Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [17,4,Mod(16,17)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(17, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("17.16");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 17.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: | \(1.00303247010\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.4669632.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 74x^{2} + 1072 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 16.4 | ||
Root | \(4.44593i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 17.16 |
Dual form | 17.4.b.a.16.3 |
$q$-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 \(\left(\mathbb{Z}/17\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.37228 | 0.838728 | 0.419364 | − | 0.907818i | \(-0.362253\pi\) | ||||
0.419364 | + | 0.907818i | \(0.362253\pi\) | |||||||
\(3\) | 4.44593i | 0.855620i | 0.903869 | + | 0.427810i | \(0.140715\pi\) | ||||
−0.903869 | + | 0.427810i | \(0.859285\pi\) | |||||||
\(4\) | −2.37228 | −0.296535 | ||||||||
\(5\) | − | 19.4389i | − | 1.73867i | −0.494228 | − | 0.869333i | \(-0.664549\pi\) | ||
0.494228 | − | 0.869333i | \(-0.335451\pi\) | |||||||
\(6\) | 10.5470i | 0.717633i | ||||||||
\(7\) | 14.9929i | 0.809542i | 0.914418 | + | 0.404771i | \(0.132649\pi\) | ||||
−0.914418 | + | 0.404771i | \(0.867351\pi\) | |||||||
\(8\) | −24.6060 | −1.08744 | ||||||||
\(9\) | 7.23369 | 0.267914 | ||||||||
\(10\) | − | 46.1145i | − | 1.45827i | ||||||
\(11\) | 31.1215i | 0.853045i | 0.904477 | + | 0.426522i | \(0.140261\pi\) | ||||
−0.904477 | + | 0.426522i | \(0.859739\pi\) | |||||||
\(12\) | − | 10.5470i | − | 0.253721i | ||||||
\(13\) | −5.21194 | −0.111195 | −0.0555974 | − | 0.998453i | \(-0.517706\pi\) | ||||
−0.0555974 | + | 0.998453i | \(0.517706\pi\) | |||||||
\(14\) | 35.5675i | 0.678986i | ||||||||
\(15\) | 86.4239 | 1.48764 | ||||||||
\(16\) | −39.3940 | −0.615532 | ||||||||
\(17\) | 68.2119 | − | 16.1286i | 0.973166 | − | 0.230103i | ||||
\(18\) | 17.1603 | 0.224707 | ||||||||
\(19\) | −28.0000 | −0.338086 | −0.169043 | − | 0.985609i | \(-0.554068\pi\) | ||||
−0.169043 | + | 0.985609i | \(0.554068\pi\) | |||||||
\(20\) | 46.1145i | 0.515575i | ||||||||
\(21\) | −66.6576 | −0.692661 | ||||||||
\(22\) | 73.8290i | 0.715473i | ||||||||
\(23\) | − | 167.194i | − | 1.51575i | −0.652399 | − | 0.757875i | \(-0.726237\pi\) | ||
0.652399 | − | 0.757875i | \(-0.273763\pi\) | |||||||
\(24\) | − | 109.396i | − | 0.930436i | ||||||
\(25\) | −252.870 | −2.02296 | ||||||||
\(26\) | −12.3642 | −0.0932622 | ||||||||
\(27\) | 152.201i | 1.08485i | ||||||||
\(28\) | − | 35.5675i | − | 0.240058i | ||||||
\(29\) | 136.072i | 0.871309i | 0.900114 | + | 0.435654i | \(0.143483\pi\) | ||||
−0.900114 | + | 0.435654i | \(0.856517\pi\) | |||||||
\(30\) | 205.022 | 1.24772 | ||||||||
\(31\) | − | 50.5604i | − | 0.292933i | −0.989216 | − | 0.146466i | \(-0.953210\pi\) | ||
0.989216 | − | 0.146466i | \(-0.0467900\pi\) | |||||||
\(32\) | 103.394 | 0.571177 | ||||||||
\(33\) | −138.364 | −0.729882 | ||||||||
\(34\) | 161.818 | − | 38.2616i | 0.816222 | − | 0.192994i | ||||
\(35\) | 291.446 | 1.40752 | ||||||||
\(36\) | −17.1603 | −0.0794460 | ||||||||
\(37\) | − | 260.558i | − | 1.15772i | −0.815428 | − | 0.578858i | \(-0.803499\pi\) | ||
0.815428 | − | 0.578858i | \(-0.196501\pi\) | |||||||
\(38\) | −66.4239 | −0.283563 | ||||||||
\(39\) | − | 23.1719i | − | 0.0951404i | ||||||
\(40\) | 478.312i | 1.89069i | ||||||||
\(41\) | 183.225i | 0.697927i | 0.937136 | + | 0.348964i | \(0.113466\pi\) | ||||
−0.937136 | + | 0.348964i | \(0.886534\pi\) | |||||||
\(42\) | −158.130 | −0.580954 | ||||||||
\(43\) | −348.293 | −1.23521 | −0.617607 | − | 0.786486i | \(-0.711898\pi\) | ||||
−0.617607 | + | 0.786486i | \(0.711898\pi\) | |||||||
\(44\) | − | 73.8290i | − | 0.252958i | ||||||
\(45\) | − | 140.615i | − | 0.465813i | ||||||
\(46\) | − | 396.630i | − | 1.27130i | ||||||
\(47\) | 318.424 | 0.988232 | 0.494116 | − | 0.869396i | \(-0.335492\pi\) | ||||
0.494116 | + | 0.869396i | \(0.335492\pi\) | |||||||
\(48\) | − | 175.143i | − | 0.526661i | ||||||
\(49\) | 118.212 | 0.344641 | ||||||||
\(50\) | −599.878 | −1.69671 | ||||||||
\(51\) | 71.7066 | + | 303.266i | 0.196881 | + | 0.832660i | ||||
\(52\) | 12.3642 | 0.0329732 | ||||||||
\(53\) | −408.250 | −1.05806 | −0.529032 | − | 0.848602i | \(-0.677445\pi\) | ||||
−0.529032 | + | 0.848602i | \(0.677445\pi\) | |||||||
\(54\) | 361.063i | 0.909897i | ||||||||
\(55\) | 604.967 | 1.48316 | ||||||||
\(56\) | − | 368.916i | − | 0.880329i | ||||||
\(57\) | − | 124.486i | − | 0.289273i | ||||||
\(58\) | 322.801i | 0.730791i | ||||||||
\(59\) | 108.119 | 0.238575 | 0.119288 | − | 0.992860i | \(-0.461939\pi\) | ||||
0.119288 | + | 0.992860i | \(0.461939\pi\) | |||||||
\(60\) | −205.022 | −0.441137 | ||||||||
\(61\) | − | 123.677i | − | 0.259593i | −0.991541 | − | 0.129796i | \(-0.958568\pi\) | ||
0.991541 | − | 0.129796i | \(-0.0414324\pi\) | |||||||
\(62\) | − | 119.943i | − | 0.245691i | ||||||
\(63\) | 108.454i | 0.216888i | ||||||||
\(64\) | 560.432 | 1.09459 | ||||||||
\(65\) | 101.314i | 0.193330i | ||||||||
\(66\) | −328.239 | −0.612173 | ||||||||
\(67\) | −243.826 | −0.444598 | −0.222299 | − | 0.974979i | \(-0.571356\pi\) | ||||
−0.222299 | + | 0.974979i | \(0.571356\pi\) | |||||||
\(68\) | −161.818 | + | 38.2616i | −0.288578 | + | 0.0682338i | ||||
\(69\) | 743.331 | 1.29691 | ||||||||
\(70\) | 691.391 | 1.18053 | ||||||||
\(71\) | 42.7075i | 0.0713866i | 0.999363 | + | 0.0356933i | \(0.0113639\pi\) | ||||
−0.999363 | + | 0.0356933i | \(0.988636\pi\) | |||||||
\(72\) | −177.992 | −0.291341 | ||||||||
\(73\) | 875.172i | 1.40317i | 0.712588 | + | 0.701583i | \(0.247523\pi\) | ||||
−0.712588 | + | 0.701583i | \(0.752477\pi\) | |||||||
\(74\) | − | 618.117i | − | 0.971009i | ||||||
\(75\) | − | 1124.24i | − | 1.73088i | ||||||
\(76\) | 66.4239 | 0.100254 | ||||||||
\(77\) | −466.603 | −0.690576 | ||||||||
\(78\) | − | 54.9703i | − | 0.0797970i | ||||||
\(79\) | 750.553i | 1.06891i | 0.845197 | + | 0.534454i | \(0.179483\pi\) | ||||
−0.845197 | + | 0.534454i | \(0.820517\pi\) | |||||||
\(80\) | 765.775i | 1.07020i | ||||||||
\(81\) | −481.364 | −0.660308 | ||||||||
\(82\) | 434.662i | 0.585371i | ||||||||
\(83\) | −472.728 | −0.625165 | −0.312582 | − | 0.949891i | \(-0.601194\pi\) | ||||
−0.312582 | + | 0.949891i | \(0.601194\pi\) | |||||||
\(84\) | 158.130 | 0.205398 | ||||||||
\(85\) | −313.522 | − | 1325.96i | −0.400073 | − | 1.69201i | ||||
\(86\) | −826.250 | −1.03601 | ||||||||
\(87\) | −604.967 | −0.745509 | ||||||||
\(88\) | − | 765.775i | − | 0.927635i | ||||||
\(89\) | 376.364 | 0.448253 | 0.224127 | − | 0.974560i | \(-0.428047\pi\) | ||||
0.224127 | + | 0.974560i | \(0.428047\pi\) | |||||||
\(90\) | − | 333.578i | − | 0.390691i | ||||||
\(91\) | − | 78.1422i | − | 0.0900169i | ||||||
\(92\) | 396.630i | 0.449473i | ||||||||
\(93\) | 224.788 | 0.250639 | ||||||||
\(94\) | 755.391 | 0.828858 | ||||||||
\(95\) | 544.288i | 0.587819i | ||||||||
\(96\) | 459.683i | 0.488710i | ||||||||
\(97\) | − | 303.169i | − | 0.317342i | −0.987332 | − | 0.158671i | \(-0.949279\pi\) | ||
0.987332 | − | 0.158671i | \(-0.0507209\pi\) | |||||||
\(98\) | 280.432 | 0.289060 | ||||||||
\(99\) | 225.123i | 0.228543i | ||||||||
\(100\) | 599.878 | 0.599878 | ||||||||
\(101\) | 1484.72 | 1.46273 | 0.731363 | − | 0.681988i | \(-0.238884\pi\) | ||||
0.731363 | + | 0.681988i | \(0.238884\pi\) | |||||||
\(102\) | 170.108 | + | 719.431i | 0.165130 | + | 0.698376i | ||||
\(103\) | −168.000 | −0.160714 | −0.0803570 | − | 0.996766i | \(-0.525606\pi\) | ||||
−0.0803570 | + | 0.996766i | \(0.525606\pi\) | |||||||
\(104\) | 128.245 | 0.120918 | ||||||||
\(105\) | 1295.75i | 1.20430i | ||||||||
\(106\) | −968.484 | −0.887429 | ||||||||
