Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [720,2,Mod(241,720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(720, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("720.241");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 720.q (of order \(3\), degree \(2\), not minimal) |
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: | no |
Analytic conductor: | \(5.74922894553\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.954288.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 180) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 241.3 | ||
Root | \(1.71903 + 0.211943i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 720.241 |
Dual form | 720.2.q.k.481.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(271\) | \(577\) | \(641\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.71903 | − | 0.211943i | 0.992485 | − | 0.122365i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.36710 | − | 2.36788i | 0.516714 | − | 0.894974i | −0.483098 | − | 0.875566i | \(-0.660489\pi\) |
0.999812 | − | 0.0194079i | \(-0.00617810\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.91016 | − | 0.728674i | 0.970054 | − | 0.242891i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.76210 | − | 4.78410i | 0.832804 | − | 1.44246i | −0.0630012 | − | 0.998013i | \(-0.520067\pi\) |
0.895806 | − | 0.444446i | \(-0.146599\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.76210 | + | 3.05205i | 0.488719 | + | 0.846485i | 0.999916 | − | 0.0129781i | \(-0.00413116\pi\) |
−0.511197 | + | 0.859463i | \(0.670798\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.04307 | + | 1.38276i | 0.269318 | + | 0.357026i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.52420 | −1.33982 | −0.669908 | − | 0.742444i | \(-0.733666\pi\) | ||||
−0.669908 | + | 0.742444i | \(0.733666\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.52420 | −1.72617 | −0.863085 | − | 0.505059i | \(-0.831471\pi\) | ||||
−0.863085 | + | 0.505059i | \(0.831471\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.84823 | − | 4.36021i | 0.403317 | − | 0.951476i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.367095 | + | 0.635828i | 0.0765447 | + | 0.132579i | 0.901757 | − | 0.432243i | \(-0.142278\pi\) |
−0.825212 | + | 0.564823i | \(0.808945\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.84823 | − | 1.86940i | 0.933042 | − | 0.359767i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.23419 | − | 3.86973i | 0.414879 | − | 0.718591i | −0.580537 | − | 0.814234i | \(-0.697157\pi\) |
0.995416 | + | 0.0956427i | \(0.0304906\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.76210 | + | 6.51615i | 0.675693 | + | 1.17033i | 0.976266 | + | 0.216576i | \(0.0694889\pi\) |
−0.300573 | + | 0.953759i | \(0.597178\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.73419 | − | 8.80944i | 0.650039 | − | 1.53353i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.73419 | 0.462163 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.05582 | 0.995570 | 0.497785 | − | 0.867300i | \(-0.334147\pi\) | ||||
0.497785 | + | 0.867300i | \(0.334147\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.67597 | + | 4.87311i | 0.588626 | + | 0.780322i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.527909 | + | 0.914365i | 0.0824455 | + | 0.142800i | 0.904300 | − | 0.426898i | \(-0.140394\pi\) |
−0.821854 | + | 0.569698i | \(0.807060\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.76210 | + | 3.05205i | −0.268718 | + | 0.465433i | −0.968531 | − | 0.248893i | \(-0.919933\pi\) |
0.699813 | + | 0.714326i | \(0.253267\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.08613 | + | 2.15594i | 0.310982 | + | 0.321388i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.604996 | − | 1.04788i | 0.0882477 | − | 0.152849i | −0.818523 | − | 0.574474i | \(-0.805207\pi\) |
0.906771 | + | 0.421625i | \(0.138540\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.237900 | − | 0.412055i | −0.0339857 | − | 0.0588650i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.49629 | + | 1.17081i | −1.32975 | + | 0.163947i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.46838 | 0.201698 | 0.100849 | − | 0.994902i | \(-0.467844\pi\) | ||||
0.100849 | + | 0.994902i | \(0.467844\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.52420 | 0.744883 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12.9344 | + | 1.59470i | −1.71320 | + | 0.211223i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.734191 | − | 1.27166i | −0.0955835 | − | 0.165556i | 0.814268 | − | 0.580488i | \(-0.197138\pi\) |
−0.909852 | + | 0.414933i | \(0.863805\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.52791 | + | 7.84257i | −0.579739 | + | 1.00414i | 0.415770 | + | 0.909470i | \(0.363512\pi\) |
−0.995509 | + | 0.0946680i | \(0.969821\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.25306 | − | 7.88707i | 0.283858 | − | 0.993678i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.76210 | + | 3.05205i | −0.218562 | + | 0.378560i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.12920 | − | 3.68787i | −0.260123 | − | 0.450546i | 0.706152 | − | 0.708061i | \(-0.250430\pi\) |
−0.966274 | + | 0.257515i | \(0.917096\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.765809 | + | 1.01521i | 0.0921926 | + | 0.122217i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.0558 | −1.19341 | −0.596703 | − | 0.802462i | \(-0.703523\pi\) | ||||
−0.596703 | + | 0.802462i | \(0.703523\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.00000 | 0.936329 | 0.468165 | − | 0.883641i | \(-0.344915\pi\) | ||||
0.468165 | + | 0.883641i | \(0.344915\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.675970 | + | 1.59470i | −0.0780542 | + | 0.184140i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.55211 | − | 13.0806i | −0.860643 | − | 1.49068i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.00000 | − | 1.73205i | 0.112509 | − | 0.194871i | −0.804272 | − | 0.594261i | \(-0.797445\pi\) |
0.916781 | + | 0.399390i | \(0.130778\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.93807 | − | 4.24111i | 0.882008 | − | 0.471235i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.63290 | + | 4.56032i | −0.288999 | + | 0.500561i | −0.973571 | − | 0.228384i | \(-0.926656\pi\) |
0.684572 | + | 0.728945i | \(0.259989\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.76210 | − | 4.78410i | −0.299592 | − | 0.518908i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.02049 | − | 7.12572i | 0.323831 | − | 0.763958i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.00000 | −0.317999 | −0.159000 | − | 0.987279i | \(-0.550827\pi\) | ||||
−0.159000 | + | 0.987279i | \(0.550827\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.63583 | 1.01011 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.84823 | + | 10.4041i | 0.813824 | + | 1.07886i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.76210 | − | 6.51615i | −0.385983 | − | 0.668543i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.73419 | + | 8.19986i | −0.480684 | + | 0.832570i | −0.999754 | − | 0.0221621i | \(-0.992945\pi\) |
0.519070 | + | 0.854732i | \(0.326278\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.55211 | − | 15.9352i | 0.457504 | − | 1.60154i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.73419 | + | 11.6640i | −0.670077 | + | 1.16061i | 0.307805 | + | 0.951450i | \(0.400406\pi\) |
−0.977882 | + | 0.209158i | \(0.932928\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.28630 | + | 16.0843i | 0.915006 | + | 1.58484i | 0.806892 | + | 0.590699i | \(0.201148\pi\) |
0.108114 | + | 0.994138i | \(0.465519\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.70017 | − | 0.579492i | 0.458690 | − | 0.0565526i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −19.2510 | −1.86106 | −0.930531 | − | 0.366213i | \(-0.880654\pi\) | ||||
