LMFDB - Embedded newform 546.2.z.a.131.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(131,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("546.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.z (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.8
Character	$\chi$	$=$	546.131
Dual form			546.2.z.a.521.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(1.72106 + 0.194824i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.735814 + 1.27447i) q^{5} +(-1.39307 - 1.02925i) q^{6} +(0.322414 + 2.62603i) q^{7} -1.00000i q^{8} +(2.92409 + 0.670607i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(1.72106 + 0.194824i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.735814 + 1.27447i) q^{5} +(-1.39307 - 1.02925i) q^{6} +(0.322414 + 2.62603i) q^{7} -1.00000i q^{8} +(2.92409 + 0.670607i) q^{9} +(1.27447 - 0.735814i) q^{10} +(-5.30459 + 3.06261i) q^{11} +(0.691807 + 1.58789i) q^{12} +1.00000i q^{13} +(1.03380 - 2.43542i) q^{14} +(-1.51468 + 2.05008i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.120940 + 0.209475i) q^{17} +(-2.19703 - 2.04281i) q^{18} +(-3.75717 - 2.16920i) q^{19} -1.47163 q^{20} +(0.0432793 + 4.58237i) q^{21} +6.12521 q^{22} +(-1.69183 - 0.976779i) q^{23} +(0.194824 - 1.72106i) q^{24} +(1.41716 + 2.45459i) q^{25} +(0.500000 - 0.866025i) q^{26} +(4.90188 + 1.72384i) q^{27} +(-2.11300 + 1.59224i) q^{28} +3.00301i q^{29} +(2.33679 - 1.01808i) q^{30} +(-0.975089 + 0.562968i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-9.72618 + 4.23746i) q^{33} -0.241880i q^{34} +(-3.58403 - 1.52137i) q^{35} +(0.881281 + 2.86764i) q^{36} +(2.60288 - 4.50831i) q^{37} +(2.16920 + 3.75717i) q^{38} +(-0.194824 + 1.72106i) q^{39} +(1.27447 + 0.735814i) q^{40} +4.60565 q^{41} +(2.25370 - 3.99009i) q^{42} +1.24679 q^{43} +(-5.30459 - 3.06261i) q^{44} +(-3.00625 + 3.23321i) q^{45} +(0.976779 + 1.69183i) q^{46} +(3.84662 - 6.66255i) q^{47} +(-1.02925 + 1.39307i) q^{48} +(-6.79210 + 1.69334i) q^{49} -2.83431i q^{50} +(0.167335 + 0.384080i) q^{51} +(-0.866025 + 0.500000i) q^{52} +(6.14856 - 3.54987i) q^{53} +(-3.38323 - 3.94382i) q^{54} -9.01403i q^{55} +(2.62603 - 0.322414i) q^{56} +(-6.04370 - 4.46531i) q^{57} +(1.50150 - 2.60068i) q^{58} +(6.21031 + 10.7566i) q^{59} +(-2.53276 - 0.286708i) q^{60} +(11.5260 + 6.65454i) q^{61} +1.12594 q^{62} +(-0.818269 + 7.89496i) q^{63} -1.00000 q^{64} +(-1.27447 - 0.735814i) q^{65} +(10.5418 + 1.19334i) q^{66} +(6.58500 + 11.4055i) q^{67} +(-0.120940 + 0.209475i) q^{68} +(-2.72144 - 2.01070i) q^{69} +(2.34318 + 3.10956i) q^{70} -9.38944i q^{71} +(0.670607 - 2.92409i) q^{72} +(-8.77999 + 5.06913i) q^{73} +(-4.50831 + 2.60288i) q^{74} +(1.96080 + 4.50058i) q^{75} -4.33841i q^{76} +(-9.75277 - 12.9426i) q^{77} +(1.02925 - 1.39307i) q^{78} +(2.38049 - 4.12313i) q^{79} +(-0.735814 - 1.27447i) q^{80} +(8.10057 + 3.92182i) q^{81} +(-3.98861 - 2.30282i) q^{82} +9.45528 q^{83} +(-3.94681 + 2.32867i) q^{84} -0.355958 q^{85} +(-1.07975 - 0.623395i) q^{86} +(-0.585058 + 5.16836i) q^{87} +(3.06261 + 5.30459i) q^{88} +(1.82263 - 3.15689i) q^{89} +(4.22010 - 1.29692i) q^{90} +(-2.62603 + 0.322414i) q^{91} -1.95356i q^{92} +(-1.78786 + 0.778930i) q^{93} +(-6.66255 + 3.84662i) q^{94} +(5.52916 - 3.19226i) q^{95} +(1.58789 - 0.691807i) q^{96} +7.44495i q^{97} +(6.72880 + 1.92958i) q^{98} +(-17.5649 + 5.39803i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9}+O(q^{10}) $ 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9	$ 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{10} - 24 q^{11} + 4 q^{14} - 12 q^{15} - 16 q^{16} + 4 q^{17} + 24 q^{18} - 12 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} + 16 q^{26} - 6 q^{27} - 2 q^{28} + 10 q^{30} - 6 q^{31} - 14 q^{33} + 48 q^{35} + 4 q^{36} + 16 q^{38} + 6 q^{39} + 6 q^{40} + 16 q^{41} - 18 q^{42} + 32 q^{43} - 24 q^{44} - 20 q^{45} + 16 q^{46} + 20 q^{47} - 26 q^{49} + 44 q^{51} - 60 q^{53} - 6 q^{54} + 8 q^{56} - 8 q^{57} - 10 q^{58} + 8 q^{59} - 6 q^{60} + 36 q^{61} + 36 q^{62} - 28 q^{63} - 32 q^{64} - 6 q^{65} + 12 q^{66} - 4 q^{68} - 36 q^{69} - 18 q^{70} + 24 q^{72} - 48 q^{73} - 84 q^{74} + 14 q^{75} + 52 q^{77} + 18 q^{79} + 70 q^{81} + 24 q^{83} - 24 q^{84} - 32 q^{85} - 24 q^{86} - 26 q^{87} - 6 q^{88} - 20 q^{89} - 6 q^{90} - 8 q^{91} + 92 q^{93} - 72 q^{95} - 6 q^{96} + 32 q^{98}+O(q^{100}) $ 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9 + 6 * q^10 - 24 * q^11 + 4 * q^14 - 12 * q^15 - 16 * q^16 + 4 * q^17 + 24 * q^18 - 12 * q^21 - 12 * q^22 - 6 * q^24 - 18 * q^25 + 16 * q^26 - 6 * q^27 - 2 * q^28 + 10 * q^30 - 6 * q^31 - 14 * q^33 + 48 * q^35 + 4 * q^36 + 16 * q^38 + 6 * q^39 + 6 * q^40 + 16 * q^41 - 18 * q^42 + 32 * q^43 - 24 * q^44 - 20 * q^45 + 16 * q^46 + 20 * q^47 - 26 * q^49 + 44 * q^51 - 60 * q^53 - 6 * q^54 + 8 * q^56 - 8 * q^57 - 10 * q^58 + 8 * q^59 - 6 * q^60 + 36 * q^61 + 36 * q^62 - 28 * q^63 - 32 * q^64 - 6 * q^65 + 12 * q^66 - 4 * q^68 - 36 * q^69 - 18 * q^70 + 24 * q^72 - 48 * q^73 - 84 * q^74 + 14 * q^75 + 52 * q^77 + 18 * q^79 + 70 * q^81 + 24 * q^83 - 24 * q^84 - 32 * q^85 - 24 * q^86 - 26 * q^87 - 6 * q^88 - 20 * q^89 - 6 * q^90 - 8 * q^91 + 92 * q^93 - 72 * q^95 - 6 * q^96 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	1.72106	+	0.194824i	0.993654	+	0.112482i
$3$	1.72106	+	0.194824i	0.993654	+	0.112482i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.735814	+	1.27447i	−0.329066	+	0.569959i	−0.982327	−	0.187174i	$-0.940067\pi$
$5$	−0.735814	+	1.27447i	−0.329066	+	0.569959i	0.653261	+	0.757133i	$0.273401\pi$
$6$	−1.39307	−	1.02925i	−0.568718	−	0.420190i
$7$	0.322414	+	2.62603i	0.121861	+	0.992547i
$7$	0.322414	+	2.62603i	0.121861	+	0.992547i
$8$		−	1.00000i		−	0.353553i
$9$	2.92409	+	0.670607i	0.974696	+	0.223536i
$10$	1.27447	−	0.735814i	0.403022	−	0.232685i
$11$	−5.30459	+	3.06261i	−1.59939	+	0.923410i	−0.607789	+	0.794098i	$0.707944\pi$
$11$	−5.30459	+	3.06261i	−1.59939	+	0.923410i	−0.991604	+	0.129312i	$0.958723\pi$
$12$	0.691807	+	1.58789i	0.199707	+	0.458385i
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	1.03380	−	2.43542i	0.276294	−	0.650893i
$15$	−1.51468	+	2.05008i	−0.391088	+	0.529328i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.120940	+	0.209475i	0.0293323	+	0.0508050i	0.880319	−	0.474382i	$-0.157329\pi$
$17$	0.120940	+	0.209475i	0.0293323	+	0.0508050i	−0.850987	+	0.525187i	$0.823995\pi$
$18$	−2.19703	−	2.04281i	−0.517845	−	0.481494i
$19$	−3.75717	−	2.16920i	−0.861954	−	0.497650i	0.00271198	−	0.999996i	$-0.499137\pi$
$19$	−3.75717	−	2.16920i	−0.861954	−	0.497650i	−0.864666	+	0.502347i	$0.832470\pi$
$20$	−1.47163			−0.329066
$21$	0.0432793	+	4.58237i	0.00944432	+	0.999955i
$22$	6.12521			1.30590
$23$	−1.69183	−	0.976779i	−0.352771	−	0.203673i	0.313134	−	0.949709i	$-0.398621\pi$
$23$	−1.69183	−	0.976779i	−0.352771	−	0.203673i	−0.665905	+	0.746036i	$0.731954\pi$
$24$	0.194824	−	1.72106i	0.0397682	−	0.351310i
$25$	1.41716	+	2.45459i	0.283431	+	0.490917i
$26$	0.500000	−	0.866025i	0.0980581	−	0.169842i
$27$	4.90188	+	1.72384i	0.943367	+	0.331752i
$28$	−2.11300	+	1.59224i	−0.399320	+	0.300904i
$29$			3.00301i			0.557645i	0.960343	+	0.278822i	$0.0899441\pi$
$29$			3.00301i			0.557645i	−0.960343	+	0.278822i	$0.910056\pi$
$30$	2.33679	−	1.01808i	0.426637	−	0.185876i
$31$	−0.975089	+	0.562968i	−0.175131	+	0.101112i	−0.585003	−	0.811031i	$-0.698907\pi$
$31$	−0.975089	+	0.562968i	−0.175131	+	0.101112i	0.409872	+	0.912143i	$0.365573\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−9.72618	+	4.23746i	−1.69311	+	0.737648i
$34$		−	0.241880i		−	0.0414821i
$35$	−3.58403	−	1.52137i	−0.605812	−	0.257158i
$36$	0.881281	+	2.86764i	0.146880	+	0.477940i
$37$	2.60288	−	4.50831i	0.427910	−	0.741162i	−0.568777	−	0.822492i	$-0.692583\pi$
$37$	2.60288	−	4.50831i	0.427910	−	0.741162i	0.996687	+	0.0813296i	$0.0259166\pi$
$38$	2.16920	+	3.75717i	0.351891	+	0.609494i
$39$	−0.194824	+	1.72106i	−0.0311968	+	0.275590i
$40$	1.27447	+	0.735814i	0.201511	+	0.116342i
$41$	4.60565			0.719282			0.359641	−	0.933091i	$-0.382899\pi$
$41$	4.60565			0.719282			0.359641	+	0.933091i	$0.382899\pi$
$42$	2.25370	−	3.99009i	0.347754	−	0.615684i
$43$	1.24679			0.190134			0.0950669	−	0.995471i	$-0.469693\pi$
$43$	1.24679			0.190134			0.0950669	+	0.995471i	$0.469693\pi$
$44$	−5.30459	−	3.06261i	−0.799697	−	0.461705i
$45$	−3.00625	+	3.23321i	−0.448145	+	0.481979i
$46$	0.976779	+	1.69183i	0.144018	+	0.249447i
$47$	3.84662	−	6.66255i	0.561088	−	0.971832i	−0.436314	−	0.899794i	$-0.643716\pi$
$47$	3.84662	−	6.66255i	0.561088	−	0.971832i	0.997402	−	0.0720378i	$-0.0229502\pi$
$48$	−1.02925	+	1.39307i	−0.148560	+	0.201072i
$49$	−6.79210	+	1.69334i	−0.970300	+	0.241905i
$50$		−	2.83431i		−	0.400832i
$51$	0.167335	+	0.384080i	0.0234315	+	0.0537820i
$52$	−0.866025	+	0.500000i	−0.120096	+	0.0693375i
$53$	6.14856	−	3.54987i	0.844569	−	0.487612i	−0.0142454	−	0.999899i	$-0.504535\pi$
$53$	6.14856	−	3.54987i	0.844569	−	0.487612i	0.858815	+	0.512286i	$0.171201\pi$
$54$	−3.38323	−	3.94382i	−0.460400	−	0.536686i
$55$		−	9.01403i		−	1.21545i
$56$	2.62603	−	0.322414i	0.350918	−	0.0430844i
$57$	−6.04370	−	4.46531i	−0.800508	−	0.591445i
$58$	1.50150	−	2.60068i	0.197157	−	0.341486i
