LMFDB - Embedded newform 570.2.s.b.521.7

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			521.7
Character	$\chi$	$=$	570.521
Dual form			570.2.s.b.221.7

$q$-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 $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.500000	−	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	$0.0173606\pi$
$11$			0.361598i			0.109026i	−0.998513	+	0.0545129i	$0.982639\pi$
$12$	−1.72300	+	0.176823i	−0.497388	+	0.0510444i
$13$	2.32225	−	1.34075i	0.644075	−	0.371857i	−0.142108	−	0.989851i	$-0.545388\pi$
$13$	2.32225	−	1.34075i	0.644075	−	0.371857i	0.786183	+	0.617994i	$0.212055\pi$
$14$	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	0.324300	−	0.945954i	$-0.394871\pi$
$17$	−1.37205	−	0.792151i	−0.332770	−	0.192125i	−0.657070	+	0.753829i	$0.728205\pi$
$18$	−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	−0.813872	−	0.581045i	$-0.802644\pi$
$23$	−3.44153	+	1.98697i	−0.717608	+	0.414311i	0.0962636	+	0.995356i	$0.469311\pi$
$24$	−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	0.726327	−	0.687350i	$-0.241226\pi$
$29$	−1.24989	−	2.16488i	−0.232099	−	0.402007i	−0.958426	+	0.285342i	$0.907893\pi$
$30$	−0.176823	−	1.72300i	−0.0322833	−	0.314576i
$31$			5.44068i			0.977174i	0.872515	+	0.488587i	$0.162488\pi$
$31$			5.44068i			0.977174i	−0.872515	+	0.488587i	$0.837512\pi$
$32$	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	$0.226209\pi$
$37$			7.93595i			1.30466i	−0.757934	+	0.652331i	$0.773791\pi$
$38$	−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	−0.651324	−	0.758800i	$-0.725786\pi$
$41$	2.12250	−	3.67627i	0.331478	−	0.574137i	0.982802	+	0.184663i	$0.0591193\pi$
$42$	−2.77283	−	3.83623i	−0.427857	−	0.591943i
$43$	1.23694	−	2.14245i	0.188632	−	0.326720i	−0.756162	−	0.654384i	$-0.772928\pi$
$43$	1.23694	−	2.14245i	0.188632	−	0.326720i	0.944794	+	0.327664i	$0.106261\pi$
$44$	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	−0.898043	−	0.439908i	$-0.855011\pi$
$47$	−6.62319	+	3.82390i	−0.966092	+	0.557773i	−0.0680494	+	0.997682i	$0.521678\pi$
$48$	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	0.944855	−	0.327489i	$-0.106202\pi$
$53$	1.37459	+	2.38085i	0.188814	+	0.327035i	−0.756041	+	0.654524i	$0.772869\pi$
$54$	−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	−0.745677	−	0.666307i	$-0.767874\pi$
$59$	1.56849	−	2.71671i	0.204200	−	0.353685i	0.949878	+	0.312622i	$0.101207\pi$
$60$	−1.58057	−	0.708367i	−0.204051	−	0.0914498i
$61$	3.73492	+	6.46907i	0.478208	+	0.828280i	0.999688	−	0.0249834i	$-0.00795330\pi$
$61$	3.73492	+	6.46907i	0.478208	+	0.828280i	−0.521480	+	0.853263i	$0.674620\pi$
$62$	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	−0.544035	−	0.839062i	$-0.683104\pi$
$67$	−0.731797	+	0.422503i	−0.0894032	+	0.0516170i	0.454632	+	0.890679i	$0.349771\pi$
$68$			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	0.498870	+	0.866677i	$0.333749\pi$
$71$	−4.22259	+	7.31374i	−0.501129	+	0.867981i	−0.999999	+	0.00130440i	$0.999585\pi$
$72$	1.99643	+	2.23925i	0.235282	+	0.263899i
$73$	6.07501	−	10.5222i	0.711026	−	1.23153i	−0.253447	−	0.967349i	$-0.581564\pi$
