LMFDB - Embedded newform 280.2.bj.b.131.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(131,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

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

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

chi := DirichletCharacter("280.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.bj (of order $6$, 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:	$2.23581125660$
Analytic rank:	$1$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.2
Root			$1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	280.131
Dual form			280.2.bj.b.171.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} +(-2.72474 + 1.57313i) q^{3} -2.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.22474 - 3.85337i) q^{6} +(-2.50000 - 0.866025i) q^{7} -2.82843i q^{8} +(3.44949 - 5.97469i) q^{9} +O(q^{10})$	\(q+1.41421i q^{2} +(-2.72474 + 1.57313i) q^{3} -2.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.22474 - 3.85337i) q^{6} +(-2.50000 - 0.866025i) q^{7} -2.82843i q^{8} +(3.44949 - 5.97469i) q^{9} +(-1.22474 - 0.707107i) q^{10} +(2.44949 + 4.24264i) q^{11} +(5.44949 - 3.14626i) q^{12} +0.449490 q^{13} +(1.22474 - 3.53553i) q^{14} -3.14626i q^{15} +4.00000 q^{16} +(-1.77526 + 1.02494i) q^{17} +(8.44949 + 4.87832i) q^{18} +(-3.67423 - 2.12132i) q^{19} +(1.00000 - 1.73205i) q^{20} +(8.17423 - 1.57313i) q^{21} +(-6.00000 + 3.46410i) q^{22} +(-0.949490 - 0.548188i) q^{23} +(4.44949 + 7.70674i) q^{24} +(-0.500000 - 0.866025i) q^{25} +0.635674i q^{26} +12.2672i q^{27} +(5.00000 + 1.73205i) q^{28} -10.0745i q^{29} +4.44949 q^{30} +(-3.22474 - 5.58542i) q^{31} +5.65685i q^{32} +(-13.3485 - 7.70674i) q^{33} +(-1.44949 - 2.51059i) q^{34} +(2.00000 - 1.73205i) q^{35} +(-6.89898 + 11.9494i) q^{36} +(-3.00000 - 1.73205i) q^{37} +(3.00000 - 5.19615i) q^{38} +(-1.22474 + 0.707107i) q^{39} +(2.44949 + 1.41421i) q^{40} +2.36773i q^{41} +(2.22474 + 11.5601i) q^{42} -4.55051 q^{43} +(-4.89898 - 8.48528i) q^{44} +(3.44949 + 5.97469i) q^{45} +(0.775255 - 1.34278i) q^{46} +(3.00000 - 5.19615i) q^{47} +(-10.8990 + 6.29253i) q^{48} +(5.50000 + 4.33013i) q^{49} +(1.22474 - 0.707107i) q^{50} +(3.22474 - 5.58542i) q^{51} -0.898979 q^{52} +(-4.22474 + 2.43916i) q^{53} -17.3485 q^{54} -4.89898 q^{55} +(-2.44949 + 7.07107i) q^{56} +13.3485 q^{57} +14.2474 q^{58} +(-9.12372 + 5.26758i) q^{59} +6.29253i q^{60} +(-7.17423 + 12.4261i) q^{61} +(7.89898 - 4.56048i) q^{62} +(-13.7980 + 11.9494i) q^{63} -8.00000 q^{64} +(-0.224745 + 0.389270i) q^{65} +(10.8990 - 18.8776i) q^{66} +(1.17423 + 2.03383i) q^{67} +(3.55051 - 2.04989i) q^{68} +3.44949 q^{69} +(2.44949 + 2.82843i) q^{70} -1.41421i q^{71} +(-16.8990 - 9.75663i) q^{72} +(-2.32577 + 1.34278i) q^{73} +(2.44949 - 4.24264i) q^{74} +(2.72474 + 1.57313i) q^{75} +(7.34847 + 4.24264i) q^{76} +(-2.44949 - 12.7279i) q^{77} +(-1.00000 - 1.73205i) q^{78} +(0.674235 + 0.389270i) q^{79} +(-2.00000 + 3.46410i) q^{80} +(-8.94949 - 15.5010i) q^{81} -3.34847 q^{82} -12.2672i q^{83} +(-16.3485 + 3.14626i) q^{84} -2.04989i q^{85} -6.43539i q^{86} +(15.8485 + 27.4504i) q^{87} +(12.0000 - 6.92820i) q^{88} +(-0.398979 - 0.230351i) q^{89} +(-8.44949 + 4.87832i) q^{90} +(-1.12372 - 0.389270i) q^{91} +(1.89898 + 1.09638i) q^{92} +(17.5732 + 10.1459i) q^{93} +(7.34847 + 4.24264i) q^{94} +(3.67423 - 2.12132i) q^{95} +(-8.89898 - 15.4135i) q^{96} +5.02118i q^{97} +(-6.12372 + 7.77817i) q^{98} +33.7980 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{3} - 8 q^{4} - 2 q^{5} - 4 q^{6} - 10 q^{7} + 4 q^{9}+O(q^{10}) $ 4 * q - 6 * q^3 - 8 * q^4 - 2 * q^5 - 4 * q^6 - 10 * q^7 + 4 * q^9	$ 4 q - 6 q^{3} - 8 q^{4} - 2 q^{5} - 4 q^{6} - 10 q^{7} + 4 q^{9} + 12 q^{12} - 8 q^{13} + 16 q^{16} - 12 q^{17} + 24 q^{18} + 4 q^{20} + 18 q^{21} - 24 q^{22} + 6 q^{23} + 8 q^{24} - 2 q^{25} + 20 q^{28} + 8 q^{30} - 8 q^{31} - 24 q^{33} + 4 q^{34} + 8 q^{35} - 8 q^{36} - 12 q^{37} + 12 q^{38} + 4 q^{42} - 28 q^{43} + 4 q^{45} + 8 q^{46} + 12 q^{47} - 24 q^{48} + 22 q^{49} + 8 q^{51} + 16 q^{52} - 12 q^{53} - 40 q^{54} + 24 q^{57} + 8 q^{58} - 12 q^{59} - 14 q^{61} + 12 q^{62} - 16 q^{63} - 32 q^{64} + 4 q^{65} + 24 q^{66} - 10 q^{67} + 24 q^{68} + 4 q^{69} - 48 q^{72} - 24 q^{73} + 6 q^{75} - 4 q^{78} - 12 q^{79} - 8 q^{80} - 26 q^{81} + 16 q^{82} - 36 q^{84} + 34 q^{87} + 48 q^{88} + 18 q^{89} - 24 q^{90} + 20 q^{91} - 12 q^{92} + 36 q^{93} - 16 q^{96} + 96 q^{99}+O(q^{100}) $ 4 * q - 6 * q^3 - 8 * q^4 - 2 * q^5 - 4 * q^6 - 10 * q^7 + 4 * q^9 + 12 * q^12 - 8 * q^13 + 16 * q^16 - 12 * q^17 + 24 * q^18 + 4 * q^20 + 18 * q^21 - 24 * q^22 + 6 * q^23 + 8 * q^24 - 2 * q^25 + 20 * q^28 + 8 * q^30 - 8 * q^31 - 24 * q^33 + 4 * q^34 + 8 * q^35 - 8 * q^36 - 12 * q^37 + 12 * q^38 + 4 * q^42 - 28 * q^43 + 4 * q^45 + 8 * q^46 + 12 * q^47 - 24 * q^48 + 22 * q^49 + 8 * q^51 + 16 * q^52 - 12 * q^53 - 40 * q^54 + 24 * q^57 + 8 * q^58 - 12 * q^59 - 14 * q^61 + 12 * q^62 - 16 * q^63 - 32 * q^64 + 4 * q^65 + 24 * q^66 - 10 * q^67 + 24 * q^68 + 4 * q^69 - 48 * q^72 - 24 * q^73 + 6 * q^75 - 4 * q^78 - 12 * q^79 - 8 * q^80 - 26 * q^81 + 16 * q^82 - 36 * q^84 + 34 * q^87 + 48 * q^88 + 18 * q^89 - 24 * q^90 + 20 * q^91 - 12 * q^92 + 36 * q^93 - 16 * q^96 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$			1.41421i			1.00000i
$2$			1.41421i			1.00000i
$3$	−2.72474	+	1.57313i	−1.57313	+	0.908248i	−0.577350	+	0.816497i	$0.695913\pi$
$3$	−2.72474	+	1.57313i	−1.57313	+	0.908248i	−0.995782	+	0.0917517i	$0.970753\pi$
$4$	−2.00000			−1.00000
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−2.22474	−	3.85337i	−0.908248	−	1.57313i
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$8$		−	2.82843i		−	1.00000i
$9$	3.44949	−	5.97469i	1.14983	−	1.99156i
$10$	−1.22474	−	0.707107i	−0.387298	−	0.223607i
$11$	2.44949	+	4.24264i	0.738549	+	1.27920i	0.953149	+	0.302502i	$0.0978220\pi$
$11$	2.44949	+	4.24264i	0.738549	+	1.27920i	−0.214600	+	0.976702i	$0.568845\pi$
$12$	5.44949	−	3.14626i	1.57313	−	0.908248i
$13$	0.449490			0.124666			0.0623330	−	0.998055i	$-0.480146\pi$
$13$	0.449490			0.124666			0.0623330	+	0.998055i	$0.480146\pi$
$14$	1.22474	−	3.53553i	0.327327	−	0.944911i
$15$		−	3.14626i		−	0.812362i
$16$	4.00000			1.00000
$17$	−1.77526	+	1.02494i	−0.430563	+	0.248585i	−0.699586	−	0.714548i	$-0.746632\pi$
$17$	−1.77526	+	1.02494i	−0.430563	+	0.248585i	0.269024	+	0.963134i	$0.413299\pi$
$18$	8.44949	+	4.87832i	1.99156	+	1.14983i
$19$	−3.67423	−	2.12132i	−0.842927	−	0.486664i	0.0153309	−	0.999882i	$-0.495120\pi$
$19$	−3.67423	−	2.12132i	−0.842927	−	0.486664i	−0.858258	+	0.513218i	$0.828453\pi$
$20$	1.00000	−	1.73205i	0.223607	−	0.387298i
$21$	8.17423	−	1.57313i	1.78376	−	0.343286i
$22$	−6.00000	+	3.46410i	−1.27920	+	0.738549i
$23$	−0.949490	−	0.548188i	−0.197982	−	0.114305i	0.397732	−	0.917502i	$-0.369797\pi$
$23$	−0.949490	−	0.548188i	−0.197982	−	0.114305i	−0.595714	+	0.803197i	$0.703131\pi$
$24$	4.44949	+	7.70674i	0.908248	+	1.57313i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$			0.635674i			0.124666i
$27$			12.2672i			2.36083i
$28$	5.00000	+	1.73205i	0.944911	+	0.327327i
$29$		−	10.0745i		−	1.87078i	−0.353616	−	0.935391i	$-0.615048\pi$
$29$		−	10.0745i		−	1.87078i	0.353616	−	0.935391i	$-0.384952\pi$
$30$	4.44949			0.812362
$31$	−3.22474	−	5.58542i	−0.579181	−	1.00317i	−0.995573	−	0.0939863i	$-0.970039\pi$
$31$	−3.22474	−	5.58542i	−0.579181	−	1.00317i	0.416392	−	0.909185i	$-0.363294\pi$
$32$			5.65685i			1.00000i
$33$	−13.3485	−	7.70674i	−2.32367	−	1.34157i
$34$	−1.44949	−	2.51059i	−0.248585	−	0.430563i
$35$	2.00000	−	1.73205i	0.338062	−	0.292770i
$36$	−6.89898	+	11.9494i	−1.14983	+	1.99156i
$37$	−3.00000	−	1.73205i	−0.493197	−	0.284747i	0.232703	−	0.972548i	$-0.425243\pi$
$37$	−3.00000	−	1.73205i	−0.493197	−	0.284747i	−0.725900	+	0.687800i	$0.758576\pi$
$38$	3.00000	−	5.19615i	0.486664	−	0.842927i
$39$	−1.22474	+	0.707107i	−0.196116	+	0.113228i
$40$	2.44949	+	1.41421i	0.387298	+	0.223607i
$41$			2.36773i			0.369777i	0.982760	+	0.184888i	$0.0591923\pi$
$41$			2.36773i			0.369777i	−0.982760	+	0.184888i	$0.940808\pi$
$42$	2.22474	+	11.5601i	0.343286	+	1.78376i
$43$	−4.55051			−0.693946			−0.346973	−	0.937875i	$-0.612791\pi$
$43$	−4.55051			−0.693946			−0.346973	+	0.937875i	$0.612791\pi$
$44$	−4.89898	−	8.48528i	−0.738549	−	1.27920i
$45$	3.44949	+	5.97469i	0.514220	+	0.890654i
$46$	0.775255	−	1.34278i	0.114305	−	0.197982i
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	−0.559908	−	0.828554i	$-0.689164\pi$
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	0.997503	+	0.0706177i	$0.0224970\pi$
$48$	−10.8990	+	6.29253i	−1.57313	+	0.908248i
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$	1.22474	−	0.707107i	0.173205	−	0.100000i
$51$	3.22474	−	5.58542i	0.451555	−	0.782116i
$52$	−0.898979			−0.124666
$53$	−4.22474	+	2.43916i	−0.580313	+	0.335044i	−0.761258	−	0.648449i	$-0.775418\pi$
$53$	−4.22474	+	2.43916i	−0.580313	+	0.335044i	0.180945	+	0.983493i	$0.442085\pi$
