Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4026,2,Mod(1,4026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4026, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4026.a (trivial) |
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: | yes |
Analytic conductor: | \(32.1477718538\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 2x^{6} - 21x^{5} + 39x^{4} + 89x^{3} - 100x^{2} - 96x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.80390\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4026.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.80390 | −1.70116 | −0.850578 | − | 0.525849i | \(-0.823748\pi\) | ||||
−0.850578 | + | 0.525849i | \(0.823748\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −1.13011 | −0.427140 | −0.213570 | − | 0.976928i | \(-0.568509\pi\) | ||||
−0.213570 | + | 0.976928i | \(0.568509\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.80390 | 1.20290 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −4.24171 | −1.17644 | −0.588220 | − | 0.808701i | \(-0.700171\pi\) | ||||
−0.588220 | + | 0.808701i | \(0.700171\pi\) | |||||||
\(14\) | 1.13011 | 0.302034 | ||||||||
\(15\) | 3.80390 | 0.982163 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.128672 | −0.0312075 | −0.0156037 | − | 0.999878i | \(-0.504967\pi\) | ||||
−0.0156037 | + | 0.999878i | \(0.504967\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −0.265037 | −0.0608036 | −0.0304018 | − | 0.999538i | \(-0.509679\pi\) | ||||
−0.0304018 | + | 0.999538i | \(0.509679\pi\) | |||||||
\(20\) | −3.80390 | −0.850578 | ||||||||
\(21\) | 1.13011 | 0.246609 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 4.37039 | 0.911288 | 0.455644 | − | 0.890162i | \(-0.349409\pi\) | ||||
0.455644 | + | 0.890162i | \(0.349409\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 9.46966 | 1.89393 | ||||||||
\(26\) | 4.24171 | 0.831869 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.13011 | −0.213570 | ||||||||
\(29\) | −3.55745 | −0.660603 | −0.330301 | − | 0.943876i | \(-0.607150\pi\) | ||||
−0.330301 | + | 0.943876i | \(0.607150\pi\) | |||||||
\(30\) | −3.80390 | −0.694494 | ||||||||
\(31\) | 7.85627 | 1.41103 | 0.705514 | − | 0.708696i | \(-0.250716\pi\) | ||||
0.705514 | + | 0.708696i | \(0.250716\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 0.128672 | 0.0220670 | ||||||||
\(35\) | 4.29881 | 0.726632 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 11.0001 | 1.80841 | 0.904206 | − | 0.427097i | \(-0.140464\pi\) | ||||
0.904206 | + | 0.427097i | \(0.140464\pi\) | |||||||
\(38\) | 0.265037 | 0.0429947 | ||||||||
\(39\) | 4.24171 | 0.679218 | ||||||||
\(40\) | 3.80390 | 0.601450 | ||||||||
\(41\) | 2.09928 | 0.327852 | 0.163926 | − | 0.986473i | \(-0.447584\pi\) | ||||
0.163926 | + | 0.986473i | \(0.447584\pi\) | |||||||
\(42\) | −1.13011 | −0.174379 | ||||||||
\(43\) | 1.99798 | 0.304689 | 0.152345 | − | 0.988327i | \(-0.451318\pi\) | ||||
0.152345 | + | 0.988327i | \(0.451318\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | −3.80390 | −0.567052 | ||||||||
\(46\) | −4.37039 | −0.644378 | ||||||||
\(47\) | −0.338707 | −0.0494055 | −0.0247028 | − | 0.999695i | \(-0.507864\pi\) | ||||
−0.0247028 | + | 0.999695i | \(0.507864\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −5.72286 | −0.817551 | ||||||||
\(50\) | −9.46966 | −1.33921 | ||||||||
\(51\) | 0.128672 | 0.0180177 | ||||||||
\(52\) | −4.24171 | −0.588220 | ||||||||
\(53\) | −2.22997 | −0.306309 | −0.153155 | − | 0.988202i | \(-0.548943\pi\) | ||||
−0.153155 | + | 0.988202i | \(0.548943\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 3.80390 | 0.512918 | ||||||||
\(56\) | 1.13011 | 0.151017 | ||||||||
\(57\) | 0.265037 | 0.0351050 | ||||||||
\(58\) | 3.55745 | 0.467117 | ||||||||
\(59\) | −4.93603 | −0.642616 | −0.321308 | − | 0.946975i | \(-0.604122\pi\) | ||||
−0.321308 | + | 0.946975i | \(0.604122\pi\) | |||||||
\(60\) | 3.80390 | 0.491081 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | −7.85627 | −0.997747 | ||||||||
\(63\) | −1.13011 | −0.142380 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 16.1351 | 2.00131 | ||||||||
\(66\) | −1.00000 | −0.123091 | ||||||||
\(67\) | 13.4773 | 1.64652 | 0.823259 | − | 0.567665i | \(-0.192153\pi\) | ||||
0.823259 | + | 0.567665i | \(0.192153\pi\) | |||||||
\(68\) | −0.128672 | −0.0156037 | ||||||||
\(69\) | −4.37039 | −0.526133 | ||||||||
\(70\) | −4.29881 | −0.513806 | ||||||||
\(71\) | 2.75650 | 0.327136 | 0.163568 | − | 0.986532i | \(-0.447700\pi\) | ||||
0.163568 | + | 0.986532i | \(0.447700\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −11.1407 | −1.30391 | −0.651957 | − | 0.758256i | \(-0.726052\pi\) | ||||
−0.651957 | + | 0.758256i | \(0.726052\pi\) | |||||||
\(74\) | −11.0001 | −1.27874 | ||||||||
\(75\) | −9.46966 | −1.09346 | ||||||||
\(76\) | −0.265037 | −0.0304018 | ||||||||
\(77\) | 1.13011 | 0.128788 | ||||||||
\(78\) | −4.24171 | −0.480280 | ||||||||
\(79\) | −4.18391 | −0.470726 | −0.235363 | − | 0.971907i | \(-0.575628\pi\) | ||||
−0.235363 | + | 0.971907i | \(0.575628\pi\) | |||||||
\(80\) | −3.80390 | −0.425289 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.09928 | −0.231826 | ||||||||
\(83\) | −5.50532 | −0.604287 | −0.302143 | − | 0.953262i | \(-0.597702\pi\) | ||||
−0.302143 | + | 0.953262i | \(0.597702\pi\) | |||||||
\(84\) | 1.13011 | 0.123305 | ||||||||
\(85\) | 0.489455 | 0.0530888 | ||||||||
\(86\) | −1.99798 | −0.215448 | ||||||||
\(87\) | 3.55745 | 0.381399 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | −0.489455 | −0.0518821 | −0.0259410 | − | 0.999663i | \(-0.508258\pi\) | ||||
−0.0259410 | + | 0.999663i | \(0.508258\pi\) | |||||||
\(90\) | 3.80390 | 0.400966 | ||||||||
\(91\) | 4.79359 | 0.502505 | ||||||||
\(92\) | 4.37039 | 0.455644 | ||||||||
\(93\) | −7.85627 | −0.814657 | ||||||||
\(94\) | 0.338707 | 0.0349350 | ||||||||
\(95\) | 1.00817 | 0.103436 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 16.4339 | 1.66861 | 0.834304 | − | 0.551305i | \(-0.185870\pi\) | ||||
0.834304 | + | 0.551305i | \(0.185870\pi\) | |||||||
\(98\) | 5.72286 | 0.578096 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 9.46966 | 0.946966 | ||||||||
\(101\) | −5.19702 | −0.517123 | −0.258562 | − | 0.965995i | \(-0.583249\pi\) | ||||
−0.258562 | + | 0.965995i | \(0.583249\pi\) | |||||||
\(102\) | −0.128672 | −0.0127404 | ||||||||
\(103\) | 16.9417 | 1.66932 | 0.834660 | − | 0.550766i | \(-0.185664\pi\) | ||||
0.834660 | + | 0.550766i | \(0.185664\pi\) | |||||||
\(104\) | 4.24171 | 0.415934 | ||||||||
\(105\) | −4.29881 | −0.419521 | ||||||||
\(106\) | 2.22997 | 0.216593 | ||||||||
\(107\) | −0.918730 | −0.0888170 | −0.0444085 | − | 0.999013i | \(-0.514140\pi\) | ||||
−0.0444085 | + | 0.999013i | \(0.514140\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −4.41651 | −0.423025 | −0.211512 | − | 0.977375i | \(-0.567839\pi\) | ||||
−0.211512 | + | 0.977375i | \(0.567839\pi\) | |||||||
\(110\) | −3.80390 | −0.362688 | ||||||||
\(111\) | −11.0001 | −1.04409 | ||||||||
\(112\) | −1.13011 | −0.106785 | ||||||||
\(113\) | 9.04088 | 0.850494 | 0.425247 | − | 0.905077i | \(-0.360187\pi\) | ||||
