Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [117,4,Mod(64,117)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(117, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("117.64");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 117 = 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 117.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.90322347067\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.5054412.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 29x^{2} + 48 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 64.2 | ||
Root | \(-1.32750i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 117.64 |
Dual form | 117.4.b.d.64.3 |
$q$-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 \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(92\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.32750i | − | 0.469343i | −0.972075 | − | 0.234671i | \(-0.924599\pi\) | ||
0.972075 | − | 0.234671i | \(-0.0754014\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 6.23774 | 0.779717 | ||||||||
\(5\) | − | 15.4241i | − | 1.37957i | −0.724014 | − | 0.689785i | \(-0.757705\pi\) | ||
0.724014 | − | 0.689785i | \(-0.242295\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.96501i | 0.430070i | 0.976606 | + | 0.215035i | \(0.0689866\pi\) | ||||
−0.976606 | + | 0.215035i | \(0.931013\pi\) | |||||||
\(8\) | − | 18.9006i | − | 0.835297i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −20.4755 | −0.647491 | ||||||||
\(11\) | 12.7691i | 0.350002i | 0.984568 | + | 0.175001i | \(0.0559928\pi\) | ||||
−0.984568 | + | 0.175001i | \(0.944007\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7.47548 | − | 46.2722i | 0.159487 | − | 0.987200i | ||||
\(14\) | 10.5736 | 0.201850 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 24.8113 | 0.387677 | ||||||||
\(17\) | −54.0000 | −0.770407 | −0.385204 | − | 0.922832i | \(-0.625869\pi\) | ||||
−0.385204 | + | 0.922832i | \(0.625869\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 84.5794i | − | 1.02126i | −0.859802 | − | 0.510628i | \(-0.829413\pi\) | ||
0.859802 | − | 0.510628i | \(-0.170587\pi\) | |||||||
\(20\) | − | 96.2113i | − | 1.07568i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 16.9510 | 0.164271 | ||||||||
\(23\) | 122.853 | 1.11376 | 0.556882 | − | 0.830591i | \(-0.311997\pi\) | ||||
0.556882 | + | 0.830591i | \(0.311997\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −112.902 | −0.903215 | ||||||||
\(26\) | −61.4264 | − | 9.92371i | −0.463335 | − | 0.0748538i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 49.6837i | 0.335333i | ||||||||
\(29\) | −140.853 | −0.901921 | −0.450961 | − | 0.892544i | \(-0.648919\pi\) | ||||
−0.450961 | + | 0.892544i | \(0.648919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 116.439i | − | 0.674617i | −0.941394 | − | 0.337309i | \(-0.890483\pi\) | ||
0.941394 | − | 0.337309i | \(-0.109517\pi\) | |||||||
\(32\) | − | 184.142i | − | 1.01725i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 71.6851i | 0.361585i | ||||||||
\(35\) | 122.853 | 0.593312 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 433.898i | 1.92790i | 0.266081 | + | 0.963951i | \(0.414271\pi\) | ||||
−0.266081 | + | 0.963951i | \(0.585729\pi\) | |||||||
\(38\) | −112.279 | −0.479319 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −291.525 | −1.15235 | ||||||||
\(41\) | 205.823i | 0.784003i | 0.919965 | + | 0.392002i | \(0.128217\pi\) | ||||
−0.919965 | + | 0.392002i | \(0.871783\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 418.853 | 1.48545 | 0.742726 | − | 0.669595i | \(-0.233532\pi\) | ||||
0.742726 | + | 0.669595i | \(0.233532\pi\) | |||||||
\(44\) | 79.6501i | 0.272902i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 163.087i | − | 0.522737i | ||||||
\(47\) | 485.861i | 1.50787i | 0.656947 | + | 0.753937i | \(0.271848\pi\) | ||||
−0.656947 | + | 0.753937i | \(0.728152\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 279.559 | 0.815040 | ||||||||
\(50\) | 149.877i | 0.423918i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 46.6301 | − | 288.634i | 0.124354 | − | 0.769737i | ||||
\(53\) | 674.559 | 1.74826 | 0.874130 | − | 0.485693i | \(-0.161433\pi\) | ||||
0.874130 | + | 0.485693i | \(0.161433\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 196.951 | 0.482852 | ||||||||
\(56\) | 150.544 | 0.359236 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 186.982i | 0.423310i | ||||||||
\(59\) | 186.226i | 0.410925i | 0.978665 | + | 0.205462i | \(0.0658698\pi\) | ||||
−0.978665 | + | 0.205462i | \(0.934130\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −671.902 | −1.41030 | −0.705149 | − | 0.709059i | \(-0.749120\pi\) | ||||
−0.705149 | + | 0.709059i | \(0.749120\pi\) | |||||||
\(62\) | −154.574 | −0.316627 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −45.9584 | −0.0897626 | ||||||||
\(65\) | −713.706 | − | 115.302i | −1.36191 | − | 0.220023i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.0364i | 0.0255944i | 0.999918 | + | 0.0127972i | \(0.00407358\pi\) | ||||
−0.999918 | + | 0.0127972i | \(0.995926\pi\) | |||||||
\(68\) | −336.838 | −0.600700 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | − | 163.087i | − | 0.278467i | ||||||
\(71\) | 346.789i | 0.579665i | 0.957077 | + | 0.289833i | \(0.0935996\pi\) | ||||
−0.957077 | + | 0.289833i | \(0.906400\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 832.900i | 1.33539i | 0.744435 | + | 0.667695i | \(0.232719\pi\) | ||||
−0.744435 | + | 0.667695i | \(0.767281\pi\) | |||||||
\(74\) | 576.000 | 0.904846 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 527.584i | − | 0.796290i | ||||||
\(77\) | −101.706 | −0.150525 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −335.608 | −0.477960 | −0.238980 | − | 0.971025i | \(-0.576813\pi\) | ||||
−0.238980 | + | 0.971025i | \(0.576813\pi\) | |||||||
\(80\) | − | 382.691i | − | 0.534827i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 273.230 | 0.367966 | ||||||||
\(83\) | − | 568.797i | − | 0.752212i | −0.926577 | − | 0.376106i | \(-0.877263\pi\) | ||
0.926577 | − | 0.376106i | \(-0.122737\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 832.900i | 1.06283i | ||||||||
\(86\) | − | 556.028i | − | 0.697186i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 241.343 | 0.292355 | ||||||||
\(89\) | − | 236.671i | − | 0.281877i | −0.990018 | − | 0.140939i | \(-0.954988\pi\) | ||
0.990018 | − | 0.140939i | \(-0.0450120\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 368.559 | + | 59.5423i | 0.424565 | + | 0.0685904i | ||||
\(92\) | 766.324 | 0.868422 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 644.981 | 0.707710 | ||||||||
\(95\) | −1304.56 | −1.40889 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1278.94i | − | 1.33873i | −0.742934 | − | 0.669365i | \(-0.766566\pi\) | ||
0.742934 | − | 0.669365i | \(-0.233434\pi\) | |||||||
\(98\) | − | 371.115i | − | 0.382533i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −704.253 | −0.704253 | ||||||||
\(101\) | 632.264 | 0.622898 | 0.311449 | − | 0.950263i | \(-0.399186\pi\) | ||||
0.311449 | + | 0.950263i | \(0.399186\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1506.26 | −1.44094 | −0.720469 | − | 0.693487i | \(-0.756073\pi\) | ||||
