LMFDB - Embedded newform 56.2.m.a.19.5

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			19.5
Root			$-0.0263223 - 0.217464i$ of defining polynomial
Character	$\chi$	$=$	56.19
Dual form			56.2.m.a.3.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.13090 - 0.849154i) q^{2} +(-0.416472 + 0.240450i) q^{3} +(0.557875 - 1.92062i) q^{4} +(-1.59713 + 2.76632i) q^{5} +(-0.266810 + 0.625575i) q^{6} +(-0.694153 - 2.55307i) q^{7} +(-1.00000 - 2.64575i) q^{8} +(-1.38437 + 2.39779i) q^{9} +O(q^{10})$	\(q+(1.13090 - 0.849154i) q^{2} +(-0.416472 + 0.240450i) q^{3} +(0.557875 - 1.92062i) 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} +(0.542829 + 4.48465i) q^{10} +(0.800840 + 1.38709i) q^{11} +(0.229474 + 0.934026i) q^{12} +1.38831 q^{13} +(-2.95297 - 2.29782i) q^{14} -1.53613i q^{15} +(-3.37755 - 2.14293i) q^{16} +(3.48605 - 2.01267i) q^{17} +(0.470514 + 3.88721i) 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} +(1.05264 + 0.861432i) q^{24} +(-2.60168 - 4.50624i) q^{25} +(1.57004 - 1.17889i) q^{26} -2.77419i q^{27} +(-5.29072 - 0.0910883i) q^{28} -5.10613i q^{29} +(-1.30441 - 1.73721i) q^{30} +(0.0579809 + 0.100426i) q^{31} +(-5.63935 + 0.444621i) 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} +(-7.40801 + 0.896678i) q^{38} +(-0.578191 + 0.333819i) q^{39} +(8.91613 + 1.45930i) q^{40} +4.21689i q^{41} +(1.78234 + 0.246938i) q^{42} +(3.11085 - 0.764282i) q^{44} +(-4.42204 - 7.65920i) q^{45} +(6.20976 - 0.751640i) 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} +(0.774501 - 2.66641i) q^{52} +(-6.13514 + 3.54212i) q^{53} +(-2.35571 - 3.13733i) q^{54} -5.11619 q^{55} +(-6.06063 + 4.38962i) q^{56} +2.53747 q^{57} +(-4.33589 - 5.77453i) q^{58} +(-4.38856 + 2.53374i) q^{59} +(-2.95031 - 0.856966i) 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} +(-1.08140 + 0.130895i) q^{66} +(5.01815 + 8.69169i) q^{67} +(-1.92079 - 7.81818i) q^{68} -2.12703 q^{69} +(11.0728 - 4.49891i) q^{70} +5.29150i q^{71} +(7.72833 + 1.26490i) q^{72} +(9.30504 - 5.37227i) q^{73} +(7.50738 - 0.908707i) 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} +(11.3224 - 5.92084i) q^{80} +(-3.48605 - 6.03801i) q^{81} +(3.58079 + 4.76889i) q^{82} -14.9789i q^{83} +(2.22534 - 1.23422i) q^{84} +12.8580i q^{85} +(1.22777 + 2.12656i) q^{87} +(2.86907 - 3.50592i) 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} +(1.71917 + 14.2031i) q^{94} +(14.5965 - 8.42726i) q^{95} +(2.24173 - 1.54116i) q^{96} +2.87198i q^{97} +(-3.81669 + 9.13416i) q^{98} -4.43462 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} - 12 q^{8}+O(q^{10}) $ 12 * q - 6 * q^3 - 12 * q^8	$ 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}+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

Display 100 coefficients 10 coefficients

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 $

$2$	1.13090	−	0.849154i	0.799668	−	0.600443i
$2$	1.13090	−	0.849154i	0.799668	−	0.600443i
$3$	−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	$0.377666\pi$
$4$	0.557875	−	1.92062i	0.278937	−	0.960309i
$5$	−1.59713	+	2.76632i	−0.714260	+	1.23714i	0.248984	+	0.968508i	$0.419903\pi$
$5$	−1.59713	+	2.76632i	−0.714260	+	1.23714i	−0.963244	+	0.268628i	$0.913430\pi$
$6$	−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
$10$	0.542829	+	4.48465i	0.171658	+	1.41817i
$11$	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	$0.755706\pi$
$12$	0.229474	+	0.934026i	0.0662435	+	0.269630i
$13$	1.38831			0.385047			0.192523	−	0.981292i	$-0.438333\pi$
$13$	1.38831			0.385047			0.192523	+	0.981292i	$0.438333\pi$
$14$	−2.95297	−	2.29782i	−0.789213	−	0.614119i
$15$		−	1.53613i		−	0.396626i
$16$	−3.37755	−	2.14293i	−0.844388	−	0.535732i
$17$	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	$0.171007\pi$
$18$	0.470514	+	3.88721i	0.110901	+	0.916224i
$19$	−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	0.843017	−	0.537887i	$-0.180777\pi$
$23$	3.83044	+	2.21151i	0.798702	+	0.461131i	−0.0443149	+	0.999018i	$0.514110\pi$
$24$	1.05264	+	0.861432i	0.214870	+	0.175839i
$25$	−2.60168	−	4.50624i	−0.520336	−	0.901248i
$26$	1.57004	−	1.17889i	0.307910	−	0.231199i
$27$		−	2.77419i		−	0.533893i
$28$	−5.29072	−	0.0910883i	−0.999852	−	0.0172141i
$29$		−	5.10613i		−	0.948185i	−0.880475	−	0.474093i	$-0.842776\pi$
$29$		−	5.10613i		−	0.948185i	0.880475	−	0.474093i	$-0.157224\pi$
$30$	−1.30441	−	1.73721i	−0.238151	−	0.317169i
$31$	0.0579809	+	0.100426i	0.0104137	+	0.0180370i	0.871185	−	0.490954i	$-0.163352\pi$
$31$	0.0579809	+	0.100426i	0.0104137	+	0.0180370i	−0.860772	+	0.508991i	$0.830018\pi$
$32$	−5.63935	+	0.444621i	−0.996906	+	0.0785986i
$33$	−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	0.829766	−	0.558111i	$-0.188474\pi$
$37$	4.63087	+	2.67363i	0.761310	+	0.439543i	−0.0684556	+	0.997654i	$0.521807\pi$
$38$	−7.40801	+	0.896678i	−1.20174	+	0.145460i
$39$	−0.578191	+	0.333819i	−0.0925847	+	0.0534538i
$40$	8.91613	+	1.45930i	1.40976	+	0.230736i
$41$			4.21689i			0.658568i	0.944231	+	0.329284i	$0.106807\pi$
$41$			4.21689i			0.658568i	−0.944231	+	0.329284i	$0.893193\pi$
$42$	1.78234	+	0.246938i	0.275021	+	0.0381034i
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$	3.11085	−	0.764282i	0.468978	−	0.115220i
$45$	−4.42204	−	7.65920i	−0.659199	−	1.14177i
$46$	6.20976	−	0.751640i	0.915579	−	0.110823i
$47$	−5.05821	+	8.76108i	−0.737816	+	1.27794i	0.215660	+	0.976468i	$0.430810\pi$
$47$	−5.05821	+	8.76108i	−0.737816	+	1.27794i	−0.953477	+	0.301467i	$0.902524\pi$
$48$	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
$52$	0.774501	−	2.66641i	0.107404	−	0.369764i
$53$	−6.13514	+	3.54212i	−0.842726	+	0.486548i	−0.858190	−	0.513332i	$-0.828411\pi$
$53$	−6.13514	+	3.54212i	−0.842726	+	0.486548i	0.0154638	+	0.999880i	$0.495078\pi$
$54$	−2.35571	−	3.13733i	−0.320572	−	0.426937i
$55$	−5.11619			−0.689868
$56$	−6.06063	+	4.38962i	−0.809885	+	0.586588i
$57$	2.53747			0.336096
$58$	−4.33589	−	5.77453i	−0.569331	−	0.758233i
$59$	−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	$0.440336\pi$
$60$	−2.95031	−	0.856966i	−0.380884	−	0.110634i
$61$	4.21321	−	7.29750i	0.539447	−	0.934349i	−0.459487	−	0.888184i	$-0.651967\pi$
$61$	4.21321	−	7.29750i	0.539447	−	0.934349i	0.998934	−	0.0461646i	$-0.0146999\pi$
$62$	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
$66$	−1.08140	+	0.130895i	−0.133112	+	0.0161120i
$67$	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	$0.623270\pi$
$68$	−1.92079	−	7.81818i	−0.232930	−	0.948094i
$69$	−2.12703			−0.256064
$70$	11.0728	−	4.49891i	1.32345	−	0.537723i
$71$			5.29150i			0.627986i	0.949425	+	0.313993i	$0.101667\pi$
$71$			5.29150i			0.627986i	−0.949425	+	0.313993i	$0.898333\pi$
$72$	7.72833	+	1.26490i	0.910793	+	0.149070i
