LMFDB - Embedded newform 570.2.s.b.221.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(221,570)]

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, 0, 5]))

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

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

chi := DirichletCharacter("570.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.s (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:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			221.7
Character	$\chi$	$=$	570.221
Dual form			570.2.s.b.521.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.708367 + 1.58057i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-1.01463 + 1.40375i) q^{6} +2.73284 q^{7} -1.00000 q^{8} +(-1.99643 + 2.23925i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.708367 + 1.58057i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-1.01463 + 1.40375i) q^{6} +2.73284 q^{7} -1.00000 q^{8} +(-1.99643 + 2.23925i) q^{9} +(0.866025 + 0.500000i) q^{10} -0.361598i q^{11} +(-1.72300 - 0.176823i) q^{12} +(2.32225 + 1.34075i) q^{13} +(1.36642 + 2.36671i) q^{14} +(1.40375 + 1.01463i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.37205 + 0.792151i) q^{17} +(-2.93747 - 0.609333i) q^{18} +(2.26593 + 3.72365i) q^{19} +1.00000i q^{20} +(1.93585 + 4.31946i) q^{21} +(0.313153 - 0.180799i) q^{22} +(-3.44153 - 1.98697i) q^{23} +(-0.708367 - 1.58057i) q^{24} +(0.500000 - 0.866025i) q^{25} +2.68150i q^{26} +(-4.95352 - 1.56929i) q^{27} +(-1.36642 + 2.36671i) q^{28} +(-1.24989 + 2.16488i) q^{29} +(-0.176823 + 1.72300i) q^{30} -5.44068i q^{31} +(0.500000 - 0.866025i) q^{32} +(0.571532 - 0.256144i) q^{33} +(-1.37205 - 0.792151i) q^{34} +(2.36671 - 1.36642i) q^{35} +(-0.941036 - 2.84859i) q^{36} -7.93595i q^{37} +(-2.09181 + 3.82417i) q^{38} +(-0.474151 + 4.62022i) q^{39} +(-0.866025 + 0.500000i) q^{40} +(2.12250 + 3.67627i) q^{41} +(-2.77283 + 3.83623i) q^{42} +(1.23694 + 2.14245i) q^{43} +(0.313153 + 0.180799i) q^{44} +(-0.609333 + 2.93747i) q^{45} -3.97393i q^{46} +(-6.62319 - 3.82390i) q^{47} +(1.01463 - 1.40375i) q^{48} +0.468410 q^{49} +1.00000 q^{50} +(-2.22397 - 1.60749i) q^{51} +(-2.32225 + 1.34075i) q^{52} +(1.37459 - 2.38085i) q^{53} +(-1.11771 - 5.07452i) q^{54} +(-0.180799 - 0.313153i) q^{55} -2.73284 q^{56} +(-4.28040 + 6.21918i) q^{57} -2.49978 q^{58} +(1.56849 + 2.71671i) q^{59} +(-1.58057 + 0.708367i) q^{60} +(3.73492 - 6.46907i) q^{61} +(4.71176 - 2.72034i) q^{62} +(-5.45593 + 6.11952i) q^{63} +1.00000 q^{64} +2.68150 q^{65} +(0.507593 + 0.366889i) q^{66} +(-0.731797 - 0.422503i) q^{67} -1.58430i q^{68} +(0.702683 - 6.84709i) q^{69} +(2.36671 + 1.36642i) q^{70} +(-4.22259 - 7.31374i) q^{71} +(1.99643 - 2.23925i) q^{72} +(6.07501 + 10.5222i) q^{73} +(6.87273 - 3.96797i) q^{74} +(1.72300 + 0.176823i) q^{75} +(-4.35774 + 0.100523i) q^{76} -0.988188i q^{77} +(-4.23831 + 1.89949i) q^{78} +(3.57112 - 2.06179i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(-1.02852 - 8.94104i) q^{81} +(-2.12250 + 3.67627i) q^{82} +0.651818i q^{83} +(-4.70869 - 0.483229i) q^{84} +(-0.792151 + 1.37205i) q^{85} +(-1.23694 + 2.14245i) q^{86} +(-4.30713 - 0.442019i) q^{87} +0.361598i q^{88} +(5.47514 - 9.48321i) q^{89} +(-2.84859 + 0.941036i) q^{90} +(6.34632 + 3.66405i) q^{91} +(3.44153 - 1.98697i) q^{92} +(8.59939 - 3.85400i) q^{93} -7.64780i q^{94} +(3.82417 + 2.09181i) q^{95} +(1.72300 + 0.176823i) q^{96} +(15.3033 - 8.83538i) q^{97} +(0.234205 + 0.405655i) q^{98} +(0.809709 + 0.721905i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 q^{9}+O(q^{10}) $ 24 * q + 12 * q^2 + 2 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^7 - 24 * q^8 + 2 * q^9	$ 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 q^{9} + 2 q^{12} + 18 q^{13} - 6 q^{14} - 12 q^{16} - 12 q^{17} - 2 q^{18} + 6 q^{19} + 6 q^{21} + 18 q^{22} - 2 q^{24} + 12 q^{25} - 28 q^{27} + 6 q^{28} + 12 q^{32} - 8 q^{33} - 12 q^{34} - 4 q^{36} - 6 q^{38} + 40 q^{39} - 6 q^{41} - 6 q^{42} - 22 q^{43} + 18 q^{44} + 8 q^{45} - 12 q^{47} - 4 q^{48} + 12 q^{49} + 24 q^{50} - 4 q^{51} - 18 q^{52} - 8 q^{53} - 32 q^{54} + 12 q^{56} - 20 q^{57} - 26 q^{59} + 22 q^{61} + 18 q^{62} + 30 q^{63} + 24 q^{64} - 8 q^{65} - 22 q^{66} - 48 q^{67} + 64 q^{69} - 24 q^{71} - 2 q^{72} - 8 q^{73} - 30 q^{74} - 2 q^{75} - 12 q^{76} + 2 q^{78} + 18 q^{79} - 6 q^{81} + 6 q^{82} - 12 q^{84} + 22 q^{86} - 24 q^{87} - 28 q^{89} + 16 q^{90} + 18 q^{91} + 14 q^{93} - 2 q^{96} + 6 q^{97} + 6 q^{98} - 52 q^{99}+O(q^{100}) $ 24 * q + 12 * q^2 + 2 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^7 - 24 * q^8 + 2 * q^9 + 2 * q^12 + 18 * q^13 - 6 * q^14 - 12 * q^16 - 12 * q^17 - 2 * q^18 + 6 * q^19 + 6 * q^21 + 18 * q^22 - 2 * q^24 + 12 * q^25 - 28 * q^27 + 6 * q^28 + 12 * q^32 - 8 * q^33 - 12 * q^34 - 4 * q^36 - 6 * q^38 + 40 * q^39 - 6 * q^41 - 6 * q^42 - 22 * q^43 + 18 * q^44 + 8 * q^45 - 12 * q^47 - 4 * q^48 + 12 * q^49 + 24 * q^50 - 4 * q^51 - 18 * q^52 - 8 * q^53 - 32 * q^54 + 12 * q^56 - 20 * q^57 - 26 * q^59 + 22 * q^61 + 18 * q^62 + 30 * q^63 + 24 * q^64 - 8 * q^65 - 22 * q^66 - 48 * q^67 + 64 * q^69 - 24 * q^71 - 2 * q^72 - 8 * q^73 - 30 * q^74 - 2 * q^75 - 12 * q^76 + 2 * q^78 + 18 * q^79 - 6 * q^81 + 6 * q^82 - 12 * q^84 + 22 * q^86 - 24 * q^87 - 28 * q^89 + 16 * q^90 + 18 * q^91 + 14 * q^93 - 2 * q^96 + 6 * q^97 + 6 * q^98 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	0.708367	+	1.58057i	0.408976	+	0.912545i
$3$	0.708367	+	1.58057i	0.408976	+	0.912545i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$	−1.01463	+	1.40375i	−0.414223	+	0.573079i
$7$	2.73284			1.03292			0.516458	−	0.856312i	$-0.327250\pi$
$7$	2.73284			1.03292			0.516458	+	0.856312i	$0.327250\pi$
$8$	−1.00000			−0.353553
$9$	−1.99643	+	2.23925i	−0.665477	+	0.746418i
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$		−	0.361598i		−	0.109026i	−0.998513	−	0.0545129i	$-0.982639\pi$
$11$		−	0.361598i		−	0.109026i	0.998513	−	0.0545129i	$-0.0173606\pi$
$12$	−1.72300	−	0.176823i	−0.497388	−	0.0510444i
$13$	2.32225	+	1.34075i	0.644075	+	0.371857i	0.786183	−	0.617994i	$-0.212055\pi$
$13$	2.32225	+	1.34075i	0.644075	+	0.371857i	−0.142108	+	0.989851i	$0.545388\pi$
$14$	1.36642	+	2.36671i	0.365191	+	0.632529i
$15$	1.40375	+	1.01463i	0.362447	+	0.261977i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.37205	+	0.792151i	−0.332770	+	0.192125i	−0.657070	−	0.753829i	$-0.728205\pi$
$17$	−1.37205	+	0.792151i	−0.332770	+	0.192125i	0.324300	+	0.945954i	$0.394871\pi$
$18$	−2.93747	−	0.609333i	−0.692368	−	0.143621i
$19$	2.26593	+	3.72365i	0.519839	+	0.854264i
$19$	2.26593	+	3.72365i	0.519839	+	0.854264i
$20$			1.00000i			0.223607i
$21$	1.93585	+	4.31946i	0.422438	+	0.942583i
$22$	0.313153	−	0.180799i	0.0667644	−	0.0385464i
$23$	−3.44153	−	1.98697i	−0.717608	−	0.414311i	0.0962636	−	0.995356i	$-0.469311\pi$
$23$	−3.44153	−	1.98697i	−0.717608	−	0.414311i	−0.813872	+	0.581045i	$0.802644\pi$
$24$	−0.708367	−	1.58057i	−0.144595	−	0.322633i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$			2.68150i			0.525885i
$27$	−4.95352	−	1.56929i	−0.953305	−	0.302011i
$28$	−1.36642	+	2.36671i	−0.258229	+	0.447266i
$29$	−1.24989	+	2.16488i	−0.232099	+	0.402007i	−0.958426	−	0.285342i	$-0.907893\pi$
$29$	−1.24989	+	2.16488i	−0.232099	+	0.402007i	0.726327	+	0.687350i	$0.241226\pi$
$30$	−0.176823	+	1.72300i	−0.0322833	+	0.314576i
$31$		−	5.44068i		−	0.977174i	−0.872515	−	0.488587i	$-0.837512\pi$
$31$		−	5.44068i		−	0.977174i	0.872515	−	0.488587i	$-0.162488\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	0.571532	−	0.256144i	0.0994909	−	0.0445889i
$34$	−1.37205	−	0.792151i	−0.235304	−	0.135853i
$35$	2.36671	−	1.36642i	0.400047	−	0.230967i
$36$	−0.941036	−	2.84859i	−0.156839	−	0.474765i
$37$		−	7.93595i		−	1.30466i	−0.757934	−	0.652331i	$-0.773791\pi$
$37$		−	7.93595i		−	1.30466i	0.757934	−	0.652331i	$-0.226209\pi$
$38$	−2.09181	+	3.82417i	−0.339337	+	0.620363i
$39$	−0.474151	+	4.62022i	−0.0759249	+	0.739828i
$40$	−0.866025	+	0.500000i	−0.136931	+	0.0790569i
$41$	2.12250	+	3.67627i	0.331478	+	0.574137i	0.982802	−	0.184663i	$-0.0591193\pi$
$41$	2.12250	+	3.67627i	0.331478	+	0.574137i	−0.651324	+	0.758800i	$0.725786\pi$
$42$	−2.77283	+	3.83623i	−0.427857	+	0.591943i
$43$	1.23694	+	2.14245i	0.188632	+	0.326720i	0.944794	−	0.327664i	$-0.106261\pi$
$43$	1.23694	+	2.14245i	0.188632	+	0.326720i	−0.756162	+	0.654384i	$0.772928\pi$
$44$	0.313153	+	0.180799i	0.0472095	+	0.0272564i
$45$	−0.609333	+	2.93747i	−0.0908340	+	0.437892i
$46$		−	3.97393i		−	0.585925i
$47$	−6.62319	−	3.82390i	−0.966092	−	0.557773i	−0.0680494	−	0.997682i	$-0.521678\pi$
$47$	−6.62319	−	3.82390i	−0.966092	−	0.557773i	−0.898043	+	0.439908i	$0.855011\pi$
$48$	1.01463	−	1.40375i	0.146450	−	0.202614i
$49$	0.468410			0.0669158
$50$	1.00000			0.141421
$51$	−2.22397	−	1.60749i	−0.311417	−	0.225093i
$52$	−2.32225	+	1.34075i	−0.322037	+	0.185928i
$53$	1.37459	−	2.38085i	0.188814	−	0.327035i	−0.756041	−	0.654524i	$-0.772869\pi$
$53$	1.37459	−	2.38085i	0.188814	−	0.327035i	0.944855	+	0.327489i	$0.106202\pi$
$54$	−1.11771	−	5.07452i	−0.152101	−	0.690554i
$55$	−0.180799	−	0.313153i	−0.0243789	−	0.0422255i
$56$	−2.73284			−0.365191
$57$	−4.28040	+	6.21918i	−0.566953	+	0.823750i
