Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1275,2,Mod(1174,1275)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1275, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1275.1174");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1275 = 3 \cdot 5^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1275.b (of order \(2\), degree \(1\), 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: | \(10.1809262577\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 51) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1174.4 | ||
Root | \(2.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1275.1174 |
Dual form | 1275.2.b.d.1174.1 |
$q$-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 \(\left(\mathbb{Z}/1275\mathbb{Z}\right)^\times\).
\(n\) | \(52\) | \(751\) | \(851\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.56155i | 1.81129i | 0.424035 | + | 0.905646i | \(0.360613\pi\) | ||||
−0.424035 | + | 0.905646i | \(0.639387\pi\) | |||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | −4.56155 | −2.28078 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.56155 | 1.04575 | ||||||||
\(7\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(8\) | − 6.56155i | − 2.31986i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.56155 | 0.470826 | 0.235413 | − | 0.971895i | \(-0.424356\pi\) | ||||
0.235413 | + | 0.971895i | \(0.424356\pi\) | |||||||
\(12\) | 4.56155i | 1.31681i | ||||||||
\(13\) | 0.438447i | 0.121603i | 0.998150 | + | 0.0608017i | \(0.0193657\pi\) | ||||
−0.998150 | + | 0.0608017i | \(0.980634\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 7.68466 | 1.92116 | ||||||||
\(17\) | − 1.00000i | − 0.242536i | ||||||||
\(18\) | − 2.56155i | − 0.603764i | ||||||||
\(19\) | 4.68466 | 1.07473 | 0.537367 | − | 0.843348i | \(-0.319419\pi\) | ||||
0.537367 | + | 0.843348i | \(0.319419\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.00000i | 0.852803i | ||||||||
\(23\) | − 2.43845i | − 0.508451i | −0.967145 | − | 0.254226i | \(-0.918179\pi\) | ||||
0.967145 | − | 0.254226i | \(-0.0818206\pi\) | |||||||
\(24\) | −6.56155 | −1.33937 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.12311 | −0.220259 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.24621 | 1.53128 | 0.765641 | − | 0.643268i | \(-0.222422\pi\) | ||||
0.765641 | + | 0.643268i | \(0.222422\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.12311 | 0.560926 | 0.280463 | − | 0.959865i | \(-0.409512\pi\) | ||||
0.280463 | + | 0.959865i | \(0.409512\pi\) | |||||||
\(32\) | 6.56155i | 1.15993i | ||||||||
\(33\) | − 1.56155i | − 0.271831i | ||||||||
\(34\) | 2.56155 | 0.439303 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.56155 | 0.760259 | ||||||||
\(37\) | 5.12311i | 0.842233i | 0.907006 | + | 0.421117i | \(0.138362\pi\) | ||||
−0.907006 | + | 0.421117i | \(0.861638\pi\) | |||||||
\(38\) | 12.0000i | 1.94666i | ||||||||
\(39\) | 0.438447 | 0.0702077 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.56155 | −0.556221 | −0.278111 | − | 0.960549i | \(-0.589708\pi\) | ||||
−0.278111 | + | 0.960549i | \(0.589708\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.68466i | 0.714404i | 0.934027 | + | 0.357202i | \(0.116269\pi\) | ||||
−0.934027 | + | 0.357202i | \(0.883731\pi\) | |||||||
\(44\) | −7.12311 | −1.07385 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.24621 | 0.920954 | ||||||||
\(47\) | 11.1231i | 1.62247i | 0.584719 | + | 0.811236i | \(0.301205\pi\) | ||||
−0.584719 | + | 0.811236i | \(0.698795\pi\) | |||||||
\(48\) | − 7.68466i | − 1.10918i | ||||||||
\(49\) | 7.00000 | 1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | − 2.00000i | − 0.277350i | ||||||||
\(53\) | 12.2462i | 1.68215i | 0.540921 | + | 0.841073i | \(0.318076\pi\) | ||||
−0.540921 | + | 0.841073i | \(0.681924\pi\) | |||||||
\(54\) | −2.56155 | −0.348583 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 4.68466i | − 0.620498i | ||||||||
\(58\) | 21.1231i | 2.77360i | ||||||||
\(59\) | −7.12311 | −0.927349 | −0.463675 | − | 0.886006i | \(-0.653469\pi\) | ||||
−0.463675 | + | 0.886006i | \(0.653469\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.12311 | 1.16809 | 0.584047 | − | 0.811720i | \(-0.301468\pi\) | ||||
0.584047 | + | 0.811720i | \(0.301468\pi\) | |||||||
\(62\) | 8.00000i | 1.01600i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.43845 | −0.179806 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.00000 | 0.492366 | ||||||||
\(67\) | − 4.00000i | − 0.488678i | −0.969690 | − | 0.244339i | \(-0.921429\pi\) | ||||
0.969690 | − | 0.244339i | \(-0.0785709\pi\) | |||||||
\(68\) | 4.56155i | 0.553170i | ||||||||
\(69\) | −2.43845 | −0.293555 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.24621 | −0.741289 | −0.370644 | − | 0.928775i | \(-0.620863\pi\) | ||||
−0.370644 | + | 0.928775i | \(0.620863\pi\) | |||||||
\(72\) | 6.56155i | 0.773286i | ||||||||
\(73\) | − 12.2462i | − 1.43331i | −0.697428 | − | 0.716655i | \(-0.745672\pi\) | ||||
0.697428 | − | 0.716655i | \(-0.254328\pi\) | |||||||
\(74\) | −13.1231 | −1.52553 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −21.3693 | −2.45123 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.12311i | 0.127167i | ||||||||
\(79\) | 9.36932 | 1.05413 | 0.527065 | − | 0.849825i | \(-0.323292\pi\) | ||||
0.527065 | + | 0.849825i | \(0.323292\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − 9.12311i | − 1.00748i | ||||||||
\(83\) | − 0.876894i | − 0.0962517i | −0.998841 | − | 0.0481258i | \(-0.984675\pi\) | ||||
0.998841 | − | 0.0481258i | \(-0.0153248\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −12.0000 | −1.29399 | ||||||||
\(87\) | − 8.24621i | − 0.884087i | ||||||||
\(88\) | − 10.2462i | − 1.09225i | ||||||||
\(89\) | 1.12311 | 0.119049 | 0.0595245 | − | 0.998227i | \(-0.481042\pi\) | ||||
0.0595245 | + | 0.998227i | \(0.481042\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 11.1231i | 1.15966i | ||||||||
\(93\) | − 3.12311i | − 0.323851i | ||||||||
\(94\) | −28.4924 | −2.93877 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 6.56155 | 0.669686 | ||||||||
\(97\) | 2.87689i | 0.292104i | 0.989277 | + | 0.146052i | \(0.0466567\pi\) | ||||
−0.989277 | + | 0.146052i | \(0.953343\pi\) | |||||||
\(98\) | 17.9309i | 1.81129i | ||||||||
\(99\) | −1.56155 | −0.156942 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.8769 | 1.08229 | 0.541146 | − | 0.840929i | \(-0.317991\pi\) | ||||
0.541146 | + | 0.840929i | \(0.317991\pi\) | |||||||
\(102\) | − 2.56155i | − 0.253632i | ||||||||
\(103\) | 16.6847i | 1.64399i | 0.569496 | + | 0.821994i | \(0.307138\pi\) | ||||
−0.569496 | + | 0.821994i | \(0.692862\pi\) | |||||||
