LMFDB - Embedded newform 363.2.e.c.202.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,2,Mod(124,363)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("363.124");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	363.e (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.89856959337$
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 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			202.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	363.202
Dual form			363.2.e.c.124.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.363271i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.500000 - 1.53884i) q^{4} +(2.11803 - 1.53884i) q^{5} +(-0.500000 + 0.363271i) q^{6} +(-0.927051 - 2.85317i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.363271i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.500000 - 1.53884i) q^{4} +(2.11803 - 1.53884i) q^{5} +(-0.500000 + 0.363271i) q^{6} +(-0.927051 - 2.85317i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(-0.809017 - 0.587785i) q^{9} -1.61803 q^{10} -1.61803 q^{12} +(1.42705 + 1.03681i) q^{13} +(-0.572949 + 1.76336i) q^{14} +(-0.809017 - 2.48990i) q^{15} +(-1.50000 + 1.08981i) q^{16} +(1.30902 - 0.951057i) q^{17} +(0.190983 + 0.587785i) q^{18} +(-1.80902 + 5.56758i) q^{19} +(-3.42705 - 2.48990i) q^{20} -3.00000 q^{21} +3.47214 q^{23} +(1.80902 + 1.31433i) q^{24} +(0.572949 - 1.76336i) q^{25} +(-0.336881 - 1.03681i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-3.92705 + 2.85317i) q^{28} +(-1.38197 - 4.25325i) q^{29} +(-0.500000 + 1.53884i) q^{30} +(-2.30902 - 1.67760i) q^{31} +5.61803 q^{32} -1.00000 q^{34} +(-6.35410 - 4.61653i) q^{35} +(-0.500000 + 1.53884i) q^{36} +(0.0729490 + 0.224514i) q^{37} +(2.92705 - 2.12663i) q^{38} +(1.42705 - 1.03681i) q^{39} +(1.80902 + 5.56758i) q^{40} +(3.69098 - 11.3597i) q^{41} +(1.50000 + 1.08981i) q^{42} -6.23607 q^{43} -2.61803 q^{45} +(-1.73607 - 1.26133i) q^{46} +(0.500000 - 1.53884i) q^{47} +(0.572949 + 1.76336i) q^{48} +(-1.61803 + 1.17557i) q^{49} +(-0.927051 + 0.673542i) q^{50} +(-0.500000 - 1.53884i) q^{51} +(0.881966 - 2.71441i) q^{52} +(7.78115 + 5.65334i) q^{53} +0.618034 q^{54} +6.70820 q^{56} +(4.73607 + 3.44095i) q^{57} +(-0.854102 + 2.62866i) q^{58} +(3.19098 + 9.82084i) q^{59} +(-3.42705 + 2.48990i) q^{60} +(6.35410 - 4.61653i) q^{61} +(0.545085 + 1.67760i) q^{62} +(-0.927051 + 2.85317i) q^{63} +(0.190983 + 0.138757i) q^{64} +4.61803 q^{65} -9.56231 q^{67} +(-2.11803 - 1.53884i) q^{68} +(1.07295 - 3.30220i) q^{69} +(1.50000 + 4.61653i) q^{70} +(4.50000 - 3.26944i) q^{71} +(1.80902 - 1.31433i) q^{72} +(1.00000 + 3.07768i) q^{73} +(0.0450850 - 0.138757i) q^{74} +(-1.50000 - 1.08981i) q^{75} +9.47214 q^{76} -1.09017 q^{78} +(7.66312 + 5.56758i) q^{79} +(-1.50000 + 4.61653i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-5.97214 + 4.33901i) q^{82} +(0.572949 - 0.416272i) q^{83} +(1.50000 + 4.61653i) q^{84} +(1.30902 - 4.02874i) q^{85} +(3.11803 + 2.26538i) q^{86} -4.47214 q^{87} +0.527864 q^{89} +(1.30902 + 0.951057i) q^{90} +(1.63525 - 5.03280i) q^{91} +(-1.73607 - 5.34307i) q^{92} +(-2.30902 + 1.67760i) q^{93} +(-0.809017 + 0.587785i) q^{94} +(4.73607 + 14.5761i) q^{95} +(1.73607 - 5.34307i) q^{96} +(11.3541 + 8.24924i) q^{97} +1.23607 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 3 q^{7} - 5 q^{8} - q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 + 3 * q^7 - 5 * q^8 - q^9	$ 4 q - 2 q^{2} - q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 3 q^{7} - 5 q^{8} - q^{9} - 2 q^{10} - 2 q^{12} - q^{13} - 9 q^{14} - q^{15} - 6 q^{16} + 3 q^{17} + 3 q^{18} - 5 q^{19} - 7 q^{20} - 12 q^{21} - 4 q^{23} + 5 q^{24} + 9 q^{25} - 17 q^{26} - q^{27} - 9 q^{28} - 10 q^{29} - 2 q^{30} - 7 q^{31} + 18 q^{32} - 4 q^{34} - 12 q^{35} - 2 q^{36} + 7 q^{37} + 5 q^{38} - q^{39} + 5 q^{40} + 17 q^{41} + 6 q^{42} - 16 q^{43} - 6 q^{45} + 2 q^{46} + 2 q^{47} + 9 q^{48} - 2 q^{49} + 3 q^{50} - 2 q^{51} + 8 q^{52} + 11 q^{53} - 2 q^{54} + 10 q^{57} + 10 q^{58} + 15 q^{59} - 7 q^{60} + 12 q^{61} - 9 q^{62} + 3 q^{63} + 3 q^{64} + 14 q^{65} + 2 q^{67} - 4 q^{68} + 11 q^{69} + 6 q^{70} + 18 q^{71} + 5 q^{72} + 4 q^{73} - 11 q^{74} - 6 q^{75} + 20 q^{76} + 18 q^{78} + 15 q^{79} - 6 q^{80} - q^{81} - 6 q^{82} + 9 q^{83} + 6 q^{84} + 3 q^{85} + 8 q^{86} + 20 q^{89} + 3 q^{90} - 27 q^{91} + 2 q^{92} - 7 q^{93} - q^{94} + 10 q^{95} - 2 q^{96} + 32 q^{97} - 4 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 + 3 * q^7 - 5 * q^8 - q^9 - 2 * q^10 - 2 * q^12 - q^13 - 9 * q^14 - q^15 - 6 * q^16 + 3 * q^17 + 3 * q^18 - 5 * q^19 - 7 * q^20 - 12 * q^21 - 4 * q^23 + 5 * q^24 + 9 * q^25 - 17 * q^26 - q^27 - 9 * q^28 - 10 * q^29 - 2 * q^30 - 7 * q^31 + 18 * q^32 - 4 * q^34 - 12 * q^35 - 2 * q^36 + 7 * q^37 + 5 * q^38 - q^39 + 5 * q^40 + 17 * q^41 + 6 * q^42 - 16 * q^43 - 6 * q^45 + 2 * q^46 + 2 * q^47 + 9 * q^48 - 2 * q^49 + 3 * q^50 - 2 * q^51 + 8 * q^52 + 11 * q^53 - 2 * q^54 + 10 * q^57 + 10 * q^58 + 15 * q^59 - 7 * q^60 + 12 * q^61 - 9 * q^62 + 3 * q^63 + 3 * q^64 + 14 * q^65 + 2 * q^67 - 4 * q^68 + 11 * q^69 + 6 * q^70 + 18 * q^71 + 5 * q^72 + 4 * q^73 - 11 * q^74 - 6 * q^75 + 20 * q^76 + 18 * q^78 + 15 * q^79 - 6 * q^80 - q^81 - 6 * q^82 + 9 * q^83 + 6 * q^84 + 3 * q^85 + 8 * q^86 + 20 * q^89 + 3 * q^90 - 27 * q^91 + 2 * q^92 - 7 * q^93 - q^94 + 10 * q^95 - 2 * q^96 + 32 * q^97 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.500000	−	0.363271i	−0.353553	−	0.256872i	0.396805	−	0.917903i	$-0.370119\pi$
$2$	−0.500000	−	0.363271i	−0.353553	−	0.256872i	−0.750358	+	0.661031i	$0.770119\pi$
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$4$	−0.500000	−	1.53884i	−0.250000	−	0.769421i
$5$	2.11803	−	1.53884i	0.947214	−	0.688191i	−0.00293261	−	0.999996i	$-0.500933\pi$
$5$	2.11803	−	1.53884i	0.947214	−	0.688191i	0.950146	+	0.311805i	$0.100933\pi$
$6$	−0.500000	+	0.363271i	−0.204124	+	0.148305i
$7$	−0.927051	−	2.85317i	−0.350392	−	1.07840i	−0.958633	−	0.284644i	$-0.908125\pi$
$7$	−0.927051	−	2.85317i	−0.350392	−	1.07840i	0.608241	−	0.793752i	$-0.291875\pi$
$8$	−0.690983	+	2.12663i	−0.244299	+	0.751876i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	−1.61803			−0.511667
$11$		0			0
$11$		0			0
$12$	−1.61803			−0.467086
$13$	1.42705	+	1.03681i	0.395793	+	0.287560i	0.767825	−	0.640660i	$-0.221339\pi$
$13$	1.42705	+	1.03681i	0.395793	+	0.287560i	−0.372032	+	0.928220i	$0.621339\pi$
$14$	−0.572949	+	1.76336i	−0.153127	+	0.471277i
$15$	−0.809017	−	2.48990i	−0.208887	−	0.642889i
$16$	−1.50000	+	1.08981i	−0.375000	+	0.272453i
$17$	1.30902	−	0.951057i	0.317483	−	0.230665i	−0.417618	−	0.908623i	$-0.637135\pi$
$17$	1.30902	−	0.951057i	0.317483	−	0.230665i	0.735101	+	0.677958i	$0.237135\pi$
$18$	0.190983	+	0.587785i	0.0450151	+	0.138542i
$19$	−1.80902	+	5.56758i	−0.415017	+	1.27729i	0.497219	+	0.867625i	$0.334355\pi$
$19$	−1.80902	+	5.56758i	−0.415017	+	1.27729i	−0.912236	+	0.409666i	$0.865645\pi$
$20$	−3.42705	−	2.48990i	−0.766312	−	0.556758i
$21$	−3.00000			−0.654654
$22$		0			0
$23$	3.47214			0.723990			0.361995	−	0.932180i	$-0.382096\pi$
$23$	3.47214			0.723990			0.361995	+	0.932180i	$0.382096\pi$
$24$	1.80902	+	1.31433i	0.369264	+	0.268286i
