Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [547,2,Mod(1,547)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(547, 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("547.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 547 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 547.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: | \(4.36781699056\) |
Analytic rank: | \(0\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 547.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.760071 | 0.537451 | 0.268726 | − | 0.963217i | \(-0.413397\pi\) | ||||
0.268726 | + | 0.963217i | \(0.413397\pi\) | |||||||
\(3\) | −2.84895 | −1.64484 | −0.822422 | − | 0.568878i | \(-0.807378\pi\) | ||||
−0.822422 | + | 0.568878i | \(0.807378\pi\) | |||||||
\(4\) | −1.42229 | −0.711146 | ||||||||
\(5\) | 3.94928 | 1.76617 | 0.883086 | − | 0.469211i | \(-0.155462\pi\) | ||||
0.883086 | + | 0.469211i | \(0.155462\pi\) | |||||||
\(6\) | −2.16541 | −0.884023 | ||||||||
\(7\) | 1.21889 | 0.460696 | 0.230348 | − | 0.973108i | \(-0.426014\pi\) | ||||
0.230348 | + | 0.973108i | \(0.426014\pi\) | |||||||
\(8\) | −2.60119 | −0.919658 | ||||||||
\(9\) | 5.11653 | 1.70551 | ||||||||
\(10\) | 3.00173 | 0.949232 | ||||||||
\(11\) | −3.82257 | −1.15255 | −0.576274 | − | 0.817256i | \(-0.695494\pi\) | ||||
−0.576274 | + | 0.817256i | \(0.695494\pi\) | |||||||
\(12\) | 4.05204 | 1.16972 | ||||||||
\(13\) | −3.43145 | −0.951714 | −0.475857 | − | 0.879523i | \(-0.657862\pi\) | ||||
−0.475857 | + | 0.879523i | \(0.657862\pi\) | |||||||
\(14\) | 0.926440 | 0.247602 | ||||||||
\(15\) | −11.2513 | −2.90508 | ||||||||
\(16\) | 0.867499 | 0.216875 | ||||||||
\(17\) | 6.96790 | 1.68996 | 0.844982 | − | 0.534794i | \(-0.179611\pi\) | ||||
0.844982 | + | 0.534794i | \(0.179611\pi\) | |||||||
\(18\) | 3.88893 | 0.916629 | ||||||||
\(19\) | 5.60932 | 1.28687 | 0.643433 | − | 0.765502i | \(-0.277509\pi\) | ||||
0.643433 | + | 0.765502i | \(0.277509\pi\) | |||||||
\(20\) | −5.61703 | −1.25601 | ||||||||
\(21\) | −3.47255 | −0.757773 | ||||||||
\(22\) | −2.90543 | −0.619439 | ||||||||
\(23\) | 2.46597 | 0.514190 | 0.257095 | − | 0.966386i | \(-0.417235\pi\) | ||||
0.257095 | + | 0.966386i | \(0.417235\pi\) | |||||||
\(24\) | 7.41065 | 1.51269 | ||||||||
\(25\) | 10.5968 | 2.11936 | ||||||||
\(26\) | −2.60815 | −0.511500 | ||||||||
\(27\) | −6.02989 | −1.16045 | ||||||||
\(28\) | −1.73361 | −0.327622 | ||||||||
\(29\) | 9.86564 | 1.83200 | 0.916002 | − | 0.401175i | \(-0.131398\pi\) | ||||
0.916002 | + | 0.401175i | \(0.131398\pi\) | |||||||
\(30\) | −8.55180 | −1.56134 | ||||||||
\(31\) | −1.40756 | −0.252805 | −0.126402 | − | 0.991979i | \(-0.540343\pi\) | ||||
−0.126402 | + | 0.991979i | \(0.540343\pi\) | |||||||
\(32\) | 5.86173 | 1.03622 | ||||||||
\(33\) | 10.8903 | 1.89576 | ||||||||
\(34\) | 5.29610 | 0.908274 | ||||||||
\(35\) | 4.81373 | 0.813668 | ||||||||
\(36\) | −7.27720 | −1.21287 | ||||||||
\(37\) | −0.306868 | −0.0504488 | −0.0252244 | − | 0.999682i | \(-0.508030\pi\) | ||||
−0.0252244 | + | 0.999682i | \(0.508030\pi\) | |||||||
\(38\) | 4.26348 | 0.691628 | ||||||||
\(39\) | 9.77605 | 1.56542 | ||||||||
\(40\) | −10.2728 | −1.62427 | ||||||||
\(41\) | −4.59684 | −0.717906 | −0.358953 | − | 0.933356i | \(-0.616866\pi\) | ||||
−0.358953 | + | 0.933356i | \(0.616866\pi\) | |||||||
\(42\) | −2.63938 | −0.407266 | ||||||||
\(43\) | 8.76044 | 1.33595 | 0.667977 | − | 0.744182i | \(-0.267160\pi\) | ||||
0.667977 | + | 0.744182i | \(0.267160\pi\) | |||||||
\(44\) | 5.43681 | 0.819631 | ||||||||
\(45\) | 20.2066 | 3.01222 | ||||||||
\(46\) | 1.87431 | 0.276352 | ||||||||
\(47\) | −5.68889 | −0.829810 | −0.414905 | − | 0.909865i | \(-0.636185\pi\) | ||||
−0.414905 | + | 0.909865i | \(0.636185\pi\) | |||||||
\(48\) | −2.47146 | −0.356725 | ||||||||
\(49\) | −5.51432 | −0.787759 | ||||||||
\(50\) | 8.05434 | 1.13906 | ||||||||
\(51\) | −19.8512 | −2.77973 | ||||||||
\(52\) | 4.88053 | 0.676808 | ||||||||
\(53\) | −1.28368 | −0.176327 | −0.0881637 | − | 0.996106i | \(-0.528100\pi\) | ||||
−0.0881637 | + | 0.996106i | \(0.528100\pi\) | |||||||
\(54\) | −4.58315 | −0.623687 | ||||||||
\(55\) | −15.0964 | −2.03560 | ||||||||
\(56\) | −3.17055 | −0.423683 | ||||||||
\(57\) | −15.9807 | −2.11669 | ||||||||
\(58\) | 7.49859 | 0.984613 | ||||||||
\(59\) | −8.51290 | −1.10829 | −0.554143 | − | 0.832422i | \(-0.686954\pi\) | ||||
−0.554143 | + | 0.832422i | \(0.686954\pi\) | |||||||
\(60\) | 16.0027 | 2.06593 | ||||||||
\(61\) | 13.2410 | 1.69534 | 0.847669 | − | 0.530525i | \(-0.178005\pi\) | ||||
0.847669 | + | 0.530525i | \(0.178005\pi\) | |||||||
\(62\) | −1.06984 | −0.135870 | ||||||||
\(63\) | 6.23647 | 0.785721 | ||||||||
\(64\) | 2.72033 | 0.340042 | ||||||||
\(65\) | −13.5518 | −1.68089 | ||||||||
\(66\) | 8.27742 | 1.01888 | ||||||||
\(67\) | 14.1158 | 1.72452 | 0.862261 | − | 0.506464i | \(-0.169048\pi\) | ||||
0.862261 | + | 0.506464i | \(0.169048\pi\) | |||||||
\(68\) | −9.91039 | −1.20181 | ||||||||
\(69\) | −7.02543 | −0.845762 | ||||||||
\(70\) | 3.65877 | 0.437307 | ||||||||
\(71\) | −3.89908 | −0.462736 | −0.231368 | − | 0.972866i | \(-0.574320\pi\) | ||||
−0.231368 | + | 0.972866i | \(0.574320\pi\) | |||||||
\(72\) | −13.3090 | −1.56849 | ||||||||
\(73\) | 2.36236 | 0.276493 | 0.138246 | − | 0.990398i | \(-0.455853\pi\) | ||||
0.138246 | + | 0.990398i | \(0.455853\pi\) | |||||||
\(74\) | −0.233242 | −0.0271138 | ||||||||
\(75\) | −30.1898 | −3.48602 | ||||||||
\(76\) | −7.97809 | −0.915150 | ||||||||
\(77\) | −4.65928 | −0.530975 | ||||||||
\(78\) | 7.43049 | 0.841338 | ||||||||
\(79\) | −1.53407 | −0.172596 | −0.0862981 | − | 0.996269i | \(-0.527504\pi\) | ||||
−0.0862981 | + | 0.996269i | \(0.527504\pi\) | |||||||
\(80\) | 3.42600 | 0.383038 | ||||||||
\(81\) | 1.82928 | 0.203254 | ||||||||
\(82\) | −3.49393 | −0.385840 | ||||||||
\(83\) | 7.20051 | 0.790359 | 0.395179 | − | 0.918604i | \(-0.370682\pi\) | ||||
0.395179 | + | 0.918604i | \(0.370682\pi\) | |||||||
\(84\) | 4.93898 | 0.538887 | ||||||||
\(85\) | 27.5182 | 2.98477 | ||||||||
\(86\) | 6.65856 | 0.718011 | ||||||||
\(87\) | −28.1067 | −3.01336 | ||||||||
\(88\) | 9.94322 | 1.05995 | ||||||||
\(89\) | −8.50459 | −0.901485 | −0.450742 | − | 0.892654i | \(-0.648841\pi\) | ||||
−0.450742 | + | 0.892654i | \(0.648841\pi\) | |||||||
\(90\) | 15.3585 | 1.61892 | ||||||||
\(91\) | −4.18255 | −0.438451 | ||||||||
\(92\) | −3.50733 | −0.365664 | ||||||||
\(93\) | 4.01006 | 0.415824 | ||||||||
\(94\) | −4.32396 | −0.445982 | ||||||||
\(95\) | 22.1528 | 2.27283 | ||||||||
\(96\) | −16.6998 | −1.70442 | ||||||||
\(97\) | −4.54592 | −0.461568 | −0.230784 | − | 0.973005i | \(-0.574129\pi\) | ||||
−0.230784 | + | 0.973005i | \(0.574129\pi\) | |||||||
\(98\) | −4.19127 | −0.423382 | ||||||||
\(99\) | −19.5583 | −1.96568 | ||||||||
\(100\) | −15.0718 | −1.50718 | ||||||||
\(101\) | 6.28606 | 0.625486 | 0.312743 | − | 0.949838i | \(-0.398752\pi\) | ||||
0.312743 | + | 0.949838i | \(0.398752\pi\) | |||||||
\(102\) | −15.0883 | −1.49397 | ||||||||
\(103\) | −12.5719 | −1.23875 | −0.619373 | − | 0.785097i | \(-0.712613\pi\) | ||||
−0.619373 | + | 0.785097i | \(0.712613\pi\) | |||||||
\(104\) | 8.92585 | 0.875251 | ||||||||
