LMFDB - Embedded newform 360.2.q.d.121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(121,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))

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

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

chi := DirichletCharacter("360.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.q (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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
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			121.2
Root			$0.403374 - 1.68443i$ of defining polynomial
Character	$\chi$	$=$	360.121
Dual form			360.2.q.d.241.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.403374 + 1.68443i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(0.596626 + 1.03339i) q^{7} +(-2.67458 - 1.35891i) q^{9} +O(q^{10})$	\(q+(-0.403374 + 1.68443i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(0.596626 + 1.03339i) q^{7} +(-2.67458 - 1.35891i) q^{9} +(1.66044 + 2.87597i) q^{11} +(-0.853695 + 1.47864i) q^{13} +(-1.25707 - 1.19154i) q^{15} -6.34916 q^{17} +1.32088 q^{19} +(-1.98133 + 0.588131i) q^{21} +(-3.43165 + 5.94379i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(3.36783 - 3.95698i) q^{27} +(-1.01414 - 1.75654i) q^{29} +(1.33956 - 2.32018i) q^{31} +(-5.51414 + 1.63680i) q^{33} -1.19325 q^{35} +3.32088 q^{37} +(-2.14631 - 2.03443i) q^{39} +(-1.16044 + 2.00994i) q^{41} +(3.17458 + 5.49853i) q^{43} +(2.51414 - 1.63680i) q^{45} +(6.38470 + 11.0586i) q^{47} +(2.78807 - 4.82909i) q^{49} +(2.56108 - 10.6947i) q^{51} +1.02827 q^{53} -3.32088 q^{55} +(-0.532810 + 2.22493i) q^{57} +(5.83502 - 10.1066i) q^{59} +(4.86783 + 8.43133i) q^{61} +(-0.191448 - 3.57463i) q^{63} +(-0.853695 - 1.47864i) q^{65} +(5.28534 - 9.15448i) q^{67} +(-8.62763 - 8.17792i) q^{69} -1.06562 q^{71} +14.0565 q^{73} +(1.66044 - 0.492881i) q^{75} +(-1.98133 + 3.43176i) q^{77} +(-0.707389 - 1.22523i) q^{79} +(5.30675 + 7.26900i) q^{81} +(5.91751 + 10.2494i) q^{83} +(3.17458 - 5.49853i) q^{85} +(3.36783 - 0.999697i) q^{87} -11.0000 q^{89} -2.03735 q^{91} +(3.36783 + 3.19229i) q^{93} +(-0.660442 + 1.14392i) q^{95} +(-8.12763 - 14.0775i) q^{97} +(-0.532810 - 9.94840i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{3} - 3 q^{5} + 5 q^{7} + 5 q^{9}+O(q^{10}) $ 6 * q - q^3 - 3 * q^5 + 5 * q^7 + 5 * q^9	$ 6 q - q^{3} - 3 q^{5} + 5 q^{7} + 5 q^{9} + 2 q^{11} - q^{15} + 4 q^{17} - 8 q^{19} + 12 q^{21} + 7 q^{23} - 3 q^{25} + 2 q^{27} + 7 q^{29} + 16 q^{31} - 20 q^{33} - 10 q^{35} + 4 q^{37} - 18 q^{39} + q^{41} - 2 q^{43} + 2 q^{45} + 13 q^{47} - 10 q^{49} - 20 q^{53} - 4 q^{55} - 14 q^{57} + 6 q^{59} + 11 q^{61} + 27 q^{63} - q^{67} - 33 q^{69} - 28 q^{71} + 32 q^{73} + 2 q^{75} + 12 q^{77} + 6 q^{79} + 29 q^{81} + 21 q^{83} - 2 q^{85} + 2 q^{87} - 66 q^{89} - 60 q^{91} + 2 q^{93} + 4 q^{95} - 30 q^{97} - 14 q^{99}+O(q^{100}) $ 6 * q - q^3 - 3 * q^5 + 5 * q^7 + 5 * q^9 + 2 * q^11 - q^15 + 4 * q^17 - 8 * q^19 + 12 * q^21 + 7 * q^23 - 3 * q^25 + 2 * q^27 + 7 * q^29 + 16 * q^31 - 20 * q^33 - 10 * q^35 + 4 * q^37 - 18 * q^39 + q^41 - 2 * q^43 + 2 * q^45 + 13 * q^47 - 10 * q^49 - 20 * q^53 - 4 * q^55 - 14 * q^57 + 6 * q^59 + 11 * q^61 + 27 * q^63 - q^67 - 33 * q^69 - 28 * q^71 + 32 * q^73 + 2 * q^75 + 12 * q^77 + 6 * q^79 + 29 * q^81 + 21 * q^83 - 2 * q^85 + 2 * q^87 - 66 * q^89 - 60 * q^91 + 2 * q^93 + 4 * q^95 - 30 * q^97 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−0.403374	+	1.68443i	−0.232888	+	0.972504i
$3$	−0.403374	+	1.68443i	−0.232888	+	0.972504i
$4$		0			0
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	0.596626	+	1.03339i	0.225504	+	0.390584i	0.956470	−	0.291829i	$-0.0942640\pi$
$7$	0.596626	+	1.03339i	0.225504	+	0.390584i	−0.730967	+	0.682413i	$0.760931\pi$
$8$		0			0
$9$	−2.67458	−	1.35891i	−0.891526	−	0.452969i
$10$		0			0
$11$	1.66044	+	2.87597i	0.500642	+	0.867138i	1.00000		0.000741679i	$0.000236084\pi$
$11$	1.66044	+	2.87597i	0.500642	+	0.867138i	−0.499358	+	0.866396i	$0.666431\pi$
$12$		0			0
$13$	−0.853695	+	1.47864i	−0.236772	+	0.410102i	−0.959786	−	0.280732i	$-0.909423\pi$
$13$	−0.853695	+	1.47864i	−0.236772	+	0.410102i	0.723014	+	0.690833i	$0.242756\pi$
$14$		0			0
$15$	−1.25707	−	1.19154i	−0.324574	−	0.307656i
$16$		0			0
$17$	−6.34916			−1.53990			−0.769949	−	0.638106i	$-0.779718\pi$
$17$	−6.34916			−1.53990			−0.769949	+	0.638106i	$0.779718\pi$
$18$		0			0
$19$	1.32088			0.303032			0.151516	−	0.988455i	$-0.451585\pi$
$19$	1.32088			0.303032			0.151516	+	0.988455i	$0.451585\pi$
$20$		0			0
$21$	−1.98133	+	0.588131i	−0.432361	+	0.128341i
$22$		0			0
$23$	−3.43165	+	5.94379i	−0.715548	+	1.23937i	0.247200	+	0.968965i	$0.420490\pi$
$23$	−3.43165	+	5.94379i	−0.715548	+	1.23937i	−0.962748	+	0.270401i	$0.912844\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	3.36783	−	3.95698i	0.648139	−	0.761522i
$28$		0			0
$29$	−1.01414	−	1.75654i	−0.188321	−	0.326181i	0.756370	−	0.654144i	$-0.226971\pi$
$29$	−1.01414	−	1.75654i	−0.188321	−	0.326181i	−0.944690	+	0.327963i	$0.893638\pi$
$30$		0			0
$31$	1.33956	−	2.32018i	0.240592	−	0.416717i	−0.720291	−	0.693672i	$-0.755992\pi$
$31$	1.33956	−	2.32018i	0.240592	−	0.416717i	0.960883	+	0.276955i	$0.0893252\pi$
$32$		0			0
$33$	−5.51414	+	1.63680i	−0.959888	+	0.284930i
$34$		0			0
$35$	−1.19325			−0.201696
$36$		0			0
$37$	3.32088			0.545950			0.272975	−	0.962021i	$-0.411992\pi$
$37$	3.32088			0.545950			0.272975	+	0.962021i	$0.411992\pi$
$38$		0			0
$39$	−2.14631	−	2.03443i	−0.343684	−	0.325770i
$40$		0			0
$41$	−1.16044	+	2.00994i	−0.181231	+	0.313901i	−0.942300	−	0.334770i	$-0.891341\pi$
$41$	−1.16044	+	2.00994i	−0.181231	+	0.313901i	0.761069	+	0.648671i	$0.224675\pi$
$42$		0			0
$43$	3.17458	+	5.49853i	0.484119	+	0.838518i	0.999834	−	0.0182420i	$-0.00580692\pi$
$43$	3.17458	+	5.49853i	0.484119	+	0.838518i	−0.515715	+	0.856760i	$0.672474\pi$
$44$		0			0
$45$	2.51414	−	1.63680i	0.374785	−	0.244000i
$46$		0			0
$47$	6.38470	+	11.0586i	0.931304	+	1.61307i	0.781095	+	0.624412i	$0.214661\pi$
$47$	6.38470	+	11.0586i	0.931304	+	1.61307i	0.150209	+	0.988654i	$0.452005\pi$
$48$		0			0
$49$	2.78807	−	4.82909i	0.398296	−	0.689869i
$50$		0			0
$51$	2.56108	−	10.6947i	0.358623	−	1.49756i
$52$		0			0
$53$	1.02827			0.141244			0.0706221	−	0.997503i	$-0.477502\pi$
$53$	1.02827			0.141244			0.0706221	+	0.997503i	$0.477502\pi$
$54$		0			0
$55$	−3.32088			−0.447788
$56$		0			0
$57$	−0.532810	+	2.22493i	−0.0705724	+	0.294699i
$58$		0			0
$59$	5.83502	−	10.1066i	0.759655	−	1.31576i	−0.183371	−	0.983044i	$-0.558701\pi$
$59$	5.83502	−	10.1066i	0.759655	−	1.31576i	0.943027	−	0.332718i	$-0.107966\pi$
$60$		0			0
$61$	4.86783	+	8.43133i	0.623262	+	1.07952i	0.988874	+	0.148754i	$0.0475263\pi$
$61$	4.86783	+	8.43133i	0.623262	+	1.07952i	−0.365612	+	0.930767i	$0.619140\pi$