$73$	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	$0.116890\pi$
$74$	7.50738	−	0.908707i	0.872716	−	0.105635i
$75$	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	−0.210805	−	0.977528i	$-0.567609\pi$
$79$	−10.3349	−	5.96688i	−1.16277	−	0.671327i	−0.951967	+	0.306201i	$0.900942\pi$
$80$	11.3224	−	5.92084i	1.26589	−	0.661970i
$81$	−3.48605	−	6.03801i	−0.387338	−	0.670890i
$82$	3.58079	+	4.76889i	0.395432	+	0.526636i
$83$		−	14.9789i		−	1.64415i	−0.569382	−	0.822073i	$-0.692818\pi$
$83$		−	14.9789i		−	1.64415i	0.569382	−	0.822073i	$-0.307182\pi$
$84$	2.22534	−	1.23422i	0.242805	−	0.134664i
$85$			12.8580i			1.39465i
$86$		0			0
$87$	1.22777	+	2.12656i	0.131631	+	0.227992i
$88$	2.86907	−	3.50592i	0.305844	−	0.373732i
$89$	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
$94$	1.71917	+	14.2031i	0.177319	+	1.46494i
$95$	14.5965	−	8.42726i	1.49756	−	0.864619i
$96$	2.24173	−	1.54116i	0.228795	−	0.157294i
$97$			2.87198i			0.291606i	0.989314	+	0.145803i	$0.0465765\pi$
$97$			2.87198i			0.291606i	−0.989314	+	0.145803i	$0.953423\pi$
$98$	−3.81669	+	9.13416i	−0.385544	+	0.922690i
$99$	−4.43462			−0.445696
$100$	−10.1062	+	2.48292i	−1.01062	+	0.248292i
$101$	3.40310	+	5.89434i	0.338621	+	0.586509i	0.984174	−	0.177207i	$-0.0567062\pi$
$101$	3.40310	+	5.89434i	0.338621	+	0.586509i	−0.645553	+	0.763716i	$0.723373\pi$
$102$	0.328965	+	2.71778i	0.0325724	+	0.269101i
$103$	7.02471	−	12.1672i	0.692165	−	1.19887i	−0.278962	−	0.960302i	$-0.589990\pi$
$103$	7.02471	−	12.1672i	0.692165	−	1.19887i	0.971127	−	0.238563i	$-0.0766765\pi$
$104$	−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	$0.0867586\pi$
$108$	−5.32816	−	1.54765i	−0.512702	−	0.148923i
$109$	2.45182	−	1.41556i	0.234842	−	0.135586i	−0.377962	−	0.925821i	$-0.623375\pi$
$109$	2.45182	−	1.41556i	0.234842	−	0.135586i	0.612804	+	0.790235i	$0.290042\pi$
$110$	−5.78591	+	4.34444i	−0.551665	+	0.414226i
$111$	−2.57151			−0.244077
$112$	−3.12650	+	10.1106i	−0.295427	+	0.955365i
$113$	−1.43695			−0.135177			−0.0675887	−	0.997713i	$-0.521531\pi$
$113$	−1.43695			−0.135177			−0.0675887	+	0.997713i	$0.521531\pi$
$114$	2.86963	−	2.15470i	0.268765	−	0.201806i
$115$	−12.2355	+	7.06415i	−1.14096	+	0.658735i
$116$	−9.80694	−	2.84858i	−0.910551	−	0.264484i
$117$	−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
$122$	−1.43197	−	11.8304i	−0.129645	−	1.07108i
$123$	−1.01395	−	1.75622i	−0.0914251	−	0.158353i
$124$	0.225226	−	0.0553342i	0.0202259	−	0.00496916i
$125$	0.649581			0.0581003
$126$	9.59770	−	3.89957i	0.855031	−	0.347402i
$127$		−	4.92077i		−	0.436647i	−0.975876	−	0.218324i	$-0.929941\pi$
$127$		−	4.92077i		−	0.436647i	0.975876	−	0.218324i	$-0.0700589\pi$
$128$	−2.29211	+	11.0791i	−0.202595	+	0.979263i
$129$		0			0
$130$	0.753613	+	6.22606i	0.0660962	+	0.546062i
$131$	−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
$136$	−8.81107	−	7.21054i	−0.755543	−	0.618299i
$137$	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	$0.831935\pi$
$138$	−2.40546	+	1.80618i	−0.204767	+	0.153752i
$139$			14.9789i			1.27049i	0.772310	+	0.635246i	$0.219101\pi$
$139$			14.9789i			1.27049i	−0.772310	+	0.635246i	$0.780899\pi$
$140$	8.70197	−	14.4903i	0.735451	−	1.22466i
$141$		−	4.86500i		−	0.409707i
$142$	4.49330	+	5.98417i	0.377069	+	0.502180i
$143$	1.11181	+	1.92571i	0.0929743	+	0.161036i
$144$	9.81407	−	5.13207i	0.817840	−	0.427673i
$145$	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	0.0420645	−	0.999115i	$-0.486607\pi$
$149$	−9.79164	−	5.65320i	−0.802162	−	0.463129i	−0.844227	+	0.535986i	$0.819940\pi$
$150$	3.51314	−	0.425237i	0.286847	−	0.0347204i
$151$	−12.8351	+	7.41032i	−1.04450	+	0.603044i	−0.921105	−	0.389314i	$-0.872712\pi$
$151$	−12.8351	+	7.41032i	−1.04450	+	0.603044i	−0.123397	+	0.992357i	$0.539379\pi$
$152$	−2.41057	+	14.7282i	−0.195523	+	1.19461i
$153$			11.1451i			0.901028i
$154$	0.822447	−	5.93623i	0.0662747	−	0.478355i
$155$	−0.370413			−0.0297523
$156$	0.318580	+	1.29671i	0.0255068	+	0.103820i
$157$	0.369362	+	0.639755i	0.0294783	+	0.0510580i	0.880388	−	0.474254i	$-0.157282\pi$
$157$	0.369362	+	0.639755i	0.0294783	+	0.0510580i	−0.850910	+	0.525312i	$0.823949\pi$
$158$	−16.7546	+	2.02801i	−1.33292	+	0.161339i
$159$	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	$0.0559364\pi$
$164$	8.09904	+	2.35250i	0.632429	+	0.183699i
$165$	2.13075	−	1.23019i	0.165879	−	0.0957703i
$166$	−12.7194	−	16.9396i	−0.987215	−	1.31477i
$167$	1.38831			0.107430			0.0537152	−	0.998556i	$-0.482894\pi$
$167$	1.38831			0.107430			0.0537152	+	0.998556i	$0.482894\pi$
$168$	1.46860	−	3.28544i	0.113305	−	0.253477i
$169$	−11.0726			−0.851739
$170$	10.9184	+	14.5411i	0.837406	+	1.11526i
$171$	12.6519	−	7.30460i	0.967518	−	0.558597i
$172$		0			0
$173$	−0.485324	+	0.840606i	−0.0368985	+	0.0639101i	−0.883885	−	0.467704i	$-0.845081\pi$
$173$	−0.485324	+	0.840606i	−0.0368985	+	0.0639101i	0.846986	+	0.531615i	$0.178414\pi$
$174$	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
$178$	2.43174	−	0.294342i	0.182267	−	0.0220619i
$179$	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	$0.654288\pi$
$180$	−17.1773	+	4.22018i	−1.28032	+	0.314554i
$181$	15.3218			1.13886			0.569429	−	0.822041i	$-0.307164\pi$
$181$	15.3218			1.13886			0.569429	+	0.822041i	$0.307164\pi$
$182$	−4.09962	−	3.19008i	−0.303884	−	0.236465i
$183$			4.05228i			0.299553i
$184$	2.02065	−	12.3459i	0.148965	−	0.910152i
$185$	−14.7922	+	8.54031i	−1.08755	+	0.627896i
$186$	−0.0782938	+	0.00947682i	−0.00574078	+	0.000694874i
$187$	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	0.419599	−	0.907709i	$-0.362171\pi$
$191$	−2.16564	−	1.25033i	−0.156700	−	0.0904709i	−0.576300	+	0.817238i	$0.695504\pi$
$192$	1.22649	−	3.64647i	0.0885143	−	0.263161i
$193$	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	$0.797739\pi$
$194$	2.43876	+	3.24793i	0.175093	+	0.233188i
$195$		−	2.13261i		−	0.152720i
$196$	3.44001	+	13.5708i	0.245715	+	0.969342i
$197$		−	15.6891i		−	1.11780i	−0.829233	−	0.558902i	$-0.811223\pi$
$197$		−	15.6891i		−	1.11780i	0.829233	−	0.558902i	$-0.188777\pi$
$198$	−5.01512	+	3.76568i	−0.356409	+	0.267615i
$199$	5.91290	+	10.2414i	0.419154	+	0.725997i	0.995855	−	0.0909591i	$-0.0289933\pi$
$199$	5.91290	+	10.2414i	0.419154	+	0.725997i	−0.576700	+	0.816956i	$0.695660\pi$
$200$	−9.32071	+	11.3896i	−0.659074	+	0.805369i
$201$	−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
$206$	−2.38754	−	19.7249i	−0.166348	−	1.37430i
$207$	−10.6055	+	6.12307i	−0.737131	+	0.425583i
$208$	−4.68908	−	2.97504i	−0.325129	−	0.206282i
$209$		−	8.45124i		−	0.584585i
$210$	−3.52975	+	4.53613i	−0.243576	+	0.313023i
$211$	10.0726			0.693427			0.346713	−	0.937971i	$-0.387298\pi$
