LMFDB - Embedded newform 950.2.w.a.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(37,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([9, 10]))

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

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

chi := DirichletCharacter("950.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.w (of order $20$, degree $8$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$400$
Relative dimension:	$50$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			37.1
Character	$\chi$	$=$	950.37
Dual form			950.2.w.a.873.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.987688 + 0.156434i) q^{2} +(-1.41733 + 2.78167i) q^{3} +(0.951057 - 0.309017i) q^{4} +(2.23282 - 0.120389i) q^{5} +(0.964734 - 2.96915i) q^{6} +(3.07932 + 3.07932i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(-3.96551 - 5.45806i) q^{9} +O(q^{10})$	\(q+(-0.987688 + 0.156434i) q^{2} +(-1.41733 + 2.78167i) q^{3} +(0.951057 - 0.309017i) q^{4} +(2.23282 - 0.120389i) q^{5} +(0.964734 - 2.96915i) q^{6} +(3.07932 + 3.07932i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(-3.96551 - 5.45806i) q^{9} +(-2.18650 + 0.468198i) q^{10} +(-0.779003 - 0.565979i) q^{11} +(-0.488380 + 3.08351i) q^{12} +(5.73928 + 0.909012i) q^{13} +(-3.52312 - 2.55969i) q^{14} +(-2.82977 + 6.38162i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-6.62836 + 3.37732i) q^{17} +(4.77052 + 4.77052i) q^{18} +(4.35835 + 0.0689505i) q^{19} +(2.08634 - 0.804478i) q^{20} +(-12.9301 + 4.20123i) q^{21} +(0.857951 + 0.437148i) q^{22} +(5.87184 - 0.930008i) q^{23} -3.12194i q^{24} +(4.97101 - 0.537615i) q^{25} -5.81082 q^{26} +(11.5525 - 1.82973i) q^{27} +(3.88017 + 1.97704i) q^{28} +(1.54394 + 4.75177i) q^{29} +(1.79663 - 6.74572i) q^{30} +(3.78002 + 1.22820i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(2.67848 - 1.36475i) q^{33} +(6.01843 - 4.37264i) q^{34} +(7.24629 + 6.50486i) q^{35} +(-5.45806 - 3.96551i) q^{36} +(0.993110 - 6.27025i) q^{37} +(-4.31548 + 0.613695i) q^{38} +(-10.6630 + 14.6764i) q^{39} +(-1.93481 + 1.12095i) q^{40} +(-2.27130 - 3.12618i) q^{41} +(12.1137 - 6.17222i) q^{42} +(0.664893 - 0.664893i) q^{43} +(-0.915773 - 0.297553i) q^{44} +(-9.51139 - 11.7095i) q^{45} +(-5.65406 + 1.83712i) q^{46} +(-1.86766 + 3.66550i) q^{47} +(0.488380 + 3.08351i) q^{48} +11.9644i q^{49} +(-4.82571 + 1.30863i) q^{50} -23.2247i q^{51} +(5.73928 - 0.909012i) q^{52} +(-2.36153 + 4.63477i) q^{53} +(-11.1240 + 3.61441i) q^{54} +(-1.80752 - 1.16995i) q^{55} +(-4.14167 - 1.34571i) q^{56} +(-6.36904 + 12.0258i) q^{57} +(-2.26827 - 4.45174i) q^{58} +(3.44923 - 2.50601i) q^{59} +(-0.719246 + 6.94373i) q^{60} +(-5.03331 - 3.65691i) q^{61} +(-3.92562 - 0.621756i) q^{62} +(4.59603 - 29.0182i) q^{63} +(0.587785 - 0.809017i) q^{64} +(12.9242 + 1.33872i) q^{65} +(-2.43201 + 1.76696i) q^{66} +(-1.41499 - 2.77708i) q^{67} +(-5.26030 + 5.26030i) q^{68} +(-5.73537 + 17.6517i) q^{69} +(-8.17466 - 5.29120i) q^{70} +(-1.64638 + 0.534940i) q^{71} +(6.01121 + 3.06286i) q^{72} +(-5.64995 + 0.894865i) q^{73} +6.34841i q^{74} +(-5.55011 + 14.5897i) q^{75} +(4.16635 - 1.28123i) q^{76} +(-0.655969 - 4.14163i) q^{77} +(8.23586 - 16.1638i) q^{78} +(-2.49638 - 7.68306i) q^{79} +(1.73563 - 1.40982i) q^{80} +(-5.02960 + 15.4795i) q^{81} +(2.73238 + 2.73238i) q^{82} +(-3.00824 - 5.90400i) q^{83} +(-10.9990 + 7.99122i) q^{84} +(-14.3934 + 8.33894i) q^{85} +(-0.552695 + 0.760719i) q^{86} +(-15.4061 - 2.44009i) q^{87} +(0.951046 + 0.150631i) q^{88} +(0.480087 + 0.348803i) q^{89} +(11.2261 + 10.0774i) q^{90} +(14.8739 + 20.4722i) q^{91} +(5.29706 - 2.69899i) q^{92} +(-8.77401 + 8.77401i) q^{93} +(1.27126 - 3.91254i) q^{94} +(9.73974 - 0.370743i) q^{95} +(-0.964734 - 2.96915i) q^{96} +(-16.9465 - 8.63470i) q^{97} +(-1.87164 - 11.8171i) q^{98} +6.49625i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 400 q + 4 q^{5} - 4 q^{7}+O(q^{10}) $ 400 * q + 4 * q^5 - 4 * q^7	$ 400 q + 4 q^{5} - 4 q^{7} + 100 q^{16} + 40 q^{17} - 40 q^{19} - 76 q^{23} - 20 q^{25} - 4 q^{28} + 64 q^{30} + 8 q^{35} - 100 q^{36} + 4 q^{38} + 80 q^{39} + 32 q^{42} - 84 q^{43} - 144 q^{45} + 20 q^{47} - 16 q^{55} - 32 q^{57} - 16 q^{62} + 108 q^{63} - 100 q^{68} - 12 q^{73} + 256 q^{77} - 4 q^{80} + 100 q^{81} - 16 q^{82} + 116 q^{85} - 272 q^{87} - 4 q^{92} - 24 q^{93} - 56 q^{95}+O(q^{100}) $ 400 * q + 4 * q^5 - 4 * q^7 + 100 * q^16 + 40 * q^17 - 40 * q^19 - 76 * q^23 - 20 * q^25 - 4 * q^28 + 64 * q^30 + 8 * q^35 - 100 * q^36 + 4 * q^38 + 80 * q^39 + 32 * q^42 - 84 * q^43 - 144 * q^45 + 20 * q^47 - 16 * q^55 - 32 * q^57 - 16 * q^62 + 108 * q^63 - 100 * q^68 - 12 * q^73 + 256 * q^77 - 4 * q^80 + 100 * q^81 - 16 * q^82 + 116 * q^85 - 272 * q^87 - 4 * q^92 - 24 * q^93 - 56 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{9}{20}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.987688	+	0.156434i	−0.698401	+	0.110616i
$2$	−0.987688	+	0.156434i	−0.698401	+	0.110616i
$3$	−1.41733	+	2.78167i	−0.818298	+	1.60600i	−0.0230347	+	0.999735i	$0.507333\pi$
$3$	−1.41733	+	2.78167i	−0.818298	+	1.60600i	−0.795263	+	0.606265i	$0.792667\pi$
$4$	0.951057	−	0.309017i	0.475528	−	0.154508i
$5$	2.23282	−	0.120389i	0.998550	−	0.0538396i
$5$	2.23282	−	0.120389i	0.998550	−	0.0538396i
$6$	0.964734	−	2.96915i	0.393851	−	1.21215i
$7$	3.07932	+	3.07932i	1.16387	+	1.16387i	0.983621	+	0.180252i	$0.0576912\pi$
$7$	3.07932	+	3.07932i	1.16387	+	1.16387i	0.180252	+	0.983621i	$0.442309\pi$
$8$	−0.891007	+	0.453990i	−0.315018	+	0.160510i
$9$	−3.96551	−	5.45806i	−1.32184	−	1.81935i
$10$	−2.18650	+	0.468198i	−0.691433	+	0.148057i
$11$	−0.779003	−	0.565979i	−0.234878	−	0.170649i	0.464120	−	0.885772i	$-0.346371\pi$
$11$	−0.779003	−	0.565979i	−0.234878	−	0.170649i	−0.698998	+	0.715123i	$0.746371\pi$
$12$	−0.488380	+	3.08351i	−0.140983	+	0.890132i
$13$	5.73928	+	0.909012i	1.59179	+	0.252115i	0.888530	−	0.458819i	$-0.151727\pi$
$13$	5.73928	+	0.909012i	1.59179	+	0.252115i	0.703259	+	0.710934i	$0.251727\pi$
$14$	−3.52312	−	2.55969i	−0.941592	−	0.684107i
$15$	−2.82977	+	6.38162i	−0.730644	+	1.64773i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	−6.62836	+	3.37732i	−1.60761	+	0.819120i	−0.607930	+	0.793991i	$0.708000\pi$
$17$	−6.62836	+	3.37732i	−1.60761	+	0.819120i	−0.999684	+	0.0251292i	$0.992000\pi$
$18$	4.77052	+	4.77052i	1.12442	+	1.12442i
$19$	4.35835	+	0.0689505i	0.999875	+	0.0158183i
$19$	4.35835	+	0.0689505i	0.999875	+	0.0158183i
$20$	2.08634	−	0.804478i	0.466520	−	0.179887i
$21$	−12.9301	+	4.20123i	−2.82157	+	0.916784i
$22$	0.857951	+	0.437148i	0.182916	+	0.0932003i
$23$	5.87184	−	0.930008i	1.22436	−	0.193920i	0.489419	−	0.872049i	$-0.337209\pi$
$23$	5.87184	−	0.930008i	1.22436	−	0.193920i	0.734943	+	0.678129i	$0.237209\pi$
$24$		−	3.12194i		−	0.637264i
$25$	4.97101	−	0.537615i	0.994203	−	0.107523i
$26$	−5.81082			−1.13959
$27$	11.5525	−	1.82973i	2.22327	−	0.352132i
$28$	3.88017	+	1.97704i	0.733282	+	0.373626i
$29$	1.54394	+	4.75177i	0.286703	+	0.882381i	0.985883	+	0.167435i	$0.0535486\pi$
$29$	1.54394	+	4.75177i	0.286703	+	0.882381i	−0.699180	+	0.714946i	$0.746451\pi$
$30$	1.79663	−	6.74572i	0.328018	−	1.23160i
$31$	3.78002	+	1.22820i	0.678912	+	0.220592i	0.628119	−	0.778117i	$-0.283825\pi$
$31$	3.78002	+	1.22820i	0.678912	+	0.220592i	0.0507929	+	0.998709i	$0.483825\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	2.67848	−	1.36475i	0.466263	−	0.237573i
$34$	6.01843	−	4.37264i	1.03215	−	0.749902i
$35$	7.24629	+	6.50486i	1.22485	+	1.09952i
$36$	−5.45806	−	3.96551i	−0.909677	−	0.660919i
$37$	0.993110	−	6.27025i	0.163266	−	1.03082i	−0.760910	−	0.648857i	$-0.775247\pi$
$37$	0.993110	−	6.27025i	0.163266	−	1.03082i	0.924177	−	0.381965i	$-0.124753\pi$
$38$	−4.31548	+	0.613695i	−0.700064	+	0.0995545i
$39$	−10.6630	+	14.6764i	−1.70745	+	2.35011i
$40$	−1.93481	+	1.12095i	−0.305920	+	0.177238i
$41$	−2.27130	−	3.12618i	−0.354718	−	0.488227i	0.593950	−	0.804502i	$-0.297568\pi$
$41$	−2.27130	−	3.12618i	−0.354718	−	0.488227i	−0.948667	+	0.316275i	$0.897568\pi$
$42$	12.1137	−	6.17222i	1.86918	−	0.952394i
$43$	0.664893	−	0.664893i	0.101395	−	0.101395i	−0.654589	−	0.755985i	$-0.727158\pi$
$43$	0.664893	−	0.664893i	0.101395	−	0.101395i	0.755985	+	0.654589i	$0.227158\pi$
$44$	−0.915773	−	0.297553i	−0.138058	−	0.0448578i
$45$	−9.51139	−	11.7095i	−1.41787	−	1.74555i
$46$	−5.65406	+	1.83712i	−0.833646	+	0.270868i
$47$	−1.86766	+	3.66550i	−0.272427	+	0.534668i	−0.986169	−	0.165740i	$-0.946999\pi$
$47$	−1.86766	+	3.66550i	−0.272427	+	0.534668i	0.713743	+	0.700408i	$0.246999\pi$
$48$	0.488380	+	3.08351i	0.0704915	+	0.445066i
$49$			11.9644i			1.70920i
$50$	−4.82571	+	1.30863i	−0.682458	+	0.185069i
$51$		−	23.2247i		−	3.25211i
$52$	5.73928	−	0.909012i	0.795894	−	0.126057i
$53$	−2.36153	+	4.63477i	−0.324381	+	0.636634i	−0.994397	−	0.105713i	$-0.966287\pi$
$53$	−2.36153	+	4.63477i	−0.324381	+	0.636634i	0.670015	+	0.742347i	$0.266287\pi$
$54$	−11.1240	+	3.61441i	−1.51379	+	0.491859i
$55$	−1.80752	−	1.16995i	−0.243725	−	0.157756i
$56$	−4.14167	−	1.34571i	−0.553454	−	0.179828i
$57$	−6.36904	+	12.0258i	−0.843599	+	1.59285i
$58$	−2.26827	−	4.45174i	−0.297839	−	0.584542i
$59$	3.44923	−	2.50601i	0.449051	−	0.326255i	−0.340170	−	0.940364i	$-0.610485\pi$
$59$	3.44923	−	2.50601i	0.449051	−	0.326255i	0.789221	+	0.614109i	$0.210485\pi$
$60$	−0.719246	+	6.94373i	−0.0928542	+	0.896431i
$61$	−5.03331	−	3.65691i	−0.644449	−	0.468220i	0.216927	−	0.976188i	$-0.430397\pi$
