LMFDB - Embedded newform 462.2.k.g.89.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(89,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, 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("462.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.k (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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6 x^{19} + 19 x^{18} - 42 x^{17} + 62 x^{16} - 42 x^{15} - 25 x^{14} + 6 x^{13} + 445 x^{12} + \cdots + 59049 $ x^20 - 6x^19 + 19x^18 - 42x^17 + 62x^16 - 42x^15 - 25x^14 + 6x^13 + 445x^12 - 1764x^11 + 3864x^10 - 5292x^9 + 4005x^8 + 162x^7 - 2025x^6 - 10206x^5 + 45198x^4 - 91854x^3 + 124659x^2 - 118098*x + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.9
Root			$-1.60269 + 0.656793i$ of defining polynomial
Character	$\chi$	$=$	462.89
Dual form			462.2.k.g.353.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.232547 - 1.71637i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.92560 + 3.33524i) q^{5} +(1.05958 - 1.37015i) q^{6} +(1.58064 + 2.12169i) q^{7} +1.00000i q^{8} +(-2.89184 - 0.798273i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.232547 - 1.71637i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.92560 + 3.33524i) q^{5} +(1.05958 - 1.37015i) q^{6} +(1.58064 + 2.12169i) q^{7} +1.00000i q^{8} +(-2.89184 - 0.798273i) q^{9} +(-3.33524 + 1.92560i) q^{10} +(-0.866025 + 0.500000i) q^{11} +(1.60269 - 0.656793i) q^{12} +3.23514i q^{13} +(0.308031 + 2.62776i) q^{14} +(5.27671 + 4.08064i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.751545 + 1.30171i) q^{17} +(-2.10527 - 2.13725i) q^{18} +(-2.17488 - 1.25567i) q^{19} -3.85120 q^{20} +(4.00918 - 2.21957i) q^{21} -1.00000 q^{22} +(6.70851 + 3.87316i) q^{23} +(1.71637 + 0.232547i) q^{24} +(-4.91588 - 8.51456i) q^{25} +(-1.61757 + 2.80171i) q^{26} +(-2.04262 + 4.77783i) q^{27} +(-1.04712 + 2.42972i) q^{28} -7.71286i q^{29} +(2.52944 + 6.17229i) q^{30} +(5.23845 - 3.02442i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.656793 + 1.60269i) q^{33} +1.50309i q^{34} +(-10.1200 + 1.18629i) q^{35} +(-0.754597 - 2.90355i) q^{36} +(-0.0683071 + 0.118311i) q^{37} +(-1.25567 - 2.17488i) q^{38} +(5.55269 + 0.752322i) q^{39} +(-3.33524 - 1.92560i) q^{40} +3.85120 q^{41} +(4.58184 + 0.0823825i) q^{42} +7.22205 q^{43} +(-0.866025 - 0.500000i) q^{44} +(8.23097 - 8.10784i) q^{45} +(3.87316 + 6.70851i) q^{46} +(-5.40027 + 9.35353i) q^{47} +(1.37015 + 1.05958i) q^{48} +(-2.00314 + 6.70727i) q^{49} -9.83176i q^{50} +(2.40899 - 0.987219i) q^{51} +(-2.80171 + 1.61757i) q^{52} +(8.98451 - 5.18721i) q^{53} +(-4.15788 + 3.11642i) q^{54} -3.85120i q^{55} +(-2.12169 + 1.58064i) q^{56} +(-2.66095 + 3.44089i) q^{57} +(3.85643 - 6.67953i) q^{58} +(-1.68071 - 2.91108i) q^{59} +(-0.895586 + 6.61008i) q^{60} +(-7.45472 - 4.30399i) q^{61} +6.04884 q^{62} +(-2.87728 - 7.39738i) q^{63} -1.00000 q^{64} +(-10.7900 - 6.22959i) q^{65} +(-0.232547 + 1.71637i) q^{66} +(-5.19167 - 8.99224i) q^{67} +(-0.751545 + 1.30171i) q^{68} +(8.20782 - 10.6136i) q^{69} +(-9.35735 - 4.03266i) q^{70} -0.857105i q^{71} +(0.798273 - 2.89184i) q^{72} +(-2.12908 + 1.22922i) q^{73} +(-0.118311 + 0.0683071i) q^{74} +(-15.7573 + 6.45743i) q^{75} -2.51133i q^{76} +(-2.42972 - 1.04712i) q^{77} +(4.43261 + 3.42788i) q^{78} +(2.11856 - 3.66946i) q^{79} +(-1.92560 - 3.33524i) q^{80} +(7.72552 + 4.61696i) q^{81} +(3.33524 + 1.92560i) q^{82} -8.67372 q^{83} +(3.92679 + 2.36226i) q^{84} -5.78870 q^{85} +(6.25448 + 3.61103i) q^{86} +(-13.2381 - 1.79360i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(3.33499 - 5.77637i) q^{89} +(11.1821 - 2.90611i) q^{90} +(-6.86397 + 5.11360i) q^{91} +7.74632i q^{92} +(-3.97283 - 9.69443i) q^{93} +(-9.35353 + 5.40027i) q^{94} +(8.37589 - 4.83582i) q^{95} +(0.656793 + 1.60269i) q^{96} +10.6767i q^{97} +(-5.08840 + 4.80709i) q^{98} +(2.90355 - 0.754597i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{3} + 10 q^{4} - 6 q^{7} - 2 q^{9}+O(q^{10}) $ 20 * q - 6 * q^3 + 10 * q^4 - 6 * q^7 - 2 * q^9	$ 20 q - 6 q^{3} + 10 q^{4} - 6 q^{7} - 2 q^{9} - 18 q^{10} - 6 q^{12} - 8 q^{15} - 10 q^{16} + 4 q^{18} + 36 q^{19} + 24 q^{21} - 20 q^{22} - 12 q^{25} - 22 q^{30} + 36 q^{31} - 4 q^{36} + 16 q^{37} + 4 q^{39} - 18 q^{40} + 32 q^{42} + 32 q^{43} + 24 q^{45} + 30 q^{46} - 42 q^{49} - 24 q^{52} - 36 q^{54} - 24 q^{57} + 32 q^{58} - 4 q^{60} + 42 q^{61} - 10 q^{63} - 20 q^{64} + 6 q^{66} - 10 q^{67} - 36 q^{70} - 4 q^{72} + 12 q^{73} - 108 q^{75} + 6 q^{79} + 42 q^{81} + 18 q^{82} + 18 q^{84} - 28 q^{85} + 36 q^{87} - 10 q^{88} - 112 q^{91} - 36 q^{93} + 42 q^{94} - 8 q^{99}+O(q^{100}) $ 20 * q - 6 * q^3 + 10 * q^4 - 6 * q^7 - 2 * q^9 - 18 * q^10 - 6 * q^12 - 8 * q^15 - 10 * q^16 + 4 * q^18 + 36 * q^19 + 24 * q^21 - 20 * q^22 - 12 * q^25 - 22 * q^30 + 36 * q^31 - 4 * q^36 + 16 * q^37 + 4 * q^39 - 18 * q^40 + 32 * q^42 + 32 * q^43 + 24 * q^45 + 30 * q^46 - 42 * q^49 - 24 * q^52 - 36 * q^54 - 24 * q^57 + 32 * q^58 - 4 * q^60 + 42 * q^61 - 10 * q^63 - 20 * q^64 + 6 * q^66 - 10 * q^67 - 36 * q^70 - 4 * q^72 + 12 * q^73 - 108 * q^75 + 6 * q^79 + 42 * q^81 + 18 * q^82 + 18 * q^84 - 28 * q^85 + 36 * q^87 - 10 * q^88 - 112 * q^91 - 36 * q^93 + 42 * q^94 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	0.232547	−	1.71637i	0.134261	−	0.990946i
$3$	0.232547	−	1.71637i	0.134261	−	0.990946i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.92560	+	3.33524i	−0.861155	+	1.49156i	0.00965972	+	0.999953i	$0.496925\pi$
$5$	−1.92560	+	3.33524i	−0.861155	+	1.49156i	−0.870815	+	0.491611i	$0.836408\pi$
$6$	1.05958	−	1.37015i	0.432570	−	0.559360i
$7$	1.58064	+	2.12169i	0.597427	+	0.801924i
$7$	1.58064	+	2.12169i	0.597427	+	0.801924i
$8$			1.00000i			0.353553i
$9$	−2.89184	−	0.798273i	−0.963948	−	0.266091i
$10$	−3.33524	+	1.92560i	−1.05470	+	0.608929i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$12$	1.60269	−	0.656793i	0.462657	−	0.189600i
$13$			3.23514i			0.897267i	0.893716	+	0.448633i	$0.148089\pi$
$13$			3.23514i			0.897267i	−0.893716	+	0.448633i	$0.851911\pi$
$14$	0.308031	+	2.62776i	0.0823248	+	0.702298i
$15$	5.27671	+	4.08064i	1.36244	+	1.05362i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.751545	+	1.30171i	0.182276	+	0.315712i	0.942655	−	0.333768i	$-0.108320\pi$
$17$	0.751545	+	1.30171i	0.182276	+	0.315712i	−0.760379	+	0.649480i	$0.774987\pi$
$18$	−2.10527	−	2.13725i	−0.496218	−	0.503754i
$19$	−2.17488	−	1.25567i	−0.498951	−	0.288069i	0.229329	−	0.973349i	$-0.426347\pi$
$19$	−2.17488	−	1.25567i	−0.498951	−	0.288069i	−0.728280	+	0.685280i	$0.759680\pi$
$20$	−3.85120			−0.861155
$21$	4.00918	−	2.21957i	0.874874	−	0.484350i
$22$	−1.00000			−0.213201
$23$	6.70851	+	3.87316i	1.39882	+	0.807610i	0.994269	−	0.106905i	$-0.0340940\pi$
$23$	6.70851	+	3.87316i	1.39882	+	0.807610i	0.404552	+	0.914515i	$0.367427\pi$
$24$	1.71637	+	0.232547i	0.350352	+	0.0474685i
$25$	−4.91588	−	8.51456i	−0.983176	−	1.70291i
$26$	−1.61757	+	2.80171i	−0.317232	+	0.549461i
$27$	−2.04262	+	4.77783i	−0.393102	+	0.919495i
$28$	−1.04712	+	2.42972i	−0.197886	+	0.459174i
$29$		−	7.71286i		−	1.43224i	−0.697976	−	0.716121i	$-0.745916\pi$
$29$		−	7.71286i		−	1.43224i	0.697976	−	0.716121i	$-0.254084\pi$
$30$	2.52944	+	6.17229i	0.461811	+	1.12690i
$31$	5.23845	−	3.02442i	0.940853	−	0.543202i	0.0506253	−	0.998718i	$-0.483879\pi$
$31$	5.23845	−	3.02442i	0.940853	−	0.543202i	0.890228	+	0.455516i	$0.150545\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	0.656793	+	1.60269i	0.114333	+	0.278993i
$34$			1.50309i			0.257778i
$35$	−10.1200	+	1.18629i	−1.71060	+	0.200520i
$36$	−0.754597	−	2.90355i	−0.125766	−	0.483924i
$37$	−0.0683071	+	0.118311i	−0.0112296	+	0.0194503i	−0.871586	−	0.490243i	$-0.836908\pi$
$37$	−0.0683071	+	0.118311i	−0.0112296	+	0.0194503i	0.860356	+	0.509694i	$0.170241\pi$
$38$	−1.25567	−	2.17488i	−0.203696	−	0.352811i
$39$	5.55269	+	0.752322i	0.889143	+	0.120468i
$40$	−3.33524	−	1.92560i	−0.527348	−	0.304464i
$41$	3.85120			0.601457			0.300728	−	0.953710i	$-0.402770\pi$
$41$	3.85120			0.601457			0.300728	+	0.953710i	$0.402770\pi$
$42$	4.58184	+	0.0823825i	0.706993	+	0.0127119i
$43$	7.22205			1.10135			0.550676	−	0.834719i	$-0.314370\pi$
$43$	7.22205			1.10135			0.550676	+	0.834719i	$0.314370\pi$
$44$	−0.866025	−	0.500000i	−0.130558	−	0.0753778i
$45$	8.23097	−	8.10784i	1.22700	−	1.20864i
$46$	3.87316	+	6.70851i	0.571067	+	0.989116i
$47$	−5.40027	+	9.35353i	−0.787710	+	1.36435i	0.139657	+	0.990200i	$0.455400\pi$
$47$	−5.40027	+	9.35353i	−0.787710	+	1.36435i	−0.927367	+	0.374153i	$0.877933\pi$
$48$	1.37015	+	1.05958i	0.197763	+	0.152937i
$49$	−2.00314	+	6.70727i	−0.286163	+	0.958181i
$50$		−	9.83176i		−	1.39042i
$51$	2.40899	−	0.987219i	0.337326	−	0.138238i
$52$	−2.80171	+	1.61757i	−0.388528	+	0.224317i
$53$	8.98451	−	5.18721i	1.23412	−	0.712518i	0.266232	−	0.963909i	$-0.414221\pi$
$53$	8.98451	−	5.18721i	1.23412	−	0.712518i	0.967886	+	0.251391i	$0.0808879\pi$
$54$	−4.15788	+	3.11642i	−0.565816	+	0.424090i
$55$		−	3.85120i		−	0.519296i
$56$	−2.12169	+	1.58064i	−0.283523	+	0.211222i
$57$	−2.66095	+	3.44089i	−0.352451	+	0.455757i
$58$	3.85643	−	6.67953i	0.506374	−	0.877066i
