LMFDB - Embedded newform 143.2.e.a.133.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,2,Mod(100,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("143.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	143.e (of order $3$, degree $2$, 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:	$1.14186074890$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1714608.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 12x^{4} - 19x^{3} + 30x^{2} - 21x + 7 $ x^6 - 3x^5 + 12x^4 - 19x^3 + 30x^2 - 21*x + 7
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			133.3
Root			$0.500000 - 2.23871i$ of defining polynomial
Character	$\chi$	$=$	143.133
Dual form			143.2.e.a.100.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(1.13090 + 1.95878i) q^{3} +(0.500000 - 0.866025i) q^{4} +2.11575 q^{5} +(1.13090 - 1.95878i) q^{6} +(-1.68878 + 2.92505i) q^{7} -3.00000 q^{8} +(-1.05787 + 1.83229i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(1.13090 + 1.95878i) q^{3} +(0.500000 - 0.866025i) q^{4} +2.11575 q^{5} +(1.13090 - 1.95878i) q^{6} +(-1.68878 + 2.92505i) q^{7} -3.00000 q^{8} +(-1.05787 + 1.83229i) q^{9} +(-1.05787 - 1.83229i) q^{10} +(-0.500000 - 0.866025i) q^{11} +2.26180 q^{12} +(2.63090 - 2.46543i) q^{13} +3.37755 q^{14} +(2.39270 + 4.14428i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.07303 - 1.85854i) q^{17} +2.11575 q^{18} +(-1.57303 + 2.72456i) q^{19} +(1.05787 - 1.83229i) q^{20} -7.63935 q^{21} +(-0.500000 + 0.866025i) q^{22} +(-2.26180 - 3.91756i) q^{23} +(-3.39270 - 5.87633i) q^{24} -0.523604 q^{25} +(-3.45058 - 1.04571i) q^{26} +2.00000 q^{27} +(1.68878 + 2.92505i) q^{28} +(-1.74665 - 3.02529i) q^{29} +(2.39270 - 4.14428i) q^{30} -9.27871 q^{31} +(-2.50000 + 4.33013i) q^{32} +(1.13090 - 1.95878i) q^{33} -2.14605 q^{34} +(-3.57303 + 6.18866i) q^{35} +(1.05787 + 1.83229i) q^{36} +(4.58148 + 7.93535i) q^{37} +3.14605 q^{38} +(7.80453 + 2.36519i) q^{39} -6.34725 q^{40} +(-5.00845 - 8.67489i) q^{41} +(3.81968 + 6.61587i) q^{42} +(-1.26180 + 2.18551i) q^{43} -1.00000 q^{44} +(-2.23820 + 3.87667i) q^{45} +(-2.26180 + 3.91756i) q^{46} -1.96970 q^{47} +(-1.13090 + 1.95878i) q^{48} +(-2.20393 - 3.81731i) q^{49} +(0.261802 + 0.453455i) q^{50} +4.85395 q^{51} +(-0.819677 - 3.51114i) q^{52} +7.75510 q^{53} +(-1.00000 - 1.73205i) q^{54} +(-1.05787 - 1.83229i) q^{55} +(5.06633 - 8.77514i) q^{56} -7.11575 q^{57} +(-1.74665 + 3.02529i) q^{58} +(3.01515 - 5.22240i) q^{59} +4.78541 q^{60} +(-4.89270 + 8.47441i) q^{61} +(4.63935 + 8.03560i) q^{62} +(-3.57303 - 6.18866i) q^{63} +7.00000 q^{64} +(5.56633 - 5.21624i) q^{65} -2.26180 q^{66} +(-2.01515 - 3.49035i) q^{67} +(-1.07303 - 1.85854i) q^{68} +(5.11575 - 8.86074i) q^{69} +7.14605 q^{70} +(-3.00000 + 5.19615i) q^{71} +(3.17362 - 5.49688i) q^{72} +10.8405 q^{73} +(4.58148 - 7.93535i) q^{74} +(-0.592145 - 1.02563i) q^{75} +(1.57303 + 2.72456i) q^{76} +3.37755 q^{77} +(-1.85395 - 7.94151i) q^{78} +1.66966 q^{79} +(1.05787 + 1.83229i) q^{80} +(5.43543 + 9.41443i) q^{81} +(-5.00845 + 8.67489i) q^{82} +5.66966 q^{83} +(-3.81968 + 6.61587i) q^{84} +(2.27026 - 3.93220i) q^{85} +2.52360 q^{86} +(3.95058 - 6.84260i) q^{87} +(1.50000 + 2.59808i) q^{88} +(-4.67362 - 8.09495i) q^{89} +4.47640 q^{90} +(2.76850 + 11.8591i) q^{91} -4.52360 q^{92} +(-10.4933 - 18.1749i) q^{93} +(0.984848 + 1.70581i) q^{94} +(-3.32813 + 5.76449i) q^{95} -11.3090 q^{96} +(-5.81968 + 10.0800i) q^{97} +(-2.20393 + 3.81731i) q^{98} +2.11575 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} + 3 q^{4} + 6 q^{5} - 18 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 + 3 * q^4 + 6 * q^5 - 18 * q^8 - 3 * q^9	$ 6 q - 3 q^{2} + 3 q^{4} + 6 q^{5} - 18 q^{8} - 3 q^{9} - 3 q^{10} - 3 q^{11} + 9 q^{13} - 6 q^{15} + 3 q^{16} + 3 q^{17} + 6 q^{18} - 6 q^{19} + 3 q^{20} - 12 q^{21} - 3 q^{22} + 24 q^{25} + 3 q^{26} + 12 q^{27} + 3 q^{29} - 6 q^{30} + 12 q^{31} - 15 q^{32} - 6 q^{34} - 18 q^{35} + 3 q^{36} - 3 q^{37} + 12 q^{38} + 30 q^{39} - 18 q^{40} - 3 q^{41} + 6 q^{42} + 6 q^{43} - 6 q^{44} - 27 q^{45} - 12 q^{47} - 3 q^{49} - 12 q^{50} + 36 q^{51} + 12 q^{52} + 6 q^{53} - 6 q^{54} - 3 q^{55} - 36 q^{57} + 3 q^{58} + 18 q^{59} - 12 q^{60} - 9 q^{61} - 6 q^{62} - 18 q^{63} + 42 q^{64} + 3 q^{65} - 12 q^{67} - 3 q^{68} + 24 q^{69} + 36 q^{70} - 18 q^{71} + 9 q^{72} + 18 q^{73} - 3 q^{74} - 24 q^{75} + 6 q^{76} - 18 q^{78} - 24 q^{79} + 3 q^{80} + 9 q^{81} - 3 q^{82} - 6 q^{84} - 27 q^{85} - 12 q^{86} + 9 q^{88} - 18 q^{89} + 54 q^{90} + 30 q^{91} - 36 q^{93} + 6 q^{94} + 24 q^{95} - 18 q^{97} - 3 q^{98} + 6 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 + 3 * q^4 + 6 * q^5 - 18 * q^8 - 3 * q^9 - 3 * q^10 - 3 * q^11 + 9 * q^13 - 6 * q^15 + 3 * q^16 + 3 * q^17 + 6 * q^18 - 6 * q^19 + 3 * q^20 - 12 * q^21 - 3 * q^22 + 24 * q^25 + 3 * q^26 + 12 * q^27 + 3 * q^29 - 6 * q^30 + 12 * q^31 - 15 * q^32 - 6 * q^34 - 18 * q^35 + 3 * q^36 - 3 * q^37 + 12 * q^38 + 30 * q^39 - 18 * q^40 - 3 * q^41 + 6 * q^42 + 6 * q^43 - 6 * q^44 - 27 * q^45 - 12 * q^47 - 3 * q^49 - 12 * q^50 + 36 * q^51 + 12 * q^52 + 6 * q^53 - 6 * q^54 - 3 * q^55 - 36 * q^57 + 3 * q^58 + 18 * q^59 - 12 * q^60 - 9 * q^61 - 6 * q^62 - 18 * q^63 + 42 * q^64 + 3 * q^65 - 12 * q^67 - 3 * q^68 + 24 * q^69 + 36 * q^70 - 18 * q^71 + 9 * q^72 + 18 * q^73 - 3 * q^74 - 24 * q^75 + 6 * q^76 - 18 * q^78 - 24 * q^79 + 3 * q^80 + 9 * q^81 - 3 * q^82 - 6 * q^84 - 27 * q^85 - 12 * q^86 + 9 * q^88 - 18 * q^89 + 54 * q^90 + 30 * q^91 - 36 * q^93 + 6 * q^94 + 24 * q^95 - 18 * q^97 - 3 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i	0.633316	−	0.773893i	$-0.281693\pi$
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i	−0.986869	+	0.161521i	$0.948360\pi$
$3$	1.13090	+	1.95878i	0.652926	+	1.13090i	0.982409	+	0.186740i	$0.0597921\pi$
$3$	1.13090	+	1.95878i	0.652926	+	1.13090i	−0.329483	+	0.944161i	$0.606875\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	2.11575			0.946192			0.473096	−	0.881011i	$-0.343136\pi$
$5$	2.11575			0.946192			0.473096	+	0.881011i	$0.343136\pi$
$6$	1.13090	−	1.95878i	0.461688	−	0.799668i
$7$	−1.68878	+	2.92505i	−0.638297	+	1.10556i	0.347509	+	0.937677i	$0.387028\pi$
$7$	−1.68878	+	2.92505i	−0.638297	+	1.10556i	−0.985806	+	0.167887i	$0.946306\pi$
$8$	−3.00000			−1.06066
$9$	−1.05787	+	1.83229i	−0.352625	+	0.610764i
$10$	−1.05787	−	1.83229i	−0.334529	−	0.579422i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$	2.26180			0.652926
$13$	2.63090	−	2.46543i	0.729681	−	0.683788i
$13$	2.63090	−	2.46543i	0.729681	−	0.683788i
$14$	3.37755			0.902689
$15$	2.39270	+	4.14428i	0.617793	+	1.07005i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.07303	−	1.85854i	0.260247	−	0.450761i	−0.706060	−	0.708152i	$-0.749529\pi$
$17$	1.07303	−	1.85854i	0.260247	−	0.450761i	0.966308	+	0.257390i	$0.0828626\pi$
$18$	2.11575			0.498687
$19$	−1.57303	+	2.72456i	−0.360877	+	0.625057i	−0.988105	−	0.153778i	$-0.950856\pi$
$19$	−1.57303	+	2.72456i	−0.360877	+	0.625057i	0.627228	+	0.778835i	$0.284189\pi$
$20$	1.05787	−	1.83229i	0.236548	−	0.409713i
$21$	−7.63935			−1.66704
$22$	−0.500000	+	0.866025i	−0.106600	+	0.184637i
$23$	−2.26180	−	3.91756i	−0.471618	−	0.816867i	0.527854	−	0.849335i	$-0.322997\pi$
