LMFDB - Embedded newform 731.2.e.a.307.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(307,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("731.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.e (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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$58$
Relative dimension:	$29$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			307.19
Character	$\chi$	$=$	731.307
Dual form			731.2.e.a.681.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.715873 q^{2} +(-1.27871 + 2.21478i) q^{3} -1.48753 q^{4} +(0.380045 - 0.658258i) q^{5} +(-0.915390 + 1.58550i) q^{6} +(-1.25160 - 2.16783i) q^{7} -2.49662 q^{8} +(-1.77018 - 3.06604i) q^{9} +O(q^{10})$	\(q+0.715873 q^{2} +(-1.27871 + 2.21478i) q^{3} -1.48753 q^{4} +(0.380045 - 0.658258i) q^{5} +(-0.915390 + 1.58550i) q^{6} +(-1.25160 - 2.16783i) q^{7} -2.49662 q^{8} +(-1.77018 - 3.06604i) q^{9} +(0.272064 - 0.471229i) q^{10} +3.64255 q^{11} +(1.90211 - 3.29455i) q^{12} +(-0.946091 - 1.63868i) q^{13} +(-0.895984 - 1.55189i) q^{14} +(0.971932 + 1.68344i) q^{15} +1.18779 q^{16} +(0.500000 + 0.866025i) q^{17} +(-1.26722 - 2.19489i) q^{18} +(3.30791 - 5.72947i) q^{19} +(-0.565328 + 0.979176i) q^{20} +6.40170 q^{21} +2.60761 q^{22} +(-1.37206 + 2.37648i) q^{23} +(3.19245 - 5.52948i) q^{24} +(2.21113 + 3.82979i) q^{25} +(-0.677281 - 1.17308i) q^{26} +1.38191 q^{27} +(1.86178 + 3.22470i) q^{28} +(-1.32854 - 2.30110i) q^{29} +(0.695780 + 1.20513i) q^{30} +(3.99769 - 6.92420i) q^{31} +5.84355 q^{32} +(-4.65776 + 8.06747i) q^{33} +(0.357936 + 0.619964i) q^{34} -1.90265 q^{35} +(2.63318 + 4.56081i) q^{36} +(0.162196 - 0.280931i) q^{37} +(2.36804 - 4.10157i) q^{38} +4.83909 q^{39} +(-0.948831 + 1.64342i) q^{40} +3.56122 q^{41} +4.58280 q^{42} +(5.24004 + 3.94234i) q^{43} -5.41840 q^{44} -2.69099 q^{45} +(-0.982221 + 1.70126i) q^{46} -1.45379 q^{47} +(-1.51883 + 2.63069i) q^{48} +(0.367011 - 0.635682i) q^{49} +(1.58289 + 2.74164i) q^{50} -2.55741 q^{51} +(1.40734 + 2.43758i) q^{52} +(4.87867 - 8.45010i) q^{53} +0.989269 q^{54} +(1.38434 - 2.39774i) q^{55} +(3.12477 + 5.41226i) q^{56} +(8.45969 + 14.6526i) q^{57} +(-0.951067 - 1.64730i) q^{58} -11.5260 q^{59} +(-1.44578 - 2.50416i) q^{60} +(-4.32567 - 7.49228i) q^{61} +(2.86184 - 4.95685i) q^{62} +(-4.43109 + 7.67488i) q^{63} +1.80767 q^{64} -1.43823 q^{65} +(-3.33436 + 5.77528i) q^{66} +(4.90932 - 8.50320i) q^{67} +(-0.743763 - 1.28824i) q^{68} +(-3.50892 - 6.07763i) q^{69} -1.36206 q^{70} +(-1.74234 - 3.01783i) q^{71} +(4.41947 + 7.65474i) q^{72} +(7.33800 + 12.7098i) q^{73} +(0.116111 - 0.201111i) q^{74} -11.3095 q^{75} +(-4.92060 + 8.52273i) q^{76} +(-4.55901 - 7.89644i) q^{77} +3.46417 q^{78} +(-4.69908 - 8.13904i) q^{79} +(0.451413 - 0.781870i) q^{80} +(3.54348 - 6.13749i) q^{81} +2.54938 q^{82} +(0.889198 - 1.54014i) q^{83} -9.52269 q^{84} +0.760091 q^{85} +(3.75120 + 2.82221i) q^{86} +6.79526 q^{87} -9.09409 q^{88} +(6.92596 - 11.9961i) q^{89} -1.92641 q^{90} +(-2.36825 + 4.10193i) q^{91} +(2.04098 - 3.53507i) q^{92} +(10.2237 + 17.7080i) q^{93} -1.04073 q^{94} +(-2.51431 - 4.35492i) q^{95} +(-7.47219 + 12.9422i) q^{96} +14.8714 q^{97} +(0.262733 - 0.455067i) q^{98} +(-6.44797 - 11.1682i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9}+O(q^{10}) $ 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9	\( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9} + 4 q^{10} + 16 q^{11} + 12 q^{12} + 2 q^{13} - 11 q^{14} + 7 q^{15} + 30 q^{16} + 29 q^{17} + 8 q^{18} + 8 q^{19} - 33 q^{20} - 26 q^{21} - 22 q^{22} - 5 q^{23} + 12 q^{24} - 36 q^{25} - 12 q^{27} + 15 q^{28} + 2 q^{29} + 11 q^{30} + 3 q^{31} - 40 q^{32} + 17 q^{33} - 3 q^{34} + 38 q^{35} - 7 q^{36} + 2 q^{37} + q^{38} - 54 q^{39} + 5 q^{40} + 14 q^{41} - 112 q^{42} + 31 q^{43} - 24 q^{44} - 46 q^{45} - 13 q^{46} - 28 q^{47} - 28 q^{49} - 13 q^{50} + 6 q^{51} + 85 q^{52} - 10 q^{53} + 34 q^{54} + 36 q^{55} - 54 q^{56} - 23 q^{57} + 3 q^{58} + 12 q^{59} + 2 q^{60} - q^{61} - q^{62} - 14 q^{63} + 28 q^{64} + 80 q^{65} - 74 q^{66} + 11 q^{67} + 27 q^{68} - 11 q^{69} + 2 q^{70} + 16 q^{71} + 21 q^{72} + 14 q^{73} + 21 q^{74} - 54 q^{75} + 44 q^{76} + 25 q^{77} + 88 q^{78} - 4 q^{79} - 112 q^{80} + 11 q^{81} - 176 q^{82} - 3 q^{83} + 100 q^{84} - 2 q^{85} + 44 q^{86} + 8 q^{87} - 106 q^{88} + 82 q^{89} + 54 q^{90} - 15 q^{91} + 42 q^{92} + 88 q^{94} + 29 q^{95} + 20 q^{96} + 20 q^{97} + 44 q^{98} - 54 q^{99}+O(q^{100}) \) 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9 + 4 * q^10 + 16 * q^11 + 12 * q^12 + 2 * q^13 - 11 * q^14 + 7 * q^15 + 30 * q^16 + 29 * q^17 + 8 * q^18 + 8 * q^19 - 33 * q^20 - 26 * q^21 - 22 * q^22 - 5 * q^23 + 12 * q^24 - 36 * q^25 - 12 * q^27 + 15 * q^28 + 2 * q^29 + 11 * q^30 + 3 * q^31 - 40 * q^32 + 17 * q^33 - 3 * q^34 + 38 * q^35 - 7 * q^36 + 2 * q^37 + q^38 - 54 * q^39 + 5 * q^40 + 14 * q^41 - 112 * q^42 + 31 * q^43 - 24 * q^44 - 46 * q^45 - 13 * q^46 - 28 * q^47 - 28 * q^49 - 13 * q^50 + 6 * q^51 + 85 * q^52 - 10 * q^53 + 34 * q^54 + 36 * q^55 - 54 * q^56 - 23 * q^57 + 3 * q^58 + 12 * q^59 + 2 * q^60 - q^61 - q^62 - 14 * q^63 + 28 * q^64 + 80 * q^65 - 74 * q^66 + 11 * q^67 + 27 * q^68 - 11 * q^69 + 2 * q^70 + 16 * q^71 + 21 * q^72 + 14 * q^73 + 21 * q^74 - 54 * q^75 + 44 * q^76 + 25 * q^77 + 88 * q^78 - 4 * q^79 - 112 * q^80 + 11 * q^81 - 176 * q^82 - 3 * q^83 + 100 * q^84 - 2 * q^85 + 44 * q^86 + 8 * q^87 - 106 * q^88 + 82 * q^89 + 54 * q^90 - 15 * q^91 + 42 * q^92 + 88 * q^94 + 29 * q^95 + 20 * q^96 + 20 * q^97 + 44 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.715873			0.506198			0.253099	−	0.967440i	$-0.418550\pi$
$2$	0.715873			0.506198			0.253099	+	0.967440i	$0.418550\pi$
$3$	−1.27871	+	2.21478i	−0.738261	+	1.27871i	0.215017	+	0.976610i	$0.431019\pi$
$3$	−1.27871	+	2.21478i	−0.738261	+	1.27871i	−0.953278	+	0.302095i	$0.902314\pi$
$4$	−1.48753			−0.743763
$5$	0.380045	−	0.658258i	0.169961	−	0.294382i	−0.768445	−	0.639916i	$-0.778969\pi$
$5$	0.380045	−	0.658258i	0.169961	−	0.294382i	0.938406	+	0.345534i	$0.112302\pi$
$6$	−0.915390	+	1.58550i	−0.373707	+	0.647279i
$7$	−1.25160	−	2.16783i	−0.473059	−	0.819362i	0.526465	−	0.850197i	$-0.323517\pi$
$7$	−1.25160	−	2.16783i	−0.473059	−	0.819362i	−0.999525	+	0.0308342i	$0.990184\pi$
$8$	−2.49662			−0.882690
$9$	−1.77018	−	3.06604i	−0.590059	−	1.02201i
$10$	0.272064	−	0.471229i	0.0860342	−	0.149016i
$11$	3.64255			1.09827			0.549136	−	0.835733i	$-0.314957\pi$
$11$	3.64255			1.09827			0.549136	+	0.835733i	$0.314957\pi$
$12$	1.90211	−	3.29455i	0.549091	−	0.951054i
$13$	−0.946091	−	1.63868i	−0.262398	−	0.454487i	0.704480	−	0.709724i	$-0.251180\pi$
$13$	−0.946091	−	1.63868i	−0.262398	−	0.454487i	−0.966879	+	0.255236i	$0.917847\pi$
$14$	−0.895984	−	1.55189i	−0.239462	−	0.414760i
$15$	0.971932	+	1.68344i	0.250952	+	0.434661i
$16$	1.18779			0.296947
$17$	0.500000	+	0.866025i	0.121268	+	0.210042i
$17$	0.500000	+	0.866025i	0.121268	+	0.210042i
$18$	−1.26722	−	2.19489i	−0.298687	−	0.517341i
$19$	3.30791	−	5.72947i	0.758886	−	1.31443i	−0.184532	−	0.982826i	$-0.559077\pi$
$19$	3.30791	−	5.72947i	0.758886	−	1.31443i	0.943419	−	0.331603i	$-0.107590\pi$
$20$	−0.565328	+	0.979176i	−0.126411	+	0.218950i
$21$	6.40170			1.39696
$22$	2.60761			0.555943
$23$	−1.37206	+	2.37648i	−0.286094	+	0.495530i	−0.972874	−	0.231336i	$-0.925690\pi$
$23$	−1.37206	+	2.37648i	−0.286094	+	0.495530i	0.686780	+	0.726866i	$0.259024\pi$
$24$	3.19245	−	5.52948i	0.651656	−	1.12870i
$25$	2.21113	+	3.82979i	0.442226	+	0.765958i
$26$	−0.677281	−	1.17308i	−0.132826	−	0.230061i
$27$	1.38191			0.265948
$28$	1.86178	+	3.22470i	0.351844	+	0.609412i
$29$	−1.32854	−	2.30110i	−0.246704	−	0.427304i	0.715905	−	0.698198i	$-0.246014\pi$
$29$	−1.32854	−	2.30110i	−0.246704	−	0.427304i	−0.962609	+	0.270893i	$0.912681\pi$
$30$	0.695780	+	1.20513i	0.127031	+	0.220025i
$31$	3.99769	−	6.92420i	0.718006	−	1.24362i	−0.243782	−	0.969830i	$-0.578388\pi$
$31$	3.99769	−	6.92420i	0.718006	−	1.24362i	0.961789	−	0.273793i	$-0.0882785\pi$
$32$	5.84355			1.03300
$33$	−4.65776	+	8.06747i	−0.810811	+	1.40437i
$34$	0.357936	+	0.619964i	0.0613856	+	0.106323i
$35$	−1.90265			−0.321607
$36$	2.63318	+	4.56081i	0.438864	+	0.760135i
$37$	0.162196	−	0.280931i	0.0266648	−	0.0461848i	−0.852385	−	0.522915i	$-0.824845\pi$
$37$	0.162196	−	0.280931i	0.0266648	−	0.0461848i	0.879050	+	0.476730i	$0.158178\pi$
$38$	2.36804	−	4.10157i	0.384147	−	0.665362i
$39$	4.83909			0.774874
$40$	−0.948831	+	1.64342i	−0.150023	+	0.259848i
$41$	3.56122			0.556169			0.278084	−	0.960557i	$-0.410300\pi$
$41$	3.56122			0.556169			0.278084	+	0.960557i	$0.410300\pi$
$42$	4.58280			0.707141
$43$	5.24004	+	3.94234i	0.799098	+	0.601201i
$43$	5.24004	+	3.94234i	0.799098	+	0.601201i
$44$	−5.41840			−0.816854
$45$	−2.69099			−0.401149
$46$	−0.982221	+	1.70126i	−0.144821	+	0.250837i