$59$	−1.68071	−	2.91108i	−0.218810	−	0.378991i	0.735634	−	0.677379i	$-0.236884\pi$
$59$	−1.68071	−	2.91108i	−0.218810	−	0.378991i	−0.954445	+	0.298388i	$0.903551\pi$
$60$	−0.895586	+	6.61008i	−0.115620	+	0.853358i
$61$	−7.45472	−	4.30399i	−0.954480	−	0.551069i	−0.0600100	−	0.998198i	$-0.519113\pi$
$61$	−7.45472	−	4.30399i	−0.954480	−	0.551069i	−0.894470	+	0.447129i	$0.852447\pi$
$62$	6.04884			0.768203
$63$	−2.87728	−	7.39738i	−0.362504	−	0.931982i
$64$	−1.00000			−0.125000
$65$	−10.7900	−	6.22959i	−1.33833	−	0.772686i
$66$	−0.232547	+	1.71637i	−0.0286246	+	0.211270i
$67$	−5.19167	−	8.99224i	−0.634263	−	1.09858i	−0.986671	−	0.162730i	$-0.947970\pi$
$67$	−5.19167	−	8.99224i	−0.634263	−	1.09858i	0.352407	−	0.935847i	$-0.385363\pi$
$68$	−0.751545	+	1.30171i	−0.0911382	+	0.157856i
$69$	8.20782	−	10.6136i	0.988105	−	1.27773i
$70$	−9.35735	−	4.03266i	−1.11842	−	0.481995i
$71$		−	0.857105i		−	0.101720i	−0.998706	−	0.0508598i	$-0.983804\pi$
$71$		−	0.857105i		−	0.101720i	0.998706	−	0.0508598i	$-0.0161962\pi$
$72$	0.798273	−	2.89184i	0.0940774	−	0.340807i
$73$	−2.12908	+	1.22922i	−0.249190	+	0.143870i	−0.619393	−	0.785081i	$-0.712621\pi$
$73$	−2.12908	+	1.22922i	−0.249190	+	0.143870i	0.370204	+	0.928951i	$0.379288\pi$
$74$	−0.118311	+	0.0683071i	−0.0137534	+	0.00794054i
$75$	−15.7573	+	6.45743i	−1.81950	+	0.745640i
$76$		−	2.51133i		−	0.288069i
$77$	−2.42972	−	1.04712i	−0.276892	−	0.119330i
$78$	4.43261	+	3.42788i	0.501895	+	0.388131i
$79$	2.11856	−	3.66946i	0.238357	−	0.412847i	−0.721886	−	0.692012i	$-0.756724\pi$
$79$	2.11856	−	3.66946i	0.238357	−	0.412847i	0.960243	+	0.279165i	$0.0900578\pi$
$80$	−1.92560	−	3.33524i	−0.215289	−	0.372891i
$81$	7.72552	+	4.61696i	0.858391	+	0.512996i
$82$	3.33524	+	1.92560i	0.368316	+	0.212647i
$83$	−8.67372			−0.952064			−0.476032	−	0.879428i	$-0.657925\pi$
$83$	−8.67372			−0.952064			−0.476032	+	0.879428i	$0.657925\pi$
$84$	3.92679	+	2.36226i	0.428448	+	0.257744i
$85$	−5.78870			−0.627873
$86$	6.25448	+	3.61103i	0.674438	+	0.389387i
$87$	−13.2381	−	1.79360i	−1.41927	−	0.192294i
$88$	−0.500000	−	0.866025i	−0.0533002	−	0.0923186i
$89$	3.33499	−	5.77637i	0.353508	−	0.612294i	−0.633353	−	0.773863i	$-0.718322\pi$
$89$	3.33499	−	5.77637i	0.353508	−	0.612294i	0.986861	+	0.161569i	$0.0516554\pi$
$90$	11.1821	−	2.90611i	1.17870	−	0.306331i
$91$	−6.86397	+	5.11360i	−0.719539	+	0.536051i
$92$			7.74632i			0.807610i
$93$	−3.97283	−	9.69443i	−0.411964	−	1.00527i
$94$	−9.35353	+	5.40027i	−0.964743	+	0.556995i
$95$	8.37589	−	4.83582i	0.859348	−	0.496145i
$96$	0.656793	+	1.60269i	0.0670336	+	0.163574i
$97$			10.6767i			1.08406i	0.840360	+	0.542029i	$0.182344\pi$
$97$			10.6767i			1.08406i	−0.840360	+	0.542029i	$0.817656\pi$
$98$	−5.08840	+	4.80709i	−0.514006	+	0.485590i
$99$	2.90355	−	0.754597i	0.291817	−	0.0758399i
$100$	4.91588	−	8.51456i	0.491588	−	0.851456i
$101$	4.33142	+	7.50224i	0.430992	+	0.746501i	0.996959	−	0.0779275i	$-0.0248303\pi$
$101$	4.33142	+	7.50224i	0.430992	+	0.746501i	−0.565967	+	0.824428i	$0.691497\pi$
$102$	2.57986	+	0.349539i	0.255444	+	0.0346095i
$103$	2.93643	+	1.69535i	0.289335	+	0.167048i	0.637642	−	0.770333i	$-0.279910\pi$
$103$	2.93643	+	1.69535i	0.289335	+	0.167048i	−0.348307	+	0.937381i	$0.613243\pi$
$104$	−3.23514			−0.317232
$105$	−0.317272	+	17.6456i	−0.0309626	+	1.72203i
$106$	10.3744			1.00765
$107$	14.1527	+	8.17106i	1.36819	+	0.789926i	0.990697	−	0.136085i	$-0.0434521\pi$
$107$	14.1527	+	8.17106i	1.36819	+	0.789926i	0.377495	+	0.926012i	$0.376785\pi$
$108$	−5.15904	+	0.619956i	−0.496428	+	0.0596553i
$109$	−3.21222	−	5.56372i	−0.307675	−	0.532908i	0.670179	−	0.742200i	$-0.266217\pi$
$109$	−3.21222	−	5.56372i	−0.307675	−	0.532908i	−0.977853	+	0.209292i	$0.932884\pi$
$110$	1.92560	−	3.33524i	0.183599	−	0.318003i
$111$	0.187181	+	0.144753i	0.0177665	+	0.0137394i
$112$	−2.62776	+	0.308031i	−0.248300	+	0.0291062i
$113$		−	9.69766i		−	0.912279i	−0.889908	−	0.456140i	$-0.849232\pi$
$113$		−	9.69766i		−	0.912279i	0.889908	−	0.456140i	$-0.150768\pi$
$114$	−4.02489	+	1.64942i	−0.376965	+	0.154483i
$115$	−25.8358	+	14.9163i	−2.40920	+	1.39096i
$116$	6.67953	−	3.85643i	0.620179	−	0.358061i
$117$	2.58253	−	9.35552i	0.238755	−	0.864918i
$118$		−	3.36143i		−	0.309445i
$119$	−1.57391	+	3.65209i	−0.144280	+	0.334787i
$120$	−4.08064	+	5.27671i	−0.372510	+	0.481695i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$	−4.30399	−	7.45472i	−0.389665	−	0.674919i
$123$	0.895586	−	6.61008i	0.0807522	−	0.596011i
$124$	5.23845	+	3.02442i	0.470426	+	0.271601i
$125$	18.6081			1.66436
$126$	1.20689	−	7.84496i	0.107518	−	0.698885i
$127$	−13.2555			−1.17624			−0.588119	−	0.808775i	$-0.700131\pi$
$127$	−13.2555			−1.17624			−0.588119	+	0.808775i	$0.700131\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	1.67947	−	12.3957i	0.147869	−	1.09138i
$130$	−6.22959	−	10.7900i	−0.546371	−	0.946343i
$131$	8.33693	−	14.4400i	0.728401	−	1.26163i	−0.229158	−	0.973389i	$-0.573597\pi$
$131$	8.33693	−	14.4400i	0.728401	−	1.26163i	0.957559	−	0.288238i	$-0.0930696\pi$
$132$	−1.05958	+	1.37015i	−0.0922243	+	0.119256i
$133$	−0.773568	−	6.59917i	−0.0670768	−	0.572221i
$134$		−	10.3833i		−	0.896984i
$135$	−12.0019	−	16.0128i	−1.03296	−	1.37817i
$136$	−1.30171	+	0.751545i	−0.111621	+	0.0644444i
$137$	11.3547	−	6.55564i	0.970097	−	0.560086i	0.0708312	−	0.997488i	$-0.477435\pi$
$137$	11.3547	−	6.55564i	0.970097	−	0.560086i	0.899266	+	0.437402i	$0.144101\pi$
$138$	12.4150	−	5.08773i	1.05683	−	0.433096i
$139$			15.8729i			1.34632i	0.739497	+	0.673160i	$0.235064\pi$
$139$			15.8729i			1.34632i	−0.739497	+	0.673160i	$0.764936\pi$
$140$	−6.08737	−	8.17106i	−0.514477	−	0.690581i
$141$	14.7983	+	11.4440i	1.24624	+	0.963757i
$142$	0.428552	−	0.742275i	0.0359633	−	0.0622903i
$143$	−1.61757	−	2.80171i	−0.135268	−	0.234291i
$144$	2.13725	−	2.10527i	0.178104	−	0.175439i
$145$	25.7242	+	14.8519i	2.13628	+	1.23338i
$146$	−2.45845			−0.203462
$147$	11.0463	+	4.99788i	0.911085	+	0.412218i
$148$	−0.136614			−0.0112296
$149$	2.60352	+	1.50314i	0.213288	+	0.123142i	0.602839	−	0.797863i	$-0.294036\pi$
$149$	2.60352	+	1.50314i	0.213288	+	0.123142i	−0.389550	+	0.921005i	$0.627370\pi$
$150$	−16.8749	−	2.28635i	−1.37783	−	0.186679i
$151$	6.16568	+	10.6793i	0.501756	+	0.869067i	0.999998	+	0.00202885i	$0.000645802\pi$
$151$	6.16568	+	10.6793i	0.501756	+	0.869067i	−0.498242	+	0.867038i	$0.666021\pi$
$152$	1.25567	−	2.17488i	0.101848	−	0.176406i
$153$	−1.13423	−	4.36429i	−0.0916969	−	0.352832i
$154$	−1.58064	−	2.12169i	−0.127372	−	0.170971i
$155$			23.2953i			1.87112i
$156$	2.12482	+	5.18494i	0.170122	+	0.415127i
$157$	4.17140	−	2.40836i	0.332914	−	0.192208i	−0.324220	−	0.945982i	$-0.605102\pi$
$157$	4.17140	−	2.40836i	0.332914	−	0.192208i	0.657134	+	0.753774i	$0.271769\pi$
$158$	3.66946	−	2.11856i	0.291927	−	0.168544i
$159$	−6.81385	−	16.6270i	−0.540373	−	1.31861i
$160$		−	3.85120i		−	0.304464i
$161$	2.38611	+	20.3555i	0.188052	+	1.60424i
$162$	4.38202	+	7.86117i	0.344284	+	0.617632i
$163$	7.26751	−	12.5877i	0.569236	−	0.985945i	−0.427406	−	0.904060i	$-0.640573\pi$
$163$	7.26751	−	12.5877i	0.569236	−	0.985945i	0.996642	−	0.0818853i	$-0.0260941\pi$
$164$	1.92560	+	3.33524i	0.150364	+	0.260438i
$165$	−6.61008	−	0.895586i	−0.514594	−	0.0697213i
$166$	−7.51166	−	4.33686i	−0.583018	−	0.336606i
$167$	20.9824			1.62367			0.811834	−	0.583888i	$-0.198469\pi$
$167$	20.9824			1.62367			0.811834	+	0.583888i	$0.198469\pi$
$168$	2.21957	+	4.00918i	0.171244	+	0.309315i
$169$	2.53386			0.194913
$170$	−5.01316	−	2.89435i	−0.384492	−	0.221987i
$171$	5.28704	+	5.36733i	0.404310	+	0.410450i
$172$	3.61103	+	6.25448i	0.275338	+	0.476900i
$173$	0.506658	−	0.877558i	0.0385205	−	0.0667195i	−0.846122	−	0.532989i	$-0.821069\pi$
$173$	0.506658	−	0.877558i	0.0385205	−	0.0667195i	0.884643	+	0.466269i	$0.154402\pi$
$174$	−10.5677	−	8.17236i	−0.801138	−	0.619545i
$175$	10.2950	−	23.8884i	0.778229	−	1.80580i
$176$		−	1.00000i		−	0.0753778i
$177$	−5.38734	+	2.20776i	−0.404937	+	0.165946i
$178$	5.77637	−	3.33499i	0.432957	−	0.249968i
$179$	−15.5742	+	8.99179i	−1.16407	+	0.672078i	−0.952277	−	0.305236i	$-0.901265\pi$
$179$	−15.5742	+	8.99179i	−1.16407	+	0.672078i	−0.211796	+	0.977314i	$0.567931\pi$
$180$	11.1371	+	3.07431i	0.830109	+	0.229146i
$181$		−	16.2893i		−	1.21078i	−0.795930	−	0.605389i	$-0.793018\pi$
$181$		−	16.2893i		−	1.21078i	0.795930	−	0.605389i	$-0.206982\pi$
$182$	−8.50117	+	0.996524i	−0.630149	+	0.0738673i
$183$	−9.12080	+	11.7942i	−0.674229	+	0.871851i
$184$	−3.87316	+	6.70851i	−0.285533	+	0.494558i
$185$	−0.263065	−	0.455641i	−0.0193409	−	0.0334994i
$186$	1.40664	−	10.3820i	0.103140	−	0.761248i
$187$	−1.30171	−	0.751545i	−0.0951908	−	0.0549584i
$188$	−10.8005			−0.787710
$189$	−13.3657	+	3.21824i	−0.972214	+	0.234092i
$190$	9.67164			0.701655
$191$	−6.35746	−	3.67048i	−0.460009	−	0.265587i	0.252039	−	0.967717i	$-0.418899\pi$
$191$	−6.35746	−	3.67048i	−0.460009	−	0.265587i	−0.712048	+	0.702131i	$0.752232\pi$
$192$	−0.232547	+	1.71637i	−0.0167826	+	0.123868i
$193$	9.83302	+	17.0313i	0.707796	+	1.22594i	0.965673	+	0.259761i	$0.0836438\pi$
$193$	9.83302	+	17.0313i	0.707796	+	1.22594i	−0.257877	+	0.966178i	$0.583023\pi$
