LMFDB - Embedded newform 462.2.k.g.89.5

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			89.5
Root			$-0.232547 - 1.71637i$ of defining polynomial
Character	$\chi$	$=$	462.89
Dual form			462.2.k.g.353.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(1.60269 + 0.656793i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.92560 - 3.33524i) q^{5} +(-1.05958 - 1.37015i) q^{6} +(1.58064 + 2.12169i) q^{7} -1.00000i q^{8} +(2.13725 + 2.10527i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(1.60269 + 0.656793i) 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} +(2.13725 + 2.10527i) q^{9} +(-3.33524 + 1.92560i) q^{10} +(0.866025 - 0.500000i) q^{11} +(0.232547 + 1.71637i) 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} +(-0.798273 - 2.89184i) q^{18} +(-2.17488 - 1.25567i) q^{19} +3.85120 q^{20} +(1.13977 + 4.43857i) q^{21} -1.00000 q^{22} +(-6.70851 - 3.87316i) q^{23} +(0.656793 - 1.60269i) 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} +(-6.61008 + 0.895586i) q^{30} +(5.23845 - 3.02442i) q^{31} +(0.866025 - 0.500000i) q^{32} +(1.71637 - 0.232547i) 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} +(-2.12482 + 5.18494i) q^{39} +(-3.33524 - 1.92560i) q^{40} -3.85120 q^{41} +(1.23221 - 4.41380i) q^{42} +7.22205 q^{43} +(0.866025 + 0.500000i) q^{44} +(11.1371 - 3.07431i) 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} +(-0.349539 - 2.57986i) q^{51} +(-2.80171 + 1.61757i) q^{52} +(-8.98451 + 5.18721i) q^{53} +(0.619956 - 5.15904i) 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} +(6.17229 + 2.52944i) q^{60} +(-7.45472 - 4.30399i) q^{61} -6.04884 q^{62} +(-1.08852 + 7.86226i) q^{63} -1.00000 q^{64} +(10.7900 + 6.22959i) q^{65} +(-1.60269 - 0.656793i) 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} +(2.10527 - 2.13725i) q^{72} +(-2.12908 + 1.22922i) q^{73} +(0.118311 - 0.0683071i) q^{74} +(-2.28635 - 16.8749i) 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} +(0.135645 + 8.99898i) q^{81} +(3.33524 + 1.92560i) q^{82} +8.67372 q^{83} +(-3.27403 + 3.20636i) q^{84} -5.78870 q^{85} +(-6.25448 - 3.61103i) q^{86} +(-5.06575 + 12.3613i) 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} +(10.3820 - 1.40664i) q^{93} +(-9.35353 + 5.40027i) q^{94} +(-8.37589 + 4.83582i) q^{95} +(1.71637 - 0.232547i) 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
$3$	1.60269	+	0.656793i	0.925315	+	0.379199i
$3$	1.60269	+	0.656793i	0.925315	+	0.379199i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.92560	−	3.33524i	0.861155	−	1.49156i	−0.00965972	−	0.999953i	$-0.503075\pi$
$5$	1.92560	−	3.33524i	0.861155	−	1.49156i	0.870815	−	0.491611i	$-0.163592\pi$
$6$	−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
$9$	2.13725	+	2.10527i	0.712415	+	0.701758i
$10$	−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
$12$	0.232547	+	1.71637i	0.0671305	+	0.495473i
$13$			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	0.760379	−	0.649480i	$-0.225013\pi$
$17$	−0.751545	−	1.30171i	−0.182276	−	0.315712i	−0.942655	+	0.333768i	$0.891680\pi$
$18$	−0.798273	−	2.89184i	−0.188155	−	0.681614i
$19$	−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
$21$	1.13977	+	4.43857i	0.248719	+	0.968576i
$22$	−1.00000			−0.213201
$23$	−6.70851	−	3.87316i	−1.39882	−	0.807610i	−0.404552	−	0.914515i	$-0.632573\pi$
$23$	−6.70851	−	3.87316i	−1.39882	−	0.807610i	−0.994269	+	0.106905i	$0.965906\pi$
$24$	0.656793	−	1.60269i	0.134067	−	0.327148i
$25$	−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	$0.745916\pi$
$30$	−6.61008	+	0.895586i	−1.20683	+	0.163511i
$31$	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
$33$	1.71637	−	0.232547i	0.298781	−	0.0404812i
$34$			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
$39$	−2.12482	+	5.18494i	−0.340243	+	0.830254i
$40$	−3.33524	−	1.92560i	−0.527348	−	0.304464i
$41$	−3.85120			−0.601457			−0.300728	−	0.953710i	$-0.597230\pi$
$41$	−3.85120			−0.601457			−0.300728	+	0.953710i	$0.597230\pi$
$42$	1.23221	−	4.41380i	0.190135	−	0.681064i
$43$	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
$45$	11.1371	−	3.07431i	1.66022	−	0.458291i
$46$	3.87316	+	6.70851i	0.571067	+	0.989116i
$47$	5.40027	−	9.35353i	0.787710	−	1.36435i	−0.139657	−	0.990200i	$-0.544600\pi$
$47$	5.40027	−	9.35353i	0.787710	−	1.36435i	0.927367	−	0.374153i	$-0.122067\pi$
$48$	−1.37015	+	1.05958i	−0.197763	+	0.152937i
$49$	−2.00314	+	6.70727i	−0.286163	+	0.958181i
$50$			9.83176i			1.39042i
$51$	−0.349539	−	2.57986i	−0.0489453	−	0.361252i
$52$	−2.80171	+	1.61757i	−0.388528	+	0.224317i
$53$	−8.98451	+	5.18721i	−1.23412	+	0.712518i	−0.967886	−	0.251391i	$-0.919112\pi$
$53$	−8.98451	+	5.18721i	−1.23412	+	0.712518i	−0.266232	+	0.963909i	$0.585779\pi$
$54$	0.619956	−	5.15904i	0.0843654	−	0.702056i
$55$		−	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	$-0.0964490\pi$
$59$	1.68071	+	2.91108i	0.218810	+	0.378991i	−0.735634	+	0.677379i	$0.763116\pi$
$60$	6.17229	+	2.52944i	0.796840	+	0.326550i
$61$	−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
$63$	−1.08852	+	7.86226i	−0.137140	+	0.990552i
$64$	−1.00000			−0.125000
$65$	10.7900	+	6.22959i	1.33833	+	0.772686i
$66$	−1.60269	−	0.656793i	−0.197278	−	0.0808456i
$67$	−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	$0.0161962\pi$
$71$			0.857105i			0.101720i	−0.998706	+	0.0508598i	$0.983804\pi$
$72$	2.10527	−	2.13725i	0.248109	−	0.251877i
$73$	−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
$75$	−2.28635	−	16.8749i	−0.264005	−	1.94855i