$62$		0			0
$63$	−0.191448	−	3.57463i	−0.0241202	−	0.450362i
$64$		0			0
$65$	−0.853695	−	1.47864i	−0.105888	−	0.183403i
$66$		0			0
$67$	5.28534	−	9.15448i	0.645707	−	1.11840i	−0.338430	−	0.940991i	$-0.609896\pi$
$67$	5.28534	−	9.15448i	0.645707	−	1.11840i	0.984138	−	0.177406i	$-0.0567707\pi$
$68$		0			0
$69$	−8.62763	−	8.17792i	−1.03864	−	0.984506i
$70$		0			0
$71$	−1.06562			−0.126466			−0.0632329	−	0.997999i	$-0.520141\pi$
$71$	−1.06562			−0.126466			−0.0632329	+	0.997999i	$0.520141\pi$
$72$		0			0
$73$	14.0565			1.64519			0.822597	−	0.568624i	$-0.192524\pi$
$73$	14.0565			1.64519			0.822597	+	0.568624i	$0.192524\pi$
$74$		0			0
$75$	1.66044	−	0.492881i	0.191731	−	0.0569130i
$76$		0			0
$77$	−1.98133	+	3.43176i	−0.225793	+	0.391085i
$78$		0			0
$79$	−0.707389	−	1.22523i	−0.0795875	−	0.137850i	0.823485	−	0.567339i	$-0.192027\pi$
$79$	−0.707389	−	1.22523i	−0.0795875	−	0.137850i	−0.903072	+	0.429489i	$0.858694\pi$
$80$		0			0
$81$	5.30675	+	7.26900i	0.589639	+	0.807667i
$82$		0			0
$83$	5.91751	+	10.2494i	0.649531	+	1.12502i	0.983235	+	0.182343i	$0.0583681\pi$
$83$	5.91751	+	10.2494i	0.649531	+	1.12502i	−0.333704	+	0.942678i	$0.608299\pi$
$84$		0			0
$85$	3.17458	−	5.49853i	0.344331	−	0.596400i
$86$		0			0
$87$	3.36783	−	0.999697i	0.361069	−	0.107179i
$88$		0			0
$89$	−11.0000			−1.16600			−0.582999	−	0.812473i	$-0.698121\pi$
$89$	−11.0000			−1.16600			−0.582999	+	0.812473i	$0.698121\pi$
$90$		0			0
$91$	−2.03735			−0.213572
$92$		0			0
$93$	3.36783	+	3.19229i	0.349228	+	0.331025i
$94$		0			0
$95$	−0.660442	+	1.14392i	−0.0677599	+	0.117364i
$96$		0			0
$97$	−8.12763	−	14.0775i	−0.825236	−	1.42935i	−0.901739	−	0.432281i	$-0.857709\pi$
$97$	−8.12763	−	14.0775i	−0.825236	−	1.42935i	0.0765028	−	0.997069i	$-0.475625\pi$
$98$		0			0
$99$	−0.532810	−	9.94840i	−0.0535494	−	0.999851i
$100$		0			0
$101$	1.19325	+	2.06677i	0.118733	+	0.205652i	0.919266	−	0.393637i	$-0.128783\pi$
$101$	1.19325	+	2.06677i	0.118733	+	0.205652i	−0.800533	+	0.599289i	$0.795450\pi$
$102$		0			0
$103$	−4.88197	+	8.45582i	−0.481035	+	0.833176i	−0.999763	−	0.0217626i	$-0.993072\pi$
$103$	−4.88197	+	8.45582i	−0.481035	+	0.833176i	0.518729	+	0.854939i	$0.326406\pi$
$104$		0			0
$105$	0.481327	−	2.00994i	0.0469727	−	0.196151i
$106$		0			0
$107$	−7.57976			−0.732763			−0.366381	−	0.930465i	$-0.619403\pi$
$107$	−7.57976			−0.732763			−0.366381	+	0.930465i	$0.619403\pi$
$108$		0			0
$109$	16.5761			1.58771			0.793854	−	0.608109i	$-0.208072\pi$
$109$	16.5761			1.58771			0.793854	+	0.608109i	$0.208072\pi$
$110$		0			0
$111$	−1.33956	+	5.59378i	−0.127145	+	0.530938i
$112$		0			0
$113$	10.5424	−	18.2600i	0.991747	−	1.71776i	0.384837	−	0.922985i	$-0.374258\pi$
$113$	10.5424	−	18.2600i	0.991747	−	1.71776i	0.606909	−	0.794771i	$-0.292409\pi$
$114$		0			0
$115$	−3.43165	−	5.94379i	−0.320003	−	0.554261i
$116$		0			0
$117$	4.29261	−	2.79466i	0.396852	−	0.258366i
$118$		0			0
$119$	−3.78807	−	6.56114i	−0.347252	−	0.601458i
$120$		0			0
$121$	−0.0141369	+	0.0244859i	−0.00128518	+	0.00222599i
$122$		0			0
$123$	−2.91751	−	2.76544i	−0.263063	−	0.249351i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−15.4112			−1.36752			−0.683760	−	0.729707i	$-0.739657\pi$
$127$	−15.4112			−1.36752			−0.683760	+	0.729707i	$0.739657\pi$
$128$		0			0
$129$	−10.5424	+	3.12938i	−0.928208	+	0.275526i
$130$		0			0
$131$	1.67912	−	2.90831i	0.146705	−	0.254101i	−0.783303	−	0.621640i	$-0.786467\pi$
$131$	1.67912	−	2.90831i	0.146705	−	0.254101i	0.930008	+	0.367540i	$0.119800\pi$
$132$		0			0
$133$	0.788074	+	1.36498i	0.0683347	+	0.118359i
$134$		0			0
$135$	1.74293	+	4.89512i	0.150008	+	0.421305i
$136$		0			0
$137$	3.80675	+	6.59348i	0.325232	+	0.563319i	0.981559	−	0.191158i	$-0.0612241\pi$
$137$	3.80675	+	6.59348i	0.325232	+	0.563319i	−0.656327	+	0.754477i	$0.727891\pi$
$138$		0			0
$139$	−6.64177	+	11.5039i	−0.563347	+	0.975746i	0.433854	+	0.900983i	$0.357153\pi$
$139$	−6.64177	+	11.5039i	−0.563347	+	0.975746i	−0.997201	+	0.0747632i	$0.976180\pi$
$140$		0			0
$141$	−21.2029	+	6.29379i	−1.78560	+	0.530033i
$142$		0			0
$143$	−5.67004			−0.474153
$144$		0			0
$145$	2.02827			0.168439
$146$		0			0
$147$	7.00960	+	6.64423i	0.578142	+	0.548007i
$148$		0			0
$149$	8.99546	−	15.5806i	0.736937	−	1.27641i	−0.216931	−	0.976187i	$-0.569605\pi$
$149$	8.99546	−	15.5806i	0.736937	−	1.27641i	0.953868	−	0.300226i	$-0.0970620\pi$
$150$		0			0
$151$	4.33956	+	7.51633i	0.353148	+	0.611671i	0.986799	−	0.161948i	$-0.0517778\pi$
$151$	4.33956	+	7.51633i	0.353148	+	0.611671i	−0.633651	+	0.773619i	$0.718444\pi$
$152$		0			0
$153$	16.9813	+	8.62791i	1.37286	+	0.697525i
$154$		0			0
$155$	1.33956	+	2.32018i	0.107596	+	0.186362i
$156$		0			0
$157$	−9.44852	+	16.3653i	−0.754074	+	1.30609i	0.191760	+	0.981442i	$0.438581\pi$
$157$	−9.44852	+	16.3653i	−0.754074	+	1.30609i	−0.945834	+	0.324652i	$0.894753\pi$
$158$		0			0
$159$	−0.414779	+	1.73205i	−0.0328941	+	0.137361i
$160$		0			0
$161$	−8.18964			−0.645434
$162$		0			0
$163$	−0.990927			−0.0776154			−0.0388077	−	0.999247i	$-0.512356\pi$
$163$	−0.990927			−0.0776154			−0.0388077	+	0.999247i	$0.512356\pi$
$164$		0			0
$165$	1.33956	−	5.59378i	0.104284	−	0.435475i
$166$		0			0
$167$	−6.79948	+	11.7770i	−0.526160	+	0.911335i	0.473376	+	0.880860i	$0.343035\pi$
$167$	−6.79948	+	11.7770i	−0.526160	+	0.911335i	−0.999536	+	0.0304745i	$0.990298\pi$
$168$		0			0
$169$	5.04241	+	8.73371i	0.387878	+	0.671824i
$170$		0			0
$171$	−3.53281	−	1.79496i	−0.270161	−	0.137264i
$172$		0			0
$173$	0.0938942	+	0.162630i	0.00713865	+	0.0123645i	0.869573	−	0.493805i	$-0.164394\pi$
$173$	0.0938942	+	0.162630i	0.00713865	+	0.0123645i	−0.862434	+	0.506170i	$0.831061\pi$
$174$		0			0
$175$	0.596626	−	1.03339i	0.0451007	−	0.0781167i
$176$		0			0
$177$	14.6700	+	13.9054i	1.10267	+	1.04519i
$178$		0			0
$179$	9.76394			0.729791			0.364895	−	0.931048i	$-0.381105\pi$
$179$	9.76394			0.729791			0.364895	+	0.931048i	$0.381105\pi$
$180$		0			0
$181$	−16.0848			−1.19558			−0.597788	−	0.801654i	$-0.703953\pi$
$181$	−16.0848			−1.19558			−0.597788	+	0.801654i	$0.703953\pi$
$182$		0			0
$183$	−16.1655	+	4.79852i	−1.19499	+	0.354717i
$184$		0			0
$185$	−1.66044	+	2.87597i	−0.122078	+	0.211446i
$186$		0			0
$187$	−10.5424	−	18.2600i	−0.770937	−	1.33530i
$188$		0			0
$189$	6.09843	+	1.11943i	0.443596	+	0.0814268i
$190$		0			0
$191$	1.53281	+	2.65491i	0.110910	+	0.192102i	0.916138	−	0.400864i	$-0.131290\pi$
$191$	1.53281	+	2.65491i	0.110910	+	0.192102i	−0.805227	+	0.592966i	$0.797957\pi$
$192$		0			0
$193$	−0.118031	+	0.204436i	−0.00849609	+	0.0147157i	−0.870242	−	0.492624i	$-0.836038\pi$
$193$	−0.118031	+	0.204436i	−0.00849609	+	0.0147157i	0.861746	+	0.507340i	$0.169371\pi$
$194$		0			0
$195$	2.83502	−	0.841540i	0.203020	−	0.0602639i
