Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(841,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4020.841");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.q (of order \(3\), degree \(2\), 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: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - x^{13} + 11 x^{12} - 8 x^{11} + 88 x^{10} - 57 x^{9} + 270 x^{8} + 17 x^{7} + 458 x^{6} + \cdots + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 841.7 | ||
Root | \(-0.647766 + 1.12196i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4020.841 |
Dual form | 4020.2.q.k.3781.7 |
$q$-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 \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.01447 | − | 3.48916i | 0.761396 | − | 1.31878i | −0.180735 | − | 0.983532i | \(-0.557848\pi\) |
0.942131 | − | 0.335245i | \(-0.108819\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.47884 | − | 2.56142i | 0.445887 | − | 0.772298i | −0.552227 | − | 0.833694i | \(-0.686222\pi\) |
0.998114 | + | 0.0613955i | \(0.0195551\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.795531 | − | 1.37790i | −0.220641 | − | 0.382161i | 0.734362 | − | 0.678758i | \(-0.237481\pi\) |
−0.955003 | + | 0.296597i | \(0.904148\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.62284 | − | 4.54289i | −0.636131 | − | 1.10181i | −0.986274 | − | 0.165115i | \(-0.947200\pi\) |
0.350143 | − | 0.936696i | \(-0.386133\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.339201 | + | 0.587513i | 0.0778180 | + | 0.134785i | 0.902308 | − | 0.431091i | \(-0.141871\pi\) |
−0.824490 | + | 0.565876i | \(0.808538\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.01447 | + | 3.48916i | −0.439592 | + | 0.761396i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.358507 | − | 0.620953i | −0.0747539 | − | 0.129478i | 0.826225 | − | 0.563340i | \(-0.190484\pi\) |
−0.900979 | + | 0.433862i | \(0.857150\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.40670 | − | 5.90058i | 0.632608 | − | 1.09571i | −0.354408 | − | 0.935091i | \(-0.615318\pi\) |
0.987016 | − | 0.160619i | \(-0.0513490\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.61034 | − | 2.78918i | 0.289225 | − | 0.500952i | −0.684400 | − | 0.729107i | \(-0.739936\pi\) |
0.973625 | + | 0.228155i | \(0.0732692\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.47884 | + | 2.56142i | −0.257433 | + | 0.445887i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.01447 | − | 3.48916i | 0.340507 | − | 0.589775i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.94572 | − | 3.37008i | −0.319874 | − | 0.554038i | 0.660588 | − | 0.750749i | \(-0.270307\pi\) |
−0.980461 | + | 0.196711i | \(0.936974\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.795531 | + | 1.37790i | 0.127387 | + | 0.220641i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.662081 | + | 1.14676i | −0.103400 | + | 0.179094i | −0.913083 | − | 0.407773i | \(-0.866305\pi\) |
0.809684 | + | 0.586867i | \(0.199639\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.8759 | −1.65856 | −0.829282 | − | 0.558830i | \(-0.811250\pi\) | ||||
−0.829282 | + | 0.558830i | \(0.811250\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.03954 | + | 5.26464i | −0.443363 | + | 0.767927i | −0.997937 | − | 0.0642075i | \(-0.979548\pi\) |
0.554574 | + | 0.832135i | \(0.312881\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.61614 | − | 7.99539i | −0.659449 | − | 1.14220i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.62284 | + | 4.54289i | 0.367271 | + | 0.636131i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.84141 | 0.252937 | 0.126468 | − | 0.991971i | \(-0.459636\pi\) | ||||
0.126468 | + | 0.991971i | \(0.459636\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.47884 | − | 2.56142i | 0.199407 | − | 0.345382i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.339201 | − | 0.587513i | −0.0449282 | − | 0.0778180i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.21856 | 0.419021 | 0.209511 | − | 0.977806i | \(-0.432813\pi\) | ||||
0.209511 | + | 0.977806i | \(0.432813\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.514400 | + | 0.890968i | 0.0658622 | + | 0.114077i | 0.897076 | − | 0.441876i | \(-0.145687\pi\) |
−0.831214 | + | 0.555953i | \(0.812354\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.01447 | − | 3.48916i | 0.253799 | − | 0.439592i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.795531 | − | 1.37790i | −0.0986735 | − | 0.170908i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.98224 | + | 7.62274i | −0.364339 | + | 0.931266i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.358507 | + | 0.620953i | 0.0431592 | + | 0.0747539i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.97238 | + | 12.0765i | −0.827469 | + | 1.43322i | 0.0725490 | + | 0.997365i | \(0.476887\pi\) |
−0.900018 | + | 0.435853i | \(0.856447\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.44466 | − | 5.96633i | −0.403167 | − | 0.698306i | 0.590939 | − | 0.806716i | \(-0.298757\pi\) |
−0.994106 | + | 0.108410i | \(0.965424\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.95814 | − | 10.3198i | −0.678993 | − | 1.17605i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.19415 | − | 8.99654i | 0.584388 | − | 1.01219i | −0.410563 | − | 0.911832i | \(-0.634668\pi\) |
0.994951 | − | 0.100358i | \(-0.0319987\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.85758 | + | 6.68153i | 0.423425 | + | 0.733393i | 0.996272 | − | 0.0862691i | \(-0.0274945\pi\) |
−0.572847 | + | 0.819662i | \(0.694161\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.62284 | − | 4.54289i | −0.284487 | − | 0.492745i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.40670 | + | 5.90058i | −0.365237 | + | 0.632608i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.969090 | −0.102723 | −0.0513617 | − | 0.998680i | \(-0.516356\pi\) | ||||
−0.0513617 | + | 0.998680i | \(0.516356\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.41028 | −0.671980 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.61034 | + | 2.78918i | −0.166984 | + | 0.289225i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.339201 | + | 0.587513i | 0.0348012 | + | 0.0602775i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.77014 | + | 8.26213i | 0.484335 | + | 0.838893i | 0.999838 | − | 0.0179951i | \(-0.00572832\pi\) |
−0.515503 | + | 0.856888i | \(0.672395\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.47884 | − | 2.56142i | 0.148629 | − | 0.257433i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.10709 | + | 3.64959i | −0.209663 | + | 0.363147i | −0.951608 | − | 0.307313i | \(-0.900570\pi\) |
0.741945 | + | 0.670460i | \(0.233903\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.25035 | − | 2.16566i | 0.123200 | − | 0.213389i | −0.797828 | − | 0.602886i | \(-0.794018\pi\) |
0.921028 | + | 0.389496i | \(0.127351\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.01447 | + | 3.48916i | −0.196592 | + | 0.340507i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.117103 | −0.0113208 | −0.00566041 | − | 0.999984i | \(-0.501802\pi\) | ||||
−0.00566041 | + | 0.999984i | \(0.501802\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.47281 | 0.619983 | 0.309992 | − | 0.950739i | \(-0.399674\pi\) | ||||
0.309992 | + | 0.950739i | \(0.399674\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.94572 | + | 3.37008i | 0.184679 | + | 0.319874i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.71169 | + | 16.8211i | −0.913599 | + | 1.58240i | −0.104660 | + | 0.994508i | \(0.533375\pi\) |
