LMFDB - Embedded newform 720.2.bd.f.523.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [720,2,Mod(307,720)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("720.307"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(720, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.bd (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,-2,0,8,8,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 14 x^{14} - 10 x^{13} - 26 x^{12} + 78 x^{11} - 66 x^{10} - 74 x^{9} + 233 x^{8} + \cdots + 256 $ x^16 - 6x^15 + 14x^14 - 10x^13 - 26x^12 + 78x^11 - 66x^10 - 74x^9 + 233x^8 - 148x^7 - 264x^6 + 624x^5 - 416x^4 - 320x^3 + 896x^2 - 768*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			523.4
Root			$-1.20803 - 0.735291i$ of defining polynomial
Character	$\chi$	$=$	720.523
Dual form			720.2.bd.f.307.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.873858 + 1.11192i) q^{2} +(-0.472743 - 1.94333i) q^{4} +(-1.54804 + 1.61356i) q^{5} +(0.143894 - 0.143894i) q^{7} +(2.57394 + 1.17254i) q^{8} +(-0.441393 - 3.13132i) q^{10} +(-0.749545 + 0.749545i) q^{11} +3.29132 q^{13} +(0.0342559 + 0.285741i) q^{14} +(-3.55303 + 1.83739i) q^{16} +(-1.35709 + 1.35709i) q^{17} +(-4.25468 + 4.25468i) q^{19} +(3.86750 + 2.24554i) q^{20} +(-0.178440 - 1.48843i) q^{22} +(-0.837388 - 0.837388i) q^{23} +(-0.207170 - 4.99571i) q^{25} +(-2.87614 + 3.65969i) q^{26} +(-0.347657 - 0.211607i) q^{28} +(-2.77462 - 2.77462i) q^{29} +6.60915i q^{31} +(1.06181 - 5.55631i) q^{32} +(-0.323074 - 2.69488i) q^{34} +(0.00942893 + 0.454934i) q^{35} -10.0194 q^{37} +(-1.01289 - 8.44886i) q^{38} +(-5.87651 + 2.33808i) q^{40} -1.72608i q^{41} -4.17171 q^{43} +(1.81095 + 1.10227i) q^{44} +(1.66287 - 0.199352i) q^{46} +(-8.54502 - 8.54502i) q^{47} +6.95859i q^{49} +(5.73588 + 4.13518i) q^{50} +(-1.55595 - 6.39610i) q^{52} +5.05524i q^{53} +(-0.0491155 - 2.36976i) q^{55} +(0.539094 - 0.201653i) q^{56} +(5.50979 - 0.660538i) q^{58} +(3.08237 + 3.08237i) q^{59} +(-5.00346 + 5.00346i) q^{61} +(-7.34887 - 5.77546i) q^{62} +(5.25031 + 6.03608i) q^{64} +(-5.09507 + 5.31074i) q^{65} -4.26739 q^{67} +(3.27881 + 1.99571i) q^{68} +(-0.514091 - 0.387064i) q^{70} -13.2111 q^{71} +(11.6889 - 11.6889i) q^{73} +(8.75550 - 11.1407i) q^{74} +(10.2796 + 6.25686i) q^{76} +0.215710i q^{77} -9.95558 q^{79} +(2.53547 - 8.57738i) q^{80} +(1.91927 + 1.50835i) q^{82} +10.0134i q^{83} +(-0.0889259 - 4.29056i) q^{85} +(3.64549 - 4.63862i) q^{86} +(-2.80815 + 1.05041i) q^{88} +5.76005 q^{89} +(0.473599 - 0.473599i) q^{91} +(-1.23145 + 2.02319i) q^{92} +(16.9685 - 2.03426i) q^{94} +(-0.278797 - 13.4516i) q^{95} +(11.7668 - 11.7668i) q^{97} +(-7.73741 - 6.08082i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} + 8 q^{4} + 8 q^{5} - 4 q^{7} - 8 q^{8} - 2 q^{10} - 8 q^{13} - 4 q^{14} - 8 q^{16} + 8 q^{17} - 8 q^{19} - 4 q^{20} - 32 q^{25} - 20 q^{26} + 12 q^{28} + 12 q^{29} + 28 q^{32} - 12 q^{35}+ \cdots - 62 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 + 8 * q^4 + 8 * q^5 - 4 * q^7 - 8 * q^8 - 2 * q^10 - 8 * q^13 - 4 * q^14 - 8 * q^16 + 8 * q^17 - 8 * q^19 - 4 * q^20 - 32 * q^25 - 20 * q^26 + 12 * q^28 + 12 * q^29 + 28 * q^32 - 12 * q^35 - 24 * q^37 - 16 * q^38 + 16 * q^40 + 24 * q^43 + 52 * q^44 - 16 * q^46 - 32 * q^47 - 6 * q^50 + 24 * q^52 - 4 * q^55 - 20 * q^56 + 12 * q^58 - 24 * q^59 + 40 * q^61 - 28 * q^62 + 8 * q^64 + 4 * q^65 + 16 * q^67 + 8 * q^68 + 12 * q^70 - 8 * q^73 + 64 * q^74 + 16 * q^76 + 48 * q^79 - 32 * q^82 - 8 * q^85 + 8 * q^86 + 24 * q^88 - 40 * q^91 + 16 * q^92 + 20 * q^94 + 8 * q^95 + 48 * q^97 - 62 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−0.873858	+	1.11192i	−0.617911	+	0.786248i
$2$	−0.873858	+	1.11192i	−0.617911	+	0.786248i
$3$		0			0
$3$		0			0
$4$	−0.472743	−	1.94333i	−0.236372	−	0.971663i
$5$	−1.54804	+	1.61356i	−0.692303	+	0.721607i
$5$	−1.54804	+	1.61356i	−0.692303	+	0.721607i
$6$		0			0
$7$	0.143894	−	0.143894i	0.0543867	−	0.0543867i	−0.679390	−	0.733777i	$-0.737756\pi$
$7$	0.143894	−	0.143894i	0.0543867	−	0.0543867i	0.733777	+	0.679390i	$0.237756\pi$
$8$	2.57394	+	1.17254i	0.910024	+	0.414554i
$9$		0			0
$10$	−0.441393	−	3.13132i	−0.139581	−	0.990211i
$11$	−0.749545	+	0.749545i	−0.225996	+	0.225996i	−0.811018	−	0.585021i	$-0.801086\pi$
$11$	−0.749545	+	0.749545i	−0.225996	+	0.225996i	0.585021	+	0.811018i	$0.301086\pi$
$12$		0			0
$13$	3.29132			0.912847			0.456423	−	0.889763i	$-0.349130\pi$
$13$	3.29132			0.912847			0.456423	+	0.889763i	$0.349130\pi$
$14$	0.0342559	+	0.285741i	0.00915528	+	0.0763676i
$15$		0			0
$16$	−3.55303	+	1.83739i	−0.888257	+	0.459347i
$17$	−1.35709	+	1.35709i	−0.329142	+	0.329142i	−0.852260	−	0.523118i	$-0.824769\pi$
$17$	−1.35709	+	1.35709i	−0.329142	+	0.329142i	0.523118	+	0.852260i	$0.324769\pi$
$18$		0			0
$19$	−4.25468	+	4.25468i	−0.976091	+	0.976091i	−0.999721	−	0.0236300i	$-0.992478\pi$
$19$	−4.25468	+	4.25468i	−0.976091	+	0.976091i	0.0236300	+	0.999721i	$0.492478\pi$
$20$	3.86750	+	2.24554i	0.864800	+	0.502117i
$21$		0			0
$22$	−0.178440	−	1.48843i	−0.0380435	−	0.317335i
$23$	−0.837388	−	0.837388i	−0.174608	−	0.174608i	0.614393	−	0.789000i	$-0.289401\pi$
$23$	−0.837388	−	0.837388i	−0.174608	−	0.174608i	−0.789000	+	0.614393i	$0.789401\pi$
$24$		0			0
$25$	−0.207170	−	4.99571i	−0.0414341	−	0.999141i
$26$	−2.87614	+	3.65969i	−0.564058	+	0.717724i
$27$		0			0
$28$	−0.347657	−	0.211607i	−0.0657010	−	0.0399900i
$29$	−2.77462	−	2.77462i	−0.515234	−	0.515234i	0.400891	−	0.916126i	$-0.368701\pi$
$29$	−2.77462	−	2.77462i	−0.515234	−	0.515234i	−0.916126	+	0.400891i	$0.868701\pi$
$30$		0			0
$31$			6.60915i			1.18704i	0.804820	+	0.593520i	$0.202262\pi$
$31$			6.60915i			1.18704i	−0.804820	+	0.593520i	$0.797738\pi$
$32$	1.06181	−	5.55631i	0.187703	−	0.982226i
$33$		0			0
$34$	−0.323074	−	2.69488i	−0.0554067	−	0.462167i
$35$	0.00942893	+	0.454934i	0.00159378	+	0.0768979i
$36$		0			0
$37$	−10.0194			−1.64717			−0.823586	−	0.567191i	$-0.808030\pi$
$37$	−10.0194			−1.64717			−0.823586	+	0.567191i	$0.808030\pi$
$38$	−1.01289	−	8.44886i	−0.164312	−	1.37059i
$39$		0			0
$40$	−5.87651	+	2.33808i	−0.929158	+	0.369683i
$41$		−	1.72608i		−	0.269569i	−0.990875	−	0.134784i	$-0.956966\pi$
$41$		−	1.72608i		−	0.269569i	0.990875	−	0.134784i	$-0.0430342\pi$
$42$		0			0
$43$	−4.17171			−0.636180			−0.318090	−	0.948061i	$-0.603041\pi$
$43$	−4.17171			−0.636180			−0.318090	+	0.948061i	$0.603041\pi$
$44$	1.81095	+	1.10227i	0.273011	+	0.166173i
$45$		0			0
$46$	1.66287	−	0.199352i	0.245177	−	0.0293929i
$47$	−8.54502	−	8.54502i	−1.24642	−	1.24642i	−0.957290	−	0.289128i	$-0.906635\pi$
$47$	−8.54502	−	8.54502i	−1.24642	−	1.24642i	−0.289128	−	0.957290i	$-0.593365\pi$
$48$		0			0
$49$			6.95859i			0.994084i
$50$	5.73588	+	4.13518i	0.811175	+	0.584803i
$51$		0			0
$52$	−1.55595	−	6.39610i	−0.215771	−	0.886979i
$53$			5.05524i			0.694391i	0.937793	+	0.347196i	$0.112866\pi$
$53$			5.05524i			0.694391i	−0.937793	+	0.347196i	$0.887134\pi$
$54$		0			0
$55$	−0.0491155	−	2.36976i	−0.00662273	−	0.319538i
$56$	0.539094	−	0.201653i	0.0720395	−	0.0269470i
$57$		0			0
$58$	5.50979	−	0.660538i	0.723471	−	0.0867329i
$59$	3.08237	+	3.08237i	0.401290	+	0.401290i	0.878687	−	0.477398i	$-0.158420\pi$
$59$	3.08237	+	3.08237i	0.401290	+	0.401290i	−0.477398	+	0.878687i	$0.658420\pi$
$60$		0			0
$61$	−5.00346	+	5.00346i	−0.640627	+	0.640627i	−0.950710	−	0.310083i	$-0.899643\pi$
$61$	−5.00346	+	5.00346i	−0.640627	+	0.640627i	0.310083	+	0.950710i	$0.399643\pi$
$62$	−7.34887	−	5.77546i	−0.933307	−	0.733485i
$63$		0			0
$64$	5.25031	+	6.03608i	0.656289	+	0.754509i
