LMFDB - Embedded newform 570.2.k.b.533.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(77,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("570.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.k (of order $4$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			533.14
Character	$\chi$	$=$	570.533
Dual form			570.2.k.b.77.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.336929 - 1.69896i) q^{3} +1.00000i q^{4} +(-2.14526 - 0.630765i) q^{5} +(1.43959 - 0.963104i) q^{6} +(0.804978 - 0.804978i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.77296 - 1.14486i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.336929 - 1.69896i) q^{3} +1.00000i q^{4} +(-2.14526 - 0.630765i) q^{5} +(1.43959 - 0.963104i) q^{6} +(0.804978 - 0.804978i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.77296 - 1.14486i) q^{9} +(-1.07091 - 1.96295i) q^{10} -3.15590i q^{11} +(1.69896 + 0.336929i) q^{12} +(-2.72994 - 2.72994i) q^{13} +1.13841 q^{14} +(-1.79445 + 3.43220i) q^{15} -1.00000 q^{16} +(-2.04213 - 2.04213i) q^{17} +(-1.15124 - 2.77032i) q^{18} +1.00000i q^{19} +(0.630765 - 2.14526i) q^{20} +(-1.09641 - 1.63885i) q^{21} +(2.23156 - 2.23156i) q^{22} +(1.82163 - 1.82163i) q^{23} +(0.963104 + 1.43959i) q^{24} +(4.20427 + 2.70631i) q^{25} -3.86071i q^{26} +(-2.87936 + 4.32542i) q^{27} +(0.804978 + 0.804978i) q^{28} -5.49359 q^{29} +(-3.69579 + 1.15806i) q^{30} +5.07413 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-5.36176 - 1.06331i) q^{33} -2.88801i q^{34} +(-2.23464 + 1.21913i) q^{35} +(1.14486 - 2.77296i) q^{36} +(7.25575 - 7.25575i) q^{37} +(-0.707107 + 0.707107i) q^{38} +(-5.55786 + 3.71827i) q^{39} +(1.96295 - 1.07091i) q^{40} -6.31900i q^{41} +(0.383563 - 1.93412i) q^{42} +(0.643335 + 0.643335i) q^{43} +3.15590 q^{44} +(5.22658 + 4.20510i) q^{45} +2.57617 q^{46} +(-3.22573 - 3.22573i) q^{47} +(-0.336929 + 1.69896i) q^{48} +5.70402i q^{49} +(1.05922 + 4.88652i) q^{50} +(-4.15756 + 2.78145i) q^{51} +(2.72994 - 2.72994i) q^{52} +(-3.16898 + 3.16898i) q^{53} +(-5.09455 + 1.02252i) q^{54} +(-1.99063 + 6.77022i) q^{55} +1.13841i q^{56} +(1.69896 + 0.336929i) q^{57} +(-3.88456 - 3.88456i) q^{58} -1.26612 q^{59} +(-3.43220 - 1.79445i) q^{60} +2.70369 q^{61} +(3.58795 + 3.58795i) q^{62} +(-3.15376 + 1.31058i) q^{63} -1.00000i q^{64} +(4.13447 + 7.57837i) q^{65} +(-3.03946 - 4.54321i) q^{66} +(3.86878 - 3.86878i) q^{67} +(2.04213 - 2.04213i) q^{68} +(-2.48112 - 3.70864i) q^{69} +(-2.44219 - 0.718070i) q^{70} +0.944610i q^{71} +(2.77032 - 1.15124i) q^{72} +(3.61892 + 3.61892i) q^{73} +10.2612 q^{74} +(6.01446 - 6.23107i) q^{75} -1.00000 q^{76} +(-2.54043 - 2.54043i) q^{77} +(-6.55921 - 1.30079i) q^{78} +15.0264i q^{79} +(2.14526 + 0.630765i) q^{80} +(6.37859 + 6.34930i) q^{81} +(4.46821 - 4.46821i) q^{82} +(5.54904 - 5.54904i) q^{83} +(1.63885 - 1.09641i) q^{84} +(3.09279 + 5.66900i) q^{85} +0.909814i q^{86} +(-1.85095 + 9.33342i) q^{87} +(2.23156 + 2.23156i) q^{88} +3.27340 q^{89} +(0.722289 + 6.66921i) q^{90} -4.39508 q^{91} +(1.82163 + 1.82163i) q^{92} +(1.70962 - 8.62077i) q^{93} -4.56187i q^{94} +(0.630765 - 2.14526i) q^{95} +(-1.43959 + 0.963104i) q^{96} +(2.89748 - 2.89748i) q^{97} +(-4.03335 + 4.03335i) q^{98} +(-3.61306 + 8.75117i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{3} + 4 q^{6} + 20 q^{7}+O(q^{10}) $ 36 * q + 4 * q^3 + 4 * q^6 + 20 * q^7	$ 36 q + 4 q^{3} + 4 q^{6} + 20 q^{7} - 4 q^{10} - 4 q^{12} + 8 q^{13} + 4 q^{15} - 36 q^{16} + 16 q^{21} - 4 q^{22} + 16 q^{25} - 44 q^{27} + 20 q^{28} + 32 q^{30} - 24 q^{31} - 4 q^{33} + 4 q^{36} - 8 q^{40} + 12 q^{42} - 8 q^{43} + 28 q^{45} - 16 q^{46} - 4 q^{48} + 40 q^{51} - 8 q^{52} - 36 q^{55} - 4 q^{57} + 44 q^{58} + 16 q^{60} - 120 q^{61} - 12 q^{63} + 80 q^{67} - 36 q^{70} + 44 q^{73} + 4 q^{75} - 36 q^{76} - 64 q^{78} + 36 q^{81} + 8 q^{82} - 24 q^{85} - 28 q^{87} - 4 q^{88} + 44 q^{90} - 72 q^{93} - 4 q^{96} + 92 q^{97}+O(q^{100}) $ 36 * q + 4 * q^3 + 4 * q^6 + 20 * q^7 - 4 * q^10 - 4 * q^12 + 8 * q^13 + 4 * q^15 - 36 * q^16 + 16 * q^21 - 4 * q^22 + 16 * q^25 - 44 * q^27 + 20 * q^28 + 32 * q^30 - 24 * q^31 - 4 * q^33 + 4 * q^36 - 8 * q^40 + 12 * q^42 - 8 * q^43 + 28 * q^45 - 16 * q^46 - 4 * q^48 + 40 * q^51 - 8 * q^52 - 36 * q^55 - 4 * q^57 + 44 * q^58 + 16 * q^60 - 120 * q^61 - 12 * q^63 + 80 * q^67 - 36 * q^70 + 44 * q^73 + 4 * q^75 - 36 * q^76 - 64 * q^78 + 36 * q^81 + 8 * q^82 - 24 * q^85 - 28 * q^87 - 4 * q^88 + 44 * q^90 - 72 * q^93 - 4 * q^96 + 92 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	0.336929	−	1.69896i	0.194526	−	0.980897i
$3$	0.336929	−	1.69896i	0.194526	−	0.980897i
$4$			1.00000i			0.500000i
$5$	−2.14526	−	0.630765i	−0.959389	−	0.282087i
$5$	−2.14526	−	0.630765i	−0.959389	−	0.282087i
$6$	1.43959	−	0.963104i	0.587712	−	0.393186i
$7$	0.804978	−	0.804978i	0.304253	−	0.304253i	−0.538422	−	0.842675i	$-0.680979\pi$
$7$	0.804978	−	0.804978i	0.304253	−	0.304253i	0.842675	+	0.538422i	$0.180979\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−2.77296	−	1.14486i	−0.924319	−	0.381620i
$10$	−1.07091	−	1.96295i	−0.338651	−	0.620738i
$11$		−	3.15590i		−	0.951539i	−0.879570	−	0.475769i	$-0.842170\pi$
$11$		−	3.15590i		−	0.951539i	0.879570	−	0.475769i	$-0.157830\pi$
$12$	1.69896	+	0.336929i	0.490449	+	0.0972629i
$13$	−2.72994	−	2.72994i	−0.757148	−	0.757148i	0.218654	−	0.975802i	$-0.429833\pi$
$13$	−2.72994	−	2.72994i	−0.757148	−	0.757148i	−0.975802	+	0.218654i	$0.929833\pi$
$14$	1.13841			0.304253
$15$	−1.79445	+	3.43220i	−0.463324	+	0.886189i
$16$	−1.00000			−0.250000
$17$	−2.04213	−	2.04213i	−0.495289	−	0.495289i	0.414679	−	0.909968i	$-0.363894\pi$
$17$	−2.04213	−	2.04213i	−0.495289	−	0.495289i	−0.909968	+	0.414679i	$0.863894\pi$
$18$	−1.15124	−	2.77032i	−0.271350	−	0.652970i
$19$			1.00000i			0.229416i
$19$			1.00000i			0.229416i
$20$	0.630765	−	2.14526i	0.141043	−	0.479694i
$21$	−1.09641	−	1.63885i	−0.239256	−	0.357626i
$22$	2.23156	−	2.23156i	0.475769	−	0.475769i
$23$	1.82163	−	1.82163i	0.379835	−	0.379835i	−0.491207	−	0.871043i	$-0.663444\pi$
$23$	1.82163	−	1.82163i	0.379835	−	0.379835i	0.871043	+	0.491207i	$0.163444\pi$
$24$	0.963104	+	1.43959i	0.196593	+	0.293856i
$25$	4.20427	+	2.70631i	0.840854	+	0.541262i
$26$		−	3.86071i		−	0.757148i
$27$	−2.87936	+	4.32542i	−0.554134	+	0.832428i
$28$	0.804978	+	0.804978i	0.152127	+	0.152127i
$29$	−5.49359			−1.02013			−0.510067	−	0.860134i	$-0.670380\pi$
$29$	−5.49359			−1.02013			−0.510067	+	0.860134i	$0.670380\pi$
$30$	−3.69579	+	1.15806i	−0.674756	+	0.211432i
$31$	5.07413			0.911341			0.455671	−	0.890148i	$-0.349400\pi$
$31$	5.07413			0.911341			0.455671	+	0.890148i	$0.349400\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−5.36176	−	1.06331i	−0.933362	−	0.185099i
$34$		−	2.88801i		−	0.495289i
$35$	−2.23464	+	1.21913i	−0.377723	+	0.206071i
$36$	1.14486	−	2.77296i	0.190810	−	0.462160i
$37$	7.25575	−	7.25575i	1.19284	−	1.19284i	0.216570	−	0.976267i	$-0.430513\pi$
$37$	7.25575	−	7.25575i	1.19284	−	1.19284i	0.976267	−	0.216570i	$-0.0694871\pi$
$38$	−0.707107	+	0.707107i	−0.114708	+	0.114708i
$39$	−5.55786	+	3.71827i	−0.889970	+	0.595400i
$40$	1.96295	−	1.07091i	0.310369	−	0.169326i
$41$		−	6.31900i		−	0.986862i	−0.869785	−	0.493431i	$-0.835743\pi$
$41$		−	6.31900i		−	0.986862i	0.869785	−	0.493431i	$-0.164257\pi$
$42$	0.383563	−	1.93412i	0.0591851	−	0.298441i
$43$	0.643335	+	0.643335i	0.0981077	+	0.0981077i	0.754457	−	0.656349i	$-0.227900\pi$
$43$	0.643335	+	0.643335i	0.0981077	+	0.0981077i	−0.656349	+	0.754457i	$0.727900\pi$
$44$	3.15590			0.475769
$45$	5.22658	+	4.20510i	0.779132	+	0.626860i
$46$	2.57617			0.379835
$47$	−3.22573	−	3.22573i	−0.470521	−	0.470521i	0.431562	−	0.902083i	$-0.357963\pi$
$47$	−3.22573	−	3.22573i	−0.470521	−	0.470521i	−0.902083	+	0.431562i	$0.857963\pi$
$48$	−0.336929	+	1.69896i	−0.0486315	+	0.245224i
$49$			5.70402i			0.814860i
$50$	1.05922	+	4.88652i	0.149796	+	0.691058i
$51$	−4.15756	+	2.78145i	−0.582174	+	0.389481i
$52$	2.72994	−	2.72994i	0.378574	−	0.378574i
$53$	−3.16898	+	3.16898i	−0.435292	+	0.435292i	−0.890424	−	0.455132i	$-0.849592\pi$
$53$	−3.16898	+	3.16898i	−0.435292	+	0.435292i	0.455132	+	0.890424i	$0.349592\pi$
$54$	−5.09455	+	1.02252i	−0.693281	+	0.139147i
$55$	−1.99063	+	6.77022i	−0.268416	+	0.912896i
$56$			1.13841i			0.152127i
$57$	1.69896	+	0.336929i	0.225033	+	0.0446273i
$58$	−3.88456	−	3.88456i	−0.510067	−	0.510067i
$59$	−1.26612			−0.164834			−0.0824171	−	0.996598i	$-0.526264\pi$
$59$	−1.26612			−0.164834			−0.0824171	+	0.996598i	$0.526264\pi$
$60$	−3.43220	−	1.79445i	−0.443094	−	0.231662i
$61$	2.70369			0.346172			0.173086	−	0.984907i	$-0.444626\pi$
$61$	2.70369			0.346172			0.173086	+	0.984907i	$0.444626\pi$
$62$	3.58795	+	3.58795i	0.455671	+	0.455671i
$63$	−3.15376	+	1.31058i	−0.397336	+	0.165118i