$59$	6.21031	+	10.7566i	0.808514	+	1.40039i	0.913893	+	0.405955i	$0.133061\pi$
$59$	6.21031	+	10.7566i	0.808514	+	1.40039i	−0.105379	+	0.994432i	$0.533606\pi$
$60$	−2.53276	−	0.286708i	−0.326978	−	0.0370139i
$61$	11.5260	+	6.65454i	1.47575	+	0.852026i	0.999626	−	0.0273504i	$-0.00870698\pi$
$61$	11.5260	+	6.65454i	1.47575	+	0.852026i	0.476127	+	0.879377i	$0.342040\pi$
$62$	1.12594			0.142994
$63$	−0.818269	+	7.89496i	−0.103092	+	0.994672i
$64$	−1.00000			−0.125000
$65$	−1.27447	−	0.735814i	−0.158078	−	0.0912665i
$66$	10.5418	+	1.19334i	1.29761	+	0.146890i
$67$	6.58500	+	11.4055i	0.804485	+	1.39341i	0.916638	+	0.399718i	$0.130892\pi$
$67$	6.58500	+	11.4055i	0.804485	+	1.39341i	−0.112153	+	0.993691i	$0.535775\pi$
$68$	−0.120940	+	0.209475i	−0.0146662	+	0.0254025i
$69$	−2.72144	−	2.01070i	−0.327623	−	0.242060i
$70$	2.34318	+	3.10956i	0.280063	+	0.371663i
$71$		−	9.38944i		−	1.11432i	−0.830405	−	0.557161i	$-0.811891\pi$
$71$		−	9.38944i		−	1.11432i	0.830405	−	0.557161i	$-0.188109\pi$
$72$	0.670607	−	2.92409i	0.0790317	−	0.344607i
$73$	−8.77999	+	5.06913i	−1.02762	+	0.593297i	−0.916302	−	0.400488i	$-0.868841\pi$
$73$	−8.77999	+	5.06913i	−1.02762	+	0.593297i	−0.111318	+	0.993785i	$0.535507\pi$
$74$	−4.50831	+	2.60288i	−0.524081	+	0.302578i
$75$	1.96080	+	4.50058i	0.226413	+	0.519682i
$76$		−	4.33841i		−	0.497650i
$77$	−9.75277	−	12.9426i	−1.11143	−	1.47495i
$78$	1.02925	−	1.39307i	0.116540	−	0.157734i
$79$	2.38049	−	4.12313i	0.267826	−	0.463888i	−0.700474	−	0.713678i	$-0.747028\pi$
$79$	2.38049	−	4.12313i	0.267826	−	0.463888i	0.968300	+	0.249789i	$0.0803614\pi$
$80$	−0.735814	−	1.27447i	−0.0822665	−	0.142490i
$81$	8.10057	+	3.92182i	0.900064	+	0.435758i
$82$	−3.98861	−	2.30282i	−0.440468	−	0.254304i
$83$	9.45528			1.03785			0.518926	−	0.854819i	$-0.326332\pi$
$83$	9.45528			1.03785			0.518926	+	0.854819i	$0.326332\pi$
$84$	−3.94681	+	2.32867i	−0.430632	+	0.254078i
$85$	−0.355958			−0.0386091
$86$	−1.07975	−	0.623395i	−0.116433	−	0.0672225i
$87$	−0.585058	+	5.16836i	−0.0627248	+	0.554106i
$88$	3.06261	+	5.30459i	0.326475	+	0.565471i
$89$	1.82263	−	3.15689i	0.193198	−	0.334630i	−0.753110	−	0.657895i	$-0.771447\pi$
$89$	1.82263	−	3.15689i	0.193198	−	0.334630i	0.946308	+	0.323265i	$0.104781\pi$
$90$	4.22010	−	1.29692i	0.444837	−	0.136707i
$91$	−2.62603	+	0.322414i	−0.275283	+	0.0337981i
$92$		−	1.95356i		−	0.203673i
$93$	−1.78786	+	0.778930i	−0.185393	+	0.0807713i
$94$	−6.66255	+	3.84662i	−0.687189	+	0.396749i
$95$	5.52916	−	3.19226i	0.567280	−	0.327519i
$96$	1.58789	−	0.691807i	0.162064	−	0.0706073i
$97$			7.44495i			0.755920i	0.925822	+	0.377960i	$0.123374\pi$
$97$			7.44495i			0.755920i	−0.925822	+	0.377960i	$0.876626\pi$
$98$	6.72880	+	1.92958i	0.679711	+	0.194917i
$99$	−17.5649	+	5.39803i	−1.76534	+	0.542523i
$100$	−1.41716	+	2.45459i	−0.141716	+	0.245459i
$101$	−1.22181	−	2.11624i	−0.121575	−	0.210574i	0.798814	−	0.601578i	$-0.205461\pi$
$101$	−1.22181	−	2.11624i	−0.121575	−	0.210574i	−0.920389	+	0.391004i	$0.872128\pi$
$102$	0.0471241	−	0.416290i	0.00466598	−	0.0412189i
$103$	−7.84682	−	4.53036i	−0.773170	−	0.446390i	0.0608342	−	0.998148i	$-0.480624\pi$
$103$	−7.84682	−	4.53036i	−0.773170	−	0.446390i	−0.834004	+	0.551758i	$0.813957\pi$
$104$	1.00000			0.0980581
$105$	−5.87193	−	3.31662i	−0.573042	−	0.323669i
$106$	−7.09974			−0.689588
$107$	7.06421	+	4.07852i	0.682923	+	0.394286i	0.800955	−	0.598724i	$-0.204325\pi$
$107$	7.06421	+	4.07852i	0.682923	+	0.394286i	−0.118033	+	0.993010i	$0.537659\pi$
$108$	0.958053	+	5.10707i	0.0921887	+	0.491428i
$109$	4.09144	+	7.08658i	0.391889	+	0.678771i	0.992699	−	0.120621i	$-0.0384886\pi$
$109$	4.09144	+	7.08658i	0.391889	+	0.678771i	−0.600810	+	0.799392i	$0.705155\pi$
$110$	−4.50702	+	7.80638i	−0.429727	+	0.744309i
$111$	5.35803	−	7.25197i	0.508562	−	0.688326i
$112$	−2.43542	−	1.03380i	−0.230125	−	0.0976847i
$113$		−	9.84547i		−	0.926184i	−0.886310	−	0.463092i	$-0.846740\pi$
$113$		−	9.84547i		−	0.926184i	0.886310	−	0.463092i	$-0.153260\pi$
$114$	3.00134	+	6.88893i	0.281101	+	0.645207i
$115$	2.48975	−	1.43746i	0.232170	−	0.134043i
$116$	−2.60068	+	1.50150i	−0.241467	+	0.139411i
$117$	−0.670607	+	2.92409i	−0.0619976	+	0.270332i
$118$		−	12.4206i		−	1.14341i
$119$	−0.511094	+	0.385130i	−0.0468519	+	0.0353048i
$120$	2.05008	+	1.51468i	0.187146	+	0.138270i
$121$	13.2591	−	22.9654i	1.20537	−	2.08777i
$122$	−6.65454	−	11.5260i	−0.602474	−	1.04351i
$123$	7.92659	+	0.897290i	0.714717	+	0.0809059i
$124$	−0.975089	−	0.562968i	−0.0875656	−	0.0505560i
$125$	−11.5292			−1.03120
$126$	4.65612	−	6.42810i	0.414800	−	0.572661i
$127$	−19.8655			−1.76278			−0.881391	−	0.472387i	$-0.843392\pi$
$127$	−19.8655			−1.76278			−0.881391	+	0.472387i	$0.843392\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	2.14580	+	0.242905i	0.188927	+	0.0213866i
$130$	0.735814	+	1.27447i	0.0645352	+	0.111778i
$131$	−0.561211	+	0.972047i	−0.0490333	+	0.0849281i	−0.889500	−	0.456935i	$-0.848947\pi$
$131$	−0.561211	+	0.972047i	−0.0490333	+	0.0849281i	0.840467	+	0.541863i	$0.182281\pi$
$132$	−8.53284	−	6.30438i	−0.742688	−	0.548726i
$133$	4.48504	−	10.5658i	0.388902	−	0.916174i
$134$		−	13.1700i		−	1.13771i
$135$	−5.80384	+	4.97886i	−0.499515	+	0.428512i
$136$	0.209475	−	0.120940i	0.0179623	−	0.0103705i
$137$	7.96943	−	4.60115i	0.680875	−	0.393103i	−0.119310	−	0.992857i	$-0.538068\pi$
$137$	7.96943	−	4.60115i	0.680875	−	0.393103i	0.800184	+	0.599754i	$0.204735\pi$
$138$	1.35149	+	3.10204i	0.115046	+	0.264063i
$139$		−	15.4994i		−	1.31464i	−0.753611	−	0.657320i	$-0.771690\pi$
$139$		−	15.4994i		−	1.31464i	0.753611	−	0.657320i	$-0.228310\pi$
$140$	−0.474473	−	3.86454i	−0.0401003	−	0.326614i
$141$	7.91829	−	10.7172i	0.666840	−	0.902553i
$142$	−4.69472	+	8.13150i	−0.393972	+	0.682380i
$143$	−3.06261	−	5.30459i	−0.256108	−	0.443592i
$144$	−2.04281	+	2.19703i	−0.170234	+	0.183086i
$145$	−3.82724	−	2.20966i	−0.317835	−	0.183502i
$146$	10.1383			0.839049
$147$	−12.0195	+	1.59107i	−0.991352	+	0.131229i
$148$	5.20575			0.427910
$149$	−4.52977	−	2.61527i	−0.371094	−	0.214251i	0.302843	−	0.953041i	$-0.402064\pi$
$149$	−4.52977	−	2.61527i	−0.371094	−	0.214251i	−0.673936	+	0.738790i	$0.735398\pi$
$150$	0.552191	−	4.87802i	0.0450862	−	0.398288i
$151$	−12.1680	−	21.0756i	−0.990216	−	1.71510i	−0.615956	−	0.787780i	$-0.711230\pi$
$151$	−12.1680	−	21.0756i	−0.990216	−	1.71510i	−0.374260	−	0.927324i	$-0.622103\pi$
$152$	−2.16920	+	3.75717i	−0.175946	+	0.304747i
$153$	0.213165	+	0.693625i	0.0172333	+	0.0560763i
$154$	1.97485	+	16.0850i	0.159138	+	1.29617i
$155$		−	1.65696i		−	0.133090i
$156$	−1.58789	+	0.691807i	−0.127133	+	0.0553889i
$157$	14.7389	−	8.50948i	1.17629	−	0.679131i	0.221136	−	0.975243i	$-0.429024\pi$
$157$	14.7389	−	8.50948i	1.17629	−	0.679131i	0.955153	+	0.296113i	$0.0956903\pi$
$158$	−4.12313	+	2.38049i	−0.328019	+	0.189382i
$159$	11.2736	−	4.91165i	0.894057	−	0.389519i
$160$			1.47163i			0.116342i
$161$	2.01958	−	4.75773i	0.159166	−	0.374962i
$162$	−5.05439	−	7.44669i	−0.397110	−	0.585067i
$163$	4.78175	−	8.28223i	0.374535	−	0.648714i	−0.615722	−	0.787964i	$-0.711136\pi$
$163$	4.78175	−	8.28223i	0.374535	−	0.648714i	0.990257	+	0.139249i	$0.0444689\pi$
$164$	2.30282	+	3.98861i	0.179820	+	0.311458i
$165$	1.75615	−	15.5137i	0.136716	−	1.20774i
$166$	−8.18851	−	4.72764i	−0.635552	−	0.366936i
$167$	−17.5663			−1.35932			−0.679659	−	0.733528i	$-0.737872\pi$
$167$	−17.5663			−1.35932			−0.679659	+	0.733528i	$0.737872\pi$
$168$	4.58237	−	0.0432793i	0.353538	−	0.00333907i
$169$	−1.00000			−0.0769231
$170$	0.308269	+	0.177979i	0.0236431	+	0.0136504i
$171$	−9.53162	−	8.86253i	−0.728901	−	0.677734i
$172$	0.623395	+	1.07975i	0.0475335	+	0.0823304i
$173$	−6.79512	+	11.7695i	−0.516624	+	0.894818i	0.483190	+	0.875515i	$0.339478\pi$
$173$	−6.79512	+	11.7695i	−0.516624	+	0.894818i	−0.999814	+	0.0193028i	$0.993855\pi$
$174$	3.09085	−	4.18340i	0.234317	−	0.317143i
$175$	−5.98891	+	4.51289i	−0.452719	+	0.341142i
$176$		−	6.12521i		−	0.461705i
$177$	8.59267	+	19.7226i	0.645865	+	1.48244i
$178$	−3.15689	+	1.82263i	−0.236619	+	0.136612i
$179$	−8.79586	+	5.07829i	−0.657434	+	0.379569i	−0.791298	−	0.611430i	$-0.790595\pi$
$179$	−8.79586	+	5.07829i	−0.657434	+	0.379569i	0.133865	+	0.991000i	$0.457261\pi$
$180$	−4.30317	−	0.986883i	−0.320739	−	0.0735579i
$181$			6.07777i			0.451757i	0.974155	+	0.225879i	$0.0725253\pi$
$181$			6.07777i			0.451757i	−0.974155	+	0.225879i	$0.927475\pi$
$182$	2.43542	+	1.03380i	0.180525	+	0.0766302i
$183$	18.5405	+	13.6984i	1.37055	+	1.01261i
$184$	−0.976779	+	1.69183i	−0.0720091	+	0.124723i
$185$	3.83046	+	6.63456i	0.281621	+	0.487783i
$186$	1.93780	+	0.219359i	0.142087	+	0.0160842i
$187$	−1.28308	−	0.740784i	−0.0938278	−	0.0541715i
$188$	7.69324			0.561088
$189$	−2.94642	+	13.4283i	−0.214320	+	0.976763i
$190$	−6.38452			−0.463182
$191$	5.48179	+	3.16492i	0.396649	+	0.229005i	0.685037	−	0.728508i	$-0.259786\pi$
$191$	5.48179	+	3.16492i	0.396649	+	0.229005i	−0.288388	+	0.957514i	$0.593119\pi$
$192$	−1.72106	−	0.194824i	−0.124207	−	0.0140602i
$193$	2.63368	+	4.56167i	0.189576	+	0.328356i	0.945109	−	0.326755i	$-0.105955\pi$
$193$	2.63368	+	4.56167i	0.189576	+	0.328356i	−0.755533	+	0.655111i	$0.772622\pi$
$194$	3.72247	−	6.44752i	0.267258	−	0.462905i
$195$	−2.05008	−	1.51468i	−0.146809	−	0.108468i
