LMFDB - Embedded newform 186.2.p.a.17.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [186,2,Mod(11,186)] 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("186.11"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(186, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([15, 23])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 186 = 2 \cdot 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	186.p (of order $30$, degree $8$, 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:	$1.48521747760$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			17.5
Character	$\chi$	$=$	186.17
Dual form			186.2.p.a.11.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.951057 - 0.309017i) q^{2} +(1.72891 + 0.104282i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.24540 - 0.719033i) q^{5} +(-1.61207 - 0.633440i) q^{6} +(0.425612 - 4.04943i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(2.97825 + 0.360587i) q^{9} +(0.962254 + 1.06869i) q^{10} +(1.88938 - 0.841206i) q^{11} +(1.33742 + 1.10059i) q^{12} +(-0.489854 + 2.30458i) q^{13} +(-1.65612 + 3.71971i) q^{14} +(-2.07820 - 1.37301i) q^{15} +(0.309017 + 0.951057i) q^{16} +(4.03564 + 1.79678i) q^{17} +(-2.72106 - 1.26327i) q^{18} +(0.442727 - 0.0941045i) q^{19} +(-0.584914 - 1.31374i) q^{20} +(1.15813 - 6.95671i) q^{21} +(-2.05685 + 0.216184i) q^{22} +(-6.27809 + 4.56130i) q^{23} +(-0.931861 - 1.46001i) q^{24} +(-1.46598 - 2.53916i) q^{25} +(1.17803 - 2.04042i) q^{26} +(5.11152 + 0.934000i) q^{27} +(2.72452 - 3.02589i) q^{28} +(0.220199 - 0.677704i) q^{29} +(1.55220 + 1.94802i) q^{30} +(4.15673 - 3.70427i) q^{31} -1.00000i q^{32} +(3.35429 - 1.25734i) q^{33} +(-3.28288 - 2.95592i) q^{34} +(-3.44173 + 4.73713i) q^{35} +(2.19751 + 2.04229i) q^{36} +(-10.0495 + 5.80206i) q^{37} +(-0.450138 - 0.0473114i) q^{38} +(-1.08724 + 3.93333i) q^{39} +(0.150319 + 1.43019i) q^{40} +(-2.77250 + 2.49637i) q^{41} +(-3.25118 + 6.25834i) q^{42} +(2.05128 + 9.65052i) q^{43} +(2.02299 + 0.429999i) q^{44} +(-3.44984 - 2.59054i) q^{45} +(7.38033 - 2.39802i) q^{46} +(-4.67994 + 1.52061i) q^{47} +(0.435084 + 1.67651i) q^{48} +(-9.36969 - 1.99159i) q^{49} +(0.609590 + 2.86790i) q^{50} +(6.78987 + 3.52731i) q^{51} +(-1.75090 + 1.57652i) q^{52} +(0.0558542 + 0.531418i) q^{53} +(-4.57272 - 2.46783i) q^{54} +(-2.95789 - 0.310887i) q^{55} +(-3.52622 + 2.03587i) q^{56} +(0.775247 - 0.116530i) q^{57} +(-0.418844 + 0.576489i) q^{58} +(-2.82498 - 2.54362i) q^{59} +(-0.874264 - 2.33233i) q^{60} +9.02543i q^{61} +(-5.09797 + 2.23847i) q^{62} +(2.72775 - 11.9067i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(2.26714 - 2.51791i) q^{65} +(-3.57866 + 0.159270i) q^{66} +(2.69535 - 4.66849i) q^{67} +(2.20878 + 3.82571i) q^{68} +(-11.3299 + 7.23138i) q^{69} +(4.73713 - 3.44173i) q^{70} +(16.2430 - 1.70721i) q^{71} +(-1.45885 - 2.62140i) q^{72} +(-0.136883 - 0.307444i) q^{73} +(11.3505 - 2.41263i) q^{74} +(-2.26976 - 4.54285i) q^{75} +(0.413487 + 0.184096i) q^{76} +(-2.60226 - 8.00893i) q^{77} +(2.24949 - 3.40484i) q^{78} +(-1.04215 + 2.34070i) q^{79} +(0.298991 - 1.40664i) q^{80} +(8.73995 + 2.14784i) q^{81} +(3.40822 - 1.51744i) q^{82} +(6.20154 + 6.88751i) q^{83} +(5.02599 - 4.94736i) q^{84} +(-3.73404 - 5.13947i) q^{85} +(1.03129 - 9.81207i) q^{86} +(0.451377 - 1.14873i) q^{87} +(-1.79110 - 1.03409i) q^{88} +(-2.82961 - 2.05583i) q^{89} +(2.48048 + 3.52981i) q^{90} +(9.12375 + 2.96449i) q^{91} -7.76014 q^{92} +(7.57289 - 5.97087i) q^{93} +4.92078 q^{94} +(-0.619037 - 0.201137i) q^{95} +(0.104282 - 1.72891i) q^{96} +(-4.33278 - 3.14795i) q^{97} +(8.29567 + 4.78950i) q^{98} +(5.93037 - 1.82404i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 20 q^{4} + 8 q^{7} + 4 q^{9} - 4 q^{10} - 10 q^{15} - 20 q^{16} - 8 q^{18} - 4 q^{19} + 30 q^{21} - 2 q^{22} + 12 q^{25} - 38 q^{28} - 86 q^{31} - 28 q^{34} - 4 q^{36} - 144 q^{37} - 16 q^{39} - 6 q^{40}+ \cdots + 150 q^{99}+O(q^{100}) $ 80 * q + 20 * q^4 + 8 * q^7 + 4 * q^9 - 4 * q^10 - 10 * q^15 - 20 * q^16 - 8 * q^18 - 4 * q^19 + 30 * q^21 - 2 * q^22 + 12 * q^25 - 38 * q^28 - 86 * q^31 - 28 * q^34 - 4 * q^36 - 144 * q^37 - 16 * q^39 - 6 * q^40 - 6 * q^42 + 40 * q^43 - 24 * q^45 - 20 * q^46 + 10 * q^48 - 14 * q^49 - 92 * q^51 - 92 * q^55 - 96 * q^57 + 20 * q^58 - 10 * q^60 + 88 * q^63 + 20 * q^64 + 12 * q^66 + 40 * q^67 - 60 * q^69 + 24 * q^70 + 8 * q^72 + 56 * q^73 - 30 * q^75 - 36 * q^76 + 32 * q^78 + 32 * q^79 + 128 * q^81 + 36 * q^82 + 10 * q^84 + 100 * q^85 + 34 * q^87 + 42 * q^88 + 34 * q^90 + 60 * q^91 + 172 * q^93 + 24 * q^94 - 4 * q^97 + 150 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/186\mathbb{Z}\right)^\times$.

$n$	$125$	$127$
$\chi(n)$	$-1$	$e\left(\frac{7}{30}\right)$

Coefficient data

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

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

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

$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$3$	1.72891	+	0.104282i	0.998186	+	0.0602071i
$3$	1.72891	+	0.104282i	0.998186	+	0.0602071i
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	−1.24540	−	0.719033i	−0.556960	−	0.321561i	0.194964	−	0.980810i	$-0.437541\pi$
$5$	−1.24540	−	0.719033i	−0.556960	−	0.321561i	−0.751925	+	0.659249i	$0.770874\pi$
$6$	−1.61207	−	0.633440i	−0.658123	−	0.258601i
$7$	0.425612	−	4.04943i	0.160866	−	1.53054i	−0.554733	−	0.832029i	$-0.687180\pi$
$7$	0.425612	−	4.04943i	0.160866	−	1.53054i	0.715599	−	0.698511i	$-0.246154\pi$
$8$	−0.587785	−	0.809017i	−0.207813	−	0.286031i
$9$	2.97825	+	0.360587i	0.992750	+	0.120196i
$10$	0.962254	+	1.06869i	0.304291	+	0.337950i
$11$	1.88938	−	0.841206i	0.569669	−	0.253633i	−0.101627	−	0.994823i	$-0.532405\pi$
$11$	1.88938	−	0.841206i	0.569669	−	0.253633i	0.671296	+	0.741190i	$0.265738\pi$
$12$	1.33742	+	1.10059i	0.386080	+	0.317714i
$13$	−0.489854	+	2.30458i	−0.135861	+	0.639176i	0.856535	+	0.516089i	$0.172613\pi$
$13$	−0.489854	+	2.30458i	−0.135861	+	0.639176i	−0.992396	+	0.123087i	$0.960721\pi$
$14$	−1.65612	+	3.71971i	−0.442617	+	0.994135i
$15$	−2.07820	−	1.37301i	−0.536590	−	0.354511i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	4.03564	+	1.79678i	0.978785	+	0.435783i	0.832843	−	0.553510i	$-0.186712\pi$
$17$	4.03564	+	1.79678i	0.978785	+	0.435783i	0.145943	+	0.989293i	$0.453379\pi$
$18$	−2.72106	−	1.26327i	−0.641359	−	0.297755i
$19$	0.442727	−	0.0941045i	0.101568	−	0.0215890i	−0.156847	−	0.987623i	$-0.550133\pi$
$19$	0.442727	−	0.0941045i	0.101568	−	0.0215890i	0.258416	+	0.966034i	$0.416800\pi$
$20$	−0.584914	−	1.31374i	−0.130791	−	0.293761i
$21$	1.15813	−	6.95671i	0.252724	−	1.51808i
$22$	−2.05685	+	0.216184i	−0.438523	+	0.0460906i
$23$	−6.27809	+	4.56130i	−1.30907	+	0.951096i	−0.309072	+	0.951039i	$0.600018\pi$
$23$	−6.27809	+	4.56130i	−1.30907	+	0.951096i	−1.00000		5.74047e-5i	$0.999982\pi$
$24$	−0.931861	−	1.46001i	−0.190215	−	0.298024i
$25$	−1.46598	−	2.53916i	−0.293197	−	0.507832i
$26$	1.17803	−	2.04042i	0.231032	−	0.400158i
$27$	5.11152	+	0.934000i	0.983713	+	0.179748i
$28$	2.72452	−	3.02589i	0.514886	−	0.571839i
$29$	0.220199	−	0.677704i	0.0408900	−	0.125846i	−0.928528	−	0.371263i	$-0.878925\pi$
$29$	0.220199	−	0.677704i	0.0408900	−	0.125846i	0.969418	+	0.245417i	$0.0789248\pi$
$30$	1.55220	+	1.94802i	0.283392	+	0.355657i
$31$	4.15673	−	3.70427i	0.746570	−	0.665307i
$31$	4.15673	−	3.70427i	0.746570	−	0.665307i
$32$		−	1.00000i		−	0.176777i
$33$	3.35429	−	1.25734i	0.583906	−	0.218875i
$34$	−3.28288	−	2.95592i	−0.563010	−	0.506936i
$35$	−3.44173	+	4.73713i	−0.581758	+	0.800722i
$36$	2.19751	+	2.04229i	0.366251	+	0.340382i
$37$	−10.0495	+	5.80206i	−1.65212	+	0.953853i	−0.675925	+	0.736971i	$0.736256\pi$
$37$	−10.0495	+	5.80206i	−1.65212	+	0.953853i	−0.976198	+	0.216883i	$0.930411\pi$
$38$	−0.450138	−	0.0473114i	−0.0730220	−	0.00767492i
$39$	−1.08724	+	3.93333i	−0.174098	+	0.629837i
$40$	0.150319	+	1.43019i	0.0237675	+	0.226133i
$41$	−2.77250	+	2.49637i	−0.432991	+	0.389867i	−0.856602	−	0.515977i	$-0.827429\pi$
$41$	−2.77250	+	2.49637i	−0.432991	+	0.389867i	0.423611	+	0.905844i	$0.360762\pi$
$42$	−3.25118	+	6.25834i	−0.501669	+	0.965683i
$43$	2.05128	+	9.65052i	0.312818	+	1.47169i	0.800850	+	0.598865i	$0.204382\pi$
$43$	2.05128	+	9.65052i	0.312818	+	1.47169i	−0.488032	+	0.872826i	$0.662285\pi$
$44$	2.02299	+	0.429999i	0.304977	+	0.0648249i
$45$	−3.44984	−	2.59054i	−0.514272	−	0.386174i
$46$	7.38033	−	2.39802i	1.08817	−	0.353568i
$47$	−4.67994	+	1.52061i	−0.682640	+	0.221803i	−0.629751	−	0.776797i	$-0.716843\pi$
$47$	−4.67994	+	1.52061i	−0.682640	+	0.221803i	−0.0528892	+	0.998600i	$0.516843\pi$
$48$	0.435084	+	1.67651i	0.0627990	+	0.241984i
$49$	−9.36969	−	1.99159i	−1.33853	−	0.284513i
$50$	0.609590	+	2.86790i	0.0862091	+	0.405582i
$51$	6.78987	+	3.52731i	0.950772	+	0.493923i
$52$	−1.75090	+	1.57652i	−0.242806	+	0.218624i
$53$	0.0558542	+	0.531418i	0.00767217	+	0.0729958i	0.997688	−	0.0679601i	$-0.0216491\pi$
$53$	0.0558542	+	0.531418i	0.00767217	+	0.0729958i	−0.990016	+	0.140956i	$0.954982\pi$
$54$	−4.57272	−	2.46783i	−0.622269	−	0.335830i
$55$	−2.95789	−	0.310887i	−0.398842	−	0.0419200i
$56$	−3.52622	+	2.03587i	−0.471212	+	0.272054i
$57$	0.775247	−	0.116530i	0.102684	−	0.0154347i
$58$	−0.418844	+	0.576489i	−0.0549969	+	0.0756967i
$59$	−2.82498	−	2.54362i	−0.367781	−	0.331151i	0.464431	−	0.885609i	$-0.346259\pi$
$59$	−2.82498	−	2.54362i	−0.367781	−	0.331151i	−0.832212	+	0.554458i	$0.812926\pi$
$60$	−0.874264	−	2.33233i	−0.112867	−	0.301102i
$61$			9.02543i			1.15559i	0.816183	+	0.577794i	$0.196086\pi$
$61$			9.02543i			1.15559i	−0.816183	+	0.577794i	$0.803914\pi$
