Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3640,2,Mod(1,3640)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3640, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("3640.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3640 = 2^{3} \cdot 5 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3640.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: | \(29.0655463357\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.4913.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 6x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.344151\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3640.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.34415 | 0.776046 | 0.388023 | − | 0.921650i | \(-0.373158\pi\) | ||||
0.388023 | + | 0.921650i | \(0.373158\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.19326 | −0.397753 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.02414 | 0.308791 | 0.154395 | − | 0.988009i | \(-0.450657\pi\) | ||||
0.154395 | + | 0.988009i | \(0.450657\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.34415 | −0.347058 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.881560 | −0.213810 | −0.106905 | − | 0.994269i | \(-0.534094\pi\) | ||||
−0.106905 | + | 0.994269i | \(0.534094\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.90570 | 0.896030 | 0.448015 | − | 0.894026i | \(-0.352131\pi\) | ||||
0.448015 | + | 0.894026i | \(0.352131\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.34415 | −0.293318 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.975857 | 0.203480 | 0.101740 | − | 0.994811i | \(-0.467559\pi\) | ||||
0.101740 | + | 0.994811i | \(0.467559\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.63637 | −1.08472 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.320007 | 0.0594239 | 0.0297119 | − | 0.999559i | \(-0.490541\pi\) | ||||
0.0297119 | + | 0.999559i | \(0.490541\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.46726 | −0.802343 | −0.401171 | − | 0.916003i | \(-0.631397\pi\) | ||||
−0.401171 | + | 0.916003i | \(0.631397\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.37660 | 0.239636 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.56622 | 1.07948 | 0.539740 | − | 0.841832i | \(-0.318523\pi\) | ||||
0.539740 | + | 0.841832i | \(0.318523\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.34415 | 0.215236 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12.5044 | 1.95286 | 0.976428 | − | 0.215845i | \(-0.0692507\pi\) | ||||
0.976428 | + | 0.215845i | \(0.0692507\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.71244 | 0.566143 | 0.283071 | − | 0.959099i | \(-0.408647\pi\) | ||||
0.283071 | + | 0.959099i | \(0.408647\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.19326 | 0.177881 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.12311 | 0.747282 | 0.373641 | − | 0.927573i | \(-0.378109\pi\) | ||||
0.373641 | + | 0.927573i | \(0.378109\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.18495 | −0.165926 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.12311 | −0.154270 | −0.0771352 | − | 0.997021i | \(-0.524577\pi\) | ||||
−0.0771352 | + | 0.997021i | \(0.524577\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.02414 | −0.138095 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.24985 | 0.695360 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.91926 | 0.249867 | 0.124933 | − | 0.992165i | \(-0.460128\pi\) | ||||
0.124933 | + | 0.992165i | \(0.460128\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.24621 | −1.05582 | −0.527910 | − | 0.849301i | \(-0.677024\pi\) | ||||
−0.527910 | + | 0.849301i | \(0.677024\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.19326 | 0.150336 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.430138 | 0.0525498 | 0.0262749 | − | 0.999655i | \(-0.491635\pi\) | ||||
0.0262749 | + | 0.999655i | \(0.491635\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.31170 | 0.157910 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.6569 | −1.62077 | −0.810386 | − | 0.585896i | \(-0.800743\pi\) | ||||
−0.810386 | + | 0.585896i | \(0.800743\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.49971 | 0.994816 | 0.497408 | − | 0.867517i | \(-0.334285\pi\) | ||||
0.497408 | + | 0.867517i | \(0.334285\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.34415 | 0.155209 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.02414 | −0.116712 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.3912 | 1.61913 | 0.809567 | − | 0.587027i | \(-0.199702\pi\) | ||||
0.809567 | + | 0.587027i | \(0.199702\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.99636 | −0.444040 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.7459 | 1.83810 | 0.919052 | − | 0.394137i | \(-0.128956\pi\) | ||||
0.919052 | + | 0.394137i | \(0.128956\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.881560 | 0.0956186 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.430138 | 0.0461157 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.55630 | −0.164968 | −0.0824839 | − | 0.996592i | \(-0.526285\pi\) | ||||
−0.0824839 | + | 0.996592i | \(0.526285\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.00467 | −0.622655 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.90570 | −0.400717 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.5090 | −1.67624 | −0.838120 | − | 0.545487i | \(-0.816345\pi\) | ||||
−0.838120 | + | 0.545487i | \(0.816345\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.22207 | −0.122822 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 19.3210 | 1.92251 | 0.961257 | − | 0.275653i | \(-0.0888941\pi\) | ||||
0.961257 | + | 0.275653i | \(0.0888941\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.40541 | −0.434078 | −0.217039 | − | 0.976163i | \(-0.569640\pi\) | ||||
−0.217039 | + | 0.976163i | \(0.569640\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.34415 | 0.131176 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.36237 | 0.711748 | 0.355874 | − | 0.934534i | \(-0.384183\pi\) | ||||
0.355874 | + | 0.934534i | \(0.384183\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.1225 | 1.35269 | 0.676346 | − | 0.736584i | \(-0.263562\pi\) | ||||
0.676346 | + | 0.736584i | \(0.263562\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.82599 | 0.837726 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.7366 | 1.01001 | 0.505007 | − | 0.863115i | \(-0.331490\pi\) | ||||