−0.808939 | + | 0.587892i | \(0.799958\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.358507 | − | 0.620953i | −0.0334310 | − | 0.0579042i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.795531 | − | 1.37790i | −0.0735469 | − | 0.127387i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −21.1345 | −1.93739 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.12607 | + | 1.95041i | 0.102370 | + | 0.177310i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.662081 | − | 1.14676i | 0.0596979 | − | 0.103400i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.70520 | + | 2.95350i | −0.151312 | + | 0.262081i | −0.931710 | − | 0.363203i | \(-0.881683\pi\) |
0.780398 | + | 0.625283i | \(0.215017\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.8759 | 0.957573 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.5182 | 1.00635 | 0.503173 | − | 0.864185i | \(-0.332166\pi\) | ||||
0.503173 | + | 0.864185i | \(0.332166\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.73323 | 0.237001 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.14095 | −0.182913 | −0.0914567 | − | 0.995809i | \(-0.529152\pi\) | ||||
−0.0914567 | + | 0.995809i | \(0.529152\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.56402 | −0.471934 | −0.235967 | − | 0.971761i | \(-0.575826\pi\) | ||||
−0.235967 | + | 0.971761i | \(0.575826\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.03954 | − | 5.26464i | 0.255976 | − | 0.443363i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.70585 | −0.393523 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.40670 | − | 5.90058i | 0.282911 | − | 0.490016i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.61614 | + | 7.99539i | 0.380733 | + | 0.659449i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.7958 | 0.966348 | 0.483174 | − | 0.875524i | \(-0.339484\pi\) | ||||
0.483174 | + | 0.875524i | \(0.339484\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.51228 | + | 2.61935i | 0.123068 | + | 0.213160i | 0.920976 | − | 0.389619i | \(-0.127393\pi\) |
−0.797908 | + | 0.602779i | \(0.794060\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.62284 | − | 4.54289i | −0.212044 | − | 0.367271i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.61034 | − | 2.78918i | 0.129345 | − | 0.224033i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.96108 | − | 3.39669i | −0.156511 | − | 0.271086i | 0.777097 | − | 0.629381i | \(-0.216691\pi\) |
−0.933608 | + | 0.358295i | \(0.883358\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.84141 | −0.146033 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.88880 | −0.227670 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.37206 | − | 4.10853i | 0.185794 | − | 0.321805i | −0.758050 | − | 0.652197i | \(-0.773848\pi\) |
0.943844 | + | 0.330392i | \(0.107181\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.47884 | + | 2.56142i | −0.115127 | + | 0.199407i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.13784 | + | 1.97079i | −0.0880485 | + | 0.152504i | −0.906686 | − | 0.421806i | \(-0.861396\pi\) |
0.818638 | + | 0.574310i | \(0.194730\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.23426 | − | 9.06600i | 0.402635 | − | 0.697385i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.339201 | + | 0.587513i | 0.0259393 | + | 0.0449282i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.382324 | + | 0.662205i | 0.0290676 | + | 0.0503465i | 0.880193 | − | 0.474615i | \(-0.157413\pi\) |
−0.851126 | + | 0.524962i | \(0.824080\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.01447 | − | 3.48916i | 0.152279 | − | 0.263755i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.21856 | −0.241922 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.9147 | −1.18952 | −0.594759 | − | 0.803904i | \(-0.702753\pi\) | ||||
−0.594759 | + | 0.803904i | \(0.702753\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.99097 | − | 5.18051i | 0.222317 | − | 0.385064i | −0.733194 | − | 0.680019i | \(-0.761971\pi\) |
0.955511 | + | 0.294955i | \(0.0953047\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.514400 | − | 0.890968i | −0.0380256 | − | 0.0658622i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.94572 | − | 3.37008i | −0.143052 | − | 0.247773i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.5150 | −1.13457 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.01447 | + | 3.48916i | −0.146531 | + | 0.253799i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.91365 | + | 3.31454i | 0.138467 | + | 0.239832i | 0.926916 | − | 0.375268i | \(-0.122449\pi\) |
−0.788450 | + | 0.615099i | \(0.789116\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.18305 | −0.517047 | −0.258523 | − | 0.966005i | \(-0.583236\pi\) | ||||
−0.258523 | + | 0.966005i | \(0.583236\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.795531 | + | 1.37790i | 0.0569692 | + | 0.0986735i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.5593 | − | 20.0213i | 0.823566 | − | 1.42646i | −0.0794451 | − | 0.996839i | \(-0.525315\pi\) |
0.903011 | − | 0.429618i | \(-0.141352\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.4217 | − | 23.2470i | −0.951436 | − | 1.64794i | −0.742321 | − | 0.670044i | \(-0.766275\pi\) |
−0.209114 | − | 0.977891i | \(-0.567058\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.98224 | − | 7.62274i | 0.210351 | − | 0.537667i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.7254 | − | 23.7730i | −0.963331 | − | 1.66854i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.662081 | + | 1.14676i | −0.0462418 | + | 0.0800931i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.358507 | − | 0.620953i | −0.0249180 | − | 0.0431592i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.00649 | 0.138792 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.30980 | − | 2.26864i | −0.0901704 | − | 0.156180i | 0.817412 | − | 0.576053i | \(-0.195408\pi\) |
−0.907583 | + | 0.419873i | \(0.862075\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.97238 | − | 12.0765i | 0.477739 | − | 0.827469i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.8759 | −0.741733 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.48793 | − | 11.2374i | −0.440429 | − | 0.762846i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.44466 | + | 5.96633i | 0.232769 | + | 0.403167i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.17310 | + | 7.22802i | −0.280713 | + | 0.486209i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.5929 | −1.17811 | −0.589055 | − | 0.808093i | \(-0.700500\pi\) | ||||
−0.589055 | + | 0.808093i | \(0.700500\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.78070 | − | 3.08427i | 0.118189 | − | 0.204710i | −0.800861 | − | 0.598851i | \(-0.795624\pi\) |
0.919050 | + | 0.394140i | \(0.128958\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.9704 | − | 20.7333i | −0.791025 | − | 1.37010i | −0.925333 | − | 0.379157i | \(-0.876214\pi\) |
0.134307 | − | 0.990940i | \(-0.457119\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.95814 | + | 10.3198i | 0.392017 | + | 0.678993i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.5277 | − | 19.9665i | 0.755203 | − | 1.30805i | −0.190071 | − | 0.981770i | \(-0.560872\pi\) |
0.945274 | − | 0.326279i | \(-0.105795\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.03954 | + | 5.26464i | −0.198278 | + | 0.343427i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.19415 | + | 8.99654i | −0.337397 | + | 0.584388i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.785887 | + | 1.36120i | −0.0508348 | + | 0.0880484i | −0.890323 | − | 0.455329i | \(-0.849522\pi\) |
