LMFDB - Embedded newform 462.2.k.g.353.9

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			353.9
Root			$-1.60269 - 0.656793i$ of defining polynomial
Character	$\chi$	$=$	462.353
Dual form			462.2.k.g.89.9

$q$-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 $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

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

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	−0.870815	−	0.491611i	$-0.836408\pi$
$5$	−1.92560	−	3.33524i	−0.861155	−	1.49156i	0.00965972	−	0.999953i	$-0.496925\pi$
$6$	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	$-0.851911\pi$
$13$		−	3.23514i		−	0.897267i	0.893716	−	0.448633i	$-0.148089\pi$
$14$	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	−0.760379	−	0.649480i	$-0.774987\pi$
$17$	0.751545	−	1.30171i	0.182276	−	0.315712i	0.942655	+	0.333768i	$0.108320\pi$
$18$	−2.10527	+	2.13725i	−0.496218	+	0.503754i
$19$	−2.17488	+	1.25567i	−0.498951	+	0.288069i	−0.728280	−	0.685280i	$-0.759680\pi$
$19$	−2.17488	+	1.25567i	−0.498951	+	0.288069i	0.229329	+	0.973349i	$0.426347\pi$
$20$	−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	0.404552	−	0.914515i	$-0.367427\pi$
$23$	6.70851	−	3.87316i	1.39882	−	0.807610i	0.994269	+	0.106905i	$0.0340940\pi$
$24$	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	$0.254084\pi$
$29$			7.71286i			1.43224i	−0.697976	+	0.716121i	$0.745916\pi$
$30$	2.52944	−	6.17229i	0.461811	−	1.12690i
$31$	5.23845	+	3.02442i	0.940853	+	0.543202i	0.890228	−	0.455516i	$-0.150545\pi$
$31$	5.23845	+	3.02442i	0.940853	+	0.543202i	0.0506253	+	0.998718i	$0.483879\pi$
$32$	−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	0.860356	−	0.509694i	$-0.170241\pi$
$37$	−0.0683071	−	0.118311i	−0.0112296	−	0.0194503i	−0.871586	+	0.490243i	$0.836908\pi$
$38$	−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	−0.927367	−	0.374153i	$-0.877933\pi$
$47$	−5.40027	−	9.35353i	−0.787710	−	1.36435i	0.139657	−	0.990200i	$-0.455400\pi$
$48$	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	0.967886	−	0.251391i	$-0.0808879\pi$
$53$	8.98451	+	5.18721i	1.23412	+	0.712518i	0.266232	+	0.963909i	$0.414221\pi$
$54$	−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	−0.954445	−	0.298388i	$-0.903551\pi$
$59$	−1.68071	+	2.91108i	−0.218810	+	0.378991i	0.735634	+	0.677379i	$0.236884\pi$
$60$	−0.895586	−	6.61008i	−0.115620	−	0.853358i
$61$	−7.45472	+	4.30399i	−0.954480	+	0.551069i	−0.894470	−	0.447129i	$-0.852447\pi$
$61$	−7.45472	+	4.30399i	−0.954480	+	0.551069i	−0.0600100	+	0.998198i	$0.519113\pi$
$62$	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	0.352407	+	0.935847i	$0.385363\pi$
$67$	−5.19167	+	8.99224i	−0.634263	+	1.09858i	−0.986671	+	0.162730i	$0.947970\pi$
$68$	−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	$0.0161962\pi$
$71$			0.857105i			0.101720i	−0.998706	+	0.0508598i	$0.983804\pi$
$72$	0.798273	+	2.89184i	0.0940774	+	0.340807i
$73$	−2.12908	−	1.22922i	−0.249190	−	0.143870i	0.370204	−	0.928951i	$-0.379288\pi$
$73$	−2.12908	−	1.22922i	−0.249190	−	0.143870i	−0.619393	+	0.785081i	$0.712621\pi$
$74$	−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	0.960243	−	0.279165i	$-0.0900578\pi$
$79$	2.11856	+	3.66946i	0.238357	+	0.412847i	−0.721886	+	0.692012i	$0.756724\pi$