\(107\) | − | 1096.53i | − | 0.990703i | −0.868693 | − | 0.495351i | \(-0.835039\pi\) | ||
0.868693 | − | 0.495351i | \(-0.164961\pi\) | |||||||
\(108\) | − | 361.063i | − | 0.321697i | ||||||
\(109\) | 828.018i | 0.727613i | 0.931475 | + | 0.363806i | \(0.118523\pi\) | ||||
−0.931475 | + | 0.363806i | \(0.881477\pi\) | |||||||
\(110\) | 1435.15 | 1.24397 | ||||||||
\(111\) | 1158.42 | 0.990565 | ||||||||
\(112\) | − | 590.632i | − | 0.498299i | ||||||
\(113\) | − | 1711.01i | − | 1.42441i | −0.701973 | − | 0.712204i | \(-0.747697\pi\) | ||
0.701973 | − | 0.712204i | \(-0.252303\pi\) | |||||||
\(114\) | − | 295.316i | − | 0.242622i | ||||||
\(115\) | −3250.05 | −2.63538 | ||||||||
\(116\) | − | 322.801i | − | 0.258374i | ||||||
\(117\) | −37.7015 | −0.0297907 | ||||||||
\(118\) | 256.490 | 0.200100 | ||||||||
\(119\) | 241.815 | + | 1022.70i | 0.186278 | + | 0.787819i | ||||
\(120\) | −2126.54 | −1.61772 | ||||||||
\(121\) | 362.451 | 0.272315 | ||||||||
\(122\) | − | 293.396i | − | 0.217728i | ||||||
\(123\) | −814.608 | −0.597160 | ||||||||
\(124\) | 119.943i | 0.0868649i | ||||||||
\(125\) | 2485.64i | 1.77858i | ||||||||
\(126\) | 257.284i | 0.181910i | ||||||||
\(127\) | −1131.46 | −0.790555 | −0.395277 | − | 0.918562i | \(-0.629352\pi\) | ||||
−0.395277 | + | 0.918562i | \(0.629352\pi\) | |||||||
\(128\) | 502.350 | 0.346890 | ||||||||
\(129\) | − | 1548.49i | − | 1.05687i | ||||||
\(130\) | 240.346i | 0.162152i | ||||||||
\(131\) | − | 1525.41i | − | 1.01737i | −0.860952 | − | 0.508687i | \(-0.830131\pi\) | ||
0.860952 | − | 0.508687i | \(-0.169869\pi\) | |||||||
\(132\) | 328.239 | 0.216436 | ||||||||
\(133\) | − | 419.802i | − | 0.273695i | ||||||
\(134\) | −578.424 | −0.372897 | ||||||||
\(135\) | 2958.61 | 1.88620 | ||||||||
\(136\) | −1678.42 | + | 396.860i | −1.05826 | + | 0.250224i | ||||
\(137\) | 430.495 | 0.268465 | 0.134232 | − | 0.990950i | \(-0.457143\pi\) | ||||
0.134232 | + | 0.990950i | \(0.457143\pi\) | |||||||
\(138\) | 1763.39 | 1.08775 | ||||||||
\(139\) | − | 1073.93i | − | 0.655323i | −0.944795 | − | 0.327662i | \(-0.893739\pi\) | ||
0.944795 | − | 0.327662i | \(-0.106261\pi\) | |||||||
\(140\) | −691.391 | −0.417380 | ||||||||
\(141\) | 1415.69i | 0.845551i | ||||||||
\(142\) | 101.314i | 0.0598739i | ||||||||
\(143\) | − | 162.203i | − | 0.0948541i | ||||||
\(144\) | −284.964 | −0.164910 | ||||||||
\(145\) | 2645.09 | 1.51491 | ||||||||
\(146\) | 2076.15i | 1.17687i | ||||||||
\(147\) | 525.562i | 0.294882i | ||||||||
\(148\) | 618.117i | 0.343304i | ||||||||
\(149\) | −1821.57 | −1.00153 | −0.500767 | − | 0.865582i | \(-0.666948\pi\) | ||||
−0.500767 | + | 0.865582i | \(0.666948\pi\) | |||||||
\(150\) | − | 2667.02i | − | 1.45174i | ||||||
\(151\) | 150.608 | 0.0811676 | 0.0405838 | − | 0.999176i | \(-0.487078\pi\) | ||||
0.0405838 | + | 0.999176i | \(0.487078\pi\) | |||||||
\(152\) | 688.967 | 0.367649 | ||||||||
\(153\) | 493.424 | − | 116.669i | 0.260725 | − | 0.0616480i | ||||
\(154\) | −1106.91 | −0.579205 | ||||||||
\(155\) | −982.837 | −0.509312 | ||||||||
\(156\) | 54.9703i | 0.0282125i | ||||||||
\(157\) | 1457.75 | 0.741026 | 0.370513 | − | 0.928827i | \(-0.379182\pi\) | ||||
0.370513 | + | 0.928827i | \(0.379182\pi\) | |||||||
\(158\) | 1780.52i | 0.896524i | ||||||||
\(159\) | − | 1815.05i | − | 0.905301i | ||||||
\(160\) | − | 2009.86i | − | 0.993085i | ||||||
\(161\) | 2506.72 | 1.22706 | ||||||||
\(162\) | −1141.93 | −0.553818 | ||||||||
\(163\) | 2573.11i | 1.23645i | 0.786001 | + | 0.618225i | \(0.212148\pi\) | ||||
−0.786001 | + | 0.618225i | \(0.787852\pi\) | |||||||
\(164\) | − | 434.662i | − | 0.206960i | ||||||
\(165\) | 2689.64i | 1.26902i | ||||||||
\(166\) | −1121.44 | −0.524343 | ||||||||
\(167\) | 1563.48i | 0.724466i | 0.932088 | + | 0.362233i | \(0.117986\pi\) | ||||
−0.932088 | + | 0.362233i | \(0.882014\pi\) | |||||||
\(168\) | 1640.17 | 0.753227 | ||||||||
\(169\) | −2169.84 | −0.987636 | ||||||||
\(170\) | −743.761 | − | 3145.56i | −0.335552 | − | 1.41914i | ||||
\(171\) | −202.543 | −0.0905782 | ||||||||
\(172\) | 826.250 | 0.366285 | ||||||||
\(173\) | − | 340.850i | − | 0.149794i | −0.997191 | − | 0.0748970i | \(-0.976137\pi\) | ||
0.997191 | − | 0.0748970i | \(-0.0238628\pi\) | |||||||
\(174\) | −1435.15 | −0.625279 | ||||||||
\(175\) | − | 3791.26i | − | 1.63767i | ||||||
\(176\) | − | 1226.00i | − | 0.525076i | ||||||
\(177\) | 480.691i | 0.204130i | ||||||||
\(178\) | 892.842 | 0.375962 | ||||||||
\(179\) | −1674.72 | −0.699297 | −0.349649 | − | 0.936881i | \(-0.613699\pi\) | ||||
−0.349649 | + | 0.936881i | \(0.613699\pi\) | |||||||
\(180\) | 333.578i | 0.138130i | ||||||||
\(181\) | − | 1178.76i | − | 0.484071i | −0.970267 | − | 0.242035i | \(-0.922185\pi\) | ||
0.970267 | − | 0.242035i | \(-0.0778150\pi\) | |||||||
\(182\) | − | 185.375i | − | 0.0754997i | ||||||
\(183\) | 549.857 | 0.222113 | ||||||||
\(184\) | 4113.96i | 1.64829i | ||||||||
\(185\) | −5064.96 | −2.01288 | ||||||||
\(186\) | 533.261 | 0.210218 | ||||||||
\(187\) | 501.946 | + | 2122.86i | 0.196289 | + | 0.830154i | ||||
\(188\) | −755.391 | −0.293045 | ||||||||
\(189\) | −2281.93 | −0.878234 | ||||||||
\(190\) | 1291.20i | 0.493020i | ||||||||
\(191\) | 3686.60 | 1.39661 | 0.698306 | − | 0.715799i | \(-0.253938\pi\) | ||||
0.698306 | + | 0.715799i | \(0.253938\pi\) | |||||||
\(192\) | 2491.64i | 0.936556i | ||||||||
\(193\) | − | 1499.75i | − | 0.559350i | −0.960095 | − | 0.279675i | \(-0.909773\pi\) | ||
0.960095 | − | 0.279675i | \(-0.0902267\pi\) | |||||||
\(194\) | − | 719.202i | − | 0.266163i | ||||||
\(195\) | −450.436 | −0.165417 | ||||||||
\(196\) | −280.432 | −0.102198 | ||||||||
\(197\) | − | 4359.97i | − | 1.57683i | −0.615145 | − | 0.788414i | \(-0.710902\pi\) | ||
0.615145 | − | 0.788414i | \(-0.289098\pi\) | |||||||
\(198\) | 534.056i | 0.191685i | ||||||||
\(199\) | − | 473.286i | − | 0.168595i | −0.996441 | − | 0.0842974i | \(-0.973135\pi\) | ||
0.996441 | − | 0.0842974i | \(-0.0268646\pi\) | |||||||
\(200\) | 6222.10 | 2.19984 | ||||||||
\(201\) | − | 1084.03i | − | 0.380407i | ||||||
\(202\) | 3522.18 | 1.22683 | ||||||||
\(203\) | −2040.12 | −0.705361 | ||||||||
\(204\) | −170.108 | − | 719.431i | −0.0583822 | − | 0.246913i | ||||
\(205\) | 3561.70 | 1.21346 | ||||||||
\(206\) | −398.543 | −0.134795 | ||||||||
\(207\) | − | 1209.43i | − | 0.406091i | ||||||
\(208\) | 205.319 | 0.0684439 | ||||||||
\(209\) | − | 871.403i | − | 0.288403i | ||||||
\(210\) | 3073.88i | 1.01008i | ||||||||
\(211\) | 4192.78i | 1.36798i | 0.729493 | + | 0.683988i | \(0.239756\pi\) | ||||
−0.729493 | + | 0.683988i | \(0.760244\pi\) | |||||||
\(212\) | 968.484 | 0.313753 | ||||||||
\(213\) | −189.875 | −0.0610798 | ||||||||
\(214\) | − | 2601.27i | − | 0.830930i | ||||||
\(215\) | 6770.43i | 2.14763i | ||||||||
\(216\) | − | 3745.04i | − | 1.17971i | ||||||
\(217\) | 758.049 | 0.237141 | ||||||||
\(218\) | 1964.29i | 0.610269i | ||||||||
\(219\) | −3890.95 | −1.20058 | ||||||||
\(220\) | −1435.15 | −0.439809 | ||||||||
\(221\) | −355.516 | + | 84.0612i | −0.108211 | + | 0.0255863i | ||||
\(222\) | 2748.11 | 0.830815 | ||||||||
\(223\) | 3017.07 | 0.906001 | 0.453001 | − | 0.891510i | \(-0.350354\pi\) | ||||
0.453001 | + | 0.891510i | \(0.350354\pi\) | |||||||
\(224\) | 1550.18i | 0.462392i | ||||||||
\(225\) | −1829.18 | −0.541979 | ||||||||
\(226\) | − | 4058.99i | − | 1.19469i | ||||||
\(227\) | 535.758i | 0.156650i | 0.996928 | + | 0.0783250i | \(0.0249572\pi\) | ||||
−0.996928 | + | 0.0783250i | \(0.975043\pi\) | |||||||
\(228\) | 295.316i | 0.0857797i | ||||||||
\(229\) | −4029.45 | −1.16277 | −0.581383 | − | 0.813630i | \(-0.697488\pi\) | ||||
−0.581383 | + | 0.813630i | \(0.697488\pi\) | |||||||
\(230\) | −7710.04 | −2.21037 | ||||||||
\(231\) | − | 2074.49i | − | 0.590871i | ||||||
