LMFDB - Embedded newform 570.2.n.a.179.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(179,570)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("570.179");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.n (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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			179.19
Character	$\chi$	$=$	570.179
Dual form			570.2.n.a.449.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(1.71127 + 0.267475i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.56298 - 1.59909i) q^{5} +(-1.34827 - 1.08728i) q^{6} -1.36390i q^{7} -1.00000i q^{8} +(2.85691 + 0.915446i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(1.71127 + 0.267475i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.56298 - 1.59909i) q^{5} +(-1.34827 - 1.08728i) q^{6} -1.36390i q^{7} -1.00000i q^{8} +(2.85691 + 0.915446i) q^{9} +(0.554035 + 2.16634i) q^{10} -5.06802i q^{11} +(0.623997 + 1.61574i) q^{12} +(1.22067 + 2.11426i) q^{13} +(-0.681949 + 1.18117i) q^{14} +(-2.24697 - 3.15454i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.98489 + 3.43793i) q^{17} +(-2.01644 - 2.22126i) q^{18} +(1.02155 - 4.23750i) q^{19} +(0.603364 - 2.15313i) q^{20} +(0.364808 - 2.33400i) q^{21} +(-2.53401 + 4.38904i) q^{22} +(-3.14511 - 5.44749i) q^{23} +(0.267475 - 1.71127i) q^{24} +(-0.114186 + 4.99870i) q^{25} -2.44133i q^{26} +(4.64410 + 2.33073i) q^{27} +(1.18117 - 0.681949i) q^{28} +(-2.36769 - 4.10097i) q^{29} +(0.368662 + 3.85540i) q^{30} -8.32731i q^{31} +(0.866025 - 0.500000i) q^{32} +(1.35557 - 8.67278i) q^{33} +(3.43793 - 1.98489i) q^{34} +(-2.18100 + 2.13174i) q^{35} +(0.635658 + 2.93188i) q^{36} -3.47648 q^{37} +(-3.00344 + 3.15901i) q^{38} +(1.52338 + 3.94457i) q^{39} +(-1.59909 + 1.56298i) q^{40} +(2.09732 - 3.63266i) q^{41} +(-1.48293 + 1.83890i) q^{42} +(8.08295 + 4.66669i) q^{43} +(4.38904 - 2.53401i) q^{44} +(-3.00142 - 5.99929i) q^{45} +6.29022i q^{46} +(4.62919 + 8.01800i) q^{47} +(-1.08728 + 1.34827i) q^{48} +5.13978 q^{49} +(2.59824 - 4.27190i) q^{50} +(-4.31625 + 5.35234i) q^{51} +(-1.22067 + 2.11426i) q^{52} +(6.37085 - 3.67821i) q^{53} +(-2.85655 - 4.34052i) q^{54} +(-8.10423 + 7.92122i) q^{55} -1.36390 q^{56} +(2.88158 - 6.97829i) q^{57} +4.73539i q^{58} +(0.294619 - 0.510294i) q^{59} +(1.60843 - 3.52320i) q^{60} +(3.56020 + 6.16645i) q^{61} +(-4.16366 + 7.21167i) q^{62} +(1.24857 - 3.89654i) q^{63} -1.00000 q^{64} +(1.47301 - 5.25650i) q^{65} +(-5.51035 + 6.83306i) q^{66} +(-5.50663 - 9.53776i) q^{67} -3.96978 q^{68} +(-3.92508 - 10.1634i) q^{69} +(2.95467 - 0.755647i) q^{70} +(-5.35146 + 9.26899i) q^{71} +(0.915446 - 2.85691i) q^{72} +(-6.55246 - 3.78306i) q^{73} +(3.01072 + 1.73824i) q^{74} +(-1.53243 + 8.52359i) q^{75} +(4.18056 - 1.23406i) q^{76} -6.91226 q^{77} +(0.652996 - 4.17779i) q^{78} +(-6.44300 - 3.71987i) q^{79} +(2.16634 - 0.554035i) q^{80} +(7.32392 + 5.23070i) q^{81} +(-3.63266 + 2.09732i) q^{82} +10.1667 q^{83} +(2.20371 - 0.851067i) q^{84} +(8.59992 - 2.19940i) q^{85} +(-4.66669 - 8.08295i) q^{86} +(-2.95487 - 7.65117i) q^{87} -5.06802 q^{88} +(3.62450 + 6.27782i) q^{89} +(-0.400340 + 6.69625i) q^{90} +(2.88363 - 1.66486i) q^{91} +(3.14511 - 5.44749i) q^{92} +(2.22735 - 14.2503i) q^{93} -9.25839i q^{94} +(-8.37282 + 4.98958i) q^{95} +(1.61574 - 0.623997i) q^{96} +(-5.42307 + 9.39303i) q^{97} +(-4.45118 - 2.56989i) q^{98} +(4.63950 - 14.4789i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 40 q^{4}+O(q^{10}) $ 80 * q + 40 * q^4	$ 80 q + 40 q^{4} + 30 q^{15} - 40 q^{16} + 8 q^{19} + 8 q^{25} - 4 q^{30} + 48 q^{39} + 12 q^{45} - 128 q^{49} - 36 q^{54} + 12 q^{55} + 30 q^{60} - 24 q^{61} - 80 q^{64} + 4 q^{66} + 36 q^{70} + 16 q^{76} + 24 q^{79} + 32 q^{81} - 8 q^{85} - 54 q^{90} + 24 q^{91} - 60 q^{99}+O(q^{100}) $ 80 * q + 40 * q^4 + 30 * q^15 - 40 * q^16 + 8 * q^19 + 8 * q^25 - 4 * q^30 + 48 * q^39 + 12 * q^45 - 128 * q^49 - 36 * q^54 + 12 * q^55 + 30 * q^60 - 24 * q^61 - 80 * q^64 + 4 * q^66 + 36 * q^70 + 16 * q^76 + 24 * q^79 + 32 * q^81 - 8 * q^85 - 54 * q^90 + 24 * q^91 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$

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
$3$	1.71127	+	0.267475i	0.988004	+	0.154427i
$3$	1.71127	+	0.267475i	0.988004	+	0.154427i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.56298	−	1.59909i	−0.698986	−	0.715135i
$5$	−1.56298	−	1.59909i	−0.698986	−	0.715135i
$6$	−1.34827	−	1.08728i	−0.550428	−	0.443879i
$7$		−	1.36390i		−	0.515505i	−0.966211	−	0.257752i	$-0.917018\pi$
$7$		−	1.36390i		−	0.515505i	0.966211	−	0.257752i	$-0.0829819\pi$
$8$		−	1.00000i		−	0.353553i
$9$	2.85691	+	0.915446i	0.952305	+	0.305149i
$10$	0.554035	+	2.16634i	0.175201	+	0.685058i
$11$		−	5.06802i		−	1.52807i	−0.645177	−	0.764033i	$-0.723216\pi$
$11$		−	5.06802i		−	1.52807i	0.645177	−	0.764033i	$-0.276784\pi$
$12$	0.623997	+	1.61574i	0.180132	+	0.466425i
$13$	1.22067	+	2.11426i	0.338552	+	0.586390i	0.984161	−	0.177279i	$-0.0567295\pi$
$13$	1.22067	+	2.11426i	0.338552	+	0.586390i	−0.645608	+	0.763669i	$0.723396\pi$
$14$	−0.681949	+	1.18117i	−0.182258	+	0.315681i
$15$	−2.24697	−	3.15454i	−0.580165	−	0.814499i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.98489	+	3.43793i	−0.481407	+	0.833821i	−0.999772	−	0.0213379i	$-0.993207\pi$
$17$	−1.98489	+	3.43793i	−0.481407	+	0.833821i	0.518365	+	0.855159i	$0.326541\pi$
$18$	−2.01644	−	2.22126i	−0.475279	−	0.523555i
$19$	1.02155	−	4.23750i	0.234359	−	0.972150i
$19$	1.02155	−	4.23750i	0.234359	−	0.972150i
$20$	0.603364	−	2.15313i	0.134916	−	0.481454i
$21$	0.364808	−	2.33400i	0.0796077	−	0.509321i
$22$	−2.53401	+	4.38904i	−0.540253	+	0.935746i
$23$	−3.14511	−	5.44749i	−0.655801	−	1.13588i	−0.981692	−	0.190473i	$-0.938998\pi$
$23$	−3.14511	−	5.44749i	−0.655801	−	1.13588i	0.325892	−	0.945407i	$-0.394336\pi$
$24$	0.267475	−	1.71127i	0.0545981	−	0.349312i
$25$	−0.114186	+	4.99870i	−0.0228372	+	0.999739i
$26$		−	2.44133i		−	0.478785i
$27$	4.64410	+	2.33073i	0.893758	+	0.448549i
$28$	1.18117	−	0.681949i	0.223220	−	0.128876i
$29$	−2.36769	−	4.10097i	−0.439670	−	0.761530i	0.557994	−	0.829845i	$-0.311571\pi$
$29$	−2.36769	−	4.10097i	−0.439670	−	0.761530i	−0.997664	+	0.0683147i	$0.978238\pi$
$30$	0.368662	+	3.85540i	0.0673082	+	0.703896i
$31$		−	8.32731i		−	1.49563i	−0.663907	−	0.747815i	$-0.731103\pi$
$31$		−	8.32731i		−	1.49563i	0.663907	−	0.747815i	$-0.268897\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	1.35557	−	8.67278i	0.235974	−	1.50974i
$34$	3.43793	−	1.98489i	0.589601	−	0.340406i
$35$	−2.18100	+	2.13174i	−0.368656	+	0.360331i
$36$	0.635658	+	2.93188i	0.105943	+	0.488647i
$37$	−3.47648			−0.571530			−0.285765	−	0.958300i	$-0.592248\pi$
$37$	−3.47648			−0.571530			−0.285765	+	0.958300i	$0.592248\pi$
$38$	−3.00344	+	3.15901i	−0.487222	+	0.512459i
$39$	1.52338	+	3.94457i	0.243937	+	0.631637i
$40$	−1.59909	+	1.56298i	−0.252839	+	0.247129i
$41$	2.09732	−	3.63266i	0.327546	−	0.567327i	−0.654478	−	0.756081i	$-0.727112\pi$
$41$	2.09732	−	3.63266i	0.327546	−	0.567327i	0.982024	+	0.188754i	$0.0604449\pi$
$42$	−1.48293	+	1.83890i	−0.228822	+	0.283748i
$43$	8.08295	+	4.66669i	1.23264	+	0.711664i	0.967579	−	0.252568i	$-0.0812753\pi$
$43$	8.08295	+	4.66669i	1.23264	+	0.711664i	0.265059	+	0.964232i	$0.414609\pi$
$44$	4.38904	−	2.53401i	0.661672	−	0.382017i
$45$	−3.00142	−	5.99929i	−0.447425	−	0.894321i
$46$			6.29022i			0.927442i
$47$	4.62919	+	8.01800i	0.675237	+	1.16955i	0.976400	+	0.215972i	$0.0692921\pi$
$47$	4.62919	+	8.01800i	0.675237	+	1.16955i	−0.301162	+	0.953573i	$0.597375\pi$
$48$	−1.08728	+	1.34827i	−0.156935	+	0.194606i
$49$	5.13978			0.734255
$50$	2.59824	−	4.27190i	0.367446	−	0.604139i
$51$	−4.31625	+	5.35234i	−0.604397	+	0.749477i
$52$	−1.22067	+	2.11426i	−0.169276	+	0.293195i
$53$	6.37085	−	3.67821i	0.875104	−	0.505242i	0.00606311	−	0.999982i	$-0.498070\pi$
$53$	6.37085	−	3.67821i	0.875104	−	0.505242i	0.869041	+	0.494740i	$0.164737\pi$
$54$	−2.85655	−	4.34052i	−0.388727	−	0.590670i
$55$	−8.10423	+	7.92122i	−1.09277	+	1.06810i
$56$	−1.36390			−0.182258
$57$	2.88158	−	6.97829i	0.381674	−	0.924297i
$58$			4.73539i			0.621787i
$59$	0.294619	−	0.510294i	0.0383561	−	0.0664347i	−0.846210	−	0.532849i	$-0.821121\pi$
$59$	0.294619	−	0.510294i	0.0383561	−	0.0664347i	0.884566	+	0.466415i	$0.154455\pi$
$60$	1.60843	−	3.52320i	0.207647	−	0.454844i
$61$	3.56020	+	6.16645i	0.455837	+	0.789534i	0.998736	−	0.0502647i	$-0.0160065\pi$
$61$	3.56020	+	6.16645i	0.455837	+	0.789534i	−0.542898	+	0.839798i	$0.682673\pi$
$62$	−4.16366	+	7.21167i	−0.528785	+	0.915882i
$63$	1.24857	−	3.89654i	0.157306	−	0.490918i
$64$	−1.00000			−0.125000
$65$	1.47301	−	5.25650i	0.182705	−	0.651989i
$66$	−5.51035	+	6.83306i	−0.678277	+	0.841091i
$67$	−5.50663	−	9.53776i	−0.672742	−	1.16522i	−0.977124	−	0.212673i	$-0.931783\pi$
$67$	−5.50663	−	9.53776i	−0.672742	−	1.16522i	0.304382	−	0.952550i	$-0.401550\pi$
$68$	−3.96978			−0.481407
$69$	−3.92508	−	10.1634i	−0.472524	−	1.22353i
$70$	2.95467	−	0.755647i	0.353151	−	0.0903170i
