Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [867,2,Mod(616,867)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(867, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("867.616");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 867 = 3 \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 867.e (of order \(4\), degree \(2\), not 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: | \(6.92302985525\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 51) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 616.1 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 867.616 |
Dual form | 867.2.e.e.829.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/867\mathbb{Z}\right)^\times\).
\(n\) | \(290\) | \(292\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | 2.00000 | 1.00000 | ||||||||
\(5\) | 2.12132 | − | 2.12132i | 0.948683 | − | 0.948683i | −0.0500628 | − | 0.998746i | \(-0.515942\pi\) |
0.998746 | + | 0.0500628i | \(0.0159421\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.82843 | − | 2.82843i | −1.06904 | − | 1.06904i | −0.997433 | − | 0.0716124i | \(-0.977186\pi\) |
−0.0716124 | − | 0.997433i | \(-0.522814\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.12132 | + | 2.12132i | 0.639602 | + | 0.639602i | 0.950457 | − | 0.310855i | \(-0.100615\pi\) |
−0.310855 | + | 0.950457i | \(0.600615\pi\) | |||||||
\(12\) | −1.41421 | + | 1.41421i | −0.408248 | + | 0.408248i | ||||
\(13\) | 1.00000 | 0.277350 | 0.138675 | − | 0.990338i | \(-0.455716\pi\) | ||||
0.138675 | + | 0.990338i | \(0.455716\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.00000i | 0.774597i | ||||||||
\(16\) | 4.00000 | 1.00000 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.00000i | − | 0.229416i | −0.993399 | − | 0.114708i | \(-0.963407\pi\) | ||
0.993399 | − | 0.114708i | \(-0.0365932\pi\) | |||||||
\(20\) | 4.24264 | − | 4.24264i | 0.948683 | − | 0.948683i | ||||
\(21\) | 4.00000 | 0.872872 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.36396 | − | 6.36396i | −1.32698 | − | 1.32698i | −0.907994 | − | 0.418984i | \(-0.862386\pi\) |
−0.418984 | − | 0.907994i | \(-0.637614\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 4.00000i | − | 0.800000i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | −5.65685 | − | 5.65685i | −1.06904 | − | 1.06904i | ||||
\(29\) | 4.24264 | − | 4.24264i | 0.787839 | − | 0.787839i | −0.193301 | − | 0.981140i | \(-0.561919\pi\) |
0.981140 | + | 0.193301i | \(0.0619194\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.41421 | + | 1.41421i | −0.254000 | + | 0.254000i | −0.822608 | − | 0.568608i | \(-0.807482\pi\) |
0.568608 | + | 0.822608i | \(0.307482\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.00000 | −0.522233 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −12.0000 | −2.02837 | ||||||||
\(36\) | − | 2.00000i | − | 0.333333i | ||||||
\(37\) | 2.82843 | − | 2.82843i | 0.464991 | − | 0.464991i | −0.435297 | − | 0.900287i | \(-0.643356\pi\) |
0.900287 | + | 0.435297i | \(0.143356\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.707107 | + | 0.707107i | −0.113228 | + | 0.113228i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.12132 | − | 2.12132i | −0.331295 | − | 0.331295i | 0.521783 | − | 0.853078i | \(-0.325267\pi\) |
−0.853078 | + | 0.521783i | \(0.825267\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.00000i | 1.06749i | 0.845645 | + | 0.533745i | \(0.179216\pi\) | ||||
−0.845645 | + | 0.533745i | \(0.820784\pi\) | |||||||
\(44\) | 4.24264 | + | 4.24264i | 0.639602 | + | 0.639602i | ||||
\(45\) | −2.12132 | − | 2.12132i | −0.316228 | − | 0.316228i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.00000 | 0.875190 | 0.437595 | − | 0.899172i | \(-0.355830\pi\) | ||||
0.437595 | + | 0.899172i | \(0.355830\pi\) | |||||||
\(48\) | −2.82843 | + | 2.82843i | −0.408248 | + | 0.408248i | ||||
\(49\) | 9.00000i | 1.28571i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.00000 | 0.277350 | ||||||||
\(53\) | − | 6.00000i | − | 0.824163i | −0.911147 | − | 0.412082i | \(-0.864802\pi\) | ||
0.911147 | − | 0.412082i | \(-0.135198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.00000 | 1.21356 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.707107 | + | 0.707107i | 0.0936586 | + | 0.0936586i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 6.00000i | − | 0.781133i | −0.920575 | − | 0.390567i | \(-0.872279\pi\) | ||
0.920575 | − | 0.390567i | \(-0.127721\pi\) | |||||||
\(60\) | 6.00000i | 0.774597i | ||||||||
\(61\) | 5.65685 | + | 5.65685i | 0.724286 | + | 0.724286i | 0.969475 | − | 0.245189i | \(-0.0788501\pi\) |
−0.245189 | + | 0.969475i | \(0.578850\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.82843 | + | 2.82843i | −0.356348 | + | 0.356348i | ||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 2.12132 | − | 2.12132i | 0.263117 | − | 0.263117i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.00000 | 1.08347 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.48528 | + | 8.48528i | −1.00702 | + | 1.00702i | −0.00704243 | + | 0.999975i | \(0.502242\pi\) |
−0.999975 | + | 0.00704243i | \(0.997758\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.41421 | − | 1.41421i | 0.165521 | − | 0.165521i | −0.619486 | − | 0.785007i | \(-0.712659\pi\) |
0.785007 | + | 0.619486i | \(0.212659\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.82843 | + | 2.82843i | 0.326599 | + | 0.326599i | ||||
\(76\) | − | 2.00000i | − | 0.229416i | ||||||
\(77\) | − | 12.0000i | − | 1.36753i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.07107 | + | 7.07107i | 0.795557 | + | 0.795557i | 0.982391 | − | 0.186834i | \(-0.0598227\pi\) |
−0.186834 | + | 0.982391i | \(0.559823\pi\) | |||||||
\(80\) | 8.48528 | − | 8.48528i | 0.948683 | − | 0.948683i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 6.00000i | − | 0.658586i | −0.944228 | − | 0.329293i | \(-0.893190\pi\) | ||
0.944228 | − | 0.329293i | \(-0.106810\pi\) | |||||||
\(84\) | 8.00000 | 0.872872 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.00000i | 0.643268i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.82843 | − | 2.82843i | −0.296500 | − | 0.296500i | ||||
\(92\) | −12.7279 | − | 12.7279i | −1.32698 | − | 1.32698i | ||||
\(93\) | − | 2.00000i | − | 0.207390i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.12132 | − | 2.12132i | −0.217643 | − | 0.217643i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.3137 | + | 11.3137i | −1.14873 | + | 1.14873i | −0.161931 | + | 0.986802i | \(0.551772\pi\) |
−0.986802 | + | 0.161931i | \(0.948228\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.12132 | − | 2.12132i | 0.213201 | − | 0.213201i | ||||
\(100\) | − | 8.00000i | − | 0.800000i | ||||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.00000 | 0.492665 | 0.246332 | − | 0.969185i | \(-0.420775\pi\) | ||||
0.246332 | + | 0.969185i | \(0.420775\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.48528 | − | 8.48528i | 0.828079 | − | 0.828079i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.36396 | − | 6.36396i | 0.615227 | − | 0.615227i | −0.329076 | − | 0.944303i | \(-0.606737\pi\) |
0.944303 | + | 0.329076i | \(0.106737\pi\) | |||||||
\(108\) | 1.41421 | + | 1.41421i | 0.136083 | + | 0.136083i | ||||
\(109\) | 14.1421 | + | 14.1421i | 1.35457 | + | 1.35457i | 0.880471 | + | 0.474100i | \(0.157226\pi\) |
0.474100 | + | 0.880471i | \(0.342774\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.00000i | 0.379663i | ||||||||
