Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5265,2,Mod(1,5265)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5265, 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("5265.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5265 = 3^{4} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5265.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: | \(42.0412366642\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 8x^{6} + 31x^{5} - x^{4} - 70x^{3} + 66x^{2} - 19x + 1 \) |
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 | 1.6 | ||
Root | \(1.63404\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5265.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.63404 | 1.15544 | 0.577719 | − | 0.816235i | \(-0.303943\pi\) | ||||
0.577719 | + | 0.816235i | \(0.303943\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.670078 | 0.335039 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.13012 | 0.805108 | 0.402554 | − | 0.915396i | \(-0.368123\pi\) | ||||
0.402554 | + | 0.915396i | \(0.368123\pi\) | |||||||
\(8\) | −2.17314 | −0.768322 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.63404 | −0.516728 | ||||||||
\(11\) | −0.0526457 | −0.0158733 | −0.00793664 | − | 0.999969i | \(-0.502526\pi\) | ||||
−0.00793664 | + | 0.999969i | \(0.502526\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 3.48069 | 0.930253 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.89115 | −1.22279 | ||||||||
\(17\) | −2.48047 | −0.601603 | −0.300801 | − | 0.953687i | \(-0.597254\pi\) | ||||
−0.300801 | + | 0.953687i | \(0.597254\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.13105 | 0.488895 | 0.244448 | − | 0.969662i | \(-0.421393\pi\) | ||||
0.244448 | + | 0.969662i | \(0.421393\pi\) | |||||||
\(20\) | −0.670078 | −0.149834 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.0860250 | −0.0183406 | ||||||||
\(23\) | 4.93083 | 1.02815 | 0.514075 | − | 0.857745i | \(-0.328135\pi\) | ||||
0.514075 | + | 0.857745i | \(0.328135\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.63404 | −0.320461 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.42734 | 0.269743 | ||||||||
\(29\) | −2.48694 | −0.461812 | −0.230906 | − | 0.972976i | \(-0.574169\pi\) | ||||
−0.230906 | + | 0.972976i | \(0.574169\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.16059 | −1.46569 | −0.732843 | − | 0.680398i | \(-0.761807\pi\) | ||||
−0.732843 | + | 0.680398i | \(0.761807\pi\) | |||||||
\(32\) | −3.64604 | −0.644535 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.05318 | −0.695115 | ||||||||
\(35\) | −2.13012 | −0.360055 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.11963 | −0.184066 | −0.0920331 | − | 0.995756i | \(-0.529337\pi\) | ||||
−0.0920331 | + | 0.995756i | \(0.529337\pi\) | |||||||
\(38\) | 3.48221 | 0.564889 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.17314 | 0.343604 | ||||||||
\(41\) | −5.47417 | −0.854922 | −0.427461 | − | 0.904034i | \(-0.640592\pi\) | ||||
−0.427461 | + | 0.904034i | \(0.640592\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.47722 | −1.44526 | −0.722632 | − | 0.691233i | \(-0.757068\pi\) | ||||
−0.722632 | + | 0.691233i | \(0.757068\pi\) | |||||||
\(44\) | −0.0352767 | −0.00531816 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.05716 | 1.18796 | ||||||||
\(47\) | 9.76560 | 1.42446 | 0.712230 | − | 0.701946i | \(-0.247685\pi\) | ||||
0.712230 | + | 0.701946i | \(0.247685\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.46260 | −0.351801 | ||||||||
\(50\) | 1.63404 | 0.231088 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.670078 | −0.0929231 | ||||||||
\(53\) | −3.64091 | −0.500118 | −0.250059 | − | 0.968231i | \(-0.580450\pi\) | ||||
−0.250059 | + | 0.968231i | \(0.580450\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.0526457 | 0.00709875 | ||||||||
\(56\) | −4.62905 | −0.618582 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.06374 | −0.533596 | ||||||||
\(59\) | 7.49087 | 0.975228 | 0.487614 | − | 0.873059i | \(-0.337867\pi\) | ||||
0.487614 | + | 0.873059i | \(0.337867\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.78404 | −0.740570 | −0.370285 | − | 0.928918i | \(-0.620740\pi\) | ||||
−0.370285 | + | 0.928918i | \(0.620740\pi\) | |||||||
\(62\) | −13.3347 | −1.69351 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.82454 | 0.478067 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.23591 | −0.761837 | −0.380919 | − | 0.924609i | \(-0.624392\pi\) | ||||
−0.380919 | + | 0.924609i | \(0.624392\pi\) | |||||||
\(68\) | −1.66211 | −0.201560 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.48069 | −0.416022 | ||||||||
\(71\) | 2.50050 | 0.296755 | 0.148377 | − | 0.988931i | \(-0.452595\pi\) | ||||
0.148377 | + | 0.988931i | \(0.452595\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.10245 | −0.129032 | −0.0645159 | − | 0.997917i | \(-0.520550\pi\) | ||||
−0.0645159 | + | 0.997917i | \(0.520550\pi\) | |||||||
\(74\) | −1.82952 | −0.212677 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.42797 | 0.163799 | ||||||||
\(77\) | −0.112141 | −0.0127797 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.6156 | −1.75689 | −0.878445 | − | 0.477844i | \(-0.841418\pi\) | ||||
−0.878445 | + | 0.477844i | \(0.841418\pi\) | |||||||
\(80\) | 4.89115 | 0.546847 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8.94500 | −0.987810 | ||||||||
\(83\) | 0.489152 | 0.0536914 | 0.0268457 | − | 0.999640i | \(-0.491454\pi\) | ||||
0.0268457 | + | 0.999640i | \(0.491454\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.48047 | 0.269045 | ||||||||
\(86\) | −15.4861 | −1.66991 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.114407 | 0.0121958 | ||||||||
\(89\) | −4.64901 | −0.492794 | −0.246397 | − | 0.969169i | \(-0.579247\pi\) | ||||
−0.246397 | + | 0.969169i | \(0.579247\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.13012 | −0.223297 | ||||||||
\(92\) | 3.30404 | 0.344470 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 15.9574 | 1.64588 | ||||||||
\(95\) | −2.13105 | −0.218641 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.34097 | 0.745363 | 0.372682 | − | 0.927959i | \(-0.378438\pi\) | ||||
0.372682 | + | 0.927959i | \(0.378438\pi\) | |||||||
\(98\) | −4.02399 | −0.406484 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.670078 | 0.0670078 | ||||||||
\(101\) | 0.552859 | 0.0550115 | 0.0275058 | − | 0.999622i | \(-0.491244\pi\) | ||||
0.0275058 | + | 0.999622i | \(0.491244\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.83795 | −0.772296 | −0.386148 | − | 0.922437i | \(-0.626195\pi\) | ||||
−0.386148 | + | 0.922437i | \(0.626195\pi\) | |||||||
\(104\) | 2.17314 | 0.213094 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.94939 | −0.577855 | ||||||||