$71$	−5.35146	+	9.26899i	−0.635101	+	1.10003i	0.351393	+	0.936228i	$0.385708\pi$
$71$	−5.35146	+	9.26899i	−0.635101	+	1.10003i	−0.986494	+	0.163799i	$0.947625\pi$
$72$	0.915446	−	2.85691i	0.107886	−	0.336691i
$73$	−6.55246	−	3.78306i	−0.766908	−	0.442774i	0.0648628	−	0.997894i	$-0.479339\pi$
$73$	−6.55246	−	3.78306i	−0.766908	−	0.442774i	−0.831770	+	0.555120i	$0.812672\pi$
$74$	3.01072	+	1.73824i	0.349989	+	0.202067i
$75$	−1.53243	+	8.52359i	−0.176950	+	0.984220i
$76$	4.18056	−	1.23406i	0.479543	−	0.141557i
$77$	−6.91226			−0.787725
$78$	0.652996	−	4.17779i	0.0739372	−	0.473042i
$79$	−6.44300	−	3.71987i	−0.724894	−	0.418518i	0.0916575	−	0.995791i	$-0.470783\pi$
$79$	−6.44300	−	3.71987i	−0.724894	−	0.418518i	−0.816551	+	0.577273i	$0.804117\pi$
$80$	2.16634	−	0.554035i	0.242205	−	0.0619430i
$81$	7.32392	+	5.23070i	0.813769	+	0.581189i
$82$	−3.63266	+	2.09732i	−0.401161	+	0.231610i
$83$	10.1667			1.11594			0.557970	−	0.829861i	$-0.311580\pi$
$83$	10.1667			1.11594			0.557970	+	0.829861i	$0.311580\pi$
$84$	2.20371	−	0.851067i	0.240444	−	0.0928590i
$85$	8.59992	−	2.19940i	0.932792	−	0.238558i
$86$	−4.66669	−	8.08295i	−0.503222	−	0.871607i
$87$	−2.95487	−	7.65117i	−0.316795	−	0.820292i
$88$	−5.06802			−0.540253
$89$	3.62450	+	6.27782i	0.384196	+	0.665448i	0.991657	−	0.128902i	$-0.0411452\pi$
$89$	3.62450	+	6.27782i	0.384196	+	0.665448i	−0.607461	+	0.794350i	$0.707812\pi$
$90$	−0.400340	+	6.69625i	−0.0421995	+	0.705846i
$91$	2.88363	−	1.66486i	0.302287	−	0.174525i
$92$	3.14511	−	5.44749i	0.327900	−	0.567940i
$93$	2.22735	−	14.2503i	0.230965	−	1.47769i
$94$		−	9.25839i		−	0.954930i
$95$	−8.37282	+	4.98958i	−0.859033	+	0.511920i
$96$	1.61574	−	0.623997i	0.164906	−	0.0636864i
$97$	−5.42307	+	9.39303i	−0.550629	+	0.953718i	0.447600	+	0.894234i	$0.352279\pi$
$97$	−5.42307	+	9.39303i	−0.550629	+	0.953718i	−0.998229	+	0.0594842i	$0.981054\pi$
$98$	−4.45118	−	2.56989i	−0.449638	−	0.259598i
$99$	4.63950	−	14.4789i	0.466287	−	1.45519i
$100$	−4.38609	+	2.40046i	−0.438609	+	0.240046i
$101$	−12.4759	+	7.20295i	−1.24140	+	0.716720i	−0.969378	−	0.245572i	$-0.921024\pi$
$101$	−12.4759	+	7.20295i	−1.24140	+	0.716720i	−0.272018	+	0.962292i	$0.587691\pi$
$102$	6.41415	−	2.47713i	0.635096	−	0.245273i
$103$	1.39554			0.137506			0.0687532	−	0.997634i	$-0.478098\pi$
$103$	1.39554			0.137506			0.0687532	+	0.997634i	$0.478098\pi$
$104$	2.11426	−	1.22067i	0.207320	−	0.119696i
$105$	−4.30247	+	3.06464i	−0.419878	+	0.299078i
$106$	−7.35643			−0.714520
$107$			13.5423i			1.30919i	0.755981	+	0.654593i	$0.227160\pi$
$107$			13.5423i			1.30919i	−0.755981	+	0.654593i	$0.772840\pi$
$108$	0.303579	+	5.18728i	0.0292119	+	0.499146i
$109$	−1.72498	−	0.995917i	−0.165223	−	0.0953916i	0.415108	−	0.909772i	$-0.363744\pi$
$109$	−1.72498	−	0.995917i	−0.165223	−	0.0953916i	−0.580331	+	0.814380i	$0.697077\pi$
$110$	10.9791	−	2.80786i	1.04681	−	0.267719i
$111$	−5.94921	−	0.929872i	−0.564674	−	0.0882596i
$112$	1.18117	+	0.681949i	0.111610	+	0.0644381i
$113$			9.35520i			0.880063i	0.897982	+	0.440032i	$0.145033\pi$
$113$			9.35520i			0.880063i	−0.897982	+	0.440032i	$0.854967\pi$
$114$	−5.98466	+	4.60259i	−0.560515	+	0.431072i
$115$	−3.79529	+	13.5436i	−0.353913	+	1.26295i
$116$	2.36769	−	4.10097i	0.219835	−	0.380765i
$117$	1.55185	+	7.15771i	0.143469	+	0.661730i
$118$	−0.510294	+	0.294619i	−0.0469764	+	0.0271218i
$119$	4.68899	+	2.70719i	0.429839	+	0.248168i
$120$	−3.15454	+	2.24697i	−0.287969	+	0.205119i
$121$	−14.6849			−1.33499
$122$		−	7.12041i		−	0.644651i
$123$	4.56074	−	5.65550i	0.411228	−	0.509939i
$124$	7.21167	−	4.16366i	0.647627	−	0.373907i
$125$	8.17184	−	7.63027i	0.730912	−	0.682472i
$126$	−3.02957	+	2.75021i	−0.269895	+	0.245008i
$127$	6.15762	+	10.6653i	0.546400	+	0.946393i	0.998517	+	0.0544343i	$0.0173356\pi$
$127$	6.15762	+	10.6653i	0.546400	+	0.946393i	−0.452117	+	0.891959i	$0.649331\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	12.5839	+	10.1480i	1.10795	+	0.893479i
$130$	−3.90392	+	3.81576i	−0.342396	+	0.334664i
$131$	18.6976	+	10.7951i	1.63362	+	0.943170i	0.982964	+	0.183797i	$0.0588389\pi$
$131$	18.6976	+	10.7951i	1.63362	+	0.943170i	0.650655	+	0.759374i	$0.274494\pi$
$132$	8.18863	−	3.16243i	0.712729	−	0.275254i
$133$	−5.77952	−	1.39329i	−0.501148	−	0.120813i
$134$			11.0133i			0.951400i
$135$	−3.53159	−	11.0692i	−0.303951	−	0.952688i
$136$	3.43793	+	1.98489i	0.294800	+	0.170203i
$137$	−3.24209	−	5.61546i	−0.276990	−	0.479761i	0.693645	−	0.720317i	$-0.256004\pi$
$137$	−3.24209	−	5.61546i	−0.276990	−	0.479761i	−0.970635	+	0.240556i	$0.922670\pi$
$138$	−1.68248	+	10.7643i	−0.143222	+	0.916317i
$139$	−0.586315	−	1.01553i	−0.0497306	−	0.0861360i	0.840089	−	0.542449i	$-0.182503\pi$
$139$	−0.586315	−	1.01553i	−0.0497306	−	0.0861360i	−0.889819	+	0.456313i	$0.849170\pi$
$140$	−2.93664	−	0.822926i	−0.248192	−	0.0695499i
$141$	5.77720	+	14.9592i	0.486528	+	1.25979i
$142$	9.26899	−	5.35146i	0.777837	−	0.449084i
$143$	10.7151	−	6.18637i	0.896043	−	0.517330i
$144$	−2.22126	+	2.01644i	−0.185105	+	0.168036i
$145$	−2.85716	+	10.1959i	−0.237274	+	0.846722i
$146$	3.78306	+	6.55246i	0.313089	+	0.542285i
$147$	8.79558	+	1.37476i	0.725447	+	0.113389i
$148$	−1.73824	−	3.01072i	−0.142883	−	0.247480i
$149$	14.5597	+	8.40607i	1.19278	+	0.688652i	0.958936	−	0.283622i	$-0.0915360\pi$
$149$	14.5597	+	8.40607i	1.19278	+	0.688652i	0.233844	+	0.972274i	$0.424869\pi$
$150$	5.58892	−	6.61543i	0.456333	−	0.540148i
$151$		−	0.483534i		−	0.0393494i	−0.999806	−	0.0196747i	$-0.993737\pi$
$151$		−	0.483534i		−	0.0393494i	0.999806	−	0.0196747i	$-0.00626306\pi$
$152$	−4.23750	−	1.02155i	−0.343707	−	0.0828586i
$153$	−8.81791	+	8.00482i	−0.712886	+	0.647151i
$154$	5.98620	+	3.45613i	0.482381	+	0.278503i
$155$	−13.3161	+	13.0154i	−1.06958	+	1.04542i
$156$	−2.65441	+	3.29158i	−0.212523	+	0.263537i
$157$	0.0466968	+	0.0269604i	0.00372681	+	0.00215167i	0.501862	−	0.864948i	$-0.332648\pi$
$157$	0.0466968	+	0.0269604i	0.00372681	+	0.00215167i	−0.498135	+	0.867099i	$0.665982\pi$
$158$	3.71987	+	6.44300i	0.295937	+	0.512577i
$159$	11.8861	−	4.59039i	0.942629	−	0.364041i
$160$	−2.15313	−	0.603364i	−0.170220	−	0.0477001i
$161$	−7.42982	+	4.28961i	−0.585551	+	0.338068i
$162$	−3.72735	−	8.19188i	−0.292848	−	0.643615i
$163$			19.2029i			1.50409i	0.659111	+	0.752045i	$0.270933\pi$
$163$			19.2029i			1.50409i	−0.659111	+	0.752045i	$0.729067\pi$
$164$	4.19464			0.327546
$165$	−15.9873	+	11.3877i	−1.24461	+	0.886531i
$166$	−8.80462	−	5.08335i	−0.683371	−	0.394544i
$167$	0.292128	−	0.168660i	0.0226055	−	0.0130513i	−0.488655	−	0.872477i	$-0.662512\pi$
$167$	0.292128	−	0.168660i	0.0226055	−	0.0130513i	0.511260	+	0.859426i	$0.329179\pi$
$168$	−2.33400	−	0.364808i	−0.180072	−	0.0281456i
$169$	3.51994	−	6.09672i	0.270765	−	0.468978i
$170$	−8.54745	−	2.39522i	−0.655559	−	0.183705i
$171$	6.79768	−	11.1710i	0.519832	−	0.854269i
$172$			9.33338i			0.711664i
$173$	5.13617	+	2.96537i	0.390496	+	0.225453i	0.682375	−	0.731002i	$-0.260947\pi$
$173$	5.13617	+	2.96537i	0.390496	+	0.225453i	−0.291879	+	0.956455i	$0.594280\pi$
$174$	−1.26660	+	8.10354i	−0.0960205	+	0.614328i
$175$	6.81771	+	0.155738i	0.515370	+	0.0117727i
$176$	4.38904	+	2.53401i	0.330836	+	0.191008i
$177$	0.640664	−	0.794450i	0.0481552	−	0.0597145i
$178$		−	7.24900i		−	0.543336i
$179$	−15.4657			−1.15596			−0.577979	−	0.816052i	$-0.696159\pi$
$179$	−15.4657			−1.15596			−0.577979	+	0.816052i	$0.696159\pi$
$180$	3.69483	−	5.59895i	0.275396	−	0.417321i
$181$	13.0595	−	7.53991i	0.970705	−	0.560437i	0.0712539	−	0.997458i	$-0.477300\pi$
$181$	13.0595	−	7.53991i	0.970705	−	0.560437i	0.899451	+	0.437021i	$0.143967\pi$
$182$	−3.32973			−0.246816
$183$	4.44311	+	11.5048i	0.328444	+	0.850456i
$184$	−5.44749	+	3.14511i	−0.401594	+	0.231861i
$185$	5.43368	+	5.55922i	0.399492	+	0.408722i
$186$	−9.05410	+	11.2275i	−0.663879	+	0.823237i
$187$	17.4235	+	10.0595i	1.27413	+	0.735622i
$188$	−4.62919	+	8.01800i	−0.337619	+	0.584773i
$189$	3.17888	−	6.33408i	0.231229	−	0.460736i
$190$	9.74586	−	0.134698i	0.707039	−	0.00977203i
$191$		−	3.72983i		−	0.269881i	−0.990854	−	0.134941i	$-0.956916\pi$
$191$		−	3.72983i		−	0.269881i	0.990854	−	0.134941i	$-0.0430844\pi$
$192$	−1.71127	−	0.267475i	−0.123501	−	0.0193033i
$193$	−1.12403	+	1.94688i	−0.0809094	+	0.140139i	−0.903641	−	0.428291i	$-0.859116\pi$
$193$	−1.12403	+	1.94688i	−0.0809094	+	0.140139i	0.822731	+	0.568430i	$0.192449\pi$
$194$	9.39303	−	5.42307i	0.674381	−	0.389354i
$195$	3.92671	−	8.60132i	0.281198	−	0.615953i
$196$	2.56989	+	4.45118i	0.183564	+	0.317942i
$197$	−24.7183			−1.76110			−0.880552	−	0.473949i	$-0.842828\pi$
$197$	−24.7183			−1.76110			−0.880552	+	0.473949i	$0.842828\pi$
$198$	−11.2574	+	10.2194i	−0.800027	+	0.726258i
$199$	−7.54694	−	13.0717i	−0.534988	−	0.926627i	−0.999164	−	0.0408837i	$-0.986983\pi$
$199$	−7.54694	−	13.0717i	−0.534988	−	0.926627i	0.464176	−	0.885743i	$-0.346351\pi$
$200$	4.99870	+	0.114186i	0.353461	+	0.00807417i
$201$	−6.87223	−	17.7946i	−0.484730	−	1.25513i
$202$	14.4059			1.01360
$203$	−5.59329	+	3.22929i	−0.392572	+	0.226652i
