LMFDB - Embedded newform 462.2.k.g.353.5

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			353.5
Root			$-0.232547 + 1.71637i$ of defining polynomial
Character	$\chi$	$=$	462.353
Dual form			462.2.k.g.89.5

$q$-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} +(-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} - 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}+ \cdots - 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

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
$3$	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	0.870815	+	0.491611i	$0.163592\pi$
$5$	1.92560	+	3.33524i	0.861155	+	1.49156i	−0.00965972	+	0.999953i	$0.503075\pi$
$6$	−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	$-0.851911\pi$
$13$		−	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	−0.942655	−	0.333768i	$-0.891680\pi$
$17$	−0.751545	+	1.30171i	−0.182276	+	0.315712i	0.760379	+	0.649480i	$0.225013\pi$
$18$	−0.798273	+	2.89184i	−0.188155	+	0.681614i
$19$	−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
$21$	1.13977	−	4.43857i	0.248719	−	0.968576i
$22$	−1.00000			−0.213201
$23$	−6.70851	+	3.87316i	−1.39882	+	0.807610i	−0.994269	−	0.106905i	$-0.965906\pi$
$23$	−6.70851	+	3.87316i	−1.39882	+	0.807610i	−0.404552	+	0.914515i	$0.632573\pi$
$24$	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	$-0.745916\pi$
$29$		−	7.71286i		−	1.43224i	0.697976	−	0.716121i	$-0.254084\pi$
$30$	−6.61008	−	0.895586i	−1.20683	−	0.163511i
$31$	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
$33$	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	0.860356	−	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
$39$	−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	0.927367	+	0.374153i	$0.122067\pi$
$47$	5.40027	+	9.35353i	0.787710	+	1.36435i	−0.139657	+	0.990200i	$0.544600\pi$
$48$	−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	−0.266232	−	0.963909i	$-0.585779\pi$
$53$	−8.98451	−	5.18721i	−1.23412	−	0.712518i	−0.967886	+	0.251391i	$0.919112\pi$
$54$	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	−0.735634	−	0.677379i	$-0.763116\pi$
$59$	1.68071	−	2.91108i	0.218810	−	0.378991i	0.954445	+	0.298388i	$0.0964490\pi$
$60$	6.17229	−	2.52944i	0.796840	−	0.326550i
$61$	−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
$63$	−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	0.352407	+	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	$-0.983804\pi$
$71$		−	0.857105i		−	0.101720i	0.998706	−	0.0508598i	$-0.0161962\pi$
$72$	2.10527	+	2.13725i	0.248109	+	0.251877i
$73$	−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
$75$	−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	0.960243	−	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
$81$	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	0.633353	−	0.773863i	$-0.281678\pi$
$89$	−3.33499	−	5.77637i	−0.353508	−	0.612294i	−0.986861	+	0.161569i	$0.948345\pi$
$90$	−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	$-0.817656\pi$
$97$		−	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	−0.996959	−	0.0779275i	$-0.975170\pi$
$101$	−4.33142	+	7.50224i	−0.430992	+	0.746501i	0.565967	+	0.824428i	$0.308503\pi$
$102$	−0.987219	−	2.40899i	−0.0977492	−	0.238526i
$103$	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
$105$	16.9984	−	4.74551i	1.65888	−	0.463114i
$106$	10.3744			1.00765
$107$	−14.1527	+	8.17106i	−1.36819	+	0.789926i	−0.990697	−	0.136085i	$-0.956548\pi$
$107$	−14.1527	+	8.17106i	−1.36819	+	0.789926i	−0.377495	+	0.926012i	$0.623215\pi$
$108$	−3.11642	−	4.15788i	−0.299877	−	0.400092i
$109$	−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	$-0.849232\pi$
$113$		−	9.69766i		−	0.912279i	0.889908	−	0.456140i	$-0.150768\pi$
$114$	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	−0.957559	−	0.288238i	$-0.906930\pi$
$131$	−8.33693	−	14.4400i	−0.728401	−	1.26163i	0.229158	−	0.973389i	$-0.426403\pi$
$132$	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	−0.0708312	−	0.997488i	$-0.522565\pi$
$137$	−11.3547	−	6.55564i	−0.970097	−	0.560086i	−0.899266	+	0.437402i	$0.855899\pi$
$138$	1.80138	−	13.2955i	0.153344	−	1.13179i
$139$		−	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
