Properties

Label 280.2.bv.d.213.1
Level $280$
Weight $2$
Character 280.213
Analytic conductor $2.236$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [280,2,Mod(117,280)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(280, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 6, 3, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("280.117");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.bv (of order \(12\), 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: \(2.23581125660\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 213.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 280.213
Dual form 280.2.bv.d.117.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(1.86603 - 0.500000i) q^{3} +2.00000i q^{4} +(-0.133975 - 2.23205i) q^{5} +(2.36603 + 1.36603i) q^{6} +(0.866025 + 2.50000i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(0.633975 - 0.366025i) q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(1.86603 - 0.500000i) q^{3} +2.00000i q^{4} +(-0.133975 - 2.23205i) q^{5} +(2.36603 + 1.36603i) q^{6} +(0.866025 + 2.50000i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(0.633975 - 0.366025i) q^{9} +(2.09808 - 2.36603i) q^{10} +(0.633975 + 0.366025i) q^{11} +(1.00000 + 3.73205i) q^{12} +(-3.00000 - 3.00000i) q^{13} +(-1.63397 + 3.36603i) q^{14} +(-1.36603 - 4.09808i) q^{15} -4.00000 q^{16} +(4.09808 - 1.09808i) q^{17} +(1.00000 + 0.267949i) q^{18} +(3.00000 - 1.73205i) q^{19} +(4.46410 - 0.267949i) q^{20} +(2.86603 + 4.23205i) q^{21} +(0.267949 + 1.00000i) q^{22} +(0.401924 - 1.50000i) q^{23} +(-2.73205 + 4.73205i) q^{24} +(-4.96410 + 0.598076i) q^{25} -6.00000i q^{26} +(-3.09808 + 3.09808i) q^{27} +(-5.00000 + 1.73205i) q^{28} -4.46410 q^{29} +(2.73205 - 5.46410i) q^{30} +(-8.83013 - 5.09808i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(1.36603 + 0.366025i) q^{33} +(5.19615 + 3.00000i) q^{34} +(5.46410 - 2.26795i) q^{35} +(0.732051 + 1.26795i) q^{36} +(-1.73205 + 6.46410i) q^{37} +(4.73205 + 1.26795i) q^{38} +(-7.09808 - 4.09808i) q^{39} +(4.73205 + 4.19615i) q^{40} +0.464102i q^{41} +(-1.36603 + 7.09808i) q^{42} +(2.36603 - 2.36603i) q^{43} +(-0.732051 + 1.26795i) q^{44} +(-0.901924 - 1.36603i) q^{45} +(1.90192 - 1.09808i) q^{46} +(0.169873 - 0.633975i) q^{47} +(-7.46410 + 2.00000i) q^{48} +(-5.50000 + 4.33013i) q^{49} +(-5.56218 - 4.36603i) q^{50} +(7.09808 - 4.09808i) q^{51} +(6.00000 - 6.00000i) q^{52} +(-0.803848 - 3.00000i) q^{53} -6.19615 q^{54} +(0.732051 - 1.46410i) q^{55} +(-6.73205 - 3.26795i) q^{56} +(4.73205 - 4.73205i) q^{57} +(-4.46410 - 4.46410i) q^{58} +(7.73205 + 4.46410i) q^{59} +(8.19615 - 2.73205i) q^{60} +(4.96410 + 8.59808i) q^{61} +(-3.73205 - 13.9282i) q^{62} +(1.46410 + 1.26795i) q^{63} -8.00000i q^{64} +(-6.29423 + 7.09808i) q^{65} +(1.00000 + 1.73205i) q^{66} +(-3.86603 + 1.03590i) q^{67} +(2.19615 + 8.19615i) q^{68} -3.00000i q^{69} +(7.73205 + 3.19615i) q^{70} +15.4641 q^{71} +(-0.535898 + 2.00000i) q^{72} +(-2.16987 - 8.09808i) q^{73} +(-8.19615 + 4.73205i) q^{74} +(-8.96410 + 3.59808i) q^{75} +(3.46410 + 6.00000i) q^{76} +(-0.366025 + 1.90192i) q^{77} +(-3.00000 - 11.1962i) q^{78} +(11.1962 - 6.46410i) q^{79} +(0.535898 + 8.92820i) q^{80} +(-5.33013 + 9.23205i) q^{81} +(-0.464102 + 0.464102i) q^{82} +(-4.56218 - 4.56218i) q^{83} +(-8.46410 + 5.73205i) q^{84} +(-3.00000 - 9.00000i) q^{85} +4.73205 q^{86} +(-8.33013 + 2.23205i) q^{87} +(-2.00000 + 0.535898i) q^{88} +(8.59808 + 14.8923i) q^{89} +(0.464102 - 2.26795i) q^{90} +(4.90192 - 10.0981i) q^{91} +(3.00000 + 0.803848i) q^{92} +(-19.0263 - 5.09808i) q^{93} +(0.803848 - 0.464102i) q^{94} +(-4.26795 - 6.46410i) q^{95} +(-9.46410 - 5.46410i) q^{96} +(-6.26795 - 6.26795i) q^{97} +(-9.83013 - 1.16987i) q^{98} +0.535898 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{2} + 4 q^{3} - 4 q^{5} + 6 q^{6} - 8 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{2} + 4 q^{3} - 4 q^{5} + 6 q^{6} - 8 q^{8} + 6 q^{9} - 2 q^{10} + 6 q^{11} + 4 q^{12} - 12 q^{13} - 10 q^{14} - 2 q^{15} - 16 q^{16} + 6 q^{17} + 4 q^{18} + 12 q^{19} + 4 q^{20} + 8 q^{21} + 8 q^{22} + 12 q^{23} - 4 q^{24} - 6 q^{25} - 2 q^{27} - 20 q^{28} - 4 q^{29} + 4 q^{30} - 18 q^{31} - 16 q^{32} + 2 q^{33} + 8 q^{35} - 4 q^{36} + 12 q^{38} - 18 q^{39} + 12 q^{40} - 2 q^{42} + 6 q^{43} + 4 q^{44} - 14 q^{45} + 18 q^{46} + 18 q^{47} - 16 q^{48} - 22 q^{49} + 2 q^{50} + 18 q^{51} + 24 q^{52} - 24 q^{53} - 4 q^{54} - 4 q^{55} - 20 q^{56} + 12 q^{57} - 4 q^{58} + 24 q^{59} + 12 q^{60} + 6 q^{61} - 8 q^{62} - 8 q^{63} + 6 q^{65} + 4 q^{66} - 12 q^{67} - 12 q^{68} + 24 q^{70} + 48 q^{71} - 16 q^{72} - 26 q^{73} - 12 q^{74} - 22 q^{75} + 2 q^{77} - 12 q^{78} + 24 q^{79} + 16 q^{80} - 4 q^{81} + 12 q^{82} + 6 q^{83} - 20 q^{84} - 12 q^{85} + 12 q^{86} - 16 q^{87} - 8 q^{88} + 24 q^{89} - 12 q^{90} + 30 q^{91} + 12 q^{92} - 38 q^{93} + 24 q^{94} - 24 q^{95} - 24 q^{96} - 32 q^{97} - 22 q^{98} + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(141\) \(241\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.00000i 0.707107 + 0.707107i
\(3\) 1.86603 0.500000i 1.07735 0.288675i 0.323840 0.946112i \(-0.395026\pi\)
0.753510 + 0.657437i \(0.228359\pi\)
\(4\) 2.00000i 1.00000i
\(5\) −0.133975 2.23205i −0.0599153 0.998203i
\(6\) 2.36603 + 1.36603i 0.965926 + 0.557678i
\(7\) 0.866025 + 2.50000i 0.327327 + 0.944911i
\(8\) −2.00000 + 2.00000i −0.707107 + 0.707107i
\(9\) 0.633975 0.366025i 0.211325 0.122008i
\(10\) 2.09808 2.36603i 0.663470 0.748203i
\(11\) 0.633975 + 0.366025i 0.191151 + 0.110361i 0.592521 0.805555i \(-0.298133\pi\)
−0.401371 + 0.915916i \(0.631466\pi\)
\(12\) 1.00000 + 3.73205i 0.288675 + 1.07735i
\(13\) −3.00000 3.00000i −0.832050 0.832050i 0.155747 0.987797i \(-0.450222\pi\)
−0.987797 + 0.155747i \(0.950222\pi\)
\(14\) −1.63397 + 3.36603i −0.436698 + 0.899608i
\(15\) −1.36603 4.09808i −0.352706 1.05812i
\(16\) −4.00000 −1.00000
\(17\) 4.09808 1.09808i 0.993929 0.266323i 0.275029 0.961436i \(-0.411312\pi\)
0.718900 + 0.695113i \(0.244646\pi\)
\(18\) 1.00000 + 0.267949i 0.235702 + 0.0631562i
\(19\) 3.00000 1.73205i 0.688247 0.397360i −0.114708 0.993399i \(-0.536593\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) 4.46410 0.267949i 0.998203 0.0599153i
\(21\) 2.86603 + 4.23205i 0.625418 + 0.923509i
\(22\) 0.267949 + 1.00000i 0.0571270 + 0.213201i
\(23\) 0.401924 1.50000i 0.0838069 0.312772i −0.911279 0.411790i \(-0.864904\pi\)
0.995086 + 0.0990186i \(0.0315703\pi\)
\(24\) −2.73205 + 4.73205i −0.557678 + 0.965926i
\(25\) −4.96410 + 0.598076i −0.992820 + 0.119615i
\(26\) 6.00000i 1.17670i
\(27\) −3.09808 + 3.09808i −0.596225 + 0.596225i
\(28\) −5.00000 + 1.73205i −0.944911 + 0.327327i
\(29\) −4.46410 −0.828963 −0.414481 0.910058i \(-0.636037\pi\)
−0.414481 + 0.910058i \(0.636037\pi\)
\(30\) 2.73205 5.46410i 0.498802 0.997604i
\(31\) −8.83013 5.09808i −1.58594 0.915642i −0.993967 0.109682i \(-0.965017\pi\)
−0.591971 0.805959i \(-0.701650\pi\)
\(32\) −4.00000 4.00000i −0.707107 0.707107i
\(33\) 1.36603 + 0.366025i 0.237795 + 0.0637168i
\(34\) 5.19615 + 3.00000i 0.891133 + 0.514496i
\(35\) 5.46410 2.26795i 0.923602 0.383353i
\(36\) 0.732051 + 1.26795i 0.122008 + 0.211325i
\(37\) −1.73205 + 6.46410i −0.284747 + 1.06269i 0.664276 + 0.747487i \(0.268740\pi\)
−0.949024 + 0.315205i \(0.897927\pi\)
\(38\) 4.73205 + 1.26795i 0.767640 + 0.205689i
\(39\) −7.09808 4.09808i −1.13660 0.656217i
\(40\) 4.73205 + 4.19615i 0.748203 + 0.663470i
\(41\) 0.464102i 0.0724805i 0.999343 + 0.0362402i \(0.0115382\pi\)
−0.999343 + 0.0362402i \(0.988462\pi\)
\(42\) −1.36603 + 7.09808i −0.210782 + 1.09526i
\(43\) 2.36603 2.36603i 0.360815 0.360815i −0.503298 0.864113i \(-0.667880\pi\)
0.864113 + 0.503298i \(0.167880\pi\)
\(44\) −0.732051 + 1.26795i −0.110361 + 0.191151i
\(45\) −0.901924 1.36603i −0.134451 0.203635i
\(46\) 1.90192 1.09808i 0.280423 0.161903i
\(47\) 0.169873 0.633975i 0.0247785 0.0924747i −0.952429 0.304760i \(-0.901424\pi\)
