LMFDB - Embedded newform 286.2.h.d.157.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [286,2,Mod(27,286)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(286, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("286.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 286 = 2 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	286.h (of order $5$, degree $4$, 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:	$2.28372149781$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 17x^{10} + 99x^{8} + 233x^{6} + 226x^{4} + 80x^{2} + 5 $ x^12 + 17x^10 + 99x^8 + 233x^6 + 226x^4 + 80*x^2 + 5
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			157.3
Root			$1.49180i$ of defining polynomial
Character	$\chi$	$=$	286.157
Dual form			286.2.h.d.235.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(0.946538 + 2.91314i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.34055 + 1.70051i) q^{5} +(2.47807 + 1.80042i) q^{6} +(1.35095 - 4.15779i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-5.16342 + 3.75145i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(0.946538 + 2.91314i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.34055 + 1.70051i) q^{5} +(2.47807 + 1.80042i) q^{6} +(1.35095 - 4.15779i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-5.16342 + 3.75145i) q^{9} +2.89308 q^{10} +(-2.76994 - 1.82413i) q^{11} +3.06306 q^{12} +(-0.809017 + 0.587785i) q^{13} +(-1.35095 - 4.15779i) q^{14} +(-2.73841 + 8.42795i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-5.51457 - 4.00657i) q^{17} +(-1.97225 + 6.06997i) q^{18} +(1.53211 + 4.71534i) q^{19} +(2.34055 - 1.70051i) q^{20} +13.3910 q^{21} +(-3.31312 + 0.152375i) q^{22} -0.809862 q^{23} +(2.47807 - 1.80042i) q^{24} +(1.04135 + 3.20495i) q^{25} +(-0.309017 + 0.951057i) q^{26} +(-8.38168 - 6.08964i) q^{27} +(-3.53682 - 2.56965i) q^{28} +(-0.260083 + 0.800454i) q^{29} +(2.73841 + 8.42795i) q^{30} +(1.82718 - 1.32753i) q^{31} -1.00000 q^{32} +(2.69211 - 9.79583i) q^{33} -6.81638 q^{34} +(10.2323 - 7.43420i) q^{35} +(1.97225 + 6.06997i) q^{36} +(-2.90290 + 8.93420i) q^{37} +(4.01111 + 2.91424i) q^{38} +(-2.47807 - 1.80042i) q^{39} +(0.894010 - 2.75148i) q^{40} +(-1.43071 - 4.40327i) q^{41} +(10.8335 - 7.87100i) q^{42} +5.08386 q^{43} +(-2.59081 + 2.07068i) q^{44} -18.4646 q^{45} +(-0.655192 + 0.476025i) q^{46} +(-1.22018 - 3.75531i) q^{47} +(0.946538 - 2.91314i) q^{48} +(-9.79901 - 7.11940i) q^{49} +(2.72630 + 1.98077i) q^{50} +(6.45197 - 19.8571i) q^{51} +(0.309017 + 0.951057i) q^{52} +(-0.564906 + 0.410428i) q^{53} -10.3603 q^{54} +(-3.38122 - 8.97976i) q^{55} -4.37176 q^{56} +(-12.2863 + 8.92650i) q^{57} +(0.260083 + 0.800454i) q^{58} +(0.482452 - 1.48483i) q^{59} +(7.16924 + 5.20876i) q^{60} +(5.55670 + 4.03718i) q^{61} +(0.697921 - 2.14798i) q^{62} +(8.62220 + 26.5364i) q^{63} +(-0.809017 + 0.587785i) q^{64} -2.89308 q^{65} +(-3.57989 - 9.50737i) q^{66} +11.6321 q^{67} +(-5.51457 + 4.00657i) q^{68} +(-0.766565 - 2.35924i) q^{69} +(3.90839 - 12.0288i) q^{70} +(7.37778 + 5.36027i) q^{71} +(5.16342 + 3.75145i) q^{72} +(-2.00779 + 6.17934i) q^{73} +(2.90290 + 8.93420i) q^{74} +(-8.35081 + 6.06722i) q^{75} +4.95800 q^{76} +(-11.3264 + 9.05250i) q^{77} -3.06306 q^{78} +(4.02790 - 2.92644i) q^{79} +(-0.894010 - 2.75148i) q^{80} +(3.88968 - 11.9712i) q^{81} +(-3.74565 - 2.72137i) q^{82} +(0.353069 + 0.256519i) q^{83} +(4.13803 - 12.7356i) q^{84} +(-6.09391 - 18.7551i) q^{85} +(4.11293 - 2.98822i) q^{86} -2.57802 q^{87} +(-0.878894 + 3.19805i) q^{88} -4.15808 q^{89} +(-14.9382 + 10.8532i) q^{90} +(1.35095 + 4.15779i) q^{91} +(-0.250261 + 0.770225i) q^{92} +(5.59677 + 4.06629i) q^{93} +(-3.19446 - 2.32091i) q^{94} +(-4.43250 + 13.6418i) q^{95} +(-0.946538 - 2.91314i) q^{96} +(-4.46094 + 3.24106i) q^{97} -12.1122 q^{98} +(21.1455 - 0.972511i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 2 q^{7} + 3 q^{8} - 17 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 2 * q^7 + 3 * q^8 - 17 * q^9	\( 12 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 2 q^{7} + 3 q^{8} - 17 q^{9} + 12 q^{10} - 3 q^{13} + 2 q^{14} - 18 q^{15} - 3 q^{16} - 10 q^{17} - 13 q^{18} + 3 q^{19} + 3 q^{20} + 30 q^{21} + 5 q^{22} + 8 q^{23} - 2 q^{25} + 3 q^{26} - 9 q^{27} - 7 q^{28} - 6 q^{29} + 18 q^{30} - 29 q^{31} - 12 q^{32} + 7 q^{33} - 10 q^{34} + 22 q^{35} + 13 q^{36} - 16 q^{37} + 12 q^{38} - 3 q^{40} + 16 q^{41} + 10 q^{42} + 38 q^{43} - 5 q^{44} - 20 q^{45} + 2 q^{46} + 9 q^{47} + 3 q^{49} - 8 q^{50} + 3 q^{51} - 3 q^{52} - 21 q^{53} - 6 q^{54} - 4 q^{55} - 18 q^{56} - 8 q^{57} + 6 q^{58} - 5 q^{59} + 22 q^{60} + 6 q^{61} - 36 q^{62} + 27 q^{63} - 3 q^{64} - 12 q^{65} - 12 q^{66} + 14 q^{67} - 10 q^{68} - 16 q^{69} + 18 q^{70} + 39 q^{71} + 17 q^{72} - 18 q^{73} + 16 q^{74} - 50 q^{75} + 18 q^{76} - 30 q^{77} - 12 q^{79} + 3 q^{80} + 19 q^{81} + 19 q^{82} + 16 q^{83} - 5 q^{84} - 21 q^{85} + 12 q^{86} - 4 q^{87} - 10 q^{88} - 10 q^{89} - 20 q^{90} - 2 q^{91} - 2 q^{92} + 47 q^{93} - 14 q^{94} - 67 q^{95} - 16 q^{97} - 18 q^{98} - 2 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 2 * q^7 + 3 * q^8 - 17 * q^9 + 12 * q^10 - 3 * q^13 + 2 * q^14 - 18 * q^15 - 3 * q^16 - 10 * q^17 - 13 * q^18 + 3 * q^19 + 3 * q^20 + 30 * q^21 + 5 * q^22 + 8 * q^23 - 2 * q^25 + 3 * q^26 - 9 * q^27 - 7 * q^28 - 6 * q^29 + 18 * q^30 - 29 * q^31 - 12 * q^32 + 7 * q^33 - 10 * q^34 + 22 * q^35 + 13 * q^36 - 16 * q^37 + 12 * q^38 - 3 * q^40 + 16 * q^41 + 10 * q^42 + 38 * q^43 - 5 * q^44 - 20 * q^45 + 2 * q^46 + 9 * q^47 + 3 * q^49 - 8 * q^50 + 3 * q^51 - 3 * q^52 - 21 * q^53 - 6 * q^54 - 4 * q^55 - 18 * q^56 - 8 * q^57 + 6 * q^58 - 5 * q^59 + 22 * q^60 + 6 * q^61 - 36 * q^62 + 27 * q^63 - 3 * q^64 - 12 * q^65 - 12 * q^66 + 14 * q^67 - 10 * q^68 - 16 * q^69 + 18 * q^70 + 39 * q^71 + 17 * q^72 - 18 * q^73 + 16 * q^74 - 50 * q^75 + 18 * q^76 - 30 * q^77 - 12 * q^79 + 3 * q^80 + 19 * q^81 + 19 * q^82 + 16 * q^83 - 5 * q^84 - 21 * q^85 + 12 * q^86 - 4 * q^87 - 10 * q^88 - 10 * q^89 - 20 * q^90 - 2 * q^91 - 2 * q^92 + 47 * q^93 - 14 * q^94 - 67 * q^95 - 16 * q^97 - 18 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/286\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	0.946538	+	2.91314i	0.546484	+	1.68190i	0.717435	+	0.696625i	$0.245316\pi$
$3$	0.946538	+	2.91314i	0.546484	+	1.68190i	−0.170951	+	0.985279i	$0.554684\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	2.34055	+	1.70051i	1.04672	+	0.760490i	0.971587	−	0.236683i	$-0.0760603\pi$
$5$	2.34055	+	1.70051i	1.04672	+	0.760490i	0.0751378	+	0.997173i	$0.476060\pi$
$6$	2.47807	+	1.80042i	1.01167	+	0.735019i
$7$	1.35095	−	4.15779i	0.510610	−	1.57150i	−0.280521	−	0.959848i	$-0.590507\pi$
$7$	1.35095	−	4.15779i	0.510610	−	1.57150i	0.791130	−	0.611648i	$-0.209493\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	−5.16342	+	3.75145i	−1.72114	+	1.25048i
$10$	2.89308			0.914871
$11$	−2.76994	−	1.82413i	−0.835167	−	0.549996i
$11$	−2.76994	−	1.82413i	−0.835167	−	0.549996i
$12$	3.06306			0.884230
$13$	−0.809017	+	0.587785i	−0.224381	+	0.163022i
$13$	−0.809017	+	0.587785i	−0.224381	+	0.163022i
$14$	−1.35095	−	4.15779i	−0.361056	−	1.11122i
$15$	−2.73841	+	8.42795i	−0.707053	+	2.17609i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−5.51457	−	4.00657i	−1.33748	−	0.971736i	−0.999533	−	0.0305707i	$-0.990268\pi$
$17$	−5.51457	−	4.00657i	−1.33748	−	0.971736i	−0.337947	−	0.941165i	$-0.609732\pi$
$18$	−1.97225	+	6.06997i	−0.464864	+	1.43071i
$19$	1.53211	+	4.71534i	0.351490	+	1.08177i	0.958017	+	0.286711i	$0.0925620\pi$
$19$	1.53211	+	4.71534i	0.351490	+	1.08177i	−0.606527	+	0.795063i	$0.707438\pi$
$20$	2.34055	−	1.70051i	0.523362	−	0.380245i
$21$	13.3910			2.92215
$22$	−3.31312	+	0.152375i	−0.706360	+	0.0324865i
$23$	−0.809862			−0.168868			−0.0844339	−	0.996429i	$-0.526908\pi$
$23$	−0.809862			−0.168868			−0.0844339	+	0.996429i	$0.526908\pi$
$24$	2.47807	−	1.80042i	0.505834	−	0.367510i
$25$	1.04135	+	3.20495i	0.208271	+	0.640991i
$26$	−0.309017	+	0.951057i	−0.0606032	+	0.186518i
$27$	−8.38168	−	6.08964i	−1.61305	−	1.17195i
$28$	−3.53682	−	2.56965i	−0.668397	−	0.485619i
$29$	−0.260083	+	0.800454i	−0.0482962	+	0.148641i	−0.972296	−	0.233752i	$-0.924900\pi$
$29$	−0.260083	+	0.800454i	−0.0482962	+	0.148641i	0.924000	+	0.382392i	$0.124900\pi$
$30$	2.73841	+	8.42795i	0.499962	+	1.53873i
$31$	1.82718	−	1.32753i	0.328171	−	0.238431i	−0.411483	−	0.911417i	$-0.634989\pi$
$31$	1.82718	−	1.32753i	0.328171	−	0.238431i	0.739654	+	0.672987i	$0.234989\pi$
$32$	−1.00000			−0.176777
$33$	2.69211	−	9.79583i	0.468635	−	1.70524i
$34$	−6.81638			−1.16900
$35$	10.2323	−	7.43420i	1.72957	−	1.25661i
$36$	1.97225	+	6.06997i	0.328709	+	1.01166i
$37$	−2.90290	+	8.93420i	−0.477233	+	1.46877i	0.365688	+	0.930737i	$0.380834\pi$
$37$	−2.90290	+	8.93420i	−0.477233	+	1.46877i	−0.842922	+	0.538036i	$0.819166\pi$
$38$	4.01111	+	2.91424i	0.650688	+	0.472752i
$39$	−2.47807	−	1.80042i	−0.396809	−	0.288298i
$40$	0.894010	−	2.75148i	0.141355	−	0.435047i
$41$	−1.43071	−	4.40327i	−0.223439	−	0.687676i	−0.998446	−	0.0557231i	$-0.982254\pi$
$41$	−1.43071	−	4.40327i	−0.223439	−	0.687676i	0.775007	−	0.631953i	$-0.217746\pi$
$42$	10.8335	−	7.87100i	1.67165	−	1.21452i
$43$	5.08386			0.775281			0.387641	−	0.921811i	$-0.373290\pi$
$43$	5.08386			0.775281			0.387641	+	0.921811i	$0.373290\pi$
$44$	−2.59081	+	2.07068i	−0.390579	+	0.312167i
$45$	−18.4646			−2.75254
