LMFDB - Embedded newform 950.2.l.b.251.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(101,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("950.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.l (of order $9$, degree $6$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			251.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	950.251
Dual form			950.2.l.b.651.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 + 0.342020i) q^{2} +(0.439693 + 2.49362i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.439693 + 2.49362i) q^{6} +(-0.326352 + 0.565258i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-3.20574 + 1.16679i) q^{9} +O(q^{10})$	\(q+(0.939693 + 0.342020i) q^{2} +(0.439693 + 2.49362i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.439693 + 2.49362i) q^{6} +(-0.326352 + 0.565258i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-3.20574 + 1.16679i) q^{9} +(0.500000 + 0.866025i) q^{11} +(-1.26604 + 2.19285i) q^{12} +(-0.500000 + 2.83564i) q^{13} +(-0.500000 + 0.419550i) q^{14} +(0.173648 + 0.984808i) q^{16} +(0.439693 + 0.160035i) q^{17} -3.41147 q^{18} +(-4.07398 - 1.55007i) q^{19} +(-1.55303 - 0.565258i) q^{21} +(0.173648 + 0.984808i) q^{22} +(2.56418 + 2.15160i) q^{23} +(-1.93969 + 1.62760i) q^{24} +(-1.43969 + 2.49362i) q^{26} +(-0.520945 - 0.902302i) q^{27} +(-0.613341 + 0.223238i) q^{28} +(-6.41147 + 2.33359i) q^{29} +(2.03209 - 3.51968i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-1.93969 + 1.62760i) q^{33} +(0.358441 + 0.300767i) q^{34} +(-3.20574 - 1.16679i) q^{36} +7.63816 q^{37} +(-3.29813 - 2.84997i) q^{38} -7.29086 q^{39} +(-0.854570 - 4.84651i) q^{41} +(-1.26604 - 1.06234i) q^{42} +(-2.40760 + 2.02022i) q^{43} +(-0.173648 + 0.984808i) q^{44} +(1.67365 + 2.89884i) q^{46} +(6.02481 - 2.19285i) q^{47} +(-2.37939 + 0.866025i) q^{48} +(3.28699 + 5.69323i) q^{49} +(-0.205737 + 1.16679i) q^{51} +(-2.20574 + 1.85083i) q^{52} +(-2.96064 - 2.48427i) q^{53} +(-0.180922 - 1.02606i) q^{54} -0.652704 q^{56} +(2.07398 - 10.8405i) q^{57} -6.82295 q^{58} +(5.68479 + 2.06910i) q^{59} +(-3.96064 - 3.32337i) q^{61} +(3.11334 - 2.61240i) q^{62} +(0.386659 - 2.19285i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-2.37939 + 0.866025i) q^{66} +(-0.826352 + 0.300767i) q^{67} +(0.233956 + 0.405223i) q^{68} +(-4.23783 + 7.34013i) q^{69} +(9.35504 - 7.84981i) q^{71} +(-2.61334 - 2.19285i) q^{72} +(-0.0885259 - 0.502055i) q^{73} +(7.17752 + 2.61240i) q^{74} +(-2.12449 - 3.80612i) q^{76} -0.652704 q^{77} +(-6.85117 - 2.49362i) q^{78} +(-1.51367 - 8.58445i) q^{79} +(-5.81908 + 4.88279i) q^{81} +(0.854570 - 4.84651i) q^{82} +(8.95471 - 15.5100i) q^{83} +(-0.826352 - 1.43128i) q^{84} +(-2.95336 + 1.07494i) q^{86} +(-8.63816 - 14.9617i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(-3.06418 + 17.3778i) q^{89} +(-1.43969 - 1.20805i) q^{91} +(0.581252 + 3.29644i) q^{92} +(9.67024 + 3.51968i) q^{93} +6.41147 q^{94} -2.53209 q^{96} +(13.6284 + 4.96032i) q^{97} +(1.14156 + 6.47410i) q^{98} +(-2.61334 - 2.19285i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{3} + 3 q^{6} - 3 q^{7} + 3 q^{8} - 9 q^{9}+O(q^{10}) $ 6 * q - 3 * q^3 + 3 * q^6 - 3 * q^7 + 3 * q^8 - 9 * q^9	$ 6 q - 3 q^{3} + 3 q^{6} - 3 q^{7} + 3 q^{8} - 9 q^{9} + 3 q^{11} - 3 q^{12} - 3 q^{13} - 3 q^{14} - 3 q^{17} - 9 q^{19} + 3 q^{21} - 3 q^{23} - 6 q^{24} - 3 q^{26} + 3 q^{28} - 18 q^{29} + 3 q^{31} - 6 q^{33} - 6 q^{34} - 9 q^{36} + 12 q^{37} - 6 q^{38} - 12 q^{39} - 21 q^{41} - 3 q^{42} - 18 q^{43} + 9 q^{46} + 9 q^{47} - 3 q^{48} + 12 q^{49} + 9 q^{51} - 3 q^{52} - 9 q^{53} - 18 q^{54} - 6 q^{56} - 3 q^{57} + 27 q^{59} - 15 q^{61} + 12 q^{62} + 9 q^{63} - 3 q^{64} - 3 q^{66} - 6 q^{67} + 6 q^{68} - 6 q^{69} + 6 q^{71} - 9 q^{72} - 21 q^{73} + 18 q^{74} - 6 q^{77} - 15 q^{78} + 12 q^{79} - 18 q^{81} + 21 q^{82} + 18 q^{83} - 6 q^{84} + 9 q^{86} - 18 q^{87} - 3 q^{88} - 3 q^{91} + 6 q^{92} + 15 q^{93} + 18 q^{94} - 6 q^{96} + 45 q^{97} + 15 q^{98} - 9 q^{99}+O(q^{100}) $ 6 * q - 3 * q^3 + 3 * q^6 - 3 * q^7 + 3 * q^8 - 9 * q^9 + 3 * q^11 - 3 * q^12 - 3 * q^13 - 3 * q^14 - 3 * q^17 - 9 * q^19 + 3 * q^21 - 3 * q^23 - 6 * q^24 - 3 * q^26 + 3 * q^28 - 18 * q^29 + 3 * q^31 - 6 * q^33 - 6 * q^34 - 9 * q^36 + 12 * q^37 - 6 * q^38 - 12 * q^39 - 21 * q^41 - 3 * q^42 - 18 * q^43 + 9 * q^46 + 9 * q^47 - 3 * q^48 + 12 * q^49 + 9 * q^51 - 3 * q^52 - 9 * q^53 - 18 * q^54 - 6 * q^56 - 3 * q^57 + 27 * q^59 - 15 * q^61 + 12 * q^62 + 9 * q^63 - 3 * q^64 - 3 * q^66 - 6 * q^67 + 6 * q^68 - 6 * q^69 + 6 * q^71 - 9 * q^72 - 21 * q^73 + 18 * q^74 - 6 * q^77 - 15 * q^78 + 12 * q^79 - 18 * q^81 + 21 * q^82 + 18 * q^83 - 6 * q^84 + 9 * q^86 - 18 * q^87 - 3 * q^88 - 3 * q^91 + 6 * q^92 + 15 * q^93 + 18 * q^94 - 6 * q^96 + 45 * q^97 + 15 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$

Coefficient data

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

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

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

$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$3$	0.439693	+	2.49362i	0.253857	+	1.43969i	0.798991	+	0.601344i	$0.205368\pi$
$3$	0.439693	+	2.49362i	0.253857	+	1.43969i	−0.545134	+	0.838349i	$0.683521\pi$
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$		0			0
$5$		0			0
$6$	−0.439693	+	2.49362i	−0.179504	+	1.01802i
$7$	−0.326352	+	0.565258i	−0.123349	+	0.213647i	−0.921087	−	0.389358i	$-0.872697\pi$
$7$	−0.326352	+	0.565258i	−0.123349	+	0.213647i	0.797737	+	0.603005i	$0.206030\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−3.20574	+	1.16679i	−1.06858	+	0.388931i
$10$		0			0
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	0.931505	−	0.363727i	$-0.118496\pi$
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	−0.780750	+	0.624844i	$0.785163\pi$
$12$	−1.26604	+	2.19285i	−0.365476	+	0.633022i
$13$	−0.500000	+	2.83564i	−0.138675	+	0.786465i	0.833555	+	0.552437i	$0.186302\pi$
$13$	−0.500000	+	2.83564i	−0.138675	+	0.786465i	−0.972230	+	0.234028i	$0.924809\pi$
$14$	−0.500000	+	0.419550i	−0.133631	+	0.112129i
$15$		0			0
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	0.439693	+	0.160035i	0.106641	+	0.0388142i	0.394790	−	0.918772i	$-0.370817\pi$
$17$	0.439693	+	0.160035i	0.106641	+	0.0388142i	−0.288149	+	0.957586i	$0.593040\pi$
$18$	−3.41147			−0.804092
$19$	−4.07398	−	1.55007i	−0.934635	−	0.355609i
$19$	−4.07398	−	1.55007i	−0.934635	−	0.355609i
$20$		0			0
$21$	−1.55303	−	0.565258i	−0.338900	−	0.123349i
$22$	0.173648	+	0.984808i	0.0370219	+	0.209962i
$23$	2.56418	+	2.15160i	0.534668	+	0.448640i	0.869710	−	0.493564i	$-0.164306\pi$
$23$	2.56418	+	2.15160i	0.534668	+	0.448640i	−0.335042	+	0.942203i	$0.608750\pi$
$24$	−1.93969	+	1.62760i	−0.395938	+	0.332232i
$25$		0			0
$26$	−1.43969	+	2.49362i	−0.282347	+	0.489039i
$27$	−0.520945	−	0.902302i	−0.100256	−	0.173648i
$28$	−0.613341	+	0.223238i	−0.115911	+	0.0421880i
$29$	−6.41147	+	2.33359i	−1.19058	+	0.433336i	−0.859927	−	0.510416i	$-0.829491\pi$
$29$	−6.41147	+	2.33359i	−1.19058	+	0.433336i	−0.330653	+	0.943752i	$0.607269\pi$
$30$		0			0
$31$	2.03209	−	3.51968i	0.364974	−	0.632153i	−0.623798	−	0.781586i	$-0.714411\pi$
$31$	2.03209	−	3.51968i	0.364974	−	0.632153i	0.988772	+	0.149432i	$0.0477446\pi$
$32$	−0.173648	+	0.984808i	−0.0306970	+	0.174091i
$33$	−1.93969	+	1.62760i	−0.337657	+	0.283328i
$34$	0.358441	+	0.300767i	0.0614721	+	0.0515812i
$35$		0			0
$36$	−3.20574	−	1.16679i	−0.534290	−	0.194465i
$37$	7.63816			1.25571			0.627853	−	0.778332i	$-0.283934\pi$
$37$	7.63816			1.25571			0.627853	+	0.778332i	$0.283934\pi$
$38$	−3.29813	−	2.84997i	−0.535028	−	0.462326i
$39$	−7.29086			−1.16747
$40$		0			0
$41$	−0.854570	−	4.84651i	−0.133461	−	0.756898i	−0.975919	−	0.218134i	$-0.930003\pi$
$41$	−0.854570	−	4.84651i	−0.133461	−	0.756898i	0.842457	−	0.538763i	$-0.181108\pi$
$42$	−1.26604	−	1.06234i	−0.195355	−	0.163922i
$43$	−2.40760	+	2.02022i	−0.367156	+	0.308081i	−0.807635	−	0.589682i	$-0.799253\pi$
$43$	−2.40760	+	2.02022i	−0.367156	+	0.308081i	0.440479	+	0.897763i	$0.354809\pi$
$44$	−0.173648	+	0.984808i	−0.0261784	+	0.148465i
$45$		0			0
$46$	1.67365	+	2.89884i	0.246766	+	0.427411i
$47$	6.02481	−	2.19285i	0.878810	−	0.319861i	0.137080	−	0.990560i	$-0.456228\pi$
$47$	6.02481	−	2.19285i	0.878810	−	0.319861i	0.741729	+	0.670699i	$0.234006\pi$
$48$	−2.37939	+	0.866025i	−0.343435	+	0.125000i
$49$	3.28699	+	5.69323i	0.469570	+	0.813319i
$50$		0			0
$51$	−0.205737	+	1.16679i	−0.0288090	+	0.163384i
$52$	−2.20574	+	1.85083i	−0.305881	+	0.256664i
$53$	−2.96064	−	2.48427i	−0.406675	−	0.341241i	0.416392	−	0.909185i	$-0.363294\pi$
