LMFDB - Embedded newform 180.2.n.d.59.18

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			59.18
Character	$\chi$	$=$	180.59
Dual form			180.2.n.d.119.18

$q$-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} +(0.959839 + 1.44177i) q^{3} +(-0.242609 - 1.98523i) q^{4} +(0.520093 - 2.17474i) q^{5} +(2.42646 + 0.335110i) q^{6} +(-0.550457 - 0.953419i) q^{7} +(-2.32961 - 1.60403i) q^{8} +(-1.15742 + 2.76774i) q^{9} +(-1.81534 - 2.58931i) q^{10} +(2.84126 + 4.92120i) q^{11} +(2.62939 - 2.25529i) q^{12} +(-2.07548 - 1.19828i) q^{13} +(-1.52558 - 0.310835i) q^{14} +(3.63469 - 1.33755i) q^{15} +(-3.88228 + 0.963271i) q^{16} +1.29175 q^{17} +(1.84586 + 3.82005i) q^{18} +2.78362i q^{19} +(-4.44354 - 0.504891i) q^{20} +(0.846263 - 1.70876i) q^{21} +(7.87450 + 1.60442i) q^{22} +(1.82546 + 1.05393i) q^{23} +(0.0765889 - 4.89838i) 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} +(1.99076 - 5.10263i) q^{30} +(-2.78385 - 1.60725i) q^{31} +(-2.61918 + 5.01397i) q^{32} +(-4.36810 + 8.82001i) q^{33} +(1.21087 - 1.36785i) q^{34} +(-2.35973 + 0.701235i) q^{35} +(5.77540 + 1.62626i) q^{36} -6.51687i q^{37} +(2.94763 + 2.60933i) q^{38} +(-0.264482 - 4.14253i) q^{39} +(-4.69996 + 4.23206i) q^{40} +(6.35642 + 3.66988i) q^{41} +(-1.01616 - 2.49789i) 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} +(-5.11518 - 4.67278i) q^{48} +(2.89400 - 5.01255i) q^{49} +(-6.57523 + 2.60122i) q^{50} +(1.23987 + 1.86240i) q^{51} +(-1.87533 + 4.41103i) q^{52} +11.5954 q^{53} +(-3.73592 + 6.32794i) q^{54} +(12.1801 - 3.61952i) q^{55} +(-0.246959 + 3.10404i) q^{56} +(-4.01335 + 2.67183i) q^{57} +(-1.79874 + 8.82821i) q^{58} +(3.66237 - 6.34341i) q^{59} +(-3.53715 - 6.89120i) 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} +(5.24505 + 12.8932i) q^{66} +(-1.85016 + 3.20457i) q^{67} +(-0.313389 - 2.56441i) q^{68} +(0.232621 + 3.64351i) q^{69} +(-1.46943 + 3.15608i) q^{70} -12.6950 q^{71} +(7.13586 - 4.59123i) q^{72} -9.86891i q^{73} +(-6.90082 - 6.10883i) q^{74} +(-1.01844 - 8.60016i) q^{75} +(5.52614 - 0.675333i) q^{76} +(3.12798 - 5.41781i) q^{77} +(-4.63452 - 3.60310i) q^{78} +(0.975531 - 0.563223i) q^{79} +(0.0757197 + 8.94395i) q^{80} +(-6.32077 - 6.40686i) q^{81} +(9.84453 - 3.29082i) q^{82} +(9.98138 - 5.76275i) q^{83} +(-3.59760 - 1.26547i) q^{84} +(0.671827 - 2.80921i) q^{85} +(-6.24894 - 1.27321i) q^{86} +(-9.88823 - 4.89714i) q^{87} +(1.27471 - 16.0219i) q^{88} -9.16815i q^{89} +(9.26765 - 2.02748i) q^{90} +2.63841i q^{91} +(1.64942 - 3.87966i) q^{92} +(-0.354749 - 5.55638i) q^{93} +(-2.63956 + 12.9550i) q^{94} +(6.05366 + 1.44774i) q^{95} +(-9.74300 + 1.03635i) 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 $

$2$	0.937387	−	1.05892i	0.662833	−	0.748767i
$2$	0.937387	−	1.05892i	0.662833	−	0.748767i
$3$	0.959839	+	1.44177i	0.554163	+	0.832408i
$3$	0.959839	+	1.44177i	0.554163	+	0.832408i
$4$	−0.242609	−	1.98523i	−0.121305	−	0.992615i
$5$	0.520093	−	2.17474i	0.232593	−	0.972574i
$5$	0.520093	−	2.17474i	0.232593	−	0.972574i
$6$	2.42646	+	0.335110i	0.990598	+	0.136808i
$7$	−0.550457	−	0.953419i	−0.208053	−	0.360358i	0.743048	−	0.669238i	$-0.233379\pi$
$7$	−0.550457	−	0.953419i	−0.208053	−	0.360358i	−0.951101	+	0.308880i	$0.900046\pi$
$8$	−2.32961	−	1.60403i	−0.823643	−	0.567109i
$9$	−1.15742	+	2.76774i	−0.385806	+	0.922580i
$10$	−1.81534	−	2.58931i	−0.574062	−	0.818812i
$11$	2.84126	+	4.92120i	0.856671	+	1.48380i	0.875086	+	0.483967i	$0.160805\pi$
$11$	2.84126	+	4.92120i	0.856671	+	1.48380i	−0.0184153	+	0.999830i	$0.505862\pi$
$12$	2.62939	−	2.25529i	0.759038	−	0.651046i
$13$	−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	$0.774506\pi$
$14$	−1.52558	−	0.310835i	−0.407729	−	0.0830742i
$15$	3.63469	−	1.33755i	0.938473	−	0.345353i
$16$	−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	$0.449931\pi$
$18$	1.84586	+	3.82005i	0.435073	+	0.900395i
$19$			2.78362i			0.638607i	0.947652	+	0.319304i	$0.103449\pi$
$19$			2.78362i			0.638607i	−0.947652	+	0.319304i	$0.896551\pi$
$20$	−4.44354	−	0.504891i	−0.993607	−	0.112897i
$21$	0.846263	−	1.70876i	0.184670	−	0.372882i
$22$	7.87450	+	1.60442i	1.67885	+	0.342063i
$23$	1.82546	+	1.05393i	0.380635	+	0.219760i	0.678095	−	0.734975i	$-0.262806\pi$
$23$	1.82546	+	1.05393i	0.380635	+	0.219760i	−0.297459	+	0.954735i	$0.596139\pi$
$24$	0.0765889	−	4.89838i	0.0156336	−	0.999878i
$25$	−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	$0.534801\pi$
$30$	1.99076	−	5.10263i	0.363462	−	0.931609i
$31$	−2.78385	−	1.60725i	−0.499994	−	0.288671i	0.228717	−	0.973493i	$-0.426547\pi$
$31$	−2.78385	−	1.60725i	−0.499994	−	0.288671i	−0.728711	+	0.684821i	$0.759880\pi$
$32$	−2.61918	+	5.01397i	−0.463010	+	0.886353i
$33$	−4.36810	+	8.82001i	−0.760389	+	1.53537i
$34$	1.21087	−	1.36785i	0.207662	−	0.234584i
$35$	−2.35973	+	0.701235i	−0.398867	+	0.118530i
$36$	5.77540	+	1.62626i	0.962567	+	0.271043i
$37$		−	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
$39$	−0.264482	−	4.14253i	−0.0423510	−	0.663336i
$40$	−4.69996	+	4.23206i	−0.743129	+	0.669148i
$41$	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	$0.472392\pi$
$42$	−1.01616	−	2.49789i	−0.156797	−	0.385434i
$43$	−2.25473	−	3.90530i	−0.343843	−	0.595553i	0.641300	−	0.767290i	$-0.278395\pi$
$43$	−2.25473	−	3.90530i	−0.343843	−	0.595553i	−0.985143	+	0.171737i	$0.945062\pi$
$44$	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	−0.956237	−	0.292592i	$-0.905482\pi$
$47$	−8.09628	+	4.67439i	−1.18096	+	0.681830i	−0.224726	+	0.974422i	$0.572149\pi$
$48$	−5.11518	−	4.67278i	−0.738313	−	0.674458i
$49$	2.89400	−	5.01255i	0.413428	−	0.716078i
$50$	−6.57523	+	2.60122i	−0.929878	+	0.367868i
$51$	1.23987	+	1.86240i	0.173616	+	0.260789i
$52$	−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	$0.206747\pi$
$54$	−3.73592	+	6.32794i	−0.508395	+	0.861124i
$55$	12.1801	−	3.61952i	1.64236	−	0.488056i
$56$	−0.246959	+	3.10404i	−0.0330013	+	0.414795i
$57$	−4.01335	+	2.67183i	−0.531582	+	0.353893i
$58$	−1.79874	+	8.82821i	−0.236186	+	1.15920i
$59$	3.66237	−	6.34341i	0.476800	−	0.825842i	−0.522846	−	0.852427i	$-0.675130\pi$
$59$	3.66237	−	6.34341i	0.476800	−	0.825842i	0.999647	+	0.0265849i	$0.00846323\pi$
$60$	−3.53715	−	6.89120i	−0.456644	−	0.889649i
$61$	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
$66$	5.24505	+	12.8932i	0.645621	+	1.58705i
$67$	−1.85016	+	3.20457i	−0.226033	+	0.391500i	−0.956629	−	0.291310i	$-0.905909\pi$
$67$	−1.85016	+	3.20457i	−0.226033	+	0.391500i	0.730596	+	0.682810i	$0.239242\pi$
$68$	−0.313389	−	2.56441i	−0.0380041	−	0.310981i
$69$	0.232621	+	3.64351i	0.0280043	+	0.438627i
$70$	−1.46943	+	3.15608i	−0.175631	+	0.377224i
$71$	−12.6950			−1.50662			−0.753311	−	0.657664i	$-0.771545\pi$
$71$	−12.6950			−1.50662			−0.753311	+	0.657664i	$0.771545\pi$
$72$	7.13586	−	4.59123i	0.840970	−	0.541082i
$73$		−	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
$75$	−1.01844	−	8.60016i	−0.117600	−	0.993061i
$76$	5.52614	−	0.675333i	0.633891	−	0.0774660i
$77$	3.12798	−	5.41781i	0.356466	−	0.617417i
$78$	−4.63452	−	3.60310i	−0.524756	−	0.407970i
$79$	0.975531	−	0.563223i	0.109756	−	0.0633676i	−0.444117	−	0.895969i	$-0.646483\pi$