$47$	−1.45379			−0.212057			−0.106028	−	0.994363i	$-0.533813\pi$
$47$	−1.45379			−0.212057			−0.106028	+	0.994363i	$0.533813\pi$
$48$	−1.51883	+	2.63069i	−0.219224	+	0.379708i
$49$	0.367011	−	0.635682i	0.0524302	−	0.0908117i
$50$	1.58289	+	2.74164i	0.223854	+	0.387727i
$51$	−2.55741			−0.358109
$52$	1.40734	+	2.43758i	0.195162	+	0.338031i
$53$	4.87867	−	8.45010i	0.670137	−	1.16071i	−0.307728	−	0.951474i	$-0.599569\pi$
$53$	4.87867	−	8.45010i	0.670137	−	1.16071i	0.977865	−	0.209237i	$-0.0670979\pi$
$54$	0.989269			0.134622
$55$	1.38434	−	2.39774i	0.186664	−	0.323311i
$56$	3.12477	+	5.41226i	0.417565	+	0.723243i
$57$	8.45969	+	14.6526i	1.12051	+	1.94078i
$58$	−0.951067	−	1.64730i	−0.124881	−	0.216301i
$59$	−11.5260			−1.50056			−0.750278	−	0.661122i	$-0.770080\pi$
$59$	−11.5260			−1.50056			−0.750278	+	0.661122i	$0.770080\pi$
$60$	−1.44578	−	2.50416i	−0.186649	−	0.323285i
$61$	−4.32567	−	7.49228i	−0.553845	−	0.959289i	−0.997992	−	0.0633345i	$-0.979826\pi$
$61$	−4.32567	−	7.49228i	−0.553845	−	0.959289i	0.444147	−	0.895954i	$-0.353507\pi$
$62$	2.86184	−	4.95685i	0.363454	−	0.629520i
$63$	−4.43109	+	7.67488i	−0.558265	+	0.966944i
$64$	1.80767			0.225958
$65$	−1.43823			−0.178391
$66$	−3.33436	+	5.77528i	−0.410431	+	0.710888i
$67$	4.90932	−	8.50320i	0.599769	−	1.03883i	−0.393085	−	0.919502i	$-0.628592\pi$
$67$	4.90932	−	8.50320i	0.599769	−	1.03883i	0.992855	−	0.119329i	$-0.0380743\pi$
$68$	−0.743763	−	1.28824i	−0.0901945	−	0.156222i
$69$	−3.50892	−	6.07763i	−0.422425	−	0.731661i
$70$	−1.36206			−0.162797
$71$	−1.74234	−	3.01783i	−0.206778	−	0.358150i	0.743920	−	0.668269i	$-0.232964\pi$
$71$	−1.74234	−	3.01783i	−0.206778	−	0.358150i	−0.950698	+	0.310119i	$0.899631\pi$
$72$	4.41947	+	7.65474i	0.520839	+	0.902120i
$73$	7.33800	+	12.7098i	0.858848	+	1.48757i	0.873029	+	0.487668i	$0.162152\pi$
$73$	7.33800	+	12.7098i	0.858848	+	1.48757i	−0.0141816	+	0.999899i	$0.504514\pi$
$74$	0.116111	−	0.201111i	0.0134977	−	0.0233786i
$75$	−11.3095			−1.30591
$76$	−4.92060	+	8.52273i	−0.564432	+	0.977625i
$77$	−4.55901	−	7.89644i	−0.519547	−	0.899882i
$78$	3.46417			0.392240
$79$	−4.69908	−	8.13904i	−0.528688	−	0.915714i	−0.999440	−	0.0334488i	$-0.989351\pi$
$79$	−4.69908	−	8.13904i	−0.528688	−	0.915714i	0.470753	−	0.882265i	$-0.343982\pi$
$80$	0.451413	−	0.781870i	0.0504695	−	0.0874158i
$81$	3.54348	−	6.13749i	0.393720	−	0.681943i
$82$	2.54938			0.281532
$83$	0.889198	−	1.54014i	0.0976022	−	0.169052i	−0.813089	−	0.582139i	$-0.802216\pi$
$83$	0.889198	−	1.54014i	0.0976022	−	0.169052i	0.910692	+	0.413087i	$0.135549\pi$
$84$	−9.52269			−1.03901
$85$	0.760091			0.0824434
$86$	3.75120	+	2.82221i	0.404502	+	0.304327i
$87$	6.79526			0.728528
$88$	−9.09409			−0.969434
$89$	6.92596	−	11.9961i	0.734150	−	1.27158i	−0.220945	−	0.975286i	$-0.570914\pi$
$89$	6.92596	−	11.9961i	0.734150	−	1.27158i	0.955095	−	0.296299i	$-0.0957524\pi$
$90$	−1.92641			−0.203061
$91$	−2.36825	+	4.10193i	−0.248260	+	0.429999i
$92$	2.04098	−	3.53507i	0.212786	−	0.368557i
$93$	10.2237	+	17.7080i	1.06015	+	1.83624i
$94$	−1.04073			−0.107343
$95$	−2.51431	−	4.35492i	−0.257963	−	0.446805i
$96$	−7.47219	+	12.9422i	−0.762627	+	1.32091i
$97$	14.8714			1.50996			0.754982	−	0.655745i	$-0.227645\pi$
$97$	14.8714			1.50996			0.754982	+	0.655745i	$0.227645\pi$
$98$	0.262733	−	0.455067i	0.0265401	−	0.0459688i
$99$	−6.44797	−	11.1682i	−0.648045	−	1.12245i
$100$	−3.28912	−	5.69692i	−0.328912	−	0.569692i
$101$	4.08019	+	7.06710i	0.405994	+	0.703202i	0.994437	−	0.105337i	$-0.0335920\pi$
$101$	4.08019	+	7.06710i	0.405994	+	0.703202i	−0.588443	+	0.808539i	$0.700259\pi$
$102$	−1.83078			−0.181274
$103$	−8.55020	−	14.8094i	−0.842476	−	1.45921i	−0.887795	−	0.460239i	$-0.847764\pi$
$103$	−8.55020	−	14.8094i	−0.842476	−	1.45921i	0.0453191	−	0.998973i	$-0.485570\pi$
$104$	2.36203	+	4.09116i	0.231617	+	0.401172i
$105$	2.43294	−	4.21397i	0.237430	−	0.411241i
$106$	3.49251	−	6.04920i	0.339222	−	0.587550i
$107$	−7.75826			−0.750020			−0.375010	−	0.927021i	$-0.622361\pi$
$107$	−7.75826			−0.750020			−0.375010	+	0.927021i	$0.622361\pi$
$108$	−2.05562			−0.197802
$109$	−3.74818	+	6.49204i	−0.359011	+	0.621825i	−0.987796	−	0.155754i	$-0.950219\pi$
$109$	−3.74818	+	6.49204i	−0.359011	+	0.621825i	0.628785	+	0.777579i	$0.283553\pi$
$110$	0.991009	−	1.71648i	0.0944890	−	0.163660i
$111$	0.414801	+	0.718456i	0.0393711	+	0.0681928i
$112$	−1.48663	−	2.57492i	−0.140473	−	0.243307i
$113$	−15.7319			−1.47993			−0.739967	−	0.672644i	$-0.765159\pi$
$113$	−15.7319			−1.47993			−0.739967	+	0.672644i	$0.765159\pi$
$114$	6.05606	+	10.4894i	0.567202	+	0.982422i
$115$	1.04289	+	1.80634i	0.0972501	+	0.168442i
$116$	1.97624	+	3.42295i	0.183489	+	0.317813i
$117$	−3.34950	+	5.80150i	−0.309661	+	0.536349i
$118$	−8.25114			−0.759579
$119$	1.25160	−	2.16783i	0.114734	−	0.198725i
$120$	−2.42655	−	4.20291i	−0.221513	−	0.383671i
$121$	2.26821			0.206201
$122$	−3.09663	−	5.36352i	−0.280356	−	0.485590i
$123$	−4.55375	+	7.88733i	−0.410598	+	0.711176i
$124$	−5.94667	+	10.2999i	−0.534027	+	0.924961i
$125$	7.16177			0.640569
$126$	−3.17210	+	5.49424i	−0.282593	+	0.489466i
$127$	−12.5597			−1.11449			−0.557246	−	0.830347i	$-0.688142\pi$
$127$	−12.5597			−1.11449			−0.557246	+	0.830347i	$0.688142\pi$
$128$	−10.3930			−0.918624
$129$	−15.4319	+	6.56445i	−1.35870	+	0.577968i
$130$	−1.02959			−0.0903010
$131$	3.30173			0.288473			0.144237	−	0.989543i	$-0.453927\pi$
$131$	3.30173			0.288473			0.144237	+	0.989543i	$0.453927\pi$
$132$	6.92853	−	12.0006i	0.603052	−	1.04452i
$133$	−16.5607			−1.43599
$134$	3.51445	−	6.08721i	0.303602	−	0.525855i
$135$	0.525187	−	0.909651i	0.0452009	−	0.0782903i
$136$	−1.24831	−	2.16214i	−0.107042	−	0.185402i
$137$	−0.977597			−0.0835218			−0.0417609	−	0.999128i	$-0.513297\pi$
$137$	−0.977597			−0.0835218			−0.0417609	+	0.999128i	$0.513297\pi$
$138$	−2.51194	−	4.35081i	−0.213831	−	0.370366i
$139$	3.68381	−	6.38055i	0.312457	−	0.541191i	−0.666437	−	0.745562i	$-0.732181\pi$
$139$	3.68381	−	6.38055i	0.312457	−	0.541191i	0.978894	+	0.204370i	$0.0655147\pi$
$140$	2.83025			0.239200
$141$	1.85897	−	3.21983i	0.156553	−	0.271158i
$142$	−1.24730	−	2.16038i	−0.104671	−	0.181295i
$143$	−3.44619	−	5.96897i	−0.288185	−	0.499151i
$144$	−2.10259	−	3.64180i	−0.175216	−	0.303483i
$145$	−2.01963			−0.167721
$146$	5.25307	+	9.09859i	0.434747	+	0.753004i
$147$	0.938599	+	1.62570i	0.0774143	+	0.134086i
$148$	−0.241270	+	0.417892i	−0.0198323	+	0.0343505i
$149$	−2.01327	+	3.48708i	−0.164933	+	0.285673i	−0.936632	−	0.350316i	$-0.886074\pi$
$149$	−2.01327	+	3.48708i	−0.164933	+	0.285673i	0.771698	+	0.635989i	$0.219408\pi$
$150$	−8.09619			−0.661051
$151$	−14.6830			−1.19488			−0.597441	−	0.801913i	$-0.703816\pi$
$151$	−14.6830			−1.19488			−0.597441	+	0.801913i	$0.703816\pi$
$152$	−8.25861	+	14.3043i	−0.669862	+	1.16023i
$153$	1.77018	−	3.06604i	0.143110	−	0.247874i
$154$	−3.26367	−	5.65284i	−0.262994	−	0.455519i
$155$	−3.03861	−	5.26302i	−0.244067	−	0.422736i
$156$	−7.19827			−0.576323
$157$	−1.97089	−	3.41369i	−0.157294	−	0.272442i	0.776598	−	0.629997i	$-0.216944\pi$
$157$	−1.97089	−	3.41369i	−0.157294	−	0.272442i	−0.933892	+	0.357555i	$0.883610\pi$
$158$	−3.36394	−	5.82652i	−0.267621	−	0.463533i
$159$	12.4768	+	21.6104i	0.989472	+	1.71382i
$160$	2.22082	−	3.84657i	0.175571	−	0.304098i
$161$	6.86907			0.541358
$162$	2.53668	−	4.39366i	0.199300	−	0.345198i
$163$	4.12820	+	7.15026i	0.323346	+	0.560051i	0.981176	−	0.193115i	$-0.0618590\pi$
$163$	4.12820	+	7.15026i	0.323346	+	0.560051i	−0.657830	+	0.753166i	$0.728526\pi$
$164$	−5.29741			−0.413658
$165$	3.54032	+	6.13201i	0.275613	+	0.477376i
$166$	0.636552	−	1.10254i	0.0494061	−	0.0855738i
$167$	−3.61749	+	6.26568i	−0.279930	+	0.484853i	−0.971367	−	0.237584i	$-0.923645\pi$
$167$	−3.61749	+	6.26568i	−0.279930	+	0.484853i	0.691437	+	0.722437i	$0.256978\pi$
$168$	−15.9826			−1.23309
$169$	4.70982	−	8.15765i	0.362294	−	0.627512i
$170$	0.544128			0.0417327
$171$	−23.4223			−1.79115
$172$	−7.79469	−	5.86433i	−0.594340	−	0.447151i
$173$	12.1075			0.920518			0.460259	−	0.887785i	$-0.347756\pi$
$173$	12.1075			0.920518			0.460259	+	0.887785i	$0.347756\pi$
$174$	4.86454			0.368780
$175$	5.53489	−	9.58671i	0.418398	−	0.724687i
$176$	4.32658			0.326128
$177$	14.7383	−	25.5276i	1.10780	−	1.91877i
$178$	4.95810	−	8.58769i	0.371625	−	0.643674i
$179$	8.12878	+	14.0795i	0.607573	+	1.05235i	0.991639	+	0.129042i	$0.0411903\pi$
$179$	8.12878	+	14.0795i	0.607573	+	1.05235i	−0.384066	+	0.923306i	$0.625476\pi$
$180$	4.00292			0.298360
$181$	5.54624	+	9.60638i	0.412249	+	0.714036i	0.995135	−	0.0985174i	$-0.0314100\pi$
$181$	5.54624	+	9.60638i	0.412249	+	0.714036i	−0.582886	+	0.812554i	$0.698077\pi$
$182$	−1.69536	+	2.93646i	−0.125669	+	0.217665i
$183$	22.1250			1.63553
$184$	3.42552	−	5.93318i	0.252533	−	0.437399i
$185$	−0.123283	−	0.213533i	−0.00906397	−	0.0156993i
$186$	7.31889	+	12.6767i	0.536647	+	0.929501i