$58$	−2.49978			−0.328238
$59$	1.56849	+	2.71671i	0.204200	+	0.353685i	0.949878	−	0.312622i	$-0.101207\pi$
$59$	1.56849	+	2.71671i	0.204200	+	0.353685i	−0.745677	+	0.666307i	$0.767874\pi$
$60$	−1.58057	+	0.708367i	−0.204051	+	0.0914498i
$61$	3.73492	−	6.46907i	0.478208	−	0.828280i	−0.521480	−	0.853263i	$-0.674620\pi$
$61$	3.73492	−	6.46907i	0.478208	−	0.828280i	0.999688	+	0.0249834i	$0.00795330\pi$
$62$	4.71176	−	2.72034i	0.598395	−	0.345483i
$63$	−5.45593	+	6.11952i	−0.687382	+	0.770987i
$64$	1.00000			0.125000
$65$	2.68150			0.332599
$66$	0.507593	+	0.366889i	0.0624804	+	0.0451609i
$67$	−0.731797	−	0.422503i	−0.0894032	−	0.0516170i	0.454632	−	0.890679i	$-0.349771\pi$
$67$	−0.731797	−	0.422503i	−0.0894032	−	0.0516170i	−0.544035	+	0.839062i	$0.683104\pi$
$68$		−	1.58430i		−	0.192125i
$69$	0.702683	−	6.84709i	0.0845931	−	0.824293i
$70$	2.36671	+	1.36642i	0.282876	+	0.163318i
$71$	−4.22259	−	7.31374i	−0.501129	−	0.867981i	−0.999999	−	0.00130440i	$-0.999585\pi$
$71$	−4.22259	−	7.31374i	−0.501129	−	0.867981i	0.498870	−	0.866677i	$-0.333749\pi$
$72$	1.99643	−	2.23925i	0.235282	−	0.263899i
$73$	6.07501	+	10.5222i	0.711026	+	1.23153i	0.964472	+	0.264184i	$0.0851025\pi$
$73$	6.07501	+	10.5222i	0.711026	+	1.23153i	−0.253447	+	0.967349i	$0.581564\pi$
$74$	6.87273	−	3.96797i	0.798939	−	0.461268i
$75$	1.72300	+	0.176823i	0.198955	+	0.0204178i
$76$	−4.35774	+	0.100523i	−0.499867	+	0.0115308i
$77$		−	0.988188i		−	0.112614i
$78$	−4.23831	+	1.89949i	−0.479894	+	0.215074i
$79$	3.57112	−	2.06179i	0.401783	−	0.231969i	−0.285470	−	0.958388i	$-0.592150\pi$
$79$	3.57112	−	2.06179i	0.401783	−	0.231969i	0.687253	+	0.726418i	$0.258816\pi$
$80$	−0.866025	−	0.500000i	−0.0968246	−	0.0559017i
$81$	−1.02852	−	8.94104i	−0.114280	−	0.993449i
$82$	−2.12250	+	3.67627i	−0.234391	+	0.405976i
$83$			0.651818i			0.0715463i	0.999360	+	0.0357732i	$0.0113894\pi$
$83$			0.651818i			0.0715463i	−0.999360	+	0.0357732i	$0.988611\pi$
$84$	−4.70869	−	0.483229i	−0.513760	−	0.0527246i
$85$	−0.792151	+	1.37205i	−0.0859208	+	0.148819i
$86$	−1.23694	+	2.14245i	−0.133383	+	0.231026i
$87$	−4.30713	−	0.442019i	−0.461773	−	0.0473895i
$88$			0.361598i			0.0385464i
$89$	5.47514	−	9.48321i	0.580363	−	1.00522i	−0.415073	−	0.909788i	$-0.636244\pi$
$89$	5.47514	−	9.48321i	0.580363	−	1.00522i	0.995436	−	0.0954304i	$-0.0304227\pi$
$90$	−2.84859	+	0.941036i	−0.300268	+	0.0991939i
$91$	6.34632	+	3.66405i	0.665275	+	0.384097i
$92$	3.44153	−	1.98697i	0.358804	−	0.207156i
$93$	8.59939	−	3.85400i	0.891716	−	0.399641i
$94$		−	7.64780i		−	0.788811i
$95$	3.82417	+	2.09181i	0.392352	+	0.214616i
$96$	1.72300	+	0.176823i	0.175853	+	0.0180469i
$97$	15.3033	−	8.83538i	1.55382	−	0.897097i	0.555992	−	0.831187i	$-0.312338\pi$
$97$	15.3033	−	8.83538i	1.55382	−	0.897097i	0.997826	−	0.0659098i	$-0.0209950\pi$
$98$	0.234205	+	0.405655i	0.0236583	+	0.0409774i
$99$	0.809709	+	0.721905i	0.0813788	+	0.0725542i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−0.597354	−	0.344883i	−0.0594390	−	0.0343171i	0.469986	−	0.882674i	$-0.344259\pi$
$101$	−0.597354	−	0.344883i	−0.0594390	−	0.0343171i	−0.529425	+	0.848357i	$0.677592\pi$
$102$	0.280141	−	2.72975i	0.0277381	−	0.270286i
$103$			15.3946i			1.51688i	0.651744	+	0.758439i	$0.274038\pi$
$103$			15.3946i			1.51688i	−0.651744	+	0.758439i	$0.725962\pi$
$104$	−2.32225	−	1.34075i	−0.227715	−	0.131471i
$105$	3.83623	+	2.77283i	0.374377	+	0.270601i
$106$	2.74917			0.267023
$107$	−0.902808			−0.0872778			−0.0436389	−	0.999047i	$-0.513895\pi$
$107$	−0.902808			−0.0872778			−0.0436389	+	0.999047i	$0.513895\pi$
$108$	3.83581	−	3.50522i	0.369101	−	0.337290i
$109$	8.27239	−	4.77607i	0.792351	−	0.457464i	−0.0484384	−	0.998826i	$-0.515424\pi$
$109$	8.27239	−	4.77607i	0.792351	−	0.457464i	0.840790	+	0.541362i	$0.182091\pi$
$110$	0.180799	−	0.313153i	0.0172385	−	0.0298579i
$111$	12.5434	−	5.62157i	1.19056	−	0.533575i
$112$	−1.36642	−	2.36671i	−0.129115	−	0.223633i
$113$	−18.0868			−1.70146			−0.850731	−	0.525602i	$-0.823840\pi$
$113$	−18.0868			−1.70146			−0.850731	+	0.525602i	$0.823840\pi$
$114$	−7.52617	−	0.597347i	−0.704890	−	0.0559467i
$115$	−3.97393			−0.370571
$116$	−1.24989	−	2.16488i	−0.116050	−	0.201004i
$117$	−7.63848	+	2.52339i	−0.706178	+	0.233287i
$118$	−1.56849	+	2.71671i	−0.144391	+	0.250093i
$119$	−3.74958	+	2.16482i	−0.343723	+	0.198449i
$120$	−1.40375	−	1.01463i	−0.128144	−	0.0926230i
$121$	10.8692			0.988113
$122$	7.46984			0.676288
$123$	−4.30712	+	5.95892i	−0.388360	+	0.537297i
$124$	4.71176	+	2.72034i	0.423129	+	0.244294i
$125$		−	1.00000i		−	0.0894427i
$126$	−8.02763	−	1.66521i	−0.715158	−	0.148349i
$127$	−3.08394	−	1.78051i	−0.273655	−	0.157995i	0.356892	−	0.934145i	$-0.383836\pi$
$127$	−3.08394	−	1.78051i	−0.273655	−	0.157995i	−0.630548	+	0.776151i	$0.717170\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−2.51009	+	3.47272i	−0.221001	+	0.305756i
$130$	1.34075	+	2.32225i	0.117591	+	0.203674i
$131$	4.10014	−	2.36722i	0.358231	−	0.206825i	−0.310073	−	0.950713i	$-0.600354\pi$
$131$	4.10014	−	2.36722i	0.358231	−	0.206825i	0.668305	+	0.743888i	$0.267020\pi$
$132$	−0.0639388	+	0.623033i	−0.00556516	+	0.0542281i
$133$	6.19241	+	10.1761i	0.536950	+	0.882383i
$134$		−	0.845006i		−	0.0729974i
$135$	−5.07452	+	1.11771i	−0.436745	+	0.0961971i
$136$	1.37205	−	0.792151i	0.117652	−	0.0679264i
$137$	4.07740	+	2.35409i	0.348356	+	0.201123i	0.663961	−	0.747767i	$-0.268874\pi$
$137$	4.07740	+	2.35409i	0.348356	+	0.201123i	−0.315605	+	0.948891i	$0.602207\pi$
$138$	6.28110	−	2.81500i	0.534683	−	0.239629i
$139$	−7.46724	+	12.9336i	−0.633363	+	1.09702i	0.353497	+	0.935436i	$0.384993\pi$
$139$	−7.46724	+	12.9336i	−0.633363	+	1.09702i	−0.986860	+	0.161581i	$0.948341\pi$
$140$			2.73284i			0.230967i
$141$	1.35231	−	13.1772i	0.113885	−	1.10972i
$142$	4.22259	−	7.31374i	0.354352	−	0.613755i
$143$	0.484812	−	0.839718i	0.0405420	−	0.0702208i
$144$	2.93747	+	0.609333i	0.244789	+	0.0507777i
$145$			2.49978i			0.207596i
$146$	−6.07501	+	10.5222i	−0.502771	+	0.870825i
$147$	0.331807	+	0.740357i	0.0273669	+	0.0610636i
$148$	6.87273	+	3.96797i	0.564935	+	0.326165i
$149$	19.6035	−	11.3181i	1.60598	−	0.927215i	0.615726	−	0.787960i	$-0.288863\pi$
$149$	19.6035	−	11.3181i	1.60598	−	0.927215i	0.990257	−	0.139254i	$-0.0444706\pi$
$150$	0.708367	+	1.58057i	0.0578380	+	0.129053i
$151$		−	3.63440i		−	0.295763i	−0.989005	−	0.147882i	$-0.952755\pi$
$151$		−	3.63440i		−	0.295763i	0.989005	−	0.147882i	$-0.0472455\pi$
$152$	−2.26593	−	3.72365i	−0.183791	−	0.302028i
$153$	0.965367	−	4.65383i	0.0780453	−	0.376240i
$154$	0.855796	−	0.494094i	0.0689620	−	0.0398152i
$155$	−2.72034	−	4.71176i	−0.218503	−	0.378458i
$156$	−3.76416	−	2.72074i	−0.301374	−	0.217833i
$157$	−6.76442	−	11.7163i	−0.539859	−	0.935064i	−0.998911	−	0.0466542i	$-0.985144\pi$
$157$	−6.76442	−	11.7163i	−0.539859	−	0.935064i	0.459052	−	0.888410i	$-0.348189\pi$
$158$	3.57112	+	2.06179i	0.284103	+	0.164027i
$159$	4.73683	+	0.486117i	0.375655	+	0.0385516i
$160$		−	1.00000i		−	0.0790569i
$161$	−9.40514	−	5.43006i	−0.741229	−	0.427949i
$162$	7.22890	−	5.36125i	0.567956	−	0.421219i
$163$	−18.9557			−1.48472			−0.742361	−	0.670000i	$-0.766294\pi$
$163$	−18.9557			−1.48472			−0.742361	+	0.670000i	$0.766294\pi$
$164$	−4.24499			−0.331478
$165$	0.366889	−	0.507593i	0.0285623	−	0.0395161i
$166$	−0.564491	+	0.325909i	−0.0438130	+	0.0252954i
$167$	2.66087	−	4.60877i	0.205905	−	0.356637i	−0.744516	−	0.667605i	$-0.767320\pi$
$167$	2.66087	−	4.60877i	0.205905	−	0.356637i	0.950421	+	0.310967i	$0.100653\pi$
$168$	−1.93585	−	4.31946i	−0.149354	−	0.333253i
$169$	−2.90478	−	5.03123i	−0.223445	−	0.387018i
$170$	−1.58430			−0.121510
$171$	−12.8620	−	2.36003i	−0.983579	−	0.180476i
$172$	−2.47389			−0.188632
$173$	5.01989	+	8.69470i	0.381655	+	0.661046i	0.991299	−	0.131630i	$-0.0420209\pi$
$173$	5.01989	+	8.69470i	0.381655	+	0.661046i	−0.609644	+	0.792675i	$0.708688\pi$
$174$	−1.77076	−	3.95109i	−0.134241	−	0.299532i
$175$	1.36642	−	2.36671i	0.103292	−	0.178906i
$176$	−0.313153	+	0.180799i	−0.0236048	+	0.0136282i
$177$	−3.18289	+	4.40355i	−0.239241	+	0.330991i
$178$	10.9503			0.820757
$179$	6.28120			0.469479			0.234739	−	0.972058i	$-0.424576\pi$
$179$	6.28120			0.469479			0.234739	+	0.972058i	$0.424576\pi$
$180$	−2.23925	−	1.99643i	−0.166904	−	0.148805i
$181$	−21.3026	−	12.2990i	−1.58341	−	0.914180i	−0.994357	−	0.106083i	$-0.966169\pi$
$181$	−21.3026	−	12.2990i	−1.58341	−	0.914180i	−0.589049	−	0.808097i	$-0.700498\pi$
$182$			7.32810i			0.543195i
$183$	12.8705	+	1.32084i	0.951418	+	0.0976394i
$184$	3.44153	+	1.98697i	0.253713	+	0.146481i
$185$	−3.96797	−	6.87273i	−0.291731	−	0.505293i
$186$	7.63736	+	5.52029i	0.559998	+	0.404768i
$187$	0.286440	+	0.496128i	0.0209466	+	0.0362805i
$188$	6.62319	−	3.82390i	0.483046	−	0.278887i
$189$	−13.5372	−	4.28863i	−0.984684	−	0.311952i
$190$	0.100523	+	4.35774i	0.00729274	+	0.316144i
$191$		−	25.6046i		−	1.85268i	−0.376683	−	0.926342i	$-0.622935\pi$
$191$		−	25.6046i		−	1.85268i	0.376683	−	0.926342i	$-0.377065\pi$
$192$	0.708367	+	1.58057i	0.0511220	+	0.114068i
$193$	2.59120	−	1.49603i	0.186519	−	0.107687i	−0.403833	−	0.914833i	$-0.632322\pi$
$193$	2.59120	−	1.49603i	0.186519	−	0.107687i	0.590352	+	0.807146i	$0.298989\pi$