$25$	0.572949	−	1.76336i	0.114590	−	0.352671i
$26$	−0.336881	−	1.03681i	−0.0660678	−	0.203336i
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	−3.92705	+	2.85317i	−0.742143	+	0.539198i
$29$	−1.38197	−	4.25325i	−0.256625	−	0.789809i	−0.993505	−	0.113787i	$-0.963702\pi$
$29$	−1.38197	−	4.25325i	−0.256625	−	0.789809i	0.736881	−	0.676023i	$-0.236298\pi$
$30$	−0.500000	+	1.53884i	−0.0912871	+	0.280953i
$31$	−2.30902	−	1.67760i	−0.414712	−	0.301306i	0.360795	−	0.932645i	$-0.382505\pi$
$31$	−2.30902	−	1.67760i	−0.414712	−	0.301306i	−0.775507	+	0.631340i	$0.782505\pi$
$32$	5.61803			0.993137
$33$		0			0
$34$	−1.00000			−0.171499
$35$	−6.35410	−	4.61653i	−1.07404	−	0.780335i
$36$	−0.500000	+	1.53884i	−0.0833333	+	0.256474i
$37$	0.0729490	+	0.224514i	0.0119927	+	0.0369099i	0.956874	−	0.290504i	$-0.0938229\pi$
$37$	0.0729490	+	0.224514i	0.0119927	+	0.0369099i	−0.944881	+	0.327414i	$0.893823\pi$
$38$	2.92705	−	2.12663i	0.474830	−	0.344984i
$39$	1.42705	−	1.03681i	0.228511	−	0.166023i
$40$	1.80902	+	5.56758i	0.286031	+	0.880312i
$41$	3.69098	−	11.3597i	0.576435	−	1.77408i	−0.0548065	−	0.998497i	$-0.517454\pi$
$41$	3.69098	−	11.3597i	0.576435	−	1.77408i	0.631241	−	0.775587i	$-0.282546\pi$
$42$	1.50000	+	1.08981i	0.231455	+	0.168162i
$43$	−6.23607			−0.950991			−0.475496	−	0.879718i	$-0.657731\pi$
$43$	−6.23607			−0.950991			−0.475496	+	0.879718i	$0.657731\pi$
$44$		0			0
$45$	−2.61803			−0.390273
$46$	−1.73607	−	1.26133i	−0.255969	−	0.185973i
$47$	0.500000	−	1.53884i	0.0729325	−	0.224463i	−0.907945	−	0.419089i	$-0.862349\pi$
$47$	0.500000	−	1.53884i	0.0729325	−	0.224463i	0.980877	+	0.194626i	$0.0623494\pi$
$48$	0.572949	+	1.76336i	0.0826981	+	0.254518i
$49$	−1.61803	+	1.17557i	−0.231148	+	0.167939i
$50$	−0.927051	+	0.673542i	−0.131105	+	0.0952532i
$51$	−0.500000	−	1.53884i	−0.0700140	−	0.215481i
$52$	0.881966	−	2.71441i	0.122307	−	0.376421i
$53$	7.78115	+	5.65334i	1.06882	+	0.776546i	0.975700	−	0.219109i	$-0.0703150\pi$
$53$	7.78115	+	5.65334i	1.06882	+	0.776546i	0.0931231	+	0.995655i	$0.470315\pi$
$54$	0.618034			0.0841038
$55$		0			0
$56$	6.70820			0.896421
$57$	4.73607	+	3.44095i	0.627308	+	0.455766i
$58$	−0.854102	+	2.62866i	−0.112149	+	0.345159i
$59$	3.19098	+	9.82084i	0.415431	+	1.27856i	0.911865	+	0.410490i	$0.134642\pi$
$59$	3.19098	+	9.82084i	0.415431	+	1.27856i	−0.496435	+	0.868074i	$0.665358\pi$
$60$	−3.42705	+	2.48990i	−0.442430	+	0.321444i
$61$	6.35410	−	4.61653i	0.813559	−	0.591085i	−0.101301	−	0.994856i	$-0.532301\pi$
$61$	6.35410	−	4.61653i	0.813559	−	0.591085i	0.914860	+	0.403770i	$0.132301\pi$
$62$	0.545085	+	1.67760i	0.0692259	+	0.213055i
$63$	−0.927051	+	2.85317i	−0.116797	+	0.359466i
$64$	0.190983	+	0.138757i	0.0238729	+	0.0173447i
$65$	4.61803			0.572797
$66$		0			0
$67$	−9.56231			−1.16822			−0.584111	−	0.811674i	$-0.698557\pi$
$67$	−9.56231			−1.16822			−0.584111	+	0.811674i	$0.698557\pi$
$68$	−2.11803	−	1.53884i	−0.256849	−	0.186612i
$69$	1.07295	−	3.30220i	0.129168	−	0.397538i
$70$	1.50000	+	4.61653i	0.179284	+	0.551780i
$71$	4.50000	−	3.26944i	0.534052	−	0.388011i	−0.287819	−	0.957685i	$-0.592930\pi$
$71$	4.50000	−	3.26944i	0.534052	−	0.388011i	0.821871	+	0.569673i	$0.192930\pi$
$72$	1.80902	−	1.31433i	0.213195	−	0.154895i
$73$	1.00000	+	3.07768i	0.117041	+	0.360216i	0.992367	−	0.123317i	$-0.0393533\pi$
$73$	1.00000	+	3.07768i	0.117041	+	0.360216i	−0.875326	+	0.483533i	$0.839353\pi$
$74$	0.0450850	−	0.138757i	0.00524102	−	0.0161302i
$75$	−1.50000	−	1.08981i	−0.173205	−	0.125841i
$76$	9.47214			1.08653
$77$		0			0
$78$	−1.09017			−0.123437
$79$	7.66312	+	5.56758i	0.862168	+	0.626402i	0.928474	−	0.371397i	$-0.121121\pi$
$79$	7.66312	+	5.56758i	0.862168	+	0.626402i	−0.0663057	+	0.997799i	$0.521121\pi$
$80$	−1.50000	+	4.61653i	−0.167705	+	0.516143i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	−5.97214	+	4.33901i	−0.659512	+	0.479164i
$83$	0.572949	−	0.416272i	0.0628893	−	0.0456918i	−0.555896	−	0.831252i	$-0.687625\pi$
$83$	0.572949	−	0.416272i	0.0628893	−	0.0456918i	0.618786	+	0.785560i	$0.287625\pi$
$84$	1.50000	+	4.61653i	0.163663	+	0.503704i
$85$	1.30902	−	4.02874i	0.141983	−	0.436978i
$86$	3.11803	+	2.26538i	0.336226	+	0.244283i
$87$	−4.47214			−0.479463
$88$		0			0
$89$	0.527864			0.0559535			0.0279767	−	0.999609i	$-0.491094\pi$
$89$	0.527864			0.0559535			0.0279767	+	0.999609i	$0.491094\pi$
$90$	1.30902	+	0.951057i	0.137983	+	0.100250i
$91$	1.63525	−	5.03280i	0.171421	−	0.527580i
$92$	−1.73607	−	5.34307i	−0.180998	−	0.557053i
$93$	−2.30902	+	1.67760i	−0.239434	+	0.173959i
$94$	−0.809017	+	0.587785i	−0.0834437	+	0.0606254i
$95$	4.73607	+	14.5761i	0.485910	+	1.49548i
$96$	1.73607	−	5.34307i	0.177187	−	0.545325i
$97$	11.3541	+	8.24924i	1.15283	+	0.837583i	0.988855	−	0.148881i	$-0.0475670\pi$
$97$	11.3541	+	8.24924i	1.15283	+	0.837583i	0.163979	+	0.986464i	$0.447567\pi$
$98$	1.23607			0.124862
$99$		0			0
$100$	−3.00000			−0.300000
$101$	−2.42705	−	1.76336i	−0.241501	−	0.175460i	0.460451	−	0.887685i	$-0.347688\pi$
$101$	−2.42705	−	1.76336i	−0.241501	−	0.175460i	−0.701952	+	0.712225i	$0.747688\pi$
$102$	−0.309017	+	0.951057i	−0.0305972	+	0.0941686i
$103$	−1.85410	−	5.70634i	−0.182690	−	0.562262i	0.817211	−	0.576339i	$-0.195519\pi$
$103$	−1.85410	−	5.70634i	−0.182690	−	0.562262i	−0.999901	+	0.0140765i	$0.995519\pi$
$104$	−3.19098	+	2.31838i	−0.312902	+	0.227336i
$105$	−6.35410	+	4.61653i	−0.620097	+	0.450527i
$106$	−1.83688	−	5.65334i	−0.178414	−	0.549101i
$107$	1.30902	−	4.02874i	0.126547	−	0.389473i	−0.867632	−	0.497206i	$-0.834359\pi$
$107$	1.30902	−	4.02874i	0.126547	−	0.389473i	0.994180	+	0.107733i	$0.0343592\pi$
$108$	1.30902	+	0.951057i	0.125960	+	0.0915155i
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$		0			0
$111$	0.236068			0.0224066
$112$	4.50000	+	3.26944i	0.425210	+	0.308933i
$113$	0.218847	−	0.673542i	0.0205874	−	0.0633615i	−0.940235	−	0.340526i	$-0.889395\pi$
$113$	0.218847	−	0.673542i	0.0205874	−	0.0633615i	0.960822	+	0.277165i	$0.0893948\pi$
$114$	−1.11803	−	3.44095i	−0.104713	−	0.322275i
$115$	7.35410	−	5.34307i	0.685774	−	0.498244i
$116$	−5.85410	+	4.25325i	−0.543540	+	0.394905i
$117$	−0.545085	−	1.67760i	−0.0503931	−	0.155094i
$118$	1.97214	−	6.06961i	0.181550	−	0.558753i
$119$	−3.92705	−	2.85317i	−0.359992	−	0.261550i
$120$	5.85410			0.534404
$121$		0			0
$122$	−4.85410			−0.439470
$123$	−9.66312	−	7.02067i	−0.871294	−	0.633032i
$124$	−1.42705	+	4.39201i	−0.128153	+	0.394414i
$125$	2.54508	+	7.83297i	0.227639	+	0.700602i
$126$	1.50000	−	1.08981i	0.133631	−	0.0970883i
$127$	−3.00000	+	2.17963i	−0.266207	+	0.193411i	−0.712879	−	0.701287i	$-0.752609\pi$
$127$	−3.00000	+	2.17963i	−0.266207	+	0.193411i	0.446672	+	0.894698i	$0.352609\pi$
$128$	−3.51722	−	10.8249i	−0.310881	−	0.956794i
$129$	−1.92705	+	5.93085i	−0.169667	+	0.522182i
$130$	−2.30902	−	1.67760i	−0.202514	−	0.147135i
$131$	7.14590			0.624340			0.312170	−	0.950026i	$-0.398944\pi$
$131$	7.14590			0.624340			0.312170	+	0.950026i	$0.398944\pi$
$132$		0			0
$133$	17.5623			1.52285
$134$	4.78115	+	3.47371i	0.413029	+	0.300083i
$135$	−0.809017	+	2.48990i	−0.0696291	+	0.214296i
$136$	1.11803	+	3.44095i	0.0958706	+	0.295059i
$137$	−6.04508	+	4.39201i	−0.516466	+	0.375235i	−0.815271	−	0.579079i	$-0.803412\pi$