\(112\) | −11.3137 | − | 11.3137i | −1.06904 | − | 1.06904i | ||||
\(113\) | 6.36396 | + | 6.36396i | 0.598671 | + | 0.598671i | 0.939959 | − | 0.341288i | \(-0.110863\pi\) |
−0.341288 | + | 0.939959i | \(0.610863\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −27.0000 | −2.51776 | ||||||||
\(116\) | 8.48528 | − | 8.48528i | 0.787839 | − | 0.787839i | ||||
\(117\) | − | 1.00000i | − | 0.0924500i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 2.00000i | − | 0.181818i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.00000 | 0.270501 | ||||||||
\(124\) | −2.82843 | + | 2.82843i | −0.254000 | + | 0.254000i | ||||
\(125\) | 2.12132 | + | 2.12132i | 0.189737 | + | 0.189737i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.0000i | 1.15356i | 0.816898 | + | 0.576782i | \(0.195692\pi\) | ||||
−0.816898 | + | 0.576782i | \(0.804308\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.94975 | − | 4.94975i | −0.435801 | − | 0.435801i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.12132 | − | 2.12132i | 0.185341 | − | 0.185341i | −0.608338 | − | 0.793678i | \(-0.708163\pi\) |
0.793678 | + | 0.608338i | \(0.208163\pi\) | |||||||
\(132\) | −6.00000 | −0.522233 | ||||||||
\(133\) | −2.82843 | + | 2.82843i | −0.245256 | + | 0.245256i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.00000 | 0.258199 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.00000 | −0.512615 | −0.256307 | − | 0.966595i | \(-0.582506\pi\) | ||||
−0.256307 | + | 0.966595i | \(0.582506\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.41421 | + | 1.41421i | −0.119952 | + | 0.119952i | −0.764535 | − | 0.644583i | \(-0.777031\pi\) |
0.644583 | + | 0.764535i | \(0.277031\pi\) | |||||||
\(140\) | −24.0000 | −2.02837 | ||||||||
\(141\) | −4.24264 | + | 4.24264i | −0.357295 | + | 0.357295i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.12132 | + | 2.12132i | 0.177394 | + | 0.177394i | ||||
\(144\) | − | 4.00000i | − | 0.333333i | ||||||
\(145\) | − | 18.0000i | − | 1.49482i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.36396 | − | 6.36396i | −0.524891 | − | 0.524891i | ||||
\(148\) | 5.65685 | − | 5.65685i | 0.464991 | − | 0.464991i | ||||
\(149\) | 18.0000 | 1.47462 | 0.737309 | − | 0.675556i | \(-0.236096\pi\) | ||||
0.737309 | + | 0.675556i | \(0.236096\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000i | 0.651031i | 0.945537 | + | 0.325515i | \(0.105538\pi\) | ||||
−0.945537 | + | 0.325515i | \(0.894462\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.00000i | 0.481932i | ||||||||
\(156\) | −1.41421 | + | 1.41421i | −0.113228 | + | 0.113228i | ||||
\(157\) | −11.0000 | −0.877896 | −0.438948 | − | 0.898513i | \(-0.644649\pi\) | ||||
−0.438948 | + | 0.898513i | \(0.644649\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.24264 | + | 4.24264i | 0.336463 | + | 0.336463i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 36.0000i | 2.83720i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.41421 | + | 1.41421i | 0.110770 | + | 0.110770i | 0.760319 | − | 0.649550i | \(-0.225042\pi\) |
−0.649550 | + | 0.760319i | \(0.725042\pi\) | |||||||
\(164\) | −4.24264 | − | 4.24264i | −0.331295 | − | 0.331295i | ||||
\(165\) | −6.36396 | + | 6.36396i | −0.495434 | + | 0.495434i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.8492 | + | 14.8492i | −1.14907 | + | 1.14907i | −0.162333 | + | 0.986736i | \(0.551902\pi\) |
−0.986736 | + | 0.162333i | \(0.948098\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | 14.0000i | 1.06749i | ||||||||
\(173\) | −10.6066 | + | 10.6066i | −0.806405 | + | 0.806405i | −0.984088 | − | 0.177683i | \(-0.943140\pi\) |
0.177683 | + | 0.984088i | \(0.443140\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.3137 | + | 11.3137i | −0.855236 | + | 0.855236i | ||||
\(176\) | 8.48528 | + | 8.48528i | 0.639602 | + | 0.639602i | ||||
\(177\) | 4.24264 | + | 4.24264i | 0.318896 | + | 0.318896i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.00000i | 0.448461i | 0.974536 | + | 0.224231i | \(0.0719869\pi\) | ||||
−0.974536 | + | 0.224231i | \(0.928013\pi\) | |||||||
\(180\) | −4.24264 | − | 4.24264i | −0.316228 | − | 0.316228i | ||||
\(181\) | −9.89949 | − | 9.89949i | −0.735824 | − | 0.735824i | 0.235943 | − | 0.971767i | \(-0.424182\pi\) |
−0.971767 | + | 0.235943i | \(0.924182\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.00000 | −0.591377 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 12.0000i | − | 0.882258i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 12.0000 | 0.875190 | ||||||||
\(189\) | − | 4.00000i | − | 0.290957i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.0000 | −1.30243 | −0.651217 | − | 0.758891i | \(-0.725741\pi\) | ||||
−0.651217 | + | 0.758891i | \(0.725741\pi\) | |||||||
\(192\) | −5.65685 | + | 5.65685i | −0.408248 | + | 0.408248i | ||||
\(193\) | 15.5563 | + | 15.5563i | 1.11977 | + | 1.11977i | 0.991775 | + | 0.127996i | \(0.0408544\pi\) |
0.127996 | + | 0.991775i | \(0.459146\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.00000i | 0.214834i | ||||||||
\(196\) | 18.0000i | 1.28571i | ||||||||
\(197\) | 2.12132 | + | 2.12132i | 0.151138 | + | 0.151138i | 0.778626 | − | 0.627488i | \(-0.215917\pi\) |
−0.627488 | + | 0.778626i | \(0.715917\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.3137 | + | 11.3137i | −0.802008 | + | 0.802008i | −0.983409 | − | 0.181402i | \(-0.941937\pi\) |
0.181402 | + | 0.983409i | \(0.441937\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.82843 | − | 2.82843i | 0.199502 | − | 0.199502i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −24.0000 | −1.68447 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.00000 | −0.628587 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.36396 | + | 6.36396i | −0.442326 | + | 0.442326i | ||||
\(208\) | 4.00000 | 0.277350 | ||||||||
\(209\) | 2.12132 | − | 2.12132i | 0.146735 | − | 0.146735i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.41421 | + | 1.41421i | 0.0973585 | + | 0.0973585i | 0.754108 | − | 0.656750i | \(-0.228069\pi\) |
−0.656750 | + | 0.754108i | \(0.728069\pi\) | |||||||
\(212\) | − | 12.0000i | − | 0.824163i | ||||||
\(213\) | − | 12.0000i | − | 0.822226i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 14.8492 | + | 14.8492i | 1.01271 | + | 1.01271i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.00000 | 0.543075 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.00000i | 0.135147i | ||||||||
\(220\) | 18.0000 | 1.21356 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.00000i | − | 0.0669650i | −0.999439 | − | 0.0334825i | \(-0.989340\pi\) | ||
0.999439 | − | 0.0334825i | \(-0.0106598\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.00000 | −0.266667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.12132 | − | 2.12132i | −0.140797 | − | 0.140797i | 0.633195 | − | 0.773992i | \(-0.281743\pi\) |
−0.773992 | + | 0.633195i | \(0.781743\pi\) | |||||||
\(228\) | 1.41421 | + | 1.41421i | 0.0936586 | + | 0.0936586i | ||||
\(229\) | − | 14.0000i | − | 0.925146i | −0.886581 | − | 0.462573i | \(-0.846926\pi\) | ||
0.886581 | − | 0.462573i | \(-0.153074\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.48528 | + | 8.48528i | 0.558291 | + | 0.558291i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.8492 | − | 14.8492i | 0.972806 | − | 0.972806i | −0.0268337 | − | 0.999640i | \(-0.508542\pi\) |