0.505007 | + | 0.863115i | \(0.331490\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.975857 | −0.0909991 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.19326 | −0.110317 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.881560 | 0.0808125 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.95113 | −0.904648 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 16.8078 | 1.51551 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.6470 | 1.29971 | 0.649854 | − | 0.760059i | \(-0.274830\pi\) | ||||
0.649854 | + | 0.760059i | \(0.274830\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.99009 | 0.439353 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.12311 | 0.797089 | 0.398545 | − | 0.917149i | \(-0.369515\pi\) | ||||
0.398545 | + | 0.917149i | \(0.369515\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.90570 | −0.338667 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.63637 | 0.485102 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.63171 | 0.139406 | 0.0697030 | − | 0.997568i | \(-0.477795\pi\) | ||||
0.0697030 | + | 0.997568i | \(0.477795\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.23630 | 0.613775 | 0.306887 | − | 0.951746i | \(-0.400713\pi\) | ||||
0.306887 | + | 0.951746i | \(0.400713\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.88623 | 0.579925 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.02414 | 0.0856432 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.320007 | −0.0265752 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.34415 | 0.110864 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.12311 | 0.0920084 | 0.0460042 | − | 0.998941i | \(-0.485351\pi\) | ||||
0.0460042 | + | 0.998941i | \(0.485351\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.03406 | 0.165529 | 0.0827646 | − | 0.996569i | \(-0.473625\pi\) | ||||
0.0827646 | + | 0.996569i | \(0.473625\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.05193 | 0.0850435 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.46726 | 0.358819 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.3194 | 1.38224 | 0.691120 | − | 0.722740i | \(-0.257117\pi\) | ||||
0.691120 | + | 0.722740i | \(0.257117\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.50962 | −0.119721 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.975857 | −0.0769083 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.4908 | −1.13501 | −0.567504 | − | 0.823371i | \(-0.692091\pi\) | ||||
−0.567504 | + | 0.823371i | \(0.692091\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.37660 | −0.107168 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.4608 | −1.58330 | −0.791650 | − | 0.610974i | \(-0.790778\pi\) | ||||
−0.791650 | + | 0.610974i | \(0.790778\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.66052 | −0.356399 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.43320 | 0.184993 | 0.0924963 | − | 0.995713i | \(-0.470515\pi\) | ||||
0.0924963 | + | 0.995713i | \(0.470515\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.57978 | 0.193908 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.51224 | 0.113030 | 0.0565152 | − | 0.998402i | \(-0.482001\pi\) | ||||
0.0565152 | + | 0.998402i | \(0.482001\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.8862 | −1.25514 | −0.627572 | − | 0.778559i | \(-0.715951\pi\) | ||||
−0.627572 | + | 0.778559i | \(0.715951\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.0842 | −0.819364 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.56622 | −0.482758 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.902844 | −0.0660225 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.63637 | 0.409986 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.75481 | −0.633476 | −0.316738 | − | 0.948513i | \(-0.602588\pi\) | ||||
−0.316738 | + | 0.948513i | \(0.602588\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.95638 | 0.140823 | 0.0704116 | − | 0.997518i | \(-0.477569\pi\) | ||||
0.0704116 | + | 0.997518i | \(0.477569\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.34415 | −0.0962566 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.6628 | −0.759692 | −0.379846 | − | 0.925050i | \(-0.624023\pi\) | ||||
−0.379846 | + | 0.925050i | \(0.624023\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.0847 | 1.28199 | 0.640996 | − | 0.767544i | \(-0.278521\pi\) | ||||
0.640996 | + | 0.767544i | \(0.278521\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.578171 | 0.0407810 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.320007 | −0.0224601 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.5044 | −0.873343 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.16445 | −0.0809348 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.00000 | 0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.8155 | 1.57068 | 0.785342 | − | 0.619063i | \(-0.212487\pi\) | ||||
0.785342 | + | 0.619063i | \(0.212487\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −18.3569 | −1.25779 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.71244 | −0.253187 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.46726 | 0.303257 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.4249 | 0.772022 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.881560 | −0.0593002 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −25.5839 | −1.71322 | −0.856611 | − | 0.515963i | \(-0.827434\pi\) | ||||
−0.856611 | + | 0.515963i | \(0.827434\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.19326 | −0.0795506 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 25.5190 | 1.69375 | 0.846876 | − | 0.531790i | \(-0.178480\pi\) | ||||
0.846876 | + | 0.531790i | \(0.178480\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.5216 | −1.29002 | −0.645011 | − | 0.764173i | \(-0.723147\pi\) | ||||
−0.645011 | + | 0.764173i | \(0.723147\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.37660 | −0.0905738 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.7459 | 0.703989 | 0.351994 | − | 0.936002i | \(-0.385504\pi\) | ||||
0.351994 | + | 0.936002i | \(0.385504\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.12311 | −0.334195 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 19.3439 | 1.25652 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.40075 | 0.543399 | 0.271700 | − | 0.962382i | \(-0.412414\pi\) | ||||
