Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4275,2,Mod(1,4275)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4275, 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("4275.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4275 = 3^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4275.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: | \(34.1360468641\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 475) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.24698\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4275.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.246980 | 0.174641 | 0.0873205 | − | 0.996180i | \(-0.472170\pi\) | ||||
0.0873205 | + | 0.996180i | \(0.472170\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.93900 | −0.969501 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.69202 | 0.639524 | 0.319762 | − | 0.947498i | \(-0.396397\pi\) | ||||
0.319762 | + | 0.947498i | \(0.396397\pi\) | |||||||
\(8\) | −0.972853 | −0.343955 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.911854 | 0.274934 | 0.137467 | − | 0.990506i | \(-0.456104\pi\) | ||||
0.137467 | + | 0.990506i | \(0.456104\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.55496 | 0.431268 | 0.215634 | − | 0.976474i | \(-0.430818\pi\) | ||||
0.215634 | + | 0.976474i | \(0.430818\pi\) | |||||||
\(14\) | 0.417895 | 0.111687 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.63773 | 0.909432 | ||||||||
\(17\) | −5.29590 | −1.28444 | −0.642222 | − | 0.766519i | \(-0.721987\pi\) | ||||
−0.642222 | + | 0.766519i | \(0.721987\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.225209 | 0.0480148 | ||||||||
\(23\) | −4.24698 | −0.885556 | −0.442778 | − | 0.896631i | \(-0.646007\pi\) | ||||
−0.442778 | + | 0.896631i | \(0.646007\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.384043 | 0.0753170 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.28083 | −0.620019 | ||||||||
\(29\) | −5.00969 | −0.930276 | −0.465138 | − | 0.885238i | \(-0.653995\pi\) | ||||
−0.465138 | + | 0.885238i | \(0.653995\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.82908 | 0.328513 | 0.164257 | − | 0.986418i | \(-0.447477\pi\) | ||||
0.164257 | + | 0.986418i | \(0.447477\pi\) | |||||||
\(32\) | 2.84415 | 0.502779 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.30798 | −0.224316 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.29590 | 1.03504 | 0.517520 | − | 0.855671i | \(-0.326855\pi\) | ||||
0.517520 | + | 0.855671i | \(0.326855\pi\) | |||||||
\(38\) | −0.246980 | −0.0400654 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.18060 | −0.652901 | −0.326450 | − | 0.945214i | \(-0.605853\pi\) | ||||
−0.326450 | + | 0.945214i | \(0.605853\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.31767 | 1.11593 | 0.557967 | − | 0.829863i | \(-0.311582\pi\) | ||||
0.557967 | + | 0.829863i | \(0.311582\pi\) | |||||||
\(44\) | −1.76809 | −0.266549 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.04892 | −0.154654 | ||||||||
\(47\) | 2.04892 | 0.298865 | 0.149433 | − | 0.988772i | \(-0.452255\pi\) | ||||
0.149433 | + | 0.988772i | \(0.452255\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.13706 | −0.591009 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.01507 | −0.418114 | ||||||||
\(53\) | 2.70171 | 0.371108 | 0.185554 | − | 0.982634i | \(-0.440592\pi\) | ||||
0.185554 | + | 0.982634i | \(0.440592\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.64609 | −0.219968 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.23729 | −0.162464 | ||||||||
\(59\) | −9.87800 | −1.28601 | −0.643003 | − | 0.765864i | \(-0.722312\pi\) | ||||
−0.643003 | + | 0.765864i | \(0.722312\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.542877 | 0.0695082 | 0.0347541 | − | 0.999396i | \(-0.488935\pi\) | ||||
0.0347541 | + | 0.999396i | \(0.488935\pi\) | |||||||
\(62\) | 0.451747 | 0.0573719 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.57301 | −0.821626 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.9976 | −1.71008 | −0.855040 | − | 0.518562i | \(-0.826467\pi\) | ||||
−0.855040 | + | 0.518562i | \(0.826467\pi\) | |||||||
\(68\) | 10.2687 | 1.24527 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.8780 | 1.52834 | 0.764169 | − | 0.645016i | \(-0.223149\pi\) | ||||
0.764169 | + | 0.645016i | \(0.223149\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.80731 | −0.328571 | −0.164286 | − | 0.986413i | \(-0.552532\pi\) | ||||
−0.164286 | + | 0.986413i | \(0.552532\pi\) | |||||||
\(74\) | 1.55496 | 0.180760 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.93900 | 0.222419 | ||||||||
\(77\) | 1.54288 | 0.175827 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.59419 | 0.179360 | 0.0896800 | − | 0.995971i | \(-0.471416\pi\) | ||||
0.0896800 | + | 0.995971i | \(0.471416\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.03252 | −0.114023 | ||||||||
\(83\) | −12.2349 | −1.34295 | −0.671477 | − | 0.741025i | \(-0.734340\pi\) | ||||
−0.671477 | + | 0.741025i | \(0.734340\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.80731 | 0.194888 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.887100 | −0.0945652 | ||||||||
\(89\) | −2.91723 | −0.309226 | −0.154613 | − | 0.987975i | \(-0.549413\pi\) | ||||
−0.154613 | + | 0.987975i | \(0.549413\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.63102 | 0.275806 | ||||||||
\(92\) | 8.23490 | 0.858547 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.506041 | 0.0521941 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.55496 | 0.157882 | 0.0789410 | − | 0.996879i | \(-0.474846\pi\) | ||||
0.0789410 | + | 0.996879i | \(0.474846\pi\) | |||||||
\(98\) | −1.02177 | −0.103214 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.6015 | 1.65191 | 0.825955 | − | 0.563737i | \(-0.190637\pi\) | ||||
0.825955 | + | 0.563737i | \(0.190637\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.84548 | −0.477439 | −0.238720 | − | 0.971089i | \(-0.576728\pi\) | ||||
−0.238720 | + | 0.971089i | \(0.576728\pi\) | |||||||
\(104\) | −1.51275 | −0.148337 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.667267 | 0.0648107 | ||||||||
