Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(149,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.149");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.u (of order \(6\), 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: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.303595776.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 149.4 | ||
Root | \(0.396143 + 1.68614i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.149 |
Dual form | 900.3.u.a.749.4 |
$q$-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 \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(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 | ||||||||
\(3\) | 2.92048 | + | 0.686141i | 0.973494 | + | 0.228714i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.89542 | − | 4.55842i | 1.12792 | − | 0.651203i | 0.184507 | − | 0.982831i | \(-0.440931\pi\) |
0.943410 | + | 0.331628i | \(0.107598\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.05842 | + | 4.00772i | 0.895380 | + | 0.445302i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.383156 | + | 0.221215i | −0.0348324 | + | 0.0201105i | −0.517315 | − | 0.855795i | \(-0.673068\pi\) |
0.482483 | + | 0.875906i | \(0.339735\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −9.62747 | − | 5.55842i | −0.740575 | − | 0.427571i | 0.0817036 | − | 0.996657i | \(-0.473964\pi\) |
−0.822278 | + | 0.569086i | \(0.807297\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 8.01544 | 0.471497 | 0.235748 | − | 0.971814i | \(-0.424246\pi\) | ||||
0.235748 | + | 0.971814i | \(0.424246\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.11684 | 0.427202 | 0.213601 | − | 0.976921i | \(-0.431481\pi\) | ||||
0.213601 | + | 0.976921i | \(0.431481\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 26.1861 | − | 7.89542i | 1.24696 | − | 0.375972i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 11.8020 | − | 20.4416i | 0.513128 | − | 0.888764i | −0.486756 | − | 0.873538i | \(-0.661820\pi\) |
0.999884 | − | 0.0152262i | \(-0.00484683\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 20.7846 | + | 17.2337i | 0.769800 | + | 0.638285i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 45.9090 | − | 26.5055i | 1.58307 | − | 0.913984i | 0.588659 | − | 0.808381i | \(-0.299656\pi\) |
0.994408 | − | 0.105603i | \(-0.0336772\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −14.6753 | + | 25.4183i | −0.473396 | + | 0.819945i | −0.999536 | − | 0.0304523i | \(-0.990305\pi\) |
0.526141 | + | 0.850398i | \(0.323639\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.27078 | + | 0.383156i | −0.0385086 | + | 0.0116108i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 18.4674i | 0.499118i | 0.968360 | + | 0.249559i | \(0.0802857\pi\) | ||||
−0.968360 | + | 0.249559i | \(0.919714\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −24.3030 | − | 22.8391i | −0.623153 | − | 0.585617i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −38.9674 | − | 22.4978i | −0.950424 | − | 0.548727i | −0.0572112 | − | 0.998362i | \(-0.518221\pi\) |
−0.893213 | + | 0.449635i | \(0.851554\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −19.9186 | + | 11.5000i | −0.463223 | + | 0.267442i | −0.713398 | − | 0.700759i | \(-0.752845\pi\) |
0.250176 | + | 0.968200i | \(0.419512\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.22894 | − | 7.32473i | −0.0899774 | − | 0.155845i | 0.817524 | − | 0.575895i | \(-0.195346\pi\) |
−0.907501 | + | 0.420049i | \(0.862013\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 17.0584 | − | 29.5461i | 0.348131 | − | 0.602981i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 23.4090 | + | 5.49972i | 0.458999 | + | 0.107838i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 60.5841 | 1.14310 | 0.571548 | − | 0.820569i | \(-0.306343\pi\) | ||||
0.571548 | + | 0.820569i | \(0.306343\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 23.7051 | + | 5.56930i | 0.415879 | + | 0.0977070i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −65.9674 | − | 38.0863i | −1.11809 | − | 0.645530i | −0.177178 | − | 0.984179i | \(-0.556697\pi\) |
−0.940913 | + | 0.338649i | \(0.890030\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.67527 | − | 4.63370i | −0.0438568 | − | 0.0759622i | 0.843264 | − | 0.537500i | \(-0.180631\pi\) |
−0.887121 | + | 0.461538i | \(0.847298\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 81.8935 | − | 5.09105i | 1.29990 | − | 0.0808103i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 95.0039 | + | 54.8505i | 1.41797 | + | 0.818665i | 0.996120 | − | 0.0880017i | \(-0.0280481\pi\) |
0.421848 | + | 0.906666i | \(0.361381\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 48.4932 | − | 51.6014i | 0.702800 | − | 0.747847i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.0309i | 0.225787i | 0.993607 | + | 0.112894i | \(0.0360119\pi\) | ||||
−0.993607 | + | 0.112894i | \(0.963988\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.35053i | 0.0595963i | 0.999556 | + | 0.0297982i | \(0.00948645\pi\) | ||||
−0.999556 | + | 0.0297982i | \(0.990514\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.01678 | + | 3.49317i | −0.0261920 | + | 0.0453659i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.792110 | + | 1.37197i | 0.0100267 | + | 0.0173668i | 0.870995 | − | 0.491291i | \(-0.163475\pi\) |
−0.860969 | + | 0.508658i | \(0.830142\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 48.8763 | + | 64.5918i | 0.603411 | + | 0.797430i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.22894 | + | 7.32473i | 0.0509511 | + | 0.0882498i | 0.890376 | − | 0.455226i | \(-0.150441\pi\) |
−0.839425 | + | 0.543475i | \(0.817108\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 152.263 | − | 45.9090i | 1.75015 | − | 0.527689i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 64.1236i | − | 0.720489i | −0.932858 | − | 0.360245i | \(-0.882693\pi\) | ||
0.932858 | − | 0.360245i | \(-0.117307\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −101.351 | −1.11374 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −60.2994 | + | 64.1644i | −0.648380 | + | 0.689940i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 99.7953 | − | 57.6168i | 1.02882 | − | 0.593988i | 0.112172 | − | 0.993689i | \(-0.464219\pi\) |
0.916646 | + | 0.399701i | \(0.130886\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.97420 | + | 0.247063i | −0.0401435 | + | 0.00249558i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 114.558 | − | 66.1403i | 1.13424 | − | 0.654855i | 0.189244 | − | 0.981930i | \(-0.439396\pi\) |
0.944998 | + | 0.327075i | \(0.106063\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 108.557 | + | 62.6753i | 1.05395 | + | 0.608498i | 0.923752 | − | 0.382990i | \(-0.125106\pi\) |
