LMFDB - Embedded newform 240.2.t.b.59.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(59,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2, 2]))

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

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

chi := DirichletCharacter("240.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.t (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			59.27
Character	$\chi$	$=$	240.59
Dual form			240.2.t.b.179.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.743883 + 1.20276i) q^{2} +(-1.39602 + 1.02525i) q^{3} +(-0.893276 + 1.78943i) q^{4} +(0.920160 + 2.03797i) q^{5} +(-2.27161 - 0.916409i) q^{6} +0.440232i q^{7} +(-2.81675 + 0.256728i) q^{8} +(0.897721 - 2.86253i) q^{9} +O(q^{10})$	\(q+(0.743883 + 1.20276i) q^{2} +(-1.39602 + 1.02525i) q^{3} +(-0.893276 + 1.78943i) q^{4} +(0.920160 + 2.03797i) q^{5} +(-2.27161 - 0.916409i) q^{6} +0.440232i q^{7} +(-2.81675 + 0.256728i) q^{8} +(0.897721 - 2.86253i) q^{9} +(-1.76670 + 2.62274i) q^{10} +(-3.34512 - 3.34512i) q^{11} +(-0.587588 - 3.41390i) q^{12} +(3.79299 + 3.79299i) q^{13} +(-0.529495 + 0.327481i) q^{14} +(-3.37398 - 1.90164i) q^{15} +(-2.40412 - 3.19691i) q^{16} -3.44344 q^{17} +(4.11075 - 1.04965i) q^{18} +(3.74228 + 3.74228i) q^{19} +(-4.46875 - 0.173904i) q^{20} +(-0.451349 - 0.614571i) q^{21} +(1.53501 - 6.51176i) q^{22} -0.0184980 q^{23} +(3.66902 - 3.24627i) q^{24} +(-3.30661 + 3.75051i) q^{25} +(-1.74053 + 7.38361i) q^{26} +(1.68158 + 4.91653i) q^{27} +(-0.787765 - 0.393249i) q^{28} +(4.40505 + 4.40505i) q^{29} +(-0.222632 - 5.47270i) q^{30} -3.65248i q^{31} +(2.05674 - 5.26971i) q^{32} +(8.09943 + 1.24025i) q^{33} +(-2.56152 - 4.14164i) q^{34} +(-0.897179 + 0.405084i) q^{35} +(4.32039 + 4.16344i) q^{36} +(2.54315 - 2.54315i) q^{37} +(-1.71726 + 7.28489i) q^{38} +(-9.18384 - 1.40631i) q^{39} +(-3.11507 - 5.50421i) q^{40} +7.93346 q^{41} +(0.403433 - 1.00003i) q^{42} +(4.73534 + 4.73534i) q^{43} +(8.97397 - 2.99774i) q^{44} +(6.65979 - 0.804465i) q^{45} +(-0.0137604 - 0.0222487i) q^{46} +3.28433i q^{47} +(6.63382 + 1.99811i) q^{48} +6.80620 q^{49} +(-6.97071 - 1.18713i) q^{50} +(4.80709 - 3.53039i) q^{51} +(-10.1755 + 3.39910i) q^{52} +(-5.57793 - 5.57793i) q^{53} +(-4.66252 + 5.67987i) q^{54} +(3.73920 - 9.89529i) q^{55} +(-0.113020 - 1.24003i) q^{56} +(-9.06106 - 1.38751i) q^{57} +(-2.02139 + 8.57508i) q^{58} +(-0.447338 - 0.447338i) q^{59} +(6.41675 - 4.33882i) q^{60} +(-0.162615 + 0.162615i) q^{61} +(4.39306 - 2.71702i) q^{62} +(1.26018 + 0.395206i) q^{63} +(7.86818 - 1.44628i) q^{64} +(-4.23983 + 11.2201i) q^{65} +(4.53330 + 10.6643i) q^{66} +(-6.98489 + 6.98489i) q^{67} +(3.07594 - 6.16179i) q^{68} +(0.0258235 - 0.0189651i) q^{69} +(-1.15462 - 0.777758i) q^{70} -5.70676i q^{71} +(-1.79376 + 8.29352i) q^{72} -5.51755 q^{73} +(4.95061 + 1.16700i) q^{74} +(0.770867 - 8.62588i) q^{75} +(-10.0394 + 3.35366i) q^{76} +(1.47263 - 1.47263i) q^{77} +(-5.14025 - 12.0921i) q^{78} +2.95205i q^{79} +(4.30302 - 7.84118i) q^{80} +(-7.38820 - 5.13951i) q^{81} +(5.90156 + 9.54206i) q^{82} +(5.11440 + 5.11440i) q^{83} +(1.50291 - 0.258675i) q^{84} +(-3.16851 - 7.01761i) q^{85} +(-2.17295 + 9.21803i) q^{86} +(-10.6658 - 1.63324i) q^{87} +(10.2812 + 8.56359i) q^{88} -10.9541 q^{89} +(5.92169 + 7.41172i) q^{90} +(-1.66980 + 1.66980i) q^{91} +(0.0165238 - 0.0331009i) q^{92} +(3.74471 + 5.09892i) q^{93} +(-3.95027 + 2.44316i) q^{94} +(-4.18314 + 11.0701i) q^{95} +(2.53153 + 9.46527i) q^{96} -17.0870i q^{97} +(5.06301 + 8.18624i) q^{98} +(-12.5785 + 6.57254i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 8 q^{4} - 4 q^{6}+O(q^{10}) $ 80 * q - 8 * q^4 - 4 * q^6	$ 80 q - 8 q^{4} - 4 q^{6} + 16 q^{10} - 32 q^{16} + 16 q^{19} + 8 q^{21} - 56 q^{24} + 8 q^{30} - 16 q^{34} - 40 q^{36} - 8 q^{39} - 8 q^{40} - 12 q^{45} - 24 q^{46} - 112 q^{49} + 32 q^{51} + 60 q^{54} - 40 q^{55} + 40 q^{60} + 16 q^{61} - 32 q^{64} - 56 q^{66} - 40 q^{69} + 48 q^{70} - 36 q^{75} - 128 q^{76} + 64 q^{81} + 128 q^{84} - 64 q^{85} + 72 q^{90} + 48 q^{91} + 56 q^{94} - 24 q^{96} - 8 q^{99}+O(q^{100}) $ 80 * q - 8 * q^4 - 4 * q^6 + 16 * q^10 - 32 * q^16 + 16 * q^19 + 8 * q^21 - 56 * q^24 + 8 * q^30 - 16 * q^34 - 40 * q^36 - 8 * q^39 - 8 * q^40 - 12 * q^45 - 24 * q^46 - 112 * q^49 + 32 * q^51 + 60 * q^54 - 40 * q^55 + 40 * q^60 + 16 * q^61 - 32 * q^64 - 56 * q^66 - 40 * q^69 + 48 * q^70 - 36 * q^75 - 128 * q^76 + 64 * q^81 + 128 * q^84 - 64 * q^85 + 72 * q^90 + 48 * q^91 + 56 * q^94 - 24 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.743883	+	1.20276i	0.526005	+	0.850482i
$2$	0.743883	+	1.20276i	0.526005	+	0.850482i
$3$	−1.39602	+	1.02525i	−0.805990	+	0.591929i
$3$	−1.39602	+	1.02525i	−0.805990	+	0.591929i
$4$	−0.893276	+	1.78943i	−0.446638	+	0.894715i
$5$	0.920160	+	2.03797i	0.411508	+	0.911406i
$5$	0.920160	+	2.03797i	0.411508	+	0.911406i
$6$	−2.27161	−	0.916409i	−0.927379	−	0.374122i
$7$			0.440232i			0.166392i	0.996533	+	0.0831961i	$0.0265128\pi$
$7$			0.440232i			0.166392i	−0.996533	+	0.0831961i	$0.973487\pi$
$8$	−2.81675	+	0.256728i	−0.995872	+	0.0907671i
$9$	0.897721	−	2.86253i	0.299240	−	0.954178i
$10$	−1.76670	+	2.62274i	−0.558679	+	0.829384i
$11$	−3.34512	−	3.34512i	−1.00859	−	1.00859i	−0.999963	−	0.00862901i	$-0.997253\pi$
$11$	−3.34512	−	3.34512i	−1.00859	−	1.00859i	−0.00862901	−	0.999963i	$-0.502747\pi$
$12$	−0.587588	−	3.41390i	−0.169622	−	0.985509i
$13$	3.79299	+	3.79299i	1.05199	+	1.05199i	0.998572	+	0.0534141i	$0.0170103\pi$
$13$	3.79299	+	3.79299i	1.05199	+	1.05199i	0.0534141	+	0.998572i	$0.482990\pi$
$14$	−0.529495	+	0.327481i	−0.141514	+	0.0875231i
$15$	−3.37398	−	1.90164i	−0.871159	−	0.491001i
$16$	−2.40412	−	3.19691i	−0.601029	−	0.799227i
$17$	−3.44344			−0.835156			−0.417578	−	0.908641i	$-0.637121\pi$
$17$	−3.44344			−0.835156			−0.417578	+	0.908641i	$0.637121\pi$
$18$	4.11075	−	1.04965i	0.968912	−	0.247404i
$19$	3.74228	+	3.74228i	0.858538	+	0.858538i	0.991166	−	0.132628i	$-0.0423416\pi$
$19$	3.74228	+	3.74228i	0.858538	+	0.858538i	−0.132628	+	0.991166i	$0.542342\pi$
$20$	−4.46875	−	0.173904i	−0.999244	−	0.0388860i
$21$	−0.451349	−	0.614571i	−0.0984924	−	0.134110i
$22$	1.53501	−	6.51176i	0.327265	−	1.38831i
$23$	−0.0184980			−0.00385710			−0.00192855	−	0.999998i	$-0.500614\pi$
$23$	−0.0184980			−0.00385710			−0.00192855	+	0.999998i	$0.500614\pi$
$24$	3.66902	−	3.24627i	0.748935	−	0.662643i
$25$	−3.30661	+	3.75051i	−0.661322	+	0.750102i
$26$	−1.74053	+	7.38361i	−0.341345	+	1.44805i
$27$	1.68158	+	4.91653i	0.323621	+	0.946187i
$28$	−0.787765	−	0.393249i	−0.148874	−	0.0743171i
$29$	4.40505	+	4.40505i	0.817998	+	0.817998i	0.985818	−	0.167820i	$-0.0536728\pi$
$29$	4.40505	+	4.40505i	0.817998	+	0.817998i	−0.167820	+	0.985818i	$0.553673\pi$
$30$	−0.222632	−	5.47270i	−0.0406468	−	0.999174i
$31$		−	3.65248i		−	0.656004i	−0.944677	−	0.328002i	$-0.893625\pi$
$31$		−	3.65248i		−	0.656004i	0.944677	−	0.328002i	$-0.106375\pi$
$32$	2.05674	−	5.26971i	0.363584	−	0.931562i
$33$	8.09943	+	1.24025i	1.40993	+	0.215900i
$34$	−2.56152	−	4.14164i	−0.439296	−	0.710285i
$35$	−0.897179	+	0.405084i	−0.151651	+	0.0684717i
$36$	4.32039	+	4.16344i	0.720065	+	0.693907i
$37$	2.54315	−	2.54315i	0.418091	−	0.418091i	−0.466454	−	0.884545i	$-0.654469\pi$
$37$	2.54315	−	2.54315i	0.418091	−	0.418091i	0.884545	+	0.466454i	$0.154469\pi$
$38$	−1.71726	+	7.28489i	−0.278576	+	1.18177i
$39$	−9.18384	−	1.40631i	−1.47059	−	0.225189i
$40$	−3.11507	−	5.50421i	−0.492535	−	0.870293i
$41$	7.93346			1.23900			0.619499	−	0.784998i	$-0.287336\pi$
$41$	7.93346			1.23900			0.619499	+	0.784998i	$0.287336\pi$
$42$	0.403433	−	1.00003i	0.0622510	−	0.154309i
$43$	4.73534	+	4.73534i	0.722133	+	0.722133i	0.969039	−	0.246907i	$-0.0794141\pi$
$43$	4.73534	+	4.73534i	0.722133	+	0.722133i	−0.246907	+	0.969039i	$0.579414\pi$
$44$	8.97397	−	2.99774i	1.35288	−	0.451927i
$45$	6.65979	−	0.804465i	0.992783	−	0.119923i
$46$	−0.0137604	−	0.0222487i	−0.00202885	−	0.00328039i
$47$			3.28433i			0.479069i	0.970888	+	0.239535i	$0.0769948\pi$
$47$			3.28433i			0.479069i	−0.970888	+	0.239535i	$0.923005\pi$
$48$	6.63382	+	1.99811i	0.957509	+	0.288402i
$49$	6.80620			0.972314
$50$	−6.97071	−	1.18713i	−0.985807	−	0.167885i
$51$	4.80709	−	3.53039i	0.673128	−	0.494353i
$52$	−10.1755	+	3.39910i	−1.41108	+	0.471371i
$53$	−5.57793	−	5.57793i	−0.766188	−	0.766188i	0.211245	−	0.977433i	$-0.432248\pi$
$53$	−5.57793	−	5.57793i	−0.766188	−	0.766188i	−0.977433	+	0.211245i	$0.932248\pi$
$54$	−4.66252	+	5.67987i	−0.634488	+	0.772932i
$55$	3.73920	−	9.89529i	0.504193	−	1.33428i
$56$	−0.113020	−	1.24003i	−0.0151029	−	0.165705i
$57$	−9.06106	−	1.38751i	−1.20017	−	0.183780i
$58$	−2.02139	+	8.57508i	−0.265421	+	1.12596i
$59$	−0.447338	−	0.447338i	−0.0582385	−	0.0582385i	0.677388	−	0.735626i	$-0.263112\pi$
$59$	−0.447338	−	0.447338i	−0.0582385	−	0.0582385i	−0.735626	+	0.677388i	$0.763112\pi$
$60$	6.41675	−	4.33882i	0.828398	−	0.560139i
$61$	−0.162615	+	0.162615i	−0.0208208	+	0.0208208i	−0.717441	−	0.696620i	$-0.754686\pi$
$61$	−0.162615	+	0.162615i	−0.0208208	+	0.0208208i	0.696620	+	0.717441i	$0.254686\pi$
$62$	4.39306	−	2.71702i	0.557920	−	0.345061i
$63$	1.26018	+	0.395206i	0.158768	+	0.0497912i
$64$	7.86818	−	1.44628i	0.983523	−	0.180785i
