Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(1,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, 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("825.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.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: | \(6.58765816676\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.311108\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.21432 | 0.858654 | 0.429327 | − | 0.903149i | \(-0.358751\pi\) | ||||
0.429327 | + | 0.903149i | \(0.358751\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −0.525428 | −0.262714 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.21432 | 0.495744 | ||||||||
\(7\) | −4.90321 | −1.85324 | −0.926620 | − | 0.375999i | \(-0.877300\pi\) | ||||
−0.926620 | + | 0.375999i | \(0.877300\pi\) | |||||||
\(8\) | −3.06668 | −1.08423 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −0.525428 | −0.151678 | ||||||||
\(13\) | −4.14764 | −1.15035 | −0.575175 | − | 0.818031i | \(-0.695066\pi\) | ||||
−0.575175 | + | 0.818031i | \(0.695066\pi\) | |||||||
\(14\) | −5.95407 | −1.59129 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.67307 | −0.668268 | ||||||||
\(17\) | 5.33185 | 1.29316 | 0.646582 | − | 0.762845i | \(-0.276198\pi\) | ||||
0.646582 | + | 0.762845i | \(0.276198\pi\) | |||||||
\(18\) | 1.21432 | 0.286218 | ||||||||
\(19\) | −5.18421 | −1.18934 | −0.594669 | − | 0.803970i | \(-0.702717\pi\) | ||||
−0.594669 | + | 0.803970i | \(0.702717\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.90321 | −1.06997 | ||||||||
\(22\) | −1.21432 | −0.258894 | ||||||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | −3.06668 | −0.625983 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.03657 | −0.987752 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.57628 | 0.486872 | ||||||||
\(29\) | 1.80642 | 0.335444 | 0.167722 | − | 0.985834i | \(-0.446359\pi\) | ||||
0.167722 | + | 0.985834i | \(0.446359\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.62222 | 0.470964 | 0.235482 | − | 0.971879i | \(-0.424333\pi\) | ||||
0.235482 | + | 0.971879i | \(0.424333\pi\) | |||||||
\(32\) | 2.88739 | 0.510423 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 6.47457 | 1.11038 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.525428 | −0.0875713 | ||||||||
\(37\) | −5.80642 | −0.954570 | −0.477285 | − | 0.878749i | \(-0.658379\pi\) | ||||
−0.477285 | + | 0.878749i | \(0.658379\pi\) | |||||||
\(38\) | −6.29529 | −1.02123 | ||||||||
\(39\) | −4.14764 | −0.664154 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.80642 | 0.282116 | 0.141058 | − | 0.990001i | \(-0.454950\pi\) | ||||
0.141058 | + | 0.990001i | \(0.454950\pi\) | |||||||
\(42\) | −5.95407 | −0.918732 | ||||||||
\(43\) | −4.90321 | −0.747733 | −0.373866 | − | 0.927483i | \(-0.621968\pi\) | ||||
−0.373866 | + | 0.927483i | \(0.621968\pi\) | |||||||
\(44\) | 0.525428 | 0.0792112 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.85728 | −0.716167 | ||||||||
\(47\) | −7.05086 | −1.02847 | −0.514236 | − | 0.857648i | \(-0.671925\pi\) | ||||
−0.514236 | + | 0.857648i | \(0.671925\pi\) | |||||||
\(48\) | −2.67307 | −0.385825 | ||||||||
\(49\) | 17.0415 | 2.43450 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.33185 | 0.746609 | ||||||||
\(52\) | 2.17929 | 0.302213 | ||||||||
\(53\) | 7.18421 | 0.986827 | 0.493413 | − | 0.869795i | \(-0.335749\pi\) | ||||
0.493413 | + | 0.869795i | \(0.335749\pi\) | |||||||
\(54\) | 1.21432 | 0.165248 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 15.0366 | 2.00935 | ||||||||
\(57\) | −5.18421 | −0.686665 | ||||||||
\(58\) | 2.19358 | 0.288031 | ||||||||
\(59\) | 1.67307 | 0.217815 | 0.108908 | − | 0.994052i | \(-0.465265\pi\) | ||||
0.108908 | + | 0.994052i | \(0.465265\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.755569 | 0.0967407 | 0.0483703 | − | 0.998829i | \(-0.484597\pi\) | ||||
0.0483703 | + | 0.998829i | \(0.484597\pi\) | |||||||
\(62\) | 3.18421 | 0.404395 | ||||||||
\(63\) | −4.90321 | −0.617747 | ||||||||
\(64\) | 8.85236 | 1.10654 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.21432 | −0.149472 | ||||||||
\(67\) | 4.85728 | 0.593411 | 0.296706 | − | 0.954969i | \(-0.404112\pi\) | ||||
0.296706 | + | 0.954969i | \(0.404112\pi\) | |||||||
\(68\) | −2.80150 | −0.339732 | ||||||||
\(69\) | −4.00000 | −0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.428639 | 0.0508701 | 0.0254351 | − | 0.999676i | \(-0.491903\pi\) | ||||
0.0254351 | + | 0.999676i | \(0.491903\pi\) | |||||||
\(72\) | −3.06668 | −0.361411 | ||||||||
\(73\) | −12.7096 | −1.48755 | −0.743775 | − | 0.668430i | \(-0.766967\pi\) | ||||
−0.743775 | + | 0.668430i | \(0.766967\pi\) | |||||||
\(74\) | −7.05086 | −0.819645 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.72393 | 0.312456 | ||||||||
\(77\) | 4.90321 | 0.558773 | ||||||||
\(78\) | −5.03657 | −0.570279 | ||||||||
\(79\) | −6.42864 | −0.723278 | −0.361639 | − | 0.932318i | \(-0.617783\pi\) | ||||
−0.361639 | + | 0.932318i | \(0.617783\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.19358 | 0.242240 | ||||||||
\(83\) | 2.90321 | 0.318669 | 0.159334 | − | 0.987225i | \(-0.449065\pi\) | ||||
0.159334 | + | 0.987225i | \(0.449065\pi\) | |||||||
\(84\) | 2.57628 | 0.281095 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.95407 | −0.642044 | ||||||||
\(87\) | 1.80642 | 0.193669 | ||||||||
\(88\) | 3.06668 | 0.326909 | ||||||||
\(89\) | 0.622216 | 0.0659547 | 0.0329774 | − | 0.999456i | \(-0.489501\pi\) | ||||
0.0329774 | + | 0.999456i | \(0.489501\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 20.3368 | 2.13187 | ||||||||
\(92\) | 2.10171 | 0.219118 | ||||||||
\(93\) | 2.62222 | 0.271911 | ||||||||
\(94\) | −8.56199 | −0.883102 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.88739 | 0.294693 | ||||||||
\(97\) | 2.75557 | 0.279786 | 0.139893 | − | 0.990167i | \(-0.455324\pi\) | ||||
0.139893 | + | 0.990167i | \(0.455324\pi\) | |||||||
\(98\) | 20.6938 | 2.09039 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.8064 | −1.77181 | −0.885903 | − | 0.463871i | \(-0.846460\pi\) | ||||
−0.885903 | + | 0.463871i | \(0.846460\pi\) | |||||||
\(102\) | 6.47457 | 0.641078 | ||||||||
\(103\) | −4.94914 | −0.487654 | −0.243827 | − | 0.969819i | \(-0.578403\pi\) | ||||
−0.243827 | + | 0.969819i | \(0.578403\pi\) | |||||||
\(104\) | 12.7195 | 1.24725 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.72393 | 0.847343 | ||||||||
\(107\) | −11.1985 | −1.08260 | −0.541300 | − | 0.840830i | \(-0.682068\pi\) | ||||
−0.541300 | + | 0.840830i | \(0.682068\pi\) | |||||||
\(108\) | −0.525428 | −0.0505593 | ||||||||
\(109\) | 15.7146 | 1.50518 | 0.752591 | − | 0.658488i | \(-0.228804\pi\) | ||||
0.752591 | + | 0.658488i | \(0.228804\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.80642 | −0.551121 | ||||||||
\(112\) | 13.1066 | 1.23846 | ||||||||
\(113\) | 1.76494 | 0.166031 | 0.0830156 | − | 0.996548i | \(-0.473545\pi\) | ||||
0.0830156 | + | 0.996548i | \(0.473545\pi\) | |||||||
