LMFDB - Embedded newform 640.2.bm.a.101.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [640,2,Mod(21,640)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("640.21"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(640, base_ring=CyclotomicField(32)) chi = DirichletCharacter(H, H._module([0, 13, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.bm (of order $32$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			101.16
Character	$\chi$	$=$	640.101
Dual form			640.2.bm.a.621.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.03208 + 0.966858i) q^{2} +(-1.37880 + 0.736983i) q^{3} +(0.130372 - 1.99575i) q^{4} +(-0.634393 - 0.773010i) q^{5} +(0.710470 - 2.09372i) q^{6} +(-3.10331 + 2.07356i) q^{7} +(1.79505 + 2.18582i) q^{8} +(-0.308772 + 0.462110i) q^{9} +(1.40213 + 0.184439i) q^{10} +(-2.82139 + 0.855861i) q^{11} +(1.29107 + 2.84781i) q^{12} +(2.98376 + 2.44871i) q^{13} +(1.19802 - 5.14054i) q^{14} +(1.44440 + 0.598288i) q^{15} +(-3.96601 - 0.520378i) q^{16} +(0.554169 - 0.229544i) q^{17} +(-0.128118 - 0.775472i) q^{18} +(0.0238327 + 0.241977i) q^{19} +(-1.62544 + 1.16531i) q^{20} +(2.75065 - 5.14611i) q^{21} +(2.08440 - 3.61120i) q^{22} +(1.30055 - 0.258696i) q^{23} +(-4.08592 - 1.69088i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(-5.44703 + 0.357613i) q^{26} +(0.544888 - 5.53234i) q^{27} +(3.73372 + 6.46375i) q^{28} +(2.17948 - 7.18478i) q^{29} +(-2.06919 + 0.779045i) q^{30} +(-7.25600 - 7.25600i) q^{31} +(4.59636 - 3.29749i) q^{32} +(3.25938 - 3.25938i) q^{33} +(-0.350009 + 0.772710i) q^{34} +(3.57160 + 1.08343i) q^{35} +(0.881998 + 0.676476i) q^{36} +(1.61093 + 0.158662i) q^{37} +(-0.258555 - 0.226697i) q^{38} +(-5.91866 - 1.17729i) q^{39} +(0.550893 - 2.77426i) q^{40} +(-1.48887 - 7.48507i) q^{41} +(2.13667 + 7.97068i) q^{42} +(-4.15462 - 2.22069i) q^{43} +(1.34025 + 5.74237i) q^{44} +(0.553098 - 0.0544754i) q^{45} +(-1.09215 + 1.52445i) q^{46} +(1.45195 + 3.50531i) q^{47} +(5.85183 - 2.20538i) q^{48} +(2.65207 - 6.40266i) q^{49} +(-0.746931 - 1.20087i) q^{50} +(-0.594916 + 0.724908i) q^{51} +(5.27600 - 5.63559i) q^{52} +(0.554534 + 1.82806i) q^{53} +(4.78662 + 6.23663i) q^{54} +(2.45146 + 1.63801i) q^{55} +(-10.1030 - 3.06112i) q^{56} +(-0.211194 - 0.316073i) q^{57} +(4.69727 + 9.52250i) q^{58} +(11.5747 - 9.49908i) q^{59} +(1.38234 - 2.80465i) q^{60} +(4.17502 + 7.81091i) q^{61} +(14.5043 + 0.473240i) q^{62} -2.07433i q^{63} +(-1.55560 + 7.84730i) q^{64} -3.85992i q^{65} +(-0.212578 + 6.51529i) q^{66} +(3.16225 + 5.91615i) q^{67} +(-0.385864 - 1.13591i) q^{68} +(-1.60255 + 1.31518i) q^{69} +(-4.73370 + 2.33504i) q^{70} +(0.0539030 + 0.0806715i) q^{71} +(-1.56435 + 0.154591i) q^{72} +(-5.76292 - 3.85066i) q^{73} +(-1.81601 + 1.39378i) q^{74} +(-0.453832 - 1.49608i) q^{75} +(0.486033 - 0.0160170i) q^{76} +(6.98097 - 8.50634i) q^{77} +(7.24680 - 4.50744i) q^{78} +(-0.358853 + 0.866348i) q^{79} +(2.11375 + 3.39589i) q^{80} +(2.68789 + 6.48914i) q^{81} +(8.77364 + 6.28565i) q^{82} +(-1.07931 + 0.106303i) q^{83} +(-9.91172 - 6.16051i) q^{84} +(-0.529001 - 0.282757i) q^{85} +(6.43498 - 1.72500i) q^{86} +(2.29000 + 11.5126i) q^{87} +(-6.93530 - 4.63074i) q^{88} +(7.59436 + 1.51061i) q^{89} +(-0.518171 + 0.590990i) q^{90} +(-14.3371 - 1.41208i) q^{91} +(-0.346737 - 2.62930i) q^{92} +(15.3521 + 4.65701i) q^{93} +(-4.88766 - 2.21393i) q^{94} +(0.171932 - 0.171932i) q^{95} +(-3.90726 + 7.93401i) q^{96} +(-11.9444 - 11.9444i) q^{97} +(3.45332 + 9.17222i) q^{98} +(0.475665 - 1.56806i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) $ 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{9}{32}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.03208	+	0.966858i	−0.729790	+	0.683672i
$2$	−1.03208	+	0.966858i	−0.729790	+	0.683672i
$3$	−1.37880	+	0.736983i	−0.796049	+	0.425497i	−0.818682	−	0.574247i	$-0.805295\pi$
$3$	−1.37880	+	0.736983i	−0.796049	+	0.425497i	0.0226332	+	0.999744i	$0.492795\pi$
$4$	0.130372	−	1.99575i	0.0651859	−	0.997873i
$5$	−0.634393	−	0.773010i	−0.283709	−	0.345701i
$5$	−0.634393	−	0.773010i	−0.283709	−	0.345701i
$6$	0.710470	−	2.09372i	0.290048	−	0.854760i
$7$	−3.10331	+	2.07356i	−1.17294	+	0.783733i	−0.980296	−	0.197535i	$-0.936706\pi$
$7$	−3.10331	+	2.07356i	−1.17294	+	0.783733i	−0.192644	+	0.981269i	$0.561706\pi$
$8$	1.79505	+	2.18582i	0.634646	+	0.772803i
$9$	−0.308772	+	0.462110i	−0.102924	+	0.154037i
$10$	1.40213	+	0.184439i	0.443394	+	0.0583248i
$11$	−2.82139	+	0.855861i	−0.850682	+	0.258052i	−0.685375	−	0.728190i	$-0.740362\pi$
$11$	−2.82139	+	0.855861i	−0.850682	+	0.258052i	−0.165307	+	0.986242i	$0.552862\pi$
$12$	1.29107	+	2.84781i	0.372701	+	0.822092i
$13$	2.98376	+	2.44871i	0.827547	+	0.679150i	0.949631	−	0.313370i	$-0.101458\pi$
$13$	2.98376	+	2.44871i	0.827547	+	0.679150i	−0.122084	+	0.992520i	$0.538958\pi$
$14$	1.19802	−	5.14054i	0.320183	−	1.37387i
$15$	1.44440	+	0.598288i	0.372941	+	0.154477i
$16$	−3.96601	−	0.520378i	−0.991502	−	0.130094i
$17$	0.554169	−	0.229544i	0.134406	−	0.0556727i	−0.314467	−	0.949268i	$-0.601826\pi$
$17$	0.554169	−	0.229544i	0.134406	−	0.0556727i	0.448873	+	0.893596i	$0.351826\pi$
$18$	−0.128118	−	0.775472i	−0.0301976	−	0.182780i
$19$	0.0238327	+	0.241977i	0.00546759	+	0.0555134i	0.997531	−	0.0702223i	$-0.0223709\pi$
$19$	0.0238327	+	0.241977i	0.00546759	+	0.0555134i	−0.992064	+	0.125736i	$0.959871\pi$
$20$	−1.62544	+	1.16531i	−0.363459	+	0.260571i
$21$	2.75065	−	5.14611i	0.600242	−	1.12297i
$22$	2.08440	−	3.61120i	0.444397	−	0.769911i
$23$	1.30055	−	0.258696i	0.271184	−	0.0539419i	−0.0576248	−	0.998338i	$-0.518353\pi$
$23$	1.30055	−	0.258696i	0.271184	−	0.0539419i	0.328809	+	0.944396i	$0.393353\pi$
$24$	−4.08592	−	1.69088i	−0.834035	−	0.345149i
$25$	−0.195090	+	0.980785i	−0.0390181	+	0.196157i
$26$	−5.44703	+	0.357613i	−1.06825	+	0.0701337i
$27$	0.544888	−	5.53234i	0.104864	−	1.06470i
$28$	3.73372	+	6.46375i	0.705607	+	1.22153i
$29$	2.17948	−	7.18478i	0.404719	−	1.33418i	−0.483735	−	0.875215i	$-0.660720\pi$
$29$	2.17948	−	7.18478i	0.404719	−	1.33418i	0.888454	−	0.458966i	$-0.151780\pi$
$30$	−2.06919	+	0.779045i	−0.377780	+	0.142233i
$31$	−7.25600	−	7.25600i	−1.30322	−	1.30322i	−0.926211	−	0.377005i	$-0.876954\pi$
$31$	−7.25600	−	7.25600i	−1.30322	−	1.30322i	−0.377005	−	0.926211i	$-0.623046\pi$
$32$	4.59636	−	3.29749i	0.812530	−	0.582920i
$33$	3.25938	−	3.25938i	0.567385	−	0.567385i
$34$	−0.350009	+	0.772710i	−0.0600261	+	0.132519i
$35$	3.57160	+	1.08343i	0.603711	+	0.183134i
$36$	0.881998	+	0.676476i	0.147000	+	0.112746i
$37$	1.61093	+	0.158662i	0.264834	+	0.0260839i	0.229563	−	0.973294i	$-0.426270\pi$
$37$	1.61093	+	0.158662i	0.264834	+	0.0260839i	0.0352716	+	0.999378i	$0.488770\pi$
$38$	−0.258555	−	0.226697i	−0.0419431	−	0.0367751i
$39$	−5.91866	−	1.17729i	−0.947744	−	0.188518i
$40$	0.550893	−	2.77426i	0.0871038	−	0.438649i
$41$	−1.48887	−	7.48507i	−0.232523	−	1.16897i	−0.903863	−	0.427822i	$-0.859281\pi$
$41$	−1.48887	−	7.48507i	−0.232523	−	1.16897i	0.671340	−	0.741150i	$-0.265719\pi$
$42$	2.13667	+	7.97068i	0.329695	+	1.22990i
$43$	−4.15462	−	2.22069i	−0.633573	−	0.338652i	0.123149	−	0.992388i	$-0.460701\pi$
$43$	−4.15462	−	2.22069i	−0.633573	−	0.338652i	−0.756722	+	0.653736i	$0.773201\pi$
$44$	1.34025	+	5.74237i	0.202050	+	0.865694i
$45$	0.553098	−	0.0544754i	0.0824510	−	0.00812072i
$46$	−1.09215	+	1.52445i	−0.161029	+	0.224767i
$47$	1.45195	+	3.50531i	0.211788	+	0.511302i	0.993698	−	0.112089i	$-0.0357543\pi$
$47$	1.45195	+	3.50531i	0.211788	+	0.511302i	−0.781910	+	0.623392i	$0.785754\pi$
$48$	5.85183	−	2.20538i	0.844639	−	0.318319i
$49$	2.65207	−	6.40266i	0.378867	−	0.914665i
$50$	−0.746931	−	1.20087i	−0.105632	−	0.169829i
$51$	−0.594916	+	0.724908i	−0.0833050	+	0.101507i
$52$	5.27600	−	5.63559i	0.731650	−	0.781516i
$53$	0.554534	+	1.82806i	0.0761712	+	0.251103i	0.986754	−	0.162224i	$-0.0518667\pi$
$53$	0.554534	+	1.82806i	0.0761712	+	0.251103i	−0.910583	+	0.413327i	$0.864367\pi$
$54$	4.78662	+	6.23663i	0.651376	+	0.848698i
$55$	2.45146	+	1.63801i	0.330555	+	0.220870i
$56$	−10.1030	−	3.06112i	−1.35007	−	0.409059i
$57$	−0.211194	−	0.316073i	−0.0279733	−	0.0418650i
$58$	4.69727	+	9.52250i	0.616782	+	1.25037i
$59$	11.5747	−	9.49908i	1.50689	−	1.23667i	0.611624	−	0.791149i	$-0.290517\pi$
$59$	11.5747	−	9.49908i	1.50689	−	1.23667i	0.895269	−	0.445526i	$-0.146983\pi$
$60$	1.38234	−	2.80465i	0.178459	−	0.362078i
$61$	4.17502	+	7.81091i	0.534556	+	1.00008i	0.993737	+	0.111742i	$0.0356430\pi$
$61$	4.17502	+	7.81091i	0.534556	+	1.00008i	−0.459181	+	0.888343i	$0.651857\pi$
$62$	14.5043	+	0.473240i	1.84205	+	0.0601016i
$63$		−	2.07433i		−	0.261341i
$64$	−1.55560	+	7.84730i	−0.194450	+	0.980913i
$65$		−	3.85992i		−	0.478765i
$66$	−0.212578	+	6.51529i	−0.0261666	+	0.801976i
$67$	3.16225	+	5.91615i	0.386330	+	0.722773i	0.997643	−	0.0686160i	$-0.0218583\pi$
$67$	3.16225	+	5.91615i	0.386330	+	0.722773i	−0.611313	+	0.791389i	$0.709358\pi$
$68$	−0.385864	−	1.13591i	−0.0467929	−	0.137749i
$69$	−1.60255	+	1.31518i	−0.192924	+	0.158329i
$70$	−4.73370	+	2.33504i	−0.565786	+	0.279091i
$71$	0.0539030	+	0.0806715i	0.00639710	+	0.00957394i	0.834654	−	0.550774i	$-0.185667\pi$
$71$	0.0539030	+	0.0806715i	0.00639710	+	0.00957394i	−0.828257	+	0.560348i	$0.810667\pi$
$72$	−1.56435	+	0.154591i	−0.184360	+	0.0182187i
$73$	−5.76292	−	3.85066i	−0.674499	−	0.450686i	0.170568	−	0.985346i	$-0.445440\pi$