$65$	−4.23983	+	11.2201i	−0.525886	+	1.39169i
$66$	4.53330	+	10.6643i	0.558011	+	1.31268i
$67$	−6.98489	+	6.98489i	−0.853340	+	0.853340i	−0.990543	−	0.137203i	$-0.956189\pi$
$67$	−6.98489	+	6.98489i	−0.853340	+	0.853340i	0.137203	+	0.990543i	$0.456189\pi$
$68$	3.07594	−	6.16179i	0.373012	−	0.747227i
$69$	0.0258235	−	0.0189651i	0.00310879	−	0.00228313i
$70$	−1.15462	−	0.777758i	−0.138003	−	0.0929598i
$71$		−	5.70676i		−	0.677268i	−0.940918	−	0.338634i	$-0.890035\pi$
$71$		−	5.70676i		−	0.677268i	0.940918	−	0.338634i	$-0.109965\pi$
$72$	−1.79376	+	8.29352i	−0.211397	+	0.977400i
$73$	−5.51755			−0.645781			−0.322890	−	0.946436i	$-0.604655\pi$
$73$	−5.51755			−0.645781			−0.322890	+	0.946436i	$0.604655\pi$
$74$	4.95061	+	1.16700i	0.575497	+	0.135661i
$75$	0.770867	−	8.62588i	0.0890120	−	0.996031i
$76$	−10.0394	+	3.35366i	−1.15160	+	0.384691i
$77$	1.47263	−	1.47263i	0.167822	−	0.167822i
$78$	−5.14025	−	12.0921i	−0.582019	−	1.36916i
$79$			2.95205i			0.332131i	0.986115	+	0.166066i	$0.0531063\pi$
$79$			2.95205i			0.332131i	−0.986115	+	0.166066i	$0.946894\pi$
$80$	4.30302	−	7.84118i	0.481092	−	0.876670i
$81$	−7.38820	−	5.13951i	−0.820911	−	0.571057i
$82$	5.90156	+	9.54206i	0.651719	+	1.05374i
$83$	5.11440	+	5.11440i	0.561379	+	0.561379i	0.929699	−	0.368320i	$-0.120067\pi$
$83$	5.11440	+	5.11440i	0.561379	+	0.561379i	−0.368320	+	0.929699i	$0.620067\pi$
$84$	1.50291	−	0.258675i	0.163981	−	0.0282238i
$85$	−3.16851	−	7.01761i	−0.343674	−	0.761167i
$86$	−2.17295	+	9.21803i	−0.234315	+	0.994006i
$87$	−10.6658	−	1.63324i	−1.14349	−	0.175102i
$88$	10.2812	+	8.56359i	1.09598	+	0.912882i
$89$	−10.9541			−1.16113			−0.580565	−	0.814214i	$-0.697168\pi$
$89$	−10.9541			−1.16113			−0.580565	+	0.814214i	$0.697168\pi$
$90$	5.92169	+	7.41172i	0.624201	+	0.781264i
$91$	−1.66980	+	1.66980i	−0.175042	+	0.175042i
$92$	0.0165238	−	0.0331009i	0.00172273	−	0.00345101i
$93$	3.74471	+	5.09892i	0.388308	+	0.528733i
$94$	−3.95027	+	2.44316i	−0.407439	+	0.251993i
$95$	−4.18314	+	11.0701i	−0.429181	+	1.13577i
$96$	2.53153	+	9.46527i	0.258374	+	0.966045i
$97$		−	17.0870i		−	1.73492i	−0.497507	−	0.867460i	$-0.665751\pi$
$97$		−	17.0870i		−	1.73492i	0.497507	−	0.867460i	$-0.334249\pi$
$98$	5.06301	+	8.18624i	0.511442	+	0.826935i
$99$	−12.5785	+	6.57254i	−1.26419	+	0.660565i
$100$	−3.75756	−	9.26719i	−0.375756	−	0.926719i
$101$	5.66895	−	5.66895i	0.564081	−	0.564081i	−0.366383	−	0.930464i	$-0.619404\pi$
$101$	5.66895	−	5.66895i	0.564081	−	0.564081i	0.930464	+	0.366383i	$0.119404\pi$
$102$	7.82214	+	3.15560i	0.774507	+	0.312451i
$103$		−	15.2221i		−	1.49987i	−0.661509	−	0.749937i	$-0.730084\pi$
$103$		−	15.2221i		−	1.49987i	0.661509	−	0.749937i	$-0.269916\pi$
$104$	−11.6577	−	9.71015i	−1.14313	−	0.952158i
$105$	0.837163	−	1.48534i	0.0816987	−	0.144954i
$106$	2.55960	−	10.8583i	0.248610	−	1.05465i
$107$	7.84406	−	7.84406i	0.758314	−	0.758314i	−0.217701	−	0.976015i	$-0.569856\pi$
$107$	7.84406	−	7.84406i	0.758314	−	0.758314i	0.976015	+	0.217701i	$0.0698559\pi$
$108$	−10.2999	−	1.38274i	−0.991109	−	0.133054i
$109$	10.7241	−	10.7241i	1.02718	−	1.02718i	0.0275633	−	0.999620i	$-0.491225\pi$
$109$	10.7241	−	10.7241i	1.02718	−	1.02718i	0.999620	−	0.0275633i	$-0.00877479\pi$
$110$	14.6832	−	2.86357i	1.39999	−	0.273031i
$111$	−0.942911	+	6.15764i	−0.0894971	+	0.584458i
$112$	1.40738	−	1.05837i	0.132985	−	0.100007i
$113$	−0.615365			−0.0578886			−0.0289443	−	0.999581i	$-0.509215\pi$
$113$	−0.615365			−0.0578886			−0.0289443	+	0.999581i	$0.509215\pi$
$114$	−5.07153	−	11.9304i	−0.474992	−	1.11739i
$115$	−0.0170211	−	0.0376983i	−0.00158723	−	0.00351539i
$116$	−11.8175	+	3.94760i	−1.09722	+	0.366526i
$117$	14.2626	−	7.45252i	1.31858	−	0.688986i
$118$	0.205274	−	0.870809i	0.0188970	−	0.0801645i
$119$		−	1.51591i		−	0.138964i
$120$	9.99188	+	4.49024i	0.912130	+	0.409901i
$121$			11.3797i			1.03451i
$122$	−0.316555	−	0.0746209i	−0.0286595	−	0.00675586i
$123$	−11.0752	+	8.13378i	−0.998620	+	0.733399i
$124$	6.53585	+	3.26267i	0.586937	+	0.292996i
$125$	−10.6860	−	3.28769i	−0.955787	−	0.294060i
$126$	0.462088	+	1.80968i	0.0411661	+	0.161219i
$127$	5.73070			0.508517			0.254259	−	0.967136i	$-0.418169\pi$
$127$	5.73070			0.508517			0.254259	+	0.967136i	$0.418169\pi$
$128$	7.59254	+	8.38769i	0.671092	+	0.741374i
$129$	−11.4655	−	1.75570i	−1.00948	−	0.154581i
$130$	−16.6491	+	3.24697i	−1.46022	+	0.284778i
$131$	8.58881	−	8.58881i	0.750407	−	0.750407i	−0.224148	−	0.974555i	$-0.571960\pi$
$131$	8.58881	−	8.58881i	0.750407	−	0.750407i	0.974555	+	0.224148i	$0.0719598\pi$
$132$	−9.45437	+	13.3855i	−0.822897	+	1.16506i
$133$	−1.64747	+	1.64747i	−0.142854	+	0.142854i
$134$	−13.5971	−	3.20522i	−1.17461	−	0.276889i
$135$	−8.47240	+	7.95101i	−0.729188	+	0.684314i
$136$	9.69931	−	0.884027i	0.831709	−	0.0758047i
$137$			4.92640i			0.420890i	0.977606	+	0.210445i	$0.0674914\pi$
$137$			4.92640i			0.420890i	−0.977606	+	0.210445i	$0.932509\pi$
$138$	0.0420202	+	0.0169517i	0.00357700	+	0.00144303i
$139$	−6.73849	+	6.73849i	−0.571551	+	0.571551i	−0.932562	−	0.361011i	$-0.882432\pi$
$139$	−6.73849	+	6.73849i	−0.571551	+	0.571551i	0.361011	+	0.932562i	$0.382432\pi$
$140$	0.0765580	−	1.96729i	0.00647033	−	0.166266i
$141$	−3.36727	−	4.58498i	−0.283575	−	0.386125i
$142$	6.86388	−	4.24516i	0.576004	−	0.356246i
$143$		−	25.3760i		−	2.12205i
$144$	−11.3095	+	4.01194i	−0.942457	+	0.334328i
$145$	−4.92399	+	13.0307i	−0.408915	+	1.08214i
$146$	−4.10442	−	6.63631i	−0.339684	−	0.549225i
$147$	−9.50156	+	6.97806i	−0.783675	+	0.575541i
$148$	2.27905	+	6.82252i	0.187337	+	0.560808i
$149$	−7.93902	+	7.93902i	−0.650390	+	0.650390i	−0.953087	−	0.302697i	$-0.902113\pi$
$149$	−7.93902	+	7.93902i	−0.650390	+	0.650390i	0.302697	+	0.953087i	$0.402113\pi$
$150$	10.9483	−	5.48948i	0.893926	−	0.448214i
$151$	−3.77736			−0.307397			−0.153699	−	0.988118i	$-0.549119\pi$
$151$	−3.77736			−0.307397			−0.153699	+	0.988118i	$0.549119\pi$
$152$	−11.5018	−	9.58033i	−0.932921	−	0.777067i
$153$	−3.09125	+	9.85696i	−0.249912	+	0.796888i
$154$	2.86669	+	0.675760i	0.231004	+	0.0544543i
$155$	7.44362	−	3.36086i	0.597886	−	0.269951i
$156$	10.7202	−	15.1776i	0.858302	−	1.21518i
$157$	−6.35205	−	6.35205i	−0.506949	−	0.506949i	0.406640	−	0.913589i	$-0.366700\pi$
$157$	−6.35205	−	6.35205i	−0.506949	−	0.506949i	−0.913589	+	0.406640i	$0.866700\pi$
$158$	−3.55061	+	2.19598i	−0.282471	+	0.174703i
$159$	13.5057	+	2.06810i	1.07107	+	0.164011i
$160$	12.6320	−	0.657411i	0.998648	−	0.0519729i
$161$		−	0.00814343i		−	0.000641792i
$162$	0.685657	−	12.7094i	0.0538703	−	0.998548i
$163$	−0.640327	+	0.640327i	−0.0501543	+	0.0501543i	−0.731739	−	0.681585i	$-0.761291\pi$
$163$	−0.640327	+	0.640327i	−0.0501543	+	0.0501543i	0.681585	+	0.731739i	$0.261291\pi$
$164$	−7.08676	+	14.1964i	−0.553383	+	1.10855i
$165$	4.92518	+	17.6476i	0.383425	+	1.37386i
$166$	−2.34689	+	9.95593i	−0.182154	+	0.772730i
$167$	23.3549			1.80726			0.903630	−	0.428314i	$-0.140892\pi$
$167$	23.3549			1.80726			0.903630	+	0.428314i	$0.140892\pi$
$168$	1.42912	+	1.61522i	0.110259	+	0.124617i
$169$			15.7736i			1.21335i
$170$	6.08351	−	9.03125i	0.466584	−	0.692665i
$171$	14.0719	−	7.35288i	1.07611	−	0.562289i
$172$	−12.7035	+	4.24359i	−0.968635	+	0.323571i
$173$	−6.68054	+	6.68054i	−0.507912	+	0.507912i	−0.913885	−	0.405973i	$-0.866933\pi$
$173$	−6.68054	+	6.68054i	−0.507912	+	0.507912i	0.405973	+	0.913885i	$0.366933\pi$
$174$	−5.96972	−	14.0434i	−0.452563	−	1.06463i
$175$	−1.65110	−	1.45568i	−0.124811	−	0.110039i
$176$	−2.65198	+	18.7361i	−0.199901	+	1.41229i
$177$	1.08313	+	0.165857i	0.0814127	+	0.0124666i
$178$	−8.14856	−	13.1752i	−0.610760	−	0.987520i
$179$	−10.3007	+	10.3007i	−0.769913	+	0.769913i	−0.978091	−	0.208178i	$-0.933247\pi$
$179$	−10.3007	+	10.3007i	−0.769913	+	0.769913i	0.208178	+	0.978091i	$0.433247\pi$
$180$	−4.50950	+	12.6358i	−0.336118	+	0.941820i
$181$	−4.40418	−	4.40418i	−0.327360	−	0.327360i	0.524222	−	0.851582i	$-0.324356\pi$
$181$	−4.40418	−	4.40418i	−0.327360	−	0.327360i	−0.851582	+	0.524222i	$0.824356\pi$
$182$	−3.25050	−	0.766236i	−0.240943	−	0.0567972i
$183$	0.0602921	−	0.393735i	0.00445692	−	0.0291058i
$184$	0.0521043	−	0.00474896i	0.00384118	−	0.000350098i
$185$	7.52296	+	2.84275i	0.553099	+	0.209003i
$186$	−3.34716	+	8.29699i	−0.245426	+	0.608365i
$187$	11.5187	+	11.5187i	0.842332	+	0.842332i
$188$	−5.87708	−	2.93381i	−0.428630	−	0.213970i
$189$	−2.16442	+	0.740287i	−0.157438	+	0.0538480i
$190$	−16.4265	+	3.20356i	−1.19170	+	0.232411i
$191$	3.25481			0.235510			0.117755	−	0.993043i	$-0.462430\pi$
$191$	3.25481			0.235510			0.117755	+	0.993043i	$0.462430\pi$
$192$	−9.50131	+	10.0859i	−0.685698	+	0.727886i
$193$			3.29429i			0.237128i	0.992946	+	0.118564i	$0.0378291\pi$
$193$			3.29429i			0.237128i	−0.992946	+	0.118564i	$0.962171\pi$
$194$	20.5516	−	12.7107i	1.47552	−	0.912576i
$195$	−5.58460	−	20.0104i	−0.399921	−	1.43297i
$196$	−6.07981	+	12.1792i	−0.434272	+	0.869943i
$197$	−3.74538	−	3.74538i	−0.266847	−	0.266847i	0.560981	−	0.827829i	$-0.310424\pi$
$197$	−3.74538	−	3.74538i	−0.266847	−	0.266847i	−0.827829	+	0.560981i	$0.810424\pi$
$198$	−17.2621	−	10.2398i	−1.22677	−	0.727708i
$199$	23.2982			1.65157			0.825784	−	0.563986i	$-0.190733\pi$
$199$	23.2982			1.65157			0.825784	+	0.563986i	$0.190733\pi$