$46$	−0.655192	+	0.476025i	−0.0966028	+	0.0701860i
$47$	−1.22018	−	3.75531i	−0.177981	−	0.547769i	0.821776	−	0.569810i	$-0.192983\pi$
$47$	−1.22018	−	3.75531i	−0.177981	−	0.547769i	−0.999757	+	0.0220416i	$0.992983\pi$
$48$	0.946538	−	2.91314i	0.136621	−	0.420476i
$49$	−9.79901	−	7.11940i	−1.39986	−	1.01706i
$50$	2.72630	+	1.98077i	0.385557	+	0.280123i
$51$	6.45197	−	19.8571i	0.903456	−	2.78055i
$52$	0.309017	+	0.951057i	0.0428529	+	0.131888i
$53$	−0.564906	+	0.410428i	−0.0775958	+	0.0563766i	−0.625907	−	0.779898i	$-0.715271\pi$
$53$	−0.564906	+	0.410428i	−0.0775958	+	0.0563766i	0.548311	+	0.836274i	$0.315271\pi$
$54$	−10.3603			−1.40986
$55$	−3.38122	−	8.97976i	−0.455924	−	1.21083i
$56$	−4.37176			−0.584200
$57$	−12.2863	+	8.92650i	−1.62736	+	1.18234i
$58$	0.260083	+	0.800454i	0.0341506	+	0.105105i
$59$	0.482452	−	1.48483i	0.0628099	−	0.193309i	−0.914727	−	0.404072i	$-0.867595\pi$
$59$	0.482452	−	1.48483i	0.0628099	−	0.193309i	0.977537	+	0.210763i	$0.0675947\pi$
$60$	7.16924	+	5.20876i	0.925545	+	0.672448i
$61$	5.55670	+	4.03718i	0.711462	+	0.516908i	0.883645	−	0.468157i	$-0.155082\pi$
$61$	5.55670	+	4.03718i	0.711462	+	0.516908i	−0.172183	+	0.985065i	$0.555082\pi$
$62$	0.697921	−	2.14798i	0.0886361	−	0.272794i
$63$	8.62220	+	26.5364i	1.08630	+	3.34327i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−2.89308			−0.358842
$66$	−3.57989	−	9.50737i	−0.440654	−	1.17028i
$67$	11.6321			1.42109			0.710545	−	0.703652i	$-0.248449\pi$
$67$	11.6321			1.42109			0.710545	+	0.703652i	$0.248449\pi$
$68$	−5.51457	+	4.00657i	−0.668740	+	0.485868i
$69$	−0.766565	−	2.35924i	−0.0922836	−	0.284020i
$70$	3.90839	−	12.0288i	0.467142	−	1.43772i
$71$	7.37778	+	5.36027i	0.875582	+	0.636147i	0.932079	−	0.362255i	$-0.117993\pi$
$71$	7.37778	+	5.36027i	0.875582	+	0.636147i	−0.0564971	+	0.998403i	$0.517993\pi$
$72$	5.16342	+	3.75145i	0.608515	+	0.442112i
$73$	−2.00779	+	6.17934i	−0.234994	+	0.723237i	0.762128	+	0.647426i	$0.224155\pi$
$73$	−2.00779	+	6.17934i	−0.234994	+	0.723237i	−0.997122	+	0.0758109i	$0.975845\pi$
$74$	2.90290	+	8.93420i	0.337455	+	1.03858i
$75$	−8.35081	+	6.06722i	−0.964269	+	0.700582i
$76$	4.95800			0.568722
$77$	−11.3264	+	9.05250i	−1.29076	+	1.03163i
$78$	−3.06306			−0.346823
$79$	4.02790	−	2.92644i	0.453174	−	0.329250i	−0.337674	−	0.941263i	$-0.609640\pi$
$79$	4.02790	−	2.92644i	0.453174	−	0.329250i	0.790848	+	0.612013i	$0.209640\pi$
$80$	−0.894010	−	2.75148i	−0.0999533	−	0.307625i
$81$	3.88968	−	11.9712i	0.432187	−	1.33013i
$82$	−3.74565	−	2.72137i	−0.413638	−	0.300525i
$83$	0.353069	+	0.256519i	0.0387543	+	0.0281567i	0.606994	−	0.794707i	$-0.292375\pi$
$83$	0.353069	+	0.256519i	0.0387543	+	0.0281567i	−0.568239	+	0.822863i	$0.692375\pi$
$84$	4.13803	−	12.7356i	0.451496	−	1.38956i
$85$	−6.09391	−	18.7551i	−0.660978	−	2.03428i
$86$	4.11293	−	2.98822i	0.443508	−	0.322228i
$87$	−2.57802			−0.276392
$88$	−0.878894	+	3.19805i	−0.0936904	+	0.340914i
$89$	−4.15808			−0.440756			−0.220378	−	0.975415i	$-0.570729\pi$
$89$	−4.15808			−0.440756			−0.220378	+	0.975415i	$0.570729\pi$
$90$	−14.9382	+	10.8532i	−1.57462	+	1.14403i
$91$	1.35095	+	4.15779i	0.141618	+	0.435854i
$92$	−0.250261	+	0.770225i	−0.0260915	+	0.0803015i
$93$	5.59677	+	4.06629i	0.580358	+	0.421655i
$94$	−3.19446	−	2.32091i	−0.329484	−	0.239384i
$95$	−4.43250	+	13.6418i	−0.454765	+	1.39962i
$96$	−0.946538	−	2.91314i	−0.0966056	−	0.297322i
$97$	−4.46094	+	3.24106i	−0.452940	+	0.329080i	−0.790755	−	0.612132i	$-0.790312\pi$
$97$	−4.46094	+	3.24106i	−0.452940	+	0.329080i	0.337816	+	0.941212i	$0.390312\pi$
$98$	−12.1122			−1.22352
$99$	21.1455	−	0.972511i	2.12520	−	0.0977410i
$100$	3.36989			0.336989
$101$	−8.25215	+	5.99554i	−0.821119	+	0.596578i	−0.917033	−	0.398811i	$-0.869423\pi$
$101$	−8.25215	+	5.99554i	−0.821119	+	0.596578i	0.0959135	+	0.995390i	$0.469423\pi$
$102$	−6.45197	−	19.8571i	−0.638840	−	1.96615i
$103$	4.92796	−	15.1667i	0.485566	−	1.49442i	−0.345592	−	0.938385i	$-0.612322\pi$
$103$	4.92796	−	15.1667i	0.485566	−	1.49442i	0.831159	−	0.556035i	$-0.187678\pi$
$104$	0.809017	+	0.587785i	0.0793306	+	0.0576371i
$105$	31.3422	+	22.7714i	3.05868	+	2.22226i
$106$	−0.215775	+	0.664087i	−0.0209579	+	0.0645018i
$107$	−0.360892	−	1.11071i	−0.0348887	−	0.107377i	0.932096	−	0.362212i	$-0.117979\pi$
$107$	−0.360892	−	1.11071i	−0.0348887	−	0.107377i	−0.966984	+	0.254836i	$0.917979\pi$
$108$	−8.38168	+	6.08964i	−0.806527	+	0.585976i
$109$	5.24668			0.502541			0.251270	−	0.967917i	$-0.419152\pi$
$109$	5.24668			0.502541			0.251270	+	0.967917i	$0.419152\pi$
$110$	−8.01364	−	5.27735i	−0.764070	−	0.503175i
$111$	−28.7743			−2.73114
$112$	−3.53682	+	2.56965i	−0.334198	+	0.242809i
$113$	−0.376850	−	1.15983i	−0.0354511	−	0.109107i	0.931765	−	0.363062i	$-0.118269\pi$
$113$	−0.376850	−	1.15983i	−0.0354511	−	0.109107i	−0.967216	+	0.253955i	$0.918269\pi$
$114$	−4.69294	+	14.4434i	−0.439534	+	1.35275i
$115$	−1.89552	−	1.37718i	−0.176758	−	0.128422i
$116$	0.680907	+	0.494708i	0.0632206	+	0.0459324i
$117$	1.97225	−	6.06997i	0.182335	−	0.561169i
$118$	−0.482452	−	1.48483i	−0.0444133	−	0.136690i
$119$	−24.1084	+	17.5157i	−2.21001	+	1.60567i
$120$	8.86167			0.808956
$121$	4.34510	+	10.1055i	0.395009	+	0.918677i
$122$	6.86846			0.621841
$123$	11.4732	−	8.33573i	1.03450	−	0.751608i
$124$	−0.697921	−	2.14798i	−0.0626752	−	0.192894i
$125$	1.45734	−	4.48522i	0.130348	−	0.401170i
$126$	22.5732	+	16.4004i	2.01098	+	1.46106i
$127$	−4.47744	−	3.25305i	−0.397309	−	0.288662i	0.371135	−	0.928579i	$-0.378969\pi$
$127$	−4.47744	−	3.25305i	−0.397309	−	0.288662i	−0.768444	+	0.639917i	$0.778969\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	4.81207	+	14.8100i	0.423679	+	1.30395i
$130$	−2.34055	+	1.70051i	−0.205280	+	0.149144i
$131$	−8.99775			−0.786137			−0.393069	−	0.919509i	$-0.628587\pi$
$131$	−8.99775			−0.786137			−0.393069	+	0.919509i	$0.628587\pi$
$132$	−8.48448	−	5.58742i	−0.738480	−	0.486323i
$133$	21.6752			1.87948
$134$	9.41058	−	6.83719i	0.812951	−	0.590643i
$135$	−9.26223	−	28.5062i	−0.797166	−	2.45342i
$136$	−2.10638	+	6.48277i	−0.180620	+	0.555893i
$137$	15.4773	+	11.2449i	1.32231	+	0.960717i	0.999900	+	0.0141172i	$0.00449381\pi$
$137$	15.4773	+	11.2449i	1.32231	+	0.960717i	0.322412	+	0.946599i	$0.395506\pi$
$138$	−2.00689	−	1.45809i	−0.170838	−	0.124121i
$139$	3.41439	−	10.5084i	0.289605	−	0.891312i	−0.695376	−	0.718646i	$-0.744762\pi$
$139$	3.41439	−	10.5084i	0.289605	−	0.891312i	0.984981	−	0.172666i	$-0.0552380\pi$
$140$	−3.90839	−	12.0288i	−0.330319	−	1.01662i
$141$	9.78483	−	7.10909i	0.824031	−	0.598694i
$142$	9.11944			0.765287
$143$	3.31312	−	0.152375i	0.277057	−	0.0127423i
$144$	6.38234			0.531862
$145$	−1.96991	+	1.43123i	−0.163592	+	0.118857i
$146$	2.00779	+	6.17934i	0.166166	+	0.511406i
$147$	11.4647	−	35.2847i	0.945592	−	2.91023i
$148$	7.59989	+	5.52164i	0.624707	+	0.453876i
$149$	−18.8055	−	13.6630i	−1.54060	−	1.11931i	−0.949956	−	0.312383i	$-0.898873\pi$
$149$	−18.8055	−	13.6630i	−1.54060	−	1.11931i	−0.590647	−	0.806930i	$-0.701127\pi$
$150$	−3.18973	+	9.81697i	−0.260440	+	0.801552i
$151$	6.63712	+	20.4270i	0.540121	+	1.66232i	0.732316	+	0.680965i	$0.238440\pi$
$151$	6.63712	+	20.4270i	0.540121	+	1.66232i	−0.192194	+	0.981357i	$0.561560\pi$
$152$	4.01111	−	2.91424i	0.325344	−	0.236376i
$153$	43.5045			3.51713
$154$	−3.84231	+	13.9811i	−0.309622	+	1.12663i
$155$	6.53407			0.524829
$156$	−2.47807	+	1.80042i	−0.198404	+	0.144149i
$157$	−0.587582	−	1.80839i	−0.0468941	−	0.144325i	0.924868	−	0.380289i	$-0.124175\pi$
$157$	−0.587582	−	1.80839i	−0.0468941	−	0.144325i	−0.971762	+	0.235964i	$0.924175\pi$
$158$	1.53852	−	4.73508i	0.122398	−	0.376703i
$159$	−1.73034	−	1.25717i	−0.137225	−	0.0996998i
$160$	−2.34055	−	1.70051i	−0.185037	−	0.134437i
$161$	−1.09408	+	3.36723i	−0.0862256	+	0.265375i
$162$	−3.88968	−	11.9712i	−0.305602	−	0.940547i
$163$	−3.23203	+	2.34821i	−0.253152	+	0.183926i	−0.707123	−	0.707091i	$-0.750007\pi$
$163$	−3.23203	+	2.34821i	−0.253152	+	0.183926i	0.453970	+	0.891017i	$0.350007\pi$
$164$	−4.62988			−0.361533
$165$	22.9589	−	18.3497i	1.78735	−	1.42852i
$166$	0.436417			0.0338725
$167$	10.0502	−	7.30192i	0.777710	−	0.565039i	−0.126581	−	0.991956i	$-0.540400\pi$
$167$	10.0502	−	7.30192i	0.777710	−	0.565039i	0.904291	+	0.426917i	$0.140400\pi$
$168$	−4.13803	−	12.7356i	−0.319256	−	0.982569i
$169$	0.309017	−	0.951057i	0.0237705	−	0.0731582i
$170$	−15.9541	−	11.5913i	−1.22362	−	0.889013i
$171$	−25.6003	−	18.5997i	−1.95770	−	1.42235i
$172$	1.57100	−	4.83504i	0.119788	−	0.368668i
$173$	2.38687	+	7.34604i	0.181471	+	0.558509i	0.999870	−	0.0161413i	$-0.00513816\pi$
$173$	2.38687	+	7.34604i	0.181471	+	0.558509i	−0.818399	+	0.574650i	$0.805138\pi$
$174$	−2.08566	+	1.51532i	−0.158113	+	0.114876i
$175$	14.7323			1.11366
$176$	1.16873	+	3.10388i	0.0880962	+	0.233964i
$177$	4.78220			0.359452
$178$	−3.36396	+	2.44406i	−0.252140	+	0.183190i
$179$	3.65472	+	11.2481i	0.273167	+	0.840720i	0.989699	+	0.143166i	$0.0457284\pi$
$179$	3.65472	+	11.2481i	0.273167	+	0.840720i	−0.716532	+	0.697554i	$0.754272\pi$
$180$	−5.70588	+	17.5609i	−0.425291	+	1.30891i
$181$	14.2920	+	10.3837i	1.06231	+	0.771817i	0.974515	−	0.224321i	$-0.0720165\pi$
$181$	14.2920	+	10.3837i	1.06231	+	0.771817i	0.0877995	+	0.996138i	$0.472017\pi$
$182$	3.53682	+	2.56965i	0.262167	+	0.190475i
$183$	−6.50126	+	20.0088i	−0.480587	+	1.47909i
$184$	0.250261	+	0.770225i	0.0184495	+	0.0567817i
