LMFDB - Embedded newform 280.2.bj.c.131.1

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:	$0$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.1
Root			$-1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	280.131
Dual form			280.2.bj.c.171.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 + 0.707107i) q^{2} +(-2.72474 + 1.57313i) q^{3} +(1.00000 - 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +(2.22474 - 3.85337i) q^{6} +(2.50000 + 0.866025i) q^{7} +2.82843i q^{8} +(3.44949 - 5.97469i) q^{9} +O(q^{10})$	\(q+(-1.22474 + 0.707107i) q^{2} +(-2.72474 + 1.57313i) q^{3} +(1.00000 - 1.73205i) 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} +1.41421i q^{10} +(2.44949 + 4.24264i) q^{11} +6.29253i q^{12} -0.449490 q^{13} +(-3.67423 + 0.707107i) q^{14} +3.14626i q^{15} +(-2.00000 - 3.46410i) q^{16} +(-1.77526 + 1.02494i) q^{17} +9.75663i 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} +(0.550510 - 0.317837i) q^{26} +12.2672i q^{27} +(4.00000 - 3.46410i) q^{28} +10.0745i q^{29} +(-2.22474 - 3.85337i) q^{30} +(3.22474 + 5.58542i) q^{31} +(4.89898 + 2.82843i) 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} +6.00000 q^{38} +(1.22474 - 0.707107i) q^{39} +(2.44949 + 1.41421i) q^{40} +2.36773i q^{41} +(8.89898 - 7.70674i) q^{42} -4.55051 q^{43} +9.79796 q^{44} +(-3.44949 - 5.97469i) q^{45} -1.55051 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} +(-0.449490 + 0.778539i) q^{52} +(4.22474 - 2.43916i) q^{53} +(-8.67423 - 15.0242i) q^{54} +4.89898 q^{55} +(-2.44949 + 7.07107i) q^{56} +13.3485 q^{57} +(-7.12372 - 12.3387i) q^{58} +(-9.12372 + 5.26758i) q^{59} +(5.44949 + 3.14626i) 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} +21.7980 q^{66} +(1.17423 + 2.03383i) q^{67} +4.09978i q^{68} -3.44949 q^{69} +(-1.22474 + 3.53553i) q^{70} +1.41421i q^{71} +(16.8990 + 9.75663i) q^{72} +(-2.32577 + 1.34278i) q^{73} -4.89898 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} -4.00000 q^{80} +(-8.94949 - 15.5010i) q^{81} +(-1.67423 - 2.89986i) q^{82} -12.2672i q^{83} +(-5.44949 + 15.7313i) q^{84} +2.04989i q^{85} +(5.57321 - 3.21770i) 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} -8.48528i q^{94} +(-3.67423 + 2.12132i) q^{95} -17.7980 q^{96} +5.02118i q^{97} +(-9.79796 - 1.41421i) q^{98} +33.7980 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{3} + 4 q^{4} + 2 q^{5} + 4 q^{6} + 10 q^{7} + 4 q^{9}+O(q^{10}) $ 4 * q - 6 * q^3 + 4 * q^4 + 2 * q^5 + 4 * q^6 + 10 * q^7 + 4 * q^9	$ 4 q - 6 q^{3} + 4 q^{4} + 2 q^{5} + 4 q^{6} + 10 q^{7} + 4 q^{9} + 8 q^{13} - 8 q^{16} - 12 q^{17} - 4 q^{20} - 18 q^{21} - 24 q^{22} - 6 q^{23} - 8 q^{24} - 2 q^{25} + 12 q^{26} + 16 q^{28} - 4 q^{30} + 8 q^{31} - 24 q^{33} - 4 q^{34} + 8 q^{35} - 8 q^{36} + 12 q^{37} + 24 q^{38} + 16 q^{42} - 28 q^{43} - 4 q^{45} - 16 q^{46} - 12 q^{47} + 24 q^{48} + 22 q^{49} + 8 q^{51} + 8 q^{52} + 12 q^{53} - 20 q^{54} + 24 q^{57} - 4 q^{58} - 12 q^{59} + 12 q^{60} + 14 q^{61} - 12 q^{62} + 16 q^{63} - 32 q^{64} + 4 q^{65} + 48 q^{66} - 10 q^{67} - 4 q^{69} + 48 q^{72} - 24 q^{73} + 6 q^{75} - 4 q^{78} + 12 q^{79} - 16 q^{80} - 26 q^{81} + 8 q^{82} - 12 q^{84} - 12 q^{86} - 34 q^{87} - 48 q^{88} + 18 q^{89} + 24 q^{90} + 20 q^{91} - 12 q^{92} - 36 q^{93} - 32 q^{96} + 96 q^{99}+O(q^{100}) $ 4 * q - 6 * q^3 + 4 * q^4 + 2 * q^5 + 4 * q^6 + 10 * q^7 + 4 * q^9 + 8 * q^13 - 8 * q^16 - 12 * q^17 - 4 * q^20 - 18 * q^21 - 24 * q^22 - 6 * q^23 - 8 * q^24 - 2 * q^25 + 12 * q^26 + 16 * q^28 - 4 * q^30 + 8 * q^31 - 24 * q^33 - 4 * q^34 + 8 * q^35 - 8 * q^36 + 12 * q^37 + 24 * q^38 + 16 * q^42 - 28 * q^43 - 4 * q^45 - 16 * q^46 - 12 * q^47 + 24 * q^48 + 22 * q^49 + 8 * q^51 + 8 * q^52 + 12 * q^53 - 20 * q^54 + 24 * q^57 - 4 * q^58 - 12 * q^59 + 12 * q^60 + 14 * q^61 - 12 * q^62 + 16 * q^63 - 32 * q^64 + 4 * q^65 + 48 * q^66 - 10 * q^67 - 4 * q^69 + 48 * q^72 - 24 * q^73 + 6 * q^75 - 4 * q^78 + 12 * q^79 - 16 * q^80 - 26 * q^81 + 8 * q^82 - 12 * q^84 - 12 * q^86 - 34 * q^87 - 48 * q^88 + 18 * q^89 + 24 * q^90 + 20 * q^91 - 12 * q^92 - 36 * q^93 - 32 * 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 $

$2$	−1.22474	+	0.707107i	−0.866025	+	0.500000i
$2$	−1.22474	+	0.707107i	−0.866025	+	0.500000i
$3$	−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	$0.970753\pi$
$4$	1.00000	−	1.73205i	0.500000	−	0.866025i
$5$	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
$10$			1.41421i			0.447214i
$11$	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	$0.568845\pi$
$12$			6.29253i			1.81650i
$13$	−0.449490			−0.124666			−0.0623330	−	0.998055i	$-0.519854\pi$
$13$	−0.449490			−0.124666			−0.0623330	+	0.998055i	$0.519854\pi$
$14$	−3.67423	+	0.707107i	−0.981981	+	0.188982i
$15$			3.14626i			0.812362i
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$	−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	$0.413299\pi$
$18$			9.75663i			2.29966i
$19$	−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	0.595714	−	0.803197i	$-0.296869\pi$
$23$	0.949490	+	0.548188i	0.197982	+	0.114305i	−0.397732	+	0.917502i	$0.630203\pi$
$24$	−4.44949	−	7.70674i	−0.908248	−	1.57313i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	0.550510	−	0.317837i	0.107964	−	0.0623330i
$27$			12.2672i			2.36083i
$28$	4.00000	−	3.46410i	0.755929	−	0.654654i
$29$			10.0745i			1.87078i	0.353616	+	0.935391i	$0.384952\pi$
$29$			10.0745i			1.87078i	−0.353616	+	0.935391i	$0.615048\pi$
$30$	−2.22474	−	3.85337i	−0.406181	−	0.703526i
$31$	3.22474	+	5.58542i	0.579181	+	1.00317i	0.995573	+	0.0939863i	$0.0299610\pi$
$31$	3.22474	+	5.58542i	0.579181	+	1.00317i	−0.416392	+	0.909185i	$0.636706\pi$
$32$	4.89898	+	2.82843i	0.866025	+	0.500000i
$33$	−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	0.725900	−	0.687800i	$-0.241424\pi$
$37$	3.00000	+	1.73205i	0.493197	+	0.284747i	−0.232703	+	0.972548i	$0.574757\pi$
$38$	6.00000			0.973329
$39$	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	$0.940808\pi$
$42$	8.89898	−	7.70674i	1.37314	−	1.18918i
$43$	−4.55051			−0.693946			−0.346973	−	0.937875i	$-0.612791\pi$
$43$	−4.55051			−0.693946			−0.346973	+	0.937875i	$0.612791\pi$
$44$	9.79796			1.47710
$45$	−3.44949	−	5.97469i	−0.514220	−	0.890654i
$46$	−1.55051			−0.228610
