LMFDB - Embedded newform 547.2.c.a.40.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,2,Mod(40,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("547.40");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	547.c (of order $3$, 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:	$4.36781699056$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$45$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			40.16
Character	$\chi$	$=$	547.40
Dual form			547.2.c.a.506.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.467669 - 0.810027i) q^{2} +3.30105 q^{3} +(0.562571 - 0.974402i) q^{4} +(-0.395260 + 0.684610i) q^{5} +(-1.54380 - 2.67394i) q^{6} +(-2.17986 - 3.77563i) q^{7} -2.92307 q^{8} +7.89696 q^{9} +O(q^{10})$	\(q+(-0.467669 - 0.810027i) q^{2} +3.30105 q^{3} +(0.562571 - 0.974402i) q^{4} +(-0.395260 + 0.684610i) q^{5} +(-1.54380 - 2.67394i) q^{6} +(-2.17986 - 3.77563i) q^{7} -2.92307 q^{8} +7.89696 q^{9} +0.739403 q^{10} +(-1.40680 - 2.43665i) q^{11} +(1.85708 - 3.21655i) q^{12} +(2.07590 + 3.59557i) q^{13} +(-2.03891 + 3.53149i) q^{14} +(-1.30477 + 2.25994i) q^{15} +(0.241885 + 0.418957i) q^{16} +(-1.02890 - 1.78211i) q^{17} +(-3.69317 - 6.39675i) q^{18} +(-3.21026 + 5.56033i) q^{19} +(0.444724 + 0.770284i) q^{20} +(-7.19584 - 12.4636i) q^{21} +(-1.31584 + 2.27910i) q^{22} +(3.98906 - 6.90925i) q^{23} -9.64920 q^{24} +(2.18754 + 3.78893i) q^{25} +(1.94167 - 3.36307i) q^{26} +16.1651 q^{27} -4.90531 q^{28} +1.13972 q^{29} +2.44081 q^{30} -4.21623 q^{31} +(-2.69682 + 4.67103i) q^{32} +(-4.64393 - 8.04353i) q^{33} +(-0.962369 + 1.66687i) q^{34} +3.44644 q^{35} +(4.44260 - 7.69481i) q^{36} +(5.47554 + 9.48392i) q^{37} +6.00536 q^{38} +(6.85266 + 11.8692i) q^{39} +(1.15537 - 2.00116i) q^{40} +(2.41154 + 4.17691i) q^{41} +(-6.73054 + 11.6576i) q^{42} +(2.24247 + 3.88408i) q^{43} -3.16571 q^{44} +(-3.12135 + 5.40634i) q^{45} -7.46224 q^{46} +(6.12874 - 10.6153i) q^{47} +(0.798476 + 1.38300i) q^{48} +(-6.00358 + 10.3985i) q^{49} +(2.04609 - 3.54393i) q^{50} +(-3.39645 - 5.88283i) q^{51} +4.67137 q^{52} +(3.15175 + 5.45899i) q^{53} +(-7.55994 - 13.0942i) q^{54} +2.22421 q^{55} +(6.37187 + 11.0364i) q^{56} +(-10.5972 + 18.3550i) q^{57} +(-0.533012 - 0.923205i) q^{58} +(1.12124 + 1.94205i) q^{59} +(1.46806 + 2.54275i) q^{60} +(-1.84448 - 3.19473i) q^{61} +(1.97180 + 3.41526i) q^{62} +(-17.2143 - 29.8160i) q^{63} +6.01242 q^{64} -3.28208 q^{65} +(-4.34365 + 7.52342i) q^{66} +(-1.96420 - 3.40209i) q^{67} -2.31532 q^{68} +(13.1681 - 22.8078i) q^{69} +(-1.61180 - 2.79171i) q^{70} +(-5.25365 - 9.09959i) q^{71} -23.0833 q^{72} +(-0.0563340 - 0.0975733i) q^{73} +(5.12148 - 8.87067i) q^{74} +(7.22119 + 12.5075i) q^{75} +(3.61200 + 6.25616i) q^{76} +(-6.13327 + 10.6231i) q^{77} +(6.40956 - 11.1017i) q^{78} +2.29837 q^{79} -0.382430 q^{80} +29.6711 q^{81} +(2.25561 - 3.90683i) q^{82} +(2.78860 + 4.83000i) q^{83} -16.1927 q^{84} +1.62673 q^{85} +(2.09747 - 3.63293i) q^{86} +3.76228 q^{87} +(4.11218 + 7.12250i) q^{88} -1.30316 q^{89} +5.83904 q^{90} +(9.05034 - 15.6757i) q^{91} +(-4.48826 - 7.77389i) q^{92} -13.9180 q^{93} -11.4649 q^{94} +(-2.53777 - 4.39555i) q^{95} +(-8.90235 + 15.4193i) q^{96} +(-6.68150 + 11.5727i) q^{97} +11.2308 q^{98} +(-11.1095 - 19.2422i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - q^{2} - 4 q^{3} - 47 q^{4} + q^{5} - 3 q^{6} + 2 q^{7} - 30 q^{8} + 82 q^{9}+O(q^{10}) $ 90 * q - q^2 - 4 * q^3 - 47 * q^4 + q^5 - 3 * q^6 + 2 * q^7 - 30 * q^8 + 82 * q^9	\( 90 q - q^{2} - 4 q^{3} - 47 q^{4} + q^{5} - 3 q^{6} + 2 q^{7} - 30 q^{8} + 82 q^{9} - 10 q^{10} + q^{11} + 4 q^{12} - 3 q^{13} + 2 q^{14} - 7 q^{15} - 39 q^{16} - 4 q^{17} - 11 q^{18} - 2 q^{19} + 25 q^{20} - 27 q^{21} - 7 q^{22} + q^{23} + 32 q^{24} - 40 q^{25} - 10 q^{26} - 34 q^{27} - 28 q^{28} + 26 q^{29} - 40 q^{30} - 24 q^{31} + 19 q^{32} + q^{33} - 6 q^{34} - 8 q^{35} - 36 q^{36} - 10 q^{37} + 24 q^{38} + 22 q^{39} + 20 q^{40} + 3 q^{41} + 38 q^{42} - 12 q^{43} - 30 q^{44} - 2 q^{45} - 40 q^{46} + 32 q^{47} + 14 q^{48} - 43 q^{49} + 14 q^{50} + 13 q^{51} + 46 q^{52} + 9 q^{53} - 8 q^{54} + 4 q^{55} - 8 q^{56} - 8 q^{57} + 4 q^{58} + 22 q^{59} - 2 q^{60} - 12 q^{61} + 11 q^{62} + 8 q^{63} + 22 q^{64} + 18 q^{65} + 12 q^{66} - 22 q^{67} + 6 q^{68} - q^{69} - 6 q^{70} - 4 q^{71} - 140 q^{72} + 17 q^{73} + 17 q^{74} + 39 q^{75} + 84 q^{76} - 4 q^{77} + 33 q^{78} - 72 q^{79} - 40 q^{80} + 18 q^{81} - 9 q^{82} + 24 q^{83} + 114 q^{84} + 40 q^{85} - 72 q^{86} - 78 q^{87} - 22 q^{88} + 14 q^{89} + 96 q^{90} - 8 q^{92} - 76 q^{93} + 108 q^{94} - 11 q^{95} - 34 q^{96} - 74 q^{98} - 62 q^{99}+O(q^{100}) \) 90 * q - q^2 - 4 * q^3 - 47 * q^4 + q^5 - 3 * q^6 + 2 * q^7 - 30 * q^8 + 82 * q^9 - 10 * q^10 + q^11 + 4 * q^12 - 3 * q^13 + 2 * q^14 - 7 * q^15 - 39 * q^16 - 4 * q^17 - 11 * q^18 - 2 * q^19 + 25 * q^20 - 27 * q^21 - 7 * q^22 + q^23 + 32 * q^24 - 40 * q^25 - 10 * q^26 - 34 * q^27 - 28 * q^28 + 26 * q^29 - 40 * q^30 - 24 * q^31 + 19 * q^32 + q^33 - 6 * q^34 - 8 * q^35 - 36 * q^36 - 10 * q^37 + 24 * q^38 + 22 * q^39 + 20 * q^40 + 3 * q^41 + 38 * q^42 - 12 * q^43 - 30 * q^44 - 2 * q^45 - 40 * q^46 + 32 * q^47 + 14 * q^48 - 43 * q^49 + 14 * q^50 + 13 * q^51 + 46 * q^52 + 9 * q^53 - 8 * q^54 + 4 * q^55 - 8 * q^56 - 8 * q^57 + 4 * q^58 + 22 * q^59 - 2 * q^60 - 12 * q^61 + 11 * q^62 + 8 * q^63 + 22 * q^64 + 18 * q^65 + 12 * q^66 - 22 * q^67 + 6 * q^68 - q^69 - 6 * q^70 - 4 * q^71 - 140 * q^72 + 17 * q^73 + 17 * q^74 + 39 * q^75 + 84 * q^76 - 4 * q^77 + 33 * q^78 - 72 * q^79 - 40 * q^80 + 18 * q^81 - 9 * q^82 + 24 * q^83 + 114 * q^84 + 40 * q^85 - 72 * q^86 - 78 * q^87 - 22 * q^88 + 14 * q^89 + 96 * q^90 - 8 * q^92 - 76 * q^93 + 108 * q^94 - 11 * q^95 - 34 * q^96 - 74 * q^98 - 62 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/547\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.467669	−	0.810027i	−0.330692	−	0.572775i	0.651956	−	0.758257i	$-0.273949\pi$
$2$	−0.467669	−	0.810027i	−0.330692	−	0.572775i	−0.982648	+	0.185482i	$0.940615\pi$
$3$	3.30105			1.90586			0.952932	−	0.303183i	$-0.0980493\pi$
$3$	3.30105			1.90586			0.952932	+	0.303183i	$0.0980493\pi$
$4$	0.562571	−	0.974402i	0.281286	−	0.487201i
$5$	−0.395260	+	0.684610i	−0.176766	+	0.306167i	−0.940771	−	0.339043i	$-0.889897\pi$
$5$	−0.395260	+	0.684610i	−0.176766	+	0.306167i	0.764005	+	0.645210i	$0.223230\pi$
$6$	−1.54380	−	2.67394i	−0.630254	−	1.09163i
$7$	−2.17986	−	3.77563i	−0.823910	−	1.42705i	−0.902750	−	0.430166i	$-0.858455\pi$
$7$	−2.17986	−	3.77563i	−0.823910	−	1.42705i	0.0788402	−	0.996887i	$-0.474878\pi$
$8$	−2.92307			−1.03346
$9$	7.89696			2.63232
$10$	0.739403			0.233820
$11$	−1.40680	−	2.43665i	−0.424167	−	0.734679i	0.572175	−	0.820131i	$-0.306100\pi$
$11$	−1.40680	−	2.43665i	−0.424167	−	0.734679i	−0.996342	+	0.0854526i	$0.972766\pi$
$12$	1.85708	−	3.21655i	0.536092	−	0.928539i
$13$	2.07590	+	3.59557i	0.575751	+	0.997230i	0.995960	+	0.0898027i	$0.0286237\pi$
$13$	2.07590	+	3.59557i	0.575751	+	0.997230i	−0.420208	+	0.907428i	$0.638043\pi$
$14$	−2.03891	+	3.53149i	−0.544921	+	0.943830i
$15$	−1.30477	+	2.25994i	−0.336891	+	0.583513i
$16$	0.241885	+	0.418957i	0.0604713	+	0.104739i
$17$	−1.02890	−	1.78211i	−0.249545	−	0.432224i	0.713855	−	0.700294i	$-0.246948\pi$
$17$	−1.02890	−	1.78211i	−0.249545	−	0.432224i	−0.963400	+	0.268069i	$0.913614\pi$
$18$	−3.69317	−	6.39675i	−0.870487	−	1.50773i
$19$	−3.21026	+	5.56033i	−0.736484	+	1.27563i	0.217585	+	0.976041i	$0.430182\pi$
$19$	−3.21026	+	5.56033i	−0.736484	+	1.27563i	−0.954069	+	0.299586i	$0.903151\pi$
$20$	0.444724	+	0.770284i	0.0994432	+	0.172241i
$21$	−7.19584	−	12.4636i	−1.57026	−	2.71977i
$22$	−1.31584	+	2.27910i	−0.280537	+	0.485905i
$23$	3.98906	−	6.90925i	0.831776	−	1.44068i	−0.0648521	−	0.997895i	$-0.520658\pi$
$23$	3.98906	−	6.90925i	0.831776	−	1.44068i	0.896628	−	0.442784i	$-0.146009\pi$
$24$	−9.64920			−1.96963
$25$	2.18754	+	3.78893i	0.437508	+	0.757786i
$26$	1.94167	−	3.36307i	0.380793	−	0.659552i
$27$	16.1651			3.11098
$28$	−4.90531			−0.927016
$29$	1.13972			0.211641			0.105820	−	0.994385i	$-0.466253\pi$
$29$	1.13972			0.211641			0.105820	+	0.994385i	$0.466253\pi$
$30$	2.44081			0.445629
$31$	−4.21623			−0.757257			−0.378629	−	0.925549i	$-0.623604\pi$
$31$	−4.21623			−0.757257			−0.378629	+	0.925549i	$0.623604\pi$
$32$	−2.69682	+	4.67103i	−0.476735	+	0.825729i
$33$	−4.64393	−	8.04353i	−0.808405	−	1.40020i
$34$	−0.962369	+	1.66687i	−0.165045	+	0.285866i
$35$	3.44644			0.582555
$36$	4.44260	−	7.69481i	0.740434	−	1.28247i
$37$	5.47554	+	9.48392i	0.900174	+	1.55915i	0.827268	+	0.561808i	$0.189894\pi$
$37$	5.47554	+	9.48392i	0.900174	+	1.55915i	0.0729059	+	0.997339i	$0.476773\pi$
$38$	6.00536			0.974197
$39$	6.85266	+	11.8692i	1.09730	+	1.90059i
$40$	1.15537	−	2.00116i	0.182680	−	0.316411i
$41$	2.41154	+	4.17691i	0.376620	+	0.652324i	0.990568	−	0.137022i	$-0.0437530\pi$