$185$	−21.9870	+	15.9745i	−1.61652	+	1.17447i
$186$	6.91799			0.507251
$187$	7.96650	+	21.1572i	0.582568	+	1.54717i
$188$	−3.94857			−0.287979
$189$	−36.6426	+	26.6224i	−2.66536	+	1.93650i
$190$	4.43250	+	13.6418i	0.321568	+	0.989683i
$191$	−4.87954	+	15.0177i	−0.353071	+	1.08664i	0.604048	+	0.796948i	$0.293554\pi$
$191$	−4.87954	+	15.0177i	−0.353071	+	1.08664i	−0.957119	+	0.289694i	$0.906446\pi$
$192$	−2.47807	−	1.80042i	−0.178839	−	0.129934i
$193$	−16.3841	−	11.9038i	−1.17936	−	0.856853i	−0.187258	−	0.982311i	$-0.559960\pi$
$193$	−16.3841	−	11.9038i	−1.17936	−	0.856853i	−0.992099	+	0.125458i	$0.959960\pi$
$194$	−1.70393	+	5.24415i	−0.122335	+	0.376508i
$195$	−2.73841	−	8.42795i	−0.196101	−	0.603538i
$196$	−9.79901	+	7.11940i	−0.699929	+	0.508528i
$197$	−7.51561			−0.535465			−0.267732	−	0.963493i	$-0.586274\pi$
$197$	−7.51561			−0.535465			−0.267732	+	0.963493i	$0.586274\pi$
$198$	16.5354	−	13.2158i	1.17512	−	0.939205i
$199$	−10.6352			−0.753910			−0.376955	−	0.926232i	$-0.623029\pi$
$199$	−10.6352			−0.753910			−0.376955	+	0.926232i	$0.623029\pi$
$200$	2.72630	−	1.98077i	0.192778	−	0.140062i
$201$	11.0102	+	33.8860i	0.776603	+	2.39014i
$202$	−3.15204	+	9.70098i	−0.221777	+	0.682559i
$203$	2.97676	+	2.16274i	0.208927	+	0.151795i
$204$	−16.8915	−	12.2724i	−1.18264	−	0.859238i
$205$	4.13915	−	12.7390i	0.289091	−	0.889731i
$206$	−4.92796	−	15.1667i	−0.343347	−	1.05671i
$207$	4.18166	−	3.03815i	0.290646	−	0.211166i
$208$	1.00000			0.0693375
$209$	4.35756	−	15.8560i	0.301419	−	1.09678i
$210$	38.7410			2.67339
$211$	0.334859	−	0.243289i	0.0230526	−	0.0167487i	−0.576199	−	0.817309i	$-0.695465\pi$
$211$	0.334859	−	0.243289i	0.0230526	−	0.0167487i	0.599252	+	0.800561i	$0.295465\pi$
$212$	0.215775	+	0.664087i	0.0148195	+	0.0456096i
$213$	−8.63190	+	26.5662i	−0.591448	+	1.82029i
$214$	−0.944828	−	0.686457i	−0.0645871	−	0.0469253i
$215$	11.8990	+	8.64514i	0.811506	+	0.589594i
$216$	−3.20152	+	9.85325i	−0.217836	+	0.670429i
$217$	−3.05114	−	9.39045i	−0.207125	−	0.637465i
$218$	4.24465	−	3.08392i	0.287484	−	0.208869i
$219$	−19.9018			−1.34484
$220$	−9.58512	+	0.440833i	−0.646228	+	0.0297210i
$221$	6.81638			0.458520
$222$	−23.2789	+	16.9131i	−1.56238	+	1.13513i
$223$	−5.41799	−	16.6749i	−0.362815	−	1.11663i	−0.951338	−	0.308150i	$-0.900290\pi$
$223$	−5.41799	−	16.6749i	−0.362815	−	1.11663i	0.588522	−	0.808481i	$-0.299710\pi$
$224$	−1.35095	+	4.15779i	−0.0902639	+	0.277804i
$225$	−17.4002	−	12.6420i	−1.16001	−	0.842797i
$226$	−0.986607	−	0.716812i	−0.0656281	−	0.0476816i
$227$	−4.55222	+	14.0103i	−0.302142	+	0.929896i	0.678587	+	0.734520i	$0.262593\pi$
$227$	−4.55222	+	14.0103i	−0.302142	+	0.929896i	−0.980728	+	0.195376i	$0.937407\pi$
$228$	4.69294	+	14.4434i	0.310797	+	0.956536i
$229$	−5.04484	+	3.66529i	−0.333373	+	0.242209i	−0.741860	−	0.670554i	$-0.766056\pi$
$229$	−5.04484	+	3.66529i	−0.333373	+	0.242209i	0.408488	+	0.912764i	$0.366056\pi$
$230$	−2.34299			−0.154492
$231$	−37.0921	−	24.4268i	−2.44048	−	1.60717i
$232$	0.841647			0.0552568
$233$	7.48789	−	5.44027i	0.490548	−	0.356404i	−0.314847	−	0.949142i	$-0.601953\pi$
$233$	7.48789	−	5.44027i	0.490548	−	0.356404i	0.805395	+	0.592738i	$0.201953\pi$
$234$	−1.97225	−	6.06997i	−0.128930	−	0.396806i
$235$	3.53006	−	10.8644i	0.230276	−	0.708716i
$236$	−1.26308	−	0.917678i	−0.0822192	−	0.0597358i
$237$	12.3377	+	8.96386i	0.801420	+	0.582265i
$238$	−9.20857	+	28.3411i	−0.596903	+	1.83708i
$239$	−4.16409	−	12.8158i	−0.269353	−	0.828983i	−0.990659	−	0.136366i	$-0.956458\pi$
$239$	−4.16409	−	12.8158i	−0.269353	−	0.828983i	0.721306	−	0.692617i	$-0.243542\pi$
$240$	7.16924	−	5.20876i	0.462772	−	0.336224i
$241$	−18.5633			−1.19577			−0.597883	−	0.801584i	$-0.703991\pi$
$241$	−18.5633			−1.19577			−0.597883	+	0.801584i	$0.703991\pi$
$242$	9.45509	+	5.62150i	0.607796	+	0.361364i
$243$	7.47461			0.479497
$244$	5.55670	−	4.03718i	0.355731	−	0.258454i
$245$	−10.8285	−	33.3266i	−0.691805	−	2.12916i
$246$	4.38235	−	13.4875i	0.279409	−	0.859931i
$247$	−4.01111	−	2.91424i	−0.255221	−	0.185429i
$248$	−1.82718	−	1.32753i	−0.116026	−	0.0842979i
$249$	−0.413085	+	1.27134i	−0.0261782	+	0.0805682i
$250$	−1.45734	−	4.48522i	−0.0921700	−	0.283670i
$251$	1.12520	−	0.817508i	0.0710222	−	0.0516007i	−0.551708	−	0.834038i	$-0.686024\pi$
$251$	1.12520	−	0.817508i	0.0710222	−	0.0516007i	0.622730	+	0.782437i	$0.286024\pi$
$252$	27.9020			1.75766
$253$	2.24327	+	1.47729i	0.141033	+	0.0928767i
$254$	−5.53442			−0.347260
$255$	48.8683	−	35.5049i	3.06025	−	2.22340i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	6.93217	−	21.3350i	0.432417	−	1.33084i	−0.463293	−	0.886205i	$-0.653332\pi$
$257$	6.93217	−	21.3350i	0.432417	−	1.33084i	0.895710	−	0.444638i	$-0.146668\pi$
$258$	12.5982	+	9.15309i	0.784327	+	0.569847i
$259$	33.2248	+	24.1393i	2.06449	+	1.49994i
$260$	−0.894010	+	2.75148i	−0.0554441	+	0.170639i
$261$	−1.65994	−	5.10877i	−0.102748	−	0.316225i
$262$	−7.27934	+	5.28875i	−0.449719	+	0.326740i
$263$	−5.84685			−0.360532			−0.180266	−	0.983618i	$-0.557696\pi$
$263$	−5.84685			−0.360532			−0.180266	+	0.983618i	$0.557696\pi$
$264$	−10.1483	+	0.466735i	−0.624584	+	0.0287255i
$265$	−2.02012			−0.124095
$266$	17.5356	−	12.7404i	1.07518	−	0.781161i
$267$	−3.93578	−	12.1131i	−0.240866	−	0.741310i
$268$	3.59452	−	11.0628i	0.219570	−	0.675768i
$269$	−8.62711	−	6.26796i	−0.526004	−	0.382164i	0.292857	−	0.956156i	$-0.405394\pi$
$269$	−8.62711	−	6.26796i	−0.526004	−	0.382164i	−0.818861	+	0.573992i	$0.805394\pi$
$270$	−24.2488	−	17.6178i	−1.47574	−	1.07219i
$271$	−0.307829	+	0.947400i	−0.0186993	+	0.0575504i	−0.959971	−	0.280100i	$-0.909632\pi$
$271$	−0.307829	+	0.947400i	−0.0186993	+	0.0575504i	0.941271	+	0.337651i	$0.109632\pi$
$272$	2.10638	+	6.48277i	0.127718	+	0.393075i
$273$	−10.8335	+	7.87100i	−0.655674	+	0.476375i
$274$	19.1310			1.15574
$275$	2.96177	−	10.7771i	0.178602	−	0.649882i
$276$	−2.48066			−0.149318
$277$	−11.8886	+	8.63755i	−0.714315	+	0.518980i	−0.884563	−	0.466421i	$-0.845543\pi$
$277$	−11.8886	+	8.63755i	−0.714315	+	0.518980i	0.170248	+	0.985401i	$0.445543\pi$
$278$	−3.41439	−	10.5084i	−0.204782	−	0.630253i
$279$	−4.45437	+	13.7091i	−0.266676	+	0.820745i
$280$	−10.2323	−	7.43420i	−0.611497	−	0.444279i
$281$	2.17255	+	1.57845i	0.129603	+	0.0941624i	0.650698	−	0.759336i	$-0.274476\pi$
$281$	2.17255	+	1.57845i	0.129603	+	0.0941624i	−0.521095	+	0.853499i	$0.674476\pi$
$282$	3.73747	−	11.5028i	0.222563	−	0.684979i
$283$	−1.79485	−	5.52398i	−0.106693	−	0.328367i	0.883431	−	0.468561i	$-0.155227\pi$
$283$	−1.79485	−	5.52398i	−0.106693	−	0.328367i	−0.990124	+	0.140194i	$0.955227\pi$
$284$	7.37778	−	5.36027i	0.437791	−	0.318074i
$285$	−43.9362			−2.60256
$286$	2.59081	−	2.07068i	0.153198	−	0.122442i
$287$	−20.2407			−1.19477
$288$	5.16342	−	3.75145i	0.304258	−	0.221056i
$289$	9.10459	+	28.0211i	0.535564	+	1.64830i
$290$	−0.752440	+	2.31577i	−0.0441848	+	0.135987i
$291$	−13.6641	−	9.92757i	−0.801005	−	0.581964i
$292$	5.25646	+	3.81904i	0.307611	+	0.223493i
$293$	−7.17443	+	22.0806i	−0.419135	+	1.28996i	0.489365	+	0.872079i	$0.337228\pi$
$293$	−7.17443	+	22.0806i	−0.419135	+	1.28996i	−0.908500	+	0.417885i	$0.862772\pi$
$294$	−11.4647	−	35.2847i	−0.668635	−	2.05785i
$295$	3.65417	−	2.65491i	0.212754	−	0.154575i
$296$	9.39397			0.546014
$297$	12.1084	+	32.1572i	0.702601	+	1.86595i
$298$	−23.2448			−1.34654
$299$	0.655192	−	0.476025i	0.0378907	−	0.0275292i
$300$	3.18973	+	9.81697i	0.184159	+	0.566783i
$301$	6.86802	−	21.1376i	0.395866	−	1.21835i
$302$	17.3762	+	12.6246i	0.999888	+	0.726461i
$303$	−25.2768	−	18.3647i	−1.45212	−	1.05502i
$304$	1.53211	−	4.71534i	0.0878724	−	0.270443i
$305$	6.14047	+	18.8984i	0.351602	+	1.08212i
$306$	35.1959	−	25.5713i	2.01201	−	1.46181i
$307$	10.9581			0.625413			0.312706	−	0.949850i	$-0.398764\pi$
$307$	10.9581			0.625413			0.312706	+	0.949850i	$0.398764\pi$
$308$	5.10940	+	13.5694i	0.291135	+	0.773189i
$309$	48.8473			2.77883
$310$	5.28617	−	3.84063i	0.300235	−	0.218133i
$311$	−9.17298	−	28.2315i	−0.520152	−	1.60086i	−0.773708	−	0.633542i	$-0.781600\pi$
$311$	−9.17298	−	28.2315i	−0.520152	−	1.60086i	0.253556	−	0.967321i	$-0.418400\pi$
$312$	−0.946538	+	2.91314i	−0.0535872	+	0.164924i
$313$	9.74631	+	7.08111i	0.550894	+	0.400248i	0.828115	−	0.560558i	$-0.189413\pi$
$313$	9.74631	+	7.08111i	0.550894	+	0.400248i	−0.277221	+	0.960806i	$0.589413\pi$
$314$	−1.53831	−	1.11765i	−0.0868118	−	0.0630725i
$315$	−24.9447	+	76.7719i	−1.40547	+	4.32560i
$316$	−1.53852	−	4.73508i	−0.0865485	−	0.266369i
$317$	−11.5108	+	8.36309i	−0.646511	+	0.469718i	−0.862081	−	0.506771i	$-0.830839\pi$
$317$	−11.5108	+	8.36309i	−0.646511	+	0.469718i	0.215570	+	0.976488i	$0.430839\pi$
$318$	−2.13882			−0.119939
$319$	2.18055	−	1.74278i	0.122087	−	0.0975770i
$320$	−2.89308			−0.161728
$321$	2.89406	−	2.10266i	0.161531	−	0.117359i
$322$	1.09408	+	3.36723i	0.0609707	+	0.187649i
$323$	10.4434	−	32.1416i	0.581088	−	1.78841i
$324$	−10.1833	−	7.39861i	−0.565740	−	0.411034i
$325$	−2.72630	−	1.98077i	−0.151228	−	0.109873i
$326$	−1.23453	+	3.79948i	−0.0683741	+	0.210434i
$327$	4.96618	+	15.2843i	0.274630	+	0.845225i
$328$	−3.74565	+	2.72137i	−0.206819	+	0.150263i
$329$	−17.2622			−0.951695
$330$	7.78846	−	28.3401i	0.428741	−	1.56007i
$331$	−21.9012			−1.20380			−0.601899	−	0.798572i	$-0.705589\pi$
$331$	−21.9012			−1.20380			−0.601899	+	0.798572i	$0.705589\pi$
$332$	0.353069	−	0.256519i	0.0193772	−	0.0140783i