0.839488 | + | 0.543378i | \(0.182855\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.751633 | 0.0484170 | 0.0242085 | − | 0.999707i | \(-0.492293\pi\) | ||||
0.0242085 | + | 0.999707i | \(0.492293\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.61614 | − | 7.99539i | −0.294914 | − | 0.510807i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.539689 | − | 0.934769i | 0.0343396 | − | 0.0594780i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.85758 | − | 6.68153i | −0.244464 | − | 0.423425i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.1397 | + | 26.2227i | 0.955607 | + | 1.65516i | 0.732973 | + | 0.680258i | \(0.238132\pi\) |
0.222634 | + | 0.974902i | \(0.428534\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.12070 | −0.133327 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.62284 | + | 4.54289i | 0.164248 | + | 0.284487i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.51598 | − | 7.82191i | 0.281699 | − | 0.487917i | −0.690104 | − | 0.723710i | \(-0.742435\pi\) |
0.971803 | + | 0.235793i | \(0.0757687\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15.6783 | −0.974203 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.40670 | − | 5.90058i | 0.210869 | − | 0.365237i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.4758 | −0.830952 | −0.415476 | − | 0.909604i | \(-0.636385\pi\) | ||||
−0.415476 | + | 0.909604i | \(0.636385\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.84141 | 0.113117 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.969090 | 0.0593074 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.93750 | −0.240074 | −0.120037 | − | 0.992769i | \(-0.538301\pi\) | ||||
−0.120037 | + | 0.992769i | \(0.538301\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.11307 | 0.371342 | 0.185671 | − | 0.982612i | \(-0.440554\pi\) | ||||
0.185671 | + | 0.982612i | \(0.440554\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.41028 | 0.387968 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.47884 | − | 2.56142i | 0.0891773 | − | 0.154460i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.2321 | 0.614786 | 0.307393 | − | 0.951583i | \(-0.400543\pi\) | ||||
0.307393 | + | 0.951583i | \(0.400543\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.61034 | − | 2.78918i | 0.0964082 | − | 0.166984i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.432633 | + | 0.749342i | 0.0258087 | + | 0.0447020i | 0.878641 | − | 0.477482i | \(-0.158451\pi\) |
−0.852833 | + | 0.522184i | \(0.825117\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −31.6110 | −1.87908 | −0.939541 | − | 0.342437i | \(-0.888748\pi\) | ||||
−0.939541 | + | 0.342437i | \(0.888748\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.339201 | − | 0.587513i | −0.0200925 | − | 0.0348012i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.66748 | + | 4.62021i | 0.157456 | + | 0.272722i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.25854 | + | 9.10806i | −0.309326 | + | 0.535768i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.77014 | − | 8.26213i | −0.279631 | − | 0.484335i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.7027 | 1.32631 | 0.663154 | − | 0.748483i | \(-0.269217\pi\) | ||||
0.663154 | + | 0.748483i | \(0.269217\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.21856 | 0.187392 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.47884 | + | 2.56142i | −0.0858109 | + | 0.148629i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.570408 | + | 0.987975i | −0.0329875 | + | 0.0571361i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.9092 | + | 37.9478i | −1.26282 | + | 2.18728i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.10709 | − | 3.64959i | 0.121049 | − | 0.209663i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.514400 | + | 0.890968i | 0.0294545 | + | 0.0510167i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.1406 | − | 27.9564i | −0.921193 | − | 1.59555i | −0.797572 | − | 0.603224i | \(-0.793883\pi\) |
−0.123621 | − | 0.992329i | \(-0.539451\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.25035 | + | 2.16566i | −0.0711297 | + | 0.123200i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.42942 | −0.364579 | −0.182289 | − | 0.983245i | \(-0.558351\pi\) | ||||
−0.182289 | + | 0.983245i | \(0.558351\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.54276 | −0.0872018 | −0.0436009 | − | 0.999049i | \(-0.513883\pi\) | ||||
−0.0436009 | + | 0.999049i | \(0.513883\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.01447 | − | 3.48916i | 0.113502 | − | 0.196592i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.825808 | − | 1.43034i | −0.0463820 | − | 0.0803360i | 0.841902 | − | 0.539630i | \(-0.181436\pi\) |
−0.888284 | + | 0.459294i | \(0.848102\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.0759 | − | 17.4520i | −0.564143 | − | 0.977125i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.117103 | 0.00653608 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.77934 | − | 3.08190i | 0.0990049 | − | 0.171481i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.795531 | − | 1.37790i | −0.0441281 | − | 0.0764322i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.47281 | −0.357947 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.2461 | + | 21.2109i | 0.675150 | + | 1.16939i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.91944 | − | 11.9848i | 0.380327 | − | 0.658745i | −0.610782 | − | 0.791799i | \(-0.709145\pi\) |
0.991109 | + | 0.133054i | \(0.0424783\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.94572 | − | 3.37008i | −0.106625 | − | 0.184679i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.98224 | + | 7.62274i | −0.162937 | + | 0.416475i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.03143 | − | 10.4467i | −0.328553 | − | 0.569070i | 0.653672 | − | 0.756778i | \(-0.273228\pi\) |
−0.982225 | + | 0.187708i | \(0.939894\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.71169 | − | 16.8211i | 0.527467 | − | 0.913599i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.76285 | − | 8.24950i | −0.257923 | − | 0.446736i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.99370 | −0.485614 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.358507 | + | 0.620953i | 0.0193014 | + | 0.0334310i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.2895 | − | 21.2860i | 0.659735 | − | 1.14269i | −0.320950 | − | 0.947096i | \(-0.604002\pi\) |
0.980684 | − | 0.195598i | \(-0.0626647\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.16779 | 0.383683 | 0.191841 | − | 0.981426i | \(-0.438554\pi\) | ||||
0.191841 | + | 0.981426i | \(0.438554\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.795531 | + | 1.37790i | 0.0424623 | + | 0.0735469i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.327236 | − | 0.566790i | −0.0174170 | − | 0.0301672i | 0.857186 | − | 0.515008i | \(-0.172211\pi\) |
−0.874603 | + | 0.484841i | \(0.838878\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.97238 | + | 12.0765i | −0.370055 | + | 0.640955i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 21.1345 | 1.11855 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.17595 | −0.167620 | −0.0838100 | − | 0.996482i | \(-0.526709\pi\) | ||||
−0.0838100 | + | 0.996482i | \(0.526709\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.26989 | − | 16.0559i | 0.487889 | − | 0.845048i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.12607 | − | 1.95041i | −0.0591034 | − | 0.102370i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.44466 | − | 5.96633i | −0.180302 | − | 0.312292i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.51684 | + | 7.82339i | −0.235777 | + | 0.408378i | −0.959498 | − | 0.281715i | \(-0.909097\pi\) |