$76$		−	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
$81$	0.135645	+	8.99898i	0.0150717	+	0.999886i
$82$	3.33524	+	1.92560i	0.368316	+	0.212647i
$83$	8.67372			0.952064			0.476032	−	0.879428i	$-0.342075\pi$
$83$	8.67372			0.952064			0.476032	+	0.879428i	$0.342075\pi$
$84$	−3.27403	+	3.20636i	−0.357226	+	0.349842i
$85$	−5.78870			−0.627873
$86$	−6.25448	−	3.61103i	−0.674438	−	0.389387i
$87$	−5.06575	+	12.3613i	−0.543105	+	1.32528i
$88$	−0.500000	−	0.866025i	−0.0533002	−	0.0923186i
$89$	−3.33499	+	5.77637i	−0.353508	+	0.612294i	−0.986861	−	0.161569i	$-0.948345\pi$
$89$	−3.33499	+	5.77637i	−0.353508	+	0.612294i	0.633353	+	0.773863i	$0.281678\pi$
$90$	−11.1821	−	2.90611i	−1.17870	−	0.306331i
$91$	−6.86397	+	5.11360i	−0.719539	+	0.536051i
$92$		−	7.74632i		−	0.807610i
$93$	10.3820	−	1.40664i	1.07657	−	0.145862i
$94$	−9.35353	+	5.40027i	−0.964743	+	0.556995i
$95$	−8.37589	+	4.83582i	−0.859348	+	0.496145i
$96$	1.71637	−	0.232547i	0.175176	−	0.0237342i
$97$			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	0.565967	−	0.824428i	$-0.308503\pi$
$101$	−4.33142	−	7.50224i	−0.430992	−	0.746501i	−0.996959	+	0.0779275i	$0.975170\pi$
$102$	−0.987219	+	2.40899i	−0.0977492	+	0.238526i
$103$	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
$105$	16.9984	+	4.74551i	1.65888	+	0.463114i
$106$	10.3744			1.00765
$107$	−14.1527	−	8.17106i	−1.36819	−	0.789926i	−0.377495	−	0.926012i	$-0.623215\pi$
$107$	−14.1527	−	8.17106i	−1.36819	−	0.789926i	−0.990697	+	0.136085i	$0.956548\pi$
$108$	−3.11642	+	4.15788i	−0.299877	+	0.400092i
$109$	−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	$0.150768\pi$
$113$			9.69766i			0.912279i	−0.889908	+	0.456140i	$0.849232\pi$
$114$	0.584002	+	4.31037i	0.0546968	+	0.403703i
$115$	−25.8358	+	14.9163i	−2.40920	+	1.39096i
$116$	−6.67953	+	3.85643i	−0.620179	+	0.358061i
$117$	−6.81086	+	6.91429i	−0.629664	+	0.639227i
$118$		−	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
$123$	−6.17229	−	2.52944i	−0.556537	−	0.228072i
$124$	5.23845	+	3.02442i	0.470426	+	0.271601i
$125$	−18.6081			−1.66436
$126$	4.87381	−	6.26466i	0.434194	−	0.558100i
$127$	−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
$129$	11.5747	+	4.74339i	1.01910	+	0.417632i
$130$	−6.22959	−	10.7900i	−0.546371	−	0.946343i
$131$	−8.33693	+	14.4400i	−0.728401	+	1.26163i	0.229158	+	0.973389i	$0.426403\pi$
$131$	−8.33693	+	14.4400i	−0.728401	+	1.26163i	−0.957559	+	0.288238i	$0.906930\pi$
$132$	1.05958	+	1.37015i	0.0922243	+	0.119256i
$133$	−0.773568	−	6.59917i	−0.0670768	−	0.572221i
$134$			10.3833i			0.896984i
$135$	19.8685	+	2.38758i	1.71001	+	0.205490i
$136$	−1.30171	+	0.751545i	−0.111621	+	0.0644444i
$137$	−11.3547	+	6.55564i	−0.970097	+	0.560086i	−0.899266	−	0.437402i	$-0.855899\pi$
$137$	−11.3547	+	6.55564i	−0.970097	+	0.560086i	−0.0708312	+	0.997488i	$0.522565\pi$
$138$	1.80138	+	13.2955i	0.153344	+	1.13179i
$139$			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
$144$	−2.89184	+	0.798273i	−0.240987	+	0.0665227i
$145$	25.7242	+	14.8519i	2.13628	+	1.23338i
$146$	2.45845			0.203462
$147$	−7.61570	+	9.43404i	−0.628133	+	0.778106i
$148$	−0.136614			−0.0112296
$149$	−2.60352	−	1.50314i	−0.213288	−	0.123142i	0.389550	−	0.921005i	$-0.372630\pi$
$149$	−2.60352	−	1.50314i	−0.213288	−	0.123142i	−0.602839	+	0.797863i	$0.705964\pi$
$150$	−6.45743	+	15.7573i	−0.527247	+	1.28658i
$151$	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
$156$	−5.55269	+	0.752322i	−0.444571	+	0.0602340i
$157$	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
$159$	−17.8063	+	2.41254i	−1.41213	+	0.191327i
$160$		−	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
$165$	2.52944	−	6.17229i	0.196917	−	0.480512i
$166$	−7.51166	−	4.33686i	−0.583018	−	0.336606i
$167$	−20.9824			−1.62367			−0.811834	−	0.583888i	$-0.801531\pi$
$167$	−20.9824			−1.62367			−0.811834	+	0.583888i	$0.801531\pi$
$168$	4.43857	−	1.13977i	0.342443	−	0.0879354i
$169$	2.53386			0.194913
$170$	5.01316	+	2.89435i	0.384492	+	0.221987i
$171$	−2.00473	−	7.26237i	−0.153305	−	0.555368i
$172$	3.61103	+	6.25448i	0.275338	+	0.476900i
$173$	−0.506658	+	0.877558i	−0.0385205	+	0.0667195i	−0.884643	−	0.466269i	$-0.845598\pi$
$173$	−0.506658	+	0.877558i	−0.0385205	+	0.0667195i	0.846122	+	0.532989i	$0.178931\pi$
$174$	10.5677	−	8.17236i	0.801138	−	0.619545i
$175$	10.2950	−	23.8884i	0.778229	−	1.80580i
$176$			1.00000i			0.0753778i
$177$	0.781690	+	5.76945i	0.0587555	+	0.433659i
$178$	5.77637	−	3.33499i	0.432957	−	0.249968i
$179$	15.5742	−	8.99179i	1.16407	−	0.672078i	0.211796	−	0.977314i	$-0.432069\pi$
$179$	15.5742	−	8.99179i	1.16407	−	0.672078i	0.952277	+	0.305236i	$0.0987354\pi$
$180$	8.23097	+	8.10784i	0.613500	+	0.604322i
$181$		−	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
$186$	−9.69443	−	3.97283i	−0.710830	−	0.291302i
$187$	−1.30171	−	0.751545i	−0.0951908	−	0.0549584i
$188$	10.8005			0.787710
$189$	−6.90843	+	11.8859i	−0.502515	+	0.864569i
$190$	9.67164			0.701655
$191$	6.35746	+	3.67048i	0.460009	+	0.265587i	0.712048	−	0.702131i	$-0.247768\pi$
$191$	6.35746	+	3.67048i	0.460009	+	0.265587i	−0.252039	+	0.967717i	$0.581101\pi$
$192$	−1.60269	−	0.656793i	−0.115664	−	0.0473999i
$193$	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	$-0.697397\pi$
$197$		−	22.8444i		−	1.62759i	0.581150	−	0.813797i	$-0.302603\pi$
$198$	−2.13725	−	2.10527i	−0.151887	−	0.149615i
$199$	−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
$201$	−2.41461	−	17.8216i	−0.170314	−	1.25704i