$61$	−5.03331	−	3.65691i	−0.644449	−	0.468220i	−0.861376	+	0.507968i	$0.830397\pi$
$62$	−3.92562	−	0.621756i	−0.498554	−	0.0789631i
$63$	4.59603	−	29.0182i	0.579045	−	3.65595i
$64$	0.587785	−	0.809017i	0.0734732	−	0.101127i
$65$	12.9242	+	1.33872i	1.60305	+	0.166048i
$66$	−2.43201	+	1.76696i	−0.299359	+	0.217497i
$67$	−1.41499	−	2.77708i	−0.172869	−	0.339274i	0.788275	−	0.615323i	$-0.210975\pi$
$67$	−1.41499	−	2.77708i	−0.172869	−	0.339274i	−0.961143	+	0.276050i	$0.910975\pi$
$68$	−5.26030	+	5.26030i	−0.637905	+	0.637905i
$69$	−5.73537	+	17.6517i	−0.690458	+	2.12501i
$70$	−8.17466	−	5.29120i	−0.977059	−	0.632420i
$71$	−1.64638	+	0.534940i	−0.195389	+	0.0634857i	−0.405077	−	0.914283i	$-0.632755\pi$
$71$	−1.64638	+	0.534940i	−0.195389	+	0.0634857i	0.209688	+	0.977768i	$0.432755\pi$
$72$	6.01121	+	3.06286i	0.708428	+	0.360962i
$73$	−5.64995	+	0.894865i	−0.661277	+	0.104736i	−0.478047	−	0.878334i	$-0.658655\pi$
$73$	−5.64995	+	0.894865i	−0.661277	+	0.104736i	−0.183230	+	0.983070i	$0.558655\pi$
$74$			6.34841i			0.737987i
$75$	−5.55011	+	14.5897i	−0.640872	+	1.68467i
$76$	4.16635	−	1.28123i	0.477913	−	0.146967i
$77$	−0.655969	−	4.14163i	−0.0747546	−	0.471982i
$78$	8.23586	−	16.1638i	0.932528	−	1.83019i
$79$	−2.49638	−	7.68306i	−0.280864	−	0.864411i	−0.987608	−	0.156942i	$-0.949837\pi$
$79$	−2.49638	−	7.68306i	−0.280864	−	0.864411i	0.706744	−	0.707470i	$-0.250163\pi$
$80$	1.73563	−	1.40982i	0.194049	−	0.157622i
$81$	−5.02960	+	15.4795i	−0.558845	+	1.71995i
$82$	2.73238	+	2.73238i	0.301741	+	0.301741i
$83$	−3.00824	−	5.90400i	−0.330197	−	0.648049i	0.664902	−	0.746931i	$-0.268473\pi$
$83$	−3.00824	−	5.90400i	−0.330197	−	0.648049i	−0.995099	+	0.0988821i	$0.968473\pi$
$84$	−10.9990	+	7.99122i	−1.20009	+	0.871914i
$85$	−14.3934	+	8.33894i	−1.56118	+	0.904485i
$86$	−0.552695	+	0.760719i	−0.0595986	+	0.0820304i
$87$	−15.4061	−	2.44009i	−1.65171	−	0.261605i
$88$	0.951046	+	0.150631i	0.101382	+	0.0160573i
$89$	0.480087	+	0.348803i	0.0508891	+	0.0369731i	0.612939	−	0.790130i	$-0.289987\pi$
$89$	0.480087	+	0.348803i	0.0508891	+	0.0369731i	−0.562050	+	0.827103i	$0.689987\pi$
$90$	11.2261	+	10.0774i	1.18333	+	1.06225i
$91$	14.8739	+	20.4722i	1.55921	+	2.14607i
$92$	5.29706	−	2.69899i	0.552257	−	0.281389i
$93$	−8.77401	+	8.77401i	−0.909822	+	0.909822i
$94$	1.27126	−	3.91254i	0.131120	−	0.403547i
$95$	9.73974	−	0.370743i	0.999276	−	0.0380375i
$96$	−0.964734	−	2.96915i	−0.0984627	−	0.303037i
$97$	−16.9465	−	8.63470i	−1.72066	−	0.876721i	−0.978431	−	0.206576i	$-0.933768\pi$
$97$	−16.9465	−	8.63470i	−1.72066	−	0.876721i	−0.742230	−	0.670145i	$-0.766232\pi$
$98$	−1.87164	−	11.8171i	−0.189064	−	1.19371i
$99$			6.49625i			0.652897i
$100$	4.56158	−	2.04743i	0.456158	−	0.204743i
$101$	−17.7984			−1.77101			−0.885506	−	0.464628i	$-0.846188\pi$
$101$	−17.7984			−1.77101			−0.885506	+	0.464628i	$0.846188\pi$
$102$	3.63315	+	22.9388i	0.359735	+	2.27128i
$103$	−3.71410	+	7.28933i	−0.365961	+	0.718239i	−0.998410	−	0.0563627i	$-0.982050\pi$
$103$	−3.71410	+	7.28933i	−0.365961	+	0.718239i	0.632449	+	0.774602i	$0.282050\pi$
$104$	−5.52642	+	1.79564i	−0.541910	+	0.176077i
$105$	−28.3648	+	10.9373i	−2.76812	+	1.06737i
$106$	1.60742	−	4.94713i	0.156126	−	0.480508i
$107$	−4.50109	+	4.50109i	−0.435137	+	0.435137i	−0.890372	−	0.455235i	$-0.849555\pi$
$107$	−4.50109	+	4.50109i	−0.435137	+	0.435137i	0.455235	+	0.890372i	$0.349555\pi$
$108$	10.4216	−	5.31009i	1.00282	−	0.510963i
$109$	−1.71528	+	1.24622i	−0.164294	+	0.119367i	−0.666894	−	0.745152i	$-0.732377\pi$
$109$	−1.71528	+	1.24622i	−0.164294	+	0.119367i	0.502600	+	0.864519i	$0.332377\pi$
$110$	1.96828	+	0.872787i	0.187668	+	0.0832170i
$111$	16.0342	+	11.6495i	1.52190	+	1.10572i
$112$	4.30120	+	0.681243i	0.406425	+	0.0643714i
$113$	2.20253	+	0.348847i	0.207197	+	0.0328168i	0.259170	−	0.965832i	$-0.416551\pi$
$113$	2.20253	+	0.348847i	0.207197	+	0.0328168i	−0.0519730	+	0.998648i	$0.516551\pi$
$114$	4.40938	−	12.8741i	0.412976	−	1.20577i
$115$	12.9988	−	2.78345i	1.21215	−	0.259558i
$116$	2.93675	+	4.04209i	0.272671	+	0.375299i
$117$	−17.7977	−	34.9300i	−1.64540	−	3.22928i
$118$	−3.01473	+	3.01473i	−0.277529	+	0.277529i
$119$	−30.8107	−	10.0110i	−2.82441	−	0.917706i
$120$	−0.375848	−	6.97075i	−0.0343101	−	0.636340i
$121$	−3.11267	−	9.57982i	−0.282970	−	0.870893i
$122$	5.54341	+	2.82451i	0.501877	+	0.255719i
$123$	11.9152	−	1.88718i	1.07436	−	0.170161i
$124$	3.97455			0.356925
$125$	11.0347	−	1.79886i	0.986972	−	0.160895i
$126$			29.3799i			2.61737i
$127$	15.5753	−	2.46688i	1.38208	−	0.218901i	0.579273	−	0.815134i	$-0.303337\pi$
$127$	15.5753	−	2.46688i	1.38208	−	0.218901i	0.802811	+	0.596233i	$0.203337\pi$
$128$	−0.453990	+	0.891007i	−0.0401275	+	0.0787546i
$129$	0.907139	+	2.79189i	0.0798692	+	0.245812i
$130$	−12.9745	+	0.699559i	−1.13794	+	0.0613553i
$131$	2.91774	−	8.97989i	0.254924	−	0.784576i	−0.738920	−	0.673793i	$-0.764664\pi$
$131$	2.91774	−	8.97989i	0.254924	−	0.784576i	0.993845	−	0.110783i	$-0.0353360\pi$
$132$	2.12565	−	2.12565i	0.185014	−	0.185014i
$133$	13.2084	+	13.6331i	1.14532	+	1.18214i
$134$	1.83200	+	2.52153i	0.158261	+	0.217827i
$135$	25.5744	−	5.47626i	2.20109	−	0.471321i
$136$	4.37264	−	6.01843i	0.374951	−	0.516076i
$137$	11.9632	+	1.89478i	1.02208	+	0.161882i	0.644908	−	0.764260i	$-0.276896\pi$
$137$	11.9632	+	1.89478i	1.02208	+	0.161882i	0.377174	+	0.926142i	$0.376896\pi$
$138$	2.90343	−	18.3315i	0.247157	−	1.56049i
$139$	−4.52370	+	6.22633i	−0.383695	+	0.528111i	−0.956559	−	0.291540i	$-0.905832\pi$
$139$	−4.52370	+	6.22633i	−0.383695	+	0.528111i	0.572864	+	0.819651i	$0.305832\pi$
$140$	8.90174	+	3.94726i	0.752335	+	0.333604i
$141$	−7.54911	−	10.3905i	−0.635750	−	0.875035i
$142$	1.54242	−	0.785904i	0.129437	−	0.0659516i
$143$	−3.95643	−	3.95643i	−0.330854	−	0.330854i
$144$	−6.41634	−	2.08479i	−0.534695	−	0.173733i
$145$	4.01941	+	10.4240i	0.333794	+	0.865665i
$146$	5.44041	−	1.76770i	0.450251	−	0.146296i
$147$	−33.2810	−	16.9575i	−2.74497	−	1.39863i
$148$	−0.993110	−	6.27025i	−0.0816331	−	0.515411i
$149$		−	2.53561i		−	0.207725i	−0.994592	−	0.103863i	$-0.966880\pi$
$149$		−	2.53561i		−	0.207725i	0.994592	−	0.103863i	$-0.0331202\pi$
$150$	3.19945	−	15.2783i	0.261234	−	1.24747i
$151$		−	17.2068i		−	1.40027i	−0.714009	−	0.700136i	$-0.753122\pi$
$151$		−	17.2068i		−	1.40027i	0.714009	−	0.700136i	$-0.246878\pi$
$152$	−3.91462	+	1.91722i	−0.317518	+	0.155507i
$153$	44.7185	+	22.7852i	3.61527	+	1.84207i
$154$	1.29579	+	3.98802i	0.104417	+	0.321364i
$155$	8.58799	+	2.28729i	0.689804	+	0.183719i
$156$	−5.60589	+	17.2532i	−0.448831	+	1.38136i
$157$	−4.12610	−	4.12610i	−0.329299	−	0.329299i	0.523021	−	0.852320i	$-0.324805\pi$
$157$	−4.12610	−	4.12610i	−0.329299	−	0.329299i	−0.852320	+	0.523021i	$0.824805\pi$
$158$	3.66754	+	7.19795i	0.291774	+	0.572638i
$159$	−9.54533	−	13.1380i	−0.756994	−	1.04191i
$160$	−1.49372	+	1.66397i	−0.118089	+	0.131549i
$161$	20.9450	+	15.2175i	1.65070	+	1.19930i
$162$	2.54615	−	16.0757i	0.200044	−	1.26303i
$163$	−1.14746	+	7.24480i	−0.0898762	+	0.567456i	0.901120	+	0.433569i	$0.142746\pi$
$163$	−1.14746	+	7.24480i	−0.0898762	+	0.567456i	−0.990997	+	0.133887i	$0.957254\pi$
$164$	−3.12618	−	2.27130i	−0.244113	−	0.177359i
$165$	5.81627	−	3.36971i	0.452796	−	0.262332i
$166$	3.89479	+	5.36072i	0.302295	+	0.416073i
$167$	0.580608	+	1.13951i	0.0449288	+	0.0881777i	0.912379	−	0.409346i	$-0.134243\pi$
$167$	0.580608	+	1.13951i	0.0449288	+	0.0881777i	−0.867451	+	0.497523i	$0.834243\pi$
$168$	9.61345	−	9.61345i	0.741694	−	0.741694i
$169$	19.7493	+	6.41692i	1.51917	+	0.493609i
$170$	12.9117	−	10.4879i	0.990280	−	0.804385i
$171$	−16.9068	−	24.0616i	−1.29289	−	1.84004i
$172$	0.426887	−	0.837814i	0.0325499	−	0.0638827i
$173$	−3.97910	−	25.1230i	−0.302525	−	1.91007i	−0.403129	−	0.915143i	$-0.632077\pi$
$173$	−3.97910	−	25.1230i	−0.302525	−	1.91007i	0.100604	−	0.994927i	$-0.467923\pi$
$174$	15.5982			1.18249
$175$	16.9628	+	13.6518i	1.28227	+	1.03198i
$176$	−0.962901			−0.0725814
$177$	2.08220	+	13.1465i	0.156507	+	0.988149i
$178$	−0.528741	−	0.269407i	−0.0396308	−	0.0201929i
$179$	5.57696	+	17.1641i	0.416842	+	1.28291i	0.910593	+	0.413304i	$0.135625\pi$
$179$	5.57696	+	17.1641i	0.416842	+	1.28291i	−0.493751	+	0.869603i	$0.664375\pi$
$180$	−12.6643	−	8.19721i	−0.943941	−	0.610984i
$181$	−4.41329	−	1.43397i	−0.328037	−	0.106586i	0.140368	−	0.990099i	$-0.455171\pi$
$181$	−4.41329	−	1.43397i	−0.328037	−	0.106586i	−0.468406	+	0.883514i	$0.655171\pi$
$182$	−17.8933	−	17.8933i	−1.32634	−	1.32634i
$183$	17.3062	−	8.81796i	1.27931	−	0.651842i
$184$	−4.80963	+	3.49440i	−0.354571	+	0.257611i
$185$	1.46257	−	14.1199i	0.107530	−	1.03812i
$186$	7.29343	−	10.0385i	0.534780	−	0.736062i
$187$	7.07501	+	1.12057i	0.517376	+	0.0819443i
$188$	−0.643553	+	4.06324i	−0.0469360	+	0.296342i
$189$	41.2080	+	29.9394i	2.99744	+	2.17777i
$190$	−9.56183	+	1.88981i	−0.693688	+	0.137101i
$191$	2.36339	−	1.71710i	0.171009	−	0.124245i	−0.498989	−	0.866608i	$-0.666295\pi$
$191$	2.36339	−	1.71710i	0.171009	−	0.124245i	0.669997	+	0.742363i	$0.266295\pi$
$192$	1.41733	+	2.78167i	0.102287	+	0.200750i
$193$	7.74133	+	7.74133i	0.557233	+	0.557233i	0.928519	−	0.371285i	$-0.121083\pi$
$193$	7.74133	+	7.74133i	0.557233	+	0.557233i	−0.371285	+	0.928519i	$0.621083\pi$
$194$	18.0887	+	5.87736i	1.29869	+	0.421970i
$195$	−22.0418	+	34.0536i	−1.57845	+	2.43863i
$196$	3.69720	+	11.3788i	0.264085	+	0.812771i