$194$	−5.33837	+	9.24632i	−0.383272	+	0.663847i
$195$	−13.2015	+	17.0709i	−0.945376	+	1.22247i
$196$	−6.81023	+	1.61886i	−0.486445	+	0.115633i
$197$			22.8444i			1.62759i	0.581150	+	0.813797i	$0.302603\pi$
$197$			22.8444i			1.62759i	−0.581150	+	0.813797i	$0.697397\pi$
$198$	2.89184	+	0.798273i	0.205514	+	0.0567308i
$199$	−1.58668	+	0.916069i	−0.112477	+	0.0649384i	−0.555183	−	0.831728i	$-0.687352\pi$
$199$	−1.58668	+	0.916069i	−0.112477	+	0.0649384i	0.442706	+	0.896667i	$0.354018\pi$
$200$	8.51456	−	4.91588i	0.602070	−	0.347605i
$201$	−16.6413	+	6.81970i	−1.17379	+	0.481025i
$202$			8.66284i			0.609515i
$203$	16.3643	−	12.1913i	1.14855	−	0.855660i
$204$	2.05945	+	1.59264i	0.144190	+	0.111507i
$205$	−7.41588	+	12.8447i	−0.517948	+	0.897112i
$206$	1.69535	+	2.93643i	0.118120	+	0.204591i
$207$	−16.3081	−	16.5558i	−1.13349	−	1.15071i
$208$	−2.80171	−	1.61757i	−0.194264	−	0.112158i
$209$	2.51133			0.173712
$210$	−9.09755	+	15.1229i	−0.627791	+	1.04358i
$211$	−9.95762			−0.685511			−0.342755	−	0.939425i	$-0.611360\pi$
$211$	−9.95762			−0.685511			−0.342755	+	0.939425i	$0.611360\pi$
$212$	8.98451	+	5.18721i	0.617059	+	0.356259i
$213$	−1.47111	−	0.199317i	−0.100799	−	0.0136570i
$214$	8.17106	+	14.1527i	0.558562	+	0.967458i
$215$	−13.9068	+	24.0873i	−0.948436	+	1.64274i
$216$	−4.77783	−	2.04262i	−0.325090	−	0.138983i
$217$	14.6970	+	6.33384i	0.997697	+	0.429969i
$218$		−	6.42443i		−	0.435118i
$219$	1.61469	+	3.94013i	0.109111	+	0.266250i
$220$	3.33524	−	1.92560i	0.224862	−	0.129824i
$221$	−4.21123	+	2.43135i	−0.283278	+	0.163551i
$222$	0.0897272	+	0.218951i	0.00602210	+	0.0146950i
$223$		−	15.5834i		−	1.04354i	−0.853086	−	0.521770i	$-0.825272\pi$
$223$		−	15.5834i		−	1.04354i	0.853086	−	0.521770i	$-0.174728\pi$
$224$	−2.42972	−	1.04712i	−0.162343	−	0.0699634i
$225$	7.41902	+	28.5470i	0.494601	+	1.90313i
$226$	4.84883	−	8.39842i	0.322539	−	0.558655i
$227$	−6.90336	−	11.9570i	−0.458192	−	0.793612i	0.540674	−	0.841232i	$-0.318169\pi$
$227$	−6.90336	−	11.9570i	−0.458192	−	0.793612i	−0.998865	+	0.0476209i	$0.984836\pi$
$228$	−4.31037	−	0.584002i	−0.285461	−	0.0386765i
$229$	18.8937	+	10.9083i	1.24853	+	0.720839i	0.970816	−	0.239824i	$-0.0770898\pi$
$229$	18.8937	+	10.9083i	1.24853	+	0.720839i	0.277714	+	0.960664i	$0.410423\pi$
$230$	−29.8327			−1.96711
$231$	−2.36226	+	3.92679i	−0.155425	+	0.258364i
$232$	7.71286			0.506374
$233$	−1.71010	−	0.987329i	−0.112033	−	0.0646821i	0.442937	−	0.896553i	$-0.353937\pi$
$233$	−1.71010	−	0.987329i	−0.112033	−	0.0646821i	−0.554969	+	0.831871i	$0.687270\pi$
$234$	6.91429	−	6.81086i	0.452001	−	0.445240i
$235$	−20.7975	−	36.0224i	−1.35668	−	2.34984i
$236$	1.68071	−	2.91108i	0.109405	−	0.189495i
$237$	−5.80548	−	4.48956i	−0.377107	−	0.291628i
$238$	−3.18909	+	2.37585i	−0.206718	+	0.154003i
$239$			8.61931i			0.557536i	0.960358	+	0.278768i	$0.0899261\pi$
$239$			8.61931i			0.557536i	−0.960358	+	0.278768i	$0.910074\pi$
$240$	−6.17229	+	2.52944i	−0.398420	+	0.163275i
$241$	−7.63695	+	4.40920i	−0.491939	+	0.284021i	−0.725379	−	0.688350i	$-0.758335\pi$
$241$	−7.63695	+	4.40920i	−0.491939	+	0.284021i	0.233439	+	0.972371i	$0.425002\pi$
$242$	0.866025	−	0.500000i	0.0556702	−	0.0321412i
$243$	9.72095	−	12.1862i	0.623600	−	0.781744i
$244$		−	8.60797i		−	0.551069i
$245$	−18.5131	−	19.5965i	−1.18276	−	1.25197i
$246$	4.08064	−	5.27671i	0.260172	−	0.336431i
$247$	4.06225	−	7.03603i	0.258475	−	0.447692i
$248$	3.02442	+	5.23845i	0.192051	+	0.332642i
$249$	−2.01705	+	14.8873i	−0.127825	+	0.943444i
$250$	16.1151	+	9.30405i	1.01921	+	0.588440i
$251$	−10.3975			−0.656283			−0.328141	−	0.944629i	$-0.606422\pi$
$251$	−10.3975			−0.656283			−0.328141	+	0.944629i	$0.606422\pi$
$252$	4.96768	−	6.19049i	0.312934	−	0.389964i
$253$	−7.74632			−0.487007
$254$	−11.4796	−	6.62776i	−0.720295	−	0.415863i
$255$	−1.34615	+	9.93555i	−0.0842989	+	0.622188i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.03225	−	10.4482i	0.376282	−	0.651739i	−0.614236	−	0.789122i	$-0.710536\pi$
$257$	6.03225	−	10.4482i	0.376282	−	0.651739i	0.990518	+	0.137383i	$0.0438692\pi$
$258$	7.65232	−	9.89527i	0.476412	−	0.616052i
$259$	−0.358989	+	0.0420814i	−0.0223065	+	0.00261481i
$260$		−	12.4592i		−	0.772686i
$261$	−6.15697	+	22.3044i	−0.381107	+	1.38061i
$262$	14.4400	−	8.33693i	0.892106	−	0.515057i
$263$	−20.5474	+	11.8631i	−1.26701	+	0.731508i	−0.974421	−	0.224730i	$-0.927850\pi$
$263$	−20.5474	+	11.8631i	−1.26701	+	0.731508i	−0.292588	+	0.956239i	$0.594517\pi$
$264$	−1.60269	+	0.656793i	−0.0986389	+	0.0404228i
$265$			39.9540i			2.45435i
$266$	2.62966	−	6.10183i	0.161235	−	0.374127i
$267$	−9.13884	−	7.06735i	−0.559288	−	0.432515i
$268$	5.19167	−	8.99224i	0.317132	−	0.549288i
$269$	−15.3296	−	26.5516i	−0.934661	−	1.61888i	−0.775238	−	0.631669i	$-0.782370\pi$
$269$	−15.3296	−	26.5516i	−0.934661	−	1.61888i	−0.159422	−	0.987210i	$-0.550963\pi$
$270$	−2.38758	−	19.8685i	−0.145303	−	1.20916i
$271$	21.6186	+	12.4815i	1.31323	+	0.758196i	0.982630	−	0.185573i	$-0.0594142\pi$
$271$	21.6186	+	12.4815i	1.31323	+	0.758196i	0.330604	+	0.943770i	$0.392748\pi$
$272$	−1.50309			−0.0911382
$273$	7.18063	+	12.9703i	0.434591	+	0.784995i
$274$	13.1113			0.792081
$275$	8.51456	+	4.91588i	0.513447	+	0.296439i
$276$	13.2955	+	1.80138i	0.800298	+	0.108431i
$277$	−0.993044	−	1.72000i	−0.0596662	−	0.103345i	0.834649	−	0.550782i	$-0.185670\pi$
$277$	−0.993044	−	1.72000i	−0.0596662	−	0.103345i	−0.894316	+	0.447437i	$0.852337\pi$
$278$	−7.93644	+	13.7463i	−0.475996	+	0.824450i
$279$	−17.5631	+	4.56444i	−1.05147	+	0.273266i
$280$	−1.18629	−	10.1200i	−0.0708944	−	0.604788i
$281$		−	0.837366i		−	0.0499531i	−0.999688	−	0.0249765i	$-0.992049\pi$
$281$		−	0.837366i		−	0.0499531i	0.999688	−	0.0249765i	$-0.00795110\pi$
$282$	7.09371	+	17.3099i	0.422424	+	1.03079i
$283$	−7.13062	+	4.11687i	−0.423871	+	0.244722i	−0.696732	−	0.717331i	$-0.745363\pi$
$283$	−7.13062	+	4.11687i	−0.423871	+	0.244722i	0.272861	+	0.962054i	$0.412030\pi$
$284$	0.742275	−	0.428552i	0.0440459	−	0.0254299i
$285$	−6.35226	−	15.5007i	−0.376276	−	0.918180i
$286$		−	3.23514i		−	0.191298i
$287$	6.08737	+	8.17106i	0.359326	+	0.482322i
$288$	2.90355	−	0.754597i	0.171093	−	0.0444651i
$289$	7.37036	−	12.7658i	0.433551	−	0.750932i
$290$	14.8519	+	25.7242i	0.872133	+	1.51058i
$291$	18.3252	+	2.48284i	1.07424	+	0.145547i
$292$	−2.12908	−	1.22922i	−0.124595	−	0.0719348i
$293$	−1.75825			−0.102718			−0.0513591	−	0.998680i	$-0.516355\pi$
$293$	−1.75825			−0.102718			−0.0513591	+	0.998680i	$0.516355\pi$
$294$	7.06745	+	9.85145i	0.412182	+	0.574548i
$295$	12.9455			0.753719
$296$	−0.118311	−	0.0683071i	−0.00687671	−	0.00397027i
$297$	−0.619956	−	5.15904i	−0.0359735	−	0.299358i
$298$	1.50314	+	2.60352i	0.0870746	+	0.150818i
$299$	−12.5302	+	21.7030i	−0.724641	+	1.25512i
$300$	−13.4709	−	10.4175i	−0.777745	−	0.601455i
$301$	11.4155	+	15.3230i	0.657978	+	0.883201i
$302$			12.3314i			0.709590i
$303$	13.8839	−	5.68969i	0.797607	−	0.326864i
$304$	2.17488	−	1.25567i	0.124738	−	0.0720173i
$305$	28.7097	−	16.5755i	1.64391	−	0.949112i
$306$	1.19988	−	4.34670i	0.0685923	−	0.248484i
$307$		−	10.9981i		−	0.627694i	−0.949474	−	0.313847i	$-0.898382\pi$
$307$		−	10.9981i		−	0.627694i	0.949474	−	0.313847i	$-0.101618\pi$
$308$	−0.308031	−	2.62776i	−0.0175517	−	0.149730i
$309$	3.59270	−	4.64575i	0.204382	−	0.264287i
$310$	−11.6476	+	20.1743i	−0.661542	+	1.14582i
$311$	−4.02080	−	6.96424i	−0.227999	−	0.394906i	0.729216	−	0.684283i	$-0.239885\pi$
$311$	−4.02080	−	6.96424i	−0.227999	−	0.394906i	−0.957215	+	0.289378i	$0.906552\pi$
$312$	−0.752322	+	5.55269i	−0.0425919	+	0.314359i
$313$	−11.0635	−	6.38750i	−0.625345	−	0.361043i	0.153602	−	0.988133i	$-0.450913\pi$
$313$	−11.0635	−	6.38750i	−0.625345	−	0.361043i	−0.778947	+	0.627090i	$0.784246\pi$
$314$	4.81671			0.271823
$315$	30.2125	+	4.64798i	1.70228	+	0.261884i
$316$	4.23713			0.238357
$317$	7.12754	+	4.11509i	0.400323	+	0.231126i	0.686623	−	0.727013i	$-0.259092\pi$
$317$	7.12754	+	4.11509i	0.400323	+	0.231126i	−0.286301	+	0.958140i	$0.592426\pi$
$318$	2.41254	−	17.8063i	0.135289	−	0.998530i
$319$	3.85643	+	6.67953i	0.215919	+	0.373982i
$320$	1.92560	−	3.33524i	0.107644	−	0.186446i
$321$	17.3157	−	22.3911i	0.966469	−	1.24975i
$322$	−8.11130	+	18.8214i	−0.452025	+	1.04888i
$323$		−	3.77475i		−	0.210033i
$324$	−0.135645	+	8.99898i	−0.00753583	+	0.499943i
$325$	27.5458	−	15.9036i	1.52797	−	0.882171i
$326$	12.5877	−	7.26751i	0.697168	−	0.402510i
$327$	−10.2964	+	4.21952i	−0.569392	+	0.233340i
$328$			3.85120i			0.212647i
$329$	−28.3812	+	3.32690i	−1.56471	+	0.183418i
$330$	−5.27671	−	4.08064i	−0.290473	−	0.224632i
$331$	−6.00504	+	10.4010i	−0.330067	+	0.571693i	−0.982525	−	0.186132i	$-0.940405\pi$
$331$	−6.00504	+	10.4010i	−0.330067	+	0.571693i	0.652458	+	0.757825i	$0.273738\pi$
$332$	−4.33686	−	7.51166i	−0.238016	−	0.412256i
$333$	0.291978	−	0.287610i	0.0160003	−	0.0157609i
$334$	18.1713	+	10.4912i	0.994290	+	0.574053i
$335$	39.9883			2.18480
$336$	−0.0823825	+	4.58184i	−0.00449434	+	0.249960i
$337$	−21.0070			−1.14432			−0.572162	−	0.820141i	$-0.693895\pi$
$337$	−21.0070			−1.14432			−0.572162	+	0.820141i	$0.693895\pi$
