Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4016,2,Mod(1,4016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4016 = 2^{4} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4016.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0679214517\) |
Analytic rank: | \(0\) |
Dimension: | \(23\) |
Twist minimal: | no (minimal twist has level 2008) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 4016.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.0812979 | 0.0469374 | 0.0234687 | − | 0.999725i | \(-0.492529\pi\) | ||||
0.0234687 | + | 0.999725i | \(0.492529\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.08000 | 1.82463 | 0.912315 | − | 0.409489i | \(-0.134293\pi\) | ||||
0.912315 | + | 0.409489i | \(0.134293\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.55548 | −1.72181 | −0.860905 | − | 0.508765i | \(-0.830102\pi\) | ||||
−0.860905 | + | 0.508765i | \(0.830102\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.99339 | −0.997797 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.53247 | −1.06508 | −0.532540 | − | 0.846405i | \(-0.678762\pi\) | ||||
−0.532540 | + | 0.846405i | \(0.678762\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.88643 | −0.523203 | −0.261601 | − | 0.965176i | \(-0.584251\pi\) | ||||
−0.261601 | + | 0.965176i | \(0.584251\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.331695 | 0.0856434 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.25153 | 1.75875 | 0.879377 | − | 0.476127i | \(-0.157960\pi\) | ||||
0.879377 | + | 0.476127i | \(0.157960\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.82679 | 1.56617 | 0.783087 | − | 0.621912i | \(-0.213644\pi\) | ||||
0.783087 | + | 0.621912i | \(0.213644\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.370351 | −0.0808173 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.510976 | 0.106546 | 0.0532729 | − | 0.998580i | \(-0.483035\pi\) | ||||
0.0532729 | + | 0.998580i | \(0.483035\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.6464 | 2.32928 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.487250 | −0.0937714 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.891263 | −0.165503 | −0.0827517 | − | 0.996570i | \(-0.526371\pi\) | ||||
−0.0827517 | + | 0.996570i | \(0.526371\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.69490 | −0.843229 | −0.421614 | − | 0.906775i | \(-0.638536\pi\) | ||||
−0.421614 | + | 0.906775i | \(0.638536\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.287182 | −0.0499920 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −18.5864 | −3.14167 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.85500 | 0.962557 | 0.481278 | − | 0.876568i | \(-0.340173\pi\) | ||||
0.481278 | + | 0.876568i | \(0.340173\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.153363 | −0.0245578 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.5623 | −1.64955 | −0.824775 | − | 0.565461i | \(-0.808698\pi\) | ||||
−0.824775 | + | 0.565461i | \(0.808698\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.97649 | 0.911407 | 0.455703 | − | 0.890132i | \(-0.349388\pi\) | ||||
0.455703 | + | 0.890132i | \(0.349388\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −12.2130 | −1.82061 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.59740 | 0.524734 | 0.262367 | − | 0.964968i | \(-0.415497\pi\) | ||||
0.262367 | + | 0.964968i | \(0.415497\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.7524 | 1.96463 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.589534 | 0.0825513 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.13887 | −0.980600 | −0.490300 | − | 0.871554i | \(-0.663113\pi\) | ||||
−0.490300 | + | 0.871554i | \(0.663113\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −14.4125 | −1.94338 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.555004 | 0.0735121 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.2148 | 1.46004 | 0.730021 | − | 0.683425i | \(-0.239510\pi\) | ||||
0.730021 | + | 0.683425i | \(0.239510\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.92985 | 0.759240 | 0.379620 | − | 0.925142i | \(-0.376055\pi\) | ||||
0.379620 | + | 0.925142i | \(0.376055\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 13.6363 | 1.71802 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.69665 | −0.954652 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.31848 | 1.01626 | 0.508132 | − | 0.861279i | \(-0.330336\pi\) | ||||
0.508132 | + | 0.861279i | \(0.330336\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.0415413 | 0.00500098 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.26092 | 0.980391 | 0.490196 | − | 0.871613i | \(-0.336925\pi\) | ||||
0.490196 | + | 0.871613i | \(0.336925\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.74189 | −1.14020 | −0.570101 | − | 0.821575i | \(-0.693096\pi\) | ||||
−0.570101 | + | 0.821575i | \(0.693096\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.946827 | 0.109330 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 16.0921 | 1.83386 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.0811 | −1.13421 | −0.567107 | − | 0.823644i | \(-0.691937\pi\) | ||||
−0.567107 | + | 0.823644i | \(0.691937\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.94056 | 0.993396 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.97449 | 0.985078 | 0.492539 | − | 0.870290i | \(-0.336069\pi\) | ||||
0.492539 | + | 0.870290i | \(0.336069\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 29.5862 | 3.20908 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.0724579 | −0.00776830 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.15098 | 0.334003 | 0.167002 | − | 0.985957i | \(-0.446591\pi\) | ||||
0.167002 | + | 0.985957i | \(0.446591\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.59362 | 0.900856 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.381685 | −0.0395789 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 27.8533 | 2.85769 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.31571 | −0.539729 | −0.269864 | − | 0.962898i | \(-0.586979\pi\) | ||||
−0.269864 | + | 0.962898i | \(0.586979\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.5741 | 1.06273 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.10417 | 0.806395 | 0.403198 | − | 0.915113i | \(-0.367899\pi\) | ||||
0.403198 | + | 0.915113i | \(0.367899\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.08265 | −0.599341 | −0.299670 | − | 0.954043i | \(-0.596877\pi\) | ||||
