LMFDB - Embedded newform 462.2.k.e.89.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(89,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("462.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.k (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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
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			89.4
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	462.89
Dual form			462.2.k.e.353.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(1.62484 + 0.599900i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.758819 + 1.31431i) q^{5} +(1.10721 + 1.33195i) q^{6} +(-1.48356 + 2.19067i) q^{7} +1.00000i q^{8} +(2.28024 + 1.94949i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(1.62484 + 0.599900i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.758819 + 1.31431i) q^{5} +(1.10721 + 1.33195i) q^{6} +(-1.48356 + 2.19067i) q^{7} +1.00000i q^{8} +(2.28024 + 1.94949i) q^{9} +(-1.31431 + 0.758819i) q^{10} +(0.866025 - 0.500000i) q^{11} +(0.292893 + 1.70711i) q^{12} -5.44949i q^{13} +(-2.38014 + 1.15539i) q^{14} +(-2.02142 + 1.68034i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.34108 + 4.05487i) q^{17} +(1.00000 + 2.82843i) q^{18} +(-6.12983 - 3.53906i) q^{19} -1.51764 q^{20} +(-3.72474 + 2.66951i) q^{21} +1.00000 q^{22} +(0.680339 + 0.392794i) q^{23} +(-0.599900 + 1.62484i) q^{24} +(1.34839 + 2.33548i) q^{25} +(2.72474 - 4.71940i) q^{26} +(2.53553 + 4.53553i) q^{27} +(-2.63896 - 0.189469i) q^{28} -2.48477i q^{29} +(-2.59077 + 0.444506i) q^{30} +(7.11597 - 4.10841i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.70711 - 0.292893i) q^{33} +4.68216i q^{34} +(-1.75347 - 3.61219i) q^{35} +(-0.548188 + 2.94949i) q^{36} +(0.996476 - 1.72595i) q^{37} +(-3.53906 - 6.12983i) q^{38} +(3.26915 - 8.85457i) q^{39} +(-1.31431 - 0.758819i) q^{40} +8.74567 q^{41} +(-4.56048 + 0.449490i) q^{42} +2.14626 q^{43} +(0.866025 + 0.500000i) q^{44} +(-4.29253 + 1.51764i) q^{45} +(0.392794 + 0.680339i) q^{46} +(1.58579 - 2.74666i) q^{47} +(-1.33195 + 1.10721i) q^{48} +(-2.59808 - 6.50000i) q^{49} +2.69677i q^{50} +(1.37137 + 7.99295i) q^{51} +(4.71940 - 2.72474i) q^{52} +(-4.99149 + 2.88184i) q^{53} +(-0.0719302 + 5.19565i) q^{54} +1.51764i q^{55} +(-2.19067 - 1.48356i) q^{56} +(-7.83694 - 9.42771i) q^{57} +(1.24238 - 2.15187i) q^{58} +(-2.55670 - 4.42833i) q^{59} +(-2.46593 - 0.910432i) q^{60} +(-8.29227 - 4.78754i) q^{61} +8.21682 q^{62} +(-7.65357 + 2.10306i) q^{63} -1.00000 q^{64} +(7.16234 + 4.13518i) q^{65} +(1.62484 + 0.599900i) q^{66} +(3.83926 + 6.64979i) q^{67} +(-2.34108 + 4.05487i) q^{68} +(0.869807 + 1.04636i) q^{69} +(0.287545 - 4.00498i) q^{70} -3.76028i q^{71} +(-1.94949 + 2.28024i) q^{72} +(8.74919 - 5.05135i) q^{73} +(1.72595 - 0.996476i) q^{74} +(0.789867 + 4.60368i) q^{75} -7.07812i q^{76} +(-0.189469 + 2.63896i) q^{77} +(7.25845 - 6.03371i) q^{78} +(1.25177 - 2.16813i) q^{79} +(-0.758819 - 1.31431i) q^{80} +(1.39898 + 8.89060i) q^{81} +(7.57397 + 4.37283i) q^{82} -14.9747 q^{83} +(-4.17423 - 1.89097i) q^{84} -7.10583 q^{85} +(1.85872 + 1.07313i) q^{86} +(1.49061 - 4.03736i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-4.91189 + 8.50765i) q^{89} +(-4.47626 - 0.831951i) q^{90} +(11.9380 + 8.08467i) q^{91} +0.785587i q^{92} +(14.0270 - 2.40665i) q^{93} +(2.74666 - 1.58579i) q^{94} +(9.30286 - 5.37101i) q^{95} +(-1.70711 + 0.292893i) q^{96} -9.37481i q^{97} +(1.00000 - 6.92820i) q^{98} +(2.94949 + 0.548188i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6}+O(q^{10}) $ 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6	$ 8 q + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} + 8 q^{12} - 4 q^{16} + 20 q^{17} + 8 q^{18} - 12 q^{19} - 8 q^{20} - 20 q^{21} + 8 q^{22} - 12 q^{23} - 4 q^{24} + 8 q^{25} + 12 q^{26} - 8 q^{27} - 4 q^{30} + 12 q^{31} + 8 q^{33} + 16 q^{35} - 8 q^{38} + 24 q^{39} + 40 q^{41} - 8 q^{43} + 16 q^{45} + 8 q^{46} + 24 q^{47} + 4 q^{48} + 32 q^{51} - 60 q^{53} - 4 q^{54} - 20 q^{57} - 4 q^{58} + 4 q^{59} - 12 q^{60} - 36 q^{61} + 24 q^{62} - 32 q^{63} - 8 q^{64} - 12 q^{65} + 4 q^{66} + 12 q^{67} - 20 q^{68} - 12 q^{69} - 20 q^{70} + 4 q^{72} + 48 q^{73} - 12 q^{74} + 8 q^{75} - 8 q^{79} - 4 q^{80} - 28 q^{81} - 24 q^{82} - 72 q^{83} - 4 q^{84} - 32 q^{85} + 12 q^{86} + 16 q^{87} + 4 q^{88} - 4 q^{89} - 28 q^{90} + 36 q^{91} + 16 q^{93} + 24 q^{95} - 8 q^{96} + 8 q^{98} + 4 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 + 8 * q^12 - 4 * q^16 + 20 * q^17 + 8 * q^18 - 12 * q^19 - 8 * q^20 - 20 * q^21 + 8 * q^22 - 12 * q^23 - 4 * q^24 + 8 * q^25 + 12 * q^26 - 8 * q^27 - 4 * q^30 + 12 * q^31 + 8 * q^33 + 16 * q^35 - 8 * q^38 + 24 * q^39 + 40 * q^41 - 8 * q^43 + 16 * q^45 + 8 * q^46 + 24 * q^47 + 4 * q^48 + 32 * q^51 - 60 * q^53 - 4 * q^54 - 20 * q^57 - 4 * q^58 + 4 * q^59 - 12 * q^60 - 36 * q^61 + 24 * q^62 - 32 * q^63 - 8 * q^64 - 12 * q^65 + 4 * q^66 + 12 * q^67 - 20 * q^68 - 12 * q^69 - 20 * q^70 + 4 * q^72 + 48 * q^73 - 12 * q^74 + 8 * q^75 - 8 * q^79 - 4 * q^80 - 28 * q^81 - 24 * q^82 - 72 * q^83 - 4 * q^84 - 32 * q^85 + 12 * q^86 + 16 * q^87 + 4 * q^88 - 4 * q^89 - 28 * q^90 + 36 * q^91 + 16 * q^93 + 24 * q^95 - 8 * q^96 + 8 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	1.62484	+	0.599900i	0.938104	+	0.346353i
$3$	1.62484	+	0.599900i	0.938104	+	0.346353i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.758819	+	1.31431i	−0.339354	+	0.587779i	−0.984311	−	0.176440i	$-0.943542\pi$
$5$	−0.758819	+	1.31431i	−0.339354	+	0.587779i	0.644957	+	0.764219i	$0.276875\pi$
$6$	1.10721	+	1.33195i	0.452015	+	0.543767i
$7$	−1.48356	+	2.19067i	−0.560734	+	0.827996i
$7$	−1.48356	+	2.19067i	−0.560734	+	0.827996i
$8$			1.00000i			0.353553i
$9$	2.28024	+	1.94949i	0.760080	+	0.649830i
$10$	−1.31431	+	0.758819i	−0.415622	+	0.239960i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$12$	0.292893	+	1.70711i	0.0845510	+	0.492799i
$13$		−	5.44949i		−	1.51142i	−0.654908	−	0.755708i	$-0.727293\pi$
$13$		−	5.44949i		−	1.51142i	0.654908	−	0.755708i	$-0.272707\pi$
$14$	−2.38014	+	1.15539i	−0.636119	+	0.308792i
$15$	−2.02142	+	1.68034i	−0.521928	+	0.433862i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.34108	+	4.05487i	0.567796	+	0.983451i	0.996784	+	0.0801407i	$0.0255370\pi$
$17$	2.34108	+	4.05487i	0.567796	+	0.983451i	−0.428988	+	0.903310i	$0.641130\pi$
$18$	1.00000	+	2.82843i	0.235702	+	0.666667i
$19$	−6.12983	−	3.53906i	−1.40628	−	0.811916i	−0.411252	−	0.911522i	$-0.634908\pi$
$19$	−6.12983	−	3.53906i	−1.40628	−	0.811916i	−0.995027	+	0.0996061i	$0.968242\pi$
$20$	−1.51764			−0.339354
$21$	−3.72474	+	2.66951i	−0.812806	+	0.582535i
$22$	1.00000			0.213201
$23$	0.680339	+	0.392794i	0.141860	+	0.0819031i	0.569250	−	0.822164i	$-0.307234\pi$
$23$	0.680339	+	0.392794i	0.141860	+	0.0819031i	−0.427390	+	0.904067i	$0.640567\pi$
$24$	−0.599900	+	1.62484i	−0.122454	+	0.331670i
$25$	1.34839	+	2.33548i	0.269677	+	0.467095i
$26$	2.72474	−	4.71940i	0.534366	−	0.925550i
$27$	2.53553	+	4.53553i	0.487964	+	0.872864i
$28$	−2.63896	−	0.189469i	−0.498716	−	0.0358062i
$29$		−	2.48477i		−	0.461409i	−0.973024	−	0.230705i	$-0.925897\pi$
$29$		−	2.48477i		−	0.461409i	0.973024	−	0.230705i	$-0.0741031\pi$
$30$	−2.59077	+	0.444506i	−0.473008	+	0.0811553i
$31$	7.11597	−	4.10841i	1.27807	−	0.737892i	0.301574	−	0.953443i	$-0.402488\pi$
$31$	7.11597	−	4.10841i	1.27807	−	0.737892i	0.976493	+	0.215551i	$0.0691547\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	1.70711	−	0.292893i	0.297169	−	0.0509862i
$34$			4.68216i			0.802984i
$35$	−1.75347	−	3.61219i	−0.296391	−	0.610572i
$36$	−0.548188	+	2.94949i	−0.0913647	+	0.491582i
$37$	0.996476	−	1.72595i	0.163820	−	0.283744i	−0.772416	−	0.635117i	$-0.780952\pi$
$37$	0.996476	−	1.72595i	0.163820	−	0.283744i	0.936235	+	0.351373i	$0.114285\pi$
$38$	−3.53906	−	6.12983i	−0.574111	−	0.994389i
$39$	3.26915	−	8.85457i	0.523483	−	1.41787i
$40$	−1.31431	−	0.758819i	−0.207811	−	0.119980i
$41$	8.74567			1.36584			0.682922	−	0.730491i	$-0.260709\pi$
$41$	8.74567			1.36584			0.682922	+	0.730491i	$0.260709\pi$
$42$	−4.56048	+	0.449490i	−0.703697	+	0.0693578i
$43$	2.14626			0.327302			0.163651	−	0.986518i	$-0.447673\pi$
$43$	2.14626			0.327302			0.163651	+	0.986518i	$0.447673\pi$
$44$	0.866025	+	0.500000i	0.130558	+	0.0753778i
$45$	−4.29253	+	1.51764i	−0.639892	+	0.226236i
$46$	0.392794	+	0.680339i	0.0579143	+	0.100310i
$47$	1.58579	−	2.74666i	0.231311	−	0.400642i	−0.726883	−	0.686761i	$-0.759032\pi$
$47$	1.58579	−	2.74666i	0.231311	−	0.400642i	0.958194	+	0.286119i	$0.0923653\pi$
$48$	−1.33195	+	1.10721i	−0.192251	+	0.159811i
$49$	−2.59808	−	6.50000i	−0.371154	−	0.928571i
$50$			2.69677i			0.381382i
$51$	1.37137	+	7.99295i	0.192031	+	1.11924i
$52$	4.71940	−	2.72474i	0.654463	−	0.377854i
$53$	−4.99149	+	2.88184i	−0.685634	+	0.395851i	−0.801974	−	0.597358i	$-0.796217\pi$
$53$	−4.99149	+	2.88184i	−0.685634	+	0.395851i	0.116340	+	0.993209i	$0.462884\pi$
$54$	−0.0719302	+	5.19565i	−0.00978846	+	0.707039i
$55$			1.51764i			0.204638i
$56$	−2.19067	−	1.48356i	−0.292741	−	0.198250i
$57$	−7.83694	−	9.42771i	−1.03803	−	1.24873i
$58$	1.24238	−	2.15187i	0.163133	−	0.282554i