$23$	−2.26180	−	3.91756i	−0.471618	−	0.816867i	−0.999473	+	0.0324679i	$0.989663\pi$
$24$	−3.39270	−	5.87633i	−0.692533	−	1.19950i
$25$	−0.523604			−0.104721
$26$	−3.45058	−	1.04571i	−0.676714	−	0.205081i
$27$	2.00000			0.384900
$28$	1.68878	+	2.92505i	0.319149	+	0.552782i
$29$	−1.74665	−	3.02529i	−0.324345	−	0.561782i	0.657035	−	0.753860i	$-0.271810\pi$
$29$	−1.74665	−	3.02529i	−0.324345	−	0.561782i	−0.981380	+	0.192079i	$0.938477\pi$
$30$	2.39270	−	4.14428i	0.436846	−	0.756639i
$31$	−9.27871			−1.66651			−0.833253	−	0.552893i	$-0.813524\pi$
$31$	−9.27871			−1.66651			−0.833253	+	0.552893i	$0.813524\pi$
$32$	−2.50000	+	4.33013i	−0.441942	+	0.765466i
$33$	1.13090	−	1.95878i	0.196865	−	0.340980i
$34$	−2.14605			−0.368045
$35$	−3.57303	+	6.18866i	−0.603952	+	1.04608i
$36$	1.05787	+	1.83229i	0.176312	+	0.305382i
$37$	4.58148	+	7.93535i	0.753191	+	1.30456i	0.946269	+	0.323381i	$0.104820\pi$
$37$	4.58148	+	7.93535i	0.753191	+	1.30456i	−0.193078	+	0.981183i	$0.561847\pi$
$38$	3.14605			0.510357
$39$	7.80453	+	2.36519i	1.24972	+	0.378734i
$40$	−6.34725			−1.00359
$41$	−5.00845	−	8.67489i	−0.782189	−	1.35479i	−0.930664	−	0.365875i	$-0.880770\pi$
$41$	−5.00845	−	8.67489i	−0.782189	−	1.35479i	0.148475	−	0.988916i	$-0.452563\pi$
$42$	3.81968	+	6.61587i	0.589389	+	1.02085i
$43$	−1.26180	+	2.18551i	−0.192423	+	0.333286i	−0.946053	−	0.324013i	$-0.894968\pi$
$43$	−1.26180	+	2.18551i	−0.192423	+	0.333286i	0.753630	+	0.657299i	$0.228301\pi$
$44$	−1.00000			−0.150756
$45$	−2.23820	+	3.87667i	−0.333651	+	0.577900i
$46$	−2.26180	+	3.91756i	−0.333485	+	0.577612i
$47$	−1.96970			−0.287310			−0.143655	−	0.989628i	$-0.545886\pi$
$47$	−1.96970			−0.287310			−0.143655	+	0.989628i	$0.545886\pi$
$48$	−1.13090	+	1.95878i	−0.163232	+	0.282725i
$49$	−2.20393	−	3.81731i	−0.314847	−	0.545331i
$50$	0.261802	+	0.453455i	0.0370244	+	0.0641282i
$51$	4.85395			0.679689
$52$	−0.819677	−	3.51114i	−0.113669	−	0.486908i
$53$	7.75510			1.06525			0.532623	−	0.846353i	$-0.321206\pi$
$53$	7.75510			1.06525			0.532623	+	0.846353i	$0.321206\pi$
$54$	−1.00000	−	1.73205i	−0.136083	−	0.235702i
$55$	−1.05787	−	1.83229i	−0.142644	−	0.247066i
$56$	5.06633	−	8.77514i	0.677016	−	1.17263i
$57$	−7.11575			−0.942504
$58$	−1.74665	+	3.02529i	−0.229346	+	0.397240i
$59$	3.01515	−	5.22240i	0.392539	−	0.679898i	−0.600244	−	0.799817i	$-0.704930\pi$
$59$	3.01515	−	5.22240i	0.392539	−	0.679898i	0.992784	+	0.119919i	$0.0382634\pi$
$60$	4.78541			0.617793
$61$	−4.89270	+	8.47441i	−0.626446	+	1.08504i	0.361813	+	0.932251i	$0.382158\pi$
$61$	−4.89270	+	8.47441i	−0.626446	+	1.08504i	−0.988259	+	0.152786i	$0.951175\pi$
$62$	4.63935	+	8.03560i	0.589199	+	1.02052i
$63$	−3.57303	−	6.18866i	−0.450159	−	0.779698i
$64$	7.00000			0.875000
$65$	5.56633	−	5.21624i	0.690418	−	0.646995i
$66$	−2.26180			−0.278409
$67$	−2.01515	−	3.49035i	−0.246190	−	0.426414i	0.716276	−	0.697818i	$-0.245845\pi$
$67$	−2.01515	−	3.49035i	−0.246190	−	0.426414i	−0.962466	+	0.271404i	$0.912512\pi$
$68$	−1.07303	−	1.85854i	−0.130124	−	0.225381i
$69$	5.11575	−	8.86074i	0.615864	−	1.06671i
$70$	7.14605			0.854117
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	−0.987294	−	0.158901i	$-0.949205\pi$
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	0.631260	+	0.775571i	$0.282538\pi$
$72$	3.17362	−	5.49688i	0.374015	−	0.647813i
$73$	10.8405			1.26879			0.634395	−	0.773009i	$-0.281249\pi$
$73$	10.8405			1.26879			0.634395	+	0.773009i	$0.281249\pi$
$74$	4.58148	−	7.93535i	0.532586	−	0.922466i
$75$	−0.592145	−	1.02563i	−0.0683750	−	0.118429i
$76$	1.57303	+	2.72456i	0.180439	+	0.312529i
$77$	3.37755			0.384908
$78$	−1.85395	−	7.94151i	−0.209918	−	0.899199i
$79$	1.66966			0.187851			0.0939256	−	0.995579i	$-0.470058\pi$
$79$	1.66966			0.187851			0.0939256	+	0.995579i	$0.470058\pi$
$80$	1.05787	+	1.83229i	0.118274	+	0.204857i
$81$	5.43543	+	9.41443i	0.603936	+	1.04605i
$82$	−5.00845	+	8.67489i	−0.553091	+	0.957982i
$83$	5.66966			0.622326			0.311163	−	0.950357i	$-0.399282\pi$
$83$	5.66966			0.622326			0.311163	+	0.950357i	$0.399282\pi$
$84$	−3.81968	+	6.61587i	−0.416761	+	0.721851i
$85$	2.27026	−	3.93220i	0.246244	−	0.426507i
$86$	2.52360			0.272127
$87$	3.95058	−	6.84260i	0.423546	−	0.733604i
$88$	1.50000	+	2.59808i	0.159901	+	0.276956i
$89$	−4.67362	−	8.09495i	−0.495403	−	0.858063i	0.504583	−	0.863363i	$-0.331646\pi$
$89$	−4.67362	−	8.09495i	−0.495403	−	0.858063i	−0.999986	+	0.00529986i	$0.998313\pi$
$90$	4.47640			0.471854
$91$	2.76850	+	11.8591i	0.290218	+	1.24317i
$92$	−4.52360			−0.471618
$93$	−10.4933	−	18.1749i	−1.08810	−	1.88465i
$94$	0.984848	+	1.70581i	0.101579	+	0.175941i
$95$	−3.32813	+	5.76449i	−0.341459	+	0.591424i
$96$	−11.3090			−1.15422
$97$	−5.81968	+	10.0800i	−0.590899	+	1.02347i	0.403213	+	0.915106i	$0.367893\pi$
$97$	−5.81968	+	10.0800i	−0.590899	+	1.02347i	−0.994112	+	0.108360i	$0.965440\pi$
$98$	−2.20393	+	3.81731i	−0.222630	+	0.385607i
$99$	2.11575			0.212641
$100$	−0.261802	+	0.453455i	−0.0261802	+	0.0453455i
$101$	−0.450578	−	0.780424i	−0.0448342	−	0.0776551i	0.842737	−	0.538325i	$-0.180943\pi$
$101$	−0.450578	−	0.780424i	−0.0448342	−	0.0776551i	−0.887572	+	0.460670i	$0.847609\pi$
$102$	−2.42697	−	4.20364i	−0.240306	−	0.416223i
$103$	13.0472			1.28558			0.642790	−	0.766043i	$-0.277777\pi$
$103$	13.0472			1.28558			0.642790	+	0.766043i	$0.277777\pi$
$104$	−7.89270	+	7.39630i	−0.773943	+	0.725267i
$105$	−16.1630			−1.57734
$106$	−3.87755	−	6.71612i	−0.376621	−	0.652327i
$107$	6.80453	+	11.7858i	0.657818	+	1.13937i	0.981179	+	0.193099i	$0.0618539\pi$
$107$	6.80453	+	11.7858i	0.657818	+	1.13937i	−0.323361	+	0.946276i	$0.604813\pi$
$108$	1.00000	−	1.73205i	0.0962250	−	0.166667i
$109$	18.6866			1.78985			0.894924	−	0.446218i	$-0.147230\pi$
$109$	18.6866			1.78985			0.894924	+	0.446218i	$0.147230\pi$
$110$	−1.05787	+	1.83229i	−0.100864	+	0.174702i
$111$	−10.3624	+	17.9482i	−0.983555	+	1.70357i
$112$	−3.37755			−0.319149
$113$	−6.31968	+	10.9460i	−0.594505	+	1.02971i	0.399111	+	0.916902i	$0.369319\pi$
$113$	−6.31968	+	10.9460i	−0.594505	+	1.02971i	−0.993616	+	0.112811i	$0.964015\pi$
$114$	3.55787	+	6.16242i	0.333225	+	0.577163i
$115$	−4.78541	−	8.28857i	−0.446241	−	0.772913i
$116$	−3.49330			−0.324345
$117$	1.73423	+	7.42870i	0.160330	+	0.686784i
$118$	−6.03030			−0.555134
$119$	3.62420	+	6.27730i	0.332230	+	0.575439i
$120$	−7.17811	−	12.4329i	−0.655269	−	1.13496i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	9.78541			0.885929
$123$	11.3281	−	19.6209i	1.02142	−	1.76916i
$124$	−4.63935	+	8.03560i	−0.416626	+	0.721618i
$125$	−11.6866			−1.04528
$126$	−3.57303	+	6.18866i	−0.318310	+	0.551330i
$127$	−5.75510	−	9.96813i	−0.510683	−	0.884529i	−0.999923	−	0.0123797i	$-0.996059\pi$
$127$	−5.75510	−	9.96813i	−0.510683	−	0.884529i	0.489241	−	0.872149i	$-0.337274\pi$
$128$	1.50000	+	2.59808i	0.132583	+	0.229640i
$129$	−5.70789			−0.502552
$130$	−7.30056	−	2.21246i	−0.640301	−	0.194046i
$131$	13.6091			1.18903			0.594514	−	0.804085i	$-0.297344\pi$
$131$	13.6091			1.18903			0.594514	+	0.804085i	$0.297344\pi$
$132$	−1.13090	−	1.95878i	−0.0984323	−	0.170490i
$133$	−5.31298	−	9.20235i	−0.460694	−	0.797945i
$134$	−2.01515	+	3.49035i	−0.174083	+	0.301520i
$135$	4.23150			0.364189
