Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4022,2,Mod(1,4022)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4022, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4022.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4022 = 2 \cdot 2011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4022.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: | \(32.1158316930\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.169.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.65109\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4022.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | −0.288675 | − | 0.957427i | \(-0.593215\pi\) | ||||
−0.288675 | + | 0.957427i | \(0.593215\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.65109 | 1.18561 | 0.592803 | − | 0.805348i | \(-0.298021\pi\) | ||||
0.592803 | + | 0.805348i | \(0.298021\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0.273891 | 0.103521 | 0.0517604 | − | 0.998660i | \(-0.483517\pi\) | ||||
0.0517604 | + | 0.998660i | \(0.483517\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.00000 | −0.666667 | ||||||||
\(10\) | 2.65109 | 0.838349 | ||||||||
\(11\) | 4.10331 | 1.23720 | 0.618598 | − | 0.785708i | \(-0.287701\pi\) | ||||
0.618598 | + | 0.785708i | \(0.287701\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −4.75441 | −1.31863 | −0.659317 | − | 0.751865i | \(-0.729155\pi\) | ||||
−0.659317 | + | 0.751865i | \(0.729155\pi\) | |||||||
\(14\) | 0.273891 | 0.0732003 | ||||||||
\(15\) | −2.65109 | −0.684509 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.57608 | −1.83747 | −0.918734 | − | 0.394876i | \(-0.870787\pi\) | ||||
−0.918734 | + | 0.394876i | \(0.870787\pi\) | |||||||
\(18\) | −2.00000 | −0.471405 | ||||||||
\(19\) | −1.65109 | −0.378787 | −0.189393 | − | 0.981901i | \(-0.560652\pi\) | ||||
−0.189393 | + | 0.981901i | \(0.560652\pi\) | |||||||
\(20\) | 2.65109 | 0.592803 | ||||||||
\(21\) | −0.273891 | −0.0597678 | ||||||||
\(22\) | 4.10331 | 0.874829 | ||||||||
\(23\) | −3.27389 | −0.682653 | −0.341327 | − | 0.939945i | \(-0.610876\pi\) | ||||
−0.341327 | + | 0.939945i | \(0.610876\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 2.02830 | 0.405659 | ||||||||
\(26\) | −4.75441 | −0.932416 | ||||||||
\(27\) | 5.00000 | 0.962250 | ||||||||
\(28\) | 0.273891 | 0.0517604 | ||||||||
\(29\) | −7.27389 | −1.35073 | −0.675364 | − | 0.737485i | \(-0.736013\pi\) | ||||
−0.675364 | + | 0.737485i | \(0.736013\pi\) | |||||||
\(30\) | −2.65109 | −0.484021 | ||||||||
\(31\) | −8.12386 | −1.45909 | −0.729544 | − | 0.683934i | \(-0.760268\pi\) | ||||
−0.729544 | + | 0.683934i | \(0.760268\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −4.10331 | −0.714295 | ||||||||
\(34\) | −7.57608 | −1.29929 | ||||||||
\(35\) | 0.726109 | 0.122735 | ||||||||
\(36\) | −2.00000 | −0.333333 | ||||||||
\(37\) | −4.10331 | −0.674580 | −0.337290 | − | 0.941401i | \(-0.609510\pi\) | ||||
−0.337290 | + | 0.941401i | \(0.609510\pi\) | |||||||
\(38\) | −1.65109 | −0.267843 | ||||||||
\(39\) | 4.75441 | 0.761314 | ||||||||
\(40\) | 2.65109 | 0.419175 | ||||||||
\(41\) | 3.36945 | 0.526220 | 0.263110 | − | 0.964766i | \(-0.415252\pi\) | ||||
0.263110 | + | 0.964766i | \(0.415252\pi\) | |||||||
\(42\) | −0.273891 | −0.0422622 | ||||||||
\(43\) | −5.37720 | −0.820016 | −0.410008 | − | 0.912082i | \(-0.634474\pi\) | ||||
−0.410008 | + | 0.912082i | \(0.634474\pi\) | |||||||
\(44\) | 4.10331 | 0.618598 | ||||||||
\(45\) | −5.30219 | −0.790403 | ||||||||
\(46\) | −3.27389 | −0.482709 | ||||||||
\(47\) | −7.35878 | −1.07339 | −0.536694 | − | 0.843777i | \(-0.680327\pi\) | ||||
−0.536694 | + | 0.843777i | \(0.680327\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −6.92498 | −0.989283 | ||||||||
\(50\) | 2.02830 | 0.286844 | ||||||||
\(51\) | 7.57608 | 1.06086 | ||||||||
\(52\) | −4.75441 | −0.659317 | ||||||||
\(53\) | −3.10331 | −0.426273 | −0.213136 | − | 0.977022i | \(-0.568368\pi\) | ||||
−0.213136 | + | 0.977022i | \(0.568368\pi\) | |||||||
\(54\) | 5.00000 | 0.680414 | ||||||||
\(55\) | 10.8783 | 1.46682 | ||||||||
\(56\) | 0.273891 | 0.0366002 | ||||||||
\(57\) | 1.65109 | 0.218693 | ||||||||
\(58\) | −7.27389 | −0.955109 | ||||||||
\(59\) | 12.4621 | 1.62243 | 0.811213 | − | 0.584751i | \(-0.198808\pi\) | ||||
0.811213 | + | 0.584751i | \(0.198808\pi\) | |||||||
\(60\) | −2.65109 | −0.342255 | ||||||||
\(61\) | 5.13161 | 0.657035 | 0.328518 | − | 0.944498i | \(-0.393451\pi\) | ||||
0.328518 | + | 0.944498i | \(0.393451\pi\) | |||||||
\(62\) | −8.12386 | −1.03173 | ||||||||
\(63\) | −0.547781 | −0.0690139 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −12.6044 | −1.56338 | ||||||||
\(66\) | −4.10331 | −0.505083 | ||||||||
\(67\) | −1.26614 | −0.154684 | −0.0773418 | − | 0.997005i | \(-0.524643\pi\) | ||||
−0.0773418 | + | 0.997005i | \(0.524643\pi\) | |||||||
\(68\) | −7.57608 | −0.918734 | ||||||||
\(69\) | 3.27389 | 0.394130 | ||||||||
\(70\) | 0.726109 | 0.0867867 | ||||||||
\(71\) | 0.754406 | 0.0895315 | 0.0447657 | − | 0.998998i | \(-0.485746\pi\) | ||||
0.0447657 | + | 0.998998i | \(0.485746\pi\) | |||||||
\(72\) | −2.00000 | −0.235702 | ||||||||
\(73\) | 7.70769 | 0.902116 | 0.451058 | − | 0.892495i | \(-0.351047\pi\) | ||||
0.451058 | + | 0.892495i | \(0.351047\pi\) | |||||||
\(74\) | −4.10331 | −0.477000 | ||||||||
\(75\) | −2.02830 | −0.234207 | ||||||||
\(76\) | −1.65109 | −0.189393 | ||||||||
\(77\) | 1.12386 | 0.128076 | ||||||||
\(78\) | 4.75441 | 0.538330 | ||||||||
\(79\) | 11.3695 | 1.27916 | 0.639582 | − | 0.768723i | \(-0.279108\pi\) | ||||
0.639582 | + | 0.768723i | \(0.279108\pi\) | |||||||
\(80\) | 2.65109 | 0.296401 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.36945 | 0.372094 | ||||||||
\(83\) | −5.03605 | −0.552778 | −0.276389 | − | 0.961046i | \(-0.589138\pi\) | ||||
−0.276389 | + | 0.961046i | \(0.589138\pi\) | |||||||
\(84\) | −0.273891 | −0.0298839 | ||||||||
\(85\) | −20.0849 | −2.17851 | ||||||||
\(86\) | −5.37720 | −0.579839 | ||||||||
\(87\) | 7.27389 | 0.779843 | ||||||||
\(88\) | 4.10331 | 0.437415 | ||||||||
\(89\) | 3.25547 | 0.345079 | 0.172539 | − | 0.985003i | \(-0.444803\pi\) | ||||
0.172539 | + | 0.985003i | \(0.444803\pi\) | |||||||
\(90\) | −5.30219 | −0.558900 | ||||||||
\(91\) | −1.30219 | −0.136506 | ||||||||
\(92\) | −3.27389 | −0.341327 | ||||||||
\(93\) | 8.12386 | 0.842405 | ||||||||
\(94\) | −7.35878 | −0.759000 | ||||||||
\(95\) | −4.37720 | −0.449092 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 13.1239 | 1.33253 | 0.666263 | − | 0.745717i | \(-0.267893\pi\) | ||||
0.666263 | + | 0.745717i | \(0.267893\pi\) | |||||||
\(98\) | −6.92498 | −0.699529 | ||||||||
\(99\) | −8.20662 | −0.824797 | ||||||||
\(100\) | 2.02830 | 0.202830 | ||||||||
\(101\) | 4.72611 | 0.470265 | 0.235133 | − | 0.971963i | \(-0.424448\pi\) | ||||
0.235133 | + | 0.971963i | \(0.424448\pi\) | |||||||
\(102\) | 7.57608 | 0.750143 | ||||||||
\(103\) | −12.0750 | −1.18979 | −0.594893 | − | 0.803805i | \(-0.702806\pi\) | ||||
−0.594893 | + | 0.803805i | \(0.702806\pi\) | |||||||
\(104\) | −4.75441 | −0.466208 | ||||||||
\(105\) | −0.726109 | −0.0708610 | ||||||||
\(106\) | −3.10331 | −0.301420 | ||||||||