$54$	−17.3485			−2.36083
$55$	−4.89898			−0.660578
$56$	−2.44949	+	7.07107i	−0.327327	+	0.944911i
$57$	13.3485			1.76805
$58$	14.2474			1.87078
$59$	−9.12372	+	5.26758i	−1.18781	+	0.685781i	−0.957808	−	0.287410i	$-0.907206\pi$
$59$	−9.12372	+	5.26758i	−1.18781	+	0.685781i	−0.230000	+	0.973191i	$0.573873\pi$
$60$			6.29253i			0.812362i
$61$	−7.17423	+	12.4261i	−0.918567	+	1.59100i	−0.116973	+	0.993135i	$0.537319\pi$
$61$	−7.17423	+	12.4261i	−0.918567	+	1.59100i	−0.801594	+	0.597869i	$0.796014\pi$
$62$	7.89898	−	4.56048i	1.00317	−	0.579181i
$63$	−13.7980	+	11.9494i	−1.73838	+	1.50548i
$64$	−8.00000			−1.00000
$65$	−0.224745	+	0.389270i	−0.0278762	+	0.0482829i
$66$	10.8990	−	18.8776i	1.34157	−	2.32367i
$67$	1.17423	+	2.03383i	0.143456	+	0.248472i	0.928796	−	0.370592i	$-0.120845\pi$
$67$	1.17423	+	2.03383i	0.143456	+	0.248472i	−0.785340	+	0.619065i	$0.787512\pi$
$68$	3.55051	−	2.04989i	0.430563	−	0.248585i
$69$	3.44949			0.415270
$70$	2.44949	+	2.82843i	0.292770	+	0.338062i
$71$		−	1.41421i		−	0.167836i	−0.996473	−	0.0839181i	$-0.973257\pi$
$71$		−	1.41421i		−	0.167836i	0.996473	−	0.0839181i	$-0.0267434\pi$
$72$	−16.8990	−	9.75663i	−1.99156	−	1.14983i
$73$	−2.32577	+	1.34278i	−0.272210	+	0.157161i	−0.629892	−	0.776683i	$-0.716901\pi$
$73$	−2.32577	+	1.34278i	−0.272210	+	0.157161i	0.357681	+	0.933844i	$0.383567\pi$
$74$	2.44949	−	4.24264i	0.284747	−	0.493197i
$75$	2.72474	+	1.57313i	0.314626	+	0.181650i
$76$	7.34847	+	4.24264i	0.842927	+	0.486664i
$77$	−2.44949	−	12.7279i	−0.279145	−	1.45048i
$78$	−1.00000	−	1.73205i	−0.113228	−	0.196116i
$79$	0.674235	+	0.389270i	0.0758573	+	0.0437962i	0.537449	−	0.843296i	$-0.319388\pi$
$79$	0.674235	+	0.389270i	0.0758573	+	0.0437962i	−0.461592	+	0.887093i	$0.652721\pi$
$80$	−2.00000	+	3.46410i	−0.223607	+	0.387298i
$81$	−8.94949	−	15.5010i	−0.994388	−	1.72233i
$82$	−3.34847			−0.369777
$83$		−	12.2672i		−	1.34650i	−0.739414	−	0.673251i	$-0.764897\pi$
$83$		−	12.2672i		−	1.34650i	0.739414	−	0.673251i	$-0.235103\pi$
$84$	−16.3485	+	3.14626i	−1.78376	+	0.343286i
$85$		−	2.04989i		−	0.222342i
$86$		−	6.43539i		−	0.693946i
$87$	15.8485	+	27.4504i	1.69913	+	2.94299i
$88$	12.0000	−	6.92820i	1.27920	−	0.738549i
$89$	−0.398979	−	0.230351i	−0.0422917	−	0.0244171i	0.478705	−	0.877976i	$-0.341106\pi$
$89$	−0.398979	−	0.230351i	−0.0422917	−	0.0244171i	−0.520997	+	0.853559i	$0.674440\pi$
$90$	−8.44949	+	4.87832i	−0.890654	+	0.514220i
$91$	−1.12372	−	0.389270i	−0.117798	−	0.0408065i
$92$	1.89898	+	1.09638i	0.197982	+	0.114305i
$93$	17.5732	+	10.1459i	1.82226	+	1.05208i
$94$	7.34847	+	4.24264i	0.757937	+	0.437595i
$95$	3.67423	−	2.12132i	0.376969	−	0.217643i
$96$	−8.89898	−	15.4135i	−0.908248	−	1.57313i
$97$			5.02118i			0.509824i	0.966964	+	0.254912i	$0.0820464\pi$
$97$			5.02118i			0.509824i	−0.966964	+	0.254912i	$0.917954\pi$
$98$	−6.12372	+	7.77817i	−0.618590	+	0.785714i
$99$	33.7980			3.39682
$100$	1.00000	+	1.73205i	0.100000	+	0.173205i
$101$	−4.62372	−	8.00853i	−0.460078	−	0.796878i	0.538887	−	0.842378i	$-0.318845\pi$
$101$	−4.62372	−	8.00853i	−0.460078	−	0.796878i	−0.998964	+	0.0455003i	$0.985512\pi$
$102$	7.89898	+	4.56048i	0.782116	+	0.451555i
$103$	1.39898	−	2.42310i	0.137846	−	0.238755i	−0.788835	−	0.614605i	$-0.789316\pi$
$103$	1.39898	−	2.42310i	0.137846	−	0.238755i	0.926681	+	0.375849i	$0.122649\pi$
$104$		−	1.27135i		−	0.124666i
$105$	−2.72474	+	7.86566i	−0.265908	+	0.767610i
$106$	−3.44949	−	5.97469i	−0.335044	−	0.580313i
$107$	0.275255	−	0.476756i	0.0266099	−	0.0460897i	−0.852414	−	0.522868i	$-0.824862\pi$
$107$	0.275255	−	0.476756i	0.0266099	−	0.0460897i	0.879024	+	0.476778i	$0.158195\pi$
$108$		−	24.5344i		−	2.36083i
$109$	−14.1742	+	8.18350i	−1.35765	+	0.783837i	−0.989306	−	0.145854i	$-0.953407\pi$
$109$	−14.1742	+	8.18350i	−1.35765	+	0.783837i	−0.368339	+	0.929691i	$0.620074\pi$
$110$		−	6.92820i		−	0.660578i
$111$	10.8990			1.03449
$112$	−10.0000	−	3.46410i	−0.944911	−	0.327327i
$113$	3.55051			0.334004			0.167002	−	0.985957i	$-0.446591\pi$
$113$	3.55051			0.334004			0.167002	+	0.985957i	$0.446591\pi$
$114$			18.8776i			1.76805i
$115$	0.949490	−	0.548188i	0.0885404	−	0.0511188i
$116$			20.1489i			1.87078i
$117$	1.55051	−	2.68556i	0.143345	−	0.248280i
$118$	−7.44949	−	12.9029i	−0.685781	−	1.18781i
$119$	5.32577	−	1.02494i	0.488212	−	0.0939565i
$120$	−8.89898			−0.812362
$121$	−6.50000	+	11.2583i	−0.590909	+	1.02348i
$122$	−17.5732	−	10.1459i	−1.59100	−	0.918567i
$123$	−3.72474	−	6.45145i	−0.335849	−	0.581707i
$124$	6.44949	+	11.1708i	0.579181	+	1.00317i
$125$	1.00000			0.0894427
$126$	−16.8990	−	19.5133i	−1.50548	−	1.73838i
$127$			6.92820i			0.614779i	0.951584	+	0.307389i	$0.0994554\pi$
$127$			6.92820i			0.614779i	−0.951584	+	0.307389i	$0.900545\pi$
$128$		−	11.3137i		−	1.00000i
$129$	12.3990	−	7.15855i	1.09167	−	0.630276i
$130$	−0.550510	−	0.317837i	−0.0482829	−	0.0278762i
$131$	9.79796	+	5.65685i	0.856052	+	0.494242i	0.862688	−	0.505736i	$-0.168779\pi$
$131$	9.79796	+	5.65685i	0.856052	+	0.494242i	−0.00663646	+	0.999978i	$0.502112\pi$
$132$	26.6969	+	15.4135i	2.32367	+	1.34157i
$133$	7.34847	+	8.48528i	0.637193	+	0.735767i
$134$	−2.87628	+	1.66062i	−0.248472	+	0.143456i
$135$	−10.6237	−	6.13361i	−0.914345	−	0.527897i
$136$	2.89898	+	5.02118i	0.248585	+	0.430563i
$137$	−4.89898	−	8.48528i	−0.418548	−	0.724947i	0.577246	−	0.816571i	$-0.304128\pi$
$137$	−4.89898	−	8.48528i	−0.418548	−	0.724947i	−0.995794	+	0.0916241i	$0.970794\pi$
$138$			4.87832i			0.415270i
$139$			6.92820i			0.587643i	0.955860	+	0.293821i	$0.0949270\pi$
$139$			6.92820i			0.587643i	−0.955860	+	0.293821i	$0.905073\pi$
$140$	−4.00000	+	3.46410i	−0.338062	+	0.292770i
$141$			18.8776i			1.58978i
$142$	2.00000			0.167836
$143$	1.10102	+	1.90702i	0.0920720	+	0.159473i
$144$	13.7980	−	23.8988i	1.14983	−	1.99156i
$145$	8.72474	+	5.03723i	0.724551	+	0.418319i
$146$	−1.89898	−	3.28913i	−0.157161	−	0.272210i
$147$	−21.7980	−	3.14626i	−1.79787	−	0.259500i
$148$	6.00000	+	3.46410i	0.493197	+	0.284747i
$149$	4.37628	+	2.52664i	0.358518	+	0.206991i	0.668431	−	0.743774i	$-0.266966\pi$
$149$	4.37628	+	2.52664i	0.358518	+	0.206991i	−0.309912	+	0.950765i	$0.600300\pi$
$150$	−2.22474	+	3.85337i	−0.181650	+	0.314626i
$151$	0.674235	−	0.389270i	0.0548684	−	0.0316783i	−0.472315	−	0.881430i	$-0.656581\pi$
$151$	0.674235	−	0.389270i	0.0548684	−	0.0316783i	0.527183	+	0.849752i	$0.323248\pi$
$152$	−6.00000	+	10.3923i	−0.486664	+	0.842927i
$153$			14.1421i			1.14332i
$154$	18.0000	−	3.46410i	1.45048	−	0.279145i
$155$	6.44949			0.518035
$156$	2.44949	−	1.41421i	0.196116	−	0.113228i
$157$	−9.34847	−	16.1920i	−0.746089	−	1.29226i	−0.949684	−	0.313209i	$-0.898596\pi$
$157$	−9.34847	−	16.1920i	−0.746089	−	1.29226i	0.203595	−	0.979055i	$-0.434737\pi$
$158$	−0.550510	+	0.953512i	−0.0437962	+	0.0758573i
$159$	7.67423	−	13.2922i	0.608606	−	1.05414i
$160$	−4.89898	−	2.82843i	−0.387298	−	0.223607i
$161$	1.89898	+	2.19275i	0.149661	+	0.172813i
$162$	21.9217	−	12.6565i	1.72233	−	0.994388i
$163$	6.89898	−	11.9494i	0.540370	−	0.935948i	−0.458513	−	0.888688i	$-0.651618\pi$
$163$	6.89898	−	11.9494i	0.540370	−	0.935948i	0.998883	−	0.0472601i	$-0.0150490\pi$
$164$		−	4.73545i		−	0.369777i
$165$	13.3485	−	7.70674i	1.03918	−	0.599969i
$166$	17.3485			1.34650
$167$	−3.00000			−0.232147			−0.116073	−	0.993241i	$-0.537031\pi$
$167$	−3.00000			−0.232147			−0.116073	+	0.993241i	$0.537031\pi$
$168$	−4.44949	−	23.1202i	−0.343286	−	1.78376i
$169$	−12.7980			−0.984458
$170$	2.89898			0.222342
$171$	−25.3485	+	14.6349i	−1.93845	+	1.11916i
$172$	9.10102			0.693946
$173$	−0.550510	+	0.953512i	−0.0418545	+	0.0724942i	−0.886194	−	0.463315i	$-0.846660\pi$
$173$	−0.550510	+	0.953512i	−0.0418545	+	0.0724942i	0.844339	+	0.535809i	$0.179993\pi$
$174$	−38.8207	+	22.4131i	−2.94299	+	1.69913i
$175$	0.500000	+	2.59808i	0.0377964	+	0.196396i
$176$	9.79796	+	16.9706i	0.738549	+	1.27920i
$177$	16.5732	−	28.7056i	1.24572	−	2.15765i
$178$	0.325765	−	0.564242i	0.0244171	−	0.0422917i
$179$	−7.22474	−	12.5136i	−0.540003	−	0.935312i	−0.998903	−	0.0468245i	$-0.985090\pi$
$179$	−7.22474	−	12.5136i	−0.540003	−	0.935312i	0.458900	−	0.888488i	$-0.348243\pi$
$180$	−6.89898	−	11.9494i	−0.514220	−	0.890654i
$181$	2.34847			0.174560			0.0872802	−	0.996184i	$-0.472182\pi$
$181$	2.34847			0.174560			0.0872802	+	0.996184i	$0.472182\pi$
$182$	0.550510	−	1.58919i	0.0408065	−	0.117798i
$183$		−	45.1441i		−	3.33715i
$184$	−1.55051	+	2.68556i	−0.114305	+	0.197982i
$185$	3.00000	−	1.73205i	0.220564	−	0.127343i
$186$	−14.3485	+	24.8523i	−1.05208	+	1.82226i
$187$	−8.69694	−	5.02118i	−0.635983	−	0.367185i
$188$	−6.00000	+	10.3923i	−0.437595	+	0.757937i
$189$	10.6237	−	30.6681i	0.772762	−	2.23077i
$190$	3.00000	+	5.19615i	0.217643	+	0.376969i
$191$	−13.1010	−	7.56388i	−0.947957	−	0.547303i	−0.0555110	−	0.998458i	$-0.517679\pi$
$191$	−13.1010	−	7.56388i	−0.947957	−	0.547303i	−0.892446	+	0.451155i	$0.851012\pi$