$196$	−4.86252	−	5.03546i	−0.347323	−	0.359676i
$197$		−	1.52379i		−	0.108565i	−0.998526	−	0.0542827i	$-0.982713\pi$
$197$		−	1.52379i		−	0.108565i	0.998526	−	0.0542827i	$-0.0172872\pi$
$198$	17.9106	+	4.10761i	1.27285	+	0.291915i
$199$	−2.93279	+	1.69325i	−0.207900	+	0.120031i	−0.600335	−	0.799749i	$-0.704966\pi$
$199$	−2.93279	+	1.69325i	−0.207900	+	0.120031i	0.392435	+	0.919780i	$0.371633\pi$
$200$	2.45459	−	1.41716i	0.173565	−	0.100208i
$201$	9.11109	+	20.9125i	0.642647	+	1.47506i
$202$			2.44363i			0.171933i
$203$	−7.88600	+	0.968212i	−0.553489	+	0.0679551i
$204$	−0.248956	+	0.336956i	−0.0174304	+	0.0235916i
$205$	−3.38890	+	5.86975i	−0.236691	+	0.409961i
$206$	4.53036	+	7.84682i	0.315645	+	0.546714i
$207$	−4.29203	−	3.99074i	−0.298317	−	0.277376i
$208$	−0.866025	−	0.500000i	−0.0600481	−	0.0346688i
$209$	26.5737			1.83814
$210$	3.42693	+	5.80824i	0.236481	+	0.400806i
$211$	−21.4236			−1.47486			−0.737432	−	0.675421i	$-0.763962\pi$
$211$	−21.4236			−1.47486			−0.737432	+	0.675421i	$0.763962\pi$
$212$	6.14856	+	3.54987i	0.422285	+	0.243806i
$213$	1.82929	−	16.1598i	0.125341	−	1.10725i
$214$	−4.07852	−	7.06421i	−0.278802	−	0.482899i
$215$	−0.917406	+	1.58899i	−0.0625666	+	0.108369i
$216$	1.72384	−	4.90188i	0.117292	−	0.333530i
$217$	−1.79275	−	2.37911i	−0.121700	−	0.161504i
$218$		−	8.18287i		−	0.554214i
$219$	−16.0985	+	7.01372i	−1.08783	+	0.473943i
$220$	7.80638	−	4.50702i	0.526306	−	0.303863i
$221$	−0.209475	+	0.120940i	−0.0140908	+	0.00813532i
$222$	−8.26617	+	3.60138i	−0.554789	+	0.241708i
$223$		−	1.44986i		−	0.0970896i	−0.998821	−	0.0485448i	$-0.984542\pi$
$223$		−	1.44986i		−	0.0970896i	0.998821	−	0.0485448i	$-0.0154584\pi$
$224$	1.59224	+	2.11300i	0.106386	+	0.141181i
$225$	2.49783	+	8.12777i	0.166522	+	0.541852i
$226$	−4.92273	+	8.52643i	−0.327455	+	0.567169i
$227$	10.2279	+	17.7152i	0.678849	+	1.17580i	0.975328	+	0.220762i	$0.0708544\pi$
$227$	10.2279	+	17.7152i	0.678849	+	1.17580i	−0.296478	+	0.955040i	$0.595812\pi$
$228$	0.845225	−	7.46666i	0.0559764	−	0.494491i
$229$	18.3031	+	10.5673i	1.20950	+	0.698308i	0.962651	−	0.270745i	$-0.0872700\pi$
$229$	18.3031	+	10.5673i	1.20950	+	0.698308i	0.246853	+	0.969053i	$0.420603\pi$
$230$	−2.87491			−0.189566
$231$	−14.2636	−	24.1750i	−0.938474	−	1.59060i
$232$	3.00301			0.197157
$233$	−6.22889	−	3.59625i	−0.408068	−	0.235598i	0.281891	−	0.959446i	$-0.409038\pi$
$233$	−6.22889	−	3.59625i	−0.408068	−	0.235598i	−0.689959	+	0.723848i	$0.742372\pi$
$234$	2.04281	−	2.19703i	0.133542	−	0.143624i
$235$	5.66080	+	9.80479i	0.369270	+	0.639594i
$236$	−6.21031	+	10.7566i	−0.404257	+	0.700193i
$237$	4.90025	−	6.63237i	0.318305	−	0.430819i
$238$	0.635186	−	0.0779856i	0.0411730	−	0.00505505i
$239$		−	0.933935i		−	0.0604113i	−0.999544	−	0.0302056i	$-0.990384\pi$
$239$		−	0.933935i		−	0.0604113i	0.999544	−	0.0302056i	$-0.00961621\pi$
$240$	−1.01808	−	2.33679i	−0.0657170	−	0.150839i
$241$	13.4530	−	7.76708i	0.866582	−	0.500322i	0.000371405	−	1.00000i	$-0.499882\pi$
$241$	13.4530	−	7.76708i	0.866582	−	0.500322i	0.866211	+	0.499678i	$0.166548\pi$
$242$	−22.9654	+	13.2591i	−1.47627	+	0.852327i
$243$	13.1775	+	8.32787i	0.845337	+	0.534233i
$244$			13.3091i			0.852026i
$245$	2.83962	−	9.90229i	0.181416	−	0.632634i
$246$	−6.41599	−	4.74037i	−0.409068	−	0.302235i
$247$	2.16920	−	3.75717i	0.138023	−	0.239063i
$248$	0.562968	+	0.975089i	0.0357485	+	0.0619182i
$249$	16.2731	+	1.84211i	1.03127	+	0.116739i
$250$	9.98457	+	5.76460i	0.631480	+	0.364585i
$251$	17.5062			1.10498			0.552489	−	0.833520i	$-0.313678\pi$
$251$	17.5062			1.10498			0.552489	+	0.833520i	$0.313678\pi$
$252$	−7.24637	+	3.23884i	−0.456479	+	0.204028i
$253$	11.9660			0.752293
$254$	17.2041	+	9.93277i	1.07948	+	0.623238i
$255$	−0.612625	−	0.0693491i	−0.0383640	−	0.00434281i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−8.58522	+	14.8700i	−0.535531	+	0.927567i	0.463606	+	0.886041i	$0.346555\pi$
$257$	−8.58522	+	14.8700i	−0.535531	+	0.927567i	−0.999137	+	0.0415259i	$0.986778\pi$
$258$	−1.73687	−	1.28326i	−0.108133	−	0.0798924i
$259$	12.6782	+	5.38170i	0.787784	+	0.334402i
$260$		−	1.47163i		−	0.0912665i
$261$	−2.01384	+	8.78106i	−0.124653	+	0.543534i
$262$	0.972047	−	0.561211i	0.0600532	−	0.0346718i
$263$	−24.5992	+	14.2023i	−1.51685	+	0.875753i	−0.517045	+	0.855958i	$0.672968\pi$
$263$	−24.5992	+	14.2023i	−1.51685	+	0.875753i	−0.999804	+	0.0197947i	$0.993699\pi$
$264$	4.23746	+	9.72618i	0.260798	+	0.598605i
$265$			10.4482i			0.641827i
$266$	−9.16708	+	6.90777i	−0.562069	+	0.423542i
$267$	3.75189	−	5.07810i	0.229612	−	0.310775i
$268$	−6.58500	+	11.4055i	−0.402243	+	0.696705i
$269$	−1.10919	−	1.92117i	−0.0676285	−	0.117136i	0.830228	−	0.557423i	$-0.188210\pi$
$269$	−1.10919	−	1.92117i	−0.0676285	−	0.117136i	−0.897857	+	0.440287i	$0.854877\pi$
$270$	7.51570	−	1.40990i	0.457391	−	0.0858037i
$271$	9.69571	+	5.59782i	0.588972	+	0.340043i	0.764691	−	0.644397i	$-0.222892\pi$
$271$	9.69571	+	5.59782i	0.588972	+	0.340043i	−0.175719	+	0.984440i	$0.556225\pi$
$272$	−0.241880			−0.0146662
$273$	−4.58237	+	0.0432793i	−0.277338	+	0.00261938i
$274$	−9.20231			−0.555932
$275$	−15.0348	−	8.68037i	−0.906636	−	0.523446i
$276$	0.380600	−	3.36219i	0.0229094	−	0.202380i
$277$	2.65822	+	4.60417i	0.159717	+	0.276638i	0.934767	−	0.355263i	$-0.115609\pi$
$277$	2.65822	+	4.60417i	0.159717	+	0.276638i	−0.775050	+	0.631900i	$0.782275\pi$
$278$	−7.74969	+	13.4229i	−0.464796	+	0.805050i
$279$	−3.22877	+	0.992266i	−0.193302	+	0.0594054i
$280$	−1.52137	+	3.58403i	−0.0909190	+	0.214187i
$281$		−	10.6377i		−	0.634593i	−0.948326	−	0.317296i	$-0.897225\pi$
$281$		−	10.6377i		−	0.634593i	0.948326	−	0.317296i	$-0.102775\pi$
$282$	−12.2160	+	5.32224i	−0.727455	+	0.316935i
$283$	−0.252739	+	0.145919i	−0.0150238	+	0.00867399i	−0.507493	−	0.861656i	$-0.669428\pi$
$283$	−0.252739	+	0.145919i	−0.0150238	+	0.00867399i	0.492469	+	0.870330i	$0.336094\pi$
$284$	8.13150	−	4.69472i	0.482516	−	0.278580i
$285$	10.1379	−	4.41686i	0.600520	−	0.261632i
$286$			6.12521i			0.362191i
$287$	1.48492	+	12.0946i	0.0876523	+	0.713921i
$288$	2.86764	−	0.881281i	0.168977	−	0.0519300i
$289$	8.47075	−	14.6718i	0.498279	−	0.863045i
$290$	2.20966	+	3.82724i	0.129756	+	0.224743i
$291$	−1.45045	+	12.8132i	−0.0850271	+	0.751123i
$292$	−8.77999	−	5.06913i	−0.513810	−	0.296648i
$293$	29.4133			1.71834			0.859171	−	0.511689i	$-0.170980\pi$
$293$	29.4133			1.71834			0.859171	+	0.511689i	$0.170980\pi$
$294$	11.2047	+	4.63184i	0.653473	+	0.270135i
$295$	−18.2785			−1.06422
$296$	−4.50831	−	2.60288i	−0.262040	−	0.151289i
$297$	−31.2819	+	5.86828i	−1.81516	+	0.340512i
$298$	2.61527	+	4.52977i	0.151498	+	0.262403i
$299$	0.976779	−	1.69183i	0.0564886	−	0.0978411i
$300$	−2.91722	+	3.94839i	−0.168426	+	0.227960i
$301$	0.401983	+	3.27411i	0.0231699	+	0.188717i
$302$			24.3360i			1.40038i
$303$	−1.69052	−	3.88021i	−0.0971177	−	0.222913i
$304$	3.75717	−	2.16920i	0.215489	−	0.124412i
$305$	−16.9620	+	9.79300i	−0.971240	+	0.560746i
$306$	0.162207	−	0.707279i	0.00927273	−	0.0404325i
$307$			26.2231i			1.49663i	0.663343	+	0.748316i	$0.269137\pi$
$307$			26.2231i			1.49663i	−0.663343	+	0.748316i	$0.730863\pi$
$308$	6.33223	−	14.9174i	0.360812	−	0.850000i
$309$	−12.6222	−	9.32577i	−0.718053	−	0.530524i
$310$	−0.828479	+	1.43497i	−0.0470545	+	0.0815007i
$311$	9.67225	+	16.7528i	0.548463	+	0.949966i	0.998380	+	0.0568956i	$0.0181202\pi$
$311$	9.67225	+	16.7528i	0.548463	+	0.949966i	−0.449917	+	0.893070i	$0.648546\pi$
$312$	1.72106	+	0.194824i	0.0974358	+	0.0110297i
$313$	17.6672	+	10.2001i	0.998608	+	0.576546i	0.907836	−	0.419325i	$-0.137733\pi$
$313$	17.6672	+	10.2001i	0.998608	+	0.576546i	0.0907717	+	0.995872i	$0.471067\pi$
$314$	−17.0190			−0.960436
$315$	−9.45978	−	6.85208i	−0.532998	−	0.386071i
$316$	4.76098			0.267826
$317$	−27.9888	−	16.1594i	−1.57201	−	0.907600i	−0.995923	−	0.0902118i	$-0.971246\pi$
$317$	−27.9888	−	16.1594i	−1.57201	−	0.907600i	−0.576087	−	0.817388i	$-0.695421\pi$
$318$	−12.2191	−	1.38320i	−0.685212	−	0.0775660i
$319$	−9.19703	−	15.9297i	−0.514935	−	0.891893i
$320$	0.735814	−	1.27447i	0.0411333	−	0.0712449i
$321$	11.3633	+	8.39565i	0.634239	+	0.468600i
$322$	−4.12788	+	3.11052i	−0.230038	+	0.173343i
$323$		−	1.04938i		−	0.0583888i
$324$	0.653888	+	8.97621i	0.0363271	+	0.498679i
$325$	−2.45459	+	1.41716i	−0.136156	+	0.0786096i
$326$	−8.28223	+	4.78175i	−0.458710	+	0.264837i
$327$	5.66097	+	12.9935i	0.313052	+	0.718543i
$328$		−	4.60565i		−	0.254304i
$329$	18.7363	+	7.95326i	1.03296	+	0.438477i
$330$	−9.27771	+	12.5572i	−0.510721	+	0.691249i
$331$	13.4800	−	23.3481i	0.740929	−	1.28333i	−0.211144	−	0.977455i	$-0.567719\pi$
$331$	13.4800	−	23.3481i	0.740929	−	1.28333i	0.952073	−	0.305871i	$-0.0989477\pi$
$332$	4.72764	+	8.18851i	0.259463	+	0.449403i
$333$	10.6343	−	11.4372i	0.582758	−	0.626754i
$334$	15.2128	+	8.78313i	0.832409	+	0.480592i
$335$	−19.3813			−1.05892
$336$	−3.99009	−	2.25370i	−0.217677	−	0.122950i
$337$	32.9960			1.79741			0.898704	−	0.438557i	$-0.144510\pi$
$337$	32.9960			1.79741			0.898704	+	0.438557i	$0.144510\pi$
$338$	0.866025	+	0.500000i	0.0471056	+	0.0271964i
$339$	1.91813	−	16.9446i	0.104179	−	0.920306i
$340$	−0.177979	−	0.308269i	−0.00965227	−	0.0167182i