$59$	−2.55670	−	4.42833i	−0.332853	−	0.576519i	0.650217	−	0.759749i	$-0.274678\pi$
$59$	−2.55670	−	4.42833i	−0.332853	−	0.576519i	−0.983070	+	0.183230i	$0.941345\pi$
$60$	−2.46593	−	0.910432i	−0.318350	−	0.117536i
$61$	−8.29227	−	4.78754i	−1.06172	−	0.612982i	−0.135810	−	0.990735i	$-0.543364\pi$
$61$	−8.29227	−	4.78754i	−1.06172	−	0.612982i	−0.925907	+	0.377753i	$0.876697\pi$
$62$	8.21682			1.04354
$63$	−7.65357	+	2.10306i	−0.964259	+	0.264961i
$64$	−1.00000			−0.125000
$65$	7.16234	+	4.13518i	0.888378	+	0.512906i
$66$	1.62484	+	0.599900i	0.200005	+	0.0738426i
$67$	3.83926	+	6.64979i	0.469040	+	0.812401i	0.999374	−	0.0353880i	$-0.0112667\pi$
$67$	3.83926	+	6.64979i	0.469040	+	0.812401i	−0.530334	+	0.847789i	$0.677933\pi$
$68$	−2.34108	+	4.05487i	−0.283898	+	0.491725i
$69$	0.869807	+	1.04636i	0.104712	+	0.125967i
$70$	0.287545	−	4.00498i	0.0343682	−	0.478687i
$71$		−	3.76028i		−	0.446263i	−0.974788	−	0.223131i	$-0.928372\pi$
$71$		−	3.76028i		−	0.446263i	0.974788	−	0.223131i	$-0.0716279\pi$
$72$	−1.94949	+	2.28024i	−0.229750	+	0.268729i
$73$	8.74919	−	5.05135i	1.02402	−	0.591216i	0.108751	−	0.994069i	$-0.465315\pi$
$73$	8.74919	−	5.05135i	1.02402	−	0.591216i	0.915264	+	0.402853i	$0.131982\pi$
$74$	1.72595	−	0.996476i	0.200637	−	0.115838i
$75$	0.789867	+	4.60368i	0.0912060	+	0.531587i
$76$		−	7.07812i		−	0.811916i
$77$	−0.189469	+	2.63896i	−0.0215920	+	0.300737i
$78$	7.25845	−	6.03371i	0.821858	−	0.683183i
$79$	1.25177	−	2.16813i	0.140835	−	0.243934i	−0.786976	−	0.616983i	$-0.788355\pi$
$79$	1.25177	−	2.16813i	0.140835	−	0.243934i	0.927811	+	0.373050i	$0.121688\pi$
$80$	−0.758819	−	1.31431i	−0.0848385	−	0.146945i
$81$	1.39898	+	8.89060i	0.155442	+	0.987845i
$82$	7.57397	+	4.37283i	0.836405	+	0.482899i
$83$	−14.9747			−1.64369			−0.821843	−	0.569714i	$-0.807054\pi$
$83$	−14.9747			−1.64369			−0.821843	+	0.569714i	$0.807054\pi$
$84$	−4.17423	−	1.89097i	−0.455446	−	0.206322i
$85$	−7.10583			−0.770735
$86$	1.85872	+	1.07313i	0.200431	+	0.115719i
$87$	1.49061	−	4.03736i	0.159810	−	0.432850i
$88$	0.500000	+	0.866025i	0.0533002	+	0.0923186i
$89$	−4.91189	+	8.50765i	−0.520659	+	0.901809i	0.479052	+	0.877787i	$0.340981\pi$
$89$	−4.91189	+	8.50765i	−0.520659	+	0.901809i	−0.999711	+	0.0240221i	$0.992353\pi$
$90$	−4.47626	−	0.831951i	−0.471839	−	0.0876954i
$91$	11.9380	+	8.08467i	1.25145	+	0.847503i
$92$			0.785587i			0.0819031i
$93$	14.0270	−	2.40665i	1.45453	−	0.249558i
$94$	2.74666	−	1.58579i	0.283297	−	0.163561i
$95$	9.30286	−	5.37101i	0.954453	−	0.551054i
$96$	−1.70711	+	0.292893i	−0.174231	+	0.0298933i
$97$		−	9.37481i		−	0.951868i	−0.879481	−	0.475934i	$-0.842110\pi$
$97$		−	9.37481i		−	0.951868i	0.879481	−	0.475934i	$-0.157890\pi$
$98$	1.00000	−	6.92820i	0.101015	−	0.699854i
$99$	2.94949	+	0.548188i	0.296435	+	0.0550950i
$100$	−1.34839	+	2.33548i	−0.134839	+	0.233548i
$101$	−4.34046	−	7.51790i	−0.431892	−	0.748059i	0.565144	−	0.824992i	$-0.308820\pi$
$101$	−4.34046	−	7.51790i	−0.431892	−	0.748059i	−0.997036	+	0.0769334i	$0.975487\pi$
$102$	−2.80883	+	7.60779i	−0.278116	+	0.753283i
$103$	−12.9739	−	7.49051i	−1.27836	−	0.738061i	−0.301813	−	0.953367i	$-0.597592\pi$
$103$	−12.9739	−	7.49051i	−1.27836	−	0.738061i	−0.976547	+	0.215306i	$0.930925\pi$
$104$	5.44949			0.534366
$105$	−0.682163	−	6.92116i	−0.0665723	−	0.675436i
$106$	−5.76368			−0.559818
$107$	−11.0899	−	6.40276i	−1.07210	−	0.618978i	−0.143347	−	0.989673i	$-0.545786\pi$
$107$	−11.0899	−	6.40276i	−1.07210	−	0.618978i	−0.928755	+	0.370694i	$0.879120\pi$
$108$	−2.66012	+	4.46360i	−0.255970	+	0.429510i
$109$	2.11634	+	3.66560i	0.202708	+	0.351101i	0.949400	−	0.314069i	$-0.101692\pi$
$109$	2.11634	+	3.66560i	0.202708	+	0.351101i	−0.746692	+	0.665170i	$0.768359\pi$
$110$	−0.758819	+	1.31431i	−0.0723506	+	0.125315i
$111$	2.65451	−	2.20661i	0.251955	−	0.209442i
$112$	−1.15539	−	2.38014i	−0.109175	−	0.224902i
$113$			20.3443i			1.91383i	0.290361	+	0.956917i	$0.406225\pi$
$113$			20.3443i			1.91383i	−0.290361	+	0.956917i	$0.593775\pi$
$114$	−2.07313	−	12.0831i	−0.194167	−	1.13169i
$115$	−1.03251	+	0.596119i	−0.0962818	+	0.0555883i
$116$	2.15187	−	1.24238i	0.199796	−	0.115352i
$117$	10.6237	−	12.4261i	0.982164	−	1.14880i
$118$		−	5.11339i		−	0.470726i
$119$	−12.3560	−	0.887123i	−1.13268	−	0.0813225i
$120$	−1.68034	−	2.02142i	−0.153393	−	0.184530i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$	−4.78754	−	8.29227i	−0.433444	−	0.750747i
$123$	14.2103	+	5.24653i	1.28130	+	0.473064i
$124$	7.11597	+	4.10841i	0.639033	+	0.368946i
$125$	−11.6809			−1.04477
$126$	−7.67972	−	2.00548i	−0.684164	−	0.178663i
$127$	5.14402			0.456458			0.228229	−	0.973607i	$-0.426706\pi$
$127$	5.14402			0.456458			0.228229	+	0.973607i	$0.426706\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	3.48735	+	1.28754i	0.307044	+	0.113362i
$130$	4.13518	+	7.16234i	0.362679	+	0.628178i
$131$	−4.97394	+	8.61511i	−0.434575	+	0.752706i	−0.997261	−	0.0739651i	$-0.976435\pi$
$131$	−4.97394	+	8.61511i	−0.434575	+	0.752706i	0.562686	+	0.826671i	$0.309768\pi$
$132$	1.10721	+	1.33195i	0.0963699	+	0.115931i
$133$	16.8469	−	8.17802i	1.46081	−	0.709124i
$134$			7.67851i			0.663323i
$135$	−7.88512	−	0.109164i	−0.678643	−	0.00939534i
$136$	−4.05487	+	2.34108i	−0.347702	+	0.200746i
$137$	8.16560	−	4.71441i	0.697634	−	0.402779i	−0.108831	−	0.994060i	$-0.534711\pi$
$137$	8.16560	−	4.71441i	0.697634	−	0.402779i	0.806466	+	0.591281i	$0.201377\pi$
$138$	0.230093	+	1.34108i	0.0195868	+	0.114160i
$139$			7.37945i			0.625917i	0.949767	+	0.312959i	$0.101320\pi$
$139$			7.37945i			0.625917i	−0.949767	+	0.312959i	$0.898680\pi$
$140$	2.25151	−	3.32465i	0.190288	−	0.280984i
$141$	4.22438	−	3.51159i	0.355757	−	0.295729i
$142$	1.88014	−	3.25650i	0.157778	−	0.273279i
$143$	−2.72474	−	4.71940i	−0.227855	−	0.394656i
$144$	−2.82843	+	1.00000i	−0.235702	+	0.0833333i
$145$	3.26576	+	1.88549i	0.271207	+	0.156581i
$146$	10.1027			0.836105
$147$	−0.322117	−	12.1201i	−0.0265678	−	0.999647i
$148$	1.99295			0.163820
$149$	2.65515	+	1.53295i	0.217519	+	0.125584i	0.604801	−	0.796377i	$-0.293253\pi$
$149$	2.65515	+	1.53295i	0.217519	+	0.125584i	−0.387282	+	0.921961i	$0.626586\pi$
$150$	−1.61780	+	4.38184i	−0.132093	+	0.357776i
$151$	−7.38770	−	12.7959i	−0.601203	−	1.04131i	−0.992639	−	0.121109i	$-0.961355\pi$
$151$	−7.38770	−	12.7959i	−0.601203	−	1.04131i	0.391437	−	0.920205i	$-0.371978\pi$
$152$	3.53906	−	6.12983i	0.287056	−	0.497195i
$153$	−2.56671	+	13.8100i	−0.207506	+	1.11647i
$154$	−1.48356	+	2.19067i	−0.119549	+	0.176529i
$155$			12.4702i			1.00163i
$156$	9.30286	−	1.59612i	0.744825	−	0.127792i
$157$	11.0826	−	6.39853i	0.884487	−	0.510659i	0.0123515	−	0.999924i	$-0.496068\pi$
$157$	11.0826	−	6.39853i	0.884487	−	0.510659i	0.872135	+	0.489265i	$0.162735\pi$
$158$	2.16813	−	1.25177i	0.172487	−	0.0995855i
$159$	−9.83921	+	1.68814i	−0.780300	+	0.133878i
$160$		−	1.51764i		−	0.119980i
$161$	−1.86981	+	0.907663i	−0.147361	+	0.0715339i
$162$	−3.23375	+	8.39898i	−0.254067	+	0.659886i
$163$	1.07433	−	1.86080i	0.0841483	−	0.145749i	−0.820880	−	0.571101i	$-0.806516\pi$
$163$	1.07433	−	1.86080i	0.0841483	−	0.145749i	0.905028	+	0.425352i	$0.139850\pi$
$164$	4.37283	+	7.57397i	0.341461	+	0.591428i
$165$	−0.910432	+	2.46593i	−0.0708770	+	0.191972i
$166$	−12.9685	−	7.48735i	−1.00655	−	0.581131i
$167$	−10.7736			−0.833690			−0.416845	−	0.908978i	$-0.636864\pi$
$167$	−10.7736			−0.833690			−0.416845	+	0.908978i	$0.636864\pi$
$168$	−2.66951	−	3.72474i	−0.205957	−	0.287370i
$169$	−16.6969			−1.28438
$170$	−6.15383	−	3.55291i	−0.471977	−	0.272496i
$171$	−7.07812	−	20.0199i	−0.541277	−	1.53096i
$172$	1.07313	+	1.85872i	0.0818256	+	0.141726i
$173$	11.0455	−	19.1314i	0.839774	−	1.45453i	−0.0503096	−	0.998734i	$-0.516021\pi$
$173$	11.0455	−	19.1314i	0.839774	−	1.45453i	0.890084	−	0.455797i	$-0.150646\pi$
$174$	3.30959	−	2.75115i	0.250899	−	0.208564i
$175$	−7.11668	−	0.510954i	−0.537970	−	0.0386245i
$176$			1.00000i			0.0753778i
$177$	−1.49768	−	8.72911i	−0.112572	−	0.656120i
$178$	−8.50765	+	4.91189i	−0.637675	+	0.368162i
$179$	−2.33800	+	1.34985i	−0.174751	+	0.100892i	−0.584824	−	0.811160i	$-0.698836\pi$
$179$	−2.33800	+	1.34985i	−0.174751	+	0.100892i	0.410073	+	0.912053i	$0.365503\pi$
$180$	−3.46058	−	2.95862i	−0.257936	−	0.220523i
$181$			13.5013i			1.00354i	0.865000	+	0.501772i	$0.167318\pi$
$181$			13.5013i			1.00354i	−0.865000	+	0.501772i	$0.832682\pi$
$182$	6.29631	+	12.9705i	0.466714	+	0.961441i
$183$	−10.6016	−	12.7536i	−0.783693	−	0.942770i
$184$	−0.392794	+	0.680339i	−0.0289571	+	0.0501552i
$185$	1.51229	+	2.61936i	0.111186	+	0.192579i
$186$	13.3510	+	4.92927i	0.978946	+	0.361432i
$187$	4.05487	+	2.34108i	0.296522	+	0.171197i
$188$	3.17157			0.231311
$189$	−13.6975	−	1.17423i	−0.996346	−	0.0854130i
$190$	10.7420			0.779308
$191$	18.2850	+	10.5568i	1.32305	+	0.763865i	0.984215	−	0.176979i	$-0.0566325\pi$
$191$	18.2850	+	10.5568i	1.32305	+	0.763865i	0.338839	+	0.940844i	$0.389966\pi$
$192$	−1.62484	−	0.599900i	−0.117263	−	0.0432941i
$193$	8.44232	+	14.6225i	0.607691	+	1.05255i	0.991620	+	0.129189i	$0.0412375\pi$
$193$	8.44232	+	14.6225i	0.607691	+	1.05255i	−0.383929	+	0.923363i	$0.625429\pi$
$194$	4.68740	−	8.11882i	0.336536	−	0.582897i