$41$	2.41154	+	4.17691i	0.376620	+	0.652324i	−0.613948	+	0.789346i	$0.710420\pi$
$42$	−6.73054	+	11.6576i	−1.03855	+	1.79881i
$43$	2.24247	+	3.88408i	0.341974	+	0.592316i	0.984799	−	0.173696i	$-0.0555712\pi$
$43$	2.24247	+	3.88408i	0.341974	+	0.592316i	−0.642825	+	0.766013i	$0.722238\pi$
$44$	−3.16571			−0.477248
$45$	−3.12135	+	5.40634i	−0.465304	+	0.805930i
$46$	−7.46224			−1.10025
$47$	6.12874	−	10.6153i	0.893968	−	1.54840i	0.0588916	−	0.998264i	$-0.481243\pi$
$47$	6.12874	−	10.6153i	0.893968	−	1.54840i	0.835077	−	0.550134i	$-0.185423\pi$
$48$	0.798476	+	1.38300i	0.115250	+	0.199619i
$49$	−6.00358	+	10.3985i	−0.857654	+	1.48550i
$50$	2.04609	−	3.54393i	0.289361	−	0.501187i
$51$	−3.39645	−	5.88283i	−0.475599	−	0.823761i
$52$	4.67137			0.647802
$53$	3.15175	+	5.45899i	0.432926	+	0.749851i	0.997124	−	0.0757893i	$-0.0241477\pi$
$53$	3.15175	+	5.45899i	0.432926	+	0.749851i	−0.564197	+	0.825640i	$0.690814\pi$
$54$	−7.55994	−	13.0942i	−1.02878	−	1.78189i
$55$	2.22421			0.299913
$56$	6.37187	+	11.0364i	0.851477	+	1.47480i
$57$	−10.5972	+	18.3550i	−1.40364	+	2.43117i
$58$	−0.533012	−	0.923205i	−0.0699880	−	0.121223i
$59$	1.12124	+	1.94205i	0.145973	+	0.252833i	0.929736	−	0.368228i	$-0.120035\pi$
$59$	1.12124	+	1.94205i	0.145973	+	0.252833i	−0.783762	+	0.621061i	$0.786702\pi$
$60$	1.46806	+	2.54275i	0.189525	+	0.328268i
$61$	−1.84448	−	3.19473i	−0.236161	−	0.409043i	0.723448	−	0.690379i	$-0.242556\pi$
$61$	−1.84448	−	3.19473i	−0.236161	−	0.409043i	−0.959610	+	0.281335i	$0.909223\pi$
$62$	1.97180	+	3.41526i	0.250419	+	0.433738i
$63$	−17.2143	−	29.8160i	−2.16879	−	3.75646i
$64$	6.01242			0.751552
$65$	−3.28208			−0.407092
$66$	−4.34365	+	7.52342i	−0.534666	+	0.926069i
$67$	−1.96420	−	3.40209i	−0.239965	−	0.415631i	0.720739	−	0.693206i	$-0.243803\pi$
$67$	−1.96420	−	3.40209i	−0.239965	−	0.415631i	−0.960704	+	0.277575i	$0.910469\pi$
$68$	−2.31532			−0.280773
$69$	13.1681	−	22.8078i	1.58525	−	2.74574i
$70$	−1.61180	−	2.79171i	−0.192646	−	0.333673i
$71$	−5.25365	−	9.09959i	−0.623494	−	1.07992i	−0.988830	−	0.149047i	$-0.952379\pi$
$71$	−5.25365	−	9.09959i	−0.623494	−	1.07992i	0.365336	−	0.930876i	$-0.380954\pi$
$72$	−23.0833			−2.72040
$73$	−0.0563340	−	0.0975733i	−0.00659339	−	0.0114201i	0.862710	−	0.505699i	$-0.168765\pi$
$73$	−0.0563340	−	0.0975733i	−0.00659339	−	0.0114201i	−0.869303	+	0.494279i	$0.835432\pi$
$74$	5.12148	−	8.87067i	0.595361	−	1.03119i
$75$	7.22119	+	12.5075i	0.833831	+	1.44424i
$76$	3.61200	+	6.25616i	0.414325	+	0.717631i
$77$	−6.13327	+	10.6231i	−0.698951	+	1.21062i
$78$	6.40956	−	11.1017i	0.725739	−	1.25702i
$79$	2.29837			0.258586			0.129293	−	0.991606i	$-0.458729\pi$
$79$	2.29837			0.258586			0.129293	+	0.991606i	$0.458729\pi$
$80$	−0.382430			−0.0427569
$81$	29.6711			3.29679
$82$	2.25561	−	3.90683i	0.249090	−	0.431437i
$83$	2.78860	+	4.83000i	0.306089	+	0.530161i	0.977503	−	0.210921i	$-0.0676462\pi$
$83$	2.78860	+	4.83000i	0.306089	+	0.530161i	−0.671414	+	0.741082i	$0.734313\pi$
$84$	−16.1927			−1.76677
$85$	1.62673			0.176444
$86$	2.09747	−	3.63293i	0.226176	−	0.391749i
$87$	3.76228			0.403359
$88$	4.11218	+	7.12250i	0.438359	+	0.759261i
$89$	−1.30316			−0.138135			−0.0690675	−	0.997612i	$-0.522002\pi$
$89$	−1.30316			−0.138135			−0.0690675	+	0.997612i	$0.522002\pi$
$90$	5.83904			0.615489
$91$	9.05034	−	15.6757i	0.948734	−	1.64326i
$92$	−4.48826	−	7.77389i	−0.467933	−	0.810484i
$93$	−13.9180			−1.44323
$94$	−11.4649			−1.18251
$95$	−2.53777	−	4.39555i	−0.260370	−	0.450974i
$96$	−8.90235	+	15.4193i	−0.908593	+	1.57373i
$97$	−6.68150	+	11.5727i	−0.678403	+	1.17503i	0.297058	+	0.954859i	$0.403994\pi$
$97$	−6.68150	+	11.5727i	−0.678403	+	1.17503i	−0.975462	+	0.220170i	$0.929339\pi$
$98$	11.2308			1.13448
$99$	−11.1095	−	19.2422i	−1.11654	−	1.93391i
$100$	4.92259			0.492259
$101$	−7.77429			−0.773571			−0.386785	−	0.922170i	$-0.626415\pi$
$101$	−7.77429			−0.773571			−0.386785	+	0.922170i	$0.626415\pi$
$102$	−3.17683	+	5.50244i	−0.314553	+	0.544823i
$103$	−19.3802			−1.90959			−0.954796	−	0.297263i	$-0.903926\pi$
$103$	−19.3802			−1.90959			−0.954796	+	0.297263i	$0.903926\pi$
$104$	−6.06799	−	10.5101i	−0.595016	−	1.03060i
$105$	11.3769			1.11027
$106$	2.94795	−	5.10601i	0.286331	−	0.495939i
$107$	−16.3465			−1.58028			−0.790140	−	0.612927i	$-0.789992\pi$
$107$	−16.3465			−1.58028			−0.790140	+	0.612927i	$0.789992\pi$
$108$	9.09404	−	15.7513i	0.875075	−	1.51567i
$109$	6.74182	−	11.6772i	0.645749	−	1.11847i	−0.338379	−	0.941010i	$-0.609878\pi$
$109$	6.74182	−	11.6772i	0.645749	−	1.11847i	0.984128	−	0.177460i	$-0.0567882\pi$
$110$	−1.04019	−	1.80167i	−0.0991787	−	0.171783i
$111$	18.0751	+	31.3069i	1.71561	+	2.97152i
$112$	1.05455	−	1.82654i	0.0996457	−	0.172591i
$113$	−0.822577	+	1.42474i	−0.0773815	+	0.134029i	−0.902119	−	0.431486i	$-0.857989\pi$
$113$	−0.822577	+	1.42474i	−0.0773815	+	0.134029i	0.824738	+	0.565515i	$0.191323\pi$
$114$	19.8240			1.85669
$115$	3.15343	+	5.46190i	0.294059	+	0.509325i
$116$	0.641174	−	1.11055i	0.0595315	−	0.103112i
$117$	16.3933	+	28.3940i	1.51556	+	2.62503i
$118$	1.04874	−	1.81647i	0.0965443	−	0.167220i
$119$	−4.48571	+	7.76949i	−0.411205	+	0.712228i
$120$	3.81394	−	6.60594i	0.348164	−	0.603037i
$121$	1.54181	−	2.67050i	0.140165	−	0.242772i
$122$	−1.72521	+	2.98815i	−0.156193	+	0.270535i
$123$	7.96063	+	13.7882i	0.717786	+	1.24324i
$124$	−2.37193	+	4.10830i	−0.213006	+	0.368936i
$125$	−7.41118			−0.662876
$126$	−16.1012	+	27.8880i	−1.43441	+	2.48446i
$127$	−4.95778	+	8.58712i	−0.439932	+	0.761984i	−0.997684	−	0.0680237i	$-0.978331\pi$
$127$	−4.95778	+	8.58712i	−0.439932	+	0.761984i	0.557752	+	0.830008i	$0.311664\pi$
$128$	2.58182	+	4.47184i	0.228203	+	0.395259i
$129$	7.40253	+	12.8216i	0.651756	+	1.12888i
$130$	1.53493	+	2.65857i	0.134622	+	0.233172i
$131$	8.53420			0.745637			0.372818	−	0.927904i	$-0.378391\pi$
$131$	8.53420			0.745637			0.372818	+	0.927904i	$0.378391\pi$
$132$	−10.4502			−0.909571
$133$	27.9917			2.42718
$134$	−1.83719	+	3.18210i	−0.158709	+	0.274892i
$135$	−6.38943	+	11.0668i	−0.549915	+	0.952480i
$136$	3.00754	+	5.20921i	0.257895	+	0.446686i
$137$	5.99157	+	10.3777i	0.511894	+	0.886627i	0.999905	+	0.0137892i	$0.00438936\pi$
$137$	5.99157	+	10.3777i	0.511894	+	0.886627i	−0.488011	+	0.872838i	$0.662277\pi$
$138$	−24.6333			−2.09692
$139$	0.840040	+	1.45499i	0.0712512	+	0.123411i	0.899450	−	0.437024i	$-0.143967\pi$
$139$	0.840040	+	1.45499i	0.0712512	+	0.123411i	−0.828199	+	0.560435i	$0.810634\pi$
$140$	1.93887	−	3.35822i	0.163864	−	0.283822i
$141$	20.2313	−	35.0416i	1.70378	−	2.95104i
$142$	−4.91394	+	8.51120i	−0.412369	+	0.714244i
$143$	5.84077	−	10.1165i	0.488429	−	0.845985i
$144$	1.91016	+	3.30849i	0.159180	+	0.275707i
$145$	−0.450486	+	0.780265i	−0.0374108	+	0.0647975i
$146$	−0.0526913	+	0.0912641i	−0.00436077	+	0.00755307i
$147$	−19.8181	+	34.3260i	−1.63457	+	2.83116i
$148$	12.3215			1.01282
$149$	−3.20323			−0.262418			−0.131209	−	0.991355i	$-0.541886\pi$
$149$	−3.20323			−0.262418			−0.131209	+	0.991355i	$0.541886\pi$
$150$	6.75425	−	11.6987i	0.551482	−	0.955196i
$151$	4.92575			0.400852			0.200426	−	0.979709i	$-0.435767\pi$
$151$	4.92575			0.400852			0.200426	+	0.979709i	$0.435767\pi$
$152$	9.38380	−	16.2532i	0.761126	−	1.31831i
$153$	−8.12518	−	14.0732i	−0.656882	−	1.13775i
$154$	11.4734			0.924549
$155$	1.66651	−	2.88647i	0.133857	−	0.231847i
$156$	15.4204			1.23462
$157$	−2.02871	−	3.51383i	−0.161909	−	0.280435i	0.773644	−	0.633620i	$-0.218432\pi$
$157$	−2.02871	−	3.51383i	−0.161909	−	0.280435i	−0.935553	+	0.353186i	$0.885098\pi$
$158$	−1.07487	−	1.86174i	−0.0855124	−	0.148112i
$159$	10.4041	+	18.0204i	0.825099	+	1.42911i
$160$	−2.13189	−	3.69254i	−0.168541	−	0.291921i
$161$	−34.7824			−2.74123
$162$	−13.8763	−	24.0344i	−1.09022	−	1.88832i
$163$	1.40544	+	2.43429i	0.110082	+	0.190668i	0.915803	−	0.401627i	$-0.131555\pi$
$163$	1.40544	+	2.43429i	0.110082	+	0.190668i	−0.805721	+	0.592295i	$0.798222\pi$
$164$	5.42666			0.423751
$165$	7.34224			0.571593
$166$	2.60829	−	4.51768i	0.202442	−	0.350640i
$167$	−18.0243			−1.39476			−0.697380	−	0.716701i	$-0.745651\pi$
$167$	−18.0243			−1.39476			−0.697380	+	0.716701i	$0.745651\pi$
$168$	21.0339	+	36.4318i	1.62280	+	2.81077i
$169$	−2.11873	+	3.66974i	−0.162979	+	0.282288i
$170$	−0.760772	−	1.31770i	−0.0583485	−	0.101063i
$171$	−25.3513	+	43.9097i	−1.93866	+	3.35786i
$172$	5.04620			0.384769
$173$	5.38220			0.409201			0.204601	−	0.978846i	$-0.434410\pi$
$173$	5.38220			0.409201			0.204601	+	0.978846i	$0.434410\pi$
$174$	−1.75950	−	3.04755i	−0.133388	−	0.231034i
$175$	9.53706	−	16.5187i	0.720934	−	1.24869i
$176$	0.680569	−	1.17878i	0.0512998	−	0.0888539i
$177$	3.70128	+	6.41080i	0.278205	+	0.481866i
$178$	0.609449	+	1.05560i	0.0456801	+	0.0791203i
$179$	−4.13417			−0.309003			−0.154501	−	0.987993i	$-0.549377\pi$
$179$	−4.13417			−0.309003			−0.154501	+	0.987993i	$0.549377\pi$
$180$	3.51197	+	6.08290i	0.261766	+	0.453393i