0.271700 | + | 0.962382i | \(0.412414\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.12835 | −0.394762 | −0.197381 | − | 0.980327i | \(-0.563244\pi\) | ||||
−0.197381 | + | 0.980327i | \(0.563244\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.5374 | 0.740125 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.90570 | 0.248514 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 22.5090 | 1.42645 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.3105 | −1.72383 | −0.861913 | − | 0.507057i | \(-0.830734\pi\) | ||||
−0.861913 | + | 0.507057i | \(0.830734\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.999417 | 0.0628328 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.18495 | 0.0742044 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 29.6155 | 1.84737 | 0.923683 | − | 0.383158i | \(-0.125163\pi\) | ||||
0.923683 | + | 0.383158i | \(0.125163\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.56622 | −0.408005 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.381852 | −0.0236360 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23.3234 | 1.43818 | 0.719092 | − | 0.694915i | \(-0.244558\pi\) | ||||
0.719092 | + | 0.694915i | \(0.244558\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.12311 | 0.0689918 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.09191 | −0.128023 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.0748 | 0.797186 | 0.398593 | − | 0.917128i | \(-0.369499\pi\) | ||||
0.398593 | + | 0.917128i | \(0.369499\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.5021 | −1.12392 | −0.561961 | − | 0.827164i | \(-0.689953\pi\) | ||||
−0.561961 | + | 0.827164i | \(0.689953\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.34415 | −0.0813517 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.02414 | 0.0617582 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.3760 | −1.10411 | −0.552054 | − | 0.833808i | \(-0.686156\pi\) | ||||
−0.552054 | + | 0.833808i | \(0.686156\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.33059 | 0.319134 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −28.8591 | −1.72159 | −0.860795 | − | 0.508952i | \(-0.830033\pi\) | ||||
−0.860795 | + | 0.508952i | \(0.830033\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.0071 | 1.18930 | 0.594648 | − | 0.803986i | \(-0.297291\pi\) | ||||
0.594648 | + | 0.803986i | \(0.297291\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.24985 | −0.310975 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.5044 | −0.738110 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.2229 | −0.954285 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −22.1906 | −1.30084 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.8645 | −0.926812 | −0.463406 | − | 0.886146i | \(-0.653373\pi\) | ||||
−0.463406 | + | 0.886146i | \(0.653373\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.91926 | −0.111744 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.77245 | −0.334952 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.975857 | 0.0564353 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.71244 | −0.213982 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 25.9704 | 1.49196 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.24621 | 0.472177 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.69822 | 0.325214 | 0.162607 | − | 0.986691i | \(-0.448010\pi\) | ||||
0.162607 | + | 0.986691i | \(0.448010\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.92154 | −0.336865 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 32.5018 | 1.84301 | 0.921503 | − | 0.388372i | \(-0.126962\pi\) | ||||
0.921503 | + | 0.388372i | \(0.126962\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.34654 | 0.189158 | 0.0945788 | − | 0.995517i | \(-0.469850\pi\) | ||||
0.0945788 | + | 0.995517i | \(0.469850\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.19326 | −0.0672325 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −30.7188 | −1.72534 | −0.862670 | − | 0.505767i | \(-0.831209\pi\) | ||||
−0.862670 | + | 0.505767i | \(0.831209\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.327733 | 0.0183496 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.89614 | 0.552349 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.44311 | −0.191580 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 18.9828 | 1.04975 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.12311 | −0.282446 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.2221 | 0.946610 | 0.473305 | − | 0.880898i | \(-0.343061\pi\) | ||||
0.473305 | + | 0.880898i | \(0.343061\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.83520 | −0.429366 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.430138 | −0.0235010 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −29.1491 | −1.58785 | −0.793925 | − | 0.608016i | \(-0.791966\pi\) | ||||
−0.793925 | + | 0.608016i | \(0.791966\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.4316 | 0.783817 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.57511 | −0.247756 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.31170 | −0.0706195 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.77065 | −0.470833 | −0.235416 | − | 0.971895i | \(-0.575645\pi\) | ||||
−0.235416 | + | 0.971895i | \(0.575645\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.0566 | −1.34125 | −0.670624 | − | 0.741797i | \(-0.733974\pi\) | ||||
−0.670624 | + | 0.741797i | \(0.733974\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.63637 | −0.300847 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.3766 | 0.818414 | 0.409207 | − | 0.912442i | \(-0.365805\pi\) | ||||
0.409207 | + | 0.912442i | \(0.365805\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.6569 | 0.724832 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.18495 | 0.0627142 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.0896 | 0.532510 | 0.266255 | − | 0.963903i | \(-0.414214\pi\) | ||||
0.266255 | + | 0.963903i | \(0.414214\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.74548 | −0.197131 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −13.3758 | −0.702048 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.49971 | −0.444895 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.0422 | −1.56819 | −0.784096 | − | 0.620640i | \(-0.786873\pi\) | ||||
