Properties

Label 285.2.k.b.77.2
Level $285$
Weight $2$
Character 285.77
Analytic conductor $2.276$
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] = [285,2,Mod(77,285)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(285, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("285.77");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 285 = 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 285.k (of order \(4\), 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: \(2.27573645761\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
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: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 77.2
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 285.77
Dual form 285.2.k.b.248.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 - 1.00000i) q^{2} +1.73205 q^{3} +(0.133975 - 2.23205i) q^{5} +(1.73205 - 1.73205i) q^{6} +(-2.36603 - 2.36603i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+(1.00000 - 1.00000i) q^{2} +1.73205 q^{3} +(0.133975 - 2.23205i) q^{5} +(1.73205 - 1.73205i) q^{6} +(-2.36603 - 2.36603i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +(-2.09808 - 2.36603i) q^{10} +0.267949i q^{11} +(-3.73205 + 3.73205i) q^{13} -4.73205 q^{14} +(0.232051 - 3.86603i) q^{15} +4.00000 q^{16} +(-0.0980762 + 0.0980762i) q^{17} +(3.00000 - 3.00000i) q^{18} -1.00000i q^{19} +(-4.09808 - 4.09808i) q^{21} +(0.267949 + 0.267949i) q^{22} +(6.46410 + 6.46410i) q^{23} +(3.46410 + 3.46410i) q^{24} +(-4.96410 - 0.598076i) q^{25} +7.46410i q^{26} +5.19615 q^{27} +(-3.63397 - 4.09808i) q^{30} -8.73205 q^{31} +0.464102i q^{33} +0.196152i q^{34} +(-5.59808 + 4.96410i) q^{35} +(2.46410 + 2.46410i) q^{37} +(-1.00000 - 1.00000i) q^{38} +(-6.46410 + 6.46410i) q^{39} +(4.73205 - 4.19615i) q^{40} -7.66025i q^{41} -8.19615 q^{42} +(0.0980762 - 0.0980762i) q^{43} +(0.401924 - 6.69615i) q^{45} +12.9282 q^{46} +(-3.56218 + 3.56218i) q^{47} +6.92820 q^{48} +4.19615i q^{49} +(-5.56218 + 4.36603i) q^{50} +(-0.169873 + 0.169873i) q^{51} +(-2.26795 - 2.26795i) q^{53} +(5.19615 - 5.19615i) q^{54} +(0.598076 + 0.0358984i) q^{55} -9.46410i q^{56} -1.73205i q^{57} -10.1962 q^{59} -4.26795 q^{61} +(-8.73205 + 8.73205i) q^{62} +(-7.09808 - 7.09808i) q^{63} +8.00000i q^{64} +(7.83013 + 8.83013i) q^{65} +(0.464102 + 0.464102i) q^{66} +(8.19615 + 8.19615i) q^{67} +(11.1962 + 11.1962i) q^{69} +(-0.633975 + 10.5622i) q^{70} -7.26795i q^{71} +(6.00000 + 6.00000i) q^{72} +(3.63397 - 3.63397i) q^{73} +4.92820 q^{74} +(-8.59808 - 1.03590i) q^{75} +(0.633975 - 0.633975i) q^{77} +12.9282i q^{78} -10.3923i q^{79} +(0.535898 - 8.92820i) q^{80} +9.00000 q^{81} +(-7.66025 - 7.66025i) q^{82} +(3.73205 + 3.73205i) q^{83} +(0.205771 + 0.232051i) q^{85} -0.196152i q^{86} +(-0.535898 + 0.535898i) q^{88} +10.7321 q^{89} +(-6.29423 - 7.09808i) q^{90} +17.6603 q^{91} -15.1244 q^{93} +7.12436i q^{94} +(-2.23205 - 0.133975i) q^{95} +(0.464102 + 0.464102i) q^{97} +(4.19615 + 4.19615i) q^{98} +0.803848i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{2} + 4 q^{5} - 6 q^{7} + 8 q^{8} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{2} + 4 q^{5} - 6 q^{7} + 8 q^{8} + 12 q^{9} + 2 q^{10} - 8 q^{13} - 12 q^{14} - 6 q^{15} + 16 q^{16} + 10 q^{17} + 12 q^{18} - 6 q^{21} + 8 q^{22} + 12 q^{23} - 6 q^{25} - 18 q^{30} - 28 q^{31} - 12 q^{35} - 4 q^{37} - 4 q^{38} - 12 q^{39} + 12 q^{40} - 12 q^{42} - 10 q^{43} + 12 q^{45} + 24 q^{46} + 10 q^{47} + 2 q^{50} - 18 q^{51} - 16 q^{53} - 8 q^{55} - 20 q^{59} - 24 q^{61} - 28 q^{62} - 18 q^{63} + 14 q^{65} - 12 q^{66} + 12 q^{67} + 24 q^{69} - 6 q^{70} + 24 q^{72} + 18 q^{73} - 8 q^{74} - 24 q^{75} + 6 q^{77} + 16 q^{80} + 36 q^{81} + 4 q^{82} + 8 q^{83} + 32 q^{85} - 16 q^{88} + 36 q^{89} + 6 q^{90} + 36 q^{91} - 12 q^{93} - 2 q^{95} - 12 q^{97} - 4 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/285\mathbb{Z}\right)^\times\).

\(n\) \(172\) \(191\) \(211\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
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 −0.258819 0.965926i \(-0.583333\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(3\) 1.73205 1.00000
\(4\) 0 0
\(5\) 0.133975 2.23205i 0.0599153 0.998203i
\(6\) 1.73205 1.73205i 0.707107 0.707107i
\(7\) −2.36603 2.36603i −0.894274 0.894274i 0.100649 0.994922i \(-0.467908\pi\)
−0.994922 + 0.100649i \(0.967908\pi\)
\(8\) 2.00000 + 2.00000i 0.707107 + 0.707107i
\(9\) 3.00000 1.00000
\(10\) −2.09808 2.36603i −0.663470 0.748203i
\(11\) 0.267949i 0.0807897i 0.999184 + 0.0403949i \(0.0128616\pi\)
−0.999184 + 0.0403949i \(0.987138\pi\)
\(12\) 0 0
\(13\) −3.73205 + 3.73205i −1.03508 + 1.03508i −0.0357229 + 0.999362i \(0.511373\pi\)
−0.999362 + 0.0357229i \(0.988627\pi\)
\(14\) −4.73205 −1.26469
\(15\) 0.232051 3.86603i 0.0599153 0.998203i
\(16\) 4.00000 1.00000
\(17\) −0.0980762 + 0.0980762i −0.0237870 + 0.0237870i −0.718900 0.695113i \(-0.755354\pi\)
0.695113 + 0.718900i \(0.255354\pi\)
\(18\) 3.00000 3.00000i 0.707107 0.707107i
\(19\) 1.00000i 0.229416i
\(20\) 0 0
\(21\) −4.09808 4.09808i −0.894274 0.894274i
\(22\) 0.267949 + 0.267949i 0.0571270 + 0.0571270i
