Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7605,2,Mod(1,7605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7605, 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("7605.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7605 = 3^{2} \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7605.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: | \(60.7262307372\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 585) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7605.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.56155 | 1.10418 | 0.552092 | − | 0.833783i | \(-0.313830\pi\) | ||||
0.552092 | + | 0.833783i | \(0.313830\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.438447 | 0.219224 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.56155 | 1.72410 | 0.862052 | − | 0.506819i | \(-0.169179\pi\) | ||||
0.862052 | + | 0.506819i | \(0.169179\pi\) | |||||||
\(8\) | −2.43845 | −0.862121 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.56155 | −0.493806 | ||||||||
\(11\) | −2.56155 | −0.772337 | −0.386169 | − | 0.922428i | \(-0.626202\pi\) | ||||
−0.386169 | + | 0.922428i | \(0.626202\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 7.12311 | 1.90373 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.68466 | −1.17116 | ||||||||
\(17\) | −2.56155 | −0.621268 | −0.310634 | − | 0.950530i | \(-0.600541\pi\) | ||||
−0.310634 | + | 0.950530i | \(0.600541\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.12311 | −0.716490 | −0.358245 | − | 0.933628i | \(-0.616625\pi\) | ||||
−0.358245 | + | 0.933628i | \(0.616625\pi\) | |||||||
\(20\) | −0.438447 | −0.0980398 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.00000 | −0.852803 | ||||||||
\(23\) | 6.56155 | 1.36818 | 0.684089 | − | 0.729398i | \(-0.260200\pi\) | ||||
0.684089 | + | 0.729398i | \(0.260200\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.00000 | 0.377964 | ||||||||
\(29\) | 1.12311 | 0.208555 | 0.104278 | − | 0.994548i | \(-0.466747\pi\) | ||||
0.104278 | + | 0.994548i | \(0.466747\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.00000 | −1.07763 | −0.538816 | − | 0.842424i | \(-0.681128\pi\) | ||||
−0.538816 | + | 0.842424i | \(0.681128\pi\) | |||||||
\(32\) | −2.43845 | −0.431061 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.00000 | −0.685994 | ||||||||
\(35\) | −4.56155 | −0.771043 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.68466 | −0.276956 | −0.138478 | − | 0.990366i | \(-0.544221\pi\) | ||||
−0.138478 | + | 0.990366i | \(0.544221\pi\) | |||||||
\(38\) | −4.87689 | −0.791137 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.43845 | 0.385552 | ||||||||
\(41\) | 0.561553 | 0.0876998 | 0.0438499 | − | 0.999038i | \(-0.486038\pi\) | ||||
0.0438499 | + | 0.999038i | \(0.486038\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.12311 | −0.781266 | −0.390633 | − | 0.920546i | \(-0.627744\pi\) | ||||
−0.390633 | + | 0.920546i | \(0.627744\pi\) | |||||||
\(44\) | −1.12311 | −0.169315 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 10.2462 | 1.51072 | ||||||||
\(47\) | −2.87689 | −0.419638 | −0.209819 | − | 0.977740i | \(-0.567288\pi\) | ||||
−0.209819 | + | 0.977740i | \(0.567288\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.8078 | 1.97254 | ||||||||
\(50\) | 1.56155 | 0.220837 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.68466 | 1.05557 | 0.527785 | − | 0.849378i | \(-0.323023\pi\) | ||||
0.527785 | + | 0.849378i | \(0.323023\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.56155 | 0.345400 | ||||||||
\(56\) | −11.1231 | −1.48639 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.75379 | 0.230284 | ||||||||
\(59\) | −12.0000 | −1.56227 | −0.781133 | − | 0.624364i | \(-0.785358\pi\) | ||||
−0.781133 | + | 0.624364i | \(0.785358\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.68466 | 0.727846 | 0.363923 | − | 0.931429i | \(-0.381437\pi\) | ||||
0.363923 | + | 0.931429i | \(0.381437\pi\) | |||||||
\(62\) | −9.36932 | −1.18990 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.56155 | 0.695194 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.3693 | −1.63332 | −0.816661 | − | 0.577118i | \(-0.804177\pi\) | ||||
−0.816661 | + | 0.577118i | \(0.804177\pi\) | |||||||
\(68\) | −1.12311 | −0.136197 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −7.12311 | −0.851374 | ||||||||
\(71\) | −14.5616 | −1.72814 | −0.864069 | − | 0.503373i | \(-0.832092\pi\) | ||||
−0.864069 | + | 0.503373i | \(0.832092\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.00000 | 0.702247 | 0.351123 | − | 0.936329i | \(-0.385800\pi\) | ||||
0.351123 | + | 0.936329i | \(0.385800\pi\) | |||||||
\(74\) | −2.63068 | −0.305811 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.36932 | −0.157071 | ||||||||
\(77\) | −11.6847 | −1.33159 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.68466 | −0.864592 | −0.432296 | − | 0.901732i | \(-0.642296\pi\) | ||||
−0.432296 | + | 0.901732i | \(0.642296\pi\) | |||||||
\(80\) | 4.68466 | 0.523761 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.876894 | 0.0968368 | ||||||||
\(83\) | −16.4924 | −1.81028 | −0.905139 | − | 0.425115i | \(-0.860234\pi\) | ||||
−0.905139 | + | 0.425115i | \(0.860234\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.56155 | 0.277839 | ||||||||
\(86\) | −8.00000 | −0.862662 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.24621 | 0.665848 | ||||||||
\(89\) | 1.68466 | 0.178573 | 0.0892867 | − | 0.996006i | \(-0.471541\pi\) | ||||
0.0892867 | + | 0.996006i | \(0.471541\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.87689 | 0.299937 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.49242 | −0.463358 | ||||||||
\(95\) | 3.12311 | 0.320424 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.9309 | 1.21140 | 0.605698 | − | 0.795695i | \(-0.292894\pi\) | ||||
0.605698 | + | 0.795695i | \(0.292894\pi\) | |||||||
\(98\) | 21.5616 | 2.17805 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.438447 | 0.0438447 | ||||||||
\(101\) | −6.24621 | −0.621521 | −0.310761 | − | 0.950488i | \(-0.600584\pi\) | ||||
−0.310761 | + | 0.950488i | \(0.600584\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.87689 | −0.677601 | −0.338800 | − | 0.940858i | \(-0.610021\pi\) | ||||
−0.338800 | + | 0.940858i | \(0.610021\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.0000 | 1.16554 | ||||||||
\(107\) | −17.9309 | −1.73344 | −0.866721 | − | 0.498793i | \(-0.833777\pi\) | ||||
