LMFDB - Embedded newform 570.2.k.b.533.1

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			533.1
Character	$\chi$	$=$	570.533
Dual form			570.2.k.b.77.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-1.69896 + 0.336929i) q^{3} +1.00000i q^{4} +(2.14526 + 0.630765i) q^{5} +(1.43959 + 0.963104i) q^{6} +(0.804978 - 0.804978i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.77296 - 1.14486i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.69896 + 0.336929i) 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} +(-0.336929 - 1.69896i) q^{12} +(-2.72994 - 2.72994i) q^{13} -1.13841 q^{14} +(-3.85724 - 0.348848i) q^{15} -1.00000 q^{16} +(2.04213 + 2.04213i) q^{17} +(-2.77032 - 1.15124i) 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} +(-4.32542 + 2.87936i) q^{27} +(0.804978 + 0.804978i) q^{28} +5.49359 q^{29} +(2.48081 + 2.97415i) q^{30} +5.07413 q^{31} +(0.707107 + 0.707107i) q^{32} +(-1.06331 - 5.36176i) 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} +(1.93412 - 0.383563i) q^{42} +(0.643335 + 0.643335i) q^{43} -3.15590 q^{44} +(6.67085 - 0.706935i) q^{45} +2.57617 q^{46} +(3.22573 + 3.22573i) q^{47} +(1.69896 - 0.336929i) 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} +(-0.336929 - 1.69896i) q^{57} +(-3.88456 - 3.88456i) q^{58} +1.26612 q^{59} +(0.348848 - 3.85724i) q^{60} +2.70369 q^{61} +(-3.58795 - 3.58795i) q^{62} +(1.31058 - 3.15376i) 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} +(1.15124 - 2.77032i) q^{72} +(3.61892 + 3.61892i) q^{73} -10.2612 q^{74} +(-8.05474 - 3.18138i) q^{75} -1.00000 q^{76} +(2.54043 + 2.54043i) q^{77} +(-1.30079 - 6.55921i) 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} +(-9.33342 + 1.85095i) q^{87} +(2.23156 + 2.23156i) q^{88} -3.27340 q^{89} +(-5.21688 - 4.21712i) q^{90} -4.39508 q^{91} +(-1.82163 - 1.82163i) q^{92} +(-8.62077 + 1.70962i) 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
$3$	−1.69896	+	0.336929i	−0.980897	+	0.194526i
$3$	−1.69896	+	0.336929i	−0.980897	+	0.194526i
$4$			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	$0.157830\pi$
$11$			3.15590i			0.951539i	−0.879570	+	0.475769i	$0.842170\pi$
$12$	−0.336929	−	1.69896i	−0.0972629	−	0.490449i
$13$	−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
$15$	−3.85724	−	0.348848i	−0.995935	−	0.0900721i
$16$	−1.00000			−0.250000
$17$	2.04213	+	2.04213i	0.495289	+	0.495289i	0.909968	−	0.414679i	$-0.136106\pi$
$17$	2.04213	+	2.04213i	0.495289	+	0.495289i	−0.414679	+	0.909968i	$0.636106\pi$
$18$	−2.77032	−	1.15124i	−0.652970	−	0.271350i
$19$			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	−0.871043	−	0.491207i	$-0.836556\pi$
$23$	−1.82163	+	1.82163i	−0.379835	+	0.379835i	0.491207	+	0.871043i	$0.336556\pi$
$24$	−0.963104	+	1.43959i	−0.196593	+	0.293856i
$25$	4.20427	+	2.70631i	0.840854	+	0.541262i
$26$			3.86071i			0.757148i
$27$	−4.32542	+	2.87936i	−0.832428	+	0.554134i
$28$	0.804978	+	0.804978i	0.152127	+	0.152127i
$29$	5.49359			1.02013			0.510067	−	0.860134i	$-0.329620\pi$
$29$	5.49359			1.02013			0.510067	+	0.860134i	$0.329620\pi$
$30$	2.48081	+	2.97415i	0.452932	+	0.543004i
$31$	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
$33$	−1.06331	−	5.36176i	−0.185099	−	0.933362i
$34$		−	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	$0.164257\pi$
$41$			6.31900i			0.986862i	−0.869785	+	0.493431i	$0.835743\pi$
$42$	1.93412	−	0.383563i	0.298441	−	0.0591851i
$43$	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
$45$	6.67085	−	0.706935i	0.994432	−	0.105384i
$46$	2.57617			0.379835
$47$	3.22573	+	3.22573i	0.470521	+	0.470521i	0.902083	−	0.431562i	$-0.142037\pi$
$47$	3.22573	+	3.22573i	0.470521	+	0.470521i	−0.431562	+	0.902083i	$0.642037\pi$
$48$	1.69896	−	0.336929i	0.245224	−	0.0486315i
$49$			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	−0.455132	−	0.890424i	$-0.650408\pi$
$53$	3.16898	−	3.16898i	0.435292	−	0.435292i	0.890424	+	0.455132i	$0.150408\pi$
$54$	5.09455	+	1.02252i	0.693281	+	0.139147i
$55$	−1.99063	+	6.77022i	−0.268416	+	0.912896i
$56$		−	1.13841i		−	0.152127i
$57$	−0.336929	−	1.69896i	−0.0446273	−	0.225033i
$58$	−3.88456	−	3.88456i	−0.510067	−	0.510067i
$59$	1.26612			0.164834			0.0824171	−	0.996598i	$-0.473736\pi$
$59$	1.26612			0.164834			0.0824171	+	0.996598i	$0.473736\pi$
$60$	0.348848	−	3.85724i	0.0450360	−	0.497968i
$61$	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
$63$	1.31058	−	3.15376i	0.165118	−	0.397336i
$64$		−	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	$-0.982149\pi$
$71$		−	0.944610i		−	0.112105i	0.998428	−	0.0560523i	$-0.0178514\pi$
$72$	1.15124	−	2.77032i	0.135675	−	0.326485i
$73$	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
$75$	−8.05474	−	3.18138i	−0.930081	−	0.367354i
$76$	−1.00000			−0.114708
$77$	2.54043	+	2.54043i	0.289509	+	0.289509i