$79$	0.975531	−	0.563223i	0.109756	−	0.0633676i	0.553873	+	0.832601i	$0.313149\pi$
$80$	0.0757197	+	8.94395i	0.00846572	+	0.999964i
$81$	−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	0.160537	−	0.987030i	$-0.448677\pi$
$83$	9.98138	−	5.76275i	1.09560	−	0.632544i	0.935062	+	0.354485i	$0.115344\pi$
$84$	−3.59760	−	1.26547i	−0.392530	−	0.138074i
$85$	0.671827	−	2.80921i	0.0728699	−	0.304702i
$86$	−6.24894	−	1.27321i	−0.673841	−	0.137294i
$87$	−9.88823	−	4.89714i	−1.06013	−	0.525029i
$88$	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	$-0.161512\pi$
$90$	9.26765	−	2.02748i	0.976896	−	0.213715i
$91$			2.63841i			0.276580i
$92$	1.64942	−	3.87966i	0.171964	−	0.404482i
$93$	−0.354749	−	5.55638i	−0.0367858	−	0.576170i
$94$	−2.63956	+	12.9550i	−0.272250	+	1.33621i
$95$	6.05366	+	1.44774i	0.621093	+	0.148535i
$96$	−9.74300	+	1.03635i	−0.994390	+	0.105772i
$97$	−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
$100$	−3.40906	+	9.40097i	−0.340906	+	0.940097i
$101$	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	$0.0199575\pi$
$102$	3.13437	+	0.432877i	0.310348	+	0.0428612i
$103$	0.679292	−	1.17657i	0.0669327	−	0.115931i	−0.830617	−	0.556844i	$-0.812012\pi$
$103$	0.679292	−	1.17657i	0.0669327	−	0.115931i	0.897550	+	0.440913i	$0.145345\pi$
$104$	2.91300	+	6.12066i	0.285643	+	0.600181i
$105$	−3.27598	−	2.72912i	−0.319703	−	0.266335i
$106$	10.8694	−	12.2786i	1.05573	−	1.19260i
$107$			2.97211i			0.287324i	0.989627	+	0.143662i	$0.0458879\pi$
$107$			2.97211i			0.287324i	−0.989627	+	0.143662i	$0.954112\pi$
$108$	3.19876	+	9.88777i	0.307801	+	0.951451i
$109$	5.12076			0.490480			0.245240	−	0.969462i	$-0.421133\pi$
$109$	5.12076			0.490480			0.245240	+	0.969462i	$0.421133\pi$
$110$	7.58466	−	16.2906i	0.723169	−	1.55324i
$111$	9.39584	−	6.25515i	0.891814	−	0.593712i
$112$	3.05543	+	3.17120i	0.288711	+	0.299650i
$113$	−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	$0.295476\pi$
$114$	−0.932820	+	6.75435i	−0.0873666	+	0.632603i
$115$	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
$120$	−10.6129	−	2.71417i	−0.968819	−	0.247769i
$121$	−10.6455	+	18.4385i	−0.967770	+	1.67623i
$122$	6.90071	+	1.40601i	0.624761	+	0.127294i
$123$	0.810007	+	12.6870i	0.0730359	+	1.14395i
$124$	−2.51538	+	5.91651i	−0.225888	+	0.531318i
$125$	−7.23866	+	8.52067i	−0.647445	+	0.762112i
$126$	2.62605	−	3.86265i	0.233947	−	0.344112i
$127$	−5.14729			−0.456748			−0.228374	−	0.973573i	$-0.573341\pi$
$127$	−5.14729			−0.456748			−0.228374	+	0.973573i	$0.573341\pi$
$128$	10.5893	+	3.98324i	0.935973	+	0.352072i
$129$	3.46638	−	6.99926i	0.305198	−	0.616251i
$130$	0.664991	+	7.54937i	0.0583236	+	0.662123i
$131$	7.10028	−	12.2980i	0.620354	−	1.07449i	−0.369065	−	0.929403i	$-0.620322\pi$
$131$	7.10028	−	12.2980i	0.620354	−	1.07449i	0.989420	−	0.145082i	$-0.0463445\pi$
$132$	18.5695	+	6.53188i	1.61627	+	0.568527i
$133$	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	$0.929180\pi$
$138$	4.07623	+	3.16905i	0.346992	+	0.269768i
$139$	10.3321	+	5.96523i	0.876356	+	0.505964i	0.869455	−	0.494012i	$-0.164470\pi$
$139$	10.3321	+	5.96523i	0.876356	+	0.505964i	0.00690070	+	0.999976i	$0.497803\pi$
$140$	1.96461	+	4.51448i	0.166039	+	0.381543i
$141$	−14.5105	−	7.18633i	−1.22201	−	0.605198i
$142$	−11.9002	+	13.4430i	−0.998640	+	1.12811i
$143$		−	13.6185i		−	1.13884i
$144$	1.82734	−	11.8601i	0.152278	−	0.988338i
$145$	4.05789	+	13.6552i	0.336990	+	1.13401i
$146$	−10.4504	−	9.25100i	−0.864878	−	0.765618i
$147$	10.0047	−	0.638756i	0.825176	−	0.0526837i
$148$	−12.9375	+	1.58105i	−1.06345	+	0.129962i
$149$	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	$0.590976\pi$
$150$	−10.0615	−	6.98324i	−0.821521	−	0.570179i
$151$	−1.85084	+	1.06858i	−0.150619	+	0.0869599i	−0.573415	−	0.819265i	$-0.694382\pi$
$151$	−1.85084	+	1.06858i	−0.150619	+	0.0869599i	0.422796	+	0.906225i	$0.361049\pi$
$152$	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
$156$	−8.15972	+	1.53007i	−0.653300	+	0.122504i
$157$	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	$0.535236\pi$
$158$	0.318044	−	1.56097i	0.0253022	−	0.124184i
$159$	11.1297	+	16.7180i	0.882646	+	1.32582i
$160$	9.54188	+	8.30377i	0.754352	+	0.656470i
$161$		−	2.32057i		−	0.182887i
$162$	−12.7093	+	0.687459i	−0.998540	+	0.0540119i
$163$	−18.2146			−1.42668			−0.713339	−	0.700819i	$-0.752818\pi$
$163$	−18.2146			−1.42668			−0.713339	+	0.700819i	$0.752818\pi$
$164$	5.74343	−	13.5093i	0.448487	−	1.05490i
$165$	16.9094	+	14.0867i	1.31640	+	1.09665i
$166$	3.25415	−	15.9714i	0.252571	−	1.23962i
$167$	−6.44716	−	3.72227i	−0.498896	−	0.288038i	0.229362	−	0.973341i	$-0.426336\pi$
$167$	−6.44716	−	3.72227i	−0.498896	−	0.288038i	−0.728258	+	0.685304i	$0.759670\pi$
$168$	−4.71237	+	2.62332i	−0.363567	+	0.202394i
$169$	−3.62824	−	6.28430i	−0.279096	−	0.483408i
$170$	−2.34496	−	3.34473i	−0.179850	−	0.256529i
$171$	−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	$0.726440\pi$
$174$	−14.4548	+	5.88030i	−1.09581	+	0.445784i
$175$	0.297727	+	5.49651i	0.0225061	+	0.415497i
$176$	−15.7710	−	16.3686i	−1.18878	−	1.23383i
$177$	12.6610	−	0.808350i	0.951663	−	0.0607593i
$178$	−9.70831	−	8.59411i	−0.727668	−	0.644156i
$179$	1.10988			0.0829560			0.0414780	−	0.999139i	$-0.486793\pi$
$179$	1.10988			0.0829560			0.0414780	+	0.999139i	$0.486793\pi$
$180$	6.54044	−	11.7142i	0.487496	−	0.873125i
$181$	−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
$183$	−3.82793	+	7.72930i	−0.282969	+	0.571366i
$184$	−2.56209	−	5.38335i	−0.188880	−	0.396866i
$185$	−14.1725	−	3.38938i	−1.04198	−	0.249192i
$186$	−6.21628	−	4.83283i	−0.455800	−	0.354360i
$187$	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
$190$	7.20767	−	5.05323i	0.522899	−	0.366600i
$191$	11.3827	+	19.7154i	0.823625	+	1.42656i	0.902966	+	0.429712i	$0.141385\pi$
$191$	11.3827	+	19.7154i	0.823625	+	1.42656i	−0.0793411	+	0.996848i	$0.525282\pi$
$192$	−8.03556	+	11.2885i	−0.579916	+	0.814676i
$193$	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	$0.529243\pi$
$194$	−3.62723	+	17.8025i	−0.260420	+	1.27814i
$195$	−9.14650	−	1.57932i	−0.654994	−	0.113098i
$196$	−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	$0.643117\pi$
$198$	−13.5547	+	19.9376i	−0.963290	+	1.41690i
$199$		−	7.07921i		−	0.501832i	−0.968009	−	0.250916i	$-0.919268\pi$
$199$		−	7.07921i		−	0.501832i	0.968009	−	0.250916i	$-0.0807318\pi$
$200$	6.75923	+	12.4223i	0.477950	+	0.878387i
$201$	−6.39612	+	0.408363i	−0.451147	+	0.0288037i
$202$	4.72727	−	23.2015i	0.332609	−	1.63245i
$203$	6.07399	+	3.50682i	0.426310	+	0.246130i
$204$	3.39650	−	2.91326i	0.237802	−	0.203969i
$205$	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
$210$	−5.96077	+	0.910749i	−0.411333	+	0.0628477i
$211$	−5.61368	−	3.24106i	−0.386462	−	0.223124i	0.294164	−	0.955755i	$-0.404959\pi$
$211$	−5.61368	−	3.24106i	−0.386462	−	0.223124i	−0.680626	+	0.732631i	$0.738292\pi$
$212$	−2.81316	−	23.0196i	−0.193209	−	1.58099i
$213$	−12.1852	−	18.3033i	−0.834915	−	1.25412i
$214$	3.14721	+	2.78601i	0.215139	+	0.190448i
$215$	−9.66569	+	2.87233i	−0.659195	+	0.195891i
$216$	13.4688	+	5.88145i	0.916436	+	0.400182i
$217$			3.53890i			0.240236i