$192$	21.7980	−	12.5851i	1.57313	−	0.908248i
$193$	3.34847	+	5.79972i	0.241028	+	0.417473i	0.961007	−	0.276523i	$-0.0891821\pi$
$193$	3.34847	+	5.79972i	0.241028	+	0.417473i	−0.719979	+	0.693996i	$0.755849\pi$
$194$	−7.10102			−0.509824
$195$		−	1.41421i		−	0.101274i
$196$	−11.0000	−	8.66025i	−0.785714	−	0.618590i
$197$			21.7060i			1.54649i	0.634108	+	0.773245i	$0.281368\pi$
$197$			21.7060i			1.54649i	−0.634108	+	0.773245i	$0.718632\pi$
$198$			47.7975i			3.39682i
$199$	2.34847	+	4.06767i	0.166479	+	0.288349i	0.937179	−	0.348848i	$-0.113427\pi$
$199$	2.34847	+	4.06767i	0.166479	+	0.288349i	−0.770701	+	0.637197i	$0.780094\pi$
$200$	−2.44949	+	1.41421i	−0.173205	+	0.100000i
$201$	−6.39898	−	3.69445i	−0.451349	−	0.260587i
$202$	11.3258	−	6.53893i	0.796878	−	0.460078i
$203$	−8.72474	+	25.1862i	−0.612357	+	1.76772i
$204$	−6.44949	+	11.1708i	−0.451555	+	0.782116i
$205$	−2.05051	−	1.18386i	−0.143214	−	0.0826846i
$206$	3.42679	+	1.97846i	0.238755	+	0.137846i
$207$	−6.55051	+	3.78194i	−0.455292	+	0.262863i
$208$	1.79796			0.124666
$209$		−	20.7846i		−	1.43770i
$210$	−11.1237	−	3.85337i	−0.767610	−	0.265908i
$211$	−16.2474			−1.11852			−0.559260	−	0.828992i	$-0.688915\pi$
$211$	−16.2474			−1.11852			−0.559260	+	0.828992i	$0.688915\pi$
$212$	8.44949	−	4.87832i	0.580313	−	0.335044i
$213$	2.22474	+	3.85337i	0.152437	+	0.264029i
$214$	0.674235	+	0.389270i	0.0460897	+	0.0266099i
$215$	2.27526	−	3.94086i	0.155171	−	0.268764i
$216$	34.6969			2.36083
$217$	3.22474	+	16.7563i	0.218910	+	1.13749i
$218$	−11.5732	−	20.0454i	−0.783837	−	1.35765i
$219$	4.22474	−	7.31747i	0.285482	−	0.494469i
$220$	9.79796			0.660578
$221$	−0.797959	+	0.460702i	−0.0536765	+	0.0309902i
$222$			15.4135i			1.03449i
$223$	−4.69694			−0.314530			−0.157265	−	0.987556i	$-0.550268\pi$
$223$	−4.69694			−0.314530			−0.157265	+	0.987556i	$0.550268\pi$
$224$	4.89898	−	14.1421i	0.327327	−	0.944911i
$225$	−6.89898			−0.459932
$226$			5.02118i			0.334004i
$227$	15.2474	−	8.80312i	1.01201	−	0.584284i	0.100230	−	0.994964i	$-0.468042\pi$
$227$	15.2474	−	8.80312i	1.01201	−	0.584284i	0.911779	+	0.410681i	$0.134709\pi$
$228$	−26.6969			−1.76805
$229$	−6.34847	+	10.9959i	−0.419519	+	0.726628i	−0.995891	−	0.0905595i	$-0.971134\pi$
$229$	−6.34847	+	10.9959i	−0.419519	+	0.726628i	0.576372	+	0.817187i	$0.304468\pi$
$230$	0.775255	+	1.34278i	0.0511188	+	0.0885404i
$231$	26.6969	+	30.8270i	1.75653	+	2.02827i
$232$	−28.4949			−1.87078
$233$	−12.1237	+	20.9989i	−0.794252	+	1.37568i	0.129062	+	0.991637i	$0.458803\pi$
$233$	−12.1237	+	20.9989i	−0.794252	+	1.37568i	−0.923313	+	0.384048i	$0.874530\pi$
$234$	3.79796	+	2.19275i	0.248280	+	0.143345i
$235$	3.00000	+	5.19615i	0.195698	+	0.338960i
$236$	18.2474	−	10.5352i	1.18781	−	0.685781i
$237$	−2.44949			−0.159111
$238$	1.44949	+	7.53177i	0.0939565	+	0.488212i
$239$			17.4634i			1.12961i	0.825224	+	0.564806i	$0.191049\pi$
$239$			17.4634i			1.12961i	−0.825224	+	0.564806i	$0.808951\pi$
$240$		−	12.5851i		−	0.812362i
$241$	11.6969	−	6.75323i	0.753466	−	0.435014i	−0.0734789	−	0.997297i	$-0.523410\pi$
$241$	11.6969	−	6.75323i	0.753466	−	0.435014i	0.826945	+	0.562283i	$0.190077\pi$
$242$	−15.9217	−	9.19239i	−1.02348	−	0.590909i
$243$	16.8990	+	9.75663i	1.08407	+	0.625888i
$244$	14.3485	−	24.8523i	0.918567	−	1.59100i
$245$	−6.50000	+	2.59808i	−0.415270	+	0.165985i
$246$	9.12372	−	5.26758i	0.581707	−	0.335849i
$247$	−1.65153	−	0.953512i	−0.105084	−	0.0606705i
$248$	−15.7980	+	9.12096i	−1.00317	+	0.579181i
$249$	19.2980	+	33.4250i	1.22296	+	2.11823i
$250$			1.41421i			0.0894427i
$251$		−	27.8557i		−	1.75823i	−0.476605	−	0.879117i	$-0.658133\pi$
$251$		−	27.8557i		−	1.75823i	0.476605	−	0.879117i	$-0.341867\pi$
$252$	27.5959	−	23.8988i	1.73838	−	1.50548i
$253$		−	5.37113i		−	0.337680i
$254$	−9.79796			−0.614779
$255$	3.22474	+	5.58542i	0.201941	+	0.349773i
$256$	16.0000			1.00000
$257$	−6.55051	−	3.78194i	−0.408610	−	0.235911i	0.281583	−	0.959537i	$-0.409141\pi$
$257$	−6.55051	−	3.78194i	−0.408610	−	0.235911i	−0.690192	+	0.723626i	$0.742474\pi$
$258$	10.1237	+	17.5348i	0.630276	+	1.09167i
$259$	6.00000	+	6.92820i	0.372822	+	0.430498i
$260$	0.449490	−	0.778539i	0.0278762	−	0.0482829i
$261$	−60.1918	−	34.7518i	−3.72578	−	2.15108i
$262$	−8.00000	+	13.8564i	−0.494242	+	0.856052i
$263$	−19.7474	+	11.4012i	−1.21768	+	0.703028i	−0.964421	−	0.264371i	$-0.914836\pi$
$263$	−19.7474	+	11.4012i	−1.21768	+	0.703028i	−0.253259	+	0.967399i	$0.581502\pi$
$264$	−21.7980	+	37.7552i	−1.34157	+	2.32367i
$265$		−	4.87832i		−	0.299673i
$266$	−12.0000	+	10.3923i	−0.735767	+	0.637193i
$267$	1.44949			0.0887073
$268$	−2.34847	−	4.06767i	−0.143456	−	0.248472i
$269$	−0.825765	−	1.43027i	−0.0503478	−	0.0872050i	0.839753	−	0.542968i	$-0.182700\pi$
$269$	−0.825765	−	1.43027i	−0.0503478	−	0.0872050i	−0.890101	+	0.455763i	$0.849366\pi$
$270$	8.67423	−	15.0242i	0.527897	−	0.914345i
$271$	−5.67423	+	9.82806i	−0.344685	+	0.597012i	−0.985297	−	0.170853i	$-0.945348\pi$
$271$	−5.67423	+	9.82806i	−0.344685	+	0.597012i	0.640611	+	0.767865i	$0.278681\pi$
$272$	−7.10102	+	4.09978i	−0.430563	+	0.248585i
$273$	3.67423	−	0.707107i	0.222375	−	0.0427960i
$274$	12.0000	−	6.92820i	0.724947	−	0.418548i
$275$	2.44949	−	4.24264i	0.147710	−	0.255841i
$276$	−6.89898			−0.415270
$277$	−17.0227	+	9.82806i	−1.02280	+	0.590511i	−0.914912	−	0.403653i	$-0.867740\pi$
$277$	−17.0227	+	9.82806i	−1.02280	+	0.590511i	−0.107883	+	0.994164i	$0.534407\pi$
$278$	−9.79796			−0.587643
$279$	−44.4949			−2.66384
$280$	−4.89898	−	5.65685i	−0.292770	−	0.338062i
$281$	7.10102			0.423611			0.211806	−	0.977312i	$-0.432066\pi$
$281$	7.10102			0.423611			0.211806	+	0.977312i	$0.432066\pi$
$282$	−26.6969			−1.58978
$283$	7.34847	−	4.24264i	0.436821	−	0.252199i	−0.265427	−	0.964131i	$-0.585513\pi$
$283$	7.34847	−	4.24264i	0.436821	−	0.252199i	0.702248	+	0.711932i	$0.252180\pi$
$284$			2.82843i			0.167836i
$285$	−6.67423	+	11.5601i	−0.395348	+	0.684762i
$286$	−2.69694	+	1.55708i	−0.159473	+	0.0920720i
$287$	2.05051	−	5.91931i	0.121038	−	0.349406i
$288$	33.7980	+	19.5133i	1.99156	+	1.14983i
$289$	−6.39898	+	11.0834i	−0.376411	+	0.651962i
$290$	−7.12372	+	12.3387i	−0.418319	+	0.724551i
$291$	−7.89898	−	13.6814i	−0.463046	−	0.802020i
$292$	4.65153	−	2.68556i	0.272210	−	0.157161i
$293$	24.4949			1.43101			0.715504	−	0.698609i	$-0.246197\pi$
$293$	24.4949			1.43101			0.715504	+	0.698609i	$0.246197\pi$
$294$	4.44949	−	30.8270i	0.259500	−	1.79787i
$295$		−	10.5352i		−	0.613381i
$296$	−4.89898	+	8.48528i	−0.284747	+	0.493197i
$297$	−52.0454	+	30.0484i	−3.01998	+	1.74359i
$298$	−3.57321	+	6.18899i	−0.206991	+	0.358518i
$299$	−0.426786	−	0.246405i	−0.0246817	−	0.0142500i
$300$	−5.44949	−	3.14626i	−0.314626	−	0.181650i
$301$	11.3763	+	3.94086i	0.655718	+	0.227147i
$302$	0.550510	+	0.953512i	0.0316783	+	0.0548684i
$303$	25.1969	+	14.5475i	1.44753	+	0.835730i
$304$	−14.6969	−	8.48528i	−0.842927	−	0.486664i
$305$	−7.17423	−	12.4261i	−0.410795	−	0.711519i
$306$	−20.0000			−1.14332
$307$		−	31.4305i		−	1.79384i	−0.442197	−	0.896918i	$-0.645801\pi$
$307$		−	31.4305i		−	1.79384i	0.442197	−	0.896918i	$-0.354199\pi$
$308$	4.89898	+	25.4558i	0.279145	+	1.45048i
$309$			8.80312i			0.500792i
$310$			9.12096i			0.518035i
$311$	11.5732	+	20.0454i	0.656257	+	1.13667i	0.981577	+	0.191066i	$0.0611945\pi$
$311$	11.5732	+	20.0454i	0.656257	+	1.13667i	−0.325320	+	0.945604i	$0.605472\pi$
$312$	2.00000	+	3.46410i	0.113228	+	0.196116i
$313$	23.6969	+	13.6814i	1.33943	+	0.773320i	0.986723	−	0.162413i	$-0.0519278\pi$
$313$	23.6969	+	13.6814i	1.33943	+	0.773320i	0.352707	+	0.935734i	$0.385261\pi$
$314$	22.8990	−	13.2207i	1.29226	−	0.746089i
$315$	−3.44949	−	17.9241i	−0.194357	−	1.00991i
$316$	−1.34847	−	0.778539i	−0.0758573	−	0.0437962i
$317$	17.5732	+	10.1459i	0.987010	+	0.569851i	0.904379	−	0.426730i	$-0.140334\pi$
$317$	17.5732	+	10.1459i	0.987010	+	0.569851i	0.0826308	+	0.996580i	$0.473668\pi$
$318$	18.7980	+	10.8530i	1.05414	+	0.608606i
$319$	42.7423	−	24.6773i	2.39311	−	1.38166i
$320$	4.00000	−	6.92820i	0.223607	−	0.387298i
$321$			1.73205i			0.0966736i
$322$	−3.10102	+	2.68556i	−0.172813	+	0.149661i
$323$	8.69694			0.483911
$324$	17.8990	+	31.0019i	0.994388	+	1.72233i
$325$	−0.224745	−	0.389270i	−0.0124666	−	0.0215928i
$326$	16.8990	+	9.75663i	0.935948	+	0.540370i
$327$	25.7474	−	44.5959i	1.42384	−	2.46616i
$328$	6.69694			0.369777
$329$	−12.0000	+	10.3923i	−0.661581	+	0.572946i
$330$	10.8990	+	18.8776i	0.599969	+	1.03918i
$331$	−15.5732	+	26.9736i	−0.855981	+	1.48260i	0.0197504	+	0.999805i	$0.493713\pi$
$331$	−15.5732	+	26.9736i	−0.855981	+	1.48260i	−0.875732	+	0.482798i	$0.839621\pi$
$332$			24.5344i			1.34650i
$333$	−20.6969	+	11.9494i	−1.13419	+	0.654822i
$334$		−	4.24264i		−	0.232147i
$335$	−2.34847			−0.128311
$336$	32.6969	−	6.29253i	1.78376	−	0.343286i
$337$	−4.24745			−0.231373			−0.115687	−	0.993286i	$-0.536907\pi$
$337$	−4.24745			−0.231373			−0.115687	+	0.993286i	$0.536907\pi$
$338$		−	18.0990i		−	0.984458i
