LMFDB - Embedded newform 462.2.p.b.241.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(241,462)]

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([0, 1, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("462.241");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.p (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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 74 x^{14} - 378 x^{13} + 1878 x^{12} - 6718 x^{11} + 22086 x^{10} - 56904 x^{9} + \cdots + 13417 $ x^16 - 8x^15 + 74x^14 - 378x^13 + 1878x^12 - 6718x^11 + 22086x^10 - 56904x^9 + 130215x^8 - 239606x^7 + 378750x^6 - 477124x^5 + 493030x^4 - 386266x^3 + 223844x^2 - 82874*x + 13417
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			241.4
Root			$0.500000 + 3.43554i$ of defining polynomial
Character	$\chi$	$=$	462.241
Dual form			462.2.p.b.439.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(3.72526 - 2.15078i) q^{5} +1.00000 q^{6} +(1.43173 + 2.22489i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(3.72526 - 2.15078i) q^{5} +1.00000 q^{6} +(1.43173 + 2.22489i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.15078 + 3.72526i) q^{10} +(1.15591 + 3.10868i) q^{11} +(-0.866025 + 0.500000i) q^{12} -1.00074 q^{13} +(-2.35236 - 1.21095i) q^{14} -4.30156 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.66854 - 2.89000i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(-1.61555 - 2.79822i) q^{19} -4.30156i q^{20} +(-0.127470 - 2.64268i) q^{21} +(-2.55539 - 2.11424i) q^{22} +(2.86499 + 4.96231i) q^{23} +(0.500000 - 0.866025i) q^{24} +(6.75173 - 11.6943i) q^{25} +(0.866669 - 0.500372i) q^{26} -1.00000i q^{27} +(2.64268 - 0.127470i) q^{28} +7.74872i q^{29} +(3.72526 - 2.15078i) q^{30} +(-2.77407 - 1.60161i) q^{31} +(0.866025 + 0.500000i) q^{32} +(0.553289 - 3.27015i) q^{33} +3.33708i q^{34} +(10.1188 + 5.20897i) q^{35} +1.00000 q^{36} +(1.26472 + 2.19056i) q^{37} +(2.79822 + 1.61555i) q^{38} +(0.866669 + 0.500372i) q^{39} +(2.15078 + 3.72526i) q^{40} -1.45111 q^{41} +(1.43173 + 2.22489i) q^{42} -4.14572i q^{43} +(3.27015 + 0.553289i) q^{44} +(3.72526 + 2.15078i) q^{45} +(-4.96231 - 2.86499i) q^{46} +(2.77216 - 1.60050i) q^{47} +1.00000i q^{48} +(-2.90029 + 6.37090i) q^{49} +13.5035i q^{50} +(-2.89000 + 1.66854i) q^{51} +(-0.500372 + 0.866669i) q^{52} +(5.65774 - 9.79949i) q^{53} +(0.500000 + 0.866025i) q^{54} +(10.9922 + 9.09452i) q^{55} +(-2.22489 + 1.43173i) q^{56} +3.23111i q^{57} +(-3.87436 - 6.71059i) q^{58} +(2.98113 + 1.72116i) q^{59} +(-2.15078 + 3.72526i) q^{60} +(-7.42522 - 12.8609i) q^{61} +3.20322 q^{62} +(-1.21095 + 2.35236i) q^{63} -1.00000 q^{64} +(-3.72803 + 2.15238i) q^{65} +(1.15591 + 3.10868i) q^{66} +(0.165196 - 0.286128i) q^{67} +(-1.66854 - 2.89000i) q^{68} -5.72998i q^{69} +(-11.3677 + 0.548319i) q^{70} +2.84974 q^{71} +(-0.866025 + 0.500000i) q^{72} +(7.44790 - 12.9001i) q^{73} +(-2.19056 - 1.26472i) q^{74} +(-11.6943 + 6.75173i) q^{75} -3.23111 q^{76} +(-5.26151 + 7.02257i) q^{77} -1.00074 q^{78} +(-13.9363 + 8.04614i) q^{79} +(-3.72526 - 2.15078i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.25670 - 0.725556i) q^{82} -1.75062 q^{83} +(-2.35236 - 1.21095i) q^{84} -14.3547i q^{85} +(2.07286 + 3.59030i) q^{86} +(3.87436 - 6.71059i) q^{87} +(-3.10868 + 1.15591i) q^{88} +(-2.41153 + 1.39230i) q^{89} -4.30156 q^{90} +(-1.43280 - 2.22655i) q^{91} +5.72998 q^{92} +(1.60161 + 2.77407i) q^{93} +(-1.60050 + 2.77216i) q^{94} +(-12.0367 - 6.94940i) q^{95} +(-0.500000 - 0.866025i) q^{96} +12.3347i q^{97} +(-0.673723 - 6.96750i) q^{98} +(-2.11424 + 2.55539i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 12 q^{5} + 16 q^{6} + 6 q^{7} + 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 + 12 * q^5 + 16 * q^6 + 6 * q^7 + 8 * q^9	$ 16 q + 8 q^{4} + 12 q^{5} + 16 q^{6} + 6 q^{7} + 8 q^{9} - 2 q^{10} - 4 q^{11} + 8 q^{14} - 4 q^{15} - 8 q^{16} + 10 q^{19} + 4 q^{21} + 2 q^{22} - 4 q^{23} + 8 q^{24} + 10 q^{25} + 12 q^{26} + 12 q^{30} + 6 q^{31} + 4 q^{33} + 8 q^{35} + 16 q^{36} + 14 q^{37} - 12 q^{38} + 12 q^{39} + 2 q^{40} - 32 q^{41} + 6 q^{42} + 4 q^{44} + 12 q^{45} - 18 q^{46} - 24 q^{47} - 6 q^{49} - 6 q^{51} + 8 q^{54} + 14 q^{55} + 4 q^{56} - 2 q^{60} - 28 q^{61} + 8 q^{62} + 6 q^{63} - 16 q^{64} - 72 q^{65} - 4 q^{66} - 16 q^{67} - 30 q^{70} - 56 q^{71} + 44 q^{73} - 24 q^{74} - 12 q^{75} + 20 q^{76} - 52 q^{77} + 30 q^{79} - 12 q^{80} - 8 q^{81} - 12 q^{82} - 8 q^{83} + 8 q^{84} - 12 q^{86} - 2 q^{88} - 36 q^{89} - 4 q^{90} - 8 q^{91} - 8 q^{92} + 4 q^{93} - 14 q^{94} - 72 q^{95} - 8 q^{96} + 40 q^{98} - 8 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 12 * q^5 + 16 * q^6 + 6 * q^7 + 8 * q^9 - 2 * q^10 - 4 * q^11 + 8 * q^14 - 4 * q^15 - 8 * q^16 + 10 * q^19 + 4 * q^21 + 2 * q^22 - 4 * q^23 + 8 * q^24 + 10 * q^25 + 12 * q^26 + 12 * q^30 + 6 * q^31 + 4 * q^33 + 8 * q^35 + 16 * q^36 + 14 * q^37 - 12 * q^38 + 12 * q^39 + 2 * q^40 - 32 * q^41 + 6 * q^42 + 4 * q^44 + 12 * q^45 - 18 * q^46 - 24 * q^47 - 6 * q^49 - 6 * q^51 + 8 * q^54 + 14 * q^55 + 4 * q^56 - 2 * q^60 - 28 * q^61 + 8 * q^62 + 6 * q^63 - 16 * q^64 - 72 * q^65 - 4 * q^66 - 16 * q^67 - 30 * q^70 - 56 * q^71 + 44 * q^73 - 24 * q^74 - 12 * q^75 + 20 * q^76 - 52 * q^77 + 30 * q^79 - 12 * q^80 - 8 * q^81 - 12 * q^82 - 8 * q^83 + 8 * q^84 - 12 * q^86 - 2 * q^88 - 36 * q^89 - 4 * q^90 - 8 * q^91 - 8 * q^92 + 4 * q^93 - 14 * q^94 - 72 * q^95 - 8 * q^96 + 40 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	3.72526	−	2.15078i	1.66599	−	0.961859i	0.696221	−	0.717827i	$-0.254863\pi$
$5$	3.72526	−	2.15078i	1.66599	−	0.961859i	0.969767	−	0.244032i	$-0.0784701\pi$
$6$	1.00000			0.408248
$7$	1.43173	+	2.22489i	0.541144	+	0.840930i
$7$	1.43173	+	2.22489i	0.541144	+	0.840930i
$8$			1.00000i			0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−2.15078	+	3.72526i	−0.680137	+	1.17803i
$11$	1.15591	+	3.10868i	0.348521	+	0.937301i
$11$	1.15591	+	3.10868i	0.348521	+	0.937301i
$12$	−0.866025	+	0.500000i	−0.250000	+	0.144338i
$13$	−1.00074			−0.277556			−0.138778	−	0.990324i	$-0.544317\pi$
$13$	−1.00074			−0.277556			−0.138778	+	0.990324i	$0.544317\pi$
$14$	−2.35236	−	1.21095i	−0.628695	−	0.323639i
$15$	−4.30156			−1.11066
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.66854	−	2.89000i	0.404681	−	0.700927i	−0.589604	−	0.807693i	$-0.700716\pi$
$17$	1.66854	−	2.89000i	0.404681	−	0.700927i	0.994284	+	0.106765i	$0.0340494\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$	−1.61555	−	2.79822i	−0.370633	−	0.641956i	0.619030	−	0.785367i	$-0.287526\pi$
$19$	−1.61555	−	2.79822i	−0.370633	−	0.641956i	−0.989663	+	0.143412i	$0.954193\pi$
$20$		−	4.30156i		−	0.961859i
$21$	−0.127470	−	2.64268i	−0.0278162	−	0.576680i
$22$	−2.55539	−	2.11424i	−0.544810	−	0.450757i
$23$	2.86499	+	4.96231i	0.597392	+	1.03471i	0.993205	+	0.116382i	$0.0371296\pi$
$23$	2.86499	+	4.96231i	0.597392	+	1.03471i	−0.395813	+	0.918331i	$0.629537\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	6.75173	−	11.6943i	1.35035	−	2.33887i
$26$	0.866669	−	0.500372i	0.169968	−	0.0981309i
$27$		−	1.00000i		−	0.192450i
$28$	2.64268	−	0.127470i	0.499419	−	0.0240895i
$29$			7.74872i			1.43890i	0.694544	+	0.719450i	$0.255606\pi$
$29$			7.74872i			1.43890i	−0.694544	+	0.719450i	$0.744394\pi$
$30$	3.72526	−	2.15078i	0.680137	−	0.392677i
$31$	−2.77407	−	1.60161i	−0.498237	−	0.287657i	0.229748	−	0.973250i	$-0.426210\pi$
$31$	−2.77407	−	1.60161i	−0.498237	−	0.287657i	−0.727985	+	0.685593i	$0.759543\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	0.553289	−	3.27015i	0.0963152	−	0.569260i
$34$			3.33708i			0.572305i
$35$	10.1188	+	5.20897i	1.71040	+	0.880476i
$36$	1.00000			0.166667
$37$	1.26472	+	2.19056i	0.207918	+	0.360125i	0.951059	−	0.309010i	$-0.0999978\pi$
$37$	1.26472	+	2.19056i	0.207918	+	0.360125i	−0.743140	+	0.669136i	$0.766664\pi$
$38$	2.79822	+	1.61555i	0.453931	+	0.262077i
$39$	0.866669	+	0.500372i	0.138778	+	0.0801236i
$40$	2.15078	+	3.72526i	0.340068	+	0.589016i
$41$	−1.45111			−0.226625			−0.113313	−	0.993559i	$-0.536146\pi$
$41$	−1.45111			−0.226625			−0.113313	+	0.993559i	$0.536146\pi$
$42$	1.43173	+	2.22489i	0.220921	+	0.343308i
$43$		−	4.14572i		−	0.632216i	−0.948723	−	0.316108i	$-0.897624\pi$
$43$		−	4.14572i		−	0.632216i	0.948723	−	0.316108i	$-0.102376\pi$
$44$	3.27015	+	0.553289i	0.492993	+	0.0834114i
$45$	3.72526	+	2.15078i	0.555330	+	0.320620i
$46$	−4.96231	−	2.86499i	−0.731653	−	0.422420i
$47$	2.77216	−	1.60050i	0.404360	−	0.233458i	−0.284003	−	0.958823i	$-0.591663\pi$
$47$	2.77216	−	1.60050i	0.404360	−	0.233458i	0.688364	+	0.725366i	$0.258329\pi$
$48$			1.00000i			0.144338i
$49$	−2.90029	+	6.37090i	−0.414327	+	0.910128i
$50$			13.5035i			1.90968i
$51$	−2.89000	+	1.66854i	−0.404681	+	0.233642i
$52$	−0.500372	+	0.866669i	−0.0693890	+	0.120185i
$53$	5.65774	−	9.79949i	0.777150	−	1.34606i	−0.156428	−	0.987689i	$-0.549998\pi$
$53$	5.65774	−	9.79949i	0.777150	−	1.34606i	0.933578	−	0.358374i	$-0.116669\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	10.9922	+	9.09452i	1.48218	+	1.22631i
$56$	−2.22489	+	1.43173i	−0.297314	+	0.191323i