0.425247 | + | 0.905077i | \(0.360187\pi\) | |||||||
\(114\) | −0.265037 | −0.0248230 | ||||||||
\(115\) | −16.6245 | −1.55024 | ||||||||
\(116\) | −3.55745 | −0.330301 | ||||||||
\(117\) | −4.24171 | −0.392147 | ||||||||
\(118\) | 4.93603 | 0.454398 | ||||||||
\(119\) | 0.145413 | 0.0133300 | ||||||||
\(120\) | −3.80390 | −0.347247 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 1.00000 | 0.0905357 | ||||||||
\(123\) | −2.09928 | −0.189285 | ||||||||
\(124\) | 7.85627 | 0.705514 | ||||||||
\(125\) | −17.0021 | −1.52072 | ||||||||
\(126\) | 1.13011 | 0.100678 | ||||||||
\(127\) | 14.9447 | 1.32613 | 0.663065 | − | 0.748562i | \(-0.269255\pi\) | ||||
0.663065 | + | 0.748562i | \(0.269255\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −1.99798 | −0.175912 | ||||||||
\(130\) | −16.1351 | −1.41514 | ||||||||
\(131\) | −5.68475 | −0.496679 | −0.248340 | − | 0.968673i | \(-0.579885\pi\) | ||||
−0.248340 | + | 0.968673i | \(0.579885\pi\) | |||||||
\(132\) | 1.00000 | 0.0870388 | ||||||||
\(133\) | 0.299520 | 0.0259717 | ||||||||
\(134\) | −13.4773 | −1.16426 | ||||||||
\(135\) | 3.80390 | 0.327388 | ||||||||
\(136\) | 0.128672 | 0.0110335 | ||||||||
\(137\) | −13.2285 | −1.13019 | −0.565095 | − | 0.825026i | \(-0.691160\pi\) | ||||
−0.565095 | + | 0.825026i | \(0.691160\pi\) | |||||||
\(138\) | 4.37039 | 0.372032 | ||||||||
\(139\) | −14.6777 | −1.24494 | −0.622472 | − | 0.782642i | \(-0.713872\pi\) | ||||
−0.622472 | + | 0.782642i | \(0.713872\pi\) | |||||||
\(140\) | 4.29881 | 0.363316 | ||||||||
\(141\) | 0.338707 | 0.0285243 | ||||||||
\(142\) | −2.75650 | −0.231320 | ||||||||
\(143\) | 4.24171 | 0.354710 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 13.5322 | 1.12379 | ||||||||
\(146\) | 11.1407 | 0.922007 | ||||||||
\(147\) | 5.72286 | 0.472013 | ||||||||
\(148\) | 11.0001 | 0.904206 | ||||||||
\(149\) | 7.90661 | 0.647735 | 0.323868 | − | 0.946102i | \(-0.395017\pi\) | ||||
0.323868 | + | 0.946102i | \(0.395017\pi\) | |||||||
\(150\) | 9.46966 | 0.773195 | ||||||||
\(151\) | 1.15571 | 0.0940505 | 0.0470252 | − | 0.998894i | \(-0.485026\pi\) | ||||
0.0470252 | + | 0.998894i | \(0.485026\pi\) | |||||||
\(152\) | 0.265037 | 0.0214973 | ||||||||
\(153\) | −0.128672 | −0.0104025 | ||||||||
\(154\) | −1.13011 | −0.0910666 | ||||||||
\(155\) | −29.8845 | −2.40038 | ||||||||
\(156\) | 4.24171 | 0.339609 | ||||||||
\(157\) | 9.07230 | 0.724048 | 0.362024 | − | 0.932169i | \(-0.382086\pi\) | ||||
0.362024 | + | 0.932169i | \(0.382086\pi\) | |||||||
\(158\) | 4.18391 | 0.332854 | ||||||||
\(159\) | 2.22997 | 0.176848 | ||||||||
\(160\) | 3.80390 | 0.300725 | ||||||||
\(161\) | −4.93900 | −0.389248 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −8.13603 | −0.637263 | −0.318631 | − | 0.947879i | \(-0.603223\pi\) | ||||
−0.318631 | + | 0.947879i | \(0.603223\pi\) | |||||||
\(164\) | 2.09928 | 0.163926 | ||||||||
\(165\) | −3.80390 | −0.296133 | ||||||||
\(166\) | 5.50532 | 0.427295 | ||||||||
\(167\) | −3.11680 | −0.241186 | −0.120593 | − | 0.992702i | \(-0.538480\pi\) | ||||
−0.120593 | + | 0.992702i | \(0.538480\pi\) | |||||||
\(168\) | −1.13011 | −0.0871896 | ||||||||
\(169\) | 4.99214 | 0.384010 | ||||||||
\(170\) | −0.489455 | −0.0375395 | ||||||||
\(171\) | −0.265037 | −0.0202679 | ||||||||
\(172\) | 1.99798 | 0.152345 | ||||||||
\(173\) | −7.76547 | −0.590398 | −0.295199 | − | 0.955436i | \(-0.595386\pi\) | ||||
−0.295199 | + | 0.955436i | \(0.595386\pi\) | |||||||
\(174\) | −3.55745 | −0.269690 | ||||||||
\(175\) | −10.7017 | −0.808974 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 4.93603 | 0.371014 | ||||||||
\(178\) | 0.489455 | 0.0366862 | ||||||||
\(179\) | −3.25320 | −0.243156 | −0.121578 | − | 0.992582i | \(-0.538795\pi\) | ||||
−0.121578 | + | 0.992582i | \(0.538795\pi\) | |||||||
\(180\) | −3.80390 | −0.283526 | ||||||||
\(181\) | −2.50450 | −0.186158 | −0.0930789 | − | 0.995659i | \(-0.529671\pi\) | ||||
−0.0930789 | + | 0.995659i | \(0.529671\pi\) | |||||||
\(182\) | −4.79359 | −0.355324 | ||||||||
\(183\) | 1.00000 | 0.0739221 | ||||||||
\(184\) | −4.37039 | −0.322189 | ||||||||
\(185\) | −41.8434 | −3.07639 | ||||||||
\(186\) | 7.85627 | 0.576049 | ||||||||
\(187\) | 0.128672 | 0.00940941 | ||||||||
\(188\) | −0.338707 | −0.0247028 | ||||||||
\(189\) | 1.13011 | 0.0822031 | ||||||||
\(190\) | −1.00817 | −0.0731406 | ||||||||
\(191\) | −23.2019 | −1.67883 | −0.839415 | − | 0.543491i | \(-0.817102\pi\) | ||||
−0.839415 | + | 0.543491i | \(0.817102\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −19.7378 | −1.42076 | −0.710379 | − | 0.703819i | \(-0.751477\pi\) | ||||
−0.710379 | + | 0.703819i | \(0.751477\pi\) | |||||||
\(194\) | −16.4339 | −1.17988 | ||||||||
\(195\) | −16.1351 | −1.15546 | ||||||||
\(196\) | −5.72286 | −0.408776 | ||||||||
\(197\) | 4.50236 | 0.320780 | 0.160390 | − | 0.987054i | \(-0.448725\pi\) | ||||
0.160390 | + | 0.987054i | \(0.448725\pi\) | |||||||
\(198\) | 1.00000 | 0.0710669 | ||||||||
\(199\) | 7.90054 | 0.560055 | 0.280027 | − | 0.959992i | \(-0.409656\pi\) | ||||
0.280027 | + | 0.959992i | \(0.409656\pi\) | |||||||
\(200\) | −9.46966 | −0.669606 | ||||||||
\(201\) | −13.4773 | −0.950618 | ||||||||
\(202\) | 5.19702 | 0.365661 | ||||||||
\(203\) | 4.02030 | 0.282170 | ||||||||
\(204\) | 0.128672 | 0.00900883 | ||||||||
\(205\) | −7.98544 | −0.557727 | ||||||||
\(206\) | −16.9417 | −1.18039 | ||||||||
\(207\) | 4.37039 | 0.303763 | ||||||||
\(208\) | −4.24171 | −0.294110 | ||||||||
\(209\) | 0.265037 | 0.0183330 | ||||||||
\(210\) | 4.29881 | 0.296646 | ||||||||
\(211\) | 25.2862 | 1.74077 | 0.870387 | − | 0.492368i | \(-0.163869\pi\) | ||||
0.870387 | + | 0.492368i | \(0.163869\pi\) | |||||||
\(212\) | −2.22997 | −0.153155 | ||||||||
\(213\) | −2.75650 | −0.188872 | ||||||||
\(214\) | 0.918730 | 0.0628031 | ||||||||
\(215\) | −7.60012 | −0.518324 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −8.87842 | −0.602706 | ||||||||
\(218\) | 4.41651 | 0.299124 | ||||||||
\(219\) | 11.1407 | 0.752815 | ||||||||
\(220\) | 3.80390 | 0.256459 | ||||||||
\(221\) | 0.545789 | 0.0367137 | ||||||||
\(222\) | 11.0001 | 0.738281 | ||||||||
\(223\) | −0.909127 | −0.0608796 | −0.0304398 | − | 0.999537i | \(-0.509691\pi\) | ||||
−0.0304398 | + | 0.999537i | \(0.509691\pi\) | |||||||
\(224\) | 1.13011 | 0.0755084 | ||||||||
\(225\) | 9.46966 | 0.631311 | ||||||||
\(226\) | −9.04088 | −0.601390 | ||||||||
\(227\) | −6.58569 | −0.437108 | −0.218554 | − | 0.975825i | \(-0.570134\pi\) | ||||
−0.218554 | + | 0.975825i | \(0.570134\pi\) | |||||||
\(228\) | 0.265037 | 0.0175525 | ||||||||
\(229\) | −24.9926 | −1.65156 | −0.825780 | − | 0.563993i | \(-0.809264\pi\) | ||||
−0.825780 | + | 0.563993i | \(0.809264\pi\) | |||||||
\(230\) | 16.6245 | 1.09619 | ||||||||
\(231\) | −1.13011 | −0.0743555 | ||||||||
\(232\) | 3.55745 | 0.233558 | ||||||||
\(233\) | −0.0101462 | −0.000664701 0 | −0.000332350 | − | 1.00000i | \(-0.500106\pi\) | ||||
−0.000332350 | 1.00000i | \(0.500106\pi\) | ||||||||
\(234\) | 4.24171 | 0.277290 | ||||||||
\(235\) | 1.28841 | 0.0840465 | ||||||||
\(236\) | −4.93603 | −0.321308 | ||||||||