\(105\) | −13.7141 | −1.33836 | ||||||||
\(106\) | −0.975690 | −0.0947674 | ||||||||
\(107\) | 2.18850 | 0.211570 | 0.105785 | − | 0.994389i | \(-0.466264\pi\) | ||||
0.105785 | + | 0.994389i | \(0.466264\pi\) | |||||||
\(108\) | 8.57627 | 0.825252 | ||||||||
\(109\) | −15.4204 | −1.47700 | −0.738502 | − | 0.674251i | \(-0.764467\pi\) | ||||
−0.738502 | + | 0.674251i | \(0.764467\pi\) | |||||||
\(110\) | −11.4743 | −1.09404 | ||||||||
\(111\) | 0.874252 | 0.0829804 | ||||||||
\(112\) | 1.05738 | 0.0999133 | ||||||||
\(113\) | −6.83811 | −0.643275 | −0.321638 | − | 0.946863i | \(-0.604233\pi\) | ||||
−0.321638 | + | 0.946863i | \(0.604233\pi\) | |||||||
\(114\) | −12.1465 | −1.13762 | ||||||||
\(115\) | 9.73880 | 0.908148 | ||||||||
\(116\) | −14.0318 | −1.30282 | ||||||||
\(117\) | −17.5571 | −1.62316 | ||||||||
\(118\) | −6.47041 | −0.595650 | ||||||||
\(119\) | 8.49308 | 0.778560 | ||||||||
\(120\) | 29.2667 | 2.67168 | ||||||||
\(121\) | 3.61206 | 0.328369 | ||||||||
\(122\) | 10.0641 | 0.911162 | ||||||||
\(123\) | 13.0962 | 1.18084 | ||||||||
\(124\) | 2.00196 | 0.179781 | ||||||||
\(125\) | 22.1034 | 1.97699 | ||||||||
\(126\) | 4.74016 | 0.422287 | ||||||||
\(127\) | −4.15923 | −0.369072 | −0.184536 | − | 0.982826i | \(-0.559078\pi\) | ||||
−0.184536 | + | 0.982826i | \(0.559078\pi\) | |||||||
\(128\) | −9.65581 | −0.853461 | ||||||||
\(129\) | −24.9581 | −2.19744 | ||||||||
\(130\) | −10.3003 | −0.903397 | ||||||||
\(131\) | −3.86580 | −0.337756 | −0.168878 | − | 0.985637i | \(-0.554014\pi\) | ||||
−0.168878 | + | 0.985637i | \(0.554014\pi\) | |||||||
\(132\) | −15.4892 | −1.34816 | ||||||||
\(133\) | 6.83713 | 0.592854 | ||||||||
\(134\) | 10.7290 | 0.926847 | ||||||||
\(135\) | −23.8137 | −2.04956 | ||||||||
\(136\) | −18.1248 | −1.55419 | ||||||||
\(137\) | −11.8207 | −1.00991 | −0.504955 | − | 0.863146i | \(-0.668491\pi\) | ||||
−0.504955 | + | 0.863146i | \(0.668491\pi\) | |||||||
\(138\) | −5.33982 | −0.454556 | ||||||||
\(139\) | 5.35879 | 0.454526 | 0.227263 | − | 0.973833i | \(-0.427022\pi\) | ||||
0.227263 | + | 0.973833i | \(0.427022\pi\) | |||||||
\(140\) | −6.84652 | −0.578637 | ||||||||
\(141\) | 16.2074 | 1.36491 | ||||||||
\(142\) | −2.96358 | −0.248698 | ||||||||
\(143\) | 13.1170 | 1.09690 | ||||||||
\(144\) | 4.43858 | 0.369882 | ||||||||
\(145\) | 38.9622 | 3.23563 | ||||||||
\(146\) | 1.79556 | 0.148601 | ||||||||
\(147\) | 15.7100 | 1.29574 | ||||||||
\(148\) | 0.436456 | 0.0358765 | ||||||||
\(149\) | 11.4674 | 0.939442 | 0.469721 | − | 0.882815i | \(-0.344354\pi\) | ||||
0.469721 | + | 0.882815i | \(0.344354\pi\) | |||||||
\(150\) | −22.9464 | −1.87357 | ||||||||
\(151\) | 18.0123 | 1.46582 | 0.732910 | − | 0.680326i | \(-0.238162\pi\) | ||||
0.732910 | + | 0.680326i | \(0.238162\pi\) | |||||||
\(152\) | −14.5909 | −1.18348 | ||||||||
\(153\) | 35.6515 | 2.88225 | ||||||||
\(154\) | −3.54139 | −0.285373 | ||||||||
\(155\) | −5.55884 | −0.446497 | ||||||||
\(156\) | −13.9044 | −1.11324 | ||||||||
\(157\) | 17.1473 | 1.36850 | 0.684250 | − | 0.729247i | \(-0.260130\pi\) | ||||
0.684250 | + | 0.729247i | \(0.260130\pi\) | |||||||
\(158\) | −1.16600 | −0.0927621 | ||||||||
\(159\) | 3.65715 | 0.290031 | ||||||||
\(160\) | 23.1496 | 1.83014 | ||||||||
\(161\) | 3.00574 | 0.236885 | ||||||||
\(162\) | 1.39039 | 0.109239 | ||||||||
\(163\) | −23.1476 | −1.81306 | −0.906531 | − | 0.422140i | \(-0.861279\pi\) | ||||
−0.906531 | + | 0.422140i | \(0.861279\pi\) | |||||||
\(164\) | 6.53805 | 0.510536 | ||||||||
\(165\) | 43.0090 | 3.34824 | ||||||||
\(166\) | 5.47290 | 0.424780 | ||||||||
\(167\) | 12.4285 | 0.961743 | 0.480872 | − | 0.876791i | \(-0.340320\pi\) | ||||
0.480872 | + | 0.876791i | \(0.340320\pi\) | |||||||
\(168\) | 9.03275 | 0.696891 | ||||||||
\(169\) | −1.22512 | −0.0942399 | ||||||||
\(170\) | 20.9158 | 1.60417 | ||||||||
\(171\) | 28.7003 | 2.19476 | ||||||||
\(172\) | −12.4599 | −0.950059 | ||||||||
\(173\) | 21.2502 | 1.61562 | 0.807812 | − | 0.589440i | \(-0.200652\pi\) | ||||
0.807812 | + | 0.589440i | \(0.200652\pi\) | |||||||
\(174\) | −21.3631 | −1.61953 | ||||||||
\(175\) | 12.9163 | 0.976382 | ||||||||
\(176\) | −3.31608 | −0.249959 | ||||||||
\(177\) | 24.2529 | 1.82296 | ||||||||
\(178\) | −6.46409 | −0.484504 | ||||||||
\(179\) | 1.46923 | 0.109816 | 0.0549079 | − | 0.998491i | \(-0.482513\pi\) | ||||
0.0549079 | + | 0.998491i | \(0.482513\pi\) | |||||||
\(180\) | −28.7397 | −2.14213 | ||||||||
\(181\) | −13.2169 | −0.982404 | −0.491202 | − | 0.871046i | \(-0.663442\pi\) | ||||
−0.491202 | + | 0.871046i | \(0.663442\pi\) | |||||||
\(182\) | −3.17904 | −0.235646 | ||||||||
\(183\) | −37.7230 | −2.78857 | ||||||||
\(184\) | −6.41444 | −0.472879 | ||||||||
\(185\) | −1.21191 | −0.0891013 | ||||||||
\(186\) | 3.04793 | 0.223485 | ||||||||
\(187\) | −26.6353 | −1.94777 | ||||||||
\(188\) | 8.09126 | 0.590116 | ||||||||
\(189\) | −7.34975 | −0.534616 | ||||||||
\(190\) | 16.8377 | 1.22153 | ||||||||
\(191\) | −10.7370 | −0.776902 | −0.388451 | − | 0.921469i | \(-0.626990\pi\) | ||||
−0.388451 | + | 0.921469i | \(0.626990\pi\) | |||||||
\(192\) | −7.75010 | −0.559316 | ||||||||
\(193\) | −12.0744 | −0.869138 | −0.434569 | − | 0.900639i | \(-0.643099\pi\) | ||||
−0.434569 | + | 0.900639i | \(0.643099\pi\) | |||||||
\(194\) | −3.45522 | −0.248071 | ||||||||
\(195\) | 38.6084 | 2.76480 | ||||||||
\(196\) | 7.84297 | 0.560212 | ||||||||
\(197\) | 0.419140 | 0.0298625 | 0.0149313 | − | 0.999889i | \(-0.495247\pi\) | ||||
0.0149313 | + | 0.999889i | \(0.495247\pi\) | |||||||
\(198\) | −14.8657 | −1.05646 | ||||||||
\(199\) | 3.46652 | 0.245735 | 0.122867 | − | 0.992423i | \(-0.460791\pi\) | ||||
0.122867 | + | 0.992423i | \(0.460791\pi\) | |||||||
\(200\) | −27.5643 | −1.94909 | ||||||||
\(201\) | −40.2153 | −2.83657 | ||||||||
\(202\) | 4.77785 | 0.336169 | ||||||||
\(203\) | 12.0251 | 0.843996 | ||||||||
\(204\) | 28.2342 | 1.97679 | ||||||||
\(205\) | −18.1542 | −1.26795 | ||||||||
\(206\) | −9.55553 | −0.665765 | ||||||||
\(207\) | 12.6172 | 0.876956 | ||||||||
\(208\) | −2.97678 | −0.206403 | ||||||||
\(209\) | −21.4420 | −1.48318 | ||||||||
\(210\) | −10.4237 | −0.719302 | ||||||||
\(211\) | −13.4797 | −0.927978 | −0.463989 | − | 0.885841i | \(-0.653582\pi\) | ||||
−0.463989 | + | 0.885841i | \(0.653582\pi\) | |||||||
\(212\) | 1.82577 | 0.125395 | ||||||||
\(213\) | 11.1083 | 0.761128 | ||||||||
\(214\) | 1.66342 | 0.113709 | ||||||||
\(215\) | 34.5974 | 2.35953 | ||||||||
\(216\) | 15.6849 | 1.06722 | ||||||||
\(217\) | −1.71565 | −0.116466 | ||||||||
\(218\) | −11.7206 | −0.793818 | ||||||||
\(219\) | −6.73024 | −0.454787 | ||||||||
\(220\) | 21.4715 | 1.44761 | ||||||||
\(221\) | −23.9100 | −1.60836 | ||||||||
\(222\) | 0.664494 | 0.0445979 | ||||||||
\(223\) | −19.8072 | −1.32639 | −0.663195 | − | 0.748446i | \(-0.730800\pi\) | ||||
−0.663195 | + | 0.748446i | \(0.730800\pi\) | |||||||
\(224\) | 7.14479 | 0.477381 | ||||||||
\(225\) | 54.2190 | 3.61460 | ||||||||
\(226\) | −5.19745 | −0.345729 | ||||||||
\(227\) | 26.6313 | 1.76758 | 0.883789 | − | 0.467885i | \(-0.154984\pi\) | ||||
0.883789 | + | 0.467885i | \(0.154984\pi\) | |||||||
\(228\) | 22.7292 | 1.50528 | ||||||||
