LMFDB - Embedded newform 180.2.n.d.59.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [180,2,Mod(59,180)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(180, 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("180.59"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	180.n (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.43730723638$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			59.2
Character	$\chi$	$=$	180.59
Dual form			180.2.n.d.119.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.38574 + 0.282343i) q^{2} +(-0.959839 - 1.44177i) q^{3} +(1.84056 - 0.782509i) q^{4} +(0.520093 - 2.17474i) q^{5} +(1.73716 + 1.72692i) q^{6} +(0.550457 + 0.953419i) q^{7} +(-2.32961 + 1.60403i) q^{8} +(-1.15742 + 2.76774i) q^{9} +(-0.106691 + 3.16048i) q^{10} +(-2.84126 - 4.92120i) q^{11} +(-2.89485 - 1.90259i) q^{12} +(-2.07548 - 1.19828i) q^{13} +(-1.03198 - 1.16578i) q^{14} +(-3.63469 + 1.33755i) q^{15} +(2.77536 - 2.88052i) q^{16} +1.29175 q^{17} +(0.822430 - 4.16216i) q^{18} -2.78362i q^{19} +(-0.744492 - 4.40973i) q^{20} +(0.846263 - 1.70876i) q^{21} +(5.32672 + 6.01731i) q^{22} +(-1.82546 - 1.05393i) q^{23} +(4.54870 + 1.81916i) q^{24} +(-4.45901 - 2.26214i) q^{25} +(3.21441 + 1.07451i) q^{26} +(5.10139 - 0.987853i) q^{27} +(1.75921 + 1.32409i) q^{28} +(-5.51723 + 3.18537i) q^{29} +(4.65910 - 2.87973i) q^{30} +(2.78385 + 1.60725i) q^{31} +(-3.03264 + 4.77526i) q^{32} +(-4.36810 + 8.82001i) q^{33} +(-1.79003 + 0.364715i) q^{34} +(2.35973 - 0.701235i) q^{35} +(0.0354812 + 5.99990i) q^{36} -6.51687i q^{37} +(0.785937 + 3.85739i) q^{38} +(0.264482 + 4.14253i) q^{39} +(2.27673 + 5.90055i) q^{40} +(6.35642 + 3.66988i) q^{41} +(-0.690246 + 2.60684i) q^{42} +(2.25473 + 3.90530i) q^{43} +(-9.08040 - 6.83448i) q^{44} +(5.41716 + 3.95657i) q^{45} +(2.82719 + 0.945071i) q^{46} +(8.09628 - 4.67439i) q^{47} +(-6.81695 - 1.23660i) q^{48} +(2.89400 - 5.01255i) q^{49} +(6.81773 + 1.87577i) q^{50} +(-1.23987 - 1.86240i) q^{51} +(-4.75773 - 0.581429i) q^{52} +11.5954 q^{53} +(-6.79030 + 2.80925i) q^{54} +(-12.1801 + 3.61952i) q^{55} +(-2.81166 - 1.33815i) q^{56} +(-4.01335 + 2.67183i) q^{57} +(6.74609 - 5.97186i) q^{58} +(-3.66237 + 6.34341i) q^{59} +(-5.64324 + 5.30602i) q^{60} +(2.48990 + 4.31263i) q^{61} +(-4.31149 - 1.44124i) q^{62} +(-3.27592 + 0.420017i) q^{63} +(2.85419 - 7.47353i) q^{64} +(-3.68540 + 3.89043i) q^{65} +(3.56280 - 13.4556i) q^{66} +(1.85016 - 3.20457i) q^{67} +(2.37754 - 1.01080i) q^{68} +(0.232621 + 3.64351i) q^{69} +(-3.07199 + 1.63798i) q^{70} +12.6950 q^{71} +(-1.74320 - 8.30429i) q^{72} -9.86891i q^{73} +(1.83999 + 9.03070i) q^{74} +(1.01844 + 8.60016i) q^{75} +(-2.17821 - 5.12344i) q^{76} +(3.12798 - 5.41781i) q^{77} +(-1.53612 - 5.66581i) q^{78} +(-0.975531 + 0.563223i) q^{79} +(-4.82094 - 7.53382i) q^{80} +(-6.32077 - 6.40686i) q^{81} +(-9.84453 - 3.29082i) q^{82} +(-9.98138 + 5.76275i) q^{83} +(0.220480 - 3.80730i) q^{84} +(0.671827 - 2.80921i) q^{85} +(-4.22710 - 4.77514i) q^{86} +(9.88823 + 4.89714i) q^{87} +(14.5128 + 6.90704i) q^{88} -9.16815i q^{89} +(-8.62389 - 3.95329i) q^{90} -2.63841i q^{91} +(-4.18460 - 0.511387i) q^{92} +(-0.354749 - 5.55638i) q^{93} +(-9.89957 + 8.76343i) q^{94} +(-6.05366 - 1.44774i) q^{95} +(9.79568 - 0.211108i) q^{96} +(-11.1257 + 6.42344i) q^{97} +(-2.59507 + 7.76320i) q^{98} +(16.9091 - 2.16798i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 2 q^{4} - 18 q^{5} - 12 q^{9} - 16 q^{10} - 42 q^{14} + 30 q^{16} - 12 q^{21} - 6 q^{24} - 26 q^{25} - 12 q^{30} - 4 q^{34} + 96 q^{36} + 10 q^{40} + 96 q^{41} - 66 q^{45} + 4 q^{46} + 32 q^{49}+ \cdots + 54 q^{96}+O(q^{100}) $ 48 * q - 2 * q^4 - 18 * q^5 - 12 * q^9 - 16 * q^10 - 42 * q^14 + 30 * q^16 - 12 * q^21 - 6 * q^24 - 26 * q^25 - 12 * q^30 - 4 * q^34 + 96 * q^36 + 10 * q^40 + 96 * q^41 - 66 * q^45 + 4 * q^46 + 32 * q^49 - 90 * q^50 - 30 * q^54 + 6 * q^56 - 42 * q^60 + 8 * q^61 - 20 * q^64 - 6 * q^65 + 36 * q^66 - 96 * q^69 + 4 * q^70 + 72 * q^74 + 36 * q^81 - 6 * q^84 - 4 * q^85 + 108 * q^86 - 6 * q^90 - 62 * q^94 + 54 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.38574	+	0.282343i	−0.979868	+	0.199647i
$2$	−1.38574	+	0.282343i	−0.979868	+	0.199647i
$3$	−0.959839	−	1.44177i	−0.554163	−	0.832408i
$3$	−0.959839	−	1.44177i	−0.554163	−	0.832408i
$4$	1.84056	−	0.782509i	0.920282	−	0.391255i
$5$	0.520093	−	2.17474i	0.232593	−	0.972574i
$5$	0.520093	−	2.17474i	0.232593	−	0.972574i
$6$	1.73716	+	1.72692i	0.709194	+	0.705013i
$7$	0.550457	+	0.953419i	0.208053	+	0.360358i	0.951101	−	0.308880i	$-0.0999540\pi$
$7$	0.550457	+	0.953419i	0.208053	+	0.360358i	−0.743048	+	0.669238i	$0.766621\pi$
$8$	−2.32961	+	1.60403i	−0.823643	+	0.567109i
$9$	−1.15742	+	2.76774i	−0.385806	+	0.922580i
$10$	−0.106691	+	3.16048i	−0.0337388	+	0.999431i
$11$	−2.84126	−	4.92120i	−0.856671	−	1.48380i	−0.875086	−	0.483967i	$-0.839195\pi$
$11$	−2.84126	−	4.92120i	−0.856671	−	1.48380i	0.0184153	−	0.999830i	$-0.494138\pi$
$12$	−2.89485	−	1.90259i	−0.835670	−	0.549231i
$13$	−2.07548	−	1.19828i	−0.575636	−	0.332343i	0.183761	−	0.982971i	$-0.441173\pi$
$13$	−2.07548	−	1.19828i	−0.575636	−	0.332343i	−0.759397	+	0.650627i	$0.774506\pi$
$14$	−1.03198	−	1.16578i	−0.275809	−	0.311567i
$15$	−3.63469	+	1.33755i	−0.938473	+	0.345353i
$16$	2.77536	−	2.88052i	0.693839	−	0.720130i
$17$	1.29175			0.313294			0.156647	−	0.987655i	$-0.449931\pi$
$17$	1.29175			0.313294			0.156647	+	0.987655i	$0.449931\pi$
$18$	0.822430	−	4.16216i	0.193849	−	0.981031i
$19$		−	2.78362i		−	0.638607i	−0.947652	−	0.319304i	$-0.896551\pi$
$19$		−	2.78362i		−	0.638607i	0.947652	−	0.319304i	$-0.103449\pi$
$20$	−0.744492	−	4.40973i	−0.166473	−	0.986046i
$21$	0.846263	−	1.70876i	0.184670	−	0.372882i
$22$	5.32672	+	6.01731i	1.13566	+	1.28289i
$23$	−1.82546	−	1.05393i	−0.380635	−	0.219760i	0.297459	−	0.954735i	$-0.403861\pi$
$23$	−1.82546	−	1.05393i	−0.380635	−	0.219760i	−0.678095	+	0.734975i	$0.737194\pi$
$24$	4.54870	+	1.81916i	0.928499	+	0.371335i
$25$	−4.45901	−	2.26214i	−0.891801	−	0.452427i
$26$	3.21441	+	1.07451i	0.630398	+	0.210729i
$27$	5.10139	−	0.987853i	0.981762	−	0.190112i
$28$	1.75921	+	1.32409i	0.332459	+	0.250230i
$29$	−5.51723	+	3.18537i	−1.02452	+	0.591509i	−0.915411	−	0.402521i	$-0.868134\pi$
$29$	−5.51723	+	3.18537i	−1.02452	+	0.591509i	−0.109112	+	0.994029i	$0.534801\pi$
$30$	4.65910	−	2.87973i	0.850631	−	0.525763i
$31$	2.78385	+	1.60725i	0.499994	+	0.288671i	0.728711	−	0.684821i	$-0.240120\pi$
$31$	2.78385	+	1.60725i	0.499994	+	0.288671i	−0.228717	+	0.973493i	$0.573453\pi$
$32$	−3.03264	+	4.77526i	−0.536100	+	0.844155i
$33$	−4.36810	+	8.82001i	−0.760389	+	1.53537i
$34$	−1.79003	+	0.364715i	−0.306987	+	0.0625481i
$35$	2.35973	−	0.701235i	0.398867	−	0.118530i
$36$	0.0354812	+	5.99990i	0.00591353	+	0.999983i
$37$		−	6.51687i		−	1.07137i	−0.844419	−	0.535683i	$-0.820054\pi$
$37$		−	6.51687i		−	1.07137i	0.844419	−	0.535683i	$-0.179946\pi$
$38$	0.785937	+	3.85739i	0.127496	+	0.625751i
$39$	0.264482	+	4.14253i	0.0423510	+	0.663336i
$40$	2.27673	+	5.90055i	0.359983	+	0.932959i
$41$	6.35642	+	3.66988i	0.992706	+	0.573139i	0.906082	−	0.423102i	$-0.139059\pi$
$41$	6.35642	+	3.66988i	0.992706	+	0.573139i	0.0866240	+	0.996241i	$0.472392\pi$
$42$	−0.690246	+	2.60684i	−0.106507	+	0.402244i
$43$	2.25473	+	3.90530i	0.343843	+	0.595553i	0.985143	−	0.171737i	$-0.0549380\pi$
$43$	2.25473	+	3.90530i	0.343843	+	0.595553i	−0.641300	+	0.767290i	$0.721605\pi$
$44$	−9.08040	−	6.83448i	−1.36892	−	1.03034i
$45$	5.41716	+	3.95657i	0.807542	+	0.589810i
$46$	2.82719	+	0.945071i	0.416847	+	0.139343i
$47$	8.09628	−	4.67439i	1.18096	−	0.681830i	0.224726	−	0.974422i	$-0.427851\pi$
$47$	8.09628	−	4.67439i	1.18096	−	0.681830i	0.956237	+	0.292592i	$0.0945179\pi$
$48$	−6.81695	−	1.23660i	−0.983942	−	0.178488i
$49$	2.89400	−	5.01255i	0.413428	−	0.716078i
$50$	6.81773	+	1.87577i	0.964173	+	0.265274i
$51$	−1.23987	−	1.86240i	−0.173616	−	0.260789i
$52$	−4.75773	−	0.581429i	−0.659778	−	0.0806296i
$53$	11.5954			1.59275			0.796377	−	0.604800i	$-0.206747\pi$
$53$	11.5954			1.59275			0.796377	+	0.604800i	$0.206747\pi$
$54$	−6.79030	+	2.80925i	−0.924042	+	0.382291i
$55$	−12.1801	+	3.61952i	−1.64236	+	0.488056i
$56$	−2.81166	−	1.33815i	−0.375724	−	0.178818i
$57$	−4.01335	+	2.67183i	−0.531582	+	0.353893i
$58$	6.74609	−	5.97186i	0.885805	−	0.784143i
$59$	−3.66237	+	6.34341i	−0.476800	+	0.825842i	−0.999647	−	0.0265849i	$-0.991537\pi$
$59$	−3.66237	+	6.34341i	−0.476800	+	0.825842i	0.522846	+	0.852427i	$0.324870\pi$
$60$	−5.64324	+	5.30602i	−0.728539	+	0.685004i
$61$	2.48990	+	4.31263i	0.318799	+	0.552175i	0.980238	−	0.197823i	$-0.0633873\pi$
$61$	2.48990	+	4.31263i	0.318799	+	0.552175i	−0.661439	+	0.749999i	$0.730054\pi$
$62$	−4.31149	−	1.44124i	−0.547560	−	0.183038i
$63$	−3.27592	+	0.420017i	−0.412728	+	0.0529172i
$64$	2.85419	−	7.47353i	0.356774	−	0.934191i
$65$	−3.68540	+	3.89043i	−0.457117	+	0.482548i
$66$	3.56280	−	13.4556i	0.438550	−	1.65627i
$67$	1.85016	−	3.20457i	0.226033	−	0.391500i	−0.730596	−	0.682810i	$-0.760758\pi$
$67$	1.85016	−	3.20457i	0.226033	−	0.391500i	0.956629	+	0.291310i	$0.0940910\pi$
$68$	2.37754	−	1.01080i	0.288319	−	0.122578i
$69$	0.232621	+	3.64351i	0.0280043	+	0.438627i
$70$	−3.07199	+	1.63798i	−0.367173	+	0.195777i
$71$	12.6950			1.50662			0.753311	−	0.657664i	$-0.228455\pi$