$62$	−5.09797	+	2.23847i	−0.647442	+	0.284286i
$63$	2.72775	−	11.9067i	0.343664	−	1.50011i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	2.26714	−	2.51791i	0.281204	−	0.312308i
$66$	−3.57866	+	0.159270i	−0.440502	+	0.0196048i
$67$	2.69535	−	4.66849i	0.329290	−	0.570346i	−0.653081	−	0.757288i	$-0.726524\pi$
$67$	2.69535	−	4.66849i	0.329290	−	0.570346i	0.982371	+	0.186941i	$0.0598574\pi$
$68$	2.20878	+	3.82571i	0.267853	+	0.463936i
$69$	−11.3299	+	7.23138i	−1.36396	+	0.870555i
$70$	4.73713	−	3.44173i	0.566196	−	0.411365i
$71$	16.2430	−	1.70721i	1.92769	−	0.202609i	0.938086	−	0.346403i	$-0.112597\pi$
$71$	16.2430	−	1.70721i	1.92769	−	0.202609i	0.989608	+	0.143794i	$0.0459302\pi$
$72$	−1.45885	−	2.62140i	−0.171927	−	0.308935i
$73$	−0.136883	−	0.307444i	−0.0160209	−	0.0359836i	0.905358	−	0.424650i	$-0.139603\pi$
$73$	−0.136883	−	0.307444i	−0.0160209	−	0.0359836i	−0.921379	+	0.388666i	$0.872936\pi$
$74$	11.3505	−	2.41263i	1.31947	−	0.280463i
$75$	−2.26976	−	4.54285i	−0.262090	−	0.524563i
$76$	0.413487	+	0.184096i	0.0474302	+	0.0211173i
$77$	−2.60226	−	8.00893i	−0.296555	−	0.912702i
$78$	2.24949	−	3.40484i	0.254705	−	0.385523i
$79$	−1.04215	+	2.34070i	−0.117251	+	0.263349i	−0.962631	−	0.270815i	$-0.912707\pi$
$79$	−1.04215	+	2.34070i	−0.117251	+	0.263349i	0.845381	+	0.534164i	$0.179373\pi$
$80$	0.298991	−	1.40664i	0.0334282	−	0.157267i
$81$	8.73995	+	2.14784i	0.971106	+	0.238649i
$82$	3.40822	−	1.51744i	0.376375	−	0.167573i
$83$	6.20154	+	6.88751i	0.680708	+	0.756002i	0.980181	−	0.198102i	$-0.0634777\pi$
$83$	6.20154	+	6.88751i	0.680708	+	0.756002i	−0.299474	+	0.954105i	$0.596811\pi$
$84$	5.02599	−	4.94736i	0.548381	−	0.539802i
$85$	−3.73404	−	5.13947i	−0.405014	−	0.557454i
$86$	1.03129	−	9.81207i	0.111207	−	1.05806i
$87$	0.451377	−	1.14873i	0.0483927	−	0.123156i
$88$	−1.79110	−	1.03409i	−0.190932	−	0.110235i
$89$	−2.82961	−	2.05583i	−0.299938	−	0.217917i	0.427629	−	0.903954i	$-0.359349\pi$
$89$	−2.82961	−	2.05583i	−0.299938	−	0.217917i	−0.727567	+	0.686037i	$0.759349\pi$
$90$	2.48048	+	3.52981i	0.261465	+	0.372074i
$91$	9.12375	+	2.96449i	0.956429	+	0.310763i
$92$	−7.76014			−0.809051
$93$	7.57289	−	5.97087i	0.785272	−	0.619151i
$94$	4.92078			0.507540
$95$	−0.619037	−	0.201137i	−0.0635118	−	0.0206362i
$96$	0.104282	−	1.72891i	0.0106432	−	0.176456i
$97$	−4.33278	−	3.14795i	−0.439927	−	0.319626i	0.345679	−	0.938353i	$-0.387649\pi$
$97$	−4.33278	−	3.14795i	−0.439927	−	0.319626i	−0.785606	+	0.618727i	$0.787649\pi$
$98$	8.29567	+	4.78950i	0.837989	+	0.483813i
$99$	5.93037	−	1.82404i	0.596025	−	0.183322i
$100$	0.306474	−	2.91591i	0.0306474	−	0.291591i
$101$	−8.50038	−	11.6998i	−0.845819	−	1.16417i	−0.984768	−	0.173871i	$-0.944372\pi$
$101$	−8.50038	−	11.6998i	−0.845819	−	1.16417i	0.138949	−	0.990300i	$-0.455628\pi$
$102$	−5.36755	−	5.45286i	−0.531467	−	0.539914i
$103$	−1.56952	−	1.74313i	−0.154650	−	0.171756i	0.660841	−	0.750526i	$-0.270200\pi$
$103$	−1.56952	−	1.74313i	−0.154650	−	0.171756i	−0.815491	+	0.578770i	$0.803533\pi$
$104$	2.15238	−	0.958299i	0.211058	−	0.0939690i
$105$	−6.44443	+	7.83116i	−0.628912	+	0.764243i
$106$	0.111097	−	0.522668i	0.0107906	−	0.0507660i
$107$	1.78969	−	4.01970i	0.173016	−	0.388600i	−0.806136	−	0.591730i	$-0.798445\pi$
$107$	1.78969	−	4.01970i	0.173016	−	0.388600i	0.979152	+	0.203131i	$0.0651117\pi$
$108$	3.58632	+	3.76010i	0.345093	+	0.361816i
$109$	0.998447	+	3.07290i	0.0956339	+	0.294331i	0.987418	−	0.158130i	$-0.0505464\pi$
$109$	0.998447	+	3.07290i	0.0956339	+	0.294331i	−0.891784	+	0.452460i	$0.850546\pi$
$110$	2.71705	+	1.20971i	0.259061	+	0.115341i
$111$	−17.9797	+	8.98326i	−1.70655	+	0.852653i
$112$	3.98276	−	0.846561i	0.376335	−	0.0799925i
$113$	−5.16390	−	11.5983i	−0.485779	−	1.09108i	−0.975660	−	0.219288i	$-0.929627\pi$
$113$	−5.16390	−	11.5983i	−0.485779	−	1.09108i	0.489881	−	0.871789i	$-0.337040\pi$
$114$	−0.773314	−	0.128738i	−0.0724275	−	0.0120574i
$115$	11.0985	−	1.16650i	1.03494	−	0.108776i
$116$	0.576489	−	0.418844i	0.0535257	−	0.0388887i
$117$	−2.28991	+	6.68699i	−0.211702	+	0.618212i
$118$	1.90069	+	3.29209i	0.174973	+	0.303062i
$119$	8.99355	−	15.5773i	0.824437	−	1.42797i
$120$	0.110745	+	2.48834i	0.0101096	+	0.227153i
$121$	−4.49831	+	4.99588i	−0.408937	+	0.454171i
$122$	2.78901	−	8.58370i	0.252505	−	0.777131i
$123$	−5.05372	+	4.02687i	−0.455679	+	0.363091i
$124$	5.54018	−	0.553555i	0.497523	−	0.0497107i
$125$			11.4067i			1.02025i
$126$	−6.27363	+	10.4811i	−0.558900	+	0.933727i
$127$	10.3939	+	9.35867i	0.922306	+	0.830448i	0.985867	−	0.167530i	$-0.0535792\pi$
$127$	10.3939	+	9.35867i	0.922306	+	0.830448i	−0.0635613	+	0.997978i	$0.520246\pi$
$128$	0.587785	−	0.809017i	0.0519534	−	0.0715077i
$129$	2.54011	+	16.8988i	0.223644	+	1.48786i
$130$	−2.93425	+	1.69409i	−0.257351	+	0.148582i
$131$	16.1183	+	1.69410i	1.40826	+	0.148015i	0.777950	−	0.628326i	$-0.216259\pi$
$131$	16.1183	+	1.69410i	1.40826	+	0.148015i	0.630314	+	0.776340i	$0.282926\pi$
$132$	3.45272	+	0.954391i	0.300521	+	0.0830690i
$133$	−0.192639	−	1.83284i	−0.0167040	−	0.158928i
$134$	−4.00607	+	3.60709i	−0.346072	+	0.311605i
$135$	−5.69432	−	4.83856i	−0.490089	−	0.416437i
$136$	−0.918461	−	4.32102i	−0.0787574	−	0.370524i
$137$	−18.9117	−	4.01982i	−1.61574	−	0.343436i	−0.690651	−	0.723188i	$-0.742676\pi$
$137$	−18.9117	−	4.01982i	−1.61574	−	0.343436i	−0.925088	+	0.379752i	$0.876009\pi$
$138$	13.0100	−	3.37632i	1.10748	−	0.287411i
$139$	−16.8882	+	5.48730i	−1.43244	+	0.465427i	−0.919531	−	0.393018i	$-0.871431\pi$
$139$	−16.8882	+	5.48730i	−1.43244	+	0.465427i	−0.512906	+	0.858445i	$0.671431\pi$
$140$	−5.56884	+	1.80942i	−0.470652	+	0.152924i
$141$	−8.24977	+	2.14096i	−0.694756	+	0.180301i
$142$	−15.9756	−	3.39572i	−1.34064	−	0.284962i
$143$	1.01311	+	4.76630i	0.0847204	+	0.398578i
$144$	0.577391	+	2.94391i	0.0481159	+	0.245326i
$145$	−0.761528	+	0.685683i	−0.0632414	+	0.0569429i
$146$	0.0351779	+	0.334696i	0.00291135	+	0.0276996i
$147$	−15.9916	−	4.42036i	−1.31897	−	0.364585i
$148$	−11.5406	−	1.21296i	−0.948628	−	0.0997048i
$149$	16.5985	−	9.58313i	1.35980	−	0.785081i	0.370203	−	0.928951i	$-0.379288\pi$
$149$	16.5985	−	9.58313i	1.35980	−	0.785081i	0.989597	+	0.143870i	$0.0459547\pi$
$150$	0.754856	+	5.02190i	0.0616338	+	0.410036i
$151$	5.05799	−	6.96172i	0.411613	−	0.566537i	−0.551998	−	0.833846i	$-0.686134\pi$
$151$	5.05799	−	6.96172i	0.411613	−	0.566537i	0.963611	+	0.267309i	$0.0861343\pi$
$152$	−0.336360	−	0.302860i	−0.0272824	−	0.0245652i
$153$	11.3712	+	6.80646i	0.919310	+	0.550270i
$154$			8.42109i			0.678591i
$155$	−7.84029	+	1.62448i	−0.629747	+	0.130481i
$156$	−3.19155	+	2.54307i	−0.255528	+	0.203608i
$157$	6.08148	−	18.7169i	0.485355	−	1.49377i	−0.346112	−	0.938193i	$-0.612498\pi$
$157$	6.08148	−	18.7169i	0.485355	−	1.49377i	0.831466	−	0.555575i	$-0.187502\pi$
$158$	1.71445	−	1.90409i	0.136395	−	0.151482i
$159$	0.0411497	+	0.924597i	0.00326338	+	0.0733253i
$160$	−0.719033	+	1.24540i	−0.0568445	+	0.0984576i
$161$	15.7986	+	27.3640i	1.24511	+	2.15659i
$162$	−7.64847	−	4.74351i	−0.600921	−	0.372685i
$163$	12.1149	−	8.80199i	0.948912	−	0.689425i	−0.00163732	−	0.999999i	$-0.500521\pi$
$163$	12.1149	−	8.80199i	0.948912	−	0.689425i	0.950549	+	0.310574i	$0.100521\pi$
$164$	−3.71032	+	0.389971i	−0.289728	+	0.0304516i
$165$	−5.08150	−	0.845949i	−0.395594	−	0.0658570i
$166$	−3.76966	−	8.46679i	−0.292582	−	0.657151i
$167$	−16.5066	+	3.50858i	−1.27732	+	0.271502i	−0.796135	−	0.605119i	$-0.793126\pi$
$167$	−16.5066	+	3.50858i	−1.27732	+	0.271502i	−0.481182	+	0.876621i	$0.659792\pi$
$168$	−6.30882	+	3.15211i	−0.486736	+	0.243190i
$169$	6.80495	+	3.02976i	0.523457	+	0.233058i
$170$	1.96310	+	6.04181i	0.150563	+	0.463385i
$171$	1.35248	−	0.120625i	0.103427	−	0.00922442i
$172$	−4.01291	+	9.01315i	−0.305982	+	0.687246i
$173$	−0.431356	+	2.02937i	−0.0327954	+	0.154290i	−0.991498	−	0.130119i	$-0.958464\pi$
$173$	−0.431356	+	2.02937i	−0.0327954	+	0.154290i	0.958703	+	0.284409i	$0.0917974\pi$
$174$	−0.784260	+	0.953020i	−0.0594546	+	0.0722482i
$175$	−10.9061	+	4.85570i	−0.824422	+	0.367056i
$176$	1.38388	+	1.53696i	0.104314	+	0.115853i
$177$	−4.61887	−	4.69228i	−0.347176	−	0.352693i
$178$	2.05583	+	2.82961i	0.154091	+	0.212088i
$179$	−0.916463	+	8.71956i	−0.0684997	+	0.651731i	0.905370	+	0.424623i	$0.139594\pi$
$179$	−0.916463	+	8.71956i	−0.0684997	+	0.651731i	−0.973870	+	0.227107i	$0.927073\pi$
$180$	−1.26830	−	4.12356i	−0.0945337	−	0.307352i
$181$	−7.99449	−	4.61562i	−0.594226	−	0.343076i	0.172541	−	0.985002i	$-0.444802\pi$
$181$	−7.99449	−	4.61562i	−0.594226	−	0.343076i	−0.766767	+	0.641926i	$0.778136\pi$
$182$	−7.76113	−	5.63879i	−0.575293	−	0.417975i
$183$	−0.941188	+	15.6041i	−0.0695747	+	1.15349i
$184$	7.38033	+	2.39802i	0.544085	+	0.176784i
$185$	16.6875			1.22689
$186$	−9.04735	+	3.33849i	−0.663384	+	0.244790i
$187$	9.13631			0.668113
$188$	−4.67994	−	1.52061i	−0.341320	−	0.110902i
$189$	5.95769	−	20.3012i	0.433358	−	1.47670i
$190$	0.526584	+	0.382586i	0.0382024	+	0.0277557i
$191$	11.1116	+	6.41531i	0.804010	+	0.464195i	0.844871	−	0.534970i	$-0.179677\pi$
$191$	11.1116	+	6.41531i	0.804010	+	0.464195i	−0.0408616	+	0.999165i	$0.513010\pi$
$192$	−0.633440	+	1.61207i	−0.0457146	+	0.116341i
$193$	0.412810	−	3.92763i	0.0297147	−	0.282717i	−0.969567	−	0.244826i	$-0.921269\pi$
$193$	0.412810	−	3.92763i	0.0297147	−	0.282717i	0.999282	−	0.0378913i	$-0.0120641\pi$
$194$	3.14795	+	4.33278i	0.226010	+	0.311075i
$195$	4.18224	−	4.11681i	0.299497	−	0.294811i
$196$	−6.40961	−	7.11859i	−0.457829	−	0.508471i
$197$	5.02180	−	2.23585i	0.357788	−	0.159298i	−0.219968	−	0.975507i	$-0.570595\pi$