−0.866721 | + | 0.498793i | \(0.833777\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 4.00000 | 0.381385 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −21.3693 | −2.01921 | ||||||||
\(113\) | −13.1231 | −1.23452 | −0.617259 | − | 0.786760i | \(-0.711757\pi\) | ||||
−0.617259 | + | 0.786760i | \(0.711757\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.56155 | −0.611868 | ||||||||
\(116\) | 0.492423 | 0.0457203 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −18.7386 | −1.72503 | ||||||||
\(119\) | −11.6847 | −1.07113 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.43845 | −0.403495 | ||||||||
\(122\) | 8.87689 | 0.803676 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.63068 | −0.236242 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.2462 | 1.61909 | 0.809545 | − | 0.587058i | \(-0.199714\pi\) | ||||
0.809545 | + | 0.587058i | \(0.199714\pi\) | |||||||
\(128\) | 13.5616 | 1.19868 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14.2462 | −1.23530 | ||||||||
\(134\) | −20.8769 | −1.80349 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.24621 | 0.535608 | ||||||||
\(137\) | 7.12311 | 0.608568 | 0.304284 | − | 0.952581i | \(-0.401583\pi\) | ||||
0.304284 | + | 0.952581i | \(0.401583\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.6847 | 1.33036 | 0.665178 | − | 0.746685i | \(-0.268356\pi\) | ||||
0.665178 | + | 0.746685i | \(0.268356\pi\) | |||||||
\(140\) | −2.00000 | −0.169031 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −22.7386 | −1.90818 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.12311 | −0.0932688 | ||||||||
\(146\) | 9.36932 | 0.775410 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.738634 | −0.0607153 | ||||||||
\(149\) | −2.80776 | −0.230021 | −0.115010 | − | 0.993364i | \(-0.536690\pi\) | ||||
−0.115010 | + | 0.993364i | \(0.536690\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.3693 | 1.08798 | 0.543990 | − | 0.839092i | \(-0.316913\pi\) | ||||
0.543990 | + | 0.839092i | \(0.316913\pi\) | |||||||
\(152\) | 7.61553 | 0.617701 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −18.2462 | −1.47032 | ||||||||
\(155\) | 6.00000 | 0.481932 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.3693 | −1.70546 | −0.852729 | − | 0.522354i | \(-0.825054\pi\) | ||||
−0.852729 | + | 0.522354i | \(0.825054\pi\) | |||||||
\(158\) | −12.0000 | −0.954669 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.43845 | 0.192776 | ||||||||
\(161\) | 29.9309 | 2.35888 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.0540 | 1.64907 | 0.824537 | − | 0.565808i | \(-0.191436\pi\) | ||||
0.824537 | + | 0.565808i | \(0.191436\pi\) | |||||||
\(164\) | 0.246211 | 0.0192259 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −25.7538 | −1.99888 | ||||||||
\(167\) | −13.1231 | −1.01550 | −0.507748 | − | 0.861506i | \(-0.669522\pi\) | ||||
−0.507748 | + | 0.861506i | \(0.669522\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 4.00000 | 0.306786 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.24621 | −0.171272 | ||||||||
\(173\) | 21.1231 | 1.60596 | 0.802980 | − | 0.596006i | \(-0.203247\pi\) | ||||
0.802980 | + | 0.596006i | \(0.203247\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.56155 | 0.344821 | ||||||||
\(176\) | 12.0000 | 0.904534 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.63068 | 0.197178 | ||||||||
\(179\) | −13.1231 | −0.980867 | −0.490433 | − | 0.871479i | \(-0.663162\pi\) | ||||
−0.490433 | + | 0.871479i | \(0.663162\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.6847 | 1.90913 | 0.954563 | − | 0.298010i | \(-0.0963228\pi\) | ||||
0.954563 | + | 0.298010i | \(0.0963228\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −16.0000 | −1.17954 | ||||||||
\(185\) | 1.68466 | 0.123859 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.56155 | 0.479828 | ||||||||
\(188\) | −1.26137 | −0.0919946 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.87689 | 0.353807 | ||||||||
\(191\) | −21.6155 | −1.56404 | −0.782022 | − | 0.623250i | \(-0.785812\pi\) | ||||
−0.782022 | + | 0.623250i | \(0.785812\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.4384 | −1.11128 | −0.555642 | − | 0.831422i | \(-0.687527\pi\) | ||||
−0.555642 | + | 0.831422i | \(0.687527\pi\) | |||||||
\(194\) | 18.6307 | 1.33761 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.05398 | 0.432427 | ||||||||
\(197\) | −21.3693 | −1.52250 | −0.761250 | − | 0.648458i | \(-0.775414\pi\) | ||||
−0.761250 | + | 0.648458i | \(0.775414\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.00000 | −0.567105 | −0.283552 | − | 0.958957i | \(-0.591513\pi\) | ||||
−0.283552 | + | 0.958957i | \(0.591513\pi\) | |||||||
\(200\) | −2.43845 | −0.172424 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.75379 | −0.686274 | ||||||||
\(203\) | 5.12311 | 0.359572 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.561553 | −0.0392205 | ||||||||
\(206\) | −10.7386 | −0.748196 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.00000 | 0.553372 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.2462 | −0.705378 | −0.352689 | − | 0.935741i | \(-0.614733\pi\) | ||||
−0.352689 | + | 0.935741i | \(0.614733\pi\) | |||||||
\(212\) | 3.36932 | 0.231406 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −28.0000 | −1.91404 | ||||||||
\(215\) | 5.12311 | 0.349393 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −27.3693 | −1.85795 | ||||||||
\(218\) | 3.12311 | 0.211523 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.12311 | 0.0757198 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.36932 | −0.627416 | −0.313708 | − | 0.949520i | \(-0.601571\pi\) | ||||
−0.313708 | + | 0.949520i | \(0.601571\pi\) | |||||||
\(224\) | −11.1231 | −0.743194 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −20.4924 | −1.36314 | ||||||||
\(227\) | −22.2462 | −1.47653 | −0.738266 | − | 0.674509i | \(-0.764355\pi\) | ||||
−0.738266 | + | 0.674509i | \(0.764355\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.87689 | −0.586602 | −0.293301 | − | 0.956020i | \(-0.594754\pi\) | ||||
−0.293301 | + | 0.956020i | \(0.594754\pi\) | |||||||
\(230\) | −10.2462 | −0.675615 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.73863 | −0.179800 | ||||||||
\(233\) | −7.19224 | −0.471179 | −0.235590 | − | 0.971853i | \(-0.575702\pi\) | ||||
−0.235590 | + | 0.971853i | \(0.575702\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.87689 | 0.187668 | ||||||||
\(236\) | −5.26137 | −0.342486 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −18.2462 | −1.18273 | ||||||||
