LMFDB - Embedded newform 726.2.e.a.487.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [726,2,Mod(487,726)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(726, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("726.487"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 726 = 2 \cdot 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	726.e (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,-1,-1,-1,-5,-1,-3,-1,-1,10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$5.79713918674$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 66)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			487.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	726.487
Dual form			726.2.e.a.565.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-2.92705 - 2.12663i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(-0.190983 + 0.587785i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +3.61803 q^{10} +1.00000 q^{12} +(2.61803 - 1.90211i) q^{13} +(-0.190983 - 0.587785i) q^{14} +(1.11803 - 3.44095i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(3.23607 + 2.35114i) q^{17} +(0.309017 - 0.951057i) q^{18} +(1.76393 + 5.42882i) q^{19} +(-2.92705 + 2.12663i) q^{20} -0.618034 q^{21} -5.70820 q^{23} +(-0.809017 + 0.587785i) q^{24} +(2.50000 + 7.69421i) q^{25} +(-1.00000 + 3.07768i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(0.500000 + 0.363271i) q^{28} +(-2.11803 + 6.51864i) q^{29} +(1.11803 + 3.44095i) q^{30} +(2.73607 - 1.98787i) q^{31} +1.00000 q^{32} -4.00000 q^{34} +(1.80902 - 1.31433i) q^{35} +(0.309017 + 0.951057i) q^{36} +(-2.76393 + 8.50651i) q^{37} +(-4.61803 - 3.35520i) q^{38} +(2.61803 + 1.90211i) q^{39} +(1.11803 - 3.44095i) q^{40} +(1.76393 + 5.42882i) q^{41} +(0.500000 - 0.363271i) q^{42} +4.76393 q^{43} +3.61803 q^{45} +(4.61803 - 3.35520i) q^{46} +(1.23607 + 3.80423i) q^{47} +(0.309017 - 0.951057i) q^{48} +(5.35410 + 3.88998i) q^{49} +(-6.54508 - 4.75528i) q^{50} +(-1.23607 + 3.80423i) q^{51} +(-1.00000 - 3.07768i) q^{52} +(-1.11803 + 0.812299i) q^{53} +1.00000 q^{54} -0.618034 q^{56} +(-4.61803 + 3.35520i) q^{57} +(-2.11803 - 6.51864i) q^{58} +(3.19098 - 9.82084i) q^{59} +(-2.92705 - 2.12663i) q^{60} +(-3.00000 - 2.17963i) q^{61} +(-1.04508 + 3.21644i) q^{62} +(-0.190983 - 0.587785i) q^{63} +(-0.809017 + 0.587785i) q^{64} -11.7082 q^{65} +4.94427 q^{67} +(3.23607 - 2.35114i) q^{68} +(-1.76393 - 5.42882i) q^{69} +(-0.690983 + 2.12663i) q^{70} +(-4.85410 - 3.52671i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(-4.50000 + 13.8496i) q^{73} +(-2.76393 - 8.50651i) q^{74} +(-6.54508 + 4.75528i) q^{75} +5.70820 q^{76} -3.23607 q^{78} +(-5.54508 + 4.02874i) q^{79} +(1.11803 + 3.44095i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-4.61803 - 3.35520i) q^{82} +(1.30902 + 0.951057i) q^{83} +(-0.190983 + 0.587785i) q^{84} +(-4.47214 - 13.7638i) q^{85} +(-3.85410 + 2.80017i) q^{86} -6.85410 q^{87} +6.76393 q^{89} +(-2.92705 + 2.12663i) q^{90} +(0.618034 + 1.90211i) q^{91} +(-1.76393 + 5.42882i) q^{92} +(2.73607 + 1.98787i) q^{93} +(-3.23607 - 2.35114i) q^{94} +(6.38197 - 19.6417i) q^{95} +(0.309017 + 0.951057i) q^{96} +(7.78115 - 5.65334i) q^{97} -6.61803 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - q^{3} - q^{4} - 5 q^{5} - q^{6} - 3 q^{7} - q^{8} - q^{9} + 10 q^{10} + 4 q^{12} + 6 q^{13} - 3 q^{14} - q^{16} + 4 q^{17} - q^{18} + 16 q^{19} - 5 q^{20} + 2 q^{21} + 4 q^{23} - q^{24}+ \cdots - 22 q^{98}+O(q^{100}) $ 4 * q - q^2 - q^3 - q^4 - 5 * q^5 - q^6 - 3 * q^7 - q^8 - q^9 + 10 * q^10 + 4 * q^12 + 6 * q^13 - 3 * q^14 - q^16 + 4 * q^17 - q^18 + 16 * q^19 - 5 * q^20 + 2 * q^21 + 4 * q^23 - q^24 + 10 * q^25 - 4 * q^26 - q^27 + 2 * q^28 - 4 * q^29 + 2 * q^31 + 4 * q^32 - 16 * q^34 + 5 * q^35 - q^36 - 20 * q^37 - 14 * q^38 + 6 * q^39 + 16 * q^41 + 2 * q^42 + 28 * q^43 + 10 * q^45 + 14 * q^46 - 4 * q^47 - q^48 + 8 * q^49 - 15 * q^50 + 4 * q^51 - 4 * q^52 + 4 * q^54 + 2 * q^56 - 14 * q^57 - 4 * q^58 + 15 * q^59 - 5 * q^60 - 12 * q^61 + 7 * q^62 - 3 * q^63 - q^64 - 20 * q^65 - 16 * q^67 + 4 * q^68 - 16 * q^69 - 5 * q^70 - 6 * q^71 - q^72 - 18 * q^73 - 20 * q^74 - 15 * q^75 - 4 * q^76 - 4 * q^78 - 11 * q^79 - q^81 - 14 * q^82 + 3 * q^83 - 3 * q^84 - 2 * q^86 - 14 * q^87 + 36 * q^89 - 5 * q^90 - 2 * q^91 - 16 * q^92 + 2 * q^93 - 4 * q^94 + 30 * q^95 - q^96 + 11 * q^97 - 22 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/726\mathbb{Z}\right)^\times$.

$n$	$485$	$607$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−2.92705	−	2.12663i	−1.30902	−	0.951057i	−0.309017	−	0.951057i	$-0.600000\pi$
$5$	−2.92705	−	2.12663i	−1.30902	−	0.951057i	−1.00000			$\pi$
$6$	−0.809017	−	0.587785i	−0.330280	−	0.239962i
$7$	−0.190983	+	0.587785i	−0.0721848	+	0.222162i	−0.980640	−	0.195821i	$-0.937263\pi$
$7$	−0.190983	+	0.587785i	−0.0721848	+	0.222162i	0.908455	+	0.417983i	$0.137263\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	3.61803			1.14412
$11$		0			0
$11$		0			0
$12$	1.00000			0.288675
$13$	2.61803	−	1.90211i	0.726112	−	0.527551i	−0.162219	−	0.986755i	$-0.551865\pi$
$13$	2.61803	−	1.90211i	0.726112	−	0.527551i	0.888331	+	0.459204i	$0.151865\pi$
$14$	−0.190983	−	0.587785i	−0.0510424	−	0.157092i
$15$	1.11803	−	3.44095i	0.288675	−	0.888451i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	3.23607	+	2.35114i	0.784862	+	0.570235i	0.906434	−	0.422347i	$-0.138794\pi$
$17$	3.23607	+	2.35114i	0.784862	+	0.570235i	−0.121572	+	0.992583i	$0.538794\pi$
$18$	0.309017	−	0.951057i	0.0728360	−	0.224166i
$19$	1.76393	+	5.42882i	0.404674	+	1.24546i	0.921167	+	0.389167i	$0.127237\pi$
$19$	1.76393	+	5.42882i	0.404674	+	1.24546i	−0.516494	+	0.856291i	$0.672763\pi$
$20$	−2.92705	+	2.12663i	−0.654508	+	0.475528i
$21$	−0.618034			−0.134866
$22$		0			0
$23$	−5.70820			−1.19024			−0.595121	−	0.803636i	$-0.702896\pi$
$23$	−5.70820			−1.19024			−0.595121	+	0.803636i	$0.702896\pi$
$24$	−0.809017	+	0.587785i	−0.165140	+	0.119981i
$25$	2.50000	+	7.69421i	0.500000	+	1.53884i
$26$	−1.00000	+	3.07768i	−0.196116	+	0.603583i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	0.500000	+	0.363271i	0.0944911	+	0.0686518i
$29$	−2.11803	+	6.51864i	−0.393309	+	1.21048i	0.536962	+	0.843607i	$0.319572\pi$
$29$	−2.11803	+	6.51864i	−0.393309	+	1.21048i	−0.930271	+	0.366874i	$0.880428\pi$
$30$	1.11803	+	3.44095i	0.204124	+	0.628230i
$31$	2.73607	−	1.98787i	0.491412	−	0.357032i	−0.314315	−	0.949319i	$-0.601775\pi$
$31$	2.73607	−	1.98787i	0.491412	−	0.357032i	0.805727	+	0.592287i	$0.201775\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−4.00000			−0.685994
$35$	1.80902	−	1.31433i	0.305780	−	0.222162i
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	−2.76393	+	8.50651i	−0.454388	+	1.39846i	0.417465	+	0.908693i	$0.362919\pi$
$37$	−2.76393	+	8.50651i	−0.454388	+	1.39846i	−0.871853	+	0.489768i	$0.837081\pi$
$38$	−4.61803	−	3.35520i	−0.749144	−	0.544285i
$39$	2.61803	+	1.90211i	0.419221	+	0.304582i
$40$	1.11803	−	3.44095i	0.176777	−	0.544063i
$41$	1.76393	+	5.42882i	0.275480	+	0.847840i	0.989092	+	0.147299i	$0.0470579\pi$
$41$	1.76393	+	5.42882i	0.275480	+	0.847840i	−0.713612	+	0.700541i	$0.752942\pi$
$42$	0.500000	−	0.363271i	0.0771517	−	0.0560540i
$43$	4.76393			0.726493			0.363246	−	0.931693i	$-0.381668\pi$
$43$	4.76393			0.726493			0.363246	+	0.931693i	$0.381668\pi$
$44$		0			0
$45$	3.61803			0.539345
$46$	4.61803	−	3.35520i	0.680892	−	0.494697i
$47$	1.23607	+	3.80423i	0.180299	+	0.554903i	0.999836	−	0.0181233i	$-0.00576913\pi$
$47$	1.23607	+	3.80423i	0.180299	+	0.554903i	−0.819537	+	0.573027i	$0.805769\pi$
$48$	0.309017	−	0.951057i	0.0446028	−	0.137273i
$49$	5.35410	+	3.88998i	0.764872	+	0.555712i
$50$	−6.54508	−	4.75528i	−0.925615	−	0.672499i
$51$	−1.23607	+	3.80423i	−0.173084	+	0.532698i
$52$	−1.00000	−	3.07768i	−0.138675	−	0.426798i
$53$	−1.11803	+	0.812299i	−0.153574	+	0.111578i	−0.661919	−	0.749576i	$-0.730258\pi$
$53$	−1.11803	+	0.812299i	−0.153574	+	0.111578i	0.508345	+	0.861154i	$0.330258\pi$
$54$	1.00000			0.136083
$55$		0			0
$56$	−0.618034			−0.0825883
$57$	−4.61803	+	3.35520i	−0.611674	+	0.444407i
$58$	−2.11803	−	6.51864i	−0.278111	−	0.855939i
$59$	3.19098	−	9.82084i	0.415431	−	1.27856i	−0.496435	−	0.868074i	$-0.665358\pi$
$59$	3.19098	−	9.82084i	0.415431	−	1.27856i	0.911865	−	0.410490i	$-0.134642\pi$
$60$	−2.92705	−	2.12663i	−0.377881	−	0.274546i
$61$	−3.00000	−	2.17963i	−0.384111	−	0.279073i	0.378927	−	0.925426i	$-0.376293\pi$
$61$	−3.00000	−	2.17963i	−0.384111	−	0.279073i	−0.763038	+	0.646354i	$0.776293\pi$
$62$	−1.04508	+	3.21644i	−0.132726	+	0.408488i
$63$	−0.190983	−	0.587785i	−0.0240616	−	0.0740540i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−11.7082			−1.45222
$66$		0			0