$194$	15.3033	+	8.83538i	1.09872	+	0.634344i
$195$	1.89949	+	4.23831i	0.136025	+	0.303511i
$196$	−0.234205	+	0.405655i	−0.0167289	+	0.0289754i
$197$			17.7186i			1.26240i	0.775620	+	0.631201i	$0.217438\pi$
$197$			17.7186i			1.26240i	−0.775620	+	0.631201i	$0.782562\pi$
$198$	−0.220333	+	1.06218i	−0.0156584	+	0.0754859i
$199$	−10.2862	+	17.8162i	−0.729170	+	1.26296i	0.228065	+	0.973646i	$0.426760\pi$
$199$	−10.2862	+	17.8162i	−0.729170	+	1.26296i	−0.957235	+	0.289313i	$0.906573\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	0.149417	−	1.45595i	0.0105390	−	0.102695i
$202$		−	0.689765i		−	0.0485317i
$203$	−3.41575	+	5.91626i	−0.239739	+	0.415240i
$204$	2.50411	−	1.12227i	0.175323	−	0.0785744i
$205$	3.67627	+	2.12250i	0.256762	+	0.148242i
$206$	−13.3321	+	7.69731i	−0.928894	+	0.536297i
$207$	11.3201	−	3.73961i	0.786801	−	0.259921i
$208$		−	2.68150i		−	0.185928i
$209$	1.34646	−	0.819353i	0.0931368	−	0.0566758i
$210$	−0.483229	+	4.70869i	−0.0333460	+	0.324930i
$211$	0.240924	−	0.139098i	0.0165859	−	0.00957587i	−0.491684	−	0.870774i	$-0.663619\pi$
$211$	0.240924	−	0.139098i	0.0165859	−	0.00957587i	0.508270	+	0.861198i	$0.330285\pi$
$212$	1.37459	+	2.38085i	0.0944069	+	0.163518i
$213$	8.56877	−	11.8549i	0.587122	−	0.812287i
$214$	−0.451404	−	0.781855i	−0.0308573	−	0.0534465i
$215$	2.14245	+	1.23694i	0.146114	+	0.0843588i
$216$	4.95352	+	1.56929i	0.337044	+	0.106777i
$217$		−	14.8685i		−	1.00934i
$218$	8.27239	+	4.77607i	0.560277	+	0.323476i
$219$	−12.3278	+	17.0556i	−0.833037	+	1.15251i
$220$	0.361598			0.0243789
$221$	−4.24830			−0.285772
$222$	11.1401	+	8.05208i	0.747674	+	0.540420i
$223$	4.55894	−	2.63211i	0.305290	−	0.176259i	−0.339527	−	0.940596i	$-0.610267\pi$
$223$	4.55894	−	2.63211i	0.305290	−	0.176259i	0.644817	+	0.764337i	$0.276934\pi$
$224$	1.36642	−	2.36671i	0.0912978	−	0.158132i
$225$	0.941036	+	2.84859i	0.0627357	+	0.189906i
$226$	−9.04339	−	15.6636i	−0.601557	−	1.04193i
$227$	−18.1853			−1.20700			−0.603500	−	0.797363i	$-0.706227\pi$
$227$	−18.1853			−1.20700			−0.603500	+	0.797363i	$0.706227\pi$
$228$	−3.24577	−	6.81652i	−0.214956	−	0.451435i
$229$	−0.0923898			−0.00610529			−0.00305265	−	0.999995i	$-0.500972\pi$
$229$	−0.0923898			−0.00610529			−0.00305265	+	0.999995i	$0.500972\pi$
$230$	−1.98697	−	3.44153i	−0.131017	−	0.226928i
$231$	1.56190	−	0.700000i	0.102766	−	0.0460566i
$232$	1.24989	−	2.16488i	0.0820594	−	0.142131i
$233$	−12.3845	+	7.15019i	−0.811335	+	0.468425i	−0.847419	−	0.530924i	$-0.821845\pi$
$233$	−12.3845	+	7.15019i	−0.811335	+	0.468425i	0.0360842	+	0.999349i	$0.488512\pi$
$234$	−6.00456	−	5.35343i	−0.392530	−	0.349964i
$235$	−7.64780			−0.498888
$236$	−3.13699			−0.204200
$237$	5.78848	+	4.18392i	0.376002	+	0.271775i
$238$	−3.74958	−	2.16482i	−0.243049	−	0.140324i
$239$			26.1968i			1.69453i	0.531172	+	0.847264i	$0.321752\pi$
$239$			26.1968i			1.69453i	−0.531172	+	0.847264i	$0.678248\pi$
$240$	0.176823	−	1.72300i	0.0114139	−	0.111219i
$241$	−16.7185	−	9.65242i	−1.07693	−	0.621767i	−0.146865	−	0.989157i	$-0.546918\pi$
$241$	−16.7185	−	9.65242i	−1.07693	−	0.621767i	−0.930067	+	0.367390i	$0.880251\pi$
$242$	5.43462	+	9.41304i	0.349351	+	0.605093i
$243$	13.4034	−	7.95920i	0.859829	−	0.510583i
$244$	3.73492	+	6.46907i	0.239104	+	0.414140i
$245$	0.405655	−	0.234205i	0.0259164	−	0.0149628i
$246$	−7.31413	−	0.750613i	−0.466332	−	0.0478573i
$247$	0.269553	+	11.6853i	0.0171513	+	0.743516i
$248$			5.44068i			0.345483i
$249$	−1.03025	+	0.461727i	−0.0652892	+	0.0292607i
$250$	0.866025	−	0.500000i	0.0547723	−	0.0316228i
$251$	9.65147	+	5.57228i	0.609195	+	0.351719i	0.772650	−	0.634832i	$-0.218931\pi$
$251$	9.65147	+	5.57228i	0.609195	+	0.351719i	−0.163455	+	0.986551i	$0.552264\pi$
$252$	−2.57170	−	7.78473i	−0.162002	−	0.490392i
$253$	−0.718482	+	1.24445i	−0.0451706	+	0.0782378i
$254$		−	3.56102i		−	0.223438i
$255$	−2.72975	−	0.280141i	−0.170944	−	0.0175431i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.98490	+	6.90205i	−0.248571	+	0.430538i	−0.963130	−	0.269038i	$-0.913294\pi$
$257$	−3.98490	+	6.90205i	−0.248571	+	0.430538i	0.714558	+	0.699576i	$0.246628\pi$
$258$	−4.26251	−	0.437440i	−0.265372	−	0.0272338i
$259$		−	21.6877i		−	1.34761i
$260$	−1.34075	+	2.32225i	−0.0831497	+	0.144020i
$261$	−2.35238	−	7.12085i	−0.145609	−	0.440770i
$262$	4.10014	+	2.36722i	0.253308	+	0.146247i
$263$	−14.1470	+	8.16779i	−0.872343	+	0.503647i	−0.868126	−	0.496344i	$-0.834676\pi$
$263$	−14.1470	+	8.16779i	−0.872343	+	0.503647i	−0.00421689	+	0.999991i	$0.501342\pi$
$264$	−0.571532	+	0.256144i	−0.0351754	+	0.0157646i
$265$		−	2.74917i		−	0.168880i
$266$	−5.71659	+	10.4509i	−0.350507	+	0.640783i
$267$	18.8673	+	1.93626i	1.15466	+	0.118497i
$268$	0.731797	−	0.422503i	0.0447016	−	0.0258085i
$269$	−15.6050	−	27.0287i	−0.951456	−	1.64797i	−0.742277	−	0.670093i	$-0.766254\pi$
$269$	−15.6050	−	27.0287i	−0.951456	−	1.64797i	−0.209179	−	0.977877i	$-0.567079\pi$
$270$	−3.50522	−	3.83581i	−0.213321	−	0.233440i
$271$	15.8830	+	27.5101i	0.964823	+	1.67112i	0.710090	+	0.704111i	$0.248654\pi$
$271$	15.8830	+	27.5101i	0.964823	+	1.67112i	0.254733	+	0.967011i	$0.418012\pi$
$272$	1.37205	+	0.792151i	0.0831925	+	0.0480312i
$273$	−1.29578	+	12.6263i	−0.0784241	+	0.764180i
$274$			4.70818i			0.284431i
$275$	−0.313153	−	0.180799i	−0.0188838	−	0.0109026i
$276$	5.57841	+	4.03209i	0.335781	+	0.242703i
$277$	−20.8653			−1.25367			−0.626836	−	0.779151i	$-0.715651\pi$
$277$	−20.8653			−1.25367			−0.626836	+	0.779151i	$0.715651\pi$
$278$	−14.9345			−0.895710
$279$	12.1831	+	10.8619i	0.729381	+	0.650287i
$280$	−2.36671	+	1.36642i	−0.141438	+	0.0816592i
$281$	−0.194045	+	0.336095i	−0.0115757	+	0.0200498i	−0.871755	−	0.489942i	$-0.837018\pi$
$281$	−0.194045	+	0.336095i	−0.0115757	+	0.0200498i	0.860180	+	0.509991i	$0.170351\pi$
$282$	12.0879	−	5.41746i	0.719825	−	0.322605i
$283$	−10.8411	−	18.7773i	−0.644434	−	1.11619i	−0.984432	−	0.175767i	$-0.943760\pi$
$283$	−10.8411	−	18.7773i	−0.644434	−	1.11619i	0.339997	−	0.940426i	$-0.389574\pi$
$284$	8.44518			0.501129
$285$	−0.597347	+	7.52617i	−0.0353838	+	0.445812i
$286$	0.969623			0.0573350
$287$	5.80044	+	10.0467i	0.342389	+	0.593036i
$288$	0.941036	+	2.84859i	0.0554511	+	0.167855i
$289$	−7.24499	+	12.5487i	−0.426176	+	0.738159i
$290$	−2.16488	+	1.24989i	−0.127126	+	0.0733961i
$291$	24.8054	+	17.9294i	1.45412	+	1.05104i
$292$	−12.1500			−0.711026
$293$	32.2855			1.88614			0.943069	−	0.332596i	$-0.107924\pi$
$293$	32.2855			1.88614			0.943069	+	0.332596i	$0.107924\pi$
$294$	−0.475265	+	0.657532i	−0.0277180	+	0.0383480i
$295$	2.71671	+	1.56849i	0.158173	+	0.0913212i
$296$			7.93595i			0.461268i
$297$	−0.567453	+	1.79118i	−0.0329269	+	0.103935i
$298$	19.6035	+	11.3181i	1.13560	+	0.655640i
$299$	−5.32805	−	9.22845i	−0.308129	−	0.533695i
$300$	−1.01463	+	1.40375i	−0.0585799	+	0.0810456i
$301$	3.38037	+	5.85497i	0.194841	+	0.337475i
$302$	3.14748	−	1.81720i	0.181117	−	0.104568i
$303$	0.121966	−	1.18847i	0.00700679	−	0.0682756i
$304$	2.09181	−	3.82417i	0.119974	−	0.219331i
$305$		−	7.46984i		−	0.427722i
$306$	4.51302	−	1.49088i	0.257992	−	0.0852282i
$307$	−16.9205	+	9.76906i	−0.965705	+	0.557550i	−0.897924	−	0.440150i	$-0.854925\pi$
$307$	−16.9205	+	9.76906i	−0.965705	+	0.557550i	−0.0677805	+	0.997700i	$0.521592\pi$
$308$	0.855796	+	0.494094i	0.0487635	+	0.0281536i
$309$	−24.3324	+	10.9051i	−1.38422	+	0.620367i
$310$	2.72034	−	4.71176i	0.154505	−	0.267610i
$311$			30.7306i			1.74257i	0.490775	+	0.871287i	$0.336714\pi$
$311$			30.7306i			1.74257i	−0.490775	+	0.871287i	$0.663286\pi$
$312$	0.474151	−	4.62022i	0.0268435	−	0.261569i
$313$	−5.11644	+	8.86194i	−0.289198	+	0.500906i	−0.973619	−	0.228181i	$-0.926722\pi$
$313$	−5.11644	+	8.86194i	−0.289198	+	0.500906i	0.684420	+	0.729088i	$0.260055\pi$
$314$	6.76442	−	11.7163i	0.381738	−	0.661190i
$315$	−1.66521	+	8.02763i	−0.0938239	+	0.452305i
$316$			4.12358i			0.231969i
$317$	−0.252084	+	0.436622i	−0.0141584	+	0.0245231i	−0.873018	−	0.487688i	$-0.837840\pi$
$317$	−0.252084	+	0.436622i	−0.0141584	+	0.0245231i	0.858859	+	0.512211i	$0.171174\pi$
$318$	1.94742	+	4.34527i	0.109206	+	0.243671i
$319$	0.782814	+	0.451958i	0.0438291	+	0.0253048i
$320$	0.866025	−	0.500000i	0.0484123	−	0.0279508i
$321$	−0.639520	−	1.42696i	−0.0356945	−	0.0796449i
$322$		−	10.8601i		−	0.605211i
$323$	−6.05865	−	3.31406i	−0.337112	−	0.184399i
$324$	8.25743	+	3.57979i	0.458746	+	0.198877i
$325$	2.32225	−	1.34075i	0.128815	−	0.0743714i
$326$	−9.47783	−	16.4161i	−0.524929	−	0.909203i
$327$	13.4088	+	9.69192i	0.741509	+	0.535964i
$328$	−2.12250	−	3.67627i	−0.117195	−	0.202988i
$329$	−18.1001	−	10.4501i	−0.997892	−	0.576133i
$330$	0.623033	+	0.0639388i	0.0342968	+	0.00351972i
$331$		−	16.7161i		−	0.918800i	−0.888229	−	0.459400i	$-0.848064\pi$
$331$		−	16.7161i		−	0.918800i	0.888229	−	0.459400i	$-0.151936\pi$
$332$	−0.564491	−	0.325909i	−0.0309805	−	0.0178866i
$333$	17.7706	+	15.8436i	0.973823	+	0.868223i
$334$	5.32175			0.291193
$335$	−0.845006			−0.0461676
$336$	2.77283	−	3.83623i	0.151270	−	0.209283i
$337$	5.81314	−	3.35622i	0.316662	−	0.182825i	−0.333242	−	0.942841i	$-0.608143\pi$
$337$	5.81314	−	3.35622i	0.316662	−	0.182825i	0.649904	+	0.760017i	$0.274809\pi$
$338$	2.90478	−	5.03123i	0.157999	−	0.273663i