\(104\) | 2.87689 | 0.282103 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −31.3693 | −3.04686 | ||||||||
\(107\) | 4.68466i | 0.452883i | 0.974025 | + | 0.226442i | \(0.0727092\pi\) | ||||
−0.974025 | + | 0.226442i | \(0.927291\pi\) | |||||||
\(108\) | − 4.56155i | − 0.438936i | ||||||||
\(109\) | 6.87689 | 0.658687 | 0.329344 | − | 0.944210i | \(-0.393173\pi\) | ||||
0.329344 | + | 0.944210i | \(0.393173\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.12311 | 0.486264 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 0.438447i | − 0.0412456i | −0.999787 | − | 0.0206228i | \(-0.993435\pi\) | ||||
0.999787 | − | 0.0206228i | \(-0.00656491\pi\) | |||||||
\(114\) | 12.0000 | 1.12390 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −37.6155 | −3.49251 | ||||||||
\(117\) | − 0.438447i | − 0.0405345i | ||||||||
\(118\) | − 18.2462i | − 1.67970i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.56155 | −0.778323 | ||||||||
\(122\) | 23.3693i | 2.11576i | ||||||||
\(123\) | 3.56155i | 0.321134i | ||||||||
\(124\) | −14.2462 | −1.27935 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 19.8078i | − 1.75765i | −0.477140 | − | 0.878827i | \(-0.658326\pi\) | ||||
0.477140 | − | 0.878827i | \(-0.341674\pi\) | |||||||
\(128\) | 9.43845i | 0.834249i | ||||||||
\(129\) | 4.68466 | 0.412461 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.4384 | 1.26149 | 0.630746 | − | 0.775989i | \(-0.282749\pi\) | ||||
0.630746 | + | 0.775989i | \(0.282749\pi\) | |||||||
\(132\) | 7.12311i | 0.619987i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 10.2462 | 0.885138 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.56155 | −0.562649 | ||||||||
\(137\) | − 0.246211i | − 0.0210352i | −0.999945 | − | 0.0105176i | \(-0.996652\pi\) | ||||
0.999945 | − | 0.0105176i | \(-0.00334793\pi\) | |||||||
\(138\) | − 6.24621i | − 0.531713i | ||||||||
\(139\) | 0.876894 | 0.0743772 | 0.0371886 | − | 0.999308i | \(-0.488160\pi\) | ||||
0.0371886 | + | 0.999308i | \(0.488160\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.1231 | 0.936734 | ||||||||
\(142\) | − 16.0000i | − 1.34269i | ||||||||
\(143\) | 0.684658i | 0.0572540i | ||||||||
\(144\) | −7.68466 | −0.640388 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 31.3693 | 2.59614 | ||||||||
\(147\) | − 7.00000i | − 0.577350i | ||||||||
\(148\) | − 23.3693i | − 1.92095i | ||||||||
\(149\) | −12.2462 | −1.00325 | −0.501624 | − | 0.865086i | \(-0.667264\pi\) | ||||
−0.501624 | + | 0.865086i | \(0.667264\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | 0.651031 | 0.325515 | − | 0.945537i | \(-0.394462\pi\) | ||||
0.325515 | + | 0.945537i | \(0.394462\pi\) | |||||||
\(152\) | − 30.7386i | − 2.49323i | ||||||||
\(153\) | 1.00000i | 0.0808452i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.00000 | −0.160128 | ||||||||
\(157\) | − 6.68466i | − 0.533494i | −0.963767 | − | 0.266747i | \(-0.914051\pi\) | ||||
0.963767 | − | 0.266747i | \(-0.0859488\pi\) | |||||||
\(158\) | 24.0000i | 1.90934i | ||||||||
\(159\) | 12.2462 | 0.971188 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.56155i | 0.201255i | ||||||||
\(163\) | − 15.1231i | − 1.18453i | −0.805742 | − | 0.592267i | \(-0.798233\pi\) | ||||
0.805742 | − | 0.592267i | \(-0.201767\pi\) | |||||||
\(164\) | 16.2462 | 1.26862 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.24621 | 0.174340 | ||||||||
\(167\) | − 19.8078i | − 1.53277i | −0.642381 | − | 0.766385i | \(-0.722053\pi\) | ||||
0.642381 | − | 0.766385i | \(-0.277947\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.8078 | 0.985213 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.68466 | −0.358245 | ||||||||
\(172\) | − 21.3693i | − 1.62940i | ||||||||
\(173\) | 1.80776i | 0.137442i | 0.997636 | + | 0.0687209i | \(0.0218918\pi\) | ||||
−0.997636 | + | 0.0687209i | \(0.978108\pi\) | |||||||
\(174\) | 21.1231 | 1.60134 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 12.0000 | 0.904534 | ||||||||
\(177\) | 7.12311i | 0.535405i | ||||||||
\(178\) | 2.87689i | 0.215632i | ||||||||
\(179\) | 0.876894 | 0.0655422 | 0.0327711 | − | 0.999463i | \(-0.489567\pi\) | ||||
0.0327711 | + | 0.999463i | \(0.489567\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.00000 | 0.445976 | 0.222988 | − | 0.974821i | \(-0.428419\pi\) | ||||
0.222988 | + | 0.974821i | \(0.428419\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 9.12311i | − 0.674399i | ||||||||
\(184\) | −16.0000 | −1.17954 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 8.00000 | 0.586588 | ||||||||
\(187\) | − 1.56155i | − 0.114192i | ||||||||
\(188\) | − 50.7386i | − 3.70050i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.87689 | −0.352880 | −0.176440 | − | 0.984311i | \(-0.556458\pi\) | ||||
−0.176440 | + | 0.984311i | \(0.556458\pi\) | |||||||
\(192\) | 1.43845i | 0.103811i | ||||||||
\(193\) | − 7.75379i | − 0.558130i | −0.960272 | − | 0.279065i | \(-0.909976\pi\) | ||||
0.960272 | − | 0.279065i | \(-0.0900245\pi\) | |||||||
\(194\) | −7.36932 | −0.529086 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −31.9309 | −2.28078 | ||||||||
\(197\) | 8.93087i | 0.636298i | 0.948041 | + | 0.318149i | \(0.103061\pi\) | ||||
−0.948041 | + | 0.318149i | \(0.896939\pi\) | |||||||
\(198\) | − 4.00000i | − 0.284268i | ||||||||
\(199\) | −16.0000 | −1.13421 | −0.567105 | − | 0.823646i | \(-0.691937\pi\) | ||||
−0.567105 | + | 0.823646i | \(0.691937\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.00000 | −0.282138 | ||||||||
\(202\) | 27.8617i | 1.96035i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 4.56155 | 0.319373 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −42.7386 | −2.97774 | ||||||||
\(207\) | 2.43845i | 0.169484i | ||||||||
\(208\) | 3.36932i | 0.233620i | ||||||||
\(209\) | 7.31534 | 0.506013 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.3693 | 0.920382 | 0.460191 | − | 0.887820i | \(-0.347781\pi\) | ||||
0.460191 | + | 0.887820i | \(0.347781\pi\) | |||||||
\(212\) | − 55.8617i | − 3.83660i | ||||||||
\(213\) | 6.24621i | 0.427983i | ||||||||
\(214\) | −12.0000 | −0.820303 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 6.56155 | 0.446457 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 17.6155i | 1.19307i | ||||||||
\(219\) | −12.2462 | −0.827522 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.438447 | 0.0294931 | ||||||||
\(222\) | 13.1231i | 0.880765i | ||||||||
\(223\) | − 14.9309i | − 0.999845i | −0.866070 | − | 0.499922i | \(-0.833362\pi\) | ||||
0.866070 | − | 0.499922i | \(-0.166638\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.12311 | 0.0747079 | ||||||||
\(227\) | 14.0540i | 0.932795i | 0.884575 | + | 0.466398i | \(0.154448\pi\) | ||||
