LMFDB - Embedded newform 56.2.m.a.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [56,2,Mod(3,56)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(56, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("56.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 56 = 2^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	56.m (of order $6$, 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:	$0.447162251319$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.144054149089536.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3x^{11} + x^{9} + 48x^{8} - 189x^{7} + 431x^{6} - 654x^{5} + 624x^{4} - 340x^{3} + 96x^{2} - 12x + 4 $ x^12 - 3x^11 + x^9 + 48x^8 - 189x^7 + 431x^6 - 654x^5 + 624x^4 - 340x^3 + 96x^2 - 12*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.3
Root			$0.609850 + 0.457915i$ of defining polynomial
Character	$\chi$	$=$	56.19
Dual form			56.2.m.a.3.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.169938 - 1.40397i) q^{2} +(-0.416472 + 0.240450i) q^{3} +(-1.94224 - 0.477176i) q^{4} +(1.59713 - 2.76632i) q^{5} +(0.266810 + 0.625575i) q^{6} +(0.694153 + 2.55307i) q^{7} +(-1.00000 + 2.64575i) q^{8} +(-1.38437 + 2.39779i) q^{9} +(-3.61240 - 2.71243i) q^{10} +(0.800840 + 1.38709i) q^{11} +(0.923627 - 0.268282i) q^{12} -1.38831 q^{13} +(3.70238 - 0.540703i) q^{14} +1.53613i q^{15} +(3.54461 + 1.85358i) q^{16} +(3.48605 - 2.01267i) q^{17} +(3.13116 + 2.35108i) q^{18} +(-4.56957 - 2.63824i) q^{19} +(-4.42204 + 4.61075i) q^{20} +(-0.902982 - 0.896373i) q^{21} +(2.08353 - 0.888631i) q^{22} +(-3.83044 - 2.21151i) q^{23} +(-0.219700 - 1.34233i) q^{24} +(-2.60168 - 4.50624i) q^{25} +(-0.235927 + 1.94913i) q^{26} -2.77419i q^{27} +(-0.129952 - 5.28991i) q^{28} +5.10613i q^{29} +(2.15667 + 0.261047i) q^{30} +(-0.0579809 - 0.100426i) q^{31} +(3.20473 - 4.66151i) q^{32} +(-0.667055 - 0.385124i) q^{33} +(-2.23331 - 5.23632i) q^{34} +(8.17125 + 2.15734i) q^{35} +(3.83294 - 3.99651i) q^{36} +(-4.63087 - 2.67363i) q^{37} +(-4.48055 + 5.96719i) q^{38} +(0.578191 - 0.333819i) q^{39} +(5.72186 + 6.99194i) q^{40} +4.21689i q^{41} +(-1.41193 + 1.11543i) q^{42} +(-0.893536 - 3.07621i) q^{44} +(4.42204 + 7.65920i) q^{45} +(-3.75582 + 5.00199i) q^{46} +(5.05821 - 8.76108i) q^{47} +(-1.92193 + 0.0803370i) q^{48} +(-6.03630 + 3.54444i) q^{49} +(-6.76873 + 2.88689i) q^{50} +(-0.967895 + 1.67644i) q^{51} +(2.69643 + 0.662466i) q^{52} +(6.13514 - 3.54212i) q^{53} +(-3.89487 - 0.471441i) q^{54} +5.11619 q^{55} +(-7.44893 - 0.716511i) q^{56} +2.53747 q^{57} +(7.16884 + 0.867728i) q^{58} +(-4.38856 + 2.53374i) q^{59} +(0.733002 - 2.98353i) q^{60} +(-4.21321 + 7.29750i) q^{61} +(-0.150848 + 0.0643370i) q^{62} +(-7.08269 - 1.86995i) q^{63} +(-6.00000 - 5.29150i) q^{64} +(-2.21731 + 3.84050i) q^{65} +(-0.654060 + 0.871075i) q^{66} +(5.01815 + 8.69169i) q^{67} +(-7.73114 + 2.24564i) q^{68} +2.12703 q^{69} +(4.41745 - 11.1055i) q^{70} -5.29150i q^{71} +(-4.95960 - 6.06049i) q^{72} +(9.30504 - 5.37227i) q^{73} +(-4.54066 + 6.04723i) q^{74} +(2.16706 + 1.25115i) q^{75} +(7.61631 + 7.30460i) q^{76} +(-2.98544 + 3.00745i) q^{77} +(-0.370413 - 0.868490i) q^{78} +(10.3349 + 5.96688i) q^{79} +(10.7888 - 6.84509i) q^{80} +(-3.48605 - 6.03801i) q^{81} +(5.92037 + 0.716612i) q^{82} -14.9789i q^{83} +(1.32608 + 2.17185i) q^{84} -12.8580i q^{85} +(-1.22777 - 2.12656i) q^{87} +(-4.47075 + 0.731728i) q^{88} +(1.50000 + 0.866025i) q^{89} +(11.5047 - 4.90680i) q^{90} +(-0.963697 - 3.54444i) q^{91} +(6.38437 + 6.12307i) q^{92} +(0.0482949 + 0.0278831i) q^{93} +(-11.4407 - 8.59041i) q^{94} +(-14.5965 + 8.42726i) q^{95} +(-0.213819 + 2.71197i) q^{96} +2.87198i q^{97} +(3.95047 + 9.07710i) q^{98} -4.43462 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} - 12 q^{8} + 6 q^{10} - 6 q^{11} - 18 q^{12} + 6 q^{14} - 6 q^{17} + 6 q^{18} - 6 q^{19} + 24 q^{22} + 6 q^{24} + 6 q^{26} + 6 q^{28} - 12 q^{30} - 6 q^{33} + 18 q^{35} + 48 q^{36} - 24 q^{38}+ \cdots - 24 q^{99}+O(q^{100}) $ 12 * q - 6 * q^3 - 12 * q^8 + 6 * q^10 - 6 * q^11 - 18 * q^12 + 6 * q^14 - 6 * q^17 + 6 * q^18 - 6 * q^19 + 24 * q^22 + 6 * q^24 + 6 * q^26 + 6 * q^28 - 12 * q^30 - 6 * q^33 + 18 * q^35 + 48 * q^36 - 24 * q^38 + 42 * q^40 - 30 * q^42 + 6 * q^44 - 18 * q^46 - 12 * q^49 - 48 * q^50 + 6 * q^51 - 24 * q^52 - 36 * q^54 - 36 * q^57 + 18 * q^58 + 42 * q^59 - 6 * q^60 - 72 * q^64 - 12 * q^65 + 12 * q^66 + 30 * q^67 - 36 * q^68 + 30 * q^70 + 18 * q^73 + 12 * q^74 + 24 * q^75 + 60 * q^78 + 36 * q^80 + 6 * q^81 + 54 * q^82 + 12 * q^84 + 6 * q^88 + 18 * q^89 - 72 * q^91 + 60 * q^92 - 12 * q^94 + 60 * q^96 - 6 * q^98 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/56\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$29$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.169938	−	1.40397i	0.120165	−	0.992754i
$2$	0.169938	−	1.40397i	0.120165	−	0.992754i
$3$	−0.416472	+	0.240450i	−0.240450	+	0.138824i	−0.615384	−	0.788228i	$-0.710999\pi$
$3$	−0.416472	+	0.240450i	−0.240450	+	0.138824i	0.374933	+	0.927052i	$0.377666\pi$
$4$	−1.94224	−	0.477176i	−0.971121	−	0.238588i
$5$	1.59713	−	2.76632i	0.714260	−	1.23714i	−0.248984	−	0.968508i	$-0.580097\pi$
$5$	1.59713	−	2.76632i	0.714260	−	1.23714i	0.963244	−	0.268628i	$-0.0865701\pi$
$6$	0.266810	+	0.625575i	0.108925	+	0.255390i
$7$	0.694153	+	2.55307i	0.262365	+	0.964969i
$7$	0.694153	+	2.55307i	0.262365	+	0.964969i
$8$	−1.00000	+	2.64575i	−0.353553	+	0.935414i
$9$	−1.38437	+	2.39779i	−0.461456	+	0.799265i
$10$	−3.61240	−	2.71243i	−1.14234	−	0.857745i
$11$	0.800840	+	1.38709i	0.241462	+	0.418225i	0.961131	−	0.276093i	$-0.0890397\pi$
$11$	0.800840	+	1.38709i	0.241462	+	0.418225i	−0.719669	+	0.694318i	$0.755706\pi$
$12$	0.923627	−	0.268282i	0.266628	−	0.0774465i
$13$	−1.38831			−0.385047			−0.192523	−	0.981292i	$-0.561667\pi$
$13$	−1.38831			−0.385047			−0.192523	+	0.981292i	$0.561667\pi$
$14$	3.70238	−	0.540703i	0.989503	−	0.144509i
$15$			1.53613i			0.396626i
$16$	3.54461	+	1.85358i	0.886152	+	0.463395i
$17$	3.48605	−	2.01267i	0.845490	−	0.488144i	−0.0136363	−	0.999907i	$-0.504341\pi$
$17$	3.48605	−	2.01267i	0.845490	−	0.488144i	0.859127	+	0.511763i	$0.171007\pi$
$18$	3.13116	+	2.35108i	0.738023	+	0.554155i
$19$	−4.56957	−	2.63824i	−1.04833	−	0.605255i	−0.126150	−	0.992011i	$-0.540262\pi$
$19$	−4.56957	−	2.63824i	−1.04833	−	0.605255i	−0.922182	+	0.386756i	$0.873595\pi$
$20$	−4.42204	+	4.61075i	−0.988799	+	1.03099i
$21$	−0.902982	−	0.896373i	−0.197047	−	0.195605i
$22$	2.08353	−	0.888631i	0.444210	−	0.189457i
$23$	−3.83044	−	2.21151i	−0.798702	−	0.461131i	0.0443149	−	0.999018i	$-0.485890\pi$
$23$	−3.83044	−	2.21151i	−0.798702	−	0.461131i	−0.843017	+	0.537887i	$0.819223\pi$
$24$	−0.219700	−	1.34233i	−0.0448460	−	0.274003i
$25$	−2.60168	−	4.50624i	−0.520336	−	0.901248i
$26$	−0.235927	+	1.94913i	−0.0462690	+	0.382257i
$27$		−	2.77419i		−	0.533893i
$28$	−0.129952	−	5.28991i	−0.0245586	−	0.999698i
$29$			5.10613i			0.948185i	0.880475	+	0.474093i	$0.157224\pi$
$29$			5.10613i			0.948185i	−0.880475	+	0.474093i	$0.842776\pi$
$30$	2.15667	+	0.261047i	0.393752	+	0.0476605i
$31$	−0.0579809	−	0.100426i	−0.0104137	−	0.0180370i	0.860772	−	0.508991i	$-0.169982\pi$
$31$	−0.0579809	−	0.100426i	−0.0104137	−	0.0180370i	−0.871185	+	0.490954i	$0.836648\pi$
$32$	3.20473	−	4.66151i	0.566522	−	0.824047i
$33$	−0.667055	−	0.385124i	−0.116119	−	0.0670416i
$34$	−2.23331	−	5.23632i	−0.383009	−	0.898022i
$35$	8.17125	+	2.15734i	1.38119	+	0.364658i
$36$	3.83294	−	3.99651i	0.638824	−	0.666085i
$37$	−4.63087	−	2.67363i	−0.761310	−	0.439543i	0.0684556	−	0.997654i	$-0.478193\pi$
$37$	−4.63087	−	2.67363i	−0.761310	−	0.439543i	−0.829766	+	0.558111i	$0.811526\pi$
$38$	−4.48055	+	5.96719i	−0.726842	+	0.968006i
$39$	0.578191	−	0.333819i	0.0925847	−	0.0534538i
$40$	5.72186	+	6.99194i	0.904705	+	1.10552i
$41$			4.21689i			0.658568i	0.944231	+	0.329284i	$0.106807\pi$
$41$			4.21689i			0.658568i	−0.944231	+	0.329284i	$0.893193\pi$
$42$	−1.41193	+	1.11543i	−0.217865	+	0.172114i
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$	−0.893536	−	3.07621i	−0.134706	−	0.463757i
$45$	4.42204	+	7.65920i	0.659199	+	1.14177i
$46$	−3.75582	+	5.00199i	−0.553765	+	0.737503i
$47$	5.05821	−	8.76108i	0.737816	−	1.27794i	−0.215660	−	0.976468i	$-0.569190\pi$
$47$	5.05821	−	8.76108i	0.737816	−	1.27794i	0.953477	−	0.301467i	$-0.0974763\pi$
$48$	−1.92193	+	0.0803370i	−0.277406	+	0.0115956i
$49$	−6.03630	+	3.54444i	−0.862329	+	0.506348i
$50$	−6.76873	+	2.88689i	−0.957244	+	0.408267i
$51$	−0.967895	+	1.67644i	−0.135532	+	0.234749i
$52$	2.69643	+	0.662466i	0.373927	+	0.0918675i
$53$	6.13514	−	3.54212i	0.842726	−	0.486548i	−0.0154638	−	0.999880i	$-0.504922\pi$
$53$	6.13514	−	3.54212i	0.842726	−	0.486548i	0.858190	+	0.513332i	$0.171589\pi$
$54$	−3.89487	−	0.471441i	−0.530024	−	0.0641551i
$55$	5.11619			0.689868
$56$	−7.44893	−	0.716511i	−0.995406	−	0.0957478i
$57$	2.53747			0.336096
$58$	7.16884	+	0.867728i	0.941315	+	0.113938i
$59$	−4.38856	+	2.53374i	−0.571342	+	0.329865i	−0.757685	−	0.652620i	$-0.773670\pi$
$59$	−4.38856	+	2.53374i	−0.571342	+	0.329865i	0.186343	+	0.982485i	$0.440336\pi$
$60$	0.733002	−	2.98353i	0.0946302	−	0.385172i
$61$	−4.21321	+	7.29750i	−0.539447	+	0.934349i	0.459487	+	0.888184i	$0.348033\pi$
$61$	−4.21321	+	7.29750i	−0.539447	+	0.934349i	−0.998934	+	0.0461646i	$0.985300\pi$