0.999640 | + | 0.0268337i | \(0.00854246\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.7279 | − | 12.7279i | 0.830278 | − | 0.830278i | ||||
\(236\) | − | 12.0000i | − | 0.781133i | ||||||
\(237\) | −10.0000 | −0.649570 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.0000 | −0.776215 | −0.388108 | − | 0.921614i | \(-0.626871\pi\) | ||||
−0.388108 | + | 0.921614i | \(0.626871\pi\) | |||||||
\(240\) | 12.0000i | 0.774597i | ||||||||
\(241\) | −5.65685 | + | 5.65685i | −0.364390 | + | 0.364390i | −0.865426 | − | 0.501036i | \(-0.832952\pi\) |
0.501036 | + | 0.865426i | \(0.332952\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 11.3137 | + | 11.3137i | 0.724286 | + | 0.724286i | ||||
\(245\) | 19.0919 | + | 19.0919i | 1.21974 | + | 1.21974i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1.00000i | − | 0.0636285i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.24264 | + | 4.24264i | 0.268866 | + | 0.268866i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.0000 | −1.51487 | −0.757433 | − | 0.652913i | \(-0.773547\pi\) | ||||
−0.757433 | + | 0.652913i | \(0.773547\pi\) | |||||||
\(252\) | −5.65685 | + | 5.65685i | −0.356348 | + | 0.356348i | ||||
\(253\) | − | 27.0000i | − | 1.69748i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 12.0000i | 0.748539i | 0.927320 | + | 0.374270i | \(0.122107\pi\) | ||||
−0.927320 | + | 0.374270i | \(0.877893\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.0000 | −0.994192 | ||||||||
\(260\) | 4.24264 | − | 4.24264i | 0.263117 | − | 0.263117i | ||||
\(261\) | −4.24264 | − | 4.24264i | −0.262613 | − | 0.262613i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 12.0000i | − | 0.739952i | −0.929041 | − | 0.369976i | \(-0.879366\pi\) | ||
0.929041 | − | 0.369976i | \(-0.120634\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.7279 | − | 12.7279i | −0.781870 | − | 0.781870i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −8.00000 | −0.488678 | ||||||||
\(269\) | 10.6066 | − | 10.6066i | 0.646696 | − | 0.646696i | −0.305497 | − | 0.952193i | \(-0.598823\pi\) |
0.952193 | + | 0.305497i | \(0.0988226\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.0000 | 0.668202 | 0.334101 | − | 0.942537i | \(-0.391567\pi\) | ||||
0.334101 | + | 0.942537i | \(0.391567\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.00000 | 0.242091 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.48528 | − | 8.48528i | 0.511682 | − | 0.511682i | ||||
\(276\) | 18.0000 | 1.08347 | ||||||||
\(277\) | 1.41421 | − | 1.41421i | 0.0849719 | − | 0.0849719i | −0.663343 | − | 0.748315i | \(-0.730863\pi\) |
0.748315 | + | 0.663343i | \(0.230863\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.41421 | + | 1.41421i | 0.0846668 | + | 0.0846668i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 12.0000i | − | 0.715860i | −0.933748 | − | 0.357930i | \(-0.883483\pi\) | ||
0.933748 | − | 0.357930i | \(-0.116517\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.07107 | + | 7.07107i | 0.420331 | + | 0.420331i | 0.885318 | − | 0.464986i | \(-0.153941\pi\) |
−0.464986 | + | 0.885318i | \(0.653941\pi\) | |||||||
\(284\) | −16.9706 | + | 16.9706i | −1.00702 | + | 1.00702i | ||||
\(285\) | 3.00000 | 0.177705 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.0000i | 0.708338i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 16.0000i | − | 0.937937i | ||||||
\(292\) | 2.82843 | − | 2.82843i | 0.165521 | − | 0.165521i | ||||
\(293\) | 24.0000 | 1.40209 | 0.701047 | − | 0.713115i | \(-0.252716\pi\) | ||||
0.701047 | + | 0.713115i | \(0.252716\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.7279 | − | 12.7279i | −0.741048 | − | 0.741048i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.00000i | 0.174078i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.36396 | − | 6.36396i | −0.368037 | − | 0.368037i | ||||
\(300\) | 5.65685 | + | 5.65685i | 0.326599 | + | 0.326599i | ||||
\(301\) | 19.7990 | − | 19.7990i | 1.14119 | − | 1.14119i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 4.00000i | − | 0.229416i | ||||||
\(305\) | 24.0000 | 1.37424 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.0000 | 1.14146 | 0.570730 | − | 0.821138i | \(-0.306660\pi\) | ||||
0.570730 | + | 0.821138i | \(0.306660\pi\) | |||||||
\(308\) | − | 24.0000i | − | 1.36753i | ||||||
\(309\) | −3.53553 | + | 3.53553i | −0.201129 | + | 0.201129i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.9706 | + | 16.9706i | −0.962312 | + | 0.962312i | −0.999315 | − | 0.0370028i | \(-0.988219\pi\) |
0.0370028 | + | 0.999315i | \(0.488219\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.3137 | − | 11.3137i | −0.639489 | − | 0.639489i | 0.310941 | − | 0.950429i | \(-0.399356\pi\) |
−0.950429 | + | 0.310941i | \(0.899356\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 12.0000i | 0.676123i | ||||||||
\(316\) | 14.1421 | + | 14.1421i | 0.795557 | + | 0.795557i | ||||
\(317\) | 4.24264 | + | 4.24264i | 0.238290 | + | 0.238290i | 0.816142 | − | 0.577851i | \(-0.196109\pi\) |
−0.577851 | + | 0.816142i | \(0.696109\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.0000 | 1.00781 | ||||||||
\(320\) | 16.9706 | − | 16.9706i | 0.948683 | − | 0.948683i | ||||
\(321\) | 9.00000i | 0.502331i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −2.00000 | −0.111111 | ||||||||
\(325\) | − | 4.00000i | − | 0.221880i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −20.0000 | −1.10600 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16.9706 | − | 16.9706i | −0.935617 | − | 0.935617i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.0000i | 0.714545i | 0.934000 | + | 0.357272i | \(0.116293\pi\) | ||||
−0.934000 | + | 0.357272i | \(0.883707\pi\) | |||||||
\(332\) | − | 12.0000i | − | 0.658586i | ||||||
\(333\) | −2.82843 | − | 2.82843i | −0.154997 | − | 0.154997i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.48528 | + | 8.48528i | −0.463600 | + | 0.463600i | ||||
\(336\) | 16.0000 | 0.872872 | ||||||||
\(337\) | −9.89949 | + | 9.89949i | −0.539260 | + | 0.539260i | −0.923312 | − | 0.384052i | \(-0.874528\pi\) |
0.384052 | + | 0.923312i | \(0.374528\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.00000 | −0.488813 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.00000 | −0.324918 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.65685 | − | 5.65685i | 0.305441 | − | 0.305441i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 19.0919 | − | 19.0919i | 1.02787 | − | 1.02787i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.48528 | − | 8.48528i | −0.455514 | − | 0.455514i | 0.441666 | − | 0.897180i | \(-0.354388\pi\) |
−0.897180 | + | 0.441666i | \(0.854388\pi\) | |||||||
\(348\) | 12.0000i | 0.643268i | ||||||||
\(349\) | 19.0000i | 1.01705i | 0.861048 | + | 0.508523i | \(0.169808\pi\) | ||||
−0.861048 | + | 0.508523i | \(0.830192\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.707107 | + | 0.707107i | 0.0377426 | + | 0.0377426i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.00000 | −0.319348 | −0.159674 | − | 0.987170i | \(-0.551044\pi\) | ||||
−0.159674 | + | 0.987170i | \(0.551044\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 36.0000i | 1.91068i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.0000 | 0.947368 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.41421 | + | 1.41421i | 0.0742270 | + | 0.0742270i | ||||
\(364\) | −5.65685 | − | 5.65685i | −0.296500 | − | 0.296500i | ||||