$197$	9.00342	−	17.6702i	0.641467	−	1.25895i	−0.309865	−	0.950781i	$-0.600284\pi$
$197$	9.00342	−	17.6702i	0.641467	−	1.25895i	0.951332	−	0.308169i	$-0.0997162\pi$
$198$	−1.01624	−	6.41627i	−0.0722208	−	0.455984i
$199$		−	3.09157i		−	0.219156i	−0.993978	−	0.109578i	$-0.965050\pi$
$199$		−	3.09157i		−	0.219156i	0.993978	−	0.109578i	$-0.0349499\pi$
$200$	−4.18513	+	2.73581i	−0.295934	+	0.193451i
$201$	9.73043			0.686331
$202$	17.5793	−	2.78429i	1.23688	−	0.195902i
$203$	−9.87791	+	19.3865i	−0.693293	+	1.36066i
$204$	−7.17683	−	22.0880i	−0.502479	−	1.54647i
$205$	−5.44777	−	6.70677i	−0.380489	−	0.468421i
$206$	2.52807	−	7.78060i	0.176139	−	0.542100i
$207$	−28.3609	−	28.3609i	−1.97122	−	1.97122i
$208$	5.17748	−	2.63806i	0.358993	−	0.182916i
$209$	−3.35615	−	2.52045i	−0.232150	−	0.174343i
$210$	26.3046	−	15.2398i	1.81519	−	1.05165i
$211$	−5.33674	+	7.34539i	−0.367396	+	0.505677i	−0.952191	−	0.305504i	$-0.901175\pi$
$211$	−5.33674	+	7.34539i	−0.367396	+	0.505677i	0.584795	+	0.811181i	$0.301175\pi$
$212$	−0.813728	+	5.13768i	−0.0558871	+	0.352857i
$213$	0.845436	−	5.33787i	0.0579283	−	0.365745i
$214$	3.74155	−	5.14980i	0.255767	−	0.352033i
$215$	1.40454	−	1.56463i	0.0957890	−	0.106707i
$216$	−9.46265	+	6.87502i	−0.643852	+	0.467786i
$217$	7.85785	+	15.4219i	0.533426	+	1.04691i
$218$	1.49921	−	1.49921i	0.101539	−	0.101539i
$219$	5.51865	−	16.9846i	0.372916	−	1.14772i
$220$	−2.08058	−	0.554134i	−0.140273	−	0.0373597i
$221$	−41.1120	+	13.3581i	−2.76549	+	0.898563i
$222$	−17.6592	−	8.99781i	−1.18521	−	0.603893i
$223$	2.22074	+	14.0212i	0.148712	+	0.938928i	0.943339	+	0.331831i	$0.107666\pi$
$223$	2.22074	+	14.0212i	0.148712	+	0.938928i	−0.794627	+	0.607097i	$0.792334\pi$
$224$	−4.35481			−0.290968
$225$	−22.6470	−	25.0002i	−1.50980	−	1.66668i
$226$	−2.22999			−0.148337
$227$	−5.03707	+	0.797794i	−0.334322	+	0.0529515i	−0.321339	−	0.946964i	$-0.604133\pi$
$227$	−5.03707	+	0.797794i	−0.334322	+	0.0529515i	−0.0129834	+	0.999916i	$0.504133\pi$
$228$	−2.34114	+	13.4053i	−0.155046	+	0.887791i
$229$	1.53942	−	0.500186i	0.101727	−	0.0330532i	−0.257711	−	0.966222i	$-0.582968\pi$
$229$	1.53942	−	0.500186i	0.101727	−	0.0330532i	0.359438	+	0.933169i	$0.382968\pi$
$230$	−12.4034	+	4.78264i	−0.817853	+	0.315358i
$231$	12.4504	+	4.04537i	0.819175	+	0.266166i
$232$	−3.53292	−	3.53292i	−0.231948	−	0.231948i
$233$	9.89560	+	19.4212i	0.648282	+	1.27233i	0.947992	+	0.318295i	$0.103110\pi$
$233$	9.89560	+	19.4212i	0.648282	+	1.27233i	−0.299709	+	0.954031i	$0.596890\pi$
$234$	23.0429	+	31.7158i	1.50636	+	2.07333i
$235$	−3.72888	+	8.40926i	−0.243245	+	0.548560i
$236$	2.50601	−	3.44923i	0.163127	−	0.224525i
$237$	24.9099	+	3.94535i	1.61807	+	0.256278i
$238$	31.9974	+	5.06789i	2.07408	+	0.328502i
$239$	6.10938	−	8.40884i	0.395183	−	0.543923i	−0.564344	−	0.825540i	$-0.690871\pi$
$239$	6.10938	−	8.40884i	0.395183	−	0.543923i	0.959527	+	0.281617i	$0.0908707\pi$
$240$	1.46169	+	6.82614i	0.0943515	+	0.440625i
$241$	−3.54401	−	4.87791i	−0.228290	−	0.314214i	0.679471	−	0.733702i	$-0.262209\pi$
$241$	−3.54401	−	4.87791i	−0.228290	−	0.314214i	−0.907761	+	0.419489i	$0.862209\pi$
$242$	4.57297	+	8.97495i	0.293961	+	0.576932i
$243$	−11.1184	−	11.1184i	−0.713244	−	0.713244i
$244$	−5.91701	−	1.92255i	−0.378798	−	0.123079i
$245$	1.44038	+	26.7144i	0.0920225	+	1.70672i
$246$	−11.4733	+	3.72789i	−0.731509	+	0.237682i
$247$	24.9511	+	4.35752i	1.58760	+	0.277262i
$248$	−3.92562	+	0.621756i	−0.249277	+	0.0394816i
$249$	20.6867			1.31097
$250$	−10.6174	+	3.50291i	−0.671505	+	0.221544i
$251$	−19.1615			−1.20946			−0.604732	−	0.796429i	$-0.706720\pi$
$251$	−19.1615			−1.20946			−0.604732	+	0.796429i	$0.706720\pi$
$252$	−4.59603	−	29.0182i	−0.289522	−	1.82797i
$253$	−5.10055	−	2.59886i	−0.320669	−	0.163389i
$254$	−14.9976	+	4.87303i	−0.941035	+	0.305761i
$255$	−2.79600	−	51.8567i	−0.175092	−	3.24739i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−0.884381	+	0.884381i	−0.0551662	+	0.0551662i	−0.734152	−	0.678986i	$-0.762420\pi$
$257$	−0.884381	+	0.884381i	−0.0551662	+	0.0551662i	0.678986	+	0.734152i	$0.262420\pi$
$258$	−1.33272	−	2.61561i	−0.0829714	−	0.162841i
$259$	22.3662	−	16.2500i	1.38977	−	1.00972i
$260$	12.7054	−	2.72061i	0.787953	−	0.168725i
$261$	19.8129	−	27.2701i	1.22639	−	1.68798i
$262$	−1.47706	+	9.32576i	−0.0912528	+	0.576148i
$263$	−0.255961	+	1.61607i	−0.0157832	+	0.0996514i	−0.994322	−	0.106410i	$-0.966065\pi$
$263$	−0.255961	+	1.61607i	−0.0157832	+	0.0996514i	0.978539	+	0.206061i	$0.0660645\pi$
$264$	−1.76696	+	2.43201i	−0.108749	+	0.149680i
$265$	−4.71491	+	10.6329i	−0.289635	+	0.653175i
$266$	−15.1785	−	11.3990i	−0.930653	−	0.698916i
$267$	−1.65070	+	0.841073i	−0.101021	+	0.0514729i
$268$	−2.20390	−	2.20390i	−0.134625	−	0.134625i
$269$	−0.155382	+	0.478216i	−0.00947379	+	0.0291573i	−0.955682	−	0.294402i	$-0.904880\pi$
$269$	−0.155382	+	0.478216i	−0.00947379	+	0.0291573i	0.946208	+	0.323559i	$0.104880\pi$
$270$	−24.4028	+	9.40955i	−1.48511	+	0.572647i
$271$	−1.20427	−	3.70636i	−0.0731542	−	0.225145i	0.907794	−	0.419417i	$-0.137766\pi$
$271$	−1.20427	−	3.70636i	−0.0731542	−	0.225145i	−0.980948	+	0.194272i	$0.937766\pi$
$272$	−3.37732	+	6.62836i	−0.204780	+	0.401903i
$273$	−78.0282	+	12.3585i	−4.72248	+	0.747968i
$274$	−12.1123			−0.731730
$275$	−4.17671	−	2.39469i	−0.251865	−	0.144405i
$276$			18.5601i			1.11718i
$277$	−1.34258	−	8.47673i	−0.0806680	−	0.509317i	−0.994628	−	0.103513i	$-0.966992\pi$
$277$	−1.34258	−	8.47673i	−0.0806680	−	0.509317i	0.913960	−	0.405804i	$-0.133008\pi$
$278$	3.49399	−	6.85734i	0.209556	−	0.411276i
$279$	−8.28612	−	25.5020i	−0.496077	−	1.52677i
$280$	−9.40964	−	2.50612i	−0.562333	−	0.149770i
$281$	−22.7195	−	7.38201i	−1.35533	−	0.440374i	−0.460849	−	0.887478i	$-0.652455\pi$
$281$	−22.7195	−	7.38201i	−1.35533	−	0.440374i	−0.894482	+	0.447105i	$0.852455\pi$
$282$	9.08160	+	9.08160i	0.540801	+	0.540801i
$283$	10.5227	+	20.6520i	0.625510	+	1.22763i	0.958605	+	0.284739i	$0.0919068\pi$
$283$	10.5227	+	20.6520i	0.625510	+	1.22763i	−0.333096	+	0.942893i	$0.608093\pi$
$284$	−1.40049	+	1.01752i	−0.0831039	+	0.0603785i
$285$	−12.7732	+	27.6182i	−0.756617	+	1.63596i
$286$	4.52665	+	3.28880i	0.267666	+	0.194471i
$287$	2.63244	−	16.6205i	0.155388	−	0.981080i
$288$	6.66347	+	1.05539i	0.392649	+	0.0621895i
$289$	22.5365	−	31.0189i	1.32568	−	1.82464i
$290$	−5.60060	−	9.66688i	−0.328879	−	0.567659i
$291$	48.0378	−	34.9015i	2.81603	−	2.04596i
$292$	−5.09690	+	2.59700i	−0.298273	+	0.151978i
$293$	−8.85200	−	8.85200i	−0.517139	−	0.517139i	0.399565	−	0.916705i	$-0.369161\pi$
$293$	−8.85200	−	8.85200i	−0.517139	−	0.517139i	−0.916705	+	0.399565i	$0.869161\pi$
$294$	35.5240	+	11.5424i	2.07180	+	0.673169i
$295$	7.39982	−	6.01073i	0.430834	−	0.349958i
$296$	1.96177	+	6.03769i	0.114025	+	0.350934i
$297$	−10.0350	−	5.11309i	−0.582290	−	0.296692i
$298$	0.396657	+	2.50439i	0.0229777	+	0.145075i
$299$	34.5455			1.99782
$300$	−0.770001	+	15.5907i	−0.0444560	+	0.900131i
$301$	4.09483			0.236022
$302$	2.69174	+	16.9950i	0.154892	+	0.977952i
$303$	25.2263	−	49.5094i	1.44921	−	2.84424i
$304$	3.56651	−	2.50599i	0.204553	−	0.143729i
$305$	−11.6788	−	7.55929i	−0.668723	−	0.432844i
$306$	−47.7323	−	15.5092i	−2.72867	−	0.886600i
$307$	−21.9862	+	21.9862i	−1.25482	+	1.25482i	−0.301280	+	0.953536i	$0.597414\pi$
$307$	−21.9862	+	21.9862i	−1.25482	+	1.25482i	−0.953536	+	0.301280i	$0.902586\pi$
$308$	−1.90370	−	3.73622i	−0.108473	−	0.212891i
$309$	−15.0124	−	20.6628i	−0.854027	−	1.17547i
$310$	−8.84006	−	0.915672i	−0.502082	−	0.0520067i
$311$	−5.06004	−	3.67633i	−0.286928	−	0.208466i	0.435005	−	0.900428i	$-0.356746\pi$
$311$	−5.06004	−	3.67633i	−0.286928	−	0.208466i	−0.721934	+	0.691962i	$0.756746\pi$
$312$	2.83788	−	17.9177i	0.160664	−	1.01439i
$313$	2.47572	−	15.6311i	0.139936	−	0.883520i	−0.813421	−	0.581675i	$-0.802398\pi$
$313$	2.47572	−	15.6311i	0.139936	−	0.883520i	0.953357	−	0.301845i	$-0.0976024\pi$
$314$	4.72077	+	3.42984i	0.266408	+	0.193557i
$315$	6.76865	−	65.3458i	0.381370	−	3.68182i
$316$	−4.74839	−	6.53560i	−0.267118	−	0.367656i
$317$	14.9849	+	29.4096i	0.841638	+	1.65181i	0.755148	+	0.655554i	$0.227565\pi$
$317$	14.9849	+	29.4096i	0.841638	+	1.65181i	0.0864897	+	0.996253i	$0.472435\pi$
$318$	11.4830	+	11.4830i	0.643937	+	0.643937i
$319$	1.48666	−	4.57548i	0.0832372	−	0.256178i
$320$	1.21502	−	1.87716i	0.0679219	−	0.104936i
$321$	−6.14102	−	18.9001i	−0.342758	−	1.05490i
$322$	−23.0677	−	11.7536i	−1.28551	−	0.655001i
$323$	−29.1216	+	14.2625i	−1.62037	+	0.793588i
$324$			16.2761i			0.904230i
$325$	29.0187	+	1.43319i	1.60967	+	0.0794990i
$326$		−	7.33510i		−	0.406254i
$327$	−1.03546	−	6.53766i	−0.0572612	−	0.361533i
$328$	3.44300	+	1.75430i	0.190108	+	0.0968648i
$329$	−17.0384	+	5.53610i	−0.939355	+	0.305215i
$330$	−5.21752	+	4.23809i	−0.287215	+	0.233299i
$331$	22.6426	+	7.35704i	1.24455	+	0.404380i	0.855966	−	0.517033i	$-0.172963\pi$
$331$	22.6426	+	7.35704i	1.24455	+	0.404380i	0.388587	+	0.921412i	$0.372963\pi$
$332$	−4.68544	−	4.68544i	−0.257147	−	0.257147i
$333$	−38.1616	+	19.4443i	−2.09124	+	1.06554i
$334$	−0.751718	−	1.03465i	−0.0411322	−	0.0566136i
$335$	−3.49376	−	6.03037i	−0.190884	−	0.329474i
$336$	−7.99122	+	10.9990i	−0.435957	+	0.600043i
$337$	0.781481	−	4.93408i	0.0425700	−	0.268776i	−0.957218	−	0.289368i	$-0.906555\pi$
$337$	0.781481	−	4.93408i	0.0425700	−	0.268776i	0.999788	+	0.0205914i	$0.00655491\pi$
$338$	−20.5099	−	3.24845i	−1.11559	−	0.176693i