\(237\) | 4.18391 | 0.271774 | ||||||||
\(238\) | −0.145413 | −0.00942571 | ||||||||
\(239\) | −1.36601 | −0.0883598 | −0.0441799 | − | 0.999024i | \(-0.514067\pi\) | ||||
−0.0441799 | + | 0.999024i | \(0.514067\pi\) | |||||||
\(240\) | 3.80390 | 0.245541 | ||||||||
\(241\) | 23.3974 | 1.50716 | 0.753578 | − | 0.657358i | \(-0.228326\pi\) | ||||
0.753578 | + | 0.657358i | \(0.228326\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −1.00000 | −0.0640184 | ||||||||
\(245\) | 21.7692 | 1.39078 | ||||||||
\(246\) | 2.09928 | 0.133845 | ||||||||
\(247\) | 1.12421 | 0.0715318 | ||||||||
\(248\) | −7.85627 | −0.498873 | ||||||||
\(249\) | 5.50532 | 0.348885 | ||||||||
\(250\) | 17.0021 | 1.07531 | ||||||||
\(251\) | −13.0600 | −0.824343 | −0.412171 | − | 0.911106i | \(-0.635229\pi\) | ||||
−0.412171 | + | 0.911106i | \(0.635229\pi\) | |||||||
\(252\) | −1.13011 | −0.0711900 | ||||||||
\(253\) | −4.37039 | −0.274764 | ||||||||
\(254\) | −14.9447 | −0.937715 | ||||||||
\(255\) | −0.489455 | −0.0306508 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 16.2686 | 1.01481 | 0.507404 | − | 0.861708i | \(-0.330605\pi\) | ||||
0.507404 | + | 0.861708i | \(0.330605\pi\) | |||||||
\(258\) | 1.99798 | 0.124389 | ||||||||
\(259\) | −12.4313 | −0.772445 | ||||||||
\(260\) | 16.1351 | 1.00065 | ||||||||
\(261\) | −3.55745 | −0.220201 | ||||||||
\(262\) | 5.68475 | 0.351205 | ||||||||
\(263\) | 6.16069 | 0.379884 | 0.189942 | − | 0.981795i | \(-0.439170\pi\) | ||||
0.189942 | + | 0.981795i | \(0.439170\pi\) | |||||||
\(264\) | −1.00000 | −0.0615457 | ||||||||
\(265\) | 8.48257 | 0.521080 | ||||||||
\(266\) | −0.299520 | −0.0183647 | ||||||||
\(267\) | 0.489455 | 0.0299541 | ||||||||
\(268\) | 13.4773 | 0.823259 | ||||||||
\(269\) | −21.6824 | −1.32200 | −0.661000 | − | 0.750386i | \(-0.729868\pi\) | ||||
−0.661000 | + | 0.750386i | \(0.729868\pi\) | |||||||
\(270\) | −3.80390 | −0.231498 | ||||||||
\(271\) | −19.0960 | −1.16000 | −0.579999 | − | 0.814617i | \(-0.696947\pi\) | ||||
−0.579999 | + | 0.814617i | \(0.696947\pi\) | |||||||
\(272\) | −0.128672 | −0.00780187 | ||||||||
\(273\) | −4.79359 | −0.290121 | ||||||||
\(274\) | 13.2285 | 0.799164 | ||||||||
\(275\) | −9.46966 | −0.571042 | ||||||||
\(276\) | −4.37039 | −0.263066 | ||||||||
\(277\) | −21.4653 | −1.28973 | −0.644863 | − | 0.764298i | \(-0.723086\pi\) | ||||
−0.644863 | + | 0.764298i | \(0.723086\pi\) | |||||||
\(278\) | 14.6777 | 0.880309 | ||||||||
\(279\) | 7.85627 | 0.470342 | ||||||||
\(280\) | −4.29881 | −0.256903 | ||||||||
\(281\) | −20.1406 | −1.20149 | −0.600743 | − | 0.799442i | \(-0.705128\pi\) | ||||
−0.600743 | + | 0.799442i | \(0.705128\pi\) | |||||||
\(282\) | −0.338707 | −0.0201697 | ||||||||
\(283\) | 6.60060 | 0.392365 | 0.196182 | − | 0.980567i | \(-0.437146\pi\) | ||||
0.196182 | + | 0.980567i | \(0.437146\pi\) | |||||||
\(284\) | 2.75650 | 0.163568 | ||||||||
\(285\) | −1.00817 | −0.0597191 | ||||||||
\(286\) | −4.24171 | −0.250818 | ||||||||
\(287\) | −2.37240 | −0.140039 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −16.9834 | −0.999026 | ||||||||
\(290\) | −13.5322 | −0.794638 | ||||||||
\(291\) | −16.4339 | −0.963371 | ||||||||
\(292\) | −11.1407 | −0.651957 | ||||||||
\(293\) | 27.0042 | 1.57760 | 0.788801 | − | 0.614649i | \(-0.210702\pi\) | ||||
0.788801 | + | 0.614649i | \(0.210702\pi\) | |||||||
\(294\) | −5.72286 | −0.333764 | ||||||||
\(295\) | 18.7762 | 1.09319 | ||||||||
\(296\) | −11.0001 | −0.639370 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | −7.90661 | −0.458018 | ||||||||
\(299\) | −18.5379 | −1.07208 | ||||||||
\(300\) | −9.46966 | −0.546731 | ||||||||
\(301\) | −2.25793 | −0.130145 | ||||||||
\(302\) | −1.15571 | −0.0665037 | ||||||||
\(303\) | 5.19702 | 0.298561 | ||||||||
\(304\) | −0.265037 | −0.0152009 | ||||||||
\(305\) | 3.80390 | 0.217811 | ||||||||
\(306\) | 0.128672 | 0.00735568 | ||||||||
\(307\) | −21.1225 | −1.20553 | −0.602763 | − | 0.797921i | \(-0.705933\pi\) | ||||
−0.602763 | + | 0.797921i | \(0.705933\pi\) | |||||||
\(308\) | 1.13011 | 0.0643938 | ||||||||
\(309\) | −16.9417 | −0.963782 | ||||||||
\(310\) | 29.8845 | 1.69732 | ||||||||
\(311\) | −25.0386 | −1.41981 | −0.709903 | − | 0.704299i | \(-0.751261\pi\) | ||||
−0.709903 | + | 0.704299i | \(0.751261\pi\) | |||||||
\(312\) | −4.24171 | −0.240140 | ||||||||
\(313\) | −24.5109 | −1.38544 | −0.692719 | − | 0.721208i | \(-0.743587\pi\) | ||||
−0.692719 | + | 0.721208i | \(0.743587\pi\) | |||||||
\(314\) | −9.07230 | −0.511980 | ||||||||
\(315\) | 4.29881 | 0.242211 | ||||||||
\(316\) | −4.18391 | −0.235363 | ||||||||
\(317\) | 29.1713 | 1.63842 | 0.819210 | − | 0.573493i | \(-0.194412\pi\) | ||||
0.819210 | + | 0.573493i | \(0.194412\pi\) | |||||||
\(318\) | −2.22997 | −0.125050 | ||||||||
\(319\) | 3.55745 | 0.199179 | ||||||||
\(320\) | −3.80390 | −0.212645 | ||||||||
\(321\) | 0.918730 | 0.0512785 | ||||||||
\(322\) | 4.93900 | 0.275240 | ||||||||
\(323\) | 0.0341028 | 0.00189753 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −40.1676 | −2.22810 | ||||||||
\(326\) | 8.13603 | 0.450613 | ||||||||
\(327\) | 4.41651 | 0.244234 | ||||||||
\(328\) | −2.09928 | −0.115913 | ||||||||
\(329\) | 0.382775 | 0.0211031 | ||||||||
\(330\) | 3.80390 | 0.209398 | ||||||||
\(331\) | 11.8658 | 0.652204 | 0.326102 | − | 0.945335i | \(-0.394265\pi\) | ||||
0.326102 | + | 0.945335i | \(0.394265\pi\) | |||||||
\(332\) | −5.50532 | −0.302143 | ||||||||
\(333\) | 11.0001 | 0.602804 | ||||||||
\(334\) | 3.11680 | 0.170544 | ||||||||
\(335\) | −51.2665 | −2.80099 | ||||||||
\(336\) | 1.13011 | 0.0616524 | ||||||||
\(337\) | 18.0097 | 0.981051 | 0.490525 | − | 0.871427i | \(-0.336805\pi\) | ||||
0.490525 | + | 0.871427i | \(0.336805\pi\) | |||||||
\(338\) | −4.99214 | −0.271536 | ||||||||
\(339\) | −9.04088 | −0.491033 | ||||||||
\(340\) | 0.489455 | 0.0265444 | ||||||||
\(341\) | −7.85627 | −0.425441 | ||||||||
\(342\) | 0.265037 | 0.0143316 | ||||||||
\(343\) | 14.3782 | 0.776349 | ||||||||
\(344\) | −1.99798 | −0.107724 | ||||||||
\(345\) | 16.6245 | 0.895034 | ||||||||
\(346\) | 7.76547 | 0.417474 | ||||||||
\(347\) | −12.1166 | −0.650454 | −0.325227 | − | 0.945636i | \(-0.605441\pi\) | ||||
−0.325227 | + | 0.945636i | \(0.605441\pi\) | |||||||
\(348\) | 3.55745 | 0.190700 | ||||||||
\(349\) | −21.1577 | −1.13255 | −0.566274 | − | 0.824217i | \(-0.691616\pi\) | ||||
−0.566274 | + | 0.824217i | \(0.691616\pi\) | |||||||
\(350\) | 10.7017 | 0.572031 | ||||||||
\(351\) | 4.24171 | 0.226406 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −2.82372 | −0.150292 | −0.0751458 | − | 0.997173i | \(-0.523942\pi\) | ||||
−0.0751458 | + | 0.997173i | \(0.523942\pi\) | |||||||
\(354\) | −4.93603 | −0.262347 | ||||||||
\(355\) | −10.4854 | −0.556510 | ||||||||
\(356\) | −0.489455 | −0.0259410 | ||||||||
\(357\) | −0.145413 | −0.00769606 | ||||||||
\(358\) | 3.25320 | 0.171937 | ||||||||
\(359\) | 18.0948 | 0.955008 | 0.477504 | − | 0.878630i | \(-0.341542\pi\) | ||||
0.477504 | + | 0.878630i | \(0.341542\pi\) | |||||||
\(360\) | 3.80390 | 0.200483 | ||||||||
\(361\) | −18.9298 | −0.996303 | ||||||||