−0.720469 | + | 0.693487i | \(0.756073\pi\) | |||||||
\(104\) | −874.574 | − | 141.291i | −0.824606 | − | 0.133219i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 895.478i | − | 0.820533i | ||||||
\(107\) | 1268.56 | 1.14613 | 0.573066 | − | 0.819509i | \(-0.305754\pi\) | ||||
0.573066 | + | 0.819509i | \(0.305754\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 347.425i | 0.305296i | 0.988281 | + | 0.152648i | \(0.0487801\pi\) | ||||
−0.988281 | + | 0.152648i | \(0.951220\pi\) | |||||||
\(110\) | − | 261.453i | − | 0.226623i | ||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 197.622i | 0.166728i | ||||||||
\(113\) | −659.706 | −0.549203 | −0.274601 | − | 0.961558i | \(-0.588546\pi\) | ||||
−0.274601 | + | 0.961558i | \(0.588546\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1894.89i | − | 1.53652i | ||||||
\(116\) | −878.603 | −0.703244 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 247.215 | 0.192865 | ||||||||
\(119\) | − | 430.111i | − | 0.331329i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1167.95 | 0.877499 | ||||||||
\(122\) | 891.951i | 0.661913i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 726.319i | − | 0.526011i | ||||||
\(125\) | − | 186.602i | − | 0.133521i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −275.019 | −0.192157 | −0.0960787 | − | 0.995374i | \(-0.530630\pi\) | ||||
−0.0960787 | + | 0.995374i | \(0.530630\pi\) | |||||||
\(128\) | − | 1412.13i | − | 0.975121i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −153.064 | + | 947.446i | −0.103266 | + | 0.639204i | ||||
\(131\) | 1183.97 | 0.789648 | 0.394824 | − | 0.918757i | \(-0.370805\pi\) | ||||
0.394824 | + | 0.918757i | \(0.370805\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 673.676 | 0.439211 | ||||||||
\(134\) | 18.6334 | 0.0120125 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1020.63i | 0.643519i | ||||||||
\(137\) | 2557.36i | 1.59482i | 0.603438 | + | 0.797410i | \(0.293797\pi\) | ||||
−0.603438 | + | 0.797410i | \(0.706203\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 545.736 | 0.333012 | 0.166506 | − | 0.986040i | \(-0.446751\pi\) | ||||
0.166506 | + | 0.986040i | \(0.446751\pi\) | |||||||
\(140\) | 766.324 | 0.462616 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 460.362 | 0.272062 | ||||||||
\(143\) | 590.853 | + | 95.4549i | 0.345522 | + | 0.0558205i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2172.52i | 1.24426i | ||||||||
\(146\) | 1105.68 | 0.626756 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2706.54i | 1.50322i | ||||||||
\(149\) | − | 1376.78i | − | 0.756981i | −0.925605 | − | 0.378491i | \(-0.876443\pi\) | ||
0.925605 | − | 0.378491i | \(-0.123557\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2733.47i | − | 1.47316i | −0.676352 | − | 0.736579i | \(-0.736440\pi\) | ||
0.676352 | − | 0.736579i | \(-0.263560\pi\) | |||||||
\(152\) | −1598.60 | −0.853052 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 135.015i | 0.0706479i | ||||||||
\(155\) | −1795.97 | −0.930683 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1029.97 | 0.523570 | 0.261785 | − | 0.965126i | \(-0.415689\pi\) | ||||
0.261785 | + | 0.965126i | \(0.415689\pi\) | |||||||
\(158\) | 445.520i | 0.224327i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2840.22 | −1.40337 | ||||||||
\(161\) | 978.524i | 0.478997i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2882.91i | 1.38532i | 0.721264 | + | 0.692660i | \(0.243561\pi\) | ||||
−0.721264 | + | 0.692660i | \(0.756439\pi\) | |||||||
\(164\) | 1283.87i | 0.611301i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −755.079 | −0.353045 | ||||||||
\(167\) | 1153.90i | 0.534679i | 0.963602 | + | 0.267340i | \(0.0861446\pi\) | ||||
−0.963602 | + | 0.267340i | \(0.913855\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2085.23 | − | 691.814i | −0.949128 | − | 0.314890i | ||||
\(170\) | 1105.68 | 0.498832 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2612.69 | 1.15823 | ||||||||
\(173\) | −1688.85 | −0.742203 | −0.371101 | − | 0.928592i | \(-0.621020\pi\) | ||||
−0.371101 | + | 0.928592i | \(0.621020\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 899.265i | − | 0.388446i | ||||||
\(176\) | 316.817i | 0.135687i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −314.181 | −0.132297 | ||||||||
\(179\) | −942.793 | −0.393674 | −0.196837 | − | 0.980436i | \(-0.563067\pi\) | ||||
−0.196837 | + | 0.980436i | \(0.563067\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −482.030 | −0.197950 | −0.0989751 | − | 0.995090i | \(-0.531556\pi\) | ||||
−0.0989751 | + | 0.995090i | \(0.531556\pi\) | |||||||
\(182\) | 79.0425 | − | 489.262i | 0.0321924 | − | 0.199267i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 2322.00i | − | 0.930325i | ||||||
\(185\) | 6692.47 | 2.65968 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 689.530i | − | 0.269644i | ||||||
\(188\) | 3030.67i | 1.17572i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1731.80i | 0.661254i | ||||||||
\(191\) | −4223.32 | −1.59994 | −0.799971 | − | 0.600039i | \(-0.795152\pi\) | ||||
−0.799971 | + | 0.600039i | \(0.795152\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 229.092i | 0.0854424i | 0.999087 | + | 0.0427212i | \(0.0136027\pi\) | ||||
−0.999087 | + | 0.0427212i | \(0.986397\pi\) | |||||||
\(194\) | −1697.80 | −0.628323 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1743.81 | 0.635501 | ||||||||
\(197\) | 228.335i | 0.0825798i | 0.999147 | + | 0.0412899i | \(0.0131467\pi\) | ||||
−0.999147 | + | 0.0412899i | \(0.986853\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2939.02 | −1.04694 | −0.523471 | − | 0.852043i | \(-0.675363\pi\) | ||||
−0.523471 | + | 0.852043i | \(0.675363\pi\) | |||||||
\(200\) | 2133.92i | 0.754453i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 839.332i | − | 0.292352i | ||||||
\(203\) | − | 1121.89i | − | 0.387889i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3174.63 | 1.08159 | ||||||||
\(206\) | 1999.57i | 0.676294i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 185.476 | − | 1148.07i | 0.0618292 | − | 0.382714i | ||||
\(209\) | 1080.00 | 0.357441 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1607.02 | −0.524321 | −0.262161 | − | 0.965024i | \(-0.584435\pi\) | ||||
−0.262161 | + | 0.965024i | \(0.584435\pi\) | |||||||
\(212\) | 4207.72 | 1.36315 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 1684.01i | − | 0.537929i | ||||||
\(215\) | − | 6460.42i | − | 2.04929i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 927.441 | 0.290133 | ||||||||
\(218\) | 461.207 | 0.143288 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1228.53 | 0.376488 | ||||||||
\(221\) | −403.676 | + | 2498.70i | −0.122870 | + | 0.760546i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 130.867i | 0.0392981i | 0.999807 | + | 0.0196490i | \(0.00625488\pi\) | ||||
−0.999807 | + | 0.0196490i | \(0.993745\pi\) | |||||||
\(224\) | 1466.69 | 0.437489 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 875.761i | 0.257764i | ||||||||
\(227\) | − | 4325.19i | − | 1.26464i | −0.774708 | − | 0.632319i | \(-0.782103\pi\) | ||