\(107\) | −10.1783 | −0.983976 | −0.491988 | − | 0.870602i | \(-0.663730\pi\) | ||||
−0.491988 | + | 0.870602i | \(0.663730\pi\) | |||||||
\(108\) | 5.00000 | 0.481125 | ||||||||
\(109\) | −2.27389 | −0.217799 | −0.108900 | − | 0.994053i | \(-0.534733\pi\) | ||||
−0.108900 | + | 0.994053i | \(0.534733\pi\) | |||||||
\(110\) | 10.8783 | 1.03720 | ||||||||
\(111\) | 4.10331 | 0.389469 | ||||||||
\(112\) | 0.273891 | 0.0258802 | ||||||||
\(113\) | −4.58383 | −0.431210 | −0.215605 | − | 0.976481i | \(-0.569172\pi\) | ||||
−0.215605 | + | 0.976481i | \(0.569172\pi\) | |||||||
\(114\) | 1.65109 | 0.154639 | ||||||||
\(115\) | −8.67939 | −0.809357 | ||||||||
\(116\) | −7.27389 | −0.675364 | ||||||||
\(117\) | 9.50881 | 0.879090 | ||||||||
\(118\) | 12.4621 | 1.14723 | ||||||||
\(119\) | −2.07502 | −0.190216 | ||||||||
\(120\) | −2.65109 | −0.242011 | ||||||||
\(121\) | 5.83717 | 0.530652 | ||||||||
\(122\) | 5.13161 | 0.464594 | ||||||||
\(123\) | −3.36945 | −0.303813 | ||||||||
\(124\) | −8.12386 | −0.729544 | ||||||||
\(125\) | −7.87826 | −0.704653 | ||||||||
\(126\) | −0.547781 | −0.0488002 | ||||||||
\(127\) | 12.1132 | 1.07487 | 0.537436 | − | 0.843305i | \(-0.319393\pi\) | ||||
0.537436 | + | 0.843305i | \(0.319393\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 5.37720 | 0.473436 | ||||||||
\(130\) | −12.6044 | −1.10548 | ||||||||
\(131\) | 2.57608 | 0.225073 | 0.112536 | − | 0.993648i | \(-0.464102\pi\) | ||||
0.112536 | + | 0.993648i | \(0.464102\pi\) | |||||||
\(132\) | −4.10331 | −0.357147 | ||||||||
\(133\) | −0.452219 | −0.0392124 | ||||||||
\(134\) | −1.26614 | −0.109378 | ||||||||
\(135\) | 13.2555 | 1.14085 | ||||||||
\(136\) | −7.57608 | −0.649643 | ||||||||
\(137\) | −1.95328 | −0.166880 | −0.0834400 | − | 0.996513i | \(-0.526591\pi\) | ||||
−0.0834400 | + | 0.996513i | \(0.526591\pi\) | |||||||
\(138\) | 3.27389 | 0.278692 | ||||||||
\(139\) | −16.4805 | −1.39786 | −0.698930 | − | 0.715191i | \(-0.746340\pi\) | ||||
−0.698930 | + | 0.715191i | \(0.746340\pi\) | |||||||
\(140\) | 0.726109 | 0.0613674 | ||||||||
\(141\) | 7.35878 | 0.619721 | ||||||||
\(142\) | 0.754406 | 0.0633083 | ||||||||
\(143\) | −19.5088 | −1.63141 | ||||||||
\(144\) | −2.00000 | −0.166667 | ||||||||
\(145\) | −19.2838 | −1.60143 | ||||||||
\(146\) | 7.70769 | 0.637893 | ||||||||
\(147\) | 6.92498 | 0.571163 | ||||||||
\(148\) | −4.10331 | −0.337290 | ||||||||
\(149\) | 15.8110 | 1.29529 | 0.647644 | − | 0.761943i | \(-0.275755\pi\) | ||||
0.647644 | + | 0.761943i | \(0.275755\pi\) | |||||||
\(150\) | −2.02830 | −0.165610 | ||||||||
\(151\) | 17.7643 | 1.44564 | 0.722818 | − | 0.691038i | \(-0.242846\pi\) | ||||
0.722818 | + | 0.691038i | \(0.242846\pi\) | |||||||
\(152\) | −1.65109 | −0.133921 | ||||||||
\(153\) | 15.1522 | 1.22498 | ||||||||
\(154\) | 1.12386 | 0.0905631 | ||||||||
\(155\) | −21.5371 | −1.72990 | ||||||||
\(156\) | 4.75441 | 0.380657 | ||||||||
\(157\) | 11.5371 | 0.920761 | 0.460381 | − | 0.887722i | \(-0.347713\pi\) | ||||
0.460381 | + | 0.887722i | \(0.347713\pi\) | |||||||
\(158\) | 11.3695 | 0.904505 | ||||||||
\(159\) | 3.10331 | 0.246109 | ||||||||
\(160\) | 2.65109 | 0.209587 | ||||||||
\(161\) | −0.896688 | −0.0706689 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 9.18820 | 0.719675 | 0.359838 | − | 0.933015i | \(-0.382832\pi\) | ||||
0.359838 | + | 0.933015i | \(0.382832\pi\) | |||||||
\(164\) | 3.36945 | 0.263110 | ||||||||
\(165\) | −10.8783 | −0.846872 | ||||||||
\(166\) | −5.03605 | −0.390873 | ||||||||
\(167\) | 5.44447 | 0.421306 | 0.210653 | − | 0.977561i | \(-0.432441\pi\) | ||||
0.210653 | + | 0.977561i | \(0.432441\pi\) | |||||||
\(168\) | −0.273891 | −0.0211311 | ||||||||
\(169\) | 9.60437 | 0.738798 | ||||||||
\(170\) | −20.0849 | −1.54044 | ||||||||
\(171\) | 3.30219 | 0.252525 | ||||||||
\(172\) | −5.37720 | −0.410008 | ||||||||
\(173\) | 18.6893 | 1.42092 | 0.710459 | − | 0.703738i | \(-0.248487\pi\) | ||||
0.710459 | + | 0.703738i | \(0.248487\pi\) | |||||||
\(174\) | 7.27389 | 0.551432 | ||||||||
\(175\) | 0.555531 | 0.0419942 | ||||||||
\(176\) | 4.10331 | 0.309299 | ||||||||
\(177\) | −12.4621 | −0.936708 | ||||||||
\(178\) | 3.25547 | 0.244008 | ||||||||
\(179\) | −2.96103 | −0.221318 | −0.110659 | − | 0.993858i | \(-0.535296\pi\) | ||||
−0.110659 | + | 0.993858i | \(0.535296\pi\) | |||||||
\(180\) | −5.30219 | −0.395202 | ||||||||
\(181\) | 1.54778 | 0.115046 | 0.0575228 | − | 0.998344i | \(-0.481680\pi\) | ||||
0.0575228 | + | 0.998344i | \(0.481680\pi\) | |||||||
\(182\) | −1.30219 | −0.0965245 | ||||||||
\(183\) | −5.13161 | −0.379339 | ||||||||
\(184\) | −3.27389 | −0.241354 | ||||||||
\(185\) | −10.8783 | −0.799786 | ||||||||
\(186\) | 8.12386 | 0.595670 | ||||||||
\(187\) | −31.0870 | −2.27331 | ||||||||
\(188\) | −7.35878 | −0.536694 | ||||||||
\(189\) | 1.36945 | 0.0996130 | ||||||||
\(190\) | −4.37720 | −0.317556 | ||||||||
\(191\) | 2.90444 | 0.210158 | 0.105079 | − | 0.994464i | \(-0.466490\pi\) | ||||
0.105079 | + | 0.994464i | \(0.466490\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −11.9172 | −0.857821 | −0.428911 | − | 0.903347i | \(-0.641102\pi\) | ||||
−0.428911 | + | 0.903347i | \(0.641102\pi\) | |||||||
\(194\) | 13.1239 | 0.942238 | ||||||||
\(195\) | 12.6044 | 0.902618 | ||||||||
\(196\) | −6.92498 | −0.494642 | ||||||||
\(197\) | 6.63055 | 0.472407 | 0.236203 | − | 0.971704i | \(-0.424097\pi\) | ||||
0.236203 | + | 0.971704i | \(0.424097\pi\) | |||||||
\(198\) | −8.20662 | −0.583219 | ||||||||
\(199\) | 14.4415 | 1.02373 | 0.511867 | − | 0.859065i | \(-0.328954\pi\) | ||||
0.511867 | + | 0.859065i | \(0.328954\pi\) | |||||||
\(200\) | 2.02830 | 0.143422 | ||||||||
\(201\) | 1.26614 | 0.0893067 | ||||||||
\(202\) | 4.72611 | 0.332528 | ||||||||
\(203\) | −1.99225 | −0.139829 | ||||||||
\(204\) | 7.57608 | 0.530432 | ||||||||
\(205\) | 8.93273 | 0.623889 | ||||||||
\(206\) | −12.0750 | −0.841306 | ||||||||
\(207\) | 6.54778 | 0.455102 | ||||||||
\(208\) | −4.75441 | −0.329659 | ||||||||
\(209\) | −6.77495 | −0.468633 | ||||||||
\(210\) | −0.726109 | −0.0501063 | ||||||||
\(211\) | 3.43380 | 0.236392 | 0.118196 | − | 0.992990i | \(-0.462289\pi\) | ||||
0.118196 | + | 0.992990i | \(0.462289\pi\) | |||||||
\(212\) | −3.10331 | −0.213136 | ||||||||
\(213\) | −0.754406 | −0.0516910 | ||||||||
\(214\) | −10.1783 | −0.695776 | ||||||||
\(215\) | −14.2555 | −0.972215 | ||||||||
\(216\) | 5.00000 | 0.340207 | ||||||||
\(217\) | −2.22505 | −0.151046 | ||||||||
\(218\) | −2.27389 | −0.154007 | ||||||||
\(219\) | −7.70769 | −0.520837 | ||||||||
\(220\) | 10.8783 | 0.733412 | ||||||||
\(221\) | 36.0197 | 2.42295 | ||||||||
\(222\) | 4.10331 | 0.275396 | ||||||||
\(223\) | −10.1599 | −0.680358 | −0.340179 | − | 0.940361i | \(-0.610488\pi\) | ||||
−0.340179 | + | 0.940361i | \(0.610488\pi\) | |||||||
\(224\) | 0.273891 | 0.0183001 | ||||||||
\(225\) | −4.05659 | −0.270440 | ||||||||
\(226\) | −4.58383 | −0.304912 | ||||||||
\(227\) | −4.96103 | −0.329275 | −0.164638 | − | 0.986354i | \(-0.552645\pi\) | ||||
−0.164638 | + | 0.986354i | \(0.552645\pi\) | |||||||
\(228\) | 1.65109 | 0.109346 | ||||||||
\(229\) | −14.7184 | −0.972617 | −0.486308 | − | 0.873787i | \(-0.661657\pi\) | ||||
