LMFDB - Embedded newform 363.2.e.h.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.h.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	0.750358	−	0.661031i	$-0.229881\pi$
$2$	0.500000	+	0.363271i	0.353553	+	0.256872i	−0.396805	+	0.917903i	$0.629881\pi$
$3$	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	$0.0918755\pi$
$7$	0.927051	+	2.85317i	0.350392	+	1.07840i	−0.608241	+	0.793752i	$0.708125\pi$
$8$	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	0.372032	−	0.928220i	$-0.378661\pi$
$13$	−1.42705	−	1.03681i	−0.395793	−	0.287560i	−0.767825	+	0.640660i	$0.778661\pi$
$14$	−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	−0.735101	−	0.677958i	$-0.762865\pi$
$17$	−1.30902	+	0.951057i	−0.317483	+	0.230665i	0.417618	+	0.908623i	$0.362865\pi$
$18$	−0.190983	−	0.587785i	−0.0450151	−	0.138542i
$19$	1.80902	−	5.56758i	0.415017	−	1.27729i	−0.497219	−	0.867625i	$-0.665645\pi$
$19$	1.80902	−	5.56758i	0.415017	−	1.27729i	0.912236	−	0.409666i	$-0.134355\pi$
$20$	−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	$0.0362980\pi$
$29$	1.38197	+	4.25325i	0.256625	+	0.789809i	−0.736881	+	0.676023i	$0.763702\pi$
$30$	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	$0.482546\pi$
$41$	−3.69098	+	11.3597i	−0.576435	+	1.77408i	−0.631241	+	0.775587i	$0.717454\pi$
$42$	1.50000	+	1.08981i	0.231455	+	0.168162i
$43$	6.23607			0.950991			0.475496	−	0.879718i	$-0.342269\pi$
$43$	6.23607			0.950991			0.475496	+	0.879718i	$0.342269\pi$
$44$		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	−0.914860	−	0.403770i	$-0.867699\pi$
$61$	−6.35410	+	4.61653i	−0.813559	+	0.591085i	0.101301	+	0.994856i	$0.467699\pi$
$62$	−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	0.875326	−	0.483533i	$-0.160647\pi$
$73$	−1.00000	−	3.07768i	−0.117041	−	0.360216i	−0.992367	+	0.123317i	$0.960647\pi$
$74$	−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	0.0663057	−	0.997799i	$-0.478879\pi$
$79$	−7.66312	−	5.56758i	−0.862168	−	0.626402i	−0.928474	+	0.371397i	$0.878879\pi$
$80$	−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	−0.618786	−	0.785560i	$-0.712375\pi$
$83$	−0.572949	+	0.416272i	−0.0628893	+	0.0456918i	0.555896	+	0.831252i	$0.312375\pi$
$84$	−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	0.701952	−	0.712225i	$-0.252312\pi$
$101$	2.42705	+	1.76336i	0.241501	+	0.175460i	−0.460451	+	0.887685i	$0.652312\pi$
$102$	−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	−0.994180	−	0.107733i	$-0.965641\pi$
$107$	−1.30902	+	4.02874i	−0.126547	+	0.389473i	0.867632	+	0.497206i	$0.165641\pi$
$108$	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	−0.446672	−	0.894698i	$-0.647391\pi$
$127$	3.00000	−	2.17963i	0.266207	−	0.193411i	0.712879	+	0.701287i	$0.247391\pi$
$128$	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	$-0.601056\pi$
$131$	−7.14590			−0.624340			−0.312170	+	0.950026i	$0.601056\pi$
$132$		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	0.939239	−	0.343263i	$-0.111532\pi$
$139$	−0.263932	−	0.812299i	−0.0223864	−	0.0688983i	−0.961626	+	0.274365i	$0.911532\pi$
$140$	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	−0.960828	−	0.277146i	$-0.910612\pi$
$149$	−12.1353	+	8.81678i	−0.994159	+	0.722299i	−0.0333309	+	0.999444i	$0.510612\pi$
$150$	−0.354102	−	1.08981i	−0.0289123	−	0.0889829i
$151$	0.618034	−	1.90211i	0.0502949	−	0.154792i	−0.922755	−	0.385388i	$-0.874068\pi$
$151$	0.618034	−	1.90211i	0.0502949	−	0.154792i	0.973050	+	0.230596i	$0.0740676\pi$
$152$	−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	0.227581	−	0.973759i	$-0.426918\pi$
$167$	−8.11803	−	5.89810i	−0.628192	−	0.456408i	−0.855774	+	0.517351i	$0.826918\pi$
$168$	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	$-0.701199\pi$
$173$	4.75329	−	14.6291i	0.361386	−	1.11223i	0.952213	−	0.305433i	$-0.0988014\pi$
$174$	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	0.103113	−	0.994670i	$-0.467120\pi$
$193$	15.0172	−	10.9106i	1.08096	−	0.785366i	0.977851	+	0.209304i	$0.0671198\pi$