$80$	−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	0.986861	−	0.161569i	$-0.0516554\pi$
$89$	3.33499	+	5.77637i	0.353508	+	0.612294i	−0.633353	+	0.773863i	$0.718322\pi$
$90$	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	$-0.817656\pi$
$97$		−	10.6767i		−	1.08406i	0.840360	−	0.542029i	$-0.182344\pi$
$98$	−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	−0.565967	−	0.824428i	$-0.691497\pi$
$101$	4.33142	−	7.50224i	0.430992	−	0.746501i	0.996959	+	0.0779275i	$0.0248303\pi$
$102$	2.57986	−	0.349539i	0.255444	−	0.0346095i
$103$	2.93643	−	1.69535i	0.289335	−	0.167048i	−0.348307	−	0.937381i	$-0.613243\pi$
$103$	2.93643	−	1.69535i	0.289335	−	0.167048i	0.637642	+	0.770333i	$0.279910\pi$
$104$	−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	0.377495	−	0.926012i	$-0.376785\pi$
$107$	14.1527	−	8.17106i	1.36819	−	0.789926i	0.990697	+	0.136085i	$0.0434521\pi$
$108$	−5.15904	−	0.619956i	−0.496428	−	0.0596553i
$109$	−3.21222	+	5.56372i	−0.307675	+	0.532908i	−0.977853	−	0.209292i	$-0.932884\pi$
$109$	−3.21222	+	5.56372i	−0.307675	+	0.532908i	0.670179	+	0.742200i	$0.266217\pi$
$110$	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	$0.150768\pi$
$113$			9.69766i			0.912279i	−0.889908	+	0.456140i	$0.849232\pi$
$114$	−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	0.957559	+	0.288238i	$0.0930696\pi$
$131$	8.33693	+	14.4400i	0.728401	+	1.26163i	−0.229158	+	0.973389i	$0.573597\pi$
$132$	−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	0.899266	−	0.437402i	$-0.144101\pi$
$137$	11.3547	+	6.55564i	0.970097	+	0.560086i	0.0708312	+	0.997488i	$0.477435\pi$
$138$	12.4150	+	5.08773i	1.05683	+	0.433096i
$139$		−	15.8729i		−	1.34632i	−0.739497	−	0.673160i	$-0.764936\pi$
$139$		−	15.8729i		−	1.34632i	0.739497	−	0.673160i	$-0.235064\pi$
$140$	−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	−0.389550	−	0.921005i	$-0.627370\pi$
$149$	2.60352	−	1.50314i	0.213288	−	0.123142i	0.602839	+	0.797863i	$0.294036\pi$
$150$	−16.8749	+	2.28635i	−1.37783	+	0.186679i
$151$	6.16568	−	10.6793i	0.501756	−	0.869067i	−0.498242	−	0.867038i	$-0.666021\pi$
$151$	6.16568	−	10.6793i	0.501756	−	0.869067i	0.999998	−	0.00202885i	$-0.000645802\pi$
$152$	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	0.657134	−	0.753774i	$-0.271769\pi$
$157$	4.17140	+	2.40836i	0.332914	+	0.192208i	−0.324220	+	0.945982i	$0.605102\pi$
$158$	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	0.996642	+	0.0818853i	$0.0260941\pi$
$163$	7.26751	+	12.5877i	0.569236	+	0.985945i	−0.427406	+	0.904060i	$0.640573\pi$
$164$	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	0.884643	−	0.466269i	$-0.154402\pi$
$173$	0.506658	+	0.877558i	0.0385205	+	0.0667195i	−0.846122	+	0.532989i	$0.821069\pi$
$174$	−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	−0.211796	−	0.977314i	$-0.567931\pi$
$179$	−15.5742	−	8.99179i	−1.16407	−	0.672078i	−0.952277	+	0.305236i	$0.901265\pi$
$180$	11.1371	−	3.07431i	0.830109	−	0.229146i
$181$			16.2893i			1.21078i	0.795930	+	0.605389i	$0.206982\pi$
$181$			16.2893i			1.21078i	−0.795930	+	0.605389i	$0.793018\pi$
$182$	−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	−0.712048	−	0.702131i	$-0.752232\pi$