−0.486308 | + | 0.873787i | \(0.661657\pi\) | |||||||
\(230\) | −8.67939 | −0.572302 | ||||||||
\(231\) | −1.12386 | −0.0739445 | ||||||||
\(232\) | −7.27389 | −0.477554 | ||||||||
\(233\) | −14.9426 | −0.978923 | −0.489461 | − | 0.872025i | \(-0.662807\pi\) | ||||
−0.489461 | + | 0.872025i | \(0.662807\pi\) | |||||||
\(234\) | 9.50881 | 0.621610 | ||||||||
\(235\) | −19.5088 | −1.27261 | ||||||||
\(236\) | 12.4621 | 0.811213 | ||||||||
\(237\) | −11.3695 | −0.738525 | ||||||||
\(238\) | −2.07502 | −0.134503 | ||||||||
\(239\) | 8.02055 | 0.518806 | 0.259403 | − | 0.965769i | \(-0.416474\pi\) | ||||
0.259403 | + | 0.965769i | \(0.416474\pi\) | |||||||
\(240\) | −2.65109 | −0.171127 | ||||||||
\(241\) | −11.5499 | −0.743995 | −0.371997 | − | 0.928234i | \(-0.621327\pi\) | ||||
−0.371997 | + | 0.928234i | \(0.621327\pi\) | |||||||
\(242\) | 5.83717 | 0.375228 | ||||||||
\(243\) | −16.0000 | −1.02640 | ||||||||
\(244\) | 5.13161 | 0.328518 | ||||||||
\(245\) | −18.3588 | −1.17290 | ||||||||
\(246\) | −3.36945 | −0.214828 | ||||||||
\(247\) | 7.84997 | 0.499481 | ||||||||
\(248\) | −8.12386 | −0.515866 | ||||||||
\(249\) | 5.03605 | 0.319146 | ||||||||
\(250\) | −7.87826 | −0.498265 | ||||||||
\(251\) | −9.18608 | −0.579820 | −0.289910 | − | 0.957054i | \(-0.593625\pi\) | ||||
−0.289910 | + | 0.957054i | \(0.593625\pi\) | |||||||
\(252\) | −0.547781 | −0.0345070 | ||||||||
\(253\) | −13.4338 | −0.844575 | ||||||||
\(254\) | 12.1132 | 0.760049 | ||||||||
\(255\) | 20.0849 | 1.25776 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −3.42100 | −0.213396 | −0.106698 | − | 0.994291i | \(-0.534028\pi\) | ||||
−0.106698 | + | 0.994291i | \(0.534028\pi\) | |||||||
\(258\) | 5.37720 | 0.334770 | ||||||||
\(259\) | −1.12386 | −0.0698332 | ||||||||
\(260\) | −12.6044 | −0.781690 | ||||||||
\(261\) | 14.5478 | 0.900485 | ||||||||
\(262\) | 2.57608 | 0.159151 | ||||||||
\(263\) | −19.1444 | −1.18049 | −0.590247 | − | 0.807222i | \(-0.700970\pi\) | ||||
−0.590247 | + | 0.807222i | \(0.700970\pi\) | |||||||
\(264\) | −4.10331 | −0.252541 | ||||||||
\(265\) | −8.22717 | −0.505391 | ||||||||
\(266\) | −0.452219 | −0.0277273 | ||||||||
\(267\) | −3.25547 | −0.199231 | ||||||||
\(268\) | −1.26614 | −0.0773418 | ||||||||
\(269\) | −27.7565 | −1.69235 | −0.846173 | − | 0.532909i | \(-0.821099\pi\) | ||||
−0.846173 | + | 0.532909i | \(0.821099\pi\) | |||||||
\(270\) | 13.2555 | 0.806702 | ||||||||
\(271\) | −13.6999 | −0.832212 | −0.416106 | − | 0.909316i | \(-0.636605\pi\) | ||||
−0.416106 | + | 0.909316i | \(0.636605\pi\) | |||||||
\(272\) | −7.57608 | −0.459367 | ||||||||
\(273\) | 1.30219 | 0.0788119 | ||||||||
\(274\) | −1.95328 | −0.118002 | ||||||||
\(275\) | 8.32273 | 0.501880 | ||||||||
\(276\) | 3.27389 | 0.197065 | ||||||||
\(277\) | −6.48827 | −0.389842 | −0.194921 | − | 0.980819i | \(-0.562445\pi\) | ||||
−0.194921 | + | 0.980819i | \(0.562445\pi\) | |||||||
\(278\) | −16.4805 | −0.988436 | ||||||||
\(279\) | 16.2477 | 0.972725 | ||||||||
\(280\) | 0.726109 | 0.0433933 | ||||||||
\(281\) | −28.5937 | −1.70576 | −0.852879 | − | 0.522109i | \(-0.825145\pi\) | ||||
−0.852879 | + | 0.522109i | \(0.825145\pi\) | |||||||
\(282\) | 7.35878 | 0.438209 | ||||||||
\(283\) | −14.8959 | −0.885469 | −0.442734 | − | 0.896653i | \(-0.645991\pi\) | ||||
−0.442734 | + | 0.896653i | \(0.645991\pi\) | |||||||
\(284\) | 0.754406 | 0.0447657 | ||||||||
\(285\) | 4.37720 | 0.259283 | ||||||||
\(286\) | −19.5088 | −1.15358 | ||||||||
\(287\) | 0.922861 | 0.0544748 | ||||||||
\(288\) | −2.00000 | −0.117851 | ||||||||
\(289\) | 40.3969 | 2.37629 | ||||||||
\(290\) | −19.2838 | −1.13238 | ||||||||
\(291\) | −13.1239 | −0.769334 | ||||||||
\(292\) | 7.70769 | 0.451058 | ||||||||
\(293\) | −14.4776 | −0.845790 | −0.422895 | − | 0.906179i | \(-0.638986\pi\) | ||||
−0.422895 | + | 0.906179i | \(0.638986\pi\) | |||||||
\(294\) | 6.92498 | 0.403873 | ||||||||
\(295\) | 33.0382 | 1.92356 | ||||||||
\(296\) | −4.10331 | −0.238500 | ||||||||
\(297\) | 20.5166 | 1.19049 | ||||||||
\(298\) | 15.8110 | 0.915907 | ||||||||
\(299\) | 15.5654 | 0.900171 | ||||||||
\(300\) | −2.02830 | −0.117104 | ||||||||
\(301\) | −1.47277 | −0.0848888 | ||||||||
\(302\) | 17.7643 | 1.02222 | ||||||||
\(303\) | −4.72611 | −0.271508 | ||||||||
\(304\) | −1.65109 | −0.0946967 | ||||||||
\(305\) | 13.6044 | 0.778984 | ||||||||
\(306\) | 15.1522 | 0.866191 | ||||||||
\(307\) | −20.8315 | −1.18892 | −0.594460 | − | 0.804126i | \(-0.702634\pi\) | ||||
−0.594460 | + | 0.804126i | \(0.702634\pi\) | |||||||
\(308\) | 1.12386 | 0.0640378 | ||||||||
\(309\) | 12.0750 | 0.686924 | ||||||||
\(310\) | −21.5371 | −1.22323 | ||||||||
\(311\) | −14.9795 | −0.849407 | −0.424703 | − | 0.905333i | \(-0.639622\pi\) | ||||
−0.424703 | + | 0.905333i | \(0.639622\pi\) | |||||||
\(312\) | 4.75441 | 0.269165 | ||||||||
\(313\) | 21.5216 | 1.21647 | 0.608237 | − | 0.793756i | \(-0.291877\pi\) | ||||
0.608237 | + | 0.793756i | \(0.291877\pi\) | |||||||
\(314\) | 11.5371 | 0.651077 | ||||||||
\(315\) | −1.45222 | −0.0818233 | ||||||||
\(316\) | 11.3695 | 0.639582 | ||||||||
\(317\) | −17.5470 | −0.985537 | −0.492768 | − | 0.870161i | \(-0.664015\pi\) | ||||
−0.492768 | + | 0.870161i | \(0.664015\pi\) | |||||||
\(318\) | 3.10331 | 0.174025 | ||||||||
\(319\) | −29.8470 | −1.67111 | ||||||||
\(320\) | 2.65109 | 0.148201 | ||||||||
\(321\) | 10.1783 | 0.568099 | ||||||||
\(322\) | −0.896688 | −0.0499705 | ||||||||
\(323\) | 12.5088 | 0.696009 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −9.64334 | −0.534916 | ||||||||
\(326\) | 9.18820 | 0.508887 | ||||||||
\(327\) | 2.27389 | 0.125746 | ||||||||
\(328\) | 3.36945 | 0.186047 | ||||||||
\(329\) | −2.01550 | −0.111118 | ||||||||
\(330\) | −10.8783 | −0.598829 | ||||||||
\(331\) | 3.80888 | 0.209355 | 0.104677 | − | 0.994506i | \(-0.466619\pi\) | ||||
0.104677 | + | 0.994506i | \(0.466619\pi\) | |||||||
\(332\) | −5.03605 | −0.276389 | ||||||||
\(333\) | 8.20662 | 0.449720 | ||||||||
\(334\) | 5.44447 | 0.297908 | ||||||||
\(335\) | −3.35666 | −0.183394 | ||||||||
\(336\) | −0.273891 | −0.0149420 | ||||||||
\(337\) | 34.9036 | 1.90132 | 0.950661 | − | 0.310231i | \(-0.100406\pi\) | ||||
0.950661 | + | 0.310231i | \(0.100406\pi\) | |||||||
\(338\) | 9.60437 | 0.522409 | ||||||||
\(339\) | 4.58383 | 0.248959 | ||||||||
\(340\) | −20.0849 | −1.08926 | ||||||||
\(341\) | −33.3347 | −1.80518 | ||||||||
\(342\) | 3.30219 | 0.178562 | ||||||||
\(343\) | −3.81392 | −0.205932 | ||||||||
\(344\) | −5.37720 | −0.289919 | ||||||||
\(345\) | 8.67939 | 0.467283 | ||||||||
\(346\) | 18.6893 | 1.00474 | ||||||||
\(347\) | −16.5478 | −0.888331 | −0.444166 | − | 0.895945i | \(-0.646500\pi\) | ||||
−0.444166 | + | 0.895945i | \(0.646500\pi\) | |||||||
\(348\) | 7.27389 | 0.389921 | ||||||||
\(349\) | −31.2341 | −1.67192 | −0.835962 | − | 0.548787i | \(-0.815090\pi\) | ||||
−0.835962 | + | 0.548787i | \(0.815090\pi\) | |||||||
\(350\) | 0.555531 | 0.0296944 | ||||||||
\(351\) | −23.7720 | −1.26886 | ||||||||
\(352\) | 4.10331 | 0.218707 | ||||||||
\(353\) | 11.6327 | 0.619145 | 0.309572 | − | 0.950876i | \(-0.399814\pi\) | ||||
0.309572 | + | 0.950876i | \(0.399814\pi\) | |||||||
\(354\) | −12.4621 | −0.662353 | ||||||||