0.723721 | + | 0.690092i | \(0.242430\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.662081 | + | 1.14676i | −0.0344666 | + | 0.0596979i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.70945 | − | 6.42496i | 0.192585 | − | 0.333567i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.5611 | − | 18.2923i | 0.546831 | − | 0.947140i | −0.451658 | − | 0.892191i | \(-0.649167\pi\) |
0.998489 | − | 0.0549485i | \(-0.0174995\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.8405 | −0.558316 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.31206 | − | 5.73666i | −0.170129 | − | 0.294673i | 0.768336 | − | 0.640047i | \(-0.221085\pi\) |
−0.938465 | + | 0.345375i | \(0.887752\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.70520 | − | 2.95350i | 0.0873603 | − | 0.151312i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.133978 | + | 0.232057i | 0.00684598 | + | 0.0118576i | 0.869428 | − | 0.494059i | \(-0.164488\pi\) |
−0.862582 | + | 0.505917i | \(0.831154\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.95814 | − | 10.3198i | −0.303655 | − | 0.525946i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.8759 | −0.552855 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.38734 | + | 11.0632i | 0.323851 | + | 0.560926i | 0.981279 | − | 0.192591i | \(-0.0616890\pi\) |
−0.657428 | + | 0.753517i | \(0.728356\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.88061 | + | 3.25732i | −0.0951066 | + | 0.164730i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.5182 | −0.581015 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.19415 | − | 8.99654i | 0.261346 | − | 0.452665i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.4347 | 1.62785 | 0.813924 | − | 0.580971i | \(-0.197327\pi\) | ||||
0.813924 | + | 0.580971i | \(0.197327\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.73323 | −0.136833 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.0300 | 1.00025 | 0.500126 | − | 0.865953i | \(-0.333287\pi\) | ||||
0.500126 | + | 0.865953i | \(0.333287\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.12429 | −0.255259 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.5096 | −0.570510 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.2965 | + | 21.2982i | −0.608024 | + | 1.05313i | 0.383542 | + | 0.923523i | \(0.374704\pi\) |
−0.991566 | + | 0.129605i | \(0.958629\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.14095 | 0.105605 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.48368 | − | 11.2301i | 0.319041 | − | 0.552595i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.85758 | + | 6.68153i | 0.189361 | + | 0.327983i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.56402 | 0.272471 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.19377 | − | 2.06766i | −0.0583193 | − | 0.101012i | 0.835392 | − | 0.549655i | \(-0.185241\pi\) |
−0.893711 | + | 0.448643i | \(0.851907\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.238338 | − | 0.412813i | −0.0116159 | − | 0.0201193i | 0.860159 | − | 0.510026i | \(-0.170364\pi\) |
−0.871775 | + | 0.489907i | \(0.837031\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.03954 | + | 5.26464i | −0.147788 | + | 0.255976i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.62284 | − | 4.54289i | −0.127226 | − | 0.220362i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.14497 | 0.200589 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.70585 | 0.227201 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.80478 | − | 6.59007i | 0.183270 | − | 0.317433i | −0.759722 | − | 0.650248i | \(-0.774665\pi\) |
0.942992 | + | 0.332815i | \(0.107998\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.433672 | − | 0.751142i | 0.0208409 | − | 0.0360976i | −0.855417 | − | 0.517940i | \(-0.826699\pi\) |
0.876258 | + | 0.481843i | \(0.160032\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.40670 | + | 5.90058i | −0.163339 | + | 0.282911i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.243212 | − | 0.421255i | 0.0116344 | − | 0.0201514i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.4885 | + | 26.8268i | 0.739224 | + | 1.28037i | 0.952845 | + | 0.303457i | \(0.0981409\pi\) |
−0.213621 | + | 0.976917i | \(0.568526\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.61614 | − | 7.99539i | −0.219816 | − | 0.380733i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.0873 | + | 26.1320i | −0.716820 | + | 1.24157i | 0.245433 | + | 0.969414i | \(0.421070\pi\) |
−0.962253 | + | 0.272155i | \(0.912263\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.969090 | −0.0459393 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.7958 | −0.557921 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.98151 | − | 10.3603i | 0.282285 | − | 0.488932i | −0.689662 | − | 0.724131i | \(-0.742241\pi\) |
0.971947 | + | 0.235199i | \(0.0755743\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.95822 | + | 3.39174i | 0.0922091 | + | 0.159711i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.51228 | − | 2.61935i | −0.0710533 | − | 0.123068i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.41028 | −0.300519 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.14859 | + | 12.3817i | −0.334397 | + | 0.579192i | −0.983369 | − | 0.181620i | \(-0.941866\pi\) |
0.648972 | + | 0.760812i | \(0.275199\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.62284 | + | 4.54289i | 0.122424 | + | 0.212044i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.9836 | 0.837582 | 0.418791 | − | 0.908083i | \(-0.362454\pi\) | ||||
0.418791 | + | 0.908083i | \(0.362454\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.2327 | − | 17.7236i | −0.475555 | − | 0.823686i | 0.524053 | − | 0.851686i | \(-0.324420\pi\) |
−0.999608 | + | 0.0279998i | \(0.991086\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.61034 | + | 2.78918i | −0.0746775 | + | 0.129345i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.59920 | + | 4.50194i | 0.120277 | + | 0.208325i | 0.919877 | − | 0.392208i | \(-0.128289\pi\) |
−0.799600 | + | 0.600533i | \(0.794955\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.5893 | + | 25.7613i | 0.950727 | + | 1.18954i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.96108 | + | 3.39669i | 0.0903619 | + | 0.156511i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −16.0838 | + | 27.8579i | −0.739532 | + | 1.28091i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.339201 | + | 0.587513i | 0.0155636 | + | 0.0269569i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.84141 | 0.0843123 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.34803 | + | 10.9951i | 0.290049 | + | 0.502379i | 0.973821 | − | 0.227316i | \(-0.0729952\pi\) |
−0.683772 | + | 0.729695i | \(0.739662\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.09576 | + | 5.36201i | −0.141154 | + | 0.244487i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.88880 | 0.131445 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.77014 | + | 8.26213i | 0.216601 | + | 0.375164i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.08345 | − | 12.2689i | −0.320982 | − | 0.555957i | 0.659709 | − | 0.751521i | \(-0.270680\pi\) |
−0.980691 | + | 0.195564i | \(0.937346\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.37206 | + | 4.10853i | −0.107268 | + | 0.185794i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.0080 | 1.44450 | 0.722250 | − | 0.691632i | \(-0.243108\pi\) | ||||