$62$	−0.150848	+	0.0643370i	−0.0191577	+	0.00817081i
$63$	−7.08269	−	1.86995i	−0.892335	−	0.235591i
$64$	−6.00000	−	5.29150i	−0.750000	−	0.661438i
$65$	−2.21731	+	3.84050i	−0.275024	+	0.476355i
$66$	−0.654060	+	0.871075i	−0.0805092	+	0.107222i
$67$	5.01815	+	8.69169i	0.613065	+	1.06186i	0.990721	+	0.135913i	$0.0433969\pi$
$67$	5.01815	+	8.69169i	0.613065	+	1.06186i	−0.377656	+	0.925946i	$0.623270\pi$
$68$	−7.73114	+	2.24564i	−0.937539	+	0.272323i
$69$	2.12703			0.256064
$70$	4.41745	−	11.1055i	0.527986	−	1.32737i
$71$		−	5.29150i		−	0.627986i	−0.949425	−	0.313993i	$-0.898333\pi$
$71$		−	5.29150i		−	0.627986i	0.949425	−	0.313993i	$-0.101667\pi$
$72$	−4.95960	−	6.06049i	−0.584494	−	0.714235i
$73$	9.30504	−	5.37227i	1.08907	−	0.628776i	0.155743	−	0.987798i	$-0.450223\pi$
$73$	9.30504	−	5.37227i	1.08907	−	0.628776i	0.933329	+	0.359021i	$0.116890\pi$
$74$	−4.54066	+	6.04723i	−0.527840	+	0.702976i
$75$	2.16706	+	1.25115i	0.250230	+	0.144470i
$76$	7.61631	+	7.30460i	0.873651	+	0.837895i
$77$	−2.98544	+	3.00745i	−0.340223	+	0.342731i
$78$	−0.370413	−	0.868490i	−0.0419411	−	0.0983371i
$79$	10.3349	+	5.96688i	1.16277	+	0.671327i	0.951967	−	0.306201i	$-0.0990581\pi$
$79$	10.3349	+	5.96688i	1.16277	+	0.671327i	0.210805	+	0.977528i	$0.432391\pi$
$80$	10.7888	−	6.84509i	1.20623	−	0.765305i
$81$	−3.48605	−	6.03801i	−0.387338	−	0.670890i
$82$	5.92037	+	0.716612i	0.653796	+	0.0791366i
$83$		−	14.9789i		−	1.64415i	−0.569382	−	0.822073i	$-0.692818\pi$
$83$		−	14.9789i		−	1.64415i	0.569382	−	0.822073i	$-0.307182\pi$
$84$	1.32608	+	2.17185i	0.144687	+	0.236969i
$85$		−	12.8580i		−	1.39465i
$86$		0			0
$87$	−1.22777	−	2.12656i	−0.131631	−	0.227992i
$88$	−4.47075	+	0.731728i	−0.476583	+	0.0780024i
$89$	1.50000	+	0.866025i	0.159000	+	0.0917985i	0.577389	−	0.816469i	$-0.304072\pi$
$89$	1.50000	+	0.866025i	0.159000	+	0.0917985i	−0.418389	+	0.908268i	$0.637405\pi$
$90$	11.5047	−	4.90680i	1.21271	−	0.517223i
$91$	−0.963697	−	3.54444i	−0.101023	−	0.371558i
$92$	6.38437	+	6.12307i	0.665616	+	0.638375i
$93$	0.0482949	+	0.0278831i	0.00500795	+	0.00289134i
$94$	−11.4407	−	8.59041i	−1.18002	−	0.886033i
$95$	−14.5965	+	8.42726i	−1.49756	+	0.864619i
$96$	−0.213819	+	2.71197i	−0.0218228	+	0.276789i
$97$			2.87198i			0.291606i	0.989314	+	0.145803i	$0.0465765\pi$
$97$			2.87198i			0.291606i	−0.989314	+	0.145803i	$0.953423\pi$
$98$	3.95047	+	9.07710i	0.399058	+	0.916926i
$99$	−4.43462			−0.445696
$100$	2.90282	+	9.99367i	0.290282	+	0.999367i
$101$	−3.40310	−	5.89434i	−0.338621	−	0.586509i	0.645553	−	0.763716i	$-0.276627\pi$
$101$	−3.40310	−	5.89434i	−0.338621	−	0.586509i	−0.984174	+	0.177207i	$0.943294\pi$
$102$	2.18919	+	1.64378i	0.216762	+	0.162759i
$103$	−7.02471	+	12.1672i	−0.692165	+	1.19887i	0.278962	+	0.960302i	$0.410010\pi$
$103$	−7.02471	+	12.1672i	−0.692165	+	1.19887i	−0.971127	+	0.238563i	$0.923324\pi$
$104$	1.38831	−	3.67311i	0.136135	−	0.360178i
$105$	−3.92184	+	1.06631i	−0.382732	+	0.104061i
$106$	−3.93043	−	9.21547i	−0.381757	−	0.895086i
$107$	2.56957	−	4.45063i	0.248410	−	0.430259i	−0.714675	−	0.699457i	$-0.753425\pi$
$107$	2.56957	−	4.45063i	0.248410	−	0.430259i	0.963085	+	0.269198i	$0.0867586\pi$
$108$	−1.32378	+	5.38815i	−0.127380	+	0.518475i
$109$	−2.45182	+	1.41556i	−0.234842	+	0.135586i	−0.612804	−	0.790235i	$-0.709958\pi$
$109$	−2.45182	+	1.41556i	−0.234842	+	0.135586i	0.377962	+	0.925821i	$0.376625\pi$
$110$	0.869438	−	7.18296i	0.0828977	−	0.684869i
$111$	2.57151			0.244077
$112$	−2.27182	+	10.3363i	−0.214667	+	0.976687i
$113$	−1.43695			−0.135177			−0.0675887	−	0.997713i	$-0.521531\pi$
$113$	−1.43695			−0.135177			−0.0675887	+	0.997713i	$0.521531\pi$
$114$	0.431213	−	3.56252i	0.0403868	−	0.333661i
$115$	−12.2355	+	7.06415i	−1.14096	+	0.658735i
$116$	2.43652	−	9.91735i	0.226225	−	0.920803i
$117$	1.92193	−	3.32887i	0.177682	−	0.307754i
$118$	2.81150	+	6.59198i	0.258819	+	0.606841i
$119$	7.55833	+	7.50301i	0.692871	+	0.687800i
$120$	−4.06421	−	1.53613i	−0.371010	−	0.140229i
$121$	4.21731	−	7.30460i	0.383392	−	0.664054i
$122$	9.52946	+	7.15533i	0.862756	+	0.647814i
$123$	−1.01395	−	1.75622i	−0.0914251	−	0.158353i
$124$	0.0646922	+	0.222719i	0.00580953	+	0.0200007i
$125$	−0.649581			−0.0581003
$126$	−3.82896	+	9.62608i	−0.341111	+	0.857560i
$127$			4.92077i			0.436647i	0.975876	+	0.218324i	$0.0700589\pi$
$127$			4.92077i			0.436647i	−0.975876	+	0.218324i	$0.929941\pi$
$128$	−8.44872	+	7.52457i	−0.746769	+	0.665084i
$129$		0			0
$130$	5.01512	+	3.76568i	0.439855	+	0.330272i
$131$	−3.41647	−	1.97250i	−0.298499	−	0.172338i	0.343270	−	0.939237i	$-0.388466\pi$
$131$	−3.41647	−	1.97250i	−0.298499	−	0.172338i	−0.641768	+	0.766899i	$0.721799\pi$
$132$	1.11181	+	1.06631i	0.0967707	+	0.0928101i
$133$	3.56363	−	13.4978i	0.309006	−	1.17041i
$134$	13.0556	−	5.56826i	1.12783	−	0.481025i
$135$	−7.67429	−	4.43075i	−0.660498	−	0.381339i
$136$	1.83898	+	11.2359i	0.157691	+	0.963469i
$137$	0.0514223	+	0.0890661i	0.00439331	+	0.00760943i	0.868214	−	0.496190i	$-0.165268\pi$
$137$	0.0514223	+	0.0890661i	0.00439331	+	0.00760943i	−0.863820	+	0.503800i	$0.831935\pi$
$138$	0.361464	−	2.98628i	0.0307699	−	0.254209i
$139$			14.9789i			1.27049i	0.772310	+	0.635246i	$0.219101\pi$
$139$			14.9789i			1.27049i	−0.772310	+	0.635246i	$0.780899\pi$
$140$	−14.8411	−	8.08921i	−1.25430	−	0.683663i
$141$			4.86500i			0.409707i
$142$	−7.42909	−	0.899230i	−0.623435	−	0.0754617i
$143$	−1.11181	−	1.92571i	−0.0929743	−	0.161036i
$144$	−9.35154	+	5.93320i	−0.779295	+	0.494433i
$145$	14.1252	+	8.15518i	1.17303	+	0.677251i
$146$	−5.96120	−	13.9769i	−0.493352	−	1.15674i
$147$	1.66169	−	2.92759i	0.137054	−	0.241464i
$148$	7.71848	+	7.40258i	0.634455	+	0.608489i
$149$	9.79164	+	5.65320i	0.802162	+	0.463129i	0.844227	−	0.535986i	$-0.180060\pi$
$149$	9.79164	+	5.65320i	0.802162	+	0.463129i	−0.0420645	+	0.999115i	$0.513393\pi$
$150$	2.12484	−	2.82985i	0.173492	−	0.231057i
$151$	12.8351	−	7.41032i	1.04450	−	0.603044i	0.123397	−	0.992357i	$-0.460621\pi$
$151$	12.8351	−	7.41032i	1.04450	−	0.603044i	0.921105	+	0.389314i	$0.127288\pi$
$152$	11.5497	−	9.45171i	0.936805	−	0.766635i
$153$			11.1451i			0.901028i
$154$	3.71502	+	4.70254i	0.299365	+	0.378941i
$155$	−0.370413			−0.0297523
$156$	−1.28228	+	0.372458i	−0.102664	+	0.0298205i
$157$	−0.369362	−	0.639755i	−0.0294783	−	0.0510580i	0.850910	−	0.525312i	$-0.176051\pi$
$157$	−0.369362	−	0.639755i	−0.0294783	−	0.0510580i	−0.880388	+	0.474254i	$0.842718\pi$
$158$	10.1336	−	13.4959i	0.806186	−	1.07368i
$159$	−1.70341	+	2.95039i	−0.135089	+	0.233981i
$160$	−7.77685	−	16.3104i	−0.614814	−	1.28945i
$161$	2.98721	−	11.3145i	0.235425	−	0.891707i
$162$	−9.06957	+	3.86820i	−0.712573	+	0.303915i
$163$	4.35226	−	7.53834i	0.340895	−	0.590448i	−0.643704	−	0.765275i	$-0.722603\pi$
$163$	4.35226	−	7.53834i	0.340895	−	0.590448i	0.984599	+	0.174826i	$0.0559364\pi$
$164$	2.01220	−	8.19022i	0.157126	−	0.639549i
$165$	−2.13075	+	1.23019i	−0.165879	+	0.0957703i
$166$	−21.0298	−	2.54549i	−1.63223	−	0.197568i
$167$	−1.38831			−0.107430			−0.0537152	−	0.998556i	$-0.517106\pi$
$167$	−1.38831			−0.107430			−0.0537152	+	0.998556i	$0.517106\pi$
$168$	3.27456	−	1.49269i	0.252638	−	0.115164i
$169$	−11.0726			−0.851739
$170$	−18.0522	−	2.18507i	−1.38454	−	0.167587i
$171$	12.6519	−	7.30460i	0.967518	−	0.558597i
$172$		0			0
$173$	0.485324	−	0.840606i	0.0368985	−	0.0639101i	−0.846986	−	0.531615i	$-0.821586\pi$
$173$	0.485324	−	0.840606i	0.0368985	−	0.0639101i	0.883885	+	0.467704i	$0.154919\pi$
$174$	−3.19427	+	1.36237i	−0.242157	+	0.103281i
$175$	9.69877	−	9.77028i	0.733158	−	0.738564i
$176$	0.267569	+	6.40113i	0.0201688	+	0.482503i
$177$	1.21848	−	2.11046i	0.0915864	−	0.158632i
$178$	1.47078	−	1.95878i	0.110239	−	0.146817i
$179$	7.13495	+	12.3581i	0.533291	+	0.923687i	0.999244	+	0.0388779i	$0.0123783\pi$
$179$	7.13495	+	12.3581i	0.533291	+	0.923687i	−0.465953	+	0.884810i	$0.654288\pi$
$180$	−4.93389	−	16.9861i	−0.367750	−	1.26607i
$181$	−15.3218			−1.13886			−0.569429	−	0.822041i	$-0.692836\pi$
$181$	−15.3218			−1.13886			−0.569429	+	0.822041i	$0.692836\pi$
$182$	−5.14004	+	0.750661i	−0.381005	+	0.0556427i
$183$		−	4.05228i		−	0.299553i
$184$	9.68154	−	7.92289i	0.713732	−	0.584083i
$185$	−14.7922	+	8.54031i	−1.08755	+	0.627896i
$186$	0.0473541	−	0.0630660i	0.00347217	−	0.00462422i
$187$	5.58353	+	3.22365i	0.408308	+	0.235737i
$188$	−14.0049	+	14.6025i	−1.02141	+	1.06500i
$189$	7.08269	−	1.92571i	0.515190	−	0.140075i
$190$	9.35110	+	21.9250i	0.678400	+	1.59061i
$191$	2.16564	+	1.25033i	0.156700	+	0.0904709i	0.576300	−	0.817238i	$-0.304496\pi$
$191$	2.16564	+	1.25033i	0.156700	+	0.0904709i	−0.419599	+	0.907709i	$0.637829\pi$
$192$	3.77118	+	0.761062i	0.272161	+	0.0549249i
$193$	1.55026	+	2.68512i	0.111590	+	0.193279i	0.916411	−	0.400237i	$-0.131072\pi$
$193$	1.55026	+	2.68512i	0.111590	+	0.193279i	−0.804822	+	0.593517i	$0.797739\pi$
$194$	4.03217	+	0.488061i	0.289493	+	0.0350407i
$195$		−	2.13261i		−	0.152720i
$196$	13.4153	−	4.00378i	0.958234	−	0.285984i
$197$			15.6891i			1.11780i	0.829233	+	0.558902i	$0.188777\pi$
$197$			15.6891i			1.11780i	−0.829233	+	0.558902i	$0.811223\pi$
$198$	−0.753613	+	6.22606i	−0.0535570	+	0.442467i
$199$	−5.91290	−	10.2414i	−0.419154	−	0.725997i	0.576700	−	0.816956i	$-0.304340\pi$
$199$	−5.91290	−	10.2414i	−0.419154	−	0.725997i	−0.995855	+	0.0909591i	$0.971007\pi$