$78$	−1.30079	−	6.55921i	−0.147285	−	0.742685i
$79$			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	−0.942707	−	0.333621i	$-0.891729\pi$
$83$	−5.54904	+	5.54904i	−0.609086	+	0.609086i	0.333621	+	0.942707i	$0.391729\pi$
$84$	−1.63885	−	1.09641i	−0.178813	−	0.119628i
$85$	3.09279	+	5.66900i	0.335460	+	0.614889i
$86$		−	0.909814i		−	0.0981077i
$87$	−9.33342	+	1.85095i	−1.00065	+	0.198443i
$88$	2.23156	+	2.23156i	0.237885	+	0.237885i
$89$	−3.27340			−0.346979			−0.173490	−	0.984836i	$-0.555504\pi$
$89$	−3.27340			−0.346979			−0.173490	+	0.984836i	$0.555504\pi$
$90$	−5.21688	−	4.21712i	−0.549908	−	0.444524i
$91$	−4.39508			−0.460729
$92$	−1.82163	−	1.82163i	−0.189918	−	0.189918i
$93$	−8.62077	+	1.70962i	−0.893932	+	0.177279i
$94$		−	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	$-0.682641\pi$
$101$		−	16.8808i		−	1.67971i	0.542813	−	0.839853i	$-0.317359\pi$
$102$	0.973053	+	4.90662i	0.0963466	+	0.485828i
$103$	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
$105$	−3.38581	+	2.82418i	−0.330421	+	0.275612i
$106$	−4.48161			−0.435292
$107$	−8.84697	−	8.84697i	−0.855269	−	0.855269i	0.135507	−	0.990776i	$-0.456734\pi$
$107$	−8.84697	−	8.84697i	−0.855269	−	0.855269i	−0.990776	+	0.135507i	$0.956734\pi$
$108$	−2.87936	−	4.32542i	−0.277067	−	0.416214i
$109$		−	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	$0.654089\pi$
$113$	−14.3560	+	14.3560i	−1.35050	+	1.35050i	−0.885101	+	0.465400i	$0.845911\pi$
$114$	−0.963104	+	1.43959i	−0.0902030	+	0.134830i
$115$	−5.05688	+	2.75884i	−0.471556	+	0.257263i
$116$			5.49359i			0.510067i
$117$	−10.6954	−	4.44461i	−0.988790	−	0.410904i
$118$	−0.895279	−	0.895279i	−0.0824171	−	0.0824171i
$119$	3.28774			0.301386
$120$	−2.97415	+	2.48081i	−0.271502	+	0.226466i
$121$	1.04032			0.0945742
$122$	−1.91180	−	1.91180i	−0.173086	−	0.173086i
$123$	−2.12905	−	10.7357i	−0.191970	−	0.968010i
$124$			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	$0.311757\pi$
$131$			19.0035i			1.66034i	−0.557509	+	0.830171i	$0.688243\pi$
$132$	5.36176	−	1.06331i	0.466681	−	0.0925494i
$133$	0.804978	+	0.804978i	0.0698004	+	0.0698004i
$134$	−5.47128			−0.472647
$135$	−11.0953	+	3.44866i	−0.954936	+	0.296813i
$136$	2.88801			0.247645
$137$	−15.2239	−	15.2239i	−1.30066	−	1.30066i	−0.927944	−	0.372720i	$-0.878425\pi$
$137$	−15.2239	−	15.2239i	−1.30066	−	1.30066i	−0.372720	−	0.927944i	$-0.621575\pi$
$138$	−4.37682	+	0.867985i	−0.372580	+	0.0738878i
$139$		−	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
$147$	−1.92185	−	9.69093i	−0.158511	−	0.799294i
$148$	7.25575	+	7.25575i	0.596419	+	0.596419i
$149$	13.7188			1.12389			0.561945	−	0.827174i	$-0.310053\pi$
$149$	13.7188			1.12389			0.561945	+	0.827174i	$0.310053\pi$
$150$	3.44598	+	7.94514i	0.281363	+	0.648718i
$151$	−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
$153$	8.00069	+	3.32479i	0.646818	+	0.268793i
$154$		−	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
$162$	−8.99998	−	0.0207168i	−0.707105	−	0.00162767i
$163$	−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
$165$	1.10093	−	12.1731i	0.0857071	−	0.947671i
$166$	7.84753			0.609086
$167$	2.26247	+	2.26247i	0.175075	+	0.175075i	0.789205	−	0.614130i	$-0.210493\pi$
$167$	2.26247	+	2.26247i	0.175075	+	0.175075i	−0.614130	+	0.789205i	$0.710493\pi$
$168$	0.383563	+	1.93412i	0.0295925	+	0.149221i
$169$			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	−0.897402	−	0.441214i	$-0.854548\pi$
$173$	−6.00022	+	6.00022i	−0.456189	+	0.456189i	0.441214	+	0.897402i	$0.354548\pi$
$174$	7.90854	+	5.29091i	0.599545	+	0.401103i
$175$	5.56286	−	1.20583i	0.420513	−	0.0911520i
$176$		−	3.15590i		−	0.237885i
$177$	−2.15108	+	0.426591i	−0.161685	+	0.0320645i
$178$	2.31464	+	2.31464i	0.173490	+	0.173490i
$179$	10.5263			0.786776			0.393388	−	0.919373i	$-0.371303\pi$
$179$	10.5263			0.786776			0.393388	+	0.919373i	$0.371303\pi$
$180$	0.706935	+	6.67085i	0.0526919	+	0.497216i
$181$	−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
$183$	−4.59347	+	0.910950i	−0.339559	+	0.0673394i
$184$			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	$-0.645803\pi$
$191$		−	24.7912i		−	1.79383i	0.442204	−	0.896915i	$-0.354197\pi$
$192$	0.336929	+	1.69896i	0.0243157	+	0.122612i
$193$	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
$195$	9.57769	+	11.4824i	0.685873	+	0.822268i
$196$	−5.70402			−0.407430
$197$	1.66630	+	1.66630i	0.118719	+	0.118719i	0.763970	−	0.645252i	$-0.223247\pi$
$197$	1.66630	+	1.66630i	0.118719	+	0.118719i	−0.645252	+	0.763970i	$0.723247\pi$
$198$	3.63319	−	8.74283i	0.258200	−	0.621326i
$199$		−	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
$207$	−2.96579	+	7.13680i	−0.206137	+	0.496042i
$208$	2.72994	+	2.72994i	0.189287	+	0.189287i
$209$	−3.15590			−0.218298
$210$	4.39112	+	0.397132i	0.303016	+	0.0274047i
$211$	−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
