LMFDB - Embedded newform 570.2.n.a.179.15

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			179.15
Character	$\chi$	$=$	570.179
Dual form			570.2.n.a.449.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(1.08728 + 1.34827i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.16634 + 0.554035i) q^{5} +(-0.267475 - 1.71127i) q^{6} +1.36390i q^{7} -1.00000i q^{8} +(-0.635658 + 2.93188i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(1.08728 + 1.34827i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.16634 + 0.554035i) q^{5} +(-0.267475 - 1.71127i) q^{6} +1.36390i q^{7} -1.00000i q^{8} +(-0.635658 + 2.93188i) q^{9} +(-1.59909 - 1.56298i) q^{10} +5.06802i q^{11} +(-0.623997 + 1.61574i) q^{12} +(-1.22067 - 2.11426i) q^{13} +(0.681949 - 1.18117i) q^{14} +(1.60843 + 3.52320i) 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} +(-1.83890 + 1.48293i) q^{21} +(2.53401 - 4.38904i) q^{22} +(-3.14511 - 5.44749i) q^{23} +(1.34827 - 1.08728i) q^{24} +(4.38609 + 2.40046i) 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} +(-6.83306 + 5.51035i) q^{33} +(3.43793 - 1.98489i) q^{34} +(-0.755647 + 2.95467i) q^{35} +(-2.85691 + 0.915446i) q^{36} +3.47648 q^{37} +(-3.00344 + 3.15901i) q^{38} +(1.52338 - 3.94457i) q^{39} +(0.554035 - 2.16634i) q^{40} +(-2.09732 + 3.63266i) q^{41} +(2.33400 - 0.364808i) 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} +(-1.71127 + 0.267475i) q^{48} +5.13978 q^{49} +(-2.59824 - 4.27190i) q^{50} +(-6.79339 + 1.06182i) q^{51} +(1.22067 - 2.11426i) q^{52} +(6.37085 - 3.67821i) q^{53} +(5.18728 + 0.303579i) q^{54} +(-2.80786 + 10.9791i) q^{55} +1.36390 q^{56} +(6.82400 - 3.23002i) q^{57} -4.73539i q^{58} +(-0.294619 + 0.510294i) q^{59} +(-2.24697 + 3.15454i) q^{60} +(3.56020 + 6.16645i) q^{61} +(-4.16366 + 7.21167i) q^{62} +(-3.99879 - 0.866972i) q^{63} -1.00000 q^{64} +(-1.47301 - 5.25650i) q^{65} +(8.67278 - 1.35557i) q^{66} +(5.50663 + 9.53776i) q^{67} -3.96978 q^{68} +(3.92508 - 10.1634i) q^{69} +(2.13174 - 2.18100i) q^{70} +(5.35146 - 9.26899i) q^{71} +(2.93188 + 0.635658i) 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} +(-3.29158 + 2.65441i) q^{78} +(-6.44300 - 3.71987i) q^{79} +(-1.56298 + 1.59909i) q^{80} +(-8.19188 - 3.72735i) q^{81} +(3.63266 - 2.09732i) q^{82} +10.1667 q^{83} +(-2.20371 - 0.851067i) q^{84} +(-6.20469 + 6.34805i) q^{85} +(4.66669 + 8.08295i) q^{86} +(-2.95487 + 7.65117i) q^{87} +5.06802 q^{88} +(-3.62450 - 6.27782i) q^{89} +(5.59895 - 3.69483i) q^{90} +(2.88363 - 1.66486i) q^{91} +(3.14511 - 5.44749i) q^{92} +(11.2275 - 9.05410i) q^{93} -9.25839i q^{94} +(4.56075 - 8.61392i) q^{95} +(1.61574 + 0.623997i) q^{96} +(5.42307 - 9.39303i) q^{97} +(-4.45118 - 2.56989i) q^{98} +(-14.8589 - 3.22153i) 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
$3$	1.08728	+	1.34827i	0.627740	+	0.778423i
$3$	1.08728	+	1.34827i	0.627740	+	0.778423i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	2.16634	+	0.554035i	0.968818	+	0.247772i
$5$	2.16634	+	0.554035i	0.968818	+	0.247772i
$6$	−0.267475	−	1.71127i	−0.109196	−	0.698624i
$7$			1.36390i			0.515505i	0.966211	+	0.257752i	$0.0829819\pi$
$7$			1.36390i			0.515505i	−0.966211	+	0.257752i	$0.917018\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.635658	+	2.93188i	−0.211886	+	0.977294i
$10$	−1.59909	−	1.56298i	−0.505677	−	0.494258i
$11$			5.06802i			1.52807i	0.645177	+	0.764033i	$0.276784\pi$
$11$			5.06802i			1.52807i	−0.645177	+	0.764033i	$0.723216\pi$
$12$	−0.623997	+	1.61574i	−0.180132	+	0.466425i
$13$	−1.22067	−	2.11426i	−0.338552	−	0.586390i	0.645608	−	0.763669i	$-0.276604\pi$
$13$	−1.22067	−	2.11426i	−0.338552	−	0.586390i	−0.984161	+	0.177279i	$0.943271\pi$
$14$	0.681949	−	1.18117i	0.182258	−	0.315681i
$15$	1.60843	+	3.52320i	0.415294	+	0.909687i
$16$	−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
$21$	−1.83890	+	1.48293i	−0.401281	+	0.323603i
$22$	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	$-0.394336\pi$
$24$	1.34827	−	1.08728i	0.275214	−	0.221939i
$25$	4.38609	+	2.40046i	0.877218	+	0.480092i
$26$			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	0.997664	−	0.0683147i	$-0.0217622\pi$
$29$	2.36769	+	4.10097i	0.439670	+	0.761530i	−0.557994	+	0.829845i	$0.688429\pi$
$30$	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
$33$	−6.83306	+	5.51035i	−1.18948	+	0.959228i
$34$	3.43793	−	1.98489i	0.589601	−	0.340406i
$35$	−0.755647	+	2.95467i	−0.127728	+	0.499430i
$36$	−2.85691	+	0.915446i	−0.476152	+	0.152574i
$37$	3.47648			0.571530			0.285765	−	0.958300i	$-0.407752\pi$
$37$	3.47648			0.571530			0.285765	+	0.958300i	$0.407752\pi$
$38$	−3.00344	+	3.15901i	−0.487222	+	0.512459i
$39$	1.52338	−	3.94457i	0.243937	−	0.631637i
$40$	0.554035	−	2.16634i	0.0876006	−	0.342529i
$41$	−2.09732	+	3.63266i	−0.327546	+	0.567327i	−0.982024	−	0.188754i	$-0.939555\pi$
$41$	−2.09732	+	3.63266i	−0.327546	+	0.567327i	0.654478	+	0.756081i	$0.272888\pi$
$42$	2.33400	−	0.364808i	0.360144	−	0.0562911i
$43$	−8.08295	−	4.66669i	−1.23264	−	0.711664i	−0.265059	−	0.964232i	$-0.585391\pi$
$43$	−8.08295	−	4.66669i	−1.23264	−	0.711664i	−0.967579	+	0.252568i	$0.918725\pi$
$44$	−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	$0.597375\pi$
$48$	−1.71127	+	0.267475i	−0.247001	+	0.0386067i
$49$	5.13978			0.734255
$50$	−2.59824	−	4.27190i	−0.367446	−	0.604139i
$51$	−6.79339	+	1.06182i	−0.951264	+	0.148684i
$52$	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	$0.164737\pi$
$54$	5.18728	+	0.303579i	0.705899	+	0.0413119i
$55$	−2.80786	+	10.9791i	−0.378612	+	1.48042i
$56$	1.36390			0.182258
$57$	6.82400	−	3.23002i	0.903861	−	0.427826i
$58$		−	4.73539i		−	0.621787i
$59$	−0.294619	+	0.510294i	−0.0383561	+	0.0664347i	−0.884566	−	0.466415i	$-0.845545\pi$
$59$	−0.294619	+	0.510294i	−0.0383561	+	0.0664347i	0.846210	+	0.532849i	$0.178879\pi$
$60$	−2.24697	+	3.15454i	−0.290083	+	0.407249i
$61$	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
$63$	−3.99879	−	0.866972i	−0.503800	−	0.109228i
$64$	−1.00000			−0.125000
$65$	−1.47301	−	5.25650i	−0.182705	−	0.651989i
$66$	8.67278	−	1.35557i	1.06754	−	0.166859i
$67$	5.50663	+	9.53776i	0.672742	+	1.16522i	0.977124	+	0.212673i	$0.0682168\pi$
$67$	5.50663	+	9.53776i	0.672742	+	1.16522i	−0.304382	+	0.952550i	$0.598450\pi$
$68$	−3.96978			−0.481407
$69$	3.92508	−	10.1634i	0.472524	−	1.22353i
$70$	2.13174	−	2.18100i	0.254792	−	0.260679i