$200$	8.35104	−	11.4132i	0.590508	−	0.807032i
$201$	2.58975	−	16.9123i	0.182667	−	1.19290i
$202$	11.0354	+	2.60136i	0.776450	+	0.183031i
$203$	−1.93925	+	1.93925i	−0.136108	+	0.136108i
$204$	2.02332	+	11.7556i	0.141661	+	0.823054i
$205$	7.30005	+	16.1681i	0.509858	+	1.12923i
$206$	18.3085	−	11.3234i	1.27561	−	0.788941i
$207$	−0.0166060	+	0.0529512i	−0.00115420	+	0.00368036i
$208$	3.00705	−	21.2446i	0.208501	−	1.47305i
$209$		−	25.0368i		−	1.73183i
$210$	2.40926	−	0.0980097i	0.166255	−	0.00676331i
$211$	−10.8276	−	10.8276i	−0.745401	−	0.745401i	0.228211	−	0.973612i	$-0.426713\pi$
$211$	−10.8276	−	10.8276i	−0.745401	−	0.745401i	−0.973612	+	0.228211i	$0.926713\pi$
$212$	14.9640	−	4.99869i	1.02773	−	0.343311i
$213$	5.85086	+	7.96673i	0.400894	+	0.545871i
$214$	15.2696	+	3.59948i	1.04381	+	0.246055i
$215$	−5.29319	+	14.0077i	−0.360993	+	0.955320i
$216$	−5.99881	−	13.4169i	−0.408168	−	0.912907i
$217$	1.60794			0.109154
$218$	20.8760	+	4.92107i	1.41390	+	0.333297i
$219$	7.70259	−	5.65688i	0.520493	−	0.382256i
$220$	14.3668	+	15.5302i	0.968609	+	1.04705i
$221$	−13.0609	−	13.0609i	−0.878573	−	0.878573i
$222$	−8.10760	+	3.44647i	−0.544146	+	0.231312i
$223$	−12.4106			−0.831075			−0.415538	−	0.909576i	$-0.636407\pi$
$223$	−12.4106			−0.831075			−0.415538	+	0.909576i	$0.636407\pi$
$224$	2.31990	+	0.905443i	0.155005	+	0.0604975i
$225$	7.76755	+	12.8322i	0.517837	+	0.855480i
$226$	−0.457759	−	0.740138i	−0.0304497	−	0.0492332i
$227$	2.72995	+	2.72995i	0.181193	+	0.181193i	0.791876	−	0.610682i	$-0.209105\pi$
$227$	2.72995	+	2.72995i	0.181193	+	0.181193i	−0.610682	+	0.791876i	$0.709105\pi$
$228$	10.5769	−	14.9747i	0.700470	−	0.991724i
$229$	−10.5245	−	10.5245i	−0.695480	−	0.695480i	0.267952	−	0.963432i	$-0.413653\pi$
$229$	−10.5245	−	10.5245i	−0.695480	−	0.695480i	−0.963432	+	0.267952i	$0.913653\pi$
$230$	0.0326804	−	0.0485155i	0.00215488	−	0.00319902i
$231$	−0.546000	+	3.56563i	−0.0359241	+	0.234601i
$232$	−13.5388	−	11.2770i	−0.888868	−	0.740374i
$233$		−	11.6936i		−	0.766074i	−0.923733	−	0.383037i	$-0.874878\pi$
$233$		−	11.6936i		−	0.766074i	0.923733	−	0.383037i	$-0.125122\pi$
$234$	19.5733	+	11.6107i	1.27955	+	0.759017i
$235$	−6.69336	+	3.02211i	−0.436627	+	0.197141i
$236$	1.20008	−	0.400884i	0.0781184	−	0.0260953i
$237$	−3.02659	−	4.12110i	−0.196598	−	0.267694i
$238$	1.82328	−	1.12766i	0.118186	−	0.0730955i
$239$	19.5159			1.26238			0.631190	−	0.775628i	$-0.282567\pi$
$239$	19.5159			1.26238			0.631190	+	0.775628i	$0.282567\pi$
$240$	2.03209	+	15.3581i	0.131171	+	0.991360i
$241$	14.9628			0.963837			0.481919	−	0.876216i	$-0.339940\pi$
$241$	14.9628			0.963837			0.481919	+	0.876216i	$0.339940\pi$
$242$	−13.6870	+	8.46514i	−0.879836	+	0.544160i
$243$	15.5833	−	0.399917i	0.999671	−	0.0256547i
$244$	−0.145728	−	0.436249i	−0.00932931	−	0.0279280i
$245$	6.26279	+	13.8708i	0.400115	+	0.886173i
$246$	−18.0217	−	7.27029i	−1.14902	−	0.463537i
$247$			28.3889i			1.80634i
$248$	0.937694	+	10.2881i	0.0595436	+	0.653296i
$249$	−12.3833	−	1.89624i	−0.784762	−	0.120169i
$250$	−3.99484	−	15.2984i	−0.252656	−	0.967556i
$251$	9.52848	+	9.52848i	0.601432	+	0.601432i	0.940693	−	0.339260i	$-0.110177\pi$
$251$	9.52848	+	9.52848i	0.601432	+	0.601432i	−0.339260	+	0.940693i	$0.610177\pi$
$252$	−1.83288	+	1.90198i	−0.115461	+	0.119813i
$253$	0.0618781	+	0.0618781i	0.00389024	+	0.00389024i
$254$	4.26297	+	6.89267i	0.267482	+	0.432484i
$255$	11.6181	+	6.54817i	0.727554	+	0.410062i
$256$	−4.44044	+	15.3715i	−0.277528	+	0.960718i
$257$	−9.63886			−0.601256			−0.300628	−	0.953742i	$-0.597196\pi$
$257$	−9.63886			−0.601256			−0.300628	+	0.953742i	$0.597196\pi$
$258$	−6.41732	−	15.0963i	−0.399525	−	0.939857i
$259$	1.11958	+	1.11958i	0.0695671	+	0.0695671i
$260$	−16.2903	−	17.6096i	−1.01028	−	1.09210i
$261$	16.5641	−	8.65510i	1.02529	−	0.535737i
$262$	16.7194	+	3.94123i	1.03293	+	0.243490i
$263$	0.238312			0.0146949			0.00734746	−	0.999973i	$-0.497661\pi$
$263$	0.238312			0.0146949			0.00734746	+	0.999973i	$0.497661\pi$
$264$	−23.1325	−	1.41413i	−1.42371	−	0.0870339i
$265$	6.23505	−	16.5002i	0.383016	−	1.01360i
$266$	−3.20705	−	0.755991i	−0.196637	−	0.0463528i
$267$	15.2921	−	11.2307i	0.935860	−	0.687307i
$268$	−6.25954	−	18.7384i	−0.382362	−	1.14463i
$269$	22.4266	+	22.4266i	1.36737	+	1.36737i	0.864165	+	0.503208i	$0.167847\pi$
$269$	22.4266	+	22.4266i	1.36737	+	1.36737i	0.503208	+	0.864165i	$0.332153\pi$
$270$	−15.8656	−	4.27566i	−0.965552	−	0.260209i
$271$		−	15.3922i		−	0.935011i	−0.883990	−	0.467505i	$-0.845153\pi$
$271$		−	15.3922i		−	0.935011i	0.883990	−	0.467505i	$-0.154847\pi$
$272$	8.27843	+	11.0084i	0.501953	+	0.667480i
$273$	0.619102	−	4.04303i	0.0374698	−	0.244695i
$274$	−5.92528	+	3.66466i	−0.357960	+	0.221390i
$275$	23.6069	−	1.48490i	1.42355	−	0.0895426i
$276$	0.0108692	+	0.0631504i	0.000654249	+	0.00380121i
$277$	−4.32796	+	4.32796i	−0.260042	+	0.260042i	−0.825071	−	0.565029i	$-0.808865\pi$
$277$	−4.32796	+	4.32796i	−0.260042	+	0.260042i	0.565029	+	0.825071i	$0.308865\pi$
$278$	−13.1174	−	3.09215i	−0.786732	−	0.185455i
$279$	−10.4553	−	3.27890i	−0.625945	−	0.196303i
$280$	2.42313	−	1.37135i	0.144810	−	0.0819540i
$281$	−17.7037			−1.05611			−0.528057	−	0.849209i	$-0.677079\pi$
$281$	−17.7037			−1.05611			−0.528057	+	0.849209i	$0.677079\pi$
$282$	3.00979	−	7.46071i	0.179230	−	0.444279i
$283$	−9.86424	−	9.86424i	−0.586368	−	0.586368i	0.350278	−	0.936646i	$-0.386087\pi$
$283$	−9.86424	−	9.86424i	−0.586368	−	0.586368i	−0.936646	+	0.350278i	$0.886087\pi$
$284$	10.2118	+	5.09771i	0.605962	+	0.302493i
$285$	−5.50993	−	19.7429i	−0.326380	−	1.16947i
$286$	30.5213	−	18.8768i	1.80476	−	1.11621i
$287$			3.49256i			0.206160i
$288$	−13.2383	−	10.6182i	−0.780077	−	0.625684i
$289$	−5.14273			−0.302514
$290$	−19.3357	+	3.77092i	−1.13543	+	0.221436i
$291$	17.5184	+	23.8537i	1.02695	+	1.39833i
$292$	4.92870	−	9.87328i	0.288430	−	0.577790i
$293$	−15.2467	−	15.2467i	−0.890721	−	0.890721i	0.103870	−	0.994591i	$-0.466877\pi$
$293$	−15.2467	−	15.2467i	−0.890721	−	0.890721i	−0.994591	+	0.103870i	$0.966877\pi$
$294$	−15.4610	−	6.23726i	−0.901704	−	0.363764i
$295$	0.500037	−	1.32328i	0.0291133	−	0.0770445i
$296$	−6.51052	+	7.81632i	−0.378417	+	0.454314i
$297$	10.8213	−	22.0715i	0.627915	−	1.28072i
$298$	−15.4545	−	3.64305i	−0.895253	−	0.211036i
$299$	−0.0701628	−	0.0701628i	−0.00405762	−	0.00405762i
$300$	14.7468	+	9.08470i	0.851407	+	0.524505i
$301$	−2.08465	+	2.08465i	−0.120157	+	0.120157i
$302$	−2.80992	−	4.54327i	−0.161693	−	0.261436i
$303$	−2.10185	+	13.7260i	−0.120748	+	0.788540i
$304$	2.96684	−	20.9606i	0.170160	−	1.20217i
$305$	−0.481037	−	0.181772i	−0.0275441	−	0.0104083i
$306$	−14.1551	+	3.61439i	−0.809193	+	0.206621i
$307$	1.97950	−	1.97950i	0.112976	−	0.112976i	−0.648359	−	0.761335i	$-0.724544\pi$
$307$	1.97950	−	1.97950i	0.112976	−	0.112976i	0.761335	+	0.648359i	$0.224544\pi$
$308$	1.31970	+	3.95063i	0.0751971	+	0.225108i
$309$	15.6064	+	21.2502i	0.887819	+	1.20888i
$310$	9.57951	+	6.45282i	0.544080	+	0.366496i
$311$			10.4775i			0.594124i	0.954858	+	0.297062i	$0.0960067\pi$
$311$			10.4775i			0.594124i	−0.954858	+	0.297062i	$0.903993\pi$
$312$	26.2296	+	1.60347i	1.48496	+	0.0907786i
$313$	21.3133			1.20470			0.602348	−	0.798234i	$-0.294232\pi$
$313$	21.3133			1.20470			0.602348	+	0.798234i	$0.294232\pi$
$314$	2.91483	−	12.3652i	0.164493	−	0.697808i
$315$	0.354152	+	2.93186i	0.0199542	+	0.165191i
$316$	−5.28248	−	2.63699i	−0.297163	−	0.148342i
$317$	−2.64044	+	2.64044i	−0.148302	+	0.148302i	−0.777359	−	0.629057i	$-0.783441\pi$
$317$	−2.64044	+	2.64044i	−0.148302	+	0.148302i	0.629057	+	0.777359i	$0.283441\pi$
$318$	7.55920	+	17.7825i	0.423899	+	0.997195i
$319$		−	29.4709i		−	1.65005i
$320$	10.1875	+	14.7043i	0.569496	+	0.821994i
$321$	−2.90830	+	18.9926i	−0.162326	+	1.06006i
$322$	0.00979461	−	0.00605776i	0.000545832	−	0.000337586i
$323$	−12.8863	−	12.8863i	−0.717013	−	0.717013i
$324$	15.7965	−	8.62966i	0.877583	−	0.479425i
$325$	−26.7676	+	1.68371i	−1.48480	+	0.0933952i
$326$	−1.24649	−	0.293833i	−0.0690367	−	0.0162739i
$327$	−3.97612	+	25.9659i	−0.219880	+	1.43592i
$328$	−22.3466	+	2.03674i	−1.23388	+	0.112460i
$329$	−1.44587			−0.0797134
$330$	−17.5621	+	19.0516i	−0.966762	+	1.04875i
$331$	−18.8251	+	18.8251i	−1.03472	+	1.03472i	−0.0353466	+	0.999375i	$0.511254\pi$
$331$	−18.8251	+	18.8251i	−1.03472	+	1.03472i	−0.999375	+	0.0353466i	$0.988746\pi$
$332$	−13.7204	+	4.58329i	−0.753007	+	0.251541i
$333$	−4.99681	−	9.56289i	−0.273824	−	0.524043i
$334$	17.3733	+	28.0904i	0.950627	+	1.53704i
$335$	−20.6622	−	7.80775i	−1.12890	−	0.426583i
$336$	−0.879633	+	2.92042i	−0.0479879	+	0.159322i
$337$			0.0498334i			0.00271460i	0.999999	+	0.00135730i	$0.000432042\pi$
$337$			0.0498334i			0.00271460i	−0.999999	+	0.00135730i	$0.999568\pi$
$338$	−18.9719	+	11.7337i	−1.03193	+	0.638229i
$339$	0.859059	−	0.630903i	0.0466577	−	0.0342660i
$340$	15.3879	+	0.598826i	0.834525	+	0.0324759i
$341$	−12.2180	+	12.2180i	−0.661641	+	0.661641i
$342$	19.3116	+	11.4555i	1.04425	+	0.619442i
$343$			6.07793i			0.328178i
$344$	−14.5540	−	12.1226i	−0.784698	−	0.653606i
$345$	0.0624120	+	0.0351765i	0.00336015	+	0.00189384i
$346$	−13.0047	−	3.06556i	−0.699134	−	0.164806i
$347$	−24.0018	+	24.0018i	−1.28848	+	1.28848i	−0.352774	+	0.935709i	$0.614762\pi$