$73$	6.07501	−	10.5222i	0.711026	−	1.23153i	0.964472	−	0.264184i	$-0.0851025\pi$
$74$	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	0.687253	−	0.726418i	$-0.258816\pi$
$79$	3.57112	+	2.06179i	0.401783	+	0.231969i	−0.285470	+	0.958388i	$0.592150\pi$
$80$	−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	$-0.988611\pi$
$83$		−	0.651818i		−	0.0715463i	0.999360	−	0.0357732i	$-0.0113894\pi$
$84$	−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	0.995436	+	0.0954304i	$0.0304227\pi$
$89$	5.47514	+	9.48321i	0.580363	+	1.00522i	−0.415073	+	0.909788i	$0.636244\pi$
$90$	−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	0.997826	+	0.0659098i	$0.0209950\pi$
$97$	15.3033	+	8.83538i	1.55382	+	0.897097i	0.555992	+	0.831187i	$0.312338\pi$
$98$	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	−0.529425	−	0.848357i	$-0.677592\pi$
$101$	−0.597354	+	0.344883i	−0.0594390	+	0.0343171i	0.469986	+	0.882674i	$0.344259\pi$
$102$	0.280141	+	2.72975i	0.0277381	+	0.270286i
$103$		−	15.3946i		−	1.51688i	−0.651744	−	0.758439i	$-0.725962\pi$
$103$		−	15.3946i		−	1.51688i	0.651744	−	0.758439i	$-0.274038\pi$
$104$	−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	0.840790	−	0.541362i	$-0.182091\pi$
$109$	8.27239	+	4.77607i	0.792351	+	0.457464i	−0.0484384	+	0.998826i	$0.515424\pi$
$110$	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	−0.630548	−	0.776151i	$-0.717170\pi$
$127$	−3.08394	+	1.78051i	−0.273655	+	0.157995i	0.356892	+	0.934145i	$0.383836\pi$
$128$	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	0.668305	−	0.743888i	$-0.267020\pi$
$131$	4.10014	+	2.36722i	0.358231	+	0.206825i	−0.310073	+	0.950713i	$0.600354\pi$
$132$	−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	−0.315605	−	0.948891i	$-0.602207\pi$
$137$	4.07740	−	2.35409i	0.348356	−	0.201123i	0.663961	+	0.747767i	$0.268874\pi$
$138$	6.28110	+	2.81500i	0.534683	+	0.239629i
$139$	−7.46724	−	12.9336i	−0.633363	−	1.09702i	−0.986860	−	0.161581i	$-0.948341\pi$
$139$	−7.46724	−	12.9336i	−0.633363	−	1.09702i	0.353497	−	0.935436i	$-0.384993\pi$
$140$		−	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	0.990257	+	0.139254i	$0.0444706\pi$
$149$	19.6035	+	11.3181i	1.60598	+	0.927215i	0.615726	+	0.787960i	$0.288863\pi$
$150$	0.708367	−	1.58057i	0.0578380	−	0.129053i
$151$			3.63440i			0.295763i	0.989005	+	0.147882i	$0.0472455\pi$
$151$			3.63440i			0.295763i	−0.989005	+	0.147882i	$0.952755\pi$
$152$	−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	0.459052	+	0.888410i	$0.348189\pi$
$157$	−6.76442	+	11.7163i	−0.539859	+	0.935064i	−0.998911	+	0.0466542i	$0.985144\pi$
$158$	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	0.950421	−	0.310967i	$-0.100653\pi$
$167$	2.66087	+	4.60877i	0.205905	+	0.356637i	−0.744516	+	0.667605i	$0.767320\pi$
$168$	−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	−0.609644	−	0.792675i	$-0.708688\pi$
$173$	5.01989	−	8.69470i	0.381655	−	0.661046i	0.991299	+	0.131630i	$0.0420209\pi$
$174$	−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	−0.589049	+	0.808097i	$0.700498\pi$
$181$	−21.3026	+	12.2990i	−1.58341	+	0.914180i	−0.994357	+	0.106083i	$0.966169\pi$
$182$		−	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	$0.377065\pi$