\(365\) | − | 6.00000i | − | 0.314054i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.65685 | + | 5.65685i | 0.295285 | + | 0.295285i | 0.839164 | − | 0.543879i | \(-0.183045\pi\) |
−0.543879 | + | 0.839164i | \(0.683045\pi\) | |||||||
\(368\) | −25.4558 | − | 25.4558i | −1.32698 | − | 1.32698i | ||||
\(369\) | −2.12132 | + | 2.12132i | −0.110432 | + | 0.110432i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −16.9706 | + | 16.9706i | −0.881068 | + | 0.881068i | ||||
\(372\) | − | 4.00000i | − | 0.207390i | ||||||
\(373\) | −22.0000 | −1.13912 | −0.569558 | − | 0.821951i | \(-0.692886\pi\) | ||||
−0.569558 | + | 0.821951i | \(0.692886\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.00000 | −0.154919 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.24264 | − | 4.24264i | 0.218507 | − | 0.218507i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.6274 | − | 22.6274i | 1.16229 | − | 1.16229i | 0.178320 | − | 0.983973i | \(-0.442934\pi\) |
0.983973 | − | 0.178320i | \(-0.0570661\pi\) | |||||||
\(380\) | −4.24264 | − | 4.24264i | −0.217643 | − | 0.217643i | ||||
\(381\) | −9.19239 | − | 9.19239i | −0.470940 | − | 0.470940i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.0000i | 0.613171i | 0.951843 | + | 0.306586i | \(0.0991866\pi\) | ||||
−0.951843 | + | 0.306586i | \(0.900813\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −25.4558 | − | 25.4558i | −1.29735 | − | 1.29735i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.00000 | 0.355830 | ||||||||
\(388\) | −22.6274 | + | 22.6274i | −1.14873 | + | 1.14873i | ||||
\(389\) | 36.0000i | 1.82527i | 0.408773 | + | 0.912636i | \(0.365957\pi\) | ||||
−0.408773 | + | 0.912636i | \(0.634043\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.00000i | 0.151330i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 30.0000 | 1.50946 | ||||||||
\(396\) | 4.24264 | − | 4.24264i | 0.213201 | − | 0.213201i | ||||
\(397\) | −14.1421 | − | 14.1421i | −0.709773 | − | 0.709773i | 0.256714 | − | 0.966487i | \(-0.417360\pi\) |
−0.966487 | + | 0.256714i | \(0.917360\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 4.00000i | − | 0.200250i | ||||||
\(400\) | − | 16.0000i | − | 0.800000i | ||||||
\(401\) | −10.6066 | − | 10.6066i | −0.529668 | − | 0.529668i | 0.390805 | − | 0.920473i | \(-0.372197\pi\) |
−0.920473 | + | 0.390805i | \(0.872197\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.41421 | + | 1.41421i | −0.0704470 | + | 0.0704470i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.12132 | + | 2.12132i | −0.105409 | + | 0.105409i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.0000 | 0.594818 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.0000 | −0.939490 | −0.469745 | − | 0.882802i | \(-0.655654\pi\) | ||||
−0.469745 | + | 0.882802i | \(0.655654\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.24264 | − | 4.24264i | 0.209274 | − | 0.209274i | ||||
\(412\) | 10.0000 | 0.492665 | ||||||||
\(413\) | −16.9706 | + | 16.9706i | −0.835067 | + | 0.835067i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.7279 | − | 12.7279i | −0.624789 | − | 0.624789i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 2.00000i | − | 0.0979404i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.48528 | − | 8.48528i | −0.414533 | − | 0.414533i | 0.468781 | − | 0.883314i | \(-0.344693\pi\) |
−0.883314 | + | 0.468781i | \(0.844693\pi\) | |||||||
\(420\) | 16.9706 | − | 16.9706i | 0.828079 | − | 0.828079i | ||||
\(421\) | 25.0000 | 1.21843 | 0.609213 | − | 0.793007i | \(-0.291486\pi\) | ||||
0.609213 | + | 0.793007i | \(0.291486\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 6.00000i | − | 0.291730i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 32.0000i | − | 1.54859i | ||||||
\(428\) | 12.7279 | − | 12.7279i | 0.615227 | − | 0.615227i | ||||
\(429\) | −3.00000 | −0.144841 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.9706 | + | 16.9706i | 0.817443 | + | 0.817443i | 0.985737 | − | 0.168294i | \(-0.0538257\pi\) |
−0.168294 | + | 0.985737i | \(0.553826\pi\) | |||||||
\(432\) | 2.82843 | + | 2.82843i | 0.136083 | + | 0.136083i | ||||
\(433\) | 1.00000i | 0.0480569i | 0.999711 | + | 0.0240285i | \(0.00764923\pi\) | ||||
−0.999711 | + | 0.0240285i | \(0.992351\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12.7279 | + | 12.7279i | 0.610257 | + | 0.610257i | ||||
\(436\) | 28.2843 | + | 28.2843i | 1.35457 | + | 1.35457i | ||||
\(437\) | −6.36396 | + | 6.36396i | −0.304430 | + | 0.304430i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.7990 | − | 19.7990i | 0.944954 | − | 0.944954i | −0.0536078 | − | 0.998562i | \(-0.517072\pi\) |
0.998562 | + | 0.0536078i | \(0.0170721\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.00000 | 0.428571 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.00000 | 0.285069 | 0.142534 | − | 0.989790i | \(-0.454475\pi\) | ||||
0.142534 | + | 0.989790i | \(0.454475\pi\) | |||||||
\(444\) | 8.00000i | 0.379663i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.7279 | + | 12.7279i | −0.602010 | + | 0.602010i | ||||
\(448\) | −22.6274 | − | 22.6274i | −1.06904 | − | 1.06904i | ||||
\(449\) | −4.24264 | − | 4.24264i | −0.200223 | − | 0.200223i | 0.599873 | − | 0.800095i | \(-0.295218\pi\) |
−0.800095 | + | 0.599873i | \(0.795218\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 9.00000i | − | 0.423793i | ||||||
\(452\) | 12.7279 | + | 12.7279i | 0.598671 | + | 0.598671i | ||||
\(453\) | −5.65685 | − | 5.65685i | −0.265782 | − | 0.265782i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12.0000 | −0.562569 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 19.0000i | − | 0.888783i | −0.895833 | − | 0.444391i | \(-0.853420\pi\) | ||
0.895833 | − | 0.444391i | \(-0.146580\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −54.0000 | −2.51776 | ||||||||
\(461\) | 30.0000i | 1.39724i | 0.715493 | + | 0.698620i | \(0.246202\pi\) | ||||
−0.715493 | + | 0.698620i | \(0.753798\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.00000 | −0.371792 | −0.185896 | − | 0.982569i | \(-0.559519\pi\) | ||||
−0.185896 | + | 0.982569i | \(0.559519\pi\) | |||||||
\(464\) | 16.9706 | − | 16.9706i | 0.787839 | − | 0.787839i | ||||
\(465\) | −4.24264 | − | 4.24264i | −0.196748 | − | 0.196748i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 42.0000i | − | 1.94353i | −0.235954 | − | 0.971764i | \(-0.575822\pi\) | ||
0.235954 | − | 0.971764i | \(-0.424178\pi\) | |||||||
\(468\) | − | 2.00000i | − | 0.0924500i | ||||||
\(469\) | 11.3137 | + | 11.3137i | 0.522419 | + | 0.522419i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.77817 | − | 7.77817i | 0.358399 | − | 0.358399i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −14.8492 | + | 14.8492i | −0.682769 | + | 0.682769i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.00000 | −0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.00000 | −0.274721 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.0919 | − | 19.0919i | 0.872330 | − | 0.872330i | −0.120396 | − | 0.992726i | \(-0.538416\pi\) |
0.992726 | + | 0.120396i | \(0.0384163\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.82843 | − | 2.82843i | 0.128965 | − | 0.128965i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −25.4558 | − | 25.4558i | −1.15828 | − | 1.15828i | ||||
\(484\) | − | 4.00000i | − | 0.181818i | ||||||
\(485\) | 48.0000i | 2.17957i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.5563 | + | 15.5563i | 0.704925 | + | 0.704925i | 0.965464 | − | 0.260538i | \(-0.0839000\pi\) |