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	−0.997503	−	0.0706177i	$-0.977503\pi$
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	0.559908	+	0.828554i	$0.310836\pi$
$48$	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
$52$	−0.449490	+	0.778539i	−0.0623330	+	0.107964i
$53$	4.22474	−	2.43916i	0.580313	−	0.335044i	−0.180945	−	0.983493i	$-0.557915\pi$
$53$	4.22474	−	2.43916i	0.580313	−	0.335044i	0.761258	+	0.648449i	$0.224582\pi$
$54$	−8.67423	−	15.0242i	−1.18041	−	2.04454i
$55$	4.89898			0.660578
$56$	−2.44949	+	7.07107i	−0.327327	+	0.944911i
$57$	13.3485			1.76805
$58$	−7.12372	−	12.3387i	−0.935391	−	1.62014i
$59$	−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	$0.573873\pi$
$60$	5.44949	+	3.14626i	0.703526	+	0.406181i
$61$	7.17423	−	12.4261i	0.918567	−	1.59100i	0.116973	−	0.993135i	$-0.462681\pi$
$61$	7.17423	−	12.4261i	0.918567	−	1.59100i	0.801594	−	0.597869i	$-0.203986\pi$
$62$	−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
$66$	21.7980			2.68314
$67$	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	$0.787512\pi$
$68$			4.09978i			0.497171i
$69$	−3.44949			−0.415270
$70$	−1.22474	+	3.53553i	−0.146385	+	0.422577i
$71$			1.41421i			0.167836i	0.996473	+	0.0839181i	$0.0267434\pi$
$71$			1.41421i			0.167836i	−0.996473	+	0.0839181i	$0.973257\pi$
$72$	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	$0.383567\pi$
$74$	−4.89898			−0.569495
$75$	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	0.461592	−	0.887093i	$-0.347279\pi$
$79$	−0.674235	−	0.389270i	−0.0758573	−	0.0437962i	−0.537449	+	0.843296i	$0.680612\pi$
$80$	−4.00000			−0.447214
$81$	−8.94949	−	15.5010i	−0.994388	−	1.72233i
$82$	−1.67423	−	2.89986i	−0.184888	−	0.320236i
$83$		−	12.2672i		−	1.34650i	−0.739414	−	0.673251i	$-0.764897\pi$
$83$		−	12.2672i		−	1.34650i	0.739414	−	0.673251i	$-0.235103\pi$
$84$	−5.44949	+	15.7313i	−0.594588	+	1.71643i
$85$			2.04989i			0.222342i
$86$	5.57321	−	3.21770i	0.600975	−	0.346973i
$87$	−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
$94$		−	8.48528i		−	0.875190i
$95$	−3.67423	+	2.12132i	−0.376969	+	0.217643i
$96$	−17.7980			−1.81650
$97$			5.02118i			0.509824i	0.966964	+	0.254912i	$0.0820464\pi$
$97$			5.02118i			0.509824i	−0.966964	+	0.254912i	$0.917954\pi$
$98$	−9.79796	−	1.41421i	−0.989743	−	0.142857i
$99$	33.7980			3.39682
$100$	−2.00000			−0.200000
$101$	4.62372	+	8.00853i	0.460078	+	0.796878i	0.998964	−	0.0455003i	$-0.0144882\pi$
$101$	4.62372	+	8.00853i	0.460078	+	0.796878i	−0.538887	+	0.842378i	$0.681155\pi$
$102$			9.12096i			0.903109i
$103$	−1.39898	+	2.42310i	−0.137846	+	0.238755i	−0.926681	−	0.375849i	$-0.877351\pi$
$103$	−1.39898	+	2.42310i	−0.137846	+	0.238755i	0.788835	+	0.614605i	$0.210684\pi$
$104$		−	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	$0.158195\pi$
$108$	21.2474	+	12.2672i	2.04454	+	1.18041i
$109$	14.1742	−	8.18350i	1.35765	−	0.783837i	0.368339	−	0.929691i	$-0.379926\pi$
$109$	14.1742	−	8.18350i	1.35765	−	0.783837i	0.989306	+	0.145854i	$0.0465931\pi$
$110$	−6.00000	+	3.46410i	−0.572078	+	0.330289i
$111$	−10.8990			−1.03449
$112$	−2.00000	−	10.3923i	−0.188982	−	0.981981i
$113$	3.55051			0.334004			0.167002	−	0.985957i	$-0.446591\pi$
$113$	3.55051			0.334004			0.167002	+	0.985957i	$0.446591\pi$
$114$	−16.3485	+	9.43879i	−1.53117	+	0.884024i
$115$	0.949490	−	0.548188i	0.0885404	−	0.0511188i
$116$	17.4495	+	10.0745i	1.62014	+	0.935391i
$117$	−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
$122$			20.2918i			1.83713i
$123$	−3.72474	−	6.45145i	−0.335849	−	0.581707i
$124$	12.8990			1.15836
$125$	−1.00000			−0.0894427
$126$	−8.44949	+	24.3916i	−0.752740	+	2.17297i
$127$		−	6.92820i		−	0.614779i	−0.951584	−	0.307389i	$-0.900545\pi$
$127$		−	6.92820i		−	0.614779i	0.951584	−	0.307389i	$-0.0994554\pi$
$128$	9.79796	−	5.65685i	0.866025	−	0.500000i
$129$	12.3990	−	7.15855i	1.09167	−	0.630276i
$130$		−	0.635674i		−	0.0557523i
$131$	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	$0.970794\pi$
$138$	4.22474	−	2.43916i	0.359634	−	0.207635i
$139$			6.92820i			0.587643i	0.955860	+	0.293821i	$0.0949270\pi$
$139$			6.92820i			0.587643i	−0.955860	+	0.293821i	$0.905073\pi$
$140$	−1.00000	−	5.19615i	−0.0845154	−	0.439155i
$141$		−	18.8776i		−	1.58978i
$142$	−1.00000	−	1.73205i	−0.0839181	−	0.145350i
$143$	−1.10102	−	1.90702i	−0.0920720	−	0.159473i
$144$	−27.5959			−2.29966
$145$	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	0.309912	−	0.950765i	$-0.399700\pi$
$149$	−4.37628	−	2.52664i	−0.358518	−	0.206991i	−0.668431	+	0.743774i	$0.733034\pi$
$150$	−4.44949			−0.363299
$151$	−0.674235	+	0.389270i	−0.0548684	+	0.0316783i	−0.527183	−	0.849752i	$-0.676752\pi$
$151$	−0.674235	+	0.389270i	−0.0548684	+	0.0316783i	0.472315	+	0.881430i	$0.343419\pi$
$152$	6.00000	−	10.3923i	0.486664	−	0.842927i
$153$			14.1421i			1.14332i
$154$	−12.0000	−	13.8564i	−0.966988	−	1.11658i
$155$	6.44949			0.518035
$156$		−	2.82843i		−	0.226455i
$157$	9.34847	+	16.1920i	0.746089	+	1.29226i	0.949684	+	0.313209i	$0.101404\pi$
$157$	9.34847	+	16.1920i	0.746089	+	1.29226i	−0.203595	+	0.979055i	$0.565263\pi$
$158$	1.10102			0.0875925
$159$	−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	$-0.0150490\pi$
$164$	4.10102	+	2.36773i	0.320236	+	0.184888i
$165$	−13.3485	+	7.70674i	−1.03918	+	0.599969i
$166$	8.67423	+	15.0242i	0.673251	+	1.16611i
$167$	3.00000			0.232147			0.116073	−	0.993241i	$-0.462969\pi$
$167$	3.00000			0.232147			0.116073	+	0.993241i	$0.462969\pi$
$168$	−4.44949	−	23.1202i	−0.343286	−	1.78376i
$169$	−12.7980			−0.984458
$170$	−1.44949	−	2.51059i	−0.111171	−	0.192553i
$171$	−25.3485	+	14.6349i	−1.93845	+	1.11916i
$172$	−4.55051	+	7.88171i	−0.346973	+	0.600975i
$173$	0.550510	−	0.953512i	0.0418545	−	0.0724942i	−0.844339	−	0.535809i	$-0.820007\pi$
$173$	0.550510	−	0.953512i	0.0418545	−	0.0724942i	0.886194	+	0.463315i	$0.153340\pi$
$174$	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
$178$	0.651531			0.0488343
$179$	−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	$-0.348243\pi$
$180$	−13.7980			−1.02844
$181$	−2.34847			−0.174560			−0.0872802	−	0.996184i	$-0.527818\pi$
$181$	−2.34847			−0.174560			−0.0872802	+	0.996184i	$0.527818\pi$
$182$	1.65153	−	0.317837i	0.122420	−	0.0235597i