0.774708 | − | 0.632319i | \(-0.217897\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2621.57i | 0.756499i | 0.925704 | + | 0.378250i | \(0.123474\pi\) | ||||
−0.925704 | + | 0.378250i | \(0.876526\pi\) | |||||||
\(230\) | −2515.47 | −0.721153 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2662.21i | 0.753373i | ||||||||
\(233\) | −4643.12 | −1.30550 | −0.652748 | − | 0.757575i | \(-0.726384\pi\) | ||||
−0.652748 | + | 0.757575i | \(0.726384\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7493.95 | 2.08022 | ||||||||
\(236\) | 1161.63i | 0.320405i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −570.972 | −0.155507 | ||||||||
\(239\) | − | 6696.69i | − | 1.81244i | −0.422809 | − | 0.906219i | \(-0.638956\pi\) | ||
0.422809 | − | 0.906219i | \(-0.361044\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 2301.47i | − | 0.615148i | −0.951524 | − | 0.307574i | \(-0.900483\pi\) | ||
0.951524 | − | 0.307574i | \(-0.0995171\pi\) | |||||||
\(242\) | − | 1550.46i | − | 0.411848i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4191.15 | −1.09963 | ||||||||
\(245\) | − | 4311.93i | − | 1.12440i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3913.68 | − | 632.272i | −1.00818 | − | 0.162876i | ||||
\(248\) | −2200.78 | −0.563506 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −247.714 | −0.0626673 | ||||||||
\(251\) | 828.000 | 0.208219 | 0.104109 | − | 0.994566i | \(-0.466801\pi\) | ||||
0.104109 | + | 0.994566i | \(0.466801\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1568.72i | 0.389820i | ||||||||
\(254\) | 365.088i | 0.0901877i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2242.27 | −0.547429 | ||||||||
\(257\) | 884.763 | 0.214747 | 0.107374 | − | 0.994219i | \(-0.465756\pi\) | ||||
0.107374 | + | 0.994219i | \(0.465756\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3456.00 | −0.829133 | ||||||||
\(260\) | −4451.91 | − | 719.226i | −1.06191 | − | 0.171556i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 1571.72i | − | 0.370616i | ||||||
\(263\) | 8343.94 | 1.95631 | 0.978155 | − | 0.207878i | \(-0.0666557\pi\) | ||||
0.978155 | + | 0.207878i | \(0.0666557\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 10404.4i | − | 2.41185i | ||||||
\(266\) | − | 894.306i | − | 0.206141i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 87.5556i | 0.0199564i | ||||||||
\(269\) | −2762.56 | −0.626157 | −0.313078 | − | 0.949727i | \(-0.601360\pi\) | ||||
−0.313078 | + | 0.949727i | \(0.601360\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3116.54i | 0.698585i | 0.937014 | + | 0.349293i | \(0.113578\pi\) | ||||
−0.937014 | + | 0.349293i | \(0.886422\pi\) | |||||||
\(272\) | −1339.81 | −0.298669 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3394.91 | 0.748517 | ||||||||
\(275\) | − | 1441.65i | − | 0.316127i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 502.060 | 0.108902 | 0.0544510 | − | 0.998516i | \(-0.482659\pi\) | ||||
0.0544510 | + | 0.998516i | \(0.482659\pi\) | |||||||
\(278\) | − | 724.465i | − | 0.156297i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | − | 2322.00i | − | 0.495592i | ||||||
\(281\) | 6607.56i | 1.40275i | 0.712791 | + | 0.701377i | \(0.247431\pi\) | ||||
−0.712791 | + | 0.701377i | \(0.752569\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4368.98 | 0.917699 | 0.458850 | − | 0.888514i | \(-0.348262\pi\) | ||||
0.458850 | + | 0.888514i | \(0.348262\pi\) | |||||||
\(284\) | 2163.18i | 0.451975i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 126.717 | − | 784.358i | 0.0261990 | − | 0.162168i | ||||
\(287\) | −1639.38 | −0.337176 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1997.00 | −0.406473 | ||||||||
\(290\) | 2884.03 | 0.583986 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5195.41i | 1.04123i | ||||||||
\(293\) | 5348.12i | 1.06635i | 0.846005 | + | 0.533175i | \(0.179001\pi\) | ||||
−0.846005 | + | 0.533175i | \(0.820999\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2872.36 | 0.566900 | ||||||||
\(296\) | 8200.94 | 1.61037 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1827.68 | −0.355284 | ||||||||
\(299\) | 918.384 | − | 5684.67i | 0.177630 | − | 1.09951i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3336.17i | 0.638849i | ||||||||
\(302\) | −3628.69 | −0.691416 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 2098.53i | − | 0.395917i | ||||||
\(305\) | 10363.5i | 1.94561i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 4502.46i | − | 0.837032i | −0.908210 | − | 0.418516i | \(-0.862550\pi\) | ||
0.908210 | − | 0.418516i | \(-0.137450\pi\) | |||||||
\(308\) | −634.414 | −0.117367 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2384.15i | 0.436809i | ||||||||
\(311\) | −7447.20 | −1.35785 | −0.678926 | − | 0.734207i | \(-0.737554\pi\) | ||||
−0.678926 | + | 0.734207i | \(0.737554\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6508.93 | −1.17542 | −0.587710 | − | 0.809072i | \(-0.699970\pi\) | ||||
−0.587710 | + | 0.809072i | \(0.699970\pi\) | |||||||
\(314\) | − | 1367.29i | − | 0.245734i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2093.43 | −0.372673 | ||||||||
\(317\) | 2465.57i | 0.436846i | 0.975854 | + | 0.218423i | \(0.0700913\pi\) | ||||
−0.975854 | + | 0.218423i | \(0.929909\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 1798.56i | − | 0.315674i | ||||||
\(320\) | 708.866i | 0.123834i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1298.99 | 0.224814 | ||||||||
\(323\) | 4567.29i | 0.786782i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −843.996 | + | 5224.22i | −0.144051 | + | 0.891654i | ||||
\(326\) | 3827.07 | 0.650190 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3890.18 | 0.654876 | ||||||||
\(329\) | −3869.89 | −0.648491 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4114.84i | 0.683300i | 0.939827 | + | 0.341650i | \(0.110986\pi\) | ||||
−0.939827 | + | 0.341650i | \(0.889014\pi\) | |||||||
\(332\) | − | 3548.01i | − | 0.586513i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1531.80 | 0.250948 | ||||||||
\(335\) | 216.499 | 0.0353092 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4798.05 | −0.775568 | −0.387784 | − | 0.921750i | \(-0.626759\pi\) | ||||
−0.387784 | + | 0.921750i | \(0.626759\pi\) | |||||||
\(338\) | −918.384 | + | 2768.15i | −0.147791 | + | 0.445466i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5195.41i | 0.828708i | ||||||||
\(341\) | 1486.82 | 0.236117 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4958.69i | 0.780594i | ||||||||
\(344\) | − | 7916.58i | − | 1.24079i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2241.96i | 0.348348i | ||||||||
\(347\) | 3314.76 | 0.512812 | 0.256406 | − | 0.966569i | \(-0.417462\pi\) | ||||
0.256406 | + | 0.966569i | \(0.417462\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 371.740i | − | 0.0570166i | −0.999594 | − | 0.0285083i | \(-0.990924\pi\) | ||
0.999594 | − | 0.0285083i | \(-0.00907570\pi\) | |||||||
\(350\) | −1193.78 | −0.182314 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2351.32 | 0.356039 | ||||||||
\(353\) | 7539.10i | 1.13673i | 0.822776 | + | 0.568365i | \(0.192424\pi\) | ||||
−0.822776 | + | 0.568365i | \(0.807576\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5348.89 | 0.799689 | ||||||||