\(107\) | 4.46681 | 0.431823 | 0.215912 | − | 0.976413i | \(-0.430728\pi\) | ||||
0.215912 | + | 0.976413i | \(0.430728\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.8267 | 1.80327 | 0.901635 | − | 0.432498i | \(-0.142368\pi\) | ||||
0.901635 | + | 0.432498i | \(0.142368\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 6.15511 | 0.581603 | ||||||||
\(113\) | −20.0368 | −1.88491 | −0.942453 | − | 0.334337i | \(-0.891488\pi\) | ||||
−0.942453 | + | 0.334337i | \(0.891488\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 9.71379 | 0.901903 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.43967 | −0.224589 | ||||||||
\(119\) | −8.96077 | −0.821433 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.1685 | −0.924411 | ||||||||
\(122\) | 0.134079 | 0.0121390 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.54660 | −0.318494 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.8702 | −1.58573 | −0.792863 | − | 0.609399i | \(-0.791411\pi\) | ||||
−0.792863 | + | 0.609399i | \(0.791411\pi\) | |||||||
\(128\) | −7.31170 | −0.646269 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.44265 | −0.650267 | −0.325134 | − | 0.945668i | \(-0.605409\pi\) | ||||
−0.325134 | + | 0.945668i | \(0.605409\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.69202 | −0.146717 | ||||||||
\(134\) | −3.45712 | −0.298650 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.15213 | 0.441791 | ||||||||
\(137\) | −5.68664 | −0.485843 | −0.242921 | − | 0.970046i | \(-0.578106\pi\) | ||||
−0.242921 | + | 0.970046i | \(0.578106\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.61596 | 0.306701 | 0.153351 | − | 0.988172i | \(-0.450994\pi\) | ||||
0.153351 | + | 0.988172i | \(0.450994\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.18060 | 0.266910 | ||||||||
\(143\) | 1.41789 | 0.118570 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.693349 | −0.0573820 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −12.2078 | −1.00347 | ||||||||
\(149\) | −3.29052 | −0.269570 | −0.134785 | − | 0.990875i | \(-0.543034\pi\) | ||||
−0.134785 | + | 0.990875i | \(0.543034\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.2131 | −0.831133 | −0.415566 | − | 0.909563i | \(-0.636417\pi\) | ||||
−0.415566 | + | 0.909563i | \(0.636417\pi\) | |||||||
\(152\) | 0.972853 | 0.0789088 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.381059 | 0.0307066 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.3448 | 1.14484 | 0.572420 | − | 0.819960i | \(-0.306005\pi\) | ||||
0.572420 | + | 0.819960i | \(0.306005\pi\) | |||||||
\(158\) | 0.393732 | 0.0313236 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.18598 | −0.566335 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.5308 | −1.52977 | −0.764885 | − | 0.644167i | \(-0.777204\pi\) | ||||
−0.764885 | + | 0.644167i | \(0.777204\pi\) | |||||||
\(164\) | 8.10620 | 0.632988 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.02177 | −0.234535 | ||||||||
\(167\) | −11.8823 | −0.919481 | −0.459741 | − | 0.888053i | \(-0.652058\pi\) | ||||
−0.459741 | + | 0.888053i | \(0.652058\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.5821 | −0.814008 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −14.1890 | −1.08190 | ||||||||
\(173\) | −15.4722 | −1.17633 | −0.588164 | − | 0.808741i | \(-0.700149\pi\) | ||||
−0.588164 | + | 0.808741i | \(0.700149\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.31708 | 0.250034 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.720497 | −0.0540035 | ||||||||
\(179\) | −2.16421 | −0.161761 | −0.0808803 | − | 0.996724i | \(-0.525773\pi\) | ||||
−0.0808803 | + | 0.996724i | \(0.525773\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.8974 | 1.25597 | 0.627986 | − | 0.778225i | \(-0.283879\pi\) | ||||
0.627986 | + | 0.778225i | \(0.283879\pi\) | |||||||
\(182\) | 0.649809 | 0.0481670 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.13169 | 0.304592 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.82908 | −0.353138 | ||||||||
\(188\) | −3.97285 | −0.289750 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.92394 | −0.428641 | −0.214320 | − | 0.976763i | \(-0.568754\pi\) | ||||
−0.214320 | + | 0.976763i | \(0.568754\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.43535 | −0.319264 | −0.159632 | − | 0.987177i | \(-0.551031\pi\) | ||||
−0.159632 | + | 0.987177i | \(0.551031\pi\) | |||||||
\(194\) | 0.384043 | 0.0275727 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.02177 | 0.572984 | ||||||||
\(197\) | −16.4722 | −1.17359 | −0.586797 | − | 0.809734i | \(-0.699612\pi\) | ||||
−0.586797 | + | 0.809734i | \(0.699612\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.4131 | −1.73060 | −0.865300 | − | 0.501255i | \(-0.832872\pi\) | ||||
−0.865300 | + | 0.501255i | \(0.832872\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.10023 | 0.288491 | ||||||||
\(203\) | −8.47650 | −0.594934 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.19673 | −0.0833804 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.65651 | 0.392209 | ||||||||
\(209\) | −0.911854 | −0.0630743 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.34050 | −0.298813 | −0.149406 | − | 0.988776i | \(-0.547736\pi\) | ||||
−0.149406 | + | 0.988776i | \(0.547736\pi\) | |||||||
\(212\) | −5.23862 | −0.359790 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.10321 | 0.0754140 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.09485 | 0.210092 | ||||||||
\(218\) | 4.64981 | 0.314925 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.23490 | −0.553939 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.2379 | 1.75702 | 0.878509 | − | 0.477725i | \(-0.158539\pi\) | ||||
0.878509 | + | 0.477725i | \(0.158539\pi\) | |||||||
\(224\) | 4.81236 | 0.321540 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.94869 | −0.329182 | ||||||||
\(227\) | −14.6853 | −0.974699 | −0.487349 | − | 0.873207i | \(-0.662036\pi\) | ||||
−0.487349 | + | 0.873207i | \(0.662036\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.6407 | −1.43006 | −0.715029 | − | 0.699095i | \(-0.753587\pi\) | ||||