$137$	−6.04508	+	4.39201i	−0.516466	+	0.375235i	0.298805	+	0.954314i	$0.403412\pi$
$138$	−1.73607	+	1.26133i	−0.147784	+	0.107371i
$139$	0.263932	+	0.812299i	0.0223864	+	0.0688983i	0.961626	−	0.274365i	$-0.0884677\pi$
$139$	0.263932	+	0.812299i	0.0223864	+	0.0688983i	−0.939239	+	0.343263i	$0.888468\pi$
$140$	−3.92705	+	12.0862i	−0.331896	+	1.02147i
$141$	−1.30902	−	0.951057i	−0.110239	−	0.0800934i
$142$	−3.43769			−0.288485
$143$		0			0
$144$	1.85410			0.154508
$145$	−9.47214	−	6.88191i	−0.786618	−	0.571511i
$146$	0.618034	−	1.90211i	0.0511489	−	0.157420i
$147$	0.618034	+	1.90211i	0.0509746	+	0.156884i
$148$	0.309017	−	0.224514i	0.0254010	−	0.0184549i
$149$	12.1353	−	8.81678i	0.994159	−	0.722299i	0.0333309	−	0.999444i	$-0.489388\pi$
$149$	12.1353	−	8.81678i	0.994159	−	0.722299i	0.960828	+	0.277146i	$0.0893885\pi$
$150$	0.354102	+	1.08981i	0.0289123	+	0.0889829i
$151$	−0.618034	+	1.90211i	−0.0502949	+	0.154792i	−0.973050	−	0.230596i	$-0.925932\pi$
$151$	−0.618034	+	1.90211i	−0.0502949	+	0.154792i	0.922755	+	0.385388i	$0.125932\pi$
$152$	−10.5902	−	7.69421i	−0.858976	−	0.624083i
$153$	−1.61803			−0.130810
$154$		0			0
$155$	−7.47214			−0.600176
$156$	−2.30902	−	1.67760i	−0.184869	−	0.134315i
$157$	−1.14590	+	3.52671i	−0.0914526	+	0.281462i	−0.986313	−	0.164884i	$-0.947275\pi$
$157$	−1.14590	+	3.52671i	−0.0914526	+	0.281462i	0.894860	+	0.446346i	$0.147275\pi$
$158$	−1.80902	−	5.56758i	−0.143918	−	0.442933i
$159$	7.78115	−	5.65334i	0.617086	−	0.448339i
$160$	11.8992	−	8.64527i	0.940713	−	0.683468i
$161$	−3.21885	−	9.90659i	−0.253681	−	0.780749i
$162$	0.190983	−	0.587785i	0.0150050	−	0.0461808i
$163$	−14.7812	−	10.7391i	−1.15775	−	0.841154i	−0.168257	−	0.985743i	$-0.553814\pi$
$163$	−14.7812	−	10.7391i	−1.15775	−	0.841154i	−0.989492	+	0.144589i	$0.953814\pi$
$164$	−19.3262			−1.50913
$165$		0			0
$166$	−0.437694			−0.0339717
$167$	8.11803	+	5.89810i	0.628192	+	0.456408i	0.855774	−	0.517351i	$-0.173082\pi$
$167$	8.11803	+	5.89810i	0.628192	+	0.456408i	−0.227581	+	0.973759i	$0.573082\pi$
$168$	2.07295	−	6.37988i	0.159931	−	0.492219i
$169$	−3.05573	−	9.40456i	−0.235056	−	0.723428i
$170$	−2.11803	+	1.53884i	−0.162446	+	0.118024i
$171$	4.73607	−	3.44095i	0.362176	−	0.263136i
$172$	3.11803	+	9.59632i	0.237748	+	0.731713i
$173$	−4.75329	+	14.6291i	−0.361386	+	1.11223i	0.590828	+	0.806798i	$0.298801\pi$
$173$	−4.75329	+	14.6291i	−0.361386	+	1.11223i	−0.952213	+	0.305433i	$0.901199\pi$
$174$	2.23607	+	1.62460i	0.169516	+	0.123160i
$175$	−5.56231			−0.420471
$176$		0			0
$177$	10.3262			0.776168
$178$	−0.263932	−	0.191758i	−0.0197825	−	0.0143729i
$179$	−0.690983	+	2.12663i	−0.0516465	+	0.158952i	−0.973553	−	0.228460i	$-0.926631\pi$
$179$	−0.690983	+	2.12663i	−0.0516465	+	0.158952i	0.921907	+	0.387412i	$0.126631\pi$
$180$	1.30902	+	4.02874i	0.0975684	+	0.300285i
$181$	14.1353	−	10.2699i	1.05067	−	0.763353i	0.0783264	−	0.996928i	$-0.475042\pi$
$181$	14.1353	−	10.2699i	1.05067	−	0.763353i	0.972339	+	0.233575i	$0.0750424\pi$
$182$	−2.64590	+	1.92236i	−0.196127	+	0.142495i
$183$	−2.42705	−	7.46969i	−0.179413	−	0.552176i
$184$	−2.39919	+	7.38394i	−0.176870	+	0.544351i
$185$	0.500000	+	0.363271i	0.0367607	+	0.0267082i
$186$	1.76393			0.129338
$187$		0			0
$188$	−2.61803			−0.190940
$189$	2.42705	+	1.76336i	0.176542	+	0.128265i
$190$	2.92705	−	9.00854i	0.212351	−	0.653548i
$191$	−2.30902	−	7.10642i	−0.167075	−	0.514203i	0.832109	−	0.554613i	$-0.187134\pi$
$191$	−2.30902	−	7.10642i	−0.167075	−	0.514203i	−0.999183	+	0.0404100i	$0.987134\pi$
$192$	0.190983	−	0.138757i	0.0137830	−	0.0100139i
$193$	−15.0172	+	10.9106i	−1.08096	+	0.785366i	−0.977851	−	0.209304i	$-0.932880\pi$
$193$	−15.0172	+	10.9106i	−1.08096	+	0.785366i	−0.103113	+	0.994670i	$0.532880\pi$
$194$	−2.68034	−	8.24924i	−0.192437	−	0.592261i
$195$	1.42705	−	4.39201i	0.102193	−	0.314518i
$196$	2.61803	+	1.90211i	0.187002	+	0.135865i
$197$	−24.3820			−1.73714			−0.868572	−	0.495564i	$-0.834961\pi$
$197$	−24.3820			−1.73714			−0.868572	+	0.495564i	$0.834961\pi$
$198$		0			0
$199$	−16.7082			−1.18441			−0.592207	−	0.805786i	$-0.701743\pi$
$199$	−16.7082			−1.18441			−0.592207	+	0.805786i	$0.701743\pi$
$200$	3.35410	+	2.43690i	0.237171	+	0.172315i
$201$	−2.95492	+	9.09429i	−0.208424	+	0.641462i
$202$	0.572949	+	1.76336i	0.0403126	+	0.124069i
$203$	−10.8541	+	7.88597i	−0.761809	+	0.553486i
$204$	−2.11803	+	1.53884i	−0.148292	+	0.107740i
$205$	−9.66312	−	29.7400i	−0.674902	−	2.07713i
$206$	−1.14590	+	3.52671i	−0.0798385	+	0.245718i
$207$	−2.80902	−	2.04087i	−0.195240	−	0.141850i
$208$	−3.27051			−0.226769
$209$		0			0
$210$	4.85410			0.334965
$211$	−18.0172	−	13.0903i	−1.24036	−	0.901172i	−0.242735	−	0.970093i	$-0.578044\pi$
$211$	−18.0172	−	13.0903i	−1.24036	−	0.901172i	−0.997622	+	0.0689209i	$0.978044\pi$
$212$	4.80902	−	14.8006i	0.330285	−	1.01651i
$213$	−1.71885	−	5.29007i	−0.117773	−	0.362469i
$214$	−2.11803	+	1.53884i	−0.144786	+	0.105193i
$215$	−13.2082	+	9.59632i	−0.900792	+	0.654464i
$216$	−0.690983	−	2.12663i	−0.0470154	−	0.144699i
$217$	−2.64590	+	8.14324i	−0.179615	+	0.552799i
$218$		0			0
$219$	3.23607			0.218673
$220$		0			0
$221$	2.85410			0.191988
$222$	−0.118034	−	0.0857567i	−0.00792192	−	0.00575561i
$223$	0.218847	−	0.673542i	0.0146551	−	0.0451037i	−0.943462	−	0.331482i	$-0.892451\pi$
$223$	0.218847	−	0.673542i	0.0146551	−	0.0451037i	0.958117	+	0.286378i	$0.0924514\pi$
$224$	−5.20820	−	16.0292i	−0.347988	−	1.07100i
$225$	−1.50000	+	1.08981i	−0.100000	+	0.0726543i
$226$	−0.354102	+	0.257270i	−0.0235545	+	0.0171134i
$227$	7.69098	+	23.6704i	0.510468	+	1.57106i	0.791379	+	0.611326i	$0.209364\pi$
$227$	7.69098	+	23.6704i	0.510468	+	1.57106i	−0.280910	+	0.959734i	$0.590636\pi$
$228$	2.92705	−	9.00854i	0.193849	−	0.596605i
$229$	−8.09017	−	5.87785i	−0.534613	−	0.388419i	0.287467	−	0.957790i	$-0.407187\pi$
$229$	−8.09017	−	5.87785i	−0.534613	−	0.388419i	−0.822081	+	0.569371i	$0.807187\pi$
$230$	−5.61803			−0.370442
$231$		0			0
$232$	10.0000			0.656532
$233$	19.6803	+	14.2986i	1.28930	+	0.936733i	0.999791	−	0.0204420i	$-0.00650735\pi$
$233$	19.6803	+	14.2986i	1.28930	+	0.936733i	0.289511	+	0.957175i	$0.406507\pi$
$234$	−0.336881	+	1.03681i	−0.0220226	+	0.0677786i
$235$	−1.30902	−	4.02874i	−0.0853909	−	0.262806i
$236$	13.5172	−	9.82084i	0.879896	−	0.639282i
$237$	7.66312	−	5.56758i	0.497773	−	0.361653i
$238$	0.927051	+	2.85317i	0.0600918	+	0.184944i
$239$	−0.791796	+	2.43690i	−0.0512170	+	0.157630i	−0.973394	−	0.229139i	$-0.926409\pi$
$239$	−0.791796	+	2.43690i	−0.0512170	+	0.157630i	0.922177	+	0.386769i	$0.126409\pi$
$240$	3.92705	+	2.85317i	0.253490	+	0.184171i
$241$	23.1246			1.48959			0.744794	−	0.667295i	$-0.232548\pi$
$241$	23.1246			1.48959			0.744794	+	0.667295i	$0.232548\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$	−10.2812	−	7.46969i	−0.658183	−	0.478198i
$245$	−1.61803	+	4.97980i	−0.103372	+	0.318148i
$246$	2.28115	+	7.02067i	0.145441	+	0.447621i
$247$	−8.35410	+	6.06961i	−0.531559	+	0.386200i
$248$	5.16312	−	3.75123i	0.327858	−	0.238203i
$249$	−0.218847	−	0.673542i	−0.0138689	−	0.0426840i
$250$	1.57295	−	4.84104i	0.0994820	−	0.306174i