$187$	1.82128	+	3.15455i	0.133185	+	0.230683i
$188$	2.16255			0.157720
$189$	−1.72959	−	2.99574i	−0.125809	−	0.217908i
$190$	−1.79993	−	3.11756i	−0.130580	−	0.226172i
$191$	−5.59162	+	9.68497i	−0.404595	+	0.700780i	−0.994274	−	0.106858i	$-0.965921\pi$
$191$	−5.59162	+	9.68497i	−0.404595	+	0.700780i	0.589679	+	0.807638i	$0.299254\pi$
$192$	−2.31147	+	4.00359i	−0.166816	+	0.288934i
$193$	17.3139			1.24629			0.623143	−	0.782108i	$-0.285856\pi$
$193$	17.3139			1.24629			0.623143	+	0.782108i	$0.285856\pi$
$194$	10.6460			0.764342
$195$	1.83907	−	3.18537i	0.131699	−	0.228109i
$196$	−0.545939	+	0.945594i	−0.0389956	+	0.0675424i
$197$	12.2009	+	21.1326i	0.869280	+	1.50564i	0.862733	+	0.505659i	$0.168751\pi$
$197$	12.2009	+	21.1326i	0.869280	+	1.50564i	0.00654679	+	0.999979i	$0.497916\pi$
$198$	−4.61592	−	7.99501i	−0.328039	−	0.568181i
$199$	−10.6885			−0.757689			−0.378844	−	0.925460i	$-0.623678\pi$
$199$	−10.6885			−0.757689			−0.378844	+	0.925460i	$0.623678\pi$
$200$	−5.52036	−	9.56155i	−0.390349	−	0.676104i
$201$	12.5552	+	21.7462i	0.885573	+	1.53386i
$202$	2.92090	+	5.05914i	0.205514	+	0.355960i
$203$	−3.32560	+	5.76011i	−0.233411	+	0.404280i
$204$	3.80422			0.266348
$205$	1.35342	−	2.34420i	0.0945273	−	0.163726i
$206$	−6.12085	−	10.6016i	−0.426460	−	0.738650i
$207$	9.71516			0.675250
$208$	−1.12376	−	1.94640i	−0.0779184	−	0.134959i
$209$	12.0492	−	20.8699i	0.833463	−	1.44360i
$210$	1.74167	−	3.01666i	0.120187	−	0.208170i
$211$	1.58767			0.109300			0.0546499	−	0.998506i	$-0.482596\pi$
$211$	1.58767			0.109300			0.0546499	+	0.998506i	$0.482596\pi$
$212$	−7.25715	+	12.5698i	−0.498423	+	0.863294i
$213$	8.91177			0.610625
$214$	−5.55393			−0.379659
$215$	4.58653	−	1.95103i	0.312799	−	0.133059i
$216$	−3.45010			−0.234750
$217$	−20.0140			−1.35864
$218$	−2.68322	+	4.64748i	−0.181731	+	0.314767i
$219$	−37.5326			−2.53621
$220$	−2.05924	+	3.56670i	−0.138834	+	0.240467i
$221$	0.946091	−	1.63868i	0.0636410	−	0.110229i
$222$	0.296944	+	0.514323i	0.0199296	+	0.0345191i
$223$	14.1780			0.949428			0.474714	−	0.880140i	$-0.342551\pi$
$223$	14.1780			0.949428			0.474714	+	0.880140i	$0.342551\pi$
$224$	−7.31377	−	12.6678i	−0.488672	−	0.846405i
$225$	7.82819	−	13.5588i	0.521879	−	0.903921i
$226$	−11.2620			−0.749140
$227$	−8.35460	+	14.4706i	−0.554514	+	0.960447i	0.443427	+	0.896310i	$0.353763\pi$
$227$	−8.35460	+	14.4706i	−0.554514	+	0.960447i	−0.997941	+	0.0641362i	$0.979571\pi$
$228$	−12.5840	−	21.7961i	−0.833396	−	1.44348i
$229$	2.57047	+	4.45219i	0.169862	+	0.294209i	0.938371	−	0.345630i	$-0.112335\pi$
$229$	2.57047	+	4.45219i	0.169862	+	0.294209i	−0.768510	+	0.639838i	$0.779001\pi$
$230$	0.746577	+	1.29311i	0.0492278	+	0.0852651i
$231$	23.3185			1.53425
$232$	3.31687	+	5.74499i	0.217763	+	0.377177i
$233$	−3.94162	−	6.82709i	−0.258224	−	0.447258i	0.707542	−	0.706671i	$-0.249804\pi$
$233$	−3.94162	−	6.82709i	−0.258224	−	0.447258i	−0.965766	+	0.259414i	$0.916471\pi$
$234$	−2.39781	+	4.15313i	−0.156750	+	0.271499i
$235$	−0.552506	+	0.956968i	−0.0360415	+	0.0624257i
$236$	17.1452			1.11606
$237$	24.0350			1.56124
$238$	0.895984	−	1.55189i	0.0580780	−	0.100594i
$239$	10.4912	−	18.1713i	0.678620	−	1.17540i	−0.296776	−	0.954947i	$-0.595912\pi$
$239$	10.4912	−	18.1713i	0.678620	−	1.17540i	0.975397	−	0.220458i	$-0.0707551\pi$
$240$	1.15445	+	1.99956i	0.0745194	+	0.129071i
$241$	7.57065	+	13.1127i	0.487668	+	0.844666i	0.999899	−	0.0141814i	$-0.00451424\pi$
$241$	7.57065	+	13.1127i	0.487668	+	0.844666i	−0.512231	+	0.858848i	$0.671181\pi$
$242$	1.62375			0.104378
$243$	11.1350	+	19.2864i	0.714310	+	1.23722i
$244$	6.43455	+	11.1450i	0.411930	+	0.713483i
$245$	−0.278962	−	0.483176i	−0.0178222	−	0.0308690i
$246$	−3.25991	+	5.64632i	−0.207844	+	0.359996i
$247$	−12.5183			−0.796523
$248$	−9.98073	+	17.2871i	−0.633777	+	1.09773i
$249$	2.27404	+	3.93876i	0.144112	+	0.249609i
$250$	5.12692			0.324255
$251$	−5.74892	−	9.95742i	−0.362868	−	0.628507i	0.625563	−	0.780173i	$-0.284869\pi$
$251$	−5.74892	−	9.95742i	−0.362868	−	0.628507i	−0.988432	+	0.151667i	$0.951536\pi$
$252$	6.59137	−	11.4166i	0.415217	−	0.719177i
$253$	−4.99781	+	8.65645i	−0.314209	+	0.544227i
$254$	−8.99114			−0.564154
$255$	−0.971932	+	1.68344i	−0.0608648	+	0.105421i
$256$	−11.0554			−0.690964
$257$	5.37055			0.335006			0.167503	−	0.985872i	$-0.446430\pi$
$257$	5.37055			0.335006			0.167503	+	0.985872i	$0.446430\pi$
$258$	−11.0473	+	4.69931i	−0.687773	+	0.292566i
$259$	−0.812014			−0.0504561
$260$	2.13941			0.132680
$261$	−4.70351	+	8.14672i	−0.291140	+	0.504269i
$262$	2.36362			0.146025
$263$	−6.48108	+	11.2256i	−0.399640	+	0.692197i	−0.993681	−	0.112237i	$-0.964198\pi$
$263$	−6.48108	+	11.2256i	−0.399640	+	0.692197i	0.594041	+	0.804435i	$0.297532\pi$
$264$	11.6287	−	20.1414i	0.715695	−	1.23962i
$265$	−3.70823	−	6.42285i	−0.227795	−	0.394552i
$266$	−11.8553			−0.726897
$267$	17.7125	+	30.6790i	1.08399	+	1.87752i
$268$	−7.30275	+	12.6487i	−0.446086	+	0.772644i
$269$	14.5397			0.886498			0.443249	−	0.896398i	$-0.353826\pi$
$269$	14.5397			0.886498			0.443249	+	0.896398i	$0.353826\pi$
$270$	0.375967	−	0.651194i	0.0228806	−	0.0396304i
$271$	−7.91602	−	13.7110i	−0.480864	−	0.832881i	0.518895	−	0.854838i	$-0.326344\pi$
$271$	−7.91602	−	13.7110i	−0.480864	−	0.832881i	−0.999759	+	0.0219570i	$0.993010\pi$
$272$	0.593894	+	1.02865i	0.0360101	+	0.0623713i
$273$	−6.05659	−	10.4903i	−0.366561	−	0.634903i
$274$	−0.699835			−0.0422786
$275$	8.05417	+	13.9502i	0.485684	+	0.841230i
$276$	5.21962	+	9.04064i	0.314184	+	0.544183i
$277$	−12.5521	+	21.7409i	−0.754184	+	1.30628i	0.191595	+	0.981474i	$0.438634\pi$
$277$	−12.5521	+	21.7409i	−0.754184	+	1.30628i	−0.945779	+	0.324811i	$0.894699\pi$
$278$	2.63714	−	4.56766i	0.158165	−	0.273950i
$279$	−28.3065			−1.69466
$280$	4.75021			0.283880
$281$	−2.81287	+	4.87204i	−0.167802	+	0.290641i	−0.937647	−	0.347590i	$-0.887000\pi$
$281$	−2.81287	+	4.87204i	−0.167802	+	0.290641i	0.769845	+	0.638231i	$0.220334\pi$
$282$	1.33078	−	2.30499i	0.0792471	−	0.137260i
$283$	0.417605	+	0.723314i	0.0248241	+	0.0429965i	0.878171	−	0.478348i	$-0.158764\pi$
$283$	0.417605	+	0.723314i	0.0248241	+	0.0429965i	−0.853346	+	0.521344i	$0.825431\pi$
$284$	2.59178	+	4.48910i	0.153794	+	0.266379i
$285$	12.8603			0.761776
$286$	−2.46703	−	4.27303i	−0.145879	−	0.252669i
$287$	−4.45721	−	7.72011i	−0.263101	−	0.455704i
$288$	−10.3441	−	17.9165i	−0.609533	−	1.05574i
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$	−1.44580			−0.0849000
$291$	−19.0162	+	32.9370i	−1.11475	+	1.93080i
$292$	−10.9155	−	18.9061i	−0.638779	−	1.10640i
$293$	12.7737			0.746249			0.373125	−	0.927781i	$-0.378286\pi$
$293$	12.7737			0.746249			0.373125	+	0.927781i	$0.378286\pi$
$294$	0.671917	+	1.16379i	0.0391870	+	0.0678739i
$295$	−4.38040	+	7.58707i	−0.255037	+	0.441737i
$296$	−0.404941	+	0.701379i	−0.0235367	+	0.0407668i
$297$	5.03367			0.292083
$298$	−1.44124	+	2.49631i	−0.0834890	+	0.144607i
$299$	5.19238			0.300283
$300$	16.8232			0.971290
$301$	1.98790	−	16.2937i	0.114581	−	0.939154i
$302$	−10.5111			−0.604847
$303$	−20.8694			−1.19892
$304$	3.92909	−	6.80539i	0.225349	−	0.390316i
$305$	−6.57581			−0.376530
$306$	1.26722	−	2.19489i	0.0724422	−	0.125474i
$307$	15.9704	−	27.6616i	0.911482	−	1.57873i	0.0995089	−	0.995037i	$-0.468273\pi$
$307$	15.9704	−	27.6616i	0.911482	−	1.57873i	0.811973	−	0.583696i	$-0.198394\pi$
$308$	6.78165	+	11.7462i	0.386420	+	0.669299i
$309$	43.7327			2.48787
$310$	−2.17526	−	3.76765i	−0.123546	−	0.213988i
$311$	−5.24146	+	9.07847i	−0.297216	+	0.514793i	−0.975498	−	0.220009i	$-0.929391\pi$
$311$	−5.24146	+	9.07847i	−0.297216	+	0.514793i	0.678282	+	0.734802i	$0.262725\pi$
$312$	−12.0814			−0.683974
$313$	3.38555	−	5.86395i	0.191363	−	0.331450i	−0.754339	−	0.656485i	$-0.772043\pi$
$313$	3.38555	−	5.86395i	0.191363	−	0.331450i	0.945702	+	0.325035i	$0.105376\pi$
$314$	−1.41091	−	2.44377i	−0.0796222	−	0.137910i
$315$	3.36803	+	5.83361i	0.189767	+	0.328687i
$316$	6.99000	+	12.1070i	0.393218	+	0.681074i
$317$	−16.7433			−0.940400			−0.470200	−	0.882560i	$-0.655818\pi$
$317$	−16.7433			−0.940400			−0.470200	+	0.882560i	$0.655818\pi$
$318$	8.93178	+	15.4703i	0.500869	+	0.867531i
$319$	−4.83929	−	8.38190i	−0.270948	−	0.469296i
$320$	0.686995	−	1.18991i	0.0384042	−	0.0665180i
$321$	9.92053	−	17.1829i	0.553710	−	0.959054i
$322$	4.91738			0.274035
$323$	6.61582			0.368114
$324$	−5.27102	+	9.12967i	−0.292834	+	0.507204i
$325$	4.18386	−	7.24666i	0.232079	−	0.401973i
$326$	2.95527	+	5.11867i	0.163677	+	0.283497i
$327$	−9.58564	−	16.6028i	−0.530087	−	0.918138i
$328$	−8.89103			−0.490925
$329$	1.81956	+	3.15157i	0.100315	+	0.173751i
$330$	2.53442	+	4.38974i	0.139515	+	0.241647i
$331$	−6.67211	−	11.5564i	−0.366733	−	0.635199i	0.622320	−	0.782763i	$-0.286190\pi$
$331$	−6.67211	−	11.5564i	−0.366733	−	0.635199i	−0.989053	+	0.147563i	$0.952857\pi$
$332$	−1.32271	+	2.29099i	−0.0725929	+	0.125735i