$202$			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
$207$	−6.18368	−	22.4012i	−0.429795	−	1.55699i
$208$	−2.80171	−	1.61757i	−0.194264	−	0.112158i
$209$	−2.51133			−0.173712
$210$	−12.3483	−	12.6090i	−0.852116	−	0.870100i
$211$	−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
$213$	−0.562940	+	1.37368i	−0.0385720	+	0.0941227i
$214$	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
$219$	−4.21960	+	0.571704i	−0.285134	+	0.0386322i
$220$	3.33524	−	1.92560i	0.224862	−	0.129824i
$221$	4.21123	−	2.43135i	0.283278	−	0.163551i
$222$	0.234480	−	0.0317692i	0.0157373	−	0.00213221i
$223$		−	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	0.998865	−	0.0476209i	$-0.0151639\pi$
$227$	6.90336	+	11.9570i	0.458192	+	0.793612i	−0.540674	+	0.841232i	$0.681831\pi$
$228$	1.64942	−	4.02489i	0.109236	−	0.266555i
$229$	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
$231$	3.20636	+	3.27403i	0.210963	+	0.215415i
$232$	7.71286			0.506374
$233$	1.71010	+	0.987329i	0.112033	+	0.0646821i	0.554969	−	0.831871i	$-0.312730\pi$
$233$	1.71010	+	0.987329i	0.112033	+	0.0646821i	−0.442937	+	0.896553i	$0.646063\pi$
$234$	9.35552	−	2.58253i	0.611590	−	0.168825i
$235$	−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	$-0.0899261\pi$
$240$	0.895586	+	6.61008i	0.0578098	+	0.426679i
$241$	−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
$243$	−5.69307	+	14.5117i	−0.365210	+	0.930925i
$244$		−	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
$249$	13.9013	+	5.69684i	0.880959	+	0.361022i
$250$	16.1151	+	9.30405i	1.01921	+	0.588440i
$251$	10.3975			0.656283			0.328141	−	0.944629i	$-0.393578\pi$
$251$	10.3975			0.656283			0.328141	+	0.944629i	$0.393578\pi$
$252$	−7.35318	+	2.98845i	−0.463207	+	0.188254i
$253$	−7.74632			−0.487007
$254$	11.4796	+	6.62776i	0.720295	+	0.415863i
$255$	−9.27751	−	3.80198i	−0.580980	−	0.238089i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.03225	+	10.4482i	−0.376282	+	0.651739i	−0.990518	−	0.137383i	$-0.956131\pi$
$257$	−6.03225	+	10.4482i	−0.376282	+	0.651739i	0.614236	+	0.789122i	$0.289464\pi$
$258$	−7.65232	−	9.89527i	−0.476412	−	0.616052i
$259$	−0.358989	+	0.0420814i	−0.0223065	+	0.00261481i
$260$			12.4592i			0.772686i
$261$	−16.2377	+	16.4843i	−1.00509	+	1.02035i
$262$	14.4400	−	8.33693i	0.892106	−	0.515057i
$263$	20.5474	−	11.8631i	1.26701	−	0.731508i	0.292588	−	0.956239i	$-0.405483\pi$
$263$	20.5474	−	11.8631i	1.26701	−	0.731508i	0.974421	+	0.224730i	$0.0721501\pi$
$264$	−0.232547	−	1.71637i	−0.0143123	−	0.105635i
$265$			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	$0.217630\pi$
$269$	15.3296	+	26.5516i	0.934661	+	1.61888i	0.159422	+	0.987210i	$0.449037\pi$
$270$	−16.0128	−	12.0019i	−0.974510	−	0.730415i
$271$	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
$273$	−14.3594	+	3.68732i	−0.869071	+	0.223167i
$274$	13.1113			0.792081
$275$	−8.51456	−	4.91588i	−0.513447	−	0.296439i
$276$	5.08773	−	12.4150i	0.306245	−	0.747294i
$277$	−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	$0.00795110\pi$
$281$			0.837366i			0.0499531i	−0.999688	+	0.0249765i	$0.992049\pi$
$282$	−18.5377	+	2.51163i	−1.10390	+	0.149565i
$283$	−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
$285$	−16.6001	+	2.24911i	−0.983305	+	0.133226i
$286$		−	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
$291$	−7.01240	+	17.1115i	−0.411074	+	1.00310i
$292$	−2.12908	−	1.22922i	−0.124595	−	0.0719348i
$293$	1.75825			0.102718			0.0513591	−	0.998680i	$-0.483645\pi$
$293$	1.75825			0.102718			0.0513591	+	0.998680i	$0.483645\pi$
$294$	11.3124	−	4.36227i	0.659753	−	0.254412i
$295$	12.9455			0.753719
$296$	0.118311	+	0.0683071i	0.00687671	+	0.00397027i
$297$	4.15788	+	3.11642i	0.241265	+	0.180833i
$298$	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
$303$	−2.01452	−	14.8686i	−0.115731	−	0.854180i
$304$	2.17488	−	1.25567i	0.124738	−	0.0720173i
$305$	−28.7097	+	16.5755i	−1.64391	+	0.949112i
$306$	−3.16442	+	3.21247i	−0.180898	+	0.183645i
$307$		−	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	0.957215	−	0.289378i	$-0.0934484\pi$
$311$	4.02080	+	6.96424i	0.227999	+	0.394906i	−0.729216	+	0.684283i	$0.760115\pi$
$312$	5.18494	+	2.12482i	0.293539	+	0.120294i
$313$	−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
$315$	24.1265	+	18.7700i	1.35937	+	1.05757i
$316$	4.23713			0.238357
$317$	−7.12754	−	4.11509i	−0.400323	−	0.231126i	0.286301	−	0.958140i	$-0.407574\pi$
$317$	−7.12754	−	4.11509i	−0.400323	−	0.231126i	−0.686623	+	0.727013i	$0.740908\pi$
$318$	16.6270	+	6.81385i	0.932396	+	0.382101i
$319$	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
$324$	−7.72552	+	4.61696i	−0.429196	+	0.256498i
$325$	27.5458	−	15.9036i	1.52797	−	0.882171i
$326$	−12.5877	+	7.26751i	−0.697168	+	0.402510i
$327$	−1.49398	−	11.0267i	−0.0826174	−	0.609778i
$328$			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
$333$	−0.395067	+	0.109055i	−0.0216495	+	0.00597620i
$334$	18.1713	+	10.4912i	0.994290	+	0.574053i
$335$	−39.9883			−2.18480
$336$	−4.41380	−	1.23221i	−0.240793	−	0.0672228i
$337$	−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
$339$	−6.36935	+	15.5424i	−0.345936	+	0.844146i
$340$	−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
$345$	−51.2039	+	6.93750i	−2.75672	+	0.373502i
$346$	0.877558	−	0.506658i	0.0471778	−	0.0272381i
$347$	23.8900	−	13.7929i	1.28248	−	0.740440i	0.305179	−	0.952295i	$-0.401284\pi$
$347$	23.8900	−	13.7929i	1.28248	−	0.740440i	0.977301	+	0.211854i	$0.0679503\pi$