$251$	6.30902	+	4.58377i	0.398222	+	0.289325i	0.768816	−	0.639470i	$-0.220846\pi$
$251$	6.30902	+	4.58377i	0.398222	+	0.289325i	−0.370595	+	0.928795i	$0.620846\pi$
$252$	4.85410			0.305780
$253$		0			0
$254$	2.29180			0.143800
$255$	−3.42705	−	2.48990i	−0.214610	−	0.155923i
$256$	−2.02786	+	6.24112i	−0.126742	+	0.390070i
$257$	−3.60739	−	11.1024i	−0.225023	−	0.692549i	−0.998289	−	0.0584679i	$-0.981378\pi$
$257$	−3.60739	−	11.1024i	−0.225023	−	0.692549i	0.773266	−	0.634081i	$-0.218622\pi$
$258$	3.11803	−	2.26538i	0.194120	−	0.141037i
$259$	0.572949	−	0.416272i	0.0356013	−	0.0258659i
$260$	−2.30902	−	7.10642i	−0.143199	−	0.440722i
$261$	−1.38197	+	4.25325i	−0.0855415	+	0.263270i
$262$	−3.57295	−	2.59590i	−0.220738	−	0.160375i
$263$	16.3262			1.00672			0.503359	−	0.864077i	$-0.332097\pi$
$263$	16.3262			1.00672			0.503359	+	0.864077i	$0.332097\pi$
$264$		0			0
$265$	25.1803			1.54682
$266$	−8.78115	−	6.37988i	−0.538407	−	0.391176i
$267$	0.163119	−	0.502029i	0.00998272	−	0.0307236i
$268$	4.78115	+	14.7149i	0.292055	+	0.898854i
$269$	−12.5623	+	9.12705i	−0.765937	+	0.556486i	−0.900726	−	0.434388i	$-0.856965\pi$
$269$	−12.5623	+	9.12705i	−0.765937	+	0.556486i	0.134788	+	0.990874i	$0.456965\pi$
$270$	1.30902	−	0.951057i	0.0796642	−	0.0578795i
$271$	8.42705	+	25.9358i	0.511907	+	1.57549i	0.788840	+	0.614598i	$0.210682\pi$
$271$	8.42705	+	25.9358i	0.511907	+	1.57549i	−0.276933	+	0.960889i	$0.589318\pi$
$272$	−0.927051	+	2.85317i	−0.0562107	+	0.172999i
$273$	−4.28115	−	3.11044i	−0.259107	−	0.188252i
$274$	4.61803			0.278986
$275$		0			0
$276$	−5.61803			−0.338166
$277$	24.7254	+	17.9641i	1.48561	+	1.07936i	0.975696	+	0.219129i	$0.0703217\pi$
$277$	24.7254	+	17.9641i	1.48561	+	1.07936i	0.509911	+	0.860227i	$0.329678\pi$
$278$	0.163119	−	0.502029i	0.00978323	−	0.0301097i
$279$	0.881966	+	2.71441i	0.0528019	+	0.162508i
$280$	14.2082	−	10.3229i	0.849103	−	0.616909i
$281$	−0.618034	+	0.449028i	−0.0368688	+	0.0267868i	−0.606067	−	0.795414i	$-0.707254\pi$
$281$	−0.618034	+	0.449028i	−0.0368688	+	0.0267868i	0.569198	+	0.822200i	$0.307254\pi$
$282$	0.309017	+	0.951057i	0.0184017	+	0.0566346i
$283$	−0.0557281	+	0.171513i	−0.00331269	+	0.0101954i	−0.952699	−	0.303915i	$-0.901706\pi$
$283$	−0.0557281	+	0.171513i	−0.00331269	+	0.0101954i	0.949387	+	0.314110i	$0.101706\pi$
$284$	−7.28115	−	5.29007i	−0.432057	−	0.313908i
$285$	15.3262			0.907848
$286$		0			0
$287$	−35.8328			−2.11514
$288$	−4.54508	−	3.30220i	−0.267822	−	0.194584i
$289$	−4.44427	+	13.6781i	−0.261428	+	0.804592i
$290$	2.23607	+	6.88191i	0.131306	+	0.404120i
$291$	11.3541	−	8.24924i	0.665589	−	0.483579i
$292$	4.23607	−	3.07768i	0.247897	−	0.180108i
$293$	−0.0172209	−	0.0530006i	−0.00100606	−	0.00309633i	0.950552	−	0.310565i	$-0.100518\pi$
$293$	−0.0172209	−	0.0530006i	−0.00100606	−	0.00309633i	−0.951558	+	0.307468i	$0.900518\pi$
$294$	0.381966	−	1.17557i	0.0222767	−	0.0685607i
$295$	21.8713	+	15.8904i	1.27340	+	0.925178i
$296$	−0.527864			−0.0306815
$297$		0			0
$298$	−9.27051			−0.537026
$299$	4.95492	+	3.59996i	0.286550	+	0.208191i
$300$	−0.927051	+	2.85317i	−0.0535233	+	0.164728i
$301$	5.78115	+	17.7926i	0.333220	+	1.02555i
$302$	1.00000	−	0.726543i	0.0575435	−	0.0418078i
$303$	−2.42705	+	1.76336i	−0.139430	+	0.101302i
$304$	−3.35410	−	10.3229i	−0.192371	−	0.592057i
$305$	6.35410	−	19.5559i	0.363835	−	1.11977i
$306$	0.809017	+	0.587785i	0.0462484	+	0.0336014i
$307$	−0.562306			−0.0320925			−0.0160462	−	0.999871i	$-0.505108\pi$
$307$	−0.562306			−0.0320925			−0.0160462	+	0.999871i	$0.505108\pi$
$308$		0			0
$309$	−6.00000			−0.341328
$310$	3.73607	+	2.71441i	0.212194	+	0.154168i
$311$	0.781153	−	2.40414i	0.0442951	−	0.136326i	−0.926463	−	0.376385i	$-0.877167\pi$
$311$	0.781153	−	2.40414i	0.0442951	−	0.136326i	0.970758	+	0.240059i	$0.0771668\pi$
$312$	1.21885	+	3.75123i	0.0690036	+	0.212371i
$313$	−20.8992	+	15.1841i	−1.18129	+	0.858259i	−0.992317	−	0.123723i	$-0.960517\pi$
$313$	−20.8992	+	15.1841i	−1.18129	+	0.858259i	−0.188975	+	0.981982i	$0.560517\pi$
$314$	1.85410	−	1.34708i	0.104633	−	0.0760203i
$315$	2.42705	+	7.46969i	0.136749	+	0.420870i
$316$	4.73607	−	14.5761i	0.266425	−	0.819971i
$317$	15.6631	+	11.3799i	0.879728	+	0.639160i	0.933180	−	0.359410i	$-0.117022\pi$
$317$	15.6631	+	11.3799i	0.879728	+	0.639160i	−0.0534512	+	0.998570i	$0.517022\pi$
$318$	−5.94427			−0.333338
$319$		0			0
$320$	0.618034			0.0345492
$321$	−3.42705	−	2.48990i	−0.191279	−	0.138973i
$322$	−1.98936	+	6.12261i	−0.110863	+	0.341200i
$323$	2.92705	+	9.00854i	0.162865	+	0.501248i
$324$	1.30902	−	0.951057i	0.0727232	−	0.0528365i
$325$	2.64590	−	1.92236i	0.146768	−	0.106633i
$326$	3.48936	+	10.7391i	0.193258	+	0.594786i
$327$		0			0
$328$	21.6074	+	15.6987i	1.19307	+	0.866815i
$329$	−4.85410			−0.267615
$330$		0			0
$331$	26.5967			1.46189			0.730945	−	0.682437i	$-0.239080\pi$
$331$	26.5967			1.46189			0.730945	+	0.682437i	$0.239080\pi$
$332$	−0.927051	−	0.673542i	−0.0508785	−	0.0369654i
$333$	0.0729490	−	0.224514i	0.00399758	−	0.0123033i
$334$	−1.91641	−	5.89810i	−0.104861	−	0.322730i
$335$	−20.2533	+	14.7149i	−1.10656	+	0.803960i
$336$	4.50000	−	3.26944i	0.245495	−	0.178363i
$337$	0.0901699	+	0.277515i	0.00491187	+	0.0151172i	0.953482	−	0.301449i	$-0.0974702\pi$
$337$	0.0901699	+	0.277515i	0.00491187	+	0.0151172i	−0.948571	+	0.316566i	$0.897470\pi$
$338$	−1.88854	+	5.81234i	−0.102723	+	0.316150i
$339$	−0.572949	−	0.416272i	−0.0311183	−	0.0226088i
$340$	−6.85410			−0.371716
$341$		0			0
$342$	−3.61803			−0.195641
$343$	−12.1353	−	8.81678i	−0.655242	−	0.476061i
$344$	4.30902	−	13.2618i	0.232327	−	0.715028i
$345$	−2.80902	−	8.64527i	−0.151232	−	0.465445i
$346$	7.69098	−	5.58783i	0.413470	−	0.300403i
$347$	−16.9443	+	12.3107i	−0.909616	+	0.660875i	−0.940918	−	0.338635i	$-0.890035\pi$
$347$	−16.9443	+	12.3107i	−0.909616	+	0.660875i	0.0313016	+	0.999510i	$0.490035\pi$
$348$	2.23607	+	6.88191i	0.119866	+	0.368909i
$349$	3.12868	−	9.62908i	0.167474	−	0.515433i	−0.831736	−	0.555172i	$-0.812653\pi$
$349$	3.12868	−	9.62908i	0.167474	−	0.515433i	0.999210	+	0.0397388i	$0.0126526\pi$
$350$	2.78115	+	2.02063i	0.148659	+	0.108007i
$351$	−1.76393			−0.0941517
$352$		0			0
$353$	−10.4721			−0.557376			−0.278688	−	0.960382i	$-0.589899\pi$
$353$	−10.4721			−0.557376			−0.278688	+	0.960382i	$0.589899\pi$
$354$	−5.16312	−	3.75123i	−0.274417	−	0.199375i
$355$	4.50000	−	13.8496i	0.238835	−	0.735059i
$356$	−0.263932	−	0.812299i	−0.0139884	−	0.0430518i
$357$	−3.92705	+	2.85317i	−0.207842	+	0.151006i
$358$	1.11803	−	0.812299i	0.0590899	−	0.0429313i
$359$	3.94427	+	12.1392i	0.208171	+	0.640684i	0.999568	+	0.0293817i	$0.00935385\pi$
$359$	3.94427	+	12.1392i	0.208171	+	0.640684i	−0.791398	+	0.611302i	$0.790646\pi$
$360$	1.80902	−	5.56758i	0.0953436	−	0.293437i
$361$	−12.3541	−	8.97578i	−0.650216	−	0.472409i
$362$	−10.7984			−0.567550
$363$		0			0
$364$	−8.56231			−0.448787
$365$	6.85410	+	4.97980i	0.358760	+	0.260654i
$366$	−1.50000	+	4.61653i	−0.0784063	+	0.241310i
$367$	1.71885	+	5.29007i	0.0897231	+	0.276139i	0.985843	−	0.167674i	$-0.0536255\pi$
$367$	1.71885	+	5.29007i	0.0897231	+	0.276139i	−0.896119	+	0.443813i	$0.853625\pi$
$368$	−5.20820	+	3.78398i	−0.271496	+	0.197254i
$369$	−9.66312	+	7.02067i	−0.503042	+	0.365481i