$211$	10.0726			0.693427			0.346713	+	0.937971i	$0.387298\pi$
$212$	3.38043	+	13.7593i	0.232169	+	0.944994i
$213$	−1.27234	−	2.20376i	−0.0871796	−	0.150999i
$214$	−0.873339	−	7.21519i	−0.0597002	−	0.493220i
$215$		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
$220$	−2.85420	+	9.82626i	−0.192430	+	0.662486i
$221$	4.83970	−	2.79420i	0.325553	−	0.187958i
$222$	−2.90812	+	2.18361i	−0.195180	+	0.146554i
$223$	24.3086			1.62783			0.813913	−	0.580987i	$-0.197333\pi$
$223$	24.3086			1.62783			0.813913	+	0.580987i	$0.197333\pi$
$224$	5.04972	+	14.0890i	0.337399	+	0.941362i
$225$	14.4067			0.960448
$226$	−1.62505	+	1.22020i	−0.108097	+	0.0811662i
$227$	−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	$0.491014\pi$
$228$	1.41559	−	4.87351i	0.0937497	−	0.322756i
$229$	5.32502	−	9.22321i	0.351887	−	0.609487i	−0.634693	−	0.772765i	$-0.718873\pi$
$229$	5.32502	−	9.22321i	0.351887	−	0.609487i	0.986580	+	0.163278i	$0.0522066\pi$
$230$	−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	$0.160014\pi$
$234$	0.653218	+	5.39664i	0.0427022	+	0.352789i
$235$	−16.1573	−	27.9853i	−1.05399	−	1.82556i
$236$	2.41808	+	9.84227i	0.157403	+	0.640677i
$237$	5.73896			0.372785
$238$	−14.9189	−	2.06697i	−0.967051	−	0.133982i
$239$			4.73540i			0.306307i	0.988202	+	0.153154i	$0.0489430\pi$
$239$			4.73540i			0.306307i	−0.988202	+	0.153154i	$0.951057\pi$
$240$	−3.29181	+	5.18835i	−0.212486	+	0.334906i
$241$	−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	$0.456390\pi$
$242$	−1.43337	−	11.8419i	−0.0921403	−	0.761228i
$243$	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
$248$	0.207721	−	0.253829i	0.0131903	−	0.0161182i
$249$	3.60168	+	6.23829i	0.228247	+	0.395336i
$250$	0.734612	−	0.551594i	0.0464609	−	0.0348859i
$251$			11.5631i			0.729858i	0.931035	+	0.364929i	$0.118907\pi$
$251$			11.5631i			0.729858i	−0.931035	+	0.364929i	$0.881093\pi$
$252$	7.54271	−	12.5600i	0.475146	−	0.791203i
$253$			7.08425i			0.445383i
$254$	−4.17849	−	5.56490i	−0.262182	−	0.349173i
$255$	−3.09172	−	5.35501i	−0.193611	−	0.335344i
$256$	6.81571	+	14.4757i	0.425982	+	0.904732i
$257$	−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
$262$	−5.53865	+	0.670408i	−0.342179	+	0.0414179i
$263$	9.24833	−	5.33953i	0.570277	−	0.329249i	−0.186983	−	0.982363i	$-0.559871\pi$
$263$	9.24833	−	5.33953i	0.570277	−	0.329249i	0.757260	+	0.653114i	$0.226538\pi$
$264$	−0.351888	+	2.14999i	−0.0216572	+	0.132323i
$265$		−	22.6290i		−	1.39009i
$266$	7.43157	+	18.2907i	0.455659	+	1.12148i
$267$	−0.832945			−0.0509754
$268$	19.4929	−	4.78908i	1.19072	−	0.292540i
$269$	11.6690	+	20.2113i	0.711471	+	1.23230i	0.964305	+	0.264794i	$0.0853040\pi$
$269$	11.6690	+	20.2113i	0.711471	+	1.23230i	−0.252834	+	0.967510i	$0.581363\pi$
$270$	12.4413	−	1.50591i	0.757151	−	0.0916468i
$271$	−6.81961	+	11.8119i	−0.414262	+	0.717522i	−0.995351	−	0.0963179i	$-0.969293\pi$
$271$	−6.81961	+	11.8119i	−0.414262	+	0.717522i	0.581089	+	0.813840i	$0.302627\pi$
$272$	−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
$276$	−1.18662	+	4.08522i	−0.0714259	+	0.245901i
$277$	0.396180	−	0.228735i	0.0238042	−	0.0137433i	−0.488051	−	0.872815i	$-0.662292\pi$
$277$	0.396180	−	0.228735i	0.0238042	−	0.0137433i	0.511855	+	0.859072i	$0.328959\pi$
$278$	12.7194	+	16.9396i	0.762858	+	1.01597i
$279$	−0.321068			−0.0192218
$280$	−2.46346	−	23.7764i	−0.147220	−	1.42091i
$281$	1.43695			0.0857215			0.0428608	−	0.999081i	$-0.486353\pi$
$281$	1.43695			0.0857215			0.0428608	+	0.999081i	$0.486353\pi$
$282$	−4.13113	−	5.50183i	−0.246005	−	0.327629i
$283$	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	$-0.0452318\pi$
$284$	10.1630	+	2.95200i	0.603061	+	0.175169i
$285$	−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
$290$	22.8992	−	2.77176i	1.34469	−	0.162763i
$291$	−0.690570	−	1.19610i	−0.0404819	−	0.0701168i
$292$	−5.12703	−	20.8685i	−0.300037	−	1.22124i
$293$	−31.3006			−1.82860			−0.914299	−	0.405040i	$-0.867258\pi$
$293$	−31.3006			−1.82860			−0.914299	+	0.405040i	$0.867258\pi$
$294$	−0.606768	−	4.72185i	−0.0353874	−	0.275384i
$295$		−	16.1869i		−	0.942437i
$296$	2.44290	−	14.9258i	0.141991	−	0.867543i
$297$	3.84806	−	2.22168i	0.223287	−	0.128915i
$298$	−15.8738	+	1.92139i	−0.919545	+	0.111303i
$299$	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
$304$	9.78040	+	18.7031i	0.560944	+	1.07270i
$305$	13.4581	+	23.3102i	0.770611	+	1.33474i
$306$	9.46390	+	12.6040i	0.541015	+	0.720523i
$307$			14.7215i			0.840202i	0.907477	+	0.420101i	$0.138005\pi$
$307$			14.7215i			0.840202i	−0.907477	+	0.420101i	$0.861995\pi$
$308$	−4.11067	−	7.41168i	−0.234227	−	0.422319i
$309$			6.75638i			0.384357i
$310$	−0.418901	+	0.314538i	−0.0237920	+	0.0178646i
$311$	−7.79025	−	13.4931i	−0.441745	−	0.765124i	0.556074	−	0.831133i	$-0.312307\pi$
$311$	−7.79025	−	13.4931i	−0.441745	−	0.765124i	−0.997819	+	0.0660082i	$0.978974\pi$
$312$	1.46139	+	1.19593i	0.0827351	+	0.0677063i
$313$	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	0.947815	−	0.318821i	$-0.103287\pi$
$317$	20.3971	+	11.7763i	1.14562	+	0.661422i	0.197801	+	0.980242i	$0.436620\pi$
$318$	−0.578950	−	4.78306i	−0.0324659	−	0.268221i
$319$	7.08269	−	4.08919i	0.396555	−	0.228951i
$320$	−5.05517	−	25.0492i	−0.282593	−	1.40029i
$321$			2.47142i			0.137941i
$322$	−6.22951	−	15.3322i	−0.347157	−	0.854429i
$323$	−21.2397			−1.18181
$324$	−13.5415	+	3.32691i	−0.752305	+	0.184828i
$325$	−3.61193	−	6.25604i	−0.200354	−	0.347023i
$326$	−1.47923	−	12.2209i	−0.0819272	−	0.676851i
$327$	−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	$0.803937\pi$
$332$	−28.7687	−	8.35634i	−1.57889	−	0.458614i
$333$	−12.8217	+	7.40258i	−0.702622	+	0.405659i
$334$	1.57004	−	1.17889i	0.0859086	−	0.0645058i
$335$	−32.0587			−1.75155
$336$	−1.12900	−	4.96257i	−0.0615923	−	0.270730i
$337$	−15.5096			−0.844860			−0.422430	−	0.906396i	$-0.638823\pi$
$337$	−15.5096			−0.844860			−0.422430	+	0.906396i	$0.638823\pi$
$338$	−12.5220	+	9.40235i	−0.681108	+	0.511420i
$339$	0.598452	−	0.345516i	0.0325035	−	0.0187659i
$340$	24.6954	+	7.17316i	1.33929	+	0.389019i
$341$	−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
$346$	0.164951	+	1.36276i	0.00886780	+	0.0732623i
$347$	−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	$-0.373054\pi$
$348$	4.76926	−	1.17173i	0.255659	−	0.0628111i
$349$	−28.4735			−1.52415			−0.762077	−	0.647486i	$-0.775820\pi$
$349$	−28.4735			−1.52415			−0.762077	+	0.647486i	$0.775820\pi$
$350$	−2.67188	+	19.2850i	−0.142818	+	1.03083i
$351$		−	3.85142i		−	0.205574i
$352$	−5.13295	−	7.46625i	−0.273587	−	0.397952i
$353$	−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	$0.415336\pi$
$354$	−0.414132	−	3.42140i	−0.0220109	−	0.181845i