−0.299670 | + | 0.954043i | \(0.596877\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.51103 | −0.147462 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.24257 | −0.410145 | −0.205072 | − | 0.978747i | \(-0.565743\pi\) | ||||
−0.205072 | + | 0.978747i | \(0.565743\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.1124 | 1.83064 | 0.915320 | − | 0.402727i | \(-0.131938\pi\) | ||||
0.915320 | + | 0.402727i | \(0.131938\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.476000 | 0.0451799 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.811208 | −0.0763121 | −0.0381560 | − | 0.999272i | \(-0.512148\pi\) | ||||
−0.0381560 | + | 0.999272i | \(0.512148\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.08478 | 0.194407 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.64683 | 0.522050 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −33.0342 | −3.02824 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.47833 | 0.134393 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.858691 | −0.0774255 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 27.1172 | 2.42544 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.0145 | 1.77600 | 0.887998 | − | 0.459848i | \(-0.152096\pi\) | ||||
0.887998 | + | 0.459848i | \(0.152096\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.485877 | 0.0427790 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.7560 | 1.37661 | 0.688304 | − | 0.725422i | \(-0.258355\pi\) | ||||
0.688304 | + | 0.725422i | \(0.258355\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −31.0993 | −2.69665 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.98798 | −0.171098 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.6854 | 1.68183 | 0.840917 | − | 0.541165i | \(-0.182016\pi\) | ||||
0.840917 | + | 0.541165i | \(0.182016\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.46512 | 0.718002 | 0.359001 | − | 0.933337i | \(-0.383117\pi\) | ||||
0.359001 | + | 0.933337i | \(0.383117\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.292461 | 0.0246297 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.66377 | 0.557252 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.63635 | −0.301983 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.11804 | 0.0922146 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.07600 | 0.251996 | 0.125998 | − | 0.992031i | \(-0.459787\pi\) | ||||
0.125998 | + | 0.992031i | \(0.459787\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.28405 | −0.592768 | −0.296384 | − | 0.955069i | \(-0.595781\pi\) | ||||
−0.296384 | + | 0.955069i | \(0.595781\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −21.7066 | −1.75488 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −19.1552 | −1.53858 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.36041 | −0.747042 | −0.373521 | − | 0.927622i | \(-0.621850\pi\) | ||||
−0.373521 | + | 0.927622i | \(0.621850\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.580376 | −0.0460268 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.32774 | −0.183452 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.991367 | −0.0776498 | −0.0388249 | − | 0.999246i | \(-0.512361\pi\) | ||||
−0.0388249 | + | 0.999246i | \(0.512361\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.17170 | −0.0912170 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.81810 | 0.604982 | 0.302491 | − | 0.953152i | \(-0.402182\pi\) | ||||
0.302491 | + | 0.953152i | \(0.402182\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.44137 | −0.726259 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −20.4353 | −1.56272 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.88338 | 0.675391 | 0.337695 | − | 0.941255i | \(-0.390353\pi\) | ||||
0.337695 | + | 0.941255i | \(0.390353\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −53.0549 | −4.01057 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.911739 | 0.0685305 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −25.0766 | −1.87431 | −0.937156 | − | 0.348911i | \(-0.886552\pi\) | ||||
−0.937156 | + | 0.348911i | \(0.886552\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.1745 | 0.979254 | 0.489627 | − | 0.871932i | \(-0.337133\pi\) | ||||
0.489627 | + | 0.871932i | \(0.337133\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.482085 | 0.0356367 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 23.8884 | 1.75631 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −25.6158 | −1.87321 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.21966 | 0.161456 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.38371 | 0.172479 | 0.0862396 | − | 0.996274i | \(-0.472515\pi\) | ||||
0.0862396 | + | 0.996274i | \(0.472515\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.28291 | 0.308291 | 0.154145 | − | 0.988048i | \(-0.450738\pi\) | ||||
0.154145 | + | 0.988048i | \(0.450738\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.625721 | −0.0448088 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.2113 | 1.01252 | 0.506258 | − | 0.862382i | \(-0.331029\pi\) | ||||
0.506258 | + | 0.862382i | \(0.331029\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25.4472 | −1.80390 | −0.901952 | − | 0.431837i | \(-0.857866\pi\) | ||||
−0.901952 | + | 0.431837i | \(0.857866\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.676275 | 0.0477008 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.06013 | 0.284966 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −43.0940 | −3.00982 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.52955 | −0.106311 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −24.1154 | −1.66810 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.9641 | 1.64976 | 0.824878 | − | 0.565311i | \(-0.191244\pi\) | ||||
0.824878 | + | 0.565311i | \(0.191244\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.671596 | 0.0460170 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 24.3841 | 1.66298 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 21.3875 | 1.45188 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.791996 | −0.0535181 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.6795 | −0.920184 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.8891 | 0.796156 | 0.398078 | − | 0.917352i | \(-0.369677\pi\) | ||||
0.398078 | + | 0.917352i | \(0.369677\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −34.8622 | −2.32414 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.0493739 | −0.00327706 | −0.00163853 | − | 0.999999i | \(-0.500522\pi\) | ||||