$64$		−	1.00000i		−	0.125000i
$65$	4.13447	+	7.57837i	0.512818	+	0.939981i
$66$	−3.03946	−	4.54321i	−0.374131	−	0.559230i
$67$	3.86878	−	3.86878i	0.472647	−	0.472647i	−0.430123	−	0.902770i	$-0.641530\pi$
$67$	3.86878	−	3.86878i	0.472647	−	0.472647i	0.902770	+	0.430123i	$0.141530\pi$
$68$	2.04213	−	2.04213i	0.247645	−	0.247645i
$69$	−2.48112	−	3.70864i	−0.298692	−	0.446467i
$70$	−2.44219	−	0.718070i	−0.291897	−	0.0858257i
$71$			0.944610i			0.112105i	0.998428	+	0.0560523i	$0.0178514\pi$
$71$			0.944610i			0.112105i	−0.998428	+	0.0560523i	$0.982149\pi$
$72$	2.77032	−	1.15124i	0.326485	−	0.135675i
$73$	3.61892	+	3.61892i	0.423563	+	0.423563i	0.886428	−	0.462866i	$-0.153179\pi$
$73$	3.61892	+	3.61892i	0.423563	+	0.423563i	−0.462866	+	0.886428i	$0.653179\pi$
$74$	10.2612			1.19284
$75$	6.01446	−	6.23107i	0.694490	−	0.719502i
$76$	−1.00000			−0.114708
$77$	−2.54043	−	2.54043i	−0.289509	−	0.289509i
$78$	−6.55921	−	1.30079i	−0.742685	−	0.147285i
$79$			15.0264i			1.69060i	0.534292	+	0.845300i	$0.320578\pi$
$79$			15.0264i			1.69060i	−0.534292	+	0.845300i	$0.679422\pi$
$80$	2.14526	+	0.630765i	0.239847	+	0.0705217i
$81$	6.37859	+	6.34930i	0.708733	+	0.705477i
$82$	4.46821	−	4.46821i	0.493431	−	0.493431i
$83$	5.54904	−	5.54904i	0.609086	−	0.609086i	−0.333621	−	0.942707i	$-0.608271\pi$
$83$	5.54904	−	5.54904i	0.609086	−	0.609086i	0.942707	+	0.333621i	$0.108271\pi$
$84$	1.63885	−	1.09641i	0.178813	−	0.119628i
$85$	3.09279	+	5.66900i	0.335460	+	0.614889i
$86$			0.909814i			0.0981077i
$87$	−1.85095	+	9.33342i	−0.198443	+	1.00065i
$88$	2.23156	+	2.23156i	0.237885	+	0.237885i
$89$	3.27340			0.346979			0.173490	−	0.984836i	$-0.444496\pi$
$89$	3.27340			0.346979			0.173490	+	0.984836i	$0.444496\pi$
$90$	0.722289	+	6.66921i	0.0761359	+	0.702996i
$91$	−4.39508			−0.460729
$92$	1.82163	+	1.82163i	0.189918	+	0.189918i
$93$	1.70962	−	8.62077i	0.177279	−	0.893932i
$94$		−	4.56187i		−	0.470521i
$95$	0.630765	−	2.14526i	0.0647151	−	0.220099i
$96$	−1.43959	+	0.963104i	−0.146928	+	0.0982964i
$97$	2.89748	−	2.89748i	0.294195	−	0.294195i	−0.544540	−	0.838735i	$-0.683296\pi$
$97$	2.89748	−	2.89748i	0.294195	−	0.294195i	0.838735	+	0.544540i	$0.183296\pi$
$98$	−4.03335	+	4.03335i	−0.407430	+	0.407430i
$99$	−3.61306	+	8.75117i	−0.363126	+	0.879526i
$100$	−2.70631	+	4.20427i	−0.270631	+	0.420427i
$101$			16.8808i			1.67971i	0.542813	+	0.839853i	$0.317359\pi$
$101$			16.8808i			1.67971i	−0.542813	+	0.839853i	$0.682641\pi$
$102$	−4.90662	−	0.973053i	−0.485828	−	0.0963466i
$103$	1.47281	+	1.47281i	0.145121	+	0.145121i	0.775934	−	0.630814i	$-0.217279\pi$
$103$	1.47281	+	1.47281i	0.145121	+	0.145121i	−0.630814	+	0.775934i	$0.717279\pi$
$104$	3.86071			0.378574
$105$	1.31835	+	4.20733i	0.128658	+	0.410593i
$106$	−4.48161			−0.435292
$107$	8.84697	+	8.84697i	0.855269	+	0.855269i	0.990776	−	0.135507i	$-0.0432665\pi$
$107$	8.84697	+	8.84697i	0.855269	+	0.855269i	−0.135507	+	0.990776i	$0.543266\pi$
$108$	−4.32542	−	2.87936i	−0.416214	−	0.277067i
$109$		−	6.83921i		−	0.655077i	−0.944838	−	0.327539i	$-0.893781\pi$
$109$		−	6.83921i		−	0.655077i	0.944838	−	0.327539i	$-0.106219\pi$
$110$	−6.19485	+	3.37968i	−0.590656	+	0.322240i
$111$	−9.88258	−	14.7719i	−0.938013	−	1.40209i
$112$	−0.804978	+	0.804978i	−0.0760633	+	0.0760633i
$113$	14.3560	−	14.3560i	1.35050	−	1.35050i	0.465400	−	0.885101i	$-0.345911\pi$
$113$	14.3560	−	14.3560i	1.35050	−	1.35050i	0.885101	−	0.465400i	$-0.154089\pi$
$114$	0.963104	+	1.43959i	0.0902030	+	0.134830i
$115$	−5.05688	+	2.75884i	−0.471556	+	0.257263i
$116$		−	5.49359i		−	0.510067i
$117$	4.44461	+	10.6954i	0.410904	+	0.988790i
$118$	−0.895279	−	0.895279i	−0.0824171	−	0.0824171i
$119$	−3.28774			−0.301386
$120$	−1.15806	−	3.69579i	−0.105716	−	0.337378i
$121$	1.04032			0.0945742
$122$	1.91180	+	1.91180i	0.173086	+	0.173086i
$123$	−10.7357	−	2.12905i	−0.968010	−	0.191970i
$124$			5.07413i			0.455671i
$125$	−7.31221	−	8.45764i	−0.654024	−	0.756474i
$126$	−3.15677	−	1.30332i	−0.281227	−	0.116109i
$127$	−1.57598	+	1.57598i	−0.139845	+	0.139845i	−0.773564	−	0.633718i	$-0.781528\pi$
$127$	−1.57598	+	1.57598i	−0.139845	+	0.139845i	0.633718	+	0.773564i	$0.281528\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	1.30976	−	0.876246i	0.115318	−	0.0771491i
$130$	−2.43520	+	8.28223i	−0.213581	+	0.726400i
$131$		−	19.0035i		−	1.66034i	−0.557509	−	0.830171i	$-0.688243\pi$
$131$		−	19.0035i		−	1.66034i	0.557509	−	0.830171i	$-0.311757\pi$
$132$	1.06331	−	5.36176i	0.0925494	−	0.466681i
$133$	0.804978	+	0.804978i	0.0698004	+	0.0698004i
$134$	5.47128			0.472647
$135$	8.90531	−	7.46294i	0.766447	−	0.642308i
$136$	2.88801			0.247645
$137$	15.2239	+	15.2239i	1.30066	+	1.30066i	0.927944	+	0.372720i	$0.121575\pi$
$137$	15.2239	+	15.2239i	1.30066	+	1.30066i	0.372720	+	0.927944i	$0.378425\pi$
$138$	0.867985	−	4.37682i	0.0738878	−	0.372580i
$139$		−	15.0510i		−	1.27661i	−0.769785	−	0.638304i	$-0.779636\pi$
$139$		−	15.0510i		−	1.27661i	0.769785	−	0.638304i	$-0.220364\pi$
$140$	−1.21913	−	2.23464i	−0.103036	−	0.188861i
$141$	−6.56724	+	4.39356i	−0.553061	+	0.370004i
$142$	−0.667940	+	0.667940i	−0.0560523	+	0.0560523i
$143$	−8.61540	+	8.61540i	−0.720456	+	0.720456i
$144$	2.77296	+	1.14486i	0.231080	+	0.0954050i
$145$	11.7852	+	3.46517i	0.978706	+	0.287766i
$146$			5.11793i			0.423563i
$147$	9.69093	+	1.92185i	0.799294	+	0.158511i
$148$	7.25575	+	7.25575i	0.596419	+	0.596419i
$149$	−13.7188			−1.12389			−0.561945	−	0.827174i	$-0.689947\pi$
$149$	−13.7188			−1.12389			−0.561945	+	0.827174i	$0.689947\pi$
$150$	8.65890	−	0.153169i	0.706996	−	0.0125062i
$151$	−14.9068			−1.21310			−0.606549	−	0.795046i	$-0.707447\pi$
$151$	−14.9068			−1.21310			−0.606549	+	0.795046i	$0.707447\pi$
$152$	−0.707107	−	0.707107i	−0.0573539	−	0.0573539i
$153$	3.32479	+	8.00069i	0.268793	+	0.646818i
$154$		−	3.59271i		−	0.289509i
$155$	−10.8853	−	3.20058i	−0.874331	−	0.257077i
$156$	−3.71827	−	5.55786i	−0.297700	−	0.444985i
$157$	2.63322	−	2.63322i	0.210153	−	0.210153i	−0.594179	−	0.804333i	$-0.702523\pi$
$157$	2.63322	−	2.63322i	0.210153	−	0.210153i	0.804333	+	0.594179i	$0.202523\pi$
$158$	−10.6253	+	10.6253i	−0.845300	+	0.845300i
$159$	4.31626	+	6.45170i	0.342301	+	0.511653i
$160$	1.07091	+	1.96295i	0.0846628	+	0.155184i
$161$		−	2.93274i		−	0.231132i
$162$	0.0207168	+	8.99998i	0.00162767	+	0.707105i
$163$	−8.49310	−	8.49310i	−0.665231	−	0.665231i	0.291377	−	0.956608i	$-0.405887\pi$
$163$	−8.49310	−	8.49310i	−0.665231	−	0.665231i	−0.956608	+	0.291377i	$0.905887\pi$
$164$	6.31900			0.493431
$165$	10.8317	+	5.66309i	0.843243	+	0.440871i
$166$	7.84753			0.609086
$167$	−2.26247	−	2.26247i	−0.175075	−	0.175075i	0.614130	−	0.789205i	$-0.289507\pi$
$167$	−2.26247	−	2.26247i	−0.175075	−	0.175075i	−0.789205	+	0.614130i	$0.789507\pi$
$168$	1.93412	+	0.383563i	0.149221	+	0.0295925i
$169$			1.90511i			0.146547i
$170$	−1.82165	+	6.19552i	−0.139714	+	0.475175i
$171$	1.14486	−	2.77296i	0.0875496	−	0.212053i
$172$	−0.643335	+	0.643335i	−0.0490539	+	0.0490539i
$173$	6.00022	−	6.00022i	0.456189	−	0.456189i	−0.441214	−	0.897402i	$-0.645452\pi$
$173$	6.00022	−	6.00022i	0.456189	−	0.456189i	0.897402	+	0.441214i	$0.145452\pi$
$174$	−7.90854	+	5.29091i	−0.599545	+	0.401103i
$175$	5.56286	−	1.20583i	0.420513	−	0.0911520i
$176$			3.15590i			0.237885i
$177$	−0.426591	+	2.15108i	−0.0320645	+	0.161685i
$178$	2.31464	+	2.31464i	0.173490	+	0.173490i
$179$	−10.5263			−0.786776			−0.393388	−	0.919373i	$-0.628697\pi$
$179$	−10.5263			−0.786776			−0.393388	+	0.919373i	$0.628697\pi$
$180$	−4.20510	+	5.22658i	−0.313430	+	0.389566i
$181$	−20.9226			−1.55516			−0.777582	−	0.628781i	$-0.783554\pi$
$181$	−20.9226			−1.55516			−0.777582	+	0.628781i	$0.783554\pi$
$182$	−3.10779	−	3.10779i	−0.230365	−	0.230365i
$183$	0.910950	−	4.59347i	0.0673394	−	0.339559i
$184$			2.57617i			0.189918i
$185$	−20.1421	+	10.9888i	−1.48088	+	0.807912i
$186$	7.30469	−	4.88692i	0.535606	−	0.358326i
$187$	−6.44475	+	6.44475i	−0.471287	+	0.471287i
$188$	3.22573	−	3.22573i	0.235260	−	0.235260i
$189$	1.16404	+	5.79969i	0.0846717	+	0.421866i
$190$	1.96295	−	1.07091i	0.142407	−	0.0776919i
$191$			24.7912i			1.79383i	0.442204	+	0.896915i	$0.354197\pi$
$191$			24.7912i			1.79383i	−0.442204	+	0.896915i	$0.645803\pi$
$192$	−1.69896	−	0.336929i	−0.122612	−	0.0243157i
$193$	17.4625	+	17.4625i	1.25698	+	1.25698i	0.952528	+	0.304450i	$0.0984726\pi$
$193$	17.4625	+	17.4625i	1.25698	+	1.25698i	0.304450	+	0.952528i	$0.401527\pi$
$194$	4.09766			0.294195
$195$	14.2684	−	4.47095i	1.02178	−	0.320171i
$196$	−5.70402			−0.407430
$197$	−1.66630	−	1.66630i	−0.118719	−	0.118719i	0.645252	−	0.763970i	$-0.276753\pi$
$197$	−1.66630	−	1.66630i	−0.118719	−	0.118719i	−0.763970	+	0.645252i	$0.776753\pi$
$198$	−8.74283	+	3.63319i	−0.621326	+	0.258200i