$339$	−12.8121	−	28.5875i	−0.695857	−	1.55266i
$340$	−0.792151	−	1.37205i	−0.0429604	−	0.0744096i
$341$	−1.96733			−0.106537
$342$	−4.38714	−	12.3188i	−0.237229	−	0.666125i
$343$	−17.8498			−0.963798
$344$	−1.23694	−	2.14245i	−0.0666915	−	0.115513i
$345$	−2.81500	−	6.28110i	−0.151555	−	0.338163i
$346$	−5.01989	+	8.69470i	−0.269871	+	0.467430i
$347$	−28.1207	+	16.2355i	−1.50960	+	0.871566i	−0.509660	+	0.860376i	$0.670229\pi$
$347$	−28.1207	+	16.2355i	−1.50960	+	0.871566i	−0.999937	+	0.0111900i	$0.996438\pi$
$348$	2.53636	−	3.50907i	0.135963	−	0.188106i
$349$	2.90700			0.155608			0.0778040	−	0.996969i	$-0.475209\pi$
$349$	2.90700			0.155608			0.0778040	+	0.996969i	$0.475209\pi$
$350$	2.73284			0.146076
$351$	−9.39925	−	10.2857i	−0.501695	−	0.549010i
$352$	−0.313153	−	0.180799i	−0.0166911	−	0.00963661i
$353$			10.7325i			0.571233i	0.958344	+	0.285616i	$0.0921983\pi$
$353$			10.7325i			0.571233i	−0.958344	+	0.285616i	$0.907802\pi$
$354$	−5.40503	−	0.554692i	−0.287274	−	0.0294815i
$355$	−7.31374	−	4.22259i	−0.388173	−	0.224112i
$356$	5.47514	+	9.48321i	0.290182	+	0.502609i
$357$	−6.07774	−	4.39300i	−0.321668	−	0.232502i
$358$	3.14060	+	5.43967i	0.165986	+	0.287496i
$359$	−1.09849	+	0.634215i	−0.0579762	+	0.0334726i	−0.528708	−	0.848804i	$-0.677323\pi$
$359$	−1.09849	+	0.634215i	−0.0579762	+	0.0334726i	0.470732	+	0.882276i	$0.343990\pi$
$360$	0.609333	−	2.93747i	0.0321147	−	0.154818i
$361$	−8.73116	+	16.8750i	−0.459535	+	0.888160i
$362$		−	24.5981i		−	1.29285i
$363$	7.69942	+	17.1797i	0.404115	+	0.901698i
$364$	−6.34632	+	3.66405i	−0.332638	+	0.192048i
$365$	10.5222	+	6.07501i	0.550758	+	0.317980i
$366$	5.29139	+	11.8066i	0.276586	+	0.617143i
$367$	−4.80585	+	8.32397i	−0.250863	+	0.434508i	−0.963764	−	0.266757i	$-0.914048\pi$
$367$	−4.80585	+	8.32397i	−0.250863	+	0.434508i	0.712900	+	0.701265i	$0.247381\pi$
$368$			3.97393i			0.207156i
$369$	−12.4695	−	2.58661i	−0.649138	−	0.134654i
$370$	3.96797	−	6.87273i	0.206285	−	0.357296i
$371$	3.75652	−	6.50649i	0.195029	−	0.337800i
$372$	−0.962037	+	9.37429i	−0.0498793	+	0.486034i
$373$		−	13.3101i		−	0.689173i	−0.938755	−	0.344586i	$-0.888019\pi$
$373$		−	13.3101i		−	0.689173i	0.938755	−	0.344586i	$-0.111981\pi$
$374$	−0.286440	+	0.496128i	−0.0148114	+	0.0256542i
$375$	1.58057	−	0.708367i	0.0816205	−	0.0365799i
$376$	6.62319	+	3.82390i	0.341565	+	0.197203i
$377$	−5.80511	+	3.35158i	−0.298978	+	0.172615i
$378$	−3.05452	−	13.8678i	−0.157108	−	0.713285i
$379$			6.83849i			0.351270i	0.984455	+	0.175635i	$0.0561978\pi$
$379$			6.83849i			0.351270i	−0.984455	+	0.175635i	$0.943802\pi$
$380$	−3.72365	+	2.26593i	−0.191019	+	0.116240i
$381$	0.629671	−	6.13565i	0.0322590	−	0.314339i
$382$	22.1742	−	12.8023i	1.13453	−	0.655023i
$383$	−10.2329	−	17.7238i	−0.522874	−	0.905645i	−0.999646	−	0.0266177i	$-0.991526\pi$
$383$	−10.2329	−	17.7238i	−0.522874	−	0.905645i	0.476771	−	0.879027i	$-0.341807\pi$
$384$	−1.01463	+	1.40375i	−0.0517778	+	0.0716349i
$385$	−0.494094	−	0.855796i	−0.0251814	−	0.0436154i
$386$	2.59120	+	1.49603i	0.131889	+	0.0761460i
$387$	−7.26696	−	1.50742i	−0.369400	−	0.0766265i
$388$			17.6708i			0.897097i
$389$	9.69169	+	5.59550i	0.491388	+	0.283703i	0.725150	−	0.688591i	$-0.241770\pi$
$389$	9.69169	+	5.59550i	0.491388	+	0.283703i	−0.233762	+	0.972294i	$0.575104\pi$
$390$	−2.72074	+	3.76416i	−0.137770	+	0.190605i
$391$	6.29591			0.318398
$392$	−0.468410			−0.0236583
$393$	6.64598	+	4.80372i	0.335245	+	0.242316i
$394$	−15.3448	+	8.85932i	−0.773060	+	0.446326i
$395$	2.06179	−	3.57112i	0.103740	−	0.179683i
$396$	−1.03004	+	0.340276i	−0.0517616	+	0.0170995i
$397$	19.4671	+	33.7181i	0.977028	+	1.69226i	0.673074	+	0.739575i	$0.264973\pi$
$397$	19.4671	+	33.7181i	0.977028	+	1.69226i	0.303953	+	0.952687i	$0.401693\pi$
$398$	−20.5724			−1.03120
$399$	−11.6976	+	16.9960i	−0.585615	+	0.850865i
$400$	−1.00000			−0.0500000
$401$	14.6051	+	25.2968i	0.729345	+	1.26326i	0.957160	+	0.289559i	$0.0935085\pi$
$401$	14.6051	+	25.2968i	0.729345	+	1.26326i	−0.227815	+	0.973704i	$0.573158\pi$
$402$	1.33560	−	0.598575i	0.0666134	−	0.0298542i
$403$	7.29458	−	12.6346i	0.363369	−	0.629373i
$404$	0.597354	−	0.344883i	0.0297195	−	0.0171586i
$405$	−5.36125	−	7.22890i	−0.266402	−	0.359207i
$406$	−6.83150			−0.339042
$407$	−2.86962			−0.142242
$408$	2.22397	+	1.60749i	0.110103	+	0.0795824i
$409$	−13.1471	−	7.59047i	−0.650081	−	0.375325i	0.138406	−	0.990376i	$-0.455802\pi$
$409$	−13.1471	−	7.59047i	−0.650081	−	0.375325i	−0.788487	+	0.615051i	$0.789135\pi$
$410$			4.24499i			0.209645i
$411$	−0.832515	+	8.11220i	−0.0410649	+	0.400145i
$412$	−13.3321	−	7.69731i	−0.656827	−	0.379219i
$413$	4.28644	+	7.42433i	0.210922	+	0.365327i
$414$	8.89865	+	7.93369i	0.437345	+	0.389919i
$415$	0.325909	+	0.564491i	0.0159982	+	0.0277098i
$416$	2.32225	−	1.34075i	0.113857	−	0.0657356i
$417$	−25.7321	−	2.64076i	−1.26011	−	0.129319i
$418$	1.38281	+	0.756395i	0.0676356	+	0.0369965i
$419$		−	18.6245i		−	0.909864i	−0.890526	−	0.454932i	$-0.849663\pi$
$419$		−	18.6245i		−	0.909864i	0.890526	−	0.454932i	$-0.150337\pi$
$420$	−4.31946	+	1.93585i	−0.210768	+	0.0944600i
$421$	0.995150	−	0.574550i	0.0485006	−	0.0280019i	−0.475554	−	0.879687i	$-0.657752\pi$
$421$	0.995150	−	0.574550i	0.0485006	−	0.0280019i	0.524054	+	0.851685i	$0.324419\pi$
$422$	0.240924	+	0.139098i	0.0117280	+	0.00677117i
$423$	21.7854	−	7.19686i	1.05924	−	0.349923i
$424$	−1.37459	+	2.38085i	−0.0667558	+	0.115624i
$425$			1.58430i			0.0768499i
$426$	14.5511	+	1.49330i	0.705001	+	0.0723508i
$427$	10.2069	−	17.6789i	0.493948	−	0.855544i
$428$	0.451404	−	0.781855i	0.0218194	−	0.0377924i
$429$	1.67066	+	0.171452i	0.0806603	+	0.00827777i
$430$			2.47389i			0.119301i
$431$	0.361329	−	0.625840i	0.0174046	−	0.0301457i	−0.857192	−	0.514997i	$-0.827793\pi$
$431$	0.361329	−	0.625840i	0.0174046	−	0.0301457i	0.874597	+	0.484851i	$0.161126\pi$
$432$	1.11771	+	5.07452i	0.0537758	+	0.244148i
$433$	−20.1778	−	11.6497i	−0.969684	−	0.559847i	−0.0705439	−	0.997509i	$-0.522473\pi$
$433$	−20.1778	−	11.6497i	−0.969684	−	0.559847i	−0.899140	+	0.437662i	$0.855807\pi$
$434$	12.8765	−	7.43425i	0.618091	−	0.356855i
$435$	−3.95109	+	1.77076i	−0.189440	+	0.0849017i
$436$			9.55213i			0.457464i
$437$	−0.399474	−	17.3174i	−0.0191094	−	0.828402i
$438$	−20.9345	−	2.14840i	−1.00029	−	0.102655i
$439$	4.96102	−	2.86425i	0.236776	−	0.136703i	−0.376918	−	0.926247i	$-0.623016\pi$
$439$	4.96102	−	2.86425i	0.236776	−	0.136703i	0.613694	+	0.789544i	$0.289683\pi$
$440$	0.180799	+	0.313153i	0.00861924	+	0.0149290i
$441$	−0.935149	+	1.04889i	−0.0445309	+	0.0499471i
$442$	−2.12415	−	3.67914i	−0.101036	−	0.174999i
$443$	20.0773	+	11.5917i	0.953903	+	0.550736i	0.894291	−	0.447486i	$-0.147680\pi$
$443$	20.0773	+	11.5917i	0.953903	+	0.550736i	0.0596116	+	0.998222i	$0.481014\pi$
$444$	−1.40326	+	13.6736i	−0.0665957	+	0.648923i
$445$		−	10.9503i		−	0.519093i
$446$	4.55894	+	2.63211i	0.215872	+	0.124634i
$447$	31.7756	+	22.9675i	1.50293	+	1.08632i
$448$	2.73284			0.129115
$449$	12.0455			0.568464			0.284232	−	0.958755i	$-0.408261\pi$
$449$	12.0455			0.568464			0.284232	+	0.958755i	$0.408261\pi$
$450$	−1.99643	+	2.23925i	−0.0941127	+	0.105559i
$451$	1.32933	−	0.767490i	0.0625958	−	0.0361397i
$452$	9.04339	−	15.6636i	0.425365	−	0.736754i
$453$	5.74444	−	2.57449i	0.269897	−	0.120960i
$454$	−9.09264	−	15.7489i	−0.426739	−	0.739133i
$455$	7.32810			0.343547
$456$	4.28040	−	6.21918i	0.200448	−	0.291240i
$457$	30.1464			1.41019			0.705094	−	0.709113i	$-0.250905\pi$
$457$	30.1464			1.41019			0.705094	+	0.709113i	$0.250905\pi$
$458$	−0.0461949	−	0.0800119i	−0.00215855	−	0.00373871i
$459$	8.03957	−	1.77079i	0.375255	−	0.0826534i
$460$	1.98697	−	3.44153i	0.0926428	−	0.160462i
$461$	34.0561	−	19.6623i	1.58615	−	0.915765i	0.592218	−	0.805778i	$-0.298252\pi$
$461$	34.0561	−	19.6623i	1.58615	−	0.915765i	0.993933	−	0.109987i	$-0.0350811\pi$
$462$	1.38717	+	1.00265i	0.0645370	+	0.0466475i
$463$	−16.6034			−0.771624			−0.385812	−	0.922577i	$-0.626079\pi$
$463$	−16.6034			−0.771624			−0.385812	+	0.922577i	$0.626079\pi$
$464$	2.49978			0.116050
$465$	5.52029	−	7.63736i	0.255998	−	0.354174i
$466$	−12.3845	−	7.15019i	−0.573701	−	0.331226i
$467$		−	17.0263i		−	0.787884i	−0.919135	−	0.393942i	$-0.871111\pi$
$467$		−	17.0263i		−	0.787884i	0.919135	−	0.393942i	$-0.128889\pi$
$468$	1.63393	−	7.87681i	0.0755282	−	0.364106i
$469$	−1.99988	−	1.15463i	−0.0923460	−	0.0533160i
$470$	−3.82390	−	6.62319i	−0.176383	−	0.305505i
$471$	13.7268	−	18.9911i	0.632498	−	0.875065i
$472$	−1.56849	−	2.71671i	−0.0721957	−	0.125047i
$473$	0.774704	−	0.447276i	0.0356209	−	0.0205658i
$474$	−0.729144	+	7.10493i	−0.0334907	+	0.326340i
$475$	4.35774	−	0.100523i	0.199947	−	0.00461233i
$476$		−	4.32964i		−	0.198449i
$477$	2.58707	+	7.83126i	0.118454	+	0.358569i
$478$	−22.6871	+	13.0984i	−1.03768	+	0.599106i
$479$	10.9769	+	6.33750i	0.501546	+	0.289568i	0.729352	−	0.684139i	$-0.239822\pi$
$479$	10.9769	+	6.33750i	0.501546	+	0.289568i	−0.227806	+	0.973707i	$0.573155\pi$
$480$	1.58057	−	0.708367i	0.0721430	−	0.0323324i
$481$	10.6401	−	18.4292i	0.485147	−	0.840300i
$482$		−	19.3048i		−	0.879311i
$483$	1.92032	−	18.7120i	0.0873776	−	0.851426i
$484$	−5.43462	+	9.41304i	−0.247028	+	0.427866i