$333$	−1.14846			−0.0629352
$334$	−2.58967	+	4.48543i	−0.141700	+	0.245432i
$335$	−3.73153	−	6.46320i	−0.203875	−	0.353122i
$336$	7.60385			0.414824
$337$	1.58319	+	2.74217i	0.0862418	+	0.149375i	0.905920	−	0.423449i	$-0.139181\pi$
$337$	1.58319	+	2.74217i	0.0862418	+	0.149375i	−0.819678	+	0.572825i	$0.805848\pi$
$338$	3.37163	−	5.83984i	0.183393	−	0.317645i
$339$	20.1165	−	34.8428i	1.09258	−	1.89240i
$340$	−1.13066			−0.0613184
$341$	14.5618	−	25.2218i	0.788566	−	1.36584i
$342$	−16.7674			−0.906678
$343$	−19.3598			−1.04533
$344$	−13.0824	−	9.84254i	−0.705356	−	0.530674i
$345$	−5.33420			−0.287184
$346$	8.66745			0.465965
$347$	9.65269	−	16.7189i	0.518183	−	0.897520i	−0.481593	−	0.876395i	$-0.659942\pi$
$347$	9.65269	−	16.7189i	0.518183	−	0.897520i	0.999777	−	0.0211253i	$-0.00672489\pi$
$348$	−10.1081			−0.541853
$349$	8.73134	−	15.1231i	0.467378	−	0.809523i	−0.531927	−	0.846790i	$-0.678532\pi$
$349$	8.73134	−	15.1231i	0.467378	−	0.809523i	0.999305	+	0.0372675i	$0.0118654\pi$
$350$	3.96228	−	6.86286i	0.211793	−	0.366835i
$351$	−1.30741	−	2.26450i	−0.0697843	−	0.120870i
$352$	21.2855			1.13452
$353$	10.5329	+	18.2436i	0.560612	+	0.971009i	0.997443	+	0.0714650i	$0.0227674\pi$
$353$	10.5329	+	18.2436i	0.560612	+	0.971009i	−0.436831	+	0.899544i	$0.643899\pi$
$354$	10.5508	−	18.2745i	0.560768	−	0.971278i
$355$	−2.64868			−0.140577
$356$	−10.3025	+	17.8445i	−0.546034	+	0.945758i
$357$	3.20085	+	5.54403i	0.169407	+	0.293421i
$358$	5.81917	+	10.0791i	0.307553	+	0.532697i
$359$	−14.0774	−	24.3828i	−0.742977	−	1.28687i	−0.951134	−	0.308779i	$-0.900080\pi$
$359$	−14.0774	−	24.3828i	−0.742977	−	1.28687i	0.208157	−	0.978096i	$-0.433254\pi$
$360$	6.71839			0.354090
$361$	−12.3845	−	21.4506i	−0.651817	−	1.12898i
$362$	3.97040	+	6.87694i	0.208680	+	0.361444i
$363$	−2.90037	+	5.02359i	−0.152230	+	0.263670i
$364$	3.52283	−	6.10173i	0.184647	−	0.319817i
$365$	11.1551			0.583884
$366$	15.8387			0.827903
$367$	−16.0711	+	27.8359i	−0.838903	+	1.45302i	0.0519103	+	0.998652i	$0.483469\pi$
$367$	−16.0711	+	27.8359i	−0.838903	+	1.45302i	−0.890813	+	0.454370i	$0.849864\pi$
$368$	−1.62972	+	2.82275i	−0.0849548	+	0.147146i
$369$	−6.30399	−	10.9188i	−0.328172	−	0.568411i
$370$	−0.0882552	−	0.152862i	−0.00458817	−	0.00794694i
$371$	−24.4245			−1.26806
$372$	−15.2081	−	26.3412i	−0.788502	−	1.36573i
$373$	−14.4614	−	25.0478i	−0.748782	−	1.29693i	−0.948407	−	0.317056i	$-0.897306\pi$
$373$	−14.4614	−	25.0478i	−0.748782	−	1.29693i	0.199625	−	0.979872i	$-0.436028\pi$
$374$	1.30380	+	2.25825i	0.0674180	+	0.116771i
$375$	−9.15780	+	15.8618i	−0.472907	+	0.819099i
$376$	3.62957			0.187181
$377$	−2.51384	+	4.35411i	−0.129470	+	0.224248i
$378$	−1.23817	−	2.14457i	−0.0636844	−	0.110305i
$379$	4.28489			0.220100			0.110050	−	0.993926i	$-0.464899\pi$
$379$	4.28489			0.220100			0.110050	+	0.993926i	$0.464899\pi$
$380$	3.74010	+	6.47805i	0.191863	+	0.332317i
$381$	16.0601	−	27.8170i	0.822786	−	1.42511i
$382$	−4.00289	+	6.93321i	−0.204806	+	0.354734i
$383$	19.4623			0.994478			0.497239	−	0.867614i	$-0.334347\pi$
$383$	19.4623			0.994478			0.497239	+	0.867614i	$0.334347\pi$
$384$	13.2897	−	23.0184i	0.678185	−	1.17465i
$385$	−6.93052			−0.353212
$386$	12.3946			0.630868
$387$	2.81156	−	23.0448i	0.142920	−	1.17143i
$388$	−22.1216			−1.12306
$389$	−15.2120			−0.771279			−0.385640	−	0.922649i	$-0.626019\pi$
$389$	−15.2120			−0.771279			−0.385640	+	0.922649i	$0.626019\pi$
$390$	1.31654	−	2.28032i	0.0666657	−	0.115468i
$391$	−2.74412			−0.138776
$392$	−0.916289	+	1.58706i	−0.0462796	+	0.0801586i
$393$	−4.22194	+	7.31262i	−0.212969	+	0.368873i
$394$	8.73431	+	15.1283i	0.440028	+	0.762151i
$395$	−7.14345			−0.359426
$396$	9.59152	+	16.6130i	0.481992	+	0.834835i
$397$	−8.05785	+	13.9566i	−0.404412	+	0.700462i	−0.994253	−	0.107058i	$-0.965857\pi$
$397$	−8.05785	+	13.9566i	−0.404412	+	0.700462i	0.589841	+	0.807519i	$0.299190\pi$
$398$	−7.65162			−0.383541
$399$	21.1762	−	36.6783i	1.06014	−	1.83621i
$400$	2.62635	+	4.54898i	0.131318	+	0.227449i
$401$	19.2367	+	33.3190i	0.960635	+	1.66387i	0.720911	+	0.693028i	$0.243724\pi$
$401$	19.2367	+	33.3190i	0.960635	+	1.66387i	0.239725	+	0.970841i	$0.422943\pi$
$402$	8.98790	+	15.5675i	0.448276	+	0.776436i
$403$	−15.1287			−0.753615
$404$	−6.06939	−	10.5125i	−0.301963	−	0.523016i
$405$	−2.69337	−	4.66505i	−0.133834	−	0.231808i
$406$	−2.38071	+	4.12350i	−0.118152	+	0.204646i
$407$	0.590806	−	1.02331i	0.0292852	−	0.0507234i
$408$	6.38490			0.316099
$409$	−32.2260			−1.59347			−0.796736	−	0.604327i	$-0.793442\pi$
$409$	−32.2260			−1.59347			−0.796736	+	0.604327i	$0.793442\pi$
$410$	0.968880	−	1.67815i	0.0478496	−	0.0828779i
$411$	1.25006	−	2.16517i	0.0616609	−	0.106800i
$412$	12.7186	+	22.0293i	0.626603	+	1.08531i
$413$	14.4259	+	24.9864i	0.709852	+	1.22950i
$414$	6.95482			0.341811
$415$	−0.675871	−	1.17064i	−0.0331772	−	0.0574646i
$416$	−5.52853	−	9.57570i	−0.271059	−	0.469487i
$417$	9.42102	+	16.3177i	0.461349	+	0.799081i
$418$	8.62572	−	14.9402i	0.421898	−	0.730749i
$419$	10.1950			0.498059			0.249030	−	0.968496i	$-0.419888\pi$
$419$	10.1950			0.498059			0.249030	+	0.968496i	$0.419888\pi$
$420$	−3.61906	+	6.26839i	−0.176592	+	0.305866i
$421$	−7.88602	−	13.6590i	−0.384341	−	0.665699i	0.607336	−	0.794445i	$-0.292238\pi$
$421$	−7.88602	−	13.6590i	−0.384341	−	0.665699i	−0.991678	+	0.128746i	$0.958905\pi$
$422$	1.13657			0.0553273
$423$	2.57346	+	4.45737i	0.125126	+	0.216725i
$424$	−12.1802	+	21.0967i	−0.591523	+	1.02455i
$425$	−2.21113	+	3.82979i	−0.107256	+	0.185772i
$426$	6.37970			0.309097
$427$	−10.8280	+	18.7546i	−0.524003	+	0.907600i
$428$	11.5406			0.557837
$429$	17.6266			0.851023
$430$	3.28337	−	1.39669i	0.158338	−	0.0673542i
$431$	19.7859			0.953053			0.476527	−	0.879160i	$-0.341896\pi$
$431$	19.7859			0.953053			0.476527	+	0.879160i	$0.341896\pi$
$432$	1.64141			0.0789724
$433$	6.30712	−	10.9243i	0.303101	−	0.524986i	−0.673736	−	0.738972i	$-0.735311\pi$
$433$	6.30712	−	10.9243i	0.303101	−	0.524986i	0.976837	+	0.213986i	$0.0686447\pi$
$434$	−14.3275			−0.687740
$435$	2.58251	−	4.47303i	0.123822	−	0.214466i
$436$	5.57552	−	9.65708i	0.267019	−	0.462490i
$437$	9.07730	+	15.7224i	0.434226	+	0.752102i
$438$	−26.8685			−1.28383
$439$	5.76511	+	9.98547i	0.275154	+	0.476580i	0.970174	−	0.242410i	$-0.0779379\pi$
$439$	5.76511	+	9.98547i	0.275154	+	0.476580i	−0.695020	+	0.718990i	$0.744605\pi$
$440$	−3.45617	+	5.98626i	−0.164766	+	0.285384i
$441$	−2.59870			−0.123748
$442$	0.677281	−	1.17308i	0.0322150	−	0.0557979i
$443$	11.2179	+	19.4300i	0.532979	+	0.923147i	0.999258	+	0.0385092i	$0.0122609\pi$
$443$	11.2179	+	19.4300i	0.532979	+	0.923147i	−0.466279	+	0.884638i	$0.654406\pi$
$444$	−0.617027	−	1.06872i	−0.0292828	−	0.0507193i
$445$	−5.26436	−	9.11813i	−0.249554	−	0.432241i
$446$	10.1496			0.480599
$447$	−5.14875	−	8.91790i	−0.243528	−	0.421802i
$448$	−2.26247	−	3.91871i	−0.106892	−	0.185142i
$449$	−18.8451	+	32.6407i	−0.889357	+	1.54041i	−0.0487194	+	0.998813i	$0.515514\pi$
$449$	−18.8451	+	32.6407i	−0.889357	+	1.54041i	−0.840637	+	0.541598i	$0.817819\pi$
$450$	5.60398	−	9.70638i	0.264174	−	0.457563i
$451$	12.9719			0.610824
$452$	23.4016			1.10072
$453$	18.7752	−	32.5196i	0.882135	−	1.52790i
$454$	−5.98083	+	10.3591i	−0.280694	+	0.486177i
$455$	1.80008	+	3.11784i	0.0843893	+	0.146166i
$456$	−21.1207	−	36.5821i	−0.989066	−	1.71311i
$457$	−28.5256			−1.33437			−0.667186	−	0.744891i	$-0.732501\pi$
$457$	−28.5256			−1.33437			−0.667186	+	0.744891i	$0.732501\pi$
$458$	1.84013	+	3.18720i	0.0859836	+	0.148928i
$459$	0.690953	+	1.19677i	0.0322509	+	0.0558602i
$460$	−1.55133	−	2.68698i	−0.0723310	−	0.125281i
$461$	−15.6485	+	27.1040i	−0.728823	+	1.26236i	0.228559	+	0.973530i	$0.426599\pi$
$461$	−15.6485	+	27.1040i	−0.728823	+	1.26236i	−0.957381	+	0.288827i	$0.906735\pi$
$462$	16.6931			0.776633
$463$	12.0557	−	20.8810i	0.560275	−	0.970424i	−0.437197	−	0.899366i	$-0.644029\pi$
$463$	12.0557	−	20.8810i	0.560275	−	0.970424i	0.997472	−	0.0710588i	$-0.0226378\pi$
$464$	−1.57803	−	2.73322i	−0.0732580	−	0.126887i
$465$	15.5419			0.720740
$466$	−2.82170	−	4.88733i	−0.130713	−	0.226401i
$467$	1.69581	−	2.93722i	0.0784725	−	0.135918i	−0.824119	−	0.566417i	$-0.808329\pi$
$467$	1.69581	−	2.93722i	0.0784725	−	0.135918i	0.902591	+	0.430499i	$0.141662\pi$
$468$	4.98247	−	8.62988i	0.230315	−	0.398916i
$469$	−24.5780			−1.13491
$470$	−0.395524	+	0.685067i	−0.0182442	+	0.0315998i
$471$	10.0808			0.464497
$472$	28.7761			1.32453
$473$	19.0871	+	14.3602i	0.877627	+	0.660282i
$474$	17.2060			0.790296
$475$	29.2569			1.34240
$476$	−1.86178	+	3.22470i	−0.0853347	+	0.147804i
$477$	−34.5444			−1.58168
$478$	7.51037	−	13.0083i	0.343516	−	0.594988i
$479$	17.0912	−	29.6029i	0.780919	−	1.35259i	−0.150489	−	0.988612i	$-0.548085\pi$
$479$	17.0912	−	29.6029i	0.780919	−	1.35259i	0.931407	−	0.363979i	$-0.118582\pi$
$480$	5.67954	+	9.83725i	0.259234	+	0.449007i