\(355\) | 2.00000 | 0.106149 | ||||||||
\(356\) | 3.25547 | 0.172539 | ||||||||
\(357\) | 2.07502 | 0.109821 | ||||||||
\(358\) | −2.96103 | −0.156495 | ||||||||
\(359\) | 15.8753 | 0.837868 | 0.418934 | − | 0.908017i | \(-0.362404\pi\) | ||||
0.418934 | + | 0.908017i | \(0.362404\pi\) | |||||||
\(360\) | −5.30219 | −0.279450 | ||||||||
\(361\) | −16.2739 | −0.856521 | ||||||||
\(362\) | 1.54778 | 0.0813496 | ||||||||
\(363\) | −5.83717 | −0.306372 | ||||||||
\(364\) | −1.30219 | −0.0682531 | ||||||||
\(365\) | 20.4338 | 1.06955 | ||||||||
\(366\) | −5.13161 | −0.268233 | ||||||||
\(367\) | 31.6142 | 1.65025 | 0.825125 | − | 0.564950i | \(-0.191105\pi\) | ||||
0.825125 | + | 0.564950i | \(0.191105\pi\) | |||||||
\(368\) | −3.27389 | −0.170663 | ||||||||
\(369\) | −6.73891 | −0.350813 | ||||||||
\(370\) | −10.8783 | −0.565534 | ||||||||
\(371\) | −0.849968 | −0.0441281 | ||||||||
\(372\) | 8.12386 | 0.421202 | ||||||||
\(373\) | 33.6249 | 1.74103 | 0.870516 | − | 0.492140i | \(-0.163785\pi\) | ||||
0.870516 | + | 0.492140i | \(0.163785\pi\) | |||||||
\(374\) | −31.0870 | −1.60747 | ||||||||
\(375\) | 7.87826 | 0.406832 | ||||||||
\(376\) | −7.35878 | −0.379500 | ||||||||
\(377\) | 34.5830 | 1.78112 | ||||||||
\(378\) | 1.36945 | 0.0704371 | ||||||||
\(379\) | −1.42897 | −0.0734012 | −0.0367006 | − | 0.999326i | \(-0.511685\pi\) | ||||
−0.0367006 | + | 0.999326i | \(0.511685\pi\) | |||||||
\(380\) | −4.37720 | −0.224546 | ||||||||
\(381\) | −12.1132 | −0.620577 | ||||||||
\(382\) | 2.90444 | 0.148604 | ||||||||
\(383\) | −36.1076 | −1.84501 | −0.922505 | − | 0.385985i | \(-0.873862\pi\) | ||||
−0.922505 | + | 0.385985i | \(0.873862\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 2.97945 | 0.151847 | ||||||||
\(386\) | −11.9172 | −0.606571 | ||||||||
\(387\) | 10.7544 | 0.546677 | ||||||||
\(388\) | 13.1239 | 0.666263 | ||||||||
\(389\) | 32.8081 | 1.66344 | 0.831718 | − | 0.555199i | \(-0.187358\pi\) | ||||
0.831718 | + | 0.555199i | \(0.187358\pi\) | |||||||
\(390\) | 12.6044 | 0.638247 | ||||||||
\(391\) | 24.8032 | 1.25435 | ||||||||
\(392\) | −6.92498 | −0.349765 | ||||||||
\(393\) | −2.57608 | −0.129946 | ||||||||
\(394\) | 6.63055 | 0.334042 | ||||||||
\(395\) | 30.1415 | 1.51658 | ||||||||
\(396\) | −8.20662 | −0.412398 | ||||||||
\(397\) | −18.7622 | −0.941646 | −0.470823 | − | 0.882228i | \(-0.656043\pi\) | ||||
−0.470823 | + | 0.882228i | \(0.656043\pi\) | |||||||
\(398\) | 14.4415 | 0.723889 | ||||||||
\(399\) | 0.452219 | 0.0226393 | ||||||||
\(400\) | 2.02830 | 0.101415 | ||||||||
\(401\) | 35.9730 | 1.79641 | 0.898204 | − | 0.439580i | \(-0.144873\pi\) | ||||
0.898204 | + | 0.439580i | \(0.144873\pi\) | |||||||
\(402\) | 1.26614 | 0.0631493 | ||||||||
\(403\) | 38.6241 | 1.92400 | ||||||||
\(404\) | 4.72611 | 0.235133 | ||||||||
\(405\) | 2.65109 | 0.131734 | ||||||||
\(406\) | −1.99225 | −0.0988737 | ||||||||
\(407\) | −16.8372 | −0.834588 | ||||||||
\(408\) | 7.57608 | 0.375072 | ||||||||
\(409\) | 20.4989 | 1.01361 | 0.506804 | − | 0.862062i | \(-0.330827\pi\) | ||||
0.506804 | + | 0.862062i | \(0.330827\pi\) | |||||||
\(410\) | 8.93273 | 0.441156 | ||||||||
\(411\) | 1.95328 | 0.0963482 | ||||||||
\(412\) | −12.0750 | −0.594893 | ||||||||
\(413\) | 3.41325 | 0.167955 | ||||||||
\(414\) | 6.54778 | 0.321806 | ||||||||
\(415\) | −13.3510 | −0.655376 | ||||||||
\(416\) | −4.75441 | −0.233104 | ||||||||
\(417\) | 16.4805 | 0.807054 | ||||||||
\(418\) | −6.77495 | −0.331374 | ||||||||
\(419\) | −12.4445 | −0.607952 | −0.303976 | − | 0.952680i | \(-0.598314\pi\) | ||||
−0.303976 | + | 0.952680i | \(0.598314\pi\) | |||||||
\(420\) | −0.726109 | −0.0354305 | ||||||||
\(421\) | −33.8881 | −1.65161 | −0.825803 | − | 0.563958i | \(-0.809278\pi\) | ||||
−0.825803 | + | 0.563958i | \(0.809278\pi\) | |||||||
\(422\) | 3.43380 | 0.167155 | ||||||||
\(423\) | 14.7176 | 0.715592 | ||||||||
\(424\) | −3.10331 | −0.150710 | ||||||||
\(425\) | −15.3665 | −0.745386 | ||||||||
\(426\) | −0.754406 | −0.0365511 | ||||||||
\(427\) | 1.40550 | 0.0680169 | ||||||||
\(428\) | −10.1783 | −0.491988 | ||||||||
\(429\) | 19.5088 | 0.941894 | ||||||||
\(430\) | −14.2555 | −0.687460 | ||||||||
\(431\) | −13.5470 | −0.652535 | −0.326268 | − | 0.945277i | \(-0.605791\pi\) | ||||
−0.326268 | + | 0.945277i | \(0.605791\pi\) | |||||||
\(432\) | 5.00000 | 0.240563 | ||||||||
\(433\) | −3.49602 | −0.168008 | −0.0840039 | − | 0.996465i | \(-0.526771\pi\) | ||||
−0.0840039 | + | 0.996465i | \(0.526771\pi\) | |||||||
\(434\) | −2.22505 | −0.106806 | ||||||||
\(435\) | 19.2838 | 0.924586 | ||||||||
\(436\) | −2.27389 | −0.108900 | ||||||||
\(437\) | 5.40550 | 0.258580 | ||||||||
\(438\) | −7.70769 | −0.368287 | ||||||||
\(439\) | 21.1394 | 1.00893 | 0.504463 | − | 0.863433i | \(-0.331690\pi\) | ||||
0.504463 | + | 0.863433i | \(0.331690\pi\) | |||||||
\(440\) | 10.8783 | 0.518601 | ||||||||
\(441\) | 13.8500 | 0.659522 | ||||||||
\(442\) | 36.0197 | 1.71328 | ||||||||
\(443\) | −37.5158 | −1.78243 | −0.891214 | − | 0.453583i | \(-0.850145\pi\) | ||||
−0.891214 | + | 0.453583i | \(0.850145\pi\) | |||||||
\(444\) | 4.10331 | 0.194735 | ||||||||
\(445\) | 8.63055 | 0.409127 | ||||||||
\(446\) | −10.1599 | −0.481085 | ||||||||
\(447\) | −15.8110 | −0.747835 | ||||||||
\(448\) | 0.273891 | 0.0129401 | ||||||||
\(449\) | 9.81180 | 0.463047 | 0.231524 | − | 0.972829i | \(-0.425629\pi\) | ||||
0.231524 | + | 0.972829i | \(0.425629\pi\) | |||||||
\(450\) | −4.05659 | −0.191230 | ||||||||
\(451\) | 13.8259 | 0.651037 | ||||||||
\(452\) | −4.58383 | −0.215605 | ||||||||
\(453\) | −17.7643 | −0.834639 | ||||||||
\(454\) | −4.96103 | −0.232833 | ||||||||
\(455\) | −3.45222 | −0.161843 | ||||||||
\(456\) | 1.65109 | 0.0773195 | ||||||||
\(457\) | 28.5598 | 1.33597 | 0.667985 | − | 0.744175i | \(-0.267157\pi\) | ||||
0.667985 | + | 0.744175i | \(0.267157\pi\) | |||||||
\(458\) | −14.7184 | −0.687744 | ||||||||
\(459\) | −37.8804 | −1.76811 | ||||||||
\(460\) | −8.67939 | −0.404679 | ||||||||
\(461\) | 38.1826 | 1.77834 | 0.889170 | − | 0.457577i | \(-0.151283\pi\) | ||||
0.889170 | + | 0.457577i | \(0.151283\pi\) | |||||||
\(462\) | −1.12386 | −0.0522866 | ||||||||
\(463\) | −1.85772 | −0.0863355 | −0.0431677 | − | 0.999068i | \(-0.513745\pi\) | ||||
−0.0431677 | + | 0.999068i | \(0.513745\pi\) | |||||||
\(464\) | −7.27389 | −0.337682 | ||||||||
\(465\) | 21.5371 | 0.998759 | ||||||||
\(466\) | −14.9426 | −0.692203 | ||||||||
\(467\) | −11.0360 | −0.510687 | −0.255344 | − | 0.966850i | \(-0.582189\pi\) | ||||
−0.255344 | + | 0.966850i | \(0.582189\pi\) | |||||||
\(468\) | 9.50881 | 0.439545 | ||||||||
\(469\) | −0.346784 | −0.0160130 | ||||||||
\(470\) | −19.5088 | −0.899874 | ||||||||
\(471\) | −11.5371 | −0.531602 | ||||||||
\(472\) | 12.4621 | 0.573614 | ||||||||
\(473\) | −22.0643 | −1.01452 | ||||||||
\(474\) | −11.3695 | −0.522216 | ||||||||
\(475\) | −3.34891 | −0.153658 | ||||||||
\(476\) | −2.07502 | −0.0951082 | ||||||||
\(477\) | 6.20662 | 0.284182 | ||||||||
\(478\) | 8.02055 | 0.366851 | ||||||||
\(479\) | −24.9194 | −1.13859 | −0.569297 | − | 0.822132i | \(-0.692785\pi\) | ||||
−0.569297 | + | 0.822132i | \(0.692785\pi\) | |||||||
\(480\) | −2.65109 | −0.121005 | ||||||||
