LMFDB - Embedded newform 462.2.k.f.353.2

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			353.2
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	462.353
Dual form			462.2.k.f.89.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(1.70711 + 0.292893i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.241181 + 0.417738i) q^{5} +(-1.62484 + 0.599900i) q^{6} +(1.48356 + 2.19067i) q^{7} +1.00000i q^{8} +(2.82843 + 1.00000i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(1.70711 + 0.292893i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.241181 + 0.417738i) q^{5} +(-1.62484 + 0.599900i) q^{6} +(1.48356 + 2.19067i) q^{7} +1.00000i q^{8} +(2.82843 + 1.00000i) q^{9} +(-0.417738 - 0.241181i) q^{10} +(-0.866025 - 0.500000i) q^{11} +(1.10721 - 1.33195i) q^{12} +0.550510i q^{13} +(-2.38014 - 1.15539i) q^{14} +(0.289369 + 0.783763i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.926868 + 1.60538i) q^{17} +(-2.94949 + 0.548188i) q^{18} +(-0.334273 + 0.192993i) q^{19} +0.482362 q^{20} +(1.89097 + 4.17423i) q^{21} +1.00000 q^{22} +(0.216237 - 0.124844i) q^{23} +(-0.292893 + 1.70711i) q^{24} +(2.38366 - 4.12863i) q^{25} +(-0.275255 - 0.476756i) q^{26} +(4.53553 + 2.53553i) q^{27} +(2.63896 - 0.189469i) q^{28} +4.48477i q^{29} +(-0.642483 - 0.534074i) q^{30} +(1.08018 + 0.623642i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.33195 - 1.10721i) q^{33} -1.85374i q^{34} +(-0.557318 + 1.14809i) q^{35} +(2.28024 - 1.94949i) q^{36} +(-2.72853 - 4.72595i) q^{37} +(0.192993 - 0.334273i) q^{38} +(-0.161241 + 0.939780i) q^{39} +(-0.417738 + 0.241181i) q^{40} +5.67387 q^{41} +(-3.72474 - 2.66951i) q^{42} -0.682163 q^{43} +(-0.866025 + 0.500000i) q^{44} +(0.264425 + 1.42272i) q^{45} +(-0.124844 + 0.216237i) q^{46} +(-4.41421 - 7.64564i) q^{47} +(-0.599900 - 1.62484i) q^{48} +(-2.59808 + 6.50000i) q^{49} +4.76733i q^{50} +(-2.05247 + 2.46909i) q^{51} +(0.476756 + 0.275255i) q^{52} +(6.54441 + 3.77841i) q^{53} +(-5.19565 + 0.0719302i) q^{54} -0.482362i q^{55} +(-2.19067 + 1.48356i) q^{56} +(-0.627167 + 0.231553i) q^{57} +(-2.24238 - 3.88392i) q^{58} +(-1.82465 + 3.16038i) q^{59} +(0.823443 + 0.141281i) q^{60} +(-7.63593 + 4.40861i) q^{61} -1.24728 q^{62} +(2.00548 + 7.67972i) q^{63} -1.00000 q^{64} +(-0.229969 + 0.132773i) q^{65} +(1.70711 + 0.292893i) q^{66} +(4.35690 - 7.54636i) q^{67} +(0.926868 + 1.60538i) q^{68} +(0.405706 - 0.149788i) q^{69} +(-0.0913925 - 1.27293i) q^{70} +5.76028i q^{71} +(-1.00000 + 2.82843i) q^{72} +(-1.94534 - 1.12314i) q^{73} +(4.72595 + 2.72853i) q^{74} +(5.27841 - 6.34985i) q^{75} +0.385986i q^{76} +(-0.189469 - 2.63896i) q^{77} +(-0.330251 - 0.894494i) q^{78} +(-6.71587 - 11.6322i) q^{79} +(0.241181 - 0.417738i) q^{80} +(7.00000 + 5.65685i) q^{81} +(-4.91372 + 2.83694i) q^{82} +6.48941 q^{83} +(4.56048 + 0.449490i) q^{84} -0.894171 q^{85} +(0.590770 - 0.341081i) q^{86} +(-1.31356 + 7.65597i) q^{87} +(0.500000 - 0.866025i) q^{88} +(-5.64394 - 9.77559i) q^{89} +(-0.940360 - 1.09990i) q^{90} +(-1.20599 + 0.816717i) q^{91} -0.249689i q^{92} +(1.66132 + 1.38100i) q^{93} +(7.64564 + 4.41421i) q^{94} +(-0.161241 - 0.0930924i) q^{95} +(1.33195 + 1.10721i) q^{96} -16.8389i q^{97} +(-1.00000 - 6.92820i) q^{98} +(-1.94949 - 2.28024i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{3} + 4 q^{4} + 4 q^{5} - 4 q^{6}+O(q^{10}) $ 8 * q + 8 * q^3 + 4 * q^4 + 4 * q^5 - 4 * q^6	$ 8 q + 8 q^{3} + 4 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{12} - 4 q^{16} - 20 q^{17} - 4 q^{18} - 12 q^{19} + 8 q^{20} + 8 q^{22} + 12 q^{23} - 8 q^{24} + 8 q^{25} - 12 q^{26} + 8 q^{27} + 8 q^{30} + 12 q^{31} + 4 q^{33} - 16 q^{35} + 8 q^{38} - 24 q^{39} - 40 q^{41} - 20 q^{42} - 8 q^{43} + 8 q^{45} + 8 q^{46} - 24 q^{47} - 4 q^{48} - 4 q^{51} + 60 q^{53} + 4 q^{54} - 20 q^{57} - 4 q^{58} - 4 q^{59} + 12 q^{60} - 36 q^{61} - 24 q^{62} - 8 q^{63} - 8 q^{64} + 12 q^{65} + 8 q^{66} + 12 q^{67} + 20 q^{68} + 12 q^{69} - 20 q^{70} - 8 q^{72} + 48 q^{73} + 12 q^{74} + 4 q^{75} - 8 q^{79} + 4 q^{80} + 56 q^{81} - 24 q^{82} + 72 q^{83} - 32 q^{85} - 12 q^{86} - 16 q^{87} + 4 q^{88} + 4 q^{89} + 28 q^{90} + 36 q^{91} - 20 q^{93} - 24 q^{95} - 4 q^{96} - 8 q^{98} + 4 q^{99}+O(q^{100}) $ 8 * q + 8 * q^3 + 4 * q^4 + 4 * q^5 - 4 * q^6 + 4 * q^12 - 4 * q^16 - 20 * q^17 - 4 * q^18 - 12 * q^19 + 8 * q^20 + 8 * q^22 + 12 * q^23 - 8 * q^24 + 8 * q^25 - 12 * q^26 + 8 * q^27 + 8 * q^30 + 12 * q^31 + 4 * q^33 - 16 * q^35 + 8 * q^38 - 24 * q^39 - 40 * q^41 - 20 * q^42 - 8 * q^43 + 8 * q^45 + 8 * q^46 - 24 * q^47 - 4 * q^48 - 4 * q^51 + 60 * q^53 + 4 * q^54 - 20 * q^57 - 4 * q^58 - 4 * q^59 + 12 * q^60 - 36 * q^61 - 24 * q^62 - 8 * q^63 - 8 * q^64 + 12 * q^65 + 8 * q^66 + 12 * q^67 + 20 * q^68 + 12 * q^69 - 20 * q^70 - 8 * q^72 + 48 * q^73 + 12 * q^74 + 4 * q^75 - 8 * q^79 + 4 * q^80 + 56 * q^81 - 24 * q^82 + 72 * q^83 - 32 * q^85 - 12 * q^86 - 16 * q^87 + 4 * q^88 + 4 * q^89 + 28 * q^90 + 36 * q^91 - 20 * q^93 - 24 * q^95 - 4 * q^96 - 8 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	1.70711	+	0.292893i	0.985599	+	0.169102i
$3$	1.70711	+	0.292893i	0.985599	+	0.169102i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.241181	+	0.417738i	0.107859	+	0.186818i	0.914903	−	0.403674i	$-0.132267\pi$
$5$	0.241181	+	0.417738i	0.107859	+	0.186818i	−0.807043	+	0.590492i	$0.798934\pi$
$6$	−1.62484	+	0.599900i	−0.663340	+	0.244908i
$7$	1.48356	+	2.19067i	0.560734	+	0.827996i
$7$	1.48356	+	2.19067i	0.560734	+	0.827996i
$8$			1.00000i			0.353553i
$9$	2.82843	+	1.00000i	0.942809	+	0.333333i
$10$	−0.417738	−	0.241181i	−0.132100	−	0.0762681i
$11$	−0.866025	−	0.500000i	−0.261116	−	0.150756i
$11$	−0.866025	−	0.500000i	−0.261116	−	0.150756i
$12$	1.10721	−	1.33195i	0.319623	−	0.384501i
$13$			0.550510i			0.152684i	0.997082	+	0.0763420i	$0.0243241\pi$
$13$			0.550510i			0.152684i	−0.997082	+	0.0763420i	$0.975676\pi$
$14$	−2.38014	−	1.15539i	−0.636119	−	0.308792i
$15$	0.289369	+	0.783763i	0.0747148	+	0.202367i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.926868	+	1.60538i	−0.224798	+	0.389362i	−0.956259	−	0.292521i	$-0.905506\pi$
$17$	−0.926868	+	1.60538i	−0.224798	+	0.389362i	0.731460	+	0.681884i	$0.238839\pi$
$18$	−2.94949	+	0.548188i	−0.695201	+	0.129209i
$19$	−0.334273	+	0.192993i	−0.0766876	+	0.0442756i	−0.537853	−	0.843038i	$-0.680765\pi$
$19$	−0.334273	+	0.192993i	−0.0766876	+	0.0442756i	0.461166	+	0.887314i	$0.347431\pi$
$20$	0.482362			0.107859
$21$	1.89097	+	4.17423i	0.412643	+	0.910893i
$22$	1.00000			0.213201
$23$	0.216237	−	0.124844i	0.0450885	−	0.0260319i	−0.477286	−	0.878748i	$-0.658380\pi$
$23$	0.216237	−	0.124844i	0.0450885	−	0.0260319i	0.522375	+	0.852716i	$0.325046\pi$
$24$	−0.292893	+	1.70711i	−0.0597866	+	0.348462i
$25$	2.38366	−	4.12863i	0.476733	−	0.825725i
$26$	−0.275255	−	0.476756i	−0.0539820	−	0.0934995i
$27$	4.53553	+	2.53553i	0.872864	+	0.487964i
$28$	2.63896	−	0.189469i	0.498716	−	0.0358062i
$29$			4.48477i			0.832800i	0.909181	+	0.416400i	$0.136708\pi$
$29$			4.48477i			0.832800i	−0.909181	+	0.416400i	$0.863292\pi$
$30$	−0.642483	−	0.534074i	−0.117301	−	0.0975082i
$31$	1.08018	+	0.623642i	0.194006	+	0.112009i	0.593857	−	0.804571i	$-0.297605\pi$
$31$	1.08018	+	0.623642i	0.194006	+	0.112009i	−0.399851	+	0.916580i	$0.630938\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−1.33195	−	1.10721i	−0.231863	−	0.192740i
$34$		−	1.85374i		−	0.317913i
$35$	−0.557318	+	1.14809i	−0.0942040	+	0.194062i
$36$	2.28024	−	1.94949i	0.380040	−	0.324915i
$37$	−2.72853	−	4.72595i	−0.448567	−	0.776941i	0.549726	−	0.835345i	$-0.314732\pi$
$37$	−2.72853	−	4.72595i	−0.448567	−	0.776941i	−0.998293	+	0.0584042i	$0.981399\pi$
$38$	0.192993	−	0.334273i	0.0313076	−	0.0542263i
$39$	−0.161241	+	0.939780i	−0.0258192	+	0.150485i
$40$	−0.417738	+	0.241181i	−0.0660501	+	0.0381341i
$41$	5.67387			0.886110			0.443055	−	0.896495i	$-0.353895\pi$
$41$	5.67387			0.886110			0.443055	+	0.896495i	$0.353895\pi$
$42$	−3.72474	−	2.66951i	−0.574741	−	0.411914i
$43$	−0.682163			−0.104029			−0.0520144	−	0.998646i	$-0.516564\pi$
$43$	−0.682163			−0.104029			−0.0520144	+	0.998646i	$0.516564\pi$
$44$	−0.866025	+	0.500000i	−0.130558	+	0.0753778i
$45$	0.264425	+	1.42272i	0.0394182	+	0.212087i
$46$	−0.124844	+	0.216237i	−0.0184073	+	0.0318824i
$47$	−4.41421	−	7.64564i	−0.643879	−	1.11523i	−0.984559	−	0.175052i	$-0.943991\pi$
$47$	−4.41421	−	7.64564i	−0.643879	−	1.11523i	0.340680	−	0.940179i	$-0.389343\pi$
$48$	−0.599900	−	1.62484i	−0.0865882	−	0.234526i
$49$	−2.59808	+	6.50000i	−0.371154	+	0.928571i
$50$			4.76733i			0.674202i
$51$	−2.05247	+	2.46909i	−0.287403	+	0.345741i
$52$	0.476756	+	0.275255i	0.0661141	+	0.0381710i
$53$	6.54441	+	3.77841i	0.898943	+	0.519005i	0.876857	−	0.480751i	$-0.159636\pi$
$53$	6.54441	+	3.77841i	0.898943	+	0.519005i	0.0220861	+	0.999756i	$0.492969\pi$
$54$	−5.19565	+	0.0719302i	−0.707039	+	0.00978846i
$55$		−	0.482362i		−	0.0650417i
$56$	−2.19067	+	1.48356i	−0.292741	+	0.198250i
$57$	−0.627167	+	0.231553i	−0.0830702	+	0.0306699i
$58$	−2.24238	−	3.88392i	−0.294439	−	0.509984i
$59$	−1.82465	+	3.16038i	−0.237549	+	0.411446i	−0.960010	−	0.279965i	$-0.909677\pi$
$59$	−1.82465	+	3.16038i	−0.237549	+	0.411446i	0.722462	+	0.691411i	$0.243011\pi$
$60$	0.823443	+	0.141281i	0.106306	+	0.0182392i
