LMFDB - Embedded newform 540.2.n.d.359.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [540,2,Mod(179,540)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(540, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("540.179"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 540 = 2^{2} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	540.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,-2,18,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.31192170915$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			359.18
Character	$\chi$	$=$	540.359
Dual form			540.2.n.d.179.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.937387 + 1.05892i) q^{2} +(-0.242609 + 1.98523i) q^{4} +(1.62334 + 1.53778i) q^{5} +(0.550457 - 0.953419i) q^{7} +(-2.32961 + 1.60403i) q^{8} +(-0.106691 + 3.16048i) q^{10} +(-2.84126 + 4.92120i) q^{11} +(2.07548 - 1.19828i) q^{13} +(1.52558 - 0.310835i) q^{14} +(-3.88228 - 0.963271i) q^{16} +1.29175 q^{17} -2.78362i q^{19} +(-3.44669 + 2.84961i) q^{20} +(-7.87450 + 1.60442i) q^{22} +(1.82546 - 1.05393i) q^{23} +(0.270437 + 4.99268i) q^{25} +(3.21441 + 1.07451i) q^{26} +(1.75921 + 1.32409i) q^{28} +(5.51723 + 3.18537i) q^{29} +(-2.78385 + 1.60725i) q^{31} +(-2.61918 - 5.01397i) q^{32} +(1.21087 + 1.36785i) q^{34} +(2.35973 - 0.701235i) q^{35} -6.51687i q^{37} +(2.94763 - 2.60933i) q^{38} +(-6.24839 - 0.978569i) q^{40} +(-6.35642 + 3.66988i) q^{41} +(2.25473 - 3.90530i) q^{43} +(-9.08040 - 6.83448i) q^{44} +(2.82719 + 0.945071i) q^{46} +(-8.09628 - 4.67439i) q^{47} +(2.89400 + 5.01255i) q^{49} +(-5.03333 + 4.96645i) q^{50} +(1.87533 + 4.41103i) q^{52} +11.5954 q^{53} +(-12.1801 + 3.61952i) q^{55} +(0.246959 + 3.10404i) q^{56} +(1.79874 + 8.82821i) q^{58} +(-3.66237 - 6.34341i) q^{59} +(2.48990 - 4.31263i) q^{61} +(-4.31149 - 1.44124i) q^{62} +(2.85419 - 7.47353i) q^{64} +(5.21191 + 1.24643i) q^{65} +(1.85016 + 3.20457i) q^{67} +(-0.313389 + 2.56441i) q^{68} +(2.95453 + 1.84143i) q^{70} +12.6950 q^{71} -9.86891i q^{73} +(6.90082 - 6.10883i) q^{74} +(5.52614 + 0.675333i) q^{76} +(3.12798 + 5.41781i) q^{77} +(0.975531 + 0.563223i) q^{79} +(-4.82094 - 7.53382i) q^{80} +(-9.84453 - 3.29082i) q^{82} +(9.98138 + 5.76275i) q^{83} +(2.09694 + 1.98643i) q^{85} +(6.24894 - 1.27321i) q^{86} +(-1.27471 - 16.0219i) q^{88} -9.16815i q^{89} -2.63841i q^{91} +(1.64942 + 3.87966i) q^{92} +(-2.63956 - 12.9550i) q^{94} +(4.28061 - 4.51876i) q^{95} +(11.1257 + 6.42344i) q^{97} +(-2.59507 + 7.76320i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 2 q^{4} + 18 q^{5} - 16 q^{10} + 42 q^{14} + 30 q^{16} - 26 q^{25} - 4 q^{34} + 10 q^{40} - 96 q^{41} + 4 q^{46} + 32 q^{49} + 90 q^{50} - 6 q^{56} + 8 q^{61} - 20 q^{64} + 6 q^{65} + 4 q^{70} - 72 q^{74}+ \cdots - 62 q^{94}+O(q^{100}) $ 48 * q - 2 * q^4 + 18 * q^5 - 16 * q^10 + 42 * q^14 + 30 * q^16 - 26 * q^25 - 4 * q^34 + 10 * q^40 - 96 * q^41 + 4 * q^46 + 32 * q^49 + 90 * q^50 - 6 * q^56 + 8 * q^61 - 20 * q^64 + 6 * q^65 + 4 * q^70 - 72 * q^74 - 4 * q^85 - 108 * q^86 - 62 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/540\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$461$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.937387	+	1.05892i	0.662833	+	0.748767i
$2$	0.937387	+	1.05892i	0.662833	+	0.748767i
$3$		0			0
$3$		0			0
$4$	−0.242609	+	1.98523i	−0.121305	+	0.992615i
$5$	1.62334	+	1.53778i	0.725978	+	0.687718i
$5$	1.62334	+	1.53778i	0.725978	+	0.687718i
$6$		0			0
$7$	0.550457	−	0.953419i	0.208053	−	0.360358i	−0.743048	−	0.669238i	$-0.766621\pi$
$7$	0.550457	−	0.953419i	0.208053	−	0.360358i	0.951101	+	0.308880i	$0.0999540\pi$
$8$	−2.32961	+	1.60403i	−0.823643	+	0.567109i
$9$		0			0
$10$	−0.106691	+	3.16048i	−0.0337388	+	0.999431i
$11$	−2.84126	+	4.92120i	−0.856671	+	1.48380i	0.0184153	+	0.999830i	$0.494138\pi$
$11$	−2.84126	+	4.92120i	−0.856671	+	1.48380i	−0.875086	+	0.483967i	$0.839195\pi$
$12$		0			0
$13$	2.07548	−	1.19828i	0.575636	−	0.332343i	−0.183761	−	0.982971i	$-0.558827\pi$
$13$	2.07548	−	1.19828i	0.575636	−	0.332343i	0.759397	+	0.650627i	$0.225494\pi$
$14$	1.52558	−	0.310835i	0.407729	−	0.0830742i
$15$		0			0
$16$	−3.88228	−	0.963271i	−0.970570	−	0.240818i
$17$	1.29175			0.313294			0.156647	−	0.987655i	$-0.449931\pi$
$17$	1.29175			0.313294			0.156647	+	0.987655i	$0.449931\pi$
$18$		0			0
$19$		−	2.78362i		−	0.638607i	−0.947652	−	0.319304i	$-0.896551\pi$
$19$		−	2.78362i		−	0.638607i	0.947652	−	0.319304i	$-0.103449\pi$
$20$	−3.44669	+	2.84961i	−0.770704	+	0.637193i
$21$		0			0
$22$	−7.87450	+	1.60442i	−1.67885	+	0.342063i
$23$	1.82546	−	1.05393i	0.380635	−	0.219760i	−0.297459	−	0.954735i	$-0.596139\pi$
$23$	1.82546	−	1.05393i	0.380635	−	0.219760i	0.678095	+	0.734975i	$0.262806\pi$
$24$		0			0
$25$	0.270437	+	4.99268i	0.0540873	+	0.998536i
$26$	3.21441	+	1.07451i	0.630398	+	0.210729i
$27$		0			0
$28$	1.75921	+	1.32409i	0.332459	+	0.250230i
$29$	5.51723	+	3.18537i	1.02452	+	0.591509i	0.915411	−	0.402521i	$-0.131866\pi$
$29$	5.51723	+	3.18537i	1.02452	+	0.591509i	0.109112	+	0.994029i	$0.465199\pi$
$30$		0			0
$31$	−2.78385	+	1.60725i	−0.499994	+	0.288671i	−0.728711	−	0.684821i	$-0.759880\pi$
$31$	−2.78385	+	1.60725i	−0.499994	+	0.288671i	0.228717	+	0.973493i	$0.426547\pi$
$32$	−2.61918	−	5.01397i	−0.463010	−	0.886353i
$33$		0			0
$34$	1.21087	+	1.36785i	0.207662	+	0.234584i
$35$	2.35973	−	0.701235i	0.398867	−	0.118530i
$36$		0			0
$37$		−	6.51687i		−	1.07137i	−0.844419	−	0.535683i	$-0.820054\pi$
$37$		−	6.51687i		−	1.07137i	0.844419	−	0.535683i	$-0.179946\pi$
$38$	2.94763	−	2.60933i	0.478168	−	0.423290i
$39$		0			0
$40$	−6.24839	−	0.978569i	−0.987958	−	0.154725i
$41$	−6.35642	+	3.66988i	−0.992706	+	0.573139i	−0.906082	−	0.423102i	$-0.860941\pi$
$41$	−6.35642	+	3.66988i	−0.992706	+	0.573139i	−0.0866240	+	0.996241i	$0.527608\pi$
$42$		0			0
$43$	2.25473	−	3.90530i	0.343843	−	0.595553i	−0.641300	−	0.767290i	$-0.721605\pi$
$43$	2.25473	−	3.90530i	0.343843	−	0.595553i	0.985143	+	0.171737i	$0.0549380\pi$
$44$	−9.08040	−	6.83448i	−1.36892	−	1.03034i
$45$		0			0
$46$	2.82719	+	0.945071i	0.416847	+	0.139343i
$47$	−8.09628	−	4.67439i	−1.18096	−	0.681830i	−0.224726	−	0.974422i	$-0.572149\pi$
$47$	−8.09628	−	4.67439i	−1.18096	−	0.681830i	−0.956237	+	0.292592i	$0.905482\pi$
$48$		0			0
$49$	2.89400	+	5.01255i	0.413428	+	0.716078i
$50$	−5.03333	+	4.96645i	−0.711820	+	0.702362i
$51$		0			0
$52$	1.87533	+	4.41103i	0.260062	+	0.611700i
$53$	11.5954			1.59275			0.796377	−	0.604800i	$-0.206747\pi$
$53$	11.5954			1.59275			0.796377	+	0.604800i	$0.206747\pi$
$54$		0			0
$55$	−12.1801	+	3.61952i	−1.64236	+	0.488056i
$56$	0.246959	+	3.10404i	0.0330013	+	0.414795i
$57$		0			0
$58$	1.79874	+	8.82821i	0.236186	+	1.15920i
$59$	−3.66237	−	6.34341i	−0.476800	−	0.825842i	0.522846	−	0.852427i	$-0.324870\pi$
$59$	−3.66237	−	6.34341i	−0.476800	−	0.825842i	−0.999647	+	0.0265849i	$0.991537\pi$
$60$		0			0
$61$	2.48990	−	4.31263i	0.318799	−	0.552175i	−0.661439	−	0.749999i	$-0.730054\pi$
$61$	2.48990	−	4.31263i	0.318799	−	0.552175i	0.980238	+	0.197823i	$0.0633873\pi$
$62$	−4.31149	−	1.44124i	−0.547560	−	0.183038i
$63$		0			0
$64$	2.85419	−	7.47353i	0.356774	−	0.934191i
$65$	5.21191	+	1.24643i	0.646457	+	0.154601i
$66$		0			0
$67$	1.85016	+	3.20457i	0.226033	+	0.391500i	0.956629	−	0.291310i	$-0.0940910\pi$
$67$	1.85016	+	3.20457i	0.226033	+	0.391500i	−0.730596	+	0.682810i	$0.760758\pi$
$68$	−0.313389	+	2.56441i	−0.0380041	+	0.310981i
$69$		0			0
$70$	2.95453	+	1.84143i	0.353134	+	0.220093i
$71$	12.6950			1.50662			0.753311	−	0.657664i	$-0.228455\pi$
$71$	12.6950			1.50662			0.753311	+	0.657664i	$0.228455\pi$