0.977208 + 0.212285i \(0.0680905\pi\)
\(48\) −7.46410 + 2.00000i −1.07735 + 0.288675i
\(49\) −5.50000 + 4.33013i −0.785714 + 0.618590i
\(50\) −5.56218 4.36603i −0.786611 0.617449i
\(51\) 7.09808 4.09808i 0.993929 0.573845i
\(52\) 6.00000 6.00000i 0.832050 0.832050i
\(53\) −0.803848 3.00000i −0.110417 0.412082i 0.888486 0.458903i \(-0.151757\pi\)
−0.998903 + 0.0468214i \(0.985091\pi\)
\(54\) −6.19615 −0.843190
\(55\) 0.732051 1.46410i 0.0987097 0.197419i
\(56\) −6.73205 3.26795i −0.899608 0.436698i
\(57\) 4.73205 4.73205i 0.626775 0.626775i
\(58\) −4.46410 4.46410i −0.586165 0.586165i
\(59\) 7.73205 + 4.46410i 1.00663 + 0.581177i 0.910202 0.414164i \(-0.135926\pi\)
0.0964249 + 0.995340i \(0.469259\pi\)
\(60\) 8.19615 2.73205i 1.05812 0.352706i
\(61\) 4.96410 + 8.59808i 0.635588 + 1.10087i 0.986390 + 0.164421i \(0.0525756\pi\)
−0.350802 + 0.936450i \(0.614091\pi\)
\(62\) −3.73205 13.9282i −0.473971 1.76888i
\(63\) 1.46410 + 1.26795i 0.184459 + 0.159747i
\(64\) 8.00000i 1.00000i
\(65\) −6.29423 + 7.09808i −0.780703 + 0.880408i
\(66\) 1.00000 + 1.73205i 0.123091 + 0.213201i
\(67\) −3.86603 + 1.03590i −0.472310 + 0.126555i −0.487120 0.873335i \(-0.661952\pi\)
0.0148095 + 0.999890i \(0.495286\pi\)
\(68\) 2.19615 + 8.19615i 0.266323 + 0.993929i
\(69\) 3.00000i 0.361158i
\(70\) 7.73205 + 3.19615i 0.924157 + 0.382013i
\(71\) 15.4641 1.83525 0.917626 0.397446i \(-0.130103\pi\)
0.917626 + 0.397446i \(0.130103\pi\)
\(72\) −0.535898 + 2.00000i −0.0631562 + 0.235702i
\(73\) −2.16987 8.09808i −0.253964 0.947808i −0.968664 0.248376i \(-0.920103\pi\)
0.714699 0.699432i \(-0.246564\pi\)
\(74\) −8.19615 + 4.73205i −0.952783 + 0.550090i
\(75\) −8.96410 + 3.59808i −1.03509 + 0.415470i
\(76\) 3.46410 + 6.00000i 0.397360 + 0.688247i
\(77\) −0.366025 + 1.90192i −0.0417125 + 0.216744i
\(78\) −3.00000 11.1962i −0.339683 1.26771i
\(79\) 11.1962 6.46410i 1.25967 0.727268i 0.286656 0.958034i \(-0.407456\pi\)
0.973009 + 0.230765i \(0.0741230\pi\)
\(80\) 0.535898 + 8.92820i 0.0599153 + 0.998203i
\(81\) −5.33013 + 9.23205i −0.592236 + 1.02578i
\(82\) −0.464102 + 0.464102i −0.0512514 + 0.0512514i
\(83\) −4.56218 4.56218i −0.500764 0.500764i 0.410911 0.911675i \(-0.365211\pi\)
−0.911675 + 0.410911i \(0.865211\pi\)
\(84\) −8.46410 + 5.73205i −0.923509 + 0.625418i
\(85\) −3.00000 9.00000i −0.325396 0.976187i
\(86\) 4.73205 0.510270
\(87\) −8.33013 + 2.23205i −0.893083 + 0.239301i
\(88\) −2.00000 + 0.535898i −0.213201 + 0.0571270i
\(89\) 8.59808 + 14.8923i 0.911394 + 1.57858i 0.812096 + 0.583523i \(0.198326\pi\)
0.0992979 + 0.995058i \(0.468340\pi\)
\(90\) 0.464102 2.26795i 0.0489206 0.239063i
\(91\) 4.90192 10.0981i 0.513861 1.05857i
\(92\) 3.00000 + 0.803848i 0.312772 + 0.0838069i
\(93\) −19.0263 5.09808i −1.97293 0.528646i
\(94\) 0.803848 0.464102i 0.0829105 0.0478684i
\(95\) −4.26795 6.46410i −0.437882 0.663203i
\(96\) −9.46410 5.46410i −0.965926 0.557678i
\(97\) −6.26795 6.26795i −0.636414 0.636414i 0.313255 0.949669i \(-0.398580\pi\)
−0.949669 + 0.313255i \(0.898580\pi\)
\(98\) −9.83013 1.16987i −0.992993 0.118175i
\(99\) 0.535898 0.0538598
\(100\) −1.19615 9.92820i −0.119615 0.992820i
\(101\) −5.06218 + 8.76795i −0.503706 + 0.872444i 0.496285 + 0.868159i \(0.334697\pi\)
−0.999991 + 0.00428406i \(0.998636\pi\)
\(102\) 11.1962 + 3.00000i 1.10858 + 0.297044i
\(103\) 12.4282 + 3.33013i 1.22459 + 0.328127i 0.812470 0.583003i \(-0.198123\pi\)
0.412118 + 0.911131i \(0.364789\pi\)
\(104\) 12.0000 1.17670
\(105\) 9.06218 6.96410i 0.884378 0.679627i
\(106\) 2.19615 3.80385i 0.213309 0.369462i
\(107\) 1.42820 5.33013i 0.138070 0.515283i −0.861897 0.507084i \(-0.830723\pi\)
0.999966 0.00819905i \(-0.00260987\pi\)
\(108\) −6.19615 6.19615i −0.596225 0.596225i
\(109\) 2.13397 3.69615i 0.204398 0.354027i −0.745543 0.666458i \(-0.767810\pi\)
0.949941 + 0.312430i \(0.101143\pi\)
\(110\) 2.19615 0.732051i 0.209395 0.0697983i
\(111\) 12.9282i 1.22709i
\(112\) −3.46410 10.0000i −0.327327 0.944911i
\(113\) 2.53590 + 2.53590i 0.238557 + 0.238557i 0.816253 0.577695i \(-0.196048\pi\)
−0.577695 + 0.816253i \(0.696048\pi\)
\(114\) 9.46410 0.886394
\(115\) −3.40192 0.696152i −0.317231 0.0649165i
\(116\) 8.92820i 0.828963i
\(117\) −3.00000 0.803848i −0.277350 0.0743157i
\(118\) 3.26795 + 12.1962i 0.300839 + 1.12275i
\(119\) 6.29423 + 9.29423i 0.576991 + 0.852001i
\(120\) 10.9282 + 5.46410i 0.997604 + 0.498802i
\(121\) −5.23205 9.06218i −0.475641 0.823834i
\(122\) −3.63397 + 13.5622i −0.329005 + 1.22786i
\(123\) 0.232051 + 0.866025i 0.0209233 + 0.0780869i
\(124\) 10.1962 17.6603i 0.915642 1.58594i
\(125\) 2.00000 + 11.0000i 0.178885 + 0.983870i
\(126\) 0.196152 + 2.73205i 0.0174746 + 0.243390i
\(127\) −11.0000 + 11.0000i −0.976092 + 0.976092i −0.999721 0.0236286i \(-0.992478\pi\)
0.0236286 + 0.999721i \(0.492478\pi\)
\(128\) 8.00000 8.00000i 0.707107 0.707107i
\(129\) 3.23205 5.59808i 0.284566 0.492883i
\(130\) −13.3923 + 0.803848i −1.17458 + 0.0705021i
\(131\) 3.73205 + 6.46410i 0.326071 + 0.564771i 0.981728 0.190287i \(-0.0609419\pi\)
−0.655658 + 0.755058i \(0.727609\pi\)
\(132\) −0.732051 + 2.73205i −0.0637168 + 0.237795i
\(133\) 6.92820 + 6.00000i 0.600751 + 0.520266i
\(134\) −4.90192 2.83013i −0.423462 0.244486i
\(135\) 7.33013 + 6.50000i 0.630877 + 0.559431i
\(136\) −6.00000 + 10.3923i −0.514496 + 0.891133i
\(137\) 2.19615 + 8.19615i 0.187630 + 0.700245i 0.994052 + 0.108904i \(0.0347343\pi\)
−0.806422 + 0.591340i \(0.798599\pi\)
\(138\) 3.00000 3.00000i 0.255377 0.255377i
\(139\) 1.26795i 0.107546i −0.998553 0.0537730i \(-0.982875\pi\)
0.998553 0.0537730i \(-0.0171247\pi\)
\(140\) 4.53590 + 10.9282i 0.383353 + 0.923602i
\(141\) 1.26795i 0.106781i
\(142\) 15.4641 + 15.4641i 1.29772 + 1.29772i
\(143\) −0.803848 3.00000i −0.0672211 0.250873i
\(144\) −2.53590 + 1.46410i −0.211325 + 0.122008i
\(145\) 0.598076 + 9.96410i 0.0496675 + 0.827474i
\(146\) 5.92820 10.2679i 0.490622 0.849782i
\(147\) −8.09808 + 10.8301i −0.667918 + 0.893254i
\(148\) −12.9282 3.46410i −1.06269 0.284747i
\(149\) 11.3301 + 19.6244i 0.928200 + 1.60769i 0.786332 + 0.617804i \(0.211978\pi\)
0.141868 + 0.989886i \(0.454689\pi\)
\(150\) −12.5622 5.36603i −1.02570 0.438134i
\(151\) −6.90192 + 11.9545i −0.561671 + 0.972842i 0.435680 + 0.900101i \(0.356508\pi\)
−0.997351 + 0.0727405i \(0.976826\pi\)
\(152\) −2.53590 + 9.46410i −0.205689 + 0.767640i
\(153\) 2.19615 2.19615i 0.177548 0.177548i
\(154\) −2.26795 + 1.53590i −0.182757 + 0.123766i
\(155\) −10.1962 + 20.3923i −0.818975 + 1.63795i
\(156\) 8.19615 14.1962i 0.656217 1.13660i
\(157\) −4.56218 17.0263i −0.364101 1.35885i −0.868635 0.495453i \(-0.835002\pi\)
0.504533 0.863392i \(-0.331665\pi\)
\(158\) 17.6603 + 4.73205i 1.40497 + 0.376462i
\(159\) −3.00000 5.19615i −0.237915 0.412082i
\(160\) −8.39230 + 9.46410i −0.663470 + 0.748203i
\(161\) 4.09808 0.294229i 0.322974 0.0231885i
\(162\) −14.5622 + 3.90192i −1.14411 + 0.306564i
\(163\) −3.63397 0.973721i −0.284635 0.0762677i 0.113677 0.993518i \(-0.463737\pi\)
−0.398312 + 0.917250i \(0.630404\pi\)
\(164\) −0.928203 −0.0724805
\(165\) 0.633975 3.09808i 0.0493549 0.241185i
\(166\) 9.12436i 0.708187i
\(167\) −3.29423 3.29423i −0.254915 0.254915i 0.568067 0.822982i \(-0.307691\pi\)
−0.822982 + 0.568067i \(0.807691\pi\)
\(168\) −14.1962 2.73205i −1.09526 0.210782i
\(169\) 5.00000i 0.384615i
\(170\) 6.00000 12.0000i 0.460179 0.920358i
\(171\) 1.26795 2.19615i 0.0969625 0.167944i
\(172\) 4.73205 + 4.73205i 0.360815 + 0.360815i
\(173\) −0.124356 + 0.464102i −0.00945459 + 0.0352850i −0.970492 0.241133i \(-0.922481\pi\)
0.961037 + 0.276418i \(0.0891475\pi\)
\(174\) −10.5622 6.09808i −0.800717 0.462294i
\(175\) −5.79423 11.8923i −0.438003 0.898974i
\(176\) −2.53590 1.46410i −0.191151 0.110361i
\(177\) 16.6603 + 4.46410i 1.25226 + 0.335542i
\(178\) −6.29423 + 23.4904i −0.471772 + 1.76068i
\(179\) 7.02628 12.1699i 0.525169 0.909619i −0.474402 0.880309i \(-0.657336\pi\)