\(481\) | 19.5088 | 0.889525 | ||||||||
\(482\) | −11.5499 | −0.526084 | ||||||||
\(483\) | 0.896688 | 0.0408007 | ||||||||
\(484\) | 5.83717 | 0.265326 | ||||||||
\(485\) | 34.7926 | 1.57985 | ||||||||
\(486\) | −16.0000 | −0.725775 | ||||||||
\(487\) | 17.6588 | 0.800199 | 0.400099 | − | 0.916472i | \(-0.368976\pi\) | ||||
0.400099 | + | 0.916472i | \(0.368976\pi\) | |||||||
\(488\) | 5.13161 | 0.232297 | ||||||||
\(489\) | −9.18820 | −0.415505 | ||||||||
\(490\) | −18.3588 | −0.829365 | ||||||||
\(491\) | −24.1231 | −1.08866 | −0.544329 | − | 0.838872i | \(-0.683216\pi\) | ||||
−0.544329 | + | 0.838872i | \(0.683216\pi\) | |||||||
\(492\) | −3.36945 | −0.151907 | ||||||||
\(493\) | 55.1076 | 2.48192 | ||||||||
\(494\) | 7.84997 | 0.353187 | ||||||||
\(495\) | −21.7565 | −0.977883 | ||||||||
\(496\) | −8.12386 | −0.364772 | ||||||||
\(497\) | 0.206625 | 0.00926838 | ||||||||
\(498\) | 5.03605 | 0.225671 | ||||||||
\(499\) | 17.7728 | 0.795621 | 0.397811 | − | 0.917468i | \(-0.369770\pi\) | ||||
0.397811 | + | 0.917468i | \(0.369770\pi\) | |||||||
\(500\) | −7.87826 | −0.352327 | ||||||||
\(501\) | −5.44447 | −0.243241 | ||||||||
\(502\) | −9.18608 | −0.409995 | ||||||||
\(503\) | −26.8881 | −1.19888 | −0.599441 | − | 0.800419i | \(-0.704611\pi\) | ||||
−0.599441 | + | 0.800419i | \(0.704611\pi\) | |||||||
\(504\) | −0.547781 | −0.0244001 | ||||||||
\(505\) | 12.5294 | 0.557549 | ||||||||
\(506\) | −13.4338 | −0.597205 | ||||||||
\(507\) | −9.60437 | −0.426545 | ||||||||
\(508\) | 12.1132 | 0.537436 | ||||||||
\(509\) | 3.36653 | 0.149219 | 0.0746094 | − | 0.997213i | \(-0.476229\pi\) | ||||
0.0746094 | + | 0.997213i | \(0.476229\pi\) | |||||||
\(510\) | 20.0849 | 0.889374 | ||||||||
\(511\) | 2.11106 | 0.0933879 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −8.25547 | −0.364488 | ||||||||
\(514\) | −3.42100 | −0.150894 | ||||||||
\(515\) | −32.0120 | −1.41062 | ||||||||
\(516\) | 5.37720 | 0.236718 | ||||||||
\(517\) | −30.1954 | −1.32799 | ||||||||
\(518\) | −1.12386 | −0.0493795 | ||||||||
\(519\) | −18.6893 | −0.820368 | ||||||||
\(520\) | −12.6044 | −0.552738 | ||||||||
\(521\) | −17.6588 | −0.773648 | −0.386824 | − | 0.922154i | \(-0.626428\pi\) | ||||
−0.386824 | + | 0.922154i | \(0.626428\pi\) | |||||||
\(522\) | 14.5478 | 0.636739 | ||||||||
\(523\) | −40.9066 | −1.78872 | −0.894359 | − | 0.447349i | \(-0.852368\pi\) | ||||
−0.894359 | + | 0.447349i | \(0.852368\pi\) | |||||||
\(524\) | 2.57608 | 0.112536 | ||||||||
\(525\) | −0.555531 | −0.0242454 | ||||||||
\(526\) | −19.1444 | −0.834736 | ||||||||
\(527\) | 61.5470 | 2.68103 | ||||||||
\(528\) | −4.10331 | −0.178574 | ||||||||
\(529\) | −12.2816 | −0.533984 | ||||||||
\(530\) | −8.22717 | −0.357365 | ||||||||
\(531\) | −24.9242 | −1.08162 | ||||||||
\(532\) | −0.452219 | −0.0196062 | ||||||||
\(533\) | −16.0197 | −0.693892 | ||||||||
\(534\) | −3.25547 | −0.140878 | ||||||||
\(535\) | −26.9837 | −1.16661 | ||||||||
\(536\) | −1.26614 | −0.0546889 | ||||||||
\(537\) | 2.96103 | 0.127778 | ||||||||
\(538\) | −27.7565 | −1.19667 | ||||||||
\(539\) | −28.4154 | −1.22394 | ||||||||
\(540\) | 13.2555 | 0.570424 | ||||||||
\(541\) | 34.6455 | 1.48952 | 0.744762 | − | 0.667330i | \(-0.232563\pi\) | ||||
0.744762 | + | 0.667330i | \(0.232563\pi\) | |||||||
\(542\) | −13.6999 | −0.588463 | ||||||||
\(543\) | −1.54778 | −0.0664216 | ||||||||
\(544\) | −7.57608 | −0.324822 | ||||||||
\(545\) | −6.02830 | −0.258224 | ||||||||
\(546\) | 1.30219 | 0.0557285 | ||||||||
\(547\) | −22.6404 | −0.968034 | −0.484017 | − | 0.875058i | \(-0.660823\pi\) | ||||
−0.484017 | + | 0.875058i | \(0.660823\pi\) | |||||||
\(548\) | −1.95328 | −0.0834400 | ||||||||
\(549\) | −10.2632 | −0.438023 | ||||||||
\(550\) | 8.32273 | 0.354883 | ||||||||
\(551\) | 12.0099 | 0.511638 | ||||||||
\(552\) | 3.27389 | 0.139346 | ||||||||
\(553\) | 3.11399 | 0.132420 | ||||||||
\(554\) | −6.48827 | −0.275660 | ||||||||
\(555\) | 10.8783 | 0.461757 | ||||||||
\(556\) | −16.4805 | −0.698930 | ||||||||
\(557\) | 41.0219 | 1.73815 | 0.869076 | − | 0.494678i | \(-0.164714\pi\) | ||||
0.869076 | + | 0.494678i | \(0.164714\pi\) | |||||||
\(558\) | 16.2477 | 0.687821 | ||||||||
\(559\) | 25.5654 | 1.08130 | ||||||||
\(560\) | 0.726109 | 0.0306837 | ||||||||
\(561\) | 31.0870 | 1.31249 | ||||||||
\(562\) | −28.5937 | −1.20615 | ||||||||
\(563\) | −24.9378 | −1.05100 | −0.525501 | − | 0.850793i | \(-0.676122\pi\) | ||||
−0.525501 | + | 0.850793i | \(0.676122\pi\) | |||||||
\(564\) | 7.35878 | 0.309861 | ||||||||
\(565\) | −12.1522 | −0.511245 | ||||||||
\(566\) | −14.8959 | −0.626121 | ||||||||
\(567\) | 0.273891 | 0.0115023 | ||||||||
\(568\) | 0.754406 | 0.0316542 | ||||||||
\(569\) | −14.0616 | −0.589495 | −0.294747 | − | 0.955575i | \(-0.595235\pi\) | ||||
−0.294747 | + | 0.955575i | \(0.595235\pi\) | |||||||
\(570\) | 4.37720 | 0.183341 | ||||||||
\(571\) | 32.0304 | 1.34043 | 0.670216 | − | 0.742166i | \(-0.266202\pi\) | ||||
0.670216 | + | 0.742166i | \(0.266202\pi\) | |||||||
\(572\) | −19.5088 | −0.815704 | ||||||||
\(573\) | −2.90444 | −0.121335 | ||||||||
\(574\) | 0.922861 | 0.0385195 | ||||||||
\(575\) | −6.64042 | −0.276925 | ||||||||
\(576\) | −2.00000 | −0.0833333 | ||||||||
\(577\) | −41.6941 | −1.73575 | −0.867874 | − | 0.496785i | \(-0.834514\pi\) | ||||
−0.867874 | + | 0.496785i | \(0.834514\pi\) | |||||||
\(578\) | 40.3969 | 1.68029 | ||||||||
\(579\) | 11.9172 | 0.495263 | ||||||||
\(580\) | −19.2838 | −0.800715 | ||||||||
\(581\) | −1.37933 | −0.0572241 | ||||||||
\(582\) | −13.1239 | −0.544001 | ||||||||
\(583\) | −12.7339 | −0.527383 | ||||||||
\(584\) | 7.70769 | 0.318946 | ||||||||
\(585\) | 25.2087 | 1.04225 | ||||||||
\(586\) | −14.4776 | −0.598064 | ||||||||
\(587\) | 35.1642 | 1.45138 | 0.725690 | − | 0.688022i | \(-0.241521\pi\) | ||||
0.725690 | + | 0.688022i | \(0.241521\pi\) | |||||||
\(588\) | 6.92498 | 0.285582 | ||||||||
\(589\) | 13.4132 | 0.552683 | ||||||||
\(590\) | 33.0382 | 1.36016 | ||||||||
\(591\) | −6.63055 | −0.272744 | ||||||||
\(592\) | −4.10331 | −0.168645 | ||||||||
\(593\) | −3.18045 | −0.130605 | −0.0653027 | − | 0.997865i | \(-0.520801\pi\) | ||||
−0.0653027 | + | 0.997865i | \(0.520801\pi\) | |||||||
\(594\) | 20.5166 | 0.841805 | ||||||||
\(595\) | −5.50106 | −0.225522 | ||||||||
\(596\) | 15.8110 | 0.647644 | ||||||||
\(597\) | −14.4415 | −0.591053 | ||||||||
\(598\) | 15.5654 | 0.636517 | ||||||||
\(599\) | −20.0013 | −0.817232 | −0.408616 | − | 0.912706i | \(-0.633988\pi\) | ||||
−0.408616 | + | 0.912706i | \(0.633988\pi\) | |||||||
\(600\) | −2.02830 | −0.0828048 | ||||||||
\(601\) | −7.59450 | −0.309786 | −0.154893 | − | 0.987931i | \(-0.549503\pi\) | ||||
−0.154893 | + | 0.987931i | \(0.549503\pi\) | |||||||
\(602\) | −1.47277 | −0.0600254 | ||||||||
\(603\) | 2.53228 | 0.103122 | ||||||||
\(604\) | 17.7643 | 0.722818 | ||||||||
\(605\) | 15.4749 | 0.629144 | ||||||||
\(606\) | −4.72611 | −0.191985 | ||||||||
\(607\) | 4.34036 | 0.176170 | 0.0880848 | − | 0.996113i | \(-0.471925\pi\) | ||||
0.0880848 | + | 0.996113i | \(0.471925\pi\) | |||||||
\(608\) | −1.65109 | −0.0669607 | ||||||||
\(609\) | 1.99225 | 0.0807300 | ||||||||
\(610\) | 13.6044 | 0.550825 | ||||||||