\(362\) | 2.50450 | 0.131633 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 4.79359 | 0.251252 | ||||||||
\(365\) | 42.3779 | 2.21816 | ||||||||
\(366\) | −1.00000 | −0.0522708 | ||||||||
\(367\) | −20.6125 | −1.07596 | −0.537982 | − | 0.842956i | \(-0.680813\pi\) | ||||
−0.537982 | + | 0.842956i | \(0.680813\pi\) | |||||||
\(368\) | 4.37039 | 0.227822 | ||||||||
\(369\) | 2.09928 | 0.109284 | ||||||||
\(370\) | 41.8434 | 2.17534 | ||||||||
\(371\) | 2.52010 | 0.130837 | ||||||||
\(372\) | −7.85627 | −0.407328 | ||||||||
\(373\) | 25.1657 | 1.30303 | 0.651516 | − | 0.758634i | \(-0.274133\pi\) | ||||
0.651516 | + | 0.758634i | \(0.274133\pi\) | |||||||
\(374\) | −0.128672 | −0.00665346 | ||||||||
\(375\) | 17.0021 | 0.877987 | ||||||||
\(376\) | 0.338707 | 0.0174675 | ||||||||
\(377\) | 15.0897 | 0.777159 | ||||||||
\(378\) | −1.13011 | −0.0581264 | ||||||||
\(379\) | 2.60869 | 0.134000 | 0.0669998 | − | 0.997753i | \(-0.478657\pi\) | ||||
0.0669998 | + | 0.997753i | \(0.478657\pi\) | |||||||
\(380\) | 1.00817 | 0.0517182 | ||||||||
\(381\) | −14.9447 | −0.765641 | ||||||||
\(382\) | 23.2019 | 1.18711 | ||||||||
\(383\) | 10.1177 | 0.516989 | 0.258495 | − | 0.966013i | \(-0.416774\pi\) | ||||
0.258495 | + | 0.966013i | \(0.416774\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −4.29881 | −0.219088 | ||||||||
\(386\) | 19.7378 | 1.00463 | ||||||||
\(387\) | 1.99798 | 0.101563 | ||||||||
\(388\) | 16.4339 | 0.834304 | ||||||||
\(389\) | 12.2480 | 0.621000 | 0.310500 | − | 0.950573i | \(-0.399504\pi\) | ||||
0.310500 | + | 0.950573i | \(0.399504\pi\) | |||||||
\(390\) | 16.1351 | 0.817030 | ||||||||
\(391\) | −0.562345 | −0.0284390 | ||||||||
\(392\) | 5.72286 | 0.289048 | ||||||||
\(393\) | 5.68475 | 0.286758 | ||||||||
\(394\) | −4.50236 | −0.226826 | ||||||||
\(395\) | 15.9152 | 0.800779 | ||||||||
\(396\) | −1.00000 | −0.0502519 | ||||||||
\(397\) | −21.9214 | −1.10020 | −0.550101 | − | 0.835098i | \(-0.685411\pi\) | ||||
−0.550101 | + | 0.835098i | \(0.685411\pi\) | |||||||
\(398\) | −7.90054 | −0.396018 | ||||||||
\(399\) | −0.299520 | −0.0149948 | ||||||||
\(400\) | 9.46966 | 0.473483 | ||||||||
\(401\) | −21.0450 | −1.05094 | −0.525468 | − | 0.850813i | \(-0.676110\pi\) | ||||
−0.525468 | + | 0.850813i | \(0.676110\pi\) | |||||||
\(402\) | 13.4773 | 0.672189 | ||||||||
\(403\) | −33.3240 | −1.65999 | ||||||||
\(404\) | −5.19702 | −0.258562 | ||||||||
\(405\) | −3.80390 | −0.189017 | ||||||||
\(406\) | −4.02030 | −0.199524 | ||||||||
\(407\) | −11.0001 | −0.545257 | ||||||||
\(408\) | −0.128672 | −0.00637020 | ||||||||
\(409\) | 26.3348 | 1.30217 | 0.651086 | − | 0.759004i | \(-0.274314\pi\) | ||||
0.651086 | + | 0.759004i | \(0.274314\pi\) | |||||||
\(410\) | 7.98544 | 0.394373 | ||||||||
\(411\) | 13.2285 | 0.652515 | ||||||||
\(412\) | 16.9417 | 0.834660 | ||||||||
\(413\) | 5.57824 | 0.274487 | ||||||||
\(414\) | −4.37039 | −0.214793 | ||||||||
\(415\) | 20.9417 | 1.02799 | ||||||||
\(416\) | 4.24171 | 0.207967 | ||||||||
\(417\) | 14.6777 | 0.718769 | ||||||||
\(418\) | −0.265037 | −0.0129634 | ||||||||
\(419\) | 16.1013 | 0.786602 | 0.393301 | − | 0.919410i | \(-0.371333\pi\) | ||||
0.393301 | + | 0.919410i | \(0.371333\pi\) | |||||||
\(420\) | −4.29881 | −0.209761 | ||||||||
\(421\) | −17.0787 | −0.832363 | −0.416181 | − | 0.909282i | \(-0.636632\pi\) | ||||
−0.416181 | + | 0.909282i | \(0.636632\pi\) | |||||||
\(422\) | −25.2862 | −1.23091 | ||||||||
\(423\) | −0.338707 | −0.0164685 | ||||||||
\(424\) | 2.22997 | 0.108297 | ||||||||
\(425\) | −1.21848 | −0.0591049 | ||||||||
\(426\) | 2.75650 | 0.133553 | ||||||||
\(427\) | 1.13011 | 0.0546897 | ||||||||
\(428\) | −0.918730 | −0.0444085 | ||||||||
\(429\) | −4.24171 | −0.204792 | ||||||||
\(430\) | 7.60012 | 0.366510 | ||||||||
\(431\) | 25.0261 | 1.20546 | 0.602732 | − | 0.797944i | \(-0.294079\pi\) | ||||
0.602732 | + | 0.797944i | \(0.294079\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −4.76689 | −0.229082 | −0.114541 | − | 0.993419i | \(-0.536540\pi\) | ||||
−0.114541 | + | 0.993419i | \(0.536540\pi\) | |||||||
\(434\) | 8.87842 | 0.426178 | ||||||||
\(435\) | −13.5322 | −0.648819 | ||||||||
\(436\) | −4.41651 | −0.211512 | ||||||||
\(437\) | −1.15831 | −0.0554097 | ||||||||
\(438\) | −11.1407 | −0.532321 | ||||||||
\(439\) | −19.2883 | −0.920582 | −0.460291 | − | 0.887768i | \(-0.652255\pi\) | ||||
−0.460291 | + | 0.887768i | \(0.652255\pi\) | |||||||
\(440\) | −3.80390 | −0.181344 | ||||||||
\(441\) | −5.72286 | −0.272517 | ||||||||
\(442\) | −0.545789 | −0.0259605 | ||||||||
\(443\) | −21.1686 | −1.00575 | −0.502876 | − | 0.864359i | \(-0.667725\pi\) | ||||
−0.502876 | + | 0.864359i | \(0.667725\pi\) | |||||||
\(444\) | −11.0001 | −0.522044 | ||||||||
\(445\) | 1.86184 | 0.0882595 | ||||||||
\(446\) | 0.909127 | 0.0430484 | ||||||||
\(447\) | −7.90661 | −0.373970 | ||||||||
\(448\) | −1.13011 | −0.0533925 | ||||||||
\(449\) | 4.72877 | 0.223164 | 0.111582 | − | 0.993755i | \(-0.464408\pi\) | ||||
0.111582 | + | 0.993755i | \(0.464408\pi\) | |||||||
\(450\) | −9.46966 | −0.446404 | ||||||||
\(451\) | −2.09928 | −0.0988510 | ||||||||
\(452\) | 9.04088 | 0.425247 | ||||||||
\(453\) | −1.15571 | −0.0543001 | ||||||||
\(454\) | 6.58569 | 0.309082 | ||||||||
\(455\) | −18.2343 | −0.854839 | ||||||||
\(456\) | −0.265037 | −0.0124115 | ||||||||
\(457\) | 11.3987 | 0.533210 | 0.266605 | − | 0.963806i | \(-0.414098\pi\) | ||||
0.266605 | + | 0.963806i | \(0.414098\pi\) | |||||||
\(458\) | 24.9926 | 1.16783 | ||||||||
\(459\) | 0.128672 | 0.00600588 | ||||||||
\(460\) | −16.6245 | −0.775122 | ||||||||
\(461\) | −2.01992 | −0.0940772 | −0.0470386 | − | 0.998893i | \(-0.514978\pi\) | ||||
−0.0470386 | + | 0.998893i | \(0.514978\pi\) | |||||||
\(462\) | 1.13011 | 0.0525773 | ||||||||
\(463\) | 1.91078 | 0.0888014 | 0.0444007 | − | 0.999014i | \(-0.485862\pi\) | ||||
0.0444007 | + | 0.999014i | \(0.485862\pi\) | |||||||
\(464\) | −3.55745 | −0.165151 | ||||||||
\(465\) | 29.8845 | 1.38586 | ||||||||
\(466\) | 0.0101462 | 0.000470014 0 | ||||||||
\(467\) | 15.1715 | 0.702052 | 0.351026 | − | 0.936366i | \(-0.385833\pi\) | ||||
0.351026 | + | 0.936366i | \(0.385833\pi\) | |||||||
\(468\) | −4.24171 | −0.196073 | ||||||||
\(469\) | −15.2308 | −0.703294 | ||||||||
\(470\) | −1.28841 | −0.0594299 | ||||||||
\(471\) | −9.07230 | −0.418030 | ||||||||
\(472\) | 4.93603 | 0.227199 | ||||||||
\(473\) | −1.99798 | −0.0918673 | ||||||||
\(474\) | −4.18391 | −0.192173 | ||||||||
\(475\) | −2.50981 | −0.115158 | ||||||||
\(476\) | 0.145413 | 0.00666499 | ||||||||
\(477\) | −2.22997 | −0.102103 | ||||||||
\(478\) | 1.36601 | 0.0624798 | ||||||||
\(479\) | 32.5688 | 1.48810 | 0.744052 | − | 0.668121i | \(-0.232901\pi\) | ||||
0.744052 | + | 0.668121i | \(0.232901\pi\) | |||||||
\(480\) | −3.80390 | −0.173624 | ||||||||
\(481\) | −46.6594 | −2.12749 | ||||||||
\(482\) | −23.3974 | −1.06572 | ||||||||
\(483\) | 4.93900 | 0.224732 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −62.5129 | −2.83856 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 1.71068 | 0.0775184 | 0.0387592 | − | 0.999249i | \(-0.487659\pi\) | ||||