$67$	4.94427			0.604039			0.302019	−	0.953302i	$-0.402339\pi$
$67$	4.94427			0.604039			0.302019	+	0.953302i	$0.402339\pi$
$68$	3.23607	−	2.35114i	0.392431	−	0.285118i
$69$	−1.76393	−	5.42882i	−0.212352	−	0.653554i
$70$	−0.690983	+	2.12663i	−0.0825883	+	0.254181i
$71$	−4.85410	−	3.52671i	−0.576076	−	0.418544i	0.261231	−	0.965276i	$-0.415871\pi$
$71$	−4.85410	−	3.52671i	−0.576076	−	0.418544i	−0.837307	+	0.546733i	$0.815871\pi$
$72$	−0.809017	−	0.587785i	−0.0953436	−	0.0692712i
$73$	−4.50000	+	13.8496i	−0.526685	+	1.62097i	0.234274	+	0.972171i	$0.424729\pi$
$73$	−4.50000	+	13.8496i	−0.526685	+	1.62097i	−0.760959	+	0.648800i	$0.775271\pi$
$74$	−2.76393	−	8.50651i	−0.321301	−	0.988861i
$75$	−6.54508	+	4.75528i	−0.755761	+	0.549093i
$76$	5.70820			0.654776
$77$		0			0
$78$	−3.23607			−0.366413
$79$	−5.54508	+	4.02874i	−0.623871	+	0.453269i	−0.854271	−	0.519827i	$-0.825996\pi$
$79$	−5.54508	+	4.02874i	−0.623871	+	0.453269i	0.230401	+	0.973096i	$0.425996\pi$
$80$	1.11803	+	3.44095i	0.125000	+	0.384710i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−4.61803	−	3.35520i	−0.509977	−	0.370520i
$83$	1.30902	+	0.951057i	0.143683	+	0.104392i	0.657305	−	0.753625i	$-0.271696\pi$
$83$	1.30902	+	0.951057i	0.143683	+	0.104392i	−0.513621	+	0.858017i	$0.671696\pi$
$84$	−0.190983	+	0.587785i	−0.0208380	+	0.0641326i
$85$	−4.47214	−	13.7638i	−0.485071	−	1.49290i
$86$	−3.85410	+	2.80017i	−0.415599	+	0.301950i
$87$	−6.85410			−0.734837
$88$		0			0
$89$	6.76393			0.716975			0.358488	−	0.933534i	$-0.383293\pi$
$89$	6.76393			0.716975			0.358488	+	0.933534i	$0.383293\pi$
$90$	−2.92705	+	2.12663i	−0.308538	+	0.224166i
$91$	0.618034	+	1.90211i	0.0647876	+	0.199396i
$92$	−1.76393	+	5.42882i	−0.183903	+	0.565994i
$93$	2.73607	+	1.98787i	0.283717	+	0.206132i
$94$	−3.23607	−	2.35114i	−0.333775	−	0.242502i
$95$	6.38197	−	19.6417i	0.654776	−	2.01519i
$96$	0.309017	+	0.951057i	0.0315389	+	0.0970668i
$97$	7.78115	−	5.65334i	0.790056	−	0.574010i	−0.117924	−	0.993023i	$-0.537624\pi$
$97$	7.78115	−	5.65334i	0.790056	−	0.574010i	0.907980	+	0.419013i	$0.137624\pi$
$98$	−6.61803			−0.668522
$99$		0			0
$100$	8.09017			0.809017
$101$	−1.69098	+	1.22857i	−0.168259	+	0.122247i	−0.668728	−	0.743507i	$-0.733161\pi$
$101$	−1.69098	+	1.22857i	−0.168259	+	0.122247i	0.500469	+	0.865754i	$0.333161\pi$
$102$	−1.23607	−	3.80423i	−0.122389	−	0.376675i
$103$	−3.04508	+	9.37181i	−0.300041	+	0.923432i	0.681440	+	0.731874i	$0.261354\pi$
$103$	−3.04508	+	9.37181i	−0.300041	+	0.923432i	−0.981481	+	0.191558i	$0.938646\pi$
$104$	2.61803	+	1.90211i	0.256719	+	0.186518i
$105$	1.80902	+	1.31433i	0.176542	+	0.128265i
$106$	0.427051	−	1.31433i	0.0414789	−	0.127659i
$107$	−0.336881	−	1.03681i	−0.0325675	−	0.100233i	0.933451	−	0.358704i	$-0.116781\pi$
$107$	−0.336881	−	1.03681i	−0.0325675	−	0.100233i	−0.966019	+	0.258471i	$0.916781\pi$
$108$	−0.809017	+	0.587785i	−0.0778477	+	0.0565597i
$109$	2.94427			0.282010			0.141005	−	0.990009i	$-0.454967\pi$
$109$	2.94427			0.282010			0.141005	+	0.990009i	$0.454967\pi$
$110$		0			0
$111$	−8.94427			−0.848953
$112$	0.500000	−	0.363271i	0.0472456	−	0.0343259i
$113$	2.14590	+	6.60440i	0.201869	+	0.621289i	0.999827	+	0.0185766i	$0.00591346\pi$
$113$	2.14590	+	6.60440i	0.201869	+	0.621289i	−0.797958	+	0.602713i	$0.794087\pi$
$114$	1.76393	−	5.42882i	0.165207	−	0.508456i
$115$	16.7082	+	12.1392i	1.55805	+	1.13199i
$116$	5.54508	+	4.02874i	0.514848	+	0.374059i
$117$	−1.00000	+	3.07768i	−0.0924500	+	0.284532i
$118$	3.19098	+	9.82084i	0.293754	+	0.904081i
$119$	−2.00000	+	1.45309i	−0.183340	+	0.133204i
$120$	3.61803			0.330280
$121$		0			0
$122$	3.70820			0.335725
$123$	−4.61803	+	3.35520i	−0.416394	+	0.302528i
$124$	−1.04508	−	3.21644i	−0.0938514	−	0.288845i
$125$	3.45492	−	10.6331i	0.309017	−	0.951057i
$126$	0.500000	+	0.363271i	0.0445435	+	0.0323628i
$127$	3.23607	+	2.35114i	0.287155	+	0.208630i	0.722032	−	0.691860i	$-0.243208\pi$
$127$	3.23607	+	2.35114i	0.287155	+	0.208630i	−0.434877	+	0.900490i	$0.643208\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	1.47214	+	4.53077i	0.129614	+	0.398912i
$130$	9.47214	−	6.88191i	0.830761	−	0.603583i
$131$	−3.85410			−0.336734			−0.168367	−	0.985724i	$-0.553849\pi$
$131$	−3.85410			−0.336734			−0.168367	+	0.985724i	$0.553849\pi$
$132$		0			0
$133$	−3.52786			−0.305905
$134$	−4.00000	+	2.90617i	−0.345547	+	0.251055i
$135$	1.11803	+	3.44095i	0.0962250	+	0.296150i
$136$	−1.23607	+	3.80423i	−0.105992	+	0.326210i
$137$	11.4721	+	8.33499i	0.980131	+	0.712107i	0.957738	−	0.287643i	$-0.0928715\pi$
$137$	11.4721	+	8.33499i	0.980131	+	0.712107i	0.0223929	+	0.999749i	$0.492872\pi$
$138$	4.61803	+	3.35520i	0.393113	+	0.285613i
$139$	4.85410	−	14.9394i	0.411720	−	1.26714i	−0.503433	−	0.864034i	$-0.667930\pi$
$139$	4.85410	−	14.9394i	0.411720	−	1.26714i	0.915152	−	0.403108i	$-0.132070\pi$
$140$	−0.690983	−	2.12663i	−0.0583987	−	0.179733i
$141$	−3.23607	+	2.35114i	−0.272526	+	0.198002i
$142$	6.00000			0.503509
$143$		0			0
$144$	1.00000			0.0833333
$145$	20.0623	−	14.5761i	1.66608	−	1.21048i
$146$	−4.50000	−	13.8496i	−0.372423	−	1.14620i
$147$	−2.04508	+	6.29412i	−0.168676	+	0.519131i
$148$	7.23607	+	5.25731i	0.594801	+	0.432148i
$149$	4.88197	+	3.54696i	0.399946	+	0.290578i	0.769519	−	0.638624i	$-0.220496\pi$
$149$	4.88197	+	3.54696i	0.399946	+	0.290578i	−0.369573	+	0.929202i	$0.620496\pi$
$150$	2.50000	−	7.69421i	0.204124	−	0.628230i
$151$	−6.11803	−	18.8294i	−0.497879	−	1.53231i	−0.812422	−	0.583070i	$-0.801851\pi$
$151$	−6.11803	−	18.8294i	−0.497879	−	1.53231i	0.314544	−	0.949243i	$-0.398149\pi$
$152$	−4.61803	+	3.35520i	−0.374572	+	0.272143i
$153$	−4.00000			−0.323381
$154$		0			0
$155$	−12.2361			−0.982825
$156$	2.61803	−	1.90211i	0.209610	−	0.152291i
$157$	−5.56231	−	17.1190i	−0.443920	−	1.36625i	−0.883663	−	0.468123i	$-0.844931\pi$
$157$	−5.56231	−	17.1190i	−0.443920	−	1.36625i	0.439743	−	0.898124i	$-0.355069\pi$
$158$	2.11803	−	6.51864i	0.168502	−	0.518595i
$159$	−1.11803	−	0.812299i	−0.0886659	−	0.0644195i
$160$	−2.92705	−	2.12663i	−0.231404	−	0.168125i
$161$	1.09017	−	3.35520i	0.0859174	−	0.264427i
$162$	0.309017	+	0.951057i	0.0242787	+	0.0747221i
$163$	−0.381966	+	0.277515i	−0.0299179	+	0.0217366i	−0.602644	−	0.798010i	$-0.705886\pi$
$163$	−0.381966	+	0.277515i	−0.0299179	+	0.0217366i	0.572726	+	0.819747i	$0.305886\pi$
$164$	5.70820			0.445736
$165$		0			0
$166$	−1.61803			−0.125584
$167$	−5.09017	+	3.69822i	−0.393889	+	0.286177i	−0.767047	−	0.641591i	$-0.778275\pi$
$167$	−5.09017	+	3.69822i	−0.393889	+	0.286177i	0.373158	+	0.927768i	$0.378275\pi$
$168$	−0.190983	−	0.587785i	−0.0147347	−	0.0453486i
$169$	−0.781153	+	2.40414i	−0.0600887	+	0.184934i
$170$	11.7082	+	8.50651i	0.897978	+	0.652419i
$171$	−4.61803	−	3.35520i	−0.353150	−	0.256578i
$172$	1.47214	−	4.53077i	0.112249	−	0.345468i
$173$	4.42705	+	13.6251i	0.336582	+	1.03589i	0.965937	+	0.258776i	$0.0833192\pi$
$173$	4.42705	+	13.6251i	0.336582	+	1.03589i	−0.629355	+	0.777118i	$0.716681\pi$
$174$	5.54508	−	4.02874i	0.420372	−	0.305418i
$175$	−5.00000			−0.377964
$176$		0			0
$177$	10.3262			0.776168
$178$	−5.47214	+	3.97574i	−0.410154	+	0.297994i
$179$	−5.73607	−	17.6538i	−0.428734	−	1.31951i	−0.899373	−	0.437181i	$-0.855977\pi$
$179$	−5.73607	−	17.6538i	−0.428734	−	1.31951i	0.470639	−	0.882326i	$-0.344023\pi$
$180$	1.11803	−	3.44095i	0.0833333	−	0.256474i
$181$	−17.3262	−	12.5882i	−1.28785	−	0.935677i	−0.288090	−	0.957603i	$-0.593020\pi$
$181$	−17.3262	−	12.5882i	−1.28785	−	0.935677i	−0.999760	+	0.0219263i	$0.993020\pi$
$182$	−1.61803	−	1.17557i	−0.119937	−	0.0871391i
$183$	1.14590	−	3.52671i	0.0847072	−	0.260702i
$184$	−1.76393	−	5.42882i	−0.130039	−	0.400218i
$185$	26.1803	−	19.0211i	1.92482	−	1.39846i
$186$	−3.38197			−0.247978
$187$		0			0
$188$	4.00000			0.291730
$189$	0.500000	−	0.363271i	0.0363696	−	0.0264241i
$190$	6.38197	+	19.6417i	0.462996	+	1.42496i
$191$	−0.944272	+	2.90617i	−0.0683251	+	0.210283i	−0.979389	−	0.201981i	$-0.935262\pi$
$191$	−0.944272	+	2.90617i	−0.0683251	+	0.210283i	0.911064	+	0.412264i	$0.135262\pi$
$192$	−0.809017	−	0.587785i	−0.0583858	−	0.0424197i
$193$	−3.73607	−	2.71441i	−0.268928	−	0.195388i	0.445146	−	0.895458i	$-0.353152\pi$
$193$	−3.73607	−	2.71441i	−0.268928	−	0.195388i	−0.714074	+	0.700070i	$0.753152\pi$
$194$	−2.97214	+	9.14729i	−0.213387	+	0.656737i
$195$	−3.61803	−	11.1352i	−0.259093	−	0.797406i
$196$	5.35410	−	3.88998i	0.382436	−	0.277856i
$197$	25.5066			1.81727			0.908634	−	0.417593i	$-0.137126\pi$
$197$	25.5066			1.81727			0.908634	+	0.417593i	$0.137126\pi$
$198$		0			0
$199$	−0.381966			−0.0270769			−0.0135384	−	0.999908i	$-0.504310\pi$
$199$	−0.381966			−0.0270769			−0.0135384	+	0.999908i	$0.504310\pi$