\(356\) | − | 1476.29i | − | 0.219785i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1251.56i | 0.184768i | ||||||||
\(359\) | − | 12741.5i | − | 1.87317i | −0.350437 | − | 0.936586i | \(-0.613967\pi\) | ||
0.350437 | − | 0.936586i | \(-0.386033\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −294.676 | −0.0429619 | ||||||||
\(362\) | 639.896i | 0.0929065i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2298.97 | + | 371.409i | 0.331041 | + | 0.0534811i | ||||
\(365\) | 12846.7 | 1.84227 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7187.26 | 1.02227 | 0.511134 | − | 0.859501i | \(-0.329226\pi\) | ||||
0.511134 | + | 0.859501i | \(0.329226\pi\) | |||||||
\(368\) | 3048.14 | 0.431781 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 8884.26i | − | 1.24830i | ||||||
\(371\) | 5372.87i | 0.751874i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2087.99 | −0.289845 | −0.144922 | − | 0.989443i | \(-0.546293\pi\) | ||||
−0.144922 | + | 0.989443i | \(0.546293\pi\) | |||||||
\(374\) | −915.352 | −0.126555 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9183.07 | 1.25952 | ||||||||
\(377\) | −1052.94 | + | 6517.57i | −0.143844 | + | 0.890377i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 3982.08i | − | 0.539699i | −0.962902 | − | 0.269850i | \(-0.913026\pi\) | ||
0.962902 | − | 0.269850i | \(-0.0869740\pi\) | |||||||
\(380\) | −8137.50 | −1.09854 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5606.47i | 0.750921i | ||||||||
\(383\) | 8638.43i | 1.15249i | 0.817278 | + | 0.576244i | \(0.195482\pi\) | ||||
−0.817278 | + | 0.576244i | \(0.804518\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1568.72i | 0.207660i | ||||||||
\(386\) | 304.120 | 0.0401018 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 7977.70i | − | 1.04383i | ||||||
\(389\) | −1275.74 | −0.166279 | −0.0831393 | − | 0.996538i | \(-0.526495\pi\) | ||||
−0.0831393 | + | 0.996538i | \(0.526495\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6634.06 | −0.858053 | ||||||||
\(392\) | − | 5283.83i | − | 0.680801i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 303.115 | 0.0387582 | ||||||||
\(395\) | 5176.44i | 0.659379i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 4622.65i | − | 0.584394i | −0.956358 | − | 0.292197i | \(-0.905614\pi\) | ||
0.956358 | − | 0.292197i | \(-0.0943862\pi\) | |||||||
\(398\) | 3901.55i | 0.491375i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2801.24 | −0.350155 | ||||||||
\(401\) | 138.075i | 0.0171949i | 0.999963 | + | 0.00859743i | \(0.00273668\pi\) | ||||
−0.999963 | + | 0.00859743i | \(0.997263\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5387.91 | − | 870.441i | −0.665982 | − | 0.107592i | ||||
\(404\) | 3943.90 | 0.485684 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1489.32 | −0.182053 | ||||||||
\(407\) | −5540.47 | −0.674769 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1204.64i | 0.145637i | 0.997345 | + | 0.0728186i | \(0.0231994\pi\) | ||||
−0.997345 | + | 0.0728186i | \(0.976801\pi\) | |||||||
\(410\) | − | 4214.32i | − | 0.507635i | ||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9395.68 | −1.12352 | ||||||||
\(413\) | −1483.29 | −0.176726 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8773.16 | −1.03773 | ||||||||
\(416\) | −8520.66 | − | 1376.55i | −1.00423 | − | 0.162238i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 1433.70i | − | 0.167762i | ||||||
\(419\) | −5199.85 | −0.606275 | −0.303138 | − | 0.952947i | \(-0.598034\pi\) | ||||
−0.303138 | + | 0.952947i | \(0.598034\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14136.5i | 1.63651i | 0.574854 | + | 0.818256i | \(0.305059\pi\) | ||||
−0.574854 | + | 0.818256i | \(0.694941\pi\) | |||||||
\(422\) | 2133.32i | 0.246086i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 12749.6i | − | 1.46032i | ||||||
\(425\) | 6096.70 | 0.695844 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 5351.71i | − | 0.606527i | ||||||
\(428\) | 7912.94 | 0.893660 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8576.21 | −0.961818 | ||||||||
\(431\) | − | 2279.83i | − | 0.254793i | −0.991852 | − | 0.127396i | \(-0.959338\pi\) | ||
0.991852 | − | 0.127396i | \(-0.0406620\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13298.7 | 1.47597 | 0.737984 | − | 0.674819i | \(-0.235778\pi\) | ||||
0.737984 | + | 0.674819i | \(0.235778\pi\) | |||||||
\(434\) | − | 1231.18i | − | 0.136172i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2167.14i | 0.238045i | ||||||||
\(437\) | − | 10390.8i | − | 1.13744i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10452.3 | 1.13635 | 0.568177 | − | 0.822907i | \(-0.307649\pi\) | ||||
0.568177 | + | 0.822907i | \(0.307649\pi\) | |||||||
\(440\) | − | 3722.50i | − | 0.403325i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3317.03 | + | 535.880i | 0.356957 | + | 0.0576679i | ||||
\(443\) | −5363.50 | −0.575232 | −0.287616 | − | 0.957746i | \(-0.592863\pi\) | ||||
−0.287616 | + | 0.957746i | \(0.592863\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3650.43 | −0.388870 | ||||||||
\(446\) | 173.726 | 0.0184443 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 366.059i | − | 0.0386042i | ||||||
\(449\) | − | 9681.73i | − | 1.01762i | −0.860880 | − | 0.508808i | \(-0.830086\pi\) | ||
0.860880 | − | 0.508808i | \(-0.169914\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2628.17 | −0.274402 | ||||||||
\(452\) | −4115.07 | −0.428223 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −5741.69 | −0.593548 | ||||||||
\(455\) | 918.384 | − | 5684.67i | 0.0946253 | − | 0.585718i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3537.94i | 0.362139i | 0.983470 | + | 0.181070i | \(0.0579560\pi\) | ||||
−0.983470 | + | 0.181070i | \(0.942044\pi\) | |||||||
\(458\) | 3480.14 | 0.355057 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 11819.8i | − | 1.19805i | ||||||
\(461\) | − | 15074.9i | − | 1.52302i | −0.648156 | − | 0.761508i | \(-0.724459\pi\) | ||
0.648156 | − | 0.761508i | \(-0.275541\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 11070.0i | − | 1.11116i | −0.831463 | − | 0.555580i | \(-0.812496\pi\) | ||
0.831463 | − | 0.555580i | \(-0.187504\pi\) | |||||||
\(464\) | −3494.74 | −0.349654 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6163.75i | 0.612725i | ||||||||
\(467\) | 13252.8 | 1.31320 | 0.656600 | − | 0.754239i | \(-0.271994\pi\) | ||||
0.656600 | + | 0.754239i | \(0.271994\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −111.800 | −0.0110074 | ||||||||
\(470\) | − | 9948.23i | − | 0.976335i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3519.79 | 0.343244 | ||||||||
\(473\) | 5348.36i | 0.519911i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9549.18i | 0.922413i | ||||||||
\(476\) | − | 2682.92i | − | 0.258343i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8889.86 | −0.850654 | ||||||||
\(479\) | − | 12241.4i | − | 1.16769i | −0.811866 | − | 0.583843i | \(-0.801548\pi\) | ||
0.811866 | − | 0.583843i | \(-0.198452\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20077.4 | + | 3243.59i | 1.90322 | + | 0.307474i | ||||
\(482\) | −3055.20 | −0.288715 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7285.37 | 0.684201 | ||||||||