−0.260538 | + | 0.965464i | \(0.583900\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.00000 | −0.0904431 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 6.00000i | − | 0.270776i | −0.990793 | − | 0.135388i | \(-0.956772\pi\) | ||
0.990793 | − | 0.135388i | \(-0.0432281\pi\) | |||||||
\(492\) | 6.00000 | 0.270501 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 9.00000i | − | 0.404520i | ||||||
\(496\) | −5.65685 | + | 5.65685i | −0.254000 | + | 0.254000i | ||||
\(497\) | 48.0000 | 2.15309 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.5563 | + | 15.5563i | 0.696398 | + | 0.696398i | 0.963632 | − | 0.267234i | \(-0.0861096\pi\) |
−0.267234 | + | 0.963632i | \(0.586110\pi\) | |||||||
\(500\) | 4.24264 | + | 4.24264i | 0.189737 | + | 0.189737i | ||||
\(501\) | − | 21.0000i | − | 0.938211i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.6066 | + | 10.6066i | 0.472925 | + | 0.472925i | 0.902860 | − | 0.429935i | \(-0.141463\pi\) |
−0.429935 | + | 0.902860i | \(0.641463\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.48528 | − | 8.48528i | 0.376845 | − | 0.376845i | ||||
\(508\) | 26.0000i | 1.15356i | ||||||||
\(509\) | 36.0000 | 1.59567 | 0.797836 | − | 0.602875i | \(-0.205978\pi\) | ||||
0.797836 | + | 0.602875i | \(0.205978\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.00000 | −0.353899 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.707107 | − | 0.707107i | 0.0312195 | − | 0.0312195i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.6066 | − | 10.6066i | 0.467383 | − | 0.467383i | ||||
\(516\) | −9.89949 | − | 9.89949i | −0.435801 | − | 0.435801i | ||||
\(517\) | 12.7279 | + | 12.7279i | 0.559773 | + | 0.559773i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 15.0000i | − | 0.658427i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.8492 | − | 14.8492i | −0.650557 | − | 0.650557i | 0.302570 | − | 0.953127i | \(-0.402155\pi\) |
−0.953127 | + | 0.302570i | \(0.902155\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.0000 | −0.874539 | −0.437269 | − | 0.899331i | \(-0.644054\pi\) | ||||
−0.437269 | + | 0.899331i | \(0.644054\pi\) | |||||||
\(524\) | 4.24264 | − | 4.24264i | 0.185341 | − | 0.185341i | ||||
\(525\) | − | 16.0000i | − | 0.698297i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −12.0000 | −0.522233 | ||||||||
\(529\) | 58.0000i | 2.52174i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.00000 | −0.260378 | ||||||||
\(532\) | −5.65685 | + | 5.65685i | −0.245256 | + | 0.245256i | ||||
\(533\) | −2.12132 | − | 2.12132i | −0.0918846 | − | 0.0918846i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 27.0000i | − | 1.16731i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.24264 | − | 4.24264i | −0.183083 | − | 0.183083i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −19.0919 | + | 19.0919i | −0.822346 | + | 0.822346i | ||||
\(540\) | 6.00000 | 0.258199 | ||||||||
\(541\) | 11.3137 | − | 11.3137i | 0.486414 | − | 0.486414i | −0.420758 | − | 0.907173i | \(-0.638236\pi\) |
0.907173 | + | 0.420758i | \(0.138236\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 14.0000 | 0.600798 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 60.0000 | 2.57012 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.65685 | + | 5.65685i | −0.241870 | + | 0.241870i | −0.817623 | − | 0.575754i | \(-0.804709\pi\) |
0.575754 | + | 0.817623i | \(0.304709\pi\) | |||||||
\(548\) | −12.0000 | −0.512615 | ||||||||
\(549\) | 5.65685 | − | 5.65685i | 0.241429 | − | 0.241429i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.24264 | − | 4.24264i | −0.180743 | − | 0.180743i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 40.0000i | − | 1.70097i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.48528 | + | 8.48528i | 0.360180 | + | 0.360180i | ||||
\(556\) | −2.82843 | + | 2.82843i | −0.119952 | + | 0.119952i | ||||
\(557\) | 30.0000 | 1.27114 | 0.635570 | − | 0.772043i | \(-0.280765\pi\) | ||||
0.635570 | + | 0.772043i | \(0.280765\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.00000i | 0.296068i | ||||||||
\(560\) | −48.0000 | −2.02837 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 30.0000i | − | 1.26435i | −0.774826 | − | 0.632175i | \(-0.782163\pi\) | ||
0.774826 | − | 0.632175i | \(-0.217837\pi\) | |||||||
\(564\) | −8.48528 | + | 8.48528i | −0.357295 | + | 0.357295i | ||||
\(565\) | 27.0000 | 1.13590 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.82843 | + | 2.82843i | 0.118783 | + | 0.118783i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.0000i | 1.00613i | 0.864248 | + | 0.503066i | \(0.167795\pi\) | ||||
−0.864248 | + | 0.503066i | \(0.832205\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.65685 | + | 5.65685i | 0.236732 | + | 0.236732i | 0.815495 | − | 0.578763i | \(-0.196465\pi\) |
−0.578763 | + | 0.815495i | \(0.696465\pi\) | |||||||
\(572\) | 4.24264 | + | 4.24264i | 0.177394 | + | 0.177394i | ||||
\(573\) | 12.7279 | − | 12.7279i | 0.531717 | − | 0.531717i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −25.4558 | + | 25.4558i | −1.06158 | + | 1.06158i | ||||
\(576\) | − | 8.00000i | − | 0.333333i | ||||||
\(577\) | −7.00000 | −0.291414 | −0.145707 | − | 0.989328i | \(-0.546546\pi\) | ||||
−0.145707 | + | 0.989328i | \(0.546546\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −22.0000 | −0.914289 | ||||||||
\(580\) | − | 36.0000i | − | 1.49482i | ||||||
\(581\) | −16.9706 | + | 16.9706i | −0.704058 | + | 0.704058i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.7279 | − | 12.7279i | 0.527137 | − | 0.527137i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.12132 | − | 2.12132i | −0.0877058 | − | 0.0877058i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 36.0000i | 1.48588i | 0.669359 | + | 0.742940i | \(0.266569\pi\) | ||||
−0.669359 | + | 0.742940i | \(0.733431\pi\) | |||||||
\(588\) | −12.7279 | − | 12.7279i | −0.524891 | − | 0.524891i | ||||
\(589\) | 1.41421 | + | 1.41421i | 0.0582717 | + | 0.0582717i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.00000 | −0.123404 | ||||||||
\(592\) | 11.3137 | − | 11.3137i | 0.464991 | − | 0.464991i | ||||
\(593\) | − | 18.0000i | − | 0.739171i | −0.929197 | − | 0.369586i | \(-0.879500\pi\) | ||
0.929197 | − | 0.369586i | \(-0.120500\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 36.0000 | 1.47462 | ||||||||
\(597\) | − | 16.0000i | − | 0.654836i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.00000 | 0.245153 | 0.122577 | − | 0.992459i | \(-0.460884\pi\) | ||||
0.122577 | + | 0.992459i | \(0.460884\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.8701 | − | 26.8701i | −1.09605 | − | 1.09605i | −0.994868 | − | 0.101185i | \(-0.967737\pi\) |
−0.101185 | − | 0.994868i | \(-0.532263\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.00000i | 0.162893i | ||||||||
\(604\) | 16.0000i | 0.651031i | ||||||||
\(605\) | −4.24264 | − | 4.24264i | −0.172488 | − | 0.172488i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.8701 | − | 26.8701i | 1.09062 | − | 1.09062i | 0.0951600 | − | 0.995462i | \(-0.469664\pi\) |
0.995462 | − | 0.0951600i | \(-0.0303363\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 16.9706 | − | 16.9706i | 0.687682 | − | 0.687682i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.00000 | 0.242734 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.0000 | 0.444286 | 0.222143 | − | 0.975014i | \(-0.428695\pi\) | ||||