$191$	−6.35746	+	3.67048i	−0.460009	+	0.265587i	0.252039	+	0.967717i	$0.418899\pi$
$192$	−0.232547	−	1.71637i	−0.0167826	−	0.123868i
$193$	9.83302	−	17.0313i	0.707796	−	1.22594i	−0.257877	−	0.966178i	$-0.583023\pi$
$193$	9.83302	−	17.0313i	0.707796	−	1.22594i	0.965673	−	0.259761i	$-0.0836438\pi$
$194$	−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	$-0.697397\pi$
$197$		−	22.8444i		−	1.62759i	0.581150	−	0.813797i	$-0.302603\pi$
$198$	2.89184	−	0.798273i	0.205514	−	0.0567308i
$199$	−1.58668	−	0.916069i	−0.112477	−	0.0649384i	0.442706	−	0.896667i	$-0.354018\pi$
$199$	−1.58668	−	0.916069i	−0.112477	−	0.0649384i	−0.555183	+	0.831728i	$0.687352\pi$
$200$	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	$0.174728\pi$
$223$			15.5834i			1.04354i	−0.853086	+	0.521770i	$0.825272\pi$
$224$	−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	−0.998865	−	0.0476209i	$-0.984836\pi$
$227$	−6.90336	+	11.9570i	−0.458192	+	0.793612i	0.540674	+	0.841232i	$0.318169\pi$
$228$	−4.31037	+	0.584002i	−0.285461	+	0.0386765i
$229$	18.8937	−	10.9083i	1.24853	−	0.720839i	0.277714	−	0.960664i	$-0.410423\pi$
$229$	18.8937	−	10.9083i	1.24853	−	0.720839i	0.970816	+	0.239824i	$0.0770898\pi$
$230$	−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	−0.554969	−	0.831871i	$-0.687270\pi$
$233$	−1.71010	+	0.987329i	−0.112033	+	0.0646821i	0.442937	+	0.896553i	$0.353937\pi$
$234$	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	$-0.910074\pi$
$239$		−	8.61931i		−	0.557536i	0.960358	−	0.278768i	$-0.0899261\pi$
$240$	−6.17229	−	2.52944i	−0.398420	−	0.163275i
$241$	−7.63695	−	4.40920i	−0.491939	−	0.284021i	0.233439	−	0.972371i	$-0.425002\pi$
$241$	−7.63695	−	4.40920i	−0.491939	−	0.284021i	−0.725379	+	0.688350i	$0.758335\pi$
$242$	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	0.990518	−	0.137383i	$-0.0438692\pi$
$257$	6.03225	+	10.4482i	0.376282	+	0.651739i	−0.614236	+	0.789122i	$0.710536\pi$
$258$	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	−0.292588	−	0.956239i	$-0.594517\pi$
$263$	−20.5474	−	11.8631i	−1.26701	−	0.731508i	−0.974421	+	0.224730i	$0.927850\pi$
$264$	−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	−0.159422	+	0.987210i	$0.550963\pi$
$269$	−15.3296	+	26.5516i	−0.934661	+	1.61888i	−0.775238	+	0.631669i	$0.782370\pi$
$270$	−2.38758	+	19.8685i	−0.145303	+	1.20916i
$271$	21.6186	−	12.4815i	1.31323	−	0.758196i	0.330604	−	0.943770i	$-0.392748\pi$
$271$	21.6186	−	12.4815i	1.31323	−	0.758196i	0.982630	+	0.185573i	$0.0594142\pi$
$272$	−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	−0.894316	−	0.447437i	$-0.852337\pi$
$277$	−0.993044	+	1.72000i	−0.0596662	+	0.103345i	0.834649	+	0.550782i	$0.185670\pi$
$278$	−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	$0.00795110\pi$
$281$			0.837366i			0.0499531i	−0.999688	+	0.0249765i	$0.992049\pi$
$282$	7.09371	−	17.3099i	0.422424	−	1.03079i
$283$	−7.13062	−	4.11687i	−0.423871	−	0.244722i	0.272861	−	0.962054i	$-0.412030\pi$
$283$	−7.13062	−	4.11687i	−0.423871	−	0.244722i	−0.696732	+	0.717331i	$0.745363\pi$
$284$	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	$0.101618\pi$
$307$			10.9981i			0.627694i	−0.949474	+	0.313847i	$0.898382\pi$
$308$	−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	−0.957215	−	0.289378i	$-0.906552\pi$