$144$	−2.89184	−	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	−0.602839	−	0.797863i	$-0.705964\pi$
$149$	−2.60352	+	1.50314i	−0.213288	+	0.123142i	0.389550	+	0.921005i	$0.372630\pi$
$150$	−6.45743	−	15.7573i	−0.527247	−	1.28658i
$151$	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
$156$	−5.55269	−	0.752322i	−0.444571	−	0.0602340i
$157$	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
$159$	−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	0.996642	+	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
$165$	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	0.846122	−	0.532989i	$-0.178931\pi$
$173$	−0.506658	−	0.877558i	−0.0385205	−	0.0667195i	−0.884643	+	0.466269i	$0.845598\pi$
$174$	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	0.952277	−	0.305236i	$-0.0987354\pi$
$179$	15.5742	+	8.99179i	1.16407	+	0.672078i	0.211796	+	0.977314i	$0.432069\pi$
$180$	8.23097	−	8.10784i	0.613500	−	0.604322i
$181$			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
$186$	−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	−0.252039	−	0.967717i	$-0.581101\pi$
$191$	6.35746	−	3.67048i	0.460009	−	0.265587i	0.712048	+	0.702131i	$0.247768\pi$
$192$	−1.60269	+	0.656793i	−0.115664	+	0.0473999i
$193$	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	$0.302603\pi$
$197$			22.8444i			1.62759i	−0.581150	+	0.813797i	$0.697397\pi$
$198$	−2.13725	+	2.10527i	−0.151887	+	0.149615i
$199$	−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
$201$	−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	$0.174728\pi$
$223$			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	−0.540674	−	0.841232i	$-0.681831\pi$
$227$	6.90336	−	11.9570i	0.458192	−	0.793612i	0.998865	+	0.0476209i	$0.0151639\pi$
$228$	1.64942	+	4.02489i	0.109236	+	0.266555i
$229$	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
$231$	3.20636	−	3.27403i	0.210963	−	0.215415i
$232$	7.71286			0.506374
$233$	1.71010	−	0.987329i	0.112033	−	0.0646821i	−0.442937	−	0.896553i	$-0.646063\pi$
$233$	1.71010	−	0.987329i	0.112033	−	0.0646821i	0.554969	+	0.831871i	$0.312730\pi$
$234$	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	$0.0899261\pi$
$239$			8.61931i			0.557536i	−0.960358	+	0.278768i	$0.910074\pi$
$240$	0.895586	−	6.61008i	0.0578098	−	0.426679i
$241$	−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
$243$	−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	0.614236	−	0.789122i	$-0.289464\pi$
$257$	−6.03225	−	10.4482i	−0.376282	−	0.651739i	−0.990518	+	0.137383i	$0.956131\pi$
$258$	−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	0.974421	−	0.224730i	$-0.0721501\pi$
$263$	20.5474	+	11.8631i	1.26701	+	0.731508i	0.292588	+	0.956239i	$0.405483\pi$
$264$	−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	0.159422	−	0.987210i	$-0.449037\pi$
$269$	15.3296	−	26.5516i	0.934661	−	1.61888i	0.775238	−	0.631669i	$-0.217630\pi$
$270$	−16.0128	+	12.0019i	−0.974510	+	0.730415i
$271$	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
$273$	−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	−0.894316	−	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	$-0.992049\pi$
$281$		−	0.837366i		−	0.0499531i	0.999688	−	0.0249765i	$-0.00795110\pi$
$282$	−18.5377	−	2.51163i	−1.10390	−	0.149565i
$283$	−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
$285$	−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	$0.101618\pi$
$307$			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	−0.729216	−	0.684283i	$-0.760115\pi$
$311$	4.02080	−	6.96424i	0.227999	−	0.394906i	0.957215	+	0.289378i	$0.0934484\pi$
$312$	5.18494	−	2.12482i	0.293539	−	0.120294i
$313$	−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
$315$	24.1265	−	18.7700i	1.35937	−	1.05757i
$316$	4.23713			0.238357
$317$	−7.12754	+	4.11509i	−0.400323	+	0.231126i	−0.686623	−	0.727013i	$-0.740908\pi$
$317$	−7.12754	+	4.11509i	−0.400323	+	0.231126i	0.286301	+	0.958140i	$0.407574\pi$
$318$	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	0.652458	−	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
$333$	−0.395067	−	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	0.977301	−	0.211854i	$-0.0679503\pi$
$347$	23.8900	+	13.7929i	1.28248	+	0.740440i	0.305179	+	0.952295i	$0.401284\pi$
$348$	−13.2381	−	1.79360i	−0.709637	−	0.0961472i