$196$		0			0
$197$	−1.74474			−0.124307			−0.0621536	−	0.998067i	$-0.519797\pi$
$197$	−1.74474			−0.124307			−0.0621536	+	0.998067i	$0.519797\pi$
$198$		0			0
$199$	−22.7922			−1.61570			−0.807848	−	0.589390i	$-0.799368\pi$
$199$	−22.7922			−1.61570			−0.807848	+	0.589390i	$0.799368\pi$
$200$		0			0
$201$	13.2881	+	12.5954i	0.937268	+	0.888414i
$202$		0			0
$203$	1.21012	−	2.09599i	0.0849339	−	0.147110i
$204$		0			0
$205$	−1.16044	−	2.00994i	−0.0810488	−	0.140381i
$206$		0			0
$207$	17.2553	−	11.2338i	1.19932	−	0.780806i
$208$		0			0
$209$	2.19325	+	3.79882i	0.151710	+	0.262770i
$210$		0			0
$211$	6.68872	−	11.5852i	0.460470	−	0.797558i	−0.538514	−	0.842616i	$-0.681014\pi$
$211$	6.68872	−	11.5852i	0.460470	−	0.797558i	0.998984	+	0.0450587i	$0.0143475\pi$
$212$		0			0
$213$	0.429843	−	1.79496i	0.0294524	−	0.122989i
$214$		0			0
$215$	−6.34916			−0.433009
$216$		0			0
$217$	3.19686			0.217017
$218$		0			0
$219$	−5.67004	+	23.6772i	−0.383146	+	1.59996i
$220$		0			0
$221$	5.42024	−	9.38814i	0.364605	−	0.631514i
$222$		0			0
$223$	4.74293	+	8.21500i	0.317610	+	0.550117i	0.979989	−	0.199052i	$-0.0637863\pi$
$223$	4.74293	+	8.21500i	0.317610	+	0.550117i	−0.662379	+	0.749169i	$0.730453\pi$
$224$		0			0
$225$	0.160442	+	2.99571i	0.0106961	+	0.199714i
$226$		0			0
$227$	−1.75434	−	3.03860i	−0.116439	−	0.201679i	0.801915	−	0.597438i	$-0.203815\pi$
$227$	−1.75434	−	3.03860i	−0.116439	−	0.201679i	−0.918354	+	0.395759i	$0.870481\pi$
$228$		0			0
$229$	−9.36330	+	16.2177i	−0.618744	+	1.07170i	0.370971	+	0.928644i	$0.379025\pi$
$229$	−9.36330	+	16.2177i	−0.618744	+	1.07170i	−0.989715	+	0.143052i	$0.954308\pi$
$230$		0			0
$231$	−4.98133	−	4.72168i	−0.327747	−	0.310664i
$232$		0			0
$233$	2.15044			0.140880			0.0704401	−	0.997516i	$-0.477560\pi$
$233$	2.15044			0.140880			0.0704401	+	0.997516i	$0.477560\pi$
$234$		0			0
$235$	−12.7694			−0.832984
$236$		0			0
$237$	2.34916	−	0.697317i	0.152594	−	0.0452956i
$238$		0			0
$239$	12.7977	−	22.1662i	0.827813	−	1.43381i	−0.0719377	−	0.997409i	$-0.522918\pi$
$239$	12.7977	−	22.1662i	0.827813	−	1.43381i	0.899751	−	0.436405i	$-0.143748\pi$
$240$		0			0
$241$	−2.38197	−	4.12569i	−0.153436	−	0.265759i	0.779052	−	0.626959i	$-0.215701\pi$
$241$	−2.38197	−	4.12569i	−0.153436	−	0.265759i	−0.932488	+	0.361200i	$0.882367\pi$
$242$		0			0
$243$	−14.3847	+	6.00670i	−0.922779	+	0.385330i
$244$		0			0
$245$	2.78807	+	4.82909i	0.178124	+	0.308519i
$246$		0			0
$247$	−1.12763	+	1.95312i	−0.0717495	+	0.124274i
$248$		0			0
$249$	−19.6514	+	5.83326i	−1.24535	+	0.369668i
$250$		0			0
$251$	7.76394			0.490055			0.245028	−	0.969516i	$-0.421203\pi$
$251$	7.76394			0.490055			0.245028	+	0.969516i	$0.421203\pi$
$252$		0			0
$253$	−22.7922			−1.43293
$254$		0			0
$255$	7.98133	+	7.56531i	0.499810	+	0.473758i
$256$		0			0
$257$	−9.64177	+	16.7000i	−0.601437	+	1.04172i	0.391167	+	0.920320i	$0.372072\pi$
$257$	−9.64177	+	16.7000i	−0.601437	+	1.04172i	−0.992604	+	0.121400i	$0.961262\pi$
$258$		0			0
$259$	1.98133	+	3.43176i	0.123114	+	0.213239i
$260$		0			0
$261$	0.325421	+	6.07611i	0.0201430	+	0.376102i
$262$		0			0
$263$	−3.85369	−	6.67479i	−0.237629	−	0.411585i	0.722404	−	0.691471i	$-0.243037\pi$
$263$	−3.85369	−	6.67479i	−0.237629	−	0.411585i	−0.960033	+	0.279885i	$0.909704\pi$
$264$		0			0
$265$	−0.514137	+	0.890511i	−0.0315832	+	0.0547037i
$266$		0			0
$267$	4.43711	−	18.5287i	0.271547	−	1.13394i
$268$		0			0
$269$	14.1222			0.861044			0.430522	−	0.902580i	$-0.358330\pi$
$269$	14.1222			0.861044			0.430522	+	0.902580i	$0.358330\pi$
$270$		0			0
$271$	−3.26434			−0.198294			−0.0991472	−	0.995073i	$-0.531611\pi$
$271$	−3.26434			−0.198294			−0.0991472	+	0.995073i	$0.531611\pi$
$272$		0			0
$273$	0.821812	−	3.43176i	0.0497383	−	0.207699i
$274$		0			0
$275$	1.66044	−	2.87597i	0.100128	−	0.173428i
$276$		0			0
$277$	−13.2311	−	22.9170i	−0.794981	−	1.37695i	−0.922851	−	0.385157i	$-0.874147\pi$
$277$	−13.2311	−	22.9170i	−0.794981	−	1.37695i	0.127870	−	0.991791i	$-0.459186\pi$
$278$		0			0
$279$	−6.73566	+	4.38518i	−0.403254	+	0.262534i
$280$		0			0
$281$	−9.70285	−	16.8058i	−0.578824	−	1.00255i	−0.995615	−	0.0935497i	$-0.970179\pi$
$281$	−9.70285	−	16.8058i	−0.578824	−	1.00255i	0.416791	−	0.909002i	$-0.363155\pi$
$282$		0			0
$283$	2.69598	−	4.66958i	0.160260	−	0.277578i	−0.774702	−	0.632326i	$-0.782100\pi$
$283$	2.69598	−	4.66958i	0.160260	−	0.277578i	0.934962	+	0.354749i	$0.115434\pi$
$284$		0			0
$285$	−1.66044	−	1.57389i	−0.0983561	−	0.0932294i
$286$		0			0
$287$	−2.76940			−0.163473
$288$		0			0
$289$	23.3118			1.37128
$290$		0			0
$291$	26.9909	−	8.01191i	1.58224	−	0.469666i
$292$		0			0
$293$	16.4581	−	28.5063i	0.961493	−	1.66536i	0.242739	−	0.970092i	$-0.421954\pi$
$293$	16.4581	−	28.5063i	0.961493	−	1.66536i	0.718755	−	0.695264i	$-0.244712\pi$
$294$		0			0
$295$	5.83502	+	10.1066i	0.339728	+	0.588426i
$296$		0			0
$297$	16.9723	+	3.11544i	0.984830	+	0.180776i
$298$		0			0
$299$	−5.85916	−	10.1484i	−0.338844	−	0.586895i
$300$		0			0
$301$	−3.78807	+	6.56114i	−0.218341	+	0.378178i
$302$		0			0
$303$	−3.96265	+	1.17626i	−0.227648	+	0.0675745i
$304$		0			0
$305$	−9.73566			−0.557462
$306$		0			0
$307$	6.27807			0.358309			0.179154	−	0.983821i	$-0.442664\pi$
$307$	6.27807			0.358309			0.179154	+	0.983821i	$0.442664\pi$
$308$		0			0
$309$	−12.2739	−	11.6342i	−0.698240	−	0.661845i
$310$		0			0
$311$	10.2311	−	17.7208i	0.580154	−	1.00486i	−0.415307	−	0.909681i	$-0.636326\pi$
$311$	10.2311	−	17.7208i	0.580154	−	1.00486i	0.995461	−	0.0951747i	$-0.0303410\pi$
$312$		0			0
$313$	−11.6887	−	20.2455i	−0.660685	−	1.14434i	−0.980436	−	0.196839i	$-0.936932\pi$
$313$	−11.6887	−	20.2455i	−0.660685	−	1.14434i	0.319751	−	0.947502i	$-0.396401\pi$
$314$		0			0
$315$	3.19145	+	1.62152i	0.179818	+	0.0913622i
$316$		0			0
$317$	1.04695	+	1.81337i	0.0588024	+	0.101849i	0.893928	−	0.448210i	$-0.147938\pi$
$317$	1.04695	+	1.81337i	0.0588024	+	0.101849i	−0.835126	+	0.550059i	$0.814605\pi$
$318$		0			0
$319$	3.36783	−	5.83326i	0.188562	−	0.326600i
$320$		0			0
$321$	3.05748	−	12.7675i	0.170652	−	0.712614i
$322$		0			0
$323$	−8.38650			−0.466638
$324$		0			0
$325$	1.70739			0.0947089
$326$		0			0
$327$	−6.68638	+	27.9213i	−0.369758	+	1.54405i
$328$		0			0
$329$	−7.61856	+	13.1957i	−0.420025	+	0.727504i
$330$		0			0
$331$	13.1559	+	22.7867i	0.723114	+	1.25247i	0.959746	+	0.280871i	$0.0906232\pi$
$331$	13.1559	+	22.7867i	0.723114	+	1.25247i	−0.236632	+	0.971599i	$0.576043\pi$
$332$		0			0
$333$	−8.88197	−	4.51277i	−0.486729	−	0.247298i
$334$		0			0
$335$	5.28534	+	9.15448i	0.288769	+	0.500163i
$336$		0			0
$337$	11.5333	−	19.9763i	0.628261	−	1.08818i	−0.359640	−	0.933091i	$-0.617100\pi$
$337$	11.5333	−	19.9763i	0.628261	−	1.08818i	0.987901	−	0.155089i	$-0.0495663\pi$