$53$	−2.96064	−	2.48427i	−0.406675	−	0.341241i	−0.823067	+	0.567944i	$0.807739\pi$
$54$	−0.180922	−	1.02606i	−0.0246204	−	0.139629i
$55$		0			0
$56$	−0.652704			−0.0872212
$57$	2.07398	−	10.8405i	0.274705	−	1.43586i
$58$	−6.82295			−0.895897
$59$	5.68479	+	2.06910i	0.740097	+	0.269373i	0.684432	−	0.729076i	$-0.260050\pi$
$59$	5.68479	+	2.06910i	0.740097	+	0.269373i	0.0556645	+	0.998450i	$0.482272\pi$
$60$		0			0
$61$	−3.96064	−	3.32337i	−0.507108	−	0.425514i	0.353002	−	0.935622i	$-0.385161\pi$
$61$	−3.96064	−	3.32337i	−0.507108	−	0.425514i	−0.860110	+	0.510109i	$0.829605\pi$
$62$	3.11334	−	2.61240i	0.395395	−	0.331776i
$63$	0.386659	−	2.19285i	0.0487145	−	0.276274i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$		0			0
$66$	−2.37939	+	0.866025i	−0.292882	+	0.106600i
$67$	−0.826352	+	0.300767i	−0.100955	+	0.0367446i	−0.392004	−	0.919964i	$-0.628218\pi$
$67$	−0.826352	+	0.300767i	−0.100955	+	0.0367446i	0.291049	+	0.956708i	$0.405996\pi$
$68$	0.233956	+	0.405223i	0.0283713	+	0.0491405i
$69$	−4.23783	+	7.34013i	−0.510174	+	0.883648i
$70$		0			0
$71$	9.35504	−	7.84981i	1.11024	−	0.931601i	0.112168	−	0.993689i	$-0.464221\pi$
$71$	9.35504	−	7.84981i	1.11024	−	0.931601i	0.998071	+	0.0620884i	$0.0197761\pi$
$72$	−2.61334	−	2.19285i	−0.307985	−	0.258430i
$73$	−0.0885259	−	0.502055i	−0.0103612	−	0.0587611i	0.979189	−	0.202951i	$-0.0650534\pi$
$73$	−0.0885259	−	0.502055i	−0.0103612	−	0.0587611i	−0.989550	+	0.144190i	$0.953942\pi$
$74$	7.17752	+	2.61240i	0.834370	+	0.303686i
$75$		0			0
$76$	−2.12449	−	3.80612i	−0.243695	−	0.436592i
$77$	−0.652704			−0.0743825
$78$	−6.85117	−	2.49362i	−0.775742	−	0.282347i
$79$	−1.51367	−	8.58445i	−0.170301	−	0.965826i	−0.943429	−	0.331576i	$-0.892420\pi$
$79$	−1.51367	−	8.58445i	−0.170301	−	0.965826i	0.773127	−	0.634251i	$-0.218691\pi$
$80$		0			0
$81$	−5.81908	+	4.88279i	−0.646564	+	0.542532i
$82$	0.854570	−	4.84651i	0.0943715	−	0.535207i
$83$	8.95471	−	15.5100i	0.982907	−	1.70244i	0.332015	−	0.943274i	$-0.392272\pi$
$83$	8.95471	−	15.5100i	0.982907	−	1.70244i	0.650892	−	0.759170i	$-0.274395\pi$
$84$	−0.826352	−	1.43128i	−0.0901624	−	0.156166i
$85$		0			0
$86$	−2.95336	+	1.07494i	−0.318469	+	0.115913i
$87$	−8.63816	−	14.9617i	−0.926108	−	1.60407i
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	−3.06418	+	17.3778i	−0.324802	+	1.84204i	0.186259	+	0.982501i	$0.440364\pi$
$89$	−3.06418	+	17.3778i	−0.324802	+	1.84204i	−0.511061	+	0.859544i	$0.670748\pi$
$90$		0			0
$91$	−1.43969	−	1.20805i	−0.150921	−	0.126638i
$92$	0.581252	+	3.29644i	0.0605997	+	0.343678i
$93$	9.67024	+	3.51968i	1.00276	+	0.364974i
$94$	6.41147			0.661293
$95$		0			0
$96$	−2.53209			−0.258430
$97$	13.6284	+	4.96032i	1.38375	+	0.503644i	0.923313	−	0.384049i	$-0.125471\pi$
$97$	13.6284	+	4.96032i	1.38375	+	0.503644i	0.460437	+	0.887692i	$0.347693\pi$
$98$	1.14156	+	6.47410i	0.115315	+	0.653983i
$99$	−2.61334	−	2.19285i	−0.262651	−	0.220390i
$100$		0			0
$101$	−2.59580	+	14.7215i	−0.258292	+	1.46485i	0.529188	+	0.848505i	$0.322497\pi$
$101$	−2.59580	+	14.7215i	−0.258292	+	1.46485i	−0.787480	+	0.616341i	$0.788614\pi$
$102$	−0.592396	+	1.02606i	−0.0586560	+	0.101595i
$103$	−3.61334	−	6.25849i	−0.356033	−	0.616667i	0.631261	−	0.775570i	$-0.282538\pi$
$103$	−3.61334	−	6.25849i	−0.356033	−	0.616667i	−0.987294	+	0.158903i	$0.949204\pi$
$104$	−2.70574	+	0.984808i	−0.265319	+	0.0965683i
$105$		0			0
$106$	−1.93242	−	3.34705i	−0.187693	−	0.325094i
$107$	−3.63429	+	6.29477i	−0.351340	+	0.608538i	−0.986484	−	0.163855i	$-0.947607\pi$
$107$	−3.63429	+	6.29477i	−0.351340	+	0.608538i	0.635145	+	0.772393i	$0.280940\pi$
$108$	0.180922	−	1.02606i	0.0174092	−	0.0987327i
$109$	6.77584	−	5.68561i	0.649008	−	0.544583i	−0.257762	−	0.966209i	$-0.582985\pi$
$109$	6.77584	−	5.68561i	0.649008	−	0.544583i	0.906770	+	0.421626i	$0.138540\pi$
$110$		0			0
$111$	3.35844	+	19.0467i	0.318769	+	1.80783i
$112$	−0.613341	−	0.223238i	−0.0579553	−	0.0210940i
$113$	−1.49020			−0.140186			−0.0700931	−	0.997540i	$-0.522330\pi$
$113$	−1.49020			−0.140186			−0.0700931	+	0.997540i	$0.522330\pi$
$114$	5.65657	−	9.47740i	0.529787	−	0.887640i
$115$		0			0
$116$	−6.41147	−	2.33359i	−0.595290	−	0.216668i
$117$	−1.70574	−	9.67372i	−0.157695	−	0.894335i
$118$	4.63429	+	3.88863i	0.426621	+	0.357977i
$119$	−0.233956	+	0.196312i	−0.0214467	+	0.0179959i
$120$		0			0
$121$	5.00000	−	8.66025i	0.454545	−	0.787296i
$122$	−2.58512	−	4.47756i	−0.234046	−	0.405380i
$123$	11.7096	−	4.26195i	1.05582	−	0.384287i
$124$	3.81908	−	1.39003i	0.342963	−	0.124828i
$125$		0			0
$126$	1.11334	−	1.92836i	0.0991843	−	0.171792i
$127$	−3.18392	+	18.0569i	−0.282527	+	1.60229i	0.431461	+	0.902131i	$0.357998\pi$
$127$	−3.18392	+	18.0569i	−0.282527	+	1.60229i	−0.713988	+	0.700158i	$0.753113\pi$
$128$	−0.766044	+	0.642788i	−0.0677094	+	0.0568149i
$129$	−6.09627	−	5.11538i	−0.536746	−	0.450384i
$130$		0			0
$131$	−6.72416	−	2.44739i	−0.587492	−	0.213830i	0.0311339	−	0.999515i	$-0.490088\pi$
$131$	−6.72416	−	2.44739i	−0.587492	−	0.213830i	−0.618626	+	0.785686i	$0.712310\pi$
$132$	−2.53209			−0.220390
$133$	2.20574	−	1.79698i	0.191262	−	0.155818i
$134$	−0.879385			−0.0759673
$135$		0			0
$136$	0.0812519	+	0.460802i	0.00696729	+	0.0395135i
$137$	12.9855	+	10.8961i	1.10942	+	0.930916i	0.998022	−	0.0628601i	$-0.0200222\pi$
$137$	12.9855	+	10.8961i	1.10942	+	0.930916i	0.111400	+	0.993776i	$0.464467\pi$
$138$	−6.49273	+	5.44804i	−0.552698	+	0.463768i
$139$	2.20321	−	12.4950i	0.186874	−	1.05981i	−0.736650	−	0.676274i	$-0.763594\pi$
$139$	2.20321	−	12.4950i	0.186874	−	1.05981i	0.923524	−	0.383541i	$-0.125295\pi$
$140$		0			0
$141$	8.11721	+	14.0594i	0.683592	+	1.18402i
$142$	11.4757	−	4.17680i	0.963015	−	0.350509i
$143$	−2.70574	+	0.984808i	−0.226265	+	0.0823538i
$144$	−1.70574	−	2.95442i	−0.142145	−	0.246202i
$145$		0			0
$146$	0.0885259	−	0.502055i	0.00732645	−	0.0415504i
$147$	−12.7515	+	10.6998i	−1.05173	+	0.882503i
$148$	5.85117	+	4.90971i	0.480963	+	0.403576i
$149$	−0.593740	−	3.36727i	−0.0486411	−	0.275857i	0.950780	−	0.309865i	$-0.100284\pi$
$149$	−0.593740	−	3.36727i	−0.0486411	−	0.275857i	−0.999422	+	0.0340079i	$0.989173\pi$
$150$		0			0
$151$	15.5594			1.26621			0.633104	−	0.774067i	$-0.281780\pi$
$151$	15.5594			1.26621			0.633104	+	0.774067i	$0.281780\pi$
$152$	−0.694593	−	4.30320i	−0.0563389	−	0.349036i
$153$	−1.59627			−0.129051
$154$	−0.613341	−	0.223238i	−0.0494244	−	0.0179890i
$155$		0			0
$156$	−5.58512	−	4.68647i	−0.447168	−	0.375218i
$157$	10.1762	−	8.53882i	0.812147	−	0.681472i	−0.138972	−	0.990296i	$-0.544380\pi$
$157$	10.1762	−	8.53882i	0.812147	−	0.681472i	0.951119	+	0.308824i	$0.0999354\pi$
$158$	1.51367	−	8.58445i	0.120421	−	0.682942i
$159$	4.89306	−	8.47502i	0.388045	−	0.672113i
$160$		0			0
$161$	−2.05303	+	0.747243i	−0.161802	+	0.0588910i
$162$	−7.13816	+	2.59808i	−0.560826	+	0.204124i
$163$	2.63563	+	4.56504i	0.206438	+	0.357562i	0.950590	−	0.310449i	$-0.100479\pi$
$163$	2.63563	+	4.56504i	0.206438	+	0.357562i	−0.744152	+	0.668011i	$0.767146\pi$
$164$	2.46064	−	4.26195i	0.192143	−	0.332802i
$165$		0			0
$166$	13.7194	−	11.5119i	1.06483	−	0.893501i
$167$	−1.66843	−	1.39998i	−0.129107	−	0.108334i	0.575948	−	0.817487i	$-0.304633\pi$
$167$	−1.66843	−	1.39998i	−0.129107	−	0.108334i	−0.705055	+	0.709153i	$0.749078\pi$
$168$	−0.286989	−	1.62760i	−0.0221417	−	0.125572i
$169$	4.42514	+	1.61062i	0.340396	+	0.123894i
$170$		0			0
$171$	14.8687	+	0.215615i	1.13704	+	0.0164885i
$172$	−3.14290			−0.239644
$173$	6.99912	+	2.54747i	0.532133	+	0.193681i	0.594091	−	0.804398i	$-0.297512\pi$
$173$	6.99912	+	2.54747i	0.532133	+	0.193681i	−0.0619572	+	0.998079i	$0.519734\pi$
$174$	−3.00000	−	17.0138i	−0.227429	−	1.28982i
$175$		0			0
$176$	−0.766044	+	0.642788i	−0.0577428	+	0.0484519i
$177$	−2.65998	+	15.0855i	−0.199936	+	1.13389i
$178$	−8.82295	+	15.2818i	−0.661308	+	1.14542i
$179$	−3.17617	−	5.50130i	−0.237398	−	0.411186i	0.722569	−	0.691299i	$-0.242961\pi$
$179$	−3.17617	−	5.50130i	−0.237398	−	0.411186i	−0.959967	+	0.280113i	$0.909628\pi$
$180$		0			0
$181$	−12.5449	+	4.56596i	−0.932454	+	0.339385i	−0.763182	−	0.646184i	$-0.776364\pi$
$181$	−12.5449	+	4.56596i	−0.932454	+	0.339385i	−0.169272	+	0.985569i	$0.554142\pi$
$182$	−0.939693	−	1.62760i	−0.0696547	−	0.120645i
$183$	6.54576	−	11.3376i	0.483876	−	0.838099i
$184$	−0.581252	+	3.29644i	−0.0428505	+	0.243017i
$185$		0			0
$186$	7.88326	+	6.61484i	0.578028	+	0.485023i
$187$	0.0812519	+	0.460802i	0.00594173	+	0.0336972i
$188$	6.02481	+	2.19285i	0.439405	+	0.159930i
$189$	0.680045			0.0494660
$190$		0			0
$191$	9.17530			0.663901			0.331951	−	0.943297i	$-0.392293\pi$
$191$	9.17530			0.663901			0.331951	+	0.943297i	$0.392293\pi$