$195$	9.15699	+	11.0157i	0.655746	+	0.788851i
$196$	4.33013	−	5.50000i	0.309295	−	0.392857i
$197$			27.8291i			1.98274i	0.131087	+	0.991371i	$0.458153\pi$
$197$			27.8291i			1.98274i	−0.131087	+	0.991371i	$0.541847\pi$
$198$	2.28024	+	1.94949i	0.162050	+	0.138544i
$199$	−7.81358	+	4.51117i	−0.553890	+	0.319788i	−0.750689	−	0.660655i	$-0.770278\pi$
$199$	−7.81358	+	4.51117i	−0.553890	+	0.319788i	0.196800	+	0.980444i	$0.436945\pi$
$200$	−2.33548	+	1.34839i	−0.165143	+	0.0953454i
$201$	2.24898	+	13.1080i	0.158631	+	0.924570i
$202$		−	8.68092i		−	0.610787i
$203$	5.44330	+	3.68631i	0.382045	+	0.258728i
$204$	−6.23641	+	5.18412i	−0.436636	+	0.362961i
$205$	−6.63638	+	11.4945i	−0.463505	+	0.802814i
$206$	−7.49051	−	12.9739i	−0.521888	−	0.903937i
$207$	0.785587	+	2.22198i	0.0546021	+	0.154438i
$208$	4.71940	+	2.72474i	0.327231	+	0.188927i
$209$	−7.07812			−0.489604
$210$	2.86981	−	6.33498i	0.198036	−	0.437155i
$211$	−15.2636			−1.05079			−0.525394	−	0.850859i	$-0.676082\pi$
$211$	−15.2636			−1.05079			−0.525394	+	0.850859i	$0.676082\pi$
$212$	−4.99149	−	2.88184i	−0.342817	−	0.197926i
$213$	2.25579	−	6.10987i	0.154564	−	0.418641i
$214$	−6.40276	−	11.0899i	−0.437684	−	0.758090i
$215$	−1.62863	+	2.82086i	−0.111071	+	0.192381i
$216$	−4.53553	+	2.53553i	−0.308604	+	0.172521i
$217$	−1.55683	+	21.6838i	−0.105684	+	1.47199i
$218$			4.23267i			0.286673i
$219$	17.2464	−	2.95901i	1.16540	−	0.199951i
$220$	−1.31431	+	0.758819i	−0.0886110	+	0.0511596i
$221$	22.0970	−	12.7577i	1.48640	−	0.858176i
$222$	3.40218	−	0.583722i	0.228339	−	0.0391769i
$223$			14.5622i			0.975154i	0.873080	+	0.487577i	$0.162119\pi$
$223$			14.5622i			0.975154i	−0.873080	+	0.487577i	$0.837881\pi$
$224$	0.189469	−	2.63896i	0.0126594	−	0.176323i
$225$	−1.47834	+	7.95411i	−0.0985560	+	0.530274i
$226$	−10.1722	+	17.6187i	−0.676643	+	1.17198i
$227$	−9.32316	−	16.1482i	−0.618800	−	1.07179i	−0.989705	−	0.143122i	$-0.954286\pi$
$227$	−9.32316	−	16.1482i	−0.618800	−	1.07179i	0.370905	−	0.928671i	$-0.379048\pi$
$228$	4.24616	−	11.5008i	0.281209	−	0.761662i
$229$	−9.75323	−	5.63103i	−0.644512	−	0.372109i	0.141839	−	0.989890i	$-0.454699\pi$
$229$	−9.75323	−	5.63103i	−0.644512	−	0.372109i	−0.786350	+	0.617781i	$0.788032\pi$
$230$	−1.19224			−0.0786138
$231$	−1.89097	+	4.17423i	−0.124417	+	0.274644i
$232$	2.48477			0.163133
$233$	8.40498	+	4.85262i	0.550628	+	0.317905i	0.749375	−	0.662145i	$-0.230354\pi$
$233$	8.40498	+	4.85262i	0.550628	+	0.317905i	−0.198747	+	0.980051i	$0.563687\pi$
$234$	15.4135	−	5.44949i	1.00761	−	0.356244i
$235$	2.40665	+	4.16844i	0.156993	+	0.271919i
$236$	2.55670	−	4.42833i	0.166427	−	0.288260i
$237$	3.33460	−	2.77194i	0.216605	−	0.180057i
$238$	−10.2571	−	6.94629i	−0.664868	−	0.450261i
$239$			11.2896i			0.730264i	0.930956	+	0.365132i	$0.118976\pi$
$239$			11.2896i			0.730264i	−0.930956	+	0.365132i	$0.881024\pi$
$240$	−0.444506	−	2.59077i	−0.0286927	−	0.167234i
$241$	26.1036	−	15.0709i	1.68148	−	0.970805i	0.720806	−	0.693137i	$-0.243772\pi$
$241$	26.1036	−	15.0709i	1.68148	−	0.970805i	0.960677	−	0.277668i	$-0.0895616\pi$
$242$	0.866025	−	0.500000i	0.0556702	−	0.0321412i
$243$	−3.06035	+	15.2851i	−0.196322	+	0.980540i
$244$		−	9.57509i		−	0.612982i
$245$	10.5145	+	1.51764i	0.671747	+	0.0969583i
$246$	9.68326	+	11.6488i	0.617382	+	0.742700i
$247$	−19.2861	+	33.4044i	−1.22714	+	2.12547i
$248$	4.10841	+	7.11597i	0.260884	+	0.451865i
$249$	−24.3315	−	8.98332i	−1.54195	−	0.569295i
$250$	−10.1160	−	5.84046i	−0.639790	−	0.369383i
$251$	−11.5357			−0.728126			−0.364063	−	0.931374i	$-0.618611\pi$
$251$	−11.5357			−0.728126			−0.364063	+	0.931374i	$0.618611\pi$
$252$	−5.64809	−	5.57666i	−0.355796	−	0.351296i
$253$	0.785587			0.0493894
$254$	4.45486	+	2.57201i	0.279523	+	0.161382i
$255$	−11.5459	−	4.26279i	−0.723030	−	0.266946i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.93658	+	6.81835i	−0.245557	+	0.425317i	−0.962288	−	0.272033i	$-0.912304\pi$
$257$	−3.93658	+	6.81835i	−0.245557	+	0.425317i	0.716731	+	0.697350i	$0.245638\pi$
$258$	2.37636	+	2.85872i	0.147946	+	0.177976i
$259$	2.30265	+	4.74350i	0.143079	+	0.294747i
$260$			8.27035i			0.512906i
$261$	4.84403	−	5.66586i	0.299838	−	0.350708i
$262$	−8.61511	+	4.97394i	−0.532243	+	0.307291i
$263$	−17.6811	+	10.2082i	−1.09026	+	0.629465i	−0.933647	−	0.358195i	$-0.883392\pi$
$263$	−17.6811	+	10.2082i	−1.09026	+	0.629465i	−0.156618	+	0.987659i	$0.550059\pi$
$264$	0.292893	+	1.70711i	0.0180263	+	0.105065i
$265$		−	8.74718i		−	0.537335i
$266$	18.6789	+	1.34108i	1.14527	+	0.0822270i
$267$	−13.0848	+	10.8770i	−0.800777	+	0.665659i
$268$	−3.83926	+	6.64979i	−0.234520	+	0.406200i
$269$	8.53225	+	14.7783i	0.520220	+	0.901048i	0.999724	+	0.0235081i	$0.00748356\pi$
$269$	8.53225	+	14.7783i	0.520220	+	0.901048i	−0.479503	+	0.877540i	$0.659183\pi$
$270$	−6.77414	−	4.03710i	−0.412261	−	0.245690i
$271$	−21.0954	−	12.1795i	−1.28146	−	0.739849i	−0.304342	−	0.952563i	$-0.598437\pi$
$271$	−21.0954	−	12.1795i	−1.28146	−	0.739849i	−0.977115	+	0.212713i	$0.931770\pi$
$272$	−4.68216			−0.283898
$273$	14.5475	+	20.2980i	0.880452	+	1.22849i
$274$	9.42883			0.569616
$275$	2.33548	+	1.34839i	0.140834	+	0.0813108i
$276$	−0.471274	+	1.27646i	−0.0283674	+	0.0768337i
$277$	−6.73231	−	11.6607i	−0.404505	−	0.700624i	0.589759	−	0.807580i	$-0.299223\pi$
$277$	−6.73231	−	11.6607i	−0.404505	−	0.700624i	−0.994264	+	0.106956i	$0.965890\pi$
$278$	−3.68973	+	6.39079i	−0.221295	+	0.383294i
$279$	24.2354	+	4.50436i	1.45094	+	0.269669i
$280$	3.61219	−	1.75347i	0.215870	−	0.104790i
$281$		−	20.0803i		−	1.19789i	−0.800791	−	0.598944i	$-0.795587\pi$
$281$		−	20.0803i		−	1.19789i	0.800791	−	0.598944i	$-0.204413\pi$
$282$	5.41421	−	0.928932i	0.322412	−	0.0553171i
$283$	−11.6196	+	6.70857i	−0.690712	+	0.398783i	−0.803879	−	0.594793i	$-0.797234\pi$
$283$	−11.6196	+	6.70857i	−0.690712	+	0.398783i	0.113167	+	0.993576i	$0.463901\pi$
$284$	3.25650	−	1.88014i	0.193238	−	0.111566i
$285$	18.3378	−	3.14626i	1.08624	−	0.186369i
$286$		−	5.44949i		−	0.322235i
$287$	−12.9748	+	19.1589i	−0.765876	+	1.13091i
$288$	−2.94949	−	0.548188i	−0.173800	−	0.0323023i
$289$	−2.46132	+	4.26314i	−0.144784	+	0.250773i
$290$	1.88549	+	3.26576i	0.110720	+	0.191772i
$291$	5.62395	−	15.2326i	0.329682	−	0.892951i
$292$	8.74919	+	5.05135i	0.512008	+	0.295608i
$293$	13.7994			0.806168			0.403084	−	0.915163i	$-0.367938\pi$
$293$	13.7994			0.806168			0.403084	+	0.915163i	$0.367938\pi$
$294$	5.78108	−	10.6574i	0.337159	−	0.621549i
$295$	7.76028			0.451821
$296$	1.72595	+	0.996476i	0.100319	+	0.0579190i
$297$	4.46360	+	2.66012i	0.259005	+	0.154356i
$298$	1.53295	+	2.65515i	0.0888016	+	0.153809i
$299$	2.14052	−	3.70750i	0.123790	−	0.214410i
$300$	−3.59197	+	2.98589i	−0.207383	+	0.172390i
$301$	−3.18412	+	4.70176i	−0.183530	+	0.271005i
$302$		−	14.7754i		−	0.850229i
$303$	−2.54258	−	14.8193i	−0.146068	−	0.851344i
$304$	6.12983	−	3.53906i	0.351570	−	0.202979i
$305$	12.5847	−	7.26576i	0.720596	−	0.416036i
$306$	−9.12783	+	10.6764i	−0.521803	+	0.610332i
$307$			25.9970i			1.48373i	0.670550	+	0.741864i	$0.266058\pi$
$307$			25.9970i			1.48373i	−0.670550	+	0.741864i	$0.733942\pi$
$308$	−2.38014	+	1.15539i	−0.135621	+	0.0658347i
$309$	−16.5871	−	19.9540i	−0.943605	−	1.13514i
$310$	−6.23508	+	10.7995i	−0.354129	+	0.613369i
$311$	−0.607206	−	1.05171i	−0.0344315	−	0.0596371i	0.848296	−	0.529522i	$-0.177629\pi$
$311$	−0.607206	−	1.05171i	−0.0344315	−	0.0596371i	−0.882728	+	0.469885i	$0.844295\pi$
$312$	8.85457	+	3.26915i	0.501291	+	0.185079i
$313$	20.4649	+	11.8154i	1.15674	+	0.667846i	0.950521	−	0.310659i	$-0.100550\pi$
$313$	20.4649	+	11.8154i	1.15674	+	0.667846i	0.206222	+	0.978505i	$0.433883\pi$
$314$	12.7971			0.722180
$315$	3.04360	−	11.6550i	0.171487	−	0.656687i
$316$	2.50354			0.140835
$317$	−24.4579	−	14.1208i	−1.37369	−	0.793102i	−0.382302	−	0.924037i	$-0.624869\pi$
$317$	−24.4579	−	14.1208i	−1.37369	−	0.793102i	−0.991391	+	0.130935i	$0.958202\pi$
$318$	−9.36508	−	3.45763i	−0.525168	−	0.193894i
$319$	−1.24238	−	2.15187i	−0.0695601	−	0.120482i
$320$	0.758819	−	1.31431i	0.0424193	−	0.0734723i
$321$	−14.1784	−	17.0563i	−0.791359	−	0.951992i
$322$	−2.07313	−	0.148844i	−0.115531	−	0.00829476i
$323$		−	33.1409i		−	1.84401i
$324$	−7.00000	+	5.65685i	−0.388889	+	0.314270i
$325$	12.7271	−	7.34802i	0.705975	−	0.407595i
$326$	1.86080	−	1.07433i	0.103060	−	0.0595019i
$327$	1.23972	+	7.22562i	0.0685567	+	0.399578i
$328$			8.74567i			0.482899i
$329$	3.66442	+	7.54879i	0.202026	+	0.416178i
$330$	−2.02142	+	1.68034i	−0.111276	+	0.0924996i
$331$	−3.89279	+	6.74252i	−0.213967	+	0.370602i	−0.952953	−	0.303119i	$-0.901972\pi$
$331$	−3.89279	+	6.74252i	−0.213967	+	0.370602i	0.738985	+	0.673722i	$0.235305\pi$
$332$	−7.48735	−	12.9685i	−0.410921	−	0.711737i
$333$	5.63692	−	1.99295i	0.308901	−	0.109213i
$334$	−9.33025	−	5.38682i	−0.510529	−	0.294754i
$335$	−11.6532			−0.636683
$336$	−0.449490	−	4.56048i	−0.0245217	−	0.248794i
$337$	−0.772220			−0.0420655			−0.0210327	−	0.999779i	$-0.506695\pi$
$337$	−0.772220			−0.0420655			−0.0210327	+	0.999779i	$0.506695\pi$
$338$	−14.4600	−	8.34847i	−0.786519	−	0.454097i
$339$	−12.2046	+	33.0564i	−0.662862	+	1.79538i
$340$	−3.55291	−	6.15383i	−0.192684	−	0.333738i