\(23\) 6.46410 + 6.46410i 1.34786 + 1.34786i 0.887984 + 0.459874i \(0.152106\pi\)
0.459874 + 0.887984i \(0.347894\pi\)
\(24\) 3.46410 + 3.46410i 0.707107 + 0.707107i
\(25\) −4.96410 0.598076i −0.992820 0.119615i
\(26\) 7.46410i 1.46383i
\(27\) 5.19615 1.00000
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) −3.63397 4.09808i −0.663470 0.748203i
\(31\) −8.73205 −1.56832 −0.784161 0.620557i \(-0.786907\pi\)
−0.784161 + 0.620557i \(0.786907\pi\)
\(32\) 0 0
\(33\) 0.464102i 0.0807897i
\(34\) 0.196152i 0.0336399i
\(35\) −5.59808 + 4.96410i −0.946248 + 0.839086i
\(36\) 0 0
\(37\) 2.46410 + 2.46410i 0.405096 + 0.405096i 0.880024 0.474929i \(-0.157526\pi\)
−0.474929 + 0.880024i \(0.657526\pi\)
\(38\) −1.00000 1.00000i −0.162221 0.162221i
\(39\) −6.46410 + 6.46410i −1.03508 + 1.03508i
\(40\) 4.73205 4.19615i 0.748203 0.663470i
\(41\) 7.66025i 1.19633i −0.801373 0.598165i \(-0.795897\pi\)
0.801373 0.598165i \(-0.204103\pi\)
\(42\) −8.19615 −1.26469
\(43\) 0.0980762 0.0980762i 0.0149565 0.0149565i −0.699589 0.714545i \(-0.746634\pi\)
0.714545 + 0.699589i \(0.246634\pi\)
\(44\) 0 0
\(45\) 0.401924 6.69615i 0.0599153 0.998203i
\(46\) 12.9282 1.90616
\(47\) −3.56218 + 3.56218i −0.519597 + 0.519597i −0.917449 0.397852i \(-0.869756\pi\)
0.397852 + 0.917449i \(0.369756\pi\)
\(48\) 6.92820 1.00000
\(49\) 4.19615i 0.599450i
\(50\) −5.56218 + 4.36603i −0.786611 + 0.617449i
\(51\) −0.169873 + 0.169873i −0.0237870 + 0.0237870i
\(52\) 0 0
\(53\) −2.26795 2.26795i −0.311527 0.311527i 0.533974 0.845501i \(-0.320698\pi\)
−0.845501 + 0.533974i \(0.820698\pi\)
\(54\) 5.19615 5.19615i 0.707107 0.707107i
\(55\) 0.598076 + 0.0358984i 0.0806446 + 0.00484054i
\(56\) 9.46410i 1.26469i
\(57\) 1.73205i 0.229416i
\(58\) 0 0
\(59\) −10.1962 −1.32743 −0.663713 0.747987i \(-0.731020\pi\)
−0.663713 + 0.747987i \(0.731020\pi\)
\(60\) 0 0
\(61\) −4.26795 −0.546455 −0.273227 0.961949i \(-0.588091\pi\)
−0.273227 + 0.961949i \(0.588091\pi\)
\(62\) −8.73205 + 8.73205i −1.10897 + 1.10897i
\(63\) −7.09808 7.09808i −0.894274 0.894274i
\(64\) 8.00000i 1.00000i
\(65\) 7.83013 + 8.83013i 0.971208 + 1.09524i
\(66\) 0.464102 + 0.464102i 0.0571270 + 0.0571270i
\(67\) 8.19615 + 8.19615i 1.00132 + 1.00132i 0.999999 + 0.00132026i \(0.000420252\pi\)
0.00132026 + 0.999999i \(0.499580\pi\)
\(68\) 0 0
\(69\) 11.1962 + 11.1962i 1.34786 + 1.34786i
\(70\) −0.633975 + 10.5622i −0.0757745 + 1.26242i
\(71\) 7.26795i 0.862547i −0.902221 0.431273i \(-0.858064\pi\)
0.902221 0.431273i \(-0.141936\pi\)
\(72\) 6.00000 + 6.00000i 0.707107 + 0.707107i
\(73\) 3.63397 3.63397i 0.425325 0.425325i −0.461708 0.887032i \(-0.652763\pi\)
0.887032 + 0.461708i \(0.152763\pi\)
\(74\) 4.92820 0.572892
\(75\) −8.59808 1.03590i −0.992820 0.119615i
\(76\) 0 0
\(77\) 0.633975 0.633975i 0.0722481 0.0722481i
\(78\) 12.9282i 1.46383i
\(79\) 10.3923i 1.16923i −0.811312 0.584613i \(-0.801246\pi\)
0.811312 0.584613i \(-0.198754\pi\)
\(80\) 0.535898 8.92820i 0.0599153 0.998203i
\(81\) 9.00000 1.00000
\(82\) −7.66025 7.66025i −0.845934 0.845934i
\(83\) 3.73205 + 3.73205i 0.409646 + 0.409646i 0.881615 0.471969i \(-0.156457\pi\)
−0.471969 + 0.881615i \(0.656457\pi\)
\(84\) 0 0
\(85\) 0.205771 + 0.232051i 0.0223190 + 0.0251694i
\(86\) 0.196152i 0.0211517i
\(87\) 0 0
\(88\) −0.535898 + 0.535898i −0.0571270 + 0.0571270i
\(89\) 10.7321 1.13760 0.568798 0.822478i \(-0.307409\pi\)
0.568798 + 0.822478i \(0.307409\pi\)
\(90\) −6.29423 7.09808i −0.663470 0.748203i
\(91\) 17.6603 1.85130
\(92\) 0 0
\(93\) −15.1244 −1.56832
\(94\) 7.12436i 0.734821i
\(95\) −2.23205 0.133975i −0.229004 0.0137455i
\(96\) 0 0
\(97\) 0.464102 + 0.464102i 0.0471224 + 0.0471224i 0.730275 0.683153i \(-0.239392\pi\)
−0.683153 + 0.730275i \(0.739392\pi\)
\(98\) 4.19615 + 4.19615i 0.423875 + 0.423875i
\(99\) 0.803848i 0.0807897i
\(100\) 0 0
\(101\) 2.39230i 0.238043i 0.992892 + 0.119022i \(0.0379758\pi\)
−0.992892 + 0.119022i \(0.962024\pi\)
\(102\) 0.339746i 0.0336399i
\(103\) −11.6603 + 11.6603i −1.14892 + 1.14892i −0.162153 + 0.986766i \(0.551844\pi\)
−0.986766 + 0.162153i \(0.948156\pi\)
\(104\) −14.9282 −1.46383
\(105\) −9.69615 + 8.59808i −0.946248 + 0.839086i
\(106\) −4.53590 −0.440565
\(107\) 7.46410 7.46410i 0.721582 0.721582i −0.247345 0.968927i \(-0.579558\pi\)
0.968927 + 0.247345i \(0.0795582\pi\)
\(108\) 0 0
\(109\) 16.9282i 1.62143i −0.585443 0.810714i \(-0.699079\pi\)
0.585443 0.810714i \(-0.300921\pi\)
\(110\) 0.633975 0.562178i 0.0604471 0.0536016i
\(111\) 4.26795 + 4.26795i 0.405096 + 0.405096i
\(112\) −9.46410 9.46410i −0.894274 0.894274i
\(113\) −5.46410 5.46410i −0.514019 0.514019i 0.401736 0.915756i \(-0.368407\pi\)
−0.915756 + 0.401736i \(0.868407\pi\)
\(114\) −1.73205 1.73205i −0.162221 0.162221i
\(115\) 15.2942 13.5622i 1.42619 1.26468i
\(116\) 0 0
\(117\) −11.1962 + 11.1962i −1.03508 + 1.03508i
\(118\) −10.1962 + 10.1962i −0.938632 + 0.938632i
\(119\) 0.464102 0.0425441
\(120\) 8.19615 7.26795i 0.748203 0.663470i
\(121\) 10.9282 0.993473
\(122\) −4.26795 + 4.26795i −0.386402 + 0.386402i
\(123\) 13.2679i 1.19633i
\(124\) 0 0
\(125\) −2.00000 + 11.0000i −0.178885 + 0.983870i