$333$	−18.5273	−	57.0211i	−1.01529	−	3.12474i
$334$	3.83884	−	11.8147i	0.210052	−	0.646474i
$335$	27.2255	+	19.7805i	1.48749	+	1.08072i
$336$	−10.8335	−	7.87100i	−0.591016	−	0.429399i
$337$	7.26831	−	22.3695i	0.395930	−	1.21855i	−0.532305	−	0.846553i	$-0.678674\pi$
$337$	7.26831	−	22.3695i	0.395930	−	1.21855i	0.928235	−	0.371994i	$-0.121326\pi$
$338$	−0.309017	−	0.951057i	−0.0168083	−	0.0517307i
$339$	3.02204	−	2.19564i	0.164135	−	0.119251i
$340$	−19.7203			−1.06948
$341$	−7.48276	+	0.344143i	−0.405214	+	0.0186364i
$342$	−31.6437			−1.71109
$343$	−18.0811	+	13.1367i	−0.976288	+	0.709315i
$344$	−1.57100	−	4.83504i	−0.0847026	−	0.260688i
$345$	2.21773	−	6.82547i	0.119399	−	0.367471i
$346$	6.24891	+	4.54010i	0.335944	+	0.244077i
$347$	17.8543	+	12.9719i	0.958470	+	0.696369i	0.952795	−	0.303614i	$-0.0981935\pi$
$347$	17.8543	+	12.9719i	0.958470	+	0.696369i	0.00567535	+	0.999984i	$0.498193\pi$
$348$	−0.796651	+	2.45184i	−0.0427050	+	0.131432i
$349$	−7.20212	−	22.1658i	−0.385520	−	1.18651i	−0.936102	−	0.351729i	$-0.885594\pi$
$349$	−7.20212	−	22.1658i	−0.385520	−	1.18651i	0.550582	−	0.834781i	$-0.314406\pi$
$350$	11.9187	−	8.65944i	0.637081	−	0.462867i
$351$	10.3603			0.552993
$352$	2.76994	+	1.82413i	0.147638	+	0.0972265i
$353$	15.1457			0.806126			0.403063	−	0.915172i	$-0.367946\pi$
$353$	15.1457			0.806126			0.403063	+	0.915172i	$0.367946\pi$
$354$	3.86888	−	2.81090i	0.205629	−	0.149398i
$355$	8.15287	+	25.0919i	0.432709	+	1.33174i
$356$	−1.28492	+	3.95457i	−0.0681006	+	0.209592i
$357$	−73.8453	−	53.6518i	−3.90831	−	2.83955i
$358$	9.56818	+	6.95169i	0.505694	+	0.367408i
$359$	−2.85258	+	8.77934i	−0.150553	+	0.463356i	−0.997683	−	0.0680301i	$-0.978329\pi$
$359$	−2.85258	+	8.77934i	−0.150553	+	0.463356i	0.847130	+	0.531386i	$0.178329\pi$
$360$	5.70588	+	17.5609i	0.300726	+	0.925540i
$361$	−4.51578	+	3.28090i	−0.237672	+	0.172679i
$362$	17.6659			0.928497
$363$	−25.3258	+	22.2231i	−1.32926	+	1.16641i
$364$	4.37176			0.229142
$365$	−15.2073	+	11.0488i	−0.795988	+	0.578319i
$366$	6.50126	+	20.0088i	0.339826	+	1.04588i
$367$	6.03315	−	18.5681i	0.314928	−	0.969248i	−0.660856	−	0.750513i	$-0.729807\pi$
$367$	6.03315	−	18.5681i	0.314928	−	0.969248i	0.975784	−	0.218736i	$-0.0701933\pi$
$368$	0.655192	+	0.476025i	0.0341543	+	0.0248145i
$369$	23.9060	+	17.3687i	1.24450	+	0.904180i
$370$	−8.39830	+	25.8473i	−0.436607	+	1.34374i
$371$	0.943315	+	2.90322i	0.0489745	+	0.150728i
$372$	5.59677	−	4.06629i	0.290179	−	0.210827i
$373$	−7.35092			−0.380616			−0.190308	−	0.981724i	$-0.560949\pi$
$373$	−7.35092			−0.380616			−0.190308	+	0.981724i	$0.560949\pi$
$374$	18.8809	+	12.4340i	0.976311	+	0.642945i
$375$	14.4455			0.745963
$376$	−3.19446	+	2.32091i	−0.164742	+	0.119692i
$377$	−0.260083	−	0.800454i	−0.0133950	−	0.0412255i
$378$	−13.9962	+	43.0760i	−0.719889	+	2.21559i
$379$	19.8323	+	14.4090i	1.01872	+	0.740142i	0.966020	−	0.258468i	$-0.0832177\pi$
$379$	19.8323	+	14.4090i	1.01872	+	0.740142i	0.0526987	+	0.998610i	$0.483218\pi$
$380$	11.6044	+	8.43112i	0.595295	+	0.432507i
$381$	5.23854	−	16.1226i	0.268379	−	0.825984i
$382$	4.87954	+	15.0177i	0.249659	+	0.768372i
$383$	−11.2833	+	8.19781i	−0.576551	+	0.418888i	−0.837479	−	0.546470i	$-0.815971\pi$
$383$	−11.2833	+	8.19781i	−0.576551	+	0.418888i	0.260928	+	0.965358i	$0.415971\pi$
$384$	−3.06306			−0.156311
$385$	−41.9038	+	1.92721i	−2.13561	+	0.0982199i
$386$	−20.2519			−1.03080
$387$	−26.2501	+	19.0718i	−1.33437	+	0.969476i
$388$	1.70393	+	5.24415i	0.0865038	+	0.266231i
$389$	−5.39998	+	16.6194i	−0.273790	+	0.842639i	0.715747	+	0.698360i	$0.246086\pi$
$389$	−5.39998	+	16.6194i	−0.273790	+	0.842639i	−0.989537	+	0.144279i	$0.953914\pi$
$390$	−7.16924	−	5.20876i	−0.363029	−	0.263756i
$391$	4.46604	+	3.24477i	0.225857	+	0.164095i
$392$	−3.74289	+	11.5194i	−0.189044	+	0.581819i
$393$	−8.51672	−	26.2118i	−0.429611	−	1.32221i
$394$	−6.08025	+	4.41756i	−0.306319	+	0.222554i
$395$	14.4039			0.724740
$396$	5.60940	−	20.4111i	0.281883	−	1.02570i
$397$	37.5524			1.88470			0.942351	−	0.334625i	$-0.108610\pi$
$397$	37.5524			1.88470			0.942351	+	0.334625i	$0.108610\pi$
$398$	−8.60406	+	6.25122i	−0.431283	+	0.313345i
$399$	20.5164	+	63.1429i	1.02710	+	3.16110i
$400$	1.04135	−	3.20495i	0.0520676	−	0.160248i
$401$	5.48228	+	3.98311i	0.273772	+	0.198907i	0.716196	−	0.697899i	$-0.245881\pi$
$401$	5.48228	+	3.98311i	0.273772	+	0.198907i	−0.442424	+	0.896806i	$0.645881\pi$
$402$	28.8252	+	20.9427i	1.43767	+	1.04453i
$403$	−0.697921	+	2.14798i	−0.0347659	+	0.106999i
$404$	3.15204	+	9.70098i	0.156820	+	0.482642i
$405$	29.4611	−	21.4047i	1.46393	−	1.06361i
$406$	3.67947			0.182609
$407$	24.3380	−	19.4519i	1.20639	−	0.964195i
$408$	−20.8790			−1.03366
$409$	10.2721	−	7.46313i	0.507924	−	0.369028i	−0.304112	−	0.952636i	$-0.598360\pi$
$409$	10.2721	−	7.46313i	0.507924	−	0.369028i	0.812035	+	0.583608i	$0.198360\pi$
$410$	−4.13915	−	12.7390i	−0.204418	−	0.629135i
$411$	−18.1082	+	55.7313i	−0.893211	+	2.74902i
$412$	−12.9016	−	9.37354i	−0.635615	−	0.461801i
$413$	−5.52186	−	4.01187i	−0.271713	−	0.197411i
$414$	1.59725	−	4.91584i	0.0785007	−	0.241600i
$415$	0.390161	+	1.20079i	0.0191522	+	0.0589445i
$416$	0.809017	−	0.587785i	0.0396653	−	0.0288185i
$417$	33.8444			1.65737
$418$	−5.79456	−	15.3891i	−0.283421	−	0.752703i
$419$	−25.4600			−1.24380			−0.621900	−	0.783097i	$-0.713639\pi$
$419$	−25.4600			−1.24380			−0.621900	+	0.783097i	$0.713639\pi$
$420$	31.3422	−	22.7714i	1.52934	−	1.11113i
$421$	−10.5706	−	32.5328i	−0.515178	−	1.58555i	−0.782959	−	0.622074i	$-0.786290\pi$
$421$	−10.5706	−	32.5328i	−0.515178	−	1.58555i	0.267781	−	0.963480i	$-0.413710\pi$
$422$	0.127905	−	0.393650i	0.00622630	−	0.0191626i
$423$	20.3881	+	14.8129i	0.991306	+	0.720226i
$424$	0.564906	+	0.410428i	0.0274342	+	0.0199321i
$425$	7.09826	−	21.8462i	0.344316	−	1.05970i
$426$	8.63190	+	26.5662i	0.418217	+	1.28714i
$427$	24.2925	−	17.6496i	1.17560	−	0.854122i
$428$	−1.16787			−0.0564512
$429$	3.57989	+	9.50737i	0.172839	+	0.459020i
$430$	14.7080			0.709282
$431$	8.39410	−	6.09867i	0.404330	−	0.293763i	−0.366973	−	0.930232i	$-0.619606\pi$
$431$	8.39410	−	6.09867i	0.404330	−	0.293763i	0.771302	+	0.636469i	$0.219606\pi$
$432$	3.20152	+	9.85325i	0.154033	+	0.474065i
$433$	6.05478	−	18.6347i	0.290974	−	0.895527i	−0.693570	−	0.720389i	$-0.743963\pi$
$433$	6.05478	−	18.6347i	0.290974	−	0.895527i	0.984544	−	0.175137i	$-0.0560369\pi$
$434$	−7.98799	−	5.80361i	−0.383436	−	0.278582i
$435$	−6.03397	−	4.38393i	−0.289307	−	0.210194i
$436$	1.62131	−	4.98989i	0.0776468	−	0.238972i
$437$	−1.24080	−	3.81878i	−0.0593553	−	0.182677i
$438$	−16.1009	+	11.6980i	−0.769329	+	0.558950i
$439$	0.706509			0.0337199			0.0168599	−	0.999858i	$-0.494633\pi$
$439$	0.706509			0.0337199			0.0168599	+	0.999858i	$0.494633\pi$
$440$	−7.49541	+	5.99063i	−0.357329	+	0.285592i
$441$	77.3045			3.68117
$442$	5.51457	−	4.00657i	0.262301	−	0.190573i
$443$	−7.87544	−	24.2381i	−0.374174	−	1.15159i	−0.944034	−	0.329847i	$-0.893003\pi$
$443$	−7.87544	−	24.2381i	−0.374174	−	1.15159i	0.569861	−	0.821741i	$-0.306997\pi$
$444$	−8.89175	+	27.3660i	−0.421984	+	1.29873i
$445$	−9.73219	−	7.07085i	−0.461350	−	0.335191i
$446$	−14.1845	−	10.3056i	−0.671655	−	0.487986i
$447$	22.0021	−	67.7155i	1.04066	−	3.20283i
$448$	1.35095	+	4.15779i	0.0638262	+	0.196437i
$449$	16.6390	−	12.0889i	0.785244	−	0.570513i	−0.121305	−	0.992615i	$-0.538708\pi$
$449$	16.6390	−	12.0889i	0.785244	−	0.570513i	0.906548	+	0.422103i	$0.138708\pi$
$450$	−21.5078			−1.01389
$451$	−4.06917	+	14.8066i	−0.191610	+	0.697215i
$452$	−1.21951			−0.0573611
$453$	−53.2244	+	38.6698i	−2.50070	+	1.81686i
$454$	4.55222	+	14.0103i	0.213646	+	0.657536i
$455$	−3.90839	+	12.0288i	−0.183228	+	0.563918i
$456$	12.2863	+	8.92650i	0.575358	+	0.418022i
$457$	21.9744	+	15.9653i	1.02792	+	0.746827i	0.967891	−	0.251369i	$-0.0808809\pi$
$457$	21.9744	+	15.9653i	1.02792	+	0.746827i	0.0600284	+	0.998197i	$0.480881\pi$
$458$	−1.92696	+	5.93057i	−0.0900409	+	0.277117i
$459$	21.8228	+	67.1635i	1.01860	+	3.13493i
$460$	−1.89552	+	1.37718i	−0.0883791	+	0.0642112i
$461$	13.3542			0.621967			0.310983	−	0.950415i	$-0.399342\pi$
$461$	13.3542			0.621967			0.310983	+	0.950415i	$0.399342\pi$
$462$	−44.3659	+	2.04045i	−2.06409	+	0.0949303i
$463$	19.8061			0.920469			0.460234	−	0.887797i	$-0.347765\pi$
$463$	19.8061			0.920469			0.460234	+	0.887797i	$0.347765\pi$
$464$	0.680907	−	0.494708i	0.0316103	−	0.0229662i
$465$	6.18475	+	19.0347i	0.286811	+	0.882713i
$466$	2.86012	−	8.80254i	0.132492	−	0.407770i
$467$	−30.9115	−	22.4585i	−1.43042	−	1.03926i	−0.989939	−	0.141494i	$-0.954810\pi$
$467$	−30.9115	−	22.4585i	−1.43042	−	1.03926i	−0.440476	−	0.897764i	$-0.645190\pi$
$468$	−5.16342	−	3.75145i	−0.238679	−	0.173411i
$469$	15.7144	−	48.3639i	0.725622	−	2.23324i
$470$	−3.53006	−	10.8644i	−0.162830	−	0.501138i
$471$	4.71194	−	3.42342i	0.217115	−	0.157743i
$472$	−1.56125			−0.0718623
$473$	−14.0820	−	9.27362i	−0.647490	−	0.426402i
$474$	15.2502			0.700466
$475$	−13.5170	+	9.82067i	−0.620202	+	0.450603i
$476$	9.20857	+	28.3411i	0.422074	+	1.29901i
$477$	1.37715	−	4.23843i	0.0630553	−	0.194064i
$478$	−10.9017	−	7.92058i	−0.498634	−	0.362279i
$479$	11.3900	+	8.27535i	0.520424	+	0.378111i	0.816764	−	0.576972i	$-0.195766\pi$
$479$	11.3900	+	8.27535i	0.520424	+	0.378111i	−0.296339	+	0.955083i	$0.595766\pi$
$480$	2.73841	−	8.42795i	0.124991	−	0.384681i
$481$	−2.90290	−	8.93420i	−0.132361	−	0.407365i