$191$			25.6046i			1.85268i	−0.376683	+	0.926342i	$0.622935\pi$
$192$	0.708367	−	1.58057i	0.0511220	−	0.114068i
$193$	2.59120	+	1.49603i	0.186519	+	0.107687i	0.590352	−	0.807146i	$-0.298989\pi$
$193$	2.59120	+	1.49603i	0.186519	+	0.107687i	−0.403833	+	0.914833i	$0.632322\pi$
$194$	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	$-0.782562\pi$
$197$		−	17.7186i		−	1.26240i	0.775620	−	0.631201i	$-0.217438\pi$
$198$	−0.220333	−	1.06218i	−0.0156584	−	0.0754859i
$199$	−10.2862	−	17.8162i	−0.729170	−	1.26296i	−0.957235	−	0.289313i	$-0.906573\pi$
$199$	−10.2862	−	17.8162i	−0.729170	−	1.26296i	0.228065	−	0.973646i	$-0.426760\pi$
$200$	−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	0.508270	−	0.861198i	$-0.330285\pi$
$211$	0.240924	+	0.139098i	0.0165859	+	0.00957587i	−0.491684	+	0.870774i	$0.663619\pi$
$212$	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	0.644817	−	0.764337i	$-0.276934\pi$
$223$	4.55894	+	2.63211i	0.305290	+	0.176259i	−0.339527	+	0.940596i	$0.610267\pi$
$224$	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	0.0360842	−	0.999349i	$-0.488512\pi$
$233$	−12.3845	−	7.15019i	−0.811335	−	0.468425i	−0.847419	+	0.530924i	$0.821845\pi$
$234$	−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	$-0.678248\pi$
$239$		−	26.1968i		−	1.69453i	0.531172	−	0.847264i	$-0.321752\pi$
$240$	0.176823	+	1.72300i	0.0114139	+	0.111219i
$241$	−16.7185	+	9.65242i	−1.07693	+	0.621767i	−0.930067	−	0.367390i	$-0.880251\pi$
$241$	−16.7185	+	9.65242i	−1.07693	+	0.621767i	−0.146865	+	0.989157i	$0.546918\pi$
$242$	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	−0.163455	−	0.986551i	$-0.552264\pi$
$251$	9.65147	−	5.57228i	0.609195	−	0.351719i	0.772650	+	0.634832i	$0.218931\pi$
$252$	−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	0.714558	−	0.699576i	$-0.246628\pi$
$257$	−3.98490	−	6.90205i	−0.248571	−	0.430538i	−0.963130	+	0.269038i	$0.913294\pi$
$258$	−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	−0.00421689	−	0.999991i	$-0.501342\pi$
$263$	−14.1470	−	8.16779i	−0.872343	−	0.503647i	−0.868126	+	0.496344i	$0.834676\pi$
$264$	−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	−0.209179	+	0.977877i	$0.567079\pi$
$269$	−15.6050	+	27.0287i	−0.951456	+	1.64797i	−0.742277	+	0.670093i	$0.766254\pi$
$270$	−3.50522	+	3.83581i	−0.213321	+	0.233440i
$271$	15.8830	−	27.5101i	0.964823	−	1.67112i	0.254733	−	0.967011i	$-0.418012\pi$
$271$	15.8830	−	27.5101i	0.964823	−	1.67112i	0.710090	−	0.704111i	$-0.248654\pi$
$272$	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	0.860180	−	0.509991i	$-0.170351\pi$
$281$	−0.194045	−	0.336095i	−0.0115757	−	0.0200498i	−0.871755	+	0.489942i	$0.837018\pi$
$282$	12.0879	+	5.41746i	0.719825	+	0.322605i
$283$	−10.8411	+	18.7773i	−0.644434	+	1.11619i	0.339997	+	0.940426i	$0.389574\pi$
$283$	−10.8411	+	18.7773i	−0.644434	+	1.11619i	−0.984432	+	0.175767i	$0.943760\pi$
$284$	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	−0.0677805	−	0.997700i	$-0.521592\pi$
$307$	−16.9205	−	9.76906i	−0.965705	−	0.557550i	−0.897924	+	0.440150i	$0.854925\pi$
$308$	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	$-0.663286\pi$