$183$			45.1441i			3.33715i
$184$	−1.55051	+	2.68556i	−0.114305	+	0.197982i
$185$	3.00000	−	1.73205i	0.220564	−	0.127343i
$186$	28.6969			2.10416
$187$	−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	0.892446	−	0.451155i	$-0.148988\pi$
$191$	13.1010	+	7.56388i	0.947957	+	0.547303i	0.0555110	+	0.998458i	$0.482321\pi$
$192$	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	$0.755849\pi$
$194$	−3.55051	−	6.14966i	−0.254912	−	0.441520i
$195$		−	1.41421i		−	0.101274i
$196$	13.0000	−	5.19615i	0.928571	−	0.371154i
$197$		−	21.7060i		−	1.54649i	−0.634108	−	0.773245i	$-0.718632\pi$
$197$		−	21.7060i		−	1.54649i	0.634108	−	0.773245i	$-0.281368\pi$
$198$	−41.3939	+	23.8988i	−2.94173	+	1.69841i
$199$	−2.34847	−	4.06767i	−0.166479	−	0.288349i	0.770701	−	0.637197i	$-0.219906\pi$
$199$	−2.34847	−	4.06767i	−0.166479	−	0.288349i	−0.937179	+	0.348848i	$0.886573\pi$
$200$	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
$206$		−	3.95691i		−	0.275691i
$207$	6.55051	−	3.78194i	0.455292	−	0.262863i
$208$	0.898979	+	1.55708i	0.0623330	+	0.107964i
$209$		−	20.7846i		−	1.43770i
$210$	−2.22474	−	11.5601i	−0.153522	−	0.797724i
$211$	−16.2474			−1.11852			−0.559260	−	0.828992i	$-0.688915\pi$
$211$	−16.2474			−1.11852			−0.559260	+	0.828992i	$0.688915\pi$
$212$		−	9.75663i		−	0.670088i
$213$	−2.22474	−	3.85337i	−0.152437	−	0.264029i
$214$			0.778539i			0.0532198i
$215$	−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
$220$	4.89898	−	8.48528i	0.330289	−	0.572078i
$221$	0.797959	−	0.460702i	0.0536765	−	0.0309902i
$222$	13.3485	−	7.70674i	0.895891	−	0.517243i
$223$	4.69694			0.314530			0.157265	−	0.987556i	$-0.449732\pi$
$223$	4.69694			0.314530			0.157265	+	0.987556i	$0.449732\pi$
$224$	9.79796	+	11.3137i	0.654654	+	0.755929i
$225$	−6.89898			−0.459932
$226$	−4.34847	+	2.51059i	−0.289256	+	0.167002i
$227$	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	$0.134709\pi$
$228$	13.3485	−	23.1202i	0.884024	−	1.53117i
$229$	6.34847	−	10.9959i	0.419519	−	0.726628i	−0.576372	−	0.817187i	$-0.695532\pi$
$229$	6.34847	−	10.9959i	0.419519	−	0.726628i	0.995891	+	0.0905595i	$0.0288655\pi$
$230$	−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	$0.874530\pi$
$234$		−	4.38551i		−	0.286689i
$235$	3.00000	+	5.19615i	0.195698	+	0.338960i
$236$			21.0703i			1.37156i
$237$	2.44949			0.159111
$238$	5.79796	−	5.02118i	0.375826	−	0.325475i
$239$		−	17.4634i		−	1.12961i	−0.825224	−	0.564806i	$-0.808951\pi$
$239$		−	17.4634i		−	1.12961i	0.825224	−	0.564806i	$-0.191049\pi$
$240$	10.8990	−	6.29253i	0.703526	−	0.406181i
$241$	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	$0.190077\pi$
$242$		−	18.3848i		−	1.18182i
$243$	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
$250$	1.22474	−	0.707107i	0.0774597	−	0.0447214i
$251$		−	27.8557i		−	1.75823i	−0.476605	−	0.879117i	$-0.658133\pi$
$251$		−	27.8557i		−	1.75823i	0.476605	−	0.879117i	$-0.341867\pi$
$252$	−6.89898	−	35.8481i	−0.434595	−	2.25822i
$253$			5.37113i			0.337680i
$254$	4.89898	+	8.48528i	0.307389	+	0.532414i
$255$	−3.22474	−	5.58542i	−0.201941	−	0.349773i
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−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
$262$	−16.0000			−0.988483
$263$	19.7474	−	11.4012i	1.21768	−	0.703028i	0.253259	−	0.967399i	$-0.418498\pi$
$263$	19.7474	−	11.4012i	1.21768	−	0.703028i	0.964421	+	0.264371i	$0.0851643\pi$
$264$	21.7980	−	37.7552i	1.34157	−	2.32367i
$265$		−	4.87832i		−	0.299673i
$266$	15.0000	+	5.19615i	0.919709	+	0.318597i
$267$	1.44949			0.0887073
$268$	4.69694			0.286911
$269$	0.825765	+	1.43027i	0.0503478	+	0.0872050i	0.890101	−	0.455763i	$-0.150634\pi$
$269$	0.825765	+	1.43027i	0.0503478	+	0.0872050i	−0.839753	+	0.542968i	$0.817300\pi$
$270$	−17.3485			−1.05579
$271$	5.67423	−	9.82806i	0.344685	−	0.597012i	−0.640611	−	0.767865i	$-0.721319\pi$
$271$	5.67423	−	9.82806i	0.344685	−	0.597012i	0.985297	+	0.170853i	$0.0546523\pi$
$272$	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
$276$	−3.44949	+	5.97469i	−0.207635	+	0.359634i
$277$	17.0227	−	9.82806i	1.02280	−	0.590511i	0.107883	−	0.994164i	$-0.465593\pi$
$277$	17.0227	−	9.82806i	1.02280	−	0.590511i	0.914912	+	0.403653i	$0.132260\pi$
$278$	−4.89898	−	8.48528i	−0.293821	−	0.508913i
$279$	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	$0.432066\pi$
$282$	13.3485	+	23.1202i	0.794890	+	1.37679i
$283$	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	$0.252180\pi$
$284$	2.44949	+	1.41421i	0.145350	+	0.0839181i
$285$	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
$290$	−14.2474			−0.836639
$291$	−7.89898	−	13.6814i	−0.463046	−	0.802020i
$292$			5.37113i			0.314321i
$293$	−24.4949			−1.43101			−0.715504	−	0.698609i	$-0.753803\pi$
$293$	−24.4949			−1.43101			−0.715504	+	0.698609i	$0.753803\pi$
$294$	28.9217	−	11.5601i	1.68675	−	0.674200i
$295$			10.5352i			0.613381i
$296$	−4.89898	+	8.48528i	−0.284747	+	0.493197i
$297$	−52.0454	+	30.0484i	−3.01998	+	1.74359i
$298$	7.14643			0.413981
$299$	−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
$304$			16.9706i			0.973329i
$305$	−7.17423	−	12.4261i	−0.410795	−	0.711519i
$306$	−10.0000	−	17.3205i	−0.571662	−	0.990148i
$307$		−	31.4305i		−	1.79384i	−0.442197	−	0.896918i	$-0.645801\pi$
$307$		−	31.4305i		−	1.79384i	0.442197	−	0.896918i	$-0.354199\pi$
$308$	24.4949	+	8.48528i	1.39573	+	0.483494i
$309$		−	8.80312i		−	0.500792i
$310$	−7.89898	+	4.56048i	−0.448632	+	0.259018i
$311$	−11.5732	−	20.0454i	−0.656257	−	1.13667i	−0.981577	−	0.191066i	$-0.938805\pi$
$311$	−11.5732	−	20.0454i	−0.656257	−	1.13667i	0.325320	−	0.945604i	$-0.394528\pi$
$312$	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	−0.0826308	−	0.996580i	$-0.526332\pi$
$317$	−17.5732	−	10.1459i	−0.987010	−	0.569851i	−0.904379	+	0.426730i	$0.859666\pi$
$318$		−	21.7060i		−	1.21721i
$319$	−42.7423	+	24.6773i	−2.39311	+	1.38166i
$320$	−4.00000	+	6.92820i	−0.223607	+	0.387298i
$321$			1.73205i			0.0966736i
$322$	−3.87628	−	1.34278i	−0.216016	−	0.0748303i
$323$	8.69694			0.483911
$324$	−35.7980			−1.98878
$325$	0.224745	+	0.389270i	0.0124666	+	0.0215928i
$326$			19.5133i			1.08074i
$327$	−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	$0.839621\pi$