$199$		−	27.4124i		−	1.94321i	−0.236606	−	0.971606i	$-0.576035\pi$
$199$		−	27.4124i		−	1.94321i	0.236606	−	0.971606i	$-0.423965\pi$
$200$	−4.88652	+	1.05922i	−0.345529	+	0.0748982i
$201$	−5.26942	−	7.87642i	−0.371676	−	0.555560i
$202$	−11.9366	+	11.9366i	−0.839853	+	0.839853i
$203$	−4.42222	+	4.42222i	−0.310379	+	0.310379i
$204$	−2.78145	−	4.15756i	−0.194741	−	0.291087i
$205$	−3.98580	+	13.5559i	−0.278380	+	0.946784i
$206$			2.08287i			0.145121i
$207$	−7.13680	+	2.96579i	−0.496042	+	0.206137i
$208$	2.72994	+	2.72994i	0.189287	+	0.189287i
$209$	3.15590			0.218298
$210$	−2.04282	+	3.90725i	−0.140968	+	0.269626i
$211$	−3.68643			−0.253785			−0.126892	−	0.991917i	$-0.540500\pi$
$211$	−3.68643			−0.253785			−0.126892	+	0.991917i	$0.540500\pi$
$212$	−3.16898	−	3.16898i	−0.217646	−	0.217646i
$213$	1.60486	+	0.318266i	0.109963	+	0.0218073i
$214$			12.5115i			0.855269i
$215$	−0.974328	−	1.78591i	−0.0664486	−	0.121798i
$216$	−1.02252	−	5.09455i	−0.0695734	−	0.346640i
$217$	4.08457	−	4.08457i	0.277278	−	0.277278i
$218$	4.83605	−	4.83605i	0.327539	−	0.327539i
$219$	7.36773	−	4.92910i	0.497865	−	0.333078i
$220$	−6.77022	−	1.99063i	−0.456448	−	0.134208i
$221$			11.1498i			0.750015i
$222$	3.45728	−	17.4334i	0.232038	−	1.17005i
$223$	−18.9631	−	18.9631i	−1.26987	−	1.26987i	−0.946157	−	0.323709i	$-0.895070\pi$
$223$	−18.9631	−	18.9631i	−1.26987	−	1.26987i	−0.323709	−	0.946157i	$-0.604930\pi$
$224$	−1.13841			−0.0760633
$225$	−8.55993	−	12.3178i	−0.570662	−	0.821185i
$226$	20.3025			1.35050
$227$	2.05681	+	2.05681i	0.136515	+	0.136515i	0.772062	−	0.635547i	$-0.219225\pi$
$227$	2.05681	+	2.05681i	0.136515	+	0.136515i	−0.635547	+	0.772062i	$0.719225\pi$
$228$	−0.336929	+	1.69896i	−0.0223136	+	0.112517i
$229$		−	15.8734i		−	1.04895i	−0.851427	−	0.524473i	$-0.824262\pi$
$229$		−	15.8734i		−	1.04895i	0.851427	−	0.524473i	$-0.175738\pi$
$230$	−5.52655	−	1.62496i	−0.364410	−	0.107147i
$231$	−5.17204	+	3.46015i	−0.340295	+	0.227661i
$232$	3.88456	−	3.88456i	0.255034	−	0.255034i
$233$	15.6011	−	15.6011i	1.02206	−	1.02206i	0.0223132	−	0.999751i	$-0.492897\pi$
$233$	15.6011	−	15.6011i	1.02206	−	1.02206i	0.999751	−	0.0223132i	$-0.00710309\pi$
$234$	−4.41997	+	10.7056i	−0.288943	+	0.699847i
$235$	4.88535	+	8.95470i	0.318685	+	0.584140i
$236$		−	1.26612i		−	0.0824171i
$237$	25.5293	+	5.06282i	1.65830	+	0.328865i
$238$	−2.32478	−	2.32478i	−0.150693	−	0.150693i
$239$	−4.84839			−0.313616			−0.156808	−	0.987629i	$-0.550120\pi$
$239$	−4.84839			−0.313616			−0.156808	+	0.987629i	$0.550120\pi$
$240$	1.79445	−	3.43220i	0.115831	−	0.221547i
$241$	−17.0520			−1.09842			−0.549209	−	0.835685i	$-0.685071\pi$
$241$	−17.0520			−1.09842			−0.549209	+	0.835685i	$0.685071\pi$
$242$	0.735615	+	0.735615i	0.0472871	+	0.0472871i
$243$	12.9364	−	8.69774i	0.829868	−	0.557960i
$244$			2.70369i			0.173086i
$245$	3.59790	−	12.2366i	0.229861	−	0.781768i
$246$	−6.08585	−	9.09679i	−0.388020	−	0.579990i
$247$	2.72994	−	2.72994i	0.173702	−	0.173702i
$248$	−3.58795	+	3.58795i	−0.227835	+	0.227835i
$249$	−7.55799	−	11.2973i	−0.478968	−	0.715934i
$250$	0.809943	−	11.1510i	0.0512253	−	0.705249i
$251$			7.93870i			0.501087i	0.968105	+	0.250543i	$0.0806092\pi$
$251$			7.93870i			0.501087i	−0.968105	+	0.250543i	$0.919391\pi$
$252$	−1.31058	−	3.15376i	−0.0825590	−	0.198668i
$253$	−5.74887	−	5.74887i	−0.361428	−	0.361428i
$254$	−2.22877			−0.139845
$255$	10.6735	−	3.34450i	0.668399	−	0.209440i
$256$	1.00000			0.0625000
$257$	−16.9891	−	16.9891i	−1.05975	−	1.05975i	−0.998098	−	0.0616541i	$-0.980362\pi$
$257$	−16.9891	−	16.9891i	−1.05975	−	1.05975i	−0.0616541	−	0.998098i	$-0.519638\pi$
$258$	1.54574	+	0.306542i	0.0962336	+	0.0190845i
$259$		−	11.6814i		−	0.725849i
$260$	−7.57837	+	4.13447i	−0.469990	+	0.256409i
$261$	15.2335	+	6.28939i	0.942930	+	0.389304i
$262$	13.4375	−	13.4375i	0.830171	−	0.830171i
$263$	−2.30249	+	2.30249i	−0.141977	+	0.141977i	−0.774523	−	0.632546i	$-0.782010\pi$
$263$	−2.30249	+	2.30249i	−0.141977	+	0.141977i	0.632546	+	0.774523i	$0.282010\pi$
$264$	4.54321	−	3.03946i	0.279615	−	0.187066i
$265$	8.79715	−	4.79939i	0.540405	−	0.294824i
$266$			1.13841i			0.0698004i
$267$	1.10290	−	5.56138i	0.0674965	−	0.340351i
$268$	3.86878	+	3.86878i	0.236323	+	0.236323i
$269$	15.9676			0.973559			0.486780	−	0.873525i	$-0.338171\pi$
$269$	15.9676			0.973559			0.486780	+	0.873525i	$0.338171\pi$
$270$	11.5741	+	1.01990i	0.704377	+	0.0620694i
$271$	−5.91297			−0.359188			−0.179594	−	0.983741i	$-0.557478\pi$
$271$	−5.91297			−0.359188			−0.179594	+	0.983741i	$0.557478\pi$
$272$	2.04213	+	2.04213i	0.123822	+	0.123822i
$273$	−1.48083	+	7.46708i	−0.0896238	+	0.451928i
$274$			21.5298i			1.30066i
$275$	8.54083	−	13.2682i	0.515031	−	0.800105i
$276$	3.70864	−	2.48112i	0.223234	−	0.149346i
$277$	17.6393	−	17.6393i	1.05984	−	1.05984i	0.0617480	−	0.998092i	$-0.480332\pi$
$277$	17.6393	−	17.6393i	1.05984	−	1.05984i	0.998092	−	0.0617480i	$-0.0196675\pi$
$278$	10.6426	−	10.6426i	0.638304	−	0.638304i
$279$	−14.0704	−	5.80917i	−0.842370	−	0.347786i
$280$	0.718070	−	2.44219i	0.0429129	−	0.145949i
$281$			11.7923i			0.703472i	0.936099	+	0.351736i	$0.114408\pi$
$281$			11.7923i			0.703472i	−0.936099	+	0.351736i	$0.885592\pi$
$282$	−7.75045	−	1.53702i	−0.461533	−	0.0915285i
$283$	−4.82604	−	4.82604i	−0.286878	−	0.286878i	0.548966	−	0.835845i	$-0.315022\pi$
$283$	−4.82604	−	4.82604i	−0.286878	−	0.286878i	−0.835845	+	0.548966i	$0.815022\pi$
$284$	−0.944610			−0.0560523
$285$	−3.43220	−	1.79445i	−0.203306	−	0.106294i
$286$	−12.1840			−0.720456
$287$	−5.08665	−	5.08665i	−0.300256	−	0.300256i
$288$	1.15124	+	2.77032i	0.0678374	+	0.163242i
$289$		−	8.65941i		−	0.509377i
$290$	5.88314	+	10.7836i	0.345470	+	0.633236i
$291$	−3.94648	−	5.89897i	−0.231346	−	0.345804i
$292$	−3.61892	+	3.61892i	−0.211781	+	0.211781i
$293$	11.3784	−	11.3784i	0.664732	−	0.664732i	−0.291760	−	0.956492i	$-0.594241\pi$
$293$	11.3784	−	11.3784i	0.664732	−	0.664732i	0.956492	+	0.291760i	$0.0942408\pi$
$294$	5.49357	+	8.21147i	0.320391	+	0.478903i
$295$	2.71614	+	0.798621i	0.158140	+	0.0464975i
$296$			10.2612i			0.596419i
$297$	13.6506	+	9.08698i	0.792087	+	0.527280i
$298$	−9.70068	−	9.70068i	−0.561945	−	0.561945i
$299$	−9.94585			−0.575183
$300$	6.23107	+	6.01446i	0.359751	+	0.347245i
$301$	1.03574			0.0596992
$302$	−10.5407	−	10.5407i	−0.606549	−	0.606549i
$303$	28.6799	+	5.68764i	1.64762	+	0.326746i
$304$		−	1.00000i		−	0.0573539i
$305$	−5.80011	−	1.70539i	−0.332113	−	0.0976504i
$306$	−3.30636	+	8.00832i	−0.189012	+	0.457805i
$307$	3.22856	−	3.22856i	0.184264	−	0.184264i	−0.608947	−	0.793211i	$-0.708408\pi$
$307$	3.22856	−	3.22856i	0.184264	−	0.184264i	0.793211	+	0.608947i	$0.208408\pi$
$308$	2.54043	−	2.54043i	0.144754	−	0.144754i
$309$	2.99849	−	2.00602i	0.170578	−	0.114119i
$310$	−5.43393	−	9.96024i	−0.308627	−	0.565704i
$311$		−	8.13102i		−	0.461068i	−0.973064	−	0.230534i	$-0.925953\pi$
$311$		−	8.13102i		−	0.461068i	0.973064	−	0.230534i	$-0.0740473\pi$
$312$	1.30079	−	6.55921i	0.0736425	−	0.371342i
$313$	19.8596	+	19.8596i	1.12253	+	1.12253i	0.991359	+	0.131173i	$0.0418744\pi$
$313$	19.8596	+	19.8596i	1.12253	+	1.12253i	0.131173	+	0.991359i	$0.458126\pi$
$314$	3.72393			0.210153
$315$	7.59230	−	0.822262i	0.427777	−	0.0463292i
$316$	−15.0264			−0.845300
$317$	7.90002	+	7.90002i	0.443709	+	0.443709i	0.893257	−	0.449547i	$-0.148415\pi$
$317$	7.90002	+	7.90002i	0.443709	+	0.443709i	−0.449547	+	0.893257i	$0.648415\pi$
$318$	−1.50998	+	7.61409i	−0.0846756	+	0.426977i
$319$			17.3372i			0.970698i
$320$	−0.630765	+	2.14526i	−0.0352608	+	0.119924i
$321$	18.0115	−	12.0499i	1.00530	−	0.672559i
$322$	2.07376	−	2.07376i	0.115566	−	0.115566i
$323$	2.04213	−	2.04213i	0.113627	−	0.113627i
$324$	−6.34930	+	6.37859i	−0.352739	+	0.354366i
$325$	−4.08934	−	18.8654i	−0.226836	−	1.04647i
$326$		−	12.0111i		−	0.665231i
$327$	−11.6196	−	2.30432i	−0.642563	−	0.127429i
$328$	4.46821	+	4.46821i	0.246715	+	0.246715i
$329$	−5.19328			−0.286315
$330$	3.65473	+	11.6635i	0.201186	+	0.642057i
$331$	29.2265			1.60643			0.803217	−	0.595687i	$-0.203120\pi$
$331$	29.2265			1.60643			0.803217	+	0.595687i	$0.203120\pi$
$332$	5.54904	+	5.54904i	0.304543	+	0.304543i
$333$	−28.4267	+	11.8131i	−1.55777	+	0.647352i
$334$		−	3.19962i		−	0.175075i
$335$	−10.7398	+	5.85925i	−0.586779	+	0.320125i
$336$	1.09641	+	1.63885i	0.0598140	+	0.0894065i
$337$	−10.9958	+	10.9958i	−0.598982	+	0.598982i	−0.940042	−	0.341060i	$-0.889214\pi$
$337$	−10.9958	+	10.9958i	−0.598982	+	0.598982i	0.341060	+	0.940042i	$0.389214\pi$
$338$	−1.34711	+	1.34711i	−0.0732734	+	0.0732734i
$339$	−19.5534	−	29.2273i	−1.06200	−	1.58741i
$340$	−5.66900	+	3.09279i	−0.307445	+	0.167730i
$341$		−	16.0134i		−	0.867176i
$342$	2.77032	−	1.15124i	0.149802	−	0.0622519i
$343$	10.2265	+	10.2265i	0.552177	+	0.552177i