$311$		−	30.7306i		−	1.74257i	0.490775	−	0.871287i	$-0.336714\pi$
$312$	0.474151	+	4.62022i	0.0268435	+	0.261569i
$313$	−5.11644	−	8.86194i	−0.289198	−	0.500906i	0.684420	−	0.729088i	$-0.260055\pi$
$313$	−5.11644	−	8.86194i	−0.289198	−	0.500906i	−0.973619	+	0.228181i	$0.926722\pi$
$314$	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	0.858859	−	0.512211i	$-0.171174\pi$
$317$	−0.252084	−	0.436622i	−0.0141584	−	0.0245231i	−0.873018	+	0.487688i	$0.837840\pi$
$318$	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	$0.151936\pi$
$331$			16.7161i			0.918800i	−0.888229	+	0.459400i	$0.848064\pi$
$332$	−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	0.649904	−	0.760017i	$-0.274809\pi$
$337$	5.81314	+	3.35622i	0.316662	+	0.182825i	−0.333242	+	0.942841i	$0.608143\pi$
$338$	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	−0.999937	−	0.0111900i	$-0.996438\pi$
$347$	−28.1207	−	16.2355i	−1.50960	−	0.871566i	−0.509660	−	0.860376i	$-0.670229\pi$
$348$	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	$-0.907802\pi$
$353$		−	10.7325i		−	0.571233i	0.958344	−	0.285616i	$-0.0921983\pi$
$354$	−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	0.470732	−	0.882276i	$-0.343990\pi$
$359$	−1.09849	−	0.634215i	−0.0579762	−	0.0334726i	−0.528708	+	0.848804i	$0.677323\pi$
$360$	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	0.712900	−	0.701265i	$-0.247381\pi$
$367$	−4.80585	−	8.32397i	−0.250863	−	0.434508i	−0.963764	+	0.266757i	$0.914048\pi$
$368$		−	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	$0.111981\pi$
$373$			13.3101i			0.689173i	−0.938755	+	0.344586i	$0.888019\pi$
$374$	−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	$-0.943802\pi$
$379$		−	6.83849i		−	0.351270i	0.984455	−	0.175635i	$-0.0561978\pi$
$380$	−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	0.476771	+	0.879027i	$0.341807\pi$
$383$	−10.2329	+	17.7238i	−0.522874	+	0.905645i	−0.999646	+	0.0266177i	$0.991526\pi$
$384$	−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	−0.233762	−	0.972294i	$-0.575104\pi$
$389$	9.69169	−	5.59550i	0.491388	−	0.283703i	0.725150	+	0.688591i	$0.241770\pi$
$390$	−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	0.303953	−	0.952687i	$-0.401693\pi$
$397$	19.4671	−	33.7181i	0.977028	−	1.69226i	0.673074	−	0.739575i	$-0.264973\pi$
$398$	−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	−0.227815	−	0.973704i	$-0.573158\pi$
$401$	14.6051	−	25.2968i	0.729345	−	1.26326i	0.957160	−	0.289559i	$-0.0935085\pi$
$402$	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	−0.788487	−	0.615051i	$-0.789135\pi$
$409$	−13.1471	+	7.59047i	−0.650081	+	0.375325i	0.138406	+	0.990376i	$0.455802\pi$
$410$		−	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	$0.150337\pi$
$419$			18.6245i			0.909864i	−0.890526	+	0.454932i	$0.849663\pi$
$420$	−4.31946	−	1.93585i	−0.210768	−	0.0944600i
$421$	0.995150	+	0.574550i	0.0485006	+	0.0280019i	0.524054	−	0.851685i	$-0.324419\pi$
$421$	0.995150	+	0.574550i	0.0485006	+	0.0280019i	−0.475554	+	0.879687i	$0.657752\pi$
$422$	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	0.874597	−	0.484851i	$-0.161126\pi$