$341$	4.10841	−	7.11597i	0.222483	−	0.385351i
$342$	3.88014	−	20.8768i	0.209814	−	1.12889i
$343$	18.0938	+	3.95164i	0.976972	+	0.213368i
$344$			2.14626i			0.115719i
$345$	−2.03528	+	0.349198i	−0.109576	+	0.0188002i
$346$	19.1314	−	11.0455i	1.02851	−	0.593810i
$347$	8.58736	−	4.95792i	0.460994	−	0.266155i	−0.251468	−	0.967866i	$-0.580913\pi$
$347$	8.58736	−	4.95792i	0.460994	−	0.266155i	0.712462	+	0.701711i	$0.247580\pi$
$348$	4.24176	−	0.727771i	0.227382	−	0.0390126i
$349$			0.520394i			0.0278560i	0.999903	+	0.0139280i	$0.00443357\pi$
$349$			0.520394i			0.0278560i	−0.999903	+	0.0139280i	$0.995566\pi$
$350$	−5.90775	−	4.00084i	−0.315782	−	0.213854i
$351$	24.7163	−	13.8174i	1.31926	−	0.737516i
$352$	−0.500000	+	0.866025i	−0.0266501	+	0.0461593i
$353$	3.20220	+	5.54638i	0.170436	+	0.295204i	0.938572	−	0.345082i	$-0.112149\pi$
$353$	3.20220	+	5.54638i	0.170436	+	0.295204i	−0.768136	+	0.640286i	$0.778816\pi$
$354$	3.06753	−	8.30847i	0.163037	−	0.441590i
$355$	4.94218	+	2.85337i	0.262304	+	0.151441i
$356$	−9.82378			−0.520659
$357$	−19.5444	−	8.85383i	−1.03440	−	0.468594i
$358$	−2.69969			−0.142683
$359$	−10.9896	−	6.34486i	−0.580010	−	0.334869i	0.181127	−	0.983460i	$-0.442025\pi$
$359$	−10.9896	−	6.34486i	−0.580010	−	0.334869i	−0.761137	+	0.648591i	$0.775359\pi$
$360$	−1.51764	−	4.29253i	−0.0799866	−	0.226236i
$361$	15.5499	+	26.9332i	0.818414	+	1.41753i
$362$	−6.75065	+	11.6925i	−0.354806	+	0.614543i
$363$	1.33195	−	1.10721i	0.0699093	−	0.0581133i
$364$	−1.03251	+	14.3810i	−0.0541181	+	0.753768i
$365$			15.3322i			0.802526i
$366$	−2.80448	−	16.3457i	−0.146592	−	0.854403i
$367$	−13.3308	+	7.69653i	−0.695862	+	0.401756i	−0.805804	−	0.592182i	$-0.798267\pi$
$367$	−13.3308	+	7.69653i	−0.695862	+	0.401756i	0.109943	+	0.993938i	$0.464933\pi$
$368$	−0.680339	+	0.392794i	−0.0354651	+	0.0204758i
$369$	19.9422	+	17.0496i	1.03815	+	0.887566i
$370$			3.02458i			0.157240i
$371$	1.09204	−	15.2101i	0.0566957	−	0.789669i
$372$	9.09771	+	10.9444i	0.471694	+	0.567441i
$373$	−1.02362	+	1.77296i	−0.0530009	+	0.0918003i	−0.891309	−	0.453397i	$-0.850212\pi$
$373$	−1.02362	+	1.77296i	−0.0530009	+	0.0918003i	0.838308	+	0.545197i	$0.183545\pi$
$374$	2.34108	+	4.05487i	0.121054	+	0.209672i
$375$	−18.9797	−	7.00739i	−0.980106	−	0.361860i
$376$	2.74666	+	1.58579i	0.141648	+	0.0817807i
$377$	−13.5407			−0.697382
$378$	−11.2753	−	7.86566i	−0.579937	−	0.404566i
$379$	8.98462			0.461509			0.230755	−	0.973012i	$-0.425881\pi$
$379$	8.98462			0.461509			0.230755	+	0.973012i	$0.425881\pi$
$380$	9.30286	+	5.37101i	0.477227	+	0.275527i
$381$	8.35824	+	3.08590i	0.428206	+	0.158096i
$382$	10.5568	+	18.2850i	0.540134	+	0.935540i
$383$	14.2861	−	24.7442i	0.729984	−	1.26437i	−0.226906	−	0.973917i	$-0.572861\pi$
$383$	14.2861	−	24.7442i	0.729984	−	1.26437i	0.956890	−	0.290452i	$-0.0938057\pi$
$384$	−1.10721	−	1.33195i	−0.0565019	−	0.0679709i
$385$	−3.32465	−	2.25151i	−0.169440	−	0.114748i
$386$			16.8846i			0.859405i
$387$	4.89400	+	4.18412i	0.248776	+	0.212691i
$388$	8.11882	−	4.68740i	0.412171	−	0.237967i
$389$	2.37424	−	1.37077i	0.120379	−	0.0695008i	−0.438602	−	0.898682i	$-0.644526\pi$
$389$	2.37424	−	1.37077i	0.120379	−	0.0695008i	0.558980	+	0.829181i	$0.311193\pi$
$390$	2.42233	+	14.1184i	0.122659	+	0.714912i
$391$			3.67825i			0.186017i
$392$	6.50000	−	2.59808i	0.328300	−	0.131223i
$393$	−13.2501	+	11.0143i	−0.668378	+	0.555600i
$394$	−13.9146	+	24.1007i	−0.701005	+	1.21418i
$395$	1.89974	+	3.29044i	0.0955860	+	0.165560i
$396$	1.00000	+	2.82843i	0.0502519	+	0.142134i
$397$	11.2031	+	6.46809i	0.562265	+	0.324624i	0.754054	−	0.656812i	$-0.228096\pi$
$397$	11.2031	+	6.46809i	0.562265	+	0.324624i	−0.191789	+	0.981436i	$0.561429\pi$
$398$	−9.02234			−0.452249
$399$	32.2796	−	3.18154i	1.61600	−	0.159276i
$400$	−2.69677			−0.134839
$401$	−22.3078	−	12.8794i	−1.11400	−	0.643166i	−0.174135	−	0.984722i	$-0.555713\pi$
$401$	−22.3078	−	12.8794i	−1.11400	−	0.643166i	−0.939862	+	0.341556i	$0.889046\pi$
$402$	−4.60634	+	12.4764i	−0.229744	+	0.622266i
$403$	−22.3887	−	38.7784i	−1.11526	−	1.93169i
$404$	4.34046	−	7.51790i	0.215946	−	0.374029i
$405$	−12.7466	−	4.90766i	−0.633384	−	0.243864i
$406$	2.87088	+	5.91409i	0.142480	+	0.293511i
$407$		−	1.99295i		−	0.0987870i
$408$	−7.99295	+	1.37137i	−0.395710	+	0.0678931i
$409$	−5.61478	+	3.24170i	−0.277633	+	0.160292i	−0.632351	−	0.774682i	$-0.717910\pi$
$409$	−5.61478	+	3.24170i	−0.277633	+	0.160292i	0.354718	+	0.934973i	$0.384577\pi$
$410$	−11.4945	+	6.63638i	−0.567675	+	0.327747i
$411$	16.0960	−	2.76164i	0.793958	−	0.136222i
$412$		−	14.9810i		−	0.738061i
$413$	13.4940	+	0.968828i	0.663998	+	0.0476729i
$414$	−0.430650	+	2.31708i	−0.0211653	+	0.113878i
$415$	11.3631	−	19.6814i	0.557792	−	0.966124i
$416$	2.72474	+	4.71940i	0.133592	+	0.231387i
$417$	−4.42694	+	11.9905i	−0.216788	+	0.587175i
$418$	−6.12983	−	3.53906i	−0.299820	−	0.173101i
$419$	−3.54875			−0.173368			−0.0866839	−	0.996236i	$-0.527627\pi$
$419$	−3.54875			−0.173368			−0.0866839	+	0.996236i	$0.527627\pi$
$420$	5.65281	−	4.05135i	0.275829	−	0.197686i
$421$	−10.8092			−0.526807			−0.263403	−	0.964686i	$-0.584845\pi$
$421$	−10.8092			−0.526807			−0.263403	+	0.964686i	$0.584845\pi$
$422$	−13.2186	−	7.63179i	−0.643473	−	0.371510i
$423$	8.97056	−	3.17157i	0.436164	−	0.154207i
$424$	−2.88184	−	4.99149i	−0.139954	−	0.242408i
$425$	−6.31337	+	10.9351i	−0.306243	+	0.530429i
$426$	5.00851	−	4.16340i	0.242663	−	0.201718i
$427$	22.7900	−	11.0630i	1.10289	−	0.535376i
$428$		−	12.8055i		−	0.618978i
$429$	−1.59612	−	9.30286i	−0.0770613	−	0.449146i
$430$	−2.82086	+	1.62863i	−0.136034	+	0.0785393i
$431$	23.7313	−	13.7013i	1.14310	−	0.659966i	0.195900	−	0.980624i	$-0.437237\pi$
$431$	23.7313	−	13.7013i	1.14310	−	0.659966i	0.947195	+	0.320657i	$0.103904\pi$
$432$	−5.19565	−	0.0719302i	−0.249976	−	0.00346074i
$433$		−	21.8530i		−	1.05019i	−0.851044	−	0.525094i	$-0.824030\pi$
$433$		−	21.8530i		−	1.05019i	0.851044	−	0.525094i	$-0.175970\pi$
$434$	−12.1902	+	18.0003i	−0.585147	+	0.864044i
$435$	4.17525	+	5.02276i	0.200188	+	0.240823i
$436$	−2.11634	+	3.66560i	−0.101354	+	0.175551i
$437$	−2.78024	−	4.81552i	−0.132997	−	0.230357i
$438$	16.4153	+	6.06061i	0.784354	+	0.289587i
$439$	−31.4237	−	18.1425i	−1.49977	−	0.865892i	−0.499769	−	0.866158i	$-0.666582\pi$
$439$	−31.4237	−	18.1425i	−1.49977	−	0.865892i	−1.00000		0.000266220i	$0.999915\pi$
$440$	−1.51764			−0.0723506
$441$	6.74745	−	19.8865i	0.321307	−	0.946975i
$442$	25.5154			1.21364
$443$	0.638443	+	0.368605i	0.0303333	+	0.0175130i	0.515090	−	0.857136i	$-0.327758\pi$
$443$	0.638443	+	0.368605i	0.0303333	+	0.0175130i	−0.484757	+	0.874649i	$0.661092\pi$
$444$	3.23824	+	1.19557i	0.153680	+	0.0567394i
$445$	−7.45447	−	12.9115i	−0.353376	−	0.612065i
$446$	−7.28108	+	12.6112i	−0.344769	+	0.597157i
$447$	3.39459	+	4.08364i	0.160559	+	0.193150i
$448$	1.48356	−	2.19067i	0.0700918	−	0.103499i
$449$		−	31.9095i		−	1.50590i	−0.658077	−	0.752950i	$-0.728630\pi$
$449$		−	31.9095i		−	1.50590i	0.658077	−	0.752950i	$-0.271370\pi$
$450$	−5.25733	+	6.14929i	−0.247833	+	0.289880i
$451$	7.57397	−	4.37283i	0.356644	−	0.205909i
$452$	−17.6187	+	10.1722i	−0.828715	+	0.478459i
$453$	−4.32762	−	25.2232i	−0.203329	−	1.18509i
$454$		−	18.6463i		−	0.875115i
$455$	−19.6846	+	9.55552i	−0.922828	+	0.447970i
$456$	9.42771	−	7.83694i	0.441493	−	0.366998i
$457$	10.7640	−	18.6438i	0.503520	−	0.872121i	−0.496472	−	0.868053i	$-0.665372\pi$
$457$	10.7640	−	18.6438i	0.503520	−	0.872121i	0.999992	−	0.00406879i	$-0.00129514\pi$
$458$	−5.63103	−	9.75323i	−0.263121	−	0.455739i
$459$	−12.4551	+	20.8993i	−0.581355	+	0.975497i
$460$	−1.03251	−	0.596119i	−0.0481409	−	0.0277942i
$461$	−1.43738			−0.0669457			−0.0334728	−	0.999440i	$-0.510657\pi$
$461$	−1.43738			−0.0669457			−0.0334728	+	0.999440i	$0.510657\pi$
$462$	−3.72474	+	2.66951i	−0.173291	+	0.124197i
$463$	7.15018			0.332297			0.166149	−	0.986101i	$-0.446867\pi$
$463$	7.15018			0.332297			0.166149	+	0.986101i	$0.446867\pi$
$464$	2.15187	+	1.24238i	0.0998981	+	0.0576762i
$465$	−7.48085	+	20.2621i	−0.346916	+	0.939631i
$466$	4.85262	+	8.40498i	0.224793	+	0.389353i
$467$	−0.641199	+	1.11059i	−0.0296711	+	0.0513919i	−0.880480	−	0.474084i	$-0.842779\pi$
$467$	−0.641199	+	1.11059i	−0.0296711	+	0.0513919i	0.850809	+	0.525476i	$0.176113\pi$
$468$	16.0732	+	2.98735i	0.742985	+	0.138090i
$469$	−20.2633	−	1.45484i	−0.935671	−	0.0671782i
$470$			4.81330i			0.222021i
$471$	21.8460	−	3.74817i	1.00661	−	0.172707i
$472$	4.42833	−	2.55670i	0.203830	−	0.117681i
$473$	1.85872	−	1.07313i	0.0854640	−	0.0493427i
$474$	4.27381	−	0.733270i	0.196303	−	0.0336802i
$475$		−	19.0881i		−	0.875821i
$476$	−5.40975	−	11.1442i	−0.247955	−	0.510794i
$477$	−16.9999	−	3.15958i	−0.778372	−	0.144667i
$478$	−5.64480	+	9.77709i	−0.258187	+	0.447194i
$479$	−1.91275	−	3.31299i	−0.0873960	−	0.151374i	0.819014	−	0.573774i	$-0.194521\pi$
$479$	−1.91275	−	3.31299i	−0.0873960	−	0.151374i	−0.906410	+	0.422400i	$0.861188\pi$
$480$	0.910432	−	2.46593i	0.0415553	−	0.112554i
$481$	−9.40553	−	5.43029i	−0.428855	−	0.247600i
$482$	30.1419			1.37293
$483$	−3.58265	+	0.353113i	−0.163016	+	0.0160672i
$484$	1.00000			0.0454545