−0.715029 | + | 0.699095i | \(0.753587\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.87369 | 0.319973 | ||||||||
\(233\) | −27.1183 | −1.77658 | −0.888289 | − | 0.459286i | \(-0.848105\pi\) | ||||
−0.888289 | + | 0.459286i | \(0.848105\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 19.1535 | 1.24678 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.21313 | −0.143456 | ||||||||
\(239\) | 11.5308 | 0.745865 | 0.372933 | − | 0.927858i | \(-0.378352\pi\) | ||||
0.372933 | + | 0.927858i | \(0.378352\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.8194 | 0.761354 | 0.380677 | − | 0.924708i | \(-0.375691\pi\) | ||||
0.380677 | + | 0.924708i | \(0.375691\pi\) | |||||||
\(242\) | −2.51142 | −0.161440 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.05264 | −0.0673883 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.55496 | −0.0989396 | ||||||||
\(248\) | −1.77943 | −0.112994 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.66487 | 0.610041 | 0.305021 | − | 0.952346i | \(-0.401337\pi\) | ||||
0.305021 | + | 0.952346i | \(0.401337\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.87263 | −0.243470 | ||||||||
\(254\) | −4.41358 | −0.276933 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 11.3402 | 0.708761 | ||||||||
\(257\) | −14.1860 | −0.884897 | −0.442449 | − | 0.896794i | \(-0.645890\pi\) | ||||
−0.442449 | + | 0.896794i | \(0.645890\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.6528 | 0.661932 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.83818 | −0.113563 | ||||||||
\(263\) | 21.7942 | 1.34389 | 0.671943 | − | 0.740603i | \(-0.265460\pi\) | ||||
0.671943 | + | 0.740603i | \(0.265460\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.417895 | −0.0256228 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 27.1414 | 1.65792 | ||||||||
\(269\) | 24.7265 | 1.50760 | 0.753800 | − | 0.657104i | \(-0.228219\pi\) | ||||
0.753800 | + | 0.657104i | \(0.228219\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.2295 | −0.803636 | −0.401818 | − | 0.915720i | \(-0.631622\pi\) | ||||
−0.401818 | + | 0.915720i | \(0.631622\pi\) | |||||||
\(272\) | −19.2650 | −1.16811 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.40449 | −0.0848481 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.560335 | −0.0336673 | −0.0168336 | − | 0.999858i | \(-0.505359\pi\) | ||||
−0.0168336 | + | 0.999858i | \(0.505359\pi\) | |||||||
\(278\) | 0.893068 | 0.0535626 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −27.6039 | −1.64671 | −0.823355 | − | 0.567527i | \(-0.807900\pi\) | ||||
−0.823355 | + | 0.567527i | \(0.807900\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.9608 | −0.948769 | −0.474385 | − | 0.880318i | \(-0.657329\pi\) | ||||
−0.474385 | + | 0.880318i | \(0.657329\pi\) | |||||||
\(284\) | −24.9705 | −1.48172 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.350191 | 0.0207072 | ||||||||
\(287\) | −7.07367 | −0.417546 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.0465 | 0.649796 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.44339 | 0.318550 | ||||||||
\(293\) | −25.3327 | −1.47995 | −0.739977 | − | 0.672632i | \(-0.765164\pi\) | ||||
−0.739977 | + | 0.672632i | \(0.765164\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.12498 | −0.356007 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.812691 | −0.0470779 | ||||||||
\(299\) | −6.60388 | −0.381912 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.3817 | 0.713666 | ||||||||
\(302\) | −2.52243 | −0.145150 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.63773 | −0.208638 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.5574 | −0.659613 | −0.329806 | − | 0.944049i | \(-0.606983\pi\) | ||||
−0.329806 | + | 0.944049i | \(0.606983\pi\) | |||||||
\(308\) | −2.99164 | −0.170464 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.3424 | 1.04010 | 0.520052 | − | 0.854135i | \(-0.325913\pi\) | ||||
0.520052 | + | 0.854135i | \(0.325913\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.9119 | −1.06896 | −0.534481 | − | 0.845181i | \(-0.679493\pi\) | ||||
−0.534481 | + | 0.845181i | \(0.679493\pi\) | |||||||
\(314\) | 3.54288 | 0.199936 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.09113 | −0.173890 | ||||||||
\(317\) | −20.2784 | −1.13895 | −0.569475 | − | 0.822008i | \(-0.692854\pi\) | ||||
−0.569475 | + | 0.822008i | \(0.692854\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.56810 | −0.255765 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.77479 | −0.0989052 | ||||||||
\(323\) | 5.29590 | 0.294672 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.82371 | −0.267160 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.06711 | 0.224569 | ||||||||
\(329\) | 3.46681 | 0.191132 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.77479 | −0.262446 | −0.131223 | − | 0.991353i | \(-0.541890\pi\) | ||||
−0.131223 | + | 0.991353i | \(0.541890\pi\) | |||||||
\(332\) | 23.7235 | 1.30200 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.93469 | −0.160579 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.3967 | 1.32897 | 0.664487 | − | 0.747300i | \(-0.268650\pi\) | ||||
0.664487 | + | 0.747300i | \(0.268650\pi\) | |||||||
\(338\) | −2.61356 | −0.142159 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.66786 | 0.0903196 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.8442 | −1.01749 | ||||||||
\(344\) | −7.11901 | −0.383832 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.82132 | −0.205435 | ||||||||
\(347\) | 9.99761 | 0.536700 | 0.268350 | − | 0.963322i | \(-0.413522\pi\) | ||||
0.268350 | + | 0.963322i | \(0.413522\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.9584 | 1.17541 | 0.587703 | − | 0.809077i | \(-0.300033\pi\) | ||||
0.587703 | + | 0.809077i | \(0.300033\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.59345 | 0.138231 | ||||||||
\(353\) | 36.8786 | 1.96285 | 0.981425 | − | 0.191848i | \(-0.0614479\pi\) | ||||
0.981425 | + | 0.191848i | \(0.0614479\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.65651 | 0.299795 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.534516 | −0.0282500 | ||||||||