−0.884575 | + | 0.466398i | \(0.845552\pi\) | |||||||
\(228\) | 21.3693i | 1.41522i | ||||||||
\(229\) | −6.00000 | −0.396491 | −0.198246 | − | 0.980152i | \(-0.563524\pi\) | ||||
−0.198246 | + | 0.980152i | \(0.563524\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 54.1080i | − 3.55236i | ||||||||
\(233\) | − 3.56155i | − 0.233325i | −0.993172 | − | 0.116663i | \(-0.962780\pi\) | ||||
0.993172 | − | 0.116663i | \(-0.0372196\pi\) | |||||||
\(234\) | 1.12311 | 0.0734197 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 32.4924 | 2.11508 | ||||||||
\(237\) | − 9.36932i | − 0.608603i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.24621 | 0.404034 | 0.202017 | − | 0.979382i | \(-0.435250\pi\) | ||||
0.202017 | + | 0.979382i | \(0.435250\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.36932 | 0.217037 | 0.108518 | − | 0.994094i | \(-0.465389\pi\) | ||||
0.108518 | + | 0.994094i | \(0.465389\pi\) | |||||||
\(242\) | − 21.9309i | − 1.40977i | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | −41.6155 | −2.66416 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −9.12311 | −0.581668 | ||||||||
\(247\) | 2.05398i | 0.130691i | ||||||||
\(248\) | − 20.4924i | − 1.30127i | ||||||||
\(249\) | −0.876894 | −0.0555709 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.49242 | 0.536037 | 0.268018 | − | 0.963414i | \(-0.413631\pi\) | ||||
0.268018 | + | 0.963414i | \(0.413631\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 3.80776i | − 0.239392i | ||||||||
\(254\) | 50.7386 | 3.18363 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −27.0540 | −1.69087 | ||||||||
\(257\) | 15.3693i | 0.958712i | 0.877621 | + | 0.479356i | \(0.159130\pi\) | ||||
−0.877621 | + | 0.479356i | \(0.840870\pi\) | |||||||
\(258\) | 12.0000i | 0.747087i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.24621 | −0.510428 | ||||||||
\(262\) | 36.9848i | 2.28493i | ||||||||
\(263\) | − 20.4924i | − 1.26362i | −0.775125 | − | 0.631808i | \(-0.782313\pi\) | ||||
0.775125 | − | 0.631808i | \(-0.217687\pi\) | |||||||
\(264\) | −10.2462 | −0.630611 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 1.12311i | − 0.0687329i | ||||||||
\(268\) | 18.2462i | 1.11456i | ||||||||
\(269\) | −16.4384 | −1.00227 | −0.501135 | − | 0.865369i | \(-0.667084\pi\) | ||||
−0.501135 | + | 0.865369i | \(0.667084\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.8078 | 1.20324 | 0.601618 | − | 0.798784i | \(-0.294523\pi\) | ||||
0.601618 | + | 0.798784i | \(0.294523\pi\) | |||||||
\(272\) | − 7.68466i | − 0.465951i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.630683 | 0.0381010 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 11.1231 | 0.669532 | ||||||||
\(277\) | − 6.00000i | − 0.360505i | −0.983620 | − | 0.180253i | \(-0.942309\pi\) | ||||
0.983620 | − | 0.180253i | \(-0.0576915\pi\) | |||||||
\(278\) | 2.24621i | 0.134719i | ||||||||
\(279\) | −3.12311 | −0.186975 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.8769 | −0.648861 | −0.324431 | − | 0.945910i | \(-0.605173\pi\) | ||||
−0.324431 | + | 0.945910i | \(0.605173\pi\) | |||||||
\(282\) | 28.4924i | 1.69670i | ||||||||
\(283\) | 21.3693i | 1.27027i | 0.772399 | + | 0.635137i | \(0.219056\pi\) | ||||
−0.772399 | + | 0.635137i | \(0.780944\pi\) | |||||||
\(284\) | 28.4924 | 1.69071 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.75379 | −0.103704 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − 6.56155i | − 0.386643i | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.87689 | 0.168647 | ||||||||
\(292\) | 55.8617i | 3.26906i | ||||||||
\(293\) | 1.12311i | 0.0656125i | 0.999462 | + | 0.0328063i | \(0.0104444\pi\) | ||||
−0.999462 | + | 0.0328063i | \(0.989556\pi\) | |||||||
\(294\) | 17.9309 | 1.04575 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 33.6155 | 1.95386 | ||||||||
\(297\) | 1.56155i | 0.0906105i | ||||||||
\(298\) | − 31.3693i | − 1.81718i | ||||||||
\(299\) | 1.06913 | 0.0618294 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 20.4924i | 1.17921i | ||||||||
\(303\) | − 10.8769i | − 0.624861i | ||||||||
\(304\) | 36.0000 | 2.06474 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.56155 | −0.146434 | ||||||||
\(307\) | − 32.4924i | − 1.85444i | −0.374516 | − | 0.927220i | \(-0.622191\pi\) | ||||
0.374516 | − | 0.927220i | \(-0.377809\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.6847 | 0.949157 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | − 2.87689i | − 0.162872i | ||||||||
\(313\) | 33.6155i | 1.90006i | 0.312156 | + | 0.950031i | \(0.398949\pi\) | ||||
−0.312156 | + | 0.950031i | \(0.601051\pi\) | |||||||
\(314\) | 17.1231 | 0.966313 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −42.7386 | −2.40424 | ||||||||
\(317\) | 18.0000i | 1.01098i | 0.862832 | + | 0.505490i | \(0.168688\pi\) | ||||
−0.862832 | + | 0.505490i | \(0.831312\pi\) | |||||||
\(318\) | 31.3693i | 1.75910i | ||||||||
\(319\) | 12.8769 | 0.720968 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.68466 | 0.261472 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 4.68466i | − 0.260661i | ||||||||
\(324\) | −4.56155 | −0.253420 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 38.7386 | 2.14553 | ||||||||
\(327\) | − 6.87689i | − 0.380293i | ||||||||
\(328\) | 23.3693i | 1.29035i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −34.9309 | −1.91997 | −0.959987 | − | 0.280044i | \(-0.909651\pi\) | ||||
−0.959987 | + | 0.280044i | \(0.909651\pi\) | |||||||
\(332\) | 4.00000i | 0.219529i | ||||||||
\(333\) | − 5.12311i | − 0.280744i | ||||||||
\(334\) | 50.7386 | 2.77629 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.7386i | 0.911811i | 0.890028 | + | 0.455906i | \(0.150685\pi\) | ||||
−0.890028 | + | 0.455906i | \(0.849315\pi\) | |||||||
\(338\) | 32.8078i | 1.78451i | ||||||||
\(339\) | −0.438447 | −0.0238132 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.87689 | 0.264099 | ||||||||
\(342\) | − 12.0000i | − 0.648886i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 30.7386 | 1.65732 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.63068 | −0.248947 | ||||||||
\(347\) | 8.49242i | 0.455897i | 0.973673 | + | 0.227949i | \(0.0732018\pi\) | ||||
−0.973673 | + | 0.227949i | \(0.926798\pi\) | |||||||
\(348\) | 37.6155i | 2.01640i | ||||||||
\(349\) | −11.5616 | −0.618876 | −0.309438 | − | 0.950920i | \(-0.600141\pi\) | ||||
−0.309438 | + | 0.950920i | \(0.600141\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.438447 | −0.0234026 | ||||||||
\(352\) | 10.2462i | 0.546125i | ||||||||
\(353\) | − 10.4924i | − 0.558455i | −0.960225 | − | 0.279228i | \(-0.909922\pi\) | ||||
0.960225 | − | 0.279228i | \(-0.0900784\pi\) | |||||||