$192$	−2.37939	−	0.866025i	−0.171717	−	0.0625000i
$193$	2.64022	+	14.9734i	0.190047	+	1.07781i	0.919298	+	0.393563i	$0.128758\pi$
$193$	2.64022	+	14.9734i	0.190047	+	1.07781i	−0.729251	+	0.684246i	$0.760131\pi$
$194$	11.1099	+	9.32234i	0.797647	+	0.669305i
$195$		0			0
$196$	−1.14156	+	6.47410i	−0.0815399	+	0.462436i
$197$	−8.97906	+	15.5522i	−0.639731	+	1.10805i	0.345760	+	0.938323i	$0.387621\pi$
$197$	−8.97906	+	15.5522i	−0.639731	+	1.10805i	−0.985492	+	0.169724i	$0.945712\pi$
$198$	−1.70574	−	2.95442i	−0.121221	−	0.209962i
$199$	23.2729	−	8.47065i	1.64977	−	0.600468i	0.661065	−	0.750328i	$-0.270105\pi$
$199$	23.2729	−	8.47065i	1.64977	−	0.600468i	0.988707	+	0.149860i	$0.0478823\pi$
$200$		0			0
$201$	−1.11334	−	1.92836i	−0.0785290	−	0.136016i
$202$	−7.47431	+	12.9459i	−0.525890	+	0.910869i
$203$	0.773318	−	4.38571i	0.0542763	−	0.307816i
$204$	−0.907604	+	0.761570i	−0.0635450	+	0.0533206i
$205$		0			0
$206$	−1.25490	−	7.11689i	−0.0874330	−	0.495857i
$207$	−10.7306	−	3.90560i	−0.745825	−	0.271458i
$208$	−2.87939			−0.199649
$209$	−0.694593	−	4.30320i	−0.0480460	−	0.297659i
$210$		0			0
$211$	−10.0522	−	3.65869i	−0.692019	−	0.251874i	−0.0280195	−	0.999607i	$-0.508920\pi$
$211$	−10.0522	−	3.65869i	−0.692019	−	0.251874i	−0.663999	+	0.747733i	$0.731142\pi$
$212$	−0.671122	−	3.80612i	−0.0460928	−	0.261406i
$213$	23.6878	+	19.8764i	1.62306	+	1.36191i
$214$	−5.56805	+	4.67215i	−0.380624	+	0.319381i
$215$		0			0
$216$	0.520945	−	0.902302i	0.0354458	−	0.0613939i
$217$	1.32635	+	2.29731i	0.0900386	+	0.155951i
$218$	8.31180	−	3.02525i	0.562946	−	0.204896i
$219$	1.21301	−	0.441500i	0.0819677	−	0.0298338i
$220$		0			0
$221$	−0.673648	+	1.16679i	−0.0453145	+	0.0784870i
$222$	−3.35844	+	19.0467i	−0.225404	+	1.27833i
$223$	−8.76857	+	7.35770i	−0.587187	+	0.492708i	−0.887298	−	0.461196i	$-0.847421\pi$
$223$	−8.76857	+	7.35770i	−0.587187	+	0.492708i	0.300111	+	0.953904i	$0.402976\pi$
$224$	−0.500000	−	0.419550i	−0.0334077	−	0.0280324i
$225$		0			0
$226$	−1.40033	−	0.509678i	−0.0931486	−	0.0339033i
$227$	−14.3250			−0.950784			−0.475392	−	0.879774i	$-0.657694\pi$
$227$	−14.3250			−0.950784			−0.475392	+	0.879774i	$0.657694\pi$
$228$	8.55690	−	6.97118i	0.566695	−	0.461678i
$229$	−6.08647			−0.402205			−0.201103	−	0.979570i	$-0.564452\pi$
$229$	−6.08647			−0.402205			−0.201103	+	0.979570i	$0.564452\pi$
$230$		0			0
$231$	−0.286989	−	1.62760i	−0.0188825	−	0.107088i
$232$	−5.22668	−	4.38571i	−0.343148	−	0.287936i
$233$	8.46451	−	7.10257i	0.554528	−	0.465305i	−0.321943	−	0.946759i	$-0.604336\pi$
$233$	8.46451	−	7.10257i	0.554528	−	0.465305i	0.876471	+	0.481455i	$0.159891\pi$
$234$	1.70574	−	9.67372i	0.111508	−	0.632391i
$235$		0			0
$236$	3.02481	+	5.23913i	0.196899	+	0.341039i
$237$	20.7408	−	7.54904i	1.34726	−	0.490363i
$238$	−0.286989	+	0.104455i	−0.0186027	+	0.00677084i
$239$	4.02481	+	6.97118i	0.260344	+	0.450928i	0.966333	−	0.257294i	$-0.0828308\pi$
$239$	4.02481	+	6.97118i	0.260344	+	0.450928i	−0.705990	+	0.708222i	$0.749497\pi$
$240$		0			0
$241$	4.80019	−	27.2232i	0.309208	−	1.75360i	−0.293799	−	0.955867i	$-0.594920\pi$
$241$	4.80019	−	27.2232i	0.309208	−	1.75360i	0.603007	−	0.797736i	$-0.293969\pi$
$242$	7.66044	−	6.42788i	0.492432	−	0.413200i
$243$	−17.1288	−	14.3728i	−1.09881	−	0.922015i
$244$	−0.897804	−	5.09170i	−0.0574760	−	0.325962i
$245$		0			0
$246$	12.4611			0.794491
$247$	6.43242	−	10.7773i	0.409285	−	0.685744i
$248$	4.06418			0.258076
$249$	42.6134	+	15.5100i	2.70051	+	0.982907i
$250$		0			0
$251$	−16.8648	−	14.1513i	−1.06450	−	0.893221i	−0.0699563	−	0.997550i	$-0.522286\pi$
$251$	−16.8648	−	14.1513i	−1.06450	−	0.893221i	−0.994543	+	0.104329i	$0.966730\pi$
$252$	1.70574	−	1.43128i	0.107451	−	0.0901624i
$253$	−0.581252	+	3.29644i	−0.0365430	+	0.207246i
$254$	−9.16772	+	15.8790i	−0.575234	+	0.996334i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−13.4547	+	4.89711i	−0.839282	+	0.305474i	−0.725662	−	0.688051i	$-0.758467\pi$
$257$	−13.4547	+	4.89711i	−0.839282	+	0.305474i	−0.113619	+	0.993524i	$0.536244\pi$
$258$	−3.97906	−	6.89193i	−0.247725	−	0.429073i
$259$	−2.49273	+	4.31753i	−0.154890	+	0.268278i
$260$		0			0
$261$	17.8307	−	14.9617i	1.10369	−	0.926108i
$262$	−5.48158	−	4.59959i	−0.338653	−	0.284164i
$263$	−0.828411	−	4.69815i	−0.0510820	−	0.289701i	0.948556	−	0.316610i	$-0.102545\pi$
$263$	−0.828411	−	4.69815i	−0.0510820	−	0.289701i	−0.999638	+	0.0269093i	$0.991433\pi$
$264$	−2.37939	−	0.866025i	−0.146441	−	0.0533002i
$265$		0			0
$266$	2.68732	−	0.934204i	0.164770	−	0.0572797i
$267$	−44.6810			−2.73443
$268$	−0.826352	−	0.300767i	−0.0504775	−	0.0183723i
$269$	0.384133	+	2.17853i	0.0234210	+	0.132827i	0.994276	−	0.106839i	$-0.0340730\pi$
$269$	0.384133	+	2.17853i	0.0234210	+	0.132827i	−0.970855	+	0.239666i	$0.922962\pi$
$270$		0			0
$271$	16.3917	−	13.7543i	0.995726	−	0.835513i	0.00933905	−	0.999956i	$-0.497027\pi$
$271$	16.3917	−	13.7543i	0.995726	−	0.835513i	0.986387	+	0.164443i	$0.0525828\pi$
$272$	−0.0812519	+	0.460802i	−0.00492662	+	0.0279403i
$273$	2.37939	−	4.12122i	0.144007	−	0.249427i
$274$	8.47565	+	14.6803i	0.512033	+	0.886867i
$275$		0			0
$276$	−7.96451	+	2.89884i	−0.479407	+	0.174490i
$277$	−3.87211	−	6.70669i	−0.232653	−	0.402966i	0.725935	−	0.687763i	$-0.241407\pi$
$277$	−3.87211	−	6.70669i	−0.232653	−	0.402966i	−0.958588	+	0.284797i	$0.908074\pi$
$278$	6.34389	−	10.9879i	0.380481	−	0.659013i
$279$	−2.40760	+	13.6542i	−0.144139	+	0.817456i
$280$		0			0
$281$	−10.7968	−	9.05958i	−0.644082	−	0.540449i	0.261186	−	0.965288i	$-0.415886\pi$
$281$	−10.7968	−	9.05958i	−0.644082	−	0.540449i	−0.905269	+	0.424839i	$0.860331\pi$
$282$	2.81908	+	15.9878i	0.167874	+	0.952059i
$283$	4.89053	+	1.78001i	0.290712	+	0.105810i	0.483259	−	0.875477i	$-0.339453\pi$
$283$	4.89053	+	1.78001i	0.290712	+	0.105810i	−0.192548	+	0.981288i	$0.561675\pi$
$284$	12.2121			0.724657
$285$		0			0
$286$	−2.87939			−0.170262
$287$	3.01842	+	1.09861i	0.178172	+	0.0648492i
$288$	−0.592396	−	3.35965i	−0.0349073	−	0.197969i
$289$	−12.8550	−	10.7867i	−0.756179	−	0.634509i
$290$		0			0
$291$	−6.37686	+	36.1650i	−0.373818	+	2.12003i
$292$	0.254900	−	0.441500i	0.0149169	−	0.0258368i
$293$	−13.3341	−	23.0953i	−0.778986	−	1.34924i	−0.932527	−	0.361101i	$-0.882401\pi$
$293$	−13.3341	−	23.0953i	−0.778986	−	1.34924i	0.153541	−	0.988142i	$-0.450932\pi$
$294$	−15.6420	+	5.69323i	−0.912261	+	0.332036i
$295$		0			0
$296$	3.81908	+	6.61484i	0.221979	+	0.384480i
$297$	0.520945	−	0.902302i	0.0302283	−	0.0523569i
$298$	0.593740	−	3.36727i	0.0343945	−	0.195061i
$299$	−7.38326	+	6.19529i	−0.426985	+	0.358283i
$300$		0			0
$301$	−0.356219	−	2.02022i	−0.0205321	−	0.116444i
$302$	14.6211	+	5.32164i	0.841349	+	0.306226i
$303$	−37.8512			−2.17450
$304$	0.819078	−	4.28125i	0.0469773	−	0.245547i
$305$		0			0
$306$	−1.50000	−	0.545955i	−0.0857493	−	0.0312102i
$307$	−5.90925	−	33.5130i	−0.337259	−	1.91269i	−0.403684	−	0.914899i	$-0.632270\pi$
$307$	−5.90925	−	33.5130i	−0.337259	−	1.91269i	0.0664248	−	0.997791i	$-0.478841\pi$
$308$	−0.500000	−	0.419550i	−0.0284901	−	0.0239061i
$309$	14.0175	−	11.7621i	0.797430	−	0.669123i
$310$		0			0
$311$	9.52347	−	16.4951i	0.540026	−	0.935353i	−0.458875	−	0.888501i	$-0.651748\pi$
$311$	9.52347	−	16.4951i	0.540026	−	0.935353i	0.998902	−	0.0468526i	$-0.0149191\pi$
$312$	−3.64543	−	6.31407i	−0.206382	−	0.357464i
$313$	−3.37211	+	1.22735i	−0.190603	+	0.0693738i	−0.435558	−	0.900161i	$-0.643449\pi$
$313$	−3.37211	+	1.22735i	−0.190603	+	0.0693738i	0.244955	+	0.969534i	$0.421227\pi$
$314$	12.4829	−	4.54341i	0.704452	−	0.256400i
$315$		0			0
$316$	4.35844	−	7.54904i	0.245181	−	0.424667i
$317$	−4.89827	+	27.7795i	−0.275114	+	1.56025i	0.463484	+	0.886105i	$0.346599\pi$
$317$	−4.89827	+	27.7795i	−0.275114	+	1.56025i	−0.738599	+	0.674145i	$0.764512\pi$
$318$	7.49660	−	6.29039i	0.420388	−	0.352748i
$319$	−5.22668	−	4.38571i	−0.292638	−	0.245552i
$320$		0			0
$321$	−17.2947	−	6.29477i	−0.965298	−	0.351340i
$322$	−2.18479			−0.121754
$323$	−1.54323	−	1.33353i	−0.0858678	−	0.0741997i
$324$	−7.59627			−0.422015
$325$		0			0
$326$	0.915345	+	5.19118i	0.0506962	+	0.287513i
$327$	17.1570	+	14.3965i	0.948787	+	0.796126i
$328$	3.76991	−	3.16333i	0.208159	−	0.174666i
$329$	−0.726682	+	4.12122i	−0.0400633	+	0.227210i
$330$		0			0
$331$	−4.12108	−	7.13792i	−0.226515	−	0.392336i	0.730258	−	0.683172i	$-0.239400\pi$
$331$	−4.12108	−	7.13792i	−0.226515	−	0.392336i	−0.956773	+	0.290836i	$0.906067\pi$
$332$	16.8293	−	6.12538i	0.923630	−	0.336174i
$333$	−24.4859	+	8.91215i	−1.34182	+	0.488383i
$334$	−1.08899	−	1.88619i	−0.0595870	−	0.103208i
$335$		0			0
$336$	0.286989	−	1.62760i	0.0156565	−	0.0887926i