\(107\) | 19.4173 | 1.87714 | 0.938572 | − | 0.345084i | \(-0.112149\pi\) | ||||
0.938572 | + | 0.345084i | \(0.112149\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.13502 | −0.204498 | −0.102249 | − | 0.994759i | \(-0.532604\pi\) | ||||
−0.102249 | + | 0.994759i | \(0.532604\pi\) | |||||||
\(110\) | 0.0860250 | 0.00820217 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −10.4187 | −0.984477 | ||||||||
\(113\) | −6.23529 | −0.586567 | −0.293283 | − | 0.956026i | \(-0.594748\pi\) | ||||
−0.293283 | + | 0.956026i | \(0.594748\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.93083 | −0.459802 | ||||||||
\(116\) | −1.66644 | −0.154725 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 12.2404 | 1.12682 | ||||||||
\(119\) | −5.28369 | −0.484355 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9972 | −0.999748 | ||||||||
\(122\) | −9.45133 | −0.855683 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.46823 | −0.491062 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.6036 | −0.940918 | −0.470459 | − | 0.882422i | \(-0.655912\pi\) | ||||
−0.470459 | + | 0.882422i | \(0.655912\pi\) | |||||||
\(128\) | 13.5415 | 1.19691 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.63404 | 0.143315 | ||||||||
\(131\) | −16.1923 | −1.41473 | −0.707365 | − | 0.706849i | \(-0.750116\pi\) | ||||
−0.707365 | + | 0.706849i | \(0.750116\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.53938 | 0.393614 | ||||||||
\(134\) | −10.1897 | −0.880256 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.39042 | 0.462224 | ||||||||
\(137\) | −20.7686 | −1.77438 | −0.887189 | − | 0.461406i | \(-0.847345\pi\) | ||||
−0.887189 | + | 0.461406i | \(0.847345\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.50075 | −0.212111 | −0.106055 | − | 0.994360i | \(-0.533822\pi\) | ||||
−0.106055 | + | 0.994360i | \(0.533822\pi\) | |||||||
\(140\) | −1.42734 | −0.120633 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.08591 | 0.342882 | ||||||||
\(143\) | 0.0526457 | 0.00440245 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.48694 | 0.206529 | ||||||||
\(146\) | −1.80144 | −0.149088 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.750240 | −0.0616693 | ||||||||
\(149\) | −1.89025 | −0.154856 | −0.0774279 | − | 0.996998i | \(-0.524671\pi\) | ||||
−0.0774279 | + | 0.996998i | \(0.524671\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.88685 | −0.397686 | −0.198843 | − | 0.980031i | \(-0.563718\pi\) | ||||
−0.198843 | + | 0.980031i | \(0.563718\pi\) | |||||||
\(152\) | −4.63107 | −0.375629 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.183243 | −0.0147662 | ||||||||
\(155\) | 8.16059 | 0.655475 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.9998 | −1.43654 | −0.718269 | − | 0.695765i | \(-0.755065\pi\) | ||||
−0.718269 | + | 0.695765i | \(0.755065\pi\) | |||||||
\(158\) | −25.5164 | −2.02998 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.64604 | 0.288245 | ||||||||
\(161\) | 10.5032 | 0.827772 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.41748 | 0.737634 | 0.368817 | − | 0.929502i | \(-0.379763\pi\) | ||||
0.368817 | + | 0.929502i | \(0.379763\pi\) | |||||||
\(164\) | −3.66812 | −0.286432 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.799292 | 0.0620371 | ||||||||
\(167\) | −15.4905 | −1.19869 | −0.599344 | − | 0.800492i | \(-0.704572\pi\) | ||||
−0.599344 | + | 0.800492i | \(0.704572\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 4.05318 | 0.310865 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.35048 | −0.484219 | ||||||||
\(173\) | −9.67663 | −0.735700 | −0.367850 | − | 0.929885i | \(-0.619906\pi\) | ||||
−0.367850 | + | 0.929885i | \(0.619906\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.13012 | 0.161022 | ||||||||
\(176\) | 0.257498 | 0.0194096 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.59665 | −0.569393 | ||||||||
\(179\) | −3.31630 | −0.247872 | −0.123936 | − | 0.992290i | \(-0.539552\pi\) | ||||
−0.123936 | + | 0.992290i | \(0.539552\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.6189 | −1.68125 | −0.840623 | − | 0.541621i | \(-0.817811\pi\) | ||||
−0.840623 | + | 0.541621i | \(0.817811\pi\) | |||||||
\(182\) | −3.48069 | −0.258006 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −10.7154 | −0.789950 | ||||||||
\(185\) | 1.11963 | 0.0823169 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.130586 | 0.00954940 | ||||||||
\(188\) | 6.54371 | 0.477249 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.48221 | −0.252626 | ||||||||
\(191\) | 5.88211 | 0.425614 | 0.212807 | − | 0.977094i | \(-0.431739\pi\) | ||||
0.212807 | + | 0.977094i | \(0.431739\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.459539 | −0.0330783 | −0.0165392 | − | 0.999863i | \(-0.505265\pi\) | ||||
−0.0165392 | + | 0.999863i | \(0.505265\pi\) | |||||||
\(194\) | 11.9954 | 0.861221 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.65014 | −0.117867 | ||||||||
\(197\) | −2.31119 | −0.164665 | −0.0823326 | − | 0.996605i | \(-0.526237\pi\) | ||||
−0.0823326 | + | 0.996605i | \(0.526237\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.3734 | 1.72779 | 0.863893 | − | 0.503675i | \(-0.168019\pi\) | ||||
0.863893 | + | 0.503675i | \(0.168019\pi\) | |||||||
\(200\) | −2.17314 | −0.153664 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.903392 | 0.0635624 | ||||||||
\(203\) | −5.29746 | −0.371809 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.47417 | 0.382333 | ||||||||
\(206\) | −12.8075 | −0.892341 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.89115 | 0.339140 | ||||||||
\(209\) | −0.112190 | −0.00776037 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 27.3938 | 1.88587 | 0.942934 | − | 0.332980i | \(-0.108054\pi\) | ||||
0.942934 | + | 0.332980i | \(0.108054\pi\) | |||||||
\(212\) | −2.43969 | −0.167559 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 31.7286 | 2.16893 | ||||||||
\(215\) | 9.47722 | 0.646341 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.3830 | −1.18004 | ||||||||
\(218\) | −3.48870 | −0.236285 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.0352767 | 0.00237836 | ||||||||
\(221\) | 2.48047 | 0.166855 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.3359 | 1.69661 | 0.848307 | − | 0.529504i | \(-0.177622\pi\) | ||||
0.848307 | + | 0.529504i | \(0.177622\pi\) | |||||||
\(224\) | −7.76649 | −0.518920 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.1887 | −0.677742 | ||||||||
\(227\) | −21.2417 | −1.40986 | −0.704931 | − | 0.709276i | \(-0.749022\pi\) | ||||
−0.704931 | + | 0.709276i | \(0.749022\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.2337 | 0.808427 | 0.404214 | − | 0.914665i | \(-0.367545\pi\) | ||||
0.404214 | + | 0.914665i | \(0.367545\pi\) | |||||||