$71$	12.6950			1.50662			0.753311	+	0.657664i	$0.228455\pi$
$72$	−1.74320	−	8.30429i	−0.205438	−	0.978670i
$73$		−	9.86891i		−	1.15507i	−0.816366	−	0.577534i	$-0.804015\pi$
$73$		−	9.86891i		−	1.15507i	0.816366	−	0.577534i	$-0.195985\pi$
$74$	1.83999	+	9.03070i	0.213895	+	1.04980i
$75$	1.01844	+	8.60016i	0.117600	+	0.993061i
$76$	−2.17821	−	5.12344i	−0.249858	−	0.587699i
$77$	3.12798	−	5.41781i	0.356466	−	0.617417i
$78$	−1.53612	−	5.66581i	−0.173931	−	0.641527i
$79$	−0.975531	+	0.563223i	−0.109756	+	0.0633676i	−0.553873	−	0.832601i	$-0.686851\pi$
$79$	−0.975531	+	0.563223i	−0.109756	+	0.0633676i	0.444117	+	0.895969i	$0.353517\pi$
$80$	−4.82094	−	7.53382i	−0.538998	−	0.842307i
$81$	−6.32077	−	6.40686i	−0.702308	−	0.711873i
$82$	−9.84453	−	3.29082i	−1.08715	−	0.363410i
$83$	−9.98138	+	5.76275i	−1.09560	+	0.632544i	−0.935062	−	0.354485i	$-0.884656\pi$
$83$	−9.98138	+	5.76275i	−1.09560	+	0.632544i	−0.160537	+	0.987030i	$0.551323\pi$
$84$	0.220480	−	3.80730i	0.0240564	−	0.415410i
$85$	0.671827	−	2.80921i	0.0728699	−	0.304702i
$86$	−4.22710	−	4.77514i	−0.455820	−	0.514916i
$87$	9.88823	+	4.89714i	1.06013	+	0.525029i
$88$	14.5128	+	6.90704i	1.54707	+	0.736293i
$89$		−	9.16815i		−	0.971822i	−0.874008	−	0.485911i	$-0.838488\pi$
$89$		−	9.16815i		−	0.971822i	0.874008	−	0.485911i	$-0.161512\pi$
$90$	−8.62389	−	3.95329i	−0.909038	−	0.416713i
$91$		−	2.63841i		−	0.276580i
$92$	−4.18460	−	0.511387i	−0.436274	−	0.0533158i
$93$	−0.354749	−	5.55638i	−0.0367858	−	0.576170i
$94$	−9.89957	+	8.76343i	−1.02106	+	0.903878i
$95$	−6.05366	−	1.44774i	−0.621093	−	0.148535i
$96$	9.79568	−	0.211108i	0.999768	−	0.0215462i
$97$	−11.1257	+	6.42344i	−1.12965	+	0.652202i	−0.943846	−	0.330386i	$-0.892821\pi$
$97$	−11.1257	+	6.42344i	−1.12965	+	0.652202i	−0.185801	+	0.982587i	$0.559488\pi$
$98$	−2.59507	+	7.76320i	−0.262142	+	0.784201i
$99$	16.9091	−	2.16798i	1.69943	−	0.217890i
$100$	−9.97723	−	0.674392i	−0.997723	−	0.0674392i
$101$	14.4999	−	8.37150i	1.44279	−	0.832995i	0.444755	−	0.895652i	$-0.353291\pi$
$101$	14.4999	−	8.37150i	1.44279	−	0.832995i	0.998035	+	0.0626572i	$0.0199575\pi$
$102$	2.24397	+	2.23074i	0.222187	+	0.220876i
$103$	−0.679292	+	1.17657i	−0.0669327	+	0.115931i	−0.897550	−	0.440913i	$-0.854655\pi$
$103$	−0.679292	+	1.17657i	−0.0669327	+	0.115931i	0.830617	+	0.556844i	$0.187988\pi$
$104$	6.75715	−	0.537601i	0.662593	−	0.0527162i
$105$	−3.27598	−	2.72912i	−0.319703	−	0.266335i
$106$	−16.0683	+	3.27389i	−1.56069	+	0.317988i
$107$		−	2.97211i		−	0.287324i	−0.989627	−	0.143662i	$-0.954112\pi$
$107$		−	2.97211i		−	0.287324i	0.989627	−	0.143662i	$-0.0458879\pi$
$108$	8.61643	−	5.81009i	0.829116	−	0.559076i
$109$	5.12076			0.490480			0.245240	−	0.969462i	$-0.421133\pi$
$109$	5.12076			0.490480			0.245240	+	0.969462i	$0.421133\pi$
$110$	15.8565	−	8.45468i	1.51186	−	0.806122i
$111$	−9.39584	+	6.25515i	−0.891814	+	0.593712i
$112$	4.27405	+	1.06048i	0.403860	+	0.100206i
$113$	−4.18521	+	7.24900i	−0.393711	+	0.681928i	−0.992936	−	0.118653i	$-0.962142\pi$
$113$	−4.18521	+	7.24900i	−0.393711	+	0.681928i	0.599224	+	0.800581i	$0.295476\pi$
$114$	4.80710	−	4.83561i	0.450226	−	0.452897i
$115$	−3.24144	+	3.42177i	−0.302266	+	0.319082i
$116$	−7.66223	+	10.1802i	−0.711420	+	0.945205i
$117$	5.71873	−	4.35749i	0.528697	−	0.402850i
$118$	3.28409	−	9.82438i	0.302325	−	0.904408i
$119$	0.711050	+	1.23157i	0.0651818	+	0.112898i
$120$	6.32196	−	8.94611i	0.577113	−	0.816664i
$121$	−10.6455	+	18.4385i	−0.967770	+	1.67623i
$122$	−4.66800	−	5.27319i	−0.422621	−	0.477412i
$123$	−0.810007	−	12.6870i	−0.0730359	−	1.14395i
$124$	6.38154	+	0.779870i	0.573079	+	0.0700344i
$125$	−7.23866	+	8.52067i	−0.647445	+	0.762112i
$126$	4.42100	−	1.50697i	0.393854	−	0.134252i
$127$	5.14729			0.456748			0.228374	−	0.973573i	$-0.426659\pi$
$127$	5.14729			0.456748			0.228374	+	0.973573i	$0.426659\pi$
$128$	−1.84508	+	11.1622i	−0.163084	+	0.986612i
$129$	3.46638	−	6.99926i	0.305198	−	0.616251i
$130$	4.00858	−	6.43167i	0.351576	−	0.564095i
$131$	−7.10028	+	12.2980i	−0.620354	+	1.07449i	0.369065	+	0.929403i	$0.379678\pi$
$131$	−7.10028	+	12.2980i	−0.620354	+	1.07449i	−0.989420	+	0.145082i	$0.953656\pi$
$132$	−1.13804	+	19.6519i	−0.0990535	+	1.71048i
$133$	2.65396	−	1.53226i	0.230127	−	0.132864i
$134$	−1.65906	+	4.96309i	−0.143321	+	0.428746i
$135$	0.504869	−	11.6080i	0.0434522	−	0.999056i
$136$	−3.00927	+	2.07199i	−0.258042	+	0.177672i
$137$	−3.47139	−	6.01263i	−0.296581	−	0.513693i	0.678770	−	0.734351i	$-0.262513\pi$
$137$	−3.47139	−	6.01263i	−0.296581	−	0.513693i	−0.975351	+	0.220657i	$0.929180\pi$
$138$	−1.35107	−	4.98329i	−0.115011	−	0.424205i
$139$	−10.3321	−	5.96523i	−0.876356	−	0.505964i	−0.00690070	−	0.999976i	$-0.502197\pi$
$139$	−10.3321	−	5.96523i	−0.876356	−	0.505964i	−0.869455	+	0.494012i	$0.835530\pi$
$140$	3.79451	−	3.13718i	0.320695	−	0.265140i
$141$	−14.5105	−	7.18633i	−1.22201	−	0.605198i
$142$	−17.5920	+	3.58435i	−1.47629	+	0.300792i
$143$			13.6185i			1.13884i
$144$	4.76028	+	11.0154i	0.396690	+	0.917953i
$145$	4.05789	+	13.6552i	0.336990	+	1.13401i
$146$	2.78642	+	13.6758i	0.230606	+	1.13182i
$147$	−10.0047	+	0.638756i	−0.825176	+	0.0526837i
$148$	−5.09951	−	11.9947i	−0.419177	−	0.985960i
$149$	4.98019	+	2.87531i	0.407993	+	0.235555i	0.689927	−	0.723879i	$-0.257643\pi$
$149$	4.98019	+	2.87531i	0.407993	+	0.235555i	−0.281934	+	0.959434i	$0.590976\pi$
$150$	−3.83950	−	11.6301i	−0.313494	−	0.949590i
$151$	1.85084	−	1.06858i	0.150619	−	0.0869599i	−0.422796	−	0.906225i	$-0.638951\pi$
$151$	1.85084	−	1.06858i	0.150619	−	0.0869599i	0.573415	+	0.819265i	$0.305618\pi$
$152$	4.46501	+	6.48477i	0.362160	+	0.525984i
$153$	−1.49509	+	3.57521i	−0.120871	+	0.289039i
$154$	−2.80489	+	8.39086i	−0.226024	+	0.676155i
$155$	4.94322	−	5.21823i	0.397049	−	0.419138i
$156$	3.72837	+	7.41764i	0.298508	+	0.593887i
$157$	8.70855	+	5.02788i	0.695018	+	0.401269i	0.805489	−	0.592611i	$-0.201903\pi$
$157$	8.70855	+	5.02788i	0.695018	+	0.401269i	−0.110471	+	0.993879i	$0.535236\pi$
$158$	1.19281	−	1.05592i	0.0948951	−	0.0840042i
$159$	−11.1297	−	16.7180i	−0.882646	−	1.32582i
$160$	8.80771	+	9.07878i	0.696310	+	0.717741i
$161$		−	2.32057i		−	0.182887i
$162$	10.5679	+	7.09363i	0.830292	+	0.557329i
$163$	18.2146			1.42668			0.713339	−	0.700819i	$-0.247182\pi$
$163$	18.2146			1.42668			0.713339	+	0.700819i	$0.247182\pi$
$164$	14.5711	+	1.78069i	1.13781	+	0.139049i
$165$	16.9094	+	14.0867i	1.31640	+	1.09665i
$166$	12.2046	−	10.8039i	0.947257	−	0.838543i
$167$	6.44716	+	3.72227i	0.498896	+	0.288038i	0.728258	−	0.685304i	$-0.240330\pi$
$167$	6.44716	+	3.72227i	0.498896	+	0.288038i	−0.229362	+	0.973341i	$0.573664\pi$
$168$	0.769435	+	5.33818i	0.0593632	+	0.411850i
$169$	−3.62824	−	6.28430i	−0.279096	−	0.483408i
$170$	−0.137818	+	4.08253i	−0.0105702	+	0.313116i
$171$	7.70435	+	3.22181i	0.589166	+	0.246378i
$172$	7.20591	+	5.42361i	0.549445	+	0.413547i
$173$	4.33441	+	7.50742i	0.329539	+	0.570778i	0.982420	−	0.186682i	$-0.0597734\pi$
$173$	4.33441	+	7.50742i	0.329539	+	0.570778i	−0.652881	+	0.757460i	$0.726440\pi$
$174$	−15.0852	−	3.99430i	−1.14361	−	0.302807i
$175$	−0.297727	−	5.49651i	−0.0225061	−	0.415497i
$176$	−22.0611	−	5.47380i	−1.66292	−	0.412603i
$177$	12.6610	−	0.808350i	0.951663	−	0.0607593i
$178$	2.58856	+	12.7047i	0.194021	+	0.952257i
$179$	−1.10988			−0.0829560			−0.0414780	−	0.999139i	$-0.513207\pi$
$179$	−1.10988			−0.0829560			−0.0414780	+	0.999139i	$0.513207\pi$
$180$	13.0667	+	3.04334i	0.973933	+	0.226837i
$181$	−12.6629			−0.941229			−0.470615	−	0.882339i	$-0.655968\pi$
$181$	−12.6629			−0.941229			−0.470615	+	0.882339i	$0.655968\pi$
$182$	0.744936	+	3.65615i	0.0552183	+	0.271012i
$183$	3.82793	−	7.72930i	0.282969	−	0.571366i
$184$	5.94316	−	0.472840i	0.438135	−	0.0348582i
$185$	−14.1725	−	3.38938i	−1.04198	−	0.249192i
$186$	2.06040	+	7.59955i	0.151076	+	0.557226i
$187$	−3.67018	−	6.35694i	−0.268390	−	0.464865i
$188$	11.2440	−	14.9389i	0.820051	−	1.08953i
$189$	3.74993	+	4.31999i	0.272767	+	0.314233i
$190$	8.79758	+	0.296989i	0.638244	+	0.0215458i
$191$	−11.3827	−	19.7154i	−0.823625	−	1.42656i	−0.902966	−	0.429712i	$-0.858615\pi$
$191$	−11.3827	−	19.7154i	−0.823625	−	1.42656i	0.0793411	−	0.996848i	$-0.474718\pi$
$192$	−13.5147	+	3.05829i	−0.975339	+	0.220713i
$193$	10.0687	+	5.81319i	0.724764	+	0.418443i	0.816504	−	0.577340i	$-0.195909\pi$
$193$	10.0687	+	5.81319i	0.724764	+	0.418443i	−0.0917396	+	0.995783i	$0.529243\pi$
$194$	13.6038	−	12.0425i	0.976695	−	0.864602i
$195$	9.14650	+	1.57932i	0.654994	+	0.113098i
$196$	1.40422	−	11.4905i	0.100301	−	0.820750i
$197$	−12.2003			−0.869238			−0.434619	−	0.900614i	$-0.643117\pi$
$197$	−12.2003			−0.869238			−0.434619	+	0.900614i	$0.643117\pi$
$198$	−22.8196	+	7.77843i	−1.62172	+	0.552789i
$199$			7.07921i			0.501832i	0.968009	+	0.250916i	$0.0807318\pi$
$199$			7.07921i			0.501832i	−0.968009	+	0.250916i	$0.919268\pi$
$200$	14.0163	−	1.88247i	0.991101	−	0.133111i
$201$	−6.39612	+	0.408363i	−0.451147	+	0.0288037i
$202$	−17.7294	+	15.6947i	−1.24744	+	1.10427i
$203$	−6.07399	−	3.50682i	−0.426310	−	0.246130i
$204$	−3.73940	−	2.45767i	−0.261811	−	0.172071i
$205$	11.2870	−	11.9149i	0.788316	−	0.832172i
$206$	0.609128	−	1.82222i	0.0424400	−	0.126960i
$207$	5.02983	−	3.83257i	0.349597	−	0.266382i
$208$	−9.21188	+	2.65281i	−0.638729	+	0.183939i
$209$	−13.6988	+	7.90899i	−0.947564	+	0.547076i