$213$	0.318266	+	1.60486i	0.0218073	+	0.109963i
$214$			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
$222$	17.4334	−	3.45728i	1.17005	−	0.232038i
$223$	−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
$225$	14.7566	+	2.69118i	0.983774	+	0.179412i
$226$	20.3025			1.35050
$227$	−2.05681	−	2.05681i	−0.136515	−	0.136515i	0.635547	−	0.772062i	$-0.280775\pi$
$227$	−2.05681	−	2.05681i	−0.136515	−	0.136515i	−0.772062	+	0.635547i	$0.780775\pi$
$228$	1.69896	−	0.336929i	0.112517	−	0.0223136i
$229$		−	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	$0.507103\pi$
$233$	−15.6011	+	15.6011i	−1.02206	+	1.02206i	−0.999751	+	0.0223132i	$0.992897\pi$
$234$	4.41997	+	10.7056i	0.288943	+	0.699847i
$235$	4.88535	+	8.95470i	0.318685	+	0.584140i
$236$			1.26612i			0.0824171i
$237$	−5.06282	−	25.5293i	−0.328865	−	1.65830i
$238$	−2.32478	−	2.32478i	−0.150693	−	0.150693i
$239$	4.84839			0.313616			0.156808	−	0.987629i	$-0.449880\pi$
$239$	4.84839			0.313616			0.156808	+	0.987629i	$0.449880\pi$
$240$	3.85724	+	0.348848i	0.248984	+	0.0225180i
$241$	−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
$243$	−8.69774	+	12.9364i	−0.557960	+	0.829868i
$244$			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	$-0.919391\pi$
$251$		−	7.93870i		−	0.501087i	0.968105	−	0.250543i	$-0.0806092\pi$
$252$	3.15376	+	1.31058i	0.198668	+	0.0825590i
$253$	−5.74887	−	5.74887i	−0.361428	−	0.361428i
$254$	2.22877			0.139845
$255$	−7.16459	−	8.58938i	−0.448664	−	0.537888i
$256$	1.00000			0.0625000
$257$	16.9891	+	16.9891i	1.05975	+	1.05975i	0.998098	+	0.0616541i	$0.0196376\pi$
$257$	16.9891	+	16.9891i	1.05975	+	1.05975i	0.0616541	+	0.998098i	$0.480362\pi$
$258$	0.306542	+	1.54574i	0.0190845	+	0.0962336i
$259$		−	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	−0.632546	−	0.774523i	$-0.717990\pi$
$263$	2.30249	−	2.30249i	0.141977	−	0.141977i	0.774523	+	0.632546i	$0.217990\pi$
$264$	−4.54321	−	3.03946i	−0.279615	−	0.187066i
$265$	8.79715	−	4.79939i	0.540405	−	0.294824i
$266$		−	1.13841i		−	0.0698004i
$267$	5.56138	−	1.10290i	0.340351	−	0.0674965i
$268$	3.86878	+	3.86878i	0.236323	+	0.236323i
$269$	−15.9676			−0.973559			−0.486780	−	0.873525i	$-0.661829\pi$
$269$	−15.9676			−0.973559			−0.486780	+	0.873525i	$0.661829\pi$
$270$	10.2842	+	5.40703i	0.625874	+	0.329061i
$271$	−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
$273$	7.46708	−	1.48083i	0.451928	−	0.0896238i
$274$			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	$-0.885592\pi$
$281$		−	11.7923i		−	0.703472i	0.936099	−	0.351736i	$-0.114408\pi$
$282$	1.53702	+	7.75045i	0.0915285	+	0.461533i
$283$	−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
$285$	0.348848	−	3.85724i	0.0206640	−	0.228483i
$286$	−12.1840			−0.720456
$287$	5.08665	+	5.08665i	0.300256	+	0.300256i
$288$	2.77032	+	1.15124i	0.163242	+	0.0678374i
$289$		−	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	−0.956492	−	0.291760i	$-0.905759\pi$
$293$	−11.3784	+	11.3784i	−0.664732	+	0.664732i	0.291760	+	0.956492i	$0.405759\pi$
$294$	−5.49357	+	8.21147i	−0.320391	+	0.478903i
$295$	2.71614	+	0.798621i	0.158140	+	0.0464975i
$296$		−	10.2612i		−	0.596419i
$297$	−9.08698	−	13.6506i	−0.527280	−	0.792087i
$298$	−9.70068	−	9.70068i	−0.561945	−	0.561945i
$299$	9.94585			0.575183
$300$	3.18138	−	8.05474i	0.183677	−	0.465041i
$301$	1.03574			0.0596992
$302$	10.5407	+	10.5407i	0.606549	+	0.606549i
$303$	5.68764	+	28.6799i	0.326746	+	1.64762i
$304$		−	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	$0.0740473\pi$
$311$			8.13102i			0.461068i	−0.973064	+	0.230534i	$0.925953\pi$
$312$	6.55921	−	1.30079i	0.371342	−	0.0736425i
$313$	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
$315$	4.80082	−	5.93895i	0.270496	−	0.334622i
$316$	−15.0264			−0.845300
$317$	−7.90002	−	7.90002i	−0.443709	−	0.443709i	0.449547	−	0.893257i	$-0.351585\pi$
$317$	−7.90002	−	7.90002i	−0.443709	−	0.443709i	−0.893257	+	0.449547i	$0.851585\pi$
$318$	7.61409	−	1.50998i	0.426977	−	0.0846756i
$319$			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
$327$	2.30432	+	11.6196i	0.127429	+	0.642563i
$328$	4.46821	+	4.46821i	0.246715	+	0.246715i
$329$	5.19328			0.286315
$330$	−9.38612	+	7.82917i	−0.516689	+	0.430982i
$331$	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
$333$	11.8131	−	28.4267i	0.647352	−	1.55777i
$334$		−	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
$342$	1.15124	−	2.77032i	0.0622519	−	0.149802i
$343$	10.2265	+	10.2265i	0.552177	+	0.552177i
$344$	0.909814			0.0490539
$345$	7.66192	−	6.39098i	0.412504	−	0.344079i
$346$	8.48560			0.456189
$347$	19.5400	+	19.5400i	1.04896	+	1.04896i	0.998738	+	0.0502218i	$0.0159928\pi$
$347$	19.5400	+	19.5400i	1.04896	+	1.04896i	0.0502218	+	0.998738i	$0.484007\pi$
$348$	−1.85095	−	9.33342i	−0.0992213	−	0.500324i