$197$	5.02180	−	2.23585i	0.357788	−	0.159298i	0.577756	+	0.816210i	$0.303929\pi$
$198$	−6.20378	−	0.0978254i	−0.440883	−	0.00695215i
$199$	4.54600	−	21.3873i	0.322258	−	1.51610i	−0.457039	−	0.889447i	$-0.651090\pi$
$199$	4.54600	−	21.3873i	0.322258	−	1.51610i	0.779296	−	0.626656i	$-0.215577\pi$
$200$	−1.19254	+	2.67848i	−0.0843252	+	0.189397i
$201$	5.14686	−	7.79031i	0.363031	−	0.549486i
$202$	4.46891	+	13.7539i	0.314432	+	0.967721i
$203$	−2.65059	−	1.18012i	−0.186035	−	0.0828282i
$204$	3.41982	+	6.84464i	0.239435	+	0.479221i
$205$	5.24784	−	1.11546i	0.366525	−	0.0779073i
$206$	0.954047	+	2.14282i	0.0664716	+	0.149298i
$207$	−20.3425	+	11.3209i	−1.41390	+	0.786856i
$208$	−2.34316	+	0.246276i	−0.162469	+	0.0170762i
$209$	0.757317	−	0.550223i	0.0523847	−	0.0380597i
$210$	8.54898	−	5.45644i	0.589936	−	0.376530i
$211$	1.08137	+	1.87299i	0.0744445	+	0.128942i	0.900845	−	0.434142i	$-0.142948\pi$
$211$	1.08137	+	1.87299i	0.0744445	+	0.128942i	−0.826400	+	0.563083i	$0.809615\pi$
$212$	−0.267172	+	0.462756i	−0.0183495	+	0.0317822i
$213$	28.2608	−	1.25776i	1.93640	−	0.0861803i
$214$	−2.94425	+	3.26992i	−0.201265	+	0.223527i
$215$	4.38437	−	13.4937i	0.299012	−	0.920264i
$216$	−2.24885	−	4.68430i	−0.153015	−	0.318726i
$217$	−13.2310	−	18.4089i	−0.898180	−	1.24968i
$218$		−	3.23104i		−	0.218834i
$219$	−0.204597	−	0.545817i	−0.0138254	−	0.0368829i
$220$	−2.21025	−	1.99012i	−0.149015	−	0.134174i
$221$	−6.11770	+	8.42029i	−0.411521	+	0.566410i
$222$	19.8757	−	2.98757i	1.33397	−	0.200512i
$223$	−10.1327	+	5.85010i	−0.678533	+	0.391751i	−0.799302	−	0.600929i	$-0.794797\pi$
$223$	−10.1327	+	5.85010i	−0.678533	+	0.391751i	0.120769	+	0.992681i	$0.461464\pi$
$224$	−4.04943	−	0.425612i	−0.270564	−	0.0284374i
$225$	−3.45048	−	8.09086i	−0.230032	−	0.539391i
$226$	1.32709	+	12.6264i	0.0882764	+	0.839894i
$227$	−21.3974	+	19.2663i	−1.42019	+	1.27875i	−0.512770	+	0.858526i	$0.671381\pi$
$227$	−21.3974	+	19.2663i	−1.42019	+	1.27875i	−0.907422	+	0.420221i	$0.861953\pi$
$228$	0.695683	+	0.361404i	0.0460727	+	0.0239346i
$229$	−0.219386	−	1.03213i	−0.0144974	−	0.0682050i	0.970304	−	0.241888i	$-0.0777666\pi$
$229$	−0.219386	−	1.03213i	−0.0144974	−	0.0682050i	−0.984802	+	0.173683i	$0.944433\pi$
$230$	−10.9157	−	2.32021i	−0.719762	−	0.152990i
$231$	−3.66388	−	14.1181i	−0.241066	−	0.928901i
$232$	−0.677704	+	0.220199i	−0.0444934	+	0.0144568i
$233$	0.111969	−	0.0363808i	0.00733530	−	0.00238338i	−0.305347	−	0.952241i	$-0.598772\pi$
$233$	0.111969	−	0.0363808i	0.00733530	−	0.00238338i	0.312682	+	0.949858i	$0.398772\pi$
$234$	4.24423	−	5.65208i	0.277454	−	0.369488i
$235$	6.92178	+	1.47127i	0.451527	+	0.0959750i
$236$	−0.790352	−	3.71831i	−0.0514475	−	0.242041i
$237$	−2.04587	+	3.93817i	−0.132893	+	0.255812i
$238$	−13.3670	+	12.0357i	−0.866455	+	0.780160i
$239$	−2.37231	−	22.5710i	−0.153452	−	1.46000i	−0.752133	−	0.659012i	$-0.770975\pi$
$239$	−2.37231	−	22.5710i	−0.153452	−	1.46000i	0.598681	−	0.800988i	$-0.295692\pi$
$240$	0.663615	−	2.40077i	0.0428361	−	0.154969i
$241$	5.06281	+	0.532123i	0.326124	+	0.0342771i	0.266176	−	0.963924i	$-0.414240\pi$
$241$	5.06281	+	0.532123i	0.326124	+	0.0342771i	0.0599483	+	0.998201i	$0.480906\pi$
$242$	5.82196	−	3.36131i	0.374250	−	0.216073i
$243$	14.8866	+	4.62484i	0.954976	+	0.296683i
$244$	−5.30502	+	7.30173i	−0.339619	+	0.467445i
$245$	10.2370	+	9.21744i	0.654018	+	0.588881i
$246$	6.05074	−	2.26810i	0.385781	−	0.144609i
$247$			1.06640i			0.0678533i
$248$	−5.44008	−	1.18555i	−0.345445	−	0.0752823i
$249$	10.0037	+	12.5546i	0.633956	+	0.795614i
$250$	3.52486	−	10.8484i	0.222932	−	0.686113i
$251$	−8.55467	+	9.50093i	−0.539966	+	0.599693i	−0.949951	−	0.312399i	$-0.898867\pi$
$251$	−8.55467	+	9.50093i	−0.539966	+	0.599693i	0.409985	+	0.912092i	$0.365534\pi$
$252$	9.20540	−	8.02942i	0.579886	−	0.505806i
$253$	−8.02470	+	13.8992i	−0.504508	+	0.873834i
$254$	−6.99316	−	12.1125i	−0.438790	−	0.760006i
$255$	−5.91986	−	9.27506i	−0.370716	−	0.580827i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−23.2516	+	2.44384i	−1.45039	+	0.152443i	−0.796727	−	0.604340i	$-0.793437\pi$
$257$	−23.2516	+	2.44384i	−1.45039	+	0.152443i	−0.653667	+	0.756782i	$0.726770\pi$
$258$	2.80623	−	16.8566i	0.174708	−	1.04945i
$259$	19.2179	+	43.1640i	1.19414	+	2.68208i
$260$	3.31414	−	0.704442i	0.205534	−	0.0436877i
$261$	0.900180	−	1.93897i	0.0557198	−	0.120019i
$262$	−14.8059	−	6.59202i	−0.914713	−	0.407257i
$263$	−9.01395	−	27.7421i	−0.555824	−	1.71065i	−0.693757	−	0.720209i	$-0.744046\pi$
$263$	−9.01395	−	27.7421i	−0.555824	−	1.71065i	0.137933	−	0.990442i	$-0.455954\pi$
$264$	−2.98881	−	1.97463i	−0.183949	−	0.121530i
$265$	0.312546	−	0.701989i	0.0191995	−	0.0431229i
$266$	−0.383168	+	1.80266i	−0.0234936	+	0.110528i
$267$	−4.67775	−	3.84942i	−0.286273	−	0.235581i
$268$	4.92465	−	2.19260i	0.300821	−	0.133934i
$269$	12.5620	+	13.9515i	0.765916	+	0.850636i	0.992358	−	0.123388i	$-0.0393761\pi$
$269$	12.5620	+	13.9515i	0.765916	+	0.850636i	−0.226442	+	0.974025i	$0.572709\pi$
$270$	3.92042	+	6.36138i	0.238589	+	0.387141i
$271$	1.82684	+	2.51443i	0.110973	+	0.152741i	0.860891	−	0.508790i	$-0.169907\pi$
$271$	1.82684	+	2.51443i	0.110973	+	0.152741i	−0.749918	+	0.661531i	$0.769907\pi$
$272$	−0.461760	+	4.39335i	−0.0279983	+	0.266386i
$273$	15.4650	+	6.07677i	0.935984	+	0.367783i
$274$	16.7440	+	9.66712i	1.01154	+	0.584012i
$275$	−4.90575	−	3.56424i	−0.295828	−	0.214932i
$276$	−13.4166	−	0.809242i	−0.807583	−	0.0487106i
$277$	8.48710	+	2.75763i	0.509940	+	0.165690i	0.552675	−	0.833397i	$-0.313607\pi$
$277$	8.48710	+	2.75763i	0.509940	+	0.165690i	−0.0427348	+	0.999086i	$0.513607\pi$
$278$	17.7573			1.06501
$279$	13.7155	−	9.53338i	0.821125	−	0.570749i
$280$	5.85542			0.349928
$281$	−14.3209	−	4.65313i	−0.854312	−	0.277583i	−0.151061	−	0.988524i	$-0.548269\pi$
$281$	−14.3209	−	4.65313i	−0.854312	−	0.277583i	−0.703251	+	0.710942i	$0.748269\pi$
$282$	8.50759	+	0.513148i	0.506619	+	0.0305575i
$283$	−12.7816	−	9.28640i	−0.759789	−	0.552019i	0.139057	−	0.990284i	$-0.455593\pi$
$283$	−12.7816	−	9.28640i	−0.759789	−	0.552019i	−0.898846	+	0.438265i	$0.855593\pi$
$284$	14.1444	+	8.16625i	0.839314	+	0.484578i
$285$	−1.04928	−	0.412302i	−0.0621542	−	0.0244227i
$286$	0.509344	−	4.84609i	0.0301182	−	0.286555i
$287$	8.92885	+	12.2895i	0.527053	+	0.725427i
$288$	0.360587	−	2.97825i	0.0212478	−	0.175495i
$289$	1.68271	+	1.86884i	0.0989830	+	0.109932i
$290$	0.936144	−	0.416798i	0.0549722	−	0.0244752i
$291$	−7.16271	−	5.89435i	−0.419885	−	0.345533i
$292$	0.0699705	−	0.329185i	0.00409471	−	0.0192641i
$293$	−4.05504	+	9.10777i	−0.236898	+	0.532081i	−0.992398	−	0.123067i	$-0.960727\pi$
$293$	−4.05504	+	9.10777i	−0.236898	+	0.532081i	0.755501	+	0.655148i	$0.227394\pi$
$294$	13.8430	+	9.14570i	0.807340	+	0.533388i
$295$	1.68928	+	5.19908i	0.0983539	+	0.302702i
$296$	10.6009	+	4.71982i	0.616165	+	0.274334i
$297$	10.4433	−	2.53516i	0.605981	−	0.147105i
$298$	−18.7474	+	3.98489i	−1.08601	+	0.230839i
$299$	−7.43654	−	16.7027i	−0.430066	−	0.965944i
$300$	0.833941	−	5.00937i	0.0481476	−	0.289216i
$301$	39.9521	−	4.19914i	2.30280	−	0.242034i
$302$	−6.96172	+	5.05799i	−0.400602	+	0.291054i
$303$	−13.4763	−	21.1143i	−0.774194	−	1.21298i
$304$	0.226309	+	0.391978i	0.0129797	+	0.0224815i
$305$	6.48958	−	11.2403i	0.371592	−	0.643617i
$306$	−8.71138	−	9.98724i	−0.497996	−	0.570932i
$307$	7.64357	−	8.48905i	0.436242	−	0.484496i	−0.484432	−	0.874829i	$-0.660974\pi$
$307$	7.64357	−	8.48905i	0.436242	−	0.484496i	0.920674	+	0.390333i	$0.127640\pi$
$308$	2.60226	−	8.00893i	0.148278	−	0.456351i
$309$	−2.53178	−	3.17739i	−0.144028	−	0.180755i
$310$	7.95855	+	0.877809i	0.452015	+	0.0498562i
$311$		−	12.1902i		−	0.691241i	−0.938374	−	0.345620i	$-0.887669\pi$
$311$		−	12.1902i		−	0.691241i	0.938374	−	0.345620i	$-0.112331\pi$
$312$	3.82119	−	1.43236i	0.216333	−	0.0810913i
$313$	−10.0563	−	9.05474i	−0.568416	−	0.511804i	0.334055	−	0.942553i	$-0.391583\pi$
$313$	−10.0563	−	9.05474i	−0.568416	−	0.511804i	−0.902472	+	0.430749i	$0.858249\pi$
$314$	−11.5677	+	15.9215i	−0.652801	+	0.898503i
$315$	−11.9585	+	12.8673i	−0.673784	+	0.724992i
$316$	−2.21894	+	1.28111i	−0.124825	+	0.0720678i
$317$	−24.6676	−	2.59267i	−1.38547	−	0.145619i	−0.617737	−	0.786385i	$-0.711950\pi$
$317$	−24.6676	−	2.59267i	−1.38547	−	0.145619i	−0.767736	+	0.640766i	$0.778617\pi$
$318$	0.246581	−	0.892060i	0.0138276	−	0.0500242i
$319$	−0.154048	−	1.46567i	−0.00862505	−	0.0820619i
$320$	1.06869	−	0.962254i	0.0597417	−	0.0537916i
$321$	3.51339	−	6.76307i	0.196098	−	0.377478i
$322$	−6.56943	−	30.9068i	−0.366100	−	1.72237i
$323$	1.95577	+	0.415711i	0.108822	+	0.0231308i
$324$	5.80830	+	6.87485i	0.322683	+	0.381936i
$325$	6.56982	−	2.13466i	0.364428	−	0.118410i
$326$	−14.2419	+	4.62748i	−0.788787	+	0.256292i
$327$	1.40578	+	5.41689i	0.0777396	+	0.299555i
$328$	3.64924	+	0.775669i	0.201495	+	0.0428292i
$329$	4.16574	+	19.5983i	0.229665	+	1.08049i
$330$	4.57138	+	2.37482i	0.251646	+	0.130729i
$331$	6.49954	−	5.85221i	0.357247	−	0.321667i	−0.470891	−	0.882192i	$-0.656067\pi$
$331$	6.49954	−	5.85221i	0.357247	−	0.321667i	0.828137	+	0.560525i	$0.189401\pi$
$332$	0.968776	+	9.21729i	0.0531685	+	0.505864i
$333$	−32.0220	+	13.6563i	−1.75479	+	0.748360i
$334$	16.7829	+	1.76395i	0.918319	+	0.0965192i
$335$	−6.71359	+	3.87609i	−0.366803	+	0.211774i
$336$	6.97410	−	1.04830i	0.380468	−	0.0571893i
$337$	−2.88381	+	3.96922i	−0.157091	+	0.216217i	−0.880307	−	0.474405i	$-0.842663\pi$
$337$	−2.88381	+	3.96922i	−0.157091	+	0.216217i	0.723216	+	0.690622i	$0.242663\pi$
$338$	−5.53564	−	4.98432i	−0.301099	−	0.271111i