0.222143 | + | 0.975014i | \(0.428695\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.36396 | − | 6.36396i | 0.256620 | − | 0.256620i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.24264 | + | 4.24264i | −0.170802 | + | 0.170802i | −0.787332 | − | 0.616530i | \(-0.788538\pi\) |
0.616530 | + | 0.787332i | \(0.288538\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.07107 | − | 7.07107i | −0.284210 | − | 0.284210i | 0.550575 | − | 0.834786i | \(-0.314408\pi\) |
−0.834786 | + | 0.550575i | \(0.814408\pi\) | |||||||
\(620\) | 12.0000i | 0.481932i | ||||||||
\(621\) | − | 9.00000i | − | 0.361158i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −2.82843 | + | 2.82843i | −0.113228 | + | 0.113228i | ||||
\(625\) | 29.0000 | 1.16000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.00000i | 0.119808i | ||||||||
\(628\) | −22.0000 | −0.877896 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 37.0000i | − | 1.47295i | −0.676467 | − | 0.736473i | \(-0.736490\pi\) | ||
0.676467 | − | 0.736473i | \(-0.263510\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.00000 | −0.0794929 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 27.5772 | + | 27.5772i | 1.09437 | + | 1.09437i | ||||
\(636\) | 8.48528 | + | 8.48528i | 0.336463 | + | 0.336463i | ||||
\(637\) | 9.00000i | 0.356593i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.48528 | + | 8.48528i | 0.335673 | + | 0.335673i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.3345 | + | 23.3345i | −0.921658 | + | 0.921658i | −0.997147 | − | 0.0754884i | \(-0.975948\pi\) |
0.0754884 | + | 0.997147i | \(0.475948\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.6274 | + | 22.6274i | −0.892338 | + | 0.892338i | −0.994743 | − | 0.102405i | \(-0.967346\pi\) |
0.102405 | + | 0.994743i | \(0.467346\pi\) | |||||||
\(644\) | 72.0000i | 2.83720i | ||||||||
\(645\) | −21.0000 | −0.826874 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.0000 | 0.707653 | 0.353827 | − | 0.935311i | \(-0.384880\pi\) | ||||
0.353827 | + | 0.935311i | \(0.384880\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.7279 | − | 12.7279i | 0.499615 | − | 0.499615i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.65685 | + | 5.65685i | −0.221710 | + | 0.221710i | ||||
\(652\) | 2.82843 | + | 2.82843i | 0.110770 | + | 0.110770i | ||||
\(653\) | 19.0919 | + | 19.0919i | 0.747123 | + | 0.747123i | 0.973938 | − | 0.226815i | \(-0.0728312\pi\) |
−0.226815 | + | 0.973938i | \(0.572831\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 9.00000i | − | 0.351659i | ||||||
\(656\) | −8.48528 | − | 8.48528i | −0.331295 | − | 0.331295i | ||||
\(657\) | −1.41421 | − | 1.41421i | −0.0551737 | − | 0.0551737i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.00000 | −0.233727 | −0.116863 | − | 0.993148i | \(-0.537284\pi\) | ||||
−0.116863 | + | 0.993148i | \(0.537284\pi\) | |||||||
\(660\) | −12.7279 | + | 12.7279i | −0.495434 | + | 0.495434i | ||||
\(661\) | − | 31.0000i | − | 1.20576i | −0.797832 | − | 0.602880i | \(-0.794020\pi\) | ||
0.797832 | − | 0.602880i | \(-0.205980\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.0000i | 0.465340i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −54.0000 | −2.09089 | ||||||||
\(668\) | −29.6985 | + | 29.6985i | −1.14907 | + | 1.14907i | ||||
\(669\) | 0.707107 | + | 0.707107i | 0.0273383 | + | 0.0273383i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.0000i | 0.926510i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.5563 | − | 15.5563i | −0.599653 | − | 0.599653i | 0.340567 | − | 0.940220i | \(-0.389381\pi\) |
−0.940220 | + | 0.340567i | \(0.889381\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.82843 | − | 2.82843i | 0.108866 | − | 0.108866i | ||||
\(676\) | −24.0000 | −0.923077 | ||||||||
\(677\) | 19.0919 | − | 19.0919i | 0.733761 | − | 0.733761i | −0.237602 | − | 0.971363i | \(-0.576361\pi\) |
0.971363 | + | 0.237602i | \(0.0763614\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 64.0000 | 2.45609 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.00000 | 0.114960 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.12132 | + | 2.12132i | −0.0811701 | + | 0.0811701i | −0.746526 | − | 0.665356i | \(-0.768280\pi\) |
0.665356 | + | 0.746526i | \(0.268280\pi\) | |||||||
\(684\) | −2.00000 | −0.0764719 | ||||||||
\(685\) | −12.7279 | + | 12.7279i | −0.486309 | + | 0.486309i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.89949 | + | 9.89949i | 0.377689 | + | 0.377689i | ||||
\(688\) | 28.0000i | 1.06749i | ||||||||
\(689\) | − | 6.00000i | − | 0.228582i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.1421 | − | 14.1421i | −0.537992 | − | 0.537992i | 0.384947 | − | 0.922939i | \(-0.374220\pi\) |
−0.922939 | + | 0.384947i | \(0.874220\pi\) | |||||||
\(692\) | −21.2132 | + | 21.2132i | −0.806405 | + | 0.806405i | ||||
\(693\) | −12.0000 | −0.455842 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.00000i | 0.227593i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 21.0000i | 0.794293i | ||||||||
\(700\) | −22.6274 | + | 22.6274i | −0.855236 | + | 0.855236i | ||||
\(701\) | −24.0000 | −0.906467 | −0.453234 | − | 0.891392i | \(-0.649730\pi\) | ||||
−0.453234 | + | 0.891392i | \(0.649730\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.82843 | − | 2.82843i | −0.106676 | − | 0.106676i | ||||
\(704\) | 16.9706 | + | 16.9706i | 0.639602 | + | 0.639602i | ||||
\(705\) | 18.0000i | 0.677919i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 8.48528 | + | 8.48528i | 0.318896 | + | 0.318896i | ||||
\(709\) | 9.89949 | − | 9.89949i | 0.371783 | − | 0.371783i | −0.496343 | − | 0.868126i | \(-0.665324\pi\) |
0.868126 | + | 0.496343i | \(0.165324\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.07107 | − | 7.07107i | 0.265186 | − | 0.265186i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18.0000 | 0.674105 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.00000 | 0.336581 | ||||||||
\(716\) | 12.0000i | 0.448461i | ||||||||
\(717\) | 8.48528 | − | 8.48528i | 0.316889 | − | 0.316889i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.12132 | − | 2.12132i | 0.0791119 | − | 0.0791119i | −0.666444 | − | 0.745555i | \(-0.732184\pi\) |
0.745555 | + | 0.666444i | \(0.232184\pi\) | |||||||
\(720\) | −8.48528 | − | 8.48528i | −0.316228 | − | 0.316228i | ||||
\(721\) | −14.1421 | − | 14.1421i | −0.526681 | − | 0.526681i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 8.00000i | − | 0.297523i | ||||||
\(724\) | −19.7990 | − | 19.7990i | −0.735824 | − | 0.735824i | ||||
\(725\) | −16.9706 | − | 16.9706i | −0.630271 | − | 0.630271i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.00000 | −0.296704 | −0.148352 | − | 0.988935i | \(-0.547397\pi\) | ||||
−0.148352 | + | 0.988935i | \(0.547397\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −16.0000 | −0.591377 | ||||||||
\(733\) | 2.00000i | 0.0738717i | 0.999318 | + | 0.0369358i | \(0.0117597\pi\) | ||||
−0.999318 | + | 0.0369358i | \(0.988240\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −27.0000 | −0.995910 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.48528 | − | 8.48528i | −0.312559 | − | 0.312559i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.00000i | 0.0367856i | 0.999831 | + | 0.0183928i | \(0.00585494\pi\) | ||||
−0.999831 | + | 0.0183928i | \(0.994145\pi\) | |||||||
\(740\) | − | 24.0000i | − | 0.882258i | ||||||
\(741\) | 0.707107 | + | 0.707107i | 0.0259762 | + | 0.0259762i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.9706 | − | 16.9706i | 0.622590 | − | 0.622590i | −0.323603 | − | 0.946193i | \(-0.604894\pi\) |