$218$	4.80014	−	5.42246i	0.325106	−	0.367255i
$219$	14.2287	−	9.47257i	0.961488	−	0.640097i
$220$	−10.1406	−	23.3021i	−0.683677	−	1.57103i
$221$	−2.68100	−	1.54787i	−0.180343	−	0.104121i
$222$	2.18387	−	15.8129i	0.146572	−	1.06129i
$223$	7.84799	+	13.5931i	0.525540	+	0.910263i	0.999557	+	0.0297470i	$0.00947015\pi$
$223$	7.84799	+	13.5931i	0.525540	+	0.910263i	−0.474017	+	0.880516i	$0.657197\pi$
$224$	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	−0.505623	−	0.862755i	$-0.668737\pi$
$227$	−0.169745	+	0.0980022i	−0.0112664	+	0.00650463i	0.494356	+	0.869259i	$0.335404\pi$
$228$	6.27788	+	7.31922i	0.415763	+	0.484727i
$229$	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	$0.149302\pi$
$230$	−0.584884	−	6.63994i	−0.0385661	−	0.437825i
$231$	10.8136	−	0.690399i	0.711483	−	0.0454249i
$232$	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	$0.730530\pi$
$234$	0.746450	−	10.1403i	0.0487970	−	0.662893i
$235$	5.95477	+	20.0384i	0.388447	+	1.30716i
$236$	−13.4817	−	5.73168i	−0.877581	−	0.373101i
$237$	1.74839	+	0.865891i	0.113570	+	0.0562456i
$238$	−1.97066	−	0.401520i	−0.127739	−	0.0260267i
$239$	−10.1646	+	17.6056i	−0.657494	+	1.13881i	0.323769	+	0.946136i	$0.395050\pi$
$239$	−10.1646	+	17.6056i	−0.657494	+	1.13881i	−0.981262	+	0.192676i	$0.938283\pi$
$240$	−12.8225	+	8.69393i	−0.827687	+	0.561191i
$241$	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
$246$	14.1938	+	11.0349i	0.904962	+	0.703560i
$247$	3.33556	−	5.77737i	0.212237	−	0.367605i
$248$	3.90720	+	8.20965i	0.248108	+	0.521313i
$249$	17.8891	+	8.85957i	1.13368	+	0.561452i
$250$	2.23725	+	15.6523i	0.141496	+	0.989939i
$251$	9.92020			0.626157			0.313079	−	0.949727i	$-0.398640\pi$
$251$	9.92020			0.626157			0.313079	+	0.949727i	$0.398640\pi$
$252$	−1.62860	−	6.40156i	−0.102592	−	0.403261i
$253$			11.9780i			0.753048i
$254$	−4.82501	+	5.45055i	−0.302748	+	0.341998i
$255$	4.69509	−	1.72777i	0.294018	−	0.108197i
$256$	14.1442	−	7.47938i	0.884014	−	0.467461i
$257$	−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	$0.984666\pi$
$258$	−4.16230	−	10.2316i	−0.259133	−	0.636994i
$259$	−6.21330	+	3.58725i	−0.386076	+	0.222901i
$260$	8.61750	+	6.37251i	0.534435	+	0.395206i
$261$	−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	−0.734203	−	0.678930i	$-0.762444\pi$
$263$	−8.32487	+	4.80637i	−0.513334	+	0.296373i	0.220869	+	0.975303i	$0.429111\pi$
$264$	24.3235	−	13.5406i	1.49701	−	0.833369i
$265$	6.03070	−	25.2171i	0.370463	−	1.54907i
$266$	0.865248	−	4.24665i	0.0530518	−	0.260379i
$267$	13.2184	−	8.79995i	0.808952	−	0.538548i
$268$	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	$0.986946\pi$
$270$	11.8186	+	11.4158i	0.719258	+	0.694743i
$271$		−	21.7288i		−	1.31993i	−0.751297	−	0.659964i	$-0.770571\pi$
$271$		−	21.7288i		−	1.31993i	0.751297	−	0.659964i	$-0.229429\pi$
$272$	−5.01492	+	1.24430i	−0.304074	+	0.0754468i
$273$	−3.80398	+	2.53245i	−0.230228	+	0.153271i
$274$	−9.62091	−	1.96025i	−0.581221	−	0.118423i
$275$	−1.53676	−	28.3710i	−0.0926701	−	1.71083i
$276$	7.17677	−	1.34576i	0.431991	−	0.0810050i
$277$	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
$280$	6.62205	+	2.15146i	0.395743	+	0.128575i
$281$	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	$0.220302\pi$
$282$	−21.2117	+	8.62907i	−1.26314	+	0.513853i
$283$	6.21367	−	10.7624i	0.369365	−	0.639758i	−0.620102	−	0.784521i	$-0.712909\pi$
$283$	6.21367	−	10.7624i	0.369365	−	0.639758i	0.989466	+	0.144763i	$0.0462420\pi$
$284$	3.07993	+	25.2026i	0.182760	+	1.49550i
$285$	3.72323	+	10.1176i	0.220545	+	0.599315i
$286$	−14.4209	−	12.7658i	−0.852723	−	0.754858i
$287$		−	8.08044i		−	0.476973i
$288$	−10.8459	−	13.0525i	−0.639100	−	0.769124i
$289$	−15.3314			−0.901847
$290$	18.2636	+	8.50328i	1.07247	+	0.499330i
$291$	−19.9401	−	9.87530i	−1.16891	−	0.578900i
$292$	−19.5921	+	2.39429i	−1.14654	+	0.140115i
$293$	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	$0.0766829\pi$
$294$	8.70191	−	11.1929i	0.507506	−	0.652785i
$295$	−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
$300$	−16.8262	+	4.10833i	−0.971462	+	0.237194i
$301$	−2.48226	+	4.29940i	−0.143075	+	0.247813i
$302$	−0.603413	+	2.96156i	−0.0347225	+	0.170418i
$303$	25.9873	+	12.8702i	1.49293	+	0.739374i
$304$	−2.68138	−	10.8068i	−0.153788	−	0.619813i
$305$	10.6738	−	3.17192i	0.611182	−	0.181623i
$306$	2.38438	+	4.93454i	0.136306	+	0.282089i
$307$	13.4685			0.768689			0.384345	−	0.923190i	$-0.374427\pi$
$307$	13.4685			0.768689			0.384345	+	0.923190i	$0.374427\pi$
$308$	−11.5145	−	4.89534i	−0.656099	−	0.278938i
$309$	2.34836	−	0.149932i	0.133593	−	0.00852932i
$310$	0.891953	+	10.1260i	0.0506595	+	0.575116i
$311$	−5.13110	+	8.88732i	−0.290958	+	0.503954i	−0.974037	−	0.226391i	$-0.927307\pi$
$311$	−5.13110	+	8.88732i	−0.290958	+	0.503954i	0.683079	+	0.730345i	$0.260641\pi$
$312$	−6.02860	+	10.0747i	−0.341302	+	0.570370i
$313$	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	$0.793337\pi$
$318$	28.1358	+	3.88574i	1.57778	+	0.217902i
$319$	−31.3517	−	18.1009i	−1.75536	−	1.01346i
$320$	17.7374	−	2.32021i	0.991553	−	0.129704i
$321$	−4.28510	+	2.85274i	−0.239171	+	0.159225i
$322$	−2.45730	−	2.17528i	−0.136940	−	0.121223i
$323$			3.59573i			0.200072i
$324$	−11.1856	+	14.1026i	−0.621423	+	0.783475i
$325$	6.54392	+	10.0382i	0.362992	+	0.556818i
$326$	−17.0741	+	19.2878i	−0.945649	+	1.06825i
$327$	4.91511	+	7.38297i	0.271806	+	0.408279i
$328$	−8.92141	−	18.7453i	−0.492602	−	1.03503i
$329$	8.91330	+	5.14610i	0.491406	+	0.283713i
$330$	30.7673	−	4.70095i	1.69369	−	0.258779i
$331$	−10.2107	+	5.89512i	−0.561228	+	0.324025i	−0.753638	−	0.657289i	$-0.771703\pi$
$331$	−10.2107	+	5.89512i	−0.561228	+	0.324025i	0.192410	+	0.981315i	$0.438370\pi$
$332$	−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
$336$	−1.63943	+	7.44908i	−0.0894383	+	0.406380i
$337$	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	$0.573783\pi$
$338$	−10.0556	−	2.04882i	−0.546954	−	0.111441i
$339$	−14.4685	+	0.923749i	−0.785823	+	0.0501712i
$340$	−5.73993	−	0.652191i	−0.311291	−	0.0353700i
$341$		−	18.2665i		−	0.989186i
$342$	−10.6336	+	5.13817i	−0.574999	+	0.277841i
$343$	−14.0785			−0.760166
$344$	−1.01157	+	12.7145i	−0.0545401	+	0.685519i
$345$	8.04468	+	1.38907i	0.433111	+	0.0747851i
$346$	12.0127	+	2.44758i	0.645809	+	0.131583i
$347$	20.1864	+	11.6546i	1.08366	+	0.625652i	0.931882	−	0.362763i	$-0.118166\pi$
$347$	20.1864	+	11.6546i	1.08366	+	0.625652i	0.151779	+	0.988414i	$0.451500\pi$
$348$	−7.32298	+	20.8185i	−0.392553	+	1.11599i
$349$	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	$0.784636\pi$
$350$	6.09943	+	4.83709i	0.326028	+	0.258553i
$351$	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	$0.846236\pi$
$354$	11.0123	−	14.1647i	0.585299	−	0.752847i
$355$	−6.60259	+	27.6084i	−0.350429	+	1.46530i
$356$	−18.2009	+	2.22428i	−0.964645	+	0.117887i
$357$	1.09316	−	2.20729i	0.0578560	−	0.116822i
$358$	1.04038	−	1.17527i	0.0549860	−	0.0621148i
$359$	−9.46115			−0.499341			−0.249670	−	0.968331i	$-0.580322\pi$
$359$	−9.46115			−0.499341			−0.249670	+	0.968331i	$0.580322\pi$
$360$	−6.27344	−	17.9065i	−0.330639	−	0.943757i
$361$	11.2514			0.592181
