LMFDB - Embedded newform 666.2.k.a.175.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [666,2,Mod(175,666)] 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("666.175"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(666, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.k (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			175.4
Character	$\chi$	$=$	666.175
Dual form			666.2.k.a.529.23

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} +(-1.46639 - 0.921793i) q^{3} -1.00000 q^{4} +1.15671i q^{5} +(-0.921793 + 1.46639i) q^{6} +(-1.84738 + 3.19976i) q^{7} +1.00000i q^{8} +(1.30060 + 2.70341i) q^{9} +1.15671 q^{10} +(-1.20873 - 2.09357i) q^{11} +(1.46639 + 0.921793i) q^{12} -6.88028i q^{13} +(3.19976 + 1.84738i) q^{14} +(1.06625 - 1.69619i) q^{15} +1.00000 q^{16} +(4.89370 + 2.82538i) q^{17} +(2.70341 - 1.30060i) q^{18} +(2.91946 - 1.68555i) q^{19} -1.15671i q^{20} +(5.65849 - 2.98919i) q^{21} +(-2.09357 + 1.20873i) q^{22} +(-4.06860 - 2.34901i) q^{23} +(0.921793 - 1.46639i) q^{24} +3.66202 q^{25} -6.88028 q^{26} +(0.584805 - 5.16314i) q^{27} +(1.84738 - 3.19976i) q^{28} +(6.50368 - 3.75490i) q^{29} +(-1.69619 - 1.06625i) q^{30} +(7.08217 + 4.08889i) q^{31} -1.00000i q^{32} +(-0.157378 + 4.18419i) q^{33} +(2.82538 - 4.89370i) q^{34} +(-3.70120 - 2.13689i) q^{35} +(-1.30060 - 2.70341i) q^{36} +(3.81202 - 4.74010i) q^{37} +(-1.68555 - 2.91946i) q^{38} +(-6.34219 + 10.0892i) q^{39} -1.15671 q^{40} -9.35395 q^{41} +(-2.98919 - 5.65849i) q^{42} +(-1.53830 + 0.888135i) q^{43} +(1.20873 + 2.09357i) q^{44} +(-3.12707 + 1.50442i) q^{45} +(-2.34901 + 4.06860i) q^{46} +(0.781422 + 1.35346i) q^{47} +(-1.46639 - 0.921793i) q^{48} +(-3.32563 - 5.76017i) q^{49} -3.66202i q^{50} +(-4.57165 - 8.65408i) q^{51} +6.88028i q^{52} +(-0.0906763 + 0.157056i) q^{53} +(-5.16314 - 0.584805i) q^{54} +(2.42166 - 1.39815i) q^{55} +(-3.19976 - 1.84738i) q^{56} +(-5.83479 - 0.219462i) q^{57} +(-3.75490 - 6.50368i) q^{58} +(3.21227 - 1.85460i) q^{59} +(-1.06625 + 1.69619i) q^{60} +(-0.931466 - 0.537782i) q^{61} +(4.08889 - 7.08217i) q^{62} +(-11.0530 - 0.832641i) q^{63} -1.00000 q^{64} +7.95850 q^{65} +(4.18419 + 0.157378i) q^{66} +5.28380 q^{67} +(-4.89370 - 2.82538i) q^{68} +(3.80086 + 7.19497i) q^{69} +(-2.13689 + 3.70120i) q^{70} +(-0.405092 - 0.701640i) q^{71} +(-2.70341 + 1.30060i) q^{72} +6.14056 q^{73} +(-4.74010 - 3.81202i) q^{74} +(-5.36994 - 3.37562i) q^{75} +(-2.91946 + 1.68555i) q^{76} +8.93190 q^{77} +(10.0892 + 6.34219i) q^{78} +(10.1075 + 5.83555i) q^{79} +1.15671i q^{80} +(-5.61690 + 7.03210i) q^{81} +9.35395i q^{82} -4.32347 q^{83} +(-5.65849 + 2.98919i) q^{84} +(-3.26815 + 5.66060i) q^{85} +(0.888135 + 1.53830i) q^{86} +(-12.9982 - 0.488895i) q^{87} +(2.09357 - 1.20873i) q^{88} +(13.0129 + 7.51299i) q^{89} +(1.50442 + 3.12707i) q^{90} +(22.0152 + 12.7105i) q^{91} +(4.06860 + 2.34901i) q^{92} +(-6.61611 - 12.5242i) q^{93} +(1.35346 - 0.781422i) q^{94} +(1.94969 + 3.37697i) q^{95} +(-0.921793 + 1.46639i) q^{96} +(14.5488 - 8.39978i) q^{97} +(-5.76017 + 3.32563i) q^{98} +(4.08773 - 5.99058i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 4 q^{3} - 76 q^{4} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{12} + 12 q^{15} + 76 q^{16} + 6 q^{21} + 12 q^{23} - 100 q^{25} - 24 q^{26} + 4 q^{27} + 2 q^{28} + 18 q^{29} - 12 q^{30} + 6 q^{31} - 32 q^{33}+ \cdots - 76 q^{99}+O(q^{100}) $ 76 * q + 4 * q^3 - 76 * q^4 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^12 + 12 * q^15 + 76 * q^16 + 6 * q^21 + 12 * q^23 - 100 * q^25 - 24 * q^26 + 4 * q^27 + 2 * q^28 + 18 * q^29 - 12 * q^30 + 6 * q^31 - 32 * q^33 - 18 * q^35 + 4 * q^36 + 10 * q^37 + 12 * q^38 + 24 * q^39 + 72 * q^41 + 6 * q^42 + 6 * q^43 + 4 * q^44 + 12 * q^45 - 20 * q^47 + 4 * q^48 - 36 * q^49 - 18 * q^51 + 14 * q^53 + 36 * q^54 + 42 * q^57 - 6 * q^59 - 12 * q^60 - 16 * q^62 + 46 * q^63 - 76 * q^64 + 32 * q^65 + 40 * q^67 + 6 * q^69 + 2 * q^71 + 28 * q^73 - 2 * q^74 - 78 * q^75 - 24 * q^77 - 2 * q^78 + 6 * q^79 - 28 * q^81 - 64 * q^83 - 6 * q^84 - 12 * q^85 + 4 * q^86 - 78 * q^87 + 60 * q^89 - 16 * q^90 + 42 * q^91 - 12 * q^92 + 6 * q^93 - 14 * q^95 - 12 * q^97 - 24 * q^98 - 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−1.46639	−	0.921793i	−0.846620	−	0.532197i
$3$	−1.46639	−	0.921793i	−0.846620	−	0.532197i
$4$	−1.00000			−0.500000
$5$			1.15671i			0.517297i	0.965971	+	0.258649i	$0.0832772\pi$
$5$			1.15671i			0.517297i	−0.965971	+	0.258649i	$0.916723\pi$
$6$	−0.921793	+	1.46639i	−0.376320	+	0.598651i
$7$	−1.84738	+	3.19976i	−0.698244	+	1.20939i	0.270830	+	0.962627i	$0.412702\pi$
$7$	−1.84738	+	3.19976i	−0.698244	+	1.20939i	−0.969075	+	0.246768i	$0.920632\pi$
$8$			1.00000i			0.353553i
$9$	1.30060	+	2.70341i	0.433532	+	0.901138i
$10$	1.15671			0.365785
$11$	−1.20873	−	2.09357i	−0.364444	−	0.631236i	0.624242	−	0.781231i	$-0.285408\pi$
$11$	−1.20873	−	2.09357i	−0.364444	−	0.631236i	−0.988687	+	0.149995i	$0.952074\pi$
$12$	1.46639	+	0.921793i	0.423310	+	0.266099i
$13$		−	6.88028i		−	1.90825i	−0.299415	−	0.954123i	$-0.596791\pi$
$13$		−	6.88028i		−	1.90825i	0.299415	−	0.954123i	$-0.403209\pi$
$14$	3.19976	+	1.84738i	0.855171	+	0.493733i
$15$	1.06625	−	1.69619i	0.275304	−	0.437955i
$16$	1.00000			0.250000
$17$	4.89370	+	2.82538i	1.18690	+	0.685254i	0.957600	−	0.288102i	$-0.0930243\pi$
$17$	4.89370	+	2.82538i	1.18690	+	0.685254i	0.229296	+	0.973357i	$0.426358\pi$
$18$	2.70341	−	1.30060i	0.637201	−	0.306554i
$19$	2.91946	−	1.68555i	0.669769	−	0.386691i	−0.126220	−	0.992002i	$-0.540285\pi$
$19$	2.91946	−	1.68555i	0.669769	−	0.386691i	0.795989	+	0.605311i	$0.206951\pi$
$20$		−	1.15671i		−	0.258649i
$21$	5.65849	−	2.98919i	1.23478	−	0.652295i
$22$	−2.09357	+	1.20873i	−0.446351	+	0.257701i
$23$	−4.06860	−	2.34901i	−0.848362	−	0.489802i	0.0117358	−	0.999931i	$-0.496264\pi$
$23$	−4.06860	−	2.34901i	−0.848362	−	0.489802i	−0.860098	+	0.510129i	$0.829598\pi$
$24$	0.921793	−	1.46639i	0.188160	−	0.299326i
$25$	3.66202			0.732403
$26$	−6.88028			−1.34933
$27$	0.584805	−	5.16314i	0.112546	−	0.993647i
$28$	1.84738	−	3.19976i	0.349122	−	0.604697i
$29$	6.50368	−	3.75490i	1.20770	−	0.697267i	0.245446	−	0.969410i	$-0.421066\pi$
$29$	6.50368	−	3.75490i	1.20770	−	0.697267i	0.962257	+	0.272143i	$0.0877324\pi$
$30$	−1.69619	−	1.06625i	−0.309681	−	0.194670i
$31$	7.08217	+	4.08889i	1.27199	+	0.734386i	0.975363	−	0.220606i	$-0.0708034\pi$
$31$	7.08217	+	4.08889i	1.27199	+	0.734386i	0.296631	+	0.954992i	$0.404137\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−0.157378	+	4.18419i	−0.0273961	+	0.728374i
$34$	2.82538	−	4.89370i	0.484548	−	0.839262i
$35$	−3.70120	−	2.13689i	−0.625617	−	0.361200i
$36$	−1.30060	−	2.70341i	−0.216766	−	0.450569i
$37$	3.81202	−	4.74010i	0.626692	−	0.779267i
$37$	3.81202	−	4.74010i	0.626692	−	0.779267i
$38$	−1.68555	−	2.91946i	−0.273432	−	0.473598i
$39$	−6.34219	+	10.0892i	−1.01556	+	1.61556i
$40$	−1.15671			−0.182892
$41$	−9.35395			−1.46084			−0.730421	−	0.682998i	$-0.760676\pi$
$41$	−9.35395			−1.46084			−0.730421	+	0.682998i	$0.760676\pi$
$42$	−2.98919	−	5.65849i	−0.461242	−	0.873124i
$43$	−1.53830	+	0.888135i	−0.234588	+	0.135439i	−0.612687	−	0.790326i	$-0.709911\pi$
$43$	−1.53830	+	0.888135i	−0.234588	+	0.135439i	0.378099	+	0.925765i	$0.376578\pi$
$44$	1.20873	+	2.09357i	0.182222	+	0.315618i
$45$	−3.12707	+	1.50442i	−0.466156	+	0.224265i
$46$	−2.34901	+	4.06860i	−0.346342	+	0.599883i
$47$	0.781422	+	1.35346i	0.113982	+	0.197423i	0.917372	−	0.398030i	$-0.130306\pi$
$47$	0.781422	+	1.35346i	0.113982	+	0.197423i	−0.803390	+	0.595453i	$0.796973\pi$
$48$	−1.46639	−	0.921793i	−0.211655	−	0.133049i
$49$	−3.32563	−	5.76017i	−0.475090	−	0.822881i
$50$		−	3.66202i		−	0.517887i
$51$	−4.57165	−	8.65408i	−0.640160	−	1.21181i
$52$			6.88028i			0.954123i
$53$	−0.0906763	+	0.157056i	−0.0124553	+	0.0215733i	−0.872186	−	0.489175i	$-0.837298\pi$
$53$	−0.0906763	+	0.157056i	−0.0124553	+	0.0215733i	0.859731	+	0.510748i	$0.170631\pi$
$54$	−5.16314	−	0.584805i	−0.702614	−	0.0795819i
$55$	2.42166	−	1.39815i	0.326537	−	0.188526i
$56$	−3.19976	−	1.84738i	−0.427586	−	0.246867i
$57$	−5.83479	−	0.219462i	−0.772836	−	0.0290684i
$58$	−3.75490	−	6.50368i	−0.493042	−	0.853975i
$59$	3.21227	−	1.85460i	0.418202	−	0.241449i	−0.276106	−	0.961127i	$-0.589044\pi$
$59$	3.21227	−	1.85460i	0.418202	−	0.241449i	0.694308	+	0.719678i	$0.255711\pi$
$60$	−1.06625	+	1.69619i	−0.137652	+	0.218977i
$61$	−0.931466	−	0.537782i	−0.119262	−	0.0688560i	0.439182	−	0.898398i	$-0.355268\pi$
$61$	−0.931466	−	0.537782i	−0.119262	−	0.0688560i	−0.558444	+	0.829542i	$0.688602\pi$
$62$	4.08889	−	7.08217i	0.519290	−	0.899436i
$63$	−11.0530	−	0.832641i	−1.39254	−	0.104903i
$64$	−1.00000			−0.125000
$65$	7.95850			0.987131
$66$	4.18419	+	0.157378i	0.515038	+	0.0193719i
$67$	5.28380			0.645519			0.322760	−	0.946481i	$-0.395389\pi$
$67$	5.28380			0.645519			0.322760	+	0.946481i	$0.395389\pi$
$68$	−4.89370	−	2.82538i	−0.593448	−	0.342627i