$349$			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	−0.997665	−	0.0682931i	$-0.978245\pi$
$353$	−17.4613	+	17.4613i	−0.929372	+	0.929372i	0.0682931	+	0.997665i	$0.478245\pi$
$354$	1.82269	+	1.21940i	0.0968750	+	0.0648104i
$355$	0.595827	−	2.02643i	0.0316232	−	0.107552i
$356$		−	3.27340i		−	0.173490i
$357$	−5.58575	+	1.10773i	−0.295629	+	0.0586275i
$358$	−7.44325	−	7.44325i	−0.393388	−	0.393388i
$359$	−25.1531			−1.32753			−0.663766	−	0.747940i	$-0.731043\pi$
$359$	−25.1531			−1.32753			−0.663766	+	0.747940i	$0.731043\pi$
$360$	4.21712	−	5.21688i	0.222262	−	0.274954i
$361$	−1.00000			−0.0526316
$362$	14.7945	+	14.7945i	0.777582	+	0.777582i
$363$	−1.76746	+	0.350513i	−0.0927676	+	0.0183971i
$364$		−	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
$372$	−1.70962	−	8.62077i	−0.0886397	−	0.446966i
$373$	−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
$375$	−15.2728	−	11.9055i	−0.788684	−	0.614799i
$376$	4.56187			0.235260
$377$	−14.9972	−	14.9972i	−0.772393	−	0.772393i
$378$	4.92411	−	3.27790i	0.253269	−	0.168597i
$379$		−	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	−0.547446	−	0.836841i	$-0.684400\pi$
$383$	5.66358	−	5.66358i	0.289396	−	0.289396i	0.836841	+	0.547446i	$0.184400\pi$
$384$	0.963104	−	1.43959i	0.0491482	−	0.0734640i
$385$	3.84746	+	7.05229i	0.196085	+	0.359418i
$386$		−	24.6957i		−	1.25698i
$387$	2.52047	+	1.04741i	0.128123	+	0.0532430i
$388$	2.89748	+	2.89748i	0.147097	+	0.147097i
$389$	1.77092			0.0897890			0.0448945	−	0.998992i	$-0.485705\pi$
$389$	1.77092			0.0897890			0.0448945	+	0.998992i	$0.485705\pi$
$390$	1.34680	−	14.8917i	0.0681979	−	0.754071i
$391$	−7.44000			−0.376257
$392$	4.03335	+	4.03335i	0.203715	+	0.203715i
$393$	−6.40282	−	32.2862i	−0.322980	−	1.62863i
$394$		−	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	$-0.690425\pi$
$401$		−	33.0944i		−	1.65266i	0.563188	−	0.826329i	$-0.309575\pi$
$402$	9.29551	−	1.84343i	0.463618	−	0.0919420i
$403$	−13.8521	−	13.8521i	−0.690020	−	0.690020i
$404$	16.8808			0.839853
$405$	17.6886	−	9.59749i	0.878956	−	0.476903i
$406$	−6.25397			−0.310379
$407$	22.8984	+	22.8984i	1.13503	+	1.13503i
$408$	−4.90662	+	0.973053i	−0.242914	+	0.0481733i
$409$		−	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
$417$	5.07111	+	25.5711i	0.248333	+	1.25222i
$418$	2.23156	+	2.23156i	0.109149	+	0.109149i
$419$	−33.5096			−1.63705			−0.818525	−	0.574471i	$-0.805208\pi$
$419$	−33.5096			−1.63705			−0.818525	+	0.574471i	$0.805208\pi$
$420$	−2.82418	−	3.38581i	−0.137806	−	0.165211i
$421$	−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
$423$	12.6378	+	5.25180i	0.614472	+	0.255351i
$424$		−	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	$-0.867661\pi$
$431$		−	16.7696i		−	0.807763i	0.914811	−	0.403882i	$-0.132339\pi$
$432$	4.32542	−	2.87936i	0.208107	−	0.138533i
$433$	−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
$435$	−21.1901	−	1.91643i	−1.01599	−	0.0918857i
$436$	6.83921			0.327539
$437$	−1.82163	−	1.82163i	−0.0871402	−	0.0871402i
$438$	1.72438	+	8.69517i	0.0823939	+	0.415471i
$439$			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	−0.239405	−	0.970920i	$-0.576952\pi$
$443$	15.3966	−	15.3966i	0.731515	−	0.731515i	0.970920	+	0.239405i	$0.0769523\pi$
$444$	−14.7719	−	9.88258i	−0.701044	−	0.469007i
$445$	−7.02228	−	2.06474i	−0.332888	−	0.0978782i
$446$			26.8179i			1.26987i
$447$	−23.3078	+	4.62227i	−1.10242	+	0.218626i
$448$	−0.804978	−	0.804978i	−0.0380316	−	0.0380316i
$449$	−3.69496			−0.174376			−0.0871879	−	0.996192i	$-0.527788\pi$
$449$	−3.69496			−0.174376			−0.0871879	+	0.996192i	$0.527788\pi$
$450$	−8.53155	−	12.3375i	−0.402181	−	0.581593i
$451$	−19.9421			−0.939037
$452$	−14.3560	−	14.3560i	−0.675250	−	0.675250i
$453$	25.3261	−	5.02253i	1.18992	−	0.235979i
$454$			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	$0.0223898\pi$
$461$			3.01803i			0.140563i	−0.997527	+	0.0702817i	$0.977610\pi$
$462$	1.21049	+	6.10388i	0.0563169	+	0.283978i
$463$	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
$465$	−19.5722	−	1.77010i	−0.907637	−	0.0820864i
$466$	22.0633			1.02206
$467$	−3.42627	−	3.42627i	−0.158549	−	0.158549i	0.623375	−	0.781923i	$-0.285761\pi$
$467$	−3.42627	−	3.42627i	−0.158549	−	0.158549i	−0.781923	+	0.623375i	$0.785761\pi$
$468$	4.44461	−	10.6954i	0.205452	−	0.494395i
$469$		−	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
$477$	5.15941	−	12.4155i	0.236233	−	0.568465i
$478$	−3.42833	−	3.42833i	−0.156808	−	0.156808i
$479$	18.0199			0.823349			0.411674	−	0.911331i	$-0.364944\pi$
$479$	18.0199			0.823349			0.411674	+	0.911331i	$0.364944\pi$
$480$	−2.48081	−	2.97415i	−0.113233	−	0.135751i
$481$	−39.6155			−1.80631
$482$	12.0576	+	12.0576i	0.549209	+	0.549209i
$483$	−0.988124	−	4.98262i	−0.0449612	−	0.226717i
$484$			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	$-0.628173\pi$