$200$	14.5241	−	2.37716i	1.02701	−	0.168090i
$201$	−4.17984	−	2.41323i	−0.294823	−	0.170216i
$202$	−8.85377	+	3.77616i	−0.622949	+	0.265690i
$203$	−13.0363	+	3.54444i	−0.914969	+	0.248771i
$204$	2.67984	−	2.79420i	0.187627	−	0.195633i
$205$	11.6653	+	6.73495i	0.814738	+	0.470389i
$206$	15.8885	+	11.9301i	1.10700	+	0.831211i
$207$	10.6055	−	6.12307i	0.737131	−	0.425583i
$208$	−4.92100	−	2.57334i	−0.341210	−	0.178429i
$209$		−	8.45124i		−	0.584585i
$210$	0.830589	+	5.68733i	0.0573161	+	0.392463i
$211$	10.0726			0.693427			0.346713	−	0.937971i	$-0.387298\pi$
$211$	10.0726			0.693427			0.346713	+	0.937971i	$0.387298\pi$
$212$	−13.6061	+	3.95212i	−0.934473	+	0.271433i
$213$	1.27234	+	2.20376i	0.0871796	+	0.150999i
$214$	−5.81187	−	4.36393i	−0.397291	−	0.298312i
$215$		0			0
$216$	7.33982	+	2.77419i	0.499411	+	0.188760i
$217$	0.216146	−	0.217740i	0.0146730	−	0.0147812i
$218$	1.57074	+	3.68283i	0.106384	+	0.249433i
$219$	−2.58353	+	4.47480i	−0.174579	+	0.302379i
$220$	−9.93689	−	2.44132i	−0.669945	−	0.164594i
$221$	−4.83970	+	2.79420i	−0.325553	+	0.187958i
$222$	0.436998	−	3.61031i	0.0293294	−	0.242308i
$223$	−24.3086			−1.62783			−0.813913	−	0.580987i	$-0.802667\pi$
$223$	−24.3086			−1.62783			−0.813913	+	0.580987i	$0.802667\pi$
$224$	14.1257	+	4.94609i	0.943815	+	0.330474i
$225$	14.4067			0.960448
$226$	−0.244194	+	2.01744i	−0.0162435	+	0.134198i
$227$	−12.4048	+	7.16194i	−0.823339	+	0.475355i	−0.851566	−	0.524247i	$-0.824347\pi$
$227$	−12.4048	+	7.16194i	−0.823339	+	0.475355i	0.0282277	+	0.999602i	$0.491014\pi$
$228$	−4.92838	−	1.21082i	−0.326390	−	0.0801884i
$229$	−5.32502	+	9.22321i	−0.351887	+	0.609487i	−0.986580	−	0.163278i	$-0.947793\pi$
$229$	−5.32502	+	9.22321i	−0.351887	+	0.609487i	0.634693	+	0.772765i	$0.281127\pi$
$230$	7.83855	+	18.3786i	0.516859	+	1.21185i
$231$	0.520210	−	1.97037i	0.0342273	−	0.129641i
$232$	−13.5096	−	5.10613i	−0.886946	−	0.335234i
$233$	0.318991	−	0.552509i	0.0208978	−	0.0361961i	−0.855387	−	0.517989i	$-0.826681\pi$
$233$	0.318991	−	0.552509i	0.0208978	−	0.0361961i	0.876285	+	0.481793i	$0.160014\pi$
$234$	−4.34702	−	3.26402i	−0.284173	−	0.213376i
$235$	−16.1573	−	27.9853i	−1.05399	−	1.82556i
$236$	9.73269	−	2.82702i	0.633544	−	0.184023i
$237$	−5.73896			−0.372785
$238$	11.8184	−	9.33659i	0.766075	−	0.605201i
$239$		−	4.73540i		−	0.306307i	−0.988202	−	0.153154i	$-0.951057\pi$
$239$		−	4.73540i		−	0.306307i	0.988202	−	0.153154i	$-0.0489430\pi$
$240$	−2.84734	+	5.44497i	−0.183795	+	0.351471i
$241$	−10.1380	+	5.85317i	−0.653045	+	0.377036i	−0.789622	−	0.613594i	$-0.789723\pi$
$241$	−10.1380	+	5.85317i	−0.653045	+	0.377036i	0.136577	+	0.990629i	$0.456390\pi$
$242$	−9.53873	−	7.16230i	−0.613173	−	0.460410i
$243$	10.1112	+	5.83773i	0.648636	+	0.374490i
$244$	11.6653	−	12.1631i	0.746792	−	0.778661i
$245$	0.164257	+	22.3593i	0.0104940	+	1.42848i
$246$	−2.63798	+	1.12511i	−0.168192	+	0.0717342i
$247$	6.34397	+	3.66269i	0.403657	+	0.233051i
$248$	0.323683	−	0.0529772i	0.0205539	−	0.00336406i
$249$	3.60168	+	6.23829i	0.228247	+	0.395336i
$250$	−0.110389	+	0.911990i	−0.00698160	+	0.0576793i
$251$			11.5631i			0.729858i	0.931035	+	0.364929i	$0.118907\pi$
$251$			11.5631i			0.729858i	−0.931035	+	0.364929i	$0.881093\pi$
$252$	12.8640	+	7.01158i	0.810356	+	0.441688i
$253$		−	7.08425i		−	0.445383i
$254$	6.90859	+	0.836227i	0.433483	+	0.0524696i
$255$	3.09172	+	5.35501i	0.193611	+	0.335344i
$256$	9.12847	+	13.1404i	0.570530	+	0.821277i
$257$	−20.4302	−	11.7954i	−1.27440	−	0.735777i	−0.298589	−	0.954382i	$-0.596516\pi$
$257$	−20.4302	−	11.7954i	−1.27440	−	0.735777i	−0.975813	+	0.218605i	$0.929849\pi$
$258$		0			0
$259$	3.61144	−	13.6788i	0.224404	−	0.849961i
$260$	6.13915	−	6.40113i	0.380734	−	0.396981i
$261$	−12.2435	−	7.06876i	−0.757851	−	0.437546i
$262$	−3.34991	+	4.46141i	−0.206958	+	0.275627i
$263$	−9.24833	+	5.33953i	−0.570277	+	0.329249i	−0.757260	−	0.653114i	$-0.773462\pi$
$263$	−9.24833	+	5.33953i	−0.570277	+	0.329249i	0.186983	+	0.982363i	$0.440129\pi$
$264$	1.68600	−	1.37974i	0.103766	−	0.0849170i
$265$		−	22.6290i		−	1.39009i
$266$	−18.3448	−	7.29701i	−1.12479	−	0.447408i
$267$	−0.832945			−0.0509754
$268$	−5.59900	−	19.2759i	−0.342013	−	1.17746i
$269$	−11.6690	−	20.2113i	−0.711471	−	1.23230i	−0.964305	−	0.264794i	$-0.914696\pi$
$269$	−11.6690	−	20.2113i	−0.711471	−	1.23230i	0.252834	−	0.967510i	$-0.418637\pi$
$270$	−7.52479	+	10.0215i	−0.457944	+	0.609889i
$271$	6.81961	−	11.8119i	0.414262	−	0.717522i	−0.581089	−	0.813840i	$-0.697373\pi$
$271$	6.81961	−	11.8119i	0.414262	−	0.717522i	0.995351	+	0.0963179i	$0.0307066\pi$
$272$	16.0873	−	0.672454i	0.975436	−	0.0407735i
$273$	1.25362	+	1.24444i	0.0758722	+	0.0753169i
$274$	0.133784	−	0.0570595i	0.00808221	−	0.00344709i
$275$	4.16706	−	7.21755i	0.251283	−	0.435235i
$276$	−4.13121	−	1.01497i	−0.248670	−	0.0610939i
$277$	−0.396180	+	0.228735i	−0.0238042	+	0.0137433i	−0.511855	−	0.859072i	$-0.671041\pi$
$277$	−0.396180	+	0.228735i	−0.0238042	+	0.0137433i	0.488051	+	0.872815i	$0.337708\pi$
$278$	21.0298	+	2.54549i	1.26129	+	0.152668i
$279$	0.321068			0.0192218
$280$	−13.8790	+	19.4618i	−0.829432	+	1.16306i
$281$	1.43695			0.0857215			0.0428608	−	0.999081i	$-0.486353\pi$
$281$	1.43695			0.0857215			0.0428608	+	0.999081i	$0.486353\pi$
$282$	6.83029	+	0.826750i	0.406738	+	0.0492323i
$283$	27.0428	−	15.6132i	1.60753	−	0.928108i	0.617609	−	0.786486i	$-0.288102\pi$
$283$	27.0428	−	15.6132i	1.60753	−	0.928108i	0.989921	−	0.141622i	$-0.0452318\pi$
$284$	−2.52498	+	10.2774i	−0.149830	+	0.609850i
$285$	4.05268	−	7.01945i	0.240060	−	0.415796i
$286$	−2.89257	+	1.23369i	−0.171041	+	0.0729497i
$287$	−10.7660	+	2.92717i	−0.635497	+	0.172785i
$288$	6.74083	+	14.1375i	0.397207	+	0.833062i
$289$	−0.398321	+	0.689912i	−0.0234306	+	0.0405831i
$290$	13.8500	−	18.4454i	0.813301	−	1.08315i
$291$	−0.690570	−	1.19610i	−0.0404819	−	0.0701168i
$292$	−20.6361	+	5.99410i	−1.20764	+	0.350778i
$293$	31.3006			1.82860			0.914299	−	0.405040i	$-0.132742\pi$
$293$	31.3006			1.82860			0.914299	+	0.405040i	$0.132742\pi$
$294$	−3.82786	−	2.83047i	−0.223245	−	0.165076i
$295$			16.1869i			0.942437i
$296$	11.7046	−	9.57850i	0.680319	−	0.556739i
$297$	3.84806	−	2.22168i	0.223287	−	0.128915i
$298$	9.60088	−	12.7864i	0.556164	−	0.740698i
$299$	5.31783	+	3.07025i	0.307538	+	0.177557i
$300$	−3.61193	−	3.46410i	−0.208535	−	0.200000i
$301$		0			0
$302$	−8.22268	−	19.2793i	−0.473162	−	1.10940i
$303$	2.83459	+	1.63655i	0.162843	+	0.0940175i
$304$	−11.3071	−	17.8216i	−0.648509	−	1.02214i
$305$	13.4581	+	23.3102i	0.770611	+	1.33474i
$306$	15.6473	+	1.89398i	0.894499	+	0.108272i
$307$			14.7215i			0.840202i	0.907477	+	0.420101i	$0.138005\pi$
$307$			14.7215i			0.840202i	−0.907477	+	0.420101i	$0.861995\pi$
$308$	7.23353	−	4.41662i	0.412169	−	0.251660i
$309$		−	6.75638i		−	0.384357i
$310$	−0.0629475	+	0.520048i	−0.00357518	+	0.0295367i
$311$	7.79025	+	13.4931i	0.441745	+	0.765124i	0.997819	−	0.0660082i	$-0.0210263\pi$
$311$	7.79025	+	13.4931i	0.441745	+	0.765124i	−0.556074	+	0.831133i	$0.687693\pi$
$312$	0.305010	+	1.86357i	0.0172678	+	0.105504i
$313$	11.3329	+	6.54308i	0.640576	+	0.369837i	0.784836	−	0.619703i	$-0.212747\pi$
$313$	11.3329	+	6.54308i	0.640576	+	0.369837i	−0.144260	+	0.989540i	$0.546080\pi$
$314$	−0.960963	+	0.409854i	−0.0542303	+	0.0231294i
$315$	−16.4849	+	16.6064i	−0.928818	+	0.935666i
$316$	−17.2257	−	16.5207i	−0.969022	−	0.929363i
$317$	−20.3971	−	11.7763i	−1.14562	−	0.661422i	−0.197801	−	0.980242i	$-0.563380\pi$
$317$	−20.3971	−	11.7763i	−1.14562	−	0.661422i	−0.947815	+	0.318821i	$0.896713\pi$
$318$	3.85278	+	2.89292i	0.216053	+	0.162227i
$319$	−7.08269	+	4.08919i	−0.396555	+	0.228951i
$320$	−24.2208	+	8.14667i	−1.35398	+	0.455413i
$321$			2.47142i			0.137941i
$322$	−15.3775	−	6.11671i	−0.856956	−	0.340871i
$323$	−21.2397			−1.18181
$324$	3.88955	+	13.3907i	0.216086	+	0.743929i
$325$	3.61193	+	6.25604i	0.200354	+	0.347023i
$326$	−9.84396	−	7.39148i	−0.545206	−	0.409376i
$327$	0.680744	−	1.17908i	0.0376452	−	0.0652035i
$328$	−11.1568	−	4.21689i	−0.616034	−	0.232839i
$329$	25.8788	+	6.83243i	1.42674	+	0.376684i
$330$	1.36505	+	3.20056i	0.0751435	+	0.176185i
$331$	−16.5277	+	28.6268i	−0.908445	+	1.57347i	−0.0922207	+	0.995739i	$0.529397\pi$
$331$	−16.5277	+	28.6268i	−0.908445	+	1.57347i	−0.816225	+	0.577735i	$0.803937\pi$
$332$	−7.14756	+	29.0926i	−0.392273	+	1.59666i
$333$	12.8217	−	7.40258i	0.702622	−	0.405659i
$334$	−0.235927	+	1.94913i	−0.0129093	+	0.106652i
$335$	32.0587			1.75155
$336$	−1.53922	−	4.85104i	−0.0839711	−	0.264646i
$337$	−15.5096			−0.844860			−0.422430	−	0.906396i	$-0.638823\pi$
$337$	−15.5096			−0.844860			−0.422430	+	0.906396i	$0.638823\pi$
$338$	−1.88166	+	15.5456i	−0.102349	+	0.845567i
$339$	0.598452	−	0.345516i	0.0325035	−	0.0187659i
$340$	−6.13553	+	24.9734i	−0.332746	+	1.35437i
$341$	0.0928668	−	0.160850i	0.00502902	−	0.00871052i
$342$	−8.10536	−	19.0042i	−0.438288	−	1.02763i
$343$	−13.2393	−	12.9507i	−0.714855	−	0.699272i
$344$		0			0
$345$	3.39716	−	5.88405i	0.182897	−	0.316786i
$346$	−1.09771	−	0.824230i	−0.0590131	−	0.0443109i
$347$	−11.2494	−	19.4846i	−0.603900	−	1.04599i	−0.992224	−	0.124463i	$-0.960279\pi$
$347$	−11.2494	−	19.4846i	−0.603900	−	1.04599i	0.388324	−	0.921523i	$-0.373054\pi$
$348$	1.36989	+	4.71616i	0.0734336	+	0.252813i