$370$	−0.118034	−	0.363271i	−0.00613629	−	0.0188856i
$371$	8.91641	−	27.4419i	0.462917	−	1.42471i
$372$	3.73607	+	2.71441i	0.193706	+	0.140736i
$373$	4.41641			0.228673			0.114336	−	0.993442i	$-0.463526\pi$
$373$	4.41641			0.228673			0.114336	+	0.993442i	$0.463526\pi$
$374$		0			0
$375$	8.23607			0.425309
$376$	2.92705	+	2.12663i	0.150951	+	0.109672i
$377$	2.43769	−	7.50245i	0.125548	−	0.386396i
$378$	−0.572949	−	1.76336i	−0.0294693	−	0.0906972i
$379$	−1.28115	+	0.930812i	−0.0658084	+	0.0478126i	−0.620203	−	0.784441i	$-0.712950\pi$
$379$	−1.28115	+	0.930812i	−0.0658084	+	0.0478126i	0.554395	+	0.832254i	$0.312950\pi$
$380$	20.0623	−	14.5761i	1.02917	−	0.747739i
$381$	1.14590	+	3.52671i	0.0587061	+	0.180679i
$382$	−1.42705	+	4.39201i	−0.0730143	+	0.224715i
$383$	−21.7533	−	15.8047i	−1.11154	−	0.807582i	−0.128635	−	0.991692i	$-0.541060\pi$
$383$	−21.7533	−	15.8047i	−1.11154	−	0.807582i	−0.982906	+	0.184110i	$0.941060\pi$
$384$	−11.3820			−0.580834
$385$		0			0
$386$	11.4721			0.583916
$387$	5.04508	+	3.66547i	0.256456	+	0.186326i
$388$	7.01722	−	21.5968i	0.356245	−	1.09641i
$389$	7.50000	+	23.0826i	0.380265	+	1.17034i	0.939857	+	0.341567i	$0.110958\pi$
$389$	7.50000	+	23.0826i	0.380265	+	1.17034i	−0.559592	+	0.828768i	$0.689042\pi$
$390$	−2.30902	+	1.67760i	−0.116922	+	0.0849485i
$391$	4.54508	−	3.30220i	0.229855	−	0.166999i
$392$	−1.38197	−	4.25325i	−0.0697998	−	0.214822i
$393$	2.20820	−	6.79615i	0.111389	−	0.342821i
$394$	12.1910	+	8.85727i	0.614173	+	0.446223i
$395$	24.7984			1.24774
$396$		0			0
$397$	−38.7082			−1.94271			−0.971355	−	0.237635i	$-0.923628\pi$
$397$	−38.7082			−1.94271			−0.971355	+	0.237635i	$0.923628\pi$
$398$	8.35410	+	6.06961i	0.418753	+	0.304242i
$399$	5.42705	−	16.7027i	0.271692	−	0.836183i
$400$	1.06231	+	3.26944i	0.0531153	+	0.163472i
$401$	21.1074	−	15.3354i	1.05405	−	0.765814i	0.0810739	−	0.996708i	$-0.474165\pi$
$401$	21.1074	−	15.3354i	1.05405	−	0.765814i	0.972979	+	0.230894i	$0.0741650\pi$
$402$	4.78115	−	3.47371i	0.238462	−	0.173253i
$403$	−1.55573	−	4.78804i	−0.0774963	−	0.238509i
$404$	−1.50000	+	4.61653i	−0.0746278	+	0.229681i
$405$	2.11803	+	1.53884i	0.105246	+	0.0764657i
$406$	8.29180			0.411515
$407$		0			0
$408$	3.61803			0.179119
$409$	−8.94427	−	6.49839i	−0.442266	−	0.321325i	0.344269	−	0.938871i	$-0.388127\pi$
$409$	−8.94427	−	6.49839i	−0.442266	−	0.321325i	−0.786535	+	0.617546i	$0.788127\pi$
$410$	−5.97214	+	18.3803i	−0.294943	+	0.907741i
$411$	2.30902	+	7.10642i	0.113895	+	0.350534i
$412$	−7.85410	+	5.70634i	−0.386944	+	0.281131i
$413$	25.0623	−	18.2088i	1.23324	−	0.895998i
$414$	0.663119	+	2.04087i	0.0325905	+	0.100303i
$415$	0.572949	−	1.76336i	0.0281250	−	0.0865597i
$416$	8.01722	+	5.82485i	0.393077	+	0.285587i
$417$	0.854102			0.0418256
$418$		0			0
$419$	16.5066			0.806399			0.403200	−	0.915112i	$-0.367898\pi$
$419$	16.5066			0.806399			0.403200	+	0.915112i	$0.367898\pi$
$420$	10.2812	+	7.46969i	0.501669	+	0.364484i
$421$	−11.5172	+	35.4464i	−0.561315	+	1.72755i	0.117339	+	0.993092i	$0.462564\pi$
$421$	−11.5172	+	35.4464i	−0.561315	+	1.72755i	−0.678654	+	0.734458i	$0.737436\pi$
$422$	4.25329	+	13.0903i	0.207047	+	0.637225i
$423$	−1.30902	+	0.951057i	−0.0636466	+	0.0462420i
$424$	−17.3992	+	12.6412i	−0.844979	+	0.613913i
$425$	−0.927051	−	2.85317i	−0.0449686	−	0.138399i
$426$	−1.06231	+	3.26944i	−0.0514689	+	0.158405i
$427$	−19.0623	−	13.8496i	−0.922490	−	0.670228i
$428$	−6.85410			−0.331306
$429$		0			0
$430$	10.0902			0.486591
$431$	−31.9615	−	23.2214i	−1.53953	−	1.11853i	−0.950629	−	0.310330i	$-0.899560\pi$
$431$	−31.9615	−	23.2214i	−1.53953	−	1.11853i	−0.588902	−	0.808204i	$-0.700440\pi$
$432$	0.572949	−	1.76336i	0.0275660	−	0.0848395i
$433$	−1.85410	−	5.70634i	−0.0891025	−	0.274229i	0.896569	−	0.442903i	$-0.146051\pi$
$433$	−1.85410	−	5.70634i	−0.0891025	−	0.274229i	−0.985672	+	0.168674i	$0.946051\pi$
$434$	4.28115	−	3.11044i	0.205502	−	0.149306i
$435$	−9.47214	+	6.88191i	−0.454154	+	0.329962i
$436$		0			0
$437$	−6.28115	+	19.3314i	−0.300468	+	0.924746i
$438$	−1.61803	−	1.17557i	−0.0773127	−	0.0561709i
$439$	−3.29180			−0.157109			−0.0785544	−	0.996910i	$-0.525030\pi$
$439$	−3.29180			−0.157109			−0.0785544	+	0.996910i	$0.525030\pi$
$440$		0			0
$441$	2.00000			0.0952381
$442$	−1.42705	−	1.03681i	−0.0678779	−	0.0493162i
$443$	−12.7082	+	39.1118i	−0.603785	+	1.85826i	−0.0988488	+	0.995102i	$0.531516\pi$
$443$	−12.7082	+	39.1118i	−0.603785	+	1.85826i	−0.504936	+	0.863157i	$0.668484\pi$
$444$	−0.118034	−	0.363271i	−0.00560165	−	0.0172401i
$445$	1.11803	−	0.812299i	0.0529999	−	0.0385067i
$446$	−0.354102	+	0.257270i	−0.0167672	+	0.0121821i
$447$	−4.63525	−	14.2658i	−0.219240	−	0.674751i
$448$	0.218847	−	0.673542i	0.0103396	−	0.0318219i
$449$	19.7984	+	14.3844i	0.934343	+	0.678840i	0.947052	−	0.321079i	$-0.104046\pi$
$449$	19.7984	+	14.3844i	0.934343	+	0.678840i	−0.0127093	+	0.999919i	$0.504046\pi$
$450$	1.14590			0.0540182
$451$		0			0
$452$	−1.14590			−0.0538985
$453$	1.61803	+	1.17557i	0.0760219	+	0.0552331i
$454$	4.75329	−	14.6291i	0.223083	−	0.686579i
$455$	−4.28115	−	13.1760i	−0.200704	−	0.617702i
$456$	−10.5902	+	7.69421i	−0.495930	+	0.360314i
$457$	6.63525	−	4.82079i	0.310384	−	0.225507i	−0.421677	−	0.906746i	$-0.638558\pi$
$457$	6.63525	−	4.82079i	0.310384	−	0.225507i	0.732061	+	0.681239i	$0.238558\pi$
$458$	1.90983	+	5.87785i	0.0892405	+	0.274654i
$459$	−0.500000	+	1.53884i	−0.0233380	+	0.0718270i
$460$	−11.8992	−	8.64527i	−0.554802	−	0.403088i
$461$	21.0902			0.982267			0.491134	−	0.871084i	$-0.336583\pi$
$461$	21.0902			0.982267			0.491134	+	0.871084i	$0.336583\pi$
$462$		0			0
$463$	−15.7984			−0.734213			−0.367106	−	0.930179i	$-0.619651\pi$
$463$	−15.7984			−0.734213			−0.367106	+	0.930179i	$0.619651\pi$
$464$	6.70820	+	4.87380i	0.311421	+	0.226260i
$465$	−2.30902	+	7.10642i	−0.107078	+	0.329553i
$466$	−4.64590	−	14.2986i	−0.215217	−	0.662370i
$467$	7.89919	−	5.73910i	0.365531	−	0.265574i	−0.389824	−	0.920889i	$-0.627464\pi$
$467$	7.89919	−	5.73910i	0.365531	−	0.265574i	0.755355	+	0.655316i	$0.227464\pi$
$468$	−2.30902	+	1.67760i	−0.106734	+	0.0775470i
$469$	8.86475	+	27.2829i	0.409336	+	1.25981i
$470$	−0.809017	+	2.48990i	−0.0373172	+	0.114850i
$471$	3.00000	+	2.17963i	0.138233	+	0.100432i
$472$	−23.0902			−1.06281
$473$		0			0
$474$	−5.85410			−0.268888
$475$	8.78115	+	6.37988i	0.402907	+	0.292729i
$476$	−2.42705	+	7.46969i	−0.111244	+	0.342373i
$477$	−2.97214	−	9.14729i	−0.136085	−	0.418826i
$478$	1.28115	−	0.930812i	0.0585986	−	0.0425744i
$479$	−22.7254	+	16.5110i	−1.03835	+	0.754406i	−0.969963	−	0.243253i	$-0.921786\pi$
$479$	−22.7254	+	16.5110i	−1.03835	+	0.754406i	−0.0683882	+	0.997659i	$0.521786\pi$
$480$	−4.54508	−	13.9883i	−0.207454	−	0.638477i
$481$	−0.128677	+	0.396027i	−0.00586717	+	0.0180573i
$482$	−11.5623	−	8.40051i	−0.526649	−	0.382633i
$483$	−10.4164			−0.473963
$484$		0			0
$485$	36.7426			1.66840
$486$	−0.500000	−	0.363271i	−0.0226805	−	0.0164783i
$487$	5.19756	−	15.9964i	0.235524	−	0.724868i	−0.761528	−	0.648133i	$-0.775550\pi$
$487$	5.19756	−	15.9964i	0.235524	−	0.724868i	0.997051	−	0.0767356i	$-0.0244497\pi$
$488$	5.42705	+	16.7027i	0.245671	+	0.756098i