$338$		0			0
$339$	26.5051	+	25.1235i	1.43956	+	1.36452i
$340$		0			0
$341$	8.89703			0.481801
$342$		0			0
$343$	15.0065			0.810276
$344$		0			0
$345$	11.3961	−	3.38279i	0.613546	−	0.182123i
$346$		0			0
$347$	7.26847	−	12.5894i	0.390192	−	0.675833i	−0.602283	−	0.798283i	$-0.705742\pi$
$347$	7.26847	−	12.5894i	0.390192	−	0.675833i	0.992475	+	0.122450i	$0.0390753\pi$
$348$		0			0
$349$	11.4909	+	19.9029i	0.615095	+	1.06538i	0.990368	+	0.138462i	$0.0442158\pi$
$349$	11.4909	+	19.9029i	0.615095	+	1.06538i	−0.375273	+	0.926915i	$0.622451\pi$
$350$		0			0
$351$	2.97586	+	8.35787i	0.158840	+	0.446110i
$352$		0			0
$353$	−10.6983	−	18.5300i	−0.569414	−	0.986254i	−0.996624	−	0.0821015i	$-0.973837\pi$
$353$	−10.6983	−	18.5300i	−0.569414	−	0.986254i	0.427210	−	0.904152i	$-0.359496\pi$
$354$		0			0
$355$	0.532810	−	0.922854i	0.0282786	−	0.0489800i
$356$		0			0
$357$	12.5798	−	3.73414i	0.665791	−	0.197632i
$358$		0			0
$359$	22.5935			1.19244			0.596220	−	0.802821i	$-0.296669\pi$
$359$	22.5935			1.19244			0.596220	+	0.802821i	$0.296669\pi$
$360$		0			0
$361$	−17.2553			−0.908172
$362$		0			0
$363$	−0.0355422	−	0.0336896i	−0.00186548	−	0.00176824i
$364$		0			0
$365$	−7.02827	+	12.1733i	−0.367877	+	0.637181i
$366$		0			0
$367$	−4.14631	−	7.18161i	−0.216435	−	0.374877i	0.737280	−	0.675587i	$-0.236110\pi$
$367$	−4.14631	−	7.18161i	−0.216435	−	0.374877i	−0.953716	+	0.300710i	$0.902776\pi$
$368$		0			0
$369$	5.83502	−	3.79882i	0.303759	−	0.197759i
$370$		0			0
$371$	0.613495	+	1.06260i	0.0318511	+	0.0551677i
$372$		0			0
$373$	−9.74113	+	16.8721i	−0.504376	+	0.873606i	0.495611	+	0.868545i	$0.334944\pi$
$373$	−9.74113	+	16.8721i	−0.504376	+	0.873606i	−0.999987	+	0.00506088i	$0.998389\pi$
$374$		0			0
$375$	−0.403374	+	1.68443i	−0.0208301	+	0.0869834i
$376$		0			0
$377$	3.46305			0.178356
$378$		0			0
$379$	22.0000			1.13006			0.565032	−	0.825069i	$-0.308864\pi$
$379$	22.0000			1.13006			0.565032	+	0.825069i	$0.308864\pi$
$380$		0			0
$381$	6.21646	−	25.9590i	0.318479	−	1.32992i
$382$		0			0
$383$	−5.75980	+	9.97627i	−0.294312	+	0.509763i	−0.974825	−	0.222973i	$-0.928424\pi$
$383$	−5.75980	+	9.97627i	−0.294312	+	0.509763i	0.680513	+	0.732736i	$0.261757\pi$
$384$		0			0
$385$	−1.98133	−	3.43176i	−0.100978	−	0.174899i
$386$		0			0
$387$	−1.01867	−	19.0202i	−0.0517821	−	0.966852i
$388$		0			0
$389$	11.1887	+	19.3794i	0.567290	+	0.982576i	0.996833	+	0.0795290i	$0.0253416\pi$
$389$	11.1887	+	19.3794i	0.567290	+	0.982576i	−0.429542	+	0.903047i	$0.641325\pi$
$390$		0			0
$391$	21.7881	−	37.7381i	1.10187	−	1.90850i
$392$		0			0
$393$	4.22153	+	4.00148i	0.212948	+	0.201848i
$394$		0			0
$395$	1.41478			0.0711852
$396$		0			0
$397$	−9.34009			−0.468765			−0.234383	−	0.972144i	$-0.575307\pi$
$397$	−9.34009			−0.468765			−0.234383	+	0.972144i	$0.575307\pi$
$398$		0			0
$399$	−2.61710	+	0.776853i	−0.131019	+	0.0388913i
$400$		0			0
$401$	4.86330	−	8.42347i	0.242861	−	0.420648i	−0.718667	−	0.695355i	$-0.755247\pi$
$401$	4.86330	−	8.42347i	0.242861	−	0.420648i	0.961528	+	0.274706i	$0.0885807\pi$
$402$		0			0
$403$	2.28715	+	3.96145i	0.113931	+	0.197334i
$404$		0			0
$405$	−8.94852	+	0.961276i	−0.444655	+	0.0477662i
$406$		0			0
$407$	5.51414	+	9.55077i	0.273326	+	0.473414i
$408$		0			0
$409$	−5.09389	+	8.82288i	−0.251877	+	0.436264i	−0.964043	−	0.265748i	$-0.914381\pi$
$409$	−5.09389	+	8.82288i	−0.251877	+	0.436264i	0.712166	+	0.702011i	$0.247714\pi$
$410$		0			0
$411$	−12.6418	+	3.75255i	−0.623572	+	0.185099i
$412$		0			0
$413$	13.9253			0.685220
$414$		0			0
$415$	−11.8350			−0.580958
$416$		0			0
$417$	−16.6983	−	15.8279i	−0.817720	−	0.775097i
$418$		0			0
$419$	−6.00960	+	10.4089i	−0.293588	+	0.508510i	−0.974655	−	0.223711i	$-0.928183\pi$
$419$	−6.00960	+	10.4089i	−0.293588	+	0.508510i	0.681067	+	0.732221i	$0.261516\pi$
$420$		0			0
$421$	−9.73566	−	16.8627i	−0.474487	−	0.821836i	0.525086	−	0.851049i	$-0.324033\pi$
$421$	−9.73566	−	16.8627i	−0.474487	−	0.821836i	−0.999573	+	0.0292132i	$0.990700\pi$
$422$		0			0
$423$	−2.04875	−	38.2534i	−0.0996137	−	1.85994i
$424$		0			0
$425$	3.17458	+	5.49853i	0.153990	+	0.266718i
$426$		0			0
$427$	−5.80855	+	10.0607i	−0.281096	+	0.486872i
$428$		0			0
$429$	2.28715	−	9.55077i	0.110424	−	0.461115i
$430$		0			0
$431$	−16.8296			−0.810651			−0.405326	−	0.914172i	$-0.632842\pi$
$431$	−16.8296			−0.810651			−0.405326	+	0.914172i	$0.632842\pi$
$432$		0			0
$433$	−8.40571			−0.403952			−0.201976	−	0.979390i	$-0.564736\pi$
$433$	−8.40571			−0.403952			−0.201976	+	0.979390i	$0.564736\pi$
$434$		0			0
$435$	−0.818153	+	3.41648i	−0.0392274	+	0.163808i
$436$		0			0
$437$	−4.53281	+	7.85106i	−0.216834	+	0.375567i
$438$		0			0
$439$	14.5424	+	25.1882i	0.694071	+	1.20217i	0.970493	+	0.241130i	$0.0775181\pi$
$439$	14.5424	+	25.1882i	0.694071	+	1.20217i	−0.276421	+	0.961037i	$0.589149\pi$
$440$		0			0
$441$	−14.0192	+	9.12704i	−0.667581	+	0.434621i
$442$		0			0
$443$	−7.09209	−	12.2839i	−0.336955	−	0.583624i	0.646903	−	0.762572i	$-0.276064\pi$
$443$	−7.09209	−	12.2839i	−0.336955	−	0.583624i	−0.983858	+	0.178948i	$0.942730\pi$
$444$		0			0
$445$	5.50000	−	9.52628i	0.260725	−	0.451589i
$446$		0			0
$447$	22.6158	+	21.4370i	1.06969	+	1.01394i
$448$		0			0
$449$	−26.6874			−1.25946			−0.629728	−	0.776816i	$-0.716834\pi$
$449$	−26.6874			−1.25946			−0.629728	+	0.776816i	$0.716834\pi$
$450$		0			0
$451$	−7.70739			−0.362927
$452$		0			0
$453$	−14.4112	+	4.27777i	−0.677096	+	0.200987i
$454$		0			0
$455$	1.01867	−	1.76439i	0.0477561	−	0.0827161i
$456$		0			0
$457$	−7.95305	−	13.7751i	−0.372028	−	0.644372i	0.617849	−	0.786297i	$-0.288004\pi$
$457$	−7.95305	−	13.7751i	−0.372028	−	0.644372i	−0.989877	+	0.141925i	$0.954671\pi$
$458$		0			0
$459$	−21.3829	+	25.1235i	−0.998068	+	1.17266i
$460$		0			0
$461$	19.0333	+	32.9667i	0.886471	+	1.53541i	0.844018	+	0.536314i	$0.180184\pi$
$461$	19.0333	+	32.9667i	0.886471	+	1.53541i	0.0424525	+	0.999098i	$0.486483\pi$
$462$		0			0
$463$	17.9723	−	31.1289i	0.835241	−	1.44668i	−0.0585922	−	0.998282i	$-0.518661\pi$
$463$	17.9723	−	31.1289i	0.835241	−	1.44668i	0.893834	−	0.448399i	$-0.148006\pi$
$464$		0			0
$465$	−4.44852	+	1.32048i	−0.206295	+	0.0612360i
$466$		0			0
$467$	−26.4623			−1.22453			−0.612264	−	0.790654i	$-0.709741\pi$
$467$	−26.4623			−1.22453			−0.612264	+	0.790654i	$0.709741\pi$
$468$		0			0
$469$	12.6135			0.582437
$470$		0			0
$471$	−23.7549	−	22.5167i	−1.09457	−	1.03751i
$472$		0			0
$473$	−10.5424	+	18.2600i	−0.484741	+	0.839595i
$474$		0			0
$475$	−0.660442	−	1.14392i	−0.0303032	−	0.0524866i
$476$		0			0
$477$	−2.75020	−	1.39733i	−0.125923	−	0.0639792i
$478$		0			0
$479$	−19.0565	−	33.0069i	−0.870716	−	1.50812i	−0.861257	−	0.508169i	$-0.830323\pi$
$479$	−19.0565	−	33.0069i	−0.870716	−	1.50812i	−0.00945845	−	0.999955i	$-0.503011\pi$