$71$	5.35146	−	9.26899i	0.635101	−	1.10003i	−0.351393	−	0.936228i	$-0.614292\pi$
$71$	5.35146	−	9.26899i	0.635101	−	1.10003i	0.986494	−	0.163799i	$-0.0523749\pi$
$72$	2.93188	+	0.635658i	0.345526	+	0.0749130i
$73$	6.55246	+	3.78306i	0.766908	+	0.442774i	0.831770	−	0.555120i	$-0.187328\pi$
$73$	6.55246	+	3.78306i	0.766908	+	0.442774i	−0.0648628	+	0.997894i	$0.520661\pi$
$74$	−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
$78$	−3.29158	+	2.65441i	−0.372698	+	0.300552i
$79$	−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	$0.804117\pi$
$80$	−1.56298	+	1.59909i	−0.174746	+	0.178784i
$81$	−8.19188	−	3.72735i	−0.910209	−	0.414150i
$82$	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
$85$	−6.20469	+	6.34805i	−0.672994	+	0.688542i
$86$	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	0.607461	−	0.794350i	$-0.292188\pi$
$89$	−3.62450	−	6.27782i	−0.384196	−	0.665448i	−0.991657	+	0.128902i	$0.958855\pi$
$90$	5.59895	−	3.69483i	0.590181	−	0.389469i
$91$	2.88363	−	1.66486i	0.302287	−	0.174525i
$92$	3.14511	−	5.44749i	0.327900	−	0.567940i
$93$	11.2275	−	9.05410i	1.16423	−	0.938866i
$94$		−	9.25839i		−	0.954930i
$95$	4.56075	−	8.61392i	0.467923	−	0.883769i
$96$	1.61574	+	0.623997i	0.164906	+	0.0636864i
$97$	5.42307	−	9.39303i	0.550629	−	0.953718i	−0.447600	−	0.894234i	$-0.647721\pi$
$97$	5.42307	−	9.39303i	0.550629	−	0.953718i	0.998229	−	0.0594842i	$-0.0189456\pi$
$98$	−4.45118	−	2.56989i	−0.449638	−	0.259598i
$99$	−14.8589	−	3.22153i	−1.49337	−	0.323776i
$100$	0.114186	+	4.99870i	0.0114186	+	0.499870i
$101$	12.4759	−	7.20295i	1.24140	−	0.716720i	0.272018	−	0.962292i	$-0.412309\pi$
$101$	12.4759	−	7.20295i	1.24140	−	0.716720i	0.969378	+	0.245572i	$0.0789757\pi$
$102$	6.41415	+	2.47713i	0.635096	+	0.245273i
$103$	−1.39554			−0.137506			−0.0687532	−	0.997634i	$-0.521902\pi$
$103$	−1.39554			−0.137506			−0.0687532	+	0.997634i	$0.521902\pi$
$104$	−2.11426	+	1.22067i	−0.207320	+	0.119696i
$105$	−4.80529	+	2.19373i	−0.468948	+	0.214086i
$106$	−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	$0.772840\pi$
$108$	−4.34052	−	2.85655i	−0.417667	−	0.274871i
$109$	−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	$0.697077\pi$
$110$	7.92122	−	8.10423i	0.755259	−	0.772708i
$111$	3.77990	+	4.68724i	0.358772	+	0.444893i
$112$	−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	$0.854967\pi$
$114$	−7.52477	−	0.614724i	−0.704759	−	0.0575742i
$115$	−3.79529	−	13.5436i	−0.353913	−	1.26295i
$116$	−2.36769	+	4.10097i	−0.219835	+	0.380765i
$117$	6.97468	−	2.23491i	0.644810	−	0.206617i
$118$	0.510294	−	0.294619i	0.0469764	−	0.0271218i
$119$	−4.68899	−	2.70719i	−0.429839	−	0.248168i
$120$	3.52320	−	1.60843i	0.321623	−	0.146829i
$121$	−14.6849			−1.33499
$122$		−	7.12041i		−	0.644651i
$123$	−7.17818	+	1.12196i	−0.647234	+	0.101164i
$124$	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	$-0.982664\pi$
$127$	−6.15762	−	10.6653i	−0.546400	−	0.946393i	0.452117	−	0.891959i	$-0.350669\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−2.49645	−	15.9720i	−0.219800	−	1.40625i
$130$	−1.35258	+	5.28877i	−0.118630	+	0.463856i
$131$	−18.6976	−	10.7951i	−1.63362	−	0.943170i	−0.982964	−	0.183797i	$-0.941161\pi$
$131$	−18.6976	−	10.7951i	−1.63362	−	0.943170i	−0.650655	−	0.759374i	$-0.725506\pi$
$132$	−8.18863	−	3.16243i	−0.712729	−	0.275254i
$133$	5.77952	+	1.39329i	0.501148	+	0.120813i
$134$		−	11.0133i		−	0.951400i
$135$	−11.3520	+	2.47617i	−0.977027	+	0.213115i
$136$	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	$0.922670\pi$
$138$	−8.48091	+	6.83921i	−0.721943	+	0.582192i
$139$	−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
$147$	5.58837	+	6.92981i	0.460921	+	0.571561i
$148$	1.73824	+	3.01072i	0.142883	+	0.247480i
$149$	−14.5597	−	8.40607i	−1.19278	−	0.688652i	−0.233844	−	0.972274i	$-0.575131\pi$
$149$	−14.5597	−	8.40607i	−1.19278	−	0.688652i	−0.958936	+	0.283622i	$0.908464\pi$
$150$	2.93467	−	8.14786i	0.239615	−	0.665270i
$151$		−	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
$155$	4.61362	−	18.0398i	0.370575	−	1.44899i
$156$	4.17779	−	0.652996i	0.334491	−	0.0522815i
$157$	−0.0466968	−	0.0269604i	−0.00372681	−	0.00215167i	0.498135	−	0.867099i	$-0.334018\pi$
$157$	−0.0466968	−	0.0269604i	−0.00372681	−	0.00215167i	−0.501862	+	0.864948i	$0.667352\pi$
$158$	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
$162$	5.23070	+	7.32392i	0.410963	+	0.575421i
$163$		−	19.2029i		−	1.50409i	−0.659111	−	0.752045i	$-0.729067\pi$
$163$		−	19.2029i		−	1.50409i	0.659111	−	0.752045i	$-0.270933\pi$
$164$	−4.19464			−0.327546
$165$	−17.8557	+	8.15155i	−1.39006	+	0.634597i
$166$	−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	$0.329179\pi$
$168$	1.48293	+	1.83890i	0.114411	+	0.141874i
$169$	3.51994	−	6.09672i	0.270765	−	0.468978i
$170$	8.54745	−	2.39522i	0.655559	−	0.183705i
$171$	11.7745	+	5.68867i	0.900419	+	0.435023i
$172$		−	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	$0.594280\pi$
$174$	6.38457	−	5.14868i	0.484013	−	0.390320i
$175$	−3.27398	+	5.98218i	−0.247490	+	0.452210i
$176$	−4.38904	−	2.53401i	−0.330836	−	0.191008i
$177$	−1.00835	+	0.157606i	−0.0757919	+	0.0118464i
$178$			7.24900i			0.543336i
$179$	15.4657			1.15596			0.577979	−	0.816052i	$-0.303841\pi$
$179$	15.4657			1.15596			0.577979	+	0.816052i	$0.303841\pi$
$180$	−6.69625	+	0.400340i	−0.499109	+	0.0298396i
$181$	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
$185$	7.53126	+	1.92609i	0.553709	+	0.141609i
$186$	−14.2503	+	2.22735i	−1.04488	+	0.163317i
$187$	−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
$190$	−8.25668	+	5.17949i	−0.599003	+	0.375760i
$191$			3.72983i			0.269881i	0.990854	+	0.134941i	$0.0430844\pi$
$191$			3.72983i			0.269881i	−0.990854	+	0.134941i	$0.956916\pi$
$192$	−1.08728	−	1.34827i	−0.0784675	−	0.0973029i
$193$	1.12403	−	1.94688i	0.0809094	−	0.140139i	−0.822731	−	0.568430i	$-0.807551\pi$
$193$	1.12403	−	1.94688i	0.0809094	−	0.140139i	0.903641	+	0.428291i	$0.140884\pi$
$194$	−9.39303	+	5.42307i	−0.674381	+	0.389354i
$195$	5.48561	−	7.70129i	0.392832	−	0.551501i
$196$	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	$-0.346351\pi$
$200$	2.40046	−	4.38609i	0.169738	−	0.310143i
$201$	−6.87223	+	17.7946i	−0.484730	+	1.25513i
$202$	−14.4059			−1.01360
$203$	−5.59329	+	3.22929i	−0.392572	+	0.226652i
$204$	−4.31625	−	5.35234i	−0.302198	−	0.374738i