$65$	−5.09507	+	5.31074i	−0.631966	+	0.658717i
$66$		0			0
$67$	−4.26739			−0.521345			−0.260672	−	0.965427i	$-0.583944\pi$
$67$	−4.26739			−0.521345			−0.260672	+	0.965427i	$0.583944\pi$
$68$	3.27881	+	1.99571i	0.397614	+	0.242015i
$69$		0			0
$70$	−0.514091	−	0.387064i	−0.0614456	−	0.0462629i
$71$	−13.2111			−1.56786			−0.783932	−	0.620846i	$-0.786789\pi$
$71$	−13.2111			−1.56786			−0.783932	+	0.620846i	$0.786789\pi$
$72$		0			0
$73$	11.6889	−	11.6889i	1.36808	−	1.36808i	0.504904	−	0.863175i	$-0.331528\pi$
$73$	11.6889	−	11.6889i	1.36808	−	1.36808i	0.863175	−	0.504904i	$-0.168472\pi$
$74$	8.75550	−	11.1407i	1.01781	−	1.29509i
$75$		0			0
$76$	10.2796	+	6.25686i	1.17915	+	0.717711i
$77$			0.215710i			0.0245824i
$78$		0			0
$79$	−9.95558			−1.12009			−0.560045	−	0.828462i	$-0.689216\pi$
$79$	−9.95558			−1.12009			−0.560045	+	0.828462i	$0.689216\pi$
$80$	2.53547	−	8.57738i	0.283474	−	0.958980i
$81$		0			0
$82$	1.91927	+	1.50835i	0.211948	+	0.166570i
$83$			10.0134i			1.09912i	0.835455	+	0.549559i	$0.185204\pi$
$83$			10.0134i			1.09912i	−0.835455	+	0.549559i	$0.814796\pi$
$84$		0			0
$85$	−0.0889259	−	4.29056i	−0.00964537	−	0.465377i
$86$	3.64549	−	4.63862i	0.393103	−	0.500195i
$87$		0			0
$88$	−2.80815	+	1.05041i	−0.299350	+	0.111974i
$89$	5.76005			0.610564			0.305282	−	0.952262i	$-0.401249\pi$
$89$	5.76005			0.610564			0.305282	+	0.952262i	$0.401249\pi$
$90$		0			0
$91$	0.473599	−	0.473599i	0.0496467	−	0.0496467i
$92$	−1.23145	+	2.02319i	−0.128387	+	0.210932i
$93$		0			0
$94$	16.9685	−	2.03426i	1.75017	−	0.209818i
$95$	−0.278797	−	13.4516i	−0.0286040	−	1.38010i
$96$		0			0
$97$	11.7668	−	11.7668i	1.19474	−	1.19474i	0.219021	−	0.975720i	$-0.429714\pi$
$97$	11.7668	−	11.7668i	1.19474	−	1.19474i	0.975720	−	0.219021i	$-0.0702865\pi$
$98$	−7.73741	−	6.08082i	−0.781597	−	0.614256i
$99$		0			0
$100$	−9.61034	+	2.76429i	−0.961034	+	0.276429i
$101$	1.29314	+	1.29314i	0.128672	+	0.128672i	0.768510	−	0.639838i	$-0.220998\pi$
$101$	1.29314	+	1.29314i	0.128672	+	0.128672i	−0.639838	+	0.768510i	$0.720998\pi$
$102$		0			0
$103$	−11.2892	−	11.2892i	−1.11236	−	1.11236i	−0.992830	−	0.119532i	$-0.961861\pi$
$103$	−11.2892	−	11.2892i	−1.11236	−	1.11236i	−0.119532	−	0.992830i	$-0.538139\pi$
$104$	8.47164	+	3.85919i	0.830713	+	0.378425i
$105$		0			0
$106$	−5.62104	−	4.41757i	−0.545964	−	0.429072i
$107$			1.39451i			0.134812i	0.997726	+	0.0674060i	$0.0214723\pi$
$107$			1.39451i			0.134812i	−0.997726	+	0.0674060i	$0.978528\pi$
$108$		0			0
$109$	4.55325	+	4.55325i	0.436123	+	0.436123i	0.890705	−	0.454582i	$-0.150211\pi$
$109$	4.55325	+	4.55325i	0.436123	+	0.436123i	−0.454582	+	0.890705i	$0.650211\pi$
$110$	2.67791	+	2.01622i	0.255329	+	0.192239i
$111$		0			0
$112$	−0.246870	+	0.775647i	−0.0233270	+	0.0732917i
$113$	11.4501	+	11.4501i	1.07714	+	1.07714i	0.996765	+	0.0803726i	$0.0256110\pi$
$113$	11.4501	+	11.4501i	1.07714	+	1.07714i	0.0803726	+	0.996765i	$0.474389\pi$
$114$		0			0
$115$	2.64749	−	0.0548716i	0.246879	−	0.00511680i
$116$	−4.08031	+	6.70368i	−0.378847	+	0.622421i
$117$		0			0
$118$	−6.12090	+	0.733801i	−0.563475	+	0.0675519i
$119$			0.390552i			0.0358018i
$120$		0			0
$121$			9.87636i			0.897851i
$122$	−1.19114	−	9.93577i	−0.107841	−	0.899542i
$123$		0			0
$124$	12.8437	−	3.12443i	1.15340	−	0.280582i
$125$	8.38159	+	7.39925i	0.749672	+	0.661809i
$126$		0			0
$127$	4.94562	+	4.94562i	0.438853	+	0.438853i	0.891626	−	0.452773i	$-0.149565\pi$
$127$	4.94562	+	4.94562i	0.438853	+	0.438853i	−0.452773	+	0.891626i	$0.649565\pi$
$128$	−11.2997	+	0.563267i	−0.998760	+	0.0497862i
$129$		0			0
$130$	−1.45276	−	10.3062i	−0.127416	−	0.903910i
$131$	12.7313	+	12.7313i	1.11234	+	1.11234i	0.992833	+	0.119509i	$0.0381319\pi$
$131$	12.7313	+	12.7313i	1.11234	+	1.11234i	0.119509	+	0.992833i	$0.461868\pi$
$132$		0			0
$133$			1.22444i			0.106173i
$134$	3.72909	−	4.74501i	0.322145	−	0.409906i
$135$		0			0
$136$	−5.08429	+	1.90182i	−0.435974	+	0.163080i
$137$	−6.06032	−	6.06032i	−0.517768	−	0.517768i	0.399127	−	0.916896i	$-0.369313\pi$
$137$	−6.06032	−	6.06032i	−0.517768	−	0.517768i	−0.916896	+	0.399127i	$0.869313\pi$
$138$		0			0
$139$	−10.3543	−	10.3543i	−0.878239	−	0.878239i	0.115114	−	0.993352i	$-0.463277\pi$
$139$	−10.3543	−	10.3543i	−0.878239	−	0.878239i	−0.993352	+	0.115114i	$0.963277\pi$
$140$	0.879627	−	0.233390i	0.0743421	−	0.0197251i
$141$		0			0
$142$	11.5446	−	14.6897i	0.968801	−	1.23273i
$143$	−2.46699	+	2.46699i	−0.206300	+	0.206300i
$144$		0			0
$145$	8.77224	−	0.181813i	0.728495	−	0.0150987i
$146$	2.78270	+	23.2115i	0.230298	+	1.92100i
$147$		0			0
$148$	4.73658	+	19.4709i	0.389345	+	1.60050i
$149$	0.485009	−	0.485009i	0.0397335	−	0.0397335i	−0.686961	−	0.726694i	$-0.741056\pi$
$149$	0.485009	−	0.485009i	0.0397335	−	0.0397335i	0.726694	+	0.686961i	$0.241056\pi$
$150$		0			0
$151$	6.47302			0.526767			0.263383	−	0.964691i	$-0.415162\pi$
$151$	6.47302			0.526767			0.263383	+	0.964691i	$0.415162\pi$
$152$	−15.9401	+	5.96251i	−1.29291	+	0.483624i
$153$		0			0
$154$	−0.239852	−	0.188500i	−0.0193278	−	0.0151897i
$155$	−10.6643	−	10.2312i	−0.856576	−	0.821790i
$156$		0			0
$157$			11.7463i			0.937455i	0.883343	+	0.468728i	$0.155287\pi$
$157$			11.7463i			0.937455i	−0.883343	+	0.468728i	$0.844713\pi$
$158$	8.69977	−	11.0698i	0.692117	−	0.880669i
$159$		0			0
$160$	7.32173	+	10.3147i	0.578834	+	0.815445i
$161$	−0.240990			−0.0189926
$162$		0			0
$163$			1.87143i			0.146582i	0.997311	+	0.0732908i	$0.0233501\pi$
$163$			1.87143i			0.146582i	−0.997311	+	0.0732908i	$0.976650\pi$
$164$	−3.35434	+	0.815994i	−0.261930	+	0.0637184i
$165$		0			0
$166$	−11.1342	−	8.75033i	−0.864179	−	0.679157i
$167$	−4.79897	+	4.79897i	−0.371355	+	0.371355i	−0.867971	−	0.496615i	$-0.834576\pi$
$167$	−4.79897	+	4.79897i	−0.371355	+	0.371355i	0.496615	+	0.867971i	$0.334576\pi$
$168$		0			0
$169$	−2.16724			−0.166711
$170$	4.84848	+	3.65046i	0.371861	+	0.279978i
$171$		0			0
$172$	1.97215	+	8.10699i	0.150375	+	0.618152i
$173$	−12.8446			−0.976560			−0.488280	−	0.872687i	$-0.662375\pi$
$173$	−12.8446			−0.976560			−0.488280	+	0.872687i	$0.662375\pi$
$174$		0			0
$175$	−0.748661	−	0.689040i	−0.0565934	−	0.0520865i
$176$	1.28595	−	4.04036i	0.0969320	−	0.304554i
$177$		0			0
$178$	−5.03346	+	6.40473i	−0.377274	+	0.480054i
$179$	−3.47791	+	3.47791i	−0.259951	+	0.259951i	−0.825034	−	0.565083i	$-0.808844\pi$
$179$	−3.47791	+	3.47791i	−0.259951	+	0.259951i	0.565083	+	0.825034i	$0.308844\pi$
$180$		0			0
$181$	16.3185	+	16.3185i	1.21295	+	1.21295i	0.970053	+	0.242893i	$0.0780965\pi$
$181$	16.3185	+	16.3185i	1.21295	+	1.21295i	0.242893	+	0.970053i	$0.421903\pi$
$182$	0.112747	+	0.940464i	0.00835737	+	0.0697119i
$183$		0			0
$184$	−1.17352	−	3.13725i	−0.0865128	−	0.231281i
$185$	15.5103	−	16.1669i	1.14034	−	1.18861i
$186$		0			0
$187$		−	2.03439i		−	0.148770i
$188$	−12.5661	+	20.6453i	−0.916480	+	1.50572i
$189$		0			0
$190$	15.2008	+	11.4448i	1.10278	+	0.830292i
$191$			21.5483i			1.55918i	0.626289	+	0.779591i	$0.284573\pi$
$191$			21.5483i			1.55918i	−0.626289	+	0.779591i	$0.715427\pi$
$192$		0			0
$193$	11.3161	+	11.3161i	0.814552	+	0.814552i	0.985313	−	0.170760i	$-0.0546224\pi$
$193$	11.3161	+	11.3161i	0.814552	+	0.814552i	−0.170760	+	0.985313i	$0.554622\pi$
$194$	2.80126	+	23.3664i	0.201119	+	1.67761i
$195$		0			0
$196$	13.5228	−	3.28963i	0.965915	−	0.234973i
$197$	23.3109			1.66083			0.830417	−	0.557142i	$-0.188102\pi$
$197$	23.3109			1.66083			0.830417	+	0.557142i	$0.188102\pi$
$198$		0			0
$199$		−	2.14992i		−	0.152404i	−0.997092	−	0.0762018i	$-0.975721\pi$