$136$	−3.21908	+	5.57561i	−0.276034	+	0.478105i
$137$	7.55118	−	13.0790i	0.645140	−	1.11742i	−0.339129	−	0.940740i	$-0.610132\pi$
$137$	7.55118	−	13.0790i	0.645140	−	1.11742i	0.984269	−	0.176676i	$-0.0565345\pi$
$138$	−10.2315			−0.870963
$139$	7.63935	−	13.2317i	0.647962	−	1.12230i	−0.335647	−	0.941988i	$-0.608955\pi$
$139$	7.63935	−	13.2317i	0.647962	−	1.12230i	0.983609	−	0.180315i	$-0.0577116\pi$
$140$	3.57303	+	6.18866i	0.301976	+	0.523038i
$141$	−2.22753	−	3.85820i	−0.187592	−	0.324919i
$142$	6.00000			0.503509
$143$	−3.45058	−	1.04571i	−0.288552	−	0.0874467i
$144$	−2.11575			−0.176312
$145$	−3.69547	−	6.40075i	−0.306892	−	0.531553i
$146$	−5.42027	−	9.38819i	−0.448585	−	0.776972i
$147$	4.98485	−	8.63401i	0.411143	−	0.712121i
$148$	9.16296			0.753191
$149$	−2.18878	+	3.79107i	−0.179312	+	0.310577i	−0.941645	−	0.336608i	$-0.890720\pi$
$149$	−2.18878	+	3.79107i	−0.179312	+	0.310577i	0.762333	+	0.647184i	$0.224054\pi$
$150$	−0.592145	+	1.02563i	−0.0483484	+	0.0837419i
$151$	2.29211			0.186529			0.0932645	−	0.995641i	$-0.470270\pi$
$151$	2.29211			0.186529			0.0932645	+	0.995641i	$0.470270\pi$
$152$	4.71908	−	8.17369i	0.382768	−	0.662973i
$153$	2.27026	+	3.93220i	0.183539	+	0.317899i
$154$	−1.68878	−	2.92505i	−0.136085	−	0.235707i
$155$	−19.6314			−1.57683
$156$	5.95058	−	5.57632i	0.476428	−	0.446463i
$157$	−24.0472			−1.91918			−0.959588	−	0.281408i	$-0.909198\pi$
$157$	−24.0472			−1.91918			−0.959588	+	0.281408i	$0.909198\pi$
$158$	−0.834829	−	1.44597i	−0.0664154	−	0.115035i
$159$	8.77026	+	15.1905i	0.695526	+	1.20469i
$160$	−5.28937	+	9.16146i	−0.418162	+	0.724277i
$161$	15.2787			1.20413
$162$	5.43543	−	9.41443i	0.427047	−	0.739668i
$163$	3.27695	−	5.67585i	0.256671	−	0.444567i	−0.708677	−	0.705533i	$-0.750708\pi$
$163$	3.27695	−	5.67585i	0.256671	−	0.444567i	0.965348	+	0.260966i	$0.0840410\pi$
$164$	−10.0169			−0.782189
$165$	2.39270	−	4.14428i	0.186272	−	0.322632i
$166$	−2.83483	−	4.91007i	−0.220025	−	0.381095i
$167$	9.16296	+	15.8707i	0.709051	+	1.22811i	0.965210	+	0.261478i	$0.0842098\pi$
$167$	9.16296	+	15.8707i	0.709051	+	1.22811i	−0.256159	+	0.966635i	$0.582457\pi$
$168$	22.9181			1.76817
$169$	0.843281	−	12.9726i	0.0648678	−	0.997894i
$170$	−4.54051			−0.348241
$171$	−3.32813	−	5.76449i	−0.254508	−	0.440822i
$172$	1.26180	+	2.18551i	0.0962115	+	0.166643i
$173$	−7.34328	+	12.7189i	−0.558299	+	0.967003i	0.439339	+	0.898321i	$0.355213\pi$
$173$	−7.34328	+	12.7189i	−0.558299	+	0.967003i	−0.997639	+	0.0686816i	$0.978121\pi$
$174$	−7.90116			−0.598985
$175$	0.884251	−	1.53157i	0.0668431	−	0.115776i
$176$	0.500000	−	0.866025i	0.0376889	−	0.0652791i
$177$	13.6394			1.02520
$178$	−4.67362	+	8.09495i	−0.350303	+	0.606742i
$179$	3.24665	+	5.62336i	0.242666	+	0.420310i	0.961473	−	0.274900i	$-0.0886447\pi$
$179$	3.24665	+	5.62336i	0.242666	+	0.420310i	−0.718807	+	0.695210i	$0.755311\pi$
$180$	2.23820	+	3.87667i	0.166825	+	0.288950i
$181$	−17.1630			−1.27571			−0.637856	−	0.770155i	$-0.720179\pi$
$181$	−17.1630			−1.27571			−0.637856	+	0.770155i	$0.720179\pi$
$182$	8.88600	−	8.32713i	0.658674	−	0.617248i
$183$	−22.1327			−1.63609
$184$	6.78541	+	11.7527i	0.500227	+	0.866418i
$185$	9.69326	+	16.7892i	0.712663	+	1.23437i
$186$	−10.4933	+	18.1749i	−0.769406	+	1.33265i
$187$	−2.14605			−0.156935
$188$	−0.984848	+	1.70581i	−0.0718274	+	0.124409i
$189$	−3.37755	+	5.85009i	−0.245681	+	0.425532i
$190$	6.65626			0.482896
$191$	−8.98485	+	15.5622i	−0.650121	+	1.12604i	0.332972	+	0.942937i	$0.391948\pi$
$191$	−8.98485	+	15.5622i	−0.650121	+	1.12604i	−0.983093	+	0.183106i	$0.941385\pi$
$192$	7.91631	+	13.7114i	0.571310	+	0.989538i
$193$	1.48485	+	2.57183i	0.106882	+	0.185125i	0.914505	−	0.404574i	$-0.132580\pi$
$193$	1.48485	+	2.57183i	0.106882	+	0.185125i	−0.807624	+	0.589698i	$0.799247\pi$
$194$	11.6394			0.835657
$195$	16.5124	+	5.00415i	1.18248	+	0.358355i
$196$	−4.40786			−0.314847
$197$	−6.11575	−	10.5928i	−0.435729	−	0.754705i	0.561626	−	0.827391i	$-0.310176\pi$
$197$	−6.11575	−	10.5928i	−0.435729	−	0.754705i	−0.997355	+	0.0726865i	$0.976843\pi$
$198$	−1.05787	−	1.83229i	−0.0751799	−	0.130215i
$199$	0.100598	−	0.174240i	0.00713118	−	0.0123516i	−0.862438	−	0.506163i	$-0.831063\pi$
$199$	0.100598	−	0.174240i	0.00713118	−	0.0123516i	0.869569	+	0.493812i	$0.164397\pi$
$200$	1.57081			0.111073
$201$	4.55787	−	7.89447i	0.321488	−	0.556833i
$202$	−0.450578	+	0.780424i	−0.0317026	+	0.0549104i
$203$	11.7988			0.828114
$204$	2.42697	−	4.20364i	0.169922	−	0.294314i
$205$	−10.5966	−	18.3539i	−0.740101	−	1.28189i
$206$	−6.52360	−	11.2992i	−0.454521	−	0.787254i
$207$	9.57081			0.665218
$208$	3.45058	+	1.04571i	0.239255	+	0.0725070i
$209$	3.14605			0.217617
$210$	8.08148	+	13.9975i	0.557675	+	0.965922i
$211$	−5.83483	−	10.1062i	−0.401686	−	0.695741i	0.592243	−	0.805759i	$-0.298242\pi$
$211$	−5.83483	−	10.1062i	−0.401686	−	0.695741i	−0.993930	+	0.110018i	$0.964909\pi$
$212$	3.87755	−	6.71612i	0.266311	−	0.461265i
$213$	−13.5708			−0.929857
$214$	6.80453	−	11.7858i	0.465148	−	0.805660i
$215$	−2.66966	+	4.62398i	−0.182069	+	0.315353i
$216$	−6.00000			−0.408248
$217$	15.6697	−	27.1406i	1.06373	−	1.84243i
$218$	−9.34328	−	16.1830i	−0.632807	−	1.09605i
$219$	12.2596	+	21.2342i	0.828426	+	1.43488i
$220$	−2.11575			−0.142644
$221$	−1.75907	−	7.53510i	−0.118328	−	0.506866i
$222$	20.7248			1.39096
$223$	3.75335	+	6.50099i	0.251343	+	0.435339i	0.963896	−	0.266280i	$-0.0857945\pi$
$223$	3.75335	+	6.50099i	0.251343	+	0.435339i	−0.712553	+	0.701618i	$0.752461\pi$
$224$	−8.44388	−	14.6252i	−0.564180	−	0.977189i
$225$	0.553908	−	0.959397i	0.0369272	−	0.0639598i
$226$	12.6394			0.840757
$227$	1.73820	−	3.01065i	0.115368	−	0.199824i	−0.802559	−	0.596573i	$-0.796529\pi$
$227$	1.73820	−	3.01065i	0.115368	−	0.199824i	0.917927	+	0.396750i	$0.129862\pi$
$228$	−3.55787	+	6.16242i	−0.235626	+	0.408116i
$229$	13.4079			0.886016			0.443008	−	0.896518i	$-0.353911\pi$
$229$	13.4079			0.886016			0.443008	+	0.896518i	$0.353911\pi$
$230$	−4.78541	+	8.28857i	−0.315540	+	0.546532i
$231$	3.81968	+	6.61587i	0.251316	+	0.435293i
$232$	5.23995	+	9.07586i	0.344020	+	0.595860i
$233$	0.292106			0.0191365			0.00956824	−	0.999954i	$-0.496954\pi$
$233$	0.292106			0.0191365			0.00956824	+	0.999954i	$0.496954\pi$
$234$	5.56633	−	5.21624i	0.363882	−	0.340996i
$235$	−4.16738			−0.271850
$236$	−3.01515	−	5.22240i	−0.196270	−	0.339949i
$237$	1.88822	+	3.27049i	0.122653	+	0.212441i
$238$	3.62420	−	6.27730i	0.234922	−	0.406897i
$239$	−21.8023			−1.41027			−0.705137	−	0.709071i	$-0.749115\pi$
$239$	−21.8023			−1.41027			−0.705137	+	0.709071i	$0.749115\pi$
$240$	−2.39270	+	4.14428i	−0.154448	+	0.267512i
$241$	1.27422	−	2.20702i	0.0820798	−	0.142166i	−0.822063	−	0.569396i	$-0.807177\pi$
$241$	1.27422	−	2.20702i	0.0820798	−	0.142166i	0.904143	+	0.427230i	$0.140510\pi$
$242$	1.00000			0.0642824
$243$	−9.29386	+	16.0974i	−0.596201	+	1.03265i
$244$	4.89270	+	8.47441i	0.313223	+	0.542519i
$245$	−4.66296	−	8.07648i	−0.297905	−	0.515987i
$246$	−22.6563			−1.44451
$247$	2.57875	+	11.0462i	0.164082	+	0.702856i
$248$	27.8361			1.76760
$249$	6.41182	+	11.1056i	0.406333	+	0.703789i
$250$	5.84328	+	10.1209i	0.369562	+	0.640099i