$347$	−24.0018	+	24.0018i	−1.28848	+	1.28848i	−0.935709	+	0.352774i	$0.885238\pi$
$348$	12.4501	−	17.6268i	0.667394	−	0.944894i
$349$	−21.9261	+	21.9261i	−1.17368	+	1.17368i	−0.192351	+	0.981326i	$0.561611\pi$
$349$	−21.9261	+	21.9261i	−1.17368	+	1.17368i	−0.981326	+	0.192351i	$0.938389\pi$
$350$	0.522612	−	3.06873i	0.0279348	−	0.164031i
$351$	−12.2701	+	25.0266i	−0.654931	+	1.33582i
$352$	−24.5078	+	10.7478i	−1.30627	+	0.572858i
$353$	16.8045			0.894413			0.447206	−	0.894431i	$-0.352419\pi$
$353$	16.8045			0.894413			0.447206	+	0.894431i	$0.352419\pi$
$354$	0.606232	+	1.42612i	0.0322209	+	0.0757975i
$355$	11.6302	−	5.25113i	0.617266	−	0.278701i
$356$	9.78502	−	19.6016i	0.518605	−	1.03888i
$357$	1.55419	+	2.11624i	0.0822565	+	0.112003i
$358$	−20.0519	−	4.72679i	−1.05977	−	0.249819i
$359$		−	29.9327i		−	1.57979i	−0.613245	−	0.789893i	$-0.710136\pi$
$359$		−	29.9327i		−	1.57979i	0.613245	−	0.789893i	$-0.289864\pi$
$360$	−18.5525	+	3.97573i	−0.977800	+	0.209540i
$361$			9.00932i			0.474175i
$362$	2.02099	−	8.57337i	0.106221	−	0.450606i
$363$	−11.6670	−	15.8862i	−0.612359	−	0.833809i
$364$	−1.49640	−	4.47958i	−0.0784325	−	0.234794i
$365$	−5.07703	−	11.2446i	−0.265744	−	0.588569i
$366$	0.518420	−	0.220376i	0.0270983	−	0.0115192i
$367$	−8.55600			−0.446619			−0.223310	−	0.974748i	$-0.571686\pi$
$367$	−8.55600			−0.446619			−0.223310	+	0.974748i	$0.571686\pi$
$368$	0.0444714	+	0.0591365i	0.00231823	+	0.00308270i
$369$	7.12203	−	22.7098i	0.370758	−	1.18222i
$370$	2.17705	+	11.1630i	0.113179	+	0.580337i
$371$	2.45559	−	2.45559i	0.127488	−	0.127488i
$372$	−12.4692	+	2.14615i	−0.646498	+	0.111273i
$373$	−14.5653	+	14.5653i	−0.754163	+	0.754163i	−0.975253	−	0.221090i	$-0.929039\pi$
$373$	−14.5653	+	14.5653i	−0.754163	+	0.754163i	0.221090	+	0.975253i	$0.429039\pi$
$374$	−5.28570	+	22.4229i	−0.273317	+	1.15946i
$375$	18.2886	−	6.36619i	0.944417	−	0.328749i
$376$	−0.843180	−	9.25115i	−0.0434837	−	0.477092i
$377$			33.4166i			1.72104i
$378$	−2.50046	−	2.05259i	−0.128610	−	0.105574i
$379$	6.98000	−	6.98000i	0.358539	−	0.358539i	−0.504735	−	0.863274i	$-0.668410\pi$
$379$	6.98000	−	6.98000i	0.358539	−	0.358539i	0.863274	+	0.504735i	$0.168410\pi$
$380$	−16.0725	−	17.3741i	−0.824503	−	0.891274i
$381$	−8.00014	+	5.87540i	−0.409860	+	0.301006i
$382$	2.42120	+	3.91476i	0.123879	+	0.200297i
$383$			19.2617i			0.984227i	0.870531	+	0.492113i	$0.163775\pi$
$383$			19.2617i			0.984227i	−0.870531	+	0.492113i	$0.836225\pi$
$384$	−19.1988	−	3.92509i	−0.979734	−	0.200302i
$385$	4.35623	+	1.64612i	0.222014	+	0.0838938i
$386$	−3.96225	+	2.45057i	−0.201673	+	0.124731i
$387$	17.8061	−	9.30406i	0.905134	−	0.472952i
$388$	30.5760	+	15.2634i	1.55226	+	0.774881i
$389$	12.7288	−	12.7288i	0.645378	−	0.645378i	−0.306494	−	0.951872i	$-0.599156\pi$
$389$	12.7288	−	12.7288i	0.645378	−	0.645378i	0.951872	+	0.306494i	$0.0991561\pi$
$390$	19.9135	−	21.6023i	1.00836	−	1.09388i
$391$	0.0636968			0.00322128
$392$	−19.1714	+	1.74734i	−0.968300	+	0.0882541i
$393$	−3.18443	+	20.7958i	−0.160633	+	1.04901i
$394$	1.71868	−	7.29093i	0.0865858	−	0.367312i
$395$	−6.01617	+	2.71636i	−0.302706	+	0.136675i
$396$	−0.525020	−	28.3794i	−0.0263833	−	1.42612i
$397$	−17.6330	−	17.6330i	−0.884976	−	0.884976i	0.109060	−	0.994035i	$-0.465216\pi$
$397$	−17.6330	−	17.6330i	−0.884976	−	0.884976i	−0.994035	+	0.109060i	$0.965216\pi$
$398$	17.3312	+	28.0223i	0.868733	+	1.40463i
$399$	0.610825	−	3.98897i	0.0305795	−	0.199698i
$400$	19.9395	+	1.55426i	0.996976	+	0.0777132i
$401$			14.6077i			0.729475i	0.931110	+	0.364737i	$0.118841\pi$
$401$			14.6077i			0.729475i	−0.931110	+	0.364737i	$0.881159\pi$
$402$	22.2679	−	9.46590i	1.11062	−	0.472116i
$403$	13.8538	−	13.8538i	0.690108	−	0.690108i
$404$	5.08025	+	15.2081i	0.252752	+	0.756632i
$405$	3.67583	−	19.7861i	0.182653	−	0.983177i
$406$	−3.77503	−	0.889880i	−0.187351	−	0.0441640i
$407$	−17.0143			−0.843367
$408$	−12.6340	+	11.1783i	−0.625478	+	0.553411i
$409$		−	15.8009i		−	0.781306i	−0.920538	−	0.390653i	$-0.872249\pi$
$409$		−	15.8009i		−	0.781306i	0.920538	−	0.390653i	$-0.127751\pi$
$410$	−14.0160	+	20.8074i	−0.692202	+	1.02760i
$411$	−5.05079	−	6.87733i	−0.249137	−	0.339234i
$412$	27.2388	+	13.5975i	1.34196	+	0.669900i
$413$	0.196933	−	0.196933i	0.00969043	−	0.00969043i
$414$	−0.0760407	+	0.0194164i	−0.00373719	+	0.000954262i
$415$	−5.71691	+	15.1290i	−0.280632	+	0.742656i
$416$	27.7892	−	12.1868i	1.36248	−	0.597505i
$417$	2.49839	−	16.3157i	0.122347	−	0.798982i
$418$	30.1133	−	18.6244i	1.47289	−	0.910950i
$419$	−25.6978	+	25.6978i	−1.25542	+	1.25542i	−0.302161	+	0.953257i	$0.597708\pi$
$419$	−25.6978	+	25.6978i	−1.25542	+	1.25542i	−0.953257	+	0.302161i	$0.902292\pi$
$420$	1.91009	+	2.82486i	0.0932029	+	0.137839i
$421$	3.85429	+	3.85429i	0.187847	+	0.187847i	0.794764	−	0.606918i	$-0.207594\pi$
$421$	3.85429	+	3.85429i	0.187847	+	0.187847i	−0.606918	+	0.794764i	$0.707594\pi$
$422$	4.96855	−	21.0775i	0.241865	−	1.02603i
$423$	9.40151	+	2.94841i	0.457117	+	0.143357i
$424$	17.1437	+	14.2796i	0.832570	+	0.693481i
$425$	11.3861	−	12.9146i	0.552307	−	0.626452i
$426$	−5.22972	+	12.9635i	−0.253381	+	0.628084i
$427$	−0.0715886	−	0.0715886i	−0.00346441	−	0.00346441i
$428$	7.02949	+	21.0433i	0.339783	+	1.01717i
$429$	26.0168	+	35.4253i	1.25610	+	1.71035i
$430$	−20.7855	+	4.05367i	−1.00237	+	0.195485i
$431$	−29.8465			−1.43765			−0.718827	−	0.695189i	$-0.755321\pi$
$431$	−29.8465			−1.43765			−0.718827	+	0.695189i	$0.755321\pi$
$432$	11.6750	−	17.1958i	0.561712	−	0.827333i
$433$		−	9.24672i		−	0.444369i	−0.975005	−	0.222184i	$-0.928681\pi$
$433$		−	9.24672i		−	0.444369i	0.975005	−	0.222184i	$-0.0713187\pi$
$434$	1.19612	+	1.93397i	0.0574155	+	0.0928335i
$435$	−6.48576	−	23.2394i	−0.310969	−	1.11424i
$436$	9.61045	+	28.7696i	0.460257	+	1.37782i
$437$	−0.0692248	−	0.0692248i	−0.00331147	−	0.00331147i
$438$	12.5337	+	5.05633i	0.598884	+	0.241601i
$439$	−11.2775			−0.538246			−0.269123	−	0.963106i	$-0.586734\pi$
$439$	−11.2775			−0.538246			−0.269123	+	0.963106i	$0.586734\pi$
$440$	−7.99199	+	28.8325i	−0.381003	+	1.37454i
$441$	6.11006	−	19.4830i	0.290955	−	0.927760i
$442$	5.99339	−	25.4250i	0.285077	−	1.20934i
$443$	18.7172	−	18.7172i	0.889282	−	0.889282i	−0.105172	−	0.994454i	$-0.533539\pi$
$443$	18.7172	−	18.7172i	0.889282	−	0.889282i	0.994454	+	0.105172i	$0.0335395\pi$
$444$	−10.1764	−	7.18775i	−0.482950	−	0.341115i
$445$	−10.0795	−	22.3240i	−0.477815	−	1.05826i
$446$	−9.23203	−	14.9270i	−0.437150	−	0.706814i
$447$	2.94351	−	19.2225i	0.139223	−	0.909192i
$448$	0.636699	+	3.46383i	0.0300812	+	0.163651i
$449$			7.78422i			0.367360i	0.982986	+	0.183680i	$0.0588010\pi$
$449$			7.78422i			0.367360i	−0.982986	+	0.183680i	$0.941199\pi$
$450$	−9.65594	+	18.8882i	−0.455185	+	0.890397i
$451$	−26.5384	−	26.5384i	−1.24964	−	1.24964i
$452$	0.549690	−	1.10115i	0.0258553	−	0.0517938i
$453$	5.27326	−	3.87275i	0.247759	−	0.181957i
$454$	−1.25272	+	5.31425i	−0.0587930	+	0.249410i
$455$	−4.93947	−	1.86651i	−0.231566	−	0.0875033i
$456$	25.8790	+	1.58203i	1.21189	+	0.0740854i
$457$	18.3732			0.859460			0.429730	−	0.902957i	$-0.358609\pi$
$457$	18.3732			0.859460			0.429730	+	0.902957i	$0.358609\pi$
$458$	4.82949	−	20.4875i	0.225667	−	0.957319i
$459$	−5.79043	−	16.9298i	−0.270274	−	0.790214i
$460$	0.0826631	+	0.00321687i	0.00385419	+	0.000149987i
$461$	17.1622	+	17.1622i	0.799325	+	0.799325i	0.982989	−	0.183664i	$-0.0587958\pi$
$461$	17.1622	+	17.1622i	0.799325	+	0.799325i	−0.183664	+	0.982989i	$0.558796\pi$
$462$	−4.69477	+	1.99571i	−0.218420	+	0.0928486i
$463$	8.80346			0.409132			0.204566	−	0.978853i	$-0.434422\pi$
$463$	8.80346			0.409132			0.204566	+	0.978853i	$0.434422\pi$
$464$	3.49228	−	24.6728i	0.162125	−	1.14541i
$465$	−6.94569	+	12.3234i	−0.322099	+	0.571484i
$466$	14.0646	−	8.69869i	0.651532	−	0.402959i
$467$	−20.7474	−	20.7474i	−0.960073	−	0.960073i	0.0391596	−	0.999233i	$-0.487532\pi$
$467$	−20.7474	−	20.7474i	−0.960073	−	0.960073i	−0.999233	+	0.0391596i	$0.987532\pi$
$468$	0.595314	+	32.1791i	0.0275184	+	1.48748i
$469$	−3.07497	−	3.07497i	−0.141989	−	0.141989i
$470$	−8.61396	−	5.80242i	−0.397332	−	0.267646i
$471$	15.3800	+	2.35512i	0.708674	+	0.108518i
$472$	1.37489	+	1.14520i	0.0632842	+	0.0527120i
$473$		−	31.6806i		−	1.45667i
$474$	2.70528	−	6.70589i	0.124258	−	0.308012i
$475$	−26.4097	+	1.66119i	−1.21176	+	0.0762208i
$476$	2.71262	+	1.35413i	0.124333	+	0.0620664i
$477$	−20.9744	+	10.9596i	−0.960354	+	0.501805i
$478$	14.5176	+	23.4730i	0.664018	+	1.07363i
$479$	21.1247			0.965212			0.482606	−	0.875838i	$-0.339690\pi$
$479$	21.1247			0.965212			0.482606	+	0.875838i	$0.339690\pi$
$480$	−16.9605	+	13.8687i	−0.774137	+	0.633019i
$481$	19.2923			0.879653
$482$	11.1306	+	17.9967i	0.506983	+	0.819726i
$483$	0.00834906	+	0.0113684i	0.000379895	+	0.000517278i
$484$	−20.3631	−	10.1652i	−0.925596	−	0.462053i
$485$	34.8227	−	15.7228i	1.58122	−	0.713934i
$486$	12.0732	+	18.4456i	0.547651	+	0.836707i
$487$		−	14.1021i		−	0.639026i	−0.947582	−	0.319513i	$-0.896481\pi$
$487$		−	14.1021i		−	0.639026i	0.947582	−	0.319513i	$-0.103519\pi$
$488$	0.416299	−	0.499795i	0.0188450	−	0.0226247i
$489$	0.237411	−	1.55040i	0.0107361	−	0.0701117i
$490$	−12.0245	+	17.8509i	−0.543211	+	0.806421i