−0.00163853 | + | 0.999999i | \(0.500522\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.0320 | 0.729013 | 0.364507 | − | 0.931201i | \(-0.381238\pi\) | ||||
0.364507 | + | 0.931201i | \(0.381238\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.30825 | 0.0860768 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.3230 | 1.06935 | 0.534677 | − | 0.845057i | \(-0.320433\pi\) | ||||
0.534677 | + | 0.845057i | \(0.320433\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.6774 | 0.957446 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.819574 | −0.0532370 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.21570 | 0.337376 | 0.168688 | − | 0.985670i | \(-0.446047\pi\) | ||||
0.168688 | + | 0.985670i | \(0.446047\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.0438 | −1.29114 | −0.645568 | − | 0.763703i | \(-0.723379\pi\) | ||||
−0.645568 | + | 0.763703i | \(0.723379\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.18860 | 0.140399 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 56.1098 | 3.58473 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.8783 | −0.819426 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.729608 | 0.0462370 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.00000 | 0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.80500 | −0.113480 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.40530 | 0.150626 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.26409 | 0.515499 | 0.257750 | − | 0.966212i | \(-0.417019\pi\) | ||||
0.257750 | + | 0.966212i | \(0.417019\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −26.6724 | −1.65734 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.66790 | 0.165139 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.14540 | −0.378942 | −0.189471 | − | 0.981886i | \(-0.560677\pi\) | ||||
−0.189471 | + | 0.981886i | \(0.560677\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −29.1266 | −1.78923 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.256168 | 0.0156772 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −28.2396 | −1.72180 | −0.860901 | − | 0.508773i | \(-0.830099\pi\) | ||||
−0.860901 | + | 0.508773i | \(0.830099\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.25843 | −0.562409 | −0.281205 | − | 0.959648i | \(-0.590734\pi\) | ||||
−0.281205 | + | 0.959648i | \(0.590734\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.698643 | 0.0422838 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −41.1405 | −2.48086 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.8351 | −1.13169 | −0.565847 | − | 0.824510i | \(-0.691451\pi\) | ||||
−0.565847 | + | 0.824510i | \(0.691451\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 14.0537 | 0.841371 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.15954 | 0.0691721 | 0.0345860 | − | 0.999402i | \(-0.488989\pi\) | ||||
0.0345860 | + | 0.999402i | \(0.488989\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.2403 | 1.44094 | 0.720468 | − | 0.693488i | \(-0.243927\pi\) | ||||
0.720468 | + | 0.693488i | \(0.243927\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.26442 | 0.134132 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 48.1162 | 2.84021 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 35.5846 | 2.09321 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.432156 | −0.0253334 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.1841 | 0.828641 | 0.414321 | − | 0.910131i | \(-0.364019\pi\) | ||||
0.414321 | + | 0.910131i | \(0.364019\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 45.7563 | 2.66404 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.72120 | 0.0998739 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.963922 | −0.0557450 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −27.2258 | −1.56927 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.658852 | 0.0378501 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 24.1938 | 1.38533 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.1114 | −1.03367 | −0.516836 | − | 0.856085i | \(-0.672890\pi\) | ||||
−0.516836 | + | 0.856085i | \(0.672890\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.494507 | −0.0281315 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.7357 | −1.23252 | −0.616261 | − | 0.787542i | \(-0.711353\pi\) | ||||
−0.616261 | + | 0.787542i | \(0.711353\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.3780 | −1.37793 | −0.688963 | − | 0.724796i | \(-0.741934\pi\) | ||||
−0.688963 | + | 0.724796i | \(0.741934\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 55.6362 | 3.13475 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.3696 | 1.08791 | 0.543953 | − | 0.839116i | \(-0.316927\pi\) | ||||
0.543953 | + | 0.839116i | \(0.316927\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.14836 | 0.176274 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.344912 | −0.0192511 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 49.5047 | 2.75451 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −21.9701 | −1.21868 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.55380 | 0.0859255 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16.3879 | −0.903493 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.55908 | −0.305555 | −0.152777 | − | 0.988261i | \(-0.548822\pi\) | ||||
−0.152777 | + | 0.988261i | \(0.548822\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −17.5263 | −0.960436 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 33.9394 | 1.85431 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −30.5103 | −1.66200 | −0.831001 | − | 0.556271i | \(-0.812232\pi\) | ||||
−0.831001 | + | 0.556271i | \(0.812232\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.0659496 | −0.00358189 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.5846 | 0.898105 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −30.7605 | −1.66091 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.169488 | 0.00912494 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.1759 | −0.546269 | −0.273134 | − | 0.961976i | \(-0.588060\pi\) | ||||
−0.273134 | + | 0.961976i | \(0.588060\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.86972 | −0.260670 | −0.130335 | − | 0.991470i | \(-0.541605\pi\) | ||||
−0.130335 | + | 0.991470i | \(0.541605\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.919165 | 0.0490614 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.6941 | −0.622415 | −0.311208 | − | 0.950342i | \(-0.600733\pi\) | ||||