$199$		−	2.14992i		−	0.152404i	0.997092	−	0.0762018i	$-0.0242793\pi$
$200$	5.32441	−	13.1016i	0.376492	−	0.926420i
$201$		0			0
$202$	−2.56789	+	0.307850i	−0.180676	+	0.0216603i
$203$	−0.798501			−0.0560438
$204$		0			0
$205$	2.78514	+	2.67204i	0.194523	+	0.186623i
$206$	22.4180	−	2.68756i	1.56193	−	0.187251i
$207$		0			0
$208$	−11.6941	+	6.04742i	−0.810842	+	0.419313i
$209$		−	6.37815i		−	0.441186i
$210$		0			0
$211$	6.27270	+	6.27270i	0.431830	+	0.431830i	0.889251	−	0.457420i	$-0.151226\pi$
$211$	6.27270	+	6.27270i	0.431830	+	0.431830i	−0.457420	+	0.889251i	$0.651226\pi$
$212$	9.82398	−	2.38983i	0.674714	−	0.164134i
$213$		0			0
$214$	−1.55058	−	1.21860i	−0.105996	−	0.0833019i
$215$	6.45796	−	6.73132i	0.440429	−	0.459072i
$216$		0			0
$217$	0.951015	+	0.951015i	0.0645591	+	0.0645591i
$218$	−9.04176	+	1.08397i	−0.612385	+	0.0734155i
$219$		0			0
$220$	−4.58200	+	1.21574i	−0.308918	+	0.0819649i
$221$	−4.46660	+	4.46660i	−0.300456	+	0.300456i
$222$		0			0
$223$	5.00009	−	5.00009i	0.334831	−	0.334831i	−0.519587	−	0.854418i	$-0.673914\pi$
$223$	5.00009	−	5.00009i	0.334831	−	0.334831i	0.854418	+	0.519587i	$0.173914\pi$
$224$	−0.646730	−	0.952305i	−0.0432115	−	0.0636286i
$225$		0			0
$226$	−22.7374	+	2.72587i	−1.51247	+	0.181322i
$227$	22.5630			1.49756			0.748778	−	0.662821i	$-0.230641\pi$
$227$	22.5630			1.49756			0.748778	+	0.662821i	$0.230641\pi$
$228$		0			0
$229$	6.83720	−	6.83720i	0.451815	−	0.451815i	−0.444142	−	0.895957i	$-0.646491\pi$
$229$	6.83720	−	6.83720i	0.451815	−	0.451815i	0.895957	+	0.444142i	$0.146491\pi$
$230$	−2.25251	+	2.99175i	−0.148526	+	0.197270i
$231$		0			0
$232$	−3.88836	−	10.3951i	−0.255283	−	0.682469i
$233$	3.10894	−	3.10894i	0.203673	−	0.203673i	−0.597899	−	0.801572i	$-0.703997\pi$
$233$	3.10894	−	3.10894i	0.203673	−	0.203673i	0.801572	+	0.597899i	$0.203997\pi$
$234$		0			0
$235$	27.0159	−	0.559930i	1.76232	−	0.0365258i
$236$	4.53287	−	7.44721i	0.295065	−	0.484772i
$237$		0			0
$238$	−0.434264	−	0.341287i	−0.0281491	−	0.0221224i
$239$	11.0671			0.715873			0.357937	−	0.933746i	$-0.383480\pi$
$239$	11.0671			0.715873			0.357937	+	0.933746i	$0.383480\pi$
$240$		0			0
$241$	−23.4743			−1.51211			−0.756056	−	0.654507i	$-0.772876\pi$
$241$	−23.4743			−1.51211			−0.756056	+	0.654507i	$0.772876\pi$
$242$	−10.9818	−	8.63054i	−0.705934	−	0.554792i
$243$		0			0
$244$	12.0887	+	7.35799i	0.773899	+	0.471047i
$245$	−11.2281	−	10.7721i	−0.717338	−	0.688207i
$246$		0			0
$247$	−14.0035	+	14.0035i	−0.891021	+	0.891021i
$248$	−7.74948	+	17.0116i	−0.492092	+	1.08023i
$249$		0			0
$250$	−15.5517	+	2.85379i	−0.983577	+	0.180489i
$251$	1.76187	−	1.76187i	0.111209	−	0.111209i	−0.649313	−	0.760521i	$-0.724943\pi$
$251$	1.76187	−	1.76187i	0.111209	−	0.111209i	0.760521	+	0.649313i	$0.224943\pi$
$252$		0			0
$253$	1.25532			0.0789213
$254$	−9.82092	+	1.17738i	−0.616219	+	0.0738751i
$255$		0			0
$256$	9.24801	−	13.0566i	0.578001	−	0.816036i
$257$	4.05693	−	4.05693i	0.253064	−	0.253064i	−0.569162	−	0.822226i	$-0.692732\pi$
$257$	4.05693	−	4.05693i	0.253064	−	0.253064i	0.822226	+	0.569162i	$0.192732\pi$
$258$		0			0
$259$	−1.44172	+	1.44172i	−0.0895842	+	0.0895842i
$260$	12.7292	+	7.39077i	0.789429	+	0.458356i
$261$		0			0
$262$	−25.2816	+	3.03087i	−1.56190	+	0.187248i
$263$	−22.2576	−	22.2576i	−1.37246	−	1.37246i	−0.856784	−	0.515676i	$-0.827541\pi$
$263$	−22.2576	−	22.2576i	−1.37246	−	1.37246i	−0.515676	−	0.856784i	$-0.672459\pi$
$264$		0			0
$265$	−8.15695	−	7.82570i	−0.501078	−	0.480729i
$266$	−1.36149	−	1.06999i	−0.0834781	−	0.0656053i
$267$		0			0
$268$	2.01738	+	8.29293i	0.123231	+	0.506571i
$269$	−11.9600	−	11.9600i	−0.729217	−	0.729217i	0.241247	−	0.970464i	$-0.422444\pi$
$269$	−11.9600	−	11.9600i	−0.729217	−	0.729217i	−0.970464	+	0.241247i	$0.922444\pi$
$270$		0			0
$271$		−	15.7162i		−	0.954691i	−0.878716	−	0.477346i	$-0.841599\pi$
$271$		−	15.7162i		−	0.954691i	0.878716	−	0.477346i	$-0.158401\pi$
$272$	2.32827	−	7.31526i	0.141172	−	0.443553i
$273$		0			0
$274$	12.0345	−	1.44275i	0.727029	−	0.0871595i
$275$	3.89979	+	3.58922i	0.235166	+	0.216438i
$276$		0			0
$277$	4.59363			0.276004			0.138002	−	0.990432i	$-0.455932\pi$
$277$	4.59363			0.276004			0.138002	+	0.990432i	$0.455932\pi$
$278$	20.5613	−	2.46498i	1.23319	−	0.147840i
$279$		0			0
$280$	−0.509157	+	1.18203i	−0.0304280	+	0.0706397i
$281$		−	20.5117i		−	1.22363i	−0.791002	−	0.611814i	$-0.790440\pi$
$281$		−	20.5117i		−	1.22363i	0.791002	−	0.611814i	$-0.209560\pi$
$282$		0			0
$283$	−28.8990			−1.71787			−0.858933	−	0.512088i	$-0.828872\pi$
$283$	−28.8990			−1.71787			−0.858933	+	0.512088i	$0.828872\pi$
$284$	6.24544	+	25.6734i	0.370599	+	1.52344i
$285$		0			0
$286$	−0.587302	−	4.89890i	−0.0347279	−	0.289678i
$287$	−0.248372	−	0.248372i	−0.0146610	−	0.0146610i
$288$		0			0
$289$			13.3166i			0.783332i
$290$	−7.46353	+	9.91293i	−0.438274	+	0.582107i
$291$		0			0
$292$	−28.2411	−	17.1895i	−1.65269	−	1.00594i
$293$		−	8.86723i		−	0.518029i	−0.965873	−	0.259014i	$-0.916602\pi$
$293$		−	8.86723i		−	0.518029i	0.965873	−	0.259014i	$-0.0833977\pi$
$294$		0			0
$295$	−9.74521	+	0.201978i	−0.567388	+	0.0117596i
$296$	−25.7892	−	11.7481i	−1.49897	−	0.682843i
$297$		0			0
$298$	0.115463	+	0.963122i	0.00668861	+	0.0557921i
$299$	−2.75611	−	2.75611i	−0.159390	−	0.159390i
$300$		0			0
$301$	−0.600283	+	0.600283i	−0.0345997	+	0.0345997i
$302$	−5.65650	+	7.19749i	−0.325495	+	0.414169i
$303$		0			0
$304$	7.29950	−	22.9345i	0.418655	−	1.31538i
$305$	−0.327862	−	15.8189i	−0.0187733	−	0.905789i
$306$		0			0
$307$	14.1518			0.807684			0.403842	−	0.914829i	$-0.367675\pi$
$307$	14.1518			0.807684			0.403842	+	0.914829i	$0.367675\pi$
$308$	0.419194	−	0.101975i	0.0238858	−	0.00581058i
$309$		0			0
$310$	20.6954	−	2.91723i	1.17542	−	0.165688i
$311$	−7.15165			−0.405533			−0.202766	−	0.979227i	$-0.564993\pi$
$311$	−7.15165			−0.405533			−0.202766	+	0.979227i	$0.564993\pi$
$312$		0			0
$313$	5.98016	−	5.98016i	0.338019	−	0.338019i	−0.517602	−	0.855621i	$-0.673175\pi$
$313$	5.98016	−	5.98016i	0.338019	−	0.338019i	0.855621	+	0.517602i	$0.173175\pi$
$314$	−13.0610	−	10.2646i	−0.737072	−	0.579264i
$315$		0			0
$316$	4.70644	+	19.3469i	0.264758	+	1.08835i
$317$			7.76996i			0.436404i	0.975904	+	0.218202i	$0.0700192\pi$
$317$			7.76996i			0.436404i	−0.975904	+	0.218202i	$0.929981\pi$
$318$		0			0
$319$	4.15941			0.232882
$320$	−17.8673	−	0.872350i	−0.998810	−	0.0487659i
$321$		0			0
$322$	0.210591	−	0.267962i	0.0117358	−	0.0149329i
$323$		−	11.5479i		−	0.642544i
$324$		0			0
$325$	−0.681863	−	16.4424i	−0.0378229	−	0.912063i
$326$	−2.08088	−	1.63536i	−0.115249	−	0.0905744i
$327$		0			0
$328$	2.02390	−	4.44283i	0.111751	−	0.245314i
$329$	−2.45915			−0.135577
$330$		0			0
$331$	−0.751395	+	0.751395i	−0.0413004	+	0.0413004i	−0.727455	−	0.686155i	$-0.759297\pi$
$331$	−0.751395	+	0.751395i	−0.0413004	+	0.0413004i	0.686155	+	0.727455i	$0.259297\pi$
$332$	19.4594	−	4.73379i	1.06797	−	0.259800i
$333$		0			0
$334$	−1.14246	−	9.52970i	−0.0625127	−	0.521442i
$335$	6.60607	−	6.88570i	0.360928	−	0.376206i
$336$		0			0
$337$	−0.379414	+	0.379414i	−0.0206680	+	0.0206680i	−0.717365	−	0.696697i	$-0.754652\pi$
$337$	−0.379414	+	0.379414i	−0.0206680	+	0.0206680i	0.696697	+	0.717365i	$0.254652\pi$
$338$	1.89386	−	2.40981i	0.103013	−	0.131076i
$339$		0			0
$340$	−8.29592	+	2.20115i	−0.449909	+	0.119374i
$341$	−4.95386	−	4.95386i	−0.268266	−	0.268266i
$342$		0			0
$343$	2.00855	+	2.00855i	0.108452	+	0.108452i
$344$	−10.7377	−	4.89149i	−0.578939	−	0.263731i
$345$		0			0
$346$	11.2244	−	14.2822i	0.603427	−	0.767818i