0.722250 | + | 0.691632i | \(0.243108\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −35.7409 | −1.60969 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.47884 | − | 2.56142i | 0.0664689 | − | 0.115127i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 28.0912 | + | 48.6554i | 1.26006 | + | 2.18249i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.2186 | − | 28.0914i | −0.726043 | − | 1.25754i | −0.958543 | − | 0.284947i | \(-0.908024\pi\) |
0.232500 | − | 0.972596i | \(-0.425309\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.13784 | − | 1.97079i | 0.0508348 | − | 0.0880485i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.7195 | − | 28.9591i | 0.745487 | − | 1.29122i | −0.204480 | − | 0.978871i | \(-0.565550\pi\) |
0.949967 | − | 0.312350i | \(-0.101116\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.10709 | + | 3.64959i | −0.0937642 | + | 0.162404i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.23426 | + | 9.06600i | −0.232462 | + | 0.402635i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.2804 | −0.765940 | −0.382970 | − | 0.923761i | \(-0.625099\pi\) | ||||
−0.382970 | + | 0.923761i | \(0.625099\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.7566 | −1.22788 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.339201 | − | 0.587513i | −0.0149761 | − | 0.0259393i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.25035 | − | 2.16566i | 0.0550968 | − | 0.0954305i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.98999 | + | 15.5711i | 0.395379 | + | 0.684817i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.382324 | − | 0.662205i | −0.0167822 | − | 0.0290676i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.5957 | −0.508015 | −0.254008 | − | 0.967202i | \(-0.581749\pi\) | ||||
−0.254008 | + | 0.967202i | \(0.581749\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.86867 | + | 8.43278i | 0.212892 | + | 0.368740i | 0.952618 | − | 0.304168i | \(-0.0983784\pi\) |
−0.739726 | + | 0.672908i | \(0.765045\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.01447 | + | 3.48916i | −0.0879185 | + | 0.152279i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16.8946 | −0.735940 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.2429 | − | 19.4734i | 0.488824 | − | 0.846667i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.21856 | 0.139674 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.10683 | 0.0912568 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.117103 | −0.00506283 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.9147 | 0.686769 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −27.3061 | −1.17616 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.8255 | 0.551411 | 0.275706 | − | 0.961242i | \(-0.411088\pi\) | ||||
0.275706 | + | 0.961242i | \(0.411088\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.99097 | + | 5.18051i | −0.128355 | + | 0.222317i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.47281 | 0.277265 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.47486 | − | 12.9468i | 0.319602 | − | 0.553567i | −0.660803 | − | 0.750559i | \(-0.729784\pi\) |
0.980405 | + | 0.196992i | \(0.0631174\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.514400 | + | 0.890968i | 0.0219541 | + | 0.0380256i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.62222 | 0.196913 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.9269 | − | 36.2464i | −0.889902 | − | 1.54136i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.94572 | + | 3.37008i | 0.0825911 | + | 0.143052i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.2541 | − | 33.3490i | 0.815821 | − | 1.41304i | −0.0929167 | − | 0.995674i | \(-0.529619\pi\) |
0.908737 | − | 0.417369i | \(-0.137048\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.65215 | + | 14.9860i | 0.365947 | + | 0.633838i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.5150 | 0.655044 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.97968 | −0.167724 | −0.0838618 | − | 0.996477i | \(-0.526725\pi\) | ||||
−0.0838618 | + | 0.996477i | \(0.526725\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.71169 | + | 16.8211i | −0.408574 | + | 0.707671i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.01447 | − | 3.48916i | 0.0845996 | − | 0.146531i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.8974 | + | 37.9274i | −0.917987 | + | 1.59000i | −0.115520 | + | 0.993305i | \(0.536853\pi\) |
−0.802468 | + | 0.596696i | \(0.796480\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.86063 | + | 8.41885i | −0.203411 | + | 0.352318i | −0.949625 | − | 0.313388i | \(-0.898536\pi\) |
0.746214 | + | 0.665706i | \(0.231869\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.91365 | − | 3.31454i | −0.0799439 | − | 0.138467i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.358507 | − | 0.620953i | −0.0149508 | − | 0.0258955i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.9145 | + | 24.1006i | −0.579267 | + | 1.00332i | 0.416296 | + | 0.909229i | \(0.363328\pi\) |
−0.995564 | + | 0.0940915i | \(0.970005\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.18305 | 0.298517 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 31.0839 | 1.28958 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.72315 | − | 4.71663i | 0.112781 | − | 0.195343i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.795531 | − | 1.37790i | −0.0328912 | − | 0.0569692i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.88217 | + | 6.72411i | 0.160234 | + | 0.277534i | 0.934953 | − | 0.354773i | \(-0.115442\pi\) |
−0.774718 | + | 0.632306i | \(0.782108\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.18491 | 0.0900275 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.5593 | + | 20.0213i | −0.475486 | + | 0.823566i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.59382 | + | 9.68879i | 0.229711 | + | 0.397871i | 0.957722 | − | 0.287694i | \(-0.0928886\pi\) |
−0.728012 | + | 0.685565i | \(0.759555\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −21.1345 | −0.866428 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.4217 | + | 23.2470i | 0.549312 | + | 0.951436i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.91450 | − | 3.31600i | 0.0782242 | − | 0.135488i | −0.824260 | − | 0.566212i | \(-0.808408\pi\) |
0.902484 | + | 0.430724i | \(0.141742\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.2689 | + | 22.9825i | 0.541251 | + | 0.937474i | 0.998833 | + | 0.0483065i | \(0.0153824\pi\) |
−0.457582 | + | 0.889168i | \(0.651284\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.98224 | + | 7.62274i | −0.121446 | + | 0.310422i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.12607 | + | 1.95041i | 0.0457813 | + | 0.0792956i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.4414 | + | 35.4055i | −0.829690 | + | 1.43707i | 0.0685917 | + | 0.997645i | \(0.478149\pi\) |
−0.898282 | + | 0.439420i | \(0.855184\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 13.7254 | + | 23.7730i | 0.556180 | + | 0.963331i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.67221 | 0.391296 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.3259 | − | 19.6170i | −0.457448 | − | 0.792324i | 0.541377 | − | 0.840780i | \(-0.317903\pi\) |
−0.998825 | + | 0.0484563i | \(0.984570\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.662081 | − | 1.14676i | 0.0266977 | − | 0.0462418i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 40.4341 | 1.62782 | 0.813908 | − | 0.580994i | \(-0.197336\pi\) | ||||