$339$	−7.71842	−	20.5909i	−0.419207	−	1.11835i
$340$		−	6.35273i		−	0.344525i
$341$	4.73758	−	10.4954i	0.256554	−	0.568360i
$342$	−1.32356	−	0.303219i	−0.0715701	−	0.0163962i
$343$	−3.24500	+	9.98708i	−0.175213	+	0.539252i
$344$	6.60172	−	7.33196i	0.355941	−	0.395313i
$345$	19.3099	−	0.859396i	1.03961	−	0.0462683i
$346$	1.03735	−	1.79675i	0.0557685	−	0.0965938i
$347$	12.0328	+	20.8414i	0.645953	+	1.11882i	0.984080	+	0.177723i	$0.0568732\pi$
$347$	12.0328	+	20.8414i	0.645953	+	1.11882i	−0.338127	+	0.941100i	$0.609793\pi$
$348$	1.04038	−	0.664026i	0.0557700	−	0.0355955i
$349$	−12.8600	+	9.34336i	−0.688382	+	0.500139i	−0.876128	−	0.482079i	$-0.839882\pi$
$349$	−12.8600	+	9.34336i	−0.688382	+	0.500139i	0.187746	+	0.982218i	$0.439882\pi$
$350$	11.8728	−	1.24788i	0.634627	−	0.0667020i
$351$	−4.65638	+	11.3224i	−0.248539	+	0.604345i
$352$	−0.841206	−	1.88938i	−0.0448364	−	0.100704i
$353$	19.8157	−	4.21195i	1.05468	−	0.224180i	0.352232	−	0.935913i	$-0.385423\pi$
$353$	19.8157	−	4.21195i	1.05468	−	0.224180i	0.702450	+	0.711733i	$0.252089\pi$
$354$	2.94281	+	5.88993i	0.156409	+	0.313046i
$355$	−21.4566	−	9.55311i	−1.13880	−	0.507027i
$356$	−1.08081	−	3.32640i	−0.0572830	−	0.176299i
$357$	17.1734	−	25.9938i	0.908915	−	1.37574i
$358$	3.56610	−	8.00960i	0.188474	−	0.423320i
$359$	2.36308	−	11.1174i	0.124718	−	0.586754i	−0.870755	−	0.491716i	$-0.836370\pi$
$359$	2.36308	−	11.1174i	0.124718	−	0.586754i	0.995474	−	0.0950372i	$-0.0302970\pi$
$360$	−0.0680208	+	4.31366i	−0.00358501	+	0.227350i
$361$	−17.1702	+	7.64467i	−0.903695	+	0.402351i
$362$	6.17691	+	6.86015i	0.324651	+	0.360561i
$363$	−8.29815	+	8.16833i	−0.435540	+	0.428726i
$364$	5.63879	+	7.76113i	0.295553	+	0.406794i
$365$	−0.0505882	+	0.481314i	−0.00264791	+	0.0251931i
$366$	5.71707	−	14.5496i	0.298836	−	0.760519i
$367$	−15.2168	−	8.78541i	−0.794310	−	0.458595i	0.0471680	−	0.998887i	$-0.484980\pi$
$367$	−15.2168	−	8.78541i	−0.794310	−	0.458595i	−0.841477	+	0.540292i	$0.818314\pi$
$368$	−6.27809	−	4.56130i	−0.327268	−	0.237774i
$369$	−9.15735	+	6.43508i	−0.476713	+	0.334997i
$370$	−15.8708	−	5.15672i	−0.825081	−	0.268085i
$371$	2.17571			0.112957
$372$	9.63619	−	0.379305i	0.499613	−	0.0196661i
$373$	4.28959			0.222107			0.111053	−	0.993814i	$-0.464578\pi$
$373$	4.28959			0.222107			0.111053	+	0.993814i	$0.464578\pi$
$374$	−8.68914	−	2.82327i	−0.449305	−	0.145988i
$375$	−1.18951	+	19.7211i	−0.0614261	+	1.01839i
$376$	3.98100	+	2.89236i	0.205304	+	0.149162i
$377$	1.45396	+	0.839443i	0.0748827	+	0.0432335i
$378$	−11.9395	+	17.4666i	−0.614103	+	0.898383i
$379$	3.01915	−	28.7253i	0.155083	−	1.47552i	−0.589381	−	0.807855i	$-0.700628\pi$
$379$	3.01915	−	28.7253i	0.155083	−	1.47552i	0.744464	−	0.667662i	$-0.232705\pi$
$380$	−0.382586	−	0.526584i	−0.0196262	−	0.0270132i
$381$	16.9941	+	17.2642i	0.870634	+	0.884471i
$382$	−8.58535	−	9.53500i	−0.439265	−	0.487853i
$383$	−13.1924	+	5.87362i	−0.674098	+	0.300128i	−0.715091	−	0.699032i	$-0.753615\pi$
$383$	−13.1924	+	5.87362i	−0.674098	+	0.300128i	0.0409927	+	0.999159i	$0.486948\pi$
$384$	1.10059	−	1.33742i	0.0561644	−	0.0682500i
$385$	−2.51783	+	11.8454i	−0.128320	+	0.603700i
$386$	−1.60631	+	3.60783i	−0.0817590	+	0.183634i
$387$	2.62937	+	29.4813i	0.133659	+	1.49862i
$388$	−1.65497	−	5.09349i	−0.0840186	−	0.258583i
$389$	3.95500	+	1.76088i	0.200526	+	0.0892801i	0.504543	−	0.863387i	$-0.331661\pi$
$389$	3.95500	+	1.76088i	0.200526	+	0.0892801i	−0.304016	+	0.952667i	$0.598328\pi$
$390$	−5.24971	+	2.62294i	−0.265830	+	0.132818i
$391$	−33.5317	+	7.12739i	−1.69577	+	0.360447i
$392$	3.89613	+	8.75086i	0.196784	+	0.441985i
$393$	27.6904	+	4.60980i	1.39680	+	0.232534i
$394$	−5.46693	+	0.574598i	−0.275420	+	0.0289478i
$395$	2.98093	−	2.16577i	0.149987	−	0.108972i
$396$	5.86991	+	2.01011i	0.294974	+	0.101012i
$397$	18.1339	+	31.4089i	0.910115	+	1.57637i	0.813900	+	0.581005i	$0.197340\pi$
$397$	18.1339	+	31.4089i	0.910115	+	1.57637i	0.0962150	+	0.995361i	$0.469326\pi$
$398$	−10.9325	+	18.9357i	−0.547998	+	0.949161i
$399$	−0.141924	−	3.18890i	−0.00710508	−	0.159645i
$400$	1.96187	−	2.17888i	0.0980934	−	0.108944i
$401$	−4.38451	+	13.4941i	−0.218952	+	0.673865i	0.779897	+	0.625907i	$0.215271\pi$
$401$	−4.38451	+	13.4941i	−0.218952	+	0.673865i	−0.998849	+	0.0479574i	$0.984729\pi$
$402$	−7.30229	+	5.81856i	−0.364205	+	0.290203i
$403$	6.50061	+	11.3941i	0.323818	+	0.567579i
$404$		−	14.4617i		−	0.719497i
$405$	−9.34038	−	8.95924i	−0.464127	−	0.445188i
$406$	2.15619	+	1.94144i	0.107010	+	0.0963520i
$407$	−14.1065	+	19.4160i	−0.699235	+	0.962414i
$408$	−1.13733	−	7.56643i	−0.0563063	−	0.374594i
$409$	6.93530	−	4.00410i	0.342928	−	0.197990i	−0.318638	−	0.947877i	$-0.603225\pi$
$409$	6.93530	−	4.00410i	0.342928	−	0.197990i	0.661566	+	0.749887i	$0.269892\pi$
$410$	−5.33569	−	0.560804i	−0.263511	−	0.0276961i
$411$	−32.2775	−	8.92205i	−1.59213	−	0.440092i
$412$	−0.245183	−	2.33276i	−0.0120793	−	0.114927i
$413$	−11.5026	+	10.3569i	−0.566003	+	0.509632i
$414$	22.8452	−	4.48064i	1.12278	−	0.220211i
$415$	−2.77106	−	13.0368i	−0.136026	−	0.639953i
$416$	2.30458	+	0.489854i	0.112991	+	0.0240171i
$417$	−29.7703	+	7.72591i	−1.45786	+	0.378340i
$418$	−0.890280	+	0.289269i	−0.0435450	+	0.0141486i
$419$	−7.90530	+	2.56859i	−0.386199	+	0.125484i	−0.495680	−	0.868505i	$-0.665081\pi$
$419$	−7.90530	+	2.56859i	−0.386199	+	0.125484i	0.109481	+	0.993989i	$0.465081\pi$
$420$	−9.81670	+	2.54760i	−0.479006	+	0.124310i
$421$	−12.5650	−	2.67078i	−0.612383	−	0.130166i	−0.108729	−	0.994071i	$-0.534678\pi$
$421$	−12.5650	−	2.67078i	−0.612383	−	0.130166i	−0.503654	+	0.863906i	$0.668011\pi$
$422$	−0.449658	−	2.11548i	−0.0218890	−	0.102980i
$423$	−14.4864	+	2.84122i	−0.704351	+	0.138145i
$424$	0.397096	−	0.357546i	0.0192847	−	0.0173640i
$425$	−1.35386	−	12.8812i	−0.0656721	−	0.624828i
$426$	−27.2662	−	7.53685i	−1.32105	−	0.365162i
$427$	36.5478	+	3.84133i	1.76867	+	0.185895i
$428$	3.81061	−	2.20006i	0.184193	−	0.106344i
$429$	1.25453	+	8.34614i	0.0605694	+	0.402956i
$430$	−8.33958	+	11.4784i	−0.402170	+	0.553540i
$431$	−0.201295	−	0.181247i	−0.00969602	−	0.00873034i	0.664268	−	0.747494i	$-0.268743\pi$
$431$	−0.201295	−	0.181247i	−0.00969602	−	0.00873034i	−0.673964	+	0.738764i	$0.735410\pi$
$432$	0.691260	+	5.14997i	0.0332583	+	0.247778i
$433$		−	36.7430i		−	1.76575i	−0.469605	−	0.882877i	$-0.655604\pi$
$433$		−	36.7430i		−	1.76575i	0.469605	−	0.882877i	$-0.344396\pi$
$434$	6.89477	+	21.5966i	0.330960	+	1.03667i
$435$	−1.38812	+	1.10607i	−0.0665551	+	0.0530320i
$436$	−0.998447	+	3.07290i	−0.0478169	+	0.147165i
$437$	−2.35024	+	2.61020i	−0.112427	+	0.124863i
$438$	0.0259168	+	0.582327i	0.00123835	+	0.0278246i
$439$	−14.7218	+	25.4990i	−0.702635	+	1.21700i	0.264904	+	0.964275i	$0.414660\pi$
$439$	−14.7218	+	25.4990i	−0.702635	+	1.21700i	−0.967538	+	0.252724i	$0.918673\pi$
$440$	1.48709	+	2.57572i	0.0708943	+	0.122793i
$441$	−27.1871	−	9.31004i	−1.29463	−	0.443335i
$442$	8.42029	−	6.11770i	0.400513	−	0.290989i
$443$	19.1133	−	2.00889i	0.908102	−	0.0954454i	0.361052	−	0.932546i	$-0.382418\pi$
$443$	19.1133	−	2.00889i	0.908102	−	0.0954454i	0.547050	+	0.837100i	$0.315751\pi$
$444$	−19.8261	−	3.30057i	−0.940904	−	0.156638i
$445$	2.04579	+	4.59491i	0.0969796	+	0.217820i
$446$	11.4445	−	2.43261i	0.541913	−	0.115187i
$447$	29.6966	−	14.8374i	1.40460	−	0.701787i
$448$	3.71971	+	1.65612i	0.175740	+	0.0782445i
$449$	−6.90826	−	21.2614i	−0.326021	−	1.00339i	−0.970978	−	0.239170i	$-0.923125\pi$
$449$	−6.90826	−	21.2614i	−0.326021	−	1.00339i	0.644957	−	0.764219i	$-0.276875\pi$
$450$	0.781385	+	8.76112i	0.0368348	+	0.413003i
$451$	−3.13834	+	7.04882i	−0.147779	+	0.331916i
$452$	2.63963	−	12.4185i	0.124158	−	0.584117i
$453$	9.47078	−	11.5087i	0.444976	−	0.540727i
$454$	26.3037	−	11.7112i	1.23449	−	0.549632i
$455$	−9.23117	−	10.2523i	−0.432764	−	0.480633i
$456$	−0.549953	−	0.558694i	−0.0257539	−	0.0261632i
$457$	−4.23607	−	5.83045i	−0.198155	−	0.272737i	0.698364	−	0.715743i	$-0.253912\pi$
$457$	−4.23607	−	5.83045i	−0.198155	−	0.272737i	−0.896518	+	0.443006i	$0.853912\pi$
$458$	−0.110297	+	1.04941i	−0.00515384	+	0.0490355i
$459$	18.9500	+	12.9536i	0.884512	+	0.604621i
$460$	9.66449	+	5.57980i	0.450609	+	0.260159i
$461$	20.3773	+	14.8050i	0.949066	+	0.689537i	0.950586	−	0.310462i	$-0.100484\pi$
$461$	20.3773	+	14.8050i	0.949066	+	0.689537i	−0.00151996	+	0.999999i	$0.500484\pi$
$462$	−0.878166	+	14.5593i	−0.0408560	+	0.677360i
$463$	22.6248	+	7.35124i	1.05146	+	0.341641i	0.783243	−	0.621716i	$-0.213564\pi$
$463$	22.6248	+	7.35124i	1.05146	+	0.341641i	0.268221	+	0.963357i	$0.413564\pi$
$464$	0.712580			0.0330807
$465$	−13.7245	+	1.99098i	−0.636460	+	0.0923294i
$466$	−0.117731			−0.00545377
$467$	12.0482	+	3.91471i	0.557526	+	0.181151i	0.574208	−	0.818710i	$-0.305310\pi$
$467$	12.0482	+	3.91471i	0.557526	+	0.181151i	−0.0166817	+	0.999861i	$0.505310\pi$
$468$	−5.78309	+	4.06391i	−0.267323	+	0.187854i
$469$	−17.7575	−	12.9016i	−0.819966	−	0.595740i
$470$	−6.12835	−	3.53821i	−0.282680	−	0.163205i
$471$	12.4661	−	31.7256i	0.574410	−	1.46184i
$472$	−0.397353	+	3.78056i	−0.0182896	+	0.174014i
$473$	11.9937	+	16.5079i	0.551472	+	0.759036i
$474$	3.16270	−	3.11322i	0.145267	−	0.142995i
$475$	−0.887976	−	0.986197i	−0.0407431	−	0.0452498i
$476$	16.4320	−	7.31601i	0.753161	−	0.335329i
$477$	−0.0252746	+	1.60284i	−0.00115724	+	0.0733888i
$478$	−4.71863	+	22.1994i	−0.215825	+	1.01538i
$479$	−6.13255	+	13.7739i	−0.280203	+	0.629347i	−0.997741	−	0.0671721i	$-0.978602\pi$
$479$	−6.13255	+	13.7739i	−0.280203	+	0.629347i	0.717538	+	0.696519i	$0.245269\pi$
$480$	−1.37301	+	2.07820i	−0.0626693	+	0.0948566i