$72$		0			0
$73$		−	9.86891i		−	1.15507i	−0.816366	−	0.577534i	$-0.804015\pi$
$73$		−	9.86891i		−	1.15507i	0.816366	−	0.577534i	$-0.195985\pi$
$74$	6.90082	−	6.10883i	0.802204	−	0.710137i
$75$		0			0
$76$	5.52614	+	0.675333i	0.633891	+	0.0774660i
$77$	3.12798	+	5.41781i	0.356466	+	0.617417i
$78$		0			0
$79$	0.975531	+	0.563223i	0.109756	+	0.0633676i	0.553873	−	0.832601i	$-0.313149\pi$
$79$	0.975531	+	0.563223i	0.109756	+	0.0633676i	−0.444117	+	0.895969i	$0.646483\pi$
$80$	−4.82094	−	7.53382i	−0.538998	−	0.842307i
$81$		0			0
$82$	−9.84453	−	3.29082i	−1.08715	−	0.363410i
$83$	9.98138	+	5.76275i	1.09560	+	0.632544i	0.935062	−	0.354485i	$-0.115344\pi$
$83$	9.98138	+	5.76275i	1.09560	+	0.632544i	0.160537	+	0.987030i	$0.448677\pi$
$84$		0			0
$85$	2.09694	+	1.98643i	0.227445	+	0.215458i
$86$	6.24894	−	1.27321i	0.673841	−	0.137294i
$87$		0			0
$88$	−1.27471	−	16.0219i	−0.135885	−	1.70794i
$89$		−	9.16815i		−	0.971822i	−0.874008	−	0.485911i	$-0.838488\pi$
$89$		−	9.16815i		−	0.971822i	0.874008	−	0.485911i	$-0.161512\pi$
$90$		0			0
$91$		−	2.63841i		−	0.276580i
$92$	1.64942	+	3.87966i	0.171964	+	0.404482i
$93$		0			0
$94$	−2.63956	−	12.9550i	−0.272250	−	1.33621i
$95$	4.28061	−	4.51876i	0.439182	−	0.463615i
$96$		0			0
$97$	11.1257	+	6.42344i	1.12965	+	0.652202i	0.943846	−	0.330386i	$-0.107179\pi$
$97$	11.1257	+	6.42344i	1.12965	+	0.652202i	0.185801	+	0.982587i	$0.440512\pi$
$98$	−2.59507	+	7.76320i	−0.262142	+	0.784201i
$99$		0			0
$100$	−9.97723	−	0.674392i	−0.997723	−	0.0674392i
$101$	−14.4999	−	8.37150i	−1.44279	−	0.832995i	−0.444755	−	0.895652i	$-0.646709\pi$
$101$	−14.4999	−	8.37150i	−1.44279	−	0.832995i	−0.998035	+	0.0626572i	$0.980043\pi$
$102$		0			0
$103$	−0.679292	−	1.17657i	−0.0669327	−	0.115931i	0.830617	−	0.556844i	$-0.187988\pi$
$103$	−0.679292	−	1.17657i	−0.0669327	−	0.115931i	−0.897550	+	0.440913i	$0.854655\pi$
$104$	−2.91300	+	6.12066i	−0.285643	+	0.600181i
$105$		0			0
$106$	10.8694	+	12.2786i	1.05573	+	1.19260i
$107$		−	2.97211i		−	0.287324i	−0.989627	−	0.143662i	$-0.954112\pi$
$107$		−	2.97211i		−	0.287324i	0.989627	−	0.143662i	$-0.0458879\pi$
$108$		0			0
$109$	5.12076			0.490480			0.245240	−	0.969462i	$-0.421133\pi$
$109$	5.12076			0.490480			0.245240	+	0.969462i	$0.421133\pi$
$110$	−15.2502	−	9.50478i	−1.45405	−	0.906245i
$111$		0			0
$112$	−3.05543	+	3.17120i	−0.288711	+	0.299650i
$113$	−4.18521	−	7.24900i	−0.393711	−	0.681928i	0.599224	−	0.800581i	$-0.295476\pi$
$113$	−4.18521	−	7.24900i	−0.393711	−	0.681928i	−0.992936	+	0.118653i	$0.962142\pi$
$114$		0			0
$115$	4.58406	+	1.09628i	0.427466	+	0.102229i
$116$	−7.66223	+	10.1802i	−0.711420	+	0.945205i
$117$		0			0
$118$	3.28409	−	9.82438i	0.302325	−	0.904408i
$119$	0.711050	−	1.23157i	0.0651818	−	0.112898i
$120$		0			0
$121$	−10.6455	−	18.4385i	−0.967770	−	1.67623i
$122$	6.90071	−	1.40601i	0.624761	−	0.127294i
$123$		0			0
$124$	−2.51538	−	5.91651i	−0.225888	−	0.531318i
$125$	−7.23866	+	8.52067i	−0.647445	+	0.762112i
$126$		0			0
$127$	5.14729			0.456748			0.228374	−	0.973573i	$-0.426659\pi$
$127$	5.14729			0.456748			0.228374	+	0.973573i	$0.426659\pi$
$128$	10.5893	−	3.98324i	0.935973	−	0.352072i
$129$		0			0
$130$	3.56570	+	6.68737i	0.312733	+	0.586521i
$131$	−7.10028	−	12.2980i	−0.620354	−	1.07449i	−0.989420	−	0.145082i	$-0.953656\pi$
$131$	−7.10028	−	12.2980i	−0.620354	−	1.07449i	0.369065	−	0.929403i	$-0.379678\pi$
$132$		0			0
$133$	−2.65396	−	1.53226i	−0.230127	−	0.132864i
$134$	−1.65906	+	4.96309i	−0.143321	+	0.428746i
$135$		0			0
$136$	−3.00927	+	2.07199i	−0.258042	+	0.177672i
$137$	−3.47139	+	6.01263i	−0.296581	+	0.513693i	−0.975351	−	0.220657i	$-0.929180\pi$
$137$	−3.47139	+	6.01263i	−0.296581	+	0.513693i	0.678770	+	0.734351i	$0.262513\pi$
$138$		0			0
$139$	10.3321	−	5.96523i	0.876356	−	0.505964i	0.00690070	−	0.999976i	$-0.497803\pi$
$139$	10.3321	−	5.96523i	0.876356	−	0.505964i	0.869455	+	0.494012i	$0.164470\pi$
$140$	0.819621	+	4.85473i	0.0692706	+	0.410300i
$141$		0			0
$142$	11.9002	+	13.4430i	0.998640	+	1.12811i
$143$			13.6185i			1.13884i
$144$		0			0
$145$	4.05789	+	13.6552i	0.336990	+	1.13401i
$146$	10.4504	−	9.25100i	0.864878	−	0.765618i
$147$		0			0
$148$	12.9375	+	1.58105i	1.06345	+	0.129962i
$149$	−4.98019	+	2.87531i	−0.407993	+	0.235555i	−0.689927	−	0.723879i	$-0.742357\pi$
$149$	−4.98019	+	2.87531i	−0.407993	+	0.235555i	0.281934	+	0.959434i	$0.409024\pi$
$150$		0			0
$151$	−1.85084	−	1.06858i	−0.150619	−	0.0869599i	0.422796	−	0.906225i	$-0.361049\pi$
$151$	−1.85084	−	1.06858i	−0.150619	−	0.0869599i	−0.573415	+	0.819265i	$0.694382\pi$
$152$	4.46501	+	6.48477i	0.362160	+	0.525984i
$153$		0			0
$154$	−2.80489	+	8.39086i	−0.226024	+	0.676155i
$155$	−6.99073	−	1.67184i	−0.561509	−	0.134286i
$156$		0			0
$157$	−8.70855	+	5.02788i	−0.695018	+	0.401269i	−0.805489	−	0.592611i	$-0.798097\pi$
$157$	−8.70855	+	5.02788i	−0.695018	+	0.401269i	0.110471	+	0.993879i	$0.464764\pi$
$158$	0.318044	+	1.56097i	0.0253022	+	0.124184i
$159$		0			0
$160$	3.45860	−	12.1671i	0.273427	−	0.961893i
$161$		−	2.32057i		−	0.182887i
$162$		0			0
$163$	18.2146			1.42668			0.713339	−	0.700819i	$-0.247182\pi$
$163$	18.2146			1.42668			0.713339	+	0.700819i	$0.247182\pi$
$164$	−5.74343	−	13.5093i	−0.448487	−	1.05490i
$165$		0			0
$166$	3.25415	+	15.9714i	0.252571	+	1.23962i
$167$	−6.44716	+	3.72227i	−0.498896	+	0.288038i	−0.728258	−	0.685304i	$-0.759670\pi$
$167$	−6.44716	+	3.72227i	−0.498896	+	0.288038i	0.229362	+	0.973341i	$0.426336\pi$
$168$		0			0
$169$	−3.62824	+	6.28430i	−0.279096	+	0.483408i
$170$	−0.137818	+	4.08253i	−0.0105702	+	0.313116i
$171$		0			0
$172$	7.20591	+	5.42361i	0.549445	+	0.413547i
$173$	4.33441	−	7.50742i	0.329539	−	0.570778i	−0.652881	−	0.757460i	$-0.726440\pi$
$173$	4.33441	−	7.50742i	0.329539	−	0.570778i	0.982420	+	0.186682i	$0.0597734\pi$
$174$		0			0
$175$	4.90898	+	2.49041i	0.371084	+	0.188258i
$176$	15.7710	−	16.3686i	1.18878	−	1.23383i
$177$		0			0
$178$	9.70831	−	8.59411i	0.727668	−	0.644156i
$179$	−1.10988			−0.0829560			−0.0414780	−	0.999139i	$-0.513207\pi$
$179$	−1.10988			−0.0829560			−0.0414780	+	0.999139i	$0.513207\pi$
$180$		0			0
$181$	−12.6629			−0.941229			−0.470615	−	0.882339i	$-0.655968\pi$
$181$	−12.6629			−0.941229			−0.470615	+	0.882339i	$0.655968\pi$
$182$	2.79385	−	2.47321i	0.207094	−	0.183327i
$183$		0			0
$184$	−2.56209	+	5.38335i	−0.188880	+	0.396866i
$185$	10.0215	−	10.5791i	0.736798	−	0.777788i
$186$		0			0
$187$	−3.67018	+	6.35694i	−0.268390	+	0.464865i
$188$	11.2440	−	14.9389i	0.820051	−	1.08953i
$189$		0			0
$190$	8.79758	+	0.296989i	0.638244	+	0.0215458i
$191$	−11.3827	+	19.7154i	−0.823625	+	1.42656i	0.0793411	+	0.996848i	$0.474718\pi$
$191$	−11.3827	+	19.7154i	−0.823625	+	1.42656i	−0.902966	+	0.429712i	$0.858615\pi$
$192$		0			0
$193$	−10.0687	+	5.81319i	−0.724764	+	0.418443i	−0.816504	−	0.577340i	$-0.804091\pi$
$193$	−10.0687	+	5.81319i	−0.724764	+	0.418443i	0.0917396	+	0.995783i	$0.470757\pi$
$194$	3.62723	+	17.8025i	0.260420	+	1.27814i
$195$		0			0
$196$	−10.6532	+	4.52916i	−0.760941	+	0.323511i
$197$	−12.2003			−0.869238			−0.434619	−	0.900614i	$-0.643117\pi$
$197$	−12.2003			−0.869238			−0.434619	+	0.900614i	$0.643117\pi$
$198$		0			0
$199$			7.07921i			0.501832i	0.968009	+	0.250916i	$0.0807318\pi$
$199$			7.07921i			0.501832i	−0.968009	+	0.250916i	$0.919268\pi$
$200$	−8.63841	−	11.1972i	−0.610828	−	0.791763i
$201$		0			0
$202$	−4.72727	−	23.2015i	−0.332609	−	1.63245i
$203$	6.07399	−	3.50682i	0.426310	−	0.246130i
$204$		0			0
$205$	−15.9621	−	3.81736i	−1.11484	−	0.266616i
$206$	0.609128	−	1.82222i	0.0424400	−	0.126960i
$207$		0			0
$208$	−9.21188	+	2.65281i	−0.638729	+	0.183939i