$339$	−9.67423	+	5.58542i	−0.525432	+	0.303358i
$340$			4.09978i			0.222342i
$341$	15.7980	−	27.3629i	0.855507	−	1.48178i
$342$	−20.6969	−	35.8481i	−1.11916	−	1.93845i
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$			12.8708i			0.693946i
$345$	−1.72474	+	2.98735i	−0.0928571	+	0.160833i
$346$	−1.34847	−	0.778539i	−0.0724942	−	0.0418545i
$347$	11.1742	+	19.3543i	0.599864	+	1.03900i	0.992841	+	0.119447i	$0.0381121\pi$
$347$	11.1742	+	19.3543i	0.599864	+	1.03900i	−0.392976	+	0.919549i	$0.628555\pi$
$348$	−31.6969	−	54.9007i	−1.69913	−	2.94299i
$349$	−17.2474			−0.923235			−0.461617	−	0.887079i	$-0.652731\pi$
$349$	−17.2474			−0.923235			−0.461617	+	0.887079i	$0.652731\pi$
$350$	−3.67423	+	0.707107i	−0.196396	+	0.0377964i
$351$			5.51399i			0.294315i
$352$	−24.0000	+	13.8564i	−1.27920	+	0.738549i
$353$	−11.8207	+	6.82466i	−0.629150	+	0.363240i	−0.780423	−	0.625252i	$-0.784996\pi$
$353$	−11.8207	+	6.82466i	−0.629150	+	0.363240i	0.151273	+	0.988492i	$0.451663\pi$
$354$	40.5959	+	23.4381i	2.15765	+	1.24572i
$355$	1.22474	+	0.707107i	0.0650027	+	0.0375293i
$356$	0.797959	+	0.460702i	0.0422917	+	0.0244171i
$357$	−12.8990	+	11.1708i	−0.682686	+	0.591224i
$358$	17.6969	−	10.2173i	0.935312	−	0.540003i
$359$	22.2247	+	12.8315i	1.17298	+	0.677219i	0.954379	−	0.298596i	$-0.0965184\pi$
$359$	22.2247	+	12.8315i	1.17298	+	0.677219i	0.218598	+	0.975815i	$0.429852\pi$
$360$	16.8990	−	9.75663i	0.890654	−	0.514220i
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$			3.32124i			0.174560i
$363$		−	40.9014i		−	2.14677i
$364$	2.24745	+	0.778539i	0.117798	+	0.0408065i
$365$		−	2.68556i		−	0.140569i
$366$	63.8434			3.33715
$367$	−8.94949	−	15.5010i	−0.467160	−	0.809144i	0.532137	−	0.846659i	$-0.321389\pi$
$367$	−8.94949	−	15.5010i	−0.467160	−	0.809144i	−0.999296	+	0.0375145i	$0.988056\pi$
$368$	−3.79796	−	2.19275i	−0.197982	−	0.114305i
$369$	14.1464	+	8.16744i	0.736434	+	0.425180i
$370$	2.44949	+	4.24264i	0.127343	+	0.220564i
$371$	12.6742	−	2.43916i	0.658013	−	0.126635i
$372$	−35.1464	−	20.2918i	−1.82226	−	1.05208i
$373$	−15.0000	−	8.66025i	−0.776671	−	0.448411i	0.0585785	−	0.998283i	$-0.481343\pi$
$373$	−15.0000	−	8.66025i	−0.776671	−	0.448411i	−0.835249	+	0.549872i	$0.814677\pi$
$374$	7.10102	−	12.2993i	0.367185	−	0.635983i
$375$	−2.72474	+	1.57313i	−0.140705	+	0.0812362i
$376$	−14.6969	−	8.48528i	−0.757937	−	0.437595i
$377$		−	4.52837i		−	0.233223i
$378$	43.3712	+	15.0242i	2.23077	+	0.772762i
$379$	−2.65153			−0.136200			−0.0681000	−	0.997679i	$-0.521694\pi$
$379$	−2.65153			−0.136200			−0.0681000	+	0.997679i	$0.521694\pi$
$380$	−7.34847	+	4.24264i	−0.376969	+	0.217643i
$381$	−10.8990	−	18.8776i	−0.558372	−	0.967128i
$382$	10.6969	−	18.5276i	0.547303	−	0.947957i
$383$	−12.3990	+	21.4757i	−0.633558	+	1.09736i	0.353260	+	0.935525i	$0.385073\pi$
$383$	−12.3990	+	21.4757i	−0.633558	+	1.09736i	−0.986819	+	0.161830i	$0.948260\pi$
$384$	17.7980	+	30.8270i	0.908248	+	1.57313i
$385$	12.2474	+	4.24264i	0.624188	+	0.216225i
$386$	−8.20204	+	4.73545i	−0.417473	+	0.241028i
$387$	−15.6969	+	27.1879i	−0.797920	+	1.38204i
$388$		−	10.0424i		−	0.509824i
$389$	9.79796	−	5.65685i	0.496776	−	0.286814i	−0.230605	−	0.973047i	$-0.574071\pi$
$389$	9.79796	−	5.65685i	0.496776	−	0.286814i	0.727381	+	0.686234i	$0.240737\pi$
$390$	2.00000			0.101274
$391$	2.24745			0.113658
$392$	12.2474	−	15.5563i	0.618590	−	0.785714i
$393$	−35.5959			−1.79558
$394$	−30.6969			−1.54649
$395$	−0.674235	+	0.389270i	−0.0339244	+	0.0195863i
$396$	−67.5959			−3.39682
$397$	14.3485	−	24.8523i	0.720129	−	1.24730i	−0.240819	−	0.970570i	$-0.577416\pi$
$397$	14.3485	−	24.8523i	0.720129	−	1.24730i	0.960948	−	0.276730i	$-0.0892507\pi$
$398$	−5.75255	+	3.32124i	−0.288349	+	0.166479i
$399$	−33.3712	−	11.5601i	−1.67065	−	0.578730i
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	5.60102	−	9.70125i	0.279702	−	0.484457i	−0.691609	−	0.722272i	$-0.743098\pi$
$401$	5.60102	−	9.70125i	0.279702	−	0.484457i	0.971311	+	0.237815i	$0.0764311\pi$
$402$	5.22474	−	9.04952i	0.260587	−	0.451349i
$403$	−1.44949	−	2.51059i	−0.0722042	−	0.125061i
$404$	9.24745	+	16.0171i	0.460078	+	0.796878i
$405$	17.8990			0.889407
$406$	−35.6186	−	12.3387i	−1.76772	−	0.612357i
$407$		−	16.9706i		−	0.841200i
$408$	−15.7980	−	9.12096i	−0.782116	−	0.451555i
$409$	19.1969	−	11.0834i	0.949228	−	0.548037i	0.0563866	−	0.998409i	$-0.482042\pi$
$409$	19.1969	−	11.0834i	0.949228	−	0.548037i	0.892841	+	0.450372i	$0.148709\pi$
$410$	1.67423	−	2.89986i	0.0826846	−	0.143214i
$411$	26.6969	+	15.4135i	1.31686	+	0.760291i
$412$	−2.79796	+	4.84621i	−0.137846	+	0.238755i
$413$	27.3712	−	5.26758i	1.34685	−	0.259201i
$414$	−5.34847	−	9.26382i	−0.262863	−	0.455292i
$415$	10.6237	+	6.13361i	0.521498	+	0.301087i
$416$			2.54270i			0.124666i
$417$	−10.8990	−	18.8776i	−0.533725	−	0.924439i
$418$	29.3939			1.43770
$419$			11.0280i			0.538752i	0.963035	+	0.269376i	$0.0868174\pi$
$419$			11.0280i			0.538752i	−0.963035	+	0.269376i	$0.913183\pi$
$420$	5.44949	−	15.7313i	0.265908	−	0.767610i
$421$		−	21.3882i		−	1.04240i	−0.853436	−	0.521198i	$-0.825485\pi$
$421$		−	21.3882i		−	1.04240i	0.853436	−	0.521198i	$-0.174515\pi$
$422$		−	22.9774i		−	1.11852i
$423$	−20.6969	−	35.8481i	−1.00632	−	1.74300i
$424$	6.89898	+	11.9494i	0.335044	+	0.580313i
$425$	1.77526	+	1.02494i	0.0861125	+	0.0497171i
$426$	−5.44949	+	3.14626i	−0.264029	+	0.152437i
$427$	28.6969	−	24.8523i	1.38874	−	1.20269i
$428$	−0.550510	+	0.953512i	−0.0266099	+	0.0460897i
$429$	−6.00000	−	3.46410i	−0.289683	−	0.167248i
$430$	5.57321	+	3.21770i	0.268764	+	0.155171i
$431$	27.7980	−	16.0492i	1.33898	−	0.773061i	0.352324	−	0.935878i	$-0.385391\pi$
$431$	27.7980	−	16.0492i	1.33898	−	0.773061i	0.986656	+	0.162817i	$0.0520581\pi$
$432$			49.0689i			2.36083i
$433$			0.778539i			0.0374142i	0.999825	+	0.0187071i	$0.00595500\pi$
$433$			0.778539i			0.0374142i	−0.999825	+	0.0187071i	$0.994045\pi$
$434$	−23.6969	+	4.56048i	−1.13749	+	0.218910i
$435$	−31.6969			−1.51975
$436$	28.3485	−	16.3670i	1.35765	−	0.783837i
$437$	2.32577	+	4.02834i	0.111256	+	0.192702i
$438$	10.3485	+	5.97469i	0.494469	+	0.285482i
$439$	−10.4495	+	18.0990i	−0.498727	+	0.863820i	−0.999999	−	0.00146939i	$-0.999532\pi$
$439$	−10.4495	+	18.0990i	−0.498727	+	0.863820i	0.501272	+	0.865290i	$0.332866\pi$
$440$			13.8564i			0.660578i
$441$	44.8434	−	17.9241i	2.13540	−	0.853527i
$442$	−0.651531	−	1.12848i	−0.0309902	−	0.0536765i
$443$	0.825765	−	1.43027i	0.0392333	−	0.0679541i	−0.845742	−	0.533592i	$-0.820842\pi$
$443$	0.825765	−	1.43027i	0.0392333	−	0.0679541i	0.884975	+	0.465638i	$0.154175\pi$
$444$	−21.7980			−1.03449
$445$	0.398979	−	0.230351i	0.0189134	−	0.0109197i
$446$		−	6.64247i		−	0.314530i
$447$	−15.8990			−0.751996
$448$	20.0000	+	6.92820i	0.944911	+	0.327327i
$449$	−40.5959			−1.91584			−0.957920	−	0.287036i	$-0.907330\pi$
$449$	−40.5959			−1.91584			−0.957920	+	0.287036i	$0.907330\pi$
$450$		−	9.75663i		−	0.459932i
$451$	−10.0454	+	5.79972i	−0.473020	+	0.273098i
$452$	−7.10102			−0.334004
$453$	−1.22474	+	2.12132i	−0.0575435	+	0.0996683i
$454$	12.4495	+	21.5631i	0.584284	+	1.01201i
$455$	0.898979	−	0.778539i	0.0421448	−	0.0364985i
$456$		−	37.7552i		−	1.76805i
$457$	14.7980	−	25.6308i	0.692219	−	1.19896i	−0.278890	−	0.960323i	$-0.589966\pi$
$457$	14.7980	−	25.6308i	0.692219	−	1.19896i	0.971109	−	0.238636i	$-0.0767003\pi$
$458$	−15.5505	−	8.97809i	−0.726628	−	0.419519i
$459$	−12.5732	−	21.7774i	−0.586867	−	1.01648i
$460$	−1.89898	+	1.09638i	−0.0885404	+	0.0511188i
$461$	−9.30306			−0.433287			−0.216643	−	0.976251i	$-0.569511\pi$
$461$	−9.30306			−0.433287			−0.216643	+	0.976251i	$0.569511\pi$
$462$	−43.5959	+	37.7552i	−2.02827	+	1.75653i
$463$			12.1244i			0.563467i	0.959493	+	0.281733i	$0.0909093\pi$
$463$			12.1244i			0.563467i	−0.959493	+	0.281733i	$0.909091\pi$
$464$		−	40.2979i		−	1.87078i
$465$	−17.5732	+	10.1459i	−0.814938	+	0.470505i
$466$	−29.6969	−	17.1455i	−1.37568	−	0.794252i
$467$	−7.37628	−	4.25869i	−0.341333	−	0.197069i	0.319528	−	0.947577i	$-0.396476\pi$
$467$	−7.37628	−	4.25869i	−0.341333	−	0.197069i	−0.660861	+	0.750508i	$0.729809\pi$
$468$	−3.10102	+	5.37113i	−0.143345	+	0.248280i
$469$	−1.17423	−	6.10150i	−0.0542211	−	0.281741i
$470$	−7.34847	+	4.24264i	−0.338960	+	0.195698i
$471$	50.9444	+	29.4128i	2.34739	+	1.35527i
$472$	14.8990	+	25.8058i	0.685781	+	1.18781i
$473$	−11.1464	−	19.3062i	−0.512513	−	0.887699i
$474$		−	3.46410i		−	0.159111i
$475$			4.24264i			0.194666i
$476$	−10.6515	+	2.04989i	−0.488212	+	0.0939565i
$477$			33.6554i			1.54097i
$478$	−24.6969			−1.12961
$479$	−1.77526	−	3.07483i	−0.0811135	−	0.140493i	0.822615	−	0.568599i	$-0.192514\pi$
$479$	−1.77526	−	3.07483i	−0.0811135	−	0.140493i	−0.903728	+	0.428106i	$0.859181\pi$
$480$	17.7980			0.812362
$481$	−1.34847	−	0.778539i	−0.0614849	−	0.0354983i
$482$	9.55051	+	16.5420i	0.435014	+	0.753466i
$483$	−8.62372	−	2.98735i	−0.392393	−	0.135929i
$484$	13.0000	−	22.5167i	0.590909	−	1.02348i