$481$	−8.44856	−	26.0020i	−0.385221	−	1.18559i
$482$	−4.65058	−	2.07057i	−0.211828	−	0.0943120i
$483$	24.4608	+	48.9574i	1.11300	+	2.22764i
$484$	−6.57571	+	1.39771i	−0.298896	+	0.0635323i
$485$	3.13257	+	7.03587i	0.142243	+	0.319482i
$486$	−12.7288	−	8.99869i	−0.577392	−	0.408189i
$487$	−9.27414	+	0.974751i	−0.420251	+	0.0441702i	−0.312294	−	0.949985i	$-0.601098\pi$
$487$	−9.27414	+	0.974751i	−0.420251	+	0.0441702i	−0.107957	+	0.994156i	$0.534431\pi$
$488$	7.30173	−	5.30502i	0.330534	−	0.240147i
$489$	21.8634	−	13.9545i	0.988699	−	0.631043i
$490$	−6.88762	−	11.9297i	−0.311151	−	0.538929i
$491$	11.7564	−	20.3627i	0.530559	−	0.918955i	−0.468805	−	0.883302i	$-0.655315\pi$
$491$	11.7564	−	20.3627i	0.530559	−	0.918955i	0.999364	−	0.0356535i	$-0.0113513\pi$
$492$	−6.45548	+	0.287305i	−0.291036	+	0.0129527i
$493$	2.10633	−	2.33932i	0.0948643	−	0.105357i
$494$	0.329535	−	1.01420i	0.0148265	−	0.0456312i
$495$	−8.69724	−	1.99248i	−0.390912	−	0.0895552i
$496$	4.80747	+	2.80860i	0.215862	+	0.126110i
$497$		−	66.5016i		−	2.98300i
$498$	−5.63446	−	15.0314i	−0.252486	−	0.673574i
$499$	−6.25793	−	5.63466i	−0.280143	−	0.252242i	0.517065	−	0.855946i	$-0.327024\pi$
$499$	−6.25793	−	5.63466i	−0.280143	−	0.252242i	−0.797209	+	0.603704i	$0.793691\pi$
$500$	−6.70468	+	9.22821i	−0.299843	+	0.412698i
$501$	−28.9042	+	4.34468i	−1.29135	+	0.194106i
$502$	11.0719	−	6.39238i	0.494164	−	0.285306i
$503$	9.67154	+	1.01652i	0.431233	+	0.0453244i	0.317659	−	0.948205i	$-0.397103\pi$
$503$	9.67154	+	1.01652i	0.431233	+	0.0453244i	0.113574	+	0.993530i	$0.463770\pi$
$504$	−11.2361	+	4.79181i	−0.500495	+	0.213444i
$505$	2.17387	+	20.6830i	0.0967358	+	0.920380i
$506$	11.9270	−	10.7391i	0.530221	−	0.477413i
$507$	11.4492	+	5.94781i	0.508476	+	0.264151i
$508$	2.90792	+	13.6807i	0.129018	+	0.606982i
$509$	−2.67655	−	0.568918i	−0.118636	−	0.0252169i	0.148211	−	0.988956i	$-0.452649\pi$
$509$	−2.67655	−	0.568918i	−0.118636	−	0.0252169i	−0.266847	+	0.963739i	$0.585982\pi$
$510$	2.76397	+	10.6504i	0.122391	+	0.471610i
$511$	−1.30323	+	0.423445i	−0.0576515	+	0.0187321i
$512$	0.951057	−	0.309017i	0.0420312	−	0.0136568i
$513$	2.35090	−	0.0675101i	0.103795	−	0.00298064i
$514$	22.8688	+	4.86090i	1.00870	+	0.214405i
$515$	0.701317	+	3.29944i	0.0309037	+	0.145391i
$516$	−7.87787	+	15.1644i	−0.346804	+	0.667577i
$517$	−7.56305	+	6.80980i	−0.332622	+	0.299495i
$518$	−4.93886	−	46.9901i	−0.217001	−	2.06463i
$519$	−0.957401	+	3.46361i	−0.0420252	+	0.152036i
$520$	−3.36962	−	0.354161i	−0.147768	−	0.0155310i
$521$	−31.2326	+	18.0321i	−1.36832	+	0.790002i	−0.990714	−	0.135963i	$-0.956587\pi$
$521$	−31.2326	+	18.0321i	−1.36832	+	0.790002i	−0.377610	+	0.925965i	$0.623254\pi$
$522$	−1.45530	+	1.56590i	−0.0636966	+	0.0685376i
$523$	6.63417	−	9.13115i	0.290092	−	0.399277i	−0.638952	−	0.769247i	$-0.720632\pi$
$523$	6.63417	−	9.13115i	0.290092	−	0.399277i	0.929044	+	0.369969i	$0.120632\pi$
$524$	12.0442	+	10.8447i	0.526155	+	0.473752i
$525$	−19.3620	+	7.25775i	−0.845026	+	0.316754i
$526$			29.1698i			1.27186i
$527$	23.4308	−	7.48036i	1.02066	−	0.325849i
$528$	2.23233	+	2.80158i	0.0971498	+	0.121923i
$529$	11.5016	−	35.3981i	0.500067	−	1.53905i
$530$	−0.514175	+	0.571050i	−0.0223343	+	0.0248048i
$531$	−7.49629	−	8.59419i	−0.325311	−	0.372956i
$532$	0.921469	−	1.59603i	0.0399507	−	0.0691967i
$533$	−4.39497	−	7.61230i	−0.190367	−	0.329725i
$534$	3.25927	+	5.10652i	0.141042	+	0.220981i
$535$	−5.11918	+	3.71930i	−0.221321	+	0.160799i
$536$	−5.36117	+	0.563482i	−0.231567	+	0.0243387i
$537$	−2.49377	+	14.9798i	−0.107614	+	0.646424i
$538$	−7.63589	−	17.1505i	−0.329207	−	0.739410i
$539$	−19.3782	+	4.11897i	−0.834679	+	0.177417i
$540$	−1.76277	−	7.26151i	−0.0758575	−	0.312486i
$541$	25.0455	+	11.1510i	1.07679	+	0.479418i	0.866990	−	0.498326i	$-0.166052\pi$
$541$	25.0455	+	11.1510i	1.07679	+	0.479418i	0.209801	+	0.977744i	$0.432718\pi$
$542$	−0.960426	−	2.95589i	−0.0412538	−	0.126966i
$543$	−13.3404	−	8.81367i	−0.572492	−	0.378231i
$544$	1.79678	−	4.03564i	0.0770363	−	0.173026i
$545$	0.966052	−	4.54492i	0.0413811	−	0.194683i
$546$	−12.8303	−	10.5583i	−0.549084	−	0.451853i
$547$	9.96337	−	4.43598i	0.426003	−	0.189669i	−0.182525	−	0.983201i	$-0.558427\pi$
$547$	9.96337	−	4.43598i	0.426003	−	0.189669i	0.608528	+	0.793532i	$0.291760\pi$
$548$	−12.9371	−	14.3681i	−0.552647	−	0.613777i
$549$	−3.25446	+	26.8800i	−0.138897	+	1.14721i
$550$	3.56424	+	4.90575i	0.151980	+	0.209182i
$551$	0.0337132	−	0.320759i	0.00143623	−	0.0136648i
$552$	12.5099	+	4.91558i	0.532455	+	0.209221i
$553$	9.03493	+	5.21632i	0.384204	+	0.221820i
$554$	−7.21956	−	5.24532i	−0.306730	−	0.222852i
$555$	28.8512	+	1.74020i	1.22466	+	0.0738675i
$556$	−16.8882	−	5.48730i	−0.716218	−	0.232713i
$557$	35.7007			1.51269			0.756344	−	0.654175i	$-0.226984\pi$
$557$	35.7007			1.51269			0.756344	+	0.654175i	$0.226984\pi$
$558$	−15.9902	+	4.82847i	−0.676918	+	0.204405i
$559$	−23.2453			−0.983170
$560$	−5.56884	−	1.80942i	−0.235326	−	0.0764621i
$561$	15.7958	+	0.952751i	0.666901	+	0.0402252i
$562$	12.1821	+	8.85079i	0.513869	+	0.373348i
$563$	12.6306	+	7.29230i	0.532318	+	0.307334i	0.741960	−	0.670444i	$-0.233896\pi$
$563$	12.6306	+	7.29230i	0.532318	+	0.307334i	−0.209642	+	0.977778i	$0.567230\pi$
$564$	−7.93262	−	3.11702i	−0.334024	−	0.131250i
$565$	−1.90844	+	18.1576i	−0.0802885	+	0.763894i
$566$	9.28640	+	12.7816i	0.390336	+	0.537252i
$567$	12.4174	−	34.4777i	0.521480	−	1.44793i
$568$	−10.9286	−	12.1374i	−0.458553	−	0.509275i
$569$	9.06517	−	4.03607i	0.380032	−	0.169201i	−0.207825	−	0.978166i	$-0.566639\pi$
$569$	9.06517	−	4.03607i	0.380032	−	0.169201i	0.587857	+	0.808965i	$0.299972\pi$
$570$	0.870519	+	0.716369i	0.0364620	+	0.0300054i
$571$	1.61967	−	7.61997i	0.0677813	−	0.318886i	−0.931174	−	0.364574i	$-0.881215\pi$
$571$	1.61967	−	7.61997i	0.0677813	−	0.318886i	0.998956	+	0.0456881i	$0.0145480\pi$
$572$	−1.98194	+	4.45151i	−0.0828690	+	0.186127i
$573$	18.5420	+	12.2502i	0.774603	+	0.511760i
$574$	−4.69417	−	14.4472i	−0.195931	−	0.603014i
$575$	20.7854	+	9.25427i	0.866812	+	0.385930i
$576$	−1.26327	+	2.72106i	−0.0526362	+	0.113377i
$577$	−17.5297	+	3.72606i	−0.729772	+	0.155118i	−0.557790	−	0.829982i	$-0.688350\pi$
$577$	−17.5297	+	3.72606i	−0.729772	+	0.155118i	−0.171982	+	0.985100i	$0.555017\pi$
$578$	−1.02285	−	2.29736i	−0.0425449	−	0.0955575i
$579$	1.12329	−	6.74746i	0.0466824	−	0.280415i
$580$	−1.01912	+	0.107114i	−0.0423168	+	0.00444767i
$581$	30.5299	−	22.1813i	1.26659	−	0.920235i
$582$	4.99068	+	7.81925i	0.206871	+	0.324118i
$583$	0.552561	+	0.957064i	0.0228848	+	0.0396376i
$584$	−0.168270	+	0.291452i	−0.00696305	+	0.0120604i
$585$	7.66003	−	6.68146i	0.316703	−	0.276245i
$586$	6.67102	−	7.40892i	0.275578	−	0.306060i
$587$	8.79662	−	27.0732i	0.363075	−	1.11743i	−0.588102	−	0.808787i	$-0.700125\pi$
$587$	8.79662	−	27.0732i	0.363075	−	1.11743i	0.951178	−	0.308644i	$-0.0998753\pi$
$588$	−10.3393	−	12.9758i	−0.426385	−	0.535113i
$589$	1.49171	−	2.03115i	0.0614647	−	0.0836919i
$590$		−	5.46664i		−	0.225058i
$591$	8.91539	−	3.34190i	0.366730	−	0.137467i
$592$	−8.62355	−	7.76468i	−0.354426	−	0.319126i
$593$	13.0709	−	17.9905i	0.536757	−	0.738783i	−0.451384	−	0.892330i	$-0.649070\pi$
$593$	13.0709	−	17.9905i	0.536757	−	0.738783i	0.988141	+	0.153547i	$0.0490696\pi$
$594$	−10.7156	−	0.816072i	−0.439665	−	0.0334839i
$595$	−22.4012	+	12.9333i	−0.918358	+	0.530214i
$596$	19.0613	+	2.00342i	0.780780	+	0.0820633i
$597$	10.0899	−	36.5025i	0.412953	−	1.49395i
$598$	1.91114	+	18.1833i	0.0781523	+	0.743569i
$599$	15.2451	−	13.7268i	0.622898	−	0.560860i	−0.296083	−	0.955162i	$-0.595680\pi$
$599$	15.2451	−	13.7268i	0.622898	−	0.560860i	0.918981	+	0.394302i	$0.129014\pi$
$600$	−2.34111	+	4.50650i	−0.0955753	+	0.183977i
$601$	4.32730	+	20.3583i	0.176514	+	0.830434i	0.973902	+	0.226967i	$0.0728811\pi$
$601$	4.32730	+	20.3583i	0.176514	+	0.830434i	−0.797388	+	0.603467i	$0.793786\pi$
$602$	−39.2944	−	8.35227i	−1.60152	−	0.340413i
$603$	9.71083	−	12.9320i	0.395456	−	0.526632i
$604$	8.18399	−	2.65914i	0.333002	−	0.108199i
$605$	9.19440	−	2.98744i	0.373806	−	0.121457i
$606$	6.29206	+	24.2453i	0.255598	+	0.984897i
$607$	41.0769	+	8.73116i	1.66726	+	0.354387i	0.942394	−	0.334504i	$-0.108569\pi$
$607$	41.0769	+	8.73116i	1.66726	+	0.354387i	0.724865	+	0.688891i	$0.241902\pi$
$608$	−0.0941045	−	0.442727i	−0.00381644	−	0.0179549i
$609$	−4.45957	−	2.31673i	−0.180711	−	0.0938786i
$610$	−9.64540	+	8.68476i	−0.390531	+	0.351636i
$611$	−1.21187	−	11.5302i	−0.0490271	−	0.466462i
$612$	5.19879	+	12.1904i	0.210148	+	0.492767i
$613$	−14.9681	−	1.57321i	−0.604557	−	0.0635415i	−0.202695	−	0.979242i	$-0.564970\pi$
$613$	−14.9681	−	1.57321i	−0.604557	−	0.0635415i	−0.401862	+	0.915700i	$0.631637\pi$
$614$	−9.89273	+	5.71157i	−0.399238	+	0.230500i
$615$	9.18936	−	1.38128i	0.370551	−	0.0556986i
$616$	−4.94979	+	6.81280i	−0.199433	+	0.274496i
$617$	−15.1978	−	13.6842i	−0.611841	−	0.550905i	0.303884	−	0.952709i	$-0.401716\pi$
$617$	−15.1978	−	13.6842i	−0.611841	−	0.550905i	−0.915725	+	0.401805i	$0.868383\pi$
$618$	1.42600	+	3.80424i	0.0573622	+	0.153029i
$619$			0.902063i			0.0362570i	0.999836	+	0.0181285i	$0.00577079\pi$
$619$			0.902063i			0.0362570i	−0.999836	+	0.0181285i	$0.994229\pi$
$620$	−7.29777	−	3.29417i	−0.293086	−	0.132297i
$621$	−36.3508	+	17.4514i	−1.45871	+	0.700302i
$622$	−3.76697	+	11.5935i	−0.151042	+	0.464858i
$623$	−9.52925	+	10.5833i	−0.381781	+	0.424011i
$624$	−4.07679	+	0.181440i	−0.163202	+	0.00726341i
$625$	0.871868	−	1.51012i	0.0348747	−	0.0604048i
$626$	6.76605	+	11.7191i	0.270426	+	0.468391i