0.0387592 | + | 0.999249i | \(0.487659\pi\) | |||||||
\(488\) | 1.00000 | 0.0452679 | ||||||||
\(489\) | 8.13603 | 0.367924 | ||||||||
\(490\) | −21.7692 | −0.983432 | ||||||||
\(491\) | −6.63332 | −0.299357 | −0.149679 | − | 0.988735i | \(-0.547824\pi\) | ||||
−0.149679 | + | 0.988735i | \(0.547824\pi\) | |||||||
\(492\) | −2.09928 | −0.0946426 | ||||||||
\(493\) | 0.457744 | 0.0206158 | ||||||||
\(494\) | −1.12421 | −0.0505806 | ||||||||
\(495\) | 3.80390 | 0.170973 | ||||||||
\(496\) | 7.85627 | 0.352757 | ||||||||
\(497\) | −3.11514 | −0.139733 | ||||||||
\(498\) | −5.50532 | −0.246699 | ||||||||
\(499\) | −14.8590 | −0.665180 | −0.332590 | − | 0.943072i | \(-0.607922\pi\) | ||||
−0.332590 | + | 0.943072i | \(0.607922\pi\) | |||||||
\(500\) | −17.0021 | −0.760359 | ||||||||
\(501\) | 3.11680 | 0.139249 | ||||||||
\(502\) | 13.0600 | 0.582898 | ||||||||
\(503\) | 3.36636 | 0.150099 | 0.0750493 | − | 0.997180i | \(-0.476089\pi\) | ||||
0.0750493 | + | 0.997180i | \(0.476089\pi\) | |||||||
\(504\) | 1.13011 | 0.0503389 | ||||||||
\(505\) | 19.7690 | 0.879707 | ||||||||
\(506\) | 4.37039 | 0.194287 | ||||||||
\(507\) | −4.99214 | −0.221709 | ||||||||
\(508\) | 14.9447 | 0.663065 | ||||||||
\(509\) | 11.0387 | 0.489281 | 0.244641 | − | 0.969614i | \(-0.421330\pi\) | ||||
0.244641 | + | 0.969614i | \(0.421330\pi\) | |||||||
\(510\) | 0.489455 | 0.0216734 | ||||||||
\(511\) | 12.5901 | 0.556954 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0.265037 | 0.0117017 | ||||||||
\(514\) | −16.2686 | −0.717578 | ||||||||
\(515\) | −64.4447 | −2.83977 | ||||||||
\(516\) | −1.99798 | −0.0879562 | ||||||||
\(517\) | 0.338707 | 0.0148963 | ||||||||
\(518\) | 12.4313 | 0.546201 | ||||||||
\(519\) | 7.76547 | 0.340866 | ||||||||
\(520\) | −16.1351 | −0.707569 | ||||||||
\(521\) | 34.7021 | 1.52033 | 0.760163 | − | 0.649732i | \(-0.225119\pi\) | ||||
0.760163 | + | 0.649732i | \(0.225119\pi\) | |||||||
\(522\) | 3.55745 | 0.155706 | ||||||||
\(523\) | −22.1747 | −0.969633 | −0.484817 | − | 0.874616i | \(-0.661114\pi\) | ||||
−0.484817 | + | 0.874616i | \(0.661114\pi\) | |||||||
\(524\) | −5.68475 | −0.248340 | ||||||||
\(525\) | 10.7017 | 0.467062 | ||||||||
\(526\) | −6.16069 | −0.268619 | ||||||||
\(527\) | −1.01088 | −0.0440346 | ||||||||
\(528\) | 1.00000 | 0.0435194 | ||||||||
\(529\) | −3.89973 | −0.169553 | ||||||||
\(530\) | −8.48257 | −0.368459 | ||||||||
\(531\) | −4.93603 | −0.214205 | ||||||||
\(532\) | 0.299520 | 0.0129858 | ||||||||
\(533\) | −8.90453 | −0.385698 | ||||||||
\(534\) | −0.489455 | −0.0211808 | ||||||||
\(535\) | 3.49476 | 0.151092 | ||||||||
\(536\) | −13.4773 | −0.582132 | ||||||||
\(537\) | 3.25320 | 0.140386 | ||||||||
\(538\) | 21.6824 | 0.934795 | ||||||||
\(539\) | 5.72286 | 0.246501 | ||||||||
\(540\) | 3.80390 | 0.163694 | ||||||||
\(541\) | 19.2666 | 0.828336 | 0.414168 | − | 0.910200i | \(-0.364073\pi\) | ||||
0.414168 | + | 0.910200i | \(0.364073\pi\) | |||||||
\(542\) | 19.0960 | 0.820242 | ||||||||
\(543\) | 2.50450 | 0.107478 | ||||||||
\(544\) | 0.128672 | 0.00551676 | ||||||||
\(545\) | 16.8000 | 0.719631 | ||||||||
\(546\) | 4.79359 | 0.205147 | ||||||||
\(547\) | −34.1442 | −1.45990 | −0.729951 | − | 0.683499i | \(-0.760457\pi\) | ||||
−0.729951 | + | 0.683499i | \(0.760457\pi\) | |||||||
\(548\) | −13.2285 | −0.565095 | ||||||||
\(549\) | −1.00000 | −0.0426790 | ||||||||
\(550\) | 9.46966 | 0.403788 | ||||||||
\(551\) | 0.942857 | 0.0401671 | ||||||||
\(552\) | 4.37039 | 0.186016 | ||||||||
\(553\) | 4.72826 | 0.201066 | ||||||||
\(554\) | 21.4653 | 0.911974 | ||||||||
\(555\) | 41.8434 | 1.77616 | ||||||||
\(556\) | −14.6777 | −0.622472 | ||||||||
\(557\) | −21.0969 | −0.893903 | −0.446952 | − | 0.894558i | \(-0.647490\pi\) | ||||
−0.446952 | + | 0.894558i | \(0.647490\pi\) | |||||||
\(558\) | −7.85627 | −0.332582 | ||||||||
\(559\) | −8.47486 | −0.358448 | ||||||||
\(560\) | 4.29881 | 0.181658 | ||||||||
\(561\) | −0.128672 | −0.00543253 | ||||||||
\(562\) | 20.1406 | 0.849578 | ||||||||
\(563\) | −15.6125 | −0.657990 | −0.328995 | − | 0.944332i | \(-0.606710\pi\) | ||||
−0.328995 | + | 0.944332i | \(0.606710\pi\) | |||||||
\(564\) | 0.338707 | 0.0142621 | ||||||||
\(565\) | −34.3906 | −1.44682 | ||||||||
\(566\) | −6.60060 | −0.277444 | ||||||||
\(567\) | −1.13011 | −0.0474600 | ||||||||
\(568\) | −2.75650 | −0.115660 | ||||||||
\(569\) | 1.28802 | 0.0539966 | 0.0269983 | − | 0.999635i | \(-0.491405\pi\) | ||||
0.0269983 | + | 0.999635i | \(0.491405\pi\) | |||||||
\(570\) | 1.00817 | 0.0422278 | ||||||||
\(571\) | −15.7671 | −0.659834 | −0.329917 | − | 0.944010i | \(-0.607021\pi\) | ||||
−0.329917 | + | 0.944010i | \(0.607021\pi\) | |||||||
\(572\) | 4.24171 | 0.177355 | ||||||||
\(573\) | 23.2019 | 0.969273 | ||||||||
\(574\) | 2.37240 | 0.0990223 | ||||||||
\(575\) | 41.3861 | 1.72592 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 1.85705 | 0.0773099 | 0.0386549 | − | 0.999253i | \(-0.487693\pi\) | ||||
0.0386549 | + | 0.999253i | \(0.487693\pi\) | |||||||
\(578\) | 16.9834 | 0.706418 | ||||||||
\(579\) | 19.7378 | 0.820276 | ||||||||
\(580\) | 13.5322 | 0.561894 | ||||||||
\(581\) | 6.22159 | 0.258115 | ||||||||
\(582\) | 16.4339 | 0.681206 | ||||||||
\(583\) | 2.22997 | 0.0923558 | ||||||||
\(584\) | 11.1407 | 0.461003 | ||||||||
\(585\) | 16.1351 | 0.667103 | ||||||||
\(586\) | −27.0042 | −1.11553 | ||||||||
\(587\) | −31.2101 | −1.28818 | −0.644088 | − | 0.764951i | \(-0.722763\pi\) | ||||
−0.644088 | + | 0.764951i | \(0.722763\pi\) | |||||||
\(588\) | 5.72286 | 0.236007 | ||||||||
\(589\) | −2.08220 | −0.0857956 | ||||||||
\(590\) | −18.7762 | −0.773002 | ||||||||
\(591\) | −4.50236 | −0.185202 | ||||||||
\(592\) | 11.0001 | 0.452103 | ||||||||
\(593\) | −39.1914 | −1.60940 | −0.804699 | − | 0.593683i | \(-0.797673\pi\) | ||||
−0.804699 | + | 0.593683i | \(0.797673\pi\) | |||||||
\(594\) | −1.00000 | −0.0410305 | ||||||||
\(595\) | −0.553136 | −0.0226764 | ||||||||
\(596\) | 7.90661 | 0.323868 | ||||||||
\(597\) | −7.90054 | −0.323348 | ||||||||
\(598\) | 18.5379 | 0.758072 | ||||||||
\(599\) | −44.7511 | −1.82848 | −0.914241 | − | 0.405172i | \(-0.867212\pi\) | ||||
−0.914241 | + | 0.405172i | \(0.867212\pi\) | |||||||
\(600\) | 9.46966 | 0.386597 | ||||||||
\(601\) | 26.7372 | 1.09063 | 0.545316 | − | 0.838231i | \(-0.316410\pi\) | ||||
0.545316 | + | 0.838231i | \(0.316410\pi\) | |||||||
\(602\) | 2.25793 | 0.0920264 | ||||||||
\(603\) | 13.4773 | 0.548840 | ||||||||
\(604\) | 1.15571 | 0.0470252 | ||||||||
\(605\) | −3.80390 | −0.154651 | ||||||||
\(606\) | −5.19702 | −0.211115 | ||||||||
\(607\) | −13.2882 | −0.539350 | −0.269675 | − | 0.962951i | \(-0.586916\pi\) | ||||
−0.269675 | + | 0.962951i | \(0.586916\pi\) | |||||||
\(608\) | 0.265037 | 0.0107487 | ||||||||
\(609\) | −4.02030 | −0.162911 | ||||||||
\(610\) | −3.80390 | −0.154015 | ||||||||
\(611\) | 1.43670 | 0.0581226 | ||||||||
\(612\) | −0.128672 | −0.00520125 | ||||||||
\(613\) | 29.6723 | 1.19845 | 0.599227 | − | 0.800579i | \(-0.295475\pi\) | ||||
0.599227 | + | 0.800579i | \(0.295475\pi\) | |||||||
\(614\) | 21.1225 | 0.852435 | ||||||||
\(615\) | 7.98544 | 0.322004 | ||||||||