$481$	−0.613807			−0.0279872
$482$	5.41962	+	9.38706i	0.246857	+	0.427569i
$483$	−8.78351	+	15.2135i	−0.399664	+	0.692238i
$484$	−3.37402			−0.153364
$485$	5.65182	−	9.78924i	0.256636	−	0.444506i
$486$	7.97124	+	13.8066i	0.361583	+	0.626280i
$487$	−9.40789	−	16.2949i	−0.426312	−	0.738394i	0.570230	−	0.821485i	$-0.306854\pi$
$487$	−9.40789	−	16.2949i	−0.426312	−	0.738394i	−0.996542	+	0.0830909i	$0.973521\pi$
$488$	10.7996	+	18.7054i	0.488874	+	0.846755i
$489$	−21.1150			−0.954855
$490$	−0.199701	−	0.345893i	−0.00902158	−	0.0156258i
$491$	10.8434	+	18.7813i	0.489356	+	0.847589i	0.999925	−	0.0122475i	$-0.00389859\pi$
$491$	10.8434	+	18.7813i	0.489356	+	0.847589i	−0.510569	+	0.859837i	$0.670565\pi$
$492$	6.77382	−	11.7326i	0.305388	−	0.528947i
$493$	1.32854	−	2.30110i	0.0598346	−	0.103636i
$494$	−8.96153			−0.403198
$495$	−9.80208			−0.440571
$496$	4.74841	−	8.22448i	0.213210	−	0.369290i
$497$	−4.36142	+	7.55420i	−0.195636	+	0.338852i
$498$	1.62793	+	2.81965i	0.0729491	+	0.126352i
$499$	−10.0596	−	17.4238i	−0.450331	−	0.779996i	0.548075	−	0.836429i	$-0.315361\pi$
$499$	−10.0596	−	17.4238i	−0.450331	−	0.779996i	−0.998406	+	0.0564329i	$0.982027\pi$
$500$	−10.6533			−0.476431
$501$	−9.25142	−	16.0239i	−0.413323	−	0.715897i
$502$	−4.11549	−	7.12824i	−0.183683	−	0.318149i
$503$	−2.20467	−	3.81860i	−0.0983014	−	0.170263i	0.812680	−	0.582710i	$-0.198008\pi$
$503$	−2.20467	−	3.81860i	−0.0983014	−	0.170263i	−0.910982	+	0.412447i	$0.864674\pi$
$504$	11.0628	−	19.1613i	0.492775	−	0.853512i
$505$	6.20263			0.276013
$506$	−3.57779	+	6.19692i	−0.159052	+	0.275487i
$507$	12.0450	+	20.8625i	0.534935	+	0.926535i
$508$	18.6829			0.828918
$509$	4.01279	+	6.95036i	0.177864	+	0.308069i	0.941149	−	0.337993i	$-0.109748\pi$
$509$	4.01279	+	6.95036i	0.177864	+	0.308069i	−0.763285	+	0.646062i	$0.776415\pi$
$510$	−0.695780	+	1.20513i	−0.0308097	+	0.0533639i
$511$	18.3684	−	31.8150i	0.812571	−	1.40741i
$512$	12.8718			0.568859
$513$	4.57122	−	7.91759i	0.201824	−	0.349570i
$514$	3.84463			0.169579
$515$	−12.9979			−0.572754
$516$	22.9553	−	9.76480i	1.01055	−	0.429871i
$517$	−5.29551			−0.232896
$518$	−0.581298			−0.0255408
$519$	−15.4820	+	26.8156i	−0.679583	+	1.17707i
$520$	3.59072			0.157464
$521$	20.5791	−	35.6440i	0.901586	−	1.56159i	0.0761516	−	0.997096i	$-0.475737\pi$
$521$	20.5791	−	35.6440i	0.901586	−	1.56159i	0.825435	−	0.564497i	$-0.190930\pi$
$522$	−3.36711	+	5.83201i	−0.147375	+	0.255260i
$523$	6.90801	+	11.9650i	0.302066	+	0.523194i	0.976604	−	0.215047i	$-0.0689903\pi$
$523$	6.90801	+	11.9650i	0.302066	+	0.523194i	−0.674538	+	0.738240i	$0.735657\pi$
$524$	−4.91141			−0.214556
$525$	14.1550	+	24.5172i	0.617774	+	1.07002i
$526$	−4.63963	+	8.03607i	−0.202297	+	0.350389i
$527$	7.99538			0.348284
$528$	−5.53242	+	9.58244i	−0.240768	+	0.417022i
$529$	7.73490	+	13.3972i	0.336300	+	0.582489i
$530$	−2.65462	−	4.59794i	−0.115309	−	0.199722i
$531$	20.4030	+	35.3391i	0.885416	+	1.53359i
$532$	24.6344			1.06804
$533$	−3.36924	−	5.83569i	−0.145938	−	0.252772i
$534$	12.6799	+	21.9622i	0.548713	+	0.950399i
$535$	−2.94849	+	5.10694i	−0.127474	+	0.220792i
$536$	−12.2567	+	21.2293i	−0.529410	+	0.916966i
$537$	−41.5773			−1.79419
$538$	10.4085			0.448744
$539$	1.33686	−	2.31551i	0.0575826	−	0.0997359i
$540$	−0.781230	+	1.35313i	−0.0336188	+	0.0582294i
$541$	2.58176	+	4.47174i	0.110999	+	0.192255i	0.916173	−	0.400783i	$-0.131262\pi$
$541$	2.58176	+	4.47174i	0.110999	+	0.192255i	−0.805175	+	0.593038i	$0.797928\pi$
$542$	−5.66686	−	9.81530i	−0.243413	−	0.421603i
$543$	−28.3681			−1.21739
$544$	2.92178	+	5.06067i	0.125270	+	0.216974i
$545$	2.84896	+	4.93454i	0.122036	+	0.211373i
$546$	−4.33575	−	7.50973i	−0.185553	−	0.321387i
$547$	−9.52713	+	16.5015i	−0.407351	+	0.705552i	−0.994592	−	0.103860i	$-0.966881\pi$
$547$	−9.52713	+	16.5015i	−0.407351	+	0.705552i	0.587241	+	0.809412i	$0.300214\pi$
$548$	1.45420			0.0621204
$549$	−15.3144	+	26.5253i	−0.653603	+	1.13207i
$550$	5.76576	+	9.98658i	0.245853	+	0.425829i
$551$	−17.5788			−0.748882
$552$	8.76047	+	15.1736i	0.372870	+	0.645830i
$553$	−11.7627	+	20.3736i	−0.500201	+	0.866374i
$554$	−8.98572	+	15.5637i	−0.381767	+	0.661239i
$555$	0.630572			0.0267663
$556$	−5.47977	+	9.49123i	−0.232394	+	0.402518i
$557$	25.3072			1.07230			0.536150	−	0.844123i	$-0.319878\pi$
$557$	25.3072			1.07230			0.536150	+	0.844123i	$0.319878\pi$
$558$	−20.2638			−0.857836
$559$	1.50267	−	12.3165i	0.0635562	−	0.520934i
$560$	−2.25995			−0.0955003
$561$	−9.31551			−0.393301
$562$	−2.01366	+	3.48776i	−0.0849411	+	0.147122i
$563$	25.0035			1.05377			0.526885	−	0.849936i	$-0.323360\pi$
$563$	25.0035			1.05377			0.526885	+	0.849936i	$0.323360\pi$
$564$	−2.76526	+	4.78958i	−0.116439	+	0.201678i
$565$	−5.97884	+	10.3557i	−0.251532	+	0.435666i
$566$	0.298952	+	0.517800i	0.0125659	+	0.0217648i
$567$	−17.7400			−0.745011
$568$	4.34998	+	7.53438i	0.182521	+	0.316136i
$569$	0.394091	−	0.682585i	0.0165211	−	0.0286155i	−0.857647	−	0.514239i	$-0.828074\pi$
$569$	0.394091	−	0.682585i	0.0165211	−	0.0286155i	0.874168	+	0.485624i	$0.161408\pi$
$570$	9.20631			0.385610
$571$	18.0687	−	31.2960i	0.756153	−	1.30970i	−0.188646	−	0.982045i	$-0.560410\pi$
$571$	18.0687	−	31.2960i	0.756153	−	1.30970i	0.944799	−	0.327651i	$-0.106257\pi$
$572$	5.12630	+	8.87901i	0.214341	+	0.371250i
$573$	−14.3001	−	24.7685i	−0.597394	−	1.03472i
$574$	−3.19079	−	5.52662i	−0.133181	−	0.230677i
$575$	−12.1352			−0.506074
$576$	−3.19989	−	5.54237i	−0.133329	−	0.230932i
$577$	−12.4603	−	21.5820i	−0.518731	−	0.898469i	−0.999763	−	0.0217655i	$-0.993071\pi$
$577$	−12.4603	−	21.5820i	−0.518731	−	0.898469i	0.481032	−	0.876703i	$-0.340262\pi$
$578$	−0.357936	+	0.619964i	−0.0148882	+	0.0257871i
$579$	−22.1394	+	38.3466i	−0.920084	+	1.59363i
$580$	3.00425			0.124745
$581$	−4.45167			−0.184686
$582$	−13.6132	+	23.5787i	−0.564284	+	0.977368i
$583$	17.7708	−	30.7800i	0.735992	−	1.27478i
$584$	−18.3202	−	31.7316i	−0.758096	−	1.31306i
$585$	2.54592	+	4.40967i	0.105261	+	0.182317i
$586$	9.14436			0.377750
$587$	−0.417401	−	0.722960i	−0.0172280	−	0.0298398i	0.857283	−	0.514846i	$-0.172151\pi$
$587$	−0.417401	−	0.722960i	−0.0172280	−	0.0298398i	−0.874511	+	0.485006i	$0.838817\pi$
$588$	−1.39619	−	2.41827i	−0.0575779	−	0.0997279i
$589$	−26.4480	−	45.8093i	−1.08977	−	1.88754i
$590$	−3.13581	+	5.43138i	−0.129099	+	0.223606i
$591$	−62.4056			−2.56702
$592$	0.192654	−	0.333686i	0.00791802	−	0.0137144i
$593$	−1.99330	−	3.45251i	−0.0818552	−	0.141777i	0.822192	−	0.569211i	$-0.192751\pi$
$593$	−1.99330	−	3.45251i	−0.0818552	−	0.141777i	−0.904047	+	0.427433i	$0.859418\pi$
$594$	3.60347			0.147852
$595$	−0.951327	−	1.64775i	−0.0390006	−	0.0675510i
$596$	2.99479	−	5.18713i	0.122671	−	0.212473i
$597$	13.6675	−	23.6727i	0.559372	−	0.968861i
$598$	3.71708			0.152003
$599$	−14.7598	+	25.5648i	−0.603071	+	1.04455i	0.389283	+	0.921118i	$0.372723\pi$
$599$	−14.7598	+	25.5648i	−0.603071	+	1.04455i	−0.992353	+	0.123431i	$0.960610\pi$
$600$	28.2357			1.15272
$601$	2.24560			0.0916000			0.0458000	−	0.998951i	$-0.485416\pi$
$601$	2.24560			0.0916000			0.0458000	+	0.998951i	$0.485416\pi$
$602$	1.42309	−	11.6642i	0.0580007	−	0.475398i
$603$	−34.7615			−1.41560
$604$	21.8413			0.888709
$605$	0.862022	−	1.49307i	0.0350462	−	0.0607017i
$606$	−14.9399			−0.606891
$607$	1.60838	−	2.78580i	0.0652821	−	0.113072i	−0.831537	−	0.555469i	$-0.812539\pi$
$607$	1.60838	−	2.78580i	0.0652821	−	0.113072i	0.896819	+	0.442397i	$0.145872\pi$
$608$	19.3299	−	33.4805i	0.783933	−	1.35781i
$609$	−8.50493	−	14.7310i	−0.344637	−	0.596929i
$610$	−4.70744			−0.190599
$611$	1.37542	+	2.38229i	0.0556434	+	0.0963772i
$612$	−2.63318	+	4.56081i	−0.106440	+	0.184360i
$613$	−28.1969			−1.13886			−0.569430	−	0.822040i	$-0.692836\pi$
$613$	−28.1969			−1.13886			−0.569430	+	0.822040i	$0.692836\pi$
$614$	11.4328	−	19.8022i	0.461390	−	0.799152i
$615$	3.46126	+	5.99508i	0.139572	+	0.241745i
$616$	11.3821	+	19.7144i	0.458599	+	0.794317i
$617$	6.70101	+	11.6065i	0.269773	+	0.467260i	0.968803	−	0.247832i	$-0.0797181\pi$
$617$	6.70101	+	11.6065i	0.269773	+	0.467260i	−0.699030	+	0.715092i	$0.746385\pi$
$618$	31.3071			1.25936
$619$	8.17065	+	14.1520i	0.328406	+	0.568816i	0.982196	−	0.187860i	$-0.0601552\pi$
$619$	8.17065	+	14.1520i	0.328406	+	0.568816i	−0.653790	+	0.756676i	$0.726822\pi$
$620$	4.52001	+	7.82888i	0.181528	+	0.314416i
$621$	−1.89606	+	3.28407i	−0.0760862	+	0.131785i
$622$	−3.75221	+	6.49903i	−0.150450	+	0.260587i
$623$	−34.6740			−1.38919
$624$	5.74781			0.230096
$625$	−8.33386	+	14.4347i	−0.333354	+	0.577386i
$626$	2.42362	−	4.19784i	0.0968675	−	0.167779i
$627$	30.8149	+	53.3729i	1.23063	+	2.13151i
$628$	2.93176	+	5.07795i	0.116990	+	0.202632i
$629$	0.324391			0.0129343
$630$	2.41108	+	4.17612i	0.0960599	+	0.166381i
$631$	6.37912	+	11.0490i	0.253949	+	0.439852i	0.964609	−	0.263683i	$-0.0849372\pi$