$491$	−2.84188	−	2.84188i	−0.128252	−	0.128252i	0.640067	−	0.768319i	$-0.278907\pi$
$491$	−2.84188	−	2.84188i	−0.128252	−	0.128252i	−0.768319	+	0.640067i	$0.778907\pi$
$492$	−4.66160	−	27.0841i	−0.210161	−	1.22104i
$493$	−15.1685	−	15.1685i	−0.683156	−	0.683156i
$494$	−34.1451	+	21.1180i	−1.53626	+	0.950144i
$495$	−24.9688	−	19.5868i	−1.12227	−	0.880360i
$496$	−11.6766	+	8.78098i	−0.524296	+	0.394278i
$497$	2.51230			0.112692
$498$	−6.93103	−	16.3048i	−0.310587	−	0.730635i
$499$	14.3965	+	14.3965i	0.644475	+	0.644475i	0.951652	−	0.307177i	$-0.0993844\pi$
$499$	14.3965	+	14.3965i	0.644475	+	0.644475i	−0.307177	+	0.951652i	$0.599384\pi$
$500$	15.4287	−	16.1851i	0.689990	−	0.723818i
$501$	−32.6039	+	23.9447i	−1.45663	+	1.06977i
$502$	−4.37242	+	18.5486i	−0.195151	+	0.827863i
$503$	−20.3925			−0.909257			−0.454628	−	0.890681i	$-0.650228\pi$
$503$	−20.3925			−0.909257			−0.454628	+	0.890681i	$0.650228\pi$
$504$	−3.65107	−	0.789673i	−0.162632	−	0.0351748i
$505$	16.7695	+	6.33678i	0.746231	+	0.281983i
$506$	−0.0283946	+	0.120455i	−0.00126229	+	0.00535487i
$507$	−16.1719	−	22.0202i	−0.718218	−	0.977949i
$508$	−5.11909	+	10.2547i	−0.227123	+	0.454978i
$509$	−0.999850	−	0.999850i	−0.0443176	−	0.0443176i	0.684601	−	0.728918i	$-0.259977\pi$
$509$	−0.999850	−	0.999850i	−0.0443176	−	0.0443176i	−0.728918	+	0.684601i	$0.759977\pi$
$510$	0.766619	+	18.8449i	0.0339464	+	0.834466i
$511$		−	2.42901i		−	0.107453i
$512$	−21.7914	+	6.09379i	−0.963054	+	0.269310i
$513$	−12.1061	+	24.6920i	−0.534497	+	1.09018i
$514$	−7.17019	−	11.5933i	−0.316263	−	0.511357i
$515$	31.0220	−	14.0067i	1.36699	−	0.617210i
$516$	13.3836	−	18.9484i	0.589179	−	0.834158i
$517$	10.9865	−	10.9865i	0.483185	−	0.483185i
$518$	−0.513751	+	2.17942i	−0.0225729	+	0.0957582i
$519$	2.47691	−	16.1754i	0.108724	−	0.710020i
$520$	9.06202	−	32.6929i	0.397396	−	1.43368i
$521$	40.7689			1.78612			0.893059	−	0.449940i	$-0.148555\pi$
$521$	40.7689			1.78612			0.893059	+	0.449940i	$0.148555\pi$
$522$	22.7318	+	13.4843i	0.994944	+	0.590192i
$523$	1.05115	+	1.05115i	0.0459634	+	0.0459634i	0.729715	−	0.683752i	$-0.239653\pi$
$523$	1.05115	+	1.05115i	0.0459634	+	0.0459634i	−0.683752	+	0.729715i	$0.739653\pi$
$524$	7.69689	+	23.0412i	0.336240	+	1.00656i
$525$	3.79739	+	0.339361i	0.165732	+	0.0148109i
$526$	0.177276	+	0.286632i	0.00772960	+	0.0124978i
$527$			12.5771i			0.547866i
$528$	−15.5070	−	28.8748i	−0.674856	−	1.25662i
$529$	−22.9997			−0.999985
$530$	24.4840	−	4.77496i	1.06352	−	0.207411i
$531$	−1.68211	+	0.878936i	−0.0729972	+	0.0381426i
$532$	−1.47639	−	4.41968i	−0.0640096	−	0.191618i
$533$	30.0915	+	30.0915i	1.30341	+	1.30341i
$534$	24.8834	+	10.0384i	1.07681	+	0.434405i
$535$	23.2037	+	8.76814i	1.00318	+	0.379080i
$536$	17.8815	−	21.4679i	0.772362	−	0.927273i
$537$	3.81915	−	24.9408i	0.164808	−	1.07628i
$538$	−10.2911	+	43.6566i	−0.443681	+	1.88217i
$539$	−22.7675	−	22.7675i	−0.980668	−	0.980668i
$540$	−6.65958	−	22.2632i	−0.286583	−	0.958056i
$541$	15.5806	−	15.5806i	0.669863	−	0.669863i	−0.287821	−	0.957684i	$-0.592931\pi$
$541$	15.5806	−	15.5806i	0.669863	−	0.669863i	0.957684	+	0.287821i	$0.0929308\pi$
$542$	18.5132	−	11.4500i	0.795210	−	0.491820i
$543$	10.6637	+	1.63291i	0.457623	+	0.0700750i
$544$	−7.08225	+	18.1459i	−0.303649	+	0.778000i
$545$	31.7233	+	11.9875i	1.35888	+	0.513487i
$546$	5.32334	−	2.26291i	0.227818	−	0.0968434i
$547$	−4.34516	+	4.34516i	−0.185785	+	0.185785i	−0.793871	−	0.608086i	$-0.791938\pi$
$547$	−4.34516	+	4.34516i	−0.185785	+	0.185785i	0.608086	+	0.793871i	$0.291938\pi$
$548$	−8.81544	−	4.40063i	−0.376577	−	0.187986i
$549$	0.319509	+	0.611475i	0.0136363	+	0.0260971i
$550$	19.3468	+	27.2889i	0.824949	+	1.16360i
$551$			32.9699i			1.40456i
$552$	−0.0678696	+	0.0600496i	−0.00288872	+	0.00255588i
$553$	−1.29959			−0.0552640
$554$	−8.42500	−	1.98601i	−0.357944	−	0.0843775i
$555$	−13.4167	+	3.74440i	−0.569507	+	0.158941i
$556$	−6.03872	−	18.0774i	−0.256099	−	0.766651i
$557$	20.8571	−	20.8571i	0.883745	−	0.883745i	−0.110168	−	0.993913i	$-0.535139\pi$
$557$	20.8571	−	20.8571i	0.883745	−	0.883745i	0.993913	+	0.110168i	$0.0351389\pi$
$558$	−3.83381	−	15.0144i	−0.162298	−	0.635611i
$559$			35.9222i			1.51935i
$560$	3.45194	+	1.89433i	0.145871	+	0.0800500i
$561$	−27.8899	−	4.27073i	−1.17751	−	0.180311i
$562$	−13.1695	−	21.2934i	−0.555522	−	0.898206i
$563$	−11.6633	−	11.6633i	−0.491551	−	0.491551i	0.417244	−	0.908795i	$-0.362996\pi$
$563$	−11.6633	−	11.6633i	−0.491551	−	0.491551i	−0.908795	+	0.417244i	$0.862996\pi$
$564$	11.2124	−	1.92983i	0.472127	−	0.0812606i
$565$	−0.566234	−	1.25409i	−0.0238216	−	0.0527601i
$566$	4.52650	−	19.2022i	0.190263	−	0.807128i
$567$	2.26258	−	3.25252i	0.0950194	−	0.136593i
$568$	1.46509	+	16.0745i	0.0614736	+	0.674472i
$569$	−16.4311			−0.688826			−0.344413	−	0.938818i	$-0.611922\pi$
$569$	−16.4311			−0.688826			−0.344413	+	0.938818i	$0.611922\pi$
$570$	19.6472	−	21.3135i	0.822932	−	0.892725i
$571$	1.93896	−	1.93896i	0.0811431	−	0.0811431i	−0.665370	−	0.746513i	$-0.731726\pi$
$571$	1.93896	−	1.93896i	0.0811431	−	0.0811431i	0.746513	+	0.665370i	$0.231726\pi$
$572$	45.4086	+	22.6678i	1.89863	+	0.947788i
$573$	−4.54377	+	3.33700i	−0.189819	+	0.139405i
$574$	−4.20073	+	2.59806i	−0.175335	+	0.108441i
$575$	0.0611657	−	0.0693770i	0.00255079	−	0.00289322i
$576$	2.92341	−	23.8213i	0.121809	−	0.992554i
$577$			3.38706i			0.141005i	0.997512	+	0.0705027i	$0.0224603\pi$
$577$			3.38706i			0.141005i	−0.997512	+	0.0705027i	$0.977540\pi$
$578$	−3.82559	−	6.18549i	−0.159124	−	0.257282i
$579$	−3.37748	−	4.59888i	−0.140363	−	0.191123i
$580$	−18.9190	−	20.4511i	−0.785570	−	0.849188i
$581$	−2.25153	+	2.25153i	−0.0934090	+	0.0934090i
$582$	−15.6587	+	38.8149i	−0.649072	+	1.60893i
$583$			37.3177i			1.54554i
$584$	15.5416	−	1.41651i	0.643115	−	0.0586157i
$585$	28.3119	+	22.2092i	1.17055	+	0.918238i
$586$	6.99639	−	29.6799i	0.289018	−	1.22606i
$587$	−15.5032	+	15.5032i	−0.639887	+	0.639887i	−0.950528	−	0.310640i	$-0.899457\pi$
$587$	−15.5032	+	15.5032i	−0.639887	+	0.639887i	0.310640	+	0.950528i	$0.399457\pi$
$588$	−3.99924	−	23.2357i	−0.164926	−	0.958224i
$589$	13.6686	−	13.6686i	0.563205	−	0.563205i
$590$	1.96356	−	0.382942i	0.0808387	−	0.0157655i
$591$	9.06857	+	1.38866i	0.373031	+	0.0571217i
$592$	−14.2442	−	2.01619i	−0.585435	−	0.0828647i
$593$	−28.5801			−1.17365			−0.586823	−	0.809715i	$-0.699621\pi$
$593$	−28.5801			−1.17365			−0.586823	+	0.809715i	$0.699621\pi$
$594$	34.5965	−	3.40316i	1.41951	−	0.139634i
$595$	3.08938	−	1.39488i	0.126652	−	0.0571846i
$596$	−7.11458	−	21.2980i	−0.291425	−	0.872402i
$597$	−32.5247	+	23.8865i	−1.33115	+	0.977611i
$598$	0.0321963	−	0.136582i	0.00131660	−	0.00558526i
$599$		−	20.1902i		−	0.824951i	−0.910969	−	0.412475i	$-0.864664\pi$
$599$		−	20.1902i		−	0.824951i	0.910969	−	0.412475i	$-0.135336\pi$
$600$	0.0431643	+	24.4949i	0.00176217	+	0.999998i
$601$			8.70832i			0.355220i	0.984101	+	0.177610i	$0.0568365\pi$
$601$			8.70832i			0.355220i	−0.984101	+	0.177610i	$0.943163\pi$
$602$	−4.05808	−	0.956603i	−0.165395	−	0.0389882i
$603$	13.7240	+	26.2650i	0.558884	+	1.06959i
$604$	3.37423	−	6.75933i	0.137295	−	0.275033i
$605$	−23.1914	+	10.4711i	−0.942863	+	0.425711i
$606$	−18.0727	+	7.68254i	−0.734153	+	0.312082i
$607$	−15.7460			−0.639110			−0.319555	−	0.947568i	$-0.603534\pi$
$607$	−15.7460			−0.639110			−0.319555	+	0.947568i	$0.603534\pi$
$608$	27.4176	−	12.0238i	1.11193	−	0.487631i
$609$	0.719004	−	4.69543i	0.0291355	−	0.190269i
$610$	−0.139206	−	0.713791i	−0.00563629	−	0.0289005i
$611$	−12.4574	+	12.4574i	−0.503974	+	0.503974i
$612$	−14.8770	−	14.3365i	−0.601367	−	0.579521i
$613$	1.95644	−	1.95644i	0.0790199	−	0.0790199i	−0.666492	−	0.745512i	$-0.732205\pi$
$613$	1.95644	−	1.95644i	0.0790199	−	0.0790199i	0.745512	+	0.666492i	$0.232205\pi$
$614$	3.85339	+	0.908353i	0.155510	+	0.0366582i
$615$	−26.7674	−	15.0866i	−1.07936	−	0.608349i
$616$	−3.76997	+	4.52610i	−0.151896	+	0.182362i
$617$		−	4.13547i		−	0.166488i	−0.996529	−	0.0832440i	$-0.973472\pi$
$617$		−	4.13547i		−	0.166488i	0.996529	−	0.0832440i	$-0.0265281\pi$
$618$	−13.9496	+	34.5785i	−0.561136	+	1.39095i
$619$	−18.6898	+	18.6898i	−0.751206	+	0.751206i	−0.974704	−	0.223498i	$-0.928252\pi$
$619$	−18.6898	+	18.6898i	−0.751206	+	0.751206i	0.223498	+	0.974704i	$0.428252\pi$
$620$	−0.635179	+	16.3220i	−0.0255094	+	0.655508i
$621$	−0.0311060	−	0.0909461i	−0.00124824	−	0.00364954i
$622$	−12.6019	+	7.79402i	−0.505291	+	0.312512i
$623$		−	4.82234i		−	0.193203i
$624$	17.5832	+	32.7408i	0.703891	+	1.31068i
$625$	−3.13265	−	24.8030i	−0.125306	−	0.992118i
$626$	15.8546	+	25.6348i	0.633676	+	1.02457i
$627$	25.6690	+	34.9517i	1.02512	+	1.39584i
$628$	17.0407	−	5.69242i	0.679997	−	0.227152i
$629$	−8.75718	+	8.75718i	−0.349172	+	0.349172i
$630$	−3.26288	+	2.60692i	−0.129996	+	0.103862i
$631$	16.1144			0.641504			0.320752	−	0.947163i	$-0.396064\pi$
$631$	16.1144			0.641504			0.320752	+	0.947163i	$0.396064\pi$
$632$	−0.757873	−	8.31518i	−0.0301466	−	0.330760i
$633$	26.2165	+	4.01449i	1.04201	+	0.159561i
$634$	−5.14000	−	1.21164i	−0.204135	−	0.0481205i
$635$	5.27316	+	11.6790i	0.209259	+	0.463466i
$636$	−15.7650	+	22.3201i	−0.625123	+	0.885048i
$637$	25.8158	+	25.8158i	1.02286	+	1.02286i
$638$	35.4464	−	21.9229i	1.40334	−	0.867935i