$311$	−4.02080	+	6.96424i	−0.227999	+	0.394906i	0.729216	+	0.684283i	$0.239885\pi$
$312$	−0.752322	−	5.55269i	−0.0425919	−	0.314359i
$313$	−11.0635	+	6.38750i	−0.625345	+	0.361043i	−0.778947	−	0.627090i	$-0.784246\pi$
$313$	−11.0635	+	6.38750i	−0.625345	+	0.361043i	0.153602	+	0.988133i	$0.450913\pi$
$314$	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	−0.286301	−	0.958140i	$-0.592426\pi$
$317$	7.12754	−	4.11509i	0.400323	−	0.231126i	0.686623	+	0.727013i	$0.259092\pi$
$318$	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	0.652458	−	0.757825i	$-0.273738\pi$
$331$	−6.00504	−	10.4010i	−0.330067	−	0.571693i	−0.982525	+	0.186132i	$0.940405\pi$
$332$	−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	−0.305179	−	0.952295i	$-0.598716\pi$
$347$	−23.8900	−	13.7929i	−1.28248	−	0.740440i	−0.977301	+	0.211854i	$0.932050\pi$
$348$	−5.06575	+	12.3613i	−0.271553	+	0.662638i
$349$			9.51035i			0.509078i	0.967063	+	0.254539i	$0.0819237\pi$
$349$			9.51035i			0.509078i	−0.967063	+	0.254539i	$0.918076\pi$
$350$	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	−0.994231	−	0.107263i	$-0.965791\pi$
$353$	−7.59466	+	13.1543i	−0.404223	+	0.700134i	0.590008	+	0.807398i	$0.299125\pi$
$354$	−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	−0.179987	−	0.983669i	$-0.557605\pi$
$359$	11.0255	−	6.36556i	0.581902	−	0.335962i	0.761889	+	0.647708i	$0.224272\pi$
$360$	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	0.208900	−	0.977937i	$-0.433012\pi$
$367$	−10.2217	−	5.90150i	−0.533568	−	0.308056i	−0.742468	+	0.669881i	$0.766345\pi$
$368$	−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	0.920401	+	0.390977i	$0.127863\pi$
$373$	15.4273	+	26.7209i	0.798796	+	1.38356i	−0.121604	+	0.992579i	$0.538804\pi$
$374$	−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	0.997191	+	0.0748992i	$0.0238635\pi$
$383$	11.0271	+	19.0996i	0.563460	+	0.975942i	−0.433731	+	0.901042i	$0.642803\pi$
$384$	−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	−0.0492785	−	0.998785i	$-0.515692\pi$
$389$	−18.5178	−	10.6913i	−0.938891	−	0.542069i	−0.889613	+	0.456716i	$0.849026\pi$
$390$	−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	−0.807087	−	0.590433i	$-0.798957\pi$
$397$	−13.9335	+	8.04449i	−0.699301	+	0.403742i	0.107786	+	0.994174i	$0.465624\pi$
$398$	−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	−0.885769	−	0.464127i	$-0.846368\pi$
$401$	−18.5573	+	10.7141i	−0.926707	+	0.535034i	−0.0409384	+	0.999162i	$0.513035\pi$
$402$	−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	0.742962	−	0.669334i	$-0.233420\pi$
$409$	10.8153	+	6.24422i	0.534783	+	0.308757i	−0.208179	+	0.978091i	$0.566754\pi$
$410$	−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	0.0365139	−	0.999333i	$-0.488375\pi$
$431$	−16.8301	−	9.71686i	−0.810677	−	0.468045i	−0.847191	+	0.531289i	$0.821708\pi$
$432$	−3.11642	+	4.15788i	−0.149939	+	0.200046i
$433$			2.90858i			0.139778i	0.997555	+	0.0698888i	$0.0222645\pi$
$433$			2.90858i			0.139778i	−0.997555	+	0.0698888i	$0.977736\pi$
$434$	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	−0.119980	−	0.992776i	$-0.538283\pi$
$439$	14.2434	−	8.22341i	0.679799	−	0.392482i	0.799779	+	0.600294i	$0.204950\pi$