$341$	3.44830	−	5.97262i	0.186736	−	0.323436i
$342$	3.82336	+	12.4410i	0.206744	+	0.672731i
$343$	−6.63663	−	17.2903i	−0.358344	−	0.933590i
$344$		−	1.24679i		−	0.0672225i
$345$	4.56505	−	1.98888i	0.245774	−	0.107078i
$346$	11.7695	−	6.79512i	0.632732	−	0.365308i
$347$	−29.4603	+	17.0089i	−1.58151	+	0.913086i	−0.586873	+	0.809679i	$0.699641\pi$
$347$	−29.4603	+	17.0089i	−1.58151	+	0.913086i	−0.994639	+	0.103407i	$0.967025\pi$
$348$	−4.76846	+	2.07750i	−0.255616	+	0.111366i
$349$		−	14.2931i		−	0.765091i	−0.923937	−	0.382545i	$-0.875048\pi$
$349$		−	14.2931i		−	0.765091i	0.923937	−	0.382545i	$-0.124952\pi$
$350$	7.44299	−	0.913821i	0.397845	−	0.0488458i
$351$	−1.72384	+	4.90188i	−0.0920115	+	0.261643i
$352$	−3.06261	+	5.30459i	−0.163237	+	0.282735i
$353$	12.1947	+	21.1218i	0.649057	+	1.12420i	0.983348	+	0.181730i	$0.0581697\pi$
$353$	12.1947	+	21.1218i	0.649057	+	1.12420i	−0.334291	+	0.942470i	$0.608497\pi$
$354$	2.41983	−	21.3766i	0.128613	−	1.13615i
$355$	11.9665	+	6.90888i	0.635118	+	0.366685i
$356$	3.64526			0.193198
$357$	−0.954656	+	0.563259i	−0.0505257	+	0.0298108i
$358$	10.1566			0.536792
$359$	−3.79649	−	2.19190i	−0.200371	−	0.115684i	0.396458	−	0.918053i	$-0.370239\pi$
$359$	−3.79649	−	2.19190i	−0.200371	−	0.115684i	−0.596828	+	0.802369i	$0.703573\pi$
$360$	3.23321	+	3.00625i	0.170405	+	0.158443i
$361$	−0.0891083	−	0.154340i	−0.00468991	−	0.00812317i
$362$	3.03889	−	5.26351i	0.159720	−	0.276644i
$363$	27.2939	−	36.9417i	1.43256	−	1.93894i
$364$	−1.59224	−	2.11300i	−0.0834558	−	0.110752i
$365$		−	14.9198i		−	0.780936i
$366$	−9.20731	−	21.1334i	−0.481274	−	1.10466i
$367$	14.4278	−	8.32987i	0.753123	−	0.434816i	−0.0736983	−	0.997281i	$-0.523480\pi$
$367$	14.4278	−	8.32987i	0.753123	−	0.434816i	0.826821	+	0.562465i	$0.190147\pi$
$368$	1.69183	−	0.976779i	0.0881928	−	0.0509181i
$369$	13.4673	+	3.08858i	0.701081	+	0.160785i
$370$		−	7.66093i		−	0.398273i
$371$	11.3045	+	15.0018i	0.586898	+	0.778854i
$372$	−1.56851	−	1.15887i	−0.0813232	−	0.0600847i
$373$	2.34560	−	4.06270i	0.121451	−	0.210359i	−0.798889	−	0.601478i	$-0.794579\pi$
$373$	2.34560	−	4.06270i	0.121451	−	0.210359i	0.920340	+	0.391119i	$0.127912\pi$
$374$	0.740784	+	1.28308i	0.0383050	+	0.0663463i
$375$	−19.8424	−	2.24616i	−1.02466	−	0.115991i
$376$	−6.66255	−	3.84662i	−0.343595	−	0.198374i
$377$	−3.00301			−0.154663
$378$	9.26581	−	10.1560i	0.476582	−	0.522369i
$379$	−23.1300			−1.18811			−0.594055	−	0.804425i	$-0.702474\pi$
$379$	−23.1300			−1.18811			−0.594055	+	0.804425i	$0.702474\pi$
$380$	5.52916	+	3.19226i	0.283640	+	0.163760i
$381$	−34.1898	−	3.87028i	−1.75160	−	0.198281i
$382$	−3.16492	−	5.48179i	−0.161931	−	0.280473i
$383$	12.1551	−	21.0533i	0.621099	−	1.07577i	−0.368183	−	0.929754i	$-0.620020\pi$
$383$	12.1551	−	21.0533i	0.621099	−	1.07577i	0.989281	−	0.146021i	$-0.0466468\pi$
$384$	1.39307	+	1.02925i	0.0710897	+	0.0525238i
$385$	23.6711	−	2.90625i	1.20639	−	0.148116i
$386$		−	5.26736i		−	0.268101i
$387$	3.64573	+	0.836106i	0.185323	+	0.0425017i
$388$	−6.44752	+	3.72247i	−0.327323	+	0.188980i
$389$	3.20230	−	1.84885i	0.162363	−	0.0937402i	−0.416617	−	0.909082i	$-0.636784\pi$
$389$	3.20230	−	1.84885i	0.162363	−	0.0937402i	0.578980	+	0.815342i	$0.303451\pi$
$390$	1.01808	+	2.33679i	0.0515526	+	0.118328i
$391$		−	0.472527i		−	0.0238967i
$392$	1.69334	+	6.79210i	0.0855265	+	0.343053i
$393$	−1.15526	+	1.56361i	−0.0582749	+	0.0788738i
$394$	−0.761894	+	1.31964i	−0.0383836	+	0.0664824i
$395$	3.50320	+	6.06772i	0.176265	+	0.305300i
$396$	−13.4573	−	12.5126i	−0.676253	−	0.628783i
$397$	−28.7638	−	16.6068i	−1.44361	−	0.833471i	−0.445526	−	0.895269i	$-0.646983\pi$
$397$	−28.7638	−	16.6068i	−1.44361	−	0.833471i	−0.998089	+	0.0617976i	$0.980317\pi$
$398$	3.38650			0.169750
$399$	9.77749	−	17.3106i	0.489487	−	0.866616i
$400$	−2.83431			−0.141716
$401$	−15.2442	−	8.80123i	−0.761258	−	0.439512i	0.0684893	−	0.997652i	$-0.478182\pi$
$401$	−15.2442	−	8.80123i	−0.761258	−	0.439512i	−0.829747	+	0.558139i	$0.811515\pi$
$402$	2.56583	−	22.6663i	0.127972	−	1.13049i
$403$	−0.562968	−	0.975089i	−0.0280434	−	0.0485726i
$404$	1.22181	−	2.11624i	0.0607875	−	0.105287i
$405$	−10.9588	+	7.43818i	−0.544545	+	0.369606i
$406$	7.31358	+	3.10451i	0.362967	+	0.154074i
$407$			31.8863i			1.58055i
$408$	0.384080	−	0.167335i	0.0190148	−	0.00828429i
$409$	−24.0466	+	13.8833i	−1.18903	+	0.686487i	−0.958086	−	0.286480i	$-0.907515\pi$
$409$	−24.0466	+	13.8833i	−1.18903	+	0.686487i	−0.230944	+	0.972967i	$0.574181\pi$
$410$	5.86975	−	3.38890i	0.289886	−	0.167366i
$411$	14.6123	−	6.36622i	0.720771	−	0.314023i
$412$		−	9.06073i		−	0.446390i
$413$	−26.2448	+	19.7766i	−1.29142	+	0.973140i
$414$	1.72163	+	5.60210i	0.0846137	+	0.275328i
$415$	−6.95733	+	12.0504i	−0.341522	+	0.591533i
$416$	0.500000	+	0.866025i	0.0245145	+	0.0424604i
$417$	3.01965	−	26.6754i	0.147873	−	1.30630i
$418$	−23.0135	−	13.2868i	−1.12563	−	0.649880i
$419$	−21.2291			−1.03711			−0.518555	−	0.855044i	$-0.673530\pi$
$419$	−21.2291			−1.03711			−0.518555	+	0.855044i	$0.673530\pi$
$420$	−0.0636911	−	6.74355i	−0.00310781	−	0.329051i
$421$	−7.23407			−0.352567			−0.176283	−	0.984339i	$-0.556408\pi$
$421$	−7.23407			−0.352567			−0.176283	+	0.984339i	$0.556408\pi$
$422$	18.5534	+	10.7118i	0.903166	+	0.521443i
$423$	15.7158	−	16.9023i	0.764129	−	0.821818i
$424$	−3.54987	−	6.14856i	−0.172397	−	0.298600i
$425$	−0.342782	+	0.593716i	−0.0166274	+	0.0287995i
$426$	−9.66410	+	13.0801i	−0.468227	+	0.633735i
$427$	−13.7589	+	32.4132i	−0.665840	+	1.56858i
$428$			8.15704i			0.394286i
$429$	−4.23746	−	9.72618i	−0.204587	−	0.469584i
$430$	1.58899	−	0.917406i	0.0766281	−	0.0442413i
$431$	24.1661	−	13.9523i	1.16404	−	0.672060i	0.211772	−	0.977319i	$-0.432076\pi$
$431$	24.1661	−	13.9523i	1.16404	−	0.672060i	0.952269	+	0.305259i	$0.0987431\pi$
$432$	−3.94382	+	3.38323i	−0.189747	+	0.162776i
$433$		−	14.4459i		−	0.694224i	−0.937824	−	0.347112i	$-0.887162\pi$
$433$		−	14.4459i		−	0.694224i	0.937824	−	0.347112i	$-0.112838\pi$
$434$	0.363017	+	2.95674i	0.0174254	+	0.141928i
$435$	−6.15641	−	4.54859i	−0.295177	−	0.218088i
$436$	−4.09144	+	7.08658i	−0.195944	+	0.339385i
$437$	4.23767	+	7.33985i	0.202715	+	0.351113i
$438$	17.4485	+	1.97518i	0.833724	+	0.0943775i
$439$	−1.68649	−	0.973694i	−0.0804916	−	0.0464719i	0.459214	−	0.888326i	$-0.348131\pi$
$439$	−1.68649	−	0.973694i	−0.0804916	−	0.0464719i	−0.539706	+	0.841854i	$0.681464\pi$
$440$	−9.01403			−0.429727
$441$	−20.9963	+	0.396644i	−0.999822	+	0.0188878i
$442$	0.241880			0.0115051
$443$	20.3804	+	11.7666i	0.968302	+	0.559050i	0.898718	−	0.438526i	$-0.144499\pi$
$443$	20.3804	+	11.7666i	0.968302	+	0.559050i	0.0695841	+	0.997576i	$0.477833\pi$
$444$	8.95940	+	1.01420i	0.425195	+	0.0481320i
$445$	2.68223	+	4.64577i	0.127150	+	0.220230i
$446$	−0.724929	+	1.25561i	−0.0343264	+	0.0594550i
$447$	−7.28649	−	5.38353i	−0.344639	−	0.254632i
$448$	−0.322414	−	2.62603i	−0.0152326	−	0.124068i
$449$			0.0486516i			0.00229601i	0.999999	+	0.00114801i	$0.000365422\pi$
$449$			0.0486516i			0.00229601i	−0.999999	+	0.00114801i	$0.999635\pi$
$450$	1.90071	−	8.28777i	0.0896002	−	0.390689i
$451$	−24.4311	+	14.1053i	−1.15041	+	0.664192i
$452$	8.52643	−	4.92273i	0.401049	−	0.231546i
$453$	−16.8358	−	38.6429i	−0.791014	−	1.81560i
$454$		−	20.4558i		−	0.960038i
$455$	1.52137	−	3.58403i	0.0713227	−	0.168022i
$456$	−4.46531	+	6.04370i	−0.209107	+	0.283022i
$457$	−16.4837	+	28.5507i	−0.771077	+	1.33555i	0.165896	+	0.986143i	$0.446948\pi$
$457$	−16.4837	+	28.5507i	−0.771077	+	1.33555i	−0.936973	+	0.349402i	$0.886385\pi$
$458$	−10.5673	−	18.3031i	−0.493778	−	0.855249i
$459$	0.231734	+	1.23530i	0.0108164	+	0.0576588i
$460$	2.48975	+	1.43746i	0.116085	+	0.0670217i
$461$	41.1926			1.91853			0.959265	−	0.282509i	$-0.0911668\pi$
$461$	41.1926			1.91853			0.959265	+	0.282509i	$0.0911668\pi$
$462$	0.265095	+	28.0680i	0.0123333	+	1.30584i
$463$	29.2647			1.36005			0.680024	−	0.733190i	$-0.261970\pi$
$463$	29.2647			1.36005			0.680024	+	0.733190i	$0.261970\pi$
$464$	−2.60068	−	1.50150i	−0.120734	−	0.0697056i
$465$	0.322815	−	2.85172i	0.0149702	−	0.132245i
$466$	3.59625	+	6.22889i	0.166593	+	0.288548i
$467$	−11.3867	+	19.7223i	−0.526911	+	0.912637i	0.472597	+	0.881279i	$0.343317\pi$
$467$	−11.3867	+	19.7223i	−0.526911	+	0.912637i	−0.999508	+	0.0313585i	$0.990017\pi$
$468$	−2.86764	+	0.881281i	−0.132557	+	0.0407372i
$469$	−27.8282	+	20.9697i	−1.28499	+	0.968292i
$470$		−	11.3216i		−	0.522226i
$471$	27.0243	−	11.7738i	1.24521	−	0.542510i
$472$	10.7566	−	6.21031i	0.495112	−	0.285853i
$473$	−6.61371	+	3.81843i	−0.304099	+	0.175572i
$474$	−7.55993	+	3.29368i	−0.347239	+	0.151284i
$475$		−	12.2964i		−	0.564197i
$476$	−0.589080	−	0.250055i	−0.0270004	−	0.0114613i
$477$	20.3595	−	6.25687i	0.932197	−	0.286482i
$478$	−0.466968	+	0.808812i	−0.0213586	+	0.0369942i
$479$	2.22189	+	3.84842i	0.101521	+	0.175839i	0.912311	−	0.409497i	$-0.134296\pi$
$479$	2.22189	+	3.84842i	0.101521	+	0.175839i	−0.810791	+	0.585336i	$0.800963\pi$
$480$	−0.286708	+	2.53276i	−0.0130864	+	0.115604i
$481$	4.50831	+	2.60288i	0.205561	+	0.118681i
$482$	−15.5342			−0.707562
$483$	4.40274	−	7.79487i	0.200332	−	0.354679i
$484$	26.5182			1.20537
$485$	−9.48835	−	5.47810i	−0.430844	−	0.248748i