$339$	−4.09210	+	5.63230i	−0.222253	+	0.305904i
$340$	−11.1120	+	12.3786i	−0.602635	+	0.671324i
$341$	−2.24951	−	3.09619i	−0.121818	−	0.167668i
$342$	20.4627	+	21.1205i	1.10650	+	1.14207i
$343$	−15.2869	+	15.2869i	−0.825415	+	0.825415i
$344$	−0.290569	+	0.894279i	−0.0156664	+	0.0482163i
$345$	−10.6810	+	40.1035i	−0.575047	+	2.15910i
$346$	7.86022	+	24.1913i	0.422568	+	1.30053i
$347$	2.84860	−	5.59069i	0.152921	−	0.300124i	−0.801819	−	0.597568i	$-0.796134\pi$
$347$	2.84860	−	5.59069i	0.152921	−	0.300124i	0.954739	+	0.297443i	$0.0961340\pi$
$348$	−15.4061	+	2.44009i	−0.825856	+	0.130803i
$349$			1.49716i			0.0801410i	0.999197	+	0.0400705i	$0.0127582\pi$
$349$			1.49716i			0.0801410i	−0.999197	+	0.0400705i	$0.987242\pi$
$350$	−18.8896	−	10.8302i	−1.00969	−	0.578898i
$351$	67.9661			3.62776
$352$	0.951046	−	0.150631i	0.0506909	−	0.00802866i
$353$	13.6710	+	6.96575i	0.727636	+	0.370749i	0.778238	−	0.627970i	$-0.216114\pi$
$353$	13.6710	+	6.96575i	0.727636	+	0.370749i	−0.0506015	+	0.998719i	$0.516114\pi$
$354$	−4.11312	−	12.6589i	−0.218610	−	0.672812i
$355$	−3.61167	+	1.39263i	−0.191688	+	0.0739133i
$356$	0.564376	+	0.183377i	0.0299119	+	0.00971895i
$357$	71.5163	−	71.5163i	3.78504	−	3.78504i
$358$	−8.19336	−	16.0804i	−0.433033	−	0.849874i
$359$	−6.73340	−	9.26772i	−0.355375	−	0.489132i	0.593478	−	0.804850i	$-0.297754\pi$
$359$	−6.73340	−	9.26772i	−0.355375	−	0.489132i	−0.948853	+	0.315719i	$0.897754\pi$
$360$	13.7907	+	6.11515i	0.726834	+	0.322297i
$361$	18.9905	+	0.601022i	0.999500	+	0.0316327i
$362$	4.58328	+	0.725920i	0.240892	+	0.0381535i
$363$	31.0596	+	4.91936i	1.63021	+	0.258199i
$364$	20.4722	+	14.8739i	1.07303	+	0.779605i
$365$	−12.5076	+	2.67827i	−0.654679	+	0.140187i
$366$	−15.7137	+	11.4167i	−0.821369	+	0.596759i
$367$	−19.0817	+	9.72260i	−0.996055	+	0.507515i	−0.874477	−	0.485066i	$-0.838795\pi$
$367$	−19.0817	+	9.72260i	−0.996055	+	0.507515i	−0.121578	+	0.992582i	$0.538795\pi$
$368$	4.20377	−	4.20377i	0.219137	−	0.219137i
$369$	−8.05599	+	24.7938i	−0.419378	+	1.29071i
$370$	0.764278	+	14.1749i	0.0397329	+	0.736917i
$371$	−21.5438	+	7.00001i	−1.11850	+	0.363422i
$372$	−5.63326	+	11.0559i	−0.292071	+	0.573221i
$373$	3.76932	+	23.7986i	0.195168	+	1.23224i	0.869544	+	0.493855i	$0.164413\pi$
$373$	3.76932	+	23.7986i	0.195168	+	1.23224i	−0.674376	+	0.738388i	$0.735587\pi$
$374$	−7.16320			−0.370400
$375$	−10.6360	+	33.2444i	−0.549240	+	1.71674i
$376$		−	4.11388i		−	0.212157i
$377$	4.54170	+	28.6752i	0.233909	+	1.47685i
$378$	−45.3843	−	23.1244i	−2.33431	−	1.18939i
$379$	8.68010	+	26.7146i	0.445867	+	1.37224i	0.881530	+	0.472128i	$0.156514\pi$
$379$	8.68010	+	26.7146i	0.445867	+	1.37224i	−0.435663	+	0.900110i	$0.643486\pi$
$380$	9.14848	−	3.36234i	0.469307	−	0.172485i
$381$	−15.2133	+	46.8218i	−0.779402	+	2.39875i
$382$	−2.06567	+	2.06567i	−0.105689	+	0.105689i
$383$	−16.7344	+	8.52660i	−0.855088	+	0.435689i	−0.825854	−	0.563884i	$-0.809307\pi$
$383$	−16.7344	+	8.52660i	−0.855088	+	0.435689i	−0.0292334	+	0.999573i	$0.509307\pi$
$384$	−1.83503	−	2.52571i	−0.0936436	−	0.128889i
$385$	−1.96327	−	9.16856i	−0.100058	−	0.467273i
$386$	−8.85703	−	6.43501i	−0.450811	−	0.327533i
$387$	−6.26567	−	0.992384i	−0.318502	−	0.0504457i
$388$	−18.7854	−	2.97531i	−0.953684	−	0.151049i
$389$	15.2520	−	20.9926i	0.773309	−	1.06437i	−0.222680	−	0.974892i	$-0.571480\pi$
$389$	15.2520	−	20.9926i	0.773309	−	1.06437i	0.995989	−	0.0894771i	$-0.0285196\pi$
$390$	16.4433	−	37.0824i	0.832639	−	1.87774i
$391$	−35.7797	+	25.9955i	−1.80946	+	1.31465i
$392$	−5.43171	−	10.6603i	−0.274343	−	0.538428i
$393$	20.8437	+	20.8437i	1.05143	+	1.05143i
$394$	−6.12834	+	18.8611i	−0.308741	+	0.950208i
$395$	−6.49893	−	16.8544i	−0.326996	−	0.848036i
$396$	2.00745	+	6.17830i	0.100878	+	0.310471i
$397$	−12.4226	+	24.3808i	−0.623474	+	1.22364i	0.336006	+	0.941860i	$0.390924\pi$
$397$	−12.4226	+	24.3808i	−0.623474	+	1.22364i	−0.959480	+	0.281777i	$0.909076\pi$
$398$	0.483628	+	3.05351i	0.0242421	+	0.153058i
$399$	−56.6435	+	17.4189i	−2.83572	+	0.872037i
$400$	3.70563	−	3.35683i	0.185282	−	0.167841i
$401$			4.79693i			0.239547i	0.992801	+	0.119774i	$0.0382169\pi$
$401$			4.79693i			0.239547i	−0.992801	+	0.119774i	$0.961783\pi$
$402$	−9.61063	+	1.52217i	−0.479335	+	0.0759191i
$403$	20.5781	+	10.4851i	1.02507	+	0.522299i
$404$	−16.9273	+	5.50002i	−0.842166	+	0.273636i
$405$	−9.36666	+	35.1686i	−0.465433	+	1.74754i
$406$	6.72358	−	20.6930i	0.333686	−	1.02698i
$407$	−4.32246	+	4.32246i	−0.214257	+	0.214257i
$408$	10.5438	+	20.6934i	0.521996	+	1.02447i
$409$	18.8544	−	13.6985i	0.932289	−	0.677348i	−0.0142629	−	0.999898i	$-0.504540\pi$
$409$	18.8544	−	13.6985i	0.932289	−	0.677348i	0.946552	+	0.322550i	$0.104540\pi$
$410$	6.42987	+	5.77198i	0.317549	+	0.285058i
$411$	−22.2264	+	30.5921i	−1.09635	+	1.50900i
$412$	−1.27979	+	8.08029i	−0.0630508	+	0.398087i
$413$	18.3381	+	2.90446i	0.902357	+	0.142919i
$414$	32.4483	+	23.5751i	1.59475	+	1.15865i
$415$	−7.42765	−	12.8204i	−0.364609	−	0.629331i
$416$	−4.70105	+	3.41551i	−0.230488	+	0.167459i
$417$	−10.9080	−	21.4082i	−0.534169	−	1.04837i
$418$	3.70911	+	1.96440i	0.181419	+	0.0960820i
$419$	4.45222	+	1.44661i	0.217505	+	0.0706717i	0.415743	−	0.909482i	$-0.363522\pi$
$419$	4.45222	+	1.44661i	0.217505	+	0.0706717i	−0.198237	+	0.980154i	$0.563522\pi$
$420$	−23.5967	+	19.1672i	−1.15140	+	0.935261i
$421$	−2.74623	+	0.892303i	−0.133843	+	0.0434882i	−0.375172	−	0.926955i	$-0.622417\pi$
$421$	−2.74623	+	0.892303i	−0.133843	+	0.0434882i	0.241330	+	0.970443i	$0.422417\pi$
$422$	4.12196	−	8.08980i	0.200654	−	0.393805i
$423$	27.4128	−	4.34176i	1.33285	−	0.211103i
$424$		−	5.20172i		−	0.252618i
$425$	−31.1340	+	20.3522i	−1.51022	+	0.987227i
$426$			5.40441i			0.261844i
$427$	−4.23836	−	26.7599i	−0.205109	−	1.29500i
$428$	−2.88988	+	5.67171i	−0.139688	+	0.274152i
$429$	16.6131	−	5.39792i	0.802087	−	0.260614i
$430$	−1.14249	+	1.76509i	−0.0550957	+	0.0851202i
$431$	22.1142	+	7.18535i	1.06521	+	0.346106i	0.788619	−	0.614883i	$-0.210797\pi$
$431$	22.1142	+	7.18535i	1.06521	+	0.346106i	0.276587	+	0.960989i	$0.410797\pi$
$432$	8.27066	−	8.27066i	0.397922	−	0.397922i
$433$	26.4762	−	13.4903i	1.27237	−	0.648303i	0.318326	−	0.947981i	$-0.396879\pi$
$433$	26.4762	−	13.4903i	1.27237	−	0.648303i	0.954040	+	0.299679i	$0.0968795\pi$
$434$	−10.1736	−	14.0028i	−0.488350	−	0.672156i
$435$	−34.6930	−	3.59357i	−1.66340	−	0.172298i
$436$	−1.24622	+	1.71528i	−0.0596833	+	0.0821470i
$437$	25.6557	−	3.64844i	1.22728	−	0.174528i
$438$	−2.79372	+	17.6388i	−0.133489	+	0.842817i
$439$	5.19914	+	3.77740i	0.248142	+	0.180285i	0.704903	−	0.709304i	$-0.250991\pi$
$439$	5.19914	+	3.77740i	0.248142	+	0.180285i	−0.456761	+	0.889589i	$0.650991\pi$
$440$	2.14165	+	0.221837i	0.102099	+	0.0105757i
$441$	65.3023	−	47.4449i	3.10963	−	2.25928i
$442$	38.5162	−	19.6250i	1.83203	−	0.933465i
$443$	24.1776	−	24.1776i	1.14871	−	1.14871i	0.161909	−	0.986806i	$-0.448235\pi$
$443$	24.1776	−	24.1776i	1.14871	−	1.14871i	0.986806	−	0.161909i	$-0.0517650\pi$
$444$	18.8493	+	6.12452i	0.894550	+	0.290657i
$445$	1.11394	+	0.721020i	0.0528059	+	0.0341796i
$446$	−4.38679	−	13.5012i	−0.207721	−	0.639298i
$447$	7.05323	+	3.59380i	0.333606	+	0.169981i
$448$	4.30120	−	0.681243i	0.203212	−	0.0321857i
$449$	3.09635			0.146126			0.0730629	−	0.997327i	$-0.476723\pi$
$449$	3.09635			0.146126			0.0730629	+	0.997327i	$0.476723\pi$
$450$	26.2790	+	21.1496i	1.23881	+	0.997003i
$451$			3.72081i			0.175206i
$452$	2.20253	−	0.348847i	0.103599	−	0.0164084i
$453$	47.8638	+	24.3878i	2.24884	+	1.14584i
$454$	4.85026	−	1.57594i	0.227634	−	0.0739627i
$455$	35.6755	+	43.9201i	1.67249	+	2.05901i
$456$	0.215260	−	13.6065i	0.0100805	−	0.637184i
$457$	−10.2083	−	10.2083i	−0.477526	−	0.477526i	0.426814	−	0.904339i	$-0.359636\pi$
$457$	−10.2083	−	10.2083i	−0.477526	−	0.477526i	−0.904339	+	0.426814i	$0.859636\pi$
$458$	−1.44222	+	0.734846i	−0.0673903	+	0.0343371i
$459$	−70.3944	+	51.1445i	−3.28573	+	2.38722i
$460$	11.5025	−	6.66407i	0.536306	−	0.310714i
$461$	−17.4303	−	12.6638i	−0.811810	−	0.589814i	0.102545	−	0.994728i	$-0.467301\pi$
$461$	−17.4303	−	12.6638i	−0.811810	−	0.589814i	−0.914355	+	0.404914i	$0.867301\pi$
$462$	−12.9299	−	2.04790i	−0.601555	−	0.0952769i
$463$	−4.26255	+	26.9127i	−0.198098	+	1.25074i	0.665439	+	0.746452i	$0.268244\pi$
$463$	−4.26255	+	26.9127i	−0.198098	+	1.25074i	−0.863536	+	0.504286i	$0.831756\pi$
$464$	4.04209	+	2.93675i	0.187650	+	0.136335i
$465$	−18.5345	+	20.6471i	−0.859518	+	0.957487i
$466$	−12.8119	−	17.6341i	−0.593500	−	0.816883i
$467$	26.5126	−	13.5089i	1.22686	−	0.625115i	0.284165	−	0.958776i	$-0.408284\pi$
$467$	26.5126	−	13.5089i	1.22686	−	0.625115i	0.942693	+	0.333660i	$0.108284\pi$
$468$	−27.7206	−	27.7206i	−1.28139	−	1.28139i
$469$	4.19429	−	12.9087i	0.193674	−	0.596068i
$470$	2.36747	−	8.88905i	0.109203	−	0.410022i
$471$	17.3255	−	5.62941i	0.798318	−	0.259389i
$472$	−1.93558	+	3.79879i	−0.0890922	+	0.174853i
$473$	−0.894269	+	0.141638i	−0.0411185	+	0.00651254i
$474$	−25.2204			−1.15841
$475$	21.7025	−	2.00036i	0.995779	−	0.0917829i
$476$	−32.3962			−1.48488
$477$	34.6615	−	5.48985i	1.58704	−	0.251363i
$478$	−4.71873	+	9.26104i	−0.215830	+	0.423590i
$479$	23.9102	−	7.76889i	1.09248	−	0.354970i	0.293278	−	0.956027i	$-0.405254\pi$
$479$	23.9102	−	7.76889i	1.09248	−	0.354970i	0.799206	+	0.601057i	$0.205254\pi$
$480$	−2.51153	−	6.51344i	−0.114635	−	0.297296i
$481$	11.3995	−	35.0839i	0.519771	−	1.59969i