$210$	5.31021	+	2.85691i	0.366440	+	0.197145i
$211$	5.61368	+	3.24106i	0.386462	+	0.223124i	0.680626	−	0.732631i	$-0.261708\pi$
$211$	5.61368	+	3.24106i	0.386462	+	0.223124i	−0.294164	+	0.955755i	$0.595041\pi$
$212$	21.3421	−	9.07353i	1.46578	−	0.623173i
$213$	−12.1852	−	18.3033i	−0.834915	−	1.25412i
$214$	0.839153	+	4.11857i	0.0573633	+	0.281540i
$215$	9.66569	−	2.87233i	0.659195	−	0.195891i
$216$	−10.2997	+	10.4841i	−0.700807	+	0.713351i
$217$			3.53890i			0.240236i
$218$	−7.09606	+	1.44581i	−0.480606	+	0.0979227i
$219$	−14.2287	+	9.47257i	−0.961488	+	0.640097i
$220$	−19.5859	+	16.1930i	−1.32048	+	1.09173i
$221$	−2.68100	−	1.54787i	−0.180343	−	0.104121i
$222$	11.2541	−	11.3209i	0.755327	−	0.759807i
$223$	−7.84799	−	13.5931i	−0.525540	−	0.910263i	−0.999557	−	0.0297470i	$-0.990530\pi$
$223$	−7.84799	−	13.5931i	−0.525540	−	0.910263i	0.474017	−	0.880516i	$-0.342803\pi$
$224$	−6.22216	−	0.262800i	−0.415735	−	0.0175590i
$225$	11.4219	−	9.72314i	0.761462	−	0.648209i
$226$	3.75292	−	11.2269i	0.249640	−	0.746803i
$227$	0.169745	−	0.0980022i	0.0112664	−	0.00650463i	−0.494356	−	0.869259i	$-0.664596\pi$
$227$	0.169745	−	0.0980022i	0.0112664	−	0.00650463i	0.505623	+	0.862755i	$0.331263\pi$
$228$	−5.29610	+	8.05817i	−0.350743	+	0.533665i
$229$	0.825139	−	1.42918i	0.0545267	−	0.0944431i	−0.837474	−	0.546478i	$-0.815968\pi$
$229$	0.825139	−	1.42918i	0.0545267	−	0.0944431i	0.892000	+	0.452035i	$0.149302\pi$
$230$	3.52569	−	5.65689i	0.232477	−	0.373004i
$231$	−10.8136	+	0.690399i	−0.711483	+	0.0454249i
$232$	7.74358	−	16.2705i	0.508391	−	1.06821i
$233$	−20.2270			−1.32512			−0.662559	−	0.749010i	$-0.730530\pi$
$233$	−20.2270			−1.32512			−0.662559	+	0.749010i	$0.730530\pi$
$234$	−6.69438	+	7.65300i	−0.437626	+	0.500292i
$235$	−5.95477	−	20.0384i	−0.388447	−	1.30716i
$236$	−1.77705	+	14.5413i	−0.115676	+	0.946558i
$237$	1.74839	+	0.865891i	0.113570	+	0.0562456i
$238$	−1.33306	−	1.50588i	−0.0864093	−	0.0976120i
$239$	10.1646	−	17.6056i	0.657494	−	1.13881i	−0.323769	−	0.946136i	$-0.604950\pi$
$239$	10.1646	−	17.6056i	0.657494	−	1.13881i	0.981262	−	0.192676i	$-0.0617168\pi$
$240$	−6.23473	+	14.1820i	−0.402450	+	0.915442i
$241$	8.62268	+	14.9349i	0.555436	+	0.962043i	0.997869	+	0.0652417i	$0.0207818\pi$
$241$	8.62268	+	14.9349i	0.555436	+	0.962043i	−0.442434	+	0.896801i	$0.645885\pi$
$242$	9.54590	−	28.5567i	0.613634	−	1.83569i
$243$	−3.17031	+	15.2627i	−0.203376	+	0.979101i
$244$	7.95749	+	5.98930i	0.509426	+	0.383426i
$245$	−9.39585	−	8.90068i	−0.600279	−	0.568644i
$246$	4.70455	+	17.3522i	0.299951	+	1.10634i
$247$	−3.33556	+	5.77737i	−0.212237	+	0.367605i
$248$	−9.06336	+	0.721085i	−0.575524	+	0.0457889i
$249$	17.8891	+	8.85957i	1.13368	+	0.561452i
$250$	7.62517	−	13.8512i	0.482258	−	0.876029i
$251$	−9.92020			−0.626157			−0.313079	−	0.949727i	$-0.601360\pi$
$251$	−9.92020			−0.626157			−0.313079	+	0.949727i	$0.601360\pi$
$252$	−5.70088	+	3.33651i	−0.359122	+	0.210180i
$253$			11.9780i			0.753048i
$254$	−7.13282	+	1.45330i	−0.447553	+	0.0911883i
$255$	−4.69509	+	1.72777i	−0.294018	+	0.108197i
$256$	−0.594777	−	15.9889i	−0.0371735	−	0.999309i
$257$	−8.67485	+	15.0253i	−0.541122	+	0.937252i	0.457717	+	0.889098i	$0.348667\pi$
$257$	−8.67485	+	15.0253i	−0.541122	+	0.937252i	−0.998840	+	0.0481539i	$0.984666\pi$
$258$	−2.82732	+	10.6779i	−0.176021	+	0.664776i
$259$	6.21330	−	3.58725i	0.386076	−	0.222901i
$260$	−3.73892	+	10.0444i	−0.231878	+	0.622930i
$261$	−2.43055	−	18.9571i	−0.150447	−	1.17341i
$262$	6.36689	−	19.0466i	0.393348	−	1.17671i
$263$	8.32487	−	4.80637i	0.513334	−	0.296373i	−0.220869	−	0.975303i	$-0.570889\pi$
$263$	8.32487	−	4.80637i	0.513334	−	0.296373i	0.734203	+	0.678930i	$0.237556\pi$
$264$	−3.97154	−	27.5538i	−0.244431	−	1.69582i
$265$	6.03070	−	25.2171i	0.370463	−	1.54907i
$266$	−3.24508	+	2.87265i	−0.198969	+	0.176134i
$267$	−13.2184	+	8.79995i	−0.808952	+	0.538548i
$268$	0.897732	−	7.34599i	0.0548377	−	0.448727i
$269$			1.34482i			0.0819953i	0.999159	+	0.0409977i	$0.0130536\pi$
$269$			1.34482i			0.0819953i	−0.999159	+	0.0409977i	$0.986946\pi$
$270$	2.57781	+	16.2282i	0.156881	+	0.987618i
$271$			21.7288i			1.31993i	0.751297	+	0.659964i	$0.229429\pi$
$271$			21.7288i			1.31993i	−0.751297	+	0.659964i	$0.770571\pi$
$272$	3.58506	−	3.72090i	0.217376	−	0.225612i
$273$	−3.80398	+	2.53245i	−0.230228	+	0.153271i
$274$	6.50808	+	7.35183i	0.393167	+	0.444140i
$275$	1.53676	+	28.3710i	0.0926701	+	1.71083i
$276$	3.27923	+	6.52409i	0.197387	+	0.392704i
$277$	12.0501	−	6.95713i	0.724021	−	0.418014i	−0.0922100	−	0.995740i	$-0.529393\pi$
$277$	12.0501	−	6.95713i	0.724021	−	0.418014i	0.816231	+	0.577726i	$0.196060\pi$
$278$	16.0018	+	5.34908i	0.959727	+	0.320817i
$279$	−7.67053	+	5.84470i	−0.459223	+	0.349913i
$280$	−4.37245	+	5.41867i	−0.261304	+	0.323828i
$281$	10.0948	−	5.82824i	0.602206	−	0.347684i	−0.167703	−	0.985838i	$-0.553635\pi$
$281$	10.0948	−	5.82824i	0.602206	−	0.347684i	0.769909	+	0.638154i	$0.220302\pi$
$282$	22.1369	+	5.86146i	1.31823	+	0.349045i
$283$	−6.21367	+	10.7624i	−0.369365	+	0.639758i	−0.989466	−	0.144763i	$-0.953758\pi$
$283$	−6.21367	+	10.7624i	−0.369365	+	0.639758i	0.620102	+	0.784521i	$0.287091\pi$
$284$	23.3660	−	9.93398i	1.38652	−	0.589473i
$285$	3.72323	+	10.1176i	0.220545	+	0.599315i
$286$	−3.84509	−	18.8717i	−0.227365	−	1.11591i
$287$			8.08044i			0.476973i
$288$	−9.70665	−	13.9205i	−0.571970	−	0.820275i
$289$	−15.3314			−0.901847
$290$	−9.47866	−	17.7769i	−0.556606	−	1.04390i
$291$	19.9401	+	9.87530i	1.16891	+	0.578900i
$292$	−7.72252	−	18.1644i	−0.451926	−	1.06299i
$293$	4.77472	−	8.27006i	0.278942	−	0.483142i	−0.692180	−	0.721725i	$-0.743350\pi$
$293$	4.77472	−	8.27006i	0.278942	−	0.483142i	0.971122	+	0.238583i	$0.0766829\pi$
$294$	13.6836	−	3.70991i	0.798045	−	0.216367i
$295$	11.8905	+	11.2639i	0.692292	+	0.655808i
$296$	10.4532	+	15.1818i	0.607582	+	0.882423i
$297$	−19.3558	−	22.2982i	−1.12314	−	1.29387i
$298$	−7.71308	−	2.57832i	−0.446807	−	0.149358i
$299$	2.52581	+	4.37484i	0.146072	+	0.253003i
$300$	8.60422	+	15.0322i	0.496765	+	0.867885i
$301$	−2.48226	+	4.29940i	−0.143075	+	0.247813i
$302$	−2.26308	+	2.00335i	−0.130225	+	0.115280i
$303$	−25.9873	−	12.8702i	−1.49293	−	0.739374i
$304$	−8.01828	−	7.72555i	−0.459880	−	0.443091i
$305$	10.6738	−	3.17192i	0.611182	−	0.181623i
$306$	1.06237	−	5.37646i	0.0607317	−	0.307351i
$307$	−13.4685			−0.768689			−0.384345	−	0.923190i	$-0.625573\pi$
$307$	−13.4685			−0.768689			−0.384345	+	0.923190i	$0.625573\pi$
$308$	1.51775	−	12.4195i	0.0864820	−	0.707667i
$309$	2.34836	−	0.149932i	0.133593	−	0.00852932i
$310$	−5.37670	+	8.62680i	−0.305376	+	0.489969i
$311$	5.13110	−	8.88732i	0.290958	−	0.503954i	−0.683079	−	0.730345i	$-0.739359\pi$
$311$	5.13110	−	8.88732i	0.290958	−	0.503954i	0.974037	+	0.226391i	$0.0726927\pi$
$312$	−7.26088	−	9.22626i	−0.411066	−	0.522334i
$313$	1.39067	−	0.802903i	0.0786052	−	0.0453827i	−0.460182	−	0.887824i	$-0.652216\pi$
$313$	1.39067	−	0.802903i	0.0786052	−	0.0453827i	0.538787	+	0.842442i	$0.318883\pi$
$314$	−13.4874	−	4.50855i	−0.761138	−	0.254432i
$315$	−0.790355	+	7.34274i	−0.0445314	+	0.413716i
$316$	−1.35480	+	1.80001i	−0.0762135	+	0.101259i
$317$	2.23127	+	3.86467i	0.125320	+	0.217061i	0.921858	−	0.387528i	$-0.126671\pi$
$317$	2.23127	+	3.86467i	0.125320	+	0.217061i	−0.796538	+	0.604589i	$0.793337\pi$
$318$	20.1432	+	20.0244i	1.12957	+	1.12291i
$319$	31.3517	+	18.1009i	1.75536	+	1.01346i
$320$	−14.7685	−	10.0941i	−0.825587	−	0.564275i
$321$	−4.28510	+	2.85274i	−0.239171	+	0.159225i
$322$	0.655198	+	3.21572i	0.0365128	+	0.179205i
$323$		−	3.59573i		−	0.200072i
$324$	−16.6472	−	6.84618i	−0.924845	−	0.380343i
$325$	6.54392	+	10.0382i	0.362992	+	0.556818i
$326$	−25.2408	+	5.14277i	−1.39796	+	0.284832i
$327$	−4.91511	−	7.38297i	−0.271806	−	0.408279i
$328$	−20.6946	+	1.64647i	−1.14267	+	0.0909110i
$329$	8.91330	+	5.14610i	0.491406	+	0.283713i
$330$	−27.4094	−	14.7463i	−1.50884	−	0.811758i
$331$	10.2107	−	5.89512i	0.561228	−	0.324025i	−0.192410	−	0.981315i	$-0.561630\pi$
$331$	10.2107	−	5.89512i	0.561228	−	0.324025i	0.753638	+	0.657289i	$0.228297\pi$
$332$	−13.8620	+	18.4172i	−0.760775	+	1.01078i
$333$	18.0370	+	7.54274i	0.988421	+	0.413339i
$334$	−9.98506	−	3.33780i	−0.546358	−	0.182636i
$335$	−6.00686	−	5.69029i	−0.328190	−	0.310894i
$336$	−2.57344	−	7.18010i	−0.140393	−	0.391707i
$337$	9.14715	+	5.28111i	0.498277	+	0.287680i	0.728002	−	0.685575i	$-0.240449\pi$
$337$	9.14715	+	5.28111i	0.498277	+	0.287680i	−0.229725	+	0.973256i	$0.573783\pi$
$338$	6.80214	+	7.68402i	0.369988	+	0.417955i
$339$	14.4685	−	0.923749i	0.785823	−	0.0501712i
$340$	−0.961694	−	5.69625i	−0.0521552	−	0.308922i
$341$		−	18.2665i		−	0.989186i
$342$	−11.5859	−	2.28934i	−0.626494	−	0.123793i
$343$	14.0785			0.760166
$344$	−11.5168	−	5.48120i	−0.620947	−	0.295526i
$345$	8.04468	+	1.38907i	0.433111	+	0.0747851i
$346$	−8.12604	−	9.17956i	−0.436859	−	0.493496i
$347$	−20.1864	−	11.6546i	−1.08366	−	0.625652i	−0.151779	−	0.988414i	$-0.548500\pi$
$347$	−20.1864	−	11.6546i	−1.08366	−	0.625652i	−0.931882	+	0.362763i	$0.881834\pi$
$348$	22.0320	+	1.27587i	1.18104	+	0.0683939i
$349$	2.84689	+	4.93095i	0.152390	+	0.263948i	0.932106	−	0.362186i	$-0.117970\pi$
$349$	2.84689	+	4.93095i	0.152390	+	0.263948i	−0.779715	+	0.626134i	$0.784636\pi$
$350$	1.96447	+	7.53268i	0.105006	+	0.402639i
$351$	−11.7716	−	4.06262i	−0.628320	−	0.216847i