\(616\) | −1.13011 | −0.0455333 | ||||||||
\(617\) | 13.6157 | 0.548146 | 0.274073 | − | 0.961709i | \(-0.411629\pi\) | ||||
0.274073 | + | 0.961709i | \(0.411629\pi\) | |||||||
\(618\) | 16.9417 | 0.681497 | ||||||||
\(619\) | −14.7681 | −0.593580 | −0.296790 | − | 0.954943i | \(-0.595916\pi\) | ||||
−0.296790 | + | 0.954943i | \(0.595916\pi\) | |||||||
\(620\) | −29.8845 | −1.20019 | ||||||||
\(621\) | −4.37039 | −0.175378 | ||||||||
\(622\) | 25.0386 | 1.00395 | ||||||||
\(623\) | 0.553136 | 0.0221609 | ||||||||
\(624\) | 4.24171 | 0.169804 | ||||||||
\(625\) | 17.3262 | 0.693047 | ||||||||
\(626\) | 24.5109 | 0.979652 | ||||||||
\(627\) | −0.265037 | −0.0105846 | ||||||||
\(628\) | 9.07230 | 0.362024 | ||||||||
\(629\) | −1.41541 | −0.0564360 | ||||||||
\(630\) | −4.29881 | −0.171269 | ||||||||
\(631\) | −19.9567 | −0.794465 | −0.397232 | − | 0.917718i | \(-0.630029\pi\) | ||||
−0.397232 | + | 0.917718i | \(0.630029\pi\) | |||||||
\(632\) | 4.18391 | 0.166427 | ||||||||
\(633\) | −25.2862 | −1.00504 | ||||||||
\(634\) | −29.1713 | −1.15854 | ||||||||
\(635\) | −56.8482 | −2.25595 | ||||||||
\(636\) | 2.22997 | 0.0884239 | ||||||||
\(637\) | 24.2747 | 0.961800 | ||||||||
\(638\) | −3.55745 | −0.140841 | ||||||||
\(639\) | 2.75650 | 0.109045 | ||||||||
\(640\) | 3.80390 | 0.150362 | ||||||||
\(641\) | 31.5939 | 1.24789 | 0.623943 | − | 0.781470i | \(-0.285530\pi\) | ||||
0.623943 | + | 0.781470i | \(0.285530\pi\) | |||||||
\(642\) | −0.918730 | −0.0362594 | ||||||||
\(643\) | 11.2434 | 0.443398 | 0.221699 | − | 0.975115i | \(-0.428840\pi\) | ||||
0.221699 | + | 0.975115i | \(0.428840\pi\) | |||||||
\(644\) | −4.93900 | −0.194624 | ||||||||
\(645\) | 7.60012 | 0.299254 | ||||||||
\(646\) | −0.0341028 | −0.00134176 | ||||||||
\(647\) | 0.806620 | 0.0317115 | 0.0158558 | − | 0.999874i | \(-0.494953\pi\) | ||||
0.0158558 | + | 0.999874i | \(0.494953\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 4.93603 | 0.193756 | ||||||||
\(650\) | 40.1676 | 1.57550 | ||||||||
\(651\) | 8.87842 | 0.347973 | ||||||||
\(652\) | −8.13603 | −0.318631 | ||||||||
\(653\) | 31.5647 | 1.23522 | 0.617611 | − | 0.786484i | \(-0.288101\pi\) | ||||
0.617611 | + | 0.786484i | \(0.288101\pi\) | |||||||
\(654\) | −4.41651 | −0.172699 | ||||||||
\(655\) | 21.6242 | 0.844929 | ||||||||
\(656\) | 2.09928 | 0.0819629 | ||||||||
\(657\) | −11.1407 | −0.434638 | ||||||||
\(658\) | −0.382775 | −0.0149221 | ||||||||
\(659\) | −27.7659 | −1.08161 | −0.540804 | − | 0.841149i | \(-0.681880\pi\) | ||||
−0.540804 | + | 0.841149i | \(0.681880\pi\) | |||||||
\(660\) | −3.80390 | −0.148067 | ||||||||
\(661\) | 30.8385 | 1.19948 | 0.599740 | − | 0.800195i | \(-0.295271\pi\) | ||||
0.599740 | + | 0.800195i | \(0.295271\pi\) | |||||||
\(662\) | −11.8658 | −0.461178 | ||||||||
\(663\) | −0.545789 | −0.0211967 | ||||||||
\(664\) | 5.50532 | 0.213648 | ||||||||
\(665\) | −1.13934 | −0.0441819 | ||||||||
\(666\) | −11.0001 | −0.426247 | ||||||||
\(667\) | −15.5474 | −0.602000 | ||||||||
\(668\) | −3.11680 | −0.120593 | ||||||||
\(669\) | 0.909127 | 0.0351489 | ||||||||
\(670\) | 51.2665 | 1.98060 | ||||||||
\(671\) | 1.00000 | 0.0386046 | ||||||||
\(672\) | −1.13011 | −0.0435948 | ||||||||
\(673\) | 34.6630 | 1.33616 | 0.668080 | − | 0.744089i | \(-0.267116\pi\) | ||||
0.668080 | + | 0.744089i | \(0.267116\pi\) | |||||||
\(674\) | −18.0097 | −0.693708 | ||||||||
\(675\) | −9.46966 | −0.364487 | ||||||||
\(676\) | 4.99214 | 0.192005 | ||||||||
\(677\) | −29.8345 | −1.14663 | −0.573317 | − | 0.819334i | \(-0.694344\pi\) | ||||
−0.573317 | + | 0.819334i | \(0.694344\pi\) | |||||||
\(678\) | 9.04088 | 0.347213 | ||||||||
\(679\) | −18.5720 | −0.712729 | ||||||||
\(680\) | −0.489455 | −0.0187697 | ||||||||
\(681\) | 6.58569 | 0.252364 | ||||||||
\(682\) | 7.85627 | 0.300832 | ||||||||
\(683\) | 22.5557 | 0.863068 | 0.431534 | − | 0.902097i | \(-0.357972\pi\) | ||||
0.431534 | + | 0.902097i | \(0.357972\pi\) | |||||||
\(684\) | −0.265037 | −0.0101339 | ||||||||
\(685\) | 50.3200 | 1.92263 | ||||||||
\(686\) | −14.3782 | −0.548962 | ||||||||
\(687\) | 24.9926 | 0.953528 | ||||||||
\(688\) | 1.99798 | 0.0761723 | ||||||||
\(689\) | 9.45888 | 0.360355 | ||||||||
\(690\) | −16.6245 | −0.632884 | ||||||||
\(691\) | −11.0236 | −0.419356 | −0.209678 | − | 0.977771i | \(-0.567242\pi\) | ||||
−0.209678 | + | 0.977771i | \(0.567242\pi\) | |||||||
\(692\) | −7.76547 | −0.295199 | ||||||||
\(693\) | 1.13011 | 0.0429292 | ||||||||
\(694\) | 12.1166 | 0.459941 | ||||||||
\(695\) | 55.8324 | 2.11784 | ||||||||
\(696\) | −3.55745 | −0.134845 | ||||||||
\(697\) | −0.270118 | −0.0102314 | ||||||||
\(698\) | 21.1577 | 0.800832 | ||||||||
\(699\) | 0.0101462 | 0.000383765 0 | ||||||||
\(700\) | −10.7017 | −0.404487 | ||||||||
\(701\) | −1.35614 | −0.0512207 | −0.0256103 | − | 0.999672i | \(-0.508153\pi\) | ||||
−0.0256103 | + | 0.999672i | \(0.508153\pi\) | |||||||
\(702\) | −4.24171 | −0.160093 | ||||||||
\(703\) | −2.91544 | −0.109958 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | −1.28841 | −0.0485243 | ||||||||
\(706\) | 2.82372 | 0.106272 | ||||||||
\(707\) | 5.87319 | 0.220884 | ||||||||
\(708\) | 4.93603 | 0.185507 | ||||||||
\(709\) | −27.9823 | −1.05090 | −0.525449 | − | 0.850825i | \(-0.676103\pi\) | ||||
−0.525449 | + | 0.850825i | \(0.676103\pi\) | |||||||
\(710\) | 10.4854 | 0.393512 | ||||||||
\(711\) | −4.18391 | −0.156909 | ||||||||
\(712\) | 0.489455 | 0.0183431 | ||||||||
\(713\) | 34.3349 | 1.28585 | ||||||||
\(714\) | 0.145413 | 0.00544194 | ||||||||
\(715\) | −16.1351 | −0.603417 | ||||||||
\(716\) | −3.25320 | −0.121578 | ||||||||
\(717\) | 1.36601 | 0.0510145 | ||||||||
\(718\) | −18.0948 | −0.675293 | ||||||||
\(719\) | −8.95333 | −0.333903 | −0.166951 | − | 0.985965i | \(-0.553392\pi\) | ||||
−0.166951 | + | 0.985965i | \(0.553392\pi\) | |||||||
\(720\) | −3.80390 | −0.141763 | ||||||||
\(721\) | −19.1460 | −0.713033 | ||||||||
\(722\) | 18.9298 | 0.704493 | ||||||||
\(723\) | −23.3974 | −0.870157 | ||||||||
\(724\) | −2.50450 | −0.0930789 | ||||||||
\(725\) | −33.6879 | −1.25114 | ||||||||
\(726\) | 1.00000 | 0.0371135 | ||||||||
\(727\) | 21.7053 | 0.805006 | 0.402503 | − | 0.915419i | \(-0.368140\pi\) | ||||
0.402503 | + | 0.915419i | \(0.368140\pi\) | |||||||
\(728\) | −4.79359 | −0.177662 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −42.3779 | −1.56848 | ||||||||
\(731\) | −0.257084 | −0.00950859 | ||||||||
\(732\) | 1.00000 | 0.0369611 | ||||||||
\(733\) | −40.4633 | −1.49455 | −0.747274 | − | 0.664517i | \(-0.768638\pi\) | ||||
−0.747274 | + | 0.664517i | \(0.768638\pi\) | |||||||
\(734\) | 20.6125 | 0.760821 | ||||||||
\(735\) | −21.7692 | −0.802969 | ||||||||
\(736\) | −4.37039 | −0.161095 | ||||||||
\(737\) | −13.4773 | −0.496444 | ||||||||
\(738\) | −2.09928 | −0.0772754 | ||||||||
\(739\) | −22.9213 | −0.843173 | −0.421586 | − | 0.906788i | \(-0.638527\pi\) | ||||
−0.421586 | + | 0.906788i | \(0.638527\pi\) | |||||||
\(740\) | −41.8434 | −1.53820 | ||||||||
\(741\) | −1.12421 | −0.0412989 | ||||||||
\(742\) | −2.52010 | −0.0925158 | ||||||||
\(743\) | 9.71416 | 0.356378 | 0.178189 | − | 0.983996i | \(-0.442976\pi\) | ||||