$57$			3.23111i			0.427970i
$58$	−3.87436	−	6.71059i	−0.508728	−	0.881143i
$59$	2.98113	+	1.72116i	0.388110	+	0.224075i	0.681341	−	0.731966i	$-0.261397\pi$
$59$	2.98113	+	1.72116i	0.388110	+	0.224075i	−0.293231	+	0.956042i	$0.594730\pi$
$60$	−2.15078	+	3.72526i	−0.277665	+	0.480929i
$61$	−7.42522	−	12.8609i	−0.950702	−	1.64666i	−0.743911	−	0.668279i	$-0.767031\pi$
$61$	−7.42522	−	12.8609i	−0.950702	−	1.64666i	−0.206791	−	0.978385i	$-0.566302\pi$
$62$	3.20322			0.406809
$63$	−1.21095	+	2.35236i	−0.152565	+	0.296370i
$64$	−1.00000			−0.125000
$65$	−3.72803	+	2.15238i	−0.462405	+	0.266970i
$66$	1.15591	+	3.10868i	0.142283	+	0.382652i
$67$	0.165196	−	0.286128i	0.0201819	−	0.0349560i	−0.855758	−	0.517376i	$-0.826909\pi$
$67$	0.165196	−	0.286128i	0.0201819	−	0.0349560i	0.875940	+	0.482420i	$0.160242\pi$
$68$	−1.66854	−	2.89000i	−0.202340	−	0.350464i
$69$		−	5.72998i		−	0.689809i
$70$	−11.3677	+	0.548319i	−1.35869	+	0.0655367i
$71$	2.84974			0.338201			0.169101	−	0.985599i	$-0.445914\pi$
$71$	2.84974			0.338201			0.169101	+	0.985599i	$0.445914\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	7.44790	−	12.9001i	0.871710	−	1.50985i	0.0114838	−	0.999934i	$-0.496345\pi$
$73$	7.44790	−	12.9001i	0.871710	−	1.50985i	0.860226	−	0.509912i	$-0.170322\pi$
$74$	−2.19056	−	1.26472i	−0.254647	−	0.147021i
$75$	−11.6943	+	6.75173i	−1.35035	+	0.779622i
$76$	−3.23111			−0.370633
$77$	−5.26151	+	7.02257i	−0.599605	+	0.800296i
$78$	−1.00074			−0.113312
$79$	−13.9363	+	8.04614i	−1.56796	+	0.905261i	−0.571552	+	0.820566i	$0.693658\pi$
$79$	−13.9363	+	8.04614i	−1.56796	+	0.905261i	−0.996407	+	0.0846953i	$0.973008\pi$
$80$	−3.72526	−	2.15078i	−0.416497	−	0.240465i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	1.25670	−	0.725556i	0.138779	−	0.0801242i
$83$	−1.75062			−0.192155			−0.0960777	−	0.995374i	$-0.530630\pi$
$83$	−1.75062			−0.192155			−0.0960777	+	0.995374i	$0.530630\pi$
$84$	−2.35236	−	1.21095i	−0.256664	−	0.132125i
$85$		−	14.3547i		−	1.55698i
$86$	2.07286	+	3.59030i	0.223522	+	0.387152i
$87$	3.87436	−	6.71059i	0.415375	−	0.719450i
$88$	−3.10868	+	1.15591i	−0.331386	+	0.123221i
$89$	−2.41153	+	1.39230i	−0.255622	+	0.147583i	−0.622336	−	0.782750i	$-0.713816\pi$
$89$	−2.41153	+	1.39230i	−0.255622	+	0.147583i	0.366714	+	0.930334i	$0.380483\pi$
$90$	−4.30156			−0.453425
$91$	−1.43280	−	2.22655i	−0.150198	−	0.233405i
$92$	5.72998			0.597392
$93$	1.60161	+	2.77407i	0.166079	+	0.287657i
$94$	−1.60050	+	2.77216i	−0.165079	+	0.285926i
$95$	−12.0367	−	6.94940i	−1.23494	−	0.712994i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$			12.3347i			1.25240i	0.779661	+	0.626201i	$0.215391\pi$
$97$			12.3347i			1.25240i	−0.779661	+	0.626201i	$0.784609\pi$
$98$	−0.673723	−	6.96750i	−0.0680563	−	0.703824i
$99$	−2.11424	+	2.55539i	−0.212489	+	0.256826i
$100$	−6.75173	−	11.6943i	−0.675173	−	1.16943i
$101$	−0.0281224	+	0.0487094i	−0.00279828	+	0.00484677i	−0.867421	−	0.497575i	$-0.834224\pi$
$101$	−0.0281224	+	0.0487094i	−0.00279828	+	0.00484677i	0.864623	+	0.502421i	$0.167557\pi$
$102$	1.66854	−	2.89000i	0.165210	−	0.286152i
$103$	−12.8128	+	7.39746i	−1.26248	+	0.728893i	−0.973554	−	0.228458i	$-0.926632\pi$
$103$	−12.8128	+	7.39746i	−1.26248	+	0.728893i	−0.288926	+	0.957351i	$0.593298\pi$
$104$		−	1.00074i		−	0.0981309i
$105$	−6.15868	−	9.57052i	−0.601026	−	0.933987i
$106$			11.3155i			1.09906i
$107$	9.19190	−	5.30694i	0.888614	−	0.513042i	0.0151251	−	0.999886i	$-0.495185\pi$
$107$	9.19190	−	5.30694i	0.888614	−	0.513042i	0.873489	+	0.486844i	$0.161852\pi$
$108$	−0.866025	−	0.500000i	−0.0833333	−	0.0481125i
$109$	−0.301553	−	0.174102i	−0.0288836	−	0.0166759i	0.485489	−	0.874243i	$-0.338642\pi$
$109$	−0.301553	−	0.174102i	−0.0288836	−	0.0166759i	−0.514372	+	0.857567i	$0.671975\pi$
$110$	−14.0668	−	2.38001i	−1.34121	−	0.226925i
$111$		−	2.52944i		−	0.240084i
$112$	1.21095	−	2.35236i	0.114424	−	0.222277i
$113$	−18.9549			−1.78313			−0.891564	−	0.452895i	$-0.850391\pi$
$113$	−18.9549			−1.78313			−0.891564	+	0.452895i	$0.850391\pi$
$114$	−1.61555	−	2.79822i	−0.151310	−	0.262077i
$115$	21.3457	+	12.3239i	1.99050	+	1.14921i
$116$	6.71059	+	3.87436i	0.623062	+	0.359725i
$117$	−0.500372	−	0.866669i	−0.0462594	−	0.0801236i
$118$	−3.44231			−0.316890
$119$	8.81883	−	0.425377i	0.808421	−	0.0389942i
$120$		−	4.30156i		−	0.392677i
$121$	−8.32774	+	7.18671i	−0.757067	+	0.653337i
$122$	12.8609	+	7.42522i	1.16437	+	0.672248i
$123$	1.25670	+	0.725556i	0.113313	+	0.0654211i
$124$	−2.77407	+	1.60161i	−0.249119	+	0.143829i
$125$		−	36.5781i		−	3.27165i
$126$	−0.127470	−	2.64268i	−0.0113559	−	0.235429i
$127$			5.90909i			0.524347i	0.965021	+	0.262173i	$0.0844392\pi$
$127$			5.90909i			0.524347i	−0.965021	+	0.262173i	$0.915561\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−2.07286	+	3.59030i	−0.182505	+	0.316108i
$130$	2.15238	−	3.72803i	0.188776	−	0.326970i
$131$	6.05214	+	10.4826i	0.528778	+	0.915870i	0.999437	+	0.0335545i	$0.0106827\pi$
$131$	6.05214	+	10.4826i	0.528778	+	0.915870i	−0.470659	+	0.882315i	$0.655984\pi$
$132$	−2.55539	−	2.11424i	−0.222418	−	0.184021i
$133$	3.91270	−	7.60073i	0.339274	−	0.659067i
$134$			0.330392i			0.0285415i
$135$	−2.15078	−	3.72526i	−0.185110	−	0.320620i
$136$	2.89000	+	1.66854i	0.247815	+	0.143076i
$137$	−4.94560	+	8.56604i	−0.422532	+	0.731846i	−0.996186	−	0.0872511i	$-0.972192\pi$
$137$	−4.94560	+	8.56604i	−0.422532	+	0.731846i	0.573655	+	0.819097i	$0.305525\pi$
$138$	2.86499	+	4.96231i	0.243884	+	0.422420i
$139$	1.58746			0.134647			0.0673235	−	0.997731i	$-0.478554\pi$
$139$	1.58746			0.134647			0.0673235	+	0.997731i	$0.478554\pi$
$140$	9.57052	−	6.15868i	0.808856	−	0.520504i
$141$	−3.20101			−0.269574
$142$	−2.46794	+	1.42487i	−0.207105	+	0.119572i
$143$	−1.15677	−	3.11099i	−0.0967340	−	0.260154i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	16.6658	+	28.8660i	1.38402	+	2.39719i
$146$			14.8958i			1.23278i
$147$	5.69717	−	4.06721i	0.469895	−	0.335458i
$148$	2.52944			0.207918
$149$	−14.7912	+	8.53970i	−1.21174	+	0.699599i	−0.963138	−	0.269006i	$-0.913305\pi$
$149$	−14.7912	+	8.53970i	−1.21174	+	0.699599i	−0.248603	+	0.968605i	$0.579971\pi$
$150$	6.75173	−	11.6943i	0.551276	−	0.954838i
$151$	−7.20145	−	4.15776i	−0.586046	−	0.338354i	0.177487	−	0.984123i	$-0.443203\pi$
$151$	−7.20145	−	4.15776i	−0.586046	−	0.338354i	−0.763532	+	0.645770i	$0.776537\pi$
$152$	2.79822	−	1.61555i	0.226966	−	0.131039i
$153$	3.33708			0.269787
$154$	1.04532	−	8.71248i	0.0842343	−	0.702072i
$155$	−13.7788			−1.10674
$156$	0.866669	−	0.500372i	0.0693890	−	0.0400618i
$157$	−1.08351	−	0.625565i	−0.0864735	−	0.0499255i	0.456140	−	0.889908i	$-0.349232\pi$
$157$	−1.08351	−	0.625565i	−0.0864735	−	0.0499255i	−0.542613	+	0.839983i	$0.682565\pi$
$158$	8.04614	−	13.9363i	0.640116	−	1.10871i
$159$	−9.79949	+	5.65774i	−0.777150	+	0.448688i
$160$	4.30156			0.340068
$161$	−6.93871	+	13.4790i	−0.546847	+	1.06229i
$162$		−	1.00000i		−	0.0785674i
$163$	−3.60786	−	6.24899i	−0.282589	−	0.489459i	0.689433	−	0.724350i	$-0.257860\pi$
$163$	−3.60786	−	6.24899i	−0.282589	−	0.489459i	−0.972022	+	0.234891i	$0.924527\pi$
$164$	−0.725556	+	1.25670i	−0.0566564	+	0.0981317i
$165$	−4.97223	−	13.3722i	−0.387088	−	1.04102i
$166$	1.51608	−	0.875309i	0.117671	−	0.0679372i
$167$	−15.4393			−1.19473			−0.597364	−	0.801970i	$-0.703785\pi$
$167$	−15.4393			−1.19473			−0.597364	+	0.801970i	$0.703785\pi$
$168$	2.64268	−	0.127470i	0.203887	−	0.00983450i
$169$	−11.9985			−0.922963
$170$	7.17733	+	12.4315i	0.550476	+	0.953453i
$171$	1.61555	−	2.79822i	0.123544	−	0.213985i
$172$	−3.59030	−	2.07286i	−0.273757	−	0.158054i
$173$	3.11021	+	5.38705i	0.236465	+	0.409569i	0.959697	−	0.281035i	$-0.0906778\pi$
$173$	3.11021	+	5.38705i	0.236465	+	0.409569i	−0.723232	+	0.690605i	$0.757344\pi$
$174$			7.74872i			0.587429i
$175$	35.6853	−	1.72128i	2.69755	−	0.130117i
$176$	2.11424	−	2.55539i	0.159367	−	0.192620i
$177$	−1.72116	−	2.98113i	−0.129370	−	0.224075i
$178$	1.39230	−	2.41153i	0.104357	−	0.180752i
$179$	−1.53946	+	2.66643i	−0.115065	+	0.199298i	−0.917806	−	0.397030i	$-0.870041\pi$
$179$	−1.53946	+	2.66643i	−0.115065	+	0.199298i	0.802741	+	0.596328i	$0.203374\pi$
$180$	3.72526	−	2.15078i	0.277665	−	0.160310i
$181$			18.3243i			1.36203i	0.732268	+	0.681016i	$0.238462\pi$
$181$			18.3243i			1.36203i	−0.732268	+	0.681016i	$0.761538\pi$
$182$	2.35411	+	1.21185i	0.174498	+	0.0898281i
$183$			14.8504i			1.09778i
$184$	−4.96231	+	2.86499i	−0.365826	+	0.211210i
$185$	9.42282	+	5.44027i	0.692779	+	0.399976i
$186$	−2.77407	−	1.60161i	−0.203404	−	0.117436i
$187$	10.9128	+	1.84637i	0.798019	+	0.135020i
$188$		−	3.20101i		−	0.233458i
$189$	2.22489	−	1.43173i	0.161837	−	0.104143i
$190$	13.8988			1.00833
$191$	−10.4101	−	18.0308i	−0.753248	−	1.30466i	−0.946241	−	0.323464i	$-0.895153\pi$
$191$	−10.4101	−	18.0308i	−0.753248	−	1.30466i	0.192992	−	0.981200i	$-0.438181\pi$
$192$	0.866025	+	0.500000i	0.0625000	+	0.0360844i
$193$	3.91133	+	2.25821i	0.281544	+	0.162549i	0.634122	−	0.773233i	$-0.281362\pi$
$193$	3.91133	+	2.25821i	0.281544	+	0.162549i	−0.352578	+	0.935782i	$0.614695\pi$