0.130197 | + | 0.991488i | \(0.458439\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −36.5378 | −0.341475 | −0.170737 | − | 0.985317i | \(-0.554615\pi\) | ||||
−0.170737 | + | 0.985317i | \(0.554615\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −134.701 | −1.23579 | −0.617895 | − | 0.786261i | \(-0.712014\pi\) | ||||
−0.617895 | + | 0.786261i | \(0.712014\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.6712 | + | 53.9336i | −0.114155 | + | 0.485889i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −95.1051 | + | 164.727i | −0.841638 | + | 1.45776i | 0.0468711 | + | 0.998901i | \(0.485075\pi\) |
−0.888509 | + | 0.458859i | \(0.848258\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −55.3056 | − | 83.3763i | −0.472697 | − | 0.712618i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 63.2853 | − | 36.5378i | 0.531809 | − | 0.307040i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −60.4021 | + | 104.620i | −0.499191 | + | 0.864624i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −98.3668 | − | 92.4416i | −0.799730 | − | 0.751558i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 184.103i | 1.44963i | 0.688943 | + | 0.724816i | \(0.258075\pi\) | ||||
−0.688943 | + | 0.724816i | \(0.741925\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −66.0625 | + | 19.9186i | −0.512112 | + | 0.154408i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −109.194 | − | 63.0433i | −0.833544 | − | 0.481247i | 0.0215207 | − | 0.999768i | \(-0.493149\pi\) |
−0.855064 | + | 0.518522i | \(0.826483\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 64.0859 | − | 37.0000i | 0.481849 | − | 0.278195i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 62.1326 | + | 107.617i | 0.453523 | + | 0.785524i | 0.998602 | − | 0.0528602i | \(-0.0168338\pi\) |
−0.545079 | + | 0.838385i | \(0.683500\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.3832 | − | 23.1803i | 0.0962817 | − | 0.166765i | −0.813861 | − | 0.581059i | \(-0.802638\pi\) |
0.910143 | + | 0.414295i | \(0.135972\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.32473 | − | 24.2934i | −0.0519485 | − | 0.172294i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.91843 | 0.0343946 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 70.0916 | − | 74.5842i | 0.476813 | − | 0.507376i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −69.8437 | − | 40.3243i | −0.468750 | − | 0.270633i | 0.246966 | − | 0.969024i | \(-0.420566\pi\) |
−0.715716 | + | 0.698391i | \(0.753900\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −49.9742 | − | 86.5579i | −0.330955 | − | 0.573231i | 0.651744 | − | 0.758439i | \(-0.274037\pi\) |
−0.982699 | + | 0.185208i | \(0.940704\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 64.5918 | + | 32.1237i | 0.422169 | + | 0.209959i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 60.1487 | + | 34.7269i | 0.383113 | + | 0.221190i | 0.679172 | − | 0.733979i | \(-0.262339\pi\) |
−0.296059 | + | 0.955170i | \(0.595673\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 176.935 | + | 41.5692i | 1.11280 | + | 0.261442i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 215.193i | − | 1.33660i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 162.467i | − | 0.996732i | −0.866967 | − | 0.498366i | \(-0.833934\pi\) | ||
0.866967 | − | 0.498366i | \(-0.166066\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −48.3397 | + | 83.7269i | −0.289459 | + | 0.501358i | −0.973681 | − | 0.227916i | \(-0.926809\pi\) |
0.684221 | + | 0.729274i | \(0.260142\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −22.7079 | − | 39.3312i | −0.134366 | − | 0.232729i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 65.4090 | + | 32.5301i | 0.382509 | + | 0.190234i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.0141 | + | 24.2731i | 0.0810064 | + | 0.140307i | 0.903682 | − | 0.428203i | \(-0.140853\pi\) |
−0.822676 | + | 0.568510i | \(0.807520\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −166.524 | − | 156.493i | −0.940813 | − | 0.884142i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 35.6012i | 0.198889i | 0.995043 | + | 0.0994447i | \(0.0317067\pi\) | ||||
−0.995043 | + | 0.0994447i | \(0.968293\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.6358 | −0.108485 | −0.0542426 | − | 0.998528i | \(-0.517274\pi\) | ||||
−0.0542426 | + | 0.998528i | \(0.517274\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.63370 | − | 15.3682i | −0.0253207 | − | 0.0839794i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.07117 | + | 1.77314i | −0.0164233 | + | 0.00948202i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 242.662 | + | 41.3222i | 1.28392 | + | 0.218636i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 188.662 | − | 108.924i | 0.987757 | − | 0.570282i | 0.0831540 | − | 0.996537i | \(-0.473501\pi\) |
0.904603 | + | 0.426255i | \(0.140167\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −42.4352 | − | 24.5000i | −0.219872 | − | 0.126943i | 0.386019 | − | 0.922491i | \(-0.373850\pi\) |
−0.605891 | + | 0.795548i | \(0.707183\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −359.965 | −1.82723 | −0.913617 | − | 0.406575i | \(-0.866723\pi\) | ||||
−0.913617 | + | 0.406575i | \(0.866723\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 61.0652 | 0.306861 | 0.153430 | − | 0.988159i | \(-0.450968\pi\) | ||||
0.153430 | + | 0.988159i | \(0.450968\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 239.822 | + | 225.376i | 1.19314 | + | 1.12127i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 241.647 | − | 418.545i | 1.19038 | − | 2.06180i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 177.029 | − | 117.428i | 0.855214 | − | 0.567285i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.11002 | + | 1.79557i | −0.0148805 | + | 0.00859124i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −193.493 | + | 335.140i | −0.917029 | + | 1.58834i | −0.113126 | + | 0.993581i | \(0.536087\pi\) |
−0.803903 | + | 0.594761i | \(0.797247\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.9994 | + | 46.8179i | −0.0516406 | + | 0.219802i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 267.584i | 1.23311i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.98508 | + | 12.7056i | −0.0136305 | + | 0.0580167i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −77.1684 | − | 44.5532i | −0.349178 | − | 0.201598i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −88.9864 | + | 51.3763i | −0.399042 | + | 0.230387i | −0.686071 | − | 0.727535i | \(-0.740666\pi\) |
0.287028 | + | 0.957922i | \(0.407333\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −169.482 | − | 293.552i | −0.746617 | − | 1.29318i | −0.949435 | − | 0.313962i | \(-0.898343\pi\) |
0.202818 | − | 0.979216i | \(-0.434990\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −148.376 | + | 256.995i | −0.647932 | + | 1.12225i | 0.335685 | + | 0.941974i | \(0.391032\pi\) |