$631$	6.37912	+	11.0490i	0.253949	+	0.439852i	−0.710661	+	0.703535i	$0.751604\pi$
$632$	11.7318	+	20.3201i	0.466667	+	0.808292i
$633$	−2.03016	+	3.51634i	−0.0806917	+	0.139762i
$634$	−11.9861			−0.476029
$635$	−4.77325	+	8.26752i	−0.189421	+	0.328086i
$636$	−18.5595	−	32.1460i	−0.735933	−	1.27467i
$637$	−1.38890			−0.0550304
$638$	−3.46432	−	6.00037i	−0.137154	−	0.237557i
$639$	−6.16851	+	10.6842i	−0.244022	+	0.422659i
$640$	−3.94983	+	6.84131i	−0.156131	+	0.270426i
$641$	34.5437			1.36439			0.682197	−	0.731168i	$-0.261025\pi$
$641$	34.5437			1.36439			0.682197	+	0.731168i	$0.261025\pi$
$642$	7.10184	−	12.3007i	0.280287	−	0.485472i
$643$	−6.53101			−0.257558			−0.128779	−	0.991673i	$-0.541106\pi$
$643$	−6.53101			−0.257558			−0.128779	+	0.991673i	$0.541106\pi$
$644$	−10.2179			−0.402642
$645$	−1.54372	+	12.6530i	−0.0607837	+	0.498210i
$646$	4.73608			0.186339
$647$	−35.2094			−1.38422			−0.692112	−	0.721790i	$-0.743320\pi$
$647$	−35.2094			−1.38422			−0.692112	+	0.721790i	$0.743320\pi$
$648$	−8.84674	+	15.3230i	−0.347533	+	0.601944i
$649$	−41.9841			−1.64802
$650$	2.99511	−	5.18769i	0.117478	−	0.203478i
$651$	25.5920	−	44.3266i	1.00303	−	1.73730i
$652$	−6.14081	−	10.6362i	−0.240493	−	0.416546i
$653$	−33.6405			−1.31645			−0.658227	−	0.752820i	$-0.728693\pi$
$653$	−33.6405			−1.31645			−0.658227	+	0.752820i	$0.728693\pi$
$654$	−6.86210	−	11.8855i	−0.268329	−	0.464760i
$655$	1.25481	−	2.17339i	0.0490294	−	0.0849214i
$656$	4.22997			0.165153
$657$	25.9791	−	44.9971i	1.01354	−	1.75550i
$658$	1.30257	+	2.25612i	0.0507795	+	0.0879527i
$659$	3.81676	+	6.61083i	0.148680	+	0.257521i	0.930740	−	0.365682i	$-0.119164\pi$
$659$	3.81676	+	6.61083i	0.148680	+	0.257521i	−0.782060	+	0.623203i	$0.785831\pi$
$660$	−5.26632	−	9.12153i	−0.204991	−	0.355055i
$661$	25.0604			0.974738			0.487369	−	0.873196i	$-0.337957\pi$
$661$	25.0604			0.974738			0.487369	+	0.873196i	$0.337957\pi$
$662$	−4.77638	−	8.27294i	−0.185639	−	0.321537i
$663$	2.41954	+	4.19077i	0.0939673	+	0.162756i
$664$	−2.21999	+	3.84514i	−0.0861525	+	0.149220i
$665$	−6.29381	+	10.9012i	−0.244063	+	0.422730i
$666$	−0.822150			−0.0318577
$667$	7.29136			0.282323
$668$	5.38112	−	9.32037i	0.208202	−	0.360616i
$669$	−18.1295	+	31.4012i	−0.700926	+	1.21404i
$670$	−2.67130	−	4.62683i	−0.103201	−	0.178750i
$671$	−15.7565	−	27.2911i	−0.608273	−	1.05356i
$672$	37.4087			1.44307
$673$	−21.9911	−	38.0897i	−0.847695	−	1.46825i	−0.883260	−	0.468884i	$-0.844656\pi$
$673$	−21.9911	−	38.0897i	−0.847695	−	1.46825i	0.0355644	−	0.999367i	$-0.488677\pi$
$674$	1.13336	+	1.96304i	0.0436555	+	0.0756135i
$675$	3.05558	+	5.29241i	0.117609	+	0.203705i
$676$	−7.00599	+	12.1347i	−0.269461	+	0.466720i
$677$	14.8738			0.571645			0.285822	−	0.958283i	$-0.407733\pi$
$677$	14.8738			0.571645			0.285822	+	0.958283i	$0.407733\pi$
$678$	14.4008	−	24.9430i	0.553061	−	0.957929i
$679$	−18.6130	−	32.2387i	−0.714303	−	1.23721i
$680$	−1.89766			−0.0727720
$681$	−21.3661	−	37.0072i	−0.818752	−	1.41812i
$682$	10.4244	−	18.0556i	0.399171	−	0.691384i
$683$	3.03887	−	5.26348i	0.116279	−	0.201402i	−0.802011	−	0.597309i	$-0.796237\pi$
$683$	3.03887	−	5.26348i	0.116279	−	0.201402i	0.918290	+	0.395908i	$0.129570\pi$
$684$	34.8413			1.33219
$685$	−0.371531	+	0.643511i	−0.0141955	+	0.0245873i
$686$	−13.8591			−0.529144
$687$	−13.1475			−0.501609
$688$	6.22405	+	4.68266i	0.237290	+	0.178525i
$689$	−18.4627			−0.703371
$690$	−3.81861			−0.145372
$691$	−16.5272	+	28.6259i	−0.628724	+	1.08898i	0.359084	+	0.933305i	$0.383089\pi$
$691$	−16.5272	+	28.6259i	−0.628724	+	1.08898i	−0.987808	+	0.155677i	$0.950244\pi$
$692$	−18.0103			−0.684648
$693$	−16.1405	+	27.9562i	−0.613127	+	1.06197i
$694$	6.91010	−	11.9686i	0.262304	−	0.454323i
$695$	−2.80003	−	4.84980i	−0.106211	−	0.183963i
$696$	−16.9652			−0.643065
$697$	1.78061	+	3.08411i	0.0674454	+	0.116819i
$698$	6.25053	−	10.8262i	0.236586	−	0.409779i
$699$	20.1607			0.762548
$700$	−8.23329	+	14.2605i	−0.311189	+	0.538996i
$701$	13.0361	+	22.5792i	0.492367	+	0.852805i	0.999961	−	0.00879148i	$-0.00279845\pi$
$701$	13.0361	+	22.5792i	0.492367	+	0.852805i	−0.507594	+	0.861596i	$0.669465\pi$
$702$	−0.935938	−	1.62109i	−0.0353247	−	0.0611842i
$703$	−1.07306	−	1.85859i	−0.0404711	−	0.0700980i
$704$	6.58452			0.248164
$705$	−1.41298	−	2.44736i	−0.0532161	−	0.0921730i
$706$	7.54025	+	13.0601i	0.283781	+	0.491523i
$707$	10.2135	−	17.6903i	0.384118	−	0.665312i
$708$	−21.9237	+	37.9729i	−0.823942	+	1.42711i
$709$	18.5267			0.695787			0.347893	−	0.937534i	$-0.386897\pi$
$709$	18.5267			0.695787			0.347893	+	0.937534i	$0.386897\pi$
$710$	−1.89612			−0.0711600
$711$	−16.6364	+	28.8151i	−0.623914	+	1.08065i
$712$	−17.2915	+	29.9498i	−0.648027	+	1.12242i
$713$	10.9701	+	19.0009i	0.410835	+	0.711587i
$714$	2.29140	+	3.96882i	0.0857535	+	0.148529i
$715$	−5.23883			−0.195921
$716$	−12.0918	−	20.9436i	−0.451891	−	0.782698i
$717$	26.8303	+	46.4715i	1.00200	+	1.73551i
$718$	−10.0776	−	17.4550i	−0.376094	−	0.651414i
$719$	17.2430	−	29.8657i	0.643054	−	1.11380i	−0.341693	−	0.939812i	$-0.611000\pi$
$719$	17.2430	−	29.8657i	0.643054	−	1.11380i	0.984747	−	0.173991i	$-0.0556665\pi$
$720$	−3.19632			−0.119120
$721$	−21.4028	+	37.0707i	−0.797082	+	1.38059i
$722$	−8.86575	−	15.3559i	−0.329949	−	0.571488i
$723$	−38.7225			−1.44011
$724$	−8.25018	−	14.2897i	−0.306616	−	0.531074i
$725$	5.87516	−	10.1761i	0.218198	−	0.377930i
$726$	−2.07629	+	3.59625i	−0.0770585	+	0.133469i
$727$	−40.8914			−1.51658			−0.758290	−	0.651918i	$-0.773965\pi$
$727$	−40.8914			−1.51658			−0.758290	+	0.651918i	$0.773965\pi$
$728$	5.91263	−	10.2410i	0.219137	−	0.379556i
$729$	−35.6926			−1.32195
$730$	7.98562			0.295561
$731$	−0.794147	+	6.50917i	−0.0293726	+	0.240750i
$732$	−32.9116			−1.21645
$733$	19.2856			0.712330			0.356165	−	0.934423i	$-0.384084\pi$
$733$	19.2856			0.712330			0.356165	+	0.934423i	$0.384084\pi$
$734$	−11.5048	+	19.9270i	−0.424651	+	0.735517i
$735$	1.42684			0.0526298
$736$	−8.01771	+	13.8871i	−0.295537	+	0.511885i
$737$	17.8825	−	30.9734i	0.658710	−	1.14092i
$738$	−4.51285	−	7.81649i	−0.166120	−	0.287729i
$739$	−7.88800			−0.290165			−0.145082	−	0.989420i	$-0.546345\pi$
$739$	−7.88800			−0.290165			−0.145082	+	0.989420i	$0.546345\pi$
$740$	0.183387	+	0.317636i	0.00674145	+	0.0116765i
$741$	16.0073	−	27.7254i	0.588042	−	1.01852i
$742$	−17.4848			−0.641889
$743$	13.4564	−	23.3072i	0.493669	−	0.855060i	−0.506304	−	0.862355i	$-0.668989\pi$
$743$	13.4564	−	23.3072i	0.493669	−	0.855060i	0.999973	+	0.00729512i	$0.00232213\pi$
$744$	−25.5248	−	44.2103i	−0.935786	−	1.62083i
$745$	1.53027	+	2.65050i	0.0560646	+	0.0971068i
$746$	−10.3525	−	17.9311i	−0.379032	−	0.656503i
$747$	−6.29615			−0.230364
$748$	−2.70920	−	4.69247i	−0.0990581	−	0.171574i
$749$	9.71022	+	16.8186i	0.354804	+	0.614538i
$750$	−6.55582	+	11.3550i	−0.239385	+	0.414626i
$751$	−14.8378	+	25.6999i	−0.541440	+	0.937801i	0.457382	+	0.889270i	$0.348787\pi$
$751$	−14.8378	+	25.6999i	−0.541440	+	0.937801i	−0.998822	+	0.0485308i	$0.984546\pi$
$752$	−1.72679			−0.0629696
$753$	29.4047			1.07157
$754$	−1.79959	+	3.11699i	−0.0655373	+	0.113514i
$755$	−5.58019	+	9.66517i	−0.203084	+	0.351752i
$756$	2.57281	+	4.45624i	0.0935722	+	0.162072i
$757$	12.6905	+	21.9806i	0.461244	+	0.798898i	0.999023	−	0.0441880i	$-0.0140700\pi$
$757$	12.6905	+	21.9806i	0.461244	+	0.798898i	−0.537780	+	0.843086i	$0.680737\pi$
$758$	3.06744			0.111414
$759$	−12.7814	−	22.1381i	−0.463937	−	0.803563i
$760$	6.27729	+	10.8726i	0.227701	+	0.394390i
$761$	8.79880	+	15.2400i	0.318956	+	0.552448i	0.980271	−	0.197660i	$-0.0633344\pi$
$761$	8.79880	+	15.2400i	0.318956	+	0.552448i	−0.661314	+	0.750109i	$0.730001\pi$
$762$	11.4970	−	19.9134i	0.416493	−	0.721387i
$763$	18.7649			0.679333
$764$	8.31768	−	14.4066i	0.300923	−	0.521214i
$765$	−1.34550	−	2.33047i	−0.0486465	−	0.0842582i
$766$	13.9325			0.503403
$767$	10.9046	+	18.8874i	0.393744	+	0.681984i
$768$	14.1366	−	24.4854i	0.510112	−	0.883540i
$769$	−1.91849	+	3.32292i	−0.0691825	+	0.119828i	−0.898542	−	0.438888i	$-0.855372\pi$
$769$	−1.91849	+	3.32292i	−0.0691825	+	0.119828i	0.829359	+	0.558716i	$0.188706\pi$
$770$	−4.96137			−0.178795
$771$	−6.86735	+	11.8946i	−0.247322	+	0.428374i
$772$	−25.7550			−0.926941
$773$	−14.7386			−0.530111			−0.265055	−	0.964233i	$-0.585390\pi$
$773$	−14.7386			−0.530111			−0.265055	+	0.964233i	$0.585390\pi$
$774$	2.01272	−	16.4971i	0.0723457	−	0.592977i
$775$	35.3577			1.27008
$776$	−37.1284			−1.33283
$777$	1.03833	−	1.79843i	0.0372498	−	0.0645185i
$778$	−10.8899			−0.390420
$779$	11.7802	−	20.4039i	0.422069	−	0.731045i
$780$	−2.73567	+	4.73832i	−0.0979527	+	0.169659i
$781$	−6.34658	−	10.9926i	−0.227098	−	0.393346i
$782$	−1.96444			−0.0702483
$783$	−1.83592	−	3.17991i	−0.0656105	−	0.113641i
$784$	0.435931	−	0.755055i	0.0155690	−	0.0269663i
$785$	−2.99612			−0.106936
$786$	−3.02237	+	5.23490i	−0.107804	+	0.186723i