\(239\) | 5.93087 | 0.383636 | 0.191818 | − | 0.981431i | \(-0.438562\pi\) | ||||
0.191818 | + | 0.981431i | \(0.438562\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.7386 | 1.59356 | 0.796778 | − | 0.604272i | \(-0.206536\pi\) | ||||
0.796778 | + | 0.604272i | \(0.206536\pi\) | |||||||
\(242\) | −6.93087 | −0.445533 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.49242 | 0.159561 | ||||||||
\(245\) | −13.8078 | −0.882146 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 14.6307 | 0.929049 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.56155 | −0.0987613 | ||||||||
\(251\) | 9.75379 | 0.615654 | 0.307827 | − | 0.951442i | \(-0.400398\pi\) | ||||
0.307827 | + | 0.951442i | \(0.400398\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.8078 | −1.05670 | ||||||||
\(254\) | 28.4924 | 1.78777 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 10.0540 | 0.628373 | ||||||||
\(257\) | −21.1231 | −1.31762 | −0.658812 | − | 0.752308i | \(-0.728941\pi\) | ||||
−0.658812 | + | 0.752308i | \(0.728941\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.68466 | −0.477501 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.2462 | 0.878459 | 0.439230 | − | 0.898375i | \(-0.355251\pi\) | ||||
0.439230 | + | 0.898375i | \(0.355251\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.68466 | −0.472065 | ||||||||
\(266\) | −22.2462 | −1.36400 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.86174 | −0.358063 | ||||||||
\(269\) | −9.12311 | −0.556246 | −0.278123 | − | 0.960546i | \(-0.589712\pi\) | ||||
−0.278123 | + | 0.960546i | \(0.589712\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.36932 | −0.326163 | −0.163081 | − | 0.986613i | \(-0.552143\pi\) | ||||
−0.163081 | + | 0.986613i | \(0.552143\pi\) | |||||||
\(272\) | 12.0000 | 0.727607 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.1231 | 0.671971 | ||||||||
\(275\) | −2.56155 | −0.154467 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.24621 | 0.255130 | 0.127565 | − | 0.991830i | \(-0.459284\pi\) | ||||
0.127565 | + | 0.991830i | \(0.459284\pi\) | |||||||
\(278\) | 24.4924 | 1.46896 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 11.1231 | 0.664733 | ||||||||
\(281\) | 12.2462 | 0.730548 | 0.365274 | − | 0.930900i | \(-0.380975\pi\) | ||||
0.365274 | + | 0.930900i | \(0.380975\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.00000 | −0.237775 | −0.118888 | − | 0.992908i | \(-0.537933\pi\) | ||||
−0.118888 | + | 0.992908i | \(0.537933\pi\) | |||||||
\(284\) | −6.38447 | −0.378849 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.56155 | 0.151204 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.4384 | −0.614026 | ||||||||
\(290\) | −1.75379 | −0.102986 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.63068 | 0.153949 | ||||||||
\(293\) | 3.75379 | 0.219299 | 0.109649 | − | 0.993970i | \(-0.465027\pi\) | ||||
0.109649 | + | 0.993970i | \(0.465027\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.0000 | 0.698667 | ||||||||
\(296\) | 4.10795 | 0.238770 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.38447 | −0.253986 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −23.3693 | −1.34699 | ||||||||
\(302\) | 20.8769 | 1.20133 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 14.6307 | 0.839127 | ||||||||
\(305\) | −5.68466 | −0.325503 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.43845 | −0.196243 | −0.0981213 | − | 0.995174i | \(-0.531283\pi\) | ||||
−0.0981213 | + | 0.995174i | \(0.531283\pi\) | |||||||
\(308\) | −5.12311 | −0.291916 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 9.36932 | 0.532141 | ||||||||
\(311\) | 27.3693 | 1.55197 | 0.775986 | − | 0.630750i | \(-0.217253\pi\) | ||||
0.775986 | + | 0.630750i | \(0.217253\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.8769 | 1.18003 | 0.590016 | − | 0.807392i | \(-0.299121\pi\) | ||||
0.590016 | + | 0.807392i | \(0.299121\pi\) | |||||||
\(314\) | −33.3693 | −1.88314 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.36932 | −0.189539 | ||||||||
\(317\) | −34.4924 | −1.93729 | −0.968644 | − | 0.248454i | \(-0.920078\pi\) | ||||
−0.968644 | + | 0.248454i | \(0.920078\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.87689 | −0.161075 | ||||||||
\(320\) | −5.56155 | −0.310900 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 46.7386 | 2.60464 | ||||||||
\(323\) | 8.00000 | 0.445132 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 32.8769 | 1.82088 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.36932 | −0.0756079 | ||||||||
\(329\) | −13.1231 | −0.723500 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.8769 | −1.14750 | −0.573749 | − | 0.819031i | \(-0.694511\pi\) | ||||
−0.573749 | + | 0.819031i | \(0.694511\pi\) | |||||||
\(332\) | −7.23106 | −0.396856 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −20.4924 | −1.12130 | ||||||||
\(335\) | 13.3693 | 0.730444 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.49242 | 0.135771 | 0.0678855 | − | 0.997693i | \(-0.478375\pi\) | ||||
0.0678855 | + | 0.997693i | \(0.478375\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.12311 | 0.0609090 | ||||||||
\(341\) | 15.3693 | 0.832295 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 31.0540 | 1.67676 | ||||||||
\(344\) | 12.4924 | 0.673546 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 32.9848 | 1.77328 | ||||||||
\(347\) | 11.0540 | 0.593408 | 0.296704 | − | 0.954969i | \(-0.404112\pi\) | ||||
0.296704 | + | 0.954969i | \(0.404112\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.36932 | −0.0732979 | −0.0366489 | − | 0.999328i | \(-0.511668\pi\) | ||||
−0.0366489 | + | 0.999328i | \(0.511668\pi\) | |||||||
\(350\) | 7.12311 | 0.380746 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.24621 | 0.332924 | ||||||||
\(353\) | −10.4924 | −0.558455 | −0.279228 | − | 0.960225i | \(-0.590078\pi\) | ||||
−0.279228 | + | 0.960225i | \(0.590078\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.5616 | 0.772847 | ||||||||
\(356\) | 0.738634 | 0.0391475 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −20.4924 | −1.08306 | ||||||||
\(359\) | −2.24621 | −0.118550 | −0.0592752 | − | 0.998242i | \(-0.518879\pi\) | ||||
−0.0592752 | + | 0.998242i | \(0.518879\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.24621 | −0.486643 | ||||||||
\(362\) | 40.1080 | 2.10803 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.00000 | −0.314054 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.2462 | −0.952444 | −0.476222 | − | 0.879325i | \(-0.657994\pi\) | ||||