$489$	−14.7812	+	10.7391i	−0.668427	+	0.485641i
$490$	2.61803	−	1.90211i	0.118271	−	0.0859287i
$491$	−7.79180	−	23.9807i	−0.351639	−	1.08223i	−0.957933	−	0.286992i	$-0.907345\pi$
$491$	−7.79180	−	23.9807i	−0.351639	−	1.08223i	0.606294	−	0.795241i	$-0.292655\pi$
$492$	−5.97214	+	18.3803i	−0.269245	+	0.828650i
$493$	−5.85410	−	4.25325i	−0.263655	−	0.191557i
$494$	6.38197			0.287138
$495$		0			0
$496$	5.29180			0.237609
$497$	−13.5000	−	9.80832i	−0.605558	−	0.439963i
$498$	−0.135255	+	0.416272i	−0.00606092	+	0.0186536i
$499$	−5.42705	−	16.7027i	−0.242948	−	0.747718i	−0.995967	−	0.0897188i	$-0.971403\pi$
$499$	−5.42705	−	16.7027i	−0.242948	−	0.747718i	0.753019	−	0.657999i	$-0.228597\pi$
$500$	10.7812	−	7.83297i	0.482148	−	0.350301i
$501$	8.11803	−	5.89810i	0.362687	−	0.263508i
$502$	−1.48936	−	4.58377i	−0.0664733	−	0.204584i
$503$	−8.67376	+	26.6951i	−0.386744	+	1.19028i	0.548463	+	0.836175i	$0.315213\pi$
$503$	−8.67376	+	26.6951i	−0.386744	+	1.19028i	−0.935207	+	0.354101i	$0.884787\pi$
$504$	−5.42705	−	3.94298i	−0.241740	−	0.175634i
$505$	−7.85410			−0.349503
$506$		0			0
$507$	−9.88854			−0.439166
$508$	4.85410	+	3.52671i	0.215366	+	0.156473i
$509$	7.29837	−	22.4621i	0.323495	−	0.995614i	−0.648621	−	0.761112i	$-0.724654\pi$
$509$	7.29837	−	22.4621i	0.323495	−	0.995614i	0.972115	−	0.234503i	$-0.0753462\pi$
$510$	0.809017	+	2.48990i	0.0358239	+	0.110255i
$511$	7.85410	−	5.70634i	0.347445	−	0.252434i
$512$	−15.1353	+	10.9964i	−0.668890	+	0.485977i
$513$	−1.80902	−	5.56758i	−0.0798701	−	0.245815i
$514$	−2.22949	+	6.86167i	−0.0983386	+	0.302655i
$515$	−12.7082	−	9.23305i	−0.559990	−	0.406857i
$516$	10.0902			0.444195
$517$		0			0
$518$	−0.437694			−0.0192312
$519$	12.4443	+	9.04129i	0.546243	+	0.396869i
$520$	−3.19098	+	9.82084i	−0.139934	+	0.430672i
$521$	−4.58359	−	14.1068i	−0.200811	−	0.618032i	−0.999859	−	0.0167657i	$-0.994663\pi$
$521$	−4.58359	−	14.1068i	−0.200811	−	0.618032i	0.799049	−	0.601266i	$-0.205337\pi$
$522$	2.23607	−	1.62460i	0.0978700	−	0.0711067i
$523$	−9.69098	+	7.04091i	−0.423757	+	0.307878i	−0.779148	−	0.626840i	$-0.784348\pi$
$523$	−9.69098	+	7.04091i	−0.423757	+	0.307878i	0.355391	+	0.934718i	$0.384348\pi$
$524$	−3.57295	−	10.9964i	−0.156085	−	0.480380i
$525$	−1.71885	+	5.29007i	−0.0750166	+	0.230877i
$526$	−8.16312	−	5.93085i	−0.355929	−	0.258597i
$527$	−4.61803			−0.201165
$528$		0			0
$529$	−10.9443			−0.475838
$530$	−12.5902	−	9.14729i	−0.546882	−	0.397333i
$531$	3.19098	−	9.82084i	0.138477	−	0.426188i
$532$	−8.78115	−	27.0256i	−0.380711	−	1.17171i
$533$	17.0451	−	12.3840i	0.738305	−	0.536410i
$534$	−0.263932	+	0.191758i	−0.0114215	+	0.00829817i
$535$	−3.42705	−	10.5474i	−0.148164	−	0.456003i
$536$	6.60739	−	20.3355i	0.285396	−	0.878358i
$537$	1.80902	+	1.31433i	0.0780648	+	0.0567174i
$538$	9.59675			0.413745
$539$		0			0
$540$	4.23607			0.182291
$541$	15.8262	+	11.4984i	0.680423	+	0.494356i	0.873498	−	0.486828i	$-0.161846\pi$
$541$	15.8262	+	11.4984i	0.680423	+	0.494356i	−0.193075	+	0.981184i	$0.561846\pi$
$542$	5.20820	−	16.0292i	0.223712	−	0.688513i
$543$	−5.39919	−	16.6170i	−0.231701	−	0.713103i
$544$	7.35410	−	5.34307i	0.315305	−	0.229082i
$545$		0			0
$546$	1.01064	+	3.11044i	0.0432515	+	0.133115i
$547$	−6.68034	+	20.5600i	−0.285631	+	0.879081i	0.700578	+	0.713576i	$0.252925\pi$
$547$	−6.68034	+	20.5600i	−0.285631	+	0.879081i	−0.986209	+	0.165505i	$0.947075\pi$
$548$	9.78115	+	7.10642i	0.417830	+	0.303571i
$549$	−7.85410			−0.335205
$550$		0			0
$551$	26.1803			1.11532
$552$	6.28115	+	4.56352i	0.267344	+	0.194237i
$553$	8.78115	−	27.0256i	0.373413	−	1.14925i
$554$	−5.83688	−	17.9641i	−0.247985	−	0.763220i
$555$	0.500000	−	0.363271i	0.0212238	−	0.0154200i
$556$	1.11803	−	0.812299i	0.0474152	−	0.0344492i
$557$	−4.60739	−	14.1801i	−0.195221	−	0.600830i	−0.999974	−	0.00721928i	$-0.997702\pi$
$557$	−4.60739	−	14.1801i	−0.195221	−	0.600830i	0.804753	−	0.593610i	$-0.202298\pi$
$558$	0.545085	−	1.67760i	0.0230753	−	0.0710184i
$559$	−8.89919	−	6.46564i	−0.376396	−	0.273467i
$560$	14.5623			0.615370
$561$		0			0
$562$	0.472136			0.0199159
$563$	−7.19098	−	5.22455i	−0.303064	−	0.220189i	0.425851	−	0.904793i	$-0.359975\pi$
$563$	−7.19098	−	5.22455i	−0.303064	−	0.220189i	−0.728915	+	0.684605i	$0.759975\pi$
$564$	−0.809017	+	2.48990i	−0.0340658	+	0.104844i
$565$	−0.572949	−	1.76336i	−0.0241041	−	0.0741849i
$566$	0.0901699	−	0.0655123i	0.00379013	−	0.00275369i
$567$	2.42705	−	1.76336i	0.101927	−	0.0740540i
$568$	3.84346	+	11.8290i	0.161268	+	0.496332i
$569$	7.43769	−	22.8909i	0.311804	−	0.959635i	−0.665246	−	0.746625i	$-0.731673\pi$
$569$	7.43769	−	22.8909i	0.311804	−	0.959635i	0.977050	−	0.213010i	$-0.0683269\pi$
$570$	−7.66312	−	5.56758i	−0.320973	−	0.233200i
$571$	−34.6869			−1.45160			−0.725801	−	0.687905i	$-0.758531\pi$
$571$	−34.6869			−1.45160			−0.725801	+	0.687905i	$0.758531\pi$
$572$		0			0
$573$	−7.47214			−0.312153
$574$	17.9164	+	13.0170i	0.747816	+	0.543320i
$575$	1.98936	−	6.12261i	0.0829619	−	0.255331i
$576$	−0.0729490	−	0.224514i	−0.00303954	−	0.00935475i
$577$	−8.70820	+	6.32688i	−0.362527	+	0.263391i	−0.754105	−	0.656753i	$-0.771929\pi$
$577$	−8.70820	+	6.32688i	−0.362527	+	0.263391i	0.391578	+	0.920145i	$0.371929\pi$
$578$	7.19098	−	5.22455i	0.299105	−	0.217313i
$579$	5.73607	+	17.6538i	0.238383	+	0.733667i
$580$	−5.85410	+	18.0171i	−0.243078	+	0.748118i
$581$	−1.71885	−	1.24882i	−0.0713098	−	0.0518096i
$582$	−8.67376			−0.359539
$583$		0			0
$584$	−7.23607			−0.299431
$585$	−3.73607	−	2.71441i	−0.154467	−	0.112227i
$586$	−0.0106431	+	0.0327561i	−0.000439663	+	0.00135314i
$587$	−11.8369	−	36.4302i	−0.488560	−	1.50363i	−0.826757	−	0.562559i	$-0.809817\pi$
$587$	−11.8369	−	36.4302i	−0.488560	−	1.50363i	0.338197	−	0.941075i	$-0.390183\pi$
$588$	2.61803	−	1.90211i	0.107966	−	0.0784418i
$589$	13.5172	−	9.82084i	0.556967	−	0.404660i
$590$	−5.16312	−	15.8904i	−0.212562	−	0.654199i
$591$	−7.53444	+	23.1886i	−0.309926	+	0.953853i
$592$	−0.354102	−	0.257270i	−0.0145535	−	0.0105737i
$593$	−22.2148			−0.912252			−0.456126	−	0.889915i	$-0.650763\pi$
$593$	−22.2148			−0.912252			−0.456126	+	0.889915i	$0.650763\pi$
$594$		0			0
$595$	−12.7082			−0.520986
$596$	−19.6353	−	14.2658i	−0.804291	−	0.584352i
$597$	−5.16312	+	15.8904i	−0.211312	+	0.650353i
$598$	−1.16970	−	3.59996i	−0.0478325	−	0.147213i
$599$	6.70820	−	4.87380i	0.274090	−	0.199138i	−0.442246	−	0.896894i	$-0.645818\pi$
$599$	6.70820	−	4.87380i	0.274090	−	0.199138i	0.716335	+	0.697756i	$0.245818\pi$
$600$	3.35410	−	2.43690i	0.136931	−	0.0994859i
$601$	−10.4549	−	32.1769i	−0.426465	−	1.31252i	−0.901585	−	0.432603i	$-0.857595\pi$
$601$	−10.4549	−	32.1769i	−0.426465	−	1.31252i	0.475120	−	0.879921i	$-0.342405\pi$
$602$	3.57295	−	10.9964i	0.145623	−	0.448180i
$603$	7.73607	+	5.62058i	0.315037	+	0.228888i
$604$	3.23607			0.131674
$605$		0			0
$606$	1.85410			0.0753177
$607$	10.7812	+	7.83297i	0.437593	+	0.317930i	0.784678	−	0.619904i	$-0.212828\pi$
$607$	10.7812	+	7.83297i	0.437593	+	0.317930i	−0.347084	+	0.937834i	$0.612828\pi$
$608$	−10.1631	+	31.2789i	−0.412169	+	1.26853i
$609$	4.14590	+	12.7598i	0.168000	+	0.517052i
$610$	−10.2812	+	7.46969i	−0.416272	+	0.302439i
$611$	2.30902	−	1.67760i	0.0934128	−	0.0678684i