0.813908 | + | 0.580994i | \(0.197336\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.51336 | + | 9.54942i | 0.221601 | + | 0.383823i | 0.955294 | − | 0.295657i | \(-0.0955386\pi\) |
−0.733694 | + | 0.679480i | \(0.762205\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.358507 | + | 0.620953i | 0.0143864 | + | 0.0249180i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.95220 | + | 3.38131i | −0.0782132 | + | 0.135469i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.00649 | −0.0801316 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.2066 | + | 17.6783i | −0.406964 | + | 0.704882i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.30826 | − | 16.1224i | −0.370556 | − | 0.641821i | 0.619095 | − | 0.785316i | \(-0.287499\pi\) |
−0.989651 | + | 0.143494i | \(0.954166\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.30980 | + | 2.26864i | 0.0520599 | + | 0.0901704i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.70520 | + | 2.95350i | −0.0676690 | + | 0.117206i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.34457 | + | 12.7212i | −0.291002 | + | 0.504031i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.97238 | + | 12.0765i | −0.275823 | + | 0.477739i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.3550 | + | 21.3996i | −0.487995 | + | 0.845232i | −0.999905 | − | 0.0138072i | \(-0.995605\pi\) |
0.511910 | + | 0.859039i | \(0.328938\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.5875 | 1.32456 | 0.662282 | − | 0.749255i | \(-0.269588\pi\) | ||||
0.662282 | + | 0.749255i | \(0.269588\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.8759 | 0.428239 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.6888 | − | 39.2982i | −0.891990 | − | 1.54497i | −0.837486 | − | 0.546459i | \(-0.815975\pi\) |
−0.0545048 | − | 0.998514i | \(-0.517358\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.75973 | − | 8.24410i | 0.186836 | − | 0.323609i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.48793 | + | 11.2374i | 0.254282 | + | 0.440429i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.60834 | + | 7.98188i | 0.180338 | + | 0.312355i | 0.941996 | − | 0.335625i | \(-0.108947\pi\) |
−0.761657 | + | 0.647980i | \(0.775614\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.5182 | 0.450052 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.44466 | − | 5.96633i | −0.134389 | − | 0.232769i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.09361 | − | 8.82238i | 0.198419 | − | 0.343671i | −0.749597 | − | 0.661894i | \(-0.769753\pi\) |
0.948016 | + | 0.318223i | \(0.103086\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.9987 | 1.28350 | 0.641751 | − | 0.766913i | \(-0.278208\pi\) | ||||
0.641751 | + | 0.766913i | \(0.278208\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.17310 | − | 7.22802i | 0.162070 | − | 0.280713i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.73323 | 0.105990 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.88531 | −0.189160 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 17.5929 | 0.680182 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.04286 | 0.117468 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.6692 | −1.10512 | −0.552558 | − | 0.833475i | \(-0.686348\pi\) | ||||
−0.552558 | + | 0.833475i | \(0.686348\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.59788 | − | 11.4279i | 0.253577 | − | 0.439208i | −0.710931 | − | 0.703262i | \(-0.751726\pi\) |
0.964508 | + | 0.264053i | \(0.0850595\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 38.4372 | 1.47508 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.78070 | + | 3.08427i | −0.0682367 | + | 0.118189i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.35528 | − | 14.4718i | −0.319706 | − | 0.553747i | 0.660721 | − | 0.750632i | \(-0.270251\pi\) |
−0.980427 | + | 0.196885i | \(0.936917\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.14095 | −0.0818013 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.9704 | + | 20.7333i | 0.456699 | + | 0.791025i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.46490 | − | 2.53728i | −0.0558082 | − | 0.0966626i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.3246 | − | 31.7392i | 0.697101 | − | 1.20742i | −0.272366 | − | 0.962194i | \(-0.587806\pi\) |
0.969467 | − | 0.245221i | \(-0.0788606\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.95814 | − | 10.3198i | −0.226331 | − | 0.392017i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.56402 | −0.211055 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.94613 | 0.263103 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11.5277 | + | 19.9665i | −0.436016 | + | 0.755203i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.0317333 | + | 0.0549637i | −0.00119855 | + | 0.00207595i | −0.866624 | − | 0.498962i | \(-0.833715\pi\) |
0.865426 | + | 0.501038i | \(0.167048\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.31998 | − | 2.28627i | 0.0497839 | − | 0.0862282i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.03954 | − | 5.26464i | 0.114476 | − | 0.198278i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.48932 | + | 14.7039i | 0.319274 | + | 0.552998i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.92424 | − | 10.2611i | −0.222490 | − | 0.385363i | 0.733074 | − | 0.680149i | \(-0.238085\pi\) |
−0.955563 | + | 0.294786i | \(0.904752\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.19415 | − | 8.99654i | 0.194796 | − | 0.337397i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.30927 | −0.0864828 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.70585 | −0.175989 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.785887 | − | 1.36120i | 0.0293495 | − | 0.0508348i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.5290 | + | 23.4328i | 0.504545 | + | 0.873897i | 0.999986 | + | 0.00525586i | \(0.00167300\pi\) |
−0.495441 | + | 0.868641i | \(0.664994\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.03756 | − | 8.72531i | −0.187609 | − | 0.324947i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.751633 | −0.0279535 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.40670 | − | 5.90058i | 0.126522 | − | 0.219142i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.11684 | − | 5.39852i | −0.115597 | − | 0.200220i | 0.802421 | − | 0.596758i | \(-0.203545\pi\) |
−0.918018 | + | 0.396538i | \(0.870211\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28.5258 | + | 49.4081i | 1.05506 | + | 1.82743i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.7516 | − | 39.4069i | 0.840349 | − | 1.45553i | −0.0492511 | − | 0.998786i | \(-0.515683\pi\) |
0.889600 | − | 0.456741i | \(-0.150983\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.61614 | + | 7.99539i | 0.170269 | + | 0.294914i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15.1148 | + | 18.9116i | 0.556762 | + | 0.696618i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.89645 | − | 10.2130i | −0.216904 | − | 0.375690i | 0.736956 | − | 0.675941i | \(-0.236263\pi\) |
−0.953860 | + | 0.300252i | \(0.902929\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.539689 | + | 0.934769i | −0.0198260 | + | 0.0343396i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.3166 | + | 24.7970i | 0.525224 | + | 0.909715i | 0.999568 | + | 0.0293756i | \(0.00935189\pi\) |
−0.474344 | + | 0.880339i | \(0.657315\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.7958 | 0.432164 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.85758 | + | 6.68153i | 0.141142 | + | 0.244464i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.235901 | + | 0.408592i | −0.00861963 | + | 0.0149296i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.0352 | 0.658112 | 0.329056 | − | 0.944310i | \(-0.393269\pi\) | ||||