$61$	−7.63593	+	4.40861i	−0.977681	+	0.564464i	−0.901569	−	0.432635i	$-0.857584\pi$
$61$	−7.63593	+	4.40861i	−0.977681	+	0.564464i	−0.0761117	+	0.997099i	$0.524251\pi$
$62$	−1.24728			−0.158405
$63$	2.00548	+	7.67972i	0.252667	+	0.967553i
$64$	−1.00000			−0.125000
$65$	−0.229969	+	0.132773i	−0.0285241	+	0.0164684i
$66$	1.70711	+	0.292893i	0.210130	+	0.0360527i
$67$	4.35690	−	7.54636i	0.532279	−	0.921935i	−0.467010	−	0.884252i	$-0.654669\pi$
$67$	4.35690	−	7.54636i	0.532279	−	0.921935i	0.999290	−	0.0376832i	$-0.0119978\pi$
$68$	0.926868	+	1.60538i	0.112399	+	0.194681i
$69$	0.405706	−	0.149788i	0.0488412	−	0.0180324i
$70$	−0.0913925	−	1.27293i	−0.0109235	−	0.152145i
$71$			5.76028i			0.683619i	0.939769	+	0.341810i	$0.111040\pi$
$71$			5.76028i			0.683619i	−0.939769	+	0.341810i	$0.888960\pi$
$72$	−1.00000	+	2.82843i	−0.117851	+	0.333333i
$73$	−1.94534	−	1.12314i	−0.227685	−	0.131454i	0.381819	−	0.924237i	$-0.375298\pi$
$73$	−1.94534	−	1.12314i	−0.227685	−	0.131454i	−0.609504	+	0.792783i	$0.708631\pi$
$74$	4.72595	+	2.72853i	0.549380	+	0.317185i
$75$	5.27841	−	6.34985i	0.609499	−	0.733217i
$76$			0.385986i			0.0442756i
$77$	−0.189469	−	2.63896i	−0.0215920	−	0.300737i
$78$	−0.330251	−	0.894494i	−0.0373936	−	0.101281i
$79$	−6.71587	−	11.6322i	−0.755595	−	1.30873i	−0.945078	−	0.326844i	$-0.894015\pi$
$79$	−6.71587	−	11.6322i	−0.755595	−	1.30873i	0.189483	−	0.981884i	$-0.439319\pi$
$80$	0.241181	−	0.417738i	0.0269649	−	0.0467045i
$81$	7.00000	+	5.65685i	0.777778	+	0.628539i
$82$	−4.91372	+	2.83694i	−0.542629	+	0.313287i
$83$	6.48941			0.712305			0.356153	−	0.934428i	$-0.384088\pi$
$83$	6.48941			0.712305			0.356153	+	0.934428i	$0.384088\pi$
$84$	4.56048	+	0.449490i	0.497589	+	0.0490434i
$85$	−0.894171			−0.0969865
$86$	0.590770	−	0.341081i	0.0637044	−	0.0367798i
$87$	−1.31356	+	7.65597i	−0.140828	+	0.820807i
$88$	0.500000	−	0.866025i	0.0533002	−	0.0923186i
$89$	−5.64394	−	9.77559i	−0.598257	−	1.03621i	−0.993078	−	0.117453i	$-0.962527\pi$
$89$	−5.64394	−	9.77559i	−0.598257	−	1.03621i	0.394822	−	0.918758i	$-0.370806\pi$
$90$	−0.940360	−	1.09990i	−0.0991226	−	0.115940i
$91$	−1.20599	+	0.816717i	−0.126422	+	0.0856152i
$92$		−	0.249689i		−	0.0260319i
$93$	1.66132	+	1.38100i	0.172271	+	0.143203i
$94$	7.64564	+	4.41421i	0.788588	+	0.455291i
$95$	−0.161241	−	0.0930924i	−0.0165429	−	0.00955108i
$96$	1.33195	+	1.10721i	0.135942	+	0.113004i
$97$		−	16.8389i		−	1.70973i	−0.518849	−	0.854866i	$-0.673639\pi$
$97$		−	16.8389i		−	1.70973i	0.518849	−	0.854866i	$-0.326361\pi$
$98$	−1.00000	−	6.92820i	−0.101015	−	0.699854i
$99$	−1.94949	−	2.28024i	−0.195931	−	0.229173i
$100$	−2.38366	−	4.12863i	−0.238366	−	0.412863i
$101$	0.855693	−	1.48210i	0.0851447	−	0.147475i	−0.820308	−	0.571922i	$-0.806198\pi$
$101$	0.855693	−	1.48210i	0.0851447	−	0.147475i	0.905453	+	0.424447i	$0.139531\pi$
$102$	0.542947	−	3.16452i	0.0537597	−	0.313335i
$103$	0.170088	−	0.0982005i	0.0167593	−	0.00967599i	−0.491597	−	0.870823i	$-0.663587\pi$
$103$	0.170088	−	0.0982005i	0.0167593	−	0.00967599i	0.508356	+	0.861147i	$0.330253\pi$
$104$	−0.550510			−0.0539820
$105$	−1.28767	+	1.79668i	−0.125664	+	0.175338i
$106$	−7.55683			−0.733984
$107$	−8.08991	+	4.67071i	−0.782081	+	0.451535i	−0.837167	−	0.546947i	$-0.815790\pi$
$107$	−8.08991	+	4.67071i	−0.782081	+	0.451535i	0.0550863	+	0.998482i	$0.482457\pi$
$108$	4.46360	−	2.66012i	0.429510	−	0.255970i
$109$	3.15161	−	5.45875i	0.301870	−	0.522854i	−0.674690	−	0.738101i	$-0.735723\pi$
$109$	3.15161	−	5.45875i	0.301870	−	0.522854i	0.976559	+	0.215248i	$0.0690559\pi$
$110$	0.241181	+	0.417738i	0.0229957	+	0.0398297i
$111$	−3.27369	−	8.86686i	−0.310725	−	0.841605i
$112$	1.15539	−	2.38014i	0.109175	−	0.224902i
$113$		−	19.8084i		−	1.86342i	−0.363201	−	0.931711i	$-0.618316\pi$
$113$		−	19.8084i		−	1.86342i	0.363201	−	0.931711i	$-0.381684\pi$
$114$	0.427366	−	0.514114i	0.0400265	−	0.0481512i
$115$	0.104304	+	0.0602202i	0.00972644	+	0.00561556i
$116$	3.88392	+	2.24238i	0.360613	+	0.208200i
$117$	−0.550510	+	1.55708i	−0.0508947	+	0.143952i
$118$		−	3.64929i		−	0.335944i
$119$	−4.89193	+	0.351225i	−0.448443	+	0.0321967i
$120$	−0.783763	+	0.289369i	−0.0715475	+	0.0264157i
$121$	0.500000	+	0.866025i	0.0454545	+	0.0787296i
$122$	4.40861	−	7.63593i	0.399137	−	0.691325i
$123$	9.68590	+	1.66184i	0.873348	+	0.149843i
$124$	1.08018	−	0.623642i	0.0970031	−	0.0560047i
$125$	4.71139			0.421399
$126$	−5.57666	−	5.64809i	−0.496808	−	0.503172i
$127$	−21.1440			−1.87623			−0.938114	−	0.346326i	$-0.887429\pi$
$127$	−21.1440			−1.87623			−0.938114	+	0.346326i	$0.887429\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−1.16452	−	0.199801i	−0.102531	−	0.0175915i
$130$	0.132773	−	0.229969i	0.0116449	−	0.0201696i
$131$	−8.17009	−	14.1510i	−0.713824	−	1.23638i	−0.963411	−	0.268027i	$-0.913628\pi$
$131$	−8.17009	−	14.1510i	−0.713824	−	1.23638i	0.249587	−	0.968352i	$-0.419705\pi$
$132$	−1.62484	+	0.599900i	−0.141425	+	0.0522146i
$133$	−0.918700	−	0.445966i	−0.0796614	−	0.0386701i
$134$			8.71379i			0.752757i
$135$	0.0346964	+	2.50619i	0.00298619	+	0.215698i
$136$	−1.60538	−	0.926868i	−0.137660	−	0.0794783i
$137$	−9.95875	−	5.74969i	−0.850834	−	0.491229i	0.0100984	−	0.999949i	$-0.496786\pi$
$137$	−9.95875	−	5.74969i	−0.850834	−	0.491229i	−0.860932	+	0.508720i	$0.830119\pi$
$138$	−0.276457	+	0.332573i	−0.0235336	+	0.0283105i
$139$			3.37945i			0.286641i	0.989676	+	0.143321i	$0.0457780\pi$
$139$			3.37945i			0.286641i	−0.989676	+	0.143321i	$0.954222\pi$
$140$	0.715615	+	1.05670i	0.0604805	+	0.0893071i
$141$	−5.29618	−	14.3448i	−0.446019	−	1.20805i
$142$	−2.88014	−	4.98855i	−0.241696	−	0.418630i
$143$	0.275255	−	0.476756i	0.0230180	−	0.0398683i
$144$	−0.548188	−	2.94949i	−0.0456823	−	0.245791i
$145$	−1.87346	+	1.08164i	−0.155582	+	0.0898253i
$146$	2.24629			0.185904
$147$	−6.33900	+	10.3352i	−0.522832	+	0.852436i
$148$	−5.45705			−0.448567
$149$	14.3154	−	8.26500i	1.17276	−	0.677096i	0.218434	−	0.975852i	$-0.429905\pi$
$149$	14.3154	−	8.26500i	1.17276	−	0.677096i	0.954330	+	0.298756i	$0.0965717\pi$
$150$	−1.39632	+	8.13834i	−0.114009	+	0.664492i
$151$	−0.0763986	+	0.132326i	−0.00621723	+	0.0107686i	−0.869117	−	0.494606i	$-0.835312\pi$
$151$	−0.0763986	+	0.132326i	−0.00621723	+	0.0107686i	0.862900	+	0.505375i	$0.168646\pi$
$152$	−0.192993	−	0.334273i	−0.0156538	−	0.0271131i
$153$	−4.22696	+	3.61384i	−0.341729	+	0.292162i
$154$	1.48356	+	2.19067i	0.119549	+	0.176529i
$155$			0.601643i			0.0483251i
$156$	0.733253	+	0.609528i	0.0587072	+	0.0488013i
$157$	9.11357	+	5.26172i	0.727342	+	0.419931i	0.817449	−	0.576001i	$-0.195388\pi$
$157$	9.11357	+	5.26172i	0.727342	+	0.419931i	−0.0901071	+	0.995932i	$0.528721\pi$
$158$	11.6322	+	6.71587i	0.925411	+	0.534286i
$159$	10.0653	+	8.36697i	0.798232	+	0.663544i
$160$			0.482362i			0.0381341i
$161$	0.594294	+	0.288489i	0.0468370	+	0.0227361i
$162$	−8.89060	−	1.39898i	−0.698512	−	0.109914i
$163$	−4.34228	−	7.52106i	−0.340114	−	0.589095i	0.644340	−	0.764739i	$-0.277132\pi$
$163$	−4.34228	−	7.52106i	−0.340114	−	0.589095i	−0.984454	+	0.175645i	$0.943799\pi$
$164$	2.83694	−	4.91372i	0.221527	−	0.383697i
$165$	0.141281	−	0.823443i	0.0109987	−	0.0641050i
$166$	−5.61999	+	3.24471i	−0.436196	+	0.251838i
$167$	2.01096			0.155613			0.0778065	−	0.996968i	$-0.475208\pi$
$167$	2.01096			0.155613			0.0778065	+	0.996968i	$0.475208\pi$
$168$	−4.17423	+	1.89097i	−0.322049	+	0.145891i
$169$	12.6969			0.976688
$170$	0.774375	−	0.447086i	0.0593919	−	0.0342899i
$171$	−1.13846	+	0.211593i	−0.0870603	+	0.0161809i
$172$	−0.341081	+	0.590770i	−0.0260072	+	0.0450458i
$173$	6.58140	+	11.3993i	0.500375	+	0.866674i	1.00000		0.000432574i	$0.000137693\pi$
$173$	6.58140	+	11.3993i	0.500375	+	0.866674i	−0.499625	+	0.866242i	$0.666529\pi$
$174$	−2.69041	−	7.28705i	−0.203960	−	0.552430i
$175$	12.5808	−	0.903259i	0.951017	−	0.0682800i
$176$			1.00000i			0.0753778i
$177$	−4.04052	+	4.86068i	−0.303704	+	0.365351i
$178$	9.77559	+	5.64394i	0.732712	+	0.423031i
$179$	−11.4624	−	6.61780i	−0.856737	−	0.494637i	0.00618127	−	0.999981i	$-0.498032\pi$
$179$	−11.4624	−	6.61780i	−0.856737	−	0.494637i	−0.862918	+	0.505344i	$0.831366\pi$
$180$	1.36433	+	0.482362i	0.101691	+	0.0359531i
$181$			25.8936i			1.92466i	0.271890	+	0.962328i	$0.412351\pi$
$181$			25.8936i			1.92466i	−0.271890	+	0.962328i	$0.587649\pi$
$182$	0.636057	−	1.31029i	0.0471476	−	0.0971252i
$183$	−14.3266	+	5.28945i	−1.05905	+	0.391007i
$184$	0.124844	+	0.216237i	0.00920365	+	0.0159412i
$185$	1.31614	−	2.27962i	0.0967643	−	0.167601i
$186$	−2.12925	−	0.365321i	−0.156124	−	0.0267867i
$187$	1.60538	−	0.926868i	0.117397	−	0.0677793i
$188$	−8.82843			−0.643879
$189$	1.17423	+	13.6975i	0.0854130	+	0.996346i
$190$	0.186185			0.0135073
$191$	−15.1791	+	8.76368i	−1.09832	+	0.634118i	−0.935780	−	0.352584i	$-0.885303\pi$
$191$	−15.1791	+	8.76368i	−1.09832	+	0.634118i	−0.162544	+	0.986701i	$0.551970\pi$
$192$	−1.70711	−	0.292893i	−0.123200	−	0.0211377i
$193$	3.68204	−	6.37748i	0.265039	−	0.459061i	−0.702535	−	0.711649i	$-0.747949\pi$
$193$	3.68204	−	6.37748i	0.265039	−	0.459061i	0.967574	+	0.252588i	$0.0812819\pi$
$194$	8.41946	+	14.5829i	0.604482	+	1.04699i
$195$	−0.431470	+	0.159301i	−0.0308982	+	0.0114078i
$196$	4.33013	+	5.50000i	0.309295	+	0.392857i