\(232\) | − | 3348.18i | − | 0.947496i | ||||||
\(233\) | − | 1415.69i | − | 0.398047i | −0.979995 | − | 0.199024i | \(-0.936223\pi\) | ||
0.979995 | − | 0.199024i | \(-0.0637770\pi\) | |||||||
\(234\) | −89.4387 | −0.0249863 | ||||||||
\(235\) | − | 6189.80i | − | 1.71820i | ||||||
\(236\) | −256.490 | −0.0707460 | ||||||||
\(237\) | −3336.91 | −0.914580 | ||||||||
\(238\) | 573.653 | + | 2426.13i | 0.156237 | + | 0.660766i | ||||
\(239\) | 3584.18 | 0.970049 | 0.485024 | − | 0.874501i | \(-0.338811\pi\) | ||||
0.485024 | + | 0.874501i | \(0.338811\pi\) | |||||||
\(240\) | −3404.58 | −0.915688 | ||||||||
\(241\) | 6042.91i | 1.61518i | 0.589744 | + | 0.807590i | \(0.299228\pi\) | ||||
−0.589744 | + | 0.807590i | \(0.700772\pi\) | |||||||
\(242\) | 859.835 | 0.228398 | ||||||||
\(243\) | 1969.31i | 0.519881i | ||||||||
\(244\) | 293.396i | 0.0769784i | ||||||||
\(245\) | − | 2297.91i | − | 0.599216i | ||||||
\(246\) | −1932.48 | −0.500855 | ||||||||
\(247\) | 145.934 | 0.0375934 | ||||||||
\(248\) | 1244.09i | 0.318547i | ||||||||
\(249\) | − | 2101.72i | − | 0.534904i | ||||||
\(250\) | 5896.63i | 1.49174i | ||||||||
\(251\) | 5801.33 | 1.45887 | 0.729435 | − | 0.684050i | \(-0.239783\pi\) | ||||
0.729435 | + | 0.684050i | \(0.239783\pi\) | |||||||
\(252\) | − | 257.284i | − | 0.0643149i | ||||||
\(253\) | 5203.32 | 1.29300 | ||||||||
\(254\) | −2684.13 | −0.663061 | ||||||||
\(255\) | 5895.14 | − | 1393.90i | 1.44772 | − | 0.342310i | ||||
\(256\) | −3291.74 | −0.803647 | ||||||||
\(257\) | −2865.09 | −0.695407 | −0.347703 | − | 0.937605i | \(-0.613038\pi\) | ||||
−0.347703 | + | 0.937605i | \(0.613038\pi\) | |||||||
\(258\) | − | 3673.45i | − | 0.886430i | ||||||
\(259\) | 3906.53 | 0.937220 | ||||||||
\(260\) | − | 240.346i | − | 0.0573293i | ||||||
\(261\) | 984.303i | 0.233436i | ||||||||
\(262\) | − | 3618.71i | − | 0.853300i | ||||||
\(263\) | 542.066 | 0.127092 | 0.0635460 | − | 0.997979i | \(-0.479759\pi\) | ||||
0.0635460 | + | 0.997979i | \(0.479759\pi\) | |||||||
\(264\) | 3404.58 | 0.793703 | ||||||||
\(265\) | 7935.91i | 1.83962i | ||||||||
\(266\) | − | 995.889i | − | 0.229556i | ||||||
\(267\) | 1673.29i | 0.383534i | ||||||||
\(268\) | 578.424 | 0.131839 | ||||||||
\(269\) | 1759.85i | 0.398885i | 0.979910 | + | 0.199442i | \(0.0639131\pi\) | ||||
−0.979910 | + | 0.199442i | \(0.936087\pi\) | |||||||
\(270\) | 7018.65 | 1.58201 | ||||||||
\(271\) | −3596.70 | −0.806215 | −0.403107 | − | 0.915153i | \(-0.632070\pi\) | ||||
−0.403107 | + | 0.915153i | \(0.632070\pi\) | |||||||
\(272\) | −2687.14 | + | 635.370i | −0.599015 | + | 0.141636i | ||||
\(273\) | 347.415 | 0.0770202 | ||||||||
\(274\) | 1021.25 | 0.225169 | ||||||||
\(275\) | − | 7869.68i | − | 1.72567i | ||||||
\(276\) | −1763.39 | −0.384578 | ||||||||
\(277\) | 4539.43i | 0.984649i | 0.870412 | + | 0.492325i | \(0.163853\pi\) | ||||
−0.870412 | + | 0.492325i | \(0.836147\pi\) | |||||||
\(278\) | − | 2547.67i | − | 0.549638i | ||||||
\(279\) | − | 365.738i | − | 0.0784809i | ||||||
\(280\) | −7171.30 | −1.53060 | ||||||||
\(281\) | 1838.52 | 0.390309 | 0.195155 | − | 0.980772i | \(-0.437479\pi\) | ||||
0.195155 | + | 0.980772i | \(0.437479\pi\) | |||||||
\(282\) | 3358.42i | 0.709187i | ||||||||
\(283\) | − | 3934.41i | − | 0.826418i | −0.910636 | − | 0.413209i | \(-0.864408\pi\) | ||
0.910636 | − | 0.413209i | \(-0.135592\pi\) | |||||||
\(284\) | − | 101.314i | − | 0.0211686i | ||||||
\(285\) | −2419.87 | −0.502950 | ||||||||
\(286\) | − | 384.792i | − | 0.0795568i | ||||||
\(287\) | −2747.09 | −0.565002 | ||||||||
\(288\) | 747.920 | 0.153026 | ||||||||
\(289\) | 4392.74 | − | 2200.32i | 0.894105 | − | 0.447858i | ||||
\(290\) | 6274.89 | 1.27060 | ||||||||
\(291\) | 1347.87 | 0.271524 | ||||||||
\(292\) | − | 2076.15i | − | 0.416088i | ||||||
\(293\) | −4739.91 | −0.945080 | −0.472540 | − | 0.881309i | \(-0.656663\pi\) | ||||
−0.472540 | + | 0.881309i | \(0.656663\pi\) | |||||||
\(294\) | 1246.78i | 0.247326i | ||||||||
\(295\) | − | 2101.72i | − | 0.414803i | ||||||
\(296\) | 6411.29i | 1.25895i | ||||||||
\(297\) | −4736.72 | −0.925428 | ||||||||
\(298\) | −4321.26 | −0.840014 | ||||||||
\(299\) | 871.403i | 0.168544i | ||||||||
\(300\) | 2667.02i | 0.513267i | ||||||||
\(301\) | − | 5221.94i | − | 0.999959i | ||||||
\(302\) | 357.285 | 0.0680776 | ||||||||
\(303\) | 6600.97i | 1.25154i | ||||||||
\(304\) | 1103.03 | 0.208103 | ||||||||
\(305\) | −2404.13 | −0.451345 | ||||||||
\(306\) | 1170.54 | − | 276.772i | 0.218678 | − | 0.0517059i | ||||
\(307\) | −4965.81 | −0.923173 | −0.461586 | − | 0.887095i | \(-0.652720\pi\) | ||||
−0.461586 | + | 0.887095i | \(0.652720\pi\) | |||||||
\(308\) | 1106.91 | 0.204780 | ||||||||
\(309\) | − | 746.917i | − | 0.137510i | ||||||
\(310\) | −2331.57 | −0.427174 | ||||||||
\(311\) | 6039.28i | 1.10114i | 0.834787 | + | 0.550572i | \(0.185591\pi\) | ||||
−0.834787 | + | 0.550572i | \(0.814409\pi\) | |||||||
\(312\) | 570.168i | 0.103460i | ||||||||
\(313\) | − | 6495.68i | − | 1.17303i | −0.809940 | − | 0.586513i | \(-0.800500\pi\) | ||
0.809940 | − | 0.586513i | \(-0.199500\pi\) | |||||||
\(314\) | 3458.19 | 0.621519 | ||||||||
\(315\) | 2108.23 | 0.377096 | ||||||||
\(316\) | − | 1780.52i | − | 0.316969i | ||||||
\(317\) | − | 3036.97i | − | 0.538086i | −0.963128 | − | 0.269043i | \(-0.913293\pi\) | ||
0.963128 | − | 0.269043i | \(-0.0867074\pi\) | |||||||
\(318\) | − | 4305.81i | − | 0.759302i | ||||||
\(319\) | −4234.77 | −0.743265 | ||||||||
\(320\) | − | 10894.2i | − | 1.90313i | ||||||
\(321\) | 4875.08 | 0.847665 | ||||||||
\(322\) | 5946.65 | 1.02917 | ||||||||
\(323\) | −1909.93 | + | 451.601i | −0.329014 | + | 0.0777948i | ||||
\(324\) | 1141.93 | 0.195804 | ||||||||
\(325\) | 1317.94 | 0.224942 | ||||||||
\(326\) | 6104.13i | 1.03704i | ||||||||
\(327\) | −3681.31 | −0.622560 | ||||||||
\(328\) | − | 4508.44i | − | 0.758954i | ||||||
\(329\) | 4774.11i | 0.800015i | ||||||||
\(330\) | 6380.59i | 1.06436i | ||||||||
\(331\) | −7769.51 | −1.29018 | −0.645092 | − | 0.764105i | \(-0.723181\pi\) | ||||
−0.645092 | + | 0.764105i | \(0.723181\pi\) | |||||||
\(332\) | 1121.44 | 0.185383 | ||||||||
\(333\) | − | 1884.80i | − | 0.310169i | ||||||
\(334\) | 3709.02i | 0.607630i | ||||||||
\(335\) | 4739.70i | 0.773008i | ||||||||
\(336\) | 2625.91 | 0.426355 | ||||||||
\(337\) | 6053.47i | 0.978498i | 0.872144 | + | 0.489249i | \(0.162729\pi\) | ||||
−0.872144 | + | 0.489249i | \(0.837271\pi\) | |||||||
\(338\) | −5147.46 | −0.828358 | ||||||||
\(339\) | 7607.02 | 1.21875 | ||||||||
\(340\) | 743.761 | + | 3145.56i | 0.118636 | + | 0.501740i | ||||
\(341\) | 1573.52 | 0.249885 | ||||||||
\(342\) | −480.490 | −0.0759705 | ||||||||
\(343\) | 6914.92i | 1.08854i | ||||||||
\(344\) | 8570.10 | 1.34322 | ||||||||
\(345\) | − | 14449.5i | − | 2.25489i | ||||||
\(346\) | − | 808.593i | − | 0.125636i | ||||||
\(347\) | − | 336.418i | − | 0.0520457i | −0.999661 | − | 0.0260228i | \(-0.991716\pi\) | ||
0.999661 | − | 0.0260228i | \(-0.00828426\pi\) | |||||||
\(348\) | 1435.15 | 0.221070 | ||||||||
\(349\) | 8360.05 | 1.28224 | 0.641122 | − | 0.767439i | \(-0.278469\pi\) | ||||
0.641122 | + | 0.767439i | \(0.278469\pi\) | |||||||
\(350\) | − | 8993.93i | − | 1.37356i | ||||||
\(351\) | − | 793.260i | − | 0.120630i | ||||||
\(352\) | 3217.78i | 0.487239i | ||||||||
\(353\) | 2040.04 | 0.307593 | 0.153797 | − | 0.988103i | \(-0.450850\pi\) | ||||
0.153797 | + | 0.988103i | \(0.450850\pi\) | |||||||
\(354\) | 1140.34i | 0.171209i | ||||||||
\(355\) | 830.185 | 0.124117 | ||||||||
\(356\) | −892.842 | −0.132923 | ||||||||
\(357\) | −4546.84 | + | 1075.09i | −0.674074 | + | 0.159384i | ||||
\(358\) | −3972.90 | −0.586520 | ||||||||
\(359\) | −594.357 | −0.0873788 | −0.0436894 | − | 0.999045i | \(-0.513911\pi\) | ||||
−0.0436894 | + | 0.999045i | \(0.513911\pi\) | |||||||