$485$	−4.34847	−	2.51059i	−0.197454	−	0.114000i
$486$	−13.7980	+	23.8988i	−0.625888	+	1.08407i
$487$	−32.3939	+	18.7026i	−1.46791	+	0.847496i	−0.999354	−	0.0359392i	$-0.988558\pi$
$487$	−32.3939	+	18.7026i	−1.46791	+	0.847496i	−0.468553	+	0.883436i	$0.655224\pi$
$488$	35.1464	+	20.2918i	1.59100	+	0.918567i
$489$			43.4120i			1.96316i
$490$	−3.67423	−	9.19239i	−0.165985	−	0.415270i
$491$	35.1464			1.58614			0.793068	−	0.609133i	$-0.208482\pi$
$491$	35.1464			1.58614			0.793068	+	0.609133i	$0.208482\pi$
$492$	7.44949	+	12.9029i	0.335849	+	0.581707i
$493$	10.3258	+	17.8848i	0.465049	+	0.805489i
$494$	1.34847	−	2.33562i	0.0606705	−	0.105084i
$495$	−16.8990	+	29.2699i	−0.759553	+	1.31558i
$496$	−12.8990	−	22.3417i	−0.579181	−	1.00317i
$497$	−1.22474	+	3.53553i	−0.0549373	+	0.158590i
$498$	−47.2702	+	27.2914i	−2.11823	+	1.22296i
$499$	−15.6969	+	27.1879i	−0.702691	+	1.21710i	0.264827	+	0.964296i	$0.414685\pi$
$499$	−15.6969	+	27.1879i	−0.702691	+	1.21710i	−0.967518	+	0.252801i	$0.918648\pi$
$500$	−2.00000			−0.0894427
$501$	8.17423	−	4.71940i	0.365198	−	0.210847i
$502$	39.3939			1.75823
$503$	−5.69694			−0.254014			−0.127007	−	0.991902i	$-0.540537\pi$
$503$	−5.69694			−0.254014			−0.127007	+	0.991902i	$0.540537\pi$
$504$	33.7980	+	39.0265i	1.50548	+	1.73838i
$505$	9.24745			0.411506
$506$	7.59592			0.337680
$507$	34.8712	−	20.1329i	1.54868	−	0.894133i
$508$		−	13.8564i		−	0.614779i
$509$	−6.27526	+	10.8691i	−0.278146	+	0.481763i	−0.970924	−	0.239388i	$-0.923053\pi$
$509$	−6.27526	+	10.8691i	−0.278146	+	0.481763i	0.692778	+	0.721151i	$0.256387\pi$
$510$	−7.89898	+	4.56048i	−0.349773	+	0.201941i
$511$	6.97730	−	1.34278i	0.308657	−	0.0594011i
$512$			22.6274i			1.00000i
$513$	26.0227	−	45.0726i	1.14893	−	1.99001i
$514$	5.34847	−	9.26382i	0.235911	−	0.408610i
$515$	1.39898	+	2.42310i	0.0616464	+	0.106775i
$516$	−24.7980	+	14.3171i	−1.09167	+	0.630276i
$517$	29.3939			1.29274
$518$	−9.79796	+	8.48528i	−0.430498	+	0.372822i
$519$		−	3.46410i		−	0.152057i
$520$	1.10102	+	0.635674i	0.0482829	+	0.0278762i
$521$	15.2474	−	8.80312i	0.668003	−	0.385672i	−0.127317	−	0.991862i	$-0.540636\pi$
$521$	15.2474	−	8.80312i	0.668003	−	0.385672i	0.795319	+	0.606190i	$0.207303\pi$
$522$	49.1464	−	85.1241i	2.15108	−	3.72578i
$523$	4.34847	+	2.51059i	0.190145	+	0.109780i	0.592051	−	0.805901i	$-0.298319\pi$
$523$	4.34847	+	2.51059i	0.190145	+	0.109780i	−0.401905	+	0.915681i	$0.631652\pi$
$524$	−19.5959	−	11.3137i	−0.856052	−	0.494242i
$525$	−5.44949	−	6.29253i	−0.237835	−	0.274628i
$526$	−16.1237	−	27.9271i	−0.703028	−	1.21768i
$527$	11.4495	+	6.61037i	0.498748	+	0.287952i
$528$	−53.3939	−	30.8270i	−2.32367	−	1.34157i
$529$	−10.8990	−	18.8776i	−0.473869	−	0.820765i
$530$	6.89898			0.299673
$531$			72.6819i			3.15413i
$532$	−14.6969	−	16.9706i	−0.637193	−	0.735767i
$533$			1.06427i			0.0460986i
$534$			2.04989i			0.0887073i
$535$	0.275255	+	0.476756i	0.0119003	+	0.0206120i
$536$	5.75255	−	3.32124i	0.248472	−	0.143456i
$537$	39.3712	+	22.7310i	1.69899	+	0.980913i
$538$	2.02270	−	1.16781i	0.0872050	−	0.0503478i
$539$	−4.89898	+	33.9411i	−0.211014	+	1.46195i
$540$	21.2474	+	12.2672i	0.914345	+	0.527897i
$541$	2.47730	+	1.43027i	0.106507	+	0.0614920i	0.552307	−	0.833641i	$-0.313747\pi$
$541$	2.47730	+	1.43027i	0.106507	+	0.0614920i	−0.445800	+	0.895133i	$0.647081\pi$
$542$	−13.8990	−	8.02458i	−0.597012	−	0.344685i
$543$	−6.39898	+	3.69445i	−0.274606	+	0.158544i
$544$	−5.79796	−	10.0424i	−0.248585	−	0.430563i
$545$		−	16.3670i		−	0.701085i
$546$	1.00000	+	5.19615i	0.0427960	+	0.222375i
$547$	−35.0454			−1.49843			−0.749217	−	0.662325i	$-0.769570\pi$
$547$	−35.0454			−1.49843			−0.749217	+	0.662325i	$0.769570\pi$
$548$	9.79796	+	16.9706i	0.418548	+	0.724947i
$549$	49.4949	+	85.7277i	2.11239	+	3.65877i
$550$	6.00000	+	3.46410i	0.255841	+	0.147710i
$551$	−21.3712	+	37.0160i	−0.910443	+	1.57693i
$552$		−	9.75663i		−	0.415270i
$553$	−1.34847	−	1.55708i	−0.0573427	−	0.0662137i
$554$	−13.8990	−	24.0737i	−0.590511	−	1.02280i
$555$	−5.44949	+	9.43879i	−0.231318	+	0.400654i
$556$		−	13.8564i		−	0.587643i
$557$	4.10102	−	2.36773i	0.173766	−	0.100324i	−0.410595	−	0.911818i	$-0.634679\pi$
$557$	4.10102	−	2.36773i	0.173766	−	0.100324i	0.584360	+	0.811494i	$0.301345\pi$
$558$		−	62.9253i		−	2.66384i
$559$	−2.04541			−0.0865115
$560$	8.00000	−	6.92820i	0.338062	−	0.292770i
$561$	31.5959			1.33398
$562$			10.0424i			0.423611i
$563$	4.37628	−	2.52664i	0.184438	−	0.106485i	−0.404938	−	0.914344i	$-0.632707\pi$
$563$	4.37628	−	2.52664i	0.184438	−	0.106485i	0.589376	+	0.807859i	$0.299374\pi$
$564$		−	37.7552i		−	1.58978i
$565$	−1.77526	+	3.07483i	−0.0746855	+	0.129359i
$566$	6.00000	+	10.3923i	0.252199	+	0.436821i
$567$	8.94949	+	46.5029i	0.375843	+	1.95294i
$568$	−4.00000			−0.167836
$569$	8.69694	−	15.0635i	0.364595	−	0.631496i	−0.624116	−	0.781331i	$-0.714541\pi$
$569$	8.69694	−	15.0635i	0.364595	−	0.631496i	0.988711	+	0.149835i	$0.0478742\pi$
$570$	−16.3485	−	9.43879i	−0.684762	−	0.395348i
$571$	−2.77526	−	4.80688i	−0.116141	−	0.201162i	0.802094	−	0.597197i	$-0.203719\pi$
$571$	−2.77526	−	4.80688i	−0.116141	−	0.201162i	−0.918235	+	0.396035i	$0.870386\pi$
$572$	−2.20204	−	3.81405i	−0.0920720	−	0.159473i
$573$	47.5959			1.98835
$574$	8.37117	+	2.89986i	0.349406	+	0.121038i
$575$			1.09638i			0.0457221i
$576$	−27.5959	+	47.7975i	−1.14983	+	1.99156i
$577$	10.6515	−	6.14966i	0.443429	−	0.256014i	−0.261622	−	0.965170i	$-0.584257\pi$
$577$	10.6515	−	6.14966i	0.443429	−	0.256014i	0.705051	+	0.709157i	$0.250924\pi$
$578$	−15.6742	−	9.04952i	−0.651962	−	0.376411i
$579$	−18.2474	−	10.5352i	−0.758338	−	0.437827i
$580$	−17.4495	−	10.0745i	−0.724551	−	0.418319i
$581$	−10.6237	+	30.6681i	−0.440746	+	1.27233i
$582$	19.3485	−	11.1708i	0.802020	−	0.463046i
$583$	−20.6969	−	11.9494i	−0.857180	−	0.494893i
$584$	3.79796	+	6.57826i	0.157161	+	0.272210i
$585$	1.55051	+	2.68556i	0.0641057	+	0.111034i
$586$			34.6410i			1.43101i
$587$			39.9479i			1.64883i	0.565988	+	0.824414i	$0.308495\pi$
$587$			39.9479i			1.64883i	−0.565988	+	0.824414i	$0.691505\pi$
$588$	43.5959	+	6.29253i	1.79787	+	0.259500i
$589$			27.3629i			1.12747i
$590$	14.8990			0.613381
$591$	−34.1464	−	59.1433i	−1.40460	−	2.43283i
$592$	−12.0000	−	6.92820i	−0.493197	−	0.284747i
$593$	−8.57321	−	4.94975i	−0.352060	−	0.203262i	0.313532	−	0.949578i	$-0.398488\pi$
$593$	−8.57321	−	4.94975i	−0.352060	−	0.203262i	−0.665592	+	0.746316i	$0.731821\pi$
$594$	−42.4949	−	73.6033i	−1.74359	−	3.01998i
$595$	−1.77526	+	5.12472i	−0.0727784	+	0.210093i
$596$	−8.75255	−	5.05329i	−0.358518	−	0.206991i
$597$	−12.7980	−	7.38891i	−0.523786	−	0.302408i
$598$	0.348469	−	0.603566i	0.0142500	−	0.0246817i
$599$	23.1464	−	13.3636i	0.945737	−	0.546022i	0.0539832	−	0.998542i	$-0.482808\pi$
$599$	23.1464	−	13.3636i	0.945737	−	0.546022i	0.891754	+	0.452520i	$0.149475\pi$
$600$	4.44949	−	7.70674i	0.181650	−	0.314626i
$601$			8.83523i			0.360396i	0.983630	+	0.180198i	$0.0576739\pi$
$601$			8.83523i			0.360396i	−0.983630	+	0.180198i	$0.942326\pi$
$602$	−5.57321	+	16.0885i	−0.227147	+	0.655718i
$603$	16.2020			0.659798
$604$	−1.34847	+	0.778539i	−0.0548684	+	0.0316783i
$605$	−6.50000	−	11.2583i	−0.264263	−	0.457716i
$606$	−20.5732	+	35.6339i	−0.835730	+	1.44753i
$607$	3.84847	−	6.66574i	0.156205	−	0.270554i	−0.777292	−	0.629139i	$-0.783407\pi$
$607$	3.84847	−	6.66574i	0.156205	−	0.270554i	0.933497	+	0.358585i	$0.116741\pi$
$608$	12.0000	−	20.7846i	0.486664	−	0.842927i
$609$	−15.8485	−	82.3511i	−0.642212	−	3.33703i
$610$	17.5732	−	10.1459i	0.711519	−	0.410795i
$611$	1.34847	−	2.33562i	0.0545532	−	0.0944890i
$612$		−	28.2843i		−	1.14332i
$613$	−6.67423	+	3.85337i	−0.269570	+	0.155636i	−0.628692	−	0.777654i	$-0.716409\pi$
$613$	−6.67423	+	3.85337i	−0.269570	+	0.155636i	0.359122	+	0.933290i	$0.383076\pi$
$614$	44.4495			1.79384
$615$	7.44949			0.300392
$616$	−36.0000	+	6.92820i	−1.45048	+	0.279145i
$617$	32.6969			1.31633			0.658165	−	0.752874i	$-0.271333\pi$
$617$	32.6969			1.31633			0.658165	+	0.752874i	$0.271333\pi$
$618$	−12.4495			−0.500792
$619$	1.34847	−	0.778539i	0.0541996	−	0.0312921i	−0.472655	−	0.881247i	$-0.656704\pi$
$619$	1.34847	−	0.778539i	0.0541996	−	0.0312921i	0.526855	+	0.849955i	$0.323371\pi$
$620$	−12.8990			−0.518035
$621$	6.72474	−	11.6476i	0.269855	−	0.467402i
$622$	−28.3485	+	16.3670i	−1.13667	+	0.656257i
$623$	0.797959	+	0.921404i	0.0319696	+	0.0369153i
$624$	−4.89898	+	2.82843i	−0.196116	+	0.113228i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−19.3485	+	33.5125i	−0.773320	+	1.33943i
$627$	32.6969	+	56.6328i	1.30579	+	2.26169i
$628$	18.6969	+	32.3840i	0.746089	+	1.29226i
$629$	7.10102			0.283136
$630$	25.3485	−	4.87832i	1.00991	−	0.194357i
$631$		−	11.5994i		−	0.461766i	−0.972981	−	0.230883i	$-0.925838\pi$
$631$		−	11.5994i		−	0.461766i	0.972981	−	0.230883i	$-0.0741615\pi$
$632$	1.10102	−	1.90702i	0.0437962	−	0.0758573i
$633$	44.2702	−	25.5594i	1.75958	−	1.01589i