$73$	−5.76292	−	3.85066i	−0.674499	−	0.450686i	−0.845067	+	0.534660i	$0.820440\pi$
$74$	−1.81601	+	1.39378i	−0.211106	+	0.162024i
$75$	−0.453832	−	1.49608i	−0.0524040	−	0.172753i
$76$	0.486033	−	0.0160170i	0.0557518	−	0.00183728i
$77$	6.98097	−	8.50634i	0.795556	−	0.969387i
$78$	7.24680	−	4.50744i	0.820538	−	0.510367i
$79$	−0.358853	+	0.866348i	−0.0403741	+	0.0974718i	−0.942780	−	0.333415i	$-0.891799\pi$
$79$	−0.358853	+	0.866348i	−0.0403741	+	0.0974718i	0.902406	+	0.430887i	$0.141799\pi$
$80$	2.11375	+	3.39589i	0.236324	+	0.379672i
$81$	2.68789	+	6.48914i	0.298654	+	0.721015i
$82$	8.77364	+	6.28565i	0.968886	+	0.694134i
$83$	−1.07931	+	0.106303i	−0.118470	+	0.0116682i	−0.157078	−	0.987586i	$-0.550207\pi$
$83$	−1.07931	+	0.106303i	−0.118470	+	0.0116682i	0.0386086	+	0.999254i	$0.487707\pi$
$84$	−9.91172	−	6.16051i	−1.08146	−	0.672167i
$85$	−0.529001	−	0.282757i	−0.0573782	−	0.0306693i
$86$	6.43498	−	1.72500i	0.693902	−	0.186011i
$87$	2.29000	+	11.5126i	0.245514	+	1.23428i
$88$	−6.93530	−	4.63074i	−0.739305	−	0.493639i
$89$	7.59436	+	1.51061i	0.805000	+	0.160125i	0.580405	−	0.814328i	$-0.302894\pi$
$89$	7.59436	+	1.51061i	0.805000	+	0.160125i	0.224595	+	0.974452i	$0.427894\pi$
$90$	−0.518171	+	0.590990i	−0.0546200	+	0.0622958i
$91$	−14.3371	−	1.41208i	−1.50294	−	0.148026i
$92$	−0.346737	−	2.62930i	−0.0361498	−	0.274124i
$93$	15.3521	+	4.65701i	1.59194	+	0.482909i
$94$	−4.88766	−	2.21393i	−0.504124	−	0.228349i
$95$	0.171932	−	0.171932i	0.0176398	−	0.0176398i
$96$	−3.90726	+	7.93401i	−0.398783	+	0.809762i
$97$	−11.9444	−	11.9444i	−1.21277	−	1.21277i	−0.970113	−	0.242652i	$-0.921983\pi$
$97$	−11.9444	−	11.9444i	−1.21277	−	1.21277i	−0.242652	−	0.970113i	$-0.578017\pi$
$98$	3.45332	+	9.17222i	0.348838	+	0.926534i
$99$	0.475665	−	1.56806i	0.0478062	−	0.157596i
$100$	1.93196	+	0.517217i	0.193196	+	0.0517217i
$101$	0.732419	−	7.43637i	0.0728784	−	0.739947i	−0.887418	−	0.460965i	$-0.847503\pi$
$101$	0.732419	−	7.43637i	0.0728784	−	0.739947i	0.960297	−	0.278981i	$-0.0899967\pi$
$102$	−0.0868824	−	1.32336i	−0.00860264	−	0.131032i
$103$	−1.73086	+	8.70161i	−0.170546	+	0.857395i	0.796860	+	0.604165i	$0.206493\pi$
$103$	−1.73086	+	8.70161i	−0.170546	+	0.857395i	−0.967406	+	0.253230i	$0.918507\pi$
$104$	0.00356566	+	10.9175i	0.000349642	+	1.07055i
$105$	−5.72299	+	1.13837i	−0.558507	+	0.111094i
$106$	−2.33979	−	1.35054i	−0.227261	−	0.131176i
$107$	0.486534	−	0.910241i	0.0470350	−	0.0879963i	−0.857306	−	0.514808i	$-0.827863\pi$
$107$	0.486534	−	0.910241i	0.0470350	−	0.0879963i	0.904341	+	0.426812i	$0.140363\pi$
$108$	−10.9701	−	1.80872i	−1.05560	−	0.174044i
$109$	−0.144710	−	1.46927i	−0.0138608	−	0.140731i	0.985764	−	0.168137i	$-0.0537751\pi$
$109$	−0.144710	−	1.46927i	−0.0138608	−	0.140731i	−0.999624	+	0.0274065i	$0.991275\pi$
$110$	−4.11383	+	0.679656i	−0.392238	+	0.0648027i
$111$	−2.33807	+	0.968461i	−0.221920	+	0.0919222i
$112$	13.3868	−	6.60888i	1.26493	−	0.624480i
$113$	−18.5238	−	7.67281i	−1.74257	−	0.721797i	−0.998561	−	0.0536299i	$-0.982921\pi$
$113$	−18.5238	−	7.67281i	−1.74257	−	0.721797i	−0.744011	−	0.668167i	$-0.767079\pi$
$114$	0.523566	+	0.122018i	0.0490365	+	0.0114281i
$115$	−1.02504	−	0.841227i	−0.0955853	−	0.0784448i
$116$	−14.0549	−	5.28638i	−1.30496	−	0.490828i
$117$	−2.05287	+	0.622733i	−0.189788	+	0.0575716i
$118$	−2.76170	+	20.9948i	−0.254235	+	1.93273i
$119$	−1.24378	+	1.86145i	−0.114017	+	0.170639i
$120$	1.28501	+	4.23114i	0.117305	+	0.386249i
$121$	−1.91840	+	1.28183i	−0.174400	+	0.116530i
$122$	−11.8610	−	4.02482i	−1.07384	−	0.364390i
$123$	7.56922	+	9.22312i	0.682494	+	0.831621i
$124$	−15.4271	+	13.5352i	−1.38540	+	1.21549i
$125$	0.881921	−	0.471397i	0.0788814	−	0.0421630i
$126$	2.00558	+	2.14087i	0.178671	+	0.190724i
$127$	−4.18421			−0.371289			−0.185644	−	0.982617i	$-0.559437\pi$
$127$	−4.18421			−0.371289			−0.185644	+	0.982617i	$0.559437\pi$
$128$	−5.98173	−	9.60307i	−0.528715	−	0.848800i
$129$	7.36498			0.648451
$130$	3.73200	+	3.98375i	0.327318	+	0.349398i
$131$	−9.07591	+	4.85118i	−0.792966	+	0.423849i	−0.817556	−	0.575848i	$-0.804672\pi$
$131$	−9.07591	+	4.85118i	−0.792966	+	0.423849i	0.0245904	+	0.999698i	$0.492172\pi$
$132$	−6.07996	−	6.92982i	−0.529192	−	0.603163i
$133$	−0.575716	−	0.701512i	−0.0499209	−	0.0608288i
$134$	−8.98377	−	3.04849i	−0.776079	−	0.263349i
$135$	−4.62223	+	3.08847i	−0.397818	+	0.265813i
$136$	1.49650	+	0.799269i	0.128324	+	0.0685367i
$137$	3.93533	−	5.88964i	0.336218	−	0.503186i	−0.624382	−	0.781119i	$-0.714649\pi$
$137$	3.93533	−	5.88964i	0.336218	−	0.503186i	0.960600	+	0.277933i	$0.0896493\pi$
$138$	0.382365	−	2.90680i	0.0325491	−	0.247443i
$139$	10.3632	−	3.14363i	0.878992	−	0.266639i	0.181637	−	0.983366i	$-0.441860\pi$
$139$	10.3632	−	3.14363i	0.878992	−	0.266639i	0.697355	+	0.716726i	$0.254360\pi$
$140$	2.62790	−	6.98677i	0.222098	−	0.590490i
$141$	−4.58529	−	3.76305i	−0.386151	−	0.316906i
$142$	−0.133630	−	0.0311428i	−0.0112140	−	0.00261345i
$143$	−10.5141	−	4.35509i	−0.879235	−	0.364191i
$144$	1.46506	−	1.67205i	0.122089	−	0.139338i
$145$	−6.93656	+	2.87322i	−0.576050	+	0.238608i
$146$	9.67083	−	1.59774i	0.800364	−	0.132230i
$147$	1.06198	+	10.7825i	0.0875909	+	0.889325i
$148$	0.526669	−	3.19431i	0.0432919	−	0.262571i
$149$	8.55529	−	16.0058i	0.700877	−	1.31125i	−0.239428	−	0.970914i	$-0.576960\pi$
$149$	8.55529	−	16.0058i	0.700877	−	1.31125i	0.940305	−	0.340334i	$-0.110540\pi$
$150$	1.91489	+	1.10528i	0.156350	+	0.0902460i
$151$	0.943368	−	0.187647i	0.0767702	−	0.0152705i	−0.156556	−	0.987669i	$-0.550039\pi$
$151$	0.943368	−	0.187647i	0.0767702	−	0.0152705i	0.233326	+	0.972399i	$0.425039\pi$
$152$	−0.486138	+	0.486455i	−0.0394310	+	0.0394567i
$153$	−0.0650371	+	0.326963i	−0.00525794	+	0.0264334i
$154$	1.01951	+	15.5288i	0.0821545	+	1.25135i
$155$	−1.00581	+	10.2121i	−0.0807883	+	0.820258i
$156$	−3.12121	+	11.6587i	−0.249897	+	0.933440i
$157$	−4.38848	+	14.4669i	−0.350239	+	1.15458i	0.588078	+	0.808804i	$0.299885\pi$
$157$	−4.38848	+	14.4669i	−0.350239	+	1.15458i	−0.938317	+	0.345777i	$0.887615\pi$
$158$	−0.467271	−	1.24110i	−0.0371741	−	0.0987366i
$159$	−2.11184	−	2.11184i	−0.167479	−	0.167479i
$160$	−5.46490	−	1.46113i	−0.432038	−	0.115512i
$161$	−3.49960	+	3.49960i	−0.275807	+	0.275807i
$162$	−9.04819	−	4.09849i	−0.710893	−	0.322008i
$163$	3.19174	+	0.968202i	0.249996	+	0.0758355i	0.412796	−	0.910824i	$-0.364552\pi$
$163$	3.19174	+	0.968202i	0.249996	+	0.0758355i	−0.162800	+	0.986659i	$0.552052\pi$
$164$	−15.1324	+	1.99557i	−1.18164	+	0.155828i
$165$	−4.58726	−	0.451806i	−0.357118	−	0.0351730i
$166$	1.01115	−	1.15325i	0.0784807	−	0.0895097i
$167$	−23.9240	−	4.75877i	−1.85129	−	0.368245i	−0.861155	−	0.508343i	$-0.830258\pi$
$167$	−23.9240	−	4.75877i	−1.85129	−	0.368245i	−0.990138	+	0.140098i	$0.955258\pi$
$168$	16.1860	−	3.22509i	1.24878	−	0.248821i
$169$	0.370480	+	1.86253i	0.0284985	+	0.143272i
$170$	0.819356	−	0.219641i	0.0628418	−	0.0168457i
$171$	−0.119179	−	0.0637025i	−0.00911384	−	0.00487145i
$172$	−4.97358	+	8.00205i	−0.379232	+	0.610150i
$173$	14.8282	−	1.46045i	1.12736	−	0.111036i	0.482904	−	0.875673i	$-0.339582\pi$
$173$	14.8282	−	1.46045i	1.12736	−	0.111036i	0.644460	+	0.764638i	$0.277082\pi$
$174$	−13.4945	−	9.66780i	−1.02302	−	0.732914i
$175$	−1.42830	−	3.44821i	−0.107969	−	0.260660i
$176$	11.6350	−	1.92616i	0.877024	−	0.145190i
$177$	−8.95846	+	21.6276i	−0.673359	+	1.62563i
$178$	−9.29852	+	5.78360i	−0.696954	+	0.433499i
$179$	9.31809	−	11.3541i	0.696467	−	0.848647i	−0.297905	−	0.954596i	$-0.596288\pi$
$179$	9.31809	−	11.3541i	0.696467	−	0.848647i	0.994372	+	0.105948i	$0.0337878\pi$
$180$	−0.0366108	−	1.11095i	−0.00272880	−	0.0828050i
$181$	4.24645	+	13.9987i	0.315636	+	1.04051i	0.960979	+	0.276620i	$0.0892143\pi$
$181$	4.24645	+	13.9987i	0.315636	+	1.04051i	−0.645343	+	0.763893i	$0.723286\pi$
$182$	16.1623	−	12.4046i	1.19803	−	0.919487i
$183$	−11.5130	−	7.69275i	−0.851066	−	0.568664i
$184$	2.90002	+	2.37840i	0.213792	+	0.175338i
$185$	−0.899313	−	1.34592i	−0.0661188	−	0.0989537i
$186$	−20.3472	+	10.0369i	−1.49193	+	0.735941i
$187$	−1.36707	+	1.12193i	−0.0999701	+	0.0820433i
$188$	7.18501	−	2.44073i	0.524020	−	0.178008i
$189$	9.78070	+	18.2984i	0.711441	+	1.33101i
$190$	−0.0112135	+	0.343681i	−0.000813512	+	0.0249332i
$191$		−	8.71045i		−	0.630266i	−0.949047	−	0.315133i	$-0.897951\pi$
$191$		−	8.71045i		−	0.630266i	0.949047	−	0.315133i	$-0.102049\pi$
$192$	−3.63847	−	11.9663i	−0.262584	−	0.863592i
$193$		−	18.2879i		−	1.31639i	−0.752847	−	0.658196i	$-0.771320\pi$
$193$		−	18.2879i		−	1.31639i	0.752847	−	0.658196i	$-0.228680\pi$
$194$	23.8760	+	0.779017i	1.71420	+	0.0559302i
$195$	2.84470	+	5.32205i	0.203713	+	0.381120i
$196$	−12.4323	−	6.12758i	−0.888023	−	0.437684i
$197$	−0.959496	+	0.787438i	−0.0683612	+	0.0561026i	−0.667953	−	0.744203i	$-0.732829\pi$
$197$	−0.959496	+	0.787438i	−0.0683612	+	0.0561026i	0.599592	+	0.800306i	$0.295329\pi$
$198$	1.02517	+	2.07826i	0.0728554	+	0.147696i
$199$	15.0952	+	22.5915i	1.07007	+	1.60147i	0.759012	+	0.651077i	$0.225682\pi$
$199$	15.0952	+	22.5915i	1.07007	+	1.60147i	0.311055	+	0.950392i	$0.399318\pi$
$200$	−2.49401	+	1.33413i	−0.176353	+	0.0943369i
$201$	−8.72020	−	5.82665i	−0.615076	−	0.410980i
$202$	6.43400	+	8.38306i	0.452695	+	0.589830i
$203$	8.13451	+	26.8159i	0.570930	+	1.88211i
$204$	1.36917	+	1.28181i	0.0958612	+	0.0897446i