$349$	28.4735			1.52415			0.762077	−	0.647486i	$-0.224180\pi$
$349$	28.4735			1.52415			0.762077	+	0.647486i	$0.224180\pi$
$350$	−12.0690	−	15.2771i	−0.645113	−	0.816595i
$351$			3.85142i			0.205574i
$352$	9.03244	+	0.712140i	0.481430	+	0.0379572i
$353$	−8.29108	+	4.78686i	−0.441290	+	0.254779i	−0.704145	−	0.710057i	$-0.748669\pi$
$353$	−8.29108	+	4.78686i	−0.441290	+	0.254779i	0.262855	+	0.964835i	$0.415336\pi$
$354$	−2.75596	−	2.06935i	−0.146477	−	0.109985i
$355$	−14.6380	−	8.45124i	−0.776903	−	0.448545i
$356$	−2.50012	−	2.39779i	−0.132506	−	0.127083i
$357$	−4.95194	−	1.30739i	−0.262084	−	0.0691945i
$358$	18.5629	−	7.91711i	0.981077	−	0.418432i
$359$	3.25225	+	1.87769i	0.171647	+	0.0991006i	0.583362	−	0.812212i	$-0.301737\pi$
$359$	3.25225	+	1.87769i	0.171647	+	0.0991006i	−0.411715	+	0.911313i	$0.635070\pi$
$360$	−24.6864	+	4.04042i	−1.30109	+	0.212949i
$361$	4.42067	+	7.65683i	0.232667	+	0.402991i
$362$	−2.60376	+	21.5112i	−0.136850	+	1.13061i
$363$			4.05622i			0.212896i
$364$	0.180413	+	7.34401i	0.00945620	+	0.384931i
$365$		−	34.3209i		−	1.79644i
$366$	−5.68926	−	0.688638i	−0.297382	−	0.0359957i
$367$	8.41302	+	14.5718i	0.439156	+	0.760640i	0.997625	−	0.0688852i	$-0.0219442\pi$
$367$	8.41302	+	14.5718i	0.439156	+	0.760640i	−0.558469	+	0.829526i	$0.688611\pi$
$368$	−9.47820	−	14.9390i	−0.494086	−	0.778747i
$369$	−10.1112	−	5.83773i	−0.526370	−	0.303900i
$370$	9.47653	+	22.2191i	0.492661	+	1.15512i
$371$	13.3020	+	13.2046i	0.690606	+	0.685551i
$372$	−0.0804953	−	0.0772008i	−0.00417349	−	0.00400268i
$373$	11.1354	+	6.42901i	0.576568	+	0.332882i	0.759768	−	0.650194i	$-0.225312\pi$
$373$	11.1354	+	6.42901i	0.576568	+	0.332882i	−0.183200	+	0.983076i	$0.558646\pi$
$374$	5.47475	−	7.29126i	0.283093	−	0.377022i
$375$	0.270533	−	0.156192i	0.0139702	−	0.00806572i
$376$	18.1214	+	22.1439i	0.934542	+	1.14198i
$377$		−	7.08888i		−	0.365096i
$378$	−1.50001	−	10.2711i	−0.0771523	−	0.528289i
$379$	25.5822			1.31407			0.657034	−	0.753861i	$-0.271811\pi$
$379$	25.5822			1.31407			0.657034	+	0.753861i	$0.271811\pi$
$380$	32.3711	−	9.40272i	1.66060	−	0.482349i
$381$	−1.18320	−	2.04936i	−0.0606172	−	0.104992i
$382$	2.12345	−	2.82801i	0.108645	−	0.144693i
$383$	−13.4846	+	23.3561i	−0.689033	+	1.19344i	0.283118	+	0.959085i	$0.408631\pi$
$383$	−13.4846	+	23.3561i	−0.689033	+	1.19344i	−0.972151	+	0.234355i	$0.924702\pi$
$384$	1.70937	−	5.16527i	0.0872311	−	0.263589i
$385$	3.55142	+	13.0620i	0.180997	+	0.665701i
$386$	4.03327	−	1.72020i	0.205288	−	0.0875560i
$387$		0			0
$388$	1.37044	−	5.57809i	0.0695736	−	0.283185i
$389$	−27.7043	+	15.9951i	−1.40466	+	0.810983i	−0.994867	−	0.101195i	$-0.967734\pi$
$389$	−27.7043	+	15.9951i	−1.40466	+	0.810983i	−0.409796	+	0.912177i	$0.634400\pi$
$390$	−2.99412	−	0.362413i	−0.151613	−	0.0183515i
$391$	−17.8041			−0.900394
$392$	−3.34140	−	19.5150i	−0.168766	−	0.985656i
$393$	1.89716			0.0956988
$394$	22.0270	+	2.66619i	1.10971	+	0.134321i
$395$	33.0126	−	19.0598i	1.66104	−	0.959004i
$396$	8.61311	+	2.11609i	0.432825	+	0.106338i
$397$	8.51929	−	14.7558i	0.427571	−	0.740575i	−0.569086	−	0.822278i	$-0.692703\pi$
$397$	8.51929	−	14.7558i	0.427571	−	0.740575i	0.996657	+	0.0817035i	$0.0260360\pi$
$398$	−15.3835	+	6.56110i	−0.771104	+	0.328878i
$399$	1.76139	+	6.47833i	0.0881799	+	0.324322i
$400$	−0.869248	−	20.7953i	−0.0434624	−	1.03976i
$401$	2.94858	−	5.10709i	0.147245	−	0.255036i	−0.782963	−	0.622068i	$-0.786293\pi$
$401$	2.94858	−	5.10709i	0.147245	−	0.255036i	0.930208	+	0.367032i	$0.119626\pi$
$402$	−4.09841	+	5.45826i	−0.204410	+	0.272233i
$403$	0.0804953	+	0.139422i	0.00400976	+	0.00694510i
$404$	3.79700	+	13.0721i	0.188908	+	0.650362i
$405$	−22.2707			−1.10664
$406$	2.76090	+	18.9049i	0.137021	+	0.938233i
$407$		−	8.56461i		−	0.424532i
$408$	−3.46756	−	4.23725i	−0.171670	−	0.209775i
$409$	−0.207751	+	0.119945i	−0.0102726	+	0.00593090i	−0.505128	−	0.863045i	$-0.668555\pi$
$409$	−0.207751	+	0.119945i	−0.0102726	+	0.00593090i	0.494855	+	0.868976i	$0.335221\pi$
$410$	11.4380	−	15.2331i	0.564883	−	0.752310i
$411$	−0.0428320	−	0.0247290i	−0.00211274	−	0.00121979i
$412$	19.4496	−	20.2795i	0.958211	−	0.999101i
$413$	−9.51514	−	9.44550i	−0.468210	−	0.464783i
$414$	−6.79431	−	15.9303i	−0.333922	−	0.782930i
$415$	−41.4364	−	23.9233i	−2.03403	−	1.17435i
$416$	−4.44915	+	6.47161i	−0.218137	+	0.317297i
$417$	−3.60168	−	6.23829i	−0.176375	−	0.305490i
$418$	−11.8653	−	1.43619i	−0.580349	−	0.0702464i
$419$		−	29.4140i		−	1.43697i	−0.695544	−	0.718484i	$-0.744837\pi$
$419$		−	29.4140i		−	1.43697i	0.695544	−	0.718484i	$-0.255163\pi$
$420$	8.12597	−	0.199622i	0.396507	−	0.00974057i
$421$			32.1265i			1.56575i	0.622180	+	0.782874i	$0.286247\pi$
$421$			32.1265i			1.56575i	−0.622180	+	0.782874i	$0.713753\pi$
$422$	1.71172	−	14.1416i	0.0833254	−	0.688402i
$423$	14.0049	+	24.2571i	0.680939	+	1.17942i
$424$	3.23644	+	19.7742i	0.157175	+	0.960319i
$425$	−18.1391	−	10.4726i	−0.879878	−	0.507998i
$426$	3.31023	−	1.41182i	0.160381	−	0.0684031i
$427$	−21.5556	−	5.69103i	−1.04315	−	0.275408i
$428$	−7.11447	+	7.41807i	−0.343891	+	0.358566i
$429$	0.926077	+	0.534671i	0.0447114	+	0.0258141i
$430$		0			0
$431$	32.7662	−	18.9176i	1.57829	−	0.911228i	0.583196	−	0.812332i	$-0.301802\pi$
$431$	32.7662	−	18.9176i	1.57829	−	0.911228i	0.995098	−	0.0988962i	$-0.0315312\pi$
$432$	5.14219	−	9.83341i	0.247404	−	0.473110i
$433$		−	25.4835i		−	1.22466i	−0.790602	−	0.612330i	$-0.790232\pi$
$433$		−	25.4835i		−	1.22466i	0.790602	−	0.612330i	$-0.209768\pi$
$434$	−0.268968	−	0.340465i	−0.0129109	−	0.0163428i
$435$	−7.84367			−0.376075
$436$	5.43750	−	1.57941i	0.260409	−	0.0756400i
$437$	11.6690	+	20.2113i	0.558204	+	0.966837i
$438$	5.84343	+	4.38763i	0.279210	+	0.209649i
$439$	11.9804	−	20.7506i	0.571792	−	0.990373i	−0.424590	−	0.905386i	$-0.639582\pi$
$439$	11.9804	−	20.7506i	0.571792	−	0.990373i	0.996382	−	0.0849871i	$-0.0270849\pi$
$440$	−5.11619	+	13.5362i	−0.243905	+	0.645312i
$441$	−0.142375	−	19.3806i	−0.00677975	−	0.922887i
$442$	3.10051	+	7.26962i	0.147476	+	0.345780i
$443$	−5.13495	+	8.89399i	−0.243969	+	0.422566i	−0.961841	−	0.273608i	$-0.911783\pi$
$443$	−5.13495	+	8.89399i	−0.243969	+	0.422566i	0.717872	+	0.696175i	$0.245116\pi$
$444$	−4.99449	−	1.22706i	−0.237028	−	0.0582337i
$445$	4.79140	−	2.76632i	0.227134	−	0.131136i
$446$	−4.13097	+	34.1285i	−0.195607	+	1.61603i
$447$	−5.43726			−0.257174
$448$	9.34464	−	18.9915i	0.441493	−	0.897265i
$449$	11.5096			0.543170			0.271585	−	0.962414i	$-0.412452\pi$
$449$	11.5096			0.543170			0.271585	+	0.962414i	$0.412452\pi$
$450$	2.44825	−	20.2265i	0.115412	−	0.953488i
$451$	−5.84923	+	3.37705i	−0.275429	+	0.159019i
$452$	2.79091	+	0.685680i	0.131274	+	0.0322517i
$453$	−3.56363	+	6.17239i	−0.167434	+	0.290004i
$454$	7.94707	+	18.6331i	0.372974	+	0.874494i
$455$	−11.3442	−	2.99505i	−0.531824	−	0.140410i
$456$	−2.53747	+	6.71351i	−0.118828	+	0.314389i
$457$	−15.3050	+	26.5091i	−0.715939	+	1.24004i	0.246657	+	0.969103i	$0.420668\pi$
$457$	−15.3050	+	26.5091i	−0.715939	+	1.24004i	−0.962596	+	0.270941i	$0.912665\pi$
$458$	12.0442	+	9.04353i	0.562786	+	0.422576i
$459$	−5.58353	−	9.67095i	−0.260617	−	0.451401i
$460$	27.1351	−	7.88182i	1.26518	−	0.367492i
$461$	−17.3671			−0.808866			−0.404433	−	0.914568i	$-0.632531\pi$
$461$	−17.3671			−0.808866			−0.404433	+	0.914568i	$0.632531\pi$
$462$	−2.67793	−	1.06520i	−0.124589	−	0.0495576i
$463$		−	21.7288i		−	1.00983i	−0.863171	−	0.504913i	$-0.831525\pi$
$463$		−	21.7288i		−	1.00983i	0.863171	−	0.504913i	$-0.168475\pi$
$464$	−9.46463	+	18.0992i	−0.439385	+	0.840236i
$465$	0.154267	−	0.0890661i	0.00715396	−	0.00413034i
$466$	−0.721495	−	0.541745i	−0.0334226	−	0.0250959i
$467$	−0.585859	−	0.338246i	−0.0271103	−	0.0156521i	0.486384	−	0.873745i	$-0.338316\pi$
$467$	−0.585859	−	0.338246i	−0.0271103	−	0.0156521i	−0.513494	+	0.858093i	$0.671649\pi$
$468$	−5.32130	+	5.54838i	−0.245977	+	0.256474i
$469$	−18.7071	+	18.8450i	−0.863814	+	0.870183i
$470$	−42.0361	+	17.9285i	−1.93898	+	0.826981i
$471$	0.307659	+	0.177627i	0.0141762	+	0.00818461i
$472$	−2.31508	−	14.1448i	−0.106560	−	0.651067i
$473$		0			0
$474$	−0.975270	+	8.05730i	−0.0447956	+	0.370084i
$475$			27.4555i			1.25974i
$476$	−11.0999	−	18.1793i	−0.508761	−	0.833247i
$477$			19.6144i			0.898082i
$478$	−6.64834	−	0.804726i	−0.304088	−	0.0368073i
$479$	−14.3839	−	24.9136i	−0.657217	−	1.13833i	−0.981333	−	0.192316i	$-0.938400\pi$
$479$	−14.3839	−	24.9136i	−0.657217	−	1.13833i	0.324116	−	0.946017i	$-0.394933\pi$
$480$	7.16068	+	4.92287i	0.326839	+	0.224697i
$481$	6.42907	+	3.71182i	0.293140	+	0.169245i
$482$	6.49482	+	15.2281i	0.295831	+	0.693619i
$483$	1.47649	+	5.43045i	0.0671824	+	0.247094i
$484$	−11.6766	+	12.1749i	−0.530755	+	0.553404i
$485$	7.94483	+	4.58695i	0.360756	+	0.208283i
$486$	9.91426	−	13.2038i	0.449720	−	0.598936i
$487$	1.58745	−	0.916514i	0.0719342	−	0.0415312i	−0.463602	−	0.886044i	$-0.653443\pi$
$487$	1.58745	−	0.916514i	0.0719342	−	0.0415312i	0.535536	+	0.844513i	$0.320110\pi$
$488$	−15.0942	−	18.4446i	−0.683280	−	0.834948i
$489$			4.18601i			0.189298i
$490$	31.4196	+	3.56909i	1.41939	+	0.161235i
$491$	13.4370			0.606401			0.303201	−	0.952927i	$-0.401945\pi$
$491$	13.4370			0.606401			0.303201	+	0.952927i	$0.401945\pi$
$492$	1.13132	+	3.89484i	0.0510038	+	0.175593i
$493$	10.2770	+	17.8002i	0.462851	+	0.801682i