$362$	−11.8701	+	13.4090i	−0.623878	+	0.704762i
$363$	−36.8021	+	2.34964i	−1.93161	+	0.123324i
$364$	5.23785	−	0.640102i	0.274538	−	0.0335505i
$365$	−21.4623	−	5.13275i	−1.12339	−	0.268660i
$366$	4.59643	+	11.2988i	0.240259	+	0.590598i
$367$	−4.06621	−	7.04288i	−0.212254	−	0.367635i	0.740165	−	0.672425i	$-0.234747\pi$
$367$	−4.06621	−	7.04288i	−0.212254	−	0.367635i	−0.952420	+	0.304790i	$0.901414\pi$
$368$	−8.10218	−	2.33324i	−0.422356	−	0.121629i
$369$	−17.5143	+	13.3453i	−0.911758	+	0.694730i
$370$	−16.8742	+	11.8303i	−0.877248	+	0.615031i
$371$	−6.38278	−	11.0553i	−0.331377	−	0.573963i
$372$	−10.9446	+	2.05229i	−0.567453	+	0.106406i
$373$	−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	$0.763892\pi$
$374$	10.1718	+	2.07250i	0.525974	+	0.107166i
$375$	−19.2328	−	2.25803i	−0.993178	−	0.116604i
$376$	26.3590	+	2.09713i	1.35936	+	0.108151i
$377$	15.2679			0.786336
$378$	8.08964	+	0.0786396i	0.416086	+	0.00404478i
$379$		−	0.194316i		−	0.00998136i	−0.999988	−	0.00499068i	$-0.998411\pi$
$379$		−	0.194316i		−	0.00998136i	0.999988	−	0.00499068i	$-0.00158859\pi$
$380$	1.40543	−	12.3692i	0.0720969	−	0.634524i
$381$	−4.94057	−	7.42123i	−0.253113	−	0.380201i
$382$	31.5470	+	6.42766i	1.61409	+	0.328868i
$383$	−16.0220	−	9.25031i	−0.818686	−	0.472669i	0.0312769	−	0.999511i	$-0.490043\pi$
$383$	−16.0220	−	9.25031i	−0.818686	−	0.472669i	−0.849963	+	0.526842i	$0.823376\pi$
$384$	4.42113	+	19.0907i	0.225615	+	0.974217i
$385$	−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	$0.536888\pi$
$390$	−10.2462	+	8.20494i	−0.518836	+	0.415473i
$391$	2.35803	+	1.36141i	0.119251	+	0.0688495i
$392$	−14.7821	+	7.03525i	−0.746611	+	0.355334i
$393$	24.5461	−	1.56716i	1.23819	−	0.0790526i
$394$	−11.4364	+	12.9191i	−0.576160	+	0.650857i
$395$	−0.717499	−	2.41446i	−0.0361013	−	0.121485i
$396$	8.40624	+	33.0425i	0.422430	+	1.66045i
$397$			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
$399$	4.75655	+	2.35568i	0.238125	+	0.117931i
$400$	19.4902	+	4.48701i	0.974508	+	0.224351i
$401$	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	$0.397933\pi$
$402$	−5.56322	+	7.15575i	−0.277468	+	0.356896i
$403$	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
$408$	0.0989333	−	6.32746i	0.00489793	−	0.313256i
$409$	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	$0.150289\pi$
$410$	−2.03662	−	23.1208i	−0.100581	−	1.14186i
$411$	5.33686	−	10.7761i	0.263248	−	0.531547i
$412$	−2.50056	−	1.06311i	−0.123194	−	0.0523754i
$413$	−8.06390			−0.396799
$414$	−0.656530	+	8.91878i	−0.0322667	+	0.438334i
$415$	−7.34126	−	24.7041i	−0.360368	−	1.21268i
$416$	11.4442	−	7.26791i	0.561099	−	0.356338i
$417$	1.31663	+	20.6222i	0.0644757	+	1.00987i
$418$	−4.46610	+	21.9196i	−0.218444	+	1.07212i
$419$	4.89021	−	8.47010i	0.238903	−	0.413791i	−0.721497	−	0.692417i	$-0.756546\pi$
$419$	4.89021	−	8.47010i	0.238903	−	0.413791i	0.960400	+	0.278626i	$0.0898790\pi$
$420$	−4.62315	+	7.16569i	−0.225587	+	0.349650i
$421$	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
$426$	−30.8040	−	4.25423i	−1.49246	−	0.206118i
$427$	2.74116	−	4.74783i	0.132654	−	0.229764i
$428$	5.90031	−	0.721061i	0.285202	−	0.0348538i
$429$	19.6348	−	13.0716i	0.947976	−	0.631101i
$430$	−6.01894	+	12.9276i	−0.290259	+	0.623426i
$431$	−3.84204			−0.185064			−0.0925322	−	0.995710i	$-0.529496\pi$
$431$	−3.84204			−0.185064			−0.0925322	+	0.995710i	$0.529496\pi$
$432$	18.8534	−	8.74914i	0.907087	−	0.420943i
$433$		−	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
$435$	−15.7928	+	18.9574i	−0.757208	+	0.908937i
$436$	−1.24234	−	10.1659i	−0.0594975	−	0.486858i
$437$	−2.93375	+	5.08140i	−0.140340	+	0.243077i
$438$	3.30717	−	23.9465i	0.158023	−	1.14421i
$439$	33.5536	−	19.3722i	1.60143	−	0.924585i	0.610225	−	0.792228i	$-0.291079\pi$
$439$	33.5536	−	19.3722i	1.60143	−	0.924585i	0.991202	−	0.132357i	$-0.0422544\pi$
$440$	−34.1806	−	11.1051i	−1.62950	−	0.529413i
$441$	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	−0.897289	−	0.441443i	$-0.854467\pi$
$443$	−20.2821	+	11.7099i	−0.963633	+	0.556354i	−0.0663436	+	0.997797i	$0.521133\pi$
$444$	−14.6974	−	17.1354i	−0.697509	−	0.813208i
$445$	−19.9384	−	4.76829i	−0.945169	−	0.226039i
$446$	21.7506	+	4.43165i	1.02992	+	0.209845i
$447$	0.634632	+	9.94014i	0.0300171	+	0.470152i
$448$	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	$-0.121501\pi$
$450$	0.410786	−	21.2092i	0.0193646	−	0.999812i
$451$			41.7083i			1.96397i
$452$	15.4063	+	6.54993i	0.724651	+	0.308083i
$453$	−3.31716	−	1.64282i	−0.155854	−	0.0771864i
$454$	−0.0553404	+	0.271612i	−0.00259726	+	0.0127474i
$455$	5.73786	+	1.37222i	0.268995	+	0.0643305i
$456$	13.6353	+	0.213195i	0.638529	+	0.00998375i
$457$	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
$460$	−7.57941	−	5.60485i	−0.353392	−	0.261328i
$461$	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	$0.137326\pi$
$462$	9.40547	−	12.0979i	0.437582	−	0.562845i
$463$	10.3598	−	17.9437i	0.481460	−	0.833913i	−0.518314	−	0.855191i	$-0.673440\pi$
$463$	10.3598	−	17.9437i	0.481460	−	0.833913i	0.999774	+	0.0212774i	$0.00677331\pi$
$464$	18.3511	−	17.6811i	0.851926	−	0.820824i
$465$	−12.2682	−	2.11834i	−0.568924	−	0.0982359i
$466$	−18.9606	+	21.4188i	−0.878332	+	0.992205i
$467$		−	1.59588i		−	0.0738487i	−0.999318	−	0.0369243i	$-0.988244\pi$
$467$		−	1.59588i		−	0.0738487i	0.999318	−	0.0369243i	$-0.0117561\pi$
$468$	−10.0380	−	10.2958i	−0.464009	−	0.475925i
$469$	4.07373			0.188107
$470$	26.8010	+	12.4782i	1.23624	+	0.575575i
$471$	1.10974	+	17.3817i	0.0511342	+	0.800907i
$472$	−18.7069	+	8.90315i	−0.861055	+	0.409801i
$473$	12.8125	−	22.1919i	0.589120	−	1.02039i
$474$	2.55583	−	1.03973i	0.117393	−	0.0477563i
$475$	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	0.789612	−	0.613606i	$-0.210282\pi$
$479$	−2.98947	−	5.17791i	−0.136592	−	0.236585i	−0.926205	+	0.377021i	$0.876948\pi$
$480$	−2.81348	+	21.7275i	−0.128417	+	0.991720i
$481$	−7.80904	+	13.5257i	−0.356062	+	0.616717i
$482$	23.8976	+	4.86911i	1.08851	+	0.221782i
$483$	3.34574	−	2.22738i	0.152237	−	0.101349i
$484$	39.1874	+	16.6604i	1.78124	+	0.757289i
$485$	8.18292	+	27.5364i	0.371567	+	1.25036i
$486$	−13.1901	−	17.6641i	−0.598314	−	0.801261i
$487$	16.5971			0.752086			0.376043	−	0.926602i	$-0.377284\pi$
$487$	16.5971			0.752086			0.376043	+	0.926602i	$0.377284\pi$
$488$	1.11708	−	14.0406i	0.0505677	−	0.635589i
$489$	−17.4831	−	26.2613i	−0.790613	−	1.18758i
$490$	−18.2326	+	1.60603i	−0.823666	+	0.0725533i
$491$	−6.66941	+	11.5518i	−0.300986	+	0.521323i	−0.976360	−	0.216153i	$-0.930649\pi$
$491$	−6.66941	+	11.5518i	−0.300986	+	0.521323i	0.675373	+	0.737476i	$0.263982\pi$
$492$	24.9901	−	4.68604i	1.12664	−	0.211263i
$493$	−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
$498$	26.1506	−	10.6382i	1.17183	−	0.476710i
$499$	35.7135	+	20.6192i	1.59875	+	0.923041i	0.991728	+	0.128359i	$0.0409711\pi$
$499$	35.7135	+	20.6192i	1.59875	+	0.923041i	0.607026	+	0.794682i	$0.292362\pi$
$500$	18.6717	+	12.3032i	0.835022	+	0.550216i
$501$	−0.821570	−	12.8681i	−0.0367050	−	0.574905i
$502$	9.29907	−	10.5047i	0.415038	−	0.468846i
$503$			24.1634i			1.07739i	0.842500	+	0.538696i	$0.181083\pi$