$355$	−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	0.411715	−	0.911313i	$-0.364930\pi$
$359$	−3.25225	−	1.87769i	−0.171647	−	0.0991006i	−0.583362	+	0.812212i	$0.698263\pi$
$360$	−15.8423	+	19.3588i	−0.834963	+	1.02030i
$361$	4.42067	+	7.65683i	0.232667	+	0.402991i
$362$	17.3274	−	13.0105i	0.910708	−	0.683819i
$363$			4.05622i			0.212896i
$364$	−7.34514	−	0.126458i	−0.384990	−	0.00662822i
$365$			34.3209i			1.79644i
$366$	3.44101	+	4.58272i	0.179864	+	0.239543i
$367$	−8.41302	−	14.5718i	−0.439156	−	0.760640i	0.558469	−	0.829526i	$-0.311389\pi$
$367$	−8.41302	−	14.5718i	−0.439156	−	0.760640i	−0.997625	+	0.0688852i	$0.978056\pi$
$368$	−8.19841	−	15.6778i	−0.427372	−	0.817264i
$369$	−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	0.183200	−	0.983076i	$-0.441354\pi$
$373$	−11.1354	−	6.42901i	−0.576568	−	0.332882i	−0.759768	+	0.650194i	$0.774688\pi$
$374$	9.05179	−	1.09564i	0.468057	−	0.0566544i
$375$	−0.270533	+	0.156192i	−0.0139702	+	0.00806572i
$376$	28.2379	+	4.62169i	1.45626	+	0.238346i
$377$		−	7.08888i		−	0.365096i
$378$	−6.37460	+	8.19209i	−0.327874	+	0.421355i
$379$	25.5822			1.31407			0.657034	−	0.753861i	$-0.271811\pi$
$379$	25.5822			1.31407			0.657034	+	0.753861i	$0.271811\pi$
$380$	−8.04257	−	32.7356i	−0.412575	−	1.67930i
$381$	1.18320	+	2.04936i	0.0606172	+	0.104992i
$382$	−3.51085	+	0.424959i	−0.179631	+	0.0217428i
$383$	13.4846	−	23.3561i	0.689033	−	1.19344i	−0.283118	−	0.959085i	$-0.591369\pi$
$383$	13.4846	−	23.3561i	0.689033	−	1.19344i	0.972151	−	0.234355i	$-0.0752978\pi$
$384$	−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
$388$	5.51599	+	1.60221i	0.280032	+	0.0813398i
$389$	27.7043	−	15.9951i	1.40466	−	0.810983i	0.409796	−	0.912177i	$-0.365600\pi$
$389$	27.7043	−	15.9951i	1.40466	−	0.810983i	0.994867	+	0.101195i	$0.0322665\pi$
$390$	−1.81092	−	2.41178i	−0.0916994	−	0.122125i
$391$	17.8041			0.900394
$392$	15.4140	+	12.4261i	0.778525	+	0.627614i
$393$	1.89716			0.0956988
$394$	−13.3225	−	17.7429i	−0.671178	−	0.893873i
$395$	33.0126	−	19.0598i	1.66104	−	0.959004i
$396$	−2.47396	+	8.51722i	−0.124321	+	0.428006i
$397$	−8.51929	+	14.7558i	−0.427571	+	0.740575i	−0.996657	−	0.0817035i	$-0.973964\pi$
$397$	−8.51929	+	14.7558i	−0.427571	+	0.740575i	0.569086	+	0.822278i	$0.307297\pi$
$398$	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	$0.119626\pi$
$402$	−6.77620	+	0.820202i	−0.337966	+	0.0409080i
$403$	0.0804953	+	0.139422i	0.00400976	+	0.00694510i
$404$	13.2193	−	3.24775i	0.657684	−	0.161582i
$405$	22.2707			1.10664
$406$	−11.7330	+	15.0782i	−0.582299	+	0.748320i
$407$			8.56461i			0.424532i
$408$	5.40335	+	0.884366i	0.267505	+	0.0437826i
$409$	−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	$0.335221\pi$
$410$	−18.9113	+	2.28905i	−0.933961	+	0.113048i
$411$	−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
$416$	−7.82915	+	0.617270i	−0.383856	+	0.0302641i
$417$	−3.60168	−	6.23829i	−0.176375	−	0.305490i
$418$	−7.17641	−	9.55752i	−0.351010	−	0.467474i
$419$		−	29.4140i		−	1.43697i	−0.695544	−	0.718484i	$-0.744837\pi$
$419$		−	29.4140i		−	1.43697i	0.695544	−	0.718484i	$-0.255163\pi$
$420$	−0.139923	+	8.12722i	−0.00682755	+	0.396568i
$421$		−	32.1265i		−	1.56575i	−0.622180	−	0.782874i	$-0.713753\pi$
$421$		−	32.1265i		−	1.56575i	0.622180	−	0.782874i	$-0.286247\pi$
$422$	11.3911	−	8.55319i	0.554511	−	0.416363i
$423$	−14.0049	−	24.2571i	−0.680939	−	1.17942i
$424$	15.5067	+	12.6899i	0.753073	+	0.616277i
$425$	−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	$0.698198\pi$
$431$	−32.7662	+	18.9176i	−1.57829	+	0.911228i	−0.995098	+	0.0988962i	$0.968469\pi$
$432$	−5.94489	+	9.36997i	−0.286024	+	0.450813i
$433$		−	25.4835i		−	1.22466i	−0.790602	−	0.612330i	$-0.790232\pi$
$433$		−	25.4835i		−	1.22466i	0.790602	−	0.612330i	$-0.209768\pi$
$434$	0.0595453	−	0.429784i	0.00285827	−	0.0206303i
$435$	−7.84367			−0.376075
$436$	−1.35094	−	5.49872i	−0.0646984	−	0.263341i
$437$	−11.6690	−	20.2113i	−0.558204	−	0.966837i
$438$	0.878081	+	7.25437i	0.0419563	+	0.346627i
$439$	−11.9804	+	20.7506i	−0.571792	+	0.990373i	0.424590	+	0.905386i	$0.360418\pi$
$439$	−11.9804	+	20.7506i	−0.571792	+	0.990373i	−0.996382	+	0.0849871i	$0.972915\pi$
$440$	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	$0.245116\pi$
$444$	−1.43458	+	4.93888i	−0.0680821	+	0.234389i
$445$	−4.79140	+	2.76632i	−0.227134	+	0.131136i
$446$	27.4907	−	20.6418i	1.30172	−	0.977416i
$447$	5.43726			0.257174
$448$	17.6745	+	11.6453i	0.835041	+	0.550188i
$449$	11.5096			0.543170			0.271585	−	0.962414i	$-0.412452\pi$
$449$	11.5096			0.543170			0.271585	+	0.962414i	$0.412452\pi$
$450$	16.2926	−	12.2335i	0.768039	−	0.576694i
$451$	−5.84923	+	3.37705i	−0.275429	+	0.159019i
$452$	−0.801641	+	2.75984i	−0.0377060	+	0.129812i
$453$	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	$0.912665\pi$
$458$	−1.80985	−	14.9523i	−0.0845689	−	0.698675i
$459$	−5.58353	−	9.67095i	−0.260617	−	0.451401i
$460$	6.74168	+	27.4406i	0.314332	+	1.27942i
$461$	17.3671			0.808866			0.404433	−	0.914568i	$-0.367469\pi$
$461$	17.3671			0.808866			0.404433	+	0.914568i	$0.367469\pi$
$462$	1.08484	+	2.67003i	0.0504715	+	0.124221i
$463$			21.7288i			1.00983i	0.863171	+	0.504913i	$0.168475\pi$
$463$			21.7288i			1.00983i	−0.863171	+	0.504913i	$0.831525\pi$
$464$	−10.9421	+	17.2462i	−0.507973	+	0.800636i
$465$	0.154267	−	0.0890661i	0.00715396	−	0.00413034i
$466$	−0.108418	−	0.895705i	−0.00502235	−	0.0414928i
$467$	−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
$472$	11.0922	+	9.07731i	0.510560	+	0.417817i
$473$		0			0
$474$	6.49019	−	4.87326i	0.298104	−	0.223836i
$475$			27.4555i			1.25974i
$476$	−18.6270	+	10.3309i	−0.853768	+	0.473517i
$477$		−	19.6144i		−	0.898082i
$478$	4.02108	+	5.35527i	0.183920	+	0.244944i
$479$	14.3839	+	24.9136i	0.657217	+	1.13833i	0.981333	+	0.192316i	$0.0615999\pi$
$479$	14.3839	+	24.9136i	0.657217	+	1.13833i	−0.324116	+	0.946017i	$0.605067\pi$
$480$	0.682994	+	8.66276i	0.0311743	+	0.395399i
$481$	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
$486$	16.3919	−	1.98411i	0.743554	−	0.0900010i
$487$	−1.58745	+	0.916514i	−0.0719342	+	0.0415312i	−0.535536	−	0.844513i	$-0.679890\pi$
$487$	−1.58745	+	0.916514i	−0.0719342	+	0.0415312i	0.463602	+	0.886044i	$0.346557\pi$
$488$	−23.5206	−	3.84962i	−1.06473	−	0.174264i
$489$			4.18601i			0.189298i
$490$	−19.1722	−	25.1467i	−0.866113	−	1.13601i
$491$	13.4370			0.606401			0.303201	−	0.952927i	$-0.401945\pi$
$491$	13.4370			0.606401			0.303201	+	0.952927i	$0.401945\pi$
$492$	−3.93869	+	0.967668i	−0.177570	+	0.0436258i
$493$	−10.2770	−	17.8002i	−0.462851	−	0.801682i
$494$	−10.2846	+	1.24486i	−0.462726	+	0.0560091i