$639$	−16.3358	−	5.12308i	−0.646234	−	0.202666i
$640$	−10.1075	+	23.1914i	−0.399533	+	0.916719i
$641$			26.1407i			1.03250i	0.856439	+	0.516248i	$0.172672\pi$
$641$			26.1407i			1.03250i	−0.856439	+	0.516248i	$0.827328\pi$
$642$	−25.0070	+	10.6303i	−0.986947	+	0.419543i
$643$	−4.36541	+	4.36541i	−0.172155	+	0.172155i	−0.787925	−	0.615771i	$-0.788845\pi$
$643$	−4.36541	+	4.36541i	−0.172155	+	0.172155i	0.615771	+	0.787925i	$0.288845\pi$
$644$	0.0145721	+	0.00727432i	0.000574221	+	0.000286649i
$645$	−6.97207	−	24.9819i	−0.274525	−	0.983660i
$646$	5.91326	−	25.0851i	0.232654	−	0.986959i
$647$	35.4164			1.39236			0.696182	−	0.717865i	$-0.254881\pi$
$647$	35.4164			1.39236			0.696182	+	0.717865i	$0.254881\pi$
$648$	22.1302	+	12.5800i	0.869355	+	0.494188i
$649$			2.99280i			0.117478i
$650$	−21.9371	−	30.9426i	−0.860442	−	1.21367i
$651$	−2.24471	+	1.64854i	−0.0879771	+	0.0646114i
$652$	−0.573832	−	1.71781i	−0.0224730	−	0.0672746i
$653$	34.9841	−	34.9841i	1.36903	−	1.36903i	0.507212	−	0.861822i	$-0.330676\pi$
$653$	34.9841	−	34.9841i	1.36903	−	1.36903i	0.861822	−	0.507212i	$-0.169324\pi$
$654$	−34.1886	+	14.5333i	−1.33688	+	0.568297i
$655$	25.4068	+	9.60062i	0.992725	+	0.375127i
$656$	−19.0730	−	25.3625i	−0.744674	−	0.990240i
$657$	−4.95322	+	15.7942i	−0.193244	+	0.616190i
$658$	−1.07556	−	1.73904i	−0.0419296	−	0.0677948i
$659$	−16.3292	+	16.3292i	−0.636097	+	0.636097i	−0.949590	−	0.313494i	$-0.898501\pi$
$659$	−16.3292	+	16.3292i	−0.636097	+	0.636097i	0.313494	+	0.949590i	$0.398501\pi$
$660$	−35.9787	−	6.95091i	−1.40047	−	0.270564i
$661$	33.8788	+	33.8788i	1.31773	+	1.31773i	0.915568	+	0.402162i	$0.131741\pi$
$661$	33.8788	+	33.8788i	1.31773	+	1.31773i	0.402162	+	0.915568i	$0.368259\pi$
$662$	−36.6458	−	8.63846i	−1.42428	−	0.335743i
$663$	31.6240	+	4.84253i	1.22817	+	0.188068i
$664$	−15.7190	−	13.0930i	−0.610016	−	0.508107i
$665$	−4.87343	−	1.84156i	−0.188984	−	0.0714124i
$666$	7.78484	−	13.1237i	0.301656	−	0.508531i
$667$	−0.0814847	−	0.0814847i	−0.00315510	−	0.00315510i
$668$	−20.8624	+	41.7920i	−0.807190	+	1.61698i
$669$	17.3254	−	12.7240i	0.669838	−	0.491937i
$670$	−5.97938	−	30.6598i	−0.231004	−	1.18449i
$671$	1.08794			0.0419993
$672$	−4.16692	+	1.11446i	−0.160742	+	0.0429914i
$673$			29.4380i			1.13475i	0.823459	+	0.567376i	$0.192041\pi$
$673$			29.4380i			1.13475i	−0.823459	+	0.567376i	$0.807959\pi$
$674$	−0.0599378	+	0.0370703i	−0.00230872	+	0.00142789i
$675$	−23.9998	−	9.95026i	−0.923754	−	0.382986i
$676$	−28.2257	−	14.0901i	−1.08560	−	0.541929i
$677$	−9.99478	−	9.99478i	−0.384130	−	0.384130i	0.488457	−	0.872588i	$-0.337560\pi$
$677$	−9.99478	−	9.99478i	−0.384130	−	0.384130i	−0.872588	+	0.488457i	$0.837560\pi$
$678$	1.39787	+	0.563926i	0.0536847	+	0.0216574i
$679$	7.52224			0.288677
$680$	10.7265	+	18.9534i	0.411344	+	0.726830i
$681$	−6.60994	−	1.01217i	−0.253293	−	0.0387864i
$682$	−23.7841	−	5.60658i	−0.910739	−	0.214687i
$683$	−8.48336	+	8.48336i	−0.324607	+	0.324607i	−0.850531	−	0.525925i	$-0.823719\pi$
$683$	−8.48336	+	8.48336i	−0.324607	+	0.324607i	0.525925	+	0.850531i	$0.323719\pi$
$684$	0.587355	+	31.7489i	0.0224581	+	1.21395i
$685$	−10.0398	+	4.53307i	−0.383602	+	0.173200i
$686$	−7.31031	+	4.52127i	−0.279109	+	0.172623i
$687$	25.4827	+	3.90212i	0.972225	+	0.148875i
$688$	3.75413	−	26.5228i	0.143125	−	1.01117i
$689$		−	42.3141i		−	1.61204i
$690$	0.00411825	+	0.101234i	0.000156779	+	0.00385392i
$691$	11.6149	+	11.6149i	0.441853	+	0.441853i	0.892634	−	0.450782i	$-0.148855\pi$
$691$	11.6149	+	11.6149i	0.441853	+	0.441853i	−0.450782	+	0.892634i	$0.648855\pi$
$692$	−5.98680	−	17.9219i	−0.227584	−	0.681289i
$693$	−2.89344	−	5.53746i	−0.109913	−	0.210351i
$694$	−46.7229	−	11.0139i	−1.77358	−	0.418083i
$695$	−19.9333	−	7.53232i	−0.756113	−	0.285717i
$696$	30.4622	+	1.86221i	1.15467	+	0.0705871i
$697$	−27.3184			−1.03476
$698$	−42.6824	−	10.0614i	−1.61555	−	0.380831i
$699$	11.9889	+	16.3245i	0.453462	+	0.617448i
$700$	4.07972	−	1.65420i	0.154199	−	0.0625229i
$701$	−27.1341	−	27.1341i	−1.02484	−	1.02484i	−0.999684	−	0.0251556i	$-0.991992\pi$
$701$	−27.1341	−	27.1341i	−1.02484	−	1.02484i	−0.0251556	−	0.999684i	$-0.508008\pi$
$702$	−39.2286	+	3.85881i	−1.48059	+	0.145641i
$703$	19.0344			0.717894
$704$	−31.1580	−	21.4820i	−1.17431	−	0.809635i
$705$	6.24561	−	11.0813i	0.235223	−	0.417345i
$706$	12.5006	+	20.2118i	0.470465	+	0.760681i
$707$	2.49565	+	2.49565i	0.0938587	+	0.0938587i
$708$	−1.26432	+	1.79002i	−0.0475160	+	0.0672731i
$709$	−1.84919	−	1.84919i	−0.0694477	−	0.0694477i	0.671530	−	0.740978i	$-0.265638\pi$
$709$	−1.84919	−	1.84919i	−0.0694477	−	0.0694477i	−0.740978	+	0.671530i	$0.765638\pi$
$710$	14.9674	+	10.0821i	0.561715	+	0.378375i
$711$	8.45033	+	2.65011i	0.316912	+	0.0993870i
$712$	30.8549	−	2.81222i	1.15634	−	0.105392i
$713$			0.0675636i			0.00253028i
$714$	−1.38920	+	3.44356i	−0.0519893	+	0.128872i
$715$	51.7155	−	23.3500i	1.93405	−	0.873241i
$716$	−9.23104	−	27.6338i	−0.344980	−	1.03272i
$717$	−27.2445	+	20.0087i	−1.01747	+	0.747239i
$718$	36.0019	−	22.2664i	1.34358	−	0.830975i
$719$	29.8745			1.11413			0.557064	−	0.830469i	$-0.311928\pi$
$719$	29.8745			1.11413			0.557064	+	0.830469i	$0.311928\pi$
$720$	−18.5827	−	19.3567i	−0.692537	−	0.721382i
$721$	6.70124			0.249567
$722$	−10.8361	+	6.70188i	−0.403277	+	0.249418i
$723$	−20.8883	+	15.3406i	−0.776843	+	0.570523i
$724$	11.8151	−	3.94682i	0.439105	−	0.146682i
$725$	−31.0870	+	1.95540i	−1.15454	+	0.0726217i
$726$	10.4284	−	25.8501i	0.387035	−	0.959388i
$727$		−	30.4730i		−	1.13018i	−0.825028	−	0.565091i	$-0.808841\pi$
$727$		−	30.4730i		−	1.13018i	0.825028	−	0.565091i	$-0.191159\pi$
$728$	4.27472	−	5.13209i	0.158432	−	0.190208i
$729$	−21.3446	+	16.5351i	−0.790539	+	0.612412i
$730$	9.74785	−	14.4711i	0.360784	−	0.535600i
$731$	−16.3059	−	16.3059i	−0.603094	−	0.603094i
$732$	0.650704	+	0.459603i	0.0240507	+	0.0169874i
$733$	16.5992	+	16.5992i	0.613105	+	0.613105i	0.943754	−	0.330649i	$-0.107268\pi$
$733$	16.5992	+	16.5992i	0.613105	+	0.613105i	−0.330649	+	0.943754i	$0.607268\pi$
$734$	−6.36466	−	10.2908i	−0.234924	−	0.379842i
$735$	−22.9640	−	12.9429i	−0.847040	−	0.477407i
$736$	−0.0380456	+	0.0974791i	−0.00140238	+	0.00359313i
$737$	46.7306			1.72134
$738$	32.6124	−	8.32732i	1.20048	−	0.306533i
$739$	−27.6075	−	27.6075i	−1.01556	−	1.01556i	−0.999877	−	0.0156803i	$-0.995009\pi$
$739$	−27.6075	−	27.6075i	−1.01556	−	1.01556i	−0.0156803	−	0.999877i	$-0.504991\pi$
$740$	−11.8070	+	10.9224i	−0.434033	+	0.401517i
$741$	−29.1057	−	39.6313i	−1.06923	−	1.45589i
$742$	4.78016	+	1.12682i	0.175485	+	0.0413668i
$743$	−27.3129			−1.00201			−0.501006	−	0.865444i	$-0.667037\pi$
$743$	−27.3129			−1.00201			−0.501006	+	0.865444i	$0.667037\pi$
$744$	−11.8569	−	13.4010i	−0.434697	−	0.491305i
$745$	−23.4846	−	8.87428i	−0.860410	−	0.325128i
$746$	−28.3535	−	6.68372i	−1.03810	−	0.244708i
$747$	19.2315	−	10.0488i	0.703642	−	0.367668i
$748$	−30.9013	+	10.3225i	−1.12986	+	0.377430i
$749$	3.45321	+	3.45321i	0.126178	+	0.126178i
$750$	21.2616	+	17.2611i	0.776363	+	0.630286i
$751$		−	9.64892i		−	0.352094i	−0.984382	−	0.176047i	$-0.943669\pi$
$751$		−	9.64892i		−	0.352094i	0.984382	−	0.176047i	$-0.0563311\pi$
$752$	10.4997	−	7.89592i	0.382885	−	0.287935i
$753$	−23.0710	−	3.53282i	−0.840754	−	0.128743i
$754$	−40.1923	+	24.8581i	−1.46372	+	0.905278i
$755$	−3.47578	−	7.69814i	−0.126497	−	0.280164i
$756$	0.608728	−	4.53435i	0.0221392	−	0.164913i
$757$	−5.65329	+	5.65329i	−0.205472	+	0.205472i	−0.802340	−	0.596868i	$-0.796412\pi$
$757$	−5.65329	+	5.65329i	−0.205472	+	0.205472i	0.596868	+	0.802340i	$0.296412\pi$
$758$	13.5876	+	3.20298i	0.493523	+	0.116337i
$759$	−0.149823	−	0.0229422i	−0.00543824	−	0.000832750i
$760$	8.94086	−	32.2558i	0.324319	−	1.17004i
$761$	−38.4858			−1.39511			−0.697554	−	0.716533i	$-0.745728\pi$
$761$	−38.4858			−1.39511			−0.697554	+	0.716533i	$0.745728\pi$
$762$	−13.0179	−	5.25166i	−0.471588	−	0.190248i
$763$	4.72110	+	4.72110i	0.170915	+	0.170915i
$764$	−2.90744	+	5.82425i	−0.105188	+	0.210714i
$765$	−22.9326	+	2.77013i	−0.829129	+	0.100154i
$766$	−23.1672	+	14.3285i	−0.837067	+	0.517708i
$767$		−	3.39350i		−	0.122532i
$768$	−9.56070	−	26.0114i	−0.344992	−	0.938606i
$769$	24.1959			0.872528			0.436264	−	0.899819i	$-0.356301\pi$
$769$	24.1959			0.872528			0.436264	+	0.899819i	$0.356301\pi$
$770$	1.26064	+	6.46402i	0.0454302	+	0.232947i
$771$	13.4560	−	9.88225i	0.484606	−	0.355901i
$772$	−5.89490	−	2.94271i	−0.212162	−	0.105910i
$773$	19.0814	+	19.0814i	0.686312	+	0.686312i	0.961415	−	0.275103i	$-0.0887120\pi$
$773$	19.0814	+	19.0814i	0.686312	+	0.686312i	−0.275103	+	0.961415i	$0.588712\pi$
$774$	24.4362	+	14.4954i	0.878342	+	0.521025i
$775$	13.6987	+	12.0773i	0.492070	+	0.433830i
$776$	4.38671	+	48.1298i	0.157474	+	1.72776i
$777$	−2.71079	−	0.415100i	−0.0972492	−	0.0148916i
$778$	24.7786	+	5.84101i	0.888354	+	0.209410i
$779$	29.6892	+	29.6892i	1.06373	+	1.06373i
$780$	40.7958	+	7.88155i	1.46072	+	0.282205i
$781$	−19.0898	+	19.0898i	−0.683087	+	0.683087i
$782$	0.0473830	+	0.0766121i	0.00169441	+	0.00273964i
$783$	−14.2501	+	29.0650i	−0.509257	+	1.03870i
$784$	−16.3629	−	21.7588i	−0.584389	−	0.777099i
$785$	7.10036	−	18.7902i	0.253423	−	0.670650i
$786$	−27.3812	+	11.6395i	−0.976656	+	0.415168i