−0.476222 | + | 0.879325i | \(0.657994\pi\) | |||||||
\(368\) | −30.7386 | −1.60236 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.63068 | 0.136763 | ||||||||
\(371\) | 35.0540 | 1.81991 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.24621 | −0.219860 | −0.109930 | − | 0.993939i | \(-0.535063\pi\) | ||||
−0.109930 | + | 0.993939i | \(0.535063\pi\) | |||||||
\(374\) | 10.2462 | 0.529819 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.01515 | 0.361779 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.49242 | −0.128027 | −0.0640136 | − | 0.997949i | \(-0.520390\pi\) | ||||
−0.0640136 | + | 0.997949i | \(0.520390\pi\) | |||||||
\(380\) | 1.36932 | 0.0702445 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −33.7538 | −1.72699 | ||||||||
\(383\) | −36.4924 | −1.86468 | −0.932338 | − | 0.361588i | \(-0.882235\pi\) | ||||
−0.932338 | + | 0.361588i | \(0.882235\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.6847 | 0.595505 | ||||||||
\(386\) | −24.1080 | −1.22706 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.23106 | 0.265567 | ||||||||
\(389\) | −19.8617 | −1.00703 | −0.503515 | − | 0.863986i | \(-0.667960\pi\) | ||||
−0.503515 | + | 0.863986i | \(0.667960\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.8078 | −0.850005 | ||||||||
\(392\) | −33.6695 | −1.70057 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −33.3693 | −1.68112 | ||||||||
\(395\) | 7.68466 | 0.386657 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.56155 | 0.429692 | 0.214846 | − | 0.976648i | \(-0.431075\pi\) | ||||
0.214846 | + | 0.976648i | \(0.431075\pi\) | |||||||
\(398\) | −12.4924 | −0.626189 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.68466 | −0.234233 | ||||||||
\(401\) | −20.2462 | −1.01105 | −0.505524 | − | 0.862813i | \(-0.668701\pi\) | ||||
−0.505524 | + | 0.862813i | \(0.668701\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −2.73863 | −0.136252 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.00000 | 0.397033 | ||||||||
\(407\) | 4.31534 | 0.213904 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.1231 | 0.747789 | 0.373895 | − | 0.927471i | \(-0.378022\pi\) | ||||
0.373895 | + | 0.927471i | \(0.378022\pi\) | |||||||
\(410\) | −0.876894 | −0.0433067 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.01515 | −0.148546 | ||||||||
\(413\) | −54.7386 | −2.69351 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16.4924 | 0.809581 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 12.4924 | 0.611024 | ||||||||
\(419\) | −33.6155 | −1.64223 | −0.821113 | − | 0.570766i | \(-0.806646\pi\) | ||||
−0.821113 | + | 0.570766i | \(0.806646\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.6307 | −0.713056 | −0.356528 | − | 0.934285i | \(-0.616040\pi\) | ||||
−0.356528 | + | 0.934285i | \(0.616040\pi\) | |||||||
\(422\) | −16.0000 | −0.778868 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −18.7386 | −0.910029 | ||||||||
\(425\) | −2.56155 | −0.124254 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 25.9309 | 1.25488 | ||||||||
\(428\) | −7.86174 | −0.380012 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.00000 | 0.385794 | ||||||||
\(431\) | 36.4924 | 1.75778 | 0.878889 | − | 0.477026i | \(-0.158285\pi\) | ||||
0.878889 | + | 0.477026i | \(0.158285\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.6155 | 1.51935 | 0.759673 | − | 0.650306i | \(-0.225359\pi\) | ||||
0.759673 | + | 0.650306i | \(0.225359\pi\) | |||||||
\(434\) | −42.7386 | −2.05152 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.876894 | 0.0419956 | ||||||||
\(437\) | −20.4924 | −0.980286 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.0540 | −0.718487 | −0.359244 | − | 0.933244i | \(-0.616965\pi\) | ||||
−0.359244 | + | 0.933244i | \(0.616965\pi\) | |||||||
\(440\) | −6.24621 | −0.297776 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.8078 | 0.608515 | 0.304258 | − | 0.952590i | \(-0.401592\pi\) | ||||
0.304258 | + | 0.952590i | \(0.401592\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.68466 | −0.0798605 | ||||||||
\(446\) | −14.6307 | −0.692783 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 25.3693 | 1.19859 | ||||||||
\(449\) | −10.1771 | −0.480286 | −0.240143 | − | 0.970738i | \(-0.577194\pi\) | ||||
−0.240143 | + | 0.970738i | \(0.577194\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.43845 | −0.0677338 | ||||||||
\(452\) | −5.75379 | −0.270635 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −34.7386 | −1.63036 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.6847 | 1.20148 | 0.600739 | − | 0.799445i | \(-0.294873\pi\) | ||||
0.600739 | + | 0.799445i | \(0.294873\pi\) | |||||||
\(458\) | −13.8617 | −0.647717 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.87689 | −0.134136 | ||||||||
\(461\) | 29.0540 | 1.35318 | 0.676589 | − | 0.736361i | \(-0.263457\pi\) | ||||
0.676589 | + | 0.736361i | \(0.263457\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.0691303 | 0.00321276 | 0.00160638 | − | 0.999999i | \(-0.499489\pi\) | ||||
0.00160638 | + | 0.999999i | \(0.499489\pi\) | |||||||
\(464\) | −5.26137 | −0.244253 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.2311 | −0.520269 | ||||||||
\(467\) | −21.9309 | −1.01484 | −0.507420 | − | 0.861699i | \(-0.669401\pi\) | ||||
−0.507420 | + | 0.861699i | \(0.669401\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −60.9848 | −2.81602 | ||||||||
\(470\) | 4.49242 | 0.207220 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 29.2614 | 1.34686 | ||||||||
\(473\) | 13.1231 | 0.603401 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.12311 | −0.143298 | ||||||||
\(476\) | −5.12311 | −0.234817 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9.26137 | 0.423605 | ||||||||
\(479\) | 11.0540 | 0.505069 | 0.252535 | − | 0.967588i | \(-0.418736\pi\) | ||||
0.252535 | + | 0.967588i | \(0.418736\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 38.6307 | 1.75958 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.94602 | −0.0884557 | ||||||||
\(485\) | −11.9309 | −0.541753 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.05398 | −0.229017 | −0.114509 | − | 0.993422i | \(-0.536529\pi\) | ||||
−0.114509 | + | 0.993422i | \(0.536529\pi\) | |||||||
\(488\) | −13.8617 | −0.627491 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −21.5616 | −0.974052 | ||||||||
\(491\) | 13.6155 | 0.614460 | 0.307230 | − | 0.951635i | \(-0.400598\pi\) | ||||
