Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [735,2,Mod(146,735)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(735, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("735.146");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 735 = 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 735.b (of order \(2\), degree \(1\), 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: | \(5.86900454856\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.856615824.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 146.5 | ||
Root | \(-0.385731i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 735.146 |
Dual form | 735.2.b.c.146.4 |
$q$-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 \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).
\(n\) | \(346\) | \(442\) | \(491\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.385731i | 0.272753i | 0.990657 | + | 0.136376i | \(0.0435457\pi\) | ||||
−0.990657 | + | 0.136376i | \(0.956454\pi\) | |||||||
\(3\) | 1.56470 | − | 0.742765i | 0.903382 | − | 0.428836i | ||||
\(4\) | 1.85121 | 0.925606 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0.286507 | + | 0.603555i | 0.116966 | + | 0.246400i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.48553i | 0.525214i | ||||||||
\(9\) | 1.89660 | − | 2.32442i | 0.632200 | − | 0.774806i | ||||
\(10\) | 0.385731i | 0.121979i | ||||||||
\(11\) | − | 2.54224i | − | 0.766514i | −0.923642 | − | 0.383257i | \(-0.874802\pi\) | ||
0.923642 | − | 0.383257i | \(-0.125198\pi\) | |||||||
\(12\) | 2.89660 | − | 1.37502i | 0.836176 | − | 0.396933i | ||||
\(13\) | − | 3.06718i | − | 0.850683i | −0.905033 | − | 0.425342i | \(-0.860154\pi\) | ||
0.905033 | − | 0.425342i | \(-0.139846\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.56470 | − | 0.742765i | 0.404005 | − | 0.191781i | ||||
\(16\) | 3.12941 | 0.782352 | ||||||||
\(17\) | −6.46130 | −1.56710 | −0.783548 | − | 0.621331i | \(-0.786592\pi\) | ||||
−0.783548 | + | 0.621331i | \(0.786592\pi\) | |||||||
\(18\) | 0.896599 | + | 0.731577i | 0.211330 | + | 0.172434i | ||||
\(19\) | − | 1.19592i | − | 0.274363i | −0.990546 | − | 0.137181i | \(-0.956196\pi\) | ||
0.990546 | − | 0.137181i | \(-0.0438043\pi\) | |||||||
\(20\) | 1.85121 | 0.413944 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.980620 | 0.209069 | ||||||||
\(23\) | 3.05599i | 0.637219i | 0.947886 | + | 0.318609i | \(0.103216\pi\) | ||||
−0.947886 | + | 0.318609i | \(0.896784\pi\) | |||||||
\(24\) | 1.10340 | + | 2.32442i | 0.225231 | + | 0.474470i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.18311 | 0.232026 | ||||||||
\(27\) | 1.24112 | − | 5.04575i | 0.238854 | − | 0.971056i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.77029i | 1.44291i | 0.692463 | + | 0.721454i | \(0.256526\pi\) | ||||
−0.692463 | + | 0.721454i | \(0.743474\pi\) | |||||||
\(30\) | 0.286507 | + | 0.603555i | 0.0523089 | + | 0.110193i | ||||
\(31\) | 6.87392i | 1.23459i | 0.786731 | + | 0.617297i | \(0.211772\pi\) | ||||
−0.786731 | + | 0.617297i | \(0.788228\pi\) | |||||||
\(32\) | 4.17817i | 0.738603i | ||||||||
\(33\) | −1.88829 | − | 3.97785i | −0.328709 | − | 0.692456i | ||||
\(34\) | − | 2.49232i | − | 0.427430i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.51101 | − | 4.30299i | 0.585168 | − | 0.717165i | ||||
\(37\) | −3.55208 | −0.583958 | −0.291979 | − | 0.956425i | \(-0.594314\pi\) | ||||
−0.291979 | + | 0.956425i | \(0.594314\pi\) | |||||||
\(38\) | 0.461303 | 0.0748333 | ||||||||
\(39\) | −2.27820 | − | 4.79923i | −0.364803 | − | 0.768492i | ||||
\(40\) | 1.48553i | 0.234883i | ||||||||
\(41\) | −2.31252 | −0.361154 | −0.180577 | − | 0.983561i | \(-0.557797\pi\) | ||||
−0.180577 | + | 0.983561i | \(0.557797\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.46130 | 0.832841 | 0.416420 | − | 0.909172i | \(-0.363284\pi\) | ||||
0.416420 | + | 0.909172i | \(0.363284\pi\) | |||||||
\(44\) | − | 4.70623i | − | 0.709490i | ||||||
\(45\) | 1.89660 | − | 2.32442i | 0.282728 | − | 0.346504i | ||||
\(46\) | −1.17879 | −0.173803 | ||||||||
\(47\) | −3.22018 | −0.469712 | −0.234856 | − | 0.972030i | \(-0.575462\pi\) | ||||
−0.234856 | + | 0.972030i | \(0.575462\pi\) | |||||||
\(48\) | 4.89660 | − | 2.32442i | 0.706763 | − | 0.335501i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.385731i | 0.0545506i | ||||||||
\(51\) | −10.1100 | + | 4.79923i | −1.41569 | + | 0.672027i | ||||
\(52\) | − | 5.67800i | − | 0.787397i | ||||||
\(53\) | 13.2548i | 1.82069i | 0.413853 | + | 0.910344i | \(0.364183\pi\) | ||||
−0.413853 | + | 0.910344i | \(0.635817\pi\) | |||||||
\(54\) | 1.94630 | + | 0.478738i | 0.264858 | + | 0.0651480i | ||||
\(55\) | − | 2.54224i | − | 0.342796i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.888288 | − | 1.87126i | −0.117657 | − | 0.247855i | ||||
\(58\) | −2.99724 | −0.393557 | ||||||||
\(59\) | −3.96292 | −0.515929 | −0.257964 | − | 0.966154i | \(-0.583052\pi\) | ||||
−0.257964 | + | 0.966154i | \(0.583052\pi\) | |||||||
\(60\) | 2.89660 | − | 1.37502i | 0.373949 | − | 0.177514i | ||||
\(61\) | − | 9.34076i | − | 1.19596i | −0.801511 | − | 0.597981i | \(-0.795970\pi\) | ||
0.801511 | − | 0.597981i | \(-0.204030\pi\) | |||||||
\(62\) | −2.65148 | −0.336739 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.64717 | 0.580896 | ||||||||
\(65\) | − | 3.06718i | − | 0.380437i | ||||||
\(66\) | 1.53438 | − | 0.728371i | 0.188869 | − | 0.0896563i | ||||
\(67\) | −3.51932 | −0.429953 | −0.214977 | − | 0.976619i | \(-0.568967\pi\) | ||||
−0.214977 | + | 0.976619i | \(0.568967\pi\) | |||||||
\(68\) | −11.9612 | −1.45051 | ||||||||
\(69\) | 2.26989 | + | 4.78173i | 0.273262 | + | 0.575652i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.921861i | 0.109405i | 0.998503 | + | 0.0547024i | \(0.0174210\pi\) | ||||
−0.998503 | + | 0.0547024i | \(0.982579\pi\) | |||||||
\(72\) | 3.45299 | + | 2.81746i | 0.406939 | + | 0.332040i | ||||
\(73\) | − | 0.296437i | − | 0.0346953i | −0.999850 | − | 0.0173477i | \(-0.994478\pi\) | ||
0.999850 | − | 0.0173477i | \(-0.00552221\pi\) | |||||||
\(74\) | − | 1.37015i | − | 0.159276i | ||||||
\(75\) | 1.56470 | − | 0.742765i | 0.180676 | − | 0.0857672i | ||||
\(76\) | − | 2.21390i | − | 0.253952i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.85121 | − | 0.878771i | 0.209608 | − | 0.0995012i | ||||
\(79\) | 8.29482 | 0.933240 | 0.466620 | − | 0.884458i | \(-0.345472\pi\) | ||||
0.466620 | + | 0.884458i | \(0.345472\pi\) | |||||||
\(80\) | 3.12941 | 0.349879 | ||||||||
\(81\) | −1.80582 | − | 8.81697i | −0.200647 | − | 0.979664i | ||||
\(82\) | − | 0.892008i | − | 0.0985058i | ||||||
\(83\) | −2.11171 | −0.231790 | −0.115895 | − | 0.993261i | \(-0.536974\pi\) | ||||
−0.115895 | + | 0.993261i | \(0.536974\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.46130 | −0.700827 | ||||||||
\(86\) | 2.10659i | 0.227160i | ||||||||
\(87\) | 5.77151 | + | 12.1582i | 0.618770 | + | 1.30350i | ||||
\(88\) | 3.77658 | 0.402584 | ||||||||
\(89\) | 18.8301 | 1.99599 | 0.997996 | − | 0.0632783i | \(-0.0201556\pi\) | ||||
0.997996 | + | 0.0632783i | \(0.0201556\pi\) | |||||||
\(90\) | 0.896599 | + | 0.731577i | 0.0945098 | + | 0.0771149i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.65729i | 0.589813i | ||||||||
\(93\) | 5.10571 | + | 10.7557i | 0.529438 | + | 1.11531i | ||||
\(94\) | − | 1.24212i | − | 0.128115i | ||||||
\(95\) | − | 1.19592i | − | 0.122699i | ||||||
\(96\) | 3.10340 | + | 6.53760i | 0.316740 | + | 0.667241i | ||||
\(97\) | 12.3692i | 1.25590i | 0.778252 | + | 0.627952i | \(0.216106\pi\) | ||||
−0.778252 | + | 0.627952i | \(0.783894\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.90923 | − | 4.82161i | −0.593900 | − | 0.484590i | ||||
\(100\) | 1.85121 | 0.185121 | ||||||||
\(101\) | −6.97630 | −0.694168 | −0.347084 | − | 0.937834i | \(-0.612828\pi\) | ||||
−0.347084 | + | 0.937834i | \(0.612828\pi\) | |||||||
\(102\) | −1.85121 | − | 3.89975i | −0.183297 | − | 0.386133i | ||||
\(103\) | 3.77318i | 0.371782i | 0.982570 | + | 0.185891i | \(0.0595171\pi\) | ||||
−0.982570 | + | 0.185891i | \(0.940483\pi\) | |||||||
\(104\) | 4.55639 | 0.446791 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.11279 | −0.496598 | ||||||||
\(107\) | − | 13.2337i | − | 1.27935i | −0.768646 | − | 0.639674i | \(-0.779069\pi\) | ||
0.768646 | − | 0.639674i | \(-0.220931\pi\) | |||||||
\(108\) | 2.29758 | − | 9.34076i | 0.221084 | − | 0.898815i | ||||