$352$	32.1165	+	1.35648i	1.71182	+	0.0723004i
$353$	−0.761369	−	1.31873i	−0.0405236	−	0.0701889i	0.845052	−	0.534684i	$-0.179569\pi$
$353$	−0.761369	−	1.31873i	−0.0405236	−	0.0701889i	−0.885576	+	0.464495i	$0.846236\pi$
$354$	−17.3167	+	4.69492i	−0.920373	+	0.249532i
$355$	6.60259	−	27.6084i	0.350429	−	1.46530i
$356$	−7.17416	−	16.8746i	−0.380230	−	0.894351i
$357$	1.09316	−	2.20729i	0.0578560	−	0.116822i
$358$	1.53800	−	0.313366i	0.0812860	−	0.0165619i
$359$	9.46115			0.499341			0.249670	−	0.968331i	$-0.419678\pi$
$359$	9.46115			0.499341			0.249670	+	0.968331i	$0.419678\pi$
$360$	−18.9663	−	0.528000i	−0.999613	−	0.0278281i
$361$	11.2514			0.592181
$362$	17.5476	−	3.57529i	0.922280	−	0.187913i
$363$	36.8021	−	2.34964i	1.93161	−	0.123324i
$364$	−2.06458	−	4.85616i	−0.108213	−	0.254532i
$365$	−21.4623	−	5.13275i	−1.12339	−	0.268660i
$366$	−3.12221	+	11.7916i	−0.163201	+	0.616357i
$367$	4.06621	+	7.04288i	0.212254	+	0.367635i	0.952420	−	0.304790i	$-0.0985862\pi$
$367$	4.06621	+	7.04288i	0.212254	+	0.367635i	−0.740165	+	0.672425i	$0.765253\pi$
$368$	−8.10218	+	2.33324i	−0.422356	+	0.121629i
$369$	−17.5143	+	13.3453i	−0.911758	+	0.694730i
$370$	20.5964	+	0.695294i	1.07076	+	0.0361466i
$371$	6.38278	+	11.0553i	0.331377	+	0.573963i
$372$	−5.00086	−	9.94928i	−0.259282	−	0.515846i
$373$	−10.0593	−	5.80775i	−0.520851	−	0.300714i	0.216432	−	0.976298i	$-0.430558\pi$
$373$	−10.0593	−	5.80775i	−0.520851	−	0.300714i	−0.737283	+	0.675584i	$0.763892\pi$
$374$	6.88076	+	7.77283i	0.355796	+	0.401923i
$375$	19.2328	+	2.25803i	0.993178	+	0.116604i
$376$	−11.3633	+	23.8762i	−0.586020	+	1.23132i
$377$	15.2679			0.786336
$378$	−6.41616	−	4.92762i	−0.330011	−	0.253450i
$379$			0.194316i			0.00998136i	0.999988	+	0.00499068i	$0.00158859\pi$
$379$			0.194316i			0.00998136i	−0.999988	+	0.00499068i	$0.998411\pi$
$380$	−12.2750	+	2.07239i	−0.629696	+	0.106311i
$381$	−4.94057	−	7.42123i	−0.253113	−	0.380201i
$382$	21.3400	+	24.1067i	1.09185	+	1.23341i
$383$	16.0220	+	9.25031i	0.818686	+	0.472669i	0.849963	−	0.526842i	$-0.176624\pi$
$383$	16.0220	+	9.25031i	0.818686	+	0.472669i	−0.0312769	+	0.999511i	$0.509957\pi$
$384$	17.8644	−	8.05377i	0.911639	−	0.410992i
$385$	−10.1555	−	9.62031i	−0.517573	−	0.490296i
$386$	−15.5940	−	5.21275i	−0.793714	−	0.265322i
$387$	−13.4185	+	1.72043i	−0.682102	+	0.0874546i
$388$	−15.4512	+	20.5288i	−0.784417	+	1.04219i
$389$	−20.3869	+	11.7704i	−1.03366	+	0.596783i	−0.918031	−	0.396509i	$-0.870221\pi$
$389$	−20.3869	+	11.7704i	−1.03366	+	0.596783i	−0.115628	+	0.993293i	$0.536888\pi$
$390$	−13.1206	+	0.393916i	−0.664388	+	0.0199467i
$391$	−2.35803	−	1.36141i	−0.119251	−	0.0688495i
$392$	1.29837	+	16.3193i	0.0655777	+	0.824251i
$393$	24.5461	−	1.56716i	1.23819	−	0.0790526i
$394$	16.9065	−	3.44468i	0.851739	−	0.173541i
$395$	0.717499	+	2.41446i	0.0361013	+	0.121485i
$396$	29.4259	−	17.2218i	1.47871	−	0.865430i
$397$			23.4091i			1.17487i	0.809272	+	0.587435i	$0.199862\pi$
$397$			23.4091i			1.17487i	−0.809272	+	0.587435i	$0.800138\pi$
$398$	−1.99877	−	9.80996i	−0.100189	−	0.491729i
$399$	−4.75655	−	2.35568i	−0.238125	−	0.117931i
$400$	−18.8915	+	6.56602i	−0.944573	+	0.328301i
$401$	25.9256	+	14.9681i	1.29466	+	0.747474i	0.979477	−	0.201557i	$-0.0646000\pi$
$401$	25.9256	+	14.9681i	1.29466	+	0.747474i	0.315185	+	0.949030i	$0.397933\pi$
$402$	8.74807	−	2.37178i	0.436314	−	0.118294i
$403$	−3.85189	−	6.67166i	−0.191876	−	0.332339i
$404$	20.1372	−	26.7546i	1.00186	−	1.33109i
$405$	−17.2207	+	10.4139i	−0.855701	+	0.517470i
$406$	9.40711	+	3.14460i	0.466867	+	0.156064i
$407$	−32.0708	+	18.5161i	−1.58969	+	0.917809i
$408$	5.87576	+	2.34990i	0.290893	+	0.116337i
$409$	1.04012	−	1.80153i	0.0514304	−	0.0890800i	−0.839164	−	0.543878i	$-0.816955\pi$
$409$	1.04012	−	1.80153i	0.0514304	−	0.0890800i	0.890594	+	0.454798i	$0.150289\pi$
$410$	−12.2768	+	19.6978i	−0.606306	+	0.972804i
$411$	−5.33686	+	10.7761i	−0.263248	+	0.531547i
$412$	−0.329605	+	2.69710i	−0.0162385	+	0.132877i
$413$	−8.06390			−0.396799
$414$	−5.88795	+	6.73109i	−0.289377	+	0.330815i
$415$	7.34126	+	24.7041i	0.360368	+	1.21268i
$416$	12.0163	−	6.27702i	0.589147	−	0.307756i
$417$	1.31663	+	20.6222i	0.0644757	+	1.00987i
$418$	16.7499	−	14.8276i	0.819265	−	0.725240i
$419$	−4.89021	+	8.47010i	−0.238903	+	0.413791i	−0.960400	−	0.278626i	$-0.910121\pi$
$419$	−4.89021	+	8.47010i	−0.238903	+	0.413791i	0.721497	+	0.692417i	$0.243454\pi$
$420$	−8.16522	−	2.45964i	−0.398422	−	0.120018i
$421$	1.05097	+	1.82034i	0.0512212	+	0.0887177i	0.890499	−	0.454985i	$-0.150355\pi$
$421$	1.05097	+	1.82034i	0.0512212	+	0.0887177i	−0.839278	+	0.543703i	$0.817022\pi$
$422$	−8.69420	−	2.90629i	−0.423227	−	0.141476i
$423$	3.56672	+	27.8186i	0.173420	+	1.35259i
$424$	−27.0129	+	18.5994i	−1.31186	+	0.903266i
$425$	−5.75990	−	2.92210i	−0.279396	−	0.141743i
$426$	22.0534	+	21.9233i	1.06849	+	1.06219i
$427$	−2.74116	+	4.74783i	−0.132654	+	0.229764i
$428$	−2.32570	−	5.47035i	−0.112417	−	0.264419i
$429$	19.6348	−	13.0716i	0.947976	−	0.631101i
$430$	−12.5832	+	6.70935i	−0.606815	+	0.323554i
$431$	3.84204			0.185064			0.0925322	−	0.995710i	$-0.470504\pi$
$431$	3.84204			0.185064			0.0925322	+	0.995710i	$0.470504\pi$
$432$	11.3126	−	17.4363i	0.544280	−	0.838904i
$433$		−	6.66853i		−	0.320469i	−0.987079	−	0.160235i	$-0.948775\pi$
$433$		−	6.66853i		−	0.320469i	0.987079	−	0.160235i	$-0.0512251\pi$
$434$	−0.999182	−	4.90400i	−0.0479623	−	0.235399i
$435$	15.7928	−	18.9574i	0.757208	−	0.908937i
$436$	9.42509	−	4.00704i	0.451380	−	0.191903i
$437$	−2.93375	+	5.08140i	−0.140340	+	0.243077i
$438$	17.0428	−	17.1439i	0.814339	−	0.819168i
$439$	−33.5536	+	19.3722i	−1.60143	+	0.924585i	−0.610225	+	0.792228i	$0.708921\pi$
$439$	−33.5536	+	19.3722i	−1.60143	+	0.924585i	−0.991202	+	0.132357i	$0.957746\pi$
$440$	22.5690	−	27.9692i	1.07594	−	1.33338i
$441$	10.5239	+	13.8114i	0.501136	+	0.657687i
$442$	4.15220	+	1.38799i	0.197500	+	0.0660202i
$443$	20.2821	−	11.7099i	0.963633	−	0.556354i	0.0663436	−	0.997797i	$-0.478867\pi$
$443$	20.2821	−	11.7099i	0.963633	−	0.556354i	0.897289	+	0.441443i	$0.145533\pi$
$444$	−12.3989	+	18.8653i	−0.588428	+	0.895309i
$445$	−19.9384	−	4.76829i	−0.945169	−	0.226039i
$446$	14.7132	+	16.6207i	0.696691	+	0.787015i
$447$	−0.634632	−	9.94014i	−0.0300171	−	0.470152i
$448$	8.69651	−	1.39261i	0.410871	−	0.0657946i
$449$		−	15.7865i		−	0.745011i	−0.928030	−	0.372506i	$-0.878499\pi$
$449$		−	15.7865i		−	0.745011i	0.928030	−	0.372506i	$-0.121501\pi$
$450$	−13.0826	+	16.6987i	−0.616720	+	0.787183i
$451$		−	41.7083i		−	1.96397i
$452$	−2.03074	+	16.6172i	−0.0955181	+	0.781608i
$453$	−3.31716	−	1.64282i	−0.155854	−	0.0771864i
$454$	−0.207552	+	0.183732i	−0.00974091	+	0.00862297i
$455$	−5.73786	−	1.37222i	−0.268995	−	0.0643305i
$456$	5.06387	−	12.6619i	0.237137	−	0.592946i
$457$	7.28867	−	4.20812i	0.340950	−	0.196847i	−0.319742	−	0.947505i	$-0.603596\pi$
$457$	7.28867	−	4.20812i	0.340950	−	0.196847i	0.660692	+	0.750657i	$0.270263\pi$
$458$	−0.739911	+	2.21345i	−0.0345738	+	0.103428i
$459$	6.58969	−	1.27605i	0.307580	−	0.0595611i
$460$	−3.28851	+	8.83445i	−0.153328	+	0.411908i
$461$	21.4798	−	12.4014i	1.00042	−	0.577590i	0.0920445	−	0.995755i	$-0.470660\pi$
$461$	21.4798	−	12.4014i	1.00042	−	0.577590i	0.908371	+	0.418165i	$0.137326\pi$
$462$	14.7900	−	4.00986i	0.688091	−	0.186556i
$463$	−10.3598	+	17.9437i	−0.481460	+	0.833913i	−0.999774	−	0.0212774i	$-0.993227\pi$
$463$	−10.3598	+	17.9437i	−0.481460	+	0.833913i	0.518314	+	0.855191i	$0.326560\pi$
$464$	−6.13675	+	24.7330i	−0.284892	+	1.14820i
$465$	−12.2682	−	2.11834i	−0.568924	−	0.0982359i
$466$	28.0295	−	5.71097i	1.29844	−	0.264555i
$467$			1.59588i			0.0738487i	0.999318	+	0.0369243i	$0.0117561\pi$
$467$			1.59588i			0.0738487i	−0.999318	+	0.0369243i	$0.988244\pi$
$468$	7.11592	−	12.4952i	0.328934	−	0.577591i
$469$	4.07373			0.188107
$470$	13.9095	+	26.0868i	0.641597	+	1.20330i
$471$	−1.10974	−	17.3817i	−0.0511342	−	0.800907i
$472$	−1.64310	−	20.6522i	−0.0756298	−	0.950596i
$473$	12.8125	−	22.1919i	0.589120	−	1.02039i
$474$	−2.66730	−	0.706255i	−0.122513	−	0.0324394i
$475$	−6.29693	+	12.4122i	−0.288923	+	0.569511i
$476$	2.27245	+	1.71039i	0.104158	+	0.0783955i
$477$	−13.4207	+	32.0931i	−0.614494	+	1.46944i
$478$	−9.11471	+	27.2668i	−0.416897	+	1.24715i
$479$	2.98947	+	5.17791i	0.136592	+	0.236585i	0.926205	−	0.377021i	$-0.123052\pi$
$479$	2.98947	+	5.17791i	0.136592	+	0.236585i	−0.789612	+	0.613606i	$0.789718\pi$
$480$	4.63556	−	21.4129i	0.211583	−	0.977360i
$481$	−7.80904	+	13.5257i	−0.356062	+	0.616717i
$482$	−16.1656	−	18.2614i	−0.736322	−	0.831784i
$483$	−3.34574	+	2.22738i	−0.152237	+	0.101349i
$484$	−5.16538	+	42.2674i	−0.234790	+	1.92125i
$485$	8.18292	+	27.5364i	0.371567	+	1.25036i
$486$	0.0839300	−	22.0452i	0.00380714	−	0.999993i
$487$	−16.5971			−0.752086			−0.376043	−	0.926602i	$-0.622716\pi$
$487$	−16.5971			−0.752086			−0.376043	+	0.926602i	$0.622716\pi$
$488$	−12.7181	−	6.05289i	−0.575720	−	0.274002i
$489$	−17.4831	−	26.2613i	−0.790613	−	1.18758i
$490$	15.5333	+	9.68120i	0.701722	+	0.437352i
$491$	6.66941	−	11.5518i	0.300986	−	0.521323i	−0.675373	−	0.737476i	$-0.736018\pi$
$491$	6.66941	−	11.5518i	0.300986	−	0.521323i	0.976360	+	0.216153i	$0.0693509\pi$
$492$	−11.4186	−	22.7174i	−0.514789	−	1.02418i
$493$	−7.12685	+	4.11469i	−0.320977	+	0.185316i