\(359\) | −16.5187 | −0.871824 | −0.435912 | − | 0.899989i | \(-0.643574\pi\) | ||||
−0.435912 | + | 0.899989i | \(0.643574\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 4.17331 | 0.219344 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.10156 | −0.267394 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.83148 | −0.356600 | −0.178300 | − | 0.983976i | \(-0.557060\pi\) | ||||
−0.178300 | + | 0.983976i | \(0.557060\pi\) | |||||||
\(368\) | −15.4494 | −0.805353 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.57135 | 0.237333 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.76271 | −0.246604 | −0.123302 | − | 0.992369i | \(-0.539348\pi\) | ||||
−0.123302 | + | 0.992369i | \(0.539348\pi\) | |||||||
\(374\) | −1.19269 | −0.0616723 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.99330 | −0.102796 | ||||||||
\(377\) | −7.78986 | −0.401198 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.3773 | 0.738514 | 0.369257 | − | 0.929327i | \(-0.379612\pi\) | ||||
0.369257 | + | 0.929327i | \(0.379612\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.46309 | −0.0748583 | ||||||||
\(383\) | 30.6708 | 1.56721 | 0.783603 | − | 0.621261i | \(-0.213379\pi\) | ||||
0.783603 | + | 0.621261i | \(0.213379\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.09544 | −0.0557565 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.01507 | −0.153067 | ||||||||
\(389\) | 12.9215 | 0.655148 | 0.327574 | − | 0.944825i | \(-0.393769\pi\) | ||||
0.327574 | + | 0.944825i | \(0.393769\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 22.4916 | 1.13745 | ||||||||
\(392\) | 4.02475 | 0.203281 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.06829 | −0.204958 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.8471 | −1.49798 | −0.748992 | − | 0.662579i | \(-0.769462\pi\) | ||||
−0.748992 | + | 0.662579i | \(0.769462\pi\) | |||||||
\(398\) | −6.02954 | −0.302234 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 28.7101 | 1.43371 | 0.716856 | − | 0.697221i | \(-0.245580\pi\) | ||||
0.716856 | + | 0.697221i | \(0.245580\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.84415 | 0.141677 | ||||||||
\(404\) | −32.1903 | −1.60153 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.09352 | −0.103900 | ||||||||
\(407\) | 5.74094 | 0.284568 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.6203 | −0.673479 | −0.336739 | − | 0.941598i | \(-0.609324\pi\) | ||||
−0.336739 | + | 0.941598i | \(0.609324\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9.39539 | 0.462878 | ||||||||
\(413\) | −16.7138 | −0.822432 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.42253 | 0.216833 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.225209 | −0.0110153 | ||||||||
\(419\) | 2.13946 | 0.104519 | 0.0522596 | − | 0.998634i | \(-0.483358\pi\) | ||||
0.0522596 | + | 0.998634i | \(0.483358\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.0562 | −0.733795 | −0.366897 | − | 0.930261i | \(-0.619580\pi\) | ||||
−0.366897 | + | 0.930261i | \(0.619580\pi\) | |||||||
\(422\) | −1.07202 | −0.0521849 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.62837 | −0.127645 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.918559 | 0.0444522 | ||||||||
\(428\) | −8.66115 | −0.418653 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.37435 | −0.210705 | −0.105353 | − | 0.994435i | \(-0.533597\pi\) | ||||
−0.105353 | + | 0.994435i | \(0.533597\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −33.1564 | −1.59340 | −0.796698 | − | 0.604377i | \(-0.793422\pi\) | ||||
−0.796698 | + | 0.604377i | \(0.793422\pi\) | |||||||
\(434\) | 0.764365 | 0.0366907 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −36.5050 | −1.74827 | ||||||||
\(437\) | 4.24698 | 0.203161 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.2368 | 1.53858 | 0.769290 | − | 0.638900i | \(-0.220610\pi\) | ||||
0.769290 | + | 0.638900i | \(0.220610\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.03385 | −0.0967405 | ||||||||
\(443\) | −21.7362 | −1.03272 | −0.516358 | − | 0.856373i | \(-0.672713\pi\) | ||||
−0.516358 | + | 0.856373i | \(0.672713\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 6.48022 | 0.306847 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −11.1217 | −0.525450 | ||||||||
\(449\) | 24.9584 | 1.17786 | 0.588929 | − | 0.808185i | \(-0.299550\pi\) | ||||
0.588929 | + | 0.808185i | \(0.299550\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.81210 | −0.179505 | ||||||||
\(452\) | 38.8514 | 1.82742 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.62697 | −0.170222 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.1347 | 0.614414 | 0.307207 | − | 0.951643i | \(-0.400606\pi\) | ||||
0.307207 | + | 0.951643i | \(0.400606\pi\) | |||||||
\(458\) | −5.34481 | −0.249747 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 35.3726 | 1.64746 | 0.823732 | − | 0.566979i | \(-0.191888\pi\) | ||||
0.823732 | + | 0.566979i | \(0.191888\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.6963 | 0.682997 | 0.341498 | − | 0.939882i | \(-0.389066\pi\) | ||||
0.341498 | + | 0.939882i | \(0.389066\pi\) | |||||||
\(464\) | −18.2239 | −0.846022 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.69766 | −0.310263 | ||||||||
\(467\) | 33.2121 | 1.53687 | 0.768435 | − | 0.639927i | \(-0.221036\pi\) | ||||
0.768435 | + | 0.639927i | \(0.221036\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −23.6843 | −1.09364 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 9.60984 | 0.442329 | ||||||||
\(473\) | 6.67264 | 0.306809 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 17.3749 | 0.796379 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.84787 | 0.130259 | ||||||||
\(479\) | −24.6219 | −1.12500 | −0.562502 | − | 0.826796i | \(-0.690161\pi\) | ||||
−0.562502 | + | 0.826796i | \(0.690161\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.78986 | 0.446379 | ||||||||
\(482\) | 2.91915 | 0.132964 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 19.7168 | 0.896217 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −29.5646 | −1.33970 | −0.669851 | − | 0.742496i | \(-0.733642\pi\) | ||||