$485$	8.83538	−	15.3033i	0.401194	−	0.694889i
$486$	13.5946	+	7.62809i	0.616662	+	0.346017i
$487$			32.6229i			1.47829i	0.673549	+	0.739143i	$0.264769\pi$
$487$			32.6229i			1.47829i	−0.673549	+	0.739143i	$0.735231\pi$
$488$	−3.73492	+	6.46907i	−0.169072	+	0.292841i
$489$	−13.4276	−	29.9608i	−0.607216	−	1.35488i
$490$	0.405655	+	0.234205i	0.0183256	+	0.0105803i
$491$	−6.27240	+	3.62137i	−0.283070	+	0.163430i	−0.634812	−	0.772666i	$-0.718923\pi$
$491$	−6.27240	+	3.62137i	−0.283070	+	0.163430i	0.351743	+	0.936097i	$0.385589\pi$
$492$	−3.00702	−	6.70953i	−0.135567	−	0.302489i
$493$		−	3.96041i		−	0.178368i
$494$	−9.98496	+	6.07608i	−0.449245	+	0.273376i
$495$	1.06218	+	0.220333i	0.0477415	+	0.00990325i
$496$	−4.71176	+	2.72034i	−0.211564	+	0.122147i
$497$	−11.5397	−	19.9873i	−0.517624	−	0.896552i
$498$	−0.914990	−	0.661357i	−0.0410017	−	0.0296361i
$499$	8.51878	+	14.7550i	0.381353	+	0.660522i	0.991256	−	0.131954i	$-0.0421250\pi$
$499$	8.51878	+	14.7550i	0.381353	+	0.660522i	−0.609903	+	0.792476i	$0.708792\pi$
$500$	0.866025	+	0.500000i	0.0387298	+	0.0223607i
$501$	9.16938	+	0.941008i	0.409658	+	0.0420412i
$502$			11.1446i			0.497406i
$503$	−24.2478	−	13.9995i	−1.08115	−	0.624205i	−0.149947	−	0.988694i	$-0.547910\pi$
$503$	−24.2478	−	13.9995i	−1.08115	−	0.624205i	−0.931208	+	0.364489i	$0.881244\pi$
$504$	5.45593	−	6.11952i	0.243026	−	0.272585i
$505$	−0.689765			−0.0306942
$506$	−1.43696			−0.0638809
$507$	5.89459	−	8.15519i	0.261788	−	0.362185i
$508$	3.08394	−	1.78051i	0.136828	−	0.0789974i
$509$	16.1465	−	27.9666i	0.715683	−	1.23960i	−0.247012	−	0.969012i	$-0.579449\pi$
$509$	16.1465	−	27.9666i	0.715683	−	1.23960i	0.962695	−	0.270587i	$-0.0872178\pi$
$510$	−1.12227	−	2.50411i	−0.0496948	−	0.110884i
$511$	16.6020	+	28.7555i	0.734430	+	1.27207i
$512$	−1.00000			−0.0441942
$513$	−5.38080	−	22.0011i	−0.237568	−	0.971371i
$514$	−7.96980			−0.351533
$515$	7.69731	+	13.3321i	0.339184	+	0.587484i
$516$	−1.75242	−	3.91016i	−0.0771460	−	0.172135i
$517$	−1.38271	+	2.39493i	−0.0608117	+	0.105329i
$518$	18.7821	−	10.8438i	0.825237	−	0.476451i
$519$	−10.1867	+	14.0933i	−0.447146	+	0.618629i
$520$	−2.68150			−0.117591
$521$	32.0134			1.40253			0.701266	−	0.712900i	$-0.252619\pi$
$521$	32.0134			1.40253			0.701266	+	0.712900i	$0.252619\pi$
$522$	4.99064	−	5.59765i	0.218435	−	0.245002i
$523$	−15.0870	−	8.71046i	−0.659707	−	0.380882i	0.132458	−	0.991189i	$-0.457713\pi$
$523$	−15.0870	−	8.71046i	−0.659707	−	0.380882i	−0.792165	+	0.610307i	$0.791046\pi$
$524$			4.73444i			0.206825i
$525$	4.70869	+	0.483229i	0.205504	+	0.0210899i
$526$	−14.1470	−	8.16779i	−0.616840	−	0.356133i
$527$	4.30984	+	7.46485i	0.187739	+	0.325174i
$528$	−0.507593	−	0.366889i	−0.0220902	−	0.0159668i
$529$	−3.60393	−	6.24218i	−0.156692	−	0.271399i
$530$	2.38085	−	1.37459i	0.103418	−	0.0597082i
$531$	−9.21479	−	1.91147i	−0.399888	−	0.0829507i
$532$	−11.9090	+	0.274714i	−0.516321	+	0.0119104i
$533$			11.3829i			0.493050i
$534$	7.75681	+	17.3077i	0.335670	+	0.748978i
$535$	−0.781855	+	0.451404i	−0.0338025	+	0.0195159i
$536$	0.731797	+	0.422503i	0.0316088	+	0.0182494i
$537$	4.44939	+	9.92790i	0.192006	+	0.428420i
$538$	15.6050	−	27.0287i	0.672781	−	1.16529i
$539$		−	0.169376i		−	0.00729554i
$540$	1.56929	−	4.95352i	0.0675316	−	0.213165i
$541$	−14.8276	+	25.6821i	−0.637487	+	1.10416i	0.348495	+	0.937311i	$0.386693\pi$
$541$	−14.8276	+	25.6821i	−0.637487	+	1.10416i	−0.985982	+	0.166850i	$0.946641\pi$
$542$	−15.8830	+	27.5101i	−0.682233	+	1.18166i
$543$	4.34951	−	42.3825i	0.186655	−	1.81881i
$544$			1.58430i			0.0679264i
$545$	4.77607	−	8.27239i	0.204584	−	0.354350i
$546$	−11.5826	+	5.19099i	−0.495690	+	0.222154i
$547$	−20.9812	−	12.1135i	−0.897093	−	0.517937i	−0.0208373	−	0.999783i	$-0.506633\pi$
$547$	−20.9812	−	12.1135i	−0.897093	−	0.517937i	−0.876256	+	0.481846i	$0.839967\pi$
$548$	−4.07740	+	2.35409i	−0.174178	+	0.100562i
$549$	7.02939	+	21.2785i	0.300007	+	0.908144i
$550$		−	0.361598i		−	0.0154186i
$551$	−10.8934	+	0.251287i	−0.464075	+	0.0107052i
$552$	−0.702683	+	6.84709i	−0.0299082	+	0.291432i
$553$	9.75931	−	5.63454i	0.415008	−	0.239605i
$554$	−10.4326	−	18.0699i	−0.443240	−	0.767715i
$555$	8.05208	−	11.1401i	0.341792	−	0.472871i
$556$	−7.46724	−	12.9336i	−0.316681	−	0.548508i
$557$	−16.2011	−	9.35371i	−0.686463	−	0.396329i	0.115823	−	0.993270i	$-0.463049\pi$
$557$	−16.2011	−	9.35371i	−0.686463	−	0.396329i	−0.802285	+	0.596941i	$0.796383\pi$
$558$	−3.31518	+	15.9818i	−0.140343	+	0.676564i
$559$			6.63372i			0.280577i
$560$	−2.36671	−	1.36642i	−0.100012	−	0.0577418i
$561$	−0.581263	+	0.804180i	−0.0245409	+	0.0339525i
$562$	−0.388089			−0.0163706
$563$	−37.5624			−1.58307			−0.791534	−	0.611125i	$-0.790717\pi$
$563$	−37.5624			−1.58307			−0.791534	+	0.611125i	$0.790717\pi$
$564$	10.7356	+	7.75972i	0.452051	+	0.326743i
$565$	−15.6636	+	9.04339i	−0.658973	+	0.380458i
$566$	10.8411	−	18.7773i	0.455684	−	0.789268i
$567$	−2.81079	−	24.4344i	−0.118042	−	1.02615i
$568$	4.22259	+	7.31374i	0.177176	+	0.306878i
$569$	21.0817			0.883790			0.441895	−	0.897067i	$-0.354306\pi$
$569$	21.0817			0.883790			0.441895	+	0.897067i	$0.354306\pi$
$570$	−6.81652	+	3.24577i	−0.285513	+	0.135950i
$571$	23.5374			0.985009			0.492505	−	0.870310i	$-0.336082\pi$
$571$	23.5374			0.985009			0.492505	+	0.870310i	$0.336082\pi$
$572$	0.484812	+	0.839718i	0.0202710	+	0.0351104i
$573$	40.4700	−	18.1375i	1.69066	−	0.757704i
$574$	−5.80044	+	10.0467i	−0.242106	+	0.419340i
$575$	−3.44153	+	1.98697i	−0.143522	+	0.0828622i
$576$	−1.99643	+	2.23925i	−0.0831846	+	0.0933023i
$577$	−7.74252			−0.322325			−0.161163	−	0.986928i	$-0.551524\pi$
$577$	−7.74252			−0.322325			−0.161163	+	0.986928i	$0.551524\pi$
$578$	−14.4900			−0.602704
$579$	4.20011	+	3.03585i	0.174551	+	0.126166i
$580$	−2.16488	−	1.24989i	−0.0898916	−	0.0518989i
$581$			1.78131i			0.0739014i
$582$	−3.12460	+	30.4468i	−0.129519	+	1.26206i
$583$	−0.860910	−	0.497047i	−0.0356553	−	0.0205856i
$584$	−6.07501	−	10.5222i	−0.251386	−	0.435413i
$585$	−5.35343	+	6.00456i	−0.221337	+	0.248258i
$586$	16.1427	+	27.9601i	0.666851	+	1.15502i
$587$	33.6896	−	19.4507i	1.39052	−	0.802816i	0.397146	−	0.917755i	$-0.370001\pi$
$587$	33.6896	−	19.4507i	1.39052	−	0.802816i	0.993373	+	0.114939i	$0.0366674\pi$
$588$	−0.807072	−	0.0828258i	−0.0332831	−	0.00341568i
$589$	20.2592	−	12.3282i	0.834765	−	0.507973i
$590$			3.13699i			0.129148i
$591$	−28.0056	+	12.5513i	−1.15200	+	0.516292i
$592$	−6.87273	+	3.96797i	−0.282468	+	0.163083i
$593$	−7.33331	−	4.23389i	−0.301143	−	0.173865i	0.341813	−	0.939768i	$-0.388959\pi$
$593$	−7.33331	−	4.23389i	−0.301143	−	0.173865i	−0.642956	+	0.765903i	$0.722292\pi$
$594$	−1.83493	+	0.404161i	−0.0752882	+	0.0165829i
$595$	−2.16482	+	3.74958i	−0.0887490	+	0.153718i
$596$			22.6362i			0.927215i
$597$	−35.4463	−	3.63768i	−1.45072	−	0.148880i
$598$	5.32805	−	9.22845i	0.217880	−	0.377379i
$599$	−18.3405	+	31.7667i	−0.749372	+	1.29795i	0.198752	+	0.980050i	$0.436311\pi$
$599$	−18.3405	+	31.7667i	−0.749372	+	1.29795i	−0.948124	+	0.317901i	$0.897022\pi$
$600$	−1.72300	−	0.176823i	−0.0703412	−	0.00721877i
$601$			9.79356i			0.399488i	0.979848	+	0.199744i	$0.0640110\pi$
$601$			9.79356i			0.399488i	−0.979848	+	0.199744i	$0.935989\pi$
$602$	−3.38037	+	5.85497i	−0.137773	+	0.238631i
$603$	2.40707	−	0.795181i	0.0980236	−	0.0323823i
$604$	3.14748	+	1.81720i	0.128069	+	0.0739408i
$605$	9.41304	−	5.43462i	0.382695	−	0.220949i
$606$	1.09023	−	0.488607i	0.0442874	−	0.0198483i
$607$			12.9985i			0.527593i	0.964578	+	0.263796i	$0.0849747\pi$
$607$			12.9985i			0.527593i	−0.964578	+	0.263796i	$0.915025\pi$
$608$	4.35774	−	0.100523i	0.176730	−	0.00407676i
$609$	−11.7707	−	1.20797i	−0.476972	−	0.0489493i
$610$	6.46907	−	3.73492i	0.261925	−	0.151223i
$611$	−10.2538	−	17.7601i	−0.414824	−	0.718496i
$612$	3.54765	+	3.16295i	0.143405	+	0.127855i
$613$	−14.8471	−	25.7160i	−0.599669	−	1.03866i	−0.992870	−	0.119205i	$-0.961965\pi$
$613$	−14.8471	−	25.7160i	−0.599669	−	1.03866i	0.393200	−	0.919453i	$-0.371368\pi$
$614$	−16.9205	−	9.76906i	−0.682856	−	0.394247i
$615$	−0.750613	+	7.31413i	−0.0302676	+	0.294934i
$616$			0.988188i			0.0398152i
$617$	11.7412	+	6.77878i	0.472683	+	0.272904i	0.717362	−	0.696700i	$-0.245349\pi$
$617$	11.7412	+	6.77878i	0.472683	+	0.272904i	−0.244679	+	0.969604i	$0.578683\pi$
$618$	−21.6102	−	15.6199i	−0.869291	−	0.628325i
$619$	11.0205			0.442953			0.221476	−	0.975166i	$-0.428912\pi$
$619$	11.0205			0.442953			0.221476	+	0.975166i	$0.428912\pi$
$620$	5.44068			0.218503
$621$	13.9295	+	15.2432i	0.558973	+	0.611690i
$622$	−26.6135	+	15.3653i	−1.06710	+	0.616093i
$623$	14.9627	−	25.9161i	0.599466	−	1.03831i
$624$	4.23831	−	1.89949i	0.169668	−	0.0760403i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−10.2329			−0.408988
$627$	2.24884	+	1.54778i	0.0898100	+	0.0618125i
$628$	13.5288			0.539859
$629$	6.28647	+	10.8885i	0.250658	+	0.434152i
$630$	−7.78473	+	2.57170i	−0.310151	+	0.102459i
$631$	4.03125	−	6.98234i	0.160482	−	0.277962i	−0.774560	−	0.632501i	$-0.782029\pi$
$631$	4.03125	−	6.98234i	0.160482	−	0.277962i	0.935042	+	0.354538i	$0.115362\pi$
$632$	−3.57112	+	2.06179i	−0.142052	+	0.0820136i
$633$	0.390517	+	0.282266i	0.0155217	+	0.0112191i