$251$	13.4096	−	23.2261i	0.846407	−	1.46602i	−0.0379867	−	0.999278i	$-0.512094\pi$
$251$	13.4096	−	23.2261i	0.846407	−	1.46602i	0.884394	−	0.466742i	$-0.154572\pi$
$252$	−7.14605			−0.450159
$253$	−2.26180	+	3.91756i	−0.142198	+	0.246295i
$254$	−5.75510	+	9.96813i	−0.361107	+	0.625456i
$255$	10.2697			0.643116
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	−1.53427	−	2.65743i	−0.0957051	−	0.165766i	0.814198	−	0.580588i	$-0.197177\pi$
$257$	−1.53427	−	2.65743i	−0.0957051	−	0.165766i	−0.909903	+	0.414822i	$0.863844\pi$
$258$	2.85395	+	4.94318i	0.177679	+	0.307749i
$259$	−30.9484			−1.92304
$260$	−1.73423	−	7.42870i	−0.107552	−	0.460708i
$261$	7.39095			0.457488
$262$	−6.80453	−	11.7858i	−0.420385	−	0.728128i
$263$	−1.14605	−	1.98502i	−0.0706686	−	0.122402i	0.828526	−	0.559951i	$-0.189180\pi$
$263$	−1.14605	−	1.98502i	−0.0706686	−	0.122402i	−0.899195	+	0.437549i	$0.855847\pi$
$264$	−3.39270	+	5.87633i	−0.208806	+	0.361663i
$265$	16.4079			1.00793
$266$	−5.31298	+	9.20235i	−0.325760	+	0.564232i
$267$	10.5708	−	18.3092i	0.646923	−	1.12050i
$268$	−4.03030			−0.246190
$269$	−5.62245	+	9.73837i	−0.342807	+	0.593759i	−0.984953	−	0.172824i	$-0.944711\pi$
$269$	−5.62245	+	9.73837i	−0.342807	+	0.593759i	0.642146	+	0.766582i	$0.278044\pi$
$270$	−2.11575	−	3.66459i	−0.128760	−	0.223020i
$271$	2.14605	+	3.71707i	0.130363	+	0.225796i	0.923817	−	0.382835i	$-0.125052\pi$
$271$	2.14605	+	3.71707i	0.130363	+	0.225796i	−0.793453	+	0.608631i	$0.791719\pi$
$272$	2.14605			0.130124
$273$	−20.0984	+	18.8343i	−1.21641	+	1.13990i
$274$	−15.1024			−0.912366
$275$	0.261802	+	0.453455i	0.0157873	+	0.0273444i
$276$	−5.11575	−	8.86074i	−0.307932	−	0.533354i
$277$	2.41631	−	4.18517i	0.145182	−	0.251462i	−0.784259	−	0.620434i	$-0.786957\pi$
$277$	2.41631	−	4.18517i	0.145182	−	0.251462i	0.929441	+	0.368971i	$0.120290\pi$
$278$	−15.2787			−0.916356
$279$	9.81571	−	17.0013i	0.587651	−	1.01784i
$280$	10.7191	−	18.5660i	0.640588	−	1.10953i
$281$	3.78541			0.225818			0.112909	−	0.993605i	$-0.463983\pi$
$281$	3.78541			0.225818			0.112909	+	0.993605i	$0.463983\pi$
$282$	−2.22753	+	3.85820i	−0.132648	+	0.229752i
$283$	6.21238	+	10.7602i	0.369288	+	0.639625i	0.989454	−	0.144845i	$-0.0462684\pi$
$283$	6.21238	+	10.7602i	0.369288	+	0.639625i	−0.620167	+	0.784470i	$0.712935\pi$
$284$	3.00000	+	5.19615i	0.178017	+	0.308335i
$285$	−15.0551			−0.891790
$286$	0.819677	+	3.51114i	0.0484685	+	0.207618i
$287$	33.8326			1.99708
$288$	−5.28937	−	9.16146i	−0.311679	−	0.539844i
$289$	6.19723	+	10.7339i	0.364543	+	0.631407i
$290$	−3.69547	+	6.40075i	−0.217006	+	0.375865i
$291$	−26.3259			−1.54325
$292$	5.42027	−	9.38819i	0.317198	−	0.549402i
$293$	−8.45058	+	14.6368i	−0.493688	+	0.855093i	−0.999974	−	0.00727315i	$-0.997685\pi$
$293$	−8.45058	+	14.6368i	−0.493688	+	0.855093i	0.506286	+	0.862366i	$0.331018\pi$
$294$	−9.96970			−0.581445
$295$	6.37931	−	11.0493i	0.371418	−	0.643314i
$296$	−13.7444	−	23.8061i	−0.798879	−	1.38370i
$297$	−1.00000	−	1.73205i	−0.0580259	−	0.100504i
$298$	4.37755			0.253585
$299$	−15.6091	−	4.73038i	−0.902695	−	0.273565i
$300$	−1.18429			−0.0683750
$301$	−4.26180	−	7.38166i	−0.245646	−	0.425472i
$302$	−1.14605	−	1.98502i	−0.0659479	−	0.114225i
$303$	1.01912	−	1.76516i	0.0585468	−	0.101406i
$304$	−3.14605			−0.180439
$305$	−10.3517	+	17.9297i	−0.592739	+	1.02665i
$306$	2.27026	−	3.93220i	0.129782	−	0.224789i
$307$	−8.42476			−0.480826			−0.240413	−	0.970671i	$-0.577283\pi$
$307$	−8.42476			−0.480826			−0.240413	+	0.970671i	$0.577283\pi$
$308$	1.68878	−	2.92505i	0.0962269	−	0.166670i
$309$	14.7551	+	25.5566i	0.839388	+	1.45386i
$310$	9.81571	+	17.0013i	0.557495	+	0.965609i
$311$	−28.5877			−1.62106			−0.810530	−	0.585697i	$-0.800821\pi$
$311$	−28.5877			−1.62106			−0.810530	+	0.585697i	$0.800821\pi$
$312$	−23.4136	−	7.09557i	−1.32553	−	0.401708i
$313$	22.3945			1.26581			0.632905	−	0.774230i	$-0.281862\pi$
$313$	22.3945			1.26581			0.632905	+	0.774230i	$0.281862\pi$
$314$	12.0236	+	20.8255i	0.678531	+	1.17525i
$315$	−7.55963	−	13.0937i	−0.425937	−	0.737744i
$316$	0.834829	−	1.44597i	0.0469628	−	0.0813419i
$317$	−26.2708			−1.47551			−0.737757	−	0.675067i	$-0.764115\pi$
$317$	−26.2708			−1.47551			−0.737757	+	0.675067i	$0.764115\pi$
$318$	8.77026	−	15.1905i	0.491811	−	0.851842i
$319$	−1.74665	+	3.02529i	−0.0977937	+	0.169384i
$320$	14.8102			0.827918
$321$	−15.3905	+	26.6571i	−0.859013	+	1.48785i
$322$	−7.63935	−	13.2317i	−0.425725	−	0.737377i
$323$	3.37580	+	5.84705i	0.187834	+	0.325339i
$324$	10.8709			0.603936
$325$	−1.37755	+	1.29091i	−0.0764128	+	0.0716069i
$326$	−6.55391			−0.362987
$327$	21.1327	+	36.6028i	1.16864	+	2.02414i
$328$	15.0254	+	26.0247i	0.829637	+	1.43697i
$329$	3.32638	−	5.76145i	0.183389	−	0.317639i
$330$	−4.78541			−0.263428
$331$	4.14605	−	7.18117i	0.227888	−	0.394713i	−0.729294	−	0.684200i	$-0.760151\pi$
$331$	4.14605	−	7.18117i	0.227888	−	0.394713i	0.957182	+	0.289487i	$0.0934848\pi$
$332$	2.83483	−	4.91007i	0.155581	−	0.269475i
$333$	−19.3865			−1.06237
$334$	9.16296	−	15.8707i	0.501375	−	0.868407i
$335$	−4.26356	−	7.38470i	−0.232943	−	0.403469i
$336$	−3.81968	−	6.61587i	−0.208380	−	0.360926i
$337$	−0.0516349			−0.00281273			−0.00140637	−	0.999999i	$-0.500448\pi$
$337$	−0.0516349			−0.00281273			−0.00140637	+	0.999999i	$0.500448\pi$
$338$	−11.6563	+	5.75601i	−0.634017	+	0.313086i
$339$	−28.5877			−1.55267
$340$	−2.27026	−	3.93220i	−0.123122	−	0.213253i
$341$	4.63935	+	8.03560i	0.251235	+	0.435152i
$342$	−3.32813	+	5.76449i	−0.179965	+	0.311708i
$343$	−8.75510			−0.472731
$344$	3.78541	−	6.55652i	0.204095	−	0.353504i
$345$	10.8236	−	18.7471i	0.582725	−	1.00931i
$346$	14.6866			0.789555
$347$	4.31122	−	7.46726i	0.231439	−	0.400863i	−0.726793	−	0.686856i	$-0.758990\pi$
$347$	4.31122	−	7.46726i	0.231439	−	0.400863i	0.958232	+	0.285993i	$0.0923234\pi$
$348$	−3.95058	−	6.84260i	−0.211773	−	0.366802i
$349$	−15.0000	−	25.9808i	−0.802932	−	1.39072i	−0.917679	−	0.397324i	$-0.869939\pi$
$349$	−15.0000	−	25.9808i	−0.802932	−	1.39072i	0.114747	−	0.993395i	$-0.463394\pi$
$350$	−1.76850			−0.0945304
$351$	5.26180	−	4.93087i	0.280854	−	0.263190i
$352$	5.00000			0.266501
$353$	0.238198	+	0.412571i	0.0126780	+	0.0219589i	0.872295	−	0.488980i	$-0.162631\pi$
$353$	0.238198	+	0.412571i	0.0126780	+	0.0219589i	−0.859617	+	0.510939i	$0.829298\pi$
$354$	−6.81968	−	11.8120i	−0.362462	−	0.627802i
$355$	−6.34725	+	10.9938i	−0.336877	+	0.583488i
$356$	−9.34725			−0.495403
$357$	−8.19723	+	14.1980i	−0.433843	+	0.751439i
$358$	3.24665	−	5.62336i	0.171591	−	0.297204i
$359$	−10.2315			−0.539998			−0.269999	−	0.962861i	$-0.587023\pi$
$359$	−10.2315			−0.539998			−0.269999	+	0.962861i	$0.587023\pi$
$360$	6.71459	−	11.6300i	0.353890	−	0.612956i
$361$	4.55118	+	7.88287i	0.239536	+	0.414888i
$362$	8.58148	+	14.8636i	0.451033	+	0.781211i
$363$	−2.26180			−0.118714
$364$	11.6545	+	3.53194i	0.610862	+	0.185124i
$365$	22.9359			1.20052
$366$	11.0663	+	19.1674i	0.578446	+	1.00190i
$367$	−10.6697	−	18.4804i	−0.556952	−	0.964668i	−0.997749	−	0.0670617i	$-0.978638\pi$
$367$	−10.6697	−	18.4804i	−0.556952	−	0.964668i	0.440797	−	0.897607i	$-0.354696\pi$
$368$	2.26180	−	3.91756i	0.117905	−	0.204217i
$369$	21.1933			1.10328
$370$	9.69326	−	16.7892i	0.503929	−	0.872830i