$494$	2.99103	−	8.94772i	0.134573	−	0.402577i
$495$	4.07952	−	37.9005i	0.183361	−	1.70350i
$496$	12.3559	−	3.55822i	0.554796	−	0.159769i
$497$	6.98806	+	12.1037i	0.313457	+	0.542924i
$498$	−27.2911	−	7.22622i	−1.22294	−	0.323815i
$499$	−35.7135	−	20.6192i	−1.59875	−	0.923041i	−0.991728	−	0.128359i	$-0.959029\pi$
$499$	−35.7135	−	20.6192i	−1.59875	−	0.923041i	−0.607026	−	0.794682i	$-0.707638\pi$
$500$	−6.65572	+	21.3472i	−0.297653	+	0.954674i
$501$	−0.821570	−	12.8681i	−0.0367050	−	0.574905i
$502$	13.7468	−	2.80090i	0.613551	−	0.125010i
$503$		−	24.1634i		−	1.07739i	−0.842500	−	0.538696i	$-0.818917\pi$
$503$		−	24.1634i		−	1.07739i	0.842500	−	0.538696i	$-0.181083\pi$
$504$	6.95791	−	6.23315i	0.309930	−	0.277646i
$505$	−10.6646	−	35.8874i	−0.474567	−	1.59697i
$506$	−3.38189	−	16.5984i	−0.150343	−	0.737887i
$507$	−5.57801	+	11.2630i	−0.247728	+	0.500208i
$508$	9.47393	−	4.02781i	0.420338	−	0.178705i
$509$	10.2084	+	5.89380i	0.452478	+	0.261238i	0.708876	−	0.705333i	$-0.249203\pi$
$509$	10.2084	+	5.89380i	0.452478	+	0.261238i	−0.256398	+	0.966571i	$0.582536\pi$
$510$	6.01837	−	3.71987i	0.266498	−	0.164719i
$511$	9.40921	−	5.43241i	0.416239	−	0.240316i
$512$	5.33857	+	21.9886i	0.235934	+	0.971769i
$513$	−2.74981	−	14.2003i	−0.121407	−	0.626960i
$514$	7.77883	−	23.2705i	0.343109	−	1.02642i
$515$	2.20544	+	2.08921i	0.0971833	+	0.0920616i
$516$	0.903109	−	15.5951i	0.0397572	−	0.686535i
$517$	−46.0072	−	26.5623i	−2.02339	−	1.16821i
$518$	−7.59721	+	6.72529i	−0.333802	+	0.295492i
$519$	6.66365	−	13.4551i	0.292502	−	0.590615i
$520$	2.34520	−	14.9747i	0.102844	−	0.656682i
$521$			32.5010i			1.42389i	0.702234	+	0.711947i	$0.252186\pi$
$521$			32.5010i			1.42389i	−0.702234	+	0.711947i	$0.747814\pi$
$522$	8.72051	+	25.5834i	0.381686	+	1.11975i
$523$	11.2435			0.491645			0.245822	−	0.969315i	$-0.420942\pi$
$523$	11.2435			0.491645			0.245822	+	0.969315i	$0.420942\pi$
$524$	−3.44519	+	28.1914i	−0.150504	+	1.23155i
$525$	−7.63895	+	5.70502i	−0.333391	+	0.248987i
$526$	−10.1791	+	9.01086i	−0.443829	+	0.392892i
$527$	3.59602	+	2.07616i	0.156645	+	0.0904391i
$528$	13.2831	+	37.0611i	0.578075	+	1.61288i
$529$	−9.27846	−	16.0708i	−0.403411	−	0.698729i
$530$	−1.23713	+	36.6471i	−0.0537376	+	1.59185i
$531$	−13.3180	−	17.4785i	−0.577953	−	0.758501i
$532$	3.68577	−	4.89698i	0.159799	−	0.212311i
$533$	−8.79510	−	15.2336i	−0.380958	−	0.659839i
$534$	15.8327	−	15.9266i	0.685147	−	0.689211i
$535$	−6.46356	−	1.54577i	−0.279444	−	0.0668295i
$536$	0.830062	+	10.4331i	0.0358532	+	0.450642i
$537$	1.06530	+	1.60019i	0.0459712	+	0.0690533i
$538$	−0.379701	−	1.86358i	−0.0163701	−	0.0803446i
$539$	−32.8903			−1.41669
$540$	−8.15411	−	21.7603i	−0.350897	−	0.936414i
$541$	−8.40855			−0.361512			−0.180756	−	0.983528i	$-0.557854\pi$
$541$	−8.40855			−0.361512			−0.180756	+	0.983528i	$0.557854\pi$
$542$	−6.13496	−	30.1105i	−0.263519	−	1.29336i
$543$	12.1544	+	18.2571i	0.521595	+	0.783487i
$544$	−3.91739	+	6.16842i	−0.167957	+	0.264469i
$545$	2.66327	−	11.1363i	0.114082	−	0.477028i
$546$	4.55632	−	4.58335i	0.194993	−	0.196149i
$547$	−2.12301	−	3.67716i	−0.0907734	−	0.157224i	0.817063	−	0.576548i	$-0.195601\pi$
$547$	−2.12301	−	3.67716i	−0.0907734	−	0.157224i	−0.907837	+	0.419324i	$0.862267\pi$
$548$	−11.0943	−	8.35023i	−0.473923	−	0.356704i
$549$	−14.8181	+	1.89988i	−0.632420	+	0.0810848i
$550$	−10.1399	−	38.8810i	−0.432367	−	1.65789i
$551$	8.86688	+	15.3579i	0.377742	+	0.654268i
$552$	−6.38620	−	8.11483i	−0.271815	−	0.345390i
$553$	−1.07398	−	0.620060i	−0.0456701	−	0.0263676i
$554$	−14.7340	+	13.0431i	−0.625990	+	0.554146i
$555$	8.71662	+	23.6868i	0.370000	+	1.00545i
$556$	−23.6847	−	2.89444i	−1.00446	−	0.122752i
$557$	21.0221			0.890734			0.445367	−	0.895348i	$-0.353073\pi$
$557$	21.0221			0.890734			0.445367	+	0.895348i	$0.353073\pi$
$558$	8.97918	−	10.2650i	0.380119	−	0.434551i
$559$		−	10.8072i		−	0.457095i
$560$	4.52917	−	8.74342i	0.191392	−	0.369477i
$561$	−5.64248	+	11.3932i	−0.238225	+	0.481021i
$562$	−12.3433	+	10.9266i	−0.520669	+	0.460913i
$563$	−18.9272	−	10.9277i	−0.797688	−	0.460546i	0.0449739	−	0.998988i	$-0.485680\pi$
$563$	−18.9272	−	10.9277i	−0.797688	−	0.460546i	−0.842662	+	0.538443i	$0.819013\pi$
$564$	−32.3309	−	1.87228i	−1.36138	−	0.0788373i
$565$	13.5880	+	12.8719i	0.571651	+	0.541525i
$566$	5.57187	−	16.6683i	0.234203	−	0.700621i
$567$	2.62911	−	9.55304i	0.110412	−	0.401190i
$568$	−29.5745	+	20.3632i	−1.24092	+	0.854420i
$569$	12.7253	−	7.34697i	0.533473	−	0.308001i	−0.208956	−	0.977925i	$-0.567007\pi$
$569$	12.7253	−	7.34697i	0.533473	−	0.308001i	0.742430	+	0.669924i	$0.233673\pi$
$570$	−8.01607	−	12.9692i	−0.335756	−	0.543219i
$571$	−15.5333	−	8.96816i	−0.650049	−	0.375306i	0.138426	−	0.990373i	$-0.455796\pi$
$571$	−15.5333	−	8.96816i	−0.650049	−	0.375306i	−0.788475	+	0.615067i	$0.789129\pi$
$572$	10.6566	+	25.0657i	0.445575	+	1.04805i
$573$	−17.4996	+	35.3350i	−0.731057	+	1.47614i
$574$	−2.28146	−	11.1974i	−0.0952261	−	0.467371i
$575$	5.75562	+	8.82893i	0.240026	+	0.368192i
$576$	17.3813	+	16.5497i	0.724220	+	0.689569i
$577$		−	38.2696i		−	1.59318i	−0.604517	−	0.796592i	$-0.706634\pi$
$577$		−	38.2696i		−	1.59318i	0.604517	−	0.796592i	$-0.293366\pi$
$578$	21.2454	−	4.32871i	0.883691	−	0.180051i
$579$	−1.28307	−	20.0966i	−0.0533227	−	0.835185i
$580$	18.1542	+	21.9580i	0.753811	+	0.911757i
$581$	−10.9886	−	6.34429i	−0.455885	−	0.263206i
$582$	−30.4200	−	8.05469i	−1.26095	−	0.333878i
$583$	−32.9456	−	57.0634i	−1.36447	−	2.36333i
$584$	15.8300	+	22.9907i	0.655050	+	0.951364i
$585$	−6.50214	−	14.7031i	−0.268831	−	0.607897i
$586$	−4.28154	+	12.8083i	−0.176869	+	0.529105i
$587$	7.27939	−	4.20276i	0.300453	−	0.173466i	−0.342194	−	0.939629i	$-0.611170\pi$
$587$	7.27939	−	4.20276i	0.300453	−	0.173466i	0.642646	+	0.766163i	$0.277837\pi$
$588$	−17.9145	+	9.00446i	−0.738782	+	0.371338i
$589$	4.47399	−	7.74918i	0.184348	−	0.319299i
$590$	−19.6575	−	12.2516i	−0.809285	−	0.504392i
$591$	11.7104	+	17.5901i	0.481700	+	0.723561i
$592$	−18.7720	−	18.0866i	−0.771523	−	0.743356i
$593$	35.1831			1.44480			0.722398	−	0.691477i	$-0.243040\pi$
$593$	35.1831			1.44480			0.722398	+	0.691477i	$0.243040\pi$
$594$	33.1179	+	25.4346i	1.35884	+	1.04359i
$595$	3.04817	−	0.905817i	0.124963	−	0.0371349i
$596$	11.4163	+	1.39516i	0.467631	+	0.0571478i
$597$	10.2066	−	6.79490i	0.417729	−	0.278097i
$598$	−4.73533	−	5.34925i	−0.193642	−	0.218747i
$599$	7.34116	−	12.7153i	0.299952	−	0.519532i	−0.676173	−	0.736743i	$-0.736363\pi$
$599$	7.34116	−	12.7153i	0.299952	−	0.519532i	0.976125	+	0.217211i	$0.0696961\pi$
$600$	−16.1675	−	18.4014i	−0.660034	−	0.751235i
$601$	13.6252	+	23.5995i	0.555783	+	0.962644i	0.997842	+	0.0656584i	$0.0209148\pi$
$601$	13.6252	+	23.5995i	0.555783	+	0.962644i	−0.442059	+	0.896986i	$0.645752\pi$
$602$	2.22587	−	6.65871i	0.0907195	−	0.271389i
$603$	6.72801	+	8.82978i	0.273986	+	0.359577i
$604$	2.57041	−	3.41509i	0.104589	−	0.138958i
$605$	34.5623	+	32.7409i	1.40516	+	1.33111i
$606$	39.6456	+	10.4975i	1.61049	+	0.426430i
$607$	3.91627	−	6.78317i	0.158956	−	0.275320i	−0.775536	−	0.631303i	$-0.782520\pi$
$607$	3.91627	−	6.78317i	0.158956	−	0.275320i	0.934493	+	0.355983i	$0.115854\pi$
$608$	13.2925	+	8.44172i	0.539083	+	0.342357i
$609$	0.774017	+	12.1233i	0.0313647	+	0.491261i
$610$	−13.8956	+	7.40914i	−0.562617	+	0.299987i
$611$	−22.4049			−0.906406
$612$	0.0458326	+	7.75034i	0.00185267	+	0.313289i
$613$			1.17677i			0.0475293i	0.999718	+	0.0237646i	$0.00756523\pi$
$613$			1.17677i			0.0475293i	−0.999718	+	0.0237646i	$0.992435\pi$
$614$	18.6639	−	3.80274i	0.753214	−	0.153466i
$615$	−28.0123	−	4.83687i	−1.12956	−	0.195041i
$616$	1.40335	+	17.6388i	0.0565425	+	0.710686i
$617$	20.4261	−	35.3790i	0.822322	−	1.42430i	−0.0816263	−	0.996663i	$-0.526011\pi$
$617$	20.4261	−	35.3790i	0.822322	−	1.42430i	0.903949	−	0.427641i	$-0.140655\pi$
$618$	−3.21189	+	0.870809i	−0.129201	+	0.0350291i
$619$	42.7230	−	24.6661i	1.71718	−	0.991416i	0.793218	−	0.608938i	$-0.208404\pi$
$619$	42.7230	−	24.6661i	1.71718	−	0.991416i	0.923965	−	0.382478i	$-0.124929\pi$
$620$	5.01501	−	13.4726i	0.201408	−	0.541073i
$621$	−10.3535	−	3.57322i	−0.415473	−	0.143389i
$622$	−4.60111	+	13.7643i	−0.184488	+	0.551897i
$623$	8.74109	−	5.04667i	0.350204	−	0.202190i
$624$	12.6667	+	10.7352i	0.507073	+	0.429751i
$625$	14.7655	+	20.1738i	0.590619	+	0.806950i
$626$	−1.70041	+	1.50526i	−0.0679622	+	0.0601624i
$627$	24.5516	+	12.1592i	0.980496	+	0.485590i
$628$	19.9630	+	2.43962i	0.796611	+	0.0973515i
$629$		−	8.41813i		−	0.335653i
$630$	−0.977942	−	10.3983i	−0.0389622	−	0.414278i
$631$			27.6752i			1.10173i	0.834594	+	0.550866i	$0.185703\pi$
$631$			27.6752i			1.10173i	−0.834594	+	0.550866i	$0.814297\pi$
$632$	1.36919	−	2.87687i	0.0544633	−	0.114436i
$633$	−0.715359	−	11.2045i	−0.0284329	−	0.445341i
$634$	−4.18312	−	4.72545i	−0.166133	−	0.187672i
$635$	2.67707	−	11.1940i	0.106236	−	0.444222i
$636$	−33.5670	−	22.0614i	−1.33102	−	0.874791i
$637$	−12.0129	+	6.93564i	−0.475968	+	0.274800i
$638$	−48.5561	−	16.2313i	−1.92235	−	0.642602i
$639$	−14.6934	+	35.1365i	−0.581264	+	1.38998i
$640$	23.3154	+	9.81797i	0.921622	+	0.388089i
$641$	−13.0424	+	7.53005i	−0.515145	+	0.297419i	−0.734946	−	0.678126i	$-0.762793\pi$
$641$	−13.0424	+	7.53005i	−0.515145	+	0.297419i	0.219801	+	0.975545i	$0.429459\pi$
$642$	5.13259	−	5.16304i	0.202567	−	0.203769i