$486$	−7.24811	−	13.8009i	−0.328781	−	0.626022i
$487$	5.72440	+	9.91496i	0.259398	+	0.449290i	0.966081	−	0.258240i	$-0.0831427\pi$
$487$	5.72440	+	9.91496i	0.259398	+	0.449290i	−0.706683	+	0.707530i	$0.749809\pi$
$488$	6.65454	−	11.5260i	0.301237	−	0.521757i
$489$	9.84325	−	13.3226i	0.445127	−	0.602469i
$490$	−7.41033	+	7.15583i	−0.334764	+	0.323267i
$491$		−	42.0968i		−	1.89980i	−0.312548	−	0.949902i	$-0.601183\pi$
$491$		−	42.0968i		−	1.89980i	0.312548	−	0.949902i	$-0.398817\pi$
$492$	3.18622	+	7.31328i	0.143646	+	0.329708i
$493$	−0.629054	+	0.363185i	−0.0283312	+	0.0163570i
$494$	−3.75717	+	2.16920i	−0.169043	+	0.0975971i
$495$	6.04487	−	26.3578i	0.271697	−	1.18470i
$496$		−	1.12594i		−	0.0505560i
$497$	24.6570	−	3.02729i	1.10602	−	0.135792i
$498$	−13.1719	−	9.73186i	−0.590245	−	0.436095i
$499$	−13.9620	+	24.1829i	−0.625026	+	1.08258i	0.363510	+	0.931590i	$0.381578\pi$
$499$	−13.9620	+	24.1829i	−0.625026	+	1.08258i	−0.988536	+	0.150986i	$0.951755\pi$
$500$	−5.76460	−	9.98457i	−0.257801	−	0.446524i
$501$	−30.2326	−	3.42233i	−1.35069	−	0.152898i
$502$	−15.1608	−	8.75308i	−0.676659	−	0.390669i
$503$	−15.9380			−0.710642			−0.355321	−	0.934744i	$-0.615629\pi$
$503$	−15.9380			−0.710642			−0.355321	+	0.934744i	$0.615629\pi$
$504$	7.89496	+	0.818269i	0.351670	+	0.0364486i
$505$	3.59611			0.160025
$506$	−10.3628	−	5.98298i	−0.460684	−	0.265976i
$507$	−1.72106	−	0.194824i	−0.0764349	−	0.00865243i
$508$	−9.93277	−	17.2041i	−0.440696	−	0.763307i
$509$	9.03310	−	15.6458i	0.400385	−	0.693487i	−0.593387	−	0.804917i	$-0.702210\pi$
$509$	9.03310	−	15.6458i	0.400385	−	0.693487i	0.993772	+	0.111430i	$0.0355430\pi$
$510$	0.495874	+	0.366370i	0.0219577	+	0.0162232i
$511$	−16.1425	−	21.4222i	−0.714102	−	0.947662i
$512$			1.00000i			0.0441942i
$513$	−14.6778	−	17.1099i	−0.648042	−	0.755421i
$514$	14.8700	−	8.58522i	0.655889	−	0.378678i
$515$	11.5476	−	6.66701i	0.508848	−	0.293784i
$516$	0.862539	+	1.97977i	0.0379712	+	0.0871545i
$517$			47.1227i			2.07246i
$518$	−8.28878	−	10.9998i	−0.364188	−	0.483302i
$519$	−13.9878	+	18.9321i	−0.613996	+	0.831029i
$520$	−0.735814	+	1.27447i	−0.0322676	+	0.0558891i
$521$	−1.53454	−	2.65790i	−0.0672295	−	0.116445i	0.830451	−	0.557091i	$-0.188083\pi$
$521$	−1.53454	−	2.65790i	−0.0672295	−	0.116445i	−0.897681	+	0.440646i	$0.854749\pi$
$522$	6.13457	−	6.59770i	0.268503	−	0.288774i
$523$	−9.75361	−	5.63125i	−0.426496	−	0.246237i	0.271357	−	0.962479i	$-0.412528\pi$
$523$	−9.75361	−	5.63125i	−0.426496	−	0.246237i	−0.697853	+	0.716241i	$0.745861\pi$
$524$	−1.12242			−0.0490333
$525$	−11.1865	+	6.60016i	−0.488218	+	0.288055i
$526$	28.4047			1.23850
$527$	−0.235855	−	0.136171i	−0.0102740	−	0.00593170i
$528$	1.19334	−	10.5418i	0.0519333	−	0.458775i
$529$	−9.59180	−	16.6135i	−0.417035	−	0.722326i
$530$	5.22409	−	9.04839i	0.226920	−	0.393037i
$531$	10.9461	+	35.6178i	0.475019	+	1.54568i
$532$	11.3928	−	1.39876i	0.493941	−	0.0606440i
$533$			4.60565i			0.199493i
$534$	−5.78828	+	2.52182i	−0.250484	+	0.109130i
$535$	−10.3959	+	6.00207i	−0.449453	+	0.259492i
$536$	11.4055	−	6.58500i	0.492645	−	0.284428i
$537$	−16.1276	+	7.02640i	−0.695956	+	0.303211i
$538$			2.21838i			0.0956411i
$539$	30.8433	−	29.7840i	1.32851	−	1.28289i
$540$	−7.21374	−	2.53684i	−0.310430	−	0.109168i
$541$	18.5411	−	32.1142i	0.797145	−	1.38070i	−0.124322	−	0.992242i	$-0.539676\pi$
$541$	18.5411	−	32.1142i	0.797145	−	1.38070i	0.921468	−	0.388455i	$-0.126991\pi$
$542$	−5.59782	−	9.69571i	−0.240447	−	0.416466i
$543$	−1.18410	+	10.4602i	−0.0508144	+	0.448890i
$544$	0.209475	+	0.120940i	0.00898115	+	0.00518527i
$545$	−12.0421			−0.515829
$546$	3.99009	+	2.25370i	0.170760	+	0.0964497i
$547$	−19.6521			−0.840264			−0.420132	−	0.907463i	$-0.638016\pi$
$547$	−19.6521			−0.840264			−0.420132	+	0.907463i	$0.638016\pi$
$548$	7.96943	+	4.60115i	0.340437	+	0.196552i
$549$	29.2404	+	27.1879i	1.24795	+	1.16035i
$550$	8.68037	+	15.0348i	0.370132	+	0.641088i
$551$	6.51414	−	11.2828i	0.277512	−	0.480664i
$552$	−2.01070	+	2.72144i	−0.0855812	+	0.115832i
$553$	11.5950	+	4.92189i	0.493069	+	0.209300i
$554$		−	5.31644i		−	0.225874i
$555$	5.29989	+	12.1647i	0.224968	+	0.516364i
$556$	13.4229	−	7.74969i	0.569256	−	0.328660i
$557$	−28.3504	+	16.3681i	−1.20125	+	0.693539i	−0.960832	−	0.277131i	$-0.910616\pi$
$557$	−28.3504	+	16.3681i	−1.20125	+	0.693539i	−0.240413	+	0.970671i	$0.577283\pi$
$558$	3.29233	+	0.755060i	0.139376	+	0.0319642i
$559$			1.24679i			0.0527336i
$560$	3.10956	−	2.34318i	0.131403	−	0.0990173i
$561$	−2.06393	−	1.52491i	−0.0871390	−	0.0643816i
$562$	−5.31886	+	9.21253i	−0.224362	+	0.388607i
$563$	2.98943	+	5.17784i	0.125989	+	0.218220i	0.922119	−	0.386906i	$-0.126456\pi$
$563$	2.98943	+	5.17784i	0.125989	+	0.218220i	−0.796130	+	0.605126i	$0.793123\pi$
$564$	13.2405	+	1.49883i	0.557527	+	0.0631120i
$565$	12.5477	+	7.24443i	0.527887	+	0.304776i
$566$	0.291838			0.0122669
$567$	−7.68710	+	22.5368i	−0.322828	+	0.946458i
$568$	−9.38944			−0.393972
$569$	29.2382	+	16.8807i	1.22573	+	0.707676i	0.966134	−	0.258041i	$-0.0830771\pi$
$569$	29.2382	+	16.8807i	1.22573	+	0.707676i	0.259597	+	0.965717i	$0.416410\pi$
$570$	−10.9881	−	1.24386i	−0.460243	−	0.0520994i
$571$	4.28031	+	7.41372i	0.179126	+	0.310255i	0.941581	−	0.336786i	$-0.109340\pi$
$571$	4.28031	+	7.41372i	0.179126	+	0.310255i	−0.762456	+	0.647040i	$0.776006\pi$
$572$	3.06261	−	5.30459i	0.128054	−	0.221796i
$573$	8.81789	+	6.51499i	0.368373	+	0.272168i
$574$	4.76131	−	11.2167i	0.198733	−	0.468175i
$575$		−	5.53699i		−	0.230909i
$576$	−2.92409	−	0.670607i	−0.121837	−	0.0279419i
$577$	25.2807	−	14.5958i	1.05245	−	0.607631i	0.129114	−	0.991630i	$-0.458787\pi$
$577$	25.2807	−	14.5958i	1.05245	−	0.607631i	0.923334	+	0.383999i	$0.125453\pi$
$578$	−14.6718	+	8.47075i	−0.610265	+	0.352337i
$579$	3.64400	+	8.36400i	0.151439	+	0.347596i
$580$		−	4.41931i		−	0.183502i
$581$	3.04851	+	24.8299i	0.126474	+	1.03012i
$582$	7.66273	−	10.3713i	0.317630	−	0.429905i
$583$	−21.7437	+	37.6612i	−0.900532	+	1.55977i
$584$	5.06913	+	8.77999i	0.209762	+	0.363319i
$585$	−3.23321	−	3.00625i	−0.133677	−	0.124293i
$586$	−25.4726	−	14.7066i	−1.05226	−	0.607525i
$587$	−2.67417			−0.110375			−0.0551874	−	0.998476i	$-0.517576\pi$
$587$	−2.67417			−0.110375			−0.0551874	+	0.998476i	$0.517576\pi$
$588$	−7.38766	−	9.61366i	−0.304662	−	0.396461i
$589$	4.88477			0.201273
$590$	15.8297	+	9.13927i	0.651698	+	0.376258i
$591$	0.296870	−	2.62253i	0.0122116	−	0.107876i
$592$	2.60288	+	4.50831i	0.106978	+	0.185291i
$593$	−6.45813	+	11.1858i	−0.265204	+	0.459346i	−0.967617	−	0.252423i	$-0.918773\pi$
$593$	−6.45813	+	11.1858i	−0.265204	+	0.459346i	0.702413	+	0.711769i	$0.252106\pi$
$594$	30.0250	+	10.5589i	1.23194	+	0.433235i
$595$	−0.114766	−	0.934757i	−0.00470494	−	0.0383213i
$596$		−	5.23053i		−	0.214251i
$597$	−5.37740	+	2.34280i	−0.220082	+	0.0958846i
$598$	−1.69183	+	0.976779i	−0.0691841	+	0.0399435i
$599$	−16.6641	+	9.62105i	−0.680879	+	0.393106i	−0.800186	−	0.599752i	$-0.795266\pi$
$599$	−16.6641	+	9.62105i	−0.680879	+	0.393106i	0.119307	+	0.992857i	$0.461933\pi$
$600$	4.50058	−	1.96080i	0.183735	−	0.0800492i
$601$			20.6157i			0.840933i	0.907308	+	0.420467i	$0.138134\pi$
$601$			20.6157i			0.840933i	−0.907308	+	0.420467i	$0.861866\pi$
$602$	1.28893	−	3.03646i	0.0525329	−	0.123757i
$603$	11.6065	+	37.7668i	0.472652	+	1.53798i
$604$	12.1680	−	21.0756i	0.495108	−	0.857552i
$605$	19.5125	+	33.7966i	0.793294	+	1.37403i
$606$	−0.476076	+	4.20562i	−0.0193393	+	0.170842i
$607$	−11.1052	−	6.41157i	−0.450745	−	0.260238i	0.257400	−	0.966305i	$-0.417134\pi$
$607$	−11.1052	−	6.41157i	−0.450745	−	0.260238i	−0.708145	+	0.706067i	$0.750468\pi$
$608$	−4.33841			−0.175946
$609$	−13.7609	+	0.129968i	−0.557620	+	0.00526658i
$610$	19.5860			0.793014
$611$	6.66255	+	3.84662i	0.269538	+	0.155618i
$612$	−0.494115	+	0.531419i	−0.0199734	+	0.0214813i
$613$	−8.64760	−	14.9781i	−0.349273	−	0.604959i	0.636847	−	0.770990i	$-0.280238\pi$
$613$	−8.64760	−	14.9781i	−0.349273	−	0.604959i	−0.986121	+	0.166031i	$0.946905\pi$
$614$	13.1115	−	22.7099i	0.529139	−	0.916496i
$615$	−6.97607	+	9.44195i	−0.281302	+	0.380736i
$616$	−12.9426	+	9.75277i	−0.521472	+	0.392950i
$617$		−	32.8435i		−	1.32223i	−0.750286	−	0.661114i	$-0.770084\pi$
$617$		−	32.8435i		−	1.32223i	0.750286	−	0.661114i	$-0.229916\pi$
$618$	6.26827	+	14.3875i	0.252147	+	0.578749i
$619$	2.25547	−	1.30220i	0.0906551	−	0.0523397i	−0.453987	−	0.891008i	$-0.649999\pi$
$619$	2.25547	−	1.30220i	0.0906551	−	0.0523397i	0.544642	+	0.838669i	$0.316665\pi$
$620$	1.43497	−	0.828479i	0.0576297	−	0.0332725i
$621$	−6.60934	−	7.70449i	−0.265224	−	0.309171i
$622$		−	19.3445i		−	0.775644i
$623$	8.87774	+	3.76846i	0.355679	+	0.150980i
$624$	−1.39307	−	1.02925i	−0.0557674	−	0.0412030i
$625$	1.39757	−	2.42065i	0.0559026	−	0.0968261i
$626$	−10.2001	−	17.6672i	−0.407680	−	0.706122i
$627$	45.7348	+	5.17718i	1.82647	+	0.206757i
$628$	14.7389	+	8.50948i	0.588144	+	0.339565i
$629$	1.25917			0.0502064
$630$	4.76637	+	10.6640i	0.189897	+	0.424863i
$631$	14.9260			0.594195			0.297098	−	0.954847i	$-0.403981\pi$
$631$	14.9260			0.594195			0.297098	+	0.954847i	$0.403981\pi$
$632$	−4.12313	−	2.38049i	−0.164009	−	0.0946908i
$633$	−36.8713	−	4.17384i	−1.46550	−	0.165895i