$337$	−3.15451	+	2.64695i	−0.171837	+	0.144189i	−0.724650	−	0.689117i	$-0.757999\pi$
$337$	−3.15451	+	2.64695i	−0.171837	+	0.144189i	0.552813	+	0.833305i	$0.313554\pi$
$338$	3.60741	+	3.02698i	0.196217	+	0.164646i
$339$	−0.655230	−	3.71599i	−0.0355872	−	0.201825i
$340$		0			0
$341$	4.06418			0.220088
$342$	13.8983	+	5.28801i	0.751532	+	0.285943i
$343$	−8.85978			−0.478383
$344$	−2.95336	−	1.07494i	−0.159235	−	0.0579567i
$345$		0			0
$346$	5.70574	+	4.78768i	0.306742	+	0.257387i
$347$	−0.716881	+	0.601535i	−0.0384842	+	0.0322921i	−0.661827	−	0.749657i	$-0.730219\pi$
$347$	−0.716881	+	0.601535i	−0.0384842	+	0.0322921i	0.623343	+	0.781949i	$0.285774\pi$
$348$	3.00000	−	17.0138i	0.160817	−	0.912038i
$349$	7.03936	−	12.1925i	0.376808	−	0.652651i	−0.613787	−	0.789471i	$-0.710355\pi$
$349$	7.03936	−	12.1925i	0.376808	−	0.652651i	0.990596	+	0.136820i	$0.0436882\pi$
$350$		0			0
$351$	2.81908	−	1.02606i	0.150471	−	0.0547671i
$352$	−0.939693	+	0.342020i	−0.0500858	+	0.0182297i
$353$	−9.39780	−	16.2775i	−0.500195	−	0.866362i	−1.00000		0.000224734i	$-0.999928\pi$
$353$	−9.39780	−	16.2775i	−0.500195	−	0.866362i	0.499805	−	0.866138i	$-0.333405\pi$
$354$	−7.65910	+	13.2660i	−0.407077	+	0.705077i
$355$		0			0
$356$	−13.5175	+	11.3426i	−0.716428	+	0.601155i
$357$	−0.592396	−	0.497079i	−0.0313529	−	0.0263082i
$358$	−1.10307	−	6.25584i	−0.0582993	−	0.330632i
$359$	−27.3307	−	9.94756i	−1.44246	−	0.525012i	−0.501984	−	0.864877i	$-0.667396\pi$
$359$	−27.3307	−	9.94756i	−1.44246	−	0.525012i	−0.940474	+	0.339865i	$0.889619\pi$
$360$		0			0
$361$	14.1946	+	12.6299i	0.747084	+	0.664730i
$362$	−13.3500			−0.701660
$363$	23.7939	+	8.66025i	1.24885	+	0.454545i
$364$	−0.326352	−	1.85083i	−0.0171055	−	0.0970100i
$365$		0			0
$366$	10.0287	−	8.41507i	0.524208	−	0.439863i
$367$	2.94831	−	16.7207i	0.153901	−	0.872813i	−0.805883	−	0.592074i	$-0.798309\pi$
$367$	2.94831	−	16.7207i	0.153901	−	0.872813i	0.959784	−	0.280739i	$-0.0905796\pi$
$368$	−1.67365	+	2.89884i	−0.0872449	+	0.151113i
$369$	8.39440	+	14.5395i	0.436995	+	0.756898i
$370$		0			0
$371$	2.37046	−	0.862778i	0.123068	−	0.0447932i
$372$	5.14543	+	8.91215i	0.266778	+	0.462073i
$373$	−2.06371	+	3.57445i	−0.106855	+	0.185078i	−0.914495	−	0.404598i	$-0.867411\pi$
$373$	−2.06371	+	3.57445i	−0.106855	+	0.185078i	0.807640	+	0.589676i	$0.200745\pi$
$374$	−0.0812519	+	0.460802i	−0.00420144	+	0.0238275i
$375$		0			0
$376$	4.91147	+	4.12122i	0.253290	+	0.212535i
$377$	−3.41147	−	19.3474i	−0.175700	−	0.996443i
$378$	0.639033	+	0.232589i	0.0328683	+	0.0119631i
$379$	−23.1702			−1.19018			−0.595088	−	0.803661i	$-0.702883\pi$
$379$	−23.1702			−1.19018			−0.595088	+	0.803661i	$0.702883\pi$
$380$		0			0
$381$	−46.4270			−2.37852
$382$	8.62196	+	3.13814i	0.441138	+	0.160561i
$383$	5.54664	+	31.4565i	0.283420	+	1.60735i	0.710876	+	0.703318i	$0.248299\pi$
$383$	5.54664	+	31.4565i	0.283420	+	1.60735i	−0.427456	+	0.904036i	$0.640590\pi$
$384$	−1.93969	−	1.62760i	−0.0989845	−	0.0830579i
$385$		0			0
$386$	−2.64022	+	14.9734i	−0.134383	+	0.762126i
$387$	5.36097	−	9.28547i	0.272513	−	0.472007i
$388$	7.25150	+	12.5600i	0.368139	+	0.637635i
$389$	25.8717	−	9.41653i	1.31175	−	0.477437i	0.410943	−	0.911661i	$-0.365200\pi$
$389$	25.8717	−	9.41653i	1.31175	−	0.477437i	0.900805	+	0.434224i	$0.142977\pi$
$390$		0			0
$391$	0.783119	+	1.35640i	0.0396040	+	0.0685962i
$392$	−3.28699	+	5.69323i	−0.166018	+	0.287552i
$393$	3.14631	−	17.8436i	0.158710	−	0.900090i
$394$	−13.7567	+	11.5433i	−0.693053	+	0.581541i
$395$		0			0
$396$	−0.592396	−	3.35965i	−0.0297690	−	0.168829i
$397$	25.7977	+	9.38960i	1.29475	+	0.471251i	0.895284	−	0.445497i	$-0.146973\pi$
$397$	25.7977	+	9.38960i	1.29475	+	0.471251i	0.399467	+	0.916748i	$0.369195\pi$
$398$	24.7665			1.24143
$399$	5.45084	+	4.71015i	0.272883	+	0.235803i
$400$		0			0
$401$	−24.0624	−	8.75801i	−1.20162	−	0.437354i	−0.337831	−	0.941207i	$-0.609693\pi$
$401$	−24.0624	−	8.75801i	−1.20162	−	0.437354i	−0.863789	+	0.503853i	$0.831915\pi$
$402$	−0.386659	−	2.19285i	−0.0192848	−	0.109370i
$403$	8.96451	+	7.52211i	0.446554	+	0.374703i
$404$	−11.4513	+	9.60878i	−0.569724	+	0.478055i
$405$		0			0
$406$	2.22668	−	3.85673i	0.110508	−	0.191406i
$407$	3.81908	+	6.61484i	0.189305	+	0.327885i
$408$	−1.11334	+	0.405223i	−0.0551186	+	0.0200615i
$409$	16.4675	−	5.99368i	0.814265	−	0.296368i	0.0988809	−	0.995099i	$-0.468474\pi$
$409$	16.4675	−	5.99368i	0.814265	−	0.296368i	0.715385	+	0.698731i	$0.246252\pi$
$410$		0			0
$411$	−21.4611	+	37.1717i	−1.05860	+	1.83355i
$412$	1.25490	−	7.11689i	0.0618245	−	0.350624i
$413$	−3.02481	+	2.53812i	−0.148841	+	0.124893i
$414$	−8.74763	−	7.34013i	−0.429922	−	0.360748i
$415$		0			0
$416$	−2.70574	−	0.984808i	−0.132660	−	0.0482842i
$417$	32.1266			1.57325
$418$	0.819078	−	4.28125i	0.0400624	−	0.209403i
$419$	−32.8776			−1.60618			−0.803089	−	0.595860i	$-0.796812\pi$
$419$	−32.8776			−1.60618			−0.803089	+	0.595860i	$0.796812\pi$
$420$		0			0
$421$	−0.931074	−	5.28039i	−0.0453778	−	0.257350i	0.953676	−	0.300835i	$-0.0972652\pi$
$421$	−0.931074	−	5.28039i	−0.0453778	−	0.257350i	−0.999054	+	0.0434844i	$0.986154\pi$
$422$	−8.19459	−	6.87608i	−0.398907	−	0.334722i
$423$	−16.7554	+	14.0594i	−0.814674	+	0.683592i
$424$	0.671122	−	3.80612i	0.0325926	−	0.184842i
$425$		0			0
$426$	15.4611	+	26.7794i	0.749093	+	1.29747i
$427$	3.17112	−	1.15419i	0.153461	−	0.0558554i
$428$	−6.83022	+	2.48600i	−0.330151	+	0.120165i
$429$	−3.64543	−	6.31407i	−0.176003	−	0.304846i
$430$		0			0
$431$	−3.80557	+	21.5825i	−0.183308	+	1.03959i	0.744802	+	0.667285i	$0.232544\pi$
$431$	−3.80557	+	21.5825i	−0.183308	+	1.03959i	−0.928110	+	0.372305i	$0.878567\pi$
$432$	0.798133	−	0.669713i	0.0384002	−	0.0322216i
$433$	−6.11515	−	5.13122i	−0.293875	−	0.246591i	0.483914	−	0.875115i	$-0.339215\pi$
$433$	−6.11515	−	5.13122i	−0.293875	−	0.246591i	−0.777790	+	0.628525i	$0.783659\pi$
$434$	0.460637	+	2.61240i	0.0221113	+	0.125399i
$435$		0			0
$436$	8.84524			0.423610
$437$	−7.11128	−	12.7402i	−0.340179	−	0.609447i
$438$	1.29086			0.0616796
$439$	26.2456	+	9.55261i	1.25263	+	0.455921i	0.881290	−	0.472575i	$-0.156675\pi$
$439$	26.2456	+	9.55261i	1.25263	+	0.455921i	0.371342	+	0.928496i	$0.378898\pi$
$440$		0			0
$441$	−17.1800	−	14.4158i	−0.818097	−	0.686465i
$442$	−1.03209	+	0.866025i	−0.0490915	+	0.0411926i
$443$	−1.33069	+	7.54671i	−0.0632229	+	0.358555i	0.936741	+	0.350024i	$0.113827\pi$
$443$	−1.33069	+	7.54671i	−0.0632229	+	0.358555i	−0.999964	+	0.00853096i	$0.997284\pi$
$444$	−9.67024	+	16.7494i	−0.458929	+	0.794889i
$445$		0			0
$446$	−10.7562	+	3.91495i	−0.509323	+	0.185378i
$447$	8.13563	−	2.96113i	0.384802	−	0.140057i
$448$	−0.326352	−	0.565258i	−0.0154187	−	0.0267059i
$449$	−10.4807	+	18.1531i	−0.494615	+	0.856698i	−0.999981	−	0.00620692i	$-0.998024\pi$
$449$	−10.4807	+	18.1531i	−0.494615	+	0.856698i	0.505366	+	0.862905i	$0.331358\pi$
$450$		0			0
$451$	3.76991	−	3.16333i	0.177518	−	0.148956i
$452$	−1.14156	−	0.957882i	−0.0536944	−	0.0450550i
$453$	6.84137	+	38.7993i	0.321435	+	1.82295i
$454$	−13.4611	−	4.89944i	−0.631761	−	0.229942i
$455$		0			0
$456$	10.4251	−	3.62414i	0.488202	−	0.169716i
$457$	−26.6563			−1.24693			−0.623465	−	0.781851i	$-0.714276\pi$
$457$	−26.6563			−1.24693			−0.623465	+	0.781851i	$0.714276\pi$
$458$	−5.71941	−	2.08169i	−0.267250	−	0.0972712i
$459$	−0.0846555	−	0.480105i	−0.00395138	−	0.0224094i
$460$		0			0
$461$	−4.47178	+	3.75227i	−0.208272	+	0.174761i	−0.740957	−	0.671553i	$-0.765628\pi$
$461$	−4.47178	+	3.75227i	−0.208272	+	0.174761i	0.532685	+	0.846314i	$0.321183\pi$
$462$	0.286989	−	1.62760i	0.0133519	−	0.0757226i
$463$	−13.8610	+	24.0079i	−0.644174	+	1.11574i	0.340318	+	0.940310i	$0.389465\pi$
$463$	−13.8610	+	24.0079i	−0.644174	+	1.11574i	−0.984492	+	0.175431i	$0.943868\pi$
$464$	−3.41147	−	5.90885i	−0.158374	−	0.274311i
$465$		0			0
$466$	10.3833	−	3.77920i	0.480995	−	0.175068i
$467$	−10.0312	−	17.3746i	−0.464189	−	0.803999i	0.534975	−	0.844868i	$-0.320321\pi$
$467$	−10.0312	−	17.3746i	−0.464189	−	0.803999i	−0.999165	+	0.0408685i	$0.986988\pi$
$468$	4.91147	−	8.50692i	0.227033	−	0.393233i
$469$	0.0996702	−	0.565258i	0.00460234	−	0.0261012i
$470$		0			0
$471$	25.7670	+	21.6211i	1.18728	+	0.996246i
$472$	1.05051	+	5.95772i	0.0483535	+	0.274226i
$473$	−2.95336	−	1.07494i	−0.135796	−	0.0494256i
$474$	22.0719			1.01380
$475$		0			0
$476$	−0.305407			−0.0139983
$477$	12.3897	+	4.50946i	0.567283	+	0.206474i
$478$	1.39780	+	7.92734i	0.0639340	+	0.362588i
$479$	−14.9199	−	12.5193i	−0.681709	−	0.572022i	0.234796	−	0.972045i	$-0.424558\pi$
$479$	−14.9199	−	12.5193i	−0.681709	−	0.572022i	−0.916505	+	0.400023i	$0.869002\pi$
$480$		0			0
$481$	−3.81908	+	21.6591i	−0.174135	+	0.987568i