\(485\) | −19726.5 | −1.84687 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13413.3i | 1.24808i | 0.781392 | + | 0.624041i | \(0.214510\pi\) | ||||
−0.781392 | + | 0.624041i | \(0.785490\pi\) | |||||||
\(488\) | 12699.4i | 1.17802i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5724.10 | −0.527731 | ||||||||
\(491\) | −737.885 | −0.0678214 | −0.0339107 | − | 0.999425i | \(-0.510796\pi\) | ||||
−0.0339107 | + | 0.999425i | \(0.510796\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7606.06 | 0.694847 | ||||||||
\(494\) | −839.342 | + | 5195.41i | −0.0764449 | + | 0.473183i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 2889.01i | − | 0.261533i | ||||||
\(497\) | −2762.17 | −0.249297 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 1865.65i | − | 0.167370i | −0.996492 | − | 0.0836852i | \(-0.973331\pi\) | ||
0.996492 | − | 0.0836852i | \(-0.0266690\pi\) | |||||||
\(500\) | − | 1163.97i | − | 0.104109i | ||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 1099.17i | − | 0.0977259i | ||||||
\(503\) | 16632.0 | 1.47432 | 0.737161 | − | 0.675717i | \(-0.236166\pi\) | ||||
0.737161 | + | 0.675717i | \(0.236166\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 9752.09i | − | 0.859331i | ||||||
\(506\) | 2082.47 | 0.182959 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1715.50 | −0.149829 | ||||||||
\(509\) | 4128.91i | 0.359549i | 0.983708 | + | 0.179775i | \(0.0575368\pi\) | ||||
−0.983708 | + | 0.179775i | \(0.942463\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6634.06 | −0.574312 | ||||||||
\(512\) | − | 8320.40i | − | 0.718190i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 1174.52i | − | 0.100790i | ||||||
\(515\) | 23232.7i | 1.98788i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6203.99 | −0.527758 | ||||||||
\(518\) | 4587.85i | 0.389147i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2179.29 | + | 13489.5i | −0.183785 | + | 1.13760i | ||||
\(521\) | 988.234 | 0.0831005 | 0.0415502 | − | 0.999136i | \(-0.486770\pi\) | ||||
0.0415502 | + | 0.999136i | \(0.486770\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9441.62 | −0.789394 | −0.394697 | − | 0.918811i | \(-0.629150\pi\) | ||||
−0.394697 | + | 0.918811i | \(0.629150\pi\) | |||||||
\(524\) | 7385.30 | 0.615703 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 11076.6i | − | 0.918180i | ||||||
\(527\) | 6287.73i | 0.519730i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2925.83 | 0.240472 | ||||||||
\(530\) | −13811.9 | −1.13198 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4202.21 | 0.342461 | ||||||||
\(533\) | 9523.88 | + | 1538.62i | 0.773968 | + | 0.125038i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 19566.3i | − | 1.58117i | ||||||
\(536\) | 265.297 | 0.0213789 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3667.30i | 0.293882i | ||||||||
\(539\) | 3569.70i | 0.285265i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14001.5i | 1.11270i | 0.830948 | + | 0.556351i | \(0.187799\pi\) | ||||
−0.830948 | + | 0.556351i | \(0.812201\pi\) | |||||||
\(542\) | 4137.22 | 0.327876 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 9943.67i | 0.783697i | ||||||||
\(545\) | 5358.70 | 0.421177 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4244.85 | −0.331804 | −0.165902 | − | 0.986142i | \(-0.553053\pi\) | ||||
−0.165902 | + | 0.986142i | \(0.553053\pi\) | |||||||
\(548\) | 15952.2i | 1.24351i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1913.80 | −0.148372 | ||||||||
\(551\) | 11913.3i | 0.921092i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 2673.12i | − | 0.205556i | ||||||
\(554\) | − | 666.485i | − | 0.0511124i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3404.16 | 0.259655 | ||||||||
\(557\) | 11732.2i | 0.892473i | 0.894915 | + | 0.446236i | \(0.147236\pi\) | ||||
−0.894915 | + | 0.446236i | \(0.852764\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3131.13 | − | 19381.2i | 0.236910 | − | 1.46644i | ||||
\(560\) | 3048.14 | 0.230013 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8771.54 | 0.658372 | ||||||||
\(563\) | −9941.80 | −0.744222 | −0.372111 | − | 0.928188i | \(-0.621366\pi\) | ||||
−0.372111 | + | 0.928188i | \(0.621366\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10175.3i | 0.757664i | ||||||||
\(566\) | − | 5799.83i | − | 0.430716i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6554.52 | 0.484193 | ||||||||
\(569\) | 3690.77 | 0.271925 | 0.135962 | − | 0.990714i | \(-0.456587\pi\) | ||||
0.135962 | + | 0.990714i | \(0.456587\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5685.09 | 0.416661 | 0.208331 | − | 0.978058i | \(-0.433197\pi\) | ||||
0.208331 | + | 0.978058i | \(0.433197\pi\) | |||||||
\(572\) | 3685.59 | + | 595.423i | 0.269409 | + | 0.0435242i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2176.28i | 0.158251i | ||||||||
\(575\) | −13870.3 | −1.00597 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 7746.50i | − | 0.558910i | −0.960159 | − | 0.279455i | \(-0.909846\pi\) | ||
0.960159 | − | 0.279455i | \(-0.0901537\pi\) | |||||||
\(578\) | 2651.02i | 0.190775i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 13551.6i | 0.970175i | ||||||||
\(581\) | 4530.47 | 0.323504 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8613.48i | 0.611894i | ||||||||
\(584\) | 15742.3 | 1.11545 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7099.64 | 0.500484 | ||||||||
\(587\) | − | 2766.54i | − | 0.194527i | −0.995259 | − | 0.0972635i | \(-0.968991\pi\) | ||
0.995259 | − | 0.0972635i | \(-0.0310089\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9848.38 | −0.688957 | ||||||||
\(590\) | − | 3813.07i | − | 0.266070i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10765.6i | 0.747402i | ||||||||
\(593\) | 1440.79i | 0.0997743i | 0.998755 | + | 0.0498871i | \(0.0158862\pi\) | ||||
−0.998755 | + | 0.0498871i | \(0.984114\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6634.06 | −0.457092 | ||||||||
\(596\) | − | 8587.99i | − | 0.590231i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7546.41 | − | 1219.16i | −0.516047 | − | 0.0833696i | ||||
\(599\) | −23837.5 | −1.62600 | −0.813001 | − | 0.582263i | \(-0.802168\pi\) | ||||
−0.813001 | + | 0.582263i | \(0.802168\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6694.23 | −0.454348 | −0.227174 | − | 0.973854i | \(-0.572949\pi\) | ||||
−0.227174 | + | 0.973854i | \(0.572949\pi\) | |||||||
\(602\) | 4428.77 | 0.299839 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 17050.7i | − | 1.14865i | ||||||
\(605\) | − | 18014.6i | − | 1.21057i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3330.50 | 0.222703 | 0.111352 | − | 0.993781i | \(-0.464482\pi\) | ||||
0.111352 | + | 0.993781i | \(0.464482\pi\) | |||||||
\(608\) | −15574.6 | −1.03887 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 13757.5 | 0.913156 | ||||||||
\(611\) | 22481.8 | + | 3632.04i | 1.48857 | + | 0.240486i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13490.3i | 0.888857i | 0.895814 | + | 0.444428i | \(0.146593\pi\) | ||||
−0.895814 | + | 0.444428i | \(0.853407\pi\) | |||||||
\(614\) | −5977.02 | −0.392855 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1922.30i | 0.125733i | ||||||||