$440$	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	−0.174393	−	0.984676i	$-0.555796\pi$
$443$	12.4426	−	7.18373i	0.591165	−	0.341309i	0.765558	+	0.643367i	$0.222463\pi$
$444$	−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	$0.00645701\pi$
$449$			0.859617i			0.0405678i	−0.999794	+	0.0202839i	$0.993543\pi$
$450$	−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	0.992186	+	0.124771i	$0.0398197\pi$
$457$	12.9152	+	22.3698i	0.604148	+	1.04641i	−0.388038	+	0.921644i	$0.626847\pi$
$458$	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	0.692807	−	0.721123i	$-0.256374\pi$
$467$	−6.00996	−	10.4096i	−0.278108	−	0.481697i	−0.970914	+	0.239427i	$0.923041\pi$
$468$	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	−0.721559	−	0.692353i	$-0.756574\pi$
$479$	5.22673	−	9.05296i	0.238815	−	0.413640i	0.960375	+	0.278712i	$0.0899076\pi$
$480$	−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	−0.987936	−	0.154864i	$-0.950506\pi$
$487$	−7.94123	+	13.7546i	−0.359851	+	0.623281i	0.628084	+	0.778145i	$0.283839\pi$
$488$	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	$-0.878517\pi$
$491$		−	16.5060i		−	0.744907i	0.928051	−	0.372454i	$-0.121483\pi$
$492$	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	−0.945139	−	0.326669i	$-0.894074\pi$
$499$	−16.8760	−	29.2301i	−0.755473	−	1.30852i	0.189666	−	0.981849i	$-0.439259\pi$
$500$	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	0.994667	+	0.103141i	$0.0328894\pi$
$509$	13.2356	+	22.9247i	0.586656	+	1.01612i	−0.408010	+	0.912977i	$0.633777\pi$
$510$	−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	−0.949042	−	0.315150i	$-0.897945\pi$
$521$	−4.60146	+	7.96995i	−0.201593	+	0.349170i	0.747449	+	0.664320i	$0.231279\pi$
$522$	−16.4843	−	16.2377i	−0.721497	−	0.710704i
$523$	9.07236	−	5.23793i	0.396707	−	0.229039i	−0.288355	−	0.957523i	$-0.593108\pi$
$523$	9.07236	−	5.23793i	0.396707	−	0.229039i	0.685062	+	0.728485i	$0.259775\pi$
$524$	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	0.985995	−	0.166773i	$-0.0533347\pi$
$541$	8.10749	+	14.0426i	0.348568	+	0.603738i	−0.637427	+	0.770511i	$0.720001\pi$
$542$	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	0.0420097	−	0.999117i	$-0.486624\pi$
$557$	−18.9337	−	10.9314i	−0.802246	−	0.463177i	−0.844256	+	0.535940i	$0.819957\pi$
$558$	−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	−0.760664	−	0.649145i	$-0.775127\pi$
$563$	4.31473	−	7.47333i	0.181844	−	0.314963i	0.942509	+	0.334182i	$0.108460\pi$
$564$	−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	−0.614001	−	0.789305i	$-0.710441\pi$
$569$	−5.66393	+	3.27007i	−0.237444	+	0.137088i	0.376557	+	0.926393i	$0.377108\pi$
$570$	2.24911	+	16.6001i	0.0942049	+	0.695302i
$571$	−14.2418	+	24.6675i	−0.596000	+	1.03230i	0.397405	+	0.917643i	$0.369911\pi$
$571$	−14.2418	+	24.6675i	−0.596000	+	1.03230i	−0.993405	+	0.114658i	$0.963423\pi$
$572$	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	−0.118512	−	0.992953i	$-0.537812\pi$
$577$	−24.9262	−	14.3911i	−1.03769	−	0.599111i	−0.919178	+	0.393842i	$0.871146\pi$
$578$	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	0.849644	−	0.527356i	$-0.176817\pi$
$593$	−0.776378	−	1.34473i	−0.0318820	−	0.0552213i	−0.881526	+	0.472135i	$0.843483\pi$