$348$	−13.2381	+	1.79360i	−0.709637	+	0.0961472i
$349$		−	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	0.994231	−	0.107263i	$-0.0342087\pi$
$353$	7.59466	+	13.1543i	0.404223	+	0.700134i	−0.590008	+	0.807398i	$0.700875\pi$
$354$	2.20776	−	5.38734i	0.117341	−	0.286334i
$355$	2.85865	+	1.65044i	0.151721	+	0.0875964i
$356$	−6.66998			−0.353508
$357$	4.92116	−	4.81944i	0.260455	−	0.255072i
$358$	−17.9836			−0.950462
$359$	−11.0255	−	6.36556i	−0.581902	−	0.335962i	0.179987	−	0.983669i	$-0.442395\pi$
$359$	−11.0255	−	6.36556i	−0.581902	−	0.335962i	−0.761889	+	0.647708i	$0.775728\pi$
$360$	−3.07431	−	11.1371i	−0.162030	−	0.586975i
$361$	−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
$366$	2.00176	+	14.7745i	0.104634	+	0.772273i
$367$	−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
$369$	−8.23097	−	8.10784i	−0.428487	−	0.422077i
$370$		−	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
$375$	−29.8231	−	12.2217i	−1.54006	−	0.631124i
$376$	−9.35353	−	5.40027i	−0.482372	−	0.278497i
$377$	−24.9522			−1.28510
$378$	11.9258	−	6.83924i	0.613397	−	0.351772i
$379$	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
$381$	−21.2445	−	8.70613i	−1.08839	−	0.446028i
$382$	−3.67048	−	6.35746i	−0.187798	−	0.325276i
$383$	−11.0271	+	19.0996i	−0.563460	+	0.975942i	0.433731	+	0.901042i	$0.357197\pi$
$383$	−11.0271	+	19.0996i	−0.563460	+	0.975942i	−0.997191	+	0.0748992i	$0.976136\pi$
$384$	1.05958	+	1.37015i	0.0540713	+	0.0699199i
$385$	8.17106	−	6.08737i	0.416436	−	0.310241i
$386$		−	19.6660i		−	1.00098i
$387$	15.4353	+	15.2044i	0.784621	+	0.772883i
$388$	−9.24632	+	5.33837i	−0.469411	+	0.271015i
$389$	18.5178	−	10.6913i	0.938891	−	0.542069i	0.0492785	−	0.998785i	$-0.484308\pi$
$389$	18.5178	−	10.6913i	0.938891	−	0.542069i	0.889613	+	0.456716i	$0.150974\pi$
$390$	−2.89735	−	21.3846i	−0.146713	−	1.08285i
$391$			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
$396$	0.798273	+	2.89184i	0.0401147	+	0.145321i
$397$	−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
$399$	3.09450	−	11.0845i	0.154919	−	0.554920i
$400$	9.83176			0.491588
$401$	18.5573	+	10.7141i	0.926707	+	0.535034i	0.885769	−	0.464127i	$-0.153632\pi$
$401$	18.5573	+	10.7141i	0.926707	+	0.535034i	0.0409384	+	0.999162i	$0.486965\pi$
$402$	−6.81970	+	16.6413i	−0.340136	+	0.829993i
$403$	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
$408$	−2.57986	+	0.349539i	−0.127722	+	0.0173048i
$409$	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
$411$	−22.5038	+	3.04899i	−1.11003	+	0.150395i
$412$			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
$417$	−10.4252	+	25.4394i	−0.510524	+	1.24577i
$418$	2.17488	+	1.25567i	0.106377	+	0.0614166i
$419$	28.3825			1.38657			0.693287	−	0.720662i	$-0.256162\pi$
$419$	28.3825			1.38657			0.693287	+	0.720662i	$0.256162\pi$
$420$	4.38949	+	17.0938i	0.214185	+	0.834094i
$421$	−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
$423$	31.2335	−	8.62177i	1.51862	−	0.419205i
$424$	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
$429$	0.752322	+	5.55269i	0.0363225	+	0.268087i
$430$	−24.0873	+	13.9068i	−1.16159	+	0.670645i
$431$	16.8301	−	9.71686i	0.810677	−	0.468045i	−0.0365139	−	0.999333i	$-0.511625\pi$
$431$	16.8301	−	9.71686i	0.810677	−	0.468045i	0.847191	+	0.531289i	$0.178292\pi$
$432$	−5.15904	−	0.619956i	−0.248214	−	0.0298277i
$433$		−	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
$438$	3.94013	+	1.61469i	0.188267	+	0.0771529i
$439$	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
$441$	−18.4018	+	10.1179i	−0.876278	+	0.481806i
$442$	−4.86271			−0.231295
$443$	−12.4426	−	7.18373i	−0.591165	−	0.341309i	0.174393	−	0.984676i	$-0.444204\pi$
$443$	−12.4426	−	7.18373i	−0.591165	−	0.341309i	−0.765558	+	0.643367i	$0.777537\pi$
$444$	−0.218951	−	0.0897272i	−0.0103909	−	0.00425827i
$445$	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	$0.993543\pi$
$450$	−20.6986	+	21.0129i	−0.975739	+	0.990558i
$451$	−3.33524	+	1.92560i	−0.157050	+	0.0906730i
$452$	−8.39842	+	4.84883i	−0.395029	+	0.228070i
$453$	2.86762	+	21.1652i	0.134733	+	0.994426i
$454$		−	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
$459$	4.68425	−	6.24966i	0.218642	−	0.291709i
$460$	−25.8358	−	14.9163i	−1.20460	−	0.695478i
$461$	9.74250			0.453754			0.226877	−	0.973923i	$-0.427149\pi$
$461$	9.74250			0.453754			0.226877	+	0.973923i	$0.427149\pi$
$462$	−1.13977	−	4.43857i	−0.0530270	−	0.206501i
$463$	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
$465$	15.3002	−	37.3352i	0.709529	−	1.73138i
$466$	−0.987329	−	1.71010i	−0.0457371	−	0.0792191i
$467$	6.00996	−	10.4096i	0.278108	−	0.481697i	−0.692807	−	0.721123i	$-0.743626\pi$
$467$	6.00996	−	10.4096i	0.278108	−	0.481697i	0.970914	+	0.239427i	$0.0769594\pi$
$468$	−9.39338	−	2.44123i	−0.434209	−	0.112846i
$469$	10.8726	−	25.2286i	0.502049	−	1.16495i
$470$			41.5950i			1.91864i
$471$	8.26726	−	1.12011i	0.380935	−	0.0516120i
$472$	2.91108	−	1.68071i	0.133993	−	0.0773612i
$473$	6.25448	−	3.61103i	0.287581	−	0.166035i
$474$	−7.27248	+	0.985332i	−0.334036	+	0.0452578i
$475$			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	$-0.243426\pi$
$479$	−5.22673	−	9.05296i	−0.238815	−	0.413640i	−0.960375	+	0.278712i	$0.910092\pi$
$480$	2.52944	−	6.17229i	0.115453	−	0.281725i
$481$	−0.382754	−	0.220983i	−0.0174521	−	0.0100760i
$482$	8.81839			0.401667
$483$	9.54513	−	34.1907i	0.434318	−	1.55573i
$484$	1.00000			0.0454545
$485$	35.6095	+	20.5591i	1.61694	+	0.933542i
$486$	12.1862	−	9.72095i	0.552776	−	0.440951i