\(109\) | 2.50162 | 0.239612 | 0.119806 | − | 0.992797i | \(-0.461773\pi\) | ||||
0.119806 | + | 0.992797i | \(0.461773\pi\) | |||||||
\(110\) | 0.980620 | 0.0934985 | ||||||||
\(111\) | −5.55795 | + | 2.63836i | −0.527537 | + | 0.250422i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 7.18425i | − | 0.675837i | −0.941175 | − | 0.337919i | \(-0.890277\pi\) | ||
0.941175 | − | 0.337919i | \(-0.109723\pi\) | |||||||
\(114\) | 0.721803 | − | 0.342640i | 0.0676031 | − | 0.0320912i | ||||
\(115\) | 3.05599i | 0.284973i | ||||||||
\(116\) | 14.3845i | 1.33556i | ||||||||
\(117\) | −7.12941 | − | 5.81721i | −0.659114 | − | 0.537802i | ||||
\(118\) | − | 1.52862i | − | 0.140721i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.10340 | + | 2.32442i | 0.100726 | + | 0.212189i | ||||
\(121\) | 4.53701 | 0.412456 | ||||||||
\(122\) | 3.60302 | 0.326202 | ||||||||
\(123\) | −3.61840 | + | 1.71766i | −0.326260 | + | 0.154876i | ||||
\(124\) | 12.7251i | 1.14275i | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.1965 | −0.993528 | −0.496764 | − | 0.867886i | \(-0.665478\pi\) | ||||
−0.496764 | + | 0.867886i | \(0.665478\pi\) | |||||||
\(128\) | 10.1489i | 0.897044i | ||||||||
\(129\) | 8.54532 | − | 4.05647i | 0.752374 | − | 0.357152i | ||||
\(130\) | 1.18311 | 0.103765 | ||||||||
\(131\) | −15.6637 | −1.36854 | −0.684270 | − | 0.729228i | \(-0.739879\pi\) | ||||
−0.684270 | + | 0.729228i | \(0.739879\pi\) | |||||||
\(132\) | −3.49562 | − | 7.36385i | −0.304255 | − | 0.640941i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 1.35751i | − | 0.117271i | ||||||
\(135\) | 1.24112 | − | 5.04575i | 0.106819 | − | 0.434269i | ||||
\(136\) | − | 9.59847i | − | 0.823062i | ||||||
\(137\) | − | 5.82840i | − | 0.497954i | −0.968509 | − | 0.248977i | \(-0.919906\pi\) | ||
0.968509 | − | 0.248977i | \(-0.0800944\pi\) | |||||||
\(138\) | −1.84446 | + | 0.875565i | −0.157011 | + | 0.0745330i | ||||
\(139\) | 12.0365i | 1.02092i | 0.859900 | + | 0.510462i | \(0.170525\pi\) | ||||
−0.859900 | + | 0.510462i | \(0.829475\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.03863 | + | 2.39184i | −0.424330 | + | 0.201429i | ||||
\(142\) | −0.355590 | −0.0298405 | ||||||||
\(143\) | −7.79751 | −0.652061 | ||||||||
\(144\) | 5.93523 | − | 7.27405i | 0.494603 | − | 0.606171i | ||||
\(145\) | 7.77029i | 0.645288i | ||||||||
\(146\) | 0.114345 | 0.00946324 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.57565 | −0.540515 | ||||||||
\(149\) | − | 18.6975i | − | 1.53176i | −0.642985 | − | 0.765879i | \(-0.722304\pi\) | ||
0.642985 | − | 0.765879i | \(-0.277696\pi\) | |||||||
\(150\) | 0.286507 | + | 0.603555i | 0.0233932 | + | 0.0492800i | ||||
\(151\) | −5.95062 | −0.484254 | −0.242127 | − | 0.970245i | \(-0.577845\pi\) | ||||
−0.242127 | + | 0.970245i | \(0.577845\pi\) | |||||||
\(152\) | 1.77658 | 0.144099 | ||||||||
\(153\) | −12.2545 | + | 15.0188i | −0.990718 | + | 1.21419i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.87392i | 0.552127i | ||||||||
\(156\) | −4.21742 | − | 8.88440i | −0.337664 | − | 0.711321i | ||||
\(157\) | − | 6.41279i | − | 0.511796i | −0.966704 | − | 0.255898i | \(-0.917629\pi\) | ||
0.966704 | − | 0.255898i | \(-0.0823711\pi\) | |||||||
\(158\) | 3.19957i | 0.254544i | ||||||||
\(159\) | 9.84521 | + | 20.7399i | 0.780776 | + | 1.64478i | ||||
\(160\) | 4.17817i | 0.330313i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 3.40098 | − | 0.696562i | 0.267206 | − | 0.0547271i | ||||
\(163\) | −16.4435 | −1.28795 | −0.643976 | − | 0.765045i | \(-0.722717\pi\) | ||||
−0.643976 | + | 0.765045i | \(0.722717\pi\) | |||||||
\(164\) | −4.28096 | −0.334286 | ||||||||
\(165\) | −1.88829 | − | 3.97785i | −0.147003 | − | 0.309676i | ||||
\(166\) | − | 0.814552i | − | 0.0632215i | ||||||
\(167\) | 4.81089 | 0.372278 | 0.186139 | − | 0.982523i | \(-0.440402\pi\) | ||||
0.186139 | + | 0.982523i | \(0.440402\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.59239 | 0.276338 | ||||||||
\(170\) | − | 2.49232i | − | 0.191152i | ||||||
\(171\) | −2.77982 | − | 2.26818i | −0.212578 | − | 0.173452i | ||||
\(172\) | 10.1100 | 0.770882 | ||||||||
\(173\) | −6.81521 | −0.518151 | −0.259075 | − | 0.965857i | \(-0.583418\pi\) | ||||
−0.259075 | + | 0.965857i | \(0.583418\pi\) | |||||||
\(174\) | −4.68980 | + | 2.22625i | −0.355533 | + | 0.168771i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 7.95571i | − | 0.599684i | ||||||
\(177\) | −6.20080 | + | 2.94352i | −0.466081 | + | 0.221249i | ||||
\(178\) | 7.26337i | 0.544412i | ||||||||
\(179\) | − | 19.9684i | − | 1.49251i | −0.665661 | − | 0.746254i | \(-0.731850\pi\) | ||
0.665661 | − | 0.746254i | \(-0.268150\pi\) | |||||||
\(180\) | 3.51101 | − | 4.30299i | 0.261695 | − | 0.320726i | ||||
\(181\) | 5.18808i | 0.385627i | 0.981235 | + | 0.192813i | \(0.0617612\pi\) | ||||
−0.981235 | + | 0.192813i | \(0.938239\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.93799 | − | 14.6155i | −0.512871 | − | 1.08041i | ||||
\(184\) | −4.53977 | −0.334676 | ||||||||
\(185\) | −3.55208 | −0.261154 | ||||||||
\(186\) | −4.14879 | + | 1.96943i | −0.304204 | + | 0.144406i | ||||
\(187\) | 16.4262i | 1.20120i | ||||||||
\(188\) | −5.96124 | −0.434768 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.461303 | 0.0334665 | ||||||||
\(191\) | 8.64099i | 0.625240i | 0.949878 | + | 0.312620i | \(0.101207\pi\) | ||||
−0.949878 | + | 0.312620i | \(0.898793\pi\) | |||||||
\(192\) | 7.27144 | − | 3.45176i | 0.524771 | − | 0.249109i | ||||
\(193\) | −23.7721 | −1.71116 | −0.855578 | − | 0.517674i | \(-0.826798\pi\) | ||||
−0.855578 | + | 0.517674i | \(0.826798\pi\) | |||||||
\(194\) | −4.77119 | −0.342551 | ||||||||
\(195\) | −2.27820 | − | 4.79923i | −0.163145 | − | 0.343680i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 11.6843i | − | 0.832475i | −0.909256 | − | 0.416238i | \(-0.863348\pi\) | ||
0.909256 | − | 0.416238i | \(-0.136652\pi\) | |||||||
\(198\) | 1.85984 | − | 2.27937i | 0.132173 | − | 0.161988i | ||||
\(199\) | 14.1268i | 1.00142i | 0.865615 | + | 0.500709i | \(0.166927\pi\) | ||||
−0.865615 | + | 0.500709i | \(0.833073\pi\) | |||||||
\(200\) | 1.48553i | 0.105043i | ||||||||
\(201\) | −5.50669 | + | 2.61403i | −0.388412 | + | 0.184379i | ||||
\(202\) | − | 2.69098i | − | 0.189336i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −18.7158 | + | 8.88440i | −1.31037 | + | 0.622032i | ||||
\(205\) | −2.31252 | −0.161513 | ||||||||
\(206\) | −1.45543 | −0.101405 | ||||||||
\(207\) | 7.10340 | + | 5.79599i | 0.493720 | + | 0.402849i | ||||
\(208\) | − | 9.59847i | − | 0.665534i | ||||||
\(209\) | −3.04032 | −0.210303 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.49838 | 0.309681 | 0.154841 | − | 0.987939i | \(-0.450514\pi\) | ||||
0.154841 | + | 0.987939i | \(0.450514\pi\) | |||||||
\(212\) | 24.5375i | 1.68524i | ||||||||
\(213\) | 0.684727 | + | 1.44244i | 0.0469167 | + | 0.0988344i | ||||
\(214\) | 5.10464 | 0.348946 | ||||||||
\(215\) | 5.46130 | 0.372458 | ||||||||
\(216\) | 7.49562 | + | 1.84372i | 0.510012 | + | 0.125449i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.964952i | 0.0653548i | ||||||||
\(219\) | −0.220183 | − | 0.463836i | −0.0148786 | − | 0.0313431i | ||||
\(220\) | − | 4.70623i | − | 0.317294i | ||||||
\(221\) | 19.8180i | 1.33310i | ||||||||
\(222\) | −1.01770 | − | 2.14387i | −0.0683033 | − | 0.143887i | ||||
\(223\) | − | 7.20662i | − | 0.482591i | −0.970452 | − | 0.241296i | \(-0.922428\pi\) | ||
0.970452 | − | 0.241296i | \(-0.0775724\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.89660 | − | 2.32442i | 0.126440 | − | 0.154961i | ||||
\(226\) | 2.77119 | 0.184336 | ||||||||
\(227\) | 1.86304 | 0.123654 | 0.0618270 | − | 0.998087i | \(-0.480307\pi\) | ||||
0.0618270 | + | 0.998087i | \(0.480307\pi\) | |||||||
\(228\) | −1.64441 | − | 3.46410i | −0.108904 | − | 0.229416i | ||||
\(229\) | − | 20.1064i | − | 1.32867i | −0.747437 | − | 0.664333i | \(-0.768716\pi\) | ||
0.747437 | − | 0.664333i | \(-0.231284\pi\) | |||||||
\(230\) | −1.17879 | −0.0777271 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −11.5430 | −0.757836 | ||||||||
\(233\) | − | 1.56530i | − | 0.102546i | −0.998685 | − | 0.0512731i | \(-0.983672\pi\) | ||
0.998685 | − | 0.0512731i | \(-0.0163279\pi\) | |||||||
\(234\) | 2.24388 | − | 2.75003i | 0.146687 | − | 0.179775i | ||||
\(235\) | −3.22018 | −0.210062 | ||||||||
\(236\) | −7.33621 | −0.477547 | ||||||||