$612$	0.809017	+	2.48990i	0.0327026	+	0.100648i
$613$	−10.7082	+	32.9565i	−0.432500	+	1.33110i	0.463126	+	0.886292i	$0.346728\pi$
$613$	−10.7082	+	32.9565i	−0.432500	+	1.33110i	−0.895627	+	0.444807i	$0.853272\pi$
$614$	0.281153	+	0.204270i	0.0113464	+	0.00824365i
$615$	−31.2705			−1.26095
$616$		0			0
$617$	19.5836			0.788406			0.394203	−	0.919023i	$-0.371021\pi$
$617$	19.5836			0.788406			0.394203	+	0.919023i	$0.371021\pi$
$618$	3.00000	+	2.17963i	0.120678	+	0.0876775i
$619$	−2.72542	+	8.38800i	−0.109544	+	0.337142i	−0.990770	−	0.135553i	$-0.956719\pi$
$619$	−2.72542	+	8.38800i	−0.109544	+	0.337142i	0.881226	+	0.472695i	$0.156719\pi$
$620$	3.73607	+	11.4984i	0.150044	+	0.461788i
$621$	−2.80902	+	2.04087i	−0.112722	+	0.0818973i
$622$	−1.26393	+	0.918300i	−0.0506791	+	0.0368205i
$623$	−0.489357	−	1.50609i	−0.0196057	−	0.0603400i
$624$	−1.01064	+	3.11044i	−0.0404581	+	0.124517i
$625$	24.9443	+	18.1231i	0.997771	+	0.724923i
$626$	15.9656			0.638112
$627$		0			0
$628$	6.00000			0.239426
$629$	0.309017	+	0.224514i	0.0123213	+	0.00895196i
$630$	1.50000	−	4.61653i	0.0597614	−	0.183927i
$631$	14.2984	+	44.0059i	0.569209	+	1.75185i	0.655101	+	0.755542i	$0.272626\pi$
$631$	14.2984	+	44.0059i	0.569209	+	1.75185i	−0.0858915	+	0.996304i	$0.527374\pi$
$632$	−17.1353	+	12.4495i	−0.681604	+	0.495214i
$633$	−18.0172	+	13.0903i	−0.716120	+	0.520292i
$634$	−3.69756	−	11.3799i	−0.146849	−	0.451954i
$635$	−3.00000	+	9.23305i	−0.119051	+	0.366402i
$636$	−12.5902	−	9.14729i	−0.499233	−	0.362714i
$637$	−3.52786			−0.139779
$638$		0			0
$639$	−5.56231			−0.220041
$640$	−24.1074	−	17.5150i	−0.952928	−	0.692343i
$641$	11.0451	−	33.9933i	0.436255	−	1.34265i	−0.455541	−	0.890215i	$-0.650554\pi$
$641$	11.0451	−	33.9933i	0.436255	−	1.34265i	0.891795	−	0.452439i	$-0.149446\pi$
$642$	0.809017	+	2.48990i	0.0319294	+	0.0982684i
$643$	31.1976	−	22.6664i	1.23031	−	0.893874i	0.233398	−	0.972381i	$-0.425015\pi$
$643$	31.1976	−	22.6664i	1.23031	−	0.893874i	0.996914	+	0.0785075i	$0.0250154\pi$
$644$	−13.6353	+	9.90659i	−0.537304	+	0.390374i
$645$	5.04508	+	15.5272i	0.198650	+	0.611382i
$646$	1.80902	−	5.56758i	0.0711748	−	0.219054i
$647$	−22.4894	−	16.3395i	−0.884148	−	0.642371i	0.0501977	−	0.998739i	$-0.484015\pi$
$647$	−22.4894	−	16.3395i	−0.884148	−	0.642371i	−0.934346	+	0.356368i	$0.884015\pi$
$648$	−2.23607			−0.0878410
$649$		0			0
$650$	−2.02129			−0.0792814
$651$	6.92705	+	5.03280i	0.271493	+	0.197251i
$652$	−9.13525	+	28.1154i	−0.357764	+	1.10108i
$653$	15.7705	+	48.5366i	0.617148	+	1.89939i	0.359488	+	0.933150i	$0.382951\pi$
$653$	15.7705	+	48.5366i	0.617148	+	1.89939i	0.257660	+	0.966236i	$0.417049\pi$
$654$		0			0
$655$	15.1353	−	10.9964i	0.591383	−	0.429665i
$656$	6.84346	+	21.0620i	0.267192	+	0.822333i
$657$	1.00000	−	3.07768i	0.0390137	−	0.120072i
$658$	2.42705	+	1.76336i	0.0946163	+	0.0687428i
$659$	10.6525			0.414962			0.207481	−	0.978239i	$-0.433474\pi$
$659$	10.6525			0.414962			0.207481	+	0.978239i	$0.433474\pi$
$660$		0			0
$661$	−9.90983			−0.385448			−0.192724	−	0.981253i	$-0.561732\pi$
$661$	−9.90983			−0.385448			−0.192724	+	0.981253i	$0.561732\pi$
$662$	−13.2984	−	9.66183i	−0.516856	−	0.375518i
$663$	0.881966	−	2.71441i	0.0342527	−	0.105419i
$664$	0.489357	+	1.50609i	0.0189907	+	0.0584475i
$665$	37.1976	−	27.0256i	1.44246	−	1.04801i
$666$	−0.118034	+	0.0857567i	−0.00457372	+	0.00332301i
$667$	−4.79837	−	14.7679i	−0.185794	−	0.571814i
$668$	5.01722	−	15.4414i	0.194122	−	0.597446i
$669$	−0.572949	−	0.416272i	−0.0221515	−	0.0160940i
$670$	15.4721			0.597741
$671$		0			0
$672$	−16.8541			−0.650161
$673$	10.0451	+	7.29818i	0.387210	+	0.281324i	0.764311	−	0.644848i	$-0.223079\pi$
$673$	10.0451	+	7.29818i	0.387210	+	0.281324i	−0.377102	+	0.926172i	$0.623079\pi$
$674$	0.0557281	−	0.171513i	0.00214657	−	0.00660645i
$675$	0.572949	+	1.76336i	0.0220528	+	0.0678716i
$676$	−12.9443	+	9.40456i	−0.497857	+	0.361714i
$677$	10.9443	−	7.95148i	0.420623	−	0.305600i	−0.357266	−	0.934003i	$-0.616291\pi$
$677$	10.9443	−	7.95148i	0.420623	−	0.305600i	0.777888	+	0.628403i	$0.216291\pi$
$678$	0.135255	+	0.416272i	0.00519443	+	0.0159868i
$679$	13.0106	−	40.0426i	0.499303	−	1.53670i
$680$	7.66312	+	5.56758i	0.293867	+	0.213507i
$681$	24.8885			0.953731
$682$		0			0
$683$	−3.11146			−0.119057			−0.0595283	−	0.998227i	$-0.518960\pi$
$683$	−3.11146			−0.119057			−0.0595283	+	0.998227i	$0.518960\pi$
$684$	−7.66312	−	5.56758i	−0.293007	−	0.212882i
$685$	−6.04508	+	18.6049i	−0.230971	+	0.710855i
$686$	2.86475	+	8.81678i	0.109376	+	0.336626i
$687$	−8.09017	+	5.87785i	−0.308659	+	0.224254i
$688$	9.35410	−	6.79615i	0.356622	−	0.259101i
$689$	5.24265	+	16.1352i	0.199729	+	0.614702i
$690$	−1.73607	+	5.34307i	−0.0660910	+	0.203407i
$691$	21.2705	+	15.4539i	0.809168	+	0.587895i	0.913589	−	0.406638i	$-0.133299\pi$
$691$	21.2705	+	15.4539i	0.809168	+	0.587895i	−0.104421	+	0.994533i	$0.533299\pi$
$692$	24.8885			0.946120
$693$		0			0
$694$	12.9443			0.491358
$695$	1.80902	+	1.31433i	0.0686199	+	0.0498553i
$696$	3.09017	−	9.51057i	0.117133	−	0.360497i
$697$	−5.97214	−	18.3803i	−0.226211	−	0.696205i
$698$	−5.06231	+	3.67798i	−0.191611	+	0.139214i
$699$	19.6803	−	14.2986i	0.744379	−	0.540823i
$700$	2.78115	+	8.55951i	0.105118	+	0.323519i
$701$	3.30244	−	10.1639i	0.124731	−	0.383884i	−0.869121	−	0.494600i	$-0.835315\pi$
$701$	3.30244	−	10.1639i	0.124731	−	0.383884i	0.993852	+	0.110716i	$0.0353145\pi$
$702$	0.881966	+	0.640786i	0.0332877	+	0.0241849i
$703$	−1.38197			−0.0521218
$704$		0			0
$705$	−4.23607			−0.159540
$706$	5.23607	+	3.80423i	0.197062	+	0.143174i
$707$	−2.78115	+	8.55951i	−0.104596	+	0.321913i
$708$	−5.16312	−	15.8904i	−0.194042	−	0.597200i
$709$	−39.4336	+	28.6502i	−1.48096	+	1.07598i	−0.503716	+	0.863870i	$0.668034\pi$
$709$	−39.4336	+	28.6502i	−1.48096	+	1.07598i	−0.977245	+	0.212112i	$0.931966\pi$
$710$	−7.28115	+	5.29007i	−0.273257	+	0.198533i
$711$	−2.92705	−	9.00854i	−0.109773	−	0.337847i
$712$	−0.364745	+	1.12257i	−0.0136694	+	0.0420701i
$713$	−8.01722	−	5.82485i	−0.300247	−	0.218142i
$714$	3.00000			0.112272
$715$		0			0
$716$	3.61803			0.135212
$717$	2.07295	+	1.50609i	0.0774157	+	0.0562458i
$718$	2.43769	−	7.50245i	0.0909739	−	0.279989i
$719$	−0.489357	−	1.50609i	−0.0182499	−	0.0561675i	0.941517	−	0.336966i	$-0.109401\pi$
$719$	−0.489357	−	1.50609i	−0.0182499	−	0.0561675i	−0.959767	+	0.280798i	$0.909401\pi$
$720$	3.92705	−	2.85317i	0.146353	−	0.106331i
$721$	−14.5623	+	10.5801i	−0.542329	+	0.394025i
$722$	2.91641	+	8.97578i	0.108537	+	0.334044i
$723$	7.14590	−	21.9928i	0.265759	−	0.817922i
$724$	−22.8713	−	16.6170i	−0.850006	−	0.617566i
$725$	−8.29180			−0.307950
$726$		0			0
$727$	38.8541			1.44102			0.720509	−	0.693445i	$-0.243908\pi$
$727$	38.8541			1.44102			0.720509	+	0.693445i	$0.243908\pi$
$728$	9.57295	+	6.95515i	0.354797	+	0.257775i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−1.61803	−	4.97980i	−0.0598861	−	0.184311i
$731$	−8.16312	+	5.93085i	−0.301924	+	0.219361i
$732$	−10.2812	+	7.46969i	−0.380002	+	0.276088i
$733$	11.6525	+	35.8626i	0.430394	+	1.32462i	0.897734	+	0.440539i	$0.145213\pi$
$733$	11.6525	+	35.8626i	0.430394	+	1.32462i	−0.467340	+	0.884078i	$0.654787\pi$