$332$	−21.2474	−	12.2672i	−1.16611	−	0.673251i
$333$	20.6969	−	11.9494i	1.13419	−	0.654822i
$334$	−3.67423	+	2.12132i	−0.201045	+	0.116073i
$335$	2.34847			0.128311
$336$	21.7980	+	25.1701i	1.18918	+	1.37314i
$337$	−4.24745			−0.231373			−0.115687	−	0.993286i	$-0.536907\pi$
$337$	−4.24745			−0.231373			−0.115687	+	0.993286i	$0.536907\pi$
$338$	15.6742	−	9.04952i	0.852566	−	0.492229i
$339$	−9.67423	+	5.58542i	−0.525432	+	0.303358i
$340$	3.55051	+	2.04989i	0.192553	+	0.111171i
$341$	−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
$346$			1.55708i			0.0837090i
$347$	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	$0.628555\pi$
$348$	−63.3939			−3.39827
$349$	17.2474			0.923235			0.461617	−	0.887079i	$-0.347269\pi$
$349$	17.2474			0.923235			0.461617	+	0.887079i	$0.347269\pi$
$350$	2.44949	+	2.82843i	0.130931	+	0.151186i
$351$		−	5.51399i		−	0.294315i
$352$			27.7128i			1.47710i
$353$	−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	$0.451663\pi$
$354$			46.8761i			2.49144i
$355$	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	−0.218598	−	0.975815i	$-0.570148\pi$
$359$	−22.2247	−	12.8315i	−1.17298	−	0.677219i	−0.954379	+	0.298596i	$0.903482\pi$
$360$	16.8990	−	9.75663i	0.890654	−	0.514220i
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$	2.87628	−	1.66062i	0.151174	−	0.0872802i
$363$		−	40.9014i		−	2.14677i
$364$	−1.79796	+	1.55708i	−0.0942387	+	0.0816131i
$365$			2.68556i			0.140569i
$366$	−31.9217	−	55.2900i	−1.66857	−	2.89005i
$367$	8.94949	+	15.5010i	0.467160	+	0.809144i	0.999296	−	0.0375145i	$-0.0119440\pi$
$367$	8.94949	+	15.5010i	0.467160	+	0.809144i	−0.532137	+	0.846659i	$0.678611\pi$
$368$		−	4.38551i		−	0.228610i
$369$	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	0.835249	−	0.549872i	$-0.185323\pi$
$373$	15.0000	+	8.66025i	0.776671	+	0.448411i	−0.0585785	+	0.998283i	$0.518657\pi$
$374$	14.2020			0.734370
$375$	2.72474	−	1.57313i	0.140705	−	0.0812362i
$376$	−14.6969	−	8.48528i	−0.757937	−	0.437595i
$377$		−	4.52837i		−	0.233223i
$378$	−8.67423	−	45.0726i	−0.446154	−	2.31829i
$379$	−2.65153			−0.136200			−0.0681000	−	0.997679i	$-0.521694\pi$
$379$	−2.65153			−0.136200			−0.0681000	+	0.997679i	$0.521694\pi$
$380$			8.48528i			0.435286i
$381$	10.8990	+	18.8776i	0.558372	+	0.967128i
$382$	−21.3939			−1.09461
$383$	12.3990	−	21.4757i	0.633558	−	1.09736i	−0.353260	−	0.935525i	$-0.614927\pi$
$383$	12.3990	−	21.4757i	0.633558	−	1.09736i	0.986819	−	0.161830i	$-0.0517396\pi$
$384$	−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
$388$	8.69694	+	5.02118i	0.441520	+	0.254912i
$389$	−9.79796	+	5.65685i	−0.496776	+	0.286814i	−0.727381	−	0.686234i	$-0.759263\pi$
$389$	−9.79796	+	5.65685i	−0.496776	+	0.286814i	0.230605	+	0.973047i	$0.425929\pi$
$390$	1.00000	+	1.73205i	0.0506370	+	0.0877058i
$391$	−2.24745			−0.113658
$392$	−12.2474	+	15.5563i	−0.618590	+	0.785714i
$393$	−35.5959			−1.79558
$394$	15.3485	+	26.5843i	0.773245	+	1.33930i
$395$	−0.674235	+	0.389270i	−0.0339244	+	0.0195863i
$396$	33.7980	−	58.5398i	1.69841	−	2.94173i
$397$	−14.3485	+	24.8523i	−0.720129	+	1.24730i	0.240819	+	0.970570i	$0.422584\pi$
$397$	−14.3485	+	24.8523i	−0.720129	+	1.24730i	−0.960948	+	0.276730i	$0.910749\pi$
$398$	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	$0.0764311\pi$
$402$	10.4495			0.521173
$403$	−1.44949	−	2.51059i	−0.0722042	−	0.125061i
$404$	18.4949			0.920156
$405$	−17.8990			−0.889407
$406$	−7.12372	−	37.0160i	−0.353545	−	1.83707i
$407$			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	$0.148709\pi$
$410$	−3.34847			−0.165369
$411$	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
$416$	−2.20204	−	1.27135i	−0.107964	−	0.0623330i
$417$	−10.8990	−	18.8776i	−0.533725	−	0.924439i
$418$	14.6969	+	25.4558i	0.718851	+	1.24509i
$419$			11.0280i			0.538752i	0.963035	+	0.269376i	$0.0868174\pi$
$419$			11.0280i			0.538752i	−0.963035	+	0.269376i	$0.913183\pi$
$420$	10.8990	+	12.5851i	0.531816	+	0.614088i
$421$			21.3882i			1.04240i	0.853436	+	0.521198i	$0.174515\pi$
$421$			21.3882i			1.04240i	−0.853436	+	0.521198i	$0.825485\pi$
$422$	19.8990	−	11.4887i	0.968667	−	0.559260i
$423$	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
$430$		−	6.43539i		−	0.310342i
$431$	−27.7980	+	16.0492i	−1.33898	+	0.773061i	−0.986656	−	0.162817i	$-0.947942\pi$
$431$	−27.7980	+	16.0492i	−1.33898	+	0.773061i	−0.352324	+	0.935878i	$0.614609\pi$
$432$	42.4949	−	24.5344i	2.04454	−	1.18041i
$433$			0.778539i			0.0374142i	0.999825	+	0.0187071i	$0.00595500\pi$
$433$			0.778539i			0.0374142i	−0.999825	+	0.0187071i	$0.994045\pi$
$434$	−15.7980	−	18.2419i	−0.758326	−	0.875640i
$435$	−31.6969			−1.51975
$436$		−	32.7340i		−	1.56767i
$437$	−2.32577	−	4.02834i	−0.111256	−	0.192702i
$438$			11.9494i			0.570964i
$439$	10.4495	−	18.0990i	0.498727	−	0.863820i	−0.501272	−	0.865290i	$-0.667134\pi$
$439$	10.4495	−	18.0990i	0.498727	−	0.863820i	0.999999	+	0.00146939i	$0.000467720\pi$
$440$			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	$0.154175\pi$
$444$	−10.8990	+	18.8776i	−0.517243	+	0.895891i
$445$	−0.398979	+	0.230351i	−0.0189134	+	0.0109197i
$446$	−5.75255	+	3.32124i	−0.272391	+	0.157265i
$447$	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	$0.907330\pi$
$450$	8.44949	−	4.87832i	0.398313	−	0.229966i
$451$	−10.0454	+	5.79972i	−0.473020	+	0.273098i
$452$	3.55051	−	6.14966i	0.167002	−	0.289256i
$453$	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	$-0.0767003\pi$
$458$			17.9562i			0.839037i
$459$	−12.5732	−	21.7774i	−0.586867	−	1.01648i
$460$		−	2.19275i		−	0.102238i
$461$	9.30306			0.433287			0.216643	−	0.976251i	$-0.430489\pi$
$461$	9.30306			0.433287			0.216643	+	0.976251i	$0.430489\pi$
$462$	54.4949	+	18.8776i	2.53533	+	0.878265i
$463$		−	12.1244i		−	0.563467i	−0.959493	−	0.281733i	$-0.909091\pi$
$463$		−	12.1244i		−	0.563467i	0.959493	−	0.281733i	$-0.0909093\pi$
$464$	34.8990	−	20.1489i	1.62014	−	0.935391i
$465$	−17.5732	+	10.1459i	−0.814938	+	0.470505i
$466$		−	34.2911i		−	1.58850i
$467$	−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
$474$	−3.00000	+	1.73205i	−0.137795	+	0.0795557i
$475$			4.24264i			0.194666i
$476$	−3.55051	+	10.2494i	−0.162737	+	0.469782i
$477$		−	33.6554i		−	1.54097i