\(230\) | −8.05716 | −0.531274 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.40446 | 0.354820 | ||||||||
\(233\) | 11.4048 | 0.747154 | 0.373577 | − | 0.927599i | \(-0.378131\pi\) | ||||
0.373577 | + | 0.927599i | \(0.378131\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.76560 | −0.637038 | ||||||||
\(236\) | 5.01947 | 0.326739 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8.63375 | −0.559643 | ||||||||
\(239\) | 14.8571 | 0.961025 | 0.480512 | − | 0.876988i | \(-0.340451\pi\) | ||||
0.480512 | + | 0.876988i | \(0.340451\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.5908 | −1.19754 | −0.598768 | − | 0.800922i | \(-0.704343\pi\) | ||||
−0.598768 | + | 0.800922i | \(0.704343\pi\) | |||||||
\(242\) | −17.9699 | −1.15515 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.87575 | −0.248120 | ||||||||
\(245\) | 2.46260 | 0.157330 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.13105 | −0.135595 | ||||||||
\(248\) | 17.7341 | 1.12612 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.63404 | −0.103346 | ||||||||
\(251\) | 30.0723 | 1.89815 | 0.949073 | − | 0.315058i | \(-0.102024\pi\) | ||||
0.949073 | + | 0.315058i | \(0.102024\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.259587 | −0.0163201 | ||||||||
\(254\) | −17.3267 | −1.08717 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.4783 | 0.904892 | ||||||||
\(257\) | 3.04064 | 0.189670 | 0.0948348 | − | 0.995493i | \(-0.469768\pi\) | ||||
0.0948348 | + | 0.995493i | \(0.469768\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.38494 | −0.148193 | ||||||||
\(260\) | 0.670078 | 0.0415565 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −26.4588 | −1.63463 | ||||||||
\(263\) | −4.80102 | −0.296044 | −0.148022 | − | 0.988984i | \(-0.547291\pi\) | ||||
−0.148022 | + | 0.988984i | \(0.547291\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.64091 | 0.223659 | ||||||||
\(266\) | 7.41751 | 0.454797 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.17854 | −0.255245 | ||||||||
\(269\) | −16.8723 | −1.02873 | −0.514363 | − | 0.857573i | \(-0.671971\pi\) | ||||
−0.514363 | + | 0.857573i | \(0.671971\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.34099 | −0.142205 | −0.0711026 | − | 0.997469i | \(-0.522652\pi\) | ||||
−0.0711026 | + | 0.997469i | \(0.522652\pi\) | |||||||
\(272\) | 12.1324 | 0.735632 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −33.9366 | −2.05019 | ||||||||
\(275\) | −0.0526457 | −0.00317466 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.77233 | −0.226657 | −0.113329 | − | 0.993558i | \(-0.536151\pi\) | ||||
−0.113329 | + | 0.993558i | \(0.536151\pi\) | |||||||
\(278\) | −4.08632 | −0.245081 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.62905 | 0.276638 | ||||||||
\(281\) | 10.9560 | 0.653577 | 0.326789 | − | 0.945097i | \(-0.394033\pi\) | ||||
0.326789 | + | 0.945097i | \(0.394033\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.5697 | 1.04441 | 0.522204 | − | 0.852821i | \(-0.325110\pi\) | ||||
0.522204 | + | 0.852821i | \(0.325110\pi\) | |||||||
\(284\) | 1.67553 | 0.0994243 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.0860250 | 0.00508677 | ||||||||
\(287\) | −11.6606 | −0.688305 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.8473 | −0.638074 | ||||||||
\(290\) | 4.06374 | 0.238631 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.738726 | −0.0432307 | ||||||||
\(293\) | 24.5445 | 1.43391 | 0.716953 | − | 0.697122i | \(-0.245536\pi\) | ||||
0.716953 | + | 0.697122i | \(0.245536\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.49087 | −0.436135 | ||||||||
\(296\) | 2.43312 | 0.141422 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.08875 | −0.178926 | ||||||||
\(299\) | −4.93083 | −0.285157 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.1876 | −1.16359 | ||||||||
\(302\) | −7.98530 | −0.459502 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −10.4233 | −0.597815 | ||||||||
\(305\) | 5.78404 | 0.331193 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.0689 | −0.631735 | −0.315868 | − | 0.948803i | \(-0.602296\pi\) | ||||
−0.315868 | + | 0.948803i | \(0.602296\pi\) | |||||||
\(308\) | −0.0751435 | −0.00428170 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 13.3347 | 0.757361 | ||||||||
\(311\) | 14.7933 | 0.838853 | 0.419426 | − | 0.907789i | \(-0.362231\pi\) | ||||
0.419426 | + | 0.907789i | \(0.362231\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.0525 | 1.52910 | 0.764548 | − | 0.644567i | \(-0.222962\pi\) | ||||
0.764548 | + | 0.644567i | \(0.222962\pi\) | |||||||
\(314\) | −29.4123 | −1.65983 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.4636 | −0.588626 | ||||||||
\(317\) | 0.577998 | 0.0324636 | 0.0162318 | − | 0.999868i | \(-0.494833\pi\) | ||||
0.0162318 | + | 0.999868i | \(0.494833\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.130926 | 0.00733047 | ||||||||
\(320\) | −3.82454 | −0.213798 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 17.1627 | 0.956440 | ||||||||
\(323\) | −5.28600 | −0.294121 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | 15.3885 | 0.852291 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 11.8962 | 0.656855 | ||||||||
\(329\) | 20.8019 | 1.14684 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.1140 | −1.32542 | −0.662712 | − | 0.748874i | \(-0.730595\pi\) | ||||
−0.662712 | + | 0.748874i | \(0.730595\pi\) | |||||||
\(332\) | 0.327770 | 0.0179887 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −25.3120 | −1.38501 | ||||||||
\(335\) | 6.23591 | 0.340704 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.13491 | 0.334190 | 0.167095 | − | 0.985941i | \(-0.446561\pi\) | ||||
0.167095 | + | 0.985941i | \(0.446561\pi\) | |||||||
\(338\) | 1.63404 | 0.0888799 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.66211 | 0.0901405 | ||||||||
\(341\) | 0.429620 | 0.0232652 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.1564 | −1.08835 | ||||||||
\(344\) | 20.5954 | 1.11043 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.8120 | −0.850057 | ||||||||
\(347\) | −3.72399 | −0.199914 | −0.0999572 | − | 0.994992i | \(-0.531871\pi\) | ||||
−0.0999572 | + | 0.994992i | \(0.531871\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.34865 | −0.179249 | −0.0896246 | − | 0.995976i | \(-0.528567\pi\) | ||||
−0.0896246 | + | 0.995976i | \(0.528567\pi\) | |||||||
\(350\) | 3.48069 | 0.186051 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.191948 | 0.0102309 | ||||||||
\(353\) | −35.5626 | −1.89281 | −0.946403 | − | 0.322988i | \(-0.895313\pi\) | ||||
−0.946403 | + | 0.322988i | \(0.895313\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.50050 | −0.132713 | ||||||||
\(356\) | −3.11520 | −0.165105 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.41896 | −0.286401 | ||||||||