$627$	1.36671	−	0.872311i	0.0545812	−	0.0348368i
$628$	15.9215	−	11.5677i	0.635338	−	0.461600i
$629$	−50.9810	+	5.35832i	−2.03275	+	0.213650i
$630$	15.3494	−	8.54218i	0.611535	−	0.340329i
$631$	−10.5398	−	23.6728i	−0.419583	−	0.942398i	−0.992439	−	0.122742i	$-0.960831\pi$
$631$	−10.5398	−	23.6728i	−0.419583	−	0.942398i	0.572856	−	0.819656i	$-0.305835\pi$
$632$	2.50622	−	0.532714i	0.0996921	−	0.0211902i
$633$	1.67427	+	3.35099i	0.0665462	+	0.133190i
$634$	22.6591	+	10.0885i	0.899910	+	0.400666i
$635$	−6.21533	−	19.1288i	−0.246648	−	0.759104i
$636$	−0.510174	+	0.772202i	−0.0202297	+	0.0306198i
$637$	9.17956	−	20.6176i	0.363707	−	0.816900i
$638$	−0.306409	+	1.44154i	−0.0121308	+	0.0570711i
$639$	48.9914	+	0.772531i	1.93807	+	0.0305608i
$640$	−1.31374	+	0.584914i	−0.0519301	+	0.0231208i
$641$	31.3555	+	34.8239i	1.23847	+	1.37546i	0.900823	+	0.434187i	$0.142964\pi$
$641$	31.3555	+	34.8239i	1.23847	+	1.37546i	0.337647	+	0.941273i	$0.390369\pi$
$642$	−5.43134	+	5.34637i	−0.214358	+	0.211004i
$643$	−0.489492	−	0.673727i	−0.0193037	−	0.0265692i	0.799256	−	0.600991i	$-0.205227\pi$
$643$	−0.489492	−	0.673727i	−0.0193037	−	0.0265692i	−0.818560	+	0.574421i	$0.805227\pi$
$644$	−3.30281	+	31.4241i	−0.130149	+	1.23828i
$645$	8.98733	−	22.8722i	0.353876	−	0.900592i
$646$	−1.73158	−	0.999731i	−0.0681283	−	0.0393339i
$647$	−19.2520	−	13.9874i	−0.756875	−	0.549902i	0.141075	−	0.989999i	$-0.454944\pi$
$647$	−19.2520	−	13.9874i	−0.756875	−	0.549902i	−0.897950	+	0.440097i	$0.854944\pi$
$648$	−3.39958	−	8.33324i	−0.133548	−	0.327361i
$649$	−7.47716	−	2.42948i	−0.293504	−	0.0953653i
$650$	−6.90791			−0.270951
$651$	−20.9555	−	33.2071i	−0.821311	−	1.30149i
$652$	14.9748			0.586460
$653$	0.428954	+	0.139376i	0.0167863	+	0.00545419i	0.317398	−	0.948292i	$-0.397191\pi$
$653$	0.428954	+	0.139376i	0.0167863	+	0.00545419i	−0.300612	+	0.953747i	$0.597191\pi$
$654$	0.336939	−	5.58618i	0.0131754	−	0.218437i
$655$	−18.8557	−	13.6994i	−0.736752	−	0.535282i
$656$	−3.23093	−	1.86538i	−0.126147	−	0.0728309i
$657$	−0.296811	−	0.965003i	−0.0115797	−	0.0376484i
$658$	2.09434	−	19.9264i	0.0816461	−	0.776810i
$659$	2.03074	+	2.79507i	0.0791063	+	0.108880i	0.846736	−	0.532013i	$-0.178564\pi$
$659$	2.03074	+	2.79507i	0.0791063	+	0.108880i	−0.767630	+	0.640893i	$0.778564\pi$
$660$	−3.61379	−	3.67122i	−0.140666	−	0.142902i
$661$	16.1794	+	17.9691i	0.629307	+	0.698917i	0.970507	−	0.241074i	$-0.0774998\pi$
$661$	16.1794	+	17.9691i	0.629307	+	0.698917i	−0.341199	+	0.939991i	$0.610833\pi$
$662$	−7.98986	+	3.55732i	−0.310535	+	0.138259i
$663$	−11.4550	+	13.9200i	−0.444877	+	0.540606i
$664$	1.92694	−	9.06553i	0.0747797	−	0.351811i
$665$	−1.07796	+	2.42114i	−0.0418015	+	0.0938877i
$666$	34.6747	−	3.09256i	1.34362	−	0.119834i
$667$	1.70878	+	5.25908i	0.0661641	+	0.203632i
$668$	−15.4164	−	6.86382i	−0.596478	−	0.265569i
$669$	−18.1285	+	9.05763i	−0.700889	+	0.350188i
$670$	7.58278	−	1.61177i	0.292948	−	0.0622681i
$671$	7.59225	+	17.0525i	0.293095	+	0.658303i
$672$	−6.95671	−	1.15813i	−0.268361	−	0.0446757i
$673$	−5.09733	+	0.535751i	−0.196488	+	0.0206517i	−0.202261	−	0.979332i	$-0.564829\pi$
$673$	−5.09733	+	0.535751i	−0.196488	+	0.0206517i	0.00577336	+	0.999983i	$0.498162\pi$
$674$	3.96922	−	2.88381i	0.152889	−	0.111080i
$675$	−5.12183	−	14.3482i	−0.197139	−	0.552262i
$676$	3.72447	+	6.45097i	0.143249	+	0.248114i
$677$	−13.2928	+	23.0238i	−0.510884	+	0.884877i	0.489036	+	0.872263i	$0.337348\pi$
$677$	−13.2928	+	23.0238i	−0.510884	+	0.884877i	−0.999920	+	0.0126136i	$0.995985\pi$
$678$	0.977709	+	21.9682i	0.0375487	+	0.843686i
$679$	−14.5915	+	16.2055i	−0.559969	+	0.621909i
$680$	−1.96310	+	6.04181i	−0.0752815	+	0.231693i
$681$	−39.0032	+	31.0783i	−1.49461	+	1.19092i
$682$	−7.74897	+	8.51776i	−0.296724	+	0.326162i
$683$			23.6121i			0.903491i	0.892147	+	0.451745i	$0.149198\pi$
$683$			23.6121i			0.903491i	−0.892147	+	0.451745i	$0.850802\pi$
$684$	1.16508	+	0.697382i	0.0445481	+	0.0266651i
$685$	20.6623	+	18.6045i	0.789467	+	0.710840i
$686$	6.17236	−	8.49552i	0.235662	−	0.324360i
$687$	−0.271666	−	1.80733i	−0.0103647	−	0.0689541i
$688$	−8.54431	+	4.93306i	−0.325749	+	0.188071i
$689$	−1.25206	−	0.131596i	−0.0476995	−	0.00501342i
$690$	−18.6303	−	5.14974i	−0.709245	−	0.196047i
$691$	2.22822	+	21.2001i	0.0847656	+	0.806491i	0.951485	+	0.307695i	$0.0995576\pi$
$691$	2.22822	+	21.2001i	0.0847656	+	0.806491i	−0.866719	+	0.498796i	$0.833776\pi$
$692$	−1.54181	+	1.38825i	−0.0586107	+	0.0527733i
$693$	−4.86226	−	24.7909i	−0.184702	−	0.941730i
$694$	−5.00351	−	23.5397i	−0.189931	−	0.893553i
$695$	24.9781	+	5.30926i	0.947474	+	0.201392i
$696$	−1.19465	+	0.310032i	−0.0452831	+	0.0117517i
$697$	−15.6742	+	5.09286i	−0.593703	+	0.192906i
$698$	15.1179	−	4.91210i	0.572220	−	0.185926i
$699$	0.197377	−	0.0512228i	0.00746549	−	0.00193742i
$700$	−11.6773	−	2.48209i	−0.441361	−	0.0938141i
$701$	−2.57495	−	12.1142i	−0.0972545	−	0.457546i	−0.999645	−	0.0266280i	$-0.991523\pi$
$701$	−2.57495	−	12.1142i	−0.0972545	−	0.457546i	0.902391	−	0.430918i	$-0.141810\pi$
$702$	7.92729	−	9.32934i	0.299196	−	0.352113i
$703$	−3.90317	+	3.51443i	−0.147211	+	0.132549i
$704$	0.216184	+	2.05685i	0.00814774	+	0.0775206i
$705$	11.8137	+	3.26550i	0.444929	+	0.122986i
$706$	−20.1474	−	2.11758i	−0.758257	−	0.0796960i
$707$	−50.9952	+	29.4421i	−1.91787	+	1.10728i
$708$	−0.978693	−	6.51104i	−0.0367815	−	0.244700i
$709$	−18.5334	+	25.5090i	−0.696035	+	0.958010i	0.303951	+	0.952688i	$0.401694\pi$
$709$	−18.5334	+	25.5090i	−0.696035	+	0.958010i	−0.999986	+	0.00532220i	$0.998306\pi$
$710$	17.4544	+	15.7160i	0.655052	+	0.589812i
$711$	−3.94780	+	6.59540i	−0.148054	+	0.247347i
$712$			3.49759i			0.131078i
$713$	−9.20002	+	42.2158i	−0.344543	+	1.58099i
$714$	−24.3655	+	19.4147i	−0.911854	+	0.726578i
$715$	2.16540	−	6.66441i	0.0809813	−	0.249235i
$716$	−5.86667	+	6.51559i	−0.219248	+	0.243499i
$717$	−1.74776	−	39.2707i	−0.0652714	−	1.46659i
$718$	−5.68288	+	9.84304i	−0.212083	+	0.367339i
$719$	−5.25384	−	9.09991i	−0.195935	−	0.339369i	0.751272	−	0.659993i	$-0.229441\pi$
$719$	−5.25384	−	9.09991i	−0.195935	−	0.339369i	−0.947207	+	0.320624i	$0.896107\pi$
$720$	1.39769	−	4.08152i	0.0520887	−	0.152109i
$721$	−7.72669	+	5.61377i	−0.287757	+	0.209068i
$722$	18.6922	−	1.96463i	0.695651	−	0.0731158i
$723$	8.69765	+	1.44795i	0.323469	+	0.0538499i
$724$	−3.75468	−	8.43316i	−0.139542	−	0.313416i
$725$	−2.04361	+	0.434382i	−0.0758976	+	0.0161325i
$726$	10.4162	−	5.20427i	0.386580	−	0.193149i
$727$	22.2937	+	9.92579i	0.826827	+	0.368127i	0.776119	−	0.630586i	$-0.217186\pi$
$727$	22.2937	+	9.92579i	0.826827	+	0.368127i	0.0507079	+	0.998714i	$0.483852\pi$
$728$	−2.96449	−	9.12375i	−0.109871	−	0.338149i
$729$	25.2553	+	9.54832i	0.935381	+	0.353642i
$730$	0.196847	−	0.442125i	0.00728562	−	0.0163638i
$731$	−9.06165	+	42.6317i	−0.335157	+	1.57679i
$732$	−9.93333	+	12.0708i	−0.367146	+	0.446150i
$733$	−23.0637	+	10.2686i	−0.851879	+	0.379281i	−0.785760	−	0.618531i	$-0.787728\pi$
$733$	−23.0637	+	10.2686i	−0.851879	+	0.379281i	−0.0661182	+	0.997812i	$0.521061\pi$
$734$	11.7572	+	13.0577i	0.433965	+	0.481967i
$735$	16.7376	+	17.0036i	0.617377	+	0.627189i
$736$	4.56130	+	6.27809i	0.168132	+	0.231413i
$737$	1.16538	−	11.0879i	0.0429275	−	0.408428i
$738$	10.6977	−	3.29035i	0.393788	−	0.121119i
$739$	−31.2678	−	18.0525i	−1.15020	−	0.664070i	−0.201266	−	0.979537i	$-0.564506\pi$
$739$	−31.2678	−	18.0525i	−1.15020	−	0.664070i	−0.948937	+	0.315466i	$0.897839\pi$
$740$	13.5005	+	9.80867i	0.496287	+	0.360574i
$741$	−0.111206	+	1.84370i	−0.00408525	+	0.0677302i
$742$	−2.06922	−	0.672331i	−0.0759636	−	0.0246821i
$743$	20.3112			0.745147			0.372573	−	0.928003i	$-0.378476\pi$
$743$	20.3112			0.745147			0.372573	+	0.928003i	$0.378476\pi$
$744$	−9.28177	−	2.61701i	−0.340286	−	0.0959441i
$745$	−27.5624			−1.00981
$746$	−4.07965	−	1.32556i	−0.149366	−	0.0485321i
$747$	15.9862	+	22.7489i	0.584904	+	0.832340i
$748$	7.39143	+	5.37019i	0.270257	+	0.196353i
$749$	−15.5158	−	8.95805i	−0.566935	−	0.327320i
$750$	7.22545	−	18.3883i	0.263836	−	0.671447i
$751$	−3.05245	+	29.0421i	−0.111385	+	1.05976i	0.785913	+	0.618337i	$0.212193\pi$
$751$	−3.05245	+	29.0421i	−0.111385	+	1.05976i	−0.897299	+	0.441424i	$0.854473\pi$
$752$	−2.89236	−	3.98100i	−0.105474	−	0.145172i
$753$	−15.7810	+	15.5341i	−0.575092	+	0.566096i
$754$	−1.12339	−	1.24766i	−0.0409116	−	0.0454370i
$755$	−11.3049	+	5.03328i	−0.411429	+	0.183180i
$756$	16.7526	−	12.9222i	0.609287	−	0.469975i
$757$	2.29090	−	10.7779i	0.0832643	−	0.391728i	−0.916705	−	0.399565i	$-0.869161\pi$
$757$	2.29090	−	10.7779i	0.0832643	−	0.391728i	0.999969	+	0.00783696i	$0.00249461\pi$
$758$	−11.7480	+	26.3864i	−0.426706	+	0.958396i
$759$	−15.3234	+	23.1936i	−0.556204	+	0.841874i
$760$	0.201137	+	0.619037i	0.00729601	+	0.0224548i
$761$	18.3194	+	8.15632i	0.664077	+	0.295666i	0.710958	−	0.703234i	$-0.248261\pi$
$761$	18.3194	+	8.15632i	0.664077	+	0.295666i	−0.0468809	+	0.998900i	$0.514928\pi$
$762$	−10.8274	−	21.6707i	−0.392236	−	0.785046i
$763$	12.8685	−	2.73527i	0.465869	−	0.0990236i
$764$	5.21868	+	11.7213i	0.188805	+	0.424063i
$765$	−9.26768	−	16.6531i	−0.335074	−	0.602093i
$766$	14.3617	−	1.50948i	0.518910	−	0.0545397i
$767$	7.24581	−	5.26439i	0.261631	−	0.190086i
$768$	−1.46001	+	0.931861i	−0.0526836	+	0.0336256i
$769$	−16.8772	−	29.2322i	−0.608607	−	1.05414i	−0.991470	−	0.130333i	$-0.958395\pi$
$769$	−16.8772	−	29.2322i	−0.608607	−	1.05414i	0.382863	−	0.923805i	$-0.374938\pi$
$770$	6.05504	−	10.4876i	0.218208	−	0.377948i
$771$	−40.4547	+	1.80046i	−1.45694	+	0.0648419i
$772$	2.64257	−	2.93487i	0.0951083	−	0.105628i