$205$	−4.84151	+	5.89939i	−0.338146	+	0.412032i
$206$	−6.62684	−	10.6542i	−0.461714	−	0.742316i
$207$	−0.282028	+	0.680877i	−0.0196023	+	0.0473242i
$208$	−10.5594	−	11.2643i	−0.732160	−	0.781038i
$209$	−0.274340	−	0.662316i	−0.0189765	−	0.0458134i
$210$	4.80593	−	6.70821i	0.331641	−	0.462910i
$211$	−19.1737	+	1.88845i	−1.31997	+	0.130006i	−0.733349	−	0.679852i	$-0.762044\pi$
$211$	−19.1737	+	1.88845i	−1.31997	+	0.130006i	−0.586625	+	0.809858i	$0.699544\pi$
$212$	3.72063	−	0.868383i	0.255534	−	0.0596408i
$213$	−0.133775	−	0.0715041i	−0.00916609	−	0.00489938i
$214$	0.377933	+	1.40985i	0.0258349	+	0.0963753i
$215$	0.919045	+	4.62035i	0.0626784	+	0.315105i
$216$	13.0708	−	8.73979i	0.889354	−	0.594667i
$217$	37.5634	+	7.47182i	2.54997	+	0.507220i
$218$	1.56993	+	1.37649i	0.106329	+	0.0932275i
$219$	10.7838	+	1.06211i	0.728700	+	0.0717707i
$220$	3.58866	−	4.67895i	0.241948	−	0.315455i
$221$	2.21560	+	0.672094i	0.149037	+	0.0452099i
$222$	1.47671	−	3.26011i	0.0991102	−	0.218804i
$223$	17.7574	−	17.7574i	1.18912	−	1.18912i	0.211811	−	0.977311i	$-0.432064\pi$
$223$	17.7574	−	17.7574i	1.18912	−	1.18912i	0.977311	−	0.211811i	$-0.0679363\pi$
$224$	−7.42636	+	19.7640i	−0.496194	+	1.32054i
$225$	−0.392992	−	0.392992i	−0.0261995	−	0.0261995i
$226$	26.5365	−	9.99094i	1.76518	−	0.664587i
$227$	4.46393	−	14.7156i	0.296281	−	0.976709i	−0.674808	−	0.737993i	$-0.735774\pi$
$227$	4.46393	−	14.7156i	0.296281	−	0.976709i	0.971089	−	0.238716i	$-0.0767264\pi$
$228$	−0.658336	+	0.380282i	−0.0435994	+	0.0251848i
$229$	−2.27545	+	23.1030i	−0.150366	+	1.52669i	0.563328	+	0.826233i	$0.309521\pi$
$229$	−2.27545	+	23.1030i	−0.150366	+	1.52669i	−0.713694	+	0.700458i	$0.752979\pi$
$230$	1.87127	−	0.122854i	0.123388	−	0.00810074i
$231$	−3.35632	+	16.8734i	−0.220830	+	1.11019i
$232$	19.6169	−	8.13309i	1.28791	−	0.533964i
$233$	7.18136	−	1.42846i	0.470467	−	0.0935816i	0.0458373	−	0.998949i	$-0.485404\pi$
$233$	7.18136	−	1.42846i	0.470467	−	0.0935816i	0.424629	+	0.905367i	$0.360404\pi$
$234$	1.51663	−	2.62755i	0.0991454	−	0.171768i
$235$	1.78854	−	3.34612i	0.116671	−	0.218277i
$236$	−17.4487	−	24.3385i	−1.13582	−	1.58430i
$237$	−0.143698	−	1.45899i	−0.00933417	−	0.0947714i
$238$	−0.516078	−	3.12372i	−0.0334524	−	0.202481i
$239$	6.86643	−	2.84417i	0.444152	−	0.183974i	−0.149387	−	0.988779i	$-0.547730\pi$
$239$	6.86643	−	2.84417i	0.444152	−	0.183974i	0.593540	+	0.804805i	$0.297730\pi$
$240$	−5.41714	−	3.12445i	−0.349675	−	0.201682i
$241$	−22.1748	−	9.18512i	−1.42841	−	0.591666i	−0.471449	−	0.881893i	$-0.656269\pi$
$241$	−22.1748	−	9.18512i	−1.42841	−	0.591666i	−0.956958	+	0.290227i	$0.906269\pi$
$242$	0.740588	−	3.17777i	0.0476068	−	0.204275i
$243$	4.40330	+	3.61370i	0.282472	+	0.231819i
$244$	16.1329	−	7.31396i	1.03280	−	0.468228i
$245$	−6.63177	+	2.01173i	−0.423689	+	0.128525i
$246$	−16.7295	−	2.20063i	−1.06663	−	0.140307i
$247$	−0.521421	+	0.780362i	−0.0331773	+	0.0496533i
$248$	2.83542	−	28.8852i	0.180049	−	1.83421i
$249$	1.40981	−	0.942002i	0.0893428	−	0.0596970i
$250$	−0.454438	+	1.33921i	−0.0287412	+	0.0846991i
$251$	−8.82969	−	10.7590i	−0.557325	−	0.679103i	0.415780	−	0.909465i	$-0.363509\pi$
$251$	−8.82969	−	10.7590i	−0.557325	−	0.679103i	−0.973105	+	0.230363i	$0.926009\pi$
$252$	−4.13983	−	0.270433i	−0.260785	−	0.0170357i
$253$	−3.44797	+	1.84298i	−0.216772	+	0.115867i
$254$	4.31843	−	4.04554i	0.270963	−	0.253840i
$255$	0.937772			0.0587256
$256$	15.4584	+	4.12764i	0.966151	+	0.257978i
$257$	−21.0320			−1.31194			−0.655971	−	0.754786i	$-0.727741\pi$
$257$	−21.0320			−1.31194			−0.655971	+	0.754786i	$0.727741\pi$
$258$	−7.60124	+	7.12089i	−0.473233	+	0.443327i
$259$	−5.32819	+	2.84798i	−0.331078	+	0.176965i
$260$	−7.70343	−	0.503225i	−0.477746	−	0.0312087i
$261$	2.64719	+	3.22562i	0.163857	+	0.199661i
$262$	4.67665	−	13.7819i	0.288925	−	0.851449i
$263$	−23.5766	+	15.7534i	−1.45380	+	0.971397i	−0.457167	+	0.889381i	$0.651136\pi$
$263$	−23.5766	+	15.7534i	−1.45380	+	0.971397i	−0.996631	+	0.0820161i	$0.973864\pi$
$264$	12.9751	+	1.27366i	0.798565	+	0.0783884i
$265$	1.06131	−	1.58837i	0.0651959	−	0.0975726i
$266$	1.27245	+	0.167380i	0.0780187	+	0.0102627i
$267$	−11.5844	+	3.51408i	−0.708952	+	0.215058i
$268$	12.2194	−	5.53975i	0.746419	−	0.338394i
$269$	−16.8584	−	13.8353i	−1.02787	−	0.843553i	−0.0400587	−	0.999197i	$-0.512754\pi$
$269$	−16.8584	−	13.8353i	−1.02787	−	0.843553i	−0.987813	+	0.155645i	$0.950254\pi$
$270$	1.78439	−	7.65658i	0.108594	−	0.465965i
$271$	−19.8583	−	8.22559i	−1.20631	−	0.499669i	−0.313276	−	0.949662i	$-0.601427\pi$
$271$	−19.8583	−	8.22559i	−1.20631	−	0.499669i	−0.893032	+	0.449993i	$0.851427\pi$
$272$	−2.31729	+	0.621997i	−0.140506	+	0.0377141i
$273$	20.8086	−	8.61921i	1.25940	−	0.521659i
$274$	1.63287	+	9.88347i	0.0986455	+	0.597083i
$275$	−0.288989	−	2.93415i	−0.0174267	−	0.176936i
$276$	2.41583	+	3.36974i	0.145416	+	0.202834i
$277$	−5.39122	+	10.0863i	−0.323927	+	0.606024i	−0.990196	−	0.139687i	$-0.955390\pi$
$277$	−5.39122	+	10.0863i	−0.323927	+	0.606024i	0.666269	+	0.745712i	$0.267890\pi$
$278$	−7.65615	+	13.2642i	−0.459185	+	0.795532i
$279$	5.59352	−	1.11262i	0.334875	−	0.0666108i
$280$	4.04302	+	9.75169i	0.241616	+	0.582775i
$281$	−1.97777	+	9.94294i	−0.117984	+	0.593146i	0.875879	+	0.482531i	$0.160282\pi$
$281$	−1.97777	+	9.94294i	−0.117984	+	0.593146i	−0.993863	+	0.110616i	$0.964718\pi$
$282$	8.37072	−	0.549561i	0.498469	−	0.0327259i
$283$	1.76125	−	17.8823i	0.104696	−	1.06299i	−0.789023	−	0.614364i	$-0.789413\pi$
$283$	1.76125	−	17.8823i	0.104696	−	1.06299i	0.893718	−	0.448628i	$-0.148087\pi$
$284$	0.168027	−	0.0970594i	0.00997058	−	0.00575941i
$285$	−0.110348	+	0.363770i	−0.00653647	+	0.0215479i
$286$	15.0622	−	5.67087i	0.890644	−	0.335325i
$287$	20.1412	+	20.1412i	1.18890	+	1.18890i
$288$	0.104577	+	3.14220i	0.00616226	+	0.185156i
$289$	−11.7664	+	11.7664i	−0.692141	+	0.692141i
$290$	4.38108	−	9.67205i	0.257266	−	0.567962i
$291$	25.2716	+	7.66606i	1.48145	+	0.449393i
$292$	−8.43626	+	10.9993i	−0.493695	+	0.643686i
$293$	3.78529	+	0.372818i	0.221139	+	0.0217803i	0.207980	−	0.978133i	$-0.433311\pi$
$293$	3.78529	+	0.372818i	0.221139	+	0.0217803i	0.0131591	+	0.999913i	$0.495811\pi$
$294$	−11.5212	−	10.1016i	−0.671929	−	0.589137i
$295$	−14.6858	−	2.92118i	−0.855039	−	0.170078i
$296$	2.54488	+	3.80600i	0.147918	+	0.221219i
$297$	3.19757	+	16.0752i	0.185542	+	0.932780i
$298$	6.64563	+	24.7910i	0.384971	+	1.43611i
$299$	4.51402	+	2.41279i	0.261052	+	0.139535i
$300$	−3.04497	+	0.710686i	−0.175801	+	0.0410315i
$301$	17.4978	−	1.72338i	1.00856	−	0.0993341i
$302$	−0.792201	+	1.10577i	−0.0455860	+	0.0636299i
$303$	4.47062	+	10.7930i	0.256830	+	0.620043i
$304$	0.0313990	−	0.972086i	0.00180086	−	0.0557529i
$305$	3.38931	−	8.18252i	0.194071	−	0.468530i
$306$	−0.249004	−	0.400334i	−0.0142346	−	0.0228855i
$307$	16.4444	−	20.0376i	0.938533	−	1.14361i	−0.0509126	−	0.998703i	$-0.516213\pi$
$307$	16.4444	−	20.0376i	0.938533	−	1.14361i	0.989446	−	0.144903i	$-0.0462870\pi$
$308$	−16.0664	−	15.0412i	−0.915467	−	0.857054i
$309$	−4.02643	−	13.2734i	−0.229056	−	0.755095i
$310$	−8.83560	−	11.5122i	−0.501828	−	0.653848i
$311$	26.8709	+	17.9545i	1.52371	+	1.01811i	0.984389	+	0.176006i	$0.0563179\pi$
$311$	26.8709	+	17.9545i	1.52371	+	1.01811i	0.539318	+	0.842102i	$0.318682\pi$
$312$	−8.05094	−	15.0504i	−0.455794	−	0.852062i
$313$	−1.66891	−	2.49771i	−0.0943326	−	0.141179i	0.781301	−	0.624154i	$-0.214556\pi$
$313$	−1.66891	−	2.49771i	−0.0943326	−	0.141179i	−0.875634	+	0.482975i	$0.839556\pi$
$314$	−9.45815	−	19.1740i	−0.533754	−	1.08205i
$315$	−1.60348	+	1.31594i	−0.0903456	+	0.0741447i
$316$	1.68223	+	0.829127i	0.0946327	+	0.0466420i
$317$	−0.203695	−	0.381086i	−0.0114406	−	0.0214039i	0.876136	−	0.482064i	$-0.160113\pi$
$317$	−0.203695	−	0.381086i	−0.0114406	−	0.0214039i	−0.887577	+	0.460660i	$0.847613\pi$
$318$	4.22142	+	0.137735i	0.236726	+	0.00772380i
$319$			22.1364i			1.23940i
$320$	7.05291	−	3.77578i	0.394269	−	0.211073i
$321$			1.61361i			0.0900627i
$322$	0.228246	−	6.99547i	0.0127196	−	0.389842i
$323$	0.0687518	+	0.128626i	0.00382545	+	0.00715692i
$324$	13.3011	−	4.51834i	0.738950	−	0.251019i
$325$	−2.98376	+	2.44871i	−0.165509	+	0.135830i
$326$	−4.23024	+	2.08669i	−0.234291	+	0.115571i
$327$	1.28235	+	1.91918i	0.0709143	+	0.106131i
$328$	13.6884	−	16.6905i	0.755816	−	0.921578i
$329$	−11.7743	−	7.86735i	−0.649140	−	0.433741i
$330$	5.17124	−	3.96893i	0.284668	−	0.218482i
$331$	−4.92838	−	16.2467i	−0.270888	−	0.892998i	−0.981832	−	0.189750i	$-0.939232\pi$
$331$	−4.92838	−	16.2467i	−0.270888	−	0.892998i	0.710944	−	0.703248i	$-0.248268\pi$
$332$	0.0714418	+	2.16789i	0.00392088	+	0.118978i
$333$	−0.570728	+	0.695434i	−0.0312757	+	0.0381095i
$334$	29.2925	−	18.2197i	1.60281	−	0.996935i
$335$	2.56714	−	6.19762i	0.140258	−	0.338612i
$336$	−13.5870	+	18.9781i	−0.741233	+	1.03534i
$337$	7.14077	+	17.2393i	0.388982	+	0.939087i	0.990156	+	0.139968i	$0.0447001\pi$
$337$	7.14077	+	17.2393i	0.388982	+	0.939087i	−0.601174	+	0.799119i	$0.705300\pi$
$338$	−2.18317	−	1.56408i	−0.118749	−	0.0850745i
$339$	31.1953	−	3.07247i	1.69430	−	0.166874i
$340$	−0.633278	+	1.01889i	−0.0343443	+	0.0552570i
$341$	26.6822	+	14.2619i	1.44492	+	0.772326i
$342$	0.184593	−	0.0494831i	0.00998166	−	0.00267574i
$343$	−0.0508342	−	0.255561i	−0.00274479	−	0.0137990i
$344$	−2.60372	−	13.0675i	−0.140383	−	0.704551i
$345$	2.03329	+	0.404446i	0.109469	+	0.0217747i