$482$	4.26345	+	4.26345i	0.194195	+	0.194195i
$483$	−72.0161	+	36.6940i	−3.27684	+	1.66964i
$484$	−5.92066	−	8.14908i	−0.269121	−	0.370413i
$485$	−38.8782	−	17.2396i	−1.76537	−	0.782809i
$486$	12.7208	+	9.24219i	0.577027	+	0.419234i
$487$	6.75816	−	42.6694i	0.306242	−	1.93353i	−0.0490930	−	0.998794i	$-0.515633\pi$
$487$	6.75816	−	42.6694i	0.306242	−	1.93353i	0.355335	−	0.934739i	$-0.384367\pi$
$488$	6.14492	+	0.973259i	0.278167	+	0.0440574i
$489$	−18.5263	−	13.4602i	−0.837789	−	0.608689i
$490$	−5.60169	−	26.1601i	−0.253059	−	1.18179i
$491$	2.28484	−	1.66003i	0.103113	−	0.0749162i	−0.535034	−	0.844831i	$-0.679701\pi$
$491$	2.28484	−	1.66003i	0.103113	−	0.0749162i	0.638147	+	0.769914i	$0.279701\pi$
$492$	10.7488	−	5.47681i	0.484596	−	0.246914i
$493$	−26.2820	−	26.2820i	−1.18368	−	1.18368i
$494$	−25.3256	−	0.400659i	−1.13945	−	0.0180265i
$495$	0.782077	+	14.5050i	0.0351517	+	0.651950i
$496$	3.78002	−	1.22820i	0.169728	−	0.0551479i
$497$	−6.71697	−	3.42247i	−0.301297	−	0.153519i
$498$	−20.4320	+	3.23611i	−0.915580	+	0.145014i
$499$		−	37.5103i		−	1.67919i	−0.543212	−	0.839596i	$-0.682792\pi$
$499$		−	37.5103i		−	1.67919i	0.543212	−	0.839596i	$-0.317208\pi$
$500$	9.93873	−	5.12072i	0.444473	−	0.229005i
$501$	−3.99265			−0.178379
$502$	18.9256	−	2.99752i	0.844691	−	0.133786i
$503$	−27.6530	−	14.0899i	−1.23299	−	0.628238i	−0.288719	−	0.957414i	$-0.593229\pi$
$503$	−27.6530	−	14.0899i	−1.23299	−	0.628238i	−0.944269	+	0.329176i	$0.893229\pi$
$504$	9.07888	+	27.9419i	0.404406	+	1.24463i
$505$	−39.7408	+	2.14274i	−1.76844	+	0.0953506i
$506$	5.44430	+	1.76896i	0.242029	+	0.0786399i
$507$	−45.8410	+	45.8410i	−2.03587	+	2.03587i
$508$	14.0507	−	7.15918i	0.623398	−	0.317637i
$509$	−21.8693	+	15.8890i	−0.969341	+	0.704268i	−0.955301	−	0.295634i	$-0.904469\pi$
$509$	−21.8693	+	15.8890i	−0.969341	+	0.704268i	−0.0140398	+	0.999901i	$0.504469\pi$
$510$	10.8738	+	50.7809i	0.481498	+	2.24862i
$511$	−20.1536	−	14.6424i	−0.891541	−	0.647743i
$512$	−0.156434	+	0.987688i	−0.00691349	+	0.0436501i
$513$	50.4759	−	7.17807i	2.22857	−	0.316919i
$514$	0.735145	−	1.01184i	0.0324259	−	0.0446304i
$515$	−7.41538	+	16.7229i	−0.326761	+	0.736901i
$516$	1.72548	+	2.37492i	0.0759601	+	0.104550i
$517$	3.52951	−	1.79838i	0.155228	−	0.0790925i
$518$	−19.5488	+	19.5488i	−0.858923	+	0.858923i
$519$	75.5238	+	24.5392i	3.31513	+	1.07715i
$520$	−12.1233	+	4.67467i	−0.531644	+	0.204998i
$521$	38.7957	−	12.6055i	1.69967	−	0.552256i	0.711110	−	0.703081i	$-0.248193\pi$
$521$	38.7957	−	12.6055i	1.69967	−	0.552256i	0.988561	+	0.150825i	$0.0481929\pi$
$522$	−15.3030	+	30.0338i	−0.669794	+	1.31454i
$523$	−6.00738	−	37.9291i	−0.262684	−	1.65852i	−0.667862	−	0.744285i	$-0.732790\pi$
$523$	−6.00738	−	37.9291i	−0.262684	−	1.65852i	0.405178	−	0.914238i	$-0.367210\pi$
$524$		−	9.44201i		−	0.412476i
$525$	−62.0169	+	27.8358i	−2.70664	+	1.21485i
$526$		−	1.63622i		−	0.0713425i
$527$	−29.2034	+	4.62536i	−1.27212	+	0.201484i
$528$	1.36475	−	2.67848i	0.0593932	−	0.116566i
$529$	11.7393	−	3.81432i	0.510403	−	0.165840i
$530$	2.99351	−	11.2396i	0.130030	−	0.488217i
$531$	−27.3559	−	8.88847i	−1.18715	−	0.385727i
$532$	16.7748	+	8.88419i	0.727280	+	0.385179i
$533$	−10.1939	−	20.0066i	−0.441546	−	0.866583i
$534$	1.49880	−	1.08894i	0.0648596	−	0.0471232i
$535$	−9.50827	+	10.5920i	−0.411078	+	0.457933i
$536$	2.52153	+	1.83200i	0.108914	+	0.0791303i
$537$	−55.6494	−	8.81400i	−2.40145	−	0.380352i
$538$	0.0786593	−	0.496635i	0.00339124	−	0.0214115i
$539$	6.77159	−	9.32029i	0.291673	−	0.401453i
$540$	22.6304	−	13.1111i	0.973858	−	0.564214i
$541$	−26.4901	+	19.2462i	−1.13890	+	0.827458i	−0.986965	−	0.160932i	$-0.948550\pi$
$541$	−26.4901	+	19.2462i	−1.13890	+	0.827458i	−0.151933	+	0.988391i	$0.548550\pi$
$542$	1.76925	+	3.47234i	0.0759956	+	0.149150i
$543$	10.2439	−	10.2439i	0.439609	−	0.439609i
$544$	2.29883	−	7.07508i	0.0985617	−	0.303342i
$545$	−3.67989	+	2.98910i	−0.157629	+	0.128039i
$546$	75.1343	−	24.4126i	3.21545	−	1.04476i
$547$	2.77361	+	1.41323i	0.118591	+	0.0604252i	0.512280	−	0.858819i	$-0.328801\pi$
$547$	2.77361	+	1.41323i	0.118591	+	0.0604252i	−0.393689	+	0.919244i	$0.628801\pi$
$548$	11.9632	−	1.89478i	0.511041	−	0.0809410i
$549$			41.9737i			1.79139i
$550$	4.49990	+	1.71182i	0.191877	+	0.0729923i
$551$	6.40141	+	20.8163i	0.272709	+	0.886806i
$552$	−2.90343	−	18.3315i	−0.123578	−	0.780243i
$553$	15.9714	−	31.3457i	0.679174	−	1.33295i
$554$	2.65211	+	8.16234i	0.112677	+	0.346785i
$555$	37.2041	+	24.0810i	1.57922	+	1.02218i
$556$	−2.37825	+	7.31949i	−0.100860	+	0.310416i
$557$	7.02497	+	7.02497i	0.297657	+	0.297657i	0.840096	−	0.542438i	$-0.182499\pi$
$557$	7.02497	+	7.02497i	0.297657	+	0.297657i	−0.542438	+	0.840096i	$0.682499\pi$
$558$	12.1735	+	23.8918i	0.515345	+	1.01142i
$559$	4.42040	−	3.21161i	0.186963	−	0.135836i
$560$	9.68583	+	1.00328i	0.409301	+	0.0423963i
$561$	−13.1447	+	18.0921i	−0.554970	+	0.763850i
$562$	23.5946	+	3.73701i	0.995277	+	0.157636i
$563$	−25.9505	−	4.11016i	−1.09368	−	0.173222i	−0.416572	−	0.909103i	$-0.636769\pi$
$563$	−25.9505	−	4.11016i	−1.09368	−	0.173222i	−0.677112	+	0.735880i	$0.736769\pi$
$564$	−10.3905	−	7.54911i	−0.437517	−	0.317875i
$565$	4.95987	+	0.513754i	0.208663	+	0.0216138i
$566$	−13.6238	−	18.7516i	−0.572652	−	0.788188i
$567$	−63.1541	+	32.1786i	−2.65222	+	1.35137i
$568$	1.22407	−	1.22407i	0.0513610	−	0.0513610i
$569$	12.0060	−	36.9507i	0.503318	−	1.54905i	−0.300262	−	0.953857i	$-0.597074\pi$
$569$	12.0060	−	36.9507i	0.503318	−	1.54905i	0.803580	−	0.595197i	$-0.202926\pi$
$570$	8.29547	−	29.2764i	0.347459	−	1.22625i
$571$	9.55506	+	29.4075i	0.399867	+	1.23066i	0.925106	+	0.379709i	$0.123976\pi$
$571$	9.55506	+	29.4075i	0.399867	+	1.23066i	−0.525239	+	0.850955i	$0.676024\pi$
$572$	−4.98540	−	2.54019i	−0.208450	−	0.106211i
$573$	1.42671	+	9.00787i	0.0596015	+	0.376309i
$574$			16.8277i			0.702375i
$575$	28.6890	−	7.77987i	1.19641	−	0.324443i
$576$	−6.74654			−0.281106
$577$	−4.11423	−	25.9763i	−0.171278	−	1.08141i	−0.912179	−	0.409792i	$-0.865601\pi$
$577$	−4.11423	−	25.9763i	−0.171278	−	1.08141i	0.740901	−	0.671614i	$-0.234399\pi$
$578$	−17.4067	+	34.1625i	−0.724022	+	1.42097i
$579$	−32.5059	+	10.5618i	−1.35090	+	0.438934i
$580$	7.04388	+	8.67174i	0.292481	+	0.360074i
$581$	8.91697	−	27.4436i	0.369938	−	1.13855i
$582$	−41.9866	+	41.9866i	−1.74040	+	1.74040i
$583$	4.46282	−	2.27392i	0.184831	−	0.0941762i
$584$	4.62789	−	3.36236i	0.191503	−	0.139135i
$585$	−43.9444	−	75.8500i	−1.81688	−	3.13601i
$586$	10.1278	+	7.35826i	0.418375	+	0.303967i
$587$	18.3338	+	2.90379i	0.756717	+	0.119852i	0.522860	−	0.852419i	$-0.324865\pi$
$587$	18.3338	+	2.90379i	0.756717	+	0.119852i	0.233857	+	0.972271i	$0.424865\pi$
$588$	−36.8923	−	5.84316i	−1.52141	−	0.240968i
$589$	16.3900	+	5.61358i	0.675337	+	0.231303i
$590$	−6.36843	+	7.09431i	−0.262184	+	0.292068i
$591$	36.3919	+	50.0891i	1.49696	+	2.06039i
$592$	−2.88212	−	5.65647i	−0.118454	−	0.232480i
$593$	9.96736	−	9.96736i	0.409311	−	0.409311i	−0.472188	−	0.881498i	$-0.656535\pi$
$593$	9.96736	−	9.96736i	0.409311	−	0.409311i	0.881498	+	0.472188i	$0.156535\pi$
$594$	10.7113	+	3.48032i	0.439491	+	0.142799i
$595$	−70.0000	−	18.6435i	−2.86972	−	0.764310i
$596$	−0.783546	−	2.41151i	−0.0320953	−	0.0987792i
$597$	8.59974	+	4.38178i	0.351964	+	0.179334i
$598$	−34.1202	+	5.40410i	−1.39528	+	0.220990i
$599$	44.4923			1.81791			0.908954	−	0.416897i	$-0.136882\pi$
$599$	44.4923			1.81791			0.908954	+	0.416897i	$0.136882\pi$
$600$	−1.67840	−	15.5192i	−0.0685206	−	0.633570i
$601$		−	6.86201i		−	0.279907i	−0.990158	−	0.139954i	$-0.955305\pi$
$601$		−	6.86201i		−	0.279907i	0.990158	−	0.139954i	$-0.0446953\pi$
$602$	−4.04442	+	0.640572i	−0.164838	+	0.0261078i
$603$	−9.54628	+	18.7356i	−0.388755	+	0.762974i
$604$	−5.31721	−	16.3647i	−0.216354	−	0.665869i
$605$	−8.10336	−	21.0153i	−0.329448	−	0.854395i
$606$	−17.1708	+	52.8462i	−0.697515	+	2.14673i
$607$	5.47333	−	5.47333i	0.222155	−	0.222155i	−0.587250	−	0.809406i	$-0.699789\pi$
$607$	5.47333	−	5.47333i	0.222155	−	0.222155i	0.809406	+	0.587250i	$0.199789\pi$
$608$	−3.13058	+	3.03307i	−0.126962	+	0.123007i
$609$	−39.9266	−	54.9542i	−1.61791	−	2.22686i
$610$	12.7175	+	5.63927i	0.514917	+	0.228327i
$611$	−14.0510	+	19.3396i	−0.568444	+	0.782395i
$612$	49.5708	+	7.85125i	2.00378	+	0.317368i
$613$	−6.16207	+	38.9058i	−0.248884	+	1.57139i	0.474066	+	0.880489i	$0.342786\pi$
$613$	−6.16207	+	38.9058i	−0.248884	+	1.57139i	−0.722950	+	0.690900i	$0.757214\pi$
$614$	18.2761	−	25.1549i	0.737562	−	1.01517i
$615$	26.3773	−	5.64820i	1.06364	−	0.227757i
$616$	2.46473	+	3.39241i	0.0993069	+	0.136684i
$617$	2.22484	−	1.13361i	0.0895688	−	0.0456376i	−0.408632	−	0.912699i	$-0.633994\pi$
$617$	2.22484	−	1.13361i	0.0895688	−	0.0456376i	0.498201	+	0.867062i	$0.333994\pi$
$618$	18.0600	+	18.0600i	0.726478	+	0.726478i
$619$	−23.0838	−	7.50039i	−0.927817	−	0.301466i	−0.194148	−	0.980972i	$-0.562194\pi$
$619$	−23.0838	−	7.50039i	−0.927817	−	0.301466i	−0.733670	+	0.679506i	$0.762194\pi$
$620$	8.87447	−	0.478492i	0.356407	−	0.0192167i
$621$	66.1326	−	21.4878i	2.65381	−	0.862275i
$622$	5.57284	+	2.83951i	0.223451	+	0.113854i
$623$	0.404263	+	2.55241i	0.0161964	+	0.102260i
$624$			18.1410i			0.726223i
$625$	24.4219	−	5.34498i	0.976878	−	0.213799i
$626$			15.8259i			0.632530i
$627$	11.7678	−	5.76339i	0.469962	−	0.230168i
$628$	−5.19919	−	2.64912i	−0.207470	−	0.105711i
$629$	14.5939	+	44.9155i	0.581898	+	1.79090i