\(617\) | 7470.76i | 0.487458i | 0.969843 | + | 0.243729i | \(0.0783707\pi\) | ||||
−0.969843 | + | 0.243729i | \(0.921629\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24806.9i | 1.61078i | 0.592746 | + | 0.805389i | \(0.298044\pi\) | ||||
−0.592746 | + | 0.805389i | \(0.701956\pi\) | |||||||
\(620\) | −11202.8 | −0.725669 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 9886.17i | 0.637298i | ||||||||
\(623\) | 1885.09 | 0.121227 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16990.9 | −1.08742 | ||||||||
\(626\) | 8640.61i | 0.551675i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6424.68 | 0.408237 | ||||||||
\(629\) | − | 23430.5i | − | 1.48527i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 314.333i | 0.0198311i | 0.999951 | + | 0.00991554i | \(0.00315627\pi\) | ||||
−0.999951 | + | 0.00991554i | \(0.996844\pi\) | |||||||
\(632\) | 6343.19i | 0.399238i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3273.05 | 0.205031 | ||||||||
\(635\) | 4241.91i | 0.265095i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2089.83 | − | 12935.8i | 0.129988 | − | 0.804607i | ||||
\(638\) | −2387.59 | −0.148159 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −21780.7 | −1.34525 | ||||||||
\(641\) | 5550.41 | 0.342009 | 0.171005 | − | 0.985270i | \(-0.445299\pi\) | ||||
0.171005 | + | 0.985270i | \(0.445299\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 5479.48i | − | 0.336065i | −0.985781 | − | 0.168032i | \(-0.946259\pi\) | ||
0.985781 | − | 0.168032i | \(-0.0537413\pi\) | |||||||
\(644\) | 6103.78i | 0.373482i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6063.08 | 0.369271 | ||||||||
\(647\) | 4724.83 | 0.287098 | 0.143549 | − | 0.989643i | \(-0.454149\pi\) | ||||
0.143549 | + | 0.989643i | \(0.454149\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2377.93 | −0.143824 | ||||||||
\(650\) | 6935.16 | + | 1120.41i | 0.418491 | + | 0.0676091i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 17982.9i | 1.08016i | ||||||||
\(653\) | −3463.91 | −0.207585 | −0.103793 | − | 0.994599i | \(-0.533098\pi\) | ||||
−0.103793 | + | 0.994599i | \(0.533098\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 18261.6i | − | 1.08938i | ||||||
\(656\) | 5106.73i | 0.303940i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5137.28i | 0.304365i | ||||||||
\(659\) | 2606.35 | 0.154065 | 0.0770327 | − | 0.997029i | \(-0.475455\pi\) | ||||
0.0770327 | + | 0.997029i | \(0.475455\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 22436.7i | − | 1.32025i | −0.751154 | − | 0.660127i | \(-0.770502\pi\) | ||
0.751154 | − | 0.660127i | \(-0.229498\pi\) | |||||||
\(662\) | 5462.46 | 0.320702 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10750.6 | −0.628321 | ||||||||
\(665\) | − | 10390.8i | − | 0.605923i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17304.2 | −1.00453 | ||||||||
\(668\) | 7197.73i | 0.416899i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 287.403i | − | 0.0165721i | ||||||
\(671\) | − | 8579.56i | − | 0.493607i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 633.970 | 0.0363117 | 0.0181558 | − | 0.999835i | \(-0.494221\pi\) | ||||
0.0181558 | + | 0.999835i | \(0.494221\pi\) | |||||||
\(674\) | 6369.42i | 0.364007i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −13007.1 | − | 4315.35i | −0.740052 | − | 0.245525i | ||||
\(677\) | −24457.4 | −1.38844 | −0.694221 | − | 0.719762i | \(-0.744251\pi\) | ||||
−0.694221 | + | 0.719762i | \(0.744251\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10186.8 | 0.575747 | ||||||||
\(680\) | 15742.3 | 0.887780 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 1973.76i | − | 0.110820i | ||||||
\(683\) | 12367.6i | 0.692875i | 0.938073 | + | 0.346437i | \(0.112609\pi\) | ||||
−0.938073 | + | 0.346437i | \(0.887391\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 39445.0 | 2.20017 | ||||||||
\(686\) | 6582.66 | 0.366366 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 10392.3 | 0.575875 | ||||||||
\(689\) | 5042.65 | − | 31213.3i | 0.278824 | − | 1.72588i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 1050.99i | − | 0.0578605i | −0.999581 | − | 0.0289302i | \(-0.990790\pi\) | ||
0.999581 | − | 0.0289302i | \(-0.00921006\pi\) | |||||||
\(692\) | −10534.6 | −0.578709 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 4400.35i | − | 0.240685i | ||||||
\(695\) | − | 8417.46i | − | 0.459414i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 11114.4i | − | 0.604002i | ||||||
\(698\) | −493.486 | −0.0267603 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | − | 5609.38i | − | 0.302878i | ||||||
\(701\) | −24294.1 | −1.30895 | −0.654476 | − | 0.756083i | \(-0.727111\pi\) | ||||
−0.654476 | + | 0.756083i | \(0.727111\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 36698.8 | 1.96888 | ||||||||
\(704\) | − | 586.846i | − | 0.0314170i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10008.2 | 0.533516 | ||||||||
\(707\) | 5035.99i | 0.267890i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 27465.9i | − | 1.45487i | −0.686176 | − | 0.727436i | \(-0.740712\pi\) | ||
0.686176 | − | 0.727436i | \(-0.259288\pi\) | |||||||
\(710\) | − | 7100.66i | − | 0.375328i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4473.23 | −0.235451 | ||||||||
\(713\) | − | 14304.9i | − | 0.751365i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1472.30 | − | 9113.36i | 0.0770084 | − | 0.476672i | ||||
\(716\) | −5880.90 | −0.306955 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −16914.3 | −0.879160 | ||||||||
\(719\) | 36433.5 | 1.88976 | 0.944882 | − | 0.327411i | \(-0.106176\pi\) | ||||
0.944882 | + | 0.327411i | \(0.106176\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 11997.4i | − | 0.619704i | ||||||
\(722\) | 391.183i | 0.0201639i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3006.78 | −0.154345 | ||||||||
\(725\) | 15902.6 | 0.814629 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −551.608 | −0.0281403 | −0.0140701 | − | 0.999901i | \(-0.504479\pi\) | ||||
−0.0140701 | + | 0.999901i | \(0.504479\pi\) | |||||||
\(728\) | 1125.39 | − | 6965.99i | 0.0572934 | − | 0.354638i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | − | 17054.0i | − | 0.864654i | ||||||
\(731\) | −22618.1 | −1.14440 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20317.2i | 1.02379i | 0.859049 | + | 0.511893i | \(0.171055\pi\) | ||||
−0.859049 | + | 0.511893i | \(0.828945\pi\) | |||||||
\(734\) | − | 9541.10i | − | 0.479794i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 22622.4i | − | 1.13298i | ||||||
\(737\) | −179.232 | −0.00895807 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29931.6i | 1.48992i | 0.667107 | + | 0.744962i | \(0.267532\pi\) | ||||
−0.667107 | + | 0.744962i | \(0.732468\pi\) | |||||||
\(740\) | 41745.9 | 2.07380 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7132.49 | 0.352887 | ||||||||
\(743\) | − | 24376.4i | − | 1.20361i | −0.798643 | − | 0.601805i | \(-0.794448\pi\) | ||
0.798643 | − | 0.601805i | \(-0.205552\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21235.5 | −1.04431 | ||||||||
\(746\) | 2771.81i | 0.136037i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 4301.11i | − | 0.210246i | ||||||