$480$		0			0
$481$	−2.83502	+	4.91040i	−0.129266	+	0.223895i
$482$		0			0
$483$	3.30349	−	13.7948i	0.150314	−	0.627687i
$484$		0			0
$485$	16.2553			0.738114
$486$		0			0
$487$	38.6610			1.75190			0.875948	−	0.482406i	$-0.160237\pi$
$487$	38.6610			1.75190			0.875948	+	0.482406i	$0.160237\pi$
$488$		0			0
$489$	0.399714	−	1.66914i	0.0180757	−	0.0754813i
$490$		0			0
$491$	−15.8633	+	27.4760i	−0.715900	+	1.23998i	0.246711	+	0.969089i	$0.420650\pi$
$491$	−15.8633	+	27.4760i	−0.715900	+	1.23998i	−0.962611	+	0.270887i	$0.912683\pi$
$492$		0			0
$493$	6.43892	+	11.1525i	0.289994	+	0.502285i
$494$		0			0
$495$	8.88197	+	4.51277i	0.399215	+	0.202834i
$496$		0			0
$497$	−0.635777	−	1.10120i	−0.0285185	−	0.0493955i
$498$		0			0
$499$	−19.2407	+	33.3259i	−0.861333	+	1.49187i	0.00930924	+	0.999957i	$0.497037\pi$
$499$	−19.2407	+	33.3259i	−0.861333	+	1.49187i	−0.870642	+	0.491916i	$0.836297\pi$
$500$		0			0
$501$	−17.0948	−	16.2038i	−0.763740	−	0.723931i
$502$		0			0
$503$	11.0994			0.494896			0.247448	−	0.968901i	$-0.420408\pi$
$503$	11.0994			0.494896			0.247448	+	0.968901i	$0.420408\pi$
$504$		0			0
$505$	−2.38650			−0.106198
$506$		0			0
$507$	−16.7453	+	4.97062i	−0.743683	+	0.220753i
$508$		0			0
$509$	−13.2639	+	22.9738i	−0.587914	+	1.01830i	0.406592	+	0.913610i	$0.366717\pi$
$509$	−13.2639	+	22.9738i	−0.587914	+	1.01830i	−0.994505	+	0.104686i	$0.966616\pi$
$510$		0			0
$511$	8.38650	+	14.5259i	0.370997	+	0.642586i
$512$		0			0
$513$	4.44852	−	5.22672i	0.196407	−	0.230765i
$514$		0			0
$515$	−4.88197	−	8.45582i	−0.215125	−	0.372608i
$516$		0			0
$517$	−21.2029	+	36.7244i	−0.932500	+	1.61514i
$518$		0			0
$519$	−0.311812	+	0.0925573i	−0.0136870	+	0.00406282i
$520$		0			0
$521$	−9.89703			−0.433597			−0.216798	−	0.976216i	$-0.569561\pi$
$521$	−9.89703			−0.433597			−0.216798	+	0.976216i	$0.569561\pi$
$522$		0			0
$523$	28.4394			1.24357			0.621785	−	0.783188i	$-0.286408\pi$
$523$	28.4394			1.24357			0.621785	+	0.783188i	$0.286408\pi$
$524$		0			0
$525$	1.50000	+	1.42181i	0.0654654	+	0.0620530i
$526$		0			0
$527$	−8.50506	+	14.7312i	−0.370486	+	0.641701i
$528$		0			0
$529$	−12.0524	−	20.8754i	−0.524018	−	0.907626i
$530$		0			0
$531$	−29.3401	+	19.1015i	−1.27325	+	0.828936i
$532$		0			0
$533$	−1.98133	−	3.43176i	−0.0858208	−	0.148646i
$534$		0			0
$535$	3.78988	−	6.56426i	0.163851	−	0.283798i
$536$		0			0
$537$	−3.93852	+	16.4466i	−0.169960	+	0.709724i
$538$		0			0
$539$	18.5177			0.797616
$540$		0			0
$541$	13.1131			0.563776			0.281888	−	0.959447i	$-0.409039\pi$
$541$	13.1131			0.563776			0.281888	+	0.959447i	$0.409039\pi$
$542$		0			0
$543$	6.48820	−	27.0937i	0.278435	−	1.16270i
$544$		0			0
$545$	−8.28807	+	14.3554i	−0.355022	+	0.614916i
$546$		0			0
$547$	−12.3660	−	21.4186i	−0.528733	−	0.915793i	−0.999439	−	0.0335023i	$-0.989334\pi$
$547$	−12.3660	−	21.4186i	−0.528733	−	0.915793i	0.470705	−	0.882290i	$-0.343999\pi$
$548$		0			0
$549$	−1.56201	−	29.1652i	−0.0666650	−	1.24474i
$550$		0			0
$551$	−1.33956	−	2.32018i	−0.0570671	−	0.0988431i
$552$		0			0
$553$	0.844094	−	1.46201i	0.0358945	−	0.0621712i
$554$		0			0
$555$	−4.17458	−	3.95698i	−0.177201	−	0.167965i
$556$		0			0
$557$	22.7730			0.964923			0.482462	−	0.875917i	$-0.339743\pi$
$557$	22.7730			0.964923			0.482462	+	0.875917i	$0.339743\pi$
$558$		0			0
$559$	−10.8405			−0.458504
$560$		0			0
$561$	35.0101	−	10.3923i	1.47813	−	0.438763i
$562$		0			0
$563$	−14.7056	+	25.4708i	−0.619767	+	1.07347i	0.369762	+	0.929127i	$0.379439\pi$
$563$	−14.7056	+	25.4708i	−0.619767	+	1.07347i	−0.989528	+	0.144340i	$0.953894\pi$
$564$		0			0
$565$	10.5424	+	18.2600i	0.443523	+	0.768204i
$566$		0			0
$567$	−4.34555	+	9.82080i	−0.182496	+	0.412435i
$568$		0			0
$569$	18.2835	+	31.6680i	0.766486	+	1.32759i	0.939457	+	0.342666i	$0.111330\pi$
$569$	18.2835	+	31.6680i	0.766486	+	1.32759i	−0.172972	+	0.984927i	$0.555337\pi$
$570$		0			0
$571$	−2.18779	+	3.78936i	−0.0915561	+	0.158580i	−0.908166	−	0.418610i	$-0.862517\pi$
$571$	−2.18779	+	3.78936i	−0.0915561	+	0.158580i	0.816610	+	0.577190i	$0.195851\pi$
$572$		0			0
$573$	−5.09029	+	1.51099i	−0.212650	+	0.0631223i
$574$		0			0
$575$	6.86330			0.286219
$576$		0			0
$577$	9.02827			0.375852			0.187926	−	0.982183i	$-0.439823\pi$
$577$	9.02827			0.375852			0.187926	+	0.982183i	$0.439823\pi$
$578$		0			0
$579$	−0.296747	−	0.281280i	−0.0123324	−	0.0116896i
$580$		0			0
$581$	−7.06108	+	12.2302i	−0.292943	+	0.507392i
$582$		0			0
$583$	1.70739	+	2.95729i	0.0707128	+	0.122478i
$584$		0			0
$585$	0.273937	+	5.11484i	0.0113259	+	0.211473i
$586$		0			0
$587$	1.63397	+	2.83012i	0.0674413	+	0.116812i	0.897774	−	0.440456i	$-0.145183\pi$
$587$	1.63397	+	2.83012i	0.0674413	+	0.116812i	−0.830333	+	0.557267i	$0.811850\pi$
$588$		0			0
$589$	1.76940	−	3.06469i	0.0729069	−	0.126278i
$590$		0			0
$591$	0.703781	−	2.93888i	0.0289497	−	0.120889i
$592$		0			0
$593$	3.39558			0.139440			0.0697198	−	0.997567i	$-0.477789\pi$
$593$	3.39558			0.139440			0.0697198	+	0.997567i	$0.477789\pi$
$594$		0			0
$595$	7.57615			0.310592
$596$		0			0
$597$	9.19378	−	38.3918i	0.376276	−	1.57127i
$598$		0			0
$599$	−0.301683	+	0.522531i	−0.0123264	+	0.0213500i	−0.872123	−	0.489287i	$-0.837257\pi$
$599$	−0.301683	+	0.522531i	−0.0123264	+	0.0213500i	0.859796	+	0.510637i	$0.170590\pi$
$600$		0			0
$601$	20.9627	+	36.3084i	0.855084	+	1.48105i	0.876567	+	0.481281i	$0.159828\pi$
$601$	20.9627	+	36.3084i	0.855084	+	1.48105i	−0.0214822	+	0.999769i	$0.506839\pi$
$602$		0			0
$603$	−26.5761	+	17.3021i	−1.08226	+	0.704596i
$604$		0			0
$605$	−0.0141369	−	0.0244859i	−0.000574748	−	0.000995493i
$606$		0			0
$607$	2.71466	−	4.70193i	0.110185	−	0.190845i	−0.805660	−	0.592378i	$-0.798189\pi$
$607$	2.71466	−	4.70193i	0.110185	−	0.190845i	0.915845	+	0.401533i	$0.131522\pi$
$608$		0			0
$609$	3.04241	+	2.88383i	0.123285	+	0.116859i
$610$		0			0
$611$	−21.8023			−0.882028
$612$		0			0
$613$	2.42385			0.0978984			0.0489492	−	0.998801i	$-0.484413\pi$
$613$	2.42385			0.0978984			0.0489492	+	0.998801i	$0.484413\pi$
$614$		0			0
$615$	3.85369	−	1.14392i	0.155396	−	0.0461273i
$616$		0			0
$617$	−14.5424	+	25.1882i	−0.585455	+	1.01404i	0.409363	+	0.912372i	$0.365751\pi$
$617$	−14.5424	+	25.1882i	−0.585455	+	1.01404i	−0.994818	+	0.101667i	$0.967582\pi$
$618$		0			0
$619$	−3.72606	−	6.45373i	−0.149763	−	0.259397i	0.781377	−	0.624060i	$-0.214518\pi$
$619$	−3.72606	−	6.45373i	−0.149763	−	0.259397i	−0.931140	+	0.364662i	$0.881184\pi$
$620$		0			0
$621$	11.9623	+	33.5966i	0.480029	+	1.34819i
$622$		0			0
$623$	−6.56289	−	11.3673i	−0.262937	−	0.455419i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	−7.28354	+	2.16202i	−0.290876	+	0.0863429i
$628$		0			0
$629$	−21.0848			−0.840707
$630$		0			0