$630$	3.53702	+	65.6001i	0.140918	+	2.61357i
$631$	−0.837003	+	2.57603i	−0.0333206	+	0.102550i	−0.966334	−	0.257292i	$-0.917170\pi$
$631$	−0.837003	+	2.57603i	−0.0333206	+	0.102550i	0.933013	+	0.359843i	$0.117170\pi$
$632$	5.71232	+	5.71232i	0.227224	+	0.227224i
$633$	−12.8685	−	25.2559i	−0.511478	−	1.00383i
$634$	−19.4011	−	26.7033i	−0.770517	−	1.06053i
$635$	34.4799	−	7.38321i	1.36829	−	0.292994i
$636$	−13.1380	−	9.54533i	−0.520956	−	0.378497i
$637$	−10.8758	+	68.6669i	−0.430913	+	2.72068i
$638$	−0.752598	+	4.75172i	−0.0297956	+	0.188122i
$639$	9.44847	+	6.86471i	0.373776	+	0.271564i
$640$	−0.906414	+	2.04412i	−0.0358292	+	0.0808008i
$641$	−11.8640	−	16.3294i	−0.468601	−	0.644974i	0.507664	−	0.861555i	$-0.330509\pi$
$641$	−11.8640	−	16.3294i	−0.468601	−	0.644974i	−0.976264	+	0.216582i	$0.930509\pi$
$642$	9.02204	+	17.7068i	0.356072	+	0.698830i
$643$	−31.3917	+	31.3917i	−1.23797	+	1.23797i	−0.277140	+	0.960830i	$0.589386\pi$
$643$	−31.3917	+	31.3917i	−1.23797	+	1.23797i	−0.960830	+	0.277140i	$0.910614\pi$
$644$	24.6224	+	8.00029i	0.970257	+	0.315256i
$645$	2.36160	+	6.12459i	0.0929877	+	0.241155i
$646$	26.5319	−	18.6425i	1.04388	−	0.733481i
$647$	−7.07240	+	13.8804i	−0.278045	+	0.545693i	−0.987225	−	0.159334i	$-0.949065\pi$
$647$	−7.07240	+	13.8804i	−0.278045	+	0.545693i	0.709180	+	0.705027i	$0.249065\pi$
$648$	−2.54615	−	16.0757i	−0.100022	−	0.631515i
$649$	−4.10531			−0.161147
$650$	−28.8856	+	3.12398i	−1.13299	+	0.122533i
$651$	−54.0359			−2.11783
$652$	1.14746	+	7.24480i	0.0449381	+	0.283728i
$653$	26.8731	+	13.6925i	1.05163	+	0.535830i	0.892322	−	0.451399i	$-0.149075\pi$
$653$	26.8731	+	13.6925i	1.05163	+	0.535830i	0.159304	+	0.987230i	$0.449075\pi$
$654$	2.04543	+	6.29519i	0.0799826	+	0.246161i
$655$	5.43373	−	20.4018i	0.212313	−	0.797163i
$656$	−3.67504	−	1.19409i	−0.143486	−	0.0466215i
$657$	27.2892	+	27.2892i	1.06465	+	1.06465i
$658$	15.9626	−	8.13333i	0.622285	−	0.317070i
$659$	−5.57356	+	4.04943i	−0.217115	+	0.157743i	−0.691027	−	0.722829i	$-0.742841\pi$
$659$	−5.57356	+	4.04943i	−0.217115	+	0.157743i	0.473912	+	0.880572i	$0.342841\pi$
$660$	4.49030	−	5.00211i	0.174785	−	0.194707i
$661$	−13.2843	+	18.2843i	−0.516699	+	0.711175i	−0.985031	−	0.172377i	$-0.944855\pi$
$661$	−13.2843	+	18.2843i	−0.516699	+	0.711175i	0.468332	+	0.883553i	$0.344855\pi$
$662$	−23.5148	−	3.72437i	−0.913927	−	0.144752i
$663$	21.1115	−	133.293i	0.819905	−	5.17667i
$664$	5.36072	+	3.89479i	0.208036	+	0.151147i
$665$	31.1334	+	28.8501i	1.20730	+	1.11876i
$666$	34.6500	−	25.1747i	1.34266	−	0.975500i
$667$	13.4850	+	26.4657i	0.522140	+	1.02476i
$668$	0.904318	+	0.904318i	0.0349891	+	0.0349891i
$669$	−42.1499	−	13.6953i	−1.62961	−	0.529492i
$670$	4.39410	+	5.40959i	0.169759	+	0.208991i
$671$	1.85123	+	5.69750i	0.0714659	+	0.219949i
$672$	6.17222	−	12.1137i	0.238098	−	0.467295i
$673$	0.462019	+	2.91707i	0.0178095	+	0.112445i	0.994992	−	0.0999584i	$-0.0318710\pi$
$673$	0.462019	+	2.91707i	0.0178095	+	0.112445i	−0.977182	+	0.212403i	$0.931871\pi$
$674$			4.99558i			0.192423i
$675$	56.4438	−	15.3064i	2.17252	−	0.589144i
$676$	20.7656			0.798677
$677$	−23.5729	+	3.73357i	−0.905979	+	0.143493i	−0.592001	−	0.805937i	$-0.701662\pi$
$677$	−23.5729	+	3.73357i	−0.905979	+	0.143493i	−0.313978	+	0.949430i	$0.601662\pi$
$678$	3.16064	−	6.20310i	0.121384	−	0.238229i
$679$	−25.5948	−	78.7727i	−0.982239	−	3.02302i
$680$	9.03879	−	13.9645i	0.346622	−	0.535514i
$681$	4.92001	−	15.1422i	0.188535	−	0.580252i
$682$	2.70617	+	2.70617i	0.103624	+	0.103624i
$683$	17.1233	−	8.72473i	0.655203	−	0.333843i	−0.0945887	−	0.995516i	$-0.530154\pi$
$683$	17.1233	−	8.72473i	0.655203	−	0.333843i	0.749792	+	0.661674i	$0.230154\pi$
$684$	−23.5147	−	17.6594i	−0.899109	−	0.675226i
$685$	26.9398	+	2.79048i	1.02932	+	0.106619i
$686$	12.7073	−	17.4901i	0.485167	−	0.667774i
$687$	−0.790509	+	4.99108i	−0.0301598	+	0.190422i
$688$	0.147095	−	0.928723i	0.00560796	−	0.0354073i
$689$	−17.7665	+	24.4535i	−0.676851	+	0.931606i
$690$	4.27594	−	41.2807i	0.162782	−	1.57153i
$691$	0.945305	−	0.686804i	0.0359611	−	0.0261273i	−0.569660	−	0.821881i	$-0.692925\pi$
$691$	0.945305	−	0.686804i	0.0359611	−	0.0261273i	0.605621	+	0.795754i	$0.292925\pi$
$692$	−11.5478	−	22.6638i	−0.438981	−	0.861549i
$693$	−20.0040	+	20.0040i	−0.759889	+	0.759889i
$694$	−1.93895	+	5.96748i	−0.0736016	+	0.226523i
$695$	−9.35104	+	14.4469i	−0.354705	+	0.548003i
$696$	14.8348	−	4.82010i	0.562310	−	0.182706i
$697$	25.6131	+	13.0505i	0.970165	+	0.494324i
$698$	−0.234207	−	1.47872i	−0.00886486	−	0.0559706i
$699$	−68.0488			−2.57384
$700$	20.3512	+	7.74187i	0.769205	+	0.292615i
$701$	15.4443			0.583323			0.291662	−	0.956522i	$-0.405792\pi$
$701$	15.4443			0.583323			0.291662	+	0.956522i	$0.405792\pi$
$702$	−67.1293	+	10.6322i	−2.53363	+	0.401288i
$703$	4.76066	−	27.2595i	0.179552	−	1.02811i
$704$	−0.915773	+	0.297553i	−0.0345145	+	0.0112144i
$705$	−18.1067	−	22.2913i	−0.681939	−	0.839537i
$706$	−14.5924	−	4.74136i	−0.549193	−	0.178444i
$707$	−54.8070	−	54.8070i	−2.06123	−	2.06123i
$708$	6.04277	+	11.8596i	0.227101	+	0.445711i
$709$	−29.6080	−	40.7519i	−1.11195	−	1.53047i	−0.818511	−	0.574491i	$-0.805200\pi$
$709$	−29.6080	−	40.7519i	−1.11195	−	1.53047i	−0.293439	−	0.955978i	$-0.594800\pi$
$710$	3.34935	−	1.94048i	0.125699	−	0.0728248i
$711$	−32.0352	+	44.0926i	−1.20141	+	1.65360i
$712$	−0.586114	−	0.0928313i	−0.0219655	−	0.00347900i
$713$	23.3379	+	3.69636i	0.874011	+	0.138430i
$714$	−59.4482	+	81.8234i	−2.22479	+	3.06216i
$715$	−9.31033	−	8.35771i	−0.348187	−	0.312561i
$716$	10.6080	+	14.6007i	0.396440	+	0.545653i
$717$	14.7316	+	28.9124i	0.550163	+	1.07975i
$718$	8.10029	+	8.10029i	0.302300	+	0.302300i
$719$	33.5466	+	10.9000i	1.25108	+	0.406500i	0.858307	−	0.513137i	$-0.171517\pi$
$719$	33.5466	+	10.9000i	1.25108	+	0.406500i	0.392770	+	0.919637i	$0.371517\pi$
$720$	−14.5775	−	3.88252i	−0.543273	−	0.144693i
$721$	−33.8830	+	11.0093i	−1.26187	+	0.410007i
$722$	−18.8507	+	2.37715i	−0.701551	+	0.0884682i
$723$	18.5918	−	2.94465i	0.691436	−	0.109513i
$724$	−4.64041			−0.172459
$725$	10.2296	+	22.7910i	0.379917	+	0.846438i
$726$	−31.4468			−1.16710
$727$	6.37237	+	40.2336i	0.236338	+	1.49218i	0.765376	+	0.643583i	$0.222553\pi$
$727$	6.37237	+	40.2336i	0.236338	+	1.49218i	−0.529038	+	0.848598i	$0.677447\pi$
$728$	−22.5469	−	11.4882i	−0.835645	−	0.425782i
$729$	0.247554	−	0.0804351i	0.00916866	−	0.00297908i
$730$	11.9347	−	4.60192i	0.441722	−	0.170325i
$731$	−2.16159	+	6.65270i	−0.0799494	+	0.246059i
$732$	13.7343	−	13.7343i	0.507634	−	0.507634i
$733$	−13.4635	−	26.4235i	−0.497285	−	0.975976i	−0.994136	−	0.108140i	$-0.965511\pi$
$733$	−13.4635	−	26.4235i	−0.497285	−	0.975976i	0.496851	−	0.867836i	$-0.334489\pi$
$734$	17.3258	−	12.5879i	0.639507	−	0.464629i
$735$	−76.3521	−	33.8565i	−2.81629	−	1.24882i
$736$	−3.49440	+	4.80963i	−0.128805	+	0.177285i
$737$	−0.469484	+	2.96421i	−0.0172937	+	0.109188i
$738$	4.07821	−	25.7488i	0.150121	−	0.947826i
$739$	−18.2918	+	25.1766i	−0.672876	+	0.926135i	−0.999821	−	0.0189087i	$-0.993981\pi$
$739$	−18.2918	+	25.1766i	−0.672876	+	0.926135i	0.326945	+	0.945043i	$0.393981\pi$
$740$	−2.97231	−	13.8808i	−0.109264	−	0.510268i
$741$	−47.4852	+	63.2298i	−1.74441	+	2.32280i
$742$	20.1835	−	10.2840i	0.740961	−	0.377538i
$743$	−3.88078	−	3.88078i	−0.142372	−	0.142372i	0.632328	−	0.774700i	$-0.282099\pi$
$743$	−3.88078	−	3.88078i	−0.142372	−	0.142372i	−0.774700	+	0.632328i	$0.782099\pi$
$744$	3.83438	−	11.8010i	0.140575	−	0.432646i
$745$	−0.305259	−	5.66157i	−0.0111838	−	0.207424i
$746$	−7.44583	−	22.9159i	−0.272611	−	0.839011i
$747$	−20.2952	+	39.8316i	−0.742563	+	1.45736i
$748$	7.07501	−	1.12057i	0.258688	−	0.0409721i
$749$	−27.7206			−1.01289
$750$	5.30446	−	34.4990i	0.193692	−	1.25972i
$751$			19.3013i			0.704316i	0.935941	+	0.352158i	$0.114552\pi$
$751$			19.3013i			0.704316i	−0.935941	+	0.352158i	$0.885448\pi$
$752$	0.643553	+	4.06324i	0.0234680	+	0.148171i
$753$	27.1583	−	53.3011i	0.989702	−	1.94240i
$754$	−8.97157	−	27.6116i	−0.326725	−	1.00556i
$755$	−2.07151	−	38.4199i	−0.0753901	−	1.39824i
$756$	48.4430	+	15.7401i	1.76185	+	0.572461i
$757$	−19.0016	−	19.0016i	−0.690626	−	0.690626i	0.271744	−	0.962370i	$-0.412400\pi$
$757$	−19.0016	−	19.0016i	−0.690626	−	0.690626i	−0.962370	+	0.271744i	$0.912400\pi$
$758$	−12.7523	−	25.0278i	−0.463185	−	0.909052i
$759$	14.4583	−	10.5046i	0.524805	−	0.381293i
$760$	−8.50986	+	4.75208i	−0.308685	+	0.172376i
$761$	−29.7911	−	21.6445i	−1.07992	−	0.784611i	−0.102255	−	0.994758i	$-0.532606\pi$
$761$	−29.7911	−	21.6445i	−1.07992	−	0.784611i	−0.977670	+	0.210147i	$0.932606\pi$
$762$	7.70147	−	48.6252i	0.278995	−	1.76151i
$763$	−9.11940	−	1.44437i	−0.330145	−	0.0522898i
$764$	1.71710	−	2.36339i	0.0621225	−	0.0855043i
$765$	102.592	+	45.4917i	3.70921	+	1.64476i
$766$	15.1945	−	11.0395i	0.549000	−	0.398872i
$767$	22.0741	−	11.2473i	0.797048	−	0.406116i
$768$	2.20755	+	2.20755i	0.0796580	+	0.0796580i
$769$	35.9722	+	11.6881i	1.29719	+	0.421482i	0.874603	−	0.484840i	$-0.161122\pi$
$769$	35.9722	+	11.6881i	1.29719	+	0.421482i	0.422587	+	0.906322i	$0.361122\pi$
$770$	3.37338	+	8.74855i	0.121568	+	0.315276i
$771$	−1.20660	−	3.71352i	−0.0434545	−	0.133739i
$772$	9.75465	+	4.97024i	0.351077	+	0.178883i
$773$	−2.64888	−	16.7244i	−0.0952736	−	0.601534i	−0.988417	−	0.151762i	$-0.951505\pi$
$773$	−2.64888	−	16.7244i	−0.0952736	−	0.601534i	0.893143	−	0.449772i	$-0.148495\pi$