$634$	−14.3485	+	24.8523i	−0.569851	+	0.987010i
$635$	−6.00000	−	3.46410i	−0.238103	−	0.137469i
$636$	−15.3485	+	26.5843i	−0.608606	+	1.05414i
$637$	2.47219	+	1.94635i	0.0979519	+	0.0771171i
$638$	34.8990	+	60.4468i	1.38166	+	2.39311i
$639$	−8.44949	−	4.87832i	−0.334257	−	0.192983i
$640$	9.79796	+	5.65685i	0.387298	+	0.223607i
$641$	−12.6464	−	21.9043i	−0.499504	−	0.865166i	0.500496	−	0.865739i	$-0.333151\pi$
$641$	−12.6464	−	21.9043i	−0.499504	−	0.865166i	−1.00000		0.000572773i	$0.999818\pi$
$642$	−2.44949			−0.0966736
$643$			27.3629i			1.07909i	0.841958	+	0.539543i	$0.181403\pi$
$643$			27.3629i			1.07909i	−0.841958	+	0.539543i	$0.818597\pi$
$644$	−3.79796	−	4.38551i	−0.149661	−	0.172813i
$645$			14.3171i			0.563736i
$646$			12.2993i			0.483911i
$647$	14.2980	+	24.7648i	0.562111	+	0.973604i	0.997312	+	0.0732712i	$0.0233439\pi$
$647$	14.2980	+	24.7648i	0.562111	+	0.973604i	−0.435201	+	0.900333i	$0.643323\pi$
$648$	−43.8434	+	25.3130i	−1.72233	+	0.994388i
$649$	−44.6969	−	25.8058i	−1.75451	−	1.01297i
$650$	0.550510	−	0.317837i	0.0215928	−	0.0124666i
$651$	−35.1464	−	40.5836i	−1.37750	−	1.59060i
$652$	−13.7980	+	23.8988i	−0.540370	+	0.935948i
$653$	19.2247	+	11.0994i	0.752322	+	0.434354i	0.826532	−	0.562889i	$-0.190310\pi$
$653$	19.2247	+	11.0994i	0.752322	+	0.434354i	−0.0742100	+	0.997243i	$0.523644\pi$
$654$	63.0681	+	36.4124i	2.46616	+	1.42384i
$655$	−9.79796	+	5.65685i	−0.382838	+	0.221032i
$656$			9.47090i			0.369777i
$657$			18.5276i			0.722832i
$658$	−14.6969	−	16.9706i	−0.572946	−	0.661581i
$659$	36.7423			1.43128			0.715639	−	0.698470i	$-0.246135\pi$
$659$	36.7423			1.43128			0.715639	+	0.698470i	$0.246135\pi$
$660$	−26.6969	+	15.4135i	−1.03918	+	0.599969i
$661$	11.8712	+	20.5615i	0.461735	+	0.799749i	0.999048	−	0.0436346i	$-0.0138937\pi$
$661$	11.8712	+	20.5615i	0.461735	+	0.799749i	−0.537312	+	0.843383i	$0.680560\pi$
$662$	−38.1464	−	22.0239i	−1.48260	−	0.855981i
$663$	1.44949	−	2.51059i	0.0562935	−	0.0975032i
$664$	−34.6969			−1.34650
$665$	−11.0227	+	2.12132i	−0.427442	+	0.0822613i
$666$	−16.8990	−	29.2699i	−0.654822	−	1.13419i
$667$	−5.52270	+	9.56560i	−0.213840	+	0.370382i
$668$	6.00000			0.232147
$669$	12.7980	−	7.38891i	0.494798	−	0.285672i
$670$		−	3.32124i		−	0.128311i
$671$	−70.2929			−2.71363
$672$	8.89898	+	46.2405i	0.343286	+	1.78376i
$673$	−17.1010			−0.659196			−0.329598	−	0.944121i	$-0.606913\pi$
$673$	−17.1010			−0.659196			−0.329598	+	0.944121i	$0.606913\pi$
$674$		−	6.00680i		−	0.231373i
$675$	10.6237	−	6.13361i	0.408907	−	0.236083i
$676$	25.5959			0.984458
$677$	8.32577	−	14.4206i	0.319985	−	0.554231i	−0.660499	−	0.750827i	$-0.729655\pi$
$677$	8.32577	−	14.4206i	0.319985	−	0.554231i	0.980485	+	0.196596i	$0.0629887\pi$
$678$	−7.89898	−	13.6814i	−0.303358	−	0.525432i
$679$	4.34847	−	12.5529i	0.166879	−	0.481738i
$680$	−5.79796			−0.222342
$681$	−27.6969	+	47.9725i	−1.06135	+	1.83831i
$682$	38.6969	+	22.3417i	1.48178	+	0.855507i
$683$	3.27526	+	5.67291i	0.125324	+	0.217068i	0.921860	−	0.387524i	$-0.126670\pi$
$683$	3.27526	+	5.67291i	0.125324	+	0.217068i	−0.796535	+	0.604592i	$0.793336\pi$
$684$	50.6969	−	29.2699i	1.93845	−	1.11916i
$685$	9.79796			0.374361
$686$	22.0454	−	14.1421i	0.841698	−	0.539949i
$687$		−	39.9479i		−	1.52411i
$688$	−18.2020			−0.693946
$689$	−1.89898	+	1.09638i	−0.0723454	+	0.0417686i
$690$	−4.22474	−	2.43916i	−0.160833	−	0.0928571i
$691$	−27.0000	−	15.5885i	−1.02713	−	0.593013i	−0.110968	−	0.993824i	$-0.535395\pi$
$691$	−27.0000	−	15.5885i	−1.02713	−	0.593013i	−0.916161	+	0.400811i	$0.868728\pi$
$692$	1.10102	−	1.90702i	0.0418545	−	0.0724942i
$693$	−84.4949	−	29.2699i	−3.20970	−	1.11187i
$694$	−27.3712	+	15.8028i	−1.03900	+	0.599864i
$695$	−6.00000	−	3.46410i	−0.227593	−	0.131401i
$696$	77.6413	−	44.8262i	2.94299	−	1.69913i
$697$	−2.42679	−	4.20332i	−0.0919211	−	0.159212i
$698$		−	24.3916i		−	0.923235i
$699$		−	76.2889i		−	2.88551i
$700$	−1.00000	−	5.19615i	−0.0377964	−	0.196396i
$701$		−	13.1886i		−	0.498127i	−0.968487	−	0.249064i	$-0.919877\pi$
$701$		−	13.1886i		−	0.498127i	0.968487	−	0.249064i	$-0.0801229\pi$
$702$	−7.79796			−0.294315
$703$	7.34847	+	12.7279i	0.277153	+	0.480043i
$704$	−19.5959	−	33.9411i	−0.738549	−	1.27920i
$705$	−16.3485	−	9.43879i	−0.615719	−	0.355486i
$706$	−9.65153	−	16.7169i	−0.363240	−	0.629150i
$707$	4.62372	+	24.0256i	0.173893	+	0.903575i
$708$	−33.1464	+	57.4113i	−1.24572	+	2.15765i
$709$	−42.2196	−	24.3755i	−1.58559	−	0.915442i	−0.994021	−	0.109189i	$-0.965175\pi$
$709$	−42.2196	−	24.3755i	−1.58559	−	0.915442i	−0.591571	−	0.806253i	$-0.701492\pi$
$710$	−1.00000	+	1.73205i	−0.0375293	+	0.0650027i
$711$	4.65153	−	2.68556i	0.174446	−	0.100716i
$712$	−0.651531	+	1.12848i	−0.0244171	+	0.0422917i
$713$			7.07107i			0.264814i
$714$	−15.7980	−	18.2419i	−0.591224	−	0.682686i
$715$	−2.20204			−0.0823517
$716$	14.4495	+	25.0273i	0.540003	+	0.935312i
$717$	−27.4722	−	47.5832i	−1.02597	−	1.77703i
$718$	−18.1464	+	31.4305i	−0.677219	+	1.17298i
$719$	−19.5959	+	33.9411i	−0.730804	+	1.26579i	0.225735	+	0.974189i	$0.427522\pi$
$719$	−19.5959	+	33.9411i	−0.730804	+	1.26579i	−0.956540	+	0.291602i	$0.905812\pi$
$720$	13.7980	+	23.8988i	0.514220	+	0.890654i
$721$	−5.59592	+	4.84621i	−0.208403	+	0.180482i
$722$	1.22474	−	0.707107i	0.0455803	−	0.0263158i
$723$	−21.2474	+	36.8017i	−0.790201	+	1.36867i
$724$	−4.69694			−0.174560
$725$	−8.72474	+	5.03723i	−0.324029	+	0.187078i
$726$	57.8434			2.14677
$727$	−24.5959			−0.912212			−0.456106	−	0.889925i	$-0.650756\pi$
$727$	−24.5959			−0.912212			−0.456106	+	0.889925i	$0.650756\pi$
$728$	−1.10102	+	3.17837i	−0.0408065	+	0.117798i
$729$	−7.69694			−0.285072
$730$	3.79796			0.140569
$731$	8.07832	−	4.66402i	0.298787	−	0.172505i
$732$			90.2882i			3.33715i
$733$	−13.4495	+	23.2952i	−0.496768	+	0.860428i	−0.999993	−	0.00372771i	$-0.998813\pi$
$733$	−13.4495	+	23.2952i	−0.496768	+	0.860428i	0.503225	+	0.864156i	$0.332147\pi$
$734$	21.9217	−	12.6565i	0.809144	−	0.467160i
$735$	13.6237	−	17.3045i	0.502519	−	0.638284i
$736$	3.10102	−	5.37113i	0.114305	−	0.197982i
$737$	−5.75255	+	9.96371i	−0.211898	+	0.367018i
$738$	−11.5505	+	20.0061i	−0.425180	+	0.736434i
$739$	−14.3485	−	24.8523i	−0.527817	−	0.914206i	−0.999474	−	0.0324238i	$-0.989677\pi$
$739$	−14.3485	−	24.8523i	−0.527817	−	0.914206i	0.471657	−	0.881782i	$-0.343656\pi$
$740$	−6.00000	+	3.46410i	−0.220564	+	0.127343i
$741$	6.00000			0.220416
$742$	3.44949	+	17.9241i	0.126635	+	0.658013i
$743$		−	28.5235i		−	1.04642i	−0.852202	−	0.523212i	$-0.824734\pi$
$743$		−	28.5235i		−	1.04642i	0.852202	−	0.523212i	$-0.175266\pi$
$744$	28.6969	−	49.7046i	1.05208	−	1.82226i
$745$	−4.37628	+	2.52664i	−0.160334	+	0.0925691i
$746$	12.2474	−	21.2132i	0.448411	−	0.776671i
$747$	−73.2929	−	42.3157i	−2.68165	−	1.54825i
$748$	17.3939	+	10.0424i	0.635983	+	0.367185i
$749$	−1.10102	+	0.953512i	−0.0402304	+	0.0348406i
$750$	−2.22474	−	3.85337i	−0.0812362	−	0.140705i
$751$	1.04541	+	0.603566i	0.0381475	+	0.0220245i	0.518952	−	0.854803i	$-0.326322\pi$
$751$	1.04541	+	0.603566i	0.0381475	+	0.0220245i	−0.480805	+	0.876828i	$0.659655\pi$
$752$	12.0000	−	20.7846i	0.437595	−	0.757937i
$753$	43.8207	+	75.8996i	1.59691	+	2.76594i
$754$	6.40408			0.233223
$755$			0.778539i			0.0283339i
$756$	−21.2474	+	61.3361i	−0.772762	+	2.23077i
$757$			8.05669i			0.292825i	0.989224	+	0.146413i	$0.0467727\pi$
$757$			8.05669i			0.292825i	−0.989224	+	0.146413i	$0.953227\pi$
$758$		−	3.74983i		−	0.136200i
$759$	8.44949	+	14.6349i	0.306697	+	0.531215i
$760$	−6.00000	−	10.3923i	−0.217643	−	0.376969i
$761$	−28.5959	−	16.5099i	−1.03660	−	0.598482i	−0.117732	−	0.993045i	$-0.537563\pi$
$761$	−28.5959	−	16.5099i	−1.03660	−	0.598482i	−0.918869	+	0.394563i	$0.870896\pi$
$762$	26.6969	−	15.4135i	0.967128	−	0.558372i
$763$	42.5227	−	8.18350i	1.53943	−	0.296263i
$764$	26.2020	+	15.1278i	0.947957	+	0.547303i
$765$	−12.2474	−	7.07107i	−0.442807	−	0.255655i
$766$	−30.3712	−	17.5348i	−1.09736	−	0.633558i
$767$	−4.10102	+	2.36773i	−0.148079	+	0.0854936i
$768$	−43.5959	+	25.1701i	−1.57313	+	0.908248i
$769$			29.6198i			1.06812i	0.845447	+	0.534059i	$0.179334\pi$
$769$			29.6198i			1.06812i	−0.845447	+	0.534059i	$0.820666\pi$
$770$	−6.00000	+	17.3205i	−0.216225	+	0.624188i
$771$	23.7980			0.857063
$772$	−6.69694	−	11.5994i	−0.241028	−	0.417473i
$773$	−18.1237	−	31.3912i	−0.651865	−	1.12906i	−0.982670	−	0.185364i	$-0.940654\pi$
$773$	−18.1237	−	31.3912i	−0.651865	−	1.12906i	0.330805	−	0.943699i	$-0.392680\pi$
$774$	−38.4495	−	22.1988i	−1.38204	−	0.797920i
$775$	−3.22474	+	5.58542i	−0.115836	+	0.200634i
$776$	14.2020			0.509824
$777$	−27.2474	−	9.43879i	−0.977497	−	0.338615i
$778$	8.00000	+	13.8564i	0.286814	+	0.496776i
$779$	5.02270	−	8.69958i	0.179957	−	0.311695i
$780$			2.82843i			0.101274i
$781$	6.00000	−	3.46410i	0.214697	−	0.123955i
$782$			3.17837i			0.113658i
$783$	123.586			4.41659
$784$	22.0000	+	17.3205i	0.785714	+	0.618590i
$785$	18.6969			0.667322