−0.669851 | + | 0.742496i | \(0.733642\pi\) | |||||||
\(488\) | −0.528139 | −0.0239077 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −36.2978 | −1.63810 | −0.819049 | − | 0.573724i | \(-0.805498\pi\) | ||||
−0.819049 | + | 0.573724i | \(0.805498\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 26.5308 | 1.19489 | ||||||||
\(494\) | −0.384043 | −0.0172789 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.65371 | 0.298760 | ||||||||
\(497\) | 21.7899 | 0.977409 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.84415 | 0.351152 | 0.175576 | − | 0.984466i | \(-0.443821\pi\) | ||||
0.175576 | + | 0.984466i | \(0.443821\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.38703 | 0.106538 | ||||||||
\(503\) | 20.4166 | 0.910330 | 0.455165 | − | 0.890407i | \(-0.349580\pi\) | ||||
0.455165 | + | 0.890407i | \(0.349580\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.956459 | −0.0425198 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 34.6504 | 1.53736 | ||||||||
\(509\) | 14.7530 | 0.653916 | 0.326958 | − | 0.945039i | \(-0.393976\pi\) | ||||
0.326958 | + | 0.945039i | \(0.393976\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.75004 | −0.210129 | ||||||||
\(512\) | 17.4242 | 0.770048 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.50365 | −0.154539 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.86831 | 0.0821683 | ||||||||
\(518\) | 2.63102 | 0.115600 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −37.1487 | −1.62751 | −0.813756 | − | 0.581206i | \(-0.802581\pi\) | ||||
−0.813756 | + | 0.581206i | \(0.802581\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.3623 | −0.715472 | −0.357736 | − | 0.933823i | \(-0.616451\pi\) | ||||
−0.357736 | + | 0.933823i | \(0.616451\pi\) | |||||||
\(524\) | 14.4313 | 0.630434 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.38271 | 0.234698 | ||||||||
\(527\) | −9.68664 | −0.421957 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.96316 | −0.215790 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.28083 | 0.142242 | ||||||||
\(533\) | −6.50066 | −0.281575 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 13.6176 | 0.588191 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.10693 | 0.263289 | ||||||||
\(539\) | −3.77240 | −0.162489 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.08947 | −0.0898335 | −0.0449168 | − | 0.998991i | \(-0.514302\pi\) | ||||
−0.0449168 | + | 0.998991i | \(0.514302\pi\) | |||||||
\(542\) | −3.26742 | −0.140348 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −15.0623 | −0.645792 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.86054 | −0.0795511 | −0.0397756 | − | 0.999209i | \(-0.512664\pi\) | ||||
−0.0397756 | + | 0.999209i | \(0.512664\pi\) | |||||||
\(548\) | 11.0264 | 0.471025 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.00969 | 0.213420 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.69740 | 0.114705 | ||||||||
\(554\) | −0.138391 | −0.00587968 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.01134 | −0.297347 | ||||||||
\(557\) | −9.80061 | −0.415265 | −0.207633 | − | 0.978207i | \(-0.566576\pi\) | ||||
−0.207633 | + | 0.978207i | \(0.566576\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.3787 | 0.481266 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.81759 | −0.287583 | ||||||||
\(563\) | 38.0170 | 1.60222 | 0.801112 | − | 0.598514i | \(-0.204242\pi\) | ||||
0.801112 | + | 0.598514i | \(0.204242\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3.94198 | −0.165694 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.5284 | −0.525680 | ||||||||
\(569\) | 7.32975 | 0.307279 | 0.153640 | − | 0.988127i | \(-0.450901\pi\) | ||||
0.153640 | + | 0.988127i | \(0.450901\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 37.8775 | 1.58513 | 0.792563 | − | 0.609791i | \(-0.208746\pi\) | ||||
0.792563 | + | 0.609791i | \(0.208746\pi\) | |||||||
\(572\) | −2.74930 | −0.114954 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.74705 | −0.0729206 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.6993 | −1.19477 | −0.597384 | − | 0.801955i | \(-0.703793\pi\) | ||||
−0.597384 | + | 0.801955i | \(0.703793\pi\) | |||||||
\(578\) | 2.72827 | 0.113481 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −20.7017 | −0.858852 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.46357 | 0.102030 | ||||||||
\(584\) | 2.73110 | 0.113014 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.25667 | −0.258461 | ||||||||
\(587\) | 3.72348 | 0.153684 | 0.0768422 | − | 0.997043i | \(-0.475516\pi\) | ||||
0.0768422 | + | 0.997043i | \(0.475516\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.82908 | −0.0753661 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 22.9028 | 0.941297 | ||||||||
\(593\) | 27.7399 | 1.13914 | 0.569570 | − | 0.821943i | \(-0.307110\pi\) | ||||
0.569570 | + | 0.821943i | \(0.307110\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.38032 | 0.261348 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.63102 | −0.0666975 | ||||||||
\(599\) | 23.5579 | 0.962551 | 0.481276 | − | 0.876569i | \(-0.340174\pi\) | ||||
0.481276 | + | 0.876569i | \(0.340174\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.36898 | −0.300587 | −0.150293 | − | 0.988641i | \(-0.548022\pi\) | ||||
−0.150293 | + | 0.988641i | \(0.548022\pi\) | |||||||
\(602\) | 3.05802 | 0.124635 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 19.8033 | 0.805783 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.4198 | 1.15352 | 0.576762 | − | 0.816912i | \(-0.304316\pi\) | ||||
0.576762 | + | 0.816912i | \(0.304316\pi\) | |||||||
\(608\) | −2.84415 | −0.115346 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.18598 | 0.128891 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.48129 | 0.261777 | 0.130888 | − | 0.991397i | \(-0.458217\pi\) | ||||
0.130888 | + | 0.991397i | \(0.458217\pi\) | |||||||
\(614\) | −2.85443 | −0.115195 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.50099 | −0.0604767 | ||||||||
\(617\) | 24.4650 | 0.984924 | 0.492462 | − | 0.870334i | \(-0.336097\pi\) | ||||