0.946193 | + | 0.323603i | \(0.104894\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 38.1838 | − | 38.1838i | 1.39894 | − | 1.39894i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.00000 | −0.219529 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −36.0000 | −1.31541 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32.5269 | − | 32.5269i | 1.18692 | − | 1.18692i | 0.209010 | − | 0.977913i | \(-0.432976\pi\) |
0.977913 | − | 0.209010i | \(-0.0670243\pi\) | |||||||
\(752\) | 24.0000 | 0.875190 | ||||||||
\(753\) | 16.9706 | − | 16.9706i | 0.618442 | − | 0.618442i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.9706 | + | 16.9706i | 0.617622 | + | 0.617622i | ||||
\(756\) | − | 8.00000i | − | 0.290957i | ||||||
\(757\) | 43.0000i | 1.56286i | 0.623992 | + | 0.781431i | \(0.285510\pi\) | ||||
−0.623992 | + | 0.781431i | \(0.714490\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 19.0919 | + | 19.0919i | 0.692991 | + | 0.692991i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.0000 | −1.08750 | −0.543750 | − | 0.839248i | \(-0.682996\pi\) | ||||
−0.543750 | + | 0.839248i | \(0.682996\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 80.0000i | − | 2.89619i | ||||||
\(764\) | −36.0000 | −1.30243 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 6.00000i | − | 0.216647i | ||||||
\(768\) | −11.3137 | + | 11.3137i | −0.408248 | + | 0.408248i | ||||
\(769\) | −41.0000 | −1.47850 | −0.739249 | − | 0.673432i | \(-0.764819\pi\) | ||||
−0.739249 | + | 0.673432i | \(0.764819\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.48528 | − | 8.48528i | −0.305590 | − | 0.305590i | ||||
\(772\) | 31.1127 | + | 31.1127i | 1.11977 | + | 1.11977i | ||||
\(773\) | − | 24.0000i | − | 0.863220i | −0.902060 | − | 0.431610i | \(-0.857946\pi\) | ||
0.902060 | − | 0.431610i | \(-0.142054\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.65685 | + | 5.65685i | 0.203200 | + | 0.203200i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11.3137 | − | 11.3137i | 0.405877 | − | 0.405877i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.12132 | + | 2.12132i | −0.0760042 | + | 0.0760042i | ||||
\(780\) | 6.00000i | 0.214834i | ||||||||
\(781\) | −36.0000 | −1.28818 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.00000 | 0.214423 | ||||||||
\(784\) | 36.0000i | 1.28571i | ||||||||
\(785\) | −23.3345 | + | 23.3345i | −0.832845 | + | 0.832845i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.2843 | + | 28.2843i | −1.00823 | + | 1.00823i | −0.00825949 | + | 0.999966i | \(0.502629\pi\) |
−0.999966 | + | 0.00825949i | \(0.997371\pi\) | |||||||
\(788\) | 4.24264 | + | 4.24264i | 0.151138 | + | 0.151138i | ||||
\(789\) | 8.48528 | + | 8.48528i | 0.302084 | + | 0.302084i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 36.0000i | − | 1.28001i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.65685 | + | 5.65685i | 0.200881 | + | 0.200881i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 18.0000 | 0.638394 | ||||||||
\(796\) | −22.6274 | + | 22.6274i | −0.802008 | + | 0.802008i | ||||
\(797\) | − | 48.0000i | − | 1.70025i | −0.526583 | − | 0.850124i | \(-0.676527\pi\) | ||
0.526583 | − | 0.850124i | \(-0.323473\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.00000 | 0.211735 | ||||||||
\(804\) | 5.65685 | − | 5.65685i | 0.199502 | − | 0.199502i | ||||
\(805\) | 76.3675 | + | 76.3675i | 2.69160 | + | 2.69160i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.0000i | 0.528025i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −36.0624 | − | 36.0624i | −1.26789 | − | 1.26789i | −0.947177 | − | 0.320711i | \(-0.896078\pi\) |
−0.320711 | − | 0.947177i | \(-0.603922\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.07107 | + | 7.07107i | −0.248299 | + | 0.248299i | −0.820272 | − | 0.571973i | \(-0.806178\pi\) |
0.571973 | + | 0.820272i | \(0.306178\pi\) | |||||||
\(812\) | −48.0000 | −1.68447 | ||||||||
\(813\) | −7.77817 | + | 7.77817i | −0.272792 | + | 0.272792i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.00000 | 0.210171 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.00000 | 0.244899 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.82843 | + | 2.82843i | −0.0988332 | + | 0.0988332i | ||||
\(820\) | −18.0000 | −0.628587 | ||||||||
\(821\) | −14.8492 | + | 14.8492i | −0.518242 | + | 0.518242i | −0.917039 | − | 0.398797i | \(-0.869428\pi\) |
0.398797 | + | 0.917039i | \(0.369428\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.7990 | − | 19.7990i | −0.690149 | − | 0.690149i | 0.272115 | − | 0.962265i | \(-0.412277\pi\) |
−0.962265 | + | 0.272115i | \(0.912277\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12.0000i | 0.417786i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.8492 | + | 14.8492i | 0.516359 | + | 0.516359i | 0.916468 | − | 0.400109i | \(-0.131028\pi\) |
−0.400109 | + | 0.916468i | \(0.631028\pi\) | |||||||
\(828\) | −12.7279 | + | 12.7279i | −0.442326 | + | 0.442326i | ||||
\(829\) | −14.0000 | −0.486240 | −0.243120 | − | 0.969996i | \(-0.578171\pi\) | ||||
−0.243120 | + | 0.969996i | \(0.578171\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.00000i | 0.0693792i | ||||||||
\(832\) | 8.00000 | 0.277350 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 63.0000i | 2.18020i | ||||||||
\(836\) | 4.24264 | − | 4.24264i | 0.146735 | − | 0.146735i | ||||
\(837\) | −2.00000 | −0.0691301 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40.3051 | + | 40.3051i | 1.39149 | + | 1.39149i | 0.822003 | + | 0.569483i | \(0.192857\pi\) |
0.569483 | + | 0.822003i | \(0.307143\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 7.00000i | − | 0.241379i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.48528 | + | 8.48528i | 0.292249 | + | 0.292249i | ||||
\(844\) | 2.82843 | + | 2.82843i | 0.0973585 | + | 0.0973585i | ||||
\(845\) | −25.4558 | + | 25.4558i | −0.875708 | + | 0.875708i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.65685 | + | 5.65685i | −0.194372 | + | 0.194372i | ||||
\(848\) | − | 24.0000i | − | 0.824163i | ||||||
\(849\) | −10.0000 | −0.343199 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −36.0000 | −1.23406 | ||||||||
\(852\) | − | 24.0000i | − | 0.822226i | ||||||
\(853\) | −18.3848 | + | 18.3848i | −0.629483 | + | 0.629483i | −0.947938 | − | 0.318455i | \(-0.896836\pi\) |
0.318455 | + | 0.947938i | \(0.396836\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.12132 | + | 2.12132i | −0.0725476 | + | 0.0725476i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.7279 | − | 12.7279i | −0.434778 | − | 0.434778i | 0.455472 | − | 0.890250i | \(-0.349470\pi\) |
−0.890250 | + | 0.455472i | \(0.849470\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 20.0000i | − | 0.682391i | −0.939992 | − | 0.341196i | \(-0.889168\pi\) | ||
0.939992 | − | 0.341196i | \(-0.110832\pi\) | |||||||
\(860\) | 29.6985 | + | 29.6985i | 1.01271 | + | 1.01271i | ||||
\(861\) | −8.48528 | − | 8.48528i | −0.289178 | − | 0.289178i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24.0000 | −0.816970 | −0.408485 | − | 0.912765i | \(-0.633943\pi\) | ||||
−0.408485 | + | 0.912765i | \(0.633943\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 45.0000i | 1.53005i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 16.0000 | 0.543075 | ||||||||