$197$		−	19.2932i		−	1.37458i	−0.726381	−	0.687292i	$-0.758799\pi$
$197$		−	19.2932i		−	1.37458i	0.726381	−	0.687292i	$-0.241201\pi$
$198$	2.82843	+	1.00000i	0.201008	+	0.0710669i
$199$	17.4020	+	10.0471i	1.23360	+	0.712218i	0.967778	−	0.251805i	$-0.0810242\pi$
$199$	17.4020	+	10.0471i	1.23360	+	0.712218i	0.265819	+	0.964023i	$0.414358\pi$
$200$	4.12863	+	2.38366i	0.291938	+	0.168550i
$201$	9.64796	−	11.6063i	0.680515	−	0.818648i
$202$			1.71139i			0.120413i
$203$	−9.82465	+	6.65344i	−0.689555	+	0.466980i
$204$	1.11206	+	3.01203i	0.0778595	+	0.210884i
$205$	1.36843	+	2.37019i	0.0955753	+	0.165541i
$206$	−0.0982005	+	0.170088i	−0.00684196	+	0.0118506i
$207$	0.736455	−	0.136876i	0.0511872	−	0.00951357i
$208$	0.476756	−	0.275255i	0.0330571	−	0.0190855i
$209$	0.385986			0.0266992
$210$	0.216817	−	2.19980i	0.0149618	−	0.151801i
$211$	−4.98514			−0.343191			−0.171596	−	0.985167i	$-0.554892\pi$
$211$	−4.98514			−0.343191			−0.171596	+	0.985167i	$0.554892\pi$
$212$	6.54441	−	3.77841i	0.449472	−	0.259503i
$213$	−1.68715	+	9.83341i	−0.115601	+	0.673774i
$214$	4.67071	−	8.08991i	0.319283	−	0.553015i
$215$	−0.164525	−	0.284965i	−0.0112205	−	0.0194345i
$216$	−2.53553	+	4.53553i	−0.172521	+	0.308604i
$217$	0.236321	+	3.29153i	0.0160425	+	0.223444i
$218$			6.30323i			0.426908i
$219$	−2.99195	−	2.48711i	−0.202177	−	0.168063i
$220$	−0.417738	−	0.241181i	−0.0281639	−	0.0162604i
$221$	−0.883779	−	0.510250i	−0.0594494	−	0.0343231i
$222$	7.26853	+	6.04208i	0.487832	+	0.405518i
$223$			13.2416i			0.886726i	0.896342	+	0.443363i	$0.146215\pi$
$223$			13.2416i			0.886726i	−0.896342	+	0.443363i	$0.853785\pi$
$224$	0.189469	+	2.63896i	0.0126594	+	0.176323i
$225$	10.8706	−	9.29386i	0.724710	−	0.619590i
$226$	9.90422	+	17.1546i	0.658819	+	1.14111i
$227$	−13.8591	+	24.0046i	−0.919858	+	1.59324i	−0.120229	+	0.992746i	$0.538363\pi$
$227$	−13.8591	+	24.0046i	−0.919858	+	1.59324i	−0.799629	+	0.600495i	$0.794970\pi$
$228$	−0.113053	+	0.658919i	−0.00748709	+	0.0436380i
$229$	7.21733	−	4.16693i	0.476935	−	0.275358i	−0.242203	−	0.970225i	$-0.577870\pi$
$229$	7.21733	−	4.16693i	0.476935	−	0.275358i	0.719138	+	0.694867i	$0.244537\pi$
$230$	−0.120440			−0.00794161
$231$	0.449490	−	4.56048i	0.0295743	−	0.300057i
$232$	−4.48477			−0.294439
$233$	7.01267	−	4.04877i	0.459415	−	0.265244i	−0.252383	−	0.967627i	$-0.581214\pi$
$233$	7.01267	−	4.04877i	0.459415	−	0.265244i	0.711798	+	0.702384i	$0.247881\pi$
$234$	−0.301783	−	1.62372i	−0.0197282	−	0.106146i
$235$	2.12925	−	3.68797i	0.138897	−	0.240576i
$236$	1.82465	+	3.16038i	0.118774	+	0.205723i
$237$	−8.05771	−	21.8245i	−0.523404	−	1.41765i
$238$	4.06092	−	2.75014i	0.263231	−	0.178265i
$239$			23.6386i			1.52905i	0.644592	+	0.764527i	$0.277027\pi$
$239$			23.6386i			1.52905i	−0.644592	+	0.764527i	$0.722973\pi$
$240$	0.534074	−	0.642483i	0.0344743	−	0.0414721i
$241$	14.7528	+	8.51751i	0.950309	+	0.548661i	0.893177	−	0.449705i	$-0.148471\pi$
$241$	14.7528	+	8.51751i	0.950309	+	0.548661i	0.0571323	+	0.998367i	$0.481804\pi$
$242$	−0.866025	−	0.500000i	−0.0556702	−	0.0321412i
$243$	10.2929	+	11.7071i	0.660289	+	0.751011i
$244$			8.81722i			0.564464i
$245$	−3.34190	+	0.482362i	−0.213506	+	0.0308170i
$246$	−9.21916	+	3.40376i	−0.587792	+	0.217016i
$247$	−0.106245	−	0.184021i	−0.00676018	−	0.0117090i
$248$	−0.623642	+	1.08018i	−0.0396013	+	0.0685915i
$249$	11.0781	+	1.90070i	0.702047	+	0.120452i
$250$	−4.08018	+	2.35569i	−0.258053	+	0.148987i
$251$	−12.6075			−0.795777			−0.397889	−	0.917434i	$-0.630257\pi$
$251$	−12.6075			−0.795777			−0.397889	+	0.917434i	$0.630257\pi$
$252$	7.65357	+	2.10306i	0.482130	+	0.132480i
$253$	−0.249689			−0.0156978
$254$	18.3113	−	10.5720i	1.14895	−	0.663347i
$255$	−1.52645	−	0.261897i	−0.0955898	−	0.0164006i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−0.204527	−	0.354251i	−0.0127580	−	0.0220976i	0.859576	−	0.511008i	$-0.170728\pi$
$257$	−0.204527	−	0.354251i	−0.0127580	−	0.0220976i	−0.872334	+	0.488911i	$0.837394\pi$
$258$	1.10841	−	0.409230i	0.0690065	−	0.0254775i
$259$	6.30505	−	12.9885i	0.391777	−	0.807069i
$260$			0.265545i			0.0164684i
$261$	−4.48477	+	12.6848i	−0.277600	+	0.785171i
$262$	14.1510	+	8.17009i	0.874252	+	0.504750i
$263$	−12.6093	−	7.28000i	−0.777524	−	0.448904i	0.0580278	−	0.998315i	$-0.481519\pi$
$263$	−12.6093	−	7.28000i	−0.777524	−	0.448904i	−0.835552	+	0.549411i	$0.814852\pi$
$264$	1.10721	−	1.33195i	0.0681438	−	0.0819759i
$265$			3.64513i			0.223918i
$266$	1.01860	−	0.0731322i	0.0624544	−	0.00448402i
$267$	−6.77161	−	18.3411i	−0.414416	−	1.12245i
$268$	−4.35690	−	7.54636i	−0.266140	−	0.460968i
$269$	−12.3960	+	21.4704i	−0.755795	+	1.30907i	0.189184	+	0.981942i	$0.439416\pi$
$269$	−12.3960	+	21.4704i	−0.755795	+	1.30907i	−0.944978	+	0.327133i	$0.893918\pi$
$270$	−1.28314	−	2.15307i	−0.0780895	−	0.131032i
$271$	−24.6174	+	14.2128i	−1.49540	+	0.863369i	−0.999986	−	0.00528874i	$-0.998317\pi$
$271$	−24.6174	+	14.2128i	−1.49540	+	0.863369i	−0.495413	+	0.868658i	$0.664983\pi$
$272$	1.85374			0.112399
$273$	−2.29796	+	1.04100i	−0.139079	+	0.0630041i
$274$	11.4994			0.694703
$275$	−4.12863	+	2.38366i	−0.248966	+	0.143740i
$276$	0.0731322	−	0.426246i	0.00440204	−	0.0256570i
$277$	−1.73179	+	2.99955i	−0.104053	+	0.180226i	−0.913351	−	0.407173i	$-0.866515\pi$
$277$	−1.73179	+	2.99955i	−0.104053	+	0.180226i	0.809298	+	0.587399i	$0.199848\pi$
$278$	−1.68973	−	2.92669i	−0.101343	−	0.175531i
$279$	2.43157	+	2.84411i	0.145574	+	0.170272i
$280$	−1.14809	−	0.557318i	−0.0686114	−	0.0333061i
$281$		−	20.5607i		−	1.22655i	−0.789869	−	0.613276i	$-0.789852\pi$
$281$		−	20.5607i		−	1.22655i	0.789869	−	0.613276i	$-0.210148\pi$
$282$	11.7590	+	9.77489i	0.700240	+	0.582086i
$283$	6.42343	+	3.70857i	0.381833	+	0.220451i	0.678615	−	0.734494i	$-0.262580\pi$
$283$	6.42343	+	3.70857i	0.381833	+	0.220451i	−0.296782	+	0.954945i	$0.595914\pi$
$284$	4.98855	+	2.88014i	0.296016	+	0.170905i
$285$	−0.247989	−	0.206145i	−0.0146896	−	0.0122110i
$286$			0.550510i			0.0325524i
$287$	8.41755	+	12.4296i	0.496872	+	0.733695i
$288$	1.94949	+	2.28024i	0.114875	+	0.134364i
$289$	6.78183	+	11.7465i	0.398931	+	0.690969i
$290$	1.08164	−	1.87346i	0.0635161	−	0.110013i
$291$	4.93200	−	28.7458i	0.289119	−	1.68511i
$292$	−1.94534	+	1.12314i	−0.113843	+	0.0657271i
$293$	33.1199			1.93488			0.967442	−	0.253093i	$-0.0814479\pi$
$293$	33.1199			1.93488			0.967442	+	0.253093i	$0.0814479\pi$
$294$	0.322117	−	12.1201i	0.0187862	−	0.706857i
$295$	−1.76028			−0.102487
$296$	4.72595	−	2.72853i	0.274690	−	0.158592i
$297$	−2.66012	−	4.46360i	−0.154356	−	0.259005i
$298$	−8.26500	+	14.3154i	−0.478779	+	0.829269i
$299$	0.0687281	+	0.119041i	0.00397465	+	0.00688430i
$300$	−2.85992	−	7.74616i	−0.165118	−	0.447225i
$301$	−1.01203	−	1.49439i	−0.0583326	−	0.0861354i
$302$		−	0.152797i		−	0.00879249i
$303$	1.89486	−	2.27948i	0.108857	−	0.130953i
$304$	0.334273	+	0.192993i	0.0191719	+	0.0110689i
$305$	−3.68328	−	2.12654i	−0.210904	−	0.121766i
$306$	1.85374	−	5.24316i	0.105971	−	0.299731i
$307$			11.6047i			0.662317i	0.943575	+	0.331158i	$0.107439\pi$
$307$			11.6047i			0.662317i	−0.943575	+	0.331158i	$0.892561\pi$
$308$	−2.38014	−	1.15539i	−0.135621	−	0.0658347i
$309$	0.319121	−	0.117821i	0.0181542	−	0.00670261i
$310$	−0.300821	−	0.521038i	−0.0170855	−	0.0295930i
$311$	1.12484	−	1.94829i	0.0637841	−	0.110477i	−0.832370	−	0.554220i	$-0.813016\pi$
$311$	1.12484	−	1.94829i	0.0637841	−	0.110477i	0.896154	+	0.443743i	$0.146350\pi$
$312$	−0.939780	−	0.161241i	−0.0532046	−	0.00912846i
$313$	−8.92899	+	5.15515i	−0.504696	+	0.291387i	−0.730651	−	0.682751i	$-0.760783\pi$
$313$	−8.92899	+	5.15515i	−0.504696	+	0.291387i	0.225955	+	0.974138i	$0.427450\pi$
$314$	−10.5234			−0.593872
$315$	−2.72442	+	2.68997i	−0.153504	+	0.151562i
$316$	−13.4317			−0.755595
$317$	−13.7259	+	7.92463i	−0.770921	+	0.445091i	−0.833203	−	0.552967i	$-0.813495\pi$
$317$	−13.7259	+	7.92463i	−0.770921	+	0.445091i	0.0622821	+	0.998059i	$0.480162\pi$
$318$	−12.9003	−	2.21334i	−0.723414	−	0.124118i
$319$	2.24238	−	3.88392i	0.125549	−	0.217458i
$320$	−0.241181	−	0.417738i	−0.0134824	−	0.0233522i
$321$	−15.1784	+	5.60392i	−0.847173	+	0.312780i
$322$	−0.658919	+	0.0473082i	−0.0367201	+	0.00263638i
$323$		−	0.715515i		−	0.0398123i
$324$	8.39898	−	3.23375i	0.466610	−	0.179653i
$325$	2.27285	+	1.31223i	0.126075	+	0.0727895i
$326$	7.52106	+	4.34228i	0.416553	+	0.240497i
$327$	6.97897	−	8.39559i	0.385938	−	0.464277i
$328$			5.67387i			0.313287i
$329$	10.2003	−	21.0129i	0.562362	−	1.15848i
$330$	0.289369	+	0.783763i	0.0159292	+	0.0431447i
$331$	−3.37516	−	5.84594i	−0.185515	−	0.321322i	0.758235	−	0.651982i	$-0.226062\pi$
$331$	−3.37516	−	5.84594i	−0.185515	−	0.321322i	−0.943750	+	0.330660i	$0.892729\pi$
$332$	3.24471	−	5.61999i	0.178076	−	0.308437i
$333$	−2.99149	−	16.0955i	−0.163933	−	0.882029i
$334$	−1.74155	+	1.00548i	−0.0952931	+	0.0550175i
$335$	4.20320			0.229645
$336$	2.66951	−	3.72474i	0.145634	−	0.203201i
$337$	1.02093			0.0556137			0.0278068	−	0.999613i	$-0.491148\pi$
$337$	1.02093			0.0556137			0.0278068	+	0.999613i	$0.491148\pi$
$338$	−10.9959	+	6.34847i	−0.598097	+	0.345311i
$339$	5.80176	−	33.8151i	0.315108	−	1.83659i
$340$	−0.447086	+	0.774375i	−0.0242466	+	0.0419964i
$341$	−0.623642	−	1.08018i	−0.0337721	−	0.0584950i
$342$	0.880139	−	0.752475i	0.0475925	−	0.0406892i