$773$	1.86634	−	5.74400i	0.0671275	−	0.206597i	−0.911866	−	0.410487i	$-0.865359\pi$
$773$	1.86634	−	5.74400i	0.0671275	−	0.206597i	0.978994	+	0.203890i	$0.0653586\pi$
$774$	6.60955	−	28.8509i	0.237575	−	1.03703i
$775$	−15.4994	−	5.12419i	−0.556756	−	0.184066i
$776$			5.35561i			0.192255i
$777$	28.7247	+	76.6307i	1.03049	+	2.74911i
$778$	−3.21729	−	2.89686i	−0.115345	−	0.103857i
$779$	−0.992539	+	1.36611i	−0.0355614	+	0.0489461i
$780$	5.80331	−	0.872312i	0.207792	−	0.0312338i
$781$	29.2531	−	16.8893i	1.04676	−	0.604347i
$782$	34.0930	+	3.58332i	1.21916	+	0.128139i
$783$	1.75853	−	3.25843i	0.0628447	−	0.116447i
$784$	−1.00128	−	9.52653i	−0.0357600	−	0.340233i
$785$	−21.0319	+	18.9372i	−0.750661	+	0.675899i
$786$	−24.9107	−	12.9410i	−0.888534	−	0.461590i
$787$	−0.0368036	−	0.173147i	−0.00131191	−	0.00617204i	0.977487	−	0.210997i	$-0.0676709\pi$
$787$	−0.0368036	−	0.173147i	−0.00131191	−	0.00617204i	−0.978799	+	0.204825i	$0.934338\pi$
$788$	5.37692	+	1.14290i	0.191545	+	0.0407141i
$789$	−12.6913	−	48.9035i	−0.451823	−	1.74101i
$790$	−3.50429	+	1.13861i	−0.124677	+	0.0405100i
$791$	−49.1643	+	15.9745i	−1.74808	+	0.567986i
$792$	−4.96146	−	3.72563i	−0.176298	−	0.132385i
$793$	−20.7999	−	4.42115i	−0.738624	−	0.156999i
$794$	−7.54051	−	35.4753i	−0.267603	−	1.25897i
$795$	0.613568	−	1.18108i	0.0217610	−	0.0418887i
$796$	16.2489	−	14.6306i	0.575927	−	0.518567i
$797$	−0.0478694	−	0.455447i	−0.00169562	−	0.0161328i	0.993641	−	0.112591i	$-0.0359151\pi$
$797$	−0.0478694	−	0.455447i	−0.00169562	−	0.0161328i	−0.995337	+	0.0964586i	$0.969248\pi$
$798$	−0.850448	+	3.07669i	−0.0301055	+	0.108913i
$799$	−21.6187	−	2.27222i	−0.764816	−	0.0803854i
$800$	−2.53916	+	1.46598i	−0.0897728	+	0.0518303i
$801$	−7.68597	−	7.14310i	−0.271570	−	0.252389i
$802$	8.33983	−	11.4788i	0.294490	−	0.405330i
$803$	−0.517247	−	0.465732i	−0.0182533	−	0.0164353i
$804$	8.74292	−	3.27725i	0.308339	−	0.115580i
$805$		−	45.4389i		−	1.60151i
$806$	−2.66148	−	12.8452i	−0.0937467	−	0.452453i
$807$	20.2636	+	25.4308i	0.713312	+	0.895207i
$808$	−4.46891	+	13.7539i	−0.157216	+	0.483861i
$809$	−9.00966	+	10.0062i	−0.316763	+	0.351801i	−0.880409	−	0.474216i	$-0.842732\pi$
$809$	−9.00966	+	10.0062i	−0.316763	+	0.351801i	0.563646	+	0.826017i	$0.309398\pi$
$810$	6.11468	+	11.4071i	0.214848	+	0.400804i
$811$	19.5648	−	33.8873i	0.687014	−	1.18994i	−0.285786	−	0.958294i	$-0.592255\pi$
$811$	19.5648	−	33.8873i	0.687014	−	1.18994i	0.972799	−	0.231649i	$-0.0744121\pi$
$812$	−1.45072	−	2.51272i	−0.0509102	−	0.0881791i
$813$	2.89623	+	4.53772i	0.101575	+	0.159145i
$814$	19.4160	−	14.1065i	0.680529	−	0.494434i
$815$	−21.4168	+	2.25100i	−0.750199	+	0.0788491i
$816$	−1.25649	+	7.54755i	−0.0439859	+	0.264217i
$817$	1.81631	+	4.07951i	0.0635448	+	0.142724i
$818$	−7.83319	+	1.66500i	−0.273881	+	0.0582152i
$819$	26.1039	+	12.1189i	0.912143	+	0.423468i
$820$	4.90125	+	2.18218i	0.171159	+	0.0762049i
$821$	−5.71556	−	17.5907i	−0.199474	−	0.613919i	−0.999895	−	0.0144805i	$-0.995391\pi$
$821$	−5.71556	−	17.5907i	−0.199474	−	0.613919i	0.800421	−	0.599439i	$-0.204609\pi$
$822$	27.9407	+	18.4597i	0.974542	+	0.643855i
$823$	21.7146	−	48.7717i	0.756922	−	1.70007i	0.0437945	−	0.999041i	$-0.486055\pi$
$823$	21.7146	−	48.7717i	0.756922	−	1.70007i	0.713128	−	0.701034i	$-0.247278\pi$
$824$	−0.487681	+	2.29436i	−0.0169892	+	0.0799277i
$825$	−8.10991	−	6.67382i	−0.282351	−	0.232353i
$826$	14.1400	−	6.29555i	0.491995	−	0.219050i
$827$	5.78995	+	6.43039i	0.201336	+	0.223607i	0.835355	−	0.549711i	$-0.185262\pi$
$827$	5.78995	+	6.43039i	0.201336	+	0.223607i	−0.634018	+	0.773318i	$0.718596\pi$
$828$	−23.1116	−	2.79821i	−0.803185	−	0.0972445i
$829$	8.73770	+	12.0264i	0.303473	+	0.417695i	0.933332	−	0.359015i	$-0.116887\pi$
$829$	8.73770	+	12.0264i	0.303473	+	0.417695i	−0.629859	+	0.776710i	$0.716887\pi$
$830$	−1.39316	+	13.2551i	−0.0483574	+	0.460090i
$831$	14.3858	+	5.65273i	0.499040	+	0.196091i
$832$	−2.04042	−	1.17803i	−0.0707387	−	0.0408410i
$833$	−34.2342	−	24.8726i	−1.18614	−	0.861784i
$834$	30.7007	+	1.85176i	1.06308	+	0.0641213i
$835$	23.0801	+	7.49918i	0.798720	+	0.259520i
$836$	0.936096			0.0323755
$837$	24.7070	−	15.0521i	0.853998	−	0.520276i
$838$	8.31212			0.287137
$839$	−31.1934	−	10.1353i	−1.07692	−	0.349911i	−0.283738	−	0.958902i	$-0.591575\pi$
$839$	−31.1934	−	10.1353i	−1.07692	−	0.349911i	−0.793177	+	0.608991i	$0.791575\pi$
$840$	10.1235	+	0.610614i	0.349293	+	0.0210682i
$841$	23.0507	+	16.7473i	0.794852	+	0.577494i
$842$	11.1247	+	6.42288i	0.383384	+	0.221347i
$843$	−24.2742	−	9.53825i	−0.836049	−	0.328515i
$844$	−0.226068	+	2.15089i	−0.00778157	+	0.0740367i
$845$	−6.29640	−	8.66625i	−0.216603	−	0.298128i
$846$	14.6553	+	1.77437i	0.503861	+	0.0610042i
$847$	18.3159	+	20.3419i	0.629342	+	0.698956i
$848$	−0.488148	+	0.217338i	−0.0167631	+	0.00746340i
$849$	−21.1299	−	17.3882i	−0.725175	−	0.596762i
$850$	−2.69290	+	12.6691i	−0.0923656	+	0.434546i
$851$	36.6265	−	82.2645i	1.25554	−	2.81999i
$852$	23.6027	+	15.5937i	0.808616	+	0.534232i
$853$	7.06350	+	21.7392i	0.241850	+	0.744337i	0.996139	+	0.0877943i	$0.0279818\pi$
$853$	7.06350	+	21.7392i	0.241850	+	0.744337i	−0.754289	+	0.656543i	$0.772018\pi$
$854$	−33.5720	−	14.9472i	−1.14881	−	0.511484i
$855$	−1.77112	−	0.822254i	−0.0605710	−	0.0281205i
$856$	−4.30396	+	0.914835i	−0.147106	+	0.0312684i
$857$	0.275915	+	0.619716i	0.00942509	+	0.0211691i	0.918197	−	0.396125i	$-0.129645\pi$
$857$	0.275915	+	0.619716i	0.00942509	+	0.0211691i	−0.908772	+	0.417294i	$0.862979\pi$
$858$	1.38597	−	8.32533i	0.0473162	−	0.284222i
$859$	−32.8008	+	3.44750i	−1.11915	+	0.117627i	−0.645987	−	0.763348i	$-0.723554\pi$
$859$	−32.8008	+	3.44750i	−1.11915	+	0.117627i	−0.473162	+	0.880975i	$0.656887\pi$
$860$	11.4784	−	8.33958i	0.391412	−	0.284377i
$861$	14.1556	+	22.1786i	0.482421	+	0.755843i
$862$	0.135434	+	0.234579i	0.00461291	+	0.00798980i
$863$	−5.59783	+	9.69573i	−0.190552	+	0.330047i	−0.945433	−	0.325815i	$-0.894361\pi$
$863$	−5.59783	+	9.69573i	−0.190552	+	0.330047i	0.754881	+	0.655862i	$0.227695\pi$
$864$	0.934000	−	5.11152i	0.0317753	−	0.173897i
$865$	1.99639	−	2.21722i	0.0678795	−	0.0753878i
$866$	−11.3542	+	34.9446i	−0.385831	+	1.18747i
$867$	2.71437	+	3.40653i	0.0921847	+	0.115692i
$868$	0.116387	−	22.6702i	0.00395044	−	0.769475i
$869$			5.29912i			0.179760i
$870$	1.66197	−	0.622983i	0.0563461	−	0.0211211i
$871$	9.43858	+	8.49854i	0.319814	+	0.287962i
$872$	1.89916	−	2.61397i	0.0643137	−	0.0885201i
$873$	−11.7690	−	10.9377i	−0.398320	−	0.370186i
$874$	3.04181	−	1.75619i	0.102891	−	0.0594039i
$875$	46.1906	+	4.85482i	1.56153	+	0.164123i
$876$	0.155301	−	0.561834i	0.00524712	−	0.0189826i
$877$	1.43731	+	13.6751i	0.0485347	+	0.461777i	0.991616	+	0.129216i	$0.0412460\pi$
$877$	1.43731	+	13.6751i	0.0485347	+	0.461777i	−0.943082	+	0.332561i	$0.892087\pi$
$878$	21.8809	−	19.7017i	0.738445	−	0.664899i
$879$	−7.96057	+	15.3236i	−0.268503	+	0.516853i
$880$	−0.618367	−	2.90919i	−0.0208452	−	0.0980688i
$881$	−15.6300	−	3.32225i	−0.526587	−	0.111930i	−0.0630556	−	0.998010i	$-0.520085\pi$
$881$	−15.6300	−	3.32225i	−0.526587	−	0.111930i	−0.463531	+	0.886081i	$0.653418\pi$
$882$	22.9795	+	17.2557i	0.773761	+	0.581028i
$883$	−3.59994	+	1.16969i	−0.121148	+	0.0393633i	−0.368963	−	0.929444i	$-0.620287\pi$
$883$	−3.59994	+	1.16969i	−0.121148	+	0.0393633i	0.247816	+	0.968807i	$0.420287\pi$
$884$	−9.89865	+	3.21627i	−0.332928	+	0.108175i
$885$	2.37845	+	9.16490i	0.0799506	+	0.308075i
$886$	−18.7986	−	3.99578i	−0.631553	−	0.134241i
$887$	3.08507	+	14.5141i	0.103587	+	0.487337i	0.999104	+	0.0423113i	$0.0134721\pi$
$887$	3.08507	+	14.5141i	0.103587	+	0.487337i	−0.895518	+	0.445026i	$0.853195\pi$
$888$	17.8358	+	9.26563i	0.598530	+	0.310934i
$889$	42.3210	−	38.1060i	1.41940	−	1.27803i
$890$	−0.525753	−	5.00221i	−0.0176233	−	0.167674i
$891$	18.3199	−	3.29402i	0.613738	−	0.110354i
$892$	−11.6361	−	1.22300i	−0.389605	−	0.0409492i
$893$	−1.92884	+	1.11362i	−0.0645462	+	0.0372658i
$894$	−32.8282	+	4.93450i	−1.09794	+	0.165034i
$895$	7.41102	−	10.2004i	0.247723	−	0.340961i
$896$	−3.02589	−	2.72452i	−0.101088	−	0.0910199i
$897$	−11.1153	−	29.6530i	−0.371129	−	0.990085i
$898$			22.3556i			0.746016i
$899$	−1.59509	−	3.63271i	−0.0531992	−	0.121158i
$900$	1.96420	−	8.57379i	0.0654732	−	0.285793i
$901$	−0.729433	+	2.24497i	−0.0243010	+	0.0747906i
$902$	5.16294	−	5.73403i	0.171907	−	0.190922i
$903$	69.5115	−	3.09365i	2.31320	−	0.102950i
$904$	−6.34796	+	10.9950i	−0.211130	+	0.365688i
$905$	6.63757	+	11.4966i	0.220640	+	0.382160i
$906$	−12.5636	+	8.01882i	−0.417399	+	0.266407i
$907$	−30.4081	+	22.0928i	−1.00968	+	0.733579i	−0.964143	−	0.265383i	$-0.914501\pi$
$907$	−30.4081	+	22.0928i	−1.00968	+	0.733579i	−0.0455419	+	0.998962i	$0.514501\pi$
$908$	−28.6352	+	3.00969i	−0.950294	+	0.0998799i
$909$	−21.0975	−	37.9100i	−0.699759	−	1.25739i
$910$	5.61124	+	12.6031i	0.186011	+	0.417787i
$911$	48.0288	−	10.2088i	1.59127	−	0.338234i	0.674693	−	0.738099i	$-0.264276\pi$
$911$	48.0288	−	10.2088i	1.59127	−	0.338234i	0.916574	+	0.399865i	$0.130943\pi$
$912$	0.350391	+	0.701294i	0.0116026	+	0.0232222i
$913$	17.5109	+	7.79635i	0.579526	+	0.258021i
$914$	2.22703	+	6.85410i	0.0736637	+	0.226714i
$915$	12.3921	−	18.7567i	0.409669	−	0.620077i
$916$	0.429183	−	0.963961i	0.0141806	−	0.0318502i
$917$	13.7203	−	64.5489i	0.453084	−	2.13159i
$918$	−14.0197	−	18.1755i	−0.462719	−	0.599879i
$919$	46.2683	−	20.6000i	1.52625	−	0.679531i	0.539532	−	0.841965i	$-0.318601\pi$
$919$	46.2683	−	20.6000i	1.52625	−	0.679531i	0.986719	+	0.162434i	$0.0519346\pi$
$920$	−7.46723	−	8.29320i	−0.246187	−	0.273419i