\(354\) | −18.2462 | −0.969775 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5.12311 | −0.271524 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.24621i | 0.118716i | ||||||||
\(359\) | −14.2462 | −0.751886 | −0.375943 | − | 0.926643i | \(-0.622681\pi\) | ||||
−0.375943 | + | 0.926643i | \(0.622681\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.94602 | 0.155054 | ||||||||
\(362\) | 15.3693i | 0.807793i | ||||||||
\(363\) | 8.56155i | 0.449365i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 23.3693 | 1.22153 | ||||||||
\(367\) | 1.75379i | 0.0915470i | 0.998952 | + | 0.0457735i | \(0.0145753\pi\) | ||||
−0.998952 | + | 0.0457735i | \(0.985425\pi\) | |||||||
\(368\) | − 18.7386i | − 0.976819i | ||||||||
\(369\) | 3.56155 | 0.185407 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 14.2462i | 0.738632i | ||||||||
\(373\) | − 0.246211i | − 0.0127483i | −0.999980 | − | 0.00637417i | \(-0.997971\pi\) | ||||
0.999980 | − | 0.00637417i | \(-0.00202897\pi\) | |||||||
\(374\) | 4.00000 | 0.206835 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 72.9848 | 3.76391 | ||||||||
\(377\) | 3.61553i | 0.186209i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.0000 | 0.616399 | 0.308199 | − | 0.951322i | \(-0.400274\pi\) | ||||
0.308199 | + | 0.951322i | \(0.400274\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.8078 | −1.01478 | ||||||||
\(382\) | − 12.4924i | − 0.639168i | ||||||||
\(383\) | 6.24621i | 0.319166i | 0.987184 | + | 0.159583i | \(0.0510150\pi\) | ||||
−0.987184 | + | 0.159583i | \(0.948985\pi\) | |||||||
\(384\) | 9.43845 | 0.481654 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 19.8617 | 1.01094 | ||||||||
\(387\) | − 4.68466i | − 0.238135i | ||||||||
\(388\) | − 13.1231i | − 0.666225i | ||||||||
\(389\) | −35.8617 | −1.81826 | −0.909131 | − | 0.416510i | \(-0.863253\pi\) | ||||
−0.909131 | + | 0.416510i | \(0.863253\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.43845 | −0.123318 | ||||||||
\(392\) | − 45.9309i | − 2.31986i | ||||||||
\(393\) | − 14.4384i | − 0.728323i | ||||||||
\(394\) | −22.8769 | −1.15252 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 7.12311 | 0.357950 | ||||||||
\(397\) | 19.3693i | 0.972118i | 0.873926 | + | 0.486059i | \(0.161566\pi\) | ||||
−0.873926 | + | 0.486059i | \(0.838434\pi\) | |||||||
\(398\) | − 40.9848i | − 2.05438i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 39.1771 | 1.95641 | 0.978205 | − | 0.207641i | \(-0.0665787\pi\) | ||||
0.978205 | + | 0.207641i | \(0.0665787\pi\) | |||||||
\(402\) | − 10.2462i | − 0.511035i | ||||||||
\(403\) | 1.36932i | 0.0682105i | ||||||||
\(404\) | −49.6155 | −2.46846 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.00000i | 0.396545i | ||||||||
\(408\) | 6.56155i | 0.324845i | ||||||||
\(409\) | 14.6847 | 0.726110 | 0.363055 | − | 0.931768i | \(-0.381734\pi\) | ||||
0.363055 | + | 0.931768i | \(0.381734\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.246211 | −0.0121447 | ||||||||
\(412\) | − 76.1080i | − 3.74957i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −6.24621 | −0.306985 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.87689 | −0.141051 | ||||||||
\(417\) | − 0.876894i | − 0.0429417i | ||||||||
\(418\) | 18.7386i | 0.916537i | ||||||||
\(419\) | 0.492423 | 0.0240564 | 0.0120282 | − | 0.999928i | \(-0.496171\pi\) | ||||
0.0120282 | + | 0.999928i | \(0.496171\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.4384 | 1.19106 | 0.595529 | − | 0.803334i | \(-0.296943\pi\) | ||||
0.595529 | + | 0.803334i | \(0.296943\pi\) | |||||||
\(422\) | 34.2462i | 1.66708i | ||||||||
\(423\) | − 11.1231i | − 0.540824i | ||||||||
\(424\) | 80.3542 | 3.90234 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −16.0000 | −0.775203 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − 21.3693i | − 1.03292i | ||||||||
\(429\) | 0.684658 | 0.0330556 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.0000 | −1.15604 | −0.578020 | − | 0.816023i | \(-0.696174\pi\) | ||||
−0.578020 | + | 0.816023i | \(0.696174\pi\) | |||||||
\(432\) | 7.68466i | 0.369728i | ||||||||
\(433\) | 26.6847i | 1.28238i | 0.767381 | + | 0.641191i | \(0.221560\pi\) | ||||
−0.767381 | + | 0.641191i | \(0.778440\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −31.3693 | −1.50232 | ||||||||
\(437\) | − 11.4233i | − 0.546450i | ||||||||
\(438\) | − 31.3693i | − 1.49888i | ||||||||
\(439\) | 22.2462 | 1.06175 | 0.530877 | − | 0.847449i | \(-0.321863\pi\) | ||||
0.530877 | + | 0.847449i | \(0.321863\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.00000 | −0.333333 | ||||||||
\(442\) | 1.12311i | 0.0534207i | ||||||||
\(443\) | − 31.1231i | − 1.47870i | −0.673319 | − | 0.739352i | \(-0.735132\pi\) | ||||
0.673319 | − | 0.739352i | \(-0.264868\pi\) | |||||||
\(444\) | −23.3693 | −1.10906 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 38.2462 | 1.81101 | ||||||||
\(447\) | 12.2462i | 0.579226i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −36.7386 | −1.73380 | −0.866902 | − | 0.498479i | \(-0.833892\pi\) | ||||
−0.866902 | + | 0.498479i | \(0.833892\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.56155 | −0.261883 | ||||||||
\(452\) | 2.00000i | 0.0940721i | ||||||||
\(453\) | − 8.00000i | − 0.375873i | ||||||||
\(454\) | −36.0000 | −1.68956 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −30.7386 | −1.43947 | ||||||||
\(457\) | − 13.8078i | − 0.645900i | −0.946416 | − | 0.322950i | \(-0.895325\pi\) | ||||
0.946416 | − | 0.322950i | \(-0.104675\pi\) | |||||||
\(458\) | − 15.3693i | − 0.718161i | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.24621 | −0.384064 | −0.192032 | − | 0.981389i | \(-0.561508\pi\) | ||||
−0.192032 | + | 0.981389i | \(0.561508\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 40.9848i | − 1.90473i | −0.304965 | − | 0.952364i | \(-0.598645\pi\) | ||||
0.304965 | − | 0.952364i | \(-0.401355\pi\) | |||||||
\(464\) | 63.3693 | 2.94185 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.12311 | 0.422620 | ||||||||
\(467\) | − 21.3693i | − 0.988854i | −0.869219 | − | 0.494427i | \(-0.835378\pi\) | ||||
0.869219 | − | 0.494427i | \(-0.164622\pi\) | |||||||
\(468\) | 2.00000i | 0.0924500i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.68466 | −0.308013 | ||||||||
\(472\) | 46.7386i | 2.15132i | ||||||||
\(473\) | 7.31534i | 0.336360i | ||||||||
\(474\) | 24.0000 | 1.10236 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 12.2462i | − 0.560715i | ||||||||
\(478\) | 16.0000i | 0.731823i | ||||||||
\(479\) | −24.3002 | −1.11030 | −0.555152 | − | 0.831749i | \(-0.687340\pi\) | ||||