\(126\) −14.1962 −1.26469
\(127\) −14.7321 14.7321i −1.30726 1.30726i −0.923386 0.383872i \(-0.874591\pi\)
−0.383872 0.923386i \(-0.625409\pi\)
\(128\) 8.00000 + 8.00000i 0.707107 + 0.707107i
\(129\) 0.169873 0.169873i 0.0149565 0.0149565i
\(130\) 16.6603 + 1.00000i 1.46120 + 0.0877058i
\(131\) 4.46410i 0.390030i −0.980800 0.195015i \(-0.937524\pi\)
0.980800 0.195015i \(-0.0624756\pi\)
\(132\) 0 0
\(133\) −2.36603 + 2.36603i −0.205160 + 0.205160i
\(134\) 16.3923 1.41608
\(135\) 0.696152 11.5981i 0.0599153 0.998203i
\(136\) −0.392305 −0.0336399
\(137\) 6.56218 6.56218i 0.560645 0.560645i −0.368846 0.929491i \(-0.620247\pi\)
0.929491 + 0.368846i \(0.120247\pi\)
\(138\) 22.3923 1.90616
\(139\) 3.53590i 0.299911i −0.988693 0.149955i \(-0.952087\pi\)
0.988693 0.149955i \(-0.0479130\pi\)
\(140\) 0 0
\(141\) −6.16987 + 6.16987i −0.519597 + 0.519597i
\(142\) −7.26795 7.26795i −0.609913 0.609913i
\(143\) −1.00000 1.00000i −0.0836242 0.0836242i
\(144\) 12.0000 1.00000
\(145\) 0 0
\(146\) 7.26795i 0.601500i
\(147\) 7.26795i 0.599450i
\(148\) 0 0
\(149\) 7.39230 0.605601 0.302801 0.953054i \(-0.402078\pi\)
0.302801 + 0.953054i \(0.402078\pi\)
\(150\) −9.63397 + 7.56218i −0.786611 + 0.617449i
\(151\) −0.732051 −0.0595734 −0.0297867 0.999556i \(-0.509483\pi\)
−0.0297867 + 0.999556i \(0.509483\pi\)
\(152\) 2.00000 2.00000i 0.162221 0.162221i
\(153\) −0.294229 + 0.294229i −0.0237870 + 0.0237870i
\(154\) 1.26795i 0.102174i
\(155\) −1.16987 + 19.4904i −0.0939665 + 1.56551i
\(156\) 0 0
\(157\) −2.66025 2.66025i −0.212311 0.212311i 0.592937 0.805249i \(-0.297968\pi\)
−0.805249 + 0.592937i \(0.797968\pi\)
\(158\) −10.3923 10.3923i −0.826767 0.826767i
\(159\) −3.92820 3.92820i −0.311527 0.311527i
\(160\) 0 0
\(161\) 30.5885i 2.41071i
\(162\) 9.00000 9.00000i 0.707107 0.707107i
\(163\) −11.0000 + 11.0000i −0.861586 + 0.861586i −0.991522 0.129936i \(-0.958523\pi\)
0.129936 + 0.991522i \(0.458523\pi\)
\(164\) 0 0
\(165\) 1.03590 + 0.0621778i 0.0806446 + 0.00484054i
\(166\) 7.46410 0.579327
\(167\) 4.00000 4.00000i 0.309529 0.309529i −0.535198 0.844727i \(-0.679763\pi\)
0.844727 + 0.535198i \(0.179763\pi\)
\(168\) 16.3923i 1.26469i
\(169\) 14.8564i 1.14280i
\(170\) 0.437822 + 0.0262794i 0.0335794 + 0.00201554i
\(171\) 3.00000i 0.229416i
\(172\) 0 0
\(173\) −2.19615 2.19615i −0.166970 0.166970i 0.618676 0.785646i \(-0.287669\pi\)
−0.785646 + 0.618676i \(0.787669\pi\)
\(174\) 0 0
\(175\) 10.3301 + 13.1603i 0.780884 + 0.994822i
\(176\) 1.07180i 0.0807897i
\(177\) −17.6603 −1.32743
\(178\) 10.7321 10.7321i 0.804401 0.804401i
\(179\) 4.92820 0.368351 0.184176 0.982893i \(-0.441038\pi\)
0.184176 + 0.982893i \(0.441038\pi\)
\(180\) 0 0
\(181\) −2.92820 −0.217652 −0.108826 0.994061i \(-0.534709\pi\)
−0.108826 + 0.994061i \(0.534709\pi\)
\(182\) 17.6603 17.6603i 1.30907 1.30907i
\(183\) −7.39230 −0.546455
\(184\) 25.8564i 1.90616i
\(185\) 5.83013 5.16987i 0.428639 0.380097i
\(186\) −15.1244 + 15.1244i −1.10897 + 1.10897i
\(187\) −0.0262794 0.0262794i −0.00192174 0.00192174i
\(188\) 0 0
\(189\) −12.2942 12.2942i −0.894274 0.894274i
\(190\) −2.36603 + 2.09808i −0.171650 + 0.152210i
\(191\) 17.9282i 1.29724i 0.761113 + 0.648620i \(0.224653\pi\)
−0.761113 + 0.648620i \(0.775347\pi\)
\(192\) 13.8564i 1.00000i
\(193\) 12.1962 12.1962i 0.877898 0.877898i −0.115419 0.993317i \(-0.536821\pi\)
0.993317 + 0.115419i \(0.0368210\pi\)
\(194\) 0.928203 0.0666411
\(195\) 13.5622 + 15.2942i 0.971208 + 1.09524i
\(196\) 0 0
\(197\) 10.1244 10.1244i 0.721330 0.721330i −0.247546 0.968876i \(-0.579624\pi\)
0.968876 + 0.247546i \(0.0796240\pi\)
\(198\) 0.803848 + 0.803848i 0.0571270 + 0.0571270i
\(199\) 11.1962i 0.793674i 0.917889 + 0.396837i \(0.129892\pi\)
−0.917889 + 0.396837i \(0.870108\pi\)
\(200\) −8.73205 11.1244i −0.617449 0.786611i
\(201\) 14.1962 + 14.1962i 1.00132 + 1.00132i
\(202\) 2.39230 + 2.39230i 0.168322 + 0.168322i
\(203\) 0 0
\(204\) 0 0
\(205\) −17.0981 1.02628i −1.19418 0.0716785i
\(206\) 23.3205i 1.62482i
\(207\) 19.3923 + 19.3923i 1.34786 + 1.34786i
\(208\) −14.9282 + 14.9282i −1.03508 + 1.03508i
\(209\) 0.267949 0.0185344
\(210\) −1.09808 + 18.2942i −0.0757745 + 1.26242i
\(211\) −24.0526 −1.65585 −0.827923 0.560841i \(-0.810478\pi\)
−0.827923 + 0.560841i \(0.810478\pi\)
\(212\) 0 0
\(213\) 12.5885i 0.862547i
\(214\) 14.9282i 1.02047i
\(215\) −0.205771 0.232051i −0.0140335 0.0158257i
\(216\) 10.3923 + 10.3923i 0.707107 + 0.707107i
\(217\) 20.6603 + 20.6603i 1.40251 + 1.40251i
\(218\) −16.9282 16.9282i −1.14652 1.14652i
\(219\) 6.29423 6.29423i 0.425325 0.425325i
\(220\) 0 0
\(221\) 0.732051i 0.0492431i
\(222\) 8.53590 0.572892
\(223\) −9.00000 + 9.00000i −0.602685 + 0.602685i −0.941024 0.338340i \(-0.890135\pi\)
0.338340 + 0.941024i \(0.390135\pi\)
\(224\) 0 0
\(225\) −14.8923 1.79423i −0.992820 0.119615i
\(226\) −10.9282 −0.726933
\(227\) 0.803848 0.803848i 0.0533532 0.0533532i −0.679927 0.733280i \(-0.737988\pi\)
0.733280 + 0.679927i \(0.237988\pi\)
\(228\) 0 0
\(229\) 25.2487i 1.66848i −0.551400 0.834241i \(-0.685906\pi\)
0.551400 0.834241i \(-0.314094\pi\)
\(230\) 1.73205 28.8564i 0.114208 1.90274i