$204$	−6.79339	−	1.06182i	−0.475632	−	0.0743421i
$205$	−9.08703	+	2.32398i	−0.634666	+	0.162314i
$206$	−1.20857	−	0.697768i	−0.0842051	−	0.0486158i
$207$	−3.99843	−	18.4422i	−0.277910	−	1.28182i
$208$	−2.44133			−0.169276
$209$	−21.4758	−	5.17724i	−1.48551	−	0.358117i
$210$	5.25837	−	0.502818i	0.362862	−	0.0346977i
$211$	17.2731	+	9.97262i	1.18913	+	0.686543i	0.958108	−	0.286406i	$-0.0924606\pi$
$211$	17.2731	+	9.97262i	1.18913	+	0.686543i	0.231019	+	0.972949i	$0.425794\pi$
$212$	6.37085	+	3.67821i	0.437552	+	0.252621i
$213$	−11.6370	+	14.4304i	−0.797356	+	0.988755i
$214$	6.77117	−	11.7280i	0.462867	−	0.801710i
$215$	−5.17102	−	20.2193i	−0.352661	−	1.37895i
$216$	2.33073	−	4.64410i	0.158586	−	0.315991i
$217$	−11.3576			−0.771004
$218$	0.995917	+	1.72498i	0.0674520	+	0.116830i
$219$	−10.2012	−	8.22648i	−0.689332	−	0.555894i
$220$	−10.9121	−	3.05786i	−0.735693	−	0.206161i
$221$	−9.69157			−0.651926
$222$	4.68724	+	3.77990i	0.314587	+	0.253690i
$223$	7.23465	−	12.5308i	0.484468	−	0.839123i	−0.515373	−	0.856966i	$-0.672347\pi$
$223$	7.23465	−	12.5308i	0.484468	−	0.839123i	0.999841	+	0.0178430i	$0.00567991\pi$
$224$	−0.681949	−	1.18117i	−0.0455646	−	0.0789202i
$225$	−4.90225	+	14.1763i	−0.326817	+	0.945088i
$226$	4.67760	−	8.10184i	0.311149	−	0.538926i
$227$		−	7.77481i		−	0.516032i	−0.966141	−	0.258016i	$-0.916931\pi$
$227$		−	7.77481i		−	0.516032i	0.966141	−	0.258016i	$-0.0830687\pi$
$228$	7.48416	−	0.993626i	0.495651	−	0.0658045i
$229$	12.1628			0.803743			0.401872	−	0.915696i	$-0.368360\pi$
$229$	12.1628			0.803743			0.401872	+	0.915696i	$0.368360\pi$
$230$	10.0586	−	9.83149i	0.663247	−	0.648269i
$231$	−11.8288	−	1.84886i	−0.778276	−	0.121646i
$232$	−4.10097	+	2.36769i	−0.269242	+	0.155447i
$233$	4.24888	−	7.35928i	0.278354	−	0.482123i	−0.692622	−	0.721301i	$-0.743545\pi$
$233$	4.24888	−	7.35928i	0.278354	−	0.482123i	0.970976	+	0.239178i	$0.0768780\pi$
$234$	2.23491	−	6.97468i	0.146101	−	0.455949i
$235$	5.58617	−	19.9345i	0.364402	−	1.30038i
$236$	0.589237			0.0383561
$237$	−10.0308	−	8.08905i	−0.651568	−	0.525440i
$238$	−2.70719	−	4.68899i	−0.175481	−	0.303942i
$239$		−	0.321143i		−	0.0207730i	−0.999946	−	0.0103865i	$-0.996694\pi$
$239$		−	0.321143i		−	0.0207730i	0.999946	−	0.0103865i	$-0.00330619\pi$
$240$	3.85540	−	0.368662i	0.248865	−	0.0237971i
$241$	4.85412	−	2.80253i	0.312682	−	0.180527i	−0.335444	−	0.942060i	$-0.608886\pi$
$241$	4.85412	−	2.80253i	0.312682	−	0.180527i	0.648126	+	0.761533i	$0.275553\pi$
$242$	12.7175	+	7.34243i	0.817510	+	0.471989i
$243$	11.1341	+	10.9101i	0.714256	+	0.699885i
$244$	−3.56020	+	6.16645i	−0.227919	+	0.394767i
$245$	−8.03338	−	8.21899i	−0.513234	−	0.525092i
$246$	−6.77746	+	2.61744i	−0.432115	+	0.166882i
$247$	10.2061	−	3.01276i	0.649402	−	0.191698i
$248$	−8.32731			−0.528785
$249$	17.3980	+	2.71934i	1.10255	+	0.172331i
$250$	−10.8922	+	2.52209i	−0.688880	+	0.159511i
$251$	11.2207	−	6.47825i	0.708242	−	0.408904i	−0.102168	−	0.994767i	$-0.532578\pi$
$251$	11.2207	−	6.47825i	0.708242	−	0.408904i	0.810410	+	0.585864i	$0.199245\pi$
$252$	3.99879	−	0.866972i	0.251900	−	0.0546141i
$253$	−27.6080	+	15.9395i	−1.73570	+	1.00211i
$254$		−	12.3152i		−	0.772727i
$255$	15.3051	−	1.46351i	0.958442	−	0.0916486i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−9.55267	+	5.51524i	−0.595879	+	0.344031i	−0.767419	−	0.641146i	$-0.778459\pi$
$257$	−9.55267	+	5.51524i	−0.595879	+	0.344031i	0.171539	+	0.985177i	$0.445126\pi$
$258$	−5.82400	−	15.0804i	−0.362586	−	0.938862i
$259$			4.74157i			0.294627i
$260$	5.28877	−	1.35258i	0.327996	−	0.0838837i
$261$	−3.01009	−	13.8836i	−0.186320	−	0.859373i
$262$	−10.7951	−	18.6976i	−0.666922	−	1.15514i
$263$	3.48778	−	6.04100i	0.215065	−	0.372504i	−0.738227	−	0.674552i	$-0.764337\pi$
$263$	3.48778	−	6.04100i	0.215065	−	0.372504i	0.953293	+	0.302048i	$0.0976702\pi$
$264$	−8.67278	−	1.35557i	−0.533772	−	0.0834295i
$265$	−15.8393	−	4.43860i	−0.973002	−	0.272661i
$266$	4.30857	+	4.09638i	0.264175	+	0.251165i
$267$	4.52335	+	11.7125i	0.276825	+	0.716796i
$268$	5.50663	−	9.53776i	0.336371	−	0.582611i
$269$	−7.71267	+	13.3587i	−0.470250	+	0.814497i	−0.999421	−	0.0340183i	$-0.989170\pi$
$269$	−7.71267	+	13.3587i	−0.470250	+	0.814497i	0.529171	+	0.848515i	$0.322503\pi$
$270$	−2.47617	+	11.3520i	−0.150695	+	0.690863i
$271$	−10.8170	+	18.7356i	−0.657086	+	1.13811i	0.324280	+	0.945961i	$0.394878\pi$
$271$	−10.8170	+	18.7356i	−0.657086	+	1.13811i	−0.981366	+	0.192146i	$0.938455\pi$
$272$	−1.98489	−	3.43793i	−0.120352	−	0.208455i
$273$	5.37999	−	2.07774i	0.325612	−	0.125751i
$274$			6.48417i			0.391723i
$275$	25.3335	+	0.578698i	1.52767	+	0.0348968i
$276$	6.83921	−	8.48091i	0.411672	−	0.510491i
$277$		−	21.4127i		−	1.28657i	−0.765629	−	0.643283i	$-0.777572\pi$
$277$		−	21.4127i		−	1.28657i	0.765629	−	0.643283i	$-0.222428\pi$
$278$			1.17263i			0.0703297i
$279$	7.62320	−	23.7904i	0.456389	−	1.42430i
$280$	2.13174	+	2.18100i	0.127396	+	0.130339i
$281$	7.90099	+	13.6849i	0.471333	+	0.816374i	0.999462	−	0.0327908i	$-0.0104395\pi$
$281$	7.90099	+	13.6849i	0.471333	+	0.816374i	−0.528129	+	0.849164i	$0.677106\pi$
$282$	2.47639	−	15.8436i	0.147467	−	0.943474i
$283$	5.08966	+	2.93851i	0.302549	+	0.174677i	0.643587	−	0.765373i	$-0.277445\pi$
$283$	5.08966	+	2.93851i	0.302549	+	0.174677i	−0.341039	+	0.940049i	$0.610779\pi$
$284$	−10.7029			−0.635101
$285$	−15.6628	+	6.29902i	−0.927782	+	0.373122i
$286$	−12.3727			−0.731616
$287$	−4.95458	−	2.86053i	−0.292460	−	0.168852i
$288$	2.93188	−	0.635658i	0.172763	−	0.0374565i
$289$	0.620408	+	1.07458i	0.0364946	+	0.0632104i
$290$	7.57232	−	7.40132i	0.444662	−	0.434620i
$291$	−11.7928	+	14.6235i	−0.691304	+	0.857246i
$292$		−	7.56613i		−	0.442774i
$293$		−	9.50600i		−	0.555346i	−0.960676	−	0.277673i	$-0.910437\pi$
$293$		−	9.50600i		−	0.555346i	0.960676	−	0.277673i	$-0.0895633\pi$
$294$	−6.92981	−	5.58837i	−0.404155	−	0.325920i
$295$	−1.27649	+	0.326458i	−0.0743201	+	0.0190071i
$296$			3.47648i			0.202067i
$297$	11.8122	−	23.5364i	0.685413	−	1.36572i
$298$	−8.40607	−	14.5597i	−0.486951	−	0.843423i
$299$	7.67827	−	13.2991i	0.444046	−	0.769110i
$300$	−8.14786	+	2.93467i	−0.470417	+	0.169433i
$301$	6.36489	−	11.0243i	0.366866	−	0.635431i
$302$	−0.241767	+	0.418752i	−0.0139121	+	0.0240965i
$303$	−23.2762	+	8.98924i	−1.33719	+	0.516418i
$304$	3.15901	+	3.00344i	0.181182	+	0.172259i
$305$	4.29620	−	15.3311i	0.245999	−	0.877858i
$306$	11.6389	−	2.52342i	0.665354	−	0.144255i
$307$	6.33092	−	10.9655i	0.361325	−	0.625833i	−0.626855	−	0.779136i	$-0.715658\pi$
$307$	6.33092	−	10.9655i	0.361325	−	0.625833i	0.988179	+	0.153304i	$0.0489913\pi$
$308$	−3.45613	−	5.98620i	−0.196931	−	0.341095i
$309$	2.38815	+	0.373271i	0.135857	+	0.0212347i
$310$	18.0398	−	4.61362i	1.02459	−	0.262036i
$311$		−	32.0007i		−	1.81459i	−0.420494	−	0.907296i	$-0.638143\pi$
$311$		−	32.0007i		−	1.81459i	0.420494	−	0.907296i	$-0.361857\pi$
$312$	3.94457	−	1.52338i	0.223317	−	0.0862447i
$313$	15.0164	−	8.66973i	0.848778	−	0.490042i	−0.0114606	−	0.999934i	$-0.503648\pi$
$313$	15.0164	−	8.66973i	0.848778	−	0.490042i	0.860238	+	0.509892i	$0.170315\pi$
$314$	−0.0269604	−	0.0466968i	−0.00152146	−	0.00263525i
$315$	−8.18241	+	4.09363i	−0.461027	+	0.230650i
$316$		−	7.43973i		−	0.418518i
$317$	−10.3578	+	5.98008i	−0.581753	+	0.335875i	−0.761830	−	0.647778i	$-0.775699\pi$
$317$	−10.3578	+	5.98008i	−0.581753	+	0.335875i	0.180077	+	0.983653i	$0.442365\pi$
$318$	−12.5889	−	1.96766i	−0.705948	−	0.110341i
$319$	−20.7838	+	11.9995i	−1.16367	+	0.671845i
$320$	1.56298	+	1.59909i	0.0873732	+	0.0893919i
$321$	−3.62224	+	23.1746i	−0.202173	+	1.29348i
$322$	8.57921			0.478101
$323$	12.5406	+	11.9230i	0.697777	+	0.663414i
$324$	−0.867960	+	8.95805i	−0.0482200	+	0.497669i
$325$	−10.7079	+	5.86033i	−0.593968	+	0.325072i
$326$	9.60147	−	16.6302i	0.531776	−	0.921064i
$327$	−2.68553	−	2.16568i	−0.148510	−	0.119762i
$328$	−3.63266	−	2.09732i	−0.200580	−	0.115805i
$329$	10.9357	−	6.31374i	0.602906	−	0.348088i
$330$	19.5392	−	1.86839i	1.07560	−	0.102851i
$331$		−	12.2936i		−	0.675718i	−0.941197	−	0.337859i	$-0.890297\pi$
$331$		−	12.2936i		−	0.675718i	0.941197	−	0.337859i	$-0.109703\pi$
$332$	5.08335	+	8.80462i	0.278985	+	0.483216i
$333$	−9.93202	−	3.18253i	−0.544271	−	0.174402i
$334$	−0.337320			−0.0184573
$335$	−6.64500	+	23.7129i	−0.363055	+	1.29558i
$336$	1.83890	+	1.48293i	0.100320	+	0.0809007i
$337$	−2.17542	+	3.76794i	−0.118503	+	0.205253i	−0.919175	−	0.393850i	$-0.871143\pi$
$337$	−2.17542	+	3.76794i	−0.118503	+	0.205253i	0.800672	+	0.599103i	$0.204476\pi$
$338$	−6.09672	+	3.51994i	−0.331618	+	0.191460i
$339$	−2.50228	+	16.0093i	−0.135905	+	0.869506i
$340$	6.20469	+	6.34805i	0.336497	+	0.344271i
$341$	−42.2030			−2.28542
$342$	−11.4725	+	6.27554i	−0.620360	+	0.339342i
$343$		−	16.5574i		−	0.894016i
$344$	4.66669	−	8.08295i	0.251611	−	0.435803i
$345$	−10.1174	+	22.1617i	−0.544700	+	1.19315i
$346$	−2.96537	−	5.13617i	−0.159419	−	0.276122i
$347$	−0.505034	+	0.874745i	−0.0271116	+	0.0469588i	−0.879263	−	0.476337i	$-0.841964\pi$