$200$	−6.54508	+	4.75528i	−0.462807	+	0.336249i
$201$	1.52786	+	4.70228i	0.107767	+	0.331673i
$202$	0.645898	−	1.98787i	0.0454452	−	0.139866i
$203$	−3.42705	−	2.48990i	−0.240532	−	0.174757i
$204$	3.23607	+	2.35114i	0.226570	+	0.164613i
$205$	6.38197	−	19.6417i	0.445736	−	1.37183i
$206$	−3.04508	−	9.37181i	−0.212161	−	0.652965i
$207$	4.61803	−	3.35520i	0.320976	−	0.233202i
$208$	−3.23607			−0.224381
$209$		0			0
$210$	−2.23607			−0.154303
$211$	−7.47214	+	5.42882i	−0.514403	+	0.373736i	−0.814491	−	0.580176i	$-0.802984\pi$
$211$	−7.47214	+	5.42882i	−0.514403	+	0.373736i	0.300088	+	0.953911i	$0.402984\pi$
$212$	0.427051	+	1.31433i	0.0293300	+	0.0902684i
$213$	1.85410	−	5.70634i	0.127041	−	0.390992i
$214$	0.881966	+	0.640786i	0.0602900	+	0.0438032i
$215$	−13.9443	−	10.1311i	−0.950991	−	0.690936i
$216$	0.309017	−	0.951057i	0.0210259	−	0.0647112i
$217$	0.645898	+	1.98787i	0.0438464	+	0.134945i
$218$	−2.38197	+	1.73060i	−0.161327	+	0.117211i
$219$	−14.5623			−0.984029
$220$		0			0
$221$	12.9443			0.870726
$222$	7.23607	−	5.25731i	0.485653	−	0.352848i
$223$	−0.409830	−	1.26133i	−0.0274443	−	0.0844647i	0.936396	−	0.350945i	$-0.114139\pi$
$223$	−0.409830	−	1.26133i	−0.0274443	−	0.0844647i	−0.963840	+	0.266480i	$0.914139\pi$
$224$	−0.190983	+	0.587785i	−0.0127606	+	0.0392731i
$225$	−6.54508	−	4.75528i	−0.436339	−	0.317019i
$226$	−5.61803	−	4.08174i	−0.373706	−	0.271513i
$227$	−1.55573	+	4.78804i	−0.103257	+	0.317793i	−0.989317	−	0.145777i	$-0.953432\pi$
$227$	−1.55573	+	4.78804i	−0.103257	+	0.317793i	0.886060	+	0.463570i	$0.153432\pi$
$228$	1.76393	+	5.42882i	0.116819	+	0.359533i
$229$	4.38197	−	3.18368i	0.289568	−	0.210384i	−0.433512	−	0.901148i	$-0.642726\pi$
$229$	4.38197	−	3.18368i	0.289568	−	0.210384i	0.723080	+	0.690764i	$0.242726\pi$
$230$	−20.6525			−1.36178
$231$		0			0
$232$	−6.85410			−0.449994
$233$	−13.7082	+	9.95959i	−0.898054	+	0.652475i	−0.937966	−	0.346729i	$-0.887292\pi$
$233$	−13.7082	+	9.95959i	−0.898054	+	0.652475i	0.0399112	+	0.999203i	$0.487292\pi$
$234$	−1.00000	−	3.07768i	−0.0653720	−	0.201194i
$235$	4.47214	−	13.7638i	0.291730	−	0.897853i
$236$	−8.35410	−	6.06961i	−0.543806	−	0.395098i
$237$	−5.54508	−	4.02874i	−0.360192	−	0.261695i
$238$	0.763932	−	2.35114i	0.0495184	−	0.152402i
$239$	2.32624	+	7.15942i	0.150472	+	0.463105i	0.997674	−	0.0681660i	$-0.0217147\pi$
$239$	2.32624	+	7.15942i	0.150472	+	0.463105i	−0.847202	+	0.531271i	$0.821715\pi$
$240$	−2.92705	+	2.12663i	−0.188940	+	0.137273i
$241$	−8.61803			−0.555136			−0.277568	−	0.960706i	$-0.589528\pi$
$241$	−8.61803			−0.555136			−0.277568	+	0.960706i	$0.589528\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$	−3.00000	+	2.17963i	−0.192055	+	0.139536i
$245$	−7.39919	−	22.7724i	−0.472717	−	1.45487i
$246$	1.76393	−	5.42882i	0.112464	−	0.346129i
$247$	14.9443	+	10.8576i	0.950881	+	0.690856i
$248$	2.73607	+	1.98787i	0.173740	+	0.126230i
$249$	−0.500000	+	1.53884i	−0.0316862	+	0.0975201i
$250$	3.45492	+	10.6331i	0.218508	+	0.672499i
$251$	−12.3992	+	9.00854i	−0.782630	+	0.568614i	−0.905767	−	0.423776i	$-0.860704\pi$
$251$	−12.3992	+	9.00854i	−0.782630	+	0.568614i	0.123137	+	0.992390i	$0.460704\pi$
$252$	−0.618034			−0.0389325
$253$		0			0
$254$	−4.00000			−0.250982
$255$	11.7082	−	8.50651i	0.733196	−	0.532698i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	2.56231	−	7.88597i	0.159832	−	0.491913i	−0.838786	−	0.544461i	$-0.816734\pi$
$257$	2.56231	−	7.88597i	0.159832	−	0.491913i	0.998618	+	0.0525479i	$0.0167342\pi$
$258$	−3.85410	−	2.80017i	−0.239946	−	0.174331i
$259$	−4.47214	−	3.24920i	−0.277885	−	0.201895i
$260$	−3.61803	+	11.1352i	−0.224381	+	0.690574i
$261$	−2.11803	−	6.51864i	−0.131103	−	0.403494i
$262$	3.11803	−	2.26538i	0.192633	−	0.139956i
$263$	17.2361			1.06282			0.531411	−	0.847114i	$-0.321662\pi$
$263$	17.2361			1.06282			0.531411	+	0.847114i	$0.321662\pi$
$264$		0			0
$265$	5.00000			0.307148
$266$	2.85410	−	2.07363i	0.174996	−	0.127142i
$267$	2.09017	+	6.43288i	0.127916	+	0.393686i
$268$	1.52786	−	4.70228i	0.0933292	−	0.287238i
$269$	−4.85410	−	3.52671i	−0.295960	−	0.215027i	0.429889	−	0.902882i	$-0.358553\pi$
$269$	−4.85410	−	3.52671i	−0.295960	−	0.215027i	−0.725849	+	0.687854i	$0.758553\pi$
$270$	−2.92705	−	2.12663i	−0.178135	−	0.129422i
$271$	−8.18034	+	25.1765i	−0.496920	+	1.52936i	0.317022	+	0.948418i	$0.397317\pi$
$271$	−8.18034	+	25.1765i	−0.496920	+	1.52936i	−0.813943	+	0.580945i	$0.802683\pi$
$272$	−1.23607	−	3.80423i	−0.0749476	−	0.230665i
$273$	−1.61803	+	1.17557i	−0.0979279	+	0.0711488i
$274$	−14.1803			−0.856666
$275$		0			0
$276$	−5.70820			−0.343594
$277$	12.7082	−	9.23305i	0.763562	−	0.554760i	−0.136439	−	0.990648i	$-0.543566\pi$
$277$	12.7082	−	9.23305i	0.763562	−	0.554760i	0.900001	+	0.435888i	$0.143566\pi$
$278$	4.85410	+	14.9394i	0.291130	+	0.896005i
$279$	−1.04508	+	3.21644i	−0.0625676	+	0.192563i
$280$	1.80902	+	1.31433i	0.108109	+	0.0785461i
$281$	17.1803	+	12.4822i	1.02489	+	0.744628i	0.967280	−	0.253711i	$-0.0816511\pi$
$281$	17.1803	+	12.4822i	1.02489	+	0.744628i	0.0576130	+	0.998339i	$0.481651\pi$
$282$	1.23607	−	3.80423i	0.0736068	−	0.226538i
$283$	2.32624	+	7.15942i	0.138280	+	0.425584i	0.996086	−	0.0883911i	$-0.0281725\pi$
$283$	2.32624	+	7.15942i	0.138280	+	0.425584i	−0.857805	+	0.513975i	$0.828173\pi$
$284$	−4.85410	+	3.52671i	−0.288038	+	0.209272i
$285$	20.6525			1.22335
$286$		0			0
$287$	−3.52786			−0.208243
$288$	−0.809017	+	0.587785i	−0.0476718	+	0.0346356i
$289$	−0.309017	−	0.951057i	−0.0181775	−	0.0559445i
$290$	−7.66312	+	23.5847i	−0.449994	+	1.38494i
$291$	7.78115	+	5.65334i	0.456139	+	0.331405i
$292$	11.7812	+	8.55951i	0.689440	+	0.500907i
$293$	−1.66312	+	5.11855i	−0.0971604	+	0.299029i	−0.987811	−	0.155660i	$-0.950250\pi$
$293$	−1.66312	+	5.11855i	−0.0971604	+	0.299029i	0.890650	+	0.454689i	$0.150250\pi$
$294$	−2.04508	−	6.29412i	−0.119272	−	0.367081i
$295$	−30.2254	+	21.9601i	−1.75979	+	1.27856i
$296$	−8.94427			−0.519875
$297$		0			0
$298$	−6.03444			−0.349566
$299$	−14.9443	+	10.8576i	−0.864250	+	0.627914i
$300$	2.50000	+	7.69421i	0.144338	+	0.444225i
$301$	−0.909830	+	2.80017i	−0.0524417	+	0.161399i
$302$	16.0172	+	11.6372i	0.921687	+	0.669645i
$303$	−1.69098	−	1.22857i	−0.0971444	−	0.0705796i
$304$	1.76393	−	5.42882i	0.101168	−	0.311364i
$305$	4.14590	+	12.7598i	0.237393	+	0.730622i
$306$	3.23607	−	2.35114i	0.184994	−	0.134406i
$307$	17.2361			0.983714			0.491857	−	0.870676i	$-0.336318\pi$
$307$	17.2361			0.983714			0.491857	+	0.870676i	$0.336318\pi$
$308$		0			0
$309$	−9.85410			−0.560580
$310$	9.89919	−	7.19218i	0.562236	−	0.408488i
$311$	5.09017	+	15.6659i	0.288637	+	0.888334i	0.985285	+	0.170920i	$0.0546740\pi$
$311$	5.09017	+	15.6659i	0.288637	+	0.888334i	−0.696648	+	0.717413i	$0.745326\pi$
$312$	−1.00000	+	3.07768i	−0.0566139	+	0.174240i
$313$	−17.7812	−	12.9188i	−1.00505	−	0.730212i	−0.0418851	−	0.999122i	$-0.513336\pi$
$313$	−17.7812	−	12.9188i	−1.00505	−	0.730212i	−0.963165	+	0.268911i	$0.913336\pi$
$314$	14.5623	+	10.5801i	0.821798	+	0.597072i
$315$	−0.690983	+	2.12663i	−0.0389325	+	0.119822i
$316$	2.11803	+	6.51864i	0.119149	+	0.366702i
$317$	7.32624	−	5.32282i	0.411483	−	0.298960i	−0.362719	−	0.931898i	$-0.618152\pi$
$317$	7.32624	−	5.32282i	0.411483	−	0.298960i	0.774202	+	0.632939i	$0.218152\pi$
$318$	1.38197			0.0774968
$319$		0			0
$320$	3.61803			0.202254
$321$	0.881966	−	0.640786i	0.0492265	−	0.0357652i
$322$	1.09017	+	3.35520i	0.0607528	+	0.186978i
$323$	−7.05573	+	21.7153i	−0.392591	+	1.20827i
$324$	−0.809017	−	0.587785i	−0.0449454	−	0.0326547i
$325$	21.1803	+	15.3884i	1.17487	+	0.853596i
$326$	0.145898	−	0.449028i	0.00808054	−	0.0248694i
$327$	0.909830	+	2.80017i	0.0503137	+	0.154850i
$328$	−4.61803	+	3.35520i	−0.254988	+	0.185260i
$329$	−2.47214			−0.136293
$330$		0			0
$331$	−16.3607			−0.899264			−0.449632	−	0.893214i	$-0.648445\pi$
$331$	−16.3607			−0.899264			−0.449632	+	0.893214i	$0.648445\pi$
$332$	1.30902	−	0.951057i	0.0718416	−	0.0521960i
$333$	−2.76393	−	8.50651i	−0.151463	−	0.466154i
$334$	1.94427	−	5.98385i	0.106386	−	0.327422i
$335$	−14.4721	−	10.5146i	−0.790697	−	0.574475i
$336$	0.500000	+	0.363271i	0.0272772	+	0.0198181i
$337$	−6.14590	+	18.9151i	−0.334788	+	1.03037i	0.632038	+	0.774938i	$0.282219\pi$
$337$	−6.14590	+	18.9151i	−0.334788	+	1.03037i	−0.966826	+	0.255435i	$0.917781\pi$
$338$	−0.781153	−	2.40414i	−0.0424891	−	0.130768i
$339$	−5.61803	+	4.08174i	−0.305130	+	0.221690i
$340$	−14.4721			−0.784862
$341$		0			0
$342$	5.70820			0.308664
$343$	−6.80902	+	4.94704i	−0.367652	+	0.267115i
$344$	1.47214	+	4.53077i	0.0793723	+	0.244283i
$345$	−6.38197	+	19.6417i	−0.343594	+	1.05747i
$346$	−11.5902	−	8.42075i	−0.623091	−	0.452702i
$347$	−27.7705	−	20.1765i	−1.49080	−	1.08313i	−0.973871	−	0.227100i	$-0.927076\pi$