−0.983616 | + | 0.180276i | \(0.942301\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.28679 | + | 8.81795i | −0.0358736 | + | 0.0381729i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −346.537 | −1.48728 | −0.743642 | − | 0.668578i | \(-0.766903\pi\) | ||||
−0.743642 | + | 0.668578i | \(0.766903\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.37197 | + | 4.55033i | 0.00578892 | + | 0.0191997i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 140.026 | + | 80.8439i | 0.585882 | + | 0.338259i | 0.763468 | − | 0.645846i | \(-0.223495\pi\) |
−0.177586 | + | 0.984105i | \(0.556829\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 162.370 | + | 281.232i | 0.673732 | + | 1.16694i | 0.976838 | + | 0.213982i | \(0.0686433\pi\) |
−0.303105 | + | 0.952957i | \(0.598023\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 98.4233 | + | 222.175i | 0.405034 | + | 0.914302i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −78.1447 | − | 45.1168i | −0.316375 | − | 0.182659i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.32473 | + | 24.2934i | 0.0294166 | + | 0.0975638i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 384.012i | − | 1.52993i | −0.644074 | − | 0.764963i | \(-0.722757\pi\) | ||
0.644074 | − | 0.764963i | \(-0.277243\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.4431i | 0.0412770i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.46694 | − | 11.2011i | 0.0251632 | − | 0.0435839i | −0.853170 | − | 0.521634i | \(-0.825323\pi\) |
0.878333 | + | 0.478050i | \(0.158656\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 84.1821 | + | 145.808i | 0.325027 | + | 0.562964i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 476.181 | − | 29.6026i | 1.82445 | − | 0.113420i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.7358 | + | 42.8437i | 0.0940526 | + | 0.162904i | 0.909213 | − | 0.416332i | \(-0.136684\pi\) |
−0.815160 | + | 0.579236i | \(0.803351\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 43.9978 | − | 187.272i | 0.164786 | − | 0.701392i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 21.4434i | − | 0.0797154i | −0.999205 | − | 0.0398577i | \(-0.987310\pi\) | ||
0.999205 | − | 0.0398577i | \(-0.0126905\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −326.907 | −1.20630 | −0.603150 | − | 0.797628i | \(-0.706088\pi\) | ||||
−0.603150 | + | 0.797628i | \(0.706088\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −295.992 | − | 69.5407i | −1.08422 | − | 0.254728i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −413.487 | + | 238.727i | −1.49273 | + | 0.861830i | −0.999965 | − | 0.00833105i | \(-0.997348\pi\) |
−0.492768 | + | 0.870161i | \(0.664015\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −220.129 | + | 146.017i | −0.788993 | + | 0.523359i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −103.064 | + | 59.5039i | −0.366775 | + | 0.211758i | −0.672049 | − | 0.740507i | \(-0.734585\pi\) |
0.305274 | + | 0.952265i | \(0.401252\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −338.920 | − | 195.675i | −1.19760 | − | 0.691432i | −0.237577 | − | 0.971369i | \(-0.576353\pi\) |
−0.960018 | + | 0.279937i | \(0.909687\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −410.218 | −1.42933 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −224.753 | −0.777691 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 330.984 | − | 99.7953i | 1.13740 | − | 0.342939i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 35.8483 | − | 62.0910i | 0.122349 | − | 0.211915i | −0.798345 | − | 0.602201i | \(-0.794291\pi\) |
0.920694 | + | 0.390286i | \(0.127624\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −11.7761 | − | 2.00532i | −0.0396502 | − | 0.00675192i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −227.246 | + | 131.200i | −0.760020 | + | 0.438797i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −104.844 | + | 181.595i | −0.348318 | + | 0.603304i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 379.947 | − | 114.558i | 1.25395 | − | 0.378081i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 172.351i | − | 0.561402i | −0.959795 | − | 0.280701i | \(-0.909433\pi\) | ||
0.959795 | − | 0.280701i | \(-0.0905670\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 274.034 | + | 257.527i | 0.886841 | + | 0.833421i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −524.246 | − | 302.673i | −1.68568 | − | 0.973227i | −0.957763 | − | 0.287559i | \(-0.907156\pi\) |
−0.727915 | − | 0.685667i | \(-0.759511\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −283.595 | + | 163.734i | −0.906055 | + | 0.523111i | −0.879160 | − | 0.476527i | \(-0.841895\pi\) |
−0.0268949 | + | 0.999638i | \(0.508562\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −34.5210 | − | 59.7921i | −0.108899 | − | 0.188619i | 0.806425 | − | 0.591336i | \(-0.201399\pi\) |
−0.915325 | + | 0.402717i | \(0.868066\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.7269 | + | 20.3115i | −0.0367613 | + | 0.0636725i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −106.708 | − | 25.0701i | −0.332423 | − | 0.0780999i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 65.0601 | 0.201424 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −393.392 | − | 92.4239i | −1.20303 | − | 0.282642i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −66.7785 | − | 38.5546i | −0.202974 | − | 0.117187i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −254.895 | − | 441.492i | −0.770076 | − | 1.33381i | −0.937521 | − | 0.347930i | \(-0.886885\pi\) |
0.167444 | − | 0.985882i | \(-0.446449\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −74.0121 | + | 148.818i | −0.222259 | + | 0.446901i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 292.232 | + | 168.720i | 0.867156 | + | 0.500653i | 0.866402 | − | 0.499347i | \(-0.166427\pi\) |
0.000754096 | 1.00000i | \(0.499760\pi\) | ||||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −390.778 | + | 415.826i | −1.15274 | + | 1.22663i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 12.9856i | − | 0.0380808i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 135.687i | 0.395590i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −107.622 | + | 186.407i | −0.310151 | + | 0.537197i | −0.978395 | − | 0.206745i | \(-0.933713\pi\) |
0.668244 | + | 0.743942i | \(0.267046\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 181.012 | + | 313.522i | 0.518659 | + | 0.898345i | 0.999765 | + | 0.0216818i | \(0.00690207\pi\) |
−0.481105 | + | 0.876663i | \(0.659765\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −104.311 | − | 281.446i | −0.297183 | − | 0.801842i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 292.420 | + | 506.486i | 0.828385 | + | 1.43481i | 0.899304 | + | 0.437323i | \(0.144074\pi\) |