$209$	13.6988	+	7.90899i	0.947564	+	0.547076i
$210$		0			0
$211$	−5.61368	+	3.24106i	−0.386462	+	0.223124i	−0.680626	−	0.732631i	$-0.738292\pi$
$211$	−5.61368	+	3.24106i	−0.386462	+	0.223124i	0.294164	+	0.955755i	$0.404959\pi$
$212$	−2.81316	+	23.0196i	−0.193209	+	1.58099i
$213$		0			0
$214$	3.14721	−	2.78601i	0.215139	−	0.190448i
$215$	9.66569	−	2.87233i	0.659195	−	0.195891i
$216$		0			0
$217$			3.53890i			0.240236i
$218$	4.80014	+	5.42246i	0.325106	+	0.367255i
$219$		0			0
$220$	−4.23058	−	25.0584i	−0.285226	−	1.68943i
$221$	2.68100	−	1.54787i	0.180343	−	0.104121i
$222$		0			0
$223$	−7.84799	+	13.5931i	−0.525540	+	0.910263i	0.474017	+	0.880516i	$0.342803\pi$
$223$	−7.84799	+	13.5931i	−0.525540	+	0.910263i	−0.999557	+	0.0297470i	$0.990530\pi$
$224$	−6.22216	−	0.262800i	−0.415735	−	0.0175590i
$225$		0			0
$226$	3.75292	−	11.2269i	0.249640	−	0.746803i
$227$	−0.169745	−	0.0980022i	−0.0112664	−	0.00650463i	0.494356	−	0.869259i	$-0.335404\pi$
$227$	−0.169745	−	0.0980022i	−0.0112664	−	0.00650463i	−0.505623	+	0.862755i	$0.668737\pi$
$228$		0			0
$229$	0.825139	+	1.42918i	0.0545267	+	0.0944431i	0.892000	−	0.452035i	$-0.149302\pi$
$229$	0.825139	+	1.42918i	0.0545267	+	0.0944431i	−0.837474	+	0.546478i	$0.815968\pi$
$230$	3.13617	+	5.88178i	0.206793	+	0.387833i
$231$		0			0
$232$	−17.9624	+	1.42910i	−1.17929	+	0.0938248i
$233$	−20.2270			−1.32512			−0.662559	−	0.749010i	$-0.730530\pi$
$233$	−20.2270			−1.32512			−0.662559	+	0.749010i	$0.730530\pi$
$234$		0			0
$235$	−5.95477	−	20.0384i	−0.388447	−	1.30716i
$236$	13.4817	−	5.73168i	0.877581	−	0.373101i
$237$		0			0
$238$	1.97066	−	0.401520i	0.127739	−	0.0260267i
$239$	10.1646	+	17.6056i	0.657494	+	1.13881i	0.981262	+	0.192676i	$0.0617168\pi$
$239$	10.1646	+	17.6056i	0.657494	+	1.13881i	−0.323769	+	0.946136i	$0.604950\pi$
$240$		0			0
$241$	8.62268	−	14.9349i	0.555436	−	0.962043i	−0.442434	−	0.896801i	$-0.645885\pi$
$241$	8.62268	−	14.9349i	0.555436	−	0.962043i	0.997869	−	0.0652417i	$-0.0207818\pi$
$242$	9.54590	−	28.5567i	0.613634	−	1.83569i
$243$		0			0
$244$	7.95749	+	5.98930i	0.509426	+	0.383426i
$245$	−3.01029	+	12.5874i	−0.192320	+	0.804179i
$246$		0			0
$247$	−3.33556	−	5.77737i	−0.212237	−	0.367605i
$248$	3.90720	−	8.20965i	0.248108	−	0.521313i
$249$		0			0
$250$	−15.8081	+	0.322033i	−0.999793	+	0.0203671i
$251$	−9.92020			−0.626157			−0.313079	−	0.949727i	$-0.601360\pi$
$251$	−9.92020			−0.626157			−0.313079	+	0.949727i	$0.601360\pi$
$252$		0			0
$253$			11.9780i			0.753048i
$254$	4.82501	+	5.45055i	0.302748	+	0.341998i
$255$		0			0
$256$	14.1442	+	7.47938i	0.884014	+	0.467461i
$257$	−8.67485	−	15.0253i	−0.541122	−	0.937252i	−0.998840	−	0.0481539i	$-0.984666\pi$
$257$	−8.67485	−	15.0253i	−0.541122	−	0.937252i	0.457717	−	0.889098i	$-0.348667\pi$
$258$		0			0
$259$	−6.21330	−	3.58725i	−0.386076	−	0.222901i
$260$	−3.73892	+	10.0444i	−0.231878	+	0.622930i
$261$		0			0
$262$	6.36689	−	19.0466i	0.393348	−	1.17671i
$263$	−8.32487	−	4.80637i	−0.513334	−	0.296373i	0.220869	−	0.975303i	$-0.429111\pi$
$263$	−8.32487	−	4.80637i	−0.513334	−	0.296373i	−0.734203	+	0.678930i	$0.762444\pi$
$264$		0			0
$265$	18.8233	+	17.8313i	1.15630	+	1.09537i
$266$	−0.865248	−	4.24665i	−0.0530518	−	0.260379i
$267$		0			0
$268$	−6.81068	+	2.89553i	−0.416028	+	0.176873i
$269$			1.34482i			0.0819953i	0.999159	+	0.0409977i	$0.0130536\pi$
$269$			1.34482i			0.0819953i	−0.999159	+	0.0409977i	$0.986946\pi$
$270$		0			0
$271$			21.7288i			1.31993i	0.751297	+	0.659964i	$0.229429\pi$
$271$			21.7288i			1.31993i	−0.751297	+	0.659964i	$0.770571\pi$
$272$	−5.01492	−	1.24430i	−0.304074	−	0.0754468i
$273$		0			0
$274$	−9.62091	+	1.96025i	−0.581221	+	0.118423i
$275$	−25.3384	−	12.8546i	−1.52796	−	0.775162i
$276$		0			0
$277$	−12.0501	−	6.95713i	−0.724021	−	0.418014i	0.0922100	−	0.995740i	$-0.470607\pi$
$277$	−12.0501	−	6.95713i	−0.724021	−	0.418014i	−0.816231	+	0.577726i	$0.803940\pi$
$278$	16.0018	+	5.34908i	0.959727	+	0.320817i
$279$		0			0
$280$	−4.37245	+	5.41867i	−0.261304	+	0.323828i
$281$	−10.0948	−	5.82824i	−0.602206	−	0.347684i	0.167703	−	0.985838i	$-0.446365\pi$
$281$	−10.0948	−	5.82824i	−0.602206	−	0.347684i	−0.769909	+	0.638154i	$0.779698\pi$
$282$		0			0
$283$	−6.21367	−	10.7624i	−0.369365	−	0.639758i	0.620102	−	0.784521i	$-0.287091\pi$
$283$	−6.21367	−	10.7624i	−0.369365	−	0.639758i	−0.989466	+	0.144763i	$0.953758\pi$
$284$	−3.07993	+	25.2026i	−0.182760	+	1.49550i
$285$		0			0
$286$	−14.4209	+	12.7658i	−0.852723	+	0.754858i
$287$			8.08044i			0.476973i
$288$		0			0
$289$	−15.3314			−0.901847
$290$	−10.6559	+	17.0972i	−0.625738	+	1.00398i
$291$		0			0
$292$	19.5921	+	2.39429i	1.14654	+	0.140115i
$293$	4.77472	+	8.27006i	0.278942	+	0.483142i	0.971122	−	0.238583i	$-0.0766829\pi$
$293$	4.77472	+	8.27006i	0.278942	+	0.483142i	−0.692180	+	0.721725i	$0.743350\pi$
$294$		0			0
$295$	3.80955	−	15.9294i	0.221800	−	0.927447i
$296$	10.4532	+	15.1818i	0.607582	+	0.882423i
$297$		0			0
$298$	−7.71308	−	2.57832i	−0.446807	−	0.149358i
$299$	2.52581	−	4.37484i	0.146072	−	0.253003i
$300$		0			0
$301$	−2.48226	−	4.29940i	−0.143075	−	0.247813i
$302$	−0.603413	−	2.96156i	−0.0347225	−	0.170418i
$303$		0			0
$304$	−2.68138	+	10.8068i	−0.153788	+	0.619813i
$305$	10.6738	−	3.17192i	0.611182	−	0.181623i
$306$		0			0
$307$	−13.4685			−0.768689			−0.384345	−	0.923190i	$-0.625573\pi$
$307$	−13.4685			−0.768689			−0.384345	+	0.923190i	$0.625573\pi$
$308$	−11.5145	+	4.89534i	−0.656099	+	0.278938i
$309$		0			0
$310$	−4.78268	−	8.96976i	−0.271638	−	0.509448i
$311$	5.13110	+	8.88732i	0.290958	+	0.503954i	0.974037	−	0.226391i	$-0.0726927\pi$
$311$	5.13110	+	8.88732i	0.290958	+	0.503954i	−0.683079	+	0.730345i	$0.739359\pi$
$312$		0			0
$313$	−1.39067	−	0.802903i	−0.0786052	−	0.0453827i	0.460182	−	0.887824i	$-0.347784\pi$
$313$	−1.39067	−	0.802903i	−0.0786052	−	0.0453827i	−0.538787	+	0.842442i	$0.681117\pi$
$314$	−13.4874	−	4.50855i	−0.761138	−	0.254432i
$315$		0			0
$316$	−1.35480	+	1.80001i	−0.0762135	+	0.101259i
$317$	2.23127	−	3.86467i	0.125320	−	0.217061i	−0.796538	−	0.604589i	$-0.793337\pi$
$317$	2.23127	−	3.86467i	0.125320	−	0.217061i	0.921858	+	0.387528i	$0.126671\pi$
$318$		0			0
$319$	−31.3517	+	18.1009i	−1.75536	+	1.01346i
$320$	16.1260	−	7.74291i	0.901470	−	0.432842i
$321$		0			0
$322$	2.45730	−	2.17528i	0.136940	−	0.121223i
$323$		−	3.59573i		−	0.200072i
$324$		0			0
$325$	6.54392	+	10.0382i	0.362992	+	0.556818i
$326$	17.0741	+	19.2878i	0.945649	+	1.06825i
$327$		0			0
$328$	8.92141	−	18.7453i	0.492602	−	1.03503i
$329$	−8.91330	+	5.14610i	−0.491406	+	0.283713i
$330$		0			0
$331$	−10.2107	−	5.89512i	−0.561228	−	0.324025i	0.192410	−	0.981315i	$-0.438370\pi$
$331$	−10.2107	−	5.89512i	−0.561228	−	0.324025i	−0.753638	+	0.657289i	$0.771703\pi$
$332$	−13.8620	+	18.4172i	−0.760775	+	1.01078i
$333$		0			0
$334$	−9.98506	−	3.33780i	−0.546358	−	0.182636i
$335$	−1.92451	+	8.04724i	−0.105147	+	0.439668i
$336$		0			0
$337$	−9.14715	+	5.28111i	−0.498277	+	0.287680i	−0.728002	−	0.685575i	$-0.759551\pi$
$337$	−9.14715	+	5.28111i	−0.498277	+	0.287680i	0.229725	+	0.973256i	$0.426217\pi$
$338$	−10.0556	+	2.04882i	−0.546954	+	0.111441i
$339$		0			0
$340$	−4.45225	+	3.68098i	−0.241457	+	0.199629i
$341$		−	18.2665i		−	0.989186i
$342$		0			0
$343$	14.0785			0.760166
$344$	1.01157	+	12.7145i	0.0545401	+	0.685519i
$345$		0			0
$346$	12.0127	−	2.44758i	0.645809	−	0.131583i
$347$	20.1864	−	11.6546i	1.08366	−	0.625652i	0.151779	−	0.988414i	$-0.451500\pi$
$347$	20.1864	−	11.6546i	1.08366	−	0.625652i	0.931882	+	0.362763i	$0.118166\pi$
$348$		0			0
$349$	2.84689	−	4.93095i	0.152390	−	0.263948i	−0.779715	−	0.626134i	$-0.784636\pi$