$503$			24.1634i			1.07739i	−0.842500	+	0.538696i	$0.818917\pi$
$504$	−8.30535	−	4.27619i	−0.369950	−	0.190477i
$505$	−10.6646	−	35.8874i	−0.474567	−	1.59697i
$506$	12.6837	+	11.2280i	0.563858	+	0.499145i
$507$	5.57801	−	11.2630i	0.247728	−	0.500208i
$508$	1.24878	+	10.2186i	0.0554057	+	0.453375i
$509$	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	$0.582536\pi$
$510$	2.57156	−	6.59130i	0.113870	−	0.291868i
$511$	−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
$516$	−14.7361	−	5.18348i	−0.648722	−	0.228190i
$517$	−46.0072	−	26.5623i	−2.02339	−	1.16821i
$518$	−2.02567	+	9.94202i	−0.0890029	+	0.436827i
$519$	−6.66365	+	13.4551i	−0.292502	+	0.590615i
$520$	14.8259	−	3.15171i	0.650159	−	0.138212i
$521$			32.5010i			1.42389i	0.702234	+	0.711947i	$0.252186\pi$
$521$			32.5010i			1.42389i	−0.702234	+	0.711947i	$0.747814\pi$
$522$	−22.3523	−	15.1964i	−0.978334	−	0.665127i
$523$	−11.2435			−0.491645			−0.245822	−	0.969315i	$-0.579058\pi$
$523$	−11.2435			−0.491645			−0.245822	+	0.969315i	$0.579058\pi$
$524$	−26.1370	−	11.1121i	−1.14180	−	0.485433i
$525$	−7.63895	+	5.70502i	−0.333391	+	0.248987i
$526$	−2.71409	+	13.3208i	−0.118340	+	0.580813i
$527$	−3.59602	−	2.07616i	−0.156645	−	0.0904391i
$528$	8.46215	−	38.4494i	0.368268	−	1.67330i
$529$	−9.27846	−	16.0708i	−0.403411	−	0.698729i
$530$	−21.0497	−	30.0242i	−0.914339	−	1.30417i
$531$	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
$534$	3.07234	−	22.2461i	0.132953	−	0.962684i
$535$	6.46356	+	1.54577i	0.279444	+	0.0668295i
$536$	9.45037	−	4.49770i	0.408194	−	0.194271i
$537$	1.06530	+	1.60019i	0.0459712	+	0.0690533i
$538$	1.42406	+	1.26062i	0.0613954	+	0.0543492i
$539$	32.8903			1.41669
$540$	23.1670	−	1.81392i	0.996949	−	0.0780588i
$541$	−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
$543$	−12.1544	−	18.2571i	−0.521595	−	0.783487i
$544$	−3.38331	+	6.47677i	−0.145058	+	0.277689i
$545$	2.66327	−	11.1363i	0.114082	−	0.477028i
$546$	−0.884156	+	6.40199i	−0.0378384	+	0.273980i
$547$	2.12301	+	3.67716i	0.0907734	+	0.157224i	0.907837	−	0.419324i	$-0.137733\pi$
$547$	2.12301	+	3.67716i	0.0907734	+	0.157224i	−0.817063	+	0.576548i	$0.804399\pi$
$548$	−11.0943	+	8.35023i	−0.473923	+	0.356704i
$549$	−14.8181	+	1.89988i	−0.632420	+	0.0810848i
$550$	−31.4830	−	24.9673i	−1.34244	−	1.06461i
$551$	−8.86688	−	15.3579i	−0.377742	−	0.654268i
$552$	5.30237	−	8.86110i	0.225684	−	0.377153i
$553$	−1.07398	−	0.620060i	−0.0456701	−	0.0263676i
$554$	3.92860	−	19.2816i	0.166910	−	0.819196i
$555$	−8.71662	−	23.6868i	−0.370000	−	1.00545i
$556$	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	$0.353073\pi$
$558$	1.00121	−	13.6012i	0.0423847	−	0.575785i
$559$			10.8072i			0.457095i
$560$	8.48565	−	4.99545i	0.358584	−	0.211096i
$561$	−5.64248	+	11.3932i	−0.238225	+	0.481021i
$562$	3.29113	−	16.1529i	0.138828	−	0.681369i
$563$	18.9272	+	10.9277i	0.797688	+	0.460546i	0.842662	−	0.538443i	$-0.180987\pi$
$563$	18.9272	+	10.9277i	0.797688	+	0.460546i	−0.0449739	+	0.998988i	$0.514320\pi$
$564$	−10.7461	+	30.5502i	−0.452494	+	1.28640i
$565$	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	$0.233673\pi$
$570$	14.2038	+	5.54153i	0.594932	+	0.232109i
$571$	15.5333	+	8.96816i	0.650049	+	0.375306i	0.788475	−	0.615067i	$-0.210871\pi$
$571$	15.5333	+	8.96816i	0.650049	+	0.375306i	−0.138426	+	0.990373i	$0.544204\pi$
$572$	−27.0359	+	3.30397i	−1.13043	+	0.138146i
$573$	−17.4996	+	35.3350i	−0.731057	+	1.47614i
$574$	−8.55651	−	7.57450i	−0.357142	−	0.316154i
$575$	−5.75562	−	8.82893i	−0.240026	−	0.368192i
$576$	−23.9883	−	0.750323i	−0.999511	−	0.0312635i
$577$		−	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
$579$	1.28307	+	20.0966i	0.0533227	+	0.835185i
$580$	26.1243	−	11.3687i	1.08475	−	0.472061i
$581$	−10.9886	−	6.34429i	−0.455885	−	0.263206i
$582$	−29.1487	+	11.8579i	−1.20825	+	0.491525i
$583$	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	−0.642646	−	0.766163i	$-0.722163\pi$
$587$	−7.27939	+	4.20276i	−0.300453	+	0.173466i	0.342194	+	0.939629i	$0.388830\pi$
$588$	−3.69532	−	19.7067i	−0.152392	−	0.812691i
$589$	4.47399	−	7.74918i	0.184348	−	0.319299i
$590$	−23.0735	+	2.03245i	−0.949922	+	0.0836746i
$591$	−11.7104	−	17.5901i	−0.481700	−	0.723561i
$592$	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	$0.243040\pi$
$594$	−41.7558	−	0.405909i	−1.71326	−	0.0166546i
$595$	−3.04817	+	0.905817i	−0.124963	+	0.0371349i
$596$	4.49992	−	10.5844i	0.184324	−	0.433554i
$597$	10.2066	−	6.79490i	0.417729	−	0.278097i
$598$	−7.00025	−	1.42629i	−0.286262	−	0.0583254i
$599$	−7.34116	+	12.7153i	−0.299952	+	0.519532i	−0.976125	−	0.217211i	$-0.930304\pi$
$599$	−7.34116	+	12.7153i	−0.299952	+	0.519532i	0.676173	+	0.736743i	$0.263637\pi$
$600$	−11.4223	+	21.6687i	−0.466314	+	0.884619i
$601$	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
$606$	37.9887	−	15.4540i	1.54318	−	0.627778i
$607$	−3.91627	+	6.78317i	−0.158956	+	0.275320i	−0.934493	−	0.355983i	$-0.884146\pi$
$607$	−3.91627	+	6.78317i	−0.158956	+	0.275320i	0.775536	+	0.631303i	$0.217480\pi$
$608$	−13.9570	−	7.29081i	−0.566032	−	0.295681i
$609$	0.774017	+	12.1233i	0.0313647	+	0.491261i
$610$	6.64672	−	14.2760i	0.269118	−	0.578019i
$611$	22.4049			0.906406
$612$	7.46035	+	2.10071i	0.301567	+	0.0849163i
$613$			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
$615$	28.0123	+	4.83687i	1.12956	+	0.195041i
$616$	−15.9773	+	7.60405i	−0.643744	+	0.306376i
$617$	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	$-0.140655\pi$
$618$	2.04255	−	2.62726i	0.0821636	−	0.105684i
$619$	−42.7230	+	24.6661i	−1.71718	+	0.991416i	−0.793218	+	0.608938i	$0.791596\pi$
$619$	−42.7230	+	24.6661i	−1.71718	+	0.991416i	−0.923965	+	0.382478i	$0.875071\pi$
$620$	11.5587	+	8.54745i	0.464207	+	0.343274i
$621$	−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
$624$	5.01718	+	15.8277i	0.200848	+	0.633616i
$625$	14.7655	+	20.1738i	0.590619	+	0.806950i
$626$	0.453388	−	2.22523i	0.0181210	−	0.0889382i
$627$	−24.5516	−	12.1592i	−0.980496	−	0.485590i
$628$	7.86873	−	18.5083i	0.313997	−	0.738561i
$629$		−	8.41813i		−	0.335653i
$630$	−7.03448	−	7.71991i	−0.280260	−	0.307569i
$631$		−	27.6752i		−	1.10173i	−0.834594	−	0.550866i	$-0.814297\pi$
$631$		−	27.6752i		−	1.10173i	0.834594	−	0.550866i	$-0.185703\pi$
$632$	−3.17604	−	0.252687i	−0.126336	−	0.0100513i
$633$	−0.715359	−	11.2045i	−0.0284329	−	0.445341i
$634$	6.18392	+	1.25996i	0.245595	+	0.0500396i
$635$	−2.67707	+	11.1940i	−0.106236	+	0.444222i
$636$	30.4889	−	26.1511i	1.20896	−	1.03696i
$637$	−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
$640$	14.1699	−	20.9574i	0.560116	−	0.828414i
$641$	−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	$0.429459\pi$
$642$	−0.995982	+	7.21169i	−0.0393083	+	0.284623i
$643$	23.7098	−	41.0665i	0.935022	−	1.61951i	0.160427	−	0.987048i	$-0.448713\pi$
$643$	23.7098	−	41.0665i	0.935022	−	1.61951i	0.774595	−	0.632458i	$-0.217954\pi$
$644$	−4.60688	+	0.562993i	−0.181536	+	0.0221850i
$645$	−13.4188	−	11.1788i	−0.528363	−	0.440163i
$646$	3.80758	+	3.37060i	0.149807	+	0.132614i
$647$			19.7634i			0.776977i	0.921453	+	0.388489i	$0.127003\pi$
$647$			19.7634i			0.776977i	−0.921453	+	0.388489i	$0.872997\pi$