\(231\) 1.09808 1.09808i 0.0722481 0.0722481i
\(232\) 0 0
\(233\) 15.8301 + 15.8301i 1.03707 + 1.03707i 0.999286 + 0.0377800i \(0.0120286\pi\)
0.0377800 + 0.999286i \(0.487971\pi\)
\(234\) 22.3923i 1.46383i
\(235\) 7.47372 + 8.42820i 0.487532 + 0.549795i
\(236\) 0 0
\(237\) 18.0000i 1.16923i
\(238\) 0.464102 0.464102i 0.0300832 0.0300832i
\(239\) −13.0526 −0.844300 −0.422150 0.906526i \(-0.638724\pi\)
−0.422150 + 0.906526i \(0.638724\pi\)
\(240\) 0.928203 15.4641i 0.0599153 0.998203i
\(241\) −5.80385 −0.373859 −0.186929 0.982373i \(-0.559854\pi\)
−0.186929 + 0.982373i \(0.559854\pi\)
\(242\) 10.9282 10.9282i 0.702492 0.702492i
\(243\) 15.5885 1.00000
\(244\) 0 0
\(245\) 9.36603 + 0.562178i 0.598373 + 0.0359162i
\(246\) −13.2679 13.2679i −0.845934 0.845934i
\(247\) 3.73205 + 3.73205i 0.237465 + 0.237465i
\(248\) −17.4641 17.4641i −1.10897 1.10897i
\(249\) 6.46410 + 6.46410i 0.409646 + 0.409646i
\(250\) 9.00000 + 13.0000i 0.569210 + 0.822192i
\(251\) 10.8564i 0.685250i 0.939472 + 0.342625i \(0.111316\pi\)
−0.939472 + 0.342625i \(0.888684\pi\)
\(252\) 0 0
\(253\) −1.73205 + 1.73205i −0.108893 + 0.108893i
\(254\) −29.4641 −1.84874
\(255\) 0.356406 + 0.401924i 0.0223190 + 0.0251694i
\(256\) 0 0
\(257\) −13.2679 + 13.2679i −0.827632 + 0.827632i −0.987189 0.159557i \(-0.948993\pi\)
0.159557 + 0.987189i \(0.448993\pi\)
\(258\) 0.339746i 0.0211517i
\(259\) 11.6603i 0.724533i
\(260\) 0 0
\(261\) 0 0
\(262\) −4.46410 4.46410i −0.275793 0.275793i
\(263\) 13.0263 + 13.0263i 0.803235 + 0.803235i 0.983600 0.180365i \(-0.0577279\pi\)
−0.180365 + 0.983600i \(0.557728\pi\)
\(264\) −0.928203 + 0.928203i −0.0571270 + 0.0571270i
\(265\) −5.36603 + 4.75833i −0.329632 + 0.292302i
\(266\) 4.73205i 0.290141i
\(267\) 18.5885 1.13760
\(268\) 0 0
\(269\) 16.1962 0.987497 0.493748 0.869605i \(-0.335626\pi\)
0.493748 + 0.869605i \(0.335626\pi\)
\(270\) −10.9019 12.2942i −0.663470 0.748203i
\(271\) 12.3923 0.752779 0.376389 0.926462i \(-0.377165\pi\)
0.376389 + 0.926462i \(0.377165\pi\)
\(272\) −0.392305 + 0.392305i −0.0237870 + 0.0237870i
\(273\) 30.5885 1.85130
\(274\) 13.1244i 0.792871i
\(275\) 0.160254 1.33013i 0.00966368 0.0802097i
\(276\) 0 0
\(277\) −6.83013 6.83013i −0.410383 0.410383i 0.471489 0.881872i \(-0.343717\pi\)
−0.881872 + 0.471489i \(0.843717\pi\)
\(278\) −3.53590 3.53590i −0.212069 0.212069i
\(279\) −26.1962 −1.56832
\(280\) −21.1244 1.26795i −1.26242 0.0757745i
\(281\) 12.0000i 0.715860i 0.933748 + 0.357930i \(0.116517\pi\)
−0.933748 + 0.357930i \(0.883483\pi\)
\(282\) 12.3397i 0.734821i
\(283\) −0.169873 + 0.169873i −0.0100979 + 0.0100979i −0.712138 0.702040i \(-0.752273\pi\)
0.702040 + 0.712138i \(0.252273\pi\)
\(284\) 0 0
\(285\) −3.86603 0.232051i −0.229004 0.0137455i
\(286\) −2.00000 −0.118262
\(287\) −18.1244 + 18.1244i −1.06985 + 1.06985i
\(288\) 0 0
\(289\) 16.9808i 0.998868i
\(290\) 0 0
\(291\) 0.803848 + 0.803848i 0.0471224 + 0.0471224i
\(292\) 0 0
\(293\) 8.00000 + 8.00000i 0.467365 + 0.467365i 0.901060 0.433695i \(-0.142790\pi\)
−0.433695 + 0.901060i \(0.642790\pi\)
\(294\) 7.26795 + 7.26795i 0.423875 + 0.423875i
\(295\) −1.36603 + 22.7583i −0.0795331 + 1.32504i
\(296\) 9.85641i 0.572892i
\(297\) 1.39230i 0.0807897i
\(298\) 7.39230 7.39230i 0.428225 0.428225i
\(299\) −48.2487 −2.79030
\(300\) 0 0
\(301\) −0.464102 −0.0267504
\(302\) −0.732051 + 0.732051i −0.0421248 + 0.0421248i
\(303\) 4.14359i 0.238043i
\(304\) 4.00000i 0.229416i
\(305\) −0.571797 + 9.52628i −0.0327410 + 0.545473i
\(306\) 0.588457i 0.0336399i
\(307\) 16.5885 + 16.5885i 0.946753 + 0.946753i 0.998652 0.0518991i \(-0.0165274\pi\)
−0.0518991 + 0.998652i \(0.516527\pi\)
\(308\) 0 0
\(309\) −20.1962 + 20.1962i −1.14892 + 1.14892i
\(310\) 18.3205 + 20.6603i 1.04053 + 1.17342i
\(311\) 2.26795i 0.128604i 0.997930 + 0.0643018i \(0.0204820\pi\)
−0.997930 + 0.0643018i \(0.979518\pi\)
\(312\) −25.8564 −1.46383
\(313\) −1.73205 + 1.73205i −0.0979013 + 0.0979013i −0.754361 0.656460i \(-0.772053\pi\)
0.656460 + 0.754361i \(0.272053\pi\)
\(314\) −5.32051 −0.300254
\(315\) −16.7942 + 14.8923i −0.946248 + 0.839086i
\(316\) 0 0
\(317\) 8.85641 8.85641i 0.497425 0.497425i −0.413210 0.910636i \(-0.635593\pi\)
0.910636 + 0.413210i \(0.135593\pi\)
\(318\) −7.85641 −0.440565
\(319\) 0 0
\(320\) 17.8564 + 1.07180i 0.998203 + 0.0599153i
\(321\) 12.9282 12.9282i 0.721582 0.721582i
\(322\) −30.5885 30.5885i −1.70463 1.70463i
\(323\) 0.0980762 + 0.0980762i 0.00545711 + 0.00545711i
\(324\) 0 0
\(325\) 20.7583 16.2942i 1.15146 0.903841i
\(326\) 22.0000i 1.21847i
\(327\) 29.3205i 1.62143i
\(328\) 15.3205 15.3205i 0.845934 0.845934i
\(329\) 16.8564 0.929324
\(330\) 1.09808 0.973721i 0.0604471 0.0536016i
\(331\) 0.679492 0.0373483 0.0186741 0.999826i \(-0.494055\pi\)
0.0186741 + 0.999826i \(0.494055\pi\)
\(332\) 0 0
\(333\) 7.39230 + 7.39230i 0.405096 + 0.405096i
\(334\) 8.00000i 0.437741i
\(335\) 19.3923 17.1962i 1.05951 0.939526i
\(336\) −16.3923 16.3923i −0.894274 0.894274i
\(337\) 3.92820 + 3.92820i 0.213983 + 0.213983i 0.805957 0.591974i \(-0.201651\pi\)
−0.591974 + 0.805957i \(0.701651\pi\)
\(338\) −14.8564 14.8564i −0.808082 0.808082i