$349$	2.84689	−	4.93095i	0.152390	−	0.263948i	0.932106	+	0.362186i	$0.117970\pi$
$350$	1.96447	+	7.53268i	0.105006	+	0.402639i
$351$		0			0
$352$	32.1165	+	1.35648i	1.71182	+	0.0723004i
$353$	−0.761369	+	1.31873i	−0.0405236	+	0.0701889i	−0.885576	−	0.464495i	$-0.846236\pi$
$353$	−0.761369	+	1.31873i	−0.0405236	+	0.0701889i	0.845052	+	0.534684i	$0.179569\pi$
$354$		0			0
$355$	20.6083	+	19.5222i	1.09377	+	1.03613i
$356$	18.2009	+	2.22428i	0.964645	+	0.117887i
$357$		0			0
$358$	−1.04038	−	1.17527i	−0.0549860	−	0.0621148i
$359$	9.46115			0.499341			0.249670	−	0.968331i	$-0.419678\pi$
$359$	9.46115			0.499341			0.249670	+	0.968331i	$0.419678\pi$
$360$		0			0
$361$	11.2514			0.592181
$362$	−11.8701	−	13.4090i	−0.623878	−	0.704762i
$363$		0			0
$364$	5.23785	+	0.640102i	0.274538	+	0.0335505i
$365$	15.1763	−	16.0206i	0.794362	−	0.838554i
$366$		0			0
$367$	4.06621	−	7.04288i	0.212254	−	0.367635i	−0.740165	−	0.672425i	$-0.765253\pi$
$367$	4.06621	−	7.04288i	0.212254	−	0.367635i	0.952420	+	0.304790i	$0.0985862\pi$
$368$	−8.10218	+	2.33324i	−0.422356	+	0.121629i
$369$		0			0
$370$	20.5964	+	0.695294i	1.07076	+	0.0361466i
$371$	6.38278	−	11.0553i	0.331377	−	0.573963i
$372$		0			0
$373$	10.0593	−	5.80775i	0.520851	−	0.300714i	−0.216432	−	0.976298i	$-0.569442\pi$
$373$	10.0593	−	5.80775i	0.520851	−	0.300714i	0.737283	+	0.675584i	$0.236108\pi$
$374$	−10.1718	+	2.07250i	−0.525974	+	0.107166i
$375$		0			0
$376$	26.3590	−	2.09713i	1.35936	−	0.108151i
$377$	15.2679			0.786336
$378$		0			0
$379$			0.194316i			0.00998136i	0.999988	+	0.00499068i	$0.00158859\pi$
$379$			0.194316i			0.00998136i	−0.999988	+	0.00499068i	$0.998411\pi$
$380$	7.93226	+	9.59430i	0.406916	+	0.492177i
$381$		0			0
$382$	−31.5470	+	6.42766i	−1.61409	+	0.328868i
$383$	−16.0220	+	9.25031i	−0.818686	+	0.472669i	−0.849963	−	0.526842i	$-0.823376\pi$
$383$	−16.0220	+	9.25031i	−0.818686	+	0.472669i	0.0312769	+	0.999511i	$0.490043\pi$
$384$		0			0
$385$	−3.25368	+	13.6051i	−0.165823	+	0.693379i
$386$	−15.5940	−	5.21275i	−0.793714	−	0.265322i
$387$		0			0
$388$	−15.4512	+	20.5288i	−0.784417	+	1.04219i
$389$	20.3869	+	11.7704i	1.03366	+	0.596783i	0.918031	−	0.396509i	$-0.129779\pi$
$389$	20.3869	+	11.7704i	1.03366	+	0.596783i	0.115628	+	0.993293i	$0.463112\pi$
$390$		0			0
$391$	2.35803	−	1.36141i	0.119251	−	0.0688495i
$392$	−14.7821	−	7.03525i	−0.746611	−	0.355334i
$393$		0			0
$394$	−11.4364	−	12.9191i	−0.576160	−	0.650857i
$395$	0.717499	+	2.41446i	0.0361013	+	0.121485i
$396$		0			0
$397$			23.4091i			1.17487i	0.809272	+	0.587435i	$0.199862\pi$
$397$			23.4091i			1.17487i	−0.809272	+	0.587435i	$0.800138\pi$
$398$	−7.49629	+	6.63596i	−0.375755	+	0.332631i
$399$		0			0
$400$	3.75939	−	19.6435i	0.187970	−	0.982175i
$401$	−25.9256	+	14.9681i	−1.29466	+	0.747474i	−0.979477	−	0.201557i	$-0.935400\pi$
$401$	−25.9256	+	14.9681i	−1.29466	+	0.747474i	−0.315185	+	0.949030i	$0.602067\pi$
$402$		0			0
$403$	−3.85189	+	6.67166i	−0.191876	+	0.332339i
$404$	20.1372	−	26.7546i	1.00186	−	1.33109i
$405$		0			0
$406$	9.40711	+	3.14460i	0.466867	+	0.156064i
$407$	32.0708	+	18.5161i	1.58969	+	0.917809i
$408$		0			0
$409$	1.04012	+	1.80153i	0.0514304	+	0.0890800i	0.890594	−	0.454798i	$-0.150289\pi$
$409$	1.04012	+	1.80153i	0.0514304	+	0.0890800i	−0.839164	+	0.543878i	$0.816955\pi$
$410$	−10.9204	−	20.4809i	−0.539320	−	1.01148i
$411$		0			0
$412$	2.50056	−	1.06311i	0.123194	−	0.0523754i
$413$	−8.06390			−0.396799
$414$		0			0
$415$	7.34126	+	24.7041i	0.360368	+	1.21268i
$416$	−11.4442	−	7.26791i	−0.561099	−	0.356338i
$417$		0			0
$418$	4.46610	+	21.9196i	0.218444	+	1.07212i
$419$	−4.89021	−	8.47010i	−0.238903	−	0.413791i	0.721497	−	0.692417i	$-0.243454\pi$
$419$	−4.89021	−	8.47010i	−0.238903	−	0.413791i	−0.960400	+	0.278626i	$0.910121\pi$
$420$		0			0
$421$	1.05097	−	1.82034i	0.0512212	−	0.0887177i	−0.839278	−	0.543703i	$-0.817022\pi$
$421$	1.05097	−	1.82034i	0.0512212	−	0.0887177i	0.890499	+	0.454985i	$0.150355\pi$
$422$	−8.69420	−	2.90629i	−0.423227	−	0.141476i
$423$		0			0
$424$	−27.0129	+	18.5994i	−1.31186	+	0.903266i
$425$	0.349335	+	6.44927i	0.0169453	+	0.312836i
$426$		0			0
$427$	−2.74116	−	4.74783i	−0.132654	−	0.229764i
$428$	5.90031	+	0.721061i	0.285202	+	0.0348538i
$429$		0			0
$430$	12.1021	+	7.54267i	0.583613	+	0.363740i
$431$	3.84204			0.185064			0.0925322	−	0.995710i	$-0.470504\pi$
$431$	3.84204			0.185064			0.0925322	+	0.995710i	$0.470504\pi$
$432$		0			0
$433$		−	6.66853i		−	0.320469i	−0.987079	−	0.160235i	$-0.948775\pi$
$433$		−	6.66853i		−	0.320469i	0.987079	−	0.160235i	$-0.0512251\pi$
$434$	−3.74740	+	3.31732i	−0.179881	+	0.159236i
$435$		0			0
$436$	−1.24234	+	10.1659i	−0.0594975	+	0.486858i
$437$	−2.93375	−	5.08140i	−0.140340	−	0.243077i
$438$		0			0
$439$	33.5536	+	19.3722i	1.60143	+	0.924585i	0.991202	+	0.132357i	$0.0422544\pi$
$439$	33.5536	+	19.3722i	1.60143	+	0.924585i	0.610225	+	0.792228i	$0.291079\pi$
$440$	22.5690	−	27.9692i	1.07594	−	1.33338i
$441$		0			0
$442$	4.15220	+	1.38799i	0.197500	+	0.0660202i
$443$	−20.2821	−	11.7099i	−0.963633	−	0.556354i	−0.0663436	−	0.997797i	$-0.521133\pi$
$443$	−20.2821	−	11.7099i	−0.963633	−	0.556354i	−0.897289	+	0.441443i	$0.854467\pi$
$444$		0			0
$445$	14.0986	−	14.8830i	0.668340	−	0.705521i
$446$	−21.7506	+	4.43165i	−1.02992	+	0.209845i
$447$		0			0
$448$	−5.55429	−	6.83509i	−0.262416	−	0.322928i
$449$		−	15.7865i		−	0.745011i	−0.928030	−	0.372506i	$-0.878499\pi$
$449$		−	15.7865i		−	0.745011i	0.928030	−	0.372506i	$-0.121501\pi$
$450$		0			0
$451$		−	41.7083i		−	1.96397i
$452$	15.4063	−	6.54993i	0.724651	−	0.308083i
$453$		0			0
$454$	−0.0553404	−	0.271612i	−0.00259726	−	0.0127474i
$455$	4.05730	−	4.28302i	0.190209	−	0.200791i
$456$		0			0
$457$	−7.28867	−	4.20812i	−0.340950	−	0.196847i	0.319742	−	0.947505i	$-0.396404\pi$
$457$	−7.28867	−	4.20812i	−0.340950	−	0.196847i	−0.660692	+	0.750657i	$0.729737\pi$
$458$	−0.739911	+	2.21345i	−0.0345738	+	0.103428i
$459$		0			0
$460$	−3.28851	+	8.83445i	−0.153328	+	0.411908i
$461$	−21.4798	−	12.4014i	−1.00042	−	0.577590i	−0.0920445	−	0.995755i	$-0.529340\pi$
$461$	−21.4798	−	12.4014i	−1.00042	−	0.577590i	−0.908371	+	0.418165i	$0.862674\pi$
$462$		0			0
$463$	−10.3598	−	17.9437i	−0.481460	−	0.833913i	0.518314	−	0.855191i	$-0.326560\pi$
$463$	−10.3598	−	17.9437i	−0.481460	−	0.833913i	−0.999774	+	0.0212774i	$0.993227\pi$
$464$	−18.3511	−	17.6811i	−0.851926	−	0.820824i
$465$		0			0
$466$	−18.9606	−	21.4188i	−0.878332	−	0.992205i
$467$			1.59588i			0.0738487i	0.999318	+	0.0369243i	$0.0117561\pi$
$467$			1.59588i			0.0738487i	−0.999318	+	0.0369243i	$0.988244\pi$
$468$		0			0
$469$	4.07373			0.188107
$470$	15.6371	−	25.0894i	0.721286	−	1.15729i
$471$		0			0
$472$	18.7069	+	8.90315i	0.861055	+	0.409801i
$473$	12.8125	+	22.1919i	0.589120	+	1.02039i
$474$		0			0
$475$	13.8977	−	0.752794i	0.637672	−	0.0345406i
$476$	2.27245	+	1.71039i	0.104158	+	0.0783955i
$477$		0			0
$478$	−9.11471	+	27.2668i	−0.416897	+	1.24715i
$479$	2.98947	−	5.17791i	0.136592	−	0.236585i	−0.789612	−	0.613606i	$-0.789718\pi$
$479$	2.98947	−	5.17791i	0.136592	−	0.236585i	0.926205	+	0.377021i	$0.123052\pi$
$480$		0			0
$481$	−7.80904	−	13.5257i	−0.356062	−	0.616717i
$482$	23.8976	−	4.86911i	1.08851	−	0.221782i
$483$		0			0
$484$	39.1874	−	16.6604i	1.78124	−	0.757289i
$485$	8.18292	+	27.5364i	0.371567	+	1.25036i
$486$		0			0
$487$	−16.5971			−0.752086			−0.376043	−	0.926602i	$-0.622716\pi$
$487$	−16.5971			−0.752086			−0.376043	+	0.926602i	$0.622716\pi$
$488$	1.11708	+	14.0406i	0.0505677	+	0.635589i
$489$		0			0
$490$	−16.1508	+	8.61161i	−0.729619	+	0.389033i