$478$	12.3485	+	21.3882i	0.564806	+	0.978272i
$479$	1.77526	+	3.07483i	0.0811135	+	0.140493i	0.903728	−	0.428106i	$-0.140819\pi$
$479$	1.77526	+	3.07483i	0.0811135	+	0.140493i	−0.822615	+	0.568599i	$0.807486\pi$
$480$	−8.89898	+	15.4135i	−0.406181	+	0.703526i
$481$	−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
$486$	−27.5959			−1.25178
$487$	32.3939	−	18.7026i	1.46791	−	0.847496i	0.468553	−	0.883436i	$-0.344776\pi$
$487$	32.3939	−	18.7026i	1.46791	−	0.847496i	0.999354	+	0.0359392i	$0.0114423\pi$
$488$	35.1464	+	20.2918i	1.59100	+	0.918567i
$489$			43.4120i			1.96316i
$490$	−6.12372	+	7.77817i	−0.276642	+	0.351382i
$491$	35.1464			1.58614			0.793068	−	0.609133i	$-0.208482\pi$
$491$	35.1464			1.58614			0.793068	+	0.609133i	$0.208482\pi$
$492$	−14.8990			−0.671698
$493$	−10.3258	−	17.8848i	−0.465049	−	0.805489i
$494$	−2.69694			−0.121341
$495$	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	$0.918648\pi$
$500$	−1.00000	+	1.73205i	−0.0447214	+	0.0774597i
$501$	−8.17423	+	4.71940i	−0.365198	+	0.210847i
$502$	19.6969	+	34.1161i	0.879117	+	1.52268i
$503$	5.69694			0.254014			0.127007	−	0.991902i	$-0.459463\pi$
$503$	5.69694			0.254014			0.127007	+	0.991902i	$0.459463\pi$
$504$	33.7980	+	39.0265i	1.50548	+	1.73838i
$505$	9.24745			0.411506
$506$	−3.79796	−	6.57826i	−0.168840	−	0.292439i
$507$	34.8712	−	20.1329i	1.54868	−	0.894133i
$508$	−12.0000	−	6.92820i	−0.532414	−	0.307389i
$509$	6.27526	−	10.8691i	0.278146	−	0.481763i	−0.692778	−	0.721151i	$-0.743613\pi$
$509$	6.27526	−	10.8691i	0.278146	−	0.481763i	0.970924	+	0.239388i	$0.0769468\pi$
$510$	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
$514$	10.6969			0.471822
$515$	1.39898	+	2.42310i	0.0616464	+	0.106775i
$516$		−	28.6342i		−	1.26055i
$517$	−29.3939			−1.29274
$518$	−12.2474	−	4.24264i	−0.538122	−	0.186411i
$519$			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	$0.207303\pi$
$522$	−98.2929			−4.30216
$523$	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
$528$			61.6539i			2.68314i
$529$	−10.8990	−	18.8776i	−0.473869	−	0.820765i
$530$	3.44949	+	5.97469i	0.149836	+	0.259524i
$531$			72.6819i			3.15413i
$532$	−22.0454	+	4.24264i	−0.955790	+	0.183942i
$533$		−	1.06427i		−	0.0460986i
$534$	−1.77526	+	1.02494i	−0.0768228	+	0.0443537i
$535$	−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	0.445800	−	0.895133i	$-0.352919\pi$
$541$	−2.47730	−	1.43027i	−0.106507	−	0.0614920i	−0.552307	+	0.833641i	$0.686253\pi$
$542$			16.0492i			0.689370i
$543$	6.39898	−	3.69445i	0.274606	−	0.158544i
$544$	−11.5959			−0.497171
$545$		−	16.3670i		−	0.701085i
$546$	−4.00000	+	3.46410i	−0.171184	+	0.148250i
$547$	−35.0454			−1.49843			−0.749217	−	0.662325i	$-0.769570\pi$
$547$	−35.0454			−1.49843			−0.749217	+	0.662325i	$0.769570\pi$
$548$	−19.5959			−0.837096
$549$	−49.4949	−	85.7277i	−2.11239	−	3.65877i
$550$			6.92820i			0.295420i
$551$	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
$556$	12.0000	+	6.92820i	0.508913	+	0.293821i
$557$	−4.10102	+	2.36773i	−0.173766	+	0.100324i	−0.584360	−	0.811494i	$-0.698655\pi$
$557$	−4.10102	+	2.36773i	−0.173766	+	0.100324i	0.410595	+	0.911818i	$0.365321\pi$
$558$	−54.4949	+	31.4626i	−2.30695	+	1.33192i
$559$	2.04541			0.0865115
$560$	−10.0000	−	3.46410i	−0.422577	−	0.146385i
$561$	31.5959			1.33398
$562$	−8.69694	+	5.02118i	−0.366858	+	0.211806i
$563$	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	$0.299374\pi$
$564$	−32.6969	−	18.8776i	−1.37679	−	0.794890i
$565$	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	$0.0478742\pi$
$570$			18.8776i			0.790695i
$571$	−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	$0.870386\pi$
$572$	−4.40408			−0.184144
$573$	−47.5959			−1.98835
$574$	−1.67423	−	8.69958i	−0.0698812	−	0.363113i
$575$		−	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	$0.250924\pi$
$578$		−	18.0990i		−	0.752821i
$579$	−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
$586$	30.0000	−	17.3205i	1.23929	−	0.715504i
$587$			39.9479i			1.64883i	0.565988	+	0.824414i	$0.308495\pi$
$587$			39.9479i			1.64883i	−0.565988	+	0.824414i	$0.691505\pi$
$588$	−27.2474	+	34.6089i	−1.12367	+	1.42725i
$589$		−	27.3629i		−	1.12747i
$590$	−7.44949	−	12.9029i	−0.306691	−	0.531204i
$591$	34.1464	+	59.1433i	1.40460	+	2.43283i
$592$		−	13.8564i		−	0.569495i
$593$	−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
$598$	0.696938			0.0284999
$599$	−23.1464	+	13.3636i	−0.945737	+	0.546022i	−0.891754	−	0.452520i	$-0.850525\pi$
$599$	−23.1464	+	13.3636i	−0.945737	+	0.546022i	−0.0539832	+	0.998542i	$0.517192\pi$
$600$	−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	$0.942326\pi$
$602$	16.7196	−	3.21770i	0.681442	−	0.131144i
$603$	16.2020			0.659798
$604$			1.55708i			0.0633566i
$605$	6.50000	+	11.2583i	0.264263	+	0.457716i
$606$	41.1464			1.67146
$607$	−3.84847	+	6.66574i	−0.156205	+	0.270554i	−0.933497	−	0.358585i	$-0.883259\pi$
$607$	−3.84847	+	6.66574i	−0.156205	+	0.270554i	0.777292	+	0.629139i	$0.216593\pi$
$608$	−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
$612$	24.4949	+	14.1421i	0.990148	+	0.571662i
$613$	6.67423	−	3.85337i	0.269570	−	0.155636i	−0.359122	−	0.933290i	$-0.616924\pi$
$613$	6.67423	−	3.85337i	0.269570	−	0.155636i	0.628692	+	0.777654i	$0.283591\pi$
$614$	22.2247	+	38.4944i	0.896918	+	1.55351i
$615$	−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	$0.271333\pi$
$618$	6.22474	+	10.7816i	0.250396	+	0.433699i
$619$	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	$0.323371\pi$
$620$	6.44949	−	11.1708i	0.259018	−	0.448632i
$621$	−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
$626$	−38.6969			−1.54664
$627$	32.6969	+	56.6328i	1.30579	+	2.26169i
$628$	37.3939			1.49218
$629$	−7.10102			−0.283136
$630$	16.8990	+	19.5133i	0.673271	+	0.777427i
$631$			11.5994i			0.461766i	0.972981	+	0.230883i	$0.0741615\pi$
$631$			11.5994i			0.461766i	−0.972981	+	0.230883i	$0.925838\pi$
$632$	1.10102	−	1.90702i	0.0437962	−	0.0758573i
$633$	44.2702	−	25.5594i	1.75958	−	1.01589i
$634$	28.6969			1.13970
$635$	−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
$640$		−	11.3137i		−	0.447214i
$641$	−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	$0.999818\pi$
$642$	−1.22474	−	2.12132i	−0.0483368	−	0.0837218i