0.999570 0.0293105i \(-0.00933115\pi\)
\(180\) 2.73205 1.80385i 0.203635 0.134451i
\(181\) 22.5167 1.67365 0.836825 0.547470i \(-0.184409\pi\)
0.836825 + 0.547470i \(0.184409\pi\)
\(182\) 15.0000 5.19615i 1.11187 0.385164i
\(183\) 13.5622 + 13.5622i 1.00255 + 1.00255i
\(184\) 2.19615 + 3.80385i 0.161903 + 0.280423i
\(185\) 14.6603 + 3.00000i 1.07784 + 0.220564i
\(186\) −13.9282 24.1244i −1.02127 1.76888i
\(187\) 3.00000 + 0.803848i 0.219382 + 0.0587832i
\(188\) 1.26795 + 0.339746i 0.0924747 + 0.0247785i
\(189\) −10.4282 5.06218i −0.758540 0.368219i
\(190\) 2.19615 10.7321i 0.159326 0.778585i
\(191\) −1.56218 2.70577i −0.113035 0.195783i 0.803957 0.594687i \(-0.202724\pi\)
−0.916993 + 0.398904i \(0.869391\pi\)
\(192\) −4.00000 14.9282i −0.288675 1.07735i
\(193\) −11.5622 + 3.09808i −0.832264 + 0.223004i −0.649701 0.760190i \(-0.725106\pi\)
−0.182563 + 0.983194i \(0.558439\pi\)
\(194\) 12.5359i 0.900025i
\(195\) −8.19615 + 16.3923i −0.586939 + 1.17388i
\(196\) −8.66025 11.0000i −0.618590 0.785714i
\(197\) −5.53590 5.53590i −0.394416 0.394416i 0.481842 0.876258i \(-0.339968\pi\)
−0.876258 + 0.481842i \(0.839968\pi\)
\(198\) 0.535898 + 0.535898i 0.0380846 + 0.0380846i
\(199\) 1.73205 3.00000i 0.122782 0.212664i −0.798082 0.602549i \(-0.794152\pi\)
0.920864 + 0.389885i \(0.127485\pi\)
\(200\) 8.73205 11.1244i 0.617449 0.786611i
\(201\) −6.69615 + 3.86603i −0.472310 + 0.272688i
\(202\) −13.8301 + 3.70577i −0.973084 + 0.260737i
\(203\) −3.86603 11.1603i −0.271342 0.783296i
\(204\) 8.19615 + 14.1962i 0.573845 + 0.993929i
\(205\) 1.03590 0.0621778i 0.0723503 0.00434269i
\(206\) 9.09808 + 15.7583i 0.633893 + 1.09793i
\(207\) −0.294229 1.09808i −0.0204503 0.0763216i
\(208\) 12.0000 + 12.0000i 0.832050 + 0.832050i
\(209\) 2.53590 0.175412
\(210\) 16.0263 + 2.09808i 1.10592 + 0.144781i
\(211\) 20.5359i 1.41375i 0.707339 + 0.706875i \(0.249896\pi\)
−0.707339 + 0.706875i \(0.750104\pi\)
\(212\) 6.00000 1.60770i 0.412082 0.110417i
\(213\) 28.8564 7.73205i 1.97721 0.529791i
\(214\) 6.75833 3.90192i 0.461990 0.266730i
\(215\) −5.59808 4.96410i −0.381786 0.338549i
\(216\) 12.3923i 0.843190i
\(217\) 5.09808 26.4904i 0.346080 1.79828i
\(218\) 5.83013 1.56218i 0.394866 0.105804i
\(219\) −8.09808 14.0263i −0.547217 0.947808i
\(220\) 2.92820 + 1.46410i 0.197419 + 0.0987097i
\(221\) −15.5885 9.00000i −1.04859 0.605406i
\(222\) −12.9282 + 12.9282i −0.867684 + 0.867684i
\(223\) −7.92820 + 7.92820i −0.530912 + 0.530912i −0.920844 0.389932i \(-0.872499\pi\)
0.389932 + 0.920844i \(0.372499\pi\)
\(224\) 6.53590 13.4641i 0.436698 0.899608i
\(225\) −2.92820 + 2.19615i −0.195214 + 0.146410i
\(226\) 5.07180i 0.337371i
\(227\) −3.43782 12.8301i −0.228176 0.851565i −0.981107 0.193466i \(-0.938027\pi\)
0.752931 0.658100i \(-0.228639\pi\)
\(228\) 9.46410 + 9.46410i 0.626775 + 0.626775i
\(229\) 13.3923 7.73205i 0.884988 0.510948i 0.0126885 0.999919i \(-0.495961\pi\)
0.872300 + 0.488971i \(0.162628\pi\)
\(230\) −2.70577 4.09808i −0.178413 0.270219i
\(231\) 0.267949 + 3.73205i 0.0176298 + 0.245551i
\(232\) 8.92820 8.92820i 0.586165 0.586165i
\(233\) −1.90192 + 7.09808i −0.124599 + 0.465010i −0.999825 0.0187040i \(-0.994046\pi\)
0.875226 + 0.483714i \(0.160713\pi\)
\(234\) −2.19615 3.80385i −0.143567 0.248665i
\(235\) −1.43782 0.294229i −0.0937932 0.0191934i
\(236\) −8.92820 + 15.4641i −0.581177 + 1.00663i
\(237\) 17.6603 17.6603i 1.14716 1.14716i
\(238\) −3.00000 + 15.5885i −0.194461 + 1.01045i
\(239\) 4.73205i 0.306091i −0.988219 0.153045i \(-0.951092\pi\)
0.988219 0.153045i \(-0.0489081\pi\)
\(240\) 5.46410 + 16.3923i 0.352706 + 1.05812i
\(241\) −17.6603 10.1962i −1.13760 0.656792i −0.191763 0.981441i \(-0.561420\pi\)
−0.945834 + 0.324649i \(0.894754\pi\)
\(242\) 3.83013 14.2942i 0.246210 0.918868i
\(243\) −1.92820 + 7.19615i −0.123694 + 0.461633i
\(244\) −17.1962 + 9.92820i −1.10087 + 0.635588i
\(245\) 10.4019 + 11.6962i 0.664555 + 0.747240i
\(246\) −0.633975 + 1.09808i −0.0404207 + 0.0700108i
\(247\) −14.1962 3.80385i −0.903280 0.242033i
\(248\) 27.8564 7.46410i 1.76888 0.473971i
\(249\) −10.7942 6.23205i −0.684056 0.394940i
\(250\) −9.00000 + 13.0000i −0.569210 + 0.822192i
\(251\) −19.6603 −1.24094 −0.620472 0.784229i \(-0.713059\pi\)
−0.620472 + 0.784229i \(0.713059\pi\)
\(252\) −2.53590 + 2.92820i −0.159747 + 0.184459i
\(253\) 0.803848 0.803848i 0.0505375 0.0505375i
\(254\) −22.0000 −1.38040
\(255\) −10.0981 15.2942i −0.632366 0.957762i
\(256\) 16.0000 1.00000
\(257\) 6.92820 25.8564i 0.432169 1.61288i −0.315581 0.948899i \(-0.602199\pi\)
0.747751 0.663980i \(-0.231134\pi\)
\(258\) 8.83013 2.36603i 0.549740 0.147302i
\(259\) −17.6603 + 1.26795i −1.09735 + 0.0787865i
\(260\) −14.1962 12.5885i −0.880408 0.780703i
\(261\) −2.83013 + 1.63397i −0.175180 + 0.101140i
\(262\) −2.73205 + 10.1962i −0.168787 + 0.629920i
\(263\) 0.401924 0.107695i 0.0247837 0.00664077i −0.246406 0.969167i \(-0.579250\pi\)
0.271190 + 0.962526i \(0.412583\pi\)
\(264\) −3.46410 + 2.00000i −0.213201 + 0.123091i
\(265\) −6.58846 + 2.19615i −0.404726 + 0.134909i
\(266\) 0.928203 + 12.9282i 0.0569118 + 0.792679i
\(267\) 23.4904 + 23.4904i 1.43759 + 1.43759i
\(268\) −2.07180 7.73205i −0.126555 0.472310i
\(269\) −3.06218 1.76795i −0.186704 0.107794i 0.403734 0.914876i \(-0.367712\pi\)
−0.590439 + 0.807082i \(0.701045\pi\)
\(270\) 0.830127 + 13.8301i 0.0505199 + 0.841675i
\(271\) 10.3923 6.00000i 0.631288 0.364474i −0.149963 0.988692i \(-0.547915\pi\)
0.781251 + 0.624218i \(0.214582\pi\)
\(272\) −16.3923 + 4.39230i −0.993929 + 0.266323i
\(273\) 4.09808 21.2942i 0.248027 1.28879i
\(274\) −6.00000 + 10.3923i −0.362473 + 0.627822i
\(275\) −3.36603 1.43782i −0.202979 0.0867039i
\(276\) 6.00000 0.361158
\(277\) −18.7583 + 5.02628i −1.12708 + 0.302000i −0.773745 0.633497i \(-0.781619\pi\)
−0.353334 + 0.935497i \(0.614952\pi\)
\(278\) 1.26795 1.26795i 0.0760465 0.0760465i
\(279\) −7.46410 −0.446864
\(280\) −6.39230 + 15.4641i −0.382013 + 0.924157i
\(281\) −24.2487 −1.44656 −0.723278 0.690557i \(-0.757366\pi\)
−0.723278 + 0.690557i \(0.757366\pi\)
\(282\) 1.26795 1.26795i 0.0755053 0.0755053i
\(283\) 13.5622 3.63397i 0.806188 0.216017i 0.167889 0.985806i \(-0.446305\pi\)
0.638299 + 0.769789i \(0.279638\pi\)
\(284\) 30.9282i 1.83525i
\(285\) −11.1962 9.92820i −0.663203 0.588096i
\(286\) 2.19615 3.80385i 0.129861 0.224926i
\(287\) −1.16025 + 0.401924i −0.0684876 + 0.0237248i
\(288\) −4.00000 1.07180i −0.235702 0.0631562i
\(289\) 0.866025 0.500000i 0.0509427 0.0294118i
\(290\) −9.36603 + 10.5622i −0.549992 + 0.620232i
\(291\) −14.8301 8.56218i −0.869357 0.501924i
\(292\) 16.1962 4.33975i 0.947808 0.253964i
\(293\) 4.19615 + 4.19615i 0.245142 + 0.245142i 0.818973 0.573832i \(-0.194544\pi\)
−0.573832 + 0.818973i \(0.694544\pi\)
\(294\) −18.9282 + 2.73205i −1.10392 + 0.159336i
\(295\) 8.92820 17.8564i 0.519820 1.03964i
\(296\) −9.46410 16.3923i −0.550090 0.952783i
\(297\) −3.09808 + 0.830127i −0.179769 + 0.0481689i
\(298\) −8.29423 + 30.9545i −0.480472 + 1.79315i
\(299\) −5.70577 + 3.29423i −0.329973 + 0.190510i
\(300\) −7.19615 17.9282i −0.415470 1.03509i
\(301\) 7.96410 + 3.86603i 0.459043 + 0.222834i
\(302\) −18.8564 + 5.05256i −1.08506 + 0.290742i
\(303\) −5.06218 + 18.8923i −0.290815 + 1.08533i
\(304\) −12.0000 + 6.92820i −0.688247 + 0.397360i
\(305\) 18.5263 12.2321i 1.06081 0.700405i
\(306\) 4.39230 0.251091
\(307\) −0.758330 + 0.758330i −0.0432802 + 0.0432802i −0.728416 0.685135i \(-0.759743\pi\)
0.685135 + 0.728416i \(0.259743\pi\)
\(308\) −3.80385 0.732051i −0.216744 0.0417125i
\(309\) 24.8564 1.41403
\(310\) −30.5885 + 10.1962i −1.73731 + 0.579103i
\(311\) 21.5885 + 12.4641i 1.22417 + 0.706774i 0.965804 0.259273i \(-0.0834829\pi\)
0.258365 + 0.966047i \(0.416816\pi\)
\(312\) 22.3923 6.00000i 1.26771 0.339683i
\(313\) −16.1244 4.32051i −0.911402 0.244210i −0.227496 0.973779i \(-0.573054\pi\)