\(229\) | −6.04587 | −0.399522 | −0.199761 | − | 0.979845i | \(-0.564017\pi\) | ||||
−0.199761 | + | 0.979845i | \(0.564017\pi\) | |||||||
\(230\) | 7.40218 | 0.488085 | ||||||||
\(231\) | 13.2741 | 0.873370 | ||||||||
\(232\) | −25.6624 | −1.68482 | ||||||||
\(233\) | 3.31027 | 0.216863 | 0.108431 | − | 0.994104i | \(-0.465417\pi\) | ||||
0.108431 | + | 0.994104i | \(0.465417\pi\) | |||||||
\(234\) | −13.3447 | −0.872368 | ||||||||
\(235\) | −22.4670 | −1.46559 | ||||||||
\(236\) | 12.1078 | 0.788153 | ||||||||
\(237\) | 4.37049 | 0.283894 | ||||||||
\(238\) | 6.45535 | 0.418438 | ||||||||
\(239\) | 3.83678 | 0.248181 | 0.124090 | − | 0.992271i | \(-0.460399\pi\) | ||||
0.124090 | + | 0.992271i | \(0.460399\pi\) | |||||||
\(240\) | −9.76050 | −0.630038 | ||||||||
\(241\) | 0.216458 | 0.0139433 | 0.00697165 | − | 0.999976i | \(-0.497781\pi\) | ||||
0.00697165 | + | 0.999976i | \(0.497781\pi\) | |||||||
\(242\) | 2.74542 | 0.176482 | ||||||||
\(243\) | 12.8781 | 0.826132 | ||||||||
\(244\) | −18.8326 | −1.20563 | ||||||||
\(245\) | −21.7776 | −1.39132 | ||||||||
\(246\) | 9.95403 | 0.634646 | ||||||||
\(247\) | −19.2481 | −1.22473 | ||||||||
\(248\) | 3.66132 | 0.232494 | ||||||||
\(249\) | −20.5139 | −1.30002 | ||||||||
\(250\) | 16.8002 | 1.06254 | ||||||||
\(251\) | −4.08046 | −0.257556 | −0.128778 | − | 0.991673i | \(-0.541106\pi\) | ||||
−0.128778 | + | 0.991673i | \(0.541106\pi\) | |||||||
\(252\) | −8.87008 | −0.558763 | ||||||||
\(253\) | −9.42634 | −0.592629 | ||||||||
\(254\) | −3.16131 | −0.198358 | ||||||||
\(255\) | −78.3981 | −4.90948 | ||||||||
\(256\) | −12.7798 | −0.798736 | ||||||||
\(257\) | 26.0143 | 1.62273 | 0.811364 | − | 0.584541i | \(-0.198725\pi\) | ||||
0.811364 | + | 0.584541i | \(0.198725\pi\) | |||||||
\(258\) | −18.9699 | −1.18101 | ||||||||
\(259\) | −0.374037 | −0.0232416 | ||||||||
\(260\) | 19.2746 | 1.19536 | ||||||||
\(261\) | 50.4778 | 3.12450 | ||||||||
\(262\) | −2.93828 | −0.181528 | ||||||||
\(263\) | 14.0214 | 0.864600 | 0.432300 | − | 0.901730i | \(-0.357702\pi\) | ||||
0.432300 | + | 0.901730i | \(0.357702\pi\) | |||||||
\(264\) | −28.3278 | −1.74345 | ||||||||
\(265\) | −5.06962 | −0.311425 | ||||||||
\(266\) | 5.19670 | 0.318630 | ||||||||
\(267\) | 24.2292 | 1.48280 | ||||||||
\(268\) | −20.0768 | −1.22639 | ||||||||
\(269\) | −24.2888 | −1.48091 | −0.740457 | − | 0.672104i | \(-0.765391\pi\) | ||||
−0.740457 | + | 0.672104i | \(0.765391\pi\) | |||||||
\(270\) | −18.1001 | −1.10154 | ||||||||
\(271\) | −8.89062 | −0.540067 | −0.270033 | − | 0.962851i | \(-0.587035\pi\) | ||||
−0.270033 | + | 0.962851i | \(0.587035\pi\) | |||||||
\(272\) | 6.04465 | 0.366510 | ||||||||
\(273\) | 11.9159 | 0.721183 | ||||||||
\(274\) | −8.98457 | −0.542778 | ||||||||
\(275\) | −40.5071 | −2.44267 | ||||||||
\(276\) | 9.99221 | 0.601460 | ||||||||
\(277\) | −5.72979 | −0.344270 | −0.172135 | − | 0.985073i | \(-0.555066\pi\) | ||||
−0.172135 | + | 0.985073i | \(0.555066\pi\) | |||||||
\(278\) | 4.07306 | 0.244286 | ||||||||
\(279\) | −7.20181 | −0.431161 | ||||||||
\(280\) | −12.5214 | −0.748296 | ||||||||
\(281\) | −30.5950 | −1.82515 | −0.912573 | − | 0.408914i | \(-0.865908\pi\) | ||||
−0.912573 | + | 0.408914i | \(0.865908\pi\) | |||||||
\(282\) | 12.3188 | 0.733571 | ||||||||
\(283\) | 18.8658 | 1.12145 | 0.560727 | − | 0.828001i | \(-0.310522\pi\) | ||||
0.560727 | + | 0.828001i | \(0.310522\pi\) | |||||||
\(284\) | 5.54563 | 0.329073 | ||||||||
\(285\) | −63.1122 | −3.73845 | ||||||||
\(286\) | 9.96984 | 0.589529 | ||||||||
\(287\) | −5.60303 | −0.330736 | ||||||||
\(288\) | 29.9917 | 1.76728 | ||||||||
\(289\) | 31.5517 | 1.85598 | ||||||||
\(290\) | 29.6140 | 1.73900 | ||||||||
\(291\) | 12.9511 | 0.759208 | ||||||||
\(292\) | −3.35996 | −0.196627 | ||||||||
\(293\) | 2.52436 | 0.147475 | 0.0737374 | − | 0.997278i | \(-0.476507\pi\) | ||||
0.0737374 | + | 0.997278i | \(0.476507\pi\) | |||||||
\(294\) | 11.9407 | 0.696398 | ||||||||
\(295\) | −33.6199 | −1.95742 | ||||||||
\(296\) | 0.798221 | 0.0463956 | ||||||||
\(297\) | 23.0497 | 1.33748 | ||||||||
\(298\) | 8.71600 | 0.504905 | ||||||||
\(299\) | −8.46186 | −0.489362 | ||||||||
\(300\) | 42.9388 | 2.47907 | ||||||||
\(301\) | 10.6780 | 0.615469 | ||||||||
\(302\) | 13.6906 | 0.787807 | ||||||||
\(303\) | −17.9087 | −1.02883 | ||||||||
\(304\) | 4.86608 | 0.279089 | ||||||||
\(305\) | 52.2925 | 2.99426 | ||||||||
\(306\) | 27.0977 | 1.54907 | ||||||||
\(307\) | −9.63533 | −0.549917 | −0.274959 | − | 0.961456i | \(-0.588664\pi\) | ||||
−0.274959 | + | 0.961456i | \(0.588664\pi\) | |||||||
\(308\) | 6.62686 | 0.377600 | ||||||||
\(309\) | 35.8167 | 2.03754 | ||||||||
\(310\) | −4.22511 | −0.239970 | ||||||||
\(311\) | 9.41890 | 0.534097 | 0.267049 | − | 0.963683i | \(-0.413952\pi\) | ||||
0.267049 | + | 0.963683i | \(0.413952\pi\) | |||||||
\(312\) | −25.4293 | −1.43965 | ||||||||
\(313\) | 3.27757 | 0.185259 | 0.0926297 | − | 0.995701i | \(-0.470473\pi\) | ||||
0.0926297 | + | 0.995701i | \(0.470473\pi\) | |||||||
\(314\) | 13.0331 | 0.735502 | ||||||||
\(315\) | 24.6296 | 1.38772 | ||||||||
\(316\) | 2.18189 | 0.122741 | ||||||||
\(317\) | −22.6005 | −1.26937 | −0.634686 | − | 0.772770i | \(-0.718871\pi\) | ||||
−0.634686 | + | 0.772770i | \(0.718871\pi\) | |||||||
\(318\) | 2.77969 | 0.155878 | ||||||||
\(319\) | −37.7121 | −2.11147 | ||||||||
\(320\) | 10.7434 | 0.600572 | ||||||||
\(321\) | −6.23493 | −0.348000 | ||||||||
\(322\) | 2.28457 | 0.127314 | ||||||||
\(323\) | 39.0852 | 2.17476 | ||||||||
\(324\) | −2.60178 | −0.144543 | ||||||||
\(325\) | −36.3625 | −2.01703 | ||||||||
\(326\) | −17.5938 | −0.974432 | ||||||||
\(327\) | 43.9319 | 2.42944 | ||||||||
\(328\) | 11.9572 | 0.660228 | ||||||||
\(329\) | −6.93411 | −0.382290 | ||||||||
\(330\) | 32.6899 | 1.79952 | ||||||||
\(331\) | −1.06072 | −0.0583023 | −0.0291511 | − | 0.999575i | \(-0.509280\pi\) | ||||
−0.0291511 | + | 0.999575i | \(0.509280\pi\) | |||||||
\(332\) | −10.2412 | −0.562061 | ||||||||
\(333\) | −1.57010 | −0.0860409 | ||||||||
\(334\) | 9.44651 | 0.516890 | ||||||||
\(335\) | 55.7474 | 3.04580 | ||||||||
\(336\) | −3.01243 | −0.164342 | ||||||||
\(337\) | 32.4103 | 1.76550 | 0.882750 | − | 0.469842i | \(-0.155689\pi\) | ||||
0.882750 | + | 0.469842i | \(0.155689\pi\) | |||||||
\(338\) | −0.931178 | −0.0506494 | ||||||||
\(339\) | 19.4814 | 1.05809 | ||||||||
\(340\) | −39.1389 | −2.12261 | ||||||||
\(341\) | 5.38049 | 0.291370 | ||||||||
\(342\) | 21.8142 | 1.17958 | ||||||||
\(343\) | −15.2535 | −0.823613 | ||||||||
\(344\) | −22.7875 | −1.22862 | ||||||||
\(345\) | −27.7454 | −1.49376 | ||||||||
\(346\) | 16.1517 | 0.868320 | ||||||||
\(347\) | −11.4646 | −0.615451 | −0.307725 | − | 0.951475i | \(-0.599568\pi\) | ||||
−0.307725 | + | 0.951475i | \(0.599568\pi\) | |||||||
\(348\) | 39.9760 | 2.14294 | ||||||||
\(349\) | −30.1593 | −1.61439 | −0.807196 | − | 0.590284i | \(-0.799016\pi\) | ||||
−0.807196 | + | 0.590284i | \(0.799016\pi\) | |||||||
\(350\) | 9.81733 | 0.524758 | ||||||||
\(351\) | 20.6913 | 1.10442 | ||||||||
\(352\) | −22.4069 | −1.19429 | ||||||||
\(353\) | 25.8694 | 1.37689 | 0.688445 | − | 0.725289i | \(-0.258294\pi\) | ||||
0.688445 | + | 0.725289i | \(0.258294\pi\) | |||||||