0.178189 | + | 0.983996i | \(0.442976\pi\) | |||||||
\(744\) | 7.85627 | 0.288025 | ||||||||
\(745\) | −30.0760 | −1.10190 | ||||||||
\(746\) | −25.1657 | −0.921383 | ||||||||
\(747\) | −5.50532 | −0.201429 | ||||||||
\(748\) | 0.128672 | 0.00470471 | ||||||||
\(749\) | 1.03826 | 0.0379373 | ||||||||
\(750\) | −17.0021 | −0.620831 | ||||||||
\(751\) | 29.3354 | 1.07046 | 0.535231 | − | 0.844706i | \(-0.320224\pi\) | ||||
0.535231 | + | 0.844706i | \(0.320224\pi\) | |||||||
\(752\) | −0.338707 | −0.0123514 | ||||||||
\(753\) | 13.0600 | 0.475934 | ||||||||
\(754\) | −15.0897 | −0.549535 | ||||||||
\(755\) | −4.39621 | −0.159995 | ||||||||
\(756\) | 1.13011 | 0.0411016 | ||||||||
\(757\) | 37.8532 | 1.37580 | 0.687900 | − | 0.725806i | \(-0.258533\pi\) | ||||
0.687900 | + | 0.725806i | \(0.258533\pi\) | |||||||
\(758\) | −2.60869 | −0.0947520 | ||||||||
\(759\) | 4.37039 | 0.158635 | ||||||||
\(760\) | −1.00817 | −0.0365703 | ||||||||
\(761\) | 27.3474 | 0.991344 | 0.495672 | − | 0.868510i | \(-0.334922\pi\) | ||||
0.495672 | + | 0.868510i | \(0.334922\pi\) | |||||||
\(762\) | 14.9447 | 0.541390 | ||||||||
\(763\) | 4.99113 | 0.180691 | ||||||||
\(764\) | −23.2019 | −0.839415 | ||||||||
\(765\) | 0.489455 | 0.0176963 | ||||||||
\(766\) | −10.1177 | −0.365567 | ||||||||
\(767\) | 20.9372 | 0.755999 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −12.3128 | −0.444011 | −0.222005 | − | 0.975045i | \(-0.571260\pi\) | ||||
−0.222005 | + | 0.975045i | \(0.571260\pi\) | |||||||
\(770\) | 4.29881 | 0.154918 | ||||||||
\(771\) | −16.2686 | −0.585900 | ||||||||
\(772\) | −19.7378 | −0.710379 | ||||||||
\(773\) | 38.5443 | 1.38634 | 0.693171 | − | 0.720773i | \(-0.256213\pi\) | ||||
0.693171 | + | 0.720773i | \(0.256213\pi\) | |||||||
\(774\) | −1.99798 | −0.0718159 | ||||||||
\(775\) | 74.3962 | 2.67239 | ||||||||
\(776\) | −16.4339 | −0.589942 | ||||||||
\(777\) | 12.4313 | 0.445971 | ||||||||
\(778\) | −12.2480 | −0.439113 | ||||||||
\(779\) | −0.556386 | −0.0199346 | ||||||||
\(780\) | −16.1351 | −0.577728 | ||||||||
\(781\) | −2.75650 | −0.0986353 | ||||||||
\(782\) | 0.562345 | 0.0201094 | ||||||||
\(783\) | 3.55745 | 0.127133 | ||||||||
\(784\) | −5.72286 | −0.204388 | ||||||||
\(785\) | −34.5101 | −1.23172 | ||||||||
\(786\) | −5.68475 | −0.202768 | ||||||||
\(787\) | 0.241105 | 0.00859445 | 0.00429723 | − | 0.999991i | \(-0.498632\pi\) | ||||
0.00429723 | + | 0.999991i | \(0.498632\pi\) | |||||||
\(788\) | 4.50236 | 0.160390 | ||||||||
\(789\) | −6.16069 | −0.219326 | ||||||||
\(790\) | −15.9152 | −0.566236 | ||||||||
\(791\) | −10.2172 | −0.363280 | ||||||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | 4.24171 | 0.150628 | ||||||||
\(794\) | 21.9214 | 0.777960 | ||||||||
\(795\) | −8.48257 | −0.300846 | ||||||||
\(796\) | 7.90054 | 0.280027 | ||||||||
\(797\) | −8.85215 | −0.313559 | −0.156780 | − | 0.987634i | \(-0.550111\pi\) | ||||
−0.156780 | + | 0.987634i | \(0.550111\pi\) | |||||||
\(798\) | 0.299520 | 0.0106029 | ||||||||
\(799\) | 0.0435821 | 0.00154182 | ||||||||
\(800\) | −9.46966 | −0.334803 | ||||||||
\(801\) | −0.489455 | −0.0172940 | ||||||||
\(802\) | 21.0450 | 0.743124 | ||||||||
\(803\) | 11.1407 | 0.393145 | ||||||||
\(804\) | −13.4773 | −0.475309 | ||||||||
\(805\) | 18.7875 | 0.662171 | ||||||||
\(806\) | 33.3240 | 1.17379 | ||||||||
\(807\) | 21.6824 | 0.763257 | ||||||||
\(808\) | 5.19702 | 0.182831 | ||||||||
\(809\) | −19.2003 | −0.675048 | −0.337524 | − | 0.941317i | \(-0.609589\pi\) | ||||
−0.337524 | + | 0.941317i | \(0.609589\pi\) | |||||||
\(810\) | 3.80390 | 0.133655 | ||||||||
\(811\) | −51.1276 | −1.79533 | −0.897667 | − | 0.440675i | \(-0.854739\pi\) | ||||
−0.897667 | + | 0.440675i | \(0.854739\pi\) | |||||||
\(812\) | 4.02030 | 0.141085 | ||||||||
\(813\) | 19.0960 | 0.669725 | ||||||||
\(814\) | 11.0001 | 0.385555 | ||||||||
\(815\) | 30.9486 | 1.08408 | ||||||||
\(816\) | 0.128672 | 0.00450441 | ||||||||
\(817\) | −0.529539 | −0.0185262 | ||||||||
\(818\) | −26.3348 | −0.920774 | ||||||||
\(819\) | 4.79359 | 0.167502 | ||||||||
\(820\) | −7.98544 | −0.278864 | ||||||||
\(821\) | 16.4508 | 0.574136 | 0.287068 | − | 0.957910i | \(-0.407319\pi\) | ||||
0.287068 | + | 0.957910i | \(0.407319\pi\) | |||||||
\(822\) | −13.2285 | −0.461398 | ||||||||
\(823\) | 17.6294 | 0.614523 | 0.307262 | − | 0.951625i | \(-0.400587\pi\) | ||||
0.307262 | + | 0.951625i | \(0.400587\pi\) | |||||||
\(824\) | −16.9417 | −0.590194 | ||||||||
\(825\) | 9.46966 | 0.329691 | ||||||||
\(826\) | −5.57824 | −0.194092 | ||||||||
\(827\) | −41.0075 | −1.42597 | −0.712986 | − | 0.701179i | \(-0.752658\pi\) | ||||
−0.712986 | + | 0.701179i | \(0.752658\pi\) | |||||||
\(828\) | 4.37039 | 0.151881 | ||||||||
\(829\) | 23.5411 | 0.817616 | 0.408808 | − | 0.912620i | \(-0.365945\pi\) | ||||
0.408808 | + | 0.912620i | \(0.365945\pi\) | |||||||
\(830\) | −20.9417 | −0.726896 | ||||||||
\(831\) | 21.4653 | 0.744624 | ||||||||
\(832\) | −4.24171 | −0.147055 | ||||||||
\(833\) | 0.736371 | 0.0255137 | ||||||||
\(834\) | −14.6777 | −0.508246 | ||||||||
\(835\) | 11.8560 | 0.410294 | ||||||||
\(836\) | 0.265037 | 0.00916649 | ||||||||
\(837\) | −7.85627 | −0.271552 | ||||||||
\(838\) | −16.1013 | −0.556211 | ||||||||
\(839\) | 11.1533 | 0.385053 | 0.192527 | − | 0.981292i | \(-0.438332\pi\) | ||||
0.192527 | + | 0.981292i | \(0.438332\pi\) | |||||||
\(840\) | 4.29881 | 0.148323 | ||||||||
\(841\) | −16.3445 | −0.563604 | ||||||||
\(842\) | 17.0787 | 0.588569 | ||||||||
\(843\) | 20.1406 | 0.693678 | ||||||||
\(844\) | 25.2862 | 0.870387 | ||||||||
\(845\) | −18.9896 | −0.653262 | ||||||||
\(846\) | 0.338707 | 0.0116450 | ||||||||
\(847\) | −1.13011 | −0.0388309 | ||||||||
\(848\) | −2.22997 | −0.0765774 | ||||||||
\(849\) | −6.60060 | −0.226532 | ||||||||
\(850\) | 1.21848 | 0.0417935 | ||||||||
\(851\) | 48.0749 | 1.64798 | ||||||||
\(852\) | −2.75650 | −0.0944361 | ||||||||
\(853\) | −32.4544 | −1.11122 | −0.555608 | − | 0.831444i | \(-0.687515\pi\) | ||||
−0.555608 | + | 0.831444i | \(0.687515\pi\) | |||||||
\(854\) | −1.13011 | −0.0386714 | ||||||||
\(855\) | 1.00817 | 0.0344788 | ||||||||
\(856\) | 0.918730 | 0.0314016 | ||||||||
\(857\) | −5.83593 | −0.199352 | −0.0996758 | − | 0.995020i | \(-0.531781\pi\) | ||||
−0.0996758 | + | 0.995020i | \(0.531781\pi\) | |||||||
\(858\) | 4.24171 | 0.144810 | ||||||||
\(859\) | −10.8604 | −0.370551 | −0.185276 | − | 0.982687i | \(-0.559318\pi\) | ||||
−0.185276 | + | 0.982687i | \(0.559318\pi\) | |||||||
\(860\) | −7.60012 | −0.259162 | ||||||||
\(861\) | 2.37240 | 0.0808513 | ||||||||
\(862\) | −25.0261 | −0.852392 | ||||||||
\(863\) | −19.5059 | −0.663988 | −0.331994 | − | 0.943281i | \(-0.607721\pi\) | ||||
−0.331994 | + | 0.943281i | \(0.607721\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 29.5391 | 1.00436 | ||||||||
\(866\) | 4.76689 | 0.161985 | ||||||||
\(867\) | 16.9834 | 0.576788 | ||||||||
\(868\) | −8.87842 | −0.301353 | ||||||||
\(869\) | 4.18391 | 0.141929 | ||||||||
\(870\) | 13.5322 | 0.458785 | ||||||||
\(871\) | −57.1670 | −1.93703 | ||||||||
\(872\) | 4.41651 | 0.149562 | ||||||||