$774$	6.34377			0.228022
$775$	19.4508	+	4.07322i	0.698694	+	0.146314i
$776$	19.0196			0.682762
$777$	13.5018	+	85.2470i	0.484374	+	3.05822i
$778$	−11.7803	+	23.1201i	−0.422344	+	0.828897i
$779$	−9.68358	−	13.7816i	−0.346950	−	0.493777i
$780$	−10.4399	+	39.1982i	−0.373808	+	1.40352i
$781$	1.58530	+	0.515095i	0.0567264	+	0.0184315i
$782$	31.2726	−	31.2726i	1.11831	−	1.11831i
$783$	26.5308	+	52.0696i	0.948134	+	1.86082i
$784$	7.03249	+	9.67939i	0.251160	+	0.345692i
$785$	−9.70960	−	8.71613i	−0.346551	−	0.311092i
$786$	−23.8477	−	17.3264i	−0.850621	−	0.618012i
$787$	1.32701	−	8.37844i	0.0473029	−	0.298659i	−0.952683	−	0.303966i	$-0.901689\pi$
$787$	1.32701	−	8.37844i	0.0473029	−	0.298659i	0.999986	+	0.00530670i	$0.00168918\pi$
$788$	3.10237	−	19.5876i	0.110517	−	0.697778i
$789$	−4.13261	−	3.00252i	−0.147125	−	0.106892i
$790$	9.05552	+	15.6302i	0.322181	+	0.556098i
$791$	5.70809	+	7.85651i	0.202956	+	0.279345i
$792$	−2.94923	−	5.78820i	−0.104796	−	0.205675i
$793$	−25.5634	−	25.5634i	−0.907782	−	0.907782i
$794$	8.45569	−	26.0239i	0.300081	−	0.923555i
$795$	−22.8947	−	28.1857i	−0.811992	−	0.999645i
$796$	−0.955348	−	2.94026i	−0.0338614	−	0.104215i
$797$	−30.7192	−	15.6522i	−1.08813	−	0.554430i	−0.184539	−	0.982825i	$-0.559079\pi$
$797$	−30.7192	−	15.6522i	−1.08813	−	0.554430i	−0.903591	+	0.428395i	$0.859079\pi$
$798$	53.2212	−	26.0655i	1.88401	−	0.922707i
$799$		−	30.6039i		−	1.08269i
$800$	−3.13489	+	3.89519i	−0.110835	+	0.137716i
$801$		−	4.00353i		−	0.141458i
$802$	−0.750405	−	4.73787i	−0.0264977	−	0.167300i
$803$	4.90781	+	2.50065i	0.173193	+	0.0882461i
$804$	9.25419	−	3.00687i	0.326370	−	0.106044i
$805$	48.5986	+	31.4564i	1.71288	+	1.10869i
$806$	−21.9650	−	7.13686i	−0.773684	−	0.251385i
$807$	−1.11001	−	1.11001i	−0.0390743	−	0.0390743i
$808$	15.8585	−	8.08033i	0.557901	−	0.284265i
$809$	24.5014	+	33.7233i	0.861423	+	1.18565i	0.981228	+	0.192849i	$0.0617729\pi$
$809$	24.5014	+	33.7233i	0.861423	+	1.18565i	−0.119806	+	0.992797i	$0.538227\pi$
$810$	3.74976	−	36.2009i	0.131753	−	1.27197i
$811$	18.8654	−	25.9660i	0.662454	−	0.911790i	−0.337106	−	0.941467i	$-0.609448\pi$
$811$	18.8654	−	25.9660i	0.662454	−	0.911790i	0.999560	+	0.0296772i	$0.00944792\pi$
$812$	−3.40369	+	21.4901i	−0.119446	+	0.754154i
$813$	12.0167	+	1.90326i	0.421445	+	0.0667504i
$814$	3.59307	−	4.94543i	0.125937	−	0.173337i
$815$	−1.68989	+	16.3145i	−0.0591943	+	0.571472i
$816$	−13.6511	−	18.7892i	−0.477886	−	0.657753i
$817$	2.94368	−	2.85199i	0.102986	−	0.0997786i
$818$	−16.4793	+	16.4793i	−0.576187	+	0.576187i
$819$	52.7557	−	162.365i	1.84343	−	5.67351i
$820$	−7.25365	−	4.69506i	−0.253308	−	0.163959i
$821$	−4.00996	−	12.3414i	−0.139948	−	0.430717i	0.856378	−	0.516349i	$-0.172709\pi$
$821$	−4.00996	−	12.3414i	−0.139948	−	0.430717i	−0.996327	+	0.0856316i	$0.972709\pi$
$822$	17.1671	−	33.6924i	0.598773	−	1.17516i
$823$	−14.2246	+	2.25296i	−0.495839	+	0.0785331i	−0.399345	−	0.916801i	$-0.630763\pi$
$823$	−14.2246	+	2.25296i	−0.495839	+	0.0785331i	−0.0964931	+	0.995334i	$0.530763\pi$
$824$		−	8.18101i		−	0.284999i
$825$	12.5810	−	8.22419i	0.438015	−	0.286329i
$826$	−18.5666			−0.646016
$827$	−31.0148	+	4.91227i	−1.07849	+	0.170816i	−0.670307	−	0.742084i	$-0.733838\pi$
$827$	−31.0148	+	4.91227i	−1.07849	+	0.170816i	−0.408184	+	0.912900i	$0.633838\pi$
$828$	−35.7368	−	18.2088i	−1.24194	−	0.632800i
$829$	−6.95548	−	21.4068i	−0.241574	−	0.743488i	−0.996181	−	0.0873112i	$-0.972173\pi$
$829$	−6.95548	−	21.4068i	−0.241574	−	0.743488i	0.754607	−	0.656177i	$-0.227827\pi$
$830$	9.34176	+	11.5007i	0.324257	+	0.399194i
$831$	25.4824	+	8.27973i	0.883974	+	0.287221i
$832$	4.10887	−	4.10887i	0.142449	−	0.142449i
$833$	−40.4075	−	79.3042i	−1.40004	−	2.74773i
$834$	14.1227	+	19.4383i	0.489030	+	0.673092i
$835$	1.43358	+	2.47442i	0.0496111	+	0.0856309i
$836$	−3.97075	−	1.35998i	−0.137331	−	0.0470360i
$837$	45.9159	+	7.27236i	1.58708	+	0.251369i
$838$	−4.62371	−	0.732323i	−0.159723	−	0.0252977i
$839$	−0.169280	−	0.122989i	−0.00584418	−	0.00424605i	0.584859	−	0.811135i	$-0.301150\pi$
$839$	−0.169280	−	0.122989i	−0.00584418	−	0.00424605i	−0.590704	+	0.806889i	$0.701150\pi$
$840$	20.3078	−	22.6225i	0.700686	−	0.780551i
$841$	3.26596	−	2.37286i	0.112619	−	0.0818228i
$842$	2.57283	−	1.31092i	0.0886655	−	0.0451773i
$843$	52.7354	−	52.7354i	1.81630	−	1.81630i
$844$	−2.80569	+	8.63502i	−0.0965758	+	0.297230i
$845$	44.8691	+	11.9503i	1.54355	+	0.411102i
$846$	−26.3961	+	8.57660i	−0.907515	+	0.294870i
$847$	19.9144	−	39.0842i	0.684267	−	1.34295i
$848$	0.813728	+	5.13768i	0.0279435	+	0.176429i
$849$	−72.3612			−2.48343
$850$	27.5669	−	24.9721i	0.945536	−	0.856535i
$851$		−	37.7415i		−	1.29376i
$852$	−0.845436	−	5.33787i	−0.0289641	−	0.182872i
$853$	31.0884	+	15.8404i	1.06445	+	0.542363i	0.896323	−	0.443402i	$-0.146229\pi$
$853$	31.0884	+	15.8404i	1.06445	+	0.542363i	0.168125	+	0.985766i	$0.446229\pi$
$854$	8.37236	+	25.7675i	0.286496	+	0.881744i
$855$	−40.6466	−	51.6899i	−1.39009	−	1.76776i
$856$	1.96705	−	6.05396i	0.0672324	−	0.206920i
$857$	−22.8725	+	22.8725i	−0.781310	+	0.781310i	−0.980052	−	0.198742i	$-0.936315\pi$
$857$	−22.8725	+	22.8725i	−0.781310	+	0.781310i	0.198742	+	0.980052i	$0.436315\pi$
$858$	−15.5641	+	7.93032i	−0.531351	+	0.270737i
$859$	4.59731	+	6.32765i	0.156858	+	0.215897i	0.880212	−	0.474581i	$-0.157400\pi$
$859$	4.59731	+	6.32765i	0.156858	+	0.215897i	−0.723354	+	0.690478i	$0.757400\pi$
$860$	0.852301	−	1.92208i	0.0290632	−	0.0655425i
$861$	42.5019	+	30.8794i	1.44846	+	1.05237i
$862$	−22.9660	−	3.63746i	−0.782226	−	0.123892i
$863$	−19.1418	−	3.03176i	−0.651594	−	0.103202i	−0.178118	−	0.984009i	$-0.557001\pi$
$863$	−19.1418	−	3.03176i	−0.651594	−	0.103202i	−0.473476	+	0.880807i	$0.657001\pi$
$864$	−6.87502	+	9.46265i	−0.233893	+	0.321926i
$865$	−11.9092	−	55.6163i	−0.404924	−	1.89101i
$866$	−24.0399	+	17.4660i	−0.816909	+	0.593519i
$867$	54.3426	+	106.653i	1.84557	+	3.62214i
$868$	12.2389	+	12.2389i	0.415415	+	0.415415i
$869$	−2.40376	+	7.39802i	−0.0815421	+	0.250961i
$870$	34.8280	−	1.87785i	1.18078	−	0.0636651i
$871$	−5.59663	−	17.2246i	−0.189634	−	0.583635i
$872$	0.962551	−	1.88911i	0.0325961	−	0.0639734i
$873$	20.0731	+	126.736i	0.679370	+	4.28937i
$874$	−24.7691	+	7.61695i	−0.837826	+	0.257647i
$875$	39.5185	+	28.4400i	1.33597	+	0.961448i
$876$		−	17.8587i		−	0.603390i
$877$	−15.9695	+	2.52932i	−0.539251	+	0.0854089i	−0.420118	−	0.907469i	$-0.638011\pi$
$877$	−15.9695	+	2.52932i	−0.539251	+	0.0854089i	−0.119133	+	0.992878i	$0.538011\pi$
$878$	−5.72605	−	2.91757i	−0.193245	−	0.0984631i
$879$	37.1696	−	12.0771i	1.25370	−	0.407352i
$880$	−2.14999	+	0.115923i	−0.0724761	+	0.00390775i
$881$	4.62783	−	14.2430i	0.155916	−	0.479859i	−0.842337	−	0.538951i	$-0.818821\pi$
$881$	4.62783	−	14.2430i	0.155916	−	0.479859i	0.998253	+	0.0590925i	$0.0188207\pi$
$882$	−57.0763	+	57.0763i	−1.92186	+	1.92186i
$883$	4.06469	+	7.97740i	0.136788	+	0.268461i	0.949231	−	0.314579i	$-0.101863\pi$
$883$	4.06469	+	7.97740i	0.136788	+	0.268461i	−0.812444	+	0.583040i	$0.801863\pi$
$884$	−34.9720	+	25.4086i	−1.17623	+	0.854585i
$885$	6.23187	+	29.1031i	0.209482	+	0.978289i
$886$	−20.0978	+	27.6622i	−0.675197	+	0.929330i
$887$	5.31805	−	33.5768i	0.178563	−	1.12740i	−0.721749	−	0.692155i	$-0.756662\pi$
$887$	5.31805	−	33.5768i	0.178563	−	1.12740i	0.900312	−	0.435245i	$-0.143338\pi$
$888$	−19.5754	−	3.10043i	−0.656906	−	0.104044i
$889$	55.5576	+	40.3649i	1.86334	+	1.35380i
$890$	−1.21302	−	0.537884i	−0.0406605	−	0.0180299i
$891$	12.6792	−	9.21195i	0.424768	−	0.308612i
$892$	6.44483	+	12.6487i	0.215789	+	0.423510i
$893$	−8.39268	+	15.8468i	−0.280850	+	0.530292i
$894$	−7.52859	−	2.44619i	−0.251794	−	0.0818127i
$895$	14.5188	+	37.6531i	0.485308	+	1.25860i
$896$	−4.14167	+	1.34571i	−0.138364	+	0.0449570i
$897$	−48.9625	+	96.0942i	−1.63481	+	3.20849i
$898$	−3.05823	+	0.484376i	−0.102054	+	0.0161638i
$899$			19.8581i			0.662303i
$900$	−29.2640	−	16.7783i	−0.975467	−	0.559276i
$901$		−	38.6966i		−	1.28917i
$902$	−0.582063	−	3.67500i	−0.0193806	−	0.122364i
$903$	−5.80374	+	11.3905i	−0.193136	+	0.379051i
$904$	−2.12085	+	0.689105i	−0.0705383	+	0.0229193i
$905$	−10.0267	−	2.67048i	−0.333300	−	0.0887698i
$906$	−51.0896	−	16.6000i	−1.69734	−	0.551499i
$907$	7.88683	−	7.88683i	0.261878	−	0.261878i	−0.563939	−	0.825817i	$-0.690715\pi$
$907$	7.88683	−	7.88683i	0.261878	−	0.261878i	0.825817	+	0.563939i	$0.190715\pi$
$908$	−4.54401	+	2.31529i	−0.150798	+	0.0768356i
$909$	70.5800	+	97.1450i	2.34099	+	3.22210i
$910$	−42.1069	−	37.7985i	−1.39583	−	1.25301i
$911$	30.6789	−	42.2259i	1.01644	−	1.39901i	0.101768	−	0.994808i	$-0.467550\pi$
$911$	30.6789	−	42.2259i	1.01644	−	1.39901i	0.914671	−	0.404199i	$-0.132450\pi$
$912$	1.91592	+	13.4727i	0.0634425	+	0.446125i
$913$	−0.998114	+	6.30184i	−0.0330327	+	0.208560i
$914$	11.6796	+	8.48571i	0.386326	+	0.280682i
$915$	37.5802	−	21.7724i	1.24236	−	0.719774i
$916$	1.30950	−	0.951411i	0.0432673	−	0.0314355i
$917$	36.6366	−	18.6673i	1.20985	−	0.616447i
$918$	61.5269	−	61.5269i	2.03069	−	2.03069i
$919$	−6.34728	−	2.06236i	−0.209377	−	0.0680309i	0.202450	−	0.979293i	$-0.435110\pi$
$919$	−6.34728	−	2.06236i	−0.209377	−	0.0680309i	−0.411828	+	0.911262i	$0.635110\pi$
$920$	−10.3184	+	8.38141i	−0.340187	+	0.276327i
$921$	−29.9966	−	92.3200i	−0.988421	−	3.04205i
$922$	19.1968	+	9.78124i	0.632212	+	0.322128i
$923$	−9.93528	+	1.57359i	−0.327024	+	0.0517955i
$924$	13.0911			0.430666