\(749\) | 10104.1i | 0.492917i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22692.2 | −1.10260 | −0.551298 | − | 0.834308i | \(-0.685867\pi\) | ||||
−0.551298 | + | 0.834308i | \(0.685867\pi\) | |||||||
\(752\) | 12054.8i | 0.584567i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8652.09 | + | 1397.78i | 0.417892 | + | 0.0675123i | ||||
\(755\) | −42161.3 | −2.03232 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33063.5 | −1.58747 | −0.793734 | − | 0.608265i | \(-0.791866\pi\) | ||||
−0.793734 | + | 0.608265i | \(0.791866\pi\) | |||||||
\(758\) | −5286.22 | −0.253304 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 24657.0i | 1.17685i | ||||||||
\(761\) | − | 216.324i | − | 0.0103045i | −0.999987 | − | 0.00515226i | \(-0.998360\pi\) | ||
0.999987 | − | 0.00515226i | \(-0.00164002\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2767.24 | −0.131299 | ||||||||
\(764\) | −26344.0 | −1.24750 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 11467.5 | 0.540912 | ||||||||
\(767\) | 8617.09 | + | 1392.13i | 0.405665 | + | 0.0655369i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19214.4i | 0.901025i | 0.892770 | + | 0.450512i | \(0.148759\pi\) | ||||
−0.892770 | + | 0.450512i | \(0.851241\pi\) | |||||||
\(770\) | 2082.47 | 0.0974638 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1429.01i | 0.0666209i | ||||||||
\(773\) | − | 33175.6i | − | 1.54365i | −0.635834 | − | 0.771826i | \(-0.719344\pi\) | ||
0.635834 | − | 0.771826i | \(-0.280656\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13146.2i | 0.609325i | ||||||||
\(776\) | −24172.8 | −1.11824 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1693.54i | 0.0780416i | ||||||||
\(779\) | 17408.4 | 0.800667 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4428.17 | −0.202884 | ||||||||
\(782\) | 8806.72i | 0.402721i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6936.21 | 0.315972 | ||||||||
\(785\) | − | 15886.3i | − | 0.722302i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14887.9i | 0.674330i | 0.941446 | + | 0.337165i | \(0.109468\pi\) | ||||
−0.941446 | + | 0.337165i | \(0.890532\pi\) | |||||||
\(788\) | 1424.30i | 0.0643889i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6871.73 | 0.309475 | ||||||||
\(791\) | − | 5254.56i | − | 0.236196i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5022.79 | + | 31090.4i | −0.224924 | + | 1.39225i | ||||
\(794\) | −6136.58 | −0.274281 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −18332.8 | −0.816319 | ||||||||
\(797\) | 12954.5 | 0.575751 | 0.287876 | − | 0.957668i | \(-0.407051\pi\) | ||||
0.287876 | + | 0.957668i | \(0.407051\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 26236.5i | − | 1.16168i | ||||||
\(800\) | 20790.0i | 0.918796i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 183.295 | 0.00807028 | ||||||||
\(803\) | −10635.4 | −0.467389 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15092.8 | 0.660810 | ||||||||
\(806\) | −1155.51 | + | 7152.46i | −0.0504977 | + | 0.312574i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 11950.2i | − | 0.520305i | ||||||
\(809\) | −8275.59 | −0.359647 | −0.179823 | − | 0.983699i | \(-0.557553\pi\) | ||||
−0.179823 | + | 0.983699i | \(0.557553\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26327.1i | 1.13991i | 0.821675 | + | 0.569956i | \(0.193040\pi\) | ||||
−0.821675 | + | 0.569956i | \(0.806960\pi\) | |||||||
\(812\) | − | 6998.09i | − | 0.302444i | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7354.98i | 0.316698i | ||||||||
\(815\) | 44466.3 | 1.91115 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 35426.3i | − | 1.51703i | ||||||
\(818\) | 1599.16 | 0.0683538 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 19802.5 | 0.843333 | ||||||||
\(821\) | 34439.0i | 1.46398i | 0.681314 | + | 0.731992i | \(0.261409\pi\) | ||||
−0.681314 | + | 0.731992i | \(0.738591\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13870.5 | 0.587479 | 0.293739 | − | 0.955886i | \(-0.405100\pi\) | ||||
0.293739 | + | 0.955886i | \(0.405100\pi\) | |||||||
\(824\) | 28469.3i | 1.20361i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1969.07i | 0.0829453i | ||||||||
\(827\) | 2132.30i | 0.0896583i | 0.998995 | + | 0.0448292i | \(0.0142743\pi\) | ||||
−0.998995 | + | 0.0448292i | \(0.985726\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6212.39 | 0.260272 | 0.130136 | − | 0.991496i | \(-0.458459\pi\) | ||||
0.130136 | + | 0.991496i | \(0.458459\pi\) | |||||||
\(830\) | 11646.4i | 0.487051i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −343.561 | + | 2126.60i | −0.0143159 | + | 0.0886136i | ||||
\(833\) | −15096.2 | −0.627913 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17797.8 | 0.737628 | ||||||||
\(836\) | 6736.76 | 0.278703 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6902.81i | 0.284551i | ||||||||
\(839\) | − | 4550.52i | − | 0.187248i | −0.995608 | − | 0.0936242i | \(-0.970155\pi\) | ||
0.995608 | − | 0.0936242i | \(-0.0298452\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4549.47 | −0.186538 | ||||||||
\(842\) | 18766.2 | 0.768085 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10024.2 | −0.408822 | ||||||||
\(845\) | −10670.6 | + | 32162.8i | −0.434413 | + | 1.30939i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9302.74i | 0.377386i | ||||||||
\(848\) | 16736.7 | 0.677759 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 8093.38i | − | 0.326589i | ||||||
\(851\) | 53305.6i | 2.14723i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 12262.8i | − | 0.492228i | −0.969241 | − | 0.246114i | \(-0.920846\pi\) | ||
0.969241 | − | 0.246114i | \(-0.0791538\pi\) | |||||||
\(854\) | −7104.40 | −0.284669 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 23976.5i | − | 0.957362i | ||||||
\(857\) | −34949.1 | −1.39304 | −0.696521 | − | 0.717536i | \(-0.745270\pi\) | ||||
−0.696521 | + | 0.717536i | \(0.745270\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21762.1 | −0.864394 | −0.432197 | − | 0.901779i | \(-0.642261\pi\) | ||||
−0.432197 | + | 0.901779i | \(0.642261\pi\) | |||||||
\(860\) | − | 40298.4i | − | 1.59786i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3026.48 | −0.119585 | ||||||||
\(863\) | 19811.5i | 0.781450i | 0.920507 | + | 0.390725i | \(0.127776\pi\) | ||||
−0.920507 | + | 0.390725i | \(0.872224\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 26049.0i | 1.02392i | ||||||||
\(866\) | − | 17654.0i | − | 0.692735i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5785.14 | 0.226222 | ||||||||
\(869\) | − | 4285.40i | − | 0.167287i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 649.496 | + | 104.929i | 0.0252668 | + | 0.00408196i | ||||
\(872\) | 6566.54 | 0.255013 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −13793.8 | −0.533848 | ||||||||
\(875\) | 1486.28 | 0.0574235 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 25716.8i | − | 0.990186i | −0.868840 | − | 0.495093i | \(-0.835134\pi\) | ||
0.868840 | − | 0.495093i | \(-0.164866\pi\) | |||||||
\(878\) | − | 13875.4i | − | 0.533339i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4886.61 | 0.187190 | ||||||||
\(881\) | 34709.6 | 1.32735 | 0.663676 | − | 0.748020i | \(-0.268995\pi\) | ||||