$347$	−27.7705	−	20.1765i	−1.49080	−	1.08313i	−0.516928	−	0.856029i	$-0.672924\pi$
$348$	−2.11803	+	6.51864i	−0.113539	+	0.349436i
$349$	3.79837	+	11.6902i	0.203322	+	0.625762i	0.999778	+	0.0210649i	$0.00670568\pi$
$349$	3.79837	+	11.6902i	0.203322	+	0.625762i	−0.796456	+	0.604697i	$0.793294\pi$
$350$	4.04508	−	2.93893i	0.216219	−	0.157092i
$351$	−3.23607			−0.172729
$352$		0			0
$353$	6.76393			0.360008			0.180004	−	0.983666i	$-0.442389\pi$
$353$	6.76393			0.360008			0.180004	+	0.983666i	$0.442389\pi$
$354$	−8.35410	+	6.06961i	−0.444016	+	0.322596i
$355$	6.70820	+	20.6457i	0.356034	+	1.09576i
$356$	2.09017	−	6.43288i	0.110779	−	0.340942i
$357$	−2.00000	−	1.45309i	−0.105851	−	0.0769054i
$358$	15.0172	+	10.9106i	0.793685	+	0.576646i
$359$	8.70820	−	26.8011i	0.459601	−	1.41451i	−0.406046	−	0.913853i	$-0.633093\pi$
$359$	8.70820	−	26.8011i	0.459601	−	1.41451i	0.865647	−	0.500655i	$-0.166907\pi$
$360$	1.11803	+	3.44095i	0.0589256	+	0.181354i
$361$	−10.9894	+	7.98424i	−0.578387	+	0.420223i
$362$	21.4164			1.12562
$363$		0			0
$364$	2.00000			0.104828
$365$	42.6246	−	30.9686i	2.23107	−	1.62097i
$366$	1.14590	+	3.52671i	0.0598970	+	0.184344i
$367$	−5.88197	+	18.1028i	−0.307036	+	0.944960i	0.671873	+	0.740666i	$0.265490\pi$
$367$	−5.88197	+	18.1028i	−0.307036	+	0.944960i	−0.978910	+	0.204294i	$0.934510\pi$
$368$	4.61803	+	3.35520i	0.240732	+	0.174902i
$369$	−4.61803	−	3.35520i	−0.240405	−	0.174665i
$370$	−10.0000	+	30.7768i	−0.519875	+	1.60001i
$371$	−0.263932	−	0.812299i	−0.0137027	−	0.0421725i
$372$	2.73607	−	1.98787i	0.141859	−	0.103066i
$373$		0			0			−	1.00000i	$-0.5\pi$
$373$		0			0				1.00000i	$0.5\pi$
$374$		0			0
$375$	11.1803			0.577350
$376$	−3.23607	+	2.35114i	−0.166887	+	0.121251i
$377$	6.85410	+	21.0948i	0.353004	+	1.08644i
$378$	−0.190983	+	0.587785i	−0.00982311	+	0.0302324i
$379$	−21.1803	−	15.3884i	−1.08796	−	0.790450i	−0.108907	−	0.994052i	$-0.534735\pi$
$379$	−21.1803	−	15.3884i	−1.08796	−	0.790450i	−0.979054	+	0.203602i	$0.934735\pi$
$380$	−16.7082	−	12.1392i	−0.857113	−	0.622729i
$381$	−1.23607	+	3.80423i	−0.0633257	+	0.194896i
$382$	−0.944272	−	2.90617i	−0.0483132	−	0.148693i
$383$	−19.6525	+	14.2784i	−1.00419	+	0.729590i	−0.962983	−	0.269560i	$-0.913122\pi$
$383$	−19.6525	+	14.2784i	−1.00419	+	0.729590i	−0.0412111	+	0.999150i	$0.513122\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	4.61803			0.235052
$387$	−3.85410	+	2.80017i	−0.195915	+	0.142341i
$388$	−2.97214	−	9.14729i	−0.150887	−	0.464383i
$389$	5.85410	−	18.0171i	0.296815	−	0.913502i	−0.685791	−	0.727798i	$-0.740544\pi$
$389$	5.85410	−	18.0171i	0.296815	−	0.913502i	0.982606	−	0.185703i	$-0.0594564\pi$
$390$	9.47214	+	6.88191i	0.479640	+	0.348479i
$391$	−18.4721	−	13.4208i	−0.934176	−	0.678719i
$392$	−2.04508	+	6.29412i	−0.103292	+	0.317901i
$393$	−1.19098	−	3.66547i	−0.0600771	−	0.184898i
$394$	−20.6353	+	14.9924i	−1.03959	+	0.755306i
$395$	24.7984			1.24774
$396$		0			0
$397$	4.94427			0.248146			0.124073	−	0.992273i	$-0.460404\pi$
$397$	4.94427			0.248146			0.124073	+	0.992273i	$0.460404\pi$
$398$	0.309017	−	0.224514i	0.0154896	−	0.0112539i
$399$	−1.09017	−	3.35520i	−0.0545768	−	0.167970i
$400$	2.50000	−	7.69421i	0.125000	−	0.384710i
$401$	1.38197	+	1.00406i	0.0690121	+	0.0501402i	0.621756	−	0.783211i	$-0.286419\pi$
$401$	1.38197	+	1.00406i	0.0690121	+	0.0501402i	−0.552744	+	0.833351i	$0.686419\pi$
$402$	−4.00000	−	2.90617i	−0.199502	−	0.144947i
$403$	3.38197	−	10.4086i	0.168468	−	0.518490i
$404$	0.645898	+	1.98787i	0.0321346	+	0.0989002i
$405$	−2.92705	+	2.12663i	−0.145446	+	0.105673i
$406$	4.23607			0.210233
$407$		0			0
$408$	−4.00000			−0.198030
$409$	−24.2533	+	17.6210i	−1.19925	+	0.871305i	−0.994211	−	0.107449i	$-0.965732\pi$
$409$	−24.2533	+	17.6210i	−1.19925	+	0.871305i	−0.205037	+	0.978754i	$0.565732\pi$
$410$	6.38197	+	19.6417i	0.315183	+	0.970033i
$411$	−4.38197	+	13.4863i	−0.216146	+	0.665230i
$412$	7.97214	+	5.79210i	0.392759	+	0.285356i
$413$	5.16312	+	3.75123i	0.254060	+	0.184586i
$414$	−1.76393	+	5.42882i	−0.0866925	+	0.266812i
$415$	−1.80902	−	5.56758i	−0.0888012	−	0.273302i
$416$	2.61803	−	1.90211i	0.128360	−	0.0932588i
$417$	15.7082			0.769234
$418$		0			0
$419$	12.0902			0.590643			0.295322	−	0.955398i	$-0.404573\pi$
$419$	12.0902			0.590643			0.295322	+	0.955398i	$0.404573\pi$
$420$	1.80902	−	1.31433i	0.0882710	−	0.0641326i
$421$	−2.96556	−	9.12705i	−0.144532	−	0.444825i	0.852418	−	0.522861i	$-0.175135\pi$
$421$	−2.96556	−	9.12705i	−0.144532	−	0.444825i	−0.996951	+	0.0780356i	$0.975135\pi$
$422$	2.85410	−	8.78402i	0.138936	−	0.427600i
$423$	−3.23607	−	2.35114i	−0.157343	−	0.114316i
$424$	−1.11803	−	0.812299i	−0.0542965	−	0.0394487i
$425$	−10.0000	+	30.7768i	−0.485071	+	1.49290i
$426$	1.85410	+	5.70634i	0.0898315	+	0.276473i
$427$	1.85410	−	1.34708i	0.0897263	−	0.0651900i
$428$	−1.09017			−0.0526954
$429$		0			0
$430$	17.2361			0.831197
$431$	27.5623	−	20.0252i	1.32763	−	0.964579i	0.327826	−	0.944738i	$-0.393684\pi$
$431$	27.5623	−	20.0252i	1.32763	−	0.964579i	0.999803	−	0.0198414i	$-0.00631612\pi$
$432$	0.309017	+	0.951057i	0.0148676	+	0.0457577i
$433$	2.28115	−	7.02067i	0.109625	−	0.337392i	−0.881163	−	0.472813i	$-0.843239\pi$
$433$	2.28115	−	7.02067i	0.109625	−	0.337392i	0.990788	+	0.135421i	$0.0432387\pi$
$434$	−1.69098	−	1.22857i	−0.0811698	−	0.0589733i
$435$	20.0623	+	14.5761i	0.961914	+	0.698871i
$436$	0.909830	−	2.80017i	0.0435730	−	0.134104i
$437$	−10.0689	−	30.9888i	−0.481660	−	1.48240i
$438$	11.7812	−	8.55951i	0.562925	−	0.408989i
$439$	−29.9230			−1.42815			−0.714073	−	0.700071i	$-0.753152\pi$
$439$	−29.9230			−1.42815			−0.714073	+	0.700071i	$0.753152\pi$
$440$		0			0
$441$	−6.61803			−0.315144
$442$	−10.4721	+	7.60845i	−0.498109	+	0.361897i
$443$	0.0450850	+	0.138757i	0.00214205	+	0.00659256i	0.952122	−	0.305719i	$-0.0988968\pi$
$443$	0.0450850	+	0.138757i	0.00214205	+	0.00659256i	−0.949980	+	0.312311i	$0.898897\pi$
$444$	−2.76393	+	8.50651i	−0.131170	+	0.403701i
$445$	−19.7984	−	14.3844i	−0.938533	−	0.681884i
$446$	1.07295	+	0.779543i	0.0508056	+	0.0369124i
$447$	−1.86475	+	5.73910i	−0.0881994	+	0.271450i
$448$	−0.190983	−	0.587785i	−0.00902310	−	0.0277702i
$449$	−0.381966	+	0.277515i	−0.0180261	+	0.0130967i	−0.596762	−	0.802418i	$-0.703546\pi$
$449$	−0.381966	+	0.277515i	−0.0180261	+	0.0130967i	0.578736	+	0.815515i	$0.303546\pi$
$450$	8.09017			0.381374
$451$		0			0
$452$	6.94427			0.326631
$453$	16.0172	−	11.6372i	0.752555	−	0.546763i
$454$	−1.55573	−	4.78804i	−0.0730139	−	0.224714i
$455$	2.23607	−	6.88191i	0.104828	−	0.322629i
$456$	−4.61803	−	3.35520i	−0.216259	−	0.157122i
$457$	−22.7254	−	16.5110i	−1.06305	−	0.772351i	−0.0884002	−	0.996085i	$-0.528175\pi$
$457$	−22.7254	−	16.5110i	−1.06305	−	0.772351i	−0.974650	+	0.223734i	$0.928175\pi$
$458$	−1.67376	+	5.15131i	−0.0782098	+	0.240705i
$459$	−1.23607	−	3.80423i	−0.0576947	−	0.177566i
$460$	16.7082	−	12.1392i	0.779024	−	0.565994i
$461$	−22.0000			−1.02464			−0.512321	−	0.858794i	$-0.671214\pi$
$461$	−22.0000			−1.02464			−0.512321	+	0.858794i	$0.671214\pi$
$462$		0			0
$463$	−7.74265			−0.359831			−0.179916	−	0.983682i	$-0.557582\pi$
$463$	−7.74265			−0.359831			−0.179916	+	0.983682i	$0.557582\pi$
$464$	5.54508	−	4.02874i	0.257424	−	0.187030i
$465$	−3.78115	−	11.6372i	−0.175347	−	0.539662i
$466$	5.23607	−	16.1150i	0.242556	−	0.746511i
$467$	−10.3541	−	7.52270i	−0.479131	−	0.348109i	0.321858	−	0.946788i	$-0.395693\pi$
$467$	−10.3541	−	7.52270i	−0.479131	−	0.348109i	−0.800989	+	0.598679i	$0.795693\pi$
$468$	2.61803	+	1.90211i	0.121019	+	0.0879252i
$469$	−0.944272	+	2.90617i	−0.0436024	+	0.134194i
$470$	4.47214	+	13.7638i	0.206284	+	0.634878i
$471$	14.5623	−	10.5801i	0.670996	−	0.487507i
$472$	10.3262			0.475304
$473$		0			0
$474$	6.85410			0.314819
$475$	−37.3607	+	27.1441i	−1.71423	+	1.24546i
$476$	0.763932	+	2.35114i	0.0350148	+	0.107764i
$477$	0.427051	−	1.31433i	0.0195533	−	0.0601789i
$478$	−6.09017	−	4.42477i	−0.278558	−	0.202384i
$479$	7.09017	+	5.15131i	0.323958	+	0.235369i	0.737863	−	0.674951i	$-0.235835\pi$
$479$	7.09017	+	5.15131i	0.323958	+	0.235369i	−0.413904	+	0.910320i	$0.635835\pi$
$480$	1.11803	−	3.44095i	0.0510310	−	0.157057i
$481$	8.94427	+	27.5276i	0.407824	+	1.25515i
$482$	6.97214	−	5.06555i	0.317572	−	0.230730i
$483$	3.52786			0.160523
$484$		0			0
$485$	−34.7984			−1.58011
$486$	−0.809017	+	0.587785i	−0.0366978	+	0.0266625i
$487$	0.954915	+	2.93893i	0.0432713	+	0.133175i	0.970358	−	0.241671i	$-0.0776954\pi$
$487$	0.954915	+	2.93893i	0.0432713	+	0.133175i	−0.927087	+	0.374846i	$0.877695\pi$
$488$	1.14590	−	3.52671i	0.0518724	−	0.159647i
$489$	−0.381966	−	0.277515i	−0.0172731	−	0.0125496i