$495$	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	$0.0847714\pi$
$500$	0.362385	−	1.24760i	0.0162063	−	0.0557943i
$501$	−0.578191	+	0.333819i	−0.0258317	+	0.0149139i
$502$	9.81887	+	13.0767i	0.438238	+	0.583644i
$503$	−13.2022			−0.588656			−0.294328	−	0.955704i	$-0.595096\pi$
$503$	−13.2022			−0.588656			−0.294328	+	0.955704i	$0.595096\pi$
$504$	−2.13528	−	20.6090i	−0.0951129	−	0.917997i
$505$	−21.7408			−0.967454
$506$	6.01562	+	8.01158i	0.267427	+	0.356158i
$507$	4.61144	−	2.66241i	0.204801	−	0.118242i
$508$	−9.45091	−	2.74517i	−0.419317	−	0.121797i
$509$	−13.2178	+	22.8940i	−0.585870	+	1.01476i	0.408896	+	0.912581i	$0.365914\pi$
$509$	−13.2178	+	22.8940i	−0.585870	+	1.01476i	−0.994766	+	0.102176i	$0.967420\pi$
$510$	−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
$514$	−33.1207	+	4.00898i	−1.46089	+	0.176829i
$515$	22.4388	+	38.8652i	0.988773	+	1.71260i
$516$		0			0
$517$	−16.2033			−0.712619
$518$	−7.53126	−	18.5361i	−0.330905	−	0.814428i
$519$		−	0.466786i		−	0.0204896i
$520$	12.3783	+	2.02596i	0.542825	+	0.0888442i
$521$	−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	$0.418201\pi$
$522$	19.8486	−	2.40251i	0.868750	−	0.105155i
$523$	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
$528$	1.42772	+	2.73023i	0.0621335	+	0.118818i
$529$	−1.71848	−	2.97649i	−0.0747164	−	0.129413i
$530$	−19.2155	−	25.5912i	−0.834668	−	1.11161i
$531$		−	14.0305i		−	0.608872i
$532$	23.9360	+	14.3744i	1.03776	+	0.623211i
$533$			5.85434i			0.253580i
$534$	−0.941978	+	0.707298i	−0.0407634	+	0.0306078i
$535$	8.20791	+	14.2165i	0.354859	+	0.614634i
$536$	17.9779	−	21.9685i	0.776527	−	0.948894i
$537$	−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	0.535811	−	0.844338i	$-0.320006\pi$
$541$	1.68628	+	0.973573i	0.0724988	+	0.0418572i	−0.463312	+	0.886195i	$0.653339\pi$
$542$	2.31783	+	19.1490i	0.0995592	+	0.822520i
$543$	−6.38109	+	3.68413i	−0.273839	+	0.158101i
$544$	−18.7642	+	12.9001i	−0.804507	+	0.553088i
$545$			9.04336i			0.387375i
$546$	2.47444	+	0.342826i	0.105896	+	0.0146716i
$547$	28.4561			1.21669			0.608347	−	0.793671i	$-0.291833\pi$
$547$	28.4561			1.21669			0.608347	+	0.793671i	$0.291833\pi$
$548$	0.199749	−	0.0490750i	0.00853286	−	0.00209638i
$549$	11.6653	+	20.2048i	0.497862	+	0.862321i
$550$	−1.41629	−	11.7008i	−0.0603906	−	0.498924i
$551$	−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
$556$	28.7687	+	8.35634i	1.22007	+	0.354388i
$557$	7.96630	−	4.59935i	0.337543	−	0.194881i	−0.321642	−	0.946861i	$-0.604235\pi$
$557$	7.96630	−	4.59935i	0.337543	−	0.194881i	0.659185	+	0.751981i	$0.270901\pi$
$558$	−0.363096	+	0.272636i	−0.0153711	+	0.0115416i
$559$		0			0
$560$	−22.9758	−	24.7970i	−0.970905	−	1.04786i
$561$	−3.10051			−0.130904
$562$	1.62505	−	1.22020i	0.0685488	−	0.0514709i
$563$	−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	$0.527596\pi$
$564$	−9.34381	−	2.71406i	−0.393445	−	0.114283i
$565$	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	$0.00241329\pi$
$570$	1.37741	+	11.3796i	0.0576934	+	0.476641i
$571$	−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	$-0.385624\pi$
$572$	4.31881	−	1.06106i	0.180579	−	0.0443651i
$573$	1.20257			0.0502382
$574$	9.68967	−	12.4523i	0.404439	−	0.519751i
$575$		−	23.0145i		−	0.959772i
$576$	−4.38173	−	21.7121i	−0.182572	−	0.904673i
$577$	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	$0.130287\pi$
$578$	0.135380	+	1.11846i	0.00563107	+	0.0465217i
$579$	−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
$584$	−23.5187	−	19.2465i	−0.973211	−	0.796428i
$585$	−6.13915	−	10.6333i	−0.253823	−	0.439634i
$586$	−35.3978	+	26.5790i	−1.46227	+	1.09797i
$587$			15.2362i			0.628867i	0.949280	+	0.314433i	$0.101814\pi$
$587$			15.2362i			0.628867i	−0.949280	+	0.314433i	$0.898186\pi$
$588$	−4.69577	−	4.82471i	−0.193650	−	0.198968i
$589$		−	0.611872i		−	0.0252117i
$590$	−13.7452	−	18.3058i	−0.565880	−	0.753637i
$591$	3.77246	+	6.53409i	0.155178	+	0.268777i
$592$	−9.91160	−	18.9540i	−0.407364	−	0.779003i
$593$	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
$598$	8.62105	−	1.04351i	0.352541	−	0.0426721i
$599$	29.1795	−	16.8468i	1.19224	−	0.688341i	0.233427	−	0.972374i	$-0.425006\pi$
$599$	29.1795	−	16.8468i	1.19224	−	0.688341i	0.958814	+	0.284033i	$0.0916726\pi$
$600$	1.14318	−	6.98464i	0.0466700	−	0.285147i
$601$			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
$604$	7.07205	+	28.7853i	0.287758	+	1.17126i
$605$	13.4712	+	23.3329i	0.547683	+	0.948616i
$606$	−4.59533	+	0.556227i	−0.186673	+	0.0225952i
$607$	4.08757	−	7.07987i	0.165909	−	0.287363i	−0.771069	−	0.636752i	$-0.780277\pi$
$607$	4.08757	−	7.07987i	0.165909	−	0.287363i	0.936978	+	0.349389i	$0.113611\pi$
$608$	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
$612$	21.4055	+	6.21757i	0.865265	+	0.251330i
$613$	−14.7221	+	8.49981i	−0.594620	+	0.343304i	−0.766922	−	0.641740i	$-0.778213\pi$
$613$	−14.7221	+	8.49981i	−0.594620	+	0.343304i	0.172302	+	0.985044i	$0.444879\pi$
$614$	12.5009	+	16.6486i	0.504493	+	0.671883i
$615$	6.47768			0.261205
$616$	−10.9424	−	4.89128i	−0.440882	−	0.197075i
$617$	39.6548			1.59644			0.798221	−	0.602365i	$-0.205775\pi$
$617$	39.6548			1.59644			0.798221	+	0.602365i	$0.205775\pi$
$618$	5.73721	+	7.64080i	0.230784	+	0.307358i
$619$	−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	$0.426795\pi$
$620$	−0.206644	+	0.711423i	−0.00829903	+	0.0285714i
$621$	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
$626$	18.3725	−	2.22384i	0.734314	−	0.0888826i
$627$	2.03211	+	3.51971i	0.0811545	+	0.140564i
$628$	1.43478	−	0.352502i	0.0572541	−	0.0140663i
$629$	21.5246			0.858241
$630$	−4.54135	+	32.7784i	−0.180932	+	1.30592i
$631$		−	36.6698i		−	1.45980i	−0.683553	−	0.729900i	$-0.739566\pi$
$631$		−	36.6698i		−	1.45980i	0.683553	−	0.729900i	$-0.260434\pi$
$632$	−5.45194	+	33.3106i	−0.216867	+	1.32502i
$633$	−4.19496	+	2.42196i	−0.166735	+	0.0962644i
$634$	33.0670	−	4.00248i	1.31326	−	0.158959i
$635$	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
$640$	−26.9875	−	24.0355i	−1.06677	−	0.950086i
$641$	−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	$0.950874\pi$
$642$	2.09862	+	2.79493i	0.0828258	+	0.110307i
$643$		−	13.6340i		−	0.537671i	−0.963186	−	0.268836i	$-0.913361\pi$
$643$		−	13.6340i		−	0.537671i	0.963186	−	0.268836i	$-0.0866389\pi$
$644$	−20.0643	−	12.0494i	−0.790646	−	0.474812i
$645$		0			0
$646$	−24.0200	+	18.0357i	−0.945053	+	0.709607i
$647$	8.74153	+	15.1408i	0.343665	+	0.595245i	0.985110	−	0.171923i	$-0.0549982\pi$
$647$	8.74153	+	15.1408i	0.343665	+	0.595245i	−0.641445	+	0.767169i	$0.721665\pi$
$648$	−12.4890	+	15.2612i	−0.490615	+	0.599517i
$649$	−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	0.655358	−	0.755319i	$-0.272518\pi$