\(360\) | 3459.96i | 0.506544i | ||||||||
\(361\) | −6075.00 | −0.885698 | ||||||||
\(362\) | − | 2796.36i | − | 0.406004i | ||||||
\(363\) | 1611.43i | 0.232998i | ||||||||
\(364\) | 185.375i | 0.0266932i | ||||||||
\(365\) | 17012.3 | 2.43964 | ||||||||
\(366\) | 1304.42 | 0.186292 | ||||||||
\(367\) | − | 11557.1i | − | 1.64381i | −0.569628 | − | 0.821903i | \(-0.692913\pi\) | ||
0.569628 | − | 0.821903i | \(-0.307087\pi\) | |||||||
\(368\) | 6586.43i | 0.932993i | ||||||||
\(369\) | 1325.40i | 0.186985i | ||||||||
\(370\) | −12015.5 | −1.68826 | ||||||||
\(371\) | − | 6120.86i | − | 0.856548i | ||||||
\(372\) | −533.261 | −0.0743233 | ||||||||
\(373\) | 154.375 | 0.0214296 | 0.0107148 | − | 0.999943i | \(-0.496589\pi\) | ||||
0.0107148 | + | 0.999943i | \(0.496589\pi\) | |||||||
\(374\) | 1190.76 | + | 5036.02i | 0.164633 | + | 0.696274i | ||||
\(375\) | −11051.0 | −1.52179 | ||||||||
\(376\) | −7835.13 | −1.07464 | ||||||||
\(377\) | − | 709.199i | − | 0.0968849i | ||||||
\(378\) | −5413.39 | −0.736600 | ||||||||
\(379\) | 8975.51i | 1.21647i | 0.793758 | + | 0.608234i | \(0.208122\pi\) | ||||
−0.793758 | + | 0.608234i | \(0.791878\pi\) | |||||||
\(380\) | − | 1291.20i | − | 0.174309i | ||||||
\(381\) | − | 5030.38i | − | 0.676415i | ||||||
\(382\) | 8745.65 | 1.17138 | ||||||||
\(383\) | −14032.7 | −1.87216 | −0.936081 | − | 0.351784i | \(-0.885575\pi\) | ||||
−0.936081 | + | 0.351784i | \(0.885575\pi\) | |||||||
\(384\) | 2233.41i | 0.296806i | ||||||||
\(385\) | 9070.23i | 1.20068i | ||||||||
\(386\) | − | 3557.83i | − | 0.469142i | ||||||
\(387\) | −2519.45 | −0.330932 | ||||||||
\(388\) | 719.202i | 0.0941030i | ||||||||
\(389\) | −11432.1 | −1.49006 | −0.745029 | − | 0.667032i | \(-0.767564\pi\) | ||||
−0.745029 | + | 0.667032i | \(0.767564\pi\) | |||||||
\(390\) | −1068.56 | −0.138740 | ||||||||
\(391\) | −2696.60 | − | 11404.6i | −0.348779 | − | 1.47508i | ||||
\(392\) | −2908.72 | −0.374777 | ||||||||
\(393\) | 6781.88 | 0.870486 | ||||||||
\(394\) | − | 10343.1i | − | 1.32253i | ||||||
\(395\) | 14589.9 | 1.85847 | ||||||||
\(396\) | − | 534.056i | − | 0.0677710i | ||||||
\(397\) | − | 1261.59i | − | 0.159490i | −0.996815 | − | 0.0797450i | \(-0.974589\pi\) | ||
0.996815 | − | 0.0797450i | \(-0.0254106\pi\) | |||||||
\(398\) | − | 1122.77i | − | 0.141405i | ||||||
\(399\) | 1866.41 | 0.234179 | ||||||||
\(400\) | 9961.55 | 1.24519 | ||||||||
\(401\) | 14316.4i | 1.78286i | 0.453158 | + | 0.891430i | \(0.350297\pi\) | ||||
−0.453158 | + | 0.891430i | \(0.649703\pi\) | |||||||
\(402\) | − | 2571.63i | − | 0.319058i | ||||||
\(403\) | 263.518i | 0.0325726i | ||||||||
\(404\) | −3522.18 | −0.433750 | ||||||||
\(405\) | 9357.17i | 1.14805i | ||||||||
\(406\) | −4839.74 | −0.591606 | ||||||||
\(407\) | 8108.97 | 0.987584 | ||||||||
\(408\) | −1764.41 | − | 7462.15i | −0.214096 | − | 0.905469i | ||||
\(409\) | 6819.29 | 0.824431 | 0.412215 | − | 0.911086i | \(-0.364755\pi\) | ||||
0.412215 | + | 0.911086i | \(0.364755\pi\) | |||||||
\(410\) | 8449.34 | 1.01776 | ||||||||
\(411\) | 1913.95i | 0.229704i | ||||||||
\(412\) | 398.543 | 0.0476573 | ||||||||
\(413\) | 1621.03i | 0.193137i | ||||||||
\(414\) | − | 2869.10i | − | 0.340600i | ||||||
\(415\) | 9189.30i | 1.08695i | ||||||||
\(416\) | −538.883 | −0.0635118 | ||||||||
\(417\) | 4774.64 | 0.560708 | ||||||||
\(418\) | − | 2067.21i | − | 0.241892i | ||||||
\(419\) | − | 11987.4i | − | 1.39767i | −0.715282 | − | 0.698836i | \(-0.753702\pi\) | ||
0.715282 | − | 0.698836i | \(-0.246298\pi\) | |||||||
\(420\) | − | 3073.88i | − | 0.357119i | ||||||
\(421\) | 8307.55 | 0.961722 | 0.480861 | − | 0.876797i | \(-0.340324\pi\) | ||||
0.480861 | + | 0.876797i | \(0.340324\pi\) | |||||||
\(422\) | 9946.45i | 1.14736i | ||||||||
\(423\) | 2303.38 | 0.264762 | ||||||||
\(424\) | 10045.4 | 1.15058 | ||||||||
\(425\) | −17248.7 | + | 4078.43i | −1.96867 | + | 0.465489i | ||||
\(426\) | −450.436 | −0.0512293 | ||||||||
\(427\) | 1854.27 | 0.210151 | ||||||||
\(428\) | 2601.27i | 0.293778i | ||||||||
\(429\) | 721.146 | 0.0811591 | ||||||||
\(430\) | 16061.4i | 1.80127i | ||||||||
\(431\) | − | 14582.2i | − | 1.62970i | −0.579673 | − | 0.814849i | \(-0.696820\pi\) | ||
0.579673 | − | 0.814849i | \(-0.303180\pi\) | |||||||
\(432\) | − | 5995.80i | − | 0.667761i | ||||||
\(433\) | 14056.3 | 1.56006 | 0.780028 | − | 0.625744i | \(-0.215205\pi\) | ||||
0.780028 | + | 0.625744i | \(0.215205\pi\) | |||||||
\(434\) | 1798.30 | 0.198897 | ||||||||
\(435\) | 11759.9i | 1.29619i | ||||||||
\(436\) | − | 1964.29i | − | 0.215763i | ||||||
\(437\) | 4681.42i | 0.512455i | ||||||||
\(438\) | −9230.44 | −1.00696 | ||||||||
\(439\) | − | 11386.3i | − | 1.23790i | −0.785431 | − | 0.618950i | \(-0.787559\pi\) | ||
0.785431 | − | 0.618950i | \(-0.212441\pi\) | |||||||
\(440\) | −14885.8 | −1.61285 | ||||||||
\(441\) | 855.108 | 0.0923343 | ||||||||
\(442\) | −843.385 | + | 199.417i | −0.0907596 | + | 0.0214599i | ||||
\(443\) | −11695.6 | −1.25435 | −0.627173 | − | 0.778880i | \(-0.715788\pi\) | ||||
−0.627173 | + | 0.778880i | \(0.715788\pi\) | |||||||
\(444\) | −2748.11 | −0.293737 | ||||||||
\(445\) | − | 7316.09i | − | 0.779362i | ||||||
\(446\) | 7157.35 | 0.759889 | ||||||||
\(447\) | − | 8098.55i | − | 0.856932i | ||||||
\(448\) | 8402.52i | 0.886120i | ||||||||
\(449\) | − | 5124.39i | − | 0.538608i | −0.963055 | − | 0.269304i | \(-0.913206\pi\) | ||
0.963055 | − | 0.269304i | \(-0.0867937\pi\) | |||||||
\(450\) | −4339.33 | −0.454573 | ||||||||
\(451\) | −5702.26 | −0.595363 | ||||||||
\(452\) | 4058.99i | 0.422387i | ||||||||
\(453\) | 669.593i | 0.0694486i | ||||||||
\(454\) | 1270.97i | 0.131387i | ||||||||
\(455\) | −1519.00 | −0.156509 | ||||||||
\(456\) | 3063.10i | 0.314568i | ||||||||
\(457\) | 6346.71 | 0.649643 | 0.324821 | − | 0.945775i | \(-0.394696\pi\) | ||||
0.324821 | + | 0.945775i | \(0.394696\pi\) | |||||||
\(458\) | −9558.99 | −0.975245 | ||||||||
\(459\) | 2454.78 | + | 10381.9i | 0.249628 | + | 1.05574i | ||||
\(460\) | 7710.04 | 0.781484 | ||||||||
\(461\) | −4564.08 | −0.461107 | −0.230553 | − | 0.973060i | \(-0.574054\pi\) | ||||
−0.230553 | + | 0.973060i | \(0.574054\pi\) | |||||||
\(462\) | − | 4921.26i | − | 0.495580i | ||||||
\(463\) | −13669.2 | −1.37206 | −0.686028 | − | 0.727575i | \(-0.740647\pi\) | ||||
−0.686028 | + | 0.727575i | \(0.740647\pi\) | |||||||
\(464\) | − | 5360.43i | − | 0.536318i | ||||||
\(465\) | − | 4369.62i | − | 0.435777i | ||||||
\(466\) | − | 3358.42i | − | 0.333853i | ||||||
\(467\) | 7042.76 | 0.697859 | 0.348929 | − | 0.937149i | \(-0.386545\pi\) | ||||
0.348929 | + | 0.937149i | \(0.386545\pi\) | |||||||
\(468\) | 89.4387 | 0.00883398 | ||||||||
\(469\) | − | 3655.67i | − | 0.359921i | ||||||
\(470\) | − | 14683.9i | − | 1.44111i | ||||||
\(471\) | 6481.05i | 0.634037i | ||||||||
\(472\) | −2660.38 | −0.259436 | ||||||||
\(473\) | − | 10839.4i | − | 1.05369i | ||||||
\(474\) | −7916.08 | −0.767084 | ||||||||
\(475\) | 7080.35 | 0.683934 | ||||||||
\(476\) | −573.653 | − | 2426.13i | −0.0552381 | − | 0.233616i | ||||
\(477\) | −2953.15 | −0.283471 | ||||||||
\(478\) | 8502.69 | 0.813607 | ||||||||
\(479\) | 6350.78i | 0.605793i | 0.953024 | + | 0.302896i | \(0.0979536\pi\) | ||||
−0.953024 | + | 0.302896i | \(0.902046\pi\) | |||||||
\(480\) | 8935.71 | 0.849703 | ||||||||
\(481\) | 1358.01i | 0.128732i | ||||||||
\(482\) | 14335.5i | 1.35470i | ||||||||
\(483\) | 11144.7i | 1.04990i | ||||||||
\(484\) | −859.835 | −0.0807508 | ||||||||
\(485\) | −5893.26 | −0.551751 | ||||||||
\(486\) | 4671.75i | 0.436038i | ||||||||
\(487\) | 10100.7i | 0.939849i | 0.882706 | + | 0.469925i | \(0.155719\pi\) | ||||
−0.882706 | + | 0.469925i | \(0.844281\pi\) | |||||||
\(488\) | 3043.18i | 0.282292i | ||||||||
\(489\) | −11439.9 | −1.05793 | ||||||||