−0.555152 | + | 0.831749i | \(0.687340\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.24621 | −0.102418 | ||||||||
\(482\) | 8.63068i | 0.393117i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 39.0540 | 1.77518 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.56155 | 0.116194 | ||||||||
\(487\) | − 17.3693i | − 0.787079i | −0.919308 | − | 0.393539i | \(-0.871250\pi\) | ||||
0.919308 | − | 0.393539i | \(-0.128750\pi\) | |||||||
\(488\) | − 59.8617i | − 2.70981i | ||||||||
\(489\) | −15.1231 | −0.683890 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.3693 | −0.964384 | −0.482192 | − | 0.876066i | \(-0.660159\pi\) | ||||
−0.482192 | + | 0.876066i | \(0.660159\pi\) | |||||||
\(492\) | − 16.2462i | − 0.732436i | ||||||||
\(493\) | − 8.24621i | − 0.371391i | ||||||||
\(494\) | −5.26137 | −0.236720 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 24.0000 | 1.07763 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | − 2.24621i | − 0.100655i | ||||||||
\(499\) | −13.3693 | −0.598493 | −0.299246 | − | 0.954176i | \(-0.596735\pi\) | ||||
−0.299246 | + | 0.954176i | \(0.596735\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −19.8078 | −0.884946 | ||||||||
\(502\) | 21.7538i | 0.970919i | ||||||||
\(503\) | − 29.5616i | − 1.31808i | −0.752106 | − | 0.659042i | \(-0.770962\pi\) | ||||
0.752106 | − | 0.659042i | \(-0.229038\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 9.75379 | 0.433609 | ||||||||
\(507\) | − 12.8078i | − 0.568813i | ||||||||
\(508\) | 90.3542i | 4.00882i | ||||||||
\(509\) | −25.1231 | −1.11356 | −0.556781 | − | 0.830659i | \(-0.687964\pi\) | ||||
−0.556781 | + | 0.830659i | \(0.687964\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − 50.4233i | − 2.22842i | ||||||||
\(513\) | 4.68466i | 0.206833i | ||||||||
\(514\) | −39.3693 | −1.73651 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −21.3693 | −0.940732 | ||||||||
\(517\) | 17.3693i | 0.763902i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.80776 | 0.0793520 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.5616 | −1.55798 | −0.778990 | − | 0.627036i | \(-0.784268\pi\) | ||||
−0.778990 | + | 0.627036i | \(0.784268\pi\) | |||||||
\(522\) | − 21.1231i | − 0.924533i | ||||||||
\(523\) | − 20.0000i | − 0.874539i | −0.899331 | − | 0.437269i | \(-0.855946\pi\) | ||||
0.899331 | − | 0.437269i | \(-0.144054\pi\) | |||||||
\(524\) | −65.8617 | −2.87718 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 52.4924 | 2.28878 | ||||||||
\(527\) | − 3.12311i | − 0.136045i | ||||||||
\(528\) | − 12.0000i | − 0.522233i | ||||||||
\(529\) | 17.0540 | 0.741477 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.12311 | 0.309116 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 1.56155i | − 0.0676384i | ||||||||
\(534\) | 2.87689 | 0.124495 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −26.2462 | −1.13366 | ||||||||
\(537\) | − 0.876894i | − 0.0378408i | ||||||||
\(538\) | − 42.1080i | − 1.81540i | ||||||||
\(539\) | 10.9309 | 0.470826 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.1080 | 1.46642 | 0.733208 | − | 0.680005i | \(-0.238022\pi\) | ||||
0.733208 | + | 0.680005i | \(0.238022\pi\) | |||||||
\(542\) | 50.7386i | 2.17941i | ||||||||
\(543\) | − 6.00000i | − 0.257485i | ||||||||
\(544\) | 6.56155 | 0.281324 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 28.0000i | − 1.19719i | −0.801050 | − | 0.598597i | \(-0.795725\pi\) | ||||
0.801050 | − | 0.598597i | \(-0.204275\pi\) | |||||||
\(548\) | 1.12311i | 0.0479767i | ||||||||
\(549\) | −9.12311 | −0.389365 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 38.6307 | 1.64572 | ||||||||
\(552\) | 16.0000i | 0.681005i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 15.3693 | 0.652980 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.00000 | −0.169638 | ||||||||
\(557\) | − 26.4924i | − 1.12252i | −0.827640 | − | 0.561260i | \(-0.810317\pi\) | ||||
0.827640 | − | 0.561260i | \(-0.189683\pi\) | |||||||
\(558\) | − 8.00000i | − 0.338667i | ||||||||
\(559\) | −2.05398 | −0.0868739 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.56155 | −0.0659288 | ||||||||
\(562\) | − 27.8617i | − 1.17528i | ||||||||
\(563\) | 31.1231i | 1.31168i | 0.754899 | + | 0.655841i | \(0.227686\pi\) | ||||
−0.754899 | + | 0.655841i | \(0.772314\pi\) | |||||||
\(564\) | −50.7386 | −2.13648 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −54.7386 | −2.30084 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 40.9848i | 1.71969i | ||||||||
\(569\) | −21.1231 | −0.885527 | −0.442763 | − | 0.896639i | \(-0.646002\pi\) | ||||
−0.442763 | + | 0.896639i | \(0.646002\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −30.7386 | −1.28637 | −0.643186 | − | 0.765710i | \(-0.722388\pi\) | ||||
−0.643186 | + | 0.765710i | \(0.722388\pi\) | |||||||
\(572\) | − 3.12311i | − 0.130584i | ||||||||
\(573\) | 4.87689i | 0.203735i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.43845 | 0.0599353 | ||||||||
\(577\) | 3.94602i | 0.164275i | 0.996621 | + | 0.0821376i | \(0.0261747\pi\) | ||||
−0.996621 | + | 0.0821376i | \(0.973825\pi\) | |||||||
\(578\) | − 2.56155i | − 0.106547i | ||||||||
\(579\) | −7.75379 | −0.322236 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 7.36932i | 0.305468i | ||||||||
\(583\) | 19.1231i | 0.791998i | ||||||||
\(584\) | −80.3542 | −3.32508 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.87689 | −0.118843 | ||||||||
\(587\) | 28.9848i | 1.19633i | 0.801372 | + | 0.598166i | \(0.204104\pi\) | ||||
−0.801372 | + | 0.598166i | \(0.795896\pi\) | |||||||
\(588\) | 31.9309i | 1.31681i | ||||||||
\(589\) | 14.6307 | 0.602847 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.93087 | 0.367367 | ||||||||
\(592\) | 39.3693i | 1.61807i | ||||||||
\(593\) | 27.7538i | 1.13971i | 0.821745 | + | 0.569856i | \(0.193001\pi\) | ||||
−0.821745 | + | 0.569856i | \(0.806999\pi\) | |||||||
\(594\) | −4.00000 | −0.164122 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 55.8617 | 2.28819 | ||||||||
\(597\) | 16.0000i | 0.654836i | ||||||||
\(598\) | 2.73863i | 0.111991i | ||||||||
\(599\) | 0.384472 | 0.0157091 | 0.00785455 | − | 0.999969i | \(-0.497500\pi\) | ||||
0.00785455 | + | 0.999969i | \(0.497500\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.9848 | −1.26390 | −0.631949 | − | 0.775010i | \(-0.717745\pi\) | ||||
−0.631949 | + | 0.775010i | \(0.717745\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.00000i | 0.162893i | ||||||||
\(604\) | −36.4924 | −1.48486 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 27.8617 | 1.13181 | ||||||||
\(607\) | 9.36932i | 0.380289i | 0.981756 | + | 0.190144i | \(0.0608956\pi\) | ||||
−0.981756 | + | 0.190144i | \(0.939104\pi\) | |||||||