$643$			27.3629i			1.07909i	0.841958	+	0.539543i	$0.181403\pi$
$643$			27.3629i			1.07909i	−0.841958	+	0.539543i	$0.818597\pi$
$644$	5.69694	−	1.09638i	0.224491	−	0.0432033i
$645$		−	14.3171i		−	0.563736i
$646$	−10.6515	+	6.14966i	−0.419079	+	0.241955i
$647$	−14.2980	−	24.7648i	−0.562111	−	0.973604i	−0.997312	−	0.0732712i	$-0.976656\pi$
$647$	−14.2980	−	24.7648i	−0.562111	−	0.973604i	0.435201	−	0.900333i	$-0.356677\pi$
$648$	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	0.0742100	−	0.997243i	$-0.476356\pi$
$653$	−19.2247	−	11.0994i	−0.752322	−	0.434354i	−0.826532	+	0.562889i	$0.809690\pi$
$654$		−	72.8248i		−	2.84767i
$655$	9.79796	−	5.65685i	0.382838	−	0.221032i
$656$	8.20204	−	4.73545i	0.320236	−	0.184888i
$657$			18.5276i			0.722832i
$658$	7.34847	−	21.2132i	0.286473	−	0.826977i
$659$	36.7423			1.43128			0.715639	−	0.698470i	$-0.246135\pi$
$659$	36.7423			1.43128			0.715639	+	0.698470i	$0.246135\pi$
$660$			30.8270i			1.19994i
$661$	−11.8712	−	20.5615i	−0.461735	−	0.799749i	0.537312	−	0.843383i	$-0.319440\pi$
$661$	−11.8712	−	20.5615i	−0.461735	−	0.799749i	−0.999048	+	0.0436346i	$0.986106\pi$
$662$		−	44.0477i		−	1.71196i
$663$	−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
$668$	3.00000	−	5.19615i	0.116073	−	0.201045i
$669$	−12.7980	+	7.38891i	−0.494798	+	0.285672i
$670$	−2.87628	+	1.66062i	−0.111120	+	0.0641553i
$671$	70.2929			2.71363
$672$	−44.4949	−	15.4135i	−1.71643	−	0.594588i
$673$	−17.1010			−0.659196			−0.329598	−	0.944121i	$-0.606913\pi$
$673$	−17.1010			−0.659196			−0.329598	+	0.944121i	$0.606913\pi$
$674$	5.20204	−	3.00340i	0.200375	−	0.115687i
$675$	10.6237	−	6.13361i	0.408907	−	0.236083i
$676$	−12.7980	+	22.1667i	−0.492229	+	0.852566i
$677$	−8.32577	+	14.4206i	−0.319985	+	0.554231i	−0.980485	−	0.196596i	$-0.937011\pi$
$677$	−8.32577	+	14.4206i	−0.319985	+	0.554231i	0.660499	+	0.750827i	$0.270345\pi$
$678$	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
$682$		−	44.6834i		−	1.71101i
$683$	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	$0.793336\pi$
$684$			58.5398i			2.23832i
$685$	−9.79796			−0.374361
$686$	−23.2702	−	12.0208i	−0.888459	−	0.458957i
$687$			39.9479i			1.52411i
$688$	9.10102	+	15.7634i	0.346973	+	0.600975i
$689$	−1.89898	+	1.09638i	−0.0723454	+	0.0417686i
$690$		−	4.87832i		−	0.185714i
$691$	−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
$698$	−21.1237	+	12.1958i	−0.799545	+	0.461617i
$699$		−	76.2889i		−	2.88551i
$700$	−5.00000	−	1.73205i	−0.188982	−	0.0654654i
$701$			13.1886i			0.498127i	0.968487	+	0.249064i	$0.0801229\pi$
$701$			13.1886i			0.498127i	−0.968487	+	0.249064i	$0.919877\pi$
$702$	3.89898	+	6.75323i	0.147157	+	0.254884i
$703$	−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	$0.0348254\pi$
$709$	42.2196	+	24.3755i	1.58559	+	0.915442i	0.591571	+	0.806253i	$0.298508\pi$
$710$	−2.00000			−0.0750587
$711$	−4.65153	+	2.68556i	−0.174446	+	0.100716i
$712$	0.651531	−	1.12848i	0.0244171	−	0.0422917i
$713$			7.07107i			0.264814i
$714$	−7.89898	+	22.8024i	−0.295612	+	0.853358i
$715$	−2.20204			−0.0823517
$716$	−28.8990			−1.08001
$717$	27.4722	+	47.5832i	1.02597	+	1.77703i
$718$	36.2929			1.35444
$719$	19.5959	−	33.9411i	0.730804	−	1.26579i	−0.225735	−	0.974189i	$-0.572478\pi$
$719$	19.5959	−	33.9411i	0.730804	−	1.26579i	0.956540	−	0.291602i	$-0.0941882\pi$
$720$	−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
$724$	−2.34847	+	4.06767i	−0.0872802	+	0.151174i
$725$	8.72474	−	5.03723i	0.324029	−	0.187078i
$726$	28.9217	+	50.0938i	1.07338	+	1.85916i
$727$	24.5959			0.912212			0.456106	−	0.889925i	$-0.349244\pi$
$727$	24.5959			0.912212			0.456106	+	0.889925i	$0.349244\pi$
$728$	1.10102	−	3.17837i	0.0408065	−	0.117798i
$729$	−7.69694			−0.285072
$730$	−1.89898	−	3.28913i	−0.0702844	−	0.121736i
$731$	8.07832	−	4.66402i	0.298787	−	0.172505i
$732$	78.1918	+	45.1441i	2.89005	+	1.66857i
$733$	13.4495	−	23.2952i	0.496768	−	0.860428i	−0.503225	−	0.864156i	$-0.667853\pi$
$733$	13.4495	−	23.2952i	0.496768	−	0.860428i	0.999993	+	0.00372771i	$0.00118657\pi$
$734$	−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
$738$	−23.1010			−0.850360
$739$	−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	$-0.343656\pi$
$740$		−	6.92820i		−	0.254686i
$741$	−6.00000			−0.220416
$742$	−13.7980	+	11.9494i	−0.506539	+	0.438676i
$743$			28.5235i			1.04642i	0.852202	+	0.523212i	$0.175266\pi$
$743$			28.5235i			1.04642i	−0.852202	+	0.523212i	$0.824734\pi$
$744$	28.6969	−	49.7046i	1.05208	−	1.82226i
$745$	−4.37628	+	2.52664i	−0.160334	+	0.0925691i
$746$	−24.4949			−0.896822
$747$	−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	0.480805	−	0.876828i	$-0.340345\pi$
$751$	−1.04541	−	0.603566i	−0.0381475	−	0.0220245i	−0.518952	+	0.854803i	$0.673678\pi$
$752$	24.0000			0.875190
$753$	43.8207	+	75.8996i	1.59691	+	2.76594i
$754$	3.20204	+	5.54610i	0.116611	+	0.201977i
$755$			0.778539i			0.0283339i
$756$	42.4949	+	49.0689i	1.54552	+	1.78462i
$757$		−	8.05669i		−	0.292825i	−0.989224	−	0.146413i	$-0.953227\pi$
$757$		−	8.05669i		−	0.292825i	0.989224	−	0.146413i	$-0.0467727\pi$
$758$	3.24745	−	1.87492i	0.117953	−	0.0681000i
$759$	−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
$766$			35.0696i			1.26712i
$767$	4.10102	−	2.36773i	0.148079	−	0.0854936i
$768$		−	50.3402i		−	1.81650i
$769$			29.6198i			1.06812i	0.845447	+	0.534059i	$0.179334\pi$
$769$			29.6198i			1.06812i	−0.845447	+	0.534059i	$0.820666\pi$
$770$	−18.0000	+	3.46410i	−0.648675	+	0.124838i
$771$	23.7980			0.857063
$772$	13.3939			0.482056
$773$	18.1237	+	31.3912i	0.651865	+	1.12906i	0.982670	+	0.185364i	$0.0593465\pi$
$773$	18.1237	+	31.3912i	0.651865	+	1.12906i	−0.330805	+	0.943699i	$0.607320\pi$
$774$		−	44.3976i		−	1.59584i
$775$	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
$780$	−2.44949	−	1.41421i	−0.0877058	−	0.0506370i
$781$	−6.00000	+	3.46410i	−0.214697	+	0.123955i
$782$	2.75255	−	1.58919i	0.0984310	−	0.0568292i
$783$	−123.586			−4.41659
$784$	4.00000	−	27.7128i	0.142857	−	0.989743i
$785$	18.6969			0.667322
$786$	43.5959	−	25.1701i	1.55501	−	0.897788i
$787$	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	$0.130811\pi$
$788$	−37.5959	−	21.7060i	−1.33930	−	0.773245i