$344$	−0.909814			−0.0490539
$345$	2.98337	+	9.52099i	0.160619	+	0.512593i
$346$	8.48560			0.456189
$347$	−19.5400	−	19.5400i	−1.04896	−	1.04896i	−0.998738	−	0.0502218i	$-0.984007\pi$
$347$	−19.5400	−	19.5400i	−1.04896	−	1.04896i	−0.0502218	−	0.998738i	$-0.515993\pi$
$348$	−9.33342	−	1.85095i	−0.500324	−	0.0992213i
$349$			33.9607i			1.81787i	0.416934	+	0.908937i	$0.363105\pi$
$349$			33.9607i			1.81787i	−0.416934	+	0.908937i	$0.636895\pi$
$350$	4.78619	+	3.08089i	0.255832	+	0.164681i
$351$	19.6686	−	3.94764i	1.04983	−	0.210709i
$352$	−2.23156	+	2.23156i	−0.118942	+	0.118942i
$353$	17.4613	−	17.4613i	0.929372	−	0.929372i	−0.0682931	−	0.997665i	$-0.521755\pi$
$353$	17.4613	−	17.4613i	0.929372	−	0.929372i	0.997665	+	0.0682931i	$0.0217553\pi$
$354$	−1.82269	+	1.21940i	−0.0968750	+	0.0648104i
$355$	0.595827	−	2.02643i	0.0316232	−	0.107552i
$356$			3.27340i			0.173490i
$357$	−1.10773	+	5.58575i	−0.0586275	+	0.295629i
$358$	−7.44325	−	7.44325i	−0.393388	−	0.393388i
$359$	25.1531			1.32753			0.663766	−	0.747940i	$-0.268957\pi$
$359$	25.1531			1.32753			0.663766	+	0.747940i	$0.268957\pi$
$360$	−6.66921	+	0.722289i	−0.351498	+	0.0380680i
$361$	−1.00000			−0.0526316
$362$	−14.7945	−	14.7945i	−0.777582	−	0.777582i
$363$	0.350513	−	1.76746i	0.0183971	−	0.0927676i
$364$		−	4.39508i		−	0.230365i
$365$	−5.48083	−	10.0462i	−0.286880	−	0.525843i
$366$	3.89221	−	2.60393i	0.203449	−	0.136110i
$367$	−3.86210	+	3.86210i	−0.201600	+	0.201600i	−0.800685	−	0.599085i	$-0.795531\pi$
$367$	−3.86210	+	3.86210i	−0.201600	+	0.201600i	0.599085	+	0.800685i	$0.295531\pi$
$368$	−1.82163	+	1.82163i	−0.0949589	+	0.0949589i
$369$	−7.23436	+	17.5223i	−0.376606	+	0.912175i
$370$	−22.0129	−	6.47239i	−1.14440	−	0.336484i
$371$			5.10191i			0.264878i
$372$	8.62077	+	1.70962i	0.446966	+	0.0886397i
$373$	−6.37524	−	6.37524i	−0.330098	−	0.330098i	0.522526	−	0.852623i	$-0.324990\pi$
$373$	−6.37524	−	6.37524i	−0.330098	−	0.330098i	−0.852623	+	0.522526i	$0.824990\pi$
$374$	−9.11425			−0.471287
$375$	−16.8329	+	9.57355i	−0.869248	+	0.494376i
$376$	4.56187			0.235260
$377$	14.9972	+	14.9972i	0.772393	+	0.772393i
$378$	−3.27790	+	4.92411i	−0.168597	+	0.253269i
$379$		−	14.0745i		−	0.722958i	−0.932380	−	0.361479i	$-0.882272\pi$
$379$		−	14.0745i		−	0.722958i	0.932380	−	0.361479i	$-0.117728\pi$
$380$	2.14526	+	0.630765i	0.110049	+	0.0323576i
$381$	2.14654	+	3.20852i	0.109970	+	0.164378i
$382$	−17.5300	+	17.5300i	−0.896915	+	0.896915i
$383$	−5.66358	+	5.66358i	−0.289396	+	0.289396i	−0.836841	−	0.547446i	$-0.815600\pi$
$383$	−5.66358	+	5.66358i	−0.289396	+	0.289396i	0.547446	+	0.836841i	$0.315600\pi$
$384$	−0.963104	−	1.43959i	−0.0491482	−	0.0734640i
$385$	3.84746	+	7.05229i	0.196085	+	0.359418i
$386$			24.6957i			1.25698i
$387$	−1.04741	−	2.52047i	−0.0532430	−	0.128123i
$388$	2.89748	+	2.89748i	0.147097	+	0.147097i
$389$	−1.77092			−0.0897890			−0.0448945	−	0.998992i	$-0.514295\pi$
$389$	−1.77092			−0.0897890			−0.0448945	+	0.998992i	$0.514295\pi$
$390$	13.2507	+	6.92784i	0.670976	+	0.350805i
$391$	−7.44000			−0.376257
$392$	−4.03335	−	4.03335i	−0.203715	−	0.203715i
$393$	−32.2862	−	6.40282i	−1.62863	−	0.322980i
$394$		−	2.35650i		−	0.118719i
$395$	9.47811	−	32.2355i	0.476896	−	1.62194i
$396$	−8.75117	−	3.61306i	−0.439763	−	0.181563i
$397$	−13.5159	+	13.5159i	−0.678345	+	0.678345i	−0.959626	−	0.281281i	$-0.909241\pi$
$397$	−13.5159	+	13.5159i	−0.678345	+	0.678345i	0.281281	+	0.959626i	$0.409241\pi$
$398$	19.3835	−	19.3835i	0.971606	−	0.971606i
$399$	1.63885	−	1.09641i	0.0820451	−	0.0548891i
$400$	−4.20427	−	2.70631i	−0.210214	−	0.135315i
$401$			33.0944i			1.65266i	0.563188	+	0.826329i	$0.309575\pi$
$401$			33.0944i			1.65266i	−0.563188	+	0.826329i	$0.690425\pi$
$402$	1.84343	−	9.29551i	0.0919420	−	0.463618i
$403$	−13.8521	−	13.8521i	−0.690020	−	0.690020i
$404$	−16.8808			−0.839853
$405$	−9.67882	−	17.6443i	−0.480944	−	0.876751i
$406$	−6.25397			−0.310379
$407$	−22.8984	−	22.8984i	−1.13503	−	1.13503i
$408$	0.973053	−	4.90662i	0.0481733	−	0.242914i
$409$		−	12.5812i		−	0.622098i	−0.950394	−	0.311049i	$-0.899320\pi$
$409$		−	12.5812i		−	0.622098i	0.950394	−	0.311049i	$-0.100680\pi$
$410$	−12.4038	+	6.76707i	−0.612582	+	0.334202i
$411$	30.9942	−	20.7355i	1.52883	−	1.02280i
$412$	−1.47281	+	1.47281i	−0.0725603	+	0.0725603i
$413$	−1.01919	+	1.01919i	−0.0501513	+	0.0501513i
$414$	−7.14361	−	2.94935i	−0.351089	−	0.144953i
$415$	−15.4043	+	8.40399i	−0.756166	+	0.412536i
$416$			3.86071i			0.189287i
$417$	−25.5711	−	5.07111i	−1.25222	−	0.248333i
$418$	2.23156	+	2.23156i	0.109149	+	0.109149i
$419$	33.5096			1.63705			0.818525	−	0.574471i	$-0.194792\pi$
$419$	33.5096			1.63705			0.818525	+	0.574471i	$0.194792\pi$
$420$	−4.20733	+	1.31835i	−0.205297	+	0.0643290i
$421$	−29.7747			−1.45113			−0.725564	−	0.688154i	$-0.758421\pi$
$421$	−29.7747			−1.45113			−0.725564	+	0.688154i	$0.758421\pi$
$422$	−2.60670	−	2.60670i	−0.126892	−	0.126892i
$423$	5.25180	+	12.6378i	0.255351	+	0.614472i
$424$		−	4.48161i		−	0.217646i
$425$	−3.05903	−	14.1123i	−0.148385	−	0.684547i
$426$	0.909759	+	1.35986i	0.0440779	+	0.0658852i
$427$	2.17641	−	2.17641i	0.105324	−	0.105324i
$428$	−8.84697	+	8.84697i	−0.427634	+	0.427634i
$429$	11.7345	+	17.5400i	0.566546	+	0.846840i
$430$	0.573879	−	1.95179i	0.0276749	−	0.0941235i
$431$			16.7696i			0.807763i	0.914811	+	0.403882i	$0.132339\pi$
$431$			16.7696i			0.807763i	−0.914811	+	0.403882i	$0.867661\pi$
$432$	2.87936	−	4.32542i	0.138533	−	0.208107i
$433$	−0.841474	−	0.841474i	−0.0404387	−	0.0404387i	0.686598	−	0.727037i	$-0.259103\pi$
$433$	−0.841474	−	0.841474i	−0.0404387	−	0.0404387i	−0.727037	+	0.686598i	$0.759103\pi$
$434$	5.77645			0.277278
$435$	9.85796	−	18.8551i	0.472653	−	0.904032i
$436$	6.83921			0.327539
$437$	1.82163	+	1.82163i	0.0871402	+	0.0871402i
$438$	8.69517	+	1.72438i	0.415471	+	0.0823939i
$439$			32.4072i			1.54671i	0.633973	+	0.773355i	$0.281423\pi$
$439$			32.4072i			1.54671i	−0.633973	+	0.773355i	$0.718577\pi$
$440$	−3.37968	−	6.19485i	−0.161120	−	0.295328i
$441$	6.53030	−	15.8170i	0.310967	−	0.753191i
$442$	−7.88408	+	7.88408i	−0.375007	+	0.375007i
$443$	−15.3966	+	15.3966i	−0.731515	+	0.731515i	−0.970920	−	0.239405i	$-0.923048\pi$
$443$	−15.3966	+	15.3966i	−0.731515	+	0.731515i	0.239405	+	0.970920i	$0.423048\pi$
$444$	14.7719	−	9.88258i	0.701044	−	0.469007i
$445$	−7.02228	−	2.06474i	−0.332888	−	0.0978782i
$446$		−	26.8179i		−	1.26987i
$447$	−4.62227	+	23.3078i	−0.218626	+	1.10242i
$448$	−0.804978	−	0.804978i	−0.0380316	−	0.0380316i
$449$	3.69496			0.174376			0.0871879	−	0.996192i	$-0.472212\pi$
$449$	3.69496			0.174376			0.0871879	+	0.996192i	$0.472212\pi$
$450$	2.65720	−	14.7628i	0.125262	−	0.695923i
$451$	−19.9421			−0.939037
$452$	14.3560	+	14.3560i	0.675250	+	0.675250i
$453$	−5.02253	+	25.3261i	−0.235979	+	1.18992i
$454$			2.90877i			0.136515i
$455$	9.42858	+	2.77226i	0.442019	+	0.129966i
$456$	−1.43959	+	0.963104i	−0.0674151	+	0.0451015i
$457$	6.23351	−	6.23351i	0.291591	−	0.291591i	−0.546117	−	0.837709i	$-0.683895\pi$
$457$	6.23351	−	6.23351i	0.291591	−	0.291591i	0.837709	+	0.546117i	$0.183895\pi$
$458$	11.2242	−	11.2242i	0.524473	−	0.524473i
$459$	14.7131	−	2.95303i	0.686749	−	0.137836i
$460$	−2.75884	−	5.05688i	−0.128632	−	0.235778i
$461$		−	3.01803i		−	0.140563i	−0.997527	−	0.0702817i	$-0.977610\pi$
$461$		−	3.01803i		−	0.140563i	0.997527	−	0.0702817i	$-0.0223898\pi$
$462$	−6.10388	−	1.21049i	−0.283978	−	0.0563169i
$463$	17.1200	+	17.1200i	0.795634	+	0.795634i	0.982404	−	0.186770i	$-0.0598018\pi$
$463$	17.1200	+	17.1200i	0.795634	+	0.795634i	−0.186770	+	0.982404i	$0.559802\pi$
$464$	5.49359			0.255034
$465$	−9.10526	+	17.4154i	−0.422246	+	0.807620i
$466$	22.0633			1.02206
$467$	3.42627	+	3.42627i	0.158549	+	0.158549i	0.781923	−	0.623375i	$-0.214239\pi$
$467$	3.42627	+	3.42627i	0.158549	+	0.158549i	−0.623375	+	0.781923i	$0.714239\pi$
$468$	−10.6954	+	4.44461i	−0.494395	+	0.205452i
$469$		−	6.22857i		−	0.287608i
$470$	−2.87747	+	9.78639i	−0.132728	+	0.451413i
$471$	−3.58653	−	5.36094i	−0.165259	−	0.247019i
$472$	0.895279	−	0.895279i	0.0412085	−	0.0412085i
$473$	2.03030	−	2.03030i	0.0933533	−	0.0933533i
$474$	14.4720	+	21.6319i	0.664720	+	0.993585i
$475$	−2.70631	+	4.20427i	−0.124174	+	0.192905i
$476$		−	3.28774i		−	0.150693i
$477$	12.4155	−	5.15941i	0.568465	−	0.236233i
$478$	−3.42833	−	3.42833i	−0.156808	−	0.156808i
$479$	−18.0199			−0.823349			−0.411674	−	0.911331i	$-0.635056\pi$
$479$	−18.0199			−0.823349			−0.411674	+	0.911331i	$0.635056\pi$
$480$	3.69579	−	1.15806i	0.168689	−	0.0528581i
$481$	−39.6155			−1.80631
$482$	−12.0576	−	12.0576i	−0.549209	−	0.549209i
$483$	−4.98262	−	0.988124i	−0.226717	−	0.0449612i
$484$			1.04032i			0.0472871i
$485$	−8.04348	+	4.38822i	−0.365236	+	0.199259i
$486$	15.2976	+	2.99715i	0.693914	+	0.135954i