$181$	−0.302654	+	0.524212i	−0.0224961	+	0.0389644i	−0.877054	−	0.480391i	$-0.840495\pi$
$181$	−0.302654	+	0.524212i	−0.0224961	+	0.0389644i	0.854558	+	0.519356i	$0.173828\pi$
$182$	−16.9303			−1.25495
$183$	−6.08872	−	10.5460i	−0.450091	−	0.779581i
$184$	−11.6603	+	20.1962i	−0.859607	+	1.48888i
$185$	−8.65705			−0.636479
$186$	6.50902	+	11.2740i	0.477265	+	0.826646i
$187$	−2.89492	+	5.01415i	−0.211697	+	0.366671i
$188$	−6.89570	−	11.9437i	−0.502921	−	0.871084i
$189$	−35.2377	−	61.0336i	−2.56317	−	4.43954i
$190$	−2.37368	+	4.11133i	−0.172205	+	0.298267i
$191$	6.07288	−	10.5185i	0.439418	−	0.761095i	−0.558226	−	0.829689i	$-0.688518\pi$
$191$	6.07288	−	10.5185i	0.439418	−	0.761095i	0.997645	+	0.0685940i	$0.0218513\pi$
$192$	19.8473			1.43236
$193$	2.67736	−	4.63732i	0.192720	−	0.333801i	−0.753430	−	0.657528i	$-0.771602\pi$
$193$	2.67736	−	4.63732i	0.192720	−	0.333801i	0.946151	+	0.323726i	$0.104936\pi$
$194$	12.4989			0.897370
$195$	−10.8343			−0.775862
$196$	6.75488	+	11.6998i	0.482491	+	0.835700i
$197$	8.88399			0.632958			0.316479	−	0.948599i	$-0.397499\pi$
$197$	8.88399			0.632958			0.316479	+	0.948599i	$0.397499\pi$
$198$	−10.3911	+	17.9979i	−0.738464	+	1.27906i
$199$	−11.5000	+	19.9186i	−0.815214	+	1.41199i	0.0939599	+	0.995576i	$0.470047\pi$
$199$	−11.5000	+	19.9186i	−0.815214	+	1.41199i	−0.909174	+	0.416416i	$0.863286\pi$
$200$	−6.39432	−	11.0753i	−0.452147	−	0.783141i
$201$	−6.48392	−	11.2305i	−0.457340	−	0.792137i
$202$	3.63580	+	6.29738i	0.255814	+	0.443082i
$203$	−2.48443	−	4.30316i	−0.174373	−	0.302023i
$204$	−7.64299			−0.535116
$205$	−3.81274			−0.266294
$206$	9.06354	+	15.6985i	0.631487	+	1.09377i
$207$	31.5014	−	54.5621i	2.18950	−	3.79233i
$208$	−1.00426	+	1.73943i	−0.0696328	+	0.120608i
$209$	18.0648			1.24957
$210$	−5.32063	−	9.21559i	−0.367158	−	0.635936i
$211$	−7.76865	+	13.4557i	−0.534816	+	0.926329i	0.464356	+	0.885649i	$0.346286\pi$
$211$	−7.76865	+	13.4557i	−0.534816	+	0.926329i	−0.999172	+	0.0406800i	$0.987048\pi$
$212$	7.09234			0.487104
$213$	−17.3426	−	30.0382i	−1.18829	−	2.05819i
$214$	7.64477	+	13.2411i	0.522586	+	0.905145i
$215$	−3.54544			−0.241797
$216$	−47.2518			−3.21507
$217$	9.19079	+	15.9189i	0.623911	+	1.08065i
$218$	−12.6118			−0.854176
$219$	−0.185962	−	0.322095i	−0.0125661	−	0.0217652i
$220$	1.25128	−	2.16728i	0.0843611	−	0.146118i
$221$	4.27179	−	7.39895i	0.287352	−	0.497707i
$222$	16.9063	−	29.2826i	1.13468	−	1.96532i
$223$	−1.91132	+	3.31050i	−0.127991	+	0.221687i	−0.922898	−	0.385044i	$-0.874186\pi$
$223$	−1.91132	+	3.31050i	−0.127991	+	0.221687i	0.794907	+	0.606731i	$0.207520\pi$
$224$	23.5148			1.57115
$225$	17.2749	+	29.9210i	1.15166	+	1.99474i
$226$	1.53878			0.102358
$227$	−2.92645	+	5.06877i	−0.194236	+	0.336426i	−0.946650	−	0.322264i	$-0.895556\pi$
$227$	−2.92645	+	5.06877i	−0.194236	+	0.336426i	0.752414	+	0.658690i	$0.228889\pi$
$228$	11.9234	+	20.6519i	0.789647	+	1.36771i
$229$	11.1058	−	19.2357i	0.733890	−	1.27113i	−0.221319	−	0.975201i	$-0.571036\pi$
$229$	11.1058	−	19.2357i	0.733890	−	1.27113i	0.955209	−	0.295933i	$-0.0956304\pi$
$230$	2.94952	−	5.10872i	0.194486	−	0.336859i
$231$	−20.2462	+	35.0675i	−1.33211	+	2.30727i
$232$	−3.33148			−0.218722
$233$	0.150866	−	0.261308i	0.00988358	−	0.0171189i	−0.861041	−	0.508535i	$-0.830187\pi$
$233$	0.150866	−	0.261308i	0.00988358	−	0.0171189i	0.870925	+	0.491416i	$0.163521\pi$
$234$	15.3333	−	26.5580i	1.00237	−	1.73615i
$235$	4.84489	+	8.39159i	0.316046	+	0.547407i
$236$	2.52311			0.164241
$237$	7.58703			0.492830
$238$	8.39132			0.543929
$239$	0.0359822	+	0.0623229i	0.00232749	+	0.00403133i	0.867187	−	0.497983i	$-0.165926\pi$
$239$	0.0359822	+	0.0623229i	0.00232749	+	0.00403133i	−0.864859	+	0.502014i	$0.832592\pi$
$240$	−1.26242			−0.0814890
$241$	−3.92440	+	6.79725i	−0.252793	+	0.437850i	−0.964294	−	0.264835i	$-0.914682\pi$
$241$	−3.92440	+	6.79725i	−0.252793	+	0.437850i	0.711501	+	0.702685i	$0.248016\pi$
$242$	−2.88423			−0.185405
$243$	49.4506			3.17226
$244$	−4.15060			−0.265715
$245$	−4.74595	−	8.22022i	−0.303207	−	0.525171i
$246$	7.44588	−	12.8967i	0.474732	−	0.822260i
$247$	−26.6567			−1.69613
$248$	12.3243			0.782595
$249$	9.20533	+	15.9441i	0.583364	+	1.01042i
$250$	3.46598	+	6.00326i	0.219208	+	0.379679i
$251$	−8.74078	−	15.1395i	−0.551713	−	0.955595i	−0.998151	−	0.0607808i	$-0.980641\pi$
$251$	−8.74078	−	15.1395i	−0.551713	−	0.955595i	0.446438	−	0.894815i	$-0.352692\pi$
$252$	−38.7370			−2.44020
$253$	−22.4473			−1.41125
$254$	9.27440			0.581927
$255$	5.36993			0.336278
$256$	8.42729	−	14.5965i	0.526706	−	0.912281i
$257$	−2.58155			−0.161033			−0.0805164	−	0.996753i	$-0.525657\pi$
$257$	−2.58155			−0.161033			−0.0805164	+	0.996753i	$0.525657\pi$
$258$	6.92387	−	11.9925i	0.431061	−	0.746620i
$259$	23.8718	−	41.3472i	1.48332	−	2.56919i
$260$	−1.84640	+	3.19807i	−0.114509	+	0.198336i
$261$	9.00034			0.557107
$262$	−3.99118	−	6.91293i	−0.246576	−	0.427082i
$263$	−14.0309			−0.865183			−0.432591	−	0.901590i	$-0.642401\pi$
$263$	−14.0309			−0.865183			−0.432591	+	0.901590i	$0.642401\pi$
$264$	13.5745	+	23.5118i	0.835454	+	1.44705i
$265$	−4.98304			−0.306106
$266$	−13.0908	−	22.6740i	−0.802651	−	1.39023i
$267$	−4.30181			−0.263267
$268$	−4.42000			−0.269995
$269$	−6.20490	+	10.7472i	−0.378319	+	0.655268i	−0.990818	−	0.135204i	$-0.956831\pi$
$269$	−6.20490	+	10.7472i	−0.378319	+	0.655268i	0.612499	+	0.790472i	$0.290165\pi$
$270$	11.9526			0.727409
$271$	−7.45891	−	12.9192i	−0.453097	−	0.784786i	0.545480	−	0.838124i	$-0.316347\pi$
$271$	−7.45891	−	12.9192i	−0.453097	−	0.784786i	−0.998577	+	0.0533376i	$0.983014\pi$
$272$	0.497751	−	0.862130i	0.0301806	−	0.0522743i
$273$	29.8757	−	51.7462i	1.80816	−	3.13182i
$274$	5.60414	−	9.70666i	0.338559	−	0.586401i
$275$	6.15487	−	10.6606i	0.371153	−	0.642856i
$276$	−14.8160	−	25.6620i	−0.891818	−	1.54467i
$277$	28.0975			1.68822			0.844108	−	0.536174i	$-0.180131\pi$
$277$	28.0975			1.68822			0.844108	+	0.536174i	$0.180131\pi$
$278$	0.785721	−	1.36091i	0.0471244	−	0.0816219i
$279$	−33.2954			−1.99334
$280$	−10.0742			−0.602047
$281$	6.70208	+	11.6083i	0.399813	+	0.692496i	0.993703	−	0.112050i	$-0.0357418\pi$
$281$	6.70208	+	11.6083i	0.399813	+	0.692496i	−0.593890	+	0.804546i	$0.702408\pi$
$282$	−37.8462			−2.25371
$283$	−4.92176	−	8.52473i	−0.292568	−	0.506743i	0.681848	−	0.731494i	$-0.261176\pi$
$283$	−4.92176	−	8.52473i	−0.292568	−	0.506743i	−0.974416	+	0.224751i	$0.927843\pi$
$284$	−11.8222			−0.701519
$285$	−8.37733	−	14.5100i	−0.496230	−	0.859496i
$286$	−10.9262			−0.646079
$287$	10.5136	−	18.2102i	0.620601	−	1.07491i
$288$	−21.2967	+	36.8870i	−1.25492	+	2.17358i
$289$	6.38273	−	11.0552i	0.375455	−	0.650307i
$290$	0.842714			0.0494859
$291$	−22.0560	+	38.2021i	−1.29294	+	2.23945i
$292$	−0.126767			−0.00741851
$293$	−21.4325			−1.25210			−0.626050	−	0.779783i	$-0.715329\pi$
$293$	−21.4325			−1.25210			−0.626050	+	0.779783i	$0.715329\pi$
$294$	37.0733			2.16216
$295$	−1.77273			−0.103212
$296$	−16.0054	−	27.7221i	−0.930293	−	1.61132i
$297$	−22.7412	−	39.3889i	−1.31958	−	2.28557i
$298$	1.49805	+	2.59470i	0.0867797	+	0.150307i
$299$	33.1236			1.91558
$300$	16.2497			0.938178
$301$	9.77656	−	16.9335i	0.563511	−	0.976030i
$302$	−2.30362	−	3.98999i	−0.132558	−	0.229598i
$303$	−25.6634			−1.47432
$304$	−3.10605			−0.178144
$305$	2.91619			0.166981
$306$	−7.59979	+	13.1632i	−0.434451	+	0.752492i
$307$	−4.88114			−0.278582			−0.139291	−	0.990252i	$-0.544482\pi$
$307$	−4.88114			−0.278582			−0.139291	+	0.990252i	$0.544482\pi$
$308$	6.90080	+	11.9525i	0.393209	+	0.681059i
$309$	−63.9752			−3.63942
$310$	−3.11749			−0.177062
$311$	−7.61988			−0.432084			−0.216042	−	0.976384i	$-0.569315\pi$
$311$	−7.61988			−0.432084			−0.216042	+	0.976384i	$0.569315\pi$
$312$	−20.0308	−	34.6943i	−1.13402	−	1.96418i
$313$	−5.44894	+	9.43785i	−0.307993	+	0.533459i	−0.977923	−	0.208965i	$-0.932991\pi$
$313$	−5.44894	+	9.43785i	−0.307993	+	0.533459i	0.669931	+	0.742424i	$0.266324\pi$
$314$	−1.89753	+	3.28662i	−0.107084	+	0.185475i
$315$	27.2164			1.53347
$316$	1.29299	−	2.23953i	0.0727366	−	0.125983i
$317$	2.84562	−	4.92875i	0.159826	−	0.276826i	−0.774980	−	0.631986i	$-0.782240\pi$
$317$	2.84562	−	4.92875i	0.159826	−	0.276826i	0.934806	+	0.355159i	$0.115573\pi$
$318$	9.73136	−	16.8552i	0.545707	−	0.945193i
$319$	−1.60336	−	2.77711i	−0.0897711	−	0.155488i
$320$	−2.37647	+	4.11616i	−0.132849	+	0.230101i
$321$	−53.9608			−3.01180
$322$	16.2666	+	28.1746i	0.906504	+	1.57011i
$323$	13.2121			0.735143
$324$	16.6921	−	28.9116i	0.927340	−	1.60620i
$325$	−9.08223	+	15.7309i	−0.503791	+	0.872592i
$326$	1.31456	−	2.27688i	0.0728067	−	0.126105i
$327$	22.2551	−	38.5470i	1.23071	−	2.13165i
$328$	−7.04910	−	12.2094i	−0.389221	−	0.674151i
$329$	−53.4391			−2.94620
$330$	−3.43374	−	5.94741i	−0.189021	−	0.327394i
$331$	5.29427			0.290999			0.145500	−	0.989358i	$-0.453521\pi$
$331$	5.29427			0.290999			0.145500	+	0.989358i	$0.453521\pi$