$347$			16.7455i			0.898947i	0.893294	+	0.449473i	$0.148388\pi$
$347$			16.7455i			0.898947i	−0.893294	+	0.449473i	$0.851612\pi$
$348$		0			0
$349$	−21.0019	−	21.0019i	−1.12421	−	1.12421i	−0.991102	−	0.133104i	$-0.957506\pi$
$349$	−21.0019	−	21.0019i	−1.12421	−	1.12421i	−0.133104	−	0.991102i	$-0.542494\pi$
$350$	1.42038	−	0.230330i	0.0759226	−	0.0123116i
$351$		0			0
$352$	3.36883	+	4.96058i	0.179559	+	0.264400i
$353$	9.02933	+	9.02933i	0.480583	+	0.480583i	0.905318	−	0.424735i	$-0.139633\pi$
$353$	9.02933	+	9.02933i	0.480583	+	0.480583i	−0.424735	+	0.905318i	$0.639633\pi$
$354$		0			0
$355$	20.4512	−	21.3169i	1.08544	−	1.13138i
$356$	−2.72302	−	11.1936i	−0.144320	−	0.593262i
$357$		0			0
$358$	−0.827965	−	6.90636i	−0.0437593	−	0.365012i
$359$			12.2651i			0.647326i	0.946172	+	0.323663i	$0.104914\pi$
$359$			12.2651i			0.647326i	−0.946172	+	0.323663i	$0.895086\pi$
$360$		0			0
$361$		−	17.2046i		−	0.905506i
$362$	−32.4050	+	3.88486i	−1.70317	+	0.204184i
$363$		0			0
$364$	−1.14425	−	0.696467i	−0.0599749	−	0.0365048i
$365$	0.765938	+	36.9555i	0.0400910	+	1.93434i
$366$		0			0
$367$	1.25485	+	1.25485i	0.0655025	+	0.0655025i	0.739099	−	0.673597i	$-0.235251\pi$
$367$	1.25485	+	1.25485i	0.0655025	+	0.0655025i	−0.673597	+	0.739099i	$0.735251\pi$
$368$	4.51387	+	1.43666i	0.235302	+	0.0748909i
$369$		0			0
$370$	4.42247	+	31.3738i	0.229913	+	1.63105i
$371$	0.727417	+	0.727417i	0.0377656	+	0.0377656i
$372$		0			0
$373$			8.25732i			0.427548i	0.976883	+	0.213774i	$0.0685756\pi$
$373$			8.25732i			0.427548i	−0.976883	+	0.213774i	$0.931424\pi$
$374$	2.26209	+	1.77777i	0.116970	+	0.0919264i
$375$		0			0
$376$	−11.9750	−	32.0137i	−0.617563	−	1.65098i
$377$	−9.13216	−	9.13216i	−0.470330	−	0.470330i
$378$		0			0
$379$	−1.03027	−	1.03027i	−0.0529214	−	0.0529214i	0.680151	−	0.733072i	$-0.261914\pi$
$379$	−1.03027	−	1.03027i	−0.0529214	−	0.0529214i	−0.733072	+	0.680151i	$0.761914\pi$
$380$	−26.0090	+	6.90094i	−1.33423	+	0.354011i
$381$		0			0
$382$	−23.9601	−	18.8302i	−1.22590	−	0.963436i
$383$	12.3374	−	12.3374i	0.630413	−	0.630413i	−0.317759	−	0.948172i	$-0.602930\pi$
$383$	12.3374	−	12.3374i	0.630413	−	0.630413i	0.948172	+	0.317759i	$0.102930\pi$
$384$		0			0
$385$	−0.348061	−	0.333926i	−0.0177388	−	0.0170184i
$386$	−22.4713	+	2.69396i	−1.14376	+	0.137119i
$387$		0			0
$388$	−28.4295	−	17.3041i	−1.44329	−	0.878483i
$389$	−12.8354	+	12.8354i	−0.650781	+	0.650781i	−0.953181	−	0.302400i	$-0.902212\pi$
$389$	−12.8354	+	12.8354i	−0.650781	+	0.650781i	0.302400	+	0.953181i	$0.402212\pi$
$390$		0			0
$391$	2.27282			0.114941
$392$	−8.15920	+	17.9110i	−0.412102	+	0.904641i
$393$		0			0
$394$	−20.3704	+	25.9199i	−1.02625	+	1.30583i
$395$	15.4116	−	16.0640i	0.775442	−	0.808266i
$396$		0			0
$397$		−	14.3934i		−	0.722383i	−0.932492	−	0.361191i	$-0.882370\pi$
$397$		−	14.3934i		−	0.722383i	0.932492	−	0.361191i	$-0.117630\pi$
$398$	2.39054	+	1.87872i	0.119827	+	0.0941718i
$399$		0			0
$400$	9.91513	+	17.3692i	0.495757	+	0.868461i
$401$	37.4272			1.86902			0.934512	−	0.355932i	$-0.115836\pi$
$401$	37.4272			1.86902			0.934512	+	0.355932i	$0.115836\pi$
$402$		0			0
$403$			21.7528i			1.08358i
$404$	1.90167	−	3.12432i	0.0946116	−	0.155440i
$405$		0			0
$406$	0.697777	−	0.887871i	0.0346301	−	0.0440643i
$407$	7.50996	−	7.50996i	0.372255	−	0.372255i
$408$		0			0
$409$	−8.19166			−0.405052			−0.202526	−	0.979277i	$-0.564915\pi$
$409$	−8.19166			−0.405052			−0.202526	+	0.979277i	$0.564915\pi$
$410$	−5.40492	+	0.761881i	−0.266930	+	0.0376266i
$411$		0			0
$412$	−16.6018	+	27.2756i	−0.817910	+	1.34377i
$413$	0.887066			0.0436497
$414$		0			0
$415$	−16.1573	−	15.5012i	−0.793131	−	0.760922i
$416$	3.49475	−	18.2876i	0.171344	−	0.896621i
$417$		0			0
$418$	7.09201	+	5.57360i	0.346881	+	0.272614i
$419$	−22.2183	+	22.2183i	−1.08544	+	1.08544i	−0.0894455	+	0.995992i	$0.528509\pi$
$419$	−22.2183	+	22.2183i	−1.08544	+	1.08544i	−0.995992	+	0.0894455i	$0.971491\pi$
$420$		0			0
$421$	−2.75098	−	2.75098i	−0.134074	−	0.134074i	0.636885	−	0.770959i	$-0.280223\pi$
$421$	−2.75098	−	2.75098i	−0.134074	−	0.134074i	−0.770959	+	0.636885i	$0.780223\pi$
$422$	−12.4562	+	1.49331i	−0.606359	+	0.0726930i
$423$		0			0
$424$	−5.92746	+	13.0119i	−0.287863	+	0.631913i
$425$	7.06075	+	6.49845i	0.342497	+	0.315221i
$426$		0			0
$427$			1.43993i			0.0696832i
$428$	2.70998	−	0.659244i	0.130992	−	0.0318658i
$429$		0			0
$430$	1.84136	+	13.0630i	0.0887985	+	0.629952i
$431$			5.32770i			0.256626i	0.991734	+	0.128313i	$0.0409563\pi$
$431$			5.32770i			0.256626i	−0.991734	+	0.128313i	$0.959044\pi$
$432$		0			0
$433$	−3.38866	−	3.38866i	−0.162849	−	0.162849i	0.620979	−	0.783827i	$-0.286735\pi$
$433$	−3.38866	−	3.38866i	−0.162849	−	0.162849i	−0.783827	+	0.620979i	$0.786735\pi$
$434$	−1.88851	+	0.226403i	−0.0906513	+	0.0108677i
$435$		0			0
$436$	6.69593	−	11.0010i	0.320677	−	0.526851i
$437$	7.12564			0.340866
$438$		0			0
$439$		−	5.99801i		−	0.286269i	−0.989703	−	0.143135i	$-0.954282\pi$
$439$		−	5.99801i		−	0.286269i	0.989703	−	0.143135i	$-0.0457182\pi$
$440$	2.65221	−	6.15721i	0.126439	−	0.293533i
$441$		0			0
$442$	−1.06334	−	8.86968i	−0.0505778	−	0.421888i
$443$	13.3394			0.633773			0.316887	−	0.948463i	$-0.397363\pi$
$443$	13.3394			0.633773			0.316887	+	0.948463i	$0.397363\pi$
$444$		0			0
$445$	−8.91676	+	9.29420i	−0.422695	+	0.440587i
$446$	1.19034	+	9.92908i	0.0563643	+	0.470156i
$447$		0			0
$448$	1.62404	+	0.113066i	0.0767287	+	0.00534188i
$449$		−	29.7201i		−	1.40258i	−0.712877	−	0.701289i	$-0.752608\pi$
$449$		−	29.7201i		−	1.40258i	0.712877	−	0.701289i	$-0.247392\pi$
$450$		0			0
$451$	1.29378	+	1.29378i	0.0609216	+	0.0609216i
$452$	16.8384	−	27.6643i	0.792010	−	1.30122i
$453$		0			0
$454$	−19.7168	+	25.0883i	−0.925356	+	1.17745i
$455$	0.0310336	+	1.49733i	0.00145488	+	0.0701960i
$456$		0			0
$457$	13.8443	+	13.8443i	0.647611	+	0.647611i	0.952415	−	0.304804i	$-0.0985910\pi$
$457$	13.8443	+	13.8443i	0.647611	+	0.647611i	−0.304804	+	0.952415i	$0.598591\pi$
$458$	1.62769	+	13.5772i	0.0760571	+	0.634420i
$459$		0			0
$460$	−1.35821	−	5.11899i	−0.0633271	−	0.238674i
$461$	−23.8766	+	23.8766i	−1.11205	+	1.11205i	−0.119172	+	0.992874i	$0.538024\pi$
$461$	−23.8766	+	23.8766i	−1.11205	+	1.11205i	−0.992874	+	0.119172i	$0.961976\pi$
$462$		0			0
$463$	10.5750	−	10.5750i	0.491463	−	0.491463i	−0.417304	−	0.908767i	$-0.637025\pi$
$463$	10.5750	−	10.5750i	0.491463	−	0.491463i	0.908767	+	0.417304i	$0.137025\pi$
$464$	14.9564	+	4.76025i	0.694332	+	0.220989i
$465$		0			0
$466$	0.740126	+	6.17366i	0.0342857	+	0.285989i
$467$	−30.0161			−1.38898			−0.694491	−	0.719502i	$-0.744370\pi$
$467$	−30.0161			−1.38898			−0.694491	+	0.719502i	$0.744370\pi$
$468$		0			0
$469$	−0.614050	+	0.614050i	−0.0283542	+	0.0283542i
$470$	−22.9855	+	30.5289i	−1.06024	+	1.40819i
$471$		0			0
$472$	4.31963	+	11.5480i	0.198827	+	0.531540i
$473$	3.12689	−	3.12689i	0.143774	−	0.143774i
$474$		0			0
$475$	22.1366	+	20.3737i	1.01570	+	0.934809i
$476$	0.758970	−	0.184631i	0.0347873	−	0.00846254i
$477$		0			0
$478$	−9.67111	+	12.3058i	−0.442346	+	0.562854i
$479$	21.9152			1.00133			0.500665	−	0.865641i	$-0.333089\pi$
$479$	21.9152			1.00133			0.500665	+	0.865641i	$0.333089\pi$
$480$		0			0
$481$	−32.9769			−1.50362
$482$	20.5132	−	26.1016i	0.934351	−	1.18890i
$483$		0			0
$484$	19.1930	−	4.66899i	0.872409	−	0.212227i
$485$	0.771047	+	37.2020i	0.0350114	+	1.68926i
$486$		0			0
$487$	−5.66360	+	5.66360i	−0.256642	+	0.256642i	−0.823687	−	0.567045i	$-0.808087\pi$