\(339\) −9.46410 9.46410i −0.514019 0.514019i
\(340\) 0 0
\(341\) 2.33975i 0.126704i
\(342\) −3.00000 3.00000i −0.162221 0.162221i
\(343\) −6.63397 + 6.63397i −0.358201 + 0.358201i
\(344\) 0.392305 0.0211517
\(345\) 26.4904 23.4904i 1.42619 1.26468i
\(346\) −4.39230 −0.236132
\(347\) −12.9019 + 12.9019i −0.692612 + 0.692612i −0.962806 0.270194i \(-0.912912\pi\)
0.270194 + 0.962806i \(0.412912\pi\)
\(348\) 0 0
\(349\) 0.267949i 0.0143430i −0.999974 0.00717150i \(-0.997717\pi\)
0.999974 0.00717150i \(-0.00228278\pi\)
\(350\) 23.4904 + 2.83013i 1.25561 + 0.151277i
\(351\) −19.3923 + 19.3923i −1.03508 + 1.03508i
\(352\) 0 0
\(353\) −22.2679 22.2679i −1.18520 1.18520i −0.978378 0.206825i \(-0.933687\pi\)
−0.206825 0.978378i \(-0.566313\pi\)
\(354\) −17.6603 + 17.6603i −0.938632 + 0.938632i
\(355\) −16.2224 0.973721i −0.860997 0.0516797i
\(356\) 0 0
\(357\) 0.803848 0.0425441
\(358\) 4.92820 4.92820i 0.260464 0.260464i
\(359\) 8.07180 0.426013 0.213007 0.977051i \(-0.431674\pi\)
0.213007 + 0.977051i \(0.431674\pi\)
\(360\) 14.1962 12.5885i 0.748203 0.663470i
\(361\) −1.00000 −0.0526316
\(362\) −2.92820 + 2.92820i −0.153903 + 0.153903i
\(363\) 18.9282 0.993473
\(364\) 0 0
\(365\) −7.62436 8.59808i −0.399077 0.450044i
\(366\) −7.39230 + 7.39230i −0.386402 + 0.386402i
\(367\) 17.7846 + 17.7846i 0.928349 + 0.928349i 0.997599 0.0692503i \(-0.0220607\pi\)
−0.0692503 + 0.997599i \(0.522061\pi\)
\(368\) 25.8564 + 25.8564i 1.34786 + 1.34786i
\(369\) 22.9808i 1.19633i
\(370\) 0.660254 11.0000i 0.0343250 0.571863i
\(371\) 10.7321i 0.557180i
\(372\) 0 0
\(373\) −12.5885 + 12.5885i −0.651806 + 0.651806i −0.953428 0.301622i \(-0.902472\pi\)
0.301622 + 0.953428i \(0.402472\pi\)
\(374\) −0.0525589 −0.00271776
\(375\) −3.46410 + 19.0526i −0.178885 + 0.983870i
\(376\) −14.2487 −0.734821
\(377\) 0 0
\(378\) −24.5885 −1.26469
\(379\) 21.4641i 1.10254i 0.834328 + 0.551268i \(0.185856\pi\)
−0.834328 + 0.551268i \(0.814144\pi\)
\(380\) 0 0
\(381\) −25.5167 25.5167i −1.30726 1.30726i
\(382\) 17.9282 + 17.9282i 0.917287 + 0.917287i
\(383\) −25.7846 25.7846i −1.31753 1.31753i −0.915724 0.401808i \(-0.868382\pi\)
−0.401808 0.915724i \(-0.631618\pi\)
\(384\) 13.8564 + 13.8564i 0.707107 + 0.707107i
\(385\) −1.33013 1.50000i −0.0677895 0.0764471i
\(386\) 24.3923i 1.24154i
\(387\) 0.294229 0.294229i 0.0149565 0.0149565i
\(388\) 0 0
\(389\) 11.8756 0.602119 0.301060 0.953605i \(-0.402660\pi\)
0.301060 + 0.953605i \(0.402660\pi\)
\(390\) 28.8564 + 1.73205i 1.46120 + 0.0877058i
\(391\) −1.26795 −0.0641229
\(392\) −8.39230 + 8.39230i −0.423875 + 0.423875i
\(393\) 7.73205i 0.390030i
\(394\) 20.2487i 1.02012i
\(395\) −23.1962 1.39230i −1.16713 0.0700545i
\(396\) 0 0
\(397\) 15.4904 + 15.4904i 0.777440 + 0.777440i 0.979395 0.201955i \(-0.0647294\pi\)
−0.201955 + 0.979395i \(0.564729\pi\)
\(398\) 11.1962 + 11.1962i 0.561212 + 0.561212i
\(399\) −4.09808 + 4.09808i −0.205160 + 0.205160i
\(400\) −19.8564 2.39230i −0.992820 0.119615i
\(401\) 23.7128i 1.18416i −0.805879 0.592081i \(-0.798307\pi\)
0.805879 0.592081i \(-0.201693\pi\)
\(402\) 28.3923 1.41608
\(403\) 32.5885 32.5885i 1.62335 1.62335i
\(404\) 0 0
\(405\) 1.20577 20.0885i 0.0599153 0.998203i
\(406\) 0 0
\(407\) −0.660254 + 0.660254i −0.0327276 + 0.0327276i
\(408\) −0.679492 −0.0336399
\(409\) 9.80385i 0.484769i −0.970180 0.242385i \(-0.922070\pi\)
0.970180 0.242385i \(-0.0779296\pi\)
\(410\) −18.1244 + 16.0718i −0.895098 + 0.793729i
\(411\) 11.3660 11.3660i 0.560645 0.560645i
\(412\) 0 0
\(413\) 24.1244 + 24.1244i 1.18708 + 1.18708i
\(414\) 38.7846 1.90616
\(415\) 8.83013 7.83013i 0.433454 0.384366i
\(416\) 0 0
\(417\) 6.12436i 0.299911i
\(418\) 0.267949 0.267949i 0.0131058 0.0131058i
\(419\) 9.07180 0.443186 0.221593 0.975139i \(-0.428874\pi\)
0.221593 + 0.975139i \(0.428874\pi\)
\(420\) 0 0
\(421\) 30.5885 1.49079 0.745395 0.666623i \(-0.232261\pi\)
0.745395 + 0.666623i \(0.232261\pi\)
\(422\) −24.0526 + 24.0526i −1.17086 + 1.17086i
\(423\) −10.6865 + 10.6865i −0.519597 + 0.519597i
\(424\) 9.07180i 0.440565i
\(425\) 0.545517 0.428203i 0.0264615 0.0207709i
\(426\) −12.5885 12.5885i −0.609913 0.609913i
\(427\) 10.0981 + 10.0981i 0.488680 + 0.488680i
\(428\) 0 0
\(429\) −1.73205 1.73205i −0.0836242 0.0836242i
\(430\) −0.437822 0.0262794i −0.0211137 0.00126731i
\(431\) 9.51666i 0.458401i 0.973379 + 0.229201i \(0.0736112\pi\)
−0.973379 + 0.229201i \(0.926389\pi\)
\(432\) 20.7846 1.00000
\(433\) −4.87564 + 4.87564i −0.234309 + 0.234309i −0.814488 0.580180i \(-0.802982\pi\)
0.580180 + 0.814488i \(0.302982\pi\)
\(434\) 41.3205 1.98345
\(435\) 0 0
\(436\) 0 0
\(437\) 6.46410 6.46410i 0.309220 0.309220i
\(438\) 12.5885i 0.601500i
\(439\) 17.8564i 0.852240i 0.904667 + 0.426120i \(0.140120\pi\)
−0.904667 + 0.426120i \(0.859880\pi\)
\(440\) 1.12436 + 1.26795i 0.0536016 + 0.0604471i
\(441\) 12.5885i 0.599450i
\(442\) −0.732051 0.732051i −0.0348201 0.0348201i
\(443\) 18.8301 + 18.8301i 0.894646 + 0.894646i 0.994956 0.100310i \(-0.0319834\pi\)
−0.100310 + 0.994956i \(0.531983\pi\)
\(444\) 0 0
\(445\) 1.43782 23.9545i 0.0681593 1.13555i
\(446\) 18.0000i 0.852325i
\(447\) 12.8038 0.605601