$494$	6.22038	−	8.28428i	0.279868	−	0.372728i
$495$	−7.08269	+	12.2676i	−0.318343	+	0.551387i
$496$	−0.0193720	−	0.463443i	−0.000869830	−	0.0208092i
$497$	13.5096	−	3.67311i	0.605987	−	0.164762i
$498$	9.37041	−	3.99651i	0.419898	−	0.179088i
$499$	5.68404	−	9.84505i	0.254453	−	0.440725i	−0.710294	−	0.703905i	$-0.751438\pi$
$499$	5.68404	−	9.84505i	0.254453	−	0.440725i	0.964747	+	0.263180i	$0.0847714\pi$
$500$	1.26164	+	0.309964i	0.0564224	+	0.0138620i
$501$	0.578191	−	0.333819i	0.0258317	−	0.0149139i
$502$	16.2342	+	1.96502i	0.724569	+	0.0877031i
$503$	13.2022			0.588656			0.294328	−	0.955704i	$-0.404904\pi$
$503$	13.2022			0.588656			0.294328	+	0.955704i	$0.404904\pi$
$504$	12.0301	−	16.8691i	0.535863	−	0.751409i
$505$	−21.7408			−0.967454
$506$	−9.94604	−	1.20389i	−0.442156	−	0.0535193i
$507$	4.61144	−	2.66241i	0.204801	−	0.118242i
$508$	2.34807	−	9.55732i	0.104179	−	0.424037i
$509$	13.2178	−	22.8940i	0.585870	−	1.01476i	−0.408896	−	0.912581i	$-0.634086\pi$
$509$	13.2178	−	22.8940i	0.585870	−	1.01476i	0.994766	−	0.102176i	$-0.0325804\pi$
$510$	8.04365	−	3.43064i	0.356179	−	0.151911i
$511$	20.1749	+	20.0272i	0.892484	+	0.885952i
$512$	20.0000	−	10.5830i	0.883883	−	0.467707i
$513$	−7.31899	+	12.6769i	−0.323141	+	0.559697i
$514$	−20.0322	+	26.6789i	−0.883583	+	1.17675i
$515$	22.4388	+	38.8652i	0.988773	+	1.71260i
$516$		0			0
$517$	16.2033			0.712619
$518$	−18.5909	−	7.39489i	−0.816837	−	0.324913i
$519$			0.466786i			0.0204896i
$520$	−7.94369	−	9.70695i	−0.348354	−	0.425678i
$521$	−10.4163	+	6.01384i	−0.456345	+	0.263471i	−0.710506	−	0.703691i	$-0.751534\pi$
$521$	−10.4163	+	6.01384i	−0.456345	+	0.263471i	0.254161	+	0.967162i	$0.418201\pi$
$522$	−12.0049	+	15.9881i	−0.525442	+	0.699782i
$523$	2.43276	+	1.40455i	0.106377	+	0.0614168i	0.552245	−	0.833682i	$-0.313771\pi$
$523$	2.43276	+	1.40455i	0.106377	+	0.0614168i	−0.445868	+	0.895099i	$0.647105\pi$
$524$	5.69439	+	5.46133i	0.248760	+	0.238579i
$525$	−1.69000	+	6.40113i	−0.0737577	+	0.279368i
$526$	5.92487	+	13.8917i	0.258337	+	0.605708i
$527$	−0.404248	−	0.233393i	−0.0176093	−	0.0101668i
$528$	−1.65059	−	2.60156i	−0.0718327	−	0.113218i
$529$	−1.71848	−	2.97649i	−0.0747164	−	0.129413i
$530$	−31.7703	−	3.84554i	−1.38002	−	0.167039i
$531$		−	14.0305i		−	0.608872i
$532$	−13.3622	+	24.5155i	−0.579327	+	1.06288i
$533$		−	5.85434i		−	0.253580i
$534$	−0.141549	+	1.16943i	−0.00612544	+	0.0506060i
$535$	−8.20791	−	14.2165i	−0.354859	−	0.614634i
$536$	−28.0142	+	4.58509i	−1.21003	+	0.198046i
$537$	−5.94302	−	3.43120i	−0.256460	−	0.148067i
$538$	−30.3590	+	12.9482i	−1.30887	+	0.558236i
$539$	−9.75058	−	5.53440i	−0.419987	−	0.238383i
$540$	12.7911	+	12.2676i	0.550441	+	0.527913i
$541$	−1.68628	−	0.973573i	−0.0724988	−	0.0418572i	0.463312	−	0.886195i	$-0.346661\pi$
$541$	−1.68628	−	0.973573i	−0.0724988	−	0.0418572i	−0.535811	+	0.844338i	$0.679994\pi$
$542$	−15.4246	−	11.5818i	−0.662543	−	0.497481i
$543$	6.38109	−	3.68413i	0.273839	−	0.158101i
$544$	1.78975	−	22.7003i	0.0767349	−	0.973268i
$545$			9.04336i			0.387375i
$546$	1.96019	−	1.54855i	0.0838883	−	0.0662720i
$547$	28.4561			1.21669			0.608347	−	0.793671i	$-0.291833\pi$
$547$	28.4561			1.21669			0.608347	+	0.793671i	$0.291833\pi$
$548$	−0.0573744	−	0.197525i	−0.00245091	−	0.00843786i
$549$	−11.6653	−	20.2048i	−0.497862	−	0.862321i
$550$	−9.42505	−	7.07694i	−0.401886	−	0.301762i
$551$	13.4712	−	23.3329i	0.573894	−	0.994013i
$552$	−2.12703	+	5.62760i	−0.0905325	+	0.239526i
$553$	−8.05982	+	30.5277i	−0.342738	+	1.29817i
$554$	0.253810	+	0.595095i	0.0107833	+	0.0252832i
$555$	4.10704	−	7.11361i	0.174334	−	0.301956i
$556$	7.14756	−	29.0926i	0.303124	−	1.23380i
$557$	−7.96630	+	4.59935i	−0.337543	+	0.194881i	−0.659185	−	0.751981i	$-0.729099\pi$
$557$	−7.96630	+	4.59935i	−0.337543	+	0.194881i	0.321642	+	0.946861i	$0.395765\pi$
$558$	0.0545617	−	0.450768i	0.00230978	−	0.0190825i
$559$		0			0
$560$	24.9651	+	22.7930i	1.05497	+	0.963181i
$561$	−3.10051			−0.130904
$562$	0.244194	−	2.01744i	0.0103007	−	0.0851004i
$563$	−23.5533	+	13.5985i	−0.992653	+	0.573108i	−0.906066	−	0.423136i	$-0.860929\pi$
$563$	−23.5533	+	13.5985i	−0.992653	+	0.573108i	−0.0865866	+	0.996244i	$0.527596\pi$
$564$	2.32146	−	9.44901i	0.0977511	−	0.397875i
$565$	−2.29501	+	3.97508i	−0.0965518	+	0.167233i
$566$	−17.3248	−	40.6205i	−0.728214	−	1.70741i
$567$	12.9956	−	13.0914i	0.545764	−	0.549788i
$568$	14.0000	+	5.29150i	0.587427	+	0.222027i
$569$	11.7699	−	20.3861i	0.493420	−	0.854628i	−0.506551	−	0.862210i	$-0.669080\pi$
$569$	11.7699	−	20.3861i	0.493420	−	0.854628i	0.999971	+	0.00758149i	$0.00241329\pi$
$570$	−9.16636	−	6.88270i	−0.383937	−	0.288285i
$571$	−15.1713	−	26.2774i	−0.634897	−	1.09967i	−0.986537	−	0.163539i	$-0.947709\pi$
$571$	−15.1713	−	26.2774i	−0.634897	−	1.09967i	0.351640	−	0.936135i	$-0.385624\pi$
$572$	1.24050	+	4.27073i	0.0518680	+	0.178568i
$573$	−1.20257			−0.0502382
$574$	2.28009	+	15.6126i	0.0951690	+	0.651655i
$575$			23.0145i			0.959772i
$576$	20.9941	−	7.06138i	0.874756	−	0.294224i
$577$	24.7760	−	14.3044i	1.03144	−	0.595500i	0.114041	−	0.993476i	$-0.463620\pi$
$577$	24.7760	−	14.3044i	1.03144	−	0.595500i	0.917396	+	0.397976i	$0.130287\pi$
$578$	0.900923	+	0.676472i	0.0374735	+	0.0281375i
$579$	−1.29128	−	0.745520i	−0.0536637	−	0.0309828i
$580$	−23.5431	−	22.5795i	−0.977574	−	0.937564i
$581$	38.2421	−	10.3976i	1.58655	−	0.431367i
$582$	−1.79664	+	0.766273i	−0.0744732	+	0.0317630i
$583$	9.82652	+	5.67335i	0.406973	+	0.234966i
$584$	4.90864	+	29.9911i	0.203121	+	1.24104i
$585$	−6.13915	−	10.6333i	−0.253823	−	0.439634i
$586$	5.31917	−	43.9449i	0.219733	−	1.81535i
$587$			15.2362i			0.628867i	0.949280	+	0.314433i	$0.101814\pi$
$587$			15.2362i			0.628867i	−0.949280	+	0.314433i	$0.898186\pi$
$588$	−4.62438	+	4.89317i	−0.190706	+	0.201791i
$589$			0.611872i			0.0252117i
$590$	22.7258	+	2.75078i	0.935608	+	0.113248i
$591$	−3.77246	−	6.53409i	−0.155178	−	0.268777i
$592$	−11.4588	−	18.0607i	−0.470955	−	0.742289i
$593$	18.2934	+	10.5617i	0.751221	+	0.433717i	0.826135	−	0.563473i	$-0.190535\pi$
$593$	18.2934	+	10.5617i	0.751221	+	0.433717i	−0.0749142	+	0.997190i	$0.523868\pi$
$594$	−2.46523	−	5.78010i	−0.101150	−	0.237160i
$595$	32.8274	−	8.92543i	1.34579	−	0.365907i
$596$	−16.3202	−	15.6522i	−0.668500	−	0.641140i
$597$	4.92512	+	2.84352i	0.201572	+	0.116378i
$598$	5.21423	−	6.94429i	0.213226	−	0.283973i
$599$	−29.1795	+	16.8468i	−1.19224	+	0.688341i	−0.958814	−	0.284033i	$-0.908327\pi$
$599$	−29.1795	+	16.8468i	−1.19224	+	0.688341i	−0.233427	+	0.972374i	$0.574994\pi$
$600$	−5.47729	+	4.48234i	−0.223609	+	0.182991i
$601$			24.3960i			0.995132i	0.867426	+	0.497566i	$0.165773\pi$
$601$			24.3960i			0.995132i	−0.867426	+	0.497566i	$0.834227\pi$
$602$		0			0
$603$	−27.7879			−1.13161
$604$	−28.4648	+	8.26807i	−1.15822	+	0.336423i
$605$	−13.4712	−	23.3329i	−0.547683	−	0.948616i
$606$	2.77937	−	3.70156i	0.112904	−	0.150366i
$607$	−4.08757	+	7.07987i	−0.165909	+	0.287363i	−0.936978	−	0.349389i	$-0.886389\pi$
$607$	−4.08757	+	7.07987i	−0.165909	+	0.287363i	0.771069	+	0.636752i	$0.219723\pi$
$608$	−26.9425	+	12.8463i	−1.09266	+	0.520985i
$609$	4.57700	−	4.61075i	0.185469	−	0.186837i
$610$	35.0138	−	14.9335i	1.41767	−	0.604639i
$611$	−7.02235	+	12.1631i	−0.284094	+	0.492065i
$612$	5.31817	−	21.6465i	0.214974	−	0.875007i
$613$	14.7221	−	8.49981i	0.594620	−	0.343304i	−0.172302	−	0.985044i	$-0.555121\pi$
$613$	14.7221	−	8.49981i	0.594620	−	0.343304i	0.766922	+	0.641740i	$0.221787\pi$
$614$	20.6685	+	2.50175i	0.834114	+	0.100963i
$615$	−6.47768			−0.261205
$616$	−4.97153	−	10.9062i	−0.200309	−	0.439423i
$617$	39.6548			1.59644			0.798221	−	0.602365i	$-0.205775\pi$
$617$	39.6548			1.59644			0.798221	+	0.602365i	$0.205775\pi$
$618$	−9.48573	−	1.14817i	−0.381572	−	0.0461861i
$619$	−12.4719	+	7.20065i	−0.501288	+	0.289419i	−0.729245	−	0.684252i	$-0.760129\pi$
$619$	−12.4719	+	7.20065i	−0.501288	+	0.289419i	0.227957	+	0.973671i	$0.426795\pi$
$620$	0.719432	+	0.176752i	0.0288931	+	0.00709854i
$621$	−6.13514	+	10.6264i	−0.246195	+	0.426422i
$622$	20.2677	−	8.64425i	0.812662	−	0.346603i
$623$	−1.16979	+	4.43075i	−0.0468667	+	0.177514i
$624$	2.66822	−	0.111532i	0.106814	−	0.00446487i
$625$	11.9709	−	20.7343i	0.478837	−	0.829370i
$626$	11.1122	−	14.7992i	0.444131	−	0.591493i
$627$	2.03211	+	3.51971i	0.0811545	+	0.140564i
$628$	0.412116	+	1.41881i	0.0164452	+	0.0566166i
$629$	−21.5246			−0.858241
$630$	20.5134	+	25.9663i	0.817275	+	1.03452i
$631$			36.6698i			1.45980i	0.683553	+	0.729900i	$0.260434\pi$
$631$			36.6698i			1.45980i	−0.683553	+	0.729900i	$0.739566\pi$
$632$	−26.1218	+	21.3768i	−1.03907	+	0.850324i
$633$	−4.19496	+	2.42196i	−0.166735	+	0.0962644i
$634$	−19.9998	+	26.6356i	−0.794292	+	1.05784i
$635$	13.6124	+	7.85913i	0.540192	+	0.311880i
$636$	4.71629	−	4.91755i	0.187013	−	0.194994i
$637$	8.38024	−	4.92077i	0.332037	−	0.194968i
$638$	4.53747	+	10.6388i	0.179640	+	0.421193i
$639$	12.6879	+	7.32538i	0.501927	+	0.289788i
$640$	7.32160	+	35.3896i	0.289412	+	1.39890i
$641$	−9.13798	−	15.8274i	−0.360929	−	0.625147i	0.627185	−	0.778870i	$-0.284207\pi$
$641$	−9.13798	−	15.8274i	−0.360929	−	0.625147i	−0.988114	+	0.153723i	$0.950874\pi$
$642$	3.46979	+	0.419989i	0.136942	+	0.0165757i
$643$		−	13.6340i		−	0.537671i	−0.963186	−	0.268836i	$-0.913361\pi$