$332$	6.27515			0.344394
$333$	43.2402	+	74.8941i	2.36955	+	4.10417i
$334$	8.42940	+	14.6001i	0.461236	+	0.798885i
$335$	3.10547			0.169670
$336$	3.48113	−	6.02949i	0.189911	−	0.328936i
$337$	−10.7420	−	18.6057i	−0.585155	−	1.01352i	−0.994856	−	0.101299i	$-0.967700\pi$
$337$	−10.7420	−	18.6057i	−0.585155	−	1.01352i	0.409701	−	0.912220i	$-0.365633\pi$
$338$	3.96345			0.215583
$339$	−2.71537	+	4.70316i	−0.147479	+	0.255441i
$340$	0.915152	−	1.58509i	0.0496311	−	0.0859636i
$341$	5.93140	+	10.2735i	0.321204	+	0.556341i
$342$	47.4241			2.56440
$343$	21.8298			1.17870
$344$	−6.55490	−	11.3534i	−0.353416	−	0.612135i
$345$	10.4096	+	18.0300i	0.560436	+	0.970704i
$346$	−2.51709	−	4.35973i	−0.135320	−	0.234380i
$347$	10.3188	+	17.8726i	0.553940	+	0.959452i	0.997985	+	0.0634478i	$0.0202096\pi$
$347$	10.3188	+	17.8726i	0.553940	+	0.959452i	−0.444045	+	0.896004i	$0.646457\pi$
$348$	2.11655	−	3.66597i	0.113459	−	0.196517i
$349$	13.7659	−	23.8433i	0.736874	−	1.27630i	−0.217023	−	0.976167i	$-0.569635\pi$
$349$	13.7659	−	23.8433i	0.736874	−	1.27630i	0.953896	−	0.300136i	$-0.0970321\pi$
$350$	−17.8408			−0.953628
$351$	33.5572	+	58.1228i	1.79115	+	3.10237i
$352$	15.1756			0.808861
$353$	−4.65709			−0.247872			−0.123936	−	0.992290i	$-0.539552\pi$
$353$	−4.65709			−0.247872			−0.123936	+	0.992290i	$0.539552\pi$
$354$	3.46195	−	5.99627i	0.184000	−	0.318698i
$355$	8.30623			0.440849
$356$	−0.733122	+	1.26980i	−0.0388554	+	0.0672995i
$357$	−14.8076	+	25.6475i	−0.783701	+	1.35741i
$358$	1.93343	+	3.34879i	0.102185	+	0.176989i
$359$	0.615594	+	1.06624i	0.0324898	+	0.0562740i	0.881813	−	0.471599i	$-0.156323\pi$
$359$	0.615594	+	1.06624i	0.0324898	+	0.0562740i	−0.849323	+	0.527873i	$0.822990\pi$
$360$	9.12392	−	15.8031i	0.480873	−	0.832896i
$361$	−11.1115	−	19.2457i	−0.584817	−	1.01293i
$362$	0.566167			0.0297571
$363$	5.08960	−	8.81545i	0.267135	−	0.462691i
$364$	−10.1829	−	17.6373i	−0.533730	−	0.924448i
$365$	0.0890662			0.00466194
$366$	−5.69501	+	9.86405i	−0.297683	+	0.515602i
$367$	−1.80532	−	3.12690i	−0.0942368	−	0.163223i	0.815053	−	0.579386i	$-0.196708\pi$
$367$	−1.80532	−	3.12690i	−0.0942368	−	0.163223i	−0.909290	+	0.416163i	$0.863374\pi$
$368$	3.85957			0.201194
$369$	19.0439	+	32.9849i	0.991384	+	1.71713i
$370$	4.04863	+	7.01244i	0.210478	+	0.364559i
$371$	13.7408	−	23.7997i	0.713384	−	1.23562i
$372$	−7.82987	+	13.5617i	−0.405960	+	0.703143i
$373$	−9.16920	−	15.8815i	−0.474763	−	0.822314i	0.524819	−	0.851214i	$-0.324133\pi$
$373$	−9.16920	−	15.8815i	−0.474763	−	0.822314i	−0.999582	+	0.0288995i	$0.990800\pi$
$374$	5.41546			0.280027
$375$	−24.4647			−1.26335
$376$	−17.9147	+	31.0292i	−0.923880	+	1.60021i
$377$	2.36595	+	4.09794i	0.121853	+	0.211055i
$378$	−32.9592	+	57.0870i	−1.69524	+	2.93624i
$379$	0.791868	+	1.37156i	0.0406756	+	0.0704521i	0.885646	−	0.464360i	$-0.153716\pi$
$379$	0.791868	+	1.37156i	0.0406756	+	0.0704521i	−0.844971	+	0.534812i	$0.820382\pi$
$380$	−5.71071			−0.292953
$381$	−16.3659	+	28.3466i	−0.838450	+	1.45224i
$382$	−11.3604			−0.581248
$383$	2.64426			0.135116			0.0675578	−	0.997715i	$-0.478479\pi$
$383$	2.64426			0.135116			0.0675578	+	0.997715i	$0.478479\pi$
$384$	8.52272	+	14.7618i	0.434923	+	0.753310i
$385$	−4.84847	−	8.39779i	−0.247101	−	0.427991i
$386$	−5.00847			−0.254924
$387$	17.7087	+	30.6724i	0.900185	+	1.55917i
$388$	7.51764	+	13.0209i	0.381650	+	0.661037i
$389$	11.8092	+	20.4541i	0.598748	+	1.03706i	0.993006	+	0.118062i	$0.0376682\pi$
$389$	11.8092	+	20.4541i	0.598748	+	1.03706i	−0.394258	+	0.919000i	$0.628998\pi$
$390$	5.06688	+	8.77609i	0.256571	+	0.444395i
$391$	−16.4174			−0.830262
$392$	17.5489	−	30.3955i	0.886351	−	1.53520i
$393$	28.1719			1.42108
$394$	−4.15477	−	7.19627i	−0.209314	−	0.362543i
$395$	−0.908451	+	1.57348i	−0.0457092	+	0.0791706i
$396$	−24.9995			−1.25627
$397$	−1.60354	+	2.77741i	−0.0804793	+	0.139394i	−0.903456	−	0.428681i	$-0.858978\pi$
$397$	−1.60354	+	2.77741i	−0.0804793	+	0.139394i	0.822977	+	0.568075i	$0.192312\pi$
$398$	21.5128			1.07834
$399$	92.4020			4.62589
$400$	−1.05827	+	1.83297i	−0.0529133	+	0.0916485i
$401$	−5.17387	+	8.96141i	−0.258371	+	0.447512i	−0.965806	−	0.259267i	$-0.916519\pi$
$401$	−5.17387	+	8.96141i	−0.258371	+	0.447512i	0.707435	+	0.706779i	$0.249852\pi$
$402$	−6.06466	+	10.5043i	−0.302478	+	0.523907i
$403$	−8.75247	−	15.1597i	−0.435992	−	0.755160i
$404$	−4.37359	+	7.57528i	−0.217594	+	0.376884i
$405$	−11.7278	+	20.3132i	−0.582759	+	1.00937i
$406$	−2.32378	+	4.02491i	−0.115328	+	0.199753i
$407$	15.4060	−	26.6840i	0.763648	−	1.32268i
$408$	9.92806	+	17.1959i	0.491512	+	0.851324i
$409$	−12.8194			−0.633881			−0.316940	−	0.948445i	$-0.602656\pi$
$409$	−12.8194			−0.633881			−0.316940	+	0.948445i	$0.602656\pi$
$410$	1.78310	+	3.08842i	0.0880611	+	0.152526i
$411$	19.7785	+	34.2574i	0.975601	+	1.68979i
$412$	−10.9028	+	18.8841i	−0.537141	+	0.930355i
$413$	4.88830	−	8.46678i	0.240537	−	0.416623i
$414$	−58.9290			−2.89620
$415$	−4.40889			−0.216424
$416$	−22.3933			−1.09792
$417$	2.77302	+	4.80301i	0.135795	+	0.235204i
$418$	−8.44835	−	14.6330i	−0.413222	−	0.715722i
$419$	2.68056	+	4.64287i	0.130954	+	0.226819i	0.924045	−	0.382285i	$-0.124863\pi$
$419$	2.68056	+	4.64287i	0.130954	+	0.226819i	−0.793091	+	0.609104i	$0.791529\pi$
$420$	6.40032	−	11.0857i	0.312303	−	0.540925i
$421$	−10.8755	+	18.8370i	−0.530040	+	0.918057i	0.469345	+	0.883015i	$0.344490\pi$
$421$	−10.8755	+	18.8370i	−0.530040	+	0.918057i	−0.999386	+	0.0350423i	$0.988843\pi$
$422$	14.5326			0.707438
$423$	48.3984	−	83.8285i	2.35321	−	4.07588i
$424$	−9.21278	−	15.9570i	−0.447412	−	0.774940i
$425$	4.50152	−	7.79686i	0.218356	−	0.378203i
$426$	−16.2212	+	28.0959i	−0.785919	+	1.36125i
$427$	−8.04141	+	13.9281i	−0.389151	+	0.674029i
$428$	−9.19609	+	15.9281i	−0.444510	+	0.769914i
$429$	19.2807	−	33.3951i	0.930880	−	1.61233i
$430$	1.65809	+	2.87190i	0.0799603	+	0.138495i
$431$	17.9603	−	31.1082i	0.865119	−	1.49843i	−0.00180986	−	0.999998i	$-0.500576\pi$
$431$	17.9603	−	31.1082i	0.865119	−	1.49843i	0.866929	−	0.498432i	$-0.166091\pi$
$432$	3.91010	+	6.77250i	0.188125	+	0.325842i
$433$	−29.7904			−1.43164			−0.715819	−	0.698286i	$-0.753946\pi$
$433$	−29.7904			−1.43164			−0.715819	+	0.698286i	$0.753946\pi$
$434$	8.59650	−	14.8896i	0.412645	−	0.714722i
$435$	−1.48708	+	2.57570i	−0.0713000	+	0.123495i
$436$	−7.58551	−	13.1385i	−0.363280	−	0.629219i
$437$	25.6118	+	44.3610i	1.22518	+	2.12207i
$438$	−0.173937	+	0.301268i	−0.00831103	+	0.0143951i
$439$	2.32424	−	4.02571i	0.110930	−	0.192137i	−0.805215	−	0.592982i	$-0.797950\pi$
$439$	2.32424	−	4.02571i	0.110930	−	0.192137i	0.916146	+	0.400846i	$0.131284\pi$
$440$	−6.50151			−0.309947
$441$	−47.4100	+	82.1166i	−2.25762	+	3.91031i
$442$	−7.99113			−0.380099
$443$	1.33303	+	2.30887i	0.0633341	+	0.109698i	0.895954	−	0.444147i	$-0.146493\pi$
$443$	1.33303	+	2.30887i	0.0633341	+	0.109698i	−0.832620	+	0.553845i	$0.813160\pi$
$444$	40.6740			1.93030
$445$	0.515088	−	0.892159i	0.0244175	−	0.0422924i
$446$	3.57545			0.169303
$447$	−10.5740			−0.500134
$448$	−13.1062	−	22.7007i	−0.619211	−	1.07251i
$449$	18.1349			0.855840			0.427920	−	0.903817i	$-0.359247\pi$
$449$	18.1349			0.855840			0.427920	+	0.903817i	$0.359247\pi$
$450$	16.1579	−	27.9863i	0.761690	−	1.31929i
$451$	6.78513	−	11.7522i	0.319499	−	0.553389i
$452$	0.925516	+	1.60304i	0.0435326	+	0.0754007i
$453$	16.2602			0.763969
$454$	5.47445			0.256929
$455$	7.15448	+	12.3919i	0.335407	+	0.580942i
$456$	30.9764	−	53.6527i	1.45060	−	2.51252i
$457$	40.3255			1.88635			0.943173	−	0.332301i	$-0.107825\pi$
$457$	40.3255			1.88635			0.943173	+	0.332301i	$0.107825\pi$
$458$	−20.7753			−0.970766
$459$	−16.6323	−	28.8080i	−0.776330	−	1.34464i
$460$	7.09611			0.330858
$461$	11.9798	−	20.7497i	0.557956	−	0.966408i	−0.439711	−	0.898139i	$-0.644919\pi$
$461$	11.9798	−	20.7497i	0.557956	−	0.966408i	0.997667	−	0.0682690i	$-0.0217476\pi$
$462$	37.8742			1.76207
$463$	17.0690			0.793264			0.396632	−	0.917978i	$-0.370179\pi$
$463$	17.0690			0.793264			0.396632	+	0.917978i	$0.370179\pi$
$464$	0.275681	+	0.477494i	0.0127982	+	0.0221671i
$465$	5.50123	−	9.52841i	0.255113	−	0.441869i
$466$	−0.282222			−0.0130737
$467$	−18.5509			−0.858433			−0.429216	−	0.903202i	$-0.641210\pi$
$467$	−18.5509			−0.858433			−0.429216	+	0.903202i	$0.641210\pi$
$468$	36.8896			1.70522
$469$	−8.56335	+	14.8322i	−0.395419	+	0.684885i
$470$	4.53161	−	7.84898i	0.209027	−	0.362046i
$471$	−6.69689	−	11.5994i	−0.308577	−	0.534470i
$472$	−3.27746	−	5.67673i	−0.150857	−	0.261293i
$473$	6.30944	−	10.9283i	0.290108	−	0.502482i
$474$	−3.54822	−	6.14570i	−0.162975	−	0.282281i
$475$	−28.0903			−1.28887
$476$	5.04707	+	8.74178i	0.231332	+	0.400679i
$477$	24.8893	+	43.1095i	1.13960	+	1.97385i
$478$	0.0336555	−	0.0582930i	0.00153937	−	0.00266626i
$479$	−10.4594			−0.477902			−0.238951	−	0.971032i	$-0.576803\pi$
$479$	−10.4594			−0.477902			−0.238951	+	0.971032i	$0.576803\pi$