\(869\) | 30.0000i | 1.01768i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.00000 | −0.135535 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.3137 | + | 11.3137i | 0.382911 | + | 0.382911i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 12.0000i | − | 0.405674i | ||||||
\(876\) | 4.00000i | 0.135147i | ||||||||
\(877\) | 9.89949 | + | 9.89949i | 0.334282 | + | 0.334282i | 0.854210 | − | 0.519928i | \(-0.174041\pi\) |
−0.519928 | + | 0.854210i | \(0.674041\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16.9706 | + | 16.9706i | −0.572403 | + | 0.572403i | ||||
\(880\) | 36.0000 | 1.21356 | ||||||||
\(881\) | −12.7279 | + | 12.7279i | −0.428815 | + | 0.428815i | −0.888224 | − | 0.459410i | \(-0.848061\pi\) |
0.459410 | + | 0.888224i | \(0.348061\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.0000 | 0.370179 | 0.185090 | − | 0.982722i | \(-0.440742\pi\) | ||||
0.185090 | + | 0.982722i | \(0.440742\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 18.0000 | 0.605063 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.5772 | + | 27.5772i | −0.925951 | + | 0.925951i | −0.997441 | − | 0.0714907i | \(-0.977224\pi\) |
0.0714907 | + | 0.997441i | \(0.477224\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 36.7696 | − | 36.7696i | 1.23321 | − | 1.23321i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.12132 | − | 2.12132i | −0.0710669 | − | 0.0710669i | ||||
\(892\) | − | 2.00000i | − | 0.0669650i | ||||||
\(893\) | − | 6.00000i | − | 0.200782i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.7279 | + | 12.7279i | 0.425448 | + | 0.425448i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.00000 | 0.300501 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.0000i | 0.400222i | ||||||||
\(900\) | −8.00000 | −0.266667 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 28.0000i | 0.931782i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −42.0000 | −1.39613 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.41421 | − | 1.41421i | −0.0469582 | − | 0.0469582i | 0.683238 | − | 0.730196i | \(-0.260571\pi\) |
−0.730196 | + | 0.683238i | \(0.760571\pi\) | |||||||
\(908\) | −4.24264 | − | 4.24264i | −0.140797 | − | 0.140797i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.0919 | − | 19.0919i | −0.632542 | − | 0.632542i | 0.316163 | − | 0.948705i | \(-0.397605\pi\) |
−0.948705 | + | 0.316163i | \(0.897605\pi\) | |||||||
\(912\) | 2.82843 | + | 2.82843i | 0.0936586 | + | 0.0936586i | ||||
\(913\) | 12.7279 | − | 12.7279i | 0.421233 | − | 0.421233i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −16.9706 | + | 16.9706i | −0.561029 | + | 0.561029i | ||||
\(916\) | − | 28.0000i | − | 0.925146i | ||||||
\(917\) | −12.0000 | −0.396275 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.0000 | 0.362857 | 0.181428 | − | 0.983404i | \(-0.441928\pi\) | ||||
0.181428 | + | 0.983404i | \(0.441928\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14.1421 | + | 14.1421i | −0.465999 | + | 0.465999i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.48528 | + | 8.48528i | −0.279296 | + | 0.279296i | ||||
\(924\) | 16.9706 | + | 16.9706i | 0.558291 | + | 0.558291i | ||||
\(925\) | −11.3137 | − | 11.3137i | −0.371992 | − | 0.371992i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 5.00000i | − | 0.164222i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.6066 | − | 10.6066i | −0.347991 | − | 0.347991i | 0.511370 | − | 0.859361i | \(-0.329138\pi\) |
−0.859361 | + | 0.511370i | \(0.829138\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.00000 | 0.294963 | ||||||||
\(932\) | 29.6985 | − | 29.6985i | 0.972806 | − | 0.972806i | ||||
\(933\) | − | 24.0000i | − | 0.785725i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 22.0000i | − | 0.718709i | −0.933201 | − | 0.359354i | \(-0.882997\pi\) | ||
0.933201 | − | 0.359354i | \(-0.117003\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.0000 | 0.522140 | ||||||||
\(940\) | 25.4558 | − | 25.4558i | 0.830278 | − | 0.830278i | ||||
\(941\) | −12.7279 | − | 12.7279i | −0.414918 | − | 0.414918i | 0.468529 | − | 0.883448i | \(-0.344784\pi\) |
−0.883448 | + | 0.468529i | \(0.844784\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27.0000i | 0.879241i | ||||||||
\(944\) | − | 24.0000i | − | 0.781133i | ||||||
\(945\) | −8.48528 | − | 8.48528i | −0.276026 | − | 0.276026i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.4558 | − | 25.4558i | 0.827204 | − | 0.827204i | −0.159925 | − | 0.987129i | \(-0.551125\pi\) |
0.987129 | + | 0.159925i | \(0.0511253\pi\) | |||||||
\(948\) | −20.0000 | −0.649570 | ||||||||
\(949\) | 1.41421 | − | 1.41421i | 0.0459073 | − | 0.0459073i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.00000 | −0.194563 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.0000 | 1.16615 | 0.583077 | − | 0.812417i | \(-0.301849\pi\) | ||||
0.583077 | + | 0.812417i | \(0.301849\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −38.1838 | + | 38.1838i | −1.23560 | + | 1.23560i | ||||
\(956\) | −24.0000 | −0.776215 | ||||||||
\(957\) | −12.7279 | + | 12.7279i | −0.411435 | + | 0.411435i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.9706 | + | 16.9706i | 0.548008 | + | 0.548008i | ||||
\(960\) | 24.0000i | 0.774597i | ||||||||
\(961\) | 27.0000i | 0.870968i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.36396 | − | 6.36396i | −0.205076 | − | 0.205076i | ||||
\(964\) | −11.3137 | + | 11.3137i | −0.364390 | + | 0.364390i | ||||
\(965\) | 66.0000 | 2.12462 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.0000i | 1.31847i | 0.751936 | + | 0.659236i | \(0.229120\pi\) | ||||
−0.751936 | + | 0.659236i | \(0.770880\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.00000i | 0.192549i | 0.995355 | + | 0.0962746i | \(0.0306927\pi\) | ||||
−0.995355 | + | 0.0962746i | \(0.969307\pi\) | |||||||
\(972\) | 1.41421 | − | 1.41421i | 0.0453609 | − | 0.0453609i | ||||
\(973\) | 8.00000 | 0.256468 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.82843 | + | 2.82843i | 0.0905822 | + | 0.0905822i | ||||
\(976\) | 22.6274 | + | 22.6274i | 0.724286 | + | 0.724286i | ||||
\(977\) | 30.0000i | 0.959785i | 0.877327 | + | 0.479893i | \(0.159324\pi\) | ||||
−0.877327 | + | 0.479893i | \(0.840676\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 38.1838 | + | 38.1838i | 1.21974 | + | 1.21974i | ||||
\(981\) | 14.1421 | − | 14.1421i | 0.451524 | − | 0.451524i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.36396 | − | 6.36396i | 0.202979 | − | 0.202979i | −0.598296 | − | 0.801275i | \(-0.704155\pi\) |
0.801275 | + | 0.598296i | \(0.204155\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.00000 | 0.286764 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 24.0000 | 0.763928 | ||||||||
\(988\) | − | 2.00000i | − | 0.0636285i | ||||||
\(989\) | 44.5477 | − | 44.5477i | 1.41654 | − | 1.41654i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36.7696 | + | 36.7696i | −1.16802 | + | 1.16802i | −0.185351 | + | 0.982672i | \(0.559342\pi\) |
−0.982672 | + | 0.185351i | \(0.940658\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.19239 | − | 9.19239i | −0.291712 | − | 0.291712i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 48.0000i | 1.52170i | ||||||||
\(996\) | 8.48528 | + | 8.48528i | 0.268866 | + | 0.268866i | ||||
\(997\) | −43.8406 | − | 43.8406i | −1.38845 | − | 1.38845i | −0.828589 | − | 0.559857i | \(-0.810856\pi\) |
−0.559857 | − | 0.828589i | \(-0.689144\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.00000 | 0.126554 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))