−0.311208 | + | 0.950342i | \(0.600733\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 33.7045 | 1.78885 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.68561 | −0.142138 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.69853 | 0.353535 | 0.176767 | − | 0.984253i | \(-0.443436\pi\) | ||||
0.176767 | + | 0.984253i | \(0.443436\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 27.6051 | 1.45290 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.120185 | 0.00630808 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −39.7469 | −2.08045 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.72221 | −0.455296 | −0.227648 | − | 0.973744i | \(-0.573103\pi\) | ||||
−0.227648 | + | 0.973744i | \(0.573103\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 31.6170 | 1.64592 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 32.5210 | 1.68841 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.8557 | −0.976309 | −0.488154 | − | 0.872757i | \(-0.662330\pi\) | ||||
−0.488154 | + | 0.872757i | \(0.662330\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.20457 | 0.113844 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.68131 | 0.0865918 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 34.7023 | 1.78254 | 0.891268 | − | 0.453476i | \(-0.149816\pi\) | ||||
0.891268 | + | 0.453476i | \(0.149816\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.62713 | 0.0833606 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.9708 | −0.662774 | −0.331387 | − | 0.943495i | \(-0.607517\pi\) | ||||
−0.331387 | + | 0.943495i | \(0.607517\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 65.6557 | 3.34612 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −17.8900 | −0.909399 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.5551 | −0.839378 | −0.419689 | − | 0.907668i | \(-0.637861\pi\) | ||||
−0.419689 | + | 0.907668i | \(0.637861\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.70535 | 0.187388 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.28093 | 0.0646144 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −41.1309 | −2.06952 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −37.4152 | −1.87781 | −0.938907 | − | 0.344172i | \(-0.888160\pi\) | ||||
−0.938907 | + | 0.344172i | \(0.888160\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.52831 | −0.126574 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.8151 | −0.989518 | −0.494759 | − | 0.869030i | \(-0.664744\pi\) | ||||
−0.494759 | + | 0.869030i | \(0.664744\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.85662 | 0.441179 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 36.4775 | 1.81258 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −20.6826 | −1.02520 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.3248 | 1.45002 | 0.725010 | − | 0.688739i | \(-0.241835\pi\) | ||||
0.725010 | + | 0.688739i | \(0.241835\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.60038 | 0.0789408 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −51.0888 | −2.51391 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 36.6159 | 1.79740 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.688197 | 0.0337012 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.5237 | 1.29577 | 0.647884 | − | 0.761739i | \(-0.275654\pi\) | ||||
0.647884 | + | 0.761739i | \(0.275654\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.62688 | −0.420448 | −0.210224 | − | 0.977653i | \(-0.567419\pi\) | ||||
−0.210224 | + | 0.977653i | \(0.567419\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.7684 | −0.523578 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 84.4540 | 4.09662 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −27.0133 | −1.30727 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.541750 | 0.0261560 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.33946 | 0.353529 | 0.176765 | − | 0.984253i | \(-0.443437\pi\) | ||||
0.176765 | + | 0.984253i | \(0.443437\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 37.8792 | 1.82036 | 0.910180 | − | 0.414213i | \(-0.135943\pi\) | ||||
0.910180 | + | 0.414213i | \(0.135943\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.295628 | −0.0141743 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.48833 | 0.166869 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.5455 | −0.551035 | −0.275518 | − | 0.961296i | \(-0.588849\pi\) | ||||
−0.275518 | + | 0.961296i | \(0.588849\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −41.1664 | −1.96030 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.58800 | −0.265494 | −0.132747 | − | 0.991150i | \(-0.542380\pi\) | ||||
−0.132747 | + | 0.991150i | \(0.542380\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.8560 | 0.609432 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.250072 | 0.0118280 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.4504 | 0.917922 | 0.458961 | − | 0.888456i | \(-0.348222\pi\) | ||||
0.458961 | + | 0.888456i | \(0.348222\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 37.3109 | 1.75690 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.592178 | −0.0278230 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 35.0619 | 1.64373 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.5002 | 1.05251 | 0.526257 | − | 0.850325i | \(-0.323595\pi\) | ||||
0.526257 | + | 0.850325i | \(0.323595\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.53331 | −0.164921 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.2605 | −0.571027 | −0.285514 | − | 0.958375i | \(-0.592164\pi\) | ||||
−0.285514 | + | 0.958375i | \(0.592164\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.40785 | −0.297798 | −0.148899 | − | 0.988852i | \(-0.547573\pi\) | ||||
−0.148899 | + | 0.988852i | \(0.547573\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.55728 | −0.0722169 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.93134 | −0.0893718 | −0.0446859 | − | 0.999001i | \(-0.514229\pi\) | ||||
−0.0446859 | + | 0.999001i | \(0.514229\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −37.8947 | −1.74981 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.760982 | −0.0350642 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −21.1118 | −0.970720 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 79.5075 | 3.64805 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 21.3694 | 0.978439 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 32.7239 | 1.49519 | 0.747596 | − | 0.664154i | \(-0.231208\pi\) | ||||