$480$	−7.03749	−	12.1893i	−0.321216	−	0.556362i
$481$	−22.7334	+	39.3753i	−1.03655	+	1.79536i
$482$	7.34128			0.334386
$483$	−114.818			−5.22442
$484$	−1.73476	−	3.00469i	−0.0788526	−	0.136577i
$485$	−5.28186	−	9.14844i	−0.239837	−	0.415409i
$486$	−23.1265	−	40.0563i	−1.04904	−	1.81699i
$487$	−4.73718	−	8.20504i	−0.214662	−	0.371806i	0.738506	−	0.674247i	$-0.235532\pi$
$487$	−4.73718	−	8.20504i	−0.214662	−	0.371806i	−0.953168	+	0.302441i	$0.902198\pi$
$488$	5.39153	+	9.33840i	0.244063	+	0.422730i
$489$	4.63942	+	8.03572i	0.209802	+	0.363388i
$490$	−4.43907	+	7.68869i	−0.200537	+	0.347339i
$491$	−11.7796	−	20.4028i	−0.531605	−	0.920767i	−0.999319	−	0.0368873i	$-0.988256\pi$
$491$	−11.7796	−	20.4028i	−0.531605	−	0.920767i	0.467714	−	0.883880i	$-0.345078\pi$
$492$	17.9137			0.807612
$493$	−1.17266	−	2.03110i	−0.0528139	−	0.0914764i
$494$	12.4665	+	21.5926i	0.560895	+	0.971499i
$495$	17.5645			0.789466
$496$	−1.01984	−	1.76642i	−0.0457923	−	0.0793146i
$497$	−22.9044	+	39.6717i	−1.02740	+	1.77952i
$498$	8.61010	−	14.9131i	0.385828	−	0.668273i
$499$	−8.48890	−	14.7032i	−0.380016	−	0.658206i	0.611048	−	0.791593i	$-0.290748\pi$
$499$	−8.48890	−	14.7032i	−0.380016	−	0.658206i	−0.991064	+	0.133387i	$0.957415\pi$
$500$	−4.16932	+	7.22147i	−0.186458	+	0.322954i
$501$	−59.4991			−2.65823
$502$	−8.17559	+	14.1605i	−0.364894	+	0.632016i
$503$	−31.0516			−1.38452			−0.692261	−	0.721647i	$-0.743385\pi$
$503$	−31.0516			−1.38452			−0.692261	+	0.721647i	$0.743385\pi$
$504$	50.3184	+	87.1541i	2.24136	+	3.88215i
$505$	3.07287	−	5.32236i	0.136741	−	0.236842i
$506$	10.4979	+	18.1829i	0.466689	+	0.808328i
$507$	−6.99403	+	12.1140i	−0.310616	+	0.538003i
$508$	5.57820	+	9.66173i	0.247493	+	0.428670i
$509$	10.8205			0.479610			0.239805	−	0.970821i	$-0.422916\pi$
$509$	10.8205			0.479610			0.239805	+	0.970821i	$0.422916\pi$
$510$	−2.51135	−	4.34979i	−0.111204	−	0.192612i
$511$	−0.245600	+	0.425392i	−0.0108647	+	0.0188182i
$512$	−5.43746			−0.240304
$513$	−51.8943	+	89.8835i	−2.29119	+	3.96845i
$514$	1.20731	+	2.09113i	0.0532523	+	0.0922356i
$515$	7.66023	−	13.2679i	0.337550	−	0.584654i
$516$	16.6578			0.733319
$517$	−34.4877			−1.51677
$518$	−44.6565			−1.96209
$519$	17.7669			0.779882
$520$	9.59374			0.420713
$521$	20.2715	−	35.1113i	0.888110	−	1.53825i	0.0460032	−	0.998941i	$-0.485352\pi$
$521$	20.2715	−	35.1113i	0.888110	−	1.53825i	0.842107	−	0.539311i	$-0.181315\pi$
$522$	−4.20918	−	7.29051i	−0.184231	−	0.319097i
$523$	34.1451			1.49306			0.746529	−	0.665352i	$-0.231719\pi$
$523$	34.1451			1.49306			0.746529	+	0.665352i	$0.231719\pi$
$524$	4.80110	−	8.31574i	0.209737	−	0.363275i
$525$	31.4824	−	54.5290i	1.37400	−	2.37984i
$526$	6.56182	+	11.3654i	0.286109	+	0.495555i
$527$	4.33808	+	7.51377i	0.188970	+	0.327305i
$528$	2.24660	−	3.89122i	0.0977705	−	0.169344i
$529$	−20.3252	−	35.2042i	−0.883704	−	1.53062i
$530$	2.33042	+	4.03640i	0.101227	+	0.175330i
$531$	8.85440	+	15.3363i	0.384248	+	0.665538i
$532$	15.7473	−	27.2751i	0.682732	−	1.18253i
$533$	−10.0122	+	17.3417i	−0.433678	+	0.751153i
$534$	2.01182	+	3.48458i	0.0870602	+	0.150793i
$535$	6.46113	−	11.1910i	0.279339	−	0.483829i
$536$	5.74147	+	9.94453i	0.247994	+	0.429538i
$537$	−13.6471			−0.588917
$538$	11.6074			0.500429
$539$	33.7834			1.45515
$540$	7.18902	+	12.4517i	0.309366	+	0.535838i
$541$	11.3622	+	19.6799i	0.488499	+	0.846105i	0.999912	−	0.0132298i	$-0.00421130\pi$
$541$	11.3622	+	19.6799i	0.488499	+	0.846105i	−0.511414	+	0.859335i	$0.670878\pi$
$542$	−6.97660	+	12.0838i	−0.299671	+	0.519045i
$543$	−0.999077	+	1.73045i	−0.0428745	+	0.0742608i
$544$	11.0990			0.475867
$545$	5.32954	+	9.23104i	0.228292	+	0.395414i
$546$	−55.8877			−2.39177
$547$	10.7771	+	20.7570i	0.460796	+	0.887506i
$547$	10.7771	+	20.7570i	0.460796	+	0.887506i
$548$	13.4827			0.575954
$549$	−14.5658	−	25.2287i	−0.621652	−	1.07673i
$550$	−11.5138			−0.490949
$551$	−3.65880	+	6.33723i	−0.155870	+	0.269975i
$552$	−38.4912	+	66.6687i	−1.63830	+	2.83761i
$553$	−5.01011	−	8.67777i	−0.213052	−	0.369016i
$554$	−13.1403	−	22.7597i	−0.558279	−	0.966968i
$555$	−28.5774			−1.21304
$556$	1.89033			0.0801678
$557$	−29.3140			−1.24207			−0.621036	−	0.783782i	$-0.713288\pi$
$557$	−29.3140			−1.24207			−0.621036	+	0.783782i	$0.713288\pi$
$558$	15.5712	+	26.9702i	0.659183	+	1.14174i
$559$	−9.31031	+	16.1259i	−0.393784	+	0.682054i
$560$	0.833643	+	1.44391i	0.0352279	+	0.0610164i
$561$	−9.55628	+	16.5520i	−0.403467	+	0.698825i
$562$	6.26871	−	10.8577i	0.264430	−	0.458006i
$563$	−0.641623	−	1.11132i	−0.0270412	−	0.0468367i	0.852188	−	0.523236i	$-0.175275\pi$
$563$	−0.641623	−	1.11132i	−0.0270412	−	0.0468367i	−0.879229	+	0.476399i	$0.841942\pi$
$564$	−22.7631	−	39.4268i	−0.958499	−	1.66017i
$565$	−0.650263	−	1.12629i	−0.0273568	−	0.0473833i
$566$	−4.60351	+	7.97351i	−0.193500	+	0.335152i
$567$	−64.6789	−	112.027i	−2.71626	−	4.70470i
$568$	15.3568	+	26.5987i	0.644356	+	1.11606i
$569$	11.1654	−	19.3390i	0.468077	−	0.810733i	−0.531258	−	0.847210i	$-0.678280\pi$
$569$	11.1654	−	19.3390i	0.468077	−	0.810733i	0.999334	+	0.0364776i	$0.0116138\pi$
$570$	−7.83563	+	13.5717i	−0.328199	+	0.568457i
$571$	21.5359			0.901250			0.450625	−	0.892713i	$-0.351201\pi$
$571$	21.5359			0.901250			0.450625	+	0.892713i	$0.351201\pi$
$572$	−6.57169	−	11.3825i	−0.274776	−	0.475927i
$573$	20.0469	−	34.7223i	0.837472	−	1.45054i
$574$	−19.6676			−0.820911
$575$	34.9049			1.45563
$576$	47.4798			1.97833
$577$	−8.35394			−0.347779			−0.173889	−	0.984765i	$-0.555634\pi$
$577$	−8.35394			−0.347779			−0.173889	+	0.984765i	$0.555634\pi$
$578$	−11.9400			−0.496640
$579$	8.83810	−	15.3080i	0.367299	−	0.636180i
$580$	0.506861	+	0.877909i	0.0210463	+	0.0364532i
$581$	12.1575	−	21.0575i	0.504379	−	0.873610i
$582$	41.2596			1.71027
$583$	8.86779	−	15.3595i	0.367266	−	0.636124i
$584$	0.164668	+	0.285213i	0.00681401	+	0.0118022i
$585$	−25.9185			−1.07160
$586$	10.0233	+	17.3609i	0.414060	+	0.717172i
$587$	−0.254970	+	0.441621i	−0.0105237	+	0.0182276i	−0.871239	−	0.490858i	$-0.836683\pi$
$587$	−0.254970	+	0.441621i	−0.0105237	+	0.0182276i	0.860716	+	0.509086i	$0.170017\pi$
$588$	22.2982	+	38.6217i	0.919563	+	1.59273i
$589$	13.5352	−	23.4436i	0.557708	−	0.965978i
$590$	0.829050	+	1.43596i	0.0341314	+	0.0591174i
$591$	29.3265			1.20633
$592$	−2.64890	+	4.58804i	−0.108869	+	0.188567i
$593$	7.49577			0.307814			0.153907	−	0.988085i	$-0.450814\pi$
$593$	7.49577			0.307814			0.153907	+	0.988085i	$0.450814\pi$
$594$	−21.2707	+	36.8419i	−0.872747	+	1.51164i
$595$	−3.54605	−	6.14193i	−0.145374	−	0.251795i
$596$	−1.80204	+	3.12123i	−0.0738145	+	0.127851i
$597$	−37.9622	+	65.7524i	−1.55369	+	2.69107i
$598$	−15.4909	−	26.8310i	−0.633469	−	1.09720i
$599$	−5.82935			−0.238181			−0.119090	−	0.992883i	$-0.537998\pi$
$599$	−5.82935			−0.238181			−0.119090	+	0.992883i	$0.537998\pi$
$600$	−21.1080	−	36.5601i	−0.861730	−	1.49256i
$601$	−18.1578	−	31.4502i	−0.740672	−	1.28288i	−0.952190	−	0.305507i	$-0.901174\pi$
$601$	−18.1578	−	31.4502i	−0.740672	−	1.28288i	0.211518	−	0.977374i	$-0.432159\pi$
$602$	−18.2888			−0.745395
$603$	−15.5112	−	26.8662i	−0.631664	−	1.09407i
$604$	2.77108	−	4.79966i	0.112754	−	0.195295i
$605$	1.21883	+	2.11108i	0.0495526	+	0.0858276i
$606$	12.0020	+	20.7880i	0.487546	+	0.844455i
$607$	14.9457	+	25.8866i	0.606626	+	1.05071i	0.991792	+	0.127860i	$0.0408107\pi$
$607$	14.9457	+	25.8866i	0.606626	+	1.05071i	−0.385167	+	0.922847i	$0.625856\pi$
$608$	−17.3150	−	29.9904i	−0.702215	−	1.21627i
$609$	−8.20125	−	14.2050i	−0.332331	−	0.575615i
$610$	−1.36381	−	2.36219i	−0.0552192	−	0.0956424i
$611$	50.8906			2.05881
$612$	−18.2840			−0.739086
$613$	−17.9719	+	31.1282i	−0.725877	+	1.25726i	0.232735	+	0.972540i	$0.425233\pi$
$613$	−17.9719	+	31.1282i	−0.725877	+	1.25726i	−0.958612	+	0.284716i	$0.908101\pi$
$614$	2.28276	+	3.95386i	0.0921247	+	0.159565i
$615$	−12.5861			−0.507520
$616$	17.9279	−	31.0521i	0.722337	−	1.25112i
$617$	−22.4753	−	38.9284i	−0.904821	−	1.56720i	−0.821157	−	0.570703i	$-0.806671\pi$
$617$	−22.4753	−	38.9284i	−0.904821	−	1.56720i	−0.0836648	−	0.996494i	$-0.526662\pi$
$618$	29.9192	+	51.8216i	1.20353	+	2.08457i
$619$	−10.8811			−0.437350			−0.218675	−	0.975798i	$-0.570173\pi$
$619$	−10.8811			−0.437350			−0.218675	+	0.975798i	$0.570173\pi$
$620$	−1.87506	−	3.24769i	−0.0753041	−	0.130431i
$621$	64.4837	−	111.689i	2.58764	−	4.48193i
$622$	3.56358	+	6.17231i	0.142887	+	0.247487i
$623$	2.84071	+	4.92026i	0.113811	+	0.197126i
$624$	−3.31511	+	5.74194i	−0.132711	+	0.229862i
$625$	−8.00835	+	13.8709i	−0.320334	+	0.554835i
$626$	10.1932			0.407403
$627$	59.6329			2.38151
$628$	−4.56518			−0.182171
$629$	11.2676	−	19.5160i	0.449267	−	0.778154i
$630$	−12.7283	−	22.0460i	−0.507107	−	0.878335i
$631$	21.5844			0.859260			0.429630	−	0.903005i	$-0.358644\pi$
$631$	21.5844			0.859260			0.429630	+	0.903005i	$0.358644\pi$
$632$	−6.71827			−0.267238