$643$		−	13.6340i		−	0.537671i	0.963186	−	0.268836i	$-0.0866389\pi$
$644$	−11.2009	+	20.5501i	−0.441377	+	0.809786i
$645$		0			0
$646$	−3.60943	+	29.8198i	−0.142011	+	1.17324i
$647$	−8.74153	−	15.1408i	−0.343665	−	0.595245i	0.641445	−	0.767169i	$-0.278335\pi$
$647$	−8.74153	−	15.1408i	−0.343665	−	0.595245i	−0.985110	+	0.171923i	$0.945002\pi$
$648$	19.4611	−	3.18520i	0.764505	−	0.125127i
$649$	−7.02907	−	4.05824i	−0.275915	−	0.159300i
$650$	9.39708	−	4.00788i	0.368584	−	0.157202i
$651$	−0.0376633	+	0.142655i	−0.00147614	+	0.00559110i
$652$	−12.0503	+	12.5645i	−0.471924	+	0.492063i
$653$	−8.40495	−	4.85260i	−0.328911	−	0.189897i	0.326446	−	0.945216i	$-0.394149\pi$
$653$	−8.40495	−	4.85260i	−0.328911	−	0.189897i	−0.655358	+	0.755319i	$0.727482\pi$
$654$	−1.53971	−	1.15611i	−0.0602074	−	0.0452076i
$655$	−10.9131	+	6.30070i	−0.426411	+	0.246189i
$656$	−7.81635	+	14.9472i	−0.305177	+	0.583591i
$657$			29.7488i			1.16061i
$658$	13.9903	−	35.1719i	0.545399	−	1.37114i
$659$	−28.9465			−1.12760			−0.563798	−	0.825913i	$-0.690660\pi$
$659$	−28.9465			−1.12760			−0.563798	+	0.825913i	$0.690660\pi$
$660$	4.72546	−	1.37259i	0.183938	−	0.0534278i
$661$	−6.43683	−	11.1489i	−0.250364	−	0.433643i	0.713262	−	0.700897i	$-0.247217\pi$
$661$	−6.43683	−	11.1489i	−0.250364	−	0.433643i	−0.963626	+	0.267254i	$0.913884\pi$
$662$	37.3824	+	28.0691i	1.45291	+	1.09094i
$663$	1.34373	−	2.32742i	0.0521863	−	0.0903893i
$664$	39.6304	+	14.9789i	1.53796	+	0.581293i
$665$	−31.6475	−	31.4159i	−1.22724	−	1.21826i
$666$	−8.21408	−	19.2591i	−0.318289	−	0.746277i
$667$	11.2922	−	19.5587i	0.437238	−	0.757318i
$668$	2.69643	+	0.662466i	0.104328	+	0.0256316i
$669$	10.1239	−	5.84502i	0.391412	−	0.225982i
$670$	5.44800	−	45.0093i	0.210475	−	1.73886i
$671$	−13.4964			−0.521024
$672$	−7.07227	+	1.33663i	−0.272819	+	0.0515616i
$673$	−23.6548			−0.911825			−0.455912	−	0.890025i	$-0.650687\pi$
$673$	−23.6548			−0.911825			−0.455912	+	0.890025i	$0.650687\pi$
$674$	−2.63567	+	21.7749i	−0.101522	+	0.838738i
$675$	−12.5012	+	7.21755i	−0.481170	+	0.277804i
$676$	21.5057	+	5.28358i	0.827142	+	0.203215i
$677$	−1.80224	+	3.12157i	−0.0692657	+	0.119972i	−0.898578	−	0.438813i	$-0.855399\pi$
$677$	−1.80224	+	3.12157i	−0.0692657	+	0.119972i	0.829313	+	0.558785i	$0.188732\pi$
$678$	−0.383393	−	0.898923i	−0.0147241	−	0.0345229i
$679$	−7.33237	+	1.99360i	−0.281391	+	0.0765072i
$680$	34.0191	+	12.8580i	1.30457	+	0.493083i
$681$	3.44419	−	5.96550i	0.131981	−	0.228599i
$682$	−0.210046	−	0.157717i	−0.00804309	−	0.00603928i
$683$	3.80924	+	6.59779i	0.145756	+	0.252457i	0.929655	−	0.368432i	$-0.120105\pi$
$683$	3.80924	+	6.59779i	0.145756	+	0.252457i	−0.783899	+	0.620889i	$0.786772\pi$
$684$	−28.0587	+	8.15010i	−1.07285	+	0.311627i
$685$	0.328514			0.0125519
$686$	−20.4322	+	16.3867i	−0.780106	+	0.625648i
$687$		−	5.12162i		−	0.195402i
$688$		0			0
$689$	−8.51745	+	4.91755i	−0.324489	+	0.187344i
$690$	−7.68369	−	5.76942i	−0.292513	−	0.219638i
$691$	−44.9707	−	25.9639i	−1.71077	−	0.987712i	−0.933526	−	0.358509i	$-0.883285\pi$
$691$	−44.9707	−	25.9639i	−1.71077	−	0.987712i	−0.777241	−	0.629203i	$-0.783381\pi$
$692$	−1.34373	+	1.40108i	−0.0510811	+	0.0532609i
$693$	−3.07831	−	11.3219i	−0.116935	−	0.430083i
$694$	−29.2674	+	12.4826i	−1.11097	+	0.473834i
$695$	41.4364	+	23.9233i	1.57177	+	0.907462i
$696$	6.85413	−	1.12182i	0.259805	−	0.0425223i
$697$	8.48721	+	14.7003i	0.321476	+	0.556813i
$698$	4.83875	−	39.9759i	0.183149	−	1.51311i
$699$			0.306806i			0.0116045i
$700$	−23.4995	+	14.3482i	−0.888198	+	0.542312i
$701$		−	0.741474i		−	0.0280051i	−0.999902	−	0.0140025i	$-0.995543\pi$
$701$		−	0.741474i		−	0.0280051i	0.999902	−	0.0140025i	$-0.00445729\pi$
$702$	5.40727	+	0.654505i	0.204084	+	0.0247027i
$703$	14.1074	+	24.4347i	0.532071	+	0.921574i
$704$	2.53478	−	12.5602i	0.0955331	−	0.473381i
$705$	13.4581	+	7.77006i	0.506863	+	0.292637i
$706$	5.31161	+	12.4539i	0.199905	+	0.468708i
$707$	12.6864	−	12.7799i	0.477120	−	0.480638i
$708$	−3.37364	+	3.51761i	−0.126789	+	0.132200i
$709$	−35.6491	−	20.5820i	−1.33883	−	0.772974i	−0.352196	−	0.935926i	$-0.614565\pi$
$709$	−35.6491	−	20.5820i	−1.33883	−	0.772974i	−0.986634	+	0.162952i	$0.947898\pi$
$710$	−14.3528	+	19.1150i	−0.538652	+	0.717375i
$711$	−28.6147	+	16.5207i	−1.07314	+	0.619575i
$712$	−3.79129	+	3.10260i	−0.142085	+	0.116275i
$713$			0.512901i			0.0192083i
$714$	−2.67706	+	6.73018i	−0.100186	+	0.251871i
$715$	−7.10284			−0.265631
$716$	−7.96082	−	27.4070i	−0.297510	−	1.02425i
$717$	1.13863	+	1.97216i	0.0425229	+	0.0736518i
$718$	3.18889	−	4.24696i	0.119008	−	0.158495i
$719$	−7.02471	+	12.1672i	−0.261978	+	0.453758i	−0.966767	−	0.255658i	$-0.917708\pi$
$719$	−7.02471	+	12.1672i	−0.261978	+	0.453758i	0.704790	+	0.709416i	$0.251041\pi$
$720$	1.47745	+	35.3455i	0.0550613	+	1.31725i
$721$	−35.9398	−	9.48869i	−1.33847	−	0.353377i
$722$	11.5012	−	4.90528i	0.428029	−	0.182556i
$723$	2.81479	−	4.87536i	0.104683	−	0.181317i
$724$	29.7586	+	7.31117i	1.10597	+	0.271718i
$725$	23.0095	−	13.2845i	0.854550	−	0.493375i
$726$	5.69479	+	0.689307i	0.211354	+	0.0255826i
$727$	−13.2022			−0.489642			−0.244821	−	0.969568i	$-0.578729\pi$
$727$	−13.2022			−0.489642			−0.244821	+	0.969568i	$0.578729\pi$
$728$	10.3414	+	0.994736i	0.383278	+	0.0368674i
$729$	15.3015			0.566724
$730$	−48.1854	−	5.83245i	−1.78342	−	0.215868i
$731$		0			0
$732$	−1.93365	+	7.87050i	−0.0714697	+	0.290902i
$733$	−24.9797	+	43.2661i	−0.922646	+	1.59807i	−0.127342	+	0.991859i	$0.540644\pi$
$733$	−24.9797	+	43.2661i	−0.922646	+	1.59807i	−0.795304	+	0.606211i	$0.792689\pi$
$734$	21.8880	−	9.33529i	0.807900	−	0.344572i
$735$	−5.44471	−	9.27253i	−0.200831	−	0.342022i
$736$	−22.5845	+	10.7684i	−0.832476	+	0.396928i
$737$	−8.03747	+	13.9213i	−0.296064	+	0.512798i
$738$	−9.91426	+	13.2038i	−0.364949	+	0.486038i
$739$	18.2718	+	31.6476i	0.672138	+	1.16418i	0.977297	+	0.211875i	$0.0679571\pi$
$739$	18.2718	+	31.6476i	0.672138	+	1.16418i	−0.305159	+	0.952301i	$0.598710\pi$
$740$	32.8054	−	9.52884i	1.20595	−	0.350287i
$741$	−3.52278			−0.129413
$742$	20.7994	−	16.4316i	0.763570	−	0.603223i
$743$		−	15.1330i		−	0.555177i	−0.960700	−	0.277589i	$-0.910465\pi$
$743$		−	15.1330i		−	0.555177i	0.960700	−	0.277589i	$-0.0895352\pi$
$744$	−0.122067	+	0.0998933i	−0.00447518	+	0.00366226i
$745$	31.2771	−	18.0579i	1.14591	−	0.661589i
$746$	10.9184	−	14.5411i	0.399752	−	0.532389i
$747$	35.9163	+	20.7363i	1.31411	+	0.758701i
$748$	−9.30631	−	8.92543i	−0.340273	−	0.326346i
$749$	13.1464	+	3.47087i	0.480360	+	0.126823i
$750$	−0.173314	−	0.406362i	−0.00632855	−	0.0148382i
$751$	−11.9997	−	6.92806i	−0.437877	−	0.252808i	0.264820	−	0.964298i	$-0.414688\pi$
$751$	−11.9997	−	6.92806i	−0.437877	−	0.252808i	−0.702697	+	0.711490i	$0.748021\pi$
$752$	34.1688	−	21.6788i	1.24601	−	0.790544i
$753$	−2.78036	−	4.81572i	−0.101322	−	0.175495i
$754$	−9.95254	−	1.20467i	−0.362450	−	0.0438716i
$755$		−	47.3412i		−	1.72292i
$756$	−14.6752	+	0.360511i	−0.533732	+	0.0131116i
$757$		−	46.6967i		−	1.69722i	−0.529019	−	0.848610i	$-0.677440\pi$
$757$		−	46.6967i		−	1.69722i	0.529019	−	0.848610i	$-0.322560\pi$
$758$	4.34739	−	35.9165i	0.157904	−	1.30455i
$759$	1.70341	+	2.95039i	0.0618299	+	0.107093i
$760$	−7.70000	−	47.0458i	−0.279308	−	1.70653i
$761$	40.7899	+	23.5501i	1.47863	+	0.853689i	0.999708	−	0.0241662i	$-0.00769309\pi$
$761$	40.7899	+	23.5501i	1.47863	+	0.853689i	0.478925	+	0.877856i	$0.341026\pi$
$762$	−3.07831	+	1.31291i	−0.111515	+	0.0475616i
$763$	−5.31596	−	5.27705i	−0.192451	−	0.191042i
$764$	−3.60957	−	3.46184i	−0.130590	−	0.125245i
$765$	30.8309	+	17.8002i	1.11469	+	0.643568i
$766$	30.4996	+	22.9011i	1.10199	+	0.827449i
$767$	6.09267	−	3.51761i	0.219994	−	0.127013i
$768$	−6.96138	−	3.27768i	−0.251197	−	0.118273i
$769$		−	17.3071i		−	0.624110i	−0.950064	−	0.312055i	$-0.898983\pi$
$769$		−	17.3071i		−	0.624110i	0.950064	−	0.312055i	$-0.101017\pi$
$770$	18.9421	−	2.76634i	0.682626	−	0.0996921i
$771$	11.3448			0.408574
$772$	−1.72970	−	5.95490i	−0.0622532	−	0.214322i
$773$	13.5389	+	23.4501i	0.486960	+	0.843440i	0.999888	−	0.0149920i	$-0.00477229\pi$
$773$	13.5389	+	23.4501i	0.486960	+	0.843440i	−0.512927	+	0.858432i	$0.671439\pi$
$774$		0			0
$775$	−0.301696	+	0.522552i	−0.0108372	+	0.0187706i
$776$	−7.59856	−	2.87198i	−0.272772	−	0.103098i
$777$	1.78502	+	6.56523i	0.0640372	+	0.235526i
$778$	17.7485	+	41.6141i	0.636315	+	1.49194i
$779$	11.1252	−	19.2694i	0.398601	−	0.690398i
$780$	−1.01763	+	4.14205i	−0.0364371	+	0.148309i
$781$	7.33982	−	4.23764i	0.262639	−	0.151635i
$782$	−3.02561	+	24.9964i	−0.108195	+	0.893869i
$783$	14.1654			0.506230
$784$	−27.9662	+	1.37486i	−0.998794	+	0.0491023i
$785$	−2.35969			−0.0842208
$786$	0.322400	−	2.66354i	0.0114996	−	0.0950054i
$787$	−46.9684	+	27.1172i	−1.67424	+	0.966624i	−0.709023	+	0.705186i	$0.750864\pi$
$787$	−46.9684	+	27.1172i	−1.67424	+	0.966624i	−0.965220	+	0.261439i	$0.915803\pi$
$788$	7.48648	−	30.4721i	0.266695	−	1.08552i
$789$	2.56778	−	4.44753i	0.0914155	−	0.158336i
$790$	−21.1492	−	49.5876i	−0.752456	−	1.76425i
$791$	−0.997467	−	3.66864i	−0.0354658	−	0.130442i
$792$	4.43462	−	11.7329i	0.157578	−	0.416911i
$793$	5.84923	−	10.1312i	0.207712	−	0.359768i
$794$	−19.2690	−	14.4684i	−0.683830	−	0.513464i
$795$	5.44115	+	9.42435i	0.192978	+	0.334247i
$796$	6.59732	+	22.7129i	0.233836	+	0.805036i