$734$	1.06231	−	3.26944i	0.0392104	−	0.120677i
$735$	4.23607	+	3.07768i	0.156250	+	0.113522i
$736$	19.5066			0.719022
$737$		0			0
$738$	7.38197			0.271734
$739$	−20.2254	−	14.6946i	−0.744004	−	0.540551i	0.149958	−	0.988692i	$-0.452086\pi$
$739$	−20.2254	−	14.6946i	−0.744004	−	0.540551i	−0.893963	+	0.448142i	$0.852086\pi$
$740$	0.309017	−	0.951057i	0.0113597	−	0.0349615i
$741$	3.19098	+	9.82084i	0.117224	+	0.360777i
$742$	−14.4271	+	10.4819i	−0.529634	+	0.384801i
$743$	28.4615	−	20.6785i	1.04415	−	0.758620i	0.0730594	−	0.997328i	$-0.476724\pi$
$743$	28.4615	−	20.6785i	1.04415	−	0.758620i	0.971092	+	0.238708i	$0.0767237\pi$
$744$	−1.97214	−	6.06961i	−0.0723020	−	0.222523i
$745$	12.1353	−	37.3485i	0.444601	−	1.36834i
$746$	−2.20820	−	1.60435i	−0.0808481	−	0.0587396i
$747$	−0.708204			−0.0259118
$748$		0			0
$749$	−12.7082			−0.464348
$750$	−4.11803	−	2.99193i	−0.150369	−	0.109250i
$751$	3.68441	−	11.3394i	0.134446	−	0.413782i	−0.861058	−	0.508508i	$-0.830197\pi$
$751$	3.68441	−	11.3394i	0.134446	−	0.413782i	0.995503	+	0.0947257i	$0.0301974\pi$
$752$	0.927051	+	2.85317i	0.0338061	+	0.104044i
$753$	6.30902	−	4.58377i	0.229913	−	0.167042i
$754$	−3.94427	+	2.86568i	−0.143642	+	0.104362i
$755$	1.61803	+	4.97980i	0.0588863	+	0.181233i
$756$	1.50000	−	4.61653i	0.0545545	−	0.167901i
$757$	−1.57295	−	1.14281i	−0.0571698	−	0.0415363i	0.558833	−	0.829280i	$-0.311249\pi$
$757$	−1.57295	−	1.14281i	−0.0571698	−	0.0415363i	−0.616003	+	0.787744i	$0.711249\pi$
$758$	0.978714			0.0355485
$759$		0			0
$760$	−34.2705			−1.24312
$761$	−24.9894	−	18.1558i	−0.905863	−	0.658148i	0.0341018	−	0.999418i	$-0.489143\pi$
$761$	−24.9894	−	18.1558i	−0.905863	−	0.658148i	−0.939965	+	0.341270i	$0.889143\pi$
$762$	0.708204	−	2.17963i	0.0256555	−	0.0789596i
$763$		0			0
$764$	−9.78115	+	7.10642i	−0.353870	+	0.257101i
$765$	−3.42705	+	2.48990i	−0.123905	+	0.0900225i
$766$	5.13525	+	15.8047i	0.185544	+	0.571047i
$767$	−5.62868	+	17.3233i	−0.203240	+	0.625508i
$768$	5.30902	+	3.85723i	0.191573	+	0.139186i
$769$	−12.6869			−0.457502			−0.228751	−	0.973485i	$-0.573464\pi$
$769$	−12.6869			−0.457502			−0.228751	+	0.973485i	$0.573464\pi$
$770$		0			0
$771$	−11.6738			−0.420420
$772$

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	363.e (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.363271i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.500000 - 1.53884i) q^{4} +(2.11803 - 1.53884i) q^{5} +(-0.500000 + 0.363271i) q^{6} +(-0.927051 - 2.85317i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.363271i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.500000 - 1.53884i) q^{4} +(2.11803 - 1.53884i) q^{5} +(-0.500000 + 0.363271i) q^{6} +(-0.927051 - 2.85317i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(-0.809017 - 0.587785i) q^{9} -1.61803 q^{10} -1.61803 q^{12} +(1.42705 + 1.03681i) q^{13} +(-0.572949 + 1.76336i) q^{14} +(-0.809017 - 2.48990i) q^{15} +(-1.50000 + 1.08981i) q^{16} +(1.30902 - 0.951057i) q^{17} +(0.190983 + 0.587785i) q^{18} +(-1.80902 + 5.56758i) q^{19} +(-3.42705 - 2.48990i) q^{20} -3.00000 q^{21} +3.47214 q^{23} +(1.80902 + 1.31433i) q^{24} +(0.572949 - 1.76336i) q^{25} +(-0.336881 - 1.03681i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-3.92705 + 2.85317i) q^{28} +(-1.38197 - 4.25325i) q^{29} +(-0.500000 + 1.53884i) q^{30} +(-2.30902 - 1.67760i) q^{31} +5.61803 q^{32} -1.00000 q^{34} +(-6.35410 - 4.61653i) q^{35} +(-0.500000 + 1.53884i) q^{36} +(0.0729490 + 0.224514i) q^{37} +(2.92705 - 2.12663i) q^{38} +(1.42705 - 1.03681i) q^{39} +(1.80902 + 5.56758i) q^{40} +(3.69098 - 11.3597i) q^{41} +(1.50000 + 1.08981i) q^{42} -6.23607 q^{43} -2.61803 q^{45} +(-1.73607 - 1.26133i) q^{46} +(0.500000 - 1.53884i) q^{47} +(0.572949 + 1.76336i) q^{48} +(-1.61803 + 1.17557i) q^{49} +(-0.927051 + 0.673542i) q^{50} +(-0.500000 - 1.53884i) q^{51} +(0.881966 - 2.71441i) q^{52} +(7.78115 + 5.65334i) q^{53} +0.618034 q^{54} +6.70820 q^{56} +(4.73607 + 3.44095i) q^{57} +(-0.854102 + 2.62866i) q^{58} +(3.19098 + 9.82084i) q^{59} +(-3.42705 + 2.48990i) q^{60} +(6.35410 - 4.61653i) q^{61} +(0.545085 + 1.67760i) q^{62} +(-0.927051 + 2.85317i) q^{63} +(0.190983 + 0.138757i) q^{64} +4.61803 q^{65} -9.56231 q^{67} +(-2.11803 - 1.53884i) q^{68} +(1.07295 - 3.30220i) q^{69} +(1.50000 + 4.61653i) q^{70} +(4.50000 - 3.26944i) q^{71} +(1.80902 - 1.31433i) q^{72} +(1.00000 + 3.07768i) q^{73} +(0.0450850 - 0.138757i) q^{74} +(-1.50000 - 1.08981i) q^{75} +9.47214 q^{76} -1.09017 q^{78} +(7.66312 + 5.56758i) q^{79} +(-1.50000 + 4.61653i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-5.97214 + 4.33901i) q^{82} +(0.572949 - 0.416272i) q^{83} +(1.50000 + 4.61653i) q^{84} +(1.30902 - 4.02874i) q^{85} +(3.11803 + 2.26538i) q^{86} -4.47214 q^{87} +0.527864 q^{89} +(1.30902 + 0.951057i) q^{90} +(1.63525 - 5.03280i) q^{91} +(-1.73607 - 5.34307i) q^{92} +(-2.30902 + 1.67760i) q^{93} +(-0.809017 + 0.587785i) q^{94} +(4.73607 + 14.5761i) q^{95} +(1.73607 - 5.34307i) q^{96} +(11.3541 + 8.24924i) q^{97} +1.23607 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 3 q^{7} - 5 q^{8} - q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 + 3 * q^7 - 5 * q^8 - q^9	\( 4 q - 2 q^{2} - q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 3 q^{7} - 5 q^{8} - q^{9} - 2 q^{10} - 2 q^{12} - q^{13} - 9 q^{14} - q^{15} - 6 q^{16} + 3 q^{17} + 3 q^{18} - 5 q^{19} - 7 q^{20} - 12 q^{21} - 4 q^{23} + 5 q^{24} + 9 q^{25} - 17 q^{26} - q^{27} - 9 q^{28} - 10 q^{29} - 2 q^{30} - 7 q^{31} + 18 q^{32} - 4 q^{34} - 12 q^{35} - 2 q^{36} + 7 q^{37} + 5 q^{38} - q^{39} + 5 q^{40} + 17 q^{41} + 6 q^{42} - 16 q^{43} - 6 q^{45} + 2 q^{46} + 2 q^{47} + 9 q^{48} - 2 q^{49} + 3 q^{50} - 2 q^{51} + 8 q^{52} + 11 q^{53} - 2 q^{54} + 10 q^{57} + 10 q^{58} + 15 q^{59} - 7 q^{60} + 12 q^{61} - 9 q^{62} + 3 q^{63} + 3 q^{64} + 14 q^{65} + 2 q^{67} - 4 q^{68} + 11 q^{69} + 6 q^{70} + 18 q^{71} + 5 q^{72} + 4 q^{73} - 11 q^{74} - 6 q^{75} + 20 q^{76} + 18 q^{78} + 15 q^{79} - 6 q^{80} - q^{81} - 6 q^{82} + 9 q^{83} + 6 q^{84} + 3 q^{85} + 8 q^{86} + 20 q^{89} + 3 q^{90} - 27 q^{91} + 2 q^{92} - 7 q^{93} - q^{94} + 10 q^{95} - 2 q^{96} + 32 q^{97} - 4 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 + 3 * q^7 - 5 * q^8 - q^9 - 2 * q^10 - 2 * q^12 - q^13 - 9 * q^14 - q^15 - 6 * q^16 + 3 * q^17 + 3 * q^18 - 5 * q^19 - 7 * q^20 - 12 * q^21 - 4 * q^23 + 5 * q^24 + 9 * q^25 - 17 * q^26 - q^27 - 9 * q^28 - 10 * q^29 - 2 * q^30 - 7 * q^31 + 18 * q^32 - 4 * q^34 - 12 * q^35 - 2 * q^36 + 7 * q^37 + 5 * q^38 - q^39 + 5 * q^40 + 17 * q^41 + 6 * q^42 - 16 * q^43 - 6 * q^45 + 2 * q^46 + 2 * q^47 + 9 * q^48 - 2 * q^49 + 3 * q^50 - 2 * q^51 + 8 * q^52 + 11 * q^53 - 2 * q^54 + 10 * q^57 + 10 * q^58 + 15 * q^59 - 7 * q^60 + 12 * q^61 - 9 * q^62 + 3 * q^63 + 3 * q^64 + 14 * q^65 + 2 * q^67 - 4 * q^68 + 11 * q^69 + 6 * q^70 + 18 * q^71 + 5 * q^72 + 4 * q^73 - 11 * q^74 - 6 * q^75 + 20 * q^76 + 18 * q^78 + 15 * q^79 - 6 * q^80 - q^81 - 6 * q^82 + 9 * q^83 + 6 * q^84 + 3 * q^85 + 8 * q^86 + 20 * q^89 + 3 * q^90 - 27 * q^91 + 2 * q^92 - 7 * q^93 - q^94 + 10 * q^95 - 2 * q^96 + 32 * q^97 - 4 * q^98

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