$343$	−18.0938	+	3.95164i	−0.976972	+	0.213368i
$344$		−	0.682163i		−	0.0367798i
$345$	0.160421	+	0.133352i	0.00863676	+	0.00717945i
$346$	−11.3993	−	6.58140i	−0.612831	−	0.353818i
$347$	−24.6613	−	14.2382i	−1.32389	−	0.764349i	−0.339544	−	0.940590i	$-0.610273\pi$
$347$	−24.6613	−	14.2382i	−1.32389	−	0.764349i	−0.984347	+	0.176242i	$0.943606\pi$
$348$	5.97349	+	4.96556i	0.320213	+	0.266182i
$349$		−	12.9437i		−	0.692861i	−0.938076	−	0.346430i	$-0.887394\pi$
$349$		−	12.9437i		−	0.692861i	0.938076	−	0.346430i	$-0.112606\pi$
$350$	−10.4436	+	7.07263i	−0.558236	+	0.378048i
$351$	−1.39584	+	2.49686i	−0.0745043	+	0.133272i
$352$	−0.500000	−	0.866025i	−0.0266501	−	0.0461593i
$353$	8.66631	−	15.0105i	0.461261	−	0.798927i	−0.537763	−	0.843096i	$-0.680731\pi$
$353$	8.66631	−	15.0105i	0.461261	−	0.798927i	0.999024	+	0.0441686i	$0.0140639\pi$
$354$	1.06885	−	6.22973i	0.0568089	−	0.331106i
$355$	−2.40629	+	1.38927i	−0.127712	+	0.0737348i
$356$	−11.2879			−0.598257
$357$	−8.45392	−	0.833235i	−0.447429	−	0.0440995i
$358$	13.2356			0.699523
$359$	6.33088	−	3.65514i	0.334131	−	0.192911i	−0.323543	−	0.946214i	$-0.604874\pi$
$359$	6.33088	−	3.65514i	0.334131	−	0.192911i	0.657674	+	0.753303i	$0.271541\pi$
$360$	−1.42272	+	0.264425i	−0.0749840	+	0.0139364i
$361$	−9.42551	+	16.3255i	−0.496079	+	0.859235i
$362$	−12.9468	−	22.4245i	−0.680469	−	1.17861i
$363$	0.599900	+	1.62484i	0.0314866	+	0.0852822i
$364$	0.104304	+	1.45277i	0.00546704	+	0.0761460i
$365$		−	1.08352i		−	0.0567143i
$366$	9.76248	−	11.7441i	0.510293	−	0.613874i
$367$	8.47438	+	4.89269i	0.442359	+	0.255396i	0.704598	−	0.709607i	$-0.251127\pi$
$367$	8.47438	+	4.89269i	0.442359	+	0.255396i	−0.262239	+	0.965003i	$0.584461\pi$
$368$	−0.216237	−	0.124844i	−0.0112721	−	0.00650797i
$369$	16.0481	+	5.67387i	0.835432	+	0.295370i
$370$			2.63227i			0.136845i
$371$	1.43178	+	19.9422i	0.0743344	+	1.03535i
$372$	2.02664	−	0.748247i	0.105077	−	0.0387948i
$373$	−14.0289	−	24.2988i	−0.726391	−	1.25815i	−0.958399	−	0.285432i	$-0.907863\pi$
$373$	−14.0289	−	24.2988i	−0.726391	−	1.25815i	0.232008	−	0.972714i	$-0.425470\pi$
$374$	−0.926868	+	1.60538i	−0.0479272	+	0.0830123i
$375$	8.04284	+	1.37993i	0.415330	+	0.0712594i
$376$	7.64564	−	4.41421i	0.394294	−	0.227646i
$377$	−2.46891			−0.127155
$378$	−7.86566	−	11.2753i	−0.404566	−	0.579937i
$379$	29.2641			1.50320			0.751598	−	0.659622i	$-0.229284\pi$
$379$	29.2641			1.50320			0.751598	+	0.659622i	$0.229284\pi$
$380$	−0.161241	+	0.0930924i	−0.00827147	+	0.00477554i
$381$	−36.0951	−	6.19294i	−1.84921	−	0.317274i
$382$	8.76368	−	15.1791i	0.448389	−	0.776632i
$383$	4.89376	+	8.47623i	0.250059	+	0.433115i	0.963542	−	0.267558i	$-0.0862166\pi$
$383$	4.89376	+	8.47623i	0.250059	+	0.433115i	−0.713483	+	0.700673i	$0.752883\pi$
$384$	1.62484	−	0.599900i	0.0829175	−	0.0306135i
$385$	1.05670	−	0.715615i	0.0538542	−	0.0364711i
$386$			7.36408i			0.374822i
$387$	−1.92945	−	0.682163i	−0.0980793	−	0.0346763i
$388$	−14.5829	−	8.41946i	−0.740336	−	0.427433i
$389$	32.1589	+	18.5669i	1.63052	+	0.941380i	0.983933	+	0.178539i	$0.0571370\pi$
$389$	32.1589	+	18.5669i	1.63052	+	0.941380i	0.646586	+	0.762841i	$0.276196\pi$
$390$	0.294013	−	0.353693i	0.0148879	−	0.0179100i
$391$			0.462857i			0.0234077i
$392$	−6.50000	−	2.59808i	−0.328300	−	0.131223i
$393$	−9.80248	−	26.5502i	−0.494470	−	1.33928i
$394$	9.64660	+	16.7084i	0.485989	+	0.841757i
$395$	3.23948	−	5.61095i	0.162996	−	0.282317i
$396$	−2.94949	+	0.548188i	−0.148217	+	0.0275475i
$397$	−31.3992	+	18.1283i	−1.57588	+	0.909835i	−0.580456	+	0.814292i	$0.697126\pi$
$397$	−31.3992	+	18.1283i	−1.57588	+	0.909835i	−0.995425	+	0.0955439i	$0.969541\pi$
$398$	−20.0941			−1.00723
$399$	−1.43770	−	1.03039i	−0.0719749	−	0.0515841i
$400$	−4.76733			−0.238366
$401$	23.6204	−	13.6373i	1.17955	−	0.681013i	0.223638	−	0.974672i	$-0.428207\pi$
$401$	23.6204	−	13.6373i	1.17955	−	0.681013i	0.955910	+	0.293660i	$0.0948732\pi$
$402$	−2.55221	+	14.8754i	−0.127293	+	0.741916i
$403$	−0.343322	+	0.594650i	−0.0171021	+	0.0296216i
$404$	−0.855693	−	1.48210i	−0.0425723	−	0.0737374i
$405$	−0.674814	+	4.28849i	−0.0335318	+	0.213097i
$406$	5.18167	−	10.6744i	0.257162	−	0.529760i
$407$			5.45705i			0.270496i
$408$	−2.46909	−	2.05247i	−0.122238	−	0.101612i
$409$	10.8109	+	6.24170i	0.534566	+	0.308632i	0.742874	−	0.669431i	$-0.233462\pi$
$409$	10.8109	+	6.24170i	0.534566	+	0.308632i	−0.208308	+	0.978063i	$0.566796\pi$
$410$	−2.37019	−	1.36843i	−0.117055	−	0.0675819i
$411$	−15.3166	−	12.7322i	−0.755513	−	0.628032i
$412$		−	0.196401i		−	0.00967599i
$413$	−9.63033	+	0.691426i	−0.473877	+	0.0340229i
$414$	−0.569350	+	0.486766i	−0.0279820	+	0.0239232i
$415$	1.56512	+	2.71087i	0.0768288	+	0.133071i
$416$	−0.275255	+	0.476756i	−0.0134955	+	0.0233749i
$417$	−0.989819	+	5.76909i	−0.0484716	+	0.282513i
$418$	−0.334273	+	0.192993i	−0.0163498	+	0.00943959i
$419$	14.3077			0.698975			0.349487	−	0.936941i	$-0.386356\pi$
$419$	14.3077			0.698975			0.349487	+	0.936941i	$0.386356\pi$
$420$	0.912132	+	2.01349i	0.0445075	+	0.0982483i
$421$	15.2015			0.740875			0.370437	−	0.928857i	$-0.379208\pi$
$421$	15.2015			0.740875			0.370437	+	0.928857i	$0.379208\pi$
$422$	4.31726	−	2.49257i	0.210161	−	0.121336i
$423$	−4.83964	−	26.0394i	−0.235311	−	1.26608i
$424$	−3.77841	+	6.54441i	−0.183496	+	0.317824i
$425$	4.41868	+	7.65338i	0.214338	+	0.371244i
$426$	−3.45559	−	9.35956i	−0.167424	−	0.453472i
$427$	−20.9862	−	10.1874i	−1.01559	−	0.493001i
$428$			9.34142i			0.451535i
$429$	0.609528	−	0.733253i	0.0294283	−	0.0354018i
$430$	0.284965	+	0.164525i	0.0137422	+	0.00793408i
$431$	−1.44564	−	0.834638i	−0.0696338	−	0.0402031i	0.464779	−	0.885427i	$-0.346134\pi$
$431$	−1.44564	−	0.834638i	−0.0696338	−	0.0402031i	−0.534413	+	0.845224i	$0.679467\pi$
$432$	−0.0719302	−	5.19565i	−0.00346074	−	0.249976i
$433$			10.5393i			0.506486i	0.967403	+	0.253243i	$0.0814973\pi$
$433$			10.5393i			0.506486i	−0.967403	+	0.253243i	$0.918503\pi$
$434$	−1.85043	−	2.73239i	−0.0888233	−	0.131159i
$435$	−3.51499	+	1.29775i	−0.168531	+	0.0622225i
$436$	−3.15161	−	5.45875i	−0.150935	−	0.261427i
$437$	−0.0481882	+	0.0834643i	−0.00230515	+	0.00399264i
$438$	3.83466	+	0.657923i	0.183227	+	0.0314368i
$439$	19.4237	−	11.2143i	0.927041	−	0.535227i	0.0411662	−	0.999152i	$-0.486893\pi$
$439$	19.4237	−	11.2143i	0.927041	−	0.535227i	0.885874	+	0.463925i	$0.153559\pi$
$440$	0.482362			0.0229957
$441$	−13.8485	+	15.7867i	−0.659451	+	0.751748i
$442$	1.02050			0.0485403
$443$	−5.36156	+	3.09550i	−0.254735	+	0.147071i	−0.621931	−	0.783072i	$-0.713651\pi$
$443$	−5.36156	+	3.09550i	−0.254735	+	0.147071i	0.367195	+	0.930144i	$0.380318\pi$
$444$	−9.31577	−	1.59833i	−0.442107	−	0.0758536i
$445$	2.72242	−	4.71537i	0.129055	−	0.223530i
$446$	−6.62082	−	11.4676i	−0.313505	−	0.543007i
$447$	26.8587	−	9.91636i	1.27037	−	0.469028i
$448$	−1.48356	−	2.19067i	−0.0700918	−	0.103499i
$449$		−	1.55464i		−	0.0733680i	−0.999327	−	0.0366840i	$-0.988321\pi$
$449$		−	1.55464i		−	0.0733680i	0.999327	−	0.0366840i	$-0.0116795\pi$
$450$	−4.76733	+	13.4840i	−0.224734	+	0.635644i
$451$	−4.91372	−	2.83694i	−0.231378	−	0.133586i
$452$	−17.1546	−	9.90422i	−0.806885	−	0.465855i
$453$	−0.169178	+	0.203518i	−0.00794867	+	0.00956213i
$454$		−	27.7181i		−	1.30088i
$455$	−0.632035	−	0.306809i	−0.0296302	−	0.0143834i
$456$	−0.231553	−	0.627167i	−0.0108435	−	0.0293698i
$457$	−8.17556	−	14.1605i	−0.382437	−	0.662400i	0.608973	−	0.793191i	$-0.291582\pi$
$457$	−8.17556	−	14.1605i	−0.382437	−	0.662400i	−0.991410	+	0.130791i	$0.958248\pi$
$458$	−4.16693	+	7.21733i	−0.194708	+	0.337244i
$459$	−8.27434	+	4.93116i	−0.386213	+	0.230167i
$460$	0.104304	−	0.0602202i	0.00486322	−	0.00280778i
$461$	20.2754			0.944321			0.472160	−	0.881513i	$-0.343474\pi$
$461$	20.2754			0.944321			0.472160	+	0.881513i	$0.343474\pi$
$462$	1.89097	+	4.17423i	0.0879759	+	0.194203i
$463$	5.63443			0.261854			0.130927	−	0.991392i	$-0.458205\pi$
$463$	5.63443			0.261854			0.130927	+	0.991392i	$0.458205\pi$
$464$	3.88392	−	2.24238i	0.180307	−	0.104100i
$465$	−0.176217	+	1.02707i	−0.00817187	+	0.0476292i
$466$	−4.04877	+	7.01267i	−0.187556	+	0.324856i
$467$	18.8229	+	32.6022i	0.871020	+	1.50865i	0.860943	+	0.508702i	$0.169874\pi$
$467$	18.8229	+	32.6022i	0.871020	+	1.50865i	0.0100773	+	0.999949i	$0.496792\pi$
$468$	1.07321	+	1.25529i	0.0496093	+	0.0580260i
$469$	22.9953	−	1.65099i	1.06183	−	0.0762357i
$470$			4.25850i			0.196430i
$471$	14.0167	+	11.6516i	0.645856	+	0.536878i
$472$	−3.16038	−	1.82465i	−0.145468	−	0.0839861i
$473$	0.590770	+	0.341081i	0.0271636	+	0.0156829i
$474$	17.8904	+	14.8717i	0.821735	+	0.683080i
$475$			1.84012i			0.0844305i
$476$	−2.14180	+	4.41215i	−0.0981691	+	0.202231i
$477$	14.7320	+	17.2314i	0.674530	+	0.788971i
$478$	−11.8193	−	20.4716i	−0.540602	−	0.936350i
$479$	8.08725	−	14.0075i	0.369516	−	0.640020i	−0.619974	−	0.784622i	$-0.712857\pi$
$479$	8.08725	−	14.0075i	0.369516	−	0.640020i	0.989490	+	0.144602i	$0.0461903\pi$
$480$	−0.141281	+	0.823443i	−0.00644854	+	0.0375849i
$481$	2.60168	−	1.50208i	0.118626	−	0.0684890i
$482$	−17.0350			−0.775924
$483$	0.930027	+	0.666547i	0.0423177	+	0.0303289i
$484$	1.00000			0.0454545
$485$	7.03425	−	4.06122i	0.319409	−	0.184411i
$486$	−14.7675	−	4.99221i	−0.669866	−	0.226451i