$371$	−13.0966	+	22.6840i	−0.679943	+	1.17770i
$372$	−20.9866			−1.08810
$373$	−10.6135	+	18.3832i	−0.549548	+	0.951845i	0.448757	+	0.893654i	$0.351867\pi$
$373$	−10.6135	+	18.3832i	−0.549548	+	0.951845i	−0.998305	+	0.0581916i	$0.981467\pi$
$374$	1.07303	+	1.85854i	0.0554849	+	0.0961026i
$375$	−13.2163	−	22.8914i	−0.682489	−	1.18211i
$376$	5.90909			0.304738
$377$	−12.0539	−	3.65298i	−0.620808	−	0.188138i
$378$	6.75510			0.347445
$379$	0.523604	+	0.906910i	0.0268958	+	0.0465848i	0.879160	−	0.476527i	$-0.158104\pi$
$379$	0.523604	+	0.906910i	0.0268958	+	0.0465848i	−0.852264	+	0.523112i	$0.824771\pi$
$380$	3.32813	+	5.76449i	0.170729	+	0.295712i
$381$	13.0169	−	22.5459i	0.666876	−	1.15506i
$382$	17.9697			0.919410
$383$	14.4933	−	25.1031i	0.740573	−	1.28271i	−0.211662	−	0.977343i	$-0.567887\pi$
$383$	14.4933	−	25.1031i	0.740573	−	1.28271i	0.952235	−	0.305367i	$-0.0987792\pi$
$384$	−3.39270	+	5.87633i	−0.173133	+	0.299875i
$385$	7.14605			0.364197
$386$	1.48485	−	2.57183i	0.0755768	−	0.130903i
$387$	−2.66966	−	4.62398i	−0.135706	−	0.235050i
$388$	5.81968	+	10.0800i	0.295449	+	0.511733i
$389$	15.5653			0.789195			0.394597	−	0.918854i	$-0.370884\pi$
$389$	15.5653			0.789195			0.394597	+	0.918854i	$0.370884\pi$
$390$	−3.92249	−	16.8023i	−0.198623	−	0.850815i
$391$	−9.70789			−0.490949
$392$	6.61178	+	11.4519i	0.333945	+	0.578410i
$393$	15.3905	+	26.6571i	0.776348	+	1.34467i
$394$	−6.11575	+	10.5928i	−0.308107	+	0.533657i
$395$	3.53258			0.177743
$396$	1.05787	−	1.83229i	0.0531602	−	0.0920762i
$397$	−9.48933	+	16.4360i	−0.476256	+	0.824900i	−0.999630	−	0.0272035i	$-0.991340\pi$
$397$	−9.48933	+	16.4360i	−0.476256	+	0.824900i	0.523374	+	0.852103i	$0.324673\pi$
$398$	−0.201195			−0.0100850
$399$	12.0169	−	20.8139i	0.601598	−	1.04200i
$400$	−0.261802	−	0.453455i	−0.0130901	−	0.0226727i
$401$	4.76180	+	8.24768i	0.237793	+	0.411870i	0.960081	−	0.279723i	$-0.0902427\pi$
$401$	4.76180	+	8.24768i	0.237793	+	0.411870i	−0.722288	+	0.691593i	$0.756909\pi$
$402$	−9.11575			−0.454652
$403$	−24.4114	+	22.8760i	−1.21602	+	1.13954i
$404$	−0.901156			−0.0448342
$405$	11.5000	+	19.9186i	0.571440	+	0.989762i
$406$	−5.89940	−	10.2181i	−0.292782	−	0.507114i
$407$	4.58148	−	7.93535i	0.227095	−	0.393341i
$408$	−14.5618			−0.720919
$409$	−4.95728	+	8.58626i	−0.245122	+	0.424563i	−0.962166	−	0.272465i	$-0.912161\pi$
$409$	−4.95728	+	8.58626i	−0.245122	+	0.424563i	0.717044	+	0.697028i	$0.245495\pi$
$410$	−10.5966	+	18.3539i	−0.523330	+	0.906435i
$411$	34.1585			1.68492
$412$	6.52360	−	11.2992i	0.321395	−	0.556672i
$413$	10.1838	+	17.6389i	0.501114	+	0.867954i
$414$	−4.78541	−	8.28857i	−0.235190	−	0.407361i
$415$	11.9956			0.588840
$416$	4.09838	+	17.5557i	0.200940	+	0.860740i
$417$	34.5574			1.69228
$418$	−1.57303	−	2.72456i	−0.0769392	−	0.133263i
$419$	−3.50670	−	6.07378i	−0.171313	−	0.296724i	0.767566	−	0.640970i	$-0.221468\pi$
$419$	−3.50670	−	6.07378i	−0.171313	−	0.296724i	−0.938879	+	0.344246i	$0.888134\pi$
$420$	−8.08148	+	13.9975i	−0.394336	+	0.683010i
$421$	33.9787			1.65602			0.828009	−	0.560714i	$-0.189473\pi$
$421$	33.9787			1.65602			0.828009	+	0.560714i	$0.189473\pi$
$422$	−5.83483	+	10.1062i	−0.284035	+	0.491963i
$423$	2.08369	−	3.60906i	0.101313	−	0.175479i
$424$	−23.2653			−1.12986
$425$	−0.561841	+	0.973138i	−0.0272533	+	0.0472041i
$426$	6.78541	+	11.7527i	0.328754	+	0.569419i
$427$	−16.5254	−	28.6228i	−0.799718	−	1.38515i
$428$	13.6091			0.657818
$429$	−1.85395	−	7.94151i	−0.0895094	−	0.383420i
$430$	5.33931			0.257485
$431$	−3.93367	−	6.81332i	−0.189478	−	0.328186i	0.755598	−	0.655036i	$-0.227346\pi$
$431$	−3.93367	−	6.81332i	−0.189478	−	0.328186i	−0.945076	+	0.326849i	$0.894013\pi$
$432$	1.00000	+	1.73205i	0.0481125	+	0.0833333i
$433$	6.82638	−	11.8236i	0.328055	−	0.568207i	−0.654071	−	0.756433i	$-0.726940\pi$
$433$	6.82638	−	11.8236i	0.328055	−	0.568207i	0.982126	+	0.188226i	$0.0602736\pi$
$434$	−31.3393			−1.50434
$435$	8.35843	−	14.4772i	0.400756	−	0.694130i
$436$	9.34328	−	16.1830i	0.447462	−	0.775027i
$437$	14.2315			0.680785
$438$	12.2596	−	21.2342i	0.585786	−	1.01461i
$439$	4.16517	+	7.21429i	0.198793	+	0.344319i	0.948137	−	0.317861i	$-0.102965\pi$
$439$	4.16517	+	7.21429i	0.198793	+	0.344319i	−0.749344	+	0.662180i	$0.769631\pi$
$440$	3.17362	+	5.49688i	0.151297	+	0.262053i
$441$	9.32592			0.444091
$442$	−5.64605	+	5.29095i	−0.268555	+	0.251665i
$443$	−25.2484			−1.19959			−0.599794	−	0.800154i	$-0.704751\pi$
$443$	−25.2484			−1.19959			−0.599794	+	0.800154i	$0.704751\pi$
$444$	10.3624	+	17.9482i	0.491778	+	0.851784i
$445$	−9.88822	−	17.1269i	−0.468746	−	0.811893i
$446$	3.75335	−	6.50099i	0.177726	−	0.307831i
$447$	−9.90116			−0.468309
$448$	−11.8214	+	20.4753i	−0.558510	+	0.967368i
$449$	18.6354	−	32.2774i	0.879458	−	1.52327i	0.0275219	−	0.999621i	$-0.491238\pi$
$449$	18.6354	−	32.2774i	0.879458	−	1.52327i	0.851936	−	0.523645i	$-0.175428\pi$
$450$	−1.10782			−0.0522229
$451$	−5.00845	+	8.67489i	−0.235839	+	0.408485i
$452$	6.31968	+	10.9460i	0.297253	+	0.514857i
$453$	2.59214	+	4.48973i	0.121790	+	0.210946i
$454$	−3.47640			−0.163155
$455$	5.85745	+	25.0908i	0.274602	+	1.17628i
$456$	21.3472			0.999676
$457$	1.54546	+	2.67681i	0.0722933	+	0.125216i	0.899906	−	0.436084i	$-0.143635\pi$
$457$	1.54546	+	2.67681i	0.0722933	+	0.125216i	−0.827613	+	0.561300i	$0.810302\pi$
$458$	−6.70393	−	11.6115i	−0.313254	−	0.542572i
$459$	2.14605	−	3.71707i	0.100169	−	0.173498i
$460$	−9.57081			−0.446241
$461$	11.2400	−	19.4682i	0.523497	−	0.906723i	−0.476129	−	0.879375i	$-0.657961\pi$
$461$	11.2400	−	19.4682i	0.523497	−	0.906723i	0.999626	−	0.0273476i	$-0.00870611\pi$
$462$	3.81968	−	6.61587i	0.177707	−	0.307798i
$463$	−29.0507			−1.35010			−0.675051	−	0.737771i	$-0.735878\pi$
$463$	−29.0507			−1.35010			−0.675051	+	0.737771i	$0.735878\pi$
$464$	1.74665	−	3.02529i	0.0810862	−	0.140445i
$465$	−22.2012	−	38.4536i	−1.02956	−	1.78324i
$466$	−0.146053	−	0.252971i	−0.00676577	−	0.0117187i
$467$	−7.47990			−0.346129			−0.173064	−	0.984911i	$-0.555367\pi$
$467$	−7.47990			−0.346129			−0.173064	+	0.984911i	$0.555367\pi$
$468$	7.30056	+	2.21246i	0.337468	+	0.102271i
$469$	13.6126			0.628570
$470$	2.08369	+	3.60906i	0.0961136	+	0.166474i
$471$	−27.1950	−	47.1031i	−1.25308	−	2.17040i
$472$	−9.04546	+	15.6672i	−0.416351	+	0.721141i
$473$	2.52360			0.116035
$474$	1.88822	−	3.27049i	0.0867287	−	0.150219i
$475$	0.823644	−	1.42659i	0.0377914	−	0.0654566i
$476$	7.24840			0.332230
$477$	−8.20393	+	14.2096i	−0.375632	+	0.650614i
$478$	10.9012	+	18.8814i	0.498607	+	0.863613i
$479$	−4.31122	−	7.46726i	−0.196985	−	0.341188i	0.750565	−	0.660797i	$-0.229782\pi$
$479$	−4.31122	−	7.46726i	−0.196985	−	0.341188i	−0.947549	+	0.319609i	$0.896448\pi$
$480$	−23.9270			−1.09211
$481$	31.6175	+	9.58180i	1.44163	+	0.436893i
$482$	−2.54844			−0.116078
$483$	17.2787	+	29.9276i	0.786208	+	1.36175i
$484$	0.500000	+	0.866025i	0.0227273	+	0.0393648i
$485$	−12.3130	+	21.3267i	−0.559104	+	0.968396i
$486$	18.5877			0.843156
$487$	−4.04546	+	7.00693i	−0.183317	+	0.317514i	−0.943008	−	0.332770i	$-0.892017\pi$
$487$	−4.04546	+	7.00693i	−0.183317	+	0.317514i	0.759691	+	0.650284i	$0.225350\pi$
$488$	14.6781	−	25.4232i	0.664447	−	1.15086i