−0.930531 | + | 0.366213i | \(0.880654\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.524200 | −0.0502092 | −0.0251046 | − | 0.999685i | \(-0.507992\pi\) | ||||
−0.0251046 | + | 0.999685i | \(0.507992\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.4102 | − | 1.28349i | 0.988089 | − | 0.121823i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.73419 | + | 6.46781i | 0.351283 | + | 0.608440i | 0.986475 | − | 0.163915i | \(-0.0524121\pi\) |
−0.635191 | + | 0.772355i | \(0.719079\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.367095 | + | 0.635828i | −0.0342318 | + | 0.0592913i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.35194 | + | 7.59795i | 0.679687 | + | 0.702431i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.55211 | + | 13.0806i | −0.692301 | + | 1.19910i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.75839 | − | 16.9020i | −0.887126 | − | 1.53655i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.10129 | + | 1.45994i | 0.0992997 | + | 0.131638i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.25839 | −0.732814 | −0.366407 | − | 0.930455i | \(-0.619412\pi\) | ||||
−0.366407 | + | 0.930455i | \(0.619412\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.38225 | + | 5.62004i | −0.209746 | + | 0.494817i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.04840 | − | 13.9402i | −0.703192 | − | 1.21796i | −0.967340 | − | 0.253482i | \(-0.918424\pi\) |
0.264148 | − | 0.964482i | \(-0.414909\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.2863 | + | 17.8164i | −0.891935 | + | 1.54488i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.04307 | + | 3.26399i | 0.347972 | + | 0.280919i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.25839 | − | 16.0360i | 0.790998 | − | 1.37005i | −0.134352 | − | 0.990934i | \(-0.542895\pi\) |
0.925350 | − | 0.379115i | \(-0.123771\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.00000 | − | 3.46410i | −0.169638 | − | 0.293821i | 0.768655 | − | 0.639664i | \(-0.220926\pi\) |
−0.938293 | + | 0.345843i | \(0.887593\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.817917 | − | 1.92957i | 0.0688811 | − | 0.162499i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 19.4684 | 1.62803 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.46838 | 0.371079 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.496291 | − | 0.657916i | −0.0409334 | − | 0.0542640i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.78630 | − | 11.7542i | −0.555955 | − | 0.962943i | −0.997829 | − | 0.0658653i | \(-0.979019\pi\) |
0.441873 | − | 0.897078i | \(-0.354314\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.23048 | + | 10.7915i | −0.507029 | + | 0.878201i | 0.492937 | + | 0.870065i | \(0.335923\pi\) |
−0.999967 | + | 0.00813598i | \(0.997410\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −16.0763 | + | 4.02534i | −1.29969 | + | 0.325429i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.76210 | + | 6.51615i | −0.302179 | + | 0.523390i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.790009 | + | 1.36834i | 0.0630496 | + | 0.109205i | 0.895827 | − | 0.444403i | \(-0.146584\pi\) |
−0.832778 | + | 0.553608i | \(0.813251\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.52420 | − | 0.311213i | 0.200182 | − | 0.0246808i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.00742 | 0.158207 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.47580 | 0.350572 | 0.175286 | − | 0.984518i | \(-0.443915\pi\) | ||||
0.175286 | + | 0.984518i | \(0.443915\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.49629 | − | 1.17081i | 0.739285 | − | 0.0911477i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.39500 | + | 14.5406i | 0.649625 | + | 1.12518i | 0.983212 | + | 0.182464i | \(0.0584074\pi\) |
−0.333588 | + | 0.942719i | \(0.608259\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.290009 | − | 0.502310i | 0.0223084 | − | 0.0386392i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −21.8966 | + | 5.48269i | −1.67448 | + | 0.419271i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.5242 | − | 19.9605i | 0.876169 | − | 1.51757i | 0.0206561 | − | 0.999787i | \(-0.493424\pi\) |
0.855513 | − | 0.517782i | \(-0.173242\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.36710 | + | 2.36788i | 0.103343 | + | 0.178995i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.53162 | − | 2.03041i | −0.115123 | − | 0.152615i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.9926 | −0.971111 | −0.485556 | − | 0.874206i | \(-0.661383\pi\) | ||||
−0.485556 | + | 0.874206i | \(0.661383\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.5652 | −1.82592 | −0.912958 | − | 0.408054i | \(-0.866207\pi\) | ||||
−0.912958 | + | 0.408054i | \(0.866207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.12146 | + | 14.4413i | −0.452511 | + | 1.06753i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.02791 | + | 5.24449i | 0.222616 | + | 0.385583i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.2584 | + | 26.4283i | −1.11580 | + | 1.93263i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.20147 | − | 14.0357i | 0.160134 | − | 1.02094i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.55211 | − | 13.0806i | 0.546451 | − | 0.946482i | −0.452063 | − | 0.891986i | \(-0.649312\pi\) |
0.998514 | − | 0.0544954i | \(-0.0173550\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.28630 | + | 12.6202i | 0.524479 | + | 0.908425i | 0.999594 | + | 0.0285008i | \(0.00907332\pi\) |
−0.475114 | + | 0.879924i | \(0.657593\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.38225 | + | 5.62004i | −0.170597 | + | 0.402459i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.53162 | −0.322864 | −0.161432 | − | 0.986884i | \(-0.551611\pi\) | ||||
−0.161432 | + | 0.986884i | \(0.551611\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.41256 | 0.525463 | 0.262731 | − | 0.964869i | \(-0.415377\pi\) | ||||
0.262731 | + | 0.964869i | \(0.415377\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.44178 | − | 5.88832i | −0.313299 | − | 0.415330i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.10870 | − | 10.5806i | −0.428747 | − | 0.742612i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.527909 | + | 0.914365i | −0.0368708 | + | 0.0638620i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.53162 | + | 1.58287i | 0.106455 | + | 0.110017i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −20.7826 | + | 35.9965i | −1.43756 | + | 2.48993i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.70628 | − | 11.6156i | −0.461680 | − | 0.799652i | 0.537365 | − | 0.843350i | \(-0.319420\pi\) |
−0.999045 | + | 0.0436972i | \(0.986086\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −17.2863 | + | 2.13126i | −1.18444 | + | 0.146031i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.52420 | −0.240348 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 20.5726 | 1.39656 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.7523 | − | 1.69554i | 0.929293 | − | 0.114574i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.73419 | − | 16.8601i | −0.654793 | − | 1.13413i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.39500 | + | 7.61237i | −0.294311 | + | 0.509762i | −0.974824 | − | 0.222974i | \(-0.928424\pi\) |
0.680513 | + | 0.732736i | \(0.261757\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.824030 | + | 2.88461i | −0.0549354 | + | 0.192307i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.02791 | − | 3.51244i | 0.134597 | − | 0.233129i | −0.790846 | − | 0.612015i | \(-0.790359\pi\) |
0.925443 | + | 0.378886i | \(0.123693\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.29001 | − | 2.23436i | −0.0852462 | − | 0.147651i | 0.820250 | − | 0.572005i | \(-0.193834\pi\) |