$346$	−13.8918	+	15.8440i	−0.746827	+	0.851780i
$347$	−16.0878	−	1.58451i	−0.863636	−	0.0850607i	−0.343509	−	0.939150i	$-0.611615\pi$
$347$	−16.0878	−	1.58451i	−0.863636	−	0.0850607i	−0.520127	+	0.854089i	$0.674115\pi$
$348$	23.2748	−	3.06934i	1.24766	−	0.164534i
$349$	−7.95179	−	2.41215i	−0.425650	−	0.129119i	0.0701897	−	0.997534i	$-0.477640\pi$
$349$	−7.95179	−	2.41215i	−0.425650	−	0.129119i	−0.495839	+	0.868414i	$0.665140\pi$
$350$	4.80804	+	2.17787i	0.257001	+	0.116412i
$351$	15.1729	−	15.1729i	0.809870	−	0.809870i
$352$	−10.1460	+	13.2374i	−0.540781	+	0.705554i
$353$	1.90454	+	1.90454i	0.101369	+	0.101369i	0.755972	−	0.654604i	$-0.227164\pi$
$353$	1.90454	+	1.90454i	0.101369	+	0.101369i	−0.654604	+	0.755972i	$0.727164\pi$
$354$	−11.6650	−	30.9830i	−0.619988	−	1.64673i
$355$	0.0281642	−	0.0928450i	0.00149480	−	0.00492770i
$356$	4.00489	−	14.9595i	0.212259	−	0.792850i
$357$	0.343066	−	3.48321i	0.0181570	−	0.184351i
$358$	1.36083	+	20.7276i	0.0719219	+	1.09549i
$359$	0.923339	−	4.64194i	0.0487320	−	0.244992i	−0.948740	−	0.316059i	$-0.897640\pi$
$359$	0.923339	−	4.64194i	0.0487320	−	0.244992i	0.997472	+	0.0710667i	$0.0226403\pi$
$360$	1.11191	+	1.11119i	0.0586029	+	0.0585646i
$361$	18.5769	−	3.69518i	0.977733	−	0.194483i
$362$	−17.9174	−	10.3420i	−0.941717	−	0.543564i
$363$	1.70039	−	3.18121i	0.0892476	−	0.166970i
$364$	−4.68730	+	28.4291i	−0.245682	+	1.49009i
$365$	0.679357	+	6.89763i	0.0355592	+	0.361039i
$366$	19.3201	−	3.19193i	1.00988	−	0.166845i
$367$	−15.3930	+	6.37600i	−0.803509	+	0.332824i	−0.746361	−	0.665541i	$-0.768201\pi$
$367$	−15.3930	+	6.37600i	−0.803509	+	0.332824i	−0.0571481	+	0.998366i	$0.518201\pi$
$368$	−5.29263	+	0.349212i	−0.275897	+	0.0182039i
$369$	3.91865	+	1.62316i	0.203997	+	0.0844981i
$370$	2.22947	+	0.519584i	0.115905	+	0.0270119i
$371$	−5.51148	−	4.52316i	−0.286142	−	0.234831i
$372$	11.2957	−	30.0318i	0.585654	−	1.55707i
$373$	−22.0455	+	6.68743i	−1.14147	+	0.346262i	−0.803740	−	0.594980i	$-0.797160\pi$
$373$	−22.0455	+	6.68743i	−1.14147	+	0.346262i	−0.337732	+	0.941242i	$0.609660\pi$
$374$	0.326181	−	2.47968i	0.0168664	−	0.128221i
$375$	−0.868580	+	1.29992i	−0.0448533	+	0.0671276i
$376$	−5.05565	+	9.46590i	−0.260725	+	0.488166i
$377$	24.0965	−	16.1008i	1.24103	−	0.829232i
$378$	−27.7864	−	9.42884i	−1.42918	−	0.484967i
$379$	−19.4507	−	23.7007i	−0.999115	−	1.21743i	−0.976018	−	0.217692i	$-0.930147\pi$
$379$	−19.4507	−	23.7007i	−0.999115	−	1.21743i	−0.0230975	−	0.999733i	$-0.507353\pi$
$380$	−0.320717	−	0.365547i	−0.0164524	−	0.0187522i
$381$	5.76918	−	3.08369i	0.295564	−	0.157982i
$382$	8.42177	+	8.98987i	0.430895	+	0.459962i
$383$	−0.657500			−0.0335967			−0.0167983	−	0.999859i	$-0.505347\pi$
$383$	−0.657500			−0.0335967			−0.0167983	+	0.999859i	$0.505347\pi$
$384$	15.3249	+	8.83226i	0.782045	+	0.450719i
$385$	−11.0042			−0.560825
$386$	17.6818	+	18.8745i	0.899980	+	0.960689i
$387$	2.30903	−	1.23420i	0.117375	−	0.0627380i
$388$	−25.3951	+	22.2807i	−1.28924	+	1.13113i
$389$	−22.2024	−	27.0537i	−1.12571	−	1.37168i	−0.919462	−	0.393179i	$-0.871375\pi$
$389$	−22.2024	−	27.0537i	−1.12571	−	1.37168i	−0.206246	−	0.978500i	$-0.566125\pi$
$390$	−8.08162	−	2.74236i	−0.409229	−	0.138865i
$391$	0.661344	−	0.441896i	0.0334456	−	0.0223476i
$392$	18.7556	−	5.69615i	0.947302	−	0.287699i
$393$	8.93861	−	13.3776i	0.450893	−	0.674809i
$394$	0.228934	−	1.74039i	0.0115335	−	0.0876797i
$395$	0.897350	−	0.272208i	0.0451506	−	0.0136963i
$396$	−3.06743	−	1.15374i	−0.154144	−	0.0579775i
$397$	7.69179	+	6.31249i	0.386040	+	0.316815i	0.807318	−	0.590117i	$-0.200918\pi$
$397$	7.69179	+	6.31249i	0.386040	+	0.316815i	−0.421278	+	0.906932i	$0.638418\pi$
$398$	−37.4221	−	8.72133i	−1.87580	−	0.437161i
$399$	1.31080	+	0.542950i	0.0656219	+	0.0271815i
$400$	1.28411	−	3.78828i	0.0642054	−	0.189414i
$401$	3.99846	−	1.65622i	0.199674	−	0.0827075i	−0.280606	−	0.959823i	$-0.590535\pi$
$401$	3.99846	−	1.65622i	0.199674	−	0.0827075i	0.480279	+	0.877116i	$0.340535\pi$
$402$	14.6335	−	2.41763i	0.729851	−	0.120581i
$403$	−3.88234	−	39.4180i	−0.193393	−	1.96355i
$404$	−14.7456	−	2.43121i	−0.733622	−	0.120957i
$405$	3.31099	−	6.19443i	0.164525	−	0.307804i
$406$	−34.3226	−	19.8112i	−1.70340	−	0.983212i
$407$	−4.68085	+	0.931079i	−0.232021	+	0.0461518i
$408$	−2.65242		0.000866280i	−0.131314		4.28873e-5i
$409$	6.63227	−	33.3427i	0.327945	−	1.64869i	−0.367436	−	0.930049i	$-0.619764\pi$
$409$	6.63227	−	33.3427i	0.327945	−	1.64869i	0.695381	−	0.718641i	$-0.255236\pi$
$410$	−0.707060	−	10.7697i	−0.0349192	−	0.531877i
$411$	−1.08546	+	11.0209i	−0.0535419	+	0.543620i
$412$	17.1405	+	4.58880i	0.844454	+	0.226074i
$413$	−16.2228	+	53.4794i	−0.798271	+	2.63155i
$414$	−0.367236	−	0.975399i	−0.0180486	−	0.0479383i
$415$	0.766880	+	0.766880i	0.0376447	+	0.0376447i
$416$	21.7891	+	1.41622i	1.06830	+	0.0694359i
$417$	−11.9719	+	11.9719i	−0.586266	+	0.586266i
$418$	0.923506	+	0.418314i	0.0451702	+	0.0204604i
$419$	21.3870	+	6.48767i	1.04482	+	0.316944i	0.765623	−	0.643290i	$-0.222431\pi$
$419$	21.3870	+	6.48767i	1.04482	+	0.316944i	0.279200	+	0.960233i	$0.409931\pi$
$420$	1.52579	+	11.5700i	0.0744509	+	0.564561i
$421$	5.71891	+	0.563263i	0.278722	+	0.0274518i	0.236413	−	0.971653i	$-0.424028\pi$
$421$	5.71891	+	0.563263i	0.278722	+	0.0274518i	0.0423099	+	0.999105i	$0.486528\pi$
$422$	17.9629	−	20.4873i	0.874422	−	0.997306i
$423$	−2.06816	−	0.411382i	−0.100557	−	0.0200021i
$424$	−3.00038	+	4.49356i	−0.145711	+	0.218227i
$425$	0.117021	+	0.588302i	0.00567633	+	0.0285369i
$426$	0.207200	−	0.0555433i	0.0100389	−	0.00269108i
$427$	−29.1528	−	15.5825i	−1.41080	−	0.754090i
$428$	−1.75318	−	1.08967i	−0.0847431	−	0.0526711i
$429$	17.7065	−	1.74394i	0.854877	−	0.0841980i
$430$	−5.41575	−	3.87998i	−0.261171	−	0.187109i
$431$	5.82501	+	14.0628i	0.280581	+	0.677382i	0.999849	−	0.0173499i	$-0.00552293\pi$
$431$	5.82501	+	14.0628i	0.280581	+	0.677382i	−0.719269	+	0.694732i	$0.755523\pi$
$432$	−5.03993	+	21.6577i	−0.242484	+	1.04201i
$433$	7.89356	−	19.0567i	0.379340	−	0.915809i	−0.612749	−	0.790277i	$-0.709936\pi$
$433$	7.89356	−	19.0567i	0.379340	−	0.915809i	0.992090	−	0.125531i	$-0.0400636\pi$
$434$	−45.9926	+	28.6070i	−2.20771	+	1.37318i
$435$	7.44660	−	9.07371i	0.357037	−	0.435051i
$436$	−2.95116	+	0.0972541i	−0.141335	+	0.00465763i
$437$	0.0935944	+	0.308539i	0.00447723	+	0.0147594i
$438$	−12.1566	+	9.33019i	−0.580865	+	0.445814i
$439$	7.76855	+	5.19078i	0.370773	+	0.247742i	0.726971	−	0.686668i	$-0.240927\pi$
$439$	7.76855	+	5.19078i	0.370773	+	0.247742i	−0.356199	+	0.934410i	$0.615927\pi$
$440$	0.820094	+	8.29877i	0.0390964	+	0.395628i
$441$	2.13985	+	3.20251i	0.101897	+	0.152500i
$442$	−2.93649	+	1.44851i	−0.139674	+	0.0688987i
$443$	23.6150	−	19.3803i	1.12198	−	0.920787i	0.124536	−	0.992215i	$-0.460256\pi$
$443$	23.6150	−	19.3803i	1.12198	−	0.920787i	0.997446	+	0.0714281i	$0.0227557\pi$
$444$	1.62798	+	4.79246i	0.0772607	+	0.227440i
$445$	−3.65009	−	6.82884i	−0.173031	−	0.323718i
$446$	−1.15815	+	35.4959i	−0.0548398	+	1.68078i
$447$			28.3739i			1.34204i
$448$	−11.4444	−	27.5782i	−0.540696	−	1.30295i
$449$			24.4660i			1.15462i	0.816524	+	0.577311i	$0.195898\pi$
$449$			24.4660i			1.15462i	−0.816524	+	0.577311i	$0.804102\pi$
$450$	0.785566	+	0.0256311i	0.0370319	+	0.00120826i
$451$	10.6069	+	19.8441i	0.499458	+	0.934421i
$452$	−17.7280	+	35.9685i	−0.833853	+	1.69181i
$453$	−1.16242	+	0.953973i	−0.0546153	+	0.0448216i
$454$	9.62077	+	19.5036i	0.451525	+	0.915351i
$455$	8.00380	+	11.9785i	0.375224	+	0.561562i
$456$	0.311776	−	1.02900i	0.0146003	−	0.0481872i
$457$	−21.8140	−	14.5756i	−1.02041	−	0.681819i	−0.0715281	−	0.997439i	$-0.522788\pi$
$457$	−21.8140	−	14.5756i	−1.02041	−	0.681819i	−0.948886	+	0.315620i	$0.897788\pi$
$458$	−19.9889	−	26.0442i	−0.934020	−	1.21696i
$459$	−0.967956	−	3.19092i	−0.0451803	−	0.148940i
$460$	−1.81251	+	1.93604i	−0.0845088	+	0.0902685i
$461$	−9.59734	+	11.6944i	−0.446993	+	0.544662i	−0.946947	−	0.321389i	$-0.895850\pi$
$461$	−9.59734	+	11.6944i	−0.446993	+	0.544662i	0.499954	+	0.866052i	$0.333350\pi$
$462$	−12.8502	−	20.6597i	−0.597844	−	0.961178i
$463$	0.239015	−	0.577033i	0.0111080	−	0.0268170i	−0.918228	−	0.396052i	$-0.870380\pi$
$463$	0.239015	−	0.577033i	0.0111080	−	0.0268170i	0.929336	+	0.369235i	$0.120380\pi$
$464$	−12.3826	+	27.3607i	−0.574849	+	1.27019i
$465$	−6.13935	−	14.8217i	−0.284706	−	0.687340i
$466$	−6.03061	+	8.41764i	−0.279363	+	0.389940i
$467$	−23.8846	+	2.35242i	−1.10525	+	0.108857i	−0.634139	−	0.773219i	$-0.718645\pi$
$467$	−23.8846	+	2.35242i	−1.10525	+	0.108857i	−0.471106	+	0.882076i	$0.656145\pi$
$468$	0.975179	+	4.17820i	0.0450777	+	0.193137i
$469$	−22.0810	−	11.8025i	−1.01960	−	0.544989i
$470$	1.38931	+	5.18272i	0.0640841	+	0.239061i
$471$	−4.61101	−	23.1811i	−0.212464	−	1.06813i
$472$	41.5403	+	8.24879i	1.91205	+	0.379681i
$473$	13.6224	+	2.70967i	0.626359	+	0.124591i
$474$	1.55894	+	1.36685i	0.0716045	+	0.0627817i
$475$	−0.241977	−	0.0238327i	−0.0111027	−	0.00109352i
$476$	3.55283	+	2.72495i	0.162844	+	0.124898i
$477$	−1.01599	−	0.308196i	−0.0465188	−	0.0141113i
$478$	−4.33679	+	9.57427i	−0.198360	+	0.437917i
$479$	24.5230	−	24.5230i	1.12048	−	1.12048i	0.128814	−	0.991669i	$-0.458883\pi$
$479$	24.5230	−	24.5230i	1.12048	−	1.12048i	0.991669	−	0.128814i	$-0.0411170\pi$
$480$	8.61181	−	2.01294i	0.393074	−	0.0918775i