0.747596 | + | 0.664154i | \(0.231208\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.0451 | −0.503612 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.189240 | −0.00861074 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −21.6881 | −0.984805 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.0302 | −0.862339 | −0.431170 | − | 0.902271i | \(-0.641899\pi\) | ||||
−0.431170 | + | 0.902271i | \(0.641899\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.0805961 | −0.00364468 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −35.1413 | −1.58591 | −0.792953 | − | 0.609283i | \(-0.791457\pi\) | ||||
−0.792953 | + | 0.609283i | \(0.791457\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.46302 | −0.291080 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 43.1421 | 1.93909 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −37.6325 | −1.68805 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.3015 | 0.505924 | 0.252962 | − | 0.967476i | \(-0.418595\pi\) | ||||
0.252962 | + | 0.967476i | \(0.418595\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.635595 | 0.0283963 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −31.7607 | −1.41614 | −0.708069 | − | 0.706143i | \(-0.750434\pi\) | ||||
−0.708069 | + | 0.706143i | \(0.750434\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 33.0650 | 1.47137 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.767564 | −0.0340887 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −29.8144 | −1.32150 | −0.660751 | − | 0.750605i | \(-0.729762\pi\) | ||||
−0.660751 | + | 0.750605i | \(0.729762\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 44.3790 | 1.96321 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.32636 | −0.146862 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −24.8172 | −1.09358 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.7077 | −0.558883 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.722200 | 0.0317011 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.5762 | 0.726218 | 0.363109 | − | 0.931747i | \(-0.381715\pi\) | ||||
0.363109 | + | 0.931747i | \(0.381715\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.3611 | 0.934056 | 0.467028 | − | 0.884243i | \(-0.345325\pi\) | ||||
0.467028 | + | 0.884243i | \(0.345325\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.31325 | −0.188246 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −34.0452 | −1.48303 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.7389 | −0.988648 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −33.5702 | −1.45682 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.9250 | 0.863049 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17.3097 | −0.748363 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.03867 | −0.0879753 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −48.5800 | −2.09249 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.90934 | −0.383042 | −0.191521 | − | 0.981488i | \(-0.561342\pi\) | ||||
−0.191521 | + | 0.981488i | \(0.561342\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.07106 | 0.0459636 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 77.9787 | 3.34024 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.5948 | 0.666785 | 0.333392 | − | 0.942788i | \(-0.391807\pi\) | ||||
0.333392 | + | 0.942788i | \(0.391807\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −17.7504 | −0.757567 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.08447 | −0.259207 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 45.9243 | 1.95290 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.94208 | 0.0824366 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.97903 | −0.380454 | −0.190227 | − | 0.981740i | \(-0.560922\pi\) | ||||
−0.190227 | + | 0.981740i | \(0.560922\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.2743 | −0.476850 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.08251 | −0.0879236 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.47683 | 0.315111 | 0.157555 | − | 0.987510i | \(-0.449639\pi\) | ||||
0.157555 | + | 0.987510i | \(0.449639\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.30973 | −0.139241 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −40.7286 | −1.71044 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22.0584 | −0.924737 | −0.462369 | − | 0.886688i | \(-0.653000\pi\) | ||||
−0.462369 | + | 0.886688i | \(0.653000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.0514 | −1.42500 | −0.712502 | − | 0.701670i | \(-0.752438\pi\) | ||||
−0.712502 | + | 0.701670i | \(0.752438\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.193791 | 0.00809572 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.95102 | 0.248175 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −30.4513 | −1.26771 | −0.633853 | − | 0.773454i | \(-0.718527\pi\) | ||||
−0.633853 | + | 0.773454i | \(0.718527\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.348192 | 0.0144704 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −40.8831 | −1.69612 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 25.2178 | 1.04442 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 23.0391 | 0.952548 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.57228 | 0.188718 | 0.0943591 | − | 0.995538i | \(-0.469920\pi\) | ||||
0.0943591 | + | 0.995538i | \(0.469920\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −32.0511 | −1.32064 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.15535 | 0.0475248 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 33.4875 | 1.37517 | 0.687583 | − | 0.726105i | \(-0.258672\pi\) | ||||
0.687583 | + | 0.726105i | \(0.258672\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −134.779 | −5.52542 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.06880 | −0.0846705 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.13268 | 0.168857 | 0.0844283 | − | 0.996430i | \(-0.473094\pi\) | ||||
0.0844283 | + | 0.996430i | \(0.473094\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.1982 | 0.742321 | 0.371161 | − | 0.928569i | \(-0.378960\pi\) | ||||
0.371161 | + | 0.928569i | \(0.378960\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −24.9005 | −1.01402 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.03157 | 0.245218 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.6100 | 1.44537 | 0.722683 | − | 0.691180i | \(-0.242909\pi\) | ||||
0.722683 | + | 0.691180i | \(0.242909\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.330081 | 0.0133755 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.78625 | −0.274542 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.36247 | −0.176198 | −0.0880992 | − | 0.996112i | \(-0.528079\pi\) | ||||