0.663676 | + | 0.748020i | \(0.268995\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3848.68 | 0.146680 | 0.0733400 | − | 0.997307i | \(-0.476634\pi\) | ||||
0.0733400 | + | 0.997307i | \(0.476634\pi\) | |||||||
\(884\) | −2518.02 | + | 15586.2i | −0.0958035 | + | 0.593011i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7120.06i | 0.269981i | ||||||||
\(887\) | −32804.8 | −1.24180 | −0.620900 | − | 0.783890i | \(-0.713233\pi\) | ||||
−0.620900 | + | 0.783890i | \(0.713233\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 2190.53i | − | 0.0826412i | ||||||
\(890\) | 4845.95i | 0.182513i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 816.311i | 0.0306414i | ||||||||
\(893\) | 41093.8 | 1.53992 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14541.7i | 0.543101i | ||||||||
\(896\) | 11247.6 | 0.419371 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12852.5 | −0.477610 | ||||||||
\(899\) | 16400.8i | 0.608452i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36426.2 | −1.34687 | ||||||||
\(902\) | 3488.90i | 0.128789i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12468.8i | 0.458748i | ||||||||
\(905\) | 7434.86i | 0.273086i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22262.2 | 0.814999 | 0.407500 | − | 0.913205i | \(-0.366401\pi\) | ||||
0.407500 | + | 0.913205i | \(0.366401\pi\) | |||||||
\(908\) | − | 26979.4i | − | 0.986060i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −7546.41 | − | 1219.16i | −0.274902 | − | 0.0444117i | ||||
\(911\) | 13515.3 | 0.491528 | 0.245764 | − | 0.969330i | \(-0.420961\pi\) | ||||
0.245764 | + | 0.969330i | \(0.420961\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7263.01 | 0.263275 | ||||||||
\(914\) | 4696.62 | 0.169968 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 16352.7i | 0.589855i | ||||||||
\(917\) | 9430.33i | 0.339604i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26600.6 | 0.954811 | 0.477405 | − | 0.878683i | \(-0.341577\pi\) | ||||
0.477405 | + | 0.878683i | \(0.341577\pi\) | |||||||
\(920\) | −35814.6 | −1.28345 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −20012.0 | −0.714816 | ||||||||
\(923\) | 16046.7 | + | 2592.41i | 0.572246 | + | 0.0924488i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 48987.9i | − | 1.74131i | ||||||
\(926\) | −14695.5 | −0.521515 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 25936.9i | 0.917480i | ||||||||
\(929\) | 32887.7i | 1.16148i | 0.814090 | + | 0.580738i | \(0.197236\pi\) | ||||
−0.814090 | + | 0.580738i | \(0.802764\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 23644.9i | − | 0.832363i | ||||||
\(932\) | −28962.6 | −1.01792 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 17593.1i | − | 0.616341i | ||||||
\(935\) | −10635.4 | −0.371993 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9261.78 | −0.322913 | −0.161456 | − | 0.986880i | \(-0.551619\pi\) | ||||
−0.161456 | + | 0.986880i | \(0.551619\pi\) | |||||||
\(938\) | 148.415i | 0.00516623i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 46745.3 | 1.62198 | ||||||||
\(941\) | − | 12054.9i | − | 0.417619i | −0.977956 | − | 0.208810i | \(-0.933041\pi\) | ||
0.977956 | − | 0.208810i | \(-0.0669589\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25285.9i | 0.873195i | ||||||||
\(944\) | 4620.51i | 0.159306i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7099.96 | 0.244016 | ||||||||
\(947\) | 20221.4i | 0.693885i | 0.937886 | + | 0.346942i | \(0.112780\pi\) | ||||
−0.937886 | + | 0.346942i | \(0.887220\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 38540.1 | + | 6226.32i | 1.31830 | + | 0.212977i | ||||
\(950\) | 12676.5 | 0.432928 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8129.36 | −0.276758 | ||||||||
\(953\) | −20331.5 | −0.691083 | −0.345542 | − | 0.938403i | \(-0.612305\pi\) | ||||
−0.345542 | + | 0.938403i | \(0.612305\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 65140.8i | 2.20723i | ||||||||
\(956\) | − | 41772.2i | − | 1.41319i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −16250.4 | −0.548045 | ||||||||
\(959\) | −20369.4 | −0.685885 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16232.9 | 0.544891 | ||||||||
\(962\) | 4305.88 | − | 26652.8i | 0.144311 | − | 0.893265i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 14356.0i | − | 0.479641i | ||||||
\(965\) | 3533.53 | 0.117874 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 11082.2i | − | 0.368541i | −0.982876 | − | 0.184270i | \(-0.941008\pi\) | ||
0.982876 | − | 0.184270i | \(-0.0589922\pi\) | |||||||
\(968\) | − | 22075.0i | − | 0.732973i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 26186.9i | 0.866816i | ||||||||
\(971\) | 36694.1 | 1.21274 | 0.606369 | − | 0.795184i | \(-0.292626\pi\) | ||||
0.606369 | + | 0.795184i | \(0.292626\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4346.79i | 0.143219i | ||||||||
\(974\) | 17806.2 | 0.585778 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −16670.8 | −0.546740 | ||||||||
\(977\) | − | 17155.3i | − | 0.561767i | −0.959742 | − | 0.280883i | \(-0.909373\pi\) | ||
0.959742 | − | 0.280883i | \(-0.0906274\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3022.07 | 0.0986575 | ||||||||
\(980\) | − | 26896.7i | − | 0.876718i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 979.544i | 0.0318315i | ||||||||
\(983\) | − | 38419.7i | − | 1.24659i | −0.781986 | − | 0.623296i | \(-0.785793\pi\) | ||
0.781986 | − | 0.623296i | \(-0.214207\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3521.86 | 0.113925 | ||||||||
\(986\) | − | 10097.1i | − | 0.326121i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −24412.5 | − | 3943.94i | −0.786098 | − | 0.126998i | ||||
\(989\) | 51457.3 | 1.65445 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 51728.9 | 1.65815 | 0.829073 | − | 0.559140i | \(-0.188869\pi\) | ||||
0.829073 | + | 0.559140i | \(0.188869\pi\) | |||||||
\(992\) | −21441.4 | −0.686255 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3666.79i | 0.117006i | ||||||||
\(995\) | 45331.6i | 1.44433i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26846.8 | −0.852805 | −0.426403 | − | 0.904533i | \(-0.640219\pi\) | ||||
−0.426403 | + | 0.904533i | \(0.640219\pi\) | |||||||
\(998\) | −2476.65 | −0.0785541 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 117.4.b.d.64.2 | 4 | ||
3.2 | odd | 2 | 39.4.b.a.25.3 | yes | 4 | ||
12.11 | even | 2 | 624.4.c.e.337.4 | 4 | |||
13.5 | odd | 4 | 1521.4.a.x.1.2 | 4 | |||
13.8 | odd | 4 | 1521.4.a.x.1.3 | 4 | |||
13.12 | even | 2 | inner | 117.4.b.d.64.3 | 4 | ||
39.5 | even | 4 | 507.4.a.j.1.3 | 4 | |||
39.8 | even | 4 | 507.4.a.j.1.2 | 4 | |||
39.38 | odd | 2 | 39.4.b.a.25.2 | ✓ | 4 | ||
156.155 | even | 2 | 624.4.c.e.337.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.b.a.25.2 | ✓ | 4 | 39.38 | odd | 2 | ||
39.4.b.a.25.3 | yes | 4 | 3.2 | odd | 2 | ||
117.4.b.d.64.2 | 4 | 1.1 | even | 1 | trivial | ||
117.4.b.d.64.3 | 4 | 13.12 | even | 2 | inner | ||
507.4.a.j.1.2 | 4 | 39.8 | even | 4 | |||
507.4.a.j.1.3 | 4 | 39.5 | even | 4 | |||
624.4.c.e.337.1 | 4 | 156.155 | even | 2 | |||
624.4.c.e.337.4 | 4 | 12.11 | even | 2 | |||
1521.4.a.x.1.2 | 4 | 13.5 | odd | 4 | |||
1521.4.a.x.1.3 | 4 | 13.8 | odd | 4 |