$487$	−3.32991	+	3.32991i	−0.150893	+	0.150893i	−0.778517	−	0.627624i	$-0.784028\pi$
$487$	−3.32991	+	3.32991i	−0.150893	+	0.150893i	0.627624	+	0.778517i	$0.284028\pi$
$488$	−1.91180	+	1.91180i	−0.0865429	+	0.0865429i
$489$	−17.2910	+	11.5679i	−0.781928	+	0.523119i
$490$	11.1967	−	6.10849i	0.505814	−	0.275953i
$491$			40.7725i			1.84004i	0.391873	+	0.920020i	$0.371827\pi$
$491$			40.7725i			1.84004i	−0.391873	+	0.920020i	$0.628173\pi$
$492$	2.12905	−	10.7357i	0.0959851	−	0.484005i
$493$	11.2186	+	11.2186i	0.505262	+	0.505262i
$494$	3.86071			0.173702
$495$	13.2709	−	16.4945i	0.596482	−	0.741374i
$496$	−5.07413			−0.227835
$497$	0.760391	+	0.760391i	0.0341082	+	0.0341082i
$498$	2.64406	−	13.3327i	0.118483	−	0.597451i
$499$			28.4698i			1.27449i	0.770663	+	0.637243i	$0.219925\pi$
$499$			28.4698i			1.27449i	−0.770663	+	0.637243i	$0.780075\pi$
$500$	8.45764	−	7.31221i	0.378237	−	0.327012i
$501$	−4.60615	+	3.08157i	−0.205788	+	0.137674i
$502$	−5.61351	+	5.61351i	−0.250543	+	0.250543i
$503$	−19.2777	+	19.2777i	−0.859549	+	0.859549i	−0.991285	−	0.131736i	$-0.957945\pi$
$503$	−19.2777	+	19.2777i	−0.859549	+	0.859549i	0.131736	+	0.991285i	$0.457945\pi$
$504$	1.30332	−	3.15677i	0.0580545	−	0.140614i
$505$	10.6478	−	36.2138i	0.473823	−	1.61149i
$506$		−	8.13012i		−	0.361428i
$507$	3.23671	+	0.641885i	0.143747	+	0.0285071i
$508$	−1.57598	−	1.57598i	−0.0699227	−	0.0699227i
$509$	30.9140			1.37024			0.685120	−	0.728431i	$-0.259750\pi$
$509$	30.9140			1.37024			0.685120	+	0.728431i	$0.259750\pi$
$510$	9.91220	+	5.18237i	0.438920	+	0.229479i
$511$	5.82630			0.257740
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−4.32542	−	2.87936i	−0.190972	−	0.127127i
$514$		−	24.0262i		−	1.05975i
$515$	−2.23057	−	4.08856i	−0.0982905	−	0.180164i
$516$	0.876246	+	1.30976i	0.0385746	+	0.0576591i
$517$	−10.1801	+	10.1801i	−0.447719	+	0.447719i
$518$	8.26002	−	8.26002i	0.362924	−	0.362924i
$519$	−8.17252	−	12.2158i	−0.358734	−	0.536215i
$520$	−8.28223	−	2.43520i	−0.363200	−	0.106791i
$521$			24.0255i			1.05258i	0.850306	+	0.526289i	$0.176417\pi$
$521$			24.0255i			1.05258i	−0.850306	+	0.526289i	$0.823583\pi$
$522$	6.32444	+	15.2190i	0.276813	+	0.666117i
$523$	−28.0008	−	28.0008i	−1.22439	−	1.22439i	−0.966056	−	0.258331i	$-0.916828\pi$
$523$	−28.0008	−	28.0008i	−1.22439	−	1.22439i	−0.258331	−	0.966056i	$-0.583172\pi$
$524$	19.0035			0.830171
$525$	−0.174369	−	9.85738i	−0.00761008	−	0.430212i
$526$	−3.25621			−0.141977
$527$	−10.3620	−	10.3620i	−0.451377	−	0.451377i
$528$	5.36176	+	1.06331i	0.233340	+	0.0462747i
$529$			16.3634i			0.711450i
$530$	9.61421	+	2.82684i	0.417615	+	0.122790i
$531$	3.51088	+	1.44952i	0.152359	+	0.0629040i
$532$	−0.804978	+	0.804978i	−0.0349002	+	0.0349002i
$533$	−17.2505	+	17.2505i	−0.747200	+	0.747200i
$534$	4.71236	−	3.15262i	0.203924	−	0.136427i
$535$	−13.3987	−	24.5594i	−0.579276	−	1.06180i
$536$			5.47128i			0.236323i
$537$	−3.54663	+	17.8839i	−0.153048	+	0.771746i
$538$	11.2908	+	11.2908i	0.486780	+	0.486780i
$539$	18.0013			0.775371
$540$	7.46294	+	8.90531i	0.321154	+	0.383223i
$541$	30.2843			1.30202			0.651012	−	0.759067i	$-0.274345\pi$
$541$	30.2843			1.30202			0.651012	+	0.759067i	$0.274345\pi$
$542$	−4.18110	−	4.18110i	−0.179594	−	0.179594i
$543$	−7.04942	+	35.5467i	−0.302520	+	1.52546i
$544$			2.88801i			0.123822i
$545$	−4.31393	+	14.6719i	−0.184788	+	0.628474i
$546$	−6.32713	+	4.23292i	−0.270776	+	0.181152i
$547$	−20.9852	+	20.9852i	−0.897263	+	0.897263i	−0.995193	−	0.0979302i	$-0.968778\pi$
$547$	−20.9852	+	20.9852i	−0.897263	+	0.897263i	0.0979302	+	0.995193i	$0.468778\pi$
$548$	−15.2239	+	15.2239i	−0.650332	+	0.650332i
$549$	−7.49721	−	3.09534i	−0.319973	−	0.132106i
$550$	15.4213	−	3.34279i	0.657568	−	0.142537i
$551$		−	5.49359i		−	0.234035i
$552$	4.37682	+	0.867985i	0.186290	+	0.0369439i
$553$	12.0959	+	12.0959i	0.514370	+	0.514370i
$554$	24.9457			1.05984
$555$	11.8831	+	37.9232i	0.504409	+	1.60975i
$556$	15.0510			0.638304
$557$	19.6777	+	19.6777i	0.833770	+	0.833770i	0.988030	−	0.154260i	$-0.0492995\pi$
$557$	19.6777	+	19.6777i	0.833770	+	0.833770i	−0.154260	+	0.988030i	$0.549299\pi$
$558$	−5.84154	−	14.0569i	−0.247292	−	0.595078i
$559$		−	3.51253i		−	0.148564i
$560$	2.23464	−	1.21913i	0.0944307	−	0.0515178i
$561$	8.77798	+	13.1208i	0.370606	+	0.553961i
$562$	−8.33844	+	8.33844i	−0.351736	+	0.351736i
$563$	11.9658	−	11.9658i	0.504296	−	0.504296i	−0.408474	−	0.912770i	$-0.633939\pi$
$563$	11.9658	−	11.9658i	0.504296	−	0.504296i	0.912770	+	0.408474i	$0.133939\pi$
$564$	−4.39356	−	6.56724i	−0.185002	−	0.276531i
$565$	−39.8526	+	21.7421i	−1.67661	+	0.914697i
$566$		−	6.82505i		−	0.286878i
$567$	10.2457	−	0.0235843i	0.430278	−	0.000990446i
$568$	−0.667940	−	0.667940i	−0.0280262	−	0.0280262i
$569$	27.2399			1.14195			0.570977	−	0.820966i	$-0.306564\pi$
$569$	27.2399			1.14195			0.570977	+	0.820966i	$0.306564\pi$
$570$	−1.15806	−	3.69579i	−0.0485059	−	0.154800i
$571$	6.63803			0.277793			0.138896	−	0.990307i	$-0.455644\pi$
$571$	6.63803			0.277793			0.138896	+	0.990307i	$0.455644\pi$
$572$	−8.61540	−	8.61540i	−0.360228	−	0.360228i
$573$	42.1194	+	8.35287i	1.75956	+	0.348946i
$574$		−	7.19361i		−	0.300256i
$575$	12.5885	−	2.72873i	0.524977	−	0.113796i
$576$	−1.14486	+	2.77296i	−0.0477025	+	0.115540i
$577$	24.2437	−	24.2437i	1.00928	−	1.00928i	0.00932364	−	0.999957i	$-0.497032\pi$
$577$	24.2437	−	24.2437i	1.00928	−	1.00928i	0.999957	−	0.00932364i	$-0.00296785\pi$
$578$	6.12313	−	6.12313i	0.254689	−	0.254689i
$579$	35.5518	−	23.7845i	1.47748	−	0.988452i
$580$	−3.46517	+	11.7852i	−0.143883	+	0.489353i
$581$		−	8.93371i		−	0.370633i
$582$	1.38062	−	6.96178i	0.0572285	−	0.288575i
$583$	10.0010	+	10.0010i	0.414197	+	0.414197i
$584$	−5.11793			−0.211781
$585$	−2.78855	−	25.7479i	−0.115292	−	1.06454i
$586$	16.0915			0.664732
$587$	30.9059	+	30.9059i	1.27562	+	1.27562i	0.943093	+	0.332528i	$0.107902\pi$
$587$	30.9059	+	30.9059i	1.27562	+	1.27562i	0.332528	+	0.943093i	$0.392098\pi$
$588$	−1.92185	+	9.69093i	−0.0792557	+	0.399647i
$589$			5.07413i			0.209076i
$590$	1.35589	+	2.48531i	0.0558213	+	0.102319i
$591$	−3.39240	+	2.26955i	−0.139545	+	0.0933570i
$592$	−7.25575	+	7.25575i	−0.298209	+	0.298209i
$593$	25.3962	−	25.3962i	1.04290	−	1.04290i	0.0438587	−	0.999038i	$-0.486035\pi$
$593$	25.3962	−	25.3962i	1.04290	−	1.04290i	0.999038	−	0.0438587i	$-0.0139652\pi$
$594$	3.22695	+	16.0779i	0.132404	+	0.659683i
$595$	7.05305	+	2.07379i	0.289147	+	0.0850171i
$596$		−	13.7188i		−	0.561945i
$597$	−46.5726	−	9.23601i	−1.90609	−	0.378005i
$598$	−7.03278	−	7.03278i	−0.287592	−	0.287592i
$599$	−24.9746			−1.02043			−0.510217	−	0.860046i	$-0.670435\pi$
$599$	−24.9746			−1.02043			−0.510217	+	0.860046i	$0.670435\pi$
$600$	0.153169	+	8.65890i	0.00625308	+	0.353498i
$601$	32.6339			1.33116			0.665582	−	0.746325i	$-0.268183\pi$
$601$	32.6339			1.33116			0.665582	+	0.746325i	$0.268183\pi$
$602$	0.732380	+	0.732380i	0.0298496	+	0.0298496i
$603$	−15.1572	+	6.29876i	−0.617248	+	0.256505i
$604$		−	14.9068i		−	0.606549i
$605$	−2.23175	−	0.656195i	−0.0907335	−	0.0266781i
$606$	16.2580	+	24.3016i	0.660437	+	0.987183i
$607$	−8.92349	+	8.92349i	−0.362193	+	0.362193i	−0.864620	−	0.502427i	$-0.832441\pi$
$607$	−8.92349	+	8.92349i	−0.362193	+	0.362193i	0.502427	+	0.864620i	$0.332441\pi$
$608$	0.707107	−	0.707107i	0.0286770	−	0.0286770i
$609$	6.02322	+	9.00317i	0.244073	+	0.364827i
$610$	−2.89540	−	5.30719i	−0.117231	−	0.214882i
$611$			17.6121i			0.712508i
$612$	−8.00069	+	3.32479i	−0.323409	+	0.134397i
$613$	−3.94769	−	3.94769i	−0.159446	−	0.159446i	0.622875	−	0.782321i	$-0.285964\pi$
$613$	−3.94769	−	3.94769i	−0.159446	−	0.159446i	−0.782321	+	0.622875i	$0.785964\pi$
$614$	4.56587			0.184264
$615$	21.6880	+	11.3391i	0.874546	+	0.457237i
$616$	3.59271			0.144754
$617$	−4.00994	−	4.00994i	−0.161434	−	0.161434i	0.621768	−	0.783202i	$-0.286415\pi$
$617$	−4.00994	−	4.00994i	−0.161434	−	0.161434i	−0.783202	+	0.621768i	$0.786415\pi$
$618$	3.53873	+	0.701779i	0.142348	+	0.0282297i
$619$		−	13.4636i		−	0.541147i	−0.962699	−	0.270573i	$-0.912787\pi$
$619$		−	13.4636i		−	0.541147i	0.962699	−	0.270573i	$-0.0872133\pi$
$620$	3.20058	−	10.8853i	0.128539	−	0.437165i
$621$	2.63417	+	13.1244i	0.105706	+	0.526665i
$622$	5.74950	−	5.74950i	0.230534	−	0.230534i
$623$	2.63501	−	2.63501i	0.105570	−	0.105570i
$624$	5.55786	−	3.71827i	0.222492	−	0.148850i
$625$	10.3518	+	22.7561i	0.414072	+	0.910244i
$626$			28.0858i			1.12253i
$627$	1.06331	−	5.36176i	0.0424646	−	0.214128i
$628$	2.63322	+	2.63322i	0.105077	+	0.105077i
$629$	−29.6344			−1.18160
$630$	5.94999	+	4.78714i	0.237053	+	0.190724i
$631$	24.4689			0.974092			0.487046	−	0.873376i	$-0.338074\pi$
$631$	24.4689			0.974092			0.487046	+	0.873376i	$0.338074\pi$
$632$	−10.6253	−	10.6253i	−0.422650	−	0.422650i