$482$	−15.0180	+	10.9112i	−0.684051	+	0.496992i
$483$	−10.8448			−0.493457
$484$	10.9536	−	1.00968i	0.497889	−	0.0458943i
$485$	−15.9525			−0.724365
$486$	6.04709	−	4.39347i	0.274302	−	0.199292i
$487$	−0.0775001	−	0.238521i	−0.00351187	−	0.0108084i	0.949285	−	0.314416i	$-0.101809\pi$
$487$	−0.0775001	−	0.238521i	−0.00351187	−	0.0108084i	−0.952797	+	0.303608i	$0.901809\pi$
$488$	2.12247	−	6.53229i	0.0960797	−	0.295703i
$489$	−9.89991	−	7.19270i	−0.447689	−	0.325265i
$490$	−28.3493	−	20.5970i	−1.28069	−	0.930476i
$491$	12.4875	−	38.4327i	0.563555	−	1.73444i	−0.108651	−	0.994080i	$-0.534653\pi$
$491$	12.4875	−	38.4327i	0.563555	−	1.73444i	0.672206	−	0.740364i	$-0.265347\pi$
$492$	−4.38235	−	13.4875i	−0.197572	−	0.608063i
$493$	4.64132	−	3.37212i	0.209035	−	0.151872i
$494$	−4.95800			−0.223071
$495$	51.1458	+	33.6818i	2.29883	+	1.51389i
$496$	−2.25852			−0.101411
$497$	32.2539	−	23.4338i	1.44678	−	1.05115i
$498$	0.413085	+	1.27134i	0.0185108	+	0.0569703i
$499$	−10.7505	+	33.0868i	−0.481260	+	1.48117i	0.356065	+	0.934461i	$0.384118\pi$
$499$	−10.7505	+	33.0868i	−0.481260	+	1.48117i	−0.837325	+	0.546706i	$0.815882\pi$
$500$	−3.81536	−	2.77202i	−0.170628	−	0.123968i
$501$	30.7845	+	22.3662i	1.37535	+	0.999249i
$502$	0.429789	−	1.32276i	0.0191824	−	0.0590375i
$503$	3.71128	+	11.4222i	0.165478	+	0.509289i	0.999071	−	0.0430899i	$-0.0137202\pi$
$503$	3.71128	+	11.4222i	0.165478	+	0.509289i	−0.833593	+	0.552379i	$0.813720\pi$
$504$	22.5732	−	16.4004i	1.00549	−	0.730532i
$505$	−29.5100			−1.31318
$506$	2.68317	−	0.123403i	0.119282	−	0.00548593i
$507$	3.06306			0.136035
$508$	−4.47744	+	3.25305i	−0.198654	+	0.144331i
$509$	12.4997	+	38.4702i	0.554040	+	1.70516i	0.698464	+	0.715645i	$0.253867\pi$
$509$	12.4997	+	38.4702i	0.554040	+	1.70516i	−0.144424	+	0.989516i	$0.546133\pi$
$510$	18.6660	−	57.4481i	0.826545	−	2.54385i
$511$	22.9800	+	16.6959i	1.01657	+	0.738584i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	15.8731	−	48.8525i	0.700816	−	2.15689i
$514$	−6.93217	−	21.3350i	−0.305765	−	0.941048i
$515$	37.3252	−	27.1184i	1.64475	−	1.19498i
$516$	15.5722			0.685527
$517$	−3.47037	+	12.6277i	−0.152627	+	0.555367i
$518$	41.0682			1.80443
$519$	−19.1408	+	13.9066i	−0.840188	+	0.610432i
$520$	0.894010	+	2.75148i	0.0392049	+	0.120660i
$521$	8.78102	−	27.0252i	0.384703	−	1.18400i	−0.551992	−	0.833850i	$-0.686132\pi$
$521$	8.78102	−	27.0252i	0.384703	−	1.18400i	0.936695	−	0.350146i	$-0.113868\pi$
$522$	−4.34578	−	3.15739i	−0.190210	−	0.138195i
$523$	−15.5092	−	11.2681i	−0.678169	−	0.492719i	0.194581	−	0.980887i	$-0.437665\pi$
$523$	−15.5092	−	11.2681i	−0.678169	−	0.492719i	−0.872750	+	0.488168i	$0.837665\pi$
$524$	−2.78046	+	8.55737i	−0.121465	+	0.373831i
$525$	13.9447	+	42.9174i	0.608597	+	1.87307i
$526$	−4.73020	+	3.43669i	−0.206246	+	0.149847i
$527$	−15.3949			−0.670614
$528$	−7.93580	+	6.34262i	−0.345362	+	0.276027i
$529$	−22.3441			−0.971484
$530$	−1.63432	+	1.18740i	−0.0709901	+	0.0515773i
$531$	3.07917	+	9.47672i	0.133625	+	0.411255i
$532$	6.69800	−	20.6143i	0.290395	−	0.893744i
$533$	3.74565	+	2.72137i	0.162242	+	0.117876i
$534$	−10.3040	−	7.48631i	−0.445898	−	0.323964i
$535$	1.04409	−	3.21337i	0.0451399	−	0.138926i
$536$	−3.59452	−	11.0628i	−0.155260	−	0.477840i
$537$	−29.3079	+	21.2935i	−1.26473	+	0.918880i
$538$	−10.6637			−0.459745
$539$	14.1559	+	37.5950i	0.609739	+	1.61933i
$540$	−29.9732			−1.28984
$541$	−26.4942	+	19.2492i	−1.13908	+	0.827587i	−0.986990	−	0.160780i	$-0.948599\pi$
$541$	−26.4942	+	19.2492i	−1.13908	+	0.827587i	−0.152086	+	0.988367i	$0.548599\pi$
$542$	0.307829	+	0.947400i	0.0132224	+	0.0406943i
$543$	−16.7214	+	51.4632i	−0.717584	+	2.20850i
$544$	5.51457	+	4.00657i	0.236435	+	0.171780i
$545$	12.2801	+	8.92201i	0.526022	+	0.382177i
$546$	−4.13803	+	12.7356i	−0.177091	+	0.545031i
$547$	−10.4839	−	32.2663i	−0.448261	−	1.37961i	−0.878868	−	0.477066i	$-0.841700\pi$
$547$	−10.4839	−	32.2663i	−0.448261	−	1.37961i	0.430606	−	0.902540i	$-0.358300\pi$
$548$	15.4773	−	11.2449i	0.661156	−	0.480358i
$549$	−43.8369			−1.87091
$550$	−3.93848	−	10.4597i	−0.167938	−	0.446004i
$551$	−4.17289			−0.177771
$552$	−2.00689	+	1.45809i	−0.0854191	+	0.0620606i
$553$	−6.72603	−	20.7006i	−0.286020	−	0.880279i
$554$	−4.54103	+	13.9759i	−0.192930	+	0.593777i
$555$	−67.3477	−	48.9309i	−2.85875	−	2.07700i
$556$	−8.93899	−	6.49456i	−0.379098	−	0.275431i
$557$	−1.19336	+	3.67279i	−0.0505644	+	0.155621i	−0.973150	−	0.230170i	$-0.926072\pi$
$557$	−1.19336	+	3.67279i	−0.0505644	+	0.155621i	0.922586	+	0.385792i	$0.126072\pi$
$558$	4.45437	+	13.7091i	0.188569	+	0.580355i
$559$	−4.11293	+	2.98822i	−0.173958	+	0.126388i
$560$	−12.6478			−0.534468
$561$	−54.0935	+	43.2337i	−2.28383	+	1.82533i
$562$	2.68542			0.113278
$563$	14.8778	−	10.8093i	0.627023	−	0.455559i	−0.228345	−	0.973580i	$-0.573331\pi$
$563$	14.8778	−	10.8093i	0.627023	−	0.455559i	0.855367	+	0.518022i	$0.173331\pi$
$564$	−3.73747	−	11.5028i	−0.157376	−	0.484353i
$565$	1.09026	−	3.35547i	0.0458674	−	0.141165i
$566$	−4.69898	−	3.41401i	−0.197513	−	0.143502i
$567$	−44.5190	−	32.3449i	−1.86962	−	1.35836i
$568$	2.81806	−	8.67310i	0.118243	−	0.363915i
$569$	4.79538	+	14.7587i	0.201033	+	0.618716i	0.999853	+	0.0171458i	$0.00545795\pi$
$569$	4.79538	+	14.7587i	0.201033	+	0.618716i	−0.798820	+	0.601570i	$0.794542\pi$
$570$	−35.5451	+	25.8250i	−1.48882	+	1.08169i
$571$	4.17089			0.174546			0.0872732	−	0.996184i	$-0.472185\pi$
$571$	4.17089			0.174546			0.0872732	+	0.996184i	$0.472185\pi$
$572$	0.878894	−	3.19805i	0.0367484	−	0.133717i
$573$	−48.3674			−2.02058
$574$	−16.3751	+	11.8972i	−0.683482	+	0.496579i
$575$	−0.843352	−	2.59557i	−0.0351702	−	0.108243i
$576$	1.97225	−	6.06997i	0.0821772	−	0.252915i
$577$	31.9019	+	23.1781i	1.32809	+	0.964915i	0.999793	+	0.0203409i	$0.00647516\pi$
$577$	31.9019	+	23.1781i	1.32809	+	0.964915i	0.328298	+	0.944574i	$0.393525\pi$
$578$	23.8361	+	17.3180i	0.991452	+	0.720332i
$579$	19.1692	−	58.9968i	0.796645	−	2.45182i
$580$	0.752440	+	2.31577i	0.0312434	+	0.0961573i
$581$	1.54353	−	1.12144i	0.0640364	−	0.0465252i
$582$	−16.8898			−0.700104
$583$	2.31343	−	0.106398i	0.0958124	−	0.00440655i
$584$	6.49734			0.268862
$585$	14.9382	−	10.8532i	0.617618	−	0.448725i
$586$	7.17443	+	22.0806i	0.296373	+	0.912142i
$587$	9.38097	−	28.8716i	0.387194	−	1.19166i	−0.547682	−	0.836686i	$-0.684490\pi$
$587$	9.38097	−	28.8716i	0.387194	−	1.19166i	0.934876	−	0.354974i	$-0.115510\pi$
$588$	−30.0150	−	21.8072i	−1.23780	−	0.899312i
$589$	9.05917	+	6.58187i	0.373277	+	0.271201i
$590$	1.39577	−	4.29574i	0.0574630	−	0.176853i
$591$	−7.11381	−	21.8941i	−0.292623	−	0.900601i
$592$	7.59989	−	5.52164i	0.312353	−	0.226938i
$593$	41.8773			1.71970			0.859848	−	0.510551i	$-0.170558\pi$
$593$	41.8773			1.71970			0.859848	+	0.510551i	$0.170558\pi$
$594$	28.6974	+	18.8986i	1.17747	+	0.775418i
$595$	−86.2124			−3.53436
$596$	−18.8055	+	13.6630i	−0.770301	+	0.559657i
$597$	−10.0666	−	30.9819i	−0.412000	−	1.26800i
$598$	0.250261	−	0.770225i	0.0102339	−	0.0314968i
$599$	−12.2466	−	8.89766i	−0.500381	−	0.363548i	0.308781	−	0.951133i	$-0.400079\pi$
$599$	−12.2466	−	8.89766i	−0.500381	−	0.363548i	−0.809163	+	0.587585i	$0.800079\pi$
$600$	8.35081	+	6.06722i	0.340920	+	0.247693i
$601$	5.91857	−	18.2155i	0.241423	−	0.743025i	−0.754781	−	0.655977i	$-0.772257\pi$
$601$	5.91857	−	18.2155i	0.241423	−	0.743025i	0.996204	−	0.0870477i	$-0.0277432\pi$
$602$	−6.86802	−	21.1376i	−0.279920	−	0.861504i
$603$	−60.0616	+	43.6373i	−2.44590	+	1.77705i
$604$	21.4782			0.873935
$605$	−7.01449	+	31.0412i	−0.285180	+	1.26200i
$606$	−31.2439			−1.26920
$607$	22.5893	−	16.4121i	0.916873	−	0.666147i	−0.0258705	−	0.999665i	$-0.508236\pi$
$607$	22.5893	−	16.4121i	0.916873	−	0.666147i	0.942744	+	0.333518i	$0.108236\pi$
$608$	−1.53211	−	4.71534i	−0.0621352	−	0.191232i
$609$	−3.48276	+	10.7188i	−0.141129	+	0.434349i
$610$	16.0760	+	11.6799i	0.650896	+	0.472904i
$611$	3.19446	+	2.32091i	0.129234	+	0.0938940i
$612$	13.4436	−	41.3752i	0.543426	−	1.67249i
$613$	−7.54660	−	23.2261i	−0.304804	−	0.938092i	−0.979750	−	0.200224i	$-0.935833\pi$
$613$	−7.54660	−	23.2261i	−0.304804	−	0.938092i	0.674946	−	0.737867i	$-0.264167\pi$
$614$	8.86530	−	6.44102i	0.357774	−	0.259938i
$615$	41.0284			1.65443
$616$	12.1095	+	7.97465i	0.487905	+	0.321308i
$617$	−14.2826			−0.574996			−0.287498	−	0.957781i	$-0.592824\pi$
$617$	−14.2826			−0.574996			−0.287498	+	0.957781i	$0.592824\pi$
$618$	39.5183	−	28.7117i	1.58966	−	1.15495i
$619$	1.02122	+	3.14300i	0.0410465	+	0.126328i	0.969480	−	0.245171i	$-0.0788440\pi$
$619$	1.02122	+	3.14300i	0.0410465	+	0.126328i	−0.928433	+	0.371499i	$0.878844\pi$
$620$	2.01914	−	6.21427i	0.0810906	−	0.249571i
$621$	6.78800	+	4.93177i	0.272393	+	0.197905i
$622$	−24.0152	−	17.4480i	−0.962921	−	0.699603i
$623$	−5.61735	+	17.2884i	−0.225054	+	0.692646i
$624$	0.946538	+	2.91314i	0.0378918	+	0.116619i
$625$	24.6696	−	17.9235i	0.986784	−	0.716940i
$626$	12.0471			0.481499
$627$	50.3153	−	2.31407i	2.00940	−	0.0924151i
$628$	−1.90145			−0.0758763
$629$	51.8037	−	37.6376i	2.06555	−	1.50071i
$630$	24.9447	+	76.7719i	0.993820	+	3.05866i
$631$	−11.7857	+	36.2726i	−0.469180	+	1.44399i	0.384468	+	0.923138i	$0.374385\pi$
$631$	−11.7857	+	36.2726i	−0.469180	+	1.44399i	−0.853648	+	0.520850i	$0.825615\pi$
$632$	−4.02790	−	2.92644i	−0.160221	−	0.116407i
$633$	1.02569	+	0.745210i	0.0407676	+	0.0296194i