−0.905496 | + | 0.424355i | \(0.860501\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −15.7547 | − | 20.8855i | −1.03658 | − | 1.37416i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.94418 | −0.127368 | −0.0636838 | − | 0.997970i | \(-0.520285\pi\) | ||||
−0.0636838 | + | 0.997970i | \(0.520285\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.20999 | 0.0789311 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.35194 | − | 3.18940i | 0.0878179 | − | 0.207174i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.73419 | + | 6.46781i | 0.241545 | + | 0.418368i | 0.961154 | − | 0.276011i | \(-0.0890126\pi\) |
−0.719610 | + | 0.694379i | \(0.755679\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.20628 | + | 2.08934i | −0.0777035 | + | 0.134586i | −0.902259 | − | 0.431195i | \(-0.858092\pi\) |
0.824555 | + | 0.565781i | \(0.191425\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.7469 | − | 8.97304i | 0.817717 | − | 0.575621i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.237900 | − | 0.412055i | 0.0151989 | − | 0.0263252i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.2584 | − | 22.9642i | −0.843611 | − | 1.46118i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.55953 | + | 8.39738i | −0.225576 | + | 0.532162i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.99258 | 0.441368 | 0.220684 | − | 0.975345i | \(-0.429171\pi\) | ||||
0.220684 | + | 0.975345i | \(0.429171\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.05582 | 0.254987 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.76210 | − | 7.63862i | −0.360837 | − | 0.478349i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.0484 | + | 24.3325i | 0.876315 | + | 1.51782i | 0.855355 | + | 0.518042i | \(0.173339\pi\) |
0.0209598 | + | 0.999780i | \(0.493328\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.27888 | − | 14.3394i | 0.514425 | − | 0.891010i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.68208 | − | 12.8895i | 0.227915 | − | 0.797842i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.81792 | − | 6.61283i | 0.235423 | − | 0.407764i | −0.723973 | − | 0.689829i | \(-0.757686\pi\) |
0.959395 | + | 0.282064i | \(0.0910192\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.734191 | + | 1.27166i | 0.0451010 | + | 0.0781172i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.15710 | + | 0.635828i | −0.315610 | + | 0.0389120i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.6210 | −1.13534 | −0.567671 | − | 0.823255i | \(-0.692155\pi\) | ||||
−0.567671 | + | 0.823255i | \(0.692155\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.57260 | −0.399257 | −0.199628 | − | 0.979872i | \(-0.563974\pi\) | ||||
−0.199628 | + | 0.979872i | \(0.563974\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 16.5643 | − | 2.04224i | 1.00252 | − | 0.123602i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.76210 | + | 4.78410i | 0.166561 | + | 0.288492i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.762100 | + | 1.32000i | −0.0457901 | + | 0.0793108i | −0.888012 | − | 0.459820i | \(-0.847914\pi\) |
0.842222 | + | 0.539131i | \(0.181247\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 15.6965 | + | 16.2217i | 0.939722 | + | 0.971167i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.26210 | + | 12.5783i | −0.433221 | + | 0.750360i | −0.997149 | − | 0.0754640i | \(-0.975956\pi\) |
0.563928 | + | 0.825824i | \(0.309290\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.36710 | − | 14.4922i | −0.497372 | − | 0.861474i | 0.502623 | − | 0.864506i | \(-0.332368\pi\) |
−0.999995 | + | 0.00303167i | \(0.999035\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.84823 | − | 10.4041i | −0.464889 | − | 0.616288i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.88681 | 0.170403 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.5168 | 0.795105 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.40034 | + | 15.0992i | −0.375194 | + | 0.885132i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.2305 | + | 17.7197i | 0.597671 | + | 1.03520i | 0.993164 | + | 0.116728i | \(0.0372405\pi\) |
−0.395493 | + | 0.918469i | \(0.629426\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.734191 | − | 1.27166i | 0.0427463 | − | 0.0740387i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.44789 | − | 28.3579i | 0.258093 | − | 1.64549i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.29372 | + | 2.24078i | −0.0748176 | + | 0.129588i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.81792 | + | 8.34488i | 0.277700 | + | 0.480991i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.10422 | + | 21.4780i | −0.523024 | + | 1.23388i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.05582 | −0.518535 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.2026 | 1.03888 | 0.519438 | − | 0.854508i | \(-0.326141\pi\) | ||||
0.519438 | + | 0.854508i | \(0.326141\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 19.3724 | + | 25.6814i | 1.10206 | + | 1.46096i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.55211 | + | 2.68833i | 0.0880120 | + | 0.152441i | 0.906671 | − | 0.421839i | \(-0.138615\pi\) |
−0.818659 | + | 0.574280i | \(0.805282\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.55211 | − | 16.5447i | 0.539917 | − | 0.935164i | −0.458991 | − | 0.888441i | \(-0.651789\pi\) |
0.998908 | − | 0.0467228i | \(-0.0148777\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.95693 | − | 1.99233i | 0.448322 | − | 0.112255i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.50371 | + | 4.33655i | −0.140622 | + | 0.243565i | −0.927731 | − | 0.373249i | \(-0.878244\pi\) |
0.787109 | + | 0.616814i | \(0.211577\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.3421 | − | 21.3772i | −0.691026 | − | 1.19689i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −33.0931 | + | 4.08010i | −1.84708 | + | 0.227729i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 41.5652 | 2.31275 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.52420 | −0.195487 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.901117 | + | 0.111100i | −0.0498319 | + | 0.00614386i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.65417 | − | 2.86511i | −0.0911976 | − | 0.157959i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.74161 | + | 3.01656i | −0.0957275 | + | 0.165805i | −0.909912 | − | 0.414801i | \(-0.863851\pi\) |
0.814184 | + | 0.580606i | \(0.197184\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 17.6234 | − | 4.41271i | 0.965756 | − | 0.241815i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.12920 | − | 3.68787i | 0.116330 | − | 0.201490i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.79001 | − | 10.0286i | −0.315402 | − | 0.546292i | 0.664121 | − | 0.747625i | \(-0.268806\pi\) |
−0.979523 | + | 0.201333i | \(0.935473\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.79001 | + | 10.3270i | 0.423095 | + | 0.560883i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 41.5652 | 2.25088 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.8384 | 0.963183 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.496291 | + | 1.17081i | −0.0267194 | + | 0.0630345i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.2305 | + | 22.9159i | 0.710249 | + | 1.23019i | 0.964763 | + | 0.263119i | \(0.0847512\pi\) |
−0.254514 | + | 0.967069i | \(0.581915\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.0168 | − | 22.5457i | 0.696772 | − | 1.20685i | −0.272807 | − | 0.962069i | \(-0.587952\pi\) |
0.969580 | − | 0.244776i | \(-0.0787145\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.2486 | + | 11.5029i | 0.760532 | + | 0.613982i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.0000 | − | 20.7846i | 0.638696 | − | 1.10625i | −0.347024 | − | 0.937856i | \(-0.612808\pi\) |
0.985719 | − | 0.168397i | \(-0.0538590\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.02791 | − | 8.70859i | −0.266854 | − | 0.462204i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −10.2100 | + | 24.0867i | −0.540370 | + | 1.27480i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.04098 | −0.318831 | −0.159415 | − | 0.987212i | \(-0.550961\pi\) | ||||