$487$	−10.8869	+	18.8567i	−0.493335	+	0.854481i	−0.999971	−	0.00767942i	$-0.997556\pi$
$487$	−10.8869	+	18.8567i	−0.493335	+	0.854481i	0.506636	+	0.862160i	$0.330889\pi$
$488$	−4.40861	−	7.63593i	−0.199568	−	0.345662i
$489$	−5.20988	−	14.1111i	−0.235599	−	0.638125i
$490$	2.65299	−	2.08869i	0.119850	−	0.0943573i
$491$			14.3125i			0.645912i	0.946414	+	0.322956i	$0.104677\pi$
$491$			14.3125i			0.645912i	−0.946414	+	0.322956i	$0.895323\pi$
$492$	6.28215	−	7.55732i	0.283221	−	0.340710i
$493$	−7.19976	−	4.15679i	−0.324261	−	0.187212i
$494$	0.184021	+	0.106245i	0.00827949	+	0.00478017i
$495$	0.482362	−	1.36433i	0.0216806	−	0.0613219i
$496$		−	1.24728i		−	0.0560047i
$497$	−12.6189	+	8.54574i	−0.566034	+	0.383329i
$498$	−10.5443	+	3.89300i	−0.472501	+	0.174449i
$499$	−4.02874	−	6.97799i	−0.180351	−	0.312378i	0.761649	−	0.647990i	$-0.224390\pi$
$499$	−4.02874	−	6.97799i	−0.180351	−	0.312378i	−0.942000	+	0.335612i	$0.891057\pi$
$500$	2.35569	−	4.08018i	0.105350	−	0.182471i
$501$	3.43293	+	0.588998i	0.153372	+	0.0263145i
$502$	10.9184	−	6.30374i	0.487312	−	0.281350i
$503$	20.9014			0.931947			0.465973	−	0.884799i	$-0.345704\pi$
$503$	20.9014			0.931947			0.465973	+	0.884799i	$0.345704\pi$
$504$	−7.67972	+	2.00548i	−0.342082	+	0.0893313i
$505$	0.825508			0.0367346
$506$	0.216237	−	0.124844i	0.00961290	−	0.00555001i
$507$	21.6750	+	3.71885i	0.962622	+	0.165160i
$508$	−10.5720	+	18.3113i	−0.469057	+	0.812431i
$509$	20.0442	+	34.7175i	0.888442	+	1.53883i	0.841717	+	0.539920i	$0.181545\pi$
$509$	20.0442	+	34.7175i	0.888442	+	1.53883i	0.0467259	+	0.998908i	$0.485121\pi$
$510$	1.45289	−	0.536414i	0.0643350	−	0.0237528i
$511$	−0.425601	−	5.92786i	−0.0188275	−	0.262233i
$512$		−	1.00000i		−	0.0441942i
$513$	−2.00545	+	0.0277640i	−0.0885427	+	0.00122581i
$514$	0.354251	+	0.204527i	0.0156253	+	0.00902130i
$515$	0.0820441	+	0.0473682i	0.00361530	+	0.00208729i
$516$	−0.755295	+	0.908608i	−0.0332500	+	0.0399992i
$517$			8.82843i			0.388274i
$518$	1.03394	+	14.4009i	0.0454287	+	0.632741i
$519$	7.89637	+	21.3875i	0.346612	+	0.938807i
$520$	−0.132773	−	0.229969i	−0.00582246	−	0.0100848i
$521$	−2.01266	+	3.48604i	−0.0881764	+	0.152726i	−0.906740	−	0.421689i	$-0.861437\pi$
$521$	−2.01266	+	3.48604i	−0.0881764	+	0.152726i	0.818564	+	0.574415i	$0.194771\pi$
$522$	−2.45850	−	13.2278i	−0.107605	−	0.578964i
$523$	−22.8435	+	13.1887i	−0.998876	+	0.576701i	−0.907915	−	0.419153i	$-0.862327\pi$
$523$	−22.8435	+	13.1887i	−0.998876	+	0.576701i	−0.0909602	+	0.995855i	$0.528994\pi$
$524$	−16.3402			−0.713824
$525$	21.7413	+	2.14286i	0.948868	+	0.0935223i
$526$	14.5600			0.634846
$527$	−2.00237	+	1.15607i	−0.0872246	+	0.0503591i
$528$	−0.292893	+	1.70711i	−0.0127465	+	0.0742923i
$529$	−11.4688	+	19.8646i	−0.498645	+	0.863678i
$530$	−1.82256	−	3.15677i	−0.0791671	−	0.137121i
$531$	−8.32125	+	7.11425i	−0.361112	+	0.308732i
$532$	−0.845567	+	0.572634i	−0.0366600	+	0.0248268i
$533$			3.12352i			0.135295i
$534$	15.0349	+	12.4980i	0.650624	+	0.540842i
$535$	−3.90226	−	2.25297i	−0.168710	−	0.0974045i
$536$	7.54636	+	4.35690i	0.325953	+	0.188189i
$537$	−17.6292	−	14.6545i	−0.760755	−	0.632390i
$538$		−	24.7919i		−	1.06885i
$539$	5.50000	−	4.33013i	0.236902	−	0.186512i
$540$	2.18777	+	1.22304i	0.0941466	+	0.0526315i
$541$	−9.66000	−	16.7316i	−0.415316	−	0.719348i	0.580146	−	0.814513i	$-0.302996\pi$
$541$	−9.66000	−	16.7316i	−0.415316	−	0.719348i	−0.995462	+	0.0951647i	$0.969662\pi$
$542$	14.2128	−	24.6174i	0.610494	−	1.05741i
$543$	−7.58406	+	44.2032i	−0.325463	+	1.89694i
$544$	−1.60538	+	0.926868i	−0.0688302	+	0.0397391i
$545$	3.04044			0.130238
$546$	1.46959	−	2.05051i	0.0628927	−	0.0877537i
$547$	6.96837			0.297946			0.148973	−	0.988841i	$-0.452403\pi$
$547$	6.96837			0.297946			0.148973	+	0.988841i	$0.452403\pi$
$548$	−9.95875	+	5.74969i	−0.425417	+	0.245615i
$549$	−26.0063	+	4.83349i	−1.10992	+	0.206288i
$550$	2.38366	−	4.12863i	0.101640	−	0.176045i
$551$	−0.865528	−	1.49914i	−0.0368727	−	0.0638654i
$552$	0.149788	+	0.405706i	0.00637542	+	0.0172680i
$553$	15.5190	−	31.9694i	0.659933	−	1.35948i
$554$		−	3.46359i		−	0.147154i
$555$	2.91447	−	3.50606i	0.123712	−	0.148824i
$556$	2.92669	+	1.68973i	0.124119	+	0.0716604i
$557$	−12.4468	−	7.18616i	−0.527388	−	0.304487i	0.212564	−	0.977147i	$-0.431818\pi$
$557$	−12.4468	−	7.18616i	−0.527388	−	0.304487i	−0.739952	+	0.672660i	$0.765152\pi$
$558$	−3.52785	−	1.24728i	−0.149346	−	0.0528018i
$559$		−	0.375538i		−	0.0158835i
$560$	1.27293	−	0.0913925i	0.0537912	−	0.00386204i
$561$	3.01203	−	1.11206i	0.127168	−	0.0469511i
$562$	10.2804	+	17.8061i	0.433651	+	0.751106i
$563$	15.5721	−	26.9717i	0.656286	−	1.13672i	−0.325284	−	0.945616i	$-0.605460\pi$
$563$	15.5721	−	26.9717i	0.656286	−	1.13672i	0.981570	−	0.191104i	$-0.0612066\pi$
$564$	−15.0711	−	2.58579i	−0.634606	−	0.108881i
$565$	8.27473	−	4.77742i	0.348121	−	0.200988i
$566$	−7.41713			−0.311765
$567$	−2.00736	+	23.7270i	−0.0843011	+	0.996440i
$568$	−5.76028			−0.241696
$569$	−26.5762	+	15.3438i	−1.11413	+	0.643244i	−0.939896	−	0.341461i	$-0.889078\pi$
$569$	−26.5762	+	15.3438i	−1.11413	+	0.643244i	−0.174234	+	0.984704i	$0.555745\pi$
$570$	0.317837	+	0.0545323i	0.0133127	+	0.00228410i
$571$	7.29934	−	12.6428i	0.305468	−	0.529086i	−0.671898	−	0.740644i	$-0.734521\pi$
$571$	7.29934	−	12.6428i	0.305468	−	0.529086i	0.977365	+	0.211558i	$0.0678539\pi$
$572$	−0.275255	−	0.476756i	−0.0115090	−	0.0199342i
$573$	−28.4792	+	10.5147i	−1.18974	+	0.439257i
$574$	−13.5046	−	6.55556i	−0.563671	−	0.273624i
$575$		−	1.19035i		−	0.0496410i
$576$	−2.82843	−	1.00000i	−0.117851	−	0.0416667i
$577$	−23.3520	−	13.4823i	−0.972154	−	0.561274i	−0.0722621	−	0.997386i	$-0.523022\pi$
$577$	−23.3520	−	13.4823i	−0.972154	−	0.561274i	−0.899892	+	0.436112i	$0.856355\pi$
$578$	−11.7465	−	6.78183i	−0.488589	−	0.282087i
$579$	8.15355	−	9.80859i	0.338850	−	0.407631i
$580$			2.16328i			0.0898253i
$581$	9.62745	+	14.2162i	0.399414	+	0.589786i
$582$	10.1017	+	27.3606i	0.418728	+	1.13413i
$583$	−3.77841	−	6.54441i	−0.156486	−	0.271042i
$584$	1.12314	−	1.94534i	0.0464761	−	0.0804989i
$585$	−0.783223	+	0.145569i	−0.0323823	+	0.00601853i
$586$	−28.6827	+	16.5599i	−1.18487	+	0.684085i
$587$	4.39307			0.181321			0.0906607	−	0.995882i	$-0.471102\pi$
$587$	4.39307			0.181321			0.0906607	+	0.995882i	$0.471102\pi$
$588$	5.78108	+	10.6574i	0.238408	+	0.439502i
$589$	−0.481434			−0.0198371
$590$	1.52445	−	0.880139i	0.0627605	−	0.0362348i
$591$	5.65085	−	32.9356i	0.232445	−	1.35479i
$592$	−2.72853	+	4.72595i	−0.112142	+	0.194235i
$593$	−20.1436	−	34.8897i	−0.827197	−	1.43275i	−0.900229	−	0.435417i	$-0.856601\pi$
$593$	−20.1436	−	34.8897i	−0.827197	−	1.43275i	0.0730318	−	0.997330i	$-0.476733\pi$
$594$	4.53553	+	2.53553i	0.186095	+	0.104034i
$595$	−1.32656	−	1.95884i	−0.0543837	−	0.0803044i
$596$		−	16.5300i		−	0.677096i
$597$	26.7644	+	22.2484i	1.09539	+	0.910565i
$598$	−0.119041	−	0.0687281i	−0.00486793	−	0.00281050i
$599$	−24.9757	−	14.4197i	−1.02048	−	0.589173i	−0.106236	−	0.994341i	$-0.533880\pi$
$599$	−24.9757	−	14.4197i	−1.02048	−	0.589173i	−0.914242	+	0.405167i	$0.867213\pi$
$600$	6.34985	+	5.27841i	0.259231	+	0.215490i
$601$		−	24.5161i		−	1.00003i	−0.866015	−	0.500017i	$-0.833327\pi$
$601$		−	24.5161i		−	1.00003i	0.866015	−	0.500017i	$-0.166673\pi$
$602$	1.62364	+	0.788167i	0.0661747	+	0.0321233i
$603$	19.8695	−	16.9874i	0.809150	−	0.691782i
$604$	0.0763986	+	0.132326i	0.00310861	+	0.00538428i
$605$	−0.241181	+	0.417738i	−0.00980540	+	0.0169835i
$606$	−0.501254	+	2.92152i	−0.0203620	+	0.118679i
$607$	−7.37857	+	4.26002i	−0.299487	+	0.172909i	−0.642212	−	0.766527i	$-0.721983\pi$
$607$	−7.37857	+	4.26002i	−0.299487	+	0.172909i	0.342725	+	0.939436i	$0.388650\pi$
$608$	−0.385986			−0.0156538
$609$	−18.7205	+	8.48056i	−0.758592	+	0.343649i
$610$	4.25309			0.172203
$611$	4.20900	−	2.43007i	0.170278	−	0.0983101i
$612$	1.01620	+	5.46757i	0.0410773	+	0.221014i
$613$	−22.8423	+	39.5640i	−0.922592	+	1.59798i	−0.127204	+	0.991877i	$0.540600\pi$
$613$	−22.8423	+	39.5640i	−0.922592	+	1.59798i	−0.795388	+	0.606100i	$0.792733\pi$
$614$	−5.80236	−	10.0500i	−0.234164	−	0.405584i
$615$	1.64184	+	4.44697i	0.0662055	+	0.179319i
$616$	2.63896	−	0.189469i	0.106327	−	0.00763391i
$617$		−	20.7786i		−	0.836513i	−0.908329	−	0.418257i	$-0.862641\pi$
$617$		−	20.7786i		−	0.836513i	0.908329	−	0.418257i	$-0.137359\pi$
$618$	−0.217456	+	0.261597i	−0.00874738	+	0.0105230i
$619$	17.3550	+	10.0199i	0.697558	+	0.402735i	0.806437	−	0.591320i	$-0.201393\pi$
$619$	17.3550	+	10.0199i	0.697558	+	0.402735i	−0.108879	+	0.994055i	$0.534726\pi$
$620$	0.521038	+	0.300821i	0.0209254	+	0.0120813i
$621$	1.29730	−	0.0179602i	0.0520587	−	0.000720717i
$622$			2.24969i			0.0902043i
$623$	13.0420	−	26.8667i	0.522515	−	1.07639i
$624$	0.894494	−	0.330251i	0.0358084	−	0.0132206i
$625$	−10.7820	−	18.6750i	−0.431281	−	0.747000i
$626$	5.15515	−	8.92899i	0.206041	−	0.356874i
$627$	0.658919	+	0.113053i	0.0263147	+	0.00451488i
$628$	9.11357	−	5.26172i	0.363671	−	0.209966i
$629$	10.1159			0.403349
$630$	1.01444	−	3.69179i	0.0404161	−	0.147084i
$631$	6.16436			0.245399			0.122700	−	0.992444i	$-0.460845\pi$
$631$	6.16436			0.245399			0.122700	+	0.992444i	$0.460845\pi$
$632$	11.6322	−	6.71587i	0.462705	−	0.267143i