−0.0880992 | + | 0.996112i | \(0.528079\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.50346 | −0.141273 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −37.3669 | −1.50433 | −0.752167 | − | 0.658972i | \(-0.770991\pi\) | ||||
−0.752167 | + | 0.658972i | \(0.770991\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.3067 | 0.615227 | 0.307614 | − | 0.951511i | \(-0.400470\pi\) | ||||
0.307614 | + | 0.951511i | \(0.400470\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.248973 | −0.00999094 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.3542 | −0.575090 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 52.4063 | 2.09625 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.96053 | −0.0782962 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 42.4577 | 1.69290 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.68147 | −0.146557 | −0.0732786 | − | 0.997312i | \(-0.523346\pi\) | ||||
−0.0732786 | + | 0.997312i | \(0.523346\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.94823 | 0.0774352 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 81.6589 | 3.24054 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −25.9430 | −1.02790 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −24.7282 | −0.978231 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.93361 | −0.392354 | −0.196177 | − | 0.980568i | \(-0.562853\pi\) | ||||
−0.196177 | + | 0.980568i | \(0.562853\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.8635 | −1.21714 | −0.608569 | − | 0.793501i | \(-0.708256\pi\) | ||||
−0.608569 | + | 0.793501i | \(0.708256\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.98238 | 0.0780559 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.87949 | −0.388403 | −0.194201 | − | 0.980962i | \(-0.562212\pi\) | ||||
−0.194201 | + | 0.980962i | \(0.562212\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −39.6159 | −1.55506 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.73876 | 0.0681474 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.9126 | 1.09230 | 0.546152 | − | 0.837686i | \(-0.316092\pi\) | ||||
0.546152 | + | 0.837686i | \(0.316092\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 64.2845 | 2.51180 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 29.1613 | 1.13769 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23.0433 | 0.897641 | 0.448820 | − | 0.893622i | \(-0.351844\pi\) | ||||
0.448820 | + | 0.893622i | \(0.351844\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.7362 | 1.58445 | 0.792227 | − | 0.610227i | \(-0.208922\pi\) | ||||
0.792227 | + | 0.610227i | \(0.208922\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.11212 | −0.0431910 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −126.885 | −4.92040 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.455414 | −0.0176337 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.966563 | 0.0373695 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20.9470 | −0.808651 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.3600 | −0.669177 | −0.334589 | − | 0.942364i | \(-0.608597\pi\) | ||||
−0.334589 | + | 0.942364i | \(0.608597\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.67470 | −0.218419 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −42.2063 | −1.62212 | −0.811059 | − | 0.584964i | \(-0.801109\pi\) | ||||
−0.811059 | + | 0.584964i | \(0.801109\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24.2156 | 0.929310 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.00401400 | −0.000153817 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.97105 | −0.228476 | −0.114238 | − | 0.993453i | \(-0.536443\pi\) | ||||
−0.114238 | + | 0.993453i | \(0.536443\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 80.3162 | 3.06872 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.896876 | 0.0342180 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.4670 | 0.513052 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.8137 | −0.715706 | −0.357853 | − | 0.933778i | \(-0.616491\pi\) | ||||
−0.357853 | + | 0.933778i | \(0.616491\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −48.1699 | −1.82982 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 34.5377 | 1.31009 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −76.5926 | −2.90115 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.32702 | 0.0501927 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.36923 | −0.353871 | −0.176936 | − | 0.984222i | \(-0.556618\pi\) | ||||
−0.176936 | + | 0.984222i | \(0.556618\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 39.9709 | 1.50753 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.19324 | 0.0449400 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −36.9184 | −1.38846 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27.3166 | −1.02590 | −0.512948 | − | 0.858420i | \(-0.671447\pi\) | ||||
−0.512948 | + | 0.858420i | \(0.671447\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 30.1767 | 1.13172 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.39898 | −0.0898424 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 27.1882 | 1.01678 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.424026 | 0.0158355 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.3970 | 0.872562 | 0.436281 | − | 0.899810i | \(-0.356295\pi\) | ||||
0.436281 | + | 0.899810i | \(0.356295\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.7094 | 1.03195 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.62952 | −0.0606026 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10.3800 | −0.385503 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −48.2868 | −1.79086 | −0.895429 | − | 0.445205i | \(-0.853131\pi\) | ||||
−0.895429 | + | 0.445205i | \(0.853131\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.6437 | −0.986806 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 43.3387 | 1.60294 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.0508 | 0.888337 | 0.444169 | − | 0.895943i | \(-0.353499\pi\) | ||||
0.444169 | + | 0.895943i | \(0.353499\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.56161 | 0.168258 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −29.3848 | −1.08240 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26.9486 | −0.991321 | −0.495660 | − | 0.868516i | \(-0.665074\pi\) | ||||
−0.495660 | + | 0.868516i | \(0.665074\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.04698 | −0.0384617 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.23899 | 0.192200 | 0.0960999 | − | 0.995372i | \(-0.469363\pi\) | ||||