$787$	25.7932	−	25.7932i	0.919427	−	0.919427i	−0.0775609	−	0.996988i	$-0.524713\pi$
$787$	25.7932	−	25.7932i	0.919427	−	0.919427i	0.996988	+	0.0775609i	$0.0247132\pi$
$788$	10.0478	−	3.35644i	0.357937	−	0.119568i
$789$	−0.332687	+	0.244329i	−0.0118440	+	0.00869835i
$790$	−7.74246	−	5.21537i	−0.275464	−	0.185555i
$791$		−	0.270904i		−	0.00963222i
$792$	33.7432	−	21.7425i	1.19901	−	0.772585i
$793$	−1.23360			−0.0438063
$794$	8.09143	−	34.3252i	0.287154	−	1.21816i
$795$	8.21265	+	29.4271i	0.291273	+	1.04367i
$796$	−20.8118	+	41.6906i	−0.737653	+	1.47768i
$797$	20.3796	−	20.3796i	0.721884	−	0.721884i	−0.247105	−	0.968989i	$-0.579479\pi$
$797$	20.3796	−	20.3796i	0.721884	−	0.721884i	0.968989	+	0.247105i	$0.0794793\pi$
$798$	5.25217	−	2.23265i	0.185925	−	0.0790350i
$799$		−	11.3094i		−	0.400098i
$800$	12.9633	+	25.1387i	0.458320	+	0.888787i
$801$	−9.83371	+	31.3564i	−0.347457	+	1.10792i
$802$	−17.5696	+	10.8664i	−0.620405	+	0.383707i
$803$	18.4569	+	18.4569i	0.651329	+	0.651329i
$804$	27.9500	+	19.7415i	0.985720	+	0.696229i
$805$	0.0165960	−	0.00749326i	0.000584933	−	0.000264103i
$806$	26.9685	+	6.35723i	0.949924	+	0.223924i
$807$	−54.3008	−	8.31499i	−1.91148	−	0.292702i
$808$	−14.5126	+	17.4234i	−0.510553	+	0.612953i
$809$	3.22975			0.113552			0.0567760	−	0.998387i	$-0.481918\pi$
$809$	3.22975			0.113552			0.0567760	+	0.998387i	$0.481918\pi$
$810$	26.5323	−	10.2974i	0.932251	−	0.361813i
$811$	32.3802	−	32.3802i	1.13702	−	1.13702i	0.148041	−	0.988981i	$-0.452703\pi$
$811$	32.3802	−	32.3802i	1.13702	−	1.13702i	0.988981	−	0.148041i	$-0.0472968\pi$
$812$	−1.73786	−	5.20243i	−0.0609871	−	0.182569i
$813$	15.7809	+	21.4878i	0.553460	+	0.753610i
$814$	−12.6566	−	20.4641i	−0.443615	−	0.717268i
$815$	−1.89417	−	0.715762i	−0.0663498	−	0.0250720i
$816$	−22.8431	−	6.88037i	−0.799670	−	0.240861i
$817$			35.4419i			1.23996i
$818$	19.0048	−	11.7541i	0.664487	−	0.410971i
$819$	3.28084	+	6.27886i	0.114642	+	0.219401i
$820$	−35.4527	−	1.37966i	−1.23806	−	0.0481797i
$821$	18.2713	−	18.2713i	0.637673	−	0.637673i	−0.312308	−	0.949981i	$-0.601102\pi$
$821$	18.2713	−	18.2713i	0.637673	−	0.637673i	0.949981	+	0.312308i	$0.101102\pi$
$822$	4.51459	−	11.1908i	0.157464	−	0.390325i
$823$		−	25.6220i		−	0.893126i	−0.894752	−	0.446563i	$-0.852648\pi$
$823$		−	25.6220i		−	0.893126i	0.894752	−	0.446563i	$-0.147352\pi$
$824$	3.90793	+	42.8768i	0.136139	+	1.49368i
$825$	−31.4332	+	26.2760i	−1.09437	+	0.914811i
$826$	0.383358	+	0.0903684i	0.0133387	+	0.00314432i
$827$	23.8780	−	23.8780i	0.830320	−	0.830320i	−0.157240	−	0.987560i	$-0.550260\pi$
$827$	23.8780	−	23.8780i	0.830320	−	0.830320i	0.987560	+	0.157240i	$0.0502598\pi$
$828$	−0.0799186	−	0.0770154i	−0.00277736	−	0.00267647i
$829$	30.4396	−	30.4396i	1.05721	−	1.05721i	0.0589488	−	0.998261i	$-0.481225\pi$
$829$	30.4396	−	30.4396i	1.05721	−	1.05721i	0.998261	−	0.0589488i	$-0.0187749\pi$
$830$	−22.4494	+	4.37816i	−0.779229	+	0.151968i
$831$	1.60465	−	10.4791i	0.0556649	−	0.363517i
$832$	35.3297	+	24.3582i	1.22484	+	0.844469i
$833$	−23.4367			−0.812034
$834$	21.4824	−	9.13198i	0.743875	−	0.316215i
$835$	21.4903	+	47.5966i	0.743702	+	1.64715i
$836$	44.8015	+	22.3647i	1.54949	+	0.773500i
$837$	17.9575	−	6.14194i	0.620703	−	0.212297i
$838$	−50.0244	−	11.7922i	−1.72807	−	0.407354i
$839$			22.6086i			0.780537i	0.920701	+	0.390268i	$0.127618\pi$
$839$			22.6086i			0.780537i	−0.920701	+	0.390268i	$0.872382\pi$
$840$	−1.97675	+	4.39875i	−0.0682044	+	0.151771i
$841$			9.80896i			0.338240i
$842$	−1.76865	+	7.50293i	−0.0609518	+	0.258568i
$843$	24.7147	−	18.1507i	0.851218	−	0.625145i
$844$	29.0472	−	9.70318i	0.999846	−	0.333997i
$845$	−32.1460	+	14.5142i	−1.10586	+	0.499304i
$846$	3.44739	+	13.5011i	0.118524	+	0.464176i
$847$	−5.00970			−0.172135
$848$	−4.42213	+	31.2421i	−0.151857	+	1.07286i
$849$	23.8840	+	3.65731i	0.819695	+	0.125519i
$850$	24.0032	+	4.08780i	0.823303	+	0.140210i
$851$	−0.0470432	+	0.0470432i	−0.00161262	+	0.00161262i
$852$	−19.4823	+	3.35322i	−0.667454	+	0.114879i
$853$	32.2703	−	32.2703i	1.10491	−	1.10491i	0.111104	−	0.993809i	$-0.464561\pi$
$853$	32.2703	−	32.2703i	1.10491	−	1.10491i	0.993809	−	0.111104i	$-0.0354386\pi$
$854$	0.0328505	−	0.139358i	0.00112412	−	0.00476872i
$855$	27.9333	+	21.9123i	0.955300	+	0.749384i
$856$	−20.0810	+	24.1086i	−0.686354	+	0.824014i
$857$			23.8230i			0.813777i	0.913478	+	0.406888i	$0.133386\pi$
$857$			23.8230i			0.813777i	−0.913478	+	0.406888i	$0.866614\pi$
$858$	−23.2548	+	57.6443i	−0.793906	+	1.96795i
$859$	5.96611	−	5.96611i	0.203561	−	0.203561i	−0.597963	−	0.801524i	$-0.704023\pi$
$859$	5.96611	−	5.96611i	0.203561	−	0.203561i	0.801524	+	0.597963i	$0.204023\pi$
$860$	−20.3376	−	21.9846i	−0.693506	−	0.749667i
$861$	−3.58076	−	4.87568i	−0.122032	−	0.166163i
$862$	−22.2023	−	35.8982i	−0.756213	−	1.22270i
$863$			4.16475i			0.141770i	0.997485	+	0.0708849i	$0.0225823\pi$
$863$			4.16475i			0.141770i	−0.997485	+	0.0708849i	$0.977418\pi$
$864$	29.3673	+	1.25057i	0.999095	+	0.0425452i
$865$	−19.7619	−	7.46755i	−0.671924	−	0.253904i
$866$	11.1216	−	6.87848i	0.377928	−	0.233740i
$867$	7.17934	−	5.27259i	0.243823	−	0.179067i
$868$	−1.43633	+	2.87729i	−0.0487523	+	0.0976617i
$869$	9.87495	−	9.87495i	0.334985	−	0.334985i
$870$	23.1268	−	25.0882i	0.784073	−	0.850571i
$871$	−52.9872			−1.79540
$872$	−27.4540	+	32.9603i	−0.929709	+	1.11618i
$873$	−48.9121	−	15.3393i	−1.65542	−	0.519158i
$874$	0.0317658	−	0.134756i	0.00107449	−	0.00455819i
$875$	1.44735	−	4.70433i	0.0489293	−	0.159036i
$876$	3.24205	+	18.8364i	0.109539	+	0.636423i
$877$	8.45950	+	8.45950i	0.285657	+	0.285657i	0.835360	−	0.549703i	$-0.185259\pi$
$877$	8.45950	+	8.45950i	0.285657	+	0.285657i	−0.549703	+	0.835360i	$0.685259\pi$
$878$	−8.38915	−	13.5642i	−0.283120	−	0.457768i
$879$	36.9163	+	5.65293i	1.24516	+	0.190669i
$880$	−40.6238	+	11.8356i	−1.36943	+	0.398977i
$881$		−	33.8513i		−	1.14048i	−0.821479	−	0.570239i	$-0.806851\pi$
$881$		−	33.8513i		−	1.14048i	0.821479	−	0.570239i	$-0.193149\pi$
$882$	27.9785	−	7.14409i	0.942087	−	0.240554i
$883$	−38.9521	+	38.9521i	−1.31084	+	1.31084i	−0.390049	+	0.920794i	$0.627542\pi$
$883$	−38.9521	+	38.9521i	−1.31084	+	1.31084i	−0.920794	+	0.390049i	$0.872458\pi$
$884$	35.0386	−	11.7046i	1.17848	−	0.393669i
$885$	0.658637	+	2.35999i	0.0221399	+	0.0793301i
$886$	36.4358	+	8.58894i	1.22408	+	0.288551i
$887$	21.5557			0.723771			0.361885	−	0.932223i	$-0.382133\pi$
$887$	21.5557			0.723771			0.361885	+	0.932223i	$0.382133\pi$
$888$	1.07510	−	17.5866i	0.0360781	−	0.590169i
$889$			2.52284i			0.0846133i
$890$	19.3526	−	28.7297i	0.648699	−	0.963023i
$891$	7.52212	+	41.9067i	0.252001	+	1.40393i
$892$	11.0861	−	22.2079i	0.371190	−	0.743575i
$893$	−12.2909	+	12.2909i	−0.411299	+	0.411299i
$894$	25.3097	−	10.7589i	0.846483	−	0.359833i
$895$	−30.4709	−	11.5142i	−1.01853	−	0.384878i
$896$	−3.69253	+	3.34248i	−0.123359	+	0.111664i
$897$	0.169883	+	0.0260139i	0.00567222	+	0.000868579i
$898$	−9.36257	+	5.79055i	−0.312433	+	0.193233i
$899$	16.0894	−	16.0894i	0.536610	−	0.536610i
$900$	−29.9009	+	2.43679i	−0.996696	+	0.0812264i
$901$	19.2073	+	19.2073i	0.639887	+	0.639887i
$902$	12.1779	−	51.6608i	0.405480	−	1.72012i
$903$	0.772915	−	5.04750i	0.0257210	−	0.167970i
$904$	1.73333	−	0.157981i	0.0576497	−	0.00525438i
$905$	4.92301	−	13.0281i	0.163647	−	0.433069i
$906$	8.58068	+	3.46161i	0.285074	+	0.115004i
$907$	−15.9679	−	15.9679i	−0.530205	−	0.530205i	0.390428	−	0.920633i	$-0.372327\pi$
$907$	−15.9679	−	15.9679i	−0.530205	−	0.530205i	−0.920633	+	0.390428i	$0.872327\pi$
$908$	−7.32365	+	2.44646i	−0.243044	+	0.0811885i
$909$	−11.1384	−	21.3167i	−0.369438	−	0.707030i
$910$	−1.42942	−	7.32948i	−0.0473849	−	0.242970i
$911$	−0.939903			−0.0311404			−0.0155702	−	0.999879i	$-0.504956\pi$
$911$	−0.939903			−0.0311404			−0.0155702	+	0.999879i	$0.504956\pi$
$912$	17.3481	+	32.3031i	0.574454	+	1.06966i
$913$		−	34.2166i		−	1.13240i
$914$	13.6675	+	22.0985i	0.452080	+	0.730955i
$915$	0.857898	−	0.239426i	0.0283612	−	0.00791519i
$916$	28.2342	−	9.43159i	0.932884	−	0.311629i
$917$	3.78107	+	3.78107i	0.124862	+	0.124862i
$918$	16.0551	−	19.5583i	0.529897	−	0.645519i
$919$	−38.8979			−1.28312			−0.641562	−	0.767071i	$-0.721713\pi$
$919$	−38.8979			−1.28312			−0.641562	+	0.767071i	$0.721713\pi$
$920$	0.0576225	+	0.101817i	0.00189976	+	0.00335681i
$921$	−0.733930	+	4.79291i	−0.0241838	+	0.157932i
$922$	−7.87540	+	33.4088i	−0.259362	+	1.10026i
$923$	21.6457	−	21.6457i	0.712477	−	0.712477i
$924$	−5.89272	−	4.16212i	−0.193856	−	0.136924i
$925$	1.12890	+	17.9473i	0.0371181	+	0.590104i
$926$	6.54875	+	10.5885i	0.215205	+	0.347959i
$927$	−43.5736	−	13.6652i	−1.43115	−	0.448823i
$928$	32.2734	−	14.1533i	1.05943	−	0.464605i
$929$		−	5.07101i		−	0.166374i	−0.996534	−	0.0831872i	$-0.973490\pi$
$929$		−	5.07101i		−	0.166374i	0.996534	−	0.0831872i	$-0.0265099\pi$
$930$	−19.9889	+	0.813158i	−0.655462	+	0.0266645i
$931$	25.4707	+	25.4707i	0.834768	+	0.834768i
$932$	20.9249	+	10.4456i	0.685418	+	0.342158i
$933$	−10.7421	−	14.6267i	−0.351679	−	0.478858i
$934$	9.52054	−	40.3878i	0.311521	−	1.32153i
$935$	−12.8757	+	34.0738i	−0.421080	+	1.11433i
$936$	−38.2610	+	24.6535i	−1.25060	+	0.805825i
$937$	−3.58923			−0.117255			−0.0586275	−	0.998280i	$-0.518672\pi$