$194$	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	$-0.165039\pi$
$197$	24.3820			1.73714			0.868572	+	0.495564i	$0.165039\pi$
$198$		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	0.997622	−	0.0689209i	$-0.0219556\pi$
$211$	18.0172	+	13.0903i	1.24036	+	0.901172i	0.242735	+	0.970093i	$0.421956\pi$
$212$	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	$-0.790636\pi$
$227$	−7.69098	−	23.6704i	−0.510468	−	1.57106i	0.280910	−	0.959734i	$-0.409364\pi$
$228$	−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	−0.289511	−	0.957175i	$-0.593493\pi$
$233$	−19.6803	−	14.2986i	−1.28930	−	0.936733i	−0.999791	+	0.0204420i	$0.993493\pi$
$234$	−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	−0.922177	−	0.386769i	$-0.873591\pi$
$239$	0.791796	−	2.43690i	0.0512170	−	0.157630i	0.973394	+	0.229139i	$0.0735911\pi$
$240$	3.92705	+	2.85317i	0.253490	+	0.184171i
$241$	−23.1246			−1.48959			−0.744794	−	0.667295i	$-0.767452\pi$
$241$	−23.1246			−1.48959			−0.744794	+	0.667295i	$0.767452\pi$
$242$		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	$-0.667903\pi$
$263$	−16.3262			−1.00672			−0.503359	+	0.864077i	$0.667903\pi$
$264$		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	$-0.789318\pi$
$271$	−8.42705	−	25.9358i	−0.511907	−	1.57549i	0.276933	−	0.960889i	$-0.410682\pi$
$272$	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	$-0.929678\pi$
$277$	−24.7254	−	17.9641i	−1.48561	−	1.07936i	−0.509911	−	0.860227i	$-0.670322\pi$
$278$	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	−0.569198	−	0.822200i	$-0.692746\pi$
$281$	0.618034	−	0.449028i	0.0368688	−	0.0267868i	0.606067	+	0.795414i	$0.292746\pi$
$282$	−0.309017	−	0.951057i	−0.0184017	−	0.0566346i
$283$	0.0557281	−	0.171513i	0.00331269	−	0.0101954i	−0.949387	−	0.314110i	$-0.898294\pi$
$283$	0.0557281	−	0.171513i	0.00331269	−	0.0101954i	0.952699	+	0.303915i	$0.0982938\pi$
$284$	−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	0.951558	−	0.307468i	$-0.0994818\pi$
$293$	0.0172209	+	0.0530006i	0.00100606	+	0.00309633i	−0.950552	+	0.310565i	$0.899482\pi$
$294$	−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	$-0.494892\pi$
$307$	0.562306			0.0320925			0.0160462	+	0.999871i	$0.494892\pi$
$308$		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	0.948571	−	0.316566i	$-0.102530\pi$
$337$	−0.0901699	−	0.277515i	−0.00491187	−	0.0151172i	−0.953482	+	0.301449i	$0.902530\pi$
$338$	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	−0.0313016	−	0.999510i	$-0.509965\pi$
$347$	16.9443	−	12.3107i	0.909616	−	0.660875i	0.940918	+	0.338635i	$0.109965\pi$
$348$	−2.23607	−	6.88191i	−0.119866	−	0.368909i
$349$	−3.12868	+	9.62908i	−0.167474	+	0.515433i	−0.999210	−	0.0397388i	$-0.987347\pi$
$349$	−3.12868	+	9.62908i	−0.167474	+	0.515433i	0.831736	+	0.555172i	$0.187347\pi$
$350$	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	$-0.990646\pi$
$359$	−3.94427	−	12.1392i	−0.208171	−	0.640684i	0.791398	−	0.611302i	$-0.209354\pi$
$360$	−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	$-0.536474\pi$
$373$	−4.41641			−0.228673			−0.114336	+	0.993442i	$0.536474\pi$
$374$		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	0.786535	−	0.617546i	$-0.211873\pi$
$409$	8.94427	+	6.49839i	0.442266	+	0.321325i	−0.344269	+	0.938871i	$0.611873\pi$
$410$	−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	$0.100440\pi$
$431$	31.9615	+	23.2214i	1.53953	+	1.11853i	0.588902	+	0.808204i	$0.299560\pi$
$432$	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	$-0.474970\pi$
$439$	3.29180			0.157109			0.0785544	+	0.996910i	$0.474970\pi$
$440$		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	−0.732061	−	0.681239i	$-0.761442\pi$
$457$	−6.63525	+	4.82079i	−0.310384	+	0.225507i	0.421677	+	0.906746i	$0.361442\pi$
$458$	−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	$-0.663417\pi$
$461$	−21.0902			−0.982267			−0.491134	+	0.871084i	$0.663417\pi$