$487$	−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	$-0.878517\pi$
$491$		−	16.5060i		−	0.744907i	0.928051	−	0.372454i	$-0.121483\pi$
$492$	−0.895586	−	6.61008i	−0.0403761	−	0.298006i
$493$	10.0399	−	5.79656i	0.452176	−	0.261064i
$494$	−7.03603	+	4.06225i	−0.316566	+	0.182769i
$495$	8.10784	−	8.23097i	0.364420	−	0.369955i
$496$			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
$501$	−33.6284	−	13.7811i	−1.50240	−	0.615694i
$502$	−9.00448	−	5.19874i	−0.401889	−	0.232031i
$503$	−14.4126			−0.642627			−0.321313	−	0.946973i	$-0.604124\pi$
$503$	−14.4126			−0.642627			−0.321313	+	0.946973i	$0.604124\pi$
$504$	7.86226	+	1.08852i	0.350213	+	0.0484864i
$505$	−33.3624			−1.48461
$506$	6.70851	+	3.87316i	0.298230	+	0.172183i
$507$	4.06101	+	1.66422i	0.180356	+	0.0739108i
$508$	−6.62776	−	11.4796i	−0.294059	−	0.509326i
$509$	−13.2356	+	22.9247i	−0.586656	+	1.01612i	0.408010	+	0.912977i	$0.366223\pi$
$509$	−13.2356	+	22.9247i	−0.586656	+	1.01612i	−0.994667	+	0.103141i	$0.967111\pi$
$510$	6.13357	+	7.93137i	0.271599	+	0.351207i
$511$	−5.97334	−	2.57428i	−0.264245	−	0.113879i
$512$			1.00000i			0.0441942i
$513$	1.55691	−	12.9560i	0.0687395	−	0.572023i
$514$	10.4482	−	6.03225i	0.460849	−	0.266071i
$515$	11.3088	−	6.52913i	0.498325	−	0.287708i
$516$	1.67947	+	12.3957i	0.0739344	+	0.545691i
$517$		−	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	$-0.102055\pi$
$521$	4.60146	+	7.96995i	0.201593	+	0.349170i	−0.747449	+	0.664320i	$0.768721\pi$
$522$	22.3044	−	6.15697i	0.976236	−	0.269483i
$523$	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
$525$	32.1895	−	31.5242i	1.40486	−	1.37583i
$526$	−23.7261			−1.03451
$527$	−7.87386	−	4.54597i	−0.342991	−	0.198026i
$528$	−0.656793	+	1.60269i	−0.0285832	+	0.0697482i
$529$	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
$534$	11.4481	−	1.55108i	0.495409	−	0.0671219i
$535$	−54.5049	+	31.4684i	−2.35645	+	1.36050i
$536$	−8.99224	+	5.19167i	−0.388405	+	0.224246i
$537$	30.8664	−	4.18203i	1.33199	−	0.180468i
$538$		−	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
$543$	10.6987	−	26.1068i	0.459126	−	1.12035i
$544$	−1.30171	−	0.751545i	−0.0558105	−	0.0322222i
$545$	−24.7418			−1.05982
$546$	14.2793	+	3.98639i	0.611096	+	0.170602i
$547$	−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
$549$	−6.87151	−	24.8929i	−0.293269	−	1.06240i
$550$	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
$555$	0.122350	+	0.903031i	0.00519346	+	0.0383315i
$556$	−13.7463	+	7.93644i	−0.582974	+	0.336580i
$557$	18.9337	−	10.9314i	0.802246	−	0.463177i	−0.0420097	−	0.999117i	$-0.513376\pi$
$557$	18.9337	−	10.9314i	0.802246	−	0.463177i	0.844256	+	0.535940i	$0.180043\pi$
$558$	−12.9279	−	12.7345i	−0.547280	−	0.539093i
$559$			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	$-0.224873\pi$
$563$	−4.31473	−	7.47333i	−0.181844	−	0.314963i	−0.942509	+	0.334182i	$0.891540\pi$
$564$	17.3099	+	7.09371i	0.728880	+	0.298699i
$565$	32.3440	+	18.6738i	1.36072	+	0.785614i
$566$	8.23373			0.346090
$567$	−18.8786	+	14.5120i	−0.792828	+	0.609445i
$568$	0.857105			0.0359633
$569$	5.66393	+	3.27007i	0.237444	+	0.137088i	0.614001	−	0.789305i	$-0.289559\pi$
$569$	5.66393	+	3.27007i	0.237444	+	0.137088i	−0.376557	+	0.926393i	$0.622892\pi$
$570$	15.5007	+	6.35226i	0.649251	+	0.266067i
$571$	−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
$576$	−2.13725	−	2.10527i	−0.0890519	−	0.0877197i
$577$	−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
$579$	4.57328	+	33.7542i	0.190059	+	1.40278i
$580$			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
$585$	9.94583	+	36.0300i	0.411209	+	1.48966i
$586$	−1.52269	−	0.879127i	−0.0629018	−	0.0363164i
$587$	6.58973			0.271987			0.135994	−	0.990710i	$-0.456577\pi$
$587$	6.58973			0.271987			0.135994	+	0.990710i	$0.456577\pi$
$588$	−11.9780	−	1.87837i	−0.493963	−	0.0774628i
$589$	−15.1906			−0.625919
$590$	−11.2112	−	6.47277i	−0.461557	−	0.266480i
$591$	15.0040	−	36.6125i	0.617183	−	1.50604i
$592$	−0.0683071	−	0.118311i	−0.00280740	−	0.00486257i
$593$	0.776378	−	1.34473i	0.0318820	−	0.0552213i	−0.849644	−	0.527356i	$-0.823183\pi$
$593$	0.776378	−	1.34473i	0.0318820	−	0.0552213i	0.881526	+	0.472135i	$0.156517\pi$
$594$	−2.04262	−	4.77783i	−0.0838097	−	0.196037i
$595$	−9.14987	−	12.2818i	−0.375108	−	0.503506i
$596$		−	3.00628i		−	0.123142i
$597$	−3.14462	+	0.426058i	−0.128701	+	0.0174374i
$598$	−21.7030	+	12.5302i	−0.887501	+	0.512399i
$599$	22.6733	−	13.0904i	0.926405	−	0.534860i	0.0407320	−	0.999170i	$-0.487031\pi$
$599$	22.6733	−	13.0904i	0.926405	−	0.534860i	0.885673	+	0.464310i	$0.153698\pi$
$600$	−16.8749	+	2.28635i	−0.688916	+	0.0933397i
$601$		−	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
$606$	−5.68969	+	13.8839i	−0.231128	+	0.563994i
$607$	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
$609$	−34.2341	+	8.79090i	−1.38723	+	0.356225i
$610$	33.1511			1.34225
$611$	30.2600	+	17.4706i	1.22419	+	0.706786i
$612$	4.34670	−	1.19988i	0.175705	−	0.0485021i
$613$	−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	$0.0769665\pi$
$617$			11.8955i			0.478896i	−0.970909	+	0.239448i	$0.923033\pi$
$618$	−0.788496	−	5.81968i	−0.0317180	−	0.234102i
$619$	−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
$621$	4.80238	−	39.9636i	0.192713	−	1.60368i
$622$		−	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
$627$	−4.02489	−	1.64942i	−0.160739	−	0.0658716i
$628$	4.17140	+	2.40836i	0.166457	+	0.0961039i
$629$	0.205343			0.00818758