$633$	−1.24207	+	6.26312i	−0.0493677	+	0.248937i
$634$			11.1723i			0.443709i
$635$	4.37495	−	2.38681i	0.173615	−	0.0947177i
$636$	−6.45170	+	4.31626i	−0.255826	+	0.171151i
$637$	15.5716	−	15.5716i	0.616970	−	0.616970i
$638$	−12.2593	+	12.2593i	−0.485349	+	0.485349i
$639$	1.08145	−	2.61937i	0.0427814	−	0.103620i
$640$	−1.96295	+	1.07091i	−0.0775922	+	0.0423314i
$641$		−	14.3767i		−	0.567845i	−0.958847	−	0.283922i	$-0.908364\pi$
$641$		−	14.3767i		−	0.567845i	0.958847	−	0.283922i	$-0.0916358\pi$
$642$	21.2566	+	4.21549i	0.838931	+	0.166372i
$643$	2.63234	+	2.63234i	0.103809	+	0.103809i	0.757104	−	0.653294i	$-0.226614\pi$
$643$	2.63234	+	2.63234i	0.103809	+	0.103809i	−0.653294	+	0.757104i	$0.726614\pi$
$644$	2.93274			0.115566
$645$	−3.36248	+	1.05362i	−0.132398	+	0.0414863i
$646$	2.88801			0.113627
$647$	7.51216	+	7.51216i	0.295333	+	0.295333i	0.839183	−	0.543849i	$-0.183034\pi$
$647$	7.51216	+	7.51216i	0.295333	+	0.295333i	−0.543849	+	0.839183i	$0.683034\pi$
$648$	−8.99998	+	0.0207168i	−0.353552	+	0.000813834i
$649$			3.99573i			0.156846i
$650$	10.4483	−	16.2315i	0.409815	−	0.636651i
$651$	−5.56332	−	8.31574i	−0.218044	−	0.325919i
$652$	8.49310	−	8.49310i	0.332616	−	0.332616i
$653$	7.41773	−	7.41773i	0.290278	−	0.290278i	−0.546912	−	0.837190i	$-0.684197\pi$
$653$	7.41773	−	7.41773i	0.290278	−	0.290278i	0.837190	+	0.546912i	$0.184197\pi$
$654$	−6.58687	−	9.84568i	−0.257567	−	0.384996i
$655$	−11.9867	+	40.7674i	−0.468360	+	1.59291i
$656$			6.31900i			0.246715i
$657$	−5.89196	−	14.1783i	−0.229867	−	0.553147i
$658$	−3.67220	−	3.67220i	−0.143157	−	0.143157i
$659$	−31.2034			−1.21551			−0.607755	−	0.794124i	$-0.707930\pi$
$659$	−31.2034			−1.21551			−0.607755	+	0.794124i	$0.707930\pi$
$660$	−5.66309	+	10.8317i	−0.220435	+	0.421622i
$661$	−27.3601			−1.06418			−0.532092	−	0.846687i	$-0.678594\pi$
$661$	−27.3601			−1.06418			−0.532092	+	0.846687i	$0.678594\pi$
$662$	20.6663	+	20.6663i	0.803217	+	0.803217i
$663$	18.9431	+	3.75668i	0.735687	+	0.145897i
$664$			7.84753i			0.304543i
$665$	−1.21913	−	2.23464i	−0.0472760	−	0.0866555i
$666$	−28.4538	−	11.7476i	−1.10256	−	0.455210i
$667$	−10.0073	+	10.0073i	−0.387483	+	0.387483i
$668$	2.26247	−	2.26247i	0.0875377	−	0.0875377i
$669$	−38.6069	+	25.8285i	−1.49263	+	0.998586i
$670$	−11.7373	−	3.45109i	−0.453452	−	0.133327i
$671$		−	8.53256i		−	0.329396i
$672$	−0.383563	+	1.93412i	−0.0147963	+	0.0746103i
$673$	−20.4515	−	20.4515i	−0.788346	−	0.788346i	0.192877	−	0.981223i	$-0.438218\pi$
$673$	−20.4515	−	20.4515i	−0.788346	−	0.788346i	−0.981223	+	0.192877i	$0.938218\pi$
$674$	−15.5505			−0.598982
$675$	−23.8115	+	10.3928i	−0.916507	+	0.400019i
$676$	−1.90511			−0.0732734
$677$	−26.1264	−	26.1264i	−1.00412	−	1.00412i	−0.999991	−	0.00412796i	$-0.998686\pi$
$677$	−26.1264	−	26.1264i	−1.00412	−	1.00412i	−0.00412796	−	0.999991i	$-0.501314\pi$
$678$	6.84049	−	34.4932i	0.262707	−	1.32470i
$679$		−	4.66482i		−	0.179019i
$680$	−6.19552	−	1.82165i	−0.237587	−	0.0698572i
$681$	4.18744	−	2.80144i	0.160463	−	0.107352i
$682$	11.3232	−	11.3232i	0.433588	−	0.433588i
$683$	−17.6171	+	17.6171i	−0.674101	+	0.674101i	−0.958659	−	0.284558i	$-0.908153\pi$
$683$	−17.6171	+	17.6171i	−0.674101	+	0.674101i	0.284558	+	0.958659i	$0.408153\pi$
$684$	2.77296	+	1.14486i	0.106027	+	0.0437748i
$685$	−23.0565	−	42.2619i	−0.880943	−	1.61474i
$686$			14.4624i			0.552177i
$687$	−26.9684	−	5.34821i	−1.02891	−	0.204047i
$688$	−0.643335	−	0.643335i	−0.0245269	−	0.0245269i
$689$	17.3022			0.659162
$690$	−4.62280	+	8.84192i	−0.175987	+	0.336606i
$691$	31.9422			1.21514			0.607569	−	0.794267i	$-0.292145\pi$
$691$	31.9422			1.21514			0.607569	+	0.794267i	$0.292145\pi$
$692$	6.00022	+	6.00022i	0.228094	+	0.228094i
$693$	4.13607	+	9.95293i	0.157116	+	0.378081i
$694$		−	27.6337i		−	1.04896i
$695$	−9.49363	+	32.2882i	−0.360114	+	1.22476i
$696$	−5.29091	−	7.90854i	−0.200551	−	0.299773i
$697$	−12.9042	+	12.9042i	−0.488782	+	0.488782i
$698$	−24.0138	+	24.0138i	−0.908937	+	0.908937i
$699$	−21.2493	−	31.7622i	−0.803722	−	1.20136i
$700$	1.20583	+	5.56286i	0.0455760	+	0.210257i
$701$		−	25.7033i		−	0.970801i	−0.874292	−	0.485401i	$-0.838674\pi$
$701$		−	25.7033i		−	0.970801i	0.874292	−	0.485401i	$-0.161326\pi$
$702$	16.6992	+	11.1164i	0.630271	+	0.419562i
$703$	7.25575	+	7.25575i	0.273656	+	0.273656i
$704$	−3.15590			−0.118942
$705$	16.8597	−	5.28293i	0.634974	−	0.198967i
$706$	24.6940			0.929372
$707$	13.5887	+	13.5887i	0.511056	+	0.511056i
$708$	−2.15108	−	0.426591i	−0.0808427	−	0.0160323i
$709$		−	33.4122i		−	1.25482i	−0.778689	−	0.627410i	$-0.784115\pi$
$709$		−	33.4122i		−	1.25482i	0.778689	−	0.627410i	$-0.215885\pi$
$710$	1.85422	−	1.01159i	0.0695876	−	0.0379644i
$711$	17.2031	−	41.6675i	0.645166	−	1.56265i
$712$	−2.31464	+	2.31464i	−0.0867448	+	0.0867448i
$713$	9.24318	−	9.24318i	0.346160	−	0.346160i
$714$	−4.73301	+	3.16644i	−0.177128	+	0.118501i
$715$	23.9165	−	13.0480i	0.894428	−	0.487966i
$716$		−	10.5263i		−	0.393388i
$717$	−1.63356	+	8.23724i	−0.0610065	+	0.307625i
$718$	17.7860	+	17.7860i	0.663766	+	0.663766i
$719$	−0.187398			−0.00698877			−0.00349439	−	0.999994i	$-0.501112\pi$
$719$	−0.187398			−0.00698877			−0.00349439	+	0.999994i	$0.501112\pi$
$720$	−5.22658	−	4.20510i	−0.194783	−	0.156715i
$721$	2.37116			0.0883068
$722$	−0.707107	−	0.707107i	−0.0263158	−	0.0263158i
$723$	−5.74532	+	28.9708i	−0.213671	+	1.07744i
$724$		−	20.9226i		−	0.777582i
$725$	−23.0966	−	14.8674i	−0.857785	−	0.552160i
$726$	1.49763	−	1.00193i	0.0555824	−	0.0371852i
$727$	0.711792	−	0.711792i	0.0263989	−	0.0263989i	−0.693784	−	0.720183i	$-0.744058\pi$
$727$	0.711792	−	0.711792i	0.0263989	−	0.0263989i	0.720183	+	0.693784i	$0.244058\pi$
$728$	3.10779	−	3.10779i	0.115182	−	0.115182i
$729$	−10.4185	−	24.9089i	−0.385871	−	0.922553i
$730$	3.22821	−	10.9793i	0.119481	−	0.406361i
$731$		−	2.62755i		−	0.0971834i
$732$	4.59347	+	0.910950i	0.169779	+	0.0336697i
$733$	−12.3766	−	12.3766i	−0.457142	−	0.457142i	0.440574	−	0.897716i	$-0.354775\pi$
$733$	−12.3766	−	12.3766i	−0.457142	−	0.457142i	−0.897716	+	0.440574i	$0.854775\pi$
$734$	−5.46183			−0.201600
$735$	−19.5773	−	10.2356i	−0.722120	−	0.377544i
$736$	−2.57617			−0.0949589
$737$	−12.2095	−	12.2095i	−0.449742	−	0.449742i
$738$	−17.5056	+	7.27468i	−0.644391	+	0.267785i
$739$			0.0763442i			0.00280837i	0.999999	+	0.00140418i	$0.000446966\pi$
$739$			0.0763442i			0.00280837i	−0.999999	+	0.00140418i	$0.999553\pi$
$740$	−10.9888	−	20.1421i	−0.403956	−	0.740439i
$741$	−3.71827	−	5.55786i	−0.136594	−	0.204173i
$742$	−3.60760	+	3.60760i	−0.132439	+	0.132439i
$743$	−33.1046	+	33.1046i	−1.21449	+	1.21449i	−0.244956	+	0.969534i	$0.578773\pi$
$743$	−33.1046	+	33.1046i	−1.21449	+	1.21449i	−0.969534	+	0.244956i	$0.921227\pi$
$744$	4.88692	+	7.30469i	0.179163	+	0.267803i
$745$	29.4304	+	8.65336i	1.07825	+	0.317034i
$746$		−	9.01595i		−	0.330098i
$747$	−21.7401	+	9.03439i	−0.795430	+	0.330551i
$748$	−6.44475	−	6.44475i	−0.235643	−	0.235643i
$749$	14.2432			0.520436
$750$	−18.6722	−	5.13314i	−0.681812	−	0.187436i
$751$	33.2419			1.21301			0.606506	−	0.795079i	$-0.292570\pi$
$751$	33.2419			1.21301			0.606506	+	0.795079i	$0.292570\pi$
$752$	3.22573	+	3.22573i	0.117630	+	0.117630i
$753$	13.4876	+	2.67478i	0.491515	+	0.0974743i
$754$			21.2092i			0.772393i
$755$	31.9789	+	9.40269i	1.16383	+	0.342199i
$756$	−5.79969	+	1.16404i	−0.210933	+	0.0423358i
$757$	18.1270	−	18.1270i	0.658838	−	0.658838i	−0.296267	−	0.955105i	$-0.595742\pi$
$757$	18.1270	−	18.1270i	0.658838	−	0.658838i	0.955105	+	0.296267i	$0.0957420\pi$
$758$	9.95217	−	9.95217i	0.361479	−	0.361479i
$759$	−11.7041	+	7.83016i	−0.424831	+	0.284217i
$760$	1.07091	+	1.96295i	0.0388460	+	0.0712035i
$761$			16.7931i			0.608751i	0.952552	+	0.304375i	$0.0984477\pi$
$761$			16.7931i			0.608751i	−0.952552	+	0.304375i	$0.901552\pi$
$762$	−0.750937	+	3.78660i	−0.0272036	+	0.137174i
$763$	−5.50541	−	5.50541i	−0.199309	−	0.199309i
$764$	−24.7912			−0.896915
$765$	−2.08598	−	19.2607i	−0.0754186	−	0.696373i
$766$	−8.00952			−0.289396
$767$	3.45641	+	3.45641i	0.124804	+	0.124804i
$768$	0.336929	−	1.69896i	0.0121579	−	0.0613061i
$769$		−	0.877088i		−	0.0316286i	−0.999875	−	0.0158143i	$-0.994966\pi$
$769$		−	0.877088i		−	0.0316286i	0.999875	−	0.0158143i	$-0.00503406\pi$
$770$	−2.26615	+	7.70729i	−0.0816665	+	0.277751i
$771$	−34.5880	+	23.1398i	−1.24566	+	0.833359i
$772$	−17.4625	+	17.4625i	−0.628489	+	0.628489i
$773$	−19.6669	+	19.6669i	−0.707370	+	0.707370i	−0.965981	−	0.258611i	$-0.916735\pi$
$773$	−19.6669	+	19.6669i	−0.707370	+	0.707370i	0.258611	+	0.965981i	$0.416735\pi$
$774$	1.04161	−	2.52288i	0.0374399	−	0.0906829i
$775$	21.3330	+	13.7322i	0.766305	+	0.493274i
$776$			4.09766i			0.147097i
$777$	−19.8463	−	3.93581i	−0.711983	−	0.141196i