$481$	4.41810	+	4.41810i	0.201448	+	0.201448i
$482$	31.7669	−	11.9602i	1.44694	−	0.544770i
$483$	2.24609	−	7.40438i	0.102201	−	0.336911i
$484$	2.30811	+	3.99575i	0.104914	+	0.181625i
$485$	−1.65569	+	16.8105i	−0.0751811	+	0.763327i
$486$	−8.03849	+	0.527749i	−0.364633	+	0.0239392i
$487$	2.14564	−	10.7869i	0.0972282	−	0.488799i	−0.901233	−	0.433336i	$-0.857336\pi$
$487$	2.14564	−	10.7869i	0.0972282	−	0.488799i	0.998461	−	0.0554633i	$-0.0176636\pi$
$488$	−9.57886	+	23.1468i	−0.433615	+	1.04781i
$489$	−5.11430	+	1.01730i	−0.231277	+	0.0460038i
$490$	4.89946	−	8.48824i	0.221335	−	0.383460i
$491$	8.96003	−	16.7630i	0.404360	−	0.756505i	−0.594507	−	0.804091i	$-0.702653\pi$
$491$	8.96003	−	16.7630i	0.404360	−	0.756505i	0.998867	+	0.0475856i	$0.0151527\pi$
$492$	19.3938	−	13.9038i	0.874341	−	0.626832i
$493$	−0.441426	−	4.48187i	−0.0198808	−	0.201853i
$494$	−0.216352	−	1.30954i	−0.00973412	−	0.0589188i
$495$	−1.51388	+	0.627072i	−0.0680441	+	0.0281848i
$496$	25.0015	+	32.5532i	1.12260	+	1.46168i
$497$	−0.334555	−	0.138577i	−0.0150068	−	0.00621604i
$498$	−0.544248	+	2.33530i	−0.0243883	+	0.104647i
$499$	−21.8731	−	17.9508i	−0.979175	−	0.803588i	0.00134681	−	0.999999i	$-0.499571\pi$
$499$	−21.8731	−	17.9508i	−0.979175	−	0.803588i	−0.980522	+	0.196411i	$0.937071\pi$
$500$	−0.825811	−	1.82155i	−0.0369314	−	0.0814621i
$501$	36.4934	−	11.0702i	1.63041	−	0.494578i
$502$	19.5154	+	2.56709i	0.871014	+	0.114575i
$503$	−20.2922	+	30.3695i	−0.904786	+	1.35411i	0.0302446	+	0.999543i	$0.490371\pi$
$503$	−20.2922	+	30.3695i	−0.904786	+	1.35411i	−0.935031	+	0.354566i	$0.884629\pi$
$504$	4.53410	−	3.72352i	0.201965	−	0.165859i
$505$	−6.21303	+	4.15142i	−0.276476	+	0.184736i
$506$	1.77668	−	5.23579i	0.0789829	−	0.232759i
$507$	−1.88347	−	2.29502i	−0.0836479	−	0.101925i
$508$	−0.545503	+	8.35062i	−0.0242028	+	0.370499i
$509$	−33.1313	+	17.7091i	−1.46852	+	0.784940i	−0.995377	−	0.0960457i	$-0.969381\pi$
$509$	−33.1313	+	17.7091i	−1.46852	+	0.784940i	−0.473143	+	0.880986i	$0.656881\pi$
$510$	−0.967854	+	0.906692i	−0.0428573	+	0.0401490i
$511$	25.8687			1.14436
$512$	−19.9451	+	10.6860i	−0.881459	+	0.472261i
$513$	1.35169			0.0596784
$514$	21.7067	−	20.3350i	0.957441	−	0.896937i
$515$	7.82448	−	4.18227i	0.344788	−	0.184293i
$516$	0.960186	−	14.6986i	0.0422698	−	0.647072i
$517$	−7.09657	−	8.64720i	−0.312107	−	0.380303i
$518$	2.74552	−	8.09094i	0.120631	−	0.355496i
$519$	−19.3687	+	12.9418i	−0.850192	+	0.568080i
$520$	8.43709	−	6.92875i	0.369991	−	0.303846i
$521$	1.60354	−	2.39987i	0.0702524	−	0.105140i	−0.794680	−	0.607029i	$-0.792361\pi$
$521$	1.60354	−	2.39987i	0.0702524	−	0.105140i	0.864932	+	0.501889i	$0.167361\pi$
$522$	−5.85082	−	0.769628i	−0.256084	−	0.0336857i
$523$	5.30272	−	1.60856i	0.231872	−	0.0703375i	−0.172211	−	0.985060i	$-0.555091\pi$
$523$	5.30272	−	1.60856i	0.231872	−	0.0703375i	0.404082	+	0.914723i	$0.367591\pi$
$524$	8.49847	+	18.7457i	0.371258	+	0.818908i
$525$	4.51060	+	3.70176i	0.196859	+	0.161558i
$526$	9.10164	−	39.0540i	0.396850	−	1.70284i
$527$	−5.68662	−	2.35548i	−0.247713	−	0.102606i
$528$	−14.6228	+	11.2306i	−0.636376	+	0.488749i
$529$	−19.6247	+	8.12882i	−0.853248	+	0.353427i
$530$	0.440367	+	2.66546i	0.0191283	+	0.115780i
$531$	0.815687	+	8.28181i	0.0353978	+	0.359400i
$532$	−1.47510	+	1.05753i	−0.0639535	+	0.0458495i
$533$	13.8863	−	25.9795i	0.601484	−	1.12530i
$534$	8.55837	−	14.8273i	0.370357	−	0.641638i
$535$	−1.01228	+	0.201355i	−0.0437647	+	0.00870533i
$536$	−7.25524	+	17.5319i	−0.313378	+	0.757262i
$537$	−4.47997	+	22.5223i	−0.193325	+	0.971910i
$538$	30.7759	−	2.02052i	1.32684	−	0.0871110i
$539$	−2.00275	+	20.3342i	−0.0862644	+	0.875857i
$540$	5.56120	+	9.62744i	0.239316	+	0.414299i
$541$	−6.11350	+	20.1535i	−0.262840	+	0.866467i	0.721835	+	0.692065i	$0.243299\pi$
$541$	−6.11350	+	20.1535i	−0.262840	+	0.866467i	−0.984675	+	0.174401i	$0.944201\pi$
$542$	28.4483	−	10.7107i	1.22196	−	0.460065i
$543$	−16.1718	−	16.1718i	−0.693997	−	0.693997i
$544$	1.79024	−	2.88244i	0.0767559	−	0.123583i
$545$	−1.04396	+	1.04396i	−0.0447182	+	0.0447182i
$546$	−13.1426	+	29.0147i	−0.562450	+	1.24171i
$547$	−0.773673	−	0.234691i	−0.0330799	−	0.0100347i	0.273701	−	0.961815i	$-0.411752\pi$
$547$	−0.773673	−	0.234691i	−0.0330799	−	0.0100347i	−0.306781	+	0.951780i	$0.599252\pi$
$548$	−11.2412	−	8.62176i	−0.480199	−	0.368304i
$549$	−4.89862	−	0.482472i	−0.209068	−	0.0205914i
$550$	3.13517	+	2.74886i	0.133684	+	0.117212i
$551$	1.79050	+	0.356152i	0.0762777	+	0.0151726i
$552$	−5.75138	−	1.14207i	−0.244795	−	0.0486097i
$553$	−0.682797	−	3.43265i	−0.0290355	−	0.145971i
$554$	−4.18782	−	15.6223i	−0.177923	−	0.663730i
$555$	2.23189	+	1.19297i	0.0947383	+	0.0506387i
$556$	−4.92283	−	21.0921i	−0.208774	−	0.894503i
$557$	−8.95226	+	0.881721i	−0.379320	+	0.0373597i	−0.285881	−	0.958265i	$-0.592286\pi$
$557$	−8.95226	+	0.881721i	−0.379320	+	0.0373597i	−0.0934391	+	0.995625i	$0.529786\pi$
$558$	−4.69720	+	6.55645i	−0.198848	+	0.277557i
$559$	−6.95857	−	16.7995i	−0.294316	−	0.710542i
$560$	−13.6012	−	6.15549i	−0.574756	−	0.260117i
$561$	1.05807	−	2.55442i	0.0446719	−	0.107848i
$562$	−7.57219	−	12.1741i	−0.319414	−	0.513534i
$563$	−14.9100	+	18.1679i	−0.628381	+	0.765685i	−0.985739	−	0.168283i	$-0.946178\pi$
$563$	−14.9100	+	18.1679i	−0.628381	+	0.765685i	0.357358	+	0.933968i	$0.383678\pi$
$564$	−8.10789	+	8.66049i	−0.341404	+	0.364672i
$565$	5.82021	+	19.1867i	0.244858	+	0.807189i
$566$	15.4719	+	20.1588i	0.650332	+	0.847338i
$567$	−21.7970	−	14.5643i	−0.915387	−	0.611642i
$568$	−0.0795747	+	0.262631i	−0.00333888	+	0.0110198i
$569$	−9.83085	−	14.7129i	−0.412131	−	0.616797i	0.566095	−	0.824340i	$-0.308453\pi$
$569$	−9.83085	−	14.7129i	−0.412131	−	0.616797i	−0.978226	+	0.207543i	$0.933453\pi$
$570$	−0.237825	−	0.482130i	−0.00996141	−	0.0201942i
$571$	−10.8191	+	8.87899i	−0.452764	+	0.371574i	−0.832961	−	0.553332i	$-0.813356\pi$
$571$	−10.8191	+	8.87899i	−0.452764	+	0.371574i	0.380197	+	0.924906i	$0.375856\pi$
$572$	−10.0624	+	20.4157i	−0.420730	+	0.853625i
$573$	6.41945	+	12.0099i	0.268176	+	0.501723i
$574$	−40.2610	−	1.31362i	−1.68046	−	0.0548295i
$575$			1.32603i			0.0552994i
$576$	−3.14599	−	3.14188i	−0.131083	−	0.130912i
$577$			44.0410i			1.83345i	0.399519	+	0.916725i	$0.369177\pi$
$577$			44.0410i			1.83345i	−0.399519	+	0.916725i	$0.630823\pi$
$578$	0.767411	−	23.5203i	0.0319201	−	0.978315i
$579$	13.4779	+	25.2153i	0.560121	+	1.04791i
$580$	4.82988	+	14.2182i	0.200550	+	0.590378i
$581$	3.12900	−	2.56791i	0.129813	−	0.106535i
$582$	−33.4943	+	16.5221i	−1.38838	+	0.684863i
$583$	−3.12912	−	4.68306i	−0.129595	−	0.193953i
$584$	−1.92788	−	19.5088i	−0.0797764	−	0.807281i
$585$	1.78371	+	1.19184i	0.0737473	+	0.0492763i
$586$	−4.26717	+	3.27506i	−0.176275	+	0.135291i
$587$	7.53641	+	24.8442i	0.311061	+	1.02543i	0.963527	+	0.267612i	$0.0862346\pi$
$587$	7.53641	+	24.8442i	0.311061	+	1.02543i	−0.652466	+	0.757818i	$0.726265\pi$
$588$	21.6576	−	0.713716i	0.893143	−	0.0294332i
$589$	1.58286	−	1.92872i	0.0652205	−	0.0794715i
$590$	17.9812	−	11.1842i	0.740276	−	0.460445i
$591$	0.742622	−	1.79285i	0.0305474	−	0.0737479i
$592$	−6.30638	−	1.46755i	−0.259190	−	0.0603157i
$593$	9.59717	+	23.1696i	0.394108	+	0.951462i	0.989035	+	0.147682i	$0.0471812\pi$
$593$	9.59717	+	23.1696i	0.394108	+	0.951462i	−0.594926	+	0.803780i	$0.702819\pi$
$594$	−18.8426	−	13.4993i	−0.773122	−	0.553884i
$595$	2.22797	−	0.219436i	0.0913378	−	0.00899599i
$596$	−30.8282	−	19.1609i	−1.26277	−	0.784861i
$597$	−37.4627	−	20.0242i	−1.53325	−	0.819537i
$598$	−6.99165	+	1.87422i	−0.285910	+	0.0766426i
$599$	−3.83882	−	19.2990i	−0.156850	−	0.788538i	−0.976474	−	0.215636i	$-0.930818\pi$
$599$	−3.83882	−	19.2990i	−0.156850	−	0.788538i	0.819624	−	0.572902i	$-0.194182\pi$
$600$	2.45551	−	3.67753i	0.100246	−	0.150135i
$601$	8.92164	+	1.77462i	0.363921	+	0.0723885i	0.373664	−	0.927564i	$-0.378101\pi$
$601$	8.92164	+	1.77462i	0.363921	+	0.0723885i	−0.00974279	+	0.999953i	$0.503101\pi$
$602$	−16.3928	+	18.6965i	−0.668122	+	0.762014i
$603$	−3.71032	−	0.365435i	−0.151096	−	0.0148817i
$604$	−0.251508	−	1.90719i	−0.0102337	−	0.0776023i
$605$	2.20789	+	0.669756i	0.0897635	+	0.0272295i
$606$	−15.0494	−	6.81680i	−0.611338	−	0.276914i
$607$	−12.5392	+	12.5392i	−0.508948	+	0.508948i	−0.914204	−	0.405255i	$-0.867183\pi$
$607$	−12.5392	+	12.5392i	−0.508948	+	0.508948i	0.405255	+	0.914204i	$0.367183\pi$
$608$	0.907463	+	1.03363i	0.0368025	+	0.0419191i
$609$	−30.9787	−	30.9787i	−1.25532	−	1.25532i
$610$	4.41330	+	11.7220i	0.178689	+	0.474609i
$611$	−4.25123	+	14.0144i	−0.171986	+	0.566963i
$612$	0.644057	+	0.172424i	0.0260345	+	0.00696984i
$613$	2.47926	−	25.1724i	0.100136	−	1.01670i	−0.805485	−	0.592616i	$-0.798095\pi$
$613$	2.47926	−	25.1724i	0.100136	−	1.01670i	0.905622	−	0.424086i	$-0.139405\pi$
$614$	2.40157	+	36.5798i	0.0969193	+	1.47624i
$615$	2.32771	−	11.7022i	0.0938622	−	0.471877i
$616$	31.1245	−	0.0101653i	1.25404	−	0.000409570i
$617$	1.50487	−	0.299337i	0.0605838	−	0.0120509i	−0.164705	−	0.986343i	$-0.552667\pi$
$617$	1.50487	−	0.299337i	0.0605838	−	0.0120509i	0.225289	+	0.974292i	$0.427667\pi$
$618$	16.9890	+	9.80617i	0.683400	+	0.394462i
$619$	14.8997	−	27.8754i	0.598870	−	1.12041i	−0.381709	−	0.924282i	$-0.624664\pi$
$619$	14.8997	−	27.8754i	0.598870	−	1.12041i	0.980579	−	0.196124i	$-0.0628356\pi$
$620$	20.2497	+	3.33871i	0.813247	+	0.134086i