$491$		−	40.7725i		−	1.84004i	0.391873	−	0.920020i	$-0.371827\pi$
$492$	10.7357	−	2.12905i	0.484005	−	0.0959851i
$493$	11.2186	+	11.2186i	0.505262	+	0.505262i
$494$	−3.86071			−0.173702
$495$	2.23102	+	21.0525i	0.100277	+	0.946240i
$496$	−5.07413			−0.227835
$497$	−0.760391	−	0.760391i	−0.0341082	−	0.0341082i
$498$	−13.3327	+	2.64406i	−0.597451	+	0.118483i
$499$			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	−0.131736	−	0.991285i	$-0.542055\pi$
$503$	19.2777	−	19.2777i	0.859549	−	0.859549i	0.991285	+	0.131736i	$0.0420551\pi$
$504$	−1.30332	−	3.15677i	−0.0580545	−	0.140614i
$505$	10.6478	−	36.2138i	0.473823	−	1.61149i
$506$			8.13012i			0.361428i
$507$	−0.641885	−	3.23671i	−0.0285071	−	0.143747i
$508$	−1.57598	−	1.57598i	−0.0699227	−	0.0699227i
$509$	−30.9140			−1.37024			−0.685120	−	0.728431i	$-0.740250\pi$
$509$	−30.9140			−1.37024			−0.685120	+	0.728431i	$0.740250\pi$
$510$	−1.00747	+	11.1397i	−0.0446117	+	0.493276i
$511$	5.82630			0.257740
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−2.87936	−	4.32542i	−0.127127	−	0.190972i
$514$		−	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	$-0.823583\pi$
$521$		−	24.0255i		−	1.05258i	0.850306	−	0.526289i	$-0.176417\pi$
$522$	−15.2190	−	6.32444i	−0.666117	−	0.276813i
$523$	−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
$525$	−9.04483	+	3.92295i	−0.394749	+	0.171211i
$526$	−3.25621			−0.141977
$527$	10.3620	+	10.3620i	0.451377	+	0.451377i
$528$	1.06331	+	5.36176i	0.0462747	+	0.233340i
$529$			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
$537$	−17.8839	+	3.54663i	−0.771746	+	0.153048i
$538$	11.2908	+	11.2908i	0.486780	+	0.486780i
$539$	−18.0013			−0.775371
$540$	−3.44866	−	11.0953i	−0.148407	−	0.477468i
$541$	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
$543$	35.5467	−	7.04942i	1.52546	−	0.302520i
$544$			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
$552$	−0.867985	−	4.37682i	−0.0369439	−	0.186290i
$553$	12.0959	+	12.0959i	0.514370	+	0.514370i
$554$	−24.9457			−1.05984
$555$	−30.5183	+	25.4560i	−1.29543	+	1.08055i
$556$	15.0510			0.638304
$557$	−19.6777	−	19.6777i	−0.833770	−	0.833770i	0.154260	−	0.988030i	$-0.450701\pi$
$557$	−19.6777	−	19.6777i	−0.833770	−	0.833770i	−0.988030	+	0.154260i	$0.950701\pi$
$558$	−14.0569	−	5.84154i	−0.595078	−	0.247292i
$559$		−	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	−0.912770	−	0.408474i	$-0.866061\pi$
$563$	−11.9658	+	11.9658i	−0.504296	+	0.504296i	0.408474	+	0.912770i	$0.366061\pi$
$564$	4.39356	−	6.56724i	0.185002	−	0.276531i
$565$	−39.8526	+	21.7421i	−1.67661	+	0.914697i
$566$			6.82505i			0.286878i
$567$	0.0235843	−	10.2457i	0.000990446	−	0.430278i
$568$	−0.667940	−	0.667940i	−0.0280262	−	0.0280262i
$569$	−27.2399			−1.14195			−0.570977	−	0.820966i	$-0.693436\pi$
$569$	−27.2399			−1.14195			−0.570977	+	0.820966i	$0.693436\pi$
$570$	−2.97415	+	2.48081i	−0.124574	+	0.103910i
$571$	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
$573$	8.35287	+	42.1194i	0.348946	+	1.75956i
$574$		−	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
$582$	6.96178	−	1.38062i	0.288575	−	0.0572285i
$583$	10.0010	+	10.0010i	0.414197	+	0.414197i
$584$	5.11793			0.211781
$585$	−20.1409	−	16.2811i	−0.832723	−	0.673141i
$586$	16.0915			0.664732
$587$	−30.9059	−	30.9059i	−1.27562	−	1.27562i	−0.943093	−	0.332528i	$-0.892098\pi$
$587$	−30.9059	−	30.9059i	−1.27562	−	1.27562i	−0.332528	−	0.943093i	$-0.607902\pi$
$588$	9.69093	−	1.92185i	0.399647	−	0.0792557i
$589$			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	$0.513965\pi$
$593$	−25.3962	+	25.3962i	−1.04290	+	1.04290i	−0.999038	+	0.0438587i	$0.986035\pi$
$594$	−3.22695	+	16.0779i	−0.132404	+	0.659683i
$595$	7.05305	+	2.07379i	0.289147	+	0.0850171i
$596$			13.7188i			0.561945i
$597$	9.23601	+	46.5726i	0.378005	+	1.90609i
$598$	−7.03278	−	7.03278i	−0.287592	−	0.287592i
$599$	24.9746			1.02043			0.510217	−	0.860046i	$-0.329565\pi$
$599$	24.9746			1.02043			0.510217	+	0.860046i	$0.329565\pi$
$600$	−7.94514	+	3.44598i	−0.324359	+	0.140682i
$601$	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
$603$	6.29876	−	15.1572i	0.256505	−	0.617248i
$604$		−	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
$612$	−3.32479	+	8.00069i	−0.134397	+	0.323409i
$613$	−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
$615$	2.20437	−	24.3739i	0.0888887	−	0.982850i
$616$	3.59271			0.144754
$617$	4.00994	+	4.00994i	0.161434	+	0.161434i	0.783202	−	0.621768i	$-0.213585\pi$
$617$	4.00994	+	4.00994i	0.161434	+	0.161434i	−0.621768	+	0.783202i	$0.713585\pi$
$618$	0.701779	+	3.53873i	0.0282297	+	0.142348i
$619$		−	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
$627$	5.36176	−	1.06331i	0.214128	−	0.0424646i
$628$	2.63322	+	2.63322i	0.105077	+	0.105077i
$629$	29.6344			1.18160
$630$	−7.59417	+	0.804783i	−0.302559	+	0.0320633i