$349$			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	−0.590008	−	0.807398i	$-0.700875\pi$
$353$	7.59466	−	13.1543i	0.404223	−	0.700134i	0.994231	+	0.107263i	$0.0342087\pi$
$354$	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	−0.761889	−	0.647708i	$-0.775728\pi$
$359$	−11.0255	+	6.36556i	−0.581902	+	0.335962i	0.179987	+	0.983669i	$0.442395\pi$
$360$	−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	0.208900	−	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
$369$	−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	0.920401	+	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
$375$	−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	−0.997191	−	0.0748992i	$-0.976136\pi$
$383$	−11.0271	−	19.0996i	−0.563460	−	0.975942i	0.433731	−	0.901042i	$-0.357197\pi$
$384$	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	0.889613	−	0.456716i	$-0.150974\pi$
$389$	18.5178	+	10.6913i	0.938891	+	0.542069i	0.0492785	+	0.998785i	$0.484308\pi$
$390$	−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	−0.807087	−	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
$399$	3.09450	+	11.0845i	0.154919	+	0.554920i
$400$	9.83176			0.491588
$401$	18.5573	−	10.7141i	0.926707	−	0.535034i	0.0409384	−	0.999162i	$-0.486965\pi$
$401$	18.5573	−	10.7141i	0.926707	−	0.535034i	0.885769	+	0.464127i	$0.153632\pi$
$402$	−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	0.742962	−	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
$411$	−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	0.847191	−	0.531289i	$-0.178292\pi$
$431$	16.8301	+	9.71686i	0.810677	+	0.468045i	−0.0365139	+	0.999333i	$0.511625\pi$
$432$	−5.15904	+	0.619956i	−0.248214	+	0.0298277i
$433$			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
$438$	3.94013	−	1.61469i	0.188267	−	0.0771529i
$439$	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
$441$	−18.4018	−	10.1179i	−0.876278	−	0.481806i
$442$	−4.86271			−0.231295
$443$	−12.4426	+	7.18373i	−0.591165	+	0.341309i	−0.765558	−	0.643367i	$-0.777537\pi$
$443$	−12.4426	+	7.18373i	−0.591165	+	0.341309i	0.174393	+	0.984676i	$0.444204\pi$
$444$	−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	$-0.993543\pi$
$449$		−	0.859617i		−	0.0405678i	0.999794	−	0.0202839i	$-0.00645701\pi$
$450$	−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	0.992186	+	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
$459$	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	0.970914	−	0.239427i	$-0.0769594\pi$
$467$	6.00996	+	10.4096i	0.278108	+	0.481697i	−0.692807	+	0.721123i	$0.743626\pi$
$468$	−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	−0.960375	−	0.278712i	$-0.910092\pi$
$479$	−5.22673	+	9.05296i	−0.238815	+	0.413640i	0.721559	+	0.692353i	$0.243426\pi$
$480$	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	−0.987936	−	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	$0.121483\pi$
$491$			16.5060i			0.744907i	−0.928051	+	0.372454i	$0.878517\pi$
$492$	−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	−0.945139	−	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
$501$	−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	−0.994667	−	0.103141i	$-0.967111\pi$
$509$	−13.2356	−	22.9247i	−0.586656	−	1.01612i	0.408010	−	0.912977i	$-0.366223\pi$
$510$	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	−0.747449	−	0.664320i	$-0.768721\pi$
$521$	4.60146	−	7.96995i	0.201593	−	0.349170i	0.949042	+	0.315150i	$0.102055\pi$
$522$	22.3044	+	6.15697i	0.976236	+	0.269483i
$523$	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
$525$	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	0.985995	−	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
$543$	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	0.844256	−	0.535940i	$-0.180043\pi$
$557$	18.9337	+	10.9314i	0.802246	+	0.463177i	−0.0420097	+	0.999117i	$0.513376\pi$
$558$	−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	−0.942509	−	0.334182i	$-0.891540\pi$
$563$	−4.31473	+	7.47333i	−0.181844	+	0.314963i	0.760664	+	0.649145i	$0.224873\pi$
$564$	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	−0.376557	−	0.926393i	$-0.622892\pi$
$569$	5.66393	−	3.27007i	0.237444	−	0.137088i	0.614001	+	0.789305i	$0.289559\pi$