\(354\) | 18.4339 | 0.979751 | ||||||||
\(355\) | −15.3986 | −0.817271 | ||||||||
\(356\) | 12.0960 | 0.641087 | ||||||||
\(357\) | −24.1964 | −1.28061 | ||||||||
\(358\) | 1.11672 | 0.0590206 | ||||||||
\(359\) | 3.04917 | 0.160929 | 0.0804644 | − | 0.996757i | \(-0.474360\pi\) | ||||
0.0804644 | + | 0.996757i | \(0.474360\pi\) | |||||||
\(360\) | −52.5611 | −2.77022 | ||||||||
\(361\) | 12.4645 | 0.656025 | ||||||||
\(362\) | −10.0458 | −0.527994 | ||||||||
\(363\) | −10.2906 | −0.540116 | ||||||||
\(364\) | 5.94881 | 0.311803 | ||||||||
\(365\) | 9.32961 | 0.488334 | ||||||||
\(366\) | −28.6722 | −1.49872 | ||||||||
\(367\) | −22.0097 | −1.14890 | −0.574448 | − | 0.818541i | \(-0.694783\pi\) | ||||
−0.574448 | + | 0.818541i | \(0.694783\pi\) | |||||||
\(368\) | 2.13922 | 0.111515 | ||||||||
\(369\) | −23.5199 | −1.22440 | ||||||||
\(370\) | −0.921136 | −0.0478876 | ||||||||
\(371\) | −1.56466 | −0.0812333 | ||||||||
\(372\) | −5.70348 | −0.295712 | ||||||||
\(373\) | 14.8875 | 0.770845 | 0.385423 | − | 0.922740i | \(-0.374056\pi\) | ||||
0.385423 | + | 0.922740i | \(0.374056\pi\) | |||||||
\(374\) | −20.2447 | −1.04683 | ||||||||
\(375\) | −62.9716 | −3.25184 | ||||||||
\(376\) | 14.7979 | 0.763141 | ||||||||
\(377\) | −33.8535 | −1.74354 | ||||||||
\(378\) | −5.58633 | −0.287330 | ||||||||
\(379\) | 9.03119 | 0.463901 | 0.231951 | − | 0.972728i | \(-0.425489\pi\) | ||||
0.231951 | + | 0.972728i | \(0.425489\pi\) | |||||||
\(380\) | −31.5077 | −1.61631 | ||||||||
\(381\) | 11.8495 | 0.607066 | ||||||||
\(382\) | −8.16088 | −0.417547 | ||||||||
\(383\) | 11.0350 | 0.563861 | 0.281930 | − | 0.959435i | \(-0.409025\pi\) | ||||
0.281930 | + | 0.959435i | \(0.409025\pi\) | |||||||
\(384\) | 27.5090 | 1.40381 | ||||||||
\(385\) | −18.4008 | −0.937793 | ||||||||
\(386\) | −9.17744 | −0.467119 | ||||||||
\(387\) | 44.8230 | 2.27848 | ||||||||
\(388\) | 6.46563 | 0.328243 | ||||||||
\(389\) | 12.7329 | 0.645584 | 0.322792 | − | 0.946470i | \(-0.395379\pi\) | ||||
0.322792 | + | 0.946470i | \(0.395379\pi\) | |||||||
\(390\) | 29.3451 | 1.48595 | ||||||||
\(391\) | 17.1826 | 0.868963 | ||||||||
\(392\) | 14.3438 | 0.724469 | ||||||||
\(393\) | 11.0135 | 0.555556 | ||||||||
\(394\) | 0.318576 | 0.0160496 | ||||||||
\(395\) | −6.05847 | −0.304835 | ||||||||
\(396\) | 27.8176 | 1.39789 | ||||||||
\(397\) | −11.5462 | −0.579489 | −0.289744 | − | 0.957104i | \(-0.593570\pi\) | ||||
−0.289744 | + | 0.957104i | \(0.593570\pi\) | |||||||
\(398\) | 2.63480 | 0.132071 | ||||||||
\(399\) | −19.4786 | −0.975152 | ||||||||
\(400\) | 9.19273 | 0.459636 | ||||||||
\(401\) | 21.1246 | 1.05491 | 0.527455 | − | 0.849583i | \(-0.323146\pi\) | ||||
0.527455 | + | 0.849583i | \(0.323146\pi\) | |||||||
\(402\) | −30.5665 | −1.52452 | ||||||||
\(403\) | 4.82997 | 0.240598 | ||||||||
\(404\) | −8.94061 | −0.444812 | ||||||||
\(405\) | 7.22435 | 0.358981 | ||||||||
\(406\) | 9.13993 | 0.453607 | ||||||||
\(407\) | 1.17303 | 0.0581447 | ||||||||
\(408\) | 51.6367 | 2.55640 | ||||||||
\(409\) | −27.5196 | −1.36076 | −0.680379 | − | 0.732860i | \(-0.738185\pi\) | ||||
−0.680379 | + | 0.732860i | \(0.738185\pi\) | |||||||
\(410\) | −13.7985 | −0.681459 | ||||||||
\(411\) | 33.6766 | 1.66114 | ||||||||
\(412\) | 17.8809 | 0.880929 | ||||||||
\(413\) | −10.3763 | −0.510583 | ||||||||
\(414\) | 9.58997 | 0.471321 | ||||||||
\(415\) | 28.4368 | 1.39591 | ||||||||
\(416\) | −20.1143 | −0.986183 | ||||||||
\(417\) | −15.2669 | −0.747625 | ||||||||
\(418\) | −16.2975 | −0.797135 | ||||||||
\(419\) | −7.13021 | −0.348334 | −0.174167 | − | 0.984716i | \(-0.555723\pi\) | ||||
−0.174167 | + | 0.984716i | \(0.555723\pi\) | |||||||
\(420\) | 19.5054 | 0.951767 | ||||||||
\(421\) | 2.00769 | 0.0978490 | 0.0489245 | − | 0.998802i | \(-0.484421\pi\) | ||||
0.0489245 | + | 0.998802i | \(0.484421\pi\) | |||||||
\(422\) | −10.2455 | −0.498743 | ||||||||
\(423\) | −29.1074 | −1.41525 | ||||||||
\(424\) | 3.33910 | 0.162161 | ||||||||
\(425\) | 73.8376 | 3.58165 | ||||||||
\(426\) | 8.44309 | 0.409069 | ||||||||
\(427\) | 16.1393 | 0.781035 | ||||||||
\(428\) | −3.11269 | −0.150457 | ||||||||
\(429\) | −37.3697 | −1.80422 | ||||||||
\(430\) | 26.2965 | 1.26813 | ||||||||
\(431\) | −18.0920 | −0.871461 | −0.435731 | − | 0.900077i | \(-0.643510\pi\) | ||||
−0.435731 | + | 0.900077i | \(0.643510\pi\) | |||||||
\(432\) | −5.23092 | −0.251673 | ||||||||
\(433\) | 14.2457 | 0.684605 | 0.342302 | − | 0.939590i | \(-0.388793\pi\) | ||||
0.342302 | + | 0.939590i | \(0.388793\pi\) | |||||||
\(434\) | −1.30402 | −0.0625949 | ||||||||
\(435\) | −111.001 | −5.32211 | ||||||||
\(436\) | 21.9323 | 1.05037 | ||||||||
\(437\) | 13.8324 | 0.661694 | ||||||||
\(438\) | −5.11546 | −0.244426 | ||||||||
\(439\) | 28.4512 | 1.35790 | 0.678951 | − | 0.734184i | \(-0.262435\pi\) | ||||
0.678951 | + | 0.734184i | \(0.262435\pi\) | |||||||
\(440\) | 39.2686 | 1.87206 | ||||||||
\(441\) | −28.2142 | −1.34353 | ||||||||
\(442\) | −18.1733 | −0.864417 | ||||||||
\(443\) | −1.91799 | −0.0911264 | −0.0455632 | − | 0.998961i | \(-0.514508\pi\) | ||||
−0.0455632 | + | 0.998961i | \(0.514508\pi\) | |||||||
\(444\) | −1.24344 | −0.0590112 | ||||||||
\(445\) | −33.5870 | −1.59218 | ||||||||
\(446\) | −15.0549 | −0.712870 | ||||||||
\(447\) | −32.6699 | −1.54524 | ||||||||
\(448\) | 3.31578 | 0.156656 | ||||||||
\(449\) | 1.56845 | 0.0740200 | 0.0370100 | − | 0.999315i | \(-0.488217\pi\) | ||||
0.0370100 | + | 0.999315i | \(0.488217\pi\) | |||||||
\(450\) | 41.2103 | 1.94267 | ||||||||
\(451\) | 17.5718 | 0.827422 | ||||||||
\(452\) | 9.72579 | 0.457463 | ||||||||
\(453\) | −51.3162 | −2.41104 | ||||||||
\(454\) | 20.2416 | 0.949988 | ||||||||
\(455\) | −16.5181 | −0.774380 | ||||||||
\(456\) | 41.5687 | 1.94663 | ||||||||
\(457\) | 17.6913 | 0.827563 | 0.413781 | − | 0.910376i | \(-0.364208\pi\) | ||||
0.413781 | + | 0.910376i | \(0.364208\pi\) | |||||||
\(458\) | −4.59529 | −0.214724 | ||||||||
\(459\) | −42.0157 | −1.96112 | ||||||||
\(460\) | −13.8514 | −0.645826 | ||||||||
\(461\) | −33.1904 | −1.54583 | −0.772915 | − | 0.634509i | \(-0.781202\pi\) | ||||
−0.772915 | + | 0.634509i | \(0.781202\pi\) | |||||||
\(462\) | 10.0892 | 0.469394 | ||||||||
\(463\) | −0.867963 | −0.0403377 | −0.0201688 | − | 0.999797i | \(-0.506420\pi\) | ||||
−0.0201688 | + | 0.999797i | \(0.506420\pi\) | |||||||
\(464\) | 8.55843 | 0.397315 | ||||||||
\(465\) | 15.8369 | 0.734417 | ||||||||
\(466\) | 2.51604 | 0.116553 | ||||||||
\(467\) | 24.1170 | 1.11600 | 0.558000 | − | 0.829841i | \(-0.311569\pi\) | ||||
0.558000 | + | 0.829841i | \(0.311569\pi\) | |||||||
\(468\) | 24.9714 | 1.15430 | ||||||||
\(469\) | 17.2056 | 0.794481 | ||||||||
\(470\) | −17.0765 | −0.787682 | ||||||||
\(471\) | −48.8517 | −2.25097 | ||||||||
\(472\) | 22.1436 | 1.01924 | ||||||||
\(473\) | −33.4874 | −1.53975 | ||||||||
\(474\) | 3.32188 | 0.152579 | ||||||||
\(475\) | 59.4410 | 2.72734 | ||||||||
\(476\) | −12.0796 | −0.553670 | ||||||||
\(477\) | −6.56800 | −0.300728 | ||||||||
\(478\) | 2.91623 | 0.133385 | ||||||||
\(479\) | 12.1544 | 0.555348 | 0.277674 | − | 0.960675i | \(-0.410437\pi\) | ||||
0.277674 | + | 0.960675i | \(0.410437\pi\) | |||||||
\(480\) | −65.9522 | −3.01029 | ||||||||