\(237\) | 12.9789 | − | 6.16110i | 0.843073 | − | 0.400207i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.69230i | 0.368205i | 0.982907 | + | 0.184102i | \(0.0589378\pi\) | ||||
−0.982907 | + | 0.184102i | \(0.941062\pi\) | |||||||
\(240\) | 4.89660 | − | 2.32442i | 0.316074 | − | 0.150040i | ||||
\(241\) | − | 13.3329i | − | 0.858848i | −0.903103 | − | 0.429424i | \(-0.858717\pi\) | ||
0.903103 | − | 0.429424i | \(-0.141283\pi\) | |||||||
\(242\) | 1.75007i | 0.112498i | ||||||||
\(243\) | −9.37452 | − | 12.4546i | −0.601376 | − | 0.798966i | ||||
\(244\) | − | 17.2917i | − | 1.10699i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.662553 | − | 1.39573i | −0.0422428 | − | 0.0889884i | ||||
\(247\) | −3.66811 | −0.233396 | ||||||||
\(248\) | −10.2114 | −0.648426 | ||||||||
\(249\) | −3.30420 | + | 1.56851i | −0.209395 | + | 0.0994001i | ||||
\(250\) | 0.385731i | 0.0243958i | ||||||||
\(251\) | −5.32590 | −0.336168 | −0.168084 | − | 0.985773i | \(-0.553758\pi\) | ||||
−0.168084 | + | 0.985773i | \(0.553758\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.76907 | 0.488437 | ||||||||
\(254\) | − | 4.31883i | − | 0.270987i | ||||||
\(255\) | −10.1100 | + | 4.79923i | −0.633115 | + | 0.300540i | ||||
\(256\) | 5.37959 | 0.336225 | ||||||||
\(257\) | 6.50006 | 0.405463 | 0.202731 | − | 0.979234i | \(-0.435018\pi\) | ||||
0.202731 | + | 0.979234i | \(0.435018\pi\) | |||||||
\(258\) | 1.56470 | + | 3.29619i | 0.0974142 | + | 0.205212i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 5.67800i | − | 0.352135i | ||||||
\(261\) | 18.0614 | + | 14.7371i | 1.11797 | + | 0.912206i | ||||
\(262\) | − | 6.04196i | − | 0.373273i | ||||||
\(263\) | − | 14.8265i | − | 0.914242i | −0.889404 | − | 0.457121i | \(-0.848881\pi\) | ||
0.889404 | − | 0.457121i | \(-0.151119\pi\) | |||||||
\(264\) | 5.90923 | − | 2.80511i | 0.363688 | − | 0.172643i | ||||
\(265\) | 13.2548i | 0.814236i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 29.4636 | − | 13.9864i | 1.80314 | − | 0.855953i | ||||
\(268\) | −6.51500 | −0.397967 | ||||||||
\(269\) | 24.6084 | 1.50040 | 0.750201 | − | 0.661210i | \(-0.229957\pi\) | ||||
0.750201 | + | 0.661210i | \(0.229957\pi\) | |||||||
\(270\) | 1.94630 | + | 0.478738i | 0.118448 | + | 0.0291351i | ||||
\(271\) | 3.81190i | 0.231557i | 0.993275 | + | 0.115778i | \(0.0369362\pi\) | ||||
−0.993275 | + | 0.115778i | \(0.963064\pi\) | |||||||
\(272\) | −20.2201 | −1.22602 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.24819 | 0.135818 | ||||||||
\(275\) | − | 2.54224i | − | 0.153303i | ||||||
\(276\) | 4.20204 | + | 8.85199i | 0.252933 | + | 0.532827i | ||||
\(277\) | −18.7754 | −1.12810 | −0.564052 | − | 0.825740i | \(-0.690758\pi\) | ||||
−0.564052 | + | 0.825740i | \(0.690758\pi\) | |||||||
\(278\) | −4.64285 | −0.278460 | ||||||||
\(279\) | 15.9779 | + | 13.0371i | 0.956570 | + | 0.780509i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.6885i | 1.41314i | 0.707643 | + | 0.706570i | \(0.249758\pi\) | ||||
−0.707643 | + | 0.706570i | \(0.750242\pi\) | |||||||
\(282\) | −0.922607 | − | 1.94356i | −0.0549404 | − | 0.115737i | ||||
\(283\) | 5.04409i | 0.299840i | 0.988698 | + | 0.149920i | \(0.0479016\pi\) | ||||
−0.988698 | + | 0.149920i | \(0.952098\pi\) | |||||||
\(284\) | 1.70656i | 0.101266i | ||||||||
\(285\) | −0.888288 | − | 1.87126i | −0.0526177 | − | 0.110844i | ||||
\(286\) | − | 3.00774i | − | 0.177851i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 9.71181 | + | 7.92431i | 0.572274 | + | 0.466945i | ||||
\(289\) | 24.7484 | 1.45579 | ||||||||
\(290\) | −2.99724 | −0.176004 | ||||||||
\(291\) | 9.18742 | + | 19.3542i | 0.538576 | + | 1.13456i | ||||
\(292\) | − | 0.548767i | − | 0.0321142i | ||||||
\(293\) | −6.29421 | −0.367712 | −0.183856 | − | 0.982953i | \(-0.558858\pi\) | ||||
−0.183856 | + | 0.982953i | \(0.558858\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.96292 | −0.230730 | ||||||||
\(296\) | − | 5.27672i | − | 0.306703i | ||||||
\(297\) | −12.8275 | − | 3.15523i | −0.744328 | − | 0.183085i | ||||
\(298\) | 7.21219 | 0.417791 | ||||||||
\(299\) | 9.37329 | 0.542071 | ||||||||
\(300\) | 2.89660 | − | 1.37502i | 0.167235 | − | 0.0793866i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 2.29534i | − | 0.132082i | ||||||
\(303\) | −10.9159 | + | 5.18176i | −0.627099 | + | 0.297684i | ||||
\(304\) | − | 3.74252i | − | 0.214648i | ||||||
\(305\) | − | 9.34076i | − | 0.534850i | ||||||
\(306\) | −5.79320 | − | 4.72694i | −0.331175 | − | 0.270221i | ||||
\(307\) | 16.0397i | 0.915432i | 0.889099 | + | 0.457716i | \(0.151332\pi\) | ||||
−0.889099 | + | 0.457716i | \(0.848668\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.80258 | + | 5.90390i | 0.159433 | + | 0.335861i | ||||
\(310\) | −2.65148 | −0.150594 | ||||||||
\(311\) | 18.0725 | 1.02480 | 0.512398 | − | 0.858748i | \(-0.328757\pi\) | ||||
0.512398 | + | 0.858748i | \(0.328757\pi\) | |||||||
\(312\) | 7.12941 | − | 3.38433i | 0.403623 | − | 0.191600i | ||||
\(313\) | − | 18.6221i | − | 1.05258i | −0.850305 | − | 0.526291i | \(-0.823582\pi\) | ||
0.850305 | − | 0.526291i | \(-0.176418\pi\) | |||||||
\(314\) | 2.47361 | 0.139594 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.3555 | 0.863812 | ||||||||
\(317\) | 2.63650i | 0.148080i | 0.997255 | + | 0.0740402i | \(0.0235893\pi\) | ||||
−0.997255 | + | 0.0740402i | \(0.976411\pi\) | |||||||
\(318\) | −8.00000 | + | 3.79760i | −0.448618 | + | 0.212959i | ||||
\(319\) | 19.7540 | 1.10601 | ||||||||
\(320\) | 4.64717 | 0.259785 | ||||||||
\(321\) | −9.82952 | − | 20.7068i | −0.548630 | − | 1.15574i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.72720i | 0.429953i | ||||||||
\(324\) | −3.34296 | − | 16.3221i | −0.185720 | − | 0.906782i | ||||
\(325\) | − | 3.06718i | − | 0.170137i | ||||||
\(326\) | − | 6.34276i | − | 0.351293i | ||||||
\(327\) | 3.91430 | − | 1.85812i | 0.216461 | − | 0.102754i | ||||
\(328\) | − | 3.43531i | − | 0.189683i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1.53438 | − | 0.728371i | 0.0844649 | − | 0.0400955i | ||||
\(331\) | −30.3408 | −1.66768 | −0.833842 | − | 0.552004i | \(-0.813863\pi\) | ||||
−0.833842 | + | 0.552004i | \(0.813863\pi\) | |||||||
\(332\) | −3.90923 | −0.214547 | ||||||||
\(333\) | −6.73687 | + | 8.25651i | −0.369178 | + | 0.452454i | ||||
\(334\) | 1.85571i | 0.101540i | ||||||||
\(335\) | −3.51932 | −0.192281 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.84215 | −0.100348 | −0.0501741 | − | 0.998740i | \(-0.515978\pi\) | ||||
−0.0501741 | + | 0.998740i | \(0.515978\pi\) | |||||||
\(338\) | 1.38570i | 0.0753720i | ||||||||
\(339\) | −5.33621 | − | 11.2412i | −0.289823 | − | 0.610539i | ||||
\(340\) | −11.9612 | −0.648689 | ||||||||
\(341\) | 17.4752 | 0.946333 | ||||||||
\(342\) | 0.874907 | − | 1.07226i | 0.0473096 | − | 0.0579812i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 8.11293i | 0.437420i | ||||||||
\(345\) | 2.26989 | + | 4.78173i | 0.122207 | + | 0.257439i | ||||
\(346\) | − | 2.62884i | − | 0.141327i | ||||||
\(347\) | 8.19039i | 0.439683i | 0.975536 | + | 0.219842i | \(0.0705541\pi\) | ||||
−0.975536 | + | 0.219842i | \(0.929446\pi\) | |||||||
\(348\) | 10.6843 | + | 22.5074i | 0.572738 | + | 1.20652i | ||||
\(349\) | − | 36.3291i | − | 1.94465i | −0.233627 | − | 0.972326i | \(-0.575059\pi\) | ||
0.233627 | − | 0.972326i | \(-0.424941\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.4762 | − | 3.80674i | −0.826061 | − | 0.203189i | ||||
\(352\) | 10.6219 | 0.566150 | ||||||||
\(353\) | 5.71473 | 0.304164 | 0.152082 | − | 0.988368i | \(-0.451402\pi\) | ||||
0.152082 | + | 0.988368i | \(0.451402\pi\) | |||||||
\(354\) | −1.13541 | − | 2.39184i | −0.0603462 | − | 0.127125i | ||||
\(355\) | 0.921861i | 0.0489273i | ||||||||
\(356\) | 34.8586 | 1.84750 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.70242 | 0.407086 | ||||||||
\(359\) | − | 4.80564i | − | 0.253632i | −0.991926 | − | 0.126816i | \(-0.959524\pi\) | ||
0.991926 | − | 0.126816i | \(-0.0404758\pi\) | |||||||
\(360\) | 3.45299 | + | 2.81746i | 0.181989 | + | 0.148493i | ||||
\(361\) | 17.5698 | 0.924725 | ||||||||
\(362\) | −2.00120 | −0.105181 | ||||||||
\(363\) | 7.09909 | − | 3.36994i | 0.372605 | − | 0.176876i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 0.296437i | − | 0.0155162i | ||||||
\(366\) | 5.63766 | − | 2.67620i | 0.294685 | − | 0.139887i | ||||
\(367\) | 24.5762i | 1.28287i | 0.767179 | + | 0.641433i | \(0.221660\pi\) | ||||
−0.767179 | + | 0.641433i | \(0.778340\pi\) | |||||||