$634$	16.1594	+	27.9888i	0.641770	+	1.11158i
$635$	14.6173	−	25.3180i	0.580072	−	1.00471i
$636$	9.89043	+	7.30742i	0.392181	+	0.289758i
$637$	−1.69334	−	6.79210i	−0.0670925	−	0.269113i
$638$			18.3941i			0.728228i
$639$	6.29662	−	27.4556i	0.249091	−	1.08612i
$640$	−1.27447	+	0.735814i	−0.0503777	+	0.0290856i
$641$	25.2634	−	14.5858i	0.997845	−	0.576106i	0.0902348	−	0.995921i	$-0.471238\pi$
$641$	25.2634	−	14.5858i	0.997845	−	0.576106i	0.907610	+	0.419815i	$0.137905\pi$
$642$	−5.64310	−	12.9525i	−0.222715	−	0.511195i
$643$			35.4696i			1.39878i	0.714739	+	0.699391i	$0.246546\pi$
$643$			35.4696i			1.39878i	−0.714739	+	0.699391i	$0.753454\pi$
$644$	5.13011	−	0.629854i	0.202155	−	0.0248197i
$645$	−1.88848	+	2.55602i	−0.0743590	+	0.100643i
$646$	−0.524688	+	0.908786i	−0.0206436	+	0.0357557i
$647$	−17.4805	−	30.2771i	−0.687229	−	1.19032i	−0.972731	−	0.231937i	$-0.925494\pi$
$647$	−17.4805	−	30.2771i	−0.687229	−	1.19032i	0.285502	−	0.958378i	$-0.407840\pi$
$648$	3.92182	−	8.10057i	0.154064	−	0.318221i
$649$	−65.8863	−	38.0395i	−2.58626	−	1.49318i
$650$	2.83431			0.111171
$651$	−2.62193	−	4.44385i	−0.102761	−	0.174168i
$652$	9.56350			0.374535
$653$	−4.32400	−	2.49646i	−0.169211	−	0.0976941i	0.413003	−	0.910730i	$-0.364480\pi$
$653$	−4.32400	−	2.49646i	−0.169211	−	0.0976941i	−0.582214	+	0.813036i	$0.697813\pi$
$654$	1.59422	−	14.0832i	0.0623389	−	0.550697i
$655$	−0.825894	−	1.43049i	−0.0322704	−	0.0558939i
$656$	−2.30282	+	3.98861i	−0.0899102	+	0.155729i
$657$	−29.0729	+	8.93466i	−1.13424	+	0.348574i
$658$	−12.2495	−	16.2559i	−0.477533	−	0.633719i
$659$			19.8977i			0.775104i	0.921848	+	0.387552i	$0.126679\pi$
$659$			19.8977i			0.775104i	−0.921848	+	0.387552i	$0.873321\pi$
$660$	14.3133	−	6.23597i	0.557145	−	0.242735i
$661$	27.4606	−	15.8544i	1.06810	−	0.616665i	0.140435	−	0.990090i	$-0.455150\pi$
$661$	27.4606	−	15.8544i	1.06810	−	0.616665i	0.927660	+	0.373425i	$0.121817\pi$
$662$	−23.3481	+	13.4800i	−0.907449	+	0.523916i
$663$	−0.384080	+	0.167335i	−0.0149164	+	0.00649874i
$664$		−	9.45528i		−	0.366936i
$665$	10.1657	+	13.4905i	0.394207	+	0.523140i
$666$	−14.9282	+	4.58773i	−0.578456	+	0.177771i
$667$	2.93328	−	5.08059i	0.113577	−	0.196721i
$668$	−8.78313	−	15.2128i	−0.339830	−	0.588602i
$669$	0.282467	−	2.49529i	0.0109208	−	0.0964735i
$670$	16.7847	+	9.69066i	0.648450	+	0.374383i
$671$	−81.5209			−3.14708
$672$	2.32867	+	3.94681i	0.0898303	+	0.152252i
$673$	−28.2240			−1.08796			−0.543978	−	0.839100i	$-0.683082\pi$
$673$	−28.2240			−1.08796			−0.543978	+	0.839100i	$0.683082\pi$
$674$	−28.5754	−	16.4980i	−1.10068	−	0.635479i
$675$	2.71542	+	14.4750i	0.104517	+	0.557144i
$676$	−0.500000	−	0.866025i	−0.0192308	−	0.0333087i
$677$	1.05212	−	1.82233i	0.0404363	−	0.0700377i	−0.845099	−	0.534610i	$-0.820459\pi$
$677$	1.05212	−	1.82233i	0.0404363	−	0.0700377i	0.885535	+	0.464572i	$0.153792\pi$
$678$	−10.1335	+	13.7154i	−0.389173	+	0.526737i
$679$	−19.5507	+	2.40035i	−0.750286	+	0.0921171i
$680$			0.355958i			0.0136504i
$681$	14.1515	+	32.4816i	0.542285	+	1.24470i
$682$	−5.97262	+	3.44830i	−0.228704	+	0.132042i
$683$	19.5356	−	11.2789i	0.747510	−	0.431575i	−0.0772837	−	0.997009i	$-0.524625\pi$
$683$	19.5356	−	11.2789i	0.747510	−	0.431575i	0.824793	+	0.565434i	$0.191291\pi$
$684$	2.90936	−	12.6859i	0.111242	−	0.485057i
$685$			13.5424i			0.517428i
$686$	−2.89767	+	18.2922i	−0.110634	+	0.698398i
$687$	29.4420	+	21.7529i	1.12328	+	0.829923i
$688$	−0.623395	+	1.07975i	−0.0237667	+	0.0411652i
$689$	3.54987	+	6.14856i	0.135239	+	0.234241i
$690$	−4.94789	−	0.560101i	−0.188363	−	0.0213227i
$691$	28.8039	+	16.6299i	1.09575	+	0.632632i	0.935101	−	0.354380i	$-0.115308\pi$
$691$	28.8039	+	16.6299i	1.09575	+	0.632632i	0.160649	+	0.987012i	$0.448641\pi$
$692$	−13.5902			−0.516624
$693$	−19.8386	−	44.3856i	−0.753605	−	1.68607i
$694$	34.0178			1.29130
$695$	19.7535	+	11.4047i	0.749291	+	0.432604i
$696$	5.16836	+	0.585058i	0.195906	+	0.0221766i
$697$	0.557008	+	0.964766i	0.0210982	+	0.0365431i
$698$	−7.14654	+	12.3782i	−0.270500	+	0.468520i
$699$	−10.0197	−	7.40290i	−0.378978	−	0.280003i
$700$	−6.90273	−	2.93010i	−0.260899	−	0.110748i
$701$			27.6759i			1.04530i	0.852546	+	0.522651i	$0.175057\pi$
$701$			27.6759i			1.04530i	−0.852546	+	0.522651i	$0.824943\pi$
$702$	3.94382	−	3.38323i	0.148850	−	0.127692i
$703$	−19.5589	+	11.2923i	−0.737678	+	0.425899i
$704$	5.30459	−	3.06261i	0.199924	−	0.115426i
$705$	7.83236	+	17.9775i	0.294984	+	0.677071i
$706$		−	24.3893i		−	0.917905i
$707$	5.16339	−	3.89083i	0.194189	−	0.146330i
$708$	−12.7839	+	17.3028i	−0.480450	+	0.650278i
$709$	10.5089	−	18.2019i	0.394668	−	0.683585i	−0.598391	−	0.801205i	$-0.704193\pi$
$709$	10.5089	−	18.2019i	0.394668	−	0.683585i	0.993059	+	0.117619i	$0.0375262\pi$
$710$	−6.90888	−	11.9665i	−0.259286	−	0.449096i
$711$	9.72576	−	10.4600i	0.364745	−	0.392281i
$712$	−3.15689	−	1.82263i	−0.118309	−	0.0683060i
$713$	2.19958			0.0823750
$714$	1.10839	−	0.0104684i	0.0414803	−	0.000391771i
$715$	9.01403			0.337106
$716$	−8.79586	−	5.07829i	−0.328717	−	0.189785i
$717$	0.181953	−	1.60736i	0.00679515	−	0.0600279i
$718$	2.19190	+	3.79649i	0.0818011	+	0.141684i
$719$	13.2893	−	23.0177i	0.495606	−	0.858415i	−0.504381	−	0.863481i	$-0.668279\pi$
$719$	13.2893	−	23.0177i	0.495606	−	0.858415i	0.999987	+	0.00506617i	$0.00161262\pi$
$720$	−1.29692	−	4.22010i	−0.0483333	−	0.157274i
$721$	9.36696	−	22.0667i	0.348844	−	0.821805i
$722$			0.178217i			0.00663254i
$723$	24.6666	−	10.7466i	0.917360	−	0.399672i
$724$	−5.26351	+	3.03889i	−0.195617	+	0.112939i
$725$	−7.37114	+	4.25573i	−0.273757	+	0.158054i
$726$	−42.1081	+	18.3455i	−1.56278	+	0.680865i
$727$		−	6.01389i		−	0.223043i	−0.993762	−	0.111521i	$-0.964428\pi$
$727$		−	6.01389i		−	0.223043i	0.993762	−	0.111521i	$-0.0355724\pi$
$728$	0.322414	+	2.62603i	0.0119494	+	0.0973273i
$729$	21.0568	+	16.9001i	0.779881	+	0.625928i
$730$	−7.45988	+	12.9209i	−0.276102	+	0.478223i
$731$	0.150787	+	0.261171i	0.00557706	+	0.00965976i
$732$	−2.59292	+	22.9057i	−0.0958373	+	0.846619i
$733$	−30.4919	−	17.6045i	−1.12624	−	0.650237i	−0.183256	−	0.983065i	$-0.558664\pi$
$733$	−30.4919	−	17.6045i	−1.12624	−	0.650237i	−0.942987	+	0.332829i	$0.891997\pi$
$734$	−16.6597			−0.614922
$735$	6.81635	−	16.4892i	0.251425	−	0.608213i
$736$	−1.95356			−0.0720091
$737$	−69.8614	−	40.3345i	−2.57338	−	1.48574i
$738$	−10.1188	−	9.40845i	−0.372476	−	0.346330i
$739$	−24.7205	−	42.8172i	−0.909359	−	1.57506i	−0.814957	−	0.579522i	$-0.803239\pi$
$739$	−24.7205	−	42.8172i	−0.909359	−	1.57506i	−0.0944025	−	0.995534i	$-0.530094\pi$
$740$	−3.83046	+	6.63456i	−0.140811	+	0.243891i
$741$	4.46531	−	6.04370i	0.164037	−	0.222021i
$742$	−2.28905	−	18.6442i	−0.0840339	−	0.684449i
$743$		−	24.3066i		−	0.891723i	−0.895102	−	0.445861i	$-0.852897\pi$
$743$		−	24.3066i		−	0.891723i	0.895102	−	0.445861i	$-0.147103\pi$
$744$	0.778930	+	1.78786i	0.0285570	+	0.0655463i
$745$	6.66614	−	3.84870i	0.244229	−	0.141005i
$746$	−4.06270	+	2.34560i	−0.148746	+	0.0858786i
$747$	27.6481	+	6.34077i	1.01159	+	0.231997i
$748$		−	1.48157i		−	0.0541715i
$749$	−8.43273	+	19.8658i	−0.308125	+	0.725881i
$750$	16.0610	+	11.8664i	0.586463	+	0.433301i
$751$	18.4231	−	31.9097i	0.672267	−	1.16440i	−0.304993	−	0.952355i	$-0.598654\pi$
$751$	18.4231	−	31.9097i	0.672267	−	1.16440i	0.977260	−	0.212046i	$-0.0680126\pi$
$752$	3.84662	+	6.66255i	0.140272	+	0.242958i
$753$	30.1291	+	3.41062i	1.09797	+	0.124290i
$754$	2.60068	+	1.50150i	0.0947113	+	0.0546816i
$755$	35.8135			1.30339
$756$	−13.1024	+	4.16247i	−0.476531	+	0.151387i
$757$	−4.74916			−0.172611			−0.0863056	−	0.996269i	$-0.527506\pi$
$757$	−4.74916			−0.172611			−0.0863056	+	0.996269i	$0.527506\pi$
$758$	20.0312	+	11.5650i	0.727565	+	0.420060i
$759$	20.5941	+	2.33125i	0.747519	+	0.0846191i
$760$	−3.19226	−	5.52916i	−0.115795	−	0.200564i
$761$	18.3013	−	31.6988i	0.663421	−	1.14908i	−0.316290	−	0.948663i	$-0.602437\pi$
$761$	18.3013	−	31.6988i	0.663421	−	1.14908i	0.979711	−	0.200416i	$-0.0642295\pi$
$762$	27.6741	+	20.4466i	1.00253	+	0.740704i
$763$	−17.2904	+	13.0291i	−0.625956	+	0.471683i
$764$			6.32983i			0.229005i
$765$	−1.04085	−	0.238708i	−0.0376321	−	0.00863050i
$766$	−21.0533	+	12.1551i	−0.760688	+	0.439183i
$767$	−10.7566	+	6.21031i	−0.388397	+	0.224241i
$768$	−0.691807	−	1.58789i	−0.0249634	−	0.0572981i
$769$			12.7430i			0.459524i	0.973247	+	0.229762i	$0.0737948\pi$
$769$			12.7430i			0.459524i	−0.973247	+	0.229762i	$0.926205\pi$
$770$	−21.9529	−	9.31869i	−0.791129	−	0.335822i
$771$	−17.6727	+	23.9196i	−0.636467	+	0.861443i
$772$	−2.63368	+	4.56167i	−0.0947882	+	0.164178i
$773$	6.80106	+	11.7798i	0.244617	+	0.423689i	0.962024	−	0.272965i	$-0.0880045\pi$
$773$	6.80106	+	11.7798i	0.244617	+	0.423689i	−0.717407	+	0.696654i	$0.754671\pi$
$774$	−2.73924	−	2.54695i	−0.0984599	−	0.0915483i
$775$	−2.76370	−	1.59563i	−0.0992752	−	0.0573166i
$776$	7.44495			0.267258
$777$	20.7714	+	11.7322i	0.745170	+	0.420891i
$778$	−3.69769			−0.132569
$779$	−17.3042	−	9.99059i	−0.619988	−	0.357950i
$780$	0.286708	−	2.53276i	0.0102658	−	0.0906873i
$781$	28.7562	+	49.8071i	1.02898	+	1.78224i
$782$	−0.236264	+	0.409221i	−0.00844877	+	0.0146337i
$783$	−5.17669	+	14.7204i	−0.185000	+	0.526064i
$784$	1.92958	−	6.72880i	0.0689134	−	0.240314i