$621$	−0.722539	−	7.33606i	−0.0289945	−	0.294386i
$622$	−45.0923	+	7.44982i	−1.80804	+	0.298710i
$623$	−26.7000	+	11.0595i	−1.06971	+	0.443089i
$624$	22.8608	+	7.74910i	0.915165	+	0.310212i
$625$	−0.923880	−	0.382683i	−0.0369552	−	0.0153073i
$626$	4.13738	+	0.964226i	0.165363	+	0.0385382i
$627$	0.866375	+	0.711016i	0.0345997	+	0.0283952i
$628$	28.3001	+	10.6444i	1.12930	+	0.424756i
$629$	0.929145	−	0.281853i	0.0370474	−	0.0112382i
$630$	0.382587	−	2.90849i	0.0152426	−	0.115877i
$631$	6.17802	−	9.24606i	0.245943	−	0.368080i	−0.687874	−	0.725830i	$-0.741456\pi$
$631$	6.17802	−	9.24606i	0.245943	−	0.368080i	0.933817	+	0.357750i	$0.116456\pi$
$632$	−2.53784	+	0.770750i	−0.100950	+	0.0306588i
$633$	25.0449	−	16.7345i	0.995447	−	0.665137i
$634$	0.578685	+	0.196367i	0.0229825	+	0.00779872i
$635$	2.65444	+	3.23444i	0.105338	+	0.128355i
$636$	−4.49001	+	3.93936i	−0.178041	+	0.156206i
$637$	23.5914	−	12.6099i	0.934725	−	0.499621i
$638$	−21.4028	−	22.8465i	−0.847344	−	0.904503i
$639$	−0.0539228			−0.00213315
$640$	−3.62851	+	10.7161i	−0.143429	+	0.423589i
$641$	2.89388			0.114301			0.0571506	−	0.998366i	$-0.481798\pi$
$641$	2.89388			0.114301			0.0571506	+	0.998366i	$0.481798\pi$
$642$	−1.56013	−	1.66537i	−0.0615733	−	0.0657268i
$643$	12.2663	−	6.55648i	0.483736	−	0.258562i	−0.211454	−	0.977388i	$-0.567820\pi$
$643$	12.2663	−	6.55648i	0.483736	−	0.258562i	0.695191	+	0.718825i	$0.255320\pi$
$644$	6.52806	+	7.44056i	0.257242	+	0.293199i
$645$	−4.67230	−	5.69321i	−0.183971	−	0.224170i
$646$	−0.195320	−	0.0662785i	−0.00768476	−	0.00260769i
$647$	15.7828	−	10.5458i	0.620488	−	0.414597i	−0.205203	−	0.978719i	$-0.565786\pi$
$647$	15.7828	−	10.5458i	0.620488	−	0.414597i	0.825691	+	0.564123i	$0.190786\pi$
$648$	−9.35918	+	17.5236i	−0.367663	+	0.688390i
$649$	−24.5268	+	36.7069i	−0.962761	+	1.44087i
$650$	0.711922	−	5.41214i	0.0279239	−	0.212281i
$651$	−57.2989	+	17.3814i	−2.24572	+	0.681232i
$652$	2.34840	−	6.24367i	0.0919704	−	0.244521i
$653$	0.192620	+	0.158079i	0.00753779	+	0.00618610i	0.638155	−	0.769908i	$-0.279698\pi$
$653$	0.192620	+	0.158079i	0.00753779	+	0.00618610i	−0.630617	+	0.776094i	$0.717198\pi$
$654$	−3.17906	−	0.740888i	−0.124311	−	0.0289710i
$655$	9.50771	+	3.93822i	0.371497	+	0.153879i
$656$	2.00982	+	30.4606i	0.0784702	+	1.18929i
$657$	3.55885	−	1.47413i	0.138844	−	0.0575111i
$658$	19.7586	−	3.26437i	0.770272	−	0.127259i
$659$	−0.0651565	−	0.661545i	−0.00253814	−	0.0257702i	0.993832	−	0.110894i	$-0.0353714\pi$
$659$	−0.0651565	−	0.661545i	−0.00253814	−	0.0257702i	−0.996370	+	0.0851238i	$0.972871\pi$
$660$	−1.49974	+	9.09610i	−0.0583772	+	0.354065i
$661$	16.7438	−	31.3254i	0.651257	−	1.21842i	−0.312064	−	0.950061i	$-0.601020\pi$
$661$	16.7438	−	31.3254i	0.651257	−	1.21842i	0.963320	−	0.268354i	$-0.0864798\pi$
$662$	20.7947	+	12.0028i	0.808209	+	0.466502i
$663$	−3.55018	+	0.706174i	−0.137877	+	0.0274255i
$664$	−2.16977	−	2.16836i	−0.0842035	−	0.0841485i
$665$	−0.177046	+	0.890069i	−0.00686554	+	0.0345154i
$666$	−0.0833498	−	1.26955i	−0.00322974	−	0.0491942i
$667$	0.975855	−	9.90802i	0.0377852	−	0.383640i
$668$	−12.6163	+	47.1258i	−0.488140	+	1.82335i
$669$	−11.3969	+	37.5707i	−0.440631	+	1.45257i
$670$	3.34273	+	8.87849i	0.129141	+	0.343006i
$671$	−18.4644	−	18.4644i	−0.712811	−	0.712811i
$672$	−4.32627	−	32.7236i	−0.166889	−	1.26234i
$673$	−15.5630	+	15.5630i	−0.599908	+	0.599908i	−0.940288	−	0.340380i	$-0.889444\pi$
$673$	−15.5630	+	15.5630i	−0.599908	+	0.599908i	0.340380	+	0.940288i	$0.389444\pi$
$674$	−24.0378	−	10.8882i	−0.925903	−	0.419399i
$675$	5.31973	+	1.61372i	0.204757	+	0.0621122i
$676$	3.76544	−	0.496564i	0.144825	−	0.0190986i
$677$	11.4527	+	1.12799i	0.440161	+	0.0433521i	0.315671	−	0.948869i	$-0.397770\pi$
$677$	11.4527	+	1.12799i	0.440161	+	0.0433521i	0.124490	+	0.992221i	$0.460270\pi$
$678$	−29.2253	+	33.3324i	−1.12239	+	1.28012i
$679$	61.8344	+	12.2996i	2.37299	+	0.472016i
$680$	−0.331528	−	1.66386i	−0.0127135	−	0.0638062i
$681$	4.69029	+	23.5797i	0.179732	+	0.903575i
$682$	−41.3273	+	11.0784i	−1.58251	+	0.424216i
$683$	−23.0712	−	12.3318i	−0.882797	−	0.471865i	−0.0332919	−	0.999446i	$-0.510599\pi$
$683$	−23.0712	−	12.3318i	−0.882797	−	0.471865i	−0.849505	+	0.527581i	$0.823099\pi$
$684$	−0.142672	+	0.229546i	−0.00545518	+	0.00877691i
$685$	−7.04930	+	0.694295i	−0.269340	+	0.0265277i
$686$	0.299556	+	0.214609i	0.0114371	+	0.00819382i
$687$	−13.8891	−	33.5314i	−0.529904	−	1.27930i
$688$	15.3216	+	10.9692i	0.584132	+	0.418198i
$689$	−2.82178	+	6.81238i	−0.107501	+	0.259531i
$690$	−2.48956	+	1.54848i	−0.0947758	+	0.0589497i
$691$	18.4122	−	22.4353i	0.700433	−	0.853480i	−0.294328	−	0.955704i	$-0.595096\pi$
$691$	18.4122	−	22.4353i	0.700433	−	0.853480i	0.994761	+	0.102224i	$0.0325960\pi$
$692$	−0.981508	−	29.7837i	−0.0373113	−	1.13220i
$693$	1.77533	+	5.85249i	0.0674394	+	0.222318i
$694$	18.1358	−	13.9192i	0.688426	−	0.528367i
$695$	−9.00438	−	6.01653i	−0.341556	−	0.228220i
$696$	−21.0538	+	25.6712i	−0.798041	+	0.973064i
$697$	−2.54324	−	3.80623i	−0.0963322	−	0.144171i
$698$	10.5391	−	5.19873i	0.398910	−	0.196775i
$699$	−8.84889	+	7.26210i	−0.334696	+	0.274678i
$700$	−7.06796	+	2.40097i	−0.267144	+	0.0907480i
$701$	−17.5356	−	32.8069i	−0.662312	−	1.23910i	−0.958806	−	0.284063i	$-0.908317\pi$
$701$	−17.5356	−	32.8069i	−0.662312	−	1.23910i	0.296494	−	0.955035i	$-0.404183\pi$
$702$	−0.989585	+	30.3297i	−0.0373495	+	1.14472i
$703$			0.393589i			0.0148445i
$704$	−2.32724	−	23.4717i	−0.0877112	−	0.884623i
$705$			5.93174i			0.223402i
$706$	−3.80706	−	0.124215i	−0.143281	−	0.00467491i
$707$	13.1469	+	24.5961i	0.494439	+	0.925030i
$708$	41.9953	+	20.6984i	1.57828	+	0.777895i
$709$	−5.14607	+	4.22327i	−0.193265	+	0.158608i	−0.726049	−	0.687643i	$-0.758646\pi$
$709$	−5.14607	+	4.22327i	−0.193265	+	0.158608i	0.532785	+	0.846251i	$0.321146\pi$
$710$	0.0607002	+	0.123054i	0.00227804	+	0.00461814i
$711$	−0.289544	−	0.433333i	−0.0108588	−	0.0162513i
$712$	10.3303	+	19.3115i	0.387145	+	0.723729i
$713$	−11.3139	−	7.55972i	−0.423710	−	0.283114i
$714$	3.01370	+	3.92664i	0.112785	+	0.146951i
$715$	3.30356	+	10.8904i	0.123546	+	0.407277i
$716$	−21.4451	−	20.0768i	−0.801443	−	0.750305i
$717$	−7.37131	+	8.98197i	−0.275287	+	0.335438i
$718$	3.53514	+	5.68358i	0.131930	+	0.212109i
$719$	16.7484	−	40.4342i	0.624609	−	1.50794i	−0.221626	−	0.975132i	$-0.571136\pi$
$719$	16.7484	−	40.4342i	0.624609	−	1.50794i	0.846236	−	0.532809i	$-0.178864\pi$
$720$	−2.22194	−	0.0717701i	−0.0828068	−	0.00267472i
$721$	−12.6720	−	30.5928i	−0.471928	−	1.13934i
$722$	−15.6001	+	21.7750i	−0.580577	+	0.810381i
$723$	37.3439	−	3.67805i	1.38883	−	0.136788i
$724$	28.4914	−	6.64980i	1.05887	−	0.247138i
$725$	6.62153	+	3.53928i	0.245918	+	0.131446i
$726$	1.32084	+	4.92730i	0.0490210	+	0.182869i
$727$	−4.09210	−	20.5724i	−0.151767	−	0.762987i	−0.979434	−	0.201766i	$-0.935332\pi$
$727$	−4.09210	−	20.5724i	−0.151767	−	0.762987i	0.827666	−	0.561221i	$-0.189668\pi$
$728$	−22.6492	−	33.8730i	−0.839436	−	1.25542i
$729$	−29.4010	−	5.84822i	−1.08893	−	0.216601i
$730$	−7.37018	−	6.46206i	−0.272783	−	0.239171i
$731$	−2.81211	−	0.276968i	−0.104009	−	0.0102440i
$732$	−16.8537	+	21.9741i	−0.622932	+	0.812187i
$733$	26.4848	+	8.03408i	0.978238	+	0.296745i	0.738620	−	0.674122i	$-0.235478\pi$
$733$	26.4848	+	8.03408i	0.978238	+	0.296745i	0.239618	+	0.970867i	$0.422978\pi$
$734$	9.72212	−	21.4634i	0.358850	−	0.792228i
$735$	7.66127	−	7.66127i	0.282590	−	0.282590i
$736$	5.12477	−	5.47763i	0.188901	−	0.201908i
$737$	−13.9854	−	13.9854i	−0.515157	−	0.515157i
$738$	−5.61371	+	2.11355i	−0.206644	+	0.0778008i
$739$	−10.2216	+	33.6962i	−0.376009	+	1.23954i	0.541120	+	0.840945i	$0.318000\pi$
$739$	−10.2216	+	33.6962i	−0.376009	+	1.23954i	−0.917129	+	0.398590i	$0.869500\pi$
$740$	−2.80335	+	1.61933i	−0.103053	+	0.0595278i
$741$	0.143821	−	1.46024i	0.00528340	−	0.0536433i
$742$	10.0615	−	0.660567i	0.369370	−	0.0242502i
$743$	4.44920	−	22.3677i	0.163225	−	0.820590i	−0.809228	−	0.587494i	$-0.800115\pi$
$743$	4.44920	−	22.3677i	0.163225	−	0.820590i	0.972454	−	0.233096i	$-0.0748855\pi$
$744$	17.3784	+	41.9165i	0.637123	+	1.53673i
$745$	−17.8001	+	3.54066i	−0.652145	+	0.129720i
$746$	16.2869	−	28.2168i	0.596305	−	1.03309i
$747$	0.284137	−	0.531583i	0.0103960	−	0.0194496i
$748$	2.06085	+	2.87459i	0.0753522	+	0.105106i
$749$	0.377578	+	3.83362i	0.0137964	+	0.140077i
$750$	−0.360397	−	2.18141i	−0.0131598	−	0.0796540i
$751$	14.7513	−	6.11019i	0.538283	−	0.222964i	−0.0969439	−	0.995290i	$-0.530907\pi$
$751$	14.7513	−	6.11019i	0.538283	−	0.222964i	0.635227	+	0.772326i	$0.280907\pi$
$752$	−3.93435	−	14.6576i	−0.143471	−	0.534509i
$753$	20.1036	+	8.32717i	0.732615	+	0.303459i
$754$	−9.30232	+	39.9151i	−0.338771	+	1.45362i
$755$	−0.743520	−	0.610191i	−0.0270594	−	0.0222071i
$756$	37.7941	−	17.1342i	1.37456	−	0.623165i
$757$	−23.4450	+	7.11198i	−0.852124	+	0.258489i	−0.685987	−	0.727614i	$-0.740629\pi$
$757$	−23.4450	+	7.11198i	−0.852124	+	0.258489i	−0.166137	+	0.986103i	$0.553129\pi$
$758$	42.9899	+	5.65496i	1.56146	+	0.205398i
$759$	3.39581	−	5.08218i	0.123260	−	0.184472i
$760$	0.684437	+	0.0671855i	0.0248272	+	0.00243707i
$761$	−36.4810	+	24.3758i	−1.32244	+	0.883623i	−0.998057	−	0.0623043i	$-0.980155\pi$
$761$	−36.4810	+	24.3758i	−1.32244	+	0.883623i	−0.324378	+	0.945927i	$0.605155\pi$
$762$	−2.97276	+	8.76059i	−0.107692	+	0.317363i
$763$	3.49571	+	4.25953i	0.126553	+	0.154205i