$594$	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	−0.0407320	−	0.999170i	$-0.512969\pi$
$599$	−22.6733	−	13.0904i	−0.926405	−	0.534860i	−0.885673	+	0.464310i	$0.846302\pi$
$600$	−6.45743	+	15.7573i	−0.263624	+	0.643289i
$601$			32.0935i			1.30912i	0.756009	+	0.654562i	$0.227147\pi$
$601$			32.0935i			1.30912i	−0.756009	+	0.654562i	$0.772853\pi$
$602$	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	−0.160479	−	0.987039i	$-0.551304\pi$
$607$	15.1294	−	8.73495i	0.614083	−	0.354541i	0.774562	+	0.632498i	$0.217971\pi$
$608$	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	0.339922	+	0.940454i	$0.389599\pi$
$613$	−15.9570	+	27.6383i	−0.644496	+	1.11630i	−0.984418	+	0.175846i	$0.943734\pi$
$614$	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	$0.0769665\pi$
$617$			11.8955i			0.478896i	−0.970909	+	0.239448i	$0.923033\pi$
$618$	5.43424	+	2.22698i	0.218597	+	0.0895825i
$619$	−32.1638	−	18.5698i	−1.29277	−	0.746383i	−0.313628	−	0.949546i	$-0.601545\pi$
$619$	−32.1638	−	18.5698i	−1.29277	−	0.746383i	−0.979145	+	0.203163i	$0.934878\pi$
$620$	−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	0.878161	−	0.478366i	$-0.158771\pi$
$641$	22.8612	+	13.1989i	0.902964	+	0.521327i	0.0248034	+	0.999692i	$0.492104\pi$
$642$	26.1914	+	10.7334i	1.03369	+	0.423613i
$643$		−	13.3060i		−	0.524736i	−0.964968	−	0.262368i	$-0.915497\pi$
$643$		−	13.3060i		−	0.524736i	0.964968	−	0.262368i	$-0.0845034\pi$
$644$	−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	−0.637219	−	0.770683i	$-0.719915\pi$
$647$	8.87268	−	15.3679i	0.348821	−	0.604176i	0.986040	+	0.166507i	$0.0532488\pi$
$648$	−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	−0.302354	−	0.953196i	$-0.597773\pi$
$653$	9.50503	−	5.48773i	0.371961	−	0.214751i	0.674315	+	0.738444i	$0.264439\pi$
$654$	−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	$0.101504\pi$
$659$			16.0960i			0.627012i	−0.949586	+	0.313506i	$0.898496\pi$
$660$	−2.52944	+	6.17229i	−0.0984584	+	0.240256i
$661$	37.8298	+	21.8411i	1.47141	+	0.849518i	0.999484	−	0.0321202i	$-0.0102259\pi$
$661$	37.8298	+	21.8411i	1.47141	+	0.849518i	0.471925	+	0.881639i	$0.343559\pi$
$662$	−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	−0.990871	−	0.134816i	$-0.956956\pi$
$677$	−15.9287	−	27.5893i	−0.612189	−	1.06034i	0.378681	−	0.925527i	$-0.376378\pi$
$678$	−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	0.995679	−	0.0928603i	$-0.0296010\pi$
$683$	36.9303	+	21.3217i	1.41310	+	0.815853i	0.417420	+	0.908714i	$0.362934\pi$
$684$	−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	−0.600764	−	0.799427i	$-0.705137\pi$
$691$	−5.48927	+	3.16923i	−0.208822	+	0.120563i	0.391942	+	0.919990i	$0.371803\pi$
$692$	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	$0.0168694\pi$
$701$			2.80501i			0.105944i	−0.998596	+	0.0529719i	$0.983131\pi$
$702$	−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	0.987794	−	0.155766i	$-0.0497845\pi$
$709$	9.55911	+	16.5569i	0.359000	+	0.621806i	−0.628794	+	0.777572i	$0.716451\pi$
$710$	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	0.708185	−	0.706026i	$-0.249514\pi$
$719$	−6.90047	−	11.9520i	−0.257344	−	0.445733i	−0.965530	+	0.260293i	$0.916181\pi$