\(114\) | −6.29529 | −0.589608 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.949145 | −0.0881259 | ||||||||
\(117\) | −4.14764 | −0.383450 | ||||||||
\(118\) | 2.03164 | 0.187028 | ||||||||
\(119\) | −26.1432 | −2.39654 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0.917502 | 0.0830667 | ||||||||
\(123\) | 1.80642 | 0.162880 | ||||||||
\(124\) | −1.37778 | −0.123729 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −5.95407 | −0.530430 | ||||||||
\(127\) | −18.7096 | −1.66021 | −0.830106 | − | 0.557606i | \(-0.811720\pi\) | ||||
−0.830106 | + | 0.557606i | \(0.811720\pi\) | |||||||
\(128\) | 4.97481 | 0.439715 | ||||||||
\(129\) | −4.90321 | −0.431704 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.24443 | −0.108726 | −0.0543632 | − | 0.998521i | \(-0.517313\pi\) | ||||
−0.0543632 | + | 0.998521i | \(0.517313\pi\) | |||||||
\(132\) | 0.525428 | 0.0457326 | ||||||||
\(133\) | 25.4193 | 2.20413 | ||||||||
\(134\) | 5.89829 | 0.509535 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −16.3511 | −1.40209 | ||||||||
\(137\) | −18.7971 | −1.60594 | −0.802970 | − | 0.596019i | \(-0.796748\pi\) | ||||
−0.802970 | + | 0.596019i | \(0.796748\pi\) | |||||||
\(138\) | −4.85728 | −0.413479 | ||||||||
\(139\) | 14.0415 | 1.19098 | 0.595492 | − | 0.803361i | \(-0.296957\pi\) | ||||
0.595492 | + | 0.803361i | \(0.296957\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.05086 | −0.593789 | ||||||||
\(142\) | 0.520505 | 0.0436798 | ||||||||
\(143\) | 4.14764 | 0.346843 | ||||||||
\(144\) | −2.67307 | −0.222756 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −15.4336 | −1.27729 | ||||||||
\(147\) | 17.0415 | 1.40556 | ||||||||
\(148\) | 3.05086 | 0.250779 | ||||||||
\(149\) | −3.05086 | −0.249936 | −0.124968 | − | 0.992161i | \(-0.539883\pi\) | ||||
−0.124968 | + | 0.992161i | \(0.539883\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.326929 | −0.0266051 | −0.0133026 | − | 0.999912i | \(-0.504234\pi\) | ||||
−0.0133026 | + | 0.999912i | \(0.504234\pi\) | |||||||
\(152\) | 15.8983 | 1.28952 | ||||||||
\(153\) | 5.33185 | 0.431055 | ||||||||
\(154\) | 5.95407 | 0.479792 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.17929 | 0.174483 | ||||||||
\(157\) | 19.9081 | 1.58884 | 0.794421 | − | 0.607367i | \(-0.207774\pi\) | ||||
0.794421 | + | 0.607367i | \(0.207774\pi\) | |||||||
\(158\) | −7.80642 | −0.621046 | ||||||||
\(159\) | 7.18421 | 0.569745 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 19.6128 | 1.54571 | ||||||||
\(162\) | 1.21432 | 0.0954060 | ||||||||
\(163\) | −12.1748 | −0.953607 | −0.476804 | − | 0.879010i | \(-0.658205\pi\) | ||||
−0.476804 | + | 0.879010i | \(0.658205\pi\) | |||||||
\(164\) | −0.949145 | −0.0741158 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.52543 | 0.273626 | ||||||||
\(167\) | −13.0049 | −1.00635 | −0.503176 | − | 0.864184i | \(-0.667835\pi\) | ||||
−0.503176 | + | 0.864184i | \(0.667835\pi\) | |||||||
\(168\) | 15.0366 | 1.16010 | ||||||||
\(169\) | 4.20294 | 0.323303 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.18421 | −0.396446 | ||||||||
\(172\) | 2.57628 | 0.196440 | ||||||||
\(173\) | −13.8938 | −1.05633 | −0.528165 | − | 0.849142i | \(-0.677120\pi\) | ||||
−0.528165 | + | 0.849142i | \(0.677120\pi\) | |||||||
\(174\) | 2.19358 | 0.166295 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.67307 | 0.201490 | ||||||||
\(177\) | 1.67307 | 0.125756 | ||||||||
\(178\) | 0.755569 | 0.0566323 | ||||||||
\(179\) | 12.8573 | 0.960998 | 0.480499 | − | 0.876995i | \(-0.340456\pi\) | ||||
0.480499 | + | 0.876995i | \(0.340456\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.917502 | 0.0681974 | 0.0340987 | − | 0.999418i | \(-0.489144\pi\) | ||||
0.0340987 | + | 0.999418i | \(0.489144\pi\) | |||||||
\(182\) | 24.6953 | 1.83054 | ||||||||
\(183\) | 0.755569 | 0.0558532 | ||||||||
\(184\) | 12.2667 | 0.904314 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.18421 | 0.233477 | ||||||||
\(187\) | −5.33185 | −0.389904 | ||||||||
\(188\) | 3.70471 | 0.270194 | ||||||||
\(189\) | −4.90321 | −0.356656 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.3684 | 1.03966 | 0.519831 | − | 0.854269i | \(-0.325995\pi\) | ||||
0.519831 | + | 0.854269i | \(0.325995\pi\) | |||||||
\(192\) | 8.85236 | 0.638864 | ||||||||
\(193\) | 11.7605 | 0.846539 | 0.423269 | − | 0.906004i | \(-0.360882\pi\) | ||||
0.423269 | + | 0.906004i | \(0.360882\pi\) | |||||||
\(194\) | 3.34614 | 0.240239 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.95407 | −0.639576 | ||||||||
\(197\) | 3.82071 | 0.272215 | 0.136107 | − | 0.990694i | \(-0.456541\pi\) | ||||
0.136107 | + | 0.990694i | \(0.456541\pi\) | |||||||
\(198\) | −1.21432 | −0.0862979 | ||||||||
\(199\) | −13.7146 | −0.972199 | −0.486100 | − | 0.873903i | \(-0.661581\pi\) | ||||
−0.486100 | + | 0.873903i | \(0.661581\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.85728 | 0.342606 | ||||||||
\(202\) | −21.6227 | −1.52137 | ||||||||
\(203\) | −8.85728 | −0.621659 | ||||||||
\(204\) | −2.80150 | −0.196144 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6.00984 | −0.418726 | ||||||||
\(207\) | −4.00000 | −0.278019 | ||||||||
\(208\) | 11.0869 | 0.768741 | ||||||||
\(209\) | 5.18421 | 0.358599 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.95851 | 0.134830 | 0.0674148 | − | 0.997725i | \(-0.478525\pi\) | ||||
0.0674148 | + | 0.997725i | \(0.478525\pi\) | |||||||
\(212\) | −3.77478 | −0.259253 | ||||||||
\(213\) | 0.428639 | 0.0293699 | ||||||||
\(214\) | −13.5986 | −0.929578 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.06668 | −0.208661 | ||||||||
\(217\) | −12.8573 | −0.872809 | ||||||||
\(218\) | 19.0825 | 1.29243 | ||||||||
\(219\) | −12.7096 | −0.858838 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −22.1146 | −1.48759 | ||||||||
\(222\) | −7.05086 | −0.473222 | ||||||||
\(223\) | 26.0098 | 1.74175 | 0.870874 | − | 0.491506i | \(-0.163554\pi\) | ||||
0.870874 | + | 0.491506i | \(0.163554\pi\) | |||||||
\(224\) | −14.1575 | −0.945937 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.14320 | 0.142563 | ||||||||
\(227\) | 6.34122 | 0.420882 | 0.210441 | − | 0.977607i | \(-0.432510\pi\) | ||||
0.210441 | + | 0.977607i | \(0.432510\pi\) | |||||||
\(228\) | 2.72393 | 0.180396 | ||||||||
\(229\) | −23.3274 | −1.54152 | −0.770759 | − | 0.637127i | \(-0.780123\pi\) | ||||
−0.770759 | + | 0.637127i | \(0.780123\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.90321 | 0.322608 | ||||||||
\(232\) | −5.53972 | −0.363700 | ||||||||
\(233\) | 1.42372 | 0.0932708 | 0.0466354 | − | 0.998912i | \(-0.485150\pi\) | ||||
0.0466354 | + | 0.998912i | \(0.485150\pi\) | |||||||
\(234\) | −5.03657 | −0.329251 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.879077 | −0.0572231 | ||||||||
\(237\) | −6.42864 | −0.417585 | ||||||||
\(238\) | −31.7462 | −2.05780 | ||||||||
\(239\) | −18.9590 | −1.22636 | −0.613178 | − | 0.789945i | \(-0.710109\pi\) | ||||