$633$	−8.51017	−	1.46011i	−0.338249	−	0.0580343i
$634$	7.92463	−	13.7259i	0.314727	−	0.545123i
$635$	−5.09954	−	8.83266i	−0.202369	−	0.350513i
$636$	12.2787	−	4.53335i	0.486881	−	0.179759i
$637$	−3.57832	−	1.43027i	−0.141778	−	0.0566693i
$638$			4.48477i			0.177554i
$639$	−5.76028	+	16.2925i	−0.227873	+	0.644522i
$640$	0.417738	+	0.241181i	0.0165125	+	0.00953351i
$641$	21.4440	+	12.3807i	0.846988	+	0.489009i	0.859634	−	0.510911i	$-0.170692\pi$
$641$	21.4440	+	12.3807i	0.846988	+	0.489009i	−0.0126451	+	0.999920i	$0.504025\pi$
$642$	10.3429	−	12.4423i	0.408201	−	0.491059i
$643$			32.9650i			1.30001i	0.759929	+	0.650006i	$0.225234\pi$
$643$			32.9650i			1.30001i	−0.759929	+	0.650006i	$0.774766\pi$
$644$	0.546986	−	0.370429i	0.0215543	−	0.0145970i
$645$	−0.197397	−	0.534654i	−0.00777249	−	0.0210520i
$646$	0.357758	+	0.619654i	0.0140758	+	0.0243800i
$647$	−6.74037	+	11.6747i	−0.264991	+	0.458978i	−0.967561	−	0.252636i	$-0.918702\pi$
$647$	−6.74037	+	11.6747i	−0.264991	+	0.458978i	0.702570	+	0.711615i	$0.252036\pi$
$648$	−5.65685	+	7.00000i	−0.222222	+	0.274986i
$649$	3.16038	−	1.82465i	0.124056	−	0.0716236i
$650$	−2.62446			−0.102940
$651$	−0.560642	+	5.68822i	−0.0219733	+	0.222939i
$652$	−8.68457			−0.340114
$653$	−12.6035	+	7.27663i	−0.493213	+	0.284757i	−0.725906	−	0.687793i	$-0.758579\pi$
$653$	−12.6035	+	7.27663i	−0.493213	+	0.284757i	0.232693	+	0.972550i	$0.425246\pi$
$654$	−1.84617	+	10.7603i	−0.0721910	+	0.420760i
$655$	3.94094	−	6.82591i	0.153985	−	0.266710i
$656$	−2.83694	−	4.91372i	−0.110764	−	0.191848i
$657$	−4.37912	−	5.12208i	−0.170846	−	0.199831i
$658$	1.67271	+	23.2979i	0.0652090	+	0.908245i
$659$			30.1076i			1.17283i	0.810012	+	0.586413i	$0.199460\pi$
$659$			30.1076i			1.17283i	−0.810012	+	0.586413i	$0.800540\pi$
$660$	−0.642483	−	0.534074i	−0.0250086	−	0.0207888i
$661$	−30.8753	−	17.8258i	−1.20091	−	0.693345i	−0.240152	−	0.970735i	$-0.577197\pi$
$661$	−30.8753	−	17.8258i	−1.20091	−	0.693345i	−0.960757	+	0.277390i	$0.910530\pi$
$662$	5.84594	+	3.37516i	0.227209	+	0.131179i
$663$	−1.35926	−	1.12990i	−0.0527892	−	0.0438819i
$664$			6.48941i			0.251838i
$665$	−0.0352762	−	0.491334i	−0.00136795	−	0.0190531i
$666$	10.6385	+	12.4434i	0.412232	+	0.482171i
$667$	0.559898	+	0.969772i	0.0216793	+	0.0375497i
$668$	1.00548	−	1.74155i	0.0389033	−	0.0673824i
$669$	−3.87839	+	22.6049i	−0.149947	+	0.873956i
$670$	−3.64008	+	2.10160i	−0.140629	+	0.0811919i
$671$	8.81722			0.340385
$672$	−0.449490	+	4.56048i	−0.0173394	+	0.175924i
$673$	47.2677			1.82203			0.911017	−	0.412369i	$-0.135298\pi$
$673$	47.2677			1.82203			0.911017	+	0.412369i	$0.135298\pi$
$674$	−0.884152	+	0.510466i	−0.0340563	+	0.0196624i
$675$	21.2795	−	12.6817i	0.819047	−	0.488118i
$676$	6.34847	−	10.9959i	0.244172	−	0.422918i
$677$	16.9764	+	29.4040i	0.652456	+	1.13009i	0.982525	+	0.186130i	$0.0595945\pi$
$677$	16.9764	+	29.4040i	0.652456	+	1.13009i	−0.330069	+	0.943957i	$0.607072\pi$
$678$	11.8831	+	32.1856i	0.456367	+	1.23608i
$679$	36.8885	−	24.9816i	1.41565	−	0.958706i
$680$		−	0.894171i		−	0.0342899i
$681$	−30.6897	+	36.9192i	−1.17603	+	1.41475i
$682$	1.08018	+	0.623642i	0.0413622	+	0.0238805i
$683$	−30.2293	−	17.4529i	−1.15669	−	0.667817i	−0.206184	−	0.978513i	$-0.566104\pi$
$683$	−30.2293	−	17.4529i	−1.15669	−	0.667817i	−0.950509	+	0.310696i	$0.899438\pi$
$684$	−0.385986	+	1.09173i	−0.0147585	+	0.0417434i
$685$		−	5.54686i		−	0.211935i
$686$	13.6938	−	12.4691i	0.522834	−	0.476073i
$687$	13.5412	−	4.99948i	0.516630	−	0.190742i
$688$	0.341081	+	0.590770i	0.0130036	+	0.0225229i
$689$	−2.08006	+	3.60276i	−0.0792438	+	0.137254i
$690$	−0.205605	−	0.0352762i	−0.00782724	−	0.00134294i
$691$	8.04299	−	4.64362i	0.305970	−	0.176652i	−0.339152	−	0.940732i	$-0.610140\pi$
$691$	8.04299	−	4.64362i	0.305970	−	0.176652i	0.645122	+	0.764080i	$0.276807\pi$
$692$	13.1628			0.500375
$693$	2.10306	−	7.65357i	0.0798886	−	0.290735i
$694$	28.4765			1.08095
$695$	−1.41172	+	0.815060i	−0.0535498	+	0.0309170i
$696$	−7.65597	−	1.31356i	−0.290199	−	0.0497903i
$697$	−5.25893	+	9.10873i	−0.199196	+	0.345018i
$698$	6.47185	+	11.2096i	0.244963	+	0.424289i
$699$	13.1572	−	4.85772i	0.497652	−	0.183736i
$700$	5.50814	−	11.3469i	0.208188	−	0.428873i
$701$			32.9715i			1.24531i	0.782495	+	0.622657i	$0.213947\pi$
$701$			32.9715i			1.24531i	−0.782495	+	0.622657i	$0.786053\pi$
$702$	−0.0395983	−	2.86026i	−0.00149454	−	0.107954i
$703$	1.82415	+	1.05317i	0.0687990	+	0.0397211i
$704$	0.866025	+	0.500000i	0.0326396	+	0.0188445i
$705$	4.71503	−	5.67211i	0.177578	−	0.213624i
$706$			17.3326i			0.652321i
$707$	4.51628	−	0.324254i	0.169852	−	0.0121948i
$708$	2.18921	+	5.92953i	0.0822756	+	0.222845i
$709$	8.32304	+	14.4159i	0.312578	+	0.541401i	0.978920	−	0.204245i	$-0.0654740\pi$
$709$	8.32304	+	14.4159i	0.312578	+	0.541401i	−0.666342	+	0.745647i	$0.732141\pi$
$710$	1.38927	−	2.40629i	0.0521384	−	0.0903063i
$711$	−7.36312	−	39.6168i	−0.276139	−	1.48575i
$712$	9.77559	−	5.64394i	0.366356	−	0.211516i
$713$	0.311433			0.0116633
$714$	7.73793	−	3.50536i	0.289585	−	0.131185i
$715$	0.265545			0.00993083
$716$	−11.4624	+	6.61780i	−0.428368	+	0.247319i
$717$	−6.92358	+	40.3536i	−0.258566	+	1.50703i
$718$	−3.65514	+	6.33088i	−0.136408	+	0.236266i
$719$	−21.6348	−	37.4725i	−0.806841	−	1.39749i	−0.915041	−	0.403360i	$-0.867842\pi$
$719$	−21.6348	−	37.4725i	−0.806841	−	1.39749i	0.108201	−	0.994129i	$-0.465491\pi$
$720$	1.09990	−	0.940360i	0.0409909	−	0.0350451i
$721$	0.467462	+	0.226921i	0.0174092	+	0.00845097i
$722$		−	18.8510i		−	0.701562i
$723$	22.6898	+	18.8613i	0.843844	+	0.701459i
$724$	22.4245	+	12.9468i	0.833401	+	0.481164i
$725$	18.5159	+	10.6902i	0.687664	+	0.397023i
$726$	−1.33195	−	1.10721i	−0.0494333	−	0.0410923i
$727$		−	41.7432i		−	1.54817i	−0.633082	−	0.774085i	$-0.718210\pi$
$727$		−	41.7432i		−	1.54817i	0.633082	−	0.774085i	$-0.281790\pi$
$728$	−0.816717	−	1.20599i	−0.0302696	−	0.0446968i
$729$	14.1421	+	23.0000i	0.523783	+	0.851852i
$730$	0.541762	+	0.938360i	0.0200515	+	0.0347302i
$731$	0.632275	−	1.09513i	0.0233855	−	0.0405049i
$732$	−2.58250	+	15.0519i	−0.0954520	+	0.556335i
$733$	2.60675	−	1.50501i	0.0962826	−	0.0555888i	−0.451086	−	0.892481i	$-0.648963\pi$
$733$	2.60675	−	1.50501i	0.0962826	−	0.0555888i	0.547368	+	0.836892i	$0.315630\pi$
$734$	−9.78537			−0.361185
$735$	−5.84626	−	0.155377i	−0.215643	−	0.00573117i
$736$	0.249689			0.00920365
$737$	−7.54636	+	4.35690i	−0.277974	+	0.160488i
$738$	−16.7350	+	3.11035i	−0.616025	+	0.114494i
$739$	−5.43041	+	9.40575i	−0.199761	+	0.345996i	−0.948451	−	0.316924i	$-0.897350\pi$
$739$	−5.43041	+	9.40575i	−0.199761	+	0.345996i	0.748690	+	0.662920i	$0.230683\pi$
$740$	−1.31614	−	2.27962i	−0.0483822	−	0.0838004i
$741$	−0.127472	−	0.345262i	−0.00468281	−	0.0126835i
$742$	−11.2110	−	16.5545i	−0.411570	−	0.607736i
$743$		−	32.1359i		−	1.17895i	−0.807786	−	0.589476i	$-0.799334\pi$
$743$		−	32.1359i		−	1.17895i	0.807786	−	0.589476i	$-0.200666\pi$
$744$	−1.38100	+	1.66132i	−0.0506300	+	0.0609070i
$745$	6.90521	+	3.98672i	0.252987	+	0.146062i
$746$	24.2988	+	14.0289i	0.889644	+	0.513636i
$747$	18.3548	+	6.48941i	0.671568	+	0.237435i
$748$		−	1.85374i		−	0.0677793i
$749$	−22.2339	−	10.7930i	−0.812408	−	0.394369i
$750$	−7.65527	+	2.82636i	−0.279531	+	0.103204i
$751$	14.4715	+	25.0654i	0.528072	+	0.914648i	0.999464	+	0.0327241i	$0.0104183\pi$
$751$	14.4715	+	25.0654i	0.528072	+	0.914648i	−0.471392	+	0.881924i	$0.656248\pi$
$752$	−4.41421	+	7.64564i	−0.160970	+	0.278808i
$753$	−21.5223	−	3.69265i	−0.784317	−	0.134567i
$754$	2.13814	−	1.23445i	0.0778664	−	0.0449562i
$755$	−0.0737035			−0.00268235
$756$	12.4495	+	5.83183i	0.452784	+	0.212101i
$757$	11.8099			0.429239			0.214619	−	0.976698i	$-0.431149\pi$
$757$	11.8099			0.429239			0.214619	+	0.976698i	$0.431149\pi$
$758$	−25.3434	+	14.6320i	−0.920515	+	0.531460i
$759$	−0.426246	−	0.0731322i	−0.0154717	−	0.00265453i
$760$	0.0930924	−	0.161241i	0.00337682	−	0.00584882i
$761$	−2.72848	−	4.72586i	−0.0989071	−	0.171312i	0.812325	−	0.583204i	$-0.198201\pi$
$761$	−2.72848	−	4.72586i	−0.0989071	−	0.171312i	−0.911233	+	0.411892i	$0.864868\pi$
$762$	34.3558	−	12.6843i	1.24458	−	0.459504i
$763$	16.6339	−	1.19426i	0.602189	−	0.0432353i
$764$			17.5274i			0.634118i
$765$	−2.52910	−	0.894171i	−0.0914398	−	0.0323288i
$766$	−8.47623	−	4.89376i	−0.306259	−	0.176819i
$767$	−1.73982	−	1.00449i	−0.0628213	−	0.0362699i
$768$	−1.10721	+	1.33195i	−0.0399529	+	0.0480627i
$769$			20.7871i			0.749602i	0.927105	+	0.374801i	$0.122289\pi$
$769$			20.7871i			0.749602i	−0.927105	+	0.374801i	$0.877711\pi$
$770$	−0.557318	+	1.14809i	−0.0200844	+	0.0413742i
$771$	−0.245392	−	0.664649i	−0.00883756	−	0.0239367i
$772$	−3.68204	−	6.37748i	−0.132519	−	0.229530i
$773$	−23.4534	+	40.6225i	−0.843560	+	1.46109i	0.0433053	+	0.999062i	$0.486211\pi$
$773$	−23.4534	+	40.6225i	−0.843560	+	1.46109i	−0.886866	+	0.462027i	$0.847122\pi$
$774$	2.01203	−	0.373954i	0.0723210	−	0.0134415i
$775$	5.14957	−	2.97311i	0.184978	−	0.106797i
$776$	16.8389			0.604482
$777$	14.5677	−	20.3261i	0.522612	−	0.729196i
$778$	−37.1338			−1.33131
$779$	−1.89662	+	1.09502i	−0.0679536	+	0.0392330i
$780$	−0.0777764	+	0.453314i	−0.00278484	+	0.0162312i
$781$	2.88014	−	4.98855i	0.103059	−	0.178504i
$782$	−0.231429	−	0.400846i	−0.00827587	−	0.0143342i