0.492462 | + | 0.870334i | \(0.336097\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.2457 | −0.894128 | −0.447064 | − | 0.894502i | \(-0.647530\pi\) | ||||
−0.447064 | + | 0.894502i | \(0.647530\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.53020 | 0.181645 | ||||||||
\(623\) | −4.93602 | −0.197757 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −4.67084 | −0.186684 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −27.8146 | −1.10992 | ||||||||
\(629\) | −33.3424 | −1.32945 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.5888 | −0.620581 | −0.310290 | − | 0.950642i | \(-0.600426\pi\) | ||||
−0.310290 | + | 0.950642i | \(0.600426\pi\) | |||||||
\(632\) | −1.55091 | −0.0616919 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.00836 | −0.198907 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.43296 | −0.254883 | ||||||||
\(638\) | −1.12823 | −0.0446670 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.17496 | −0.322892 | −0.161446 | − | 0.986882i | \(-0.551616\pi\) | ||||
−0.161446 | + | 0.986882i | \(0.551616\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.1836 | 0.441038 | 0.220519 | − | 0.975383i | \(-0.429225\pi\) | ||||
0.220519 | + | 0.975383i | \(0.429225\pi\) | |||||||
\(644\) | 13.9336 | 0.549062 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.30798 | 0.0514617 | ||||||||
\(647\) | −16.2121 | −0.637362 | −0.318681 | − | 0.947862i | \(-0.603240\pi\) | ||||
−0.318681 | + | 0.947862i | \(0.603240\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.00730 | −0.353567 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 37.8702 | 1.48311 | ||||||||
\(653\) | −24.7952 | −0.970312 | −0.485156 | − | 0.874427i | \(-0.661237\pi\) | ||||
−0.485156 | + | 0.874427i | \(0.661237\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −15.2079 | −0.593769 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.856232 | 0.0333794 | ||||||||
\(659\) | 20.2868 | 0.790262 | 0.395131 | − | 0.918625i | \(-0.370699\pi\) | ||||
0.395131 | + | 0.918625i | \(0.370699\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.4222 | 0.794332 | 0.397166 | − | 0.917747i | \(-0.369994\pi\) | ||||
0.397166 | + | 0.917747i | \(0.369994\pi\) | |||||||
\(662\) | −1.17928 | −0.0458339 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 11.9028 | 0.461917 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.2760 | 0.823812 | ||||||||
\(668\) | 23.0398 | 0.891437 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.495024 | 0.0191102 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.7254 | 1.10728 | 0.553641 | − | 0.832755i | \(-0.313238\pi\) | ||||
0.553641 | + | 0.832755i | \(0.313238\pi\) | |||||||
\(674\) | 6.02549 | 0.232093 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 20.5187 | 0.789181 | ||||||||
\(677\) | −44.0062 | −1.69130 | −0.845648 | − | 0.533740i | \(-0.820786\pi\) | ||||
−0.845648 | + | 0.533740i | \(0.820786\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.63102 | 0.100969 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.411927 | 0.0157735 | ||||||||
\(683\) | −8.48427 | −0.324642 | −0.162321 | − | 0.986738i | \(-0.551898\pi\) | ||||
−0.162321 | + | 0.986738i | \(0.551898\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −4.65412 | −0.177695 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 26.6197 | 1.01487 | ||||||||
\(689\) | 4.20105 | 0.160047 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.2586 | 0.770673 | 0.385336 | − | 0.922776i | \(-0.374085\pi\) | ||||
0.385336 | + | 0.922776i | \(0.374085\pi\) | |||||||
\(692\) | 30.0006 | 1.14045 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.46921 | 0.0937297 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.1400 | 0.838614 | ||||||||
\(698\) | 5.42327 | 0.205274 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.4101 | 0.884188 | 0.442094 | − | 0.896969i | \(-0.354236\pi\) | ||||
0.442094 | + | 0.896969i | \(0.354236\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.29590 | −0.237454 | ||||||||
\(704\) | −5.99362 | −0.225893 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.10826 | 0.342794 | ||||||||
\(707\) | 28.0901 | 1.05644 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.3472 | 1.13971 | 0.569857 | − | 0.821744i | \(-0.306999\pi\) | ||||
0.569857 | + | 0.821744i | \(0.306999\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.83804 | 0.106360 | ||||||||
\(713\) | −7.76809 | −0.290917 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.19641 | 0.156827 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4.07979 | −0.152256 | ||||||||
\(719\) | 38.3230 | 1.42921 | 0.714604 | − | 0.699529i | \(-0.246607\pi\) | ||||
0.714604 | + | 0.699529i | \(0.246607\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.19865 | −0.305334 | ||||||||
\(722\) | 0.246980 | 0.00919163 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −32.7640 | −1.21767 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.69069 | 0.0997923 | 0.0498961 | − | 0.998754i | \(-0.484111\pi\) | ||||
0.0498961 | + | 0.998754i | \(0.484111\pi\) | |||||||
\(728\) | −2.55960 | −0.0948650 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −38.7536 | −1.43335 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.9651 | 0.700491 | 0.350246 | − | 0.936658i | \(-0.386098\pi\) | ||||
0.350246 | + | 0.936658i | \(0.386098\pi\) | |||||||
\(734\) | −1.68724 | −0.0622770 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −12.0790 | −0.445240 | ||||||||
\(737\) | −12.7638 | −0.470160 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29.8278 | 1.09723 | 0.548616 | − | 0.836075i | \(-0.315155\pi\) | ||||
0.548616 | + | 0.836075i | \(0.315155\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.12903 | 0.0414480 | ||||||||
\(743\) | −8.78448 | −0.322271 | −0.161136 | − | 0.986932i | \(-0.551516\pi\) | ||||
−0.161136 | + | 0.986932i | \(0.551516\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.17629 | −0.0430671 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 9.36360 | 0.342367 | ||||||||
\(749\) | 7.55794 | 0.276161 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.1142 | −0.660998 | −0.330499 | − | 0.943806i | \(-0.607217\pi\) | ||||