$633$	−25.6447	+	44.4180i	−1.01929	+	1.76546i
$634$	−5.32323			−0.211412
$635$	−3.91922	−	6.78829i	−0.155530	−	0.269385i
$636$	23.4122			0.928354
$637$	−49.8513			−1.97518
$638$	−1.49969	+	2.59753i	−0.0593732	+	0.102837i
$639$	−41.4879	−	71.8591i	−1.64124	−	2.84270i
$640$	−4.08196			−0.161354
$641$	22.1245			0.873865			0.436932	−	0.899494i	$-0.356065\pi$
$641$	22.1245			0.873865			0.436932	+	0.899494i	$0.356065\pi$
$642$	25.2358	+	43.7097i	0.995978	+	1.72508i
$643$	0.893058	−	1.54682i	0.0352188	−	0.0610007i	−0.847879	−	0.530190i	$-0.822121\pi$
$643$	0.893058	−	1.54682i	0.0352188	−	0.0610007i	0.883098	+	0.469189i	$0.155454\pi$
$644$	−19.5676	+	33.8920i	−0.771070	+	1.33553i
$645$	−11.7037			−0.460832
$646$	−6.17891	−	10.7022i	−0.243106	−	0.421072i
$647$	−25.4184			−0.999302			−0.499651	−	0.866227i	$-0.666538\pi$
$647$	−25.4184			−0.999302			−0.499651	+	0.866227i	$0.666538\pi$
$648$	−86.7306			−3.40710
$649$	3.15473	−	5.46416i	0.123834	−	0.214487i
$650$	16.9899			0.666399
$651$	30.3393	+	52.5492i	1.18909	+	2.05957i
$652$	3.16263			0.123858
$653$	5.86049	−	10.1507i	0.229339	−	0.397226i	−0.728274	−	0.685286i	$-0.759677\pi$
$653$	5.86049	−	10.1507i	0.229339	−	0.397226i	0.957612	+	0.288060i	$0.0930104\pi$
$654$	−41.6321			−1.62794
$655$	−3.37323	+	5.84260i	−0.131803	+	0.228289i
$656$	−1.16663	+	2.02067i	−0.0455493	+	0.0788937i
$657$	−0.444867	−	0.770533i	−0.0173559	−	0.0300613i
$658$	24.9918	+	43.2871i	0.974283	+	1.68751i
$659$	2.17542	−	3.76794i	0.0847423	−	0.146778i	−0.820539	−	0.571590i	$-0.806327\pi$
$659$	2.17542	−	3.76794i	0.0847423	−	0.146778i	0.905281	+	0.424812i	$0.139660\pi$
$660$	4.13053	−	7.15429i	0.160781	−	0.278480i
$661$	−3.67902			−0.143097			−0.0715486	−	0.997437i	$-0.522794\pi$
$661$	−3.67902			−0.143097			−0.0715486	+	0.997437i	$0.522794\pi$
$662$	−2.47597	−	4.28850i	−0.0962312	−	0.166677i
$663$	14.1014	−	24.4243i	0.547653	−	0.948563i
$664$	−8.15127	−	14.1184i	−0.316330	−	0.547900i
$665$	−11.0640	+	19.1634i	−0.429043	+	0.743124i
$666$	40.4442	−	70.0514i	1.56718	−	2.71443i
$667$	4.54642	−	7.87462i	0.176038	−	0.304907i
$668$	−10.1399	+	17.5629i	−0.392326	+	0.679529i
$669$	−6.30936	+	10.9281i	−0.243934	+	0.422506i
$670$	−1.45233	−	2.51552i	−0.0561085	−	0.0971828i
$671$	−5.18963	+	8.98871i	−0.200344	+	0.347005i
$672$	77.6235			2.99439
$673$	14.5216	−	25.1521i	0.559766	−	0.969543i	−0.437750	−	0.899097i	$-0.644224\pi$
$673$	14.5216	−	25.1521i	0.559766	−	0.969543i	0.997516	−	0.0704463i	$-0.0224423\pi$
$674$	−10.0474	+	17.4027i	−0.387012	+	0.670325i
$675$	35.3619	+	61.2486i	1.36108	+	2.35746i
$676$	2.38387	+	4.12898i	0.0916873	+	0.158807i
$677$	−20.3684	−	35.2791i	−0.782820	−	1.35588i	−0.930293	−	0.366818i	$-0.880447\pi$
$677$	−20.3684	−	35.2791i	−0.782820	−	1.35588i	0.147472	−	0.989066i	$-0.452886\pi$
$678$	5.07958			0.195080
$679$	58.2589			2.23577
$680$	−4.75504			−0.182348
$681$	−9.66039	+	16.7323i	−0.370187	+	0.641182i
$682$	5.54787	−	9.60919i	0.212439	−	0.367955i
$683$	21.6279	+	37.4606i	0.827568	+	1.43339i	0.899941	+	0.436012i	$0.143609\pi$
$683$	21.6279	+	37.4606i	0.827568	+	1.43339i	−0.0723729	+	0.997378i	$0.523057\pi$
$684$	28.5238	+	49.4047i	1.09064	+	1.88904i
$685$	−9.47291			−0.361941
$686$	−10.2091	−	17.6827i	−0.389786	−	0.675129i
$687$	36.6607	−	63.4983i	1.39869	−	2.42261i
$688$	−1.08484	+	1.87900i	−0.0413592	+	0.0716362i
$689$	−13.0854	+	22.6647i	−0.498516	+	0.863455i
$690$	9.73654	−	16.8642i	0.370664	−	0.642008i
$691$	0.992686	+	1.71938i	0.0377636	+	0.0654084i	0.884289	−	0.466939i	$-0.154643\pi$
$691$	0.992686	+	1.71938i	0.0377636	+	0.0654084i	−0.846526	+	0.532348i	$0.821310\pi$
$692$	3.02787	−	5.24443i	0.115102	−	0.199363i
$693$	−48.4342	+	83.8904i	−1.83986	+	3.18673i
$694$	9.65153	−	16.7169i	0.366367	−	0.634566i
$695$	−1.32814			−0.0503791
$696$	−10.9974			−0.416855
$697$	4.96247	−	8.59525i	0.187967	−	0.325568i
$698$	−25.7516			−0.974713
$699$	0.498018	−	0.862593i	0.0188368	−	0.0326262i
$700$	−10.7305	−	18.5859i	−0.405577	−	0.702479i
$701$	−13.9339			−0.526275			−0.263137	−	0.964758i	$-0.584757\pi$
$701$	−13.9339			−0.526275			−0.263137	+	0.964758i	$0.584757\pi$
$702$	31.3874	−	54.3645i	1.18464	−	2.05186i
$703$	−70.3116			−2.65185
$704$	−8.45829	−	14.6502i	−0.318784	−	0.552150i
$705$	15.9932	+	27.7011i	0.602340	+	1.04328i
$706$	2.17798	+	3.77237i	0.0819693	+	0.141975i
$707$	16.9469	+	29.3528i	0.637352	+	1.10393i
$708$	8.32893			0.313020
$709$	19.0345	+	32.9687i	0.714856	+	1.23817i	0.963015	+	0.269447i	$0.0868410\pi$
$709$	19.0345	+	32.9687i	0.714856	+	1.23817i	−0.248159	+	0.968719i	$0.579826\pi$
$710$	−3.88457	−	6.72827i	−0.145785	−	0.252507i
$711$	18.1501			0.680682
$712$	3.80923			0.142757
$713$	−16.8188	+	29.1310i	−0.629869	+	1.09096i
$714$	27.7002			1.03665
$715$	4.61724	+	7.99730i	0.172675	+	0.299082i
$716$	−2.32577	+	4.02835i	−0.0869180	+	0.150546i
$717$	0.118779	+	0.205731i	0.00443589	+	0.00768318i
$718$	0.575789	−	0.997295i	0.0214882	−	0.0372187i
$719$	−11.9670			−0.446295			−0.223147	−	0.974785i	$-0.571633\pi$
$719$	−11.9670			−0.446295			−0.223147	+	0.974785i	$0.571633\pi$
$720$	−3.02003			−0.112550
$721$	42.2462	+	73.1726i	1.57333	+	2.72509i
$722$	−10.3930	+	18.0013i	−0.386789	+	0.669937i
$723$	−12.9546	+	22.4381i	−0.481788	+	0.834482i
$724$	0.340529	+	0.589813i	0.0126556	+	0.0219202i
$725$	2.49319	+	4.31832i	0.0925946	+	0.160379i
$726$	−9.52100			−0.353358
$727$	8.29433	+	14.3662i	0.307620	+	0.532813i	0.977841	−	0.209348i	$-0.0671342\pi$
$727$	8.29433	+	14.3662i	0.307620	+	0.532813i	−0.670222	+	0.742161i	$0.733801\pi$
$728$	−26.4547	+	45.8210i	−0.980478	+	1.69824i
$729$	74.2257			2.74910
$730$	−0.0416535	−	0.0721460i	−0.00154167	−	0.00267024i
$731$	4.61456	−	7.99266i	0.170676	−	0.295619i
$732$	−13.7014			−0.506417
$733$	−7.99308	−	13.8444i	−0.295231	−	0.511355i	0.679807	−	0.733391i	$-0.262063\pi$
$733$	−7.99308	−	13.8444i	−0.295231	−	0.511355i	−0.975039	+	0.222035i	$0.928730\pi$
$734$	−1.68858	+	2.92471i	−0.0623267	+	0.107953i
$735$	−15.6666	−	27.1354i	−0.577872	−	1.00090i
$736$	21.5156	+	37.2660i	0.793074	+	1.37364i
$737$	−5.52647	+	9.57213i	−0.203570	+	0.352594i
$738$	17.8124	−	30.8521i	0.655685	−	1.13568i
$739$	−10.9035			−0.401094			−0.200547	−	0.979684i	$-0.564272\pi$
$739$	−10.9035			−0.401094			−0.200547	+	0.979684i	$0.564272\pi$
$740$	−4.87021	+	8.43544i	−0.179032	+	0.310093i
$741$	−87.9953			−3.23259
$742$	−25.7045			−0.943642
$743$	2.91618	+	5.05096i	0.106984	+	0.185302i	0.914547	−	0.404479i	$-0.132547\pi$
$743$	2.91618	+	5.05096i	0.106984	+	0.185302i	−0.807563	+	0.589781i	$0.799214\pi$
$744$	40.6832			1.49152
$745$	1.26611	−	2.19296i	0.0463866	−	0.0803439i
$746$	−8.57631	+	14.8546i	−0.314001	+	0.543866i
$747$	22.0215	+	38.1423i	0.805724	+	1.39556i
$748$	3.25720	+	5.64163i	0.119095	+	0.206278i
$749$	35.6332	+	61.7185i	1.30201	+	2.25514i
$750$	11.4414	+	19.8171i	0.417781	+	0.723617i
$751$	17.6151			0.642782			0.321391	−	0.946947i	$-0.395850\pi$
$751$	17.6151			0.642782			0.321391	+	0.946947i	$0.395850\pi$
$752$	5.92980			0.216237
$753$	−28.8538	−	49.9762i	−1.05149	−	1.82124i
$754$	2.21296	−	3.83296i	0.0805913	−	0.139588i
$755$	−1.94695	+	3.37222i	−0.0708568	+	0.122727i
$756$	−79.2949			−2.88393
$757$	−12.7829	−	22.1407i	−0.464603	−	0.804717i	0.534580	−	0.845118i	$-0.320470\pi$
$757$	−12.7829	−	22.1407i	−0.464603	−	0.804717i	−0.999184	+	0.0404012i	$0.987136\pi$
$758$	0.740665	−	1.28287i	0.0269022	−	0.0465959i
$759$	−74.0997			−2.68965
$760$	7.41808	+	12.8485i	0.269082	+	0.466063i
$761$	−13.1880	−	22.8423i	−0.478065	−	0.828033i	0.521619	−	0.853179i	$-0.325328\pi$
$761$	−13.1880	−	22.8423i	−0.478065	−	0.828033i	−0.999684	+	0.0251456i	$0.991995\pi$
$762$	30.6153			1.10907
$763$	−58.7849			−2.12816
$764$	−6.83285	−	11.8349i	−0.247204	−	0.428170i
$765$	12.8462			0.464457
$766$	−1.23664	−	2.14192i	−0.0446816	−	0.0773909i
$767$	−4.65517	+	8.06299i	−0.168089	+	0.291138i
$768$	27.8190	−	48.1838i	1.00383	−	1.73868i
$769$	18.3938	−	31.8590i	0.663297	−	1.14886i	−0.316447	−	0.948610i	$-0.602490\pi$
$769$	18.3938	−	31.8590i	0.663297	−	1.14886i	0.979744	−	0.200254i	$-0.0641768\pi$
$770$	−4.53496	+	7.85478i	−0.163429	+	0.283067i
$771$	−8.52185			−0.306907
$772$	−3.01241	−	5.21764i	−0.108419	−	0.187787i
$773$	−30.8775			−1.11059			−0.555294	−	0.831654i	$-0.687394\pi$
$773$	−30.8775			−1.11059			−0.555294	+	0.831654i	$0.687394\pi$
$774$	16.5637	−	28.6891i	0.595368	−	1.03121i
$775$	−9.22317	−	15.9750i	−0.331306	−	0.573839i
$776$	19.5305	−	33.8277i	0.701102	−	1.21434i
$777$	78.8022	−	136.489i	2.82701	−	4.89653i
$778$	11.0456	−	19.1315i	0.396002	−	0.685896i
$779$	−30.9667			−1.10950
$780$	−6.09508	+	10.5570i	−0.218239	+	0.378001i
$781$	−14.7817	+	25.6027i	−0.528931	+	0.916135i
$782$	7.67790	+	13.2985i	0.274561	+	0.475554i
$783$	18.4238			0.658411
$784$	−5.80870			−0.207454
$785$	3.20748			0.114480
$786$	−13.1751	−	22.8200i	−0.469941	−	0.813961i