$653$	8.40495	+	4.85260i	0.328911	+	0.189897i	−0.326446	+	0.945216i	$0.605851\pi$
$654$	0.231369	+	1.91148i	0.00904725	+	0.0747449i
$655$	10.9131	−	6.30070i	0.426411	−	0.246189i
$656$	9.03650	−	14.2428i	0.352816	−	0.556087i
$657$			29.7488i			1.16061i
$658$	35.0682	−	14.2483i	1.36710	−	0.555456i
$659$	−28.9465			−1.12760			−0.563798	−	0.825913i	$-0.690660\pi$
$659$	−28.9465			−1.12760			−0.563798	+	0.825913i	$0.690660\pi$
$660$	−1.17403	−	4.77866i	−0.0456992	−	0.186009i
$661$	6.43683	+	11.1489i	0.250364	+	0.433643i	0.963626	−	0.267254i	$-0.0861164\pi$
$661$	6.43683	+	11.1489i	0.250364	+	0.433643i	−0.713262	+	0.700897i	$0.752783\pi$
$662$	5.61739	+	46.4087i	0.218326	+	1.80373i
$663$	−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
$668$	0.774501	−	2.66641i	0.0299663	−	0.103166i
$669$	−10.1239	+	5.84502i	−0.391412	+	0.225982i
$670$	−36.2552	+	27.2227i	−1.40066	+	1.05171i
$671$	13.4964			0.521024
$672$	−5.49078	−	4.65348i	−0.211811	−	0.179512i
$673$	−23.6548			−0.911825			−0.455912	−	0.890025i	$-0.650687\pi$
$673$	−23.6548			−0.911825			−0.455912	+	0.890025i	$0.650687\pi$
$674$	−17.5398	+	13.1700i	−0.675607	+	0.507290i
$675$	−12.5012	+	7.21755i	−0.481170	+	0.277804i
$676$	−6.17713	+	21.2663i	−0.237582	+	0.817933i
$677$	1.80224	−	3.12157i	0.0692657	−	0.119972i	−0.829313	−	0.558785i	$-0.811268\pi$
$677$	1.80224	−	3.12157i	0.0692657	−	0.119972i	0.898578	+	0.438813i	$0.144601\pi$
$678$	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
$682$	0.0315633	+	0.260764i	0.00120862	+	0.00998516i
$683$	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	$0.786772\pi$
$684$	−6.97115	−	28.3746i	−0.266549	−	1.08493i
$685$	−0.328514			−0.0125519
$686$	25.9695	+	3.40375i	0.991520	+	0.129956i
$687$			5.12162i			0.195402i
$688$		0			0
$689$	−8.51745	+	4.91755i	−0.324489	+	0.187344i
$690$	−1.15461	−	9.53898i	−0.0439554	−	0.363143i
$691$	−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
$696$	4.39859	−	5.37494i	0.166728	−	0.203737i
$697$	8.48721	+	14.7003i	0.321476	+	0.556813i
$698$	−32.2008	+	24.1784i	−1.21882	+	0.915167i
$699$			0.306806i			0.0116045i
$700$	13.3543	+	24.0782i	0.504745	+	0.910072i
$701$			0.741474i			0.0280051i	0.999902	+	0.0140025i	$0.00445729\pi$
$701$			0.741474i			0.0280051i	−0.999902	+	0.0140025i	$0.995543\pi$
$702$	−3.27045	−	4.35558i	−0.123435	−	0.164391i
$703$	−14.1074	−	24.4347i	−0.532071	−	0.921574i
$704$	−12.1449	−	4.08492i	−0.457726	−	0.153956i
$705$	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	0.986634	−	0.162952i	$-0.0521016\pi$
$709$	35.6491	+	20.5820i	1.33883	+	0.772974i	0.352196	+	0.935926i	$0.385435\pi$
$710$	−23.7305	+	2.87238i	−0.890590	+	0.107799i
$711$	28.6147	−	16.5207i	1.07314	−	0.619575i
$712$	0.791288	−	4.83465i	0.0296548	−	0.181186i
$713$			0.512901i			0.0192083i
$714$	6.71033	−	2.72643i	0.251128	−	0.102034i
$715$	−7.10284			−0.265631
$716$	27.7156	−	6.80925i	1.03578	−	0.254474i
$717$	−1.13863	−	1.97216i	−0.0425229	−	0.0736518i
$718$	−5.27242	+	0.638183i	−0.196765	+	0.0238168i
$719$	7.02471	−	12.1672i	0.261978	−	0.453758i	−0.704790	−	0.709416i	$-0.748959\pi$
$719$	7.02471	−	12.1672i	0.261978	−	0.453758i	0.966767	+	0.255658i	$0.0822920\pi$
$720$	−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
$724$	8.54763	−	29.4273i	0.317670	−	1.09366i
$725$	−23.0095	+	13.2845i	−0.854550	+	0.493375i
$726$	3.44435	+	4.58718i	0.127832	+	0.170246i
$727$	13.2022			0.489642			0.244821	−	0.969568i	$-0.421271\pi$
$727$	13.2022			0.489642			0.244821	+	0.969568i	$0.421271\pi$
$728$	−8.41401	+	6.09414i	−0.311844	+	0.225864i
$729$	15.3015			0.566724
$730$	29.1438	+	38.8136i	1.07866	+	1.43656i
$731$		0			0
$732$	7.78288	+	2.26066i	0.287663	+	0.0835565i
$733$	24.9797	−	43.2661i	0.922646	−	1.59807i	0.127342	−	0.991859i	$-0.459356\pi$
$733$	24.9797	−	43.2661i	0.922646	−	1.59807i	0.795304	−	0.606211i	$-0.207311\pi$
$734$	−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
$738$	−16.3919	+	1.98411i	−0.603396	+	0.0730360i
$739$	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	$0.598710\pi$
$740$	8.15045	+	33.1747i	0.299617	+	1.21953i
$741$	3.52278			0.129413
$742$	26.2560	+	3.63770i	0.963889	+	0.133544i
$743$			15.1330i			0.555177i	0.960700	+	0.277589i	$0.0895352\pi$
$743$			15.1330i			0.555177i	−0.960700	+	0.277589i	$0.910465\pi$
$744$	−0.0254768	+	0.155659i	−0.000934024	+	0.00570675i
$745$	31.2771	−	18.0579i	1.14591	−	0.661589i
$746$	−18.0522	+	2.18507i	−0.660939	+	0.0800012i
$747$	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	0.702697	−	0.711490i	$-0.251979\pi$
$751$	11.9997	+	6.92806i	0.437877	+	0.252808i	−0.264820	+	0.964298i	$0.585312\pi$
$752$	35.8588	−	18.7516i	1.30763	−	0.683801i
$753$	−2.78036	−	4.81572i	−0.101322	−	0.175495i
$754$	−6.01955	−	8.01682i	−0.219219	−	0.291955i
$755$		−	47.3412i		−	1.72292i
$756$	−0.252696	+	14.6775i	−0.00919047	+	0.533814i
$757$			46.6967i			1.69722i	0.529019	+	0.848610i	$0.322560\pi$
$757$			46.6967i			1.69722i	−0.529019	+	0.848610i	$0.677440\pi$
$758$	28.9309	−	21.7232i	1.05082	−	0.789022i
$759$	−1.70341	−	2.95039i	−0.0618299	−	0.107093i
$760$	−36.8929	−	30.1913i	−1.33825	−	1.09515i
$761$	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
$766$	−4.58312	−	37.8640i	−0.165595	−	1.36808i
$767$	−6.09267	+	3.51761i	−0.219994	+	0.127013i
$768$	−6.31925	−	4.38989i	−0.228026	−	0.158407i
$769$		−	17.3071i		−	0.624110i	−0.950064	−	0.312055i	$-0.898983\pi$
$769$		−	17.3071i		−	0.624110i	0.950064	−	0.312055i	$-0.101017\pi$
$770$	15.1079	+	11.7561i	0.544453	+	0.423661i
$771$	11.3448			0.408574
$772$	6.02195	−	1.47949i	0.216735	−	0.0532480i
$773$	−13.5389	−	23.4501i	−0.486960	−	0.843440i	0.512927	−	0.858432i	$-0.328561\pi$
$773$	−13.5389	−	23.4501i	−0.486960	−	0.843440i	−0.999888	+	0.0149920i	$0.995228\pi$
$774$		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
$780$	−4.09594	−	1.18973i	−0.146658	−	0.0425992i
$781$	−7.33982	+	4.23764i	−0.262639	+	0.151635i
$782$	20.1347	−	15.1184i	0.720016	−	0.540635i
$783$	−14.1654			−0.506230
$784$	27.9834	+	0.963845i	0.999407	+	0.0344230i
$785$	−2.35969			−0.0842208
$786$	2.14550	−	1.61098i	0.0765273	−	0.0574617i
$787$	−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	$0.915803\pi$
$788$	−30.1329	−	8.75257i	−1.07344	−	0.311798i
$789$	−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
$794$	2.89551	+	23.9216i	0.102758	+	0.848946i
$795$	5.44115	+	9.42435i	0.192978	+	0.334247i
$796$	22.9686	−	5.64298i	0.814099	−	0.200010i
$797$	20.1437			0.713527			0.356763	−	0.934195i	$-0.383880\pi$
$797$	20.1437			0.713527			0.356763	+	0.934195i	$0.383880\pi$
$798$	−7.49306	−	5.83066i	−0.265251	−	0.206403i
$799$			40.7221i			1.44064i
$800$	16.6754	+	24.2555i	0.589563	+	0.857562i