−0.784096 | + | 0.620640i | \(0.786873\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −14.9210 | −0.776754 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.12311 | 0.0583087 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.51691 | −0.182099 | −0.0910493 | − | 0.995846i | \(-0.529022\pi\) | ||||
−0.0910493 | + | 0.995846i | \(0.529022\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.34415 | −0.0694116 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.320007 | 0.0164812 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.6735 | 1.52422 | 0.762112 | − | 0.647445i | \(-0.224162\pi\) | ||||
0.762112 | + | 0.647445i | \(0.224162\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 19.6877 | 1.00863 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.1874 | −0.724944 | −0.362472 | − | 0.931995i | \(-0.618067\pi\) | ||||
−0.362472 | + | 0.931995i | \(0.618067\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.02414 | 0.0521952 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.42991 | −0.225185 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −32.3039 | −1.63787 | −0.818937 | − | 0.573883i | \(-0.805436\pi\) | ||||
−0.818937 | + | 0.573883i | \(0.805436\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.860277 | −0.0435061 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.2628 | 0.618578 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.3912 | −0.724099 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.68160 | 0.0843970 | 0.0421985 | − | 0.999109i | \(-0.486564\pi\) | ||||
0.0421985 | + | 0.999109i | \(0.486564\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.24985 | −0.262821 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.2894 | −1.36277 | −0.681383 | − | 0.731927i | \(-0.738621\pi\) | ||||
−0.681383 | + | 0.731927i | \(0.738621\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.46726 | −0.222530 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.99636 | 0.198581 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.72475 | 0.333333 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.34949 | −0.0667279 | −0.0333639 | − | 0.999443i | \(-0.510622\pi\) | ||||
−0.0333639 | + | 0.999443i | \(0.510622\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.19326 | 0.108185 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.91926 | −0.0944407 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.7459 | −0.822025 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.72667 | 0.476317 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.6321 | −0.763680 | −0.381840 | − | 0.924228i | \(-0.624710\pi\) | ||||
−0.381840 | + | 0.924228i | \(0.624710\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.23893 | 0.401541 | 0.200770 | − | 0.979638i | \(-0.435656\pi\) | ||||
0.200770 | + | 0.979638i | \(0.435656\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.11319 | −0.297234 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.881560 | −0.0427620 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.24621 | 0.399062 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.37660 | 0.0664630 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.56759 | −0.171845 | −0.0859223 | − | 0.996302i | \(-0.527384\pi\) | ||||
−0.0859223 | + | 0.996302i | \(0.527384\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.6639 | 1.04110 | 0.520551 | − | 0.853831i | \(-0.325727\pi\) | ||||
0.520551 | + | 0.853831i | \(0.325727\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.430138 | −0.0206236 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.81141 | 0.182324 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.6711 | 0.843396 | 0.421698 | − | 0.906736i | \(-0.361434\pi\) | ||||
0.421698 | + | 0.906736i | \(0.361434\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.19326 | −0.0568218 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.01686 | 0.333381 | 0.166690 | − | 0.986009i | \(-0.446692\pi\) | ||||
0.166690 | + | 0.986009i | \(0.446692\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.55630 | 0.0737759 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.50962 | 0.0714027 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.13244 | 0.336601 | 0.168300 | − | 0.985736i | \(-0.446172\pi\) | ||||
0.168300 | + | 0.985736i | \(0.446172\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.8063 | 0.603024 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.73408 | 0.128458 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.00000 | 0.0468807 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.5346 | 0.679898 | 0.339949 | − | 0.940444i | \(-0.389590\pi\) | ||||
0.339949 | + | 0.940444i | \(0.389590\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.96880 | 0.231924 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.79318 | −0.0835169 | −0.0417584 | − | 0.999128i | \(-0.513296\pi\) | ||||
−0.0417584 | + | 0.999128i | \(0.513296\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.0041 | 1.06909 | 0.534545 | − | 0.845140i | \(-0.320483\pi\) | ||||
0.534545 | + | 0.845140i | \(0.320483\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.00467 | 0.278460 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.47090 | −0.253163 | −0.126582 | − | 0.991956i | \(-0.540401\pi\) | ||||
−0.126582 | + | 0.991956i | \(0.540401\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.430138 | −0.0198619 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 23.2799 | 1.07268 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.80208 | 0.174820 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.90570 | 0.179206 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.34016 | 0.0613615 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.6818 | 0.853593 | 0.426797 | − | 0.904348i | \(-0.359642\pi\) | ||||
0.426797 | + | 0.904348i | \(0.359642\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.56622 | 0.299394 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.31170 | −0.0596844 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.5090 | 0.749637 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.4431 | −0.518537 | −0.259268 | − | 0.965805i | \(-0.583481\pi\) | ||||
−0.259268 | + | 0.965805i | \(0.583481\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −19.4778 | −0.880818 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.869608 | −0.0392449 | −0.0196224 | − | 0.999807i | \(-0.506246\pi\) | ||||