$194$	−6.16737	−	10.6822i	−0.442791	−	0.766937i
$195$	4.30476			0.308270
$196$	4.06721	+	5.69717i	0.290515	+	0.406941i
$197$		−	17.3563i		−	1.23659i	−0.785947	−	0.618293i	$-0.787824\pi$
$197$		−	17.3563i		−	1.23659i	0.785947	−	0.618293i	$-0.212176\pi$
$198$	0.553289	−	3.27015i	0.0393205	−	0.232399i
$199$	6.76938	+	3.90830i	0.479868	+	0.277052i	0.720362	−	0.693599i	$-0.243976\pi$
$199$	6.76938	+	3.90830i	0.479868	+	0.277052i	−0.240493	+	0.970651i	$0.577309\pi$
$200$	11.6943	+	6.75173i	0.826914	+	0.477419i
$201$	−0.286128	+	0.165196i	−0.0201819	+	0.0116520i
$202$		−	0.0562448i		−	0.00395737i
$203$	−17.2401	+	11.0941i	−1.21001	+	0.778652i
$204$			3.33708i			0.233642i
$205$	−5.40577	+	3.12102i	−0.377555	+	0.217982i
$206$	7.39746	−	12.8128i	0.515405	−	0.892708i
$207$	−2.86499	+	4.96231i	−0.199131	+	0.344904i
$208$	0.500372	+	0.866669i	0.0346945	+	0.0600927i
$209$	6.83132	−	8.25673i	0.472532	−	0.571130i
$210$	10.1188	+	5.20897i	0.698266	+	0.359453i
$211$		−	21.9923i		−	1.51401i	−0.653406	−	0.757007i	$-0.726661\pi$
$211$		−	21.9923i		−	1.51401i	0.653406	−	0.757007i	$-0.273339\pi$
$212$	−5.65774	−	9.79949i	−0.388575	−	0.673032i
$213$	−2.46794	−	1.42487i	−0.169101	−	0.0976304i
$214$	−5.30694	+	9.19190i	−0.362775	+	0.628345i
$215$	−8.91653	−	15.4439i	−0.608102	−	1.05326i
$216$	1.00000			0.0680414
$217$	−0.408313	−	8.46507i	−0.0277181	−	0.574646i
$218$	0.348204			0.0235833
$219$	−12.9001	+	7.44790i	−0.871710	+	0.503282i
$220$	13.3722	−	4.97223i	0.901551	−	0.335228i
$221$	−1.66978	+	2.89214i	−0.112322	+	0.194547i
$222$	1.26472	+	2.19056i	0.0848823	+	0.147021i
$223$		−	8.30245i		−	0.555973i	−0.960585	−	0.277987i	$-0.910333\pi$
$223$		−	8.30245i		−	0.555973i	0.960585	−	0.277987i	$-0.0896671\pi$
$224$	0.127470	+	2.64268i	0.00851693	+	0.176571i
$225$	13.5035			0.900230
$226$	16.4154	−	9.47745i	1.09194	−	0.630431i
$227$	−3.95627	+	6.85245i	−0.262587	+	0.454813i	−0.966929	−	0.255048i	$-0.917909\pi$
$227$	−3.95627	+	6.85245i	−0.262587	+	0.454813i	0.704342	+	0.709861i	$0.251242\pi$
$228$	2.79822	+	1.61555i	0.185317	+	0.106993i
$229$	−9.27450	+	5.35463i	−0.612876	+	0.353844i	−0.774090	−	0.633075i	$-0.781792\pi$
$229$	−9.27450	+	5.35463i	−0.612876	+	0.353844i	0.161214	+	0.986919i	$0.448459\pi$
$230$	−24.6479			−1.62523
$231$	8.06789	−	3.45097i	0.530828	−	0.227057i
$232$	−7.74872			−0.508728
$233$	15.3378	−	8.85528i	1.00481	−	0.580129i	0.0951440	−	0.995464i	$-0.469669\pi$
$233$	15.3378	−	8.85528i	1.00481	−	0.580129i	0.909669	+	0.415335i	$0.136336\pi$
$234$	0.866669	+	0.500372i	0.0566559	+	0.0327103i
$235$	6.88467	−	11.9246i	0.449107	−	0.777876i
$236$	2.98113	−	1.72116i	0.194055	−	0.112038i
$237$	16.0923			1.04531
$238$	−7.42465	+	4.77780i	−0.481268	+	0.309699i
$239$			26.6356i			1.72291i	0.507832	+	0.861456i	$0.330447\pi$
$239$			26.6356i			1.72291i	−0.507832	+	0.861456i	$0.669553\pi$
$240$	2.15078	+	3.72526i	0.138832	+	0.240465i
$241$	−1.85521	+	3.21331i	−0.119504	+	0.206987i	−0.919571	−	0.392923i	$-0.871464\pi$
$241$	−1.85521	+	3.21331i	−0.119504	+	0.206987i	0.800067	+	0.599911i	$0.204797\pi$
$242$	3.61867	−	10.3877i	0.232617	−	0.667749i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−14.8504			−0.950702
$245$	2.89806	+	29.9712i	0.185150	+	1.91479i
$246$	−1.45111			−0.0925195
$247$	1.61675	+	2.80030i	0.102872	+	0.178179i
$248$	1.60161	−	2.77407i	0.101702	−	0.176153i
$249$	1.51608	+	0.875309i	0.0960777	+	0.0554705i
$250$	18.2891	+	31.6776i	1.15670	+	2.00347i
$251$			10.6948i			0.675051i	0.941316	+	0.337526i	$0.109590\pi$
$251$			10.6948i			0.675051i	−0.941316	+	0.337526i	$0.890410\pi$
$252$	1.43173	+	2.22489i	0.0901906	+	0.140155i
$253$	−12.1145	+	14.6423i	−0.761634	+	0.920555i
$254$	−2.95454	−	5.11742i	−0.185385	−	0.321095i
$255$	−7.17733	+	12.4315i	−0.449462	+	0.778491i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	20.6304	−	11.9110i	1.28689	−	0.742987i	0.308793	−	0.951129i	$-0.400075\pi$
$257$	20.6304	−	11.9110i	1.28689	−	0.742987i	0.978099	+	0.208142i	$0.0667416\pi$
$258$		−	4.14572i		−	0.258101i
$259$	−3.06302	+	5.95015i	−0.190327	+	0.369724i
$260$			4.30476i			0.266970i
$261$	−6.71059	+	3.87436i	−0.415375	+	0.239817i
$262$	−10.4826	−	6.05214i	−0.647618	−	0.373902i
$263$	14.7672	+	8.52582i	0.910582	+	0.525725i	0.880618	−	0.473826i	$-0.157127\pi$
$263$	14.7672	+	8.52582i	0.910582	+	0.525725i	0.0299637	+	0.999551i	$0.490461\pi$
$264$	3.27015	+	0.553289i	0.201264	+	0.0340526i
$265$		−	48.6743i		−	2.99004i
$266$	0.411868	+	8.53877i	0.0252532	+	0.523546i
$267$	2.78460			0.170414
$268$	−0.165196	−	0.286128i	−0.0100909	−	0.0174780i
$269$	8.32306	+	4.80532i	0.507466	+	0.292986i	0.731791	−	0.681529i	$-0.238685\pi$
$269$	8.32306	+	4.80532i	0.507466	+	0.292986i	−0.224326	+	0.974514i	$0.572018\pi$
$270$	3.72526	+	2.15078i	0.226712	+	0.130892i
$271$	−2.55614	−	4.42736i	−0.155274	−	0.268943i	0.777884	−	0.628407i	$-0.216293\pi$
$271$	−2.55614	−	4.42736i	−0.155274	−	0.268943i	−0.933159	+	0.359464i	$0.882960\pi$
$272$	−3.33708			−0.202340
$273$	0.127564	+	2.64464i	0.00772055	+	0.160061i
$274$		−	9.89121i		−	0.597550i
$275$	44.1583	+	7.47131i	2.66285	+	0.450537i
$276$	−4.96231	−	2.86499i	−0.298696	−	0.172452i
$277$	22.8002	+	13.1637i	1.36993	+	0.790931i	0.990919	−	0.134461i	$-0.0429302\pi$
$277$	22.8002	+	13.1637i	1.36993	+	0.790931i	0.379013	+	0.925391i	$0.376264\pi$
$278$	−1.37478	+	0.793732i	−0.0824541	+	0.0476049i
$279$		−	3.20322i		−	0.191772i
$280$	−5.20897	+	10.1188i	−0.311295	+	0.604716i
$281$			10.5684i			0.630459i	0.949015	+	0.315230i	$0.102082\pi$
$281$			10.5684i			0.630459i	−0.949015	+	0.315230i	$0.897918\pi$
$282$	2.77216	−	1.60050i	0.165079	−	0.0953087i
$283$	5.20379	−	9.01323i	0.309333	−	0.535781i	−0.668883	−	0.743367i	$-0.733227\pi$
$283$	5.20379	−	9.01323i	0.309333	−	0.535781i	0.978217	+	0.207586i	$0.0665608\pi$
$284$	1.42487	−	2.46794i	0.0845504	−	0.146446i
$285$	6.94940	+	12.0367i	0.411647	+	0.712994i
$286$	2.55729	+	2.11581i	0.151215	+	0.125110i
$287$	−2.07760	−	3.22857i	−0.122637	−	0.190576i
$288$			1.00000i			0.0589256i
$289$	2.93194	+	5.07828i	0.172467	+	0.298722i
$290$	−28.8660	−	16.6658i	−1.69507	−	0.978649i
$291$	6.16737	−	10.6822i	0.361538	−	0.626201i
$292$	−7.44790	−	12.9001i	−0.435855	−	0.754923i
$293$	31.4600			1.83792			0.918958	−	0.394356i	$-0.129032\pi$
$293$	31.4600			1.83792			0.918958	+	0.394356i	$0.129032\pi$
$294$	−2.90029	+	6.37090i	−0.169148	+	0.371558i
$295$	14.8073			0.862116
$296$	−2.19056	+	1.26472i	−0.127324	+	0.0735103i
$297$	3.10868	−	1.15591i	0.180384	−	0.0670728i
$298$	8.53970	−	14.7912i	0.494691	−	0.856831i
$299$	−2.86712	−	4.96600i	−0.165810	−	0.287191i
$300$			13.5035i			0.779622i
$301$	9.22377	−	5.93555i	0.531649	−	0.342120i
$302$	8.31552			0.478504
$303$	0.0487094	−	0.0281224i	0.00279828	−	0.00161559i
$304$	−1.61555	+	2.79822i	−0.0926583	+	0.160489i
$305$	−55.3218	−	31.9401i	−3.16772	−	1.82888i
$306$	−2.89000	+	1.66854i	−0.165210	+	0.0953841i
$307$	−18.4994			−1.05582			−0.527910	−	0.849301i	$-0.677024\pi$
$307$	−18.4994			−1.05582			−0.527910	+	0.849301i	$0.677024\pi$
$308$	3.45097	+	8.06789i	0.196637	+	0.459711i
$309$	14.7949			0.841653
$310$	11.9328	−	6.88942i	0.677739	−	0.391293i
$311$	−26.8449	−	15.4989i	−1.52224	−	0.878864i	−0.999655	−	0.0262743i	$-0.991636\pi$
$311$	−26.8449	−	15.4989i	−1.52224	−	0.878864i	−0.522582	−	0.852589i	$-0.675031\pi$
$312$	−0.500372	+	0.866669i	−0.0283280	+	0.0490655i
$313$	8.31513	−	4.80074i	0.469999	−	0.271354i	−0.246240	−	0.969209i	$-0.579195\pi$
$313$	8.31513	−	4.80074i	0.469999	−	0.271354i	0.716239	+	0.697855i	$0.245862\pi$
$314$	1.25113			0.0706053
$315$	0.548319	+	11.3677i	0.0308943	+	0.640495i
$316$			16.0923i			0.905261i
$317$	5.97126	+	10.3425i	0.335379	+	0.580894i	0.983558	−	0.180595i	$-0.0578022\pi$
$317$	5.97126	+	10.3425i	0.335379	+	0.580894i	−0.648178	+	0.761489i	$0.724469\pi$
$318$	5.65774	−	9.79949i	0.317270	−	0.549528i
$319$	−24.0882	+	8.95683i	−1.34868	+	0.501486i
$320$	−3.72526	+	2.15078i	−0.208249	+	0.120232i
$321$	−10.6139			−0.592409
$322$	−0.730399	−	15.1425i	−0.0407035	−	0.843859i
$323$	−10.7825			−0.599952
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	−6.75674	+	11.7030i	−0.374797	+	0.649167i
$326$	6.24899	+	3.60786i	0.346100	+	0.199821i
$327$	0.174102	+	0.301553i	0.00962786	+	0.0166759i
$328$		−	1.45111i		−	0.0801242i
$329$	7.52993	+	3.87625i	0.415139	+	0.213705i
$330$	10.9922	+	9.09452i	0.605099	+	0.500637i
$331$	−3.24581	−	5.62191i	−0.178406	−	0.309008i	0.762929	−	0.646482i	$-0.223761\pi$
$331$	−3.24581	−	5.62191i	−0.178406	−	0.309008i	−0.941335	+	0.337474i	$0.890427\pi$
$332$	−0.875309	+	1.51608i	−0.0480388	+	0.0832057i
$333$	−1.26472	+	2.19056i	−0.0693061	+	0.120042i
$334$	13.3708	−	7.71964i	0.731618	−	0.422400i
$335$		−	1.42120i		−	0.0776485i
$336$	−2.22489	+	1.43173i	−0.121378	+	0.0781074i
$337$			5.74869i			0.313151i	0.987666	+	0.156576i	$0.0500455\pi$
$337$			5.74869i			0.313151i	−0.987666	+	0.156576i	$0.949955\pi$
$338$	10.3910	−	5.99926i	0.565197	−	0.326317i
$339$	16.4154	+	9.47745i	0.891564	+	0.514745i
$340$	−12.4315	−	7.17733i	−0.674193	−	0.389246i
$341$	1.77230	−	10.4750i	0.0959756	−	0.567253i