0.307230 | + | 0.951635i | \(0.400598\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.87689 | −0.129569 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 28.1080 | 1.26208 | ||||||||
\(497\) | −66.4233 | −2.97949 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.9848 | 1.38707 | 0.693536 | − | 0.720422i | \(-0.256052\pi\) | ||||
0.693536 | + | 0.720422i | \(0.256052\pi\) | |||||||
\(500\) | −0.438447 | −0.0196080 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 15.2311 | 0.679795 | ||||||||
\(503\) | 30.2462 | 1.34861 | 0.674306 | − | 0.738452i | \(-0.264443\pi\) | ||||
0.674306 | + | 0.738452i | \(0.264443\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.24621 | 0.277953 | ||||||||
\(506\) | −26.2462 | −1.16679 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.00000 | 0.354943 | ||||||||
\(509\) | 19.4384 | 0.861594 | 0.430797 | − | 0.902449i | \(-0.358232\pi\) | ||||
0.430797 | + | 0.902449i | \(0.358232\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.3693 | 1.21075 | ||||||||
\(512\) | −11.4233 | −0.504843 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −32.9848 | −1.45490 | ||||||||
\(515\) | 6.87689 | 0.303032 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.36932 | 0.324102 | ||||||||
\(518\) | −12.0000 | −0.527250 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.8617 | 1.39589 | 0.697944 | − | 0.716152i | \(-0.254098\pi\) | ||||
0.697944 | + | 0.716152i | \(0.254098\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.7386 | 0.819383 | 0.409692 | − | 0.912224i | \(-0.365636\pi\) | ||||
0.409692 | + | 0.912224i | \(0.365636\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.2462 | 0.969981 | ||||||||
\(527\) | 15.3693 | 0.669498 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.0540 | 0.871912 | ||||||||
\(530\) | −12.0000 | −0.521247 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6.24621 | −0.270808 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.9309 | 0.775219 | ||||||||
\(536\) | 32.6004 | 1.40812 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −14.2462 | −0.614198 | ||||||||
\(539\) | −35.3693 | −1.52346 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.1231 | −1.16611 | −0.583057 | − | 0.812431i | \(-0.698143\pi\) | ||||
−0.583057 | + | 0.812431i | \(0.698143\pi\) | |||||||
\(542\) | −8.38447 | −0.360144 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.24621 | 0.267804 | ||||||||
\(545\) | −2.00000 | −0.0856706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.3693 | 0.828172 | 0.414086 | − | 0.910238i | \(-0.364101\pi\) | ||||
0.414086 | + | 0.910238i | \(0.364101\pi\) | |||||||
\(548\) | 3.12311 | 0.133412 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.00000 | −0.170561 | ||||||||
\(551\) | −3.50758 | −0.149428 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −35.0540 | −1.49065 | ||||||||
\(554\) | 6.63068 | 0.281711 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.87689 | 0.291645 | ||||||||
\(557\) | 26.4924 | 1.12252 | 0.561260 | − | 0.827640i | \(-0.310317\pi\) | ||||
0.561260 | + | 0.827640i | \(0.310317\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 21.3693 | 0.903018 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 19.1231 | 0.806660 | ||||||||
\(563\) | −31.6847 | −1.33535 | −0.667675 | − | 0.744453i | \(-0.732710\pi\) | ||||
−0.667675 | + | 0.744453i | \(0.732710\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.1231 | 0.552093 | ||||||||
\(566\) | −6.24621 | −0.262548 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 35.5076 | 1.48986 | ||||||||
\(569\) | −41.1231 | −1.72397 | −0.861985 | − | 0.506934i | \(-0.830779\pi\) | ||||
−0.861985 | + | 0.506934i | \(0.830779\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.0540 | 0.629989 | 0.314995 | − | 0.949093i | \(-0.397997\pi\) | ||||
0.314995 | + | 0.949093i | \(0.397997\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.00000 | 0.166957 | ||||||||
\(575\) | 6.56155 | 0.273636 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.5616 | −1.18903 | −0.594517 | − | 0.804083i | \(-0.702657\pi\) | ||||
−0.594517 | + | 0.804083i | \(0.702657\pi\) | |||||||
\(578\) | −16.3002 | −0.677998 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.492423 | −0.0204467 | ||||||||
\(581\) | −75.2311 | −3.12111 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −19.6847 | −0.815255 | ||||||||
\(584\) | −14.6307 | −0.605422 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.86174 | 0.242146 | ||||||||
\(587\) | −0.492423 | −0.0203245 | −0.0101622 | − | 0.999948i | \(-0.503235\pi\) | ||||
−0.0101622 | + | 0.999948i | \(0.503235\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.7386 | 0.772112 | ||||||||
\(590\) | 18.7386 | 0.771457 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 7.89205 | 0.324361 | ||||||||
\(593\) | −7.75379 | −0.318410 | −0.159205 | − | 0.987246i | \(-0.550893\pi\) | ||||
−0.159205 | + | 0.987246i | \(0.550893\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.6847 | 0.479024 | ||||||||
\(596\) | −1.23106 | −0.0504260 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.3693 | 0.627973 | 0.313987 | − | 0.949427i | \(-0.398335\pi\) | ||||
0.313987 | + | 0.949427i | \(0.398335\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 41.5464 | 1.69471 | 0.847356 | − | 0.531025i | \(-0.178193\pi\) | ||||
0.847356 | + | 0.531025i | \(0.178193\pi\) | |||||||
\(602\) | −36.4924 | −1.48732 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.86174 | 0.238511 | ||||||||
\(605\) | 4.43845 | 0.180449 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.0000 | −0.974130 | −0.487065 | − | 0.873366i | \(-0.661933\pi\) | ||||
−0.487065 | + | 0.873366i | \(0.661933\pi\) | |||||||
\(608\) | 7.61553 | 0.308850 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.87689 | −0.359415 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −37.5464 | −1.51648 | −0.758242 | − | 0.651973i | \(-0.773942\pi\) | ||||
−0.758242 | + | 0.651973i | \(0.773942\pi\) | |||||||
\(614\) | −5.36932 | −0.216688 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 28.4924 | 1.14799 | ||||||||
\(617\) | 48.7386 | 1.96214 | 0.981072 | − | 0.193645i | \(-0.0620308\pi\) | ||||
0.981072 | + | 0.193645i | \(0.0620308\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.3693 | 1.34123 | 0.670613 | − | 0.741807i | \(-0.266031\pi\) | ||||
0.670613 | + | 0.741807i | \(0.266031\pi\) | |||||||
\(620\) | 2.63068 | 0.105651 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 42.7386 | 1.71366 | ||||||||