$431$	0.361329	+	0.625840i	0.0174046	+	0.0301457i	−0.857192	+	0.514997i	$0.827793\pi$
$432$	1.11771	−	5.07452i	0.0537758	−	0.244148i
$433$	−20.1778	+	11.6497i	−0.969684	+	0.559847i	−0.899140	−	0.437662i	$-0.855807\pi$
$433$	−20.1778	+	11.6497i	−0.969684	+	0.559847i	−0.0705439	+	0.997509i	$0.522473\pi$
$434$	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	0.613694	−	0.789544i	$-0.289683\pi$
$439$	4.96102	+	2.86425i	0.236776	+	0.136703i	−0.376918	+	0.926247i	$0.623016\pi$
$440$	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	0.0596116	−	0.998222i	$-0.481014\pi$
$443$	20.0773	−	11.5917i	0.953903	−	0.550736i	0.894291	+	0.447486i	$0.147680\pi$
$444$	−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	0.993933	+	0.109987i	$0.0350811\pi$
$461$	34.0561	+	19.6623i	1.58615	+	0.915765i	0.592218	+	0.805778i	$0.298252\pi$
$462$	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	$0.128889\pi$
$467$			17.0263i			0.787884i	−0.919135	+	0.393942i	$0.871111\pi$
$468$	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	−0.227806	−	0.973707i	$-0.573155\pi$
$479$	10.9769	−	6.33750i	0.501546	−	0.289568i	0.729352	+	0.684139i	$0.239822\pi$
$480$	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	$-0.735231\pi$
$487$		−	32.6229i		−	1.47829i	0.673549	−	0.739143i	$-0.264769\pi$
$488$	−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	0.351743	−	0.936097i	$-0.385589\pi$
$491$	−6.27240	−	3.62137i	−0.283070	−	0.163430i	−0.634812	+	0.772666i	$0.718923\pi$
$492$	−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	−0.609903	−	0.792476i	$-0.708792\pi$
$499$	8.51878	−	14.7550i	0.381353	−	0.660522i	0.991256	+	0.131954i	$0.0421250\pi$
$500$	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	−0.931208	−	0.364489i	$-0.881244\pi$
$503$	−24.2478	+	13.9995i	−1.08115	+	0.624205i	−0.149947	+	0.988694i	$0.547910\pi$
$504$	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	0.962695	+	0.270587i	$0.0872178\pi$
$509$	16.1465	+	27.9666i	0.715683	+	1.23960i	−0.247012	+	0.969012i	$0.579449\pi$
$510$	−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	−0.792165	−	0.610307i	$-0.791046\pi$
$523$	−15.0870	+	8.71046i	−0.659707	+	0.380882i	0.132458	+	0.991189i	$0.457713\pi$
$524$		−	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	−0.985982	−	0.166850i	$-0.946641\pi$
$541$	−14.8276	−	25.6821i	−0.637487	−	1.10416i	0.348495	−	0.937311i	$-0.386693\pi$
$542$	−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	−0.876256	−	0.481846i	$-0.839967\pi$
$547$	−20.9812	+	12.1135i	−0.897093	+	0.517937i	−0.0208373	+	0.999783i	$0.506633\pi$
$548$	−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	−0.802285	−	0.596941i	$-0.796383\pi$
$557$	−16.2011	+	9.35371i	−0.686463	+	0.396329i	0.115823	+	0.993270i	$0.463049\pi$
$558$	−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	0.993373	−	0.114939i	$-0.0366674\pi$
$587$	33.6896	+	19.4507i	1.39052	+	0.802816i	0.397146	+	0.917755i	$0.370001\pi$
$588$	−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	−0.642956	−	0.765903i	$-0.722292\pi$
$593$	−7.33331	+	4.23389i	−0.301143	+	0.173865i	0.341813	+	0.939768i	$0.388959\pi$