−0.0709189 | + | 0.997482i | \(0.522593\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 209.894 | − | 63.2853i | 0.587937 | − | 0.177270i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 393.693i | − | 1.09664i | −0.836269 | − | 0.548319i | \(-0.815268\pi\) | ||
0.836269 | − | 0.548319i | \(-0.184732\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −295.117 | −0.817498 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −248.187 | + | 264.095i | −0.683711 | + | 0.727535i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 329.831 | − | 190.428i | 0.898722 | − | 0.518877i | 0.0219364 | − | 0.999759i | \(-0.493017\pi\) |
0.876785 | + | 0.480882i | \(0.159684\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −223.851 | − | 337.467i | −0.606641 | − | 0.914546i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 478.337 | − | 276.168i | 1.28932 | − | 0.744388i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 115.080 | + | 66.4416i | 0.308526 | + | 0.178128i | 0.646267 | − | 0.763112i | \(-0.276329\pi\) |
−0.337741 | + | 0.941239i | \(0.609663\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −589.316 | −1.56317 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −507.622 | −1.33937 | −0.669686 | − | 0.742644i | \(-0.733571\pi\) | ||||
−0.669686 | + | 0.742644i | \(0.733571\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −126.321 | + | 537.670i | −0.331550 | + | 1.41121i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 165.968 | − | 287.466i | 0.433338 | − | 0.750564i | −0.563820 | − | 0.825898i | \(-0.690669\pi\) |
0.997158 | + | 0.0753339i | \(0.0240023\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −206.601 | + | 12.8437i | −0.533853 | + | 0.0331879i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −296.662 | + | 171.278i | −0.762626 | + | 0.440302i | −0.830238 | − | 0.557409i | \(-0.811795\pi\) |
0.0676116 | + | 0.997712i | \(0.478462\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 94.5979 | − | 163.848i | 0.241938 | − | 0.419049i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −275.643 | − | 259.039i | −0.701382 | − | 0.659133i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 24.8043i | − | 0.0624792i | −0.999512 | − | 0.0312396i | \(-0.990055\pi\) | ||
0.999512 | − | 0.0312396i | \(-0.00994550\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 212.549 | − | 64.0859i | 0.532704 | − | 0.160616i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 52.0842 | + | 30.0708i | 0.129886 | + | 0.0749896i | 0.563535 | − | 0.826092i | \(-0.309441\pi\) |
−0.433649 | + | 0.901082i | \(0.642774\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 282.571 | − | 163.143i | 0.701170 | − | 0.404820i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.08526 | − | 7.07589i | −0.0100375 | − | 0.0173855i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −240.720 | + | 416.939i | −0.588558 | + | 1.01941i | 0.405864 | + | 0.913933i | \(0.366971\pi\) |
−0.994422 | + | 0.105478i | \(0.966363\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 107.617 | + | 356.925i | 0.261841 | + | 0.868430i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −694.453 | −1.68149 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 54.9902 | − | 58.5149i | 0.131871 | − | 0.140324i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 479.531 | + | 276.857i | 1.14447 | + | 0.660758i | 0.947533 | − | 0.319659i | \(-0.103568\pi\) |
0.196933 | + | 0.980417i | \(0.436902\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 190.947 | + | 330.730i | 0.453556 | + | 0.785581i | 0.998604 | − | 0.0528233i | \(-0.0168220\pi\) |
−0.545048 | + | 0.838405i | \(0.683489\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.72306 | − | 75.9742i | −0.0111656 | − | 0.179608i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −42.2447 | − | 24.3900i | −0.0989337 | − | 0.0571194i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 14.3642 | + | 3.37474i | 0.0334829 | + | 0.00786652i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 821.321i | 1.90562i | 0.303570 | + | 0.952809i | \(0.401821\pi\) | ||||
−0.303570 | + | 0.952809i | \(0.598179\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 199.155i | 0.459942i | 0.973198 | + | 0.229971i | \(0.0738631\pi\) | ||||
−0.973198 | + | 0.229971i | \(0.926137\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 95.7946 | − | 165.921i | 0.219210 | − | 0.379682i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −240.830 | − | 417.130i | −0.548588 | − | 0.950182i | −0.998372 | − | 0.0570445i | \(-0.981832\pi\) |
0.449784 | − | 0.893137i | \(-0.351501\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 255.876 | − | 169.729i | 0.580218 | − | 0.384873i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 270.143 | + | 467.902i | 0.609805 | + | 1.05621i | 0.991272 | + | 0.131830i | \(0.0420854\pi\) |
−0.381468 | + | 0.924382i | \(0.624581\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −176.309 | − | 165.689i | −0.394428 | − | 0.370669i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 300.318i | − | 0.668859i | −0.942421 | − | 0.334429i | \(-0.891456\pi\) | ||
0.942421 | − | 0.334429i | \(-0.108544\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.9074 | 0.0441407 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −86.5579 | − | 287.080i | −0.191077 | − | 0.633731i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 134.841 | − | 77.8505i | 0.295057 | − | 0.170351i | −0.345163 | − | 0.938543i | \(-0.612176\pi\) |
0.640220 | + | 0.768191i | \(0.278843\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 166.598 | + | 138.136i | 0.362958 | + | 0.300949i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 261.143 | − | 150.771i | 0.566470 | − | 0.327052i | −0.189268 | − | 0.981925i | \(-0.560612\pi\) |
0.755738 | + | 0.654874i | \(0.227278\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 206.790 | + | 119.390i | 0.446630 | + | 0.257862i | 0.706406 | − | 0.707807i | \(-0.250315\pi\) |
−0.259776 | + | 0.965669i | \(0.583649\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 423.152 | 0.906107 | 0.453054 | − | 0.891483i | \(-0.350335\pi\) | ||||
0.453054 | + | 0.891483i | \(0.350335\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1000.13 | 2.13247 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 151.836 | + | 142.690i | 0.322369 | + | 0.302950i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.08795 | − | 8.81259i | 0.0107568 | − | 0.0186313i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 488.212 | + | 242.804i | 1.02351 | + | 0.509024i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 379.284 | − | 218.980i | 0.791824 | − | 0.457160i | −0.0487802 | − | 0.998810i | \(-0.515533\pi\) |