$631$	−27.8013			−1.10675			−0.553376	−	0.832932i	$-0.686661\pi$
$631$	−27.8013			−1.10675			−0.553376	+	0.832932i	$0.686661\pi$
$632$		0			0
$633$	16.8163	+	15.9398i	0.668390	+	0.633551i
$634$		0			0
$635$	7.70559	−	13.3465i	0.305787	−	0.529638i
$636$		0			0
$637$	4.76033	+	8.24513i	0.188611	+	0.326684i
$638$		0			0
$639$	2.85009	+	1.44808i	0.112748	+	0.0572851i
$640$		0			0
$641$	−17.0237	−	29.4860i	−0.672397	−	1.16463i	−0.977222	−	0.212218i	$-0.931931\pi$
$641$	−17.0237	−	29.4860i	−0.672397	−	1.16463i	0.304825	−	0.952408i	$-0.401402\pi$
$642$		0			0
$643$	6.92711	−	11.9981i	0.273179	−	0.473159i	−0.696495	−	0.717561i	$-0.745258\pi$
$643$	6.92711	−	11.9981i	0.273179	−	0.473159i	0.969674	+	0.244402i	$0.0785917\pi$
$644$		0			0
$645$	2.56108	−	10.6947i	0.100843	−	0.421103i
$646$		0			0
$647$	−5.11750			−0.201190			−0.100595	−	0.994927i	$-0.532075\pi$
$647$	−5.11750			−0.201190			−0.100595	+	0.994927i	$0.532075\pi$
$648$		0			0
$649$	38.7549			1.52126
$650$		0			0
$651$	−1.28953	+	5.38487i	−0.0505407	+	0.211050i
$652$		0			0
$653$	3.69779	−	6.40476i	0.144706	−	0.250638i	−0.784557	−	0.620056i	$-0.787110\pi$
$653$	3.69779	−	6.40476i	0.144706	−	0.250638i	0.929263	+	0.369419i	$0.120443\pi$
$654$		0			0
$655$	1.67912	+	2.90831i	0.0656085	+	0.113637i
$656$		0			0
$657$	−37.5953	−	19.1015i	−1.46673	−	0.745222i
$658$		0			0
$659$	8.54241	+	14.7959i	0.332765	+	0.576366i	0.983053	−	0.183322i	$-0.0586851\pi$
$659$	8.54241	+	14.7959i	0.332765	+	0.576366i	−0.650288	+	0.759688i	$0.725352\pi$
$660$		0			0
$661$	19.3118	−	33.4490i	0.751142	−	1.30102i	−0.196127	−	0.980579i	$-0.562836\pi$
$661$	19.3118	−	33.4490i	0.751142	−	1.30102i	0.947269	−	0.320438i	$-0.103830\pi$
$662$		0			0
$663$	13.6272	+	12.9169i	0.529238	+	0.501652i
$664$		0			0
$665$	−1.57615			−0.0611204
$666$		0			0
$667$	13.9206			0.539009
$668$		0			0
$669$	−15.7507	+	4.67540i	−0.608958	+	0.180761i
$670$		0			0
$671$	−16.1655	+	27.9995i	−0.624062	+	1.08091i
$672$		0			0
$673$	−13.2649	−	22.9754i	−0.511323	−	0.885637i	−0.999914	−	0.0131244i	$-0.995822\pi$
$673$	−13.2649	−	22.9754i	−0.511323	−	0.885637i	0.488591	−	0.872513i	$-0.337511\pi$
$674$		0			0
$675$	−5.11076	−	0.938136i	−0.196713	−	0.0361089i
$676$		0			0
$677$	−19.0096	−	32.9256i	−0.730598	−	1.26543i	−0.956628	−	0.291313i	$-0.905908\pi$
$677$	−19.0096	−	32.9256i	−0.730598	−	1.26543i	0.226030	−	0.974120i	$-0.427425\pi$
$678$		0			0
$679$	9.69832	−	16.7980i	0.372187	−	0.644647i
$680$		0			0
$681$	5.82595	−	1.72936i	0.223251	−	0.0662691i
$682$		0			0
$683$	6.23606			0.238616			0.119308	−	0.992857i	$-0.461932\pi$
$683$	6.23606			0.238616			0.119308	+	0.992857i	$0.461932\pi$
$684$		0			0
$685$	−7.61350			−0.290897
$686$		0			0
$687$	−23.5406	−	22.3136i	−0.898130	−	0.851316i
$688$		0			0
$689$	−0.877832	+	1.52045i	−0.0334427	+	0.0579245i
$690$		0			0
$691$	−1.58522	−	2.74568i	−0.0603047	−	0.104451i	0.834297	−	0.551315i	$-0.185874\pi$
$691$	−1.58522	−	2.74568i	−0.0603047	−	0.104451i	−0.894602	+	0.446865i	$0.852541\pi$
$692$		0			0
$693$	9.96265	−	6.48607i	0.378450	−	0.246386i
$694$		0			0
$695$	−6.64177	−	11.5039i	−0.251937	−	0.436367i
$696$		0			0
$697$	7.36783	−	12.7615i	0.279077	−	0.483375i
$698$		0			0
$699$	−0.867432	+	3.62226i	−0.0328093	+	0.137006i
$700$		0			0
$701$	51.5863			1.94839			0.974193	−	0.225715i	$-0.0724718\pi$
$701$	51.5863			1.94839			0.974193	+	0.225715i	$0.0724718\pi$
$702$		0			0
$703$	4.38650			0.165440
$704$		0			0
$705$	5.15084	−	21.5091i	0.193992	−	0.810080i
$706$		0			0
$707$	−1.42385	+	2.46618i	−0.0535494	+	0.0927504i
$708$		0			0
$709$	−6.42892	−	11.1352i	−0.241443	−	0.418192i	0.719683	−	0.694303i	$-0.244287\pi$
$709$	−6.42892	−	11.1352i	−0.241443	−	0.418192i	−0.961126	+	0.276112i	$0.910954\pi$
$710$		0			0
$711$	0.226990	+	4.23826i	0.00851280	+	0.158947i
$712$		0			0
$713$	9.19378	+	15.9241i	0.344310	+	0.596362i
$714$		0			0
$715$	2.83502	−	4.91040i	0.106024	−	0.183639i
$716$		0			0
$717$	32.1751	+	30.4980i	1.20160	+	1.13897i
$718$		0			0
$719$	4.84049			0.180520			0.0902598	−	0.995918i	$-0.471230\pi$
$719$	4.84049			0.180520			0.0902598	+	0.995918i	$0.471230\pi$
$720$		0			0
$721$	−11.6508			−0.433900
$722$		0			0
$723$	7.91024	−	2.34805i	0.294185	−	0.0873250i
$724$		0			0
$725$	−1.01414	+	1.75654i	−0.0376641	+	0.0652361i
$726$		0			0
$727$	20.5351	+	35.5679i	0.761606	+	1.31914i	0.942022	+	0.335550i	$0.108922\pi$
$727$	20.5351	+	35.5679i	0.761606	+	1.31914i	−0.180416	+	0.983590i	$0.557744\pi$
$728$		0			0
$729$	−4.31542	−	26.6529i	−0.159830	−	0.987144i
$730$		0			0
$731$	−20.1559	−	34.9111i	−0.745493	−	1.29123i
$732$		0			0
$733$	−17.6983	+	30.6544i	−0.653702	+	1.13225i	0.328515	+	0.944499i	$0.393452\pi$
$733$	−17.6983	+	30.6544i	−0.653702	+	1.13225i	−0.982217	+	0.187747i	$0.939882\pi$
$734$		0			0
$735$	−9.25887	+	2.74838i	−0.341519	+	0.101375i
$736$		0			0
$737$	35.1040			1.29307
$738$		0			0
$739$	−19.4823			−0.716666			−0.358333	−	0.933594i	$-0.616655\pi$
$739$	−19.4823			−0.716666			−0.358333	+	0.933594i	$0.616655\pi$
$740$		0			0
$741$	−2.83502	−	2.68725i	−0.104147	−	0.0987185i
$742$		0			0
$743$	8.10169	−	14.0325i	0.297222	−	0.514804i	−0.678277	−	0.734806i	$-0.737273\pi$
$743$	8.10169	−	14.0325i	0.297222	−	0.514804i	0.975499	+	0.220002i	$0.0706065\pi$
$744$		0			0
$745$	8.99546	+	15.5806i	0.329568	+	0.570829i
$746$		0			0
$747$	−1.89884	−	35.4543i	−0.0694748	−	1.29720i
$748$		0			0
$749$	−4.52228	−	7.83282i	−0.165241	−	0.286205i
$750$		0			0
$751$	−7.17458	+	12.4267i	−0.261804	+	0.453458i	−0.966721	−	0.255832i	$-0.917651\pi$
$751$	−7.17458	+	12.4267i	−0.261804	+	0.453458i	0.704917	+	0.709290i	$0.250984\pi$
$752$		0			0
$753$	−3.13177	+	13.0778i	−0.114128	+	0.476581i
$754$		0			0
$755$	−8.67912			−0.315865
$756$		0			0
$757$	16.7466			0.608665			0.304333	−	0.952566i	$-0.401567\pi$
$757$	16.7466			0.608665			0.304333	+	0.952566i	$0.401567\pi$
$758$		0			0
$759$	9.19378	−	38.3918i	0.333713	−	1.39353i
$760$		0			0
$761$	9.81542	−	17.0008i	0.355809	−	0.616279i	−0.631447	−	0.775419i	$-0.717539\pi$
$761$	9.81542	−	17.0008i	0.355809	−	0.616279i	0.987256	+	0.159140i	$0.0508721\pi$
$762$		0			0
$763$	9.88976	+	17.1296i	0.358034	+	0.620132i
$764$		0			0
$765$	−15.9627	+	10.3923i	−0.577131	+	0.375735i
$766$		0			0
$767$	9.96265	+	17.2558i	0.359731	+	0.623072i
$768$		0			0
$769$	21.4572	−	37.1649i	0.773766	−	1.34020i	−0.161719	−	0.986837i	$-0.551704\pi$
$769$	21.4572	−	37.1649i	0.773766	−	1.34020i	0.935485	−	0.353365i	$-0.114963\pi$
$770$		0			0
$771$	−24.2407	−	22.9772i	−0.873008	−	0.827504i
$772$		0			0
$773$	−7.22699			−0.259937			−0.129968	−	0.991518i	$-0.541488\pi$
$773$	−7.22699			−0.259937			−0.129968	+	0.991518i	$0.541488\pi$
$774$		0			0
$775$	−2.67912			−0.0962367
$776$		0			0
$777$	−6.57976	+	1.95312i	−0.236047	+	0.0700676i
$778$		0			0