$338$	2.19439	+	1.26693i	0.119359	+	0.0689120i
$339$	−16.6448	−	2.25516i	−0.904019	−	0.122484i
$340$	−2.89435	−	5.01316i	−0.156968	−	0.271877i
$341$	−3.02442	+	5.23845i	−0.163781	+	0.283678i
$342$	1.89504	+	7.29176i	0.102472	+	0.394293i
$343$	−17.3970	+	6.35175i	−0.939349	+	0.342962i
$344$			7.22205i			0.389387i
$345$	19.5939	+	47.8126i	1.05490	+	2.57414i
$346$	0.877558	−	0.506658i	0.0471778	−	0.0272381i
$347$	−23.8900	+	13.7929i	−1.28248	+	0.740440i	−0.977301	−	0.211854i	$-0.932050\pi$
$347$	−23.8900	+	13.7929i	−1.28248	+	0.740440i	−0.305179	+	0.952295i	$0.598716\pi$
$348$	−5.06575	−	12.3613i	−0.271553	−	0.662638i
$349$		−	9.51035i		−	0.509078i	−0.967063	−	0.254539i	$-0.918076\pi$
$349$		−	9.51035i		−	0.509078i	0.967063	−	0.254539i	$-0.0819237\pi$
$350$	20.8600	−	15.5405i	1.11501	−	0.830675i
$351$	−15.4570	−	6.60816i	−0.825032	−	0.352718i
$352$	0.500000	−	0.866025i	0.0266501	−	0.0461593i
$353$	−7.59466	−	13.1543i	−0.404223	−	0.700134i	0.590008	−	0.807398i	$-0.299125\pi$
$353$	−7.59466	−	13.1543i	−0.404223	−	0.700134i	−0.994231	+	0.107263i	$0.965791\pi$
$354$	−5.76945	−	0.781690i	−0.306643	−	0.0415464i
$355$	2.85865	+	1.65044i	0.151721	+	0.0875964i
$356$	6.66998			0.353508
$357$	5.90232	+	3.55069i	0.312384	+	0.187923i
$358$	−17.9836			−0.950462
$359$	11.0255	+	6.36556i	0.581902	+	0.335962i	0.761889	−	0.647708i	$-0.224272\pi$
$359$	11.0255	+	6.36556i	0.581902	+	0.335962i	−0.179987	+	0.983669i	$0.557605\pi$
$360$	8.10784	+	8.23097i	0.427320	+	0.433810i
$361$	−6.34661	−	10.9927i	−0.334032	−	0.578561i
$362$	8.14467	−	14.1070i	0.428075	−	0.741447i
$363$	−1.37015	−	1.05958i	−0.0719140	−	0.0556133i
$364$	−7.86049	−	3.38757i	−0.412002	−	0.177557i
$365$		−	9.46798i		−	0.495577i
$366$	−13.7959	+	5.65366i	−0.721125	+	0.295521i
$367$	−10.2217	+	5.90150i	−0.533568	+	0.308056i	−0.742468	−	0.669881i	$-0.766345\pi$
$367$	−10.2217	+	5.90150i	−0.533568	+	0.308056i	0.208900	+	0.977937i	$0.433012\pi$
$368$	−6.70851	+	3.87316i	−0.349705	+	0.201903i
$369$	−11.1371	−	3.07431i	−0.579773	−	0.160042i
$370$		−	0.526129i		−	0.0273521i
$371$	25.2070	+	10.8632i	1.30868	+	0.563991i
$372$	6.40920	−	8.28779i	0.332302	−	0.429702i
$373$	15.4273	−	26.7209i	0.798796	−	1.38356i	−0.121604	−	0.992579i	$-0.538804\pi$
$373$	15.4273	−	26.7209i	0.798796	−	1.38356i	0.920401	−	0.390977i	$-0.127863\pi$
$374$	−0.751545	−	1.30171i	−0.0388615	−	0.0673100i
$375$	4.32726	−	31.9384i	0.223459	−	1.64929i
$376$	−9.35353	−	5.40027i	−0.482372	−	0.278497i
$377$	24.9522			1.28510
$378$	−13.1842	−	3.89579i	−0.678121	−	0.200378i
$379$	32.0563			1.64662			0.823312	−	0.567589i	$-0.192124\pi$
$379$	32.0563			1.64662			0.823312	+	0.567589i	$0.192124\pi$
$380$	8.37589	+	4.83582i	0.429674	+	0.248072i
$381$	−3.08253	+	22.7514i	−0.157923	+	1.16559i
$382$	−3.67048	−	6.35746i	−0.187798	−	0.325276i
$383$	11.0271	−	19.0996i	0.563460	−	0.975942i	−0.433731	−	0.901042i	$-0.642803\pi$
$383$	11.0271	−	19.0996i	0.563460	−	0.975942i	0.997191	−	0.0748992i	$-0.0238635\pi$
$384$	−1.05958	+	1.37015i	−0.0540713	+	0.0699199i
$385$	8.17106	−	6.08737i	0.416436	−	0.310241i
$386$			19.6660i			1.00098i
$387$	−20.8851	−	5.76517i	−1.06165	−	0.293060i
$388$	−9.24632	+	5.33837i	−0.469411	+	0.271015i
$389$	−18.5178	+	10.6913i	−0.938891	+	0.542069i	−0.889613	−	0.456716i	$-0.849026\pi$
$389$	−18.5178	+	10.6913i	−0.938891	+	0.542069i	−0.0492785	+	0.998785i	$0.515692\pi$
$390$	−19.9682	+	8.18310i	−1.01113	+	0.414367i
$391$			11.6434i			0.588833i
$392$	−6.70727	−	2.00314i	−0.338768	−	0.101174i
$393$	−22.8456	−	17.6672i	−1.15241	−	0.891194i
$394$	−11.4222	+	19.7838i	−0.575441	+	0.996693i
$395$	8.15902	+	14.1318i	0.410525	+	0.711050i
$396$	2.10527	+	2.13725i	0.105794	+	0.107401i
$397$	−13.9335	−	8.04449i	−0.699301	−	0.403742i	0.107786	−	0.994174i	$-0.465624\pi$
$397$	−13.9335	−	8.04449i	−0.699301	−	0.403742i	−0.807087	+	0.590433i	$0.798957\pi$
$398$	−1.83214			−0.0918368
$399$	−11.5065	−	0.206890i	−0.576046	−	0.0103574i
$400$	9.83176			0.491588
$401$	−18.5573	−	10.7141i	−0.926707	−	0.535034i	−0.0409384	−	0.999162i	$-0.513035\pi$
$401$	−18.5573	−	10.7141i	−0.926707	−	0.535034i	−0.885769	+	0.464127i	$0.846368\pi$
$402$	−17.8216	−	2.41461i	−0.888863	−	0.120430i
$403$	9.78442	+	16.9471i	0.487397	+	0.844196i
$404$	−4.33142	+	7.50224i	−0.215496	+	0.373250i
$405$	−30.2749	+	16.8760i	−1.50437	+	0.838577i
$406$	20.2675	−	2.37580i	1.00586	−	0.117909i
$407$		−	0.136614i		−	0.00677171i
$408$	0.987219	+	2.40899i	0.0488746	+	0.119263i
$409$	10.8153	−	6.24422i	0.534783	−	0.308757i	−0.208179	−	0.978091i	$-0.566754\pi$
$409$	10.8153	−	6.24422i	0.534783	−	0.308757i	0.742962	+	0.669334i	$0.233420\pi$
$410$	−12.8447	+	7.41588i	−0.634354	+	0.366244i
$411$	−8.61139	−	21.0133i	−0.424769	−	1.03651i
$412$			3.39070i			0.167048i
$413$	3.51981	−	8.16734i	0.173198	−	0.401888i
$414$	−5.84535	−	22.4918i	−0.287284	−	1.10541i
$415$	16.7021	−	28.9289i	0.819875	−	1.42007i
$416$	−1.61757	−	2.80171i	−0.0793079	−	0.137365i
$417$	27.2437	+	3.69119i	1.33413	+	0.180758i
$418$	2.17488	+	1.25567i	0.106377	+	0.0614166i
$419$	−28.3825			−1.38657			−0.693287	−	0.720662i	$-0.743838\pi$
$419$	−28.3825			−1.38657			−0.693287	+	0.720662i	$0.743838\pi$
$420$	−15.4402	+	8.54802i	−0.753402	+	0.417101i
$421$	−31.3231			−1.52659			−0.763296	−	0.646049i	$-0.776420\pi$
$421$	−31.3231			−1.52659			−0.763296	+	0.646049i	$0.776420\pi$
$422$	−8.62355	−	4.97881i	−0.419788	−	0.242365i
$423$	23.0834	−	22.7381i	1.12235	−	1.10556i
$424$	5.18721	+	8.98451i	0.251913	+	0.436326i
$425$	7.38901	−	12.7981i	0.358420	−	0.620801i
$426$	−1.17436	−	0.908168i	−0.0568978	−	0.0440009i
$427$	−2.65152	−	22.6197i	−0.128316	−	1.09464i
$428$			16.3421i			0.789926i
$429$	−5.18494	+	2.12482i	−0.250331	+	0.102587i
$430$	−24.0873	+	13.9068i	−1.16159	+	0.670645i
$431$	−16.8301	+	9.71686i	−0.810677	+	0.468045i	−0.847191	−	0.531289i	$-0.821708\pi$
$431$	−16.8301	+	9.71686i	−0.810677	+	0.468045i	0.0365139	+	0.999333i	$0.488375\pi$
$432$	−3.11642	−	4.15788i	−0.149939	−	0.200046i
$433$		−	2.90858i		−	0.139778i	−0.997555	−	0.0698888i	$-0.977736\pi$
$433$		−	2.90858i		−	0.139778i	0.997555	−	0.0698888i	$-0.0222645\pi$
$434$	9.56105	+	12.8338i	0.458945	+	0.616040i
$435$	31.4734	−	40.6985i	1.50904	−	1.95134i
$436$	3.21222	−	5.56372i	0.153837	−	0.266454i
$437$	−9.72679	−	16.8473i	−0.465295	−	0.805915i
$438$	−0.571704	+	4.21960i	−0.0273171	+	0.201620i
$439$	14.2434	+	8.22341i	0.679799	+	0.392482i	0.799779	−	0.600294i	$-0.204950\pi$
$439$	14.2434	+	8.22341i	0.679799	+	0.392482i	−0.119980	+	0.992776i	$0.538283\pi$
$440$	3.85120			0.183599
$441$	11.1470	−	17.7973i	0.530809	−	0.847491i
$442$	−4.86271			−0.231295
$443$	12.4426	+	7.18373i	0.591165	+	0.341309i	0.765558	−	0.643367i	$-0.222463\pi$
$443$	12.4426	+	7.18373i	0.591165	+	0.341309i	−0.174393	+	0.984676i	$0.555796\pi$
$444$	−0.0317692	+	0.234480i	−0.00150770	+	0.0111279i
$445$	12.8437	+	22.2460i	0.608851	+	1.05456i
$446$	7.79169	−	13.4956i	0.368947	−	0.639035i
$447$	3.18538	−	4.11904i	0.150663	−	0.194824i
$448$	−1.58064	−	2.12169i	−0.0746783	−	0.100240i
$449$		−	0.859617i		−	0.0405678i	−0.999794	−	0.0202839i	$-0.993543\pi$
$449$		−	0.859617i		−	0.0405678i	0.999794	−	0.0202839i	$-0.00645701\pi$
$450$	−7.84843	+	28.4319i	−0.369979	+	1.34029i
$451$	−3.33524	+	1.92560i	−0.157050	+	0.0906730i
$452$	8.39842	−	4.84883i	0.395029	−	0.228070i
$453$	19.7634	−	8.09915i	0.928565	−	0.380531i
$454$		−	13.8067i		−	0.647981i
$455$	−3.83782	−	32.7397i	−0.179920	−	1.53486i
$456$	−3.44089	−	2.66095i	−0.161134	−	0.124610i
$457$	12.9152	−	22.3698i	0.604148	−	1.04641i	−0.388038	−	0.921644i	$-0.626847\pi$
$457$	12.9152	−	22.3698i	0.604148	−	1.04641i	0.992186	−	0.124771i	$-0.0398197\pi$
$458$	10.9083	+	18.8937i	0.509710	+	0.882844i
$459$	−7.75450	+	0.931850i	−0.361949	+	0.0434950i
$460$	−25.8358	−	14.9163i	−1.20460	−	0.695478i
$461$	−9.74250			−0.453754			−0.226877	−	0.973923i	$-0.572851\pi$
$461$	−9.74250			−0.453754			−0.226877	+	0.973923i	$0.572851\pi$
$462$	−4.00918	+	2.21957i	−0.186524	+	0.103264i
$463$	19.2069			0.892618			0.446309	−	0.894879i	$-0.352738\pi$
$463$	19.2069			0.892618			0.446309	+	0.894879i	$0.352738\pi$
$464$	6.67953	+	3.85643i	0.310090	+	0.179030i
$465$	39.9833	+	5.41725i	1.85418	+	0.251219i
$466$	−0.987329	−	1.71010i	−0.0457371	−	0.0792191i
$467$	−6.00996	+	10.4096i	−0.278108	+	0.481697i	−0.970914	−	0.239427i	$-0.923041\pi$
$467$	−6.00996	+	10.4096i	−0.278108	+	0.481697i	0.692807	+	0.721123i	$0.256374\pi$
$468$	9.39338	−	2.44123i	0.434209	−	0.112846i
$469$	10.8726	−	25.2286i	0.502049	−	1.16495i
$470$		−	41.5950i		−	1.91864i
$471$	−3.16358	−	7.71971i	−0.145770	−	0.355705i
$472$	2.91108	−	1.68071i	0.133993	−	0.0773612i
$473$	−6.25448	+	3.61103i	−0.287581	+	0.166035i
$474$	−2.78292	−	6.79081i	−0.127824	−	0.311912i
$475$			24.6908i			1.13289i
$476$	−3.94976	+	0.462998i	−0.181037	+	0.0212215i
$477$	−30.1226	+	7.82851i	−1.37922	+	0.358443i
$478$	−4.30965	+	7.46454i	−0.197119	+	0.341420i
$479$	5.22673	+	9.05296i	0.238815	+	0.413640i	0.960375	−	0.278712i	$-0.0899076\pi$
$479$	5.22673	+	9.05296i	0.238815	+	0.413640i	−0.721559	+	0.692353i	$0.756574\pi$
$480$	−6.61008	−	0.895586i	−0.301708	−	0.0408777i