$487$	−5.66360	+	5.66360i	−0.256642	+	0.256642i	0.567045	+	0.823687i	$0.308087\pi$
$488$	−18.7453	+	7.01185i	−0.848561	+	0.317411i
$489$		0			0
$490$	21.7896	−	3.07147i	0.984353	−	0.138755i
$491$	25.4744	−	25.4744i	1.14964	−	1.14964i	0.163018	−	0.986623i	$-0.447877\pi$
$491$	25.4744	−	25.4744i	1.14964	−	1.14964i	0.986623	−	0.163018i	$-0.0521230\pi$
$492$		0			0
$493$	7.53080			0.339170
$494$	−3.33373	−	27.8079i	−0.149992	−	1.25114i
$495$		0			0
$496$	−12.1436	−	23.4825i	−0.545263	−	1.05440i
$497$	−1.90099	+	1.90099i	−0.0852709	+	0.0852709i
$498$		0			0
$499$	−18.8209	+	18.8209i	−0.842537	+	0.842537i	−0.989188	−	0.146651i	$-0.953151\pi$
$499$	−18.8209	+	18.8209i	−0.842537	+	0.842537i	0.146651	+	0.989188i	$0.453151\pi$
$500$	10.4168	−	19.7861i	0.465854	−	0.884862i
$501$		0			0
$502$	0.419439	+	3.49870i	0.0187205	+	0.156154i
$503$	−7.85721	−	7.85721i	−0.350336	−	0.350336i	0.509899	−	0.860234i	$-0.329683\pi$
$503$	−7.85721	−	7.85721i	−0.350336	−	0.350336i	−0.860234	+	0.509899i	$0.829683\pi$
$504$		0			0
$505$	−4.08839	+	0.0847357i	−0.181931	+	0.00377069i
$506$	−1.09697	+	1.39582i	−0.0487664	+	0.0620517i
$507$		0			0
$508$	7.27294	−	11.9490i	0.322685	−	0.530149i
$509$	−10.1248	−	10.1248i	−0.448776	−	0.448776i	0.446171	−	0.894948i	$-0.352787\pi$
$509$	−10.1248	−	10.1248i	−0.448776	−	0.448776i	−0.894948	+	0.446171i	$0.852787\pi$
$510$		0			0
$511$		−	3.36391i		−	0.148811i
$512$	6.43646	+	21.6927i	0.284454	+	0.958690i
$513$		0			0
$514$	0.965809	+	8.05617i	0.0426000	+	0.355342i
$515$	35.6920	−	0.739751i	1.57278	−	0.0325973i
$516$		0			0
$517$	12.8097			0.563372
$518$	−0.343222	−	2.86294i	−0.0150803	−	0.125791i
$519$		0			0
$520$	−19.3414	+	7.69536i	−0.848179	+	0.337464i
$521$			37.3503i			1.63634i	0.574973	+	0.818172i	$0.305013\pi$
$521$			37.3503i			1.63634i	−0.574973	+	0.818172i	$0.694987\pi$
$522$		0			0
$523$	8.27258			0.361735			0.180867	−	0.983507i	$-0.442110\pi$
$523$	8.27258			0.361735			0.180867	+	0.983507i	$0.442110\pi$
$524$	18.7225	−	30.7598i	0.817895	−	1.34375i
$525$		0			0
$526$	44.1986	−	5.29873i	1.92715	−	0.231035i
$527$	−8.96919	−	8.96919i	−0.390704	−	0.390704i
$528$		0			0
$529$		−	21.5976i		−	0.939024i
$530$	15.8296	−	2.23135i	0.687594	−	0.0969236i
$531$		0			0
$532$	2.37949	−	0.578847i	0.103164	−	0.0250962i
$533$		−	5.68108i		−	0.246075i
$534$		0			0
$535$	−2.25012	−	2.15875i	−0.0972814	−	0.0933308i
$536$	−10.9840	−	5.00367i	−0.474436	−	0.216126i
$537$		0			0
$538$	23.7500	−	2.84726i	1.02394	−	0.122754i
$539$	−5.21578	−	5.21578i	−0.224659	−	0.224659i
$540$		0			0
$541$	11.1960	−	11.1960i	0.481352	−	0.481352i	−0.424211	−	0.905563i	$-0.639449\pi$
$541$	11.1960	−	11.1960i	0.481352	−	0.481352i	0.905563	+	0.424211i	$0.139449\pi$
$542$	17.4752	+	13.7337i	0.750624	+	0.589914i
$543$		0			0
$544$	6.09942	+	8.98135i	0.261511	+	0.385072i
$545$	−14.3956	+	0.298361i	−0.616638	+	0.0127804i
$546$		0			0
$547$	26.6966			1.14147			0.570733	−	0.821136i	$-0.306659\pi$
$547$	26.6966			1.14147			0.570733	+	0.821136i	$0.306659\pi$
$548$	−8.91220	+	14.6422i	−0.380710	+	0.625482i
$549$		0			0
$550$	−7.39880	+	1.19979i	−0.315486	+	0.0511593i
$551$	23.6103			1.00583
$552$		0			0
$553$	−1.43255	+	1.43255i	−0.0609180	+	0.0609180i
$554$	−4.01418	+	5.10776i	−0.170546	+	0.217008i
$555$		0			0
$556$	−15.2268	+	25.0167i	−0.645761	+	1.06094i
$557$		−	0.715510i		−	0.0303171i	−0.999885	−	0.0151586i	$-0.995175\pi$
$557$		−	0.715510i		−	0.0303171i	0.999885	−	0.0151586i	$-0.00482531\pi$
$558$		0			0
$559$	−13.7304			−0.580735
$560$	−0.869392	−	1.59907i	−0.0367385	−	0.0675730i
$561$		0			0
$562$	22.8075	+	17.9244i	0.962075	+	0.756093i
$563$		−	16.6892i		−	0.703364i	−0.936119	−	0.351682i	$-0.885610\pi$
$563$		−	16.6892i		−	0.703364i	0.936119	−	0.351682i	$-0.114390\pi$
$564$		0			0
$565$	−36.2007	+	0.750294i	−1.52298	+	0.0315651i
$566$	25.2536	−	32.1334i	1.06149	−	1.35067i
$567$		0			0
$568$	−34.0044	−	15.4905i	−1.42679	−	0.649965i
$569$	−23.0249			−0.965253			−0.482626	−	0.875826i	$-0.660317\pi$
$569$	−23.0249			−0.965253			−0.482626	+	0.875826i	$0.660317\pi$
$570$		0			0
$571$	−7.65518	+	7.65518i	−0.320359	+	0.320359i	−0.848905	−	0.528546i	$-0.822738\pi$
$571$	−7.65518	+	7.65518i	−0.320359	+	0.320359i	0.528546	+	0.848905i	$0.322738\pi$
$572$	5.96041	+	3.62791i	0.249217	+	0.151691i
$573$		0			0
$574$	0.493213	−	0.0591286i	0.0205863	−	0.00246798i
$575$	−4.00986	+	4.35683i	−0.167223	+	0.181692i
$576$		0			0
$577$	22.0343	−	22.0343i	0.917298	−	0.917298i	−0.0795337	−	0.996832i	$-0.525343\pi$
$577$	22.0343	−	22.0343i	0.917298	−	0.917298i	0.996832	+	0.0795337i	$0.0253431\pi$
$578$	−14.8071	−	11.6369i	−0.615893	−	0.484029i
$579$		0			0
$580$	−4.50034	−	16.9614i	−0.186866	−	0.704283i
$581$	1.44087	+	1.44087i	0.0597774	+	0.0597774i
$582$		0			0
$583$	−3.78913	−	3.78913i	−0.156930	−	0.156930i
$584$	43.7921	−	16.3808i	1.81213	−	0.677842i
$585$		0			0
$586$	9.85967	+	7.74870i	0.407299	+	0.320096i
$587$			22.5696i			0.931547i	0.884904	+	0.465773i	$0.154224\pi$
$587$			22.5696i			0.931547i	−0.884904	+	0.465773i	$0.845776\pi$
$588$		0			0
$589$	−28.1198	−	28.1198i	−1.15866	−	1.15866i
$590$	8.29134	−	11.0124i	0.341349	−	0.453374i
$591$		0			0
$592$	35.5990	−	18.4094i	1.46311	−	0.756624i
$593$	26.4172	+	26.4172i	1.08482	+	1.08482i	0.996052	+	0.0887706i	$0.0282938\pi$
$593$	26.4172	+	26.4172i	1.08482	+	1.08482i	0.0887706	+	0.996052i	$0.471706\pi$
$594$		0			0
$595$	−0.630180	−	0.604589i	−0.0258349	−	0.0247857i
$596$	−1.17182	−	0.713246i	−0.0479994	−	0.0292157i
$597$		0			0
$598$	5.47303	−	0.656131i	0.223809	−	0.0268312i
$599$			17.4693i			0.713775i	0.934147	+	0.356888i	$0.116162\pi$
$599$			17.4693i			0.713775i	−0.934147	+	0.356888i	$0.883838\pi$
$600$		0			0
$601$			25.8843i			1.05584i	0.849294	+	0.527921i	$0.177028\pi$
$601$			25.8843i			1.05584i	−0.849294	+	0.527921i	$0.822972\pi$
$602$	−0.142906	−	1.19203i	−0.00582441	−	0.0485835i
$603$		0			0
$604$	−3.06008	−	12.5792i	−0.124513	−	0.511839i
$605$	−15.9361	−	15.2890i	−0.647896	−	0.621585i
$606$		0			0
$607$	22.7204	+	22.7204i	0.922193	+	0.922193i	0.997184	−	0.0749912i	$-0.0238929\pi$
$607$	22.7204	+	22.7204i	0.922193	+	0.922193i	−0.0749912	+	0.997184i	$0.523893\pi$
$608$	19.1227	+	28.1580i	0.775526	+	1.14196i
$609$		0			0
$610$	17.8759	+	13.4589i	0.723775	+	0.544937i
$611$	−28.1243	−	28.1243i	−1.13779	−	1.13779i
$612$		0			0
$613$		−	0.840532i		−	0.0339488i	−0.999856	−	0.0169744i	$-0.994597\pi$
$613$		−	0.840532i		−	0.0339488i	0.999856	−	0.0169744i	$-0.00540337\pi$
$614$	−12.3666	+	15.7357i	−0.499077	+	0.635040i
$615$		0			0
$616$	−0.252927	+	0.555223i	−0.0101907	+	0.0223706i
$617$	7.18912	+	7.18912i	0.289423	+	0.289423i	0.836852	−	0.547429i	$-0.184393\pi$
$617$	7.18912	+	7.18912i	0.289423	+	0.289423i	−0.547429	+	0.836852i	$0.684393\pi$
$618$		0			0
$619$	31.9741	+	31.9741i	1.28515	+	1.28515i	0.937700	+	0.347447i	$0.112951\pi$
$619$	31.9741	+	31.9741i	1.28515	+	1.28515i	0.347447	+	0.937700i	$0.387049\pi$
$620$	−14.8411	+	25.5609i	−0.596033	+	1.02655i
$621$		0			0
$622$	6.24953	−	7.95208i	0.250583	−	0.318849i
$623$	0.828834	−	0.828834i	0.0332065	−	0.0332065i
$624$		0			0
$625$	−24.9142	+	2.06992i	−0.996566	+	0.0827970i
$626$	1.42366	+	11.8753i	0.0569010	+	0.474632i
$627$		0			0
$628$	22.8269	−	5.55298i	0.910891	−	0.221588i
$629$	13.5971	−	13.5971i	0.542153	−	0.542153i
$630$		0			0
$631$	28.2004			1.12264			0.561320	−	0.827599i	$-0.310294\pi$
$631$	28.2004			1.12264			0.561320	+	0.827599i	$0.310294\pi$
$632$	−25.6251	−	11.6733i	−1.01931	−	0.464339i
$633$		0			0
$634$	−8.63959	−	6.78984i	−0.343122	−	0.269659i
$635$	−15.6361	+	0.324072i	−0.620498	+	0.0128604i