$785$			25.0456i			0.893915i
$786$	1.78229	−	0.776500i	0.0635721	−	0.0276968i
$787$	−14.5591	+	8.40572i	−0.518977	+	0.299631i	−0.736516	−	0.676420i	$-0.763530\pi$
$787$	−14.5591	+	8.40572i	−0.518977	+	0.299631i	0.217539	+	0.976052i	$0.430197\pi$
$788$	1.31964	−	0.761894i	0.0470102	−	0.0271413i
$789$	−45.1035	+	19.6505i	−1.60573	+	0.699578i
$790$		−	7.00639i		−	0.249276i
$791$	25.8545	−	3.17431i	0.919281	−	0.112866i
$792$	5.39803	+	17.5649i	0.191811	+	0.624141i
$793$	−6.65454	+	11.5260i	−0.236310	+	0.409300i
$794$	16.6068	+	28.7638i	0.589353	+	1.02079i
$795$	−2.03555	+	17.9819i	−0.0721937	+	0.637754i
$796$	−2.93279	−	1.69325i	−0.103950	−	0.0600156i
$797$	−38.3932			−1.35996			−0.679978	−	0.733232i	$-0.738011\pi$
$797$	−38.3932			−1.35996			−0.679978	+	0.733232i	$0.738011\pi$
$798$	−17.1229	+	10.1027i	−0.606143	+	0.357632i
$799$	1.86084			0.0658320
$800$	2.45459	+	1.41716i	0.0867827	+	0.0501040i
$801$	7.44656	−	8.00875i	0.263111	−	0.282975i
$802$	8.80123	+	15.2442i	0.310782	+	0.538291i
$803$	31.0495	−	53.7793i	1.09571	−	1.89783i
$804$	−13.5552	+	18.3467i	−0.478056	+	0.647038i
$805$	4.57754	+	6.07470i	0.161337	+	0.214105i
$806$			1.12594i			0.0396594i
$807$	−1.53469	−	3.52255i	−0.0540237	−	0.124000i
$808$	−2.11624	+	1.22181i	−0.0744491	+	0.0429832i
$809$	8.03699	−	4.64016i	0.282566	−	0.163139i	−0.352019	−	0.935993i	$-0.614505\pi$
$809$	8.03699	−	4.64016i	0.282566	−	0.163139i	0.634584	+	0.772854i	$0.281171\pi$
$810$	13.2097	−	0.962279i	0.464140	−	0.0338110i
$811$		−	2.42641i		−	0.0852028i	−0.999092	−	0.0426014i	$-0.986435\pi$
$811$		−	2.42641i		−	0.0852028i	0.999092	−	0.0426014i	$-0.0135646\pi$
$812$	−4.78150	−	6.34537i	−0.167798	−	0.222679i
$813$	15.5963	+	11.5231i	0.546986	+	0.404134i
$814$	15.9432	−	27.6144i	0.558807	−	0.967883i
$815$	7.03696	+	12.1884i	0.246494	+	0.426940i
$816$	−0.416290	−	0.0471241i	−0.0145731	−	0.00164967i
$817$	−4.68441	−	2.70454i	−0.163887	−	0.0946200i
$818$	27.7667			0.970839
$819$	−7.89496	−	0.818269i	−0.275872	−	0.0285926i
$820$	−6.77780			−0.236691
$821$	12.2745	+	7.08668i	0.428382	+	0.247327i	0.698657	−	0.715456i	$-0.253781\pi$
$821$	12.2745	+	7.08668i	0.428382	+	0.247327i	−0.270275	+	0.962783i	$0.587115\pi$
$822$	−15.8377	−	1.79283i	−0.552404	−	0.0625321i
$823$	15.4387	+	26.7407i	0.538161	+	0.932122i	0.999003	+	0.0446398i	$0.0142140\pi$
$823$	15.4387	+	26.7407i	0.538161	+	0.932122i	−0.460842	+	0.887482i	$0.652453\pi$
$824$	−4.53036	+	7.84682i	−0.157823	+	0.273357i
$825$	−24.1847	−	17.8686i	−0.842004	−	0.622104i
$826$	32.6170	−	4.00458i	1.13489	−	0.139337i
$827$		−	16.5073i		−	0.574015i	−0.957928	−	0.287008i	$-0.907340\pi$
$827$		−	16.5073i		−	0.574015i	0.957928	−	0.287008i	$-0.0926605\pi$
$828$	1.31007	−	5.71238i	0.0455280	−	0.198519i
$829$	−2.07781	+	1.19962i	−0.0721654	+	0.0416647i	−0.535649	−	0.844441i	$-0.679933\pi$
$829$	−2.07781	+	1.19962i	−0.0721654	+	0.0416647i	0.463483	+	0.886106i	$0.346599\pi$
$830$	12.0504	−	6.95733i	0.418277	−	0.241492i
$831$	3.67795	+	8.44193i	0.127587	+	0.292847i
$832$		−	1.00000i		−	0.0346688i
$833$	−1.17615	−	1.21798i	−0.0407511	−	0.0422005i
$834$	−15.9528	+	21.5917i	−0.552399	+	0.747660i
$835$	12.9255	−	22.3876i	0.447306	−	0.774756i
$836$	13.2868	+	23.0135i	0.459535	+	0.795937i
$837$	−5.75023	+	1.07871i	−0.198757	+	0.0372855i
$838$	18.3849	+	10.6146i	0.635097	+	0.366674i
$839$	−44.8138			−1.54714			−0.773572	−	0.633708i	$-0.781532\pi$
$839$	−44.8138			−1.54714			−0.773572	+	0.633708i	$0.781532\pi$
$840$	−3.31662	+	5.87193i	−0.114434	+	0.202601i
$841$	19.9819			0.689032
$842$	6.26489	+	3.61703i	0.215902	+	0.124651i
$843$	2.07248	−	18.3081i	0.0713800	−	0.630565i
$844$	−10.7118	−	18.5534i	−0.368716	−	0.638635i
$845$	0.735814	−	1.27447i	0.0253128	−	0.0438430i
$846$	−22.0614	+	6.77991i	−0.758488	+	0.233098i
$847$	64.5829	+	27.4145i	2.21909	+	0.941972i
$848$			7.09974i			0.243806i
$849$	−0.463408	+	0.201896i	−0.0159041	+	0.00692905i
$850$	0.593716	−	0.342782i	0.0203643	−	0.0117573i
$851$	−8.80725	+	5.08487i	−0.301909	+	0.174307i
$852$	14.9094	−	6.49568i	0.510789	−	0.222538i
$853$			45.0580i			1.54276i	0.636376	+	0.771379i	$0.280433\pi$
$853$			45.0580i			1.54276i	−0.636376	+	0.771379i	$0.719567\pi$
$854$	28.1221	−	21.1912i	0.962320	−	0.725147i
$855$	18.3085	−	5.62656i	0.626137	−	0.192424i
$856$	4.07852	−	7.06421i	0.139401	−	0.241450i
$857$	−10.7051	−	18.5418i	−0.365680	−	0.633376i	0.623205	−	0.782058i	$-0.285830\pi$
$857$	−10.7051	−	18.5418i	−0.365680	−	0.633376i	−0.988885	+	0.148682i	$0.952497\pi$
$858$	−1.19334	+	10.5418i	−0.0407398	+	0.359893i
$859$	32.3529	+	18.6790i	1.10387	+	0.637318i	0.937234	−	0.348701i	$-0.113377\pi$
$859$	32.3529	+	18.6790i	1.10387	+	0.637318i	0.166633	+	0.986019i	$0.446710\pi$
$860$	−1.83481			−0.0625666
$861$	0.199329	+	21.1048i	0.00679313	+	0.719250i
$862$	−27.9046			−0.950436
$863$	−27.4192	−	15.8305i	−0.933359	−	0.538875i	−0.0454868	−	0.998965i	$-0.514484\pi$
$863$	−27.4192	−	15.8305i	−0.933359	−	0.538875i	−0.887872	+	0.460090i	$0.847817\pi$
$864$	5.10707	−	0.958053i	0.173746	−	0.0325936i
$865$	−9.99989	−	17.3203i	−0.340007	−	0.588909i
$866$	−7.22293	+	12.5105i	−0.245445	+	0.425124i
$867$	17.4371	−	23.6007i	0.592194	−	0.801521i
$868$	1.16399	−	2.74212i	0.0395084	−	0.0930738i
$869$			29.1620i			0.989253i
$870$	3.05731	+	7.01740i	0.103653	+	0.237912i
$871$	−11.4055	+	6.58500i	−0.386462	+	0.223124i
$872$	7.08658	−	4.09144i	0.239982	−	0.138554i
$873$	−4.99263	+	21.7697i	−0.168975	+	0.736792i
$874$		−	8.47533i		−	0.286682i
$875$	−3.71717	−	30.2760i	−0.125663	−	1.02352i
$876$	−14.1233	−	10.4348i	−0.477182	−	0.352560i
$877$	−0.750657	+	1.30018i	−0.0253479	+	0.0439038i	−0.878421	−	0.477887i	$-0.841403\pi$
$877$	−0.750657	+	1.30018i	−0.0253479	+	0.0439038i	0.853073	+	0.521791i	$0.174736\pi$
$878$	0.973694	+	1.68649i	0.0328606	+	0.0569162i
$879$	50.6220	+	5.73041i	1.70744	+	0.193282i
$880$	7.80638	+	4.50702i	0.263153	+	0.151931i
$881$	−13.1119			−0.441752			−0.220876	−	0.975302i	$-0.570892\pi$
$881$	−13.1119			−0.441752			−0.220876	+	0.975302i	$0.570892\pi$
$882$	18.3816	+	10.1546i	0.618941	+	0.341924i
$883$	16.8946			0.568549			0.284274	−	0.958743i	$-0.408247\pi$
$883$	16.8946			0.568549			0.284274	+	0.958743i	$0.408247\pi$
$884$	−0.209475	−	0.120940i	−0.00704539	−	0.00406766i
$885$	−31.4584	−	3.56109i	−1.05746	−	0.119705i
$886$	−11.7666	−	20.3804i	−0.395308	−	0.684693i
$887$	−19.3645	+	33.5403i	−0.650197	+	1.12617i	0.332878	+	0.942970i	$0.391980\pi$
$887$	−19.3645	+	33.5403i	−0.650197	+	1.12617i	−0.983075	+	0.183204i	$0.941353\pi$
$888$	−7.25197	−	5.35803i	−0.243360	−	0.179804i
$889$	−6.40493	−	52.1676i	−0.214814	−	1.74964i
$890$		−	5.36447i		−	0.179817i
$891$	−54.9812	+	4.00520i	−1.84194	+	0.134179i
$892$	1.25561	−	0.724929i	0.0420410	−	0.0242724i
$893$	−28.9048	+	16.6882i	−0.967264	+	0.558450i
$894$	3.61852	+	8.30552i	0.121021	+	0.277778i
$895$		−	14.9467i		−	0.499614i
$896$	−1.03380	+	2.43542i	−0.0345368	+	0.0813616i
$897$	2.01070	−	2.72144i	0.0671354	−	0.0908663i
$898$	0.0243258	−	0.0421336i	0.000811763	−	0.00140602i
$899$	−1.69060	−	2.92820i	−0.0563846	−	0.0976610i
$900$	−5.78995	+	6.22707i	−0.192998	+	0.207569i
$901$	1.48722	+	0.858644i	0.0495463	+	0.0286056i
$902$	28.2106			0.939309
$903$	0.0539603	+	5.71326i	0.00179568	+	0.190125i
$904$	−9.84547			−0.327455
$905$	−7.74592	−	4.47211i	−0.257483	−	0.148658i
$906$	−4.74122	+	41.8836i	−0.157517	+	1.39149i
$907$	−6.08983	−	10.5479i	−0.202210	−	0.350237i	0.747031	−	0.664790i	$-0.231479\pi$
$907$	−6.08983	−	10.5479i	−0.202210	−	0.350237i	−0.949240	+	0.314553i	$0.898146\pi$
$908$	−10.2279	+	17.7152i	−0.339425	+	0.587901i
$909$	−2.15352	−	7.00743i	−0.0714278	−	0.232422i
$910$	−3.10956	+	2.34318i	−0.103081	+	0.0776756i
$911$			10.2294i			0.338917i	0.985537	+	0.169458i	$0.0542018\pi$
$911$			10.2294i			0.338917i	−0.985537	+	0.169458i	$0.945798\pi$
$912$	6.88893	−	3.00134i	0.228115	−	0.0993843i
$913$	−50.1563	+	28.9578i	−1.65993	+	0.958363i
$914$	28.5507	−	16.4837i	0.944373	−	0.545234i
$915$	−31.1005	+	13.5497i	−1.02815	+	0.447941i
$916$			21.1346i			0.698308i
$917$	−2.73357	−	1.16036i	−0.0902704	−	0.0383184i
$918$	0.416962	−	1.18567i	0.0137618	−	0.0391329i
$919$	25.8624	−	44.7950i	0.853121	−	1.47765i	−0.0252557	−	0.999681i	$-0.508040\pi$
$919$	25.8624	−	44.7950i	0.853121	−	1.47765i	0.878377	−	0.477968i	$-0.158627\pi$
$920$	−1.43746	−	2.48975i	−0.0473915	−	0.0820845i
$921$	−5.10888	+	45.1315i	−0.168343	+	1.48713i
$922$	−35.6738	−	20.5963i	−1.17485	−	0.678302i
$923$	9.38944			0.309057
$924$	13.8044	−	24.4401i	0.454132	−	0.804021i
$925$	14.7547			0.485132
$926$	−25.3440	−	14.6324i	−0.832855	−	0.480849i
$927$	−19.9067	−	18.5093i	−0.653822	−	0.607925i
$928$	1.50150	+	2.60068i	0.0492893	+	0.0853716i
$929$	−13.5905	+	23.5394i	−0.445888	+	0.772301i	−0.998114	−	0.0613936i	$-0.980446\pi$
$929$	−13.5905	+	23.5394i	−0.445888	+	0.772301i	0.552225	+	0.833695i	$0.313779\pi$
$930$	−1.70543	+	2.30826i	−0.0559232	+	0.0756907i
$931$	29.1923	+	8.37128i	0.956738	+	0.274358i
$932$		−	7.19250i		−	0.235598i
$933$	13.3827	+	30.7170i	0.438129	+	1.00563i
$934$	19.7223	−	11.3867i	0.645332	−	0.372583i
$935$	1.88821	−	1.09016i	0.0617511	−	0.0356520i
$936$	2.92409	+	0.670607i	0.0955768	+	0.0219195i