\(359\) | 9.06902 | 0.478645 | 0.239322 | − | 0.970940i | \(-0.423075\pi\) | ||||
0.239322 | + | 0.970940i | \(0.423075\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.4586 | −0.760981 | ||||||||
\(362\) | −36.9600 | −1.94258 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.42734 | −0.0748131 | ||||||||
\(365\) | 1.10245 | 0.0577048 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.6186 | −1.28508 | −0.642541 | − | 0.766252i | \(-0.722120\pi\) | ||||
−0.642541 | + | 0.766252i | \(0.722120\pi\) | |||||||
\(368\) | −24.1174 | −1.25721 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.82952 | 0.0951121 | ||||||||
\(371\) | −7.75557 | −0.402649 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.9758 | 1.39675 | 0.698376 | − | 0.715731i | \(-0.253906\pi\) | ||||
0.698376 | + | 0.715731i | \(0.253906\pi\) | |||||||
\(374\) | 0.213383 | 0.0110338 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −21.2220 | −1.09444 | ||||||||
\(377\) | 2.48694 | 0.128084 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.2429 | 0.731611 | 0.365805 | − | 0.930691i | \(-0.380794\pi\) | ||||
0.365805 | + | 0.930691i | \(0.380794\pi\) | |||||||
\(380\) | −1.42797 | −0.0732531 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9.61158 | 0.491771 | ||||||||
\(383\) | 25.9736 | 1.32719 | 0.663595 | − | 0.748092i | \(-0.269030\pi\) | ||||
0.663595 | + | 0.748092i | \(0.269030\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.112141 | 0.00571526 | ||||||||
\(386\) | −0.750903 | −0.0382200 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.91902 | 0.249726 | ||||||||
\(389\) | 25.7906 | 1.30764 | 0.653819 | − | 0.756651i | \(-0.273166\pi\) | ||||
0.653819 | + | 0.756651i | \(0.273166\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.2308 | −0.618537 | ||||||||
\(392\) | 5.35159 | 0.270296 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.77657 | −0.190261 | ||||||||
\(395\) | 15.6156 | 0.785705 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.2890 | −0.968086 | −0.484043 | − | 0.875044i | \(-0.660832\pi\) | ||||
−0.484043 | + | 0.875044i | \(0.660832\pi\) | |||||||
\(398\) | 39.8271 | 1.99635 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.89115 | −0.244558 | ||||||||
\(401\) | −16.4631 | −0.822128 | −0.411064 | − | 0.911607i | \(-0.634843\pi\) | ||||
−0.411064 | + | 0.911607i | \(0.634843\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.16059 | 0.406508 | ||||||||
\(404\) | 0.370458 | 0.0184310 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.65625 | −0.429602 | ||||||||
\(407\) | 0.0589438 | 0.00292173 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.7526 | −0.976704 | −0.488352 | − | 0.872647i | \(-0.662402\pi\) | ||||
−0.488352 | + | 0.872647i | \(0.662402\pi\) | |||||||
\(410\) | 8.94500 | 0.441762 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.25204 | −0.258749 | ||||||||
\(413\) | 15.9564 | 0.785164 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.489152 | −0.0240115 | ||||||||
\(416\) | 3.64604 | 0.178762 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.183323 | −0.00896664 | ||||||||
\(419\) | −17.4583 | −0.852894 | −0.426447 | − | 0.904513i | \(-0.640235\pi\) | ||||
−0.426447 | + | 0.904513i | \(0.640235\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.41596 | −0.361432 | −0.180716 | − | 0.983535i | \(-0.557841\pi\) | ||||
−0.180716 | + | 0.983535i | \(0.557841\pi\) | |||||||
\(422\) | 44.7625 | 2.17900 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.91222 | 0.384251 | ||||||||
\(425\) | −2.48047 | −0.120321 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.3207 | −0.596239 | ||||||||
\(428\) | 13.0111 | 0.628916 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 15.4861 | 0.746808 | ||||||||
\(431\) | 33.6097 | 1.61892 | 0.809461 | − | 0.587174i | \(-0.199760\pi\) | ||||
0.809461 | + | 0.587174i | \(0.199760\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.2826 | 1.45529 | 0.727644 | − | 0.685955i | \(-0.240615\pi\) | ||||
0.727644 | + | 0.685955i | \(0.240615\pi\) | |||||||
\(434\) | −28.4045 | −1.36346 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.43063 | −0.0685147 | ||||||||
\(437\) | 10.5078 | 0.502658 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −28.7370 | −1.37154 | −0.685772 | − | 0.727817i | \(-0.740535\pi\) | ||||
−0.685772 | + | 0.727817i | \(0.740535\pi\) | |||||||
\(440\) | −0.114407 | −0.00545412 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.05318 | 0.192790 | ||||||||
\(443\) | −22.4218 | −1.06529 | −0.532646 | − | 0.846338i | \(-0.678802\pi\) | ||||
−0.532646 | + | 0.846338i | \(0.678802\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.64901 | 0.220384 | ||||||||
\(446\) | 41.3997 | 1.96033 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.14671 | 0.384896 | ||||||||
\(449\) | 16.0149 | 0.755791 | 0.377895 | − | 0.925848i | \(-0.376648\pi\) | ||||
0.377895 | + | 0.925848i | \(0.376648\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.288192 | 0.0135704 | ||||||||
\(452\) | −4.17813 | −0.196523 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −34.7097 | −1.62901 | ||||||||
\(455\) | 2.13012 | 0.0998614 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.06556 | 0.0498448 | 0.0249224 | − | 0.999689i | \(-0.492066\pi\) | ||||
0.0249224 | + | 0.999689i | \(0.492066\pi\) | |||||||
\(458\) | 19.9904 | 0.934089 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.30404 | −0.154052 | ||||||||
\(461\) | 24.6387 | 1.14754 | 0.573769 | − | 0.819017i | \(-0.305481\pi\) | ||||
0.573769 | + | 0.819017i | \(0.305481\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.12328 | 0.331047 | 0.165524 | − | 0.986206i | \(-0.447069\pi\) | ||||
0.165524 | + | 0.986206i | \(0.447069\pi\) | |||||||
\(464\) | 12.1640 | 0.564698 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18.6359 | 0.863290 | ||||||||
\(467\) | 20.4662 | 0.947063 | 0.473531 | − | 0.880777i | \(-0.342979\pi\) | ||||
0.473531 | + | 0.880777i | \(0.342979\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.2832 | −0.613361 | ||||||||
\(470\) | −15.9574 | −0.736058 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −16.2787 | −0.749289 | ||||||||
\(473\) | 0.498935 | 0.0229411 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.13105 | 0.0977791 | ||||||||
\(476\) | −3.54048 | −0.162278 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 24.2770 | 1.11041 | ||||||||
\(479\) | −14.4699 | −0.661145 | −0.330573 | − | 0.943781i | \(-0.607242\pi\) | ||||
−0.330573 | + | 0.943781i | \(0.607242\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.11963 | 0.0510508 | ||||||||
\(482\) | −30.3780 | −1.38368 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.36900 | −0.334954 | ||||||||
\(485\) | −7.34097 | −0.333336 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.8595 | 1.35306 | 0.676531 | − | 0.736414i | \(-0.263483\pi\) | ||||