$347$	−0.505034	+	0.874745i	−0.0271116	+	0.0469588i	0.852151	+	0.523296i	$0.175298\pi$
$348$	5.14868	−	6.38457i	0.275998	−	0.342249i
$349$	20.0477			1.07313			0.536563	−	0.843860i	$-0.319722\pi$
$349$	20.0477			1.07313			0.536563	+	0.843860i	$0.319722\pi$
$350$	−5.82644	−	3.54373i	−0.311436	−	0.189420i
$351$	0.741138	+	12.6639i	0.0395590	+	0.675948i
$352$	−2.53401	−	4.38904i	−0.135063	−	0.233936i
$353$	9.12957			0.485918			0.242959	−	0.970037i	$-0.421882\pi$
$353$	9.12957			0.485918			0.242959	+	0.970037i	$0.421882\pi$
$354$	−0.952056	+	0.367682i	−0.0506012	+	0.0195421i
$355$	23.1862	−	5.92979i	1.23060	−	0.314720i
$356$	−3.62450	+	6.27782i	−0.192098	+	0.332724i
$357$	7.30004	+	5.88693i	0.386359	+	0.311569i
$358$	13.3937	+	7.73283i	0.707877	+	0.408693i
$359$	29.3938	+	16.9705i	1.55134	+	0.895668i	0.998033	+	0.0626932i	$0.0199689\pi$
$359$	29.3938	+	16.9705i	1.55134	+	0.895668i	0.553310	+	0.832975i	$0.313364\pi$
$360$	−5.99929	+	3.00142i	−0.316190	+	0.158189i
$361$	−16.9129	−	8.65764i	−0.890151	−	0.455665i
$362$	−15.0798			−0.792577
$363$	−25.1298	−	3.92783i	−1.31897	−	0.206158i
$364$	2.88363	+	1.66486i	0.151143	+	0.0872626i
$365$	4.19190	+	16.3908i	0.219414	+	0.857936i
$366$	1.90453	−	12.1850i	0.0995514	−	0.636918i
$367$	−6.59509	+	3.80768i	−0.344261	+	0.198759i	−0.662155	−	0.749367i	$-0.730358\pi$
$367$	−6.59509	+	3.80768i	−0.344261	+	0.198759i	0.317894	+	0.948126i	$0.397024\pi$
$368$	6.29022			0.327900
$369$	9.31737	−	8.45823i	0.485043	−	0.440318i
$370$	−1.92609	−	7.53126i	−0.100133	−	0.391532i
$371$	−5.01671	−	8.68919i	−0.260454	−	0.451120i
$372$	13.4548	−	5.19622i	0.697599	−	0.269411i
$373$	7.57854			0.392402			0.196201	−	0.980564i	$-0.437140\pi$
$373$	7.57854			0.392402			0.196201	+	0.980564i	$0.437140\pi$
$374$	−10.0595	−	17.4235i	−0.520163	−	0.900949i
$375$	16.0252	−	10.8717i	0.827536	−	0.561413i
$376$	8.01800	−	4.62919i	0.413497	−	0.238732i
$377$	5.78033	−	10.0118i	0.297702	−	0.515635i
$378$	−5.92003	+	3.89603i	−0.304493	+	0.200390i
$379$			6.21526i			0.319257i	0.987177	+	0.159628i	$0.0510296\pi$
$379$			6.21526i			0.319257i	−0.987177	+	0.159628i	$0.948970\pi$
$380$	−8.50751	−	4.75628i	−0.436426	−	0.243992i
$381$	7.68467	+	19.8983i	0.393697	+	1.01942i
$382$	−1.86492	+	3.23013i	−0.0954175	+	0.165268i
$383$	−2.47608	−	1.42957i	−0.126522	−	0.0730474i	0.435403	−	0.900235i	$-0.356606\pi$
$383$	−2.47608	−	1.42957i	−0.126522	−	0.0730474i	−0.561925	+	0.827188i	$0.689939\pi$
$384$	1.34827	+	1.08728i	0.0688036	+	0.0554849i
$385$	10.8037	+	11.0533i	0.550609	+	0.563330i
$386$	1.94688	−	1.12403i	0.0990934	−	0.0572116i
$387$	18.8202	+	20.7318i	0.956684	+	1.05386i
$388$	−10.8461			−0.550629
$389$	−6.17490	+	3.56508i	−0.313080	+	0.180757i	−0.648304	−	0.761382i	$-0.724521\pi$
$389$	−6.17490	+	3.56508i	−0.313080	+	0.180757i	0.335224	+	0.942138i	$0.391188\pi$
$390$	−7.70129	+	5.48561i	−0.389970	+	0.277774i
$391$	24.9708			1.26283
$392$		−	5.13978i		−	0.259598i
$393$	29.1093	+	23.4745i	1.46837	+	1.18413i
$394$	21.4067	+	12.3591i	1.07845	+	0.622645i
$395$	4.12187	+	16.1170i	0.207394	+	0.810935i
$396$	14.8589	−	3.22153i	0.746686	−	0.161888i
$397$	−17.6120	−	10.1683i	−0.883921	−	0.510332i	−0.0119721	−	0.999928i	$-0.503811\pi$
$397$	−17.6120	−	10.1683i	−0.883921	−	0.510332i	−0.871949	+	0.489596i	$0.837144\pi$
$398$			15.0939i			0.756588i
$399$	−9.51767	−	3.93017i	−0.476479	−	0.196755i
$400$	−4.27190	−	2.59824i	−0.213595	−	0.129912i
$401$	12.7015	−	21.9996i	0.634282	−	1.09861i	−0.352384	−	0.935855i	$-0.614629\pi$
$401$	12.7015	−	21.9996i	0.634282	−	1.09861i	0.986667	−	0.162754i	$-0.0520376\pi$
$402$	−2.94577	+	18.8467i	−0.146922	+	0.939988i
$403$	17.6061	−	10.1649i	0.877022	−	0.506349i
$404$	−12.4759	−	7.20295i	−0.620698	−	0.358360i
$405$	−3.08277	−	19.8871i	−0.153184	−	0.988198i
$406$	6.45858			0.320534
$407$			17.6189i			0.873337i
$408$	5.35234	+	4.31625i	0.264980	+	0.213686i
$409$	−31.6985	+	18.3011i	−1.56739	+	0.904933i	−0.570917	+	0.821008i	$0.693412\pi$
$409$	−31.6985	+	18.3011i	−1.56739	+	0.904933i	−0.996472	+	0.0839249i	$0.973254\pi$
$410$	9.03159	+	2.53089i	0.446038	+	0.124992i
$411$	−4.04610	−	10.4768i	−0.199580	−	0.516781i
$412$	0.697768	+	1.20857i	0.0343766	+	0.0595420i
$413$	−0.695989	−	0.401829i	−0.0342474	−	0.0197727i
$414$	−5.75835	+	17.9706i	−0.283008	+	0.883208i
$415$	−15.8903	−	16.2575i	−0.780026	−	0.798048i
$416$	2.11426	+	1.22067i	0.103660	+	0.0598481i
$417$	−0.731718	−	1.89467i	−0.0358324	−	0.0927824i
$418$	16.0099	+	15.2215i	0.783072	+	0.744508i
$419$			13.4366i			0.656421i	0.944605	+	0.328210i	$0.106446\pi$
$419$			13.4366i			0.656421i	−0.944605	+	0.328210i	$0.893554\pi$
$420$	−4.80529	−	2.19373i	−0.234474	−	0.107043i
$421$	−19.3285	−	11.1593i	−0.942012	−	0.543871i	−0.0514217	−	0.998677i	$-0.516375\pi$
$421$	−19.3285	−	11.1593i	−0.942012	−	0.543871i	−0.890591	+	0.454806i	$0.849709\pi$
$422$	−9.97262	−	17.2731i	−0.485459	−	0.840840i
$423$	5.88517	+	27.1445i	0.286147	+	1.31981i
$424$	−3.67821	−	6.37085i	−0.178630	−	0.309396i
$425$	−16.9585	−	10.3144i	−0.822610	−	0.500324i
$426$	17.2932	−	6.67858i	0.837857	−	0.323578i
$427$	8.41041	−	4.85575i	0.407008	−	0.234986i
$428$	−11.7280	+	6.77117i	−0.566895	+	0.327297i
$429$	19.9912	−	7.72055i	0.965184	−	0.372752i
$430$	−5.63142	+	20.0960i	−0.271571	+	0.969113i
$431$	11.3802	+	19.7111i	0.548166	+	0.949452i	0.998400	+	0.0565412i	$0.0180072\pi$
$431$	11.3802	+	19.7111i	0.548166	+	0.949452i	−0.450234	+	0.892911i	$0.648659\pi$
$432$	−4.34052	+	2.85655i	−0.208834	+	0.137436i
$433$	10.3152	+	17.8664i	0.495715	+	0.858603i	0.999988	−	0.00494124i	$-0.00157285\pi$
$433$	10.3152	+	17.8664i	0.495715	+	0.858603i	−0.504273	+	0.863544i	$0.668240\pi$
$434$	9.83597	+	5.67880i	0.472142	+	0.272591i
$435$	−7.61653	+	16.6837i	−0.365185	+	0.799924i
$436$		−	1.99183i		−	0.0953916i
$437$	−26.2966	+	7.76254i	−1.25794	+	0.371332i
$438$	4.72124	+	12.2249i	0.225590	+	0.584130i
$439$	−22.3956	−	12.9301i	−1.06889	−	0.617122i	−0.141009	−	0.990008i	$-0.545035\pi$
$439$	−22.3956	−	12.9301i	−1.06889	−	0.617122i	−0.927877	+	0.372887i	$0.878368\pi$
$440$	7.92122	+	8.10423i	0.377629	+	0.386354i
$441$	14.6839	+	4.70519i	0.699235	+	0.224057i
$442$	8.39315	+	4.84579i	0.399221	+	0.230491i
$443$	−12.9864	−	22.4931i	−0.617002	−	1.06868i	−0.990030	−	0.140859i	$-0.955014\pi$
$443$	−12.9864	−	22.4931i	−0.617002	−	1.06868i	0.373028	−	0.927820i	$-0.378320\pi$
$444$	−2.16931	−	5.61711i	−0.102951	−	0.266576i
$445$	4.37379	−	15.6080i	0.207337	−	0.739891i
$446$	−12.5308	+	7.23465i	−0.593350	+	0.342571i
$447$	22.6673	+	18.2795i	1.07213	+	0.864589i
$448$			1.36390i			0.0644381i
$449$	−7.37904			−0.348239			−0.174119	−	0.984725i	$-0.555708\pi$
$449$	−7.37904			−0.348239			−0.174119	+	0.984725i	$0.555708\pi$
$450$	11.3336	−	9.82592i	0.534273	−	0.463198i
$451$	−18.4104	−	10.6293i	−0.866913	−	0.500513i
$452$	−8.10184	+	4.67760i	−0.381079	+	0.220016i
$453$	0.129333	−	0.827458i	0.00607660	−	0.0388774i
$454$	−3.88740	+	6.73318i	−0.182445	+	0.316004i
$455$	−7.16933	−	2.00904i	−0.336103	−	0.0941851i
$456$	−6.97829	−	2.88158i	−0.326788	−	0.134942i
$457$		−	11.9340i		−	0.558248i	−0.960255	−	0.279124i	$-0.909956\pi$
$457$		−	11.9340i		−	0.558248i	0.960255	−	0.279124i	$-0.0900440\pi$
$458$	−10.5333	−	6.08142i	−0.492190	−	0.284166i
$459$	−17.2309	+	11.3399i	−0.804271	+	0.529300i
$460$	−13.6268	+	3.48500i	−0.635352	+	0.162489i
$461$	−4.47752	−	2.58510i	−0.208539	−	0.120400i	0.392093	−	0.919925i	$-0.371751\pi$
$461$	−4.47752	−	2.58510i	−0.208539	−	0.120400i	−0.600632	+	0.799526i	$0.705084\pi$
$462$	9.31959	+	7.51554i	0.433587	+	0.349655i
$463$		−	18.3128i		−	0.851068i	−0.904942	−	0.425534i	$-0.860086\pi$
$463$		−	18.3128i		−	0.851068i	0.904942	−	0.425534i	$-0.139914\pi$
$464$	4.73539			0.219835
$465$	−26.2689	+	18.7112i	−1.21819	+	0.867712i
$466$	−7.35928	+	4.24888i	−0.340912	+	0.196826i
$467$	−39.1850			−1.81327			−0.906633	−	0.421921i	$-0.861356\pi$
$467$	−39.1850			−1.81327			−0.906633	+	0.421921i	$0.861356\pi$
$468$	−5.42283	+	4.92280i	−0.250670	+	0.227556i
$469$	−13.0085	+	7.51047i	−0.600678	+	0.346801i
$470$	−14.8050	+	14.4707i	−0.682904	+	0.667482i
$471$	0.0726997	+	0.0586268i	0.00334983	+	0.00270138i
$472$	−0.510294	−	0.294619i	−0.0234882	−	0.0135609i
$473$	23.6509	−	40.9646i	1.08747	−	1.88355i
$474$	4.64237	+	12.0207i	0.213231	+	0.552129i
$475$	21.0653	+	5.59028i	0.966544	+	0.256500i
$476$			5.41438i			0.248168i
$477$	21.5682	−	4.67617i	0.987540	−	0.214107i
$478$	−0.160572	+	0.278118i	−0.00734437	+	0.0127208i
$479$	2.03089	−	1.17253i	0.0927936	−	0.0535744i	−0.452885	−	0.891569i	$-0.649605\pi$
$479$	2.03089	−	1.17253i	0.0927936	−	0.0535744i	0.545679	+	0.837994i	$0.316272\pi$
$480$	−3.52320	−	1.60843i	−0.160811	−	0.0734143i
$481$	−4.24363	−	7.35018i	−0.193493	−	0.335140i
$482$	−5.60506			−0.255303
$483$	−13.8618	+	5.35340i	−0.630734	+	0.243588i
$484$	−7.34243	−	12.7175i	−0.333747	−	0.578067i
$485$	23.4965	−	6.00914i	1.06692	−	0.272861i
$486$	−4.18739	−	15.0155i	−0.189944	−	0.681118i
$487$	−38.4769			−1.74355			−0.871777	−	0.489903i	$-0.837032\pi$