$342$			3.23111i			0.174718i
$343$	−18.3270	+	2.66858i	−0.989565	+	0.144090i
$344$	4.14572			0.223522
$345$	−12.3239	−	21.3457i	−0.663499	−	1.14921i
$346$	−5.38705	−	3.11021i	−0.289609	−	0.167206i
$347$	−12.6658	−	7.31263i	−0.679938	−	0.392563i	0.119893	−	0.992787i	$-0.461745\pi$
$347$	−12.6658	−	7.31263i	−0.679938	−	0.392563i	−0.799832	+	0.600224i	$0.795078\pi$
$348$	−3.87436	−	6.71059i	−0.207687	−	0.359725i
$349$	−15.2458			−0.816091			−0.408046	−	0.912962i	$-0.633790\pi$
$349$	−15.2458			−0.816091			−0.408046	+	0.912962i	$0.633790\pi$
$350$	−30.0437	+	19.3333i	−1.60590	+	1.03341i
$351$			1.00074i			0.0534157i
$352$	−0.553289	+	3.27015i	−0.0294904	+	0.174300i
$353$	−23.7709	−	13.7242i	−1.26520	−	0.730463i	−0.291124	−	0.956685i	$-0.594029\pi$
$353$	−23.7709	−	13.7242i	−1.26520	−	0.730463i	−0.974076	+	0.226222i	$0.927363\pi$
$354$	2.98113	+	1.72116i	0.158445	+	0.0914784i
$355$	10.6160	−	6.12916i	0.563440	−	0.325302i
$356$			2.78460i			0.147583i
$357$	−7.85002	−	4.04103i	−0.415467	−	0.213874i
$358$		−	3.07893i		−	0.162726i
$359$	14.1129	−	8.14808i	0.744850	−	0.430039i	−0.0789804	−	0.996876i	$-0.525166\pi$
$359$	14.1129	−	8.14808i	0.744850	−	0.430039i	0.823830	+	0.566837i	$0.191833\pi$
$360$	−2.15078	+	3.72526i	−0.113356	+	0.196339i
$361$	4.27998	−	7.41314i	0.225262	−	0.390165i
$362$	−9.16214	−	15.8693i	−0.481551	−	0.834071i
$363$	10.8054	−	2.06001i	0.567136	−	0.108122i
$364$	−2.64464	+	0.127564i	−0.138617	+	0.00668619i
$365$		−	64.0752i		−	3.35385i
$366$	−7.42522	−	12.8609i	−0.388122	−	0.672248i
$367$	−2.93922	−	1.69696i	−0.153426	−	0.0885807i	0.421321	−	0.906911i	$-0.361566\pi$
$367$	−2.93922	−	1.69696i	−0.153426	−	0.0885807i	−0.574748	+	0.818331i	$0.694900\pi$
$368$	2.86499	−	4.96231i	0.149348	−	0.258678i
$369$	−0.725556	−	1.25670i	−0.0377709	−	0.0654211i
$370$	−10.8805			−0.565652
$371$	29.9032	−	1.44238i	1.55250	−	0.0748847i
$372$	3.20322			0.166079
$373$	5.64289	−	3.25792i	0.292178	−	0.168689i	−0.346746	−	0.937959i	$-0.612713\pi$
$373$	5.64289	−	3.25792i	0.292178	−	0.168689i	0.638923	+	0.769270i	$0.279380\pi$
$374$	−10.3739	+	3.85737i	−0.536422	+	0.199460i
$375$	−18.2891	+	31.6776i	−0.944444	+	1.63582i
$376$	1.60050	+	2.77216i	0.0825397	+	0.142963i
$377$		−	7.75447i		−	0.399376i
$378$	−1.21095	+	2.35236i	−0.0622844	+	0.120992i
$379$	−27.4324			−1.40911			−0.704555	−	0.709650i	$-0.748853\pi$
$379$	−27.4324			−1.40911			−0.704555	+	0.709650i	$0.748853\pi$
$380$	−12.0367	+	6.94940i	−0.617471	+	0.356497i
$381$	2.95454	−	5.11742i	0.151366	−	0.262173i
$382$	18.0308	+	10.4101i	0.922537	+	0.532627i
$383$	−7.65298	+	4.41845i	−0.391049	+	0.225772i	−0.682615	−	0.730779i	$-0.739157\pi$
$383$	−7.65298	+	4.41845i	−0.391049	+	0.225772i	0.291565	+	0.956551i	$0.405824\pi$
$384$	−1.00000			−0.0510310
$385$	−4.49651	+	37.4773i	−0.229163	+	1.91002i
$386$	−4.51641			−0.229879
$387$	3.59030	−	2.07286i	0.182505	−	0.105369i
$388$	10.6822	+	6.16737i	0.542306	+	0.313101i
$389$	−4.46153	+	7.72760i	−0.226209	+	0.391805i	−0.956681	−	0.291137i	$-0.905966\pi$
$389$	−4.46153	+	7.72760i	−0.226209	+	0.391805i	0.730473	+	0.682942i	$0.239300\pi$
$390$	−3.72803	+	2.15238i	−0.188776	+	0.108990i
$391$	19.1214			0.967011
$392$	−6.37090	−	2.90029i	−0.321779	−	0.146487i
$393$		−	12.1043i		−	0.610580i
$394$	8.67816	+	15.0310i	0.437200	+	0.757252i
$395$	−34.6110	+	59.9480i	−1.74147	+	3.01631i
$396$	1.15591	+	3.10868i	0.0580868	+	0.156217i
$397$	−4.13575	+	2.38778i	−0.207567	+	0.119839i	−0.600180	−	0.799865i	$-0.704905\pi$
$397$	−4.13575	+	2.38778i	−0.207567	+	0.119839i	0.392613	+	0.919704i	$0.371571\pi$
$398$	−7.81660			−0.391811
$399$	−7.18886	+	4.62607i	−0.359893	+	0.231593i
$400$	−13.5035			−0.675173
$401$	−1.26986	−	2.19946i	−0.0634137	−	0.109836i	0.832576	−	0.553912i	$-0.186865\pi$
$401$	−1.26986	−	2.19946i	−0.0634137	−	0.109836i	−0.895989	+	0.444076i	$0.853532\pi$
$402$	0.165196	−	0.286128i	0.00823922	−	0.0142707i
$403$	2.77613	+	1.60280i	0.138289	+	0.0798411i
$404$	0.0281224	+	0.0487094i	0.00139914	+	0.00242338i
$405$			4.30156i			0.213746i
$406$	9.38329	−	18.2278i	0.465685	−	0.904630i
$407$	−5.34783	+	6.46369i	−0.265082	+	0.320393i
$408$	−1.66854	−	2.89000i	−0.0826051	−	0.143076i
$409$	0.0321007	−	0.0556000i	0.00158728	−	0.00274924i	−0.865231	−	0.501374i	$-0.832828\pi$
$409$	0.0321007	−	0.0556000i	0.00158728	−	0.00274924i	0.866818	+	0.498625i	$0.166161\pi$
$410$	3.12102	−	5.40577i	0.154136	−	0.266972i
$411$	8.56604	−	4.94560i	0.422532	−	0.243949i
$412$			14.7949i			0.728893i
$413$	0.438790	+	9.09692i	0.0215915	+	0.447630i
$414$		−	5.72998i		−	0.281613i
$415$	−6.52152	+	3.76520i	−0.320129	+	0.184826i
$416$	−0.866669	−	0.500372i	−0.0424919	−	0.0245327i
$417$	−1.37478	−	0.793732i	−0.0673235	−	0.0388692i
$418$	−1.78773	+	10.5662i	−0.0874410	+	0.516809i
$419$			23.7720i			1.16134i	0.814140	+	0.580669i	$0.197209\pi$
$419$			23.7720i			1.16134i	−0.814140	+	0.580669i	$0.802791\pi$
$420$	−11.3677	+	0.548319i	−0.554685	+	0.0267552i
$421$	−1.11501			−0.0543422			−0.0271711	−	0.999631i	$-0.508650\pi$
$421$	−1.11501			−0.0543422			−0.0271711	+	0.999631i	$0.508650\pi$
$422$	10.9962	+	19.0459i	0.535285	+	0.927141i
$423$	2.77216	+	1.60050i	0.134787	+	0.0778192i
$424$	9.79949	+	5.65774i	0.475905	+	0.274764i
$425$	−22.5311	−	39.0249i	−1.09292	−	1.89299i
$426$	2.84974			0.138070
$427$	17.9831	−	34.9336i	0.870263	−	1.69056i
$428$		−	10.6139i		−	0.513042i
$429$	−0.553700	+	3.27258i	−0.0267329	+	0.158002i
$430$	15.4439	+	8.91653i	0.744770	+	0.429993i
$431$	−25.4430	−	14.6895i	−1.22555	−	0.707569i	−0.259451	−	0.965756i	$-0.583542\pi$
$431$	−25.4430	−	14.6895i	−1.22555	−	0.707569i	−0.966095	+	0.258187i	$0.916875\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$			13.1705i			0.632934i	0.948604	+	0.316467i	$0.102497\pi$
$433$			13.1705i			0.632934i	−0.948604	+	0.316467i	$0.897503\pi$
$434$	4.58614	+	7.12681i	0.220142	+	0.342098i
$435$		−	33.3316i		−	1.59813i
$436$	−0.301553	+	0.174102i	−0.0144418	+	0.00833797i
$437$	9.25709	−	16.0337i	0.442826	−	0.766998i
$438$	7.44790	−	12.9001i	0.355874	−	0.616392i
$439$	5.10665	+	8.84498i	0.243727	+	0.422148i	0.961773	−	0.273848i	$-0.0882965\pi$
$439$	5.10665	+	8.84498i	0.243727	+	0.422148i	−0.718046	+	0.695996i	$0.754963\pi$
$440$	−9.09452	+	10.9922i	−0.433564	+	0.524031i
$441$	−6.96750	+	0.673723i	−0.331786	+	0.0320820i
$442$		−	3.33956i		−	0.158847i
$443$	−13.6862	−	23.7051i	−0.650250	−	1.12627i	−0.983062	−	0.183272i	$-0.941331\pi$
$443$	−13.6862	−	23.7051i	−0.650250	−	1.12627i	0.332813	−	0.942993i	$-0.392002\pi$
$444$	−2.19056	−	1.26472i	−0.103959	−	0.0600209i
$445$	−5.98906	+	10.3734i	−0.283909	+	0.491744i
$446$	4.15123	+	7.19014i	0.196566	+	0.340463i
$447$	17.0794			0.807828
$448$	−1.43173	−	2.22489i	−0.0676430	−	0.105116i
$449$	1.35953			0.0641602			0.0320801	−	0.999485i	$-0.489787\pi$
$449$	1.35953			0.0641602			0.0320801	+	0.999485i	$0.489787\pi$
$450$	−11.6943	+	6.75173i	−0.551276	+	0.318279i
$451$	−1.67736	−	4.51103i	−0.0789836	−	0.212416i
$452$	−9.47745	+	16.4154i	−0.445782	+	0.772117i
$453$	4.15776	+	7.20145i	0.195349	+	0.338354i
$454$		−	7.91253i		−	0.371354i
$455$	−10.1264	−	5.21284i	−0.474731	−	0.244382i
$456$	−3.23111			−0.151310
$457$	−18.9644	+	10.9491i	−0.887115	+	0.512176i	−0.872998	−	0.487724i	$-0.837827\pi$
$457$	−18.9644	+	10.9491i	−0.887115	+	0.512176i	−0.0141173	+	0.999900i	$0.504494\pi$
$458$	5.35463	−	9.27450i	0.250206	−	0.433369i
$459$	−2.89000	−	1.66854i	−0.134894	−	0.0778808i
$460$	21.3457	−	12.3239i	0.995248	−	0.574607i
$461$	13.4227			0.625159			0.312579	−	0.949892i	$-0.398807\pi$
$461$	13.4227			0.625159			0.312579	+	0.949892i	$0.398807\pi$
$462$	−5.26151	+	7.02257i	−0.244788	+	0.326719i
$463$	−21.1422			−0.982562			−0.491281	−	0.871001i	$-0.663471\pi$
$463$	−21.1422			−0.982562			−0.491281	+	0.871001i	$0.663471\pi$
$464$	6.71059	−	3.87436i	0.311531	−	0.179863i
$465$	11.9328	+	6.88942i	0.553371	+	0.319489i
$466$	−8.85528	+	15.3378i	−0.410213	+	0.710510i
$467$	2.48960	−	1.43737i	0.115205	−	0.0665137i	−0.441290	−	0.897364i	$-0.645479\pi$
$467$	2.48960	−	1.43737i	0.115205	−	0.0665137i	0.556495	+	0.830851i	$0.312146\pi$
$468$	−1.00074			−0.0462594
$469$	0.873119	−	0.0421149i	0.0403169	−	0.00194469i
$470$			13.7693i			0.635133i
$471$	0.625565	+	1.08351i	0.0288245	+	0.0499255i
$472$	−1.72116	+	2.98113i	−0.0792226	+	0.137218i
$473$	12.8877	−	4.79208i	0.592577	−	0.220340i
$474$	−13.9363	+	8.04614i	−0.640116	+	0.369571i
$475$	−43.6311			−2.00193
$476$	4.04103	−	7.85002i	0.185220	−	0.359805i
$477$	11.3155			0.518100
$478$	−13.3178	−	23.0671i	−0.609141	−	1.05506i
$479$	1.91941	−	3.32451i	0.0877000	−	0.151901i	−0.818839	−	0.574024i	$-0.805382\pi$
$479$	1.91941	−	3.32451i	0.0877000	−	0.151901i	0.906539	+	0.422123i	$0.138715\pi$
$480$	−3.72526	−	2.15078i	−0.170034	−	0.0981693i
$481$	−1.26566	−	2.19218i	−0.0577091	−	0.0999550i
$482$		−	3.71041i		−	0.169005i
$483$	12.7486	−	8.20379i	0.580081	−	0.373286i
$484$	2.06001	+	10.8054i	0.0936367	+	0.491154i
$485$	26.5293	+	45.9502i	1.20463	+	2.08649i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	4.84042	−	8.38386i	0.219340	−	0.379909i	−0.735266	−	0.677779i	$-0.762943\pi$