0.676531 | + | 0.736414i | \(0.263483\pi\) | |||||||
\(488\) | 12.5695 | 0.568996 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.02399 | 0.181785 | ||||||||
\(491\) | 22.0470 | 0.994965 | 0.497483 | − | 0.867474i | \(-0.334258\pi\) | ||||
0.497483 | + | 0.867474i | \(0.334258\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.16877 | 0.277827 | ||||||||
\(494\) | −3.48221 | −0.156672 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 39.9147 | 1.79222 | ||||||||
\(497\) | 5.32635 | 0.238920 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.1723 | 0.947802 | 0.473901 | − | 0.880578i | \(-0.342845\pi\) | ||||
0.473901 | + | 0.880578i | \(0.342845\pi\) | |||||||
\(500\) | −0.670078 | −0.0299668 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 49.1392 | 2.19319 | ||||||||
\(503\) | −40.3143 | −1.79752 | −0.898762 | − | 0.438436i | \(-0.855533\pi\) | ||||
−0.898762 | + | 0.438436i | \(0.855533\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.552859 | −0.0246019 | ||||||||
\(506\) | −0.424175 | −0.0188569 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.10524 | −0.315244 | ||||||||
\(509\) | 19.0167 | 0.842900 | 0.421450 | − | 0.906852i | \(-0.361521\pi\) | ||||
0.421450 | + | 0.906852i | \(0.361521\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.34834 | −0.103885 | ||||||||
\(512\) | −3.42501 | −0.151366 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.96851 | 0.219152 | ||||||||
\(515\) | 7.83795 | 0.345381 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.514117 | −0.0226108 | ||||||||
\(518\) | −3.89709 | −0.171228 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.17314 | −0.0952986 | ||||||||
\(521\) | −33.4407 | −1.46507 | −0.732533 | − | 0.680732i | \(-0.761662\pi\) | ||||
−0.732533 | + | 0.680732i | \(0.761662\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.40250 | −0.279962 | −0.139981 | − | 0.990154i | \(-0.544704\pi\) | ||||
−0.139981 | + | 0.990154i | \(0.544704\pi\) | |||||||
\(524\) | −10.8501 | −0.473989 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.84504 | −0.342060 | ||||||||
\(527\) | 20.2421 | 0.881761 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.31310 | 0.0570915 | ||||||||
\(530\) | 5.94939 | 0.258425 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.04173 | 0.131876 | ||||||||
\(533\) | 5.47417 | 0.237113 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.4173 | −0.839484 | ||||||||
\(536\) | 13.5515 | 0.585336 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −27.5700 | −1.18863 | ||||||||
\(539\) | 0.129646 | 0.00558423 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.4745 | −0.751286 | −0.375643 | − | 0.926764i | \(-0.622578\pi\) | ||||
−0.375643 | + | 0.926764i | \(0.622578\pi\) | |||||||
\(542\) | −3.82527 | −0.164309 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 9.04389 | 0.387754 | ||||||||
\(545\) | 2.13502 | 0.0914542 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.0747 | −0.430761 | −0.215381 | − | 0.976530i | \(-0.569099\pi\) | ||||
−0.215381 | + | 0.976530i | \(0.569099\pi\) | |||||||
\(548\) | −13.9166 | −0.594486 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.0860250 | −0.00366812 | ||||||||
\(551\) | −5.29977 | −0.225778 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −33.2630 | −1.41449 | ||||||||
\(554\) | −6.16413 | −0.261889 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.67570 | −0.0710654 | ||||||||
\(557\) | 21.2315 | 0.899607 | 0.449804 | − | 0.893127i | \(-0.351494\pi\) | ||||
0.449804 | + | 0.893127i | \(0.351494\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.47722 | 0.400844 | ||||||||
\(560\) | 10.4187 | 0.440271 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 17.9024 | 0.755169 | ||||||||
\(563\) | 12.3449 | 0.520276 | 0.260138 | − | 0.965571i | \(-0.416232\pi\) | ||||
0.260138 | + | 0.965571i | \(0.416232\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.23529 | 0.262321 | ||||||||
\(566\) | 28.7095 | 1.20675 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.43394 | −0.228003 | ||||||||
\(569\) | 7.75747 | 0.325210 | 0.162605 | − | 0.986691i | \(-0.448010\pi\) | ||||
0.162605 | + | 0.986691i | \(0.448010\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.2139 | −0.427440 | −0.213720 | − | 0.976895i | \(-0.568558\pi\) | ||||
−0.213720 | + | 0.976895i | \(0.568558\pi\) | |||||||
\(572\) | 0.0352767 | 0.00147499 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −19.0539 | −0.795294 | ||||||||
\(575\) | 4.93083 | 0.205630 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −44.5539 | −1.85480 | −0.927402 | − | 0.374065i | \(-0.877964\pi\) | ||||
−0.927402 | + | 0.374065i | \(0.877964\pi\) | |||||||
\(578\) | −17.7248 | −0.737256 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.66644 | 0.0691952 | ||||||||
\(581\) | 1.04195 | 0.0432274 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.191678 | 0.00793851 | ||||||||
\(584\) | 2.39578 | 0.0991380 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 40.1066 | 1.65679 | ||||||||
\(587\) | 20.9069 | 0.862921 | 0.431461 | − | 0.902132i | \(-0.357998\pi\) | ||||
0.431461 | + | 0.902132i | \(0.357998\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.3906 | −0.716567 | ||||||||
\(590\) | −12.2404 | −0.503928 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.47628 | 0.225074 | ||||||||
\(593\) | −7.48843 | −0.307513 | −0.153756 | − | 0.988109i | \(-0.549137\pi\) | ||||
−0.153756 | + | 0.988109i | \(0.549137\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.28369 | 0.216610 | ||||||||
\(596\) | −1.26662 | −0.0518827 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −8.05716 | −0.329482 | ||||||||
\(599\) | −27.9314 | −1.14125 | −0.570623 | − | 0.821212i | \(-0.693298\pi\) | ||||
−0.570623 | + | 0.821212i | \(0.693298\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.7780 | 1.33704 | 0.668521 | − | 0.743693i | \(-0.266927\pi\) | ||||
0.668521 | + | 0.743693i | \(0.266927\pi\) | |||||||
\(602\) | −32.9873 | −1.34446 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.27457 | −0.133240 | ||||||||
\(605\) | 10.9972 | 0.447101 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 39.1704 | 1.58988 | 0.794940 | − | 0.606689i | \(-0.207503\pi\) | ||||
0.794940 | + | 0.606689i | \(0.207503\pi\) | |||||||
\(608\) | −7.76988 | −0.315110 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9.45133 | 0.382673 | ||||||||
\(611\) | −9.76560 | −0.395074 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.2019 | −0.412051 | −0.206026 | − | 0.978547i | \(-0.566053\pi\) | ||||
−0.206026 | + | 0.978547i | \(0.566053\pi\) | |||||||
\(614\) | −18.0870 | −0.729932 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.243699 | 0.00981893 | ||||||||