$69$	3.80086	+	7.19497i	0.457569	+	0.866172i
$70$	−2.13689	+	3.70120i	−0.255407	+	0.442378i
$71$	−0.405092	−	0.701640i	−0.0480756	−	0.0832693i	0.840986	−	0.541057i	$-0.181975\pi$
$71$	−0.405092	−	0.701640i	−0.0480756	−	0.0832693i	−0.889062	+	0.457787i	$0.848642\pi$
$72$	−2.70341	+	1.30060i	−0.318600	+	0.153277i
$73$	6.14056			0.718698			0.359349	−	0.933203i	$-0.382999\pi$
$73$	6.14056			0.718698			0.359349	+	0.933203i	$0.382999\pi$
$74$	−4.74010	−	3.81202i	−0.551025	−	0.443138i
$75$	−5.36994	−	3.37562i	−0.620068	−	0.389783i
$76$	−2.91946	+	1.68555i	−0.334885	+	0.193346i
$77$	8.93190			1.01788
$78$	10.0892	+	6.34219i	1.14237	+	0.718112i
$79$	10.1075	+	5.83555i	1.13718	+	0.656551i	0.945731	−	0.324952i	$-0.105348\pi$
$79$	10.1075	+	5.83555i	1.13718	+	0.656551i	0.191449	+	0.981503i	$0.438681\pi$
$80$			1.15671i			0.129324i
$81$	−5.61690	+	7.03210i	−0.624099	+	0.781345i
$82$			9.35395i			1.03297i
$83$	−4.32347			−0.474562			−0.237281	−	0.971441i	$-0.576256\pi$
$83$	−4.32347			−0.474562			−0.237281	+	0.971441i	$0.576256\pi$
$84$	−5.65849	+	2.98919i	−0.617392	+	0.326147i
$85$	−3.26815	+	5.66060i	−0.354480	+	0.613978i
$86$	0.888135	+	1.53830i	0.0957701	+	0.165879i
$87$	−12.9982	−	0.488895i	−1.39355	−	0.0524151i
$88$	2.09357	−	1.20873i	0.223176	−	0.128851i
$89$	13.0129	+	7.51299i	1.37936	+	0.796375i	0.992083	−	0.125587i	$-0.0400814\pi$
$89$	13.0129	+	7.51299i	1.37936	+	0.796375i	0.387280	+	0.921962i	$0.373415\pi$
$90$	1.50442	+	3.12707i	0.158579	+	0.329622i
$91$	22.0152	+	12.7105i	2.30782	+	1.33242i
$92$	4.06860	+	2.34901i	0.424181	+	0.244901i
$93$	−6.61611	−	12.5242i	−0.686058	−	1.29870i
$94$	1.35346	−	0.781422i	0.139599	−	0.0805976i
$95$	1.94969	+	3.37697i	0.200034	+	0.346470i
$96$	−0.921793	+	1.46639i	−0.0940801	+	0.149663i
$97$	14.5488	−	8.39978i	1.47721	−	0.852868i	0.477542	−	0.878609i	$-0.341528\pi$
$97$	14.5488	−	8.39978i	1.47721	−	0.852868i	0.999669	+	0.0257406i	$0.00819440\pi$
$98$	−5.76017	+	3.32563i	−0.581865	+	0.335940i
$99$	4.08773	−	5.99058i	0.410832	−	0.602076i
$100$	−3.66202			−0.366202
$101$	−9.68183	−	16.7694i	−0.963378	−	1.66862i	−0.713911	−	0.700237i	$-0.753078\pi$
$101$	−9.68183	−	16.7694i	−0.963378	−	1.66862i	−0.249467	−	0.968383i	$-0.580255\pi$
$102$	−8.65408	+	4.57165i	−0.856881	+	0.452661i
$103$	−9.66767	−	5.58163i	−0.952583	−	0.549974i	−0.0587010	−	0.998276i	$-0.518696\pi$
$103$	−9.66767	−	5.58163i	−0.952583	−	0.549974i	−0.893883	+	0.448301i	$0.852029\pi$
$104$	6.88028			0.674667
$105$	3.45763	+	6.54525i	0.337430	+	0.638751i
$106$	0.157056	+	0.0906763i	0.0152546	+	0.00880726i
$107$	−6.12736	−	10.6129i	−0.592354	−	1.02599i	−0.993914	−	0.110155i	$-0.964865\pi$
$107$	−6.12736	−	10.6129i	−0.592354	−	1.02599i	0.401561	−	0.915832i	$-0.368468\pi$
$108$	−0.584805	+	5.16314i	−0.0562729	+	0.496823i
$109$	11.2086	+	6.47129i	1.07359	+	0.619838i	0.929160	−	0.369677i	$-0.120532\pi$
$109$	11.2086	+	6.47129i	1.07359	+	0.619838i	0.144430	+	0.989515i	$0.453865\pi$
$110$	−1.39815	−	2.42166i	−0.133308	−	0.230896i
$111$	−9.95929	+	3.43694i	−0.945294	+	0.326220i
$112$	−1.84738	+	3.19976i	−0.174561	+	0.302349i
$113$	−3.31771	+	1.91548i	−0.312104	+	0.180193i	−0.647868	−	0.761753i	$-0.724339\pi$
$113$	−3.31771	+	1.91548i	−0.312104	+	0.180193i	0.335763	+	0.941946i	$0.391006\pi$
$114$	−0.219462	+	5.83479i	−0.0205545	+	0.546478i
$115$	2.71713	−	4.70620i	0.253373	−	0.438856i
$116$	−6.50368	+	3.75490i	−0.603851	+	0.348634i
$117$	18.6002	−	8.94847i	1.71959	−	0.827286i
$118$	−1.85460	−	3.21227i	−0.170730	−	0.295713i
$119$	−18.0810	+	10.4391i	−1.65749	+	0.956950i
$120$	1.69619	+	1.06625i	0.154840	+	0.0973348i
$121$	2.57797	−	4.46517i	0.234361	−	0.405925i
$122$	−0.537782	+	0.931466i	−0.0486885	+	0.0843310i
$123$	13.7165	+	8.62240i	1.23678	+	0.777456i
$124$	−7.08217	−	4.08889i	−0.635997	−	0.367193i
$125$			10.0195i			0.896168i
$126$	−0.832641	+	11.0530i	−0.0741775	+	0.984677i
$127$	−5.93633	+	10.2820i	−0.526764	+	0.912383i	0.472749	+	0.881197i	$0.343262\pi$
$127$	−5.93633	+	10.2820i	−0.526764	+	0.912383i	−0.999514	+	0.0311857i	$0.990072\pi$
$128$			1.00000i			0.0883883i
$129$	3.07442	+	0.115637i	0.270687	+	0.0101813i
$130$		−	7.95850i		−	0.698007i
$131$	−9.44064	+	5.45056i	−0.824833	+	0.476217i	−0.852080	−	0.523411i	$-0.824659\pi$
$131$	−9.44064	+	5.45056i	−0.824833	+	0.476217i	0.0272475	+	0.999629i	$0.491326\pi$
$132$	0.157378	−	4.18419i	0.0136980	−	0.364187i
$133$			12.4554i			1.08002i
$134$		−	5.28380i		−	0.456451i
$135$	5.97227	+	0.676451i	0.514011	+	0.0582197i
$136$	−2.82538	+	4.89370i	−0.242274	+	0.419631i
$137$	−2.17905	−	3.77422i	−0.186169	−	0.322453i	0.757801	−	0.652486i	$-0.226274\pi$
$137$	−2.17905	−	3.77422i	−0.186169	−	0.322453i	−0.943970	+	0.330032i	$0.892940\pi$
$138$	7.19497	−	3.80086i	0.612476	−	0.323550i
$139$	7.01644	+	12.1528i	0.595127	+	1.03079i	0.993529	+	0.113579i	$0.0362316\pi$
$139$	7.01644	+	12.1528i	0.595127	+	1.03079i	−0.398402	+	0.917211i	$0.630435\pi$
$140$	3.70120	+	2.13689i	0.312808	+	0.180600i
$141$	0.101743	−	2.70501i	0.00856828	−	0.227803i
$142$	−0.701640	+	0.405092i	−0.0588803	+	0.0339945i
$143$	−14.4044	+	8.31637i	−1.20455	+	0.695449i
$144$	1.30060	+	2.70341i	0.108383	+	0.225285i
$145$	4.34334	+	7.52288i	0.360695	+	0.624741i
$146$		−	6.14056i		−	0.508197i
$147$	−0.433004	+	11.5122i	−0.0357136	+	0.949510i
$148$	−3.81202	+	4.74010i	−0.313346	+	0.389634i
$149$	−2.44061	+	4.22726i	−0.199943	+	0.346311i	−0.948510	−	0.316748i	$-0.897409\pi$
$149$	−2.44061	+	4.22726i	−0.199943	+	0.346311i	0.748567	+	0.663059i	$0.230742\pi$
$150$	−3.37562	+	5.36994i	−0.275618	+	0.438454i
$151$	11.7521	−	20.3552i	0.956370	−	1.65648i	0.225169	−	0.974320i	$-0.427707\pi$
$151$	11.7521	−	20.3552i	0.956370	−	1.65648i	0.731201	−	0.682162i	$-0.238960\pi$
$152$	1.68555	+	2.91946i	0.136716	+	0.236799i
$153$	−1.27344	+	16.9044i	−0.102951	+	1.36664i
$154$		−	8.93190i		−	0.719753i
$155$	−4.72967	+	8.19203i	−0.379896	+	0.658000i
$156$	6.34219	−	10.0892i	0.507782	−	0.807780i
$157$	−1.78509	−	3.09186i	−0.142466	−	0.246758i	0.785959	−	0.618279i	$-0.212170\pi$
$157$	−1.78509	−	3.09186i	−0.142466	−	0.246758i	−0.928425	+	0.371521i	$0.878836\pi$
$158$	5.83555	−	10.1075i	0.464252	−	0.804108i
$159$	0.277740	−	0.146720i	0.0220262	−	0.0116357i
$160$	1.15671			0.0914461
$161$	15.0325	−	8.67903i	1.18473	−	0.684003i
$162$	7.03210	+	5.61690i	0.552494	+	0.441305i
$163$	−3.71196	−	2.14310i	−0.290743	−	0.167861i	0.347534	−	0.937668i	$-0.387019\pi$
$163$	−3.71196	−	2.14310i	−0.290743	−	0.167861i	−0.638277	+	0.769807i	$0.720353\pi$
$164$	9.35395			0.730421
$165$	−4.83990	−	0.182041i	−0.376786	−	0.0141719i
$166$			4.32347i			0.335566i
$167$		−	3.73933i		−	0.289358i	−0.989479	−	0.144679i	$-0.953785\pi$
$167$		−	3.73933i		−	0.289358i	0.989479	−	0.144679i	$-0.0462149\pi$
$168$	2.98919	+	5.65849i	0.230621	+	0.436562i
$169$	−34.3382			−2.64140
$170$	5.66060	+	3.26815i	0.434148	+	0.250656i
$171$	8.35377	+	5.70028i	0.638829	+	0.435911i
$172$	1.53830	−	0.888135i	0.117294	−	0.0677197i
$173$	−3.77995			−0.287384			−0.143692	−	0.989622i	$-0.545898\pi$
$173$	−3.77995			−0.287384			−0.143692	+	0.989622i	$0.545898\pi$
$174$	−0.488895	+	12.9982i	−0.0370630	+	0.985388i
$175$	−6.76514	+	11.7176i	−0.511397	+	0.885765i
$176$	−1.20873	−	2.09357i	−0.0911111	−	0.157809i
$177$	−6.42000	−	0.241473i	−0.482557	−	0.0181502i
$178$	7.51299	−	13.0129i	0.563122	−	0.975357i
$179$			2.37692i			0.177660i	0.996047	+	0.0888298i	$0.0283127\pi$
$179$			2.37692i			0.177660i	−0.996047	+	0.0888298i	$0.971687\pi$
$180$	3.12707	−	1.50442i	0.233078	−	0.112133i
$181$	7.92005	+	13.7179i	0.588693	+	1.01965i	0.994404	+	0.105644i	$0.0336905\pi$
$181$	7.92005	+	13.7179i	0.588693	+	1.01965i	−0.405711	+	0.914001i	$0.632976\pi$
$182$	12.7105	−	22.0152i	0.942165	−	1.63188i
$183$	0.870169	+	1.64722i	0.0643247	+	0.121766i
$184$	2.34901	−	4.06860i	0.173171	−	0.299941i
$185$	5.48293	+	4.40941i	0.403113	+	0.324186i
$186$	−12.5242	+	6.61611i	−0.918318	+	0.485116i
$187$		−	13.6604i		−	0.998948i
$188$	−0.781422	−	1.35346i	−0.0569911	−	0.0987115i
$189$	15.4404	+	11.4095i	1.12313	+	0.829920i
$190$	3.37697	−	1.94969i	0.244991	−	0.141446i
$191$	17.3974	−	10.0444i	1.25883	−	0.726788i	0.285986	−	0.958234i	$-0.407679\pi$
$191$	17.3974	−	10.0444i	1.25883	−	0.726788i	0.972848	+	0.231446i	$0.0743456\pi$
$192$	1.46639	+	0.921793i	0.105828	+	0.0665246i
$193$	−0.877859	−	0.506832i	−0.0631896	−	0.0364826i	0.468072	−	0.883690i	$-0.344949\pi$
$193$	−0.877859	−	0.506832i	−0.0631896	−	0.0364826i	−0.531262	+	0.847208i	$0.678282\pi$
$194$	−8.39978	−	14.5488i	−0.603069	−	1.04455i
$195$	−11.6703	−	7.33609i	−0.835725	−	0.525348i
$196$	3.32563	+	5.76017i	0.237545	+	0.411440i
$197$	−0.964730	+	1.67096i	−0.0687342	+	0.119051i	−0.898344	−	0.439292i	$-0.855229\pi$
$197$	−0.964730	+	1.67096i	−0.0687342	+	0.119051i	0.829610	+	0.558343i	$0.188563\pi$
$198$	−5.99058	−	4.08773i	−0.425732	−	0.290502i
$199$		−	24.4339i		−	1.73207i	−0.499982	−	0.866036i	$-0.666660\pi$