$485$	12.3214	+	7.11378i	0.559488	+	0.323020i
$486$	−10.2929	+	11.7071i	−0.466895	+	0.531045i
$487$	1.08310	+	1.87598i	0.0490799	+	0.0850089i	0.889522	−	0.456893i	$-0.151038\pi$
$487$	1.08310	+	1.87598i	0.0490799	+	0.0850089i	−0.840442	+	0.541902i	$0.817704\pi$
$488$	4.78754	−	8.29227i	0.216722	−	0.375373i
$489$	2.86192	−	2.37902i	0.129421	−	0.107583i
$490$	8.34701	+	6.57157i	0.377079	+	0.296873i
$491$		−	12.4561i		−	0.562134i	−0.959688	−	0.281067i	$-0.909312\pi$
$491$		−	12.4561i		−	0.562134i	0.959688	−	0.281067i	$-0.0906883\pi$
$492$	2.56155	+	14.9298i	0.115483	+	0.673087i
$493$	10.0754	−	5.81704i	0.453774	−	0.261986i
$494$	−33.4044	+	19.2861i	−1.50294	+	0.867721i
$495$	−2.95862	+	3.46058i	−0.132980	+	0.155541i
$496$			8.21682i			0.368946i
$497$	8.23753	+	5.57861i	0.369504	+	0.250235i
$498$	−16.5801	−	19.9456i	−0.742971	−	0.893782i
$499$	15.4928	−	26.8344i	0.693555	−	1.20127i	−0.277110	−	0.960838i	$-0.589377\pi$
$499$	15.4928	−	26.8344i	0.693555	−	1.20127i	0.970665	−	0.240434i	$-0.0772899\pi$
$500$	−5.84046	−	10.1160i	−0.261193	−	0.452400i
$501$	−17.5055	−	6.46311i	−0.782088	−	0.288751i
$502$	−9.99020	−	5.76784i	−0.445884	−	0.257431i
$503$	−3.09862			−0.138160			−0.0690802	−	0.997611i	$-0.522006\pi$
$503$	−3.09862			−0.138160			−0.0690802	+	0.997611i	$0.522006\pi$
$504$	−2.10306	−	7.65357i	−0.0936777	−	0.340917i
$505$	13.1745			0.586257
$506$	0.680339	+	0.392794i	0.0302447	+	0.0174618i
$507$	−27.1299	−	10.0165i	−1.20488	−	0.444848i
$508$	2.57201	+	4.45486i	0.114115	+	0.197652i
$509$	−14.0084	+	24.2632i	−0.620911	+	1.07545i	0.368406	+	0.929665i	$0.379904\pi$
$509$	−14.0084	+	24.2632i	−0.620911	+	1.07545i	−0.989316	+	0.145784i	$0.953430\pi$
$510$	−7.86762	−	9.46462i	−0.348384	−	0.419100i
$511$	−1.91414	+	26.6606i	−0.0846768	+	1.17940i
$512$		−	1.00000i		−	0.0441942i
$513$	0.509130	−	36.7754i	0.0224786	−	1.62368i
$514$	−6.81835	+	3.93658i	−0.300745	+	0.173635i
$515$	19.6897	−	11.3679i	0.867634	−	0.500928i
$516$	0.628626	+	3.66390i	0.0276737	+	0.161294i
$517$		−	3.17157i		−	0.139486i
$518$	−0.377602	+	5.25932i	−0.0165909	+	0.231081i
$519$	29.4241	−	24.4593i	1.29158	−	1.07364i
$520$	−4.13518	+	7.16234i	−0.181339	+	0.314089i
$521$	16.4322	+	28.4614i	0.719908	+	1.24692i	0.961036	+	0.276424i	$0.0891493\pi$
$521$	16.4322	+	28.4614i	0.719908	+	1.24692i	−0.241128	+	0.970493i	$0.577517\pi$
$522$	7.02798	−	2.48477i	0.307606	−	0.108755i
$523$	34.0396	+	19.6528i	1.48845	+	0.859356i	0.999913	−	0.0131872i	$-0.00419774\pi$
$523$	34.0396	+	19.6528i	1.48845	+	0.859356i	0.488536	+	0.872544i	$0.337531\pi$
$524$	−9.94787			−0.434575
$525$	−11.2570	−	5.09952i	−0.491294	−	0.222561i
$526$	−20.4164			−0.890198
$527$	33.3181	+	19.2362i	1.45136	+	0.837944i
$528$	−0.599900	+	1.62484i	−0.0261073	+	0.0707123i
$529$	−11.1914	−	19.3841i	−0.486584	−	0.842788i
$530$	4.37359	−	7.57528i	0.189977	−	0.329049i
$531$	2.80310	−	15.0819i	0.121644	−	0.654499i
$532$	15.5058	+	10.5008i	0.672263	+	0.455269i
$533$		−	47.6594i		−	2.06436i
$534$	−16.7702	+	2.87732i	−0.725720	+	0.124514i
$535$	16.8305	−	9.71707i	0.727645	−	0.420106i
$536$	−6.64979	+	3.83926i	−0.287227	+	0.165831i
$537$	−4.60867	+	0.790722i	−0.198879	+	0.0341222i
$538$			17.0645i			0.735703i
$539$	−5.50000	−	4.33013i	−0.236902	−	0.186512i
$540$	−3.84802	−	6.88330i	−0.165593	−	0.296210i
$541$	−14.6605	+	25.3928i	−0.630305	+	1.09172i	0.357185	+	0.934034i	$0.383737\pi$
$541$	−14.6605	+	25.3928i	−0.630305	+	1.09172i	−0.987489	+	0.157686i	$0.949597\pi$
$542$	−12.1795	−	21.0954i	−0.523153	−	0.906127i
$543$	−8.09944	+	21.9375i	−0.347580	+	0.941429i
$544$	−4.05487	−	2.34108i	−0.173851	−	0.100373i
$545$	−6.42367			−0.275160
$546$	2.44949	+	24.8523i	0.104828	+	1.06358i
$547$	5.17522			0.221276			0.110638	−	0.993861i	$-0.464711\pi$
$547$	5.17522			0.221276			0.110638	+	0.993861i	$0.464711\pi$
$548$	8.16560	+	4.71441i	0.348817	+	0.201390i
$549$	−9.57509	−	27.0824i	−0.408655	−	1.15585i
$550$	1.34839	+	2.33548i	0.0574954	+	0.0995850i
$551$	−8.79373	+	15.2312i	−0.374626	+	0.648870i
$552$	−1.04636	+	0.869807i	−0.0445362	+	0.0370215i
$553$	2.89258	+	5.95878i	0.123005	+	0.253393i
$554$		−	13.4646i		−	0.572057i
$555$	0.885879	+	5.16328i	0.0376035	+	0.219169i
$556$	−6.39079	+	3.68973i	−0.271030	+	0.156479i
$557$	−17.4276	+	10.0618i	−0.738429	+	0.426332i	−0.821498	−	0.570211i	$-0.806861\pi$
$557$	−17.4276	+	10.0618i	−0.738429	+	0.426332i	0.0830687	+	0.996544i	$0.473528\pi$
$558$	18.7363	+	16.0186i	0.793171	+	0.678121i
$559$		−	11.6960i		−	0.494690i
$560$	4.00498	+	0.287545i	0.169241	+	0.0121510i
$561$	5.18412	+	6.23641i	0.218874	+	0.263302i
$562$	10.0401	−	17.3900i	0.423518	−	0.733554i
$563$	13.3041	+	23.0435i	0.560703	+	0.971166i	0.997435	+	0.0715744i	$0.0228023\pi$
$563$	13.3041	+	23.0435i	0.560703	+	0.971166i	−0.436732	+	0.899591i	$0.643864\pi$
$564$	5.15331	+	1.90263i	0.216994	+	0.0801151i
$565$	−26.7388	−	15.4377i	−1.12491	−	0.649468i
$566$	−13.4171			−0.563964
$567$	−21.5519	−	10.1251i	−0.905093	−	0.425213i
$568$	3.76028			0.157778
$569$	19.2277	+	11.1011i	0.806067	+	0.465383i	0.845588	−	0.533836i	$-0.179250\pi$
$569$	19.2277	+	11.1011i	0.806067	+	0.465383i	−0.0395214	+	0.999219i	$0.512583\pi$
$570$	17.4541	+	6.44414i	0.731072	+	0.269915i
$571$	−5.56729	−	9.64282i	−0.232984	−	0.403540i	0.725701	−	0.688010i	$-0.241516\pi$
$571$	−5.56729	−	9.64282i	−0.232984	−	0.403540i	−0.958685	+	0.284471i	$0.908182\pi$
$572$	2.72474	−	4.71940i	0.113927	−	0.197328i
$573$	23.3772	+	28.1224i	0.976596	+	1.17483i
$574$	−20.8159	+	10.1047i	−0.868839	+	0.421762i
$575$			2.11855i			0.0883497i
$576$	−2.28024	−	1.94949i	−0.0950100	−	0.0812287i
$577$	−4.23651	+	2.44595i	−0.176368	+	0.101826i	−0.585585	−	0.810611i	$-0.699135\pi$
$577$	−4.23651	+	2.44595i	−0.176368	+	0.101826i	0.409217	+	0.912437i	$0.365802\pi$
$578$	−4.26314	+	2.46132i	−0.177323	+	0.102378i
$579$	4.94539	+	28.8239i	0.205524	+	1.19788i
$580$			3.77098i			0.156581i
$581$	22.2159	−	32.8046i	0.921671	−	1.36096i
$582$	12.4868	−	10.3798i	0.517594	−	0.430259i
$583$	−2.88184	+	4.99149i	−0.119354	+	0.206726i
$584$	5.05135	+	8.74919i	0.209026	+	0.362044i
$585$	8.27035	+	23.3921i	0.341937	+	0.967144i
$586$	11.9506	+	6.89968i	0.493675	+	0.285023i
$587$	20.7854			0.857904			0.428952	−	0.903327i	$-0.358883\pi$
$587$	20.7854			0.857904			0.428952	+	0.903327i	$0.358883\pi$
$588$	10.3352	−	6.33900i	0.426218	−	0.261416i
$589$	−58.1596			−2.39642
$590$	6.72060	+	3.88014i	0.276683	+	0.159743i
$591$	−16.6947	+	45.2180i	−0.686728	+	1.86002i
$592$	0.996476	+	1.72595i	0.0409549	+	0.0709360i
$593$	22.1769	−	38.4116i	0.910698	−	1.57738i	0.0976177	−	0.995224i	$-0.468878\pi$
$593$	22.1769	−	38.4116i	0.910698	−	1.57738i	0.813080	−	0.582151i	$-0.197789\pi$
$594$	2.53553	+	4.53553i	0.104034	+	0.186095i
$595$	10.5420	−	15.5665i	0.432178	−	0.638166i
$596$			3.06591i			0.125584i
$597$	−15.4021	+	2.64258i	−0.630366	+	0.108154i
$598$	3.70750	−	2.14052i	0.151611	−	0.0875326i
$599$	−6.38722	+	3.68766i	−0.260975	+	0.150674i	−0.624779	−	0.780802i	$-0.714811\pi$
$599$	−6.38722	+	3.68766i	−0.260975	+	0.150674i	0.363804	+	0.931475i	$0.381478\pi$
$600$	−4.60368	+	0.789867i	−0.187945	+	0.0322462i
$601$			34.5172i			1.40798i	0.710207	+	0.703992i	$0.248601\pi$
$601$			34.5172i			1.40798i	−0.710207	+	0.703992i	$0.751399\pi$
$602$	−5.10841	+	2.47978i	−0.208203	+	0.101068i
$603$	−4.20927	+	22.6477i	−0.171415	+	0.922286i
$604$	7.38770	−	12.7959i	0.300601	−	0.520657i
$605$	0.758819	+	1.31431i	0.0308504	+	0.0534344i
$606$	5.20769	−	14.1051i	0.211548	−	0.572982i
$607$	0.450370	+	0.260021i	0.0182799	+	0.0105539i	0.509112	−	0.860700i	$-0.329974\pi$
$607$	0.450370	+	0.260021i	0.0182799	+	0.0105539i	−0.490832	+	0.871254i	$0.663307\pi$
$608$	7.07812			0.287056
$609$	6.63310	+	9.25512i	0.268787	+	0.375036i
$610$	14.5315			0.588364
$611$	−14.9679	−	8.64173i	−0.605537	−	0.349607i
$612$	−13.2432	+	4.68216i	−0.535323	+	0.189265i
$613$	−7.94230	−	13.7565i	−0.320786	−	0.555618i	0.659864	−	0.751385i	$-0.270614\pi$
$613$	−7.94230	−	13.7565i	−0.320786	−	0.555618i	−0.980651	+	0.195767i	$0.937281\pi$
$614$	−12.9985	+	22.5141i	−0.524577	+	0.908595i
$615$	−17.6787	+	14.6957i	−0.712873	+	0.592587i
$616$	−2.63896	−	0.189469i	−0.106327	−	0.00763391i
$617$		−	32.6471i		−	1.31432i	−0.753750	−	0.657161i	$-0.771757\pi$
$617$		−	32.6471i		−	1.31432i	0.753750	−	0.657161i	$-0.228243\pi$
$618$	−4.38784	−	25.5742i	−0.176505	−	1.02874i
$619$	−19.2114	+	11.0917i	−0.772173	+	0.445814i	−0.833649	−	0.552294i	$-0.813753\pi$
$619$	−19.2114	+	11.0917i	−0.772173	+	0.445814i	0.0614762	+	0.998109i	$0.480419\pi$
$620$	−10.7995	+	6.23508i	−0.433717	+	0.250407i
$621$	−0.0565074	+	4.08164i	−0.00226757	+	0.163791i
$622$		−	1.21441i		−	0.0486935i
$623$	−11.3503	−	23.3820i	−0.454742	−	0.936779i
$624$	6.03371	+	7.25845i	0.241542	+	0.290571i
$625$	2.12177	−	3.67501i	0.0848707	−	0.147000i
$626$	11.8154	+	20.4649i	0.472239	+	0.817941i
$627$	−11.5008	−	4.24616i	−0.459299	−	0.169575i
$628$	11.0826	+	6.39853i	0.442243	+	0.255329i
$629$	9.33132			0.372064
$630$	8.46335	−	8.57175i	0.337188	−	0.341507i
$631$	35.8356			1.42659			0.713297	−	0.700862i	$-0.247201\pi$
$631$	35.8356			1.42659			0.713297	+	0.700862i	$0.247201\pi$
$632$	2.16813	+	1.25177i	0.0862436	+	0.0497928i