$801$	−4.15310	+	2.39779i	−0.146743	+	0.0847219i
$802$	−1.00215	−	8.27941i	−0.0353873	−	0.292356i
$803$	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
$808$	12.1919	−	14.8981i	0.428908	−	0.524113i
$809$	−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	$-0.374467\pi$
$810$	25.1860	−	18.9113i	0.884946	−	0.664475i
$811$			13.6340i			0.478754i	0.970927	+	0.239377i	$0.0769431\pi$
$811$			13.6340i			0.478754i	−0.970927	+	0.239377i	$0.923057\pi$
$812$	−0.465109	+	27.0151i	−0.0163221	+	0.948045i
$813$		−	6.55911i		−	0.230038i
$814$	7.27267	+	9.68573i	0.254907	+	0.339485i
$815$	13.9023	+	24.0795i	0.486976	+	0.843468i
$816$	6.86161	−	3.58814i	0.240204	−	0.125610i
$817$		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	−0.0692505	−	0.997599i	$-0.522061\pi$
$821$	−27.7311	−	16.0106i	−0.967822	−	0.558772i	−0.898572	+	0.438827i	$0.855394\pi$
$822$	−0.0694375	+	0.00840483i	−0.00242191	+	0.000293152i
$823$	−26.8399	+	15.4960i	−0.935580	+	0.540158i	−0.888572	−	0.458737i	$-0.848302\pi$
$823$	−26.8399	+	15.4960i	−0.935580	+	0.540158i	−0.0470083	+	0.998894i	$0.514969\pi$
$824$	−39.2160	−	6.41848i	−1.36615	−	0.223598i
$825$			4.00788i			0.139537i
$826$	18.7814	+	2.60210i	0.653487	+	0.0905387i
$827$	−11.0191			−0.383172			−0.191586	−	0.981476i	$-0.561363\pi$
$827$	−11.0191			−0.383172			−0.191586	+	0.981476i	$0.561363\pi$
$828$	5.84356	+	23.7850i	0.203078	+	0.826585i
$829$	−18.9836	−	32.8806i	−0.659328	−	1.14199i	−0.980790	−	0.195067i	$-0.937508\pi$
$829$	−18.9836	−	32.8806i	−0.659328	−	1.14199i	0.321462	−	0.946922i	$-0.395826\pi$
$830$	67.1750	−	8.13097i	2.33168	−	0.282230i
$831$	−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
$836$	−16.2316	−	4.71473i	−0.561382	−	0.163063i
$837$	0.278601	−	0.160850i	0.00962984	−	0.00555979i
$838$	−24.9770	−	33.2643i	−0.862816	−	1.14910i
$839$	−8.32984			−0.287578			−0.143789	−	0.989608i	$-0.545929\pi$
$839$	−8.32984			−0.287578			−0.143789	+	0.989608i	$0.545929\pi$
$840$	6.74302	+	9.30989i	0.232656	+	0.321222i
$841$	2.92739			0.100945
$842$	−27.2803	−	36.3319i	−0.940142	−	1.25208i
$843$	−0.598452	+	0.345516i	−0.0206118	+	0.0119002i
$844$	5.61925	−	19.3456i	0.193423	−	0.665904i
$845$	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
$850$	−29.4065	+	3.55941i	−1.00863	+	0.122087i
$851$	11.8255	+	20.4824i	0.405374	+	0.702128i
$852$	−4.94240	+	1.21426i	−0.169324	+	0.0416000i
$853$	−6.94153			−0.237673			−0.118837	−	0.992914i	$-0.537917\pi$
$853$	−6.94153			−0.237673			−0.118837	+	0.992914i	$0.537917\pi$
$854$	−29.2098	+	11.8680i	−0.999540	+	0.406116i
$855$			46.6657i			1.59593i
$856$	−14.3448	−	2.34782i	−0.490297	−	0.0802469i
$857$	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	$0.321293\pi$
$858$	−1.50132	+	0.181722i	−0.0512542	+	0.00620389i
$859$	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	0.364159	−	0.931337i	$-0.381357\pi$
$863$	−7.64747	−	4.41527i	−0.260323	−	0.150298i	−0.624482	+	0.781039i	$0.714690\pi$
$864$	1.23346	+	15.6446i	0.0419633	+	0.532241i
$865$	−1.55026	−	2.68512i	−0.0527103	−	0.0912969i
$866$	−21.6394	−	28.8193i	−0.735338	−	0.979321i
$867$		−	0.383106i		−	0.0130110i
$868$	−0.297613	−	0.536607i	−0.0101016	−	0.0182136i
$869$		−	19.1141i		−	0.648400i
$870$	−8.87042	+	6.66049i	−0.300735	+	0.225812i
$871$	6.96673	+	12.0667i	0.236059	+	0.408866i
$872$	−6.19704	−	5.07135i	−0.209858	−	0.171738i
$873$	−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	0.315801	−	0.948825i	$-0.397727\pi$
$877$	−10.3059	−	5.95011i	−0.348005	−	0.200921i	−0.663806	+	0.747905i	$0.731060\pi$
$878$	4.07185	+	33.6401i	0.137418	+	1.13530i
$879$	13.0358	−	7.52623i	0.439687	−	0.253854i
$880$	17.2802	+	10.9636i	0.582516	+	0.369584i
$881$			53.9142i			1.81642i	0.418519	+	0.908208i	$0.362549\pi$
$881$			53.9142i			1.81642i	−0.418519	+	0.908208i	$0.637451\pi$
$882$	−16.6181	−	21.7967i	−0.559562	−	0.733932i
$883$	11.1987			0.376866			0.188433	−	0.982086i	$-0.439659\pi$
$883$	11.1987			0.376866			0.188433	+	0.982086i	$0.439659\pi$
$884$	−2.66665	−	10.8540i	−0.0896891	−	0.365061i
$885$	3.89215	+	6.74139i	0.130833	+	0.226609i
$886$	1.74525	+	14.4186i	0.0586328	+	0.484402i
$887$	18.1832	−	31.4942i	0.610531	−	1.05747i	−0.380620	−	0.924732i	$-0.624289\pi$
$887$	18.1832	−	31.4942i	0.610531	−	1.05747i	0.991151	−	0.132740i	$-0.0423774\pi$
$888$	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
$892$	13.5612	−	46.6876i	0.454062	−	1.56322i
$893$	46.2278	−	26.6896i	1.54695	−	0.893134i
$894$	6.14901	−	4.61707i	0.205654	−	0.154418i
$895$	−45.5819			−1.52364
$896$	29.8767	−	1.83868i	0.998112	−	0.0614262i
$897$	−2.95297			−0.0985968
$898$	13.0162	−	9.77339i	0.434355	−	0.326142i
$899$	0.512788	−	0.296058i	0.0171024	−	0.00987410i
$900$	8.03714	−	27.6698i	0.267905	−	0.922327i
$901$	−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
$906$	−1.21120	−	10.0064i	−0.0402393	−	0.332442i
$907$	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	$0.737578\pi$
$908$	6.83501	+	27.8205i	0.226828	+	0.923254i
$909$	−18.8446			−0.625034
$910$	15.3724	−	6.24586i	0.509591	−	0.207048i
$911$		−	11.1458i		−	0.369278i	−0.982806	−	0.184639i	$-0.940888\pi$
$911$		−	11.1458i		−	0.369278i	0.982806	−	0.184639i	$-0.0591116\pi$
$912$	−8.57043	−	5.43762i	−0.283795	−	0.180057i
$913$	20.7771	−	11.9957i	0.687623	−	0.396999i
$914$	5.20183	+	42.9755i	0.172061	+	1.42150i
$915$	−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	0.887721	−	0.460382i	$-0.152288\pi$
$919$	28.2802	+	16.3276i	0.932879	+	0.538598i	0.0451579	+	0.998980i	$0.485621\pi$
$920$	30.9254	+	25.3078i	1.01958	+	0.834375i
$921$	−3.53980	−	6.13111i	−0.116640	−	0.202027i
$922$	19.6405	−	14.7473i	0.646825	−	0.485678i
$923$			7.34623i			0.241804i
$924$	3.49412	+	2.09835i	0.114948	+	0.0690305i
$925$		−	27.8238i		−	0.914839i
$926$	18.4511	+	24.5732i	0.606342	+	0.807525i
$927$	19.4496	+	33.6876i	0.638807	+	1.10645i
$928$	2.27029	+	28.7953i	0.0745260	+	0.945252i
$929$	−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
$934$	−0.949771	+	0.114962i	−0.0310775	+	0.00376167i
$935$	−17.8353	+	10.2972i	−0.583276	+	0.336755i
$936$	10.7293	+	1.75606i	0.350698	+	0.0573988i
$937$		−	32.6476i		−	1.06655i	−0.845942	−	0.533275i	$-0.820961\pi$
$937$		−	32.6476i		−	1.06655i	0.845942	−	0.533275i	$-0.179039\pi$
$938$	5.15355	−	37.1971i	0.168269	−	1.21453i
$939$	−6.29315			−0.205369
$940$	−62.7628	+	15.4197i	−2.04710	+	0.502936i
$941$	−6.32087	−	10.9481i	−0.206055	−	0.356897i	0.744414	−	0.667719i	$-0.232729\pi$
$941$	−6.32087	−	10.9481i	−0.206055	−	0.356897i	−0.950468	+	0.310822i	$0.899396\pi$
$942$	−0.498764	+	0.0603712i	−0.0162506	+	0.00196700i
$943$	−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	$-0.0742035\pi$