$594$	−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	−0.948124	−	0.317901i	$-0.897022\pi$
$599$	−18.3405	−	31.7667i	−0.749372	−	1.29795i	0.198752	−	0.980050i	$-0.436311\pi$
$600$	−1.72300	+	0.176823i	−0.0703412	+	0.00721877i
$601$		−	9.79356i		−	0.399488i	−0.979848	−	0.199744i	$-0.935989\pi$
$601$		−	9.79356i		−	0.399488i	0.979848	−	0.199744i	$-0.0640110\pi$
$602$	−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	$-0.915025\pi$
$607$		−	12.9985i		−	0.527593i	0.964578	−	0.263796i	$-0.0849747\pi$
$608$	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	0.393200	+	0.919453i	$0.371368\pi$
$613$	−14.8471	+	25.7160i	−0.599669	+	1.03866i	−0.992870	+	0.119205i	$0.961965\pi$
$614$	−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	−0.244679	−	0.969604i	$-0.578683\pi$
$617$	11.7412	−	6.77878i	0.472683	−	0.272904i	0.717362	+	0.696700i	$0.245349\pi$
$618$	−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	0.935042	−	0.354538i	$-0.115362\pi$
$631$	4.03125	+	6.98234i	0.160482	+	0.277962i	−0.774560	+	0.632501i	$0.782029\pi$
$632$	−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	−0.915536	−	0.402235i	$-0.868233\pi$
$641$	−2.77035	+	4.79838i	−0.109422	+	0.189525i	0.806114	+	0.591760i	$0.201567\pi$
$642$	0.916020	+	1.26732i	0.0361524	+	0.0500171i
$643$	−20.2446	+	35.0647i	−0.798369	+	1.38282i	0.122308	+	0.992492i	$0.460970\pi$
$643$	−20.2446	+	35.0647i	−0.798369	+	1.38282i	−0.920678	+	0.390324i	$0.872363\pi$
$644$	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	$-0.912946\pi$
$647$		−	13.7403i		−	0.540185i	0.962834	−	0.270093i	$-0.0870543\pi$
$648$	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	$-0.898164\pi$
$653$		−	16.0733i		−	0.628997i	0.949258	−	0.314498i	$-0.101836\pi$
$654$	−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	0.866167	−	0.499755i	$-0.166577\pi$
$659$	0.00725277	+	0.0125622i	0.000282528	+	0.000489352i	−0.865884	+	0.500245i	$0.833243\pi$
$660$	0.256144	−	0.571532i	0.00997039	−	0.0222468i
$661$	1.46214	−	0.844167i	0.0568706	−	0.0328343i	−0.471295	−	0.881976i	$-0.656213\pi$
$661$	1.46214	−	0.844167i	0.0568706	−	0.0328343i	0.528166	+	0.849141i	$0.322880\pi$
$662$	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	$0.147592\pi$
$673$			23.2047i			0.894476i	−0.894415	+	0.447238i	$0.852408\pi$
$674$	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	0.261105	−	0.965310i	$-0.415913\pi$
$701$	−11.7642	−	6.79204i	−0.444326	−	0.256532i	−0.705431	+	0.708779i	$0.749247\pi$
$702$	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	0.964411	−	0.264406i	$-0.0851759\pi$
$709$	6.74259	+	11.6785i	0.253223	+	0.438596i	−0.711188	+	0.703002i	$0.751843\pi$
$710$			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	0.970019	−	0.243028i	$-0.0781408\pi$
$719$	33.3719	+	19.2672i	1.24456	+	0.718547i	0.274541	+	0.961575i	$0.411474\pi$
$720$	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	−0.873857	−	0.486184i	$-0.838389\pi$
$727$	−0.428190	+	0.741646i	−0.0158807	+	0.0275061i	0.857976	+	0.513690i	$0.171722\pi$
$728$	−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	−0.957825	−	0.287352i	$-0.907225\pi$
$739$	−6.25405	+	10.8323i	−0.230059	+	0.398474i	0.727766	+	0.685825i	$0.240559\pi$