$487$	−38.4769			−1.74355			−0.871777	+	0.489903i	$0.837032\pi$
$488$	6.16645	−	3.56020i	0.279142	−	0.161163i
$489$	−5.13631	+	32.8615i	−0.232272	+	1.48605i
$490$	2.84762	+	11.1345i	0.128642	+	0.503007i
$491$	33.6488	+	19.4272i	1.51855	+	0.876735i	0.999762	+	0.0218329i	$0.00695017\pi$
$491$	33.6488	+	19.4272i	1.51855	+	0.876735i	0.518789	+	0.854903i	$0.326383\pi$
$492$	7.17818	+	1.12196i	0.323617	+	0.0505819i
$493$	18.7985			0.846640
$494$	−10.3452	−	2.49394i	−0.465451	−	0.112208i
$495$	−30.4045	+	15.2113i	−1.36658	+	0.683695i
$496$	7.21167	+	4.16366i	0.323813	+	0.186954i
$497$	12.6420	+	7.29884i	0.567069	+	0.327398i
$498$	−13.7074	−	11.0540i	−0.614245	−	0.495342i
$499$	1.77310	−	3.07110i	0.0793749	−	0.137481i	−0.823605	−	0.567163i	$-0.808041\pi$
$499$	1.77310	−	3.07110i	0.0793749	−	0.137481i	0.902980	+	0.429682i	$0.141374\pi$
$500$	10.6939	+	3.26189i	0.478247	+	0.145876i
$501$	0.545023	−	0.210487i	0.0243498	−	0.00940385i
$502$	−12.9565			−0.578277
$503$	−0.0260442	−	0.0451098i	−0.00116125	−	0.00201135i	0.865444	−	0.501005i	$-0.167036\pi$
$503$	−0.0260442	−	0.0451098i	−0.00116125	−	0.00201135i	−0.866605	+	0.498994i	$0.833703\pi$
$504$	−3.89654	−	1.24857i	−0.173566	−	0.0556159i
$505$	31.0177	+	8.69200i	1.38027	+	0.386789i
$506$	31.8790			1.41719
$507$	7.65430	−	9.49166i	0.339940	−	0.421539i
$508$	−6.15762	+	10.6653i	−0.273200	+	0.473196i
$509$	−5.84914	−	10.1310i	−0.259259	−	0.449049i	0.706785	−	0.707428i	$-0.250145\pi$
$509$	−5.84914	−	10.1310i	−0.259259	−	0.449049i	−0.966044	+	0.258379i	$0.916812\pi$
$510$	−13.9864	−	6.38511i	−0.619326	−	0.282737i
$511$	−5.15971	+	8.93688i	−0.228252	+	0.395344i
$512$			1.00000i			0.0441942i
$513$	14.6207	−	17.2984i	0.645518	−	0.763745i
$514$	11.0305			0.486533
$515$	−2.18120	−	2.23159i	−0.0961150	−	0.0983356i
$516$	−2.49645	+	15.9720i	−0.109900	+	0.703127i
$517$	40.6354	−	23.4609i	1.78714	−	1.03181i
$518$	2.37078	−	4.10632i	0.104166	−	0.180421i
$519$	7.99623	+	6.44836i	0.350996	+	0.283051i
$520$	−5.25650	−	1.47301i	−0.230513	−	0.0645959i
$521$	−3.72071			−0.163007			−0.0815037	−	0.996673i	$-0.525972\pi$
$521$	−3.72071			−0.163007			−0.0815037	+	0.996673i	$0.525972\pi$
$522$	−4.33499	+	13.5286i	−0.189737	+	0.592130i
$523$	−4.81021	−	8.33153i	−0.210336	−	0.364312i	0.741484	−	0.670971i	$-0.234122\pi$
$523$	−4.81021	−	8.33153i	−0.210336	−	0.364312i	−0.951820	+	0.306658i	$0.900789\pi$
$524$			21.5902i			0.943170i
$525$	11.6253	+	2.09008i	0.507370	+	0.0912184i
$526$	−6.04100	+	3.48778i	−0.263400	+	0.152074i
$527$	28.6288	+	16.5288i	1.24709	+	0.720007i
$528$	6.83306	+	5.51035i	0.297371	+	0.239807i
$529$	−8.28343	+	14.3473i	−0.360149	+	0.623797i
$530$	11.4980	+	11.7636i	0.499439	+	0.510978i
$531$	1.30885	−	1.18816i	0.0567991	−	0.0515617i
$532$	−1.68314	−	5.70185i	−0.0729732	−	0.247207i
$533$	10.2405			0.443566
$534$	1.93893	−	12.4050i	0.0839056	−	0.536818i
$535$	21.6554	−	21.1664i	0.936246	−	0.915103i
$536$	−9.53776	+	5.50663i	−0.411968	+	0.237850i
$537$	−26.4660	−	4.13668i	−1.14209	−	0.178511i
$538$	13.3587	−	7.71267i	0.575936	−	0.332517i
$539$		−	26.0486i		−	1.12199i
$540$	7.82044	−	8.59306i	0.336538	−	0.369786i
$541$	12.6273	+	21.8711i	0.542890	+	0.940313i	0.998736	+	0.0502546i	$0.0160033\pi$
$541$	12.6273	+	21.8711i	0.542890	+	0.940313i	−0.455846	+	0.890058i	$0.650663\pi$
$542$	18.7356	−	10.8170i	0.804763	−	0.464630i
$543$	24.3651	−	9.40975i	1.04561	−	0.403811i
$544$			3.96978i			0.170203i
$545$	1.10355	+	4.31500i	0.0472707	+	0.184834i
$546$	−5.69808	−	0.890619i	−0.243855	−	0.0381150i
$547$	18.7690	+	32.5089i	0.802505	+	1.38998i	0.917963	+	0.396667i	$0.129833\pi$
$547$	18.7690	+	32.5089i	0.802505	+	1.38998i	−0.115458	+	0.993312i	$0.536834\pi$
$548$	3.24209	−	5.61546i	0.138495	−	0.239881i
$549$	4.52614	+	20.8762i	0.193171	+	0.890975i
$550$	−21.6501	−	13.1679i	−0.923164	−	0.561482i
$551$	−19.7966	+	5.84377i	−0.843362	+	0.248953i
$552$	−10.1634	+	3.92508i	−0.432582	+	0.167062i
$553$	−5.07351	+	8.78758i	−0.215748	+	0.373686i
$554$	−10.7064	+	18.5440i	−0.454869	+	0.787857i
$555$	7.81155	+	10.9667i	0.331582	+	0.465511i
$556$	0.586315	−	1.01553i	0.0248653	−	0.0430680i
$557$	14.2223	+	24.6337i	0.602618	+	1.04377i	0.992423	+	0.122868i	$0.0392091\pi$
$557$	14.2223	+	24.6337i	0.602618	+	1.04377i	−0.389805	+	0.920897i	$0.627458\pi$
$558$	−18.4971	+	16.7915i	−0.783045	+	0.710841i
$559$			22.7859i			0.963742i
$560$	−0.755647	−	2.95467i	−0.0319319	−	0.124858i
$561$	27.1258	+	21.8749i	1.14525	+	0.923558i
$562$		−	15.8020i		−	0.666566i
$563$		−	41.2966i		−	1.74044i	−0.492661	−	0.870221i	$-0.663976\pi$
$563$		−	41.2966i		−	1.74044i	0.492661	−	0.870221i	$-0.336024\pi$
$564$	−10.0664	+	12.4828i	−0.423873	+	0.525620i
$565$	14.9598	−	14.6220i	0.629364	−	0.615152i
$566$	−2.93851	−	5.08966i	−0.123515	−	0.213934i
$567$	7.13414	−	9.98907i	0.299606	−	0.419502i
$568$	9.26899	+	5.35146i	0.388918	+	0.224542i
$569$	−35.3619			−1.48245			−0.741224	−	0.671258i	$-0.765754\pi$
$569$	−35.3619			−1.48245			−0.741224	+	0.671258i	$0.765754\pi$
$570$	16.7139	+	2.37627i	0.700067	+	0.0995310i
$571$	12.1212			0.507258			0.253629	−	0.967302i	$-0.418376\pi$
$571$	12.1212			0.507258			0.253629	+	0.967302i	$0.418376\pi$
$572$	10.7151	+	6.18637i	0.448021	+	0.258665i
$573$	0.997637	−	6.38277i	0.0416769	−	0.266644i
$574$	2.86053	+	4.95458i	0.119396	+	0.206800i
$575$	27.5895	−	15.0994i	1.15056	−	0.629689i
$576$	−2.85691	−	0.915446i	−0.119038	−	0.0381436i
$577$		−	13.3398i		−	0.555341i	−0.960676	−	0.277671i	$-0.910438\pi$
$577$		−	13.3398i		−	0.555341i	0.960676	−	0.277671i	$-0.0895624\pi$
$578$		−	1.24082i		−	0.0516111i
$579$	−2.44426	+	3.03099i	−0.101580	+	0.125964i
$580$	−10.2585	+	2.62357i	−0.425960	+	0.108938i
$581$		−	13.8663i		−	0.575272i
$582$	17.5246	−	6.76796i	0.726418	−	0.280541i
$583$	−18.6413	−	32.2876i	−0.772043	−	1.33722i
$584$	−3.78306	+	6.55246i	−0.156544	+	0.271143i
$585$	9.02031	−	13.6689i	0.372944	−	0.565140i
$586$	−4.75300	+	8.23244i	−0.196345	+	0.340079i
$587$	−13.4351	+	23.2703i	−0.554527	+	0.960470i	0.443413	+	0.896318i	$0.353768\pi$
$587$	−13.4351	+	23.2703i	−0.554527	+	0.960470i	−0.997940	+	0.0641521i	$0.979566\pi$
$588$	3.20721	+	8.30458i	0.132263	+	0.342475i
$589$	−35.2870	−	8.50676i	−1.45398	−	0.350515i
$590$	1.26870	+	0.355524i	0.0522316	+	0.0146367i
$591$	−42.2997	−	6.61152i	−1.73998	−	0.271962i
$592$	1.73824	−	3.01072i	0.0714413	−	0.123740i
$593$	12.3146	+	21.3295i	0.505700	+	0.875898i	0.999978	+	0.00659420i	$0.00209902\pi$
$593$	12.3146	+	21.3295i	0.505700	+	0.875898i	−0.494278	+	0.869304i	$0.664568\pi$
$594$	−21.9979	+	14.4770i	−0.902584	+	0.594000i
$595$	−2.99975	−	11.7294i	−0.122978	−	0.480859i
$596$			16.8121i			0.688652i
$597$	−9.41853	−	24.3878i	−0.385475	−	0.998128i
$598$	−13.2991	+	7.67827i	−0.543843	+	0.313988i
$599$	−8.57637	−	14.8547i	−0.350421	−	0.606947i	0.635902	−	0.771770i	$-0.280628\pi$
$599$	−8.57637	−	14.8547i	−0.350421	−	0.606947i	−0.986323	+	0.164822i	$0.947295\pi$
$600$	8.52359	+	1.53243i	0.347974	+	0.0625612i
$601$		−	14.8259i		−	0.604759i	−0.953188	−	0.302380i	$-0.902219\pi$
$601$		−	14.8259i		−	0.604759i	0.953188	−	0.302380i	$-0.0977810\pi$
$602$	−11.0243	+	6.36489i	−0.449317	+	0.259413i
$603$	−7.00066	−	32.2896i	−0.285089	−	1.31493i
$604$	0.418752	−	0.241767i	0.0170388	−	0.00983735i
$605$	22.9522	+	23.4824i	0.933138	+	0.954697i
$606$	24.6524	+	3.85322i	1.00144	+	0.156526i
$607$	−14.9609			−0.607242			−0.303621	−	0.952793i	$-0.598196\pi$
$607$	−14.9609			−0.607242			−0.303621	+	0.952793i	$0.598196\pi$
$608$	−1.23406	−	4.18056i	−0.0500479	−	0.169544i
$609$	−10.4354	+	4.03013i	−0.422864	+	0.163309i
$610$	−11.3862	+	11.1291i	−0.461013	+	0.450602i
$611$	−11.3014	+	19.5746i	−0.457206	+	0.791904i
$612$	−11.3413	−	3.63412i	−0.458446	−	0.146901i
$613$	−33.9142	−	19.5804i	−1.36978	−	0.790844i	−0.378883	−	0.925445i	$-0.623692\pi$
$613$	−33.9142	−	19.5804i	−1.36978	−	0.790844i	−0.990900	+	0.134600i	$0.957025\pi$
$614$	−10.9655	+	6.33092i	−0.442530	+	0.255495i
$615$	−16.1720	+	1.54641i	−0.652118	+	0.0623571i
$616$			6.91226i			0.278503i
$617$	−15.0341	−	26.0399i	−0.605252	−	1.04833i	−0.992012	−	0.126146i	$-0.959739\pi$
$617$	−15.0341	−	26.0399i	−0.605252	−	1.04833i	0.386760	−	0.922180i	$-0.373594\pi$
$618$	−1.88156	−	1.51733i	−0.0756874	−	0.0610362i
$619$	0.945014			0.0379833			0.0189917	−	0.999820i	$-0.493954\pi$
$619$	0.945014			0.0379833			0.0189917	+	0.999820i	$0.493954\pi$
$620$	−17.9298	−	5.02440i	−0.720076	−	0.201785i
$621$	−1.90958	−	32.6291i	−0.0766288	−	1.30936i
$622$	−16.0003	+	27.7134i	−0.641555	+	1.11121i
$623$	8.56230	−	4.94345i	0.343041	−	0.198055i
$624$	−4.17779	−	0.652996i	−0.167246	−	0.0261408i
$625$	−24.9739	−	1.14156i	−0.998957	−	0.0456625i
$626$	−17.3395			−0.693024
$627$	−35.3661	−	14.6039i	−1.41239	−	0.583223i
$628$			0.0539208i			0.00215167i
$629$	6.90045	−	11.9519i	0.275139	−	0.476554i
$630$	9.13299	+	0.546023i	0.363867	+	0.0217541i
$631$	12.8312	+	22.2244i	0.510804	+	0.884738i	0.999922	+	0.0125202i	$0.00398541\pi$
$631$	12.8312	+	22.2244i	0.510804	+	0.884738i	−0.489118	+	0.872218i	$0.662681\pi$
$632$	−3.71987	+	6.44300i	−0.147968	+	0.256289i
$633$	26.8915	+	21.6860i	1.06884	+	0.861941i
$634$	11.9602			0.474999
$635$	7.43056	−	26.5163i	0.294873	−	1.05227i
$636$	9.91844	+	7.99848i	0.393292	+	0.317160i
$637$	6.27397	+	10.8668i	0.248584	+	0.430560i
$638$	23.9991			0.950132
$639$	−23.7739	+	21.5818i	−0.940481	+	0.853761i
$640$	−0.554035	−	2.16634i	−0.0219002	−	0.0856323i
$641$	9.01119	−	15.6078i	0.355921	−	0.616473i	−0.631354	−	0.775494i	$-0.717501\pi$
$641$	9.01119	−	15.6078i	0.355921	−	0.616473i	0.987275	+	0.159022i	$0.0508340\pi$
$642$	14.7243	−	18.2587i	0.581120	−	0.720614i
$643$	28.9629	+	16.7217i	1.14218	+	0.659440i	0.946970	−	0.321321i	$-0.104127\pi$
$643$	28.9629	+	16.7217i	1.14218	+	0.659440i	0.195213	+	0.980761i	$0.437460\pi$
$644$	−7.42982	−	4.28961i	−0.292776	−	0.169034i
$645$	−3.44087	−	35.9839i	−0.135484	−	1.41686i
$646$	−4.89897	−	16.5959i	−0.192747	−	0.652958i
$647$	42.8741			1.68556			0.842778	−	0.538261i	$-0.180919\pi$
$647$	42.8741			1.68556			0.842778	+	0.538261i	$0.180919\pi$
$648$	5.23070	−	7.32392i	0.205481	−	0.287711i
$649$	−2.58618	−	1.49313i	−0.101517	−	0.0586106i
$650$	12.2035	+	0.278766i	0.478660	+	0.0109341i
$651$	−19.4360	−	3.03787i	−0.761755	−	0.119064i
$652$	−16.6302	+	9.60147i	−0.651290	+	0.376023i
$653$	−6.55476			−0.256507			−0.128254	−	0.991741i	$-0.540937\pi$
$653$	−6.55476			−0.256507			−0.128254	+	0.991741i	$0.540937\pi$
$654$	1.24290	+	3.21829i	0.0486012	+	0.125845i
$655$	−11.9617	−	46.7717i	−0.467382	−	1.82752i
$656$	2.09732	+	3.63266i	0.0818866	+	0.141832i
$657$	−15.2566	−	16.8063i	−0.595218	−	0.655677i
$658$	−12.6275			−0.492271
$659$	7.36677	+	12.7596i	0.286969	+	0.497044i	0.973085	−	0.230448i	$-0.0740192\pi$
$659$	7.36677	+	12.7596i	0.286969	+	0.497044i	−0.686116	+	0.727492i	$0.740686\pi$
$660$	−17.8557	−	8.15155i	−0.695031	−	0.317299i
$661$	−16.7448	+	9.66762i	−0.651297	+	0.376027i	−0.788953	−	0.614453i	$-0.789377\pi$
$661$	−16.7448	+	9.66762i	−0.651297	+	0.376027i	0.137656	+	0.990480i	$0.456043\pi$
$662$	−6.14681	+	10.6466i	−0.238902	+	0.413791i
$663$	−16.5849	−	2.59225i	−0.644105	−	0.100675i
$664$		−	10.1667i		−	0.394544i
$665$	6.80528	+	11.4197i	0.263897	+	0.442835i
$666$	7.01011	+	7.72216i	0.271636	+	0.299228i
$667$	−14.8933	+	25.7960i	−0.576671	+	0.998824i
$668$	0.292128	+	0.168660i	0.0113028	+	0.00652566i
$669$	15.7321	−	19.5085i	0.608239	−	0.754242i
$670$	17.6112	−	17.2135i	0.680380	−	0.665015i
$671$	31.2517	−	18.0432i	1.20646	−	0.696550i
$672$	−0.851067	−	2.20371i	−0.0328306	−	0.0850099i
$673$	21.1715			0.816100			0.408050	−	0.912960i	$-0.366209\pi$
$673$	21.1715			0.816100			0.408050	+	0.912960i	$0.366209\pi$
$674$	3.76794	−	2.17542i	0.145136	−	0.0837941i
$675$	−12.1809	+	22.9483i	−0.468843	+	0.883281i
$676$	7.03988			0.270765
$677$			8.33346i			0.320281i	0.987094	+	0.160140i	$0.0511947\pi$
$677$			8.33346i			0.320281i	−0.987094	+	0.160140i	$0.948805\pi$
$678$	10.1717	−	12.6133i	0.390641	−	0.484412i
$679$	12.8111	+	7.39651i	0.491646	+	0.283852i
$680$	−2.19940	−	8.59992i	−0.0843431	−	0.329792i
$681$	2.07957	−	13.3048i	0.0796892	−	0.509842i
$682$	36.5489	+	21.1015i	1.39953	+	0.808019i
$683$		−	1.85318i		−	0.0709099i	−0.999371	−	0.0354550i	$-0.988712\pi$
$683$		−	1.85318i		−	0.0709099i	0.999371	−	0.0354550i	$-0.0112880\pi$
$684$	13.0732	+	0.301460i	0.499867	+	0.0115266i
$685$	−3.91231	+	13.9612i	−0.149482	+	0.533432i
$686$	−8.27871	+	14.3391i	−0.316083	+	0.547471i
$687$	20.8140	+	3.25326i	0.794102	+	0.124119i
$688$	−8.08295	+	4.66669i	−0.308159	+	0.177916i
$689$	15.5534	+	8.97975i	0.592537	+	0.342101i
$690$	19.8428	−	14.1339i	0.755401	−	0.538070i
$691$	2.74537			0.104439			0.0522195	−	0.998636i	$-0.483370\pi$
$691$	2.74537			0.104439			0.0522195	+	0.998636i	$0.483370\pi$
$692$			5.93074i			0.225453i
$693$	−19.7477	−	6.32780i	−0.750155	−	0.240373i
$694$	0.874745	−	0.505034i	0.0332049	−	0.0191708i
$695$	−0.707523	+	2.52482i	−0.0268379	+	0.0957720i
$696$	−7.65117	+	2.95487i	−0.290017	+	0.112004i
$697$	8.32591	+	14.4209i	0.315366	+	0.546230i
$698$	−17.3618	−	10.0238i	−0.657153	−	0.379408i
$699$	9.23943	−	11.4573i	0.349467	−	0.433354i
$700$	3.27398	+	5.98218i	0.123745	+	0.226105i
$701$	15.0883	+	8.71122i	0.569876	+	0.329018i	0.757100	−	0.653299i	$-0.226616\pi$
$701$	15.0883	+	8.71122i	0.569876	+	0.329018i	−0.187224	+	0.982317i	$0.559949\pi$
$702$	5.69010	−	11.3378i	0.214759	−	0.427918i
$703$	−3.55140	+	14.7316i	−0.133944	+	0.555613i
$704$			5.06802i			0.191008i
$705$	14.8914	−	32.6192i	0.560844	−	1.22851i
$706$	−7.90644	−	4.56479i	−0.297563	−	0.171798i
$707$	9.82408	+	17.0158i	0.369473	+	0.639946i
$708$	1.00835	+	0.157606i	0.0378960	+	0.00592320i
$709$	15.1109	+	26.1728i	0.567501	+	0.982941i	0.996812	+	0.0797839i	$0.0254230\pi$
$709$	15.1109	+	26.1728i	0.567501	+	0.982941i	−0.429311	+	0.903157i	$0.641244\pi$
$710$	−23.0447	−	6.45775i	−0.864853	−	0.242355i
$711$	−15.0018	−	16.5255i	−0.562610	−	0.619756i
$712$	6.27782	−	3.62450i	0.235271	−	0.135834i
$713$	−45.3630	+	26.1903i	−1.69886	+	0.980835i
$714$	−3.37855	−	8.74825i	−0.126439	−	0.327395i
$715$	−26.6401	−	7.46526i	−0.996282	−	0.279185i
$716$	−7.73283	−	13.3937i	−0.288990	−	0.500545i
$717$	0.0858978	−	0.549564i	0.00320791	−	0.0205238i
$718$	−16.9705	−	29.3938i	−0.633333	−	1.09697i
$719$	8.06657	+	4.65724i	0.300832	+	0.173686i	0.642817	−	0.766020i	$-0.277766\pi$
$719$	8.06657	+	4.65724i	0.300832	+	0.173686i	−0.341984	+	0.939706i	$0.611099\pi$
$720$	6.69625	+	0.400340i	0.249554	+	0.0149198i
$721$		−	1.90337i		−	0.0708851i
$722$	10.3182	+	15.9542i	0.384002	+	0.593753i
$723$	9.05634	−	3.49754i	0.336809	−	0.130075i
$724$	13.0595	+	7.53991i	0.485353	+	0.280218i
$725$	20.7698	−	11.3671i	0.771372	−	0.422164i
$726$	19.7991	+	15.9665i	0.734815	+	0.592573i
$727$	−38.9254	−	22.4736i	−1.44366	−	0.833500i	−0.445572	−	0.895246i	$-0.647000\pi$
$727$	−38.9254	−	22.4736i	−1.44366	−	0.833500i	−0.998092	+	0.0617466i	$0.980333\pi$
$728$	−1.66486	−	2.88363i	−0.0617040	−	0.106874i
$729$	16.1354	+	21.6483i	0.597607	+	0.801789i
$730$	4.56513	−	16.2908i	0.168963	−	0.602951i
$731$	−32.0876	+	18.5258i	−1.18680	+	0.685200i
$732$	−7.74186	+	9.60023i	−0.286147	+	0.354835i
$733$			29.5925i			1.09302i	0.837452	+	0.546511i	$0.184044\pi$
$733$			29.5925i			1.09302i	−0.837452	+	0.546511i	$0.815956\pi$
$734$	7.61535			0.281088
$735$	−11.5489	−	16.2137i	−0.425989	−	0.598050i
$736$	−5.44749	−	3.14511i	−0.200797	−	0.115930i
$737$	−48.3376	+	27.9077i	−1.78054	+	1.02799i
$738$	−12.2982	+	2.66636i	−0.452703	+	0.0981499i
$739$	−20.5708	+	35.6297i	−0.756711	+	1.31066i	0.187809	+	0.982206i	$0.439862\pi$
$739$	−20.5708	+	35.6297i	−0.756711	+	1.31066i	−0.944519	+	0.328456i	$0.893472\pi$
$740$	−2.09758	+	7.48531i	−0.0771087	+	0.275165i
$741$	18.2714	−	2.42577i	0.671215	−	0.0891131i
$742$			10.0334i			0.368338i
$743$	−7.23600	−	4.17770i	−0.265463	−	0.153265i	0.361361	−	0.932426i	$-0.382312\pi$
$743$	−7.23600	−	4.17770i	−0.265463	−	0.153265i	−0.626824	+	0.779161i	$0.715646\pi$
$744$	−14.2503	−	2.22735i	−0.522442	−	0.0816585i
$745$	−9.31451	−	36.4209i	−0.341257	−	1.33436i
$746$	−6.56320	−	3.78927i	−0.240296	−	0.138735i
$747$	29.0454	+	9.30706i	1.06271	+	0.340527i
$748$			20.1190i			0.735622i
$749$	18.4704			0.674892
$750$	−19.3141	+	1.40260i	−0.705250	+	0.0512157i
$751$	36.1287	−	20.8589i	1.31835	−	0.761152i	0.334890	−	0.942257i	$-0.391301\pi$
$751$	36.1287	−	20.8589i	1.31835	−	0.761152i	0.983464	+	0.181105i	$0.0579674\pi$
$752$	−9.25839			−0.337619
$753$	20.9344	−	8.08481i	0.762892	−	0.294627i
$754$	−10.0118	+	5.78033i	−0.364609	+	0.210507i
$755$	−0.773214	+	0.755753i	−0.0281401	+	0.0275047i
$756$	7.07491	−	0.414051i	0.257312	−	0.0150589i
$757$	30.7033	+	17.7266i	1.11593	+	0.644283i	0.940359	−	0.340184i	$-0.110489\pi$
$757$	30.7033	+	17.7266i	1.11593	+	0.644283i	0.175571	+	0.984467i	$0.443823\pi$
$758$	3.10763	−	5.38258i	0.112874	−	0.195504i
$759$	−51.5083	+	19.8924i	−1.86963	+	0.722048i
$760$	4.98958	+	8.37282i	0.180991	+	0.303714i
$761$		−	5.16853i		−	0.187359i	−0.995602	−	0.0936795i	$-0.970137\pi$
$761$		−	5.16853i		−	0.187359i	0.995602	−	0.0936795i	$-0.0298629\pi$
$762$	3.29402	−	21.0747i	0.119330	−	0.763457i
$763$	−1.35833	+	2.35269i	−0.0491748	+	0.0851732i
$764$	3.23013	−	1.86492i	0.116862	−	0.0674703i
$765$	26.5827	+	1.58926i	0.961098	+	0.0574599i
$766$	1.42957	+	2.47608i	0.0516523	+	0.0894644i
$767$	1.43853			0.0519421
$768$	−0.623997	−	1.61574i	−0.0225165	−	0.0583031i
$769$	4.32494	+	7.49101i	0.155961	+	0.270133i	0.933409	−	0.358815i	$-0.116819\pi$
$769$	4.32494	+	7.49101i	0.155961	+	0.270133i	−0.777447	+	0.628948i	$0.783486\pi$
$770$	−3.82963	−	14.9743i	−0.138010	−	0.539638i
$771$	−17.8224	+	6.88298i	−0.641859	+	0.247884i
$772$	−2.24806			−0.0809094
$773$	−4.26585	+	2.46289i	−0.153432	+	0.0885840i	−0.574750	−	0.818329i	$-0.694901\pi$
$773$	−4.26585	+	2.46289i	−0.153432	+	0.0885840i	0.421318	+	0.906913i	$0.361568\pi$
$774$	−5.93284	−	27.3644i	−0.213252	−	0.983593i
$775$	41.6257	+	0.950863i	1.49524	+	0.0341560i
$776$	9.39303	+	5.42307i	0.337190	+	0.194677i