0.0960999 | + | 0.995372i | \(0.469363\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.5501 | 0.459799 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −26.8642 | −0.982908 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 19.3269 | 0.706191 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.14855 | 0.297345 | 0.148672 | − | 0.988886i | \(-0.452500\pi\) | ||||
0.148672 | + | 0.988886i | \(0.452500\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.0812979 | 0.00296266 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −29.7189 | −1.08158 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.25379 | 0.0455698 | 0.0227849 | − | 0.999740i | \(-0.492747\pi\) | ||||
0.0227849 | + | 0.999740i | \(0.492747\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.146743 | −0.00532644 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.0354 | 1.01628 | 0.508141 | − | 0.861274i | \(-0.330333\pi\) | ||||
0.508141 | + | 0.861274i | \(0.330333\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −87.0664 | −3.15202 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −88.5631 | −3.20201 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −21.1560 | −0.763898 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.2123 | 1.19767 | 0.598834 | − | 0.800873i | \(-0.295631\pi\) | ||||
0.598834 | + | 0.800873i | \(0.295631\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.671853 | 0.0241962 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.493202 | −0.0177392 | −0.00886962 | − | 0.999961i | \(-0.502823\pi\) | ||||
−0.00886962 | + | 0.999961i | \(0.502823\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −54.6786 | −1.96411 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.16841 | −0.0777912 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −72.1065 | −2.58348 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29.1814 | −1.04419 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.434268 | 0.0155195 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −38.1904 | −1.36308 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.7424 | 0.810679 | 0.405339 | − | 0.914166i | \(-0.367153\pi\) | ||||
0.405339 | + | 0.914166i | \(0.367153\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.499608 | −0.0177865 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.69545 | 0.131395 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.1863 | −0.397236 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.36793 | −0.0839819 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −31.3453 | −1.11031 | −0.555154 | − | 0.831748i | \(-0.687341\pi\) | ||||
−0.555154 | + | 0.831748i | \(0.687341\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.0866 | 0.922878 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.43211 | −0.333267 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 34.4129 | 1.21441 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.49718 | −0.334731 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.29582 | −0.0808168 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20.6486 | 0.725967 | 0.362983 | − | 0.931796i | \(-0.381758\pi\) | ||||
0.362983 | + | 0.931796i | \(0.381758\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.41871 | 0.225391 | 0.112696 | − | 0.993630i | \(-0.464051\pi\) | ||||
0.112696 | + | 0.993630i | \(0.464051\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.752691 | −0.0263980 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.04477 | −0.141682 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 40.8003 | 1.42742 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −25.7241 | −0.898871 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.5844 | 0.404297 | 0.202149 | − | 0.979355i | \(-0.435208\pi\) | ||||
0.202149 | + | 0.979355i | \(0.435208\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.5089 | 0.401173 | 0.200587 | − | 0.979676i | \(-0.435715\pi\) | ||||
0.200587 | + | 0.979676i | \(0.435715\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.34464 | −0.116445 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.58063 | −0.194058 | −0.0970288 | − | 0.995282i | \(-0.530934\pi\) | ||||
−0.0970288 | + | 0.995282i | \(0.530934\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.3422 | 0.602320 | 0.301160 | − | 0.953574i | \(-0.402626\pi\) | ||||
0.301160 | + | 0.953574i | \(0.402626\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.53126 | −0.0531188 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 99.7260 | 3.45530 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 31.8978 | 1.10387 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.28759 | 0.0790707 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 14.0923 | 0.486522 | 0.243261 | − | 0.969961i | \(-0.421783\pi\) | ||||
0.243261 | + | 0.969961i | \(0.421783\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.2056 | −0.972609 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.0942678 | 0.00324676 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −38.5208 | −1.32515 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.73450 | −0.231400 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.97069 | 0.0676338 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.99176 | 0.102556 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23.0877 | −0.790508 | −0.395254 | − | 0.918572i | \(-0.629343\pi\) | ||||
−0.395254 | + | 0.918572i | \(0.629343\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −83.3758 | −2.85139 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25.4684 | 0.869983 | 0.434992 | − | 0.900434i | \(-0.356751\pi\) | ||||
0.434992 | + | 0.900434i | \(0.356751\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.9645 | −0.544702 | −0.272351 | − | 0.962198i | \(-0.587801\pi\) | ||||
−0.272351 | + | 0.962198i | \(0.587801\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.91175 | 0.133312 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −34.8405 | −1.18598 | −0.592992 | − | 0.805208i | \(-0.702054\pi\) | ||||
−0.592992 | + | 0.805208i | \(0.702054\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36.2442 | 1.23234 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.89296 | 0.0982499 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 35.6112 | 1.20803 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.6923 | −0.531712 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.9120 | 0.538540 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −123.532 | −4.17615 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −37.9157 | −1.28032 | −0.640161 | − | 0.768241i | \(-0.721132\pi\) | ||||