$797$	−20.1437			−0.713527			−0.356763	−	0.934195i	$-0.616120\pi$
$797$	−20.1437			−0.713527			−0.356763	+	0.934195i	$0.616120\pi$
$798$	9.39468	−	1.37202i	0.332568	−	0.0485689i
$799$		−	40.7221i		−	1.44064i
$800$	−29.3436	−	2.31352i	−1.03745	−	0.0817953i
$801$	−4.15310	+	2.39779i	−0.146743	+	0.0847219i
$802$	−6.66910	−	5.00759i	−0.235494	−	0.176824i
$803$	14.9037	+	8.60465i	0.525940	+	0.303651i
$804$	6.96673	+	6.68160i	0.245698	+	0.235642i
$805$	−26.5285	−	26.3344i	−0.935008	−	0.928164i
$806$	0.209423	−	0.0893195i	0.00737661	−	0.00314615i
$807$	9.71963	+	5.61163i	0.342147	+	0.197539i
$808$	18.9981	−	3.10941i	0.668349	−	0.109389i
$809$	−17.2771	−	29.9249i	−0.607432	−	1.05210i	−0.991662	−	0.128865i	$-0.958867\pi$
$809$	−17.2771	−	29.9249i	−0.607432	−	1.05210i	0.384231	−	0.923237i	$-0.374467\pi$
$810$	−3.78466	+	31.2674i	−0.132979	+	1.09862i
$811$			13.6340i			0.478754i	0.970927	+	0.239377i	$0.0769431\pi$
$811$			13.6340i			0.478754i	−0.970927	+	0.239377i	$0.923057\pi$
$812$	27.0110	−	0.663551i	0.947899	−	0.0232861i
$813$			6.55911i			0.230038i
$814$	−12.0244	−	1.45546i	−0.421456	−	0.0510137i
$815$	−13.9023	−	24.0795i	−0.486976	−	0.843468i
$816$	−6.53823	+	4.14826i	−0.228884	+	0.145218i
$817$		0			0
$818$	0.133094	+	0.312058i	0.00465352	+	0.0109109i
$819$	9.83294	+	2.59606i	0.343591	+	0.0907136i
$820$	−19.4430	−	18.6473i	−0.678980	−	0.651191i
$821$	27.7311	+	16.0106i	0.967822	+	0.558772i	0.898572	−	0.438827i	$-0.144606\pi$
$821$	27.7311	+	16.0106i	0.967822	+	0.558772i	0.0692505	+	0.997599i	$0.477939\pi$
$822$	−0.0419975	+	0.0559322i	−0.00146483	+	0.00195086i
$823$	26.8399	−	15.4960i	0.935580	−	0.540158i	0.0470083	−	0.998894i	$-0.485031\pi$
$823$	26.8399	−	15.4960i	0.935580	−	0.540158i	0.888572	+	0.458737i	$0.151698\pi$
$824$	−25.1666	−	30.7528i	−0.876719	−	1.07132i
$825$			4.00788i			0.139537i
$826$	−14.8781	+	11.7538i	−0.517677	+	0.408966i
$827$	−11.0191			−0.383172			−0.191586	−	0.981476i	$-0.561363\pi$
$827$	−11.0191			−0.383172			−0.191586	+	0.981476i	$0.561363\pi$
$828$	−23.5202	+	6.83182i	−0.817383	+	0.237422i
$829$	18.9836	+	32.8806i	0.659328	+	1.14199i	0.980790	+	0.195067i	$0.0624924\pi$
$829$	18.9836	+	32.8806i	0.659328	+	1.14199i	−0.321462	+	0.946922i	$0.604174\pi$
$830$	−40.6291	+	54.1098i	−1.41026	+	1.87818i
$831$	0.109999	−	0.190524i	0.00381582	−	0.00660919i
$832$	8.32984	+	7.34623i	0.288785	+	0.254685i
$833$	−13.9090	+	24.5052i	−0.481920	+	0.849054i
$834$	−9.37041	+	3.99651i	−0.324471	+	0.138388i
$835$	−2.21731	+	3.84050i	−0.0767332	+	0.132906i
$836$	−4.03273	+	16.4144i	−0.139475	+	0.567702i
$837$	−0.278601	+	0.160850i	−0.00962984	+	0.00555979i
$838$	−41.2962	−	4.99857i	−1.42655	−	0.172673i
$839$	8.32984			0.287578			0.143789	−	0.989608i	$-0.454071\pi$
$839$	8.32984			0.287578			0.143789	+	0.989608i	$0.454071\pi$
$840$	1.10065	−	11.4425i	0.0379761	−	0.394804i
$841$	2.92739			0.100945
$842$	45.1045	+	5.45952i	1.55440	+	0.188148i
$843$	−0.598452	+	0.345516i	−0.0206118	+	0.0119002i
$844$	−19.5634	−	4.80640i	−0.673401	−	0.165443i
$845$	−17.6844	+	30.6304i	−0.608363	+	1.05372i
$846$	36.4361	−	15.5401i	1.25270	−	0.534280i
$847$	21.5766	+	5.69657i	0.741380	+	0.195736i
$848$	28.3123	−	1.18346i	0.972247	−	0.0406402i
$849$	−7.50840	+	13.0049i	−0.257687	+	0.446328i
$850$	−17.7858	+	23.6870i	−0.610047	+	0.812459i
$851$	11.8255	+	20.4824i	0.405374	+	0.702128i
$852$	−1.41962	−	4.88738i	−0.0486353	−	0.167439i
$853$	6.94153			0.237673			0.118837	−	0.992914i	$-0.462083\pi$
$853$	6.94153			0.237673			0.118837	+	0.992914i	$0.462083\pi$
$854$	−11.6531	+	29.2962i	−0.398763	+	1.00250i
$855$		−	46.6657i		−	1.59593i
$856$	9.20569	+	11.2491i	0.314644	+	0.384486i
$857$	1.91744	−	1.10704i	0.0654986	−	0.0378156i	−0.466893	−	0.884314i	$-0.654627\pi$
$857$	1.91744	−	1.10704i	0.0654986	−	0.0378156i	0.532392	+	0.846498i	$0.321293\pi$
$858$	0.908036	−	1.20932i	0.0309998	−	0.0412855i
$859$	5.26337	+	3.03881i	0.179584	+	0.103683i	0.587097	−	0.809516i	$-0.300271\pi$
$859$	5.26337	+	3.03881i	0.179584	+	0.103683i	−0.407513	+	0.913199i	$0.633604\pi$
$860$		0			0
$861$	3.77991	−	3.80778i	0.128819	−	0.129769i
$862$	−20.9914	−	49.2175i	−0.714970	−	1.67635i
$863$	7.64747	+	4.41527i	0.260323	+	0.150298i	0.624482	−	0.781039i	$-0.285310\pi$
$863$	7.64747	+	4.41527i	0.260323	+	0.150298i	−0.364159	+	0.931337i	$0.618643\pi$
$864$	−12.9319	−	8.89053i	−0.439953	−	0.302462i
$865$	−1.55026	−	2.68512i	−0.0527103	−	0.0912969i
$866$	−35.7780	−	4.33063i	−1.21579	−	0.147161i
$867$		−	0.383106i		−	0.0130110i
$868$	−0.523709	+	0.319764i	−0.0177758	+	0.0108535i
$869$			19.1141i			0.648400i
$870$	−1.33294	+	11.0122i	−0.0451909	+	0.373350i
$871$	−6.96673	−	12.0667i	−0.236059	−	0.408866i
$872$	−1.29340	−	7.90247i	−0.0438000	−	0.267611i
$873$	−6.88643	−	3.97588i	−0.233070	−	0.134563i
$874$	30.3590	−	12.9482i	1.02691	−	0.437979i
$875$	−0.450909	−	1.65842i	−0.0152435	−	0.0560650i
$876$	7.15310	−	7.45835i	0.241681	−	0.251994i
$877$	10.3059	+	5.95011i	0.348005	+	0.200921i	0.663806	−	0.747905i	$-0.268940\pi$
$877$	10.3059	+	5.95011i	0.348005	+	0.200921i	−0.315801	+	0.948825i	$0.602273\pi$
$878$	−27.0972	−	20.3464i	−0.914487	−	0.686657i
$879$	−13.0358	+	7.52623i	−0.439687	+	0.253854i
$880$	18.1349	+	9.48328i	0.611327	+	0.319681i
$881$			53.9142i			1.81642i	0.418519	+	0.908208i	$0.362549\pi$
$881$			53.9142i			1.81642i	−0.418519	+	0.908208i	$0.637451\pi$
$882$	−27.2339	−	3.09362i	−0.917014	−	0.104168i
$883$	11.1987			0.376866			0.188433	−	0.982086i	$-0.439659\pi$
$883$	11.1987			0.376866			0.188433	+	0.982086i	$0.439659\pi$
$884$	10.7332	−	3.11763i	0.360996	−	0.104857i
$885$	−3.89215	−	6.74139i	−0.130833	−	0.226609i
$886$	11.6142	+	8.72073i	0.390188	+	0.292979i
$887$	−18.1832	+	31.4942i	−0.610531	+	1.05747i	0.380620	+	0.924732i	$0.375711\pi$
$887$	−18.1832	+	31.4942i	−0.610531	+	1.05747i	−0.991151	+	0.132740i	$0.957623\pi$
$888$	−2.57151	+	6.80357i	−0.0862941	+	0.228313i
$889$	−12.5630	+	3.41576i	−0.421351	+	0.114561i
$890$	−3.06957	−	7.19707i	−0.102892	−	0.241246i
$891$	5.58353	−	9.67095i	0.187055	−	0.323989i
$892$	47.2132	+	11.5995i	1.58082	+	0.388380i
$893$	−46.2278	+	26.6896i	−1.54695	+	0.893134i
$894$	−0.924000	+	7.63373i	−0.0309032	+	0.255310i
$895$	45.5819			1.52364
$896$	−25.0754	−	16.3470i	−0.837711	−	0.546113i
$897$	−2.95297			−0.0985968
$898$	1.95592	−	16.1590i	0.0652698	−	0.539234i
$899$	0.512788	−	0.296058i	0.0171024	−	0.00987410i
$900$	−27.9813	−	6.87453i	−0.932711	−	0.229151i
$901$	14.2583	−	24.6960i	0.475011	−	0.822744i
$902$	3.74726	+	8.78601i	0.124770	+	0.292542i
$903$		0			0
$904$	1.43695	−	3.80183i	0.0477924	−	0.126447i
$905$	−24.4709	+	42.3849i	−0.813441	+	1.40892i
$906$	8.06023	+	6.05215i	0.267783	+	0.201069i
$907$	8.92370	+	15.4563i	0.296307	+	0.513218i	0.975288	−	0.220937i	$-0.0709116\pi$
$907$	8.92370	+	15.4563i	0.296307	+	0.513218i	−0.678981	+	0.734156i	$0.737578\pi$
$908$	27.5107	−	7.99093i	0.912975	−	0.265188i
$909$	18.8446			0.625034
$910$	−6.13277	+	15.4179i	−0.203299	+	0.511098i
$911$			11.1458i			0.369278i	0.982806	+	0.184639i	$0.0591116\pi$
$911$			11.1458i			0.369278i	−0.982806	+	0.184639i	$0.940888\pi$
$912$	8.99433	+	4.70340i	0.297832	+	0.155745i
$913$	20.7771	−	11.9957i	0.687623	−	0.396999i
$914$	34.6170	+	25.9927i	1.14503	+	0.859761i
$915$	−11.2099	−	6.47203i	−0.370587	−	0.213959i
$916$	14.7436	−	15.3727i	0.487141	−	0.507929i
$917$	2.66437	−	10.0917i	0.0879854	−	0.333257i
$918$	−14.5265	+	6.19562i	−0.479448	+	0.204486i
$919$	−28.2802	−	16.3276i	−0.932879	−	0.538598i	−0.0451579	−	0.998980i	$-0.514379\pi$
$919$	−28.2802	−	16.3276i	−0.932879	−	0.538598i	−0.887721	+	0.460382i	$0.847712\pi$
$920$	−6.45452	−	39.4361i	−0.212799	−	1.30017i
$921$	−3.53980	−	6.13111i	−0.116640	−	0.202027i
$922$	−2.95134	+	24.3828i	−0.0971971	+	0.803005i
$923$			7.34623i			0.241804i
$924$	−1.95059	+	3.57871i	−0.0641696	+	0.117731i
$925$			27.8238i			0.914839i
$926$	−30.5066	−	3.69257i	−1.00251	−	0.121345i
$927$	−19.4496	−	33.6876i	−0.638807	−	1.10645i
$928$	23.8023	+	16.3638i	0.781349	+	0.537167i
$929$	−23.3027	−	13.4538i	−0.764537	−	0.441406i	0.0663853	−	0.997794i	$-0.478853\pi$
$929$	−23.3027	−	13.4538i	−0.764537	−	0.441406i	−0.830922	+	0.556388i	$0.812187\pi$
$930$	−0.0988299	−	0.231721i	−0.00324076	−	0.00759844i
$931$	36.9344	−	0.271329i	1.21048	−	0.00889246i
$932$	−0.883202	+	0.920891i	−0.0289302	+	0.0301648i
$933$	−6.48885	−	3.74634i	−0.212435	−	0.122650i
$934$	−0.574445	+	0.765045i	−0.0187964	+	0.0250330i
$935$	17.8353	−	10.2972i	0.583276	−	0.336755i
$936$	6.88544	+	8.41381i	0.225058	+	0.275014i
$937$		−	32.6476i		−	1.06655i	−0.845942	−	0.533275i	$-0.820961\pi$
$937$		−	32.6476i		−	1.06655i	0.845942	−	0.533275i	$-0.179039\pi$
$938$	23.2787	+	29.4666i	0.760078	+	0.962120i
$939$	−6.29315			−0.205369
$940$	18.0275	+	62.0640i	0.587992	+	2.02431i
$941$	6.32087	+	10.9481i	0.206055	+	0.356897i	0.950468	−	0.310822i	$-0.100604\pi$
$941$	6.32087	+	10.9481i	0.206055	+	0.356897i	−0.744414	+	0.667719i	$0.767271\pi$
$942$	0.301665	−	0.401757i	0.00982878	−	0.0130899i
$943$	9.32569	−	16.1526i	0.303686	−	0.526000i
$944$	−20.2522	+	0.846548i	−0.659154	+	0.0275528i
$945$	5.98488	−	22.6686i	0.194688	−	0.737410i
$946$		0			0
$947$	21.1271	−	36.5931i	0.686537	−	1.18912i	−0.286414	−	0.958106i	$-0.592463\pi$
$947$	21.1271	−	36.5931i	0.686537	−	1.18912i	0.972951	−	0.231011i	$-0.0742035\pi$