$643$	−23.7098	+	41.0665i	−0.935022	+	1.61951i	−0.160427	+	0.987048i	$0.551287\pi$
$643$	−23.7098	+	41.0665i	−0.935022	+	1.61951i	−0.774595	+	0.632458i	$0.782046\pi$
$644$	−1.81587	−	4.27117i	−0.0715554	−	0.168308i
$645$	−13.4188	−	11.1788i	−0.528363	−	0.440163i
$646$	1.01523	+	4.98276i	0.0399437	+	0.196044i
$647$		−	19.7634i		−	0.776977i	−0.921453	−	0.388489i	$-0.872997\pi$
$647$		−	19.7634i		−	0.776977i	0.921453	−	0.388489i	$-0.127003\pi$
$648$	25.0017	+	4.78682i	0.982161	+	0.188044i
$649$	41.6229			1.63384
$650$	−11.9024	−	12.0627i	−0.466851	−	0.473138i
$651$	5.10228	−	3.39677i	0.199974	−	0.133130i
$652$	33.5252	−	14.2531i	1.31295	−	0.558195i
$653$	−17.4740	+	30.2658i	−0.683809	+	1.18439i	0.290000	+	0.957027i	$0.406345\pi$
$653$	−17.4740	+	30.2658i	−0.683809	+	1.18439i	−0.973809	+	0.227366i	$0.926989\pi$
$654$	8.89560	+	8.84315i	0.347846	+	0.345795i
$655$	23.0523	+	21.8374i	0.900727	+	0.853258i
$656$	28.2125	−	8.12455i	1.10151	−	0.317211i
$657$	27.3146	+	11.4225i	1.06564	+	0.445632i
$658$	−13.8045	−	4.61456i	−0.538155	−	0.179894i
$659$	17.4893	+	30.2924i	0.681288	+	1.18003i	0.974588	+	0.224005i	$0.0719133\pi$
$659$	17.4893	+	30.2924i	0.681288	+	1.18003i	−0.293300	+	0.956021i	$0.594753\pi$
$660$	42.1459	+	12.6957i	1.64053	+	0.494181i
$661$	17.7487	−	30.7417i	0.690346	−	1.19571i	−0.281379	−	0.959597i	$-0.590792\pi$
$661$	17.7487	−	30.7417i	0.690346	−	1.19571i	0.971725	−	0.236117i	$-0.0758749\pi$
$662$	−12.4849	+	11.0520i	−0.485239	+	0.429549i
$663$	0.341643	+	5.35110i	0.0132683	+	0.207819i
$664$	14.0091	−	29.4354i	0.543660	−	1.14231i
$665$	−1.95197	−	6.56860i	−0.0756943	−	0.254719i
$666$	−27.1243	−	5.35967i	−1.05104	−	0.207683i
$667$	13.4287			0.519960
$668$	14.7791	+	1.80611i	0.571821	+	0.0698807i
$669$	−12.0654	+	24.3622i	−0.466475	+	0.941898i
$670$	9.93057	+	6.18929i	0.383652	+	0.239113i
$671$	14.1489	−	24.5066i	0.546211	−	0.946065i
$672$	5.59337	+	9.22318i	0.215769	+	0.355792i
$673$	−41.4746	+	23.9454i	−1.59873	+	0.923027i	−0.606997	+	0.794704i	$0.707626\pi$
$673$	−41.4746	+	23.9454i	−1.59873	+	0.923027i	−0.991733	+	0.128322i	$0.959041\pi$
$674$	−14.1667	−	4.73563i	−0.545680	−	0.182409i
$675$	−24.9818	−	7.13519i	−0.961549	−	0.274633i
$676$	−11.5955	−	8.72753i	−0.445982	−	0.335674i
$677$	0.0431856	+	0.0747996i	0.00165976	+	0.00287478i	0.866854	−	0.498562i	$-0.166138\pi$
$677$	0.0431856	+	0.0747996i	0.00165976	+	0.00287478i	−0.865194	+	0.501437i	$0.832805\pi$
$678$	−19.7888	+	5.36517i	−0.759986	+	0.206048i
$679$	−12.2485	−	7.07165i	−0.470053	−	0.271385i
$680$	2.94096	+	7.62201i	0.112781	+	0.292291i
$681$	−0.304224	−	0.150667i	−0.0116579	−	0.00577357i
$682$	5.15741	+	25.3126i	0.197488	+	0.969271i
$683$		−	24.0380i		−	0.919788i	−0.887974	−	0.459894i	$-0.847887\pi$
$683$		−	24.0380i		−	0.919788i	0.887974	−	0.459894i	$-0.152113\pi$
$684$	16.7015	−	0.0987662i	0.638596	−	0.00377642i
$685$	−14.8814	+	4.42226i	−0.568588	+	0.168966i
$686$	−19.5091	+	3.97496i	−0.744862	+	0.151765i
$687$	−2.85256	+	0.182123i	−0.108832	+	0.00694841i
$688$	17.5070	+	4.34383i	0.667447	+	0.165607i
$689$	−24.0661	−	13.8946i	−0.916846	−	0.529342i
$690$	−11.5400	+	0.346463i	−0.439322	+	0.0131896i
$691$	−36.1685	+	20.8819i	−1.37591	+	0.794384i	−0.991665	−	0.128845i	$-0.958873\pi$
$691$	−36.1685	+	20.8819i	−1.37591	+	0.794384i	−0.384249	+	0.923229i	$0.625540\pi$
$692$	13.8524	+	10.4262i	0.526589	+	0.396344i
$693$	11.3747	+	14.9281i	0.432090	+	0.567071i
$694$	31.2637	+	10.4508i	1.18675	+	0.396707i
$695$	−18.3465	+	19.3671i	−0.695922	+	0.734638i
$696$	−30.8909	+	4.45255i	−1.17092	+	0.168774i
$697$	8.21087	+	4.74055i	0.311009	+	0.179561i
$698$	−5.33727	−	6.02923i	−0.202019	−	0.228210i
$699$	19.4147	+	29.1628i	0.734332	+	1.10304i
$700$	−4.84906	−	9.88371i	−0.183277	−	0.373569i
$701$			2.12514i			0.0802654i	0.999194	+	0.0401327i	$0.0127781\pi$
$701$			2.12514i			0.0802654i	−0.999194	+	0.0401327i	$0.987222\pi$
$702$	17.4594	+	2.30613i	0.658963	+	0.0870392i
$703$	−18.1405			−0.684182
$704$	−44.8882	+	7.18814i	−1.69179	+	0.270913i
$705$	−23.1752	+	27.8191i	−0.872830	+	1.04773i
$706$	1.42739	+	1.61245i	0.0537207	+	0.0606854i
$707$	15.9631	+	9.21629i	0.600354	+	0.346614i
$708$	22.6709	−	11.3952i	0.852026	−	0.428258i
$709$	2.08824	+	3.61694i	0.0784256	+	0.135837i	0.902571	−	0.430541i	$-0.141677\pi$
$709$	2.08824	+	3.61694i	0.0784256	+	0.135837i	−0.824145	+	0.566379i	$0.808344\pi$
$710$	−1.35445	+	40.1224i	−0.0508317	+	1.50577i
$711$	−0.429759	−	3.35190i	−0.0161172	−	0.125706i
$712$	14.7060	+	21.3582i	0.551129	+	0.800434i
$713$	−3.38787	−	5.86797i	−0.126877	−	0.219757i
$714$	−0.891622	+	3.36737i	−0.0333681	+	0.126021i
$715$	29.6167	+	7.08288i	1.10760	+	0.264885i
$716$	−2.04280	+	0.868489i	−0.0763430	+	0.0324569i
$717$	−35.1397	+	2.24351i	−1.31232	+	0.0837853i
$718$	−13.1107	+	2.67129i	−0.489288	+	0.0996917i
$719$	−24.0884			−0.898346			−0.449173	−	0.893445i	$-0.648281\pi$
$719$	−24.0884			−0.898346			−0.449173	+	0.893445i	$0.648281\pi$
$720$	26.4315	−	4.62333i	0.985044	−	0.172302i
$721$	−1.49568			−0.0557022
$722$	−15.5916	+	3.17676i	−0.580259	+	0.118227i
$723$	13.2564	−	26.7671i	0.493010	−	0.995478i
$724$	−23.3070	+	9.90887i	−0.866197	+	0.368260i
$725$	31.8071	−	1.72288i	1.18129	−	0.0639863i
$726$	−50.3348	+	13.6468i	−1.86810	+	0.506480i
$727$	23.4466	+	40.6108i	0.869587	+	1.50617i	0.862419	+	0.506195i	$0.168948\pi$
$727$	23.4466	+	40.6108i	0.869587	+	1.50617i	0.00716831	+	0.999974i	$0.497718\pi$
$728$	4.23208	+	6.14647i	0.156851	+	0.227803i
$729$	25.0483	−	10.0788i	0.927715	−	0.373290i
$730$	31.1905	+	1.05293i	1.15441	+	0.0389706i
$731$	2.91253	+	5.04465i	0.107724	+	0.186583i
$732$	0.997305	−	17.2217i	0.0368614	−	0.636531i
$733$	15.3758	+	8.87721i	0.567917	+	0.327887i	0.756317	−	0.654205i	$-0.226997\pi$
$733$	15.3758	+	8.87721i	0.567917	+	0.327887i	−0.188400	+	0.982092i	$0.560330\pi$
$734$	−7.62322	−	8.61155i	−0.281378	−	0.317858i
$735$	−3.81426	+	22.0899i	−0.140691	+	0.814798i
$736$	10.5688	−	5.52087i	0.389570	−	0.203502i
$737$	−21.0271			−0.774543
$738$	20.5024	−	23.4382i	0.754702	−	0.862774i
$739$			8.50437i			0.312838i	0.987691	+	0.156419i	$0.0499951\pi$
$739$			8.50437i			0.312838i	−0.987691	+	0.156419i	$0.950005\pi$
$740$	−28.7376	+	4.85176i	−1.05642	+	0.178354i
$741$	11.5313	−	0.736218i	0.423611	−	0.0270456i
$742$	−11.9663	−	13.5177i	−0.439296	−	0.496249i
$743$	43.6052	+	25.1755i	1.59972	+	0.923598i	0.991540	+	0.129798i	$0.0414330\pi$
$743$	43.6052	+	25.1755i	1.59972	+	0.923598i	0.608179	+	0.793800i	$0.291900\pi$
$744$	9.73901	+	12.3752i	0.357050	+	0.453696i
$745$	8.84322	−	9.33519i	0.323991	−	0.342015i
$746$	15.5794	+	5.20786i	0.570402	+	0.190673i
$747$	−4.39718	−	34.2958i	−0.160884	−	1.25482i
$748$	−11.7296	−	8.82840i	−0.428875	−	0.322798i
$749$	2.83366	−	1.63601i	0.103540	−	0.0597787i
$750$	−27.2893	+	2.30121i	−0.996463	+	0.0840282i
$751$	44.8169	+	25.8750i	1.63539	+	0.944193i	0.982391	+	0.186834i	$0.0598228\pi$
$751$	44.8169	+	25.8750i	1.63539	+	0.944193i	0.652999	+	0.757359i	$0.273511\pi$
$752$	9.00541	−	36.2946i	0.328393	−	1.32353i
$753$	9.52179	+	14.3027i	0.346993	+	0.521218i
$754$	−21.1574	+	4.31078i	−0.770506	+	0.156989i
$755$	−1.36128	−	4.58085i	−0.0495421	−	0.166714i
$756$	10.2824	+	5.01686i	0.373968	+	0.182462i
$757$			16.5374i			0.601064i	0.953772	+	0.300532i	$0.0971642\pi$
$757$			16.5374i			0.601064i	−0.953772	+	0.300532i	$0.902836\pi$
$758$	−0.0548639	−	0.269272i	−0.00199275	−	0.00978042i
$759$	17.2695	−	11.4969i	0.626843	−	0.417312i
$760$	16.4249	−	6.33756i	0.595794	−	0.229888i
$761$	−30.1188	−	17.3891i	−1.09180	−	0.630354i	−0.157748	−	0.987479i	$-0.550423\pi$
$761$	−30.1188	−	17.3891i	−1.09180	−	0.630354i	−0.934056	+	0.357126i	$0.883757\pi$
$762$	8.94169	+	8.88897i	0.323923	+	0.322014i
$763$	2.81876	+	4.88223i	0.102046	+	0.176749i
$764$	−36.3782	−	27.3805i	−1.31612	−	0.990591i
$765$	6.99759	+	5.11087i	0.252998	+	0.184784i
$766$	−24.8141	−	8.29485i	−0.896571	−	0.299705i
$767$	15.2024	−	8.77710i	0.548926	−	0.316923i
$768$	−22.4815	+	16.2043i	−0.811232	+	0.584724i
$769$	−7.71708	+	13.3664i	−0.278285	+	0.482003i	−0.970959	−	0.239248i	$-0.923099\pi$
$769$	−7.71708	+	13.3664i	−0.278285	+	0.482003i	0.692674	+	0.721251i	$0.256433\pi$
$770$	16.7891	+	10.4639i	0.605039	+	0.377094i
$771$	29.9895	−	1.91469i	1.08005	−	0.0689560i
$772$	23.0811	+	2.82067i	0.830705	+	0.101518i
$773$	−29.3290			−1.05489			−0.527446	−	0.849589i	$-0.676850\pi$
$773$	−29.3290			−1.05489			−0.527446	+	0.849589i	$0.676850\pi$
$774$	18.1089	−	6.17270i	0.650909	−	0.221873i
$775$	−8.77736	−	13.4642i	−0.315292	−	0.483648i
$776$	15.6153	−	32.8101i	0.560555	−	1.17781i
$777$	−11.1358	−	5.51499i	−0.399494	−	0.197849i
$778$	24.9278	−	22.0669i	0.893703	−	0.791135i
$779$	10.2156	−	17.6939i	0.366011	−	0.633949i
$780$	18.0706	−	4.25038i	0.647030	−	0.152188i
$781$	−36.0698	−	62.4748i	−1.29068	−	2.23552i
$782$	3.65201	+	1.22079i	0.130596	+	0.0436554i
$783$	−24.9988	+	21.7000i	−0.893385	+	0.775496i
$784$	−6.40686	−	22.2478i	−0.228817	−	0.794565i
$785$	15.4636	−	16.3239i	0.551920	−	0.582624i
$786$	−33.5721	+	9.10210i	−1.19748	+	0.324661i
$787$	26.3106	−	45.5713i	0.937872	−	1.62444i	0.168442	−	0.985712i	$-0.446127\pi$
$787$	26.3106	−	45.5713i	0.937872	−	1.62444i	0.769431	−	0.638730i	$-0.220540\pi$
$788$	−22.4555	+	9.54688i	−0.799945	+	0.340094i
$789$	−14.9202	−	7.38923i	−0.531174	−	0.263064i
$790$	−1.67597	−	3.14324i	−0.0596285	−	0.111831i