$648$	4.44817	+	25.0642i	0.174741	+	0.984615i
$649$	41.6229			1.63384
$650$	16.7638	+	2.48019i	0.657530	+	0.0972809i
$651$	−5.10228	+	3.39677i	−0.199974	+	0.133130i
$652$	4.41903	+	36.1602i	0.173063	+	1.41614i
$653$	−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	$0.926989\pi$
$654$	12.4253	+	1.71602i	0.485868	+	0.0671016i
$655$	−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	$-0.928087\pi$
$659$	−17.4893	−	30.2924i	−0.681288	−	1.18003i	0.293300	−	0.956021i	$-0.405247\pi$
$660$	23.8630	−	36.9867i	0.928866	−	1.43970i
$661$	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	$-0.0758749\pi$
$662$	−3.32889	+	16.3382i	−0.129381	+	0.635004i
$663$	−0.341643	−	5.35110i	−0.0132683	−	0.207819i
$664$	−32.4964	−	2.58542i	−1.26110	−	0.100334i
$665$	−1.95197	−	6.56860i	−0.0756943	−	0.254719i
$666$	24.8948	−	12.0292i	0.964653	−	0.466123i
$667$	−13.4287			−0.519960
$668$	−5.82542	+	13.7022i	−0.225392	+	0.530152i
$669$	−12.0654	+	24.3622i	−0.466475	+	0.941898i
$670$	11.6563	−	1.02675i	0.450322	−	0.0396670i
$671$	−14.1489	+	24.5066i	−0.546211	+	0.946065i
$672$	6.35117	+	8.71869i	0.245002	+	0.336331i
$673$	−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	$0.832805\pi$
$678$	−12.5844	+	16.1869i	−0.483303	+	0.621653i
$679$	12.2485	+	7.07165i	0.470053	+	0.271385i
$680$	−6.07115	+	5.46675i	−0.232818	+	0.209640i
$681$	−0.304224	−	0.150667i	−0.0116579	−	0.00577357i
$682$	−19.3427	−	17.1228i	−0.740670	−	0.655665i
$683$			24.0380i			0.919788i	0.887974	+	0.459894i	$0.152113\pi$
$683$			24.0380i			0.919788i	−0.887974	+	0.459894i	$0.847887\pi$
$684$	−4.52690	+	16.0766i	−0.173090	+	0.614702i
$685$	−14.8814	+	4.42226i	−0.568588	+	0.168966i
$686$	−13.1970	+	14.9079i	−0.503863	+	0.569187i
$687$	2.85256	−	0.182123i	0.108832	−	0.00694841i
$688$	12.5153	+	12.9896i	0.477143	+	0.495222i
$689$	−24.0661	−	13.8946i	−0.916846	−	0.529342i
$690$	9.01189	−	7.21654i	0.343077	−	0.274729i
$691$	36.1685	−	20.8819i	1.37591	−	0.794384i	0.384249	−	0.923229i	$-0.374460\pi$
$691$	36.1685	−	20.8819i	1.37591	−	0.794384i	0.991665	+	0.128845i	$0.0411271\pi$
$692$	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
$696$	15.1806	+	27.2694i	0.575420	+	1.03365i
$697$	8.21087	+	4.74055i	0.311009	+	0.179561i
$698$	7.89010	+	1.60760i	0.298645	+	0.0608484i
$699$	−19.4147	−	29.1628i	−0.734332	−	1.10304i
$700$	10.8396	−	1.92456i	0.409699	−	0.0727416i
$701$			2.12514i			0.0802654i	0.999194	+	0.0401327i	$0.0127781\pi$
$701$			2.12514i			0.0802654i	−0.999194	+	0.0401327i	$0.987222\pi$
$702$	15.3365	−	8.65686i	0.578839	−	0.326732i
$703$	18.1405			0.684182
$704$	−28.6692	+	35.2803i	−1.08051	+	1.32967i
$705$	−23.1752	+	27.8191i	−0.872830	+	1.04773i
$706$	−2.11012	−	0.429934i	−0.0794155	−	0.0161808i
$707$	−15.9631	−	9.21629i	−0.600354	−	0.346614i
$708$	−4.67645	−	24.9390i	−0.175752	−	0.937264i
$709$	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	$0.808344\pi$
$710$	23.0458	+	32.8714i	0.864895	+	1.23364i
$711$	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
$714$	−1.31262	−	3.22664i	−0.0491236	−	0.120754i
$715$	−29.6167	−	7.08288i	−1.10760	−	0.264885i
$716$	−0.269266	−	2.20336i	−0.0100630	−	0.0823434i
$717$	−35.1397	+	2.24351i	−1.31232	+	0.0837853i
$718$	−8.86877	+	10.0186i	−0.330979	+	0.373890i
$719$	24.0884			0.898346			0.449173	−	0.893445i	$-0.351719\pi$
$719$	24.0884			0.898346			0.449173	+	0.893445i	$0.351719\pi$
$720$	−24.8422	−	10.1423i	−0.925813	−	0.377982i
$721$	−1.49568			−0.0557022
$722$	10.5470	−	11.9143i	0.392517	−	0.443406i
$723$	−13.2564	+	26.7671i	−0.493010	+	0.995478i
$724$	3.07215	+	25.1389i	0.114176	+	0.934279i
$725$	31.8071	−	1.72288i	1.18129	−	0.0639863i
$726$	−32.0097	+	41.1728i	−1.18799	+	1.52807i
$727$	−23.4466	−	40.6108i	−0.869587	−	1.50617i	−0.862419	−	0.506195i	$-0.831052\pi$
$727$	−23.4466	−	40.6108i	−0.869587	−	1.50617i	−0.00716831	−	0.999974i	$-0.502282\pi$
$728$	4.23208	−	6.14647i	0.156851	−	0.227803i
$729$	25.0483	−	10.0788i	0.927715	−	0.373290i
$730$	−25.5537	+	17.9155i	−0.945784	+	0.663081i
$731$	−2.91253	−	5.04465i	−0.107724	−	0.186583i
$732$	16.2731	+	5.72412i	0.601472	+	0.211570i
$733$	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	$0.560330\pi$
$734$	−11.2694	−	2.29613i	−0.415962	−	0.0847517i
$735$	3.81426	−	22.0899i	0.140691	−	0.814798i
$736$	−10.0656	+	6.39239i	−0.371023	+	0.235626i
$737$	−21.0271			−0.774543
$738$	−2.28609	+	31.0559i	−0.0841523	+	1.14319i
$739$		−	8.50437i		−	0.312838i	−0.987691	−	0.156419i	$-0.950005\pi$
$739$		−	8.50437i		−	0.312838i	0.987691	−	0.156419i	$-0.0499951\pi$
$740$	−3.29031	+	28.9580i	−0.120954	+	1.06452i
$741$	11.5313	−	0.736218i	0.423611	−	0.0270456i
$742$	−17.6898	−	3.60427i	−0.649412	−	0.132317i
$743$	−43.6052	−	25.1755i	−1.59972	−	0.923598i	−0.991540	−	0.129798i	$-0.958567\pi$
$743$	−43.6052	−	25.1755i	−1.59972	−	0.923598i	−0.608179	−	0.793800i	$-0.708100\pi$
$744$	−8.08616	+	13.5132i	−0.296453	+	0.495419i
$745$	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
$750$	−20.4197	+	18.2493i	−0.745621	+	0.666370i
$751$	−44.8169	−	25.8750i	−1.63539	−	0.944193i	−0.982391	−	0.186834i	$-0.940177\pi$
$751$	−44.8169	−	25.8750i	−1.63539	−	0.944193i	−0.652999	−	0.757359i	$-0.726489\pi$
$752$	26.9293	−	25.9462i	0.982011	−	0.946160i
$753$	9.52179	+	14.3027i	0.346993	+	0.521218i
$754$	14.3119	−	16.1674i	0.521210	−	0.588783i
$755$	1.36128	+	4.58085i	0.0495421	+	0.166714i
$756$	7.66640	−	8.49254i	0.278824	−	0.308871i
$757$			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
$759$	−17.2695	+	11.4969i	−0.626843	+	0.417312i
$760$	−11.7805	−	13.0829i	−0.427323	−	0.474568i
$761$	−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	$0.883757\pi$
$762$	−12.4897	−	1.72491i	−0.452454	−	0.0624869i
$763$	−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
$768$	24.3597	+	13.2137i	0.879006	+	0.476810i
$769$	−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	$0.256433\pi$
$770$	−19.7068	+	1.73588i	−0.710182	+	0.0625569i
$771$	−29.9895	+	1.91469i	−1.08005	+	0.0689560i
$772$	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	$0.676850\pi$
$774$	10.7566	−	15.8218i	0.386636	−	0.568703i
$775$	8.77736	+	13.4642i	0.315292	+	0.483648i
$776$	36.2220	+	2.88184i	1.30029	+	0.103452i
$777$	−11.1358	−	5.51499i	−0.399494	−	0.197849i
$778$	−6.64658	+	32.6215i	−0.238292	+	1.16954i
$779$	−10.2156	+	17.6939i	−0.366011	+	0.633949i
$780$	−0.916293	+	18.5411i	−0.0328086	+	0.663877i
$781$	−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
$786$	21.3497	−	27.4613i	0.761520	−	0.979513i
$787$	−26.3106	+	45.5713i	−0.937872	+	1.62444i	−0.168442	+	0.985712i	$0.553873\pi$
$787$	−26.3106	+	45.5713i	−0.937872	+	1.62444i	−0.769431	+	0.638730i	$0.779460\pi$
$788$	2.95992	+	24.2205i	0.105443	+	0.862819i
$789$	−14.9202	−	7.38923i	−0.531174	−	0.263064i
$790$	−3.22928	−	1.50351i	−0.114893	−	0.0534925i
$791$	9.21510			0.327651
$792$	42.8692	+	22.0721i	1.52329	+	0.784299i
$793$		−	11.9344i		−	0.423803i
$794$	24.7883	+	21.9434i	0.879704	+	0.778742i
$795$	42.1458	−	15.5094i	1.49476	−	0.550063i
$796$	−14.0539	+	1.71748i	−0.498126	+	0.0608746i
$797$	−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	$0.180675\pi$