−0.613178 | + | 0.789945i | \(0.710109\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.34614 | −0.0867126 | −0.0433563 | − | 0.999060i | \(-0.513805\pi\) | ||||
−0.0433563 | + | 0.999060i | \(0.513805\pi\) | |||||||
\(242\) | 1.21432 | 0.0780594 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −0.396997 | −0.0254151 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.19358 | 0.139857 | ||||||||
\(247\) | 21.5022 | 1.36816 | ||||||||
\(248\) | −8.04149 | −0.510635 | ||||||||
\(249\) | 2.90321 | 0.183984 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.08250 | 0.0683267 | 0.0341633 | − | 0.999416i | \(-0.489123\pi\) | ||||
0.0341633 | + | 0.999416i | \(0.489123\pi\) | |||||||
\(252\) | 2.57628 | 0.162291 | ||||||||
\(253\) | 4.00000 | 0.251478 | ||||||||
\(254\) | −22.7195 | −1.42555 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.6637 | −0.728981 | ||||||||
\(257\) | 0.133353 | 0.00831834 | 0.00415917 | − | 0.999991i | \(-0.498676\pi\) | ||||
0.00415917 | + | 0.999991i | \(0.498676\pi\) | |||||||
\(258\) | −5.95407 | −0.370684 | ||||||||
\(259\) | 28.4701 | 1.76905 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.80642 | 0.111815 | ||||||||
\(262\) | −1.51114 | −0.0933584 | ||||||||
\(263\) | 0.147643 | 0.00910407 | 0.00455203 | − | 0.999990i | \(-0.498551\pi\) | ||||
0.00455203 | + | 0.999990i | \(0.498551\pi\) | |||||||
\(264\) | 3.06668 | 0.188741 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 30.8671 | 1.89258 | ||||||||
\(267\) | 0.622216 | 0.0380790 | ||||||||
\(268\) | −2.55215 | −0.155897 | ||||||||
\(269\) | −26.8573 | −1.63752 | −0.818759 | − | 0.574138i | \(-0.805337\pi\) | ||||
−0.818759 | + | 0.574138i | \(0.805337\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.08250 | 0.187248 | 0.0936242 | − | 0.995608i | \(-0.470155\pi\) | ||||
0.0936242 | + | 0.995608i | \(0.470155\pi\) | |||||||
\(272\) | −14.2524 | −0.864180 | ||||||||
\(273\) | 20.3368 | 1.23084 | ||||||||
\(274\) | −22.8256 | −1.37895 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.10171 | 0.126508 | ||||||||
\(277\) | 8.70964 | 0.523311 | 0.261656 | − | 0.965161i | \(-0.415732\pi\) | ||||
0.261656 | + | 0.965161i | \(0.415732\pi\) | |||||||
\(278\) | 17.0509 | 1.02264 | ||||||||
\(279\) | 2.62222 | 0.156988 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.3783 | −1.21567 | −0.607833 | − | 0.794065i | \(-0.707961\pi\) | ||||
−0.607833 | + | 0.794065i | \(0.707961\pi\) | |||||||
\(282\) | −8.56199 | −0.509859 | ||||||||
\(283\) | 6.32248 | 0.375833 | 0.187916 | − | 0.982185i | \(-0.439827\pi\) | ||||
0.187916 | + | 0.982185i | \(0.439827\pi\) | |||||||
\(284\) | −0.225219 | −0.0133643 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.03657 | 0.297818 | ||||||||
\(287\) | −8.85728 | −0.522829 | ||||||||
\(288\) | 2.88739 | 0.170141 | ||||||||
\(289\) | 11.4286 | 0.672273 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.75557 | 0.161534 | ||||||||
\(292\) | 6.67799 | 0.390800 | ||||||||
\(293\) | −16.6780 | −0.974339 | −0.487169 | − | 0.873308i | \(-0.661971\pi\) | ||||
−0.487169 | + | 0.873308i | \(0.661971\pi\) | |||||||
\(294\) | 20.6938 | 1.20689 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 17.8064 | 1.03498 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | −3.70471 | −0.214608 | ||||||||
\(299\) | 16.5906 | 0.959458 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.0415 | 1.38573 | ||||||||
\(302\) | −0.396997 | −0.0228446 | ||||||||
\(303\) | −17.8064 | −1.02295 | ||||||||
\(304\) | 13.8578 | 0.794797 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6.47457 | 0.370127 | ||||||||
\(307\) | 9.58565 | 0.547082 | 0.273541 | − | 0.961860i | \(-0.411805\pi\) | ||||
0.273541 | + | 0.961860i | \(0.411805\pi\) | |||||||
\(308\) | −2.57628 | −0.146797 | ||||||||
\(309\) | −4.94914 | −0.281547 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.5303 | 0.823941 | 0.411970 | − | 0.911197i | \(-0.364841\pi\) | ||||
0.411970 | + | 0.911197i | \(0.364841\pi\) | |||||||
\(312\) | 12.7195 | 0.720099 | ||||||||
\(313\) | 21.0321 | 1.18881 | 0.594403 | − | 0.804167i | \(-0.297388\pi\) | ||||
0.594403 | + | 0.804167i | \(0.297388\pi\) | |||||||
\(314\) | 24.1748 | 1.36427 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.37778 | 0.190015 | ||||||||
\(317\) | 0.990632 | 0.0556394 | 0.0278197 | − | 0.999613i | \(-0.491144\pi\) | ||||
0.0278197 | + | 0.999613i | \(0.491144\pi\) | |||||||
\(318\) | 8.72393 | 0.489213 | ||||||||
\(319\) | −1.80642 | −0.101140 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.1985 | −0.625039 | ||||||||
\(322\) | 23.8163 | 1.32723 | ||||||||
\(323\) | −27.6414 | −1.53801 | ||||||||
\(324\) | −0.525428 | −0.0291904 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −14.7841 | −0.818818 | ||||||||
\(327\) | 15.7146 | 0.869017 | ||||||||
\(328\) | −5.53972 | −0.305880 | ||||||||
\(329\) | 34.5718 | 1.90601 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.5812 | −0.966350 | −0.483175 | − | 0.875524i | \(-0.660517\pi\) | ||||
−0.483175 | + | 0.875524i | \(0.660517\pi\) | |||||||
\(332\) | −1.52543 | −0.0837187 | ||||||||
\(333\) | −5.80642 | −0.318190 | ||||||||
\(334\) | −15.7921 | −0.864107 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 13.1066 | 0.715025 | ||||||||
\(337\) | 3.16992 | 0.172676 | 0.0863382 | − | 0.996266i | \(-0.472483\pi\) | ||||
0.0863382 | + | 0.996266i | \(0.472483\pi\) | |||||||
\(338\) | 5.10372 | 0.277606 | ||||||||
\(339\) | 1.76494 | 0.0958582 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.62222 | −0.142001 | ||||||||
\(342\) | −6.29529 | −0.340410 | ||||||||
\(343\) | −49.2355 | −2.65847 | ||||||||
\(344\) | 15.0366 | 0.810717 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −16.8716 | −0.907021 | ||||||||
\(347\) | −4.97634 | −0.267144 | −0.133572 | − | 0.991039i | \(-0.542645\pi\) | ||||
−0.133572 | + | 0.991039i | \(0.542645\pi\) | |||||||
\(348\) | −0.949145 | −0.0508795 | ||||||||
\(349\) | 18.2034 | 0.974407 | 0.487203 | − | 0.873289i | \(-0.338017\pi\) | ||||
0.487203 | + | 0.873289i | \(0.338017\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.14764 | −0.221385 | ||||||||
\(352\) | −2.88739 | −0.153898 | ||||||||
\(353\) | −22.4099 | −1.19276 | −0.596379 | − | 0.802703i | \(-0.703395\pi\) | ||||
−0.596379 | + | 0.802703i | \(0.703395\pi\) | |||||||
\(354\) | 2.03164 | 0.107981 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.326929 | −0.0173272 | ||||||||
\(357\) | −26.1432 | −1.38364 | ||||||||
\(358\) | 15.6128 | 0.825165 | ||||||||
\(359\) | 21.3274 | 1.12562 | 0.562809 | − | 0.826587i | \(-0.309721\pi\) | ||||
0.562809 | + | 0.826587i | \(0.309721\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.87601 | 0.414527 | ||||||||
\(362\) | 1.11414 | 0.0585579 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | −10.6855 | −0.560072 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.917502 | 0.0479586 | ||||||||
\(367\) | −35.1338 | −1.83397 | −0.916985 | − | 0.398921i | \(-0.869385\pi\) | ||||
−0.916985 | + | 0.398921i | \(0.869385\pi\) | |||||||