\(623\) | 7.68466 | 0.307879 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 32.6004 | 1.30297 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9.36932 | −0.373876 | ||||||||
\(629\) | 4.31534 | 0.172064 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.7386 | −0.666354 | −0.333177 | − | 0.942864i | \(-0.608121\pi\) | ||||
−0.333177 | + | 0.942864i | \(0.608121\pi\) | |||||||
\(632\) | 18.7386 | 0.745383 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −53.8617 | −2.13912 | ||||||||
\(635\) | −18.2462 | −0.724079 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4.49242 | −0.177857 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −13.5616 | −0.536067 | ||||||||
\(641\) | 32.9848 | 1.30282 | 0.651412 | − | 0.758725i | \(-0.274177\pi\) | ||||
0.651412 | + | 0.758725i | \(0.274177\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.68466 | −0.0664364 | −0.0332182 | − | 0.999448i | \(-0.510576\pi\) | ||||
−0.0332182 | + | 0.999448i | \(0.510576\pi\) | |||||||
\(644\) | 13.1231 | 0.517123 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.4924 | 0.491508 | ||||||||
\(647\) | 11.1922 | 0.440012 | 0.220006 | − | 0.975498i | \(-0.429392\pi\) | ||||
0.220006 | + | 0.975498i | \(0.429392\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 30.7386 | 1.20660 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.23106 | 0.361516 | ||||||||
\(653\) | −8.63068 | −0.337745 | −0.168872 | − | 0.985638i | \(-0.554013\pi\) | ||||
−0.168872 | + | 0.985638i | \(0.554013\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.63068 | −0.102711 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −20.4924 | −0.798878 | ||||||||
\(659\) | 9.12311 | 0.355386 | 0.177693 | − | 0.984086i | \(-0.443137\pi\) | ||||
0.177693 | + | 0.984086i | \(0.443137\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.4924 | 1.03044 | 0.515218 | − | 0.857059i | \(-0.327711\pi\) | ||||
0.515218 | + | 0.857059i | \(0.327711\pi\) | |||||||
\(662\) | −32.6004 | −1.26705 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 40.2159 | 1.56068 | ||||||||
\(665\) | 14.2462 | 0.552444 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.36932 | 0.285341 | ||||||||
\(668\) | −5.75379 | −0.222621 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 20.8769 | 0.806545 | ||||||||
\(671\) | −14.5616 | −0.562143 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32.7386 | −1.26198 | −0.630991 | − | 0.775790i | \(-0.717351\pi\) | ||||
−0.630991 | + | 0.775790i | \(0.717351\pi\) | |||||||
\(674\) | 3.89205 | 0.149916 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.5616 | −0.713378 | −0.356689 | − | 0.934223i | \(-0.616094\pi\) | ||||
−0.356689 | + | 0.934223i | \(0.616094\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 54.4233 | 2.08857 | ||||||||
\(680\) | −6.24621 | −0.239531 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 24.0000 | 0.919007 | ||||||||
\(683\) | 0.492423 | 0.0188420 | 0.00942101 | − | 0.999956i | \(-0.497001\pi\) | ||||
0.00942101 | + | 0.999956i | \(0.497001\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.12311 | −0.272160 | ||||||||
\(686\) | 48.4924 | 1.85145 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 24.0000 | 0.914991 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.6155 | −0.746210 | −0.373105 | − | 0.927789i | \(-0.621707\pi\) | ||||
−0.373105 | + | 0.927789i | \(0.621707\pi\) | |||||||
\(692\) | 9.26137 | 0.352064 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 17.2614 | 0.655233 | ||||||||
\(695\) | −15.6847 | −0.594953 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.43845 | −0.0544851 | ||||||||
\(698\) | −2.13826 | −0.0809344 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.00000 | 0.0755929 | ||||||||
\(701\) | 16.9848 | 0.641509 | 0.320754 | − | 0.947162i | \(-0.396064\pi\) | ||||
0.320754 | + | 0.947162i | \(0.396064\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.26137 | 0.198436 | ||||||||
\(704\) | −14.2462 | −0.536924 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −16.3845 | −0.616638 | ||||||||
\(707\) | −28.4924 | −1.07157 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.876894 | −0.0329325 | −0.0164662 | − | 0.999864i | \(-0.505242\pi\) | ||||
−0.0164662 | + | 0.999864i | \(0.505242\pi\) | |||||||
\(710\) | 22.7386 | 0.853366 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.10795 | −0.153952 | ||||||||
\(713\) | −39.3693 | −1.47439 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.75379 | −0.215029 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.50758 | −0.130902 | ||||||||
\(719\) | 36.0000 | 1.34257 | 0.671287 | − | 0.741198i | \(-0.265742\pi\) | ||||
0.671287 | + | 0.741198i | \(0.265742\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −31.3693 | −1.16825 | ||||||||
\(722\) | −14.4384 | −0.537343 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 11.2614 | 0.418525 | ||||||||
\(725\) | 1.12311 | 0.0417111 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.1231 | 0.783413 | 0.391706 | − | 0.920090i | \(-0.371885\pi\) | ||||
0.391706 | + | 0.920090i | \(0.371885\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −9.36932 | −0.346774 | ||||||||
\(731\) | 13.1231 | 0.485376 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.5616 | 0.759458 | 0.379729 | − | 0.925098i | \(-0.376017\pi\) | ||||
0.379729 | + | 0.925098i | \(0.376017\pi\) | |||||||
\(734\) | −28.4924 | −1.05167 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −16.0000 | −0.589768 | ||||||||
\(737\) | 34.2462 | 1.26148 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.738634 | 0.0271711 | 0.0135855 | − | 0.999908i | \(-0.495675\pi\) | ||||
0.0135855 | + | 0.999908i | \(0.495675\pi\) | |||||||
\(740\) | 0.738634 | 0.0271527 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 54.7386 | 2.00952 | ||||||||
\(743\) | 30.7386 | 1.12769 | 0.563846 | − | 0.825880i | \(-0.309321\pi\) | ||||
0.563846 | + | 0.825880i | \(0.309321\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.80776 | 0.102869 | ||||||||
\(746\) | −6.63068 | −0.242767 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.87689 | 0.105190 | ||||||||
\(749\) | −81.7926 | −2.98864 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.0540 | −0.841252 | −0.420626 | − | 0.907234i | \(-0.638189\pi\) | ||||
−0.420626 | + | 0.907234i | \(0.638189\pi\) | |||||||
\(752\) | 13.4773 | 0.491465 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13.3693 | −0.486559 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.4924 | 0.672119 | 0.336059 | − | 0.941841i | \(-0.390906\pi\) | ||||