$489$	14.8236			0.670348
$490$	−4.66296	+	8.07648i	−0.210651	+	0.364858i
$491$	−2.31122	−	4.00316i	−0.104304	−	0.180660i	0.809150	−	0.587603i	$-0.199928\pi$
$491$	−2.31122	−	4.00316i	−0.104304	−	0.180660i	−0.913454	+	0.406943i	$0.866595\pi$
$492$	−11.3281	−	19.6209i	−0.510712	−	0.884578i
$493$	−7.49681			−0.337639
$494$	8.27695	−	7.75638i	0.372398	−	0.348976i
$495$	4.47640			0.201199
$496$	−4.63935	−	8.03560i	−0.208313	−	0.360809i
$497$	−10.1327	−	17.5503i	−0.454512	−	0.787237i
$498$	6.41182	−	11.1056i	0.287321	−	0.497654i
$499$	39.5137			1.76888			0.884438	−	0.466657i	$-0.154542\pi$
$499$	39.5137			1.76888			0.884438	+	0.466657i	$0.154542\pi$
$500$	−5.84328	+	10.1209i	−0.261319	+	0.452619i
$501$	−20.7248	+	35.8964i	−0.925916	+	1.60373i
$502$	−26.8192			−1.19700
$503$	18.8517	−	32.6522i	0.840557	−	1.45589i	−0.0488670	−	0.998805i	$-0.515561\pi$
$503$	18.8517	−	32.6522i	0.840557	−	1.45589i	0.889424	−	0.457083i	$-0.151106\pi$
$504$	10.7191	+	18.5660i	0.477466	+	0.826995i
$505$	−0.953310	−	1.65118i	−0.0424218	−	0.0734766i
$506$	4.52360			0.201099
$507$	26.3642	−	13.0189i	1.17087	−	0.578192i
$508$	−11.5102			−0.510683
$509$	3.86065	+	6.68684i	0.171120	+	0.296389i	0.938812	−	0.344431i	$-0.111928\pi$
$509$	3.86065	+	6.68684i	0.171120	+	0.296389i	−0.767692	+	0.640819i	$0.778595\pi$
$510$	−5.13487	−	8.89385i	−0.227376	−	0.393826i
$511$	−18.3073	+	31.7091i	−0.809865	+	1.40273i
$512$	−11.0000			−0.486136
$513$	−3.14605	+	5.44912i	−0.138902	+	0.240585i
$514$	−1.53427	+	2.65743i	−0.0676738	+	0.117214i
$515$	27.6046			1.21641
$516$	−2.85395	+	4.94318i	−0.125638	+	0.217611i
$517$	0.984848	+	1.70581i	0.0433136	+	0.0750213i
$518$	15.4742	+	26.8021i	0.679897	+	1.17762i
$519$	−33.2181			−1.45811
$520$	−16.6990	+	15.6487i	−0.732299	+	0.686242i
$521$	5.48979			0.240512			0.120256	−	0.992743i	$-0.461628\pi$
$521$	5.48979			0.240512			0.120256	+	0.992743i	$0.461628\pi$
$522$	−3.69547	−	6.40075i	−0.161747	−	0.280153i
$523$	−20.6068	−	35.6921i	−0.901074	−	1.56071i	−0.826102	−	0.563520i	$-0.809447\pi$
$523$	−20.6068	−	35.6921i	−0.901074	−	1.56071i	−0.0749720	−	0.997186i	$-0.523887\pi$
$524$	6.80453	−	11.7858i	0.297257	−	0.514864i
$525$	4.00000			0.174574
$526$	−1.14605	+	1.98502i	−0.0499703	+	0.0865511i
$527$	−9.95630	+	17.2448i	−0.433703	+	0.751196i
$528$	2.26180			0.0984323
$529$	1.26850	−	2.19711i	0.0551522	−	0.0955265i
$530$	−8.20393	−	14.2096i	−0.356356	−	0.617226i
$531$	6.37931	+	11.0493i	0.276838	+	0.479498i
$532$	−10.6260			−0.460694
$533$	−34.5641	−	10.4748i	−1.49714	−	0.453713i
$534$	−21.1416			−0.914888
$535$	14.3967	+	24.9358i	0.622422	+	1.07807i
$536$	6.04546	+	10.4710i	0.261124	+	0.452280i
$537$	−7.34328	+	12.7189i	−0.316886	+	0.548863i
$538$	11.2449			0.484802
$539$	−2.20393	+	3.81731i	−0.0949299	+	0.164423i
$540$	2.11575	−	3.66459i	0.0910474	−	0.157699i
$541$	31.2539			1.34371			0.671854	−	0.740683i	$-0.265498\pi$
$541$	31.2539			1.34371			0.671854	+	0.740683i	$0.265498\pi$
$542$	2.14605	−	3.71707i	0.0921809	−	0.159662i
$543$	−19.4096	−	33.6184i	−0.832946	−	1.44270i
$544$	5.36513	+	9.29268i	0.230028	+	0.398420i
$545$	39.5361			1.69354
$546$	26.3602	+	7.98855i	1.12811	+	0.341879i
$547$	2.40239			0.102719			0.0513594	−	0.998680i	$-0.483645\pi$
$547$	2.40239			0.102719			0.0513594	+	0.998680i	$0.483645\pi$
$548$	−7.55118	−	13.0790i	−0.322570	−	0.558708i
$549$	−10.3517	−	17.9297i	−0.441801	−	0.765222i
$550$	0.261802	−	0.453455i	0.0111633	−	0.0193354i
$551$	10.9901			0.468194
$552$	−15.3472	+	26.5822i	−0.653222	+	1.13141i
$553$	−2.81968	+	4.88382i	−0.119905	+	0.207681i
$554$	−4.83262			−0.205318
$555$	−21.9242	+	37.9739i	−0.930632	+	1.61190i
$556$	−7.63935	−	13.2317i	−0.323981	−	0.561151i
$557$	−1.22305	−	2.11838i	−0.0518221	−	0.0897586i	0.838951	−	0.544207i	$-0.183170\pi$
$557$	−1.22305	−	2.11838i	−0.0518221	−	0.0897586i	−0.890773	+	0.454449i	$0.849836\pi$
$558$	−19.6314			−0.831064
$559$	2.06854	+	8.86074i	0.0874899	+	0.374769i
$560$	−7.14605			−0.301976
$561$	−2.42697	−	4.20364i	−0.102467	−	0.177478i
$562$	−1.89270	−	3.27826i	−0.0798389	−	0.138285i
$563$	−19.2293	+	33.3061i	−0.810418	+	1.40368i	0.102154	+	0.994769i	$0.467426\pi$
$563$	−19.2293	+	33.3061i	−0.810418	+	1.40368i	−0.912572	+	0.408916i	$0.865907\pi$
$564$	−4.45506			−0.187592
$565$	−13.3709	+	23.1590i	−0.562516	+	0.974306i
$566$	6.21238	−	10.7602i	0.261126	−	0.452283i
$567$	−36.7169			−1.54196
$568$	9.00000	−	15.5885i	0.377632	−	0.654077i
$569$	−19.6260	−	33.9932i	−0.822763	−	1.42507i	−0.903617	−	0.428341i	$-0.859098\pi$
$569$	−19.6260	−	33.9932i	−0.822763	−	1.42507i	0.0808542	−	0.996726i	$-0.474235\pi$
$570$	7.52757	+	13.0381i	0.315295	+	0.546107i
$571$	−39.3349			−1.64611			−0.823057	−	0.567959i	$-0.807733\pi$
$571$	−39.3349			−1.64611			−0.823057	+	0.567959i	$0.807733\pi$
$572$	−2.63090	+	2.46543i	−0.110004	+	0.103085i
$573$	−40.6439			−1.69792
$574$	−16.9163	−	29.2999i	−0.706073	−	1.22295i
$575$	1.18429	+	2.05125i	0.0493883	+	0.0855430i
$576$	−7.40512	+	12.8260i	−0.308547	+	0.534419i
$577$	−24.0890			−1.00284			−0.501418	−	0.865205i	$-0.667188\pi$
$577$	−24.0890			−1.00284			−0.501418	+	0.865205i	$0.667188\pi$
$578$	6.19723	−	10.7339i	0.257771	−	0.446472i
$579$	−3.35843	+	5.81698i	−0.139572	+	0.241745i
$580$	−7.39095			−0.306892
$581$	−9.57478	+	16.5840i	−0.397229	+	0.688020i
$582$	13.1630	+	22.7989i	0.545622	+	0.945045i
$583$	−3.87755	−	6.71612i	−0.160592	−	0.278153i
$584$	−32.5216			−1.34576
$585$	3.66920	+	15.7173i	0.151703	+	0.649829i
$586$	16.9012			0.698180
$587$	−12.2333	−	21.1886i	−0.504920	−	0.874548i	−0.999984	−	0.00569090i	$-0.998189\pi$
$587$	−12.2333	−	21.1886i	−0.504920	−	0.874548i	0.495063	−	0.868857i	$-0.335145\pi$
$588$	−4.98485	−	8.63401i	−0.205572	−	0.356061i
$589$	14.5957	−	25.2804i	0.601403	−	1.04166i
$590$	−12.7586			−0.525264
$591$	13.8326	−	23.9588i	0.568998	−	0.985533i
$592$	−4.58148	+	7.93535i	−0.188298	+	0.326141i
$593$	33.6215			1.38067			0.690335	−	0.723490i	$-0.257463\pi$
$593$	33.6215			1.38067			0.690335	+	0.723490i	$0.257463\pi$
$594$	−1.00000	+	1.73205i	−0.0410305	+	0.0710669i
$595$	7.66790	+	13.2812i	0.314353	+	0.544476i
$596$	2.18878	+	3.79107i	0.0896558	+	0.155288i
$597$	0.455064			0.0186245
$598$	3.70789	+	15.8830i	0.151627	+	0.649505i
$599$	3.01340			0.123124			0.0615621	−	0.998103i	$-0.480392\pi$
$599$	3.01340			0.123124			0.0615621	+	0.998103i	$0.480392\pi$
$600$	1.77643	+	3.07688i	0.0725226	+	0.125613i
$601$	9.28716	+	16.0858i	0.378831	+	0.656155i	0.990892	−	0.134655i	$-0.0429928\pi$
$601$	9.28716	+	16.0858i	0.378831	+	0.656155i	−0.612061	+	0.790810i	$0.709659\pi$
$602$	−4.26180	+	7.38166i	−0.173698	+	0.300854i
$603$	8.52711			0.347251
$604$	1.14605	−	1.98502i	0.0466322	−	0.0807694i
$605$	−1.05787	+	1.83229i	−0.0430087	+	0.0744933i
$606$	−2.03824			−0.0827977
$607$	9.60684	−	16.6395i	0.389930	−	0.675378i	−0.602510	−	0.798111i	$-0.705833\pi$
$607$	9.60684	−	16.6395i	0.389930	−	0.675378i	0.992440	+	0.122733i	$0.0391660\pi$
$608$	−7.86513	−	13.6228i	−0.318973	−	0.552478i
$609$	13.3433	+	23.1112i	0.540697	+	0.936515i
$610$	20.7035			0.838259
$611$	−5.18208	+	4.85615i	−0.209644	+	0.196459i
$612$	4.54051			0.183539
$613$	−9.46748	−	16.3982i	−0.382388	−	0.662316i	0.609015	−	0.793159i	$-0.291565\pi$