\(368\) | 10.6923 | 0.557374 | ||||||||
\(369\) | 1.80642 | 0.0940387 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −35.2257 | −1.82883 | ||||||||
\(372\) | −1.37778 | −0.0714348 | ||||||||
\(373\) | 17.0049 | 0.880481 | 0.440241 | − | 0.897880i | \(-0.354893\pi\) | ||||
0.440241 | + | 0.897880i | \(0.354893\pi\) | |||||||
\(374\) | −6.47457 | −0.334792 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 21.6227 | 1.11511 | ||||||||
\(377\) | −7.49240 | −0.385878 | ||||||||
\(378\) | −5.95407 | −0.306244 | ||||||||
\(379\) | 2.36842 | 0.121657 | 0.0608287 | − | 0.998148i | \(-0.480626\pi\) | ||||
0.0608287 | + | 0.998148i | \(0.480626\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.7096 | −0.958524 | ||||||||
\(382\) | 17.4479 | 0.892710 | ||||||||
\(383\) | −1.21585 | −0.0621271 | −0.0310635 | − | 0.999517i | \(-0.509889\pi\) | ||||
−0.0310635 | + | 0.999517i | \(0.509889\pi\) | |||||||
\(384\) | 4.97481 | 0.253870 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14.2810 | 0.726884 | ||||||||
\(387\) | −4.90321 | −0.249244 | ||||||||
\(388\) | −1.44785 | −0.0735035 | ||||||||
\(389\) | 2.26671 | 0.114927 | 0.0574633 | − | 0.998348i | \(-0.481699\pi\) | ||||
0.0574633 | + | 0.998348i | \(0.481699\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.3274 | −1.07857 | ||||||||
\(392\) | −52.2607 | −2.63957 | ||||||||
\(393\) | −1.24443 | −0.0627733 | ||||||||
\(394\) | 4.63957 | 0.233738 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.525428 | 0.0264037 | ||||||||
\(397\) | 18.4889 | 0.927929 | 0.463965 | − | 0.885854i | \(-0.346426\pi\) | ||||
0.463965 | + | 0.885854i | \(0.346426\pi\) | |||||||
\(398\) | −16.6539 | −0.834782 | ||||||||
\(399\) | 25.4193 | 1.27256 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.5625 | 0.877028 | 0.438514 | − | 0.898724i | \(-0.355505\pi\) | ||||
0.438514 | + | 0.898724i | \(0.355505\pi\) | |||||||
\(402\) | 5.89829 | 0.294180 | ||||||||
\(403\) | −10.8760 | −0.541773 | ||||||||
\(404\) | 9.35599 | 0.465478 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.7556 | −0.533790 | ||||||||
\(407\) | 5.80642 | 0.287814 | ||||||||
\(408\) | −16.3511 | −0.809498 | ||||||||
\(409\) | −21.3461 | −1.05550 | −0.527749 | − | 0.849400i | \(-0.676964\pi\) | ||||
−0.527749 | + | 0.849400i | \(0.676964\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.7971 | −0.927190 | ||||||||
\(412\) | 2.60042 | 0.128113 | ||||||||
\(413\) | −8.20342 | −0.403664 | ||||||||
\(414\) | −4.85728 | −0.238722 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −11.9759 | −0.587165 | ||||||||
\(417\) | 14.0415 | 0.687615 | ||||||||
\(418\) | 6.29529 | 0.307913 | ||||||||
\(419\) | 28.8573 | 1.40977 | 0.704885 | − | 0.709321i | \(-0.250999\pi\) | ||||
0.704885 | + | 0.709321i | \(0.250999\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −35.4893 | −1.72964 | −0.864822 | − | 0.502078i | \(-0.832569\pi\) | ||||
−0.864822 | + | 0.502078i | \(0.832569\pi\) | |||||||
\(422\) | 2.37826 | 0.115772 | ||||||||
\(423\) | −7.05086 | −0.342824 | ||||||||
\(424\) | −22.0316 | −1.06995 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.520505 | 0.0252186 | ||||||||
\(427\) | −3.70471 | −0.179284 | ||||||||
\(428\) | 5.88400 | 0.284414 | ||||||||
\(429\) | 4.14764 | 0.200250 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.24443 | 0.445289 | 0.222644 | − | 0.974900i | \(-0.428531\pi\) | ||||
0.222644 | + | 0.974900i | \(0.428531\pi\) | |||||||
\(432\) | −2.67307 | −0.128608 | ||||||||
\(433\) | 6.28544 | 0.302059 | 0.151030 | − | 0.988529i | \(-0.451741\pi\) | ||||
0.151030 | + | 0.988529i | \(0.451741\pi\) | |||||||
\(434\) | −15.6128 | −0.749441 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.25686 | −0.395432 | ||||||||
\(437\) | 20.7368 | 0.991977 | ||||||||
\(438\) | −15.4336 | −0.737444 | ||||||||
\(439\) | −36.5303 | −1.74350 | −0.871749 | − | 0.489952i | \(-0.837014\pi\) | ||||
−0.871749 | + | 0.489952i | \(0.837014\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17.0415 | 0.811499 | ||||||||
\(442\) | −26.8542 | −1.27732 | ||||||||
\(443\) | 38.2766 | 1.81857 | 0.909287 | − | 0.416170i | \(-0.136628\pi\) | ||||
0.909287 | + | 0.416170i | \(0.136628\pi\) | |||||||
\(444\) | 3.05086 | 0.144787 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 31.5843 | 1.49556 | ||||||||
\(447\) | −3.05086 | −0.144300 | ||||||||
\(448\) | −43.4050 | −2.05069 | ||||||||
\(449\) | −31.8479 | −1.50300 | −0.751498 | − | 0.659735i | \(-0.770668\pi\) | ||||
−0.751498 | + | 0.659735i | \(0.770668\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.80642 | −0.0850612 | ||||||||
\(452\) | −0.927346 | −0.0436187 | ||||||||
\(453\) | −0.326929 | −0.0153605 | ||||||||
\(454\) | 7.70027 | 0.361391 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 15.8983 | 0.744506 | ||||||||
\(457\) | −1.39207 | −0.0651185 | −0.0325592 | − | 0.999470i | \(-0.510366\pi\) | ||||
−0.0325592 | + | 0.999470i | \(0.510366\pi\) | |||||||
\(458\) | −28.3269 | −1.32363 | ||||||||
\(459\) | 5.33185 | 0.248870 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.70471 | −0.358844 | −0.179422 | − | 0.983772i | \(-0.557423\pi\) | ||||
−0.179422 | + | 0.983772i | \(0.557423\pi\) | |||||||
\(462\) | 5.95407 | 0.277008 | ||||||||
\(463\) | −4.68244 | −0.217611 | −0.108806 | − | 0.994063i | \(-0.534703\pi\) | ||||
−0.108806 | + | 0.994063i | \(0.534703\pi\) | |||||||
\(464\) | −4.82870 | −0.224167 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.72885 | 0.0800873 | ||||||||
\(467\) | −12.8573 | −0.594964 | −0.297482 | − | 0.954727i | \(-0.596147\pi\) | ||||
−0.297482 | + | 0.954727i | \(0.596147\pi\) | |||||||
\(468\) | 2.17929 | 0.100738 | ||||||||
\(469\) | −23.8163 | −1.09973 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 19.9081 | 0.917318 | ||||||||
\(472\) | −5.13077 | −0.236163 | ||||||||
\(473\) | 4.90321 | 0.225450 | ||||||||
\(474\) | −7.80642 | −0.358561 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 13.7364 | 0.629605 | ||||||||
\(477\) | 7.18421 | 0.328942 | ||||||||
\(478\) | −23.0223 | −1.05301 | ||||||||
\(479\) | 8.38715 | 0.383219 | 0.191609 | − | 0.981471i | \(-0.438629\pi\) | ||||
0.191609 | + | 0.981471i | \(0.438629\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.0830 | 1.09809 | ||||||||
\(482\) | −1.63465 | −0.0744561 | ||||||||
\(483\) | 19.6128 | 0.892415 | ||||||||
\(484\) | −0.525428 | −0.0238831 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.21432 | 0.0550827 | ||||||||
\(487\) | −9.83500 | −0.445667 | −0.222833 | − | 0.974857i | \(-0.571531\pi\) | ||||
−0.222833 | + | 0.974857i | \(0.571531\pi\) | |||||||
\(488\) | −2.31708 | −0.104890 | ||||||||
\(489\) | −12.1748 | −0.550565 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −32.9403 | −1.48657 | −0.743286 | − | 0.668973i | \(-0.766734\pi\) | ||||
−0.743286 | + | 0.668973i | \(0.766734\pi\) | |||||||
\(492\) | −0.949145 | −0.0427908 | ||||||||
\(493\) | 9.63158 | 0.433785 | ||||||||
\(494\) | 26.1106 | 1.17477 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.00937 | −0.314730 | ||||||||