$787$	1.48846			0.0530578			0.0265289	−	0.999648i	$-0.491555\pi$
$787$	1.48846			0.0530578			0.0265289	+	0.999648i	$0.491555\pi$
$788$	4.99788	−	8.65658i	0.178042	−	0.308378i
$789$	−46.3168			−1.64892
$790$	1.69942			0.0604626
$791$	7.17241			0.255022
$792$	32.4737	+	56.2461i	1.15390	+	1.99862i
$793$	7.65790	−	13.2639i	0.271940	−	0.471014i
$794$	2.99970			0.106455
$795$	−16.4493			−0.583397
$796$	12.9391	+	22.4113i	0.458616	+	0.794346i
$797$	17.6431	+	30.5587i	0.624949	+	1.08244i	0.988551	+	0.150889i	$0.0482137\pi$
$797$	17.6431	+	30.5587i	0.624949	+	1.08244i	−0.363602	+	0.931555i	$0.618453\pi$
$798$	−43.2136	−	74.8481i	−1.52974	−	2.64959i
$799$	−25.2234			−0.892341
$800$	−23.5976			−0.834301
$801$	−10.2910			−0.363616
$802$	9.67864			0.341765
$803$	−0.158502	+	0.274533i	−0.00559340	+	0.00968805i
$804$	−14.5907			−0.514573
$805$	13.7481	−	23.8124i	0.484556	−	0.839275i
$806$	−8.18652	+	14.1795i	−0.288358	+	0.499451i
$807$	−20.4827	+	35.4771i	−0.721025	+	1.24885i
$808$	22.7248			0.799454
$809$	18.8374	+	32.6274i	0.662289	+	1.14712i	0.980013	+	0.198935i	$0.0637484\pi$
$809$	18.8374	+	32.6274i	0.662289	+	1.14712i	−0.317723	+	0.948184i	$0.602918\pi$
$810$	21.9389			0.770855
$811$	25.9608	+	44.9654i	0.911606	+	1.57895i	0.811796	+	0.583941i	$0.198490\pi$
$811$	25.9608	+	44.9654i	0.911606	+	1.57895i	0.0998103	+	0.995006i	$0.468176\pi$
$812$	−5.59068			−0.196194
$813$	−24.6223	−	42.6470i	−0.863541	−	1.49570i
$814$	−28.8197			−1.01013
$815$	−2.22205			−0.0778351
$816$	1.64310	−	2.84594i	0.0575201	−	0.0996277i
$817$	−28.7957			−1.00743
$818$	5.99526	+	10.3841i	0.209619	+	0.363071i
$819$	71.4702	−	123.790i	2.49737	−	4.32558i
$820$	−2.14494	+	3.71514i	−0.0749045	+	0.129738i
$821$	18.1304	−	31.4027i	0.632754	−	1.09596i	−0.354232	−	0.935158i	$-0.615258\pi$
$821$	18.1304	−	31.4027i	0.632754	−	1.09596i	0.986986	−	0.160805i	$-0.0514090\pi$
$822$	18.4996	−	32.0422i	0.645247	−	1.11760i
$823$	14.6712	+	25.4113i	0.511407	+	0.885784i	0.999913	+	0.0132226i	$0.00420900\pi$
$823$	14.6712	+	25.4113i	0.511407	+	0.885784i	−0.488505	+	0.872561i	$0.662458\pi$
$824$	56.6497			1.97349
$825$	20.3176	−	35.1911i	0.707367	−	1.22520i
$826$	−9.14443			−0.318175
$827$	51.6405			1.79572			0.897859	−	0.440283i	$-0.145122\pi$
$827$	51.6405			1.79572			0.897859	+	0.440283i	$0.145122\pi$
$828$	−35.4436	−	61.3901i	−1.23175	−	2.13345i
$829$	−0.805670			−0.0279821			−0.0139910	−	0.999902i	$-0.504454\pi$
$829$	−0.805670			−0.0279821			−0.0139910	+	0.999902i	$0.504454\pi$
$830$	2.06190	+	3.57132i	0.0715697	+	0.123962i
$831$	92.7514			3.21751
$832$	12.4812	+	21.6180i	0.432707	+	0.749471i
$833$	24.7083			0.856093
$834$	2.59371	−	4.49244i	0.0898128	−	0.155560i
$835$	7.12427	−	12.3396i	0.246546	−	0.427030i
$836$	10.1627	−	17.6024i	0.351486	−	0.608791i
$837$	−68.1559			−2.35581
$838$	2.50723	−	4.34266i	0.0866110	−	0.150015i
$839$	−55.4050			−1.91279			−0.956396	−	0.292073i	$-0.905655\pi$
$839$	−55.4050			−1.91279			−0.956396	+	0.292073i	$0.905655\pi$
$840$	−33.2554			−1.14742
$841$	−27.7010			−0.955208
$842$	20.3446			0.701121
$843$	22.1239	+	38.3198i	0.761989	+	1.31980i
$844$	8.74084	+	15.1396i	0.300872	+	0.521126i
$845$	−1.67490	−	2.90100i	−0.0576182	−	0.0997976i
$846$	−90.5378			−3.11275
$847$	−13.4437			−0.461932
$848$	−1.52472	+	2.64090i	−0.0523592	+	0.0906888i
$849$	−16.2470	−	28.1406i	−0.557595	−	0.965783i
$850$	−8.42088			−0.288834
$851$	87.3691			2.99497
$852$	−39.0258			−1.33700
$853$	5.68663	−	9.84954i	0.194707	−	0.337242i	−0.752098	−	0.659052i	$-0.770958\pi$
$853$	5.68663	−	9.84954i	0.194707	−	0.337242i	0.946804	+	0.321810i	$0.104291\pi$
$854$	15.0429			0.514756
$855$	−20.0407	−	34.7115i	−0.685377	−	1.18711i
$856$	47.7820			1.63316
$857$	9.44644			0.322684			0.161342	−	0.986899i	$-0.448418\pi$
$857$	9.44644			0.322684			0.161342	+	0.986899i	$0.448418\pi$
$858$	−36.0679			−1.23134
$859$	4.99048	+	8.64376i	0.170273	+	0.294921i	0.938515	−	0.345238i	$-0.112202\pi$
$859$	4.99048	+	8.64376i	0.170273	+	0.294921i	−0.768242	+	0.640159i	$0.778868\pi$
$860$	−1.99456	+	3.45468i	−0.0680140	+	0.117804i
$861$	34.7061	−	60.1128i	1.18278	−	2.04864i
$862$	−33.5980			−1.14435
$863$	18.7846	−	32.5359i	0.639435	−	1.10753i	−0.346122	−	0.938189i	$-0.612502\pi$
$863$	18.7846	−	32.5359i	0.639435	−	1.10753i	0.985557	−	0.169344i	$-0.0541650\pi$
$864$	−43.5945	+	75.5079i	−1.48311	+	2.56883i
$865$	−2.12737	+	3.68471i	−0.0723327	+	0.125284i
$866$	13.9321	+	24.1310i	0.473431	+	0.820006i
$867$	21.0697	−	36.4939i	0.715566	−	1.23940i
$868$	20.6819			0.701989
$869$	−3.23335	−	5.60032i	−0.109684	−	0.189978i
$870$	2.78184			0.0943133
$871$	8.15495	−	14.1248i	0.276320	−	0.478600i
$872$	−19.7068	+	34.1331i	−0.667356	+	1.15589i
$873$	−52.7635	+	91.3891i	−1.78577	+	3.09305i
$874$	23.9557	−	41.4925i	0.810314	−	1.40351i
$875$	16.1553	+	27.9819i	0.546150	+	0.945960i
$876$	−0.418466			−0.0141387
$877$	15.6821	+	27.1621i	0.529545	+	0.917199i	0.999406	+	0.0344588i	$0.0109707\pi$
$877$	15.6821	+	27.1621i	0.529545	+	0.917199i	−0.469861	+	0.882740i	$0.655696\pi$
$878$	−4.34791			−0.146735
$879$	−70.7499			−2.38633
$880$	0.538003	+	0.931849i	0.0181361	+	0.0314126i
$881$	13.6639	+	23.6666i	0.460349	+	0.797347i	0.998978	−	0.0451955i	$-0.0143911\pi$
$881$	13.6639	+	23.6666i	0.460349	+	0.797347i	−0.538630	+	0.842543i	$0.681058\pi$
$882$	88.6888			2.98631
$883$	−20.9976	+	36.3688i	−0.706624	+	1.22391i	0.259478	+	0.965749i	$0.416449\pi$
$883$	−20.9976	+	36.3688i	−0.706624	+	1.22391i	−0.966102	+	0.258160i	$0.916884\pi$
$884$	−4.80637	−	8.32488i	−0.161656	−	0.279996i
$885$	−5.85187			−0.196708
$886$	1.24683	−	2.15958i	0.0418882	−	0.0725525i
$887$	−25.5875	+	44.3189i	−0.859144	+	1.48808i	0.0136017	+	0.999907i	$0.495670\pi$
$887$	−25.5875	+	44.3189i	−0.859144	+	1.48808i	−0.872746	+	0.488174i	$0.837663\pi$
$888$	−52.8346	−	91.5122i	−1.77301	−	3.07095i
$889$	43.2290			1.44986
$890$	−0.963563			−0.0322987
$891$	−41.7414	−	72.2983i	−1.39839	−	2.42208i
$892$	2.15050	+	3.72478i	0.0720041	+	0.124715i
$893$	39.3497	+	68.1556i	1.31679	+	2.28074i
$894$	4.94514	+	8.56524i	0.165390	+	0.286465i
$895$	1.63407	−	2.83030i	0.0546210	−	0.0946064i
$896$	11.2560	−	19.4960i	0.376037	−	0.651315i
$897$	109.343			3.65085
$898$	−8.48114	−	14.6898i	−0.283019	−	0.490204i
$899$	−4.80533			−0.160267
$900$	38.8735			1.29578
$901$	6.48567	−	11.2335i	0.216069	−	0.374243i
$902$	−12.6928			−0.422623
$903$	32.2730	−	55.8984i	1.07398	−	1.86018i
$904$	2.40445	−	4.16462i	0.0799707	−	0.138513i
$905$	−0.239254	−	0.414400i	−0.00795307	−	0.0137751i
$906$	−7.60437	−	13.1712i	−0.252638	−	0.437583i
$907$	13.4800	−	23.3480i	0.447596	−	0.775259i	−0.550633	−	0.834747i	$-0.685614\pi$
$907$	13.4800	−	23.3480i	0.447596	−	0.775259i	0.998229	+	0.0594886i	$0.0189470\pi$
$908$	3.29268	+	5.70309i	0.109271	+	0.189264i
$909$	−61.3933			−2.03629
$910$	6.69186	−	11.5906i	0.221833	−	0.384226i
$911$	−8.05968	−	13.9598i	−0.267029	−	0.462508i	0.701064	−	0.713098i	$-0.252709\pi$
$911$	−8.05968	−	13.9598i	−0.267029	−	0.462508i	−0.968093	+	0.250590i	$0.919375\pi$
$912$	−10.2533			−0.339519
$913$	7.84603	−	13.5897i	0.259666	−	0.449754i
$914$	−18.8590	−	32.6647i	−0.623800	−	1.08045i
$915$	9.62651			0.318243
$916$	−12.4956	−	21.6430i	−0.412865	−	0.715103i
$917$	−18.6034	−	32.2220i	−0.614337	−	1.06406i
$918$	−15.5568	+	26.9452i	−0.513452	+	0.889325i
$919$	−6.05877	+	10.4941i	−0.199860	+	0.346168i	−0.948483	−	0.316828i	$-0.897382\pi$
$919$	−6.05877	+	10.4941i	−0.199860	+	0.346168i	0.748623	+	0.662996i	$0.230716\pi$
$920$	−9.21768	−	15.9655i	−0.303898	−	0.526367i
$921$	−16.1129			−0.530939
$922$	−22.4104			−0.738047
$923$	21.8121	−	37.7797i	0.717955	−	1.24353i
$924$	22.7799	+	39.4560i	0.749404	+	1.29801i
$925$	−23.9559	+	41.4929i	−0.787666	+	1.36428i
$926$	−7.98264	−	13.8263i	−0.262326	−	0.454362i
$927$	−153.045			−5.02666
$928$	−3.07362	+	5.32367i	−0.100897	+	0.174758i
$929$	23.9947			0.787240			0.393620	−	0.919273i	$-0.371223\pi$
$929$	23.9947			0.787240			0.393620	+	0.919273i	$0.371223\pi$
$930$	−10.2910			−0.337456
$931$	−38.5461	−	66.7638i	−1.26330	−	2.18809i
$932$	−0.169746	−	0.294009i	−0.00556022	−	0.00963058i
$933$	−25.1537			−0.823494
$934$	8.67568	+	15.0267i	0.283877	+	0.491689i
$935$	−2.28849	−	3.96378i	−0.0748416	−	0.129629i
$936$	−47.9187	−	82.9976i	−1.56627	−	2.71286i
$937$	−0.131305	−	0.227427i	−0.00428956	−	0.00742973i	0.863873	−	0.503710i	$-0.168032\pi$
$937$	−0.131305	−	0.227427i	−0.00428956	−	0.00742973i	−0.868162	+	0.496281i	$0.834699\pi$
$938$	16.0193			0.523047
$939$	−17.9873	+	31.1549i	−0.586992	+	1.01670i
$940$	10.9024			0.355596
$941$	22.3862	+	38.7740i	0.729768	+	1.26400i	0.956981	+	0.290150i	$0.0937052\pi$
$941$	22.3862	+	38.7740i	0.729768	+	1.26400i	−0.227213	+	0.973845i	$0.572961\pi$
$942$	−6.26386	+	10.8493i	−0.204088	+	0.353490i
$943$	38.4791			1.25305
$944$	−0.542423	+	0.939504i	−0.0176544	+	0.0305783i
$945$	55.7123			1.81232
$946$	−11.8029			−0.383746