$634$	−0.504167			−0.0200230
$635$	−3.56102			−0.141315
$636$	−2.78940	+	3.85915i	−0.110607	+	0.153025i
$637$	1.08776	+	0.628021i	0.0430988	+	0.0248831i
$638$			0.903915i			0.0357864i
$639$	24.8074	+	5.14593i	0.981367	+	0.203570i
$640$	0.866025	+	0.500000i	0.0342327	+	0.0197642i
$641$	−2.77035	−	4.79838i	−0.109422	−	0.189525i	0.806114	−	0.591760i	$-0.201567\pi$
$641$	−2.77035	−	4.79838i	−0.109422	−	0.189525i	−0.915536	+	0.402235i	$0.868233\pi$
$642$	0.916020	−	1.26732i	0.0361524	−	0.0500171i
$643$	−20.2446	−	35.0647i	−0.798369	−	1.38282i	−0.920678	−	0.390324i	$-0.872363\pi$
$643$	−20.2446	−	35.0647i	−0.798369	−	1.38282i	0.122308	−	0.992492i	$-0.460970\pi$
$644$	9.40514	−	5.43006i	0.370614	−	0.213974i
$645$	−0.437440	+	4.26251i	−0.0172242	+	0.167836i
$646$	−0.159259	−	6.90397i	−0.00626598	−	0.271633i
$647$			13.7403i			0.540185i	0.962834	+	0.270093i	$0.0870543\pi$
$647$			13.7403i			0.540185i	−0.962834	+	0.270093i	$0.912946\pi$
$648$	1.02852	+	8.94104i	0.0404042	+	0.351237i
$649$	0.982355	−	0.567163i	0.0385608	−	0.0222631i
$650$	2.32225	+	1.34075i	0.0910860	+	0.0525885i
$651$	23.5008	−	10.5324i	0.921067	−	0.412795i
$652$	9.47783	−	16.4161i	0.371181	−	0.642904i
$653$			16.0733i			0.628997i	0.949258	+	0.314498i	$0.101836\pi$
$653$			16.0733i			0.628997i	−0.949258	+	0.314498i	$0.898164\pi$
$654$	−1.68904	+	16.4583i	−0.0660466	+	0.643572i
$655$	2.36722	−	4.10014i	0.0924949	−	0.160206i
$656$	2.12250	−	3.67627i	0.0828696	−	0.143534i
$657$	−35.6903	−	7.40340i	−1.39241	−	0.288834i
$658$		−	20.9002i		−	0.814775i
$659$	0.00725277	−	0.0125622i	0.000282528	−	0.000489352i	−0.865884	−	0.500245i	$-0.833243\pi$
$659$	0.00725277	−	0.0125622i	0.000282528	−	0.000489352i	0.866167	+	0.499755i	$0.166577\pi$
$660$	0.256144	+	0.571532i	0.00997039	+	0.0222468i
$661$	1.46214	+	0.844167i	0.0568706	+	0.0328343i	0.528166	−	0.849141i	$-0.322880\pi$
$661$	1.46214	+	0.844167i	0.0568706	+	0.0328343i	−0.471295	+	0.881976i	$0.656213\pi$
$662$	14.4766	−	8.35805i	0.562648	−	0.324845i
$663$	−3.00936	−	6.71476i	−0.116874	−	0.260780i
$664$		−	0.651818i		−	0.0252954i
$665$	10.4509	+	5.71659i	0.405267	+	0.221680i
$666$	−4.83563	+	23.3116i	−0.187377	+	0.903306i
$667$	8.60307	−	4.96699i	0.333112	−	0.192322i
$668$	2.66087	+	4.60877i	0.102952	+	0.178319i
$669$	7.38965	+	5.34125i	0.285700	+	0.206505i
$670$	−0.422503	−	0.731797i	−0.0163227	−	0.0282718i
$671$	−2.33920	−	1.35054i	−0.0903039	−	0.0521370i
$672$	4.70869	+	0.483229i	0.181641	+	0.0186410i
$673$		−	23.2047i		−	0.894476i	−0.894415	−	0.447238i	$-0.852408\pi$
$673$		−	23.2047i		−	0.894476i	0.894415	−	0.447238i	$-0.147592\pi$
$674$	5.81314	+	3.35622i	0.223914	+	0.129277i
$675$	−3.83581	+	3.50522i	−0.147640	+	0.134916i
$676$	5.80957			0.223445
$677$	41.7346			1.60399			0.801995	−	0.597330i	$-0.203772\pi$
$677$	41.7346			1.60399			0.801995	+	0.597330i	$0.203772\pi$
$678$	18.3515	−	25.3893i	0.704784	−	0.975072i
$679$	41.8215	−	24.1457i	1.60496	−	0.926626i
$680$	0.792151	−	1.37205i	0.0303776	−	0.0526155i
$681$	−12.8819	−	28.7432i	−0.493634	−	1.10144i
$682$	−0.983667	−	1.70376i	−0.0376666	−	0.0652404i
$683$	−38.4483			−1.47118			−0.735592	−	0.677424i	$-0.763096\pi$
$683$	−38.4483			−1.47118			−0.735592	+	0.677424i	$0.763096\pi$
$684$	8.47483	−	9.95878i	0.324043	−	0.380783i
$685$	4.70818			0.179890
$686$	−8.92489	−	15.4584i	−0.340754	−	0.590203i
$687$	−0.0654459	−	0.146029i	−0.00249692	−	0.00557135i
$688$	1.23694	−	2.14245i	0.0471580	−	0.0816801i
$689$	6.38425	−	3.68595i	0.243221	−	0.140423i
$690$	4.03209	−	5.57841i	0.153499	−	0.212367i
$691$	−6.15004			−0.233958			−0.116979	−	0.993134i	$-0.537321\pi$
$691$	−6.15004			−0.233958			−0.116979	+	0.993134i	$0.537321\pi$
$692$	−10.0398			−0.381655
$693$	2.21280	+	1.97285i	0.0840575	+	0.0749424i
$694$	−28.1207	−	16.2355i	−1.06745	−	0.616290i
$695$			14.9345i			0.566497i
$696$	4.30713	+	0.442019i	0.163261	+	0.0167547i
$697$	−5.82432	−	3.36268i	−0.220612	−	0.127370i
$698$	1.45350	+	2.51753i	0.0550157	+	0.0952900i
$699$	−20.0742	−	14.5097i	−0.759275	−	0.548805i
$700$	1.36642	+	2.36671i	0.0516458	+	0.0894532i
$701$	−11.7642	+	6.79204i	−0.444326	+	0.256532i	−0.705431	−	0.708779i	$-0.749247\pi$
$701$	−11.7642	+	6.79204i	−0.444326	+	0.256532i	0.261105	+	0.965310i	$0.415913\pi$
$702$	4.20806	−	13.2828i	0.158823	−	0.501329i
$703$	29.5507	−	17.9823i	1.11453	−	0.678214i
$704$		−	0.361598i		−	0.0136282i
$705$	−5.41746	−	12.0879i	−0.204033	−	0.455258i
$706$	−9.29461	+	5.36625i	−0.349807	+	0.201961i
$707$	−1.63247	−	0.942509i	−0.0613955	−	0.0354467i
$708$	−2.22214	−	4.95824i	−0.0835131	−	0.186342i
$709$	6.74259	−	11.6785i	0.253223	−	0.438596i	−0.711188	−	0.703002i	$-0.751843\pi$
$709$	6.74259	−	11.6785i	0.253223	−	0.438596i	0.964411	+	0.264406i	$0.0851759\pi$
$710$		−	8.44518i		−	0.316942i
$711$	−2.51263	+	12.1129i	−0.0942311	+	0.454268i
$712$	−5.47514	+	9.48321i	−0.205189	+	0.355398i
$713$	−10.8104	+	18.7242i	−0.404854	+	0.701228i
$714$	0.765581	−	7.45998i	0.0286511	−	0.279183i
$715$		−	0.969623i		−	0.0362618i
$716$	−3.14060	+	5.43967i	−0.117370	+	0.203290i
$717$	−41.4059	+	18.5569i	−1.54633	+	0.693022i
$718$	−1.09849	−	0.634215i	−0.0409954	−	0.0236687i
$719$	33.3719	−	19.2672i	1.24456	−	0.718547i	0.274541	−	0.961575i	$-0.411474\pi$
$719$	33.3719	−	19.2672i	1.24456	−	0.718547i	0.970019	+	0.243028i	$0.0781408\pi$
$720$	2.84859	−	0.941036i	0.106161	−	0.0350703i
$721$			42.0710i			1.56681i
$722$	−18.9798	+	0.876110i	−0.706355	+	0.0326054i
$723$	3.41354	−	33.2622i	0.126951	−	1.23704i
$724$	21.3026	−	12.2990i	0.791703	−	0.457090i
$725$	1.24989	+	2.16488i	0.0464198	+	0.0804015i
$726$	−11.0283	+	15.2577i	−0.409299	+	0.566267i
$727$	−0.428190	−	0.741646i	−0.0158807	−	0.0275061i	0.857976	−	0.513690i	$-0.171722\pi$
$727$	−0.428190	−	0.741646i	−0.0158807	−	0.0275061i	−0.873857	+	0.486184i	$0.838389\pi$
$728$	−6.34632	−	3.66405i	−0.235210	−	0.135799i
$729$	22.0746	+	15.5470i	0.817579	+	0.575816i
$730$			12.1500i			0.449692i
$731$	−3.39428	−	1.95969i	−0.125542	−	0.0724818i
$732$	−7.57916	+	10.4858i	−0.280134	+	0.387566i
$733$	4.85312			0.179254			0.0896270	−	0.995975i	$-0.471432\pi$
$733$	4.85312			0.179254			0.0896270	+	0.995975i	$0.471432\pi$
$734$	−9.61170			−0.354774
$735$	0.657532	+	0.475265i	0.0242534	+	0.0175304i
$736$	−3.44153	+	1.98697i	−0.126856	+	0.0732406i
$737$	−0.152776	+	0.264616i	−0.00562758	+	0.00974725i
$738$	−3.99469	−	12.0922i	−0.147047	−	0.445121i
$739$	−6.25405	−	10.8323i	−0.230059	−	0.398474i	0.727766	−	0.685825i	$-0.240559\pi$
$739$	−6.25405	−	10.8323i	−0.230059	−	0.398474i	−0.957825	+	0.287352i	$0.907225\pi$
$740$	7.93595			0.291731
$741$	−18.2785	+	8.70351i	−0.671477	+	0.319732i
$742$	7.51304			0.275813
$743$	8.87174	+	15.3663i	0.325473	+	0.563735i	0.981608	−	0.190908i	$-0.0611433\pi$
$743$	8.87174	+	15.3663i	0.325473	+	0.563735i	−0.656135	+	0.754643i	$0.727810\pi$
$744$	−8.59939	+	3.85400i	−0.315269	+	0.141294i
$745$	11.3181	−	19.6035i	0.414663	−	0.718217i
$746$	11.5269	−	6.65507i	0.422030	−	0.243659i
$747$	−1.45959	−	1.30131i	−0.0534035	−	0.0476124i
$748$	−0.572880			−0.0209466
$749$	−2.46723			−0.0901506
$750$	1.40375	+	1.01463i	0.0512578	+	0.0370492i
$751$	14.7151	+	8.49577i	0.536962	+	0.310015i	0.743847	−	0.668350i	$-0.232999\pi$
$751$	14.7151	+	8.49577i	0.536962	+	0.310015i	−0.206885	+	0.978365i	$0.566333\pi$
$752$			7.64780i			0.278887i
$753$	−1.97062	+	19.2021i	−0.0718132	+	0.699763i
$754$	−5.80511	−	3.35158i	−0.211410	−	0.122057i
$755$	−1.81720	−	3.14748i	−0.0661347	−	0.114549i
$756$	10.4826	−	9.57921i	0.381250	−	0.348393i
$757$	27.1732	+	47.0654i	0.987628	+	1.71062i	0.629620	+	0.776903i	$0.283211\pi$
$757$	27.1732	+	47.0654i	0.987628	+	1.71062i	0.358008	+	0.933719i	$0.383456\pi$
$758$	−5.92231	+	3.41925i	−0.215108	+	0.124193i
$759$	−2.47589	−	0.254089i	−0.0898692	−	0.00922283i
$760$	−3.82417	−	2.09181i	−0.138717	−	0.0758781i
$761$			14.7061i			0.533095i	0.963822	+	0.266547i	$0.0858829\pi$
$761$			14.7061i			0.533095i	−0.963822	+	0.266547i	$0.914117\pi$
$762$	5.62846	−	2.52251i	0.203898	−	0.0913810i
$763$	22.6071	−	13.0522i	0.818432	−	0.472522i
$764$	22.1742	+	12.8023i	0.802236	+	0.463171i
$765$	−1.49088	−	4.51302i	−0.0539030	−	0.163169i
$766$	10.2329	−	17.7238i	0.369728	−	0.640388i
$767$			8.41182i			0.303733i
$768$	−1.72300	−	0.176823i	−0.0621735	−	0.00638056i
$769$	−16.8290	+	29.1487i	−0.606869	+	1.05113i	0.384884	+	0.922965i	$0.374242\pi$
$769$	−16.8290	+	29.1487i	−0.606869	+	1.05113i	−0.991753	+	0.128164i	$0.959092\pi$
$770$	0.494094	−	0.855796i	0.0178059	−	0.0308407i
$771$	−13.7320	−	1.40924i	−0.494545	−	0.0507527i
$772$			2.99206i			0.107687i
$773$	−21.1817	+	36.6877i	−0.761851	+	1.31957i	0.180044	+	0.983659i	$0.442376\pi$
$773$	−21.1817	+	36.6877i	−0.761851	+	1.31957i	−0.941895	+	0.335907i	$0.890957\pi$
$774$	−2.32802	−	7.04708i	−0.0836788	−	0.253302i
$775$	−4.71176	−	2.72034i	−0.169252	−	0.0977174i
$776$	−15.3033	+	8.83538i	−0.549358	+	0.317172i
$777$	34.2790	−	15.3628i	1.22975	−	0.551139i
$778$			11.1910i			0.401217i
$779$	−8.87974	+	16.2336i	−0.318150	+	0.581629i
$780$	−4.62022	−	0.474151i	−0.165431	−	0.0169773i
$781$	−2.64463	+	1.52688i	−0.0946323	+	0.0546360i
$782$	3.14795	+	5.45242i	0.112571	+	0.194978i
$783$	9.58868	−	8.76230i	0.342672	−	0.313139i