$570$	15.5007	−	6.35226i	0.649251	−	0.266067i
$571$	−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
$576$	−2.13725	+	2.10527i	−0.0890519	+	0.0877197i
$577$	−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
$579$	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	0.881526	−	0.472135i	$-0.156517\pi$
$593$	0.776378	+	1.34473i	0.0318820	+	0.0552213i	−0.849644	+	0.527356i	$0.823183\pi$
$594$	−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	0.885673	−	0.464310i	$-0.153698\pi$
$599$	22.6733	+	13.0904i	0.926405	+	0.534860i	0.0407320	+	0.999170i	$0.487031\pi$
$600$	−16.8749	−	2.28635i	−0.688916	−	0.0933397i
$601$			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
$606$	−5.68969	−	13.8839i	−0.231128	−	0.563994i
$607$	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
$609$	−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	0.339922	+	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	$-0.923033\pi$
$617$		−	11.8955i		−	0.478896i	0.970909	−	0.239448i	$-0.0769665\pi$
$618$	−0.788496	+	5.81968i	−0.0317180	+	0.234102i
$619$	−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
$621$	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	−0.0248034	−	0.999692i	$-0.507896\pi$
$641$	−22.8612	−	13.1989i	−0.902964	−	0.521327i	−0.878161	+	0.478366i	$0.841229\pi$
$642$	3.80031	−	28.0491i	0.149986	−	1.10701i
$643$		−	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	−0.986040	−	0.166507i	$-0.946751\pi$
$647$	−8.87268	+	15.3679i	−0.348821	+	0.604176i	0.637219	+	0.770683i	$0.280085\pi$
$648$	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	−0.674315	−	0.738444i	$-0.735561\pi$
$653$	−9.50503	+	5.48773i	−0.371961	+	0.214751i	0.302354	+	0.953196i	$0.402227\pi$
$654$	−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	$-0.898496\pi$
$659$		−	16.0960i		−	0.627012i	0.949586	−	0.313506i	$-0.101504\pi$
$660$	6.61008	+	0.895586i	0.257297	+	0.0348606i
$661$	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
$663$	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	0.990871	+	0.134816i	$0.0430443\pi$
$677$	15.9287	+	27.5893i	0.612189	+	1.06034i	−0.378681	+	0.925527i	$0.623622\pi$
$678$	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	−0.417420	−	0.908714i	$-0.637066\pi$
$683$	−36.9303	−	21.3217i	−1.41310	−	0.815853i	−0.995679	+	0.0928603i	$0.970399\pi$
$684$	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	−0.600764	−	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
$693$	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	$-0.983131\pi$
$701$		−	2.80501i		−	0.105944i	0.998596	−	0.0529719i	$-0.0168694\pi$
$702$	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	0.987794	−	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
$711$	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	0.965530	−	0.260293i	$-0.0838193\pi$
$719$	6.90047	+	11.9520i	0.257344	+	0.445733i	−0.708185	+	0.706026i	$0.750486\pi$
$720$	−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	$0.0788344\pi$
$727$			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
$732$	5.65366	+	13.7959i	0.208965	+	0.509912i
$733$	−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
$735$	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	−0.705516	−	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	$0.0691732\pi$
$743$			11.7541i			0.431215i	−0.976480	+	0.215608i	$0.930827\pi$
$744$	−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	0.955600	+	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
$753$	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	0.815389	−	0.578913i	$-0.196523\pi$
$761$	−2.58368	−	4.47507i	−0.0936584	−	0.162221i	−0.909048	+	0.416692i	$0.863189\pi$
$762$	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	$-0.858509\pi$
$769$		−	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	−0.994142	−	0.108084i	$-0.965528\pi$
$773$	−11.2176	+	19.4294i	−0.403467	+	0.698826i	0.590674	+	0.806910i	$0.298862\pi$
$774$	−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	0.966657	−	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
$789$	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	0.825875	−	0.563853i	$-0.190682\pi$
$809$	21.3465	+	12.3244i	0.750502	+	0.433302i	−0.0753734	+	0.997155i	$0.524015\pi$