$634$	−4.39674	+	13.5318i	−0.174617	+	0.537415i
$635$	−4.94783	−	15.2278i	−0.196348	−	0.604298i
$636$	−1.73034	+	1.25717i	−0.0686125	+	0.0498499i
$637$	12.1122			0.479905
$638$	0.739718	−	2.69163i	0.0292857	−	0.106563i
$639$	−58.2034			−2.30249
$640$	−2.34055	+	1.70051i	−0.0925183	+	0.0672185i
$641$	3.39976	+	10.4634i	0.134282	+	0.413279i	0.995478	−	0.0949954i	$-0.0302836\pi$
$641$	3.39976	+	10.4634i	0.134282	+	0.413279i	−0.861195	+	0.508274i	$0.830284\pi$
$642$	1.10543	−	3.40218i	0.0436280	−	0.134273i
$643$	18.8105	+	13.6666i	0.741814	+	0.538960i	0.893279	−	0.449503i	$-0.148399\pi$
$643$	18.8105	+	13.6666i	0.741814	+	0.538960i	−0.151465	+	0.988463i	$0.548399\pi$
$644$	2.86434	+	2.08106i	0.112871	+	0.0820054i
$645$	−13.9217	+	42.8465i	−0.548165	+	1.68708i
$646$	−10.4434	−	32.1416i	−0.410891	−	1.26459i
$647$	5.77011	−	4.19223i	0.226846	−	0.164813i	−0.468557	−	0.883433i	$-0.655226\pi$
$647$	5.77011	−	4.19223i	0.226846	−	0.164813i	0.695403	+	0.718620i	$0.255226\pi$
$648$	−12.5873			−0.494475
$649$	−4.04489	+	3.23284i	−0.158776	+	0.126900i
$650$	−3.36989			−0.132178
$651$	24.4677	−	17.7768i	0.958965	−	0.696729i
$652$	1.23453	+	3.79948i	0.0483478	+	0.148799i
$653$	−9.23375	+	28.4186i	−0.361345	+	1.11210i	0.590894	+	0.806749i	$0.298775\pi$
$653$	−9.23375	+	28.4186i	−0.361345	+	1.11210i	−0.952238	+	0.305355i	$0.901225\pi$
$654$	13.0016	+	9.44623i	0.508404	+	0.369377i
$655$	−21.0597	−	15.3007i	−0.822869	−	0.597850i
$656$	−1.43071	+	4.40327i	−0.0558599	+	0.171919i
$657$	−12.8144	−	39.4387i	−0.499937	−	1.53865i
$658$	−13.9654	+	10.1465i	−0.544428	+	0.395550i
$659$	8.68335			0.338255			0.169128	−	0.985594i	$-0.445905\pi$
$659$	8.68335			0.338255			0.169128	+	0.985594i	$0.445905\pi$
$660$	−10.3569	−	27.5056i	−0.403141	−	1.07065i
$661$	−18.6996			−0.727329			−0.363664	−	0.931530i	$-0.618475\pi$
$661$	−18.6996			−0.727329			−0.363664	+	0.931530i	$0.618475\pi$
$662$	−17.7184	+	12.8732i	−0.688646	+	0.500331i
$663$	6.45197	+	19.8571i	0.250574	+	0.771186i
$664$	0.134860	−	0.415057i	0.00523359	−	0.0161073i
$665$	50.7318	+	36.8588i	1.96729	+	1.42932i
$666$	−48.5051	−	35.2410i	−1.87953	−	1.36556i
$667$	0.210631	−	0.648257i	0.00815568	−	0.0251006i
$668$	−3.83884	−	11.8147i	−0.148529	−	0.457126i
$669$	43.4479	−	31.5668i	1.67979	−	1.22044i
$670$	33.6526			1.30011
$671$	−8.02736	−	21.3189i	−0.309893	−	0.823006i
$672$	−13.3910			−0.516567
$673$	14.8425	−	10.7837i	0.572136	−	0.415681i	−0.263745	−	0.964593i	$-0.584958\pi$
$673$	14.8425	−	10.7837i	0.572136	−	0.415681i	0.835880	+	0.548912i	$0.184958\pi$
$674$	−7.26831	−	22.3695i	−0.279965	−	0.861643i
$675$	10.7887	−	33.2044i	0.415259	−	1.27804i
$676$	−0.809017	−	0.587785i	−0.0311160	−	0.0226071i
$677$	−9.30341	−	6.75932i	−0.357559	−	0.259782i	0.394474	−	0.918907i	$-0.370927\pi$
$677$	−9.30341	−	6.75932i	−0.357559	−	0.259782i	−0.752033	+	0.659125i	$0.770927\pi$
$678$	1.15432	−	3.55262i	0.0443312	−	0.136437i
$679$	7.44915	+	22.9261i	0.285872	+	0.879824i
$680$	−15.9541	+	11.5913i	−0.611811	+	0.444506i
$681$	−45.1229			−1.72911
$682$	−5.85139	+	4.67667i	−0.224061	+	0.179079i
$683$	13.6358			0.521760			0.260880	−	0.965371i	$-0.415987\pi$
$683$	13.6358			0.521760			0.260880	+	0.965371i	$0.415987\pi$
$684$	−25.6003	+	18.5997i	−0.978851	+	0.711177i
$685$	17.1033	+	52.6384i	0.653482	+	2.01121i
$686$	−6.90637	+	21.2556i	−0.263686	+	0.811543i
$687$	−15.4527	−	11.2270i	−0.589556	−	0.428337i
$688$	−4.11293	−	2.98822i	−0.156804	−	0.113925i
$689$	0.215775	−	0.664087i	0.00822036	−	0.0252997i
$690$	−2.21773	−	6.82547i	−0.0844276	−	0.259841i
$691$	−11.1744	+	8.11868i	−0.425095	+	0.308849i	−0.779684	−	0.626173i	$-0.784621\pi$
$691$	−11.1744	+	8.11868i	−0.425095	+	0.308849i	0.354590	+	0.935022i	$0.384621\pi$
$692$	7.72408			0.293625
$693$	24.5229	−	89.2322i	0.931549	−	3.38965i
$694$	22.0692			0.837734
$695$	25.8612	−	18.7892i	0.980970	−	0.712717i
$696$	0.796651	+	2.45184i	0.0301970	+	0.0929367i
$697$	−9.75227	+	30.0144i	−0.369394	+	1.13688i
$698$	−18.8554	−	13.6992i	−0.713687	−	0.518524i
$699$	22.9359	+	16.6639i	0.867514	+	0.630286i
$700$	4.55254	−	14.0113i	0.172070	−	0.529576i
$701$	12.1608	+	37.4270i	0.459306	+	1.41360i	0.866004	+	0.500036i	$0.166680\pi$
$701$	12.1608	+	37.4270i	0.459306	+	1.41360i	−0.406698	+	0.913563i	$0.633320\pi$
$702$	8.38168	−	6.08964i	0.316346	−	0.229839i
$703$	−46.5754			−1.75662
$704$	3.31312	−	0.152375i	0.124868	−	0.00574286i
$705$	34.9909			1.31783
$706$	12.2532	−	8.90244i	0.461154	−	0.335048i
$707$	13.7799	+	42.4103i	0.518248	+	1.59500i
$708$	1.47778	−	4.54814i	0.0555384	−	0.170930i
$709$	21.5770	+	15.6766i	0.810341	+	0.588747i	0.913929	−	0.405873i	$-0.133033\pi$
$709$	21.5770	+	15.6766i	0.810341	+	0.588747i	−0.103589	+	0.994620i	$0.533033\pi$
$710$	21.3445	+	15.5077i	0.801044	+	0.581993i
$711$	−9.81936	+	30.2209i	−0.368255	+	1.13337i
$712$	1.28492	+	3.95457i	0.0481544	+	0.148204i
$713$	−1.47976	+	1.07511i	−0.0554176	+	0.0402633i
$714$	−91.2779			−3.41599
$715$	8.01364	+	5.27735i	0.299693	+	0.197362i
$716$	11.8269			0.441993
$717$	33.3927	−	24.2612i	1.24707	−	0.906052i
$718$	2.85258	+	8.77934i	0.106457	+	0.327642i
$719$	−0.00999067	+	0.0307481i	−0.000372589	+	0.00114671i	−0.951243	−	0.308444i	$-0.900192\pi$
$719$	−0.00999067	+	0.0307481i	−0.000372589	+	0.00114671i	0.950870	+	0.309590i	$0.100192\pi$
$720$	14.9382	+	10.8532i	0.556713	+	0.404476i
$721$	−56.4025	−	40.9788i	−2.10054	−	1.52613i
$722$	−1.72487	+	5.30861i	−0.0641931	+	0.197566i
$723$	−17.5708	−	54.0775i	−0.653466	−	2.01116i
$724$	14.2920	−	10.3837i	0.531157	−	0.385908i
$725$	−2.83626			−0.105336
$726$	−7.42663	+	32.8650i	−0.275628	+	1.21973i
$727$	−39.6625			−1.47100			−0.735501	−	0.677524i	$-0.763053\pi$
$727$	−39.6625			−1.47100			−0.735501	+	0.677524i	$0.763053\pi$
$728$	3.53682	−	2.56965i	0.131083	−	0.0952377i
$729$	−4.59404	−	14.1390i	−0.170150	−	0.523666i
$730$	−5.80869	+	17.8773i	−0.214989	+	0.661668i
$731$	−28.0353	−	20.3688i	−1.03692	−	0.753369i
$732$	17.0205	+	12.3661i	0.629096	+	0.457065i
$733$	8.70865	−	26.8025i	0.321661	−	0.989972i	−0.651264	−	0.758851i	$-0.725761\pi$
$733$	8.70865	−	26.8025i	0.321661	−	0.989972i	0.972925	−	0.231120i	$-0.0742392\pi$
$734$	−6.03315	−	18.5681i	−0.222688	−	0.685362i
$735$	86.8356	−	63.0897i	3.20298	−	2.32710i
$736$	0.809862			0.0298519
$737$	−32.2202	−	21.2185i	−1.18685	−	0.781594i
$738$	29.5495			1.08773
$739$	−31.9017	+	23.1780i	−1.17352	+	0.852615i	−0.991427	−	0.130666i	$-0.958289\pi$
$739$	−31.9017	+	23.1780i	−1.17352	+	0.852615i	−0.182097	+	0.983281i	$0.558289\pi$
$740$	8.39830	+	25.8473i	0.308728	+	0.950166i
$741$	4.69294	−	14.4434i	0.172399	−	0.530591i
$742$	2.46963	+	1.79429i	0.0906630	+	0.0658705i
$743$	8.30204	+	6.03179i	0.304572	+	0.221285i	0.729564	−	0.683912i	$-0.239723\pi$
$743$	8.30204	+	6.03179i	0.304572	+	0.221285i	−0.424992	+	0.905197i	$0.639723\pi$
$744$	2.13778	−	6.57940i	0.0783746	−	0.241212i
$745$	−20.7811	−	63.9576i	−0.761360	−	2.34323i
$746$	−5.94702	+	4.32076i	−0.217736	+	0.158194i
$747$	−2.78536			−0.101911
$748$	22.5835	−	1.03865i	0.825735	−	0.0379767i
$749$	−5.10565			−0.186556
$750$	11.6867	−	8.49086i	0.426737	−	0.310042i
$751$	−3.99165	−	12.2850i	−0.145657	−	0.448287i	0.851438	−	0.524456i	$-0.175731\pi$
$751$	−3.99165	−	12.2850i	−0.145657	−	0.448287i	−0.997095	+	0.0761687i	$0.975731\pi$
$752$	−1.22018	+	3.75531i	−0.0444952	+	0.136942i
$753$	3.44657	+	2.50408i	0.125600	+	0.0912536i
$754$	−0.680907	−	0.494708i	−0.0247972	−	0.0180162i
$755$	−19.2017	+	59.0967i	−0.698821	+	2.15075i
$756$	13.9962	+	43.0760i	0.509038	+	1.56666i
$757$	−23.9637	+	17.4106i	−0.870975	+	0.632800i	−0.930848	−	0.365406i	$-0.880930\pi$
$757$	−23.9637	+	17.4106i	−0.870975	+	0.632800i	0.0598737	+	0.998206i	$0.480930\pi$
$758$	24.5141			0.890393
$759$	−2.18023	+	7.93327i	−0.0791375	+	0.287960i
$760$	14.3439			0.520307
$761$	−36.0164	+	26.1674i	−1.30559	+	0.948569i	−0.999994	−	0.00359144i	$-0.998857\pi$
$761$	−36.0164	+	26.1674i	−1.30559	+	0.948569i	−0.305599	+	0.952160i	$0.598857\pi$
$762$	−5.23854	−	16.1226i	−0.189772	−	0.584059i
$763$	7.08798	−	21.8146i	0.256602	−	0.789740i
$764$	12.7748	+	9.28144i	0.462176	+	0.335791i
$765$	101.824	+	73.9797i	3.68147	+	2.67474i
$766$	−4.30984	+	13.2643i	−0.155721	+	0.479260i
$767$	0.482452	+	1.48483i	0.0174203	+	0.0536143i
$768$	−2.47807	+	1.80042i	−0.0894196	+	0.0649671i
$769$	−31.2123			−1.12555			−0.562773	−	0.826611i	$-0.690266\pi$
$769$	−31.2123			−1.12555			−0.562773	+	0.826611i	$0.690266\pi$
$770$	−32.7681	+	26.1896i	−1.18088	+	0.943807i
$771$	68.7136			2.47466
$772$	−16.3841	+	11.9038i	−0.589678	+	0.428426i
$773$	10.3750	+	31.9311i	0.373164	+	1.14848i	0.944709	+	0.327911i	$0.106345\pi$
$773$	10.3750	+	31.9311i	0.373164	+	1.14848i	−0.571544	+	0.820571i	$0.693655\pi$
$774$	−10.0267	+	30.8589i	−0.360401	+	1.10920i
$775$	6.15740	+	4.47361i	0.221180	+	0.160697i
$776$	4.46094	+	3.24106i	0.160138	+	0.116347i
$777$	−38.8726	+	119.637i	−1.39455	+	4.29197i
$778$	5.39998	+	16.6194i	0.193599	+	0.595836i
$779$	18.5709	−	13.4926i	0.665373	−	0.483422i
$780$	−8.86167			−0.317299
$781$	−10.6582	−	28.3057i	−0.381379	−	1.01286i
$782$	5.52033			0.197407
$783$	7.05441	−	5.12533i	0.252104	−	0.183164i
$784$	3.74289	+	11.5194i	0.133675	+	0.411408i
$785$	1.69992	−	5.23181i	0.0606727	−	0.186731i
$786$	−22.2971	−	16.1998i	−0.795309	−	0.577826i
$787$	−15.7527	−	11.4450i	−0.561525	−	0.407971i	0.270492	−	0.962722i	$-0.412814\pi$
$787$	−15.7527	−	11.4450i	−0.561525	−	0.407971i	−0.832017	+	0.554751i	$0.812814\pi$