−0.683907 + 0.729570i \(0.739720\pi\)
\(314\) 12.4641 21.5885i 0.703390 1.21831i
\(315\) 2.63397 3.43782i 0.148408 0.193699i
\(316\) 12.9282 + 22.3923i 0.727268 + 1.25967i
\(317\) 1.16987 4.36603i 0.0657066 0.245220i −0.925259 0.379336i \(-0.876153\pi\)
0.990966 + 0.134115i \(0.0428192\pi\)
\(318\) 2.19615 8.19615i 0.123154 0.459617i
\(319\) −2.83013 1.63397i −0.158457 0.0914850i
\(320\) −17.8564 + 1.07180i −0.998203 + 0.0599153i
\(321\) 10.6603i 0.594997i
\(322\) 4.39230 + 3.80385i 0.244774 + 0.211980i
\(323\) 10.3923 10.3923i 0.578243 0.578243i
\(324\) −18.4641 10.6603i −1.02578 0.592236i
\(325\) 16.6865 + 13.0981i 0.925602 + 0.726551i
\(326\) −2.66025 4.60770i −0.147338 0.255197i
\(327\) 2.13397 7.96410i 0.118009 0.440416i
\(328\) −0.928203 0.928203i −0.0512514 0.0512514i
\(329\) 1.73205 0.124356i 0.0954911 0.00685595i
\(330\) 3.73205 2.46410i 0.205443 0.135644i
\(331\) 6.29423 3.63397i 0.345962 0.199741i −0.316943 0.948444i \(-0.602656\pi\)
0.662905 + 0.748703i \(0.269323\pi\)
\(332\) 9.12436 9.12436i 0.500764 0.500764i
\(333\) 1.26795 + 4.73205i 0.0694832 + 0.259315i
\(334\) 6.58846i 0.360504i
\(335\) 2.83013 + 8.49038i 0.154626 + 0.463879i
\(336\) −11.4641 16.9282i −0.625418 0.923509i
\(337\) −19.6603 + 19.6603i −1.07096 + 1.07096i −0.0736804 + 0.997282i \(0.523474\pi\)
−0.997282 + 0.0736804i \(0.976526\pi\)
\(338\) −5.00000 + 5.00000i −0.271964 + 0.271964i
\(339\) 6.00000 + 3.46410i 0.325875 + 0.188144i
\(340\) 18.0000 6.00000i 0.976187 0.325396i
\(341\) −3.73205 6.46410i −0.202102 0.350051i
\(342\) 3.46410 0.928203i 0.187317 0.0501915i
\(343\) −15.5885 10.0000i −0.841698 0.539949i
\(344\) 9.46410i 0.510270i
\(345\) −6.69615 + 0.401924i −0.360509 + 0.0216388i
\(346\) −0.588457 + 0.339746i −0.0316357 + 0.0182649i
\(347\) 34.9186 9.35641i 1.87453 0.502278i 0.874682 0.484697i \(-0.161070\pi\)
0.999845 0.0175817i \(-0.00559672\pi\)
\(348\) −4.46410 16.6603i −0.239301 0.893083i
\(349\) 19.9808i 1.06955i −0.844996 0.534773i \(-0.820397\pi\)
0.844996 0.534773i \(-0.179603\pi\)
\(350\) 6.09808 17.6865i 0.325956 0.945385i
\(351\) 18.5885 0.992178
\(352\) −1.07180 4.00000i −0.0571270 0.213201i
\(353\) −6.80385 25.3923i −0.362132 1.35150i −0.871267 0.490809i \(-0.836701\pi\)
0.509135 0.860687i \(-0.329965\pi\)
\(354\) 12.1962 + 21.1244i 0.648218 + 1.12275i
\(355\) −2.07180 34.5167i −0.109960 1.83195i
\(356\) −29.7846 + 17.1962i −1.57858 + 0.911394i
\(357\) 16.3923 + 14.1962i 0.867573 + 0.751340i
\(358\) 19.1962 5.14359i 1.01455 0.271847i
\(359\) −4.09808 + 2.36603i −0.216288 + 0.124874i −0.604230 0.796810i \(-0.706519\pi\)
0.387942 + 0.921684i \(0.373186\pi\)
\(360\) 4.53590 + 0.928203i 0.239063 + 0.0489206i
\(361\) −3.50000 + 6.06218i −0.184211 + 0.319062i
\(362\) 22.5167 + 22.5167i 1.18345 + 1.18345i
\(363\) −14.2942 14.2942i −0.750252 0.750252i
\(364\) 20.1962 + 9.80385i 1.05857 + 0.513861i
\(365\) −17.7846 + 5.92820i −0.930889 + 0.310296i
\(366\) 27.1244i 1.41781i
\(367\) 8.06218 2.16025i 0.420842 0.112764i −0.0421820 0.999110i \(-0.513431\pi\)
0.463024 + 0.886346i \(0.346764\pi\)
\(368\) −1.60770 + 6.00000i −0.0838069 + 0.312772i
\(369\) 0.169873 + 0.294229i 0.00884323 + 0.0153169i
\(370\) 11.6603 + 17.6603i 0.606188 + 0.918113i
\(371\) 6.80385 4.60770i 0.353238 0.239220i
\(372\) 10.1962 38.0526i 0.528646 1.97293i
\(373\) −9.46410 2.53590i −0.490033 0.131304i 0.00533769 0.999986i \(-0.498301\pi\)
−0.495370 + 0.868682i \(0.664968\pi\)
\(374\) 2.19615 + 3.80385i 0.113560 + 0.196692i
\(375\) 9.23205 + 19.5263i 0.476741 + 1.00833i
\(376\) 0.928203 + 1.60770i 0.0478684 + 0.0829105i
\(377\) 13.3923 + 13.3923i 0.689739 + 0.689739i
\(378\) −5.36603 15.4904i −0.275999 0.796739i
\(379\) −30.2487 −1.55377 −0.776886 0.629641i \(-0.783202\pi\)
−0.776886 + 0.629641i \(0.783202\pi\)
\(380\) 12.9282 8.53590i 0.663203 0.437882i
\(381\) −15.0263 + 26.0263i −0.769820 + 1.33337i
\(382\) 1.14359 4.26795i 0.0585113 0.218367i
\(383\) −7.33013 1.96410i −0.374552 0.100361i 0.0666319 0.997778i \(-0.478775\pi\)
−0.441184 + 0.897417i \(0.645441\pi\)
\(384\) 10.9282 18.9282i 0.557678 0.965926i
\(385\) 4.29423 + 0.562178i 0.218854 + 0.0286512i
\(386\) −14.6603 8.46410i −0.746187 0.430811i
\(387\) 0.633975 2.36603i 0.0322267 0.120272i
\(388\) 12.5359 12.5359i 0.636414 0.636414i
\(389\) −7.53590 + 13.0526i −0.382085 + 0.661791i −0.991360 0.131168i \(-0.958127\pi\)
0.609275 + 0.792959i \(0.291461\pi\)
\(390\) −24.5885 + 8.19615i −1.24508 + 0.415028i
\(391\) 6.58846i 0.333193i
\(392\) 2.33975 19.6603i 0.118175 0.992993i
\(393\) 10.1962 + 10.1962i 0.514328 + 0.514328i
\(394\) 11.0718i 0.557789i
\(395\) −15.9282 24.1244i −0.801435 1.21383i
\(396\) 1.07180i 0.0538598i
\(397\) −21.7583 5.83013i −1.09202 0.292606i −0.332508 0.943100i \(-0.607895\pi\)
−0.759511 + 0.650495i \(0.774562\pi\)
\(398\) 4.73205 1.26795i 0.237196 0.0635566i
\(399\) 15.9282 + 7.73205i 0.797408 + 0.387087i
\(400\) 19.8564 2.39230i 0.992820 0.119615i
\(401\) 15.3564 + 26.5981i 0.766862 + 1.32824i 0.939256 + 0.343216i \(0.111516\pi\)
−0.172394 + 0.985028i \(0.555150\pi\)
\(402\) −10.5622 2.83013i −0.526794 0.141154i
\(403\) 11.1962 + 41.7846i 0.557720 + 2.08144i
\(404\) −17.5359 10.1244i −0.872444 0.503706i
\(405\) 21.3205 + 10.6603i 1.05942 + 0.529712i
\(406\) 7.29423 15.0263i 0.362006 0.745742i
\(407\) −3.46410 + 3.46410i −0.171709 + 0.171709i
\(408\) −6.00000 + 22.3923i −0.297044 + 1.10858i
\(409\) −5.69615 + 9.86603i −0.281657 + 0.487844i −0.971793 0.235836i \(-0.924217\pi\)
0.690136 + 0.723679i \(0.257551\pi\)
\(410\) 1.09808 + 0.973721i 0.0542301 + 0.0480886i
\(411\) 8.19615 + 14.1962i 0.404286 + 0.700245i
\(412\) −6.66025 + 24.8564i −0.328127 + 1.22459i
\(413\) −4.46410 + 23.1962i −0.219664 + 1.14141i
\(414\) 0.803848 1.39230i 0.0395070 0.0684280i
\(415\) −9.57180 + 10.7942i −0.469861 + 0.529868i
\(416\) 24.0000i 1.17670i
\(417\) −0.633975 2.36603i −0.0310459 0.115865i
\(418\) 2.53590 + 2.53590i 0.124035 + 0.124035i
\(419\) 2.39230i 0.116872i −0.998291 0.0584359i \(-0.981389\pi\)
0.998291 0.0584359i \(-0.0186113\pi\)
\(420\) 13.9282 + 18.1244i 0.679627 + 0.884378i
\(421\) 30.1244i 1.46817i −0.679057 0.734086i \(-0.737611\pi\)
0.679057 0.734086i \(-0.262389\pi\)
\(422\) −20.5359 + 20.5359i −0.999672 + 0.999672i
\(423\) −0.124356 0.464102i −0.00604638 0.0225654i
\(424\) 7.60770 + 4.39230i 0.369462 + 0.213309i
\(425\) −19.6865 + 7.90192i −0.954937 + 0.383300i
\(426\) 36.5885 + 21.1244i 1.77272 + 1.02348i
\(427\) −17.1962 + 19.8564i −0.832180 + 0.960919i
\(428\) 10.6603 + 2.85641i 0.515283 + 0.138070i
\(429\) −3.00000 5.19615i −0.144841 0.250873i
\(430\) −0.633975 10.5622i −0.0305730 0.509353i
\(431\) 6.63397 11.4904i 0.319547 0.553472i −0.660846 0.750521i \(-0.729802\pi\)
0.980394 + 0.197049i \(0.0631358\pi\)
\(432\) 12.3923 12.3923i 0.596225 0.596225i
\(433\) 11.4641 11.4641i 0.550930 0.550930i −0.375780 0.926709i \(-0.622625\pi\)
0.926709 + 0.375780i \(0.122625\pi\)
\(434\) 31.5885 21.3923i 1.51629 1.02686i
\(435\) 6.09808 + 18.2942i 0.292380 + 0.877141i
\(436\) 7.39230 + 4.26795i 0.354027 + 0.204398i
\(437\) −1.39230 5.19615i −0.0666030 0.248566i
\(438\) 5.92820 22.1244i 0.283261 1.05714i
\(439\) 2.66025 + 4.60770i 0.126967 + 0.219913i 0.922500 0.385997i \(-0.126142\pi\)
−0.795533 + 0.605910i \(0.792809\pi\)
\(440\) 1.46410 + 4.39230i 0.0697983 + 0.209395i
\(441\) −1.90192 + 4.75833i −0.0905678 + 0.226587i
\(442\) −6.58846 24.5885i −0.313381 1.16955i
\(443\) 33.3564 + 8.93782i 1.58481 + 0.424649i 0.940411 0.340040i \(-0.110441\pi\)
0.644400 + 0.764689i \(0.277107\pi\)
\(444\) −25.8564 −1.22709
\(445\) 32.0885 21.1865i 1.52114 1.00434i
\(446\) −15.8564 −0.750823
\(447\) 30.9545 + 30.9545i 1.46410 + 1.46410i
\(448\) 20.0000 6.92820i 0.944911 0.327327i
\(449\) 23.1962i 1.09469i −0.836906 0.547347i \(-0.815638\pi\)
0.836906 0.547347i \(-0.184362\pi\)
\(450\) −5.12436 0.732051i −0.241564 0.0345092i
\(451\) −0.169873 + 0.294229i −0.00799901 + 0.0138547i