$798$	6.95320	−	2.82861i	0.246141	−	0.100132i
$799$	−10.4583	+	6.03812i	−0.369989	+	0.213613i
$800$	23.0212	−	16.4324i	0.813923	−	0.580973i
$801$	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
$804$	2.36245	+	12.5987i	0.0833173	+	0.444322i
$805$	−5.04665	−	1.20691i	−0.177871	−	0.0425381i
$806$	10.6754	+	2.17511i	0.376027	+	0.0766148i
$807$	−1.93893	+	1.29081i	−0.0682535	+	0.0454388i
$808$	−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	$0.851021\pi$
$810$	−5.11499	+	27.9971i	−0.179723	+	0.983717i
$811$		−	26.5970i		−	0.933948i	−0.884271	−	0.466974i	$-0.845344\pi$
$811$		−	26.5970i		−	0.933948i	0.884271	−	0.466974i	$-0.154656\pi$
$812$	5.48824	−	12.9091i	0.192599	−	0.453019i
$813$	31.3279	−	20.8561i	1.09872	−	0.731456i
$814$	10.4558	−	51.3171i	0.366475	−	1.79866i
$815$	−9.47329	+	39.6121i	−0.331835	+	1.38755i
$816$	−6.60751	−	6.03604i	−0.231309	−	0.211304i
$817$	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
$820$	−26.3921	−	19.5166i	−0.921654	−	0.681548i
$821$	−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	$0.511442\pi$
$822$	−6.40830	−	15.7527i	−0.223515	−	0.549438i
$823$	−4.23623	+	7.33737i	−0.147666	+	0.255764i	−0.930364	−	0.366636i	$-0.880509\pi$
$823$	−4.23623	+	7.33737i	−0.147666	+	0.255764i	0.782699	+	0.622401i	$0.213843\pi$
$824$	−3.46974	+	1.65135i	−0.120874	+	0.0575274i
$825$	39.4294	−	29.4472i	1.37276	−	1.02522i
$826$	−7.55900	+	8.53900i	−0.263011	+	0.297110i
$827$		−	37.2624i		−	1.29574i	−0.761750	−	0.647871i	$-0.775660\pi$
$827$		−	37.2624i		−	1.29574i	0.761750	−	0.647871i	$-0.224340\pi$
$828$	8.82882	+	9.05556i	0.306823	+	0.314702i
$829$	−18.4167			−0.639639			−0.319820	−	0.947478i	$-0.603622\pi$
$829$	−18.4167			−0.639639			−0.319820	+	0.947478i	$0.603622\pi$
$830$	−33.0412	−	15.3835i	−1.14688	−	0.533970i
$831$	21.5968	+	10.6958i	0.749184	+	0.371033i
$832$	3.03155	−	18.9313i	0.105100	−	0.656325i
$833$	3.73830	−	6.47493i	0.129525	−	0.224343i
$834$	23.0714	+	17.9368i	0.798896	+	0.621100i
$835$	−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	0.710748	−	0.703447i	$-0.248357\pi$
$839$	−7.35228	−	12.7345i	−0.253829	−	0.439645i	−0.964577	+	0.263802i	$0.915023\pi$
$840$	3.25419	+	11.6126i	0.112280	+	0.400671i
$841$	5.79320	−	10.0341i	0.199765	−	0.346004i
$842$	2.91275	+	0.593469i	0.100380	+	0.0204523i
$843$	18.0924	+	8.96025i	0.623135	+	0.308607i
$844$	−5.07232	+	11.9308i	−0.174596	+	0.410674i
$845$	−15.5538	+	4.62207i	−0.535066	+	0.159004i
$846$	−32.8010	−	22.3000i	−1.12772	−	0.766688i
$847$	23.4395			0.805390
$848$	−45.0167	+	11.1695i	−1.54588	+	0.383564i
$849$	21.4811	−	1.37147i	0.737228	−	0.0470686i
$850$	−8.49352	+	3.36011i	−0.291325	+	0.115251i
$851$	6.86833	−	11.8963i	0.235443	−	0.407800i
$852$	−33.3801	+	28.6310i	−1.14358	+	0.980881i
$853$	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	$0.870005\pi$
$858$	4.56369	−	33.0447i	0.155802	−	1.12813i
$859$	−33.3860	−	19.2754i	−1.13912	−	0.657669i	−0.192904	−	0.981218i	$-0.561791\pi$
$859$	−33.3860	−	19.2754i	−1.13912	−	0.657669i	−0.946212	+	0.323549i	$0.895124\pi$
$860$	8.04722	+	18.4918i	0.274408	+	0.630564i
$861$	11.6502	−	7.75592i	0.397036	−	0.264321i
$862$	−3.60148	+	4.06840i	−0.122667	+	0.138570i
$863$		−	13.4795i		−	0.458847i	−0.973327	−	0.229424i	$-0.926316\pi$
$863$		−	13.4795i		−	0.458847i	0.973327	−	0.229424i	$-0.0736841\pi$
$864$	8.40838	−	28.1656i	0.286059	−	0.958212i
$865$	18.5810	−	5.52167i	0.631773	−	0.187742i
$866$	−7.06142	−	6.25100i	−0.239957	−	0.212418i
$867$	−14.7157	−	22.1044i	−0.499770	−	0.750704i
$868$	7.02552	−	0.858569i	0.238462	−	0.0291417i
$869$	5.54347	+	3.20052i	0.188049	+	0.108570i
$870$	5.27031	+	34.4937i	0.178680	+	1.16945i
$871$	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
$876$	−22.2573	−	25.9492i	−0.752003	−	0.876741i
$877$	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	$0.581808\pi$
$878$	10.9392	−	53.6898i	0.369180	−	1.81194i
$879$	16.5065	−	1.05387i	0.556751	−	0.0355460i
$880$	−43.7998	+	25.7847i	−1.47649	+	0.869202i
$881$			25.0226i			0.843032i	0.906821	+	0.421516i	$0.138502\pi$
$881$			25.0226i			0.843032i	−0.906821	+	0.421516i	$0.861498\pi$
$882$	24.4901	+	1.80277i	0.824625	+	0.0607024i
$883$	−13.8202			−0.465085			−0.232543	−	0.972586i	$-0.574705\pi$
$883$	−13.8202			−0.465085			−0.232543	+	0.972586i	$0.574705\pi$
$884$	−2.42245	+	5.69793i	−0.0814759	+	0.191642i
$885$	4.82697	−	27.9549i	0.162257	−	0.939695i
$886$	−6.61241	+	32.4538i	−0.222148	+	1.09031i
$887$	16.1656	+	9.33323i	0.542789	+	0.313379i	0.746208	−	0.665712i	$-0.231872\pi$
$887$	16.1656	+	9.33323i	0.542789	+	0.313379i	−0.203420	+	0.979092i	$0.565206\pi$
$888$	−31.9221	−	0.499120i	−1.07124	−	0.0167494i
$889$	2.83336	+	4.90753i	0.0950279	+	0.164593i
$890$	−23.7392	+	16.6433i	−0.795739	+	0.557886i
$891$	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
$894$	11.1207	+	8.64574i	0.371931	+	0.289157i
$895$	0.577239	−	2.41369i	0.0192950	−	0.0806809i
$896$	−2.03127	−	12.2887i	−0.0678600	−	0.410535i
$897$	3.88315	−	7.84079i	0.129654	−	0.261796i
$898$	−16.7166	−	14.7981i	−0.557840	−	0.493818i
$899$	20.4788			0.683007
$900$	−22.0737	−	20.3163i	−0.735791	−	0.677208i
$901$	14.9783			0.499001
$902$	44.1656	+	39.0968i	1.47055	+	1.30178i
$903$	−8.58132	+	0.547878i	−0.285569	+	0.0182322i
$904$	21.3775	−	10.1742i	0.711005	−	0.338388i
$905$	−6.58591	+	27.5386i	−0.218923	+	0.915415i
$906$	−4.84907	+	1.97263i	−0.161100	+	0.0655364i
$907$	−20.7283	−	35.9025i	−0.688273	−	1.19212i	−0.972396	−	0.233336i	$-0.925036\pi$
$907$	−20.7283	−	35.9025i	−0.688273	−	1.19212i	0.284123	−	0.958788i	$-0.408297\pi$
$908$	0.235739	+	0.313206i	0.00782326	+	0.0103941i
$909$	6.38774	+	49.8212i	0.211868	+	1.65246i
$910$	6.83166	−	4.78961i	0.226467	−	0.158774i
$911$	−2.80277	−	4.85454i	−0.0928600	−	0.160838i	0.815853	−	0.578259i	$-0.196268\pi$
$911$	−2.80277	−	4.85454i	−0.0928600	−	0.160838i	−0.908713	+	0.417420i	$0.862934\pi$
$912$	13.0073	−	14.2387i	0.430714	−	0.471492i
$913$	56.7193	+	32.7469i	1.87714	+	1.08376i
$914$	2.37626	−	11.6627i	0.0785998	−	0.385769i
$915$	14.8183	+	12.3447i	0.489879	+	0.408104i
$916$	−3.03744	−	1.29136i	−0.100360	−	0.0426677i
$917$	−15.6336			−0.516266
$918$	−4.82586	+	8.17409i	−0.159277	+	0.269785i
$919$			30.8044i			1.01614i	0.861315	+	0.508072i	$0.169642\pi$
$919$			30.8044i			1.01614i	−0.861315	+	0.508072i	$0.830358\pi$
$920$	−13.0399	+	2.77204i	−0.429913	+	0.0913915i
$921$	12.9276	+	19.4186i	0.425980	+	0.639863i
$922$	7.00289	−	34.3703i	0.230628	−	1.13192i
$923$	26.3483	+	15.2122i	0.867266	+	0.500716i
$924$	−3.99408	−	21.3000i	−0.131396	−	0.700719i
$925$	−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	$0.184393\pi$
$930$	−13.7432	+	11.0053i	−0.450657	+	0.360878i
$931$	13.9530	+	8.05579i	0.457293	+	0.264018i
$932$	4.90727	+	40.1554i	0.160743	+	1.31533i
$933$	−17.7385	+	1.13252i	−0.580733	+	0.0370772i
$934$	−1.68991	−	1.49596i	−0.0552955	−	0.0489494i
$935$	15.7335	−	4.67550i	0.514541	−	0.152905i
$936$	−20.3120	+	0.978260i	−0.663917	+	0.0319754i
$937$			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
$939$	2.49242	+	1.23437i	0.0813371	+	0.0402822i
$940$	38.3362	−	16.6831i	1.25039	−	0.544143i