$784$	−0.234205	−	0.405655i	−0.00836447	−	0.0144877i
$785$	−11.7163	−	6.76442i	−0.418173	−	0.241432i
$786$	−0.837158	+	8.15744i	−0.0298604	+	0.290966i
$787$			13.6235i			0.485624i	0.970073	+	0.242812i	$0.0780698\pi$
$787$			13.6235i			0.485624i	−0.970073	+	0.242812i	$0.921930\pi$
$788$	−15.3448	−	8.85932i	−0.546636	−	0.315600i
$789$	−22.9311	−	16.5746i	−0.816368	−	0.590073i
$790$	4.12358			0.146710
$791$	−49.4283			−1.75747
$792$	−0.809709	−	0.721905i	−0.0287718	−	0.0256518i
$793$	17.3468	−	10.0152i	0.616003	−	0.355650i
$794$	−19.4671	+	33.7181i	−0.690863	+	1.19661i
$795$	4.34527	−	1.94742i	0.154111	−	0.0690680i
$796$	−10.2862	−	17.8162i	−0.364585	−	0.631480i
$797$	−23.7796			−0.842317			−0.421159	−	0.906987i	$-0.638376\pi$
$797$	−23.7796			−0.842317			−0.421159	+	0.906987i	$0.638376\pi$
$798$	−20.5678	−	1.63245i	−0.728092	−	0.0577882i
$799$	12.1164			0.428648
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	10.3046	+	31.1928i	0.364095	+	1.10214i
$802$	−14.6051	+	25.2968i	−0.515725	+	0.893262i
$803$	3.80481	−	2.19671i	0.134269	−	0.0775201i
$804$	1.18618	+	0.857372i	0.0418333	+	0.0302372i
$805$	−10.8601			−0.382769
$806$	14.5892			0.513881
$807$	31.6668	−	43.8112i	1.11472	−	1.54223i
$808$	0.597354	+	0.344883i	0.0210149	+	0.0121329i
$809$			50.2747i			1.76756i	0.467900	+	0.883781i	$0.345011\pi$
$809$			50.2747i			1.76756i	−0.467900	+	0.883781i	$0.654989\pi$
$810$	3.57979	−	8.25743i	0.125781	−	0.290136i
$811$	0.694406	+	0.400916i	0.0243839	+	0.0140781i	0.512142	−	0.858901i	$-0.328852\pi$
$811$	0.694406	+	0.400916i	0.0243839	+	0.0140781i	−0.487758	+	0.872979i	$0.662185\pi$
$812$	−3.41575	−	5.91626i	−0.119869	−	0.207620i
$813$	−32.2308	+	44.5915i	−1.13039	+	1.56389i
$814$	−1.43481	−	2.48516i	−0.0502901	−	0.0871049i
$815$	−16.4161	+	9.47783i	−0.575030	+	0.331994i
$816$	−0.280141	+	2.72975i	−0.00980690	+	0.0955605i
$817$	−5.17491	+	9.46057i	−0.181047	+	0.330984i
$818$		−	15.1809i		−	0.530789i
$819$	−20.8747	+	6.89601i	−0.729423	+	0.240966i
$820$	−3.67627	+	2.12250i	−0.128381	+	0.0741208i
$821$	−8.20297	−	4.73598i	−0.286285	−	0.165287i	0.349980	−	0.936757i	$-0.386188\pi$
$821$	−8.20297	−	4.73598i	−0.286285	−	0.165287i	−0.636265	+	0.771470i	$0.719522\pi$
$822$	−7.44163	+	3.33512i	−0.259556	+	0.116326i
$823$	−3.69096	+	6.39293i	−0.128659	+	0.222843i	−0.923157	−	0.384423i	$-0.874400\pi$
$823$	−3.69096	+	6.39293i	−0.128659	+	0.222843i	0.794498	+	0.607266i	$0.207734\pi$
$824$		−	15.3946i		−	0.536297i
$825$	0.0639388	−	0.623033i	0.00222606	−	0.0216912i
$826$	−4.28644	+	7.42433i	−0.149144	+	0.258325i
$827$	−14.7907	+	25.6182i	−0.514322	+	0.890832i	0.485540	+	0.874215i	$0.338623\pi$
$827$	−14.7907	+	25.6182i	−0.514322	+	0.890832i	−0.999862	+	0.0166175i	$0.994710\pi$
$828$	−2.42145	+	11.6733i	−0.0841512	+	0.405675i
$829$			22.9422i			0.796816i	0.917208	+	0.398408i	$0.130437\pi$
$829$			22.9422i			0.796816i	−0.917208	+	0.398408i	$0.869563\pi$
$830$	−0.325909	+	0.564491i	−0.0113125	+	0.0195938i
$831$	−14.7803	−	32.9791i	−0.512722	−	1.14403i
$832$	2.32225	+	1.34075i	0.0805094	+	0.0464821i
$833$	−0.642680	+	0.371052i	−0.0222675	+	0.0128562i
$834$	−10.5791	−	23.6050i	−0.366324	−	0.817376i
$835$		−	5.32175i		−	0.184167i
$836$	0.0363490	+	1.57575i	0.00125716	+	0.0544984i
$837$	−8.53802	+	26.9505i	−0.295117	+	0.931545i
$838$	16.1293	−	9.31223i	0.557176	−	0.321686i
$839$	4.86697	+	8.42984i	0.168026	+	0.291030i	0.937726	−	0.347376i	$-0.112927\pi$
$839$	4.86697	+	8.42984i	0.168026	+	0.291030i	−0.769699	+	0.638406i	$0.779594\pi$
$840$	−3.83623	−	2.77283i	−0.132362	−	0.0956718i
$841$	11.3755	+	19.7030i	0.392260	+	0.679414i
$842$	0.995150	+	0.574550i	0.0342951	+	0.0198003i
$843$	−0.668678	−	0.0686232i	−0.0230305	−	0.00236351i
$844$			0.278195i			0.00957587i
$845$	−5.03123	−	2.90478i	−0.173080	−	0.0999276i
$846$	17.1254	+	15.2683i	0.588783	+	0.524936i
$847$	29.7039			1.02064
$848$	−2.74917			−0.0944069
$849$	21.9994	−	30.4363i	0.755018	−	1.04457i
$850$	−1.37205	+	0.792151i	−0.0470608	+	0.0271705i
$851$	−15.7685	+	27.3118i	−0.540536	+	0.936236i
$852$	5.98229	+	13.3482i	0.204950	+	0.457303i
$853$	5.29796	+	9.17634i	0.181399	+	0.314192i	0.942357	−	0.334609i	$-0.108604\pi$
$853$	5.29796	+	9.17634i	0.181399	+	0.314192i	−0.760958	+	0.648801i	$0.775271\pi$
$854$	20.4139			0.698549
$855$	−12.3188	+	4.38714i	−0.421294	+	0.150037i
$856$	0.902808			0.0308573
$857$	26.1897	+	45.3618i	0.894622	+	1.54953i	0.834272	+	0.551354i	$0.185889\pi$
$857$	26.1897	+	45.3618i	0.894622	+	1.54953i	0.0603507	+	0.998177i	$0.480778\pi$
$858$	0.686849	+	1.53256i	0.0234487	+	0.0523208i
$859$	15.2939	−	26.4898i	0.521820	−	0.903819i	−0.477858	−	0.878437i	$-0.658587\pi$
$859$	15.2939	−	26.4898i	0.521820	−	0.903819i	0.999678	−	0.0253818i	$-0.00808014\pi$
$860$	−2.14245	+	1.23694i	−0.0730569	+	0.0421794i
$861$	−11.7707	+	16.2848i	−0.401143	+	0.554983i
$862$	0.722658			0.0246138
$863$	−4.72689			−0.160905			−0.0804525	−	0.996758i	$-0.525637\pi$
$863$	−4.72689			−0.160905			−0.0804525	+	0.996758i	$0.525637\pi$
$864$	−3.83581	+	3.50522i	−0.130497	+	0.119250i
$865$	8.69470	+	5.01989i	0.295629	+	0.170681i
$866$		−	23.2993i		−	0.791743i
$867$	−24.9663	−	2.56217i	−0.847899	−	0.0870157i
$868$	12.8765	+	7.43425i	0.437057	+	0.252335i
$869$	−0.745538	−	1.29131i	−0.0252906	−	0.0438047i
$870$	−3.50907	−	2.53636i	−0.118969	−	0.0859908i
$871$	−1.13294	−	1.96231i	−0.0383883	−	0.0664904i
$872$	−8.27239	+	4.77607i	−0.280138	+	0.161738i
$873$	−10.7674	+	51.9073i	−0.364421	+	1.75680i
$874$	14.7975	−	9.00464i	0.500534	−	0.304586i
$875$		−	2.73284i		−	0.0923868i
$876$	−8.60667	−	19.2040i	−0.290793	−	0.648843i
$877$	5.68003	−	3.27937i	0.191801	−	0.110736i	−0.401024	−	0.916067i	$-0.631346\pi$
$877$	5.68003	−	3.27937i	0.191801	−	0.110736i	0.592825	+	0.805331i	$0.298012\pi$
$878$	4.96102	+	2.86425i	0.167426	+	0.0966636i
$879$	22.8700	+	51.0296i	0.771386	+	1.72119i
$880$	−0.180799	+	0.313153i	−0.00609473	+	0.0105564i
$881$			50.0177i			1.68514i	0.538587	+	0.842570i	$0.318958\pi$
$881$			50.0177i			1.68514i	−0.538587	+	0.842570i	$0.681042\pi$
$882$	−1.37594	−	0.285418i	−0.0463303	−	0.00961052i
$883$	−15.0237	+	26.0218i	−0.505588	+	0.875704i	0.494391	+	0.869239i	$0.335391\pi$
$883$	−15.0237	+	26.0218i	−0.505588	+	0.875704i	−0.999979	+	0.00646423i	$0.997942\pi$
$884$	2.12415	−	3.67914i	0.0714429	−	0.123743i
$885$	−0.554692	+	5.40503i	−0.0186458	+	0.181688i
$886$			23.1833i			0.778858i
$887$	15.3582	−	26.6012i	0.515678	−	0.893181i	−0.484156	−	0.874982i	$-0.660873\pi$
$887$	15.3582	−	26.6012i	0.515678	−	0.893181i	0.999834	−	0.0181992i	$-0.00579330\pi$
$888$	−12.5434	+	5.62157i	−0.420927	+	0.188647i
$889$	−8.42790	−	4.86585i	−0.282663	−	0.163195i
$890$	9.48321	−	5.47514i	0.317878	−	0.183527i
$891$	−3.23306	+	0.371911i	−0.108311	+	0.0124595i
$892$			5.26422i			0.176259i
$893$	−0.768784	−	33.3271i	−0.0257264	−	1.11525i
$894$	−4.00260	+	39.0022i	−0.133867	+	1.30443i
$895$	5.43967	−	3.14060i	0.181828	−	0.104979i
$896$	1.36642	+	2.36671i	0.0456489	+	0.0790662i
$897$	10.8120	−	14.9585i	0.361003	−	0.499450i
$898$	6.02277	+	10.4317i	0.200983	+	0.348112i
$899$	11.7784	+	6.80025i	0.392831	+	0.226801i
$900$	−2.93747	−	0.609333i	−0.0979156	−	0.0203111i
$901$			4.35552i			0.145103i
$902$	1.32933	+	0.767490i	0.0442619	+	0.0255546i
$903$	−6.85967	+	9.49039i	−0.228276	+	0.315820i
$904$	18.0868			0.601557
$905$	−24.5981			−0.817668
$906$	5.10179	+	3.68759i	0.169496	+	0.122512i
$907$	−12.2972	+	7.09982i	−0.408323	+	0.235745i	−0.690069	−	0.723744i	$-0.742420\pi$
$907$	−12.2972	+	7.09982i	−0.408323	+	0.235745i	0.281746	+	0.959489i	$0.409087\pi$
$908$	9.09264	−	15.7489i	0.301750	−	0.522646i
$909$	1.96486	−	0.649094i	0.0651702	−	0.0215291i
$910$	3.66405	+	6.34632i	0.121462	+	0.210379i
$911$	0.180923			0.00599424			0.00299712	−	0.999996i	$-0.499046\pi$
$911$	0.180923			0.00599424			0.00299712	+	0.999996i	$0.499046\pi$
$912$	7.52617	+	0.597347i	0.249216	+	0.0197801i
$913$	0.235696			0.00780039
$914$	15.0732	+	26.1075i	0.498577	+	0.863561i
$915$	11.8066	−	5.29139i	0.390316	−	0.174928i
$916$	0.0461949	−	0.0800119i	0.00152632	−	0.00264367i
$917$	11.2050	−	6.46923i	0.370023	−	0.213633i
$918$	5.55333	+	6.07707i	0.183287	+	0.200573i
$919$	6.27200			0.206894			0.103447	−	0.994635i	$-0.467013\pi$
$919$	6.27200			0.206894			0.103447	+	0.994635i	$0.467013\pi$
$920$	3.97393			0.131017
$921$	−27.4267	−	19.8240i	−0.903739	−	0.653224i
$922$	34.0561	+	19.6623i	1.12158	+	0.647544i
$923$		−	22.6457i		−	0.745393i
$924$	−0.174734	+	1.70265i	−0.00574834	+	0.0560130i
$925$	−6.87273	−	3.96797i	−0.225974	−	0.130466i
$926$	−8.30169	−	14.3789i	−0.272810	−	0.472521i
$927$	−34.4725	−	30.7343i	−1.13223	−	1.00945i
$928$	1.24989	+	2.16488i	0.0410297	+	0.0710655i
$929$	12.3721	−	7.14305i	0.405916	−	0.234356i	−0.283117	−	0.959085i	$-0.591369\pi$
$929$	12.3721	−	7.14305i	0.405916	−	0.234356i	0.689033	+	0.724730i	$0.258035\pi$
$930$	9.37429	+	0.962037i	0.307395	+	0.0315464i
$931$	1.06138	+	1.74420i	0.0347854	+	0.0571637i
$932$		−	14.3004i		−	0.468425i
$933$	−48.5720	+	21.7686i	−1.59018	+	0.712671i
$934$	14.7452	−	8.51316i	0.482478	−	0.278559i
$935$	0.496128	+	0.286440i	0.0162251	+	0.00936758i
$936$	7.63848	−	2.52339i	0.249672	−	0.0824794i