\(452\) −5.07180 + 5.07180i −0.238557 + 0.238557i
\(453\) −6.90192 + 25.7583i −0.324281 + 1.21023i
\(454\) 9.39230 16.2679i 0.440803 0.763493i
\(455\) −23.1962 9.58846i −1.08745 0.449514i
\(456\) 18.9282i 0.886394i
\(457\) 13.9282 + 3.73205i 0.651534 + 0.174578i 0.569422 0.822045i \(-0.307167\pi\)
0.0821116 + 0.996623i \(0.473834\pi\)
\(458\) 21.1244 + 5.66025i 0.987076 + 0.264486i
\(459\) −9.29423 + 16.0981i −0.433817 + 0.751394i
\(460\) 1.39230 6.80385i 0.0649165 0.317231i
\(461\) −12.1436 −0.565584 −0.282792 0.959181i \(-0.591261\pi\)
−0.282792 + 0.959181i \(0.591261\pi\)
\(462\) −3.46410 + 4.00000i −0.161165 + 0.186097i
\(463\) 0.830127 + 0.830127i 0.0385793 + 0.0385793i 0.726133 0.687554i \(-0.241316\pi\)
−0.687554 + 0.726133i \(0.741316\pi\)
\(464\) 17.8564 0.828963
\(465\) −8.83013 + 43.1506i −0.409487 + 2.00106i
\(466\) −9.00000 + 5.19615i −0.416917 + 0.240707i
\(467\) 6.23205 + 1.66987i 0.288385 + 0.0772725i 0.400111 0.916466i \(-0.368971\pi\)
−0.111727 + 0.993739i \(0.535638\pi\)
\(468\) 1.60770 6.00000i 0.0743157 0.277350i
\(469\) −5.93782 8.76795i −0.274183 0.404866i
\(470\) −1.14359 1.73205i −0.0527500 0.0798935i
\(471\) −17.0263 29.4904i −0.784530 1.35885i
\(472\) −24.3923 + 6.53590i −1.12275 + 0.300839i
\(473\) 2.36603 0.633975i 0.108790 0.0291502i
\(474\) 35.3205 1.62232
\(475\) −13.8564 + 10.3923i −0.635776 + 0.476832i
\(476\) −18.5885 + 12.5885i −0.852001 + 0.576991i
\(477\) −1.60770 1.60770i −0.0736113 0.0736113i
\(478\) 4.73205 4.73205i 0.216439 0.216439i
\(479\) −1.90192 + 3.29423i −0.0869011 + 0.150517i −0.906200 0.422850i \(-0.861030\pi\)
0.819299 + 0.573367i \(0.194363\pi\)
\(480\) −10.9282 + 21.8564i −0.498802 + 0.997604i
\(481\) 24.5885 14.1962i 1.12114 0.647289i
\(482\) −7.46410 27.8564i −0.339981 1.26882i
\(483\) 7.50000 2.59808i 0.341262 0.118217i
\(484\) 18.1244 10.4641i 0.823834 0.475641i
\(485\) −13.1506 + 14.8301i −0.597140 + 0.673401i
\(486\) −9.12436 + 5.26795i −0.413889 + 0.238959i
\(487\) 5.09808 + 19.0263i 0.231016 + 0.862163i 0.979905 + 0.199467i \(0.0639211\pi\)
−0.748889 + 0.662696i \(0.769412\pi\)
\(488\) −27.1244 7.26795i −1.22786 0.329005i
\(489\) −7.26795 −0.328668
\(490\) −1.29423 + 22.0981i −0.0584673 + 0.998289i
\(491\) 12.1962i 0.550405i −0.961386 0.275202i \(-0.911255\pi\)
0.961386 0.275202i \(-0.0887448\pi\)
\(492\) −1.73205 + 0.464102i −0.0780869 + 0.0209233i
\(493\) −18.2942 + 4.90192i −0.823931 + 0.220772i
\(494\) −10.3923 18.0000i −0.467572 0.809858i
\(495\) −0.0717968 1.19615i −0.00322702 0.0537631i
\(496\) 35.3205 + 20.3923i 1.58594 + 0.915642i
\(497\) 13.3923 + 38.6603i 0.600727 + 1.73415i
\(498\) −4.56218 17.0263i −0.204436 0.762966i
\(499\) 6.75833 + 11.7058i 0.302544 + 0.524022i 0.976712 0.214556i \(-0.0688306\pi\)
−0.674167 + 0.738579i \(0.735497\pi\)
\(500\) −22.0000 + 4.00000i −0.983870 + 0.178885i
\(501\) −7.79423 4.50000i −0.348220 0.201045i
\(502\) −19.6603 19.6603i −0.877480 0.877480i
\(503\) 22.6865 22.6865i 1.01154 1.01154i 0.0116099 0.999933i \(-0.496304\pi\)
0.999933 0.0116099i \(-0.00369564\pi\)
\(504\) −5.46410 + 0.392305i −0.243390 + 0.0174746i
\(505\) 20.2487 + 10.1244i 0.901056 + 0.450528i
\(506\) 1.60770 0.0714708
\(507\) 2.50000 + 9.33013i 0.111029 + 0.414365i
\(508\) −22.0000 22.0000i −0.976092 0.976092i
\(509\) 9.57180 5.52628i 0.424262 0.244948i −0.272637 0.962117i \(-0.587896\pi\)
0.696899 + 0.717169i \(0.254562\pi\)
\(510\) 5.19615 25.3923i 0.230089 1.12439i
\(511\) 18.3660 12.4378i 0.812465 0.550217i
\(512\) 16.0000 + 16.0000i 0.707107 + 0.707107i
\(513\) −3.92820 + 14.6603i −0.173434 + 0.647266i
\(514\) 32.7846 18.9282i 1.44607 0.834887i
\(515\) 5.76795 28.1865i 0.254166 1.24205i
\(516\) 11.1962 + 6.46410i 0.492883 + 0.284566i
\(517\) 0.339746 0.339746i 0.0149420 0.0149420i
\(518\) −18.9282 16.3923i −0.831658 0.720237i
\(519\) 0.928203i 0.0407436i
\(520\) −1.60770 26.7846i −0.0705021 1.17458i
\(521\) 7.39230 + 4.26795i 0.323863 + 0.186982i 0.653113 0.757260i \(-0.273463\pi\)
−0.329250 + 0.944243i \(0.606796\pi\)
\(522\) −4.46410 1.19615i −0.195388 0.0523542i
\(523\) 6.50962 24.2942i 0.284646 1.06231i −0.664452 0.747331i \(-0.731335\pi\)
0.949098 0.314982i \(-0.101998\pi\)
\(524\) −12.9282 + 7.46410i −0.564771 + 0.326071i
\(525\) −16.7583 19.2942i −0.731393 0.842069i
\(526\) 0.509619 + 0.294229i 0.0222204 + 0.0128290i
\(527\) −41.7846 11.1962i −1.82017 0.487712i
\(528\) −5.46410 1.46410i −0.237795 0.0637168i
\(529\) 17.8301 + 10.2942i 0.775223 + 0.447575i
\(530\) −8.78461 4.39230i −0.381579 0.190790i
\(531\) 6.53590 0.283634
\(532\) −12.0000 + 13.8564i −0.520266 + 0.600751i
\(533\) 1.39230 1.39230i 0.0603074 0.0603074i
\(534\) 46.9808i 2.03306i
\(535\) −12.0885 2.47372i −0.522630 0.106948i
\(536\) 5.66025 9.80385i 0.244486 0.423462i
\(537\) 7.02628 26.2224i 0.303206 1.13158i
\(538\) −1.29423 4.83013i −0.0557982 0.208242i
\(539\) −5.07180 + 0.732051i −0.218458 + 0.0315317i
\(540\) −13.0000 + 14.6603i −0.559431 + 0.630877i
\(541\) 1.79423 1.03590i 0.0771399 0.0445368i −0.460934 0.887434i \(-0.652485\pi\)
0.538074 + 0.842898i \(0.319152\pi\)
\(542\) 16.3923 + 4.39230i 0.704110 + 0.188666i
\(543\) 42.0167 11.2583i 1.80311 0.483141i
\(544\) −20.7846 12.0000i −0.891133 0.514496i
\(545\) −8.53590 4.26795i −0.365638 0.182819i
\(546\) 25.3923 17.1962i 1.08669 0.735927i
\(547\) −14.4904 14.4904i −0.619564 0.619564i 0.325856 0.945420i \(-0.394348\pi\)
−0.945420 + 0.325856i \(0.894348\pi\)
\(548\) −16.3923 + 4.39230i −0.700245 + 0.187630i
\(549\) 6.29423 + 3.63397i 0.268631 + 0.155094i
\(550\) −1.92820 4.80385i −0.0822189 0.204837i
\(551\) −13.3923 + 7.73205i −0.570531 + 0.329396i
\(552\) 6.00000 + 6.00000i 0.255377 + 0.255377i
\(553\) 25.8564 + 22.3923i 1.09953 + 0.952218i
\(554\) −23.7846 13.7321i −1.01051 0.583419i
\(555\) 28.8564 1.73205i 1.22489 0.0735215i
\(556\) 2.53590 0.107546
\(557\) −30.7583 + 8.24167i −1.30327 + 0.349211i −0.842687 0.538404i \(-0.819027\pi\)
−0.460586 + 0.887615i \(0.652361\pi\)
\(558\) −7.46410 7.46410i −0.315981 0.315981i
\(559\) −14.1962 −0.600433
\(560\) −21.8564 + 9.07180i −0.923602 + 0.383353i
\(561\) 6.00000 0.253320
\(562\) −24.2487 24.2487i −1.02287 1.02287i
\(563\) −26.3564 + 7.06218i −1.11079 + 0.297635i −0.767151 0.641466i \(-0.778326\pi\)
−0.343639 + 0.939102i \(0.611660\pi\)
\(564\) 2.53590 0.106781
\(565\) 5.32051 6.00000i 0.223835 0.252422i
\(566\) 17.1962 + 9.92820i 0.722808 + 0.417314i
\(567\) −27.6962 5.33013i −1.16313 0.223844i
\(568\) −30.9282 + 30.9282i −1.29772 + 1.29772i
\(569\) −18.8038 + 10.8564i −0.788298 + 0.455124i −0.839363 0.543571i \(-0.817072\pi\)
0.0510648 + 0.998695i \(0.483738\pi\)
\(570\) −1.26795 21.1244i −0.0531085 0.884802i
\(571\) −14.7846 8.53590i −0.618717 0.357216i 0.157653 0.987495i \(-0.449607\pi\)
−0.776369 + 0.630278i \(0.782941\pi\)
\(572\) 6.00000 1.60770i 0.250873 0.0672211i
\(573\) −4.26795 4.26795i −0.178296 0.178296i
\(574\) −1.56218 0.758330i −0.0652040 0.0316521i
\(575\) −1.09808 + 7.68653i −0.0457929 + 0.320551i
\(576\) −2.92820 5.07180i −0.122008 0.211325i
\(577\) −16.4904 + 4.41858i −0.686504 + 0.183948i −0.585178 0.810905i \(-0.698975\pi\)
−0.101326 + 0.994853i \(0.532309\pi\)
\(578\) 1.36603 + 0.366025i 0.0568192 + 0.0152246i
\(579\) −20.0263 + 11.5622i −0.832264 + 0.480508i
\(580\) −19.9282 + 1.19615i −0.827474 + 0.0496675i
\(581\) 7.45448 15.3564i 0.309264 0.637091i
\(582\) −6.26795 23.3923i −0.259815 0.969642i
\(583\) 0.588457 2.19615i 0.0243714 0.0909553i
\(584\) 20.5359 + 11.8564i 0.849782 + 0.490622i
\(585\) −1.39230 + 6.80385i −0.0575647 + 0.281304i
\(586\) 8.39230i 0.346683i
\(587\) 9.00000 9.00000i 0.371470 0.371470i −0.496543 0.868012i \(-0.665397\pi\)
0.868012 + 0.496543i \(0.165397\pi\)
\(588\) −21.6603 16.1962i −0.893254 0.667918i
\(589\) −35.3205 −1.45536
\(590\) 26.7846 8.92820i 1.10270 0.367568i
\(591\) −13.0981 7.56218i −0.538783 0.311066i
\(592\) 6.92820 25.8564i 0.284747 1.06269i