−0.330499 | + | 0.943806i | \(0.607217\pi\) | |||||||
\(752\) | 7.45340 | 0.271798 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.92394 | −0.0700656 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.222816 | −0.00809840 | −0.00404920 | − | 0.999992i | \(-0.501289\pi\) | ||||
−0.00404920 | + | 0.999992i | \(0.501289\pi\) | |||||||
\(758\) | 3.55091 | 0.128975 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.07798 | 0.220327 | 0.110163 | − | 0.993913i | \(-0.464863\pi\) | ||||
0.110163 | + | 0.993913i | \(0.464863\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 31.8552 | 1.15323 | ||||||||
\(764\) | 11.4865 | 0.415568 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.57507 | 0.273698 | ||||||||
\(767\) | −15.3599 | −0.554613 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.6267 | −0.527453 | −0.263726 | − | 0.964598i | \(-0.584952\pi\) | ||||
−0.263726 | + | 0.964598i | \(0.584952\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8.60015 | 0.309526 | ||||||||
\(773\) | 4.05728 | 0.145930 | 0.0729651 | − | 0.997334i | \(-0.476754\pi\) | ||||
0.0729651 | + | 0.997334i | \(0.476754\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.51275 | −0.0543044 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.19136 | 0.114416 | ||||||||
\(779\) | 4.18060 | 0.149786 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.7429 | 0.420192 | ||||||||
\(782\) | 5.55496 | 0.198645 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −15.0495 | −0.537482 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.5657 | 0.697442 | 0.348721 | − | 0.937227i | \(-0.386616\pi\) | ||||
0.348721 | + | 0.937227i | \(0.386616\pi\) | |||||||
\(788\) | 31.9396 | 1.13780 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −33.9028 | −1.20544 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.844150 | 0.0299767 | ||||||||
\(794\) | −7.37163 | −0.261609 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 47.3370 | 1.67782 | ||||||||
\(797\) | −38.9051 | −1.37809 | −0.689046 | − | 0.724718i | \(-0.741970\pi\) | ||||
−0.689046 | + | 0.724718i | \(0.741970\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.8509 | −0.383876 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7.09080 | 0.250385 | ||||||||
\(803\) | −2.55986 | −0.0903355 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.702447 | 0.0247426 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −16.1508 | −0.568183 | ||||||||
\(809\) | 22.5730 | 0.793625 | 0.396812 | − | 0.917900i | \(-0.370116\pi\) | ||||
0.396812 | + | 0.917900i | \(0.370116\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −46.3605 | −1.62794 | −0.813968 | − | 0.580909i | \(-0.802697\pi\) | ||||
−0.813968 | + | 0.580909i | \(0.802697\pi\) | |||||||
\(812\) | 16.4359 | 0.576789 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.41789 | 0.0496972 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.31767 | −0.256013 | ||||||||
\(818\) | −3.36393 | −0.117617 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.8194 | 0.621901 | 0.310951 | − | 0.950426i | \(-0.399353\pi\) | ||||
0.310951 | + | 0.950426i | \(0.399353\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32.5394 | −1.13425 | −0.567126 | − | 0.823631i | \(-0.691945\pi\) | ||||
−0.567126 | + | 0.823631i | \(0.691945\pi\) | |||||||
\(824\) | 4.71394 | 0.164218 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.12797 | −0.143630 | ||||||||
\(827\) | −39.8256 | −1.38487 | −0.692436 | − | 0.721479i | \(-0.743463\pi\) | ||||
−0.692436 | + | 0.721479i | \(0.743463\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.7525 | 1.34593 | 0.672966 | − | 0.739674i | \(-0.265020\pi\) | ||||
0.672966 | + | 0.739674i | \(0.265020\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −10.2208 | −0.354341 | ||||||||
\(833\) | 21.9095 | 0.759118 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.76809 | 0.0611505 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0.528402 | 0.0182533 | ||||||||
\(839\) | −2.76749 | −0.0955445 | −0.0477723 | − | 0.998858i | \(-0.515212\pi\) | ||||
−0.0477723 | + | 0.998858i | \(0.515212\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.90302 | −0.134587 | ||||||||
\(842\) | −3.71858 | −0.128151 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.41624 | 0.289699 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.2054 | −0.591183 | ||||||||
\(848\) | 9.82808 | 0.337498 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −26.7385 | −0.916586 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.1390 | 0.826503 | 0.413252 | − | 0.910617i | \(-0.364393\pi\) | ||||
0.413252 | + | 0.910617i | \(0.364393\pi\) | |||||||
\(854\) | 0.226865 | 0.00776317 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.34555 | −0.148528 | ||||||||
\(857\) | 3.16229 | 0.108022 | 0.0540109 | − | 0.998540i | \(-0.482799\pi\) | ||||
0.0540109 | + | 0.998540i | \(0.482799\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.86426 | 0.165967 | 0.0829833 | − | 0.996551i | \(-0.473555\pi\) | ||||
0.0829833 | + | 0.996551i | \(0.473555\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.08038 | −0.0367978 | ||||||||
\(863\) | −4.54958 | −0.154870 | −0.0774348 | − | 0.996997i | \(-0.524673\pi\) | ||||
−0.0774348 | + | 0.996997i | \(0.524673\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −8.18896 | −0.278272 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.00092 | −0.203684 | ||||||||
\(869\) | 1.45367 | 0.0493122 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.7657 | −0.737502 | ||||||||
\(872\) | −18.3156 | −0.620245 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.04892 | 0.0354802 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.6595 | −0.630086 | −0.315043 | − | 0.949077i | \(-0.602019\pi\) | ||||
−0.315043 | + | 0.949077i | \(0.602019\pi\) | |||||||
\(878\) | 7.96184 | 0.268699 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.4306 | −0.654632 | −0.327316 | − | 0.944915i | \(-0.606144\pi\) | ||||
−0.327316 | + | 0.944915i | \(0.606144\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.6437 | 0.862979 | 0.431490 | − | 0.902118i | \(-0.357988\pi\) | ||||