\(497\) | −2.10171 | −0.0942746 | ||||||||
\(498\) | 3.52543 | 0.157978 | ||||||||
\(499\) | −1.63158 | −0.0730397 | −0.0365199 | − | 0.999333i | \(-0.511627\pi\) | ||||
−0.0365199 | + | 0.999333i | \(0.511627\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.0049 | −0.581017 | ||||||||
\(502\) | 1.31450 | 0.0586689 | ||||||||
\(503\) | −41.8622 | −1.86654 | −0.933272 | − | 0.359171i | \(-0.883059\pi\) | ||||
−0.933272 | + | 0.359171i | \(0.883059\pi\) | |||||||
\(504\) | 15.0366 | 0.669782 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.85728 | 0.215932 | ||||||||
\(507\) | 4.20294 | 0.186659 | ||||||||
\(508\) | 9.83056 | 0.436160 | ||||||||
\(509\) | −38.8573 | −1.72232 | −0.861159 | − | 0.508335i | \(-0.830261\pi\) | ||||
−0.861159 | + | 0.508335i | \(0.830261\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 62.3180 | 2.75679 | ||||||||
\(512\) | −24.1131 | −1.06566 | ||||||||
\(513\) | −5.18421 | −0.228888 | ||||||||
\(514\) | 0.161933 | 0.00714257 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.57628 | 0.113415 | ||||||||
\(517\) | 7.05086 | 0.310096 | ||||||||
\(518\) | 34.5718 | 1.51900 | ||||||||
\(519\) | −13.8938 | −0.609872 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.1111 | 0.486785 | 0.243393 | − | 0.969928i | \(-0.421740\pi\) | ||||
0.243393 | + | 0.969928i | \(0.421740\pi\) | |||||||
\(522\) | 2.19358 | 0.0960102 | ||||||||
\(523\) | −27.3002 | −1.19375 | −0.596877 | − | 0.802332i | \(-0.703592\pi\) | ||||
−0.596877 | + | 0.802332i | \(0.703592\pi\) | |||||||
\(524\) | 0.653858 | 0.0285639 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.179286 | 0.00781724 | ||||||||
\(527\) | 13.9813 | 0.609033 | ||||||||
\(528\) | 2.67307 | 0.116330 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.67307 | 0.0726051 | ||||||||
\(532\) | −13.3560 | −0.579055 | ||||||||
\(533\) | −7.49240 | −0.324532 | ||||||||
\(534\) | 0.755569 | 0.0326967 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −14.8957 | −0.643396 | ||||||||
\(537\) | 12.8573 | 0.554833 | ||||||||
\(538\) | −32.6133 | −1.40606 | ||||||||
\(539\) | −17.0415 | −0.734029 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.1017 | −0.692267 | −0.346133 | − | 0.938185i | \(-0.612506\pi\) | ||||
−0.346133 | + | 0.938185i | \(0.612506\pi\) | |||||||
\(542\) | 3.74314 | 0.160782 | ||||||||
\(543\) | 0.917502 | 0.0393738 | ||||||||
\(544\) | 15.3951 | 0.660061 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 24.6953 | 1.05686 | ||||||||
\(547\) | −40.0370 | −1.71186 | −0.855930 | − | 0.517091i | \(-0.827015\pi\) | ||||
−0.855930 | + | 0.517091i | \(0.827015\pi\) | |||||||
\(548\) | 9.87649 | 0.421903 | ||||||||
\(549\) | 0.755569 | 0.0322469 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.36488 | −0.398957 | ||||||||
\(552\) | 12.2667 | 0.522106 | ||||||||
\(553\) | 31.5210 | 1.34041 | ||||||||
\(554\) | 10.5763 | 0.449343 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.37778 | −0.312888 | ||||||||
\(557\) | 28.2908 | 1.19872 | 0.599361 | − | 0.800479i | \(-0.295422\pi\) | ||||
0.599361 | + | 0.800479i | \(0.295422\pi\) | |||||||
\(558\) | 3.18421 | 0.134798 | ||||||||
\(559\) | 20.3368 | 0.860154 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.33185 | −0.225111 | ||||||||
\(562\) | −24.7457 | −1.04384 | ||||||||
\(563\) | 32.7926 | 1.38204 | 0.691022 | − | 0.722834i | \(-0.257161\pi\) | ||||
0.691022 | + | 0.722834i | \(0.257161\pi\) | |||||||
\(564\) | 3.70471 | 0.155997 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 7.67752 | 0.322710 | ||||||||
\(567\) | −4.90321 | −0.205916 | ||||||||
\(568\) | −1.31450 | −0.0551551 | ||||||||
\(569\) | −8.88586 | −0.372515 | −0.186257 | − | 0.982501i | \(-0.559636\pi\) | ||||
−0.186257 | + | 0.982501i | \(0.559636\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.6953 | −0.447586 | −0.223793 | − | 0.974637i | \(-0.571844\pi\) | ||||
−0.223793 | + | 0.974637i | \(0.571844\pi\) | |||||||
\(572\) | −2.17929 | −0.0911205 | ||||||||
\(573\) | 14.3684 | 0.600249 | ||||||||
\(574\) | −10.7556 | −0.448929 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 8.85236 | 0.368848 | ||||||||
\(577\) | 27.1338 | 1.12960 | 0.564798 | − | 0.825229i | \(-0.308954\pi\) | ||||
0.564798 | + | 0.825229i | \(0.308954\pi\) | |||||||
\(578\) | 13.8780 | 0.577250 | ||||||||
\(579\) | 11.7605 | 0.488749 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.2351 | −0.590570 | ||||||||
\(582\) | 3.34614 | 0.138702 | ||||||||
\(583\) | −7.18421 | −0.297540 | ||||||||
\(584\) | 38.9763 | 1.61285 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −20.2524 | −0.836620 | ||||||||
\(587\) | 10.9590 | 0.452326 | 0.226163 | − | 0.974089i | \(-0.427382\pi\) | ||||
0.226163 | + | 0.974089i | \(0.427382\pi\) | |||||||
\(588\) | −8.95407 | −0.369260 | ||||||||
\(589\) | −13.5941 | −0.560136 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.82071 | 0.157163 | ||||||||
\(592\) | 15.5210 | 0.637908 | ||||||||
\(593\) | 23.7003 | 0.973253 | 0.486627 | − | 0.873610i | \(-0.338227\pi\) | ||||
0.486627 | + | 0.873610i | \(0.338227\pi\) | |||||||
\(594\) | −1.21432 | −0.0498241 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.60300 | 0.0656616 | ||||||||
\(597\) | −13.7146 | −0.561299 | ||||||||
\(598\) | 20.1463 | 0.823842 | ||||||||
\(599\) | 41.7146 | 1.70441 | 0.852205 | − | 0.523208i | \(-0.175265\pi\) | ||||
0.852205 | + | 0.523208i | \(0.175265\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.5906 | 0.595162 | 0.297581 | − | 0.954697i | \(-0.403820\pi\) | ||||
0.297581 | + | 0.954697i | \(0.403820\pi\) | |||||||
\(602\) | 29.1941 | 1.18986 | ||||||||
\(603\) | 4.85728 | 0.197804 | ||||||||
\(604\) | 0.171778 | 0.00698953 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −21.6227 | −0.878362 | ||||||||
\(607\) | 19.9826 | 0.811071 | 0.405535 | − | 0.914079i | \(-0.367085\pi\) | ||||
0.405535 | + | 0.914079i | \(0.367085\pi\) | |||||||
\(608\) | −14.9688 | −0.607066 | ||||||||
\(609\) | −8.85728 | −0.358915 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 29.2444 | 1.18310 | ||||||||
\(612\) | −2.80150 | −0.113244 | ||||||||
\(613\) | −19.0781 | −0.770555 | −0.385278 | − | 0.922801i | \(-0.625894\pi\) | ||||
−0.385278 | + | 0.922801i | \(0.625894\pi\) | |||||||
\(614\) | 11.6400 | 0.469754 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −15.0366 | −0.605840 | ||||||||
\(617\) | 39.3590 | 1.58454 | 0.792268 | − | 0.610174i | \(-0.208900\pi\) | ||||
0.792268 | + | 0.610174i | \(0.208900\pi\) | |||||||
\(618\) | −6.00984 | −0.241751 | ||||||||
\(619\) | −23.0923 | −0.928160 | −0.464080 | − | 0.885793i | \(-0.653615\pi\) | ||||
−0.464080 | + | 0.885793i | \(0.653615\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.00000 | −0.160514 | ||||||||
\(622\) | 17.6445 | 0.707480 | ||||||||
\(623\) | −3.05086 | −0.122230 | ||||||||
\(624\) | 11.0869 | 0.443833 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 25.5397 | 1.02077 | ||||||||