\(368\) | 9.56345i | 0.498529i | ||||||||
\(369\) | −4.38591 | + | 5.37525i | −0.228322 | + | 0.279824i | ||||
\(370\) | − | 1.37015i | − | 0.0712305i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 9.45176 | + | 19.9110i | 0.490051 | + | 1.03234i | ||||
\(373\) | 26.5026 | 1.37225 | 0.686126 | − | 0.727483i | \(-0.259310\pi\) | ||||
0.686126 | + | 0.727483i | \(0.259310\pi\) | |||||||
\(374\) | −6.33609 | −0.327631 | ||||||||
\(375\) | 1.56470 | − | 0.742765i | 0.0808010 | − | 0.0383562i | ||||
\(376\) | − | 4.78368i | − | 0.246700i | ||||||
\(377\) | 23.8329 | 1.22746 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.0939 | 0.672588 | 0.336294 | − | 0.941757i | \(-0.390826\pi\) | ||||
0.336294 | + | 0.941757i | \(0.390826\pi\) | |||||||
\(380\) | − | 2.21390i | − | 0.113571i | ||||||
\(381\) | −17.5192 | + | 8.31636i | −0.897535 | + | 0.426060i | ||||
\(382\) | −3.33310 | −0.170536 | ||||||||
\(383\) | 16.9660 | 0.866922 | 0.433461 | − | 0.901172i | \(-0.357292\pi\) | ||||
0.433461 | + | 0.901172i | \(0.357292\pi\) | |||||||
\(384\) | 7.53825 | + | 15.8800i | 0.384685 | + | 0.810374i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 9.16964i | − | 0.466723i | ||||||
\(387\) | 10.3579 | − | 12.6943i | 0.526522 | − | 0.645290i | ||||
\(388\) | 22.8980i | 1.16247i | ||||||||
\(389\) | − | 2.46478i | − | 0.124970i | −0.998046 | − | 0.0624848i | \(-0.980098\pi\) | ||
0.998046 | − | 0.0624848i | \(-0.0199025\pi\) | |||||||
\(390\) | 1.85121 | − | 0.878771i | 0.0937398 | − | 0.0444983i | ||||
\(391\) | − | 19.7457i | − | 0.998583i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −24.5090 | + | 11.6344i | −1.23632 | + | 0.586879i | ||||
\(394\) | 4.50701 | 0.227060 | ||||||||
\(395\) | 8.29482 | 0.417358 | ||||||||
\(396\) | −10.9392 | − | 8.92582i | −0.549717 | − | 0.448539i | ||||
\(397\) | 3.35368i | 0.168316i | 0.996452 | + | 0.0841582i | \(0.0268201\pi\) | ||||
−0.996452 | + | 0.0841582i | \(0.973180\pi\) | |||||||
\(398\) | −5.44912 | −0.273140 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.12941 | 0.156470 | ||||||||
\(401\) | 6.24683i | 0.311952i | 0.987761 | + | 0.155976i | \(0.0498523\pi\) | ||||
−0.987761 | + | 0.155976i | \(0.950148\pi\) | |||||||
\(402\) | −1.00831 | − | 2.12410i | −0.0502900 | − | 0.105940i | ||||
\(403\) | 21.0836 | 1.05025 | ||||||||
\(404\) | −12.9146 | −0.642526 | ||||||||
\(405\) | −1.80582 | − | 8.81697i | −0.0897321 | − | 0.438119i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.03024i | 0.447612i | ||||||||
\(408\) | −7.12941 | − | 15.0188i | −0.352958 | − | 0.743539i | ||||
\(409\) | 11.7950i | 0.583223i | 0.956537 | + | 0.291611i | \(0.0941914\pi\) | ||||
−0.956537 | + | 0.291611i | \(0.905809\pi\) | |||||||
\(410\) | − | 0.892008i | − | 0.0440531i | ||||||
\(411\) | −4.32914 | − | 9.11973i | −0.213541 | − | 0.449843i | ||||
\(412\) | 6.98495i | 0.344124i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.23569 | + | 2.74000i | −0.109878 | + | 0.134664i | ||||
\(415\) | −2.11171 | −0.103660 | ||||||||
\(416\) | 12.8152 | 0.628317 | ||||||||
\(417\) | 8.94030 | + | 18.8336i | 0.437809 | + | 0.922284i | ||||
\(418\) | − | 1.17274i | − | 0.0573608i | ||||||
\(419\) | 12.0419 | 0.588284 | 0.294142 | − | 0.955762i | \(-0.404966\pi\) | ||||
0.294142 | + | 0.955762i | \(0.404966\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.4264 | 0.556888 | 0.278444 | − | 0.960453i | \(-0.410181\pi\) | ||||
0.278444 | + | 0.960453i | \(0.410181\pi\) | |||||||
\(422\) | 1.73516i | 0.0844664i | ||||||||
\(423\) | −6.10740 | + | 7.48505i | −0.296952 | + | 0.363935i | ||||
\(424\) | −19.6904 | −0.956252 | ||||||||
\(425\) | −6.46130 | −0.313419 | ||||||||
\(426\) | −0.556394 | + | 0.264120i | −0.0269574 | + | 0.0127967i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 24.4983i | − | 1.18417i | ||||||
\(429\) | −12.2008 | + | 5.79172i | −0.589060 | + | 0.279627i | ||||
\(430\) | 2.10659i | 0.101589i | ||||||||
\(431\) | − | 32.6026i | − | 1.57041i | −0.619236 | − | 0.785205i | \(-0.712558\pi\) | ||
0.619236 | − | 0.785205i | \(-0.287442\pi\) | |||||||
\(432\) | 3.88397 | − | 15.7902i | 0.186868 | − | 0.759707i | ||||
\(433\) | − | 4.37644i | − | 0.210318i | −0.994455 | − | 0.105159i | \(-0.966465\pi\) | ||
0.994455 | − | 0.105159i | \(-0.0335352\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.77151 | + | 12.1582i | 0.276723 | + | 0.582942i | ||||
\(436\) | 4.63103 | 0.221786 | ||||||||
\(437\) | 3.65472 | 0.174829 | ||||||||
\(438\) | 0.178916 | − | 0.0849314i | 0.00854893 | − | 0.00405818i | ||||
\(439\) | − | 14.8282i | − | 0.707711i | −0.935300 | − | 0.353855i | \(-0.884871\pi\) | ||
0.935300 | − | 0.353855i | \(-0.115129\pi\) | |||||||
\(440\) | 3.77658 | 0.180041 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7.64441 | −0.363607 | ||||||||
\(443\) | 15.9124i | 0.756023i | 0.925801 | + | 0.378011i | \(0.123392\pi\) | ||||
−0.925801 | + | 0.378011i | \(0.876608\pi\) | |||||||
\(444\) | −10.2889 | + | 4.88416i | −0.488292 | + | 0.231792i | ||||
\(445\) | 18.8301 | 0.892635 | ||||||||
\(446\) | 2.77982 | 0.131628 | ||||||||
\(447\) | −13.8878 | − | 29.2560i | −0.656872 | − | 1.38376i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 35.1881i | − | 1.66063i | −0.557294 | − | 0.830315i | \(-0.688161\pi\) | ||
0.557294 | − | 0.830315i | \(-0.311839\pi\) | |||||||
\(450\) | 0.896599 | + | 0.731577i | 0.0422661 | + | 0.0344869i | ||||
\(451\) | 5.87897i | 0.276830i | ||||||||
\(452\) | − | 13.2996i | − | 0.625559i | ||||||
\(453\) | −9.31096 | + | 4.41991i | −0.437467 | + | 0.207666i | ||||
\(454\) | 0.718630i | 0.0337270i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.77982 | − | 1.31958i | 0.130177 | − | 0.0617950i | ||||
\(457\) | 14.0591 | 0.657656 | 0.328828 | − | 0.944390i | \(-0.393346\pi\) | ||||
0.328828 | + | 0.944390i | \(0.393346\pi\) | |||||||
\(458\) | 7.75564 | 0.362397 | ||||||||
\(459\) | −8.01925 | + | 32.6021i | −0.374307 | + | 1.52174i | ||||
\(460\) | 5.65729i | 0.263773i | ||||||||
\(461\) | −13.5161 | −0.629506 | −0.314753 | − | 0.949174i | \(-0.601922\pi\) | ||||
−0.314753 | + | 0.949174i | \(0.601922\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.8381 | 0.829009 | 0.414504 | − | 0.910047i | \(-0.363955\pi\) | ||||
0.414504 | + | 0.910047i | \(0.363955\pi\) | |||||||
\(464\) | 24.3164i | 1.12886i | ||||||||
\(465\) | 5.10571 | + | 10.7557i | 0.236772 | + | 0.498782i | ||||
\(466\) | 0.603785 | 0.0279698 | ||||||||
\(467\) | −9.18941 | −0.425235 | −0.212618 | − | 0.977135i | \(-0.568199\pi\) | ||||
−0.212618 | + | 0.977135i | \(0.568199\pi\) | |||||||
\(468\) | −13.1980 | − | 10.7689i | −0.610080 | − | 0.497792i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 1.24212i | − | 0.0572949i | ||||||
\(471\) | −4.76320 | − | 10.0341i | −0.219476 | − | 0.462348i | ||||
\(472\) | − | 5.88705i | − | 0.270973i | ||||||
\(473\) | − | 13.8839i | − | 0.638384i | ||||||
\(474\) | 2.37653 | + | 5.00638i | 0.109158 | + | 0.229950i | ||||
\(475\) | − | 1.19592i | − | 0.0548726i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 30.8097 | + | 25.1391i | 1.41068 | + | 1.15104i | ||||
\(478\) | −2.19570 | −0.100429 | ||||||||
\(479\) | −18.8807 | −0.862683 | −0.431341 | − | 0.902189i | \(-0.641960\pi\) | ||||
−0.431341 | + | 0.902189i | \(0.641960\pi\) | |||||||
\(480\) | 3.10340 | + | 6.53760i | 0.141650 | + | 0.298399i | ||||
\(481\) | 10.8949i | 0.496763i | ||||||||
\(482\) | 5.14291 | 0.234253 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.39897 | 0.381772 | ||||||||
\(485\) | 12.3692i | 0.561657i | ||||||||
\(486\) | 4.80414 | − | 3.61604i | 0.217920 | − | 0.164027i | ||||
\(487\) | −5.23525 | −0.237232 | −0.118616 | − | 0.992940i | \(-0.537846\pi\) | ||||
−0.118616 | + | 0.992940i | \(0.537846\pi\) | |||||||
\(488\) | 13.8760 | 0.628136 | ||||||||
\(489\) | −25.7292 | + | 12.2136i | −1.16351 | + | 0.552320i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 19.5201i | − | 0.880930i | −0.897770 | − | 0.440465i | \(-0.854814\pi\) | ||
0.897770 | − | 0.440465i | \(-0.145186\pi\) | |||||||
\(492\) | −6.69843 | + | 3.17975i | −0.301988 | + | 0.143354i | ||||
\(493\) | − | 50.2062i | − | 2.26117i | ||||||
\(494\) | − | 1.41490i | − | 0.0636594i | ||||||
\(495\) | −5.90923 | − | 4.82161i | −0.265600 | − | 0.216715i | ||||
\(496\) | 21.5113i | 0.965887i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.605021 | − | 1.27453i | −0.0271116 | − | 0.0571132i | ||||