$789$	−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
$794$		−	40.5836i		−	1.44026i
$795$	7.67423	+	13.2922i	0.272177	+	0.471424i
$796$	−9.39388			−0.332957
$797$	32.6969			1.15818			0.579092	−	0.815262i	$-0.303407\pi$
$797$	32.6969			1.15818			0.579092	+	0.815262i	$0.303407\pi$
$798$	−49.0454	+	9.43879i	−1.73619	+	0.334130i
$799$		−	12.2993i		−	0.435119i
$800$		−	5.65685i		−	0.200000i
$801$	−2.75255	+	1.58919i	−0.0972566	+	0.0561511i
$802$			15.8421i			0.559403i
$803$	−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	$0.871463\pi$
$810$	21.9217	−	12.6565i	0.770249	−	0.444704i
$811$			21.9131i			0.769473i	0.923026	+	0.384736i	$0.125708\pi$
$811$			21.9131i			0.769473i	−0.923026	+	0.384736i	$0.874292\pi$
$812$	34.8990	+	40.2979i	1.22471	+	1.41418i
$813$			35.7053i			1.25224i
$814$	−12.0000	−	20.7846i	−0.420600	−	0.728500i
$815$	−6.89898	−	11.9494i	−0.241661	−	0.418569i
$816$	−25.7980			−0.903109
$817$	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	−0.0111703	−	0.999938i	$-0.503556\pi$
$821$	−25.2929	−	14.6028i	−0.882727	−	0.509643i	−0.871557	+	0.490295i	$0.836889\pi$
$822$	−43.5959			−1.52058
$823$	−23.8485	+	13.7689i	−0.831305	+	0.479954i	−0.854299	−	0.519781i	$-0.826013\pi$
$823$	−23.8485	+	13.7689i	−0.831305	+	0.479954i	0.0229940	+	0.999736i	$0.492680\pi$
$824$	−6.85357	−	3.95691i	−0.238755	−	0.137846i
$825$			15.4135i			0.536629i
$826$	29.7980	−	25.8058i	1.03680	−	0.897898i
$827$	31.0454			1.07955			0.539777	−	0.841808i	$-0.318508\pi$
$827$	31.0454			1.07955			0.539777	+	0.841808i	$0.318508\pi$
$828$		−	15.1278i		−	0.525726i
$829$	27.3485	+	47.3689i	0.949852	+	1.64519i	0.745733	+	0.666245i	$0.232100\pi$
$829$	27.3485	+	47.3689i	0.949852	+	1.64519i	0.204119	+	0.978946i	$0.434567\pi$
$830$	17.3485			0.602174
$831$	−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
$836$	−36.0000	−	20.7846i	−1.24509	−	0.718851i
$837$	−68.5176	+	39.5587i	−2.36831	+	1.36735i
$838$	−7.79796	−	13.5065i	−0.269376	−	0.466573i
$839$	−18.4949			−0.638515			−0.319257	−	0.947668i	$-0.603433\pi$
$839$	−18.4949			−0.638515			−0.319257	+	0.947668i	$0.603433\pi$
$840$	−22.2474	−	7.70674i	−0.767610	−	0.265908i
$841$	−72.4949			−2.49982
$842$	−15.1237	−	26.1951i	−0.521198	−	0.902741i
$843$	−19.3485	+	11.1708i	−0.666397	+	0.384744i
$844$	−16.2474	+	28.1414i	−0.559260	+	0.968667i
$845$	−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
$850$	−2.89898			−0.0994342
$851$	1.89898	+	3.28913i	0.0650962	+	0.112750i
$852$	−8.89898			−0.304874
$853$	−43.5505			−1.49114			−0.745571	−	0.666427i	$-0.767823\pi$
$853$	−43.5505			−1.49114			−0.745571	+	0.666427i	$0.767823\pi$
$854$	−17.5732	+	50.7295i	−0.601343	+	1.73593i
$855$			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	$0.536356\pi$
$858$	−9.79796			−0.334497
$859$	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	0.613596	−	0.789620i	$-0.289722\pi$
$863$	6.94949	+	4.01229i	0.236563	+	0.136580i	−0.377033	+	0.926200i	$0.623056\pi$
$864$	−34.6969	+	60.0969i	−1.18041	+	2.04454i
$865$	−0.550510	−	0.953512i	−0.0187179	−	0.0324204i
$866$	−0.550510	−	0.953512i	−0.0187071	−	0.0324016i
$867$		−	40.2658i		−	1.36750i
$868$	32.2474	+	11.1708i	1.09455	+	0.379163i
$869$		−	3.81405i		−	0.129383i
$870$	38.8207	−	22.4131i	1.31614	−	0.759876i
$871$	−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	$-0.912384\pi$
$877$	−49.7196	−	28.7056i	−1.67891	−	0.969321i	−0.716557	−	0.697528i	$-0.754283\pi$
$878$			29.5556i			0.997454i
$879$	66.7423	−	38.5337i	2.25116	−	1.29971i
$880$	−9.79796	−	16.9706i	−0.330289	−	0.572078i
$881$		−	8.37452i		−	0.282145i	−0.989999	−	0.141072i	$-0.954945\pi$
$881$		−	8.37452i		−	0.282145i	0.989999	−	0.141072i	$-0.0450551\pi$
$882$	−42.2474	+	53.6615i	−1.42255	+	1.80688i
$883$	8.49490			0.285876			0.142938	−	0.989732i	$-0.454345\pi$
$883$	8.49490			0.285876			0.142938	+	0.989732i	$0.454345\pi$
$884$		−	1.84281i		−	0.0619803i
$885$	−16.5732	−	28.7056i	−0.557102	−	0.964930i
$886$			2.33562i			0.0784666i
$887$	13.5000	−	23.3827i	0.453286	−	0.785114i	−0.545302	−	0.838240i	$-0.683585\pi$
$887$	13.5000	−	23.3827i	0.453286	−	0.785114i	0.998588	+	0.0531258i	$0.0169184\pi$
$888$		−	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
$892$	4.69694	−	8.13534i	0.157265	−	0.272391i
$893$	22.0454	−	12.7279i	0.737721	−	0.425924i
$894$	−19.4722	+	11.2423i	−0.651248	+	0.375998i
$895$	−14.4495			−0.482993
$896$	29.3939	−	5.65685i	0.981981	−	0.188982i
$897$	1.55051			0.0517700
$898$	49.7196	−	28.7056i	1.65917	−	0.957920i
$899$	−56.2702	+	32.4876i	−1.87671	+	1.08352i
$900$	−6.89898	+	11.9494i	−0.229966	+	0.398313i
$901$	−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
$906$			3.46410i			0.115087i
$907$	−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	$0.866945\pi$
$908$		−	35.2125i		−	1.16857i
$909$	63.7980			2.11604
$910$	0.550510	−	1.58919i	0.0182492	−	0.0526810i
$911$			20.7204i			0.686497i	0.939245	+	0.343249i	$0.111527\pi$
$911$			20.7204i			0.686497i	−0.939245	+	0.343249i	$0.888473\pi$
$912$	−26.6969	−	46.2405i	−0.884024	−	1.53117i
$913$	52.0454	−	30.0484i	1.72245	−	0.994458i
$914$			41.8549i			1.38444i
$915$	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	0.0409130	−	0.999163i	$-0.486973\pi$
$919$	−24.3712	−	14.0707i	−0.803931	−	0.464150i	−0.844844	+	0.535013i	$0.820307\pi$
$920$	1.55051	+	2.68556i	0.0511188	+	0.0885404i
$921$	49.4444	+	85.6402i	1.62925	+	2.82194i
$922$	−11.3939	+	6.57826i	−0.375237	+	0.216643i
$923$		−	0.635674i		−	0.0209235i
$924$	−80.0908	+	15.4135i	−2.63479	+	0.507066i
$925$		−	3.46410i		−	0.113899i
$926$	8.57321	+	14.8492i	0.281733	+	0.487976i
$927$	9.65153	+	16.7169i	0.316998	+	0.549056i
$928$	−28.4949	+	49.3546i	−0.935391	+	1.62014i
$929$	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
$934$	12.0454			0.394138
$935$	−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	$0.872347\pi$
$938$	−5.75255	−	6.64247i	−0.187827	−	0.216884i
$939$	−86.0908			−2.80947
$940$	12.0000			0.391397
$941$	−1.89898	−	3.28913i	−0.0619050	−	0.107223i	0.833412	−	0.552652i	$-0.186384\pi$
$941$	−1.89898	−	3.28913i	−0.0619050	−	0.107223i	−0.895317	+	0.445430i	$0.853051\pi$
$942$	83.1918			2.71054
$943$	−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	$0.923682\pi$