$487$	4.84042	−	8.38386i	0.219340	−	0.379909i	0.954607	+	0.297870i	$0.0962761\pi$
$488$	12.8609	−	7.42522i	0.582184	−	0.336124i
$489$			7.21571i			0.326306i
$490$	−17.4954	−	24.5068i	−0.790360	−	1.10710i
$491$			15.8886i			0.717041i	0.933522	+	0.358520i	$0.116719\pi$
$491$			15.8886i			0.717041i	−0.933522	+	0.358520i	$0.883281\pi$
$492$	1.25670	−	0.725556i	0.0566564	−	0.0327106i
$493$	22.3938	+	12.9290i	1.00856	+	0.582295i
$494$	−2.80030	−	1.61675i	−0.125991	−	0.0727412i
$495$	−2.38001	+	14.0668i	−0.106973	+	0.632254i
$496$			3.20322i			0.143829i
$497$	4.08006	+	6.34036i	0.183016	+	0.284404i
$498$	−1.75062			−0.0784471
$499$	15.0220	+	26.0188i	0.672477	+	1.16476i	0.977200	+	0.212323i	$0.0681027\pi$
$499$	15.0220	+	26.0188i	0.672477	+	1.16476i	−0.304723	+	0.952441i	$0.598564\pi$
$500$	−31.6776	−	18.2891i	−1.41667	−	0.817912i
$501$	13.3708	+	7.71964i	0.597364	+	0.344888i
$502$	−5.34741	−	9.26199i	−0.238667	−	0.413383i
$503$	−4.66798			−0.208135			−0.104067	−	0.994570i	$-0.533186\pi$
$503$	−4.66798			−0.208135			−0.104067	+	0.994570i	$0.533186\pi$
$504$	−2.35236	−	1.21095i	−0.104783	−	0.0539399i
$505$			0.241941i			0.0107662i
$506$	3.17034	−	18.7379i	0.140939	−	0.833001i
$507$	10.3910	+	5.99926i	0.461481	+	0.266436i
$508$	5.11742	+	2.95454i	0.227049	+	0.131087i
$509$	26.8000	−	15.4730i	1.18789	−	0.685829i	0.230064	−	0.973175i	$-0.426106\pi$
$509$	26.8000	−	15.4730i	1.18789	−	0.685829i	0.957827	+	0.287346i	$0.0927730\pi$
$510$		−	14.3547i		−	0.635635i
$511$	39.3648	−	1.89876i	1.74140	−	0.0839963i
$512$		−	1.00000i		−	0.0441942i
$513$	−2.79822	+	1.61555i	−0.123544	+	0.0713284i
$514$	−11.9110	+	20.6304i	−0.525371	+	0.909970i
$515$	−31.8206	+	55.1150i	−1.40219	+	2.42866i
$516$	2.07286	+	3.59030i	0.0912525	+	0.158054i
$517$	8.17982	+	6.76769i	0.359748	+	0.297643i
$518$	−0.322427	−	6.68449i	−0.0141666	−	0.293700i
$519$		−	6.22042i		−	0.273046i
$520$	−2.15238	−	3.72803i	−0.0943881	−	0.163485i
$521$	9.57271	+	5.52680i	0.419388	+	0.242134i	0.694815	−	0.719188i	$-0.255486\pi$
$521$	9.57271	+	5.52680i	0.419388	+	0.242134i	−0.275427	+	0.961322i	$0.588819\pi$
$522$	3.87436	−	6.71059i	0.169576	−	0.293714i
$523$	−2.06741	−	3.58085i	−0.0904013	−	0.156580i	0.817279	−	0.576243i	$-0.195482\pi$
$523$	−2.06741	−	3.58085i	−0.0904013	−	0.156580i	−0.907680	+	0.419663i	$0.862148\pi$
$524$	12.1043			0.528778
$525$	−31.7650	−	16.3520i	−1.38634	−	0.713659i
$526$	−17.0516			−0.743487
$527$	−9.25728	+	5.34470i	−0.403254	+	0.232819i
$528$	−3.10868	+	1.15591i	−0.135288	+	0.0503046i
$529$	−4.91634	+	8.51535i	−0.213754	+	0.370233i
$530$	24.3371	+	42.1531i	1.05714	+	1.83102i
$531$			3.44231i			0.149384i
$532$	−4.62607	−	7.18886i	−0.200566	−	0.311677i
$533$	1.45219			0.0629013
$534$	−2.41153	+	1.39230i	−0.104357	+	0.0602506i
$535$	22.8282	−	39.5395i	0.986947	−	1.70944i
$536$	0.286128	+	0.165196i	0.0123588	+	0.00713537i
$537$	2.66643	−	1.53946i	0.115065	−	0.0664328i
$538$	−9.61064			−0.414344
$539$	−23.1575	−	1.65187i	−0.997466	−	0.0711510i
$540$	−4.30156			−0.185110
$541$	34.4914	−	19.9136i	1.48290	−	0.856153i	0.483088	−	0.875572i	$-0.339515\pi$
$541$	34.4914	−	19.9136i	1.48290	−	0.856153i	0.999811	+	0.0194190i	$0.00618164\pi$
$542$	4.42736	+	2.55614i	0.190172	+	0.109796i
$543$	9.16214	−	15.8693i	0.393185	−	0.681016i
$544$	2.89000	−	1.66854i	0.123908	−	0.0715381i
$545$	−1.49782			−0.0641596
$546$	−1.43280	−	2.22655i	−0.0613180	−	0.0952874i
$547$		−	37.7080i		−	1.61228i	−0.591728	−	0.806138i	$-0.701554\pi$
$547$		−	37.7080i		−	1.61228i	0.591728	−	0.806138i	$-0.298446\pi$
$548$	4.94560	+	8.56604i	0.211266	+	0.365923i
$549$	7.42522	−	12.8609i	0.316901	−	0.548888i
$550$	−41.9779	+	15.6088i	−1.78994	+	0.665562i
$551$	21.6826	−	12.5185i	0.923710	−	0.533304i
$552$	5.72998			0.243884
$553$	−37.8549	−	19.4869i	−1.60975	−	0.828667i
$554$	−26.3274			−1.11854
$555$	−5.44027	−	9.42282i	−0.230926	−	0.399976i
$556$	0.793732	−	1.37478i	0.0336617	−	0.0583039i
$557$	27.3188	+	15.7725i	1.15754	+	0.668304i	0.950712	−	0.310074i	$-0.100354\pi$
$557$	27.3188	+	15.7725i	1.15754	+	0.668304i	0.206824	+	0.978378i	$0.433687\pi$
$558$	1.60161	+	2.77407i	0.0678015	+	0.117436i
$559$			4.14880i			0.175475i
$560$	−0.548319	−	11.3677i	−0.0231707	−	0.480371i
$561$	−8.52753	−	7.05538i	−0.360033	−	0.297878i
$562$	−5.28421	−	9.15252i	−0.222901	−	0.386076i
$563$	18.8993	−	32.7345i	0.796511	−	1.37960i	−0.125365	−	0.992111i	$-0.540010\pi$
$563$	18.8993	−	32.7345i	0.796511	−	1.37960i	0.921876	−	0.387486i	$-0.126656\pi$
$564$	−1.60050	+	2.77216i	−0.0673934	+	0.116729i
$565$	−70.6120	+	40.7679i	−2.97067	+	1.71512i
$566$			10.4076i			0.437463i
$567$	−2.64268	+	0.127470i	−0.110982	+	0.00535322i
$568$			2.84974i			0.119572i
$569$	−16.0111	+	9.24404i	−0.671222	+	0.387530i	−0.796540	−	0.604586i	$-0.793338\pi$
$569$	−16.0111	+	9.24404i	−0.671222	+	0.387530i	0.125317	+	0.992117i	$0.460005\pi$
$570$	−12.0367	−	6.94940i	−0.504163	−	0.291078i
$571$	13.1984	+	7.62013i	0.552338	+	0.318892i	0.750064	−	0.661365i	$-0.230022\pi$
$571$	13.1984	+	7.62013i	0.552338	+	0.318892i	−0.197727	+	0.980257i	$0.563356\pi$
$572$	−3.27258	−	0.553700i	−0.136833	−	0.0231514i
$573$			20.8202i			0.869776i
$574$	3.41354	+	1.75722i	0.142478	+	0.0733449i
$575$	77.3745			3.22674
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−23.7188	−	13.6941i	−0.987428	−	0.570092i	−0.0829237	−	0.996556i	$-0.526426\pi$
$577$	−23.7188	−	13.6941i	−0.987428	−	0.570092i	−0.904505	+	0.426464i	$0.859759\pi$
$578$	−5.07828	−	2.93194i	−0.211228	−	0.121953i
$579$	−2.25821	−	3.91133i	−0.0938479	−	0.162549i
$580$	33.3316			1.38402
$581$	−2.50642	−	3.89494i	−0.103984	−	0.161589i
$582$			12.3347i			0.511291i
$583$	37.0033	+	6.26073i	1.53252	+	0.259293i
$584$	12.9001	+	7.44790i	0.533811	+	0.308196i
$585$	−3.72803	−	2.15238i	−0.154135	−	0.0889900i
$586$	−27.2452	+	15.7300i	−1.12549	+	0.649801i
$587$			17.1517i			0.707927i	0.935259	+	0.353964i	$0.115166\pi$
$587$			17.1517i			0.707927i	−0.935259	+	0.353964i	$0.884834\pi$
$588$	−0.673723	−	6.96750i	−0.0277839	−	0.287335i
$589$			10.3499i			0.426461i
$590$	−12.8235	+	7.40366i	−0.527936	+	0.304804i
$591$	−8.67816	+	15.0310i	−0.356972	+	0.618293i
$592$	1.26472	−	2.19056i	0.0519796	−	0.0900313i
$593$	2.63071	+	4.55652i	0.108030	+	0.187114i	0.914972	−	0.403517i	$-0.132212\pi$
$593$	2.63071	+	4.55652i	0.108030	+	0.187114i	−0.806942	+	0.590631i	$0.798879\pi$
$594$	−2.11424	+	2.55539i	−0.0867482	+	0.104849i
$595$	31.9376	−	20.5520i	1.30931	−	0.842551i
$596$			17.0794i			0.699599i
$597$	−3.90830	−	6.76938i	−0.159956	−	0.277052i
$598$	4.96600	+	2.86712i	0.203075	+	0.117245i
$599$	17.8442	−	30.9071i	0.729096	−	1.26283i	−0.228169	−	0.973621i	$-0.573274\pi$
$599$	17.8442	−	30.9071i	0.729096	−	1.26283i	0.957266	−	0.289210i	$-0.0933927\pi$
$600$	−6.75173	−	11.6943i	−0.275638	−	0.477419i
$601$	9.98679			0.407370			0.203685	−	0.979036i	$-0.434708\pi$
$601$	9.98679			0.407370			0.203685	+	0.979036i	$0.434708\pi$
$602$	−5.02024	+	9.75222i	−0.204610	+	0.397471i
$603$	0.330392			0.0134546
$604$	−7.20145	+	4.15776i	−0.293023	+	0.169177i
$605$	−15.5660	+	44.6835i	−0.632846	+	1.81664i
$606$	−0.0281224	+	0.0487094i	−0.00114239	+	0.00197868i
$607$	−11.8496	−	20.5242i	−0.480962	−	0.833050i	0.518800	−	0.854896i	$-0.326379\pi$
$607$	−11.8496	−	20.5242i	−0.480962	−	0.833050i	−0.999761	+	0.0218456i	$0.993046\pi$
$608$		−	3.23111i		−	0.131039i
$609$	20.4774	−	0.987726i	0.829785	−	0.0400247i
$610$	63.8801			2.58643
$611$	−2.77422	+	1.60169i	−0.112233	+	0.0647976i
$612$	1.66854	−	2.89000i	0.0674468	−	0.116821i
$613$	22.3572	+	12.9080i	0.903000	+	0.521347i	0.878172	−	0.478345i	$-0.158763\pi$
$613$	22.3572	+	12.9080i	0.903000	+	0.521347i	0.0248276	+	0.999692i	$0.492096\pi$
$614$	16.0210	−	9.24972i	0.646555	−	0.373288i
$615$	6.24205			0.251704
$616$	−7.02257	−	5.26151i	−0.282947	−	0.211992i
$617$	4.44499			0.178949			0.0894743	−	0.995989i	$-0.471481\pi$
$617$	4.44499			0.178949			0.0894743	+	0.995989i	$0.471481\pi$
$618$	−12.8128	+	7.39746i	−0.515405	+	0.297569i
$619$	−30.0167	−	17.3301i	−1.20647	−	0.696557i	−0.244485	−	0.969653i	$-0.578619\pi$
$619$	−30.0167	−	17.3301i	−1.20647	−	0.696557i	−0.961987	+	0.273096i	$0.911952\pi$
$620$	−6.88942	+	11.9328i	−0.276686	+	0.479234i
$621$	4.96231	−	2.86499i	0.199131	−	0.114968i
$622$	30.9979			1.24290
$623$	−6.55038	−	3.37200i	−0.262435	−	0.135096i
$624$		−	1.00074i		−	0.0400618i
$625$	−44.9130	−	77.7916i	−1.79652	−	3.11166i
$626$	−4.80074	+	8.31513i	−0.191876	+	0.332339i
$627$	−10.0445	+	3.73487i	−0.401137	+	0.149156i
$628$	−1.08351	+	0.625565i	−0.0432368	+	0.0249627i
$629$	8.44094			0.336562
$630$	−6.15868	−	9.57052i	−0.245368	−	0.381298i
$631$	32.7549			1.30395			0.651975	−	0.758240i	$-0.273941\pi$
$631$	32.7549			1.30395			0.651975	+	0.758240i	$0.273941\pi$
$632$	−8.04614	−	13.9363i	−0.320058	−	0.554357i
$633$	−10.9962	+	19.0459i	−0.437058	+	0.757007i
$634$	−10.3425	−	5.97126i	−0.410754	−	0.237149i
$635$	12.7092	+	22.0129i	0.504348	+	0.873556i
$636$			11.3155i			0.448688i
$637$	2.90245	−	6.37563i	0.114999	−	0.252612i
$638$	16.3826	−	19.8010i	0.648594	−	0.783928i