0.329056 | + | 0.944310i | \(0.393269\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15.1397 | − | 26.2227i | −0.551720 | − | 0.955607i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.51228 | + | 2.61935i | 0.0550377 | + | 0.0953280i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.56650 | + | 9.64145i | −0.202318 | + | 0.350425i | −0.949275 | − | 0.314448i | \(-0.898181\pi\) |
0.746957 | + | 0.664872i | \(0.231514\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.12070 | 0.0769765 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.62039 | −0.167489 | −0.0837446 | − | 0.996487i | \(-0.526688\pi\) | ||||
−0.0837446 | + | 0.996487i | \(0.526688\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.0393 | − | 22.5847i | 0.472053 | − | 0.817620i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.62284 | − | 4.54289i | −0.0948289 | − | 0.164248i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.56047 | − | 4.43486i | −0.0924531 | − | 0.160133i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.44864 | − | 5.97321i | 0.124361 | − | 0.215400i | −0.797122 | − | 0.603818i | \(-0.793645\pi\) |
0.921483 | + | 0.388419i | \(0.126979\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.51598 | + | 7.82191i | −0.162639 | + | 0.281699i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.0363 | − | 17.3833i | 0.360980 | − | 0.625235i | −0.627143 | − | 0.778904i | \(-0.715776\pi\) |
0.988122 | + | 0.153669i | \(0.0491090\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.61034 | − | 2.78918i | 0.0578449 | − | 0.100190i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 15.6783 | 0.562457 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.898314 | −0.0321854 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.6220 | + | 35.7184i | 0.737915 | + | 1.27811i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.40670 | + | 5.90058i | −0.121746 | + | 0.210869i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.96108 | − | 3.39669i | −0.0699940 | − | 0.121233i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.64960 | − | 8.05335i | −0.165740 | − | 0.287071i | 0.771178 | − | 0.636620i | \(-0.219668\pi\) |
−0.936918 | + | 0.349549i | \(0.886335\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 13.4758 | 0.479751 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 39.1277 | + | 67.7712i | 1.39122 | + | 2.40967i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.818443 | − | 1.41759i | 0.0290638 | − | 0.0503399i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.84141 | −0.0653080 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −18.4373 | + | 31.9343i | −0.653083 | + | 1.13117i | 0.329288 | + | 0.944230i | \(0.393191\pi\) |
−0.982371 | + | 0.186943i | \(0.940142\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 31.8889 | 1.12815 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.969090 | −0.0342411 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −20.3764 | −0.719068 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.88880 | −0.101817 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.93750 | 0.138607 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31.6865 | 1.11404 | 0.557020 | − | 0.830499i | \(-0.311945\pi\) | ||||
0.557020 | + | 0.830499i | \(0.311945\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.3188 | + | 35.1931i | −0.713488 | + | 1.23580i | 0.250052 | + | 0.968232i | \(0.419552\pi\) |
−0.963540 | + | 0.267565i | \(0.913781\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.11307 | −0.214395 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.37206 | − | 4.10853i | 0.0830898 | − | 0.143916i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.68912 | − | 6.38975i | −0.129066 | − | 0.223549i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.41028 | −0.223993 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.30966 | − | 4.00046i | −0.0806078 | − | 0.139617i | 0.822903 | − | 0.568181i | \(-0.192353\pi\) |
−0.903511 | + | 0.428565i | \(0.859019\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.7575 | − | 44.6133i | −0.897850 | − | 1.55512i | −0.830238 | − | 0.557410i | \(-0.811795\pi\) |
−0.0676122 | − | 0.997712i | \(-0.521538\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.47884 | + | 2.56142i | −0.0514866 | + | 0.0891773i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.25416 | + | 9.10048i | 0.182705 | + | 0.316455i | 0.942801 | − | 0.333357i | \(-0.108181\pi\) |
−0.760096 | + | 0.649811i | \(0.774848\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.3054 | 0.357920 | 0.178960 | − | 0.983856i | \(-0.442727\pi\) | ||||
0.178960 | + | 0.983856i | \(0.442727\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.2321 | −0.354947 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −24.2148 | + | 41.9412i | −0.838992 | + | 1.45318i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.13784 | + | 1.97079i | −0.0393765 | + | 0.0682021i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.61034 | + | 2.78918i | −0.0556613 | + | 0.0964082i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22.1873 | + | 38.4294i | −0.765989 | + | 1.32673i | 0.173733 | + | 0.984793i | \(0.444417\pi\) |
−0.939722 | + | 0.341939i | \(0.888916\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.71121 | − | 15.0883i | −0.300387 | − | 0.520285i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.432633 | − | 0.749342i | −0.0149007 | − | 0.0258087i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.23426 | − | 9.06600i | 0.180064 | − | 0.311880i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.07373 | 0.311777 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 31.6110 | 1.08489 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.39511 | + | 2.41640i | −0.0478237 | + | 0.0828330i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.96832 | − | 8.60538i | −0.170112 | − | 0.294643i | 0.768347 | − | 0.640034i | \(-0.221080\pi\) |
−0.938459 | + | 0.345391i | \(0.887746\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.339201 | + | 0.587513i | 0.0116004 | + | 0.0200925i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28.5335 | 0.974686 | 0.487343 | − | 0.873211i | \(-0.337966\pi\) | ||||
0.487343 | + | 0.873211i | \(0.337966\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.72748 | + | 6.45619i | −0.127180 | + | 0.220282i | −0.922583 | − | 0.385799i | \(-0.873926\pi\) |
0.795403 | + | 0.606081i | \(0.207259\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.66748 | − | 4.62021i | −0.0909075 | − | 0.157456i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.47929 | 0.0843962 | 0.0421981 | − | 0.999109i | \(-0.486564\pi\) | ||||
0.0421981 | + | 0.999109i | \(0.486564\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.382324 | + | 0.662205i | 0.0129994 | + | 0.0225156i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.25854 | − | 9.10806i | 0.178589 | − | 0.309326i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15.3626 | − | 26.6089i | −0.521142 | − | 0.902644i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.8759 | − | 1.95490i | 0.436282 | − | 0.0662392i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.77014 | + | 8.26213i | 0.161445 | + | 0.279631i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.01447 | − | 3.48916i | 0.0681014 | − | 0.117955i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.428389 | + | 0.741992i | 0.0144657 | + | 0.0250553i | 0.873168 | − | 0.487420i | \(-0.162062\pi\) |