$948$	2.44949	−	4.24264i	0.0795557	−	0.137795i
$949$	1.04541	−	0.603566i	0.0339354	−	0.0195926i
$950$	−3.00000	−	5.19615i	−0.0973329	−	0.168585i
$951$	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	$0.505677\pi$
$954$	23.7980	+	41.2193i	0.770487	+	1.33452i
$955$	13.1010	−	7.56388i	0.423939	−	0.244761i
$956$	−30.2474	−	17.4634i	−0.978272	−	0.564806i
$957$	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
$962$	2.20204			0.0709967
$963$	−1.89898	−	3.28913i	−0.0611938	−	0.105991i
$964$		−	27.0129i		−	0.870028i
$965$	6.69694			0.215582
$966$	12.6742	−	2.43916i	0.407787	−	0.0784786i
$967$		−	49.1796i		−	1.58151i	−0.612132	−	0.790755i	$-0.709688\pi$
$967$		−	49.1796i		−	1.58151i	0.612132	−	0.790755i	$-0.290312\pi$
$968$	−31.8434	−	18.3848i	−1.02348	−	0.590909i
$969$	−23.6969	+	13.6814i	−0.761255	+	0.439511i
$970$	−7.10102			−0.228000
$971$	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
$976$	−57.3939			−1.83713
$977$	−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	$0.989150\pi$
$978$	−30.6969	−	53.1687i	−0.981580	−	1.70015i
$979$		−	2.25697i		−	0.0721330i
$980$	2.00000	−	13.8564i	0.0638877	−	0.442627i
$981$		−	112.916i		−	3.60512i
$982$	−43.0454	+	24.8523i	−1.37363	+	0.793068i
$983$	7.50000	+	12.9904i	0.239213	+	0.414329i	0.960489	−	0.278319i	$-0.0897773\pi$
$983$	7.50000	+	12.9904i	0.239213	+	0.414329i	−0.721276	+	0.692648i	$0.756444\pi$
$984$	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
$990$			47.7975i			1.51911i
$991$	25.7196	−	14.8492i	0.817011	−	0.471702i	−0.0323734	−	0.999476i	$-0.510307\pi$
$991$	25.7196	−	14.8492i	0.817011	−	0.471702i	0.849385	+	0.527774i	$0.176973\pi$
$992$			36.4838i			1.15836i
$993$		−	97.9949i		−	3.10977i
$994$	−1.00000	−	5.19615i	−0.0317181	−	0.164812i
$995$	−4.69694			−0.148903
$996$	77.1918			2.44592
$997$	20.6742	+	35.8088i	0.654760	+	1.13408i	0.981954	+	0.189120i	$0.0605635\pi$
$997$	20.6742	+	35.8088i	0.654760	+	1.13408i	−0.327194	+	0.944957i	$0.606103\pi$
$998$		−	44.3976i		−	1.40538i
$999$	−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.c.131.1	yes	4
4.3	odd	2		1120.2.bz.c.271.2		4
7.3	odd	6		280.2.bj.b.171.1	yes	4
8.3	odd	2		280.2.bj.b.131.2	✓	4
8.5	even	2		1120.2.bz.b.271.2		4
28.3	even	6		1120.2.bz.b.591.2		4
56.3	even	6	inner	280.2.bj.c.171.1	yes	4
56.45	odd	6		1120.2.bz.c.591.2		4

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

\(f(q)\)	\(=\)	\(q+(-1.22474 + 0.707107i) q^{2} +(-2.72474 + 1.57313i) q^{3} +(1.00000 - 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +(2.22474 - 3.85337i) q^{6} +(2.50000 + 0.866025i) q^{7} +2.82843i q^{8} +(3.44949 - 5.97469i) q^{9} +O(q^{10})\)	\(q+(-1.22474 + 0.707107i) q^{2} +(-2.72474 + 1.57313i) q^{3} +(1.00000 - 1.73205i) 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} +1.41421i q^{10} +(2.44949 + 4.24264i) q^{11} +6.29253i q^{12} -0.449490 q^{13} +(-3.67423 + 0.707107i) q^{14} +3.14626i q^{15} +(-2.00000 - 3.46410i) q^{16} +(-1.77526 + 1.02494i) q^{17} +9.75663i 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} +(0.550510 - 0.317837i) q^{26} +12.2672i q^{27} +(4.00000 - 3.46410i) q^{28} +10.0745i q^{29} +(-2.22474 - 3.85337i) q^{30} +(3.22474 + 5.58542i) q^{31} +(4.89898 + 2.82843i) 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} +6.00000 q^{38} +(1.22474 - 0.707107i) q^{39} +(2.44949 + 1.41421i) q^{40} +2.36773i q^{41} +(8.89898 - 7.70674i) q^{42} -4.55051 q^{43} +9.79796 q^{44} +(-3.44949 - 5.97469i) q^{45} -1.55051 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} +(-0.449490 + 0.778539i) q^{52} +(4.22474 - 2.43916i) q^{53} +(-8.67423 - 15.0242i) q^{54} +4.89898 q^{55} +(-2.44949 + 7.07107i) q^{56} +13.3485 q^{57} +(-7.12372 - 12.3387i) q^{58} +(-9.12372 + 5.26758i) q^{59} +(5.44949 + 3.14626i) 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} +21.7980 q^{66} +(1.17423 + 2.03383i) q^{67} +4.09978i q^{68} -3.44949 q^{69} +(-1.22474 + 3.53553i) q^{70} +1.41421i q^{71} +(16.8990 + 9.75663i) q^{72} +(-2.32577 + 1.34278i) q^{73} -4.89898 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} -4.00000 q^{80} +(-8.94949 - 15.5010i) q^{81} +(-1.67423 - 2.89986i) q^{82} -12.2672i q^{83} +(-5.44949 + 15.7313i) q^{84} +2.04989i q^{85} +(5.57321 - 3.21770i) 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} -8.48528i q^{94} +(-3.67423 + 2.12132i) q^{95} -17.7980 q^{96} +5.02118i q^{97} +(-9.79796 - 1.41421i) q^{98} +33.7980 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{3} + 4 q^{4} + 2 q^{5} + 4 q^{6} + 10 q^{7} + 4 q^{9}+O(q^{10}) \) 4 * q - 6 * q^3 + 4 * q^4 + 2 * q^5 + 4 * q^6 + 10 * q^7 + 4 * q^9	\( 4 q - 6 q^{3} + 4 q^{4} + 2 q^{5} + 4 q^{6} + 10 q^{7} + 4 q^{9} + 8 q^{13} - 8 q^{16} - 12 q^{17} - 4 q^{20} - 18 q^{21} - 24 q^{22} - 6 q^{23} - 8 q^{24} - 2 q^{25} + 12 q^{26} + 16 q^{28} - 4 q^{30} + 8 q^{31} - 24 q^{33} - 4 q^{34} + 8 q^{35} - 8 q^{36} + 12 q^{37} + 24 q^{38} + 16 q^{42} - 28 q^{43} - 4 q^{45} - 16 q^{46} - 12 q^{47} + 24 q^{48} + 22 q^{49} + 8 q^{51} + 8 q^{52} + 12 q^{53} - 20 q^{54} + 24 q^{57} - 4 q^{58} - 12 q^{59} + 12 q^{60} + 14 q^{61} - 12 q^{62} + 16 q^{63} - 32 q^{64} + 4 q^{65} + 48 q^{66} - 10 q^{67} - 4 q^{69} + 48 q^{72} - 24 q^{73} + 6 q^{75} - 4 q^{78} + 12 q^{79} - 16 q^{80} - 26 q^{81} + 8 q^{82} - 12 q^{84} - 12 q^{86} - 34 q^{87} - 48 q^{88} + 18 q^{89} + 24 q^{90} + 20 q^{91} - 12 q^{92} - 36 q^{93} - 32 q^{96} + 96 q^{99}+O(q^{100}) \) 4 * q - 6 * q^3 + 4 * q^4 + 2 * q^5 + 4 * q^6 + 10 * q^7 + 4 * q^9 + 8 * q^13 - 8 * q^16 - 12 * q^17 - 4 * q^20 - 18 * q^21 - 24 * q^22 - 6 * q^23 - 8 * q^24 - 2 * q^25 + 12 * q^26 + 16 * q^28 - 4 * q^30 + 8 * q^31 - 24 * q^33 - 4 * q^34 + 8 * q^35 - 8 * q^36 + 12 * q^37 + 24 * q^38 + 16 * q^42 - 28 * q^43 - 4 * q^45 - 16 * q^46 - 12 * q^47 + 24 * q^48 + 22 * q^49 + 8 * q^51 + 8 * q^52 + 12 * q^53 - 20 * q^54 + 24 * q^57 - 4 * q^58 - 12 * q^59 + 12 * q^60 + 14 * q^61 - 12 * q^62 + 16 * q^63 - 32 * q^64 + 4 * q^65 + 48 * q^66 - 10 * q^67 - 4 * q^69 + 48 * q^72 - 24 * q^73 + 6 * q^75 - 4 * q^78 + 12 * q^79 - 16 * q^80 - 26 * q^81 + 8 * q^82 - 12 * q^84 - 12 * q^86 - 34 * q^87 - 48 * q^88 + 18 * q^89 + 24 * q^90 + 20 * q^91 - 12 * q^92 - 36 * q^93 - 32 * q^96 + 96 * q^99

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