$636$		0			0
$637$			22.9029i			0.907446i
$638$	−3.63473	+	4.62494i	−0.143900	+	0.183103i
$639$		0			0
$640$	16.5834	−	19.1047i	0.655518	−	0.755180i
$641$	−36.6103			−1.44602			−0.723011	−	0.690837i	$-0.757242\pi$
$641$	−36.6103			−1.44602			−0.723011	+	0.690837i	$0.757242\pi$
$642$		0			0
$643$			13.4647i			0.530996i	0.964111	+	0.265498i	$0.0855364\pi$
$643$			13.4647i			0.530996i	−0.964111	+	0.265498i	$0.914464\pi$
$644$	0.113926	+	0.468321i	0.00448932	+	0.0184544i
$645$		0			0
$646$	12.8404	+	10.0913i	0.505199	+	0.397035i
$647$	−23.4382	+	23.4382i	−0.921451	+	0.921451i	−0.997132	−	0.0756812i	$-0.975887\pi$
$647$	−23.4382	+	23.4382i	−0.921451	+	0.921451i	0.0756812	+	0.997132i	$0.475887\pi$
$648$		0			0
$649$	−4.62075			−0.181380
$650$	18.8786	+	13.6102i	0.740479	+	0.533835i
$651$		0			0
$652$	3.63680	−	0.884706i	0.142428	−	0.0346477i
$653$	−15.0338			−0.588318			−0.294159	−	0.955756i	$-0.595040\pi$
$653$	−15.0338			−0.588318			−0.294159	+	0.955756i	$0.595040\pi$
$654$		0			0
$655$	−40.2514	+	0.834247i	−1.57275	+	0.0325967i
$656$	3.17148	+	6.13282i	0.123826	+	0.239446i
$657$		0			0
$658$	2.14895	−	2.73438i	0.0837746	−	0.106597i
$659$	−12.8233	+	12.8233i	−0.499524	+	0.499524i	−0.911290	−	0.411766i	$-0.864912\pi$
$659$	−12.8233	+	12.8233i	−0.499524	+	0.499524i	0.411766	+	0.911290i	$0.364912\pi$
$660$		0			0
$661$	22.6599	+	22.6599i	0.881369	+	0.881369i	0.993674	−	0.112305i	$-0.0358232\pi$
$661$	22.6599	+	22.6599i	0.881369	+	0.881369i	−0.112305	+	0.993674i	$0.535823\pi$
$662$	−0.178880	−	1.49211i	−0.00695238	−	0.0579923i
$663$		0			0
$664$	−11.7411	+	25.7740i	−0.455644	+	1.00022i
$665$	−1.97572	−	1.89548i	−0.0766150	−	0.0735036i
$666$		0			0
$667$			4.64687i			0.179928i
$668$	11.5946	+	7.05727i	0.448610	+	0.273054i
$669$		0			0
$670$	1.88360	+	13.3626i	0.0727697	+	0.516241i
$671$		−	7.50063i		−	0.289559i
$672$		0			0
$673$	18.5901	+	18.5901i	0.716595	+	0.716595i	0.967906	−	0.251311i	$-0.0808617\pi$
$673$	18.5901	+	18.5901i	0.716595	+	0.716595i	−0.251311	+	0.967906i	$0.580862\pi$
$674$	−0.0903249	−	0.753433i	−0.00347918	−	0.0290211i
$675$		0			0
$676$	1.02455	+	4.21166i	0.0394058	+	0.161987i
$677$	−1.52496			−0.0586089			−0.0293044	−	0.999571i	$-0.509329\pi$
$677$	−1.52496			−0.0586089			−0.0293044	+	0.999571i	$0.509329\pi$
$678$		0			0
$679$		−	3.38635i		−	0.129956i
$680$	4.80195	−	11.1479i	0.184146	−	0.427503i
$681$		0			0
$682$	9.83728	−	1.17934i	0.376689	−	0.0451591i
$683$	−3.77382			−0.144401			−0.0722006	−	0.997390i	$-0.523002\pi$
$683$	−3.77382			−0.144401			−0.0722006	+	0.997390i	$0.523002\pi$
$684$		0			0
$685$	19.1603	−	0.397115i	0.732078	−	0.0151730i
$686$	−3.98854	+	0.478164i	−0.152283	+	0.0182564i
$687$		0			0
$688$	14.8222	−	7.66505i	0.565091	−	0.292227i
$689$			16.6384i			0.633873i
$690$		0			0
$691$	−15.9624	−	15.9624i	−0.607239	−	0.607239i	0.334984	−	0.942224i	$-0.391269\pi$
$691$	−15.9624	−	15.9624i	−0.607239	−	0.607239i	−0.942224	+	0.334984i	$0.891269\pi$
$692$	6.07222	+	24.9613i	0.230831	+	0.948887i
$693$		0			0
$694$	−18.6197	−	14.6332i	−0.706795	−	0.555469i
$695$	32.7361	−	0.678486i	1.24175	−	0.0257364i
$696$		0			0
$697$	2.34244	+	2.34244i	0.0887263	+	0.0887263i
$698$	41.7052	−	4.99980i	1.57856	−	0.189245i
$699$		0			0
$700$	−0.985104	+	1.78063i	−0.0372334	+	0.0673015i
$701$	20.1411	−	20.1411i	0.760717	−	0.760717i	−0.215735	−	0.976452i	$-0.569215\pi$
$701$	20.1411	−	20.1411i	0.760717	−	0.760717i	0.976452	+	0.215735i	$0.0692146\pi$
$702$		0			0
$703$	42.6292	−	42.6292i	1.60779	−	1.60779i
$704$	−8.45966	−	0.588964i	−0.318835	−	0.0221974i
$705$		0			0
$706$	−17.9303	+	2.14956i	−0.674814	+	0.0808997i
$707$	0.372149			0.0139961
$708$		0			0
$709$	−8.20276	+	8.20276i	−0.308061	+	0.308061i	−0.844157	−	0.536096i	$-0.819899\pi$
$709$	−8.20276	+	8.20276i	−0.308061	+	0.308061i	0.536096	+	0.844157i	$0.319899\pi$
$710$	5.83127	+	41.3681i	0.218844	+	1.55252i
$711$		0			0
$712$	14.8260	+	6.75387i	0.555628	+	0.253112i
$713$	5.53443	−	5.53443i	0.207266	−	0.207266i
$714$		0			0
$715$	−0.161655	−	7.79963i	−0.00604554	−	0.291690i
$716$	8.40286	+	5.11455i	0.314030	+	0.191140i
$717$		0			0
$718$	−13.6378	−	10.7179i	−0.508959	−	0.399990i
$719$	−23.6655			−0.882576			−0.441288	−	0.897366i	$-0.645478\pi$
$719$	−23.6655			−0.882576			−0.441288	+	0.897366i	$0.645478\pi$
$720$		0			0
$721$	−3.24890			−0.120995
$722$	19.1302	+	15.0344i	0.711952	+	0.559522i
$723$		0			0
$724$	23.9977	−	39.4267i	0.891869	−	1.46528i
$725$	−13.2864	+	14.4360i	−0.493444	+	0.536140i
$726$		0			0
$727$	−1.68416	+	1.68416i	−0.0624622	+	0.0624622i	−0.737648	−	0.675186i	$-0.764064\pi$
$727$	−1.68416	+	1.68416i	−0.0624622	+	0.0624622i	0.675186	+	0.737648i	$0.264064\pi$
$728$	1.77433	−	0.663703i	0.0657610	−	0.0245985i
$729$		0			0
$730$	−41.7610	−	31.4422i	−1.54564	−	1.16373i
$731$	5.66137	−	5.66137i	0.209393	−	0.209393i
$732$		0			0
$733$	−48.4131			−1.78818			−0.894089	−	0.447889i	$-0.852176\pi$
$733$	−48.4131			−1.78818			−0.894089	+	0.447889i	$0.852176\pi$
$734$	−2.49185	+	0.298734i	−0.0919759	+	0.0110265i
$735$		0			0
$736$	−5.54193	+	3.76364i	−0.204278	+	0.138730i
$737$	3.19860	−	3.19860i	0.117822	−	0.117822i
$738$		0			0
$739$	−2.35313	+	2.35313i	−0.0865612	+	0.0865612i	−0.749062	−	0.662500i	$-0.769495\pi$
$739$	−2.35313	+	2.35313i	−0.0865612	+	0.0865612i	0.662500	+	0.749062i	$0.269495\pi$
$740$	−38.7499	−	22.4988i	−1.42447	−	0.827073i
$741$		0			0
$742$	−1.44449	+	0.173172i	−0.0530290	+	0.00635735i
$743$	−17.6788	−	17.6788i	−0.648571	−	0.648571i	0.304076	−	0.952648i	$-0.401652\pi$
$743$	−17.6788	−	17.6788i	−0.648571	−	0.648571i	−0.952648	+	0.304076i	$0.901652\pi$
$744$		0			0
$745$	0.0317812	+	1.53340i	0.00116437	+	0.0561796i
$746$	−9.18150	−	7.21573i	−0.336159	−	0.264187i
$747$		0			0
$748$	−3.95349	+	0.961746i	−0.144554	+	0.0351649i
$749$	0.200661	+	0.200661i	0.00733198	+	0.00733198i
$750$		0			0
$751$			40.8647i			1.49117i	0.666409	+	0.745587i	$0.267831\pi$
$751$			40.8647i			1.49117i	−0.666409	+	0.745587i	$0.732169\pi$
$752$	46.0612	+	14.6602i	1.67968	+	0.534601i
$753$		0			0
$754$	18.1345	−	2.17404i	0.660418	−	0.0791738i
$755$	−10.0205	+	10.4446i	−0.364682	+	0.380119i
$756$		0			0
$757$	−24.6892			−0.897345			−0.448673	−	0.893696i	$-0.648103\pi$
$757$	−24.6892			−0.897345			−0.448673	+	0.893696i	$0.648103\pi$
$758$	2.04589	−	0.245270i	0.0743101	−	0.00890862i
$759$		0			0
$760$	15.0549	−	34.9505i	0.546098	−	1.26779i
$761$			6.54343i			0.237199i	0.992942	+	0.118600i	$0.0378405\pi$
$761$			6.54343i			0.237199i	−0.992942	+	0.118600i	$0.962160\pi$
$762$		0			0
$763$	1.31037			0.0474385
$764$	41.8754	−	10.1868i	1.51500	−	0.368546i
$765$		0			0
$766$	2.93710	+	24.4994i	0.106122	+	0.885200i
$767$	10.1450	+	10.1450i	0.366316	+	0.366316i
$768$		0			0
$769$			26.2710i			0.947357i	0.880698	+	0.473678i	$0.157074\pi$
$769$			26.2710i			0.947357i	−0.880698	+	0.473678i	$0.842926\pi$
$770$	0.675456	−	0.0952127i	0.0243417	−	0.00343123i
$771$		0			0
$772$	16.6413	−	27.3405i	0.598933	−	0.984007i
$773$			9.19242i			0.330628i	0.986241	+	0.165314i	$0.0528638\pi$
$773$			9.19242i			0.330628i	−0.986241	+	0.165314i	$0.947136\pi$
$774$		0			0
$775$	33.0174	−	1.36922i	1.18602	−	0.0491839i
$776$	44.0842	−	16.4901i	1.58253	−	0.591959i
$777$		0			0
$778$	−3.05565	−	25.4883i	−0.109550	−	0.913800i
$779$	7.34393	+	7.34393i	0.263124	+	0.263124i
$780$		0			0
$781$	9.90228	−	9.90228i	0.354332	−	0.354332i
$782$	−1.98612	+	2.52719i	−0.0710235	+	0.0903723i
$783$		0			0
$784$	−12.7856	−	24.7241i	−0.456630	−	0.883002i
$785$	−18.9534	−	18.1837i	−0.676475	−	0.649003i