\(499\) | −36.6350 | −1.64001 | −0.820005 | − | 0.572356i | \(-0.806029\pi\) | ||||
−0.820005 | + | 0.572356i | \(0.806029\pi\) | |||||||
\(500\) | 1.85121 | 0.0827887 | ||||||||
\(501\) | 7.52763 | − | 3.57337i | 0.336310 | − | 0.159646i | ||||
\(502\) | − | 2.05436i | − | 0.0916907i | ||||||
\(503\) | 40.7156 | 1.81542 | 0.907708 | − | 0.419602i | \(-0.137830\pi\) | ||||
0.907708 | + | 0.419602i | \(0.137830\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.97630 | −0.310441 | ||||||||
\(506\) | 2.99677i | 0.133223i | ||||||||
\(507\) | 5.62104 | − | 2.66831i | 0.249639 | − | 0.118504i | ||||
\(508\) | −20.7271 | −0.919615 | ||||||||
\(509\) | 17.7277 | 0.785765 | 0.392883 | − | 0.919589i | \(-0.371478\pi\) | ||||
0.392883 | + | 0.919589i | \(0.371478\pi\) | |||||||
\(510\) | −1.85121 | − | 3.89975i | −0.0819730 | − | 0.172684i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.3729i | 0.988751i | ||||||||
\(513\) | −6.03432 | − | 1.48428i | −0.266422 | − | 0.0655326i | ||||
\(514\) | 2.50727i | 0.110591i | ||||||||
\(515\) | 3.77318i | 0.166266i | ||||||||
\(516\) | 15.8192 | − | 7.50938i | 0.696402 | − | 0.330582i | ||||
\(517\) | 8.18648i | 0.360041i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.6638 | + | 5.06210i | −0.468088 | + | 0.222202i | ||||
\(520\) | 4.55639 | 0.199811 | ||||||||
\(521\) | 3.51561 | 0.154022 | 0.0770108 | − | 0.997030i | \(-0.475462\pi\) | ||||
0.0770108 | + | 0.997030i | \(0.475462\pi\) | |||||||
\(522\) | −5.68457 | + | 6.96684i | −0.248807 | + | 0.304930i | ||||
\(523\) | 4.85583i | 0.212330i | 0.994349 | + | 0.106165i | \(0.0338572\pi\) | ||||
−0.994349 | + | 0.106165i | \(0.966143\pi\) | |||||||
\(524\) | −28.9968 | −1.26673 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.71904 | 0.249362 | ||||||||
\(527\) | − | 44.4145i | − | 1.93473i | ||||||
\(528\) | −5.90923 | − | 12.4483i | −0.257166 | − | 0.541744i | ||||
\(529\) | 13.6609 | 0.593952 | ||||||||
\(530\) | −5.11279 | −0.222085 | ||||||||
\(531\) | −7.51608 | + | 9.21148i | −0.326170 | + | 0.399744i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.09290i | 0.307228i | ||||||||
\(534\) | 5.39498 | + | 11.3650i | 0.233464 | + | 0.491813i | ||||
\(535\) | − | 13.2337i | − | 0.572142i | ||||||
\(536\) | − | 5.22805i | − | 0.225818i | ||||||
\(537\) | −14.8318 | − | 31.2446i | −0.640041 | − | 1.34831i | ||||
\(538\) | 9.49222i | 0.409239i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.29758 | − | 9.34076i | 0.0988719 | − | 0.401962i | ||||
\(541\) | −0.0386341 | −0.00166101 | −0.000830506 | − | 1.00000i | \(-0.500264\pi\) | ||||
−0.000830506 | 1.00000i | \(0.500264\pi\) | ||||||||
\(542\) | −1.47037 | −0.0631577 | ||||||||
\(543\) | 3.85352 | + | 8.11781i | 0.165371 | + | 0.348368i | ||||
\(544\) | − | 26.9964i | − | 1.15746i | ||||||
\(545\) | 2.50162 | 0.107158 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.3881 | −1.55584 | −0.777921 | − | 0.628362i | \(-0.783726\pi\) | ||||
−0.777921 | + | 0.628362i | \(0.783726\pi\) | |||||||
\(548\) | − | 10.7896i | − | 0.460909i | ||||||
\(549\) | −21.7118 | − | 17.7157i | −0.926637 | − | 0.756086i | ||||
\(550\) | 0.980620 | 0.0418138 | ||||||||
\(551\) | 9.29265 | 0.395880 | ||||||||
\(552\) | −7.10340 | + | 3.37199i | −0.302341 | + | 0.143521i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 7.24224i | − | 0.307693i | ||||||
\(555\) | −5.55795 | + | 2.63836i | −0.235922 | + | 0.111992i | ||||
\(556\) | 22.2821i | 0.944973i | ||||||||
\(557\) | − | 17.3756i | − | 0.736227i | −0.929781 | − | 0.368114i | \(-0.880004\pi\) | ||
0.929781 | − | 0.368114i | \(-0.119996\pi\) | |||||||
\(558\) | −5.02880 | + | 6.16315i | −0.212886 | + | 0.260907i | ||||
\(559\) | − | 16.7508i | − | 0.708484i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.2008 | + | 25.7021i | 0.515118 | + | 1.08514i | ||||
\(562\) | −9.13740 | −0.385438 | ||||||||
\(563\) | 20.9091 | 0.881214 | 0.440607 | − | 0.897700i | \(-0.354763\pi\) | ||||
0.440607 | + | 0.897700i | \(0.354763\pi\) | |||||||
\(564\) | −9.32758 | + | 4.42780i | −0.392762 | + | 0.186444i | ||||
\(565\) | − | 7.18425i | − | 0.302244i | ||||||
\(566\) | −1.94566 | −0.0817822 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.36945 | −0.0574610 | ||||||||
\(569\) | 28.7374i | 1.20473i | 0.798219 | + | 0.602367i | \(0.205776\pi\) | ||||
−0.798219 | + | 0.602367i | \(0.794224\pi\) | |||||||
\(570\) | 0.721803 | − | 0.342640i | 0.0302330 | − | 0.0143516i | ||||
\(571\) | −30.4998 | −1.27638 | −0.638188 | − | 0.769881i | \(-0.720316\pi\) | ||||
−0.638188 | + | 0.769881i | \(0.720316\pi\) | |||||||
\(572\) | −14.4348 | −0.603551 | ||||||||
\(573\) | 6.41823 | + | 13.5206i | 0.268125 | + | 0.564831i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.05599i | 0.127444i | ||||||||
\(576\) | 8.81381 | − | 10.8020i | 0.367242 | − | 0.450081i | ||||
\(577\) | − | 23.5062i | − | 0.978577i | −0.872122 | − | 0.489289i | \(-0.837256\pi\) | ||
0.872122 | − | 0.489289i | \(-0.162744\pi\) | |||||||
\(578\) | 9.54623i | 0.397071i | ||||||||
\(579\) | −37.1964 | + | 17.6571i | −1.54583 | + | 0.733805i | ||||
\(580\) | 14.3845i | 0.597282i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −7.46549 | + | 3.54387i | −0.309455 | + | 0.146898i | ||||
\(583\) | 33.6969 | 1.39558 | ||||||||
\(584\) | 0.440366 | 0.0182225 | ||||||||
\(585\) | −7.12941 | − | 5.81721i | −0.294765 | − | 0.240512i | ||||
\(586\) | − | 2.42787i | − | 0.100294i | ||||||
\(587\) | −24.4613 | −1.00963 | −0.504813 | − | 0.863229i | \(-0.668439\pi\) | ||||
−0.504813 | + | 0.863229i | \(0.668439\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.22067 | 0.338727 | ||||||||
\(590\) | − | 1.52862i | − | 0.0629324i | ||||||
\(591\) | −8.67873 | − | 18.2825i | −0.356995 | − | 0.752043i | ||||
\(592\) | −11.1159 | −0.456861 | ||||||||
\(593\) | −3.75012 | −0.153999 | −0.0769995 | − | 0.997031i | \(-0.524534\pi\) | ||||
−0.0769995 | + | 0.997031i | \(0.524534\pi\) | |||||||
\(594\) | 1.21707 | − | 4.94797i | 0.0499369 | − | 0.203018i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 34.6130i | − | 1.41780i | ||||||
\(597\) | 10.4929 | + | 22.1042i | 0.429444 | + | 0.904664i | ||||
\(598\) | 3.61557i | 0.147851i | ||||||||
\(599\) | 33.1010i | 1.35247i | 0.736686 | + | 0.676235i | \(0.236390\pi\) | ||||
−0.736686 | + | 0.676235i | \(0.763610\pi\) | |||||||
\(600\) | 1.10340 | + | 2.32442i | 0.0450462 | + | 0.0948939i | ||||
\(601\) | 3.36032i | 0.137070i | 0.997649 | + | 0.0685352i | \(0.0218325\pi\) | ||||
−0.997649 | + | 0.0685352i | \(0.978167\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.67473 | + | 8.18036i | −0.271816 | + | 0.333130i | ||||
\(604\) | −11.0159 | −0.448229 | ||||||||
\(605\) | 4.53701 | 0.184456 | ||||||||
\(606\) | −1.99876 | − | 4.21058i | −0.0811942 | − | 0.171043i | ||||
\(607\) | 44.5044i | 1.80638i | 0.429241 | + | 0.903190i | \(0.358781\pi\) | ||||
−0.429241 | + | 0.903190i | \(0.641219\pi\) | |||||||
\(608\) | 4.99676 | 0.202645 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.60302 | 0.145882 | ||||||||
\(611\) | 9.87689i | 0.399576i | ||||||||
\(612\) | −22.6857 | + | 27.8029i | −0.917014 | + | 1.12387i | ||||
\(613\) | 40.3135 | 1.62825 | 0.814123 | − | 0.580693i | \(-0.197218\pi\) | ||||
0.814123 | + | 0.580693i | \(0.197218\pi\) | |||||||
\(614\) | −6.18699 | −0.249687 | ||||||||
\(615\) | −3.61840 | + | 1.71766i | −0.145908 | + | 0.0692626i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 37.7372i | − | 1.51924i | −0.650366 | − | 0.759621i | \(-0.725384\pi\) | ||
0.650366 | − | 0.759621i | \(-0.274616\pi\) | |||||||
\(618\) | −2.27732 | + | 1.08104i | −0.0916071 | + | 0.0434859i | ||||
\(619\) | − | 14.6788i | − | 0.589992i | −0.955499 | − | 0.294996i | \(-0.904682\pi\) | ||
0.955499 | − | 0.294996i | \(-0.0953182\pi\) | |||||||
\(620\) | 12.7251i | 0.511052i | ||||||||
\(621\) | 15.4198 | + | 3.79286i | 0.618775 | + | 0.152202i | ||||
\(622\) | 6.97111i | 0.279516i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −7.12941 | − | 15.0188i | −0.285405 | − | 0.601232i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 7.18311 | 0.287095 | ||||||||
\(627\) | −4.75720 | + | 2.25824i | −0.189984 | + | 0.0901855i | ||||
\(628\) | − | 11.8714i | − | 0.473721i | ||||||
\(629\) | 22.9511 | 0.915118 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.8363 | −1.42662 | −0.713311 | − | 0.700848i | \(-0.752805\pi\) | ||||
−0.713311 | + | 0.700848i | \(0.752805\pi\) | |||||||
\(632\) | 12.3222i | 0.490151i | ||||||||
\(633\) | 7.03863 | − | 3.34124i | 0.279761 | − | 0.132802i | ||||
\(634\) | −1.01698 | −0.0403894 | ||||||||
\(635\) | −11.1965 | −0.444319 | ||||||||
\(636\) | 18.2256 | + | 38.3939i | 0.722691 | + | 1.52242i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 7.61971i | 0.301667i | ||||||||
\(639\) | 2.14279 | + | 1.74840i | 0.0847674 | + | 0.0691657i | ||||
\(640\) | 10.1489i | 0.401170i | ||||||||
\(641\) | − | 15.6174i | − | 0.616852i | −0.951248 | − | 0.308426i | \(-0.900198\pi\) | ||
0.951248 | − | 0.308426i | \(-0.0998022\pi\) | |||||||
\(642\) | 7.98725 | − | 3.79155i | 0.315232 | − | 0.149640i | ||||
\(643\) | − | 29.3208i | − | 1.15630i | −0.815931 | − | 0.578149i | \(-0.803775\pi\) | ||
0.815931 | − | 0.578149i | \(-0.196225\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.54532 | − | 4.05647i | 0.336472 | − | 0.159723i | ||||
\(646\) | −2.98062 | −0.117271 | ||||||||
\(647\) | 6.66811 | 0.262150 | 0.131075 | − | 0.991372i | \(-0.458157\pi\) | ||||
0.131075 | + | 0.991372i | \(0.458157\pi\) | |||||||
\(648\) | 13.0979 | − | 2.68261i | 0.514533 | − | 0.105383i | ||||
\(649\) | 10.0747i | 0.395467i | ||||||||
\(650\) | 1.18311 | 0.0464053 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −30.4404 | −1.19214 | ||||||||
\(653\) | − | 44.1287i | − | 1.72689i | −0.504445 | − | 0.863444i | \(-0.668303\pi\) | ||
0.504445 | − | 0.863444i | \(-0.331697\pi\) | |||||||
\(654\) | 0.716733 | + | 1.50986i | 0.0280265 | + | 0.0590404i | ||||
\(655\) | −15.6637 | −0.612030 | ||||||||
\(656\) | −7.23680 | −0.282550 | ||||||||
\(657\) | −0.689043 | − | 0.562222i | −0.0268821 | − | 0.0219344i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.10057i | 0.276599i | 0.990390 | + | 0.138299i | \(0.0441636\pi\) | ||||
−0.990390 | + | 0.138299i | \(0.955836\pi\) | |||||||
\(660\) | −3.49562 | − | 7.36385i | −0.136067 | − | 0.286638i | ||||
\(661\) | 23.7358i | 0.923214i | 0.887085 | + | 0.461607i | \(0.152727\pi\) | ||||
−0.887085 | + | 0.461607i | \(0.847273\pi\) | |||||||
\(662\) | − | 11.7034i | − | 0.454865i | ||||||
\(663\) | 14.7201 | + | 31.0093i | 0.571682 | + | 1.20430i | ||||
\(664\) | − | 3.13701i | − | 0.121740i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.18479 | − | 2.59862i | −0.123408 | − | 0.100694i | ||||
\(667\) | −23.7460 | −0.919448 | ||||||||
\(668\) | 8.90599 | 0.344583 | ||||||||
\(669\) | −5.35283 | − | 11.2762i | −0.206952 | − | 0.435965i | ||||
\(670\) | − | 1.35751i | − | 0.0524451i | ||||||
\(671\) | −23.7464 | −0.916721 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.7915 | −0.570171 | −0.285086 | − | 0.958502i | \(-0.592022\pi\) | ||||
−0.285086 | + | 0.958502i | \(0.592022\pi\) | |||||||
\(674\) | − | 0.710573i | − | 0.0273702i | ||||||
\(675\) | 1.24112 | − | 5.04575i | 0.0477707 | − | 0.194211i | ||||
\(676\) | 6.65028 | 0.255780 | ||||||||
\(677\) | 36.5179 | 1.40350 | 0.701749 | − | 0.712424i | \(-0.252403\pi\) | ||||
0.701749 | + | 0.712424i | \(0.252403\pi\) | |||||||
\(678\) | 4.33609 | − | 2.05834i | 0.166526 | − | 0.0790501i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − | 9.59847i | − | 0.368084i | ||||||
\(681\) | 2.91510 | − | 1.38380i | 0.111707 | − | 0.0530273i | ||||
\(682\) | 6.74071i | 0.258115i | ||||||||
\(683\) | − | 21.9194i | − | 0.838723i | −0.907819 | − | 0.419362i | \(-0.862254\pi\) | ||
0.907819 | − | 0.419362i | \(-0.137746\pi\) | |||||||
\(684\) | −5.14603 | − | 4.19888i | −0.196763 | − | 0.160548i | ||||
\(685\) | − | 5.82840i | − | 0.222692i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.9343 | − | 31.4605i | −0.569779 | − | 1.20029i | ||||
\(688\) | 17.0906 | 0.651575 | ||||||||
\(689\) | 40.6549 | 1.54883 | ||||||||
\(690\) | −1.84446 | + | 0.875565i | −0.0702173 | + | 0.0333322i | ||||
\(691\) | 31.4114i | 1.19495i | 0.801889 | + | 0.597473i | \(0.203828\pi\) | ||||
−0.801889 | + | 0.597473i | \(0.796172\pi\) | |||||||
\(692\) | −12.6164 | −0.479604 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.15929 | −0.119925 | ||||||||
\(695\) | 12.0365i | 0.456571i | ||||||||
\(696\) | −18.0614 | + | 8.57375i | −0.684616 | + | 0.324987i | ||||
\(697\) | 14.9419 | 0.565963 | ||||||||
\(698\) | 14.0133 | 0.530410 | ||||||||
\(699\) | −1.16265 | − | 2.44923i | −0.0439755 | − | 0.0926385i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.6988i | 1.12171i | 0.827915 | + | 0.560854i | \(0.189527\pi\) | ||||
−0.827915 | + | 0.560854i | \(0.810473\pi\) | |||||||
\(702\) | 1.46838 | − | 5.96966i | 0.0554203 | − | 0.225310i | ||||
\(703\) | 4.24800i | 0.160216i | ||||||||
\(704\) | − | 11.8142i | − | 0.445265i | ||||||
\(705\) | −5.03863 | + | 2.39184i | −0.189766 | + | 0.0900819i | ||||
\(706\) | 2.20435i | 0.0829617i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −11.4790 | + | 5.44908i | −0.431407 | + | 0.204789i | ||||
\(709\) | 13.3268 | 0.500500 | 0.250250 | − | 0.968181i | \(-0.419487\pi\) | ||||
0.250250 | + | 0.968181i | \(0.419487\pi\) | |||||||
\(710\) | −0.355590 | −0.0133451 | ||||||||
\(711\) | 15.7319 | − | 19.2806i | 0.589994 | − | 0.723079i | ||||
\(712\) | 27.9728i | 1.04832i | ||||||||
\(713\) | −21.0067 | −0.786706 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.79751 | −0.291610 | ||||||||
\(716\) | − | 36.9657i | − | 1.38147i | ||||||
\(717\) | 4.22805 | + | 8.90677i | 0.157899 | + | 0.332630i | ||||
\(718\) | 1.85368 | 0.0691789 | ||||||||
\(719\) | −51.1725 | −1.90841 | −0.954207 | − | 0.299147i | \(-0.903298\pi\) | ||||
−0.954207 | + | 0.299147i | \(0.903298\pi\) | |||||||
\(720\) | 5.93523 | − | 7.27405i | 0.221193 | − | 0.271088i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 6.77720i | 0.252221i | ||||||||
\(723\) | −9.90323 | − | 20.8621i | −0.368305 | − | 0.775869i | ||||
\(724\) | 9.60423i | 0.356938i | ||||||||
\(725\) | 7.77029i | 0.288581i | ||||||||
\(726\) | 1.29989 | + | 2.73834i | 0.0482434 | + | 0.101629i | ||||
\(727\) | 51.6371i | 1.91511i | 0.288246 | + | 0.957556i | \(0.406928\pi\) | ||||
−0.288246 | + | 0.957556i | \(0.593072\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.9192 | − | 12.5248i | −0.885898 | − | 0.463880i | ||||
\(730\) | 0.114345 | 0.00423209 | ||||||||
\(731\) | −35.2871 | −1.30514 | ||||||||
\(732\) | −12.8437 | − | 27.0564i | −0.474716 | − | 1.00003i | ||||
\(733\) | 21.9443i | 0.810530i | 0.914199 | + | 0.405265i | \(0.132821\pi\) | ||||
−0.914199 | + | 0.405265i | \(0.867179\pi\) | |||||||
\(734\) | −9.47979 | −0.349905 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −12.7685 | −0.470652 | ||||||||
\(737\) | 8.94695i | 0.329565i | ||||||||
\(738\) | −2.07340 | − | 1.69178i | −0.0763229 | − | 0.0622754i | ||||
\(739\) | −38.5749 | −1.41900 | −0.709500 | − | 0.704705i | \(-0.751079\pi\) | ||||
−0.709500 | + | 0.704705i | \(0.751079\pi\) | |||||||
\(740\) | −6.57565 | −0.241726 | ||||||||
\(741\) | −5.73950 | + | 2.72454i | −0.210846 | + | 0.100089i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.81873i | 0.140096i | 0.997544 | + | 0.0700478i | \(0.0223152\pi\) | ||||
−0.997544 | + | 0.0700478i | \(0.977685\pi\) | |||||||
\(744\) | −15.9779 | + | 7.58469i | −0.585777 | + | 0.278068i | ||||
\(745\) | − | 18.6975i | − | 0.685023i | ||||||
\(746\) | 10.2229i | 0.374285i | ||||||||
\(747\) | −4.00507 | + | 4.90850i | −0.146538 | + | 0.179593i | ||||
\(748\) | 30.4083i | 1.11184i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0.286507 | + | 0.603555i | 0.0104618 | + | 0.0220387i | ||||
\(751\) | 21.0542 | 0.768277 | 0.384139 | − | 0.923275i | \(-0.374498\pi\) | ||||
0.384139 | + | 0.923275i | \(0.374498\pi\) | |||||||
\(752\) | −10.0773 | −0.367480 | ||||||||
\(753\) | −8.33345 | + | 3.95589i | −0.303688 | + | 0.144161i | ||||
\(754\) | 9.19309i | 0.334792i | ||||||||
\(755\) | −5.95062 | −0.216565 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.6903 | 1.04277 | 0.521383 | − | 0.853323i | \(-0.325416\pi\) | ||||
0.521383 | + | 0.853323i | \(0.325416\pi\) | |||||||
\(758\) | 5.05072i | 0.183450i | ||||||||
\(759\) | 12.1563 | − | 5.77060i | 0.441246 | − | 0.209459i | ||||
\(760\) | 1.77658 | 0.0644432 | ||||||||
\(761\) | 10.6975 | 0.387784 | 0.193892 | − | 0.981023i | \(-0.437889\pi\) | ||||
0.193892 | + | 0.981023i | \(0.437889\pi\) | |||||||
\(762\) | −3.20788 | − | 6.75769i | −0.116209 | − | 0.244805i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 15.9963i | 0.578726i | ||||||||