$787$	24.7154	+	42.8084i	0.881010	+	1.52595i	0.850219	+	0.526429i	$0.176469\pi$
$787$	24.7154	+	42.8084i	0.881010	+	1.52595i	0.0307913	+	0.999526i	$0.490197\pi$
$788$	−18.1492	−	31.4353i	−0.646539	−	1.11984i
$789$	−16.5748	−	28.7084i	−0.590078	−	1.02204i
$790$	−5.11380			−0.181941
$791$	19.6900	+	34.1041i	0.700096	+	1.21260i
$792$	16.0982	+	27.8828i	0.572023	+	0.990773i
$793$	−8.18496	+	14.1768i	−0.290656	+	0.503432i
$794$	−5.76839	+	9.99115i	−0.204713	+	0.354573i
$795$	18.9669			0.672688
$796$	15.8995			0.563541
$797$	11.3494	−	19.6577i	0.402015	−	0.696311i	−0.591954	−	0.805972i	$-0.701643\pi$
$797$	11.3494	−	19.6577i	0.402015	−	0.696311i	0.993969	+	0.109661i	$0.0349765\pi$
$798$	15.1595	−	26.2570i	0.536640	−	0.929488i
$799$	−0.726895	−	1.25902i	−0.0257157	−	0.0445409i
$800$	12.9209	+	22.3796i	0.456821	+	0.791238i
$801$	−49.0407			−1.73277
$802$	13.7710	+	23.8521i	0.486272	+	0.842248i
$803$	26.7291	+	46.2961i	0.943248	+	1.63375i
$804$	−18.6761	−	32.3480i	−0.658656	−	1.14083i
$805$	2.61056	−	4.52162i	0.0920100	−	0.159366i
$806$	−10.8302			−0.381479
$807$	−18.5919	+	32.2022i	−0.654467	+	1.13357i
$808$	−10.1867	−	17.6439i	−0.358367	−	0.620710i
$809$	−18.3774			−0.646117			−0.323058	−	0.946379i	$-0.604711\pi$
$809$	−18.3774			−0.646117			−0.323058	+	0.946379i	$0.604711\pi$
$810$	−1.92811	−	3.33958i	−0.0677468	−	0.117341i
$811$	−17.0717	+	29.5690i	−0.599468	+	1.03831i	0.393432	+	0.919354i	$0.371288\pi$
$811$	−17.0717	+	29.5690i	−0.599468	+	1.03831i	−0.992900	+	0.118955i	$0.962046\pi$
$812$	4.94692	−	8.56831i	0.173603	−	0.300689i
$813$	40.4891			1.42001
$814$	0.422942	−	0.732557i	0.0148241	−	0.0256761i
$815$	6.27562			0.219825
$816$	−3.03766			−0.106339
$817$	39.9211	−	16.9817i	1.39666	−	0.594115i
$818$	−23.0697			−0.806613
$819$	16.7689			0.585952
$820$	−2.01325	+	3.48706i	−0.0703059	+	0.121773i
$821$	−22.3934			−0.781536			−0.390768	−	0.920489i	$-0.627790\pi$
$821$	−22.3934			−0.781536			−0.390768	+	0.920489i	$0.627790\pi$
$822$	0.894883	−	1.54998i	0.0312126	−	0.0540619i
$823$	−26.9816	+	46.7335i	−0.940520	+	1.62903i	−0.176038	+	0.984383i	$0.556328\pi$
$823$	−26.9816	+	46.7335i	−0.940520	+	1.62903i	−0.764482	+	0.644645i	$0.777005\pi$
$824$	21.3466	+	36.9735i	0.743645	+	1.28803i
$825$	−41.1956			−1.43425
$826$	10.3271	+	17.8871i	0.359326	+	0.622371i
$827$	−18.4962	+	32.0363i	−0.643175	+	1.11401i	0.341545	+	0.939866i	$0.389050\pi$
$827$	−18.4962	+	32.0363i	−0.643175	+	1.11401i	−0.984720	+	0.174146i	$0.944283\pi$
$828$	−14.4516			−0.502226
$829$	−12.0306	+	20.8377i	−0.417841	+	0.723722i	−0.995722	−	0.0923990i	$-0.970546\pi$
$829$	−12.0306	+	20.8377i	−0.417841	+	0.723722i	0.577881	+	0.816121i	$0.303880\pi$
$830$	−0.483838	−	0.838031i	−0.0167943	−	0.0290885i
$831$	−32.1009	−	55.6005i	−1.11357	−	1.92876i
$832$	−1.71022	−	2.96218i	−0.0592911	−	0.102695i
$833$	0.734022			0.0254324
$834$	6.74425	+	11.6814i	0.233534	+	0.404493i
$835$	2.74962	+	4.76249i	0.0951547	+	0.164813i
$836$	−17.9236	+	31.0445i	−0.619899	+	1.07370i
$837$	5.52443	−	9.56860i	0.190952	−	0.330739i
$838$	7.29833			0.252117
$839$	−1.33263			−0.0460074			−0.0230037	−	0.999735i	$-0.507323\pi$
$839$	−1.33263			−0.0460074			−0.0230037	+	0.999735i	$0.507323\pi$
$840$	−6.07413	+	10.5207i	−0.209577	+	0.362998i
$841$	10.9699	−	19.0005i	0.378274	−	0.655190i
$842$	−5.64539	−	9.77810i	−0.194553	−	0.336976i
$843$	−7.19367	−	12.4598i	−0.247763	−	0.429139i
$844$	−2.36170			−0.0812931
$845$	−3.57989	−	6.20056i	−0.123152	−	0.213306i
$846$	1.84227	+	3.19091i	0.0633386	+	0.109706i
$847$	−2.83888	−	4.91708i	−0.0975451	−	0.168953i
$848$	5.79482	−	10.0369i	0.198995	−	0.344669i
$849$	−2.13598			−0.0733065
$850$	−1.58289	+	2.74164i	−0.0542926	+	0.0940376i
$851$	0.445084	+	0.770908i	0.0152573	+	0.0264264i
$852$	−13.2565			−0.454160
$853$	2.73629	+	4.73940i	0.0936889	+	0.162274i	0.909061	−	0.416664i	$-0.136801\pi$
$853$	2.73629	+	4.73940i	0.0936889	+	0.162274i	−0.815372	+	0.578938i	$0.803467\pi$
$854$	−7.75146	+	13.4259i	−0.265250	+	0.459426i
$855$	−8.90155	+	15.4179i	−0.304427	+	0.527282i
$856$	19.3695			0.662035
$857$	−0.770431	+	1.33442i	−0.0263174	+	0.0455831i	−0.878884	−	0.477035i	$-0.841711\pi$
$857$	−0.770431	+	1.33442i	−0.0263174	+	0.0455831i	0.852567	+	0.522618i	$0.175045\pi$
$858$	12.6184			0.430786
$859$	−14.8633			−0.507128			−0.253564	−	0.967319i	$-0.581603\pi$
$859$	−14.8633			−0.507128			−0.253564	+	0.967319i	$0.581603\pi$
$860$	−6.82258	+	2.90220i	−0.232648	+	0.0989644i
$861$	22.7978			0.776948
$862$	14.1642			0.482434
$863$	15.4116	−	26.6936i	0.524616	−	0.908662i	−0.474973	−	0.880000i	$-0.657542\pi$
$863$	15.4116	−	26.6936i	0.524616	−	0.908662i	0.999589	−	0.0286616i	$-0.00912453\pi$
$864$	8.07524			0.274725
$865$	4.60141	−	7.96988i	0.156453	−	0.270984i
$866$	4.51510	−	7.82038i	0.153429	−	0.265747i
$867$	−1.27871	−	2.21478i	−0.0434271	−	0.0752180i
$868$	29.7713			1.01050
$869$	−17.1167	−	29.6469i	−0.580643	−	1.00570i
$870$	1.84875	−	3.20212i	0.0626784	−	0.108562i
$871$	−18.5787			−0.629514
$872$	9.35780	−	16.2082i	0.316895	−	0.548879i
$873$	−26.3251	−	45.5963i	−0.890968	−	1.54320i
$874$	6.49819	+	11.2552i	0.219805	+	0.380713i
$875$	−8.96365	−	15.5255i	−0.303027	−	0.524858i
$876$	55.8307			1.88634
$877$	−5.04622	−	8.74032i	−0.170399	−	0.295140i	0.768160	−	0.640257i	$-0.221172\pi$
$877$	−5.04622	−	8.74032i	−0.170399	−	0.295140i	−0.938559	+	0.345118i	$0.887839\pi$
$878$	4.12709	+	7.14832i	0.139282	+	0.241244i
$879$	−16.3338	+	28.2910i	−0.550927	+	0.954233i
$880$	1.64430	−	2.84801i	0.0554292	−	0.0960063i
$881$	10.1426			0.341713			0.170856	−	0.985296i	$-0.445347\pi$
$881$	10.1426			0.341713			0.170856	+	0.985296i	$0.445347\pi$
$882$	−1.86034			−0.0626408
$883$	0.0782080	−	0.135460i	0.00263191	−	0.00455860i	−0.864706	−	0.502278i	$-0.832496\pi$
$883$	0.0782080	−	0.135460i	0.00263191	−	0.00455860i	0.867338	+	0.497719i	$0.165829\pi$
$884$	−1.40734	+	2.43758i	−0.0473338	+	0.0819846i
$885$	−11.2025	−	19.4033i	−0.376567	−	0.652234i
$886$	8.03060	+	13.9094i	0.269793	+	0.467295i
$887$	−20.0194			−0.672185			−0.336093	−	0.941829i	$-0.609106\pi$
$887$	−20.0194			−0.672185			−0.336093	+	0.941829i	$0.609106\pi$
$888$	−1.03560	−	1.79371i	−0.0347525	−	0.0601931i
$889$	15.7197	+	27.2273i	0.527221	+	0.913173i
$890$	−3.76861	−	6.52742i	−0.126324	−	0.218800i
$891$	12.9073	−	22.3561i	0.432411	−	0.748958i
$892$	−21.0901			−0.706150
$893$	−4.80900	+	8.32944i	−0.160927	+	0.278734i
$894$	−3.68585	−	6.38408i	−0.123273	−	0.213516i
$895$	12.3572			0.413056
$896$	13.0079	+	22.5304i	0.434564	+	0.752686i
$897$	−6.63952	+	11.5000i	−0.221687	+	0.383974i
$898$	−13.4907	+	23.3666i	−0.450191	+	0.779754i
$899$	−21.2444			−0.708541
$900$	−11.6446	+	20.1691i	−0.388154	+	0.672303i
$901$	9.75734			0.325064
$902$	9.28625			0.309198
$903$	33.5451	+	25.2376i	1.11631	+	0.839856i
$904$	39.2767			1.30632
$905$	8.43130			0.280266
$906$	13.4406	−	23.2799i	0.446535	−	0.773422i
$907$	−2.95614			−0.0981570			−0.0490785	−	0.998795i	$-0.515628\pi$
$907$	−2.95614			−0.0981570			−0.0490785	+	0.998795i	$0.515628\pi$
$908$	12.4277	−	21.5254i	0.412427	−	0.714345i
$909$	14.4453	−	25.0200i	0.479121	−	0.829861i
$910$	1.28863	+	2.23197i	0.0427177	+	0.0739892i
$911$	−8.76121			−0.290272			−0.145136	−	0.989412i	$-0.546362\pi$
$911$	−8.76121			−0.290272			−0.145136	+	0.989412i	$0.546362\pi$
$912$	10.0483	+	17.4042i	0.332733	+	0.576310i
$913$	3.23895	−	5.61003i	0.107194	−	0.185665i
$914$	−20.4207			−0.675457
$915$	8.40852	−	14.5640i	0.277977	−	0.481471i
$916$	−3.82364	−	6.62274i	−0.126337	−	0.218822i
$917$	−4.13243	−	7.15759i	−0.136465	−	0.236364i
$918$	0.494634	+	0.856732i	0.0163254	+	0.0282764i
$919$	14.9153			0.492011			0.246005	−	0.969268i	$-0.420882\pi$
$919$	14.9153			0.492011			0.246005	+	0.969268i	$0.420882\pi$
$920$	−2.60371	−	4.50975i	−0.0858417	−	0.148682i
$921$	40.8430	+	70.7422i	1.34582	+	2.33103i
$922$	−11.2023	+	19.4030i	−0.368929	+	0.639003i
$923$	−3.29683	+	5.71028i	−0.108516	+	0.187956i
$924$	−34.6869			−1.14112
$925$	1.43454			0.0471675
$926$	8.63033	−	14.9482i	0.283610	−	0.491227i
$927$	−30.2707	+	52.4304i	−0.994221	+	1.72204i
$928$	−7.76341	−	13.4466i	−0.254846	−	0.441407i
$929$	−8.14456	−	14.1068i	−0.267214	−	0.462829i	0.700927	−	0.713233i	$-0.252770\pi$
$929$	−8.14456	−	14.1068i	−0.267214	−	0.462829i	−0.968141	+	0.250404i	$0.919437\pi$
$930$	11.1260			0.364838
$931$	−2.42808	−	4.20556i	−0.0795771	−	0.137832i
$932$	5.86327	+	10.1555i	0.192058	+	0.332654i
$933$	−13.4046	−	23.2174i	−0.438846	−	0.760103i
$934$	1.21398	−	2.10268i	0.0397227	−	0.0688017i
$935$	2.76867			0.0905453
$936$	8.36244	−	14.4842i	0.273335	−	0.473430i
$937$	−12.3907	−	21.4613i	−0.404786	−	0.701110i	0.589510	−	0.807761i	$-0.299321\pi$
$937$	−12.3907	−	21.4613i	−0.404786	−	0.701110i	−0.994297	+	0.106651i	$0.965987\pi$
$938$	−17.5947			−0.574487
$939$	8.65825	+	14.9965i	0.282551	+	0.489393i
$940$	0.821867	−	1.42352i	0.0268063	−	0.0464300i