$720$	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	$0.0788344\pi$
$727$			13.2195i			0.490283i	−0.969487	+	0.245141i	$0.921166\pi$
$728$	−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	−0.967150	−	0.254207i	$-0.918185\pi$
$733$	−33.3165	+	19.2353i	−1.23057	+	0.710473i	−0.263425	+	0.964680i	$0.584852\pi$
$734$	−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	−0.705516	−	0.708694i	$-0.749285\pi$
$739$	7.09488	−	12.2887i	0.260989	−	0.452047i	0.966505	+	0.256647i	$0.0826179\pi$
$740$	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	$-0.930827\pi$
$743$		−	11.7541i		−	0.431215i	0.976480	−	0.215608i	$-0.0691732\pi$
$744$	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	0.955600	+	0.294668i	$0.0952090\pi$
$751$	20.0871	+	34.7919i	0.732990	+	1.26958i	−0.222610	+	0.974908i	$0.571458\pi$
$752$	−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	0.909048	−	0.416692i	$-0.136811\pi$
$761$	2.58368	+	4.47507i	0.0936584	+	0.162221i	−0.815389	+	0.578913i	$0.803477\pi$
$762$	−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	$-0.858509\pi$
$769$		−	23.8493i		−	0.860029i	0.902822	−	0.430014i	$-0.141491\pi$
$770$	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	−0.590674	−	0.806910i	$-0.701138\pi$
$773$	11.2176	−	19.4294i	0.403467	−	0.698826i	0.994142	+	0.108084i	$0.0344715\pi$
$774$	−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	0.966657	−	0.256073i	$-0.0824288\pi$
$787$	34.4559	+	19.8931i	1.22822	+	0.709113i	0.261563	+	0.965186i	$0.415762\pi$
$788$	−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	0.0753734	−	0.997155i	$-0.475985\pi$
$809$	−21.3465	−	12.3244i	−0.750502	−	0.433302i	−0.825875	+	0.563853i	$0.809318\pi$
$810$	−34.6569	+	0.522396i	−1.21772	+	0.0183551i
$811$		−	18.3371i		−	0.643904i	−0.946756	−	0.321952i	$-0.895661\pi$
$811$		−	18.3371i		−	0.643904i	0.946756	−	0.321952i	$-0.104339\pi$
$812$	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	−0.784904	−	0.619617i	$-0.787288\pi$
$821$	−18.3595	+	10.5999i	−0.640753	+	0.369939i	0.144152	+	0.989556i	$0.453955\pi$
$822$	3.04899	+	22.5038i	0.106346	+	0.784909i
$823$	8.64517	−	14.9739i	0.301352	−	0.521956i	−0.675091	−	0.737735i	$-0.735896\pi$
$823$	8.64517	−	14.9739i	0.301352	−	0.521956i	0.976442	+	0.215778i	$0.0692289\pi$
$824$	−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	$-0.882299\pi$
$827$		−	20.7860i		−	0.722799i	0.932411	−	0.361400i	$-0.117701\pi$
$828$	6.18368	+	22.4012i	0.214898	+	0.778494i
$829$	23.3169	+	13.4620i	0.809830	+	0.467555i	0.846897	−	0.531757i	$-0.178468\pi$
$829$	23.3169	+	13.4620i	0.809830	+	0.467555i	−0.0370670	+	0.999313i	$0.511801\pi$
$830$	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	$-0.779832\pi$
$853$		−	37.2571i		−	1.27566i	0.770177	−	0.637830i	$-0.220168\pi$
$854$	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	−0.971536	−	0.236892i	$-0.923871\pi$
$857$	−8.21484	+	14.2285i	−0.280613	+	0.486037i	0.690923	+	0.722929i	$0.257205\pi$
$858$	−5.55269	+	0.752322i	−0.189566	+	0.0256839i
$859$	−24.1277	+	13.9302i	−0.823228	+	0.475291i	−0.851528	−	0.524309i	$-0.824324\pi$
$859$	−24.1277	+	13.9302i	−0.823228	+	0.475291i	0.0283003	+	0.999599i	$0.490991\pi$
$860$	−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	−0.599411	−	0.800441i	$-0.704599\pi$