\(611\) | 34.9866 | 1.41541 | ||||||||
\(612\) | 15.1522 | 0.612490 | ||||||||
\(613\) | 9.64042 | 0.389373 | 0.194686 | − | 0.980866i | \(-0.437631\pi\) | ||||
0.194686 | + | 0.980866i | \(0.437631\pi\) | |||||||
\(614\) | −20.8315 | −0.840693 | ||||||||
\(615\) | −8.93273 | −0.360203 | ||||||||
\(616\) | 1.12386 | 0.0452815 | ||||||||
\(617\) | 15.8500 | 0.638096 | 0.319048 | − | 0.947739i | \(-0.396637\pi\) | ||||
0.319048 | + | 0.947739i | \(0.396637\pi\) | |||||||
\(618\) | 12.0750 | 0.485728 | ||||||||
\(619\) | −7.66659 | −0.308146 | −0.154073 | − | 0.988059i | \(-0.549239\pi\) | ||||
−0.154073 | + | 0.988059i | \(0.549239\pi\) | |||||||
\(620\) | −21.5371 | −0.864951 | ||||||||
\(621\) | −16.3695 | −0.656884 | ||||||||
\(622\) | −14.9795 | −0.600621 | ||||||||
\(623\) | 0.891642 | 0.0357229 | ||||||||
\(624\) | 4.75441 | 0.190329 | ||||||||
\(625\) | −31.0275 | −1.24110 | ||||||||
\(626\) | 21.5216 | 0.860176 | ||||||||
\(627\) | 6.77495 | 0.270566 | ||||||||
\(628\) | 11.5371 | 0.460381 | ||||||||
\(629\) | 31.0870 | 1.23952 | ||||||||
\(630\) | −1.45222 | −0.0578578 | ||||||||
\(631\) | 18.4466 | 0.734347 | 0.367174 | − | 0.930152i | \(-0.380325\pi\) | ||||
0.367174 | + | 0.930152i | \(0.380325\pi\) | |||||||
\(632\) | 11.3695 | 0.452253 | ||||||||
\(633\) | −3.43380 | −0.136481 | ||||||||
\(634\) | −17.5470 | −0.696880 | ||||||||
\(635\) | 32.1132 | 1.27437 | ||||||||
\(636\) | 3.10331 | 0.123054 | ||||||||
\(637\) | 32.9242 | 1.30450 | ||||||||
\(638\) | −29.8470 | −1.18166 | ||||||||
\(639\) | −1.50881 | −0.0596877 | ||||||||
\(640\) | 2.65109 | 0.104794 | ||||||||
\(641\) | 47.9944 | 1.89566 | 0.947832 | − | 0.318771i | \(-0.103270\pi\) | ||||
0.947832 | + | 0.318771i | \(0.103270\pi\) | |||||||
\(642\) | 10.1783 | 0.401707 | ||||||||
\(643\) | 12.9554 | 0.510911 | 0.255456 | − | 0.966821i | \(-0.417775\pi\) | ||||
0.255456 | + | 0.966821i | \(0.417775\pi\) | |||||||
\(644\) | −0.896688 | −0.0353344 | ||||||||
\(645\) | 14.2555 | 0.561308 | ||||||||
\(646\) | 12.5088 | 0.492153 | ||||||||
\(647\) | 9.29231 | 0.365319 | 0.182659 | − | 0.983176i | \(-0.441529\pi\) | ||||
0.182659 | + | 0.983176i | \(0.441529\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 51.1359 | 2.00726 | ||||||||
\(650\) | −9.64334 | −0.378243 | ||||||||
\(651\) | 2.22505 | 0.0872065 | ||||||||
\(652\) | 9.18820 | 0.359838 | ||||||||
\(653\) | 43.4768 | 1.70138 | 0.850689 | − | 0.525669i | \(-0.176185\pi\) | ||||
0.850689 | + | 0.525669i | \(0.176185\pi\) | |||||||
\(654\) | 2.27389 | 0.0889162 | ||||||||
\(655\) | 6.82942 | 0.266848 | ||||||||
\(656\) | 3.36945 | 0.131555 | ||||||||
\(657\) | −15.4154 | −0.601411 | ||||||||
\(658\) | −2.01550 | −0.0785724 | ||||||||
\(659\) | 25.4875 | 0.992851 | 0.496425 | − | 0.868079i | \(-0.334646\pi\) | ||||
0.496425 | + | 0.868079i | \(0.334646\pi\) | |||||||
\(660\) | −10.8783 | −0.423436 | ||||||||
\(661\) | 29.1805 | 1.13499 | 0.567494 | − | 0.823378i | \(-0.307913\pi\) | ||||
0.567494 | + | 0.823378i | \(0.307913\pi\) | |||||||
\(662\) | 3.80888 | 0.148036 | ||||||||
\(663\) | −36.0197 | −1.39889 | ||||||||
\(664\) | −5.03605 | −0.195437 | ||||||||
\(665\) | −1.19887 | −0.0464904 | ||||||||
\(666\) | 8.20662 | 0.318000 | ||||||||
\(667\) | 23.8139 | 0.922079 | ||||||||
\(668\) | 5.44447 | 0.210653 | ||||||||
\(669\) | 10.1599 | 0.392805 | ||||||||
\(670\) | −3.35666 | −0.129679 | ||||||||
\(671\) | 21.0566 | 0.812881 | ||||||||
\(672\) | −0.273891 | −0.0105656 | ||||||||
\(673\) | −10.0184 | −0.386182 | −0.193091 | − | 0.981181i | \(-0.561851\pi\) | ||||
−0.193091 | + | 0.981181i | \(0.561851\pi\) | |||||||
\(674\) | 34.9036 | 1.34444 | ||||||||
\(675\) | 10.1415 | 0.390346 | ||||||||
\(676\) | 9.60437 | 0.369399 | ||||||||
\(677\) | −7.40550 | −0.284616 | −0.142308 | − | 0.989822i | \(-0.545452\pi\) | ||||
−0.142308 | + | 0.989822i | \(0.545452\pi\) | |||||||
\(678\) | 4.58383 | 0.176041 | ||||||||
\(679\) | 3.59450 | 0.137944 | ||||||||
\(680\) | −20.0849 | −0.770220 | ||||||||
\(681\) | 4.96103 | 0.190107 | ||||||||
\(682\) | −33.3347 | −1.27645 | ||||||||
\(683\) | −32.4514 | −1.24172 | −0.620860 | − | 0.783922i | \(-0.713216\pi\) | ||||
−0.620860 | + | 0.783922i | \(0.713216\pi\) | |||||||
\(684\) | 3.30219 | 0.126262 | ||||||||
\(685\) | −5.17833 | −0.197854 | ||||||||
\(686\) | −3.81392 | −0.145616 | ||||||||
\(687\) | 14.7184 | 0.561540 | ||||||||
\(688\) | −5.37720 | −0.205004 | ||||||||
\(689\) | 14.7544 | 0.562098 | ||||||||
\(690\) | 8.67939 | 0.330419 | ||||||||
\(691\) | 8.71544 | 0.331551 | 0.165775 | − | 0.986164i | \(-0.446987\pi\) | ||||
0.165775 | + | 0.986164i | \(0.446987\pi\) | |||||||
\(692\) | 18.6893 | 0.710459 | ||||||||
\(693\) | −2.24772 | −0.0853837 | ||||||||
\(694\) | −16.5478 | −0.628145 | ||||||||
\(695\) | −43.6914 | −1.65731 | ||||||||
\(696\) | 7.27389 | 0.275716 | ||||||||
\(697\) | −25.5272 | −0.966913 | ||||||||
\(698\) | −31.2341 | −1.18223 | ||||||||
\(699\) | 14.9426 | 0.565181 | ||||||||
\(700\) | 0.555531 | 0.0209971 | ||||||||
\(701\) | 39.6794 | 1.49867 | 0.749335 | − | 0.662191i | \(-0.230373\pi\) | ||||
0.749335 | + | 0.662191i | \(0.230373\pi\) | |||||||
\(702\) | −23.7720 | −0.897217 | ||||||||
\(703\) | 6.77495 | 0.255522 | ||||||||
\(704\) | 4.10331 | 0.154649 | ||||||||
\(705\) | 19.5088 | 0.734744 | ||||||||
\(706\) | 11.6327 | 0.437801 | ||||||||
\(707\) | 1.29444 | 0.0486823 | ||||||||
\(708\) | −12.4621 | −0.468354 | ||||||||
\(709\) | −30.2653 | −1.13664 | −0.568319 | − | 0.822808i | \(-0.692406\pi\) | ||||
−0.568319 | + | 0.822808i | \(0.692406\pi\) | |||||||
\(710\) | 2.00000 | 0.0750587 | ||||||||
\(711\) | −22.7389 | −0.852776 | ||||||||
\(712\) | 3.25547 | 0.122004 | ||||||||
\(713\) | 26.5966 | 0.996051 | ||||||||
\(714\) | 2.07502 | 0.0776555 | ||||||||
\(715\) | −51.7197 | −1.93421 | ||||||||
\(716\) | −2.96103 | −0.110659 | ||||||||
\(717\) | −8.02055 | −0.299533 | ||||||||
\(718\) | 15.8753 | 0.592462 | ||||||||
\(719\) | 22.2109 | 0.828326 | 0.414163 | − | 0.910203i | \(-0.364074\pi\) | ||||
0.414163 | + | 0.910203i | \(0.364074\pi\) | |||||||
\(720\) | −5.30219 | −0.197601 | ||||||||
\(721\) | −3.30723 | −0.123168 | ||||||||
\(722\) | −16.2739 | −0.605651 | ||||||||
\(723\) | 11.5499 | 0.429546 | ||||||||
\(724\) | 1.54778 | 0.0575228 | ||||||||
\(725\) | −14.7536 | −0.547935 | ||||||||
\(726\) | −5.83717 | −0.216638 | ||||||||
\(727\) | 7.19032 | 0.266674 | 0.133337 | − | 0.991071i | \(-0.457431\pi\) | ||||
0.133337 | + | 0.991071i | \(0.457431\pi\) | |||||||
\(728\) | −1.30219 | −0.0482623 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 20.4338 | 0.756289 | ||||||||
\(731\) | 40.7381 | 1.50675 | ||||||||
\(732\) | −5.13161 | −0.189670 | ||||||||
\(733\) | −27.3532 | −1.01031 | −0.505156 | − | 0.863028i | \(-0.668565\pi\) | ||||
−0.505156 | + | 0.863028i | \(0.668565\pi\) | |||||||
\(734\) | 31.6142 | 1.16690 | ||||||||
\(735\) | 18.3588 | 0.677174 | ||||||||
\(736\) | −3.27389 | −0.120677 | ||||||||
\(737\) | −5.19537 | −0.191374 | ||||||||
\(738\) | −6.73891 | −0.248063 | ||||||||
\(739\) | −19.0841 | −0.702020 | −0.351010 | − | 0.936372i | \(-0.614162\pi\) | ||||
−0.351010 | + | 0.936372i | \(0.614162\pi\) | |||||||
\(740\) | −10.8783 | −0.399893 | ||||||||