$205$	−6.55614	+	6.70761i	−0.457901	+	0.468480i
$206$	1.20857	+	0.697768i	0.0842051	+	0.0486158i
$207$	17.9706	−	5.75835i	1.24904	−	0.400233i
$208$	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
$213$	18.3156	−	2.86276i	1.25497	−	0.196153i
$214$	6.77117	−	11.7280i	0.462867	−	0.801710i
$215$	−14.9249	−	14.5879i	−1.01787	−	0.994886i
$216$	2.33073	+	4.64410i	0.158586	+	0.315991i
$217$	11.3576			0.771004
$218$	0.995917	+	1.72498i	0.0674520	+	0.116830i
$219$	2.02375	+	12.9477i	0.136752	+	0.874926i
$220$	−10.9121	+	3.05786i	−0.735693	+	0.206161i
$221$	9.69157			0.651926
$222$	−0.929872	−	5.94921i	−0.0624090	−	0.399285i
$223$	−7.23465	+	12.5308i	−0.484468	+	0.839123i	−0.999841	−	0.0178430i	$-0.994320\pi$
$223$	−7.23465	+	12.5308i	−0.484468	+	0.839123i	0.515373	+	0.856966i	$0.327653\pi$
$224$	0.681949	+	1.18117i	0.0455646	+	0.0789202i
$225$	−9.82592	+	11.3336i	−0.655061	+	0.755576i
$226$	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	$-0.0830687\pi$
$228$	6.20928	+	4.29475i	0.411219	+	0.284427i
$229$	12.1628			0.803743			0.401872	−	0.915696i	$-0.368360\pi$
$229$	12.1628			0.803743			0.401872	+	0.915696i	$0.368360\pi$
$230$	−3.48500	+	13.6268i	−0.229794	+	0.898523i
$231$	−7.51554	−	9.31959i	−0.494486	−	0.613184i
$232$	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	$0.0768780\pi$
$234$	−7.15771	−	1.55185i	−0.467914	−	0.101448i
$235$	5.58617	+	19.9345i	0.364402	+	1.30038i
$236$	−0.589237			−0.0383561
$237$	−1.98994	−	12.7314i	−0.129261	−	0.826994i
$238$	2.70719	+	4.68899i	0.175481	+	0.303942i
$239$			0.321143i			0.0207730i	0.999946	+	0.0103865i	$0.00330619\pi$
$239$			0.321143i			0.0207730i	−0.999946	+	0.0103865i	$0.996694\pi$
$240$	−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
$243$	−3.88137	−	15.0975i	−0.248990	−	0.968506i
$244$	−3.56020	+	6.16645i	−0.227919	+	0.394767i
$245$	11.1345	+	2.84762i	0.711360	+	0.181928i
$246$	6.77746	+	2.61744i	0.432115	+	0.166882i
$247$	−10.2061	+	3.01276i	−0.649402	+	0.191698i
$248$	−8.32731			−0.528785
$249$	11.0540	+	13.7074i	0.700520	+	0.868674i
$250$	−3.26189	−	10.6939i	−0.206300	−	0.676343i
$251$	−11.2207	+	6.47825i	−0.708242	+	0.408904i	−0.810410	−	0.585864i	$-0.800755\pi$
$251$	−11.2207	+	6.47825i	−0.708242	+	0.408904i	0.102168	+	0.994767i	$0.467422\pi$
$252$	−1.24857	−	3.89654i	−0.0786528	−	0.245459i
$253$	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
$260$	3.81576	−	3.90392i	0.236643	−	0.242111i
$261$	−13.5286	+	4.33499i	−0.837399	+	0.268329i
$262$	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	$0.0976702\pi$
$264$	5.51035	+	6.83306i	0.339138	+	0.420546i
$265$	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	−0.529171	−	0.848515i	$-0.677497\pi$
$269$	7.71267	−	13.3587i	0.470250	−	0.814497i	0.999421	+	0.0340183i	$0.0108304\pi$
$270$	11.0692	+	3.53159i	0.673652	+	0.214926i
$271$	−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
$275$	−12.1656	+	22.2288i	−0.733613	+	1.34045i
$276$	10.7643	−	1.68248i	0.647934	−	0.101273i
$277$			21.4127i			1.28657i	0.765629	+	0.643283i	$0.222428\pi$
$277$			21.4127i			1.28657i	−0.765629	+	0.643283i	$0.777572\pi$
$278$			1.17263i			0.0703297i
$279$	24.4147	+	5.29332i	1.46167	+	0.316903i
$280$	2.95467	+	0.755647i	0.176575	+	0.0451585i
$281$	−7.90099	−	13.6849i	−0.471333	−	0.816374i	0.528129	−	0.849164i	$-0.322894\pi$
$281$	−7.90099	−	13.6849i	−0.471333	−	0.816374i	−0.999462	+	0.0327908i	$0.989560\pi$
$282$	12.4828	−	10.0664i	0.743339	−	0.599447i
$283$	−5.08966	−	2.93851i	−0.302549	−	0.174677i	0.341039	−	0.940049i	$-0.389221\pi$
$283$	−5.08966	−	2.93851i	−0.302549	−	0.174677i	−0.643587	+	0.765373i	$0.722555\pi$
$284$	10.7029			0.635101
$285$	16.5727	−	3.21659i	0.981680	−	0.190535i
$286$	−12.3727			−0.731616
$287$	−4.95458	−	2.86053i	−0.292460	−	0.168852i
$288$	0.915446	+	2.85691i	0.0539432	+	0.168345i
$289$	0.620408	+	1.07458i	0.0364946	+	0.0632104i
$290$	2.62357	−	10.2585i	0.154061	−	0.602398i
$291$	18.5607	−	2.90107i	1.08805	−	0.170064i
$292$			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	$-0.0895633\pi$
$294$	−1.37476	−	8.79558i	−0.0801779	−	0.512969i
$295$	−0.920966	+	0.942244i	−0.0536207	+	0.0548596i
$296$		−	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
$300$	−6.61543	+	5.58892i	−0.381942	+	0.322676i
$301$	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
$306$	3.63412	+	11.3413i	0.207749	+	0.648341i
$307$	−6.33092	+	10.9655i	−0.361325	+	0.625833i	−0.988179	−	0.153304i	$-0.951009\pi$
$307$	−6.33092	+	10.9655i	−0.361325	+	0.625833i	0.626855	+	0.779136i	$0.284342\pi$
$308$	−3.45613	−	5.98620i	−0.196931	−	0.341095i
$309$	−1.51733	−	1.88156i	−0.0863182	−	0.107038i
$310$	−13.0154	+	13.3161i	−0.739227	+	0.756306i
$311$			32.0007i			1.81459i	0.420494	+	0.907296i	$0.361857\pi$
$311$			32.0007i			1.81459i	−0.420494	+	0.907296i	$0.638143\pi$
$312$	−3.94457	−	1.52338i	−0.223317	−	0.0862447i
$313$	−15.0164	+	8.66973i	−0.848778	+	0.490042i	−0.860238	−	0.509892i	$-0.829685\pi$
$313$	−15.0164	+	8.66973i	−0.848778	+	0.490042i	0.0114606	+	0.999934i	$0.496352\pi$
$314$	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	$0.442365\pi$
$318$	−7.99848	−	9.91844i	−0.448532	−	0.556199i
$319$	−20.7838	+	11.9995i	−1.16367	+	0.671845i
$320$	−2.16634	−	0.554035i	−0.121102	−	0.0309715i
$321$	−18.2587	+	14.7243i	−1.01910	+	0.821828i
$322$	−8.57921			−0.478101
$323$	12.5406	+	11.9230i	0.697777	+	0.663414i
$324$	−0.867960	−	8.95805i	−0.0482200	−	0.497669i
$325$	−0.278766	−	12.2035i	−0.0154632	−	0.676928i
$326$	−9.60147	+	16.6302i	−0.531776	+	0.921064i
$327$	−0.532766	−	3.40857i	−0.0294620	−	0.188495i
$328$	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
$333$	−2.20985	+	10.1926i	−0.121099	+	0.558553i
$334$	−0.337320			−0.0184573
$335$	6.64500	+	23.7129i	0.363055	+	1.29558i
$336$	−0.364808	−	2.33400i	−0.0199019	−	0.127330i
$337$	2.17542	−	3.76794i	0.118503	−	0.205253i	−0.800672	−	0.599103i	$-0.795524\pi$
$337$	2.17542	−	3.76794i	0.118503	−	0.205253i	0.919175	+	0.393850i	$0.128857\pi$
$338$	−6.09672	+	3.51994i	−0.331618	+	0.191460i
$339$	−12.6133	+	10.1717i	−0.685062	+	0.552450i
$340$	−8.59992	−	2.19940i	−0.466396	−	0.119279i
$341$	42.2030			2.28542
$342$	−7.35269	−	10.8138i	−0.397588	−	0.584742i
$343$			16.5574i			0.894016i
$344$	−4.66669	+	8.08295i	−0.251611	+	0.435803i
$345$	14.1339	−	19.8428i	0.760945	−	1.06830i
$346$	−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	$0.175298\pi$
$348$	−8.10354	+	1.26660i	−0.434395	+	0.0678968i
$349$	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
$351$	10.5967	+	6.97378i	0.565609	+	0.372233i
$352$	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
$355$	16.7284	−	17.1149i	0.887853	−	0.908366i
$356$	3.62450	−	6.27782i	0.192098	−	0.332724i
$357$	−1.44821	−	9.26548i	−0.0766474	−	0.490381i
$358$	−13.3937	−	7.73283i	−0.707877	−	0.408693i
$359$	−29.3938	−	16.9705i	−1.55134	−	0.895668i	−0.998033	−	0.0626932i	$-0.980031\pi$
$359$	−29.3938	−	16.9705i	−1.55134	−	0.895668i	−0.553310	−	0.832975i	$-0.686636\pi$
$360$	5.99929	+	3.00142i	0.316190	+	0.158189i
$361$	−16.9129	−	8.65764i	−0.890151	−	0.455665i
$362$	−15.0798			−0.792577
$363$	−15.9665	−	19.7991i	−0.838025	−	1.03919i
$364$	2.88363	+	1.66486i	0.151143	+	0.0872626i
$365$	12.0989	+	11.8257i	0.633287	+	0.618986i
$366$	9.60023	−	7.74186i	0.501812	−	0.404673i
$367$	6.59509	−	3.80768i	0.344261	−	0.198759i	−0.317894	−	0.948126i	$-0.602976\pi$
$367$	6.59509	−	3.80768i	0.344261	−	0.198759i	0.662155	+	0.749367i	$0.269642\pi$
$368$	6.29022			0.327900
$369$	−9.31737	−	8.45823i	−0.485043	−	0.440318i
$370$	−5.55922	−	5.43368i	−0.289010	−	0.282483i
$371$	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	$-0.562860\pi$
$373$	−7.57854			−0.392402			−0.196201	+	0.980564i	$0.562860\pi$
$374$	10.0595	+	17.4235i	0.520163	+	0.900949i
$375$	−1.40260	+	19.3141i	−0.0724299	+	0.997374i
$376$	8.01800	−	4.62919i	0.413497	−	0.238732i
$377$	5.78033	−	10.0118i	0.297702	−	0.515635i
$378$	−0.414051	+	7.07491i	−0.0212965	+	0.363894i
$379$			6.21526i			0.319257i	0.987177	+	0.159628i	$0.0510296\pi$
$379$			6.21526i			0.319257i	−0.987177	+	0.159628i	$0.948970\pi$
$380$	9.74025	−	0.357231i	0.499664	−	0.0183256i
$381$	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	$0.689939\pi$
$384$	0.267475	+	1.71127i	0.0136495	+	0.0873281i
$385$	−14.9743	−	3.82963i	−0.763163	−	0.195176i
$386$	−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	−0.335224	−	0.942138i	$-0.608812\pi$
$389$	6.17490	−	3.56508i	0.313080	−	0.180757i	0.648304	+	0.761382i	$0.275479\pi$
$390$	−8.60132	+	3.92671i	−0.435545	+	0.198837i
$391$	24.9708			1.26283
$392$		−	5.13978i		−	0.259598i
$393$	−5.77483	−	36.9467i	−0.291301	−	1.86371i
$394$	21.4067	+	12.3591i	1.07845	+	0.622645i
$395$	−11.8968	−	11.6282i	−0.598593	−	0.585076i
$396$	−4.63950	−	14.4789i	−0.233144	−	0.727593i
$397$	17.6120	+	10.1683i	0.883921	+	0.510332i	0.871949	−	0.489596i	$-0.162856\pi$
$397$	17.6120	+	10.1683i	0.883921	+	0.510332i	0.0119721	+	0.999928i	$0.496189\pi$
$398$			15.0939i			0.756588i
$399$	4.40541	+	9.30724i	0.220546	+	0.465945i
$400$	−4.27190	+	2.59824i	−0.213595	+	0.129912i
$401$	−12.7015	+	21.9996i	−0.634282	+	1.09861i	0.352384	+	0.935855i	$0.385371\pi$
$401$	−12.7015	+	21.9996i	−0.634282	+	1.09861i	−0.986667	+	0.162754i	$0.947962\pi$
$402$	14.8488	−	11.9745i	0.740592	−	0.597232i
$403$	−17.6061	+	10.1649i	−0.877022	+	0.506349i
$404$	12.4759	+	7.20295i	0.620698	+	0.358360i
$405$	−15.6813	−	12.6133i	−0.779212	−	0.626760i
$406$	6.45858			0.320534
$407$			17.6189i			0.873337i
$408$	1.06182	+	6.79339i	0.0525678	+	0.336323i
$409$	−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
$414$	−18.4422	−	3.99843i	−0.906384	−	0.196512i
$415$	22.0246	+	5.63270i	1.08114	+	0.276499i
$416$	−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	$-0.893554\pi$
$419$		−	13.4366i		−	0.656421i	0.944605	−	0.328210i	$-0.106446\pi$
$420$	−4.30247	−	3.06464i	−0.209939	−	0.149539i
$421$	−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
$423$	−26.4504	+	8.47555i	−1.28606	+	0.412095i
$424$	−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	$-0.981993\pi$
$431$	−11.3802	−	19.7111i	−0.548166	−	0.949452i	0.450234	−	0.892911i	$-0.351341\pi$
$432$	0.303579	−	5.18728i	0.0146060	−	0.249573i
$433$	−10.3152	−	17.8664i	−0.495715	−	0.858603i	0.504273	−	0.863544i	$-0.331760\pi$
$433$	−10.3152	−	17.8664i	−0.495715	−	0.858603i	−0.999988	+	0.00494124i	$0.998427\pi$
$434$	−9.83597	−	5.67880i	−0.472142	−	0.272591i
$435$	−10.6403	+	14.9380i	−0.510162	+	0.716221i
$436$		−	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	$0.878368\pi$
$440$	10.9791	+	2.80786i	0.523407	+	0.133860i
$441$	−3.26714	+	15.0692i	−0.155578	+	0.717583i
$442$	−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
$447$	−4.49683	−	28.7702i	−0.212693	−	1.36078i
$448$		−	1.36390i		−	0.0644381i
$449$	7.37904			0.348239			0.174119	−	0.984725i	$-0.444292\pi$
$449$	7.37904			0.348239			0.174119	+	0.984725i	$0.444292\pi$
$450$	14.1763	−	4.90225i	0.668278	−	0.231094i
$451$	−18.4104	−	10.6293i	−0.866913	−	0.500513i
$452$	−8.10184	+	4.67760i	−0.381079	+	0.220016i
$453$	0.651933	−	0.525735i	0.0306305	−	0.0247012i
$454$	−3.88740	+	6.73318i	−0.182445	+	0.316004i
$455$	7.16933	−	2.00904i	0.336103	−	0.0941851i
$456$	−3.23002	−	6.82400i	−0.151259	−	0.319563i
$457$			11.9340i			0.558248i	0.960255	+	0.279124i	$0.0900440\pi$
$457$			11.9340i			0.558248i	−0.960255	+	0.279124i	$0.909956\pi$
$458$	−10.5333	−	6.08142i	−0.492190	−	0.284166i
$459$	1.20514	−	20.5924i	0.0562513	−	0.961169i
$460$	9.83149	−	10.0586i	0.458395	−	0.468986i
$461$	4.47752	+	2.58510i	0.208539	+	0.120400i	0.600632	−	0.799526i	$-0.294916\pi$
$461$	4.47752	+	2.58510i	0.208539	+	0.120400i	−0.392093	+	0.919925i	$0.628249\pi$
$462$	1.84886	+	11.8288i	0.0860166	+	0.550324i
$463$			18.3128i			0.851068i	0.904942	+	0.425534i	$0.139914\pi$
$463$			18.3128i			0.851068i	−0.904942	+	0.425534i	$0.860086\pi$
$464$	−4.73539			−0.219835
$465$	29.3388	−	13.3939i	1.36056	−	0.621126i
$466$	−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
$470$	5.12947	−	20.0568i	0.236605	−	0.925153i
$471$	−0.0144225	−	0.0922732i	−0.000664552	−	0.00425173i
$472$	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
$475$	14.6526	−	16.1339i	0.672306	−	0.740274i
$476$		−	5.41438i		−	0.248168i
$477$	6.73441	+	21.0167i	0.308348	+	0.962288i
$478$	0.160572	−	0.278118i	0.00734437	−	0.0127208i
$479$	−2.03089	+	1.17253i	−0.0927936	+	0.0535744i	−0.545679	−	0.837994i	$-0.683728\pi$
$479$	−2.03089	+	1.17253i	−0.0927936	+	0.0535744i	0.452885	+	0.891569i	$0.350395\pi$
$480$	3.15454	+	2.24697i	0.143984	+	0.102560i
$481$	−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
$485$	16.9523	−	17.3440i	0.769765	−	0.787549i
$486$	−4.18739	+	15.0155i	−0.189944	+	0.681118i
$487$	38.4769			1.74355			0.871777	−	0.489903i	$-0.162968\pi$
$487$	38.4769			1.74355			0.871777	+	0.489903i	$0.162968\pi$
$488$	6.16645	−	3.56020i	0.279142	−	0.161163i
$489$	25.8907	−	20.8789i	1.17082	−	0.944177i
$490$	−8.21899	−	8.03338i	−0.371296	−	0.362911i
$491$	−33.6488	−	19.4272i	−1.51855	−	0.876735i	−0.999762	−	0.0218329i	$-0.993050\pi$
$491$	−33.6488	−	19.4272i	−1.51855	−	0.876735i	−0.518789	−	0.854903i	$-0.673617\pi$
$492$	−4.56074	−	5.65550i	−0.205614	−	0.254970i
$493$	−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
$498$	−2.71934	−	17.3980i	−0.121856	−	0.779623i
$499$	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	$0.141374\pi$
$500$	−2.52209	+	10.8922i	−0.112791	+	0.487112i
$501$	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	$0.833703\pi$
$504$	−0.866972	+	3.99879i	−0.0386180	+	0.178120i
$505$	31.0177	−	8.69200i	1.38027	−	0.386789i
$506$	−31.8790			−1.41719
$507$	12.0472	−	1.88299i	0.535033	−	0.0836266i
$508$	6.15762	−	10.6653i	0.273200	−	0.473196i
$509$	5.84914	+	10.1310i	0.259259	+	0.449049i	0.966044	−	0.258379i	$-0.0831885\pi$
$509$	5.84914	+	10.1310i	0.259259	+	0.449049i	−0.706785	+	0.707428i	$0.749855\pi$
$510$	12.5228	+	8.91998i	0.554521	+	0.394984i
$511$	−5.15971	+	8.93688i	−0.228252	+	0.395344i
$512$			1.00000i			0.0441942i
$513$	5.13230	+	22.0604i	0.226597	+	0.973989i
$514$	11.0305			0.486533
$515$	−3.02321	−	0.773176i	−0.133219	−	0.0340702i
$516$	12.5839	−	10.1480i	0.553976	−	0.446740i
$517$	−40.6354	+	23.4609i	−1.78714	+	1.03181i
$518$	2.37078	−	4.10632i	0.104166	−	0.180421i
$519$	1.58632	+	10.1491i	0.0696319	+	0.445497i
$520$	−5.25650	+	1.47301i	−0.230513	+	0.0645959i
$521$	3.72071			0.163007			0.0815037	−	0.996673i	$-0.474028\pi$
$521$	3.72071			0.163007			0.0815037	+	0.996673i	$0.474028\pi$
$522$	13.8836	+	3.01009i	0.607669	+	0.131748i
$523$	4.81021	+	8.33153i	0.210336	+	0.364312i	0.951820	−	0.306658i	$-0.0992109\pi$
$523$	4.81021	+	8.33153i	0.210336	+	0.364312i	−0.741484	+	0.670971i	$0.765878\pi$
$524$		−	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
$528$	−1.35557	−	8.67278i	−0.0589936	−	0.377434i
$529$	−8.28343	+	14.3473i	−0.360149	+	0.623797i
$530$	−15.9366	−	4.07572i	−0.692240	−	0.177038i
$531$	−1.30885	−	1.18816i	−0.0567991	−	0.0515617i
$532$	1.68314	+	5.70185i	0.0729732	+	0.247207i
$533$	10.2405			0.443566
$534$	−9.77361	+	7.88168i	−0.422945	+	0.341073i
$535$	−7.50293	+	29.3374i	−0.324380	+	1.26836i
$536$	9.53776	−	5.50663i	0.411968	−	0.237850i
$537$	16.8155	+	20.8519i	0.725641	+	0.899825i
$538$	−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
$545$	−3.18513	−	3.11320i	−0.136436	−	0.133355i
$546$	−3.62034	−	4.48937i	−0.154936	−	0.192127i
$547$	−18.7690	−	32.5089i	−0.802505	−	1.38998i	−0.917963	−	0.396667i	$-0.870167\pi$
$547$	−18.7690	−	32.5089i	−0.802505	−	1.38998i	0.115458	−	0.993312i	$-0.463166\pi$
$548$	3.24209	−	5.61546i	0.138495	−	0.239881i
$549$	−20.3424	+	6.51835i	−0.868192	+	0.278196i
$550$	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
$555$	5.59167	+	12.2484i	0.237353	+	0.519914i
$556$	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
$560$	−2.18100	−	2.13174i	−0.0921639	−	0.0900826i
$561$	−5.38132	−	34.4290i	−0.227199	−	1.45360i
$562$			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	$-0.336024\pi$
$564$	−15.8436	+	2.47639i	−0.667137	+	0.104275i
$565$	−5.18311	+	20.2666i	−0.218055	+	0.852621i
$566$	2.93851	+	5.08966i	0.123515	+	0.213934i
$567$	5.08372	−	11.1729i	0.213496	−	0.469217i
$568$	−9.26899	−	5.35146i	−0.388918	−	0.224542i
$569$	35.3619			1.48245			0.741224	−	0.671258i	$-0.234246\pi$
$569$	35.3619			1.48245			0.741224	+	0.671258i	$0.234246\pi$
$570$	−15.9607	−	5.50069i	−0.668518	−	0.230398i
$571$	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
$573$	−5.02882	+	4.05536i	−0.210082	+	0.169415i
$574$	2.86053	+	4.95458i	0.119396	+	0.206800i
$575$	−0.718255	−	31.4429i	−0.0299533	−	1.31126i
$576$	0.635658	−	2.93188i	0.0264857	−	0.122162i
$577$			13.3398i			0.555341i	0.960676	+	0.277671i	$0.0895624\pi$
$577$			13.3398i			0.555341i	−0.960676	+	0.277671i	$0.910438\pi$
$578$		−	1.24082i		−	0.0516111i
$579$	3.84704	−	0.601300i	0.159878	−	0.0249892i
$580$	−7.40132	+	7.57232i	−0.307323	+	0.314423i
$581$			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
$585$	16.3478	−	0.977364i	0.675898	−	0.0404090i
$586$	−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
$591$	−26.8756	−	33.3269i	−1.10552	−	1.37089i
$592$	−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	$0.664568\pi$
$594$	−1.53855	+	26.2892i	−0.0631273	+	1.07866i
$595$	−8.65808	−	8.46256i	−0.354947	−	0.346931i
$596$		−	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	0.986323	−	0.164822i	$-0.0527051\pi$
$599$	8.57637	+	14.8547i	0.350421	+	0.606947i	−0.635902	+	0.771770i	$0.719372\pi$
$600$	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
$603$	−31.4639	+	10.0820i	−1.28131	+	0.410572i
$604$	0.418752	−	0.241767i	0.0170388	−	0.00983735i
$605$	−31.8125	−	8.13593i	−1.29336	−	0.330773i
$606$	−15.6632	−	19.4230i	−0.636274	−	0.789007i
$607$	14.9609			0.607242			0.303621	−	0.952793i	$-0.401804\pi$
$607$	14.9609			0.607242			0.303621	+	0.952793i	$0.401804\pi$
$608$	−1.23406	−	4.18056i	−0.0500479	−	0.169544i
$609$	−10.4354	−	4.03013i	−0.422864	−	0.163309i
$610$	3.94495	−	15.4253i	0.159727	−	0.624550i
$611$	11.3014	−	19.5746i	0.457206	−	0.791904i
$612$	2.52342	−	11.6389i	0.102003	−	0.470476i
$613$	33.9142	+	19.5804i	1.36978	+	0.790844i	0.990900	−	0.134600i	$-0.0429750\pi$
$613$	33.9142	+	19.5804i	1.36978	+	0.790844i	0.378883	+	0.925445i	$0.376308\pi$
$614$	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	$-0.373594\pi$
$618$	0.373271	+	2.38815i	0.0150152	+	0.0960653i
$619$	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
$621$	27.3028	+	17.9683i	1.09563	+	0.721043i
$622$	16.0003	−	27.7134i	0.641555	−	1.11121i
$623$	8.56230	−	4.94345i	0.343041	−	0.198055i
$624$	2.65441	+	3.29158i	0.106261	+	0.131768i
$625$	13.4756	+	21.0573i	0.539023	+	0.842291i
$626$	17.3395			0.693024
$627$	16.3698	+	34.5842i	0.653747	+	1.38116i
$628$		−	0.0539208i		−	0.00215167i
$629$	−6.90045	+	11.9519i	−0.275139	+	0.476554i
$630$	5.03937	+	7.63639i	0.200773	+	0.304241i
$631$	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
$633$	5.33485	+	34.1318i	0.212041	+	1.35662i
$634$	11.9602			0.474999
$635$	−7.43056	−	26.5163i	−0.294873	−	1.05227i