$481$	−0.382754	−	0.220983i	−0.0174521	−	0.0100760i
$482$	−8.81839			−0.401667
$483$	35.4924	+	0.638162i	1.61496	+	0.0290374i
$484$	1.00000			0.0454545
$485$	−35.6095	−	20.5591i	−1.61694	−	0.933542i
$486$	14.5117	−	5.69307i	0.658263	−	0.258243i
$487$	−7.94123	−	13.7546i	−0.359851	−	0.623281i	0.628084	−	0.778145i	$-0.283839\pi$
$487$	−7.94123	−	13.7546i	−0.359851	−	0.623281i	−0.987936	+	0.154864i	$0.950506\pi$
$488$	4.30399	−	7.45472i	0.194832	−	0.337460i
$489$	−19.9151	−	15.4010i	−0.900592	−	0.696456i
$490$	−6.23457	−	26.2276i	−0.281649	−	1.18484i
$491$			16.5060i			0.744907i	0.928051	+	0.372454i	$0.121483\pi$
$491$			16.5060i			0.744907i	−0.928051	+	0.372454i	$0.878517\pi$
$492$	6.17229	−	2.52944i	0.278268	−	0.114036i
$493$	10.0399	−	5.79656i	0.452176	−	0.261064i
$494$	7.03603	−	4.06225i	0.316566	−	0.182769i
$495$	−3.07431	+	11.1371i	−0.138180	+	0.500574i
$496$			6.04884i			0.271601i
$497$	1.81851	−	1.35478i	0.0815714	−	0.0607700i
$498$	−9.19046	+	11.8843i	−0.411835	+	0.532546i
$499$	−16.8760	+	29.2301i	−0.755473	+	1.30852i	0.189666	+	0.981849i	$0.439259\pi$
$499$	−16.8760	+	29.2301i	−0.755473	+	1.30852i	−0.945139	+	0.326669i	$0.894074\pi$
$500$	9.30405	+	16.1151i	0.416090	+	0.720689i
$501$	4.87940	−	36.0136i	0.217995	−	1.60897i
$502$	−9.00448	−	5.19874i	−0.401889	−	0.232031i
$503$	14.4126			0.642627			0.321313	−	0.946973i	$-0.395876\pi$
$503$	14.4126			0.642627			0.321313	+	0.946973i	$0.395876\pi$
$504$	7.39738	−	2.87728i	0.329506	−	0.128164i
$505$	−33.3624			−1.48461
$506$	−6.70851	−	3.87316i	−0.298230	−	0.172183i
$507$	0.589243	−	4.34905i	0.0261692	−	0.193148i
$508$	−6.62776	−	11.4796i	−0.294059	−	0.509326i
$509$	13.2356	−	22.9247i	0.586656	−	1.01612i	−0.408010	−	0.912977i	$-0.633777\pi$
$509$	13.2356	−	22.9247i	0.586656	−	1.01612i	0.994667	−	0.103141i	$-0.0328894\pi$
$510$	−6.13357	+	7.93137i	−0.271599	+	0.351207i
$511$	−5.97334	−	2.57428i	−0.264245	−	0.113879i
$512$		−	1.00000i		−	0.0441942i
$513$	10.4418	−	7.82635i	0.461017	−	0.345542i
$514$	10.4482	−	6.03225i	0.460849	−	0.266071i
$515$	−11.3088	+	6.52913i	−0.498325	+	0.287708i
$516$	11.5747	−	4.74339i	0.509549	−	0.208816i
$517$		−	10.8005i		−	0.475007i
$518$	−0.331934	−	0.143051i	−0.0145844	−	0.00628530i
$519$	−1.38839	−	1.07369i	−0.0609436	−	0.0471296i
$520$	6.22959	−	10.7900i	0.273186	−	0.473171i
$521$	−4.60146	−	7.96995i	−0.201593	−	0.349170i	0.747449	−	0.664320i	$-0.231279\pi$
$521$	−4.60146	−	7.96995i	−0.201593	−	0.349170i	−0.949042	+	0.315150i	$0.897945\pi$
$522$	−16.4843	+	16.2377i	−0.721497	+	0.710704i
$523$	9.07236	+	5.23793i	0.396707	+	0.229039i	0.685062	−	0.728485i	$-0.259775\pi$
$523$	9.07236	+	5.23793i	0.396707	+	0.229039i	−0.288355	+	0.957523i	$0.593108\pi$
$524$	16.6739			0.728401
$525$	−38.6073	−	23.2252i	−1.68496	−	1.01363i
$526$	−23.7261			−1.03451
$527$	7.87386	+	4.54597i	0.342991	+	0.198026i
$528$	−1.71637	−	0.232547i	−0.0746954	−	0.0101203i
$529$	18.5028	+	32.0477i	0.804468	+	1.39338i
$530$	−19.9770	+	34.6012i	−0.867745	+	1.50298i
$531$	2.53653	+	9.76007i	0.110076	+	0.423551i
$532$	5.32826	−	3.96951i	0.231010	−	0.172100i
$533$			12.4592i			0.539667i
$534$	−4.38079	−	10.6899i	−0.189575	−	0.462598i
$535$	−54.5049	+	31.4684i	−2.35645	+	1.36050i
$536$	8.99224	−	5.19167i	0.388405	−	0.224246i
$537$	11.8115	+	28.8221i	0.509703	+	1.24377i
$538$		−	30.6591i		−	1.32181i
$539$	−1.61886	−	6.81023i	−0.0697294	−	0.293338i
$540$	7.86655	−	18.4004i	0.338522	−	0.791828i
$541$	8.10749	−	14.0426i	0.348568	−	0.603738i	−0.637427	−	0.770511i	$-0.720001\pi$
$541$	8.10749	−	14.0426i	0.348568	−	0.603738i	0.985995	+	0.166773i	$0.0533347\pi$
$542$	12.4815	+	21.6186i	0.536126	+	0.928597i
$543$	−27.9585	−	3.78804i	−1.19982	−	0.162560i
$544$	−1.30171	−	0.751545i	−0.0558105	−	0.0322222i
$545$	24.7418			1.05982
$546$	−0.266519	+	14.8229i	−0.0114060	+	0.634361i
$547$	−22.1650			−0.947706			−0.473853	−	0.880604i	$-0.657137\pi$
$547$	−22.1650			−0.947706			−0.473853	+	0.880604i	$0.657137\pi$
$548$	11.3547	+	6.55564i	0.485049	+	0.280043i
$549$	18.1221	+	18.3974i	0.773434	+	0.785180i
$550$	4.91588	+	8.51456i	0.209614	+	0.363062i
$551$	−9.68477	+	16.7745i	−0.412585	+	0.714618i
$552$	10.6136	+	8.20782i	0.451744	+	0.349348i
$553$	11.1342	−	1.30517i	0.473472	−	0.0555014i
$554$		−	1.98609i		−	0.0843808i
$555$	−0.843223	+	0.345558i	−0.0357928	+	0.0146681i
$556$	−13.7463	+	7.93644i	−0.582974	+	0.336580i
$557$	−18.9337	+	10.9314i	−0.802246	+	0.463177i	−0.844256	−	0.535940i	$-0.819957\pi$
$557$	−18.9337	+	10.9314i	−0.802246	+	0.463177i	0.0420097	+	0.999117i	$0.486624\pi$
$558$	−17.4923	−	4.82862i	−0.740508	−	0.204412i
$559$			23.3644i			0.988207i
$560$	4.03266	−	9.35735i	0.170411	−	0.395420i
$561$	−1.59264	+	2.05945i	−0.0672412	+	0.0869501i
$562$	0.418683	−	0.725180i	0.0176611	−	0.0305899i
$563$	4.31473	+	7.47333i	0.181844	+	0.314963i	0.942509	−	0.334182i	$-0.108460\pi$
$563$	4.31473	+	7.47333i	0.181844	+	0.314963i	−0.760664	+	0.649145i	$0.775127\pi$
$564$	−2.51163	+	18.5377i	−0.105759	+	0.780578i
$565$	32.3440	+	18.6738i	1.36072	+	0.785614i
$566$	−8.23373			−0.346090
$567$	2.41552	+	23.6889i	0.101442	+	0.994841i
$568$	0.857105			0.0359633
$569$	−5.66393	−	3.27007i	−0.237444	−	0.137088i	0.376557	−	0.926393i	$-0.377108\pi$
$569$	−5.66393	−	3.27007i	−0.237444	−	0.137088i	−0.614001	+	0.789305i	$0.710441\pi$
$570$	2.24911	−	16.6001i	0.0942049	−	0.695302i
$571$	−14.2418	−	24.6675i	−0.596000	−	1.03230i	−0.993405	−	0.114658i	$-0.963423\pi$
$571$	−14.2418	−	24.6675i	−0.596000	−	1.03230i	0.397405	−	0.917643i	$-0.369911\pi$
$572$	1.61757	−	2.80171i	0.0676340	−	0.117146i
$573$	−7.77830	+	10.0582i	−0.324943	+	0.420187i
$574$	1.18629	+	10.1200i	0.0495148	+	0.422402i
$575$		−	76.1600i		−	3.17609i
$576$	2.89184	+	0.798273i	0.120493	+	0.0332614i
$577$	−24.9262	+	14.3911i	−1.03769	+	0.599111i	−0.919178	−	0.393842i	$-0.871146\pi$
$577$	−24.9262	+	14.3911i	−1.03769	+	0.599111i	−0.118512	+	0.992953i	$0.537812\pi$
$578$	12.7658	−	7.37036i	0.530989	−	0.306567i
$579$	31.5186	−	12.9165i	1.30987	−	0.536792i
$580$			29.7038i			1.23338i
$581$	−13.7100	−	18.4029i	−0.568788	−	0.763483i
$582$	14.6287	+	11.3128i	0.606378	+	0.468931i
$583$	−5.18721	+	8.98451i	−0.214832	+	0.372100i
$584$	−1.22922	−	2.12908i	−0.0508656	−	0.0881018i
$585$	26.2300	+	26.6283i	1.08448	+	1.10095i
$586$	−1.52269	−	0.879127i	−0.0629018	−	0.0363164i
$587$	−6.58973			−0.271987			−0.135994	−	0.990710i	$-0.543423\pi$
$587$	−6.58973			−0.271987			−0.135994	+	0.990710i	$0.543423\pi$
$588$	1.19487	+	12.0653i	0.0492755	+	0.497566i
$589$	−15.1906			−0.625919
$590$	11.2112	+	6.47277i	0.461557	+	0.266480i
$591$	39.2094	+	5.31239i	1.61286	+	0.218522i
$592$	−0.0683071	−	0.118311i	−0.00280740	−	0.00486257i
$593$	−0.776378	+	1.34473i	−0.0318820	+	0.0552213i	−0.881526	−	0.472135i	$-0.843483\pi$
$593$	−0.776378	+	1.34473i	−0.0318820	+	0.0552213i	0.849644	+	0.527356i	$0.176817\pi$
$594$	2.04262	−	4.77783i	0.0838097	−	0.196037i
$595$	−9.14987	−	12.2818i	−0.375108	−	0.503506i
$596$			3.00628i			0.123142i
$597$	1.20333	+	2.93635i	0.0492492	+	0.120177i
$598$	−21.7030	+	12.5302i	−0.887501	+	0.512399i
$599$	−22.6733	+	13.0904i	−0.926405	+	0.534860i	−0.885673	−	0.464310i	$-0.846302\pi$
$599$	−22.6733	+	13.0904i	−0.926405	+	0.534860i	−0.0407320	+	0.999170i	$0.512969\pi$
$600$	−6.45743	−	15.7573i	−0.263624	−	0.643289i
$601$		−	32.0935i		−	1.30912i	−0.756009	−	0.654562i	$-0.772853\pi$
$601$		−	32.0935i		−	1.30912i	0.756009	−	0.654562i	$-0.227147\pi$
$602$	2.22462	+	18.9778i	0.0906686	+	0.773478i
$603$	7.83524	+	30.1485i	0.319076	+	1.22774i
$604$	−6.16568	+	10.6793i	−0.250878	+	0.434533i
$605$	1.92560	+	3.33524i	0.0782868	+	0.135597i
$606$	14.8686	+	2.01452i	0.603997	+	0.0818342i
$607$	15.1294	+	8.73495i	0.614083	+	0.354541i	0.774562	−	0.632498i	$-0.217971\pi$
$607$	15.1294	+	8.73495i	0.614083	+	0.354541i	−0.160479	+	0.987039i	$0.551304\pi$
$608$	2.51133			0.101848
$609$	−17.1192	−	30.9222i	−0.693707	−	1.25303i
$610$	33.1511			1.34225
$611$	−30.2600	−	17.4706i	−1.22419	−	0.706786i
$612$	3.21247	−	3.16442i	0.129857	−	0.127914i
$613$	−15.9570	−	27.6383i	−0.644496	−	1.11630i	−0.984418	−	0.175846i	$-0.943734\pi$
$613$	−15.9570	−	27.6383i	−0.644496	−	1.11630i	0.339922	−	0.940454i	$-0.389599\pi$
$614$	5.49905	−	9.52463i	0.221923	−	0.384383i
$615$	20.3217	+	15.7154i	0.819449	+	0.633705i
$616$	1.04712	−	2.42972i	0.0421895	−	0.0978963i
$617$		−	11.8955i		−	0.478896i	−0.970909	−	0.239448i	$-0.923033\pi$
$617$		−	11.8955i		−	0.478896i	0.970909	−	0.239448i	$-0.0769665\pi$
$618$	5.43424	−	2.22698i	0.218597	−	0.0895825i
$619$	−32.1638	+	18.5698i	−1.29277	+	0.746383i	−0.979145	−	0.203163i	$-0.934878\pi$
$619$	−32.1638	+	18.5698i	−1.29277	+	0.746383i	−0.313628	+	0.949546i	$0.601545\pi$
$620$	−20.1743	+	11.6476i	−0.810220	+	0.467781i
$621$	−32.2083	+	24.1408i	−1.29247	+	0.968736i
$622$		−	8.04161i		−	0.322439i
$623$	17.5271	−	2.05456i	0.702208	−	0.0823142i
$624$	−3.42788	+	4.43261i	−0.137225	+	0.177447i
$625$	−11.2524	+	19.4897i	−0.450095	+	0.779588i
$626$	−6.38750	−	11.0635i	−0.255296	−	0.442186i
$627$	0.584002	−	4.31037i	0.0233228	−	0.172140i
$628$	4.17140	+	2.40836i	0.166457	+	0.0961039i
$629$	−0.205343			−0.00818758