\(481\) | 1.05300 | 0.0480128 | ||||||||
\(482\) | 0.164524 | 0.00749385 | ||||||||
\(483\) | −8.56320 | −0.389639 | ||||||||
\(484\) | −5.13740 | −0.233518 | ||||||||
\(485\) | −17.9531 | −0.815209 | ||||||||
\(486\) | 9.78829 | 0.444006 | ||||||||
\(487\) | −20.8818 | −0.946244 | −0.473122 | − | 0.880997i | \(-0.656873\pi\) | ||||
−0.473122 | + | 0.880997i | \(0.656873\pi\) | |||||||
\(488\) | −34.4423 | −1.55913 | ||||||||
\(489\) | 65.9465 | 2.98220 | ||||||||
\(490\) | −16.5525 | −0.747766 | ||||||||
\(491\) | 15.5135 | 0.700113 | 0.350057 | − | 0.936729i | \(-0.386162\pi\) | ||||
0.350057 | + | 0.936729i | \(0.386162\pi\) | |||||||
\(492\) | −18.6266 | −0.839752 | ||||||||
\(493\) | 68.7428 | 3.09602 | ||||||||
\(494\) | −14.6299 | −0.658232 | ||||||||
\(495\) | −77.2412 | −3.47174 | ||||||||
\(496\) | −1.22105 | −0.0548270 | ||||||||
\(497\) | −4.75254 | −0.213180 | ||||||||
\(498\) | −15.5920 | −0.698696 | ||||||||
\(499\) | −33.3036 | −1.49087 | −0.745437 | − | 0.666576i | \(-0.767759\pi\) | ||||
−0.745437 | + | 0.666576i | \(0.767759\pi\) | |||||||
\(500\) | −31.4375 | −1.40593 | ||||||||
\(501\) | −35.4081 | −1.58192 | ||||||||
\(502\) | −3.10144 | −0.138424 | ||||||||
\(503\) | −24.0378 | −1.07179 | −0.535896 | − | 0.844284i | \(-0.680026\pi\) | ||||
−0.535896 | + | 0.844284i | \(0.680026\pi\) | |||||||
\(504\) | −16.2222 | −0.722595 | ||||||||
\(505\) | 24.8254 | 1.10472 | ||||||||
\(506\) | −7.16469 | −0.318509 | ||||||||
\(507\) | 3.49031 | 0.155010 | ||||||||
\(508\) | 5.91565 | 0.262464 | ||||||||
\(509\) | 6.28205 | 0.278447 | 0.139224 | − | 0.990261i | \(-0.455539\pi\) | ||||
0.139224 | + | 0.990261i | \(0.455539\pi\) | |||||||
\(510\) | −59.5881 | −2.63861 | ||||||||
\(511\) | 2.87944 | 0.127379 | ||||||||
\(512\) | 9.59809 | 0.424180 | ||||||||
\(513\) | −33.8236 | −1.49335 | ||||||||
\(514\) | 19.7727 | 0.872138 | ||||||||
\(515\) | −49.6499 | −2.18784 | ||||||||
\(516\) | 35.4977 | 1.56270 | ||||||||
\(517\) | 21.7462 | 0.956396 | ||||||||
\(518\) | −0.284295 | −0.0124912 | ||||||||
\(519\) | −60.5409 | −2.65745 | ||||||||
\(520\) | 35.2507 | 1.54584 | ||||||||
\(521\) | 14.0376 | 0.614998 | 0.307499 | − | 0.951548i | \(-0.400508\pi\) | ||||
0.307499 | + | 0.951548i | \(0.400508\pi\) | |||||||
\(522\) | 38.3667 | 1.67927 | ||||||||
\(523\) | 36.1356 | 1.58010 | 0.790050 | − | 0.613042i | \(-0.210055\pi\) | ||||
0.790050 | + | 0.613042i | \(0.210055\pi\) | |||||||
\(524\) | 5.49829 | 0.240194 | ||||||||
\(525\) | −36.7980 | −1.60600 | ||||||||
\(526\) | 10.6573 | 0.464680 | ||||||||
\(527\) | −9.80772 | −0.427231 | ||||||||
\(528\) | 9.44734 | 0.411143 | ||||||||
\(529\) | −16.9190 | −0.735609 | ||||||||
\(530\) | −3.85328 | −0.167376 | ||||||||
\(531\) | −43.5565 | −1.89019 | ||||||||
\(532\) | −9.72439 | −0.421606 | ||||||||
\(533\) | 15.7739 | 0.683241 | ||||||||
\(534\) | 18.4159 | 0.796934 | ||||||||
\(535\) | 8.64300 | 0.373669 | ||||||||
\(536\) | −36.7179 | −1.58597 | ||||||||
\(537\) | −4.18578 | −0.180630 | ||||||||
\(538\) | −18.4612 | −0.795919 | ||||||||
\(539\) | 21.0789 | 0.907931 | ||||||||
\(540\) | 33.8701 | 1.45754 | ||||||||
\(541\) | −26.7385 | −1.14958 | −0.574790 | − | 0.818301i | \(-0.694916\pi\) | ||||
−0.574790 | + | 0.818301i | \(0.694916\pi\) | |||||||
\(542\) | −6.75751 | −0.290260 | ||||||||
\(543\) | 37.6543 | 1.61590 | ||||||||
\(544\) | 40.8440 | 1.75117 | ||||||||
\(545\) | −60.8994 | −2.60864 | ||||||||
\(546\) | 9.05693 | 0.387601 | ||||||||
\(547\) | 1.00000 | 0.0427569 | ||||||||
\(548\) | 16.8125 | 0.718194 | ||||||||
\(549\) | 67.7480 | 2.89142 | ||||||||
\(550\) | −30.7883 | −1.31282 | ||||||||
\(551\) | 55.3395 | 2.35754 | ||||||||
\(552\) | 18.2744 | 0.777811 | ||||||||
\(553\) | −1.86986 | −0.0795144 | ||||||||
\(554\) | −4.35505 | −0.185028 | ||||||||
\(555\) | 3.45267 | 0.146558 | ||||||||
\(556\) | −7.62176 | −0.323235 | ||||||||
\(557\) | 6.67605 | 0.282873 | 0.141437 | − | 0.989947i | \(-0.454828\pi\) | ||||
0.141437 | + | 0.989947i | \(0.454828\pi\) | |||||||
\(558\) | −5.47389 | −0.231728 | ||||||||
\(559\) | −30.0610 | −1.27145 | ||||||||
\(560\) | 4.17590 | 0.176464 | ||||||||
\(561\) | 75.8827 | 3.20377 | ||||||||
\(562\) | −23.2544 | −0.980927 | ||||||||
\(563\) | 34.4697 | 1.45272 | 0.726362 | − | 0.687313i | \(-0.241210\pi\) | ||||
0.726362 | + | 0.687313i | \(0.241210\pi\) | |||||||
\(564\) | −23.0516 | −0.970648 | ||||||||
\(565\) | −27.0056 | −1.13613 | ||||||||
\(566\) | 14.3393 | 0.602727 | ||||||||
\(567\) | 2.22969 | 0.0936381 | ||||||||
\(568\) | 10.1422 | 0.425558 | ||||||||
\(569\) | −28.4453 | −1.19249 | −0.596245 | − | 0.802803i | \(-0.703341\pi\) | ||||
−0.596245 | + | 0.802803i | \(0.703341\pi\) | |||||||
\(570\) | −47.9698 | −2.00923 | ||||||||
\(571\) | −28.4524 | −1.19069 | −0.595347 | − | 0.803469i | \(-0.702986\pi\) | ||||
−0.595347 | + | 0.803469i | \(0.702986\pi\) | |||||||
\(572\) | −18.6562 | −0.780054 | ||||||||
\(573\) | 30.5892 | 1.27788 | ||||||||
\(574\) | −4.25870 | −0.177755 | ||||||||
\(575\) | 26.1314 | 1.08976 | ||||||||
\(576\) | 13.9187 | 0.579945 | ||||||||
\(577\) | −35.8918 | −1.49419 | −0.747097 | − | 0.664716i | \(-0.768553\pi\) | ||||
−0.747097 | + | 0.664716i | \(0.768553\pi\) | |||||||
\(578\) | 23.9815 | 0.997499 | ||||||||
\(579\) | 34.3995 | 1.42960 | ||||||||
\(580\) | −55.4156 | −2.30101 | ||||||||
\(581\) | 8.77661 | 0.364115 | ||||||||
\(582\) | 9.84377 | 0.408037 | ||||||||
\(583\) | 4.90697 | 0.203226 | ||||||||
\(584\) | −6.14492 | −0.254279 | ||||||||
\(585\) | −69.3381 | −2.86678 | ||||||||
\(586\) | 1.91869 | 0.0792605 | ||||||||
\(587\) | −15.1265 | −0.624337 | −0.312168 | − | 0.950027i | \(-0.601055\pi\) | ||||
−0.312168 | + | 0.950027i | \(0.601055\pi\) | |||||||
\(588\) | −22.3442 | −0.921461 | ||||||||
\(589\) | −7.89544 | −0.325326 | ||||||||
\(590\) | −25.5535 | −1.05202 | ||||||||
\(591\) | −1.19411 | −0.0491191 | ||||||||
\(592\) | −0.266208 | −0.0109411 | ||||||||
\(593\) | −36.5335 | −1.50025 | −0.750125 | − | 0.661296i | \(-0.770007\pi\) | ||||
−0.750125 | + | 0.661296i | \(0.770007\pi\) | |||||||
\(594\) | 17.5194 | 0.718830 | ||||||||
\(595\) | 33.5416 | 1.37507 | ||||||||
\(596\) | −16.3099 | −0.668081 | ||||||||
\(597\) | −9.87594 | −0.404195 | ||||||||
\(598\) | −6.43161 | −0.263008 | ||||||||
\(599\) | 1.23685 | 0.0505361 | 0.0252681 | − | 0.999681i | \(-0.491956\pi\) | ||||
0.0252681 | + | 0.999681i | \(0.491956\pi\) | |||||||
\(600\) | 78.5294 | 3.20595 | ||||||||
\(601\) | −31.4136 | −1.28139 | −0.640693 | − | 0.767797i | \(-0.721353\pi\) | ||||
−0.640693 | + | 0.767797i | \(0.721353\pi\) | |||||||
\(602\) | 8.11603 | 0.330784 | ||||||||
\(603\) | 72.2240 | 2.94119 | ||||||||
\(604\) | −25.6187 | −1.04241 | ||||||||
\(605\) | 14.2650 | 0.579956 | ||||||||
\(606\) | −13.6119 | −0.552945 | ||||||||
\(607\) | −7.95839 | −0.323021 | −0.161511 | − | 0.986871i | \(-0.551637\pi\) | ||||
−0.161511 | + | 0.986871i | \(0.551637\pi\) | |||||||
\(608\) | 32.8803 | 1.33347 | ||||||||
\(609\) | −34.2589 | −1.38824 | ||||||||
\(610\) | 39.7460 | 1.60927 | ||||||||
\(611\) | 19.5212 | 0.789742 | ||||||||
\(612\) | −50.7068 | −2.04970 | ||||||||
\(613\) | −15.6274 | −0.631183 | −0.315591 | − | 0.948895i | \(-0.602203\pi\) | ||||