−0.640161 | + | 0.768241i | \(0.721132\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.15313 | 0.0388942 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36.6026 | 1.23317 | 0.616586 | − | 0.787287i | \(-0.288515\pi\) | ||||
0.616586 | + | 0.787287i | \(0.288515\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.5586 | 1.49952 | 0.749758 | − | 0.661712i | \(-0.230170\pi\) | ||||
0.749758 | + | 0.661712i | \(0.230170\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.71989 | 0.125043 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.66736 | 0.257445 | 0.128722 | − | 0.991681i | \(-0.458912\pi\) | ||||
0.128722 | + | 0.991681i | \(0.458912\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −91.1755 | −3.05793 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −31.5822 | −1.05804 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 24.5587 | 0.821825 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −102.312 | −3.41993 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.0783648 | −0.00261653 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.18439 | 0.139557 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −51.7677 | −1.72463 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.21340 | −0.0736574 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 53.7520 | 1.78678 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.06462 | 0.234577 | 0.117288 | − | 0.993098i | \(-0.462580\pi\) | ||||
0.117288 | + | 0.993098i | \(0.462580\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −24.2590 | −0.804619 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.80712 | 0.258661 | 0.129331 | − | 0.991602i | \(-0.458717\pi\) | ||||
0.129331 | + | 0.991602i | \(0.458717\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −31.7021 | −1.04919 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.96691 | 0.0650239 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −71.7762 | −2.37026 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 50.5634 | 1.66793 | 0.833967 | − | 0.551815i | \(-0.186064\pi\) | ||||
0.833967 | + | 0.551815i | \(0.186064\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.47242 | −0.0485178 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −15.5837 | −0.512943 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 68.1896 | 2.24206 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 18.2077 | 0.598021 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22.5151 | −0.738696 | −0.369348 | − | 0.929291i | \(-0.620419\pi\) | ||||
−0.369348 | + | 0.929291i | \(0.620419\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 93.8849 | 3.07695 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.76707 | −0.0578513 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −104.512 | −3.41792 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.7253 | 1.13443 | 0.567213 | − | 0.823571i | \(-0.308022\pi\) | ||||
0.567213 | + | 0.823571i | \(0.308022\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.98188 | −0.0646763 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.6640 | −0.445432 | −0.222716 | − | 0.974883i | \(-0.571492\pi\) | ||||
−0.222716 | + | 0.974883i | \(0.571492\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.39706 | −0.175753 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.05621 | 0.294598 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14.6968 | −0.477581 | −0.238790 | − | 0.971071i | \(-0.576751\pi\) | ||||
−0.238790 | + | 0.971071i | \(0.576751\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.3774 | 0.596557 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.57471 | 0.0510635 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.324327 | 0.0105060 | 0.00525299 | − | 0.999986i | \(-0.498328\pi\) | ||||
0.00525299 | + | 0.999986i | \(0.498328\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.72553 | 0.314711 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.255955 | 0.00827385 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −89.6763 | −2.89580 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.95793 | −0.288966 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.6997 | 0.409241 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17.4743 | 0.562517 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.81111 | −0.0582413 | −0.0291206 | − | 0.999576i | \(-0.509271\pi\) | ||||
−0.0291206 | + | 0.999576i | \(0.509271\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.02463 | 0.129290 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.3189 | 0.812521 | 0.406260 | − | 0.913757i | \(-0.366833\pi\) | ||||
0.406260 | + | 0.913757i | \(0.366833\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −38.5627 | −1.23626 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.78613 | −0.0572018 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 33.0716 | 1.05805 | 0.529027 | − | 0.848605i | \(-0.322557\pi\) | ||||
0.529027 | + | 0.848605i | \(0.322557\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.1307 | −0.355740 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −57.2110 | −1.82661 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20.1354 | −0.642221 | −0.321110 | − | 0.947042i | \(-0.604056\pi\) | ||||
−0.321110 | + | 0.947042i | \(0.604056\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 57.9822 | 1.84747 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.33230 | −0.0424076 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.05384 | 0.0971065 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.73796 | 0.0869742 | 0.0434871 | − | 0.999054i | \(-0.486153\pi\) | ||||
0.0434871 | + | 0.999054i | \(0.486153\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.451942 | −0.0143419 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −103.824 | −3.29146 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −31.8558 | −1.00888 | −0.504442 | − | 0.863446i | \(-0.668302\pi\) | ||||
−0.504442 | + | 0.863446i | \(0.668302\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.85285 | −0.0902603 |
(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 | 4016.2.a.m.1.12 | 23 | ||
4.3 | odd | 2 | 2008.2.a.d.1.12 | ✓ | 23 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2008.2.a.d.1.12 | ✓ | 23 | 4.3 | odd | 2 | ||
4016.2.a.m.1.12 | 23 | 1.1 | even | 1 | trivial |