$639$	1.42487	+	2.46794i	0.0563669	+	0.0976304i
$640$	2.15078	−	3.72526i	0.0850171	−	0.147254i
$641$	17.5417	−	30.3831i	0.692854	−	1.20006i	−0.278044	−	0.960568i	$-0.589686\pi$
$641$	17.5417	−	30.3831i	0.692854	−	1.20006i	0.970899	−	0.239491i	$-0.0769805\pi$
$642$	9.19190	−	5.30694i	0.362775	−	0.209448i
$643$			4.02224i			0.158622i	0.996850	+	0.0793109i	$0.0252720\pi$
$643$			4.02224i			0.158622i	−0.996850	+	0.0793109i	$0.974728\pi$
$644$	8.20379	+	12.7486i	0.323275	+	0.502365i
$645$			17.8331i			0.702176i
$646$	9.33788	−	5.39123i	0.367394	−	0.212115i
$647$	−4.94497	−	2.85498i	−0.194407	−	0.112241i	0.399637	−	0.916673i	$-0.369136\pi$
$647$	−4.94497	−	2.85498i	−0.194407	−	0.112241i	−0.594044	+	0.804433i	$0.702470\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	−1.90459	+	11.2569i	−0.0747618	+	0.441871i
$650$		−	13.5135i		−	0.530043i
$651$	−3.87893	+	7.53512i	−0.152027	+	0.295325i
$652$	−7.21571			−0.282589
$653$	7.19689	+	12.4654i	0.281636	+	0.487808i	0.971788	−	0.235857i	$-0.0757896\pi$
$653$	7.19689	+	12.4654i	0.281636	+	0.487808i	−0.690152	+	0.723665i	$0.742456\pi$
$654$	−0.301553	−	0.174102i	−0.0117917	−	0.00680792i
$655$	45.0916	+	26.0336i	1.76187	+	1.01722i
$656$	0.725556	+	1.25670i	0.0283282	+	0.0490659i
$657$	14.8958			0.581140
$658$	−8.45924	+	0.408032i	−0.329776	+	0.0159067i
$659$		−	1.73466i		−	0.0675728i	−0.999429	−	0.0337864i	$-0.989243\pi$
$659$		−	1.73466i		−	0.0675728i	0.999429	−	0.0337864i	$-0.0107566\pi$
$660$	−14.0668	−	2.38001i	−0.547548	−	0.0926417i
$661$	−24.2717	−	14.0132i	−0.944058	−	0.545052i	−0.0528280	−	0.998604i	$-0.516823\pi$
$661$	−24.2717	−	14.0132i	−0.944058	−	0.545052i	−0.891230	+	0.453551i	$0.850157\pi$
$662$	5.62191	+	3.24581i	0.218502	+	0.126152i
$663$	2.89214	−	1.66978i	0.112322	−	0.0648489i
$664$		−	1.75062i		−	0.0679372i
$665$	−1.77168	−	36.7301i	−0.0687027	−	1.42433i
$666$		−	2.52944i		−	0.0980137i
$667$	−38.4515	+	22.2000i	−1.48885	+	0.859587i
$668$	−7.71964	+	13.3708i	−0.298682	+	0.517332i
$669$	−4.15123	+	7.19014i	−0.160496	+	0.277987i
$670$	0.710600	+	1.23080i	0.0274529	+	0.0475498i
$671$	31.3973	−	37.9486i	1.21208	−	1.46499i
$672$	1.21095	−	2.35236i	0.0467133	−	0.0907443i
$673$			11.9436i			0.460394i	0.973144	+	0.230197i	$0.0739370\pi$
$673$			11.9436i			0.460394i	−0.973144	+	0.230197i	$0.926063\pi$
$674$	−2.87434	−	4.97851i	−0.110716	−	0.191765i
$675$	−11.6943	−	6.75173i	−0.450115	−	0.259874i
$676$	−5.99926	+	10.3910i	−0.230741	+	0.399655i
$677$	−20.2334	−	35.0453i	−0.777634	−	1.34690i	−0.933302	−	0.359092i	$-0.883086\pi$
$677$	−20.2334	−	35.0453i	−0.777634	−	1.34690i	0.155668	−	0.987809i	$-0.450247\pi$
$678$	−18.9549			−0.727959
$679$	−27.4435	+	17.6600i	−1.05318	+	0.677730i
$680$	14.3547			0.550476
$681$	6.85245	−	3.95627i	0.262587	−	0.151604i
$682$	3.70264	+	9.95776i	0.141781	+	0.381302i
$683$	9.15993	−	15.8655i	0.350495	−	0.607075i	−0.635841	−	0.771820i	$-0.719347\pi$
$683$	9.15993	−	15.8655i	0.350495	−	0.607075i	0.986336	+	0.164745i	$0.0526801\pi$
$684$	−1.61555	−	2.79822i	−0.0617722	−	0.106993i
$685$			42.5477i			1.62566i
$686$	14.5374	−	11.4746i	0.555039	−	0.438100i
$687$	10.7093			0.408584
$688$	−3.59030	+	2.07286i	−0.136879	+	0.0790270i
$689$	−5.66194	+	9.80677i	−0.215703	+	0.373608i
$690$	21.3457	+	12.3239i	0.812617	+	0.469164i
$691$	38.6960	−	22.3412i	1.47207	−	0.849898i	0.472560	−	0.881299i	$-0.343330\pi$
$691$	38.6960	−	22.3412i	1.47207	−	0.849898i	0.999507	+	0.0314005i	$0.00999673\pi$
$692$	6.22042			0.236465
$693$	−8.71248	−	1.04532i	−0.330960	−	0.0397084i
$694$	14.6253			0.555167
$695$	5.91372	−	3.41429i	0.224320	−	0.129511i
$696$	6.71059	+	3.87436i	0.254364	+	0.146857i
$697$	−2.42124	+	4.19371i	−0.0917109	+	0.158848i
$698$	13.2033	−	7.62292i	0.499752	−	0.288532i
$699$	−17.7106			−0.669875
$700$	16.3520	−	31.7650i	0.618046	−	1.20060i
$701$			18.6437i			0.704161i	0.935970	+	0.352081i	$0.114526\pi$
$701$			18.6437i			0.704161i	−0.935970	+	0.352081i	$0.885474\pi$
$702$	−0.500372	−	0.866669i	−0.0188853	−	0.0327103i
$703$	4.08644	−	7.07792i	0.154123	−	0.266949i
$704$	−1.15591	−	3.10868i	−0.0435651	−	0.117163i
$705$	−11.9246	+	6.88467i	−0.449107	+	0.259292i
$706$	27.4483			1.03303
$707$	−0.148637	+	0.00716950i	−0.00559007	+	0.000269637i
$708$	−3.44231			−0.129370
$709$	2.45067	+	4.24468i	0.0920368	+	0.159412i	0.908368	−	0.418172i	$-0.137329\pi$
$709$	2.45067	+	4.24468i	0.0920368	+	0.159412i	−0.816331	+	0.577584i	$0.803996\pi$
$710$	−6.12916	+	10.6160i	−0.230023	+	0.398412i
$711$	−13.9363	−	8.04614i	−0.522653	−	0.301754i
$712$	−1.39230	−	2.41153i	−0.0521786	−	0.0903759i
$713$		−	18.3544i		−	0.687376i
$714$	8.81883	−	0.425377i	0.330037	−	0.0159193i
$715$	−11.0003	−	9.10128i	−0.411389	−	0.340369i
$716$	1.53946	+	2.66643i	0.0575325	+	0.0996492i
$717$	13.3178	−	23.0671i	0.497362	−	0.861456i
$718$	−8.14808	+	14.1129i	−0.304084	+	0.526688i
$719$	−19.2665	+	11.1235i	−0.718518	+	0.414837i	−0.814207	−	0.580575i	$-0.802828\pi$
$719$	−19.2665	+	11.1235i	−0.718518	+	0.414837i	0.0956887	+	0.995411i	$0.469495\pi$
$720$		−	4.30156i		−	0.160310i
$721$	−34.8030	−	17.9159i	−1.29613	−	0.667222i
$722$			8.55996i			0.318569i
$723$	3.21331	−	1.85521i	0.119504	−	0.0689958i
$724$	15.8693	+	9.16214i	0.589777	+	0.340508i
$725$	90.6161	+	52.3172i	3.36540	+	1.94301i
$726$	−8.32774	+	7.18671i	−0.309071	+	0.266724i
$727$		−	27.5807i		−	1.02291i	−0.859310	−	0.511456i	$-0.829106\pi$
$727$		−	27.5807i		−	1.02291i	0.859310	−	0.511456i	$-0.170894\pi$
$728$	2.22655	−	1.43280i	0.0825213	−	0.0531029i
$729$	−1.00000			−0.0370370
$730$	32.0376	+	55.4907i	1.18576	+	2.05380i
$731$	−11.9811	−	6.91730i	−0.443137	−	0.255845i
$732$	12.8609	+	7.42522i	0.475351	+	0.274444i
$733$	8.95070	+	15.5031i	0.330602	+	0.572619i	0.982630	−	0.185576i	$-0.0594151\pi$
$733$	8.95070	+	15.5031i	0.330602	+	0.572619i	−0.652028	+	0.758195i	$0.726082\pi$
$734$	3.39392			0.125272
$735$	12.4758	−	27.4048i	0.460176	−	1.01084i
$736$			5.72998i			0.211210i
$737$	1.08043	+	0.182802i	0.0397981	+	0.00673360i
$738$	1.25670	+	0.725556i	0.0462597	+	0.0267081i
$739$	−24.9947	−	14.4307i	−0.919443	−	0.530841i	−0.0359860	−	0.999352i	$-0.511457\pi$
$739$	−24.9947	−	14.4307i	−0.919443	−	0.530841i	−0.883457	+	0.468511i	$0.844790\pi$
$740$	9.42282	−	5.44027i	0.346390	−	0.199988i
$741$		−	3.23351i		−	0.118786i
$742$	−25.1757	+	16.2007i	−0.924230	+	0.594747i
$743$			34.0656i			1.24975i	0.780726	+	0.624873i	$0.214849\pi$
$743$			34.0656i			1.24975i	−0.780726	+	0.624873i	$0.785151\pi$
$744$	−2.77407	+	1.60161i	−0.101702	+	0.0587178i
$745$	−36.7341	+	63.6253i	−1.34583	+	2.33105i
$746$	−3.25792	+	5.64289i	−0.119281	+	0.206601i
$747$	−0.875309	−	1.51608i	−0.0320259	−	0.0554705i
$748$	7.05538	−	8.52753i	0.257970	−	0.311798i
$749$	24.9677	+	12.8529i	0.912300	+	0.469633i
$750$		−	36.5781i		−	1.33565i
$751$	6.28179	+	10.8804i	0.229226	+	0.397031i	0.957579	−	0.288171i	$-0.0930472\pi$
$751$	6.28179	+	10.8804i	0.229226	+	0.397031i	−0.728353	+	0.685202i	$0.759714\pi$
$752$	−2.77216	−	1.60050i	−0.101090	−	0.0583644i
$753$	5.34741	−	9.26199i	0.194871	−	0.337526i
$754$	3.87724	+	6.71557i	0.141201	+	0.244567i
$755$	−35.7697			−1.30179
$756$	−0.127470	−	2.64268i	−0.00463603	−	0.0961133i
$757$	7.03843			0.255816			0.127908	−	0.991786i	$-0.459174\pi$
$757$	7.03843			0.255816			0.127908	+	0.991786i	$0.459174\pi$
$758$	23.7572	−	13.7162i	0.862900	−	0.498195i
$759$	17.8127	−	6.62335i	0.646558	−	0.240413i
$760$	6.94940	−	12.0367i	0.252081	−	0.436618i
$761$	−0.820725	−	1.42154i	−0.0297512	−	0.0515307i	0.850766	−	0.525544i	$-0.176138\pi$
$761$	−0.820725	−	1.42154i	−0.0297512	−	0.0515307i	−0.880518	+	0.474013i	$0.842805\pi$
$762$			5.90909i			0.214064i
$763$	−0.0443854	−	0.920191i	−0.00160686	−	0.0333131i
$764$	−20.8202			−0.753248
$765$	12.4315	−	7.17733i	0.449462	−	0.259497i
$766$	4.41845	−	7.65298i	0.159645	−	0.276514i
$767$	−2.98334	−	1.72243i	−0.107722	−	0.0621935i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$	−5.29585			−0.190973			−0.0954867	−	0.995431i	$-0.530441\pi$
$769$	−5.29585			−0.190973			−0.0954867	+	0.995431i	$0.530441\pi$
$770$	−14.8446	−	34.7045i	−0.534960	−	1.25066i
$771$	−23.8220			−0.857928
$772$	3.91133	−	2.25821i	0.140772	−	0.0812746i
$773$	−17.0683	−	9.85437i	−0.613903	−	0.354437i	0.160588	−	0.987021i	$-0.448661\pi$
$773$	−17.0683	−	9.85437i	−0.613903	−	0.354437i	−0.774491	+	0.632584i	$0.781994\pi$
$774$	−2.07286	+	3.59030i	−0.0745073	+	0.129051i
$775$	−37.4595	+	21.6272i	−1.34558	+	0.776873i
$776$	−12.3347			−0.442791
$777$	5.62772	−	3.62147i	0.201893	−	0.129920i
$778$		−	8.92306i		−	0.319907i
$779$	2.34435	+	4.06053i	0.0839949	+	0.145483i
$780$	2.15238	−	3.72803i	0.0770676	−	0.133485i
$781$	3.29404	+	8.85891i	0.117870	+	0.316997i
$782$	−16.5596	+	9.56071i	−0.592171	+	0.341890i
$783$	7.74872			0.276917
$784$	6.96750	−	0.673723i	0.248839	−	0.0240615i
$785$	−5.38181			−0.192085
$786$	6.05214	+	10.4826i	0.215873	+	0.373902i
$787$	26.0498	−	45.1196i	0.928576	−	1.60834i	0.142870	−	0.989741i	$-0.454367\pi$
$787$	26.0498	−	45.1196i	0.928576	−	1.60834i	0.785706	−	0.618600i	$-0.212300\pi$
$788$	−15.0310	−	8.67816i	−0.535458	−	0.309147i