$788$	−2.32245	+	7.14777i	−0.0827339	+	0.254629i
$789$	−5.53426	−	17.0327i	−0.197025	−	0.606381i
$790$	11.6530	−	8.46641i	0.414596	−	0.301221i
$791$	−5.33141			−0.189563
$792$	−7.45923	−	19.8100i	−0.265052	−	0.703919i
$793$	−6.86846			−0.243906
$794$	30.3806	−	22.0728i	1.07817	−	0.783333i
$795$	−1.91212	−	5.88491i	−0.0678161	−	0.208716i
$796$	−3.28646	+	10.1147i	−0.116485	+	0.358505i
$797$	−4.62420	−	3.35968i	−0.163798	−	0.119006i	0.502867	−	0.864364i	$-0.332279\pi$
$797$	−4.62420	−	3.35968i	−0.163798	−	0.119006i	−0.666664	+	0.745358i	$0.732279\pi$
$798$	53.7126	+	39.0245i	1.90140	+	1.38145i
$799$	−8.31718	+	25.5977i	−0.294241	+	0.905580i
$800$	−1.04135	−	3.20495i	−0.0368174	−	0.113312i
$801$	21.4700	−	15.5988i	0.758603	−	0.551158i
$802$	6.77647			0.239286
$803$	16.8334	−	13.4539i	0.594037	−	0.474778i
$804$	35.6299			1.25657
$805$	−8.28675	+	6.02068i	−0.292070	+	0.212201i
$806$	0.697921	+	2.14798i	0.0245832	+	0.0756594i
$807$	10.0936	−	31.0649i	0.355311	−	1.09354i
$808$	8.25215	+	5.99554i	0.290310	+	0.210922i
$809$	1.51210	+	1.09860i	0.0531626	+	0.0386249i	0.614049	−	0.789268i	$-0.289540\pi$
$809$	1.51210	+	1.09860i	0.0531626	+	0.0386249i	−0.560887	+	0.827893i	$0.689540\pi$
$810$	11.2531	−	34.6336i	0.395395	−	1.21690i
$811$	13.1332	+	40.4199i	0.461170	+	1.41933i	0.863736	+	0.503944i	$0.168118\pi$
$811$	13.1332	+	40.4199i	0.461170	+	1.41933i	−0.402567	+	0.915391i	$0.631882\pi$
$812$	2.97676	−	2.16274i	0.104464	−	0.0758973i
$813$	−3.05128			−0.107013
$814$	8.25631	−	30.0424i	0.289383	−	1.05299i
$815$	−11.5579			−0.404854
$816$	−16.8915	+	12.2724i	−0.591320	+	0.429619i
$817$	7.78902	+	23.9721i	0.272503	+	0.838679i
$818$	3.92360	−	12.0756i	0.137185	−	0.422213i
$819$	−22.5732	−	16.4004i	−0.788772	−	0.573077i
$820$	−10.8364	−	7.87314i	−0.378425	−	0.274942i
$821$	9.84539	−	30.3010i	0.343606	−	1.05751i	−0.618719	−	0.785612i	$-0.712348\pi$
$821$	9.84539	−	30.3010i	0.343606	−	1.05751i	0.962326	−	0.271900i	$-0.0876518\pi$
$822$	18.1082	+	55.7313i	0.631595	+	1.94385i
$823$	−8.11671	+	5.89714i	−0.282931	+	0.205561i	−0.720195	−	0.693772i	$-0.755948\pi$
$823$	−8.11671	+	5.89714i	−0.282931	+	0.205561i	0.437264	+	0.899333i	$0.355948\pi$
$824$	−15.9472			−0.555548
$825$	34.1986	−	1.57284i	1.19064	−	0.0547594i
$826$	−6.82539			−0.237486
$827$	−26.8916	+	19.5379i	−0.935112	+	0.679398i	−0.947239	−	0.320528i	$-0.896140\pi$
$827$	−26.8916	+	19.5379i	−0.935112	+	0.679398i	0.0121272	+	0.999926i	$0.496140\pi$
$828$	−1.59725	−	4.91584i	−0.0555084	−	0.170837i
$829$	−9.16835	+	28.2173i	−0.318430	+	0.980027i	0.655889	+	0.754857i	$0.272294\pi$
$829$	−9.16835	+	28.2173i	−0.318430	+	0.980027i	−0.974320	+	0.225170i	$0.927706\pi$
$830$	1.02145	+	0.742130i	0.0354552	+	0.0257597i
$831$	−36.4154	−	26.4574i	−1.26324	−	0.917795i
$832$	0.309017	−	0.951057i	0.0107132	−	0.0329720i
$833$	25.5130	+	78.5208i	0.883972	+	2.72059i
$834$	27.3807	−	19.8932i	0.948115	−	0.688846i
$835$	35.9400			1.24375
$836$	−13.7334	−	9.04405i	−0.474978	−	0.312795i
$837$	−23.3990			−0.808788
$838$	−20.5975	+	14.9650i	−0.711530	+	0.516957i
$839$	−8.58855	−	26.4328i	−0.296510	−	0.912563i	−0.982710	−	0.185151i	$-0.940723\pi$
$839$	−8.58855	−	26.4328i	−0.296510	−	0.912563i	0.686200	−	0.727413i	$-0.259277\pi$
$840$	11.9716	−	36.8449i	0.413061	−	1.27127i
$841$	22.8884	+	16.6294i	0.789256	+	0.573428i
$842$	−27.6741	−	20.1064i	−0.953712	−	0.692912i
$843$	−2.54185	+	7.82301i	−0.0875460	+	0.269439i
$844$	−0.127905	−	0.393650i	−0.00440266	−	0.0135500i
$845$	2.34055	−	1.70051i	0.0805173	−	0.0584992i
$846$	25.2011			0.866433
$847$	47.8863	−	4.41405i	1.64539	−	0.151669i
$848$	0.698262			0.0239784
$849$	14.3933	−	10.4573i	0.493976	−	0.358894i
$850$	−7.09826	−	21.8462i	−0.243468	−	0.749318i
$851$	2.35095	−	7.23547i	0.0805894	−	0.248029i
$852$	22.5986	+	16.4188i	0.774215	+	0.562500i
$853$	−14.2977	−	10.3879i	−0.489545	−	0.355675i	0.315464	−	0.948937i	$-0.397840\pi$
$853$	−14.2977	−	10.3879i	−0.489545	−	0.355675i	−0.805009	+	0.593262i	$0.797840\pi$
$854$	9.27892	−	28.5576i	0.317518	−	0.977220i
$855$	−28.2898	−	87.0669i	−0.967489	−	2.97763i
$856$	−0.944828	+	0.686457i	−0.0322935	+	0.0234626i
$857$	−11.1775			−0.381815			−0.190908	−	0.981608i	$-0.561143\pi$
$857$	−11.1775			−0.381815			−0.190908	+	0.981608i	$0.561143\pi$
$858$	8.48448	+	5.58742i	0.289656	+	0.190751i
$859$	−11.9590			−0.408035			−0.204018	−	0.978967i	$-0.565400\pi$
$859$	−11.9590			−0.408035			−0.204018	+	0.978967i	$0.565400\pi$
$860$	11.8990	−	8.64514i	0.405753	−	0.294797i
$861$	−19.1586	−	58.9640i	−0.652923	−	2.00949i
$862$	3.20626	−	9.86786i	0.109206	−	0.336101i
$863$	−0.493893	−	0.358834i	−0.0168123	−	0.0122149i	0.579347	−	0.815081i	$-0.303307\pi$
$863$	−0.493893	−	0.358834i	−0.0168123	−	0.0122149i	−0.596160	+	0.802866i	$0.703307\pi$
$864$	8.38168	+	6.08964i	0.285150	+	0.207174i
$865$	−6.90540	+	21.2526i	−0.234791	+	0.722611i
$866$	−6.05478	−	18.6347i	−0.205750	−	0.633233i
$867$	−73.0115	+	53.0460i	−2.47960	+	1.80154i
$868$	−9.87370			−0.335135
$869$	−16.4952	+	0.758639i	−0.559562	+	0.0257351i
$870$	−7.45839			−0.252863
$871$	−9.41058	+	6.83719i	−0.318865	+	0.231669i
$872$	−1.62131	−	4.98989i	−0.0549046	−	0.168979i
$873$	10.8750	−	33.4699i	0.368064	−	1.13279i
$874$	−3.24845	−	2.36013i	−0.109880	−	0.0798327i
$875$	−16.6798	−	12.1186i	−0.563880	−	0.409683i
$876$	−6.14998	+	18.9277i	−0.207789	+	0.639507i
$877$	0.520743	+	1.60268i	0.0175842	+	0.0541188i	0.959464	−	0.281833i	$-0.0909423\pi$
$877$	0.520743	+	1.60268i	0.0175842	+	0.0541188i	−0.941879	+	0.335951i	$0.890942\pi$
$878$	0.571578	−	0.415276i	0.0192898	−	0.0140149i
$879$	−71.1149			−2.39865
$880$	−2.54271	+	9.25221i	−0.0857146	+	0.311892i
$881$	−38.2107			−1.28735			−0.643675	−	0.765299i	$-0.722591\pi$
$881$	−38.2107			−1.28735			−0.643675	+	0.765299i	$0.722591\pi$
$882$	62.5406	−	45.4384i	2.10585	−	1.52999i
$883$	−9.39978	−	28.9296i	−0.316328	−	0.973557i	−0.975204	−	0.221306i	$-0.928968\pi$
$883$	−9.39978	−	28.9296i	−0.316328	−	0.973557i	0.658877	−	0.752251i	$-0.271032\pi$
$884$	2.10638	−	6.48277i	0.0708452	−	0.218039i
$885$	11.1930	+	8.13216i	0.376247	+	0.273360i
$886$	−20.6182	−	14.9800i	−0.692681	−	0.503262i
$887$	5.79712	−	17.8417i	0.194648	−	0.599065i	−0.805332	−	0.592824i	$-0.798013\pi$
$887$	5.79712	−	17.8417i	0.194648	−	0.599065i	0.999981	−	0.00624190i	$-0.00198687\pi$
$888$	8.89175	+	27.3660i	0.298388	+	0.918343i
$889$	−19.5743	+	14.2215i	−0.656500	+	0.476975i
$890$	−12.0297			−0.403235
$891$	−32.6112	+	26.0642i	−1.09252	+	0.873183i
$892$	−17.5330			−0.587048
$893$	15.8382	−	11.5071i	0.530004	−	0.385070i
$894$	−22.0021	−	67.7155i	−0.735860	−	2.26475i
$895$	−10.5734	+	32.5415i	−0.353429	+	1.08774i
$896$	3.53682	+	2.56965i	0.118157	+	0.0858461i
$897$	2.00689	+	1.45809i	0.0670082	+	0.0486843i
$898$	6.35554	−	19.5603i	0.212087	−	0.652737i
$899$	0.587403	+	1.80784i	0.0195910	+	0.0602949i
$900$	−17.4002	+	12.6420i	−0.580005	+	0.421399i
$901$	4.75962			0.158566
$902$	5.41107	+	14.3706i	0.180169	+	0.478488i
$903$	68.0777			2.26548
$904$	−0.986607	+	0.716812i	−0.0328141	+	0.0238408i
$905$	15.7935	+	48.6072i	0.524992	+	1.61576i
$906$	−20.3299	+	62.5690i	−0.675416	+	2.07872i
$907$	36.5408	+	26.5484i	1.21332	+	0.881526i	0.995528	−	0.0944698i	$-0.0301156\pi$
$907$	36.5408	+	26.5484i	1.21332	+	0.881526i	0.217789	+	0.975996i	$0.430116\pi$
$908$	11.9179	+	8.65884i	0.395509	+	0.287354i
$909$	20.1174	−	61.9150i	0.667252	−	2.05359i
$910$	3.90839	+	12.0288i	0.129562	+	0.398751i
$911$	−16.1817	+	11.7567i	−0.536124	+	0.389517i	−0.822643	−	0.568558i	$-0.807502\pi$
$911$	−16.1817	+	11.7567i	−0.536124	+	0.389517i	0.286520	+	0.958074i	$0.407502\pi$
$912$	15.1867			0.502881
$913$	−0.510053	−	1.35459i	−0.0168803	−	0.0448302i
$914$	27.1619			0.898435
$915$	−49.2416	+	35.7761i	−1.62788	+	1.18272i
$916$	1.92696	+	5.93057i	0.0636685	+	0.195952i
$917$	−12.1555	+	37.4107i	−0.401410	+	1.23541i
$918$	57.1327	+	41.5094i	1.88566	+	1.37001i
$919$	31.4465	+	22.8472i	1.03732	+	0.753660i	0.969761	−	0.244055i	$-0.0784778\pi$
$919$	31.4465	+	22.8472i	1.03732	+	0.753660i	0.0675624	+	0.997715i	$0.478478\pi$
$920$	−0.724024	+	2.22832i	−0.0238704	+	0.0734655i
$921$	10.3723	+	31.9226i	0.341778	+	1.05188i
$922$	10.8038	−	7.84940i	0.355803	−	0.258506i
$923$	−9.11944			−0.300170
$924$	−34.6934	+	27.7284i	−1.14133	+	0.912196i
$925$	−31.6566			−1.04086
$926$	16.0235	−	11.6418i	0.526565	−	0.382572i
$927$	31.4519	+	96.7991i	1.03302	+	3.17930i
$928$	0.260083	−	0.800454i	0.00853765	−	0.0262762i
$929$	39.5015	+	28.6995i	1.29600	+	0.941600i	0.999908	−	0.0135589i	$-0.00431605\pi$
$929$	39.5015	+	28.6995i	1.29600	+	0.941600i	0.296093	+	0.955159i	$0.404316\pi$
$930$	16.1919	+	11.7641i	0.530952	+	0.385760i
$931$	18.5573	−	57.1134i	0.608190	−	1.87182i
$932$	−2.86012	−	8.80254i	−0.0936863	−	0.288337i
$933$	73.5599	−	53.4444i	2.40824	−	1.74969i
$934$	−38.2088			−1.25023
$935$	−17.3321	+	63.0666i	−0.566819	+	2.06250i
$936$	−6.38234			−0.208613
$937$	29.1566	−	21.1835i	0.952504	−	0.692035i	0.00110636	−	0.999999i	$-0.499648\pi$
$937$	29.1566	−	21.1835i	0.952504	−	0.692035i	0.951398	+	0.307965i	$0.0996478\pi$
$938$	−15.7144	−	48.3639i	−0.513093	−	1.57914i
$939$	−11.4030	+	35.0949i	−0.372124	+	1.14528i
$940$	−9.24182	−	6.71457i	−0.301435	−	0.219005i
$941$	12.8054	+	9.30370i	0.417445	+	0.303292i	0.776609	−	0.629983i	$-0.216938\pi$
$941$	12.8054	+	9.30370i	0.417445	+	0.303292i	−0.359164	+	0.933275i	$0.616938\pi$