$630$	−11.5091	−	28.3186i	−0.458534	−	1.12824i
$631$	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
$633$	−15.9590	−	6.54009i	−0.634313	−	0.259945i
$634$	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
$639$	−1.80444	+	1.83184i	−0.0713826	+	0.0724666i
$640$	3.33524	−	1.92560i	0.131837	−	0.0761161i
$641$	−22.8612	+	13.1989i	−0.902964	+	0.521327i	−0.878161	−	0.478366i	$-0.841229\pi$
$641$	−22.8612	+	13.1989i	−0.902964	+	0.521327i	−0.0248034	+	0.999692i	$0.507896\pi$
$642$	3.80031	+	28.0491i	0.149986	+	1.10701i
$643$			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	0.637219	−	0.770683i	$-0.280085\pi$
$647$	−8.87268	−	15.3679i	−0.348821	−	0.604176i	−0.986040	+	0.166507i	$0.946751\pi$
$648$	8.99898	−	0.135645i	0.353513	−	0.00532864i
$649$	2.91108	+	1.68071i	0.114270	+	0.0659738i
$650$	−31.8071			−1.24758
$651$	19.3947	+	19.8041i	0.760140	+	0.776183i
$652$	14.5350			0.569236
$653$	−9.50503	−	5.48773i	−0.371961	−	0.214751i	0.302354	−	0.953196i	$-0.402227\pi$
$653$	−9.50503	−	5.48773i	−0.371961	−	0.214751i	−0.674315	+	0.738444i	$0.735561\pi$
$654$	−4.21952	+	10.2964i	−0.164996	+	0.402621i
$655$	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	$0.898496\pi$
$660$	6.61008	−	0.895586i	0.257297	−	0.0348606i
$661$	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
$663$	8.34620	−	1.13081i	0.324140	−	0.0439169i
$664$		−	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
$669$	10.2351	−	24.9754i	0.395710	−	0.965603i
$670$	34.6309	+	19.9942i	1.33791	+	0.772442i
$671$	−8.60797			−0.332307
$672$	3.20636	+	3.27403i	0.123688	+	0.126298i
$673$	−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
$675$	30.6399	−	40.8793i	1.17933	−	1.57344i
$676$	1.26693	+	2.19439i	0.0487282	+	0.0843997i
$677$	15.9287	−	27.5893i	0.612189	−	1.06034i	−0.378681	−	0.925527i	$-0.623622\pi$
$677$	15.9287	−	27.5893i	0.612189	−	1.06034i	0.990871	−	0.134816i	$-0.0430443\pi$
$678$	13.2872	−	10.2754i	0.510292	−	0.394625i
$679$	−22.6527	+	16.8761i	−0.869332	+	0.647645i
$680$			5.78870i			0.221987i
$681$	3.21071	+	23.6974i	0.123035	+	0.908087i
$682$	−5.23845	+	3.02442i	−0.200590	+	0.115811i
$683$	−36.9303	+	21.3217i	−1.41310	+	0.815853i	−0.995679	−	0.0928603i	$-0.970399\pi$
$683$	−36.9303	+	21.3217i	−1.41310	+	0.815853i	−0.417420	+	0.908714i	$0.637066\pi$
$684$	5.28704	−	5.36733i	0.202155	−	0.205225i
$685$			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
$690$	47.8126	+	19.5939i	1.82019	+	0.745926i
$691$	−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
$693$	2.98845	+	7.35318i	0.113522	+	0.279324i
$694$	−27.5858			−1.04714
$695$	52.9399	+	30.5649i	2.00812	+	1.15939i
$696$	12.3613	+	5.06575i	0.468555	+	0.192017i
$697$	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	$0.983131\pi$
$702$	16.6902	+	2.00565i	0.629931	+	0.0756982i
$703$	0.297119	−	0.171542i	0.0112061	−	0.00646982i
$704$	−0.866025	+	0.500000i	−0.0326396	+	0.0188445i
$705$	−9.67280	−	71.3924i	−0.364299	−	2.68879i
$706$		−	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
$711$	12.2531	−	3.38238i	0.459528	−	0.126849i
$712$	5.77637	+	3.33499i	0.216479	+	0.124984i
$713$	−46.8562			−1.75478
$714$	−6.67157	+	1.71318i	−0.249677	+	0.0641142i
$715$	12.4592			0.465947
$716$	15.5742	+	8.99179i	0.582036	+	0.336039i
$717$	5.66110	−	13.8141i	0.211418	−	0.515897i
$718$	6.36556	+	11.0255i	0.237561	+	0.411467i
$719$	6.90047	−	11.9520i	0.257344	−	0.445733i	−0.708185	−	0.706026i	$-0.750486\pi$
$719$	6.90047	−	11.9520i	0.257344	−	0.445733i	0.965530	+	0.260293i	$0.0838193\pi$
$720$	−2.90611	+	11.1821i	−0.108304	+	0.416734i
$721$	1.04444	+	8.90993i	0.0388970	+	0.331823i
$722$			12.6932i			0.472393i
$723$	−15.1356	+	2.05069i	−0.562900	+	0.0762660i
$724$	14.1070	−	8.14467i	0.524282	−	0.302694i
$725$	65.6716	−	37.9155i	2.43898	−	1.40815i
$726$	−1.71637	+	0.232547i	−0.0637004	+	0.00863063i
$727$		−	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
$732$	5.65366	−	13.7959i	0.208965	−	0.509912i
$733$	−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
$735$	16.8000	+	43.5664i	0.619676	+	1.60697i
$736$	−7.74632			−0.285533
$737$	−8.99224	−	5.19167i	−0.331233	−	0.191238i
$738$	3.07431	+	11.1371i	0.113167	+	0.409961i
$739$	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	$-0.930827\pi$
$743$		−	11.7541i		−	0.431215i	0.976480	−	0.215608i	$-0.0691732\pi$
$744$	−1.40664	−	10.3820i	−0.0515699	−	0.380624i
$745$	−10.0267	+	5.78890i	−0.367349	+	0.212089i
$746$	−26.7209	+	15.4273i	−0.978321	+	0.564834i
$747$	18.5379	+	18.2606i	0.678265	+	0.668119i
$748$		−	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
$753$	16.6640	+	6.82899i	0.607268	+	0.248862i
$754$	21.6092	+	12.4761i	0.786962	+	0.454353i
$755$	47.4906			1.72836
$756$	−13.7477	−	0.0399519i	−0.499998	−	0.00145304i
$757$	−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
$759$	−12.4150	−	5.08773i	−0.450635	−	0.184673i
$760$	4.83582	+	8.37589i	0.175414	+	0.303825i
$761$	−2.58368	+	4.47507i	−0.0936584	+	0.162221i	−0.909048	−	0.416692i	$-0.863189\pi$
$761$	−2.58368	+	4.47507i	−0.0936584	+	0.162221i	0.815389	+	0.578913i	$0.196523\pi$
$762$	14.0452	+	18.1620i	0.508805	+	0.657939i
$763$	6.72713	−	15.6096i	0.243538	−	0.565105i
$764$			7.34096i			0.265587i
$765$	−12.3719	−	12.1868i	−0.447307	−	0.440615i
$766$	19.0996	−	11.0271i	0.690095	−	0.398427i
$767$	−9.41777	+	5.43735i	−0.340056	+	0.196331i
$768$	−0.232547	−	1.71637i	−0.00839132	−	0.0619341i
$769$			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	0.590674	−	0.806910i	$-0.298862\pi$