−0.315591 | + | 0.948895i | \(0.602203\pi\) | |||||||
\(614\) | −7.32353 | −0.295554 | ||||||||
\(615\) | 51.7205 | 2.08557 | ||||||||
\(616\) | 12.1197 | 0.488315 | ||||||||
\(617\) | −0.525763 | −0.0211664 | −0.0105832 | − | 0.999944i | \(-0.503369\pi\) | ||||
−0.0105832 | + | 0.999944i | \(0.503369\pi\) | |||||||
\(618\) | 27.2233 | 1.09508 | ||||||||
\(619\) | 10.3010 | 0.414031 | 0.207015 | − | 0.978338i | \(-0.433625\pi\) | ||||
0.207015 | + | 0.978338i | \(0.433625\pi\) | |||||||
\(620\) | 7.90630 | 0.317524 | ||||||||
\(621\) | −14.8695 | −0.596693 | ||||||||
\(622\) | 7.15904 | 0.287051 | ||||||||
\(623\) | −10.3661 | −0.415310 | ||||||||
\(624\) | 8.48071 | 0.339500 | ||||||||
\(625\) | 34.3085 | 1.37234 | ||||||||
\(626\) | 2.49119 | 0.0995679 | ||||||||
\(627\) | 61.0873 | 2.43959 | ||||||||
\(628\) | −24.3884 | −0.973203 | ||||||||
\(629\) | −2.13823 | −0.0852567 | ||||||||
\(630\) | 18.7202 | 0.745832 | ||||||||
\(631\) | 16.3282 | 0.650015 | 0.325007 | − | 0.945711i | \(-0.394633\pi\) | ||||
0.325007 | + | 0.945711i | \(0.394633\pi\) | |||||||
\(632\) | 3.99040 | 0.158729 | ||||||||
\(633\) | 38.4029 | 1.52638 | ||||||||
\(634\) | −17.1780 | −0.682226 | ||||||||
\(635\) | −16.4260 | −0.651845 | ||||||||
\(636\) | −5.20154 | −0.206254 | ||||||||
\(637\) | 18.9221 | 0.749722 | ||||||||
\(638\) | −28.6639 | −1.13481 | ||||||||
\(639\) | −19.9498 | −0.789200 | ||||||||
\(640\) | −38.1335 | −1.50736 | ||||||||
\(641\) | 0.187113 | 0.00739051 | 0.00369525 | − | 0.999993i | \(-0.498824\pi\) | ||||
0.00369525 | + | 0.999993i | \(0.498824\pi\) | |||||||
\(642\) | −4.73899 | −0.187033 | ||||||||
\(643\) | −16.0572 | −0.633232 | −0.316616 | − | 0.948554i | \(-0.602547\pi\) | ||||
−0.316616 | + | 0.948554i | \(0.602547\pi\) | |||||||
\(644\) | −4.27503 | −0.168460 | ||||||||
\(645\) | −98.5664 | −3.88105 | ||||||||
\(646\) | 29.7075 | 1.16883 | ||||||||
\(647\) | −14.7244 | −0.578876 | −0.289438 | − | 0.957197i | \(-0.593468\pi\) | ||||
−0.289438 | + | 0.957197i | \(0.593468\pi\) | |||||||
\(648\) | −4.75830 | −0.186924 | ||||||||
\(649\) | 32.5412 | 1.27735 | ||||||||
\(650\) | −27.6381 | −1.08406 | ||||||||
\(651\) | 4.88781 | 0.191569 | ||||||||
\(652\) | 32.9227 | 1.28935 | ||||||||
\(653\) | −13.6065 | −0.532462 | −0.266231 | − | 0.963909i | \(-0.585778\pi\) | ||||
−0.266231 | + | 0.963909i | \(0.585778\pi\) | |||||||
\(654\) | 33.3914 | 1.30571 | ||||||||
\(655\) | −15.2671 | −0.596536 | ||||||||
\(656\) | −3.98775 | −0.155696 | ||||||||
\(657\) | 12.0871 | 0.471561 | ||||||||
\(658\) | −5.27042 | −0.205462 | ||||||||
\(659\) | −5.45992 | −0.212688 | −0.106344 | − | 0.994329i | \(-0.533915\pi\) | ||||
−0.106344 | + | 0.994329i | \(0.533915\pi\) | |||||||
\(660\) | −61.1713 | −2.38109 | ||||||||
\(661\) | −9.91685 | −0.385721 | −0.192860 | − | 0.981226i | \(-0.561776\pi\) | ||||
−0.192860 | + | 0.981226i | \(0.561776\pi\) | |||||||
\(662\) | −0.806220 | −0.0313346 | ||||||||
\(663\) | 68.1186 | 2.64551 | ||||||||
\(664\) | −18.7299 | −0.726860 | ||||||||
\(665\) | 27.0017 | 1.04708 | ||||||||
\(666\) | −1.19339 | −0.0462428 | ||||||||
\(667\) | 24.3284 | 0.941998 | ||||||||
\(668\) | −17.6769 | −0.683940 | ||||||||
\(669\) | 56.4299 | 2.18170 | ||||||||
\(670\) | 42.3720 | 1.63697 | ||||||||
\(671\) | −50.6147 | −1.95396 | ||||||||
\(672\) | −20.3552 | −0.785217 | ||||||||
\(673\) | −42.2629 | −1.62912 | −0.814558 | − | 0.580082i | \(-0.803021\pi\) | ||||
−0.814558 | + | 0.580082i | \(0.803021\pi\) | |||||||
\(674\) | 24.6341 | 0.948871 | ||||||||
\(675\) | −63.8977 | −2.45942 | ||||||||
\(676\) | 1.74248 | 0.0670184 | ||||||||
\(677\) | −24.3578 | −0.936144 | −0.468072 | − | 0.883690i | \(-0.655051\pi\) | ||||
−0.468072 | + | 0.883690i | \(0.655051\pi\) | |||||||
\(678\) | 14.8073 | 0.568670 | ||||||||
\(679\) | −5.54096 | −0.212643 | ||||||||
\(680\) | −71.5799 | −2.74497 | ||||||||
\(681\) | −75.8712 | −2.90739 | ||||||||
\(682\) | 4.08956 | 0.156597 | ||||||||
\(683\) | 46.8996 | 1.79456 | 0.897281 | − | 0.441459i | \(-0.145539\pi\) | ||||
0.897281 | + | 0.441459i | \(0.145539\pi\) | |||||||
\(684\) | −40.8201 | −1.56080 | ||||||||
\(685\) | −46.6833 | −1.78368 | ||||||||
\(686\) | −11.5938 | −0.442652 | ||||||||
\(687\) | 17.2244 | 0.657151 | ||||||||
\(688\) | 7.59967 | 0.289735 | ||||||||
\(689\) | 4.40490 | 0.167813 | ||||||||
\(690\) | −21.0885 | −0.802824 | ||||||||
\(691\) | −21.0003 | −0.798890 | −0.399445 | − | 0.916757i | \(-0.630797\pi\) | ||||
−0.399445 | + | 0.916757i | \(0.630797\pi\) | |||||||
\(692\) | −30.2240 | −1.14894 | ||||||||
\(693\) | −23.8394 | −0.905582 | ||||||||
\(694\) | −8.71389 | −0.330775 | ||||||||
\(695\) | 21.1634 | 0.802772 | ||||||||
\(696\) | 73.1108 | 2.77126 | ||||||||
\(697\) | −32.0303 | −1.21324 | ||||||||
\(698\) | −22.9232 | −0.867657 | ||||||||
\(699\) | −9.43079 | −0.356705 | ||||||||
\(700\) | −18.3708 | −0.694351 | ||||||||
\(701\) | −28.9650 | −1.09399 | −0.546997 | − | 0.837135i | \(-0.684229\pi\) | ||||
−0.546997 | + | 0.837135i | \(0.684229\pi\) | |||||||
\(702\) | 15.7269 | 0.593572 | ||||||||
\(703\) | −1.72132 | −0.0649209 | ||||||||
\(704\) | −10.3987 | −0.391915 | ||||||||
\(705\) | 64.0075 | 2.41066 | ||||||||
\(706\) | 19.6626 | 0.740011 | ||||||||
\(707\) | 7.66200 | 0.288159 | ||||||||
\(708\) | −34.4946 | −1.29639 | ||||||||
\(709\) | 21.9719 | 0.825172 | 0.412586 | − | 0.910919i | \(-0.364626\pi\) | ||||
0.412586 | + | 0.910919i | \(0.364626\pi\) | |||||||
\(710\) | −11.7040 | −0.439243 | ||||||||
\(711\) | −7.84911 | −0.294365 | ||||||||
\(712\) | 22.1220 | 0.829058 | ||||||||
\(713\) | −3.47099 | −0.129990 | ||||||||
\(714\) | −18.3910 | −0.688265 | ||||||||
\(715\) | 51.8027 | 1.93731 | ||||||||
\(716\) | −2.08968 | −0.0780950 | ||||||||
\(717\) | −10.9308 | −0.408219 | ||||||||
\(718\) | 2.31758 | 0.0864914 | ||||||||
\(719\) | 13.7391 | 0.512383 | 0.256192 | − | 0.966626i | \(-0.417532\pi\) | ||||
0.256192 | + | 0.966626i | \(0.417532\pi\) | |||||||
\(720\) | 17.5292 | 0.653275 | ||||||||
\(721\) | −15.3237 | −0.570685 | ||||||||
\(722\) | 9.47388 | 0.352581 | ||||||||
\(723\) | −0.616680 | −0.0229346 | ||||||||
\(724\) | 18.7983 | 0.698633 | ||||||||
\(725\) | 104.544 | 3.88268 | ||||||||
\(726\) | −7.82158 | −0.290286 | ||||||||
\(727\) | 25.1173 | 0.931549 | 0.465775 | − | 0.884903i | \(-0.345776\pi\) | ||||
0.465775 | + | 0.884903i | \(0.345776\pi\) | |||||||
\(728\) | 10.8796 | 0.403225 | ||||||||
\(729\) | −42.1770 | −1.56211 | ||||||||
\(730\) | 7.09116 | 0.262456 | ||||||||
\(731\) | 61.0419 | 2.25772 | ||||||||
\(732\) | 53.6531 | 1.98308 | ||||||||
\(733\) | −27.5953 | −1.01925 | −0.509627 | − | 0.860395i | \(-0.670217\pi\) | ||||
−0.509627 | + | 0.860395i | \(0.670217\pi\) | |||||||
\(734\) | −16.7289 | −0.617476 | ||||||||
\(735\) | 62.0433 | 2.28850 | ||||||||
\(736\) | 14.4548 | 0.532813 | ||||||||
\(737\) | −53.9588 | −1.98760 | ||||||||
\(738\) | −17.8768 | −0.658053 | ||||||||
\(739\) | −8.87520 | −0.326480 | −0.163240 | − | 0.986586i | \(-0.552194\pi\) | ||||
−0.163240 | + | 0.986586i | \(0.552194\pi\) | |||||||
\(740\) | 1.72369 | 0.0633640 | ||||||||
\(741\) | 54.8370 | 2.01449 | ||||||||
\(742\) | −1.18926 | −0.0436590 | ||||||||