0.840604 | + | 0.541650i | \(0.182200\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 102.649 | − | 177.794i | 0.213408 | − | 0.369634i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 147.653 | − | 628.467i | 0.305699 | − | 1.30117i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 401.945i | 0.825350i | 0.910878 | + | 0.412675i | \(0.135405\pi\) | ||||
−0.910878 | + | 0.412675i | \(0.864595\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 111.475 | − | 474.483i | 0.227966 | − | 0.970313i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −241.084 | − | 139.190i | −0.491007 | − | 0.283483i | 0.233985 | − | 0.972240i | \(-0.424823\pi\) |
−0.724992 | + | 0.688757i | \(0.758157\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 367.981 | − | 212.454i | 0.746411 | − | 0.430941i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 73.0756 | + | 126.571i | 0.147033 | + | 0.254669i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 272.655 | − | 472.252i | 0.546402 | − | 0.946397i | −0.452115 | − | 0.891960i | \(-0.649330\pi\) |
0.998517 | − | 0.0544369i | \(-0.0173364\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −198.624 | + | 211.355i | −0.396454 | + | 0.421866i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −306.460 | −0.609264 | −0.304632 | − | 0.952470i | \(-0.598534\pi\) | ||||
−0.304632 | + | 0.952470i | \(0.598534\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −39.3312 | − | 130.447i | −0.0775764 | − | 0.257292i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −480.208 | − | 277.248i | −0.943434 | − | 0.544692i | −0.0523989 | − | 0.998626i | \(-0.516687\pi\) |
−0.891035 | + | 0.453934i | \(0.850020\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.8316 | + | 34.3493i | 0.0388093 | + | 0.0672197i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 168.705 | + | 139.883i | 0.328860 | + | 0.272677i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.24069 | + | 1.87101i | 0.00626825 | + | 0.00361898i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 24.2731 | + | 80.5049i | 0.0467691 | + | 0.155115i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 154.167i | 0.295905i | 0.988994 | + | 0.147953i | \(0.0472683\pi\) | ||||
−0.988994 | + | 0.147953i | \(0.952732\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 480.598i | − | 0.918925i | −0.888197 | − | 0.459463i | \(-0.848042\pi\) | ||
0.888197 | − | 0.459463i | \(-0.151958\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −117.629 | + | 203.739i | −0.223204 | + | 0.386602i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.0721 | − | 24.3735i | −0.0266013 | − | 0.0460748i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −378.954 | − | 571.294i | −0.713660 | − | 1.07588i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 250.105 | + | 433.194i | 0.469240 | + | 0.812747i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −24.4274 | + | 103.973i | −0.0454887 | + | 0.193618i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.0943i | 0.0280043i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −300.543 | −0.555533 | −0.277766 | − | 0.960649i | \(-0.589594\pi\) | ||||
−0.277766 | + | 0.960649i | \(0.589594\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −57.3460 | − | 13.4729i | −0.105610 | − | 0.0248120i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −87.6473 | + | 50.6032i | −0.160233 | + | 0.0925104i | −0.577972 | − | 0.816056i | \(-0.696156\pi\) |
0.417739 | + | 0.908567i | \(0.362822\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.98785 | − | 48.0620i | −0.00544236 | − | 0.0875446i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 372.636 | − | 215.141i | 0.676290 | − | 0.390456i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.5081 | + | 7.22154i | 0.0226186 | + | 0.0130588i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 433.041 | 0.777452 | 0.388726 | − | 0.921353i | \(-0.372915\pi\) | ||||
0.388726 | + | 0.921353i | \(0.372915\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 255.687 | 0.457401 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.1859 | + | 3.07117i | −0.0181567 | + | 0.00547445i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 520.886 | − | 902.201i | 0.925197 | − | 1.60249i | 0.133954 | − | 0.990988i | \(-0.457233\pi\) |
0.791244 | − | 0.611501i | \(-0.209434\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 680.336 | + | 287.181i | 1.19989 | + | 0.506491i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −257.445 | + | 148.636i | −0.452452 | + | 0.261223i | −0.708865 | − | 0.705344i | \(-0.750793\pi\) |
0.256413 | + | 0.966567i | \(0.417459\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 339.524 | − | 588.073i | 0.594613 | − | 1.02990i | −0.398988 | − | 0.916956i | \(-0.630638\pi\) |
0.993601 | − | 0.112945i | \(-0.0360282\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 625.720 | − | 188.662i | 1.09201 | − | 0.329252i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 148.351i | − | 0.257107i | −0.991703 | − | 0.128553i | \(-0.958967\pi\) | ||
0.991703 | − | 0.128553i | \(-0.0410333\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −107.121 | − | 100.668i | −0.185010 | − | 0.173866i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 66.7785 | + | 38.5546i | 0.114937 | + | 0.0663590i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23.2132 | + | 13.4021i | −0.0398168 | + | 0.0229882i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 263.559 | + | 456.497i | 0.448993 | + | 0.777678i | 0.998321 | − | 0.0579287i | \(-0.0184496\pi\) |
−0.549328 | + | 0.835607i | \(0.685116\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −119.117 | + | 206.316i | −0.202236 | + | 0.350283i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1051.27 | − | 246.987i | −1.77880 | − | 0.417913i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −473.848 | −0.799069 | −0.399534 | − | 0.916718i | \(-0.630828\pi\) | ||||
−0.399534 | + | 0.916718i | \(0.630828\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 178.340 | + | 41.8993i | 0.298727 | + | 0.0701832i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 601.414 | + | 347.227i | 1.00403 | + | 0.579677i | 0.909438 | − | 0.415839i | \(-0.136512\pi\) |
0.0945922 | + | 0.995516i | \(0.469845\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −93.3559 | − | 161.697i | −0.155334 | − | 0.269047i | 0.777846 | − | 0.628454i | \(-0.216312\pi\) |
−0.933181 | + | 0.359408i | \(0.882979\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 545.756 | + | 822.758i | 0.905068 | + | 1.36444i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 712.209 | + | 411.194i | 1.17333 | + | 0.677420i | 0.954461 | − | 0.298335i | \(-0.0964311\pi\) |