0.336059 | + | 0.941841i | \(0.390906\pi\) | |||||||
\(758\) | −3.89205 | −0.141366 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7.61553 | −0.276244 | ||||||||
\(761\) | 37.2311 | 1.34962 | 0.674812 | − | 0.737989i | \(-0.264225\pi\) | ||||
0.674812 | + | 0.737989i | \(0.264225\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.12311 | 0.330279 | ||||||||
\(764\) | −9.47727 | −0.342876 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −56.9848 | −2.05895 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.0000 | 1.08183 | 0.540914 | − | 0.841078i | \(-0.318079\pi\) | ||||
0.540914 | + | 0.841078i | \(0.318079\pi\) | |||||||
\(770\) | 18.2462 | 0.657548 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.76894 | −0.243620 | ||||||||
\(773\) | 0.876894 | 0.0315397 | 0.0157698 | − | 0.999876i | \(-0.494980\pi\) | ||||
0.0157698 | + | 0.999876i | \(0.494980\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.00000 | −0.215526 | ||||||||
\(776\) | −29.0928 | −1.04437 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −31.0152 | −1.11195 | ||||||||
\(779\) | −1.75379 | −0.0628360 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 37.3002 | 1.33471 | ||||||||
\(782\) | −26.2462 | −0.938563 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −64.6847 | −2.31017 | ||||||||
\(785\) | 21.3693 | 0.762704 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.3693 | 0.476565 | 0.238282 | − | 0.971196i | \(-0.423416\pi\) | ||||
0.238282 | + | 0.971196i | \(0.423416\pi\) | |||||||
\(788\) | −9.36932 | −0.333768 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 12.0000 | 0.426941 | ||||||||
\(791\) | −59.8617 | −2.12844 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 13.3693 | 0.474459 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.50758 | −0.124323 | ||||||||
\(797\) | −7.68466 | −0.272205 | −0.136102 | − | 0.990695i | \(-0.543458\pi\) | ||||
−0.136102 | + | 0.990695i | \(0.543458\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.36932 | 0.260708 | ||||||||
\(800\) | −2.43845 | −0.0862121 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −31.6155 | −1.11638 | ||||||||
\(803\) | −15.3693 | −0.542371 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −29.9309 | −1.05492 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 15.2311 | 0.535827 | ||||||||
\(809\) | 40.4924 | 1.42364 | 0.711819 | − | 0.702363i | \(-0.247872\pi\) | ||||
0.711819 | + | 0.702363i | \(0.247872\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.2462 | 0.430023 | 0.215011 | − | 0.976612i | \(-0.431021\pi\) | ||||
0.215011 | + | 0.976612i | \(0.431021\pi\) | |||||||
\(812\) | 2.24621 | 0.0788266 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.73863 | 0.236189 | ||||||||
\(815\) | −21.0540 | −0.737489 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.0000 | 0.559769 | ||||||||
\(818\) | 23.6155 | 0.825698 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.246211 | −0.00859807 | ||||||||
\(821\) | 21.5464 | 0.751974 | 0.375987 | − | 0.926625i | \(-0.377304\pi\) | ||||
0.375987 | + | 0.926625i | \(0.377304\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −46.2462 | −1.61204 | −0.806021 | − | 0.591887i | \(-0.798383\pi\) | ||||
−0.806021 | + | 0.591887i | \(0.798383\pi\) | |||||||
\(824\) | 16.7689 | 0.584174 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −85.4773 | −2.97413 | ||||||||
\(827\) | 1.12311 | 0.0390542 | 0.0195271 | − | 0.999809i | \(-0.493784\pi\) | ||||
0.0195271 | + | 0.999809i | \(0.493784\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −48.7386 | −1.69276 | −0.846381 | − | 0.532577i | \(-0.821224\pi\) | ||||
−0.846381 | + | 0.532577i | \(0.821224\pi\) | |||||||
\(830\) | 25.7538 | 0.893927 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −35.3693 | −1.22547 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.1231 | 0.454144 | ||||||||
\(836\) | 3.50758 | 0.121312 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −52.4924 | −1.81332 | ||||||||
\(839\) | −41.7926 | −1.44284 | −0.721421 | − | 0.692497i | \(-0.756510\pi\) | ||||
−0.721421 | + | 0.692497i | \(0.756510\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.7386 | −0.956505 | ||||||||
\(842\) | −22.8466 | −0.787345 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.49242 | −0.154636 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.2462 | −0.695668 | ||||||||
\(848\) | −36.0000 | −1.23625 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4.00000 | −0.137199 | ||||||||
\(851\) | −11.0540 | −0.378925 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.4233 | 0.699280 | 0.349640 | − | 0.936884i | \(-0.386304\pi\) | ||||
0.349640 | + | 0.936884i | \(0.386304\pi\) | |||||||
\(854\) | 40.4924 | 1.38562 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 43.7235 | 1.49444 | ||||||||
\(857\) | 6.56155 | 0.224138 | 0.112069 | − | 0.993700i | \(-0.464252\pi\) | ||||
0.112069 | + | 0.993700i | \(0.464252\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.8078 | −0.573474 | −0.286737 | − | 0.958009i | \(-0.592571\pi\) | ||||
−0.286737 | + | 0.958009i | \(0.592571\pi\) | |||||||
\(860\) | 2.24621 | 0.0765952 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 56.9848 | 1.94091 | ||||||||
\(863\) | −15.3693 | −0.523178 | −0.261589 | − | 0.965179i | \(-0.584246\pi\) | ||||
−0.261589 | + | 0.965179i | \(0.584246\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.1231 | −0.718207 | ||||||||
\(866\) | 49.3693 | 1.67764 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −12.0000 | −0.407307 | ||||||||
\(869\) | 19.6847 | 0.667756 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −4.87689 | −0.165152 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −32.0000 | −1.08242 | ||||||||
\(875\) | −4.56155 | −0.154209 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.9848 | 0.641073 | 0.320536 | − | 0.947236i | \(-0.396137\pi\) | ||||
0.320536 | + | 0.947236i | \(0.396137\pi\) | |||||||
\(878\) | −23.5076 | −0.793342 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −12.0000 | −0.404520 | ||||||||
\(881\) | 3.36932 | 0.113515 | 0.0567576 | − | 0.998388i | \(-0.481924\pi\) | ||||
0.0567576 | + | 0.998388i | \(0.481924\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.1080 | 0.609381 | 0.304691 | − | 0.952451i | \(-0.401447\pi\) | ||||
0.304691 | + | 0.952451i | \(0.401447\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 20.0000 | 0.671913 | ||||||||