$199$		−	24.4339i		−	1.73207i	0.499982	−	0.866036i	$-0.333340\pi$
$200$			3.66202i			0.258944i
$201$	−7.74811	−	4.87057i	−0.546510	−	0.343544i
$202$	−16.7694	+	9.68183i	−1.17989	+	0.681211i
$203$			27.7469i			1.94745i
$204$	4.57165	+	8.65408i	0.320080	+	0.605906i
$205$		−	10.8198i		−	0.755690i
$206$	−5.58163	+	9.66767i	−0.388891	+	0.673578i
$207$	1.05873	−	14.0542i	0.0735869	−	0.976836i
$208$		−	6.88028i		−	0.477062i
$209$	−7.05764	−	4.07473i	−0.488187	−	0.281855i
$210$	6.54525	−	3.45763i	0.451665	−	0.238599i
$211$	−5.76154	+	9.97929i	−0.396641	+	0.687003i	−0.993309	−	0.115486i	$-0.963158\pi$
$211$	−5.76154	+	9.97929i	−0.396641	+	0.687003i	0.596668	+	0.802488i	$0.296491\pi$
$212$	0.0906763	−	0.157056i	0.00622767	−	0.0107866i
$213$	−0.0527437	+	1.40229i	−0.00361394	+	0.0960832i
$214$	−10.6129	+	6.12736i	−0.725482	+	0.418857i
$215$	−1.02732	−	1.77937i	−0.0700624	−	0.121352i
$216$	5.16314	+	0.584805i	0.351307	+	0.0397909i
$217$	−26.1669	+	15.1075i	−1.77633	+	1.02556i
$218$	6.47129	−	11.2086i	0.438291	−	0.759143i
$219$	−9.00446	−	5.66032i	−0.608465	−	0.382489i
$220$	−2.42166	+	1.39815i	−0.163268	+	0.0942631i
$221$	19.4394	−	33.6700i	1.30763	−	2.26489i
$222$	3.43694	+	9.95929i	0.230672	+	0.668424i
$223$	−6.31017	−	10.9295i	−0.422560	−	0.731896i	0.573629	−	0.819115i	$-0.305535\pi$
$223$	−6.31017	−	10.9295i	−0.422560	−	0.731896i	−0.996189	+	0.0872195i	$0.972202\pi$
$224$	3.19976	+	1.84738i	0.213793	+	0.123433i
$225$	4.76281	+	9.89995i	0.317521	+	0.659996i
$226$	1.91548	+	3.31771i	0.127416	+	0.220691i
$227$	−7.44015	−	4.29557i	−0.493820	−	0.285107i	0.232338	−	0.972635i	$-0.425363\pi$
$227$	−7.44015	−	4.29557i	−0.493820	−	0.285107i	−0.726158	+	0.687528i	$0.758696\pi$
$228$	5.83479	+	0.219462i	0.386418	+	0.0145342i
$229$	1.84622			0.122002			0.0610008	−	0.998138i	$-0.480571\pi$
$229$	1.84622			0.122002			0.0610008	+	0.998138i	$0.480571\pi$
$230$	−4.70620	−	2.71713i	−0.310318	−	0.179162i
$231$	−13.0977	−	8.23336i	−0.861762	−	0.541715i
$232$	3.75490	+	6.50368i	0.246521	+	0.426987i
$233$	21.8364			1.43055			0.715276	−	0.698842i	$-0.246301\pi$
$233$	21.8364			1.43055			0.715276	+	0.698842i	$0.246301\pi$
$234$	−8.94847	−	18.6002i	−0.584980	−	1.21594i
$235$	−1.56557	+	0.903881i	−0.102126	+	0.0589627i
$236$	−3.21227	+	1.85460i	−0.209101	+	0.120724i
$237$	−9.44233	−	17.8742i	−0.613345	−	1.16105i
$238$	10.4391	+	18.0810i	0.676666	+	1.17202i
$239$	−0.513338	+	0.296376i	−0.0332051	+	0.0191710i	−0.516511	−	0.856281i	$-0.672769\pi$
$239$	−0.513338	+	0.296376i	−0.0332051	+	0.0191710i	0.483306	+	0.875452i	$0.339436\pi$
$240$	1.06625	−	1.69619i	0.0688261	−	0.109489i
$241$	6.95700	+	4.01662i	0.448140	+	0.258734i	0.707044	−	0.707169i	$-0.250028\pi$
$241$	6.95700	+	4.01662i	0.448140	+	0.258734i	−0.258905	+	0.965903i	$0.583362\pi$
$242$	−4.46517	−	2.57797i	−0.287032	−	0.165718i
$243$	14.7187	−	5.13419i	0.944205	−	0.329359i
$244$	0.931466	+	0.537782i	0.0596310	+	0.0344280i
$245$	6.66286	−	3.84680i	0.425674	−	0.245763i
$246$	8.62240	−	13.7165i	0.549744	−	0.874534i
$247$	−11.5970	−	20.0867i	−0.737902	−	1.27808i
$248$	−4.08889	+	7.08217i	−0.259645	+	0.449718i
$249$	6.33989	+	3.98534i	0.401774	+	0.252561i
$250$	10.0195			0.633686
$251$			8.29688i			0.523695i	0.965109	+	0.261847i	$0.0843317\pi$
$251$			8.29688i			0.523695i	−0.965109	+	0.261847i	$0.915668\pi$
$252$	11.0530	+	0.832641i	0.696272	+	0.0524514i
$253$			11.3572i			0.714022i
$254$	10.2820	+	5.93633i	0.645152	+	0.372479i
$255$	10.0103	−	5.28809i	0.626868	−	0.331153i
$256$	1.00000			0.0625000
$257$	−15.6337	+	9.02611i	−0.975203	+	0.563033i	−0.900818	−	0.434196i	$-0.857032\pi$
$257$	−15.6337	+	9.02611i	−0.975203	+	0.563033i	−0.0743842	+	0.997230i	$0.523699\pi$
$258$	0.115637	−	3.07442i	0.00719924	−	0.191405i
$259$	8.12491	+	20.9543i	0.504857	+	1.30204i
$260$	−7.95850			−0.493565
$261$	18.6097	+	12.6985i	1.15191	+	0.786019i
$262$	5.45056	+	9.44064i	0.336737	+	0.583245i
$263$	−6.12579	+	10.6102i	−0.377732	+	0.654252i	−0.990732	−	0.135831i	$-0.956629\pi$
$263$	−6.12579	+	10.6102i	−0.377732	+	0.654252i	0.612999	+	0.790083i	$0.289963\pi$
$264$	−4.18419	−	0.157378i	−0.257519	−	0.00968597i
$265$	−0.181669	−	0.104886i	−0.0111598	−	0.00644312i
$266$	12.4554			0.763690
$267$	−12.1565	−	23.0121i	−0.743968	−	1.40832i
$268$	−5.28380			−0.322760
$269$	−24.2530			−1.47873			−0.739365	−	0.673304i	$-0.764874\pi$
$269$	−24.2530			−1.47873			−0.739365	+	0.673304i	$0.764874\pi$
$270$	0.676451	−	5.97227i	0.0411675	−	0.363461i
$271$	−3.25056	+	5.63014i	−0.197458	+	0.342007i	−0.947703	−	0.319152i	$-0.896602\pi$
$271$	−3.25056	+	5.63014i	−0.197458	+	0.342007i	0.750246	+	0.661159i	$0.229935\pi$
$272$	4.89370	+	2.82538i	0.296724	+	0.171314i
$273$	−20.5665	−	38.9320i	−1.24474	−	2.35627i
$274$	−3.77422	+	2.17905i	−0.228009	+	0.131641i
$275$	−4.42637	−	7.66670i	−0.266920	−	0.462319i
$276$	−3.80086	−	7.19497i	−0.228785	−	0.433086i
$277$	−14.1713	−	8.18179i	−0.851469	−	0.491596i	0.00967690	−	0.999953i	$-0.496920\pi$
$277$	−14.1713	−	8.18179i	−0.851469	−	0.491596i	−0.861146	+	0.508357i	$0.830253\pi$
$278$	12.1528	−	7.01644i	0.728879	−	0.420818i
$279$	−1.84292	+	24.4640i	−0.110333	+	1.46462i
$280$	2.13689	−	3.70120i	0.127704	−	0.221189i
$281$			28.5899i			1.70553i	0.522294	+	0.852765i	$0.325076\pi$
$281$			28.5899i			1.70553i	−0.522294	+	0.852765i	$0.674924\pi$
$282$	−2.70501	−	0.101743i	−0.161081	−	0.00605869i
$283$		−	5.74355i		−	0.341418i	−0.985321	−	0.170709i	$-0.945394\pi$
$283$		−	5.74355i		−	0.341418i	0.985321	−	0.170709i	$-0.0546059\pi$
$284$	0.405092	+	0.701640i	0.0240378	+	0.0416347i
$285$	0.253854	−	6.74917i	0.0150370	−	0.399786i
$286$	8.31637	+	14.4044i	0.491757	+	0.851748i
$287$	17.2803	−	29.9304i	1.02002	−	1.76673i
$288$	2.70341	−	1.30060i	0.159300	−	0.0766384i
$289$	7.46551	+	12.9306i	0.439147	+	0.760626i
$290$	7.52288	−	4.34334i	0.441759	−	0.255050i
$291$	−29.0771	−	1.09367i	−1.70453	−	0.0641119i
$292$	−6.14056			−0.359349
$293$	−15.0815			−0.881070			−0.440535	−	0.897736i	$-0.645211\pi$
$293$	−15.0815			−0.881070			−0.440535	+	0.897736i	$0.645211\pi$
$294$	11.5122	+	0.433004i	0.671405	+	0.0252533i
$295$	2.14524	+	3.71567i	0.124901	+	0.216335i
$296$	4.74010	+	3.81202i	0.275513	+	0.221569i
$297$	−11.5163	+	5.01648i	−0.668242	+	0.291086i
$298$	4.22726	+	2.44061i	0.244879	+	0.141381i
$299$	−16.1618	+	27.9931i	−0.934663	+	1.61888i
$300$	5.36994	+	3.37562i	0.310034	+	0.194891i
$301$		−	6.56290i		−	0.378279i
$302$	−20.3552	−	11.7521i	−1.17131	−	0.676256i
$303$	−1.26059	+	33.5151i	−0.0724192	+	1.92539i
$304$	2.91946	−	1.68555i	0.167442	−	0.0966728i
$305$	0.622060	−	1.07744i	0.0356190	−	0.0616940i
$306$	16.9044	+	1.27344i	0.966358	+	0.0727975i
$307$	−17.4774			−0.997490			−0.498745	−	0.866749i	$-0.666206\pi$
$307$	−17.4774			−0.997490			−0.498745	+	0.866749i	$0.666206\pi$
$308$	−8.93190			−0.508942
$309$	9.03146	+	17.0964i	0.513782	+	0.972582i
$310$	8.19203	+	4.72967i	0.465276	+	0.268627i
$311$	18.3890	−	10.6169i	1.04275	−	0.602030i	0.122137	−	0.992513i	$-0.461025\pi$
$311$	18.3890	−	10.6169i	1.04275	−	0.602030i	0.920610	+	0.390483i	$0.127692\pi$
$312$	−10.0892	−	6.34219i	−0.571187	−	0.359056i
$313$		−	18.1467i		−	1.02571i	−0.858475	−	0.512856i	$-0.828588\pi$
$313$		−	18.1467i		−	1.02571i	0.858475	−	0.512856i	$-0.171412\pi$
$314$	−3.09186	+	1.78509i	−0.174484	+	0.100738i
$315$	0.963126	−	12.7851i	0.0542660	−	0.720359i
$316$	−10.1075	−	5.83555i	−0.568590	−	0.328276i
$317$	−0.894372			−0.0502329			−0.0251165	−	0.999685i	$-0.507996\pi$
$317$	−0.894372			−0.0502329			−0.0251165	+	0.999685i	$0.507996\pi$
$318$	−0.146720	−	0.277740i	−0.00822768	−	0.0155749i
$319$	−15.7223	−	9.07728i	−0.880281	−	0.508230i
$320$		−	1.15671i		−	0.0646622i
$321$	−0.797794	+	21.2108i	−0.0445285	+	1.18387i
$322$	−8.67903	−	15.0325i	−0.483663	−	0.837729i
$323$	19.0492			1.05993
$324$	5.61690	−	7.03210i	0.312050	−	0.390672i
$325$		−	25.1957i		−	1.39761i
$326$	−2.14310	+	3.71196i	−0.118696	+	0.205587i
$327$	−10.4710	−	19.8215i	−0.579048	−	1.09613i
$328$		−	9.35395i		−	0.516485i
$329$	−5.77434			−0.318350
$330$	−0.182041	+	4.83990i	−0.0100211	+	0.266428i
$331$		−	26.8173i		−	1.47401i	−0.675885	−	0.737007i	$-0.736238\pi$
$331$		−	26.8173i		−	1.47401i	0.675885	−	0.737007i	$-0.263762\pi$
$332$	4.32347			0.237281
$333$	17.7723	+	4.14051i	0.973918	+	0.226899i
$334$	−3.73933			−0.204607
$335$			6.11184i			0.333926i
$336$	5.65849	−	2.98919i	0.308696	−	0.163074i
$337$	22.6050			1.23137			0.615687	−	0.787991i	$-0.288879\pi$
$337$	22.6050			1.23137			0.615687	+	0.787991i	$0.288879\pi$
$338$			34.3382i			1.86775i
$339$	6.63074	+	0.249400i	0.360132	+	0.0135455i
$340$	3.26815	−	5.66060i	0.177240	−	0.306989i
$341$		−	19.7694i		−	1.07057i
$342$	5.70028	−	8.35377i	0.308236	−	0.451720i
$343$	−1.28849			−0.0695717
$344$	−0.888135	−	1.53830i	−0.0478850	−	0.0829393i
$345$	−8.32251	+	4.39650i	−0.448069	+	0.236699i
$346$			3.77995i			0.203212i
$347$	22.6426	+	13.0727i	1.21552	+	0.701780i	0.963956	−	0.266061i	$-0.0857222\pi$