\(593\) −14.1962 3.80385i −0.582966 0.156205i −0.0447296 0.998999i \(-0.514243\pi\)
−0.538237 + 0.842794i \(0.680909\pi\)
\(594\) −3.92820 2.26795i −0.161176 0.0930551i
\(595\) 19.9019 15.2942i 0.815899 0.627002i
\(596\) −39.2487 + 22.6603i −1.60769 + 0.928200i
\(597\) 1.73205 6.46410i 0.0708881 0.264558i
\(598\) −9.00000 2.41154i −0.368037 0.0986153i
\(599\) −21.0000 12.1244i −0.858037 0.495388i 0.00531761 0.999986i \(-0.498307\pi\)
−0.863354 + 0.504598i \(0.831641\pi\)
\(600\) 10.7321 25.1244i 0.438134 1.02570i
\(601\) 28.3923i 1.15815i −0.815276 0.579073i \(-0.803415\pi\)
0.815276 0.579073i \(-0.196585\pi\)
\(602\) 4.09808 + 11.8301i 0.167025 + 0.482160i
\(603\) −2.07180 + 2.07180i −0.0843701 + 0.0843701i
\(604\) −23.9090 13.8038i −0.972842 0.561671i
\(605\) −19.5263 + 12.8923i −0.793856 + 0.524147i
\(606\) −23.9545 + 13.8301i −0.973084 + 0.561811i
\(607\) −6.16025 + 22.9904i −0.250037 + 0.933151i 0.720747 + 0.693198i \(0.243799\pi\)
−0.970784 + 0.239953i \(0.922868\pi\)
\(608\) −18.9282 5.07180i −0.767640 0.205689i
\(609\) −12.7942 18.8923i −0.518448 0.765555i
\(610\) 30.7583 + 6.29423i 1.24537 + 0.254846i
\(611\) −2.41154 + 1.39230i −0.0975606 + 0.0563266i
\(612\) 4.39230 + 4.39230i 0.177548 + 0.177548i
\(613\) −1.43782 5.36603i −0.0580731 0.216732i 0.930791 0.365551i \(-0.119119\pi\)
−0.988864 + 0.148819i \(0.952453\pi\)
\(614\) −1.51666 −0.0612074
\(615\) 1.90192 0.633975i 0.0766930 0.0255643i
\(616\) −3.07180 4.53590i −0.123766 0.182757i
\(617\) −0.928203 + 0.928203i −0.0373681 + 0.0373681i −0.725544 0.688176i \(-0.758412\pi\)
0.688176 + 0.725544i \(0.258412\pi\)
\(618\) 24.8564 + 24.8564i 0.999871 + 0.999871i
\(619\) 15.2942 + 8.83013i 0.614727 + 0.354913i 0.774813 0.632190i \(-0.217844\pi\)
−0.160086 + 0.987103i \(0.551177\pi\)
\(620\) −40.7846 20.3923i −1.63795 0.818975i
\(621\) 3.40192 + 5.89230i 0.136514 + 0.236450i
\(622\) 9.12436 + 34.0526i 0.365853 + 1.36538i
\(623\) −29.7846 + 34.3923i −1.19330 + 1.37790i
\(624\) 28.3923 + 16.3923i 1.13660 + 0.656217i
\(625\) 24.2846 5.93782i 0.971384 0.237513i
\(626\) −11.8038 20.4449i −0.471777 0.817141i
\(627\) 4.73205 1.26795i 0.188980 0.0506370i
\(628\) 34.0526 9.12436i 1.35885 0.364101i
\(629\) 28.3923i 1.13208i
\(630\) 6.07180 0.803848i 0.241906 0.0320261i
\(631\) −7.26795 −0.289332 −0.144666 0.989481i \(-0.546211\pi\)
−0.144666 + 0.989481i \(0.546211\pi\)
\(632\) −9.46410 + 35.3205i −0.376462 + 1.40497i
\(633\) 10.2679 + 38.3205i 0.408114 + 1.52310i
\(634\) 5.53590 3.19615i 0.219859 0.126935i
\(635\) 26.0263 + 23.0788i 1.03282 + 0.915856i
\(636\) 10.3923 6.00000i 0.412082 0.237915i
\(637\) 29.4904 + 3.50962i 1.16845 + 0.139056i
\(638\) −1.19615 4.46410i −0.0473561 0.176735i
\(639\) 9.80385 5.66025i 0.387834 0.223916i
\(640\) −18.9282 16.7846i −0.748203 0.663470i
\(641\) 16.3301 28.2846i 0.645001 1.11717i −0.339300 0.940678i \(-0.610190\pi\)
0.984301 0.176497i \(-0.0564765\pi\)
\(642\) 10.6603 10.6603i 0.420727 0.420727i
\(643\) 9.00000 + 9.00000i 0.354925 + 0.354925i 0.861938 0.507013i \(-0.169250\pi\)
−0.507013 + 0.861938i \(0.669250\pi\)
\(644\) 0.588457 + 8.19615i 0.0231885 + 0.322974i
\(645\) −12.9282 6.46410i −0.509048 0.254524i
\(646\) 20.7846 0.817760
\(647\) 26.2583 7.03590i 1.03232 0.276610i 0.297394 0.954755i \(-0.403883\pi\)
0.734928 + 0.678145i \(0.237216\pi\)
\(648\) −7.80385 29.1244i −0.306564 1.14411i
\(649\) 3.26795 + 5.66025i 0.128278 + 0.222184i
\(650\) 3.58846 + 29.7846i 0.140751 + 1.16825i
\(651\) −3.73205 51.9808i −0.146271 2.03729i
\(652\) 1.94744 7.26795i 0.0762677 0.284635i
\(653\) −31.4186 8.41858i −1.22950 0.329445i −0.415118 0.909768i \(-0.636260\pi\)
−0.814386 + 0.580323i \(0.802926\pi\)
\(654\) 10.0981 5.83013i 0.394866 0.227976i
\(655\) 13.9282 9.19615i 0.544220 0.359323i
\(656\) 1.85641i 0.0724805i
\(657\) −4.33975 4.33975i −0.169310 0.169310i
\(658\) 1.85641 + 1.60770i 0.0723703 + 0.0626745i
\(659\) 39.3205 1.53171 0.765855 0.643014i \(-0.222316\pi\)
0.765855 + 0.643014i \(0.222316\pi\)
\(660\) 6.19615 + 1.26795i 0.241185 + 0.0493549i
\(661\) −19.9641 + 34.5788i −0.776514 + 1.34496i 0.157426 + 0.987531i \(0.449680\pi\)
−0.933940 + 0.357430i \(0.883653\pi\)
\(662\) 9.92820 + 2.66025i 0.385871 + 0.103394i
\(663\) −33.5885 9.00000i −1.30447 0.349531i
\(664\) 18.2487 0.708187
\(665\) 12.4641 16.2679i 0.483337 0.630844i
\(666\) −3.46410 + 6.00000i −0.134231 + 0.232495i
\(667\) −1.79423 + 6.69615i −0.0694728 + 0.259276i
\(668\) 6.58846 6.58846i 0.254915 0.254915i
\(669\) −10.8301 + 18.7583i −0.418717 + 0.725239i
\(670\) −5.66025 + 11.3205i −0.218675 + 0.437349i
\(671\) 7.26795i 0.280576i
\(672\) 5.46410 28.3923i 0.210782 1.09526i
\(673\) −10.1962 10.1962i −0.393033 0.393033i 0.482734 0.875767i \(-0.339644\pi\)
−0.875767 + 0.482734i \(0.839644\pi\)
\(674\) −39.3205 −1.51457
\(675\) 13.5263 17.2321i 0.520627 0.663262i
\(676\) −10.0000 −0.384615
\(677\) −4.56218 1.22243i −0.175339 0.0469819i 0.170081 0.985430i \(-0.445597\pi\)
−0.345420 + 0.938448i \(0.612264\pi\)
\(678\) 2.53590 + 9.46410i 0.0973906 + 0.363467i
\(679\) 10.2417 21.0981i 0.393039 0.809670i
\(680\) 24.0000 + 12.0000i 0.920358 + 0.460179i
\(681\) −12.8301 22.2224i −0.491652 0.851565i
\(682\) 2.73205 10.1962i 0.104616 0.390431i
\(683\) 7.86603 + 29.3564i 0.300985 + 1.12329i 0.936347 + 0.351077i \(0.114184\pi\)
−0.635362 + 0.772215i \(0.719149\pi\)
\(684\) 4.39230 + 2.53590i 0.167944 + 0.0969625i
\(685\) 18.0000 6.00000i 0.687745 0.229248i
\(686\) −5.58846 25.5885i −0.213368 0.976972i
\(687\) 21.1244 21.1244i 0.805944 0.805944i
\(688\) −9.46410 + 9.46410i −0.360815 + 0.360815i
\(689\) −6.58846 + 11.4115i −0.251000 + 0.434745i
\(690\) −7.09808 6.29423i −0.270219 0.239617i
\(691\) 21.7583 + 37.6865i 0.827726 + 1.43366i 0.899818 + 0.436265i \(0.143699\pi\)
−0.0720922 + 0.997398i \(0.522968\pi\)
\(692\) −0.928203 0.248711i −0.0352850 0.00945459i
\(693\) 0.464102 + 1.33975i 0.0176298 + 0.0508927i
\(694\) 44.2750 + 25.5622i 1.68066 + 0.970327i
\(695\) −2.83013 + 0.169873i −0.107353 + 0.00644365i
\(696\) 12.1962 21.1244i 0.462294 0.800717i
\(697\) 0.509619 + 1.90192i 0.0193032 + 0.0720405i
\(698\) 19.9808 19.9808i 0.756283 0.756283i
\(699\) 14.1962i 0.536948i
\(700\) 23.7846 11.5885i 0.898974 0.438003i
\(701\) 33.9808i 1.28344i −0.766941 0.641718i \(-0.778222\pi\)
0.766941 0.641718i \(-0.221778\pi\)
\(702\) 18.5885 + 18.5885i 0.701576 + 0.701576i
\(703\) 6.00000 + 22.3923i 0.226294 + 0.844542i
\(704\) 2.92820 5.07180i 0.110361 0.191151i
\(705\) −2.83013 + 0.169873i −0.106589 + 0.00639779i
\(706\) 18.5885 32.1962i 0.699586 1.21172i
\(707\) −26.3038 5.06218i −0.989258 0.190383i
\(708\) −8.92820 + 33.3205i −0.335542 + 1.25226i
\(709\) 7.96410 + 13.7942i 0.299098 + 0.518053i 0.975930 0.218085i \(-0.0699809\pi\)
−0.676832 + 0.736138i \(0.736648\pi\)
\(710\) 32.4449 36.5885i 1.21763 1.37314i
\(711\) 4.73205 8.19615i 0.177466 0.307380i
\(712\) −46.9808 12.5885i −1.76068 0.471772i
\(713\) −11.1962 + 11.1962i −0.419299 + 0.419299i
\(714\) 2.19615 + 30.5885i 0.0821889 + 1.14474i
\(715\) −6.58846 + 2.19615i −0.246394 + 0.0821314i
\(716\) 24.3397 + 14.0526i 0.909619 + 0.525169i
\(717\) −2.36603 8.83013i −0.0883608 0.329767i
\(718\) −6.46410 1.73205i −0.241238 0.0646396i
\(719\) 5.36603 + 9.29423i 0.200119 + 0.346616i 0.948567 0.316578i \(-0.102534\pi\)
−0.748448 + 0.663194i \(0.769200\pi\)
\(720\) 3.60770 + 5.46410i 0.134451 + 0.203635i
\(721\) 2.43782 + 33.9545i 0.0907892 + 1.26453i
\(722\) −9.56218 + 2.56218i −0.355867 + 0.0953544i
\(723\) −38.0526 10.1962i −1.41519 0.379199i
\(724\) 45.0333i 1.67365i
\(725\) 22.1603 2.66987i 0.823011 0.0991566i
\(726\) 28.5885i 1.06102i
\(727\) 17.2942 + 17.2942i 0.641407 + 0.641407i 0.950901 0.309494i \(-0.100160\pi\)
−0.309494 + 0.950901i \(0.600160\pi\)
\(728\) 10.3923 + 30.0000i 0.385164 + 1.11187i
\(729\) 17.5885i 0.651424i
\(730\) −23.7128 11.8564i −0.877651 0.438825i
\(731\) 7.09808 12.2942i 0.262532 0.454718i