0.431490 | + | 0.902118i | \(0.357988\pi\) | |||||||
\(884\) | 15.9675 | 0.537044 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.36839 | −0.180354 | ||||||||
\(887\) | 31.0062 | 1.04109 | 0.520544 | − | 0.853835i | \(-0.325729\pi\) | ||||
0.520544 | + | 0.853835i | \(0.325729\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −30.2368 | −1.01411 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −50.8753 | −1.70343 | ||||||||
\(893\) | −2.04892 | −0.0685644 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −12.3716 | −0.413305 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.16421 | 0.205702 | ||||||||
\(899\) | −9.16315 | −0.305608 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.3080 | −0.476668 | ||||||||
\(902\) | −0.941511 | −0.0313489 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 19.4929 | 0.648324 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.7676 | −0.589964 | −0.294982 | − | 0.955503i | \(-0.595314\pi\) | ||||
−0.294982 | + | 0.955503i | \(0.595314\pi\) | |||||||
\(908\) | 28.4748 | 0.944971 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −41.7313 | −1.38262 | −0.691309 | − | 0.722559i | \(-0.742966\pi\) | ||||
−0.691309 | + | 0.722559i | \(0.742966\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.1564 | −0.369224 | ||||||||
\(914\) | 3.24400 | 0.107302 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 41.9614 | 1.38644 | ||||||||
\(917\) | −12.5931 | −0.415862 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.4088 | 1.00309 | 0.501547 | − | 0.865130i | \(-0.332764\pi\) | ||||
0.501547 | + | 0.865130i | \(0.332764\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8.73630 | 0.287715 | ||||||||
\(923\) | 20.0248 | 0.659123 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.62969 | 0.119279 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −14.2483 | −0.467724 | ||||||||
\(929\) | 28.8219 | 0.945616 | 0.472808 | − | 0.881165i | \(-0.343240\pi\) | ||||
0.472808 | + | 0.881165i | \(0.343240\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.13706 | 0.135587 | ||||||||
\(932\) | 52.5824 | 1.72239 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 8.20270 | 0.268401 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −50.4601 | −1.64846 | −0.824230 | − | 0.566255i | \(-0.808392\pi\) | ||||
−0.824230 | + | 0.566255i | \(0.808392\pi\) | |||||||
\(938\) | −5.84953 | −0.190994 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.10082 | −0.0358857 | −0.0179428 | − | 0.999839i | \(-0.505712\pi\) | ||||
−0.0179428 | + | 0.999839i | \(0.505712\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17.7549 | 0.578180 | ||||||||
\(944\) | −35.9335 | −1.16954 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.64801 | 0.0535813 | ||||||||
\(947\) | 13.9353 | 0.452836 | 0.226418 | − | 0.974030i | \(-0.427299\pi\) | ||||
0.226418 | + | 0.974030i | \(0.427299\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.36526 | −0.141702 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 8.71751 | 0.282536 | ||||||||
\(953\) | 41.3400 | 1.33913 | 0.669567 | − | 0.742751i | \(-0.266480\pi\) | ||||
0.669567 | + | 0.742751i | \(0.266480\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −22.3582 | −0.723117 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.08111 | −0.196472 | ||||||||
\(959\) | −9.62192 | −0.310708 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.6544 | −0.892079 | ||||||||
\(962\) | 2.41789 | 0.0779561 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −22.9178 | −0.738133 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.26875 | −0.169432 | −0.0847158 | − | 0.996405i | \(-0.526998\pi\) | ||||
−0.0847158 | + | 0.996405i | \(0.526998\pi\) | |||||||
\(968\) | 9.89248 | 0.317956 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.15346 | 0.165382 | 0.0826911 | − | 0.996575i | \(-0.473649\pi\) | ||||
0.0826911 | + | 0.996575i | \(0.473649\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.11828 | 0.196143 | ||||||||
\(974\) | −7.30186 | −0.233967 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.97484 | 0.0632130 | ||||||||
\(977\) | −4.77612 | −0.152802 | −0.0764008 | − | 0.997077i | \(-0.524343\pi\) | ||||
−0.0764008 | + | 0.997077i | \(0.524343\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.66009 | −0.0850168 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −8.96482 | −0.286079 | ||||||||
\(983\) | 28.9758 | 0.924186 | 0.462093 | − | 0.886832i | \(-0.347099\pi\) | ||||
0.462093 | + | 0.886832i | \(0.347099\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 6.55257 | 0.208676 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.01507 | 0.0959220 | ||||||||
\(989\) | −31.0780 | −0.988222 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38.5042 | −1.22313 | −0.611564 | − | 0.791195i | \(-0.709459\pi\) | ||||
−0.611564 | + | 0.791195i | \(0.709459\pi\) | |||||||
\(992\) | 5.20219 | 0.165170 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.38165 | 0.170696 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.1491 | 0.321427 | 0.160713 | − | 0.987001i | \(-0.448621\pi\) | ||||
0.160713 | + | 0.987001i | \(0.448621\pi\) | |||||||
\(998\) | 1.93735 | 0.0613256 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4275.2.a.z.1.3 | 3 | ||
3.2 | odd | 2 | 475.2.a.h.1.1 | yes | 3 | ||
5.4 | even | 2 | 4275.2.a.bn.1.1 | 3 | |||
12.11 | even | 2 | 7600.2.a.bn.1.3 | 3 | |||
15.2 | even | 4 | 475.2.b.c.324.3 | 6 | |||
15.8 | even | 4 | 475.2.b.c.324.4 | 6 | |||
15.14 | odd | 2 | 475.2.a.d.1.3 | ✓ | 3 | ||
57.56 | even | 2 | 9025.2.a.w.1.3 | 3 | |||
60.59 | even | 2 | 7600.2.a.bw.1.1 | 3 | |||
285.284 | even | 2 | 9025.2.a.be.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
475.2.a.d.1.3 | ✓ | 3 | 15.14 | odd | 2 | ||
475.2.a.h.1.1 | yes | 3 | 3.2 | odd | 2 | ||
475.2.b.c.324.3 | 6 | 15.2 | even | 4 | |||
475.2.b.c.324.4 | 6 | 15.8 | even | 4 | |||
4275.2.a.z.1.3 | 3 | 1.1 | even | 1 | trivial | ||
4275.2.a.bn.1.1 | 3 | 5.4 | even | 2 | |||
7600.2.a.bn.1.3 | 3 | 12.11 | even | 2 | |||
7600.2.a.bw.1.1 | 3 | 60.59 | even | 2 | |||
9025.2.a.w.1.3 | 3 | 57.56 | even | 2 | |||
9025.2.a.be.1.1 | 3 | 285.284 | even | 2 |