$937$			12.6284i			0.412553i	0.978494	+	0.206276i	$0.0661346\pi$
$937$			12.6284i			0.412553i	−0.978494	+	0.206276i	$0.933865\pi$
$938$	34.5848	−	4.24619i	1.12923	−	0.138643i
$939$	28.4190	+	20.9970i	0.927420	+	0.685213i
$940$	−5.66080	+	9.80479i	−0.184635	+	0.319797i
$941$	−15.3797	−	26.6385i	−0.501365	−	0.868390i	−0.999999	−	0.00157679i	$-0.999498\pi$
$941$	−15.3797	−	26.6385i	−0.501365	−	0.868390i	0.498634	−	0.866813i	$-0.333835\pi$
$942$	−29.2906	−	3.31570i	−0.954341	−	0.108031i
$943$	−7.79198	−	4.49870i	−0.253742	−	0.146498i
$944$	−12.4206			−0.404257
$945$	−14.9459	−	13.6358i	−0.486190	−	0.443573i
$946$	7.63686			0.248296
$947$	40.3586	+	23.3011i	1.31148	+	0.757183i	0.982341	−	0.187099i	$-0.0599087\pi$
$947$	40.3586	+	23.3011i	1.31148	+	0.757183i	0.329138	+	0.944282i	$0.393242\pi$
$948$	8.19393	+	0.927553i	0.266126	+	0.0301255i
$949$	−5.06913	−	8.77999i	−0.164551	−	0.285011i
$950$	−6.14820	+	10.6490i	−0.199474	+	0.345499i
$951$	−45.0222	−	33.2641i	−1.45995	−	1.07866i
$952$	0.385130	+	0.511094i	0.0124821	+	0.0165647i
$953$		−	24.0324i		−	0.778486i	−0.921135	−	0.389243i	$-0.872737\pi$
$953$		−	24.0324i		−	0.778486i	0.921135	−	0.389243i	$-0.127263\pi$
$954$	−20.7603	−	4.76113i	−0.672139	−	0.154147i
$955$	−8.06716	+	4.65758i	−0.261047	+	0.150716i
$956$	0.808812	−	0.466968i	0.0261588	−	0.0151028i
$957$	−12.7251	−	29.2078i	−0.411345	−	0.944154i
$958$		−	4.44377i		−	0.143572i
$959$	14.6522	+	19.4445i	0.473145	+	0.627896i
$960$	1.51468	−	2.05008i	0.0488860	−	0.0661660i
$961$	−14.8661	+	25.7489i	−0.479553	+	0.830610i
$962$	−2.60288	−	4.50831i	−0.0839201	−	0.145354i
$963$	17.9213	+	16.6633i	0.577505	+	0.536966i
$964$	13.4530	+	7.76708i	0.433291	+	0.250161i
$965$	−7.75159			−0.249533
$966$	−7.71033	+	4.54919i	−0.248076	+	0.146368i
$967$	−31.7256			−1.02023			−0.510114	−	0.860107i	$-0.670397\pi$
$967$	−31.7256			−1.02023			−0.510114	+	0.860107i	$0.670397\pi$
$968$	−22.9654	−	13.2591i	−0.738137	−	0.426164i
$969$	0.204443	−	1.80604i	0.00656767	−	0.0580183i
$970$	5.47810	+	9.48835i	0.175891	+	0.304652i
$971$	−4.61197	+	7.98817i	−0.148005	+	0.256353i	−0.930490	−	0.366317i	$-0.880619\pi$
$971$	−4.61197	+	7.98817i	−0.148005	+	0.256353i	0.782485	+	0.622670i	$0.213952\pi$
$972$	−0.623401	+	15.5760i	−0.0199956	+	0.499600i
$973$	40.7019	−	4.99721i	1.30484	−	0.160203i
$974$		−	11.4488i		−	0.366843i
$975$	−4.50058	+	1.96080i	−0.144134	+	0.0627957i
$976$	−11.5260	+	6.65454i	−0.368938	+	0.213007i
$977$	−22.0959	+	12.7571i	−0.706910	+	0.408135i	−0.809916	−	0.586546i	$-0.800487\pi$
$977$	−22.0959	+	12.7571i	−0.706910	+	0.408135i	0.103006	+	0.994681i	$0.467154\pi$
$978$	−15.1858	+	6.61610i	−0.485589	+	0.211559i
$979$			22.3280i			0.713606i
$980$	9.99544	−	2.49196i	0.319293	−	0.0796029i
$981$	7.21141	+	23.4655i	0.230243	+	0.749196i
$982$	−21.0484	+	36.4569i	−0.671682	+	1.16339i
$983$	−5.34687	−	9.26105i	−0.170539	−	0.295381i	0.768070	−	0.640366i	$-0.221217\pi$
$983$	−5.34687	−	9.26105i	−0.170539	−	0.295381i	−0.938608	+	0.344985i	$0.887884\pi$
$984$	0.897290	−	7.92659i	0.0286046	−	0.252691i
$985$	1.94202	+	1.12122i	0.0618778	+	0.0357252i
$986$	0.726369			0.0231323
$987$	30.6967	+	17.3383i	0.977088	+	0.551884i
$988$	4.33841			0.138023
$989$	−2.10936	−	1.21784i	−0.0670737	−	0.0387250i
$990$	−18.4139	+	19.8041i	−0.585233	+	0.629416i
$991$	−3.89063	−	6.73877i	−0.123590	−	0.214064i	0.797591	−	0.603199i	$-0.206107\pi$
$991$	−3.89063	−	6.73877i	−0.123590	−	0.214064i	−0.921181	+	0.389135i	$0.872774\pi$
$992$	−0.562968	+	0.975089i	−0.0178742	+	0.0309591i
$993$	27.7487	−	37.5572i	0.880577	−	1.19184i
$994$	−22.8672	−	9.70679i	−0.725304	−	0.307881i
$995$		−	4.98367i		−	0.157993i
$996$	6.54123	+	15.0140i	0.207267	+	0.475736i
$997$	10.1269	−	5.84674i	0.320721	−	0.185168i	−0.330993	−	0.943633i	$-0.607384\pi$
$997$	10.1269	−	5.84674i	0.320721	−	0.185168i	0.651714	+	0.758465i	$0.274050\pi$
$998$	24.1829	−	13.9620i	0.765497	−	0.441960i
$999$	20.5306	−	17.6123i	0.649558	−	0.557227i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.z.a.131.8	✓	32
3.2	odd	2		546.2.z.b.131.13	yes	32
7.3	odd	6		546.2.z.b.521.13	yes	32
21.17	even	6	inner	546.2.z.a.521.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.z.a.131.8	✓	32	1.1	even	1	trivial
546.2.z.a.521.8	yes	32	21.17	even	6	inner
546.2.z.b.131.13	yes	32	3.2	odd	2
546.2.z.b.521.13	yes	32	7.3	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.72106 + 0.194824i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.735814 + 1.27447i) q^{5} +(-1.39307 - 1.02925i) q^{6} +(0.322414 + 2.62603i) q^{7} -1.00000i q^{8} +(2.92409 + 0.670607i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.72106 + 0.194824i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.735814 + 1.27447i) q^{5} +(-1.39307 - 1.02925i) q^{6} +(0.322414 + 2.62603i) q^{7} -1.00000i q^{8} +(2.92409 + 0.670607i) q^{9} +(1.27447 - 0.735814i) q^{10} +(-5.30459 + 3.06261i) q^{11} +(0.691807 + 1.58789i) q^{12} +1.00000i q^{13} +(1.03380 - 2.43542i) q^{14} +(-1.51468 + 2.05008i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.120940 + 0.209475i) q^{17} +(-2.19703 - 2.04281i) q^{18} +(-3.75717 - 2.16920i) q^{19} -1.47163 q^{20} +(0.0432793 + 4.58237i) q^{21} +6.12521 q^{22} +(-1.69183 - 0.976779i) q^{23} +(0.194824 - 1.72106i) q^{24} +(1.41716 + 2.45459i) q^{25} +(0.500000 - 0.866025i) q^{26} +(4.90188 + 1.72384i) q^{27} +(-2.11300 + 1.59224i) q^{28} +3.00301i q^{29} +(2.33679 - 1.01808i) q^{30} +(-0.975089 + 0.562968i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-9.72618 + 4.23746i) q^{33} -0.241880i q^{34} +(-3.58403 - 1.52137i) q^{35} +(0.881281 + 2.86764i) q^{36} +(2.60288 - 4.50831i) q^{37} +(2.16920 + 3.75717i) q^{38} +(-0.194824 + 1.72106i) q^{39} +(1.27447 + 0.735814i) q^{40} +4.60565 q^{41} +(2.25370 - 3.99009i) q^{42} +1.24679 q^{43} +(-5.30459 - 3.06261i) q^{44} +(-3.00625 + 3.23321i) q^{45} +(0.976779 + 1.69183i) q^{46} +(3.84662 - 6.66255i) q^{47} +(-1.02925 + 1.39307i) q^{48} +(-6.79210 + 1.69334i) q^{49} -2.83431i q^{50} +(0.167335 + 0.384080i) q^{51} +(-0.866025 + 0.500000i) q^{52} +(6.14856 - 3.54987i) q^{53} +(-3.38323 - 3.94382i) q^{54} -9.01403i q^{55} +(2.62603 - 0.322414i) q^{56} +(-6.04370 - 4.46531i) q^{57} +(1.50150 - 2.60068i) q^{58} +(6.21031 + 10.7566i) q^{59} +(-2.53276 - 0.286708i) q^{60} +(11.5260 + 6.65454i) q^{61} +1.12594 q^{62} +(-0.818269 + 7.89496i) q^{63} -1.00000 q^{64} +(-1.27447 - 0.735814i) q^{65} +(10.5418 + 1.19334i) q^{66} +(6.58500 + 11.4055i) q^{67} +(-0.120940 + 0.209475i) q^{68} +(-2.72144 - 2.01070i) q^{69} +(2.34318 + 3.10956i) q^{70} -9.38944i q^{71} +(0.670607 - 2.92409i) q^{72} +(-8.77999 + 5.06913i) q^{73} +(-4.50831 + 2.60288i) q^{74} +(1.96080 + 4.50058i) q^{75} -4.33841i q^{76} +(-9.75277 - 12.9426i) q^{77} +(1.02925 - 1.39307i) q^{78} +(2.38049 - 4.12313i) q^{79} +(-0.735814 - 1.27447i) q^{80} +(8.10057 + 3.92182i) q^{81} +(-3.98861 - 2.30282i) q^{82} +9.45528 q^{83} +(-3.94681 + 2.32867i) q^{84} -0.355958 q^{85} +(-1.07975 - 0.623395i) q^{86} +(-0.585058 + 5.16836i) q^{87} +(3.06261 + 5.30459i) q^{88} +(1.82263 - 3.15689i) q^{89} +(4.22010 - 1.29692i) q^{90} +(-2.62603 + 0.322414i) q^{91} -1.95356i q^{92} +(-1.78786 + 0.778930i) q^{93} +(-6.66255 + 3.84662i) q^{94} +(5.52916 - 3.19226i) q^{95} +(1.58789 - 0.691807i) q^{96} +7.44495i q^{97} +(6.72880 + 1.92958i) q^{98} +(-17.5649 + 5.39803i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9}+O(q^{10}) \) 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9	\( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{10} - 24 q^{11} + 4 q^{14} - 12 q^{15} - 16 q^{16} + 4 q^{17} + 24 q^{18} - 12 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} + 16 q^{26} - 6 q^{27} - 2 q^{28} + 10 q^{30} - 6 q^{31} - 14 q^{33} + 48 q^{35} + 4 q^{36} + 16 q^{38} + 6 q^{39} + 6 q^{40} + 16 q^{41} - 18 q^{42} + 32 q^{43} - 24 q^{44} - 20 q^{45} + 16 q^{46} + 20 q^{47} - 26 q^{49} + 44 q^{51} - 60 q^{53} - 6 q^{54} + 8 q^{56} - 8 q^{57} - 10 q^{58} + 8 q^{59} - 6 q^{60} + 36 q^{61} + 36 q^{62} - 28 q^{63} - 32 q^{64} - 6 q^{65} + 12 q^{66} - 4 q^{68} - 36 q^{69} - 18 q^{70} + 24 q^{72} - 48 q^{73} - 84 q^{74} + 14 q^{75} + 52 q^{77} + 18 q^{79} + 70 q^{81} + 24 q^{83} - 24 q^{84} - 32 q^{85} - 24 q^{86} - 26 q^{87} - 6 q^{88} - 20 q^{89} - 6 q^{90} - 8 q^{91} + 92 q^{93} - 72 q^{95} - 6 q^{96} + 32 q^{98}+O(q^{100}) \) 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9 + 6 * q^10 - 24 * q^11 + 4 * q^14 - 12 * q^15 - 16 * q^16 + 4 * q^17 + 24 * q^18 - 12 * q^21 - 12 * q^22 - 6 * q^24 - 18 * q^25 + 16 * q^26 - 6 * q^27 - 2 * q^28 + 10 * q^30 - 6 * q^31 - 14 * q^33 + 48 * q^35 + 4 * q^36 + 16 * q^38 + 6 * q^39 + 6 * q^40 + 16 * q^41 - 18 * q^42 + 32 * q^43 - 24 * q^44 - 20 * q^45 + 16 * q^46 + 20 * q^47 - 26 * q^49 + 44 * q^51 - 60 * q^53 - 6 * q^54 + 8 * q^56 - 8 * q^57 - 10 * q^58 + 8 * q^59 - 6 * q^60 + 36 * q^61 + 36 * q^62 - 28 * q^63 - 32 * q^64 - 6 * q^65 + 12 * q^66 - 4 * q^68 - 36 * q^69 - 18 * q^70 + 24 * q^72 - 48 * q^73 - 84 * q^74 + 14 * q^75 + 52 * q^77 + 18 * q^79 + 70 * q^81 + 24 * q^83 - 24 * q^84 - 32 * q^85 - 24 * q^86 - 26 * q^87 - 6 * q^88 - 20 * q^89 - 6 * q^90 - 8 * q^91 + 92 * q^93 - 72 * q^95 - 6 * q^96 + 32 * q^98

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