\(608\) | 30.7386i | 1.24662i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.87689 | −0.197298 | ||||||||
\(612\) | − 4.56155i | − 0.184390i | ||||||||
\(613\) | 14.6847i | 0.593108i | 0.955016 | + | 0.296554i | \(0.0958374\pi\) | ||||
−0.955016 | + | 0.296554i | \(0.904163\pi\) | |||||||
\(614\) | 83.2311 | 3.35893 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 44.2462i | 1.78129i | 0.454704 | + | 0.890643i | \(0.349745\pi\) | ||||
−0.454704 | + | 0.890643i | \(0.650255\pi\) | |||||||
\(618\) | 42.7386i | 1.71920i | ||||||||
\(619\) | −5.36932 | −0.215811 | −0.107906 | − | 0.994161i | \(-0.534414\pi\) | ||||
−0.107906 | + | 0.994161i | \(0.534414\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.43845 | 0.0978515 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 3.36932 | 0.134881 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −86.1080 | −3.44157 | ||||||||
\(627\) | − 7.31534i | − 0.292147i | ||||||||
\(628\) | 30.4924i | 1.21678i | ||||||||
\(629\) | 5.12311 | 0.204272 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.684658 | −0.0272558 | −0.0136279 | − | 0.999907i | \(-0.504338\pi\) | ||||
−0.0136279 | + | 0.999907i | \(0.504338\pi\) | |||||||
\(632\) | − 61.4773i | − 2.44543i | ||||||||
\(633\) | − 13.3693i | − 0.531383i | ||||||||
\(634\) | −46.1080 | −1.83118 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −55.8617 | −2.21506 | ||||||||
\(637\) | 3.06913i | 0.121603i | ||||||||
\(638\) | 32.9848i | 1.30588i | ||||||||
\(639\) | 6.24621 | 0.247096 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28.9309 | −1.14270 | −0.571350 | − | 0.820706i | \(-0.693580\pi\) | ||||
−0.571350 | + | 0.820706i | \(0.693580\pi\) | |||||||
\(642\) | 12.0000i | 0.473602i | ||||||||
\(643\) | − 13.7538i | − 0.542396i | −0.962524 | − | 0.271198i | \(-0.912580\pi\) | ||||
0.962524 | − | 0.271198i | \(-0.0874199\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.0000 | 0.472134 | ||||||||
\(647\) | 9.36932i | 0.368346i | 0.982894 | + | 0.184173i | \(0.0589606\pi\) | ||||
−0.982894 | + | 0.184173i | \(0.941039\pi\) | |||||||
\(648\) | − 6.56155i | − 0.257762i | ||||||||
\(649\) | −11.1231 | −0.436620 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 68.9848i | 2.70166i | ||||||||
\(653\) | − 32.9309i | − 1.28868i | −0.764737 | − | 0.644342i | \(-0.777131\pi\) | ||||
0.764737 | − | 0.644342i | \(-0.222869\pi\) | |||||||
\(654\) | 17.6155 | 0.688822 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −27.3693 | −1.06859 | ||||||||
\(657\) | 12.2462i | 0.477770i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.86174 | 0.384159 | 0.192079 | − | 0.981379i | \(-0.438477\pi\) | ||||
0.192079 | + | 0.981379i | \(0.438477\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.3153 | 0.517907 | 0.258953 | − | 0.965890i | \(-0.416622\pi\) | ||||
0.258953 | + | 0.965890i | \(0.416622\pi\) | |||||||
\(662\) | − 89.4773i | − 3.47763i | ||||||||
\(663\) | − 0.438447i | − 0.0170279i | ||||||||
\(664\) | −5.75379 | −0.223290 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 13.1231 | 0.508510 | ||||||||
\(667\) | − 20.1080i | − 0.778583i | ||||||||
\(668\) | 90.3542i | 3.49591i | ||||||||
\(669\) | −14.9309 | −0.577261 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.2462 | 0.549969 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 0.738634i | − 0.0284722i | −0.999899 | − | 0.0142361i | \(-0.995468\pi\) | ||||
0.999899 | − | 0.0142361i | \(-0.00453165\pi\) | |||||||
\(674\) | −42.8769 | −1.65156 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −58.4233 | −2.24705 | ||||||||
\(677\) | 1.31534i | 0.0505527i | 0.999681 | + | 0.0252763i | \(0.00804657\pi\) | ||||
−0.999681 | + | 0.0252763i | \(0.991953\pi\) | |||||||
\(678\) | − 1.12311i | − 0.0431326i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.0540 | 0.538550 | ||||||||
\(682\) | 12.4924i | 0.478360i | ||||||||
\(683\) | − 9.56155i | − 0.365863i | −0.983126 | − | 0.182931i | \(-0.941441\pi\) | ||||
0.983126 | − | 0.182931i | \(-0.0585586\pi\) | |||||||
\(684\) | 21.3693 | 0.817076 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.00000i | 0.228914i | ||||||||
\(688\) | 36.0000i | 1.37249i | ||||||||
\(689\) | −5.36932 | −0.204555 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.9848 | −1.10264 | −0.551318 | − | 0.834295i | \(-0.685875\pi\) | ||||
−0.551318 | + | 0.834295i | \(0.685875\pi\) | |||||||
\(692\) | − 8.24621i | − 0.313474i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21.7538 | −0.825763 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −54.1080 | −2.05096 | ||||||||
\(697\) | 3.56155i | 0.134903i | ||||||||
\(698\) | − 29.6155i | − 1.12096i | ||||||||
\(699\) | −3.56155 | −0.134710 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.3693 | 0.580491 | 0.290246 | − | 0.956952i | \(-0.406263\pi\) | ||||
0.290246 | + | 0.956952i | \(0.406263\pi\) | |||||||
\(702\) | − 1.12311i | − 0.0423889i | ||||||||
\(703\) | 24.0000i | 0.905177i | ||||||||
\(704\) | −2.24621 | −0.0846573 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 26.8769 | 1.01153 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | − 32.4924i | − 1.22114i | ||||||||
\(709\) | 44.7386 | 1.68019 | 0.840097 | − | 0.542436i | \(-0.182498\pi\) | ||||
0.840097 | + | 0.542436i | \(0.182498\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.36932 | −0.351377 | ||||||||
\(712\) | − 7.36932i | − 0.276177i | ||||||||
\(713\) | − 7.61553i | − 0.285204i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.00000 | −0.149487 | ||||||||
\(717\) | − 6.24621i | − 0.233269i | ||||||||
\(718\) | − 36.4924i | − 1.36189i | ||||||||
\(719\) | 11.8078 | 0.440355 | 0.220178 | − | 0.975460i | \(-0.429336\pi\) | ||||
0.220178 | + | 0.975460i | \(0.429336\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 7.54640i | 0.280848i | ||||||||
\(723\) | − 3.36932i | − 0.125306i | ||||||||
\(724\) | −27.3693 | −1.01717 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −21.9309 | −0.813931 | ||||||||
\(727\) | 8.00000i | 0.296704i | 0.988935 | + | 0.148352i | \(0.0473968\pi\) | ||||
−0.988935 | + | 0.148352i | \(0.952603\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.68466 | 0.173268 | ||||||||
\(732\) | 41.6155i | 1.53815i | ||||||||
\(733\) | − 11.7538i | − 0.434136i | −0.976156 | − | 0.217068i | \(-0.930351\pi\) | ||||
0.976156 | − | 0.217068i | \(-0.0696494\pi\) | |||||||
\(734\) | −4.49242 | −0.165818 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16.0000 | 0.589768 | ||||||||
\(737\) | − 6.24621i | − 0.230082i | ||||||||
\(738\) | 9.12311i | 0.335826i | ||||||||
\(739\) | 20.6847 | 0.760897 | 0.380449 | − | 0.924802i | \(-0.375770\pi\) | ||||