$786$		−	50.3402i		−	1.79558i
$787$	28.8712	−	16.6688i	1.02915	−	0.594178i	0.112406	−	0.993662i	$-0.464144\pi$
$787$	28.8712	−	16.6688i	1.02915	−	0.594178i	0.916740	+	0.399485i	$0.130811\pi$
$788$		−	43.4120i		−	1.54649i
$789$	35.8712	−	62.1307i	1.27705	−	2.21191i
$790$	−0.550510	−	0.953512i	−0.0195863	−	0.0339244i
$791$	−8.87628	−	3.07483i	−0.315604	−	0.109328i
$792$		−	95.5951i		−	3.39682i
$793$	−3.22474	+	5.58542i	−0.114514	+	0.198344i
$794$	35.1464	+	20.2918i	1.24730	+	0.720129i
$795$	7.67423	+	13.2922i	0.272177	+	0.471424i
$796$	−4.69694	−	8.13534i	−0.166479	−	0.288349i
$797$	−32.6969			−1.15818			−0.579092	−	0.815262i	$-0.696593\pi$
$797$	−32.6969			−1.15818			−0.579092	+	0.815262i	$0.696593\pi$
$798$	16.3485	−	47.1940i	0.578730	−	1.67065i
$799$			12.2993i			0.435119i
$800$	4.89898	−	2.82843i	0.173205	−	0.100000i
$801$	−2.75255	+	1.58919i	−0.0972566	+	0.0561511i
$802$	13.7196	+	7.92104i	0.484457	+	0.279702i
$803$	−11.3939	−	6.57826i	−0.402081	−	0.232142i
$804$	12.7980	+	7.38891i	0.451349	+	0.260587i
$805$	−2.84847	+	0.548188i	−0.100395	+	0.0193211i
$806$	3.55051	−	2.04989i	0.125061	−	0.0722042i
$807$	4.50000	+	2.59808i	0.158408	+	0.0914566i
$808$	−22.6515	+	13.0779i	−0.796878	+	0.460078i
$809$	−3.39898	−	5.88721i	−0.119502	−	0.206983i	0.800069	−	0.599909i	$-0.204796\pi$
$809$	−3.39898	−	5.88721i	−0.119502	−	0.206983i	−0.919570	+	0.392925i	$0.871463\pi$
$810$			25.3130i			0.889407i
$811$			21.9131i			0.769473i	0.923026	+	0.384736i	$0.125708\pi$
$811$			21.9131i			0.769473i	−0.923026	+	0.384736i	$0.874292\pi$
$812$	17.4495	−	50.3723i	0.612357	−	1.76772i
$813$		−	35.7053i		−	1.25224i
$814$	24.0000			0.841200
$815$	6.89898	+	11.9494i	0.241661	+	0.418569i
$816$	12.8990	−	22.3417i	0.451555	−	0.782116i
$817$	16.7196	+	9.65309i	0.584946	+	0.337719i
$818$	15.6742	+	27.1486i	0.548037	+	0.949228i
$819$	−6.20204	+	5.37113i	−0.216717	+	0.187682i
$820$	4.10102	+	2.36773i	0.143214	+	0.0826846i
$821$	25.2929	+	14.6028i	0.882727	+	0.509643i	0.871557	−	0.490295i	$-0.163111\pi$
$821$	25.2929	+	14.6028i	0.882727	+	0.509643i	0.0111703	+	0.999938i	$0.496444\pi$
$822$	−21.7980	+	37.7552i	−0.760291	+	1.31686i
$823$	23.8485	−	13.7689i	0.831305	−	0.479954i	−0.0229940	−	0.999736i	$-0.507320\pi$
$823$	23.8485	−	13.7689i	0.831305	−	0.479954i	0.854299	+	0.519781i	$0.173987\pi$
$824$	−6.85357	−	3.95691i	−0.238755	−	0.137846i
$825$			15.4135i			0.536629i
$826$	7.44949	+	38.7087i	0.259201	+	1.34685i
$827$	31.0454			1.07955			0.539777	−	0.841808i	$-0.318508\pi$
$827$	31.0454			1.07955			0.539777	+	0.841808i	$0.318508\pi$
$828$	13.1010	−	7.56388i	0.455292	−	0.262863i
$829$	−27.3485	−	47.3689i	−0.949852	−	1.64519i	−0.745733	−	0.666245i	$-0.767900\pi$
$829$	−27.3485	−	47.3689i	−0.949852	−	1.64519i	−0.204119	−	0.978946i	$-0.565433\pi$
$830$	−8.67423	+	15.0242i	−0.301087	+	0.521498i
$831$	30.9217	−	53.5579i	1.07266	−	1.85790i
$832$	−3.59592			−0.124666
$833$	−14.2020	−	2.04989i	−0.492072	−	0.0710244i
$834$	26.6969	−	15.4135i	0.924439	−	0.533725i
$835$	1.50000	−	2.59808i	0.0519096	−	0.0899101i
$836$			41.5692i			1.43770i
$837$	68.5176	−	39.5587i	2.36831	−	1.36735i
$838$	−15.5959			−0.538752
$839$	18.4949			0.638515			0.319257	−	0.947668i	$-0.396567\pi$
$839$	18.4949			0.638515			0.319257	+	0.947668i	$0.396567\pi$
$840$	22.2474	+	7.70674i	0.767610	+	0.265908i
$841$	−72.4949			−2.49982
$842$	30.2474			1.04240
$843$	−19.3485	+	11.1708i	−0.666397	+	0.384744i
$844$	32.4949			1.11852
$845$	6.39898	−	11.0834i	0.220132	−	0.381279i
$846$	50.6969	−	29.2699i	1.74300	−	1.00632i
$847$	26.0000	−	22.5167i	0.893371	−	0.773682i
$848$	−16.8990	+	9.75663i	−0.580313	+	0.335044i
$849$	−13.3485	+	23.1202i	−0.458118	+	0.793484i
$850$	−1.44949	+	2.51059i	−0.0497171	+	0.0861125i
$851$	1.89898	+	3.28913i	0.0650962	+	0.112750i
$852$	−4.44949	−	7.70674i	−0.152437	−	0.264029i
$853$	43.5505			1.49114			0.745571	−	0.666427i	$-0.232177\pi$
$853$	43.5505			1.49114			0.745571	+	0.666427i	$0.232177\pi$
$854$	35.1464	+	40.5836i	1.20269	+	1.38874i
$855$		−	29.2699i		−	1.00101i
$856$	−1.34847	−	0.778539i	−0.0460897	−	0.0266099i
$857$	−30.1918	+	17.4313i	−1.03133	+	0.595441i	−0.917366	−	0.398044i	$-0.869689\pi$
$857$	−30.1918	+	17.4313i	−1.03133	+	0.595441i	−0.113967	+	0.993485i	$0.536356\pi$
$858$	4.89898	−	8.48528i	0.167248	−	0.289683i
$859$	21.0000	+	12.1244i	0.716511	+	0.413678i	0.813467	−	0.581611i	$-0.197577\pi$
$859$	21.0000	+	12.1244i	0.716511	+	0.413678i	−0.0969563	+	0.995289i	$0.530911\pi$
$860$	−4.55051	+	7.88171i	−0.155171	+	0.268764i
$861$	3.72474	+	19.3543i	0.126939	+	0.659594i
$862$	22.6969	+	39.3123i	0.773061	+	1.33898i
$863$	−6.94949	−	4.01229i	−0.236563	−	0.136580i	0.377033	−	0.926200i	$-0.376944\pi$
$863$	−6.94949	−	4.01229i	−0.236563	−	0.136580i	−0.613596	+	0.789620i	$0.710278\pi$
$864$	−69.3939			−2.36083
$865$	−0.550510	−	0.953512i	−0.0187179	−	0.0324204i
$866$	−1.10102			−0.0374142
$867$		−	40.2658i		−	1.36750i
$868$	−6.44949	−	33.5125i	−0.218910	−	1.13749i
$869$			3.81405i			0.129383i
$870$		−	44.8262i		−	1.51975i
$871$	0.527806	+	0.914188i	0.0178840	+	0.0309761i
$872$	23.1464	+	40.0908i	0.783837	+	1.35765i
$873$	30.0000	+	17.3205i	1.01535	+	0.586210i
$874$	−5.69694	+	3.28913i	−0.192702	+	0.111256i
$875$	−2.50000	−	0.866025i	−0.0845154	−	0.0292770i
$876$	−8.44949	+	14.6349i	−0.285482	+	0.494469i
$877$	49.7196	+	28.7056i	1.67891	+	0.969321i	0.962356	+	0.271792i	$0.0876164\pi$
$877$	49.7196	+	28.7056i	1.67891	+	0.969321i	0.716557	+	0.697528i	$0.245717\pi$
$878$	−25.5959	−	14.7778i	−0.863820	−	0.498727i
$879$	−66.7423	+	38.5337i	−2.25116	+	1.29971i
$880$	−19.5959			−0.660578
$881$		−	8.37452i		−	0.282145i	−0.989999	−	0.141072i	$-0.954945\pi$
$881$		−	8.37452i		−	0.282145i	0.989999	−	0.141072i	$-0.0450551\pi$
$882$	25.3485	+	63.4181i	0.853527	+	2.13540i
$883$	8.49490			0.285876			0.142938	−	0.989732i	$-0.454345\pi$
$883$	8.49490			0.285876			0.142938	+	0.989732i	$0.454345\pi$
$884$	1.59592	−	0.921404i	0.0536765	−	0.0309902i
$885$	16.5732	+	28.7056i	0.557102	+	0.964930i
$886$	2.02270	+	1.16781i	0.0679541	+	0.0392333i
$887$	−13.5000	+	23.3827i	−0.453286	+	0.785114i	−0.998588	−	0.0531258i	$-0.983082\pi$
$887$	−13.5000	+	23.3827i	−0.453286	+	0.785114i	0.545302	+	0.838240i	$0.316415\pi$
$888$		−	30.8270i		−	1.03449i
$889$	6.00000	−	17.3205i	0.201234	−	0.580911i
$890$	0.325765	+	0.564242i	0.0109197	+	0.0189134i
$891$	43.8434	−	75.9389i	1.46881	−	2.54405i
$892$	9.39388			0.314530
$893$	−22.0454	+	12.7279i	−0.737721	+	0.425924i
$894$		−	22.4846i		−	0.751996i
$895$	14.4495			0.482993
$896$	−9.79796	+	28.2843i	−0.327327	+	0.944911i
$897$	1.55051			0.0517700
$898$		−	57.4113i		−	1.91584i
$899$	−56.2702	+	32.4876i	−1.87671	+	1.08352i
$900$	13.7980			0.459932
$901$	5.00000	−	8.66025i	0.166574	−	0.288515i
$902$	−8.20204	−	14.2064i	−0.273098	−	0.473020i
$903$	−37.1969	+	7.15855i	−1.23784	+	0.238222i
$904$		−	10.0424i		−	0.334004i
$905$	−1.17423	+	2.03383i	−0.0390329	+	0.0676069i
$906$	−3.00000	−	1.73205i	−0.0996683	−	0.0575435i
$907$	−3.17423	−	5.49794i	−0.105399	−	0.182556i	0.808502	−	0.588493i	$-0.200279\pi$
$907$	−3.17423	−	5.49794i	−0.105399	−	0.182556i	−0.913901	+	0.405937i	$0.866945\pi$
$908$	−30.4949	+	17.6062i	−1.01201	+	0.584284i
$909$	−63.7980			−2.11604
$910$	1.10102	+	1.27135i	0.0364985	+	0.0421448i
$911$		−	20.7204i		−	0.686497i	−0.939245	−	0.343249i	$-0.888473\pi$
$911$		−	20.7204i		−	0.686497i	0.939245	−	0.343249i	$-0.111527\pi$
$912$	53.3939			1.76805
$913$	52.0454	−	30.0484i	1.72245	−	0.994458i
$914$	36.2474	+	20.9275i	1.19896	+	0.692219i
$915$	39.0959	+	22.5720i	1.29247	+	0.746209i
$916$	12.6969	−	21.9917i	0.419519	−	0.726628i
$917$	−19.5959	−	22.6274i	−0.647114	−	0.747223i
$918$	30.7980	−	17.7812i	1.01648	−	0.586867i
$919$	24.3712	+	14.0707i	0.803931	+	0.464150i	0.844844	−	0.535013i	$-0.179693\pi$
$919$	24.3712	+	14.0707i	0.803931	+	0.464150i	−0.0409130	+	0.999163i	$0.513027\pi$
$920$	−1.55051	−	2.68556i	−0.0511188	−	0.0885404i
$921$	49.4444	+	85.6402i	1.62925	+	2.82194i
$922$		−	13.1565i		−	0.433287i
$923$		−	0.635674i		−	0.0209235i
$924$	−53.3939	−	61.6539i	−1.75653	−	2.02827i
$925$			3.46410i			0.113899i
$926$	−17.1464			−0.563467
$927$	−9.65153	−	16.7169i	−0.316998	−	0.549056i
$928$	56.9898			1.87078
$929$	14.2980	+	8.25493i	0.469101	+	0.270835i	0.715863	−	0.698241i	$-0.246033\pi$
$929$	14.2980	+	8.25493i	0.469101	+	0.270835i	−0.246762	+	0.969076i	$0.579367\pi$
$930$	−14.3485	−	24.8523i	−0.470505	−	0.814938i
$931$	−11.0227	−	27.5772i	−0.361255	−	0.903805i
$932$	24.2474	−	41.9978i	0.794252	−	1.37568i
$933$	−63.0681	−	36.4124i	−2.06476	−	1.19209i
$934$	6.02270	−	10.4316i	0.197069	−	0.341333i
$935$	8.69694	−	5.02118i	0.284420	−	0.164210i
$936$	−7.59592	−	4.38551i	−0.248280	−	0.143345i
$937$			23.8988i			0.780739i	0.920658	+	0.390369i	$0.127653\pi$
$937$			23.8988i			0.780739i	−0.920658	+	0.390369i	$0.872347\pi$
$938$	8.62883	−	1.66062i	0.281741	−	0.0542211i
$939$	−86.0908			−2.80947