\(743\) | −8.92791 | −0.327533 | −0.163767 | − | 0.986499i | \(-0.552364\pi\) | ||||
−0.163767 | + | 0.986499i | \(0.552364\pi\) | |||||||
\(744\) | −10.4309 | −0.382416 | ||||||||
\(745\) | 45.2878 | 1.65922 | ||||||||
\(746\) | 11.3156 | 0.414292 | ||||||||
\(747\) | 36.8416 | 1.34796 | ||||||||
\(748\) | 37.8832 | 1.38515 | ||||||||
\(749\) | 2.66753 | 0.0974695 | ||||||||
\(750\) | −47.8629 | −1.74771 | ||||||||
\(751\) | −15.9026 | −0.580295 | −0.290148 | − | 0.956982i | \(-0.593704\pi\) | ||||
−0.290148 | + | 0.956982i | \(0.593704\pi\) | |||||||
\(752\) | −4.93510 | −0.179965 | ||||||||
\(753\) | 11.6250 | 0.423640 | ||||||||
\(754\) | −25.7311 | −0.937070 | ||||||||
\(755\) | 71.1356 | 2.58889 | ||||||||
\(756\) | 10.4535 | 0.380190 | ||||||||
\(757\) | 4.83918 | 0.175883 | 0.0879415 | − | 0.996126i | \(-0.471971\pi\) | ||||
0.0879415 | + | 0.996126i | \(0.471971\pi\) | |||||||
\(758\) | 6.86435 | 0.249324 | ||||||||
\(759\) | 26.8552 | 0.974782 | ||||||||
\(760\) | −57.6235 | −2.09022 | ||||||||
\(761\) | −29.7717 | −1.07923 | −0.539613 | − | 0.841913i | \(-0.681429\pi\) | ||||
−0.539613 | + | 0.841913i | \(0.681429\pi\) | |||||||
\(762\) | 9.00643 | 0.326269 | ||||||||
\(763\) | −18.7957 | −0.680450 | ||||||||
\(764\) | 15.2712 | 0.552491 | ||||||||
\(765\) | 140.798 | 5.09055 | ||||||||
\(766\) | 8.38736 | 0.303048 | ||||||||
\(767\) | 29.2116 | 1.05477 | ||||||||
\(768\) | 36.4090 | 1.31380 | ||||||||
\(769\) | −22.2455 | −0.802192 | −0.401096 | − | 0.916036i | \(-0.631371\pi\) | ||||
−0.401096 | + | 0.916036i | \(0.631371\pi\) | |||||||
\(770\) | −13.9859 | −0.504018 | ||||||||
\(771\) | −74.1135 | −2.66913 | ||||||||
\(772\) | 17.1734 | 0.618084 | ||||||||
\(773\) | 51.6779 | 1.85873 | 0.929363 | − | 0.369168i | \(-0.120357\pi\) | ||||
0.929363 | + | 0.369168i | \(0.120357\pi\) | |||||||
\(774\) | 34.0687 | 1.22457 | ||||||||
\(775\) | −14.9156 | −0.535786 | ||||||||
\(776\) | 11.8248 | 0.424485 | ||||||||
\(777\) | 1.06561 | 0.0382287 | ||||||||
\(778\) | 9.67792 | 0.346970 | ||||||||
\(779\) | −25.7852 | −0.923849 | ||||||||
\(780\) | −54.9124 | −1.96618 | ||||||||
\(781\) | 14.9045 | 0.533326 | ||||||||
\(782\) | 13.0600 | 0.467025 | ||||||||
\(783\) | −59.4887 | −2.12595 | ||||||||
\(784\) | −4.78366 | −0.170845 | ||||||||
\(785\) | 67.7193 | 2.41701 | ||||||||
\(786\) | 8.37102 | 0.298585 | ||||||||
\(787\) | −26.5874 | −0.947740 | −0.473870 | − | 0.880595i | \(-0.657143\pi\) | ||||
−0.473870 | + | 0.880595i | \(0.657143\pi\) | |||||||
\(788\) | −0.596140 | −0.0212366 | ||||||||
\(789\) | −39.9464 | −1.42213 | ||||||||
\(790\) | −4.60487 | −0.163834 | ||||||||
\(791\) | −8.33488 | −0.296354 | ||||||||
\(792\) | 50.8748 | 1.80776 | ||||||||
\(793\) | −45.4359 | −1.61348 | ||||||||
\(794\) | −8.77596 | −0.311447 | ||||||||
\(795\) | 14.4431 | 0.512245 | ||||||||
\(796\) | −4.93040 | −0.174753 | ||||||||
\(797\) | 34.9680 | 1.23863 | 0.619315 | − | 0.785142i | \(-0.287410\pi\) | ||||
0.619315 | + | 0.785142i | \(0.287410\pi\) | |||||||
\(798\) | −14.8052 | −0.524097 | ||||||||
\(799\) | −39.6396 | −1.40235 | ||||||||
\(800\) | 62.1157 | 2.19612 | ||||||||
\(801\) | −43.5140 | −1.53749 | ||||||||
\(802\) | 16.0562 | 0.566963 | ||||||||
\(803\) | −9.03028 | −0.318672 | ||||||||
\(804\) | 57.1979 | 2.01722 | ||||||||
\(805\) | 11.8705 | 0.418380 | ||||||||
\(806\) | 3.67112 | 0.129310 | ||||||||
\(807\) | 69.1976 | 2.43587 | ||||||||
\(808\) | −16.3512 | −0.575234 | ||||||||
\(809\) | 28.4777 | 1.00122 | 0.500611 | − | 0.865673i | \(-0.333109\pi\) | ||||
0.500611 | + | 0.865673i | \(0.333109\pi\) | |||||||
\(810\) | 5.49102 | 0.192935 | ||||||||
\(811\) | −35.8214 | −1.25786 | −0.628930 | − | 0.777462i | \(-0.716507\pi\) | ||||
−0.628930 | + | 0.777462i | \(0.716507\pi\) | |||||||
\(812\) | −17.1032 | −0.600205 | ||||||||
\(813\) | 25.3290 | 0.888326 | ||||||||
\(814\) | 0.891583 | 0.0312500 | ||||||||
\(815\) | −91.4164 | −3.20218 | ||||||||
\(816\) | −17.2209 | −0.602852 | ||||||||
\(817\) | 49.1401 | 1.71919 | ||||||||
\(818\) | −20.9169 | −0.731342 | ||||||||
\(819\) | −21.4002 | −0.747782 | ||||||||
\(820\) | 25.8206 | 0.901695 | ||||||||
\(821\) | −5.29485 | −0.184792 | −0.0923958 | − | 0.995722i | \(-0.529453\pi\) | ||||
−0.0923958 | + | 0.995722i | \(0.529453\pi\) | |||||||
\(822\) | 25.5966 | 0.892784 | ||||||||
\(823\) | −8.82882 | −0.307753 | −0.153877 | − | 0.988090i | \(-0.549176\pi\) | ||||
−0.153877 | + | 0.988090i | \(0.549176\pi\) | |||||||
\(824\) | 32.7018 | 1.13922 | ||||||||
\(825\) | 115.403 | 4.01781 | ||||||||
\(826\) | −7.88670 | −0.274413 | ||||||||
\(827\) | −34.3588 | −1.19477 | −0.597386 | − | 0.801954i | \(-0.703794\pi\) | ||||
−0.597386 | + | 0.801954i | \(0.703794\pi\) | |||||||
\(828\) | −17.9453 | −0.623644 | ||||||||
\(829\) | −23.0901 | −0.801952 | −0.400976 | − | 0.916089i | \(-0.631329\pi\) | ||||
−0.400976 | + | 0.916089i | \(0.631329\pi\) | |||||||
\(830\) | 21.6140 | 0.750234 | ||||||||
\(831\) | 16.3239 | 0.566270 | ||||||||
\(832\) | −9.33470 | −0.323623 | ||||||||
\(833\) | −38.4232 | −1.33129 | ||||||||
\(834\) | −11.6039 | −0.401812 | ||||||||
\(835\) | 49.0835 | 1.69860 | ||||||||
\(836\) | 30.4968 | 1.05475 | ||||||||
\(837\) | 8.48742 | 0.293368 | ||||||||
\(838\) | −5.41947 | −0.187212 | ||||||||
\(839\) | −3.97310 | −0.137166 | −0.0685832 | − | 0.997645i | \(-0.521848\pi\) | ||||
−0.0685832 | + | 0.997645i | \(0.521848\pi\) | |||||||
\(840\) | 35.6729 | 1.23083 | ||||||||
\(841\) | 68.3308 | 2.35624 | ||||||||
\(842\) | 1.52599 | 0.0525891 | ||||||||
\(843\) | 87.1638 | 3.00208 | ||||||||
\(844\) | 19.1720 | 0.659928 | ||||||||
\(845\) | −4.83834 | −0.166444 | ||||||||
\(846\) | −22.1237 | −0.760627 | ||||||||
\(847\) | 4.40269 | 0.151278 | ||||||||
\(848\) | −1.11359 | −0.0382409 | ||||||||
\(849\) | −53.7477 | −1.84462 | ||||||||
\(850\) | 56.1218 | 1.92496 | ||||||||
\(851\) | −0.756727 | −0.0259403 | ||||||||
\(852\) | −15.7992 | −0.541273 | ||||||||
\(853\) | 15.9096 | 0.544735 | 0.272368 | − | 0.962193i | \(-0.412193\pi\) | ||||
0.272368 | + | 0.962193i | \(0.412193\pi\) | |||||||
\(854\) | 12.2670 | 0.419768 | ||||||||
\(855\) | 113.345 | 3.87633 | ||||||||
\(856\) | −5.69269 | −0.194572 | ||||||||
\(857\) | 36.0112 | 1.23012 | 0.615060 | − | 0.788480i | \(-0.289132\pi\) | ||||
0.615060 | + | 0.788480i | \(0.289132\pi\) | |||||||
\(858\) | −28.4036 | −0.969683 | ||||||||
\(859\) | 54.2411 | 1.85068 | 0.925341 | − | 0.379135i | \(-0.123778\pi\) | ||||
0.925341 | + | 0.379135i | \(0.123778\pi\) | |||||||
\(860\) | −49.2077 | −1.67797 | ||||||||
\(861\) | 15.9628 | 0.544009 | ||||||||
\(862\) | −13.7512 | −0.468368 | ||||||||
\(863\) | 35.7257 | 1.21612 | 0.608058 | − | 0.793893i | \(-0.291949\pi\) | ||||
0.608058 | + | 0.793893i | \(0.291949\pi\) | |||||||
\(864\) | −35.3456 | −1.20248 | ||||||||
\(865\) | 83.9231 | 2.85347 | ||||||||
\(866\) | 10.8277 | 0.367942 | ||||||||
\(867\) | −89.8892 | −3.05280 | ||||||||
\(868\) | 2.44016 | 0.0828244 | ||||||||
\(869\) | 5.86409 | 0.198926 | ||||||||
\(870\) | −84.3690 | −2.86038 | ||||||||
\(871\) | −48.4378 | −1.64125 | ||||||||
\(872\) | 40.1113 | 1.35834 | ||||||||
\(873\) | −23.2593 | −0.787209 | ||||||||
\(874\) | 10.5136 | 0.355628 | ||||||||