$948$	11.1464	+	2.73849i	0.362020	+	0.0889421i
$949$	−12.9182	+	7.45835i	−0.419344	+	0.242108i
$950$	38.5465	+	4.66574i	1.25061	+	0.151377i
$951$	11.3264			0.367285
$952$	−27.4094	+	12.4945i	−0.888345	+	0.404948i
$953$	−44.4561			−1.44007			−0.720037	−	0.693936i	$-0.755875\pi$
$953$	−44.4561			−1.44007			−0.720037	+	0.693936i	$0.755875\pi$
$954$	27.5380	+	3.33324i	0.891574	+	0.107918i
$955$	6.91764	−	3.99390i	0.223850	−	0.129240i
$956$	−2.25962	+	9.19729i	−0.0730812	+	0.297462i
$957$	1.96650	−	3.40607i	0.0635678	−	0.110103i
$958$	−37.4223	+	15.9607i	−1.20906	+	0.515668i
$959$	−0.191697	+	0.193110i	−0.00619021	+	0.00623585i
$960$	8.12842	−	9.21676i	0.262344	−	0.297470i
$961$	15.4933	−	26.8351i	0.499783	−	0.865650i
$962$	6.30382	−	8.39541i	0.203243	−	0.270679i
$963$	7.11447	+	12.3226i	0.229261	+	0.397091i
$964$	22.4834	−	6.53067i	0.724142	−	0.210339i
$965$	9.90388			0.318817
$966$	7.87508	−	1.15009i	0.253377	−	0.0370036i
$967$			25.7160i			0.826972i	0.910510	+	0.413486i	$0.135689\pi$
$967$			25.7160i			0.826972i	−0.910510	+	0.413486i	$0.864311\pi$
$968$	15.1088	+	18.4626i	0.485616	+	0.593409i
$969$	8.84573	−	5.10709i	0.284166	−	0.164063i
$970$	7.79005	−	10.3748i	0.250123	−	0.333114i
$971$	−40.2746	−	23.2526i	−1.29247	−	0.746210i	−0.313381	−	0.949627i	$-0.601462\pi$
$971$	−40.2746	−	23.2526i	−1.29247	−	0.746210i	−0.979092	+	0.203417i	$0.934795\pi$
$972$	−16.8529	−	16.1631i	−0.540556	−	0.518432i
$973$	−38.2421	+	10.3976i	−1.22599	+	0.333333i
$974$	−1.01699	−	2.38448i	−0.0325863	−	0.0764035i
$975$	−3.00854	−	1.73698i	−0.0963503	−	0.0556278i
$976$	−28.4607	+	18.0572i	−0.911004	+	0.577998i
$977$	−17.1348	−	29.6783i	−0.548189	−	0.949492i	−0.998399	−	0.0565688i	$-0.981984\pi$
$977$	−17.1348	−	29.6783i	−0.548189	−	0.949492i	0.450209	−	0.892923i	$-0.351349\pi$
$978$	5.87702	+	0.711365i	0.187926	+	0.0227469i
$979$			2.77419i			0.0886635i
$980$	10.3503	−	43.5055i	0.330628	−	1.38973i
$981$		−	7.83862i		−	0.250268i
$982$	2.28346	−	18.8650i	0.0728680	−	0.602007i
$983$	0.777334	+	1.34638i	0.0247931	+	0.0429429i	0.878156	−	0.478375i	$-0.158774\pi$
$983$	0.777334	+	1.34638i	0.0247931	+	0.0429429i	−0.853363	+	0.521318i	$0.825441\pi$
$984$	5.66047	−	0.926450i	0.180449	−	0.0295341i
$985$	43.4012	+	25.0577i	1.38288	+	0.798404i
$986$	26.7374	−	11.4036i	0.851491	−	0.363163i
$987$	−12.4207	+	3.37705i	−0.395354	+	0.107493i
$988$	−10.5738	−	10.1410i	−0.336396	−	0.322629i
$989$		0			0
$990$	16.0196	+	12.0286i	0.509138	+	0.382294i
$991$	−22.6482	+	13.0759i	−0.719443	+	0.415371i	−0.814548	−	0.580097i	$-0.803015\pi$
$991$	−22.6482	+	13.0759i	−0.719443	+	0.415371i	0.0951047	+	0.995467i	$0.469681\pi$
$992$	−0.653950	−	0.0515591i	−0.0207629	−	0.00163700i
$993$		−	15.8964i		−	0.504457i
$994$	−2.86113	−	19.5912i	−0.0907496	−	0.621394i
$995$	−37.7748			−1.19754
$996$	−4.01857	−	13.8349i	−0.127333	−	0.438376i
$997$	−18.1467	−	31.4310i	−0.574711	−	0.995429i	−0.996073	−	0.0885360i	$-0.971781\pi$
$997$	−18.1467	−	31.4310i	−0.574711	−	0.995429i	0.421362	−	0.906893i	$-0.361552\pi$
$998$	−12.8562	−	9.65325i	−0.406955	−	0.305568i
$999$	−7.41717	+	12.8469i	−0.234669	+	0.406458i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	56.2.m.a.19.3	yes	12
3.2	odd	2		504.2.bk.a.19.4		12
4.3	odd	2		224.2.q.a.47.4		12
7.2	even	3		392.2.e.e.195.3		12
7.3	odd	6	inner	56.2.m.a.3.6	yes	12
7.4	even	3		392.2.m.g.227.6		12
7.5	odd	6		392.2.e.e.195.4		12
7.6	odd	2		392.2.m.g.19.3		12
8.3	odd	2	inner	56.2.m.a.19.5	yes	12
8.5	even	2		224.2.q.a.47.3		12
12.11	even	2		2016.2.bs.a.271.1		12
21.17	even	6		504.2.bk.a.451.1		12
24.5	odd	2		2016.2.bs.a.271.6		12
24.11	even	2		504.2.bk.a.19.2		12
28.3	even	6		224.2.q.a.143.3		12
28.11	odd	6		1568.2.q.g.815.4		12
28.19	even	6		1568.2.e.e.783.6		12
28.23	odd	6		1568.2.e.e.783.7		12
28.27	even	2		1568.2.q.g.1391.3		12
56.3	even	6	inner	56.2.m.a.3.4	✓	12
56.5	odd	6		1568.2.e.e.783.5		12
56.11	odd	6		392.2.m.g.227.4		12
56.13	odd	2		1568.2.q.g.1391.4		12
56.19	even	6		392.2.e.e.195.2		12
56.27	even	2		392.2.m.g.19.5		12
56.37	even	6		1568.2.e.e.783.8		12
56.45	odd	6		224.2.q.a.143.4		12
56.51	odd	6		392.2.e.e.195.1		12
56.53	even	6		1568.2.q.g.815.3		12
84.59	odd	6		2016.2.bs.a.1711.6		12
168.59	odd	6		504.2.bk.a.451.3		12
168.101	even	6		2016.2.bs.a.1711.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.m.a.3.4	✓	12	56.3	even	6	inner
56.2.m.a.3.6	yes	12	7.3	odd	6	inner
56.2.m.a.19.3	yes	12	1.1	even	1	trivial
56.2.m.a.19.5	yes	12	8.3	odd	2	inner
224.2.q.a.47.3		12	8.5	even	2
224.2.q.a.47.4		12	4.3	odd	2
224.2.q.a.143.3		12	28.3	even	6
224.2.q.a.143.4		12	56.45	odd	6
392.2.e.e.195.1		12	56.51	odd	6
392.2.e.e.195.2		12	56.19	even	6
392.2.e.e.195.3		12	7.2	even	3
392.2.e.e.195.4		12	7.5	odd	6
392.2.m.g.19.3		12	7.6	odd	2
392.2.m.g.19.5		12	56.27	even	2
392.2.m.g.227.4		12	56.11	odd	6
392.2.m.g.227.6		12	7.4	even	3
504.2.bk.a.19.2		12	24.11	even	2
504.2.bk.a.19.4		12	3.2	odd	2
504.2.bk.a.451.1		12	21.17	even	6
504.2.bk.a.451.3		12	168.59	odd	6
1568.2.e.e.783.5		12	56.5	odd	6
1568.2.e.e.783.6		12	28.19	even	6
1568.2.e.e.783.7		12	28.23	odd	6
1568.2.e.e.783.8		12	56.37	even	6
1568.2.q.g.815.3		12	56.53	even	6
1568.2.q.g.815.4		12	28.11	odd	6
1568.2.q.g.1391.3		12	28.27	even	2
1568.2.q.g.1391.4		12	56.13	odd	2
2016.2.bs.a.271.1		12	12.11	even	2
2016.2.bs.a.271.6		12	24.5	odd	2
2016.2.bs.a.1711.1		12	168.101	even	6
2016.2.bs.a.1711.6		12	84.59	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 56 = 2^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	56.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.169938 - 1.40397i) q^{2} +(-0.416472 + 0.240450i) q^{3} +(-1.94224 - 0.477176i) q^{4} +(1.59713 - 2.76632i) q^{5} +(0.266810 + 0.625575i) q^{6} +(0.694153 + 2.55307i) q^{7} +(-1.00000 + 2.64575i) q^{8} +(-1.38437 + 2.39779i) q^{9} +(-3.61240 - 2.71243i) q^{10} +(0.800840 + 1.38709i) q^{11} +(0.923627 - 0.268282i) q^{12} -1.38831 q^{13} +(3.70238 - 0.540703i) q^{14} +1.53613i q^{15} +(3.54461 + 1.85358i) q^{16} +(3.48605 - 2.01267i) q^{17} +(3.13116 + 2.35108i) q^{18} +(-4.56957 - 2.63824i) q^{19} +(-4.42204 + 4.61075i) q^{20} +(-0.902982 - 0.896373i) q^{21} +(2.08353 - 0.888631i) q^{22} +(-3.83044 - 2.21151i) q^{23} +(-0.219700 - 1.34233i) q^{24} +(-2.60168 - 4.50624i) q^{25} +(-0.235927 + 1.94913i) q^{26} -2.77419i q^{27} +(-0.129952 - 5.28991i) q^{28} +5.10613i q^{29} +(2.15667 + 0.261047i) q^{30} +(-0.0579809 - 0.100426i) q^{31} +(3.20473 - 4.66151i) q^{32} +(-0.667055 - 0.385124i) q^{33} +(-2.23331 - 5.23632i) q^{34} +(8.17125 + 2.15734i) q^{35} +(3.83294 - 3.99651i) q^{36} +(-4.63087 - 2.67363i) q^{37} +(-4.48055 + 5.96719i) q^{38} +(0.578191 - 0.333819i) q^{39} +(5.72186 + 6.99194i) q^{40} +4.21689i q^{41} +(-1.41193 + 1.11543i) q^{42} +(-0.893536 - 3.07621i) q^{44} +(4.42204 + 7.65920i) q^{45} +(-3.75582 + 5.00199i) q^{46} +(5.05821 - 8.76108i) q^{47} +(-1.92193 + 0.0803370i) q^{48} +(-6.03630 + 3.54444i) q^{49} +(-6.76873 + 2.88689i) q^{50} +(-0.967895 + 1.67644i) q^{51} +(2.69643 + 0.662466i) q^{52} +(6.13514 - 3.54212i) q^{53} +(-3.89487 - 0.471441i) q^{54} +5.11619 q^{55} +(-7.44893 - 0.716511i) q^{56} +2.53747 q^{57} +(7.16884 + 0.867728i) q^{58} +(-4.38856 + 2.53374i) q^{59} +(0.733002 - 2.98353i) q^{60} +(-4.21321 + 7.29750i) q^{61} +(-0.150848 + 0.0643370i) q^{62} +(-7.08269 - 1.86995i) q^{63} +(-6.00000 - 5.29150i) q^{64} +(-2.21731 + 3.84050i) q^{65} +(-0.654060 + 0.871075i) q^{66} +(5.01815 + 8.69169i) q^{67} +(-7.73114 + 2.24564i) q^{68} +2.12703 q^{69} +(4.41745 - 11.1055i) q^{70} -5.29150i q^{71} +(-4.95960 - 6.06049i) q^{72} +(9.30504 - 5.37227i) q^{73} +(-4.54066 + 6.04723i) q^{74} +(2.16706 + 1.25115i) q^{75} +(7.61631 + 7.30460i) q^{76} +(-2.98544 + 3.00745i) q^{77} +(-0.370413 - 0.868490i) q^{78} +(10.3349 + 5.96688i) q^{79} +(10.7888 - 6.84509i) q^{80} +(-3.48605 - 6.03801i) q^{81} +(5.92037 + 0.716612i) q^{82} -14.9789i q^{83} +(1.32608 + 2.17185i) q^{84} -12.8580i q^{85} +(-1.22777 - 2.12656i) q^{87} +(-4.47075 + 0.731728i) q^{88} +(1.50000 + 0.866025i) q^{89} +(11.5047 - 4.90680i) q^{90} +(-0.963697 - 3.54444i) q^{91} +(6.38437 + 6.12307i) q^{92} +(0.0482949 + 0.0278831i) q^{93} +(-11.4407 - 8.59041i) q^{94} +(-14.5965 + 8.42726i) q^{95} +(-0.213819 + 2.71197i) q^{96} +2.87198i q^{97} +(3.95047 + 9.07710i) q^{98} -4.43462 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} - 12 q^{8} + 6 q^{10} - 6 q^{11} - 18 q^{12} + 6 q^{14} - 6 q^{17} + 6 q^{18} - 6 q^{19} + 24 q^{22} + 6 q^{24} + 6 q^{26} + 6 q^{28} - 12 q^{30} - 6 q^{33} + 18 q^{35} + 48 q^{36} - 24 q^{38}+ \cdots - 24 q^{99}+O(q^{100}) \) 12 * q - 6 * q^3 - 12 * q^8 + 6 * q^10 - 6 * q^11 - 18 * q^12 + 6 * q^14 - 6 * q^17 + 6 * q^18 - 6 * q^19 + 24 * q^22 + 6 * q^24 + 6 * q^26 + 6 * q^28 - 12 * q^30 - 6 * q^33 + 18 * q^35 + 48 * q^36 - 24 * q^38 + 42 * q^40 - 30 * q^42 + 6 * q^44 - 18 * q^46 - 12 * q^49 - 48 * q^50 + 6 * q^51 - 24 * q^52 - 36 * q^54 - 36 * q^57 + 18 * q^58 + 42 * q^59 - 6 * q^60 - 72 * q^64 - 12 * q^65 + 12 * q^66 + 30 * q^67 - 36 * q^68 + 30 * q^70 + 18 * q^73 + 12 * q^74 + 24 * q^75 + 60 * q^78 + 36 * q^80 + 6 * q^81 + 54 * q^82 + 12 * q^84 + 6 * q^88 + 18 * q^89 - 72 * q^91 + 60 * q^92 - 12 * q^94 + 60 * q^96 - 6 * q^98 - 24 * q^99

Introduction

L-functions

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