0.380449 | + | 0.924802i | \(0.375770\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.05398 | 0.0754547 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.4924i | 1.04529i | 0.852552 | + | 0.522643i | \(0.175054\pi\) | ||||
−0.852552 | + | 0.522643i | \(0.824946\pi\) | |||||||
\(744\) | −20.4924 | −0.751289 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0.630683 | 0.0230909 | ||||||||
\(747\) | 0.876894i | 0.0320839i | ||||||||
\(748\) | 7.12311i | 0.260447i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.3693 | −0.925740 | −0.462870 | − | 0.886426i | \(-0.653180\pi\) | ||||
−0.462870 | + | 0.886426i | \(0.653180\pi\) | |||||||
\(752\) | 85.4773i | 3.11704i | ||||||||
\(753\) | − 8.49242i | − 0.309481i | ||||||||
\(754\) | −9.26137 | −0.337279 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 16.0540i | − 0.583492i | −0.956496 | − | 0.291746i | \(-0.905764\pi\) | ||||
0.956496 | − | 0.291746i | \(-0.0942361\pi\) | |||||||
\(758\) | 30.7386i | 1.11648i | ||||||||
\(759\) | −3.80776 | −0.138213 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.7538 | −0.571074 | −0.285537 | − | 0.958368i | \(-0.592172\pi\) | ||||
−0.285537 | + | 0.958368i | \(0.592172\pi\) | |||||||
\(762\) | − 50.7386i | − 1.83807i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 22.2462 | 0.804840 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.0000 | −0.578103 | ||||||||
\(767\) | − 3.12311i | − 0.112769i | ||||||||
\(768\) | 27.0540i | 0.976226i | ||||||||
\(769\) | −40.5464 | −1.46214 | −0.731070 | − | 0.682302i | \(-0.760979\pi\) | ||||
−0.731070 | + | 0.682302i | \(0.760979\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.3693 | 0.553512 | ||||||||
\(772\) | 35.3693i | 1.27297i | ||||||||
\(773\) | − 8.63068i | − 0.310424i | −0.987881 | − | 0.155212i | \(-0.950394\pi\) | ||||
0.987881 | − | 0.155212i | \(-0.0496061\pi\) | |||||||
\(774\) | 12.0000 | 0.431331 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 18.8769 | 0.677641 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 91.8617i | − 3.29340i | ||||||||
\(779\) | −16.6847 | −0.597790 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.75379 | −0.349018 | ||||||||
\(782\) | − 6.24621i | − 0.223364i | ||||||||
\(783\) | 8.24621i | 0.294696i | ||||||||
\(784\) | 53.7926 | 1.92116 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 36.9848 | 1.31921 | ||||||||
\(787\) | 10.2462i | 0.365238i | 0.983184 | + | 0.182619i | \(0.0584575\pi\) | ||||
−0.983184 | + | 0.182619i | \(0.941543\pi\) | |||||||
\(788\) | − 40.7386i | − 1.45125i | ||||||||
\(789\) | −20.4924 | −0.729550 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 10.2462i | 0.364083i | ||||||||
\(793\) | 4.00000i | 0.142044i | ||||||||
\(794\) | −49.6155 | −1.76079 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 72.9848 | 2.58688 | ||||||||
\(797\) | 9.61553i | 0.340599i | 0.985392 | + | 0.170300i | \(0.0544736\pi\) | ||||
−0.985392 | + | 0.170300i | \(0.945526\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.1231 | 0.393507 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.12311 | −0.0396830 | ||||||||
\(802\) | 100.354i | 3.54363i | ||||||||
\(803\) | − 19.1231i | − 0.674840i | ||||||||
\(804\) | 18.2462 | 0.643494 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.50758 | −0.123549 | ||||||||
\(807\) | 16.4384i | 0.578661i | ||||||||
\(808\) | − 71.3693i | − 2.51076i | ||||||||
\(809\) | −15.9460 | −0.560632 | −0.280316 | − | 0.959908i | \(-0.590439\pi\) | ||||
−0.280316 | + | 0.959908i | \(0.590439\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −45.3693 | −1.59313 | −0.796566 | − | 0.604551i | \(-0.793352\pi\) | ||||
−0.796566 | + | 0.604551i | \(0.793352\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 19.8078i | − 0.694689i | ||||||||
\(814\) | −20.4924 | −0.718259 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −7.68466 | −0.269017 | ||||||||
\(817\) | 21.9460i | 0.767794i | ||||||||
\(818\) | 37.6155i | 1.31520i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.4384 | −0.434105 | −0.217052 | − | 0.976160i | \(-0.569644\pi\) | ||||
−0.217052 | + | 0.976160i | \(0.569644\pi\) | |||||||
\(822\) | − 0.630683i | − 0.0219976i | ||||||||
\(823\) | 3.50758i | 0.122266i | 0.998130 | + | 0.0611332i | \(0.0194715\pi\) | ||||
−0.998130 | + | 0.0611332i | \(0.980529\pi\) | |||||||
\(824\) | 109.477 | 3.81382 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 47.4233i | − 1.64907i | −0.565811 | − | 0.824535i | \(-0.691437\pi\) | ||||
0.565811 | − | 0.824535i | \(-0.308563\pi\) | |||||||
\(828\) | − 11.1231i | − 0.386555i | ||||||||
\(829\) | −17.5076 | −0.608063 | −0.304032 | − | 0.952662i | \(-0.598333\pi\) | ||||
−0.304032 | + | 0.952662i | \(0.598333\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.00000 | −0.208138 | ||||||||
\(832\) | − 0.630683i | − 0.0218650i | ||||||||
\(833\) | − 7.00000i | − 0.242536i | ||||||||
\(834\) | 2.24621 | 0.0777799 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −33.3693 | −1.15410 | ||||||||
\(837\) | 3.12311i | 0.107950i | ||||||||
\(838\) | 1.26137i | 0.0435732i | ||||||||
\(839\) | 26.0540 | 0.899483 | 0.449742 | − | 0.893159i | \(-0.351516\pi\) | ||||
0.449742 | + | 0.893159i | \(0.351516\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 39.0000 | 1.34483 | ||||||||
\(842\) | 62.6004i | 2.15735i | ||||||||
\(843\) | 10.8769i | 0.374620i | ||||||||
\(844\) | −60.9848 | −2.09918 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 28.4924 | 0.979590 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 94.1080i | 3.23168i | ||||||||
\(849\) | 21.3693 | 0.733393 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.4924 | 0.428235 | ||||||||
\(852\) | − 28.4924i | − 0.976134i | ||||||||
\(853\) | − 28.7386i | − 0.983992i | −0.870597 | − | 0.491996i | \(-0.836267\pi\) | ||||
0.870597 | − | 0.491996i | \(-0.163733\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 30.7386 | 1.05062 | ||||||||
\(857\) | 6.00000i | 0.204956i | 0.994735 | + | 0.102478i | \(0.0326771\pi\) | ||||
−0.994735 | + | 0.102478i | \(0.967323\pi\) | |||||||
\(858\) | 1.75379i | 0.0598734i | ||||||||
\(859\) | −12.0000 | −0.409435 | −0.204717 | − | 0.978821i | \(-0.565628\pi\) | ||||
−0.204717 | + | 0.978821i | \(0.565628\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − 61.4773i | − 2.09392i | ||||||||
\(863\) | − 9.75379i | − 0.332023i | −0.986124 | − | 0.166011i | \(-0.946911\pi\) | ||||
0.986124 | − | 0.166011i | \(-0.0530889\pi\) | |||||||
\(864\) | −6.56155 | −0.223229 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −68.3542 | −2.32277 | ||||||||
\(867\) | 1.00000i | 0.0339618i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.6307 | 0.496312 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.75379 | 0.0594249 | ||||||||