$490$	19.3713	+	14.0741i	0.875107	+	0.635803i
$491$	9.05573	−	27.8707i	0.408679	−	1.25779i	−0.509104	−	0.860705i	$-0.670023\pi$
$491$	9.05573	−	27.8707i	0.408679	−	1.25779i	0.917784	−	0.397081i	$-0.129977\pi$
$492$	1.76393	+	5.42882i	0.0795242	+	0.244750i
$493$	−22.1803	+	16.1150i	−0.998952	+	0.725781i
$494$	−18.4721			−0.831101
$495$		0			0
$496$	−3.38197			−0.151855
$497$	3.00000	−	2.17963i	0.134568	−	0.0977697i
$498$	−0.500000	−	1.53884i	−0.0224055	−	0.0689571i
$499$	11.5279	−	35.4791i	0.516058	−	1.58826i	−0.265290	−	0.964169i	$-0.585468\pi$
$499$	11.5279	−	35.4791i	0.516058	−	1.58826i	0.781349	−	0.624095i	$-0.214532\pi$
$500$	−9.04508	−	6.57164i	−0.404508	−	0.293893i
$501$	−5.09017	−	3.69822i	−0.227412	−	0.165225i
$502$	4.73607	−	14.5761i	0.211381	−	0.650564i
$503$	1.41641	+	4.35926i	0.0631545	+	0.194370i	0.977655	−	0.210215i	$-0.0674163\pi$
$503$	1.41641	+	4.35926i	0.0631545	+	0.194370i	−0.914501	+	0.404584i	$0.867416\pi$
$504$	0.500000	−	0.363271i	0.0222718	−	0.0161814i
$505$	7.56231			0.336518
$506$		0			0
$507$	−2.52786			−0.112266
$508$	3.23607	−	2.35114i	0.143577	−	0.104315i
$509$	7.19098	+	22.1316i	0.318735	+	0.980965i	0.974190	+	0.225730i	$0.0724769\pi$
$509$	7.19098	+	22.1316i	0.318735	+	0.980965i	−0.655455	+	0.755234i	$0.727523\pi$
$510$	−4.47214	+	13.7638i	−0.198030	+	0.609472i
$511$	−7.28115	−	5.29007i	−0.322099	−	0.234019i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	1.76393	−	5.42882i	0.0778795	−	0.239688i
$514$	2.56231	+	7.88597i	0.113018	+	0.347835i
$515$	28.8435	−	20.9560i	1.27099	−	0.923432i
$516$	4.76393			0.209720
$517$		0			0
$518$	5.52786			0.242880
$519$	−11.5902	+	8.42075i	−0.508752	+	0.369630i
$520$	−3.61803	−	11.1352i	−0.158661	−	0.488309i
$521$	−8.65248	+	26.6296i	−0.379072	+	1.16666i	0.561618	+	0.827396i	$0.310179\pi$
$521$	−8.65248	+	26.6296i	−0.379072	+	1.16666i	−0.940690	+	0.339267i	$0.889821\pi$
$522$	5.54508	+	4.02874i	0.242702	+	0.176333i
$523$	11.8541	+	8.61251i	0.518344	+	0.376599i	0.815980	−	0.578081i	$-0.196198\pi$
$523$	11.8541	+	8.61251i	0.518344	+	0.376599i	−0.297636	+	0.954679i	$0.596198\pi$
$524$	−1.19098	+	3.66547i	−0.0520283	+	0.160127i
$525$	−1.54508	−	4.75528i	−0.0674330	−	0.207538i
$526$	−13.9443	+	10.1311i	−0.607999	+	0.441737i
$527$	13.5279			0.589283
$528$		0			0
$529$	9.58359			0.416678
$530$	−4.04508	+	2.93893i	−0.175707	+	0.127659i
$531$	3.19098	+	9.82084i	0.138477	+	0.426188i
$532$	−1.09017	+	3.35520i	−0.0472649	+	0.145466i
$533$	14.9443	+	10.8576i	0.647308	+	0.470297i
$534$	−5.47214	−	3.97574i	−0.236802	−	0.172047i
$535$	−1.21885	+	3.75123i	−0.0526954	+	0.162180i
$536$	1.52786	+	4.70228i	0.0659937	+	0.203108i
$537$	15.0172	−	10.9106i	0.648041	−	0.470829i
$538$	6.00000			0.258678
$539$		0			0
$540$	3.61803			0.155695
$541$	−3.61803	+	2.62866i	−0.155551	+	0.113015i	−0.662838	−	0.748762i	$-0.730648\pi$
$541$	−3.61803	+	2.62866i	−0.155551	+	0.113015i	0.507287	+	0.861777i	$0.330648\pi$
$542$	−8.18034	−	25.1765i	−0.351376	−	1.08142i
$543$	6.61803	−	20.3682i	0.284007	−	0.874084i
$544$	3.23607	+	2.35114i	0.138745	+	0.100804i
$545$	−8.61803	−	6.26137i	−0.369156	−	0.268208i
$546$	0.618034	−	1.90211i	0.0264494	−	0.0814029i
$547$	13.3262	+	41.0139i	0.569789	+	1.75363i	0.653275	+	0.757121i	$0.273395\pi$
$547$	13.3262	+	41.0139i	0.569789	+	1.75363i	−0.0834863	+	0.996509i	$0.526605\pi$
$548$	11.4721	−	8.33499i	0.490065	−	0.356053i
$549$	3.70820			0.158262
$550$		0			0
$551$	−39.1246			−1.66676
$552$	4.61803	−	3.35520i	0.196557	−	0.142807i
$553$	−1.30902	−	4.02874i	−0.0556651	−	0.171319i
$554$	−4.85410	+	14.9394i	−0.206231	+	0.634714i
$555$	26.1803	+	19.0211i	1.11129	+	0.807402i
$556$	−12.7082	−	9.23305i	−0.538948	−	0.391569i
$557$	0.718847	−	2.21238i	0.0304585	−	0.0937417i	−0.934672	−	0.355512i	$-0.884306\pi$
$557$	0.718847	−	2.21238i	0.0304585	−	0.0937417i	0.965130	+	0.261771i	$0.0843064\pi$
$558$	−1.04508	−	3.21644i	−0.0442420	−	0.136163i
$559$	12.4721	−	9.06154i	0.527515	−	0.383262i
$560$	−2.23607			−0.0944911
$561$		0			0
$562$	−21.2361			−0.895789
$563$	6.47214	−	4.70228i	0.272768	−	0.198178i	−0.442989	−	0.896527i	$-0.646082\pi$
$563$	6.47214	−	4.70228i	0.272768	−	0.198178i	0.715757	+	0.698350i	$0.246082\pi$
$564$	1.23607	+	3.80423i	0.0520479	+	0.160187i
$565$	7.76393	−	23.8949i	0.326631	−	1.00527i
$566$	−6.09017	−	4.42477i	−0.255989	−	0.185987i
$567$	0.500000	+	0.363271i	0.0209980	+	0.0152560i
$568$	1.85410	−	5.70634i	0.0777964	−	0.239433i
$569$	2.32624	+	7.15942i	0.0975210	+	0.300139i	0.987902	−	0.155076i	$-0.0495624\pi$
$569$	2.32624	+	7.15942i	0.0975210	+	0.300139i	−0.890382	+	0.455215i	$0.849562\pi$
$570$	−16.7082	+	12.1392i	−0.699830	+	0.508456i
$571$	−32.6525			−1.36646			−0.683232	−	0.730202i	$-0.739426\pi$
$571$	−32.6525			−1.36646			−0.683232	+	0.730202i	$0.739426\pi$
$572$		0			0
$573$	−3.05573			−0.127655
$574$	2.85410	−	2.07363i	0.119128	−	0.0865515i
$575$	−14.2705	−	43.9201i	−0.595121	−	1.83160i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	38.6246	+	28.0624i	1.60796	+	1.16825i	0.869458	+	0.494006i	$0.164468\pi$
$577$	38.6246	+	28.0624i	1.60796	+	1.16825i	0.738505	+	0.674248i	$0.235532\pi$
$578$	0.809017	+	0.587785i	0.0336507	+	0.0244486i
$579$	1.42705	−	4.39201i	0.0593062	−	0.182526i
$580$	−7.66312	−	23.5847i	−0.318194	−	0.979299i
$581$	−0.809017	+	0.587785i	−0.0335637	+	0.0243854i
$582$	−9.61803			−0.398680
$583$		0			0
$584$	−14.5623			−0.602593
$585$	9.47214	−	6.88191i	0.391625	−	0.284532i
$586$	−1.66312	−	5.11855i	−0.0687028	−	0.211446i
$587$	−14.1525	+	43.5568i	−0.584135	+	1.79778i	0.0185806	+	0.999827i	$0.494085\pi$
$587$	−14.1525	+	43.5568i	−0.584135	+	1.79778i	−0.602716	+	0.797956i	$0.705915\pi$
$588$	5.35410	+	3.88998i	0.220799	+	0.160420i
$589$	15.6180	+	11.3472i	0.643530	+	0.467552i
$590$	11.5451	−	35.5321i	0.475304	−	1.46283i
$591$	7.88197	+	24.2582i	0.324221	+	0.997849i
$592$	7.23607	−	5.25731i	0.297401	−	0.216074i
$593$	−27.8885			−1.14525			−0.572623	−	0.819819i	$-0.694074\pi$
$593$	−27.8885			−1.14525			−0.572623	+	0.819819i	$0.694074\pi$
$594$		0			0
$595$	8.94427			0.366679
$596$	4.88197	−	3.54696i	0.199973	−	0.145289i
$597$	−0.118034	−	0.363271i	−0.00483081	−	0.0148677i
$598$	5.70820	−	17.5680i	0.233426	−	0.718411i
$599$	10.0000	+	7.26543i	0.408589	+	0.296857i	0.773030	−	0.634369i	$-0.218740\pi$
$599$	10.0000	+	7.26543i	0.408589	+	0.296857i	−0.364441	+	0.931226i	$0.618740\pi$
$600$	−6.54508	−	4.75528i	−0.267202	−	0.194134i
$601$	2.75329	−	8.47375i	0.112309	−	0.345652i	−0.879067	−	0.476698i	$-0.841834\pi$
$601$	2.75329	−	8.47375i	0.112309	−	0.345652i	0.991376	+	0.131046i	$0.0418336\pi$
$602$	−0.909830	−	2.80017i	−0.0370819	−	0.114126i
$603$	−4.00000	+	2.90617i	−0.162893	+	0.118348i
$604$	−19.7984			−0.805584
$605$		0			0
$606$	2.09017			0.0849073
$607$	26.6525	−	19.3642i	1.08179	−	0.785967i	0.103796	−	0.994599i	$-0.466901\pi$
$607$	26.6525	−	19.3642i	1.08179	−	0.785967i	0.977994	+	0.208632i	$0.0669010\pi$
$608$	1.76393	+	5.42882i	0.0715369	+	0.220168i
$609$	1.30902	−	4.02874i	0.0530440	−	0.163253i
$610$	−10.8541	−	7.88597i	−0.439470	−	0.319293i
$611$	10.4721	+	7.60845i	0.423657	+	0.307805i
$612$	−1.23607	+	3.80423i	−0.0499651	+	0.153777i
$613$	−10.7082	−	32.9565i	−0.432500	−	1.33110i	−0.895627	−	0.444807i	$-0.853272\pi$
$613$	−10.7082	−	32.9565i	−0.432500	−	1.33110i	0.463126	−	0.886292i	$-0.346728\pi$
$614$	−13.9443	+	10.1311i	−0.562745	+	0.408858i
$615$	20.6525			0.832788
$616$		0			0
$617$	25.1246			1.01148			0.505739	−	0.862686i	$-0.331220\pi$
$617$	25.1246			1.01148			0.505739	+	0.862686i	$0.331220\pi$
$618$	7.97214	−	5.79210i	0.320686	−	0.232992i
$619$	1.23607	+	3.80423i	0.0496818	+	0.152905i	0.972820	−	0.231565i	$-0.0743845\pi$
$619$	1.23607	+	3.80423i	0.0496818	+	0.152905i	−0.923138	+	0.384469i	$0.874384\pi$
$620$	−3.78115	+	11.6372i	−0.151855	+	0.467361i
$621$	4.61803	+	3.35520i	0.185315	+	0.134639i
$622$	−13.3262	−	9.68208i	−0.534333	−	0.388216i
$623$	−1.29180	+	3.97574i	−0.0517547	+	0.159285i
$624$	−1.00000	−	3.07768i	−0.0400320	−	0.123206i
$625$		0			0
$626$	21.9787			0.878446
$627$		0			0
$628$	−18.0000			−0.718278
$629$	−28.9443	+	21.0292i	−1.15408	+	0.838491i
$630$	−0.690983	−	2.12663i	−0.0275294	−	0.0847268i
$631$	8.40983	−	25.8828i	0.334790	−	1.03038i	−0.632035	−	0.774940i	$-0.717780\pi$
$631$	8.40983	−	25.8828i	0.334790	−	1.03038i	0.966825	−	0.255438i	$-0.0822197\pi$
$632$	−5.54508	−	4.02874i	−0.220572	−	0.160255i
$633$	−7.47214	−	5.42882i	−0.296991	−	0.215776i
$634$	−2.79837	+	8.61251i	−0.111138	+	0.342046i
$635$	−4.47214	−	13.7638i	−0.177471	−	0.546201i
$636$	−1.11803	+	0.812299i	−0.0443329	+	0.0322098i
$637$	21.4164			0.848549
$638$		0			0
$639$	6.00000			0.237356
$640$	−2.92705	+	2.12663i	−0.115702	+	0.0840623i