\(448\) 18.9282 18.9282i 0.894274 0.894274i
\(449\) −7.85641 −0.370767 −0.185383 0.982666i \(-0.559353\pi\)
−0.185383 + 0.982666i \(0.559353\pi\)
\(450\) −16.6865 + 13.0981i −0.786611 + 0.617449i
\(451\) 2.05256 0.0966512
\(452\) 0 0
\(453\) −1.26795 −0.0595734
\(454\) 1.60770i 0.0754529i
\(455\) 2.36603 39.4186i 0.110921 1.84797i
\(456\) 3.46410 3.46410i 0.162221 0.162221i
\(457\) −14.6340 14.6340i −0.684548 0.684548i 0.276473 0.961022i \(-0.410834\pi\)
−0.961022 + 0.276473i \(0.910834\pi\)
\(458\) −25.2487 25.2487i −1.17979 1.17979i
\(459\) −0.509619 + 0.509619i −0.0237870 + 0.0237870i
\(460\) 0 0
\(461\) 13.0000i 0.605470i −0.953075 0.302735i \(-0.902100\pi\)
0.953075 0.302735i \(-0.0978998\pi\)
\(462\) 2.19615i 0.102174i
\(463\) 4.29423 4.29423i 0.199570 0.199570i −0.600246 0.799816i \(-0.704931\pi\)
0.799816 + 0.600246i \(0.204931\pi\)
\(464\) 0 0
\(465\) −2.02628 + 33.7583i −0.0939665 + 1.56551i
\(466\) 31.6603 1.46663
\(467\) 18.2224 18.2224i 0.843234 0.843234i −0.146044 0.989278i \(-0.546654\pi\)
0.989278 + 0.146044i \(0.0466543\pi\)
\(468\) 0 0
\(469\) 38.7846i 1.79091i
\(470\) 15.9019 + 0.954483i 0.733501 + 0.0440270i
\(471\) −4.60770 4.60770i −0.212311 0.212311i
\(472\) −20.3923 20.3923i −0.938632 0.938632i
\(473\) 0.0262794 + 0.0262794i 0.00120833 + 0.00120833i
\(474\) −18.0000 18.0000i −0.826767 0.826767i
\(475\) −0.598076 + 4.96410i −0.0274416 + 0.227769i
\(476\) 0 0
\(477\) −6.80385 6.80385i −0.311527 0.311527i
\(478\) −13.0526 + 13.0526i −0.597010 + 0.597010i
\(479\) 12.9282 0.590705 0.295352 0.955388i \(-0.404563\pi\)
0.295352 + 0.955388i \(0.404563\pi\)
\(480\) 0 0
\(481\) −18.3923 −0.838617
\(482\) −5.80385 + 5.80385i −0.264358 + 0.264358i
\(483\) 52.9808i 2.41071i
\(484\) 0 0
\(485\) 1.09808 0.973721i 0.0498611 0.0442144i
\(486\) 15.5885 15.5885i 0.707107 0.707107i
\(487\) −21.0526 21.0526i −0.953983 0.953983i 0.0450043 0.998987i \(-0.485670\pi\)
−0.998987 + 0.0450043i \(0.985670\pi\)
\(488\) −8.53590 8.53590i −0.386402 0.386402i
\(489\) −19.0526 + 19.0526i −0.861586 + 0.861586i
\(490\) 9.92820 8.80385i 0.448511 0.397717i
\(491\) 37.3205i 1.68425i 0.539282 + 0.842125i \(0.318696\pi\)
−0.539282 + 0.842125i \(0.681304\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 7.46410 0.335826
\(495\) 1.79423 + 0.107695i 0.0806446 + 0.00484054i
\(496\) −34.9282 −1.56832
\(497\) −17.1962 + 17.1962i −0.771353 + 0.771353i
\(498\) 12.9282 0.579327
\(499\) 14.8564i 0.665064i −0.943092 0.332532i \(-0.892097\pi\)
0.943092 0.332532i \(-0.107903\pi\)
\(500\) 0 0
\(501\) 6.92820 6.92820i 0.309529 0.309529i
\(502\) 10.8564 + 10.8564i 0.484545 + 0.484545i
\(503\) 10.0718 + 10.0718i 0.449079 + 0.449079i 0.895048 0.445969i \(-0.147141\pi\)
−0.445969 + 0.895048i \(0.647141\pi\)
\(504\) 28.3923i 1.26469i
\(505\) 5.33975 + 0.320508i 0.237616 + 0.0142624i
\(506\) 3.46410i 0.153998i
\(507\) 25.7321i 1.14280i
\(508\) 0 0
\(509\) −15.2679 −0.676740 −0.338370 0.941013i \(-0.609876\pi\)
−0.338370 + 0.941013i \(0.609876\pi\)
\(510\) 0.758330 + 0.0455173i 0.0335794 + 0.00201554i
\(511\) −17.1962 −0.760713
\(512\) −16.0000 + 16.0000i −0.707107 + 0.707107i
\(513\) 5.19615i 0.229416i
\(514\) 26.5359i 1.17045i
\(515\) 24.4641 + 27.5885i 1.07802 + 1.21569i
\(516\) 0 0
\(517\) −0.954483 0.954483i −0.0419781 0.0419781i
\(518\) −11.6603 11.6603i −0.512322 0.512322i
\(519\) −3.80385 3.80385i −0.166970 0.166970i
\(520\) −2.00000 + 33.3205i −0.0877058 + 1.46120i
\(521\) 16.0000i 0.700973i −0.936568 0.350486i \(-0.886016\pi\)
0.936568 0.350486i \(-0.113984\pi\)
\(522\) 0 0
\(523\) 1.60770 1.60770i 0.0702996 0.0702996i −0.671083 0.741382i \(-0.734171\pi\)
0.741382 + 0.671083i \(0.234171\pi\)
\(524\) 0 0
\(525\) 17.8923 + 22.7942i 0.780884 + 0.994822i
\(526\) 26.0526 1.13595
\(527\) 0.856406 0.856406i 0.0373057 0.0373057i
\(528\) 1.85641i 0.0807897i
\(529\) 60.5692i 2.63344i
\(530\) −0.607695 + 10.1244i −0.0263966 + 0.439774i
\(531\) −30.5885 −1.32743
\(532\) 0 0
\(533\) 28.5885 + 28.5885i 1.23830 + 1.23830i
\(534\) 18.5885 18.5885i 0.804401 0.804401i
\(535\) −15.6603 17.6603i −0.677052 0.763519i
\(536\) 32.7846i 1.41608i
\(537\) 8.53590 0.368351
\(538\) 16.1962 16.1962i 0.698266 0.698266i
\(539\) −1.12436 −0.0484294
\(540\) 0 0
\(541\) −20.8038 −0.894427 −0.447214 0.894427i \(-0.647584\pi\)
−0.447214 + 0.894427i \(0.647584\pi\)
\(542\) 12.3923 12.3923i 0.532295 0.532295i
\(543\) −5.07180 −0.217652
\(544\) 0 0
\(545\) −37.7846 2.26795i −1.61851 0.0971483i
\(546\) 30.5885 30.5885i 1.30907 1.30907i
\(547\) −18.3205 18.3205i −0.783328 0.783328i 0.197063 0.980391i \(-0.436860\pi\)
−0.980391 + 0.197063i \(0.936860\pi\)
\(548\) 0 0
\(549\) −12.8038 −0.546455
\(550\) −1.16987 1.49038i −0.0498836 0.0635501i
\(551\) 0 0
\(552\) 44.7846i 1.90616i
\(553\) −24.5885 + 24.5885i −1.04561 + 1.04561i
\(554\) −13.6603 −0.580369
\(555\) 10.0981 8.95448i 0.428639 0.380097i
\(556\) 0 0
\(557\) −30.6865 + 30.6865i −1.30023 + 1.30023i −0.371996 + 0.928234i \(0.621326\pi\)
−0.928234 + 0.371996i \(0.878674\pi\)
\(558\) −26.1962 + 26.1962i −1.10897 + 1.10897i
\(559\) 0.732051i 0.0309625i
\(560\) −22.3923 + 19.8564i −0.946248 + 0.839086i