\(872\) | − 45.1231i | − 1.52806i | ||||||||
\(873\) | − 2.87689i | − 0.0973681i | ||||||||
\(874\) | 29.2614 | 0.989780 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 55.8617 | 1.88739 | ||||||||
\(877\) | 34.0000i | 1.14810i | 0.818821 | + | 0.574049i | \(0.194628\pi\) | ||||
−0.818821 | + | 0.574049i | \(0.805372\pi\) | |||||||
\(878\) | 56.9848i | 1.92315i | ||||||||
\(879\) | 1.12311 | 0.0378814 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.2462 | 1.35593 | 0.677965 | − | 0.735095i | \(-0.262862\pi\) | ||||
0.677965 | + | 0.735095i | \(0.262862\pi\) | |||||||
\(882\) | − 17.9309i | − 0.603764i | ||||||||
\(883\) | − 23.4233i | − 0.788257i | −0.919055 | − | 0.394128i | \(-0.871047\pi\) | ||||
0.919055 | − | 0.394128i | \(-0.128953\pi\) | |||||||
\(884\) | −2.00000 | −0.0672673 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 79.7235 | 2.67836 | ||||||||
\(887\) | − 18.4384i | − 0.619102i | −0.950883 | − | 0.309551i | \(-0.899821\pi\) | ||||
0.950883 | − | 0.309551i | \(-0.100179\pi\) | |||||||
\(888\) | − 33.6155i | − 1.12806i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.56155 | 0.0523140 | ||||||||
\(892\) | 68.1080i | 2.28042i | ||||||||
\(893\) | 52.1080i | 1.74373i | ||||||||
\(894\) | −31.3693 | −1.04915 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 1.06913i | − 0.0356972i | ||||||||
\(898\) | − 94.1080i | − 3.14042i | ||||||||
\(899\) | 25.7538 | 0.858937 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.2462 | 0.407980 | ||||||||
\(902\) | − 14.2462i | − 0.474347i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.87689 | −0.0956841 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 20.4924 | 0.680815 | ||||||||
\(907\) | 9.86174i | 0.327454i | 0.986506 | + | 0.163727i | \(0.0523516\pi\) | ||||
−0.986506 | + | 0.163727i | \(0.947648\pi\) | |||||||
\(908\) | − 64.1080i | − 2.12750i | ||||||||
\(909\) | −10.8769 | −0.360764 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.3002 | 0.805101 | 0.402551 | − | 0.915398i | \(-0.368124\pi\) | ||||
0.402551 | + | 0.915398i | \(0.368124\pi\) | |||||||
\(912\) | − 36.0000i | − 1.19208i | ||||||||
\(913\) | − 1.36932i | − 0.0453178i | ||||||||
\(914\) | 35.3693 | 1.16991 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 27.3693 | 0.904308 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.56155i | 0.0845438i | ||||||||
\(919\) | 16.6847 | 0.550376 | 0.275188 | − | 0.961390i | \(-0.411260\pi\) | ||||
0.275188 | + | 0.961390i | \(0.411260\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −32.4924 | −1.07066 | ||||||||
\(922\) | − 21.1231i | − 0.695652i | ||||||||
\(923\) | − 2.73863i | − 0.0901432i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 104.985 | 3.45002 | ||||||||
\(927\) | − 16.6847i | − 0.547996i | ||||||||
\(928\) | 54.1080i | 1.77618i | ||||||||
\(929\) | −3.06913 | −0.100695 | −0.0503474 | − | 0.998732i | \(-0.516033\pi\) | ||||
−0.0503474 | + | 0.998732i | \(0.516033\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 32.7926 | 1.07473 | ||||||||
\(932\) | 16.2462i | 0.532162i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 54.7386 | 1.79110 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.87689 | −0.0940342 | ||||||||
\(937\) | 22.0000i | 0.718709i | 0.933201 | + | 0.359354i | \(0.117003\pi\) | ||||
−0.933201 | + | 0.359354i | \(0.882997\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 33.6155 | 1.09700 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.0000 | 0.977972 | 0.488986 | − | 0.872292i | \(-0.337367\pi\) | ||||
0.488986 | + | 0.872292i | \(0.337367\pi\) | |||||||
\(942\) | − 17.1231i | − 0.557901i | ||||||||
\(943\) | 8.68466i | 0.282811i | ||||||||
\(944\) | −54.7386 | −1.78159 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −18.7386 | −0.609246 | ||||||||
\(947\) | − 12.0000i | − 0.389948i | −0.980808 | − | 0.194974i | \(-0.937538\pi\) | ||||
0.980808 | − | 0.194974i | \(-0.0624622\pi\) | |||||||
\(948\) | 42.7386i | 1.38809i | ||||||||
\(949\) | 5.36932 | 0.174295 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18.0000 | 0.583690 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.3542i | 1.17763i | 0.808269 | + | 0.588813i | \(0.200405\pi\) | ||||
−0.808269 | + | 0.588813i | \(0.799595\pi\) | |||||||
\(954\) | 31.3693 | 1.01562 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −28.4924 | −0.921511 | ||||||||
\(957\) | − 12.8769i | − 0.416251i | ||||||||
\(958\) | − 62.2462i | − 2.01108i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.2462 | −0.685362 | ||||||||
\(962\) | − 5.75379i | − 0.185510i | ||||||||
\(963\) | − 4.68466i | − 0.150961i | ||||||||
\(964\) | −15.3693 | −0.495012 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 42.4384i | − 1.36473i | −0.731012 | − | 0.682364i | \(-0.760952\pi\) | ||||
0.731012 | − | 0.682364i | \(-0.239048\pi\) | |||||||
\(968\) | 56.1771i | 1.80560i | ||||||||
\(969\) | −4.68466 | −0.150493 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −43.6155 | −1.39969 | −0.699844 | − | 0.714295i | \(-0.746747\pi\) | ||||
−0.699844 | + | 0.714295i | \(0.746747\pi\) | |||||||
\(972\) | 4.56155i | 0.146312i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 44.4924 | 1.42563 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 70.1080 | 2.24410 | ||||||||
\(977\) | − 8.24621i | − 0.263820i | −0.991262 | − | 0.131910i | \(-0.957889\pi\) | ||||
0.991262 | − | 0.131910i | \(-0.0421109\pi\) | |||||||
\(978\) | − 38.7386i | − 1.23872i | ||||||||
\(979\) | 1.75379 | 0.0560513 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.87689 | −0.219562 | ||||||||
\(982\) | − 54.7386i | − 1.74678i | ||||||||
\(983\) | 30.9309i | 0.986542i | 0.869876 | + | 0.493271i | \(0.164199\pi\) | ||||
−0.869876 | + | 0.493271i | \(0.835801\pi\) | |||||||
\(984\) | 23.3693 | 0.744987 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 21.1231 | 0.672697 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − 9.36932i | − 0.298078i | ||||||||
\(989\) | 11.4233 | 0.363240 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42.7386 | 1.35764 | 0.678819 | − | 0.734306i | \(-0.262492\pi\) | ||||
0.678819 | + | 0.734306i | \(0.262492\pi\) | |||||||
\(992\) | 20.4924i | 0.650635i | ||||||||
\(993\) | 34.9309i | 1.10850i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 4.00000 | 0.126745 | ||||||||
\(997\) | 10.0000i | 0.316703i | 0.987383 | + | 0.158352i | \(0.0506179\pi\) | ||||
−0.987383 | + | 0.158352i | \(0.949382\pi\) | |||||||
\(998\) | − 34.2462i | − 1.08404i | ||||||||
\(999\) | −5.12311 | −0.162088 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))