$491$	6.66941	+	11.5518i	0.300986	+	0.521323i	0.976360	−	0.216153i	$-0.0693509\pi$
$491$	6.66941	+	11.5518i	0.300986	+	0.521323i	−0.675373	+	0.737476i	$0.736018\pi$
$492$		0			0
$493$	7.12685	+	4.11469i	0.320977	+	0.185316i
$494$	2.99103	−	8.94772i	0.134573	−	0.402577i
$495$		0			0
$496$	12.3559	−	3.55822i	0.554796	−	0.159769i
$497$	6.98806	−	12.1037i	0.313457	−	0.542924i
$498$		0			0
$499$	35.7135	−	20.6192i	1.59875	−	0.923041i	0.607026	−	0.794682i	$-0.292362\pi$
$499$	35.7135	−	20.6192i	1.59875	−	0.923041i	0.991728	−	0.128359i	$-0.0409711\pi$
$500$	−15.1593	−	16.4376i	−0.677946	−	0.735112i
$501$		0			0
$502$	−9.29907	−	10.5047i	−0.415038	−	0.468846i
$503$		−	24.1634i		−	1.07739i	−0.842500	−	0.538696i	$-0.818917\pi$
$503$		−	24.1634i		−	1.07739i	0.842500	−	0.538696i	$-0.181083\pi$
$504$		0			0
$505$	−10.6646	−	35.8874i	−0.474567	−	1.59697i
$506$	−12.6837	+	11.2280i	−0.563858	+	0.499145i
$507$		0			0
$508$	−1.24878	+	10.2186i	−0.0554057	+	0.453375i
$509$	−10.2084	+	5.89380i	−0.452478	+	0.261238i	−0.708876	−	0.705333i	$-0.750797\pi$
$509$	−10.2084	+	5.89380i	−0.452478	+	0.261238i	0.256398	+	0.966571i	$0.417464\pi$
$510$		0			0
$511$	−9.40921	−	5.43241i	−0.416239	−	0.240316i
$512$	5.33857	+	21.9886i	0.235934	+	0.971769i
$513$		0			0
$514$	7.77883	−	23.2705i	0.343109	−	1.02642i
$515$	0.706590	−	2.95457i	0.0311361	−	0.130194i
$516$		0			0
$517$	46.0072	−	26.5623i	2.02339	−	1.16821i
$518$	−2.02567	−	9.94202i	−0.0890029	−	0.436827i
$519$		0			0
$520$	−14.1410	+	5.45633i	−0.620126	+	0.239276i
$521$			32.5010i			1.42389i	0.702234	+	0.711947i	$0.252186\pi$
$521$			32.5010i			1.42389i	−0.702234	+	0.711947i	$0.747814\pi$
$522$		0			0
$523$	11.2435			0.491645			0.245822	−	0.969315i	$-0.420942\pi$
$523$	11.2435			0.491645			0.245822	+	0.969315i	$0.420942\pi$
$524$	26.1370	−	11.1121i	1.14180	−	0.485433i
$525$		0			0
$526$	−2.71409	−	13.3208i	−0.118340	−	0.580813i
$527$	−3.59602	+	2.07616i	−0.156645	+	0.0904391i
$528$		0			0
$529$	−9.27846	+	16.0708i	−0.403411	+	0.698729i
$530$	−1.23713	+	36.6471i	−0.0537376	+	1.59185i
$531$		0			0
$532$	3.68577	−	4.89698i	0.159799	−	0.212311i
$533$	−8.79510	+	15.2336i	−0.380958	+	0.659839i
$534$		0			0
$535$	4.57046	−	4.82472i	0.197598	−	0.208591i
$536$	−9.45037	−	4.49770i	−0.408194	−	0.194271i
$537$		0			0
$538$	−1.42406	+	1.26062i	−0.0613954	+	0.0543492i
$539$	−32.8903			−1.41669
$540$		0			0
$541$	−8.40855			−0.361512			−0.180756	−	0.983528i	$-0.557854\pi$
$541$	−8.40855			−0.361512			−0.180756	+	0.983528i	$0.557854\pi$
$542$	−23.0090	+	20.3683i	−0.988319	+	0.874892i
$543$		0			0
$544$	−3.38331	−	6.47677i	−0.145058	−	0.277689i
$545$	8.31271	+	7.87463i	0.356078	+	0.337312i
$546$		0			0
$547$	−2.12301	+	3.67716i	−0.0907734	+	0.157224i	−0.907837	−	0.419324i	$-0.862267\pi$
$547$	−2.12301	+	3.67716i	−0.0907734	+	0.157224i	0.817063	+	0.576548i	$0.195601\pi$
$548$	−11.0943	−	8.35023i	−0.473923	−	0.356704i
$549$		0			0
$550$	−10.1399	−	38.8810i	−0.432367	−	1.65789i
$551$	8.86688	−	15.3579i	0.377742	−	0.654268i
$552$		0			0
$553$	1.07398	−	0.620060i	0.0456701	−	0.0263676i
$554$	−3.92860	−	19.2816i	−0.166910	−	0.819196i
$555$		0			0
$556$	9.33570	+	21.9588i	0.395922	+	0.931260i
$557$	21.0221			0.890734			0.445367	−	0.895348i	$-0.353073\pi$
$557$	21.0221			0.890734			0.445367	+	0.895348i	$0.353073\pi$
$558$		0			0
$559$		−	10.8072i		−	0.457095i
$560$	−9.83661	+	0.449333i	−0.415673	+	0.0189878i
$561$		0			0
$562$	−3.29113	−	16.1529i	−0.138828	−	0.681369i
$563$	18.9272	−	10.9277i	0.797688	−	0.460546i	−0.0449739	−	0.998988i	$-0.514320\pi$
$563$	18.9272	−	10.9277i	0.797688	−	0.460546i	0.842662	+	0.538443i	$0.180987\pi$
$564$		0			0
$565$	4.35339	−	18.2035i	0.183149	−	0.765827i
$566$	5.57187	−	16.6683i	0.234203	−	0.700621i
$567$		0			0
$568$	−29.5745	+	20.3632i	−1.24092	+	0.854420i
$569$	−12.7253	−	7.34697i	−0.533473	−	0.308001i	0.208956	−	0.977925i	$-0.432993\pi$
$569$	−12.7253	−	7.34697i	−0.533473	−	0.308001i	−0.742430	+	0.669924i	$0.766327\pi$
$570$		0			0
$571$	15.5333	−	8.96816i	0.650049	−	0.375306i	−0.138426	−	0.990373i	$-0.544204\pi$
$571$	15.5333	−	8.96816i	0.650049	−	0.375306i	0.788475	+	0.615067i	$0.210871\pi$
$572$	−27.0359	−	3.30397i	−1.13043	−	0.138146i
$573$		0			0
$574$	−8.55651	+	7.57450i	−0.357142	+	0.316154i
$575$	5.75562	+	8.82893i	0.240026	+	0.368192i
$576$		0			0
$577$		−	38.2696i		−	1.59318i	−0.604517	−	0.796592i	$-0.706634\pi$
$577$		−	38.2696i		−	1.59318i	0.604517	−	0.796592i	$-0.293366\pi$
$578$	−14.3715	−	16.2347i	−0.597774	−	0.675273i
$579$		0			0
$580$	−28.0933	+	4.74297i	−1.16651	+	0.196941i
$581$	10.9886	−	6.34429i	0.455885	−	0.263206i
$582$		0			0
$583$	−32.9456	+	57.0634i	−1.36447	+	2.36333i
$584$	15.8300	+	22.9907i	0.655050	+	0.951364i
$585$		0			0
$586$	−4.28154	+	12.8083i	−0.176869	+	0.529105i
$587$	−7.27939	−	4.20276i	−0.300453	−	0.173466i	0.342194	−	0.939629i	$-0.388830\pi$
$587$	−7.27939	−	4.20276i	−0.300453	−	0.173466i	−0.642646	+	0.766163i	$0.722163\pi$
$588$		0			0
$589$	4.47399	+	7.74918i	0.184348	+	0.319299i
$590$	20.4390	−	10.8981i	0.841458	−	0.448666i
$591$		0			0
$592$	−6.27751	+	25.3003i	−0.258004	+	1.03984i
$593$	35.1831			1.44480			0.722398	−	0.691477i	$-0.243040\pi$
$593$	35.1831			1.44480			0.722398	+	0.691477i	$0.243040\pi$
$594$		0			0
$595$	3.04817	−	0.905817i	0.124963	−	0.0371349i
$596$	−4.49992	−	10.5844i	−0.184324	−	0.433554i
$597$		0			0
$598$	7.00025	−	1.42629i	0.286262	−	0.0583254i
$599$	7.34116	+	12.7153i	0.299952	+	0.519532i	0.976125	−	0.217211i	$-0.0696961\pi$
$599$	7.34116	+	12.7153i	0.299952	+	0.519532i	−0.676173	+	0.736743i	$0.736363\pi$
$600$		0			0
$601$	13.6252	−	23.5995i	0.555783	−	0.962644i	−0.442059	−	0.896986i	$-0.645752\pi$
$601$	13.6252	−	23.5995i	0.555783	−	0.962644i	0.997842	−	0.0656584i	$-0.0209148\pi$
$602$	2.22587	−	6.65871i	0.0907195	−	0.271389i
$603$		0			0
$604$	2.57041	−	3.41509i	0.104589	−	0.138958i
$605$	11.0733	−	46.3023i	0.450192	−	1.88246i
$606$		0			0
$607$	3.91627	+	6.78317i	0.158956	+	0.275320i	0.934493	−	0.355983i	$-0.115854\pi$
$607$	3.91627	+	6.78317i	0.158956	+	0.275320i	−0.775536	+	0.631303i	$0.782520\pi$
$608$	−13.9570	+	7.29081i	−0.566032	+	0.295681i
$609$		0			0
$610$	13.3643	+	8.32938i	0.541105	+	0.337247i
$611$	−22.4049			−0.906406
$612$		0			0
$613$			1.17677i			0.0475293i	0.999718	+	0.0237646i	$0.00756523\pi$
$613$			1.17677i			0.0475293i	−0.999718	+	0.0237646i	$0.992435\pi$
$614$	−12.6252	−	14.2620i	−0.509513	−	0.575569i
$615$		0			0
$616$	−15.9773	−	7.60405i	−0.643744	−	0.306376i
$617$	20.4261	+	35.3790i	0.822322	+	1.42430i	0.903949	+	0.427641i	$0.140655\pi$
$617$	20.4261	+	35.3790i	0.822322	+	1.42430i	−0.0816263	+	0.996663i	$0.526011\pi$
$618$		0			0
$619$	−42.7230	−	24.6661i	−1.71718	−	0.991416i	−0.923965	−	0.382478i	$-0.875071\pi$
$619$	−42.7230	−	24.6661i	−1.71718	−	0.991416i	−0.793218	−	0.608938i	$-0.791596\pi$
$620$	5.01501	−	13.4726i	0.201408	−	0.541073i
$621$		0			0
$622$	−4.60111	+	13.7643i	−0.184488	+	0.551897i
$623$	−8.74109	−	5.04667i	−0.350204	−	0.202190i
$624$		0			0
$625$	−24.8537	+	2.70041i	−0.994149	+	0.108016i
$626$	−0.453388	−	2.22523i	−0.0181210	−	0.0889382i
$627$		0			0
$628$	−7.86873	−	18.5083i	−0.313997	−	0.738561i
$629$		−	8.41813i		−	0.335653i
$630$		0			0
$631$			27.6752i			1.10173i	0.834594	+	0.550866i	$0.185703\pi$
$631$			27.6752i			1.10173i	−0.834594	+	0.550866i	$0.814297\pi$
$632$	−3.17604	+	0.252687i	−0.126336	+	0.0100513i
$633$		0			0
$634$	6.18392	−	1.25996i	0.245595	−	0.0500396i
$635$	8.35578	+	7.91543i	0.331589	+	0.314114i
$636$		0			0
$637$	12.0129	+	6.93564i	0.475968	+	0.274800i
$638$	−48.5561	−	16.2313i	−1.92235	−	0.642602i