$948$	3.20162	−	11.0223i	0.103984	−	0.357989i
$949$	12.9182	−	7.45835i	0.419344	−	0.242108i
$950$	23.3139	+	31.0494i	0.756403	+	1.00738i
$951$	−11.3264			−0.367285
$952$	−12.2928	+	27.5005i	−0.398411	+	0.891295i
$953$	−44.4561			−1.44007			−0.720037	−	0.693936i	$-0.755875\pi$
$953$	−44.4561			−1.44007			−0.720037	+	0.693936i	$0.755875\pi$
$954$	−16.6556	−	22.1819i	−0.539247	−	0.718167i
$955$	6.91764	−	3.99390i	0.223850	−	0.129240i
$956$	9.09489	+	2.64176i	0.294150	+	0.0854406i
$957$	−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
$962$	10.4225	−	1.26156i	0.336036	−	0.0406744i
$963$	7.11447	+	12.3226i	0.229261	+	0.397091i
$964$	5.58598	+	22.7365i	0.179912	+	0.732294i
$965$	−9.90388			−0.318817
$966$	6.28105	+	4.88754i	0.202089	+	0.157254i
$967$		−	25.7160i		−	0.826972i	−0.910510	−	0.413486i	$-0.864311\pi$
$967$		−	25.7160i		−	0.826972i	0.910510	−	0.413486i	$-0.135689\pi$
$968$	−23.5435	−	3.85336i	−0.756716	−	0.123852i
$969$	8.84573	−	5.10709i	0.284166	−	0.164063i
$970$	−12.8798	+	1.55900i	−0.413547	+	0.0500564i
$971$	−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
$976$	−29.8684	+	15.6191i	−0.956063	+	0.499954i
$977$	−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	$-0.351349\pi$
$978$	3.55457	+	4.73397i	0.113663	+	0.151376i
$979$			2.77419i			0.0886635i
$980$	−43.0353	−	12.1582i	−1.37471	−	0.388380i
$981$			7.83862i			0.250268i
$982$	15.1959	−	11.4100i	0.484920	−	0.364109i
$983$	−0.777334	−	1.34638i	−0.0247931	−	0.0429429i	0.853363	−	0.521318i	$-0.174559\pi$
$983$	−0.777334	−	1.34638i	−0.0247931	−	0.0429429i	−0.878156	+	0.478375i	$0.841226\pi$
$984$	−3.63257	+	4.43889i	−0.115802	+	0.141507i
$985$	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
$990$	−2.40724	−	19.8877i	−0.0765072	−	0.632073i
$991$	22.6482	−	13.0759i	0.719443	−	0.415371i	−0.0951047	−	0.995467i	$-0.530319\pi$
$991$	22.6482	−	13.0759i	0.719443	−	0.415371i	0.814548	+	0.580097i	$0.196985\pi$
$992$	−0.371626	−	0.540558i	−0.0117992	−	0.0171627i
$993$		−	15.8964i		−	0.504457i
$994$	12.1589	−	15.6256i	0.385658	−	0.495615i
$995$	−37.7748			−1.19754
$996$	13.9907	−	3.43727i	0.443311	−	0.108914i
$997$	18.1467	+	31.4310i	0.574711	+	0.995429i	0.996073	+	0.0885360i	$0.0282188\pi$
$997$	18.1467	+	31.4310i	0.574711	+	0.995429i	−0.421362	+	0.906893i	$0.638448\pi$
$998$	−1.93187	−	15.9604i	−0.0611524	−	0.505218i
$999$	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.19.5	yes	12
3.2	odd	2		504.2.bk.a.19.2		12
4.3	odd	2		224.2.q.a.47.3		12
7.2	even	3		392.2.e.e.195.1		12
7.3	odd	6	inner	56.2.m.a.3.4	✓	12
7.4	even	3		392.2.m.g.227.4		12
7.5	odd	6		392.2.e.e.195.2		12
7.6	odd	2		392.2.m.g.19.5		12
8.3	odd	2	inner	56.2.m.a.19.3	yes	12
8.5	even	2		224.2.q.a.47.4		12
12.11	even	2		2016.2.bs.a.271.6		12
21.17	even	6		504.2.bk.a.451.3		12
24.5	odd	2		2016.2.bs.a.271.1		12
24.11	even	2		504.2.bk.a.19.4		12
28.3	even	6		224.2.q.a.143.4		12
28.11	odd	6		1568.2.q.g.815.3		12
28.19	even	6		1568.2.e.e.783.5		12
28.23	odd	6		1568.2.e.e.783.8		12
28.27	even	2		1568.2.q.g.1391.4		12
56.3	even	6	inner	56.2.m.a.3.6	yes	12
56.5	odd	6		1568.2.e.e.783.6		12
56.11	odd	6		392.2.m.g.227.6		12
56.13	odd	2		1568.2.q.g.1391.3		12
56.19	even	6		392.2.e.e.195.4		12
56.27	even	2		392.2.m.g.19.3		12
56.37	even	6		1568.2.e.e.783.7		12
56.45	odd	6		224.2.q.a.143.3		12
56.51	odd	6		392.2.e.e.195.3		12
56.53	even	6		1568.2.q.g.815.4		12
84.59	odd	6		2016.2.bs.a.1711.1		12
168.59	odd	6		504.2.bk.a.451.1		12
168.101	even	6		2016.2.bs.a.1711.6		12

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

\(f(q)\)	\(=\)	\(q+(1.13090 - 0.849154i) q^{2} +(-0.416472 + 0.240450i) q^{3} +(0.557875 - 1.92062i) q^{4} +(-1.59713 + 2.76632i) q^{5} +(-0.266810 + 0.625575i) q^{6} +(-0.694153 - 2.55307i) q^{7} +(-1.00000 - 2.64575i) q^{8} +(-1.38437 + 2.39779i) q^{9} +O(q^{10})\)	\(q+(1.13090 - 0.849154i) q^{2} +(-0.416472 + 0.240450i) q^{3} +(0.557875 - 1.92062i) 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} +(0.542829 + 4.48465i) q^{10} +(0.800840 + 1.38709i) q^{11} +(0.229474 + 0.934026i) q^{12} +1.38831 q^{13} +(-2.95297 - 2.29782i) q^{14} -1.53613i q^{15} +(-3.37755 - 2.14293i) q^{16} +(3.48605 - 2.01267i) q^{17} +(0.470514 + 3.88721i) 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} +(1.05264 + 0.861432i) q^{24} +(-2.60168 - 4.50624i) q^{25} +(1.57004 - 1.17889i) q^{26} -2.77419i q^{27} +(-5.29072 - 0.0910883i) q^{28} -5.10613i q^{29} +(-1.30441 - 1.73721i) q^{30} +(0.0579809 + 0.100426i) q^{31} +(-5.63935 + 0.444621i) 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} +(-7.40801 + 0.896678i) q^{38} +(-0.578191 + 0.333819i) q^{39} +(8.91613 + 1.45930i) q^{40} +4.21689i q^{41} +(1.78234 + 0.246938i) q^{42} +(3.11085 - 0.764282i) q^{44} +(-4.42204 - 7.65920i) q^{45} +(6.20976 - 0.751640i) 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} +(0.774501 - 2.66641i) q^{52} +(-6.13514 + 3.54212i) q^{53} +(-2.35571 - 3.13733i) q^{54} -5.11619 q^{55} +(-6.06063 + 4.38962i) q^{56} +2.53747 q^{57} +(-4.33589 - 5.77453i) q^{58} +(-4.38856 + 2.53374i) q^{59} +(-2.95031 - 0.856966i) 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} +(-1.08140 + 0.130895i) q^{66} +(5.01815 + 8.69169i) q^{67} +(-1.92079 - 7.81818i) q^{68} -2.12703 q^{69} +(11.0728 - 4.49891i) q^{70} +5.29150i q^{71} +(7.72833 + 1.26490i) q^{72} +(9.30504 - 5.37227i) q^{73} +(7.50738 - 0.908707i) 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} +(11.3224 - 5.92084i) q^{80} +(-3.48605 - 6.03801i) q^{81} +(3.58079 + 4.76889i) q^{82} -14.9789i q^{83} +(2.22534 - 1.23422i) q^{84} +12.8580i q^{85} +(1.22777 + 2.12656i) q^{87} +(2.86907 - 3.50592i) 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} +(1.71917 + 14.2031i) q^{94} +(14.5965 - 8.42726i) q^{95} +(2.24173 - 1.54116i) q^{96} +2.87198i q^{97} +(-3.81669 + 9.13416i) q^{98} -4.43462 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} - 12 q^{8}+O(q^{10}) \) 12 * q - 6 * q^3 - 12 * q^8	\( 12 q - 6 q^{3} - 12 q^{8} + 6 q^{10} - 6 q^{11} - 18 q^{12} + 6 q^{14} - 6 q^{17} + 6 q^{18} - 6 q^{19} + 24 q^{22} + 6 q^{24} + 6 q^{26} + 6 q^{28} - 12 q^{30} - 6 q^{33} + 18 q^{35} + 48 q^{36} - 24 q^{38} + 42 q^{40} - 30 q^{42} + 6 q^{44} - 18 q^{46} - 12 q^{49} - 48 q^{50} + 6 q^{51} - 24 q^{52} - 36 q^{54} - 36 q^{57} + 18 q^{58} + 42 q^{59} - 6 q^{60} - 72 q^{64} - 12 q^{65} + 12 q^{66} + 30 q^{67} - 36 q^{68} + 30 q^{70} + 18 q^{73} + 12 q^{74} + 24 q^{75} + 60 q^{78} + 36 q^{80} + 6 q^{81} + 54 q^{82} + 12 q^{84} + 6 q^{88} + 18 q^{89} - 72 q^{91} + 60 q^{92} - 12 q^{94} + 60 q^{96} - 6 q^{98} - 24 q^{99}+O(q^{100}) \) 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

Modular forms

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