−0.159415 | + | 0.987212i | \(0.550961\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 37.6136 | 1.97966 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −20.3573 | − | 26.9870i | −1.06848 | − | 1.41645i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.00000 | + | 6.92820i | 0.209370 | + | 0.362639i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.2305 | − | 19.4518i | 0.586226 | − | 1.01537i | −0.408495 | − | 0.912761i | \(-0.633946\pi\) |
0.994721 | − | 0.102613i | \(-0.0327204\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.20257 | + | 2.27628i | 0.114661 | + | 0.118498i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.00742 | − | 3.47695i | 0.104220 | − | 0.180514i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.26581 | + | 2.19245i | 0.0655411 | + | 0.113521i | 0.896934 | − | 0.442165i | \(-0.145789\pi\) |
−0.831393 | + | 0.555685i | \(0.812456\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.71903 | + | 0.211943i | −0.0887706 | + | 0.0109447i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15.7475 | 0.811036 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.0484 | 1.08118 | 0.540592 | − | 0.841285i | \(-0.318200\pi\) | ||||
0.540592 | + | 0.841285i | \(0.318200\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.1965 | + | 1.75031i | −0.727307 | + | 0.0896709i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.81792 | − | 6.61283i | −0.195086 | − | 0.337900i | 0.751842 | − | 0.659343i | \(-0.229165\pi\) |
−0.946929 | + | 0.321443i | \(0.895832\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.55211 | − | 13.0806i | 0.384891 | − | 0.666651i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.90405 | + | 10.1659i | −0.147621 | + | 0.516764i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.46467 | − | 16.3933i | 0.479878 | − | 0.831173i | −0.519856 | − | 0.854254i | \(-0.674014\pi\) |
0.999734 | + | 0.0230811i | \(0.00734760\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.02791 | − | 3.51244i | −0.102556 | − | 0.177632i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −16.7900 | − | 22.2580i | −0.846944 | − | 1.12277i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.00000 | 0.100631 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.1600 | −1.46350 | −0.731750 | − | 0.681573i | \(-0.761296\pi\) | ||||
−0.731750 | + | 0.681573i | \(0.761296\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −13.9065 | + | 32.8071i | −0.696193 | + | 1.64241i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.3142 | − | 28.2570i | −0.814693 | − | 1.41109i | −0.909548 | − | 0.415598i | \(-0.863572\pi\) |
0.0948557 | − | 0.995491i | \(-0.469761\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.2584 | + | 22.9642i | −0.660447 | + | 1.14393i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.64195 | + | 4.75401i | 0.379731 | + | 0.236229i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.7268 | − | 28.9716i | 0.829115 | − | 1.43607i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.1042 | − | 27.8933i | −0.796302 | − | 1.37924i | −0.922009 | − | 0.387169i | \(-0.873453\pi\) |
0.125707 | − | 0.992067i | \(-0.459880\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.5168 | − | 29.5287i | 0.617407 | − | 1.45654i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.01484 | −0.197557 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.26581 | −0.258488 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.17226 | − | 5.53103i | −0.204316 | − | 0.270855i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.7063 | − | 18.5438i | −0.523036 | − | 0.905925i | −0.999641 | − | 0.0268073i | \(-0.991466\pi\) |
0.476605 | − | 0.879118i | \(-0.341867\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.944182 | − | 1.63537i | 0.0460166 | − | 0.0797031i | −0.842100 | − | 0.539322i | \(-0.818681\pi\) |
0.888116 | + | 0.459619i | \(0.152014\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.997070 | − | 3.49035i | 0.0484792 | − | 0.169707i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.76210 | − | 4.78410i | 0.133982 | − | 0.232063i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.3802 | + | 21.4431i | 0.599118 | + | 1.03770i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 33.4668 | − | 4.12618i | 1.61579 | − | 0.199214i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.11164 | 0.101714 | 0.0508569 | − | 0.998706i | \(-0.483805\pi\) | ||||
0.0508569 | + | 0.998706i | \(0.483805\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.52420 | −0.457704 | −0.228852 | − | 0.973461i | \(-0.573497\pi\) | ||||
−0.228852 | + | 0.973461i | \(0.573497\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.68130 | − | 0.947041i | 0.368290 | − | 0.0454071i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.76210 | − | 4.78410i | −0.132129 | − | 0.228854i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.20257 | + | 12.4752i | −0.343760 | + | 0.595410i | −0.985128 | − | 0.171824i | \(-0.945034\pi\) |
0.641368 | + | 0.767234i | \(0.278367\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.992582 | − | 1.02580i | −0.0472658 | − | 0.0488474i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.60500 | + | 16.6363i | −0.456347 | + | 0.790416i | −0.998765 | − | 0.0496927i | \(-0.984176\pi\) |
0.542417 | + | 0.840109i | \(0.317509\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.50000 | − | 2.59808i | −0.0711068 | − | 0.123161i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.1571 | − | 18.7676i | −0.669608 | − | 0.887677i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.5800 | 1.58474 | 0.792369 | − | 0.610041i | \(-0.208847\pi\) | ||||
0.792369 | + | 0.610041i | \(0.208847\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.83255 | 0.274644 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.42323 | + | 19.8715i | −0.395758 | + | 0.933644i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.81792 | + | 8.34488i | 0.225867 | + | 0.391214i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.08373 | + | 1.87707i | −0.0506946 | + | 0.0878056i | −0.890259 | − | 0.455454i | \(-0.849477\pi\) |
0.839565 | + | 0.543260i | \(0.182810\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −26.7826 | + | 10.3270i | −1.25010 | + | 0.482021i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.8700 | − | 22.2915i | 0.599417 | − | 1.03822i | −0.393490 | − | 0.919329i | \(-0.628733\pi\) |
0.992907 | − | 0.118892i | \(-0.0379341\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.02791 | + | 10.4406i | 0.280141 | + | 0.485218i | 0.971419 | − | 0.237371i | \(-0.0762855\pi\) |
−0.691279 | + | 0.722588i | \(0.742952\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.08613 | + | 11.9988i | −0.235864 | + | 0.556433i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.4610 | 0.669174 | 0.334587 | − | 0.942365i | \(-0.391403\pi\) | ||||
0.334587 | + | 0.942365i | \(0.391403\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.6433 | −0.537635 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.64806 | + | 2.18478i | 0.0759386 | + | 0.100669i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.73419 | + | 16.8601i | 0.447579 | + | 0.775229i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.76210 | − | 6.51615i | 0.172617 | − | 0.298981i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.27323 | − | 1.06997i | 0.195658 | − | 0.0489906i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.99258 | + | 17.3077i | −0.456573 | + | 0.790807i | −0.998777 | − | 0.0494395i | \(-0.984257\pi\) |