\(627\) | 5.18421 | 0.207037 | ||||||||
\(628\) | −10.4603 | −0.417411 | ||||||||
\(629\) | −30.9590 | −1.23442 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.5111 | −1.01558 | −0.507791 | − | 0.861480i | \(-0.669538\pi\) | ||||
−0.507791 | + | 0.861480i | \(0.669538\pi\) | |||||||
\(632\) | 19.7146 | 0.784203 | ||||||||
\(633\) | 1.95851 | 0.0778439 | ||||||||
\(634\) | 1.20294 | 0.0477750 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3.77478 | −0.149680 | ||||||||
\(637\) | −70.6820 | −2.80052 | ||||||||
\(638\) | −2.19358 | −0.0868445 | ||||||||
\(639\) | 0.428639 | 0.0169567 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.25380 | −0.247010 | −0.123505 | − | 0.992344i | \(-0.539414\pi\) | ||||
−0.123505 | + | 0.992344i | \(0.539414\pi\) | |||||||
\(642\) | −13.5986 | −0.536692 | ||||||||
\(643\) | −6.84743 | −0.270036 | −0.135018 | − | 0.990843i | \(-0.543109\pi\) | ||||
−0.135018 | + | 0.990843i | \(0.543109\pi\) | |||||||
\(644\) | −10.3051 | −0.406079 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −33.5655 | −1.32062 | ||||||||
\(647\) | −20.2953 | −0.797890 | −0.398945 | − | 0.916975i | \(-0.630624\pi\) | ||||
−0.398945 | + | 0.916975i | \(0.630624\pi\) | |||||||
\(648\) | −3.06668 | −0.120470 | ||||||||
\(649\) | −1.67307 | −0.0656738 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.8573 | −0.503916 | ||||||||
\(652\) | 6.39700 | 0.250526 | ||||||||
\(653\) | 10.6222 | 0.415679 | 0.207840 | − | 0.978163i | \(-0.433357\pi\) | ||||
0.207840 | + | 0.978163i | \(0.433357\pi\) | |||||||
\(654\) | 19.0825 | 0.746185 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.82870 | −0.188529 | ||||||||
\(657\) | −12.7096 | −0.495850 | ||||||||
\(658\) | 41.9813 | 1.63660 | ||||||||
\(659\) | 10.1017 | 0.393507 | 0.196753 | − | 0.980453i | \(-0.436960\pi\) | ||||
0.196753 | + | 0.980453i | \(0.436960\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.6128 | 0.840642 | 0.420321 | − | 0.907375i | \(-0.361917\pi\) | ||||
0.420321 | + | 0.907375i | \(0.361917\pi\) | |||||||
\(662\) | −21.3492 | −0.829760 | ||||||||
\(663\) | −22.1146 | −0.858861 | ||||||||
\(664\) | −8.90321 | −0.345512 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.05086 | −0.273215 | ||||||||
\(667\) | −7.22570 | −0.279780 | ||||||||
\(668\) | 6.83314 | 0.264382 | ||||||||
\(669\) | 26.0098 | 1.00560 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.755569 | −0.0291684 | ||||||||
\(672\) | −14.1575 | −0.546137 | ||||||||
\(673\) | −10.2208 | −0.393982 | −0.196991 | − | 0.980405i | \(-0.563117\pi\) | ||||
−0.196991 | + | 0.980405i | \(0.563117\pi\) | |||||||
\(674\) | 3.84929 | 0.148269 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.20834 | −0.0849363 | ||||||||
\(677\) | −13.9224 | −0.535082 | −0.267541 | − | 0.963546i | \(-0.586211\pi\) | ||||
−0.267541 | + | 0.963546i | \(0.586211\pi\) | |||||||
\(678\) | 2.14320 | 0.0823090 | ||||||||
\(679\) | −13.5111 | −0.518510 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.34122 | 0.242996 | ||||||||
\(682\) | −3.18421 | −0.121930 | ||||||||
\(683\) | 10.3970 | 0.397830 | 0.198915 | − | 0.980017i | \(-0.436258\pi\) | ||||
0.198915 | + | 0.980017i | \(0.436258\pi\) | |||||||
\(684\) | 2.72393 | 0.104152 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −59.7877 | −2.28270 | ||||||||
\(687\) | −23.3274 | −0.889996 | ||||||||
\(688\) | 13.1066 | 0.499686 | ||||||||
\(689\) | −29.7975 | −1.13520 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.977725 | −0.0371944 | −0.0185972 | − | 0.999827i | \(-0.505920\pi\) | ||||
−0.0185972 | + | 0.999827i | \(0.505920\pi\) | |||||||
\(692\) | 7.30021 | 0.277512 | ||||||||
\(693\) | 4.90321 | 0.186258 | ||||||||
\(694\) | −6.04287 | −0.229384 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.53972 | −0.209982 | ||||||||
\(697\) | 9.63158 | 0.364822 | ||||||||
\(698\) | 22.1048 | 0.836678 | ||||||||
\(699\) | 1.42372 | 0.0538499 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 48.9688 | 1.84953 | 0.924764 | − | 0.380542i | \(-0.124263\pi\) | ||||
0.924764 | + | 0.380542i | \(0.124263\pi\) | |||||||
\(702\) | −5.03657 | −0.190093 | ||||||||
\(703\) | 30.1017 | 1.13531 | ||||||||
\(704\) | −8.85236 | −0.333636 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −27.2128 | −1.02417 | ||||||||
\(707\) | 87.3087 | 3.28358 | ||||||||
\(708\) | −0.879077 | −0.0330378 | ||||||||
\(709\) | −37.2672 | −1.39960 | −0.699799 | − | 0.714340i | \(-0.746727\pi\) | ||||
−0.699799 | + | 0.714340i | \(0.746727\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.42864 | −0.241093 | ||||||||
\(712\) | −1.90813 | −0.0715103 | ||||||||
\(713\) | −10.4889 | −0.392811 | ||||||||
\(714\) | −31.7462 | −1.18807 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.75557 | −0.252467 | ||||||||
\(717\) | −18.9590 | −0.708036 | ||||||||
\(718\) | 25.8983 | 0.966516 | ||||||||
\(719\) | 5.83500 | 0.217609 | 0.108804 | − | 0.994063i | \(-0.465298\pi\) | ||||
0.108804 | + | 0.994063i | \(0.465298\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24.2667 | 0.903739 | ||||||||
\(722\) | 9.56400 | 0.355935 | ||||||||
\(723\) | −1.34614 | −0.0500635 | ||||||||
\(724\) | −0.482081 | −0.0179164 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.21432 | 0.0450676 | ||||||||
\(727\) | 46.8385 | 1.73715 | 0.868573 | − | 0.495562i | \(-0.165038\pi\) | ||||
0.868573 | + | 0.495562i | \(0.165038\pi\) | |||||||
\(728\) | −62.3663 | −2.31145 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −26.1432 | −0.966941 | ||||||||
\(732\) | −0.396997 | −0.0146734 | ||||||||
\(733\) | 45.2083 | 1.66981 | 0.834904 | − | 0.550395i | \(-0.185523\pi\) | ||||
0.834904 | + | 0.550395i | \(0.185523\pi\) | |||||||
\(734\) | −42.6637 | −1.57475 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −11.5496 | −0.425723 | ||||||||
\(737\) | −4.85728 | −0.178920 | ||||||||
\(738\) | 2.19358 | 0.0807467 | ||||||||
\(739\) | 5.65433 | 0.207998 | 0.103999 | − | 0.994577i | \(-0.466836\pi\) | ||||
0.103999 | + | 0.994577i | \(0.466836\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 21.5022 | 0.789905 | ||||||||
\(742\) | −42.7753 | −1.57033 | ||||||||
\(743\) | −4.50622 | −0.165317 | −0.0826585 | − | 0.996578i | \(-0.526341\pi\) | ||||
−0.0826585 | + | 0.996578i | \(0.526341\pi\) | |||||||
\(744\) | −8.04149 | −0.294815 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 20.6494 | 0.756029 | ||||||||
\(747\) | 2.90321 | 0.106223 | ||||||||
\(748\) | 2.80150 | 0.102433 | ||||||||
\(749\) | 54.9086 | 2.00632 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 47.5121 | 1.73374 | 0.866870 | − | 0.498534i | \(-0.166128\pi\) | ||||
0.866870 | + | 0.498534i | \(0.166128\pi\) | |||||||
\(752\) | 18.8474 | 0.687295 | ||||||||
\(753\) | 1.08250 | 0.0394484 | ||||||||
\(754\) | −9.09817 | −0.331336 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.57628 | 0.0936985 | ||||||||
\(757\) | 46.6637 | 1.69602 | 0.848011 | − | 0.529979i | \(-0.177800\pi\) | ||||
0.848011 | + | 0.529979i | \(0.177800\pi\) | |||||||