$636$	1.96766	+	12.5889i	0.0780228	+	0.499181i
$637$	−6.27397	−	10.8668i	−0.248584	−	0.430560i
$638$	23.9991			0.950132
$639$	23.7739	+	21.5818i	0.940481	+	0.853761i
$640$	1.59909	+	1.56298i	0.0632096	+	0.0617822i
$641$	−9.01119	+	15.6078i	−0.355921	+	0.616473i	−0.987275	−	0.159022i	$-0.949166\pi$
$641$	−9.01119	+	15.6078i	−0.355921	+	0.616473i	0.631354	+	0.775494i	$0.282499\pi$
$642$	23.1746	−	3.62224i	0.914630	−	0.142958i
$643$	−28.9629	−	16.7217i	−1.14218	−	0.659440i	−0.195213	−	0.980761i	$-0.562540\pi$
$643$	−28.9629	−	16.7217i	−1.14218	−	0.659440i	−0.946970	+	0.321321i	$0.895873\pi$
$644$	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	$0.180919\pi$
$648$	−3.72735	+	8.19188i	−0.146424	+	0.321807i
$649$	−2.58618	−	1.49313i	−0.101517	−	0.0586106i
$650$	−5.86033	+	10.7079i	−0.229861	+	0.419999i
$651$	12.3489	+	15.3131i	0.483990	+	0.600168i
$652$	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
$655$	−34.5246	−	33.7450i	−1.34899	−	1.31853i
$656$	−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	0.686116	−	0.727492i	$-0.259314\pi$
$659$	−7.36677	−	12.7596i	−0.286969	−	0.497044i	−0.973085	+	0.230448i	$0.925981\pi$
$660$	−15.9873	−	11.3877i	−0.622304	−	0.443265i
$661$	−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
$663$	10.5374	+	13.0668i	0.409240	+	0.507474i
$664$		−	10.1667i		−	0.394544i
$665$	11.7485	+	6.22040i	0.455587	+	0.241217i
$666$	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
$669$	−24.7609	+	3.87017i	−0.957313	+	0.149630i
$670$	6.10173	−	23.8585i	0.235730	−	0.921734i
$671$	−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	$-0.633791\pi$
$673$	−21.1715			−0.816100			−0.408050	+	0.912960i	$0.633791\pi$
$674$	−3.76794	+	2.17542i	−0.145136	+	0.0837941i
$675$	−25.9643	−	0.925185i	−0.999366	−	0.0356104i
$676$	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	$0.948805\pi$
$678$	16.0093	−	2.50228i	0.614834	−	0.0960995i
$679$	12.8111	+	7.39651i	0.491646	+	0.283852i
$680$	6.34805	+	6.20469i	0.243436	+	0.237939i
$681$	10.4825	−	8.45337i	0.401691	−	0.323934i
$682$	−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	$-0.0112880\pi$
$684$	0.960726	+	13.0414i	0.0367343	+	0.498649i
$685$	−3.91231	−	13.9612i	−0.149482	−	0.533432i
$686$	8.27871	−	14.3391i	0.316083	−	0.547471i
$687$	13.2244	+	16.3988i	0.504542	+	0.625653i
$688$	8.08295	−	4.66669i	0.308159	−	0.177916i
$689$	−15.5534	−	8.97975i	−0.592537	−	0.342101i
$690$	−22.1617	+	10.1174i	−0.843682	+	0.385161i
$691$	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
$693$	4.39383	−	20.2659i	0.166908	−	0.769840i
$694$	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
$699$	14.5420	−	2.27294i	0.550029	−	0.0859705i
$700$	−6.81771	+	0.155738i	−0.257685	+	0.00588634i
$701$	−15.0883	−	8.71122i	−0.569876	−	0.329018i	0.187224	−	0.982317i	$-0.440051\pi$
$701$	−15.0883	−	8.71122i	−0.569876	−	0.329018i	−0.757100	+	0.653299i	$0.773384\pi$
$702$	−5.69010	−	11.3378i	−0.214759	−	0.427918i
$703$	3.55140	−	14.7316i	0.133944	−	0.555613i
$704$		−	5.06802i		−	0.191008i
$705$	−20.8033	+	29.2060i	−0.783498	+	1.09996i
$706$	−7.90644	−	4.56479i	−0.297563	−	0.171798i
$707$	9.82408	+	17.0158i	0.369473	+	0.639946i
$708$	−0.640664	−	0.794450i	−0.0240776	−	0.0298573i
$709$	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
$717$	−0.432987	+	0.349172i	−0.0161702	+	0.0130401i
$718$	16.9705	+	29.3938i	0.633333	+	1.09697i
$719$	−8.06657	−	4.65724i	−0.300832	−	0.173686i	0.341984	−	0.939706i	$-0.388901\pi$
$719$	−8.06657	−	4.65724i	−0.300832	−	0.173686i	−0.642817	+	0.766020i	$0.722234\pi$
$720$	−3.69483	−	5.59895i	−0.137698	−	0.208661i
$721$		−	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
$725$	0.540715	+	23.6708i	0.0200817	+	0.879110i
$726$	3.92783	+	25.1298i	0.145776	+	0.932655i
$727$	38.9254	+	22.4736i	1.44366	+	0.833500i	0.998092	−	0.0617466i	$-0.0196671\pi$
$727$	38.9254	+	22.4736i	1.44366	+	0.833500i	0.445572	+	0.895246i	$0.353000\pi$
$728$	−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
$732$	−12.1850	+	1.90453i	−0.450369	+	0.0703935i
$733$		−	29.5925i		−	1.09302i	−0.837452	−	0.546511i	$-0.815956\pi$
$733$		−	29.5925i		−	1.09302i	0.837452	−	0.546511i	$-0.184044\pi$
$734$	−7.61535			−0.281088
$735$	8.26697	+	18.1085i	0.304932	+	0.667942i
$736$	−5.44749	−	3.14511i	−0.200797	−	0.115930i
$737$	−48.3376	+	27.9077i	−1.78054	+	1.02799i
$738$	3.83997	+	11.9837i	0.141351	+	0.441127i
$739$	−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
$741$	−15.1589	−	10.4849i	−0.556877	−	0.385173i
$742$		−	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	$0.715646\pi$
$744$	−9.05410	−	11.2275i	−0.331939	−	0.411619i
$745$	−26.8842	−	26.2770i	−0.984959	−	0.962716i
$746$	6.56320	+	3.78927i	0.240296	+	0.138735i
$747$	−6.46254	+	29.8076i	−0.236452	+	1.09060i
$748$		−	20.1190i		−	0.735622i
$749$	−18.4704			−0.674892
$750$	10.8717	−	16.0252i	0.396979	−	0.585156i
$751$	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
$755$	0.267894	−	1.04750i	0.00974968	−	0.0381224i
$756$	3.89603	−	5.92003i	0.141697	−	0.215309i
$757$	−30.7033	−	17.7266i	−1.11593	−	0.644283i	−0.175571	−	0.984467i	$-0.556177\pi$
$757$	−30.7033	−	17.7266i	−1.11593	−	0.644283i	−0.940359	+	0.340184i	$0.889511\pi$
$758$	3.10763	−	5.38258i	0.112874	−	0.195504i
$759$	51.5083	+	19.8924i	1.86963	+	0.722048i
$760$	−8.61392	−	4.56075i	−0.312460	−	0.165436i
$761$			5.16853i			0.187359i	0.995602	+	0.0936795i	$0.0298629\pi$
$761$			5.16853i			0.187359i	−0.995602	+	0.0936795i	$0.970137\pi$
$762$	−16.6042	+	13.3901i	−0.601508	+	0.485071i
$763$	1.35833	−	2.35269i	0.0491748	−	0.0851732i
$764$	−3.23013	+	1.86492i	−0.116862	+	0.0674703i
$765$	−14.6677	−	22.2266i	−0.530311	−	0.803605i
$766$	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	$0.783486\pi$
$770$	11.0533	+	10.8037i	0.398335	+	0.389339i
$771$	−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	$0.361568\pi$
$774$	−26.6647	+	8.54421i	−0.958442	+	0.307115i
$775$	19.9894	−	36.5244i	0.718040	−	1.31199i
$776$	−9.39303	−	5.42307i	−0.337190	−	0.194677i
$777$	−6.39291	+	5.15540i	−0.229344	+	0.184949i
$778$	−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
$783$	−20.5541	−	13.5268i	−0.734542	−	0.483410i
$784$	−2.56989	+	4.45118i	−0.0917819	+	0.158971i
$785$	−0.0862243	−	0.0842771i	−0.00307748	−	0.00300798i
$786$	−13.4722	+	34.8842i	−0.480537	+	1.24428i