$462$		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	0.0683882	−	0.997659i	$-0.478214\pi$
$479$	22.7254	−	16.5110i	1.03835	−	0.754406i	0.969963	+	0.243253i	$0.0782144\pi$
$480$	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	$0.0926555\pi$
$491$	7.79180	+	23.9807i	0.351639	+	1.08223i	−0.606294	+	0.795241i	$0.707345\pi$
$492$	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	$-0.684787\pi$
$503$	8.67376	−	26.6951i	0.386744	−	1.19028i	0.935207	−	0.354101i	$-0.115213\pi$
$504$	−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	−0.355391	−	0.934718i	$-0.615652\pi$
$523$	9.69098	−	7.04091i	0.423757	−	0.307878i	0.779148	+	0.626840i	$0.215652\pi$
$524$	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	0.193075	−	0.981184i	$-0.438154\pi$
$541$	−15.8262	−	11.4984i	−0.680423	−	0.494356i	−0.873498	+	0.486828i	$0.838154\pi$
$542$	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	$-0.747075\pi$
$547$	6.68034	−	20.5600i	0.285631	−	0.879081i	0.986209	−	0.165505i	$-0.0529255\pi$
$548$	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	$0.00229799\pi$
$557$	4.60739	+	14.1801i	0.195221	+	0.600830i	−0.804753	+	0.593610i	$0.797702\pi$
$558$	−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	0.728915	−	0.684605i	$-0.240025\pi$
$563$	7.19098	+	5.22455i	0.303064	+	0.220189i	−0.425851	+	0.904793i	$0.640025\pi$
$564$	−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	$0.268327\pi$
$569$	−7.43769	+	22.8909i	−0.311804	+	0.959635i	−0.977050	+	0.213010i	$0.931673\pi$
$570$	−7.66312	−	5.56758i	−0.320973	−	0.233200i
$571$	34.6869			1.45160			0.725801	−	0.687905i	$-0.241469\pi$
$571$	34.6869			1.45160			0.725801	+	0.687905i	$0.241469\pi$
$572$		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	$-0.349237\pi$
$593$	22.2148			0.912252			0.456126	+	0.889915i	$0.349237\pi$
$594$		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	$0.142405\pi$
$601$	10.4549	+	32.1769i	0.426465	+	1.31252i	−0.475120	+	0.879921i	$0.657595\pi$
$602$	−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	0.347084	−	0.937834i	$-0.387172\pi$
$607$	−10.7812	−	7.83297i	−0.437593	−	0.317930i	−0.784678	+	0.619904i	$0.787172\pi$
$608$	−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	$-0.653272\pi$
$613$	10.7082	−	32.9565i	0.432500	−	1.33110i	0.895627	−	0.444807i	$-0.146728\pi$
$614$	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	$-0.566526\pi$
$659$	−10.6525			−0.414962			−0.207481	+	0.978239i	$0.566526\pi$
$660$		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	0.377102	−	0.926172i	$-0.376921\pi$
$673$	−10.0451	−	7.29818i	−0.387210	−	0.281324i	−0.764311	+	0.644848i	$0.776921\pi$
$674$	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	−0.777888	−	0.628403i	$-0.783709\pi$
$677$	−10.9443	+	7.95148i	−0.420623	+	0.305600i	0.357266	+	0.934003i	$0.383709\pi$
$678$	−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	−0.993852	−	0.110716i	$-0.964685\pi$
$701$	−3.30244	+	10.1639i	−0.124731	+	0.383884i	0.869121	+	0.494600i	$0.164685\pi$
$702$	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	$-0.854787\pi$
$733$	−11.6525	−	35.8626i	−0.430394	−	1.32462i	0.467340	−	0.884078i	$-0.345213\pi$
$734$	−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	0.893963	−	0.448142i	$-0.147914\pi$
$739$	20.2254	+	14.6946i	0.744004	+	0.540551i	−0.149958	+	0.988692i	$0.547914\pi$
$740$	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	−0.971092	−	0.238708i	$-0.923276\pi$
$743$	−28.4615	+	20.6785i	−1.04415	+	0.758620i	−0.0730594	+	0.997328i	$0.523276\pi$
$744$	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	0.939965	−	0.341270i	$-0.110857\pi$
$761$	24.9894	+	18.1558i	0.905863	+	0.658148i	−0.0341018	+	0.999418i	$0.510857\pi$
$762$	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	$-0.426536\pi$
$769$	12.6869			0.457502			0.228751	+	0.973485i	$0.426536\pi$
$770$		0			0
$771$	−11.6738

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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