$639$		0			0
$640$	23.3154	+	9.81797i	0.921622	+	0.388089i
$641$	13.0424	+	7.53005i	0.515145	+	0.297419i	0.734946	−	0.678126i	$-0.237207\pi$
$641$	13.0424	+	7.53005i	0.515145	+	0.297419i	−0.219801	+	0.975545i	$0.570541\pi$
$642$		0			0
$643$	−23.7098	−	41.0665i	−0.935022	−	1.61951i	−0.774595	−	0.632458i	$-0.782046\pi$
$643$	−23.7098	−	41.0665i	−0.935022	−	1.61951i	−0.160427	−	0.987048i	$-0.551287\pi$
$644$	4.60688	+	0.562993i	0.181536	+	0.0221850i
$645$		0			0
$646$	3.80758	−	3.37060i	0.149807	−	0.132614i
$647$		−	19.7634i		−	0.776977i	−0.921453	−	0.388489i	$-0.872997\pi$
$647$		−	19.7634i		−	0.776977i	0.921453	−	0.388489i	$-0.127003\pi$
$648$		0			0
$649$	41.6229			1.63384
$650$	−4.49540	+	16.3391i	−0.176324	+	0.640873i
$651$		0			0
$652$	−4.41903	+	36.1602i	−0.173063	+	1.41614i
$653$	−17.4740	−	30.2658i	−0.683809	−	1.18439i	−0.973809	−	0.227366i	$-0.926989\pi$
$653$	−17.4740	−	30.2658i	−0.683809	−	1.18439i	0.290000	−	0.957027i	$-0.406345\pi$
$654$		0			0
$655$	7.38561	−	30.8826i	0.288580	−	1.20668i
$656$	28.2125	−	8.12455i	1.10151	−	0.317211i
$657$		0			0
$658$	−13.8045	−	4.61456i	−0.538155	−	0.179894i
$659$	17.4893	−	30.2924i	0.681288	−	1.18003i	−0.293300	−	0.956021i	$-0.594753\pi$
$659$	17.4893	−	30.2924i	0.681288	−	1.18003i	0.974588	−	0.224005i	$-0.0719133\pi$
$660$		0			0
$661$	17.7487	+	30.7417i	0.690346	+	1.19571i	0.971725	+	0.236117i	$0.0758749\pi$
$661$	17.7487	+	30.7417i	0.690346	+	1.19571i	−0.281379	+	0.959597i	$0.590792\pi$
$662$	−3.32889	−	16.3382i	−0.129381	−	0.635004i
$663$		0			0
$664$	−32.4964	+	2.58542i	−1.26110	+	0.100334i
$665$	−1.95197	−	6.56860i	−0.0756943	−	0.254719i
$666$		0			0
$667$	13.4287			0.519960
$668$	−5.82542	−	13.7022i	−0.225392	−	0.530152i
$669$		0			0
$670$	−10.3254	+	5.50549i	−0.398904	+	0.212695i
$671$	14.1489	+	24.5066i	0.546211	+	0.946065i
$672$		0			0
$673$	41.4746	+	23.9454i	1.59873	+	0.923027i	0.991733	+	0.128322i	$0.0409591\pi$
$673$	41.4746	+	23.9454i	1.59873	+	0.923027i	0.606997	+	0.794704i	$0.292374\pi$
$674$	−14.1667	−	4.73563i	−0.545680	−	0.182409i
$675$		0			0
$676$	−11.5955	−	8.72753i	−0.445982	−	0.335674i
$677$	0.0431856	−	0.0747996i	0.00165976	−	0.00287478i	−0.865194	−	0.501437i	$-0.832805\pi$
$677$	0.0431856	−	0.0747996i	0.00165976	−	0.00287478i	0.866854	+	0.498562i	$0.166138\pi$
$678$		0			0
$679$	12.2485	−	7.07165i	0.470053	−	0.271385i
$680$	−8.07133	−	1.26406i	−0.309521	−	0.0484745i
$681$		0			0
$682$	19.3427	−	17.1228i	0.740670	−	0.655665i
$683$		−	24.0380i		−	0.919788i	−0.887974	−	0.459894i	$-0.847887\pi$
$683$		−	24.0380i		−	0.919788i	0.887974	−	0.459894i	$-0.152113\pi$
$684$		0			0
$685$	−14.8814	+	4.42226i	−0.568588	+	0.168966i
$686$	13.1970	+	14.9079i	0.503863	+	0.569187i
$687$		0			0
$688$	−12.5153	+	12.9896i	−0.477143	+	0.495222i
$689$	24.0661	−	13.8946i	0.916846	−	0.529342i
$690$		0			0
$691$	36.1685	+	20.8819i	1.37591	+	0.794384i	0.991665	−	0.128845i	$-0.0411271\pi$
$691$	36.1685	+	20.8819i	1.37591	+	0.794384i	0.384249	+	0.923229i	$0.374460\pi$
$692$	13.8524	+	10.4262i	0.526589	+	0.396344i
$693$		0			0
$694$	31.2637	+	10.4508i	1.18675	+	0.396707i
$695$	25.9457	+	6.20495i	0.984176	+	0.235367i
$696$		0			0
$697$	−8.21087	+	4.74055i	−0.311009	+	0.179561i
$698$	7.89010	−	1.60760i	0.298645	−	0.0608484i
$699$		0			0
$700$	−6.13501	+	9.14126i	−0.231882	+	0.345507i
$701$			2.12514i			0.0802654i	0.999194	+	0.0401327i	$0.0127781\pi$
$701$			2.12514i			0.0802654i	−0.999194	+	0.0401327i	$0.987222\pi$
$702$		0			0
$703$	−18.1405			−0.684182
$704$	28.6692	+	35.2803i	1.08051	+	1.32967i
$705$		0			0
$706$	−2.11012	+	0.429934i	−0.0794155	+	0.0161808i
$707$	−15.9631	+	9.21629i	−0.600354	+	0.346614i
$708$		0			0
$709$	2.08824	−	3.61694i	0.0784256	−	0.135837i	−0.824145	−	0.566379i	$-0.808344\pi$
$709$	2.08824	−	3.61694i	0.0784256	−	0.135837i	0.902571	+	0.430541i	$0.141677\pi$
$710$	−1.35445	+	40.1224i	−0.0508317	+	1.50577i
$711$		0			0
$712$	14.7060	+	21.3582i	0.551129	+	0.800434i
$713$	−3.38787	+	5.86797i	−0.126877	+	0.219757i
$714$		0			0
$715$	−20.9423	+	22.1074i	−0.783198	+	0.826769i
$716$	0.269266	−	2.20336i	0.0100630	−	0.0823434i
$717$		0			0
$718$	8.86877	+	10.0186i	0.330979	+	0.373890i
$719$	−24.0884			−0.898346			−0.449173	−	0.893445i	$-0.648281\pi$
$719$	−24.0884			−0.898346			−0.449173	+	0.893445i	$0.648281\pi$
$720$		0			0
$721$	−1.49568			−0.0557022
$722$	10.5470	+	11.9143i	0.392517	+	0.443406i
$723$		0			0
$724$	3.07215	−	25.1389i	0.114176	−	0.934279i
$725$	−14.4115	+	28.4072i	−0.535229	+	1.05502i
$726$		0			0
$727$	23.4466	−	40.6108i	0.869587	−	1.50617i	0.00716831	−	0.999974i	$-0.497718\pi$
$727$	23.4466	−	40.6108i	0.869587	−	1.50617i	0.862419	−	0.506195i	$-0.168948\pi$
$728$	4.23208	+	6.14647i	0.156851	+	0.227803i
$729$		0			0
$730$	31.1905	+	1.05293i	1.15441	+	0.0389706i
$731$	2.91253	−	5.04465i	0.107724	−	0.186583i
$732$		0			0
$733$	−15.3758	+	8.87721i	−0.567917	+	0.327887i	−0.756317	−	0.654205i	$-0.773003\pi$
$733$	−15.3758	+	8.87721i	−0.567917	+	0.327887i	0.188400	+	0.982092i	$0.439670\pi$
$734$	11.2694	−	2.29613i	0.415962	−	0.0847517i
$735$		0			0
$736$	−10.0656	−	6.39239i	−0.371023	−	0.235626i
$737$	−21.0271			−0.774543
$738$		0			0
$739$			8.50437i			0.312838i	0.987691	+	0.156419i	$0.0499951\pi$
$739$			8.50437i			0.312838i	−0.987691	+	0.156419i	$0.950005\pi$
$740$	18.5706	+	22.4616i	0.682667	+	0.825707i
$741$		0			0
$742$	17.6898	−	3.60427i	0.649412	−	0.132317i
$743$	−43.6052	+	25.1755i	−1.59972	+	0.923598i	−0.608179	+	0.793800i	$0.708100\pi$
$743$	−43.6052	+	25.1755i	−1.59972	+	0.923598i	−0.991540	+	0.129798i	$0.958567\pi$
$744$		0			0
$745$	−12.5061	−	2.99086i	−0.458189	−	0.109577i
$746$	15.5794	+	5.20786i	0.570402	+	0.190673i
$747$		0			0
$748$	−11.7296	−	8.82840i	−0.428875	−	0.322798i
$749$	−2.83366	−	1.63601i	−0.103540	−	0.0597787i
$750$		0			0
$751$	−44.8169	+	25.8750i	−1.63539	+	0.944193i	−0.652999	+	0.757359i	$0.726489\pi$
$751$	−44.8169	+	25.8750i	−1.63539	+	0.944193i	−0.982391	+	0.186834i	$0.940177\pi$
$752$	26.9293	+	25.9462i	0.982011	+	0.946160i
$753$		0			0
$754$	14.3119	+	16.1674i	0.521210	+	0.588783i
$755$	−1.36128	−	4.58085i	−0.0495421	−	0.166714i
$756$		0			0
$757$			16.5374i			0.601064i	0.953772	+	0.300532i	$0.0971642\pi$
$757$			16.5374i			0.601064i	−0.953772	+	0.300532i	$0.902836\pi$
$758$	−0.205765	+	0.182150i	−0.00747372	+	0.00661598i
$759$		0			0
$760$	−2.72397	+	17.3932i	−0.0988087	+	0.630917i
$761$	30.1188	−	17.3891i	1.09180	−	0.630354i	0.157748	−	0.987479i	$-0.449577\pi$
$761$	30.1188	−	17.3891i	1.09180	−	0.630354i	0.934056	+	0.357126i	$0.116243\pi$
$762$		0			0
$763$	2.81876	−	4.88223i	0.102046	−	0.176749i
$764$	−36.3782	−	27.3805i	−1.31612	−	0.990591i
$765$		0			0
$766$	−24.8141	−	8.29485i	−0.896571	−	0.299705i
$767$	−15.2024	−	8.77710i	−0.548926	−	0.316923i
$768$		0			0
$769$	−7.71708	−	13.3664i	−0.278285	−	0.482003i	0.692674	−	0.721251i	$-0.256433\pi$
$769$	−7.71708	−	13.3664i	−0.278285	−	0.482003i	−0.970959	+	0.239248i	$0.923099\pi$
$770$	−17.4566	+	9.30786i	−0.629092	+	0.335432i
$771$		0			0
$772$	−9.09776	−	21.3991i	−0.327435	−	0.770171i
$773$	−29.3290			−1.05489			−0.527446	−	0.849589i	$-0.676850\pi$
$773$	−29.3290			−1.05489			−0.527446	+	0.849589i	$0.676850\pi$
$774$		0			0
$775$	−8.77736	−	13.4642i	−0.315292	−	0.483648i
$776$	−36.2220	+	2.88184i	−1.30029	+	0.103452i
$777$		0			0
$778$	6.64658	+	32.6215i	0.238292	+	1.16954i
$779$	10.2156	+	17.6939i	0.366011	+	0.633949i
$780$		0			0
$781$	−36.0698	+	62.4748i	−1.29068	+	2.23552i
$782$	3.65201	+	1.22079i	0.130596	+	0.0436554i
$783$		0			0
$784$	−6.40686	−	22.2478i	−0.228817	−	0.794565i
$785$	−21.8687	−	5.22993i	−0.780527	−	0.186664i