$631$	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
$633$	6.26312	−	1.24207i	0.248937	−	0.0493677i
$634$			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	$0.0916358\pi$
$641$			14.3767i			0.567845i	−0.958847	+	0.283922i	$0.908364\pi$
$642$	−4.21549	−	21.2566i	−0.166372	−	0.838931i
$643$	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
$645$	−2.25707	−	2.70593i	−0.0888722	−	0.106546i
$646$	2.88801			0.113627
$647$	−7.51216	−	7.51216i	−0.295333	−	0.295333i	0.543849	−	0.839183i	$-0.316966\pi$
$647$	−7.51216	−	7.51216i	−0.295333	−	0.295333i	−0.839183	+	0.543849i	$0.816966\pi$
$648$	0.0207168	−	8.99998i	0.000813834	−	0.353552i
$649$			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	−0.837190	−	0.546912i	$-0.815803\pi$
$653$	−7.41773	+	7.41773i	−0.290278	+	0.290278i	0.546912	+	0.837190i	$0.315803\pi$
$654$	6.58687	−	9.84568i	0.257567	−	0.384996i
$655$	−11.9867	+	40.7674i	−0.468360	+	1.59291i
$656$		−	6.31900i		−	0.246715i
$657$	14.1783	+	5.89196i	0.553147	+	0.229867i
$658$	−3.67220	−	3.67220i	−0.143157	−	0.143157i
$659$	31.2034			1.21551			0.607755	−	0.794124i	$-0.292070\pi$
$659$	31.2034			1.21551			0.607755	+	0.794124i	$0.292070\pi$
$660$	12.1731	+	1.10093i	0.473835	+	0.0428535i
$661$	−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
$663$	3.75668	+	18.9431i	0.145897	+	0.735687i
$664$			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
$672$	−1.93412	+	0.383563i	−0.0746103	+	0.0147963i
$673$	−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
$675$	−25.9777	+	0.399710i	−0.999882	+	0.0153848i
$676$	−1.90511			−0.0732734
$677$	26.1264	+	26.1264i	1.00412	+	1.00412i	0.999991	+	0.00412796i	$0.00131397\pi$
$677$	26.1264	+	26.1264i	1.00412	+	1.00412i	0.00412796	+	0.999991i	$0.498686\pi$
$678$	−34.4932	+	6.84049i	−1.32470	+	0.262707i
$679$		−	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	−0.284558	−	0.958659i	$-0.591847\pi$
$683$	17.6171	−	17.6171i	0.674101	−	0.674101i	0.958659	+	0.284558i	$0.0918468\pi$
$684$	−2.77296	+	1.14486i	−0.106027	+	0.0437748i
$685$	−23.0565	−	42.2619i	−0.880943	−	1.61474i
$686$		−	14.4624i		−	0.552177i
$687$	5.34821	+	26.9684i	0.204047	+	1.02891i
$688$	−0.643335	−	0.643335i	−0.0245269	−	0.0245269i
$689$	−17.3022			−0.659162
$690$	−9.93691	−	0.898691i	−0.378292	−	0.0342126i
$691$	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
$693$	9.95293	+	4.13607i	0.378081	+	0.157116i
$694$		−	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	$0.161326\pi$
$701$			25.7033i			0.970801i	−0.874292	+	0.485401i	$0.838674\pi$
$702$	−11.1164	−	16.6992i	−0.419562	−	0.630271i
$703$	7.25575	+	7.25575i	0.273656	+	0.273656i
$704$	3.15590			0.118942
$705$	−11.3171	−	13.5677i	−0.426228	−	0.510989i
$706$	24.6940			0.929372
$707$	−13.5887	−	13.5887i	−0.511056	−	0.511056i
$708$	−0.426591	−	2.15108i	−0.0160323	−	0.0808427i
$709$		−	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
$717$	−8.23724	+	1.63356i	−0.307625	+	0.0610065i
$718$	17.7860	+	17.7860i	0.663766	+	0.663766i
$719$	0.187398			0.00698877			0.00349439	−	0.999994i	$-0.498888\pi$
$719$	0.187398			0.00698877			0.00349439	+	0.999994i	$0.498888\pi$
$720$	−6.67085	+	0.706935i	−0.248608	+	0.0263459i
$721$	2.37116			0.0883068
$722$	0.707107	+	0.707107i	0.0263158	+	0.0263158i
$723$	28.9708	−	5.74532i	1.07744	−	0.213671i
$724$		−	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
$732$	−0.910950	−	4.59347i	−0.0336697	−	0.169779i
$733$	−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
$735$	1.98983	−	22.0018i	0.0733961	−	0.811548i
$736$	−2.57617			−0.0949589
$737$	12.2095	+	12.2095i	0.449742	+	0.449742i
$738$	7.27468	−	17.5056i	0.267785	−	0.644391i
$739$			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	$-0.421227\pi$
$743$	33.1046	−	33.1046i	1.21449	−	1.21449i	0.969534	−	0.244956i	$-0.0787734\pi$
$744$	−4.88692	+	7.30469i	−0.179163	+	0.267803i
$745$	29.4304	+	8.65336i	1.07825	+	0.317034i
$746$			9.01595i			0.330098i
$747$	−9.03439	+	21.7401i	−0.330551	+	0.795430i
$748$	−6.44475	−	6.44475i	−0.235643	−	0.235643i
$749$	−14.2432			−0.520436
$750$	2.38102	+	19.2180i	0.0869424	+	0.701741i
$751$	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
$753$	2.67478	+	13.4876i	0.0974743	+	0.491515i
$754$			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	$-0.901552\pi$
$761$		−	16.7931i		−	0.608751i	0.952552	−	0.304375i	$-0.0984477\pi$
$762$	−3.78660	+	0.750937i	−0.137174	+	0.0272036i
$763$	−5.50541	−	5.50541i	−0.199309	−	0.199309i
$764$	24.7912			0.896915
$765$	15.0664	+	12.1791i	0.544727	+	0.440336i
$766$	−8.00952			−0.289396
$767$	−3.45641	−	3.45641i	−0.124804	−	0.124804i
$768$	−1.69896	+	0.336929i	−0.0613061	+	0.0121579i
$769$		−	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	−0.258611	−	0.965981i	$-0.583265\pi$
$773$	19.6669	−	19.6669i	0.707370	−	0.707370i	0.965981	+	0.258611i	$0.0832649\pi$