0.218865 | + | 0.975755i | \(0.429764\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 992.906 | − | 1056.55i | 1.63039 | − | 1.73489i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 94.0249i | 0.153887i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 482.206i | 0.786634i | 0.919403 | + | 0.393317i | \(0.128672\pi\) | ||||
−0.919403 | + | 0.393317i | \(0.871328\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 344.052 | − | 595.916i | 0.557621 | − | 0.965828i | −0.440073 | − | 0.897962i | \(-0.645048\pi\) |
0.997694 | − | 0.0678661i | \(-0.0216191\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −380.253 | − | 658.617i | −0.614302 | − | 1.06400i | −0.990507 | − | 0.137465i | \(-0.956105\pi\) |
0.376205 | − | 0.926536i | \(-0.377229\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 597.583 | − | 221.479i | 0.962291 | − | 0.356649i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −292.302 | − | 506.282i | −0.469185 | − | 0.812652i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.3148 | + | 3.11002i | −0.0164510 | + | 0.00496016i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 148.024i | 0.235333i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1008.08 | 1.59758 | 0.798792 | − | 0.601607i | \(-0.205473\pi\) | ||||
0.798792 | + | 0.601607i | \(0.205473\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −795.046 | + | 846.007i | −1.25600 | + | 1.33650i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −328.459 | + | 189.636i | −0.515634 | + | 0.297701i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −64.2473 | + | 129.184i | −0.100544 | + | 0.202165i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −488.095 | + | 281.802i | −0.761458 | + | 0.439628i | −0.829819 | − | 0.558032i | \(-0.811556\pi\) |
0.0683607 | + | 0.997661i | \(0.478223\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −499.697 | − | 288.500i | −0.777133 | − | 0.448678i | 0.0582801 | − | 0.998300i | \(-0.481438\pi\) |
−0.835413 | + | 0.549622i | \(0.814772\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1024.52 | 1.58349 | 0.791744 | − | 0.610853i | \(-0.209173\pi\) | ||||
0.791744 | + | 0.610853i | \(0.209173\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 33.7011 | 0.0519277 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −183.600 | + | 781.475i | −0.282028 | + | 1.20042i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 199.697 | − | 345.885i | 0.305814 | − | 0.529686i | −0.671628 | − | 0.740888i | \(-0.734405\pi\) |
0.977442 | + | 0.211203i | \(0.0677381\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −17.4357 | + | 35.0584i | −0.0265384 | + | 0.0533614i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 646.308 | − | 373.146i | 0.980741 | − | 0.566231i | 0.0782470 | − | 0.996934i | \(-0.475068\pi\) |
0.902494 | + | 0.430703i | \(0.141734\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −475.624 | + | 823.804i | −0.719552 | + | 1.24630i | 0.241626 | + | 0.970369i | \(0.422319\pi\) |
−0.961178 | + | 0.275931i | \(0.911014\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −194.799 | − | 183.065i | −0.293815 | − | 0.276117i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1251.27i | − | 1.87596i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −295.135 | + | 88.9864i | −0.441158 | + | 0.133014i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.05009 | + | 1.18362i | 0.00305527 | + | 0.00176396i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 298.113 | − | 172.115i | 0.442961 | − | 0.255743i | −0.261892 | − | 0.965097i | \(-0.584346\pi\) |
0.704853 | + | 0.709354i | \(0.251013\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 492.832 | + | 853.610i | 0.727965 | + | 1.26087i | 0.957742 | + | 0.287628i | \(0.0928668\pi\) |
−0.229778 | + | 0.973243i | \(0.573800\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 525.284 | − | 909.818i | 0.773614 | − | 1.33994i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −293.552 | − | 973.600i | −0.431060 | − | 1.42966i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 166.658 | 0.244009 | 0.122004 | − | 0.992530i | \(-0.461068\pi\) | ||||
0.122004 | + | 0.992530i | \(0.461068\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −609.665 | + | 648.743i | −0.887431 | + | 0.944313i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −583.272 | − | 336.752i | −0.846548 | − | 0.488755i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 449.077 | + | 777.825i | 0.649895 | + | 1.12565i | 0.983148 | + | 0.182813i | \(0.0585204\pi\) |
−0.333253 | + | 0.942838i | \(0.608146\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −30.2518 | + | 20.0668i | −0.0436534 | + | 0.0289564i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −312.341 | − | 180.330i | −0.448122 | − | 0.258723i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1012.06 | − | 237.773i | −1.44786 | − | 0.340162i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 730.549i | 1.04215i | 0.853510 | + | 0.521076i | \(0.174469\pi\) | ||||
−0.853510 | + | 0.521076i | \(0.825531\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 149.897i | 0.213224i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 602.991 | − | 1044.41i | 0.852887 | − | 1.47724i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −114.961 | − | 199.118i | −0.162145 | − | 0.280843i | 0.773493 | − | 0.633805i | \(-0.218508\pi\) |
−0.935638 | + | 0.352962i | \(0.885174\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.884663 | + | 14.2305i | 0.00124425 | + | 0.0200148i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 346.394 | + | 599.971i | 0.485825 | + | 0.841474i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 353.472 | + | 332.181i | 0.492988 | + | 0.463292i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 907.095i | 1.26161i | 0.775943 | + | 0.630803i | \(0.217275\pi\) | ||||
−0.775943 | + | 0.630803i | \(0.782725\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1142.80 | 1.58502 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 281.232 | + | 932.742i | 0.388980 | + | 1.29010i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 186.838 | − | 107.871i | 0.256999 | − | 0.148378i | −0.365966 | − | 0.930628i | \(-0.619261\pi\) |
0.622965 | + | 0.782250i | \(0.285928\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 135.000 | + | 716.391i | 0.185185 | + | 0.982704i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −159.656 | + | 92.1776i | −0.218408 | + | 0.126098i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 544.963 | + | 314.634i | 0.743469 | + | 0.429242i | 0.823329 | − | 0.567564i | \(-0.192114\pi\) |
−0.0798604 | + | 0.996806i | \(0.525447\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −48.5351 | −0.0658549 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −547.649 | −0.741068 | −0.370534 | − | 0.928819i | \(-0.620825\pi\) | ||||