$779$	−1.53281	+	2.65491i	−0.0549186	+	0.0951218i
$780$		0			0
$781$	−1.76940	−	3.06469i	−0.0633141	−	0.109663i
$782$		0			0
$783$	−10.3660	−	1.90280i	−0.370452	−	0.0680004i
$784$		0			0
$785$	−9.44852	−	16.3653i	−0.337232	−	0.584103i
$786$		0			0
$787$	−15.1180	+	26.1852i	−0.538900	+	0.933402i	0.460064	+	0.887886i	$0.347826\pi$
$787$	−15.1180	+	26.1852i	−0.538900	+	0.933402i	−0.998964	+	0.0455158i	$0.985507\pi$
$788$		0			0
$789$	12.7977	−	3.79882i	0.455609	−	0.135242i
$790$		0			0
$791$	25.1595			0.894569
$792$		0			0
$793$	−16.6226			−0.590285
$794$		0			0
$795$	−1.29261	−	1.22523i	−0.0458442	−	0.0434546i
$796$		0			0
$797$	13.7079	−	23.7428i	0.485559	−	0.841013i	−0.514303	−	0.857609i	$-0.671949\pi$
$797$	13.7079	−	23.7428i	0.485559	−	0.841013i	0.999862	+	0.0165951i	$0.00528264\pi$
$798$		0			0
$799$	−40.5375	−	70.2130i	−1.43411	−	2.48396i
$800$		0			0
$801$	29.4204	+	14.9480i	1.03952	+	0.528161i
$802$		0			0
$803$	23.3401	+	40.4262i	0.823654	+	1.42661i
$804$		0			0
$805$	4.09482	−	7.09244i	0.144324	−	0.249976i
$806$		0			0
$807$	−5.69651	+	23.7877i	−0.200527	+	0.837368i
$808$		0			0
$809$	28.1806			0.990776			0.495388	−	0.868672i	$-0.335026\pi$
$809$	28.1806			0.990776			0.495388	+	0.868672i	$0.335026\pi$
$810$		0			0
$811$	20.1312			0.706903			0.353452	−	0.935453i	$-0.385008\pi$
$811$	20.1312			0.706903			0.353452	+	0.935453i	$0.385008\pi$
$812$		0			0
$813$	1.31675	−	5.49853i	0.0461804	−	0.192842i
$814$		0			0
$815$	0.495464	−	0.858168i	0.0173553	−	0.0300603i
$816$		0			0
$817$	4.19325	+	7.26293i	0.146703	+	0.254098i
$818$		0			0
$819$	5.44904	+	2.76856i	0.190405	+	0.0967414i
$820$		0			0
$821$	−6.12310	−	10.6055i	−0.213698	−	0.370135i	0.739171	−	0.673517i	$-0.235217\pi$
$821$	−6.12310	−	10.6055i	−0.213698	−	0.370135i	−0.952869	+	0.303382i	$0.901884\pi$
$822$		0			0
$823$	13.9645	−	24.1872i	0.486770	−	0.843111i	−0.513114	−	0.858321i	$-0.671508\pi$
$823$	13.9645	−	24.1872i	0.486770	−	0.843111i	0.999884	+	0.0152094i	$0.00484150\pi$
$824$		0			0
$825$	4.17458	+	3.95698i	0.145340	+	0.137764i
$826$		0			0
$827$	8.57068			0.298032			0.149016	−	0.988835i	$-0.452389\pi$
$827$	8.57068			0.298032			0.149016	+	0.988835i	$0.452389\pi$
$828$		0			0
$829$	−19.7357			−0.685448			−0.342724	−	0.939436i	$-0.611350\pi$
$829$	−19.7357			−0.685448			−0.342724	+	0.939436i	$0.611350\pi$
$830$		0			0
$831$	43.9390	−	13.0427i	1.52423	−	0.452448i
$832$		0			0
$833$	−17.7019	+	30.6606i	−0.613335	+	1.06233i
$834$		0			0
$835$	−6.79948	−	11.7770i	−0.235306	−	0.407561i
$836$		0			0
$837$	−4.66951	−	13.1146i	−0.161402	−	0.453307i
$838$		0			0
$839$	−23.3588	−	40.4586i	−0.806434	−	1.39678i	−0.915319	−	0.402730i	$-0.868061\pi$
$839$	−23.3588	−	40.4586i	−0.806434	−	1.39678i	0.108885	−	0.994054i	$-0.465272\pi$
$840$		0			0
$841$	12.4431	−	21.5520i	0.429071	−	0.743172i
$842$		0			0
$843$	32.2221	−	9.56470i	1.10979	−	0.329426i
$844$		0			0
$845$	−10.0848			−0.346928
$846$		0			0
$847$	−0.0337379			−0.00115925
$848$		0			0
$849$	6.77807	+	6.42477i	0.232623	+	0.220498i
$850$		0			0
$851$	−11.3961	+	19.7386i	−0.390653	+	0.676632i
$852$		0			0
$853$	−2.69779	−	4.67271i	−0.0923705	−	0.159990i	0.816138	−	0.577858i	$-0.196111\pi$
$853$	−2.69779	−	4.67271i	−0.0923705	−	0.159990i	−0.908508	+	0.417867i	$0.862778\pi$
$854$		0			0
$855$	3.32088	−	2.16202i	0.113572	−	0.0739397i
$856$		0			0
$857$	−14.3359	−	24.8306i	−0.489707	−	0.848197i	0.510223	−	0.860042i	$-0.329563\pi$
$857$	−14.3359	−	24.8306i	−0.489707	−	0.848197i	−0.999930	+	0.0118452i	$0.996229\pi$
$858$		0			0
$859$	−11.3733	+	19.6991i	−0.388052	+	0.672125i	−0.992187	−	0.124756i	$-0.960185\pi$
$859$	−11.3733	+	19.6991i	−0.388052	+	0.672125i	0.604136	+	0.796882i	$0.293519\pi$
$860$		0			0
$861$	1.11710	−	4.66485i	0.0380708	−	0.158978i
$862$		0			0
$863$	−0.202325			−0.00688723			−0.00344361	−	0.999994i	$-0.501096\pi$
$863$	−0.202325			−0.00688723			−0.00344361	+	0.999994i	$0.501096\pi$
$864$		0			0
$865$	−0.187788			−0.00638500
$866$		0			0
$867$	−9.40337	+	39.2670i	−0.319355	+	1.33358i
$868$		0			0
$869$	2.34916	−	4.06886i	0.0796897	−	0.138027i
$870$		0			0
$871$	9.02414	+	15.6303i	0.305771	+	0.529611i
$872$		0			0
$873$	2.60803	+	48.6960i	0.0882685	+	1.64811i
$874$		0			0
$875$	0.596626	+	1.03339i	0.0201696	+	0.0349349i
$876$		0			0
$877$	−6.48639	+	11.2348i	−0.219030	+	0.379371i	−0.954512	−	0.298174i	$-0.903623\pi$
$877$	−6.48639	+	11.2348i	−0.219030	+	0.379371i	0.735482	+	0.677545i	$0.236956\pi$
$878$		0			0
$879$	41.3780	+	39.2212i	1.39564	+	1.32290i
$880$		0			0
$881$	16.4905			0.555580			0.277790	−	0.960642i	$-0.410398\pi$
$881$	16.4905			0.555580			0.277790	+	0.960642i	$0.410398\pi$
$882$		0			0
$883$	−8.38290			−0.282107			−0.141053	−	0.990002i	$-0.545049\pi$
$883$	−8.38290			−0.282107			−0.141053	+	0.990002i	$0.545049\pi$
$884$		0			0
$885$	−19.3774	+	5.75194i	−0.651365	+	0.193349i
$886$		0			0
$887$	29.2311	−	50.6298i	0.981485	−	1.69998i	0.324866	−	0.945760i	$-0.394681\pi$
$887$	29.2311	−	50.6298i	0.981485	−	1.69998i	0.656619	−	0.754222i	$-0.271986\pi$
$888$		0			0
$889$	−9.19471	−	15.9257i	−0.308381	−	0.534131i
$890$		0			0
$891$	−12.0939	+	27.3318i	−0.405161	+	0.915650i
$892$		0			0
$893$	8.43345	+	14.6072i	0.282215	+	0.488810i
$894$		0			0
$895$	−4.88197	+	8.45582i	−0.163186	+	0.282647i
$896$		0			0
$897$	19.4576	−	5.77573i	0.649670	−	0.192846i
$898$		0			0
$899$	−5.43398			−0.181233
$900$		0			0
$901$	−6.52867			−0.217502
$902$		0			0
$903$	−9.52374	−	9.02732i	−0.316930	−	0.300410i
$904$		0			0
$905$	8.04241	−	13.9299i	0.267339	−	0.463044i
$906$		0			0
$907$	−15.3510	−	26.5886i	−0.509720	−	0.882862i	−0.999937	−	0.0112607i	$-0.996416\pi$
$907$	−15.3510	−	26.5886i	−0.509720	−	0.882862i	0.490216	−	0.871601i	$-0.336918\pi$
$908$		0			0
$909$	−0.382896	−	7.14927i	−0.0126999	−	0.237126i
$910$		0			0
$911$	17.1559	+	29.7149i	0.568401	+	0.984499i	0.996724	+	0.0808733i	$0.0257709\pi$
$911$	17.1559	+	29.7149i	0.568401	+	0.984499i	−0.428324	+	0.903625i	$0.640896\pi$
$912$		0			0
$913$	−19.6514	+	34.0372i	−0.650365	+	1.12647i
$914$		0			0
$915$	3.92711	−	16.3990i	0.129826	−	0.542134i
$916$		0			0
$917$	4.00722			0.132330
$918$		0			0
$919$	−18.8861			−0.622995			−0.311498	−	0.950247i	$-0.600831\pi$
$919$	−18.8861			−0.622995			−0.311498	+	0.950247i	$0.600831\pi$
$920$		0			0
$921$	−2.53241	+	10.5749i	−0.0834458	+	0.348456i
$922$		0			0
$923$	0.909714	−	1.57567i	0.0299436	−	0.0518639i
$924$		0			0
$925$	−1.66044	−	2.87597i	−0.0545950	−	0.0945613i
$926$		0			0
$927$	24.5479	−	15.9816i	0.806258	−	0.524905i
$928$		0			0
$929$	−4.04748	−	7.01043i	−0.132793	−	0.230005i	0.791959	−	0.610574i	$-0.209061\pi$
$929$	−4.04748	−	7.01043i	−0.132793	−	0.230005i	−0.924752	+	0.380569i	$0.875728\pi$
$930$		0			0
$931$	3.68272	−	6.37867i	0.120696	−	0.209052i