\(732\) −27.1244 + 27.1244i −1.00255 + 1.00255i
\(733\) −5.70577 + 21.2942i −0.210747 + 0.786520i 0.776873 + 0.629657i \(0.216805\pi\)
−0.987620 + 0.156863i \(0.949862\pi\)
\(734\) 10.2224 + 5.90192i 0.377317 + 0.217844i
\(735\) 25.2583 + 16.6244i 0.931668 + 0.613199i
\(736\) −7.60770 + 4.39230i −0.280423 + 0.161903i
\(737\) −2.83013 0.758330i −0.104249 0.0279335i
\(738\) −0.124356 + 0.464102i −0.00457759 + 0.0170838i
\(739\) 5.83013 10.0981i 0.214465 0.371464i −0.738642 0.674098i \(-0.764533\pi\)
0.953107 + 0.302634i \(0.0978660\pi\)
\(740\) −6.00000 + 29.3205i −0.220564 + 1.07784i
\(741\) −28.3923 −1.04302
\(742\) 11.4115 + 2.19615i 0.418931 + 0.0806233i
\(743\) −33.4186 33.4186i −1.22601 1.22601i −0.965461 0.260548i \(-0.916097\pi\)
−0.260548 0.965461i \(-0.583903\pi\)
\(744\) 48.2487 27.8564i 1.76888 1.02127i
\(745\) 42.2846 27.9186i 1.54919 1.02286i
\(746\) −6.92820 12.0000i −0.253660 0.439351i
\(747\) −4.56218 1.22243i −0.166921 0.0447264i
\(748\) −1.60770 + 6.00000i −0.0587832 + 0.219382i
\(749\) 14.5622 1.04552i 0.532090 0.0382024i
\(750\) −10.2942 + 28.7583i −0.375892 + 1.05011i
\(751\) 5.19615 + 9.00000i 0.189610 + 0.328415i 0.945120 0.326722i \(-0.105944\pi\)
−0.755510 + 0.655137i \(0.772611\pi\)
\(752\) −0.679492 + 2.53590i −0.0247785 + 0.0924747i
\(753\) −36.6865 + 9.83013i −1.33693 + 0.358230i
\(754\) 26.7846i 0.975438i
\(755\) 27.6077 + 13.8038i 1.00475 + 0.502373i
\(756\) 10.1244 20.8564i 0.368219 0.758540i
\(757\) 37.0526 + 37.0526i 1.34670 + 1.34670i 0.889222 + 0.457476i \(0.151247\pi\)
0.457476 + 0.889222i \(0.348753\pi\)
\(758\) −30.2487 30.2487i −1.09868 1.09868i
\(759\) 1.09808 1.90192i 0.0398576 0.0690355i
\(760\) 21.4641 + 4.39230i 0.778585 + 0.159326i
\(761\) −30.8038 + 17.7846i −1.11664 + 0.644692i −0.940541 0.339681i \(-0.889681\pi\)
−0.176098 + 0.984373i \(0.556348\pi\)
\(762\) −41.0526 + 11.0000i −1.48718 + 0.398488i
\(763\) 11.0885 + 2.13397i 0.401429 + 0.0772551i
\(764\) 5.41154 3.12436i 0.195783 0.113035i
\(765\) −5.19615 4.60770i −0.187867 0.166592i
\(766\) −5.36603 9.29423i −0.193882 0.335814i
\(767\) −9.80385 36.5885i −0.353996 1.32113i
\(768\) 29.8564 8.00000i 1.07735 0.288675i
\(769\) −22.6410 −0.816456 −0.408228 0.912880i \(-0.633853\pi\)
−0.408228 + 0.912880i \(0.633853\pi\)
\(770\) 3.73205 + 4.85641i 0.134494 + 0.175013i
\(771\) 51.7128i 1.86239i
\(772\) −6.19615 23.1244i −0.223004 0.832264i
\(773\) 13.0981 3.50962i 0.471105 0.126232i −0.0154528 0.999881i \(-0.504919\pi\)
0.486558 + 0.873648i \(0.338252\pi\)
\(774\) 3.00000 1.73205i 0.107833 0.0622573i
\(775\) 46.8827 + 20.0263i 1.68408 + 0.719365i
\(776\) 25.0718 0.900025
\(777\) −32.3205 + 11.1962i −1.15949 + 0.401660i
\(778\) −20.5885 + 5.51666i −0.738132 + 0.197782i
\(779\) 0.803848 + 1.39230i 0.0288008 + 0.0498845i
\(780\) −32.7846 16.3923i −1.17388 0.586939i
\(781\) 9.80385 + 5.66025i 0.350809 + 0.202540i
\(782\) 6.58846 6.58846i 0.235603 0.235603i
\(783\) 13.8301 13.8301i 0.494248 0.494248i
\(784\) 22.0000 17.3205i 0.785714 0.618590i
\(785\) −37.3923 + 12.4641i −1.33459 + 0.444863i
\(786\) 20.3923i 0.727369i
\(787\) −2.72243 10.1603i −0.0970442 0.362174i 0.900277 0.435317i \(-0.143364\pi\)
−0.997321 + 0.0731430i \(0.976697\pi\)
\(788\) 11.0718 11.0718i 0.394416 0.394416i
\(789\) 0.696152 0.401924i 0.0247837 0.0143089i
\(790\) 8.19615 40.0526i 0.291606 1.42501i
\(791\) −4.14359 + 8.53590i −0.147329 + 0.303502i
\(792\) −1.07180 + 1.07180i −0.0380846 + 0.0380846i
\(793\) 10.9019 40.6865i 0.387139 1.44482i
\(794\) −15.9282 27.5885i −0.565271 0.979078i
\(795\) −11.1962 + 7.39230i −0.397087 + 0.262178i
\(796\) 6.00000 + 3.46410i 0.212664 + 0.122782i
\(797\) −0.928203 + 0.928203i −0.0328786 + 0.0328786i −0.723355 0.690476i \(-0.757401\pi\)
0.690476 + 0.723355i \(0.257401\pi\)
\(798\) 8.19615 + 23.6603i 0.290141 + 0.837564i
\(799\) 2.78461i 0.0985124i
\(800\) 22.2487 + 17.4641i 0.786611 + 0.617449i
\(801\) 10.9019 + 6.29423i 0.385201 + 0.222396i
\(802\) −11.2417 + 41.9545i −0.396957 + 1.48146i
\(803\) 1.58846 5.92820i 0.0560554 0.209202i
\(804\) −7.73205 13.3923i −0.272688 0.472310i
\(805\) −1.20577 9.10770i −0.0424979 0.321004i
\(806\) −30.5885 + 52.9808i −1.07743 + 1.86617i
\(807\) −6.59808 1.76795i −0.232263 0.0622348i
\(808\) −7.41154 27.6603i −0.260737 0.973084i
\(809\) 40.5788 + 23.4282i 1.42668 + 0.823692i 0.996857 0.0792233i \(-0.0252440\pi\)
0.429819 + 0.902915i \(0.358577\pi\)
\(810\) 10.6603 + 31.9808i 0.374563 + 1.12369i
\(811\) −30.3397 −1.06537 −0.532686 0.846313i \(-0.678817\pi\)
−0.532686 + 0.846313i \(0.678817\pi\)
\(812\) 22.3205 7.73205i 0.783296 0.271342i
\(813\) 16.3923 16.3923i 0.574903 0.574903i
\(814\) −6.92820 −0.242833
\(815\) −1.68653 + 8.24167i −0.0590767 + 0.288693i
\(816\) −28.3923 + 16.3923i −0.993929 + 0.573845i
\(817\) 3.00000 11.1962i 0.104957 0.391704i
\(818\) −15.5622 + 4.16987i −0.544119 + 0.145796i
\(819\) −0.588457 8.19615i −0.0205624 0.286397i
\(820\) 0.124356 + 2.07180i 0.00434269 + 0.0723503i
\(821\) 9.92820 5.73205i 0.346497 0.200050i −0.316645 0.948544i \(-0.602556\pi\)
0.663141 + 0.748494i \(0.269223\pi\)
\(822\) −6.00000 + 22.3923i −0.209274 + 0.781021i
\(823\) −13.6962 + 3.66987i −0.477418 + 0.127924i −0.489500 0.872003i \(-0.662821\pi\)
0.0120822 + 0.999927i \(0.496154\pi\)
\(824\) −31.5167 + 18.1962i −1.09793 + 0.633893i
\(825\) −7.00000 1.00000i −0.243709 0.0348155i
\(826\) −27.6603 + 18.7321i −0.962423 + 0.651771i
\(827\) 17.1506 + 17.1506i 0.596386 + 0.596386i 0.939349 0.342963i \(-0.111431\pi\)
−0.342963 + 0.939349i \(0.611431\pi\)
\(828\) 2.19615 0.588457i 0.0763216 0.0204503i
\(829\) −8.19615 4.73205i −0.284664 0.164351i 0.350869 0.936425i \(-0.385886\pi\)
−0.635533 + 0.772074i \(0.719220\pi\)
\(830\) −20.3660 + 1.22243i −0.706915 + 0.0424312i
\(831\) −32.4904 + 18.7583i −1.12708 + 0.650719i
\(832\) −24.0000 + 24.0000i −0.832050 + 0.832050i
\(833\) −17.7846 + 23.7846i −0.616200 + 0.824088i
\(834\) 1.73205 3.00000i 0.0599760 0.103882i
\(835\) −6.91154 + 7.79423i −0.239184 + 0.269730i
\(836\) 5.07180i 0.175412i
\(837\) 43.1506 11.5622i 1.49150 0.399647i
\(838\) 2.39230 2.39230i 0.0826408 0.0826408i
\(839\) −14.1962 −0.490106 −0.245053 0.969510i \(-0.578805\pi\)
−0.245053 + 0.969510i \(0.578805\pi\)
\(840\) −4.19615 + 32.0526i −0.144781 + 1.10592i
\(841\) −9.07180 −0.312821
\(842\) 30.1244 30.1244i 1.03815 1.03815i
\(843\) −45.2487 + 12.1244i −1.55845 + 0.417585i
\(844\) −41.0718 −1.41375
\(845\) 11.1603 0.669873i 0.383924 0.0230443i
\(846\) 0.339746 0.588457i 0.0116807 0.0202316i
\(847\) 18.1244 20.9282i 0.622760 0.719102i
\(848\) 3.21539 + 12.0000i 0.110417 + 0.412082i
\(849\) 23.4904 13.5622i 0.806188 0.465453i
\(850\) −27.5885 11.7846i −0.946276 0.404209i
\(851\) 9.00000 + 5.19615i 0.308516 + 0.178122i
\(852\) 15.4641 + 57.7128i 0.529791 + 1.97721i
\(853\) −29.3205 29.3205i −1.00392 1.00392i −0.999992 0.00392277i \(-0.998751\pi\)
−0.00392277 0.999992i \(-0.501249\pi\)
\(854\) −37.0526 + 2.66025i −1.26791 + 0.0910320i
\(855\) −5.07180 2.53590i −0.173452 0.0867259i
\(856\) 7.80385 + 13.5167i 0.266730 + 0.461990i
\(857\) 15.7583 4.22243i 0.538294 0.144236i 0.0205786 0.999788i \(-0.493449\pi\)
0.517716 + 0.855553i \(0.326782\pi\)
\(858\) 2.19615 8.19615i 0.0749754 0.279812i
\(859\) 14.1962 8.19615i 0.484366 0.279649i −0.237868 0.971298i \(-0.576449\pi\)
0.722234 + 0.691648i \(0.243115\pi\)
\(860\) 9.92820 11.1962i 0.338549 0.381786i
\(861\) −1.96410 + 1.33013i −0.0669364 + 0.0453306i
\(862\) 18.1244 4.85641i 0.617318 0.165410i
\(863\) 6.23205 23.2583i 0.212141 0.791723i −0.775012 0.631947i \(-0.782256\pi\)
0.987153 0.159776i \(-0.0510772\pi\)
\(864\) 24.7846 0.843190
\(865\) 1.05256 + 0.215390i 0.0357881 + 0.00732349i
\(866\) 22.9282 0.779132
\(867\) 1.36603 1.36603i 0.0463927 0.0463927i
\(868\) 52.9808 + 10.1962i 1.79828 + 0.346080i
\(869\) 9.46410 0.321048
\(870\) −12.1962 + 24.3923i −0.413488 + 0.826977i