0.542204 | + | 0.840247i | \(0.317590\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.6710 | + | 18.4826i | 0.486554 | + | 0.842736i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.45082 | − | 0.425458i | 0.157018 | − | 0.0193590i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.46838 | −0.429937 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.1526 | 0.822574 | 0.411287 | − | 0.911506i | \(-0.365079\pi\) | ||||
0.411287 | + | 0.911506i | \(0.365079\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.69406 | − | 0.948613i | 0.347937 | − | 0.0428978i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.7900 | + | 34.2773i | 0.893111 | + | 1.54691i | 0.836126 | + | 0.548538i | \(0.184815\pi\) |
0.0569849 | + | 0.998375i | \(0.481851\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.3421 | + | 21.3772i | −0.555861 | + | 0.962779i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 16.0763 | − | 4.02534i | 0.722576 | − | 0.180926i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13.7473 | + | 23.8110i | −0.616649 | + | 1.06807i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.3142 | − | 36.9173i | −0.954155 | − | 1.65264i | −0.736290 | − | 0.676666i | \(-0.763424\pi\) |
−0.217865 | − | 0.975979i | \(-0.569909\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.5131 | + | 23.2165i | 0.782426 | + | 1.03724i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.1952 | −0.945045 | −0.472523 | − | 0.881319i | \(-0.656657\pi\) | ||||
−0.472523 | + | 0.881319i | \(0.656657\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.4684 | −0.599335 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.392074 | − | 0.924953i | 0.0174126 | − | 0.0410786i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.0168 | + | 19.0816i | 0.488310 | + | 0.845778i | 0.999910 | − | 0.0134460i | \(-0.00428012\pi\) |
−0.511599 | + | 0.859224i | \(0.670947\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.9368 | − | 18.9430i | 0.483814 | − | 0.837990i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −36.4791 | + | 14.0658i | −1.61059 | + | 0.621018i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.28630 | + | 16.0843i | −0.409203 | + | 0.708761i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.34212 | − | 5.78872i | −0.146986 | − | 0.254587i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15.5800 | − | 36.7553i | 0.683887 | − | 1.61338i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.40515 | 0.0615606 | 0.0307803 | − | 0.999526i | \(-0.490201\pi\) | ||||
0.0307803 | + | 0.999526i | \(0.490201\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.8532 | 0.518306 | 0.259153 | − | 0.965836i | \(-0.416557\pi\) | ||||
0.259153 | + | 0.965836i | \(0.416557\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.85194 | + | 3.78072i | 0.124469 | + | 0.165004i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.7826 | − | 35.9965i | −0.905304 | − | 1.56803i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.2305 | − | 19.4518i | 0.488282 | − | 0.845729i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.06324 | − | 3.16574i | −0.132933 | − | 0.137381i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.86046 | + | 3.22240i | −0.0805853 | + | 0.139578i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.62549 | − | 16.6718i | −0.416146 | − | 0.720786i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −22.3347 | + | 2.75368i | −0.963813 | + | 0.118830i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.62842 | −0.113214 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.98516 | −0.386302 | −0.193151 | − | 0.981169i | \(-0.561871\pi\) | ||||
−0.193151 | + | 0.981169i | \(0.561871\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −42.2284 | + | 5.20641i | −1.81219 | + | 0.223428i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.262100 | − | 0.453970i | −0.0112271 | − | 0.0194459i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.10129 | + | 5.37159i | −0.132601 | + | 0.229672i | −0.924679 | − | 0.380749i | \(-0.875666\pi\) |
0.792077 | + | 0.610421i | \(0.209000\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.46227 | + | 26.1225i | −0.318482 | + | 1.11488i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16.8105 | + | 29.1166i | −0.716151 | + | 1.24041i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.73419 | − | 4.73576i | −0.116270 | − | 0.201385i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.31661 | + | 8.37372i | 0.268125 | + | 0.355445i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.00000 | 0.254228 | 0.127114 | − | 0.991888i | \(-0.459429\pi\) | ||||
0.127114 | + | 0.991888i | \(0.459429\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.4200 | −0.525309 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −20.6284 | + | 48.6651i | −0.870932 | + | 2.05464i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.13661 | − | 3.70072i | −0.0900475 | − | 0.155967i | 0.817483 | − | 0.575952i | \(-0.195369\pi\) |
−0.907531 | + | 0.419985i | \(0.862035\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.73419 | + | 6.46781i | −0.157099 | + | 0.272103i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.809653 | − | 24.5944i | 0.0340022 | − | 1.03287i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.04840 | + | 13.9402i | −0.337406 | + | 0.584405i | −0.983944 | − | 0.178477i | \(-0.942883\pi\) |
0.646538 | + | 0.762882i | \(0.276216\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.46838 | + | 9.47152i | 0.228845 | + | 0.396371i | 0.957466 | − | 0.288546i | \(-0.0931719\pi\) |
−0.728621 | + | 0.684917i | \(0.759839\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.2100 | − | 24.0867i | 0.426529 | − | 1.00624i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.734191 | −0.0306179 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −37.6620 | −1.56789 | −0.783944 | − | 0.620831i | \(-0.786795\pi\) | ||||
−0.783944 | + | 0.620831i | \(0.786795\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15.2002 | + | 20.1504i | 0.631697 | + | 0.837420i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.19886 | + | 12.4688i | 0.298659 | + | 0.517293i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.05582 | − | 7.02488i | 0.167975 | − | 0.290941i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.90405 | + | 10.1659i | −0.120068 | + | 0.420310i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.8987 | − | 18.8771i | 0.449838 | − | 0.779142i | −0.548537 | − | 0.836126i | \(-0.684815\pi\) |
0.998375 | + | 0.0569839i | \(0.0181484\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −28.3068 | − | 49.0288i | −1.16636 | − | 2.02020i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.79001 | + | 0.960443i | −0.320438 | + | 0.0395074i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 28.2643 | 1.16067 | 0.580337 | − | 0.814377i | \(-0.302921\pi\) | ||||
0.580337 | + | 0.814377i | \(0.302921\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −15.1042 | −0.619213 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.7425 | − | 1.57104i | 0.521514 | − | 0.0642983i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.05582 | + | 12.2210i | 0.288293 | + | 0.499338i | 0.973402 | − | 0.229102i | \(-0.0735790\pi\) |
−0.685109 | + | 0.728440i | \(0.740246\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.1042 | − | 24.4292i | 0.575323 | − | 0.996489i | −0.420683 | − | 0.907207i | \(-0.638210\pi\) |
0.996006 | − | 0.0892812i | \(-0.0284570\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.88356 | − | 9.18082i | −0.361766 | − | 0.373872i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.75839 | − | 16.9020i | 0.396735 | − | 0.687165i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.1850 | + | 24.5692i | 0.575752 | + | 0.997232i | 0.995959 | + | 0.0898036i | \(0.0286239\pi\) |
−0.420208 | + | 0.907428i | \(0.638043\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12.7436 | − | 16.8937i | −0.516395 | − | 0.684567i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.26425 | 0.172513 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.5726 | 0.992478 | 0.496239 | − | 0.868186i | \(-0.334714\pi\) | ||||