$774$	−1.04161	−	2.52288i	−0.0374399	−	0.0906829i
$775$	21.3330	+	13.7322i	0.766305	+	0.493274i
$776$		−	4.09766i		−	0.147097i
$777$	3.93581	+	19.8463i	0.141196	+	0.711983i
$778$	−1.25223	−	1.25223i	−0.0448945	−	0.0448945i
$779$	−6.31900			−0.226402
$780$	−11.4824	+	9.57769i	−0.411134	+	0.342936i
$781$	2.98109			0.106672
$782$	5.26087	+	5.26087i	0.188128	+	0.188128i
$783$	−23.7621	+	15.8181i	−0.849188	+	0.565291i
$784$		−	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
$792$	8.74283	+	3.63319i	0.310663	+	0.129100i
$793$	−7.38090	−	7.38090i	−0.262103	−	0.262103i
$794$	19.1144			0.678345
$795$	−13.3290	+	11.1180i	−0.472731	+	0.394315i
$796$	27.4124			0.971606
$797$	3.11137	+	3.11137i	0.110210	+	0.110210i	0.760061	−	0.649851i	$-0.225169\pi$
$797$	3.11137	+	3.11137i	0.110210	+	0.110210i	−0.649851	+	0.760061i	$0.725169\pi$
$798$	0.383563	+	1.93412i	0.0135780	+	0.0684671i
$799$			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
$807$	27.1283	−	5.37993i	0.954962	−	0.189382i
$808$	−11.9366	−	11.9366i	−0.419927	−	0.419927i
$809$	19.2043			0.675189			0.337594	−	0.941292i	$-0.390387\pi$
$809$	19.2043			0.675189			0.337594	+	0.941292i	$0.390387\pi$
$810$	−19.2942	−	5.72131i	−0.677929	−	0.201026i
$811$	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
$813$	10.0459	−	1.99225i	0.352326	−	0.0698713i
$814$		−	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	$-0.966751\pi$
$821$		−	5.97506i		−	0.208531i	0.994549	−	0.104266i	$-0.0332492\pi$
$822$	−7.25401	−	36.5784i	−0.253013	−	1.27582i
$823$	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
$825$	10.0401	−	25.4199i	0.349552	−	0.885008i
$826$	−1.44136			−0.0501513
$827$	−3.64780	−	3.64780i	−0.126846	−	0.126846i	0.640833	−	0.767680i	$-0.278589\pi$
$827$	−3.64780	−	3.64780i	−0.126846	−	0.126846i	−0.767680	+	0.640833i	$0.778589\pi$
$828$	−7.13680	−	2.96579i	−0.248021	−	0.103068i
$829$			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
$837$	−21.9478	+	14.6103i	−0.758625	+	0.505005i
$838$	23.6948	+	23.6948i	0.818525	+	0.818525i
$839$	13.6311			0.470597			0.235299	−	0.971923i	$-0.424393\pi$
$839$	13.6311			0.470597			0.235299	+	0.971923i	$0.424393\pi$
$840$	−0.397132	+	4.39112i	−0.0137024	+	0.151508i
$841$	1.17958			0.0406753
$842$	21.0539	+	21.0539i	0.725564	+	0.725564i
$843$	3.97318	+	20.0348i	0.136843	+	0.690033i
$844$		−	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
$852$	−1.60486	+	0.318266i	−0.0549816	+	0.0109036i
$853$	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
$855$	0.706935	+	6.67085i	0.0241767	+	0.228138i
$856$	−12.5115			−0.427634
$857$	16.1672	+	16.1672i	0.552261	+	0.552261i	0.927093	−	0.374832i	$-0.122300\pi$
$857$	16.1672	+	16.1672i	0.552261	+	0.552261i	−0.374832	+	0.927093i	$0.622300\pi$
$858$	20.7002	−	4.10514i	0.706693	−	0.140147i
$859$		−	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	−0.799603	−	0.600529i	$-0.794957\pi$
$863$	−5.84818	+	5.84818i	−0.199074	+	0.199074i	0.600529	+	0.799603i	$0.294957\pi$
$864$	−5.09455	−	1.02252i	−0.173320	−	0.0347867i
$865$	−16.6568	+	9.08730i	−0.566347	+	0.308978i
$866$			1.19002i			0.0404387i
$867$	2.91761	+	14.7120i	0.0990871	+	0.499647i
$868$	4.08457	+	4.08457i	0.138639	+	0.138639i
$869$	−47.4217			−1.60867
$870$	13.6286	+	16.3388i	0.462051	+	0.553937i
$871$	−21.1231			−0.715727
$872$	−4.83605	−	4.83605i	−0.163769	−	0.163769i
$873$	4.71739	−	11.3518i	0.159659	−	0.384201i
$874$			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	$-0.966916\pi$
$881$		−	6.15899i		−	0.207502i	0.994603	−	0.103751i	$-0.0330845\pi$
$882$	6.56669	−	15.8019i	0.221112	−	0.532079i
$883$	−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
$885$	−4.88371	−	0.441681i	−0.164164	−	0.0148470i
$886$	−21.7741			−0.731515
$887$	9.89729	+	9.89729i	0.332319	+	0.332319i	0.853466	−	0.521148i	$-0.174496\pi$
$887$	9.89729	+	9.89729i	0.332319	+	0.332319i	−0.521148	+	0.853466i	$0.674496\pi$
$888$	3.45728	+	17.4334i	0.116019	+	0.585026i
$889$			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
$897$	−16.8976	+	3.35104i	−0.564196	+	0.111888i
$898$	2.61273	+	2.61273i	0.0871879	+	0.0871879i
$899$	27.8752			0.929691
$900$	−2.69118	+	14.7566i	−0.0897060	+	0.491887i
$901$	12.9429			0.431191
$902$	14.1012	+	14.1012i	0.469518	+	0.469518i
$903$	−1.75969	+	0.348971i	−0.0585588	+	0.0116130i
$904$			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	$-0.919568\pi$
$911$		−	15.0916i		−	0.500006i	0.968245	−	0.250003i	$-0.0804316\pi$
$912$	0.336929	+	1.69896i	0.0111568	+	0.0562583i
$913$	−17.5122	−	17.5122i	−0.579569	−	0.579569i
$914$	−8.81552			−0.291591
$915$	−10.4288	−	0.943175i	−0.344765	−	0.0311804i
$916$	15.8734			0.524473
$917$	15.2974	+	15.2974i	0.505164	+	0.505164i
$918$	8.31563	+	12.4918i	0.274457	+	0.412292i
$919$			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