−0.0196224 | + | 0.999807i | \(0.506246\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.282106 | −0.0127054 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.22207 | 0.0549279 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.6569 | 0.612594 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.15395 | 0.409787 | 0.204894 | − | 0.978784i | \(-0.434315\pi\) | ||||
0.204894 | + | 0.978784i | \(0.434315\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −27.5023 | −1.22871 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.5504 | 0.737945 | 0.368973 | − | 0.929440i | \(-0.379710\pi\) | ||||
0.368973 | + | 0.929440i | \(0.379710\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −19.3210 | −0.859775 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.34415 | 0.0596958 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.6176 | −0.559264 | −0.279632 | − | 0.960107i | \(-0.590212\pi\) | ||||
−0.279632 | + | 0.960107i | \(0.590212\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.49971 | −0.376005 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −22.0140 | −0.971942 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.40541 | 0.194126 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.24679 | 0.230754 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.27059 | 0.143563 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.87748 | 0.345119 | 0.172559 | − | 0.984999i | \(-0.444796\pi\) | ||||
0.172559 | + | 0.984999i | \(0.444796\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.6735 | 1.21008 | 0.605039 | − | 0.796196i | \(-0.293158\pi\) | ||||
0.605039 | + | 0.796196i | \(0.293158\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.34415 | −0.0586635 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.93816 | 0.171549 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.0477 | −0.958596 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.29018 | −0.0993851 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.5044 | 0.541625 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.36237 | −0.318303 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.03268 | 0.0877167 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.02414 | 0.0441130 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −43.7891 | −1.88264 | −0.941320 | − | 0.337517i | \(-0.890413\pi\) | ||||
−0.941320 | + | 0.337517i | \(0.890413\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −22.6976 | −0.974049 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.1225 | −0.604942 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.72178 | 0.159132 | 0.0795658 | − | 0.996830i | \(-0.474647\pi\) | ||||
0.0795658 | + | 0.996830i | \(0.474647\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.83986 | 0.419955 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.24985 | 0.0532456 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.3912 | −0.611975 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.82599 | −0.374642 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.9510 | 0.802980 | 0.401490 | − | 0.915863i | \(-0.368492\pi\) | ||||
0.401490 | + | 0.915863i | \(0.368492\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.71244 | 0.157020 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.21356 | −0.0512365 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −37.9774 | −1.60056 | −0.800279 | − | 0.599628i | \(-0.795315\pi\) | ||||
−0.800279 | + | 0.599628i | \(0.795315\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.7366 | −0.451692 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.99636 | 0.167831 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.2545 | 0.555658 | 0.277829 | − | 0.960630i | \(-0.410385\pi\) | ||||
0.277829 | + | 0.960630i | \(0.410385\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.8390 | −1.33242 | −0.666210 | − | 0.745765i | \(-0.732084\pi\) | ||||
−0.666210 | + | 0.745765i | \(0.732084\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.7678 | −0.491606 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.975857 | 0.0406960 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 43.1418 | 1.79602 | 0.898008 | − | 0.439980i | \(-0.145014\pi\) | ||||
0.898008 | + | 0.439980i | \(0.145014\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.62967 | 0.109285 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.7459 | −0.694738 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.15022 | −0.0476373 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.19326 | 0.0493352 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 32.5350 | 1.34286 | 0.671431 | − | 0.741067i | \(-0.265680\pi\) | ||||
0.671431 | + | 0.741067i | \(0.265680\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.4478 | −0.718923 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.3324 | −0.589556 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.27333 | 0.175484 | 0.0877422 | − | 0.996143i | \(-0.472035\pi\) | ||||
0.0877422 | + | 0.996143i | \(0.472035\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.881560 | −0.0361404 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 24.3086 | 0.994885 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.3964 | 0.792517 | 0.396258 | − | 0.918139i | \(-0.370308\pi\) | ||||
0.396258 | + | 0.918139i | \(0.370308\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.73717 | −0.0708607 | −0.0354303 | − | 0.999372i | \(-0.511280\pi\) | ||||
−0.0354303 | + | 0.999372i | \(0.511280\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.513266 | −0.0209018 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.95113 | 0.404571 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.3197 | −0.662395 | −0.331197 | − | 0.943562i | \(-0.607453\pi\) | ||||
−0.331197 | + | 0.943562i | \(0.607453\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.430138 | −0.0174301 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.12311 | 0.207259 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.47376 | −0.261473 | −0.130736 | − | 0.991417i | \(-0.541734\pi\) | ||||
−0.130736 | + | 0.991417i | \(0.541734\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −16.8078 | −0.677754 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.7823 | 1.15873 | 0.579365 | − | 0.815068i | \(-0.303301\pi\) | ||||