\(873\) | 16.4339 | 0.556203 | ||||||||
\(874\) | 1.15831 | 0.0391805 | ||||||||
\(875\) | 19.2142 | 0.649560 | ||||||||
\(876\) | 11.1407 | 0.376408 | ||||||||
\(877\) | 34.3417 | 1.15964 | 0.579818 | − | 0.814746i | \(-0.303124\pi\) | ||||
0.579818 | + | 0.814746i | \(0.303124\pi\) | |||||||
\(878\) | 19.2883 | 0.650950 | ||||||||
\(879\) | −27.0042 | −0.910828 | ||||||||
\(880\) | 3.80390 | 0.128229 | ||||||||
\(881\) | −17.8374 | −0.600958 | −0.300479 | − | 0.953788i | \(-0.597146\pi\) | ||||
−0.300479 | + | 0.953788i | \(0.597146\pi\) | |||||||
\(882\) | 5.72286 | 0.192699 | ||||||||
\(883\) | 34.2420 | 1.15234 | 0.576168 | − | 0.817332i | \(-0.304548\pi\) | ||||
0.576168 | + | 0.817332i | \(0.304548\pi\) | |||||||
\(884\) | 0.545789 | 0.0183569 | ||||||||
\(885\) | −18.7762 | −0.631154 | ||||||||
\(886\) | 21.1686 | 0.711174 | ||||||||
\(887\) | 2.99807 | 0.100665 | 0.0503327 | − | 0.998733i | \(-0.483972\pi\) | ||||
0.0503327 | + | 0.998733i | \(0.483972\pi\) | |||||||
\(888\) | 11.0001 | 0.369141 | ||||||||
\(889\) | −16.8891 | −0.566443 | ||||||||
\(890\) | −1.86184 | −0.0624089 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | −0.909127 | −0.0304398 | ||||||||
\(893\) | 0.0897699 | 0.00300404 | ||||||||
\(894\) | 7.90661 | 0.264437 | ||||||||
\(895\) | 12.3749 | 0.413646 | ||||||||
\(896\) | 1.13011 | 0.0377542 | ||||||||
\(897\) | 18.5379 | 0.618963 | ||||||||
\(898\) | −4.72877 | −0.157801 | ||||||||
\(899\) | −27.9483 | −0.932128 | ||||||||
\(900\) | 9.46966 | 0.315655 | ||||||||
\(901\) | 0.286934 | 0.00955915 | ||||||||
\(902\) | 2.09928 | 0.0698982 | ||||||||
\(903\) | 2.25793 | 0.0751392 | ||||||||
\(904\) | −9.04088 | −0.300695 | ||||||||
\(905\) | 9.52686 | 0.316683 | ||||||||
\(906\) | 1.15571 | 0.0383959 | ||||||||
\(907\) | −53.2408 | −1.76783 | −0.883916 | − | 0.467645i | \(-0.845103\pi\) | ||||
−0.883916 | + | 0.467645i | \(0.845103\pi\) | |||||||
\(908\) | −6.58569 | −0.218554 | ||||||||
\(909\) | −5.19702 | −0.172374 | ||||||||
\(910\) | 18.2343 | 0.604462 | ||||||||
\(911\) | −18.8795 | −0.625507 | −0.312753 | − | 0.949834i | \(-0.601251\pi\) | ||||
−0.312753 | + | 0.949834i | \(0.601251\pi\) | |||||||
\(912\) | 0.265037 | 0.00877625 | ||||||||
\(913\) | 5.50532 | 0.182199 | ||||||||
\(914\) | −11.3987 | −0.377036 | ||||||||
\(915\) | −3.80390 | −0.125753 | ||||||||
\(916\) | −24.9926 | −0.825780 | ||||||||
\(917\) | 6.42438 | 0.212152 | ||||||||
\(918\) | −0.128672 | −0.00424680 | ||||||||
\(919\) | 27.9575 | 0.922231 | 0.461116 | − | 0.887340i | \(-0.347449\pi\) | ||||
0.461116 | + | 0.887340i | \(0.347449\pi\) | |||||||
\(920\) | 16.6245 | 0.548094 | ||||||||
\(921\) | 21.1225 | 0.696010 | ||||||||
\(922\) | 2.01992 | 0.0665227 | ||||||||
\(923\) | −11.6923 | −0.384856 | ||||||||
\(924\) | −1.13011 | −0.0371778 | ||||||||
\(925\) | 104.168 | 3.42501 | ||||||||
\(926\) | −1.91078 | −0.0627921 | ||||||||
\(927\) | 16.9417 | 0.556440 | ||||||||
\(928\) | 3.55745 | 0.116779 | ||||||||
\(929\) | 7.92958 | 0.260161 | 0.130081 | − | 0.991503i | \(-0.458476\pi\) | ||||
0.130081 | + | 0.991503i | \(0.458476\pi\) | |||||||
\(930\) | −29.8845 | −0.979950 | ||||||||
\(931\) | 1.51677 | 0.0497101 | ||||||||
\(932\) | −0.0101462 | −0.000332350 0 | ||||||||
\(933\) | 25.0386 | 0.819726 | ||||||||
\(934\) | −15.1715 | −0.496426 | ||||||||
\(935\) | −0.489455 | −0.0160069 | ||||||||
\(936\) | 4.24171 | 0.138645 | ||||||||
\(937\) | 19.0547 | 0.622490 | 0.311245 | − | 0.950330i | \(-0.399254\pi\) | ||||
0.311245 | + | 0.950330i | \(0.399254\pi\) | |||||||
\(938\) | 15.2308 | 0.497304 | ||||||||
\(939\) | 24.5109 | 0.799882 | ||||||||
\(940\) | 1.28841 | 0.0420233 | ||||||||
\(941\) | 33.9522 | 1.10681 | 0.553405 | − | 0.832912i | \(-0.313328\pi\) | ||||
0.553405 | + | 0.832912i | \(0.313328\pi\) | |||||||
\(942\) | 9.07230 | 0.295592 | ||||||||
\(943\) | 9.17464 | 0.298767 | ||||||||
\(944\) | −4.93603 | −0.160654 | ||||||||
\(945\) | −4.29881 | −0.139840 | ||||||||
\(946\) | 1.99798 | 0.0649600 | ||||||||
\(947\) | 41.8174 | 1.35888 | 0.679441 | − | 0.733730i | \(-0.262222\pi\) | ||||
0.679441 | + | 0.733730i | \(0.262222\pi\) | |||||||
\(948\) | 4.18391 | 0.135887 | ||||||||
\(949\) | 47.2555 | 1.53398 | ||||||||
\(950\) | 2.50981 | 0.0814290 | ||||||||
\(951\) | −29.1713 | −0.945943 | ||||||||
\(952\) | −0.145413 | −0.00471286 | ||||||||
\(953\) | −16.0917 | −0.521262 | −0.260631 | − | 0.965439i | \(-0.583931\pi\) | ||||
−0.260631 | + | 0.965439i | \(0.583931\pi\) | |||||||
\(954\) | 2.22997 | 0.0721978 | ||||||||
\(955\) | 88.2577 | 2.85595 | ||||||||
\(956\) | −1.36601 | −0.0441799 | ||||||||
\(957\) | −3.55745 | −0.114996 | ||||||||
\(958\) | −32.5688 | −1.05225 | ||||||||
\(959\) | 14.9496 | 0.482749 | ||||||||
\(960\) | 3.80390 | 0.122770 | ||||||||
\(961\) | 30.7209 | 0.990998 | ||||||||
\(962\) | 46.6594 | 1.50436 | ||||||||
\(963\) | −0.918730 | −0.0296057 | ||||||||
\(964\) | 23.3974 | 0.753578 | ||||||||
\(965\) | 75.0807 | 2.41693 | ||||||||
\(966\) | −4.93900 | −0.158910 | ||||||||
\(967\) | 33.6948 | 1.08355 | 0.541777 | − | 0.840523i | \(-0.317752\pi\) | ||||
0.541777 | + | 0.840523i | \(0.317752\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | −0.0341028 | −0.00109554 | ||||||||
\(970\) | 62.5129 | 2.00717 | ||||||||
\(971\) | −4.90939 | −0.157550 | −0.0787749 | − | 0.996892i | \(-0.525101\pi\) | ||||
−0.0787749 | + | 0.996892i | \(0.525101\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 16.5873 | 0.531766 | ||||||||
\(974\) | −1.71068 | −0.0548138 | ||||||||
\(975\) | 40.1676 | 1.28639 | ||||||||
\(976\) | −1.00000 | −0.0320092 | ||||||||
\(977\) | 9.45469 | 0.302482 | 0.151241 | − | 0.988497i | \(-0.451673\pi\) | ||||
0.151241 | + | 0.988497i | \(0.451673\pi\) | |||||||
\(978\) | −8.13603 | −0.260161 | ||||||||
\(979\) | 0.489455 | 0.0156430 | ||||||||
\(980\) | 21.7692 | 0.695391 | ||||||||
\(981\) | −4.41651 | −0.141008 | ||||||||
\(982\) | 6.63332 | 0.211678 | ||||||||
\(983\) | 8.19968 | 0.261529 | 0.130765 | − | 0.991413i | \(-0.458257\pi\) | ||||
0.130765 | + | 0.991413i | \(0.458257\pi\) | |||||||
\(984\) | 2.09928 | 0.0669225 | ||||||||
\(985\) | −17.1265 | −0.545696 | ||||||||
\(986\) | −0.457744 | −0.0145775 | ||||||||
\(987\) | −0.382775 | −0.0121839 | ||||||||
\(988\) | 1.12421 | 0.0357659 | ||||||||
\(989\) | 8.73195 | 0.277660 | ||||||||
\(990\) | −3.80390 | −0.120896 | ||||||||
\(991\) | −0.622074 | −0.0197608 | −0.00988042 | − | 0.999951i | \(-0.503145\pi\) | ||||
−0.00988042 | + | 0.999951i | \(0.503145\pi\) | |||||||
\(992\) | −7.85627 | −0.249437 | ||||||||
\(993\) | −11.8658 | −0.376550 | ||||||||
\(994\) | 3.11514 | 0.0988061 | ||||||||
\(995\) | −30.0529 | −0.952740 | ||||||||
\(996\) | 5.50532 | 0.174443 | ||||||||
\(997\) | 11.0385 | 0.349593 | 0.174796 | − | 0.984605i | \(-0.444073\pi\) | ||||
0.174796 | + | 0.984605i | \(0.444073\pi\) | |||||||
\(998\) | 14.8590 | 0.470353 | ||||||||
\(999\) | −11.0001 | −0.348029 |
(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 | 4026.2.a.y.1.1 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4026.2.a.y.1.1 | ✓ | 7 | 1.1 | even | 1 | trivial |