$482$	13.8216	−	23.9397i	0.629557	−	1.09042i
$483$	−2.76604	−	4.79093i	−0.125859	−	0.217995i
$484$	9.39693	−	3.42020i	0.427133	−	0.155464i
$485$		0			0
$486$	−11.1800	−	19.3644i	−0.507137	−	0.878387i
$487$	15.4003	−	26.6742i	0.697856	−	1.20872i	−0.271353	−	0.962480i	$-0.587471\pi$
$487$	15.4003	−	26.6742i	0.697856	−	1.20872i	0.969209	−	0.246241i	$-0.0791956\pi$
$488$	0.897804	−	5.09170i	0.0406417	−	0.230490i
$489$	−10.2246	+	8.57948i	−0.462373	+	0.387977i
$490$		0			0
$491$	1.82383	+	10.3434i	0.0823081	+	0.466792i	0.997905	+	0.0646952i	$0.0206075\pi$
$491$	1.82383	+	10.3434i	0.0823081	+	0.466792i	−0.915597	+	0.402097i	$0.868281\pi$
$492$	11.7096	+	4.26195i	0.527910	+	0.192143i
$493$	−3.19253			−0.143784
$494$	9.73055	−	7.92734i	0.437798	−	0.356668i
$495$		0			0
$496$	3.81908	+	1.39003i	0.171482	+	0.0624142i
$497$	1.38413	+	7.84981i	0.0620868	+	0.352112i
$498$	34.7388	+	29.1493i	1.55668	+	1.30621i
$499$	6.10085	−	5.11922i	0.273112	−	0.229168i	−0.495936	−	0.868359i	$-0.665175\pi$
$499$	6.10085	−	5.11922i	0.273112	−	0.229168i	0.769048	+	0.639191i	$0.220731\pi$
$500$		0			0
$501$	2.75743	−	4.77600i	0.123193	−	0.213376i
$502$	−11.0077	−	19.0660i	−0.491300	−	0.850956i
$503$	11.1823	−	4.07001i	0.498593	−	0.181473i	−0.0804683	−	0.996757i	$-0.525642\pi$
$503$	11.1823	−	4.07001i	0.498593	−	0.181473i	0.579061	+	0.815284i	$0.303419\pi$
$504$	2.09240	−	0.761570i	0.0932027	−	0.0339230i
$505$		0			0
$506$	−1.67365	+	2.89884i	−0.0744027	+	0.128869i
$507$	−2.07057	+	11.7428i	−0.0919574	+	0.521517i
$508$	−14.0458	+	11.7858i	−0.623180	+	0.522910i
$509$	−9.73442	−	8.16815i	−0.431471	−	0.362047i	0.401036	−	0.916062i	$-0.368650\pi$
$509$	−9.73442	−	8.16815i	−0.431471	−	0.362047i	−0.832506	+	0.554016i	$0.813095\pi$
$510$		0			0
$511$	0.312681	+	0.113807i	0.0138322	+	0.00503451i
$512$	−1.00000			−0.0441942
$513$	0.723689	+	4.48346i	0.0319516	+	0.197950i
$514$	−14.3182			−0.631549
$515$		0			0
$516$	−1.38191	−	7.83721i	−0.0608353	−	0.345014i
$517$	4.91147	+	4.12122i	0.216006	+	0.181251i
$518$	−3.81908	+	3.20459i	−0.167801	+	0.140801i
$519$	−3.27497	+	18.5733i	−0.143755	+	0.815276i
$520$		0			0
$521$	12.6138	+	21.8478i	0.552621	+	0.957168i	0.998084	+	0.0618674i	$0.0197056\pi$
$521$	12.6138	+	21.8478i	0.552621	+	0.957168i	−0.445463	+	0.895300i	$0.646961\pi$
$522$	21.8726	−	7.96097i	0.957337	−	0.348442i
$523$	−41.4406	+	15.0832i	−1.81207	+	0.659540i	−0.815320	+	0.579011i	$0.803439\pi$
$523$	−41.4406	+	15.0832i	−1.81207	+	0.659540i	−0.996752	+	0.0805294i	$0.974339\pi$
$524$	−3.57785	−	6.19702i	−0.156299	−	0.270718i
$525$		0			0
$526$	0.828411	−	4.69815i	0.0361204	−	0.204849i
$527$	1.45677	−	1.22237i	0.0634578	−	0.0532474i
$528$	−1.93969	−	1.62760i	−0.0844143	−	0.0708320i
$529$	−2.04829	−	11.6164i	−0.0890559	−	0.505061i
$530$		0			0
$531$	−20.6382			−0.895620
$532$	2.84477	+	0.0412527i	0.123336	+	0.00178853i
$533$	14.1702			0.613781
$534$	−41.9864	−	15.2818i	−1.81693	−	0.661308i
$535$		0			0
$536$	−0.673648	−	0.565258i	−0.0290972	−	0.0244154i
$537$	12.3216	−	10.3391i	0.531716	−	0.446163i
$538$	−0.384133	+	2.17853i	−0.0165611	+	0.0939229i
$539$	−3.28699	+	5.69323i	−0.141581	+	0.245225i
$540$		0			0
$541$	31.7759	−	11.5655i	1.36615	−	0.497239i	0.448202	−	0.893933i	$-0.352065\pi$
$541$	31.7759	−	11.5655i	1.36615	−	0.497239i	0.917951	+	0.396694i	$0.129842\pi$
$542$	20.1074	−	7.31850i	0.863687	−	0.314356i
$543$	−16.9017	−	29.2746i	−0.725320	−	1.25629i
$544$	−0.233956	+	0.405223i	−0.0100308	+	0.0173738i
$545$		0			0
$546$	3.64543	−	3.05888i	0.156010	−	0.130908i
$547$	19.9308	+	16.7239i	0.852181	+	0.715064i	0.960269	−	0.279077i	$-0.0900284\pi$
$547$	19.9308	+	16.7239i	0.852181	+	0.715064i	−0.108088	+	0.994141i	$0.534473\pi$
$548$	2.94356	+	16.6938i	0.125743	+	0.713123i
$549$	16.5744	+	6.03260i	0.707380	+	0.257465i
$550$		0			0
$551$	29.7374	+	0.431229i	1.26686	+	0.0183710i
$552$	−8.47565			−0.360748
$553$	5.34642	+	1.94594i	0.227353	+	0.0827497i
$554$	−1.34477	−	7.62657i	−0.0571338	−	0.324022i
$555$		0			0
$556$	9.71941	−	8.15555i	0.412195	−	0.345872i
$557$	−3.32723	+	18.8697i	−0.140979	+	0.799533i	0.829529	+	0.558464i	$0.188609\pi$
$557$	−3.32723	+	18.8697i	−0.140979	+	0.799533i	−0.970508	+	0.241069i	$0.922502\pi$
$558$	−6.93242	+	12.0073i	−0.293473	+	0.508310i
$559$	−4.52481	−	7.83721i	−0.191379	−	0.331479i
$560$		0			0
$561$	−1.11334	+	0.405223i	−0.0470053	+	0.0171085i
$562$	−7.04710	−	12.2059i	−0.297264	−	0.514877i
$563$	−3.96791	+	6.87262i	−0.167228	+	0.289647i	−0.937444	−	0.348136i	$-0.886815\pi$
$563$	−3.96791	+	6.87262i	−0.167228	+	0.289647i	0.770217	+	0.637782i	$0.220148\pi$
$564$	−2.81908	+	15.9878i	−0.118705	+	0.673207i
$565$		0			0
$566$	3.98680	+	3.34532i	0.167578	+	0.140614i
$567$	−0.860967	−	4.88279i	−0.0361572	−	0.205058i
$568$	11.4757	+	4.17680i	0.481508	+	0.175254i
$569$	9.12929			0.382720			0.191360	−	0.981520i	$-0.438710\pi$
$569$	9.12929			0.382720			0.191360	+	0.981520i	$0.438710\pi$
$570$		0			0
$571$	−21.4587			−0.898020			−0.449010	−	0.893527i	$-0.648223\pi$
$571$	−21.4587			−0.898020			−0.449010	+	0.893527i	$0.648223\pi$
$572$	−2.70574	−	0.984808i	−0.113133	−	0.0411769i
$573$	4.03431	+	22.8797i	0.168536	+	0.955814i
$574$	2.46064	+	2.06472i	0.102705	+	0.0861797i
$575$		0			0
$576$	0.592396	−	3.35965i	0.0246832	−	0.139985i
$577$	17.1694	−	29.7382i	0.714770	−	1.23802i	−0.248278	−	0.968689i	$-0.579865\pi$
$577$	17.1694	−	29.7382i	0.714770	−	1.23802i	0.963048	−	0.269329i	$-0.0868020\pi$
$578$	−8.39053	−	14.5328i	−0.349000	−	0.604486i
$579$	−36.1771	+	13.1674i	−1.50347	+	0.547218i
$580$		0			0
$581$	5.84477	+	10.1234i	0.242482	+	0.419991i
$582$	−18.3614	+	31.8029i	−0.761106	+	1.31827i
$583$	0.671122	−	3.80612i	0.0277950	−	0.157633i
$584$	0.390530	−	0.327693i	0.0161602	−	0.0135600i
$585$		0			0
$586$	−4.63088	−	26.2630i	−0.191300	−	1.08492i
$587$	−21.2433	−	7.73195i	−0.876807	−	0.319132i	−0.135886	−	0.990724i	$-0.543388\pi$
$587$	−21.2433	−	7.73195i	−0.876807	−	0.319132i	−0.740920	+	0.671593i	$0.765610\pi$
$588$	−16.6459			−0.686465
$589$	−13.7344	+	11.1892i	−0.565917	+	0.461044i
$590$		0			0
$591$	−42.7293	−	15.5522i	−1.75765	−	0.639731i
$592$	1.32635	+	7.52211i	0.0545127	+	0.309157i
$593$	−24.7217	−	20.7440i	−1.01520	−	0.851852i	−0.0261814	−	0.999657i	$-0.508335\pi$
$593$	−24.7217	−	20.7440i	−1.01520	−	0.851852i	−0.989017	+	0.147805i	$0.952779\pi$
$594$	0.798133	−	0.669713i	0.0327478	−	0.0274787i
$595$		0			0
$596$	1.70961	−	2.96113i	0.0700283	−	0.121292i
$597$	31.3555	+	54.3093i	1.28330	+	2.22273i
$598$	−9.05690	+	3.29644i	−0.370364	+	0.134802i
$599$	5.03849	−	1.83386i	0.205867	−	0.0749294i	−0.237029	−	0.971503i	$-0.576173\pi$
$599$	5.03849	−	1.83386i	0.205867	−	0.0749294i	0.442895	+	0.896573i	$0.353951\pi$
$600$		0			0
$601$	−17.8319	+	30.8857i	−0.727377	+	1.25985i	0.230611	+	0.973046i	$0.425928\pi$
$601$	−17.8319	+	30.8857i	−0.727377	+	1.25985i	−0.957988	+	0.286808i	$0.907406\pi$
$602$	0.356219	−	2.02022i	0.0145184	−	0.0823380i
$603$	2.29813	−	1.92836i	0.0935872	−	0.0785290i
$604$	11.9192	+	10.0014i	0.484986	+	0.406952i
$605$		0			0
$606$	−35.5685	−	12.9459i	−1.44487	−	0.525890i
$607$	−6.93077			−0.281311			−0.140656	−	0.990059i	$-0.544921\pi$
$607$	−6.93077			−0.281311			−0.140656	+	0.990059i	$0.544921\pi$
$608$	2.23396	−	3.74292i	0.0905989	−	0.151795i
$609$	11.2763			0.456939
$610$		0			0
$611$	3.20574	+	18.1806i	0.129690	+	0.735510i
$612$	−1.22281	−	1.02606i	−0.0494292	−	0.0414760i
$613$	15.7658	−	13.2291i	0.636775	−	0.534317i	−0.266251	−	0.963904i	$-0.585785\pi$
$613$	15.7658	−	13.2291i	0.636775	−	0.534317i	0.903026	+	0.429586i	$0.141341\pi$
$614$	5.90925	−	33.5130i	0.238478	−	1.35248i
$615$		0			0
$616$	−0.326352	−	0.565258i	−0.0131491	−	0.0227749i
$617$	−25.0976	+	9.13478i	−1.01039	+	0.367753i	−0.793583	−	0.608462i	$-0.791787\pi$
$617$	−25.0976	+	9.13478i	−1.01039	+	0.367753i	−0.216808	+	0.976214i	$0.569565\pi$
$618$	17.1951	−	6.25849i	0.691687	−	0.251753i
$619$	2.15405	+	3.73092i	0.0865785	+	0.149958i	0.906063	−	0.423143i	$-0.139073\pi$
$619$	2.15405	+	3.73092i	0.0865785	+	0.149958i	−0.819484	+	0.573102i	$0.805740\pi$
$620$		0			0
$621$	0.605600	−	3.43453i	0.0243019	−	0.137823i
$622$	14.5908	−	12.2431i	0.585038	−	0.490905i
$623$	−8.82295	−	7.40333i	−0.353484	−	0.296608i
$624$	−1.26604	−	7.18009i	−0.0506823	−	0.287434i
$625$		0			0
$626$	−3.58853			−0.143426
$627$	10.4251	−	3.62414i	0.416340	−	0.144734i
$628$	13.2841			0.530091
$629$	3.35844	+	1.22237i	0.133910	+	0.0487392i
$630$		0			0
$631$	−10.5988	−	8.89344i	−0.421931	−	0.354042i	0.406966	−	0.913443i	$-0.366587\pi$
$631$	−10.5988	−	8.89344i	−0.421931	−	0.354042i	−0.828897	+	0.559401i	$0.811031\pi$