−0.858702 | + | 0.512475i | \(0.828729\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −22.7027 | −0.765745 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.2606 | − | 42.0205i | −0.817359 | − | 1.41571i | −0.907622 | − | 0.419789i | \(-0.862104\pi\) |
0.0902627 | − | 0.995918i | \(-0.471229\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.11466 | − | 12.3230i | 0.239427 | − | 0.414701i | −0.721123 | − | 0.692807i | \(-0.756374\pi\) |
0.960550 | + | 0.278107i | \(0.0897069\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.21856 | −0.108191 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 27.7264 | + | 48.0236i | 0.930963 | + | 1.61247i | 0.781680 | + | 0.623680i | \(0.214363\pi\) |
0.149283 | + | 0.988794i | \(0.452303\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.87015 | + | 11.8995i | 0.230418 | + | 0.399095i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.47884 | − | 2.56142i | 0.0495430 | − | 0.0858109i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.12406 | −0.138006 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.9147 | −0.531969 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.570408 | − | 0.987975i | 0.0190454 | − | 0.0329875i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.9719 | − | 19.0038i | −0.365932 | − | 0.633813i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.82971 | − | 8.36531i | −0.160901 | − | 0.278689i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 21.9092 | − | 37.9478i | 0.729092 | − | 1.26282i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.99097 | − | 5.18051i | 0.0994231 | − | 0.172206i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.20308 | + | 14.2082i | −0.272379 | + | 0.471774i | −0.969470 | − | 0.245208i | \(-0.921144\pi\) |
0.697092 | + | 0.716982i | \(0.254477\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.10709 | + | 3.64959i | −0.0698877 | + | 0.121049i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 46.8920 | 1.55360 | 0.776801 | − | 0.629746i | \(-0.216841\pi\) | ||||
0.776801 | + | 0.629746i | \(0.216841\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.8190 | 0.755198 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.514400 | − | 0.890968i | −0.0170056 | − | 0.0294545i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 23.2029 | − | 40.1887i | 0.766229 | − | 1.32715i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.2663 | + | 50.6907i | 0.965405 | + | 1.67213i | 0.708523 | + | 0.705688i | \(0.249362\pi\) |
0.256882 | + | 0.966443i | \(0.417305\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.1406 | + | 27.9564i | 0.531851 | + | 0.921193i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22.1870 | 0.730293 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.94572 | − | 3.37008i | −0.0639748 | − | 0.110808i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.25035 | − | 2.16566i | 0.0410668 | − | 0.0711297i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.7443 | 0.647789 | 0.323894 | − | 0.946093i | \(-0.395008\pi\) | ||||
0.323894 | + | 0.946093i | \(0.395008\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.13160 | − | 5.42408i | 0.102634 | − | 0.177767i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.42942 | 0.210490 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −15.5150 | −0.507395 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −49.9894 | −1.63308 | −0.816541 | − | 0.577287i | \(-0.804111\pi\) | ||||
−0.816541 | + | 0.577287i | \(0.804111\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.54276 | 0.0503460 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.78909 | 0.156120 | 0.0780600 | − | 0.996949i | \(-0.475127\pi\) | ||||
0.0780600 | + | 0.996949i | \(0.475127\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.949444 | 0.0309182 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.01447 | + | 3.48916i | −0.0655306 | + | 0.113502i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −32.1778 | −1.04564 | −0.522819 | − | 0.852444i | \(-0.675120\pi\) | ||||
−0.522819 | + | 0.852444i | \(0.675120\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.48067 | + | 9.49281i | −0.177910 | + | 0.308150i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.825808 | + | 1.43034i | 0.0267787 | + | 0.0463820i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.0194423 | 0.000629798 | 0.000314899 | − | 1.00000i | \(-0.499900\pi\) | ||||
0.000314899 | 1.00000i | \(0.499900\pi\) | ||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.91365 | + | 3.31454i | 0.0619243 | + | 0.107256i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.0759 | + | 17.4520i | 0.325708 | + | 0.564143i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.31286 | + | 7.47010i | −0.139270 | + | 0.241222i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.3136 | + | 17.8638i | 0.332698 | + | 0.576250i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.117103 | −0.00377361 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.18305 | −0.231230 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.72730 | − | 11.6520i | 0.216335 | − | 0.374704i | −0.737349 | − | 0.675512i | \(-0.763923\pi\) |
0.953685 | + | 0.300808i | \(0.0972562\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.77934 | + | 3.08190i | −0.0571605 | + | 0.0990049i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.0898 | + | 24.4043i | −0.452164 | + | 0.783172i | −0.998520 | − | 0.0543815i | \(-0.982681\pi\) |
0.546356 | + | 0.837553i | \(0.316015\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.2085 | + | 19.4137i | −0.359329 | + | 0.622376i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.795531 | + | 1.37790i | 0.0254774 | + | 0.0441281i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.6955 | + | 41.0418i | 0.758085 | + | 1.31304i | 0.943826 | + | 0.330443i | \(0.107198\pi\) |
−0.185740 | + | 0.982599i | \(0.559468\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.43313 | + | 2.48225i | −0.0458030 | + | 0.0793331i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.47281 | 0.206661 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.5349 | 0.399802 | 0.199901 | − | 0.979816i | \(-0.435938\pi\) | ||||
0.199901 | + | 0.979816i | \(0.435938\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.5593 | − | 20.0213i | 0.368310 | − | 0.637931i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12.2461 | − | 21.2109i | −0.389798 | − | 0.675150i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.89910 | + | 6.75344i | 0.123984 | + | 0.214747i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.3722 | 0.774208 | 0.387104 | − | 0.922036i | \(-0.373475\pi\) | ||||
0.387104 | + | 0.922036i | \(0.373475\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.91944 | + | 11.9848i | −0.219582 | + | 0.380327i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13.4217 | − | 23.2470i | −0.425495 | − | 0.736979i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.45388 | 0.109386 | 0.0546928 | − | 0.998503i | \(-0.482582\pi\) | ||||
0.0546928 | + | 0.998503i | \(0.482582\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.94572 | + | 3.37008i | 0.0615598 | + | 0.106625i |
(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 | 4020.2.q.k.841.7 | ✓ | 14 | |
67.29 | even | 3 | inner | 4020.2.q.k.3781.7 | yes | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.q.k.841.7 | ✓ | 14 | 1.1 | even | 1 | trivial | |
4020.2.q.k.3781.7 | yes | 14 | 67.29 | even | 3 | inner |