$633$	−24.8009	−	9.15662i	−0.985748	−	0.363943i
$634$	−14.1208	−	24.4579i	−0.560808	−	0.971348i
$635$	−3.90338	+	6.76086i	−0.154901	+	0.268296i
$636$	−6.38158	−	7.67694i	−0.253046	−	0.304410i
$637$	−35.4217	+	14.1582i	−1.40346	+	0.560968i
$638$		−	2.48477i		−	0.0983728i
$639$	7.33062	−	8.57433i	0.289995	−	0.339195i
$640$	1.31431	−	0.758819i	0.0519528	−	0.0299950i
$641$	−2.68032	+	1.54748i	−0.105866	+	0.0611219i	−0.551998	−	0.833845i	$-0.686135\pi$
$641$	−2.68032	+	1.54748i	−0.105866	+	0.0611219i	0.446132	+	0.894967i	$0.352801\pi$
$642$	−3.75065	−	21.8604i	−0.148026	−	0.862761i
$643$		−	40.2119i		−	1.58580i	−0.609350	−	0.792902i	$-0.708569\pi$
$643$		−	40.2119i		−	1.58580i	0.609350	−	0.792902i	$-0.291431\pi$
$644$	−1.72096	−	1.16547i	−0.0678154	−	0.0459259i
$645$	−4.33850	+	3.60645i	−0.170828	+	0.142004i
$646$	16.5704	−	28.7009i	0.651955	−	1.12922i
$647$	8.84809	+	15.3253i	0.347854	+	0.602501i	0.985868	−	0.167524i	$-0.0535771\pi$
$647$	8.84809	+	15.3253i	0.347854	+	0.602501i	−0.638014	+	0.770025i	$0.720244\pi$
$648$	−8.89060	+	1.39898i	−0.349256	+	0.0549571i
$649$	−4.42833	−	2.55670i	−0.173827	−	0.100359i
$650$	14.6960			0.576426
$651$	−15.5377	+	34.2989i	−0.608972	+	1.34428i
$652$	2.14867			0.0841483
$653$	28.5016	+	16.4554i	1.11535	+	0.643950i	0.940211	−	0.340593i	$-0.110628\pi$
$653$	28.5016	+	16.4554i	1.11535	+	0.643950i	0.175144	+	0.984543i	$0.443961\pi$
$654$	−2.53918	+	6.87744i	−0.0992899	+	0.268929i
$655$	−7.54863	−	13.0746i	−0.294950	−	0.510868i
$656$	−4.37283	+	7.57397i	−0.170730	+	0.295714i
$657$	29.7978	+	5.53818i	1.16252	+	0.216065i
$658$	−0.600914	+	8.36965i	−0.0234261	+	0.326283i
$659$			38.3898i			1.49545i	0.664006	+	0.747727i	$0.268855\pi$
$659$			38.3898i			1.49545i	−0.664006	+	0.747727i	$0.731145\pi$
$660$	−2.59077	+	0.444506i	−0.100846	+	0.0173024i
$661$	−16.3542	+	9.44210i	−0.636105	+	0.367255i	−0.783112	−	0.621880i	$-0.786369\pi$
$661$	−16.3542	+	9.44210i	−0.636105	+	0.367255i	0.147008	+	0.989135i	$0.453036\pi$
$662$	−6.74252	+	3.89279i	−0.262055	+	0.151298i
$663$	43.5575	−	7.47329i	1.69163	−	0.290238i
$664$		−	14.9747i		−	0.581131i
$665$	−2.03528	+	28.3477i	−0.0789246	+	1.09928i
$666$	5.87819	+	1.09251i	0.227775	+	0.0423340i
$667$	0.976000	−	1.69048i	0.0377909	−	0.0654557i
$668$	−5.38682	−	9.33025i	−0.208422	−	0.360998i
$669$	−8.73584	+	23.6612i	−0.337747	+	0.914796i
$670$	−10.0920	−	5.82660i	−0.389887	−	0.225101i
$671$	−9.57509			−0.369642
$672$	1.89097	−	4.17423i	0.0729457	−	0.161025i
$673$	6.83747			0.263565			0.131782	−	0.991279i	$-0.457930\pi$
$673$	6.83747			0.263565			0.131782	+	0.991279i	$0.457930\pi$
$674$	−0.668762	−	0.386110i	−0.0257597	−	0.0148724i
$675$	−7.17375	+	12.0373i	−0.276118	+	0.463317i
$676$	−8.34847	−	14.4600i	−0.321095	−	0.556153i
$677$	−14.1480	+	24.5050i	−0.543750	+	0.941803i	0.454934	+	0.890525i	$0.349663\pi$
$677$	−14.1480	+	24.5050i	−0.543750	+	0.941803i	−0.998684	+	0.0512782i	$0.983670\pi$
$678$	−27.0977	+	22.5254i	−1.04068	+	0.865082i
$679$	20.5371	+	13.9081i	0.788142	+	0.533745i
$680$		−	7.10583i		−	0.272496i
$681$	−5.46138	−	31.8313i	−0.209281	−	1.21978i
$682$	7.11597	−	4.10841i	0.272485	−	0.157319i
$683$	7.28734	−	4.20735i	0.278842	−	0.160990i	−0.354057	−	0.935224i	$-0.615198\pi$
$683$	7.28734	−	4.20735i	0.278842	−	0.160990i	0.632899	+	0.774234i	$0.281865\pi$
$684$	13.7987	−	16.1398i	0.527607	−	0.617121i
$685$			14.3095i			0.546740i
$686$	13.6938	+	12.4691i	0.522834	+	0.476073i
$687$	−12.4694	−	15.0005i	−0.475738	−	0.572305i
$688$	−1.07313	+	1.85872i	−0.0409128	+	0.0708630i
$689$	15.7046	+	27.2011i	0.598296	+	1.03628i
$690$	−1.93720	−	0.715224i	−0.0737479	−	0.0272281i
$691$	−8.38273	−	4.83977i	−0.318894	−	0.184114i	0.332005	−	0.943277i	$-0.392275\pi$
$691$	−8.38273	−	4.83977i	−0.318894	−	0.184114i	−0.650900	+	0.759164i	$0.725608\pi$
$692$	22.0910			0.839774
$693$	−5.57666	+	5.64809i	−0.211840	+	0.214553i
$694$	9.91583			0.376400
$695$	−9.69891	−	5.59967i	−0.367901	−	0.212408i
$696$	4.03736	+	1.49061i	0.153036	+	0.0565015i
$697$	20.4743	+	35.4626i	0.775520	+	1.34324i
$698$	−0.260197	+	0.450674i	−0.00984860	+	0.0170583i
$699$	10.7457	+	12.9269i	0.406439	+	0.488940i
$700$	−3.11584	−	6.41870i	−0.117768	−	0.242604i
$701$		−	18.2920i		−	0.690878i	−0.938441	−	0.345439i	$-0.887730\pi$
$701$		−	18.2920i		−	0.690878i	0.938441	−	0.345439i	$-0.112270\pi$
$702$	28.3137	+	0.391983i	1.06863	+	0.0147944i
$703$	−12.2165	+	7.05317i	−0.460752	+	0.266015i
$704$	−0.866025	+	0.500000i	−0.0326396	+	0.0188445i
$705$	1.40978	+	8.21682i	0.0530955	+	0.309463i
$706$			6.40441i			0.241033i
$707$	22.9086	+	1.64476i	0.861566	+	0.0618577i
$708$	6.81079	−	5.66158i	0.255965	−	0.212775i
$709$	−7.27048	+	12.5928i	−0.273049	+	0.472934i	−0.969641	−	0.244533i	$-0.921365\pi$
$709$	−7.27048	+	12.5928i	−0.273049	+	0.472934i	0.696592	+	0.717467i	$0.254699\pi$
$710$	2.85337	+	4.94218i	0.107085	+	0.185477i
$711$	7.08109	−	2.50354i	0.265561	−	0.0938901i
$712$	−8.50765	−	4.91189i	−0.318837	−	0.184081i
$713$	6.45503			0.241743
$714$	−12.4991	−	17.4399i	−0.467766	−	0.652670i
$715$	8.27035			0.309294
$716$	−2.33800	−	1.34985i	−0.0873753	−	0.0504462i
$717$	−6.77264	+	18.3439i	−0.252929	+	0.685064i
$718$	−6.34486	−	10.9896i	−0.236788	−	0.410129i
$719$	2.41779	−	4.18773i	0.0901683	−	0.156176i	−0.817414	−	0.576051i	$-0.804593\pi$
$719$	2.41779	−	4.18773i	0.0901683	−	0.156176i	0.907582	+	0.419875i	$0.137926\pi$
$720$	0.831951	−	4.47626i	0.0310050	−	0.166820i
$721$	35.6569	−	17.3090i	1.32793	−	0.644620i
$722$			31.0997i			1.15741i
$723$	51.4554	−	8.82835i	1.91365	−	0.328330i
$724$	−11.6925	+	6.75065i	−0.434547	+	0.250886i
$725$	5.80311	−	3.35043i	0.215522	−	0.124432i
$726$	1.70711	−	0.292893i	0.0633567	−	0.0108703i
$727$		−	20.2791i		−	0.752111i	−0.926597	−	0.376055i	$-0.877280\pi$
$727$		−	20.2791i		−	0.752111i	0.926597	−	0.376055i	$-0.122720\pi$
$728$	−8.08467	+	11.9380i	−0.299638	+	0.442453i
$729$	−14.1421	+	23.0000i	−0.523783	+	0.851852i
$730$	−7.66612	+	13.2781i	−0.283736	+	0.491445i
$731$	5.02458	+	8.70283i	0.185841	+	0.321886i
$732$	5.74410	−	15.5580i	0.212308	−	0.575041i
$733$	41.6227	+	24.0309i	1.53737	+	0.887601i	0.998992	+	0.0448982i	$0.0142963\pi$
$733$	41.6227	+	24.0309i	1.53737	+	0.887601i	0.538379	+	0.842703i	$0.319037\pi$
$734$	−15.3931			−0.568169
$735$	16.1740	+	8.77358i	0.596587	+	0.323618i
$736$	−0.785587			−0.0289571
$737$	6.64979	+	3.83926i	0.244948	+	0.141421i
$738$	8.74567	+	24.7365i	0.321932	+	0.910562i
$739$	9.09066	+	15.7455i	0.334405	+	0.579207i	0.983370	−	0.181611i	$-0.0581312\pi$
$739$	9.09066	+	15.7455i	0.334405	+	0.579207i	−0.648965	+	0.760818i	$0.724798\pi$
$740$	−1.51229	+	2.61936i	−0.0555929	+	0.0962897i
$741$	−51.3762	+	42.7073i	−1.88735	+	1.56889i
$742$	8.55079	−	12.6263i	0.313909	−	0.463527i
$743$			37.2077i			1.36502i	0.730877	+	0.682509i	$0.239111\pi$
$743$			37.2077i			1.36502i	−0.730877	+	0.682509i	$0.760889\pi$
$744$	2.40665	+	14.0270i	0.0882321	+	0.514254i
$745$	−4.02956	+	2.32647i	−0.147632	+	0.0852352i
$746$	−1.77296	+	1.02362i	−0.0649126	+	0.0374773i
$747$	−34.1459	−	29.1930i	−1.24933	−	1.06812i
$748$			4.68216i			0.171197i
$749$	30.4789	−	14.7954i	1.11368	−	0.540613i
$750$	−12.9332	−	15.5584i	−0.472253	−	0.568113i
$751$	1.18876	−	2.05900i	0.0433786	−	0.0751340i	−0.843521	−	0.537096i	$-0.819521\pi$
$751$	1.18876	−	2.05900i	0.0433786	−	0.0751340i	0.886900	+	0.461962i	$0.152854\pi$
$752$	1.58579	+	2.74666i	0.0578277	+	0.100160i
$753$	−18.7437	−	6.92026i	−0.683058	−	0.252188i
$754$	−11.7266	−	6.77035i	−0.427057	−	0.246562i
$755$	22.4237			0.816083
$756$	−5.83183	−	12.4495i	−0.212101	−	0.452784i
$757$	20.2952			0.737642			0.368821	−	0.929501i	$-0.379762\pi$
$757$	20.2952			0.737642			0.368821	+	0.929501i	$0.379762\pi$
$758$	7.78091	+	4.49231i	0.282615	+	0.163168i
$759$	1.27646	+	0.471274i	0.0463325	+	0.0171062i
$760$	5.37101	+	9.30286i	0.194827	+	0.337450i
$761$	−19.3169	+	33.4579i	−0.700238	+	1.21285i	0.268144	+	0.963379i	$0.413590\pi$
$761$	−19.3169	+	33.4579i	−0.700238	+	1.21285i	−0.968383	+	0.249470i	$0.919744\pi$
$762$	5.69550	+	6.85159i	0.206326	+	0.248207i
$763$	−11.1698	−	0.801959i	−0.404376	−	0.0290329i
$764$			21.1137i			0.763865i
$765$	−16.2030	−	13.8527i	−0.585820	−	0.500847i
$766$	24.7442	−	14.2861i	0.894044	−	0.516176i
$767$	−24.1321	+	13.9327i	−0.871361	+	0.503080i
$768$	−0.292893	−	1.70711i	−0.0105689	−	0.0615999i
$769$		−	29.0693i		−	1.04827i	−0.851636	−	0.524133i	$-0.824389\pi$
$769$		−	29.0693i		−	1.04827i	0.851636	−	0.524133i	$-0.175611\pi$
$770$	−1.75347	−	3.61219i	−0.0631907	−	0.130174i
$771$	−10.4867	+	8.71721i	−0.377668	+	0.313943i
$772$	−8.44232	+	14.6225i	−0.303846	+	0.526276i
$773$	19.8671	+	34.4108i	0.714570	+	1.23767i	0.963125	+	0.269054i	$0.0867110\pi$
$773$	19.8671	+	34.4108i	0.714570	+	1.23767i	−0.248555	+	0.968618i	$0.579956\pi$
$774$	2.14626	+	6.07055i	0.0771459	+	0.218201i
$775$	19.1902	+	11.0795i	0.689331	+	0.397986i
$776$	9.37481			0.336536
$777$	0.895811	+	9.08881i	0.0321371	+	0.326059i
$778$	2.74154			0.0982889
$779$	−53.6094	−	30.9514i	−1.92076	−	1.10895i
$780$	−4.96139	+	13.4380i	−0.177646	+	0.481159i
$781$	−1.88014	−	3.25650i	−0.0672767	−	0.116527i
$782$	−1.83912	+	3.18546i	−0.0657669	+	0.113912i