$777$	−1.26825	+	8.11412i	−0.0454982	+	0.291092i
$778$	7.13016			0.255629
$779$	−13.2509	−	12.5983i	−0.474763	−	0.451383i
$780$	9.41232	−	0.900029i	0.337015	−	0.0322262i
$781$	46.9755	+	27.1213i	1.68092	+	0.970477i
$782$	−21.6254	−	12.4854i	−0.773321	−	0.446477i
$783$	−1.43756	−	24.5638i	−0.0513744	−	0.877837i
$784$	−2.56989	+	4.45118i	−0.0917819	+	0.158971i
$785$	−0.0298740	−	0.116811i	−0.00106625	−	0.00416916i
$786$	−13.4722	−	34.8842i	−0.480537	−	1.24428i
$787$	29.6094			1.05546			0.527731	−	0.849412i	$-0.323043\pi$
$787$	29.6094			1.05546			0.527731	+	0.849412i	$0.323043\pi$
$788$	−12.3591	−	21.4067i	−0.440276	−	0.762581i
$789$	7.58436	−	9.40492i	0.270010	−	0.334824i
$790$	4.48886	−	16.0187i	0.159707	−	0.569919i
$791$	12.7595			0.453677
$792$	−14.4789	−	4.63950i	−0.514486	−	0.164857i
$793$	−8.69165	+	15.0544i	−0.308650	+	0.534597i
$794$	10.1683	+	17.6120i	0.360859	+	0.625027i
$795$	−25.9182	−	11.8323i	−0.919224	−	0.419648i
$796$	7.54694	−	13.0717i	0.267494	−	0.463313i
$797$		−	31.2636i		−	1.10741i	−0.832711	−	0.553707i	$-0.813213\pi$
$797$		−	31.2636i		−	1.10741i	0.832711	−	0.553707i	$-0.186787\pi$
$798$	6.27746	+	8.16246i	0.222220	+	0.288948i
$799$	−36.7538			−1.30026
$800$	2.40046	+	4.38609i	0.0848691	+	0.155072i
$801$	4.60789	+	21.2532i	0.162812	+	0.750946i
$802$	−21.9996	+	12.7015i	−0.776834	+	0.448505i
$803$	−19.1727	+	33.2080i	−0.676589	+	1.17189i
$804$	11.9745	−	14.8488i	0.422307	−	0.523678i
$805$	18.4721	+	5.17638i	0.651057	+	0.182444i
$806$	−20.3298			−0.716085
$807$	−16.7716	+	20.7975i	−0.590389	+	0.732107i
$808$	7.20295	+	12.4759i	0.253399	+	0.438900i
$809$		−	27.8772i		−	0.980109i	−0.871692	−	0.490054i	$-0.836977\pi$
$809$		−	27.8772i		−	0.980109i	0.871692	−	0.490054i	$-0.163023\pi$
$810$	−7.27379	+	18.7641i	−0.255575	+	0.659304i
$811$	−30.0551	+	17.3523i	−1.05538	+	0.609323i	−0.924150	−	0.382029i	$-0.875225\pi$
$811$	−30.0551	+	17.3523i	−1.05538	+	0.609323i	−0.131228	+	0.991352i	$0.541892\pi$
$812$	−5.59329	−	3.22929i	−0.196286	−	0.113326i
$813$	−23.5222	+	29.1685i	−0.824958	+	1.02298i
$814$	8.80945	−	15.2584i	0.308771	−	0.534807i
$815$	30.7073	−	30.0138i	1.07563	−	1.05134i
$816$	−2.47713	−	6.41415i	−0.0867170	−	0.224540i
$817$	28.0323	−	29.4843i	0.980724	−	1.03152i
$818$	36.6023			1.27977
$819$	9.76238	−	2.11657i	0.341125	−	0.0739589i
$820$	−6.55614	−	6.70761i	−0.228950	−	0.234240i
$821$	−2.32853	+	1.34438i	−0.0812662	+	0.0469191i	−0.540082	−	0.841612i	$-0.681607\pi$
$821$	−2.32853	+	1.34438i	−0.0812662	+	0.0469191i	0.458816	+	0.888531i	$0.348274\pi$
$822$	−1.73435	+	11.0962i	−0.0604925	+	0.387024i
$823$	−14.8455	+	8.57103i	−0.517480	+	0.298767i	−0.735903	−	0.677087i	$-0.763242\pi$
$823$	−14.8455	+	8.57103i	−0.517480	+	0.298767i	0.218423	+	0.975854i	$0.429909\pi$
$824$		−	1.39554i		−	0.0486158i
$825$	43.1978	+	7.76639i	1.50395	+	0.270391i
$826$	0.401829	+	0.695989i	0.0139814	+	0.0242166i
$827$	−15.2264	+	8.79097i	−0.529474	+	0.305692i	−0.740802	−	0.671723i	$-0.765554\pi$
$827$	−15.2264	+	8.79097i	−0.529474	+	0.305692i	0.211328	+	0.977415i	$0.432221\pi$
$828$	13.9722	−	12.6838i	0.485567	−	0.440794i
$829$			2.97562i			0.103347i	0.998664	+	0.0516737i	$0.0164556\pi$
$829$			2.97562i			0.103347i	−0.998664	+	0.0516737i	$0.983544\pi$
$830$	5.63270	+	22.0246i	0.195514	+	0.764484i
$831$	5.72736	−	36.6430i	0.198680	−	1.27113i
$832$	−1.22067	−	2.11426i	−0.0423190	−	0.0732987i
$833$	−10.2019	+	17.6702i	−0.353475	+	0.612238i
$834$	−0.313649	+	2.00669i	−0.0108608	+	0.0694861i
$835$	−0.726293	−	0.203527i	−0.0251344	−	0.00704333i
$836$	−6.25427	−	21.1872i	−0.216308	−	0.732774i
$837$	19.4087	−	38.6729i	0.670864	−	1.33673i
$838$	6.71830	−	11.6364i	0.232080	−	0.401974i
$839$	24.5444	−	42.5122i	0.847368	−	1.46768i	−0.0361815	−	0.999345i	$-0.511519\pi$
$839$	24.5444	−	42.5122i	0.847368	−	1.46768i	0.883549	−	0.468339i	$-0.155147\pi$
$840$	3.06464	+	4.30247i	0.105740	+	0.148449i
$841$	3.28806	−	5.69508i	0.113381	−	0.196382i
$842$	11.1593	+	19.3285i	0.384575	+	0.666103i
$843$	9.86038	+	25.5319i	0.339610	+	0.879367i
$844$			19.9452i			0.686543i
$845$	−15.2508	+	3.90034i	−0.524644	+	0.134176i
$846$	8.47555	−	26.4504i	0.291395	−	0.909384i
$847$			20.0286i			0.688192i
$848$			7.35643i			0.252621i
$849$	7.92382	+	6.38996i	0.271945	+	0.219303i
$850$	9.52931	+	17.4118i	0.326853	+	0.597221i
$851$	10.9339	+	18.9381i	0.374810	+	0.649190i
$852$	−18.3156	−	2.86276i	−0.627483	−	0.0980766i
$853$	23.1920	+	13.3899i	0.794081	+	0.458463i	0.841397	−	0.540417i	$-0.181734\pi$
$853$	23.1920	+	13.3899i	0.794081	+	0.458463i	−0.0473166	+	0.998880i	$0.515067\pi$
$854$	−9.71150			−0.332321
$855$	−28.4881	+	6.58995i	−0.974273	+	0.225372i
$856$	13.5423			0.462867
$857$	−22.0122	−	12.7088i	−0.751923	−	0.434123i	0.0744651	−	0.997224i	$-0.476275\pi$
$857$	−22.0122	−	12.7088i	−0.751923	−	0.434123i	−0.826388	+	0.563100i	$0.809608\pi$
$858$	−21.1731	−	3.30940i	−0.722839	−	0.112981i
$859$	−8.80496	−	15.2506i	−0.300421	−	0.520345i	0.675810	−	0.737076i	$-0.263794\pi$
$859$	−8.80496	−	15.2506i	−0.300421	−	0.520345i	−0.976231	+	0.216731i	$0.930461\pi$
$860$	14.9249	−	14.5879i	0.508936	−	0.497443i
$861$	−7.71352	−	6.22037i	−0.262876	−	0.211990i
$862$		−	22.7605i		−	0.775224i
$863$			39.1623i			1.33310i	0.745460	+	0.666551i	$0.232230\pi$
$863$			39.1623i			1.33310i	−0.745460	+	0.666551i	$0.767770\pi$
$864$	5.18728	−	0.303579i	0.176475	−	0.0103280i
$865$	−3.28584	−	12.8480i	−0.111722	−	0.436846i
$866$		−	20.6303i		−	0.701046i
$867$	0.774265	+	2.00484i	0.0262954	+	0.0680879i
$868$	−5.67880	−	9.83597i	−0.192751	−	0.333855i
$869$	−18.8524	+	32.6533i	−0.639523	+	1.10769i
$870$	14.9380	−	10.6403i	0.506445	−	0.360739i
$871$	13.4435	−	23.2849i	0.455516	−	0.788977i
$872$	−0.995917	+	1.72498i	−0.0337260	+	0.0584152i
$873$	−24.0921	+	21.8706i	−0.815393	+	0.740207i
$874$	26.6548	+	6.42577i	0.901613	+	0.217355i
$875$	−10.4069	−	11.1456i	−0.351817	−	0.376788i
$876$	2.02375	−	12.9477i	0.0683762	−	0.437463i
$877$	−19.2084	+	33.2699i	−0.648621	+	1.12344i	0.334832	+	0.942278i	$0.391320\pi$
$877$	−19.2084	+	33.2699i	−0.648621	+	1.12344i	−0.983453	+	0.181166i	$0.942013\pi$
$878$	12.9301	+	22.3956i	0.436371	+	0.755817i
$879$	2.54262	−	16.2674i	0.0857604	−	0.548685i
$880$	−2.80786	−	10.9791i	−0.0946530	−	0.370105i
$881$		−	54.5643i		−	1.83832i	−0.393888	−	0.919158i	$-0.628870\pi$
$881$		−	54.5643i		−	1.83832i	0.393888	−	0.919158i	$-0.371130\pi$
$882$	−10.3641	−	11.4168i	−0.348976	−	0.384423i
$883$	−39.3518	+	22.7198i	−1.32429	+	0.764581i	−0.984411	−	0.175886i	$-0.943721\pi$
$883$	−39.3518	+	22.7198i	−1.32429	+	0.764581i	−0.339883	+	0.940468i	$0.610388\pi$
$884$	−4.84579	−	8.39315i	−0.162981	−	0.282292i
$885$	−2.27174	+	0.217230i	−0.0763638	+	0.00730209i
$886$			25.9728i			0.872573i
$887$	39.5339	−	22.8249i	1.32742	−	0.766385i	0.342518	−	0.939511i	$-0.388720\pi$
$887$	39.5339	−	22.8249i	1.32742	−	0.766385i	0.984900	+	0.173126i	$0.0553868\pi$
$888$	−0.929872	+	5.94921i	−0.0312045	+	0.199643i
$889$	14.5464	−	8.39836i	0.487870	−	0.281672i
$890$	−11.5918	+	11.3301i	−0.388559	+	0.379784i
$891$	26.5093	−	37.1178i	0.888095	−	1.24349i
$892$	14.4693			0.484468
$893$	38.7052	−	11.4254i	1.29522	−	0.382338i
$894$	−10.4907	−	27.1641i	−0.350862	−	0.908504i
$895$	24.1725	+	24.7310i	0.807999	+	0.826667i
$896$	0.681949	−	1.18117i	0.0227823	−	0.0394601i
$897$	16.6968	−	20.7047i	0.557490	−	0.691311i
$898$	6.39044	+	3.68952i	0.213252	+	0.123121i
$899$	−34.1500	+	19.7165i	−1.13897	+	0.657583i
$900$	−14.7282	+	2.84268i	−0.490939	+	0.0947560i
$901$			29.2034i			0.972907i
$902$	10.6293	+	18.4104i	0.353916	+	0.613000i
$903$	13.8408	−	17.1632i	0.460593	−	0.571154i
$904$	9.35520			0.311149
$905$	−32.4687	−	9.09861i	−1.07930	−	0.302448i
$906$	−0.525735	+	0.651933i	−0.0174664	+	0.0216590i
$907$	−19.2054	+	33.2647i	−0.637704	+	1.10454i	0.348232	+	0.937409i	$0.386782\pi$
$907$	−19.2054	+	33.2647i	−0.637704	+	1.10454i	−0.985935	+	0.167127i	$0.946551\pi$
$908$	6.73318	−	3.88740i	0.223448	−	0.129008i
$909$	−42.2364	+	9.15723i	−1.40089	+	0.303726i
$910$	5.20430	+	5.32454i	0.172521	+	0.176507i
$911$	14.7901			0.490018			0.245009	−	0.969521i	$-0.421209\pi$
$911$	14.7901			0.490018			0.245009	+	0.969521i	$0.421209\pi$
$912$	4.60259	+	5.98466i	0.152407	+	0.198172i
$913$		−	51.5251i		−	1.70523i
$914$	−5.96698	+	10.3351i	−0.197370	+	0.341855i
$915$	11.4527	−	25.0866i	0.378613	−	0.829339i
$916$	6.08142	+	10.5333i	0.200936	+	0.348031i
$917$	14.7234	−	25.5016i	0.486209	−	0.842138i
$918$	20.5924	−	1.20514i	0.679649	−	0.0397757i
$919$	7.45175			0.245810			0.122905	−	0.992418i	$-0.460779\pi$
$919$	7.45175			0.245810			0.122905	+	0.992418i	$0.460779\pi$
$920$	13.5436	+	3.79529i	0.446520	+	0.125127i
$921$	13.7669	−	17.0716i	0.453636	−	0.562527i
$922$	2.58510	+	4.47752i	0.0851356	+	0.147459i
$923$	−26.1294			−0.860060
$924$	−4.31323	−	11.1684i	−0.141895	−	0.367415i
$925$	0.396966	−	17.3779i	0.0130522	−	0.571381i
$926$	−9.15640	+	15.8594i	−0.300898	+	0.521171i
$927$	3.98693	+	1.27754i	0.130948	+	0.0419599i