0.579365 | + | 0.815068i | \(0.303301\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 34.6713 | 1.39356 | 0.696779 | − | 0.717286i | \(-0.254616\pi\) | ||||
0.696779 | + | 0.717286i | \(0.254616\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.50029 | −0.220719 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.55630 | 0.0623520 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.37660 | 0.214721 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.78852 | −0.230803 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −44.9767 | −1.79050 | −0.895248 | − | 0.445569i | \(-0.853002\pi\) | ||||
−0.895248 | + | 0.445569i | \(0.853002\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 30.6675 | 1.21892 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.6470 | −0.581247 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | 0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 16.2962 | 0.644667 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.0228 | 0.553866 | 0.276933 | − | 0.960889i | \(-0.410682\pi\) | ||||
0.276933 | + | 0.960889i | \(0.410682\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.79957 | −0.228713 | −0.114356 | − | 0.993440i | \(-0.536481\pi\) | ||||
−0.114356 | + | 0.993440i | \(0.536481\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.99009 | −0.196484 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.2205 | 0.912891 | 0.456445 | − | 0.889751i | \(-0.349122\pi\) | ||||
0.456445 | + | 0.889751i | \(0.349122\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.96560 | 0.0771565 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.00467 | 0.235341 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.50904 | −0.254718 | −0.127359 | − | 0.991857i | \(-0.540650\pi\) | ||||
−0.127359 | + | 0.991857i | \(0.540650\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.12311 | −0.356469 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.1424 | −0.395691 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.825988 | −0.0321759 | −0.0160880 | − | 0.999871i | \(-0.505121\pi\) | ||||
−0.0160880 | + | 0.999871i | \(0.505121\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.6071 | −1.19048 | −0.595238 | − | 0.803549i | \(-0.702942\pi\) | ||||
−0.595238 | + | 0.803549i | \(0.702942\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.18495 | −0.0460196 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.90570 | 0.151457 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.312281 | 0.0120916 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −34.3886 | −1.32954 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.44530 | −0.326027 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.0887 | −0.967098 | −0.483549 | − | 0.875317i | \(-0.660653\pi\) | ||||
−0.483549 | + | 0.875317i | \(0.660653\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.63637 | −0.216944 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −38.5111 | −1.48010 | −0.740051 | − | 0.672551i | \(-0.765198\pi\) | ||||
−0.740051 | + | 0.672551i | \(0.765198\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.5090 | 0.633559 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 34.3013 | 1.31443 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.10066 | 0.271699 | 0.135850 | − | 0.990729i | \(-0.456624\pi\) | ||||
0.135850 | + | 0.990729i | \(0.456624\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.63171 | −0.0623443 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −26.2399 | −1.00112 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.12311 | −0.0427869 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.3103 | −0.544391 | −0.272195 | − | 0.962242i | \(-0.587750\pi\) | ||||
−0.272195 | + | 0.962242i | \(0.587750\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.22207 | 0.0464225 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.23630 | −0.274488 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.0234 | −0.417540 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 14.4441 | 0.546327 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.62690 | 0.325833 | 0.162917 | − | 0.986640i | \(-0.447910\pi\) | ||||
0.162917 | + | 0.986640i | \(0.447910\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.6457 | 0.967246 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.88623 | −0.259350 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −19.3210 | −0.726642 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −40.2993 | −1.51347 | −0.756736 | − | 0.653721i | \(-0.773207\pi\) | ||||
−0.756736 | + | 0.653721i | \(0.773207\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −17.1724 | −0.644016 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.35940 | −0.163261 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.02414 | −0.0383008 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11.2919 | 0.421703 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.61348 | −0.134760 | −0.0673801 | − | 0.997727i | \(-0.521464\pi\) | ||||
−0.0673801 | + | 0.997727i | \(0.521464\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.40541 | 0.164066 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.23743 | −0.306353 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.320007 | 0.0118848 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.5031 | 0.649155 | 0.324577 | − | 0.945859i | \(-0.394778\pi\) | ||||
0.324577 | + | 0.945859i | \(0.394778\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.4971 | 1.01841 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.27274 | −0.121047 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.0198 | −0.443963 | −0.221981 | − | 0.975051i | \(-0.571252\pi\) | ||||
−0.221981 | + | 0.975051i | \(0.571252\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.34415 | −0.0495797 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.440523 | 0.0162269 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.58398 | −0.278981 | −0.139491 | − | 0.990223i | \(-0.544546\pi\) | ||||
−0.139491 | + | 0.990223i | \(0.544546\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.24985 | 0.192858 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29.9552 | 1.09895 | 0.549475 | − | 0.835510i | \(-0.314828\pi\) | ||||