$942$	1.79980	−	5.53921i	0.0586406	−	0.180477i
$943$	1.15868	+	3.56604i	0.0377318	+	0.116126i
$944$	−1.26308	+	0.917678i	−0.0411096	+	0.0298679i
$945$	−131.035			−4.26258
$946$	−16.8434	+	0.774654i	−0.547628	+	0.0251862i
$947$	55.3123			1.79741			0.898705	−	0.438555i	$-0.144509\pi$
$947$	55.3123			1.79741			0.898705	+	0.438555i	$0.144509\pi$
$948$	12.3377	−	8.96386i	0.400710	−	0.291133i
$949$	−2.00779	−	6.17934i	−0.0651756	−	0.200590i
$950$	−5.16303	+	15.8902i	−0.167511	+	0.515545i
$951$	−35.2583	−	25.6167i	−1.14333	−	0.830677i
$952$	24.1084	+	17.5157i	0.781356	+	0.567688i
$953$	−9.97908	+	30.7124i	−0.323254	+	0.994874i	0.648968	+	0.760815i	$0.275201\pi$
$953$	−9.97908	+	30.7124i	−0.323254	+	0.994874i	−0.972223	+	0.234058i	$0.924799\pi$
$954$	−1.37715	−	4.23843i	−0.0445868	−	0.137224i
$955$	−36.9585	+	26.8519i	−1.19595	+	0.868908i
$956$	−13.4753			−0.435822
$957$	7.14094	+	4.70264i	0.230834	+	0.152015i
$958$	14.0789			0.454868
$959$	67.6629	−	49.1599i	2.18495	−	1.58746i
$960$	−2.73841	−	8.42795i	−0.0883817	−	0.272011i
$961$	−8.00326	+	24.6315i	−0.258170	+	0.794564i
$962$	−7.59989	−	5.52164i	−0.245030	−	0.178025i
$963$	6.03021	+	4.38121i	0.194321	+	0.141182i
$964$	−5.73637	+	17.6547i	−0.184756	+	0.568620i
$965$	−18.1054	−	55.7227i	−0.582834	−	1.79378i
$966$	−8.77365	+	6.37443i	−0.282287	+	0.205094i
$967$	51.7932			1.66556			0.832778	−	0.553607i	$-0.186749\pi$
$967$	51.7932			1.66556			0.832778	+	0.553607i	$0.186749\pi$
$968$	8.26815	−	7.25519i	0.265748	−	0.233191i
$969$	103.518			3.32548
$970$	−12.9058	+	9.37663i	−0.414381	+	0.301066i
$971$	−16.0162	−	49.2929i	−0.513986	−	1.58189i	−0.785120	−	0.619344i	$-0.787399\pi$
$971$	−16.0162	−	49.2929i	−0.513986	−	1.58189i	0.271134	−	0.962542i	$-0.412601\pi$
$972$	2.30978	−	7.10878i	0.0740863	−	0.228014i
$973$	−39.0791	−	28.3926i	−1.25282	−	0.910225i
$974$	−0.202898	−	0.147414i	−0.00650127	−	0.00472345i
$975$	3.18973	−	9.81697i	0.102153	−	0.314395i
$976$	−2.12247	−	6.53229i	−0.0679386	−	0.209094i
$977$	37.3212	−	27.1155i	1.19401	−	0.867500i	0.200329	−	0.979729i	$-0.435799\pi$
$977$	37.3212	−	27.1155i	1.19401	−	0.867500i	0.993682	+	0.112228i	$0.0357988\pi$
$978$	−12.2370			−0.391295
$979$	11.5176	+	7.58489i	0.368105	+	0.242414i
$980$	−35.0416			−1.11936
$981$	−27.0908	+	19.6826i	−0.864943	+	0.628418i
$982$	−12.4875	−	38.4327i	−0.398494	−	1.22644i
$983$	−9.00873	+	27.7260i	−0.287334	+	0.884322i	0.698356	+	0.715751i	$0.253915\pi$
$983$	−9.00873	+	27.7260i	−0.287334	+	0.884322i	−0.985689	+	0.168572i	$0.946085\pi$
$984$	−11.4732	−	8.33573i	−0.365751	−	0.265733i
$985$	−17.5906	−	12.7803i	−0.560484	−	0.407216i
$986$	1.77283	−	5.45620i	0.0564583	−	0.173761i
$987$	−16.3393	−	50.2872i	−0.520086	−	1.60066i
$988$	−4.01111	+	2.91424i	−0.127610	+	0.0927144i
$989$	−4.11722			−0.130920
$990$	61.1755	−	2.81355i	1.94428	−	0.0894204i
$991$	−44.5136			−1.41402			−0.707011	−	0.707202i	$-0.749957\pi$
$991$	−44.5136			−1.41402			−0.707011	+	0.707202i	$0.749957\pi$
$992$	−1.82718	+	1.32753i	−0.0580131	+	0.0421490i
$993$	−20.7303	−	63.8013i	−0.657856	−	2.02467i
$994$	12.3199	−	37.9167i	0.390763	−	1.20264i
$995$	−24.8922	−	18.0852i	−0.789136	−	0.573341i
$996$	1.08147	+	0.785734i	0.0342677	+	0.0248969i
$997$	−15.4960	+	47.6917i	−0.490762	+	1.51041i	0.332696	+	0.943034i	$0.392042\pi$
$997$	−15.4960	+	47.6917i	−0.490762	+	1.51041i	−0.823458	+	0.567377i	$0.807958\pi$
$998$	10.7505	+	33.0868i	0.340302	+	1.04734i
$999$	78.7373	−	57.2060i	2.49114	−	1.80992i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	286.2.h.d.157.3	✓	12
11.2	odd	10		3146.2.a.bi.1.6		6
11.4	even	5	inner	286.2.h.d.235.3	yes	12
11.9	even	5		3146.2.a.bf.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
286.2.h.d.157.3	✓	12	1.1	even	1	trivial
286.2.h.d.235.3	yes	12	11.4	even	5	inner
3146.2.a.bf.1.6		6	11.9	even	5
3146.2.a.bi.1.6		6	11.2	odd	10

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:	\( N \)	\(=\)	\( 286 = 2 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	286.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.946538 + 2.91314i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.34055 + 1.70051i) q^{5} +(2.47807 + 1.80042i) q^{6} +(1.35095 - 4.15779i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-5.16342 + 3.75145i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.946538 + 2.91314i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.34055 + 1.70051i) q^{5} +(2.47807 + 1.80042i) q^{6} +(1.35095 - 4.15779i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-5.16342 + 3.75145i) q^{9} +2.89308 q^{10} +(-2.76994 - 1.82413i) q^{11} +3.06306 q^{12} +(-0.809017 + 0.587785i) q^{13} +(-1.35095 - 4.15779i) q^{14} +(-2.73841 + 8.42795i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-5.51457 - 4.00657i) q^{17} +(-1.97225 + 6.06997i) q^{18} +(1.53211 + 4.71534i) q^{19} +(2.34055 - 1.70051i) q^{20} +13.3910 q^{21} +(-3.31312 + 0.152375i) q^{22} -0.809862 q^{23} +(2.47807 - 1.80042i) q^{24} +(1.04135 + 3.20495i) q^{25} +(-0.309017 + 0.951057i) q^{26} +(-8.38168 - 6.08964i) q^{27} +(-3.53682 - 2.56965i) q^{28} +(-0.260083 + 0.800454i) q^{29} +(2.73841 + 8.42795i) q^{30} +(1.82718 - 1.32753i) q^{31} -1.00000 q^{32} +(2.69211 - 9.79583i) q^{33} -6.81638 q^{34} +(10.2323 - 7.43420i) q^{35} +(1.97225 + 6.06997i) q^{36} +(-2.90290 + 8.93420i) q^{37} +(4.01111 + 2.91424i) q^{38} +(-2.47807 - 1.80042i) q^{39} +(0.894010 - 2.75148i) q^{40} +(-1.43071 - 4.40327i) q^{41} +(10.8335 - 7.87100i) q^{42} +5.08386 q^{43} +(-2.59081 + 2.07068i) q^{44} -18.4646 q^{45} +(-0.655192 + 0.476025i) q^{46} +(-1.22018 - 3.75531i) q^{47} +(0.946538 - 2.91314i) q^{48} +(-9.79901 - 7.11940i) q^{49} +(2.72630 + 1.98077i) q^{50} +(6.45197 - 19.8571i) q^{51} +(0.309017 + 0.951057i) q^{52} +(-0.564906 + 0.410428i) q^{53} -10.3603 q^{54} +(-3.38122 - 8.97976i) q^{55} -4.37176 q^{56} +(-12.2863 + 8.92650i) q^{57} +(0.260083 + 0.800454i) q^{58} +(0.482452 - 1.48483i) q^{59} +(7.16924 + 5.20876i) q^{60} +(5.55670 + 4.03718i) q^{61} +(0.697921 - 2.14798i) q^{62} +(8.62220 + 26.5364i) q^{63} +(-0.809017 + 0.587785i) q^{64} -2.89308 q^{65} +(-3.57989 - 9.50737i) q^{66} +11.6321 q^{67} +(-5.51457 + 4.00657i) q^{68} +(-0.766565 - 2.35924i) q^{69} +(3.90839 - 12.0288i) q^{70} +(7.37778 + 5.36027i) q^{71} +(5.16342 + 3.75145i) q^{72} +(-2.00779 + 6.17934i) q^{73} +(2.90290 + 8.93420i) q^{74} +(-8.35081 + 6.06722i) q^{75} +4.95800 q^{76} +(-11.3264 + 9.05250i) q^{77} -3.06306 q^{78} +(4.02790 - 2.92644i) q^{79} +(-0.894010 - 2.75148i) q^{80} +(3.88968 - 11.9712i) q^{81} +(-3.74565 - 2.72137i) q^{82} +(0.353069 + 0.256519i) q^{83} +(4.13803 - 12.7356i) q^{84} +(-6.09391 - 18.7551i) q^{85} +(4.11293 - 2.98822i) q^{86} -2.57802 q^{87} +(-0.878894 + 3.19805i) q^{88} -4.15808 q^{89} +(-14.9382 + 10.8532i) q^{90} +(1.35095 + 4.15779i) q^{91} +(-0.250261 + 0.770225i) q^{92} +(5.59677 + 4.06629i) q^{93} +(-3.19446 - 2.32091i) q^{94} +(-4.43250 + 13.6418i) q^{95} +(-0.946538 - 2.91314i) q^{96} +(-4.46094 + 3.24106i) q^{97} -12.1122 q^{98} +(21.1455 - 0.972511i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 2 q^{7} + 3 q^{8} - 17 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 2 * q^7 + 3 * q^8 - 17 * q^9	\( 12 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 2 q^{7} + 3 q^{8} - 17 q^{9} + 12 q^{10} - 3 q^{13} + 2 q^{14} - 18 q^{15} - 3 q^{16} - 10 q^{17} - 13 q^{18} + 3 q^{19} + 3 q^{20} + 30 q^{21} + 5 q^{22} + 8 q^{23} - 2 q^{25} + 3 q^{26} - 9 q^{27} - 7 q^{28} - 6 q^{29} + 18 q^{30} - 29 q^{31} - 12 q^{32} + 7 q^{33} - 10 q^{34} + 22 q^{35} + 13 q^{36} - 16 q^{37} + 12 q^{38} - 3 q^{40} + 16 q^{41} + 10 q^{42} + 38 q^{43} - 5 q^{44} - 20 q^{45} + 2 q^{46} + 9 q^{47} + 3 q^{49} - 8 q^{50} + 3 q^{51} - 3 q^{52} - 21 q^{53} - 6 q^{54} - 4 q^{55} - 18 q^{56} - 8 q^{57} + 6 q^{58} - 5 q^{59} + 22 q^{60} + 6 q^{61} - 36 q^{62} + 27 q^{63} - 3 q^{64} - 12 q^{65} - 12 q^{66} + 14 q^{67} - 10 q^{68} - 16 q^{69} + 18 q^{70} + 39 q^{71} + 17 q^{72} - 18 q^{73} + 16 q^{74} - 50 q^{75} + 18 q^{76} - 30 q^{77} - 12 q^{79} + 3 q^{80} + 19 q^{81} + 19 q^{82} + 16 q^{83} - 5 q^{84} - 21 q^{85} + 12 q^{86} - 4 q^{87} - 10 q^{88} - 10 q^{89} - 20 q^{90} - 2 q^{91} - 2 q^{92} + 47 q^{93} - 14 q^{94} - 67 q^{95} - 16 q^{97} - 18 q^{98} - 2 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 2 * q^7 + 3 * q^8 - 17 * q^9 + 12 * q^10 - 3 * q^13 + 2 * q^14 - 18 * q^15 - 3 * q^16 - 10 * q^17 - 13 * q^18 + 3 * q^19 + 3 * q^20 + 30 * q^21 + 5 * q^22 + 8 * q^23 - 2 * q^25 + 3 * q^26 - 9 * q^27 - 7 * q^28 - 6 * q^29 + 18 * q^30 - 29 * q^31 - 12 * q^32 + 7 * q^33 - 10 * q^34 + 22 * q^35 + 13 * q^36 - 16 * q^37 + 12 * q^38 - 3 * q^40 + 16 * q^41 + 10 * q^42 + 38 * q^43 - 5 * q^44 - 20 * q^45 + 2 * q^46 + 9 * q^47 + 3 * q^49 - 8 * q^50 + 3 * q^51 - 3 * q^52 - 21 * q^53 - 6 * q^54 - 4 * q^55 - 18 * q^56 - 8 * q^57 + 6 * q^58 - 5 * q^59 + 22 * q^60 + 6 * q^61 - 36 * q^62 + 27 * q^63 - 3 * q^64 - 12 * q^65 - 12 * q^66 + 14 * q^67 - 10 * q^68 - 16 * q^69 + 18 * q^70 + 39 * q^71 + 17 * q^72 - 18 * q^73 + 16 * q^74 - 50 * q^75 + 18 * q^76 - 30 * q^77 - 12 * q^79 + 3 * q^80 + 19 * q^81 + 19 * q^82 + 16 * q^83 - 5 * q^84 - 21 * q^85 + 12 * q^86 - 4 * q^87 - 10 * q^88 - 10 * q^89 - 20 * q^90 - 2 * q^91 - 2 * q^92 + 47 * q^93 - 14 * q^94 - 67 * q^95 - 16 * q^97 - 18 * q^98 - 2 * q^99

Introduction

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