$632$	6.67752	−	5.60310i	0.265617	−	0.222879i
$633$	4.70352	−	26.6750i	0.186948	−	1.06023i
$634$	−14.1040	+	24.4289i	−0.560142	+	0.970194i
$635$		0			0
$636$	9.19594	−	3.34705i	0.364643	−	0.132719i
$637$	−17.7875	+	6.47410i	−0.704765	+	0.256513i
$638$	−3.41147	−	5.90885i	−0.135062	−	0.233933i
$639$	−20.8307	+	36.0798i	−0.824049	+	1.42730i
$640$		0			0
$641$	2.43969	−	2.04715i	0.0963621	−	0.0808574i	−0.593334	−	0.804956i	$-0.702189\pi$
$641$	2.43969	−	2.04715i	0.0963621	−	0.0808574i	0.689696	+	0.724099i	$0.257744\pi$
$642$	−14.0988	−	11.8303i	−0.556435	−	0.466904i
$643$	−2.09327	−	11.8715i	−0.0825507	−	0.468168i	−0.997858	−	0.0654126i	$-0.979164\pi$
$643$	−2.09327	−	11.8715i	−0.0825507	−	0.468168i	0.915308	−	0.402755i	$-0.131947\pi$
$644$	−2.05303	−	0.747243i	−0.0809009	−	0.0294455i
$645$		0			0
$646$	−0.994070	−	1.78093i	−0.0391112	−	0.0700696i
$647$	−25.3105			−0.995057			−0.497528	−	0.867448i	$-0.665759\pi$
$647$	−25.3105			−0.995057			−0.497528	+	0.867448i	$0.665759\pi$
$648$	−7.13816	−	2.59808i	−0.280413	−	0.102062i
$649$	1.05051	+	5.95772i	0.0412360	+	0.233861i
$650$		0			0
$651$	−5.14543	+	4.31753i	−0.201665	+	0.169217i
$652$	−0.915345	+	5.19118i	−0.0358477	+	0.203302i
$653$	0.718226	−	1.24400i	0.0281063	−	0.0486816i	−0.851630	−	0.524143i	$-0.824386\pi$
$653$	0.718226	−	1.24400i	0.0281063	−	0.0486816i	0.879736	+	0.475462i	$0.157719\pi$
$654$	11.1985	+	19.3963i	0.437895	+	0.758456i
$655$		0			0
$656$	4.62449	−	1.68317i	0.180556	−	0.0657169i
$657$	0.869585	+	1.50617i	0.0339257	+	0.0587611i
$658$	−2.09240	+	3.62414i	−0.0815701	+	0.141284i
$659$	−0.0736733	+	0.417822i	−0.00286990	+	0.0162760i	−0.986209	−	0.165504i	$-0.947075\pi$
$659$	−0.0736733	+	0.417822i	−0.00286990	+	0.0162760i	0.983339	+	0.181780i	$0.0581860\pi$
$660$		0			0
$661$	−8.34074	−	6.99871i	−0.324417	−	0.272218i	0.466003	−	0.884783i	$-0.345693\pi$
$661$	−8.34074	−	6.99871i	−0.324417	−	0.272218i	−0.790420	+	0.612565i	$0.790138\pi$
$662$	−1.43124	−	8.11695i	−0.0556266	−	0.315474i
$663$	−3.20574	−	1.16679i	−0.124501	−	0.0453145i
$664$	17.9094			0.695020
$665$		0			0
$666$	−26.0574			−1.00970
$667$	−21.4611	−	7.81120i	−0.830977	−	0.302451i
$668$	−0.378203	−	2.14490i	−0.0146331	−	0.0829886i
$669$	−22.2028	−	18.6304i	−0.858410	−	0.720291i
$670$		0			0
$671$	0.897804	−	5.09170i	0.0346593	−	0.196563i
$672$	0.826352	−	1.43128i	0.0318772	−	0.0552130i
$673$	−17.6827	−	30.6274i	−0.681619	−	1.18060i	−0.974487	−	0.224446i	$-0.927943\pi$
$673$	−17.6827	−	30.6274i	−0.681619	−	1.18060i	0.292867	−	0.956153i	$-0.405391\pi$
$674$	−3.86959	+	1.40841i	−0.149051	+	0.0542501i
$675$		0			0
$676$	2.35457	+	4.07824i	0.0905604	+	0.156855i
$677$	−15.9757	+	27.6706i	−0.613994	+	1.06347i	0.376566	+	0.926390i	$0.377105\pi$
$677$	−15.9757	+	27.6706i	−0.613994	+	1.06347i	−0.990560	+	0.137079i	$0.956228\pi$
$678$	0.655230	−	3.71599i	0.0251640	−	0.142712i
$679$	−7.25150	+	6.08473i	−0.278287	+	0.233510i
$680$		0			0
$681$	−6.29860	−	35.7211i	−0.241363	−	1.36884i
$682$	3.81908	+	1.39003i	0.146240	+	0.0532270i
$683$	−30.2327			−1.15682			−0.578410	−	0.815746i	$-0.696327\pi$
$683$	−30.2327			−1.15682			−0.578410	+	0.815746i	$0.696327\pi$
$684$	11.2515	+	9.72259i	0.430212	+	0.371753i
$685$		0			0
$686$	−8.32547	−	3.03022i	−0.317868	−	0.115695i
$687$	−2.67617	−	15.1773i	−0.102102	−	0.579052i
$688$	−2.40760	−	2.02022i	−0.0917890	−	0.0770201i
$689$	8.52481	−	7.15317i	0.324770	−	0.272514i
$690$		0			0
$691$	20.5829	−	35.6506i	0.783010	−	1.35621i	−0.147170	−	0.989111i	$-0.547016\pi$
$691$	20.5829	−	35.6506i	0.783010	−	1.35621i	0.930180	−	0.367103i	$-0.119650\pi$
$692$	3.72416	+	6.45043i	0.141571	+	0.245208i
$693$	2.09240	−	0.761570i	0.0794836	−	0.0289297i
$694$	−0.879385	+	0.320070i	−0.0333810	+	0.0121497i
$695$		0			0
$696$	8.63816	−	14.9617i	0.327428	−	0.567123i
$697$	0.399863	−	2.26774i	0.0151459	−	0.0858966i
$698$	10.7849	−	9.04963i	0.408216	−	0.342534i
$699$	21.4329	+	17.9843i	0.810666	+	0.680230i
$700$		0			0
$701$	17.5373	+	6.38306i	0.662375	+	0.241085i	0.651261	−	0.758854i	$-0.274240\pi$
$701$	17.5373	+	6.38306i	0.662375	+	0.241085i	0.0111135	+	0.999938i	$0.496462\pi$
$702$	3.00000			0.113228
$703$	−31.1177	−	11.8396i	−1.17363	−	0.446541i
$704$	−1.00000			−0.0376889
$705$		0			0
$706$	−3.26382	−	18.5101i	−0.122836	−	0.696635i
$707$	−7.47431	−	6.27169i	−0.281100	−	0.235871i
$708$	−11.7344	+	9.84635i	−0.441007	+	0.370048i
$709$	−6.62536	+	37.5743i	−0.248821	+	1.41113i	0.562629	+	0.826710i	$0.309790\pi$
$709$	−6.62536	+	37.5743i	−0.248821	+	1.41113i	−0.811449	+	0.584423i	$0.801321\pi$
$710$		0			0
$711$	14.8687	+	25.7534i	0.557620	+	0.965826i
$712$	−16.5817	+	6.03525i	−0.621426	+	0.226181i
$713$	12.7836	−	4.65284i	0.478749	−	0.174250i
$714$	−0.386659	−	0.669713i	−0.0144704	−	0.0250634i
$715$		0			0
$716$	1.10307	−	6.25584i	0.0412238	−	0.233792i
$717$	−15.6138	+	13.1015i	−0.583108	+	0.489286i
$718$	−22.2802	−	18.6953i	−0.831489	−	0.697702i
$719$	2.94516	+	16.7028i	0.109836	+	0.622910i	0.989178	+	0.146720i	$0.0468715\pi$
$719$	2.94516	+	16.7028i	0.109836	+	0.622910i	−0.879342	+	0.476190i	$0.842017\pi$
$720$		0			0
$721$	4.71688			0.175666
$722$	9.01889	+	16.7230i	0.335648	+	0.622367i
$723$	69.9951			2.60314
$724$	−12.5449	−	4.56596i	−0.466227	−	0.169693i
$725$		0			0
$726$	19.3969	+	16.2760i	0.719887	+	0.604057i
$727$	23.9047	−	20.0584i	0.886575	−	0.743925i	−0.0809452	−	0.996719i	$-0.525794\pi$
$727$	23.9047	−	20.0584i	0.886575	−	0.743925i	0.967520	+	0.252794i	$0.0813494\pi$
$728$	0.326352	−	1.85083i	0.0120954	−	0.0685964i
$729$	16.9145	−	29.2967i	0.626462	−	1.08506i
$730$		0			0
$731$	−1.38191	+	0.502975i	−0.0511118	+	0.0186032i
$732$	12.3020	−	4.47756i	0.454695	−	0.165495i
$733$	5.54370	+	9.60197i	0.204761	+	0.354657i	0.950057	−	0.312078i	$-0.101025\pi$
$733$	5.54370	+	9.60197i	0.204761	+	0.354657i	−0.745295	+	0.666734i	$0.767692\pi$
$734$	8.48932	−	14.7039i	0.313347	−	0.542732i
$735$		0			0
$736$	−2.56418	+	2.15160i	−0.0945168	+	0.0793091i
$737$	−0.673648	−	0.565258i	−0.0248141	−	0.0208215i
$738$	2.91534	+	16.5337i	0.107315	+	0.608615i
$739$	11.0842	+	4.03434i	0.407741	+	0.148405i	0.537744	−	0.843108i	$-0.319277\pi$
$739$	11.0842	+	4.03434i	0.407741	+	0.148405i	−0.130004	+	0.991514i	$0.541499\pi$
$740$		0			0
$741$	29.7028	+	11.3013i	1.09116	+	0.415164i
$742$	2.52259			0.0926073
$743$	−10.7956	−	3.92928i	−0.396052	−	0.144151i	0.136313	−	0.990666i	$-0.456475\pi$
$743$	−10.7956	−	3.92928i	−0.396052	−	0.144151i	−0.532366	+	0.846514i	$0.678697\pi$
$744$	1.78699	+	10.1345i	0.0655142	+	0.371549i
$745$		0			0
$746$	−3.16179	+	2.65306i	−0.115761	+	0.0971353i
$747$	−10.6095	+	60.1693i	−0.388180	+	2.20148i
$748$	−0.233956	+	0.405223i	−0.00855426	+	0.0148164i
$749$	−2.37211	−	4.10862i	−0.0866751	−	0.150126i
$750$		0			0
$751$	39.2717	−	14.2937i	1.43305	−	0.521586i	0.495243	−	0.868755i	$-0.335079\pi$
$751$	39.2717	−	14.2937i	1.43305	−	0.521586i	0.937803	+	0.347169i	$0.112857\pi$
$752$	3.20574	+	5.55250i	0.116901	+	0.202479i
$753$	27.8726	−	48.2767i	1.01573	−	1.75930i
$754$	3.41147	−	19.3474i	0.124239	−	0.704592i
$755$		0			0
$756$	0.520945	+	0.437124i	0.0189466	+	0.0158981i
$757$	−7.81820	−	44.3392i	−0.284157	−	1.61154i	−0.708280	−	0.705932i	$-0.750529\pi$
$757$	−7.81820	−	44.3392i	−0.284157	−	1.61154i	0.424123	−	0.905605i	$-0.360583\pi$
$758$	−21.7729	−	7.92469i	−0.790828	−	0.287838i
$759$	−8.47565			−0.307647
$760$		0			0
$761$	−27.3604			−0.991814			−0.495907	−	0.868376i	$-0.665164\pi$
$761$	−27.3604			−0.991814			−0.495907	+	0.868376i	$0.665164\pi$
$762$	−43.6271	−	15.8790i	−1.58044	−	0.575234i
$763$	1.00253	+	5.68561i	0.0362939	+	0.205833i
$764$	7.02869	+	5.89777i	0.254289	+	0.213374i
$765$		0			0
$766$	−5.54664	+	31.4565i	−0.200408	+	1.13657i
$767$	−8.70961	+	15.0855i	−0.314486	+	0.544705i
$768$	−1.26604	−	2.19285i	−0.0456844	−	0.0791278i
$769$	31.2704	−	11.3815i	1.12764	−	0.410427i	0.290204	−	0.956965i	$-0.406277\pi$
$769$	31.2704	−	11.3815i	1.12764	−	0.410427i	0.837434	+	0.546538i	$0.184055\pi$
$770$		0			0
$771$	−18.1275	−	31.3977i	−0.652845	−	1.13076i
$772$	−7.60220	+	13.1674i	−0.273609	+	0.473905i
$773$	−4.92808	+	27.9485i	−0.177251	+	1.00524i	0.758263	+	0.651949i	$0.226048\pi$
$773$	−4.92808	+	27.9485i	−0.177251	+	1.00524i	−0.935514	+	0.353290i	$0.885063\pi$
$774$	8.21348	−	6.89193i	0.295227	−	0.247725i
$775$		0			0
$776$	2.51842	+	14.2827i	0.0904059	+	0.512718i
$777$	−11.8623	−	4.31753i	−0.425558	−	0.154890i
$778$	27.5321			0.987073
$779$	−4.03091	+	21.0692i	−0.144422	+	0.754883i
$780$		0			0
$781$	11.4757	+	4.17680i	0.410631	+	0.149458i
$782$	0.271974	+	1.54244i	0.00972578	+	0.0551576i
$783$	5.44562	+	4.56942i	0.194611	+	0.163298i