$773$	−11.2176	−	19.4294i	−0.403467	−	0.698826i	−0.994142	+	0.108084i	$0.965528\pi$
$774$	−5.76517	−	20.8851i	−0.207225	−	0.750698i
$775$	−51.5032	−	29.7354i	−1.85005	−	1.06813i
$776$	10.6767			0.383272
$777$	−0.602988	−	0.168338i	−0.0216321	−	0.00603909i
$778$	−21.3825			−0.766601
$779$	8.37589	+	4.83582i	0.300097	+	0.173261i
$780$	−8.18310	+	19.9682i	−0.293002	+	0.714978i
$781$	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
$786$	28.6185	−	3.87746i	1.02079	−	0.138304i
$787$	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
$789$	40.7228	−	5.51744i	1.44977	−	0.196426i
$790$			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
$795$	−26.2415	+	64.0340i	−0.930690	+	2.27105i
$796$	−1.58668	−	0.916069i	−0.0562383	−	0.0324692i
$797$	−7.40572			−0.262324			−0.131162	−	0.991361i	$-0.541871\pi$
$797$	−7.40572			−0.262324			−0.131162	+	0.991361i	$0.541871\pi$
$798$	−8.22217	+	8.05222i	−0.291062	+	0.285046i
$799$	−16.2342			−0.574324
$800$	−8.51456	−	4.91588i	−0.301035	−	0.173803i
$801$	−19.2885	+	5.32446i	−0.681527	+	0.188131i
$802$	−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
$807$	7.12969	+	52.6224i	0.250977	+	1.85240i
$808$	−7.50224	+	4.33142i	−0.263928	+	0.152379i
$809$	21.3465	−	12.3244i	0.750502	−	0.433302i	−0.0753734	−	0.997155i	$-0.524015\pi$
$809$	21.3465	−	12.3244i	0.750502	−	0.433302i	0.825875	+	0.563853i	$0.190682\pi$
$810$	−17.7809	−	29.7525i	−0.624755	−	1.04540i
$811$			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
$816$	2.40899	+	0.987219i	0.0843315	+	0.0345596i
$817$	−15.7071	−	9.06848i	−0.549521	−	0.317266i
$818$	−12.4884			−0.436648
$819$	−25.4355	−	3.52151i	−0.888789	−	0.123051i
$820$	−14.8318			−0.517948
$821$	18.3595	+	10.5999i	0.640753	+	0.369939i	0.784904	−	0.619617i	$-0.212712\pi$
$821$	18.3595	+	10.5999i	0.640753	+	0.369939i	−0.144152	+	0.989556i	$0.546045\pi$
$822$	21.0133	+	8.61139i	0.732924	+	0.300357i
$823$	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	$-0.882299\pi$
$827$		−	20.7860i		−	0.722799i	0.932411	−	0.361400i	$-0.117701\pi$
$828$	16.3081	−	16.5558i	0.566747	−	0.575354i
$829$	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
$831$	−0.461859	−	3.40886i	−0.0160217	−	0.118252i
$832$		−	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
$837$	25.1503	+	18.8507i	0.869323	+	0.651575i
$838$	−24.5799	−	14.1912i	−0.849100	−	0.490228i
$839$	34.6403			1.19592			0.597958	−	0.801527i	$-0.295979\pi$
$839$	34.6403			1.19592			0.597958	+	0.801527i	$0.295979\pi$
$840$	4.74551	−	16.9984i	0.163736	−	0.586502i
$841$	−30.4882			−1.05132
$842$	27.1266	+	15.6615i	0.934843	+	0.539732i
$843$	−0.549976	+	1.34204i	−0.0189422	+	0.0462223i
$844$	−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
$849$	−14.1321	+	1.91473i	−0.485013	+	0.0657134i
$850$	12.7981	−	7.38901i	0.438973	−	0.253441i
$851$	0.916478	−	0.529129i	0.0314165	−	0.0181383i
$852$	−1.47111	+	0.199317i	−0.0503993	+	0.00682849i
$853$			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	0.971536	−	0.236892i	$-0.0761288\pi$
$857$	8.21484	+	14.2285i	0.280613	+	0.486037i	−0.690923	+	0.722929i	$0.742795\pi$
$858$	2.12482	−	5.18494i	0.0725401	−	0.177011i
$859$	−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
$861$	−4.38949	−	17.0938i	−0.149594	−	0.582557i
$862$	−19.4337			−0.661915
$863$	6.04913	+	3.49247i	0.205915	+	0.118885i	0.599411	−	0.800441i	$-0.295401\pi$
$863$	6.04913	+	3.49247i	0.205915	+	0.118885i	−0.393497	+	0.919326i	$0.628735\pi$
$864$	4.15788	+	3.11642i	0.141454	+	0.106023i
$865$	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
$870$	−6.90753	−	50.9827i	−0.234187	−	1.72847i
$871$	29.0911	−	16.7958i	0.985716	−	0.569103i
$872$	−5.56372	+	3.21222i	−0.188411	+	0.108779i
$873$	−22.4774	+	22.8188i	−0.760746	+	0.772300i
$874$		−	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
$879$	2.81794	+	1.15481i	0.0950467	+	0.0389507i
$880$	3.33524	+	1.92560i	0.112431	+	0.0649120i
$881$	48.5223			1.63476			0.817379	−	0.576100i	$-0.195426\pi$
$881$	48.5223			1.63476			0.817379	+	0.576100i	$0.195426\pi$
$882$	20.9954	+	0.438540i	0.706953	+	0.0147664i
$883$	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
$885$	20.7477	+	8.50254i	0.697427	+	0.285810i
$886$	7.18373	+	12.4426i	0.241342	+	0.418017i
$887$	−3.50486	+	6.07060i	−0.117682	+	0.203831i	−0.918849	−	0.394610i	$-0.870880\pi$
$887$	−3.50486	+	6.07060i	−0.117682	+	0.203831i	0.801167	+	0.598441i	$0.204213\pi$
$888$	0.144753	+	0.187181i	0.00485760	+	0.00628139i
$889$	−20.9522	−	28.1241i	−0.702715	−	0.943252i
$890$		−	25.6874i		−	0.861045i
$891$	4.61696	+	7.72552i	0.154674	+	0.258815i
$892$	13.4956	−	7.79169i	0.451866	−	0.260885i
$893$	−23.4898	+	13.5619i	−0.786057	+	0.453830i
$894$	0.699102	+	5.15989i	0.0233815	+	0.172572i
$895$		−	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
$900$	28.4319	−	7.84843i	0.947731	−	0.261614i
$901$	13.5045	+	7.79684i	0.449901	+	0.259751i
$902$	3.85120			0.128231
$903$	8.23150	+	32.0556i	0.273927	+	1.06674i
$904$	9.69766			0.322539
$905$	−54.3289	−	31.3668i	−1.80595	−	1.04267i
$906$	8.09915	−	19.7634i	0.269076	−	0.656594i
$907$	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	$0.00516971\pi$
$911$			0.980362i			0.0324808i	−0.999868	+	0.0162404i	$0.994830\pi$
$912$	4.31037	−	0.584002i	0.142731	−	0.0193382i
$913$	7.51166	−	4.33686i	0.248600	−	0.143529i
$914$	−22.3698	+	12.9152i	−0.739927	+	0.427197i
$915$	−56.8994	+	7.70918i	−1.88104	+	0.254858i
$916$			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