\(617\) | −9.68947 | −0.390084 | −0.195042 | − | 0.980795i | \(-0.562484\pi\) | ||||
−0.195042 | + | 0.980795i | \(0.562484\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.8750 | −0.798842 | −0.399421 | − | 0.916768i | \(-0.630789\pi\) | ||||
−0.399421 | + | 0.916768i | \(0.630789\pi\) | |||||||
\(620\) | 5.46823 | 0.219610 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 24.1728 | 0.969243 | ||||||||
\(623\) | −9.90292 | −0.396752 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 44.2047 | 1.76678 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −12.0612 | −0.481296 | ||||||||
\(629\) | 2.77721 | 0.110735 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.9270 | −1.54966 | −0.774830 | − | 0.632170i | \(-0.782165\pi\) | ||||
−0.774830 | + | 0.632170i | \(0.782165\pi\) | |||||||
\(632\) | 33.9349 | 1.34986 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.944470 | 0.0375097 | ||||||||
\(635\) | 10.6036 | 0.420791 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.46260 | 0.0975719 | ||||||||
\(638\) | 0.213939 | 0.00846991 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −13.5415 | −0.535275 | ||||||||
\(641\) | −7.89412 | −0.311799 | −0.155899 | − | 0.987773i | \(-0.549828\pi\) | ||||
−0.155899 | + | 0.987773i | \(0.549828\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 35.7751 | 1.41083 | 0.705415 | − | 0.708794i | \(-0.250760\pi\) | ||||
0.705415 | + | 0.708794i | \(0.250760\pi\) | |||||||
\(644\) | 7.03799 | 0.277336 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.63752 | −0.339839 | ||||||||
\(647\) | −1.47889 | −0.0581412 | −0.0290706 | − | 0.999577i | \(-0.509255\pi\) | ||||
−0.0290706 | + | 0.999577i | \(0.509255\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.394362 | −0.0154801 | ||||||||
\(650\) | −1.63404 | −0.0640922 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.31044 | 0.247136 | ||||||||
\(653\) | −6.95046 | −0.271992 | −0.135996 | − | 0.990709i | \(-0.543423\pi\) | ||||
−0.135996 | + | 0.990709i | \(0.543423\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.1923 | 0.632686 | ||||||||
\(656\) | 26.7750 | 1.04539 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 33.9910 | 1.32511 | ||||||||
\(659\) | 30.9546 | 1.20582 | 0.602910 | − | 0.797810i | \(-0.294008\pi\) | ||||
0.602910 | + | 0.797810i | \(0.294008\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.57678 | 0.139121 | 0.0695603 | − | 0.997578i | \(-0.477840\pi\) | ||||
0.0695603 | + | 0.997578i | \(0.477840\pi\) | |||||||
\(662\) | −39.4032 | −1.53145 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.06300 | −0.0412522 | ||||||||
\(665\) | −4.53938 | −0.176029 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.2627 | −0.474812 | ||||||||
\(668\) | −10.3798 | −0.401607 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 10.1897 | 0.393663 | ||||||||
\(671\) | 0.304505 | 0.0117553 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.0993 | −1.08315 | −0.541575 | − | 0.840653i | \(-0.682172\pi\) | ||||
−0.541575 | + | 0.840653i | \(0.682172\pi\) | |||||||
\(674\) | 10.0247 | 0.386136 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.670078 | 0.0257722 | ||||||||
\(677\) | 44.2934 | 1.70233 | 0.851167 | − | 0.524895i | \(-0.175895\pi\) | ||||
0.851167 | + | 0.524895i | \(0.175895\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.6371 | 0.600098 | ||||||||
\(680\) | −5.39042 | −0.206713 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.702016 | 0.0268816 | ||||||||
\(683\) | −1.69041 | −0.0646816 | −0.0323408 | − | 0.999477i | \(-0.510296\pi\) | ||||
−0.0323408 | + | 0.999477i | \(0.510296\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.7686 | 0.793526 | ||||||||
\(686\) | −32.9364 | −1.25752 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 46.3545 | 1.76725 | ||||||||
\(689\) | 3.64091 | 0.138708 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.8144 | −0.411398 | −0.205699 | − | 0.978615i | \(-0.565947\pi\) | ||||
−0.205699 | + | 0.978615i | \(0.565947\pi\) | |||||||
\(692\) | −6.48409 | −0.246488 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.08514 | −0.230989 | ||||||||
\(695\) | 2.50075 | 0.0948589 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.5785 | 0.514323 | ||||||||
\(698\) | −5.47182 | −0.207111 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.42734 | 0.0539485 | ||||||||
\(701\) | −32.1755 | −1.21525 | −0.607626 | − | 0.794224i | \(-0.707878\pi\) | ||||
−0.607626 | + | 0.794224i | \(0.707878\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.38598 | −0.0899891 | ||||||||
\(704\) | −0.201346 | −0.00758850 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −58.1106 | −2.18702 | ||||||||
\(707\) | 1.17765 | 0.0442902 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31.9120 | 1.19848 | 0.599240 | − | 0.800570i | \(-0.295470\pi\) | ||||
0.599240 | + | 0.800570i | \(0.295470\pi\) | |||||||
\(710\) | −4.08591 | −0.153341 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 10.1030 | 0.378624 | ||||||||
\(713\) | −40.2385 | −1.50694 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.0526457 | −0.00196884 | ||||||||
\(716\) | −2.22218 | −0.0830467 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 14.8191 | 0.553045 | ||||||||
\(719\) | 20.6891 | 0.771572 | 0.385786 | − | 0.922588i | \(-0.373930\pi\) | ||||
0.385786 | + | 0.922588i | \(0.373930\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.6958 | −0.621782 | ||||||||
\(722\) | −23.6260 | −0.879267 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −15.1564 | −0.563283 | ||||||||
\(725\) | −2.48694 | −0.0923625 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.6791 | −0.915299 | −0.457649 | − | 0.889133i | \(-0.651308\pi\) | ||||
−0.457649 | + | 0.889133i | \(0.651308\pi\) | |||||||
\(728\) | 4.62905 | 0.171564 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.80144 | 0.0666744 | ||||||||
\(731\) | 23.5080 | 0.869474 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.7459 | −0.803203 | −0.401602 | − | 0.915814i | \(-0.631546\pi\) | ||||
−0.401602 | + | 0.915814i | \(0.631546\pi\) | |||||||
\(734\) | −40.2277 | −1.48483 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −17.9780 | −0.662678 | ||||||||
\(737\) | 0.328294 | 0.0120929 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.0460 | 1.58347 | 0.791736 | − | 0.610864i | \(-0.209178\pi\) | ||||
0.791736 | + | 0.610864i | \(0.209178\pi\) | |||||||
\(740\) | 0.750240 | 0.0275794 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −12.6729 | −0.465236 | ||||||||
\(743\) | 7.89816 | 0.289755 | 0.144878 | − | 0.989450i | \(-0.453721\pi\) | ||||
0.144878 | + | 0.989450i | \(0.453721\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.89025 | 0.0692536 | ||||||||