\(741\) | −7.84997 | −0.288376 | ||||||||
\(742\) | −0.849968 | −0.0312033 | ||||||||
\(743\) | −40.1132 | −1.47161 | −0.735805 | − | 0.677193i | \(-0.763196\pi\) | ||||
−0.735805 | + | 0.677193i | \(0.763196\pi\) | |||||||
\(744\) | 8.12386 | 0.297835 | ||||||||
\(745\) | 41.9164 | 1.53570 | ||||||||
\(746\) | 33.6249 | 1.23110 | ||||||||
\(747\) | 10.0721 | 0.368519 | ||||||||
\(748\) | −31.0870 | −1.13665 | ||||||||
\(749\) | −2.78775 | −0.101862 | ||||||||
\(750\) | 7.87826 | 0.287674 | ||||||||
\(751\) | −53.7819 | −1.96253 | −0.981265 | − | 0.192664i | \(-0.938287\pi\) | ||||
−0.981265 | + | 0.192664i | \(0.938287\pi\) | |||||||
\(752\) | −7.35878 | −0.268347 | ||||||||
\(753\) | 9.18608 | 0.334759 | ||||||||
\(754\) | 34.5830 | 1.25944 | ||||||||
\(755\) | 47.0948 | 1.71395 | ||||||||
\(756\) | 1.36945 | 0.0498065 | ||||||||
\(757\) | −20.6786 | −0.751576 | −0.375788 | − | 0.926706i | \(-0.622628\pi\) | ||||
−0.375788 | + | 0.926706i | \(0.622628\pi\) | |||||||
\(758\) | −1.42897 | −0.0519025 | ||||||||
\(759\) | 13.4338 | 0.487616 | ||||||||
\(760\) | −4.37720 | −0.158778 | ||||||||
\(761\) | 10.3313 | 0.374509 | 0.187254 | − | 0.982311i | \(-0.440041\pi\) | ||||
0.187254 | + | 0.982311i | \(0.440041\pi\) | |||||||
\(762\) | −12.1132 | −0.438814 | ||||||||
\(763\) | −0.622797 | −0.0225468 | ||||||||
\(764\) | 2.90444 | 0.105079 | ||||||||
\(765\) | 40.1698 | 1.45234 | ||||||||
\(766\) | −36.1076 | −1.30462 | ||||||||
\(767\) | −59.2498 | −2.13939 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −49.5235 | −1.78586 | −0.892932 | − | 0.450192i | \(-0.851356\pi\) | ||||
−0.892932 | + | 0.450192i | \(0.851356\pi\) | |||||||
\(770\) | 2.97945 | 0.107372 | ||||||||
\(771\) | 3.42100 | 0.123204 | ||||||||
\(772\) | −11.9172 | −0.428911 | ||||||||
\(773\) | −5.56058 | −0.200000 | −0.100000 | − | 0.994987i | \(-0.531884\pi\) | ||||
−0.100000 | + | 0.994987i | \(0.531884\pi\) | |||||||
\(774\) | 10.7544 | 0.386559 | ||||||||
\(775\) | −16.4776 | −0.591893 | ||||||||
\(776\) | 13.1239 | 0.471119 | ||||||||
\(777\) | 1.12386 | 0.0403182 | ||||||||
\(778\) | 32.8081 | 1.17623 | ||||||||
\(779\) | −5.56328 | −0.199325 | ||||||||
\(780\) | 12.6044 | 0.451309 | ||||||||
\(781\) | 3.09556 | 0.110768 | ||||||||
\(782\) | 24.8032 | 0.886962 | ||||||||
\(783\) | −36.3695 | −1.29974 | ||||||||
\(784\) | −6.92498 | −0.247321 | ||||||||
\(785\) | 30.5860 | 1.09166 | ||||||||
\(786\) | −2.57608 | −0.0918856 | ||||||||
\(787\) | −21.1471 | −0.753813 | −0.376907 | − | 0.926251i | \(-0.623012\pi\) | ||||
−0.376907 | + | 0.926251i | \(0.623012\pi\) | |||||||
\(788\) | 6.63055 | 0.236203 | ||||||||
\(789\) | 19.1444 | 0.681559 | ||||||||
\(790\) | 30.1415 | 1.07239 | ||||||||
\(791\) | −1.25547 | −0.0446393 | ||||||||
\(792\) | −8.20662 | −0.291610 | ||||||||
\(793\) | −24.3977 | −0.866389 | ||||||||
\(794\) | −18.7622 | −0.665844 | ||||||||
\(795\) | 8.22717 | 0.291788 | ||||||||
\(796\) | 14.4415 | 0.511867 | ||||||||
\(797\) | −14.6327 | −0.518316 | −0.259158 | − | 0.965835i | \(-0.583445\pi\) | ||||
−0.259158 | + | 0.965835i | \(0.583445\pi\) | |||||||
\(798\) | 0.452219 | 0.0160084 | ||||||||
\(799\) | 55.7507 | 1.97232 | ||||||||
\(800\) | 2.02830 | 0.0717111 | ||||||||
\(801\) | −6.51093 | −0.230053 | ||||||||
\(802\) | 35.9730 | 1.27025 | ||||||||
\(803\) | 31.6270 | 1.11609 | ||||||||
\(804\) | 1.26614 | 0.0446533 | ||||||||
\(805\) | −2.37720 | −0.0837854 | ||||||||
\(806\) | 38.6241 | 1.36048 | ||||||||
\(807\) | 27.7565 | 0.977076 | ||||||||
\(808\) | 4.72611 | 0.166264 | ||||||||
\(809\) | −4.35958 | −0.153275 | −0.0766373 | − | 0.997059i | \(-0.524418\pi\) | ||||
−0.0766373 | + | 0.997059i | \(0.524418\pi\) | |||||||
\(810\) | 2.65109 | 0.0931499 | ||||||||
\(811\) | −30.3347 | −1.06520 | −0.532598 | − | 0.846368i | \(-0.678784\pi\) | ||||
−0.532598 | + | 0.846368i | \(0.678784\pi\) | |||||||
\(812\) | −1.99225 | −0.0699143 | ||||||||
\(813\) | 13.6999 | 0.480478 | ||||||||
\(814\) | −16.8372 | −0.590143 | ||||||||
\(815\) | 24.3588 | 0.853251 | ||||||||
\(816\) | 7.57608 | 0.265216 | ||||||||
\(817\) | 8.87826 | 0.310611 | ||||||||
\(818\) | 20.4989 | 0.716729 | ||||||||
\(819\) | 2.60437 | 0.0910042 | ||||||||
\(820\) | 8.93273 | 0.311945 | ||||||||
\(821\) | −51.2440 | −1.78843 | −0.894214 | − | 0.447640i | \(-0.852265\pi\) | ||||
−0.894214 | + | 0.447640i | \(0.852265\pi\) | |||||||
\(822\) | 1.95328 | 0.0681285 | ||||||||
\(823\) | −23.6036 | −0.822769 | −0.411384 | − | 0.911462i | \(-0.634955\pi\) | ||||
−0.411384 | + | 0.911462i | \(0.634955\pi\) | |||||||
\(824\) | −12.0750 | −0.420653 | ||||||||
\(825\) | −8.32273 | −0.289760 | ||||||||
\(826\) | 3.41325 | 0.118762 | ||||||||
\(827\) | 10.9659 | 0.381320 | 0.190660 | − | 0.981656i | \(-0.438937\pi\) | ||||
0.190660 | + | 0.981656i | \(0.438937\pi\) | |||||||
\(828\) | 6.54778 | 0.227551 | ||||||||
\(829\) | 1.04460 | 0.0362804 | 0.0181402 | − | 0.999835i | \(-0.494225\pi\) | ||||
0.0181402 | + | 0.999835i | \(0.494225\pi\) | |||||||
\(830\) | −13.3510 | −0.463421 | ||||||||
\(831\) | 6.48827 | 0.225075 | ||||||||
\(832\) | −4.75441 | −0.164829 | ||||||||
\(833\) | 52.4642 | 1.81778 | ||||||||
\(834\) | 16.4805 | 0.570674 | ||||||||
\(835\) | 14.4338 | 0.499502 | ||||||||
\(836\) | −6.77495 | −0.234317 | ||||||||
\(837\) | −40.6193 | −1.40401 | ||||||||
\(838\) | −12.4445 | −0.429887 | ||||||||
\(839\) | 25.9992 | 0.897592 | 0.448796 | − | 0.893634i | \(-0.351853\pi\) | ||||
0.448796 | + | 0.893634i | \(0.351853\pi\) | |||||||
\(840\) | −0.726109 | −0.0250532 | ||||||||
\(841\) | 23.9095 | 0.824465 | ||||||||
\(842\) | −33.8881 | −1.16786 | ||||||||
\(843\) | 28.5937 | 0.984819 | ||||||||
\(844\) | 3.43380 | 0.118196 | ||||||||
\(845\) | 25.4621 | 0.875923 | ||||||||
\(846\) | 14.7176 | 0.506000 | ||||||||
\(847\) | 1.59875 | 0.0549336 | ||||||||
\(848\) | −3.10331 | −0.106568 | ||||||||
\(849\) | 14.8959 | 0.511226 | ||||||||
\(850\) | −15.3665 | −0.527068 | ||||||||
\(851\) | 13.4338 | 0.460505 | ||||||||
\(852\) | −0.754406 | −0.0258455 | ||||||||
\(853\) | 37.6786 | 1.29009 | 0.645045 | − | 0.764144i | \(-0.276839\pi\) | ||||
0.645045 | + | 0.764144i | \(0.276839\pi\) | |||||||
\(854\) | 1.40550 | 0.0480952 | ||||||||
\(855\) | 8.75441 | 0.299394 | ||||||||
\(856\) | −10.1783 | −0.347888 | ||||||||
\(857\) | 12.4239 | 0.424393 | 0.212197 | − | 0.977227i | \(-0.431938\pi\) | ||||
0.212197 | + | 0.977227i | \(0.431938\pi\) | |||||||
\(858\) | 19.5088 | 0.666020 | ||||||||
\(859\) | −29.0969 | −0.992773 | −0.496386 | − | 0.868102i | \(-0.665340\pi\) | ||||
−0.496386 | + | 0.868102i | \(0.665340\pi\) | |||||||
\(860\) | −14.2555 | −0.486107 | ||||||||
\(861\) | −0.922861 | −0.0314510 | ||||||||
\(862\) | −13.5470 | −0.461412 | ||||||||
\(863\) | 55.8873 | 1.90243 | 0.951214 | − | 0.308533i | \(-0.0998381\pi\) | ||||
0.951214 | + | 0.308533i | \(0.0998381\pi\) | |||||||
\(864\) | 5.00000 | 0.170103 | ||||||||
\(865\) | 49.5470 | 1.68465 | ||||||||
\(866\) | −3.49602 | −0.118799 | ||||||||
\(867\) | −40.3969 | −1.37195 | ||||||||
\(868\) | −2.22505 | −0.0755231 | ||||||||
\(869\) | 46.6524 | 1.58257 | ||||||||
\(870\) | 19.2838 | 0.653781 | ||||||||
\(871\) | 6.01975 | 0.203971 | ||||||||