\(561\) −0.0455173 0.0455173i −0.00192174 0.00192174i
\(562\) 12.0000 + 12.0000i 0.506189 + 0.506189i
\(563\) −20.1244 20.1244i −0.848140 0.848140i 0.141761 0.989901i \(-0.454724\pi\)
−0.989901 + 0.141761i \(0.954724\pi\)
\(564\) 0 0
\(565\) −12.9282 + 11.4641i −0.543894 + 0.482298i
\(566\) 0.339746i 0.0142806i
\(567\) −21.2942 21.2942i −0.894274 0.894274i
\(568\) 14.5359 14.5359i 0.609913 0.609913i
\(569\) −5.26795 −0.220844 −0.110422 0.993885i \(-0.535220\pi\)
−0.110422 + 0.993885i \(0.535220\pi\)
\(570\) −4.09808 + 3.63397i −0.171650 + 0.152210i
\(571\) −13.4641 −0.563455 −0.281728 0.959494i \(-0.590907\pi\)
−0.281728 + 0.959494i \(0.590907\pi\)
\(572\) 0 0
\(573\) 31.0526i 1.29724i
\(574\) 36.2487i 1.51299i
\(575\) −28.2224 35.9545i −1.17696 1.49941i
\(576\) 24.0000i 1.00000i
\(577\) −14.6865 14.6865i −0.611408 0.611408i 0.331905 0.943313i \(-0.392309\pi\)
−0.943313 + 0.331905i \(0.892309\pi\)
\(578\) 16.9808 + 16.9808i 0.706307 + 0.706307i
\(579\) 21.1244 21.1244i 0.877898 0.877898i
\(580\) 0 0
\(581\) 17.6603i 0.732671i
\(582\) 1.60770 0.0666411
\(583\) 0.607695 0.607695i 0.0251682 0.0251682i
\(584\) 14.5359 0.601500
\(585\) 23.4904 + 26.4904i 0.971208 + 1.09524i
\(586\) 16.0000 0.660954
\(587\) −23.6865 + 23.6865i −0.977648 + 0.977648i −0.999756 0.0221077i \(-0.992962\pi\)
0.0221077 + 0.999756i \(0.492962\pi\)
\(588\) 0 0
\(589\) 8.73205i 0.359798i
\(590\) 21.3923 + 24.1244i 0.880707 + 0.993184i
\(591\) 17.5359 17.5359i 0.721330 0.721330i
\(592\) 9.85641 + 9.85641i 0.405096 + 0.405096i
\(593\) −17.9282 17.9282i −0.736223 0.736223i 0.235622 0.971845i \(-0.424287\pi\)
−0.971845 + 0.235622i \(0.924287\pi\)
\(594\) 1.39230 + 1.39230i 0.0571270 + 0.0571270i
\(595\) 0.0621778 1.03590i 0.00254904 0.0424677i
\(596\) 0 0
\(597\) 19.3923i 0.793674i
\(598\) −48.2487 + 48.2487i −1.97304 + 1.97304i
\(599\) −33.3205 −1.36144 −0.680720 0.732544i \(-0.738333\pi\)
−0.680720 + 0.732544i \(0.738333\pi\)
\(600\) −15.1244 19.2679i −0.617449 0.786611i
\(601\) −2.19615 −0.0895829 −0.0447915 0.998996i \(-0.514262\pi\)
−0.0447915 + 0.998996i \(0.514262\pi\)
\(602\) −0.464102 + 0.464102i −0.0189154 + 0.0189154i
\(603\) 24.5885 + 24.5885i 1.00132 + 1.00132i
\(604\) 0 0
\(605\) 1.46410 24.3923i 0.0595242 0.991688i
\(606\) 4.14359 + 4.14359i 0.168322 + 0.168322i
\(607\) 12.1244 + 12.1244i 0.492112 + 0.492112i 0.908971 0.416859i \(-0.136869\pi\)
−0.416859 + 0.908971i \(0.636869\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 8.95448 + 10.0981i 0.362556 + 0.408859i
\(611\) 26.5885i 1.07565i
\(612\) 0 0
\(613\) −3.63397 + 3.63397i −0.146775 + 0.146775i −0.776676 0.629901i \(-0.783096\pi\)
0.629901 + 0.776676i \(0.283096\pi\)
\(614\) 33.1769 1.33891
\(615\) −29.6147 1.77757i −1.19418 0.0716785i
\(616\) 2.53590 0.102174
\(617\) 20.2224 20.2224i 0.814124 0.814124i −0.171125 0.985249i \(-0.554740\pi\)
0.985249 + 0.171125i \(0.0547402\pi\)
\(618\) 40.3923i 1.62482i
\(619\) 4.78461i 0.192310i −0.995366 0.0961549i \(-0.969346\pi\)
0.995366 0.0961549i \(-0.0306544\pi\)
\(620\) 0 0
\(621\) 33.5885 + 33.5885i 1.34786 + 1.34786i
\(622\) 2.26795 + 2.26795i 0.0909365 + 0.0909365i
\(623\) −25.3923 25.3923i −1.01732 1.01732i
\(624\) −25.8564 + 25.8564i −1.03508 + 1.03508i
\(625\) 24.2846 + 5.93782i 0.971384 + 0.237513i
\(626\) 3.46410i 0.138453i
\(627\) 0.464102 0.0185344
\(628\) 0 0
\(629\) −0.483340 −0.0192720
\(630\) −1.90192 + 31.6865i −0.0757745 + 1.26242i
\(631\) −10.6603 −0.424378 −0.212189 0.977229i \(-0.568059\pi\)
−0.212189 + 0.977229i \(0.568059\pi\)
\(632\) 20.7846 20.7846i 0.826767 0.826767i
\(633\) −41.6603 −1.65585
\(634\) 17.7128i 0.703466i
\(635\) −34.8564 + 30.9090i −1.38323 + 1.22658i
\(636\) 0 0
\(637\) −15.6603 15.6603i −0.620482 0.620482i
\(638\) 0 0
\(639\) 21.8038i 0.862547i
\(640\) 18.9282 16.7846i 0.748203 0.663470i
\(641\) 0.588457i 0.0232427i −0.999932 0.0116213i \(-0.996301\pi\)
0.999932 0.0116213i \(-0.00369927\pi\)
\(642\) 25.8564i 1.02047i
\(643\) −1.24167 + 1.24167i −0.0489667 + 0.0489667i −0.731166 0.682199i \(-0.761024\pi\)
0.682199 + 0.731166i \(0.261024\pi\)
\(644\) 0 0
\(645\) −0.356406 0.401924i −0.0140335 0.0158257i
\(646\) 0.196152 0.00771751
\(647\) 15.9019 15.9019i 0.625169 0.625169i −0.321679 0.946849i \(-0.604247\pi\)
0.946849 + 0.321679i \(0.104247\pi\)
\(648\) 18.0000 + 18.0000i 0.707107 + 0.707107i
\(649\) 2.73205i 0.107242i
\(650\) 4.46410 37.0526i 0.175096 1.45332i
\(651\) 35.7846 + 35.7846i 1.40251 + 1.40251i
\(652\) 0 0
\(653\) 17.4904 + 17.4904i 0.684452 + 0.684452i 0.961000 0.276548i \(-0.0891906\pi\)
−0.276548 + 0.961000i \(0.589191\pi\)
\(654\) −29.3205 29.3205i −1.14652 1.14652i
\(655\) −9.96410 0.598076i −0.389330 0.0233688i
\(656\) 30.6410i 1.19633i
\(657\) 10.9019 10.9019i 0.425325 0.425325i
\(658\) 16.8564 16.8564i 0.657131 0.657131i
\(659\) −4.00000 −0.155818 −0.0779089 0.996960i \(-0.524824\pi\)
−0.0779089 + 0.996960i \(0.524824\pi\)
\(660\) 0 0
\(661\) 18.7846 0.730637 0.365318 0.930883i \(-0.380960\pi\)
0.365318 + 0.930883i \(0.380960\pi\)
\(662\) 0.679492 0.679492i 0.0264092 0.0264092i
\(663\) 1.26795i 0.0492431i
\(664\) 14.9282i 0.579327i