$783$	11.2697	−	6.30021i	0.402748	−	0.225151i
$784$	6.92820	+	1.00000i	0.247436	+	0.0357143i
$785$			19.4213i			0.693176i
$786$	−16.9821	+	2.91366i	−0.605731	+	0.103927i
$787$	31.2612	−	18.0487i	1.11434	−	0.643365i	0.174391	−	0.984677i	$-0.444204\pi$
$787$	31.2612	−	18.0487i	1.11434	−	0.643365i	0.939950	+	0.341312i	$0.110871\pi$
$788$	−24.1007	+	13.9146i	−0.858552	+	0.495685i
$789$	−34.8530	+	5.97983i	−1.24080	+	0.212887i
$790$			3.79947i			0.135179i
$791$	−44.5678	−	30.1821i	−1.58465	−	1.07315i
$792$	−0.548188	+	2.94949i	−0.0194790	+	0.104806i
$793$	−26.0897	+	45.1886i	−0.926472	+	1.60470i
$794$	6.46809	+	11.2031i	0.229544	+	0.397582i
$795$	5.24744	−	14.2128i	0.186107	−	0.504076i
$796$	−7.81358	−	4.51117i	−0.276945	−	0.159894i
$797$	6.46019			0.228832			0.114416	−	0.993433i	$-0.463500\pi$
$797$	6.46019			0.228832			0.114416	+	0.993433i	$0.463500\pi$
$798$	29.5457	+	13.3845i	1.04591	+	0.473806i
$799$	14.8498			0.525349
$800$	−2.33548	−	1.34839i	−0.0825715	−	0.0476727i
$801$	−27.7859	+	9.82378i	−0.981765	+	0.347106i
$802$	−12.8794	−	22.3078i	−0.454787	−	0.787714i
$803$	5.05135	−	8.74919i	0.178258	−	0.308752i
$804$	−10.2274	+	8.50170i	−0.360693	+	0.299832i
$805$	0.225892	−	3.14626i	0.00796163	−	0.110891i
$806$		−	44.7775i		−	1.57722i
$807$	4.99808	+	29.1309i	0.175941	+	1.02546i
$808$	7.51790	−	4.34046i	0.264479	−	0.152697i
$809$	−36.1610	+	20.8776i	−1.27135	+	0.734017i	−0.975243	−	0.221137i	$-0.929023\pi$
$809$	−36.1610	+	20.8776i	−1.27135	+	0.734017i	−0.296112	+	0.955153i	$0.595690\pi$
$810$	−8.58506	−	10.6235i	−0.301648	−	0.373271i
$811$			21.7907i			0.765174i	0.923920	+	0.382587i	$0.124967\pi$
$811$			21.7907i			0.765174i	−0.923920	+	0.382587i	$0.875033\pi$
$812$	−0.470785	+	6.55719i	−0.0165213	+	0.230112i
$813$	−26.9703	−	32.4449i	−0.945891	−	1.13789i
$814$	0.996476	−	1.72595i	0.0349265	−	0.0604944i
$815$	1.63045	+	2.82402i	0.0571122	+	0.0989212i
$816$	−7.60779	−	2.80883i	−0.266326	−	0.0983288i
$817$	−13.1562	−	7.59575i	−0.460278	−	0.265742i
$818$	−6.48339			−0.226687
$819$	11.4606	+	41.7081i	0.400466	+	1.45740i
$820$	−13.2728			−0.463505
$821$	−22.8559	−	13.1959i	−0.797677	−	0.460539i	0.0449812	−	0.998988i	$-0.485677\pi$
$821$	−22.8559	−	13.1959i	−0.797677	−	0.460539i	−0.842658	+	0.538449i	$0.819011\pi$
$822$	15.3204	+	5.65636i	0.534359	+	0.197288i
$823$	−20.2534	−	35.0800i	−0.705990	−	1.22281i	−0.966333	−	0.257295i	$-0.917169\pi$
$823$	−20.2534	−	35.0800i	−0.705990	−	1.22281i	0.260343	−	0.965516i	$-0.416164\pi$
$824$	7.49051	−	12.9739i	0.260944	−	0.451968i
$825$	2.98589	+	3.59197i	0.103955	+	0.125056i
$826$	11.2018	+	7.58604i	0.389759	+	0.263952i
$827$		−	3.89142i		−	0.135318i	−0.997709	−	0.0676589i	$-0.978447\pi$
$827$		−	3.89142i		−	0.135318i	0.997709	−	0.0676589i	$-0.0215530\pi$
$828$	−1.53149	+	1.79133i	−0.0532231	+	0.0622529i
$829$	−6.20192	+	3.58068i	−0.215401	+	0.124362i	−0.603819	−	0.797121i	$-0.706355\pi$
$829$	−6.20192	+	3.58068i	−0.215401	+	0.124362i	0.388418	+	0.921483i	$0.373022\pi$
$830$	19.6814	−	11.3631i	0.683153	−	0.394418i
$831$	−3.94370	−	22.9855i	−0.136805	−	0.797360i
$832$			5.44949i			0.188927i
$833$	20.2744	−	25.7519i	0.702465	−	0.892250i
$834$	−9.82907	+	8.17058i	−0.340353	+	0.282924i
$835$	8.17525	−	14.1599i	0.282916	−	0.490025i
$836$	−3.53906	−	6.12983i	−0.122401	−	0.212005i
$837$	36.6766	+	21.8577i	1.26773	+	0.755513i
$838$	−3.07331	−	1.77438i	−0.106166	−	0.0612948i
$839$	4.88068			0.168500			0.0842500	−	0.996445i	$-0.473151\pi$
$839$	4.88068			0.168500			0.0842500	+	0.996445i	$0.473151\pi$
$840$	6.92116	−	0.682163i	0.238803	−	0.0235369i
$841$	22.8259			0.787101
$842$	−9.36102	−	5.40459i	−0.322602	−	0.186254i
$843$	12.0462	−	32.6273i	0.414892	−	1.12374i
$844$	−7.63179	−	13.2186i	−0.262697	−	0.455004i
$845$	12.6700	−	21.9450i	0.435860	−	0.754931i
$846$	9.35452	+	1.73862i	0.321615	+	0.0597749i
$847$	1.15539	+	2.38014i	0.0396998	+	0.0817826i
$848$		−	5.76368i		−	0.197926i
$849$	−22.9045	+	3.92979i	−0.786080	+	0.134870i
$850$	−10.9351	+	6.31337i	−0.375070	+	0.216547i
$851$	1.35588	−	0.782819i	0.0464790	−	0.0268347i
$852$	6.41920	−	1.10136i	0.219918	−	0.0377320i
$853$		−	1.50440i		−	0.0515097i	−0.999668	−	0.0257548i	$-0.991801\pi$
$853$		−	1.50440i		−	0.0515097i	0.999668	−	0.0257548i	$-0.00819892\pi$
$854$	25.2683	+	1.81418i	0.864662	+	0.0620800i
$855$	31.6835	+	5.88865i	1.08355	+	0.201387i
$856$	6.40276	−	11.0899i	0.218842	−	0.379045i
$857$	4.55257	+	7.88529i	0.155513	+	0.269356i	0.933246	−	0.359239i	$-0.116964\pi$
$857$	4.55257	+	7.88529i	0.155513	+	0.269356i	−0.777733	+	0.628595i	$0.783630\pi$
$858$	3.26915	−	8.85457i	0.111607	−	0.302290i
$859$	3.95854	+	2.28546i	0.135064	+	0.0779790i	0.566009	−	0.824399i	$-0.308487\pi$
$859$	3.95854	+	2.28546i	0.135064	+	0.0779790i	−0.430946	+	0.902378i	$0.641820\pi$
$860$	−3.25725			−0.111071
$861$	−32.5754	+	23.3466i	−1.11017	+	0.795651i
$862$	27.4025			0.933334
$863$	26.3799	+	15.2305i	0.897983	+	0.518451i	0.876545	−	0.481319i	$-0.159842\pi$
$863$	26.3799	+	15.2305i	0.897983	+	0.518451i	0.0214379	+	0.999770i	$0.493176\pi$
$864$	−4.46360	−	2.66012i	−0.151855	−	0.0904991i
$865$	16.7631	+	29.0345i	0.569962	+	0.987202i
$866$	10.9265	−	18.9253i	0.371298	−	0.643106i
$867$	−6.55673	+	5.45039i	−0.222678	+	0.185105i
$868$	−19.5572	+	9.49367i	−0.663814	+	0.322236i
$869$		−	2.50354i		−	0.0849268i
$870$	1.10449	+	6.43746i	0.0374458	+	0.218250i
$871$	36.2380	−	20.9220i	1.22788	−	0.708915i
$872$	−3.66560	+	2.11634i	−0.124133	+	0.0716682i
$873$	18.2761	−	21.3768i	0.618552	−	0.723495i
$874$		−	5.56048i		−	0.188086i
$875$	17.3294	−	25.5890i	0.585840	−	0.865068i
$876$	11.1858	+	13.4563i	0.377932	+	0.454646i
$877$	5.02022	−	8.69527i	0.169521	−	0.293618i	−0.768731	−	0.639573i	$-0.779111\pi$
$877$	5.02022	−	8.69527i	0.169521	−	0.293618i	0.938251	+	0.345954i	$0.112445\pi$
$878$	−18.1425	−	31.4237i	−0.612278	−	1.06050i
$879$	22.4218	+	8.27825i	0.756269	+	0.279218i
$880$	−1.31431	−	0.758819i	−0.0443055	−	0.0255798i
$881$	−32.5113			−1.09533			−0.547666	−	0.836697i	$-0.684484\pi$
$881$	−32.5113			−1.09533			−0.547666	+	0.836697i	$0.684484\pi$
$882$	15.7867	−	13.8485i	0.531566	−	0.466302i
$883$	−1.02794			−0.0345931			−0.0172965	−	0.999850i	$-0.505506\pi$
$883$	−1.02794			−0.0345931			−0.0172965	+	0.999850i	$0.505506\pi$
$884$	22.0970	+	12.7577i	0.743202	+	0.429088i
$885$	12.6092	+	4.65539i	0.423855	+	0.156489i
$886$	0.368605	+	0.638443i	0.0123835	+	0.0214489i
$887$	−3.19271	+	5.52994i	−0.107201	+	0.185677i	−0.914635	−	0.404280i	$-0.867522\pi$
$887$	−3.19271	+	5.52994i	−0.107201	+	0.185677i	0.807434	+	0.589957i	$0.200855\pi$
$888$	2.20661	+	2.65451i	0.0740489	+	0.0890797i
$889$	−7.63149	+	11.2689i	−0.255952	+	0.377946i
$890$		−	14.9089i		−	0.499749i
$891$	5.65685	+	7.00000i	0.189512	+	0.234509i
$892$	−12.6112	+	7.28108i	−0.422254	+	0.243788i
$893$	−19.4412	+	11.2244i	−0.650575	+	0.375610i
$894$	0.897984	+	5.23383i	0.0300331	+	0.175046i
$895$		−	4.09716i		−	0.136953i
$896$	2.38014	−	1.15539i	0.0795149	−	0.0385990i
$897$	5.70215	−	4.74001i	0.190389	−	0.158264i
$898$	15.9547	−	27.6344i	0.532416	−	0.922172i
$899$	−10.2084	−	17.6815i	−0.340470	−	0.589712i
$900$	−7.62763	+	2.69677i	−0.254254	+	0.0898925i
$901$	−23.3710	−	13.4932i	−0.778600	−	0.449525i
$902$	8.74567			0.291199
$903$	−7.99429	+	5.72947i	−0.266033	+	0.190665i
$904$	−20.3443			−0.676643
$905$	−17.7449	−	10.2450i	−0.589862	−	0.340557i
$906$	8.86377	−	24.0077i	0.294479	−	0.797604i
$907$	−28.5813	−	49.5043i	−0.949026	−	1.64376i	−0.747482	−	0.664282i	$-0.768737\pi$
$907$	−28.5813	−	49.5043i	−0.949026	−	1.64376i	−0.201545	−	0.979479i	$-0.564596\pi$
$908$	9.32316	−	16.1482i	0.309400	−	0.535896i
$909$	4.75878	−	25.6043i	0.157839	−	0.849240i
$910$	−21.8251	−	1.56697i	−0.723496	−	0.0519446i
$911$		−	25.3169i		−	0.838786i	−0.907805	−	0.419393i	$-0.862243\pi$
$911$		−	25.3169i		−	0.838786i	0.907805	−	0.419393i	$-0.137757\pi$
$912$	12.0831	−	2.07313i	0.400111	−	0.0686483i
$913$	−12.9685	+	7.48735i	−0.429193	+	0.247795i
$914$	18.6438	−	10.7640i	0.616683	−	0.356042i
$915$	24.8069	−	4.25618i	0.820089	−	0.140705i
$916$		−	11.2621i		−	0.372109i
$917$	−11.4937	−	23.6773i	−0.379556	−	0.781894i
$918$	−21.2361	+	11.8718i	−0.700896	+	0.391827i
$919$	−10.4999	+	18.1863i	−0.346360	+	0.599912i	−0.985600	−	0.169095i	$-0.945916\pi$
$919$	−10.4999	+	18.1863i	−0.346360	+	0.599912i	0.639240	+	0.769007i	$0.279249\pi$
$920$	−0.596119	−	1.03251i	−0.0196534	−	0.0340408i
$921$	−15.5956	+	42.2411i	−0.513893	+	1.39189i
$922$	−1.24481	−	0.718692i	−0.0409957	−	0.0236689i
$923$	−20.4916			−0.674489
$924$	−4.56048	+	0.449490i	−0.150029	+	0.0147871i
$925$	5.37454			0.176714
$926$	6.19224	+	3.57509i	0.203490	+	0.117485i
$927$	−14.9810	−	42.3727i	−0.492041	−	1.39170i
$928$	1.24238	+	2.15187i	0.0407832	+	0.0706386i
$929$	7.08549	−	12.2724i	0.232468	−	0.402646i	−0.726066	−	0.687625i	$-0.758653\pi$
$929$	7.08549	−	12.2724i	0.232468	−	0.402646i	0.958534	+	0.284979i	$0.0919867\pi$
$930$	−16.6096	+	13.8070i	−0.544651	+	0.452750i
$931$	−7.07812	+	49.0386i	−0.231976	+	1.60718i
$932$			9.70523i			0.317905i
$933$	−0.355693	−	2.07313i	−0.0116449	−	0.0678713i
$934$	−1.11059	+	0.641199i	−0.0363396	+	0.0209807i
$935$	−6.15383	+	3.55291i	−0.201252	+	0.116193i