$941$	27.4692	−	47.5781i	0.895471	−	1.55100i	0.0622500	−	0.998061i	$-0.480172\pi$
$941$	27.4692	−	47.5781i	0.895471	−	1.55100i	0.833221	−	0.552940i	$-0.186494\pi$
$942$	7.21655			0.235128
$943$	−4.88621	+	8.46316i	−0.159117	+	0.275598i
$944$	−13.6904			−0.445585
$945$	−2.62929			−0.0855308
$946$	13.6639	+	10.2801i	0.444253	+	0.334234i
$947$	34.4230			1.11860			0.559299	−	0.828966i	$-0.311070\pi$
$947$	34.4230			1.11860			0.559299	+	0.828966i	$0.311070\pi$
$948$	−35.7526			−1.16119
$949$	13.8848	−	24.0492i	0.450721	−	0.780671i
$950$	20.9442			0.679520
$951$	21.4098	−	37.0829i	0.694261	−	1.20250i
$952$	−3.12477	+	5.41226i	−0.101274	+	0.175412i
$953$	−5.94612	−	10.2990i	−0.192614	−	0.333617i	0.753502	−	0.657446i	$-0.228363\pi$
$953$	−5.94612	−	10.2990i	−0.192614	−	0.333617i	−0.946116	+	0.323829i	$0.895030\pi$
$954$	−24.7294			−0.800644
$955$	4.25014	+	7.36146i	0.137531	+	0.238211i
$956$	−15.6060	+	27.0303i	−0.504733	+	0.874223i
$957$	24.7521			0.800122
$958$	12.2351	−	21.1919i	0.395300	−	0.684679i
$959$	1.22356	+	2.11926i	0.0395107	+	0.0684346i
$960$	1.75693	+	3.04309i	0.0567046	+	0.0982153i
$961$	−16.4631	−	28.5148i	−0.531066	−	0.919834i
$962$	−0.439408			−0.0141671
$963$	13.7335	+	23.7871i	0.442556	+	0.766529i
$964$	−11.2615	−	19.5056i	−0.362710	−	0.628232i
$965$	6.58009	−	11.3970i	0.211820	−	0.366884i
$966$	−6.28788	+	10.8909i	−0.202309	+	0.350410i
$967$	41.0164			1.31900			0.659499	−	0.751705i	$-0.270768\pi$
$967$	41.0164			1.31900			0.659499	+	0.751705i	$0.270768\pi$
$968$	−5.66286			−0.182011
$969$	−8.45969	+	14.6526i	−0.271764	+	0.470709i
$970$	4.04598	−	7.00785i	0.129909	−	0.225008i
$971$	−3.88080	−	6.72174i	−0.124541	−	0.215711i	0.797013	−	0.603963i	$-0.206412\pi$
$971$	−3.88080	−	6.72174i	−0.124541	−	0.215711i	−0.921553	+	0.388252i	$0.873079\pi$
$972$	−16.5636	−	28.6890i	−0.531278	−	0.920200i
$973$	−18.4426			−0.591242
$974$	−6.73485	−	11.6651i	−0.215799	−	0.373774i
$975$	10.6999	+	18.5327i	0.342670	+	0.593521i
$976$	−5.13798	−	8.89924i	−0.164463	−	0.284858i
$977$	−6.46913	+	11.2049i	−0.206966	+	0.358475i	−0.950757	−	0.309936i	$-0.899692\pi$
$977$	−6.46913	+	11.2049i	−0.206966	+	0.358475i	0.743791	+	0.668412i	$0.233026\pi$
$978$	−15.1157			−0.483346
$979$	25.2282	−	43.6965i	0.806296	−	1.39655i
$980$	0.414963	+	0.718737i	0.0132555	+	0.0229592i
$981$	26.5398			0.847350
$982$	7.76249	+	13.4450i	0.247711	+	0.429048i
$983$	−14.9508	+	25.8956i	−0.476857	+	0.825940i	−0.999648	−	0.0265207i	$-0.991557\pi$
$983$	−14.9508	+	25.8956i	−0.476857	+	0.825940i	0.522792	+	0.852460i	$0.324891\pi$
$984$	11.3690	−	19.6917i	0.362431	−	0.627748i
$985$	18.5476			0.590977
$986$	0.951067	−	1.64730i	0.0302882	−	0.0524606i
$987$	−9.30672			−0.296236
$988$	18.6214			0.592424
$989$	−16.5585	+	7.04371i	−0.526531	+	0.223977i
$990$	−7.01704			−0.223016
$991$	2.73767			0.0869649			0.0434824	−	0.999054i	$-0.486155\pi$
$991$	2.73767			0.0869649			0.0434824	+	0.999054i	$0.486155\pi$
$992$	23.3607	−	40.4619i	0.741704	−	1.28467i
$993$	34.1267			1.08298
$994$	−3.12222	+	5.40785i	−0.0990309	+	0.171526i
$995$	−4.06212	+	7.03580i	−0.128778	+	0.223050i
$996$	−3.38270	−	5.85901i	−0.107185	−	0.185650i
$997$	−45.2214			−1.43217			−0.716087	−	0.698011i	$-0.754069\pi$
$997$	−45.2214			−1.43217			−0.716087	+	0.698011i	$0.754069\pi$
$998$	−7.20141	−	12.4732i	−0.227957	−	0.394833i
$999$	0.224139	−	0.388220i	0.00709144	−	0.0122827i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.e.a.307.19	✓	58
43.36	even	3	inner	731.2.e.a.681.19	yes	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.e.a.307.19	✓	58	1.1	even	1	trivial
731.2.e.a.681.19	yes	58	43.36	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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.715873 q^{2} +(-1.27871 + 2.21478i) q^{3} -1.48753 q^{4} +(0.380045 - 0.658258i) q^{5} +(-0.915390 + 1.58550i) q^{6} +(-1.25160 - 2.16783i) q^{7} -2.49662 q^{8} +(-1.77018 - 3.06604i) q^{9} +O(q^{10})\)	\(q+0.715873 q^{2} +(-1.27871 + 2.21478i) q^{3} -1.48753 q^{4} +(0.380045 - 0.658258i) q^{5} +(-0.915390 + 1.58550i) q^{6} +(-1.25160 - 2.16783i) q^{7} -2.49662 q^{8} +(-1.77018 - 3.06604i) q^{9} +(0.272064 - 0.471229i) q^{10} +3.64255 q^{11} +(1.90211 - 3.29455i) q^{12} +(-0.946091 - 1.63868i) q^{13} +(-0.895984 - 1.55189i) q^{14} +(0.971932 + 1.68344i) q^{15} +1.18779 q^{16} +(0.500000 + 0.866025i) q^{17} +(-1.26722 - 2.19489i) q^{18} +(3.30791 - 5.72947i) q^{19} +(-0.565328 + 0.979176i) q^{20} +6.40170 q^{21} +2.60761 q^{22} +(-1.37206 + 2.37648i) q^{23} +(3.19245 - 5.52948i) q^{24} +(2.21113 + 3.82979i) q^{25} +(-0.677281 - 1.17308i) q^{26} +1.38191 q^{27} +(1.86178 + 3.22470i) q^{28} +(-1.32854 - 2.30110i) q^{29} +(0.695780 + 1.20513i) q^{30} +(3.99769 - 6.92420i) q^{31} +5.84355 q^{32} +(-4.65776 + 8.06747i) q^{33} +(0.357936 + 0.619964i) q^{34} -1.90265 q^{35} +(2.63318 + 4.56081i) q^{36} +(0.162196 - 0.280931i) q^{37} +(2.36804 - 4.10157i) q^{38} +4.83909 q^{39} +(-0.948831 + 1.64342i) q^{40} +3.56122 q^{41} +4.58280 q^{42} +(5.24004 + 3.94234i) q^{43} -5.41840 q^{44} -2.69099 q^{45} +(-0.982221 + 1.70126i) q^{46} -1.45379 q^{47} +(-1.51883 + 2.63069i) q^{48} +(0.367011 - 0.635682i) q^{49} +(1.58289 + 2.74164i) q^{50} -2.55741 q^{51} +(1.40734 + 2.43758i) q^{52} +(4.87867 - 8.45010i) q^{53} +0.989269 q^{54} +(1.38434 - 2.39774i) q^{55} +(3.12477 + 5.41226i) q^{56} +(8.45969 + 14.6526i) q^{57} +(-0.951067 - 1.64730i) q^{58} -11.5260 q^{59} +(-1.44578 - 2.50416i) q^{60} +(-4.32567 - 7.49228i) q^{61} +(2.86184 - 4.95685i) q^{62} +(-4.43109 + 7.67488i) q^{63} +1.80767 q^{64} -1.43823 q^{65} +(-3.33436 + 5.77528i) q^{66} +(4.90932 - 8.50320i) q^{67} +(-0.743763 - 1.28824i) q^{68} +(-3.50892 - 6.07763i) q^{69} -1.36206 q^{70} +(-1.74234 - 3.01783i) q^{71} +(4.41947 + 7.65474i) q^{72} +(7.33800 + 12.7098i) q^{73} +(0.116111 - 0.201111i) q^{74} -11.3095 q^{75} +(-4.92060 + 8.52273i) q^{76} +(-4.55901 - 7.89644i) q^{77} +3.46417 q^{78} +(-4.69908 - 8.13904i) q^{79} +(0.451413 - 0.781870i) q^{80} +(3.54348 - 6.13749i) q^{81} +2.54938 q^{82} +(0.889198 - 1.54014i) q^{83} -9.52269 q^{84} +0.760091 q^{85} +(3.75120 + 2.82221i) q^{86} +6.79526 q^{87} -9.09409 q^{88} +(6.92596 - 11.9961i) q^{89} -1.92641 q^{90} +(-2.36825 + 4.10193i) q^{91} +(2.04098 - 3.53507i) q^{92} +(10.2237 + 17.7080i) q^{93} -1.04073 q^{94} +(-2.51431 - 4.35492i) q^{95} +(-7.47219 + 12.9422i) q^{96} +14.8714 q^{97} +(0.262733 - 0.455067i) q^{98} +(-6.44797 - 11.1682i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9}+O(q^{10}) \) 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9	\( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9} + 4 q^{10} + 16 q^{11} + 12 q^{12} + 2 q^{13} - 11 q^{14} + 7 q^{15} + 30 q^{16} + 29 q^{17} + 8 q^{18} + 8 q^{19} - 33 q^{20} - 26 q^{21} - 22 q^{22} - 5 q^{23} + 12 q^{24} - 36 q^{25} - 12 q^{27} + 15 q^{28} + 2 q^{29} + 11 q^{30} + 3 q^{31} - 40 q^{32} + 17 q^{33} - 3 q^{34} + 38 q^{35} - 7 q^{36} + 2 q^{37} + q^{38} - 54 q^{39} + 5 q^{40} + 14 q^{41} - 112 q^{42} + 31 q^{43} - 24 q^{44} - 46 q^{45} - 13 q^{46} - 28 q^{47} - 28 q^{49} - 13 q^{50} + 6 q^{51} + 85 q^{52} - 10 q^{53} + 34 q^{54} + 36 q^{55} - 54 q^{56} - 23 q^{57} + 3 q^{58} + 12 q^{59} + 2 q^{60} - q^{61} - q^{62} - 14 q^{63} + 28 q^{64} + 80 q^{65} - 74 q^{66} + 11 q^{67} + 27 q^{68} - 11 q^{69} + 2 q^{70} + 16 q^{71} + 21 q^{72} + 14 q^{73} + 21 q^{74} - 54 q^{75} + 44 q^{76} + 25 q^{77} + 88 q^{78} - 4 q^{79} - 112 q^{80} + 11 q^{81} - 176 q^{82} - 3 q^{83} + 100 q^{84} - 2 q^{85} + 44 q^{86} + 8 q^{87} - 106 q^{88} + 82 q^{89} + 54 q^{90} - 15 q^{91} + 42 q^{92} + 88 q^{94} + 29 q^{95} + 20 q^{96} + 20 q^{97} + 44 q^{98} - 54 q^{99}+O(q^{100}) \) 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9 + 4 * q^10 + 16 * q^11 + 12 * q^12 + 2 * q^13 - 11 * q^14 + 7 * q^15 + 30 * q^16 + 29 * q^17 + 8 * q^18 + 8 * q^19 - 33 * q^20 - 26 * q^21 - 22 * q^22 - 5 * q^23 + 12 * q^24 - 36 * q^25 - 12 * q^27 + 15 * q^28 + 2 * q^29 + 11 * q^30 + 3 * q^31 - 40 * q^32 + 17 * q^33 - 3 * q^34 + 38 * q^35 - 7 * q^36 + 2 * q^37 + q^38 - 54 * q^39 + 5 * q^40 + 14 * q^41 - 112 * q^42 + 31 * q^43 - 24 * q^44 - 46 * q^45 - 13 * q^46 - 28 * q^47 - 28 * q^49 - 13 * q^50 + 6 * q^51 + 85 * q^52 - 10 * q^53 + 34 * q^54 + 36 * q^55 - 54 * q^56 - 23 * q^57 + 3 * q^58 + 12 * q^59 + 2 * q^60 - q^61 - q^62 - 14 * q^63 + 28 * q^64 + 80 * q^65 - 74 * q^66 + 11 * q^67 + 27 * q^68 - 11 * q^69 + 2 * q^70 + 16 * q^71 + 21 * q^72 + 14 * q^73 + 21 * q^74 - 54 * q^75 + 44 * q^76 + 25 * q^77 + 88 * q^78 - 4 * q^79 - 112 * q^80 + 11 * q^81 - 176 * q^82 - 3 * q^83 + 100 * q^84 - 2 * q^85 + 44 * q^86 + 8 * q^87 - 106 * q^88 + 82 * q^89 + 54 * q^90 - 15 * q^91 + 42 * q^92 + 88 * q^94 + 29 * q^95 + 20 * q^96 + 20 * q^97 + 44 * q^98 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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