\(665\) 4.96410 + 5.59808i 0.192500 + 0.217084i
\(666\) 14.7846 0.572892
\(667\) 0 0
\(668\) 0 0
\(669\) −15.5885 + 15.5885i −0.602685 + 0.602685i
\(670\) 2.19615 36.5885i 0.0848448 1.41354i
\(671\) 1.14359i 0.0441479i
\(672\) 0 0
\(673\) −29.4449 + 29.4449i −1.13502 + 1.13502i −0.145685 + 0.989331i \(0.546539\pi\)
−0.989331 + 0.145685i \(0.953461\pi\)
\(674\) 7.85641 0.302617
\(675\) −25.7942 3.10770i −0.992820 0.119615i
\(676\) 0 0
\(677\) −5.46410 + 5.46410i −0.210002 + 0.210002i −0.804269 0.594266i \(-0.797443\pi\)
0.594266 + 0.804269i \(0.297443\pi\)
\(678\) −18.9282 −0.726933
\(679\) 2.19615i 0.0842806i
\(680\) −0.0525589 + 0.875644i −0.00201554 + 0.0335794i
\(681\) 1.39230 1.39230i 0.0533532 0.0533532i
\(682\) −2.33975 2.33975i −0.0895935 0.0895935i
\(683\) 27.1962 + 27.1962i 1.04063 + 1.04063i 0.999139 + 0.0414931i \(0.0132114\pi\)
0.0414931 + 0.999139i \(0.486789\pi\)
\(684\) 0 0
\(685\) −13.7679 15.5263i −0.526046 0.593229i
\(686\) 13.2679i 0.506573i
\(687\) 43.7321i 1.66848i
\(688\) 0.392305 0.392305i 0.0149565 0.0149565i
\(689\) 16.9282 0.644913
\(690\) 3.00000 49.9808i 0.114208 1.90274i
\(691\) 49.4449 1.88097 0.940486 0.339833i \(-0.110371\pi\)
0.940486 + 0.339833i \(0.110371\pi\)
\(692\) 0 0
\(693\) 1.90192 1.90192i 0.0722481 0.0722481i
\(694\) 25.8038i 0.979501i
\(695\) −7.89230 0.473721i −0.299372 0.0179692i
\(696\) 0 0
\(697\) 0.751289 + 0.751289i 0.0284571 + 0.0284571i
\(698\) −0.267949 0.267949i −0.0101420 0.0101420i
\(699\) 27.4186 + 27.4186i 1.03707 + 1.03707i
\(700\) 0 0
\(701\) 31.8564i 1.20320i −0.798798 0.601600i \(-0.794530\pi\)
0.798798 0.601600i \(-0.205470\pi\)
\(702\) 38.7846i 1.46383i
\(703\) 2.46410 2.46410i 0.0929354 0.0929354i
\(704\) −2.14359 −0.0807897
\(705\) 12.9449 + 14.5981i 0.487532 + 0.549795i
\(706\) −44.5359 −1.67613
\(707\) 5.66025 5.66025i 0.212876 0.212876i
\(708\) 0 0
\(709\) 31.4641i 1.18166i 0.806796 + 0.590830i \(0.201199\pi\)
−0.806796 + 0.590830i \(0.798801\pi\)
\(710\) −17.1962 + 15.2487i −0.645360 + 0.572274i
\(711\) 31.1769i 1.16923i
\(712\) 21.4641 + 21.4641i 0.804401 + 0.804401i
\(713\) −56.4449 56.4449i −2.11388 2.11388i
\(714\) 0.803848 0.803848i 0.0300832 0.0300832i
\(715\) −2.36603 + 2.09808i −0.0884843 + 0.0784636i
\(716\) 0 0
\(717\) −22.6077 −0.844300
\(718\) 8.07180 8.07180i 0.301237 0.301237i
\(719\) 47.6410 1.77671 0.888355 0.459157i \(-0.151849\pi\)
0.888355 + 0.459157i \(0.151849\pi\)
\(720\) 1.60770 26.7846i 0.0599153 0.998203i
\(721\) 55.1769 2.05490
\(722\) −1.00000 + 1.00000i −0.0372161 + 0.0372161i
\(723\) −10.0526 −0.373859
\(724\) 0 0
\(725\) 0 0
\(726\) 18.9282 18.9282i 0.702492 0.702492i
\(727\) −11.0263 11.0263i −0.408942 0.408942i 0.472427 0.881370i \(-0.343378\pi\)
−0.881370 + 0.472427i \(0.843378\pi\)
\(728\) 35.3205 + 35.3205i 1.30907 + 1.30907i
\(729\) 27.0000 1.00000
\(730\) −16.2224 0.973721i −0.600419 0.0360390i
\(731\) 0.0192379i 0.000711539i
\(732\) 0 0
\(733\) 28.6603 28.6603i 1.05859 1.05859i 0.0604174 0.998173i \(-0.480757\pi\)
0.998173 0.0604174i \(-0.0192432\pi\)
\(734\) 35.5692 1.31288
\(735\) 16.2224 + 0.973721i 0.598373 + 0.0359162i
\(736\) 0 0
\(737\) −2.19615 + 2.19615i −0.0808963 + 0.0808963i
\(738\) −22.9808 22.9808i −0.845934 0.845934i
\(739\) 19.4449i 0.715291i −0.933857 0.357645i \(-0.883580\pi\)
0.933857 0.357645i \(-0.116420\pi\)
\(740\) 0 0
\(741\) 6.46410 + 6.46410i 0.237465 + 0.237465i
\(742\) 10.7321 + 10.7321i 0.393986 + 0.393986i
\(743\) −32.2487 32.2487i −1.18309 1.18309i −0.978939 0.204151i \(-0.934557\pi\)
−0.204151 0.978939i \(-0.565443\pi\)
\(744\) −30.2487 30.2487i −1.10897 1.10897i
\(745\) 0.990381 16.5000i 0.0362848 0.604513i
\(746\) 25.1769i 0.921792i
\(747\) 11.1962 + 11.1962i 0.409646 + 0.409646i
\(748\) 0 0
\(749\) −35.3205 −1.29058
\(750\) 15.5885 + 22.5167i 0.569210 + 0.822192i
\(751\) 6.78461 0.247574 0.123787 0.992309i \(-0.460496\pi\)
0.123787 + 0.992309i \(0.460496\pi\)
\(752\) −14.2487 + 14.2487i −0.519597 + 0.519597i
\(753\) 18.8038i 0.685250i
\(754\) 0 0
\(755\) −0.0980762 + 1.63397i −0.00356936 + 0.0594664i
\(756\) 0 0
\(757\) 14.0263 + 14.0263i 0.509794 + 0.509794i 0.914463 0.404669i \(-0.132613\pi\)
−0.404669 + 0.914463i \(0.632613\pi\)
\(758\) 21.4641 + 21.4641i 0.779611 + 0.779611i
\(759\) −3.00000 + 3.00000i −0.108893 + 0.108893i
\(760\) −4.19615 4.73205i −0.152210 0.171650i
\(761\) 1.48334i 0.0537710i 0.999639 + 0.0268855i \(0.00855895\pi\)
−0.999639 + 0.0268855i \(0.991441\pi\)
\(762\) −51.0333 −1.84874
\(763\) −40.0526 + 40.0526i −1.45000 + 1.45000i
\(764\) 0 0
\(765\) 0.617314 + 0.696152i 0.0223190 + 0.0251694i
\(766\) −51.5692 −1.86327
\(767\) 38.0526 38.0526i 1.37400 1.37400i
\(768\) 0 0
\(769\) 23.0000i 0.829401i −0.909958 0.414701i \(-0.863886\pi\)
0.909958 0.414701i \(-0.136114\pi\)
\(770\) −2.83013 0.169873i −0.101991 0.00612180i
\(771\) −22.9808 + 22.9808i −0.827632 + 0.827632i
\(772\) 0 0
\(773\) 25.5885 + 25.5885i 0.920353 + 0.920353i 0.997054 0.0767013i \(-0.0244388\pi\)
−0.0767013 + 0.997054i \(0.524439\pi\)
\(774\) 0.588457i 0.0211517i
\(775\) 43.3468 + 5.22243i 1.55706 + 0.187595i
\(776\) 1.85641i 0.0666411i</