$613$	−9.46748	−	16.3982i	−0.382388	−	0.662316i	−0.991403	+	0.130843i	$0.958232\pi$
$614$	4.21238	+	7.29606i	0.169998	+	0.294445i
$615$	23.9675	−	41.5129i	0.966462	−	1.67396i
$616$	−10.1327			−0.408256
$617$	0.860646	−	1.49068i	0.0346483	−	0.0600126i	−0.848181	−	0.529706i	$-0.822302\pi$
$617$	0.860646	−	1.49068i	0.0346483	−	0.0600126i	0.882830	+	0.469693i	$0.155636\pi$
$618$	14.7551	−	25.5566i	0.593537	−	1.02804i
$619$	16.3562			0.657412			0.328706	−	0.944432i	$-0.393387\pi$
$619$	16.3562			0.657412			0.328706	+	0.944432i	$0.393387\pi$
$620$	−9.81571	+	17.0013i	−0.394208	+	0.682789i
$621$	−4.52360	−	7.83511i	−0.181526	−	0.314412i
$622$	14.2939	+	24.7577i	0.573132	+	0.992693i
$623$	31.5708			1.26486
$624$	1.85395	+	7.94151i	0.0742173	+	0.317915i
$625$	−22.1078			−0.884313
$626$	−11.1972	−	19.3942i	−0.447531	−	0.775147i
$627$	3.55787	+	6.16242i	0.142088	+	0.246103i
$628$	−12.0236	+	20.8255i	−0.479794	+	0.831028i
$629$	19.6642			0.784063
$630$	−7.55963	+	13.0937i	−0.301183	+	0.521664i
$631$	10.5388	−	18.2537i	0.419541	−	0.726667i	−0.576352	−	0.817202i	$-0.695524\pi$
$631$	10.5388	−	18.2537i	0.419541	−	0.726667i	0.995893	+	0.0905347i	$0.0288576\pi$
$632$	−5.00897			−0.199246
$633$	13.1972	−	22.8583i	0.524543	−	0.908535i
$634$	13.1354	+	22.7512i	0.521673	+	0.903564i
$635$	−12.1764	−	21.0901i	−0.483204	−	0.836934i
$636$	17.5405			0.695526
$637$	−15.2096	−	4.60934i	−0.602628	−	0.182629i
$638$	3.49330			0.138301
$639$	−6.34725	−	10.9938i	−0.251093	−	0.434906i
$640$	3.17362	+	5.49688i	0.125449	+	0.217283i
$641$	2.26850	−	3.92916i	0.0896004	−	0.155192i	−0.817742	−	0.575585i	$-0.804774\pi$
$641$	2.26850	−	3.92916i	0.0896004	−	0.155192i	0.907342	+	0.420393i	$0.138108\pi$
$642$	30.7810			1.21483
$643$	0.491547	−	0.851385i	0.0193847	−	0.0335753i	−0.856170	−	0.516694i	$-0.827163\pi$
$643$	0.491547	−	0.851385i	0.0193847	−	0.0335753i	0.875555	+	0.483118i	$0.160496\pi$
$644$	7.63935	−	13.2317i	0.301033	−	0.521404i
$645$	−12.0765			−0.475511
$646$	3.37580	−	5.84705i	0.132819	−	0.230049i
$647$	23.3428	+	40.4310i	0.917701	+	1.58950i	0.802898	+	0.596117i	$0.203290\pi$
$647$	23.3428	+	40.4310i	0.917701	+	1.58950i	0.114803	+	0.993388i	$0.463376\pi$
$648$	−16.3063	−	28.2433i	−0.640571	−	1.10950i
$649$	−6.03030			−0.236710
$650$	1.80674	+	0.547539i	0.0708661	+	0.0214762i
$651$	70.8833			2.77814
$652$	−3.27695	−	5.67585i	−0.128335	−	0.222283i
$653$	12.9354	+	22.4048i	0.506202	+	0.876768i	0.999974	+	0.00717672i	$0.00228444\pi$
$653$	12.9354	+	22.4048i	0.506202	+	0.876768i	−0.493772	+	0.869591i	$0.664382\pi$
$654$	21.1327	−	36.6028i	0.826352	−	1.43128i
$655$	28.7933			1.12505
$656$	5.00845	−	8.67489i	0.195547	−	0.338698i
$657$	−11.4679	+	19.8631i	−0.447407	+	0.774932i
$658$	−6.65275			−0.259351
$659$	−8.74938	+	15.1544i	−0.340828	+	0.590331i	−0.984587	−	0.174898i	$-0.944041\pi$
$659$	−8.74938	+	15.1544i	−0.340828	+	0.590331i	0.643759	+	0.765228i	$0.277374\pi$
$660$	−2.39270	−	4.14428i	−0.0931359	−	0.161316i
$661$	−10.8264	−	18.7518i	−0.421097	−	0.729362i	0.574950	−	0.818189i	$-0.305022\pi$
$661$	−10.8264	−	18.7518i	−0.421097	−	0.729362i	−0.996047	+	0.0888269i	$0.971688\pi$
$662$	−8.29211			−0.322282
$663$	12.7703	−	11.9671i	0.495956	−	0.464763i
$664$	−17.0090			−0.660076
$665$	−11.2409	−	19.4699i	−0.435905	−	0.755009i
$666$	9.69326	+	16.7892i	0.375606	+	0.650569i
$667$	−7.90116	+	13.6852i	−0.305934	+	0.529893i
$668$	18.3259			0.709051
$669$	−8.48933	+	14.7040i	−0.328217	+	0.568488i
$670$	−4.26356	+	7.38470i	−0.164716	+	0.285296i
$671$	9.78541			0.377761
$672$	19.0984	−	33.0794i	0.736736	−	1.27606i
$673$	11.9399	+	20.6805i	0.460250	+	0.797176i	0.998973	−	0.0453067i	$-0.0144265\pi$
$673$	11.9399	+	20.6805i	0.460250	+	0.797176i	−0.538723	+	0.842483i	$0.681093\pi$
$674$	0.0258174	+	0.0447171i	0.000994451	+	0.00172244i
$675$	−1.04721			−0.0403071
$676$	−10.8130	−	7.21661i	−0.415884	−	0.277562i
$677$	−12.6945			−0.487889			−0.243945	−	0.969789i	$-0.578441\pi$
$677$	−12.6945			−0.487889			−0.243945	+	0.969789i	$0.578441\pi$
$678$	14.2939	+	24.7577i	0.548952	+	0.950813i
$679$	−19.6563	−	34.0456i	−0.754338	−	1.30655i
$680$	−6.81077	+	11.7966i	−0.261181	+	0.452379i
$681$	7.86292			0.301308
$682$	4.63935	−	8.03560i	0.177650	−	0.307699i
$683$	18.9350	−	32.7963i	0.724526	−	1.25492i	−0.234642	−	0.972082i	$-0.575392\pi$
$683$	18.9350	−	32.7963i	0.724526	−	1.25492i	0.959169	−	0.282835i	$-0.0912748\pi$
$684$	−6.65626			−0.254508
$685$	15.9764	−	27.6719i	0.610427	−	1.05729i
$686$	4.37755	+	7.58214i	0.167136	+	0.289488i
$687$	15.1630	+	26.2630i	0.578503	+	1.00200i
$688$	−2.52360			−0.0962115
$689$	20.4029	−	19.1197i	0.777289	−	0.728402i
$690$	−21.6473			−0.824098
$691$	−12.8709	−	22.2930i	−0.489630	−	0.848065i	0.510298	−	0.859997i	$-0.329535\pi$
$691$	−12.8709	−	22.2930i	−0.489630	−	0.848065i	−0.999929	+	0.0119328i	$0.996202\pi$
$692$	7.34328	+	12.7189i	0.279150	+	0.483501i
$693$	−3.57303	+	6.18866i	−0.135728	+	0.235088i
$694$	−8.62245			−0.327304
$695$	16.1630	−	27.9951i	0.613096	−	1.06191i
$696$	−11.8517	+	20.5278i	−0.449239	+	0.778104i
$697$	−21.4968			−0.814250
$698$	−15.0000	+	25.9808i	−0.567758	+	0.983386i
$699$	0.330343	+	0.572170i	0.0124947	+	0.0216415i
$700$	−0.884251	−	1.53157i	−0.0334215	−	0.0578878i
$701$	−33.5023			−1.26536			−0.632682	−	0.774412i	$-0.718046\pi$
$701$	−33.5023			−1.26536			−0.632682	+	0.774412i	$0.718046\pi$
$702$	−6.90116	−	2.09142i	−0.260467	−	0.0789356i
$703$	−28.8272			−1.08724
$704$	−3.50000	−	6.06218i	−0.131911	−	0.228477i
$705$	−4.71290	−	8.16298i	−0.177498	−	0.307436i
$706$	0.238198	−	0.412571i	0.00896469	−	0.0155273i
$707$	3.04370			0.114470
$708$	6.81968	−	11.8120i	0.256299	−	0.443923i
$709$	15.4618	−	26.7806i	0.580679	−	1.00577i	−0.414720	−	0.909949i	$-0.636121\pi$
$709$	15.4618	−	26.7806i	0.580679	−	1.00577i	0.995399	−	0.0958161i	$-0.0305461\pi$
$710$	12.6945			0.476416
$711$	−1.76629	+	3.05930i	−0.0662410	+	0.114733i
$712$	14.0209	+	24.2849i	0.525454	+	0.910114i
$713$	20.9866	+	36.3499i	0.785954	+	1.36131i
$714$	16.3945			0.613547
$715$	−7.30056	−	2.21246i	−0.273025	−	0.0827414i
$716$	6.49330			0.242666
$717$	−24.6563	−	42.7059i	−0.920805	−	1.59488i
$718$	5.11575	+	8.86074i	0.190918	+	0.330680i
$719$	−4.60905	+	7.98311i	−0.171889	+	0.297720i	−0.939080	−	0.343698i	$-0.888320\pi$
$719$	−4.60905	+	7.98311i	−0.171889	+	0.297720i	0.767192	+	0.641418i	$0.221654\pi$
$720$	−4.47640			−0.166825
$721$	−22.0338	+	38.1637i	−0.820582	+	1.42129i
$722$	4.55118	−	7.88287i	0.169377	−	0.293370i
$723$	5.76408			0.214368
$724$	−8.58148	+	14.8636i	−0.318928	+	0.552400i
$725$	0.914554	+	1.58405i	0.0339657	+	0.0588303i
$726$	1.13090	+	1.95878i	0.0419717	+	0.0726971i
$727$	33.5102			1.24282			0.621412	−	0.783484i	$-0.286559\pi$
$727$	33.5102			1.24282			0.621412	+	0.783484i	$0.286559\pi$
$728$	−8.30550	−	35.5772i	−0.307822	−	1.31858i
$729$	−9.42919			−0.349229
$730$	−11.4679	−	19.8631i	−0.424448	−	0.735165i
$731$	2.70789	+	4.69021i	0.100155	+	0.173474i
$732$	−11.0663	+	19.1674i	−0.409023	+	0.708449i
$733$	−1.29561			−0.0478546			−0.0239273	−	0.999714i	$-0.507617\pi$
$733$	−1.29561			−0.0478546			−0.0239273	+	0.999714i	$0.507617\pi$
$734$	−10.6697	+	18.4804i	−0.393824	+	0.682124i