$347$	22.6426	+	13.0727i	1.21552	+	0.701780i	0.251563	+	0.967841i	$0.419056\pi$
$348$	12.9982	+	0.488895i	0.696775	+	0.0262075i
$349$	−3.51868			−0.188351			−0.0941753	−	0.995556i	$-0.530021\pi$
$349$	−3.51868			−0.188351			−0.0941753	+	0.995556i	$0.530021\pi$
$350$	11.7176	+	6.76514i	0.626330	+	0.361612i
$351$	−35.5238	−	4.02362i	−1.89612	−	0.214765i
$352$	−2.09357	+	1.20873i	−0.111588	+	0.0644253i
$353$			11.9475i			0.635901i	0.948107	+	0.317951i	$0.102995\pi$
$353$			11.9475i			0.635901i	−0.948107	+	0.317951i	$0.897005\pi$
$354$	−0.241473	+	6.42000i	−0.0128342	+	0.341219i
$355$	0.811595	−	0.468575i	0.0430750	−	0.0248694i
$356$	−13.0129	−	7.51299i	−0.689681	−	0.398188i
$357$	36.1365	+	1.35919i	1.91255	+	0.0719360i
$358$	2.37692			0.125624
$359$	1.30369			0.0688063			0.0344032	−	0.999408i	$-0.489047\pi$
$359$	1.30369			0.0688063			0.0344032	+	0.999408i	$0.489047\pi$
$360$	−1.50442	−	3.12707i	−0.0792897	−	0.164811i
$361$	−3.81785	+	6.61272i	−0.200940	+	0.348038i
$362$	13.7179	−	7.92005i	0.720998	−	0.416269i
$363$	−7.89626	+	4.17133i	−0.414446	+	0.218938i
$364$	−22.0152	−	12.7105i	−1.15391	−	0.666211i
$365$			7.10286i			0.371781i
$366$	1.64722	−	0.870169i	0.0861014	−	0.0454845i
$367$	−11.3509	+	19.6603i	−0.592510	+	1.02626i	0.401383	+	0.915910i	$0.368530\pi$
$367$	−11.3509	+	19.6603i	−0.592510	+	1.02626i	−0.993893	+	0.110347i	$0.964804\pi$
$368$	−4.06860	−	2.34901i	−0.212091	−	0.122451i
$369$	−12.1657	−	25.2876i	−0.633322	−	1.31642i
$370$	4.40941	−	5.48293i	0.229234	−	0.285044i
$371$	−0.335027	−	0.580284i	−0.0173938	−	0.0301269i
$372$	6.61611	+	12.5242i	0.343029	+	0.649349i
$373$	15.9364			0.825154			0.412577	−	0.910923i	$-0.364629\pi$
$373$	15.9364			0.825154			0.412577	+	0.910923i	$0.364629\pi$
$374$	−13.6604			−0.706363
$375$	9.23587	−	14.6924i	0.476938	−	0.758714i
$376$	−1.35346	+	0.781422i	−0.0697995	+	0.0402988i
$377$	−25.8348	−	44.7471i	−1.33056	−	2.30459i
$378$	11.4095	−	15.4404i	0.586842	−	0.794170i
$379$	−4.69510	+	8.13215i	−0.241171	+	0.417721i	−0.961048	−	0.276381i	$-0.910865\pi$
$379$	−4.69510	+	8.13215i	−0.241171	+	0.417721i	0.719877	+	0.694102i	$0.244198\pi$
$380$	−1.94969	−	3.37697i	−0.100017	−	0.173235i
$381$	18.1829	−	9.60540i	0.931537	−	0.492099i
$382$	−10.0444	−	17.3974i	−0.513917	−	0.890130i
$383$		−	21.3223i		−	1.08952i	−0.838593	−	0.544758i	$-0.816621\pi$
$383$		−	21.3223i		−	1.08952i	0.838593	−	0.544758i	$-0.183379\pi$
$384$	0.921793	−	1.46639i	0.0470400	−	0.0748314i
$385$			10.3316i			0.526549i
$386$	−0.506832	+	0.877859i	−0.0257971	+	0.0446818i
$387$	−4.40170	−	3.00354i	−0.223751	−	0.152679i
$388$	−14.5488	+	8.39978i	−0.738605	+	0.426434i
$389$	13.1041	+	7.56564i	0.664403	+	0.383593i	0.793953	−	0.607980i	$-0.208020\pi$
$389$	13.1041	+	7.56564i	0.664403	+	0.383593i	−0.129550	+	0.991573i	$0.541353\pi$
$390$	−7.33609	+	11.6703i	−0.371477	+	0.590947i
$391$	−13.2737	−	22.9907i	−0.671278	−	1.16269i
$392$	5.76017	−	3.32563i	0.290932	−	0.167970i
$393$	18.8679	+	0.709673i	0.951762	+	0.0357983i
$394$	1.67096	+	0.964730i	0.0841818	+	0.0486024i
$395$	−6.75006	+	11.6914i	−0.339632	+	0.588260i
$396$	−4.08773	+	5.99058i	−0.205416	+	0.301038i
$397$	−9.94610			−0.499181			−0.249590	−	0.968352i	$-0.580296\pi$
$397$	−9.94610			−0.499181			−0.249590	+	0.968352i	$0.580296\pi$
$398$	−24.4339			−1.22476
$399$	11.4813	−	18.2645i	0.574784	−	0.914367i
$400$	3.66202			0.183101
$401$	18.0046	+	10.3949i	0.899106	+	0.519099i	0.876910	−	0.480655i	$-0.159601\pi$
$401$	18.0046	+	10.3949i	0.899106	+	0.519099i	0.0221958	+	0.999754i	$0.492934\pi$
$402$	−4.87057	+	7.74811i	−0.242922	+	0.386441i
$403$	28.1327	−	48.7273i	1.40139	−	2.42728i
$404$	9.68183	+	16.7694i	0.481689	+	0.834310i
$405$	−8.13412	−	6.49713i	−0.404188	−	0.322845i
$406$	27.7469			1.37706
$407$	−14.5314	−	2.25127i	−0.720296	−	0.111591i
$408$	8.65408	−	4.57165i	0.428441	−	0.226331i
$409$	−9.50078	+	5.48528i	−0.469783	+	0.271230i	−0.716149	−	0.697947i	$-0.754097\pi$
$409$	−9.50078	+	5.48528i	−0.469783	+	0.271230i	0.246366	+	0.969177i	$0.420764\pi$
$410$	−10.8198			−0.534353
$411$	−0.283716	+	7.54311i	−0.0139947	+	0.372074i
$412$	9.66767	+	5.58163i	0.476292	+	0.274987i
$413$			13.7046i			0.674362i
$414$	−14.0542	−	1.05873i	−0.690728	−	0.0520338i
$415$		−	5.00101i		−	0.245490i
$416$	−6.88028			−0.337333
$417$	0.913555	−	24.2885i	0.0447370	−	1.18941i
$418$	−4.07473	+	7.05764i	−0.199302	+	0.345200i
$419$	9.99074	+	17.3045i	0.488080	+	0.845379i	0.999906	−	0.0137101i	$-0.00436418\pi$
$419$	9.99074	+	17.3045i	0.488080	+	0.845379i	−0.511826	+	0.859089i	$0.671031\pi$
$420$	−3.45763	−	6.54525i	−0.168715	−	0.319375i
$421$	−19.8763	+	11.4756i	−0.968714	+	0.559287i	−0.898844	−	0.438269i	$-0.855592\pi$
$421$	−19.8763	+	11.4756i	−0.968714	+	0.559287i	−0.0698697	+	0.997556i	$0.522258\pi$
$422$	9.97929	+	5.76154i	0.485784	+	0.280468i
$423$	−2.64266	+	3.87282i	−0.128490	+	0.188303i
$424$	−0.157056	−	0.0906763i	−0.00762731	−	0.00440363i
$425$	17.9208	+	10.3466i	0.869286	+	0.501883i
$426$	1.40229	+	0.0527437i	0.0679411	+	0.00255544i
$427$	3.44155	−	1.98698i	0.166548	−	0.0961566i
$428$	6.12736	+	10.6129i	0.296177	+	0.512993i
$429$	28.7884	+	1.08281i	1.38992	+	0.0522784i
$430$	−1.77937	+	1.02732i	−0.0858086	+	0.0495416i
$431$	32.1727	−	18.5749i	1.54971	−	0.894723i	0.551542	−	0.834147i	$-0.314040\pi$
$431$	32.1727	−	18.5749i	1.54971	−	0.894723i	0.998164	−	0.0605759i	$-0.0192937\pi$
$432$	0.584805	−	5.16314i	0.0281364	−	0.248412i
$433$	−5.45037			−0.261928			−0.130964	−	0.991387i	$-0.541807\pi$
$433$	−5.45037			−0.261928			−0.130964	+	0.991387i	$0.541807\pi$
$434$	15.1075	+	26.1669i	0.725182	+	1.25605i
$435$	0.565511	−	15.0351i	0.0271142	−	0.720880i
$436$	−11.2086	−	6.47129i	−0.536795	−	0.309919i
$437$	−15.8375			−0.757609
$438$	−5.66032	+	9.00446i	−0.270461	+	0.430250i
$439$	10.5689	+	6.10195i	0.504426	+	0.291230i	0.730539	−	0.682871i	$-0.239269\pi$
$439$	10.5689	+	6.10195i	0.504426	+	0.291230i	−0.226114	+	0.974101i	$0.572602\pi$
$440$	1.39815	+	2.42166i	0.0666541	+	0.115448i
$441$	11.2468	−	16.4822i	0.535562	−	0.784868i
$442$	−33.6700	−	19.4394i	−1.60152	−	0.924637i
$443$	−7.46601	−	12.9315i	−0.354721	−	0.614394i	0.632349	−	0.774683i	$-0.282091\pi$
$443$	−7.46601	−	12.9315i	−0.354721	−	0.614394i	−0.987070	+	0.160289i	$0.948757\pi$
$444$	9.95929	−	3.43694i	0.472647	−	0.163110i
$445$	−8.69037	+	15.0522i	−0.411963	+	0.713541i
$446$	−10.9295	+	6.31017i	−0.517528	+	0.298795i
$447$	7.47554	−	3.94908i	0.353581	−	0.186785i
$448$	1.84738	−	3.19976i	0.0872806	−	0.151174i
$449$	−17.4504	+	10.0750i	−0.823536	+	0.475469i	−0.851634	−	0.524136i	$-0.824388\pi$
$449$	−17.4504	+	10.0750i	−0.823536	+	0.475469i	0.0280980	+	0.999605i	$0.491055\pi$
$450$	9.89995	−	4.76281i	0.466688	−	0.224521i
$451$	11.3064	+	19.5832i	0.532395	+	0.922136i
$452$	3.31771	−	1.91548i	0.156052	−	0.0900967i
$453$	−35.9964	+	19.0157i	−1.69126	+	0.893434i
$454$	−4.29557	+	7.44015i	−0.201601	+	0.349184i
$455$	−14.7024	+	25.4653i	−0.689259	+	1.19383i
$456$	0.219462	−	5.83479i	0.0102772	−	0.273239i
$457$	18.2722	+	10.5495i	0.854739	+	0.493484i	0.862247	−	0.506488i	$-0.169057\pi$
$457$	18.2722	+	10.5495i	0.854739	+	0.493484i	−0.00750782	+	0.999972i	$0.502390\pi$
$458$		−	1.84622i		−	0.0862681i
$459$	17.4497	−	23.6145i	0.814481	−	1.10223i
$460$	−2.71713	+	4.70620i	−0.126687	+	0.219428i
$461$		−	17.9167i		−	0.834463i	−0.908800	−	0.417231i	$-0.863000\pi$
$461$		−	17.9167i		−	0.834463i	0.908800	−	0.417231i	$-0.137000\pi$
$462$	−8.23336	+	13.0977i	−0.383051	+	0.609358i
$463$		−	10.2946i		−	0.478432i	−0.970966	−	0.239216i	$-0.923110\pi$
$463$		−	10.2946i		−	0.478432i	0.970966	−	0.239216i	$-0.0768905\pi$
$464$	6.50368	−	3.75490i	0.301926	−	0.174317i
$465$	14.4869	−	7.65293i	0.671813	−	0.354896i
$466$		−	21.8364i		−	1.01155i
$467$			25.3149i			1.17143i	0.810516	+	0.585716i	$0.199187\pi$
$467$			25.3149i			1.17143i	−0.810516	+	0.585716i	$0.800813\pi$
$468$	−18.6002	+	8.94847i	−0.859797	+	0.413643i
$469$	−9.76120	+	16.9069i	−0.450730	+	0.780688i
$470$	0.903881	+	1.56557i	0.0416929	+	0.0722143i
$471$	−0.232422	+	6.17936i	−0.0107094	+	0.284730i
$472$	1.85460	+	3.21227i	0.0853651	+	0.147857i
$473$	3.71875	+	2.14702i	0.170988	+	0.0987202i
$474$	−17.8742	+	9.44233i	−0.820989	+	0.433700i
$475$	10.6911	−	6.17251i	0.490541	−	0.283214i
$476$	18.0810	−	10.4391i	0.828743	−	0.478475i
$477$	−0.542521	−	0.0408691i	−0.0248403	−	0.00187127i
$478$	0.296376	+	0.513338i	0.0135559	+	0.0234796i
$479$			20.8174i			0.951171i	0.879669	+	0.475586i	$0.157764\pi$
$479$			20.8174i			0.951171i	−0.879669	+	0.475586i	$0.842236\pi$
$480$	−1.69619	−	1.06625i	−0.0774202	−	0.0486674i
$481$	−32.6132	−	26.2278i	−1.48703	−	1.19588i
$482$	4.01662	−	6.95700i	0.182952	−	0.316883i
$483$	−30.0438	−	1.13003i	−1.36704	−	0.0514180i
$484$	−2.57797	+	4.46517i	−0.117180	+	0.202962i
$485$	9.71613	+	16.8288i	0.441187	+	0.764158i
$486$	−5.13419	−	14.7187i	−0.232892	−	0.667654i
$487$		−	34.2104i		−	1.55022i	−0.631825	−	0.775111i	$-0.717694\pi$