$783$	−11.3713	+	20.3408i	−0.406376	+	0.726921i
$784$	6.92820	−	1.00000i	0.247436	−	0.0357143i
$785$			5.07611i			0.181174i
$786$	21.7643	+	18.0919i	0.776308	+	0.645318i
$787$	−22.6920	−	13.1012i	−0.808881	−	0.467008i	0.0376861	−	0.999290i	$-0.488001\pi$
$787$	−22.6920	−	13.1012i	−0.808881	−	0.467008i	−0.846567	+	0.532282i	$0.821335\pi$
$788$	−16.7084	−	9.64660i	−0.595212	−	0.343646i
$789$	−19.3932	−	16.1209i	−0.690416	−	0.573920i
$790$			6.47896i			0.230511i
$791$	43.3938	−	29.3871i	1.54290	−	1.04488i
$792$	2.28024	−	1.94949i	0.0810248	−	0.0692721i
$793$	−2.42698	−	4.20366i	−0.0861847	−	0.149276i
$794$	18.1283	−	31.3992i	0.643351	−	1.11432i
$795$	−1.06763	+	6.22262i	−0.0378650	+	0.220694i
$796$	17.4020	−	10.0471i	0.616799	−	0.356109i
$797$	−5.14751			−0.182334			−0.0911671	−	0.995836i	$-0.529060\pi$
$797$	−5.14751			−0.182334			−0.0911671	+	0.995836i	$0.529060\pi$
$798$	1.76028	+	0.173497i	0.0623132	+	0.00614171i
$799$	16.3656			0.578972
$800$	4.12863	−	2.38366i	0.145969	−	0.0842752i
$801$	−6.18788	−	33.2935i	−0.218638	−	1.17637i
$802$	−13.6373	+	23.6204i	−0.481549	+	0.834067i
$803$	1.12314	+	1.94534i	0.0396349	+	0.0686497i
$804$	−5.22741	−	14.1586i	−0.184356	−	0.499334i
$805$	0.0228197	+	0.317837i	0.000804288	+	0.0112023i
$806$		−	0.686643i		−	0.0241860i
$807$	−27.4498	+	33.0216i	−0.966277	+	1.16242i
$808$	1.48210	+	0.855693i	0.0521402	+	0.0301032i
$809$	6.76716	+	3.90702i	0.237921	+	0.137364i	0.614221	−	0.789134i	$-0.289470\pi$
$809$	6.76716	+	3.90702i	0.237921	+	0.137364i	−0.376300	+	0.926498i	$0.622804\pi$
$810$	−1.55984	−	4.05135i	−0.0548071	−	0.142350i
$811$		−	9.92215i		−	0.348414i	−0.984709	−	0.174207i	$-0.944264\pi$
$811$		−	9.92215i		−	0.348414i	0.984709	−	0.174207i	$-0.0557362\pi$
$812$	0.849723	+	11.8351i	0.0298194	+	0.415331i
$813$	−46.1873	+	17.0526i	−1.61986	+	0.598060i
$814$	−2.72853	−	4.72595i	−0.0956348	−	0.165644i
$815$	2.09455	−	3.62787i	0.0733690	−	0.127079i
$816$	3.16452	+	0.542947i	0.110781	+	0.0190069i
$817$	0.228029	−	0.131652i	0.00797772	−	0.00460594i
$818$	−12.4834			−0.436472
$819$	−4.22776	+	1.10404i	−0.147730	+	0.0385782i
$820$	2.73686			0.0955753
$821$	−16.6405	+	9.60741i	−0.580758	+	0.335301i	−0.761435	−	0.648242i	$-0.775505\pi$
$821$	−16.6405	+	9.60741i	−0.580758	+	0.335301i	0.180676	+	0.983543i	$0.442171\pi$
$822$	19.6307	+	3.36809i	0.684698	+	0.117476i
$823$	−9.79913	+	16.9726i	−0.341576	+	0.591627i	−0.984726	−	0.174113i	$-0.944294\pi$
$823$	−9.79913	+	16.9726i	−0.341576	+	0.591627i	0.643149	+	0.765741i	$0.277627\pi$
$824$	0.0982005	+	0.170088i	0.00342098	+	0.00592531i
$825$	−7.74616	+	2.85992i	−0.269687	+	0.0995697i
$826$	7.99439	−	5.41396i	0.278161	−	0.188376i
$827$			3.35552i			0.116683i	0.998297	+	0.0583414i	$0.0185812\pi$
$827$			3.35552i			0.116683i	−0.998297	+	0.0583414i	$0.981419\pi$
$828$	0.249689	−	0.706227i	0.00867729	−	0.0245431i
$829$	−33.3865	−	19.2757i	−1.15956	−	0.669474i	−0.208363	−	0.978051i	$-0.566814\pi$
$829$	−33.3865	−	19.2757i	−1.15956	−	0.669474i	−0.951199	+	0.308578i	$0.900147\pi$
$830$	−2.71087	−	1.56512i	−0.0940957	−	0.0543262i
$831$	−3.83490	+	4.61333i	−0.133031	+	0.160035i
$832$		−	0.550510i		−	0.0190855i
$833$	−8.02691	−	10.1955i	−0.278116	−	0.353255i
$834$	−2.02734	−	5.49109i	−0.0702009	−	0.190141i
$835$	0.485006	+	0.840055i	0.0167843	+	0.0290713i
$836$	0.192993	−	0.334273i	0.00667480	−	0.0115611i
$837$	3.31793	+	5.56739i	0.114684	+	0.192437i
$838$	−12.3908	+	7.15383i	−0.428033	+	0.247125i
$839$	−33.3680			−1.15199			−0.575996	−	0.817452i	$-0.695386\pi$
$839$	−33.3680			−1.15199			−0.575996	+	0.817452i	$0.695386\pi$
$840$	−1.79668	−	1.28767i	−0.0619912	−	0.0444288i
$841$	8.88687			0.306444
$842$	−13.1649	+	7.60074i	−0.453691	+	0.261939i
$843$	6.02210	−	35.0994i	0.207412	−	1.20889i
$844$	−2.49257	+	4.31726i	−0.0857978	+	0.148606i
$845$	3.06226	+	5.30399i	0.105345	+	0.182463i
$846$	17.2109	+	20.1309i	0.591724	+	0.692115i
$847$	−1.15539	+	2.38014i	−0.0396998	+	0.0817826i
$848$		−	7.55683i		−	0.259503i
$849$	9.87926	+	8.21230i	0.339055	+	0.281845i
$850$	−7.65338	−	4.41868i	−0.262509	−	0.151560i
$851$	−1.18002	−	0.681283i	−0.0404504	−	0.0233541i
$852$	7.67241	+	6.37782i	0.262852	+	0.218500i
$853$			7.56740i			0.259103i	0.991573	+	0.129551i	$0.0413537\pi$
$853$			7.56740i			0.259103i	−0.991573	+	0.129551i	$0.958646\pi$
$854$	23.2683	−	1.67059i	0.796224	−	0.0571663i
$855$	−0.362965	−	0.424546i	−0.0124131	−	0.0145192i
$856$	−4.67071	−	8.08991i	−0.159642	−	0.276507i
$857$	−22.1795	+	38.4160i	−0.757636	+	1.31226i	0.186416	+	0.982471i	$0.440313\pi$
$857$	−22.1795	+	38.4160i	−0.757636	+	1.31226i	−0.944053	+	0.329794i	$0.893021\pi$
$858$	−0.161241	+	0.939780i	−0.00550467	+	0.0320836i
$859$	15.3094	−	8.83889i	0.522350	−	0.301579i	−0.215545	−	0.976494i	$-0.569153\pi$
$859$	15.3094	−	8.83889i	0.522350	−	0.301579i	0.737896	+	0.674915i	$0.235820\pi$
$860$	−0.329049			−0.0112205
$861$	10.7291	+	23.6841i	0.365647	+	0.807151i
$862$	1.66928			0.0568558
$863$	27.0927	−	15.6420i	0.922248	−	0.532460i	0.0378962	−	0.999282i	$-0.487934\pi$
$863$	27.0927	−	15.6420i	0.922248	−	0.532460i	0.884351	+	0.466822i	$0.154601\pi$
$864$	2.66012	+	4.46360i	0.0904991	+	0.151855i
$865$	−3.17462	+	5.49860i	−0.107940	+	0.186958i
$866$	−5.26965	−	9.12730i	−0.179070	−	0.310158i
$867$	8.13685	+	22.0388i	0.276342	+	0.748478i
$868$	2.96871	+	1.44111i	0.100765	+	0.0489143i
$869$			13.4317i			0.455641i
$870$	2.39520	−	2.88138i	0.0812048	−	0.0976881i
$871$	4.15435	+	2.39852i	0.140765	+	0.0812706i
$872$	5.45875	+	3.15161i	0.184857	+	0.106727i
$873$	16.8389	−	47.6276i	0.569911	−	1.61195i
$874$		−	0.0963763i		−	0.00325998i
$875$	6.98964	+	10.3211i	0.236293	+	0.348917i
$876$	−3.64987	+	1.34755i	−0.123318	+	0.0455295i
$877$	6.71183	+	11.6252i	0.226642	+	0.392556i	0.956811	−	0.290711i	$-0.0938918\pi$
$877$	6.71183	+	11.6252i	0.226642	+	0.392556i	−0.730168	+	0.683267i	$0.760558\pi$
$878$	−11.2143	+	19.4237i	−0.378463	+	0.655517i
$879$	56.5392	+	9.70059i	1.90702	+	0.327193i
$880$	−0.417738	+	0.241181i	−0.0140819	+	0.00813021i
$881$	−17.4395			−0.587551			−0.293775	−	0.955874i	$-0.594912\pi$
$881$	−17.4395			−0.587551			−0.293775	+	0.955874i	$0.594912\pi$
$882$	4.09978	−	20.5959i	0.138047	−	0.693501i
$883$	−46.0054			−1.54820			−0.774102	−	0.633061i	$-0.781798\pi$
$883$	−46.0054			−1.54820			−0.774102	+	0.633061i	$0.781798\pi$
$884$	−0.883779	+	0.510250i	−0.0297247	+	0.0171616i
$885$	−3.00498	−	0.515574i	−0.101011	−	0.0173308i
$886$	3.09550	−	5.36156i	0.103995	−	0.180125i
$887$	−16.2645	−	28.1710i	−0.546109	−	0.945888i	−0.998536	−	0.0540868i	$-0.982775\pi$
$887$	−16.2645	−	28.1710i	−0.546109	−	0.945888i	0.452428	−	0.891801i	$-0.350558\pi$
$888$	8.86686	−	3.27369i	0.297552	−	0.109858i
$889$	−31.3685	−	46.3196i	−1.05207	−	1.55351i
$890$			5.44485i			0.182512i
$891$	−3.23375	−	8.39898i	−0.108335	−	0.281376i
$892$	11.4676	+	6.62082i	0.383964	+	0.221682i
$893$	2.95111	+	1.70382i	0.0987551	+	0.0570163i
$894$	−18.3021	+	22.0172i	−0.612115	+	0.736364i
$895$		−	6.38435i		−	0.213405i
$896$	2.38014	+	1.15539i	0.0795149	+	0.0385990i
$897$	0.0824601	+	0.223345i	0.00275326	+	0.00745728i
$898$	0.777320	+	1.34636i	0.0259395	+	0.0449285i
$899$	−2.79689	+	4.84436i	−0.0932815	+	0.161568i
$900$	−2.61339	−	14.0612i	−0.0871131	−	0.468706i
$901$	−12.1316	+	7.00418i	−0.404162	+	0.233343i
$902$	5.67387			0.188919
$903$	−1.28995	−	2.84751i	−0.0429268	−	0.0947591i
$904$	19.8084			0.658819
$905$	−10.8167	+	6.24504i	−0.359560	+	0.207592i
$906$	0.0447532	−	0.260841i	0.00148683	−	0.00866586i
$907$	1.11719	−	1.93503i	0.0370957	−	0.0642517i	−0.846881	−	0.531782i	$-0.821523\pi$
$907$	1.11719	−	1.93503i	0.0370957	−	0.0642517i	0.883977	+	0.467530i	$0.154856\pi$
$908$	13.8591	+	24.0046i	0.459929	+	0.796620i
$909$	3.90237	−	3.33633i	0.129433	−	0.110659i
$910$	0.700763	−	0.0503125i	0.0232301	−	0.00166784i
$911$			30.4938i			1.01030i	0.863030	+	0.505152i	$0.168564\pi$
$911$			30.4938i			1.01030i	−0.863030	+	0.505152i	$0.831436\pi$
$912$	0.514114	+	0.427366i	0.0170240	+	0.0141515i
$913$	−5.61999	−	3.24471i	−0.185995	−	0.107384i
$914$	14.1605	+	8.17556i	0.468387	+	0.270424i
$915$	−5.66491	−	4.70905i	−0.187276	−	0.155676i
$916$		−	8.33386i		−	0.275358i
$917$	18.8794	−	38.8919i	0.623451	−	1.28432i
$918$	4.70021	−	8.40768i	0.155130	−	0.277495i
$919$	1.57169	+	2.72225i	0.0518453	+	0.0897986i	0.890783	−	0.454428i	$-0.150156\pi$
$919$	1.57169	+	2.72225i	0.0518453	+	0.0897986i	−0.838938	+	0.544227i	$0.816823\pi$
$920$	−0.0602202	+	0.104304i	−0.00198540	+	0.00343882i
$921$	−3.39895	+	19.8105i	−0.111999	+	0.652778i
$922$	−17.5590	+	10.1377i	−0.578276	+	0.333868i
$923$	−3.17109			−0.104378
$924$	−3.72474	−	2.66951i	−0.122535	−	0.0878204i
$925$	−26.0156			−0.855386
$926$	−4.87956	+	2.81722i	−0.160352	+	0.0925794i
$927$	0.579283	−	0.107665i	0.0190261	−	0.00353617i
$928$	−2.24238	+	3.88392i	−0.0736098	+	0.127496i
$929$	23.0663	+	39.9519i	0.756779	+	1.31078i	0.944485	+	0.328555i	$0.106562\pi$
$929$	23.0663	+	39.9519i	0.756779	+	1.31078i	−0.187706	+	0.982225i	$0.560105\pi$
$930$	−0.360926	−	0.977576i	−0.0118352	−	0.0320560i
$931$	−0.385986	−	2.67419i	−0.0126502	−	0.0876429i
$932$		−	8.09754i		−	0.265244i
$933$	2.49087	−	2.99648i	0.0815474	−	0.0981002i
$934$	−32.6022	−	18.8229i	−1.06678	−	0.615904i