$786$		0			0
$787$	−20.9534			−0.746908			−0.373454	−	0.927649i	$-0.621827\pi$
$787$	−20.9534			−0.746908			−0.373454	+	0.927649i	$0.621827\pi$
$788$	−11.0201	−	45.3007i	−0.392574	−	1.61377i
$789$		0			0
$790$	4.39432	+	31.1741i	0.156343	+	1.10913i
$791$	3.29520			0.117164
$792$		0			0
$793$	−16.4680	+	16.4680i	−0.584794	+	0.584794i
$794$	16.0043	+	12.5778i	0.567972	+	0.446368i
$795$		0			0
$796$	−4.17799	+	1.01636i	−0.148085	+	0.0360239i
$797$		−	25.5883i		−	0.906384i	−0.891413	−	0.453192i	$-0.850285\pi$
$797$		−	25.5883i		−	0.906384i	0.891413	−	0.453192i	$-0.149715\pi$
$798$		0			0
$799$	23.1926			0.820497
$800$	−27.9777	−	4.15338i	−0.989160	−	0.146844i
$801$		0			0
$802$	−32.7060	+	41.6161i	−1.15489	+	1.46952i
$803$			17.5227i			0.618362i
$804$		0			0
$805$	0.373061	−	0.388852i	0.0131487	−	0.0137052i
$806$	−24.1874	−	19.0089i	−0.851966	−	0.669559i
$807$		0			0
$808$	1.81221	+	4.84472i	0.0637532	+	0.170437i
$809$	−4.93002			−0.173330			−0.0866652	−	0.996237i	$-0.527621\pi$
$809$	−4.93002			−0.173330			−0.0866652	+	0.996237i	$0.527621\pi$
$810$		0			0
$811$	35.3133	−	35.3133i	1.24002	−	1.24002i	0.280025	−	0.959993i	$-0.409657\pi$
$811$	35.3133	−	35.3133i	1.24002	−	1.24002i	0.959993	−	0.280025i	$-0.0903426\pi$
$812$	0.377486	+	1.55175i	0.0132472	+	0.0544557i
$813$		0			0
$814$	1.78785	+	14.9131i	0.0626642	+	0.522705i
$815$	−3.01967	−	2.89704i	−0.105774	−	0.101479i
$816$		0			0
$817$	17.7493	−	17.7493i	0.620970	−	0.620970i
$818$	7.15835	−	9.10849i	0.250286	−	0.318471i
$819$		0			0
$820$	3.87598	−	6.67563i	0.135355	−	0.233123i
$821$	−36.2490	−	36.2490i	−1.26510	−	1.26510i	−0.948589	−	0.316509i	$-0.897489\pi$
$821$	−36.2490	−	36.2490i	−1.26510	−	1.26510i	−0.316509	−	0.948589i	$-0.602511\pi$
$822$		0			0
$823$	23.0235	+	23.0235i	0.802548	+	0.802548i	0.983493	−	0.180945i	$-0.0579156\pi$
$823$	23.0235	+	23.0235i	0.802548	+	0.802548i	−0.180945	+	0.983493i	$0.557916\pi$
$824$	−15.8208	−	42.2949i	−0.551142	−	1.47341i
$825$		0			0
$826$	−0.775170	+	0.986349i	−0.0269716	+	0.0343195i
$827$			44.8863i			1.56085i	0.625250	+	0.780424i	$0.284997\pi$
$827$			44.8863i			1.56085i	−0.625250	+	0.780424i	$0.715003\pi$
$828$		0			0
$829$	−7.27338	−	7.27338i	−0.252615	−	0.252615i	0.569427	−	0.822042i	$-0.307165\pi$
$829$	−7.27338	−	7.27338i	−0.252615	−	0.252615i	−0.822042	+	0.569427i	$0.807165\pi$
$830$	31.3553	−	4.41986i	1.08836	−	0.153416i
$831$		0			0
$832$	17.2804	+	19.8666i	0.599091	+	0.688751i
$833$	−9.44340	−	9.44340i	−0.327195	−	0.327195i
$834$		0			0
$835$	−0.314462	−	15.1724i	−0.0108824	−	0.525063i
$836$	−12.3948	+	3.01523i	−0.428684	+	0.104284i
$837$		0			0
$838$	−5.28939	−	44.1208i	−0.182719	−	1.52413i
$839$			6.23853i			0.215378i	0.994185	+	0.107689i	$0.0343451\pi$
$839$			6.23853i			0.215378i	−0.994185	+	0.107689i	$0.965655\pi$
$840$		0			0
$841$		−	13.6029i		−	0.469067i
$842$	5.46283	−	0.654909i	0.188262	−	0.0225696i
$843$		0			0
$844$	9.22452	−	15.1553i	0.317521	−	0.521666i
$845$	3.35497	−	3.49699i	0.115415	−	0.120300i
$846$		0			0
$847$	1.42115	+	1.42115i	0.0488312	+	0.0488312i
$848$	−9.28845	−	17.9614i	−0.318967	−	0.616798i
$849$		0			0
$850$	−13.3959	+	2.17228i	−0.459475	+	0.0745085i
$851$	8.39009	+	8.39009i	0.287609	+	0.287609i
$852$		0			0
$853$			32.1759i			1.10168i	0.834610	+	0.550841i	$0.185693\pi$
$853$			32.1759i			1.10168i	−0.834610	+	0.550841i	$0.814307\pi$
$854$	−1.60109	−	1.25830i	−0.0547882	−	0.0430580i
$855$		0			0
$856$	−1.63511	+	3.58937i	−0.0558869	+	0.122682i
$857$	−11.0467	−	11.0467i	−0.377348	−	0.377348i	0.492797	−	0.870145i	$-0.335975\pi$
$857$	−11.0467	−	11.0467i	−0.377348	−	0.377348i	−0.870145	+	0.492797i	$0.835975\pi$
$858$		0			0
$859$	1.75107	+	1.75107i	0.0597457	+	0.0597457i	0.736348	−	0.676603i	$-0.236548\pi$
$859$	1.75107	+	1.75107i	0.0597457	+	0.0597457i	−0.676603	+	0.736348i	$0.736548\pi$
$860$	−16.1341	−	9.36773i	−0.550168	−	0.319437i
$861$		0			0
$862$	−5.92399	−	4.65566i	−0.201772	−	0.158572i
$863$	−4.70982	+	4.70982i	−0.160324	+	0.160324i	−0.782710	−	0.622386i	$-0.786163\pi$
$863$	−4.70982	+	4.70982i	−0.160324	+	0.160324i	0.622386	+	0.782710i	$0.286163\pi$
$864$		0			0
$865$	19.8840	−	20.7256i	0.676075	−	0.704693i
$866$	6.72913	−	0.806718i	0.228665	−	0.0274134i
$867$		0			0
$868$	1.39855	−	2.29772i	0.0474697	−	0.0779896i
$869$	7.46216	−	7.46216i	0.253136	−	0.253136i
$870$		0			0
$871$	−14.0453			−0.475908
$872$	6.38093	+	17.0587i	0.216086	+	0.577679i
$873$		0			0
$874$	−6.22680	+	7.92316i	−0.210625	+	0.268005i
$875$	2.27076	−	0.141353i	0.0767658	−	0.00477860i
$876$		0			0
$877$			16.7655i			0.566130i	0.959101	+	0.283065i	$0.0913512\pi$
$877$			16.7655i			0.566130i	−0.959101	+	0.283065i	$0.908649\pi$
$878$	6.66932	+	5.24141i	0.225079	+	0.176889i
$879$		0			0
$880$	4.52868	+	8.32958i	0.152662	+	0.280790i
$881$	−50.5390			−1.70270			−0.851352	−	0.524595i	$-0.824217\pi$
$881$	−50.5390			−1.70270			−0.851352	+	0.524595i	$0.824217\pi$
$882$		0			0
$883$		−	27.3039i		−	0.918848i	−0.888217	−	0.459424i	$-0.848056\pi$
$883$		−	27.3039i		−	0.918848i	0.888217	−	0.459424i	$-0.151944\pi$
$884$	10.7916	+	6.56850i	0.362961	+	0.220922i
$885$		0			0
$886$	−11.6567	+	14.8324i	−0.391615	+	0.498303i
$887$	2.95052	−	2.95052i	0.0990688	−	0.0990688i	−0.655835	−	0.754904i	$-0.727683\pi$
$887$	2.95052	−	2.95052i	0.0990688	−	0.0990688i	0.754904	+	0.655835i	$0.227683\pi$
$888$		0			0
$889$	1.42329			0.0477355
$890$	−2.54244	−	18.0366i	−0.0852229	−	0.604587i
$891$		0			0
$892$	−12.0806	−	7.35304i	−0.404487	−	0.246198i
$893$	72.7126			2.43324
$894$		0			0
$895$	−0.227897	−	10.9957i	−0.00761776	−	0.367547i
$896$	−1.54490	+	1.70700i	−0.0516115	+	0.0570269i
$897$		0			0
$898$	33.0464	+	25.9711i	1.10277	+	0.866668i
$899$	18.3379	−	18.3379i	0.611603	−	0.611603i
$900$		0			0
$901$	−6.86040	−	6.86040i	−0.228553	−	0.228553i
$902$	−2.56916	+	0.308002i	−0.0855436	+	0.0102553i
$903$		0			0
$904$	16.0462	+	42.8976i	0.533689	+	1.42675i
$905$	−51.5926	+	1.06931i	−1.71500	+	0.0355449i
$906$		0			0
$907$			0.0410041i			0.00136152i	1.00000		0.000680760i	$0.000216693\pi$
$907$			0.0410041i			0.00136152i	−1.00000		0.000680760i	$0.999783\pi$
$908$	−10.6665	−	43.8472i	−0.353980	−	1.45512i
$909$		0			0
$910$	−1.69204	−	1.27395i	−0.0560904	−	0.0422310i
$911$			21.7776i			0.721525i	0.932658	+	0.360763i	$0.117484\pi$
$911$			21.7776i			0.721525i	−0.932658	+	0.360763i	$0.882516\pi$
$912$		0			0
$913$	−7.50552	−	7.50552i	−0.248397	−	0.248397i
$914$	−27.4918	+	3.29584i	−0.909349	+	0.109017i
$915$		0			0
$916$	−16.5191	−	10.0547i	−0.545808	−	0.332216i
$917$	3.66392			0.120993
$918$		0			0
$919$			34.4842i			1.13753i	0.822500	+	0.568765i	$0.192579\pi$
$919$			34.4842i			1.13753i	−0.822500	+	0.568765i	$0.807421\pi$
$920$	6.87880	+	2.96304i	0.226787	+	0.0976885i
$921$		0			0
$922$	−5.68417	−	47.4138i	−0.187198	−	1.56149i
$923$	−43.4818			−1.43122
$924$		0			0
$925$	2.07571	+	50.0538i	0.0682490	+	1.64576i
$926$	2.51754	+	20.9997i	0.0827314	+	0.690093i
$927$		0			0
$928$	−18.3628	+	12.4705i	−0.602788	+	0.409365i
$929$			19.8125i			0.650028i	0.945709	+	0.325014i	$0.105369\pi$
$929$			19.8125i			0.650028i	−0.945709	+	0.325014i	$0.894631\pi$
$930$		0			0
$931$	−29.6066	−	29.6066i	−0.970316	−	0.970316i
$932$	−7.51140	−	4.57194i	−0.246044	−	0.149759i
$933$		0			0
$934$	26.2299	−	33.3756i	0.858267	−	1.09208i
$935$	3.28262	+	3.14931i	0.107353	+	0.102994i
$936$		0			0
$937$	−20.7731	−	20.7731i	−0.678628	−	0.678628i	0.281062	−	0.959690i	$-0.409313\pi$
$937$	−20.7731	−	20.7731i	−0.678628	−	0.678628i	−0.959690	+	0.281062i	$0.909313\pi$