0.496239 | + | 0.868186i | \(0.334714\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.713701 | + | 1.68371i | −0.0287792 | + | 0.0678938i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.3142 | + | 23.0609i | 0.536010 | + | 0.928396i | 0.999114 | + | 0.0420923i | \(0.0134023\pi\) |
−0.463104 | + | 0.886304i | \(0.653264\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.2863 | − | 26.4766i | 0.614408 | − | 1.06419i | −0.376080 | − | 0.926587i | \(-0.622728\pi\) |
0.990488 | − | 0.137599i | \(-0.0439385\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.96838 | + | 2.39639i | 0.119117 | + | 0.0961639i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.10129 | + | 7.10364i | −0.164315 | + | 0.284601i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −28.0968 | + | 66.2840i | −1.12208 | + | 2.64713i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −33.4535 | −1.33388 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.4684 | −1.09350 | −0.546750 | − | 0.837296i | \(-0.684135\pi\) | ||||
−0.546750 | + | 0.837296i | \(0.684135\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −13.9902 | − | 18.5463i | −0.556060 | − | 0.737150i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.12920 | − | 7.15198i | −0.163862 | − | 0.283818i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.838408 | − | 1.45216i | 0.0332189 | − | 0.0575369i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −29.2640 | + | 7.32741i | −1.15767 | + | 0.289868i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.26952 | + | 10.8591i | −0.247631 | + | 0.428910i | −0.962868 | − | 0.269972i | \(-0.912985\pi\) |
0.715237 | + | 0.698882i | \(0.246319\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.12920 | − | 8.88403i | −0.202276 | − | 0.350352i | 0.746986 | − | 0.664840i | \(-0.231500\pi\) |
−0.949261 | + | 0.314488i | \(0.898167\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.05822 | + | 0.746928i | −0.238542 | + | 0.0294103i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.7900 | −0.660083 | −0.330042 | − | 0.943966i | \(-0.607063\pi\) | ||||
−0.330042 | + | 0.943966i | \(0.607063\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.11164 | −0.318410 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 35.3650 | − | 4.36021i | 1.38606 | − | 0.170890i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25.0131 | − | 43.3239i | −0.978837 | − | 1.69540i | −0.666643 | − | 0.745377i | \(-0.732269\pi\) |
−0.312194 | − | 0.950018i | \(-0.601064\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.04840 | − | 13.9402i | 0.314477 | − | 0.544690i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 23.2813 | − | 5.82939i | 0.908289 | − | 0.227426i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.78259 | − | 4.81959i | 0.108394 | − | 0.187744i | −0.806726 | − | 0.590926i | \(-0.798762\pi\) |
0.915120 | + | 0.403182i | \(0.132096\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.6284 | + | 33.9974i | 0.763457 | + | 1.32235i | 0.941059 | + | 0.338244i | \(0.109833\pi\) |
−0.177602 | + | 0.984102i | \(0.556834\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −20.3068 | − | 26.9200i | −0.788650 | − | 1.04549i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −20.5726 | −0.797771 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.28065 | 0.127027 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.94178 | + | 14.0174i | −0.229722 | + | 0.541945i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 25.0131 | + | 43.3239i | 0.965619 | + | 1.67250i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.97209 | + | 13.8081i | −0.307302 | + | 0.532262i | −0.977771 | − | 0.209675i | \(-0.932759\pi\) |
0.670470 | + | 0.741937i | \(0.266093\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.805165 | + | 5.13339i | −0.0309908 | + | 0.197584i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.4479 | − | 18.0963i | 0.401545 | − | 0.695497i | −0.592368 | − | 0.805668i | \(-0.701807\pi\) |
0.993913 | + | 0.110171i | \(0.0351400\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.9442 | + | 22.4200i | 0.496752 | + | 0.860400i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.74161 | − | 6.46781i | 0.105059 | − | 0.247847i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19.6358 | 0.751344 | 0.375672 | − | 0.926753i | \(-0.377412\pi\) | ||||
0.375672 | + | 0.926753i | \(0.377412\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18.5168 | 0.707490 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.69113 | − | 3.56754i | −0.102673 | − | 0.136110i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.58744 | + | 4.48157i | 0.0985734 | + | 0.170734i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.5726 | + | 37.3648i | −0.820660 | + | 1.42143i | 0.0845309 | + | 0.996421i | \(0.473061\pi\) |
−0.905191 | + | 0.425005i | \(0.860272\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −31.5094 | − | 32.5637i | −1.19694 | − | 1.23699i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.00000 | − | 3.46410i | 0.0758643 | − | 0.131401i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.91627 | − | 5.05113i | −0.110462 | − | 0.191325i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.34212 | + | 0.412055i | −0.126410 | + | 0.0155854i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.0410 | 1.02132 | 0.510662 | − | 0.859782i | \(-0.329400\pi\) | ||||
0.510662 | + | 0.859782i | \(0.329400\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −45.5652 | −1.71852 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.08002 | − | 0.256449i | 0.0783380 | − | 0.00965842i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18.4126 | + | 31.8915i | 0.692476 | + | 1.19940i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.7510 | + | 37.6738i | −0.816875 | + | 1.41487i | 0.0910989 | + | 0.995842i | \(0.470962\pi\) |
−0.907974 | + | 0.419027i | \(0.862371\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.64806 | − | 5.76922i | 0.0618071 | − | 0.216363i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.76210 | + | 4.78410i | −0.103441 | + | 0.179166i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.73419 | + | 16.8601i | 0.364038 | + | 0.630532i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.79001 | + | 10.3270i | 0.290923 | + | 0.385667i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.40515 | 0.164284 | 0.0821421 | − | 0.996621i | \(-0.473824\pi\) | ||||
0.0821421 | + | 0.996621i | \(0.473824\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 50.7810 | 1.89118 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.63082 | + | 3.84731i | −0.0606509 | + | 0.143083i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.23419 | + | 3.86973i | 0.0829758 | + | 0.143718i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.24083 | − | 10.8094i | 0.231460 | − | 0.400900i | −0.726778 | − | 0.686872i | \(-0.758983\pi\) |
0.958238 | + | 0.285972i | \(0.0923166\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.0107 | − | 18.1266i | 0.741136 | − | 0.671355i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.73419 | − | 16.8601i | 0.360032 | − | 0.623594i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.5168 | − | 33.8041i | −0.720869 | − | 1.24858i | −0.960652 | − | 0.277755i | \(-0.910410\pi\) |
0.239783 | − | 0.970826i | \(-0.422924\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.321627 | − | 0.758758i | 0.0118634 | − | 0.0279872i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −23.5242 | −0.866525 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.2935 | 0.452224 | 0.226112 | − | 0.974101i | \(-0.427398\pi\) | ||||
0.226112 | + | 0.974101i | \(0.427398\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −27.6587 | − | 36.6662i | −1.01607 | − | 1.34697i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.4155 | − | 35.3607i | −0.748972 | − | 1.29726i | −0.948316 | − | 0.317328i | \(-0.897214\pi\) |