$940$	−6.00000	−	10.3923i	−0.195698	−	0.338960i
$941$	1.89898	+	3.28913i	0.0619050	+	0.107223i	0.895317	−	0.445430i	$-0.146949\pi$
$941$	1.89898	+	3.28913i	0.0619050	+	0.107223i	−0.833412	+	0.552652i	$0.813616\pi$
$942$	−41.5959	+	72.0462i	−1.35527	+	2.34739i
$943$	1.29796	−	2.24813i	0.0422674	−	0.0732092i
$944$	−36.4949	+	21.0703i	−1.18781	+	0.685781i
$945$	21.2474	+	24.5344i	0.691180	+	0.798105i
$946$	27.3031	−	15.7634i	0.887699	−	0.512513i
$947$	−21.2753	+	36.8498i	−0.691353	+	1.19746i	0.280042	+	0.959988i	$0.409652\pi$
$947$	−21.2753	+	36.8498i	−0.691353	+	1.19746i	−0.971395	+	0.237471i	$0.923682\pi$
$948$	4.89898			0.159111
$949$	−1.04541	+	0.603566i	−0.0339354	+	0.0195926i
$950$	−6.00000			−0.194666
$951$	−63.8434			−2.07026
$952$	−2.89898	−	15.0635i	−0.0939565	−	0.488212i
$953$	−1.10102			−0.0356656			−0.0178328	−	0.999841i	$-0.505677\pi$
$953$	−1.10102			−0.0356656			−0.0178328	+	0.999841i	$0.505677\pi$
$954$	−47.5959			−1.54097
$955$	13.1010	−	7.56388i	0.423939	−	0.244761i
$956$		−	34.9267i		−	1.12961i
$957$	−77.6413	+	134.479i	−2.50979	+	4.34708i
$958$	4.34847	−	2.51059i	0.140493	−	0.0811135i
$959$	4.89898	+	25.4558i	0.158196	+	0.822012i
$960$			25.1701i			0.812362i
$961$	−5.29796	+	9.17633i	−0.170902	+	0.296011i
$962$	1.10102	−	1.90702i	0.0354983	−	0.0614849i
$963$	−1.89898	−	3.28913i	−0.0611938	−	0.105991i
$964$	−23.3939	+	13.5065i	−0.753466	+	0.435014i
$965$	−6.69694			−0.215582
$966$	4.22474	−	12.1958i	0.135929	−	0.392393i
$967$			49.1796i			1.58151i	0.612132	+	0.790755i	$0.290312\pi$
$967$			49.1796i			1.58151i	−0.612132	+	0.790755i	$0.709688\pi$
$968$	31.8434	+	18.3848i	1.02348	+	0.590909i
$969$	−23.6969	+	13.6814i	−0.761255	+	0.439511i
$970$	3.55051	−	6.14966i	0.114000	−	0.197454i
$971$	8.14643	+	4.70334i	0.261431	+	0.150937i	0.624987	−	0.780635i	$-0.285104\pi$
$971$	8.14643	+	4.70334i	0.261431	+	0.150937i	−0.363556	+	0.931572i	$0.618437\pi$
$972$	−33.7980	−	19.5133i	−1.08407	−	0.625888i
$973$	6.00000	−	17.3205i	0.192351	−	0.555270i
$974$	−26.4495	−	45.8119i	−0.847496	−	1.46791i
$975$	1.22474	+	0.707107i	0.0392232	+	0.0226455i
$976$	−28.6969	+	49.7046i	−0.918567	+	1.59100i
$977$	−14.6969	−	25.4558i	−0.470197	−	0.814405i	0.529222	−	0.848483i	$-0.322484\pi$
$977$	−14.6969	−	25.4558i	−0.470197	−	0.814405i	−0.999419	+	0.0340785i	$0.989150\pi$
$978$	−61.3939			−1.96316
$979$		−	2.25697i		−	0.0721330i
$980$	13.0000	−	5.19615i	0.415270	−	0.165985i
$981$			112.916i			3.60512i
$982$			49.7046i			1.58614i
$983$	−7.50000	−	12.9904i	−0.239213	−	0.414329i	0.721276	−	0.692648i	$-0.243556\pi$
$983$	−7.50000	−	12.9904i	−0.239213	−	0.414329i	−0.960489	+	0.278319i	$0.910223\pi$
$984$	−18.2474	+	10.5352i	−0.581707	+	0.335849i
$985$	−18.7980	−	10.8530i	−0.598953	−	0.345806i
$986$	−25.2929	+	14.6028i	−0.805489	+	0.465049i
$987$	16.3485	−	47.1940i	0.520378	−	1.50220i
$988$	3.30306	+	1.90702i	0.105084	+	0.0606705i
$989$	4.32066	+	2.49454i	0.137389	+	0.0793216i
$990$	−41.3939	−	23.8988i	−1.31558	−	0.759553i
$991$	−25.7196	+	14.8492i	−0.817011	+	0.471702i	−0.849385	−	0.527774i	$-0.823027\pi$
$991$	−25.7196	+	14.8492i	−0.817011	+	0.471702i	0.0323734	+	0.999476i	$0.489693\pi$
$992$	31.5959	−	18.2419i	1.00317	−	0.579181i
$993$		−	97.9949i		−	3.10977i
$994$	−5.00000	−	1.73205i	−0.158590	−	0.0549373i
$995$	−4.69694			−0.148903
$996$	−38.5959	−	66.8501i	−1.22296	−	2.11823i
$997$	−20.6742	−	35.8088i	−0.654760	−	1.13408i	−0.981954	−	0.189120i	$-0.939437\pi$
$997$	−20.6742	−	35.8088i	−0.654760	−	1.13408i	0.327194	−	0.944957i	$-0.393897\pi$
$998$	−38.4495	−	22.1988i	−1.21710	−	0.702691i
$999$	21.2474	−	36.8017i	0.672240	−	1.16435i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.bj.b.131.2	✓	4
4.3	odd	2		1120.2.bz.b.271.2		4
7.3	odd	6		280.2.bj.c.171.1	yes	4
8.3	odd	2		280.2.bj.c.131.1	yes	4
8.5	even	2		1120.2.bz.c.271.2		4
28.3	even	6		1120.2.bz.c.591.2		4
56.3	even	6	inner	280.2.bj.b.171.1	yes	4
56.45	odd	6		1120.2.bz.b.591.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bj.b.131.2	✓	4	1.1	even	1	trivial
280.2.bj.b.171.1	yes	4	56.3	even	6	inner
280.2.bj.c.131.1	yes	4	8.3	odd	2
280.2.bj.c.171.1	yes	4	7.3	odd	6
1120.2.bz.b.271.2		4	4.3	odd	2
1120.2.bz.b.591.2		4	56.45	odd	6
1120.2.bz.c.271.2		4	8.5	even	2
1120.2.bz.c.591.2		4	28.3	even	6

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} +(-2.72474 + 1.57313i) q^{3} -2.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.22474 - 3.85337i) q^{6} +(-2.50000 - 0.866025i) q^{7} -2.82843i q^{8} +(3.44949 - 5.97469i) q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} +(-2.72474 + 1.57313i) q^{3} -2.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.22474 - 3.85337i) q^{6} +(-2.50000 - 0.866025i) q^{7} -2.82843i q^{8} +(3.44949 - 5.97469i) q^{9} +(-1.22474 - 0.707107i) q^{10} +(2.44949 + 4.24264i) q^{11} +(5.44949 - 3.14626i) q^{12} +0.449490 q^{13} +(1.22474 - 3.53553i) q^{14} -3.14626i q^{15} +4.00000 q^{16} +(-1.77526 + 1.02494i) q^{17} +(8.44949 + 4.87832i) q^{18} +(-3.67423 - 2.12132i) q^{19} +(1.00000 - 1.73205i) q^{20} +(8.17423 - 1.57313i) q^{21} +(-6.00000 + 3.46410i) q^{22} +(-0.949490 - 0.548188i) q^{23} +(4.44949 + 7.70674i) q^{24} +(-0.500000 - 0.866025i) q^{25} +0.635674i q^{26} +12.2672i q^{27} +(5.00000 + 1.73205i) q^{28} -10.0745i q^{29} +4.44949 q^{30} +(-3.22474 - 5.58542i) q^{31} +5.65685i q^{32} +(-13.3485 - 7.70674i) q^{33} +(-1.44949 - 2.51059i) q^{34} +(2.00000 - 1.73205i) q^{35} +(-6.89898 + 11.9494i) q^{36} +(-3.00000 - 1.73205i) q^{37} +(3.00000 - 5.19615i) q^{38} +(-1.22474 + 0.707107i) q^{39} +(2.44949 + 1.41421i) q^{40} +2.36773i q^{41} +(2.22474 + 11.5601i) q^{42} -4.55051 q^{43} +(-4.89898 - 8.48528i) q^{44} +(3.44949 + 5.97469i) q^{45} +(0.775255 - 1.34278i) q^{46} +(3.00000 - 5.19615i) q^{47} +(-10.8990 + 6.29253i) q^{48} +(5.50000 + 4.33013i) q^{49} +(1.22474 - 0.707107i) q^{50} +(3.22474 - 5.58542i) q^{51} -0.898979 q^{52} +(-4.22474 + 2.43916i) q^{53} -17.3485 q^{54} -4.89898 q^{55} +(-2.44949 + 7.07107i) q^{56} +13.3485 q^{57} +14.2474 q^{58} +(-9.12372 + 5.26758i) q^{59} +6.29253i q^{60} +(-7.17423 + 12.4261i) q^{61} +(7.89898 - 4.56048i) q^{62} +(-13.7980 + 11.9494i) q^{63} -8.00000 q^{64} +(-0.224745 + 0.389270i) q^{65} +(10.8990 - 18.8776i) q^{66} +(1.17423 + 2.03383i) q^{67} +(3.55051 - 2.04989i) q^{68} +3.44949 q^{69} +(2.44949 + 2.82843i) q^{70} -1.41421i q^{71} +(-16.8990 - 9.75663i) q^{72} +(-2.32577 + 1.34278i) q^{73} +(2.44949 - 4.24264i) q^{74} +(2.72474 + 1.57313i) q^{75} +(7.34847 + 4.24264i) q^{76} +(-2.44949 - 12.7279i) q^{77} +(-1.00000 - 1.73205i) q^{78} +(0.674235 + 0.389270i) q^{79} +(-2.00000 + 3.46410i) q^{80} +(-8.94949 - 15.5010i) q^{81} -3.34847 q^{82} -12.2672i q^{83} +(-16.3485 + 3.14626i) q^{84} -2.04989i q^{85} -6.43539i q^{86} +(15.8485 + 27.4504i) q^{87} +(12.0000 - 6.92820i) q^{88} +(-0.398979 - 0.230351i) q^{89} +(-8.44949 + 4.87832i) q^{90} +(-1.12372 - 0.389270i) q^{91} +(1.89898 + 1.09638i) q^{92} +(17.5732 + 10.1459i) q^{93} +(7.34847 + 4.24264i) q^{94} +(3.67423 - 2.12132i) q^{95} +(-8.89898 - 15.4135i) q^{96} +5.02118i q^{97} +(-6.12372 + 7.77817i) q^{98} +33.7980 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{3} - 8 q^{4} - 2 q^{5} - 4 q^{6} - 10 q^{7} + 4 q^{9}+O(q^{10}) \) 4 * q - 6 * q^3 - 8 * q^4 - 2 * q^5 - 4 * q^6 - 10 * q^7 + 4 * q^9	\( 4 q - 6 q^{3} - 8 q^{4} - 2 q^{5} - 4 q^{6} - 10 q^{7} + 4 q^{9} + 12 q^{12} - 8 q^{13} + 16 q^{16} - 12 q^{17} + 24 q^{18} + 4 q^{20} + 18 q^{21} - 24 q^{22} + 6 q^{23} + 8 q^{24} - 2 q^{25} + 20 q^{28} + 8 q^{30} - 8 q^{31} - 24 q^{33} + 4 q^{34} + 8 q^{35} - 8 q^{36} - 12 q^{37} + 12 q^{38} + 4 q^{42} - 28 q^{43} + 4 q^{45} + 8 q^{46} + 12 q^{47} - 24 q^{48} + 22 q^{49} + 8 q^{51} + 16 q^{52} - 12 q^{53} - 40 q^{54} + 24 q^{57} + 8 q^{58} - 12 q^{59} - 14 q^{61} + 12 q^{62} - 16 q^{63} - 32 q^{64} + 4 q^{65} + 24 q^{66} - 10 q^{67} + 24 q^{68} + 4 q^{69} - 48 q^{72} - 24 q^{73} + 6 q^{75} - 4 q^{78} - 12 q^{79} - 8 q^{80} - 26 q^{81} + 16 q^{82} - 36 q^{84} + 34 q^{87} + 48 q^{88} + 18 q^{89} - 24 q^{90} + 20 q^{91} - 12 q^{92} + 36 q^{93} - 16 q^{96} + 96 q^{99}+O(q^{100}) \) 4 * q - 6 * q^3 - 8 * q^4 - 2 * q^5 - 4 * q^6 - 10 * q^7 + 4 * q^9 + 12 * q^12 - 8 * q^13 + 16 * q^16 - 12 * q^17 + 24 * q^18 + 4 * q^20 + 18 * q^21 - 24 * q^22 + 6 * q^23 + 8 * q^24 - 2 * q^25 + 20 * q^28 + 8 * q^30 - 8 * q^31 - 24 * q^33 + 4 * q^34 + 8 * q^35 - 8 * q^36 - 12 * q^37 + 12 * q^38 + 4 * q^42 - 28 * q^43 + 4 * q^45 + 8 * q^46 + 12 * q^47 - 24 * q^48 + 22 * q^49 + 8 * q^51 + 16 * q^52 - 12 * q^53 - 40 * q^54 + 24 * q^57 + 8 * q^58 - 12 * q^59 - 14 * q^61 + 12 * q^62 - 16 * q^63 - 32 * q^64 + 4 * q^65 + 24 * q^66 - 10 * q^67 + 24 * q^68 + 4 * q^69 - 48 * q^72 - 24 * q^73 + 6 * q^75 - 4 * q^78 - 12 * q^79 - 8 * q^80 - 26 * q^81 + 16 * q^82 - 36 * q^84 + 34 * q^87 + 48 * q^88 + 18 * q^89 - 24 * q^90 + 20 * q^91 - 12 * q^92 + 36 * q^93 - 16 * q^96 + 96 * q^99

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