$810$	−17.7809	+	29.7525i	−0.624755	+	1.04540i
$811$		−	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
$816$	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	−0.144152	−	0.989556i	$-0.546045\pi$
$821$	18.3595	−	10.5999i	0.640753	−	0.369939i	0.784904	+	0.619617i	$0.212712\pi$
$822$	21.0133	−	8.61139i	0.732924	−	0.300357i
$823$	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	$0.117701\pi$
$827$			20.7860i			0.722799i	−0.932411	+	0.361400i	$0.882299\pi$
$828$	16.3081	+	16.5558i	0.566747	+	0.575354i
$829$	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
$831$	−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	$-0.779832\pi$
$853$		−	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	−0.690923	−	0.722929i	$-0.742795\pi$
$857$	8.21484	−	14.2285i	0.280613	−	0.486037i	0.971536	+	0.236892i	$0.0761288\pi$
$858$	2.12482	+	5.18494i	0.0725401	+	0.177011i
$859$	−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
$861$	−4.38949	+	17.0938i	−0.149594	+	0.582557i
$862$	−19.4337			−0.661915
$863$	6.04913	−	3.49247i	0.205915	−	0.118885i	−0.393497	−	0.919326i	$-0.628735\pi$
$863$	6.04913	−	3.49247i	0.205915	−	0.118885i	0.599411	+	0.800441i	$0.295401\pi$
$864$	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	0.709520	−	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
$879$	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	0.801167	−	0.598441i	$-0.204213\pi$
$887$	−3.50486	−	6.07060i	−0.117682	−	0.203831i	−0.918849	+	0.394610i	$0.870880\pi$
$888$	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	−0.863786	−	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	$-0.994830\pi$
$911$		−	0.980362i		−	0.0324808i	0.999868	−	0.0162404i	$-0.00516971\pi$
$912$	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	−0.613084	−	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
$921$	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	−0.999592	−	0.0285469i	$-0.990912\pi$
$929$	−15.9871	−	27.6904i	−0.524519	−	0.908493i	0.475074	−	0.879946i	$-0.342421\pi$
$930$	−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	$0.170846\pi$
$937$			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	$-0.636395\pi$
$941$	17.7912	−	30.8152i	0.579976	−	1.00455i	0.995481	−	0.0949568i	$-0.0302713\pi$
$942$	−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	−0.581389	−	0.813625i	$-0.697491\pi$
$947$	−5.15342	+	2.97533i	−0.167464	+	0.0966852i	0.413926	+	0.910311i	$0.364157\pi$
$948$	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	$-0.798311\pi$
$953$		−	36.5553i		−	1.18414i	0.805886	−	0.592070i	$-0.201689\pi$
$954$	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	0.992391	−	0.123125i	$-0.0392917\pi$
$971$	12.1392	+	21.0257i	0.389566	+	0.674748i	−0.602825	+	0.797873i	$0.705958\pi$
$972$	−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	0.0280284	−	0.999607i	$-0.491077\pi$
$977$	−25.7446	−	14.8637i	−0.823643	−	0.475530i	−0.851671	+	0.524077i	$0.824410\pi$
$978$	−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	−0.625118	−	0.780531i	$-0.714949\pi$
$983$	11.3936	−	19.7344i	0.363401	−	0.629428i	0.988518	+	0.151102i	$0.0482823\pi$
$984$	−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	−0.763980	−	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
$996$	2.01705	−	14.8873i	0.0639126	−	0.471722i
$997$	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
$999$	−0.704798	+	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.353.5	yes	20
3.2	odd	2	inner	462.2.k.g.353.9	yes	20
7.5	odd	6	inner	462.2.k.g.89.9	yes	20
21.5	even	6	inner	462.2.k.g.89.5	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.k.g.89.5	✓	20	21.5	even	6	inner
462.2.k.g.89.9	yes	20	7.5	odd	6	inner
462.2.k.g.353.5	yes	20	1.1	even	1	trivial
462.2.k.g.353.9	yes	20	3.2	odd	2	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} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{3} + 10 q^{4} - 6 q^{7} - 2 q^{9} - 18 q^{10} - 6 q^{12} - 8 q^{15} - 10 q^{16} + 4 q^{18} + 36 q^{19} + 24 q^{21} - 20 q^{22} - 12 q^{25} - 22 q^{30} + 36 q^{31} - 4 q^{36} + 16 q^{37} + 4 q^{39}+ \cdots - 8 q^{99}+O(q^{100}) \) 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

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