$938$	−0.146183	−	1.21937i	−0.00477306	−	0.0398138i
$939$		0			0
$940$	−13.8597	−	52.2360i	−0.452054	−	1.70375i
$941$	24.6412	−	24.6412i	0.803279	−	0.803279i	−0.180328	−	0.983607i	$-0.557716\pi$
$941$	24.6412	−	24.6412i	0.803279	−	0.803279i	0.983607	+	0.180328i	$0.0577158\pi$
$942$		0			0
$943$	−1.44540	+	1.44540i	−0.0470687	+	0.0470687i
$944$	−16.6152	−	5.28823i	−0.540780	−	0.172117i
$945$		0			0
$946$	0.744400	+	6.20931i	0.0242025	+	0.201882i
$947$	46.1706			1.50034			0.750171	−	0.661244i	$-0.229971\pi$
$947$	46.1706			1.50034			0.750171	+	0.661244i	$0.229971\pi$
$948$		0			0
$949$	38.4718	−	38.4718i	1.24885	−	1.24885i
$950$	−41.9982	+	6.81044i	−1.36260	+	0.220960i
$951$		0			0
$952$	−0.457937	+	1.00526i	−0.0148418	+	0.0325806i
$953$	5.45044	−	5.45044i	0.176557	−	0.176557i	−0.613296	−	0.789853i	$-0.710157\pi$
$953$	5.45044	−	5.45044i	0.176557	−	0.176557i	0.789853	+	0.613296i	$0.210157\pi$
$954$		0			0
$955$	−34.7696	−	33.3576i	−1.12512	−	1.07943i
$956$	−5.23191	−	21.5070i	−0.169212	−	0.695588i
$957$		0			0
$958$	−19.1508	+	24.3680i	−0.618733	+	0.787294i
$959$	−1.74408			−0.0563194
$960$		0			0
$961$	−12.6809			−0.409062
$962$	28.8171	−	36.6677i	0.929101	−	1.18221i
$963$		0			0
$964$	11.0973	+	45.6182i	0.357420	+	1.46926i
$965$	−35.7770	+	0.741512i	−1.15170	+	0.0238701i
$966$		0			0
$967$	−18.1852	+	18.1852i	−0.584798	+	0.584798i	−0.936218	−	0.351420i	$-0.885699\pi$
$967$	−18.1852	+	18.1852i	−0.584798	+	0.584798i	0.351420	+	0.936218i	$0.385699\pi$
$968$	−11.5804	+	25.4211i	−0.372208	+	0.817067i
$969$		0			0
$970$	−42.0396	−	31.6520i	−1.34981	−	1.01628i
$971$	11.6265	−	11.6265i	0.373112	−	0.373112i	−0.495497	−	0.868609i	$-0.665014\pi$
$971$	11.6265	−	11.6265i	0.373112	−	0.373112i	0.868609	+	0.495497i	$0.165014\pi$
$972$		0			0
$973$	−2.97983			−0.0955290
$974$	−1.34830	−	11.2467i	−0.0432023	−	0.360366i
$975$		0			0
$976$	8.58413	−	26.9707i	0.274771	−	0.863311i
$977$	8.35835	−	8.35835i	0.267407	−	0.267407i	−0.560647	−	0.828055i	$-0.689448\pi$
$977$	8.35835	−	8.35835i	0.267407	−	0.267407i	0.828055	+	0.560647i	$0.189448\pi$
$978$		0			0
$979$	−4.31741	+	4.31741i	−0.137985	+	0.137985i
$980$	−15.6258	+	26.9124i	−0.499147	+	0.859684i
$981$		0			0
$982$	6.06453	+	50.5865i	0.193527	+	1.61428i
$983$	18.1290	+	18.1290i	0.578226	+	0.578226i	0.934414	−	0.356188i	$-0.115924\pi$
$983$	18.1290	+	18.1290i	0.578226	+	0.578226i	−0.356188	+	0.934414i	$0.615924\pi$
$984$		0			0
$985$	−36.0861	+	37.6136i	−1.14980	+	1.19847i
$986$	−6.58085	+	8.37367i	−0.209577	+	0.266672i
$987$		0			0
$988$	33.8334	+	20.5933i	1.07638	+	0.655160i
$989$	3.49334	+	3.49334i	0.111082	+	0.111082i
$990$		0			0
$991$			28.8183i			0.915444i	0.889095	+	0.457722i	$0.151334\pi$
$991$			28.8183i			0.915444i	−0.889095	+	0.457722i	$0.848666\pi$
$992$	36.7225	+	7.01766i	1.16594	+	0.222811i
$993$		0			0
$994$	−0.452557	−	3.77494i	−0.0143542	−	0.119734i
$995$	3.46903	+	3.32815i	0.109975	+	0.105509i
$996$		0			0
$997$	−30.7058			−0.972463			−0.486232	−	0.873830i	$-0.661629\pi$
$997$	−30.7058			−0.972463			−0.486232	+	0.873830i	$0.661629\pi$
$998$	−4.48057	−	37.3741i	−0.141830	−	1.18306i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.bd.f.523.4		16
3.2	odd	2		240.2.bc.e.43.5	yes	16
5.2	odd	4		720.2.z.f.667.2		16
12.11	even	2		960.2.bc.e.463.8		16
15.2	even	4		240.2.y.e.187.7	yes	16
16.3	odd	4		720.2.z.f.163.2		16
24.5	odd	2		1920.2.bc.i.1183.1		16
24.11	even	2		1920.2.bc.j.1183.1		16
48.5	odd	4		1920.2.y.j.223.5		16
48.11	even	4		1920.2.y.i.223.5		16
48.29	odd	4		960.2.y.e.943.4		16
48.35	even	4		240.2.y.e.163.7	✓	16
60.47	odd	4		960.2.y.e.847.4		16
80.67	even	4	inner	720.2.bd.f.307.4		16
120.77	even	4		1920.2.y.i.1567.5		16
120.107	odd	4		1920.2.y.j.1567.5		16
240.77	even	4		960.2.bc.e.367.8		16
240.107	odd	4		1920.2.bc.i.607.1		16
240.197	even	4		1920.2.bc.j.607.1		16
240.227	odd	4		240.2.bc.e.67.5	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.e.163.7	✓	16	48.35	even	4
240.2.y.e.187.7	yes	16	15.2	even	4
240.2.bc.e.43.5	yes	16	3.2	odd	2
240.2.bc.e.67.5	yes	16	240.227	odd	4
720.2.z.f.163.2		16	16.3	odd	4
720.2.z.f.667.2		16	5.2	odd	4
720.2.bd.f.307.4		16	80.67	even	4	inner
720.2.bd.f.523.4		16	1.1	even	1	trivial
960.2.y.e.847.4		16	60.47	odd	4
960.2.y.e.943.4		16	48.29	odd	4
960.2.bc.e.367.8		16	240.77	even	4
960.2.bc.e.463.8		16	12.11	even	2
1920.2.y.i.223.5		16	48.11	even	4
1920.2.y.i.1567.5		16	120.77	even	4
1920.2.y.j.223.5		16	48.5	odd	4
1920.2.y.j.1567.5		16	120.107	odd	4
1920.2.bc.i.607.1		16	240.107	odd	4
1920.2.bc.i.1183.1		16	24.5	odd	2
1920.2.bc.j.607.1		16	240.197	even	4
1920.2.bc.j.1183.1		16	24.11	even	2

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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.bd (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.873858 + 1.11192i) q^{2} +(-0.472743 - 1.94333i) q^{4} +(-1.54804 + 1.61356i) q^{5} +(0.143894 - 0.143894i) q^{7} +(2.57394 + 1.17254i) q^{8} +(-0.441393 - 3.13132i) q^{10} +(-0.749545 + 0.749545i) q^{11} +3.29132 q^{13} +(0.0342559 + 0.285741i) q^{14} +(-3.55303 + 1.83739i) q^{16} +(-1.35709 + 1.35709i) q^{17} +(-4.25468 + 4.25468i) q^{19} +(3.86750 + 2.24554i) q^{20} +(-0.178440 - 1.48843i) q^{22} +(-0.837388 - 0.837388i) q^{23} +(-0.207170 - 4.99571i) q^{25} +(-2.87614 + 3.65969i) q^{26} +(-0.347657 - 0.211607i) q^{28} +(-2.77462 - 2.77462i) q^{29} +6.60915i q^{31} +(1.06181 - 5.55631i) q^{32} +(-0.323074 - 2.69488i) q^{34} +(0.00942893 + 0.454934i) q^{35} -10.0194 q^{37} +(-1.01289 - 8.44886i) q^{38} +(-5.87651 + 2.33808i) q^{40} -1.72608i q^{41} -4.17171 q^{43} +(1.81095 + 1.10227i) q^{44} +(1.66287 - 0.199352i) q^{46} +(-8.54502 - 8.54502i) q^{47} +6.95859i q^{49} +(5.73588 + 4.13518i) q^{50} +(-1.55595 - 6.39610i) q^{52} +5.05524i q^{53} +(-0.0491155 - 2.36976i) q^{55} +(0.539094 - 0.201653i) q^{56} +(5.50979 - 0.660538i) q^{58} +(3.08237 + 3.08237i) q^{59} +(-5.00346 + 5.00346i) q^{61} +(-7.34887 - 5.77546i) q^{62} +(5.25031 + 6.03608i) q^{64} +(-5.09507 + 5.31074i) q^{65} -4.26739 q^{67} +(3.27881 + 1.99571i) q^{68} +(-0.514091 - 0.387064i) q^{70} -13.2111 q^{71} +(11.6889 - 11.6889i) q^{73} +(8.75550 - 11.1407i) q^{74} +(10.2796 + 6.25686i) q^{76} +0.215710i q^{77} -9.95558 q^{79} +(2.53547 - 8.57738i) q^{80} +(1.91927 + 1.50835i) q^{82} +10.0134i q^{83} +(-0.0889259 - 4.29056i) q^{85} +(3.64549 - 4.63862i) q^{86} +(-2.80815 + 1.05041i) q^{88} +5.76005 q^{89} +(0.473599 - 0.473599i) q^{91} +(-1.23145 + 2.02319i) q^{92} +(16.9685 - 2.03426i) q^{94} +(-0.278797 - 13.4516i) q^{95} +(11.7668 - 11.7668i) q^{97} +(-7.73741 - 6.08082i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} + 8 q^{4} + 8 q^{5} - 4 q^{7} - 8 q^{8} - 2 q^{10} - 8 q^{13} - 4 q^{14} - 8 q^{16} + 8 q^{17} - 8 q^{19} - 4 q^{20} - 32 q^{25} - 20 q^{26} + 12 q^{28} + 12 q^{29} + 28 q^{32} - 12 q^{35}+ \cdots - 62 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 + 8 * q^4 + 8 * q^5 - 4 * q^7 - 8 * q^8 - 2 * q^10 - 8 * q^13 - 4 * q^14 - 8 * q^16 + 8 * q^17 - 8 * q^19 - 4 * q^20 - 32 * q^25 - 20 * q^26 + 12 * q^28 + 12 * q^29 + 28 * q^32 - 12 * q^35 - 24 * q^37 - 16 * q^38 + 16 * q^40 + 24 * q^43 + 52 * q^44 - 16 * q^46 - 32 * q^47 - 6 * q^50 + 24 * q^52 - 4 * q^55 - 20 * q^56 + 12 * q^58 - 24 * q^59 + 40 * q^61 - 28 * q^62 + 8 * q^64 + 4 * q^65 + 16 * q^67 + 8 * q^68 + 12 * q^70 - 8 * q^73 + 64 * q^74 + 16 * q^76 + 48 * q^79 - 32 * q^82 - 8 * q^85 + 8 * q^86 + 24 * q^88 - 40 * q^91 + 16 * q^92 + 20 * q^94 + 8 * q^95 + 48 * q^97 - 62 * q^98

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