$791$	−9.21510			−0.327651
$792$	−35.9142	+	32.1732i	−1.27616	+	1.14323i
$793$		−	11.9344i		−	0.423803i
$794$	−6.60940	−	32.4390i	−0.234559	−	1.15122i
$795$	−42.1458	+	15.5094i	−1.49476	+	0.550063i
$796$	5.53955	+	13.0297i	0.196344	+	0.461827i
$797$	−1.24198	+	2.15117i	−0.0439931	+	0.0761983i	−0.887183	−	0.461417i	$-0.847341\pi$
$797$	−1.24198	+	2.15117i	−0.0439931	+	0.0761983i	0.843190	+	0.537615i	$0.180675\pi$
$798$	7.25647	+	1.92139i	0.256876	+	0.0680163i
$799$	10.4583	−	6.03812i	0.369989	−	0.213613i
$800$	24.3248	−	14.4327i	0.860013	−	0.510272i
$801$	25.3751	+	10.6114i	0.896583	+	0.374934i
$802$	−40.1523	−	13.4221i	−1.41783	−	0.473950i
$803$	−48.5669	+	28.0401i	−1.71389	+	0.989514i
$804$	−11.4529	+	5.75664i	−0.403913	+	0.203021i
$805$	−5.04665	−	1.20691i	−0.177871	−	0.0425381i
$806$	7.22142	+	8.15765i	0.254364	+	0.287341i
$807$	1.93893	−	1.29081i	0.0682535	−	0.0454388i
$808$	−20.3510	+	42.7605i	−0.715944	+	1.50431i
$809$			25.6629i			0.902261i	0.892458	+	0.451131i	$0.148979\pi$
$809$			25.6629i			0.902261i	−0.892458	+	0.451131i	$0.851021\pi$
$810$	20.9231	−	19.2931i	0.735163	−	0.677890i
$811$			26.5970i			0.933948i	0.884271	+	0.466974i	$0.154656\pi$
$811$			26.5970i			0.933948i	−0.884271	+	0.466974i	$0.845344\pi$
$812$	−13.9237	−	1.70157i	−0.488626	−	0.0597135i
$813$	31.3279	−	20.8561i	1.09872	−	0.731456i
$814$	39.2140	−	34.7135i	1.37445	−	1.21671i
$815$	9.47329	−	39.6121i	0.331835	−	1.38755i
$816$	−8.80576	−	1.59737i	−0.308263	−	0.0559192i
$817$	10.8709	−	6.27631i	0.380324	−	0.219580i
$818$	−0.932682	+	2.79013i	−0.0326105	+	0.0975546i
$819$	7.30243	+	3.05374i	0.255167	+	0.106706i
$820$	11.4509	−	30.7623i	0.399882	−	1.07427i
$821$	−26.3429	+	15.2091i	−0.919373	+	0.530800i	−0.883435	−	0.468554i	$-0.844775\pi$
$821$	−26.3429	+	15.2091i	−0.919373	+	0.530800i	−0.0359383	+	0.999354i	$0.511442\pi$
$822$	4.35296	−	16.4397i	0.151827	−	0.573402i
$823$	4.23623	−	7.33737i	0.147666	−	0.255764i	−0.782699	−	0.622401i	$-0.786157\pi$
$823$	4.23623	−	7.33737i	0.147666	−	0.255764i	0.930364	+	0.366636i	$0.119491\pi$
$824$	−0.304760	−	3.83055i	−0.0106168	−	0.133444i
$825$	39.4294	−	29.4472i	1.37276	−	1.02522i
$826$	11.1745	−	2.27679i	0.388810	−	0.0792196i
$827$			37.2624i			1.29574i	0.761750	+	0.647871i	$0.224340\pi$
$827$			37.2624i			1.29574i	−0.761750	+	0.647871i	$0.775660\pi$
$828$	6.25871	−	10.9900i	0.217505	−	0.381928i
$829$	−18.4167			−0.639639			−0.319820	−	0.947478i	$-0.603622\pi$
$829$	−18.4167			−0.639639			−0.319820	+	0.947478i	$0.603622\pi$
$830$	−17.1481	−	32.1608i	−0.595220	−	1.11632i
$831$	−21.5968	−	10.6958i	−0.749184	−	0.371033i
$832$	−14.8792	+	12.0911i	−0.515844	+	0.419182i
$833$	3.73830	−	6.47493i	0.129525	−	0.224343i
$834$	−7.64704	−	28.2053i	−0.264795	−	0.976669i
$835$	11.4481	−	12.0850i	0.396178	−	0.418218i
$836$	−19.0246	+	25.2764i	−0.657980	+	0.874203i
$837$	15.7892	+	5.44920i	0.545755	+	0.188352i
$838$	4.38510	−	13.1181i	0.151481	−	0.453157i
$839$	7.35228	+	12.7345i	0.253829	+	0.439645i	0.964577	−	0.263802i	$-0.0849766\pi$
$839$	7.35228	+	12.7345i	0.253829	+	0.439645i	−0.710748	+	0.703447i	$0.751643\pi$
$840$	12.0094	+	1.10303i	0.414362	+	0.0380581i
$841$	5.79320	−	10.0341i	0.199765	−	0.346004i
$842$	−1.97033	−	2.22578i	−0.0679022	−	0.0767055i
$843$	−18.0924	−	8.96025i	−0.623135	−	0.308607i
$844$	12.8685	+	1.57262i	0.442952	+	0.0541319i
$845$	−15.5538	+	4.62207i	−0.535066	+	0.159004i
$846$	−12.7969	−	37.5424i	−0.439968	−	1.29073i
$847$	−23.4395			−0.805390
$848$	32.1815	−	33.4008i	1.10512	−	1.14699i
$849$	21.4811	−	1.37147i	0.737228	−	0.0470686i
$850$	8.80677	+	2.42301i	0.302070	+	0.0831087i
$851$	−6.86833	+	11.8963i	−0.235443	+	0.407800i
$852$	−36.7502	−	24.1535i	−1.25904	−	0.827484i
$853$	11.2327	−	6.48519i	0.384600	−	0.222049i	−0.295218	−	0.955430i	$-0.595392\pi$
$853$	11.2327	−	6.48519i	0.384600	−	0.222049i	0.679818	+	0.733381i	$0.262059\pi$
$854$	2.45803	−	7.35322i	0.0841119	−	0.251622i
$855$	11.0136	−	15.0793i	0.376657	−	0.515702i
$856$	4.76734	+	6.92385i	0.162944	+	0.236652i
$857$	−3.36521	−	5.82871i	−0.114953	−	0.199105i	0.802808	−	0.596238i	$-0.203339\pi$
$857$	−3.36521	−	5.82871i	−0.114953	−	0.199105i	−0.917761	+	0.397133i	$0.870005\pi$
$858$	−23.5181	+	23.6576i	−0.802894	+	0.807656i
$859$	33.3860	+	19.2754i	1.13912	+	0.657669i	0.946212	−	0.323549i	$-0.104876\pi$
$859$	33.3860	+	19.2754i	1.13912	+	0.657669i	0.192904	+	0.981218i	$0.438209\pi$
$860$	15.5427	−	12.8502i	0.530002	−	0.438188i
$861$	11.6502	−	7.75592i	0.397036	−	0.264321i
$862$	−5.32407	+	1.08477i	−0.181339	+	0.0369475i
$863$			13.4795i			0.458847i	0.973327	+	0.229424i	$0.0736841\pi$
$863$			13.4795i			0.458847i	−0.973327	+	0.229424i	$0.926316\pi$
$864$	−10.7534	+	27.3562i	−0.365838	+	0.930678i
$865$	18.5810	−	5.52167i	0.631773	−	0.187742i
$866$	1.88281	+	9.24087i	0.0639806	+	0.314018i
$867$	14.7157	+	22.1044i	0.499770	+	0.750704i
$868$	2.76922	+	6.51357i	0.0939934	+	0.221085i
$869$	5.54347	+	3.20052i	0.188049	+	0.108570i
$870$	−16.5323	+	30.7291i	−0.560497	+	1.04181i
$871$	−7.67995	+	4.43402i	−0.260225	+	0.150241i
$872$	−11.9294	+	8.21384i	−0.403980	+	0.278156i
$873$	−4.90131	−	38.2277i	−0.165884	−	1.29381i
$874$	2.63072	−	7.86984i	0.0889855	−	0.266201i
$875$	−12.1083	−	2.21121i	−0.409336	−	0.0747527i
$876$	−18.7765	+	28.5690i	−0.634400	+	0.965257i
$877$	13.5129	+	7.80171i	0.456300	+	0.263445i	0.710487	−	0.703710i	$-0.248475\pi$
$877$	13.5129	+	7.80171i	0.456300	+	0.263445i	−0.254187	+	0.967155i	$0.581808\pi$
$878$	41.0271	−	36.3185i	1.38460	−	1.22569i
$879$	−16.5065	+	1.05387i	−0.556751	+	0.0355460i
$880$	−23.3779	+	45.1303i	−0.788070	+	1.52134i
$881$			25.0226i			0.843032i	0.906821	+	0.421516i	$0.138502\pi$
$881$			25.0226i			0.843032i	−0.906821	+	0.421516i	$0.861498\pi$
$882$	−18.4829	−	16.1678i	−0.622353	−	0.544397i
$883$	13.8202			0.465085			0.232543	−	0.972586i	$-0.425295\pi$
$883$	13.8202			0.465085			0.232543	+	0.972586i	$0.425295\pi$
$884$	−6.14577	−	0.751058i	−0.206705	−	0.0252608i
$885$	4.82697	−	27.9549i	0.162257	−	0.939695i
$886$	−24.7996	+	21.9534i	−0.833159	+	0.737539i
$887$	−16.1656	−	9.33323i	−0.542789	−	0.313379i	0.203420	−	0.979092i	$-0.434794\pi$
$887$	−16.1656	−	9.33323i	−0.542789	−	0.313379i	−0.746208	+	0.665712i	$0.768128\pi$
$888$	11.8553	−	29.6433i	0.397836	−	0.994763i
$889$	2.83336	+	4.90753i	0.0950279	+	0.164593i
$890$	28.9757	+	0.978163i	0.971269	+	0.0327881i
$891$	−13.5705	+	49.3093i	−0.454629	+	1.65192i
$892$	−25.0815	−	18.8779i	−0.839790	−	0.632079i
$893$	−13.0117	−	22.5370i	−0.435421	−	0.754172i
$894$	3.68596	+	13.5953i	0.123277	+	0.454694i
$895$	−0.577239	+	2.41369i	−0.0192950	+	0.0806809i
$896$	−11.6579	+	4.38520i	−0.389464	+	0.146499i
$897$	3.88315	−	7.84079i	0.129654	−	0.261796i
$898$	4.45721	+	21.8760i	0.148739	+	0.730013i
$899$	−20.4788			−0.683007
$900$	13.4144	−	26.8338i	0.447145	−	0.894461i
$901$	14.9783			0.499001
$902$	11.7760	+	57.7969i	0.392099	+	1.92443i
$903$	8.58132	−	0.547878i	0.285569	−	0.0182322i
$904$	−1.87767	−	23.6005i	−0.0624503	−	0.784942i
$905$	−6.58591	+	27.5386i	−0.218923	+	0.915415i
$906$	5.06056	+	1.33995i	0.168126	+	0.0445168i
$907$	20.7283	+	35.9025i	0.688273	+	1.19212i	0.972396	+	0.233336i	$0.0749642\pi$
$907$	20.7283	+	35.9025i	0.688273	+	1.19212i	−0.284123	+	0.958788i	$0.591703\pi$
$908$	0.235739	−	0.313206i	0.00782326	−	0.0103941i
$909$	6.38774	+	49.8212i	0.211868	+	1.65246i
$910$	8.33863	+	0.281496i	0.276423	+	0.00933149i
$911$	2.80277	+	4.85454i	0.0928600	+	0.160838i	0.908713	−	0.417420i	$-0.137066\pi$
$911$	2.80277	+	4.85454i	0.0928600	+	0.160838i	−0.815853	+	0.578259i	$0.803732\pi$
$912$	−3.44223	+	18.9758i	−0.113984	+	0.628352i
$913$	56.7193	+	32.7469i	1.87714	+	1.08376i
$914$	−8.91209	+	7.88927i	−0.294786	+	0.260954i
$915$	−14.8183	−	12.3447i	−0.489879	−	0.408104i
$916$	0.400373	−	3.27618i	0.0132287	−	0.108248i
$917$	−15.6336			−0.516266
$918$	−8.77133	+	3.62884i	−0.289497	+	0.119769i
$919$		−	30.8044i		−	1.01614i	−0.861315	−	0.508072i	$-0.830358\pi$
$919$		−	30.8044i		−	1.01614i	0.861315	−	0.508072i	$-0.169642\pi$
$920$	2.06269	−	13.1708i	0.0680048	−	0.434227i
$921$	12.9276	+	19.4186i	0.425980	+	0.639863i
$922$	−26.2641	+	23.2498i	−0.864961	+	0.765692i
$923$	−26.3483	−	15.2122i	−0.867266	−	0.500716i
$924$	−19.3629	+	9.73248i	−0.636993	+	0.320175i
$925$	−14.7420	+	29.0588i	−0.484715	+	0.955446i
$926$	9.28972	−	27.7903i	0.305279	−	0.913247i
$927$	−2.47021	−	3.24189i	−0.0811324	−	0.106478i
$928$	1.52077	−	36.0063i	0.0499216	−	1.18196i
$929$	23.8104	−	13.7469i	0.781194	−	0.451023i	−0.0556590	−	0.998450i	$-0.517726\pi$
$929$	23.8104	−	13.7469i	0.781194	−	0.451023i	0.836853	+	0.547427i	$0.184393\pi$
$930$	17.5987	−	0.528359i	0.577083	−	0.0173256i
$931$	−13.9530	−	8.05579i	−0.457293	−	0.264018i
$932$	−37.2292	+	15.8279i	−1.21948	+	0.518459i
$933$	−17.7385	+	1.13252i	−0.580733	+	0.0370772i
$934$	−0.450587	−	2.21148i	−0.0147436	−	0.0723620i
$935$	−15.7335	+	4.67550i	−0.514541	+	0.152905i
$936$	−6.33290	+	19.3243i	−0.206997	+	0.631633i
$937$			13.6341i			0.445407i	0.974886	+	0.222704i	$0.0714882\pi$
$937$			13.6341i			0.445407i	−0.974886	+	0.222704i	$0.928512\pi$
$938$	−5.64514	+	1.15019i	−0.184320	+	0.0375550i
$939$	−2.49242	−	1.23437i	−0.0813371	−	0.0402822i
$940$	−26.6404	−	32.2224i	−0.868914	−	1.05098i
$941$	−49.7730	−	28.7364i	−1.62255	−	0.936781i	−0.986234	−	0.165355i	$-0.947123\pi$