$863$	−6.04913	+	3.49247i	−0.205915	+	0.118885i	0.393497	+	0.919326i	$0.371265\pi$
$864$	−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	0.709520	−	0.704686i	$-0.248912\pi$
$877$	−7.56690	−	13.1062i	−0.255516	−	0.442567i	−0.965036	+	0.262119i	$0.915579\pi$
$878$	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	0.918849	−	0.394610i	$-0.129120\pi$
$887$	3.50486	+	6.07060i	0.117682	+	0.203831i	−0.801167	+	0.598441i	$0.795787\pi$
$888$	−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	−0.863786	−	0.503859i	$-0.831913\pi$
$907$	0.134375	−	0.232745i	0.00446186	−	0.00772818i	0.868248	+	0.496131i	$0.165246\pi$
$908$	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	$0.00516971\pi$
$911$			0.980362i			0.0324808i	−0.999868	+	0.0162404i	$0.994830\pi$
$912$	−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	−0.613084	−	0.790018i	$-0.710071\pi$
$919$	−30.0336	−	52.0197i	−0.990717	−	1.71597i	−0.377633	−	0.925955i	$-0.623262\pi$
$920$	−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	0.999592	+	0.0285469i	$0.00908801\pi$
$929$	15.9871	+	27.6904i	0.524519	+	0.908493i	−0.475074	+	0.879946i	$0.657579\pi$
$930$	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	$0.170846\pi$
$937$			31.3040i			1.02266i	−0.859385	+	0.511328i	$0.829154\pi$
$938$	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	0.415506	+	0.909591i	$0.363605\pi$
$941$	−17.7912	+	30.8152i	−0.579976	+	1.00455i	−0.995481	+	0.0949568i	$0.969729\pi$
$942$	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	−0.413926	−	0.910311i	$-0.635843\pi$
$947$	5.15342	−	2.97533i	0.167464	−	0.0966852i	0.581389	+	0.813625i	$0.302509\pi$
$948$	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	$0.201689\pi$
$953$			36.5553i			1.18414i	−0.805886	+	0.592070i	$0.798311\pi$
$954$	−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	0.602825	−	0.797873i	$-0.294042\pi$
$971$	−12.1392	−	21.0257i	−0.389566	−	0.674748i	−0.992391	+	0.123125i	$0.960708\pi$
$972$	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	0.851671	−	0.524077i	$-0.175590\pi$
$977$	25.7446	+	14.8637i	0.823643	+	0.475530i	−0.0280284	+	0.999607i	$0.508923\pi$
$978$	−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	−0.988518	−	0.151102i	$-0.951718\pi$
$983$	−11.3936	+	19.7344i	−0.363401	+	0.629428i	0.625118	+	0.780531i	$0.285051\pi$
$984$	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	−0.763980	−	0.645240i	$-0.776757\pi$
$991$	5.56585	−	9.64033i	0.176805	−	0.306235i	0.940784	+	0.339005i	$0.110091\pi$
$992$	−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	0.923920	−	0.382585i	$-0.124966\pi$
$997$	33.2978	+	19.2245i	1.05455	+	0.608846i	0.130632	+	0.991431i	$0.458299\pi$
$998$	−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.353.9	yes	20
3.2	odd	2	inner	462.2.k.g.353.5	yes	20
7.5	odd	6	inner	462.2.k.g.89.5	✓	20
21.5	even	6	inner	462.2.k.g.89.9	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.k.g.89.5	✓	20	7.5	odd	6	inner
462.2.k.g.89.9	yes	20	21.5	even	6	inner
462.2.k.g.353.5	yes	20	3.2	odd	2	inner
462.2.k.g.353.9	yes	20	1.1	even	1	trivial

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

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