\(490\) | − | 5451.28i | − | 0.502579i | ||||||
\(491\) | 11896.0 | 1.09340 | 0.546699 | − | 0.837329i | \(-0.315884\pi\) | ||||
0.546699 | + | 0.837329i | \(0.315884\pi\) | |||||||
\(492\) | 1932.48 | 0.177079 | ||||||||
\(493\) | 2194.65 | + | 9281.74i | 0.200491 | + | 0.847928i | ||||
\(494\) | 346.197 | 0.0315307 | ||||||||
\(495\) | 4376.14 | 0.397360 | ||||||||
\(496\) | 1991.78i | 0.180309i | ||||||||
\(497\) | −640.311 | −0.0577904 | ||||||||
\(498\) | − | 4985.87i | − | 0.448639i | ||||||
\(499\) | 19328.3i | 1.73398i | 0.498328 | + | 0.866989i | \(0.333948\pi\) | ||||
−0.498328 | + | 0.866989i | \(0.666052\pi\) | |||||||
\(500\) | − | 5896.63i | − | 0.527411i | ||||||
\(501\) | −6951.13 | −0.619868 | ||||||||
\(502\) | 13762.4 | 1.22360 | ||||||||
\(503\) | − | 20998.4i | − | 1.86138i | −0.365815 | − | 0.930688i | \(-0.619210\pi\) | ||
0.365815 | − | 0.930688i | \(-0.380790\pi\) | |||||||
\(504\) | − | 2668.62i | − | 0.235853i | ||||||
\(505\) | − | 28861.3i | − | 2.54319i | ||||||
\(506\) | 12343.7 | 1.08448 | ||||||||
\(507\) | − | 9646.94i | − | 0.845041i | ||||||
\(508\) | 2684.13 | 0.234427 | ||||||||
\(509\) | −7644.91 | −0.665727 | −0.332863 | − | 0.942975i | \(-0.608015\pi\) | ||||
−0.332863 | + | 0.942975i | \(0.608015\pi\) | |||||||
\(510\) | 13984.9 | − | 3306.71i | 1.21424 | − | 0.287105i | ||||
\(511\) | −13121.4 | −1.13592 | ||||||||
\(512\) | −11827.7 | −1.02093 | ||||||||
\(513\) | − | 4261.62i | − | 0.366774i | ||||||
\(514\) | −6796.81 | −0.583257 | ||||||||
\(515\) | 3265.73i | 0.279428i | ||||||||
\(516\) | 3673.45i | 0.313400i | ||||||||
\(517\) | 9909.84i | 0.843006i | ||||||||
\(518\) | 9267.39 | 0.786073 | ||||||||
\(519\) | 1515.40 | 0.128167 | ||||||||
\(520\) | − | 2492.93i | − | 0.210235i | ||||||
\(521\) | 19875.7i | 1.67134i | 0.549229 | + | 0.835672i | \(0.314922\pi\) | ||||
−0.549229 | + | 0.835672i | \(0.685078\pi\) | |||||||
\(522\) | 2335.04i | 0.195789i | ||||||||
\(523\) | 12054.6 | 1.00786 | 0.503930 | − | 0.863744i | \(-0.331887\pi\) | ||||
0.503930 | + | 0.863744i | \(0.331887\pi\) | |||||||
\(524\) | 3618.71i | 0.301687i | ||||||||
\(525\) | 16855.7 | 1.40122 | ||||||||
\(526\) | 1285.93 | 0.106596 | ||||||||
\(527\) | −815.468 | − | 3448.82i | −0.0674048 | − | 0.285072i | ||||
\(528\) | 5450.72 | 0.449266 | ||||||||
\(529\) | −15786.7 | −1.29750 | ||||||||
\(530\) | 18826.2i | 1.54294i | ||||||||
\(531\) | 782.102 | 0.0639178 | ||||||||
\(532\) | 995.889i | 0.0811603i | ||||||||
\(533\) | − | 954.960i | − | 0.0776058i | ||||||
\(534\) | 3969.51i | 0.321681i | ||||||||
\(535\) | −21315.2 | −1.72250 | ||||||||
\(536\) | 5999.58 | 0.483474 | ||||||||
\(537\) | − | 7445.68i | − | 0.598333i | ||||||
\(538\) | 4174.86i | 0.334556i | ||||||||
\(539\) | 3678.94i | 0.293994i | ||||||||
\(540\) | −7018.65 | −0.559323 | ||||||||
\(541\) | − | 607.633i | − | 0.0482887i | −0.999708 | − | 0.0241443i | \(-0.992314\pi\) | ||
0.999708 | − | 0.0241443i | \(-0.00768613\pi\) | |||||||
\(542\) | −8532.39 | −0.676195 | ||||||||
\(543\) | 5240.70 | 0.414181 | ||||||||
\(544\) | 7052.71 | − | 1667.60i | 0.555850 | − | 0.131430i | ||||
\(545\) | 16095.7 | 1.26507 | ||||||||
\(546\) | 824.166 | 0.0645990 | ||||||||
\(547\) | − | 7671.62i | − | 0.599662i | −0.953992 | − | 0.299831i | \(-0.903070\pi\) | ||
0.953992 | − | 0.299831i | \(-0.0969302\pi\) | |||||||
\(548\) | −1021.25 | −0.0796092 | ||||||||
\(549\) | − | 894.637i | − | 0.0695486i | ||||||
\(550\) | − | 18669.1i | − | 1.44737i | ||||||
\(551\) | − | 3810.02i | − | 0.294578i | ||||||
\(552\) | −18290.4 | −1.41031 | ||||||||
\(553\) | −11253.0 | −0.865327 | ||||||||
\(554\) | 10768.8i | 0.825853i | ||||||||
\(555\) | − | 22518.4i | − | 1.72226i | ||||||
\(556\) | 2547.67i | 0.194326i | ||||||||
\(557\) | 6613.01 | 0.503056 | 0.251528 | − | 0.967850i | \(-0.419067\pi\) | ||||
0.251528 | + | 0.967850i | \(0.419067\pi\) | |||||||
\(558\) | − | 867.634i | − | 0.0658241i | ||||||
\(559\) | 1815.28 | 0.137349 | ||||||||
\(560\) | −11481.2 | −0.866375 | ||||||||
\(561\) | −9438.09 | + | 2231.62i | −0.710297 | + | 0.167948i | ||||
\(562\) | 4361.49 | 0.327363 | ||||||||
\(563\) | 24867.1 | 1.86150 | 0.930750 | − | 0.365657i | \(-0.119156\pi\) | ||||
0.930750 | + | 0.365657i | \(0.119156\pi\) | |||||||
\(564\) | − | 3358.42i | − | 0.250736i | ||||||
\(565\) | −33260.0 | −2.47657 | ||||||||
\(566\) | − | 9333.52i | − | 0.693140i | ||||||
\(567\) | − | 7217.06i | − | 0.534547i | ||||||
\(568\) | − | 1050.86i | − | 0.0776286i | ||||||
\(569\) | −11933.7 | −0.879242 | −0.439621 | − | 0.898183i | \(-0.644887\pi\) | ||||
−0.439621 | + | 0.898183i | \(0.644887\pi\) | |||||||
\(570\) | −5740.61 | −0.421838 | ||||||||
\(571\) | 8593.93i | 0.629851i | 0.949116 | + | 0.314925i | \(0.101980\pi\) | ||||
−0.949116 | + | 0.314925i | \(0.898020\pi\) | |||||||
\(572\) | 384.792i | 0.0281276i | ||||||||
\(573\) | 16390.4i | 1.19497i | ||||||||
\(574\) | −6516.86 | −0.473883 | ||||||||
\(575\) | 42278.2i | 3.06630i | ||||||||
\(576\) | 4053.99 | 0.293257 | ||||||||
\(577\) | −2580.53 | −0.186185 | −0.0930927 | − | 0.995657i | \(-0.529675\pi\) | ||||
−0.0930927 | + | 0.995657i | \(0.529675\pi\) | |||||||
\(578\) | 10420.8 | − | 5219.79i | 0.749911 | − | 0.375631i | ||||
\(579\) | 6667.80 | 0.478591 | ||||||||
\(580\) | −6274.89 | −0.449225 | ||||||||
\(581\) | − | 7087.59i | − | 0.506097i | ||||||
\(582\) | 3197.52 | 0.227735 | ||||||||
\(583\) | − | 12705.4i | − | 0.902577i | ||||||
\(584\) | − | 21534.4i | − | 1.52586i | ||||||
\(585\) | 732.875i | 0.0517960i | ||||||||
\(586\) | −11244.4 | −0.792665 | ||||||||
\(587\) | −13533.0 | −0.951560 | −0.475780 | − | 0.879564i | \(-0.657834\pi\) | ||||
−0.475780 | + | 0.879564i | \(0.657834\pi\) | |||||||
\(588\) | − | 1246.78i | − | 0.0874429i | ||||||
\(589\) | 1415.69i | 0.0990366i | ||||||||
\(590\) | − | 4985.87i | − | 0.347907i | ||||||
\(591\) | 19384.1 | 1.34917 | ||||||||
\(592\) | 10264.4i | 0.712611i | ||||||||
\(593\) | 26998.2 | 1.86961 | 0.934807 | − | 0.355156i | \(-0.115572\pi\) | ||||
0.934807 | + | 0.355156i | \(0.115572\pi\) | |||||||
\(594\) | −11236.8 | −0.776183 | ||||||||
\(595\) | 19880.1 | − | 4700.61i | 1.36975 | − | 0.323876i | ||||
\(596\) | 4321.26 | 0.296990 | ||||||||
\(597\) | 2104.20 | 0.144253 | ||||||||
\(598\) | 2067.21i | 0.141362i | ||||||||
\(599\) | 26341.6 | 1.79681 | 0.898403 | − | 0.439172i | \(-0.144728\pi\) | ||||
0.898403 | + | 0.439172i | \(0.144728\pi\) | |||||||
\(600\) | 27663.0i | 1.88223i | ||||||||
\(601\) | − | 4099.87i | − | 0.278265i | −0.990274 | − | 0.139133i | \(-0.955569\pi\) | ||
0.990274 | − | 0.139133i | \(-0.0444314\pi\) | |||||||
\(602\) | − | 12387.9i | − | 0.838694i | ||||||
\(603\) | −1763.76 | −0.119114 | ||||||||
\(604\) | −357.285 | −0.0240690 | ||||||||
\(605\) | − | 7045.63i | − | 0.473464i | ||||||
\(606\) | 15659.4i | 1.04970i | ||||||||
\(607\) | 11101.4i | 0.742328i | 0.928567 | + | 0.371164i | \(0.121041\pi\) | ||||
−0.928567 | + | 0.371164i | \(0.878959\pi\) | |||||||
\(608\) | −2895.03 | −0.193107 | ||||||||
\(609\) | − | 9070.23i | − | 0.603521i | ||||||
\(610\) | −5703.28 | −0.378556 | ||||||||
\(611\) | −1659.61 | −0.109886 | ||||||||
\(612\) | −1170.54 | + | 276.772i | −0.0773142 | + | 0.0182808i | ||||
\(613\) | 5421.00 | 0.357182 | 0.178591 | − | 0.983923i | \(-0.442846\pi\) | ||||
0.178591 | + | 0.983923i | \(0.442846\pi\) | |||||||
\(614\) | −11780.3 | −0.774291 | ||||||||
\(615\) | 15835.1i | 1.03826i | ||||||||
\(616\) | 11481.2 | 0.750960 | ||||||||
\(617\) | 7246.58i | 0.472830i | 0.971652 | + | 0.236415i | \(0.0759725\pi\) | ||||
−0.971652 | + | 0.236415i | \(0.924027\pi\) | |||||||
\(618\) | − | 1771.90i | − | 0.115334i | ||||||
\(619\) | − | 18816.8i | − | 1.22183i | −0.791697 | − | 0.610914i | \(-0.790802\pi\) | ||