\(871\) 14.7058 + 8.49038i 0.498286 + 0.287686i
\(872\) 3.12436 + 11.6603i 0.105804 + 0.394866i
\(873\) −6.26795 1.67949i −0.212138 0.0568422i
\(874\) 3.80385 6.58846i 0.128667 0.222858i
\(875\) −25.7679 + 14.5263i −0.871116 + 0.491078i
\(876\) 28.0526 16.1962i 0.947808 0.547217i
\(877\) −5.19615 + 19.3923i −0.175462 + 0.654832i 0.821011 + 0.570912i \(0.193410\pi\)
−0.996473 + 0.0839192i \(0.973256\pi\)
\(878\) −1.94744 + 7.26795i −0.0657230 + 0.245281i
\(879\) 9.92820 + 5.73205i 0.334870 + 0.193337i
\(880\) −2.92820 + 5.85641i −0.0987097 + 0.197419i
\(881\) 27.2487i 0.918032i −0.888428 0.459016i \(-0.848202\pi\)
0.888428 0.459016i \(-0.151798\pi\)
\(882\) −6.66025 + 2.85641i −0.224262 + 0.0961802i
\(883\) 15.2487 15.2487i 0.513160 0.513160i −0.402333 0.915493i \(-0.631801\pi\)
0.915493 + 0.402333i \(0.131801\pi\)
\(884\) 18.0000 31.1769i 0.605406 1.04859i
\(885\) 7.73205 37.7846i 0.259910 1.27012i
\(886\) 24.4186 + 42.2942i 0.820358 + 1.42090i
\(887\) −0.820508 + 3.06218i −0.0275500 + 0.102818i −0.978332 0.207043i \(-0.933616\pi\)
0.950782 + 0.309861i \(0.100283\pi\)
\(888\) −25.8564 25.8564i −0.867684 0.867684i
\(889\) −37.0263 17.9737i −1.24182 0.602819i
\(890\) 53.2750 + 10.9019i 1.78578 + 0.365433i
\(891\) −6.75833 + 3.90192i −0.226413 + 0.130719i
\(892\) −15.8564 15.8564i −0.530912 0.530912i
\(893\) −0.588457 2.19615i −0.0196920 0.0734914i
\(894\) 61.9090i 2.07055i
\(895\) −28.1051 14.0526i −0.939450 0.469725i
\(896\) 26.9282 + 13.0718i 0.899608 + 0.436698i
\(897\) −9.00000 + 9.00000i −0.300501 + 0.300501i
\(898\) 23.1962 23.1962i 0.774066 0.774066i
\(899\) 39.4186 + 22.7583i 1.31468 + 0.759033i
\(900\) −4.39230 5.85641i −0.146410 0.195214i
\(901\) −6.58846 11.4115i −0.219493 0.380174i
\(902\) −0.464102 + 0.124356i −0.0154529 + 0.00414059i
\(903\) 16.7942 + 3.23205i 0.558877 + 0.107556i
\(904\) −10.1436 −0.337371
\(905\) −3.01666 50.2583i −0.100277 1.67064i
\(906\) −32.6603 + 18.8564i −1.08506 + 0.626462i
\(907\) 4.50000 1.20577i 0.149420 0.0400370i −0.183334 0.983051i \(-0.558689\pi\)
0.332754 + 0.943014i \(0.392022\pi\)
\(908\) 25.6603 6.87564i 0.851565 0.228176i
\(909\) 7.41154i 0.245825i
\(910\) −13.6077 32.7846i −0.451091 1.08680i
\(911\) 8.19615 0.271551 0.135775 0.990740i \(-0.456647\pi\)
0.135775 + 0.990740i \(0.456647\pi\)
\(912\) −18.9282 + 18.9282i −0.626775 + 0.626775i
\(913\) −1.22243 4.56218i −0.0404566 0.150986i
\(914\) 10.1962 + 17.6603i 0.337259 + 0.584149i
\(915\) 28.4545 32.0885i 0.940676 1.06081i
\(916\) 15.4641 + 26.7846i 0.510948 + 0.884988i
\(917\) −12.9282 + 14.9282i −0.426927 + 0.492973i
\(918\) −25.3923 + 6.80385i −0.838071 + 0.224560i
\(919\) 39.0000 22.5167i 1.28649 0.742756i 0.308465 0.951236i \(-0.400185\pi\)
0.978027 + 0.208480i \(0.0668515\pi\)
\(920\) 8.19615 5.41154i 0.270219 0.178413i
\(921\) −1.03590 + 1.79423i −0.0341340 + 0.0591218i
\(922\) −12.1436 12.1436i −0.399928 0.399928i
\(923\) −46.3923 46.3923i −1.52702 1.52702i
\(924\) −7.46410 + 0.535898i −0.245551 + 0.0176298i
\(925\) 4.73205 33.1244i 0.155589 1.08912i
\(926\) 1.66025i 0.0545593i
\(927\) 9.09808 2.43782i 0.298820 0.0800686i
\(928\) 17.8564 + 17.8564i 0.586165 + 0.586165i
\(929\) 4.16025 + 7.20577i 0.136494 + 0.236414i 0.926167 0.377114i \(-0.123083\pi\)
−0.789673 + 0.613527i \(0.789750\pi\)
\(930\) −51.9808 + 34.3205i −1.70452 + 1.12541i
\(931\) −9.00000 + 22.5167i −0.294963 + 0.737954i
\(932\) −14.1962 3.80385i −0.465010 0.124599i
\(933\) 46.5167 + 12.4641i 1.52289 + 0.408056i
\(934\) 4.56218 + 7.90192i 0.149279 + 0.258559i
\(935\) 1.39230 6.80385i 0.0455332 0.222510i
\(936\) 7.60770 4.39230i 0.248665 0.143567i
\(937\) −0.392305 0.392305i −0.0128160 0.0128160i 0.700670 0.713486i \(-0.252885\pi\)
−0.713486 + 0.700670i \(0.752885\pi\)
\(938\) 2.83013 14.7058i 0.0924069 0.480160i
\(939\) −32.2487 −1.05240
\(940\) 0.588457 2.87564i 0.0191934 0.0937932i
\(941\) 9.73205 16.8564i 0.317256 0.549503i −0.662659 0.748922i \(-0.730572\pi\)
0.979914 + 0.199418i \(0.0639053\pi\)
\(942\) 12.4641 46.5167i 0.406102 1.51559i
\(943\) 0.696152 + 0.186533i 0.0226698 + 0.00607437i
\(944\) −30.9282 17.8564i −1.00663 0.581177i
\(945\) −9.90192 + 23.9545i −0.322110 + 0.779239i
\(946\) 3.00000 + 1.73205i 0.0975384 + 0.0563138i
\(947\) 5.98334 22.3301i 0.194432 0.725632i −0.797981 0.602683i \(-0.794098\pi\)
0.992413 0.122949i \(-0.0392350\pi\)
\(948\) 35.3205 + 35.3205i 1.14716 + 1.14716i
\(949\) −17.7846 + 30.8038i −0.577313 + 0.999935i
\(950\) −24.2487 3.46410i −0.786732 0.112390i
\(951\) 8.73205i 0.283156i
\(952\) −31.1769 6.00000i −1.01045 0.194461i
\(953\) 3.46410 + 3.46410i 0.112213 + 0.112213i 0.760984 0.648771i \(-0.224717\pi\)
−0.648771 + 0.760984i \(0.724717\pi\)
\(954\) 3.21539i 0.104102i
\(955\) −5.83013 + 3.84936i −0.188658 + 0.124563i
\(956\) 9.46410 0.306091
\(957\) −6.09808 1.63397i −0.197123 0.0528189i
\(958\) −5.19615 + 1.39230i −0.167880 + 0.0449833i
\(959\) −18.5885 + 12.5885i −0.600253 + 0.406502i
\(960\) −32.7846 + 10.9282i −1.05812 + 0.352706i
\(961\) 36.4808 + 63.1865i 1.17680 + 2.03828i
\(962\) 38.7846 + 10.3923i 1.25047 + 0.335061i
\(963\) −1.04552 3.90192i −0.0336913 0.125738i
\(964\) 20.3923 35.3205i 0.656792 1.13760i
\(965\) 8.46410 + 25.3923i 0.272469 + 0.817407i
\(966\) 10.0981 + 4.90192i 0.324900 + 0.157717i
\(967\) −10.5096 + 10.5096i −0.337967 + 0.337967i −0.855602 0.517635i \(-0.826813\pi\)
0.517635 + 0.855602i \(0.326813\pi\)
\(968\) 28.5885 + 7.66025i 0.918868 + 0.246210i
\(969\) 14.1962 24.5885i 0.456046 0.789895i
\(970\) −27.9808 + 1.67949i −0.898408 + 0.0539252i
\(971\) −10.0000 17.3205i −0.320915 0.555842i 0.659762 0.751475i \(-0.270657\pi\)
−0.980677 + 0.195633i \(0.937324\pi\)
\(972\) −14.3923 3.85641i −0.461633 0.123694i
\(973\) 3.16987 1.09808i 0.101621 0.0352027i
\(974\) −13.9282 + 24.1244i −0.446288 + 0.772994i
\(975\) 37.6865 + 16.0981i 1.20694 + 0.515551i
\(976\) −19.8564 34.3923i −0.635588 1.10087i
\(977\) −5.36603 20.0263i −0.171674 0.640697i −0.997094 0.0761781i \(-0.975728\pi\)
0.825420 0.564519i \(-0.190938\pi\)
\(978\) −7.26795 7.26795i −0.232403 0.232403i
\(979\) 12.5885i 0.402329i
\(980\) −23.3923 + 20.8038i −0.747240 + 0.664555i
\(981\) 3.12436i 0.0997530i
\(982\) 12.1962 12.1962i 0.389195 0.389195i
\(983\) 3.27757 + 12.2321i 0.104538 + 0.390142i 0.998292 0.0584153i \(-0.0186047\pi\)
−0.893754 + 0.448557i \(0.851938\pi\)
\(984\) −2.19615 1.26795i −0.0700108 0.0404207i
\(985\) −11.6147 + 13.0981i −0.370076 + 0.417339i
\(986\) −23.1962 13.3923i −0.738716 0.426498i
\(987\) 3.16987 1.09808i 0.100898 0.0349522i
\(988\) 7.60770 28.3923i 0.242033 0.903280i
\(989\) −2.59808 4.50000i −0.0826140 0.143092i
\(990\) 1.12436 1.26795i 0.0357344 0.0402981i
\(991\) −17.6865 + 30.6340i −0.561831 + 0.973120i 0.435506 + 0.900186i \(0.356570\pi\)
−0.997337 + 0.0729342i \(0.976764\pi\)
\(992\) 14.9282 + 55.7128i 0.473971 + 1.76888i
\(993\) 9.92820 9.92820i 0.315062 0.315062i
\(994\) −25.2679 + 52.0526i −0.801451 + 1.65101i
\(995\) −6.92820 3.46410i −0.219639 0.109819i
\(996\) 12.4641 21.5885i 0.394940 0.684056i
\(997\) 3.00000 + 11.1962i 0.0950110 + 0.354586i 0.997021 0.0771291i \(-0.0245754\pi\)
−0.902010 + 0.431715i \(0.857909\pi\)
\(998\) −4.94744 + 18.4641i −0.156609 + 0.584471i
\(999\) −14.6603 25.3923i −0.463830 0.803377i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 280.2.bv.d.213.1 yes 4
5.2 odd 4 280.2.bv.a.157.1 4
7.5 odd 6 280.2.bv.b.173.1 yes 4
8.5 even 2 280.2.bv.c.213.1 yes 4
35.12 even 12 280.2.bv.c.117.1 yes 4
40.37 odd 4 280.2.bv.b.157.1 yes 4
56.5 odd 6 280.2.bv.a.173.1 yes 4
280.117 even 12 inner 280.2.bv.d.117.1 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
280.2.bv.a.157.1 4 5.2 odd 4
280.2.bv.a.173.1 yes 4 56.5 odd 6
280.2.bv.b.157.1 yes 4 40.37 odd 4
280.2.bv.b.173.1 yes 4 7.5 odd 6
280.2.bv.c.117.1 yes 4 35.12 even 12
280.2.bv.c.213.1 yes 4 8.5 even 2
280.2.bv.d.117.1 yes 4 280.117 even 12 inner
280.2.bv.d.213.1 yes 4 1.1 even 1 trivial