$937$	−3.58923			−0.117255			−0.0586275	+	0.998280i	$0.518672\pi$
$938$	1.41104	−	5.98589i	0.0460722	−	0.195446i
$939$	−29.7536	+	21.8514i	−0.970973	+	0.713095i
$940$	0.571157	−	14.6769i	0.0186291	−	0.478707i
$941$	13.4811	+	13.4811i	0.439471	+	0.439471i	0.891834	−	0.452363i	$-0.149419\pi$
$941$	13.4811	+	13.4811i	0.439471	+	0.439471i	−0.452363	+	0.891834i	$0.649419\pi$
$942$	8.60828	+	20.2504i	0.280473	+	0.659795i
$943$	−0.146753			−0.00477894
$944$	−0.354646	+	2.50555i	−0.0115427	+	0.0815488i
$945$	−3.50029	−	3.72982i	−0.113864	−	0.121331i
$946$	38.1042	−	23.5666i	1.23887	−	0.766218i
$947$	−40.8702	−	40.8702i	−1.32810	−	1.32810i	−0.907025	−	0.421077i	$-0.861652\pi$
$947$	−40.8702	−	40.8702i	−1.32810	−	1.32810i	−0.421077	−	0.907025i	$-0.638348\pi$
$948$	10.0780	−	1.73459i	0.327318	−	0.0563367i
$949$	−20.9280	−	20.9280i	−0.679353	−	0.679353i
$950$	−21.6438	−	30.5289i	−0.702217	−	0.990488i
$951$	0.978981	−	6.39320i	0.0317456	−	0.207314i
$952$	0.389177	+	4.26995i	0.0126133	+	0.138390i
$953$			41.0943i			1.33117i	0.746320	+	0.665587i	$0.231819\pi$
$953$			41.0943i			1.33117i	−0.746320	+	0.665587i	$0.768181\pi$
$954$	−28.7843	−	17.0746i	−0.931927	−	0.552811i
$955$	2.99495	+	6.63319i	0.0969142	+	0.214645i
$956$	−17.4331	+	34.9224i	−0.563826	+	1.12947i
$957$	30.2150	+	41.1418i	0.976713	+	1.32993i
$958$	15.7143	+	25.4080i	0.507706	+	0.820895i
$959$	−2.16876			−0.0700329
$960$	−29.2974	−	10.0827i	−0.945570	−	0.325418i
$961$	17.6594			0.569658
$962$	14.3512	+	23.2040i	0.462702	+	0.748128i
$963$	−15.4121	−	29.4957i	−0.496648	−	0.950484i
$964$	−13.3659	+	26.7748i	−0.430486	+	0.862360i
$965$	−6.71365	+	3.03128i	−0.216120	+	0.0975802i
$966$	−0.00746271	+	0.0184987i	−0.000240109	+	0.000595185i
$967$		−	52.4822i		−	1.68771i	−0.536568	−	0.843857i	$-0.680280\pi$
$967$		−	52.4822i		−	1.68771i	0.536568	−	0.843857i	$-0.319720\pi$
$968$	−2.92148	−	32.0537i	−0.0938999	−	1.03024i
$969$	31.2012	+	4.77779i	1.00233	+	0.153485i
$970$	44.8148	+	30.1875i	1.43892	+	0.969263i
$971$	40.3327	+	40.3327i	1.29434	+	1.29434i	0.932076	+	0.362263i	$0.117996\pi$
$971$	40.3327	+	40.3327i	1.29434	+	1.29434i	0.362263	+	0.932076i	$0.382004\pi$
$972$	−13.2046	+	28.2425i	−0.423537	+	0.905879i
$973$	−2.96650	−	2.96650i	−0.0951016	−	0.0951016i
$974$	16.9614	−	10.4903i	0.543480	−	0.336131i
$975$	35.6418	−	29.7940i	1.14145	−	0.954171i
$976$	0.910813	+	0.128920i	0.0291544	+	0.00412663i
$977$	−9.50447			−0.304075			−0.152038	−	0.988375i	$-0.548583\pi$
$977$	−9.50447			−0.304075			−0.152038	+	0.988375i	$0.548583\pi$
$978$	2.04137	−	0.867770i	0.0652759	−	0.0277482i
$979$	36.6427	+	36.6427i	1.17111	+	1.17111i
$980$	−30.4152	−	1.18362i	−0.971578	−	0.0378094i
$981$	−21.0709	−	40.3254i	−0.672741	−	1.28749i
$982$	1.30408	−	5.53213i	0.0416148	−	0.176537i
$983$	−5.07572			−0.161890			−0.0809451	−	0.996719i	$-0.525794\pi$
$983$	−5.07572			−0.161890			−0.0809451	+	0.996719i	$0.525794\pi$
$984$	29.1080	−	25.7542i	0.927929	−	0.821013i
$985$	4.18661	−	11.0793i	0.133396	−	0.353016i
$986$	6.96052	−	29.5277i	0.221668	−	0.940355i
$987$	2.01846	−	1.48238i	0.0642482	−	0.0471847i
$988$	−50.7999	−	25.3591i	−1.61616	−	0.806780i
$989$	−0.0875944	−	0.0875944i	−0.00278534	−	0.00278534i
$990$	4.98434	−	44.6019i	0.158413	−	1.41754i
$991$			14.1841i			0.450574i	0.974292	+	0.225287i	$0.0723319\pi$
$991$			14.1841i			0.450574i	−0.974292	+	0.225287i	$0.927668\pi$
$992$	−19.2475	−	7.51219i	−0.611108	−	0.238512i
$993$	6.97969	−	45.5806i	0.221494	−	1.44646i
$994$	1.86886	+	3.02170i	0.0592766	+	0.0958426i
$995$	21.4381	+	47.4810i	0.679634	+	1.50525i
$996$	14.4549	−	20.4652i	0.458022	−	0.648466i
$997$	−0.0621298	+	0.0621298i	−0.00196767	+	0.00196767i	−0.708090	−	0.706122i	$-0.750443\pi$
$997$	−0.0621298	+	0.0621298i	−0.00196767	+	0.00196767i	0.706122	+	0.708090i	$0.250443\pi$
$998$	−6.60625	+	28.0249i	−0.209117	+	0.887111i
$999$	16.7800	+	8.22696i	0.530896	+	0.260289i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.t.b.59.27	yes	80
3.2	odd	2	inner	240.2.t.b.59.13	✓	80
4.3	odd	2		960.2.t.b.719.32		80
5.4	even	2	inner	240.2.t.b.59.14	yes	80
12.11	even	2		960.2.t.b.719.29		80
15.14	odd	2	inner	240.2.t.b.59.28	yes	80
16.3	odd	4	inner	240.2.t.b.179.28	yes	80
16.13	even	4		960.2.t.b.239.12		80
20.19	odd	2		960.2.t.b.719.9		80
48.29	odd	4		960.2.t.b.239.9		80
48.35	even	4	inner	240.2.t.b.179.14	yes	80
60.59	even	2		960.2.t.b.719.12		80
80.19	odd	4	inner	240.2.t.b.179.13	yes	80
80.29	even	4		960.2.t.b.239.29		80
240.29	odd	4		960.2.t.b.239.32		80
240.179	even	4	inner	240.2.t.b.179.27	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.t.b.59.13	✓	80	3.2	odd	2	inner
240.2.t.b.59.14	yes	80	5.4	even	2	inner
240.2.t.b.59.27	yes	80	1.1	even	1	trivial
240.2.t.b.59.28	yes	80	15.14	odd	2	inner
240.2.t.b.179.13	yes	80	80.19	odd	4	inner
240.2.t.b.179.14	yes	80	48.35	even	4	inner
240.2.t.b.179.27	yes	80	240.179	even	4	inner
240.2.t.b.179.28	yes	80	16.3	odd	4	inner
960.2.t.b.239.9		80	48.29	odd	4
960.2.t.b.239.12		80	16.13	even	4
960.2.t.b.239.29		80	80.29	even	4
960.2.t.b.239.32		80	240.29	odd	4
960.2.t.b.719.9		80	20.19	odd	2
960.2.t.b.719.12		80	60.59	even	2
960.2.t.b.719.29		80	12.11	even	2
960.2.t.b.719.32		80	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.743883 + 1.20276i) q^{2} +(-1.39602 + 1.02525i) q^{3} +(-0.893276 + 1.78943i) q^{4} +(0.920160 + 2.03797i) q^{5} +(-2.27161 - 0.916409i) q^{6} +0.440232i q^{7} +(-2.81675 + 0.256728i) q^{8} +(0.897721 - 2.86253i) q^{9} +O(q^{10})\)	\(q+(0.743883 + 1.20276i) q^{2} +(-1.39602 + 1.02525i) q^{3} +(-0.893276 + 1.78943i) q^{4} +(0.920160 + 2.03797i) q^{5} +(-2.27161 - 0.916409i) q^{6} +0.440232i q^{7} +(-2.81675 + 0.256728i) q^{8} +(0.897721 - 2.86253i) q^{9} +(-1.76670 + 2.62274i) q^{10} +(-3.34512 - 3.34512i) q^{11} +(-0.587588 - 3.41390i) q^{12} +(3.79299 + 3.79299i) q^{13} +(-0.529495 + 0.327481i) q^{14} +(-3.37398 - 1.90164i) q^{15} +(-2.40412 - 3.19691i) q^{16} -3.44344 q^{17} +(4.11075 - 1.04965i) q^{18} +(3.74228 + 3.74228i) q^{19} +(-4.46875 - 0.173904i) q^{20} +(-0.451349 - 0.614571i) q^{21} +(1.53501 - 6.51176i) q^{22} -0.0184980 q^{23} +(3.66902 - 3.24627i) q^{24} +(-3.30661 + 3.75051i) q^{25} +(-1.74053 + 7.38361i) q^{26} +(1.68158 + 4.91653i) q^{27} +(-0.787765 - 0.393249i) q^{28} +(4.40505 + 4.40505i) q^{29} +(-0.222632 - 5.47270i) q^{30} -3.65248i q^{31} +(2.05674 - 5.26971i) q^{32} +(8.09943 + 1.24025i) q^{33} +(-2.56152 - 4.14164i) q^{34} +(-0.897179 + 0.405084i) q^{35} +(4.32039 + 4.16344i) q^{36} +(2.54315 - 2.54315i) q^{37} +(-1.71726 + 7.28489i) q^{38} +(-9.18384 - 1.40631i) q^{39} +(-3.11507 - 5.50421i) q^{40} +7.93346 q^{41} +(0.403433 - 1.00003i) q^{42} +(4.73534 + 4.73534i) q^{43} +(8.97397 - 2.99774i) q^{44} +(6.65979 - 0.804465i) q^{45} +(-0.0137604 - 0.0222487i) q^{46} +3.28433i q^{47} +(6.63382 + 1.99811i) q^{48} +6.80620 q^{49} +(-6.97071 - 1.18713i) q^{50} +(4.80709 - 3.53039i) q^{51} +(-10.1755 + 3.39910i) q^{52} +(-5.57793 - 5.57793i) q^{53} +(-4.66252 + 5.67987i) q^{54} +(3.73920 - 9.89529i) q^{55} +(-0.113020 - 1.24003i) q^{56} +(-9.06106 - 1.38751i) q^{57} +(-2.02139 + 8.57508i) q^{58} +(-0.447338 - 0.447338i) q^{59} +(6.41675 - 4.33882i) q^{60} +(-0.162615 + 0.162615i) q^{61} +(4.39306 - 2.71702i) q^{62} +(1.26018 + 0.395206i) q^{63} +(7.86818 - 1.44628i) q^{64} +(-4.23983 + 11.2201i) q^{65} +(4.53330 + 10.6643i) q^{66} +(-6.98489 + 6.98489i) q^{67} +(3.07594 - 6.16179i) q^{68} +(0.0258235 - 0.0189651i) q^{69} +(-1.15462 - 0.777758i) q^{70} -5.70676i q^{71} +(-1.79376 + 8.29352i) q^{72} -5.51755 q^{73} +(4.95061 + 1.16700i) q^{74} +(0.770867 - 8.62588i) q^{75} +(-10.0394 + 3.35366i) q^{76} +(1.47263 - 1.47263i) q^{77} +(-5.14025 - 12.0921i) q^{78} +2.95205i q^{79} +(4.30302 - 7.84118i) q^{80} +(-7.38820 - 5.13951i) q^{81} +(5.90156 + 9.54206i) q^{82} +(5.11440 + 5.11440i) q^{83} +(1.50291 - 0.258675i) q^{84} +(-3.16851 - 7.01761i) q^{85} +(-2.17295 + 9.21803i) q^{86} +(-10.6658 - 1.63324i) q^{87} +(10.2812 + 8.56359i) q^{88} -10.9541 q^{89} +(5.92169 + 7.41172i) q^{90} +(-1.66980 + 1.66980i) q^{91} +(0.0165238 - 0.0331009i) q^{92} +(3.74471 + 5.09892i) q^{93} +(-3.95027 + 2.44316i) q^{94} +(-4.18314 + 11.0701i) q^{95} +(2.53153 + 9.46527i) q^{96} -17.0870i q^{97} +(5.06301 + 8.18624i) q^{98} +(-12.5785 + 6.57254i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 8 q^{4} - 4 q^{6}+O(q^{10}) \) 80 * q - 8 * q^4 - 4 * q^6	\( 80 q - 8 q^{4} - 4 q^{6} + 16 q^{10} - 32 q^{16} + 16 q^{19} + 8 q^{21} - 56 q^{24} + 8 q^{30} - 16 q^{34} - 40 q^{36} - 8 q^{39} - 8 q^{40} - 12 q^{45} - 24 q^{46} - 112 q^{49} + 32 q^{51} + 60 q^{54} - 40 q^{55} + 40 q^{60} + 16 q^{61} - 32 q^{64} - 56 q^{66} - 40 q^{69} + 48 q^{70} - 36 q^{75} - 128 q^{76} + 64 q^{81} + 128 q^{84} - 64 q^{85} + 72 q^{90} + 48 q^{91} + 56 q^{94} - 24 q^{96} - 8 q^{99}+O(q^{100}) \) 80 * q - 8 * q^4 - 4 * q^6 + 16 * q^10 - 32 * q^16 + 16 * q^19 + 8 * q^21 - 56 * q^24 + 8 * q^30 - 16 * q^34 - 40 * q^36 - 8 * q^39 - 8 * q^40 - 12 * q^45 - 24 * q^46 - 112 * q^49 + 32 * q^51 + 60 * q^54 - 40 * q^55 + 40 * q^60 + 16 * q^61 - 32 * q^64 - 56 * q^66 - 40 * q^69 + 48 * q^70 - 36 * q^75 - 128 * q^76 + 64 * q^81 + 128 * q^84 - 64 * q^85 + 72 * q^90 + 48 * q^91 + 56 * q^94 - 24 * q^96 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more