$487$		−	34.2104i		−	1.55022i	0.631825	−	0.775111i	$-0.282306\pi$
$488$	0.537782	−	0.931466i	0.0243443	−	0.0421655i
$489$	3.46769	+	6.56429i	0.156814	+	0.296847i
$490$	−3.84680	−	6.66286i	−0.173781	−	0.300997i
$491$	−6.76834	+	11.7231i	−0.305451	+	0.529057i	−0.977362	−	0.211576i	$-0.932141\pi$
$491$	−6.76834	+	11.7231i	−0.305451	+	0.529057i	0.671911	+	0.740632i	$0.265474\pi$
$492$	−13.7165	−	8.62240i	−0.618389	−	0.388728i
$493$	42.4360			1.91122
$494$	−20.0867	+	11.5970i	−0.903742	+	0.521776i
$495$	6.92938	+	4.72833i	0.311452	+	0.212523i
$496$	7.08217	+	4.08889i	0.317999	+	0.183597i
$497$	2.99344			0.134274
$498$	3.98534	−	6.33989i	0.178587	−	0.284097i
$499$			24.9090i			1.11508i	0.830151	+	0.557539i	$0.188254\pi$
$499$			24.9090i			1.11508i	−0.830151	+	0.557539i	$0.811746\pi$
$500$		−	10.0195i		−	0.448084i
$501$	−3.44688	+	5.48331i	−0.153995	+	0.244976i
$502$	8.29688			0.370308
$503$	−21.7108	−	12.5347i	−0.968037	−	0.558896i	−0.0693996	−	0.997589i	$-0.522108\pi$
$503$	−21.7108	−	12.5347i	−0.968037	−	0.558896i	−0.898637	+	0.438693i	$0.855442\pi$
$504$	0.832641	−	11.0530i	0.0370888	−	0.492338i
$505$	19.3974	−	11.1991i	0.863173	−	0.498353i
$506$	11.3572			0.504890
$507$	50.3532	+	31.6527i	2.23627	+	1.40575i
$508$	5.93633	−	10.2820i	0.263382	−	0.456191i
$509$	−18.5844	−	32.1892i	−0.823740	−	1.42676i	−0.902879	−	0.429896i	$-0.858550\pi$
$509$	−18.5844	−	32.1892i	−0.823740	−	1.42676i	0.0791387	−	0.996864i	$-0.474783\pi$
$510$	−5.28809	−	10.0103i	−0.234160	−	0.443262i
$511$	−11.3440	+	19.6483i	−0.501827	+	0.869190i
$512$		−	1.00000i		−	0.0441942i
$513$	−6.99541	−	16.0593i	−0.308855	−	0.709034i
$514$	9.02611	+	15.6337i	0.398125	+	0.689572i
$515$	6.45634	−	11.1827i	0.284500	−	0.492769i
$516$	−3.07442	−	0.115637i	−0.135344	−	0.00509063i
$517$	1.88905	−	3.27193i	0.0830803	−	0.143899i
$518$	20.9543	−	8.12491i	0.920679	−	0.356988i
$519$	5.54288	+	3.48433i	0.243306	+	0.152945i
$520$			7.95850i			0.349003i
$521$	0.999460	+	1.73112i	0.0437872	+	0.0758416i	0.887088	−	0.461600i	$-0.152724\pi$
$521$	0.999460	+	1.73112i	0.0437872	+	0.0758416i	−0.843301	+	0.537441i	$0.819391\pi$
$522$	12.6985	−	18.6097i	0.555799	−	0.814525i
$523$	−18.6165	+	10.7482i	−0.814042	+	0.469988i	−0.848358	−	0.529423i	$-0.822408\pi$
$523$	−18.6165	+	10.7482i	−0.814042	+	0.469988i	0.0343153	+	0.999411i	$0.489075\pi$
$524$	9.44064	−	5.45056i	0.412416	−	0.238109i
$525$	20.7215	−	10.9465i	0.904360	−	0.477743i
$526$	10.6102	+	6.12579i	0.462626	+	0.267097i
$527$	23.1053	+	40.0196i	1.00648	+	1.74328i
$528$	−0.157378	+	4.18419i	−0.00684901	+	0.182093i
$529$	−0.464322	−	0.804230i	−0.0201879	−	0.0349665i
$530$	−0.104886	+	0.181669i	−0.00455597	+	0.00789118i
$531$	9.19163	+	6.27200i	0.398883	+	0.272182i
$532$		−	12.4554i		−	0.540010i
$533$			64.3578i			2.78764i
$534$	−23.0121	+	12.1565i	−0.995833	+	0.526065i
$535$	12.2761	−	7.08759i	0.530740	−	0.306423i
$536$			5.28380i			0.228226i
$537$	2.19103	−	3.48549i	0.0945499	−	0.150410i
$538$			24.2530i			1.04562i
$539$	−8.03955	+	13.9249i	−0.346288	+	0.599789i
$540$	−5.97227	−	0.676451i	−0.257005	−	0.0291098i
$541$			5.27769i			0.226906i	0.993543	+	0.113453i	$0.0361911\pi$
$541$			5.27769i			0.226906i	−0.993543	+	0.113453i	$0.963809\pi$
$542$	5.63014	+	3.25056i	0.241835	+	0.139624i
$543$	1.03121	−	27.4165i	0.0442533	−	1.17655i
$544$	2.82538	−	4.89370i	0.121137	−	0.209815i
$545$	−7.48543	+	12.9651i	−0.320640	+	0.555366i
$546$	−38.9320	+	20.5665i	−1.66614	+	0.880163i
$547$	24.7498	−	14.2893i	1.05822	−	0.610966i	0.133284	−	0.991078i	$-0.457448\pi$
$547$	24.7498	−	14.2893i	1.05822	−	0.610966i	0.924941	+	0.380112i	$0.124114\pi$
$548$	2.17905	+	3.77422i	0.0930843	+	0.161227i
$549$	0.242386	−	3.21758i	0.0103448	−	0.137323i
$550$	−7.66670	+	4.42637i	−0.326909	+	0.188741i
$551$	12.6581	−	21.9245i	0.539254	−	0.934016i
$552$	−7.19497	+	3.80086i	−0.306238	+	0.161775i
$553$	−37.3447	+	21.5610i	−1.58806	+	0.916866i
$554$	−8.18179	+	14.1713i	−0.347611	+	0.602080i
$555$	−3.97555	−	11.5200i	−0.168753	−	0.488998i
$556$	−7.01644	−	12.1528i	−0.297563	−	0.515395i
$557$	−38.0645	−	21.9765i	−1.61284	−	0.931176i	−0.988707	−	0.149862i	$-0.952117\pi$
$557$	−38.0645	−	21.9765i	−1.61284	−	0.931176i	−0.624138	−	0.781314i	$-0.714550\pi$
$558$	24.4640	+	1.84292i	1.03564	+	0.0780170i
$559$	6.11062	+	10.5839i	0.258452	+	0.447651i
$560$	−3.70120	−	2.13689i	−0.156404	−	0.0903000i
$561$	−12.5921	+	20.0315i	−0.531638	+	0.845730i
$562$	28.5899			1.20599
$563$	−28.7838	−	16.6184i	−1.21309	−	0.700380i	−0.249662	−	0.968333i	$-0.580320\pi$
$563$	−28.7838	−	16.6184i	−1.21309	−	0.700380i	−0.963432	+	0.267953i	$0.913653\pi$
$564$	−0.101743	+	2.70501i	−0.00428414	+	0.113902i
$565$	−2.21566	−	3.83764i	−0.0932136	−	0.161451i
$566$	−5.74355			−0.241419
$567$	−12.1245	−	30.9637i	−0.509181	−	1.30035i
$568$	0.701640	−	0.405092i	0.0294401	−	0.0169973i
$569$	13.8164	−	7.97692i	0.579215	−	0.334410i	−0.181606	−	0.983371i	$-0.558130\pi$
$569$	13.8164	−	7.97692i	0.579215	−	0.334410i	0.760821	+	0.648961i	$0.224796\pi$
$570$	−6.74917	−	0.253854i	−0.282692	−	0.0106328i
$571$	20.6148	+	35.7059i	0.862703	+	1.49425i	0.869310	+	0.494267i	$0.164564\pi$
$571$	20.6148	+	35.7059i	0.862703	+	1.49425i	−0.00660710	+	0.999978i	$0.502103\pi$
$572$	14.4044	−	8.31637i	0.602277	−	0.347725i
$573$	−34.7703	−	1.30780i	−1.45255	−	0.0546342i
$574$	−29.9304	−	17.2803i	−1.24927	−	0.721266i
$575$	−14.8993	−	8.60211i	−0.621343	−	0.358733i
$576$	−1.30060	−	2.70341i	−0.0541915	−	0.112642i
$577$	−10.1448	−	5.85711i	−0.422334	−	0.243835i	0.273741	−	0.961803i	$-0.411739\pi$
$577$	−10.1448	−	5.85711i	−0.422334	−	0.243835i	−0.696075	+	0.717969i	$0.745072\pi$
$578$	12.9306	−	7.46551i	0.537843	−	0.310524i
$579$	0.820089	+	1.55242i	0.0340817	+	0.0645162i
$580$	−4.34334	−	7.52288i	−0.180347	−	0.312371i
$581$	7.98709	−	13.8340i	0.331360	−	0.573933i
$582$	−1.09367	+	29.0771i	−0.0453340	+	1.20529i
$583$	0.438411			0.0181571
$584$			6.14056i			0.254098i
$585$	10.3508	+	21.5151i	0.427953	+	0.889541i
$586$			15.0815i			0.623010i
$587$	8.59999	+	4.96520i	0.354959	+	0.204936i	0.666867	−	0.745176i	$-0.267635\pi$
$587$	8.59999	+	4.96520i	0.354959	+	0.204936i	−0.311908	+	0.950112i	$0.600968\pi$
$588$	0.433004	−	11.5122i	0.0178568	−	0.474755i
$589$	27.5681			1.13592
$590$	3.71567	−	2.14524i	0.152972	−	0.0883183i
$591$	2.95495	−	1.56100i	0.121550	−	0.0642110i
$592$	3.81202	−	4.74010i	0.156673	−	0.194817i
$593$	−13.4398			−0.551908			−0.275954	−	0.961171i	$-0.588994\pi$
$593$	−13.4398			−0.551908			−0.275954	+	0.961171i	$0.588994\pi$
$594$	5.01648	+	11.5163i	0.205829	+	0.472519i
$595$	−12.0750	−	20.9146i	−0.495028	−	0.857414i
$596$	2.44061	−	4.22726i	0.0999713	−	0.173155i
$597$	−22.5230	+	35.8296i	−0.921804	+	1.46641i
$598$	27.9931	+	16.1618i	1.14472	+	0.660906i
$599$	34.9586			1.42837			0.714186	−	0.699956i	$-0.246797\pi$
$599$	34.9586			1.42837			0.714186	+	0.699956i	$0.246797\pi$
$600$	3.37562	−	5.36994i	0.137809	−	0.219227i
$601$	−2.14582			−0.0875296			−0.0437648	−	0.999042i	$-0.513935\pi$
$601$	−2.14582			−0.0875296			−0.0437648	+	0.999042i	$0.513935\pi$
$602$	−6.56290			−0.267484
$603$	6.87210	+	14.2843i	0.279854	+	0.581702i
$604$	−11.7521	+	20.3552i	−0.478185	+	0.828241i
$605$	5.16492	+	2.98197i	0.209984	+	0.121234i
$606$	33.5151	+	1.26059i	1.36146	+	0.0512081i
$607$	2.73920	−	1.58148i	0.111181	−	0.0641902i	−0.443378	−	0.896335i	$-0.646220\pi$
$607$	2.73920	−	1.58148i	0.111181	−	0.0641902i	0.554559	+	0.832144i	$0.312887\pi$
$608$	−1.68555	−	2.91946i	−0.0683580	−	0.118400i
$609$	25.5769	−	40.6878i	1.03643	−	1.64875i
$610$	−1.07744	−	0.622060i	−0.0436242	−	0.0251865i
$611$	9.31221	−	5.37640i	0.376732	−	0.217506i
$612$	1.27344	−	16.9044i	0.0514756	−	0.683318i
$613$	−6.59279	+	11.4191i	−0.266280	+	0.461211i	−0.967898	−	0.251342i	$-0.919128\pi$
$613$	−6.59279	+	11.4191i	−0.266280	+	0.461211i	0.701618	+	0.712553i	$0.252461\pi$
$614$			17.4774i			0.705332i
$615$	−9.97364	+	15.8661i	−0.402176	+	0.639782i
$616$			8.93190i			0.359877i
$617$	20.5014	+	35.5095i	0.825356	+	1.42956i	0.901647	+	0.432474i	$0.142359\pi$
$617$	20.5014	+	35.5095i	0.825356	+	1.42956i	−0.0762903	+	0.997086i	$0.524308\pi$
$618$	17.0964	−	9.03146i	0.687719	−	0.363299i
$619$	6.82535	+	11.8218i	0.274334	+	0.475160i	0.969967	−	0.243237i	$-0.0782093\pi$
$619$	6.82535	+	11.8218i	0.274334	+	0.475160i	−0.695633	+	0.718397i	$0.744876\pi$
$620$	4.72967	−	8.19203i	0.189948	−	0.329000i
$621$	−14.5076	+	19.6330i	−0.582170	+	0.787847i
$622$	−10.6169	−	18.3890i	−0.425700	−	0.737334i
$623$	−48.0795	+	27.7587i	−1.92626	+	1.11213i
$624$	−6.34219	+	10.0892i	−0.253891	+	0.403890i
$625$	6.72045			0.268818
$626$	−18.1467			−0.725288
$627$	6.59319	+	12.4808i	0.263307	+	0.498436i
$628$	1.78509	+	3.09186i	0.0712328	+	0.123379i
$629$	32.0474	−	12.4262i	1.27781	−	0.495465i
$630$	−12.7851	−	0.963126i	−0.509371	−	0.0383718i
$631$	−4.87333	−	2.81362i	−0.194004	−	0.112008i	0.399852	−	0.916580i	$-0.369062\pi$