$641$	0.673762	+	2.07363i	0.0266120	+	0.0819033i	0.963480	−	0.267779i	$-0.0862896\pi$
$641$	0.673762	+	2.07363i	0.0266120	+	0.0819033i	−0.936868	+	0.349682i	$0.886290\pi$
$642$	−0.336881	+	1.03681i	−0.0132956	+	0.0409198i
$643$	−4.85410	−	3.52671i	−0.191427	−	0.139080i	0.487944	−	0.872875i	$-0.337747\pi$
$643$	−4.85410	−	3.52671i	−0.191427	−	0.139080i	−0.679371	+	0.733795i	$0.737747\pi$
$644$	−2.85410	−	2.07363i	−0.112467	−	0.0817123i
$645$	5.32624	−	16.3925i	0.209720	−	0.645453i
$646$	−7.05573	−	21.7153i	−0.277604	−	0.854377i
$647$	13.5623	−	9.85359i	0.533189	−	0.387385i	−0.288360	−	0.957522i	$-0.593110\pi$
$647$	13.5623	−	9.85359i	0.533189	−	0.387385i	0.821549	+	0.570137i	$0.193110\pi$
$648$	1.00000			0.0392837
$649$		0			0
$650$	−26.1803			−1.02688
$651$	−1.69098	+	1.22857i	−0.0662748	+	0.0481515i
$652$	0.145898	+	0.449028i	0.00571381	+	0.0175853i
$653$	5.11803	−	15.7517i	0.200284	−	0.616411i	−0.799590	−	0.600546i	$-0.794950\pi$
$653$	5.11803	−	15.7517i	0.200284	−	0.616411i	0.999874	−	0.0158649i	$-0.00505018\pi$
$654$	−2.38197	−	1.73060i	−0.0931422	−	0.0676718i
$655$	11.2812	+	8.19624i	0.440791	+	0.320253i
$656$	1.76393	−	5.42882i	0.0688700	−	0.211960i
$657$	−4.50000	−	13.8496i	−0.175562	−	0.540323i
$658$	2.00000	−	1.45309i	0.0779681	−	0.0566472i
$659$	18.9230			0.737135			0.368567	−	0.929601i	$-0.379848\pi$
$659$	18.9230			0.737135			0.368567	+	0.929601i	$0.379848\pi$
$660$		0			0
$661$	37.5967			1.46234			0.731172	−	0.682193i	$-0.238974\pi$
$661$	37.5967			1.46234			0.731172	+	0.682193i	$0.238974\pi$
$662$	13.2361	−	9.61657i	0.514434	−	0.373758i
$663$	4.00000	+	12.3107i	0.155347	+	0.478109i
$664$	−0.500000	+	1.53884i	−0.0194038	+	0.0597186i
$665$	10.3262	+	7.50245i	0.400434	+	0.290933i
$666$	7.23607	+	5.25731i	0.280392	+	0.203717i
$667$	12.0902	−	37.2097i	0.468133	−	1.44077i
$668$	1.94427	+	5.98385i	0.0752261	+	0.231522i
$669$	1.07295	−	0.779543i	0.0414826	−	0.0301389i
$670$	17.8885			0.691095
$671$		0			0
$672$	−0.618034			−0.0238412
$673$	−28.1074	+	20.4212i	−1.08346	+	0.787180i	−0.978283	−	0.207274i	$-0.933541\pi$
$673$	−28.1074	+	20.4212i	−1.08346	+	0.787180i	−0.105177	+	0.994453i	$0.533541\pi$
$674$	−6.14590	−	18.9151i	−0.236731	−	0.728584i
$675$	2.50000	−	7.69421i	0.0962250	−	0.296150i
$676$	2.04508	+	1.48584i	0.0786571	+	0.0571477i
$677$	35.7148	+	25.9483i	1.37263	+	0.997274i	0.997526	+	0.0702918i	$0.0223930\pi$
$677$	35.7148	+	25.9483i	1.37263	+	0.997274i	0.375104	+	0.926983i	$0.377607\pi$
$678$	2.14590	−	6.60440i	0.0824127	−	0.253640i
$679$	1.83688	+	5.65334i	0.0704930	+	0.216955i
$680$	11.7082	−	8.50651i	0.448989	−	0.326210i
$681$	−5.03444			−0.192920
$682$		0			0
$683$	41.4508			1.58607			0.793036	−	0.609174i	$-0.208499\pi$
$683$	41.4508			1.58607			0.793036	+	0.609174i	$0.208499\pi$
$684$	−4.61803	+	3.35520i	−0.176575	+	0.128289i
$685$	−15.8541	−	48.7939i	−0.605754	−	1.86432i
$686$	2.60081	−	8.00448i	0.0992995	−	0.305612i
$687$	4.38197	+	3.18368i	0.167182	+	0.121465i
$688$	−3.85410	−	2.80017i	−0.146936	−	0.106755i
$689$	−1.38197	+	4.25325i	−0.0526487	+	0.162036i
$690$	−6.38197	−	19.6417i	−0.242957	−	0.747746i
$691$	28.4164	−	20.6457i	1.08101	−	0.785401i	0.103152	−	0.994666i	$-0.467107\pi$
$691$	28.4164	−	20.6457i	1.08101	−	0.785401i	0.977859	+	0.209265i	$0.0671071\pi$
$692$	14.3262			0.544602
$693$		0			0
$694$	34.3262			1.30301
$695$	−45.9787	+	33.4055i	−1.74407	+	1.26714i
$696$	−2.11803	−	6.51864i	−0.0802839	−	0.247088i
$697$	−7.05573	+	21.7153i	−0.267255	+	0.822526i
$698$	−9.94427	−	7.22494i	−0.376396	−	0.273468i
$699$	−13.7082	−	9.95959i	−0.518492	−	0.376706i
$700$	−1.54508	+	4.75528i	−0.0583987	+	0.179733i
$701$	−16.0344	−	49.3489i	−0.605613	−	1.86388i	−0.492524	−	0.870299i	$-0.663926\pi$
$701$	−16.0344	−	49.3489i	−0.605613	−	1.86388i	−0.113088	−	0.993585i	$-0.536074\pi$
$702$	2.61803	−	1.90211i	0.0988113	−	0.0717906i
$703$	−51.0557			−1.92560
$704$		0			0
$705$	14.4721			0.545052
$706$	−5.47214	+	3.97574i	−0.205947	+	0.149629i
$707$	−0.399187	−	1.22857i	−0.0150130	−	0.0462052i
$708$	3.19098	−	9.82084i	0.119924	−	0.369090i
$709$	26.3262	+	19.1271i	0.988703	+	0.718334i	0.959637	−	0.281243i	$-0.0907467\pi$
$709$	26.3262	+	19.1271i	0.988703	+	0.718334i	0.0290660	+	0.999577i	$0.490747\pi$
$710$	−17.5623	−	12.7598i	−0.659102	−	0.478865i
$711$	2.11803	−	6.51864i	0.0794325	−	0.244468i
$712$	2.09017	+	6.43288i	0.0783324	+	0.241082i
$713$	−15.6180	+	11.3472i	−0.584900	+	0.424955i
$714$	2.47214			0.0925174
$715$		0			0
$716$	−18.5623			−0.693706
$717$	−6.09017	+	4.42477i	−0.227442	+	0.165246i
$718$	8.70820	+	26.8011i	0.324987	+	1.00021i
$719$	5.85410	−	18.0171i	0.218321	−	0.671923i	−0.780580	−	0.625056i	$-0.785076\pi$
$719$	5.85410	−	18.0171i	0.218321	−	0.671923i	0.998901	−	0.0468675i	$-0.0149239\pi$
$720$	−2.92705	−	2.12663i	−0.109085	−	0.0792547i
$721$	−4.92705	−	3.57971i	−0.183493	−	0.133315i
$722$	4.19756	−	12.9188i	0.156217	−	0.480787i
$723$	−2.66312	−	8.19624i	−0.0990425	−	0.304821i
$724$	−17.3262	+	12.5882i	−0.643925	+	0.467839i
$725$	−55.4508			−2.05939
$726$		0			0
$727$	−4.58359			−0.169996			−0.0849980	−	0.996381i	$-0.527088\pi$
$727$	−4.58359			−0.169996			−0.0849980	+	0.996381i	$0.527088\pi$
$728$	−1.61803	+	1.17557i	−0.0599683	+	0.0435695i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−16.2812	+	50.1082i	−0.602593	+	1.85459i
$731$	15.4164	+	11.2007i	0.570196	+	0.414272i
$732$	−3.00000	−	2.17963i	−0.110883	−	0.0805614i
$733$	−5.79837	+	17.8456i	−0.214168	+	0.659141i	0.785044	+	0.619440i	$0.212640\pi$
$733$	−5.79837	+	17.8456i	−0.214168	+	0.659141i	−0.999212	+	0.0397005i	$0.987360\pi$
$734$	−5.88197	−	18.1028i	−0.217107	−	0.668188i
$735$	19.3713	−	14.0741i	0.714522	−	0.519131i
$736$	−5.70820			−0.210407
$737$		0			0
$738$	5.70820			0.210122
$739$	34.3607	−	24.9645i	1.26398	−	0.918334i	0.265032	−	0.964240i	$-0.414617\pi$
$739$	34.3607	−	24.9645i	1.26398	−	0.918334i	0.998946	+	0.0459057i	$0.0146174\pi$
$740$	−10.0000	−	30.7768i	−0.367607	−	1.13138i
$741$	−5.70820	+	17.5680i	−0.209696	+	0.645378i
$742$	0.690983	+	0.502029i	0.0253668	+	0.0184300i
$743$	−34.7426	−	25.2420i	−1.27458	−	0.926040i	−0.275209	−	0.961384i	$-0.588747\pi$
$743$	−34.7426	−	25.2420i	−1.27458	−	0.926040i	−0.999375	+	0.0353449i	$0.988747\pi$
$744$	−1.04508	+	3.21644i	−0.0383147	+	0.117920i
$745$	−6.74671	−	20.7642i	−0.247180	−	0.760743i
$746$		0			0
$747$	−1.61803			−0.0592008
$748$		0			0
$749$	0.673762			0.0246187
$750$	−9.04508	+	6.57164i	−0.330280	+	0.239962i
$751$	10.7639	+	33.1280i	0.392781	+	1.20886i	0.930676	+	0.365845i	$0.119220\pi$
$751$	10.7639	+	33.1280i	0.392781	+	1.20886i	−0.537894	+	0.843012i	$0.680780\pi$
$752$	1.23607	−	3.80423i	0.0450748	−	0.138726i
$753$	−12.3992	−	9.00854i	−0.451851	−	0.328289i
$754$	−17.9443	−	13.0373i	−0.653492	−	0.474790i
$755$	−22.1353	+	68.1253i	−0.805584	+	2.47933i
$756$	−0.190983	−	0.587785i	−0.00694598	−	0.0213775i
$757$	18.8885	−	13.7233i	0.686516	−	0.498783i	−0.188997	−	0.981978i	$-0.560524\pi$
$757$	18.8885	−	13.7233i	0.686516	−	0.498783i	0.875513	+	0.483195i	$0.160524\pi$
$758$	26.1803			0.950913
$759$		0			0
$760$	20.6525			0.749144
$761$	25.7426	−	18.7031i	0.933170	−	0.677988i	−0.0135968	−	0.999908i	$-0.504328\pi$
$761$	25.7426	−	18.7031i	0.933170	−	0.677988i	0.946767	+	0.321920i	$0.104328\pi$
$762$	−1.23607	−	3.80423i	−0.0447780	−	0.137813i
$763$	−0.562306	+	1.73060i	−0.0203568	+	0.0626519i
$764$	2.47214	+	1.79611i	0.0894387	+	0.0649810i
$765$	11.7082	+	8.50651i	0.423311	+	0.307553i
$766$	7.50658	−	23.1029i	0.271224	−	0.834741i
$767$	−10.3262	−	31.7809i	−0.372859	−	1.14754i
$768$	−0.809017	+	0.587785i	−0.0291929	+	0.0212099i
$769$	21.4377			0.773063			0.386532	−	0.922276i	$-0.373673\pi$
$769$	21.4377			0.773063			0.386532	+	0.922276i	$0.373673\pi$
$770$		0			0
$771$	8.29180			0.298622
$772$	−3.73607	+	2.71441i	−0.134464	+	0.0976938i
$773$	4.00658	+	12.3310i	0.144107	+	0.443514i	0.996895	−	0.0787421i	$-0.0250903\pi$
$773$	4.00658	+	12.3310i	0.144107	+	0.443514i	−0.852788	+	0.522257i	$0.825090\pi$
$774$	1.47214	−	4.53077i	0.0529148	−	0.162855i
$775$	22.1353	+	16.0822i	0.795122	+	0.577690i
$776$	7.78115	+	5.65334i	0.279327	+	0.202943i
$777$	1.70820	−	5.25731i	0.0612815	−	0.188605i
$778$	5.85410	+	18.0171i	0.209880	+	0.645943i
$779$	−26.3607	+	19.1522i	−0.944469	+	0.686197i
$780$	−11.7082			−0.419221
$781$		0			0
$782$	22.8328			0.816500
$783$	5.54508	−	4.02874i	0.198165	−	0.143975i
$784$	−2.04508	−	6.29412i	−0.0730387	−	0.224790i
$785$	−20.1246	+	61.9372i	−0.718278	+	2.21063i
$786$	3.11803	+	2.26538i	0.111217	+	0.0808036i
$787$	27.2705	+	19.8132i	0.972089	+	0.706264i	0.955927	−	0.293606i	$-0.0948552\pi$
$787$	27.2705	+	19.8132i	0.972089	+	0.706264i	0.0161620	+	0.999869i	$0.494855\pi$