$778$	−1.25223	−	1.25223i	−0.0448945	−	0.0448945i
$779$	6.31900			0.226402
$780$	4.47095	+	14.2684i	0.160086	+	0.510891i
$781$	2.98109			0.106672
$782$	−5.26087	−	5.26087i	−0.188128	−	0.188128i
$783$	15.8181	−	23.7621i	0.565291	−	0.849188i
$784$		−	5.70402i		−	0.203715i
$785$	−7.30987	+	3.98799i	−0.260900	+	0.142337i
$786$	−18.3023	−	27.3573i	−0.652823	−	0.975803i
$787$	−34.5105	+	34.5105i	−1.23017	+	1.23017i	−0.266268	+	0.963899i	$0.585791\pi$
$787$	−34.5105	+	34.5105i	−1.23017	+	1.23017i	−0.963899	+	0.266268i	$0.914209\pi$
$788$	1.66630	−	1.66630i	0.0593593	−	0.0593593i
$789$	3.13607	+	4.68762i	0.111647	+	0.166884i
$790$	29.4960	−	16.0919i	1.04942	−	0.572524i
$791$		−	23.1126i		−	0.821788i
$792$	−3.63319	−	8.74283i	−0.129100	−	0.310663i
$793$	−7.38090	−	7.38090i	−0.262103	−	0.262103i
$794$	−19.1144			−0.678345
$795$	−5.18999	−	16.5631i	−0.184070	−	0.587433i
$796$	27.4124			0.971606
$797$	−3.11137	−	3.11137i	−0.110210	−	0.110210i	0.649851	−	0.760061i	$-0.274831\pi$
$797$	−3.11137	−	3.11137i	−0.110210	−	0.110210i	−0.760061	+	0.649851i	$0.774831\pi$
$798$	1.93412	+	0.383563i	0.0684671	+	0.0135780i
$799$			13.1747i			0.466088i
$800$	−1.05922	−	4.88652i	−0.0374491	−	0.172764i
$801$	−9.07699	−	3.74758i	−0.320720	−	0.132414i
$802$	−23.4013	+	23.4013i	−0.826329	+	0.826329i
$803$	11.4209	−	11.4209i	0.403036	−	0.403036i
$804$	7.87642	−	5.26942i	0.277780	−	0.185838i
$805$	−1.84987	+	6.29148i	−0.0651993	+	0.221746i
$806$		−	19.5898i		−	0.690020i
$807$	5.37993	−	27.1283i	0.189382	−	0.954962i
$808$	−11.9366	−	11.9366i	−0.419927	−	0.419927i
$809$	−19.2043			−0.675189			−0.337594	−	0.941292i	$-0.609613\pi$
$809$	−19.2043			−0.675189			−0.337594	+	0.941292i	$0.609613\pi$
$810$	5.63243	−	19.3203i	0.197903	−	0.678848i
$811$	33.3734			1.17190			0.585949	−	0.810348i	$-0.300722\pi$
$811$	33.3734			1.17190			0.585949	+	0.810348i	$0.300722\pi$
$812$	−4.42222	−	4.42222i	−0.155190	−	0.155190i
$813$	−1.99225	+	10.0459i	−0.0698713	+	0.352326i
$814$		−	32.3832i		−	1.13503i
$815$	12.8628	+	23.5771i	0.450563	+	0.825868i
$816$	4.15756	−	2.78145i	0.145544	−	0.0973703i
$817$	−0.643335	+	0.643335i	−0.0225075	+	0.0225075i
$818$	8.89622	−	8.89622i	0.311049	−	0.311049i
$819$	12.1874	+	5.03175i	0.425861	+	0.175823i
$820$	−13.5559	−	3.98580i	−0.473392	−	0.139190i
$821$			5.97506i			0.208531i	0.994549	+	0.104266i	$0.0332492\pi$
$821$			5.97506i			0.208531i	−0.994549	+	0.104266i	$0.966751\pi$
$822$	36.5784	+	7.25401i	1.27582	+	0.253013i
$823$	19.3849	+	19.3849i	0.675714	+	0.675714i	0.959027	−	0.283314i	$-0.0914338\pi$
$823$	19.3849	+	19.3849i	0.675714	+	0.675714i	−0.283314	+	0.959027i	$0.591434\pi$
$824$	−2.08287			−0.0725603
$825$	−19.6646	−	18.9810i	−0.684634	−	0.660834i
$826$	−1.44136			−0.0501513
$827$	3.64780	+	3.64780i	0.126846	+	0.126846i	0.767680	−	0.640833i	$-0.221411\pi$
$827$	3.64780	+	3.64780i	0.126846	+	0.126846i	−0.640833	+	0.767680i	$0.721411\pi$
$828$	−2.96579	−	7.13680i	−0.103068	−	0.248021i
$829$			38.1534i			1.32512i	0.749008	+	0.662561i	$0.230530\pi$
$829$			38.1534i			1.32512i	−0.749008	+	0.662561i	$0.769470\pi$
$830$	−16.8350	−	4.94995i	−0.584351	−	0.171815i
$831$	−24.0253	−	35.9116i	−0.833428	−	1.24576i
$832$	−2.72994	+	2.72994i	−0.0946435	+	0.0946435i
$833$	11.6483	−	11.6483i	0.403591	−	0.403591i
$834$	−14.4957	−	21.6673i	−0.501944	−	0.750277i
$835$	3.42650	+	6.28068i	0.118579	+	0.217352i
$836$			3.15590i			0.109149i
$837$	−14.6103	+	21.9478i	−0.505005	+	0.758625i
$838$	23.6948	+	23.6948i	0.818525	+	0.818525i
$839$	−13.6311			−0.470597			−0.235299	−	0.971923i	$-0.575607\pi$
$839$	−13.6311			−0.470597			−0.235299	+	0.971923i	$0.575607\pi$
$840$	−3.90725	−	2.04282i	−0.134813	−	0.0704839i
$841$	1.17958			0.0406753
$842$	−21.0539	−	21.0539i	−0.725564	−	0.725564i
$843$	20.0348	+	3.97318i	0.690033	+	0.136843i
$844$		−	3.68643i		−	0.126892i
$845$	1.20168	−	4.08695i	0.0413389	−	0.140595i
$846$	−5.22270	+	12.6499i	−0.179560	+	0.434912i
$847$	0.837432	−	0.837432i	0.0287745	−	0.0287745i
$848$	3.16898	−	3.16898i	0.108823	−	0.108823i
$849$	−9.82530	+	6.57324i	−0.337203	+	0.225593i
$850$	7.81584	−	12.1420i	0.268081	−	0.416466i
$851$		−	26.4345i		−	0.906164i
$852$	−0.318266	+	1.60486i	−0.0109036	+	0.0549816i
$853$	26.9654	+	26.9654i	0.923279	+	0.923279i	0.997260	−	0.0739807i	$-0.0235703\pi$
$853$	26.9654	+	26.9654i	0.923279	+	0.923279i	−0.0739807	+	0.997260i	$0.523570\pi$
$854$	3.07791			0.105324
$855$	−4.20510	+	5.22658i	−0.143812	+	0.178745i
$856$	−12.5115			−0.427634
$857$	−16.1672	−	16.1672i	−0.552261	−	0.552261i	0.374832	−	0.927093i	$-0.377700\pi$
$857$	−16.1672	−	16.1672i	−0.552261	−	0.552261i	−0.927093	+	0.374832i	$0.877700\pi$
$858$	−4.10514	+	20.7002i	−0.140147	+	0.706693i
$859$		−	48.3103i		−	1.64833i	−0.566352	−	0.824164i	$-0.691646\pi$
$859$		−	48.3103i		−	1.64833i	0.566352	−	0.824164i	$-0.308354\pi$
$860$	1.78591	−	0.974328i	0.0608992	−	0.0332243i
$861$	−10.3559	+	6.92820i	−0.352928	+	0.236113i
$862$	−11.8579	+	11.8579i	−0.403882	+	0.403882i
$863$	5.84818	−	5.84818i	0.199074	−	0.199074i	−0.600529	−	0.799603i	$-0.705043\pi$
$863$	5.84818	−	5.84818i	0.199074	−	0.199074i	0.799603	+	0.600529i	$0.205043\pi$
$864$	5.09455	−	1.02252i	0.173320	−	0.0347867i
$865$	−16.6568	+	9.08730i	−0.566347	+	0.308978i
$866$		−	1.19002i		−	0.0404387i
$867$	−14.7120	−	2.91761i	−0.499647	−	0.0990871i
$868$	4.08457	+	4.08457i	0.138639	+	0.138639i
$869$	47.4217			1.60867
$870$	20.3032	−	6.36193i	0.688343	−	0.215690i
$871$	−21.1231			−0.715727
$872$	4.83605	+	4.83605i	0.163769	+	0.163769i
$873$	−11.3518	+	4.71739i	−0.384201	+	0.159659i
$874$			2.57617i			0.0871402i
$875$	−12.6944	−	0.922048i	−0.429148	−	0.0311709i
$876$	4.92910	+	7.36773i	0.166539	+	0.248933i
$877$	25.8898	−	25.8898i	0.874236	−	0.874236i	−0.118695	−	0.992931i	$-0.537871\pi$
$877$	25.8898	−	25.8898i	0.874236	−	0.874236i	0.992931	+	0.118695i	$0.0378711\pi$
$878$	−22.9153	+	22.9153i	−0.773355	+	0.773355i
$879$	−15.4978	−	23.1652i	−0.522726	−	0.781341i
$880$	1.99063	−	6.77022i	0.0671041	−	0.228224i
$881$			6.15899i			0.207502i	0.994603	+	0.103751i	$0.0330845\pi$
$881$			6.15899i			0.207502i	−0.994603	+	0.103751i	$0.966916\pi$
$882$	15.8019	−	6.56669i	0.532079	−	0.221112i
$883$	−5.40089	−	5.40089i	−0.181755	−	0.181755i	0.610365	−	0.792120i	$-0.291023\pi$
$883$	−5.40089	−	5.40089i	−0.181755	−	0.181755i	−0.792120	+	0.610365i	$0.791023\pi$
$884$	−11.1498			−0.375007
$885$	2.27198	−	4.34555i	0.0763716	−	0.146074i
$886$	−21.7741			−0.731515
$887$	−9.89729	−	9.89729i	−0.332319	−	0.332319i	0.521148	−	0.853466i	$-0.325504\pi$
$887$	−9.89729	−	9.89729i	−0.332319	−	0.332319i	−0.853466	+	0.521148i	$0.825504\pi$
$888$	17.4334	+	3.45728i	0.585026	+	0.116019i
$889$			2.53726i			0.0850968i
$890$	−3.50551	−	6.42550i	−0.117505	−	0.215383i
$891$	20.0377	−	20.1302i	0.671289	−	0.674386i
$892$	18.9631	−	18.9631i	0.634933	−	0.634933i
$893$	3.22573	−	3.22573i	0.107945	−	0.107945i
$894$	−19.7495	+	13.2127i	−0.660523	+	0.441898i
$895$	22.5817	+	6.63965i	0.754824	+	0.221939i
$896$		−	1.13841i		−	0.0380316i
$897$	−3.35104	+	16.8976i	−0.111888	+	0.564196i
$898$	2.61273	+	2.61273i	0.0871879	+	0.0871879i
$899$	−27.8752			−0.929691
$900$	12.3178	−	8.55993i	0.410593	−	0.285331i
$901$	12.9429			0.431191
$902$	−14.1012	−	14.1012i	−0.469518	−	0.469518i
$903$	0.348971	−	1.75969i	0.0116130	−	0.0585588i
$904$			20.3025i			0.675250i
$905$	44.8844	+	13.1972i	1.49201	+	0.438691i
$906$	−21.4597	+	14.3568i	−0.712952	+	0.476973i
$907$	23.0626	−	23.0626i	0.765781	−	0.765781i	−0.211580	−	0.977361i	$-0.567861\pi$
$907$	23.0626	−	23.0626i	0.765781	−	0.765781i	0.977361	+	0.211580i	$0.0678609\pi$
$908$	−2.05681	+	2.05681i	−0.0682576	+	0.0682576i
$909$	19.3262	−	46.8099i	0.641009	−	1.55259i
$910$	4.70673	+	8.62730i	0.156027	+	0.285992i
$911$			15.0916i			0.500006i	0.968245	+	0.250003i	$0.0804316\pi$
$911$			15.0916i			0.500006i	−0.968245	+	0.250003i	$0.919568\pi$
$912$	−1.69896	−	0.336929i	−0.0562583	−	0.0111568i
$913$	−17.5122	−	17.5122i	−0.579569	−	0.579569i
$914$	8.81552			0.291591
$915$	−4.85162	+	9.27958i	−0.160390	+	0.306774i
$916$	15.8734			0.524473
$917$	−15.2974	−	15.2974i	−0.505164	−	0.505164i
$918$	12.4918	+	8.31563i	0.412292	+	0.274457i
$919$			8.47668i			0.279620i	0.990178	+	0.139810i	$0.0446492\pi$
$919$			8.47668i			0.279620i	−0.990178	+	0.139810i	$0.955351\pi$
$920$	1.62496	−	5.52655i	0.0535733	−	0.182205i
$921$	−4.39741	−	6.57300i	−0.144900	−	0.216588i
$922$	2.13407	−	2.13407i	0.0702817	−	0.0702817i
$923$	2.57873	−	2.57873i	0.0848798	−	0.0848798i
$924$	−3.46015	−	5.17204i	−0.113831	−	0.170148i
$925$	50.1414	−	10.8688i	1.64864	−	0.357365i
$926$			24.2113i			0.795634i
$927$	−2.39788	−	5.77021i	−0.0787569	−	0.189519i
$928$	3.88456	+	3.88456i	0.127517	+	0.127517i
$929$	6.96249			0.228432			0.114216	−	0.993456i	$-0.463564\pi$