$947$	−15.3617	+	26.6073i	−0.499188	+	0.864620i	−1.00000		0.000936947i	$-0.999702\pi$
$947$	−15.3617	+	26.6073i	−0.499188	+	0.864620i	0.500811	+	0.865557i	$0.333035\pi$
$948$	4.26824	−	7.39282i	0.138626	−	0.240107i
$949$	0.233887	−	0.405105i	0.00759231	−	0.0131503i
$950$	13.1370	+	22.7539i	0.426219	+	0.738233i
$951$	9.39354	−	16.2701i	0.304606	−	0.527594i
$952$	13.1120	−	22.7107i	0.424964	−	0.736058i
$953$	−15.4531	+	26.7655i	−0.500574	+	0.867019i	0.499426	+	0.866357i	$0.333544\pi$
$953$	−15.4531	+	26.7655i	−0.500574	+	0.867019i	−1.00000		0.000662753i	$0.999789\pi$
$954$	23.2799	−	40.3219i	0.753714	−	1.30547i
$955$	4.80073	+	8.31511i	0.155348	+	0.269071i
$956$	0.0809701			0.00261876
$957$	−5.29279	−	9.16738i	−0.171092	−	0.296339i
$958$	4.89153	+	8.47238i	0.158038	+	0.273730i
$959$	26.1216	−	45.2439i	0.843509	−	1.46100i
$960$	−7.84485	+	13.5877i	−0.253191	+	0.438540i
$961$	−13.2234			−0.426562
$962$	42.5268			1.37112
$963$	−129.088			−4.15980
$964$	4.41550	+	7.64788i	0.142214	+	0.246322i
$965$	2.11650	+	3.66589i	0.0681326	+	0.118009i
$966$	53.6971	+	93.0060i	1.72767	+	2.99242i
$967$	−9.92331	+	17.1877i	−0.319112	+	0.552718i	−0.980303	−	0.197499i	$-0.936718\pi$
$967$	−9.92331	+	17.1877i	−0.319112	+	0.552718i	0.661191	+	0.750218i	$0.270051\pi$
$968$	−4.50682	+	7.80603i	−0.144855	+	0.250895i
$969$	43.6140			1.40108
$970$	−4.94032	+	8.55689i	−0.158624	+	0.274745i
$971$	21.0261	+	36.4183i	0.674760	+	1.16872i	0.976539	+	0.215341i	$0.0690864\pi$
$971$	21.0261	+	36.4183i	0.674760	+	1.16872i	−0.301778	+	0.953378i	$0.597580\pi$
$972$	27.8195	−	48.1847i	0.892310	−	1.54553i
$973$	3.66234	−	6.34335i	0.117409	−	0.203359i
$974$	−4.43087	+	7.67449i	−0.141974	+	0.245907i
$975$	−29.9809	+	51.9285i	−0.960158	+	1.66304i
$976$	0.892303	−	1.54551i	0.0285619	−	0.0494707i
$977$	−19.6048	−	33.9565i	−0.627212	−	1.08636i	−0.988109	−	0.153758i	$-0.950863\pi$
$977$	−19.6048	−	33.9565i	−0.627212	−	1.08636i	0.360896	−	0.932606i	$-0.382471\pi$
$978$	4.33943	−	7.51612i	0.138760	−	0.240339i
$979$	1.83329	+	3.17536i	0.0585923	+	0.101485i
$980$	−10.6797			−0.341152
$981$	53.2399	−	92.2142i	1.69982	−	2.94417i
$982$	−11.0179	+	19.0835i	−0.351595	+	0.608981i
$983$	27.1029	+	46.9435i	0.864447	+	1.49727i	0.867595	+	0.497271i	$0.165664\pi$
$983$	27.1029	+	46.9435i	0.864447	+	1.49727i	−0.00314875	+	0.999995i	$0.501002\pi$
$984$	−23.2694	−	40.3039i	−0.741803	−	1.28484i
$985$	−3.51149	+	6.08207i	−0.111885	+	0.193791i
$986$	−1.09683	+	1.89977i	−0.0349303	+	0.0605010i
$987$	−176.406			−5.61505
$988$	−14.9963	+	25.9743i	−0.477096	+	0.826354i
$989$	35.7814			1.13778
$990$	−8.21438	−	14.2277i	−0.261070	−	0.452187i
$991$	47.1653			1.49825			0.749127	−	0.662426i	$-0.230473\pi$
$991$	47.1653			1.49825			0.749127	+	0.662426i	$0.230473\pi$
$992$	11.3704	−	19.6941i	0.361011	−	0.625290i
$993$	17.4767			0.554606
$994$	42.8468			1.35902
$995$	−9.09098	−	15.7460i	−0.288204	−	0.499183i
$996$	20.7146			0.656368
$997$	−6.32985	+	10.9636i	−0.200468	+	0.347221i	−0.948679	−	0.316239i	$-0.897580\pi$
$997$	−6.32985	+	10.9636i	−0.200468	+	0.347221i	0.748211	+	0.663461i	$0.230913\pi$
$998$	−7.94000	+	13.7525i	−0.251336	+	0.435327i
$999$	88.5129	+	153.309i	2.80042	+	4.85048i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.c.a.40.16	✓	90
547.506	even	3	inner	547.2.c.a.506.16	yes	90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.c.a.40.16	✓	90	1.1	even	1	trivial
547.2.c.a.506.16	yes	90	547.506	even	3	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:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	547.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.467669 - 0.810027i) q^{2} +3.30105 q^{3} +(0.562571 - 0.974402i) q^{4} +(-0.395260 + 0.684610i) q^{5} +(-1.54380 - 2.67394i) q^{6} +(-2.17986 - 3.77563i) q^{7} -2.92307 q^{8} +7.89696 q^{9} +O(q^{10})\)	\(q+(-0.467669 - 0.810027i) q^{2} +3.30105 q^{3} +(0.562571 - 0.974402i) q^{4} +(-0.395260 + 0.684610i) q^{5} +(-1.54380 - 2.67394i) q^{6} +(-2.17986 - 3.77563i) q^{7} -2.92307 q^{8} +7.89696 q^{9} +0.739403 q^{10} +(-1.40680 - 2.43665i) q^{11} +(1.85708 - 3.21655i) q^{12} +(2.07590 + 3.59557i) q^{13} +(-2.03891 + 3.53149i) q^{14} +(-1.30477 + 2.25994i) q^{15} +(0.241885 + 0.418957i) q^{16} +(-1.02890 - 1.78211i) q^{17} +(-3.69317 - 6.39675i) q^{18} +(-3.21026 + 5.56033i) q^{19} +(0.444724 + 0.770284i) q^{20} +(-7.19584 - 12.4636i) q^{21} +(-1.31584 + 2.27910i) q^{22} +(3.98906 - 6.90925i) q^{23} -9.64920 q^{24} +(2.18754 + 3.78893i) q^{25} +(1.94167 - 3.36307i) q^{26} +16.1651 q^{27} -4.90531 q^{28} +1.13972 q^{29} +2.44081 q^{30} -4.21623 q^{31} +(-2.69682 + 4.67103i) q^{32} +(-4.64393 - 8.04353i) q^{33} +(-0.962369 + 1.66687i) q^{34} +3.44644 q^{35} +(4.44260 - 7.69481i) q^{36} +(5.47554 + 9.48392i) q^{37} +6.00536 q^{38} +(6.85266 + 11.8692i) q^{39} +(1.15537 - 2.00116i) q^{40} +(2.41154 + 4.17691i) q^{41} +(-6.73054 + 11.6576i) q^{42} +(2.24247 + 3.88408i) q^{43} -3.16571 q^{44} +(-3.12135 + 5.40634i) q^{45} -7.46224 q^{46} +(6.12874 - 10.6153i) q^{47} +(0.798476 + 1.38300i) q^{48} +(-6.00358 + 10.3985i) q^{49} +(2.04609 - 3.54393i) q^{50} +(-3.39645 - 5.88283i) q^{51} +4.67137 q^{52} +(3.15175 + 5.45899i) q^{53} +(-7.55994 - 13.0942i) q^{54} +2.22421 q^{55} +(6.37187 + 11.0364i) q^{56} +(-10.5972 + 18.3550i) q^{57} +(-0.533012 - 0.923205i) q^{58} +(1.12124 + 1.94205i) q^{59} +(1.46806 + 2.54275i) q^{60} +(-1.84448 - 3.19473i) q^{61} +(1.97180 + 3.41526i) q^{62} +(-17.2143 - 29.8160i) q^{63} +6.01242 q^{64} -3.28208 q^{65} +(-4.34365 + 7.52342i) q^{66} +(-1.96420 - 3.40209i) q^{67} -2.31532 q^{68} +(13.1681 - 22.8078i) q^{69} +(-1.61180 - 2.79171i) q^{70} +(-5.25365 - 9.09959i) q^{71} -23.0833 q^{72} +(-0.0563340 - 0.0975733i) q^{73} +(5.12148 - 8.87067i) q^{74} +(7.22119 + 12.5075i) q^{75} +(3.61200 + 6.25616i) q^{76} +(-6.13327 + 10.6231i) q^{77} +(6.40956 - 11.1017i) q^{78} +2.29837 q^{79} -0.382430 q^{80} +29.6711 q^{81} +(2.25561 - 3.90683i) q^{82} +(2.78860 + 4.83000i) q^{83} -16.1927 q^{84} +1.62673 q^{85} +(2.09747 - 3.63293i) q^{86} +3.76228 q^{87} +(4.11218 + 7.12250i) q^{88} -1.30316 q^{89} +5.83904 q^{90} +(9.05034 - 15.6757i) q^{91} +(-4.48826 - 7.77389i) q^{92} -13.9180 q^{93} -11.4649 q^{94} +(-2.53777 - 4.39555i) q^{95} +(-8.90235 + 15.4193i) q^{96} +(-6.68150 + 11.5727i) q^{97} +11.2308 q^{98} +(-11.1095 - 19.2422i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - q^{2} - 4 q^{3} - 47 q^{4} + q^{5} - 3 q^{6} + 2 q^{7} - 30 q^{8} + 82 q^{9}+O(q^{10}) \) 90 * q - q^2 - 4 * q^3 - 47 * q^4 + q^5 - 3 * q^6 + 2 * q^7 - 30 * q^8 + 82 * q^9	\( 90 q - q^{2} - 4 q^{3} - 47 q^{4} + q^{5} - 3 q^{6} + 2 q^{7} - 30 q^{8} + 82 q^{9} - 10 q^{10} + q^{11} + 4 q^{12} - 3 q^{13} + 2 q^{14} - 7 q^{15} - 39 q^{16} - 4 q^{17} - 11 q^{18} - 2 q^{19} + 25 q^{20} - 27 q^{21} - 7 q^{22} + q^{23} + 32 q^{24} - 40 q^{25} - 10 q^{26} - 34 q^{27} - 28 q^{28} + 26 q^{29} - 40 q^{30} - 24 q^{31} + 19 q^{32} + q^{33} - 6 q^{34} - 8 q^{35} - 36 q^{36} - 10 q^{37} + 24 q^{38} + 22 q^{39} + 20 q^{40} + 3 q^{41} + 38 q^{42} - 12 q^{43} - 30 q^{44} - 2 q^{45} - 40 q^{46} + 32 q^{47} + 14 q^{48} - 43 q^{49} + 14 q^{50} + 13 q^{51} + 46 q^{52} + 9 q^{53} - 8 q^{54} + 4 q^{55} - 8 q^{56} - 8 q^{57} + 4 q^{58} + 22 q^{59} - 2 q^{60} - 12 q^{61} + 11 q^{62} + 8 q^{63} + 22 q^{64} + 18 q^{65} + 12 q^{66} - 22 q^{67} + 6 q^{68} - q^{69} - 6 q^{70} - 4 q^{71} - 140 q^{72} + 17 q^{73} + 17 q^{74} + 39 q^{75} + 84 q^{76} - 4 q^{77} + 33 q^{78} - 72 q^{79} - 40 q^{80} + 18 q^{81} - 9 q^{82} + 24 q^{83} + 114 q^{84} + 40 q^{85} - 72 q^{86} - 78 q^{87} - 22 q^{88} + 14 q^{89} + 96 q^{90} - 8 q^{92} - 76 q^{93} + 108 q^{94} - 11 q^{95} - 34 q^{96} - 74 q^{98} - 62 q^{99}+O(q^{100}) \) 90 * q - q^2 - 4 * q^3 - 47 * q^4 + q^5 - 3 * q^6 + 2 * q^7 - 30 * q^8 + 82 * q^9 - 10 * q^10 + q^11 + 4 * q^12 - 3 * q^13 + 2 * q^14 - 7 * q^15 - 39 * q^16 - 4 * q^17 - 11 * q^18 - 2 * q^19 + 25 * q^20 - 27 * q^21 - 7 * q^22 + q^23 + 32 * q^24 - 40 * q^25 - 10 * q^26 - 34 * q^27 - 28 * q^28 + 26 * q^29 - 40 * q^30 - 24 * q^31 + 19 * q^32 + q^33 - 6 * q^34 - 8 * q^35 - 36 * q^36 - 10 * q^37 + 24 * q^38 + 22 * q^39 + 20 * q^40 + 3 * q^41 + 38 * q^42 - 12 * q^43 - 30 * q^44 - 2 * q^45 - 40 * q^46 + 32 * q^47 + 14 * q^48 - 43 * q^49 + 14 * q^50 + 13 * q^51 + 46 * q^52 + 9 * q^53 - 8 * q^54 + 4 * q^55 - 8 * q^56 - 8 * q^57 + 4 * q^58 + 22 * q^59 - 2 * q^60 - 12 * q^61 + 11 * q^62 + 8 * q^63 + 22 * q^64 + 18 * q^65 + 12 * q^66 - 22 * q^67 + 6 * q^68 - q^69 - 6 * q^70 - 4 * q^71 - 140 * q^72 + 17 * q^73 + 17 * q^74 + 39 * q^75 + 84 * q^76 - 4 * q^77 + 33 * q^78 - 72 * q^79 - 40 * q^80 + 18 * q^81 - 9 * q^82 + 24 * q^83 + 114 * q^84 + 40 * q^85 - 72 * q^86 - 78 * q^87 - 22 * q^88 + 14 * q^89 + 96 * q^90 - 8 * q^92 - 76 * q^93 + 108 * q^94 - 11 * q^95 - 34 * q^96 - 74 * q^98 - 62 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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