0.549475 | + | 0.835510i | \(0.314828\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.12311 | −0.0411474 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −19.9822 | −0.731111 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.36237 | −0.269015 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.1995 | 0.372186 | 0.186093 | − | 0.982532i | \(-0.440417\pi\) | ||||
0.186093 | + | 0.982532i | \(0.440417\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −36.7095 | −1.33777 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.03406 | −0.0740269 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33.0452 | −1.20105 | −0.600524 | − | 0.799607i | \(-0.705041\pi\) | ||||
−0.600524 | + | 0.799607i | \(0.705041\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.34337 | 0.0487611 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.3460 | 0.592540 | 0.296270 | − | 0.955104i | \(-0.404257\pi\) | ||||
0.296270 | + | 0.955104i | \(0.404257\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.1225 | −0.511270 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.05193 | −0.0380326 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.91926 | 0.0693005 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.4991 | −1.13589 | −0.567944 | − | 0.823067i | \(-0.692261\pi\) | ||||
−0.567944 | + | 0.823067i | \(0.692261\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 39.8077 | 1.43364 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.42489 | 0.338990 | 0.169495 | − | 0.985531i | \(-0.445786\pi\) | ||||
0.169495 | + | 0.985531i | \(0.445786\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.46726 | −0.160469 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.82599 | −0.316631 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 48.8384 | 1.74982 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.9866 | −0.500480 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.80368 | −0.0644583 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −17.3194 | −0.618157 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.3137 | 0.545876 | 0.272938 | − | 0.962032i | \(-0.412005\pi\) | ||||
0.272938 | + | 0.962032i | \(0.412005\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 31.3502 | 1.11610 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.7366 | −0.381749 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.24621 | −0.292832 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.50962 | 0.0535408 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30.8323 | 1.09213 | 0.546067 | − | 0.837741i | \(-0.316124\pi\) | ||||
0.546067 | + | 0.837741i | \(0.316124\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.51633 | −0.159776 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.85707 | 0.0656165 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.70492 | 0.307190 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.975857 | 0.0343944 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 17.5745 | 0.618653 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 34.0530 | 1.19724 | 0.598619 | − | 0.801034i | \(-0.295716\pi\) | ||||
0.598619 | + | 0.801034i | \(0.295716\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.1128 | −1.33832 | −0.669162 | − | 0.743117i | \(-0.733347\pi\) | ||||
−0.669162 | + | 0.743117i | \(0.733347\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −24.8696 | −0.872215 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14.4908 | 0.507591 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.4997 | 0.507281 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.19326 | 0.0416958 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.9828 | −0.522903 | −0.261452 | − | 0.965217i | \(-0.584201\pi\) | ||||
−0.261452 | + | 0.965217i | \(0.584201\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −29.1799 | −1.01715 | −0.508574 | − | 0.861018i | \(-0.669827\pi\) | ||||
−0.508574 | + | 0.861018i | \(0.669827\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.37660 | 0.0479272 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17.1926 | −0.597844 | −0.298922 | − | 0.954278i | \(-0.596627\pi\) | ||||
−0.298922 | + | 0.954278i | \(0.596627\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.1085 | −0.663667 | −0.331833 | − | 0.943338i | \(-0.607667\pi\) | ||||
−0.331833 | + | 0.943338i | \(0.607667\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −24.7001 | −0.856838 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.881560 | −0.0305443 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20.4608 | 0.708074 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 25.1791 | 0.870318 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −35.7960 | −1.23582 | −0.617908 | − | 0.786251i | \(-0.712020\pi\) | ||||
−0.617908 | + | 0.786251i | \(0.712020\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8976 | −0.996469 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −38.7910 | −1.33603 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.95113 | 0.341925 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 26.8925 | 0.922948 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.40769 | 0.219653 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.97883 | −0.273190 | −0.136595 | − | 0.990627i | \(-0.543616\pi\) | ||||
−0.136595 | + | 0.990627i | \(0.543616\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.66052 | 0.159386 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.1791 | −0.450190 | −0.225095 | − | 0.974337i | \(-0.572269\pi\) | ||||
−0.225095 | + | 0.974337i | \(0.572269\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −41.0040 | −1.39904 | −0.699519 | − | 0.714614i | \(-0.746602\pi\) | ||||
−0.699519 | + | 0.714614i | \(0.746602\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −16.8078 | −0.572807 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −14.3609 | −0.488849 | −0.244425 | − | 0.969668i | \(-0.578599\pi\) | ||||
−0.244425 | + | 0.969668i | \(0.578599\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.43320 | −0.0827312 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −21.8060 | −0.740569 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.7386 | 0.499974 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.430138 | 0.0145747 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 19.6996 | 0.666729 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.7678 | 1.00519 | 0.502593 | − | 0.864523i | \(-0.332379\pi\) | ||||