\(765\) | −12.2545 | + | 15.0188i | −0.443062 | + | 0.543004i | ||||
\(766\) | 6.54430i | 0.236455i | ||||||||
\(767\) | 12.1550i | 0.438892i | ||||||||
\(768\) | 8.41747 | − | 3.99578i | 0.303739 | − | 0.144185i | ||||
\(769\) | 38.6874i | 1.39510i | 0.716535 | + | 0.697551i | \(0.245727\pi\) | ||||
−0.716535 | + | 0.697551i | \(0.754273\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.1707 | − | 4.82802i | 0.366288 | − | 0.173877i | ||||
\(772\) | −44.0073 | −1.58386 | ||||||||
\(773\) | 22.8875 | 0.823207 | 0.411603 | − | 0.911363i | \(-0.364969\pi\) | ||||
0.411603 | + | 0.911363i | \(0.364969\pi\) | |||||||
\(774\) | 4.89660 | + | 3.99536i | 0.176005 | + | 0.143610i | ||||
\(775\) | 6.87392i | 0.246919i | ||||||||
\(776\) | −18.3748 | −0.659618 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.950743 | 0.0340858 | ||||||||
\(779\) | 2.76558i | 0.0990873i | ||||||||
\(780\) | −4.21742 | − | 8.88440i | −0.151008 | − | 0.318112i | ||||
\(781\) | 2.34359 | 0.0838603 | ||||||||
\(782\) | 7.61652 | 0.272366 | ||||||||
\(783\) | 39.2070 | + | 9.64387i | 1.40114 | + | 0.344644i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 6.41279i | − | 0.228882i | ||||||
\(786\) | −4.48776 | − | 9.45388i | −0.160073 | − | 0.337209i | ||||
\(787\) | − | 32.5195i | − | 1.15919i | −0.814903 | − | 0.579597i | \(-0.803210\pi\) | ||
0.814903 | − | 0.579597i | \(-0.196790\pi\) | |||||||
\(788\) | − | 21.6302i | − | 0.770544i | ||||||
\(789\) | −11.0126 | − | 23.1991i | −0.392060 | − | 0.825911i | ||||
\(790\) | 3.19957i | 0.113835i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 7.16265 | − | 8.77834i | 0.254514 | − | 0.311925i | ||||
\(793\) | −28.6498 | −1.01738 | ||||||||
\(794\) | −1.29362 | −0.0459088 | ||||||||
\(795\) | 9.84521 | + | 20.7399i | 0.349174 | + | 0.735567i | ||||
\(796\) | 26.1516i | 0.926919i | ||||||||
\(797\) | 31.9080 | 1.13024 | 0.565120 | − | 0.825009i | \(-0.308830\pi\) | ||||
0.565120 | + | 0.825009i | \(0.308830\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.8066 | 0.736084 | ||||||||
\(800\) | 4.17817i | 0.147721i | ||||||||
\(801\) | 35.7132 | − | 43.7691i | 1.26187 | − | 1.54651i | ||||
\(802\) | −2.40960 | −0.0850858 | ||||||||
\(803\) | −0.753614 | −0.0265944 | ||||||||
\(804\) | −10.1941 | + | 4.83912i | −0.359516 | + | 0.170663i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 8.13258i | 0.286458i | ||||||||
\(807\) | 38.5049 | − | 18.2783i | 1.35544 | − | 0.643426i | ||||
\(808\) | − | 10.3635i | − | 0.364587i | ||||||
\(809\) | 20.7686i | 0.730187i | 0.930971 | + | 0.365093i | \(0.118963\pi\) | ||||
−0.930971 | + | 0.365093i | \(0.881037\pi\) | |||||||
\(810\) | 3.40098 | − | 0.696562i | 0.119498 | − | 0.0244747i | ||||
\(811\) | − | 5.77041i | − | 0.202627i | −0.994855 | − | 0.101313i | \(-0.967696\pi\) | ||
0.994855 | − | 0.101313i | \(-0.0323044\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.83135 | + | 5.96450i | 0.0992998 | + | 0.209184i | ||||
\(814\) | −3.48324 | −0.122087 | ||||||||
\(815\) | −16.4435 | −0.575990 | ||||||||
\(816\) | −31.6384 | + | 15.0188i | −1.10757 | + | 0.525762i | ||||
\(817\) | − | 6.53128i | − | 0.228501i | ||||||
\(818\) | −4.54968 | −0.159076 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.28096 | −0.149497 | ||||||||
\(821\) | − | 14.7695i | − | 0.515461i | −0.966217 | − | 0.257730i | \(-0.917025\pi\) | ||
0.966217 | − | 0.257730i | \(-0.0829746\pi\) | |||||||
\(822\) | 3.51776 | − | 1.66988i | 0.122696 | − | 0.0582438i | ||||
\(823\) | 27.4108 | 0.955482 | 0.477741 | − | 0.878501i | \(-0.341456\pi\) | ||||
0.477741 | + | 0.878501i | \(0.341456\pi\) | |||||||
\(824\) | −5.60517 | −0.195265 | ||||||||
\(825\) | −1.88829 | − | 3.97785i | −0.0657418 | − | 0.138491i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 27.6521i | − | 0.961557i | −0.876842 | − | 0.480779i | \(-0.840354\pi\) | ||
0.876842 | − | 0.480779i | \(-0.159646\pi\) | |||||||
\(828\) | 13.1499 | + | 10.7296i | 0.456991 | + | 0.372880i | ||||
\(829\) | 21.5065i | 0.746953i | 0.927640 | + | 0.373476i | \(0.121834\pi\) | ||||
−0.927640 | + | 0.373476i | \(0.878166\pi\) | |||||||
\(830\) | − | 0.814552i | − | 0.0282735i | ||||||
\(831\) | −29.3779 | + | 13.9457i | −1.01911 | + | 0.483771i | ||||
\(832\) | − | 14.2537i | − | 0.494158i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −7.26469 | + | 3.44855i | −0.251556 | + | 0.119414i | ||||
\(835\) | 4.81089 | 0.166488 | ||||||||
\(836\) | −5.62827 | −0.194658 | ||||||||
\(837\) | 34.6841 | + | 8.53137i | 1.19886 | + | 0.294887i | ||||
\(838\) | 4.64492i | 0.160456i | ||||||||
\(839\) | −26.4538 | −0.913286 | −0.456643 | − | 0.889650i | \(-0.650948\pi\) | ||||
−0.456643 | + | 0.889650i | \(0.650948\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −31.3775 | −1.08198 | ||||||||
\(842\) | 4.40751i | 0.151893i | ||||||||
\(843\) | 17.5950 | + | 37.0656i | 0.606005 | + | 1.27661i | ||||
\(844\) | 8.32745 | 0.286643 | ||||||||
\(845\) | 3.59239 | 0.123582 | ||||||||
\(846\) | −2.88721 | − | 2.35581i | −0.0992644 | − | 0.0809944i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 41.4797i | 1.42442i | ||||||||
\(849\) | 3.74657 | + | 7.89251i | 0.128582 | + | 0.270870i | ||||
\(850\) | − | 2.49232i | − | 0.0854860i | ||||||
\(851\) | − | 10.8551i | − | 0.372109i | ||||||
\(852\) | 1.26757 | + | 2.67026i | 0.0434264 | + | 0.0914817i | ||||
\(853\) | 6.05997i | 0.207490i | 0.994604 | + | 0.103745i | \(0.0330825\pi\) | ||||
−0.994604 | + | 0.103745i | \(0.966917\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.77982 | − | 2.26818i | −0.0950677 | − | 0.0775702i | ||||
\(856\) | 19.6590 | 0.671932 | ||||||||
\(857\) | 10.3398 | 0.353199 | 0.176600 | − | 0.984283i | \(-0.443490\pi\) | ||||
0.176600 | + | 0.984283i | \(0.443490\pi\) | |||||||
\(858\) | −2.23405 | − | 4.70623i | −0.0762691 | − | 0.160668i | ||||
\(859\) | − | 35.4947i | − | 1.21106i | −0.795821 | − | 0.605531i | \(-0.792961\pi\) | ||
0.795821 | − | 0.605531i | \(-0.207039\pi\) | |||||||
\(860\) | 10.1100 | 0.344749 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.5758 | 0.428334 | ||||||||
\(863\) | − | 15.1410i | − | 0.515405i | −0.966224 | − | 0.257702i | \(-0.917035\pi\) | ||
0.966224 | − | 0.257702i | \(-0.0829654\pi\) | |||||||
\(864\) | 21.0820 | + | 5.18561i | 0.717225 | + | 0.176418i | ||||
\(865\) | −6.81521 | −0.231724 | ||||||||
\(866\) | 1.68813 | 0.0573649 | ||||||||
\(867\) | 38.7240 | − | 18.3823i | 1.31514 | − | 0.624295i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 21.0874i | − | 0.715342i | ||||||
\(870\) | −4.68980 | + | 2.22625i | −0.158999 | + | 0.0754769i | ||||
\(871\) | 10.7944i | 0.365754i | ||||||||
\(872\) | 3.71623i | 0.125848i | ||||||||
\(873\) | 28.7512 | + | 23.4594i | 0.973081 | + | 0.793982i | ||||
\(874\) | 1.40974i | 0.0476852i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.407605 | − | 0.858658i | −0.0137717 | − | 0.0290114i | ||||
\(877\) | 19.5895 | 0.661491 | 0.330745 | − | 0.943720i | \(-0.392700\pi\) | ||||
0.330745 | + | 0.943720i | \(0.392700\pi\) | |||||||
\(878\) | 5.71969 | 0.193030 | ||||||||
\(879\) | −9.84858 | + | 4.67512i | −0.332184 | + | 0.157688i | ||||
\(880\) | − | 7.95571i | − | 0.268187i | ||||||
\(881\) | 28.7481 | 0.968548 | 0.484274 | − | 0.874917i | \(-0.339084\pi\) | ||||
0.484274 | + | 0.874917i | \(0.339084\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.77550 | 0.194361 | 0.0971805 | − | 0.995267i | \(-0.469018\pi\) | ||||
0.0971805 | + | 0.995267i | \(0.469018\pi\) | |||||||
\(884\) | 36.6873i | 1.23393i | ||||||||
\(885\) | −6.20080 | + | 2.94352i | −0.208438 | + | 0.0989454i | ||||
\(886\) | −6.13792 | −0.206207 | ||||||||
\(887\) | 13.1383 | 0.441143 | 0.220571 | − | 0.975371i | \(-0.429208\pi\) | ||||
0.220571 | + | 0.975371i | \(0.429208\pi\) | |||||||
\(888\) | −3.91937 | − | 8.25651i | −0.131525 | − | 0.277070i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 7.26337i | 0.243469i | ||||||||
\(891\) | −22.4149 | + | 4.59084i | −0.750926 | + | 0.153799i | ||||
\(892\) | − | 13.3410i | − | 0.446689i | ||||||
\(893\) | 3.85108i | 0.128872i | ||||||||
\(894\) | 11.2849 | − | 5.35697i | 0.377425 | − | 0.179164i | ||||
\(895\) | − | 19.9684i | − | 0.667470i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14.6664 | − | 6.96215i | 0.489698 | − | 0.232460i | ||||
\(898\) | 13.5731 | 0.452942 | ||||||||
\(899\) | −53.4124 | −1.78140 | ||||||||
\(900\) | 3.51101 | − | 4.30299i | 0.117034 | − | 0.143433i | ||||