$788$	7.88197	−	24.2582i	0.280783	−	0.864162i
$789$	5.32624	+	16.3925i	0.189619	+	0.583588i
$790$	−20.0623	+	14.5761i	−0.713785	+	0.518595i
$791$	−4.29180			−0.152599
$792$		0			0
$793$	−12.0000			−0.426132
$794$	−4.00000	+	2.90617i	−0.141955	+	0.103136i
$795$	1.54508	+	4.75528i	0.0547985	+	0.168652i
$796$	−0.118034	+	0.363271i	−0.00418360	+	0.0128758i
$797$	25.5902	+	18.5923i	0.906450	+	0.658575i	0.940115	−	0.340858i	$-0.110718\pi$
$797$	25.5902	+	18.5923i	0.906450	+	0.658575i	−0.0336643	+	0.999433i	$0.510718\pi$
$798$	2.85410	+	2.07363i	0.101034	+	0.0734056i
$799$	−4.94427	+	15.2169i	−0.174916	+	0.538335i
$800$	2.50000	+	7.69421i	0.0883883	+	0.272031i
$801$	−5.47214	+	3.97574i	−0.193348	+	0.140476i
$802$	−1.70820			−0.0603188
$803$		0			0
$804$	4.94427			0.174371
$805$	−10.3262	+	7.50245i	−0.363952	+	0.264427i
$806$	3.38197	+	10.4086i	0.119125	+	0.366628i
$807$	1.85410	−	5.70634i	0.0652675	−	0.200873i
$808$	−1.69098	−	1.22857i	−0.0594886	−	0.0432210i
$809$	−16.9443	−	12.3107i	−0.595729	−	0.432822i	0.248631	−	0.968598i	$-0.420019\pi$
$809$	−16.9443	−	12.3107i	−0.595729	−	0.432822i	−0.844360	+	0.535776i	$0.820019\pi$
$810$	1.11803	−	3.44095i	0.0392837	−	0.120903i
$811$	−13.6525	−	42.0180i	−0.479403	−	1.47545i	−0.839926	−	0.542701i	$-0.817402\pi$
$811$	−13.6525	−	42.0180i	−0.479403	−	1.47545i	0.360523	−	0.932750i	$-0.382598\pi$
$812$	−3.42705	+	2.48990i	−0.120266	+	0.0873783i
$813$	−26.4721			−0.928418
$814$		0			0
$815$	1.70820			0.0598358
$816$	3.23607	−	2.35114i	0.113285	−	0.0823064i
$817$	8.40325	+	25.8626i	0.293993	+	0.904816i
$818$	9.26393	−	28.5115i	0.323906	−	0.996880i
$819$	−1.61803	−	1.17557i	−0.0565387	−	0.0410778i
$820$	−16.7082	−	12.1392i	−0.583476	−	0.423920i
$821$	−7.55166	+	23.2416i	−0.263555	+	0.811138i	0.728468	+	0.685080i	$0.240233\pi$
$821$	−7.55166	+	23.2416i	−0.263555	+	0.811138i	−0.992023	+	0.126059i	$0.959767\pi$
$822$	−4.38197	−	13.4863i	−0.152839	−	0.470389i
$823$	−13.8713	+	10.0781i	−0.483524	+	0.351301i	−0.802688	−	0.596399i	$-0.796598\pi$
$823$	−13.8713	+	10.0781i	−0.483524	+	0.351301i	0.319164	+	0.947699i	$0.396598\pi$
$824$	−9.85410			−0.343284
$825$		0			0
$826$	−6.38197			−0.222057
$827$	36.0066	−	26.1603i	1.25207	−	0.909683i	0.253731	−	0.967275i	$-0.418342\pi$
$827$	36.0066	−	26.1603i	1.25207	−	0.909683i	0.998340	+	0.0575917i	$0.0183421\pi$
$828$	−1.76393	−	5.42882i	−0.0613009	−	0.188665i
$829$	15.3820	−	47.3408i	0.534238	−	1.64421i	−0.211053	−	0.977475i	$-0.567689\pi$
$829$	15.3820	−	47.3408i	0.534238	−	1.64421i	0.745290	−	0.666740i	$-0.232311\pi$
$830$	4.73607	+	3.44095i	0.164391	+	0.119437i
$831$	12.7082	+	9.23305i	0.440843	+	0.320291i
$832$	−1.00000	+	3.07768i	−0.0346688	+	0.106699i
$833$	8.18034	+	25.1765i	0.283432	+	0.872314i
$834$	−12.7082	+	9.23305i	−0.440049	+	0.319714i
$835$	22.7639			0.787778
$836$		0			0
$837$	−3.38197			−0.116898
$838$	−9.78115	+	7.10642i	−0.337884	+	0.245487i
$839$	−7.72949	−	23.7889i	−0.266852	−	0.821285i	−0.991261	−	0.131915i	$-0.957887\pi$
$839$	−7.72949	−	23.7889i	−0.266852	−	0.821285i	0.724409	−	0.689370i	$-0.242113\pi$
$840$	−0.690983	+	2.12663i	−0.0238412	+	0.0733756i
$841$	−14.5451	−	10.5676i	−0.501555	−	0.364401i
$842$	7.76393	+	5.64083i	0.267563	+	0.194396i
$843$	−6.56231	+	20.1967i	−0.226018	+	0.695611i
$844$	2.85410	+	8.78402i	0.0982422	+	0.302359i
$845$	7.39919	−	5.37582i	0.254540	−	0.184934i
$846$	4.00000			0.137523
$847$		0			0
$848$	1.38197			0.0474569
$849$	−6.09017	+	4.42477i	−0.209014	+	0.151858i
$850$	−10.0000	−	30.7768i	−0.342997	−	1.05564i
$851$	15.7771	−	48.5569i	0.540832	−	1.66451i
$852$	−4.85410	−	3.52671i	−0.166299	−	0.120823i
$853$	10.9443	+	7.95148i	0.374725	+	0.272253i	0.759167	−	0.650895i	$-0.225606\pi$
$853$	10.9443	+	7.95148i	0.374725	+	0.272253i	−0.384443	+	0.923149i	$0.625606\pi$
$854$	−0.708204	+	2.17963i	−0.0242342	+	0.0745853i
$855$	6.38197	+	19.6417i	0.218259	+	0.671731i
$856$	0.881966	−	0.640786i	0.0301450	−	0.0219016i
$857$	−20.1803			−0.689347			−0.344674	−	0.938723i	$-0.612010\pi$
$857$	−20.1803			−0.689347			−0.344674	+	0.938723i	$0.612010\pi$
$858$		0			0
$859$	−51.9574			−1.77276			−0.886382	−	0.462954i	$-0.846789\pi$
$859$	−51.9574			−1.77276			−0.886382	+	0.462954i	$0.846789\pi$
$860$	−13.9443	+	10.1311i	−0.475496	+	0.345468i
$861$	−1.09017	−	3.35520i	−0.0371529	−	0.114345i
$862$	−10.5279	+	32.4014i	−0.358580	+	1.10360i
$863$	−5.76393	−	4.18774i	−0.196207	−	0.142552i	0.485344	−	0.874323i	$-0.338694\pi$
$863$	−5.76393	−	4.18774i	−0.196207	−	0.142552i	−0.681551	+	0.731771i	$0.738694\pi$
$864$	−0.809017	−	0.587785i	−0.0275233	−	0.0199969i
$865$	16.0172	−	49.2959i	0.544602	−	1.67611i
$866$	2.28115	+	7.02067i	0.0775167	+	0.238572i
$867$	0.809017	−	0.587785i	0.0274757	−	0.0199622i
$868$	2.09017			0.0709450
$869$		0			0
$870$	−24.7984			−0.840744
$871$	12.9443	−	9.40456i	0.438600	−	0.318661i
$872$	0.909830	+	2.80017i	0.0308107	+	0.0948257i
$873$	−2.97214	+	9.14729i	−0.100592	+	0.309589i
$874$	26.3607	+	19.1522i	0.891663	+	0.647831i
$875$	5.59017	+	4.06150i	0.188982	+	0.137304i
$876$	−4.50000	+	13.8496i	−0.152041	+	0.467934i
$877$	8.90983	+	27.4216i	0.300864	+	0.925963i	0.981188	+	0.193052i	$0.0618387\pi$
$877$	8.90983	+	27.4216i	0.300864	+	0.925963i	−0.680325	+	0.732911i	$0.738161\pi$
$878$	24.2082	−	17.5883i	0.816987	−	0.593576i
$879$	−5.38197			−0.181529
$880$		0			0
$881$	−24.0689			−0.810901			−0.405451	−	0.914117i	$-0.632885\pi$
$881$	−24.0689			−0.810901			−0.405451	+	0.914117i	$0.632885\pi$
$882$	5.35410	−	3.88998i	0.180282	−	0.130983i
$883$	−17.4721	−	53.7737i	−0.587984	−	1.80963i	−0.586941	−	0.809630i	$-0.699668\pi$
$883$	−17.4721	−	53.7737i	−0.587984	−	1.80963i	−0.00104333	−	0.999999i	$-0.500332\pi$
$884$	4.00000	−	12.3107i	0.134535	−	0.414055i
$885$	−30.2254	−	21.9601i	−1.01602	−	0.738179i
$886$	−0.118034	−	0.0857567i	−0.00396543	−	0.00288105i
$887$	18.2361	−	56.1248i	0.612307	−	1.88449i	0.176984	−	0.984214i	$-0.443366\pi$
$887$	18.2361	−	56.1248i	0.612307	−	1.88449i	0.435323	−	0.900274i	$-0.356634\pi$
$888$	−2.76393	−	8.50651i	−0.0927515	−	0.285460i
$889$	−2.00000	+	1.45309i	−0.0670778	+	0.0487349i
$890$	24.4721			0.820308
$891$		0			0
$892$	−1.32624			−0.0444057
$893$	−18.4721	+	13.4208i	−0.618146	+	0.449110i
$894$	−1.86475	−	5.73910i	−0.0623664	−	0.191944i
$895$	−20.7533	+	63.8721i	−0.693706	+	2.13501i
$896$	0.500000	+	0.363271i	0.0167038	+	0.0121360i
$897$	−14.9443	−	10.8576i	−0.498975	−	0.362526i
$898$	0.145898	−	0.449028i	0.00486868	−	0.0149843i
$899$	7.16312	+	22.0458i	0.238903	+	0.735269i
$900$	−6.54508	+	4.75528i	−0.218169	+	0.158509i
$901$	−5.52786			−0.184160
$902$		0			0
$903$	−2.94427			−0.0979792
$904$	−5.61803	+	4.08174i	−0.186853	+	0.135757i
$905$	23.9443	+	73.6929i	0.795935	+	2.44963i
$906$	−6.11803	+	18.8294i	−0.203258	+	0.625564i
$907$	1.38197	+	1.00406i	0.0458874	+	0.0333392i	0.610493	−	0.792022i	$-0.290972\pi$
$907$	1.38197	+	1.00406i	0.0458874	+	0.0333392i	−0.564605	+	0.825361i	$0.690972\pi$
$908$	4.07295	+	2.95917i	0.135166	+	0.0982035i
$909$	0.645898	−	1.98787i	0.0214231	−	0.0659335i
$910$	2.23607	+	6.88191i	0.0741249	+	0.228133i
$911$	−21.4721	+	15.6004i	−0.711404	+	0.516865i	−0.883626	−	0.468193i	$-0.844905\pi$
$911$	−21.4721	+	15.6004i	−0.711404	+	0.516865i	0.172223	+	0.985058i	$0.444905\pi$
$912$	5.70820			0.189018
$913$		0			0
$914$	28.0902			0.929140
$915$	−10.8541	+	7.88597i	−0.358826	+	0.260702i
$916$	−1.67376	−	5.15131i	−0.0553027	−	0.170204i
$917$	0.736068	−	2.26538i	0.0243071	−	0.0748096i
$918$	3.23607	+	2.35114i	0.106806	+	0.0775992i
$919$	40.1976	+	29.2052i	1.32600	+	0.963392i	0.999837	+	0.0180768i	$0.00575434\pi$
$919$	40.1976	+	29.2052i	1.32600	+	0.963392i	0.326159	+	0.945315i	$0.394246\pi$
$920$	−6.38197	+	19.6417i	−0.210407	+	0.647567i
$921$	5.32624	+	16.3925i	0.175506	+	0.540150i
$922$	17.7984	−	12.9313i	0.586158	−	0.425869i
$923$	−19.4164			−0.639099
$924$		0			0
$925$	−72.3607			−2.37920
$926$	6.26393	−	4.55101i	0.205846	−	0.149556i
$927$	−3.04508	−	9.37181i	−0.100014	−	0.307811i
$928$	−2.11803	+	6.51864i	−0.0695279	+	0.213985i
$929$	−21.1803	−	15.3884i	−0.694904	−	0.504878i	0.183364	−	0.983045i	$-0.441301\pi$
$929$	−21.1803	−	15.3884i	−0.694904	−	0.504878i	−0.878269	+	0.478167i	$0.841301\pi$
$930$	9.89919	+	7.19218i	0.324607	+	0.235841i
$931$	−11.6738	+	35.9281i	−0.382592	+	1.17750i
$932$	5.23607	+	16.1150i	0.171513	+	0.527863i
$933$	−13.3262	+	9.68208i	−0.436281	+	0.316977i
$934$	12.7984			0.418776
$935$		0			0
$936$	−3.23607			−0.105774
$937$	2.79180	−	2.02836i	0.0912040	−	0.0662636i	−0.541249	−	0.840863i	$-0.682048\pi$
$937$	2.79180	−	2.02836i	0.0912040	−	0.0662636i	0.632453	+	0.774599i	$0.282048\pi$
$938$	−0.944272	−	2.90617i	−0.0308316	−	0.0948898i