$941$	−49.7730	−	28.7364i	−1.62255	−	0.936781i	−0.636319	−	0.771426i	$-0.719544\pi$
$942$	6.44542	+	23.7732i	0.210003	+	0.774574i
$943$	−7.73561	−	13.3985i	−0.251906	−	0.436314i
$944$	8.10793	+	28.1548i	0.263891	+	0.916360i
$945$	11.3452	−	5.90833i	0.369058	−	0.192198i
$946$	−11.4891	+	34.3698i	−0.373543	+	1.11746i
$947$	16.7732	−	9.68402i	0.545056	−	0.314688i	−0.202069	−	0.979371i	$-0.564767\pi$
$947$	16.7732	−	9.68402i	0.545056	−	0.314688i	0.747126	+	0.664683i	$0.231433\pi$
$948$	3.89560	+	0.225594i	0.126523	+	0.00732695i
$949$	−11.8257	+	20.4828i	−0.383880	+	0.664899i
$950$	5.22143	−	18.9780i	0.169406	−	0.615728i
$951$	3.43031	−	6.92644i	0.111236	−	0.224605i
$952$	−3.63195	−	1.72855i	−0.117712	−	0.0560226i
$953$	4.34158			0.140638			0.0703188	−	0.997525i	$-0.477598\pi$
$953$	4.34158			0.140638			0.0703188	+	0.997525i	$0.477598\pi$
$954$	9.53643	−	48.2621i	0.308753	−	1.56254i
$955$	−48.7961	+	14.5006i	−1.57900	+	0.469229i
$956$	4.93206	−	40.3582i	0.159514	−	1.30528i
$957$	−3.99519	−	62.5760i	−0.129146	−	2.02280i
$958$	−5.60458	−	6.33119i	−0.181076	−	0.204552i
$959$	3.82170	−	6.61938i	0.123409	−	0.213751i
$960$	−0.377912	+	30.9816i	−0.0121971	+	0.999926i
$961$	−10.3335	−	17.8981i	−0.333338	−	0.577358i
$962$	7.00245	−	20.9479i	0.225768	−	0.675388i
$963$	8.22601	+	3.43997i	0.265080	+	0.110851i
$964$	27.5573	+	20.7414i	0.887561	+	0.668034i
$965$	17.8789	−	18.8735i	0.575541	−	0.607560i
$966$	4.00745	−	4.03122i	0.128938	−	0.129702i
$967$	16.5665	−	28.6939i	0.532741	−	0.922735i	−0.466528	−	0.884507i	$-0.654495\pi$
$967$	16.5665	−	28.6939i	0.532741	−	0.922735i	0.999269	−	0.0382285i	$-0.0121715\pi$
$968$	−4.77602	−	60.0302i	−0.153507	−	1.92944i
$969$	−5.18423	+	3.45133i	−0.166541	+	0.110873i
$970$	−19.1141	−	35.8479i	−0.613718	−	1.15101i
$971$	22.0082			0.706277			0.353138	−	0.935571i	$-0.385114\pi$
$971$	22.0082			0.706277			0.353138	+	0.935571i	$0.385114\pi$
$972$	6.10802	+	30.5727i	0.195915	+	0.980621i
$973$		−	13.1344i		−	0.421070i
$974$	22.9993	−	4.68607i	0.736945	−	0.150151i
$975$	8.19165	−	19.0699i	0.262343	−	0.610725i
$976$	19.3330	+	4.79689i	0.618833	+	0.153545i
$977$	−14.7558	+	25.5578i	−0.472080	+	0.817667i	−0.999490	−	0.0319442i	$-0.989830\pi$
$977$	−14.7558	+	25.5578i	−0.472080	+	0.817667i	0.527409	+	0.849611i	$0.323163\pi$
$978$	31.6418	+	31.4552i	1.01179	+	1.00583i
$979$	−45.1183	+	26.0491i	−1.44199	+	0.832532i
$980$	−24.2585	−	9.02994i	−0.774911	−	0.288451i
$981$	−5.92686	+	14.1729i	−0.189230	+	0.452507i
$982$	−5.98052	+	17.8908i	−0.190846	+	0.570919i
$983$	39.8190	−	22.9895i	1.27003	−	0.733251i	0.295035	−	0.955486i	$-0.404669\pi$
$983$	39.8190	−	22.9895i	1.27003	−	0.733251i	0.974993	+	0.222235i	$0.0713354\pi$
$984$	22.2373	+	28.2565i	0.708900	+	0.900786i
$985$	−6.34531	+	26.5326i	−0.202178	+	0.845399i
$986$	8.71423	−	7.71412i	0.277518	−	0.245668i
$987$	−1.13583	−	17.7904i	−0.0361540	−	0.566274i
$988$	−1.61848	+	13.2437i	−0.0514907	+	0.421339i
$989$		−	9.50531i		−	0.302251i
$990$	5.04778	+	53.6722i	0.160429	+	1.70581i
$991$		−	52.8232i		−	1.67798i	−0.544144	−	0.838992i	$-0.683146\pi$
$991$		−	52.8232i		−	1.67798i	0.544144	−	0.838992i	$-0.316854\pi$
$992$	−16.1175	+	8.41937i	−0.511730	+	0.267315i
$993$	−18.3000	−	9.06307i	−0.580733	−	0.287608i
$994$	−13.1010	−	14.7996i	−0.415540	−	0.469413i
$995$	15.3955	+	3.68185i	0.488069	+	0.116722i
$996$	39.8587	+	2.30822i	1.26297	+	0.0731386i
$997$	43.4452	−	25.0831i	1.37592	−	0.794389i	0.384257	−	0.923226i	$-0.374458\pi$
$997$	43.4452	−	25.0831i	1.37592	−	0.794389i	0.991666	+	0.128837i	$0.0411244\pi$
$998$	55.3113	+	18.4894i	1.75085	+	0.585272i
$999$	−6.43771	−	33.2451i	−0.203680	−	1.05183i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.2.n.d.59.2	✓	48
3.2	odd	2		540.2.n.d.179.23		48
4.3	odd	2	inner	180.2.n.d.59.18	yes	48
5.2	odd	4		900.2.r.g.851.11		48
5.3	odd	4		900.2.r.g.851.14		48
5.4	even	2	inner	180.2.n.d.59.23	yes	48
9.2	odd	6	inner	180.2.n.d.119.7	yes	48
9.7	even	3		540.2.n.d.359.18		48
12.11	even	2		540.2.n.d.179.7		48
15.14	odd	2		540.2.n.d.179.2		48
20.3	even	4		900.2.r.g.851.6		48
20.7	even	4		900.2.r.g.851.19		48
20.19	odd	2	inner	180.2.n.d.59.7	yes	48
36.7	odd	6		540.2.n.d.359.2		48
36.11	even	6	inner	180.2.n.d.119.23	yes	48
45.2	even	12		900.2.r.g.551.19		48
45.29	odd	6	inner	180.2.n.d.119.18	yes	48
45.34	even	6		540.2.n.d.359.7		48
45.38	even	12		900.2.r.g.551.6		48
60.59	even	2		540.2.n.d.179.18		48
180.47	odd	12		900.2.r.g.551.11		48
180.79	odd	6		540.2.n.d.359.23		48
180.83	odd	12		900.2.r.g.551.14		48
180.119	even	6	inner	180.2.n.d.119.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.n.d.59.2	✓	48	1.1	even	1	trivial
180.2.n.d.59.7	yes	48	20.19	odd	2	inner
180.2.n.d.59.18	yes	48	4.3	odd	2	inner
180.2.n.d.59.23	yes	48	5.4	even	2	inner
180.2.n.d.119.2	yes	48	180.119	even	6	inner
180.2.n.d.119.7	yes	48	9.2	odd	6	inner
180.2.n.d.119.18	yes	48	45.29	odd	6	inner
180.2.n.d.119.23	yes	48	36.11	even	6	inner
540.2.n.d.179.2		48	15.14	odd	2
540.2.n.d.179.7		48	12.11	even	2
540.2.n.d.179.18		48	60.59	even	2
540.2.n.d.179.23		48	3.2	odd	2
540.2.n.d.359.2		48	36.7	odd	6
540.2.n.d.359.7		48	45.34	even	6
540.2.n.d.359.18		48	9.7	even	3
540.2.n.d.359.23		48	180.79	odd	6
900.2.r.g.551.6		48	45.38	even	12
900.2.r.g.551.11		48	180.47	odd	12
900.2.r.g.551.14		48	180.83	odd	12
900.2.r.g.551.19		48	45.2	even	12
900.2.r.g.851.6		48	20.3	even	4
900.2.r.g.851.11		48	5.2	odd	4
900.2.r.g.851.14		48	5.3	odd	4
900.2.r.g.851.19		48	20.7	even	4

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:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	180.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38574 + 0.282343i) q^{2} +(-0.959839 - 1.44177i) q^{3} +(1.84056 - 0.782509i) q^{4} +(0.520093 - 2.17474i) q^{5} +(1.73716 + 1.72692i) q^{6} +(0.550457 + 0.953419i) q^{7} +(-2.32961 + 1.60403i) q^{8} +(-1.15742 + 2.76774i) q^{9} +(-0.106691 + 3.16048i) q^{10} +(-2.84126 - 4.92120i) q^{11} +(-2.89485 - 1.90259i) q^{12} +(-2.07548 - 1.19828i) q^{13} +(-1.03198 - 1.16578i) q^{14} +(-3.63469 + 1.33755i) q^{15} +(2.77536 - 2.88052i) q^{16} +1.29175 q^{17} +(0.822430 - 4.16216i) q^{18} -2.78362i q^{19} +(-0.744492 - 4.40973i) q^{20} +(0.846263 - 1.70876i) q^{21} +(5.32672 + 6.01731i) q^{22} +(-1.82546 - 1.05393i) q^{23} +(4.54870 + 1.81916i) q^{24} +(-4.45901 - 2.26214i) q^{25} +(3.21441 + 1.07451i) q^{26} +(5.10139 - 0.987853i) q^{27} +(1.75921 + 1.32409i) q^{28} +(-5.51723 + 3.18537i) q^{29} +(4.65910 - 2.87973i) q^{30} +(2.78385 + 1.60725i) q^{31} +(-3.03264 + 4.77526i) q^{32} +(-4.36810 + 8.82001i) q^{33} +(-1.79003 + 0.364715i) q^{34} +(2.35973 - 0.701235i) q^{35} +(0.0354812 + 5.99990i) q^{36} -6.51687i q^{37} +(0.785937 + 3.85739i) q^{38} +(0.264482 + 4.14253i) q^{39} +(2.27673 + 5.90055i) q^{40} +(6.35642 + 3.66988i) q^{41} +(-0.690246 + 2.60684i) q^{42} +(2.25473 + 3.90530i) q^{43} +(-9.08040 - 6.83448i) q^{44} +(5.41716 + 3.95657i) q^{45} +(2.82719 + 0.945071i) q^{46} +(8.09628 - 4.67439i) q^{47} +(-6.81695 - 1.23660i) q^{48} +(2.89400 - 5.01255i) q^{49} +(6.81773 + 1.87577i) q^{50} +(-1.23987 - 1.86240i) q^{51} +(-4.75773 - 0.581429i) q^{52} +11.5954 q^{53} +(-6.79030 + 2.80925i) q^{54} +(-12.1801 + 3.61952i) q^{55} +(-2.81166 - 1.33815i) q^{56} +(-4.01335 + 2.67183i) q^{57} +(6.74609 - 5.97186i) q^{58} +(-3.66237 + 6.34341i) q^{59} +(-5.64324 + 5.30602i) q^{60} +(2.48990 + 4.31263i) q^{61} +(-4.31149 - 1.44124i) q^{62} +(-3.27592 + 0.420017i) q^{63} +(2.85419 - 7.47353i) q^{64} +(-3.68540 + 3.89043i) q^{65} +(3.56280 - 13.4556i) q^{66} +(1.85016 - 3.20457i) q^{67} +(2.37754 - 1.01080i) q^{68} +(0.232621 + 3.64351i) q^{69} +(-3.07199 + 1.63798i) q^{70} +12.6950 q^{71} +(-1.74320 - 8.30429i) q^{72} -9.86891i q^{73} +(1.83999 + 9.03070i) q^{74} +(1.01844 + 8.60016i) q^{75} +(-2.17821 - 5.12344i) q^{76} +(3.12798 - 5.41781i) q^{77} +(-1.53612 - 5.66581i) q^{78} +(-0.975531 + 0.563223i) q^{79} +(-4.82094 - 7.53382i) q^{80} +(-6.32077 - 6.40686i) q^{81} +(-9.84453 - 3.29082i) q^{82} +(-9.98138 + 5.76275i) q^{83} +(0.220480 - 3.80730i) q^{84} +(0.671827 - 2.80921i) q^{85} +(-4.22710 - 4.77514i) q^{86} +(9.88823 + 4.89714i) q^{87} +(14.5128 + 6.90704i) q^{88} -9.16815i q^{89} +(-8.62389 - 3.95329i) q^{90} -2.63841i q^{91} +(-4.18460 - 0.511387i) q^{92} +(-0.354749 - 5.55638i) q^{93} +(-9.89957 + 8.76343i) q^{94} +(-6.05366 - 1.44774i) q^{95} +(9.79568 - 0.211108i) q^{96} +(-11.1257 + 6.42344i) q^{97} +(-2.59507 + 7.76320i) q^{98} +(16.9091 - 2.16798i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{4} - 18 q^{5} - 12 q^{9} - 16 q^{10} - 42 q^{14} + 30 q^{16} - 12 q^{21} - 6 q^{24} - 26 q^{25} - 12 q^{30} - 4 q^{34} + 96 q^{36} + 10 q^{40} + 96 q^{41} - 66 q^{45} + 4 q^{46} + 32 q^{49}+ \cdots + 54 q^{96}+O(q^{100}) \) 48 * q - 2 * q^4 - 18 * q^5 - 12 * q^9 - 16 * q^10 - 42 * q^14 + 30 * q^16 - 12 * q^21 - 6 * q^24 - 26 * q^25 - 12 * q^30 - 4 * q^34 + 96 * q^36 + 10 * q^40 + 96 * q^41 - 66 * q^45 + 4 * q^46 + 32 * q^49 - 90 * q^50 - 30 * q^54 + 6 * q^56 - 42 * q^60 + 8 * q^61 - 20 * q^64 - 6 * q^65 + 36 * q^66 - 96 * q^69 + 4 * q^70 + 72 * q^74 + 36 * q^81 - 6 * q^84 - 4 * q^85 + 108 * q^86 - 6 * q^90 - 62 * q^94 + 54 * q^96

Introduction

L-functions

Modular forms

Varieties

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Database

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