\(901\) | − | 85.6433i | − | 2.85319i | ||||||
\(902\) | −2.26770 | −0.0755061 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.6724 | 0.354959 | ||||||||
\(905\) | 5.18808i | 0.172457i | ||||||||
\(906\) | −1.70490 | − | 3.59152i | −0.0566414 | − | 0.119320i | ||||
\(907\) | −6.17008 | −0.204874 | −0.102437 | − | 0.994739i | \(-0.532664\pi\) | ||||
−0.102437 | + | 0.994739i | \(0.532664\pi\) | |||||||
\(908\) | 3.44887 | 0.114455 | ||||||||
\(909\) | −13.2313 | + | 16.2158i | −0.438853 | + | 0.537845i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 53.7961i | 1.78234i | 0.453665 | + | 0.891172i | \(0.350116\pi\) | ||||
−0.453665 | + | 0.891172i | \(0.649884\pi\) | |||||||
\(912\) | −2.77982 | − | 5.85594i | −0.0920489 | − | 0.193910i | ||||
\(913\) | 5.36848i | 0.177671i | ||||||||
\(914\) | 5.42302i | 0.179378i | ||||||||
\(915\) | −6.93799 | − | 14.6155i | −0.229363 | − | 0.483174i | ||||
\(916\) | − | 37.2211i | − | 1.22982i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −12.5756 | − | 3.09327i | −0.415058 | − | 0.102093i | ||||
\(919\) | −0.620281 | −0.0204612 | −0.0102306 | − | 0.999948i | \(-0.503257\pi\) | ||||
−0.0102306 | + | 0.999948i | \(0.503257\pi\) | |||||||
\(920\) | −4.53977 | −0.149672 | ||||||||
\(921\) | 11.9137 | + | 25.0973i | 0.392570 | + | 0.826985i | ||||
\(922\) | − | 5.21357i | − | 0.171700i | ||||||
\(923\) | 2.82752 | 0.0930688 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.55208 | −0.116792 | ||||||||
\(926\) | 6.88072i | 0.226114i | ||||||||
\(927\) | 8.77043 | + | 7.15620i | 0.288059 | + | 0.235040i | ||||
\(928\) | −32.4656 | −1.06574 | ||||||||
\(929\) | −52.9609 | −1.73759 | −0.868796 | − | 0.495170i | \(-0.835106\pi\) | ||||
−0.868796 | + | 0.495170i | \(0.835106\pi\) | |||||||
\(930\) | −4.14879 | + | 1.96943i | −0.136044 | + | 0.0645802i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 2.89770i | − | 0.0949174i | ||||||
\(933\) | 28.2781 | − | 13.4236i | 0.925783 | − | 0.439469i | ||||
\(934\) | − | 3.54464i | − | 0.115984i | ||||||
\(935\) | 16.4262i | 0.537194i | ||||||||
\(936\) | 8.64165 | − | 10.5910i | 0.282461 | − | 0.346176i | ||||
\(937\) | − | 0.667265i | − | 0.0217986i | −0.999941 | − | 0.0108993i | \(-0.996531\pi\) | ||
0.999941 | − | 0.0108993i | \(-0.00346942\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −13.8318 | − | 29.1380i | −0.451385 | − | 0.950884i | ||||
\(940\) | −5.96124 | −0.194434 | ||||||||
\(941\) | −24.9683 | −0.813944 | −0.406972 | − | 0.913441i | \(-0.633415\pi\) | ||||
−0.406972 | + | 0.913441i | \(0.633415\pi\) | |||||||
\(942\) | 3.87047 | − | 1.83731i | 0.126107 | − | 0.0598628i | ||||
\(943\) | − | 7.06703i | − | 0.230134i | ||||||
\(944\) | −12.4016 | −0.403638 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.35547 | 0.174121 | ||||||||
\(947\) | 54.9967i | 1.78715i | 0.448910 | + | 0.893577i | \(0.351812\pi\) | ||||
−0.448910 | + | 0.893577i | \(0.648188\pi\) | |||||||
\(948\) | 24.0268 | − | 11.4055i | 0.780353 | − | 0.370434i | ||||
\(949\) | −0.909226 | −0.0295147 | ||||||||
\(950\) | 0.461303 | 0.0149667 | ||||||||
\(951\) | 1.95830 | + | 4.12534i | 0.0635022 | + | 0.133773i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 35.8657i | − | 1.16180i | −0.813974 | − | 0.580902i | \(-0.802700\pi\) | ||
0.813974 | − | 0.580902i | \(-0.197300\pi\) | |||||||
\(954\) | −9.69691 | + | 11.8842i | −0.313949 | + | 0.384767i | ||||
\(955\) | 8.64099i | 0.279616i | ||||||||
\(956\) | 10.5377i | 0.340812i | ||||||||
\(957\) | 30.9091 | − | 14.6726i | 0.999149 | − | 0.474296i | ||||
\(958\) | − | 7.28288i | − | 0.235299i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 7.27144 | − | 3.45176i | 0.234685 | − | 0.111405i | ||||
\(961\) | −16.2508 | −0.524220 | ||||||||
\(962\) | −4.20249 | −0.135494 | ||||||||
\(963\) | −30.7606 | − | 25.0990i | −0.991246 | − | 0.808803i | ||||
\(964\) | − | 24.6820i | − | 0.794955i | ||||||
\(965\) | −23.7721 | −0.765252 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.8780 | 0.381971 | 0.190986 | − | 0.981593i | \(-0.438832\pi\) | ||||
0.190986 | + | 0.981593i | \(0.438832\pi\) | |||||||
\(968\) | 6.73987i | 0.216628i | ||||||||
\(969\) | 5.73950 | + | 12.0908i | 0.184379 | + | 0.388412i | ||||
\(970\) | −4.77119 | −0.153194 | ||||||||
\(971\) | 5.22666 | 0.167732 | 0.0838658 | − | 0.996477i | \(-0.473273\pi\) | ||||
0.0838658 | + | 0.996477i | \(0.473273\pi\) | |||||||
\(972\) | −17.3542 | − | 23.0562i | −0.556637 | − | 0.739528i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 2.01940i | − | 0.0647056i | ||||||
\(975\) | −2.27820 | − | 4.79923i | −0.0729607 | − | 0.153698i | ||||
\(976\) | − | 29.2310i | − | 0.935663i | ||||||
\(977\) | 17.9198i | 0.573307i | 0.958034 | + | 0.286653i | \(0.0925428\pi\) | ||||
−0.958034 | + | 0.286653i | \(0.907457\pi\) | |||||||
\(978\) | −4.71118 | − | 9.92454i | −0.150647 | − | 0.317352i | ||||
\(979\) | − | 47.8708i | − | 1.52996i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.74457 | − | 5.81481i | 0.151482 | − | 0.185653i | ||||
\(982\) | 7.52951 | 0.240276 | ||||||||
\(983\) | −41.8828 | −1.33585 | −0.667926 | − | 0.744227i | \(-0.732818\pi\) | ||||
−0.667926 | + | 0.744227i | \(0.732818\pi\) | |||||||
\(984\) | −2.55163 | − | 5.37525i | −0.0813430 | − | 0.171357i | ||||
\(985\) | − | 11.6843i | − | 0.372294i | ||||||
\(986\) | 19.3661 | 0.616742 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.79044 | −0.216033 | ||||||||
\(989\) | 16.6897i | 0.530702i | ||||||||
\(990\) | 1.85984 | − | 2.27937i | 0.0591097 | − | 0.0724431i | ||||
\(991\) | 9.76830 | 0.310300 | 0.155150 | − | 0.987891i | \(-0.450414\pi\) | ||||
0.155150 | + | 0.987891i | \(0.450414\pi\) | |||||||
\(992\) | −28.7204 | −0.911875 | ||||||||
\(993\) | −47.4744 | + | 22.5361i | −1.50656 | + | 0.715162i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.1268i | 0.447848i | ||||||||
\(996\) | −6.11678 | + | 2.90364i | −0.193818 | + | 0.0920053i | ||||
\(997\) | 35.1740i | 1.11397i | 0.830522 | + | 0.556986i | \(0.188042\pi\) | ||||
−0.830522 | + | 0.556986i | \(0.811958\pi\) | |||||||
\(998\) | − | 14.1313i | − | 0.447317i | ||||||
\(999\) | −4.40856 | + | 17.9229i | −0.139481 | + | 0.567056i |
(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 | 735.2.b.c.146.5 | 8 | ||
3.2 | odd | 2 | 735.2.b.d.146.4 | 8 | |||
7.2 | even | 3 | 105.2.s.d.101.2 | yes | 8 | ||
7.3 | odd | 6 | 105.2.s.c.26.3 | ✓ | 8 | ||
7.4 | even | 3 | 735.2.s.k.656.3 | 8 | |||
7.5 | odd | 6 | 735.2.s.l.521.2 | 8 | |||
7.6 | odd | 2 | 735.2.b.d.146.5 | 8 | |||
21.2 | odd | 6 | 105.2.s.c.101.3 | yes | 8 | ||
21.5 | even | 6 | 735.2.s.k.521.3 | 8 | |||
21.11 | odd | 6 | 735.2.s.l.656.2 | 8 | |||
21.17 | even | 6 | 105.2.s.d.26.2 | yes | 8 | ||
21.20 | even | 2 | inner | 735.2.b.c.146.4 | 8 | ||
35.2 | odd | 12 | 525.2.q.e.374.5 | 16 | |||
35.3 | even | 12 | 525.2.q.f.299.4 | 16 | |||
35.9 | even | 6 | 525.2.t.f.101.3 | 8 | |||
35.17 | even | 12 | 525.2.q.f.299.5 | 16 | |||
35.23 | odd | 12 | 525.2.q.e.374.4 | 16 | |||
35.24 | odd | 6 | 525.2.t.g.26.2 | 8 | |||
105.2 | even | 12 | 525.2.q.f.374.4 | 16 | |||
105.17 | odd | 12 | 525.2.q.e.299.4 | 16 | |||
105.23 | even | 12 | 525.2.q.f.374.5 | 16 | |||
105.38 | odd | 12 | 525.2.q.e.299.5 | 16 | |||
105.44 | odd | 6 | 525.2.t.g.101.2 | 8 | |||
105.59 | even | 6 | 525.2.t.f.26.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.s.c.26.3 | ✓ | 8 | 7.3 | odd | 6 | ||
105.2.s.c.101.3 | yes | 8 | 21.2 | odd | 6 | ||
105.2.s.d.26.2 | yes | 8 | 21.17 | even | 6 | ||
105.2.s.d.101.2 | yes | 8 | 7.2 | even | 3 | ||
525.2.q.e.299.4 | 16 | 105.17 | odd | 12 | |||
525.2.q.e.299.5 | 16 | 105.38 | odd | 12 | |||
525.2.q.e.374.4 | 16 | 35.23 | odd | 12 | |||
525.2.q.e.374.5 | 16 | 35.2 | odd | 12 | |||
525.2.q.f.299.4 | 16 | 35.3 | even | 12 | |||
525.2.q.f.299.5 | 16 | 35.17 | even | 12 | |||
525.2.q.f.374.4 | 16 | 105.2 | even | 12 | |||
525.2.q.f.374.5 | 16 | 105.23 | even | 12 | |||
525.2.t.f.26.3 | 8 | 105.59 | even | 6 | |||
525.2.t.f.101.3 | 8 | 35.9 | even | 6 | |||
525.2.t.g.26.2 | 8 | 35.24 | odd | 6 | |||
525.2.t.g.101.2 | 8 | 105.44 | odd | 6 | |||
735.2.b.c.146.4 | 8 | 21.20 | even | 2 | inner | ||
735.2.b.c.146.5 | 8 | 1.1 | even | 1 | trivial | ||
735.2.b.d.146.4 | 8 | 3.2 | odd | 2 | |||
735.2.b.d.146.5 | 8 | 7.6 | odd | 2 | |||
735.2.s.k.521.3 | 8 | 21.5 | even | 6 | |||
735.2.s.k.656.3 | 8 | 7.4 | even | 3 | |||
735.2.s.l.521.2 | 8 | 7.5 | odd | 6 | |||
735.2.s.l.656.2 | 8 | 21.11 | odd | 6 |