$939$	6.79180	−	20.9030i	0.221642	−	0.682144i
$940$	−11.7082	−	8.50651i	−0.381880	−	0.277452i
$941$	30.5623	+	22.2048i	0.996303	+	0.723856i	0.961292	−	0.275531i	$-0.0888536\pi$
$941$	30.5623	+	22.2048i	0.996303	+	0.723856i	0.0350104	+	0.999387i	$0.488854\pi$
$942$	−5.56231	+	17.1190i	−0.181230	+	0.557768i
$943$	−10.0689	−	30.9888i	−0.327888	−	1.00914i
$944$	−8.35410	+	6.06961i	−0.271903	+	0.197549i
$945$	−2.23607			−0.0727393
$946$		0			0
$947$	31.9230			1.03736			0.518679	−	0.854969i	$-0.326424\pi$
$947$	31.9230			1.03736			0.518679	+	0.854969i	$0.326424\pi$
$948$	−5.54508	+	4.02874i	−0.180096	+	0.130847i
$949$	14.5623	+	44.8182i	0.472712	+	1.45486i
$950$	14.2705	−	43.9201i	0.462996	−	1.42496i
$951$	7.32624	+	5.32282i	0.237570	+	0.172604i
$952$	−2.00000	−	1.45309i	−0.0648204	−	0.0470948i
$953$	5.41641	−	16.6700i	0.175455	−	0.539994i	−0.824199	−	0.566300i	$-0.808374\pi$
$953$	5.41641	−	16.6700i	0.175455	−	0.539994i	0.999654	+	0.0263060i	$0.00837441\pi$
$954$	0.427051	+	1.31433i	0.0138263	+	0.0425529i
$955$	8.94427	−	6.49839i	0.289430	−	0.210283i
$956$	7.52786			0.243469
$957$		0			0
$958$	−8.76393			−0.283150
$959$	−7.09017	+	5.15131i	−0.228954	+	0.166344i
$960$	1.11803	+	3.44095i	0.0360844	+	0.111056i
$961$	−6.04508	+	18.6049i	−0.195003	+	0.600157i
$962$	−23.4164	−	17.0130i	−0.754975	−	0.548522i
$963$	0.881966	+	0.640786i	0.0284210	+	0.0206490i
$964$	−2.66312	+	8.19624i	−0.0857733	+	0.263983i
$965$	5.16312	+	15.8904i	0.166207	+	0.511532i
$966$	−2.85410	+	2.07363i	−0.0918292	+	0.0667178i
$967$	19.6180			0.630873			0.315437	−	0.948947i	$-0.397849\pi$
$967$	19.6180			0.630873			0.315437	+	0.948947i	$0.397849\pi$
$968$		0			0
$969$	−22.8328			−0.733496
$970$	28.1525	−	20.4540i	0.903922	−	0.656737i
$971$	−1.70820	−	5.25731i	−0.0548189	−	0.168715i	0.919898	−	0.392157i	$-0.128271\pi$
$971$	−1.70820	−	5.25731i	−0.0548189	−	0.168715i	−0.974717	+	0.223441i	$0.928271\pi$
$972$	0.309017	−	0.951057i	0.00991172	−	0.0305052i
$973$	7.85410	+	5.70634i	0.251791	+	0.182937i
$974$	−2.50000	−	1.81636i	−0.0801052	−	0.0581998i
$975$	−8.09017	+	24.8990i	−0.259093	+	0.797406i
$976$	1.14590	+	3.52671i	0.0366793	+	0.112887i
$977$	15.3820	−	11.1757i	0.492113	−	0.357541i	−0.313884	−	0.949461i	$-0.601630\pi$
$977$	15.3820	−	11.1757i	0.492113	−	0.357541i	0.805996	+	0.591921i	$0.201630\pi$
$978$	0.472136			0.0150972
$979$		0			0
$980$	−23.9443			−0.764872
$981$	−2.38197	+	1.73060i	−0.0760503	+	0.0552538i
$982$	9.05573	+	27.8707i	0.288980	+	0.889389i
$983$	−6.05573	+	18.6376i	−0.193148	+	0.594448i	0.806845	+	0.590763i	$0.201173\pi$
$983$	−6.05573	+	18.6376i	−0.193148	+	0.594448i	−0.999993	+	0.00368505i	$0.998827\pi$
$984$	−4.61803	−	3.35520i	−0.147218	−	0.106960i
$985$	−74.6591	−	54.2430i	−2.37884	−	1.72832i
$986$	8.47214	−	26.0746i	0.269808	−	0.830383i
$987$	−0.763932	−	2.35114i	−0.0243162	−	0.0748376i
$988$	14.9443	−	10.8576i	0.475441	−	0.345428i
$989$	−27.1935			−0.864703
$990$		0			0
$991$	55.3951			1.75968			0.879842	−	0.475266i	$-0.157648\pi$
$991$	55.3951			1.75968			0.879842	+	0.475266i	$0.157648\pi$
$992$	2.73607	−	1.98787i	0.0868702	−	0.0631149i
$993$	−5.05573	−	15.5599i	−0.160439	−	0.493779i
$994$	−1.14590	+	3.52671i	−0.0363457	+	0.111860i
$995$	1.11803	+	0.812299i	0.0354441	+	0.0257516i
$996$	1.30902	+	0.951057i	0.0414778	+	0.0301354i
$997$	−7.61803	+	23.4459i	−0.241266	+	0.742539i	0.754963	+	0.655768i	$0.227655\pi$
$997$	−7.61803	+	23.4459i	−0.241266	+	0.742539i	−0.996228	+	0.0867713i	$0.972345\pi$
$998$	11.5279	+	35.4791i	0.364908	+	1.12307i
$999$	7.23607	−	5.25731i	0.228939	−	0.166334i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	726.2.e.a.487.1		4
11.2	odd	10		726.2.a.k.1.2		2
11.3	even	5		726.2.e.c.511.1		4
11.4	even	5	inner	726.2.e.a.565.1		4
11.5	even	5		726.2.e.c.493.1		4
11.6	odd	10		66.2.e.b.31.1	✓	4
11.7	odd	10		726.2.e.j.565.1		4
11.8	odd	10		66.2.e.b.49.1	yes	4
11.9	even	5		726.2.a.m.1.2		2
11.10	odd	2		726.2.e.j.487.1		4
33.2	even	10		2178.2.a.v.1.1		2
33.8	even	10		198.2.f.a.181.1		4
33.17	even	10		198.2.f.a.163.1		4
33.20	odd	10		2178.2.a.o.1.1		2
44.19	even	10		528.2.y.g.49.1		4
44.31	odd	10		5808.2.a.by.1.2		2
44.35	even	10		5808.2.a.bz.1.2		2
44.39	even	10		528.2.y.g.97.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.e.b.31.1	✓	4	11.6	odd	10
66.2.e.b.49.1	yes	4	11.8	odd	10
198.2.f.a.163.1		4	33.17	even	10
198.2.f.a.181.1		4	33.8	even	10
528.2.y.g.49.1		4	44.19	even	10
528.2.y.g.97.1		4	44.39	even	10
726.2.a.k.1.2		2	11.2	odd	10
726.2.a.m.1.2		2	11.9	even	5
726.2.e.a.487.1		4	1.1	even	1	trivial
726.2.e.a.565.1		4	11.4	even	5	inner
726.2.e.c.493.1		4	11.5	even	5
726.2.e.c.511.1		4	11.3	even	5
726.2.e.j.487.1		4	11.10	odd	2
726.2.e.j.565.1		4	11.7	odd	10
2178.2.a.o.1.1		2	33.20	odd	10
2178.2.a.v.1.1		2	33.2	even	10
5808.2.a.by.1.2		2	44.31	odd	10
5808.2.a.bz.1.2		2	44.35	even	10

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:	\( N \)	\(=\)	\( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	726.e (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-2.92705 - 2.12663i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(-0.190983 + 0.587785i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +3.61803 q^{10} +1.00000 q^{12} +(2.61803 - 1.90211i) q^{13} +(-0.190983 - 0.587785i) q^{14} +(1.11803 - 3.44095i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(3.23607 + 2.35114i) q^{17} +(0.309017 - 0.951057i) q^{18} +(1.76393 + 5.42882i) q^{19} +(-2.92705 + 2.12663i) q^{20} -0.618034 q^{21} -5.70820 q^{23} +(-0.809017 + 0.587785i) q^{24} +(2.50000 + 7.69421i) q^{25} +(-1.00000 + 3.07768i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(0.500000 + 0.363271i) q^{28} +(-2.11803 + 6.51864i) q^{29} +(1.11803 + 3.44095i) q^{30} +(2.73607 - 1.98787i) q^{31} +1.00000 q^{32} -4.00000 q^{34} +(1.80902 - 1.31433i) q^{35} +(0.309017 + 0.951057i) q^{36} +(-2.76393 + 8.50651i) q^{37} +(-4.61803 - 3.35520i) q^{38} +(2.61803 + 1.90211i) q^{39} +(1.11803 - 3.44095i) q^{40} +(1.76393 + 5.42882i) q^{41} +(0.500000 - 0.363271i) q^{42} +4.76393 q^{43} +3.61803 q^{45} +(4.61803 - 3.35520i) q^{46} +(1.23607 + 3.80423i) q^{47} +(0.309017 - 0.951057i) q^{48} +(5.35410 + 3.88998i) q^{49} +(-6.54508 - 4.75528i) q^{50} +(-1.23607 + 3.80423i) q^{51} +(-1.00000 - 3.07768i) q^{52} +(-1.11803 + 0.812299i) q^{53} +1.00000 q^{54} -0.618034 q^{56} +(-4.61803 + 3.35520i) q^{57} +(-2.11803 - 6.51864i) q^{58} +(3.19098 - 9.82084i) q^{59} +(-2.92705 - 2.12663i) q^{60} +(-3.00000 - 2.17963i) q^{61} +(-1.04508 + 3.21644i) q^{62} +(-0.190983 - 0.587785i) q^{63} +(-0.809017 + 0.587785i) q^{64} -11.7082 q^{65} +4.94427 q^{67} +(3.23607 - 2.35114i) q^{68} +(-1.76393 - 5.42882i) q^{69} +(-0.690983 + 2.12663i) q^{70} +(-4.85410 - 3.52671i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(-4.50000 + 13.8496i) q^{73} +(-2.76393 - 8.50651i) q^{74} +(-6.54508 + 4.75528i) q^{75} +5.70820 q^{76} -3.23607 q^{78} +(-5.54508 + 4.02874i) q^{79} +(1.11803 + 3.44095i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-4.61803 - 3.35520i) q^{82} +(1.30902 + 0.951057i) q^{83} +(-0.190983 + 0.587785i) q^{84} +(-4.47214 - 13.7638i) q^{85} +(-3.85410 + 2.80017i) q^{86} -6.85410 q^{87} +6.76393 q^{89} +(-2.92705 + 2.12663i) q^{90} +(0.618034 + 1.90211i) q^{91} +(-1.76393 + 5.42882i) q^{92} +(2.73607 + 1.98787i) q^{93} +(-3.23607 - 2.35114i) q^{94} +(6.38197 - 19.6417i) q^{95} +(0.309017 + 0.951057i) q^{96} +(7.78115 - 5.65334i) q^{97} -6.61803 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - q^{3} - q^{4} - 5 q^{5} - q^{6} - 3 q^{7} - q^{8} - q^{9} + 10 q^{10} + 4 q^{12} + 6 q^{13} - 3 q^{14} - q^{16} + 4 q^{17} - q^{18} + 16 q^{19} - 5 q^{20} + 2 q^{21} + 4 q^{23} - q^{24}+ \cdots - 22 q^{98}+O(q^{100}) \) 4 * q - q^2 - q^3 - q^4 - 5 * q^5 - q^6 - 3 * q^7 - q^8 - q^9 + 10 * q^10 + 4 * q^12 + 6 * q^13 - 3 * q^14 - q^16 + 4 * q^17 - q^18 + 16 * q^19 - 5 * q^20 + 2 * q^21 + 4 * q^23 - q^24 + 10 * q^25 - 4 * q^26 - q^27 + 2 * q^28 - 4 * q^29 + 2 * q^31 + 4 * q^32 - 16 * q^34 + 5 * q^35 - q^36 - 20 * q^37 - 14 * q^38 + 6 * q^39 + 16 * q^41 + 2 * q^42 + 28 * q^43 + 10 * q^45 + 14 * q^46 - 4 * q^47 - q^48 + 8 * q^49 - 15 * q^50 + 4 * q^51 - 4 * q^52 + 4 * q^54 + 2 * q^56 - 14 * q^57 - 4 * q^58 + 15 * q^59 - 5 * q^60 - 12 * q^61 + 7 * q^62 - 3 * q^63 - q^64 - 20 * q^65 - 16 * q^67 + 4 * q^68 - 16 * q^69 - 5 * q^70 - 6 * q^71 - q^72 - 18 * q^73 - 20 * q^74 - 15 * q^75 - 4 * q^76 - 4 * q^78 - 11 * q^79 - q^81 - 14 * q^82 + 3 * q^83 - 3 * q^84 - 2 * q^86 - 14 * q^87 + 36 * q^89 - 5 * q^90 - 2 * q^91 - 16 * q^92 + 2 * q^93 - 4 * q^94 + 30 * q^95 - q^96 + 11 * q^97 - 22 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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