$786$		0			0
$787$	26.3106	+	45.5713i	0.937872	+	1.62444i	0.769431	+	0.638730i	$0.220540\pi$
$787$	26.3106	+	45.5713i	0.937872	+	1.62444i	0.168442	+	0.985712i	$0.446127\pi$
$788$	2.95992	−	24.2205i	0.105443	−	0.862819i
$789$		0			0
$790$	−1.88414	+	3.02305i	−0.0670345	+	0.107555i
$791$	−9.21510			−0.327651
$792$		0			0
$793$		−	11.9344i		−	0.423803i
$794$	−24.7883	+	21.9434i	−0.879704	+	0.778742i
$795$		0			0
$796$	−14.0539	−	1.71748i	−0.498126	−	0.0608746i
$797$	−1.24198	−	2.15117i	−0.0439931	−	0.0761983i	0.843190	−	0.537615i	$-0.180675\pi$
$797$	−1.24198	−	2.15117i	−0.0439931	−	0.0761983i	−0.887183	+	0.461417i	$0.847341\pi$
$798$		0			0
$799$	−10.4583	−	6.03812i	−0.369989	−	0.213613i
$800$	24.3248	−	14.4327i	0.860013	−	0.510272i
$801$		0			0
$802$	−40.1523	−	13.4221i	−1.41783	−	0.473950i
$803$	48.5669	+	28.0401i	1.71389	+	0.989514i
$804$		0			0
$805$	3.56854	−	3.76707i	0.125775	−	0.132772i
$806$	−10.6754	+	2.17511i	−0.376027	+	0.0766148i
$807$		0			0
$808$	47.2072	−	3.75582i	1.66074	−	0.132129i
$809$			25.6629i			0.902261i	0.892458	+	0.451131i	$0.148979\pi$
$809$			25.6629i			0.902261i	−0.892458	+	0.451131i	$0.851021\pi$
$810$		0			0
$811$			26.5970i			0.933948i	0.884271	+	0.466974i	$0.154656\pi$
$811$			26.5970i			0.933948i	−0.884271	+	0.466974i	$0.845344\pi$
$812$	5.48824	+	12.9091i	0.192599	+	0.453019i
$813$		0			0
$814$	10.4558	+	51.3171i	0.366475	+	1.79866i
$815$	29.5684	+	28.0101i	1.03574	+	0.981153i
$816$		0			0
$817$	−10.8709	−	6.27631i	−0.380324	−	0.219580i
$818$	−0.932682	+	2.79013i	−0.0326105	+	0.0975546i
$819$		0			0
$820$	11.4509	−	30.7623i	0.399882	−	1.07427i
$821$	26.3429	+	15.2091i	0.919373	+	0.530800i	0.883435	−	0.468554i	$-0.155225\pi$
$821$	26.3429	+	15.2091i	0.919373	+	0.530800i	0.0359383	+	0.999354i	$0.488558\pi$
$822$		0			0
$823$	4.23623	+	7.33737i	0.147666	+	0.255764i	0.930364	−	0.366636i	$-0.119491\pi$
$823$	4.23623	+	7.33737i	0.147666	+	0.255764i	−0.782699	+	0.622401i	$0.786157\pi$
$824$	3.46974	+	1.65135i	0.120874	+	0.0575274i
$825$		0			0
$826$	−7.55900	−	8.53900i	−0.263011	−	0.297110i
$827$			37.2624i			1.29574i	0.761750	+	0.647871i	$0.224340\pi$
$827$			37.2624i			1.29574i	−0.761750	+	0.647871i	$0.775660\pi$
$828$		0			0
$829$	−18.4167			−0.639639			−0.319820	−	0.947478i	$-0.603622\pi$
$829$	−18.4167			−0.639639			−0.319820	+	0.947478i	$0.603622\pi$
$830$	−19.2780	+	30.9311i	−0.669148	+	1.07363i
$831$		0			0
$832$	−3.03155	−	18.9313i	−0.105100	−	0.656325i
$833$	3.73830	+	6.47493i	0.129525	+	0.224343i
$834$		0			0
$835$	−16.1899	−	3.87185i	−0.560276	−	0.133991i
$836$	−19.0246	+	25.2764i	−0.657980	+	0.874203i
$837$		0			0
$838$	4.38510	−	13.1181i	0.151481	−	0.453157i
$839$	7.35228	−	12.7345i	0.253829	−	0.439645i	−0.710748	−	0.703447i	$-0.751643\pi$
$839$	7.35228	−	12.7345i	0.253829	−	0.439645i	0.964577	+	0.263802i	$0.0849766\pi$
$840$		0			0
$841$	5.79320	+	10.0341i	0.199765	+	0.346004i
$842$	2.91275	−	0.593469i	0.100380	−	0.0204523i
$843$		0			0
$844$	−5.07232	−	11.9308i	−0.174596	−	0.410674i
$845$	−15.5538	+	4.62207i	−0.535066	+	0.159004i
$846$		0			0
$847$	−23.4395			−0.805390
$848$	−45.0167	−	11.1695i	−1.54588	−	0.383564i
$849$		0			0
$850$	−6.50178	+	6.41538i	−0.223009	+	0.220046i
$851$	−6.86833	−	11.8963i	−0.235443	−	0.407800i
$852$		0			0
$853$	−11.2327	−	6.48519i	−0.384600	−	0.222049i	0.295218	−	0.955430i	$-0.404608\pi$
$853$	−11.2327	−	6.48519i	−0.384600	−	0.222049i	−0.679818	+	0.733381i	$0.737941\pi$
$854$	2.45803	−	7.35322i	0.0841119	−	0.251622i
$855$		0			0
$856$	4.76734	+	6.92385i	0.162944	+	0.236652i
$857$	−3.36521	+	5.82871i	−0.114953	+	0.199105i	−0.917761	−	0.397133i	$-0.870005\pi$
$857$	−3.36521	+	5.82871i	−0.114953	+	0.199105i	0.802808	+	0.596238i	$0.203339\pi$
$858$		0			0
$859$	−33.3860	+	19.2754i	−1.13912	+	0.657669i	−0.946212	−	0.323549i	$-0.895124\pi$
$859$	−33.3860	+	19.2754i	−1.13912	+	0.657669i	−0.192904	+	0.981218i	$0.561791\pi$
$860$	3.35725	+	19.8855i	0.114481	+	0.678089i
$861$		0			0
$862$	3.60148	+	4.06840i	0.122667	+	0.138570i
$863$			13.4795i			0.458847i	0.973327	+	0.229424i	$0.0736841\pi$
$863$			13.4795i			0.458847i	−0.973327	+	0.229424i	$0.926316\pi$
$864$		0			0
$865$	18.5810	−	5.52167i	0.631773	−	0.187742i
$866$	7.06142	−	6.25100i	0.239957	−	0.212418i
$867$		0			0
$868$	−7.02552	−	0.858569i	−0.238462	−	0.0291417i
$869$	−5.54347	+	3.20052i	−0.188049	+	0.108570i
$870$		0			0
$871$	7.67995	+	4.43402i	0.260225	+	0.150241i
$872$	−11.9294	+	8.21384i	−0.403980	+	0.278156i
$873$		0			0
$874$	2.63072	−	7.86984i	0.0889855	−	0.266201i
$875$	4.13920	+	11.5917i	0.139930	+	0.391872i
$876$		0			0
$877$	−13.5129	+	7.80171i	−0.456300	+	0.263445i	−0.710487	−	0.703710i	$-0.751525\pi$
$877$	−13.5129	+	7.80171i	−0.456300	+	0.263445i	0.254187	+	0.967155i	$0.418192\pi$
$878$	10.9392	+	53.6898i	0.369180	+	1.81194i
$879$		0			0
$880$	50.7730	−	2.31929i	1.71156	−	0.0781833i
$881$			25.0226i			0.843032i	0.906821	+	0.421516i	$0.138502\pi$
$881$			25.0226i			0.843032i	−0.906821	+	0.421516i	$0.861498\pi$
$882$		0			0
$883$	13.8202			0.465085			0.232543	−	0.972586i	$-0.425295\pi$
$883$	13.8202			0.465085			0.232543	+	0.972586i	$0.425295\pi$
$884$	2.42245	+	5.69793i	0.0814759	+	0.191642i
$885$		0			0
$886$	−6.61241	−	32.4538i	−0.222148	−	1.09031i
$887$	16.1656	−	9.33323i	0.542789	−	0.313379i	−0.203420	−	0.979092i	$-0.565206\pi$
$887$	16.1656	−	9.33323i	0.542789	−	0.313379i	0.746208	+	0.665712i	$0.231872\pi$
$888$		0			0
$889$	2.83336	−	4.90753i	0.0950279	−	0.164593i
$890$	28.9757	+	0.978163i	0.971269	+	0.0327881i
$891$		0			0
$892$	−25.0815	−	18.8779i	−0.839790	−	0.632079i
$893$	−13.0117	+	22.5370i	−0.435421	+	0.754172i
$894$		0			0
$895$	−1.80170	−	1.70675i	−0.0602242	−	0.0570504i
$896$	2.03127	−	12.2887i	0.0678600	−	0.410535i
$897$		0			0
$898$	16.7166	−	14.7981i	0.557840	−	0.493818i
$899$	−20.4788			−0.683007
$900$		0			0
$901$	14.9783			0.499001
$902$	44.1656	−	39.0968i	1.47055	−	1.30178i
$903$		0			0
$904$	21.3775	+	10.1742i	0.711005	+	0.338388i
$905$	−20.5562	−	19.4729i	−0.683312	−	0.647301i
$906$		0			0
$907$	20.7283	−	35.9025i	0.688273	−	1.19212i	−0.284123	−	0.958788i	$-0.591703\pi$
$907$	20.7283	−	35.9025i	0.688273	−	1.19212i	0.972396	−	0.233336i	$-0.0749642\pi$
$908$	0.235739	−	0.313206i	0.00782326	−	0.0103941i
$909$		0			0
$910$	8.33863	+	0.281496i	0.276423	+	0.00933149i
$911$	2.80277	−	4.85454i	0.0928600	−	0.160838i	−0.815853	−	0.578259i	$-0.803732\pi$
$911$	2.80277	−	4.85454i	0.0928600	−	0.160838i	0.908713	+	0.417420i	$0.137066\pi$
$912$		0			0
$913$	−56.7193	+	32.7469i	−1.87714	+	1.08376i
$914$	−2.37626	−	11.6627i	−0.0785998	−	0.385769i
$915$		0			0
$916$	−3.03744	+	1.29136i	−0.100360	+	0.0426677i
$917$	−15.6336			−0.516266
$918$		0			0
$919$		−	30.8044i		−	1.01614i	−0.861315	−	0.508072i	$-0.830358\pi$
$919$		−	30.8044i		−	1.01614i	0.861315	−	0.508072i	$-0.169642\pi$
$920$	−12.4376	+	4.79904i	−0.410054	+	0.158220i
$921$		0			0
$922$	−7.00289	−	34.3703i	−0.230628	−	1.13192i
$923$	26.3483	−	15.2122i	0.867266	−	0.500716i
$924$		0			0
$925$	32.5366	−	1.76240i	1.06980	−	0.0579474i
$926$	9.28972	−	27.7903i	0.305279	−	0.913247i
$927$		0			0
$928$	1.52077	−	36.0063i	0.0499216	−	1.18196i
$929$	−23.8104	−	13.7469i	−0.781194	−	0.451023i	0.0556590	−	0.998450i	$-0.482274\pi$
$929$	−23.8104	−	13.7469i	−0.781194	−	0.451023i	−0.836853	+	0.547427i	$0.815607\pi$
$930$		0			0
$931$	13.9530	−	8.05579i	0.457293	−	0.264018i
$932$	4.90727	−	40.1554i	0.160743	−	1.31533i
$933$		0			0
$934$	−1.68991	+	1.49596i	−0.0552955	+	0.0489494i
$935$	−15.7335	+	4.67550i	−0.514541	+	0.152905i
$936$		0			0
$937$			13.6341i			0.445407i	0.974886	+	0.222704i	$0.0714882\pi$