$789$	−8.52582	−	14.7672i	−0.303527	−	0.525725i
$790$		−	69.2220i		−	2.46281i
$791$	−27.1383	−	42.1726i	−0.964928	−	1.49949i
$792$	−2.55539	−	2.11424i	−0.0908017	−	0.0751261i
$793$	7.43074	+	12.8704i	0.263873	+	0.457042i
$794$	2.38778	−	4.13575i	0.0847390	−	0.146772i
$795$	−24.3371	+	42.1531i	−0.863149	+	1.49502i
$796$	6.76938	−	3.90830i	0.239934	−	0.138526i
$797$			39.4609i			1.39778i	0.715230	+	0.698889i	$0.246322\pi$
$797$			39.4609i			1.39778i	−0.715230	+	0.698889i	$0.753678\pi$
$798$	3.91270	−	7.60073i	0.138508	−	0.269063i
$799$		−	10.6820i		−	0.377903i
$800$	11.6943	−	6.75173i	0.413457	−	0.238710i
$801$	−2.41153	−	1.39230i	−0.0852072	−	0.0491944i
$802$	2.19946	+	1.26986i	0.0776656	+	0.0448403i
$803$	48.7114	+	8.24168i	1.71899	+	0.290842i
$804$			0.330392i			0.0116520i
$805$	3.14186	+	65.1364i	0.110736	+	2.29576i
$806$	−3.20560			−0.112912
$807$	−4.80532	−	8.32306i	−0.169155	−	0.292986i
$808$	−0.0487094	−	0.0281224i	−0.00171359	−	0.000989342i
$809$	1.42371	+	0.821978i	0.0500549	+	0.0288992i	0.524819	−	0.851214i	$-0.324133\pi$
$809$	1.42371	+	0.821978i	0.0500549	+	0.0288992i	−0.474764	+	0.880113i	$0.657466\pi$
$810$	−2.15078	−	3.72526i	−0.0755708	−	0.130892i
$811$	−18.9381			−0.665006			−0.332503	−	0.943102i	$-0.607893\pi$
$811$	−18.9381			−0.665006			−0.332503	+	0.943102i	$0.607893\pi$
$812$	0.987726	+	20.4774i	0.0346624	+	0.718615i
$813$			5.11228i			0.179295i
$814$	1.39951	−	8.27163i	0.0490528	−	0.289921i
$815$	−26.8804	−	15.5194i	−0.941581	−	0.543622i
$816$	2.89000	+	1.66854i	0.101170	+	0.0584106i
$817$	−11.6006	+	6.69762i	−0.405854	+	0.234320i
$818$			0.0642013i			0.00224475i
$819$	1.21185	−	2.35411i	0.0423454	−	0.0822593i
$820$			6.24205i			0.217982i
$821$	14.0021	−	8.08410i	0.488676	−	0.282137i	−0.235349	−	0.971911i	$-0.575623\pi$
$821$	14.0021	−	8.08410i	0.488676	−	0.282137i	0.724025	+	0.689774i	$0.242290\pi$
$822$	−4.94560	+	8.56604i	−0.172498	+	0.298775i
$823$	−1.93640	+	3.35394i	−0.0674986	+	0.116911i	−0.897800	−	0.440404i	$-0.854835\pi$
$823$	−1.93640	+	3.35394i	−0.0674986	+	0.116911i	0.830301	+	0.557315i	$0.188168\pi$
$824$	−7.39746	−	12.8128i	−0.257703	−	0.446354i
$825$	−34.5066	−	28.5495i	−1.20136	−	0.993966i
$826$	−4.92846	−	7.65877i	−0.171483	−	0.266483i
$827$			17.5641i			0.610762i	0.952230	+	0.305381i	$0.0987838\pi$
$827$			17.5641i			0.610762i	−0.952230	+	0.305381i	$0.901216\pi$
$828$	2.86499	+	4.96231i	0.0995653	+	0.172452i
$829$	27.5947	+	15.9318i	0.958405	+	0.553335i	0.895682	−	0.444696i	$-0.146688\pi$
$829$	27.5947	+	15.9318i	0.958405	+	0.553335i	0.0627229	+	0.998031i	$0.480022\pi$
$830$	3.76520	−	6.52152i	0.130692	−	0.226365i
$831$	−13.1637	−	22.8002i	−0.456644	−	0.790931i
$832$	1.00074			0.0346945
$833$	13.5726	+	19.0119i	0.470263	+	0.658724i
$834$	1.58746			0.0549694
$835$	−57.5154	+	33.2065i	−1.99040	+	1.14916i
$836$	−3.73487	−	10.0445i	−0.129173	−	0.347395i
$837$	−1.60161	+	2.77407i	−0.0553597	+	0.0958858i
$838$	−11.8860	−	20.5872i	−0.410595	−	0.711171i
$839$			13.8360i			0.477670i	0.971060	+	0.238835i	$0.0767656\pi$
$839$			13.8360i			0.477670i	−0.971060	+	0.238835i	$0.923234\pi$
$840$	9.57052	−	6.15868i	0.330214	−	0.212495i
$841$	−31.0426			−1.07043
$842$	0.965627	−	0.557505i	0.0332777	−	0.0192129i
$843$	5.28421	−	9.15252i	0.181998	−	0.315230i
$844$	−19.0459	−	10.9962i	−0.655588	−	0.378504i
$845$	−44.6976	+	25.8062i	−1.53765	+	0.887760i
$846$	−3.20101			−0.110053
$847$	−27.9127	−	8.23887i	−0.959093	−	0.283091i
$848$	−11.3155			−0.388575
$849$	−9.01323	+	5.20379i	−0.309333	+	0.178594i
$850$	39.0249	+	22.5311i	1.33854	+	0.772809i
$851$	−7.24681	+	12.5518i	−0.248418	+	0.430272i
$852$	−2.46794	+	1.42487i	−0.0845504	+	0.0488152i
$853$	9.77894			0.334825			0.167412	−	0.985887i	$-0.446459\pi$
$853$	9.77894			0.334825			0.167412	+	0.985887i	$0.446459\pi$
$854$	1.89298	+	39.2449i	0.0647765	+	1.34293i
$855$		−	13.8988i		−	0.475329i
$856$	5.30694	+	9.19190i	0.181388	+	0.314173i
$857$	−21.8559	+	37.8555i	−0.746583	+	1.29312i	0.202869	+	0.979206i	$0.434973\pi$
$857$	−21.8559	+	37.8555i	−0.746583	+	1.29312i	−0.949452	+	0.313913i	$0.898360\pi$
$858$	−1.15677	−	3.11099i	−0.0394915	−	0.106207i
$859$	40.0841	−	23.1426i	1.36765	−	0.789614i	0.377023	−	0.926204i	$-0.376948\pi$
$859$	40.0841	−	23.1426i	1.36765	−	0.789614i	0.990628	+	0.136590i	$0.0436143\pi$
$860$	−17.8331			−0.608102
$861$	0.184973	+	3.83482i	0.00630385	+	0.130690i
$862$	29.3790			1.00065
$863$	14.3077	+	24.7817i	0.487041	+	0.843579i	0.999889	−	0.0149001i	$-0.00474303\pi$
$863$	14.3077	+	24.7817i	0.487041	+	0.843579i	−0.512848	+	0.858479i	$0.671410\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	23.1727	+	13.3788i	0.787896	+	0.454892i
$866$	−6.58525	−	11.4060i	−0.223776	−	0.387591i
$867$		−	5.86389i		−	0.199148i
$868$	−7.53512	−	3.87893i	−0.255759	−	0.131659i
$869$	−41.1220	−	34.0229i	−1.39497	−	1.15415i
$870$	16.6658	+	28.8660i	0.565024	+	0.978649i
$871$	−0.165319	+	0.286340i	−0.00560161	+	0.00970227i
$872$	0.174102	−	0.301553i	0.00589583	−	0.0102119i
$873$	−10.6822	+	6.16737i	−0.361538	+	0.208734i
$874$			18.5142i			0.626251i
$875$	81.3824	−	52.3701i	2.75123	−	1.77043i
$876$			14.8958i			0.503282i
$877$	48.1559	−	27.8028i	1.62611	−	0.938834i	0.640869	−	0.767650i	$-0.278574\pi$
$877$	48.1559	−	27.8028i	1.62611	−	0.938834i	0.985239	−	0.171184i	$-0.0547592\pi$
$878$	−8.84498	−	5.10665i	−0.298504	−	0.172341i
$879$	−27.2452	−	15.7300i	−0.918958	−	0.530561i
$880$	2.38001	−	14.0668i	0.0802300	−	0.474190i
$881$		−	31.8585i		−	1.07334i	−0.843792	−	0.536671i	$-0.819682\pi$
$881$		−	31.8585i		−	1.07334i	0.843792	−	0.536671i	$-0.180318\pi$
$882$	5.69717	−	4.06721i	0.191834	−	0.136950i
$883$	55.9427			1.88262			0.941311	−	0.337539i	$-0.109595\pi$
$883$	55.9427			1.88262			0.941311	+	0.337539i	$0.109595\pi$
$884$	1.66978	+	2.89214i	0.0561608	+	0.0972734i
$885$	−12.8235	−	7.40366i	−0.431058	−	0.248871i
$886$	23.7051	+	13.6862i	0.796390	+	0.459796i
$887$	−5.49008	−	9.50910i	−0.184339	−	0.319284i	0.759015	−	0.651073i	$-0.225681\pi$
$887$	−5.49008	−	9.50910i	−0.184339	−	0.319284i	−0.943354	+	0.331789i	$0.892348\pi$
$888$	2.52944			0.0848823
$889$	−13.1471	+	8.46023i	−0.440939	+	0.283747i
$890$		−	11.9781i		−	0.401507i
$891$	−3.27015	−	0.553289i	−0.109554	−	0.0185359i
$892$	−7.19014	−	4.15123i	−0.240744	−	0.138993i
$893$	−8.95713	−	5.17140i	−0.299739	−	0.173054i
$894$	−14.7912	+	8.53970i	−0.494691	+	0.285610i
$895$			13.2442i			0.442705i
$896$	2.35236	+	1.21095i	0.0785869	+	0.0404549i
$897$			5.73424i			0.191461i
$898$	−1.17739	+	0.679765i	−0.0392899	+	0.0226840i
$899$	12.4104	−	21.4955i	0.413910	−	0.716913i
$900$	6.75173	−	11.6943i	0.225058	−	0.389811i
$901$	−18.8803	−	32.7017i	−0.628995	−	1.08945i
$902$	3.70815	+	3.06799i	0.123468	+	0.102153i
$903$	−10.9558	+	0.528453i	−0.364586	+	0.0175858i
$904$		−	18.9549i		−	0.630431i
$905$	39.4115	+	68.2627i	1.31008	+	2.26913i
$906$	−7.20145	−	4.15776i	−0.239252	−	0.138132i
$907$	−1.05966	+	1.83539i	−0.0351856	+	0.0609432i	−0.883082	−	0.469219i	$-0.844536\pi$
$907$	−1.05966	+	1.83539i	−0.0351856	+	0.0609432i	0.847896	+	0.530162i	$0.177869\pi$
$908$	3.95627	+	6.85245i	0.131293	+	0.227407i
$909$	−0.0562448			−0.00186552
$910$	11.3761	−	0.548726i	0.377114	−	0.0181901i
$911$	1.06472			0.0352757			0.0176379	−	0.999844i	$-0.494385\pi$
$911$	1.06472			0.0352757			0.0176379	+	0.999844i	$0.494385\pi$
$912$	2.79822	−	1.61555i	0.0926583	−	0.0534963i
$913$	−2.02356	−	5.44211i	−0.0669701	−	0.180107i
$914$	10.9491	−	18.9644i	0.362163	−	0.627285i
$915$	31.9401	+	55.3218i	1.05591	+	1.82888i
$916$			10.7093i			0.353844i
$917$	−14.6576	+	28.4736i	−0.484038	+	0.940282i
$918$	3.33708			0.110140
$919$	−35.7439	+	20.6368i	−1.17908	+	0.680744i	−0.955802	−	0.294011i	$-0.905010\pi$
$919$	−35.7439	+	20.6368i	−1.17908	+	0.680744i	−0.223280	+	0.974754i	$0.571677\pi$
$920$	−12.3239	+	21.3457i	−0.406308	+	0.703747i
$921$	16.0210	+	9.24972i	0.527910	+	0.304789i
$922$	−11.6244	+	6.71136i	−0.382830	+	0.221027i
$923$	−2.85185			−0.0938699
$924$	1.04532	−	8.71248i	0.0343885	−	0.286620i
$925$	34.1561			1.12305
$926$	18.3097	−	10.5711i	0.601694	−	0.347388i
$927$	−12.8128	−	7.39746i	−0.420827	−	0.242964i
$928$	−3.87436	+	6.71059i	−0.127182	+	0.220286i
$929$	17.6201	−	10.1730i	0.578096	−	0.333764i	−0.182280	−	0.983247i	$-0.558348\pi$
$929$	17.6201	−	10.1730i	0.578096	−	0.333764i	0.760376	+	0.649483i	$0.225015\pi$
$930$	−13.7788			−0.451826
$931$	22.5127	−	2.17687i	0.737825	−	0.0713440i
$932$		−	17.7106i		−	0.580129i
$933$	15.4989	+	26.8449i	0.507412	+	0.878864i
$934$	−1.43737	+	2.48960i	−0.0470323	+	0.0814623i
$935$	44.6240	−	16.5927i	1.45936	−	0.542640i
$936$	0.866669	−	0.500372i	0.0283280	−	0.0163552i
$937$	21.9119			0.715831			0.357916	−	0.933754i	$-0.383488\pi$
$937$	21.9119			0.715831			0.357916	+	0.933754i	$0.383488\pi$
$938$	−0.735086	+	0.473032i	−0.0240014	+	0.0154450i
$939$	−9.60149			−0.313333
$940$	−6.88467	−	11.9246i	−0.224553	−	0.388938i
$941$	−26.3049	+	45.5614i	−0.857514	+	1.48526i	0.0167786	+	0.999859i	$0.494659\pi$
$941$	−26.3049	+	45.5614i	−0.857514	+	1.48526i	−0.874293	+	0.485399i	$0.838674\pi$