$929$	6.96249			0.228432			0.114216	+	0.993456i	$0.463564\pi$
$930$	−18.7529	+	5.87617i	−0.614933	+	0.192687i
$931$	−5.70402			−0.186942
$932$	15.6011	+	15.6011i	0.511032	+	0.511032i
$933$	−13.8143	−	2.73957i	−0.452260	−	0.0896896i
$934$			4.84547i			0.158549i
$935$	17.8908	−	9.76053i	0.585091	−	0.319204i
$936$	−10.7056	−	4.41997i	−0.349923	−	0.144471i
$937$	2.15425	−	2.15425i	0.0703762	−	0.0703762i	−0.671043	−	0.741419i	$-0.734153\pi$
$937$	2.15425	−	2.15425i	0.0703762	−	0.0703762i	0.741419	+	0.671043i	$0.234153\pi$
$938$	4.40426	−	4.40426i	0.143804	−	0.143804i
$939$	40.4321	−	27.0495i	1.31945	−	0.882728i
$940$	−8.95470	+	4.88535i	−0.292070	+	0.159342i
$941$		−	19.9072i		−	0.648957i	−0.945893	−	0.324479i	$-0.894811\pi$
$941$		−	19.9072i		−	0.648957i	0.945893	−	0.324479i	$-0.105189\pi$
$942$	1.25470	−	6.32682i	0.0408803	−	0.206139i
$943$	−11.5109	−	11.5109i	−0.374845	−	0.374845i
$944$	1.26612			0.0412085
$945$	1.16107	−	13.1761i	0.0377696	−	0.428618i
$946$	2.87128			0.0933533
$947$	27.8351	+	27.8351i	0.904520	+	0.904520i	0.995823	−	0.0913033i	$-0.0291033\pi$
$947$	27.8351	+	27.8351i	0.904520	+	0.904520i	−0.0913033	+	0.995823i	$0.529103\pi$
$948$	−5.06282	+	25.5293i	−0.164433	+	0.829152i
$949$		−	19.7588i		−	0.641399i
$950$	−4.88652	+	1.05922i	−0.158540	+	0.0343656i
$951$	16.0836	−	10.7601i	0.521546	−	0.348920i
$952$	2.32478	−	2.32478i	0.0753466	−	0.0753466i
$953$	10.6937	−	10.6937i	0.346402	−	0.346402i	−0.512365	−	0.858768i	$-0.671231\pi$
$953$	10.6937	−	10.6937i	0.346402	−	0.346402i	0.858768	+	0.512365i	$0.171231\pi$
$954$	12.4273	+	5.13081i	0.402349	+	0.166116i
$955$	15.6374	−	53.1836i	0.506015	−	1.72098i
$956$		−	4.84839i		−	0.156808i
$957$	29.4553	+	5.84141i	0.952155	+	0.188826i
$958$	−12.7420	−	12.7420i	−0.411674	−	0.411674i
$959$	24.5098			0.791462
$960$	3.43220	+	1.79445i	0.110774	+	0.0579155i
$961$	−5.25318			−0.169457
$962$	−28.0124	−	28.0124i	−0.903155	−	0.903155i
$963$	−14.4037	−	34.6608i	−0.464154	−	1.11693i
$964$		−	17.0520i		−	0.549209i
$965$	−26.4468	−	48.4763i	−0.851354	−	1.56051i
$966$	−2.82453	−	4.22195i	−0.0908779	−	0.135839i
$967$	−13.5193	+	13.5193i	−0.434750	+	0.434750i	−0.890241	−	0.455491i	$-0.849464\pi$
$967$	−13.5193	+	13.5193i	−0.434750	+	0.434750i	0.455491	+	0.890241i	$0.349464\pi$
$968$	−0.735615	+	0.735615i	−0.0236436	+	0.0236436i
$969$	−2.78145	−	4.15756i	−0.0893531	−	0.133560i
$970$	−8.79054	−	2.58466i	−0.282247	−	0.0829885i
$971$			10.6230i			0.340909i	0.985366	+	0.170455i	$0.0545236\pi$
$971$			10.6230i			0.340909i	−0.985366	+	0.170455i	$0.945476\pi$
$972$	8.69774	+	12.9364i	0.278980	+	0.414934i
$973$	−12.1157	−	12.1157i	−0.388412	−	0.388412i
$974$	−4.70920			−0.150893
$975$	−33.4295	+	0.591340i	−1.07060	+	0.0189380i
$976$	−2.70369			−0.0865429
$977$	−4.47372	−	4.47372i	−0.143127	−	0.143127i	0.631913	−	0.775040i	$-0.282270\pi$
$977$	−4.47372	−	4.47372i	−0.143127	−	0.143127i	−0.775040	+	0.631913i	$0.782270\pi$
$978$	−20.4064	−	4.04687i	−0.652524	−	0.129405i
$979$		−	10.3305i		−	0.330164i
$980$	12.2366	+	3.59790i	0.390884	+	0.114931i
$981$	−7.82993	+	18.9648i	−0.249990	+	0.605500i
$982$	−28.8305	+	28.8305i	−0.920020	+	0.920020i
$983$	−31.6740	+	31.6740i	−1.01024	+	1.01024i	−0.0102974	+	0.999947i	$0.503278\pi$
$983$	−31.6740	+	31.6740i	−1.01024	+	1.01024i	−0.999947	+	0.0102974i	$0.996722\pi$
$984$	9.09679	−	6.08585i	0.289995	−	0.194010i
$985$	2.52359	+	4.62568i	0.0804084	+	0.147386i
$986$			15.8655i			0.505262i
$987$	−1.74977	+	8.82320i	−0.0556957	+	0.280846i
$988$	2.72994	+	2.72994i	0.0868509	+	0.0868509i
$989$	2.34383			0.0745296
$990$	21.0473	−	2.27947i	0.668928	−	0.0724463i
$991$	12.3131			0.391138			0.195569	−	0.980690i	$-0.437345\pi$
$991$	12.3131			0.391138			0.195569	+	0.980690i	$0.437345\pi$
$992$	−3.58795	−	3.58795i	−0.113918	−	0.113918i
$993$	9.84724	−	49.6548i	0.312493	−	1.57575i
$994$			1.07535i			0.0341082i
$995$	−17.2908	+	58.8066i	−0.548154	+	1.86430i
$996$	11.2973	−	7.55799i	0.357967	−	0.239484i
$997$	−31.6019	+	31.6019i	−1.00084	+	1.00084i	−0.000842399		1.00000i	$0.500268\pi$
$997$	−31.6019	+	31.6019i	−1.00084	+	1.00084i	−1.00000		0.000842399i	$0.999732\pi$
$998$	−20.1312	+	20.1312i	−0.637243	+	0.637243i
$999$	10.4922	+	52.2761i	0.331959	+	1.65394i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.k.b.533.14	yes	36
3.2	odd	2	inner	570.2.k.b.533.1	yes	36
5.2	odd	4	inner	570.2.k.b.77.1	✓	36
15.2	even	4	inner	570.2.k.b.77.14	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.k.b.77.1	✓	36	5.2	odd	4	inner
570.2.k.b.77.14	yes	36	15.2	even	4	inner
570.2.k.b.533.1	yes	36	3.2	odd	2	inner
570.2.k.b.533.14	yes	36	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.336929 - 1.69896i) q^{3} +1.00000i q^{4} +(-2.14526 - 0.630765i) q^{5} +(1.43959 - 0.963104i) q^{6} +(0.804978 - 0.804978i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.77296 - 1.14486i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.336929 - 1.69896i) q^{3} +1.00000i q^{4} +(-2.14526 - 0.630765i) q^{5} +(1.43959 - 0.963104i) q^{6} +(0.804978 - 0.804978i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.77296 - 1.14486i) q^{9} +(-1.07091 - 1.96295i) q^{10} -3.15590i q^{11} +(1.69896 + 0.336929i) q^{12} +(-2.72994 - 2.72994i) q^{13} +1.13841 q^{14} +(-1.79445 + 3.43220i) q^{15} -1.00000 q^{16} +(-2.04213 - 2.04213i) q^{17} +(-1.15124 - 2.77032i) q^{18} +1.00000i q^{19} +(0.630765 - 2.14526i) q^{20} +(-1.09641 - 1.63885i) q^{21} +(2.23156 - 2.23156i) q^{22} +(1.82163 - 1.82163i) q^{23} +(0.963104 + 1.43959i) q^{24} +(4.20427 + 2.70631i) q^{25} -3.86071i q^{26} +(-2.87936 + 4.32542i) q^{27} +(0.804978 + 0.804978i) q^{28} -5.49359 q^{29} +(-3.69579 + 1.15806i) q^{30} +5.07413 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-5.36176 - 1.06331i) q^{33} -2.88801i q^{34} +(-2.23464 + 1.21913i) q^{35} +(1.14486 - 2.77296i) q^{36} +(7.25575 - 7.25575i) q^{37} +(-0.707107 + 0.707107i) q^{38} +(-5.55786 + 3.71827i) q^{39} +(1.96295 - 1.07091i) q^{40} -6.31900i q^{41} +(0.383563 - 1.93412i) q^{42} +(0.643335 + 0.643335i) q^{43} +3.15590 q^{44} +(5.22658 + 4.20510i) q^{45} +2.57617 q^{46} +(-3.22573 - 3.22573i) q^{47} +(-0.336929 + 1.69896i) q^{48} +5.70402i q^{49} +(1.05922 + 4.88652i) q^{50} +(-4.15756 + 2.78145i) q^{51} +(2.72994 - 2.72994i) q^{52} +(-3.16898 + 3.16898i) q^{53} +(-5.09455 + 1.02252i) q^{54} +(-1.99063 + 6.77022i) q^{55} +1.13841i q^{56} +(1.69896 + 0.336929i) q^{57} +(-3.88456 - 3.88456i) q^{58} -1.26612 q^{59} +(-3.43220 - 1.79445i) q^{60} +2.70369 q^{61} +(3.58795 + 3.58795i) q^{62} +(-3.15376 + 1.31058i) q^{63} -1.00000i q^{64} +(4.13447 + 7.57837i) q^{65} +(-3.03946 - 4.54321i) q^{66} +(3.86878 - 3.86878i) q^{67} +(2.04213 - 2.04213i) q^{68} +(-2.48112 - 3.70864i) q^{69} +(-2.44219 - 0.718070i) q^{70} +0.944610i q^{71} +(2.77032 - 1.15124i) q^{72} +(3.61892 + 3.61892i) q^{73} +10.2612 q^{74} +(6.01446 - 6.23107i) q^{75} -1.00000 q^{76} +(-2.54043 - 2.54043i) q^{77} +(-6.55921 - 1.30079i) q^{78} +15.0264i q^{79} +(2.14526 + 0.630765i) q^{80} +(6.37859 + 6.34930i) q^{81} +(4.46821 - 4.46821i) q^{82} +(5.54904 - 5.54904i) q^{83} +(1.63885 - 1.09641i) q^{84} +(3.09279 + 5.66900i) q^{85} +0.909814i q^{86} +(-1.85095 + 9.33342i) q^{87} +(2.23156 + 2.23156i) q^{88} +3.27340 q^{89} +(0.722289 + 6.66921i) q^{90} -4.39508 q^{91} +(1.82163 + 1.82163i) q^{92} +(1.70962 - 8.62077i) q^{93} -4.56187i q^{94} +(0.630765 - 2.14526i) q^{95} +(-1.43959 + 0.963104i) q^{96} +(2.89748 - 2.89748i) q^{97} +(-4.03335 + 4.03335i) q^{98} +(-3.61306 + 8.75117i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{3} + 4 q^{6} + 20 q^{7}+O(q^{10}) \) 36 * q + 4 * q^3 + 4 * q^6 + 20 * q^7	\( 36 q + 4 q^{3} + 4 q^{6} + 20 q^{7} - 4 q^{10} - 4 q^{12} + 8 q^{13} + 4 q^{15} - 36 q^{16} + 16 q^{21} - 4 q^{22} + 16 q^{25} - 44 q^{27} + 20 q^{28} + 32 q^{30} - 24 q^{31} - 4 q^{33} + 4 q^{36} - 8 q^{40} + 12 q^{42} - 8 q^{43} + 28 q^{45} - 16 q^{46} - 4 q^{48} + 40 q^{51} - 8 q^{52} - 36 q^{55} - 4 q^{57} + 44 q^{58} + 16 q^{60} - 120 q^{61} - 12 q^{63} + 80 q^{67} - 36 q^{70} + 44 q^{73} + 4 q^{75} - 36 q^{76} - 64 q^{78} + 36 q^{81} + 8 q^{82} - 24 q^{85} - 28 q^{87} - 4 q^{88} + 44 q^{90} - 72 q^{93} - 4 q^{96} + 92 q^{97}+O(q^{100}) \) 36 * q + 4 * q^3 + 4 * q^6 + 20 * q^7 - 4 * q^10 - 4 * q^12 + 8 * q^13 + 4 * q^15 - 36 * q^16 + 16 * q^21 - 4 * q^22 + 16 * q^25 - 44 * q^27 + 20 * q^28 + 32 * q^30 - 24 * q^31 - 4 * q^33 + 4 * q^36 - 8 * q^40 + 12 * q^42 - 8 * q^43 + 28 * q^45 - 16 * q^46 - 4 * q^48 + 40 * q^51 - 8 * q^52 - 36 * q^55 - 4 * q^57 + 44 * q^58 + 16 * q^60 - 120 * q^61 - 12 * q^63 + 80 * q^67 - 36 * q^70 + 44 * q^73 + 4 * q^75 - 36 * q^76 - 64 * q^78 + 36 * q^81 + 8 * q^82 - 24 * q^85 - 28 * q^87 - 4 * q^88 + 44 * q^90 - 72 * q^93 - 4 * q^96 + 92 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more