$936$	12.4261	+	10.6237i	0.406161	+	0.347247i
$937$		−	13.9042i		−	0.454230i	−0.973868	−	0.227115i	$-0.927071\pi$
$937$		−	13.9042i		−	0.454230i	0.973868	−	0.227115i	$-0.0729293\pi$
$938$	−16.8211	−	11.3916i	−0.549228	−	0.371948i
$939$	26.1642	+	31.4751i	0.853836	+	1.02715i
$940$	−2.40665	+	4.16844i	−0.0784963	+	0.135960i
$941$	−15.2917	−	26.4861i	−0.498496	−	0.863421i	0.501502	−	0.865156i	$-0.332781\pi$
$941$	−15.2917	−	26.4861i	−0.498496	−	0.863421i	−0.999998	+	0.00173560i	$0.999448\pi$
$942$	20.7932	+	7.67697i	0.677480	+	0.250129i
$943$	5.95001	+	3.43524i	0.193759	+	0.111867i
$944$	5.11339			0.166427
$945$	11.9372	−	17.1118i	0.388318	−	0.556645i
$946$	2.14626			0.0697811
$947$	−38.3205	−	22.1244i	−1.24525	−	0.718945i	−0.275091	−	0.961418i	$-0.588708\pi$
$947$	−38.3205	−	22.1244i	−1.24525	−	0.718945i	−0.970158	+	0.242473i	$0.922041\pi$
$948$	4.06787	+	1.50188i	0.132118	+	0.0487787i
$949$	−27.5273	−	47.6786i	−0.893573	−	1.54771i
$950$	9.54404	−	16.5308i	0.309650	−	0.536329i
$951$	−31.2692	−	37.6164i	−1.01397	−	1.21979i
$952$	0.887123	−	12.3560i	0.0287518	−	0.400461i
$953$		−	17.8122i		−	0.576992i	−0.957481	−	0.288496i	$-0.906845\pi$
$953$		−	17.8122i		−	0.576992i	0.957481	−	0.288496i	$-0.0931553\pi$
$954$	−13.1426	−	11.2362i	−0.425506	−	0.363786i
$955$	−27.7500	+	16.0214i	−0.897968	+	0.518442i
$956$	−9.77709	+	5.64480i	−0.316214	+	0.182566i
$957$	−0.727771	−	4.24176i	−0.0235255	−	0.137117i
$958$		−	3.82551i		−	0.123597i
$959$	−1.78647	+	24.8823i	−0.0576880	+	0.803491i
$960$	2.02142	−	1.68034i	0.0652410	−	0.0542327i
$961$	18.2580	−	31.6239i	0.588969	−	1.02012i
$962$	−5.43029	−	9.40553i	−0.175079	−	0.303246i
$963$	−12.8055	−	36.2195i	−0.412652	−	1.16716i
$964$	26.1036	+	15.0709i	0.840742	+	0.485402i
$965$	−25.6248			−0.824890
$966$	−3.27923	−	1.48552i	−0.105507	−	0.0477959i
$967$	−5.14185			−0.165351			−0.0826754	−	0.996577i	$-0.526346\pi$
$967$	−5.14185			−0.165351			−0.0826754	+	0.996577i	$0.526346\pi$
$968$	0.866025	+	0.500000i	0.0278351	+	0.0160706i
$969$	19.8812	−	53.8488i	0.638677	−	1.72987i
$970$	7.11378	+	12.3214i	0.228410	+	0.395617i
$971$	23.6997	−	41.0491i	0.760560	−	1.31733i	−0.182002	−	0.983298i	$-0.558258\pi$
$971$	23.6997	−	41.0491i	0.760560	−	1.31733i	0.942562	−	0.334031i	$-0.108409\pi$
$972$	−14.7675	+	4.99221i	−0.473667	+	0.160125i
$973$	−16.1660	−	10.9479i	−0.518257	−	0.350973i
$974$			2.16620i			0.0694095i
$975$	25.0877	−	4.30437i	0.803450	−	0.137850i
$976$	8.29227	−	4.78754i	0.265429	−	0.153246i
$977$	−25.7577	+	14.8712i	−0.824061	+	0.475772i	−0.851815	−	0.523843i	$-0.824498\pi$
$977$	−25.7577	+	14.8712i	−0.824061	+	0.475772i	0.0277536	+	0.999615i	$0.491165\pi$
$978$	3.66801	−	0.629330i	0.117290	−	0.0201238i
$979$			9.82378i			0.313969i
$980$	3.94294	+	9.86465i	0.125953	+	0.315115i
$981$	−2.32030	+	12.4842i	−0.0740815	+	0.398591i
$982$	6.22803	−	10.7873i	0.198744	−	0.344235i
$983$	16.9335	+	29.3297i	0.540096	+	0.935473i	0.998898	+	0.0469347i	$0.0149453\pi$
$983$	16.9335	+	29.3297i	0.540096	+	0.935473i	−0.458802	+	0.888538i	$0.651721\pi$
$984$	−5.24653	+	14.2103i	−0.167253	+	0.453009i
$985$	−36.5762	−	21.1173i	−1.16541	−	0.672852i
$986$	11.6341			0.370505
$987$	1.42559	+	14.4639i	0.0453770	+	0.460391i
$988$	−38.5721			−1.22714
$989$	1.46019	+	0.843039i	0.0464312	+	0.0268071i
$990$	−4.29253	+	1.51764i	−0.136426	+	0.0482337i
$991$	0.259557	+	0.449566i	0.00824510	+	0.0142809i	0.870119	−	0.492843i	$-0.164042\pi$
$991$	0.259557	+	0.449566i	0.00824510	+	0.0142809i	−0.861873	+	0.507123i	$0.830709\pi$
$992$	−4.10841	+	7.11597i	−0.130442	+	0.225932i
$993$	−10.3700	+	8.62025i	−0.329083	+	0.273555i
$994$	4.34461	+	8.94999i	0.137803	+	0.283876i
$995$		−	13.6926i		−	0.434086i
$996$	−4.38599	−	25.5634i	−0.138975	−	0.810007i
$997$	36.7828	−	21.2366i	1.16492	−	0.672569i	0.212444	−	0.977173i	$-0.431858\pi$
$997$	36.7828	−	21.2366i	1.16492	−	0.672569i	0.952479	+	0.304604i	$0.0985243\pi$
$998$	26.8344	−	15.4928i	0.849428	−	0.490417i
$999$	10.3547	+	0.143353i	0.327608	+	0.00453550i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.k.e.89.4	✓	8
3.2	odd	2		462.2.k.f.89.1	yes	8
7.3	odd	6		462.2.k.f.353.1	yes	8
21.17	even	6	inner	462.2.k.e.353.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.k.e.89.4	✓	8	1.1	even	1	trivial
462.2.k.e.353.4	yes	8	21.17	even	6	inner
462.2.k.f.89.1	yes	8	3.2	odd	2
462.2.k.f.353.1	yes	8	7.3	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(1.62484 + 0.599900i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.758819 + 1.31431i) q^{5} +(1.10721 + 1.33195i) q^{6} +(-1.48356 + 2.19067i) q^{7} +1.00000i q^{8} +(2.28024 + 1.94949i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(1.62484 + 0.599900i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.758819 + 1.31431i) q^{5} +(1.10721 + 1.33195i) q^{6} +(-1.48356 + 2.19067i) q^{7} +1.00000i q^{8} +(2.28024 + 1.94949i) q^{9} +(-1.31431 + 0.758819i) q^{10} +(0.866025 - 0.500000i) q^{11} +(0.292893 + 1.70711i) q^{12} -5.44949i q^{13} +(-2.38014 + 1.15539i) q^{14} +(-2.02142 + 1.68034i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.34108 + 4.05487i) q^{17} +(1.00000 + 2.82843i) q^{18} +(-6.12983 - 3.53906i) q^{19} -1.51764 q^{20} +(-3.72474 + 2.66951i) q^{21} +1.00000 q^{22} +(0.680339 + 0.392794i) q^{23} +(-0.599900 + 1.62484i) q^{24} +(1.34839 + 2.33548i) q^{25} +(2.72474 - 4.71940i) q^{26} +(2.53553 + 4.53553i) q^{27} +(-2.63896 - 0.189469i) q^{28} -2.48477i q^{29} +(-2.59077 + 0.444506i) q^{30} +(7.11597 - 4.10841i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.70711 - 0.292893i) q^{33} +4.68216i q^{34} +(-1.75347 - 3.61219i) q^{35} +(-0.548188 + 2.94949i) q^{36} +(0.996476 - 1.72595i) q^{37} +(-3.53906 - 6.12983i) q^{38} +(3.26915 - 8.85457i) q^{39} +(-1.31431 - 0.758819i) q^{40} +8.74567 q^{41} +(-4.56048 + 0.449490i) q^{42} +2.14626 q^{43} +(0.866025 + 0.500000i) q^{44} +(-4.29253 + 1.51764i) q^{45} +(0.392794 + 0.680339i) q^{46} +(1.58579 - 2.74666i) q^{47} +(-1.33195 + 1.10721i) q^{48} +(-2.59808 - 6.50000i) q^{49} +2.69677i q^{50} +(1.37137 + 7.99295i) q^{51} +(4.71940 - 2.72474i) q^{52} +(-4.99149 + 2.88184i) q^{53} +(-0.0719302 + 5.19565i) q^{54} +1.51764i q^{55} +(-2.19067 - 1.48356i) q^{56} +(-7.83694 - 9.42771i) q^{57} +(1.24238 - 2.15187i) q^{58} +(-2.55670 - 4.42833i) q^{59} +(-2.46593 - 0.910432i) q^{60} +(-8.29227 - 4.78754i) q^{61} +8.21682 q^{62} +(-7.65357 + 2.10306i) q^{63} -1.00000 q^{64} +(7.16234 + 4.13518i) q^{65} +(1.62484 + 0.599900i) q^{66} +(3.83926 + 6.64979i) q^{67} +(-2.34108 + 4.05487i) q^{68} +(0.869807 + 1.04636i) q^{69} +(0.287545 - 4.00498i) q^{70} -3.76028i q^{71} +(-1.94949 + 2.28024i) q^{72} +(8.74919 - 5.05135i) q^{73} +(1.72595 - 0.996476i) q^{74} +(0.789867 + 4.60368i) q^{75} -7.07812i q^{76} +(-0.189469 + 2.63896i) q^{77} +(7.25845 - 6.03371i) q^{78} +(1.25177 - 2.16813i) q^{79} +(-0.758819 - 1.31431i) q^{80} +(1.39898 + 8.89060i) q^{81} +(7.57397 + 4.37283i) q^{82} -14.9747 q^{83} +(-4.17423 - 1.89097i) q^{84} -7.10583 q^{85} +(1.85872 + 1.07313i) q^{86} +(1.49061 - 4.03736i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-4.91189 + 8.50765i) q^{89} +(-4.47626 - 0.831951i) q^{90} +(11.9380 + 8.08467i) q^{91} +0.785587i q^{92} +(14.0270 - 2.40665i) q^{93} +(2.74666 - 1.58579i) q^{94} +(9.30286 - 5.37101i) q^{95} +(-1.70711 + 0.292893i) q^{96} -9.37481i q^{97} +(1.00000 - 6.92820i) q^{98} +(2.94949 + 0.548188i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6}+O(q^{10}) \) 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6	\( 8 q + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} + 8 q^{12} - 4 q^{16} + 20 q^{17} + 8 q^{18} - 12 q^{19} - 8 q^{20} - 20 q^{21} + 8 q^{22} - 12 q^{23} - 4 q^{24} + 8 q^{25} + 12 q^{26} - 8 q^{27} - 4 q^{30} + 12 q^{31} + 8 q^{33} + 16 q^{35} - 8 q^{38} + 24 q^{39} + 40 q^{41} - 8 q^{43} + 16 q^{45} + 8 q^{46} + 24 q^{47} + 4 q^{48} + 32 q^{51} - 60 q^{53} - 4 q^{54} - 20 q^{57} - 4 q^{58} + 4 q^{59} - 12 q^{60} - 36 q^{61} + 24 q^{62} - 32 q^{63} - 8 q^{64} - 12 q^{65} + 4 q^{66} + 12 q^{67} - 20 q^{68} - 12 q^{69} - 20 q^{70} + 4 q^{72} + 48 q^{73} - 12 q^{74} + 8 q^{75} - 8 q^{79} - 4 q^{80} - 28 q^{81} - 24 q^{82} - 72 q^{83} - 4 q^{84} - 32 q^{85} + 12 q^{86} + 16 q^{87} + 4 q^{88} - 4 q^{89} - 28 q^{90} + 36 q^{91} + 16 q^{93} + 24 q^{95} - 8 q^{96} + 8 q^{98} + 4 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 + 8 * q^12 - 4 * q^16 + 20 * q^17 + 8 * q^18 - 12 * q^19 - 8 * q^20 - 20 * q^21 + 8 * q^22 - 12 * q^23 - 4 * q^24 + 8 * q^25 + 12 * q^26 - 8 * q^27 - 4 * q^30 + 12 * q^31 + 8 * q^33 + 16 * q^35 - 8 * q^38 + 24 * q^39 + 40 * q^41 - 8 * q^43 + 16 * q^45 + 8 * q^46 + 24 * q^47 + 4 * q^48 + 32 * q^51 - 60 * q^53 - 4 * q^54 - 20 * q^57 - 4 * q^58 + 4 * q^59 - 12 * q^60 - 36 * q^61 + 24 * q^62 - 32 * q^63 - 8 * q^64 - 12 * q^65 + 4 * q^66 + 12 * q^67 - 20 * q^68 - 12 * q^69 - 20 * q^70 + 4 * q^72 + 48 * q^73 - 12 * q^74 + 8 * q^75 - 8 * q^79 - 4 * q^80 - 28 * q^81 - 24 * q^82 - 72 * q^83 - 4 * q^84 - 32 * q^85 + 12 * q^86 + 16 * q^87 + 4 * q^88 - 4 * q^89 - 28 * q^90 + 36 * q^91 + 16 * q^93 + 24 * q^95 - 8 * q^96 + 8 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more