\(758\) | 2.87601 | 0.104462 | ||||||||
\(759\) | 4.00000 | 0.145191 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.9304 | 0.541227 | 0.270613 | − | 0.962688i | \(-0.412773\pi\) | ||||
0.270613 | + | 0.962688i | \(0.412773\pi\) | |||||||
\(762\) | −22.7195 | −0.823040 | ||||||||
\(763\) | −77.0518 | −2.78946 | ||||||||
\(764\) | −7.54956 | −0.273134 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.47643 | −0.0533457 | ||||||||
\(767\) | −6.93930 | −0.250564 | ||||||||
\(768\) | −11.6637 | −0.420878 | ||||||||
\(769\) | 38.8573 | 1.40123 | 0.700615 | − | 0.713540i | \(-0.252909\pi\) | ||||
0.700615 | + | 0.713540i | \(0.252909\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.133353 | 0.00480259 | ||||||||
\(772\) | −6.17929 | −0.222397 | ||||||||
\(773\) | 36.3368 | 1.30694 | 0.653471 | − | 0.756951i | \(-0.273312\pi\) | ||||
0.653471 | + | 0.756951i | \(0.273312\pi\) | |||||||
\(774\) | −5.95407 | −0.214015 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.45044 | −0.303353 | ||||||||
\(777\) | 28.4701 | 1.02136 | ||||||||
\(778\) | 2.75251 | 0.0986821 | ||||||||
\(779\) | −9.36488 | −0.335532 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.428639 | −0.0153379 | ||||||||
\(782\) | −25.8983 | −0.926121 | ||||||||
\(783\) | 1.80642 | 0.0645563 | ||||||||
\(784\) | −45.5531 | −1.62690 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.51114 | −0.0539005 | ||||||||
\(787\) | 33.5482 | 1.19586 | 0.597932 | − | 0.801547i | \(-0.295989\pi\) | ||||
0.597932 | + | 0.801547i | \(0.295989\pi\) | |||||||
\(788\) | −2.00751 | −0.0715145 | ||||||||
\(789\) | 0.147643 | 0.00525624 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.65386 | −0.307696 | ||||||||
\(792\) | 3.06668 | 0.108970 | ||||||||
\(793\) | −3.13383 | −0.111286 | ||||||||
\(794\) | 22.4514 | 0.796770 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.20601 | 0.255410 | ||||||||
\(797\) | 16.1334 | 0.571473 | 0.285736 | − | 0.958308i | \(-0.407762\pi\) | ||||
0.285736 | + | 0.958308i | \(0.407762\pi\) | |||||||
\(798\) | 30.8671 | 1.09268 | ||||||||
\(799\) | −37.5941 | −1.32998 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.622216 | 0.0219849 | ||||||||
\(802\) | 21.3265 | 0.753063 | ||||||||
\(803\) | 12.7096 | 0.448513 | ||||||||
\(804\) | −2.55215 | −0.0900073 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −13.2070 | −0.465195 | ||||||||
\(807\) | −26.8573 | −0.945421 | ||||||||
\(808\) | 54.6065 | 1.92105 | ||||||||
\(809\) | 25.7431 | 0.905081 | 0.452540 | − | 0.891744i | \(-0.350518\pi\) | ||||
0.452540 | + | 0.891744i | \(0.350518\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.4509 | 0.472325 | 0.236163 | − | 0.971714i | \(-0.424110\pi\) | ||||
0.236163 | + | 0.971714i | \(0.424110\pi\) | |||||||
\(812\) | 4.65386 | 0.163318 | ||||||||
\(813\) | 3.08250 | 0.108108 | ||||||||
\(814\) | 7.05086 | 0.247132 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −14.2524 | −0.498934 | ||||||||
\(817\) | 25.4193 | 0.889308 | ||||||||
\(818\) | −25.9210 | −0.906308 | ||||||||
\(819\) | 20.3368 | 0.710624 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.1748 | 0.843708 | 0.421854 | − | 0.906664i | \(-0.361380\pi\) | ||||
0.421854 | + | 0.906664i | \(0.361380\pi\) | |||||||
\(822\) | −22.8256 | −0.796135 | ||||||||
\(823\) | 40.9117 | 1.42609 | 0.713046 | − | 0.701118i | \(-0.247315\pi\) | ||||
0.713046 | + | 0.701118i | \(0.247315\pi\) | |||||||
\(824\) | 15.1774 | 0.528731 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.96158 | −0.346608 | ||||||||
\(827\) | 20.1476 | 0.700602 | 0.350301 | − | 0.936637i | \(-0.386079\pi\) | ||||
0.350301 | + | 0.936637i | \(0.386079\pi\) | |||||||
\(828\) | 2.10171 | 0.0730395 | ||||||||
\(829\) | 31.4322 | 1.09168 | 0.545842 | − | 0.837888i | \(-0.316210\pi\) | ||||
0.545842 | + | 0.837888i | \(0.316210\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.70964 | 0.302134 | ||||||||
\(832\) | −36.7164 | −1.27291 | ||||||||
\(833\) | 90.8627 | 3.14821 | ||||||||
\(834\) | 17.0509 | 0.590423 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.72393 | −0.0942089 | ||||||||
\(837\) | 2.62222 | 0.0906370 | ||||||||
\(838\) | 35.0420 | 1.21050 | ||||||||
\(839\) | −52.8988 | −1.82627 | −0.913134 | − | 0.407659i | \(-0.866345\pi\) | ||||
−0.913134 | + | 0.407659i | \(0.866345\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.7368 | −0.887477 | ||||||||
\(842\) | −43.0954 | −1.48517 | ||||||||
\(843\) | −20.3783 | −0.701865 | ||||||||
\(844\) | −1.02906 | −0.0354216 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −8.56199 | −0.294367 | ||||||||
\(847\) | −4.90321 | −0.168476 | ||||||||
\(848\) | −19.2039 | −0.659465 | ||||||||
\(849\) | 6.32248 | 0.216987 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 23.2257 | 0.796167 | ||||||||
\(852\) | −0.225219 | −0.00771588 | ||||||||
\(853\) | 46.9229 | 1.60661 | 0.803305 | − | 0.595568i | \(-0.203073\pi\) | ||||
0.803305 | + | 0.595568i | \(0.203073\pi\) | |||||||
\(854\) | −4.49871 | −0.153943 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 34.3422 | 1.17379 | ||||||||
\(857\) | 25.1481 | 0.859043 | 0.429522 | − | 0.903057i | \(-0.358682\pi\) | ||||
0.429522 | + | 0.903057i | \(0.358682\pi\) | |||||||
\(858\) | 5.03657 | 0.171945 | ||||||||
\(859\) | 1.84791 | 0.0630499 | 0.0315250 | − | 0.999503i | \(-0.489964\pi\) | ||||
0.0315250 | + | 0.999503i | \(0.489964\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.85728 | −0.301855 | ||||||||
\(862\) | 11.2257 | 0.382349 | ||||||||
\(863\) | −32.6824 | −1.11252 | −0.556262 | − | 0.831007i | \(-0.687765\pi\) | ||||
−0.556262 | + | 0.831007i | \(0.687765\pi\) | |||||||
\(864\) | 2.88739 | 0.0982310 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 7.63254 | 0.259364 | ||||||||
\(867\) | 11.4286 | 0.388137 | ||||||||
\(868\) | 6.75557 | 0.229299 | ||||||||
\(869\) | 6.42864 | 0.218077 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.1463 | −0.682630 | ||||||||
\(872\) | −48.1915 | −1.63197 | ||||||||
\(873\) | 2.75557 | 0.0932619 | ||||||||
\(874\) | 25.1811 | 0.851765 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.67799 | 0.225628 | ||||||||
\(877\) | −49.1798 | −1.66068 | −0.830341 | − | 0.557255i | \(-0.811855\pi\) | ||||
−0.830341 | + | 0.557255i | \(0.811855\pi\) | |||||||
\(878\) | −44.3595 | −1.49706 | ||||||||
\(879\) | −16.6780 | −0.562535 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.8163 | 1.13930 | 0.569650 | − | 0.821888i | \(-0.307079\pi\) | ||||
0.569650 | + | 0.821888i | \(0.307079\pi\) | |||||||
\(882\) | 20.6938 | 0.696797 | ||||||||
\(883\) | −24.7368 | −0.832461 | −0.416230 | − | 0.909259i | \(-0.636649\pi\) | ||||
−0.416230 | + | 0.909259i | \(0.636649\pi\) | |||||||
\(884\) | 11.6196 | 0.390810 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 46.4800 | 1.56153 | ||||||||
\(887\) | −7.64004 | −0.256528 | −0.128264 | − | 0.991740i | \(-0.540940\pi\) | ||||
−0.128264 | + | 0.991740i | \(0.540940\pi\) | |||||||
\(888\) | 17.8064 | 0.597544 | ||||||||