$735$	10.5467	−	18.2674i	0.389021	−	0.673803i
$736$	22.6180			0.833711
$737$	−2.01515	+	3.49035i	−0.0742291	+	0.128569i
$738$	−10.5966	−	18.3539i	−0.390067	−	0.675617i
$739$	−14.4248	−	24.9844i	−0.530623	−	0.919067i	−0.999361	−	0.0357295i	$-0.988625\pi$
$739$	−14.4248	−	24.9844i	−0.530623	−	0.919067i	0.468738	−	0.883337i	$-0.344709\pi$
$740$	19.3865			0.712663
$741$	−18.7208	+	17.5434i	−0.687727	+	0.644473i
$742$	26.1933			0.961585
$743$	15.8686	+	27.4853i	0.582164	+	1.00834i	0.995222	+	0.0976330i	$0.0311271\pi$
$743$	15.8686	+	27.4853i	0.582164	+	1.00834i	−0.413059	+	0.910704i	$0.635540\pi$
$744$	31.4799	+	54.5248i	1.15411	+	1.99898i
$745$	−4.63090	+	8.02096i	−0.169663	+	0.293865i
$746$	21.2271			0.777178
$747$	−5.99779	+	10.3885i	−0.219448	+	0.380094i
$748$	−1.07303	+	1.85854i	−0.0392337	+	0.0679548i
$749$	−45.9653			−1.67953
$750$	−13.2163	+	22.8914i	−0.482593	+	0.835875i
$751$	18.0641	+	31.2880i	0.659169	+	1.14171i	0.980831	+	0.194860i	$0.0624251\pi$
$751$	18.0641	+	31.2880i	0.659169	+	1.14171i	−0.321662	+	0.946854i	$0.604242\pi$
$752$	−0.984848	−	1.70581i	−0.0359137	−	0.0622044i
$753$	60.6598			2.21056
$754$	2.86338	+	12.2655i	0.104278	+	0.446682i
$755$	4.84952			0.176492
$756$	3.37755	+	5.85009i	0.122840	+	0.212766i
$757$	11.0263	+	19.0982i	0.400759	+	0.694135i	0.993818	−	0.111024i	$-0.0354131\pi$
$757$	11.0263	+	19.0982i	0.400759	+	0.694135i	−0.593059	+	0.805159i	$0.702080\pi$
$758$	0.523604	−	0.906910i	0.0190182	−	0.0329404i
$759$	−10.2315			−0.371380
$760$	9.98439	−	17.2935i	0.362172	−	0.627300i
$761$	−20.0810	+	34.7813i	−0.727936	+	1.26082i	0.229817	+	0.973234i	$0.426187\pi$
$761$	−20.0810	+	34.7813i	−0.727936	+	1.26082i	−0.957754	+	0.287589i	$0.907146\pi$
$762$	−26.0338			−0.943105
$763$	−31.5574	+	54.6590i	−1.14246	+	1.97879i
$764$	8.98485	+	15.5622i	0.325060	+	0.563021i
$765$	4.80329	+	8.31954i	0.173663	+	0.300794i
$766$	−28.9866			−1.04733
$767$	−4.94290	−	21.1733i	−0.178478	−	0.764522i
$768$	38.4506			1.38747
$769$	12.4799	+	21.6158i	0.450037	+	0.779487i	0.998388	−	0.0567617i	$-0.0180775\pi$
$769$	12.4799	+	21.6158i	0.450037	+	0.779487i	−0.548351	+	0.836248i	$0.684744\pi$
$770$	−3.57303	−	6.18866i	−0.128763	−	0.223024i

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:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	143.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.13090 + 1.95878i) q^{3} +(0.500000 - 0.866025i) q^{4} +2.11575 q^{5} +(1.13090 - 1.95878i) q^{6} +(-1.68878 + 2.92505i) q^{7} -3.00000 q^{8} +(-1.05787 + 1.83229i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.13090 + 1.95878i) q^{3} +(0.500000 - 0.866025i) q^{4} +2.11575 q^{5} +(1.13090 - 1.95878i) q^{6} +(-1.68878 + 2.92505i) q^{7} -3.00000 q^{8} +(-1.05787 + 1.83229i) q^{9} +(-1.05787 - 1.83229i) q^{10} +(-0.500000 - 0.866025i) q^{11} +2.26180 q^{12} +(2.63090 - 2.46543i) q^{13} +3.37755 q^{14} +(2.39270 + 4.14428i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.07303 - 1.85854i) q^{17} +2.11575 q^{18} +(-1.57303 + 2.72456i) q^{19} +(1.05787 - 1.83229i) q^{20} -7.63935 q^{21} +(-0.500000 + 0.866025i) q^{22} +(-2.26180 - 3.91756i) q^{23} +(-3.39270 - 5.87633i) q^{24} -0.523604 q^{25} +(-3.45058 - 1.04571i) q^{26} +2.00000 q^{27} +(1.68878 + 2.92505i) q^{28} +(-1.74665 - 3.02529i) q^{29} +(2.39270 - 4.14428i) q^{30} -9.27871 q^{31} +(-2.50000 + 4.33013i) q^{32} +(1.13090 - 1.95878i) q^{33} -2.14605 q^{34} +(-3.57303 + 6.18866i) q^{35} +(1.05787 + 1.83229i) q^{36} +(4.58148 + 7.93535i) q^{37} +3.14605 q^{38} +(7.80453 + 2.36519i) q^{39} -6.34725 q^{40} +(-5.00845 - 8.67489i) q^{41} +(3.81968 + 6.61587i) q^{42} +(-1.26180 + 2.18551i) q^{43} -1.00000 q^{44} +(-2.23820 + 3.87667i) q^{45} +(-2.26180 + 3.91756i) q^{46} -1.96970 q^{47} +(-1.13090 + 1.95878i) q^{48} +(-2.20393 - 3.81731i) q^{49} +(0.261802 + 0.453455i) q^{50} +4.85395 q^{51} +(-0.819677 - 3.51114i) q^{52} +7.75510 q^{53} +(-1.00000 - 1.73205i) q^{54} +(-1.05787 - 1.83229i) q^{55} +(5.06633 - 8.77514i) q^{56} -7.11575 q^{57} +(-1.74665 + 3.02529i) q^{58} +(3.01515 - 5.22240i) q^{59} +4.78541 q^{60} +(-4.89270 + 8.47441i) q^{61} +(4.63935 + 8.03560i) q^{62} +(-3.57303 - 6.18866i) q^{63} +7.00000 q^{64} +(5.56633 - 5.21624i) q^{65} -2.26180 q^{66} +(-2.01515 - 3.49035i) q^{67} +(-1.07303 - 1.85854i) q^{68} +(5.11575 - 8.86074i) q^{69} +7.14605 q^{70} +(-3.00000 + 5.19615i) q^{71} +(3.17362 - 5.49688i) q^{72} +10.8405 q^{73} +(4.58148 - 7.93535i) q^{74} +(-0.592145 - 1.02563i) q^{75} +(1.57303 + 2.72456i) q^{76} +3.37755 q^{77} +(-1.85395 - 7.94151i) q^{78} +1.66966 q^{79} +(1.05787 + 1.83229i) q^{80} +(5.43543 + 9.41443i) q^{81} +(-5.00845 + 8.67489i) q^{82} +5.66966 q^{83} +(-3.81968 + 6.61587i) q^{84} +(2.27026 - 3.93220i) q^{85} +2.52360 q^{86} +(3.95058 - 6.84260i) q^{87} +(1.50000 + 2.59808i) q^{88} +(-4.67362 - 8.09495i) q^{89} +4.47640 q^{90} +(2.76850 + 11.8591i) q^{91} -4.52360 q^{92} +(-10.4933 - 18.1749i) q^{93} +(0.984848 + 1.70581i) q^{94} +(-3.32813 + 5.76449i) q^{95} -11.3090 q^{96} +(-5.81968 + 10.0800i) q^{97} +(-2.20393 + 3.81731i) q^{98} +2.11575 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + 3 q^{4} + 6 q^{5} - 18 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 + 3 * q^4 + 6 * q^5 - 18 * q^8 - 3 * q^9	\( 6 q - 3 q^{2} + 3 q^{4} + 6 q^{5} - 18 q^{8} - 3 q^{9} - 3 q^{10} - 3 q^{11} + 9 q^{13} - 6 q^{15} + 3 q^{16} + 3 q^{17} + 6 q^{18} - 6 q^{19} + 3 q^{20} - 12 q^{21} - 3 q^{22} + 24 q^{25} + 3 q^{26} + 12 q^{27} + 3 q^{29} - 6 q^{30} + 12 q^{31} - 15 q^{32} - 6 q^{34} - 18 q^{35} + 3 q^{36} - 3 q^{37} + 12 q^{38} + 30 q^{39} - 18 q^{40} - 3 q^{41} + 6 q^{42} + 6 q^{43} - 6 q^{44} - 27 q^{45} - 12 q^{47} - 3 q^{49} - 12 q^{50} + 36 q^{51} + 12 q^{52} + 6 q^{53} - 6 q^{54} - 3 q^{55} - 36 q^{57} + 3 q^{58} + 18 q^{59} - 12 q^{60} - 9 q^{61} - 6 q^{62} - 18 q^{63} + 42 q^{64} + 3 q^{65} - 12 q^{67} - 3 q^{68} + 24 q^{69} + 36 q^{70} - 18 q^{71} + 9 q^{72} + 18 q^{73} - 3 q^{74} - 24 q^{75} + 6 q^{76} - 18 q^{78} - 24 q^{79} + 3 q^{80} + 9 q^{81} - 3 q^{82} - 6 q^{84} - 27 q^{85} - 12 q^{86} + 9 q^{88} - 18 q^{89} + 54 q^{90} + 30 q^{91} - 36 q^{93} + 6 q^{94} + 24 q^{95} - 18 q^{97} - 3 q^{98} + 6 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + 3 * q^4 + 6 * q^5 - 18 * q^8 - 3 * q^9 - 3 * q^10 - 3 * q^11 + 9 * q^13 - 6 * q^15 + 3 * q^16 + 3 * q^17 + 6 * q^18 - 6 * q^19 + 3 * q^20 - 12 * q^21 - 3 * q^22 + 24 * q^25 + 3 * q^26 + 12 * q^27 + 3 * q^29 - 6 * q^30 + 12 * q^31 - 15 * q^32 - 6 * q^34 - 18 * q^35 + 3 * q^36 - 3 * q^37 + 12 * q^38 + 30 * q^39 - 18 * q^40 - 3 * q^41 + 6 * q^42 + 6 * q^43 - 6 * q^44 - 27 * q^45 - 12 * q^47 - 3 * q^49 - 12 * q^50 + 36 * q^51 + 12 * q^52 + 6 * q^53 - 6 * q^54 - 3 * q^55 - 36 * q^57 + 3 * q^58 + 18 * q^59 - 12 * q^60 - 9 * q^61 - 6 * q^62 - 18 * q^63 + 42 * q^64 + 3 * q^65 - 12 * q^67 - 3 * q^68 + 24 * q^69 + 36 * q^70 - 18 * q^71 + 9 * q^72 + 18 * q^73 - 3 * q^74 - 24 * q^75 + 6 * q^76 - 18 * q^78 - 24 * q^79 + 3 * q^80 + 9 * q^81 - 3 * q^82 - 6 * q^84 - 27 * q^85 - 12 * q^86 + 9 * q^88 - 18 * q^89 + 54 * q^90 + 30 * q^91 - 36 * q^93 + 6 * q^94 + 24 * q^95 - 18 * q^97 - 3 * q^98 + 6 * q^99

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