0.199344 | − | 0.979930i | \(-0.436119\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.78630 | − | 11.7542i | 0.248631 | − | 0.430641i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.33919 | + | 15.1898i | −0.158763 | + | 0.555766i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −26.3179 | + | 45.5840i | −0.961636 | + | 1.66560i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.54469 | − | 13.0678i | −0.275310 | − | 0.476850i | 0.694904 | − | 0.719103i | \(-0.255447\pi\) |
−0.970213 | + | 0.242253i | \(0.922114\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.0205 | − | 1.48203i | 0.438051 | − | 0.0540080i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.4610 | −0.453501 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.4610 | 1.25251 | 0.626253 | − | 0.779620i | \(-0.284588\pi\) | ||||
0.626253 | + | 0.779620i | \(0.284588\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.97209 | − | 0.859601i | 0.253071 | − | 0.0312015i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.17837 | + | 7.23716i | 0.151466 | + | 0.262347i | 0.931767 | − | 0.363058i | \(-0.118267\pi\) |
−0.780301 | + | 0.625405i | \(0.784934\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.716631 | + | 1.24124i | −0.0259438 | + | 0.0449359i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −11.5242 | − | 11.9098i | −0.416658 | − | 0.430601i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.58744 | − | 4.48157i | 0.0934269 | − | 0.161820i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.17837 | + | 15.8974i | 0.330981 | + | 0.573275i | 0.982704 | − | 0.185181i | \(-0.0592872\pi\) |
−0.651724 | + | 0.758456i | \(0.725954\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 29.3068 | + | 38.8510i | 1.05546 | + | 1.39919i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10.0968 | −0.363157 | −0.181578 | − | 0.983376i | \(-0.558121\pi\) | ||||
−0.181578 | + | 0.983376i | \(0.558121\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.52420 | −0.270277 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11.1925 | − | 26.4046i | 0.401530 | − | 0.947261i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.97209 | − | 6.87986i | −0.142315 | − | 0.246497i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27.7752 | + | 48.1080i | −0.993874 | + | 1.72144i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.59778 | − | 22.9380i | 0.128574 | − | 0.819736i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.790009 | + | 1.36834i | −0.0281966 | + | 0.0488380i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.28630 | − | 12.6202i | −0.259729 | − | 0.449863i | 0.706441 | − | 0.707772i | \(-0.250300\pi\) |
−0.966169 | + | 0.257909i | \(0.916966\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.16159 | − | 12.1769i | 0.183758 | − | 0.433508i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20.4200 | 0.726051 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −31.9145 | −1.13332 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.53162 | + | 2.03041i | 0.0543209 | + | 0.0720114i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.03533 | + | 1.79324i | 0.0366732 | + | 0.0635198i | 0.883779 | − | 0.467904i | \(-0.154991\pi\) |
−0.847106 | + | 0.531424i | \(0.821657\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.34212 | + | 5.78872i | −0.118236 | + | 0.204790i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.73048 | + | 2.18602i | −0.308476 | + | 0.0772393i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 22.0968 | − | 38.2728i | 0.779779 | − | 1.35062i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.00371 | + | 1.73848i | 0.0353761 | + | 0.0612732i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −32.0101 | + | 3.94658i | −1.12681 | + | 0.138926i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.37158 | 0.118539 | 0.0592693 | − | 0.998242i | \(-0.481123\pi\) | ||||
0.0592693 | + | 0.998242i | \(0.481123\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.9368 | 0.454271 | 0.227136 | − | 0.973863i | \(-0.427064\pi\) | ||||
0.227136 | + | 0.973863i | \(0.427064\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.2985 | + | 1.39301i | −0.396257 | + | 0.0488551i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.23790 | + | 3.87616i | 0.0783902 | + | 0.135776i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.2584 | − | 22.9642i | 0.463852 | − | 0.803416i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 28.0418 | − | 7.02138i | 0.979861 | − | 0.245347i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.9963 | − | 19.0461i | 0.383773 | − | 0.664715i | −0.607825 | − | 0.794071i | \(-0.707958\pi\) |
0.991598 | + | 0.129356i | \(0.0412911\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.45082 | + | 12.9052i | 0.259719 | + | 0.449847i | 0.966167 | − | 0.257919i | \(-0.0830366\pi\) |
−0.706447 | + | 0.707766i | \(0.749703\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.76210 | + | 7.63862i | 0.200611 | + | 0.265943i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −56.5785 | −1.96743 | −0.983713 | − | 0.179747i | \(-0.942472\pi\) | ||||
−0.983713 | + | 0.179747i | \(0.942472\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.0558 | 0.939687 | 0.469844 | − | 0.882750i | \(-0.344310\pi\) | ||||
0.469844 | + | 0.882750i | \(0.344310\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.03031 | + | 2.43064i | −0.0357411 | + | 0.0843180i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.31421 | + | 2.27628i | 0.0455346 | + | 0.0788683i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.39500 | + | 14.5406i | −0.290521 | + | 0.503197i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 30.4208 | + | 24.5589i | 1.05150 | + | 0.848880i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −17.2863 | + | 29.9407i | −0.596789 | + | 1.03367i | 0.396502 | + | 0.918034i | \(0.370224\pi\) |
−0.993292 | + | 0.115636i | \(0.963109\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.51678 | + | 7.82329i | 0.155751 | + | 0.269769i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.81792 | + | 23.1617i | −0.338147 | + | 0.797732i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.580017 | 0.0199532 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −53.3626 | −1.83356 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.4549 | − | 23.1393i | −0.599049 | − | 0.794139i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.22306 | + | 3.85046i | 0.0762056 | + | 0.131992i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.48887 | + | 14.7032i | −0.290653 | + | 0.503427i | −0.973964 | − | 0.226701i | \(-0.927206\pi\) |
0.683311 | + | 0.730127i | \(0.260539\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −15.6965 | − | 16.2217i | −0.536808 | − | 0.554770i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.70628 | + | 2.95537i | −0.0582855 | + | 0.100953i | −0.893696 | − | 0.448673i | \(-0.851897\pi\) |
0.835410 | + | 0.549627i | \(0.185230\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.91627 | − | 8.51524i | −0.167741 | − | 0.290536i | 0.769884 | − | 0.638184i | \(-0.220314\pi\) |
−0.937625 | + | 0.347647i | \(0.886981\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.96252 | − | 0.611838i | 0.169122 | − | 0.0208514i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 48.9836 | 1.66742 | 0.833711 | − | 0.552202i | \(-0.186212\pi\) | ||||