\(889\) | 91.7373 | 3.07677 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | −13.6663 | −0.457581 | ||||||||
\(893\) | 36.5531 | 1.22320 | ||||||||
\(894\) | −3.70471 | −0.123904 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −24.3926 | −0.814898 | ||||||||
\(897\) | 16.5906 | 0.553943 | ||||||||
\(898\) | −38.6735 | −1.29055 | ||||||||
\(899\) | 4.73683 | 0.157982 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 38.3051 | 1.27613 | ||||||||
\(902\) | −2.19358 | −0.0730381 | ||||||||
\(903\) | 24.0415 | 0.800051 | ||||||||
\(904\) | −5.41249 | −0.180017 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.396997 | −0.0131893 | ||||||||
\(907\) | 30.3970 | 1.00932 | 0.504658 | − | 0.863319i | \(-0.331619\pi\) | ||||
0.504658 | + | 0.863319i | \(0.331619\pi\) | |||||||
\(908\) | −3.33185 | −0.110571 | ||||||||
\(909\) | −17.8064 | −0.590602 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −45.3274 | −1.50176 | −0.750882 | − | 0.660436i | \(-0.770371\pi\) | ||||
−0.750882 | + | 0.660436i | \(0.770371\pi\) | |||||||
\(912\) | 13.8578 | 0.458876 | ||||||||
\(913\) | −2.90321 | −0.0960823 | ||||||||
\(914\) | −1.69042 | −0.0559142 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 12.2569 | 0.404978 | ||||||||
\(917\) | 6.10171 | 0.201496 | ||||||||
\(918\) | 6.47457 | 0.213693 | ||||||||
\(919\) | −16.3269 | −0.538576 | −0.269288 | − | 0.963060i | \(-0.586788\pi\) | ||||
−0.269288 | + | 0.963060i | \(0.586788\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.58565 | 0.315858 | ||||||||
\(922\) | −9.35599 | −0.308123 | ||||||||
\(923\) | −1.77784 | −0.0585184 | ||||||||
\(924\) | −2.57628 | −0.0847535 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5.68598 | −0.186853 | ||||||||
\(927\) | −4.94914 | −0.162551 | ||||||||
\(928\) | 5.21585 | 0.171219 | ||||||||
\(929\) | −29.6128 | −0.971566 | −0.485783 | − | 0.874079i | \(-0.661465\pi\) | ||||
−0.485783 | + | 0.874079i | \(0.661465\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −88.3466 | −2.89544 | ||||||||
\(932\) | −0.748060 | −0.0245035 | ||||||||
\(933\) | 14.5303 | 0.475702 | ||||||||
\(934\) | −15.6128 | −0.510868 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 12.7195 | 0.415749 | ||||||||
\(937\) | −8.92195 | −0.291467 | −0.145734 | − | 0.989324i | \(-0.546554\pi\) | ||||
−0.145734 | + | 0.989324i | \(0.546554\pi\) | |||||||
\(938\) | −28.9206 | −0.944290 | ||||||||
\(939\) | 21.0321 | 0.686357 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.2766 | −0.726195 | −0.363097 | − | 0.931751i | \(-0.618281\pi\) | ||||
−0.363097 | + | 0.931751i | \(0.618281\pi\) | |||||||
\(942\) | 24.1748 | 0.787659 | ||||||||
\(943\) | −7.22570 | −0.235301 | ||||||||
\(944\) | −4.47224 | −0.145559 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.95407 | 0.193583 | ||||||||
\(947\) | −44.4612 | −1.44480 | −0.722398 | − | 0.691477i | \(-0.756960\pi\) | ||||
−0.722398 | + | 0.691477i | \(0.756960\pi\) | |||||||
\(948\) | 3.37778 | 0.109705 | ||||||||
\(949\) | 52.7150 | 1.71120 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.990632 | 0.0321234 | ||||||||
\(952\) | 80.1727 | 2.59841 | ||||||||
\(953\) | −20.5575 | −0.665924 | −0.332962 | − | 0.942940i | \(-0.608048\pi\) | ||||
−0.332962 | + | 0.942940i | \(0.608048\pi\) | |||||||
\(954\) | 8.72393 | 0.282448 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 9.96158 | 0.322180 | ||||||||
\(957\) | −1.80642 | −0.0583934 | ||||||||
\(958\) | 10.1847 | 0.329052 | ||||||||
\(959\) | 92.1659 | 2.97619 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.1240 | −0.778193 | ||||||||
\(962\) | 29.2444 | 0.942878 | ||||||||
\(963\) | −11.1985 | −0.360867 | ||||||||
\(964\) | 0.707300 | 0.0227806 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 23.8163 | 0.766276 | ||||||||
\(967\) | −27.4839 | −0.883824 | −0.441912 | − | 0.897058i | \(-0.645700\pi\) | ||||
−0.441912 | + | 0.897058i | \(0.645700\pi\) | |||||||
\(968\) | −3.06668 | −0.0985667 | ||||||||
\(969\) | −27.6414 | −0.887971 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.81532 | −0.186622 | −0.0933112 | − | 0.995637i | \(-0.529745\pi\) | ||||
−0.0933112 | + | 0.995637i | \(0.529745\pi\) | |||||||
\(972\) | −0.525428 | −0.0168531 | ||||||||
\(973\) | −68.8484 | −2.20718 | ||||||||
\(974\) | −11.9428 | −0.382673 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.01969 | −0.0646487 | ||||||||
\(977\) | −48.3912 | −1.54817 | −0.774085 | − | 0.633081i | \(-0.781790\pi\) | ||||
−0.774085 | + | 0.633081i | \(0.781790\pi\) | |||||||
\(978\) | −14.7841 | −0.472745 | ||||||||
\(979\) | −0.622216 | −0.0198861 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.7146 | 0.501727 | ||||||||
\(982\) | −40.0000 | −1.27645 | ||||||||
\(983\) | 49.9724 | 1.59387 | 0.796936 | − | 0.604064i | \(-0.206453\pi\) | ||||
0.796936 | + | 0.604064i | \(0.206453\pi\) | |||||||
\(984\) | −5.53972 | −0.176600 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 11.6958 | 0.372471 | ||||||||
\(987\) | 34.5718 | 1.10043 | ||||||||
\(988\) | −11.2979 | −0.359433 | ||||||||
\(989\) | 19.6128 | 0.623652 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.35905 | −0.233768 | −0.116884 | − | 0.993146i | \(-0.537291\pi\) | ||||
−0.116884 | + | 0.993146i | \(0.537291\pi\) | |||||||
\(992\) | 7.57136 | 0.240391 | ||||||||
\(993\) | −17.5812 | −0.557923 | ||||||||
\(994\) | −2.55215 | −0.0809492 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.52543 | −0.0483350 | ||||||||
\(997\) | 4.33138 | 0.137176 | 0.0685880 | − | 0.997645i | \(-0.478151\pi\) | ||||
0.0685880 | + | 0.997645i | \(0.478151\pi\) | |||||||
\(998\) | −1.98126 | −0.0627158 | ||||||||
\(999\) | −5.80642 | −0.183707 |
(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 | 825.2.a.h.1.3 | 3 | ||
3.2 | odd | 2 | 2475.2.a.be.1.1 | 3 | |||
5.2 | odd | 4 | 165.2.c.a.34.4 | yes | 6 | ||
5.3 | odd | 4 | 165.2.c.a.34.3 | ✓ | 6 | ||
5.4 | even | 2 | 825.2.a.n.1.1 | 3 | |||
11.10 | odd | 2 | 9075.2.a.ck.1.1 | 3 | |||
15.2 | even | 4 | 495.2.c.d.199.3 | 6 | |||
15.8 | even | 4 | 495.2.c.d.199.4 | 6 | |||
15.14 | odd | 2 | 2475.2.a.y.1.3 | 3 | |||
20.3 | even | 4 | 2640.2.d.i.529.2 | 6 | |||
20.7 | even | 4 | 2640.2.d.i.529.5 | 6 | |||
55.32 | even | 4 | 1815.2.c.d.364.3 | 6 | |||
55.43 | even | 4 | 1815.2.c.d.364.4 | 6 | |||
55.54 | odd | 2 | 9075.2.a.cc.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.c.a.34.3 | ✓ | 6 | 5.3 | odd | 4 | ||
165.2.c.a.34.4 | yes | 6 | 5.2 | odd | 4 | ||
495.2.c.d.199.3 | 6 | 15.2 | even | 4 | |||
495.2.c.d.199.4 | 6 | 15.8 | even | 4 | |||
825.2.a.h.1.3 | 3 | 1.1 | even | 1 | trivial | ||
825.2.a.n.1.1 | 3 | 5.4 | even | 2 | |||
1815.2.c.d.364.3 | 6 | 55.32 | even | 4 | |||
1815.2.c.d.364.4 | 6 | 55.43 | even | 4 | |||
2475.2.a.y.1.3 | 3 | 15.14 | odd | 2 | |||
2475.2.a.be.1.1 | 3 | 3.2 | odd | 2 | |||
2640.2.d.i.529.2 | 6 | 20.3 | even | 4 | |||
2640.2.d.i.529.5 | 6 | 20.7 | even | 4 | |||
9075.2.a.cc.1.3 | 3 | 55.54 | odd | 2 | |||
9075.2.a.ck.1.1 | 3 | 11.10 | odd | 2 |