$928$	−4.10097	−	2.36769i	−0.134621	−	0.0777233i
$929$	−1.58213	−	0.913443i	−0.0519080	−	0.0299691i	0.473821	−	0.880621i	$-0.342874\pi$
$929$	−1.58213	−	0.913443i	−0.0519080	−	0.0299691i	−0.525729	+	0.850652i	$0.676208\pi$
$930$	32.1051	−	3.06997i	1.05277	−	0.100668i
$931$	5.25054	−	21.7799i	0.172080	−	0.713806i
$932$	8.49777			0.278354
$933$	8.55938	−	54.7619i	0.280221	−	1.79282i
$934$	33.9352	+	19.5925i	1.11039	+	0.641086i
$935$	−11.1466	−	43.5846i	−0.364533	−	1.42537i
$936$	7.15771	−	1.55185i	0.233957	−	0.0507239i
$937$	−38.2667	+	22.0933i	−1.25012	+	0.721757i	−0.971133	−	0.238538i	$-0.923332\pi$
$937$	−38.2667	+	22.0933i	−1.25012	+	0.721757i	−0.278987	+	0.960295i	$0.589998\pi$
$938$	15.0209			0.490451
$939$	28.0161	−	10.8198i	0.914271	−	0.353090i
$940$	20.0568	−	5.12947i	0.654182	−	0.167305i
$941$	18.8424	+	32.6360i	0.614244	+	1.06390i	0.990517	+	0.137393i	$0.0438722\pi$
$941$	18.8424	+	32.6360i	0.614244	+	1.06390i	−0.376273	+	0.926509i	$0.622794\pi$
$942$	−0.0336464	−	0.0871222i	−0.00109626	−	0.00283859i
$943$	−26.3852			−0.859221
$944$	0.294619	+	0.510294i	0.00958902	+	0.0166087i
$945$	−15.0973	+	4.81672i	−0.491115	+	0.156688i
$946$	−40.9646	+	23.6509i	−1.33187	+	0.768957i
$947$	22.8674	−	39.6075i	0.743091	−	1.28707i	−0.207990	−	0.978131i	$-0.566692\pi$
$947$	22.8674	−	39.6075i	0.743091	−	1.28707i	0.951081	−	0.308941i	$-0.0999745\pi$
$948$	1.98994	−	12.7314i	0.0646303	−	0.413497i
$949$		−	18.4715i		−	0.599609i
$950$	−15.4480	−	15.3740i	−0.501199	−	0.498798i
$951$	−19.3246	+	7.46311i	−0.626642	+	0.242008i
$952$	2.70719	−	4.68899i	0.0877405	−	0.151971i
$953$	13.1451	+	7.58934i	0.425812	+	0.245843i	0.697561	−	0.716525i	$-0.254269\pi$
$953$	13.1451	+	7.58934i	0.425812	+	0.245843i	−0.271749	+	0.962368i	$0.587602\pi$
$954$	−21.0167	−	6.73441i	−0.680440	−	0.218035i
$955$	−5.96435	+	5.82966i	−0.193002	+	0.188643i
$956$	0.278118	−	0.160572i	0.00899498	−	0.00519326i
$957$	−38.7763	+	14.9753i	−1.25346	+	0.484084i
$958$	−2.34507			−0.0757656
$959$	−7.65891	+	4.42187i	−0.247319	+	0.142790i
$960$	2.24697	+	3.15454i	0.0725206	+	0.101812i
$961$	−38.3442			−1.23691
$962$			8.48726i			0.273640i
$963$	−12.3973	+	38.6893i	−0.399497	+	1.24674i
$964$	4.85412	+	2.80253i	0.156341	+	0.0902634i
$965$	4.87007	−	1.24550i	0.156773	−	0.0400942i
$966$	14.6814	+	2.29472i	0.472366	+	0.0738315i
$967$	−26.7384	−	15.4374i	−0.859849	−	0.496434i	0.00411251	−	0.999992i	$-0.498691\pi$
$967$	−26.7384	−	15.4374i	−0.859849	−	0.496434i	−0.863962	+	0.503557i	$0.832024\pi$
$968$			14.6849i			0.471989i
$969$	18.2713	+	23.7578i	0.586958	+	0.763211i
$970$	−23.3531	−	6.54417i	−0.749823	−	0.210121i
$971$	16.3109	−	28.2513i	0.523442	−	0.906628i	−0.476186	−	0.879345i	$-0.657981\pi$
$971$	16.3109	−	28.2513i	0.523442	−	0.906628i	0.999628	−	0.0272836i	$-0.00868571\pi$
$972$	−3.88137	+	15.0975i	−0.124495	+	0.484253i
$973$	−1.38508	+	0.799674i	−0.0444035	+	0.0256364i
$974$	33.3220	+	19.2384i	1.06770	+	0.616439i
$975$	−19.8917	+	7.16452i	−0.637043	+	0.229448i
$976$	−7.12041			−0.227919
$977$			31.6549i			1.01273i	0.862319	+	0.506366i	$0.169011\pi$
$977$			31.6549i			1.01273i	−0.862319	+	0.506366i	$0.830989\pi$
$978$	20.8789	−	25.8907i	0.667634	−	0.827894i
$979$	31.8162	−	18.3691i	1.01685	−	0.587078i
$980$	3.10116	−	11.0666i	0.0990629	−	0.353510i
$981$	−4.01641	−	4.42437i	−0.128234	−	0.141259i
$982$	−19.4272	−	33.6488i	−0.619946	−	1.07378i
$983$	−8.34970	−	4.82070i	−0.266314	−	0.153757i	0.360897	−	0.932606i	$-0.382470\pi$
$983$	−8.34970	−	4.82070i	−0.266314	−	0.153757i	−0.627211	+	0.778849i	$0.715804\pi$
$984$	−5.65550	−	4.56074i	−0.180291	−	0.145391i
$985$	38.6342	+	39.5268i	1.23099	+	1.25943i
$986$	−16.2799	−	9.39923i	−0.518459	−	0.299333i
$987$	20.4028	−	7.87951i	0.649428	−	0.250808i
$988$	7.71220	+	7.33240i	0.245358	+	0.233275i
$989$		−	58.7090i		−	1.86684i
$990$	33.9367	+	2.02893i	1.07858	+	0.0644837i
$991$	−0.799956	−	0.461855i	−0.0254114	−	0.0146713i	0.487240	−	0.873268i	$-0.338004\pi$
$991$	−0.799956	−	0.461855i	−0.0254114	−	0.0146713i	−0.512652	+	0.858597i	$0.671337\pi$
$992$	−4.16366	−	7.21167i	−0.132196	−	0.228971i
$993$	3.28823	−	21.0377i	0.104349	−	0.667612i
$994$	−7.29884	−	12.6420i	−0.231505	−	0.400978i
$995$	−9.10710	+	32.4990i	−0.288714	+	1.03029i
$996$	6.34399	+	16.4268i	0.201017	+	0.520502i
$997$	7.40601	−	4.27586i	0.234551	−	0.135418i	−0.378119	−	0.925757i	$-0.623429\pi$
$997$	7.40601	−	4.27586i	0.234551	−	0.135418i	0.612670	+	0.790339i	$0.290096\pi$
$998$	−3.07110	+	1.77310i	−0.0972140	+	0.0561265i
$999$	−16.1451	−	8.10275i	−0.510810	−	0.256360i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.n.a.179.19	yes	80
3.2	odd	2	inner	570.2.n.a.179.26	yes	80
5.4	even	2	inner	570.2.n.a.179.22	yes	80
15.14	odd	2	inner	570.2.n.a.179.15	✓	80
19.12	odd	6	inner	570.2.n.a.449.15	yes	80
57.50	even	6	inner	570.2.n.a.449.22	yes	80
95.69	odd	6	inner	570.2.n.a.449.26	yes	80
285.164	even	6	inner	570.2.n.a.449.19	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.n.a.179.15	✓	80	15.14	odd	2	inner
570.2.n.a.179.19	yes	80	1.1	even	1	trivial
570.2.n.a.179.22	yes	80	5.4	even	2	inner
570.2.n.a.179.26	yes	80	3.2	odd	2	inner
570.2.n.a.449.15	yes	80	19.12	odd	6	inner
570.2.n.a.449.19	yes	80	285.164	even	6	inner
570.2.n.a.449.22	yes	80	57.50	even	6	inner
570.2.n.a.449.26	yes	80	95.69	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.71127 + 0.267475i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.56298 - 1.59909i) q^{5} +(-1.34827 - 1.08728i) q^{6} -1.36390i q^{7} -1.00000i q^{8} +(2.85691 + 0.915446i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.71127 + 0.267475i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.56298 - 1.59909i) q^{5} +(-1.34827 - 1.08728i) q^{6} -1.36390i q^{7} -1.00000i q^{8} +(2.85691 + 0.915446i) q^{9} +(0.554035 + 2.16634i) q^{10} -5.06802i q^{11} +(0.623997 + 1.61574i) q^{12} +(1.22067 + 2.11426i) q^{13} +(-0.681949 + 1.18117i) q^{14} +(-2.24697 - 3.15454i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.98489 + 3.43793i) q^{17} +(-2.01644 - 2.22126i) q^{18} +(1.02155 - 4.23750i) q^{19} +(0.603364 - 2.15313i) q^{20} +(0.364808 - 2.33400i) q^{21} +(-2.53401 + 4.38904i) q^{22} +(-3.14511 - 5.44749i) q^{23} +(0.267475 - 1.71127i) q^{24} +(-0.114186 + 4.99870i) q^{25} -2.44133i q^{26} +(4.64410 + 2.33073i) q^{27} +(1.18117 - 0.681949i) q^{28} +(-2.36769 - 4.10097i) q^{29} +(0.368662 + 3.85540i) q^{30} -8.32731i q^{31} +(0.866025 - 0.500000i) q^{32} +(1.35557 - 8.67278i) q^{33} +(3.43793 - 1.98489i) q^{34} +(-2.18100 + 2.13174i) q^{35} +(0.635658 + 2.93188i) q^{36} -3.47648 q^{37} +(-3.00344 + 3.15901i) q^{38} +(1.52338 + 3.94457i) q^{39} +(-1.59909 + 1.56298i) q^{40} +(2.09732 - 3.63266i) q^{41} +(-1.48293 + 1.83890i) q^{42} +(8.08295 + 4.66669i) q^{43} +(4.38904 - 2.53401i) q^{44} +(-3.00142 - 5.99929i) q^{45} +6.29022i q^{46} +(4.62919 + 8.01800i) q^{47} +(-1.08728 + 1.34827i) q^{48} +5.13978 q^{49} +(2.59824 - 4.27190i) q^{50} +(-4.31625 + 5.35234i) q^{51} +(-1.22067 + 2.11426i) q^{52} +(6.37085 - 3.67821i) q^{53} +(-2.85655 - 4.34052i) q^{54} +(-8.10423 + 7.92122i) q^{55} -1.36390 q^{56} +(2.88158 - 6.97829i) q^{57} +4.73539i q^{58} +(0.294619 - 0.510294i) q^{59} +(1.60843 - 3.52320i) q^{60} +(3.56020 + 6.16645i) q^{61} +(-4.16366 + 7.21167i) q^{62} +(1.24857 - 3.89654i) q^{63} -1.00000 q^{64} +(1.47301 - 5.25650i) q^{65} +(-5.51035 + 6.83306i) q^{66} +(-5.50663 - 9.53776i) q^{67} -3.96978 q^{68} +(-3.92508 - 10.1634i) q^{69} +(2.95467 - 0.755647i) q^{70} +(-5.35146 + 9.26899i) q^{71} +(0.915446 - 2.85691i) q^{72} +(-6.55246 - 3.78306i) q^{73} +(3.01072 + 1.73824i) q^{74} +(-1.53243 + 8.52359i) q^{75} +(4.18056 - 1.23406i) q^{76} -6.91226 q^{77} +(0.652996 - 4.17779i) q^{78} +(-6.44300 - 3.71987i) q^{79} +(2.16634 - 0.554035i) q^{80} +(7.32392 + 5.23070i) q^{81} +(-3.63266 + 2.09732i) q^{82} +10.1667 q^{83} +(2.20371 - 0.851067i) q^{84} +(8.59992 - 2.19940i) q^{85} +(-4.66669 - 8.08295i) q^{86} +(-2.95487 - 7.65117i) q^{87} -5.06802 q^{88} +(3.62450 + 6.27782i) q^{89} +(-0.400340 + 6.69625i) q^{90} +(2.88363 - 1.66486i) q^{91} +(3.14511 - 5.44749i) q^{92} +(2.22735 - 14.2503i) q^{93} -9.25839i q^{94} +(-8.37282 + 4.98958i) q^{95} +(1.61574 - 0.623997i) q^{96} +(-5.42307 + 9.39303i) q^{97} +(-4.45118 - 2.56989i) q^{98} +(4.63950 - 14.4789i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 40 q^{4}+O(q^{10}) \) 80 * q + 40 * q^4	\( 80 q + 40 q^{4} + 30 q^{15} - 40 q^{16} + 8 q^{19} + 8 q^{25} - 4 q^{30} + 48 q^{39} + 12 q^{45} - 128 q^{49} - 36 q^{54} + 12 q^{55} + 30 q^{60} - 24 q^{61} - 80 q^{64} + 4 q^{66} + 36 q^{70} + 16 q^{76} + 24 q^{79} + 32 q^{81} - 8 q^{85} - 54 q^{90} + 24 q^{91} - 60 q^{99}+O(q^{100}) \) 80 * q + 40 * q^4 + 30 * q^15 - 40 * q^16 + 8 * q^19 + 8 * q^25 - 4 * q^30 + 48 * q^39 + 12 * q^45 - 128 * q^49 - 36 * q^54 + 12 * q^55 + 30 * q^60 - 24 * q^61 - 80 * q^64 + 4 * q^66 + 36 * q^70 + 16 * q^76 + 24 * q^79 + 32 * q^81 - 8 * q^85 - 54 * q^90 + 24 * q^91 - 60 * q^99

Introduction

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