−0.370534 | + | 0.928819i | \(0.620825\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −197.264 | − | 185.381i | −0.266213 | − | 0.250177i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −267.072 | + | 462.583i | −0.359451 | + | 0.622588i | −0.987869 | − | 0.155288i | \(-0.950369\pi\) |
0.628418 | + | 0.777876i | \(0.283703\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.72306 | + | 75.9742i | 0.00632271 | + | 0.101706i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −288.481 | + | 166.555i | −0.385155 | + | 0.222369i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 225.545 | − | 390.655i | 0.300326 | − | 0.520180i | −0.675884 | − | 0.737008i | \(-0.736238\pi\) |
0.976210 | + | 0.216828i | \(0.0695712\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 263.486 | − | 1121.50i | 0.349915 | − | 1.48937i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 352.391i | − | 0.465511i | −0.972535 | − | 0.232755i | \(-0.925226\pi\) | ||
0.972535 | − | 0.232755i | \(-0.0747741\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.16543 | + | 30.4988i | −0.00944061 | + | 0.0401829i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −929.923 | − | 536.891i | −1.22197 | − | 0.705507i | −0.256636 | − | 0.966508i | \(-0.582614\pi\) |
−0.965339 | + | 0.261001i | \(0.915947\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1063.52 | + | 614.024i | −1.39387 | + | 0.804750i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 423.399 | + | 733.349i | 0.552020 | + | 0.956126i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 177.988 | − | 308.284i | 0.231454 | − | 0.400889i | −0.726782 | − | 0.686868i | \(-0.758985\pi\) |
0.958236 | + | 0.285978i | \(0.0923185\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26.5721 | − | 28.2753i | 0.0344644 | − | 0.0366735i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 370.790 | 0.479677 | 0.239838 | − | 0.970813i | \(-0.422906\pi\) | ||||
0.239838 | + | 0.970813i | \(0.422906\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 145.808 | + | 483.589i | 0.187655 | + | 0.622380i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −316.292 | − | 182.611i | −0.406023 | − | 0.234418i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.54628 | − | 6.14233i | −0.00454069 | − | 0.00786470i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1410.99 | + | 240.273i | 1.80203 | + | 0.306862i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −998.581 | − | 576.531i | −1.26885 | − | 0.732568i | −0.294076 | − | 0.955782i | \(-0.595012\pi\) |
−0.974769 | + | 0.223214i | \(0.928345\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 42.8437 | + | 142.096i | 0.0543013 | + | 0.180097i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1734.12i | 2.19231i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 59.4810i | 0.0750076i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 439.873 | − | 761.882i | 0.551910 | − | 0.955937i | −0.446226 | − | 0.894920i | \(-0.647232\pi\) |
0.998137 | − | 0.0610167i | \(-0.0194343\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −33.8968 | − | 58.7110i | −0.0424240 | − | 0.0734806i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 256.989 | − | 516.735i | 0.320836 | − | 0.645112i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.962404 | − | 1.66693i | −0.00119851 | − | 0.00207588i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.7132 | − | 62.6252i | 0.0182320 | − | 0.0776025i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 884.508i | − | 1.09334i | −0.837350 | − | 0.546668i | \(-0.815896\pi\) | ||
0.837350 | − | 0.546668i | \(-0.184104\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −961.464 | −1.18553 | −0.592765 | − | 0.805376i | \(-0.701964\pi\) | ||||
−0.592765 | + | 0.805376i | \(0.701964\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −954.727 | − | 224.304i | −1.17433 | − | 0.275897i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −161.676 | + | 93.3437i | −0.197890 | + | 0.114252i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −816.725 | − | 406.185i | −0.997223 | − | 0.495952i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 778.064 | − | 449.215i | 0.947702 | − | 0.547156i | 0.0553360 | − | 0.998468i | \(-0.482377\pi\) |
0.892366 | + | 0.451312i | \(0.149044\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 187.219 | + | 108.091i | 0.227484 | + | 0.131338i | 0.609411 | − | 0.792855i | \(-0.291406\pi\) |
−0.381927 | + | 0.924193i | \(0.624739\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −113.883 | −0.137706 | −0.0688528 | − | 0.997627i | \(-0.521934\pi\) | ||||
−0.0688528 | + | 0.997627i | \(0.521934\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −101.326 | −0.122227 | −0.0611135 | − | 0.998131i | \(-0.519465\pi\) | ||||
−0.0611135 | + | 0.998131i | \(0.519465\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1371.38 | + | 413.487i | −1.65028 | + | 0.497578i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 136.731 | − | 236.825i | 0.164143 | − | 0.284303i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −743.071 | + | 275.401i | −0.887779 | + | 0.329033i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −60.4689 | + | 34.9117i | −0.0720726 | + | 0.0416111i | −0.535603 | − | 0.844470i | \(-0.679916\pi\) |
0.463531 | + | 0.886081i | \(0.346582\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 984.588 | − | 1705.36i | 1.17073 | − | 2.02777i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −341.824 | + | 103.064i | −0.405485 | + | 0.122258i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1101.35i | 1.30030i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −855.547 | − | 804.012i | −1.00771 | − | 0.947011i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 377.502 | + | 217.951i | 0.443598 | + | 0.256112i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 993.028 | − | 573.325i | 1.16416 | − | 0.672127i | 0.211862 | − | 0.977300i | \(-0.432047\pi\) |
0.952297 | + | 0.305172i | \(0.0987140\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 125.788 | + | 217.871i | 0.146777 | + | 0.254225i | 0.930035 | − | 0.367472i | \(-0.119777\pi\) |
−0.783258 | + | 0.621697i | \(0.786443\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −244.266 | + | 423.082i | −0.284361 | + | 0.492528i | −0.972454 | − | 0.233095i | \(-0.925115\pi\) |
0.688093 | + | 0.725623i | \(0.258448\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1198.03 | − | 281.467i | −1.39145 | − | 0.326908i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −596.889 | −0.691644 | −0.345822 | − | 0.938300i | \(-0.612400\pi\) | ||||