$630$	23.8408	+	19.1315i	0.949842	+	0.762219i
$631$	33.9133			1.35007			0.675033	−	0.737788i	$-0.264130\pi$
$631$	33.9133			1.35007			0.675033	+	0.737788i	$0.264130\pi$
$632$	3.66946	+	2.11856i	0.145963	+	0.0842720i
$633$	−2.31561	+	17.0909i	−0.0920374	+	0.679304i
$634$	4.11509	+	7.12754i	0.163431	+	0.283071i
$635$	25.5248	−	44.2103i	1.01292	−	1.75443i
$636$	10.9925	−	14.2145i	0.435881	−	0.563640i
$637$	−21.6990	−	6.48044i	−0.859744	−	0.256764i
$638$			7.71286i			0.305355i
$639$	−0.684204	+	2.47861i	−0.0270667	+	0.0980524i
$640$	3.33524	−	1.92560i	0.131837	−	0.0761161i
$641$	22.8612	−	13.1989i	0.902964	−	0.521327i	0.0248034	−	0.999692i	$-0.492104\pi$
$641$	22.8612	−	13.1989i	0.902964	−	0.521327i	0.878161	+	0.478366i	$0.158771\pi$
$642$	26.1914	−	10.7334i	1.03369	−	0.423613i
$643$			13.3060i			0.524736i	0.964968	+	0.262368i	$0.0845034\pi$
$643$			13.3060i			0.524736i	−0.964968	+	0.262368i	$0.915497\pi$
$644$	−16.4353	+	12.2442i	−0.647642	+	0.482488i
$645$	38.1087	+	29.4706i	1.50053	+	1.16040i
$646$	1.88738	−	3.26903i	0.0742579	−	0.128618i
$647$	8.87268	+	15.3679i	0.348821	+	0.604176i	0.986040	−	0.166507i	$-0.0532488\pi$
$647$	8.87268	+	15.3679i	0.348821	+	0.604176i	−0.637219	+	0.770683i	$0.719915\pi$
$648$	−4.61696	+	7.72552i	−0.181371	+	0.303487i
$649$	2.91108	+	1.68071i	0.114270	+	0.0659738i
$650$	31.8071			1.24758
$651$	14.2889	−	23.7525i	0.560028	−	0.930935i
$652$	14.5350			0.569236
$653$	9.50503	+	5.48773i	0.371961	+	0.214751i	0.674315	−	0.738444i	$-0.264439\pi$
$653$	9.50503	+	5.48773i	0.371961	+	0.214751i	−0.302354	+	0.953196i	$0.597773\pi$
$654$	−11.0267	−	1.49398i	−0.431178	−	0.0584193i
$655$	32.1072	+	55.6113i	1.25453	+	2.17291i
$656$	−1.92560	+	3.33524i	−0.0751821	+	0.130219i
$657$	7.13821	−	1.85514i	0.278488	−	0.0723758i
$658$	−26.2423	−	11.3094i	−1.02303	−	0.440887i
$659$		−	16.0960i		−	0.627012i	−0.949586	−	0.313506i	$-0.898496\pi$
$659$		−	16.0960i		−	0.627012i	0.949586	−	0.313506i	$-0.101504\pi$
$660$	−2.52944	−	6.17229i	−0.0984584	−	0.240256i
$661$	37.8298	−	21.8411i	1.47141	−	0.849518i	0.471925	−	0.881639i	$-0.343559\pi$
$661$	37.8298	−	21.8411i	1.47141	−	0.849518i	0.999484	+	0.0321202i	$0.0102259\pi$
$662$	−10.4010	+	6.00504i	−0.404248	+	0.233393i
$663$	3.19379	+	7.79342i	0.124037	+	0.302672i
$664$		−	8.67372i		−	0.336606i
$665$	23.4994	+	10.1273i	0.911267	+	0.392721i
$666$	0.396666	−	0.103089i	0.0153705	−	0.00399461i
$667$	29.8732	−	51.7418i	1.15669	−	2.00345i
$668$	10.4912	+	18.1713i	0.405917	+	0.703069i
$669$	−26.7468	−	3.62387i	−1.03409	−	0.140107i
$670$	34.6309	+	19.9942i	1.33791	+	0.772442i
$671$	8.60797			0.332307
$672$	−2.36226	+	3.92679i	−0.0911263	+	0.151479i
$673$	−16.2251			−0.625430			−0.312715	−	0.949847i	$-0.601238\pi$
$673$	−16.2251			−0.625430			−0.312715	+	0.949847i	$0.601238\pi$
$674$	−18.1926	−	10.5035i	−0.700753	−	0.404580i
$675$	50.7224	−	6.09526i	1.95231	−	0.234607i
$676$	1.26693	+	2.19439i	0.0487282	+	0.0843997i
$677$	−15.9287	+	27.5893i	−0.612189	+	1.06034i	0.378681	+	0.925527i	$0.376378\pi$
$677$	−15.9287	+	27.5893i	−0.612189	+	1.06034i	−0.990871	+	0.134816i	$0.956956\pi$
$678$	−13.2872	−	10.2754i	−0.510292	−	0.394625i
$679$	−22.6527	+	16.8761i	−0.869332	+	0.647645i
$680$		−	5.78870i		−	0.221987i
$681$	−22.1279	+	9.06815i	−0.847943	+	0.347492i
$682$	−5.23845	+	3.02442i	−0.200590	+	0.115811i
$683$	36.9303	−	21.3217i	1.41310	−	0.815853i	0.417420	−	0.908714i	$-0.362934\pi$
$683$	36.9303	−	21.3217i	1.41310	−	0.815853i	0.995679	+	0.0928603i	$0.0296010\pi$
$684$	−2.00473	+	7.26237i	−0.0766526	+	0.277684i
$685$			50.4942i			1.92928i
$686$	−18.2421	−	3.19772i	−0.696487	−	0.122090i
$687$	23.1163	−	29.8919i	0.881942	−	1.14045i
$688$	−3.61103	+	6.25448i	−0.137669	+	0.238450i
$689$	16.7814	+	29.0662i	0.639319	+	1.10733i
$690$	−6.93750	+	51.2039i	−0.264106	+	1.94930i
$691$	−5.48927	−	3.16923i	−0.208822	−	0.120563i	0.391942	−	0.919990i	$-0.371803\pi$
$691$	−5.48927	−	3.16923i	−0.208822	−	0.120563i	−0.600764	+	0.799427i	$0.705137\pi$
$692$	1.01332			0.0385205
$693$	6.19049	+	4.96768i	0.235157	+	0.188707i
$694$	−27.5858			−1.04714
$695$	−52.9399	−	30.5649i	−2.00812	−	1.15939i
$696$	1.79360	−	13.2381i	0.0679863	−	0.501789i
$697$	2.89435	+	5.01316i	0.109631	+	0.189887i
$698$	4.75518	−	8.23621i	0.179986	−	0.311745i
$699$	−2.09230	+	2.70557i	−0.0791381	+	0.102334i
$700$	25.8355	−	3.02849i	0.976490	−	0.114466i
$701$		−	2.80501i		−	0.105944i	−0.998596	−	0.0529719i	$-0.983131\pi$
$701$		−	2.80501i		−	0.105944i	0.998596	−	0.0529719i	$-0.0168694\pi$
$702$	−10.0820	−	13.4513i	−0.380522	−	0.507687i
$703$	0.297119	−	0.171542i	0.0112061	−	0.00646982i
$704$	0.866025	−	0.500000i	0.0326396	−	0.0188445i
$705$	−66.6641	+	27.3193i	−2.51071	+	1.02891i
$706$		−	15.1893i		−	0.571657i
$707$	−9.07100	+	21.0483i	−0.341150	+	0.791602i
$708$	−4.60565	−	3.56169i	−0.173091	−	0.133857i
$709$	9.55911	−	16.5569i	0.359000	−	0.621806i	−0.628794	−	0.777572i	$-0.716451\pi$
$709$	9.55911	−	16.5569i	0.359000	−	0.621806i	0.987794	+	0.155766i	$0.0497845\pi$
$710$	1.65044	+	2.85865i	0.0619400	+	0.107283i
$711$	−9.05579	+	8.92032i	−0.339619	+	0.334538i
$712$	5.77637	+	3.33499i	0.216479	+	0.124984i
$713$	46.8562			1.75478
$714$	3.33622	+	6.02615i	0.124855	+	0.225523i
$715$	12.4592			0.465947
$716$	−15.5742	−	8.99179i	−0.582036	−	0.336039i
$717$	14.7939	+	2.00439i	0.552489	+	0.0748555i
$718$	6.36556	+	11.0255i	0.237561	+	0.411467i
$719$	−6.90047	+	11.9520i	−0.257344	+	0.445733i	−0.965530	−	0.260293i	$-0.916181\pi$
$719$	−6.90047	+	11.9520i	−0.257344	+	0.445733i	0.708185	+	0.706026i	$0.249514\pi$
$720$	2.90611	+	11.1821i	0.108304	+	0.416734i
$721$	1.04444	+	8.90993i	0.0388970	+	0.331823i
$722$		−	12.6932i		−	0.472393i
$723$	5.79186	+	14.1332i	0.215402	+	0.525618i
$724$	14.1070	−	8.14467i	0.524282	−	0.302694i
$725$	−65.6716	+	37.9155i	−2.43898	+	1.40815i
$726$	−0.656793	−	1.60269i	−0.0243759	−	0.0594815i
$727$		−	13.2195i		−	0.490283i	−0.969487	−	0.245141i	$-0.921166\pi$
$727$		−	13.2195i		−	0.490283i	0.969487	−	0.245141i	$-0.0788344\pi$
$728$	−5.11360	−	6.86397i	−0.189523	−	0.254396i
$729$	−18.6554	−	19.5186i	−0.690941	−	0.722911i
$730$	4.73399	−	8.19951i	0.175213	−	0.303477i
$731$	5.42770	+	9.40105i	0.200751	+	0.347710i
$732$	−14.7745	−	2.00176i	−0.546080	−	0.0739871i
$733$	−33.3165	−	19.2353i	−1.23057	−	0.710473i	−0.263425	−	0.964680i	$-0.584852\pi$
$733$	−33.3165	−	19.2353i	−1.23057	−	0.710473i	−0.967150	+	0.254207i	$0.918185\pi$
$734$	−11.8030			−0.435657
$735$	−37.9399	+	27.2182i	−1.39944	+	1.00396i
$736$	−7.74632			−0.285533
$737$	8.99224	+	5.19167i	0.331233	+	0.191238i
$738$	−8.10784	−	8.23097i	−0.298454	−	0.302986i
$739$	7.09488	+	12.2887i	0.260989	+	0.452047i	0.966505	−	0.256647i	$-0.0826179\pi$
$739$	7.09488	+	12.2887i	0.260989	+	0.452047i	−0.705516	+	0.708694i	$0.749285\pi$
$740$	0.263065	−	0.455641i	0.00967044	−	0.0167497i
$741$	−11.1318	−	8.60853i	−0.408935	−	0.316242i
$742$	16.3982	+	22.0113i	0.601999	+	0.808061i
$743$			11.7541i			0.431215i	0.976480	+	0.215608i	$0.0691732\pi$
$743$			11.7541i			0.431215i	−0.976480	+	0.215608i	$0.930827\pi$
$744$	9.69443	−	3.97283i	0.355415	−	0.145651i
$745$	−10.0267	+	5.78890i	−0.367349	+	0.212089i
$746$	26.7209	−	15.4273i	0.978321	−	0.564834i
$747$	25.0830	+	6.92399i	0.917740	+	0.253336i
$748$		−	1.50309i		−	0.0549584i
$749$	5.03388	+	42.9432i	0.183934	+	1.56911i
$750$	19.7167	−	25.4958i	0.719952	−	0.930975i
$751$	20.0871	−	34.7919i	0.732990	−	1.26958i	−0.222610	−	0.974908i	$-0.571458\pi$
$751$	20.0871	−	34.7919i	0.732990	−	1.26958i	0.955600	−	0.294668i	$-0.0952090\pi$
$752$	−5.40027	−	9.35353i	−0.196927	−	0.341088i
$753$	−2.41790	+	17.8459i	−0.0881132	+	0.650341i
$754$	21.6092	+	12.4761i	0.786962	+	0.454353i
$755$	−47.4906			−1.72836
$756$	−9.46995	−	9.96595i	−0.344419	−	0.362458i
$757$	−26.7691			−0.972938			−0.486469	−	0.873698i	$-0.661715\pi$
$757$	−26.7691			−0.972938			−0.486469	+	0.873698i	$0.661715\pi$
$758$	27.7616	+	16.0282i	1.00835	+	0.582169i
$759$	−1.80138	+	13.2955i	−0.0653861	+	0.482598i
$760$	4.83582	+	8.37589i	0.175414	+	0.303825i
$761$	2.58368	−	4.47507i	0.0936584	−	0.162221i	−0.815389	−	0.578913i	$-0.803477\pi$
$761$	2.58368	−	4.47507i	0.0936584	−	0.162221i	0.909048	+	0.416692i	$0.136811\pi$
$762$	−14.0452	+	18.1620i	−0.508805	+	0.657939i
$763$	6.72713	−	15.6096i	0.243538	−	0.565105i
$764$		−	7.34096i		−	0.265587i
$765$	16.7400	+	4.62097i	0.605237	+	0.167071i
$766$	19.0996	−	11.0271i	0.690095	−	0.398427i
$767$	9.41777	−	5.43735i	0.340056	−	0.196331i
$768$	−1.60269	+	0.656793i	−0.0578322	+	0.0237000i
$769$			23.8493i			0.860029i	0.902822	+	0.430014i	$0.141491\pi$
$769$			23.8493i			0.860029i	−0.902822	+	0.430014i	$0.858509\pi$
$770$	10.1200	−	1.18629i	0.364701	−	0.0427509i
$771$	−16.5301	−	12.7833i	−0.595318	−	0.460378i
$772$	−9.83302	+	17.0313i	−0.353898	+	0.612970i
$773$	11.2176	+	19.4294i	0.403467	+	0.698826i	0.994142	−	0.108084i	$-0.0344715\pi$
$773$	11.2176	+	19.4294i	0.403467	+	0.698826i	−0.590674	+	0.806910i	$0.701138\pi$
$774$	−15.2044	−	15.4353i	−0.546511	−	0.554811i
$775$	−51.5032	−	29.7354i	−1.85005	−	1.06813i
$776$	−10.6767			−0.383272
$777$	−0.0112546	+	0.625944i	−0.000403757	+	0.0224556i