\(746\) | 44.0794 | 1.61386 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.0875029 | 0.00319942 | ||||||||
\(749\) | 41.3612 | 1.51130 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38.6450 | 1.41018 | 0.705089 | − | 0.709119i | \(-0.250907\pi\) | ||||
0.705089 | + | 0.709119i | \(0.250907\pi\) | |||||||
\(752\) | −47.7650 | −1.74181 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.06374 | 0.147993 | ||||||||
\(755\) | 4.88685 | 0.177851 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.3437 | −0.557678 | −0.278839 | − | 0.960338i | \(-0.589950\pi\) | ||||
−0.278839 | + | 0.960338i | \(0.589950\pi\) | |||||||
\(758\) | 23.2735 | 0.845331 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.63107 | 0.167986 | ||||||||
\(761\) | 48.7170 | 1.76599 | 0.882995 | − | 0.469382i | \(-0.155523\pi\) | ||||
0.882995 | + | 0.469382i | \(0.155523\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.54784 | −0.164643 | ||||||||
\(764\) | 3.94147 | 0.142597 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 42.4418 | 1.53349 | ||||||||
\(767\) | −7.49087 | −0.270480 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.37109 | 0.229747 | 0.114874 | − | 0.993380i | \(-0.463354\pi\) | ||||
0.114874 | + | 0.993380i | \(0.463354\pi\) | |||||||
\(770\) | 0.183243 | 0.00660363 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.307927 | −0.0110825 | ||||||||
\(773\) | 29.8732 | 1.07446 | 0.537232 | − | 0.843435i | \(-0.319470\pi\) | ||||
0.537232 | + | 0.843435i | \(0.319470\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.16059 | −0.293137 | ||||||||
\(776\) | −15.9530 | −0.572679 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 42.1429 | 1.51090 | ||||||||
\(779\) | −11.6657 | −0.417967 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.131641 | −0.00471047 | ||||||||
\(782\) | −19.9856 | −0.714682 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 12.0450 | 0.430178 | ||||||||
\(785\) | 17.9998 | 0.642439 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.6556 | −0.843232 | −0.421616 | − | 0.906774i | \(-0.638537\pi\) | ||||
−0.421616 | + | 0.906774i | \(0.638537\pi\) | |||||||
\(788\) | −1.54868 | −0.0551693 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 25.5164 | 0.907834 | ||||||||
\(791\) | −13.2819 | −0.472250 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.78404 | 0.205397 | ||||||||
\(794\) | −31.5189 | −1.11856 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16.3321 | 0.578876 | ||||||||
\(797\) | −30.0006 | −1.06268 | −0.531339 | − | 0.847160i | \(-0.678311\pi\) | ||||
−0.531339 | + | 0.847160i | \(0.678311\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.2233 | −0.856959 | ||||||||
\(800\) | −3.64604 | −0.128907 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −26.9013 | −0.949918 | ||||||||
\(803\) | 0.0580392 | 0.00204816 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.5032 | −0.370191 | ||||||||
\(806\) | 13.3347 | 0.469695 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.20144 | −0.0422665 | ||||||||
\(809\) | 37.0787 | 1.30362 | 0.651808 | − | 0.758384i | \(-0.274011\pi\) | ||||
0.651808 | + | 0.758384i | \(0.274011\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.7582 | −1.50144 | −0.750722 | − | 0.660618i | \(-0.770294\pi\) | ||||
−0.750722 | + | 0.660618i | \(0.770294\pi\) | |||||||
\(812\) | −3.54971 | −0.124570 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.0963163 | 0.00337588 | ||||||||
\(815\) | −9.41748 | −0.329880 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20.1964 | −0.706583 | ||||||||
\(818\) | −32.2765 | −1.12852 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.66812 | 0.128096 | ||||||||
\(821\) | 28.5669 | 0.996992 | 0.498496 | − | 0.866892i | \(-0.333886\pi\) | ||||
0.498496 | + | 0.866892i | \(0.333886\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.0041 | 1.11559 | 0.557797 | − | 0.829977i | \(-0.311647\pi\) | ||||
0.557797 | + | 0.829977i | \(0.311647\pi\) | |||||||
\(824\) | 17.0330 | 0.593372 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 26.0734 | 0.907209 | ||||||||
\(827\) | 31.4986 | 1.09531 | 0.547657 | − | 0.836703i | \(-0.315520\pi\) | ||||
0.547657 | + | 0.836703i | \(0.315520\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.3851 | 1.12478 | 0.562390 | − | 0.826872i | \(-0.309882\pi\) | ||||
0.562390 | + | 0.826872i | \(0.309882\pi\) | |||||||
\(830\) | −0.799292 | −0.0277438 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.82454 | −0.132592 | ||||||||
\(833\) | 6.10842 | 0.211644 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.4905 | 0.536070 | ||||||||
\(836\) | −0.0751763 | −0.00260003 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −28.5275 | −0.985467 | ||||||||
\(839\) | 46.0763 | 1.59073 | 0.795365 | − | 0.606131i | \(-0.207279\pi\) | ||||
0.795365 | + | 0.606131i | \(0.207279\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.8152 | −0.786729 | ||||||||
\(842\) | −12.1180 | −0.417612 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 18.3560 | 0.631839 | ||||||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −23.4254 | −0.804905 | ||||||||
\(848\) | 17.8083 | 0.611538 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4.05318 | −0.139023 | ||||||||
\(851\) | −5.52071 | −0.189248 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 48.7573 | 1.66942 | 0.834709 | − | 0.550692i | \(-0.185636\pi\) | ||||
0.834709 | + | 0.550692i | \(0.185636\pi\) | |||||||
\(854\) | −20.1324 | −0.688918 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −42.1966 | −1.44225 | ||||||||
\(857\) | 31.9479 | 1.09132 | 0.545660 | − | 0.838007i | \(-0.316279\pi\) | ||||
0.545660 | + | 0.838007i | \(0.316279\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.33499 | −0.250267 | −0.125133 | − | 0.992140i | \(-0.539936\pi\) | ||||
−0.125133 | + | 0.992140i | \(0.539936\pi\) | |||||||
\(860\) | 6.35048 | 0.216549 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 54.9195 | 1.87056 | ||||||||
\(863\) | 28.4742 | 0.969273 | 0.484637 | − | 0.874716i | \(-0.338952\pi\) | ||||
0.484637 | + | 0.874716i | \(0.338952\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.67663 | 0.329015 | ||||||||
\(866\) | 49.4829 | 1.68150 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −11.6480 | −0.395358 | ||||||||
\(869\) | 0.822093 | 0.0278876 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.23591 | 0.211296 | ||||||||
\(872\) | 4.63970 | 0.157120 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 17.1702 | 0.580790 | ||||||||
\(875\) | −2.13012 | −0.0720111 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 45.8529 | 1.54834 | 0.774171 | − | 0.632977i | \(-0.218167\pi\) | ||||
0.774171 | + | 0.632977i | \(0.218167\pi\) | |||||||