$941$	−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	$-0.719544\pi$
$942$	19.4460	+	15.1183i	0.633586	+	0.492580i
$943$	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	−0.747126	−	0.664683i	$-0.768567\pi$
$947$	−16.7732	+	9.68402i	−0.545056	+	0.314688i	0.202069	+	0.979371i	$0.435233\pi$
$948$	1.29482	−	3.68104i	0.0420537	−	0.119555i
$949$	−11.8257	+	20.4828i	−0.383880	+	0.664899i
$950$	−7.24082	−	18.3030i	−0.234923	−	0.593827i
$951$	−3.43031	+	6.92644i	−0.111236	+	0.224605i
$952$	−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	$0.477598\pi$
$954$	21.4035	+	44.2952i	0.692964	+	1.43411i
$955$	48.7961	−	14.5006i	1.57900	−	0.469229i
$956$	37.4172	+	15.9078i	1.21016	+	0.514495i
$957$	−3.99519	−	62.5760i	−0.129146	−	2.02280i
$958$	−8.28526	−	1.68811i	−0.267685	−	0.0545404i
$959$	−3.82170	+	6.61938i	−0.123409	+	0.213751i
$960$	20.3703	+	23.3463i	0.657449	+	0.753499i
$961$	−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
$966$	0.777648	−	5.63078i	0.0250204	−	0.181167i
$967$	−16.5665	+	28.6939i	−0.532741	+	0.922735i	0.466528	+	0.884507i	$0.345505\pi$
$967$	−16.5665	+	28.6939i	−0.532741	+	0.922735i	−0.999269	+	0.0382285i	$0.987829\pi$
$968$	54.3757	−	25.8789i	1.74770	−	0.831780i
$969$	−5.18423	+	3.45133i	−0.166541	+	0.110873i
$970$	36.8293	+	17.1472i	1.18252	+	0.550564i
$971$	−22.0082			−0.706277			−0.353138	−	0.935571i	$-0.614886\pi$
$971$	−22.0082			−0.706277			−0.353138	+	0.935571i	$0.614886\pi$
$972$	−31.0691	−	2.59094i	−0.996541	−	0.0831043i
$973$		−	13.1344i		−	0.421070i
$974$	15.5579	−	17.5749i	0.498508	−	0.563137i
$975$	−8.19165	+	19.0699i	−0.262343	+	0.610725i
$976$	−13.8207	−	14.3444i	−0.442390	−	0.459153i
$977$	−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	$0.323163\pi$
$978$	−44.1970	−	6.10390i	−1.41326	−	0.195181i
$979$	45.1183	−	26.0491i	1.44199	−	0.832532i
$980$	−15.3904	+	20.8123i	−0.491628	+	0.664825i
$981$	−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	−0.974993	−	0.222235i	$-0.928665\pi$
$983$	−39.8190	+	22.9895i	−1.27003	+	0.733251i	−0.295035	+	0.955486i	$0.595331\pi$
$984$	18.4633	−	30.8551i	0.588589	−	0.983624i
$985$	−6.34531	+	26.5326i	−0.202178	+	0.845399i
$986$	−2.32351	+	11.4038i	−0.0739956	+	0.363171i
$987$	1.13583	+	17.7904i	0.0361540	+	0.566274i
$988$	−12.2786	−	5.22022i	−0.390636	−	0.166077i
$989$		−	9.50531i		−	0.302251i
$990$	36.3094	+	39.8474i	1.15399	+	1.26643i
$991$			52.8232i			1.67798i	0.544144	+	0.838992i	$0.316854\pi$
$991$			52.8232i			1.67798i	−0.544144	+	0.838992i	$0.683146\pi$
$992$	15.3501	−	9.74844i	0.487367	−	0.309513i
$993$	−18.3000	−	9.06307i	−0.580733	−	0.287608i
$994$	19.3673	+	3.94606i	0.614294	+	0.125161i
$995$	−15.3955	−	3.68185i	−0.488069	−	0.116722i
$996$	13.2482	−	37.6634i	0.419786	−	1.19341i
$997$	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.59.18	yes	48
3.2	odd	2		540.2.n.d.179.7		48
4.3	odd	2	inner	180.2.n.d.59.2	✓	48
5.2	odd	4		900.2.r.g.851.19		48
5.3	odd	4		900.2.r.g.851.6		48
5.4	even	2	inner	180.2.n.d.59.7	yes	48
9.2	odd	6	inner	180.2.n.d.119.23	yes	48
9.7	even	3		540.2.n.d.359.2		48
12.11	even	2		540.2.n.d.179.23		48
15.14	odd	2		540.2.n.d.179.18		48
20.3	even	4		900.2.r.g.851.14		48
20.7	even	4		900.2.r.g.851.11		48
20.19	odd	2	inner	180.2.n.d.59.23	yes	48
36.7	odd	6		540.2.n.d.359.18		48
36.11	even	6	inner	180.2.n.d.119.7	yes	48
45.2	even	12		900.2.r.g.551.11		48
45.29	odd	6	inner	180.2.n.d.119.2	yes	48
45.34	even	6		540.2.n.d.359.23		48
45.38	even	12		900.2.r.g.551.14		48
60.59	even	2		540.2.n.d.179.2		48
180.47	odd	12		900.2.r.g.551.19		48
180.79	odd	6		540.2.n.d.359.7		48
180.83	odd	12		900.2.r.g.551.6		48
180.119	even	6	inner	180.2.n.d.119.18	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.n.d.59.2	✓	48	4.3	odd	2	inner
180.2.n.d.59.7	yes	48	5.4	even	2	inner
180.2.n.d.59.18	yes	48	1.1	even	1	trivial
180.2.n.d.59.23	yes	48	20.19	odd	2	inner
180.2.n.d.119.2	yes	48	45.29	odd	6	inner
180.2.n.d.119.7	yes	48	36.11	even	6	inner
180.2.n.d.119.18	yes	48	180.119	even	6	inner
180.2.n.d.119.23	yes	48	9.2	odd	6	inner
540.2.n.d.179.2		48	60.59	even	2
540.2.n.d.179.7		48	3.2	odd	2
540.2.n.d.179.18		48	15.14	odd	2
540.2.n.d.179.23		48	12.11	even	2
540.2.n.d.359.2		48	9.7	even	3
540.2.n.d.359.7		48	180.79	odd	6
540.2.n.d.359.18		48	36.7	odd	6
540.2.n.d.359.23		48	45.34	even	6
900.2.r.g.551.6		48	180.83	odd	12
900.2.r.g.551.11		48	45.2	even	12
900.2.r.g.551.14		48	45.38	even	12
900.2.r.g.551.19		48	180.47	odd	12
900.2.r.g.851.6		48	5.3	odd	4
900.2.r.g.851.11		48	20.7	even	4
900.2.r.g.851.14		48	20.3	even	4
900.2.r.g.851.19		48	5.2	odd	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+(0.937387 - 1.05892i) q^{2} +(0.959839 + 1.44177i) q^{3} +(-0.242609 - 1.98523i) q^{4} +(0.520093 - 2.17474i) q^{5} +(2.42646 + 0.335110i) q^{6} +(-0.550457 - 0.953419i) q^{7} +(-2.32961 - 1.60403i) q^{8} +(-1.15742 + 2.76774i) q^{9} +(-1.81534 - 2.58931i) q^{10} +(2.84126 + 4.92120i) q^{11} +(2.62939 - 2.25529i) q^{12} +(-2.07548 - 1.19828i) q^{13} +(-1.52558 - 0.310835i) q^{14} +(3.63469 - 1.33755i) q^{15} +(-3.88228 + 0.963271i) q^{16} +1.29175 q^{17} +(1.84586 + 3.82005i) q^{18} +2.78362i q^{19} +(-4.44354 - 0.504891i) q^{20} +(0.846263 - 1.70876i) q^{21} +(7.87450 + 1.60442i) q^{22} +(1.82546 + 1.05393i) q^{23} +(0.0765889 - 4.89838i) 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} +(1.99076 - 5.10263i) q^{30} +(-2.78385 - 1.60725i) q^{31} +(-2.61918 + 5.01397i) q^{32} +(-4.36810 + 8.82001i) q^{33} +(1.21087 - 1.36785i) q^{34} +(-2.35973 + 0.701235i) q^{35} +(5.77540 + 1.62626i) q^{36} -6.51687i q^{37} +(2.94763 + 2.60933i) q^{38} +(-0.264482 - 4.14253i) q^{39} +(-4.69996 + 4.23206i) q^{40} +(6.35642 + 3.66988i) q^{41} +(-1.01616 - 2.49789i) 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} +(-5.11518 - 4.67278i) q^{48} +(2.89400 - 5.01255i) q^{49} +(-6.57523 + 2.60122i) q^{50} +(1.23987 + 1.86240i) q^{51} +(-1.87533 + 4.41103i) q^{52} +11.5954 q^{53} +(-3.73592 + 6.32794i) q^{54} +(12.1801 - 3.61952i) q^{55} +(-0.246959 + 3.10404i) q^{56} +(-4.01335 + 2.67183i) q^{57} +(-1.79874 + 8.82821i) q^{58} +(3.66237 - 6.34341i) q^{59} +(-3.53715 - 6.89120i) 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} +(5.24505 + 12.8932i) q^{66} +(-1.85016 + 3.20457i) q^{67} +(-0.313389 - 2.56441i) q^{68} +(0.232621 + 3.64351i) q^{69} +(-1.46943 + 3.15608i) q^{70} -12.6950 q^{71} +(7.13586 - 4.59123i) q^{72} -9.86891i q^{73} +(-6.90082 - 6.10883i) q^{74} +(-1.01844 - 8.60016i) q^{75} +(5.52614 - 0.675333i) q^{76} +(3.12798 - 5.41781i) q^{77} +(-4.63452 - 3.60310i) q^{78} +(0.975531 - 0.563223i) q^{79} +(0.0757197 + 8.94395i) q^{80} +(-6.32077 - 6.40686i) q^{81} +(9.84453 - 3.29082i) q^{82} +(9.98138 - 5.76275i) q^{83} +(-3.59760 - 1.26547i) q^{84} +(0.671827 - 2.80921i) q^{85} +(-6.24894 - 1.27321i) q^{86} +(-9.88823 - 4.89714i) q^{87} +(1.27471 - 16.0219i) q^{88} -9.16815i q^{89} +(9.26765 - 2.02748i) q^{90} +2.63841i q^{91} +(1.64942 - 3.87966i) q^{92} +(-0.354749 - 5.55638i) q^{93} +(-2.63956 + 12.9550i) q^{94} +(6.05366 + 1.44774i) q^{95} +(-9.74300 + 1.03635i) 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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