$787$	−29.6094			−1.05546			−0.527731	−	0.849412i	$-0.676957\pi$
$787$	−29.6094			−1.05546			−0.527731	+	0.849412i	$0.676957\pi$
$788$	−12.3591	−	21.4067i	−0.440276	−	0.762581i
$789$	11.9371	−	1.86579i	0.424971	−	0.0664237i
$790$	4.48886	+	16.0187i	0.159707	+	0.569919i
$791$	−12.7595			−0.453677
$792$	−3.22153	+	14.8589i	−0.114472	+	0.527986i
$793$	8.69165	−	15.0544i	0.308650	−	0.534597i
$794$	−10.1683	−	17.6120i	−0.360859	−	0.625027i
$795$	23.2062	+	16.5297i	0.823037	+	0.586247i
$796$	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	$-0.186787\pi$
$798$	0.838420	−	10.2630i	0.0296797	−	0.363307i
$799$	−36.7538			−1.30026
$800$	4.99870	−	0.114186i	0.176731	−	0.00403709i
$801$	20.7098	−	6.63607i	0.731744	−	0.234474i
$802$	21.9996	−	12.7015i	0.776834	−	0.448505i
$803$	−19.1727	+	33.2080i	−0.676589	+	1.17189i
$804$	−18.8467	+	2.94577i	−0.664672	+	0.103889i
$805$	18.4721	−	5.17638i	0.651057	−	0.182444i
$806$	20.3298			0.716085
$807$	26.3970	−	4.12589i	0.929218	−	0.145238i
$808$	−7.20295	−	12.4759i	−0.253399	−	0.438900i
$809$			27.8772i			0.980109i	0.871692	+	0.490054i	$0.163023\pi$
$809$			27.8772i			0.980109i	−0.871692	+	0.490054i	$0.836977\pi$
$810$	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
$813$	−37.0217	+	5.78656i	−1.29841	+	0.202943i
$814$	8.80945	−	15.2584i	0.308771	−	0.534807i
$815$	10.6391	−	41.6002i	0.372671	−	1.45719i
$816$	2.47713	−	6.41415i	0.0867170	−	0.224540i
$817$	−28.0323	+	29.4843i	−0.980724	+	1.03152i
$818$	36.6023			1.27977
$819$	3.04819	+	9.51275i	0.106512	+	0.332402i
$820$	−9.08703	−	2.32398i	−0.317333	−	0.0811568i
$821$	2.32853	−	1.34438i	0.0812662	−	0.0469191i	−0.458816	−	0.888531i	$-0.651726\pi$
$821$	2.32853	−	1.34438i	0.0812662	−	0.0469191i	0.540082	+	0.841612i	$0.318393\pi$
$822$	−8.74241	+	7.05009i	−0.304927	+	0.245900i
$823$	14.8455	−	8.57103i	0.517480	−	0.298767i	−0.218423	−	0.975854i	$-0.570091\pi$
$823$	14.8455	−	8.57103i	0.517480	−	0.298767i	0.735903	+	0.677087i	$0.236758\pi$
$824$			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	$0.983544\pi$
$830$	−16.2575	−	15.8903i	−0.564305	−	0.551562i
$831$	−28.8701	+	23.2815i	−1.00149	+	0.807628i
$832$	1.22067	+	2.11426i	0.0423190	+	0.0732987i
$833$	−10.2019	+	17.6702i	−0.353475	+	0.612238i
$834$	−1.58102	+	1.27497i	−0.0547463	+	0.0441488i
$835$	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	$0.488481\pi$
$839$	−24.5444	+	42.5122i	−0.847368	+	1.46768i	−0.883549	+	0.468339i	$0.844853\pi$
$840$	2.19373	+	4.80529i	0.0756909	+	0.165798i
$841$	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
$845$	11.0032	−	11.2574i	0.378522	−	0.387267i
$846$	27.1445	+	5.88517i	0.933247	+	0.202336i
$847$		−	20.0286i		−	0.688192i
$848$			7.35643i			0.252621i
$849$	−1.57196	−	10.0572i	−0.0539495	−	0.345162i
$850$	19.8437	−	0.453294i	0.680635	−	0.0155479i
$851$	−10.9339	−	18.9381i	−0.374810	−	0.649190i
$852$	11.6370	+	14.4304i	0.398678	+	0.494378i
$853$	−23.1920	−	13.3899i	−0.794081	−	0.458463i	0.0473166	−	0.998880i	$-0.484933\pi$
$853$	−23.1920	−	13.3899i	−0.794081	−	0.458463i	−0.841397	+	0.540417i	$0.818266\pi$
$854$	9.71150			0.332321
$855$	22.3559	+	18.8471i	0.764556	+	0.644557i
$856$	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	$0.809608\pi$
$858$	−13.4526	−	16.6818i	−0.459264	−	0.569507i
$859$	−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	$0.930461\pi$
$860$	5.17102	−	20.2193i	0.176330	−	0.689473i
$861$	−1.53024	−	9.79029i	−0.0521504	−	0.333652i
$862$			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	$0.767770\pi$
$864$	−2.85655	+	4.34052i	−0.0971817	+	0.147668i
$865$	9.48380	+	9.26963i	0.322459	+	0.315177i
$866$			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
$870$	16.6837	−	7.61653i	0.565631	−	0.258224i
$871$	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
$876$	−10.2012	+	8.22648i	−0.344666	+	0.277947i
$877$	19.2084	−	33.2699i	0.648621	−	1.12344i	−0.334832	−	0.942278i	$-0.608680\pi$
$877$	19.2084	−	33.2699i	0.648621	−	1.12344i	0.983453	−	0.181166i	$-0.0579871\pi$
$878$	12.9301	+	22.3956i	0.436371	+	0.755817i
$879$	12.8166	−	10.3357i	0.432295	−	0.348613i
$880$	−8.10423	−	7.92122i	−0.273194	−	0.267024i
$881$			54.5643i			1.83832i	0.393888	+	0.919158i	$0.371130\pi$
$881$			54.5643i			1.83832i	−0.393888	+	0.919158i	$0.628870\pi$
$882$	10.3641	−	11.4168i	0.348976	−	0.384423i
$883$	39.3518	−	22.7198i	1.32429	−	0.764581i	0.339883	−	0.940468i	$-0.389612\pi$
$883$	39.3518	−	22.7198i	1.32429	−	0.764581i	0.984411	+	0.175886i	$0.0562790\pi$
$884$	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	$0.0553868\pi$
$888$	4.68724	−	3.77990i	0.157293	−	0.126845i
$889$	14.5464	−	8.39836i	0.487870	−	0.281672i
$890$	−4.01620	+	15.7038i	−0.134623	+	0.526394i
$891$	18.8903	−	41.5166i	0.632849	−	1.39086i
$892$	−14.4693			−0.484468
$893$	38.7052	−	11.4254i	1.29522	−	0.382338i
$894$	−10.4907	+	27.1641i	−0.350862	+	0.908504i
$895$	33.5040	+	8.56852i	1.11991	+	0.286414i
$896$	−0.681949	+	1.18117i	−0.0227823	+	0.0394601i
$897$	−26.2792	+	4.10749i	−0.877438	+	0.137145i
$898$	−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
$903$	21.7841	−	3.40490i	0.724930	−	0.113308i
$904$	9.35520			0.311149
$905$	32.4687	−	9.09861i	1.07930	−	0.302448i
$906$	−0.827458	+	0.129333i	−0.0274905	+	0.00429681i
$907$	19.2054	−	33.2647i	0.637704	−	1.10454i	−0.348232	−	0.937409i	$-0.613218\pi$
$907$	19.2054	−	33.2647i	0.637704	−	1.10454i	0.985935	−	0.167127i	$-0.0534489\pi$
$908$	6.73318	−	3.88740i	0.223448	−	0.129008i
$909$	13.1878	+	41.1564i	0.437412	+	1.36507i
$910$	−7.21334	−	1.84479i	−0.239120	−	0.0611541i
$911$	−14.7901			−0.490018			−0.245009	−	0.969521i	$-0.578791\pi$
$911$	−14.7901			−0.490018			−0.245009	+	0.969521i	$0.578791\pi$
$912$	−0.614724	+	7.52477i	−0.0203555	+	0.249170i
$913$			51.5251i			1.70523i
$914$	5.96698	−	10.3351i	0.197370	−	0.341855i
$915$	−15.9993	+	22.4616i	−0.528922	+	0.742558i
$916$	6.08142	+	10.5333i	0.200936	+	0.348031i
$917$	14.7234	−	25.5016i	0.486209	−	0.842138i
$918$	−11.3399	+	17.2309i	−0.374271	+	0.568706i
$919$	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
$921$	−21.6679	+	3.38672i	−0.713980	+	0.111596i
$922$	−2.58510	−	4.47752i	−0.0851356	−	0.147459i
$923$	−26.1294			−0.860060
$924$	4.31323	−	11.1684i	0.141895	−	0.367415i
$925$	15.2482	+	8.34516i	0.501357	+	0.274387i
$926$	9.15640	−	15.8594i	0.300898	−	0.521171i
$927$	0.887084	−	4.09155i	0.0291357	−	0.134384i