$764$	−17.3839	−	1.13560i	−0.628926	−	0.0410844i
$765$	0.294005	−	0.157149i	0.0106298	−	0.00568174i
$766$	0.678591	−	0.635709i	0.0245185	−	0.0229691i
$767$	57.7965			2.08691
$768$	−24.3560	+	5.70140i	−0.878872	+	0.205731i
$769$	−5.62044			−0.202678			−0.101339	−	0.994852i	$-0.532313\pi$
$769$	−5.62044			−0.202678			−0.101339	+	0.994852i	$0.532313\pi$
$770$	11.3572	−	10.6395i	0.409284	−	0.383420i
$771$	28.9989	−	15.5002i	1.04437	−	0.558227i
$772$	−36.4980	−	2.38423i	−1.31359	−	0.0858101i
$773$	11.3642	+	13.8473i	0.408740	+	0.498052i	0.936170	−	0.351547i	$-0.114344\pi$
$773$	11.3642	+	13.8473i	0.408740	+	0.498052i	−0.527430	+	0.849599i	$0.676844\pi$
$774$	−1.18980	+	3.50630i	−0.0427665	+	0.126031i
$775$	8.53216	−	5.70100i	0.306484	−	0.204786i
$776$	4.66748	−	47.5489i	0.167553	−	1.70691i
$777$	5.24759	−	7.85357i	0.188256	−	0.281745i
$778$	49.0718	+	6.45499i	1.75931	+	0.231422i
$779$	1.77573	−	0.538663i	0.0636223	−	0.0192996i
$780$	10.9923	−	4.98345i	0.393589	−	0.178436i
$781$	−0.221125	−	0.181473i	−0.00791248	−	0.00649360i
$782$	−0.255308	+	1.09550i	−0.00912981	+	0.0391749i
$783$	−38.5611	−	15.9725i	−1.37806	−	0.570811i
$784$	−13.8499	+	24.0129i	−0.494640	+	0.857604i
$785$	13.9671	−	5.78534i	0.498506	−	0.206488i
$786$	3.70887	+	22.4491i	0.132291	+	0.800732i
$787$	1.47446	+	14.9705i	0.0525590	+	0.533640i	0.985028	+	0.172392i	$0.0551494\pi$
$787$	1.47446	+	14.9705i	0.0525590	+	0.533640i	−0.932470	+	0.361249i	$0.882351\pi$
$788$	1.44643	+	2.01757i	0.0515271	+	0.0718729i
$789$	20.8974	−	39.0963i	0.743968	−	1.39187i
$790$	−0.662949	+	1.14855i	−0.0235867	+	0.0408636i
$791$	73.3951	−	14.5992i	2.60963	−	0.519088i
$792$	4.28133	−	1.77502i	0.152131	−	0.0630728i
$793$	−6.66940	+	33.5293i	−0.236837	+	1.19066i
$794$	−14.0418	+	0.921884i	−0.498325	+	0.0327164i
$795$	−0.292737	+	2.97221i	−0.0103823	+	0.105413i
$796$	47.0549	−	27.1808i	1.66782	−	0.963398i
$797$	−0.628750	+	2.07271i	−0.0222715	+	0.0734192i	−0.967372	−	0.253361i	$-0.918464\pi$
$797$	−0.628750	+	2.07271i	−0.0222715	+	0.0734192i	0.945100	+	0.326781i	$0.105964\pi$
$798$	−1.87780	+	0.706988i	−0.0664734	+	0.0250271i
$799$	1.60925	+	1.60925i	0.0569311	+	0.0569311i
$800$	2.33743	+	5.15135i	0.0826406	+	0.182128i
$801$	−3.04299	+	3.04299i	−0.107519	+	0.107519i
$802$	−2.52540	+	5.57529i	−0.0891750	+	0.196870i
$803$	19.5551	+	5.93198i	0.690085	+	0.209335i
$804$	−12.7654	+	16.6437i	−0.450201	+	0.586977i
$805$	4.92535	+	0.485104i	0.173596	+	0.0170977i
$806$	42.1185	+	36.9288i	1.48356	+	1.30076i
$807$	33.4406	+	6.65175i	1.17717	+	0.234153i
$808$	17.5693	−	11.7477i	0.618085	−	0.413283i
$809$	−1.73141	−	8.70440i	−0.0608732	−	0.306030i	0.938339	−	0.345717i	$-0.112364\pi$
$809$	−1.73141	−	8.70440i	−0.0608732	−	0.306030i	−0.999212	+	0.0396862i	$0.987364\pi$
$810$	2.57193	+	9.59440i	0.0903684	+	0.337113i
$811$	−27.4434	−	14.6688i	−0.963670	−	0.515092i	−0.0870122	−	0.996207i	$-0.527732\pi$
$811$	−27.4434	−	14.6688i	−0.963670	−	0.515092i	−0.876657	+	0.481115i	$0.840232\pi$
$812$	54.5782	−	12.7384i	1.91532	−	0.447030i
$813$	33.4428	−	3.29382i	1.17289	−	0.115519i
$814$	3.93078	−	5.48666i	0.137774	−	0.192307i
$815$	−1.27638	−	3.08147i	−0.0447098	−	0.107939i
$816$	2.73667	−	2.56541i	0.0958025	−	0.0898072i
$817$	0.438341	−	1.05825i	0.0153356	−	0.0370234i
$818$	25.3926	+	40.8247i	0.887832	+	1.42740i
$819$	5.07942	−	6.18930i	0.177489	−	0.216272i
$820$	11.1425	+	10.4315i	0.389113	+	0.364285i
$821$	−9.48723	−	31.2752i	−0.331107	−	1.09151i	−0.951610	−	0.307308i	$-0.900572\pi$
$821$	−9.48723	−	31.2752i	−0.331107	−	1.09151i	0.620504	−	0.784204i	$-0.286928\pi$
$822$	−9.53535	−	12.4239i	−0.332584	−	0.433334i
$823$	−17.9622	−	12.0019i	−0.626122	−	0.418361i	0.201625	−	0.979463i	$-0.435378\pi$
$823$	−17.9622	−	12.0019i	−0.626122	−	0.418361i	−0.827747	+	0.561102i	$0.810378\pi$
$824$	−22.1271	+	11.8365i	−0.770834	+	0.412343i
$825$	2.56088	+	3.83262i	0.0891582	+	0.133435i
$826$	−34.9638	−	70.8800i	−1.21654	−	2.46623i
$827$	43.1260	−	35.3926i	1.49964	−	1.23072i	0.595590	−	0.803288i	$-0.296918\pi$
$827$	43.1260	−	35.3926i	1.49964	−	1.23072i	0.904047	−	0.427432i	$-0.140582\pi$
$828$	1.32209	+	0.651624i	0.0459458	+	0.0226455i
$829$	19.4933	+	36.4693i	0.677029	+	1.26663i	0.952270	+	0.305257i	$0.0987423\pi$
$829$	19.4933	+	36.4693i	0.677029	+	1.26663i	−0.275241	+	0.961375i	$0.588758\pi$
$830$	−1.53294	−	0.0500163i	−0.0532093	−	0.00173609i
$831$		−	17.8801i		−	0.620255i
$832$	−23.8573	+	19.6053i	−0.827103	+	0.679690i
$833$		−	4.15692i		−	0.144029i
$834$	0.780814	−	23.9311i	0.0270374	−	0.828665i
$835$	11.4986	+	21.5124i	0.397926	+	0.744468i
$836$	−1.35758	+	0.461166i	−0.0469529	+	0.0159498i
$837$	−44.0963	+	36.1889i	−1.52419	+	1.25087i
$838$	−28.3457	+	13.9824i	−0.979186	+	0.483014i
$839$	5.98196	+	8.95264i	0.206520	+	0.309079i	0.920242	−	0.391350i	$-0.127992\pi$
$839$	5.98196	+	8.95264i	0.206520	+	0.309079i	−0.713722	+	0.700429i	$0.752992\pi$
$840$	−12.7613	−	10.4660i	−0.440308	−	0.361111i
$841$	−22.7583	−	15.2066i	−0.784770	−	0.524367i
$842$	−6.44695	+	4.94804i	−0.222177	+	0.170521i
$843$	−4.60083	−	15.1669i	−0.158461	−	0.522375i
$844$	1.26915	+	38.5121i	0.0436860	+	1.32564i
$845$	1.20473	−	1.46796i	0.0414438	−	0.0504994i
$846$	2.53225	−	1.57504i	0.0870605	−	0.0541509i
$847$	3.29542	−	7.95584i	0.113232	−	0.273366i
$848$	−1.24801	−	7.53865i	−0.0428568	−	0.258878i
$849$	10.7505	+	25.9541i	0.368957	+	0.890742i
$850$	−0.689579	−	0.494032i	−0.0236524	−	0.0169452i
$851$	2.13614	−	0.210392i	0.0732260	−	0.00721213i
$852$	−0.160144	+	0.257658i	−0.00548646	+	0.00882723i
$853$	31.6705	+	16.9282i	1.08438	+	0.579611i	0.913978	−	0.405764i	$-0.132995\pi$
$853$	31.6705	+	16.9282i	1.08438	+	0.579611i	0.170398	+	0.985375i	$0.445495\pi$
$854$	45.1540	−	12.1043i	1.54514	−	0.414199i
$855$	0.0263636	+	0.132539i	0.000901617	+	0.00453274i
$856$	2.86297	−	0.570453i	0.0978544	−	0.0194977i
$857$	21.6080	+	4.29809i	0.738114	+	0.146820i	0.549809	−	0.835291i	$-0.314701\pi$
$857$	21.6080	+	4.29809i	0.738114	+	0.146820i	0.188305	+	0.982111i	$0.439701\pi$
$858$	−16.5883	+	18.9195i	−0.566316	+	0.645902i
$859$	44.1640	+	4.34977i	1.50686	+	0.148412i	0.817466	−	0.575978i	$-0.195378\pi$
$859$	44.1640	+	4.34977i	1.50686	+	0.148412i	0.689391	+	0.724390i	$0.257878\pi$
$860$	9.34087	−	1.23182i	0.318521	−	0.0420046i
$861$	−42.6144	−	12.9269i	−1.45229	−	0.440548i
$862$	−19.6086	−	8.88198i	−0.667872	−	0.302521i
$863$	9.74105	−	9.74105i	0.331589	−	0.331589i	−0.521601	−	0.853190i	$-0.674665\pi$
$863$	9.74105	−	9.74105i	0.331589	−	0.331589i	0.853190	+	0.521601i	$0.174665\pi$
$864$	−15.7383	−	27.2254i	−0.535429	−	0.926226i
$865$	−10.5358	−	10.5358i	−0.358229	−	0.358229i
$866$	10.2784	+	27.3000i	0.349274	+	0.927692i
$867$	7.55185	−	24.8951i	0.256474	−	0.845483i
$868$	19.8091	−	73.9929i	0.672364	−	2.51148i
$869$	0.270993	−	2.75144i	0.00919281	−	0.0933361i
$870$	1.08751	+	16.5646i	0.0368701	+	0.561592i
$871$	−5.05154	+	25.3958i	−0.171165	+	0.860505i
$872$	2.95179	−	2.95372i	0.0999604	−	0.100026i
$873$	9.20768	−	1.83152i	0.311633	−	0.0619876i
$874$	−0.394910	−	0.227944i	−0.0133580	−	0.00771033i
$875$	−1.75940	+	3.29161i	−0.0594786	+	0.111277i
$876$	3.52560	−	21.3832i	0.119119	−	0.722471i
$877$	−4.61739	−	46.8812i	−0.155918	−	1.58306i	−0.681175	−	0.732121i	$-0.738531\pi$
$877$	−4.61739	−	46.8812i	−0.155918	−	1.58306i	0.525256	−	0.850944i	$-0.323969\pi$
$878$	−13.0365	+	2.15379i	−0.439961	+	0.0726870i
$879$	−5.49390	+	2.27565i	−0.185305	+	0.0767557i
$880$	−8.87013	−	7.77206i	−0.299012	−	0.261996i
$881$	30.2539	+	12.5316i	1.01928	+	0.422199i	0.828832	−	0.559498i	$-0.189006\pi$
$881$	30.2539	+	12.5316i	1.01928	+	0.422199i	0.190447	+	0.981697i	$0.439006\pi$
$882$	−5.30486	−	1.23631i	−0.178624	−	0.0416287i
$883$	−12.8118	−	10.5144i	−0.431151	−	0.353837i	0.393649	−	0.919261i	$-0.371212\pi$
$883$	−12.8118	−	10.5144i	−0.431151	−	0.353837i	−0.824800	+	0.565424i	$0.808712\pi$
$884$	1.63018	−	4.33414i	0.0548289	−	0.145773i
$885$	22.4016	−	6.79544i	0.753021	−	0.228426i
$886$	−5.63451	+	42.8344i	−0.189295	+	1.43905i
$887$	−1.34298	+	2.00991i	−0.0450929	+	0.0674862i	−0.853331	−	0.521369i	$-0.825421\pi$
$887$	−1.34298	+	2.00991i	−0.0450929	+	0.0674862i	0.808238	+	0.588856i	$0.200421\pi$
$888$	−6.31383	−	3.37216i	−0.211878	−	0.113162i
$889$	12.9849	−	8.67623i	0.435499	−	0.290991i
$890$	10.3697	+	3.51878i	0.347593	+	0.117950i
$891$	−13.1374	−	16.0080i	−0.440119	−	0.536287i
$892$	−33.1242	−	37.7543i	−1.10908	−	1.26411i
$893$	−0.813602	+	0.434879i	−0.0272262	+	0.0145527i
$894$	−27.4335	−	29.2841i	−0.917514	−	0.979406i
$895$	−14.6882			−0.490972
$896$	38.4757	+	17.3978i	1.28538	+	0.581219i
$897$	−8.00210			−0.267182
$898$	−23.6552	−	25.2508i	−0.789383	−	0.842632i
$899$	−67.9471	+	36.3185i	−2.26616	+	1.21129i
$900$	−0.835547	+	0.733077i	−0.0278516	+	0.0244359i
$901$	0.726925	+	0.885761i	0.0242174	+	0.0295090i
$902$	−30.1335	−	10.2253i	−1.00334	−	0.340465i
$903$	−22.8558	+	15.2718i	−0.760594	+	0.508213i
$904$	−16.4798	−	54.2627i	−0.548109	−	1.80475i
$905$	8.12719	−	12.1632i	0.270157	−	0.404319i
$906$	0.277352	−	2.10847i	0.00921440	−	0.0700492i
$907$	−50.0713	+	15.1890i	−1.66259	+	0.504341i	−0.975083	−	0.221838i	$-0.928794\pi$
$907$	−50.0713	+	15.1890i	−1.66259	+	0.504341i	−0.687506	+	0.726179i	$0.741294\pi$
$908$	−28.7866	−	10.8274i	−0.955318	−	0.359319i
$909$	3.21027	+	2.63460i	0.106478	+	0.0873841i