$942$	−1.08351	−	0.625565i	−0.0353027	−	0.0203820i
$943$	−4.15742	−	7.20086i	−0.135384	−	0.234492i
$944$		−	3.44231i		−	0.112038i
$945$	5.20897	−	10.1188i	0.169448	−	0.329166i
$946$	−8.76502	+	10.5939i	−0.284976	+	0.344438i
$947$	12.5178	+	21.6815i	0.406775	+	0.704555i	0.994526	−	0.104487i	$-0.0333200\pi$
$947$	12.5178	+	21.6815i	0.406775	+	0.704555i	−0.587751	+	0.809042i	$0.699987\pi$
$948$	8.04614	−	13.9363i	0.261326	−	0.452631i
$949$	−7.45343	+	12.9097i	−0.241949	+	0.419067i
$950$	37.7856	−	21.8155i	1.22593	−	0.707790i
$951$		−	11.9425i		−	0.387263i
$952$	0.425377	+	8.81883i	0.0137865	+	0.285820i
$953$		−	27.4386i		−	0.888823i	−0.895823	−	0.444411i	$-0.853413\pi$
$953$		−	27.4386i		−	0.888823i	0.895823	−	0.444411i	$-0.146587\pi$
$954$	−9.79949	+	5.65774i	−0.317270	+	0.183176i
$955$	−77.5607	−	44.7797i	−2.50981	−	1.44904i
$956$	23.0671	+	13.3178i	0.746043	+	0.430728i
$957$	25.3395	+	4.28728i	0.819108	+	0.138588i
$958$			3.83882i			0.124027i
$959$	−26.1393	+	1.26083i	−0.844082	+	0.0407143i
$960$	4.30156			0.138832
$961$	−10.3697	−	17.9609i	−0.334507	−	0.579382i
$962$	2.19218	+	1.26566i	0.0706789	+	0.0408065i
$963$	9.19190	+	5.30694i	0.296205	+	0.171014i
$964$	1.85521	+	3.21331i	0.0597521	+	0.103494i
$965$	19.4276			0.625398
$966$	−6.93871	+	13.4790i	−0.223249	+	0.433679i
$967$			44.4870i			1.43061i	0.698815	+	0.715303i	$0.253711\pi$
$967$			44.4870i			1.43061i	−0.698815	+	0.715303i	$0.746289\pi$
$968$	−7.18671	−	8.32774i	−0.230990	−	0.267664i
$969$	9.33788	+	5.39123i	0.299976	+	0.173191i
$970$	−45.9502	−	26.5293i	−1.47537	−	0.851806i
$971$	−7.16677	+	4.13774i	−0.229993	+	0.132786i	−0.610569	−	0.791963i	$-0.709059\pi$
$971$	−7.16677	+	4.13774i	−0.229993	+	0.132786i	0.380576	+	0.924750i	$0.375726\pi$
$972$		−	1.00000i		−	0.0320750i
$973$	2.27282	+	3.53194i	0.0728634	+	0.113229i
$974$			9.68084i			0.310194i
$975$	11.7030	−	6.75674i	0.374797	−	0.216389i
$976$	−7.42522	+	12.8609i	−0.237675	+	0.411666i
$977$	−14.4351	+	25.0022i	−0.461818	+	0.799893i	−0.999052	−	0.0435409i	$-0.986136\pi$
$977$	−14.4351	+	25.0022i	−0.461818	+	0.799893i	0.537233	+	0.843434i	$0.319469\pi$
$978$	−3.60786	−	6.24899i	−0.115367	−	0.199821i
$979$	−7.11572	−	5.88729i	−0.227419	−	0.188159i
$980$	27.4048	+	12.4758i	0.875415	+	0.398524i
$981$		−	0.348204i		−	0.0111173i
$982$	−7.94428	−	13.7599i	−0.253512	−	0.439096i
$983$	38.6365	+	22.3068i	1.23231	+	0.711476i	0.967511	−	0.252828i	$-0.0813606\pi$
$983$	38.6365	+	22.3068i	1.23231	+	0.711476i	0.264800	+	0.964303i	$0.414694\pi$
$984$	−0.725556	+	1.25670i	−0.0231299	+	0.0400621i
$985$	−37.3297	−	64.6569i	−1.18942	−	2.06014i
$986$	−25.8581			−0.823490
$987$	−4.58299	−	7.12190i	−0.145878	−	0.226693i
$988$	3.23351			0.102872
$989$	20.5723	−	11.8774i	0.654162	−	0.377681i
$990$	−4.97223	−	13.3722i	−0.158028	−	0.424995i
$991$	18.5281	−	32.0916i	0.588565	−	1.01942i	−0.405856	−	0.913937i	$-0.633026\pi$
$991$	18.5281	−	32.0916i	0.588565	−	1.01942i	0.994421	−	0.105487i	$-0.0336402\pi$
$992$	−1.60161	−	2.77407i	−0.0508511	−	0.0880767i
$993$			6.49162i			0.206005i
$994$	−6.70361	−	3.45088i	−0.212626	−	0.109455i
$995$	33.6236			1.06594
$996$	1.51608	−	0.875309i	0.0480388	−	0.0277352i
$997$	−17.2468	+	29.8724i	−0.546213	+	0.946068i	0.452317	+	0.891857i	$0.350598\pi$
$997$	−17.2468	+	29.8724i	−0.546213	+	0.946068i	−0.998530	+	0.0542108i	$0.982736\pi$
$998$	−26.0188	−	15.0220i	−0.823612	−	0.475513i
$999$	2.19056	−	1.26472i	0.0693061	−	0.0400139i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.p.b.241.4	yes	16
3.2	odd	2		1386.2.bk.b.703.5		16
7.3	odd	6		3234.2.e.a.2155.1		16
7.4	even	3		3234.2.e.b.2155.8		16
7.5	odd	6		462.2.p.a.439.8	yes	16
11.10	odd	2		462.2.p.a.241.8	✓	16
21.5	even	6		1386.2.bk.a.901.1		16
33.32	even	2		1386.2.bk.a.703.1		16
77.10	even	6		3234.2.e.b.2155.9		16
77.32	odd	6		3234.2.e.a.2155.16		16
77.54	even	6	inner	462.2.p.b.439.4	yes	16
231.131	odd	6		1386.2.bk.b.901.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.p.a.241.8	✓	16	11.10	odd	2
462.2.p.a.439.8	yes	16	7.5	odd	6
462.2.p.b.241.4	yes	16	1.1	even	1	trivial
462.2.p.b.439.4	yes	16	77.54	even	6	inner
1386.2.bk.a.703.1		16	33.32	even	2
1386.2.bk.a.901.1		16	21.5	even	6
1386.2.bk.b.703.5		16	3.2	odd	2
1386.2.bk.b.901.5		16	231.131	odd	6
3234.2.e.a.2155.1		16	7.3	odd	6
3234.2.e.a.2155.16		16	77.32	odd	6
3234.2.e.b.2155.8		16	7.4	even	3
3234.2.e.b.2155.9		16	77.10	even	6

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.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(3.72526 - 2.15078i) q^{5} +1.00000 q^{6} +(1.43173 + 2.22489i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(3.72526 - 2.15078i) q^{5} +1.00000 q^{6} +(1.43173 + 2.22489i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.15078 + 3.72526i) q^{10} +(1.15591 + 3.10868i) q^{11} +(-0.866025 + 0.500000i) q^{12} -1.00074 q^{13} +(-2.35236 - 1.21095i) q^{14} -4.30156 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.66854 - 2.89000i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(-1.61555 - 2.79822i) q^{19} -4.30156i q^{20} +(-0.127470 - 2.64268i) q^{21} +(-2.55539 - 2.11424i) q^{22} +(2.86499 + 4.96231i) q^{23} +(0.500000 - 0.866025i) q^{24} +(6.75173 - 11.6943i) q^{25} +(0.866669 - 0.500372i) q^{26} -1.00000i q^{27} +(2.64268 - 0.127470i) q^{28} +7.74872i q^{29} +(3.72526 - 2.15078i) q^{30} +(-2.77407 - 1.60161i) q^{31} +(0.866025 + 0.500000i) q^{32} +(0.553289 - 3.27015i) q^{33} +3.33708i q^{34} +(10.1188 + 5.20897i) q^{35} +1.00000 q^{36} +(1.26472 + 2.19056i) q^{37} +(2.79822 + 1.61555i) q^{38} +(0.866669 + 0.500372i) q^{39} +(2.15078 + 3.72526i) q^{40} -1.45111 q^{41} +(1.43173 + 2.22489i) q^{42} -4.14572i q^{43} +(3.27015 + 0.553289i) q^{44} +(3.72526 + 2.15078i) q^{45} +(-4.96231 - 2.86499i) q^{46} +(2.77216 - 1.60050i) q^{47} +1.00000i q^{48} +(-2.90029 + 6.37090i) q^{49} +13.5035i q^{50} +(-2.89000 + 1.66854i) q^{51} +(-0.500372 + 0.866669i) q^{52} +(5.65774 - 9.79949i) q^{53} +(0.500000 + 0.866025i) q^{54} +(10.9922 + 9.09452i) q^{55} +(-2.22489 + 1.43173i) q^{56} +3.23111i q^{57} +(-3.87436 - 6.71059i) q^{58} +(2.98113 + 1.72116i) q^{59} +(-2.15078 + 3.72526i) q^{60} +(-7.42522 - 12.8609i) q^{61} +3.20322 q^{62} +(-1.21095 + 2.35236i) q^{63} -1.00000 q^{64} +(-3.72803 + 2.15238i) q^{65} +(1.15591 + 3.10868i) q^{66} +(0.165196 - 0.286128i) q^{67} +(-1.66854 - 2.89000i) q^{68} -5.72998i q^{69} +(-11.3677 + 0.548319i) q^{70} +2.84974 q^{71} +(-0.866025 + 0.500000i) q^{72} +(7.44790 - 12.9001i) q^{73} +(-2.19056 - 1.26472i) q^{74} +(-11.6943 + 6.75173i) q^{75} -3.23111 q^{76} +(-5.26151 + 7.02257i) q^{77} -1.00074 q^{78} +(-13.9363 + 8.04614i) q^{79} +(-3.72526 - 2.15078i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.25670 - 0.725556i) q^{82} -1.75062 q^{83} +(-2.35236 - 1.21095i) q^{84} -14.3547i q^{85} +(2.07286 + 3.59030i) q^{86} +(3.87436 - 6.71059i) q^{87} +(-3.10868 + 1.15591i) q^{88} +(-2.41153 + 1.39230i) q^{89} -4.30156 q^{90} +(-1.43280 - 2.22655i) q^{91} +5.72998 q^{92} +(1.60161 + 2.77407i) q^{93} +(-1.60050 + 2.77216i) q^{94} +(-12.0367 - 6.94940i) q^{95} +(-0.500000 - 0.866025i) q^{96} +12.3347i q^{97} +(-0.673723 - 6.96750i) q^{98} +(-2.11424 + 2.55539i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 12 q^{5} + 16 q^{6} + 6 q^{7} + 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 + 12 * q^5 + 16 * q^6 + 6 * q^7 + 8 * q^9	\( 16 q + 8 q^{4} + 12 q^{5} + 16 q^{6} + 6 q^{7} + 8 q^{9} - 2 q^{10} - 4 q^{11} + 8 q^{14} - 4 q^{15} - 8 q^{16} + 10 q^{19} + 4 q^{21} + 2 q^{22} - 4 q^{23} + 8 q^{24} + 10 q^{25} + 12 q^{26} + 12 q^{30} + 6 q^{31} + 4 q^{33} + 8 q^{35} + 16 q^{36} + 14 q^{37} - 12 q^{38} + 12 q^{39} + 2 q^{40} - 32 q^{41} + 6 q^{42} + 4 q^{44} + 12 q^{45} - 18 q^{46} - 24 q^{47} - 6 q^{49} - 6 q^{51} + 8 q^{54} + 14 q^{55} + 4 q^{56} - 2 q^{60} - 28 q^{61} + 8 q^{62} + 6 q^{63} - 16 q^{64} - 72 q^{65} - 4 q^{66} - 16 q^{67} - 30 q^{70} - 56 q^{71} + 44 q^{73} - 24 q^{74} - 12 q^{75} + 20 q^{76} - 52 q^{77} + 30 q^{79} - 12 q^{80} - 8 q^{81} - 12 q^{82} - 8 q^{83} + 8 q^{84} - 12 q^{86} - 2 q^{88} - 36 q^{89} - 4 q^{90} - 8 q^{91} - 8 q^{92} + 4 q^{93} - 14 q^{94} - 72 q^{95} - 8 q^{96} + 40 q^{98} - 8 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 12 * q^5 + 16 * q^6 + 6 * q^7 + 8 * q^9 - 2 * q^10 - 4 * q^11 + 8 * q^14 - 4 * q^15 - 8 * q^16 + 10 * q^19 + 4 * q^21 + 2 * q^22 - 4 * q^23 + 8 * q^24 + 10 * q^25 + 12 * q^26 + 12 * q^30 + 6 * q^31 + 4 * q^33 + 8 * q^35 + 16 * q^36 + 14 * q^37 - 12 * q^38 + 12 * q^39 + 2 * q^40 - 32 * q^41 + 6 * q^42 + 4 * q^44 + 12 * q^45 - 18 * q^46 - 24 * q^47 - 6 * q^49 - 6 * q^51 + 8 * q^54 + 14 * q^55 + 4 * q^56 - 2 * q^60 - 28 * q^61 + 8 * q^62 + 6 * q^63 - 16 * q^64 - 72 * q^65 - 4 * q^66 - 16 * q^67 - 30 * q^70 - 56 * q^71 + 44 * q^73 - 24 * q^74 - 12 * q^75 + 20 * q^76 - 52 * q^77 + 30 * q^79 - 12 * q^80 - 8 * q^81 - 12 * q^82 - 8 * q^83 + 8 * q^84 - 12 * q^86 - 2 * q^88 - 36 * q^89 - 4 * q^90 - 8 * q^91 - 8 * q^92 + 4 * q^93 - 14 * q^94 - 72 * q^95 - 8 * q^96 + 40 * q^98 - 8 * q^99

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