$937$	20.2062	−	34.9981i	0.660106	−	1.14334i	−0.320481	−	0.947255i	$-0.603845\pi$
$937$	20.2062	−	34.9981i	0.660106	−	1.14334i	0.980587	−	0.196083i	$-0.0628221\pi$
$938$		−	2.30927i		−	0.0754002i
$939$	−17.6313	−	1.80941i	−0.575375	−	0.0590479i
$940$	3.82390	−	6.62319i	0.124722	−	0.216025i
$941$	−3.98704	+	6.90576i	−0.129974	+	0.225121i	−0.923666	−	0.383198i	$-0.874823\pi$
$941$	−3.98704	+	6.90576i	−0.129974	+	0.225121i	0.793692	+	0.608319i	$0.208156\pi$
$942$	23.3102	+	2.39221i	0.759487	+	0.0779424i
$943$		−	16.8693i		−	0.549341i
$944$	1.56849	−	2.71671i	0.0510501	−	0.0884214i
$945$	−13.8678	+	3.05452i	−0.451121	+	0.0993636i
$946$	0.774704	+	0.447276i	0.0251878	+	0.0145422i
$947$	−7.76421	+	4.48267i	−0.252303	+	0.145667i	−0.620818	−	0.783954i	$-0.713200\pi$
$947$	−7.76421	+	4.48267i	−0.252303	+	0.145667i	0.368515	+	0.929622i	$0.379866\pi$
$948$	−6.51762	+	2.92101i	−0.211683	+	0.0948699i
$949$			32.5802i			1.05760i
$950$	2.26593	+	3.72365i	0.0735163	+	0.120811i
$951$	−0.868681	−	0.0891484i	−0.0281689	−	0.00289084i
$952$	3.74958	−	2.16482i	0.121525	−	0.0701622i
$953$	21.0568	+	36.4715i	0.682098	+	1.18143i	0.974339	+	0.225084i	$0.0722656\pi$
$953$	21.0568	+	36.4715i	0.682098	+	1.18143i	−0.292241	+	0.956345i	$0.594401\pi$
$954$	−5.48853	+	6.15610i	−0.177698	+	0.199311i
$955$	−12.8023	−	22.1742i	−0.414273	−	0.717542i
$956$	−22.6871	−	13.0984i	−0.733752	−	0.423632i
$957$	−0.159833	+	1.55745i	−0.00516667	+	0.0503451i
$958$			12.6750i			0.409511i
$959$	11.1429	+	6.43335i	0.359822	+	0.207744i
$960$	1.40375	+	1.01463i	0.0453059	+	0.0327472i
$961$	1.39905			0.0451306
$962$	21.2802			0.686102
$963$	1.80239	−	2.02162i	0.0580814	−	0.0651457i
$964$	16.7185	−	9.65242i	0.538466	−	0.310883i
$965$	1.49603	−	2.59120i	0.0481589	−	0.0834137i
$966$	17.1652	−	7.69296i	0.552282	−	0.247517i
$967$	8.15807	+	14.1302i	0.262346	+	0.454396i	0.966865	−	0.255289i	$-0.0821705\pi$
$967$	8.15807	+	14.1302i	0.262346	+	0.454396i	−0.704519	+	0.709685i	$0.748837\pi$
$968$	−10.8692			−0.349351
$969$	0.946378	−	11.9237i	0.0304020	−	0.383045i
$970$	17.6708			0.567374
$971$	−20.4607	−	35.4390i	−0.656616	−	1.13729i	−0.981486	−	0.191533i	$-0.938654\pi$
$971$	−20.4607	−	35.4390i	−0.656616	−	1.13729i	0.324870	−	0.945759i	$-0.394679\pi$
$972$	0.191165	+	15.5873i	0.00613161	+	0.499962i
$973$	−20.4068	+	35.3455i	−0.654211	+	1.13313i
$974$	−28.2523	+	16.3115i	−0.905261	+	0.522653i
$975$	3.76416	+	2.72074i	0.120549	+	0.0871334i
$976$	−7.46984			−0.239104
$977$	13.6550			0.436863			0.218432	−	0.975852i	$-0.429906\pi$
$977$	13.6550			0.436863			0.218432	+	0.975852i	$0.429906\pi$
$978$	19.2331	−	26.6090i	0.615005	−	0.850863i
$979$	−3.42911	−	1.97980i	−0.109595	−	0.0632745i
$980$			0.468410i			0.0149628i
$981$	−5.82043	+	28.0591i	−0.185832	+	0.895857i
$982$	−6.27240	−	3.62137i	−0.200160	−	0.115563i
$983$	5.89586	+	10.2119i	0.188049	+	0.325710i	0.944600	−	0.328225i	$-0.106450\pi$
$983$	5.89586	+	10.2119i	0.188049	+	0.325710i	−0.756551	+	0.653935i	$0.773117\pi$
$984$	4.30712	−	5.95892i	0.137306	−	0.189963i
$985$	8.85932	+	15.3448i	0.282282	+	0.488926i
$986$	3.42982	−	1.98020i	0.109228	−	0.0630626i
$987$	3.69564	−	36.0111i	0.117634	−	1.14625i
$988$	−10.2545	−	5.60919i	−0.326240	−	0.178452i
$989$		−	9.83106i		−	0.312610i
$990$	0.340276	+	1.03004i	0.0108147	+	0.0327369i
$991$	−11.5357	+	6.66013i	−0.366443	+	0.211566i	−0.671903	−	0.740639i	$-0.734523\pi$
$991$	−11.5357	+	6.66013i	−0.366443	+	0.211566i	0.305460	+	0.952205i	$0.401190\pi$
$992$	−4.71176	−	2.72034i	−0.149599	−	0.0863708i
$993$	26.4211	−	11.8411i	0.838447	−	0.375767i
$994$	11.5397	−	19.9873i	0.366016	−	0.633958i
$995$			20.5724i			0.652189i
$996$	0.115257	−	1.12308i	0.00365204	−	0.0355863i
$997$	7.32126	−	12.6808i	0.231867	−	0.401605i	−0.726491	−	0.687176i	$-0.758850\pi$
$997$	7.32126	−	12.6808i	0.231867	−	0.401605i	0.958357	+	0.285571i	$0.0921833\pi$
$998$	−8.51878	+	14.7550i	−0.269657	+	0.467060i
$999$	−12.4538	+	39.3108i	−0.394022	+	1.24374i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.s.b.221.7	yes	24
3.2	odd	2		570.2.s.a.221.3	✓	24
19.8	odd	6		570.2.s.a.521.3	yes	24
57.8	even	6	inner	570.2.s.b.521.7	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.s.a.221.3	✓	24	3.2	odd	2
570.2.s.a.521.3	yes	24	19.8	odd	6
570.2.s.b.221.7	yes	24	1.1	even	1	trivial
570.2.s.b.521.7	yes	24	57.8	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.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.708367 + 1.58057i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-1.01463 + 1.40375i) q^{6} +2.73284 q^{7} -1.00000 q^{8} +(-1.99643 + 2.23925i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.708367 + 1.58057i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-1.01463 + 1.40375i) q^{6} +2.73284 q^{7} -1.00000 q^{8} +(-1.99643 + 2.23925i) q^{9} +(0.866025 + 0.500000i) q^{10} -0.361598i q^{11} +(-1.72300 - 0.176823i) q^{12} +(2.32225 + 1.34075i) q^{13} +(1.36642 + 2.36671i) q^{14} +(1.40375 + 1.01463i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.37205 + 0.792151i) q^{17} +(-2.93747 - 0.609333i) q^{18} +(2.26593 + 3.72365i) q^{19} +1.00000i q^{20} +(1.93585 + 4.31946i) q^{21} +(0.313153 - 0.180799i) q^{22} +(-3.44153 - 1.98697i) q^{23} +(-0.708367 - 1.58057i) q^{24} +(0.500000 - 0.866025i) q^{25} +2.68150i q^{26} +(-4.95352 - 1.56929i) q^{27} +(-1.36642 + 2.36671i) q^{28} +(-1.24989 + 2.16488i) q^{29} +(-0.176823 + 1.72300i) q^{30} -5.44068i q^{31} +(0.500000 - 0.866025i) q^{32} +(0.571532 - 0.256144i) q^{33} +(-1.37205 - 0.792151i) q^{34} +(2.36671 - 1.36642i) q^{35} +(-0.941036 - 2.84859i) q^{36} -7.93595i q^{37} +(-2.09181 + 3.82417i) q^{38} +(-0.474151 + 4.62022i) q^{39} +(-0.866025 + 0.500000i) q^{40} +(2.12250 + 3.67627i) q^{41} +(-2.77283 + 3.83623i) q^{42} +(1.23694 + 2.14245i) q^{43} +(0.313153 + 0.180799i) q^{44} +(-0.609333 + 2.93747i) q^{45} -3.97393i q^{46} +(-6.62319 - 3.82390i) q^{47} +(1.01463 - 1.40375i) q^{48} +0.468410 q^{49} +1.00000 q^{50} +(-2.22397 - 1.60749i) q^{51} +(-2.32225 + 1.34075i) q^{52} +(1.37459 - 2.38085i) q^{53} +(-1.11771 - 5.07452i) q^{54} +(-0.180799 - 0.313153i) q^{55} -2.73284 q^{56} +(-4.28040 + 6.21918i) q^{57} -2.49978 q^{58} +(1.56849 + 2.71671i) q^{59} +(-1.58057 + 0.708367i) q^{60} +(3.73492 - 6.46907i) q^{61} +(4.71176 - 2.72034i) q^{62} +(-5.45593 + 6.11952i) q^{63} +1.00000 q^{64} +2.68150 q^{65} +(0.507593 + 0.366889i) q^{66} +(-0.731797 - 0.422503i) q^{67} -1.58430i q^{68} +(0.702683 - 6.84709i) q^{69} +(2.36671 + 1.36642i) q^{70} +(-4.22259 - 7.31374i) q^{71} +(1.99643 - 2.23925i) q^{72} +(6.07501 + 10.5222i) q^{73} +(6.87273 - 3.96797i) q^{74} +(1.72300 + 0.176823i) q^{75} +(-4.35774 + 0.100523i) q^{76} -0.988188i q^{77} +(-4.23831 + 1.89949i) q^{78} +(3.57112 - 2.06179i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(-1.02852 - 8.94104i) q^{81} +(-2.12250 + 3.67627i) q^{82} +0.651818i q^{83} +(-4.70869 - 0.483229i) q^{84} +(-0.792151 + 1.37205i) q^{85} +(-1.23694 + 2.14245i) q^{86} +(-4.30713 - 0.442019i) q^{87} +0.361598i q^{88} +(5.47514 - 9.48321i) q^{89} +(-2.84859 + 0.941036i) q^{90} +(6.34632 + 3.66405i) q^{91} +(3.44153 - 1.98697i) q^{92} +(8.59939 - 3.85400i) q^{93} -7.64780i q^{94} +(3.82417 + 2.09181i) q^{95} +(1.72300 + 0.176823i) q^{96} +(15.3033 - 8.83538i) q^{97} +(0.234205 + 0.405655i) q^{98} +(0.809709 + 0.721905i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 q^{9}+O(q^{10}) \) 24 * q + 12 * q^2 + 2 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^7 - 24 * q^8 + 2 * q^9	\( 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 q^{9} + 2 q^{12} + 18 q^{13} - 6 q^{14} - 12 q^{16} - 12 q^{17} - 2 q^{18} + 6 q^{19} + 6 q^{21} + 18 q^{22} - 2 q^{24} + 12 q^{25} - 28 q^{27} + 6 q^{28} + 12 q^{32} - 8 q^{33} - 12 q^{34} - 4 q^{36} - 6 q^{38} + 40 q^{39} - 6 q^{41} - 6 q^{42} - 22 q^{43} + 18 q^{44} + 8 q^{45} - 12 q^{47} - 4 q^{48} + 12 q^{49} + 24 q^{50} - 4 q^{51} - 18 q^{52} - 8 q^{53} - 32 q^{54} + 12 q^{56} - 20 q^{57} - 26 q^{59} + 22 q^{61} + 18 q^{62} + 30 q^{63} + 24 q^{64} - 8 q^{65} - 22 q^{66} - 48 q^{67} + 64 q^{69} - 24 q^{71} - 2 q^{72} - 8 q^{73} - 30 q^{74} - 2 q^{75} - 12 q^{76} + 2 q^{78} + 18 q^{79} - 6 q^{81} + 6 q^{82} - 12 q^{84} + 22 q^{86} - 24 q^{87} - 28 q^{89} + 16 q^{90} + 18 q^{91} + 14 q^{93} - 2 q^{96} + 6 q^{97} + 6 q^{98} - 52 q^{99}+O(q^{100}) \) 24 * q + 12 * q^2 + 2 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^7 - 24 * q^8 + 2 * q^9 + 2 * q^12 + 18 * q^13 - 6 * q^14 - 12 * q^16 - 12 * q^17 - 2 * q^18 + 6 * q^19 + 6 * q^21 + 18 * q^22 - 2 * q^24 + 12 * q^25 - 28 * q^27 + 6 * q^28 + 12 * q^32 - 8 * q^33 - 12 * q^34 - 4 * q^36 - 6 * q^38 + 40 * q^39 - 6 * q^41 - 6 * q^42 - 22 * q^43 + 18 * q^44 + 8 * q^45 - 12 * q^47 - 4 * q^48 + 12 * q^49 + 24 * q^50 - 4 * q^51 - 18 * q^52 - 8 * q^53 - 32 * q^54 + 12 * q^56 - 20 * q^57 - 26 * q^59 + 22 * q^61 + 18 * q^62 + 30 * q^63 + 24 * q^64 - 8 * q^65 - 22 * q^66 - 48 * q^67 + 64 * q^69 - 24 * q^71 - 2 * q^72 - 8 * q^73 - 30 * q^74 - 2 * q^75 - 12 * q^76 + 2 * q^78 + 18 * q^79 - 6 * q^81 + 6 * q^82 - 12 * q^84 + 22 * q^86 - 24 * q^87 - 28 * q^89 + 16 * q^90 + 18 * q^91 + 14 * q^93 - 2 * q^96 + 6 * q^97 + 6 * q^98 - 52 * q^99

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