$910$	−19.8421	−	4.62425i	−0.657759	−	0.153292i
$911$	14.4329	+	5.97829i	0.478182	+	0.198069i	0.608738	−	0.793372i	$-0.291676\pi$
$911$	14.4329	+	5.97829i	0.478182	+	0.198069i	−0.130556	+	0.991441i	$0.541676\pi$
$912$	0.673117	+	1.36345i	0.0222891	+	0.0451483i
$913$	2.95418	−	1.22366i	0.0977690	−	0.0404972i
$914$	36.6063	−	6.04781i	1.21083	−	0.200044i
$915$	1.35720	+	13.7799i	0.0448677	+	0.455550i
$916$	45.8111	+	7.55320i	1.51364	+	0.249565i
$917$	18.1061	−	33.8742i	0.597917	−	1.11862i
$918$	4.08418	+	2.35741i	0.134798	+	0.0778060i
$919$	−9.08771	+	1.80766i	−0.299776	+	0.0596291i	−0.342687	−	0.939450i	$-0.611337\pi$
$919$	−9.08771	+	1.80766i	−0.299776	+	0.0596291i	0.0429108	+	0.999079i	$0.486337\pi$
$920$	−0.00122494	−	3.75059i	−4.03851e−5	−	0.123653i
$921$	−7.90618	+	39.7470i	−0.260517	+	1.30971i
$922$	−1.40161	−	21.3488i	−0.0461595	−	0.703085i
$923$	−0.0367075	+	0.372697i	−0.00120824	+	0.0122675i
$924$	33.2374	+	8.89818i	1.09343	+	0.292729i
$925$	−0.469890	+	1.54902i	−0.0154499	+	0.0509314i
$926$	0.311227	+	0.826637i	0.0102276	+	0.0271650i
$927$	−3.48666	−	3.48666i	−0.114517	−	0.114517i
$928$	−13.6741	−	40.2107i	−0.448874	−	1.31998i
$929$	−11.4778	+	11.4778i	−0.376576	+	0.376576i	−0.869865	−	0.493289i	$-0.835794\pi$
$929$	−11.4778	+	11.4778i	−0.376576	+	0.376576i	0.493289	+	0.869865i	$0.335794\pi$
$930$	20.6668	+	9.36129i	0.677691	+	0.306969i
$931$	1.61250	+	0.489148i	0.0528477	+	0.0160312i
$932$	−1.91460	−	14.5184i	−0.0627148	−	0.475566i
$933$	−50.2817	−	4.95231i	−1.64615	−	0.162131i
$934$	22.3763	−	25.5209i	0.732174	−	0.835068i
$935$	1.73452	+	0.345018i	0.0567249	+	0.0112833i
$936$	−5.04619	−	3.36937i	−0.164940	−	0.110131i
$937$	−5.58227	−	28.0640i	−0.182365	−	0.916810i	−0.958249	−	0.285935i	$-0.907696\pi$
$937$	−5.58227	−	28.0640i	−0.182365	−	0.916810i	0.775884	−	0.630875i	$-0.217304\pi$
$938$	34.2006	−	9.16802i	1.11669	−	0.299347i
$939$	4.14186	+	2.21387i	0.135164	+	0.0722469i
$940$	−6.44483	−	4.00570i	−0.210207	−	0.130652i
$941$	−42.8704	+	4.22236i	−1.39753	+	0.137645i	−0.768558	−	0.639780i	$-0.779025\pi$
$941$	−42.8704	+	4.22236i	−1.39753	+	0.137645i	−0.628976	+	0.777425i	$0.716525\pi$
$942$	27.1718	+	19.4665i	0.885304	+	0.634254i
$943$	−3.87272	−	9.34958i	−0.126113	−	0.304464i
$944$	−50.8483	+	31.6502i	−1.65497	+	1.03013i
$945$	7.94005	−	19.1690i	0.258290	−	0.623566i
$946$	−16.6793	+	10.3743i	−0.542289	+	0.337299i
$947$	−7.80993	+	9.51642i	−0.253789	+	0.309242i	−0.884283	−	0.466952i	$-0.845352\pi$
$947$	−7.80993	+	9.51642i	−0.253789	+	0.309242i	0.630494	+	0.776194i	$0.282852\pi$
$948$	−2.93050	+	0.0965735i	−0.0951783	+	0.00313656i
$949$	−7.76603	−	25.6012i	−0.252096	−	0.831050i
$950$	0.272782	−	0.209361i	0.00885023	−	0.00679255i
$951$	0.561708	+	0.375321i	0.0182146	+	0.0121706i
$952$	−6.30144	+	0.622716i	−0.204231	+	0.0201823i
$953$	11.7583	+	17.5975i	0.380888	+	0.570039i	0.971537	−	0.236890i	$-0.0761280\pi$
$953$	11.7583	+	17.5975i	0.380888	+	0.570039i	−0.590649	+	0.806929i	$0.701128\pi$
$954$	1.34656	−	0.664232i	0.0435965	−	0.0215053i
$955$	−6.73327	+	5.52585i	−0.217883	+	0.178812i
$956$	−4.78105	−	14.0744i	−0.154630	−	0.455200i
$957$	−16.3142	−	30.5217i	−0.527362	−	0.986625i
$958$	−1.59940	+	49.0198i	−0.0516743	+	1.58376i
$959$			26.4375i			0.853712i
$960$	−6.94184	+	10.4039i	−0.224047	+	0.335785i
$961$			74.2991i			2.39675i
$962$	−8.83150	−	0.288151i	−0.284739	−	0.00929036i
$963$	0.270403	+	0.505889i	0.00871362	+	0.0163020i
$964$	−21.2221	+	43.0579i	−0.683519	+	1.38680i
$965$	−14.1367	+	11.6017i	−0.455078	+	0.373473i
$966$	4.84084	+	9.81355i	0.155751	+	0.315746i
$967$	−3.49456	−	5.22998i	−0.112377	−	0.168185i	0.771018	−	0.636814i	$-0.219748\pi$
$967$	−3.49456	−	5.22998i	−0.112377	−	0.168185i	−0.883395	+	0.468629i	$0.844748\pi$
$968$	−6.24547	−	1.89232i	−0.200737	−	0.0608213i
$969$	−0.189590	−	0.126680i	−0.00609050	−	0.00406954i
$970$	−14.5446	−	18.9506i	−0.466999	−	0.608467i
$971$	4.52222	+	14.9078i	0.145125	+	0.478413i	0.999123	−	0.0418628i	$-0.0133292\pi$
$971$	4.52222	+	14.9078i	0.145125	+	0.478413i	−0.853998	+	0.520276i	$0.825829\pi$
$972$	7.78609	−	8.31675i	0.249739	−	0.266760i
$973$	−25.6416	+	31.2443i	−0.822031	+	1.00165i
$974$	8.21489	+	13.2074i	0.263222	+	0.423193i
$975$	2.30935	−	5.57526i	0.0739583	−	0.178551i
$976$	−12.4935	−	33.1507i	−0.399908	−	1.06113i
$977$	−17.8580	−	43.1131i	−0.571330	−	1.37931i	−0.900424	−	0.435014i	$-0.856743\pi$
$977$	−17.8580	−	43.1131i	−0.571330	−	1.37931i	0.329094	−	0.944297i	$-0.393257\pi$
$978$	4.29478	−	5.99474i	0.137332	−	0.191691i
$979$	−22.7195	+	2.23768i	−0.726120	+	0.0715166i
$980$	3.15030	+	13.4976i	0.100633	+	0.431165i
$981$	0.723646	+	0.386797i	0.0231043	+	0.0123495i
$982$	6.96002	+	25.9638i	0.222103	+	0.828539i
$983$	−4.53930	−	22.8206i	−0.144781	−	0.727865i	−0.983156	−	0.182770i	$-0.941494\pi$
$983$	−4.53930	−	22.8206i	−0.144781	−	0.727865i	0.838374	−	0.545095i	$-0.183506\pi$
$984$	−6.57294	+	33.1009i	−0.209538	+	1.05522i
$985$	1.21740	+	0.242155i	0.0387894	+	0.00771570i
$986$	4.78892	+	4.19884i	0.152510	+	0.133718i
$987$	22.0325	+	2.17001i	0.701303	+	0.0690723i
$988$	1.48943	+	1.14236i	0.0473850	+	0.0363434i
$989$	−5.97779	−	1.81334i	−0.190083	−	0.0576609i
$990$	0.956159	−	2.11090i	0.0303887	−	0.0670888i
$991$	16.6985	−	16.6985i	0.530445	−	0.530445i	−0.390260	−	0.920705i	$-0.627615\pi$
$991$	16.6985	−	16.6985i	0.530445	−	0.530445i	0.920705	+	0.390260i	$0.127615\pi$
$992$	−57.2778	−	9.42458i	−1.81857	−	0.299231i
$993$	18.7688	+	18.7688i	0.595608	+	0.595608i
$994$	0.479271	−	0.180445i	0.0152016	−	0.00572335i
$995$	7.88720	−	26.0006i	0.250041	−	0.824275i
$996$	−1.69620	−	2.93643i	−0.0537461	−	0.0930442i
$997$	5.29927	−	53.8044i	0.167830	−	1.70400i	−0.430368	−	0.902654i	$-0.641616\pi$
$997$	5.29927	−	53.8044i	0.167830	−	1.70400i	0.598197	−	0.801349i	$-0.295884\pi$
$998$	39.9306	−	2.62156i	1.26398	−	0.0829840i
$999$	1.75555	−	8.82573i	0.0555430	−	0.279234i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.101.16	✓	1024
128.109	even	32	inner	640.2.bm.a.621.16	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.101.16	✓	1024	1.1	even	1	trivial
640.2.bm.a.621.16	yes	1024	128.109	even	32	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.bm (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.03208 + 0.966858i) q^{2} +(-1.37880 + 0.736983i) q^{3} +(0.130372 - 1.99575i) q^{4} +(-0.634393 - 0.773010i) q^{5} +(0.710470 - 2.09372i) q^{6} +(-3.10331 + 2.07356i) q^{7} +(1.79505 + 2.18582i) q^{8} +(-0.308772 + 0.462110i) q^{9} +(1.40213 + 0.184439i) q^{10} +(-2.82139 + 0.855861i) q^{11} +(1.29107 + 2.84781i) q^{12} +(2.98376 + 2.44871i) q^{13} +(1.19802 - 5.14054i) q^{14} +(1.44440 + 0.598288i) q^{15} +(-3.96601 - 0.520378i) q^{16} +(0.554169 - 0.229544i) q^{17} +(-0.128118 - 0.775472i) q^{18} +(0.0238327 + 0.241977i) q^{19} +(-1.62544 + 1.16531i) q^{20} +(2.75065 - 5.14611i) q^{21} +(2.08440 - 3.61120i) q^{22} +(1.30055 - 0.258696i) q^{23} +(-4.08592 - 1.69088i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(-5.44703 + 0.357613i) q^{26} +(0.544888 - 5.53234i) q^{27} +(3.73372 + 6.46375i) q^{28} +(2.17948 - 7.18478i) q^{29} +(-2.06919 + 0.779045i) q^{30} +(-7.25600 - 7.25600i) q^{31} +(4.59636 - 3.29749i) q^{32} +(3.25938 - 3.25938i) q^{33} +(-0.350009 + 0.772710i) q^{34} +(3.57160 + 1.08343i) q^{35} +(0.881998 + 0.676476i) q^{36} +(1.61093 + 0.158662i) q^{37} +(-0.258555 - 0.226697i) q^{38} +(-5.91866 - 1.17729i) q^{39} +(0.550893 - 2.77426i) q^{40} +(-1.48887 - 7.48507i) q^{41} +(2.13667 + 7.97068i) q^{42} +(-4.15462 - 2.22069i) q^{43} +(1.34025 + 5.74237i) q^{44} +(0.553098 - 0.0544754i) q^{45} +(-1.09215 + 1.52445i) q^{46} +(1.45195 + 3.50531i) q^{47} +(5.85183 - 2.20538i) q^{48} +(2.65207 - 6.40266i) q^{49} +(-0.746931 - 1.20087i) q^{50} +(-0.594916 + 0.724908i) q^{51} +(5.27600 - 5.63559i) q^{52} +(0.554534 + 1.82806i) q^{53} +(4.78662 + 6.23663i) q^{54} +(2.45146 + 1.63801i) q^{55} +(-10.1030 - 3.06112i) q^{56} +(-0.211194 - 0.316073i) q^{57} +(4.69727 + 9.52250i) q^{58} +(11.5747 - 9.49908i) q^{59} +(1.38234 - 2.80465i) q^{60} +(4.17502 + 7.81091i) q^{61} +(14.5043 + 0.473240i) q^{62} -2.07433i q^{63} +(-1.55560 + 7.84730i) q^{64} -3.85992i q^{65} +(-0.212578 + 6.51529i) q^{66} +(3.16225 + 5.91615i) q^{67} +(-0.385864 - 1.13591i) q^{68} +(-1.60255 + 1.31518i) q^{69} +(-4.73370 + 2.33504i) q^{70} +(0.0539030 + 0.0806715i) q^{71} +(-1.56435 + 0.154591i) q^{72} +(-5.76292 - 3.85066i) q^{73} +(-1.81601 + 1.39378i) q^{74} +(-0.453832 - 1.49608i) q^{75} +(0.486033 - 0.0160170i) q^{76} +(6.98097 - 8.50634i) q^{77} +(7.24680 - 4.50744i) q^{78} +(-0.358853 + 0.866348i) q^{79} +(2.11375 + 3.39589i) q^{80} +(2.68789 + 6.48914i) q^{81} +(8.77364 + 6.28565i) q^{82} +(-1.07931 + 0.106303i) q^{83} +(-9.91172 - 6.16051i) q^{84} +(-0.529001 - 0.282757i) q^{85} +(6.43498 - 1.72500i) q^{86} +(2.29000 + 11.5126i) q^{87} +(-6.93530 - 4.63074i) q^{88} +(7.59436 + 1.51061i) q^{89} +(-0.518171 + 0.590990i) q^{90} +(-14.3371 - 1.41208i) q^{91} +(-0.346737 - 2.62930i) q^{92} +(15.3521 + 4.65701i) q^{93} +(-4.88766 - 2.21393i) q^{94} +(0.171932 - 0.171932i) q^{95} +(-3.90726 + 7.93401i) q^{96} +(-11.9444 - 11.9444i) q^{97} +(3.45332 + 9.17222i) q^{98} +(0.475665 - 1.56806i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) \) 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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