$921$	7.22347	−	17.6266i	0.238021	−	0.580815i
$922$	−8.43726	−	4.87125i	−0.277866	−	0.160426i
$923$	−2.77285			−0.0912696
$924$	−1.23221	+	4.41380i	−0.0405369	+	0.145203i
$925$	1.34316			0.0441628
$926$	−16.6336	−	9.60343i	−0.546615	−	0.315588i
$927$	2.70670	+	9.80536i	0.0888997	+	0.322050i
$928$	3.85643	+	6.67953i	0.126594	+	0.219266i
$929$	−15.9871	+	27.6904i	−0.524519	+	0.908493i	0.475074	+	0.879946i	$0.342421\pi$
$929$	−15.9871	+	27.6904i	−0.524519	+	0.908493i	−0.999592	+	0.0285469i	$0.990912\pi$
$930$	−31.9179	+	24.6831i	−1.04663	+	0.809392i
$931$	12.7787	−	12.0722i	0.418804	−	0.395650i
$932$			1.97466i			0.0646821i
$933$	1.87005	+	13.8024i	0.0612227	+	0.451869i
$934$	−10.4096	+	6.00996i	−0.340611	+	0.196652i
$935$	−5.01316	+	2.89435i	−0.163948	+	0.0946554i
$936$	6.91429	+	6.81086i	0.226001	+	0.222620i
$937$		−	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	$0.0302713\pi$
$941$	17.7912	+	30.8152i	0.579976	+	1.00455i	−0.415506	+	0.909591i	$0.636395\pi$
$942$	−7.71971	−	3.16358i	−0.251522	−	0.103075i
$943$	25.8358	+	14.9163i	0.841331	+	0.485743i
$944$	−3.36143			−0.109405
$945$	26.3393	+	45.9287i	0.856817	+	1.49406i
$946$	−7.22205			−0.234809
$947$	−5.15342	−	2.97533i	−0.167464	−	0.0966852i	0.413926	−	0.910311i	$-0.364157\pi$
$947$	−5.15342	−	2.97533i	−0.167464	−	0.0966852i	−0.581389	+	0.813625i	$0.697491\pi$
$948$	6.79081	+	2.78292i	0.220555	+	0.0903849i
$949$	−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	$0.798311\pi$
$954$	22.1727	+	21.8410i	0.717868	+	0.707128i
$955$	24.4839	−	14.1358i	0.792279	−	0.457422i
$956$	7.46454	−	4.30965i	0.241420	−	0.139384i
$957$	1.79360	+	13.2381i	0.0579789	+	0.427927i
$958$			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
$963$	−13.0455	−	47.2589i	−0.420384	−	1.52290i
$964$	−7.63695	−	4.40920i	−0.245970	−	0.142011i
$965$	75.7379			2.43809
$966$	−25.3617	+	24.8375i	−0.815999	+	0.799133i
$967$	−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
$969$	−2.47923	+	6.04977i	−0.0796444	+	0.194347i
$970$	−20.5591	−	35.6095i	−0.660114	−	1.14335i
$971$	12.1392	−	21.0257i	0.389566	−	0.674748i	−0.602825	−	0.797873i	$-0.705958\pi$
$971$	12.1392	−	21.0257i	0.389566	−	0.674748i	0.992391	+	0.123125i	$0.0392917\pi$
$972$	−15.4140	+	2.32550i	−0.494405	+	0.0745905i
$973$	−33.6774	+	25.0894i	−1.07965	+	0.804328i
$974$			15.8825i			0.508907i
$975$	54.5928	−	7.39665i	1.74837	−	0.236883i
$976$	7.45472	−	4.30399i	0.238620	−	0.137767i
$977$	−25.7446	+	14.8637i	−0.823643	+	0.475530i	−0.851671	−	0.524077i	$-0.824410\pi$
$977$	−25.7446	+	14.8637i	−0.823643	+	0.475530i	0.0280284	+	0.999607i	$0.491077\pi$
$978$	−24.9475	+	3.38008i	−0.797732	+	0.108083i
$979$			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	$-0.0482823\pi$
$983$	11.3936	+	19.7344i	0.363401	+	0.629428i	−0.625118	+	0.780531i	$0.714949\pi$
$984$	−2.52944	+	6.17229i	−0.0806357	+	0.196766i
$985$	−76.1914	−	43.9891i	−2.42766	−	1.40161i
$986$	−11.5931			−0.369200
$987$	47.6714	+	13.3086i	1.51740	+	0.423616i
$988$	8.12451			0.258475
$989$	−48.4492	−	27.9722i	−1.54060	−	0.889464i
$990$	−11.1371	+	3.07431i	−0.353960	+	0.0977080i
$991$	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
$996$	2.01705	+	14.8873i	0.0639126	+	0.471722i
$997$	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
$999$	−0.704798	−	0.0846948i	−0.0222988	−	0.00267963i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.60269 + 0.656793i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.92560 - 3.33524i) q^{5} +(-1.05958 - 1.37015i) q^{6} +(1.58064 + 2.12169i) q^{7} -1.00000i q^{8} +(2.13725 + 2.10527i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.60269 + 0.656793i) 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} +(2.13725 + 2.10527i) q^{9} +(-3.33524 + 1.92560i) q^{10} +(0.866025 - 0.500000i) q^{11} +(0.232547 + 1.71637i) 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} +(-0.798273 - 2.89184i) q^{18} +(-2.17488 - 1.25567i) q^{19} +3.85120 q^{20} +(1.13977 + 4.43857i) q^{21} -1.00000 q^{22} +(-6.70851 - 3.87316i) q^{23} +(0.656793 - 1.60269i) 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} +(-6.61008 + 0.895586i) q^{30} +(5.23845 - 3.02442i) q^{31} +(0.866025 - 0.500000i) q^{32} +(1.71637 - 0.232547i) 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} +(-2.12482 + 5.18494i) q^{39} +(-3.33524 - 1.92560i) q^{40} -3.85120 q^{41} +(1.23221 - 4.41380i) q^{42} +7.22205 q^{43} +(0.866025 + 0.500000i) q^{44} +(11.1371 - 3.07431i) 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} +(-0.349539 - 2.57986i) q^{51} +(-2.80171 + 1.61757i) q^{52} +(-8.98451 + 5.18721i) q^{53} +(0.619956 - 5.15904i) 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} +(6.17229 + 2.52944i) q^{60} +(-7.45472 - 4.30399i) q^{61} -6.04884 q^{62} +(-1.08852 + 7.86226i) q^{63} -1.00000 q^{64} +(10.7900 + 6.22959i) q^{65} +(-1.60269 - 0.656793i) 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} +(2.10527 - 2.13725i) q^{72} +(-2.12908 + 1.22922i) q^{73} +(0.118311 - 0.0683071i) q^{74} +(-2.28635 - 16.8749i) 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} +(0.135645 + 8.99898i) q^{81} +(3.33524 + 1.92560i) q^{82} +8.67372 q^{83} +(-3.27403 + 3.20636i) q^{84} -5.78870 q^{85} +(-6.25448 - 3.61103i) q^{86} +(-5.06575 + 12.3613i) 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} +(10.3820 - 1.40664i) q^{93} +(-9.35353 + 5.40027i) q^{94} +(-8.37589 + 4.83582i) q^{95} +(1.71637 - 0.232547i) 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