$935$	0.774375	+	0.447086i	0.0253248	+	0.0146213i
$936$	−1.55708	−	0.550510i	−0.0508947	−	0.0179940i
$937$		−	29.7606i		−	0.972236i	−0.873893	−	0.486118i	$-0.838413\pi$
$937$		−	29.7606i		−	0.972236i	0.873893	−	0.486118i	$-0.161587\pi$
$938$	−19.0890	+	12.9275i	−0.623279	+	0.422097i
$939$	−16.7526	+	6.18516i	−0.546702	+	0.201845i
$940$	−2.12925	−	3.68797i	−0.0694484	−	0.120288i
$941$	−3.16738	+	5.48605i	−0.103253	+	0.178840i	−0.913023	−	0.407907i	$-0.866259\pi$
$941$	−3.16738	+	5.48605i	−0.103253	+	0.178840i	0.809770	+	0.586748i	$0.199592\pi$
$942$	−17.9646	−	3.08224i	−0.585320	−	0.100425i
$943$	1.22690	−	0.708351i	0.0399534	−	0.0230671i
$944$	3.64929			0.118774
$945$	−5.43875	+	3.79410i	−0.176923	+	0.123422i
$946$	−0.682163			−0.0221790
$947$	38.3205	−	22.1244i	1.24525	−	0.718945i	0.275091	−	0.961418i	$-0.411292\pi$
$947$	38.3205	−	22.1244i	1.24525	−	0.718945i	0.970158	+	0.242473i	$0.0779587\pi$
$948$	−22.9294	−	3.93407i	−0.744713	−	0.127773i
$949$	0.618303	−	1.07093i	0.0200710	−	0.0347639i
$950$	−0.920060	−	1.59359i	−0.0298507	−	0.0517029i
$951$	−25.7526	+	9.50797i	−0.835084	+	0.308317i
$952$	−0.351225	−	4.89193i	−0.0113833	−	0.158548i
$953$		−	49.7571i		−	1.61179i	−0.592059	−	0.805895i	$-0.701685\pi$
$953$		−	49.7571i		−	1.61179i	0.592059	−	0.805895i	$-0.298315\pi$
$954$	−21.3739	−	7.55683i	−0.692007	−	0.244661i
$955$	−7.32184	−	4.22726i	−0.236929	−	0.136791i
$956$	20.4716	+	11.8193i	0.662100	+	0.382263i
$957$	4.96556	−	5.97349i	0.160514	−	0.193095i
$958$			16.1745i			0.522574i
$959$	−2.17877	−	30.3464i	−0.0703562	−	0.979936i
$960$	−0.289369	−	0.783763i	−0.00933935	−	0.0252958i
$961$	−14.7221	−	25.4995i	−0.474908	−	0.822564i
$962$	−1.50208	+	2.60168i	−0.0484291	+	0.0838816i
$963$	−27.5524	+	5.12086i	−0.887865	+	0.165017i
$964$	14.7528	−	8.51751i	0.475155	−	0.274331i
$965$	3.55215			0.114348
$966$	−1.13870	−	0.112233i	−0.0366371	−	0.00361102i
$967$	−31.3556			−1.00833			−0.504164	−	0.863608i	$-0.668199\pi$
$967$	−31.3556			−1.00833			−0.504164	+	0.863608i	$0.668199\pi$
$968$	−0.866025	+	0.500000i	−0.0278351	+	0.0160706i
$969$	0.209570	−	1.22146i	0.00673234	−	0.0392390i
$970$	−4.06122	+	7.03425i	−0.130398	+	0.225856i
$971$	26.2882	+	45.5325i	0.843628	+	1.46121i	0.886807	+	0.462139i	$0.152918\pi$
$971$	26.2882	+	45.5325i	0.843628	+	1.46121i	−0.0431796	+	0.999067i	$0.513749\pi$
$972$	15.2851	−	3.06035i	0.490270	−	0.0981609i
$973$	−7.40327	+	5.01363i	−0.237338	+	0.160730i
$974$		−	21.7739i		−	0.697681i
$975$	3.49566	+	2.90582i	0.111951	+	0.0930608i
$976$	7.63593	+	4.40861i	0.244420	+	0.141116i
$977$	27.9026	+	16.1096i	0.892682	+	0.515390i	0.874819	−	0.484450i	$-0.160980\pi$
$977$	27.9026	+	16.1096i	0.892682	+	0.515390i	0.0178633	+	0.999840i	$0.494314\pi$
$978$	11.5674	+	9.61561i	0.369885	+	0.307473i
$979$			11.2879i			0.360762i
$980$	−1.25321	+	3.13535i	−0.0400324	+	0.100155i
$981$	14.3729	−	12.2881i	0.458890	−	0.392328i
$982$	−7.15623	−	12.3950i	−0.228365	−	0.395539i
$983$	9.07712	−	15.7220i	0.289515	−	0.501455i	−0.684179	−	0.729314i	$-0.739839\pi$
$983$	9.07712	−	15.7220i	0.289515	−	0.501455i	0.973694	+	0.227859i	$0.0731726\pi$
$984$	−1.66184	+	9.68590i	−0.0529775	+	0.308775i
$985$	8.05950	−	4.65315i	0.256797	−	0.148262i
$986$	8.31357			0.264758
$987$	23.5676	−	32.8836i	0.750164	−	1.04670i
$988$	−0.212489			−0.00676018
$989$	−0.147509	+	0.0851642i	−0.00469051	+	0.00270807i
$990$	0.264425	+	1.42272i	0.00840398	+	0.0452171i
$991$	24.0610	−	41.6748i	0.764321	−	1.32384i	−0.176283	−	0.984339i	$-0.556408\pi$
$991$	24.0610	−	41.6748i	0.764321	−	1.32384i	0.940605	−	0.339504i	$-0.110259\pi$
$992$	0.623642	+	1.08018i	0.0198007	+	0.0342958i
$993$	−4.04951	−	10.9682i	−0.128507	−	0.348065i
$994$	6.65539	−	13.7103i	0.211096	−	0.434863i
$995$			9.69265i			0.307278i
$996$	7.18512	−	8.64358i	0.227669	−	0.273882i
$997$	−5.51486	−	3.18400i	−0.174657	−	0.100838i	0.410123	−	0.912030i	$-0.365486\pi$
$997$	−5.51486	−	3.18400i	−0.174657	−	0.100838i	−0.584780	+	0.811192i	$0.698819\pi$
$998$	6.97799	+	4.02874i	0.220884	+	0.127528i
$999$	−0.392527	−	28.3530i	−0.0124190	−	0.897048i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.k.f.353.2	yes	8
3.2	odd	2		462.2.k.e.353.3	yes	8
7.5	odd	6		462.2.k.e.89.3	✓	8
21.5	even	6	inner	462.2.k.f.89.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.k.e.89.3	✓	8	7.5	odd	6
462.2.k.e.353.3	yes	8	3.2	odd	2
462.2.k.f.89.2	yes	8	21.5	even	6	inner
462.2.k.f.353.2	yes	8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(1.70711 + 0.292893i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.241181 + 0.417738i) q^{5} +(-1.62484 + 0.599900i) q^{6} +(1.48356 + 2.19067i) q^{7} +1.00000i q^{8} +(2.82843 + 1.00000i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(1.70711 + 0.292893i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.241181 + 0.417738i) q^{5} +(-1.62484 + 0.599900i) q^{6} +(1.48356 + 2.19067i) q^{7} +1.00000i q^{8} +(2.82843 + 1.00000i) q^{9} +(-0.417738 - 0.241181i) q^{10} +(-0.866025 - 0.500000i) q^{11} +(1.10721 - 1.33195i) q^{12} +0.550510i q^{13} +(-2.38014 - 1.15539i) q^{14} +(0.289369 + 0.783763i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.926868 + 1.60538i) q^{17} +(-2.94949 + 0.548188i) q^{18} +(-0.334273 + 0.192993i) q^{19} +0.482362 q^{20} +(1.89097 + 4.17423i) q^{21} +1.00000 q^{22} +(0.216237 - 0.124844i) q^{23} +(-0.292893 + 1.70711i) q^{24} +(2.38366 - 4.12863i) q^{25} +(-0.275255 - 0.476756i) q^{26} +(4.53553 + 2.53553i) q^{27} +(2.63896 - 0.189469i) q^{28} +4.48477i q^{29} +(-0.642483 - 0.534074i) q^{30} +(1.08018 + 0.623642i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.33195 - 1.10721i) q^{33} -1.85374i q^{34} +(-0.557318 + 1.14809i) q^{35} +(2.28024 - 1.94949i) q^{36} +(-2.72853 - 4.72595i) q^{37} +(0.192993 - 0.334273i) q^{38} +(-0.161241 + 0.939780i) q^{39} +(-0.417738 + 0.241181i) q^{40} +5.67387 q^{41} +(-3.72474 - 2.66951i) q^{42} -0.682163 q^{43} +(-0.866025 + 0.500000i) q^{44} +(0.264425 + 1.42272i) q^{45} +(-0.124844 + 0.216237i) q^{46} +(-4.41421 - 7.64564i) q^{47} +(-0.599900 - 1.62484i) q^{48} +(-2.59808 + 6.50000i) q^{49} +4.76733i q^{50} +(-2.05247 + 2.46909i) q^{51} +(0.476756 + 0.275255i) q^{52} +(6.54441 + 3.77841i) q^{53} +(-5.19565 + 0.0719302i) q^{54} -0.482362i q^{55} +(-2.19067 + 1.48356i) q^{56} +(-0.627167 + 0.231553i) q^{57} +(-2.24238 - 3.88392i) q^{58} +(-1.82465 + 3.16038i) q^{59} +(0.823443 + 0.141281i) q^{60} +(-7.63593 + 4.40861i) q^{61} -1.24728 q^{62} +(2.00548 + 7.67972i) q^{63} -1.00000 q^{64} +(-0.229969 + 0.132773i) q^{65} +(1.70711 + 0.292893i) q^{66} +(4.35690 - 7.54636i) q^{67} +(0.926868 + 1.60538i) q^{68} +(0.405706 - 0.149788i) q^{69} +(-0.0913925 - 1.27293i) q^{70} +5.76028i q^{71} +(-1.00000 + 2.82843i) q^{72} +(-1.94534 - 1.12314i) q^{73} +(4.72595 + 2.72853i) q^{74} +(5.27841 - 6.34985i) q^{75} +0.385986i q^{76} +(-0.189469 - 2.63896i) q^{77} +(-0.330251 - 0.894494i) q^{78} +(-6.71587 - 11.6322i) q^{79} +(0.241181 - 0.417738i) q^{80} +(7.00000 + 5.65685i) q^{81} +(-4.91372 + 2.83694i) q^{82} +6.48941 q^{83} +(4.56048 + 0.449490i) q^{84} -0.894171 q^{85} +(0.590770 - 0.341081i) q^{86} +(-1.31356 + 7.65597i) q^{87} +(0.500000 - 0.866025i) q^{88} +(-5.64394 - 9.77559i) q^{89} +(-0.940360 - 1.09990i) q^{90} +(-1.20599 + 0.816717i) q^{91} -0.249689i q^{92} +(1.66132 + 1.38100i) q^{93} +(7.64564 + 4.41421i) q^{94} +(-0.161241 - 0.0930924i) q^{95} +(1.33195 + 1.10721i) q^{96} -16.8389i q^{97} +(-1.00000 - 6.92820i) q^{98} +(-1.94949 - 2.28024i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{3} + 4 q^{4} + 4 q^{5} - 4 q^{6}+O(q^{10}) \) 8 * q + 8 * q^3 + 4 * q^4 + 4 * q^5 - 4 * q^6	\( 8 q + 8 q^{3} + 4 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{12} - 4 q^{16} - 20 q^{17} - 4 q^{18} - 12 q^{19} + 8 q^{20} + 8 q^{22} + 12 q^{23} - 8 q^{24} + 8 q^{25} - 12 q^{26} + 8 q^{27} + 8 q^{30} + 12 q^{31} + 4 q^{33} - 16 q^{35} + 8 q^{38} - 24 q^{39} - 40 q^{41} - 20 q^{42} - 8 q^{43} + 8 q^{45} + 8 q^{46} - 24 q^{47} - 4 q^{48} - 4 q^{51} + 60 q^{53} + 4 q^{54} - 20 q^{57} - 4 q^{58} - 4 q^{59} + 12 q^{60} - 36 q^{61} - 24 q^{62} - 8 q^{63} - 8 q^{64} + 12 q^{65} + 8 q^{66} + 12 q^{67} + 20 q^{68} + 12 q^{69} - 20 q^{70} - 8 q^{72} + 48 q^{73} + 12 q^{74} + 4 q^{75} - 8 q^{79} + 4 q^{80} + 56 q^{81} - 24 q^{82} + 72 q^{83} - 32 q^{85} - 12 q^{86} - 16 q^{87} + 4 q^{88} + 4 q^{89} + 28 q^{90} + 36 q^{91} - 20 q^{93} - 24 q^{95} - 4 q^{96} - 8 q^{98} + 4 q^{99}+O(q^{100}) \) 8 * q + 8 * q^3 + 4 * q^4 + 4 * q^5 - 4 * q^6 + 4 * q^12 - 4 * q^16 - 20 * q^17 - 4 * q^18 - 12 * q^19 + 8 * q^20 + 8 * q^22 + 12 * q^23 - 8 * q^24 + 8 * q^25 - 12 * q^26 + 8 * q^27 + 8 * q^30 + 12 * q^31 + 4 * q^33 - 16 * q^35 + 8 * q^38 - 24 * q^39 - 40 * q^41 - 20 * q^42 - 8 * q^43 + 8 * q^45 + 8 * q^46 - 24 * q^47 - 4 * q^48 - 4 * q^51 + 60 * q^53 + 4 * q^54 - 20 * q^57 - 4 * q^58 - 4 * q^59 + 12 * q^60 - 36 * q^61 - 24 * q^62 - 8 * q^63 - 8 * q^64 + 12 * q^65 + 8 * q^66 + 12 * q^67 + 20 * q^68 + 12 * q^69 - 20 * q^70 - 8 * q^72 + 48 * q^73 + 12 * q^74 + 4 * q^75 - 8 * q^79 + 4 * q^80 + 56 * q^81 - 24 * q^82 + 72 * q^83 - 32 * q^85 - 12 * q^86 - 16 * q^87 + 4 * q^88 + 4 * q^89 + 28 * q^90 + 36 * q^91 - 20 * q^93 - 24 * q^95 - 4 * q^96 - 8 * q^98 + 4 * q^99

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