0.502593 | + | 0.864523i | \(0.332379\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −21.3242 | −0.719249 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −45.3973 | −1.52947 | −0.764737 | − | 0.644342i | \(-0.777131\pi\) | ||||
−0.764737 | + | 0.644342i | \(0.777131\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.57942 | 0.120457 | 0.0602286 | − | 0.998185i | \(-0.480817\pi\) | ||||
0.0602286 | + | 0.998185i | \(0.480817\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.57978 | −0.0867182 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 58.7606 | 1.97299 | 0.986494 | − | 0.163799i | \(-0.0523749\pi\) | ||||
0.986494 | + | 0.163799i | \(0.0523749\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.6470 | −0.491243 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.09284 | −0.137115 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 20.0093 | 0.669587 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.51224 | −0.0505487 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.31170 | 0.0437963 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.42956 | −0.0476783 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.990085 | 0.0329845 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.99009 | −0.166060 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 16.8862 | 0.561317 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.00373 | 0.265760 | 0.132880 | − | 0.991132i | \(-0.457578\pi\) | ||||
0.132880 | + | 0.991132i | \(0.457578\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −23.0550 | −0.764686 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.0484 | −0.531707 | −0.265854 | − | 0.964013i | \(-0.585654\pi\) | ||||
−0.265854 | + | 0.964013i | \(0.585654\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.1502 | 0.567589 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11.0842 | 0.366431 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.12311 | −0.301271 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.6416 | 0.614930 | 0.307465 | − | 0.951559i | \(-0.400519\pi\) | ||||
0.307465 | + | 0.951559i | \(0.400519\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.65926 | 0.252381 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.6569 | −0.449521 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.56622 | 0.215896 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.25680 | 0.172656 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.6882 | 0.645948 | 0.322974 | − | 0.946408i | \(-0.395317\pi\) | ||||
0.322974 | + | 0.946408i | \(0.395317\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.90570 | 0.128004 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 43.6873 | 1.43026 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.902844 | 0.0295262 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48.8909 | 1.59720 | 0.798598 | − | 0.601865i | \(-0.205575\pi\) | ||||
0.798598 | + | 0.601865i | \(0.205575\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.49825 | 0.146795 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −36.7870 | −1.19922 | −0.599612 | − | 0.800291i | \(-0.704678\pi\) | ||||
−0.599612 | + | 0.800291i | \(0.704678\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.2025 | 0.397367 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.63637 | −0.183351 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −45.3232 | −1.47281 | −0.736403 | − | 0.676543i | \(-0.763477\pi\) | ||||
−0.736403 | + | 0.676543i | \(0.763477\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.49971 | 0.275912 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −41.2907 | −1.33894 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −28.5184 | −0.923801 | −0.461900 | − | 0.886932i | \(-0.652832\pi\) | ||||
−0.461900 | + | 0.886932i | \(0.652832\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.75481 | 0.283299 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.440523 | 0.0142401 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.63171 | −0.0526905 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.0436 | −0.356246 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.78522 | −0.283100 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.95638 | −0.0629781 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.0837 | −0.356428 | −0.178214 | − | 0.983992i | \(-0.557032\pi\) | ||||
−0.178214 | + | 0.983992i | \(0.557032\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.62806 | −0.148675 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 50.5926 | 1.62359 | 0.811797 | − | 0.583940i | \(-0.198490\pi\) | ||||
0.811797 | + | 0.583940i | \(0.198490\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.23630 | −0.231985 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.34415 | 0.0430473 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.36261 | 0.299536 | 0.149768 | − | 0.988721i | \(-0.452147\pi\) | ||||
0.149768 | + | 0.988721i | \(0.452147\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.59388 | −0.0509406 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.8518 | −0.538037 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −36.5853 | −1.16689 | −0.583445 | − | 0.812152i | \(-0.698296\pi\) | ||||
−0.583445 | + | 0.812152i | \(0.698296\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.6628 | 0.339745 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.88623 | −0.219191 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.62281 | 0.115199 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.908676 | −0.0288650 | −0.0144325 | − | 0.999896i | \(-0.504594\pi\) | ||||
−0.0144325 | + | 0.999896i | \(0.504594\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 23.1491 | 0.734613 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18.0847 | −0.573325 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.638561 | 0.0202234 | 0.0101117 | − | 0.999949i | \(-0.496781\pi\) | ||||
0.0101117 | + | 0.999949i | \(0.496781\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −37.0097 | −1.17093 |
(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 | 3640.2.a.x.1.3 | ✓ | 4 | |
4.3 | odd | 2 | 7280.2.a.br.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3640.2.a.x.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial | |
7280.2.a.br.1.2 | 4 | 4.3 | odd | 2 |