0.791697 | − | 0.610914i | \(-0.209198\pi\) | |||||||
\(620\) | 2331.57 | 0.151029 | ||||||||
\(621\) | 25447.0 | 1.64437 | ||||||||
\(622\) | 14326.9i | 0.923561i | ||||||||
\(623\) | 5642.80i | 0.362880i | ||||||||
\(624\) | 912.836i | 0.0585620i | ||||||||
\(625\) | 16709.3 | 1.06940 | ||||||||
\(626\) | − | 15409.6i | − | 0.983850i | ||||||
\(627\) | 3874.20 | 0.246763 | ||||||||
\(628\) | −3458.19 | −0.219740 | ||||||||
\(629\) | −4202.44 | − | 17773.2i | −0.266394 | − | 1.12665i | ||||
\(630\) | 5001.31 | 0.316281 | ||||||||
\(631\) | −17690.3 | −1.11607 | −0.558036 | − | 0.829817i | \(-0.688445\pi\) | ||||
−0.558036 | + | 0.829817i | \(0.688445\pi\) | |||||||
\(632\) | − | 18468.1i | − | 1.16237i | ||||||
\(633\) | −18640.8 | −1.17047 | ||||||||
\(634\) | − | 7204.55i | − | 0.451308i | ||||||
\(635\) | 21994.2i | 1.37451i | ||||||||
\(636\) | 4305.81i | 0.268454i | ||||||||
\(637\) | −616.113 | −0.0383223 | ||||||||
\(638\) | −10046.1 | −0.623397 | ||||||||
\(639\) | 308.933i | 0.0191255i | ||||||||
\(640\) | − | 9765.12i | − | 0.603125i | ||||||
\(641\) | − | 8132.02i | − | 0.501085i | −0.968106 | − | 0.250543i | \(-0.919391\pi\) | ||
0.968106 | − | 0.250543i | \(-0.0806090\pi\) | |||||||
\(642\) | 11565.1 | 0.710960 | ||||||||
\(643\) | − | 2653.40i | − | 0.162737i | −0.996684 | − | 0.0813684i | \(-0.974071\pi\) | ||
0.996684 | − | 0.0813684i | \(-0.0259290\pi\) | |||||||
\(644\) | −5946.65 | −0.363868 | ||||||||
\(645\) | −30100.9 | −1.83755 | ||||||||
\(646\) | −4530.90 | + | 1071.32i | −0.275953 | + | 0.0652487i | ||||
\(647\) | −12989.6 | −0.789297 | −0.394649 | − | 0.918832i | \(-0.629134\pi\) | ||||
−0.394649 | + | 0.918832i | \(0.629134\pi\) | |||||||
\(648\) | 11844.4 | 0.718045 | ||||||||
\(649\) | 3364.84i | 0.203515i | ||||||||
\(650\) | 3126.53 | 0.188665 | ||||||||
\(651\) | 3370.23i | 0.202903i | ||||||||
\(652\) | − | 6104.13i | − | 0.366651i | ||||||
\(653\) | 20945.7i | 1.25524i | 0.778521 | + | 0.627618i | \(0.215970\pi\) | ||||
−0.778521 | + | 0.627618i | \(0.784030\pi\) | |||||||
\(654\) | −8733.11 | −0.522158 | ||||||||
\(655\) | −29652.3 | −1.76887 | ||||||||
\(656\) | − | 7217.99i | − | 0.429596i | ||||||
\(657\) | 6330.72i | 0.375928i | ||||||||
\(658\) | 11325.5i | 0.670995i | ||||||||
\(659\) | −5888.03 | −0.348050 | −0.174025 | − | 0.984741i | \(-0.555677\pi\) | ||||
−0.174025 | + | 0.984741i | \(0.555677\pi\) | |||||||
\(660\) | − | 6380.59i | − | 0.376309i | ||||||
\(661\) | −7987.91 | −0.470036 | −0.235018 | − | 0.971991i | \(-0.575515\pi\) | ||||
−0.235018 | + | 0.971991i | \(0.575515\pi\) | |||||||
\(662\) | −18431.5 | −1.08211 | ||||||||
\(663\) | −373.730 | − | 1580.60i | −0.0218921 | − | 0.0925875i | ||||
\(664\) | 11631.9 | 0.679830 | ||||||||
\(665\) | −8160.48 | −0.475864 | ||||||||
\(666\) | − | 4471.27i | − | 0.260147i | ||||||
\(667\) | 22750.4 | 1.32069 | ||||||||
\(668\) | − | 3709.02i | − | 0.214830i | ||||||
\(669\) | 13413.7i | 0.775193i | ||||||||
\(670\) | 11243.9i | 0.648343i | ||||||||
\(671\) | 3849.00 | 0.221444 | ||||||||
\(672\) | −6891.99 | −0.395632 | ||||||||
\(673\) | 16.7490i | 0.000959325i | 1.00000 | 0.000479662i | \(0.000152681\pi\) | |||||
−1.00000 | 0.000479662i | \(0.999847\pi\) | ||||||||
\(674\) | 14360.5i | 0.820694i | ||||||||
\(675\) | − | 38486.9i | − | 2.19461i | ||||||
\(676\) | 5147.46 | 0.292869 | ||||||||
\(677\) | − | 28456.3i | − | 1.61546i | −0.589556 | − | 0.807728i | \(-0.700697\pi\) | ||
0.589556 | − | 0.807728i | \(-0.299303\pi\) | |||||||
\(678\) | 18046.0 | 1.02220 | ||||||||
\(679\) | 4545.39 | 0.256902 | ||||||||
\(680\) | 7714.50 | + | 32626.6i | 0.435055 | + | 1.83996i | ||||
\(681\) | −2381.95 | −0.134033 | ||||||||
\(682\) | 3732.82 | 0.209585 | ||||||||
\(683\) | 8066.90i | 0.451935i | 0.974135 | + | 0.225967i | \(0.0725542\pi\) | ||||
−0.974135 | + | 0.225967i | \(0.927446\pi\) | |||||||
\(684\) | 480.490 | 0.0268596 | ||||||||
\(685\) | − | 8368.33i | − | 0.466770i | ||||||
\(686\) | 16404.1i | 0.912992i | ||||||||
\(687\) | − | 17914.7i | − | 0.994887i | ||||||
\(688\) | 13720.7 | 0.760314 | ||||||||
\(689\) | 2127.77 | 0.117651 | ||||||||
\(690\) | − | 34278.3i | − | 1.89124i | ||||||
\(691\) | − | 22083.7i | − | 1.21578i | −0.794021 | − | 0.607890i | \(-0.792016\pi\) | ||
0.794021 | − | 0.607890i | \(-0.207984\pi\) | |||||||
\(692\) | 808.593i | 0.0444192i | ||||||||
\(693\) | −3375.26 | −0.185015 | ||||||||
\(694\) | − | 798.078i | − | 0.0436522i | ||||||
\(695\) | −20876.1 | −1.13939 | ||||||||
\(696\) | 14885.8 | 0.810697 | ||||||||
\(697\) | 2955.17 | + | 12498.2i | 0.160595 | + | 0.679199i | ||||
\(698\) | 19832.4 | 1.07545 | ||||||||
\(699\) | 6294.07 | 0.340577 | ||||||||
\(700\) | 8993.93i | 0.485626i | ||||||||
\(701\) | 276.484 | 0.0148968 | 0.00744839 | − | 0.999972i | \(-0.497629\pi\) | ||||
0.00744839 | + | 0.999972i | \(0.497629\pi\) | |||||||
\(702\) | − | 1881.84i | − | 0.101176i | ||||||
\(703\) | 7295.63i | 0.391408i | ||||||||
\(704\) | 17441.5i | 0.933737i | ||||||||
\(705\) | 27519.4 | 1.47013 | ||||||||
\(706\) | 4839.55 | 0.257987 | ||||||||
\(707\) | 22260.3i | 1.18414i | ||||||||
\(708\) | − | 1140.34i | − | 0.0605317i | ||||||
\(709\) | 24512.7i | 1.29844i | 0.760601 | + | 0.649219i | \(0.224904\pi\) | ||||
−0.760601 | + | 0.649219i | \(0.775096\pi\) | |||||||
\(710\) | 1969.43 | 0.104101 | ||||||||
\(711\) | 5429.27i | 0.286376i | ||||||||
\(712\) | −9260.81 | −0.487449 | ||||||||
\(713\) | −8453.37 | −0.444013 | ||||||||
\(714\) | −10786.4 | + | 2550.42i | −0.565365 | + | 0.133679i | ||||
\(715\) | −3153.05 | −0.164919 | ||||||||
\(716\) | 3972.90 | 0.207366 | ||||||||
\(717\) | 15935.0i | 0.829993i | ||||||||
\(718\) | −1409.98 | −0.0732870 | ||||||||
\(719\) | − | 10555.8i | − | 0.547518i | −0.961798 | − | 0.273759i | \(-0.911733\pi\) | ||
0.961798 | − | 0.273759i | \(-0.0882670\pi\) | |||||||
\(720\) | 5539.38i | 0.286723i | ||||||||
\(721\) | − | 2518.81i | − | 0.130105i | ||||||
\(722\) | −14411.6 | −0.742859 | ||||||||
\(723\) | −26866.4 | −1.38198 | ||||||||
\(724\) | 2796.36i | 0.143544i | ||||||||
\(725\) | − | 34408.5i | − | 1.76262i | ||||||
\(726\) | 3822.77i | 0.195422i | ||||||||
\(727\) | 26611.2 | 1.35757 | 0.678785 | − | 0.734337i | \(-0.262507\pi\) | ||||
0.678785 | + | 0.734337i | \(0.262507\pi\) | |||||||
\(728\) | 1922.77i | 0.0978880i | ||||||||
\(729\) | −21752.2 | −1.10513 | ||||||||
\(730\) | 40358.1 | 2.04619 | ||||||||
\(731\) | −23757.8 | + | 5617.48i | −1.20207 | + | 0.284227i | ||||
\(732\) | −1304.42 | −0.0658642 | ||||||||
\(733\) | 16288.7 | 0.820787 | 0.410393 | − | 0.911909i | \(-0.365391\pi\) | ||||
0.410393 | + | 0.911909i | \(0.365391\pi\) | |||||||
\(734\) | − | 27416.7i | − | 1.37871i | ||||||
\(735\) | 10216.3 | 0.512701 | ||||||||
\(736\) | − | 17286.8i | − | 0.865762i | ||||||
\(737\) | − | 7588.24i | − | 0.379262i | ||||||
\(738\) | 3144.21i | 0.156829i | ||||||||
\(739\) | −7901.82 | −0.393333 | −0.196667 | − | 0.980470i | \(-0.563012\pi\) | ||||
−0.196667 | + | 0.980470i | \(0.563012\pi\) | |||||||
\(740\) | 12015.5 | 0.596890 | ||||||||
\(741\) | 648.814i | 0.0321657i | ||||||||
\(742\) | − | 14520.4i | − | 0.718411i | ||||||
\(743\) | − | 28240.7i | − | 1.39441i | −0.716870 | − | 0.697207i | \(-0.754426\pi\) | ||
0.716870 | − | 0.697207i | \(-0.245574\pi\) | |||||||
\(744\) | −5531.13 | −0.272555 | ||||||||
\(745\) | 35409.2i | 1.74133i | ||||||||
\(746\) | 366.222 | 0.0179736 | ||||||||
\(747\) | −3419.57 | −0.167491 | ||||||||
\(748\) | −1190.76 | − | 5036.02i | −0.0582064 | − | 0.246170i | ||||
\(749\) | 16440.1 | 0.802016 | ||||||||
\(750\) | −26216.0 | −1.27637 | ||||||||
\(751\) | 520.691i | 0.0253000i | 0.999920 | + | 0.0126500i | \(0.00402673\pi\) | ||||
−0.999920 | + | 0.0126500i | \(0.995973\pi\) | |||||||
\(752\) | −12544.0 | −0.608288 | ||||||||
\(753\) | 25792.3i | 1.24824i | ||||||||