$778$	−21.3825			−0.766601
$779$	−8.37589	−	4.83582i	−0.300097	−	0.173261i
$780$	−21.3846	−	2.89735i	−0.765690	−	0.103742i
$781$	0.428552	+	0.742275i	0.0153348	+	0.0265607i
$782$	−5.82171	+	10.0835i	−0.208184	+	0.360585i
$783$	36.8508	+	15.7544i	1.31694	+	0.563018i
$784$	−4.80709	−	5.08840i	−0.171682	−	0.181729i
$785$			18.5501i			0.662083i
$786$	−10.9513	−	26.7231i	−0.390619	−	0.953181i
$787$	34.4559	−	19.8931i	1.22822	−	0.709113i	0.261563	−	0.965186i	$-0.415762\pi$
$787$	34.4559	−	19.8931i	1.22822	−	0.709113i	0.966657	+	0.256073i	$0.0824288\pi$
$788$	−19.7838	+	11.4222i	−0.704769	+	0.406898i
$789$	15.5832	+	38.0257i	0.554775	+	1.35375i
$790$			16.3180i			0.580570i
$791$	20.5754	−	15.3285i	0.731578	−	0.545020i
$792$	0.754597	+	2.90355i	0.0268134	+	0.103173i
$793$	13.9240	−	24.1171i	0.494456	−	0.856423i
$794$	−8.04449	−	13.9335i	−0.285488	−	0.494480i
$795$	68.5758	+	9.29118i	2.43213	+	0.329524i
$796$	−1.58668	−	0.916069i	−0.0562383	−	0.0324692i
$797$	7.40572			0.262324			0.131162	−	0.991361i	$-0.458129\pi$
$797$	7.40572			0.262324			0.131162	+	0.991361i	$0.458129\pi$
$798$	−9.86148	−	5.93242i	−0.349092	−	0.210005i
$799$	−16.2342			−0.574324
$800$	8.51456	+	4.91588i	0.301035	+	0.173803i
$801$	−14.2554	+	14.0421i	−0.503689	+	0.496154i
$802$	−10.7141	−	18.5573i	−0.378327	−	0.655281i
$803$	1.22922	−	2.12908i	0.0433783	−	0.0751335i
$804$	−14.2267	−	11.0019i	−0.501736	−	0.388008i
$805$	−72.4851	−	31.2383i	−2.55476	−	1.10100i
$806$			19.5688i			0.689283i
$807$	−49.1372	+	20.1367i	−1.72971	+	0.708846i
$808$	−7.50224	+	4.33142i	−0.263928	+	0.152379i
$809$	−21.3465	+	12.3244i	−0.750502	+	0.433302i	−0.825875	−	0.563853i	$-0.809318\pi$
$809$	−21.3465	+	12.3244i	−0.750502	+	0.433302i	0.0753734	+	0.997155i	$0.475985\pi$
$810$	−34.6569	−	0.522396i	−1.21772	−	0.0183551i
$811$			18.3371i			0.643904i	0.946756	+	0.321952i	$0.104339\pi$
$811$			18.3371i			0.643904i	−0.946756	+	0.321952i	$0.895661\pi$
$812$	18.7401	+	8.07626i	0.657649	+	0.283421i
$813$	26.4502	−	34.2029i	0.927648	−	1.19955i
$814$	0.0683071	−	0.118311i	0.00239416	−	0.00414681i
$815$	27.9887	+	48.4778i	0.980400	+	1.69810i
$816$	−0.349539	+	2.57986i	−0.0122363	+	0.0903130i
$817$	−15.7071	−	9.06848i	−0.549521	−	0.317266i
$818$	12.4884			0.436648
$819$	23.9316	−	9.30841i	0.836237	−	0.325262i
$820$	−14.8318			−0.517948
$821$	−18.3595	−	10.5999i	−0.640753	−	0.369939i	0.144152	−	0.989556i	$-0.453955\pi$
$821$	−18.3595	−	10.5999i	−0.640753	−	0.369939i	−0.784904	+	0.619617i	$0.787288\pi$
$822$	3.04899	−	22.5038i	0.106346	−	0.784909i
$823$	8.64517	+	14.9739i	0.301352	+	0.521956i	0.976442	−	0.215778i	$-0.0692289\pi$
$823$	8.64517	+	14.9739i	0.301352	+	0.521956i	−0.675091	+	0.737735i	$0.735896\pi$
$824$	−1.69535	+	2.93643i	−0.0590602	+	0.102295i
$825$	10.4175	−	13.4709i	0.362691	−	0.468998i
$826$	7.13191	−	5.31322i	0.248151	−	0.184870i
$827$			20.7860i			0.722799i	0.932411	+	0.361400i	$0.117701\pi$
$827$			20.7860i			0.722799i	−0.932411	+	0.361400i	$0.882299\pi$
$828$	6.18368	−	22.4012i	0.214898	−	0.778494i
$829$	23.3169	−	13.4620i	0.809830	−	0.467555i	−0.0370670	−	0.999313i	$-0.511801\pi$
$829$	23.3169	−	13.4620i	0.809830	−	0.467555i	0.846897	+	0.531757i	$0.178468\pi$
$830$	28.9289	−	16.7021i	1.00414	−	0.579739i
$831$	−3.18309	+	1.30445i	−0.110420	+	0.0452508i
$832$		−	3.23514i		−	0.112158i
$833$	−10.2364	+	2.43330i	−0.354670	+	0.0843087i
$834$	21.7482	+	16.8185i	0.753077	+	0.582378i
$835$	−40.4038	+	69.9814i	−1.39823	+	2.42181i
$836$	1.25567	+	2.17488i	0.0434281	+	0.0752196i
$837$	3.75001	+	31.2062i	0.129619	+	1.07864i
$838$	−24.5799	−	14.1912i	−0.849100	−	0.490228i
$839$	−34.6403			−1.19592			−0.597958	−	0.801527i	$-0.704021\pi$
$839$	−34.6403			−1.19592			−0.597958	+	0.801527i	$0.704021\pi$
$840$	−17.6456	−	0.317272i	−0.608830	−	0.0109469i
$841$	−30.4882			−1.05132
$842$	−27.1266	−	15.6615i	−0.934843	−	0.539732i
$843$	−1.43723	−	0.194727i	−0.0495008	−	0.00670675i
$844$	−4.97881	−	8.62355i	−0.171378	−	0.296835i
$845$	−4.87921	+	8.45105i	−0.167850	+	0.290725i
$846$	31.3598	−	8.15005i	1.07817	−	0.280205i
$847$	2.62776	−	0.308031i	0.0902909	−	0.0105841i
$848$			10.3744i			0.356259i
$849$	5.40786	+	13.1961i	0.185597	+	0.452890i
$850$	12.7981	−	7.38901i	0.438973	−	0.253441i
$851$	−0.916478	+	0.529129i	−0.0314165	+	0.0181383i
$852$	−0.562940	−	1.37368i	−0.0192860	−	0.0470613i
$853$			37.2571i			1.27566i	0.770177	+	0.637830i	$0.220168\pi$
$853$			37.2571i			1.27566i	−0.770177	+	0.637830i	$0.779832\pi$
$854$	9.01355	−	20.9150i	0.308437	−	0.715696i
$855$	−28.0821	+	7.29819i	−0.960386	+	0.249593i
$856$	−8.17106	+	14.1527i	−0.279281	+	0.483729i
$857$	−8.21484	−	14.2285i	−0.280613	−	0.486037i	0.690923	−	0.722929i	$-0.257205\pi$
$857$	−8.21484	−	14.2285i	−0.280613	−	0.486037i	−0.971536	+	0.236892i	$0.923871\pi$
$858$	−5.55269	−	0.752322i	−0.189566	−	0.0256839i
$859$	−24.1277	−	13.9302i	−0.823228	−	0.475291i	0.0283003	−	0.999599i	$-0.490991\pi$
$859$	−24.1277	−	13.9302i	−0.823228	−	0.475291i	−0.851528	+	0.524309i	$0.824324\pi$
$860$	−27.8136			−0.948436
$861$	15.4402	−	8.54802i	0.526199	−	0.291316i
$862$	−19.4337			−0.661915
$863$	−6.04913	−	3.49247i	−0.205915	−	0.118885i	0.393497	−	0.919326i	$-0.371265\pi$
$863$	−6.04913	−	3.49247i	−0.205915	−	0.118885i	−0.599411	+	0.800441i	$0.704599\pi$
$864$	−0.619956	−	5.15904i	−0.0210913	−	0.175514i
$865$	1.95124	+	3.37965i	0.0663443	+	0.114912i
$866$	1.45429	−	2.51891i	0.0494189	−	0.0855960i
$867$	−20.1969	−	15.6189i	−0.685924	−	0.530446i
$868$	1.86323	+	15.8949i	0.0632421	+	0.539508i
$869$			4.23713i			0.143735i
$870$	47.6060	−	19.5092i	1.61400	−	0.661425i
$871$	29.0911	−	16.7958i	0.985716	−	0.569103i
$872$	5.56372	−	3.21222i	0.188411	−	0.108779i
$873$	8.52295	−	30.8754i	0.288458	−	1.04498i
$874$		−	19.4536i		−	0.658027i
$875$	29.4127	+	39.4806i	0.994332	+	1.33469i
$876$	−2.60491	+	3.36843i	−0.0880118	+	0.113809i
$877$	−7.56690	+	13.1062i	−0.255516	+	0.442567i	−0.965036	−	0.262119i	$-0.915579\pi$
$877$	−7.56690	+	13.1062i	−0.255516	+	0.442567i	0.709520	+	0.704686i	$0.248912\pi$
$878$	8.22341	+	14.2434i	0.277527	+	0.480690i
$879$	−0.408877	+	3.01781i	−0.0137911	+	0.101788i
$880$	3.33524	+	1.92560i	0.112431	+	0.0649120i
$881$	−48.5223			−1.63476			−0.817379	−	0.576100i	$-0.804574\pi$
$881$	−48.5223			−1.63476			−0.817379	+	0.576100i	$0.804574\pi$
$882$	18.5522	−	9.83943i	0.624686	−	0.331311i
$883$	49.2390			1.65702			0.828512	−	0.559972i	$-0.189188\pi$
$883$	49.2390			1.65702			0.828512	+	0.559972i	$0.189188\pi$
$884$	−4.21123	−	2.43135i	−0.141639	−	0.0817753i
$885$	3.01045	−	22.2193i	0.101195	−	0.746895i
$886$	7.18373	+	12.4426i	0.241342	+	0.418017i
$887$	3.50486	−	6.07060i	0.117682	−	0.203831i	−0.801167	−	0.598441i	$-0.795787\pi$
$887$	3.50486	−	6.07060i	0.117682	−	0.203831i	0.918849	+	0.394610i	$0.129120\pi$
$888$	−0.144753	+	0.187181i	−0.00485760	+	0.00628139i
$889$	−20.9522	−	28.1241i	−0.702715	−	0.943252i
$890$			25.6874i			0.861045i
$891$	−8.99898	−	0.135645i	−0.301477	−	0.00454428i
$892$	13.4956	−	7.79169i	0.451866	−	0.260885i
$893$	23.4898	−	13.5619i	0.786057	−	0.453830i
$894$	4.81814	−	1.97450i	0.161143	−	0.0660373i
$895$		−	69.2584i		−	2.31505i
$896$	−0.308031	−	2.62776i	−0.0102906	−	0.0877873i
$897$	34.3365	+	26.5534i	1.14646	+	0.886594i
$898$	0.429809	−	0.744450i	0.0143429	−	0.0248426i
$899$	−23.3269	−	40.4034i	−0.777996	−	1.34753i
$900$	−21.0129	+	20.6986i	−0.700430	+	0.689952i
$901$	13.5045	+	7.79684i	0.449901	+	0.259751i
$902$	−3.85120			−0.128231
$903$	28.9545	−	16.0299i	0.963545	−	0.533441i
$904$	9.69766			0.322539
$905$	54.3289	+	31.3668i	1.80595	+	1.04267i
$906$	21.1652	+	2.86762i	0.703166	+	0.0952703i
$907$	0.134375	+	0.232745i	0.00446186	+	0.00772818i	0.868248	−	0.496131i	$-0.165246\pi$
$907$	0.134375	+	0.232745i	0.00446186	+	0.00772818i	−0.863786	+	0.503859i	$0.831913\pi$
$908$	6.90336	−	11.9570i	0.229096	−	0.396806i
$909$	−6.53696	−	25.1530i	−0.216817	−	0.834271i
$910$	13.0462	−	30.2723i	0.432478	−	1.00352i
$911$		−	0.980362i		−	0.0324808i	−0.999868	−	0.0162404i	$-0.994830\pi$
$911$		−	0.980362i		−	0.0324808i	0.999868	−	0.0162404i	$-0.00516971\pi$
$912$	−1.64942	−	4.02489i	−0.0546179	−	0.133277i
$913$	7.51166	−	4.33686i	0.248600	−	0.143529i
$914$	22.3698	−	12.9152i	0.739927	−	0.427197i
$915$	−21.7734	−	53.1309i	−0.719806	−	1.75645i
$916$			21.8166i			0.720839i
$917$	43.8149	−	5.13607i	1.44690	−	0.169608i
$918$	−7.18151	−	3.07024i	−0.237025	−	0.101333i
$919$	−30.0336	+	52.0197i	−0.990717	+	1.71597i	−0.377633	+	0.925955i	$0.623262\pi$
$919$	−30.0336	+	52.0197i	−0.990717	+	1.71597i	−0.613084	+	0.790018i	$0.710071\pi$
$920$	−14.9163	−	25.8358i	−0.491777	−	0.851783i
$921$	−18.8768	−	2.55757i	−0.622011	−	0.0842749i
$922$	−8.43726	−	4.87125i	−0.277866	−	0.160426i
$923$	2.77285			0.0912696
$924$	−4.58184	−	0.0823825i	−0.150731	−	0.00271019i
$925$	1.34316			0.0441628
$926$	16.6336	+	9.60343i	0.546615	+	0.315588i
$927$	−7.13834	−	7.24675i	−0.234454	−	0.238015i
$928$	3.85643	+	6.67953i	0.126594	+	0.219266i
$929$	15.9871	−	27.6904i	0.524519	−	0.908493i	−0.475074	−	0.879946i	$-0.657579\pi$
$929$	15.9871	−	27.6904i	0.524519	−	0.908493i	0.999592	−	0.0285469i	$-0.00908801\pi$