$631$	−4.87333	−	2.81362i	−0.194004	−	0.112008i	−0.593856	+	0.804572i	$0.702395\pi$
$632$	−5.83555	+	10.1075i	−0.232126	+	0.402054i
$633$	17.6475	−	9.32258i	0.701425	−	0.370539i
$634$			0.894372i			0.0355200i
$635$	−11.8934	−	6.86663i	−0.471973	−	0.272494i
$636$	−0.277740	+	0.146720i	−0.0110131	+	0.00581785i
$637$	−39.6316	+	22.8813i	−1.57026	+	0.906590i
$638$	−9.07728	+	15.7223i	−0.359373	+	0.622452i
$639$	1.36996	−	2.00768i	0.0541948	−	0.0794226i
$640$	−1.15671			−0.0457231
$641$	29.7044			1.17325			0.586626	−	0.809858i	$-0.300456\pi$
$641$	29.7044			1.17325			0.586626	+	0.809858i	$0.300456\pi$
$642$	21.2108	+	0.797794i	0.837123	+	0.0314864i
$643$	26.0040	+	15.0134i	1.02550	+	0.592072i	0.915692	−	0.401881i	$-0.131643\pi$
$643$	26.0040	+	15.0134i	1.02550	+	0.592072i	0.109807	+	0.993953i	$0.464977\pi$
$644$	−15.0325	+	8.67903i	−0.592364	+	0.342002i
$645$	−0.133759	+	3.55622i	−0.00526674	+	0.140026i
$646$		−	19.0492i		−	0.749482i
$647$	−6.79470	+	3.92292i	−0.267127	+	0.154226i	−0.627581	−	0.778551i	$-0.715955\pi$
$647$	−6.79470	+	3.92292i	−0.267127	+	0.154226i	0.360454	+	0.932777i	$0.382622\pi$
$648$	−7.03210	−	5.61690i	−0.276247	−	0.220652i
$649$	−7.76550	−	4.48341i	−0.304823	−	0.175989i
$650$	−25.1957			−0.988256
$651$	52.2969	+	1.96702i	2.04968	+	0.0770937i
$652$	3.71196	+	2.14310i	0.145372	+	0.0839304i
$653$		−	23.9730i		−	0.938137i	−0.883162	−	0.469068i	$-0.844590\pi$
$653$		−	23.9730i		−	0.938137i	0.883162	−	0.469068i	$-0.155410\pi$
$654$	−19.8215	+	10.4710i	−0.775080	+	0.409449i
$655$	−6.30473	−	10.9201i	−0.246346	−	0.426684i
$656$	−9.35395			−0.365210
$657$	7.98640	+	16.6005i	0.311579	+	0.647647i
$658$			5.77434i			0.225107i
$659$	9.18971	−	15.9170i	0.357980	−	0.620040i	−0.629643	−	0.776885i	$-0.716799\pi$
$659$	9.18971	−	15.9170i	0.357980	−	0.620040i	0.987623	+	0.156845i	$0.0501322\pi$
$660$	4.83990	+	0.182041i	0.188393	+	0.00708596i
$661$		−	6.78155i		−	0.263772i	−0.991265	−	0.131886i	$-0.957897\pi$
$661$		−	6.78155i		−	0.263772i	0.991265	−	0.131886i	$-0.0421032\pi$
$662$	−26.8173			−1.04229
$663$	−59.5425	+	31.4543i	−2.31244	+	1.22158i
$664$		−	4.32347i		−	0.167783i
$665$	−14.4073			−0.558692
$666$	4.14051	−	17.7723i	0.160441	−	0.688664i
$667$	−35.2812			−1.36609
$668$			3.73933i			0.144679i
$669$	−0.821596	+	21.8436i	−0.0317648	+	0.844523i
$670$	6.11184			0.236121
$671$			2.60012i			0.100377i
$672$	−2.98919	−	5.65849i	−0.115310	−	0.218281i
$673$	−8.38420	+	14.5219i	−0.323187	+	0.559777i	−0.981144	−	0.193279i	$-0.938088\pi$
$673$	−8.38420	+	14.5219i	−0.323187	+	0.559777i	0.657957	+	0.753056i	$0.271421\pi$
$674$		−	22.6050i		−	0.870712i
$675$	2.14157	−	18.9075i	0.0824289	−	0.727750i
$676$	34.3382			1.32070
$677$	6.38572	+	11.0604i	0.245423	+	0.425085i	0.962250	−	0.272165i	$-0.0877398\pi$
$677$	6.38572	+	11.0604i	0.245423	+	0.425085i	−0.716827	+	0.697251i	$0.754406\pi$
$678$	0.249400	−	6.63074i	0.00957813	−	0.254652i
$679$			62.0704i			2.38204i
$680$	−5.66060	−	3.26815i	−0.217074	−	0.125328i
$681$	6.95053	+	13.1573i	0.266345	+	0.504187i
$682$	−19.7694			−0.757009
$683$	29.4912	+	17.0268i	1.12845	+	0.651511i	0.943545	−	0.331245i	$-0.107469\pi$
$683$	29.4912	+	17.0268i	1.12845	+	0.651511i	0.184906	+	0.982756i	$0.440802\pi$
$684$	−8.35377	−	5.70028i	−0.319414	−	0.217956i
$685$	4.36569	−	2.52053i	0.166804	−	0.0963045i
$686$			1.28849i			0.0491946i
$687$	−2.70728	−	1.70183i	−0.103289	−	0.0649289i
$688$	−1.53830	+	0.888135i	−0.0586470	+	0.0338598i
$689$	1.08059	+	0.623878i	0.0411672	+	0.0237679i
$690$	4.39650	+	8.32251i	0.167372	+	0.316832i
$691$	15.5957			0.593288			0.296644	−	0.954988i	$-0.404133\pi$
$691$	15.5957			0.593288			0.296644	+	0.954988i	$0.404133\pi$
$692$	3.77995			0.143692
$693$	11.6168	+	24.1466i	0.441286	+	0.917255i
$694$	13.0727	−	22.6426i	0.496234	−	0.859502i
$695$	−14.0573	+	8.11601i	−0.533225	+	0.307858i
$696$	0.488895	−	12.9982i	0.0185315	−	0.492694i
$697$	−45.7754	−	26.4284i	−1.73387	−	1.00105i
$698$			3.51868i			0.133184i
$699$	−32.0207	−	20.1287i	−1.21113	−	0.761336i
$700$	6.76514	−	11.7176i	0.255698	−	0.442882i
$701$	7.84772	+	4.53089i	0.296404	+	0.171129i	0.640827	−	0.767686i	$-0.278592\pi$
$701$	7.84772	+	4.53089i	0.296404	+	0.171129i	−0.344422	+	0.938815i	$0.611925\pi$
$702$	−4.02362	+	35.5238i	−0.151862	+	1.34076i
$703$	3.13936	−	20.2638i	0.118403	−	0.764265i
$704$	1.20873	+	2.09357i	0.0455555	+	0.0789045i
$705$	3.12892	+	0.117687i	0.117842	+	0.00443235i
$706$	11.9475			0.449650
$707$	71.5441			2.69069
$708$	6.42000	+	0.241473i	0.241278	+	0.00907512i
$709$	−21.8418	+	12.6104i	−0.820285	+	0.473592i	−0.850515	−	0.525951i	$-0.823710\pi$
$709$	−21.8418	+	12.6104i	−0.820285	+	0.473592i	0.0302295	+	0.999543i	$0.490376\pi$
$710$	−0.468575	−	0.811595i	−0.0175853	−	0.0304586i
$711$	−2.63017	+	34.9144i	−0.0986389	+	1.30939i
$712$	−7.51299	+	13.0129i	−0.281561	+	0.487678i
$713$	−19.2097	−	33.2721i	−0.719408	−	1.24605i
$714$	1.35919	−	36.1365i	0.0508664	−	1.35238i
$715$	−9.61964	−	16.6617i	−0.359754	−	0.623113i
$716$		−	2.37692i		−	0.0888298i
$717$	1.02595	+	0.0385887i	0.0383149	+	0.00144112i
$718$		−	1.30369i		−	0.0486534i
$719$	−18.0843	+	31.3229i	−0.674429	+	1.16815i	0.302206	+	0.953243i	$0.402277\pi$
$719$	−18.0843	+	31.3229i	−0.674429	+	1.16815i	−0.976635	+	0.214903i	$0.931056\pi$
$720$	−3.12707	+	1.50442i	−0.116539	+	0.0560663i
$721$	35.7197	−	20.6228i	1.33027	−	0.768033i
$722$	6.61272	+	3.81785i	0.246100	+	0.142086i
$723$	−6.49917	−	12.3028i	−0.241707	−	0.457548i
$724$	−7.92005	−	13.7179i	−0.294346	−	0.509823i
$725$	23.8166	−	13.7505i	0.884525	−	0.510681i
$726$	4.17133	+	7.89626i	0.154813	+	0.293058i
$727$	−17.8514	−	10.3065i	−0.662071	−	0.382247i	0.130995	−	0.991383i	$-0.458183\pi$
$727$	−17.8514	−	10.3065i	−0.662071	−	0.382247i	−0.793066	+	0.609136i	$0.791516\pi$
$728$	−12.7105	+	22.0152i	−0.471082	+	0.815939i
$729$	−26.3160	−	6.03886i	−0.974667	−	0.223661i
$730$	7.10286			0.262889
$731$	−10.0373			−0.371242
$732$	−0.870169	−	1.64722i	−0.0321624	−	0.0608829i
$733$	−25.1489			−0.928895			−0.464447	−	0.885601i	$-0.653747\pi$
$733$	−25.1489			−0.928895			−0.464447	+	0.885601i	$0.653747\pi$
$734$	19.6603	+	11.3509i	0.725674	+	0.418968i
$735$	−13.3163	−	0.500861i	−0.491179	−	0.0184745i
$736$	−2.34901	+	4.06860i	−0.0865856	+	0.149971i
$737$	−6.38667	−	11.0620i	−0.235256	−	0.407475i
$738$	−25.2876	+	12.1657i	−0.930849	+	0.447826i
$739$	26.0675			0.958909			0.479455	−	0.877567i	$-0.340835\pi$
$739$	26.0675			0.958909			0.479455	+	0.877567i	$0.340835\pi$
$740$	−5.48293	−	4.40941i	−0.201556	−	0.162093i
$741$	−1.50996	+	40.1450i	−0.0554697	+	1.47476i
$742$	−0.580284	+	0.335027i	−0.0213029	+	0.0122992i
$743$	17.9490			0.658485			0.329243	−	0.944245i	$-0.393207\pi$
$743$	17.9490			0.658485			0.329243	+	0.944245i	$0.393207\pi$
$744$	12.5242	−	6.61611i	0.459159	−	0.242558i
$745$	−4.88972	−	2.82308i	−0.179146	−	0.103430i
$746$		−	15.9364i		−	0.583472i
$747$	−5.62309	−	11.6881i	−0.205738	−	0.427646i
$748$			13.6604i			0.499474i
$749$	45.2782			1.65443
$750$	−14.6924	−	9.23587i	−0.536492	−	0.337246i
$751$	−22.3202	+	38.6597i	−0.814475	+	1.41071i	0.0952291	+	0.995455i	$0.469642\pi$
$751$	−22.3202	+	38.6597i	−0.814475	+	1.41071i	−0.909704	+	0.415257i	$0.863692\pi$
$752$	0.781422	+	1.35346i	0.0284955	+	0.0493557i
$753$	7.64800	−	12.1665i	0.278709	−	0.443371i
$754$	−44.7471	+	25.8348i	−1.62959	+	0.940846i
$755$	23.5451	+	13.5938i	0.856894	+	0.494728i
$756$	−15.4404	−	11.4095i	−0.561563	−	0.414960i
$757$	38.2899	+	22.1067i	1.39167	+	0.803482i	0.993500	−	0.113829i	$-0.0363117\pi$
$757$	38.2899	+	22.1067i	1.39167	+	0.803482i	0.398171	+	0.917311i	$0.369645\pi$
$758$	8.13215	+	4.69510i	0.295373	+	0.170534i
$759$	10.4690	−	16.6541i	0.380001	−	0.604506i
$760$	−3.37697	+	1.94969i	−0.122496	+	0.0707229i
$761$	−14.3556	−	24.8646i	−0.520390	−	0.901341i	−0.999719	−	0.0237061i	$-0.992453\pi$
$761$	−14.3556	−	24.8646i	−0.520390	−	0.901341i	0.479329	−	0.877635i	$-0.340880\pi$
$762$	−9.60540	−	18.1829i	−0.347967	−	0.658696i
$763$	−41.4132	+	23.9099i	−1.49926	+	0.865596i
$764$	−17.3974	+	10.0444i	−0.629417	+	0.363394i
$765$	−19.5535	−	1.47300i	−0.706958	−	0.0532564i
$766$	−21.3223			−0.770404
$767$	−12.7602	−	22.1013i	−0.460744	−	0.798032i
$768$	−1.46639	−	0.921793i	−0.0529138	−	0.0332623i
$769$	−14.1433	−	8.16562i	−0.510019	−	0.294460i	0.222822	−	0.974859i	$-0.428473\pi$
$769$	−14.1433	−	8.16562i	−0.510019	−	0.294460i	−0.732841	+	0.680399i	$0.761806\pi$
$770$	10.3316			0.372327
$771$	31.2453	+	1.17522i	1.12527	+	0.0423244i
$772$	0.877859	+	0.506832i	0.0315948	+	0.0182413i
$773$	−6.96577	−	12.0651i	−0.250541	−	0.433950i	0.713134	−	0.701028i	$-0.247275\pi$
$773$	−6.96577	−	12.0651i	−0.250541	−	0.433950i	−0.963675	+	0.267078i	$0.913942\pi$
$774$	−3.00354	+	4.40170i	−0.107960	+	0.158216i
$775$	25.9350	+	14.9736i	0.931613	+	0.537867i
$776$	8.39978	+	14.5488i	0.301534	+	0.522273i
$777$	7.40124	−	38.2167i	0.265518	−	1.37101i
$778$	7.56564	−	13.1041i	0.271241	−	0.469804i