\(887\) | 1.43845 | 0.0482983 | 0.0241492 | − | 0.999708i | \(-0.492312\pi\) | ||||
0.0241492 | + | 0.999708i | \(0.492312\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 83.2311 | 2.79148 | ||||||||
\(890\) | −2.63068 | −0.0881807 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.10795 | −0.137544 | ||||||||
\(893\) | 8.98485 | 0.300666 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.1231 | 0.438657 | ||||||||
\(896\) | 61.8617 | 2.06666 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −15.8920 | −0.530325 | ||||||||
\(899\) | −6.73863 | −0.224746 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.6847 | −0.655791 | ||||||||
\(902\) | −2.24621 | −0.0747907 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 32.0000 | 1.06430 | ||||||||
\(905\) | −25.6847 | −0.853787 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27.3693 | −0.908783 | −0.454392 | − | 0.890802i | \(-0.650143\pi\) | ||||
−0.454392 | + | 0.890802i | \(0.650143\pi\) | |||||||
\(908\) | −9.75379 | −0.323691 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.0000 | −0.397578 | −0.198789 | − | 0.980042i | \(-0.563701\pi\) | ||||
−0.198789 | + | 0.980042i | \(0.563701\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 42.2462 | 1.39815 | ||||||||
\(914\) | 40.1080 | 1.32665 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.89205 | −0.128597 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 39.0540 | 1.28827 | 0.644136 | − | 0.764911i | \(-0.277217\pi\) | ||||
0.644136 | + | 0.764911i | \(0.277217\pi\) | |||||||
\(920\) | 16.0000 | 0.527504 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 45.3693 | 1.49416 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.68466 | −0.0553912 | ||||||||
\(926\) | 0.107951 | 0.00354748 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.73863 | −0.0899001 | ||||||||
\(929\) | 38.6695 | 1.26871 | 0.634353 | − | 0.773044i | \(-0.281267\pi\) | ||||
0.634353 | + | 0.773044i | \(0.281267\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −43.1231 | −1.41330 | ||||||||
\(932\) | −3.15342 | −0.103294 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −34.2462 | −1.12057 | ||||||||
\(935\) | −6.56155 | −0.214586 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.63068 | −0.0859407 | −0.0429703 | − | 0.999076i | \(-0.513682\pi\) | ||||
−0.0429703 | + | 0.999076i | \(0.513682\pi\) | |||||||
\(938\) | −95.2311 | −3.10940 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.26137 | 0.0411412 | ||||||||
\(941\) | 21.1922 | 0.690847 | 0.345424 | − | 0.938447i | \(-0.387735\pi\) | ||||
0.345424 | + | 0.938447i | \(0.387735\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.68466 | 0.119989 | ||||||||
\(944\) | 56.2159 | 1.82967 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 20.4924 | 0.666266 | ||||||||
\(947\) | 46.6004 | 1.51431 | 0.757154 | − | 0.653236i | \(-0.226589\pi\) | ||||
0.757154 | + | 0.653236i | \(0.226589\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −4.87689 | −0.158227 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 28.4924 | 0.923445 | ||||||||
\(953\) | 25.4384 | 0.824032 | 0.412016 | − | 0.911177i | \(-0.364825\pi\) | ||||
0.412016 | + | 0.911177i | \(0.364825\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.6155 | 0.699462 | ||||||||
\(956\) | 2.60037 | 0.0841021 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 17.2614 | 0.557689 | ||||||||
\(959\) | 32.4924 | 1.04924 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10.8466 | 0.349345 | ||||||||
\(965\) | 15.4384 | 0.496981 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.3693 | −0.558560 | −0.279280 | − | 0.960210i | \(-0.590096\pi\) | ||||
−0.279280 | + | 0.960210i | \(0.590096\pi\) | |||||||
\(968\) | 10.8229 | 0.347862 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −18.6307 | −0.598195 | ||||||||
\(971\) | 8.49242 | 0.272535 | 0.136267 | − | 0.990672i | \(-0.456489\pi\) | ||||
0.136267 | + | 0.990672i | \(0.456489\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 71.5464 | 2.29367 | ||||||||
\(974\) | −7.89205 | −0.252878 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −26.6307 | −0.852427 | ||||||||
\(977\) | −55.4773 | −1.77488 | −0.887438 | − | 0.460928i | \(-0.847517\pi\) | ||||
−0.887438 | + | 0.460928i | \(0.847517\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.31534 | −0.137919 | ||||||||
\(980\) | −6.05398 | −0.193387 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 21.2614 | 0.678477 | ||||||||
\(983\) | 6.73863 | 0.214929 | 0.107465 | − | 0.994209i | \(-0.465727\pi\) | ||||
0.107465 | + | 0.994209i | \(0.465727\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21.3693 | 0.680883 | ||||||||
\(986\) | −4.49242 | −0.143068 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −33.6155 | −1.06891 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.0540 | −0.859398 | −0.429699 | − | 0.902972i | \(-0.641380\pi\) | ||||
−0.429699 | + | 0.902972i | \(0.641380\pi\) | |||||||
\(992\) | 14.6307 | 0.464525 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −103.723 | −3.28991 | ||||||||
\(995\) | 8.00000 | 0.253617 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.7538 | 0.372246 | 0.186123 | − | 0.982526i | \(-0.440408\pi\) | ||||
0.186123 | + | 0.982526i | \(0.440408\pi\) | |||||||
\(998\) | 48.3845 | 1.53158 | ||||||||
\(999\) | 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 | 7605.2.a.bd.1.2 | 2 | ||
3.2 | odd | 2 | 7605.2.a.bi.1.1 | 2 | |||
13.12 | even | 2 | 585.2.a.l.1.1 | yes | 2 | ||
39.38 | odd | 2 | 585.2.a.j.1.2 | ✓ | 2 | ||
52.51 | odd | 2 | 9360.2.a.cw.1.2 | 2 | |||
65.12 | odd | 4 | 2925.2.c.p.2224.2 | 4 | |||
65.38 | odd | 4 | 2925.2.c.p.2224.3 | 4 | |||
65.64 | even | 2 | 2925.2.a.x.1.2 | 2 | |||
156.155 | even | 2 | 9360.2.a.cl.1.2 | 2 | |||
195.38 | even | 4 | 2925.2.c.o.2224.2 | 4 | |||
195.77 | even | 4 | 2925.2.c.o.2224.3 | 4 | |||
195.194 | odd | 2 | 2925.2.a.bc.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
585.2.a.j.1.2 | ✓ | 2 | 39.38 | odd | 2 | ||
585.2.a.l.1.1 | yes | 2 | 13.12 | even | 2 | ||
2925.2.a.x.1.2 | 2 | 65.64 | even | 2 | |||
2925.2.a.bc.1.1 | 2 | 195.194 | odd | 2 | |||
2925.2.c.o.2224.2 | 4 | 195.38 | even | 4 | |||
2925.2.c.o.2224.3 | 4 | 195.77 | even | 4 | |||
2925.2.c.p.2224.2 | 4 | 65.12 | odd | 4 | |||
2925.2.c.p.2224.3 | 4 | 65.38 | odd | 4 | |||
7605.2.a.bd.1.2 | 2 | 1.1 | even | 1 | trivial | ||
7605.2.a.bi.1.1 | 2 | 3.2 | odd | 2 | |||
9360.2.a.cl.1.2 | 2 | 156.155 | even | 2 | |||
9360.2.a.cw.1.2 | 2 | 52.51 | odd | 2 |