$784$	−5.03596	+	4.22567i	−0.179856	+	0.150917i
$785$		0			0
$786$	9.05943	−	15.6914i	0.323139	−	0.559693i
$787$	11.2827	+	19.5422i	0.402185	+	0.696605i	0.993989	−	0.109477i	$-0.0349175\pi$
$787$	11.2827	+	19.5422i	0.402185	+	0.696605i	−0.591804	+	0.806082i	$0.701584\pi$
$788$	−16.8751	+	6.14204i	−0.601151	+	0.218801i
$789$	11.3512	−	4.13149i	0.404112	−	0.147085i
$790$		0			0
$791$	0.486329	−	0.842347i	0.0172919	−	0.0299504i
$792$	0.592396	−	3.35965i	0.0210499	−	0.119380i
$793$	11.4042	−	9.56926i	0.404975	−	0.339814i
$794$	21.0305	+	17.6467i	0.746344	+	0.626257i
$795$		0			0
$796$	23.2729	+	8.47065i	0.824886	+	0.300234i
$797$	30.1320			1.06733			0.533665	−	0.845696i	$-0.320814\pi$
$797$	30.1320			1.06733			0.533665	+	0.845696i	$0.320814\pi$
$798$	3.51114	+	6.29039i	0.124293	+	0.222677i
$799$	3.00000			0.106132
$800$		0			0
$801$	−10.4534	−	59.2840i	−0.369351	−	2.09470i
$802$	−19.6159	−	16.4597i	−0.692660	−	0.581211i
$803$	0.390530	−	0.327693i	0.0137815	−	0.0115640i
$804$	0.386659	−	2.19285i	0.0136364	−	0.0773360i
$805$		0			0
$806$	5.85117	+	10.1345i	0.206099	+	0.356973i
$807$	−5.26352	+	1.91576i	−0.185285	+	0.0674381i
$808$	−14.0471	+	5.11273i	−0.494175	+	0.179865i
$809$	6.59714	+	11.4266i	0.231943	+	0.401737i	0.958380	−	0.285496i	$-0.0921583\pi$
$809$	6.59714	+	11.4266i	0.231943	+	0.401737i	−0.726437	+	0.687233i	$0.758825\pi$
$810$		0			0
$811$	−5.92144	+	33.5821i	−0.207930	+	1.17923i	0.684833	+	0.728700i	$0.259875\pi$
$811$	−5.92144	+	33.5821i	−0.207930	+	1.17923i	−0.892762	+	0.450528i	$0.851236\pi$
$812$	3.41147	−	2.86257i	0.119719	−	0.100456i
$813$	41.5053	+	34.8271i	1.45565	+	1.22144i
$814$	1.32635	+	7.52211i	0.0464886	+	0.263650i
$815$		0			0
$816$	−1.18479			−0.0414760
$817$	12.9400	−	4.49839i	0.452713	−	0.157379i
$818$	17.5243			0.612724
$819$	6.02481	+	2.19285i	0.210524	+	0.0766245i
$820$		0			0
$821$	4.27173	+	3.58440i	0.149084	+	0.125097i	0.714279	−	0.699861i	$-0.246755\pi$
$821$	4.27173	+	3.58440i	0.149084	+	0.125097i	−0.565195	+	0.824957i	$0.691199\pi$
$822$	−32.8803	+	27.5899i	−1.14683	+	0.962307i
$823$	−1.23648	+	7.01244i	−0.0431010	+	0.244438i	−0.998745	−	0.0500866i	$-0.984050\pi$
$823$	−1.23648	+	7.01244i	−0.0431010	+	0.244438i	0.955644	+	0.294525i	$0.0951614\pi$
$824$	3.61334	−	6.25849i	0.125877	−	0.218025i
$825$		0			0
$826$	−3.71048	+	1.35051i	−0.129104	+	0.0469901i
$827$	2.40003	−	0.873538i	0.0834570	−	0.0303759i	−0.299954	−	0.953954i	$-0.596971\pi$
$827$	2.40003	−	0.873538i	0.0834570	−	0.0303759i	0.383411	+	0.923578i	$0.374749\pi$
$828$	−5.70961	−	9.88933i	−0.198423	−	0.343678i
$829$	16.1022	−	27.8898i	0.559252	−	0.968654i	−0.438307	−	0.898826i	$-0.644422\pi$
$829$	16.1022	−	27.8898i	0.559252	−	0.968654i	0.997559	−	0.0698281i	$-0.0222451\pi$
$830$		0			0
$831$	15.0214	−	12.6045i	0.521087	−	0.437244i
$832$	−2.20574	−	1.85083i	−0.0764702	−	0.0641661i
$833$	0.534148	+	3.02931i	0.0185071	+	0.104959i
$834$	30.1891	+	10.9879i	1.04536	+	0.380481i
$835$		0			0
$836$	2.23396	−	3.74292i	0.0772630	−	0.129452i
$837$	−4.23442			−0.146363
$838$	−30.8949	−	11.2448i	−1.06725	−	0.388446i
$839$	−7.29039	−	41.3459i	−0.251692	−	1.42742i	−0.804422	−	0.594058i	$-0.797525\pi$
$839$	−7.29039	−	41.3459i	−0.251692	−	1.42742i	0.552730	−	0.833360i	$-0.313586\pi$
$840$		0			0
$841$	13.4461	−	11.2826i	0.463658	−	0.389055i
$842$	0.931074	−	5.28039i	0.0320869	−	0.181974i
$843$	17.8439	−	30.9065i	0.614576	−	1.06448i
$844$	−5.34864	−	9.26412i	−0.184108	−	0.318884i
$845$		0			0
$846$	−20.5535	+	7.48086i	−0.706644	+	0.257197i
$847$	3.26352	+	5.65258i	0.112136	+	0.194225i
$848$	1.93242	−	3.34705i	0.0663595	−	0.114938i
$849$	−2.28833	+	12.9778i	−0.0785354	+	0.445396i
$850$		0			0
$851$	19.5856	+	16.4343i	0.671385	+	0.563359i
$852$	5.36959	+	30.4524i	0.183959	+	1.04328i
$853$	34.4247	+	12.5296i	1.17868	+	0.429005i	0.855736	−	0.517413i	$-0.173105\pi$
$853$	34.4247	+	12.5296i	1.17868	+	0.429005i	0.322945	+	0.946418i	$0.395327\pi$
$854$	3.37464			0.115478
$855$		0			0
$856$	−7.26857			−0.248435
$857$	−38.2365	−	13.9170i	−1.30614	−	0.475394i	−0.407145	−	0.913363i	$-0.633476\pi$
$857$	−38.2365	−	13.9170i	−1.30614	−	0.475394i	−0.898990	+	0.437969i	$0.855698\pi$
$858$	−1.26604	−	7.18009i	−0.0432220	−	0.245124i
$859$	−10.0018	−	8.39252i	−0.341257	−	0.286349i	0.456011	−	0.889974i	$-0.349278\pi$
$859$	−10.0018	−	8.39252i	−0.341257	−	0.286349i	−0.797268	+	0.603625i	$0.793722\pi$
$860$		0			0
$861$	−1.41235	+	8.00984i	−0.0481328	+	0.272975i
$862$	−10.9577	+	18.9793i	−0.373221	+	0.646437i
$863$	22.7319	+	39.3728i	0.773803	+	1.34027i	0.935465	+	0.353420i	$0.114981\pi$
$863$	22.7319	+	39.3728i	0.773803	+	1.34027i	−0.161662	+	0.986846i	$0.551685\pi$
$864$	0.979055	−	0.356347i	0.0333081	−	0.0121232i
$865$		0			0
$866$	−3.99138	−	6.91328i	−0.135633	−	0.234923i
$867$	21.2456	−	36.7984i	0.721537	−	1.24974i
$868$	−0.460637	+	2.61240i	−0.0156350	+	0.0886707i
$869$	6.67752	−	5.60310i	0.226519	−	0.190072i
$870$		0			0
$871$	−0.439693	−	2.49362i	−0.0148984	−	0.0844931i
$872$	8.31180	+	3.02525i	0.281473	+	0.102448i
$873$	−49.4766			−1.67453
$874$	−2.32501	−	14.4041i	−0.0786446	−	0.487226i
$875$		0			0
$876$	1.21301	+	0.441500i	0.0409838	+	0.0149169i
$877$	9.29401	+	52.7090i	0.313837	+	1.77986i	0.578670	+	0.815562i	$0.303572\pi$
$877$	9.29401	+	52.7090i	0.313837	+	1.77986i	−0.264834	+	0.964294i	$0.585317\pi$
$878$	21.3956	+	17.9530i	0.722066	+	0.605885i
$879$	51.7281	−	43.4050i	1.74474	−	1.46401i
$880$		0			0
$881$	−4.08781	+	7.08030i	−0.137722	+	0.238541i	−0.926634	−	0.375965i	$-0.877311\pi$
$881$	−4.08781	+	7.08030i	−0.137722	+	0.238541i	0.788912	+	0.614506i	$0.210645\pi$
$882$	−11.2135	−	19.4223i	−0.377577	−	0.653983i
$883$	29.0672	−	10.5796i	0.978188	−	0.356031i	0.197053	−	0.980393i	$-0.436863\pi$
$883$	29.0672	−	10.5796i	0.978188	−	0.356031i	0.781136	+	0.624362i	$0.214641\pi$
$884$	−1.26604	+	0.460802i	−0.0425817	+	0.0154985i
$885$		0			0
$886$	−3.83157	+	6.63647i	−0.128724	+	0.222956i
$887$	1.81592	−	10.2986i	0.0609727	−	0.345793i	−0.939025	−	0.343848i	$-0.888270\pi$
$887$	1.81592	−	10.2986i	0.0609727	−	0.345793i	0.999998	−	0.00194565i	$-0.000619320\pi$
$888$	−14.8157	+	12.4318i	−0.497181	+	0.417185i
$889$	−9.16772	−	7.69263i	−0.307475	−	0.258002i
$890$		0			0
$891$	−7.13816	−	2.59808i	−0.239137	−	0.0870388i
$892$	−11.4466			−0.383259
$893$	−27.9440	−	0.405223i	−0.935111	−	0.0135603i
$894$	8.65776			0.289559
$895$		0			0
$896$	−0.113341	−	0.642788i	−0.00378645	−	0.0214740i
$897$	−18.6951	−	15.6870i	−0.624210	−	0.523774i
$898$	−16.0574	+	13.4737i	−0.535841	+	0.449624i
$899$	−4.81521	+	27.3084i	−0.160596	+	0.910786i
$900$		0			0
$901$	−0.904200	−	1.56612i	−0.0301233	−	0.0521750i
$902$	4.62449	−	1.68317i	0.153979	−	0.0560436i
$903$	4.88103	−	1.77655i	0.162431	−	0.0591199i
$904$	−0.745100	−	1.29055i	−0.0247817	−	0.0429231i
$905$		0			0
$906$	−6.84137	+	38.7993i	−0.227289	+	1.28902i
$907$	18.7822	−	15.7602i	0.623654	−	0.523308i	−0.275296	−	0.961360i	$-0.588776\pi$
$907$	18.7822	−	15.7602i	0.623654	−	0.523308i	0.898950	+	0.438052i	$0.144331\pi$
$908$	−10.9736	−	9.20794i	−0.364171	−	0.305576i
$909$	−8.85550	−	50.2221i	−0.293719	−	1.66576i
$910$		0			0
$911$	44.2927			1.46748			0.733742	−	0.679428i	$-0.237772\pi$
$911$	44.2927			1.46748			0.733742	+	0.679428i	$0.237772\pi$
$912$	11.0360	+	0.160035i	0.365437	+	0.00529929i
$913$	17.9094			0.592715
$914$	−25.0488	−	9.11700i	−0.828539	−	0.301564i
$915$		0			0
$916$	−4.66250	−	3.91231i	−0.154053	−	0.129266i
$917$	3.57785	−	3.00217i	0.118151	−	0.0991404i
$918$	0.0846555	−	0.480105i	0.00279405	−	0.0158458i
$919$	24.4636	−	42.3723i	0.806981	−	1.39773i	−0.107965	−	0.994155i	$-0.534433\pi$
$919$	24.4636	−	42.3723i	0.806981	−	1.39773i	0.914946	−	0.403577i	$-0.132233\pi$
$920$		0			0
$921$	80.9705	−	29.4709i	2.66807	−	0.971098i
$922$	−5.48545	+	1.99654i	−0.180654	+	0.0657526i
$923$	17.5817	+	30.4524i	0.578709	+	1.00235i
$924$	0.826352	−	1.43128i	0.0271850	−	0.0470858i
$925$		0			0
$926$	−21.2362	+	17.8193i	−0.697866	+	0.585579i
$927$	18.8858	+	15.8471i	0.620290	+	0.520485i
$928$	−1.18479	−	6.71929i	−0.0388927	−	0.220572i
$929$	−29.5685	−	10.7621i	−0.970112	−	0.353092i	−0.192123	−	0.981371i	$-0.561537\pi$
$929$	−29.5685	−	10.7621i	−0.970112	−	0.353092i	−0.777988	+	0.628279i	$0.783760\pi$
$930$		0			0
$931$	−4.56624	−	28.2892i	−0.149652	−	0.927139i
$932$	11.0496			0.361943
$933$	45.3200	+	16.4951i	1.48371	+	0.540026i
$934$	−3.48380	−	19.7576i	−0.113994	−	0.646489i
$935$		0			0
$936$	7.52481	−	6.31407i	0.245956	−	0.206382i
$937$	−1.15759	+	6.56504i	−0.0378169	+	0.214471i	−0.997860	−	0.0653804i	$-0.979174\pi$
$937$	−1.15759	+	6.56504i	−0.0378169	+	0.214471i	0.960043	+	0.279851i	$0.0902850\pi$