$740$	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	−0.656135	−	0.754643i	$-0.727810\pi$
$743$	8.87174	−	15.3663i	0.325473	−	0.563735i	0.981608	+	0.190908i	$0.0611433\pi$
$744$	−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	−0.206885	−	0.978365i	$-0.566333\pi$
$751$	14.7151	−	8.49577i	0.536962	−	0.310015i	0.743847	+	0.668350i	$0.232999\pi$
$752$		−	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	0.358008	−	0.933719i	$-0.383456\pi$
$757$	27.1732	−	47.0654i	0.987628	−	1.71062i	0.629620	−	0.776903i	$-0.283211\pi$
$758$	−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	$-0.914117\pi$
$761$		−	14.7061i		−	0.533095i	0.963822	−	0.266547i	$-0.0858829\pi$
$762$	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	−0.991753	−	0.128164i	$-0.959092\pi$
$769$	−16.8290	−	29.1487i	−0.606869	−	1.05113i	0.384884	−	0.922965i	$-0.374242\pi$
$770$	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	−0.941895	−	0.335907i	$-0.890957\pi$
$773$	−21.1817	−	36.6877i	−0.761851	−	1.31957i	0.180044	−	0.983659i	$-0.442376\pi$
$774$	−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	$-0.921930\pi$
$787$		−	13.6235i		−	0.485624i	0.970073	−	0.242812i	$-0.0780698\pi$
$788$	−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	$-0.654989\pi$
$809$		−	50.2747i		−	1.76756i	0.467900	−	0.883781i	$-0.345011\pi$
$810$	3.57979	+	8.25743i	0.125781	+	0.290136i
$811$	0.694406	−	0.400916i	0.0243839	−	0.0140781i	−0.487758	−	0.872979i	$-0.662185\pi$
$811$	0.694406	−	0.400916i	0.0243839	−	0.0140781i	0.512142	+	0.858901i	$0.328852\pi$
$812$	−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	−0.636265	−	0.771470i	$-0.719522\pi$
$821$	−8.20297	+	4.73598i	−0.286285	+	0.165287i	0.349980	+	0.936757i	$0.386188\pi$
$822$	−7.44163	−	3.33512i	−0.259556	−	0.116326i
$823$	−3.69096	−	6.39293i	−0.128659	−	0.222843i	0.794498	−	0.607266i	$-0.207734\pi$
$823$	−3.69096	−	6.39293i	−0.128659	−	0.222843i	−0.923157	+	0.384423i	$0.874400\pi$
$824$			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	−0.999862	−	0.0166175i	$-0.994710\pi$
$827$	−14.7907	−	25.6182i	−0.514322	−	0.890832i	0.485540	−	0.874215i	$-0.338623\pi$
$828$	−2.42145	−	11.6733i	−0.0841512	−	0.405675i
$829$		−	22.9422i		−	0.796816i	−0.917208	−	0.398408i	$-0.869563\pi$
$829$		−	22.9422i		−	0.796816i	0.917208	−	0.398408i	$-0.130437\pi$
$830$	−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	−0.769699	−	0.638406i	$-0.779594\pi$
$839$	4.86697	−	8.42984i	0.168026	−	0.291030i	0.937726	+	0.347376i	$0.112927\pi$
$840$	−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	−0.760958	−	0.648801i	$-0.775271\pi$
$853$	5.29796	−	9.17634i	0.181399	−	0.314192i	0.942357	+	0.334609i	$0.108604\pi$
$854$	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	0.0603507	−	0.998177i	$-0.480778\pi$
$857$	26.1897	−	45.3618i	0.894622	−	1.54953i	0.834272	−	0.551354i	$-0.185889\pi$
$858$	0.686849	−	1.53256i	0.0234487	−	0.0523208i
$859$	15.2939	+	26.4898i	0.521820	+	0.903819i	0.999678	+	0.0253818i	$0.00808014\pi$
$859$	15.2939	+	26.4898i	0.521820	+	0.903819i	−0.477858	+	0.878437i	$0.658587\pi$
$860$	−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	0.592825	−	0.805331i	$-0.298012\pi$