$779$	−27.3084	+	15.7665i	−0.978426	+	0.564895i
$780$	11.6703	+	7.33609i	0.417863	+	0.262674i
$781$	−0.979289	+	1.69618i	−0.0350417	+	0.0606941i
$782$	−22.9907	+	13.2737i	−0.822144	+	0.474665i
$783$	−15.5837	−	35.7753i	−0.556915	−	1.27850i
$784$	−3.32563	−	5.76017i	−0.118773	−	0.205720i
$785$	3.57640	−	2.06483i	0.127647	−	0.0736971i
$786$	0.709673	−	18.8679i	0.0253132	−	0.672997i
$787$	3.18847	−	5.52259i	0.113657	−	0.196859i	−0.803585	−	0.595190i	$-0.797077\pi$
$787$	3.18847	−	5.52259i	0.113657	−	0.196859i	0.917242	+	0.398331i	$0.130410\pi$
$788$	0.964730	−	1.67096i	0.0343671	−	0.0595256i
$789$	18.7632	−	9.91195i	0.667987	−	0.352875i
$790$	11.6914	+	6.75006i	0.415963	+	0.240156i
$791$		−	14.1545i		−	0.503276i
$792$	5.99058	+	4.08773i	0.212866	+	0.145251i
$793$	−3.70009	+	6.40875i	−0.131394	+	0.227581i
$794$			9.94610i			0.352974i
$795$	0.169713	+	0.321265i	0.00601911	+	0.0113941i
$796$			24.4339i			0.866036i
$797$	30.4811	−	17.5983i	1.07970	−	0.623363i	0.148881	−	0.988855i	$-0.452433\pi$
$797$	30.4811	−	17.5983i	1.07970	−	0.623363i	0.930814	+	0.365493i	$0.119099\pi$
$798$	−18.2645	−	11.4813i	−0.646555	−	0.406433i
$799$			8.83125i			0.312427i
$800$		−	3.66202i		−	0.129472i
$801$	−3.38621	+	44.9506i	−0.119646	+	1.58825i
$802$	10.3949	−	18.0046i	0.367058	−	0.635764i
$803$	−7.42225	−	12.8557i	−0.261926	−	0.453668i
$804$	7.74811	+	4.87057i	0.273255	+	0.171772i
$805$	10.0391	+	17.3883i	0.353833	+	0.612857i
$806$	−48.7273	−	28.1327i	−1.71635	−	0.990932i
$807$	35.5643	+	22.3562i	1.25192	+	0.786976i
$808$	16.7694	−	9.68183i	0.589946	−	0.340606i
$809$	−23.2128	+	13.4019i	−0.816119	+	0.471186i	−0.849076	−	0.528270i	$-0.822841\pi$
$809$	−23.2128	+	13.4019i	−0.816119	+	0.471186i	0.0329574	+	0.999457i	$0.489507\pi$
$810$	−6.49713	+	8.13412i	−0.228286	+	0.285804i
$811$	−8.89585	−	15.4081i	−0.312376	−	0.541050i	0.666501	−	0.745504i	$-0.267791\pi$
$811$	−8.89585	−	15.4081i	−0.312376	−	0.541050i	−0.978876	+	0.204454i	$0.934458\pi$
$812$		−	27.7469i		−	0.973726i
$813$	9.95641	−	5.25963i	0.349187	−	0.184463i
$814$	−2.25127	+	14.5314i	−0.0789069	+	0.509326i
$815$	2.47895	−	4.29367i	0.0868340	−	0.150401i
$816$	−4.57165	−	8.65408i	−0.160040	−	0.302953i
$817$	−2.99399	+	5.18574i	−0.104746	+	0.181426i
$818$	5.48528	+	9.50078i	0.191788	+	0.332187i
$819$	−5.72880	+	76.0475i	−0.200180	+	2.65731i
$820$			10.8198i			0.377845i
$821$	5.21092	−	9.02558i	0.181862	−	0.314995i	−0.760652	−	0.649159i	$-0.775121\pi$
$821$	5.21092	−	9.02558i	0.181862	−	0.314995i	0.942515	+	0.334164i	$0.108454\pi$
$822$	7.54311	+	0.283716i	0.263096	+	0.00989574i
$823$	−6.01151	−	10.4122i	−0.209548	−	0.362948i	0.742024	−	0.670373i	$-0.233866\pi$
$823$	−6.01151	−	10.4122i	−0.209548	−	0.362948i	−0.951572	+	0.307425i	$0.900533\pi$
$824$	5.58163	−	9.66767i	0.194445	−	0.336789i
$825$	−0.576322	+	15.3226i	−0.0200650	+	0.533463i
$826$	13.7046			0.476846
$827$	−22.9371	+	13.2427i	−0.797601	+	0.460495i	−0.842631	−	0.538491i	$-0.818995\pi$
$827$	−22.9371	+	13.2427i	−0.797601	+	0.460495i	0.0450308	+	0.998986i	$0.485661\pi$
$828$	−1.05873	+	14.0542i	−0.0367934	+	0.488418i
$829$	−34.1707	−	19.7285i	−1.18680	−	0.685198i	−0.229221	−	0.973375i	$-0.573618\pi$
$829$	−34.1707	−	19.7285i	−1.18680	−	0.685198i	−0.957577	+	0.288176i	$0.906951\pi$
$830$	−5.00101			−0.173587
$831$	13.2387	+	25.0607i	0.459245	+	0.869345i
$832$			6.88028i			0.238531i
$833$		−	37.5847i		−	1.30223i
$834$	−24.2885	−	0.913555i	−0.841042	−	0.0316338i
$835$	4.32532			0.149684
$836$	7.05764	+	4.07473i	0.244094	+	0.140927i
$837$	25.2532	−	34.1750i	0.872878	−	1.18126i
$838$	17.3045	−	9.99074i	0.597773	−	0.345124i
$839$	7.74983			0.267554			0.133777	−	0.991011i	$-0.457289\pi$
$839$	7.74983			0.267554			0.133777	+	0.991011i	$0.457289\pi$
$840$	−6.54525	+	3.45763i	−0.225833	+	0.119300i
$841$	13.6985	−	23.7266i	0.472363	−	0.818157i
$842$	11.4756	+	19.8763i	0.395476	+	0.684984i
$843$	26.3540	−	41.9239i	0.907679	−	1.44394i
$844$	5.76154	−	9.97929i	0.198321	−	0.343501i
$845$		−	39.7195i		−	1.36639i
$846$	3.87282	+	2.64266i	0.133150	+	0.0908564i
$847$	9.52498	+	16.4977i	0.327282	+	0.566869i
$848$	−0.0906763	+	0.157056i	−0.00311384	+	0.00539332i
$849$	−5.29436	+	8.42228i	−0.181702	+	0.289052i
$850$	10.3466	−	17.9208i	0.354885	−	0.614678i
$851$	−26.6441	+	10.3311i	−0.913348	+	0.354146i
$852$	0.0527437	−	1.40229i	0.00180697	−	0.0480416i
$853$		−	7.52717i		−	0.257726i	−0.991662	−	0.128863i	$-0.958867\pi$
$853$		−	7.52717i		−	0.257726i	0.991662	−	0.128863i	$-0.0411327\pi$
$854$	−1.98698	−	3.44155i	−0.0679930	−	0.117767i
$855$	−6.59358	+	9.66291i	−0.225496	+	0.330465i
$856$	10.6129	−	6.12736i	0.362741	−	0.209429i
$857$	−35.2084	+	20.3276i	−1.20270	+	0.694378i	−0.961154	−	0.276012i	$-0.910987\pi$
$857$	−35.2084	+	20.3276i	−1.20270	+	0.694378i	−0.241543	+	0.970390i	$0.577654\pi$
$858$	1.08281	−	28.7884i	0.0369664	−	0.982819i
$859$	5.31527	+	3.06877i	0.181355	+	0.104705i	0.587929	−	0.808913i	$-0.299943\pi$
$859$	5.31527	+	3.06877i	0.181355	+	0.104705i	−0.406574	+	0.913618i	$0.633277\pi$
$860$	1.02732	+	1.77937i	0.0350312	+	0.0606759i
$861$	−52.9293	+	27.9607i	−1.80382	+	0.952899i
$862$	−18.5749	−	32.1727i	−0.632665	−	1.09581i
$863$	10.6262	−	18.4050i	0.361719	−	0.626515i	−0.626525	−	0.779401i	$-0.715523\pi$
$863$	10.6262	−	18.4050i	0.361719	−	0.626515i	0.988244	+	0.152886i	$0.0488568\pi$
$864$	−5.16314	−	0.584805i	−0.175654	−	0.0198955i
$865$		−	4.37232i		−	0.148663i
$866$			5.45037i			0.185211i
$867$	0.972023	−	25.8430i	0.0330116	−	0.877674i
$868$	26.1669	−	15.1075i	0.888163	−	0.512781i
$869$		−	28.2143i		−	0.957105i
$870$	−15.0351	−	0.565511i	−0.509739	−	0.0191726i
$871$		−	36.3540i		−	1.23181i
$872$	−6.47129	+	11.2086i	−0.219146	+	0.379571i
$873$	41.6303	+	28.4068i	1.40897	+	0.961425i
$874$			15.8375i			0.535710i
$875$	−32.0599	−	18.5098i	−1.08382	−	0.625744i
$876$	9.00446	+	5.66032i	0.304232	+	0.191245i
$877$	12.9010	−	22.3451i	0.435635	−	0.754542i	−0.561712	−	0.827333i	$-0.689857\pi$
$877$	12.9010	−	22.3451i	0.435635	−	0.754542i	0.997347	+	0.0727907i	$0.0231905\pi$
$878$	6.10195	−	10.5689i	0.205931	−	0.356683i
$879$	22.1153	+	13.9020i	0.745932	+	0.468903i
$880$	2.42166	−	1.39815i	0.0816342	−	0.0471315i
$881$	−10.6443	−	18.4364i	−0.358615	−	0.621139i	0.629115	−	0.777312i	$-0.283417\pi$
$881$	−10.6443	−	18.4364i	−0.358615	−	0.621139i	−0.987730	+	0.156174i	$0.950084\pi$
$882$	−16.4822	−	11.2468i	−0.554985	−	0.378700i
$883$	23.4674	−	13.5489i	0.789742	−	0.455958i	−0.0501297	−	0.998743i	$-0.515963\pi$
$883$	23.4674	−	13.5489i	0.789742	−	0.455958i	0.839872	+	0.542785i	$0.182630\pi$
$884$	−19.4394	+	33.6700i	−0.653817	+	1.13244i
$885$	0.279315	−	7.42609i	0.00938907	−	0.249625i
$886$	−12.9315	+	7.46601i	−0.434442	+	0.250825i
$887$	−20.9076	+	36.2130i	−0.702009	+	1.21591i	0.265752	+	0.964042i	$0.414380\pi$
$887$	−20.9076	+	36.2130i	−0.702009	+	1.21591i	−0.967760	+	0.251873i	$0.918953\pi$
$888$	−3.43694	−	9.95929i	−0.115336	−	0.334212i
$889$	−21.9333	−	37.9897i	−0.735621	−	1.27413i
$890$	15.0522	+	8.69037i	0.504549	+	0.291302i
$891$	21.5115	+	3.25950i	0.720663	+	0.109197i
$892$	6.31017	+	10.9295i	0.211280	+	0.365948i
$893$	4.56266	+	2.63425i	0.152683	+	0.0881518i
$894$	−3.94908	−	7.47554i	−0.132077	−	0.250020i
$895$	−2.74942			−0.0919028
$896$	−3.19976	−	1.84738i	−0.106896	−	0.0617167i
$897$	49.5034	−	26.1510i	1.65287	−	0.873155i
$898$	10.0750	+	17.4504i	0.336207	+	0.582328i
$899$	61.4135			2.04825
$900$	−4.76281	−	9.89995i	−0.158760	−	0.329998i
$901$	−0.887484	+	0.512389i	−0.0295664	+	0.0170702i
$902$	19.5832	−	11.3064i	0.652049	−	0.376460i
$903$	−6.04963	+	9.62376i	−0.201319	+	0.320259i
$904$	−1.91548	−	3.31771i	−0.0637080	−	0.110346i
$905$	−15.8677	+	9.16122i	−0.527460	+	0.304529i
$906$	19.0157	+	35.9964i	0.631753	+	1.19590i
$907$	17.3662	+	10.0264i	0.576634	+	0.332920i	0.759794	−	0.650163i	$-0.225300\pi$
$907$	17.3662	+	10.0264i	0.576634	+	0.332920i	−0.183161	+	0.983083i	$0.558633\pi$
$908$	7.44015	+	4.29557i	0.246910	+	0.142554i
$909$	32.7425	−	47.9843i	1.08600	−	1.59154i
$910$	25.4653	+	14.7024i	0.844166	+	0.487379i
$911$	−30.8607	+	17.8174i	−1.02246	+	0.590317i	−0.914815	−	0.403872i	$-0.867664\pi$
$911$	−30.8607	+	17.8174i	−1.02246	+	0.590317i	−0.107644	+	0.994189i	$0.534331\pi$
$912$	−5.83479	−	0.219462i	−0.193209	−	0.00726710i
$913$	5.22588	+	9.05149i	0.172951	+	0.299561i
$914$	10.5495	−	18.2722i	0.348946	−	0.604392i
$915$	−1.90536	+	1.00654i	−0.0629892	+	0.0332750i
$916$	−1.84622			−0.0610008
$917$		−	40.2770i		−	1.33006i
$918$	−23.6145	−	17.4497i	−0.779396	−	0.575925i
$919$			6.68489i			0.220514i	0.993903	+	0.110257i	$0.0351674\pi$
$919$			6.68489i			0.220514i	−0.993903	+	0.110257i	$0.964833\pi$
$920$	4.70620	+	2.71713i	0.155159	+	0.0895810i
$921$	25.6287	+	16.1106i	0.844495	+	0.530861i
$922$	−17.9167			−0.590054
$923$	−4.82748	+	2.78714i	−0.158898	+	0.0917400i
$924$	13.0977	+	8.23336i	0.430881	+	0.270858i
$925$	13.9597	−	17.3583i	0.458991	−	0.570738i
$926$	−10.2946			−0.338303