$932$		0			0
$933$	25.7225	+	24.3817i	0.842115	+	0.798221i
$934$		0			0
$935$	21.0848			0.689547
$936$		0			0
$937$	29.7084			0.970533			0.485266	−	0.874366i	$-0.338723\pi$
$937$	29.7084			0.970533			0.485266	+	0.874366i	$0.338723\pi$
$938$		0			0
$939$	38.8169	−	11.5223i	1.26674	−	0.376016i
$940$		0			0
$941$	−5.24113	+	9.07790i	−0.170856	+	0.295931i	−0.938719	−	0.344682i	$-0.887987\pi$
$941$	−5.24113	+	9.07790i	−0.170856	+	0.295931i	0.767863	+	0.640614i	$0.221320\pi$
$942$		0			0
$943$	−7.96446	−	13.7948i	−0.259358	−	0.449222i
$944$		0			0
$945$	−4.01867	+	4.72168i	−0.130727	+	0.153596i
$946$		0			0
$947$	−2.32815	−	4.03248i	−0.0756548	−	0.131038i	0.825716	−	0.564086i	$-0.190771\pi$
$947$	−2.32815	−	4.03248i	−0.0756548	−	0.131038i	−0.901371	+	0.433048i	$0.857438\pi$
$948$		0			0
$949$	−12.0000	+	20.7846i	−0.389536	+	0.674697i
$950$		0			0
$951$	−3.47679	+	1.03204i	−0.112743	+	0.0334662i
$952$		0			0
$953$	−21.9445			−0.710852			−0.355426	−	0.934704i	$-0.615664\pi$
$953$	−21.9445			−0.710852			−0.355426	+	0.934704i	$0.615664\pi$
$954$		0			0
$955$	−3.06562			−0.0992011
$956$		0			0
$957$	8.46719	+	8.02584i	0.273705	+	0.259439i
$958$		0			0
$959$	−4.54241	+	7.86769i	−0.146682	+	0.254061i
$960$		0			0
$961$	11.9112	+	20.6308i	0.384231	+	0.665508i
$962$		0			0
$963$	20.2727	+	10.3002i	0.653277	+	0.331919i
$964$		0			0
$965$	−0.118031	−	0.204436i	−0.00379957	−	0.00658104i
$966$		0			0
$967$	−30.3515	+	52.5703i	−0.976038	+	1.69055i	−0.299572	+	0.954074i	$0.596844\pi$
$967$	−30.3515	+	52.5703i	−0.976038	+	1.69055i	−0.676466	+	0.736474i	$0.736489\pi$
$968$		0			0
$969$	3.38290	−	14.1264i	0.108674	−	0.453807i
$970$		0			0
$971$	38.9053			1.24853			0.624265	−	0.781212i	$-0.285398\pi$
$971$	38.9053			1.24853			0.624265	+	0.781212i	$0.285398\pi$
$972$		0			0
$973$	−15.8506			−0.508147
$974$		0			0
$975$	−0.688716	+	2.87597i	−0.0220566	+	0.0921048i
$976$		0			0
$977$	7.20832	−	12.4852i	0.230614	−	0.399436i	−0.727375	−	0.686241i	$-0.759260\pi$
$977$	7.20832	−	12.4852i	0.230614	−	0.399436i	0.957989	+	0.286805i	$0.0925930\pi$
$978$		0			0
$979$	−18.2649	−	31.6357i	−0.583748	−	1.01108i
$980$		0			0
$981$	−44.3342	−	22.5254i	−1.41548	−	0.719182i
$982$		0			0
$983$	−12.9512	−	22.4322i	−0.413081	−	0.715477i	0.582144	−	0.813086i	$-0.302214\pi$
$983$	−12.9512	−	22.4322i	−0.413081	−	0.715477i	−0.995225	+	0.0976089i	$0.968881\pi$
$984$		0			0
$985$	0.872368	−	1.51099i	0.0277960	−	0.0481440i
$986$		0			0
$987$	−19.1541	−	18.1557i	−0.609682	−	0.577903i
$988$		0			0
$989$	−43.5761			−1.38564
$990$		0			0
$991$	−26.1987			−0.832230			−0.416115	−	0.909312i	$-0.636609\pi$
$991$	−26.1987			−0.832230			−0.416115	+	0.909312i	$0.636609\pi$
$992$		0			0
$993$	−43.6892	+	12.9686i	−1.38644	+	0.411546i
$994$		0			0
$995$	11.3961	−	19.7386i	0.361281	−	0.625757i
$996$		0			0
$997$	12.3829	+	21.4478i	0.392170	+	0.679259i	0.992736	−	0.120317i	$-0.0383911\pi$
$997$	12.3829	+	21.4478i	0.392170	+	0.679259i	−0.600565	+	0.799576i	$0.705058\pi$
$998$		0			0
$999$	11.1842	−	13.1407i	0.353852	−	0.415753i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.q.d.121.2	✓	6
3.2	odd	2		1080.2.q.d.361.2		6
4.3	odd	2		720.2.q.j.481.2		6
9.2	odd	6		1080.2.q.d.721.2		6
9.4	even	3		3240.2.a.r.1.2		3
9.5	odd	6		3240.2.a.q.1.2		3
9.7	even	3	inner	360.2.q.d.241.2	yes	6
12.11	even	2		2160.2.q.j.1441.2		6
36.7	odd	6		720.2.q.j.241.2		6
36.11	even	6		2160.2.q.j.721.2		6
36.23	even	6		6480.2.a.bu.1.2		3
36.31	odd	6		6480.2.a.bx.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.q.d.121.2	✓	6	1.1	even	1	trivial
360.2.q.d.241.2	yes	6	9.7	even	3	inner
720.2.q.j.241.2		6	36.7	odd	6
720.2.q.j.481.2		6	4.3	odd	2
1080.2.q.d.361.2		6	3.2	odd	2
1080.2.q.d.721.2		6	9.2	odd	6
2160.2.q.j.721.2		6	36.11	even	6
2160.2.q.j.1441.2		6	12.11	even	2
3240.2.a.q.1.2		3	9.5	odd	6
3240.2.a.r.1.2		3	9.4	even	3
6480.2.a.bu.1.2		3	36.23	even	6
6480.2.a.bx.1.2		3	36.31	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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.403374 + 1.68443i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(0.596626 + 1.03339i) q^{7} +(-2.67458 - 1.35891i) q^{9} +O(q^{10})\)	\(q+(-0.403374 + 1.68443i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(0.596626 + 1.03339i) q^{7} +(-2.67458 - 1.35891i) q^{9} +(1.66044 + 2.87597i) q^{11} +(-0.853695 + 1.47864i) q^{13} +(-1.25707 - 1.19154i) q^{15} -6.34916 q^{17} +1.32088 q^{19} +(-1.98133 + 0.588131i) q^{21} +(-3.43165 + 5.94379i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(3.36783 - 3.95698i) q^{27} +(-1.01414 - 1.75654i) q^{29} +(1.33956 - 2.32018i) q^{31} +(-5.51414 + 1.63680i) q^{33} -1.19325 q^{35} +3.32088 q^{37} +(-2.14631 - 2.03443i) q^{39} +(-1.16044 + 2.00994i) q^{41} +(3.17458 + 5.49853i) q^{43} +(2.51414 - 1.63680i) q^{45} +(6.38470 + 11.0586i) q^{47} +(2.78807 - 4.82909i) q^{49} +(2.56108 - 10.6947i) q^{51} +1.02827 q^{53} -3.32088 q^{55} +(-0.532810 + 2.22493i) q^{57} +(5.83502 - 10.1066i) q^{59} +(4.86783 + 8.43133i) q^{61} +(-0.191448 - 3.57463i) q^{63} +(-0.853695 - 1.47864i) q^{65} +(5.28534 - 9.15448i) q^{67} +(-8.62763 - 8.17792i) q^{69} -1.06562 q^{71} +14.0565 q^{73} +(1.66044 - 0.492881i) q^{75} +(-1.98133 + 3.43176i) q^{77} +(-0.707389 - 1.22523i) q^{79} +(5.30675 + 7.26900i) q^{81} +(5.91751 + 10.2494i) q^{83} +(3.17458 - 5.49853i) q^{85} +(3.36783 - 0.999697i) q^{87} -11.0000 q^{89} -2.03735 q^{91} +(3.36783 + 3.19229i) q^{93} +(-0.660442 + 1.14392i) q^{95} +(-8.12763 - 14.0775i) q^{97} +(-0.532810 - 9.94840i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{3} - 3 q^{5} + 5 q^{7} + 5 q^{9}+O(q^{10}) \) 6 * q - q^3 - 3 * q^5 + 5 * q^7 + 5 * q^9	\( 6 q - q^{3} - 3 q^{5} + 5 q^{7} + 5 q^{9} + 2 q^{11} - q^{15} + 4 q^{17} - 8 q^{19} + 12 q^{21} + 7 q^{23} - 3 q^{25} + 2 q^{27} + 7 q^{29} + 16 q^{31} - 20 q^{33} - 10 q^{35} + 4 q^{37} - 18 q^{39} + q^{41} - 2 q^{43} + 2 q^{45} + 13 q^{47} - 10 q^{49} - 20 q^{53} - 4 q^{55} - 14 q^{57} + 6 q^{59} + 11 q^{61} + 27 q^{63} - q^{67} - 33 q^{69} - 28 q^{71} + 32 q^{73} + 2 q^{75} + 12 q^{77} + 6 q^{79} + 29 q^{81} + 21 q^{83} - 2 q^{85} + 2 q^{87} - 66 q^{89} - 60 q^{91} + 2 q^{93} + 4 q^{95} - 30 q^{97} - 14 q^{99}+O(q^{100}) \) 6 * q - q^3 - 3 * q^5 + 5 * q^7 + 5 * q^9 + 2 * q^11 - q^15 + 4 * q^17 - 8 * q^19 + 12 * q^21 + 7 * q^23 - 3 * q^25 + 2 * q^27 + 7 * q^29 + 16 * q^31 - 20 * q^33 - 10 * q^35 + 4 * q^37 - 18 * q^39 + q^41 - 2 * q^43 + 2 * q^45 + 13 * q^47 - 10 * q^49 - 20 * q^53 - 4 * q^55 - 14 * q^57 + 6 * q^59 + 11 * q^61 + 27 * q^63 - q^67 - 33 * q^69 - 28 * q^71 + 32 * q^73 + 2 * q^75 + 12 * q^77 + 6 * q^79 + 29 * q^81 + 21 * q^83 - 2 * q^85 + 2 * q^87 - 66 * q^89 - 60 * q^91 + 2 * q^93 + 4 * q^95 - 30 * q^97 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more