$925$	1.56578	−	31.7034i	0.0514826	−	1.04240i
$926$		−	27.2482i		−	0.895430i
$927$	54.5139	−	8.63416i	1.79047	−	0.283583i
$928$	−4.45174	−	2.26827i	−0.146135	−	0.0744598i
$929$	−37.3744	+	12.1437i	−1.22621	+	0.398421i	−0.849341	−	0.527844i	$-0.823001\pi$
$929$	−37.3744	+	12.1437i	−1.22621	+	0.398421i	−0.376873	+	0.926265i	$0.623001\pi$
$930$	15.0764	−	23.2924i	0.494375	−	0.763786i
$931$	−0.824950	+	52.1450i	−0.0270367	+	1.70898i
$932$	15.4128	+	15.4128i	0.504862	+	0.504862i
$933$	17.3981	−	8.86478i	0.569588	−	0.290220i
$934$	−24.0730	+	17.4900i	−0.787691	+	0.572291i
$935$	15.9322	+	1.65029i	0.521037	+	0.0539701i
$936$	31.7158	+	23.0429i	1.03666	+	0.753180i
$937$	14.4370	+	2.28659i	0.471635	+	0.0746996i	0.387728	−	0.921774i	$-0.373260\pi$
$937$	14.4370	+	2.28659i	0.471635	+	0.0746996i	0.0839071	+	0.996474i	$0.473260\pi$
$938$	−2.12329	+	13.4059i	−0.0693277	+	0.437718i
$939$	39.9716	+	29.0411i	1.30442	+	0.947719i
$940$	−0.947773	+	9.14997i	−0.0309129	+	0.298439i
$941$	22.1443	+	30.4790i	0.721883	+	0.993586i	0.999459	+	0.0328828i	$0.0104688\pi$
$941$	22.1443	+	30.4790i	0.721883	+	0.993586i	−0.277576	+	0.960704i	$0.589531\pi$
$942$	−16.2316	+	8.27041i	−0.528854	+	0.269464i
$943$	−16.2441	−	16.2441i	−0.528980	−	0.528980i
$944$	1.31749	−	4.05481i	0.0428805	−	0.131973i
$945$	95.6147	+	61.8884i	3.11035	+	2.01323i
$946$	0.861102	−	0.279789i	0.0279968	−	0.00909672i
$947$	4.66123	−	9.14817i	0.151470	−	0.297276i	−0.802786	−	0.596267i	$-0.796650\pi$
$947$	4.66123	−	9.14817i	0.151470	−	0.297276i	0.954256	+	0.298991i	$0.0966501\pi$
$948$	24.9099	−	3.94535i	0.809037	−	0.128139i
$949$	−33.2401			−1.07902
$950$	−21.1224	+	5.37075i	−0.685301	+	0.174250i
$951$	−103.046			−3.34151
$952$	31.9974	−	5.06789i	1.03704	−	0.164251i
$953$	7.81081	−	15.3296i	0.253017	−	0.496574i	−0.729205	−	0.684295i	$-0.760110\pi$
$953$	7.81081	−	15.3296i	0.253017	−	0.496574i	0.982222	+	0.187721i	$0.0601101\pi$
$954$	−33.3760	+	10.8445i	−1.08059	+	0.351104i
$955$	5.07030	−	4.11851i	0.164071	−	0.133272i
$956$	3.21189	−	9.88519i	0.103880	−	0.319710i
$957$	10.6204	+	10.6204i	0.343309	+	0.343309i
$958$	−22.4005	+	11.4136i	−0.723727	+	0.368757i
$959$	31.0038	+	42.6730i	1.00116	+	1.37798i
$960$	3.49954	+	6.04036i	0.112947	+	0.194952i
$961$	−12.2995	−	8.93608i	−0.396757	−	0.288261i
$962$	−5.77078	+	36.4353i	−0.186057	+	1.17472i
$963$	42.4164	+	6.71810i	1.36685	+	0.216488i
$964$	−4.87791	−	3.54401i	−0.157107	−	0.114145i
$965$	18.2170	+	16.3531i	0.586426	+	0.526424i
$966$	65.3892	−	47.5081i	2.10386	−	1.52855i
$967$	−6.97150	+	3.55216i	−0.224188	+	0.114230i	−0.562478	−	0.826812i	$-0.690152\pi$
$967$	−6.97150	+	3.55216i	−0.224188	+	0.114230i	0.338289	+	0.941042i	$0.390152\pi$
$968$	7.12256	+	7.12256i	0.228928	+	0.228928i
$969$	1.60136	−	101.222i	0.0514430	−	3.25170i
$970$	41.0964	+	10.9454i	1.31953	+	0.351437i
$971$	54.2166	−	17.6161i	1.73989	−	0.565326i	0.745075	−	0.666981i	$-0.232414\pi$
$971$	54.2166	−	17.6161i	1.73989	−	0.565326i	0.994820	+	0.101655i	$0.0324137\pi$
$972$	−14.0100	−	7.13844i	−0.449370	−	0.228965i
$973$	−33.1027	+	5.24296i	−1.06123	+	0.168082i
$974$			43.2012i			1.38426i
$975$	−45.1158	+	78.6893i	−1.44486	+	2.52007i
$976$	−6.22151			−0.199146
$977$	−19.7283	+	3.12466i	−0.631166	+	0.0999668i	−0.463817	−	0.885931i	$-0.653521\pi$
$977$	−19.7283	+	3.12466i	−0.631166	+	0.0999668i	−0.167349	+	0.985898i	$0.553521\pi$
$978$	20.4039	+	10.3963i	0.652443	+	0.332436i
$979$	−0.176574	−	0.543438i	−0.00564332	−	0.0173684i
$980$	9.62507	+	24.9618i	0.307462	+	0.797374i
$981$	13.6039	+	4.42018i	0.434340	+	0.141126i
$982$	−1.99702	+	1.99702i	−0.0637276	+	0.0637276i
$983$	−12.1010	+	6.16579i	−0.385963	+	0.196658i	−0.636196	−	0.771528i	$-0.719493\pi$
$983$	−12.1010	+	6.16579i	−0.385963	+	0.196658i	0.250232	+	0.968186i	$0.419493\pi$
$984$	−9.75975	+	7.09087i	−0.311129	+	0.226049i
$985$	17.9758	−	40.5384i	0.572755	−	1.29166i
$986$	30.0699	+	21.8470i	0.957620	+	0.695752i
$987$	8.74941	−	55.2416i	0.278497	−	1.75836i
$988$	25.0765	−	3.56607i	0.797789	−	0.113452i
$989$	3.28579	−	4.52250i	0.104482	−	0.143807i
$990$	−3.04153	−	14.2041i	−0.0966661	−	0.451435i
$991$	4.01997	+	5.53302i	0.127699	+	0.175762i	0.868079	−	0.496426i	$-0.165355\pi$
$991$	4.01997	+	5.53302i	0.127699	+	0.175762i	−0.740380	+	0.672188i	$0.765355\pi$
$992$	−3.54135	+	1.80441i	−0.112438	+	0.0572900i
$993$	−52.5570	+	52.5570i	−1.66785	+	1.66785i
$994$	7.16966	+	2.32956i	0.227408	+	0.0738893i
$995$	−0.372191	−	6.90293i	−0.0117992	−	0.218838i
$996$	19.6742	−	6.39254i	0.623401	−	0.202555i
$997$	−24.2899	+	47.6716i	−0.769268	+	1.50977i	0.0886927	+	0.996059i	$0.471731\pi$
$997$	−24.2899	+	47.6716i	−0.769268	+	1.50977i	−0.857961	+	0.513715i	$0.828269\pi$
$998$	5.86790	+	37.0485i	0.185745	+	1.17275i
$999$		−	74.2540i		−	2.34929i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.w.a.37.1	✓	400
19.18	odd	2	inner	950.2.w.a.37.50	yes	400
25.23	odd	20	inner	950.2.w.a.873.50	yes	400
475.398	even	20	inner	950.2.w.a.873.1	yes	400

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.w.a.37.1	✓	400	1.1	even	1	trivial
950.2.w.a.37.50	yes	400	19.18	odd	2	inner
950.2.w.a.873.1	yes	400	475.398	even	20	inner
950.2.w.a.873.50	yes	400	25.23	odd	20	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.987688 + 0.156434i) q^{2} +(-1.41733 + 2.78167i) q^{3} +(0.951057 - 0.309017i) q^{4} +(2.23282 - 0.120389i) q^{5} +(0.964734 - 2.96915i) q^{6} +(3.07932 + 3.07932i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(-3.96551 - 5.45806i) q^{9} +O(q^{10})\)	\(q+(-0.987688 + 0.156434i) q^{2} +(-1.41733 + 2.78167i) q^{3} +(0.951057 - 0.309017i) q^{4} +(2.23282 - 0.120389i) q^{5} +(0.964734 - 2.96915i) q^{6} +(3.07932 + 3.07932i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(-3.96551 - 5.45806i) q^{9} +(-2.18650 + 0.468198i) q^{10} +(-0.779003 - 0.565979i) q^{11} +(-0.488380 + 3.08351i) q^{12} +(5.73928 + 0.909012i) q^{13} +(-3.52312 - 2.55969i) q^{14} +(-2.82977 + 6.38162i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-6.62836 + 3.37732i) q^{17} +(4.77052 + 4.77052i) q^{18} +(4.35835 + 0.0689505i) q^{19} +(2.08634 - 0.804478i) q^{20} +(-12.9301 + 4.20123i) q^{21} +(0.857951 + 0.437148i) q^{22} +(5.87184 - 0.930008i) q^{23} -3.12194i q^{24} +(4.97101 - 0.537615i) q^{25} -5.81082 q^{26} +(11.5525 - 1.82973i) q^{27} +(3.88017 + 1.97704i) q^{28} +(1.54394 + 4.75177i) q^{29} +(1.79663 - 6.74572i) q^{30} +(3.78002 + 1.22820i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(2.67848 - 1.36475i) q^{33} +(6.01843 - 4.37264i) q^{34} +(7.24629 + 6.50486i) q^{35} +(-5.45806 - 3.96551i) q^{36} +(0.993110 - 6.27025i) q^{37} +(-4.31548 + 0.613695i) q^{38} +(-10.6630 + 14.6764i) q^{39} +(-1.93481 + 1.12095i) q^{40} +(-2.27130 - 3.12618i) q^{41} +(12.1137 - 6.17222i) q^{42} +(0.664893 - 0.664893i) q^{43} +(-0.915773 - 0.297553i) q^{44} +(-9.51139 - 11.7095i) q^{45} +(-5.65406 + 1.83712i) q^{46} +(-1.86766 + 3.66550i) q^{47} +(0.488380 + 3.08351i) q^{48} +11.9644i q^{49} +(-4.82571 + 1.30863i) q^{50} -23.2247i q^{51} +(5.73928 - 0.909012i) q^{52} +(-2.36153 + 4.63477i) q^{53} +(-11.1240 + 3.61441i) q^{54} +(-1.80752 - 1.16995i) q^{55} +(-4.14167 - 1.34571i) q^{56} +(-6.36904 + 12.0258i) q^{57} +(-2.26827 - 4.45174i) q^{58} +(3.44923 - 2.50601i) q^{59} +(-0.719246 + 6.94373i) q^{60} +(-5.03331 - 3.65691i) q^{61} +(-3.92562 - 0.621756i) q^{62} +(4.59603 - 29.0182i) q^{63} +(0.587785 - 0.809017i) q^{64} +(12.9242 + 1.33872i) q^{65} +(-2.43201 + 1.76696i) q^{66} +(-1.41499 - 2.77708i) q^{67} +(-5.26030 + 5.26030i) q^{68} +(-5.73537 + 17.6517i) q^{69} +(-8.17466 - 5.29120i) q^{70} +(-1.64638 + 0.534940i) q^{71} +(6.01121 + 3.06286i) q^{72} +(-5.64995 + 0.894865i) q^{73} +6.34841i q^{74} +(-5.55011 + 14.5897i) q^{75} +(4.16635 - 1.28123i) q^{76} +(-0.655969 - 4.14163i) q^{77} +(8.23586 - 16.1638i) q^{78} +(-2.49638 - 7.68306i) q^{79} +(1.73563 - 1.40982i) q^{80} +(-5.02960 + 15.4795i) q^{81} +(2.73238 + 2.73238i) q^{82} +(-3.00824 - 5.90400i) q^{83} +(-10.9990 + 7.99122i) q^{84} +(-14.3934 + 8.33894i) q^{85} +(-0.552695 + 0.760719i) q^{86} +(-15.4061 - 2.44009i) q^{87} +(0.951046 + 0.150631i) q^{88} +(0.480087 + 0.348803i) q^{89} +(11.2261 + 10.0774i) q^{90} +(14.8739 + 20.4722i) q^{91} +(5.29706 - 2.69899i) q^{92} +(-8.77401 + 8.77401i) q^{93} +(1.27126 - 3.91254i) q^{94} +(9.73974 - 0.370743i) q^{95} +(-0.964734 - 2.96915i) q^{96} +(-16.9465 - 8.63470i) q^{97} +(-1.87164 - 11.8171i) q^{98} +6.49625i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 400 q + 4 q^{5} - 4 q^{7}+O(q^{10}) \) 400 * q + 4 * q^5 - 4 * q^7	\( 400 q + 4 q^{5} - 4 q^{7} + 100 q^{16} + 40 q^{17} - 40 q^{19} - 76 q^{23} - 20 q^{25} - 4 q^{28} + 64 q^{30} + 8 q^{35} - 100 q^{36} + 4 q^{38} + 80 q^{39} + 32 q^{42} - 84 q^{43} - 144 q^{45} + 20 q^{47} - 16 q^{55} - 32 q^{57} - 16 q^{62} + 108 q^{63} - 100 q^{68} - 12 q^{73} + 256 q^{77} - 4 q^{80} + 100 q^{81} - 16 q^{82} + 116 q^{85} - 272 q^{87} - 4 q^{92} - 24 q^{93} - 56 q^{95}+O(q^{100}) \) 400 * q + 4 * q^5 - 4 * q^7 + 100 * q^16 + 40 * q^17 - 40 * q^19 - 76 * q^23 - 20 * q^25 - 4 * q^28 + 64 * q^30 + 8 * q^35 - 100 * q^36 + 4 * q^38 + 80 * q^39 + 32 * q^42 - 84 * q^43 - 144 * q^45 + 20 * q^47 - 16 * q^55 - 32 * q^57 - 16 * q^62 + 108 * q^63 - 100 * q^68 - 12 * q^73 + 256 * q^77 - 4 * q^80 + 100 * q^81 - 16 * q^82 + 116 * q^85 - 272 * q^87 - 4 * q^92 - 24 * q^93 - 56 * q^95

Introduction

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