\(754\) | − | 1682.42i | − | 0.0812601i | ||||||
\(755\) | − | 2927.65i | − | 0.141123i | ||||||
\(756\) | 5413.39 | 0.260427 | ||||||||
\(757\) | 26471.9 | 1.27099 | 0.635495 | − | 0.772105i | \(-0.280796\pi\) | ||||
0.635495 | + | 0.772105i | \(0.280796\pi\) | |||||||
\(758\) | 21292.4i | 1.02029i | ||||||||
\(759\) | 23133.6i | 1.10632i | ||||||||
\(760\) | − | 13392.7i | − | 0.639218i | ||||||
\(761\) | −8204.72 | −0.390829 | −0.195415 | − | 0.980721i | \(-0.562605\pi\) | ||||
−0.195415 | + | 0.980721i | \(0.562605\pi\) | |||||||
\(762\) | − | 11933.5i | − | 0.567328i | ||||||
\(763\) | −12414.4 | −0.589033 | ||||||||
\(764\) | −8745.65 | −0.414145 | ||||||||
\(765\) | −2267.92 | − | 9591.60i | −0.107185 | − | 0.453314i | ||||
\(766\) | −33289.6 | −1.57024 | ||||||||
\(767\) | −563.512 | −0.0265283 | ||||||||
\(768\) | − | 14634.9i | − | 0.687617i | ||||||
\(769\) | −930.048 | −0.0436130 | −0.0218065 | − | 0.999762i | \(-0.506942\pi\) | ||||
−0.0218065 | + | 0.999762i | \(0.506942\pi\) | |||||||
\(770\) | 21517.1i | 1.00704i | ||||||||
\(771\) | − | 12738.0i | − | 0.595004i | ||||||
\(772\) | 3557.83i | 0.165867i | ||||||||
\(773\) | 24346.7 | 1.13285 | 0.566423 | − | 0.824114i | \(-0.308327\pi\) | ||||
0.566423 | + | 0.824114i | \(0.308327\pi\) | |||||||
\(774\) | −5976.83 | −0.277562 | ||||||||
\(775\) | 12785.2i | 0.592590i | ||||||||
\(776\) | 7459.77i | 0.345090i | ||||||||
\(777\) | 17368.2i | 0.801904i | ||||||||
\(778\) | −27120.3 | −1.24975 | ||||||||
\(779\) | − | 5130.31i | − | 0.235960i | ||||||
\(780\) | 1068.56 | 0.0490521 | ||||||||
\(781\) | −1329.12 | −0.0608959 | ||||||||
\(782\) | −6397.09 | − | 27054.9i | −0.292531 | − | 1.23719i | ||||
\(783\) | −20710.3 | −0.945242 | ||||||||
\(784\) | −4656.84 | −0.212138 | ||||||||
\(785\) | − | 28337.0i | − | 1.28840i | ||||||
\(786\) | 16088.5 | 0.730101 | ||||||||
\(787\) | 3683.89i | 0.166857i | 0.996514 | + | 0.0834286i | \(0.0265870\pi\) | ||||
−0.996514 | + | 0.0834286i | \(0.973413\pi\) | |||||||
\(788\) | 10343.1i | 0.467585i | ||||||||
\(789\) | 2409.99i | 0.108742i | ||||||||
\(790\) | 34611.3 | 1.55875 | ||||||||
\(791\) | 25653.0 | 1.15312 | ||||||||
\(792\) | − | 5539.38i | − | 0.248527i | ||||||
\(793\) | 644.594i | 0.0288653i | ||||||||
\(794\) | − | 2992.85i | − | 0.133769i | ||||||
\(795\) | −35282.5 | −1.57402 | ||||||||
\(796\) | 1122.77i | 0.0499943i | ||||||||
\(797\) | 10785.2 | 0.479336 | 0.239668 | − | 0.970855i | \(-0.422961\pi\) | ||||
0.239668 | + | 0.970855i | \(0.422961\pi\) | |||||||
\(798\) | 4427.65 | 0.196413 | ||||||||
\(799\) | 21720.3 | − | 5135.73i | 0.961714 | − | 0.227396i | ||||
\(800\) | −26145.2 | −1.15547 | ||||||||
\(801\) | 2722.50 | 0.120093 | ||||||||
\(802\) | 33962.5i | 1.49534i | ||||||||
\(803\) | −27236.7 | −1.19696 | ||||||||
\(804\) | 2571.63i | 0.112804i | ||||||||
\(805\) | − | 48727.8i | − | 2.13345i | ||||||
\(806\) | 625.138i | 0.0273195i | ||||||||
\(807\) | −7824.18 | −0.341294 | ||||||||
\(808\) | −36533.0 | −1.59063 | ||||||||
\(809\) | − | 5287.10i | − | 0.229771i | −0.993379 | − | 0.114885i | \(-0.963350\pi\) | ||
0.993379 | − | 0.114885i | \(-0.0366501\pi\) | |||||||
\(810\) | 22197.8i | 0.962905i | ||||||||
\(811\) | 34185.5i | 1.48017i | 0.672515 | + | 0.740084i | \(0.265214\pi\) | ||||
−0.672515 | + | 0.740084i | \(0.734786\pi\) | |||||||
\(812\) | 4839.74 | 0.209164 | ||||||||
\(813\) | − | 15990.7i | − | 0.689814i | ||||||
\(814\) | 19236.8 | 0.828314 | ||||||||
\(815\) | 50018.3 | 2.14977 | ||||||||
\(816\) | −2824.81 | − | 11946.9i | −0.121187 | − | 0.512529i | ||||
\(817\) | 9752.21 | 0.417609 | ||||||||
\(818\) | 16177.3 | 0.691473 | ||||||||
\(819\) | − | 565.257i | − | 0.0241168i | ||||||
\(820\) | −8449.34 | −0.359834 | ||||||||
\(821\) | 13283.1i | 0.564655i | 0.959318 | + | 0.282327i | \(0.0911065\pi\) | ||||
−0.959318 | + | 0.282327i | \(0.908894\pi\) | |||||||
\(822\) | 4540.43i | 0.192659i | ||||||||
\(823\) | − | 37925.7i | − | 1.60633i | −0.595759 | − | 0.803164i | \(-0.703149\pi\) | ||
0.595759 | − | 0.803164i | \(-0.296851\pi\) | |||||||
\(824\) | 4133.80 | 0.174767 | ||||||||
\(825\) | 34988.1 | 1.47652 | ||||||||
\(826\) | 3845.53i | 0.161989i | ||||||||
\(827\) | 29268.3i | 1.23066i | 0.788269 | + | 0.615331i | \(0.210978\pi\) | ||||
−0.788269 | + | 0.615331i | \(0.789022\pi\) | |||||||
\(828\) | 2869.10i | 0.120420i | ||||||||
\(829\) | −13301.0 | −0.557252 | −0.278626 | − | 0.960400i | \(-0.589879\pi\) | ||||
−0.278626 | + | 0.960400i | \(0.589879\pi\) | |||||||
\(830\) | 21799.6i | 0.911657i | ||||||||
\(831\) | −20182.0 | −0.842486 | ||||||||
\(832\) | −2920.94 | −0.121713 | ||||||||
\(833\) | 8063.47 | − | 1906.59i | 0.335393 | − | 0.0793031i | ||||
\(834\) | 11326.8 | 0.470281 | ||||||||
\(835\) | 30392.3 | 1.25960 | ||||||||
\(836\) | 2067.21i | 0.0855216i | ||||||||
\(837\) | 7695.32 | 0.317789 | ||||||||
\(838\) | − | 28437.6i | − | 1.17227i | ||||||
\(839\) | − | 10311.1i | − | 0.424288i | −0.977238 | − | 0.212144i | \(-0.931955\pi\) | ||
0.977238 | − | 0.212144i | \(-0.0680446\pi\) | |||||||
\(840\) | − | 31883.1i | − | 1.30961i | ||||||
\(841\) | 5873.39 | 0.240821 | ||||||||
\(842\) | 19707.8 | 0.806623 | ||||||||
\(843\) | 8173.94i | 0.333956i | ||||||||
\(844\) | − | 9946.45i | − | 0.405653i | ||||||
\(845\) | 42179.1i | 1.71717i | ||||||||
\(846\) | 5464.26 | 0.222063 | ||||||||
\(847\) | 5434.20i | 0.220450i | ||||||||
\(848\) | 16082.6 | 0.651272 | ||||||||
\(849\) | 17492.1 | 0.707100 | ||||||||
\(850\) | −40918.8 | + | 9675.18i | −1.65118 | + | 0.390419i | ||||
\(851\) | −43563.7 | −1.75481 | ||||||||
\(852\) | 450.436 | 0.0181123 | ||||||||
\(853\) | − | 2240.96i | − | 0.0899518i | −0.998988 | − | 0.0449759i | \(-0.985679\pi\) | ||
0.998988 | − | 0.0449759i | \(-0.0143211\pi\) | |||||||
\(854\) | 4398.86 | 0.176260 | ||||||||
\(855\) | 3937.21i | 0.157485i | ||||||||
\(856\) | 26981.1i | 1.07733i | ||||||||
\(857\) | 31870.7i | 1.27034i | 0.772371 | + | 0.635171i | \(0.219070\pi\) | ||||
−0.772371 | + | 0.635171i | \(0.780930\pi\) | |||||||
\(858\) | 1710.76 | 0.0680704 | ||||||||
\(859\) | 36917.9 | 1.46638 | 0.733191 | − | 0.680022i | \(-0.238030\pi\) | ||||
0.733191 | + | 0.680022i | \(0.238030\pi\) | |||||||
\(860\) | − | 16061.4i | − | 0.636846i | ||||||
\(861\) | − | 12213.4i | − | 0.483427i | ||||||
\(862\) | − | 34593.1i | − | 1.36687i | ||||||
\(863\) | −45364.1 | −1.78936 | −0.894678 | − | 0.446712i | \(-0.852595\pi\) | ||||
−0.894678 | + | 0.446712i | \(0.852595\pi\) | |||||||
\(864\) | 15736.6i | 0.619643i | ||||||||
\(865\) | −6625.74 | −0.260442 | ||||||||
\(866\) | 33345.6 | 1.30846 | ||||||||
\(867\) | 9782.50 | + | 19529.8i | 0.383196 | + | 0.765014i | ||||
\(868\) | −1798.30 | −0.0703208 | ||||||||
\(869\) | −23358.4 | −0.911827 | ||||||||
\(870\) | 27897.7i | 1.08715i | ||||||||
\(871\) | 1270.81 | 0.0494370 | ||||||||
\(872\) | − | 20374.2i | − | 0.791235i | ||||||
\(873\) | − | 2193.03i | − | 0.0850204i | ||||||
\(874\) | 11105.6i | 0.429810i | ||||||||
\(875\) | −37267.0 | −1.43983 | ||||||||
\(876\) | 9230.44 | 0.356013 | ||||||||
\(877\) | − | 37081.4i | − | 1.42776i | −0.700266 | − | 0.713882i | \(-0.746935\pi\) | ||
0.700266 | − | 0.713882i | \(-0.253065\pi\) | |||||||
\(878\) | − | 27011.5i | − | 1.03826i | ||||||
\(879\) | − | 21073.3i | − | 0.808630i | ||||||
\(880\) | −23832.1 | −0.912932 | ||||||||
\(881\) | − | 7501.20i | − | 0.286858i | −0.989661 | − | 0.143429i | \(-0.954187\pi\) | ||
0.989661 | − | 0.143429i | \(-0.0458129\pi\) | |||||||
\(882\) | 2028.56 | 0.0774434 | ||||||||
\(883\) | −24875.8 | −0.948059 | −0.474029 | − | 0.880509i | \(-0.657201\pi\) | ||||
−0.474029 | + | 0.880509i | \(0.657201\pi\) | |||||||
\(884\) | 843.385 | − | 199.417i | 0.0320884 | − | 0.00758723i | ||||
\(885\) | 9344.10 | 0.354913 | ||||||||