$877$	5.68003	+	3.27937i	0.191801	+	0.110736i	−0.401024	+	0.916067i	$0.631346\pi$
$878$	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	$-0.681042\pi$
$881$		−	50.0177i		−	1.68514i	0.538587	−	0.842570i	$-0.318958\pi$
$882$	−1.37594	+	0.285418i	−0.0463303	+	0.00961052i
$883$	−15.0237	−	26.0218i	−0.505588	−	0.875704i	−0.999979	−	0.00646423i	$-0.997942\pi$
$883$	−15.0237	−	26.0218i	−0.505588	−	0.875704i	0.494391	−	0.869239i	$-0.335391\pi$
$884$	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	0.999834	+	0.0181992i	$0.00579330\pi$
$887$	15.3582	+	26.6012i	0.515678	+	0.893181i	−0.484156	+	0.874982i	$0.660873\pi$
$888$	−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	0.281746	−	0.959489i	$-0.409087\pi$
$907$	−12.2972	−	7.09982i	−0.408323	−	0.235745i	−0.690069	+	0.723744i	$0.742420\pi$
$908$	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	0.689033	−	0.724730i	$-0.258035\pi$
$929$	12.3721	+	7.14305i	0.405916	+	0.234356i	−0.283117	+	0.959085i	$0.591369\pi$
$930$	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	0.980587	+	0.196083i	$0.0628221\pi$
$937$	20.2062	+	34.9981i	0.660106	+	1.14334i	−0.320481	+	0.947255i	$0.603845\pi$
$938$			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	0.793692	−	0.608319i	$-0.208156\pi$
$941$	−3.98704	−	6.90576i	−0.129974	−	0.225121i	−0.923666	+	0.383198i	$0.874823\pi$
$942$	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	0.368515	−	0.929622i	$-0.379866\pi$
$947$	−7.76421	−	4.48267i	−0.252303	−	0.145667i	−0.620818	+	0.783954i	$0.713200\pi$
$948$	−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	−0.292241	−	0.956345i	$-0.594401\pi$
$953$	21.0568	−	36.4715i	0.682098	−	1.18143i	0.974339	−	0.225084i	$-0.0722656\pi$
$954$	−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	−0.704519	−	0.709685i	$-0.748837\pi$
$967$	8.15807	−	14.1302i	0.262346	−	0.454396i	0.966865	+	0.255289i	$0.0821705\pi$
$968$	−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	0.324870	+	0.945759i	$0.394679\pi$
$971$	−20.4607	+	35.4390i	−0.656616	+	1.13729i	−0.981486	+	0.191533i	$0.938654\pi$
$972$	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	−0.756551	−	0.653935i	$-0.773117\pi$
$983$	5.89586	−	10.2119i	0.188049	−	0.325710i	0.944600	+	0.328225i	$0.106450\pi$
$984$	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	0.305460	−	0.952205i	$-0.401190\pi$
$991$	−11.5357	−	6.66013i	−0.366443	−	0.211566i	−0.671903	+	0.740639i	$0.734523\pi$
$992$	−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	0.958357	−	0.285571i	$-0.0921833\pi$
$997$	7.32126	+	12.6808i	0.231867	+	0.401605i	−0.726491	+	0.687176i	$0.758850\pi$
$998$	−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.521.7	yes	24
3.2	odd	2		570.2.s.a.521.3	yes	24
19.12	odd	6		570.2.s.a.221.3	✓	24
57.50	even	6	inner	570.2.s.b.221.7	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.s.a.221.3	✓	24	19.12	odd	6
570.2.s.a.521.3	yes	24	3.2	odd	2
570.2.s.b.221.7	yes	24	57.50	even	6	inner
570.2.s.b.521.7	yes	24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
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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