$927$	5.77021	+	2.39788i	0.189519	+	0.0787569i
$928$	3.88456	+	3.88456i	0.127517	+	0.127517i
$929$	−6.96249			−0.228432			−0.114216	−	0.993456i	$-0.536436\pi$
$929$	−6.96249			−0.228432			−0.114216	+	0.993456i	$0.536436\pi$
$930$	12.5880	+	15.0912i	0.412775	+	0.494862i
$931$	−5.70402			−0.186942
$932$	−15.6011	−	15.6011i	−0.511032	−	0.511032i
$933$	−2.73957	−	13.8143i	−0.0896896	−	0.452260i
$934$			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	$0.105189\pi$
$941$			19.9072i			0.648957i	−0.945893	+	0.324479i	$0.894811\pi$
$942$	6.32682	−	1.25470i	0.206139	−	0.0408803i
$943$	−11.5109	−	11.5109i	−0.374845	−	0.374845i
$944$	−1.26612			−0.0412085
$945$	−6.15542	+	11.7076i	−0.200236	+	0.380848i
$946$	2.87128			0.0933533
$947$	−27.8351	−	27.8351i	−0.904520	−	0.904520i	0.0913033	−	0.995823i	$-0.470897\pi$
$947$	−27.8351	−	27.8351i	−0.904520	−	0.904520i	−0.995823	+	0.0913033i	$0.970897\pi$
$948$	25.5293	−	5.06282i	0.829152	−	0.164433i
$949$		−	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	−0.858768	−	0.512365i	$-0.828769\pi$
$953$	−10.6937	+	10.6937i	−0.346402	+	0.346402i	0.512365	+	0.858768i	$0.328769\pi$
$954$	−12.4273	+	5.13081i	−0.402349	+	0.166116i
$955$	15.6374	−	53.1836i	0.506015	−	1.72098i
$956$			4.84839i			0.156808i
$957$	−5.84141	−	29.4553i	−0.188826	−	0.952155i
$958$	−12.7420	−	12.7420i	−0.411674	−	0.411674i
$959$	−24.5098			−0.791462
$960$	−0.348848	+	3.85724i	−0.0112590	+	0.124492i
$961$	−5.25318			−0.169457
$962$	28.0124	+	28.0124i	0.903155	+	0.903155i
$963$	−34.6608	−	14.4037i	−1.11693	−	0.464154i
$964$		−	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	$-0.945476\pi$
$971$		−	10.6230i		−	0.340909i	0.985366	−	0.170455i	$-0.0545236\pi$
$972$	−12.9364	−	8.69774i	−0.414934	−	0.278980i
$973$	−12.1157	−	12.1157i	−0.388412	−	0.388412i
$974$	4.70920			0.150893
$975$	13.3040	+	30.6739i	0.426068	+	0.982351i
$976$	−2.70369			−0.0865429
$977$	4.47372	+	4.47372i	0.143127	+	0.143127i	0.775040	−	0.631913i	$-0.217730\pi$
$977$	4.47372	+	4.47372i	0.143127	+	0.143127i	−0.631913	+	0.775040i	$0.717730\pi$
$978$	−4.04687	−	20.4064i	−0.129405	−	0.652524i
$979$		−	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	$-0.496722\pi$
$983$	31.6740	−	31.6740i	1.01024	−	1.01024i	0.999947	−	0.0102974i	$-0.00327781\pi$
$984$	−9.09679	−	6.08585i	−0.289995	−	0.194010i
$985$	2.52359	+	4.62568i	0.0804084	+	0.147386i
$986$		−	15.8655i		−	0.505262i
$987$	−8.82320	+	1.74977i	−0.280846	+	0.0556957i
$988$	2.72994	+	2.72994i	0.0868509	+	0.0868509i
$989$	−2.34383			−0.0745296
$990$	13.3088	−	16.4639i	0.422982	−	0.523258i
$991$	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
$993$	−49.6548	+	9.84724i	−1.57575	+	0.312493i
$994$			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.533.1	yes	36
3.2	odd	2	inner	570.2.k.b.533.14	yes	36
5.2	odd	4	inner	570.2.k.b.77.14	yes	36
15.2	even	4	inner	570.2.k.b.77.1	✓	36

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

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)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.69896 + 0.336929i) q^{3} +1.00000i q^{4} +(2.14526 + 0.630765i) q^{5} +(1.43959 + 0.963104i) q^{6} +(0.804978 - 0.804978i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.77296 - 1.14486i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.69896 + 0.336929i) 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} +(-0.336929 - 1.69896i) q^{12} +(-2.72994 - 2.72994i) q^{13} -1.13841 q^{14} +(-3.85724 - 0.348848i) q^{15} -1.00000 q^{16} +(2.04213 + 2.04213i) q^{17} +(-2.77032 - 1.15124i) 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} +(-4.32542 + 2.87936i) q^{27} +(0.804978 + 0.804978i) q^{28} +5.49359 q^{29} +(2.48081 + 2.97415i) q^{30} +5.07413 q^{31} +(0.707107 + 0.707107i) q^{32} +(-1.06331 - 5.36176i) 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} +(1.93412 - 0.383563i) q^{42} +(0.643335 + 0.643335i) q^{43} -3.15590 q^{44} +(6.67085 - 0.706935i) q^{45} +2.57617 q^{46} +(3.22573 + 3.22573i) q^{47} +(1.69896 - 0.336929i) 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} +(-0.336929 - 1.69896i) q^{57} +(-3.88456 - 3.88456i) q^{58} +1.26612 q^{59} +(0.348848 - 3.85724i) q^{60} +2.70369 q^{61} +(-3.58795 - 3.58795i) q^{62} +(1.31058 - 3.15376i) 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} +(1.15124 - 2.77032i) q^{72} +(3.61892 + 3.61892i) q^{73} -10.2612 q^{74} +(-8.05474 - 3.18138i) q^{75} -1.00000 q^{76} +(2.54043 + 2.54043i) q^{77} +(-1.30079 - 6.55921i) 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} +(-9.33342 + 1.85095i) q^{87} +(2.23156 + 2.23156i) q^{88} -3.27340 q^{89} +(-5.21688 - 4.21712i) q^{90} -4.39508 q^{91} +(-1.82163 - 1.82163i) q^{92} +(-8.62077 + 1.70962i) 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

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