\(875\) | 26.9416 | 0.910791 | ||||||||
\(876\) | 9.57237 | 0.323420 | ||||||||
\(877\) | −6.96680 | −0.235252 | −0.117626 | − | 0.993058i | \(-0.537528\pi\) | ||||
−0.117626 | + | 0.993058i | \(0.537528\pi\) | |||||||
\(878\) | 21.6249 | 0.729806 | ||||||||
\(879\) | −7.19179 | −0.242573 | ||||||||
\(880\) | −13.0961 | −0.441470 | ||||||||
\(881\) | −16.9809 | −0.572101 | −0.286051 | − | 0.958215i | \(-0.592343\pi\) | ||||
−0.286051 | + | 0.958215i | \(0.592343\pi\) | |||||||
\(882\) | −21.4448 | −0.722083 | ||||||||
\(883\) | −42.8928 | −1.44346 | −0.721729 | − | 0.692176i | \(-0.756652\pi\) | ||||
−0.721729 | + | 0.692176i | \(0.756652\pi\) | |||||||
\(884\) | 34.0071 | 1.14378 | ||||||||
\(885\) | 95.7814 | 3.21966 | ||||||||
\(886\) | −1.45781 | −0.0489760 | ||||||||
\(887\) | 27.7103 | 0.930419 | 0.465210 | − | 0.885201i | \(-0.345979\pi\) | ||||
0.465210 | + | 0.885201i | \(0.345979\pi\) | |||||||
\(888\) | −2.27409 | −0.0763135 | ||||||||
\(889\) | −5.06964 | −0.170030 | ||||||||
\(890\) | −25.5285 | −0.855718 | ||||||||
\(891\) | −6.99257 | −0.234260 | ||||||||
\(892\) | 28.1717 | 0.943257 | ||||||||
\(893\) | −31.9108 | −1.06785 | ||||||||
\(894\) | −24.8315 | −0.830489 | ||||||||
\(895\) | 5.80242 | 0.193954 | ||||||||
\(896\) | −11.7693 | −0.393186 | ||||||||
\(897\) | 24.1074 | 0.804924 | ||||||||
\(898\) | 1.19214 | 0.0397821 | ||||||||
\(899\) | −13.8865 | −0.463139 | ||||||||
\(900\) | −77.1152 | −2.57051 | ||||||||
\(901\) | −8.94458 | −0.297987 | ||||||||
\(902\) | 13.3558 | 0.444699 | ||||||||
\(903\) | −30.4211 | −1.01235 | ||||||||
\(904\) | 17.7872 | 0.591593 | ||||||||
\(905\) | −52.1972 | −1.73509 | ||||||||
\(906\) | −39.0039 | −1.29582 | ||||||||
\(907\) | −56.3584 | −1.87135 | −0.935675 | − | 0.352864i | \(-0.885208\pi\) | ||||
−0.935675 | + | 0.352864i | \(0.885208\pi\) | |||||||
\(908\) | −37.8774 | −1.25701 | ||||||||
\(909\) | 32.1628 | 1.06677 | ||||||||
\(910\) | −12.5549 | −0.416191 | ||||||||
\(911\) | −49.6557 | −1.64517 | −0.822583 | − | 0.568645i | \(-0.807468\pi\) | ||||
−0.822583 | + | 0.568645i | \(0.807468\pi\) | |||||||
\(912\) | −13.8632 | −0.459057 | ||||||||
\(913\) | −27.5245 | −0.910927 | ||||||||
\(914\) | 13.4466 | 0.444775 | ||||||||
\(915\) | −148.979 | −4.92509 | ||||||||
\(916\) | 8.59899 | 0.284119 | ||||||||
\(917\) | −4.71197 | −0.155603 | ||||||||
\(918\) | −31.9349 | −1.05401 | ||||||||
\(919\) | 4.82546 | 0.159177 | 0.0795886 | − | 0.996828i | \(-0.474639\pi\) | ||||
0.0795886 | + | 0.996828i | \(0.474639\pi\) | |||||||
\(920\) | −25.3324 | −0.835185 | ||||||||
\(921\) | 27.4506 | 0.904528 | ||||||||
\(922\) | −25.2271 | −0.830809 | ||||||||
\(923\) | 13.3795 | 0.440392 | ||||||||
\(924\) | −18.8796 | −0.621094 | ||||||||
\(925\) | −3.25183 | −0.106919 | ||||||||
\(926\) | −0.659714 | −0.0216795 | ||||||||
\(927\) | −64.3245 | −2.11269 | ||||||||
\(928\) | 57.8297 | 1.89835 | ||||||||
\(929\) | 24.5788 | 0.806403 | 0.403201 | − | 0.915111i | \(-0.367897\pi\) | ||||
0.403201 | + | 0.915111i | \(0.367897\pi\) | |||||||
\(930\) | 12.0371 | 0.394714 | ||||||||
\(931\) | −30.9316 | −1.01374 | ||||||||
\(932\) | −4.70817 | −0.154221 | ||||||||
\(933\) | −26.8340 | −0.878506 | ||||||||
\(934\) | 18.3306 | 0.599796 | ||||||||
\(935\) | −105.190 | −3.44009 | ||||||||
\(936\) | 45.6694 | 1.49275 | ||||||||
\(937\) | 40.5183 | 1.32367 | 0.661837 | − | 0.749647i | \(-0.269777\pi\) | ||||
0.661837 | + | 0.749647i | \(0.269777\pi\) | |||||||
\(938\) | 13.0775 | 0.426995 | ||||||||
\(939\) | −9.33765 | −0.304723 | ||||||||
\(940\) | 31.9547 | 1.04225 | ||||||||
\(941\) | −19.8349 | −0.646599 | −0.323299 | − | 0.946297i | \(-0.604792\pi\) | ||||
−0.323299 | + | 0.946297i | \(0.604792\pi\) | |||||||
\(942\) | −37.1308 | −1.20979 | ||||||||
\(943\) | −11.3357 | −0.369140 | ||||||||
\(944\) | −7.38493 | −0.240359 | ||||||||
\(945\) | −29.0262 | −0.944224 | ||||||||
\(946\) | −25.4528 | −0.827542 | ||||||||
\(947\) | 41.6395 | 1.35310 | 0.676550 | − | 0.736397i | \(-0.263474\pi\) | ||||
0.676550 | + | 0.736397i | \(0.263474\pi\) | |||||||
\(948\) | −6.21611 | −0.201890 | ||||||||
\(949\) | −8.10632 | −0.263142 | ||||||||
\(950\) | 45.1794 | 1.46581 | ||||||||
\(951\) | 64.3878 | 2.08792 | ||||||||
\(952\) | −22.0921 | −0.716009 | ||||||||
\(953\) | −36.2310 | −1.17364 | −0.586819 | − | 0.809718i | \(-0.699620\pi\) | ||||
−0.586819 | + | 0.809718i | \(0.699620\pi\) | |||||||
\(954\) | −4.99215 | −0.161627 | ||||||||
\(955\) | −42.4034 | −1.37214 | ||||||||
\(956\) | −5.45702 | −0.176493 | ||||||||
\(957\) | 107.440 | 3.47304 | ||||||||
\(958\) | 9.23819 | 0.298472 | ||||||||
\(959\) | −14.4081 | −0.465262 | ||||||||
\(960\) | −30.6073 | −0.987848 | ||||||||
\(961\) | −29.0188 | −0.936090 | ||||||||
\(962\) | 0.800358 | 0.0258046 | ||||||||
\(963\) | 11.1975 | 0.360835 | ||||||||
\(964\) | −0.307867 | −0.00991573 | ||||||||
\(965\) | −47.6854 | −1.53505 | ||||||||
\(966\) | −6.50864 | −0.209412 | ||||||||
\(967\) | −4.48485 | −0.144223 | −0.0721115 | − | 0.997397i | \(-0.522974\pi\) | ||||
−0.0721115 | + | 0.997397i | \(0.522974\pi\) | |||||||
\(968\) | −9.39564 | −0.301987 | ||||||||
\(969\) | −111.352 | −3.57714 | ||||||||
\(970\) | −13.6456 | −0.438135 | ||||||||
\(971\) | −38.4426 | −1.23368 | −0.616841 | − | 0.787088i | \(-0.711588\pi\) | ||||
−0.616841 | + | 0.787088i | \(0.711588\pi\) | |||||||
\(972\) | −18.3165 | −0.587501 | ||||||||
\(973\) | 6.53175 | 0.209398 | ||||||||
\(974\) | −15.8716 | −0.508560 | ||||||||
\(975\) | 103.595 | 3.31770 | ||||||||
\(976\) | 11.4866 | 0.367676 | ||||||||
\(977\) | 18.9004 | 0.604679 | 0.302339 | − | 0.953200i | \(-0.402232\pi\) | ||||
0.302339 | + | 0.953200i | \(0.402232\pi\) | |||||||
\(978\) | 50.1240 | 1.60279 | ||||||||
\(979\) | 32.5094 | 1.03901 | ||||||||
\(980\) | 30.9741 | 0.989431 | ||||||||
\(981\) | −78.8988 | −2.51904 | ||||||||
\(982\) | 11.7913 | 0.376277 | ||||||||
\(983\) | 5.89154 | 0.187911 | 0.0939554 | − | 0.995576i | \(-0.470049\pi\) | ||||
0.0939554 | + | 0.995576i | \(0.470049\pi\) | |||||||
\(984\) | −34.0656 | −1.08597 | ||||||||
\(985\) | 1.65530 | 0.0527423 | ||||||||
\(986\) | 52.2494 | 1.66396 | ||||||||
\(987\) | 19.7550 | 0.628807 | ||||||||
\(988\) | 27.3765 | 0.870961 | ||||||||
\(989\) | 21.6030 | 0.686934 | ||||||||
\(990\) | −58.7088 | −1.86589 | ||||||||
\(991\) | 29.8184 | 0.947212 | 0.473606 | − | 0.880737i | \(-0.342952\pi\) | ||||
0.473606 | + | 0.880737i | \(0.342952\pi\) | |||||||
\(992\) | −8.25072 | −0.261961 | ||||||||
\(993\) | 3.02193 | 0.0958981 | ||||||||
\(994\) | −3.61227 | −0.114574 | ||||||||
\(995\) | 13.6903 | 0.434010 | ||||||||
\(996\) | 29.1768 | 0.924502 | ||||||||
\(997\) | −37.7350 | −1.19508 | −0.597540 | − | 0.801839i | \(-0.703855\pi\) | ||||
−0.597540 | + | 0.801839i | \(0.703855\pi\) | |||||||
\(998\) | −25.3131 | −0.801272 | ||||||||
\(999\) | 1.85038 | 0.0585435 |
(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 | 547.2.a.c.1.15 | ✓ | 25 | |
3.2 | odd | 2 | 4923.2.a.n.1.11 | 25 | |||
4.3 | odd | 2 | 8752.2.a.v.1.25 | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
547.2.a.c.1.15 | ✓ | 25 | 1.1 | even | 1 | trivial | |
4923.2.a.n.1.11 | 25 | 3.2 | odd | 2 | |||
8752.2.a.v.1.25 | 25 | 4.3 | odd | 2 |