0.833711 | + | 0.552202i | \(0.186212\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.0484 | 0.783669 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 23.2358 | − | 2.86478i | 0.789130 | − | 0.0972931i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.52420 | − | 9.56819i | −0.187396 | − | 0.324579i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.50371 | − | 12.9968i | 0.254253 | − | 0.440380i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.80223 | + | 27.3126i | −0.264066 | + | 0.924391i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.36710 | + | 2.36788i | −0.0462163 | + | 0.0800489i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.33470 | + | 10.9720i | 0.213908 | + | 0.370499i | 0.952934 | − | 0.303178i | \(-0.0980475\pi\) |
−0.739027 | + | 0.673676i | \(0.764714\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 21.3421 | + | 28.2925i | 0.719852 | + | 0.954283i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.0894 | −0.878974 | −0.439487 | − | 0.898249i | \(-0.644840\pi\) | ||||
−0.439487 | + | 0.898249i | \(0.644840\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.69321 | −0.0906337 | −0.0453169 | − | 0.998973i | \(-0.514430\pi\) | ||||
−0.0453169 | + | 0.998973i | \(0.514430\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.992582 | − | 2.34163i | 0.0333653 | − | 0.0787129i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.2789 | − | 21.2676i | −0.412284 | − | 0.714098i | 0.582855 | − | 0.812576i | \(-0.301936\pi\) |
−0.995139 | + | 0.0984788i | \(0.968602\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.2900 | + | 19.5549i | −0.378655 | + | 0.655849i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.63583 | − | 49.6909i | 0.0548025 | − | 1.66471i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.55211 | + | 7.88448i | −0.152330 | + | 0.263844i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.49629 | − | 11.2519i | −0.217147 | − | 0.376110i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.74903 | + | 4.12618i | −0.0583983 | + | 0.137769i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 33.6210 | 1.12132 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.11164 | −0.270238 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.0508 | + | 13.3240i | 0.334470 | + | 0.443395i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.2826 | − | 21.2741i | −0.408287 | − | 0.707174i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.1850 | − | 29.7653i | 0.570619 | − | 0.988341i | −0.425884 | − | 0.904778i | \(-0.640037\pi\) |
0.996502 | − | 0.0835631i | \(-0.0266300\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.0984 | + | 38.8510i | −0.368109 | + | 1.28861i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.7752 | − | 32.5196i | 0.622049 | − | 1.07742i | −0.367054 | − | 0.930199i | \(-0.619634\pi\) |
0.989104 | − | 0.147221i | \(-0.0470330\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.5447 | + | 25.1921i | 0.481359 | + | 0.833738i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −15.5673 | + | 1.91931i | −0.514638 | + | 0.0634506i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −44.0117 | −1.45340 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.1116 | −0.333552 | −0.166776 | − | 0.985995i | \(-0.553336\pi\) | ||||
−0.166776 | + | 0.985995i | \(0.553336\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 31.2909 | − | 3.85790i | 1.03107 | − | 0.127122i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −17.7194 | − | 30.6908i | −0.583240 | − | 1.01020i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.02791 | + | 5.24449i | −0.0995570 | + | 0.172438i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 38.7449 | + | 40.0413i | 1.27255 | + | 1.31513i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −12.4126 | + | 21.4992i | −0.407243 | + | 0.705366i | −0.994580 | − | 0.103977i | \(-0.966843\pi\) |
0.587337 | + | 0.809343i | \(0.300176\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.79001 | + | 3.10039i | 0.0586652 | + | 0.101611i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.23790 | + | 4.29238i | 0.106004 | + | 0.140526i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −30.5168 | −0.998005 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.56518 | 0.0511322 | 0.0255661 | − | 0.999673i | \(-0.491861\pi\) | ||||
0.0255661 | + | 0.999673i | \(0.491861\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12.9139 | − | 30.4655i | 0.421428 | − | 0.994203i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.23419 | + | 9.06588i | 0.170630 | + | 0.295539i | 0.938640 | − | 0.344898i | \(-0.112086\pi\) |
−0.768010 | + | 0.640437i | \(0.778753\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.387586 | + | 0.671318i | −0.0126215 | + | 0.0218611i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13.2560 | − | 5.11130i | 0.431217 | − | 0.166271i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.59758 | + | 2.76709i | −0.0519143 | + | 0.0899182i | −0.890815 | − | 0.454367i | \(-0.849866\pi\) |
0.838900 | + | 0.544285i | \(0.183199\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.0968 | + | 24.4164i | 0.457601 | + | 0.792589i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.38486 | + | 7.98533i | −0.109762 | + | 0.258942i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33.9293 | −1.09908 | −0.549540 | − | 0.835468i | \(-0.685197\pi\) | ||||
−0.549540 | + | 0.835468i | \(0.685197\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.1042 | 0.488761 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −25.7473 | − | 34.1323i | −0.832291 | − | 1.10334i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −25.3142 | − | 43.8455i | −0.817438 | − | 1.41584i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.8068 | + | 22.1820i | −0.413122 | + | 0.715549i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −56.0234 | + | 14.0277i | −1.80533 | + | 0.452036i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.28630 | + | 12.6202i | −0.234554 | + | 0.406260i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.2129 | + | 33.2778i | 0.617846 | + | 1.07014i | 0.989878 | + | 0.141921i | \(0.0453278\pi\) |
−0.372032 | + | 0.928220i | \(0.621339\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 71.4520 | − | 8.80944i | 2.29537 | − | 0.283000i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −29.7326 | −0.954166 | −0.477083 | − | 0.878858i | \(-0.658306\pi\) | ||||
−0.477083 | + | 0.878858i | \(0.658306\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.9368 | −0.350617 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.05822 | + | 0.746928i | −0.194018 | + | 0.0239209i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.4889 | + | 28.5596i | 0.527526 | + | 0.913701i | 0.999485 | + | 0.0320812i | \(0.0102135\pi\) |
−0.471960 | + | 0.881620i | \(0.656453\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.28630 | + | 14.3523i | −0.264831 | + | 0.458701i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.52551 | + | 0.381970i | −0.0487056 | + | 0.0121954i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.68872 | + | 6.38905i | −0.117652 | + | 0.203779i | −0.918837 | − | 0.394638i | \(-0.870870\pi\) |
0.801185 | + | 0.598417i | \(0.204203\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.26581 | − | 3.92450i | −0.0721947 | − | 0.125045i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.45082 | − | 4.57464i | −0.109841 | − | 0.145612i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.58744 | −0.0822757 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.51678 | 0.143480 | 0.0717401 | − | 0.997423i | \(-0.477145\pi\) | ||||
0.0717401 | + | 0.997423i | \(0.477145\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.35455 | + | 5.55469i | −0.0747194 | + | 0.176273i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.70628 | + | 6.41947i | 0.117497 | + | 0.203511i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.3142 | − | 42.1134i | 0.770039 | − | 1.33375i | −0.167502 | − | 0.985872i | \(-0.553570\pi\) |
0.937541 | − | 0.347874i | \(-0.113096\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 29.3600 | − | 11.3208i | 0.928909 | − | 0.358173i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))