$938$	0.286989	−	0.497079i	0.00937052	−	0.0162302i
$939$	−4.54323	−	7.86911i	−0.148263	−	0.256799i
$940$		0			0
$941$	−19.0415	+	6.93053i	−0.620734	+	0.225929i	−0.633194	−	0.773994i	$-0.718256\pi$
$941$	−19.0415	+	6.93053i	−0.620734	+	0.225929i	0.0124591	+	0.999922i	$0.496034\pi$
$942$	16.8182	+	29.1300i	0.547967	+	0.949106i
$943$	8.23648	−	14.2660i	0.268217	−	0.464565i
$944$	−1.05051	+	5.95772i	−0.0341911	+	0.193907i
$945$		0			0
$946$	−2.40760	−	2.02022i	−0.0782779	−	0.0656830i
$947$	−0.961819	−	5.45475i	−0.0312549	−	0.177255i	0.965184	−	0.261571i	$-0.0842407\pi$
$947$	−0.961819	−	5.45475i	−0.0312549	−	0.177255i	−0.996439	+	0.0843158i	$0.973130\pi$
$948$	20.7408	+	7.54904i	0.673630	+	0.245181i
$949$	1.46791			0.0476504
$950$		0			0
$951$	−71.4252			−2.31612
$952$	−0.286989	−	0.104455i	−0.00930137	−	0.00338542i
$953$	6.37922	+	36.1784i	0.206643	+	1.17193i	0.894833	+	0.446401i	$0.147295\pi$
$953$	6.37922	+	36.1784i	0.206643	+	1.17193i	−0.688190	+	0.725531i	$0.741594\pi$
$954$	10.1001	+	8.47502i	0.327004	+	0.274389i
$955$		0			0
$956$	−1.39780	+	7.92734i	−0.0452082	+	0.256388i
$957$	8.63816	−	14.9617i	0.279232	−	0.483644i
$958$	−9.73829	−	16.8672i	−0.314630	−	0.544955i
$959$	−10.3969	+	3.78417i	−0.335734	+	0.122197i
$960$		0			0
$961$	7.24123	+	12.5422i	0.233588	+	0.404586i
$962$	−10.9966	+	19.0467i	−0.354544	+	0.614089i
$963$	4.30587	−	24.4198i	0.138755	−	0.786918i
$964$	21.1759	−	17.7687i	0.682031	−	0.572292i
$965$		0			0
$966$	−0.960637	−	5.44804i	−0.0309080	−	0.175288i
$967$	−53.8188	−	19.5885i	−1.73070	−	0.629922i	−0.732017	−	0.681286i	$-0.761421\pi$
$967$	−53.8188	−	19.5885i	−1.73070	−	0.629922i	−0.998680	+	0.0513643i	$0.983643\pi$
$968$	10.0000			0.321412
$969$	2.64677	−	4.43458i	0.0850266	−	0.142459i
$970$		0			0
$971$	−1.88191	−	0.684960i	−0.0603934	−	0.0219814i	0.311647	−	0.950198i	$-0.399119\pi$
$971$	−1.88191	−	0.684960i	−0.0603934	−	0.0219814i	−0.372040	+	0.928217i	$0.621342\pi$
$972$	−3.88279	−	22.0204i	−0.124541	−	0.706304i
$973$	6.34389	+	5.32316i	0.203376	+	0.170653i
$974$	23.5947	−	19.7983i	0.756022	−	0.634378i
$975$		0			0
$976$	2.58512	−	4.47756i	0.0827477	−	0.143323i
$977$	13.6348	+	23.6161i	0.436214	+	0.755545i	0.997394	−	0.0721487i	$-0.0229856\pi$
$977$	13.6348	+	23.6161i	0.436214	+	0.755545i	−0.561180	+	0.827694i	$0.689652\pi$
$978$	−12.5424	+	4.56504i	−0.401060	+	0.145974i
$979$	−16.5817	+	6.03525i	−0.529954	+	0.192887i
$980$		0			0
$981$	−15.0876	+	26.1326i	−0.481712	+	0.834349i
$982$	−1.82383	+	10.3434i	−0.0582006	+	0.330072i
$983$	28.3935	−	23.8250i	0.905613	−	0.759899i	−0.0656666	−	0.997842i	$-0.520917\pi$
$983$	28.3935	−	23.8250i	0.905613	−	0.759899i	0.971279	+	0.237942i	$0.0764729\pi$
$984$	9.54576	+	8.00984i	0.304308	+	0.255344i
$985$		0			0
$986$	−3.00000	−	1.09191i	−0.0955395	−	0.0347735i
$987$	−10.5963			−0.337283
$988$	11.8550	−	4.12122i	0.377159	−	0.131113i
$989$	−10.5202			−0.334524
$990$		0			0
$991$	2.61112	+	14.8084i	0.0829449	+	0.470404i	0.997781	+	0.0665790i	$0.0212085\pi$
$991$	2.61112	+	14.8084i	0.0829449	+	0.470404i	−0.914836	+	0.403825i	$0.867680\pi$
$992$	3.11334	+	2.61240i	0.0988487	+	0.0829439i
$993$	15.9873	−	13.4149i	0.507340	−	0.425709i
$994$	−1.38413	+	7.84981i	−0.0439020	+	0.248981i
$995$		0			0
$996$	22.6741	+	39.2727i	0.718457	+	1.24440i
$997$	−14.4944	+	5.27552i	−0.459041	+	0.167077i	−0.561182	−	0.827693i	$-0.689653\pi$
$997$	−14.4944	+	5.27552i	−0.459041	+	0.167077i	0.102140	+	0.994770i	$0.467431\pi$
$998$	7.48380	−	2.72388i	0.236896	−	0.0862230i
$999$	−3.97906	−	6.89193i	−0.125892	−	0.218051i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.b.251.1	✓	6
5.2	odd	4		950.2.u.d.99.1		12
5.3	odd	4		950.2.u.d.99.2		12
5.4	even	2		950.2.l.e.251.1	yes	6
19.5	even	9	inner	950.2.l.b.651.1	yes	6
95.24	even	18		950.2.l.e.651.1	yes	6
95.43	odd	36		950.2.u.d.499.1		12
95.62	odd	36		950.2.u.d.499.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.l.b.251.1	✓	6	1.1	even	1	trivial
950.2.l.b.651.1	yes	6	19.5	even	9	inner
950.2.l.e.251.1	yes	6	5.4	even	2
950.2.l.e.651.1	yes	6	95.24	even	18
950.2.u.d.99.1		12	5.2	odd	4
950.2.u.d.99.2		12	5.3	odd	4
950.2.u.d.499.1		12	95.43	odd	36
950.2.u.d.499.2		12	95.62	odd	36

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 + 0.342020i) q^{2} +(0.439693 + 2.49362i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.439693 + 2.49362i) q^{6} +(-0.326352 + 0.565258i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-3.20574 + 1.16679i) q^{9} +O(q^{10})\)	\(q+(0.939693 + 0.342020i) q^{2} +(0.439693 + 2.49362i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.439693 + 2.49362i) q^{6} +(-0.326352 + 0.565258i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-3.20574 + 1.16679i) q^{9} +(0.500000 + 0.866025i) q^{11} +(-1.26604 + 2.19285i) q^{12} +(-0.500000 + 2.83564i) q^{13} +(-0.500000 + 0.419550i) q^{14} +(0.173648 + 0.984808i) q^{16} +(0.439693 + 0.160035i) q^{17} -3.41147 q^{18} +(-4.07398 - 1.55007i) q^{19} +(-1.55303 - 0.565258i) q^{21} +(0.173648 + 0.984808i) q^{22} +(2.56418 + 2.15160i) q^{23} +(-1.93969 + 1.62760i) q^{24} +(-1.43969 + 2.49362i) q^{26} +(-0.520945 - 0.902302i) q^{27} +(-0.613341 + 0.223238i) q^{28} +(-6.41147 + 2.33359i) q^{29} +(2.03209 - 3.51968i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-1.93969 + 1.62760i) q^{33} +(0.358441 + 0.300767i) q^{34} +(-3.20574 - 1.16679i) q^{36} +7.63816 q^{37} +(-3.29813 - 2.84997i) q^{38} -7.29086 q^{39} +(-0.854570 - 4.84651i) q^{41} +(-1.26604 - 1.06234i) q^{42} +(-2.40760 + 2.02022i) q^{43} +(-0.173648 + 0.984808i) q^{44} +(1.67365 + 2.89884i) q^{46} +(6.02481 - 2.19285i) q^{47} +(-2.37939 + 0.866025i) q^{48} +(3.28699 + 5.69323i) q^{49} +(-0.205737 + 1.16679i) q^{51} +(-2.20574 + 1.85083i) q^{52} +(-2.96064 - 2.48427i) q^{53} +(-0.180922 - 1.02606i) q^{54} -0.652704 q^{56} +(2.07398 - 10.8405i) q^{57} -6.82295 q^{58} +(5.68479 + 2.06910i) q^{59} +(-3.96064 - 3.32337i) q^{61} +(3.11334 - 2.61240i) q^{62} +(0.386659 - 2.19285i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-2.37939 + 0.866025i) q^{66} +(-0.826352 + 0.300767i) q^{67} +(0.233956 + 0.405223i) q^{68} +(-4.23783 + 7.34013i) q^{69} +(9.35504 - 7.84981i) q^{71} +(-2.61334 - 2.19285i) q^{72} +(-0.0885259 - 0.502055i) q^{73} +(7.17752 + 2.61240i) q^{74} +(-2.12449 - 3.80612i) q^{76} -0.652704 q^{77} +(-6.85117 - 2.49362i) q^{78} +(-1.51367 - 8.58445i) q^{79} +(-5.81908 + 4.88279i) q^{81} +(0.854570 - 4.84651i) q^{82} +(8.95471 - 15.5100i) q^{83} +(-0.826352 - 1.43128i) q^{84} +(-2.95336 + 1.07494i) q^{86} +(-8.63816 - 14.9617i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(-3.06418 + 17.3778i) q^{89} +(-1.43969 - 1.20805i) q^{91} +(0.581252 + 3.29644i) q^{92} +(9.67024 + 3.51968i) q^{93} +6.41147 q^{94} -2.53209 q^{96} +(13.6284 + 4.96032i) q^{97} +(1.14156 + 6.47410i) q^{98} +(-2.61334 - 2.19285i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{3} + 3 q^{6} - 3 q^{7} + 3 q^{8} - 9 q^{9}+O(q^{10}) \) 6 * q - 3 * q^3 + 3 * q^6 - 3 * q^7 + 3 * q^8 - 9 * q^9	\( 6 q - 3 q^{3} + 3 q^{6} - 3 q^{7} + 3 q^{8} - 9 q^{9} + 3 q^{11} - 3 q^{12} - 3 q^{13} - 3 q^{14} - 3 q^{17} - 9 q^{19} + 3 q^{21} - 3 q^{23} - 6 q^{24} - 3 q^{26} + 3 q^{28} - 18 q^{29} + 3 q^{31} - 6 q^{33} - 6 q^{34} - 9 q^{36} + 12 q^{37} - 6 q^{38} - 12 q^{39} - 21 q^{41} - 3 q^{42} - 18 q^{43} + 9 q^{46} + 9 q^{47} - 3 q^{48} + 12 q^{49} + 9 q^{51} - 3 q^{52} - 9 q^{53} - 18 q^{54} - 6 q^{56} - 3 q^{57} + 27 q^{59} - 15 q^{61} + 12 q^{62} + 9 q^{63} - 3 q^{64} - 3 q^{66} - 6 q^{67} + 6 q^{68} - 6 q^{69} + 6 q^{71} - 9 q^{72} - 21 q^{73} + 18 q^{74} - 6 q^{77} - 15 q^{78} + 12 q^{79} - 18 q^{81} + 21 q^{82} + 18 q^{83} - 6 q^{84} + 9 q^{86} - 18 q^{87} - 3 q^{88} - 3 q^{91} + 6 q^{92} + 15 q^{93} + 18 q^{94} - 6 q^{96} + 45 q^{97} + 15 q^{98} - 9 q^{99}+O(q^{100}) \) 6 * q - 3 * q^3 + 3 * q^6 - 3 * q^7 + 3 * q^8 - 9 * q^9 + 3 * q^11 - 3 * q^12 - 3 * q^13 - 3 * q^14 - 3 * q^17 - 9 * q^19 + 3 * q^21 - 3 * q^23 - 6 * q^24 - 3 * q^26 + 3 * q^28 - 18 * q^29 + 3 * q^31 - 6 * q^33 - 6 * q^34 - 9 * q^36 + 12 * q^37 - 6 * q^38 - 12 * q^39 - 21 * q^41 - 3 * q^42 - 18 * q^43 + 9 * q^46 + 9 * q^47 - 3 * q^48 + 12 * q^49 + 9 * q^51 - 3 * q^52 - 9 * q^53 - 18 * q^54 - 6 * q^56 - 3 * q^57 + 27 * q^59 - 15 * q^61 + 12 * q^62 + 9 * q^63 - 3 * q^64 - 3 * q^66 - 6 * q^67 + 6 * q^68 - 6 * q^69 + 6 * q^71 - 9 * q^72 - 21 * q^73 + 18 * q^74 - 6 * q^77 - 15 * q^78 + 12 * q^79 - 18 * q^81 + 21 * q^82 + 18 * q^83 - 6 * q^84 + 9 * q^86 - 18 * q^87 - 3 * q^88 - 3 * q^91 + 6 * q^92 + 15 * q^93 + 18 * q^94 - 6 * q^96 + 45 * q^97 + 15 * q^98 - 9 * q^99

Introduction

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