$937$			13.6341i			0.445407i	−0.974886	+	0.222704i	$0.928512\pi$
$938$	3.81866	+	4.31374i	0.124684	+	0.140849i
$939$		0			0
$940$	41.2256	−	6.96009i	1.34463	−	0.227013i
$941$	49.7730	−	28.7364i	1.62255	−	0.936781i	0.636319	−	0.771426i	$-0.280456\pi$
$941$	49.7730	−	28.7364i	1.62255	−	0.936781i	0.986234	−	0.165355i	$-0.0528771\pi$
$942$		0			0
$943$	−7.73561	+	13.3985i	−0.251906	+	0.436314i
$944$	8.10793	+	28.1548i	0.263891	+	0.916360i
$945$		0			0
$946$	−11.4891	+	34.3698i	−0.373543	+	1.11746i
$947$	−16.7732	−	9.68402i	−0.545056	−	0.314688i	0.202069	−	0.979371i	$-0.435233\pi$
$947$	−16.7732	−	9.68402i	−0.545056	−	0.314688i	−0.747126	+	0.664683i	$0.768567\pi$
$948$		0			0
$949$	−11.8257	−	20.4828i	−0.383880	−	0.664899i
$950$	13.8247	+	14.0109i	0.448533	+	0.454574i
$951$		0			0
$952$	0.319008	+	4.00963i	0.0103391	+	0.129953i
$953$	4.34158			0.140638			0.0703188	−	0.997525i	$-0.477598\pi$
$953$	4.34158			0.140638			0.0703188	+	0.997525i	$0.477598\pi$
$954$		0			0
$955$	−48.7961	+	14.5006i	−1.57900	+	0.469229i
$956$	−37.4172	+	15.9078i	−1.21016	+	0.514495i
$957$		0			0
$958$	8.28526	−	1.68811i	0.267685	−	0.0545404i
$959$	3.82170	+	6.61938i	0.123409	+	0.213751i
$960$		0			0
$961$	−10.3335	+	17.8981i	−0.333338	+	0.577358i
$962$	7.00245	−	20.9479i	0.225768	−	0.675388i
$963$		0			0
$964$	27.5573	+	20.7414i	0.887561	+	0.668034i
$965$	−25.2844	−	6.04680i	−0.813933	−	0.194653i
$966$		0			0
$967$	16.5665	+	28.6939i	0.532741	+	0.922735i	0.999269	+	0.0382285i	$0.0121715\pi$
$967$	16.5665	+	28.6939i	0.532741	+	0.922735i	−0.466528	+	0.884507i	$0.654495\pi$
$968$	54.3757	+	25.8789i	1.74770	+	0.831780i
$969$		0			0
$970$	−21.4882	+	34.4773i	−0.689943	+	1.10700i
$971$	22.0082			0.706277			0.353138	−	0.935571i	$-0.385114\pi$
$971$	22.0082			0.706277			0.353138	+	0.935571i	$0.385114\pi$
$972$		0			0
$973$		−	13.1344i		−	0.421070i
$974$	−15.5579	−	17.5749i	−0.498508	−	0.563137i
$975$		0			0
$976$	−13.8207	+	14.3444i	−0.442390	+	0.459153i
$977$	−14.7558	−	25.5578i	−0.472080	−	0.817667i	0.527409	−	0.849611i	$-0.323163\pi$
$977$	−14.7558	−	25.5578i	−0.472080	−	0.817667i	−0.999490	+	0.0319442i	$0.989830\pi$
$978$		0			0
$979$	45.1183	+	26.0491i	1.44199	+	0.832532i
$980$	−24.2585	−	9.02994i	−0.774911	−	0.288451i
$981$		0			0
$982$	−5.98052	+	17.8908i	−0.190846	+	0.570919i
$983$	−39.8190	−	22.9895i	−1.27003	−	0.733251i	−0.295035	−	0.955486i	$-0.595331\pi$
$983$	−39.8190	−	22.9895i	−1.27003	−	0.733251i	−0.974993	+	0.222235i	$0.928665\pi$
$984$		0			0
$985$	−19.8052	−	18.7615i	−0.631048	−	0.597791i
$986$	2.32351	+	11.4038i	0.0739956	+	0.363171i
$987$		0			0
$988$	12.2786	−	5.22022i	0.390636	−	0.166077i
$989$		−	9.50531i		−	0.302251i
$990$		0			0
$991$		−	52.8232i		−	1.67798i	−0.544144	−	0.838992i	$-0.683146\pi$
$991$		−	52.8232i		−	1.67798i	0.544144	−	0.838992i	$-0.316854\pi$
$992$	15.3501	+	9.74844i	0.487367	+	0.309513i
$993$		0			0
$994$	19.3673	−	3.94606i	0.614294	−	0.125161i
$995$	−10.8863	+	11.4919i	−0.345119	+	0.364319i
$996$		0			0
$997$	−43.4452	−	25.0831i	−1.37592	−	0.794389i	−0.384257	−	0.923226i	$-0.625542\pi$
$997$	−43.4452	−	25.0831i	−1.37592	−	0.794389i	−0.991666	+	0.128837i	$0.958876\pi$
$998$	55.3113	+	18.4894i	1.75085	+	0.585272i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	540.2.n.d.359.18		48
3.2	odd	2		180.2.n.d.119.7	yes	48
4.3	odd	2	inner	540.2.n.d.359.2		48
5.4	even	2	inner	540.2.n.d.359.7		48
9.4	even	3		180.2.n.d.59.2	✓	48
9.5	odd	6	inner	540.2.n.d.179.23		48
12.11	even	2		180.2.n.d.119.23	yes	48
15.2	even	4		900.2.r.g.551.19		48
15.8	even	4		900.2.r.g.551.6		48
15.14	odd	2		180.2.n.d.119.18	yes	48
20.19	odd	2	inner	540.2.n.d.359.23		48
36.23	even	6	inner	540.2.n.d.179.7		48
36.31	odd	6		180.2.n.d.59.18	yes	48
45.4	even	6		180.2.n.d.59.23	yes	48
45.13	odd	12		900.2.r.g.851.14		48
45.14	odd	6	inner	540.2.n.d.179.2		48
45.22	odd	12		900.2.r.g.851.11		48
60.23	odd	4		900.2.r.g.551.14		48
60.47	odd	4		900.2.r.g.551.11		48
60.59	even	2		180.2.n.d.119.2	yes	48
180.59	even	6	inner	540.2.n.d.179.18		48
180.67	even	12		900.2.r.g.851.19		48
180.103	even	12		900.2.r.g.851.6		48
180.139	odd	6		180.2.n.d.59.7	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.n.d.59.2	✓	48	9.4	even	3
180.2.n.d.59.7	yes	48	180.139	odd	6
180.2.n.d.59.18	yes	48	36.31	odd	6
180.2.n.d.59.23	yes	48	45.4	even	6
180.2.n.d.119.2	yes	48	60.59	even	2
180.2.n.d.119.7	yes	48	3.2	odd	2
180.2.n.d.119.18	yes	48	15.14	odd	2
180.2.n.d.119.23	yes	48	12.11	even	2
540.2.n.d.179.2		48	45.14	odd	6	inner
540.2.n.d.179.7		48	36.23	even	6	inner
540.2.n.d.179.18		48	180.59	even	6	inner
540.2.n.d.179.23		48	9.5	odd	6	inner
540.2.n.d.359.2		48	4.3	odd	2	inner
540.2.n.d.359.7		48	5.4	even	2	inner
540.2.n.d.359.18		48	1.1	even	1	trivial
540.2.n.d.359.23		48	20.19	odd	2	inner
900.2.r.g.551.6		48	15.8	even	4
900.2.r.g.551.11		48	60.47	odd	4
900.2.r.g.551.14		48	60.23	odd	4
900.2.r.g.551.19		48	15.2	even	4
900.2.r.g.851.6		48	180.103	even	12
900.2.r.g.851.11		48	45.22	odd	12
900.2.r.g.851.14		48	45.13	odd	12
900.2.r.g.851.19		48	180.67	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	540.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.937387 + 1.05892i) q^{2} +(-0.242609 + 1.98523i) q^{4} +(1.62334 + 1.53778i) q^{5} +(0.550457 - 0.953419i) q^{7} +(-2.32961 + 1.60403i) q^{8} +(-0.106691 + 3.16048i) q^{10} +(-2.84126 + 4.92120i) q^{11} +(2.07548 - 1.19828i) q^{13} +(1.52558 - 0.310835i) q^{14} +(-3.88228 - 0.963271i) q^{16} +1.29175 q^{17} -2.78362i q^{19} +(-3.44669 + 2.84961i) q^{20} +(-7.87450 + 1.60442i) q^{22} +(1.82546 - 1.05393i) q^{23} +(0.270437 + 4.99268i) q^{25} +(3.21441 + 1.07451i) q^{26} +(1.75921 + 1.32409i) q^{28} +(5.51723 + 3.18537i) q^{29} +(-2.78385 + 1.60725i) q^{31} +(-2.61918 - 5.01397i) q^{32} +(1.21087 + 1.36785i) q^{34} +(2.35973 - 0.701235i) q^{35} -6.51687i q^{37} +(2.94763 - 2.60933i) q^{38} +(-6.24839 - 0.978569i) q^{40} +(-6.35642 + 3.66988i) q^{41} +(2.25473 - 3.90530i) q^{43} +(-9.08040 - 6.83448i) q^{44} +(2.82719 + 0.945071i) q^{46} +(-8.09628 - 4.67439i) q^{47} +(2.89400 + 5.01255i) q^{49} +(-5.03333 + 4.96645i) q^{50} +(1.87533 + 4.41103i) q^{52} +11.5954 q^{53} +(-12.1801 + 3.61952i) q^{55} +(0.246959 + 3.10404i) q^{56} +(1.79874 + 8.82821i) q^{58} +(-3.66237 - 6.34341i) q^{59} +(2.48990 - 4.31263i) q^{61} +(-4.31149 - 1.44124i) q^{62} +(2.85419 - 7.47353i) q^{64} +(5.21191 + 1.24643i) q^{65} +(1.85016 + 3.20457i) q^{67} +(-0.313389 + 2.56441i) q^{68} +(2.95453 + 1.84143i) q^{70} +12.6950 q^{71} -9.86891i q^{73} +(6.90082 - 6.10883i) q^{74} +(5.52614 + 0.675333i) q^{76} +(3.12798 + 5.41781i) q^{77} +(0.975531 + 0.563223i) q^{79} +(-4.82094 - 7.53382i) q^{80} +(-9.84453 - 3.29082i) q^{82} +(9.98138 + 5.76275i) q^{83} +(2.09694 + 1.98643i) q^{85} +(6.24894 - 1.27321i) q^{86} +(-1.27471 - 16.0219i) q^{88} -9.16815i q^{89} -2.63841i q^{91} +(1.64942 + 3.87966i) q^{92} +(-2.63956 - 12.9550i) q^{94} +(4.28061 - 4.51876i) q^{95} +(11.1257 + 6.42344i) q^{97} +(-2.59507 + 7.76320i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{4} + 18 q^{5} - 16 q^{10} + 42 q^{14} + 30 q^{16} - 26 q^{25} - 4 q^{34} + 10 q^{40} - 96 q^{41} + 4 q^{46} + 32 q^{49} + 90 q^{50} - 6 q^{56} + 8 q^{61} - 20 q^{64} + 6 q^{65} + 4 q^{70} - 72 q^{74}+ \cdots - 62 q^{94}+O(q^{100}) \) 48 * q - 2 * q^4 + 18 * q^5 - 16 * q^10 + 42 * q^14 + 30 * q^16 - 26 * q^25 - 4 * q^34 + 10 * q^40 - 96 * q^41 + 4 * q^46 + 32 * q^49 + 90 * q^50 - 6 * q^56 + 8 * q^61 - 20 * q^64 + 6 * q^65 + 4 * q^70 - 72 * q^74 - 4 * q^85 - 108 * q^86 - 62 * q^94

Introduction

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