−0.345822 | + | 0.938300i | \(0.612400\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −656.386 | − | 154.212i | −0.757077 | − | 0.177868i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.607003 | − | 0.350454i | −0.000698508 | − | 0.000403284i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −609.765 | − | 1056.14i | −0.700074 | − | 1.21256i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1035.10 | − | 64.3490i | 1.18569 | − | 0.0737102i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −620.434 | − | 358.208i | −0.707451 | − | 0.408447i | 0.102666 | − | 0.994716i | \(-0.467263\pi\) |
−0.810116 | + | 0.586269i | \(0.800596\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 147.297 | − | 156.739i | 0.167574 | − | 0.178315i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1200.86i | 1.36306i | 0.731790 | + | 0.681531i | \(0.238685\pi\) | ||||
−0.731790 | + | 0.681531i | \(0.761315\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 22.8938i | − | 0.0259273i | −0.999916 | − | 0.0129636i | \(-0.995873\pi\) | ||
0.999916 | − | 0.0129636i | \(-0.00412657\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −301.294 | + | 521.857i | −0.339678 | + | 0.588340i | −0.984372 | − | 0.176101i | \(-0.943651\pi\) |
0.644694 | + | 0.764441i | \(0.276985\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 839.220 | + | 1453.57i | 0.944005 | + | 1.63506i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −33.0160 | − | 13.9366i | −0.0370549 | − | 0.0156415i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −34.3256 | − | 59.4537i | −0.0384385 | − | 0.0665775i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −753.689 | + | 227.246i | −0.840233 | + | 0.253340i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1555.90i | 1.73071i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 485.609 | 0.538966 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −430.794 | + | 458.406i | −0.477069 | + | 0.507648i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 366.281 | − | 211.473i | 0.403838 | − | 0.233156i | −0.284300 | − | 0.958735i | \(-0.591761\pi\) |
0.688139 | + | 0.725579i | \(0.258428\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1188.23 | − | 73.8684i | 1.30719 | − | 0.0812634i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 125.376 | − | 72.3861i | 0.137625 | − | 0.0794578i | −0.429607 | − | 0.903016i | \(-0.641348\pi\) |
0.567232 | + | 0.823558i | \(0.308014\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.24069 | − | 1.87101i | −0.00354949 | − | 0.00204930i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1149.51 | −1.25356 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 869.093 | 0.945694 | 0.472847 | − | 0.881145i | \(-0.343226\pi\) | ||||
0.472847 | + | 0.881145i | \(0.343226\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 118.257 | − | 503.347i | 0.128400 | − | 0.546522i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 89.1064 | − | 154.337i | 0.0965400 | − | 0.167212i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 623.611 | + | 940.129i | 0.672720 | + | 1.01416i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −82.2838 | + | 47.5066i | −0.0885724 | + | 0.0511373i | −0.543632 | − | 0.839324i | \(-0.682951\pi\) |
0.455060 | + | 0.890461i | \(0.349618\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 138.461 | − | 239.821i | 0.148722 | − | 0.257595i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1323.37 | − | 1243.66i | −1.41841 | − | 1.33297i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1555.55i | − | 1.66014i | −0.557657 | − | 0.830071i | \(-0.688300\pi\) | ||
0.557657 | − | 0.830071i | \(-0.311700\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −940.578 | + | 283.595i | −1.00168 | + | 0.302018i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 335.246 | + | 193.554i | 0.356265 | + | 0.205690i | 0.667441 | − | 0.744662i | \(-0.267389\pi\) |
−0.311176 | + | 0.950352i | \(0.600723\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −919.782 | + | 531.036i | −0.975379 | + | 0.563135i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −484.894 | − | 839.861i | −0.512032 | − | 0.886865i | −0.999903 | − | 0.0139492i | \(-0.995560\pi\) |
0.487871 | − | 0.872916i | \(-0.337774\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.1821 | − | 41.8846i | 0.0254817 | − | 0.0441355i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −59.7921 | − | 198.308i | −0.0628729 | − | 0.208526i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1294.65 | −1.35850 | −0.679248 | − | 0.733909i | \(-0.737694\pi\) | ||||
−0.679248 | + | 0.733909i | \(0.737694\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −48.1846 | + | 51.2731i | −0.0503497 | + | 0.0535769i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 981.126 | + | 566.453i | 1.02307 | + | 0.590671i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 49.7731 | + | 86.2096i | 0.0517931 | + | 0.0897082i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −294.437 | − | 146.433i | −0.305750 | − | 0.152059i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −713.668 | − | 412.036i | −0.738023 | − | 0.426098i | 0.0833272 | − | 0.996522i | \(-0.473445\pi\) |
−0.821350 | + | 0.570425i | \(0.806779\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 190.007 | + | 44.6404i | 0.196085 | + | 0.0460685i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1518.35i | 1.56370i | 0.623469 | + | 0.781848i | \(0.285723\pi\) | ||||
−0.623469 | + | 0.781848i | \(0.714277\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 244.024i | − | 0.250796i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 185.616 | − | 321.497i | 0.189986 | − | 0.329065i | −0.755259 | − | 0.655426i | \(-0.772489\pi\) |
0.945245 | + | 0.326361i | \(0.105822\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.1851 | + | 24.5693i | 0.0144894 | + | 0.0250963i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1085.48 | − | 539.844i | −1.10650 | − | 0.550300i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 466.522 | + | 808.039i | 0.474590 | + | 0.822014i | 0.999577 | − | 0.0290967i | \(-0.00926307\pi\) |
−0.524987 | + | 0.851110i | \(0.675930\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −168.571 | − | 158.417i | −0.170792 | − | 0.160504i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 542.890i | 0.548928i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1615.53 | 1.63020 | 0.815099 | − | 0.579321i | \(-0.196682\pi\) | ||||
0.815099 | + | 0.579321i | \(0.196682\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −441.492 | − | 1464.26i | −0.444604 | − | 1.47458i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 899.586 | − | 519.376i | 0.902293 | − | 0.520939i | 0.0243496 | − | 0.999704i | \(-0.492249\pi\) |
0.877943 | + | 0.478764i | \(0.158915\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −318.261 | + | 383.837i | −0.318580 | + | 0.384221i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))