\(878\) | −46.9574 | −1.58473 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.257498 | −0.00868026 | ||||||||
\(881\) | −37.4454 | −1.26157 | −0.630784 | − | 0.775959i | \(-0.717267\pi\) | ||||
−0.630784 | + | 0.775959i | \(0.717267\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 50.8068 | 1.70978 | 0.854892 | − | 0.518805i | \(-0.173623\pi\) | ||||
0.854892 | + | 0.518805i | \(0.173623\pi\) | |||||||
\(884\) | 1.66211 | 0.0559028 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −36.6381 | −1.23088 | ||||||||
\(887\) | −45.2968 | −1.52092 | −0.760459 | − | 0.649386i | \(-0.775026\pi\) | ||||
−0.760459 | + | 0.649386i | \(0.775026\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −22.5869 | −0.757541 | ||||||||
\(890\) | 7.59665 | 0.254640 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 16.9770 | 0.568432 | ||||||||
\(893\) | 20.8109 | 0.696412 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.31630 | 0.110852 | ||||||||
\(896\) | 28.8450 | 0.963644 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 26.1690 | 0.873270 | ||||||||
\(899\) | 20.2949 | 0.676872 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.03118 | 0.300872 | ||||||||
\(902\) | 0.470916 | 0.0156798 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13.5502 | 0.450672 | ||||||||
\(905\) | 22.6189 | 0.751876 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.3690 | 0.477116 | 0.238558 | − | 0.971128i | \(-0.423325\pi\) | ||||
0.238558 | + | 0.971128i | \(0.423325\pi\) | |||||||
\(908\) | −14.2336 | −0.472359 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.48069 | 0.115384 | ||||||||
\(911\) | 53.9063 | 1.78600 | 0.892998 | − | 0.450060i | \(-0.148597\pi\) | ||||
0.892998 | + | 0.450060i | \(0.148597\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.0257517 | −0.000852258 0 | ||||||||
\(914\) | 1.74117 | 0.0575926 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.19755 | 0.270855 | ||||||||
\(917\) | −34.4915 | −1.13901 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.6573 | −0.516487 | −0.258244 | − | 0.966080i | \(-0.583144\pi\) | ||||
−0.258244 | + | 0.966080i | \(0.583144\pi\) | |||||||
\(920\) | 10.7154 | 0.353276 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 40.2605 | 1.32591 | ||||||||
\(923\) | −2.50050 | −0.0823049 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.11963 | −0.0368132 | ||||||||
\(926\) | 11.6397 | 0.382505 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9.06746 | 0.297654 | ||||||||
\(929\) | −23.1439 | −0.759327 | −0.379664 | − | 0.925125i | \(-0.623960\pi\) | ||||
−0.379664 | + | 0.925125i | \(0.623960\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.24792 | −0.171994 | ||||||||
\(932\) | 7.64211 | 0.250326 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 33.4425 | 1.09427 | ||||||||
\(935\) | −0.130586 | −0.00427062 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.6354 | 0.478118 | 0.239059 | − | 0.971005i | \(-0.423161\pi\) | ||||
0.239059 | + | 0.971005i | \(0.423161\pi\) | |||||||
\(938\) | −21.7052 | −0.708702 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.54371 | −0.213432 | ||||||||
\(941\) | −22.0393 | −0.718462 | −0.359231 | − | 0.933249i | \(-0.616961\pi\) | ||||
−0.359231 | + | 0.933249i | \(0.616961\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −26.9922 | −0.878987 | ||||||||
\(944\) | −36.6390 | −1.19250 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.815279 | 0.0265070 | ||||||||
\(947\) | −50.3906 | −1.63747 | −0.818737 | − | 0.574168i | \(-0.805326\pi\) | ||||
−0.818737 | + | 0.574168i | \(0.805326\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.10245 | 0.0357870 | ||||||||
\(950\) | 3.48221 | 0.112978 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 11.4822 | 0.372141 | ||||||||
\(953\) | −7.28058 | −0.235841 | −0.117921 | − | 0.993023i | \(-0.537623\pi\) | ||||
−0.117921 | + | 0.993023i | \(0.537623\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.88211 | −0.190340 | ||||||||
\(956\) | 9.95540 | 0.321981 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −23.6443 | −0.763913 | ||||||||
\(959\) | −44.2395 | −1.42857 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 35.5953 | 1.14824 | ||||||||
\(962\) | 1.82952 | 0.0589861 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −12.4573 | −0.401221 | ||||||||
\(965\) | 0.459539 | 0.0147931 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.64327 | 0.0528441 | 0.0264220 | − | 0.999651i | \(-0.491589\pi\) | ||||
0.0264220 | + | 0.999651i | \(0.491589\pi\) | |||||||
\(968\) | 23.8985 | 0.768128 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −11.9954 | −0.385150 | ||||||||
\(971\) | 59.5135 | 1.90988 | 0.954939 | − | 0.296803i | \(-0.0959204\pi\) | ||||
0.954939 | + | 0.296803i | \(0.0959204\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.32689 | −0.170772 | ||||||||
\(974\) | 48.7915 | 1.56338 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 28.2906 | 0.905560 | ||||||||
\(977\) | −15.3273 | −0.490363 | −0.245181 | − | 0.969477i | \(-0.578847\pi\) | ||||
−0.245181 | + | 0.969477i | \(0.578847\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.244750 | 0.00782225 | ||||||||
\(980\) | 1.65014 | 0.0527117 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 36.0255 | 1.14962 | ||||||||
\(983\) | −3.26954 | −0.104282 | −0.0521411 | − | 0.998640i | \(-0.516605\pi\) | ||||
−0.0521411 | + | 0.998640i | \(0.516605\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.31119 | 0.0736405 | ||||||||
\(986\) | 10.0800 | 0.321013 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.42797 | −0.0454297 | ||||||||
\(989\) | −46.7306 | −1.48595 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −39.2309 | −1.24621 | −0.623106 | − | 0.782138i | \(-0.714129\pi\) | ||||
−0.623106 | + | 0.782138i | \(0.714129\pi\) | |||||||
\(992\) | 29.7538 | 0.944685 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8.70346 | 0.276057 | ||||||||
\(995\) | −24.3734 | −0.772690 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32.8254 | −1.03959 | −0.519795 | − | 0.854291i | \(-0.673992\pi\) | ||||
−0.519795 | + | 0.854291i | \(0.673992\pi\) | |||||||
\(998\) | 34.5963 | 1.09513 | ||||||||
\(999\) | 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 | 5265.2.a.bf.1.6 | 8 | ||
3.2 | odd | 2 | 5265.2.a.ba.1.3 | 8 | |||
9.2 | odd | 6 | 1755.2.i.f.1171.6 | 16 | |||
9.4 | even | 3 | 585.2.i.e.196.3 | ✓ | 16 | ||
9.5 | odd | 6 | 1755.2.i.f.586.6 | 16 | |||
9.7 | even | 3 | 585.2.i.e.391.3 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
585.2.i.e.196.3 | ✓ | 16 | 9.4 | even | 3 | ||
585.2.i.e.391.3 | yes | 16 | 9.7 | even | 3 | ||
1755.2.i.f.586.6 | 16 | 9.5 | odd | 6 | |||
1755.2.i.f.1171.6 | 16 | 9.2 | odd | 6 | |||
5265.2.a.ba.1.3 | 8 | 3.2 | odd | 2 | |||
5265.2.a.bf.1.6 | 8 | 1.1 | even | 1 | trivial |