$930$	31.9179	+	24.6831i	1.04663	+	0.809392i
$931$	12.7787	−	12.0722i	0.418804	−	0.395650i
$932$		−	1.97466i		−	0.0646821i
$933$	−12.8882	+	5.28167i	−0.421941	+	0.172914i
$934$	−10.4096	+	6.00996i	−0.340611	+	0.196652i
$935$	5.01316	−	2.89435i	0.163948	−	0.0946554i
$936$	9.35552	+	2.58253i	0.305795	+	0.0844125i
$937$		−	31.3040i		−	1.02266i	−0.859385	−	0.511328i	$-0.829154\pi$
$937$		−	31.3040i		−	1.02266i	0.859385	−	0.511328i	$-0.170846\pi$
$938$	22.0302	−	16.4123i	0.719313	−	0.535882i
$939$	−13.5361	+	17.5036i	−0.441734	+	0.571209i
$940$	20.7975	−	36.0224i	0.678340	−	1.17492i
$941$	−17.7912	−	30.8152i	−0.579976	−	1.00455i	−0.995481	−	0.0949568i	$-0.969729\pi$
$941$	−17.7912	−	30.8152i	−0.579976	−	1.00455i	0.415506	−	0.909591i	$-0.363605\pi$
$942$	1.12011	−	8.26726i	0.0364952	−	0.269362i
$943$	25.8358	+	14.9163i	0.841331	+	0.485743i
$944$	3.36143			0.109405
$945$	15.0035	−	50.7750i	0.488063	−	1.65171i
$946$	−7.22205			−0.234809
$947$	5.15342	+	2.97533i	0.167464	+	0.0966852i	0.581389	−	0.813625i	$-0.302509\pi$
$947$	5.15342	+	2.97533i	0.167464	+	0.0966852i	−0.413926	+	0.910311i	$0.635843\pi$
$948$	0.985332	−	7.27248i	0.0320021	−	0.236199i
$949$	−3.97671	−	6.88786i	−0.129089	−	0.223590i
$950$	−12.3454	+	21.3829i	−0.400538	+	0.693752i
$951$	8.72050	−	11.2765i	0.282782	−	0.365667i
$952$	−3.65209	−	1.57391i	−0.118365	−	0.0510107i
$953$		−	36.5553i		−	1.18414i	−0.805886	−	0.592070i	$-0.798311\pi$
$953$		−	36.5553i		−	1.18414i	0.805886	−	0.592070i	$-0.201689\pi$
$954$	−30.0012	−	8.28162i	−0.971325	−	0.268127i
$955$	24.4839	−	14.1358i	0.792279	−	0.457422i
$956$	−7.46454	+	4.30965i	−0.241420	+	0.139384i
$957$	12.3613	−	5.06575i	0.399585	−	0.163752i
$958$			10.4535i			0.337736i
$959$	31.8567	+	13.7290i	1.02871	+	0.443334i
$960$	−5.27671	−	4.08064i	−0.170305	−	0.131702i
$961$	2.79422	−	4.83973i	0.0901360	−	0.156120i
$962$	−0.220983	−	0.382754i	−0.00712478	−	0.0123405i
$963$	−34.4046	−	34.9271i	−1.10867	−	1.12551i
$964$	−7.63695	−	4.40920i	−0.245970	−	0.142011i
$965$	−75.7379			−2.43809
$966$	30.4182	+	18.2989i	0.978690	+	0.588756i
$967$	−9.77344			−0.314293			−0.157146	−	0.987575i	$-0.550229\pi$
$967$	−9.77344			−0.314293			−0.157146	+	0.987575i	$0.550229\pi$
$968$	0.866025	+	0.500000i	0.0278351	+	0.0160706i
$969$	−6.47887	−	0.877808i	−0.208131	−	0.0281993i
$970$	−20.5591	−	35.6095i	−0.660114	−	1.14335i
$971$	−12.1392	+	21.0257i	−0.389566	+	0.674748i	−0.992391	−	0.123125i	$-0.960708\pi$
$971$	−12.1392	+	21.0257i	−0.389566	+	0.674748i	0.602825	+	0.797873i	$0.294042\pi$
$972$	15.4140	+	2.32550i	0.494405	+	0.0745905i
$973$	−33.6774	+	25.0894i	−1.07965	+	0.804328i
$974$		−	15.8825i		−	0.508907i
$975$	−20.8907	−	50.9771i	−0.669038	−	1.63257i
$976$	7.45472	−	4.30399i	0.238620	−	0.137767i
$977$	25.7446	−	14.8637i	0.823643	−	0.475530i	−0.0280284	−	0.999607i	$-0.508923\pi$
$977$	25.7446	−	14.8637i	0.823643	−	0.475530i	0.851671	+	0.524077i	$0.175590\pi$
$978$	−9.54650	−	23.2952i	−0.305263	−	0.744898i
$979$			6.66998i			0.213173i
$980$	7.71450	−	25.8310i	0.246431	−	0.825142i
$981$	4.84786	+	18.6536i	0.154780	+	0.595565i
$982$	−8.25302	+	14.2947i	−0.263364	+	0.456161i
$983$	−11.3936	−	19.7344i	−0.363401	−	0.629428i	0.625118	−	0.780531i	$-0.285051\pi$
$983$	−11.3936	−	19.7344i	−0.363401	−	0.629428i	−0.988518	+	0.151102i	$0.951718\pi$
$984$	6.61008	+	0.895586i	0.210722	+	0.0285502i
$985$	−76.1914	−	43.9891i	−2.42766	−	1.40161i
$986$	11.5931			0.369200
$987$	−0.889775	+	49.4863i	−0.0283219	+	1.57516i
$988$	8.12451			0.258475
$989$	48.4492	+	27.9722i	1.54060	+	0.889464i
$990$	−8.23097	+	8.10784i	−0.261597	+	0.257684i
$991$	5.56585	+	9.64033i	0.176805	+	0.306235i	0.940784	−	0.339005i	$-0.110091\pi$
$991$	5.56585	+	9.64033i	0.176805	+	0.306235i	−0.763980	+	0.645240i	$0.776757\pi$
$992$	−3.02442	+	5.23845i	−0.0960254	+	0.166321i
$993$	16.4556	+	12.7256i	0.522202	+	0.403835i
$994$	2.25226	−	0.264015i	0.0714375	−	0.00837405i
$995$		−	7.05593i		−	0.223688i
$996$	−13.9013	+	5.69684i	−0.440480	+	0.180511i
$997$	33.2978	−	19.2245i	1.05455	−	0.608846i	0.130632	−	0.991431i	$-0.458299\pi$
$997$	33.2978	−	19.2245i	1.05455	−	0.608846i	0.923920	+	0.382585i	$0.124966\pi$
$998$	−29.2301	+	16.8760i	−0.925262	+	0.534200i
$999$	−0.425747	−	0.568025i	−0.0134700	−	0.0179715i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.k.g.89.9	yes	20
3.2	odd	2	inner	462.2.k.g.89.5	✓	20
7.3	odd	6	inner	462.2.k.g.353.5	yes	20
21.17	even	6	inner	462.2.k.g.353.9	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.k.g.89.5	✓	20	3.2	odd	2	inner
462.2.k.g.89.9	yes	20	1.1	even	1	trivial
462.2.k.g.353.5	yes	20	7.3	odd	6	inner
462.2.k.g.353.9	yes	20	21.17	even	6	inner

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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.232547 - 1.71637i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.92560 + 3.33524i) q^{5} +(1.05958 - 1.37015i) q^{6} +(1.58064 + 2.12169i) q^{7} +1.00000i q^{8} +(-2.89184 - 0.798273i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.232547 - 1.71637i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.92560 + 3.33524i) q^{5} +(1.05958 - 1.37015i) q^{6} +(1.58064 + 2.12169i) q^{7} +1.00000i q^{8} +(-2.89184 - 0.798273i) q^{9} +(-3.33524 + 1.92560i) q^{10} +(-0.866025 + 0.500000i) q^{11} +(1.60269 - 0.656793i) q^{12} +3.23514i q^{13} +(0.308031 + 2.62776i) q^{14} +(5.27671 + 4.08064i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.751545 + 1.30171i) q^{17} +(-2.10527 - 2.13725i) q^{18} +(-2.17488 - 1.25567i) q^{19} -3.85120 q^{20} +(4.00918 - 2.21957i) q^{21} -1.00000 q^{22} +(6.70851 + 3.87316i) q^{23} +(1.71637 + 0.232547i) q^{24} +(-4.91588 - 8.51456i) q^{25} +(-1.61757 + 2.80171i) q^{26} +(-2.04262 + 4.77783i) q^{27} +(-1.04712 + 2.42972i) q^{28} -7.71286i q^{29} +(2.52944 + 6.17229i) q^{30} +(5.23845 - 3.02442i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.656793 + 1.60269i) q^{33} +1.50309i q^{34} +(-10.1200 + 1.18629i) q^{35} +(-0.754597 - 2.90355i) q^{36} +(-0.0683071 + 0.118311i) q^{37} +(-1.25567 - 2.17488i) q^{38} +(5.55269 + 0.752322i) q^{39} +(-3.33524 - 1.92560i) q^{40} +3.85120 q^{41} +(4.58184 + 0.0823825i) q^{42} +7.22205 q^{43} +(-0.866025 - 0.500000i) q^{44} +(8.23097 - 8.10784i) q^{45} +(3.87316 + 6.70851i) q^{46} +(-5.40027 + 9.35353i) q^{47} +(1.37015 + 1.05958i) q^{48} +(-2.00314 + 6.70727i) q^{49} -9.83176i q^{50} +(2.40899 - 0.987219i) q^{51} +(-2.80171 + 1.61757i) q^{52} +(8.98451 - 5.18721i) q^{53} +(-4.15788 + 3.11642i) q^{54} -3.85120i q^{55} +(-2.12169 + 1.58064i) q^{56} +(-2.66095 + 3.44089i) q^{57} +(3.85643 - 6.67953i) q^{58} +(-1.68071 - 2.91108i) q^{59} +(-0.895586 + 6.61008i) q^{60} +(-7.45472 - 4.30399i) q^{61} +6.04884 q^{62} +(-2.87728 - 7.39738i) q^{63} -1.00000 q^{64} +(-10.7900 - 6.22959i) q^{65} +(-0.232547 + 1.71637i) q^{66} +(-5.19167 - 8.99224i) q^{67} +(-0.751545 + 1.30171i) q^{68} +(8.20782 - 10.6136i) q^{69} +(-9.35735 - 4.03266i) q^{70} -0.857105i q^{71} +(0.798273 - 2.89184i) q^{72} +(-2.12908 + 1.22922i) q^{73} +(-0.118311 + 0.0683071i) q^{74} +(-15.7573 + 6.45743i) q^{75} -2.51133i q^{76} +(-2.42972 - 1.04712i) q^{77} +(4.43261 + 3.42788i) q^{78} +(2.11856 - 3.66946i) q^{79} +(-1.92560 - 3.33524i) q^{80} +(7.72552 + 4.61696i) q^{81} +(3.33524 + 1.92560i) q^{82} -8.67372 q^{83} +(3.92679 + 2.36226i) q^{84} -5.78870 q^{85} +(6.25448 + 3.61103i) q^{86} +(-13.2381 - 1.79360i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(3.33499 - 5.77637i) q^{89} +(11.1821 - 2.90611i) q^{90} +(-6.86397 + 5.11360i) q^{91} +7.74632i q^{92} +(-3.97283 - 9.69443i) q^{93} +(-9.35353 + 5.40027i) q^{94} +(8.37589 - 4.83582i) q^{95} +(0.656793 + 1.60269i) q^{96} +10.6767i q^{97} +(-5.08840 + 4.80709i) q^{98} +(2.90355 - 0.754597i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{3} + 10 q^{4} - 6 q^{7} - 2 q^{9}+O(q^{10}) \) 20 * q - 6 * q^3 + 10 * q^4 - 6 * q^7 - 2 * q^9	\( 20 q - 6 q^{3} + 10 q^{4} - 6 q^{7} - 2 q^{9} - 18 q^{10} - 6 q^{12} - 8 q^{15} - 10 q^{16} + 4 q^{18} + 36 q^{19} + 24 q^{21} - 20 q^{22} - 12 q^{25} - 22 q^{30} + 36 q^{31} - 4 q^{36} + 16 q^{37} + 4 q^{39} - 18 q^{40} + 32 q^{42} + 32 q^{43} + 24 q^{45} + 30 q^{46} - 42 q^{49} - 24 q^{52} - 36 q^{54} - 24 q^{57} + 32 q^{58} - 4 q^{60} + 42 q^{61} - 10 q^{63} - 20 q^{64} + 6 q^{66} - 10 q^{67} - 36 q^{70} - 4 q^{72} + 12 q^{73} - 108 q^{75} + 6 q^{79} + 42 q^{81} + 18 q^{82} + 18 q^{84} - 28 q^{85} + 36 q^{87} - 10 q^{88} - 112 q^{91} - 36 q^{93} + 42 q^{94} - 8 q^{99}+O(q^{100}) \) 20 * q - 6 * q^3 + 10 * q^4 - 6 * q^7 - 2 * q^9 - 18 * q^10 - 6 * q^12 - 8 * q^15 - 10 * q^16 + 4 * q^18 + 36 * q^19 + 24 * q^21 - 20 * q^22 - 12 * q^25 - 22 * q^30 + 36 * q^31 - 4 * q^36 + 16 * q^37 + 4 * q^39 - 18 * q^40 + 32 * q^42 + 32 * q^43 + 24 * q^45 + 30 * q^46 - 42 * q^49 - 24 * q^52 - 36 * q^54 - 24 * q^57 + 32 * q^58 - 4 * q^60 + 42 * q^61 - 10 * q^63 - 20 * q^64 + 6 * q^66 - 10 * q^67 - 36 * q^70 - 4 * q^72 + 12 * q^73 - 108 * q^75 + 6 * q^79 + 42 * q^81 + 18 * q^82 + 18 * q^84 - 28 * q^85 + 36 * q^87 - 10 * q^88 - 112 * q^91 - 36 * q^93 + 42 * q^94 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more