$921$	14.1003	−	13.8797i	0.464620	−	0.457352i
$922$	−14.8050	−	20.3773i	−0.487576	−	0.671091i
$923$	−4.02231	+	38.2697i	−0.132396	+	1.25966i
$924$	5.33426	−	13.5753i	0.175484	−	0.446596i
$925$	29.4647	+	17.0115i	0.968794	+	0.559333i
$926$	−19.2458	−	13.9829i	−0.632456	−	0.459506i
$927$	−4.04588	−	5.75743i	−0.132884	−	0.189099i
$928$	−0.677704	−	0.220199i	−0.0222467	−	0.00722840i
$929$	15.8480			0.519956			0.259978	−	0.965615i	$-0.416285\pi$
$929$	15.8480			0.519956			0.259978	+	0.965615i	$0.416285\pi$
$930$	13.6681	+	2.34758i	0.448193	+	0.0769803i
$931$	−4.33563			−0.142094
$932$	0.111969	+	0.0363808i	0.00366765	+	0.00119169i
$933$	1.27121	−	21.0757i	0.0416176	−	0.689987i
$934$	−10.2488	−	7.44622i	−0.335352	−	0.243648i
$935$	−11.3784	−	6.56931i	−0.372113	−	0.214839i
$936$	6.75586	−	2.07794i	0.220822	−	0.0679195i
$937$	−5.96412	+	56.7448i	−0.194839	+	1.85377i	0.263075	+	0.964775i	$0.415263\pi$
$937$	−5.96412	+	56.7448i	−0.194839	+	1.85377i	−0.457914	+	0.888996i	$0.651403\pi$
$938$	12.9016	+	17.7575i	0.421252	+	0.579804i
$939$	−16.4422	−	16.7035i	−0.536571	−	0.545099i
$940$	4.73504	+	5.25880i	0.154440	+	0.171523i
$941$	−47.7963	+	21.2803i	−1.55811	+	0.693717i	−0.991481	−	0.130253i	$-0.958421\pi$
$941$	−47.7963	+	21.2803i	−1.55811	+	0.693717i	−0.566633	+	0.823970i	$0.691754\pi$
$942$	−21.6597	+	26.3205i	−0.705713	+	0.857570i
$943$	6.01930	−	28.3186i	0.196015	−	0.922180i
$944$	1.54616	−	3.47273i	0.0503233	−	0.113028i
$945$	−22.0170	+	20.9994i	−0.716212	+	0.683110i
$946$	−6.30548	−	19.4063i	−0.205009	−	0.630952i
$947$	−11.1518	−	4.96509i	−0.362384	−	0.161344i	0.217464	−	0.976068i	$-0.430221\pi$
$947$	−11.1518	−	4.96509i	−0.362384	−	0.161344i	−0.579848	+	0.814725i	$0.696888\pi$
$948$	−3.96994	+	1.98352i	−0.128938	+	0.0644217i
$949$	0.775583	−	0.164855i	0.0251765	−	0.00535143i
$950$	0.539764	+	1.21233i	0.0175122	+	0.0393331i
$951$	−42.3777	−	7.05488i	−1.37419	−	0.228770i
$952$	−17.8886	+	1.88016i	−0.579772	+	0.0609364i
$953$	6.60293	−	4.79731i	0.213890	−	0.155400i	−0.475682	−	0.879617i	$-0.657799\pi$
$953$	6.60293	−	4.79731i	0.213890	−	0.155400i	0.689572	+	0.724217i	$0.257799\pi$
$954$	0.519341	−	1.51658i	0.0168143	−	0.0491010i
$955$	−9.22563	−	15.9793i	−0.298534	−	0.517077i
$956$	11.3477	−	19.6548i	0.367010	−	0.635681i
$957$	−0.113493	−	2.55008i	−0.00366869	−	0.0824323i
$958$	10.0888	−	11.2047i	0.325954	−	0.362008i
$959$	−24.3270	+	74.8709i	−0.785561	+	2.41771i
$960$	1.94802	−	1.55220i	0.0628719	−	0.0500972i
$961$	3.55676	−	30.7953i	0.114734	−	0.993396i
$962$			27.3401i			0.881481i
$963$	6.77959	−	11.3263i	0.218469	−	0.364987i
$964$	3.78313	+	3.40634i	0.121846	+	0.109711i
$965$	−3.33821	+	4.59465i	−0.107461	+	0.147907i
$966$	−8.13494	−	54.1200i	−0.261737	−	1.74128i
$967$	−7.36828	+	4.25408i	−0.236948	+	0.136802i	−0.613773	−	0.789482i	$-0.710349\pi$
$967$	−7.36828	+	4.25408i	−0.236948	+	0.136802i	0.376825	+	0.926284i	$0.377016\pi$
$968$	6.68579	+	0.702705i	0.214889	+	0.0225858i
$969$	3.33799	+	0.922678i	0.107232	+	0.0296407i
$970$	−0.805049	−	7.65953i	−0.0258486	−	0.245933i
$971$	32.5622	−	29.3191i	1.04497	−	0.940896i	0.0466551	−	0.998911i	$-0.485144\pi$
$971$	32.5622	−	29.3191i	1.04497	−	0.940896i	0.998316	+	0.0580151i	$0.0184772\pi$
$972$	9.32510	+	12.4917i	0.299103	+	0.400671i
$973$	15.0326	+	70.7229i	0.481924	+	2.26727i
$974$	9.12145	+	1.93882i	0.292270	+	0.0621239i
$975$	11.5812	−	3.00552i	0.370896	−	0.0962538i
$976$	−8.58370	+	2.78901i	−0.274757	+	0.0892741i
$977$	45.3845	−	14.7463i	1.45198	−	0.471777i	0.526369	−	0.850256i	$-0.323553\pi$
$977$	45.3845	−	14.7463i	1.45198	−	0.471777i	0.925610	+	0.378479i	$0.123553\pi$
$978$	−25.1055	+	6.51532i	−0.802786	+	0.208337i
$979$	−7.07558	−	1.50396i	−0.226136	−	0.0480668i
$980$	2.86403	+	13.4742i	0.0914882	+	0.430418i
$981$	1.86558	+	9.51191i	0.0595632	+	0.303692i
$982$	−17.4734	+	15.7331i	−0.557599	+	0.502065i
$983$	2.78304	+	26.4789i	0.0887652	+	0.844545i	0.944805	+	0.327634i	$0.106251\pi$
$983$	2.78304	+	26.4789i	0.0887652	+	0.844545i	−0.856039	+	0.516911i	$0.827082\pi$
$984$	6.22831	+	1.72161i	0.198551	+	0.0548829i
$985$	−7.86181	−	0.826309i	−0.250498	−	0.0263284i
$986$	−2.72613	+	1.57393i	−0.0868175	+	0.0501241i
$987$	5.15845	+	34.3181i	0.164195	+	1.09236i
$988$	−0.626813	+	0.862734i	−0.0199416	+	0.0274472i
$989$	−56.8970	−	51.2303i	−1.80922	−	1.62903i
$990$	7.65585	+	4.58255i	0.243319	+	0.145643i
$991$		−	13.6660i		−	0.434114i	−0.976159	−	0.217057i	$-0.930354\pi$
$991$		−	13.6660i		−	0.434114i	0.976159	−	0.217057i	$-0.0696458\pi$
$992$	−3.70427	−	4.15673i	−0.117611	−	0.131976i
$993$	11.8474	−	9.44015i	0.375965	−	0.299574i
$994$	−20.5501	+	63.2468i	−0.651810	+	2.00607i
$995$	−21.0397	+	23.3670i	−0.667005	+	0.740784i
$996$	0.713730	+	16.0369i	0.0226154	+	0.508148i
$997$	2.08018	−	3.60298i	0.0658800	−	0.114108i	−0.831204	−	0.555968i	$-0.812348\pi$
$997$	2.08018	−	3.60298i	0.0658800	−	0.114108i	0.897084	+	0.441860i	$0.145681\pi$
$998$	4.21044	+	7.29269i	0.133279	+	0.230846i
$999$	−56.7872	+	20.2712i	−1.79667	+	0.641351i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	186.2.p.a.17.5	yes	80
3.2	odd	2	inner	186.2.p.a.17.8	yes	80
31.11	odd	30	inner	186.2.p.a.11.8	yes	80
93.11	even	30	inner	186.2.p.a.11.5	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
186.2.p.a.11.5	✓	80	93.11	even	30	inner
186.2.p.a.11.8	yes	80	31.11	odd	30	inner
186.2.p.a.17.5	yes	80	1.1	even	1	trivial
186.2.p.a.17.8	yes	80	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 186 = 2 \cdot 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	186.p (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.309017i) q^{2} +(1.72891 + 0.104282i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.24540 - 0.719033i) q^{5} +(-1.61207 - 0.633440i) q^{6} +(0.425612 - 4.04943i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(2.97825 + 0.360587i) q^{9} +(0.962254 + 1.06869i) q^{10} +(1.88938 - 0.841206i) q^{11} +(1.33742 + 1.10059i) q^{12} +(-0.489854 + 2.30458i) q^{13} +(-1.65612 + 3.71971i) q^{14} +(-2.07820 - 1.37301i) q^{15} +(0.309017 + 0.951057i) q^{16} +(4.03564 + 1.79678i) q^{17} +(-2.72106 - 1.26327i) q^{18} +(0.442727 - 0.0941045i) q^{19} +(-0.584914 - 1.31374i) q^{20} +(1.15813 - 6.95671i) q^{21} +(-2.05685 + 0.216184i) q^{22} +(-6.27809 + 4.56130i) q^{23} +(-0.931861 - 1.46001i) q^{24} +(-1.46598 - 2.53916i) q^{25} +(1.17803 - 2.04042i) q^{26} +(5.11152 + 0.934000i) q^{27} +(2.72452 - 3.02589i) q^{28} +(0.220199 - 0.677704i) q^{29} +(1.55220 + 1.94802i) q^{30} +(4.15673 - 3.70427i) q^{31} -1.00000i q^{32} +(3.35429 - 1.25734i) q^{33} +(-3.28288 - 2.95592i) q^{34} +(-3.44173 + 4.73713i) q^{35} +(2.19751 + 2.04229i) q^{36} +(-10.0495 + 5.80206i) q^{37} +(-0.450138 - 0.0473114i) q^{38} +(-1.08724 + 3.93333i) q^{39} +(0.150319 + 1.43019i) q^{40} +(-2.77250 + 2.49637i) q^{41} +(-3.25118 + 6.25834i) q^{42} +(2.05128 + 9.65052i) q^{43} +(2.02299 + 0.429999i) q^{44} +(-3.44984 - 2.59054i) q^{45} +(7.38033 - 2.39802i) q^{46} +(-4.67994 + 1.52061i) q^{47} +(0.435084 + 1.67651i) q^{48} +(-9.36969 - 1.99159i) q^{49} +(0.609590 + 2.86790i) q^{50} +(6.78987 + 3.52731i) q^{51} +(-1.75090 + 1.57652i) q^{52} +(0.0558542 + 0.531418i) q^{53} +(-4.57272 - 2.46783i) q^{54} +(-2.95789 - 0.310887i) q^{55} +(-3.52622 + 2.03587i) q^{56} +(0.775247 - 0.116530i) q^{57} +(-0.418844 + 0.576489i) q^{58} +(-2.82498 - 2.54362i) q^{59} +(-0.874264 - 2.33233i) q^{60} +9.02543i q^{61} +(-5.09797 + 2.23847i) q^{62} +(2.72775 - 11.9067i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(2.26714 - 2.51791i) q^{65} +(-3.57866 + 0.159270i) q^{66} +(2.69535 - 4.66849i) q^{67} +(2.20878 + 3.82571i) q^{68} +(-11.3299 + 7.23138i) q^{69} +(4.73713 - 3.44173i) q^{70} +(16.2430 - 1.70721i) q^{71} +(-1.45885 - 2.62140i) q^{72} +(-0.136883 - 0.307444i) q^{73} +(11.3505 - 2.41263i) q^{74} +(-2.26976 - 4.54285i) q^{75} +(0.413487 + 0.184096i) q^{76} +(-2.60226 - 8.00893i) q^{77} +(2.24949 - 3.40484i) q^{78} +(-1.04215 + 2.34070i) q^{79} +(0.298991 - 1.40664i) q^{80} +(8.73995 + 2.14784i) q^{81} +(3.40822 - 1.51744i) q^{82} +(6.20154 + 6.88751i) q^{83} +(5.02599 - 4.94736i) q^{84} +(-3.73404 - 5.13947i) q^{85} +(1.03129 - 9.81207i) q^{86} +(0.451377 - 1.14873i) q^{87} +(-1.79110 - 1.03409i) q^{88} +(-2.82961 - 2.05583i) q^{89} +(2.48048 + 3.52981i) q^{90} +(9.12375 + 2.96449i) q^{91} -7.76014 q^{92} +(7.57289 - 5.97087i) q^{93} +4.92078 q^{94} +(-0.619037 - 0.201137i) q^{95} +(0.104282 - 1.72891i) q^{96} +(-4.33278 - 3.14795i) q^{97} +(8.29567 + 4.78950i) q^{98} +(5.93037 - 1.82404i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 20 q^{4} + 8 q^{7} + 4 q^{9} - 4 q^{10} - 10 q^{15} - 20 q^{16} - 8 q^{18} - 4 q^{19} + 30 q^{21} - 2 q^{22} + 12 q^{25} - 38 q^{28} - 86 q^{31} - 28 q^{34} - 4 q^{36} - 144 q^{37} - 16 q^{39} - 6 q^{40}+ \cdots + 150 q^{99}+O(q^{100}) \) 80 * q + 20 * q^4 + 8 * q^7 + 4 * q^9 - 4 * q^10 - 10 * q^15 - 20 * q^16 - 8 * q^18 - 4 * q^19 + 30 * q^21 - 2 * q^22 + 12 * q^25 - 38 * q^28 - 86 * q^31 - 28 * q^34 - 4 * q^36 - 144 * q^37 - 16 * q^39 - 6 * q^40 - 6 * q^42 + 40 * q^43 - 24 * q^45 - 20 * q^46 + 10 * q^48 - 14 * q^49 - 92 * q^51 - 92 * q^55 - 96 * q^57 + 20 * q^58 - 10 * q^60 + 88 * q^63 + 20 * q^64 + 12 * q^66 + 40 * q^67 - 60 * q^69 + 24 * q^70 + 8 * q^72 + 56 * q^73 - 30 * q^75 - 36 * q^76 + 32 * q^78 + 32 * q^79 + 128 * q^81 + 36 * q^82 + 10 * q^84 + 100 * q^85 + 34 * q^87 + 42 * q^88 + 34 * q^90 + 60 * q^91 + 172 * q^93 + 24 * q^94 - 4 * q^97 + 150 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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