\(886\) | −27745.3 | −1.05205 | ||||||||
\(887\) | 6729.37i | 0.254735i | 0.991856 | + | 0.127368i | \(0.0406528\pi\) | ||||
−0.991856 | + | 0.127368i | \(0.959347\pi\) | |||||||
\(888\) | −28504.1 | −1.07718 | ||||||||
\(889\) | − | 16963.8i | − | 0.639988i | ||||||
\(890\) | − | 17355.8i | − | 0.653673i | ||||||
\(891\) | − | 14980.8i | − | 0.563272i | ||||||
\(892\) | −7157.35 | −0.268661 | ||||||||
\(893\) | −8915.87 | −0.334108 | ||||||||
\(894\) | − | 19212.0i | − | 0.718733i | ||||||
\(895\) | 32554.6i | 1.21584i | ||||||||
\(896\) | 7531.70i | 0.280822i | ||||||||
\(897\) | −3874.20 | −0.144209 | ||||||||
\(898\) | − | 12156.5i | − | 0.451746i | ||||||
\(899\) | 6879.86 | 0.255235 | ||||||||
\(900\) | 4339.33 | 0.160716 | ||||||||
\(901\) | −27847.5 | + | 6584.50i | −1.02967 | + | 0.243464i | ||||
\(902\) | −13527.4 | −0.499348 | ||||||||
\(903\) | 23216.4 | 0.855585 | ||||||||
\(904\) | 42101.0i | 1.54896i | ||||||||
\(905\) | −22913.8 | −0.841637 | ||||||||
\(906\) | 1588.46i | 0.0582485i | ||||||||
\(907\) | 25375.5i | 0.928976i | 0.885580 | + | 0.464488i | \(0.153762\pi\) | ||||
−0.885580 | + | 0.464488i | \(0.846238\pi\) | |||||||
\(908\) | − | 1270.97i | − | 0.0464522i | ||||||
\(909\) | 10740.0 | 0.391885 | ||||||||
\(910\) | −3603.49 | −0.131269 | ||||||||
\(911\) | − | 34073.4i | − | 1.23919i | −0.784922 | − | 0.619595i | \(-0.787297\pi\) | ||
0.784922 | − | 0.619595i | \(-0.212703\pi\) | |||||||
\(912\) | 4904.01i | 0.178057i | ||||||||
\(913\) | − | 14712.0i | − | 0.533294i | ||||||
\(914\) | 15056.2 | 0.544873 | ||||||||
\(915\) | − | 10688.6i | − | 0.386180i | ||||||
\(916\) | 9558.99 | 0.344801 | ||||||||
\(917\) | 22870.4 | 0.823607 | ||||||||
\(918\) | 5823.43 | + | 24628.8i | 0.209370 | + | 0.885481i | ||||
\(919\) | 2927.25 | 0.105072 | 0.0525360 | − | 0.998619i | \(-0.483270\pi\) | ||||
0.0525360 | + | 0.998619i | \(0.483270\pi\) | |||||||
\(920\) | 79970.7 | 2.86582 | ||||||||
\(921\) | − | 22077.7i | − | 0.789885i | ||||||
\(922\) | −10827.3 | −0.386743 | ||||||||
\(923\) | − | 222.589i | − | 0.00793781i | ||||||
\(924\) | 4921.26i | 0.175214i | ||||||||
\(925\) | 65887.2i | 2.34201i | ||||||||
\(926\) | −32427.2 | −1.15078 | ||||||||
\(927\) | −1215.26 | −0.0430576 | ||||||||
\(928\) | 14069.0i | 0.497671i | ||||||||
\(929\) | 10239.9i | 0.361637i | 0.983516 | + | 0.180819i | \(0.0578747\pi\) | ||||
−0.983516 | + | 0.180819i | \(0.942125\pi\) | |||||||
\(930\) | − | 10366.0i | − | 0.365499i | ||||||
\(931\) | −3309.93 | −0.116518 | ||||||||
\(932\) | 3358.42i | 0.118035i | ||||||||
\(933\) | −26850.2 | −0.942162 | ||||||||
\(934\) | 16707.4 | 0.585314 | ||||||||
\(935\) | 41266.0 | − | 9757.27i | 1.44336 | − | 0.341280i | ||||
\(936\) | 927.683 | 0.0323956 | ||||||||
\(937\) | −23319.4 | −0.813031 | −0.406516 | − | 0.913644i | \(-0.633256\pi\) | ||||
−0.406516 | + | 0.913644i | \(0.633256\pi\) | |||||||
\(938\) | − | 8672.27i | − | 0.301876i | ||||||
\(939\) | 28879.3 | 1.00366 | ||||||||
\(940\) | 14683.9i | 0.509508i | ||||||||
\(941\) | 11650.7i | 0.403617i | 0.979425 | + | 0.201808i | \(0.0646818\pi\) | ||||
−0.979425 | + | 0.201808i | \(0.935318\pi\) | |||||||
\(942\) | 15374.9i | 0.531784i | ||||||||
\(943\) | 30634.1 | 1.05788 | ||||||||
\(944\) | −4259.26 | −0.146851 | ||||||||
\(945\) | 44358.2i | 1.52696i | ||||||||
\(946\) | − | 25714.2i | − | 0.883762i | ||||||
\(947\) | − | 37562.0i | − | 1.28891i | −0.764641 | − | 0.644456i | \(-0.777084\pi\) | ||
0.764641 | − | 0.644456i | \(-0.222916\pi\) | |||||||
\(948\) | 7916.08 | 0.271205 | ||||||||
\(949\) | − | 4561.34i | − | 0.156025i | ||||||
\(950\) | 16796.6 | 0.573635 | ||||||||
\(951\) | 13502.2 | 0.460397 | ||||||||
\(952\) | −5950.09 | − | 25164.5i | −0.202567 | − | 0.856707i | ||||
\(953\) | 23737.8 | 0.806864 | 0.403432 | − | 0.915010i | \(-0.367817\pi\) | ||||
0.403432 | + | 0.915010i | \(0.367817\pi\) | |||||||
\(954\) | −7005.71 | −0.237755 | ||||||||
\(955\) | − | 71663.3i | − | 2.42824i | ||||||
\(956\) | −8502.69 | −0.287654 | ||||||||
\(957\) | − | 18827.5i | − | 0.635953i | ||||||
\(958\) | 15065.8i | 0.508095i | ||||||||
\(959\) | 6454.38i | 0.217333i | ||||||||
\(960\) | 48434.7 | 1.62836 | ||||||||
\(961\) | 27234.6 | 0.914190 | ||||||||
\(962\) | 3221.59i | 0.107971i | ||||||||
\(963\) | − | 7931.93i | − | 0.265423i | ||||||
\(964\) | − | 14335.5i | − | 0.478958i | ||||||
\(965\) | −29153.5 | −0.972522 | ||||||||
\(966\) | 26438.4i | 0.880581i | ||||||||
\(967\) | −5987.71 | −0.199123 | −0.0995614 | − | 0.995031i | \(-0.531744\pi\) | ||||
−0.0995614 | + | 0.995031i | \(0.531744\pi\) | |||||||
\(968\) | −8918.45 | −0.296126 | ||||||||
\(969\) | −2007.79 | − | 8491.44i | −0.0665628 | − | 0.281511i | ||||
\(970\) | −13980.5 | −0.462769 | ||||||||
\(971\) | −49295.6 | −1.62922 | −0.814609 | − | 0.580011i | \(-0.803048\pi\) | ||||
−0.814609 | + | 0.580011i | \(0.803048\pi\) | |||||||
\(972\) | − | 4671.75i | − | 0.154163i | ||||||
\(973\) | 16101.4 | 0.530512 | ||||||||
\(974\) | 23961.7i | 0.788278i | ||||||||
\(975\) | 5859.47i | 0.192465i | ||||||||
\(976\) | 4872.12i | 0.159788i | ||||||||
\(977\) | −14932.5 | −0.488979 | −0.244490 | − | 0.969652i | \(-0.578620\pi\) | ||||
−0.244490 | + | 0.969652i | \(0.578620\pi\) | |||||||
\(978\) | −27138.6 | −0.887316 | ||||||||
\(979\) | 11713.0i | 0.382380i | ||||||||
\(980\) | 5451.28i | 0.177689i | ||||||||
\(981\) | 5989.63i | 0.194938i | ||||||||
\(982\) | 28220.6 | 0.917064 | ||||||||
\(983\) | 10738.5i | 0.348427i | 0.984708 | + | 0.174213i | \(0.0557383\pi\) | ||||
−0.984708 | + | 0.174213i | \(0.944262\pi\) | |||||||
\(984\) | 20044.2 | 0.649376 | ||||||||
\(985\) | −84752.9 | −2.74158 | ||||||||
\(986\) | 5206.33 | + | 22018.9i | 0.168157 | + | 0.711181i | ||||
\(987\) | −21225.4 | −0.684509 | ||||||||
\(988\) | −346.197 | −0.0111478 | ||||||||
\(989\) | 58232.4i | 1.87228i | ||||||||
\(990\) | 10381.4 | 0.333277 | ||||||||
\(991\) | 27948.6i | 0.895878i | 0.894064 | + | 0.447939i | \(0.147842\pi\) | ||||
−0.894064 | + | 0.447939i | \(0.852158\pi\) | |||||||
\(992\) | − | 5227.64i | − | 0.167316i | ||||||
\(993\) | − | 34542.7i | − | 1.10391i | ||||||
\(994\) | −1519.00 | −0.0484705 | ||||||||
\(995\) | −9200.14 | −0.293130 | ||||||||
\(996\) | 4985.87i | 0.158618i | ||||||||
\(997\) | − | 28711.8i | − | 0.912049i | −0.889967 | − | 0.456025i | \(-0.849273\pi\) | ||
0.889967 | − | 0.456025i | \(-0.150727\pi\) | |||||||
\(998\) | 45852.2i | 1.45434i | ||||||||
\(999\) | 39657.1 | 1.25595 |
(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 | 17.4.b.a.16.4 | yes | 4 | |
3.2 | odd | 2 | 153.4.d.b.118.2 | 4 | |||
4.3 | odd | 2 | 272.4.b.d.33.2 | 4 | |||
5.2 | odd | 4 | 425.4.c.c.424.6 | 8 | |||
5.3 | odd | 4 | 425.4.c.c.424.3 | 8 | |||
5.4 | even | 2 | 425.4.d.c.101.1 | 4 | |||
17.4 | even | 4 | 289.4.a.e.1.2 | 4 | |||
17.13 | even | 4 | 289.4.a.e.1.1 | 4 | |||
17.16 | even | 2 | inner | 17.4.b.a.16.3 | ✓ | 4 | |
51.50 | odd | 2 | 153.4.d.b.118.1 | 4 | |||
68.67 | odd | 2 | 272.4.b.d.33.3 | 4 | |||
85.33 | odd | 4 | 425.4.c.c.424.4 | 8 | |||
85.67 | odd | 4 | 425.4.c.c.424.5 | 8 | |||
85.84 | even | 2 | 425.4.d.c.101.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.4.b.a.16.3 | ✓ | 4 | 17.16 | even | 2 | inner | |
17.4.b.a.16.4 | yes | 4 | 1.1 | even | 1 | trivial | |
153.4.d.b.118.1 | 4 | 51.50 | odd | 2 | |||
153.4.d.b.118.2 | 4 | 3.2 | odd | 2 | |||
272.4.b.d.33.2 | 4 | 4.3 | odd | 2 | |||
272.4.b.d.33.3 | 4 | 68.67 | odd | 2 | |||
289.4.a.e.1.1 | 4 | 17.13 | even | 4 | |||
289.4.a.e.1.2 | 4 | 17.4 | even | 4 | |||
425.4.c.c.424.3 | 8 | 5.3 | odd | 4 | |||
425.4.c.c.424.4 | 8 | 85.33 | odd | 4 | |||
425.4.c.c.424.5 | 8 | 85.67 | odd | 4 | |||
425.4.c.c.424.6 | 8 | 5.2 | odd | 4 | |||
425.4.d.c.101.1 | 4 | 5.4 | even | 2 | |||
425.4.d.c.101.2 | 4 | 85.84 | even | 2 |