$927$	2.51572	−	33.3952i	0.0826271	−	1.09684i
$928$	−3.75490	−	6.50368i	−0.123261	−	0.213494i
$929$	3.35778	−	5.81585i	0.110165	−	0.190812i	−0.805672	−	0.592363i	$-0.798195\pi$
$929$	3.35778	−	5.81585i	0.110165	−	0.190812i	0.915837	+	0.401551i	$0.131529\pi$
$930$	−7.65293	−	14.4869i	−0.250949	−	0.475044i
$931$	−19.4181	−	11.2110i	−0.636402	−	0.367427i
$932$	−21.8364			−0.715276
$933$	−36.7521	−	1.38234i	−1.20321	−	0.0452559i
$934$	25.3149			0.828328
$935$	15.8012			0.516754
$936$	8.94847	+	18.6002i	0.292490	+	0.607968i
$937$	25.5192	−	44.2005i	0.833674	−	1.44397i	−0.0614309	−	0.998111i	$-0.519566\pi$
$937$	25.5192	−	44.2005i	0.833674	−	1.44397i	0.895105	−	0.445855i	$-0.147100\pi$
$938$	16.9069	+	9.76120i	0.552030	+	0.318714i
$939$	−16.7275	+	26.6101i	−0.545881	+	0.868388i
$940$	1.56557	−	0.903881i	0.0510632	−	0.0294813i
$941$	6.95359	+	12.0440i	0.226681	+	0.392622i	0.956822	−	0.290673i	$-0.0938793\pi$
$941$	6.95359	+	12.0440i	0.226681	+	0.392622i	−0.730142	+	0.683296i	$0.760546\pi$
$942$	6.17936	+	0.232422i	0.201334	+	0.00757272i
$943$	38.0575	+	21.9725i	1.23932	+	0.715523i
$944$	3.21227	−	1.85460i	0.104550	−	0.0603622i
$945$	−13.1975	+	17.8601i	−0.429316	+	0.580991i
$946$	2.14702	−	3.71875i	0.0698057	−	0.120907i
$947$		−	42.1118i		−	1.36845i	−0.729272	−	0.684224i	$-0.760141\pi$
$947$		−	42.1118i		−	1.36845i	0.729272	−	0.684224i	$-0.239859\pi$
$948$	9.44233	+	17.8742i	0.306673	+	0.580527i
$949$		−	42.2488i		−	1.37145i
$950$	−6.17251	−	10.6911i	−0.200263	−	0.346865i
$951$	1.31150	+	0.824425i	0.0425282	+	0.0267338i
$952$	−10.4391	−	18.0810i	−0.338333	−	0.586010i
$953$	2.42351	−	4.19764i	0.0785051	−	0.135975i	−0.824100	−	0.566444i	$-0.808319\pi$
$953$	2.42351	−	4.19764i	0.0785051	−	0.135975i	0.902605	+	0.430469i	$0.141652\pi$
$954$	−0.0408691	+	0.542521i	−0.00132319	+	0.0175648i
$955$	11.6185	+	20.1238i	0.375966	+	0.651192i
$956$	0.513338	−	0.296376i	0.0166026	−	0.00958549i
$957$	14.6877	+	27.8035i	0.474785	+	0.898761i
$958$	20.8174			0.672579
$959$	16.1021			0.519964
$960$	−1.06625	+	1.69619i	−0.0344130	+	0.0547443i
$961$	17.9380	+	31.0696i	0.578647	+	1.00225i
$962$	−26.2278	+	32.6132i	−0.845617	+	1.05149i
$963$	20.7218	−	30.3679i	0.667751	−	0.978591i
$964$	−6.95700	−	4.01662i	−0.224070	−	0.129367i
$965$	0.586259	−	1.01543i	0.0188723	−	0.0326878i
$966$	−1.13003	+	30.0438i	−0.0363580	+	0.966643i
$967$		−	43.4011i		−	1.39569i	−0.716251	−	0.697843i	$-0.754144\pi$
$967$		−	43.4011i		−	1.39569i	0.716251	−	0.697843i	$-0.245856\pi$
$968$	4.46517	+	2.57797i	0.143516	+	0.0828590i
$969$	−27.9336	−	17.5594i	−0.897357	−	0.564091i
$970$	16.8288	−	9.71613i	0.540341	−	0.311966i
$971$	9.75877	−	16.9027i	0.313174	−	0.542433i	−0.665874	−	0.746064i	$-0.731941\pi$
$971$	9.75877	−	16.9027i	0.313174	−	0.542433i	0.979048	+	0.203631i	$0.0652744\pi$
$972$	−14.7187	+	5.13419i	−0.472102	+	0.164679i
$973$	−51.8482			−1.66218
$974$	−34.2104			−1.09617
$975$	−23.2252	+	36.9467i	−0.743802	+	1.18324i
$976$	−0.931466	−	0.537782i	−0.0298155	−	0.0172140i
$977$	−33.1026	+	19.1118i	−1.05905	+	0.611441i	−0.925168	−	0.379557i	$-0.876076\pi$
$977$	−33.1026	+	19.1118i	−1.05905	+	0.611441i	−0.133878	+	0.990998i	$0.542743\pi$
$978$	6.56429	−	3.46769i	0.209903	−	0.110884i
$979$		−	36.3246i		−	1.16094i
$980$	−6.66286	+	3.84680i	−0.212837	+	0.122882i
$981$	−2.91670	+	38.7181i	−0.0931232	+	1.23617i
$982$	11.7231	+	6.76834i	0.374099	+	0.215986i
$983$	−16.9360			−0.540176			−0.270088	−	0.962836i	$-0.587053\pi$
$983$	−16.9360			−0.540176			−0.270088	+	0.962836i	$0.587053\pi$
$984$	−8.62240	+	13.7165i	−0.274872	+	0.437267i
$985$	−1.93282	−	1.11592i	−0.0615848	−	0.0355560i
$986$		−	42.4360i		−	1.35144i
$987$	8.46743	+	5.32274i	0.269521	+	0.169425i
$988$	11.5970	+	20.0867i	0.368951	+	0.639042i
$989$	8.34495			0.265354
$990$	4.72833	−	6.92938i	0.150276	−	0.220230i
$991$			52.9569i			1.68223i	0.540856	+	0.841115i	$0.318100\pi$
$991$			52.9569i			1.68223i	−0.540856	+	0.841115i	$0.681900\pi$
$992$	4.08889	−	7.08217i	0.129822	−	0.224859i
$993$	−24.7200	+	39.3247i	−0.784466	+	1.24793i
$994$		−	2.99344i		−	0.0949460i
$995$	28.2630			0.895996
$996$	−6.33989	−	3.98534i	−0.200887	−	0.126280i
$997$			24.6223i			0.779796i	0.920858	+	0.389898i	$0.127490\pi$
$997$			24.6223i			0.779796i	−0.920858	+	0.389898i	$0.872510\pi$
$998$	24.9090			0.788479
$999$	−22.2445	−	22.4540i	−0.703784	−	0.710414i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.k.a.175.4	✓	76
3.2	odd	2		1998.2.k.a.1063.29		76
9.2	odd	6		1998.2.t.a.397.30		76
9.7	even	3		666.2.t.a.619.10	yes	76
37.11	even	6		666.2.t.a.85.10	yes	76
111.11	odd	6		1998.2.t.a.307.30		76
333.11	odd	6		1998.2.k.a.1639.10		76
333.196	even	6	inner	666.2.k.a.529.23	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.k.a.175.4	✓	76	1.1	even	1	trivial
666.2.k.a.529.23	yes	76	333.196	even	6	inner
666.2.t.a.85.10	yes	76	37.11	even	6
666.2.t.a.619.10	yes	76	9.7	even	3
1998.2.k.a.1063.29		76	3.2	odd	2
1998.2.k.a.1639.10		76	333.11	odd	6
1998.2.t.a.307.30		76	111.11	odd	6
1998.2.t.a.397.30		76	9.2	odd	6

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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-1.46639 - 0.921793i) q^{3} -1.00000 q^{4} +1.15671i q^{5} +(-0.921793 + 1.46639i) q^{6} +(-1.84738 + 3.19976i) q^{7} +1.00000i q^{8} +(1.30060 + 2.70341i) q^{9} +1.15671 q^{10} +(-1.20873 - 2.09357i) q^{11} +(1.46639 + 0.921793i) q^{12} -6.88028i q^{13} +(3.19976 + 1.84738i) q^{14} +(1.06625 - 1.69619i) q^{15} +1.00000 q^{16} +(4.89370 + 2.82538i) q^{17} +(2.70341 - 1.30060i) q^{18} +(2.91946 - 1.68555i) q^{19} -1.15671i q^{20} +(5.65849 - 2.98919i) q^{21} +(-2.09357 + 1.20873i) q^{22} +(-4.06860 - 2.34901i) q^{23} +(0.921793 - 1.46639i) q^{24} +3.66202 q^{25} -6.88028 q^{26} +(0.584805 - 5.16314i) q^{27} +(1.84738 - 3.19976i) q^{28} +(6.50368 - 3.75490i) q^{29} +(-1.69619 - 1.06625i) q^{30} +(7.08217 + 4.08889i) q^{31} -1.00000i q^{32} +(-0.157378 + 4.18419i) q^{33} +(2.82538 - 4.89370i) q^{34} +(-3.70120 - 2.13689i) q^{35} +(-1.30060 - 2.70341i) q^{36} +(3.81202 - 4.74010i) q^{37} +(-1.68555 - 2.91946i) q^{38} +(-6.34219 + 10.0892i) q^{39} -1.15671 q^{40} -9.35395 q^{41} +(-2.98919 - 5.65849i) q^{42} +(-1.53830 + 0.888135i) q^{43} +(1.20873 + 2.09357i) q^{44} +(-3.12707 + 1.50442i) q^{45} +(-2.34901 + 4.06860i) q^{46} +(0.781422 + 1.35346i) q^{47} +(-1.46639 - 0.921793i) q^{48} +(-3.32563 - 5.76017i) q^{49} -3.66202i q^{50} +(-4.57165 - 8.65408i) q^{51} +6.88028i q^{52} +(-0.0906763 + 0.157056i) q^{53} +(-5.16314 - 0.584805i) q^{54} +(2.42166 - 1.39815i) q^{55} +(-3.19976 - 1.84738i) q^{56} +(-5.83479 - 0.219462i) q^{57} +(-3.75490 - 6.50368i) q^{58} +(3.21227 - 1.85460i) q^{59} +(-1.06625 + 1.69619i) q^{60} +(-0.931466 - 0.537782i) q^{61} +(4.08889 - 7.08217i) q^{62} +(-11.0530 - 0.832641i) q^{63} -1.00000 q^{64} +7.95850 q^{65} +(4.18419 + 0.157378i) q^{66} +5.28380 q^{67} +(-4.89370 - 2.82538i) q^{68} +(3.80086 + 7.19497i) q^{69} +(-2.13689 + 3.70120i) q^{70} +(-0.405092 - 0.701640i) q^{71} +(-2.70341 + 1.30060i) q^{72} +6.14056 q^{73} +(-4.74010 - 3.81202i) q^{74} +(-5.36994 - 3.37562i) q^{75} +(-2.91946 + 1.68555i) q^{76} +8.93190 q^{77} +(10.0892 + 6.34219i) q^{78} +(10.1075 + 5.83555i) q^{79} +1.15671i q^{80} +(-5.61690 + 7.03210i) q^{81} +9.35395i q^{82} -4.32347 q^{83} +(-5.65849 + 2.98919i) q^{84} +(-3.26815 + 5.66060i) q^{85} +(0.888135 + 1.53830i) q^{86} +(-12.9982 - 0.488895i) q^{87} +(2.09357 - 1.20873i) q^{88} +(13.0129 + 7.51299i) q^{89} +(1.50442 + 3.12707i) q^{90} +(22.0152 + 12.7105i) q^{91} +(4.06860 + 2.34901i) q^{92} +(-6.61611 - 12.5242i) q^{93} +(1.35346 - 0.781422i) q^{94} +(1.94969 + 3.37697i) q^{95} +(-0.921793 + 1.46639i) q^{96} +(14.5488 - 8.39978i) q^{97} +(-5.76017 + 3.32563i) q^{98} +(4.08773 - 5.99058i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 4 q^{3} - 76 q^{4} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{12} + 12 q^{15} + 76 q^{16} + 6 q^{21} + 12 q^{23} - 100 q^{25} - 24 q^{26} + 4 q^{27} + 2 q^{28} + 18 q^{29} - 12 q^{30} + 6 q^{31} - 32 q^{33}+ \cdots - 76 q^{99}+O(q^{100}) \) 76 * q + 4 * q^3 - 76 * q^4 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^12 + 12 * q^15 + 76 * q^16 + 6 * q^21 + 12 * q^23 - 100 * q^25 - 24 * q^26 + 4 * q^27 + 2 * q^28 + 18 * q^29 - 12 * q^30 + 6 * q^31 - 32 * q^33 - 18 * q^35 + 4 * q^36 + 10 * q^37 + 12 * q^38 + 24 * q^39 + 72 * q^41 + 6 * q^42 + 6 * q^43 + 4 * q^44 + 12 * q^45 - 20 * q^47 + 4 * q^48 - 36 * q^49 - 18 * q^51 + 14 * q^53 + 36 * q^54 + 42 * q^57 - 6 * q^59 - 12 * q^60 - 16 * q^62 + 46 * q^63 - 76 * q^64 + 32 * q^65 + 40 * q^67 + 6 * q^69 + 2 * q^71 + 28 * q^73 - 2 * q^74 - 78 * q^75 - 24 * q^77 - 2 * q^78 + 6 * q^79 - 28 * q^81 - 64 * q^83 - 6 * q^84 - 12 * q^85 + 4 * q^86 - 78 * q^87 + 60 * q^89 - 16 * q^90 + 42 * q^91 - 12 * q^92 + 6 * q^93 - 14 * q^95 - 12 * q^97 - 24 * q^98 - 76 * q^99

Introduction

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