$928$	4.10097	+	2.36769i	0.134621	+	0.0777233i
$929$	1.58213	+	0.913443i	0.0519080	+	0.0299691i	0.525729	−	0.850652i	$-0.323792\pi$
$929$	1.58213	+	0.913443i	0.0519080	+	0.0299691i	−0.473821	+	0.880621i	$0.657126\pi$
$930$	−32.1051	−	3.06997i	−1.05277	−	0.100668i
$931$	5.25054	−	21.7799i	0.172080	−	0.713806i
$932$	8.49777			0.278354
$933$	−43.1455	+	34.7936i	−1.41252	+	1.13909i
$934$	33.9352	+	19.5925i	1.11039	+	0.641086i
$935$	−32.1721	−	31.4455i	−1.05214	−	1.02838i
$936$	−2.23491	−	6.97468i	−0.0730503	−	0.227975i
$937$	38.2667	−	22.0933i	1.25012	−	0.721757i	0.278987	−	0.960295i	$-0.410002\pi$
$937$	38.2667	−	22.0933i	1.25012	−	0.721757i	0.971133	+	0.238538i	$0.0766682\pi$
$938$	15.0209			0.490451
$939$	−28.0161	−	10.8198i	−0.914271	−	0.353090i
$940$	−14.4707	+	14.8050i	−0.471981	+	0.482886i
$941$	−18.8424	−	32.6360i	−0.614244	−	1.06390i	−0.990517	−	0.137393i	$-0.956128\pi$
$941$	−18.8424	−	32.6360i	−0.614244	−	1.06390i	0.376273	−	0.926509i	$-0.377206\pi$
$942$	−0.0336464	+	0.0871222i	−0.00109626	+	0.00283859i
$943$	26.3852			0.859221
$944$	−0.294619	−	0.510294i	−0.00958902	−	0.0166087i
$945$	−3.37724	−	15.4830i	−0.109862	−	0.503662i
$946$	−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	$-0.0999745\pi$
$948$	10.0308	−	8.08905i	0.325784	−	0.262720i
$949$		−	18.4715i		−	0.599609i
$950$	−20.7564	+	6.64607i	−0.673428	+	0.215627i
$951$	−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	$0.587602\pi$
$954$	4.67617	−	21.5682i	0.151397	−	0.698296i
$955$	−2.06646	+	8.08010i	−0.0668690	+	0.261466i
$956$	−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
$960$	−1.60843	−	3.52320i	−0.0519118	−	0.113711i
$961$	−38.3442			−1.23691
$962$			8.48726i			0.273640i
$963$	−39.7045	−	8.60829i	−1.27946	−	0.277398i
$964$	4.85412	+	2.80253i	0.156341	+	0.0902634i
$965$	3.51367	−	3.59485i	0.113109	−	0.115722i
$966$	−9.32798	−	11.5671i	−0.300123	−	0.372165i
$967$	26.7384	+	15.4374i	0.859849	+	0.496434i	0.863962	−	0.503557i	$-0.167976\pi$
$967$	26.7384	+	15.4374i	0.859849	+	0.496434i	−0.00411251	+	0.999992i	$0.501309\pi$
$968$			14.6849i			0.471989i
$969$	−2.44032	+	29.8717i	−0.0783944	+	0.959617i
$970$	−23.3531	+	6.54417i	−0.749823	+	0.210121i
$971$	−16.3109	+	28.2513i	−0.523442	+	0.906628i	0.476186	+	0.879345i	$0.342019\pi$
$971$	−16.3109	+	28.2513i	−0.523442	+	0.906628i	−0.999628	+	0.0272836i	$0.991314\pi$
$972$	11.1341	−	10.9101i	0.357128	−	0.349942i
$973$	1.38508	−	0.799674i	0.0444035	−	0.0256364i
$974$	−33.3220	−	19.2384i	−1.06770	−	0.616439i
$975$	16.1505	−	13.6444i	0.517230	−	0.436971i
$976$	−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	$0.830989\pi$
$978$	−32.8615	+	5.13631i	−1.05079	+	0.164241i
$979$	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	$0.715804\pi$
$984$	1.12196	+	7.17818i	0.0357668	+	0.228832i
$985$	−53.5483	−	13.6948i	−1.70619	−	0.436352i
$986$	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
$990$	18.7255	+	28.3756i	0.595135	+	0.901836i
$991$	−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
$993$	16.5751	−	13.3666i	0.525995	−	0.424175i
$994$	−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	−0.612670	−	0.790339i	$-0.709904\pi$
$997$	−7.40601	+	4.27586i	−0.234551	+	0.135418i	0.378119	+	0.925757i	$0.376571\pi$
$998$	−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.179.15	✓	80
3.2	odd	2	inner	570.2.n.a.179.22	yes	80
5.4	even	2	inner	570.2.n.a.179.26	yes	80
15.14	odd	2	inner	570.2.n.a.179.19	yes	80
19.12	odd	6	inner	570.2.n.a.449.19	yes	80
57.50	even	6	inner	570.2.n.a.449.26	yes	80
95.69	odd	6	inner	570.2.n.a.449.22	yes	80
285.164	even	6	inner	570.2.n.a.449.15	yes	80

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

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.08728 + 1.34827i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.16634 + 0.554035i) q^{5} +(-0.267475 - 1.71127i) q^{6} +1.36390i q^{7} -1.00000i q^{8} +(-0.635658 + 2.93188i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.08728 + 1.34827i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.16634 + 0.554035i) q^{5} +(-0.267475 - 1.71127i) q^{6} +1.36390i q^{7} -1.00000i q^{8} +(-0.635658 + 2.93188i) q^{9} +(-1.59909 - 1.56298i) q^{10} +5.06802i q^{11} +(-0.623997 + 1.61574i) q^{12} +(-1.22067 - 2.11426i) q^{13} +(0.681949 - 1.18117i) q^{14} +(1.60843 + 3.52320i) 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} +(-1.83890 + 1.48293i) q^{21} +(2.53401 - 4.38904i) q^{22} +(-3.14511 - 5.44749i) q^{23} +(1.34827 - 1.08728i) q^{24} +(4.38609 + 2.40046i) 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} +(-6.83306 + 5.51035i) q^{33} +(3.43793 - 1.98489i) q^{34} +(-0.755647 + 2.95467i) q^{35} +(-2.85691 + 0.915446i) q^{36} +3.47648 q^{37} +(-3.00344 + 3.15901i) q^{38} +(1.52338 - 3.94457i) q^{39} +(0.554035 - 2.16634i) q^{40} +(-2.09732 + 3.63266i) q^{41} +(2.33400 - 0.364808i) 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} +(-1.71127 + 0.267475i) q^{48} +5.13978 q^{49} +(-2.59824 - 4.27190i) q^{50} +(-6.79339 + 1.06182i) q^{51} +(1.22067 - 2.11426i) q^{52} +(6.37085 - 3.67821i) q^{53} +(5.18728 + 0.303579i) q^{54} +(-2.80786 + 10.9791i) q^{55} +1.36390 q^{56} +(6.82400 - 3.23002i) q^{57} -4.73539i q^{58} +(-0.294619 + 0.510294i) q^{59} +(-2.24697 + 3.15454i) q^{60} +(3.56020 + 6.16645i) q^{61} +(-4.16366 + 7.21167i) q^{62} +(-3.99879 - 0.866972i) q^{63} -1.00000 q^{64} +(-1.47301 - 5.25650i) q^{65} +(8.67278 - 1.35557i) q^{66} +(5.50663 + 9.53776i) q^{67} -3.96978 q^{68} +(3.92508 - 10.1634i) q^{69} +(2.13174 - 2.18100i) q^{70} +(5.35146 - 9.26899i) q^{71} +(2.93188 + 0.635658i) 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} +(-3.29158 + 2.65441i) q^{78} +(-6.44300 - 3.71987i) q^{79} +(-1.56298 + 1.59909i) q^{80} +(-8.19188 - 3.72735i) q^{81} +(3.63266 - 2.09732i) q^{82} +10.1667 q^{83} +(-2.20371 - 0.851067i) q^{84} +(-6.20469 + 6.34805i) q^{85} +(4.66669 + 8.08295i) q^{86} +(-2.95487 + 7.65117i) q^{87} +5.06802 q^{88} +(-3.62450 - 6.27782i) q^{89} +(5.59895 - 3.69483i) q^{90} +(2.88363 - 1.66486i) q^{91} +(3.14511 - 5.44749i) q^{92} +(11.2275 - 9.05410i) q^{93} -9.25839i q^{94} +(4.56075 - 8.61392i) q^{95} +(1.61574 + 0.623997i) q^{96} +(5.42307 - 9.39303i) q^{97} +(-4.45118 - 2.56989i) q^{98} +(-14.8589 - 3.22153i) 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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