\(872\) | −2.27389 | −0.0770037 | ||||||||
\(873\) | −26.2477 | −0.888351 | ||||||||
\(874\) | 5.40550 | 0.182844 | ||||||||
\(875\) | −2.15778 | −0.0729464 | ||||||||
\(876\) | −7.70769 | −0.260419 | ||||||||
\(877\) | 14.5995 | 0.492992 | 0.246496 | − | 0.969144i | \(-0.420721\pi\) | ||||
0.246496 | + | 0.969144i | \(0.420721\pi\) | |||||||
\(878\) | 21.1394 | 0.713419 | ||||||||
\(879\) | 14.4776 | 0.488317 | ||||||||
\(880\) | 10.8783 | 0.366706 | ||||||||
\(881\) | 22.6871 | 0.764349 | 0.382175 | − | 0.924090i | \(-0.375175\pi\) | ||||
0.382175 | + | 0.924090i | \(0.375175\pi\) | |||||||
\(882\) | 13.8500 | 0.466353 | ||||||||
\(883\) | 45.0072 | 1.51461 | 0.757306 | − | 0.653060i | \(-0.226515\pi\) | ||||
0.757306 | + | 0.653060i | \(0.226515\pi\) | |||||||
\(884\) | 36.0197 | 1.21148 | ||||||||
\(885\) | −33.0382 | −1.11057 | ||||||||
\(886\) | −37.5158 | −1.26037 | ||||||||
\(887\) | −45.9730 | −1.54362 | −0.771812 | − | 0.635851i | \(-0.780649\pi\) | ||||
−0.771812 | + | 0.635851i | \(0.780649\pi\) | |||||||
\(888\) | 4.10331 | 0.137698 | ||||||||
\(889\) | 3.31769 | 0.111272 | ||||||||
\(890\) | 8.63055 | 0.289297 | ||||||||
\(891\) | 4.10331 | 0.137466 | ||||||||
\(892\) | −10.1599 | −0.340179 | ||||||||
\(893\) | 12.1500 | 0.406585 | ||||||||
\(894\) | −15.8110 | −0.528799 | ||||||||
\(895\) | −7.84997 | −0.262395 | ||||||||
\(896\) | 0.273891 | 0.00915004 | ||||||||
\(897\) | −15.5654 | −0.519714 | ||||||||
\(898\) | 9.81180 | 0.327424 | ||||||||
\(899\) | 59.0921 | 1.97083 | ||||||||
\(900\) | −4.05659 | −0.135220 | ||||||||
\(901\) | 23.5109 | 0.783263 | ||||||||
\(902\) | 13.8259 | 0.460353 | ||||||||
\(903\) | 1.47277 | 0.0490106 | ||||||||
\(904\) | −4.58383 | −0.152456 | ||||||||
\(905\) | 4.10331 | 0.136399 | ||||||||
\(906\) | −17.7643 | −0.590179 | ||||||||
\(907\) | 3.69861 | 0.122810 | 0.0614052 | − | 0.998113i | \(-0.480442\pi\) | ||||
0.0614052 | + | 0.998113i | \(0.480442\pi\) | |||||||
\(908\) | −4.96103 | −0.164638 | ||||||||
\(909\) | −9.45222 | −0.313510 | ||||||||
\(910\) | −3.45222 | −0.114440 | ||||||||
\(911\) | 37.5342 | 1.24356 | 0.621782 | − | 0.783191i | \(-0.286409\pi\) | ||||
0.621782 | + | 0.783191i | \(0.286409\pi\) | |||||||
\(912\) | 1.65109 | 0.0546732 | ||||||||
\(913\) | −20.6645 | −0.683894 | ||||||||
\(914\) | 28.5598 | 0.944673 | ||||||||
\(915\) | −13.6044 | −0.449747 | ||||||||
\(916\) | −14.7184 | −0.486308 | ||||||||
\(917\) | 0.705563 | 0.0232998 | ||||||||
\(918\) | −37.8804 | −1.25024 | ||||||||
\(919\) | −22.1677 | −0.731243 | −0.365622 | − | 0.930764i | \(-0.619144\pi\) | ||||
−0.365622 | + | 0.930764i | \(0.619144\pi\) | |||||||
\(920\) | −8.67939 | −0.286151 | ||||||||
\(921\) | 20.8315 | 0.686423 | ||||||||
\(922\) | 38.1826 | 1.25748 | ||||||||
\(923\) | −3.58675 | −0.118059 | ||||||||
\(924\) | −1.12386 | −0.0369722 | ||||||||
\(925\) | −8.32273 | −0.273650 | ||||||||
\(926\) | −1.85772 | −0.0610484 | ||||||||
\(927\) | 24.1500 | 0.793191 | ||||||||
\(928\) | −7.27389 | −0.238777 | ||||||||
\(929\) | −37.6503 | −1.23527 | −0.617633 | − | 0.786466i | \(-0.711908\pi\) | ||||
−0.617633 | + | 0.786466i | \(0.711908\pi\) | |||||||
\(930\) | 21.5371 | 0.706230 | ||||||||
\(931\) | 11.4338 | 0.374728 | ||||||||
\(932\) | −14.9426 | −0.489461 | ||||||||
\(933\) | 14.9795 | 0.490405 | ||||||||
\(934\) | −11.0360 | −0.361110 | ||||||||
\(935\) | −82.4146 | −2.69524 | ||||||||
\(936\) | 9.50881 | 0.310805 | ||||||||
\(937\) | 24.4047 | 0.797267 | 0.398633 | − | 0.917110i | \(-0.369485\pi\) | ||||
0.398633 | + | 0.917110i | \(0.369485\pi\) | |||||||
\(938\) | −0.346784 | −0.0113229 | ||||||||
\(939\) | −21.5216 | −0.702331 | ||||||||
\(940\) | −19.5088 | −0.636307 | ||||||||
\(941\) | −12.5491 | −0.409089 | −0.204545 | − | 0.978857i | \(-0.565571\pi\) | ||||
−0.204545 | + | 0.978857i | \(0.565571\pi\) | |||||||
\(942\) | −11.5371 | −0.375899 | ||||||||
\(943\) | −11.0312 | −0.359226 | ||||||||
\(944\) | 12.4621 | 0.405607 | ||||||||
\(945\) | 3.63055 | 0.118102 | ||||||||
\(946\) | −22.0643 | −0.717374 | ||||||||
\(947\) | −39.4749 | −1.28276 | −0.641381 | − | 0.767223i | \(-0.721638\pi\) | ||||
−0.641381 | + | 0.767223i | \(0.721638\pi\) | |||||||
\(948\) | −11.3695 | −0.369263 | ||||||||
\(949\) | −36.6455 | −1.18956 | ||||||||
\(950\) | −3.34891 | −0.108653 | ||||||||
\(951\) | 17.5470 | 0.569000 | ||||||||
\(952\) | −2.07502 | −0.0672517 | ||||||||
\(953\) | 10.3646 | 0.335743 | 0.167872 | − | 0.985809i | \(-0.446311\pi\) | ||||
0.167872 | + | 0.985809i | \(0.446311\pi\) | |||||||
\(954\) | 6.20662 | 0.200947 | ||||||||
\(955\) | 7.69994 | 0.249164 | ||||||||
\(956\) | 8.02055 | 0.259403 | ||||||||
\(957\) | 29.8470 | 0.964818 | ||||||||
\(958\) | −24.9194 | −0.805108 | ||||||||
\(959\) | −0.534985 | −0.0172756 | ||||||||
\(960\) | −2.65109 | −0.0855637 | ||||||||
\(961\) | 34.9971 | 1.12894 | ||||||||
\(962\) | 19.5088 | 0.628989 | ||||||||
\(963\) | 20.3567 | 0.655984 | ||||||||
\(964\) | −11.5499 | −0.371997 | ||||||||
\(965\) | −31.5937 | −1.01704 | ||||||||
\(966\) | 0.896688 | 0.0288505 | ||||||||
\(967\) | −10.7029 | −0.344181 | −0.172090 | − | 0.985081i | \(-0.555052\pi\) | ||||
−0.172090 | + | 0.985081i | \(0.555052\pi\) | |||||||
\(968\) | 5.83717 | 0.187614 | ||||||||
\(969\) | −12.5088 | −0.401841 | ||||||||
\(970\) | 34.7926 | 1.11712 | ||||||||
\(971\) | −16.6015 | −0.532766 | −0.266383 | − | 0.963867i | \(-0.585829\pi\) | ||||
−0.266383 | + | 0.963867i | \(0.585829\pi\) | |||||||
\(972\) | −16.0000 | −0.513200 | ||||||||
\(973\) | −4.51386 | −0.144708 | ||||||||
\(974\) | 17.6588 | 0.565826 | ||||||||
\(975\) | 9.64334 | 0.308834 | ||||||||
\(976\) | 5.13161 | 0.164259 | ||||||||
\(977\) | 9.46289 | 0.302745 | 0.151372 | − | 0.988477i | \(-0.451631\pi\) | ||||
0.151372 | + | 0.988477i | \(0.451631\pi\) | |||||||
\(978\) | −9.18820 | −0.293806 | ||||||||
\(979\) | 13.3582 | 0.426930 | ||||||||
\(980\) | −18.3588 | −0.586450 | ||||||||
\(981\) | 4.54778 | 0.145199 | ||||||||
\(982\) | −24.1231 | −0.769798 | ||||||||
\(983\) | 47.7429 | 1.52276 | 0.761382 | − | 0.648304i | \(-0.224521\pi\) | ||||
0.761382 | + | 0.648304i | \(0.224521\pi\) | |||||||
\(984\) | −3.36945 | −0.107414 | ||||||||
\(985\) | 17.5782 | 0.560088 | ||||||||
\(986\) | 55.1076 | 1.75498 | ||||||||
\(987\) | 2.01550 | 0.0641541 | ||||||||
\(988\) | 7.84997 | 0.249741 | ||||||||
\(989\) | 17.6044 | 0.559787 | ||||||||
\(990\) | −21.7565 | −0.691468 | ||||||||
\(991\) | 2.88331 | 0.0915914 | 0.0457957 | − | 0.998951i | \(-0.485418\pi\) | ||||
0.0457957 | + | 0.998951i | \(0.485418\pi\) | |||||||
\(992\) | −8.12386 | −0.257933 | ||||||||
\(993\) | −3.80888 | −0.120871 | ||||||||
\(994\) | 0.206625 | 0.00655373 | ||||||||
\(995\) | 38.2859 | 1.21374 | ||||||||
\(996\) | 5.03605 | 0.159573 | ||||||||
\(997\) | −5.20392 | −0.164810 | −0.0824049 | − | 0.996599i | \(-0.526260\pi\) | ||||
−0.0824049 | + | 0.996599i | \(0.526260\pi\) | |||||||
\(998\) | 17.7728 | 0.562589 | ||||||||
\(999\) | −20.5166 | −0.649115 |
(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 | 4022.2.a.b.1.3 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4022.2.a.b.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial |