Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3344,2,Mod(1519,3344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 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("3344.1519");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3344 = 2^{4} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3344.o (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: | \(26.7019744359\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1519.15 | ||
Character | \(\chi\) | \(=\) | 3344.1519 |
Dual form | 3344.2.o.a.1519.16 |
$q$-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 \(\left(\mathbb{Z}/3344\mathbb{Z}\right)^\times\).
\(n\) | \(705\) | \(837\) | \(2433\) | \(2927\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
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 | 0 | ||||||||
\(3\) | −0.924782 | −0.533923 | −0.266962 | − | 0.963707i | \(-0.586020\pi\) | ||||
−0.266962 | + | 0.963707i | \(0.586020\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.57340 | −1.15086 | −0.575430 | − | 0.817851i | \(-0.695165\pi\) | ||||
−0.575430 | + | 0.817851i | \(0.695165\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.765529i | 0.289343i | 0.989480 | + | 0.144671i | \(0.0462125\pi\) | ||||
−0.989480 | + | 0.144671i | \(0.953787\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.14478 | −0.714926 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000i | 0.301511i | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.60853i | − | 0.723476i | −0.932280 | − | 0.361738i | \(-0.882184\pi\) | ||
0.932280 | − | 0.361738i | \(-0.117816\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.37984 | 0.614471 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.74816 | −0.909063 | −0.454532 | − | 0.890731i | \(-0.650193\pi\) | ||||
−0.454532 | + | 0.890731i | \(0.650193\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.28136 | − | 3.71421i | −0.523381 | − | 0.852099i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 0.707948i | − | 0.154487i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 3.60503i | − | 0.751701i | −0.926680 | − | 0.375850i | \(-0.877351\pi\) | ||
0.926680 | − | 0.375850i | \(-0.122649\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.62240 | 0.324479 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.75780 | 0.915639 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.77031i | 0.700129i | 0.936726 | + | 0.350065i | \(0.113840\pi\) | ||||
−0.936726 | + | 0.350065i | \(0.886160\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.30362 | −1.31177 | −0.655885 | − | 0.754861i | \(-0.727704\pi\) | ||||
−0.655885 | + | 0.754861i | \(0.727704\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 0.924782i | − | 0.160984i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 1.97001i | − | 0.332993i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.15874i | 1.34129i | 0.741779 | + | 0.670644i | \(0.233982\pi\) | ||||
−0.741779 | + | 0.670644i | \(0.766018\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.41232i | 0.386281i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5.25952i | − | 0.821398i | −0.911771 | − | 0.410699i | \(-0.865285\pi\) | ||
0.911771 | − | 0.410699i | \(-0.134715\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 0.574153i | − | 0.0875575i | −0.999041 | − | 0.0437788i | \(-0.986060\pi\) | ||
0.999041 | − | 0.0437788i | \(-0.0139397\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.51937 | 0.822780 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 1.77015i | − | 0.258203i | −0.991631 | − | 0.129101i | \(-0.958791\pi\) | ||
0.991631 | − | 0.129101i | \(-0.0412092\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.41396 | 0.916281 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.46624 | 0.485370 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 11.7573i | − | 1.61500i | −0.589871 | − | 0.807498i | \(-0.700821\pi\) | ||
0.589871 | − | 0.807498i | \(-0.299179\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2.57340i | − | 0.346997i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.10976 | + | 3.43484i | 0.279445 | + | 0.454955i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.11799 | −0.536117 | −0.268059 | − | 0.963403i | \(-0.586382\pi\) | ||||
−0.268059 | + | 0.963403i | \(0.586382\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.17659 | 1.17494 | 0.587471 | − | 0.809245i | \(-0.300124\pi\) | ||||
0.587471 | + | 0.809245i | \(0.300124\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 1.64189i | − | 0.206859i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.71279i | 0.832619i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.66350 | −0.203229 | −0.101614 | − | 0.994824i | \(-0.532401\pi\) | ||||
−0.101614 | + | 0.994824i | \(0.532401\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.33387i | 0.401351i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.0522 | −1.31165 | −0.655825 | − | 0.754913i | \(-0.727679\pi\) | ||||
−0.655825 | + | 0.754913i | \(0.727679\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.32984 | −0.272687 | −0.136343 | − | 0.990662i | \(-0.543535\pi\) | ||||
−0.136343 | + | 0.990662i | \(0.543535\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.50036 | −0.173247 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.765529 | −0.0872402 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.04543 | −1.01769 | −0.508845 | − | 0.860858i | \(-0.669927\pi\) | ||||
−0.508845 | + | 0.860858i | \(0.669927\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.03441 | 0.226045 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 17.2218i | 1.89034i | 0.326576 | + | 0.945171i | \(0.394105\pi\) | ||||
−0.326576 | + | 0.945171i | \(0.605895\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.64553 | 1.04620 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 3.48672i | − | 0.373815i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.39907i | 0.360301i | 0.983639 | + | 0.180150i | \(0.0576584\pi\) | ||||
−0.983639 | + | 0.180150i | \(0.942342\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.99691 | 0.209333 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.75426 | 0.700384 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.87086 | + | 9.55816i | 0.602338 | + | 0.980647i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.0585i | 1.63049i | 0.579116 | + | 0.815245i | \(0.303398\pi\) | ||||
−0.579116 | + | 0.815245i | \(0.696602\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 2.14478i | − | 0.215558i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.2482 | 1.31824 | 0.659121 | − | 0.752037i | \(-0.270928\pi\) | ||||
0.659121 | + | 0.752037i | \(0.270928\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.9964 | 1.37911 | 0.689554 | − | 0.724234i | \(-0.257806\pi\) | ||||
0.689554 | + | 0.724234i | \(0.257806\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.82183i | 0.177793i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.82819 | 0.756779 | 0.378390 | − | 0.925646i | \(-0.376478\pi\) | ||||
0.378390 | + | 0.925646i | \(0.376478\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.8017i | 1.89666i | 0.317281 | + | 0.948332i | \(0.397230\pi\) | ||||
−0.317281 | + | 0.948332i | \(0.602770\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 7.54506i | − | 0.716145i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 3.79125i | − | 0.356651i | −0.983972 | − | 0.178326i | \(-0.942932\pi\) | ||
0.983972 | − | 0.178326i | \(-0.0570680\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.27719i | 0.865102i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.59471i | 0.517232i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 2.86933i | − | 0.263031i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.86391i | 0.438564i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.69193 | 0.777430 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −21.0742 | −1.87003 | −0.935017 | − | 0.354603i | \(-0.884616\pi\) | ||||
−0.935017 | + | 0.354603i | \(0.884616\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.530966i | 0.0467490i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 17.3752i | − | 1.51808i | −0.651045 | − | 0.759039i | \(-0.725669\pi\) | ||
0.651045 | − | 0.759039i | \(-0.274331\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.84334 | − | 1.74645i | 0.246549 | − | 0.151436i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −12.2437 | −1.05377 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.90625 | −0.504605 | −0.252302 | − | 0.967648i | \(-0.581188\pi\) | ||||
−0.252302 | + | 0.967648i | \(0.581188\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 15.0930i | − | 1.28017i | −0.768305 | − | 0.640084i | \(-0.778900\pi\) | ||
0.768305 | − | 0.640084i | \(-0.221100\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.63700i | 0.137860i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.60853 | 0.218136 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 9.70253i | − | 0.805751i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.93152 | −0.489224 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.75827 | 0.635582 | 0.317791 | − | 0.948161i | \(-0.397059\pi\) | ||||
0.317791 | + | 0.948161i | \(0.397059\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.8250 | 1.85747 | 0.928737 | − | 0.370739i | \(-0.120895\pi\) | ||||
0.928737 | + | 0.370739i | \(0.120895\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.03898 | 0.649913 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 18.7952 | 1.50966 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 24.5482 | 1.95916 | 0.979581 | − | 0.201048i | \(-0.0644347\pi\) | ||||
0.979581 | + | 0.201048i | \(0.0644347\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.8730i | 0.862284i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.75976 | 0.217499 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.07574i | 0.554215i | 0.960839 | + | 0.277107i | \(0.0893758\pi\) | ||||
−0.960839 | + | 0.277107i | \(0.910624\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.37984i | 0.185270i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.8729 | 1.07352 | 0.536758 | − | 0.843736i | \(-0.319649\pi\) | ||||
0.536758 | + | 0.843736i | \(0.319649\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.19558 | 0.476583 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.89302 | + | 7.96616i | 0.374178 | + | 0.609188i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.1394i | 1.30309i | 0.758611 | + | 0.651543i | \(0.225878\pi\) | ||||
−0.758611 | + | 0.651543i | \(0.774122\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.24199i | 0.0938857i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.80825 | 0.286245 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.7633 | −1.40244 | −0.701218 | − | 0.712947i | \(-0.747360\pi\) | ||||
−0.701218 | + | 0.712947i | \(0.747360\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.8245i | 1.69653i | 0.529571 | + | 0.848265i | \(0.322353\pi\) | ||||
−0.529571 | + | 0.848265i | \(0.677647\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.48635 | −0.627329 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 20.9957i | − | 1.54364i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 3.74816i | − | 0.274093i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.64224i | 0.264934i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 23.5974i | − | 1.70745i | −0.520726 | − | 0.853724i | \(-0.674339\pi\) | ||
0.520726 | − | 0.853724i | \(-0.325661\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.0786i | 0.797452i | 0.917070 | + | 0.398726i | \(0.130547\pi\) | ||||
−0.917070 | + | 0.398726i | \(0.869453\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 6.20787i | − | 0.444555i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.34017 | −0.0954832 | −0.0477416 | − | 0.998860i | \(-0.515202\pi\) | ||||
−0.0477416 | + | 0.998860i | \(0.515202\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.1677i | 1.07521i | 0.843196 | + | 0.537606i | \(0.180671\pi\) | ||||
−0.843196 | + | 0.537606i | \(0.819329\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.53838 | 0.108509 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.88629 | −0.202578 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.5348i | 0.945315i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.73199i | 0.537410i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.71421 | − | 2.28136i | 0.256918 | − | 0.157805i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.0907 | 1.52078 | 0.760392 | − | 0.649464i | \(-0.225007\pi\) | ||||
0.760392 | + | 0.649464i | \(0.225007\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.2208 | 0.700320 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.47753i | 0.100766i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 5.59114i | − | 0.379551i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.15459 | 0.145594 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.77720i | 0.657685i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.3476 | 1.16168 | 0.580841 | − | 0.814017i | \(-0.302724\pi\) | ||||
0.580841 | + | 0.814017i | \(0.302724\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.47968 | −0.231978 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.31237 | −0.286222 | −0.143111 | − | 0.989707i | \(-0.545711\pi\) | ||||
−0.143111 | + | 0.989707i | \(0.545711\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.5294 | 1.02621 | 0.513106 | − | 0.858325i | \(-0.328495\pi\) | ||||
0.513106 | + | 0.858325i | \(0.328495\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.707948 | 0.0465796 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.8624 | −0.973666 | −0.486833 | − | 0.873495i | \(-0.661848\pi\) | ||||
−0.486833 | + | 0.873495i | \(0.661848\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.55530i | 0.297155i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.36505 | 0.543368 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.12277i | 0.201995i | 0.994887 | + | 0.100998i | \(0.0322035\pi\) | ||||
−0.994887 | + | 0.100998i | \(0.967797\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 20.2566i | − | 1.30484i | −0.757858 | − | 0.652420i | \(-0.773754\pi\) | ||
0.757858 | − | 0.652420i | \(-0.226246\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.1548 | −1.03633 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −16.5057 | −1.05451 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.68863 | + | 5.95100i | −0.616473 | + | 0.378653i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 15.9264i | − | 1.00930i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.4793i | 1.35576i | 0.735172 | + | 0.677880i | \(0.237101\pi\) | ||||
−0.735172 | + | 0.677880i | \(0.762899\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.60503 | 0.226646 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.92002 | −0.558593 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 13.0893i | − | 0.816489i | −0.912873 | − | 0.408245i | \(-0.866141\pi\) | ||
0.912873 | − | 0.408245i | \(-0.133859\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.24576 | −0.388092 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 8.08648i | − | 0.500541i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 23.0707i | − | 1.42260i | −0.702888 | − | 0.711300i | \(-0.748107\pi\) | ||
0.702888 | − | 0.711300i | \(-0.251893\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 30.2564i | 1.85863i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 3.14340i | − | 0.192373i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 5.99734i | − | 0.365664i | −0.983144 | − | 0.182832i | \(-0.941474\pi\) | ||
0.983144 | − | 0.182832i | \(-0.0585265\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.8489i | 1.08424i | 0.840300 | + | 0.542121i | \(0.182379\pi\) | ||||
−0.840300 | + | 0.542121i | \(0.817621\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.84670 | −0.111768 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.62240i | 0.0978341i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.3605 | 0.983010 | 0.491505 | − | 0.870875i | \(-0.336447\pi\) | ||||
0.491505 | + | 0.870875i | \(0.336447\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 15.6647 | 0.937818 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 9.69477i | − | 0.578342i | −0.957278 | − | 0.289171i | \(-0.906620\pi\) | ||
0.957278 | − | 0.289171i | \(-0.0933796\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 20.4923i | − | 1.21814i | −0.793117 | − | 0.609069i | \(-0.791543\pi\) | ||
0.793117 | − | 0.609069i | \(-0.208457\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.42927 | − | 8.83922i | −0.321602 | − | 0.523590i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.02631 | 0.237666 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.95126 | −0.173604 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 14.8506i | − | 0.870557i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 2.22695i | − | 0.130100i | −0.997882 | − | 0.0650500i | \(-0.979279\pi\) | ||
0.997882 | − | 0.0650500i | \(-0.0207207\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.5973 | 0.616996 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.75780i | 0.276076i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.40383 | −0.543837 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.439531 | 0.0253341 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12.2517 | −0.703841 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −23.6151 | −1.35219 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.5923 | 1.23233 | 0.616167 | − | 0.787615i | \(-0.288684\pi\) | ||||
0.616167 | + | 0.787615i | \(0.288684\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.9436 | −0.736338 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.4307i | 0.988403i | 0.869347 | + | 0.494202i | \(0.164540\pi\) | ||||
−0.869347 | + | 0.494202i | \(0.835460\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.30327 | −0.356282 | −0.178141 | − | 0.984005i | \(-0.557008\pi\) | ||||
−0.178141 | + | 0.984005i | \(0.557008\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.22524i | 0.238066i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 30.8999i | 1.73551i | 0.496989 | + | 0.867757i | \(0.334439\pi\) | ||||
−0.496989 | + | 0.867757i | \(0.665561\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.77031 | −0.211097 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.23937 | −0.404062 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.55093 | + | 13.9215i | 0.475786 | + | 0.774612i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 4.23206i | − | 0.234753i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 18.3123i | − | 1.01267i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.35510 | 0.0747091 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.5527 | −1.45947 | −0.729734 | − | 0.683731i | \(-0.760356\pi\) | ||||
−0.729734 | + | 0.683731i | \(0.760356\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 17.4987i | − | 0.958922i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.28085 | 0.233888 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 11.0220i | − | 0.600407i | −0.953875 | − | 0.300204i | \(-0.902945\pi\) | ||
0.953875 | − | 0.300204i | \(-0.0970547\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.50608i | 0.190424i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 7.30362i | − | 0.395513i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.2688i | 0.554462i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 8.57938i | − | 0.461898i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.2891i | 0.659711i | 0.944031 | + | 0.329856i | \(0.107000\pi\) | ||||
−0.944031 | + | 0.329856i | \(0.893000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.1394 | 1.18509 | 0.592546 | − | 0.805536i | \(-0.298123\pi\) | ||||
0.592546 | + | 0.805536i | \(0.298123\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 12.4109i | − | 0.662442i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.6400 | −1.36468 | −0.682339 | − | 0.731035i | \(-0.739037\pi\) | ||||
−0.682339 | + | 0.731035i | \(0.739037\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 28.4416 | 1.50952 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.65351i | 0.140438i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.13933i | 0.429577i | 0.976661 | + | 0.214789i | \(0.0689063\pi\) | ||||
−0.976661 | + | 0.214789i | \(0.931094\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.59076 | + | 16.9469i | −0.452145 | + | 0.891944i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.924782 | 0.0485385 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.99561 | 0.313825 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 30.2059i | − | 1.57674i | −0.615203 | − | 0.788369i | \(-0.710926\pi\) | ||
0.615203 | − | 0.788369i | \(-0.289074\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 11.2805i | 0.587239i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.00059 | 0.467288 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 5.16531i | − | 0.267450i | −0.991018 | − | 0.133725i | \(-0.957306\pi\) | ||
0.991018 | − | 0.133725i | \(-0.0426939\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.03815 | −0.415088 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.83497 | 0.506527 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.0822 | 0.774722 | 0.387361 | − | 0.921928i | \(-0.373387\pi\) | ||||
0.387361 | + | 0.921928i | \(0.373387\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 19.4891 | 0.998454 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.75172 | −0.293899 | −0.146949 | − | 0.989144i | \(-0.546945\pi\) | ||||
−0.146949 | + | 0.989144i | \(0.546945\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.97001 | 0.100401 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.23143i | 0.0625971i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −24.8324 | −1.25905 | −0.629527 | − | 0.776978i | \(-0.716751\pi\) | ||||
−0.629527 | + | 0.776978i | \(0.716751\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.5122i | 0.683344i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.0683i | 0.810537i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 23.2775 | 1.17122 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.0021 | 0.501991 | 0.250995 | − | 0.967988i | \(-0.419242\pi\) | ||||
0.250995 | + | 0.967988i | \(0.419242\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.62947 | + | 1.61509i | −0.131638 | + | 0.0808555i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.6318i | 0.680739i | 0.940292 | + | 0.340369i | \(0.110552\pi\) | ||||
−0.940292 | + | 0.340369i | \(0.889448\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.0517i | 0.949033i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.23534 | −0.260146 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.15874 | −0.404414 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 32.7709i | − | 1.62042i | −0.586142 | − | 0.810208i | \(-0.699354\pi\) | ||
0.586142 | − | 0.810208i | \(-0.300646\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.46199 | 0.269420 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 3.15245i | − | 0.155122i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 44.3187i | − | 2.17552i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.9577i | 0.683512i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.6469i | 1.05752i | 0.848771 | + | 0.528760i | \(0.177343\pi\) | ||||
−0.848771 | + | 0.528760i | \(0.822657\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 16.5251i | − | 0.805385i | −0.915335 | − | 0.402692i | \(-0.868074\pi\) | ||
0.915335 | − | 0.402692i | \(-0.131926\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.79657i | 0.184596i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.08100 | −0.294972 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.02495i | 0.339961i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.41232 | −0.116468 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.49914 | −0.409389 | −0.204694 | − | 0.978826i | \(-0.565620\pi\) | ||||
−0.204694 | + | 0.978826i | \(0.565620\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 8.14216i | − | 0.391287i | −0.980675 | − | 0.195644i | \(-0.937320\pi\) | ||
0.980675 | − | 0.195644i | \(-0.0626796\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.97273i | 0.430209i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −13.3899 | + | 8.22438i | −0.640523 | + | 0.393426i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.56561 | −0.456541 | −0.228271 | − | 0.973598i | \(-0.573307\pi\) | ||||
−0.228271 | + | 0.973598i | \(0.573307\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13.7565 | −0.655073 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 31.8773i | − | 1.51454i | −0.653104 | − | 0.757269i | \(-0.726533\pi\) | ||
0.653104 | − | 0.757269i | \(-0.273467\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 8.74717i | − | 0.414656i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.17471 | −0.339352 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.9188i | 0.845640i | 0.906214 | + | 0.422820i | \(0.138960\pi\) | ||||
−0.906214 | + | 0.422820i | \(0.861040\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.25952 | 0.247661 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −21.1082 | −0.991749 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.13884 | −0.240913 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.14113 | 0.193714 | 0.0968569 | − | 0.995298i | \(-0.469121\pi\) | ||||
0.0968569 | + | 0.995298i | \(0.469121\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −17.8330 | −0.832374 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.48067 | 0.394984 | 0.197492 | − | 0.980304i | \(-0.436720\pi\) | ||||
0.197492 | + | 0.980304i | \(0.436720\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.0728i | 0.979336i | 0.871909 | + | 0.489668i | \(0.162882\pi\) | ||||
−0.871909 | + | 0.489668i | \(0.837118\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −17.3814 | −0.806044 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 11.6322i | − | 0.538273i | −0.963102 | − | 0.269137i | \(-0.913262\pi\) | ||
0.963102 | − | 0.269137i | \(-0.0867383\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 1.27346i | − | 0.0588029i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −22.7018 | −1.04604 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.574153 | 0.0263996 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.70127 | − | 6.02592i | −0.169826 | − | 0.276488i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 25.2169i | 1.15460i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 21.0362i | 0.961167i | 0.876949 | + | 0.480583i | \(0.159575\pi\) | ||||
−0.876949 | + | 0.480583i | \(0.840425\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.2823 | 0.970390 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.55217 | −0.116128 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 41.3249i | − | 1.87647i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.23979 | −0.237438 | −0.118719 | − | 0.992928i | \(-0.537879\pi\) | ||||
−0.118719 | + | 0.992928i | \(0.537879\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 6.54352i | − | 0.295908i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 8.71576i | − | 0.393337i | −0.980470 | − | 0.196668i | \(-0.936988\pi\) | ||
0.980470 | − | 0.196668i | \(-0.0630122\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 14.1318i | − | 0.636462i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.51937i | 0.248077i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 8.46075i | − | 0.379516i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 24.0516i | − | 1.07670i | −0.842722 | − | 0.538349i | \(-0.819048\pi\) | ||
0.842722 | − | 0.538349i | \(-0.180952\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.8294 | −0.573175 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.14499i | 0.363167i | 0.983376 | + | 0.181583i | \(0.0581223\pi\) | ||||
−0.983376 | + | 0.181583i | \(0.941878\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −34.0929 | −1.51711 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.72956 | −0.254459 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.8864i | 1.10307i | 0.834151 | + | 0.551536i | \(0.185958\pi\) | ||||
−0.834151 | + | 0.551536i | \(0.814042\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 1.78356i | − | 0.0789000i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10.8543 | − | 17.6715i | −0.479228 | − | 0.780215i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −36.0184 | −1.58716 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.77015 | 0.0778510 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 15.8502i | − | 0.695748i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.50065i | 0.197177i | 0.995128 | + | 0.0985886i | \(0.0314328\pi\) | ||||
−0.995128 | + | 0.0985886i | \(0.968567\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.4924 | −1.24588 | −0.622942 | − | 0.782268i | \(-0.714063\pi\) | ||||
−0.622942 | + | 0.782268i | \(0.714063\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 1.14857i | − | 0.0501278i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 27.3752 | 1.19248 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.0038 | 0.434946 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.83218 | 0.383284 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13.7196 | −0.594262 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −20.1451 | −0.870947 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17.3520 | 0.748793 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.41396i | 0.276269i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.5155 | 0.796044 | 0.398022 | − | 0.917376i | \(-0.369697\pi\) | ||||
0.398022 | + | 0.917376i | \(0.369697\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 21.1077i | − | 0.905817i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 50.9578i | − | 2.18279i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.58928 | −0.238980 | −0.119490 | − | 0.992835i | \(-0.538126\pi\) | ||||
−0.119490 | + | 0.992835i | \(0.538126\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −19.6817 | −0.839997 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.0037 | − | 8.60145i | 0.596580 | − | 0.366434i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 6.92454i | − | 0.294461i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 19.4165i | 0.824183i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.1418 | −0.472092 | −0.236046 | − | 0.971742i | \(-0.575852\pi\) | ||||
−0.236046 | + | 0.971742i | \(0.575852\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.49769 | −0.0633457 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.46624i | 0.146345i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14.5096 | −0.611505 | −0.305752 | − | 0.952111i | \(-0.598908\pi\) | ||||
−0.305752 | + | 0.952111i | \(0.598908\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.75642i | 0.410456i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.55740i | 0.0654045i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 40.4383i | − | 1.69526i | −0.530587 | − | 0.847630i | \(-0.678029\pi\) | ||
0.530587 | − | 0.847630i | \(-0.321971\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.6196i | 0.486265i | 0.969993 | + | 0.243132i | \(0.0781750\pi\) | ||||
−0.969993 | + | 0.243132i | \(0.921825\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21.8225i | 0.911646i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 5.84878i | − | 0.243911i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.9948 | 0.707501 | 0.353750 | − | 0.935340i | \(-0.384906\pi\) | ||||
0.353750 | + | 0.935340i | \(0.384906\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 10.2452i | − | 0.425778i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13.1838 | −0.546957 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.7573 | 0.486940 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 14.3974i | − | 0.595261i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 9.92060i | − | 0.409467i | −0.978818 | − | 0.204734i | \(-0.934367\pi\) | ||
0.978818 | − | 0.204734i | \(-0.0656328\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.6622 | + | 27.1272i | 0.686555 | + | 1.11776i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.23937 | 0.0509807 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.16956 | −0.335483 | −0.167742 | − | 0.985831i | \(-0.553647\pi\) | ||||
−0.167742 | + | 0.985831i | \(0.553647\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.38394i | 0.302712i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 14.0268i | − | 0.574080i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.6191 | 0.556463 | 0.278231 | − | 0.960514i | \(-0.410252\pi\) | ||||
0.278231 | + | 0.960514i | \(0.410252\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 45.5092i | 1.85636i | 0.372132 | + | 0.928180i | \(0.378627\pi\) | ||||
−0.372132 | + | 0.928180i | \(0.621373\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.56784 | 0.145294 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.57340 | 0.104624 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.3767 | −0.502356 | −0.251178 | − | 0.967941i | \(-0.580818\pi\) | ||||
−0.251178 | + | 0.967941i | \(0.580818\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.66919 | 0.108161 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.61748 | −0.186803 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −33.7650 | −1.36375 | −0.681877 | − | 0.731467i | \(-0.738836\pi\) | ||||
−0.681877 | + | 0.731467i | \(0.738836\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 12.5168i | − | 0.504725i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.86095 | 0.356728 | 0.178364 | − | 0.983965i | \(-0.442919\pi\) | ||||
0.178364 | + | 0.983965i | \(0.442919\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 9.50658i | − | 0.382102i | −0.981580 | − | 0.191051i | \(-0.938810\pi\) | ||
0.981580 | − | 0.191051i | \(-0.0611895\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 17.1520i | − | 0.688286i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.60209 | −0.104250 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.4798 | −1.21919 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.43484 | + | 2.10976i | −0.137174 | + | 0.0842559i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 30.5803i | − | 1.21932i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.28201i | 0.210273i | 0.994458 | + | 0.105137i | \(0.0335280\pi\) | ||||
−0.994458 | + | 0.105137i | \(0.966472\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −20.4291 | −0.811982 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 54.2324 | 2.15215 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 16.7310i | − | 0.662907i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 23.7044 | 0.937732 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 24.0110i | − | 0.948377i | −0.880423 | − | 0.474189i | \(-0.842741\pi\) | ||
0.880423 | − | 0.474189i | \(-0.157259\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 35.1370i | − | 1.38567i | −0.721096 | − | 0.692835i | \(-0.756362\pi\) | ||
0.721096 | − | 0.692835i | \(-0.243638\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 1.36639i | − | 0.0538015i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.91965i | 0.272039i | 0.990706 | + | 0.136020i | \(0.0434311\pi\) | ||||
−0.990706 | + | 0.136020i | \(0.956569\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 4.11799i | − | 0.161645i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.17059i | 0.202651i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.56654 | −0.296102 | −0.148051 | − | 0.988980i | \(-0.547300\pi\) | ||||
−0.148051 | + | 0.988980i | \(0.547300\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 44.7133i | 1.74709i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.99699 | 0.194951 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.1971 | −0.514084 | −0.257042 | − | 0.966400i | \(-0.582748\pi\) | ||||
−0.257042 | + | 0.966400i | \(0.582748\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.4346i | 0.600338i | 0.953886 | + | 0.300169i | \(0.0970430\pi\) | ||||
−0.953886 | + | 0.300169i | \(0.902957\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 9.04178i | − | 0.351154i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.31705 | + | 4.49432i | −0.283743 | + | 0.174282i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.5921 | 0.526288 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16.0428 | −0.620249 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.17659i | 0.354258i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 36.8348i | 1.41988i | 0.704263 | + | 0.709939i | \(0.251277\pi\) | ||||
−0.704263 | + | 0.709939i | \(0.748723\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.71903 | 0.297106 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 39.0494i | − | 1.50079i | −0.660989 | − | 0.750396i | \(-0.729863\pi\) | ||
0.660989 | − | 0.750396i | \(-0.270137\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.2932 | −0.471771 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.98800 | 0.152821 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29.4734 | −1.12777 | −0.563885 | − | 0.825853i | \(-0.690694\pi\) | ||||
−0.563885 | + | 0.825853i | \(0.690694\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.1992 | 0.580730 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.3613 | −0.547918 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −30.6694 | −1.16841 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.7405i | 0.789008i | 0.918894 | + | 0.394504i | \(0.129084\pi\) | ||||
−0.918894 | + | 0.394504i | \(0.870916\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.64189 | 0.0623703 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 38.8402i | 1.47329i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.7135i | 0.746703i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.7444 | 0.519863 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 49.8681 | 1.88349 | 0.941745 | − | 0.336326i | \(-0.109185\pi\) | ||||
0.941745 | + | 0.336326i | \(0.109185\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.3033 | − | 18.6131i | 1.14291 | − | 0.702005i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 4.21266i | − | 0.158658i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.1419i | 0.381424i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.33476 | −0.200351 | −0.100176 | − | 0.994970i | \(-0.531940\pi\) | ||||
−0.100176 | + | 0.994970i | \(0.531940\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 19.4004 | 0.727573 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 26.3298i | 0.986058i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.71279 | −0.251044 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 2.88789i | − | 0.107850i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 51.1019i | − | 1.90578i | −0.303319 | − | 0.952889i | \(-0.598095\pi\) | ||
0.303319 | − | 0.952889i | \(-0.401905\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.7147i | 0.399035i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18.7329i | 0.696684i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.11694i | 0.227177i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1.04368i | − | 0.0387080i | −0.999813 | − | 0.0193540i | \(-0.993839\pi\) | ||
0.999813 | − | 0.0193540i | \(-0.00616095\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.83644 | 0.327275 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.15202i | 0.0795953i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.7389 | 1.32005 | 0.660023 | − | 0.751246i | \(-0.270547\pi\) | ||||
0.660023 | + | 0.751246i | \(0.270547\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 15.2642 | 0.563028 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.66350i | − | 0.0612758i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 23.9647i | − | 0.881555i | −0.897616 | − | 0.440778i | \(-0.854703\pi\) | ||
0.897616 | − | 0.440778i | \(-0.145297\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.95988 | − | 5.50338i | 0.329149 | − | 0.202172i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.59899 | −0.132034 | −0.0660170 | − | 0.997818i | \(-0.521029\pi\) | ||||
−0.0660170 | + | 0.997818i | \(0.521029\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19.9651 | −0.731466 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 36.9370i | − | 1.35145i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.99271i | 0.218969i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.7342 | 0.975545 | 0.487773 | − | 0.872971i | \(-0.337810\pi\) | ||||
0.487773 | + | 0.872971i | \(0.337810\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 19.8637i | − | 0.723872i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −58.7380 | −2.13769 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.86207 | −0.104024 | −0.0520119 | − | 0.998646i | \(-0.516563\pi\) | ||||
−0.0520119 | + | 0.998646i | \(0.516563\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.33387 | −0.121012 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.93442 | 0.215123 | 0.107561 | − | 0.994198i | \(-0.465696\pi\) | ||||
0.107561 | + | 0.994198i | \(0.465696\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.1588 | −0.548786 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −20.6875 | −0.747959 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10.7419i | 0.387868i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.3655 | 0.698339 | 0.349169 | − | 0.937060i | \(-0.386464\pi\) | ||||
0.349169 | + | 0.937060i | \(0.386464\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.1048i | 0.435943i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 34.7544i | 1.25003i | 0.780613 | + | 0.625015i | \(0.214907\pi\) | ||||
−0.780613 | + | 0.625015i | \(0.785093\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.8494 | −0.425642 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.77597 | 0.207212 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −19.5350 | + | 11.9989i | −0.699913 | + | 0.429904i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 11.0522i | − | 0.395477i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 17.9384i | 0.641066i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −63.1725 | −2.25472 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.5553 | −0.376254 | −0.188127 | − | 0.982145i | \(-0.560242\pi\) | ||||
−0.188127 | + | 0.982145i | \(0.560242\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21.3354i | 0.759560i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.90232 | 0.103194 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 23.9374i | − | 0.850042i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 27.9806i | − | 0.992368i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.8878i | 0.562776i | 0.959594 | + | 0.281388i | \(0.0907947\pi\) | ||||
−0.959594 | + | 0.281388i | \(0.909205\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.63480i | 0.234723i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 7.29025i | − | 0.257588i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 2.32984i | − | 0.0822182i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.10196 | −0.250311 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.54623i | 0.195237i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.0958 | −0.706532 | −0.353266 | − | 0.935523i | \(-0.614929\pi\) | ||||
−0.353266 | + | 0.935523i | \(0.614929\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.698862 | −0.0245404 | −0.0122702 | − | 0.999925i | \(-0.503906\pi\) | ||||
−0.0122702 | + | 0.999925i | \(0.503906\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 16.5063i | − | 0.578903i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 18.2087i | − | 0.637824i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.13253 | + | 1.30985i | −0.0746077 | + | 0.0458259i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.28292 | −0.149657 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.92951 | 0.102241 | 0.0511203 | − | 0.998693i | \(-0.483721\pi\) | ||||
0.0511203 | + | 0.998693i | \(0.483721\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 29.9843i | − | 1.04519i | −0.852582 | − | 0.522593i | \(-0.824965\pi\) | ||
0.852582 | − | 0.522593i | \(-0.175035\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 1.50036i | − | 0.0522359i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −32.2067 | −1.11994 | −0.559969 | − | 0.828514i | \(-0.689187\pi\) | ||||
−0.559969 | + | 0.828514i | \(0.689187\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 5.21195i | − | 0.181019i | −0.995896 | − | 0.0905093i | \(-0.971151\pi\) | ||
0.995896 | − | 0.0905093i | \(-0.0288495\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.1299 | −0.524852 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −24.0406 | −0.832957 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −35.7005 | −1.23547 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −34.7492 | −1.20111 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 43.1109 | 1.48835 | 0.744177 | − | 0.667982i | \(-0.232842\pi\) | ||||
0.744177 | + | 0.667982i | \(0.232842\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.7847 | 0.509819 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.96555i | 0.308790i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −15.9437 | −0.548480 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 0.765529i | − | 0.0263039i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 18.9509i | 0.650393i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 29.4125 | 1.00825 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.0560 | 0.583985 | 0.291993 | − | 0.956421i | \(-0.405682\pi\) | ||||
0.291993 | + | 0.956421i | \(0.405682\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12.5917 | − | 20.5001i | −0.430627 | − | 0.701090i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 47.6403i | 1.62736i | 0.581312 | + | 0.813680i | \(0.302539\pi\) | ||||
−0.581312 | + | 0.813680i | \(0.697461\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 54.4089i | 1.85641i | 0.372072 | + | 0.928204i | \(0.378648\pi\) | ||||
−0.372072 | + | 0.928204i | \(0.621352\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.72346 | −0.126895 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.0365416 | −0.00124389 | −0.000621945 | − | 1.00000i | \(-0.500198\pi\) | ||||
−0.000621945 | 1.00000i | \(0.500198\pi\) | ||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 44.1066i | − | 1.49967i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.72927 | 0.0926910 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 9.04543i | − | 0.306845i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.33929i | 0.147031i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 34.4418i | − | 1.16568i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.65393i | 0.224944i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 30.3011i | − | 1.02319i | −0.859225 | − | 0.511597i | \(-0.829054\pi\) | ||
0.859225 | − | 0.511597i | \(-0.170946\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.05945i | 0.0694635i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.0140 | −0.842743 | −0.421372 | − | 0.906888i | \(-0.638451\pi\) | ||||
−0.421372 | + | 0.906888i | \(0.638451\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 34.0342i | − | 1.14534i | −0.819785 | − | 0.572671i | \(-0.805907\pi\) | ||
0.819785 | − | 0.572671i | \(-0.194093\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.80015 | −0.329428 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.5033 | −0.587702 | −0.293851 | − | 0.955851i | \(-0.594937\pi\) | ||||
−0.293851 | + | 0.955851i | \(0.594937\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 16.1329i | − | 0.541081i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.03441i | 0.0681551i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.57471 | + | 4.03835i | −0.220014 | + | 0.135138i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 48.2855 | 1.61401 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.69649 | 0.290367 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 27.5369i | − | 0.918409i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 44.0685i | 1.46813i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.406470 | −0.0135265 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 58.7366i | − | 1.95247i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 55.3675 | 1.83845 | 0.919224 | − | 0.393735i | \(-0.128817\pi\) | ||||
0.919224 | + | 0.393735i | \(0.128817\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −28.4144 | −0.942446 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.0058 | 1.49111 | 0.745554 | − | 0.666445i | \(-0.232185\pi\) | ||||
0.745554 | + | 0.666445i | \(0.232185\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17.2218 | −0.569959 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 21.8388 | 0.721968 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.3012 | 0.439245 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.8325i | 1.11603i | 0.829830 | + | 0.558016i | \(0.188437\pi\) | ||||
−0.829830 | + | 0.558016i | \(0.811563\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −19.9681 | −0.657972 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 28.8299i | 0.948946i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13.2367i | 0.435220i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −30.0192 | −0.985961 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −40.9987 | −1.34512 | −0.672562 | − | 0.740040i | \(-0.734806\pi\) | ||||
−0.672562 | + | 0.740040i | \(0.734806\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14.6326 | − | 23.8228i | −0.479564 | − | 0.780762i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 16.1196i | − | 0.527731i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.64553i | 0.315443i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.5155 | 0.800886 | 0.400443 | − | 0.916322i | \(-0.368856\pi\) | ||||
0.400443 | + | 0.916322i | \(0.368856\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.82915 | 0.190227 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.64399i | 0.118791i | 0.998235 | + | 0.0593954i | \(0.0189173\pi\) | ||||
−0.998235 | + | 0.0593954i | \(0.981083\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.9607 | −0.617446 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 9.37293i | − | 0.304902i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 40.8600i | − | 1.32777i | −0.747834 | − | 0.663886i | \(-0.768906\pi\) | ||
0.747834 | − | 0.663886i | \(-0.231094\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.07745i | 0.197282i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 28.5757i | − | 0.926631i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 27.7349i | − | 0.898422i | −0.893426 | − | 0.449211i | \(-0.851705\pi\) | ||
0.893426 | − | 0.449211i | \(-0.148295\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 60.7256i | 1.96503i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.48672 | 0.112710 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 4.52141i | − | 0.146004i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.3429 | 0.720739 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.7897 | −0.541041 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 28.5096i | − | 0.917755i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 38.9264i | 1.25179i | 0.779908 | + | 0.625894i | \(0.215266\pi\) | ||||
−0.779908 | + | 0.625894i | \(0.784734\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.90774 | − | 12.8743i | −0.254033 | − | 0.413583i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 52.9327 | 1.69869 | 0.849346 | − | 0.527836i | \(-0.176997\pi\) | ||||
0.849346 | + | 0.527836i | \(0.176997\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.5541 | 0.370408 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.91374i | 0.125340i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 50.7846i | − | 1.62474i | −0.583140 | − | 0.812372i | \(-0.698176\pi\) | ||
0.583140 | − | 0.812372i | \(-0.301824\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.39907 | −0.108635 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 42.4703i | − | 1.35597i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23.7078 | 0.756161 | 0.378081 | − | 0.925773i | \(-0.376584\pi\) | ||||
0.378081 | + | 0.925773i | \(0.376584\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.44880 | 0.109888 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.25317 | −0.0398889 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.06984 | −0.0658170 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −39.1036 | −1.24217 | −0.621084 | − | 0.783744i | \(-0.713307\pi\) | ||||
−0.621084 | + | 0.783744i | \(0.713307\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 24.5555 | 0.779244 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 39.0326i | − | 1.23742i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −53.6755 | −1.69992 | −0.849960 | − | 0.526847i | \(-0.823374\pi\) | ||||
−0.849960 | + | 0.526847i | \(0.823374\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 38.8177i | 1.22814i |
(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 | 3344.2.o.a.1519.15 | ✓ | 36 | |
4.3 | odd | 2 | inner | 3344.2.o.a.1519.21 | yes | 36 | |
19.18 | odd | 2 | inner | 3344.2.o.a.1519.22 | yes | 36 | |
76.75 | even | 2 | inner | 3344.2.o.a.1519.16 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3344.2.o.a.1519.15 | ✓ | 36 | 1.1 | even | 1 | trivial | |
3344.2.o.a.1519.16 | yes | 36 | 76.75 | even | 2 | inner | |
3344.2.o.a.1519.21 | yes | 36 | 4.3 | odd | 2 | inner | |
3344.2.o.a.1519.22 | yes | 36 | 19.18 | odd | 2 | inner |