Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4015,2,Mod(1,4015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4015 = 5 \cdot 11 \cdot 73 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4015.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: | \(32.0599364115\) |
Analytic rank: | \(0\) |
Dimension: | \(37\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 4015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.70375 | −1.91184 | −0.955921 | − | 0.293624i | \(-0.905139\pi\) | ||||
−0.955921 | + | 0.293624i | \(0.905139\pi\) | |||||||
\(3\) | −1.27224 | −0.734530 | −0.367265 | − | 0.930116i | \(-0.619706\pi\) | ||||
−0.367265 | + | 0.930116i | \(0.619706\pi\) | |||||||
\(4\) | 5.31028 | 2.65514 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 3.43983 | 1.40431 | ||||||||
\(7\) | −0.968765 | −0.366159 | −0.183079 | − | 0.983098i | \(-0.558607\pi\) | ||||
−0.183079 | + | 0.983098i | \(0.558607\pi\) | |||||||
\(8\) | −8.95019 | −3.16437 | ||||||||
\(9\) | −1.38140 | −0.460465 | ||||||||
\(10\) | −2.70375 | −0.855002 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −6.75597 | −1.95028 | ||||||||
\(13\) | 1.17856 | 0.326875 | 0.163437 | − | 0.986554i | \(-0.447742\pi\) | ||||
0.163437 | + | 0.986554i | \(0.447742\pi\) | |||||||
\(14\) | 2.61930 | 0.700038 | ||||||||
\(15\) | −1.27224 | −0.328492 | ||||||||
\(16\) | 13.5785 | 3.39463 | ||||||||
\(17\) | −1.19285 | −0.289308 | −0.144654 | − | 0.989482i | \(-0.546207\pi\) | ||||
−0.144654 | + | 0.989482i | \(0.546207\pi\) | |||||||
\(18\) | 3.73495 | 0.880337 | ||||||||
\(19\) | 4.63111 | 1.06245 | 0.531225 | − | 0.847231i | \(-0.321732\pi\) | ||||
0.531225 | + | 0.847231i | \(0.321732\pi\) | |||||||
\(20\) | 5.31028 | 1.18742 | ||||||||
\(21\) | 1.23250 | 0.268955 | ||||||||
\(22\) | −2.70375 | −0.576442 | ||||||||
\(23\) | 3.13145 | 0.652952 | 0.326476 | − | 0.945205i | \(-0.394139\pi\) | ||||
0.326476 | + | 0.945205i | \(0.394139\pi\) | |||||||
\(24\) | 11.3868 | 2.32432 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −3.18655 | −0.624933 | ||||||||
\(27\) | 5.57420 | 1.07276 | ||||||||
\(28\) | −5.14441 | −0.972203 | ||||||||
\(29\) | 9.52697 | 1.76911 | 0.884557 | − | 0.466432i | \(-0.154461\pi\) | ||||
0.884557 | + | 0.466432i | \(0.154461\pi\) | |||||||
\(30\) | 3.43983 | 0.628025 | ||||||||
\(31\) | −7.86250 | −1.41215 | −0.706074 | − | 0.708138i | \(-0.749535\pi\) | ||||
−0.706074 | + | 0.708138i | \(0.749535\pi\) | |||||||
\(32\) | −18.8126 | −3.32563 | ||||||||
\(33\) | −1.27224 | −0.221469 | ||||||||
\(34\) | 3.22517 | 0.553112 | ||||||||
\(35\) | −0.968765 | −0.163751 | ||||||||
\(36\) | −7.33560 | −1.22260 | ||||||||
\(37\) | −4.17187 | −0.685851 | −0.342925 | − | 0.939363i | \(-0.611418\pi\) | ||||
−0.342925 | + | 0.939363i | \(0.611418\pi\) | |||||||
\(38\) | −12.5214 | −2.03124 | ||||||||
\(39\) | −1.49942 | −0.240099 | ||||||||
\(40\) | −8.95019 | −1.41515 | ||||||||
\(41\) | 2.33996 | 0.365440 | 0.182720 | − | 0.983165i | \(-0.441510\pi\) | ||||
0.182720 | + | 0.983165i | \(0.441510\pi\) | |||||||
\(42\) | −3.33239 | −0.514199 | ||||||||
\(43\) | −5.79300 | −0.883424 | −0.441712 | − | 0.897157i | \(-0.645629\pi\) | ||||
−0.441712 | + | 0.897157i | \(0.645629\pi\) | |||||||
\(44\) | 5.31028 | 0.800555 | ||||||||
\(45\) | −1.38140 | −0.205926 | ||||||||
\(46\) | −8.46666 | −1.24834 | ||||||||
\(47\) | 3.18307 | 0.464299 | 0.232149 | − | 0.972680i | \(-0.425424\pi\) | ||||
0.232149 | + | 0.972680i | \(0.425424\pi\) | |||||||
\(48\) | −17.2752 | −2.49346 | ||||||||
\(49\) | −6.06150 | −0.865928 | ||||||||
\(50\) | −2.70375 | −0.382368 | ||||||||
\(51\) | 1.51759 | 0.212506 | ||||||||
\(52\) | 6.25851 | 0.867899 | ||||||||
\(53\) | −2.16838 | −0.297850 | −0.148925 | − | 0.988849i | \(-0.547581\pi\) | ||||
−0.148925 | + | 0.988849i | \(0.547581\pi\) | |||||||
\(54\) | −15.0713 | −2.05094 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 8.67062 | 1.15866 | ||||||||
\(57\) | −5.89191 | −0.780402 | ||||||||
\(58\) | −25.7586 | −3.38227 | ||||||||
\(59\) | 9.54460 | 1.24260 | 0.621300 | − | 0.783573i | \(-0.286605\pi\) | ||||
0.621300 | + | 0.783573i | \(0.286605\pi\) | |||||||
\(60\) | −6.75597 | −0.872192 | ||||||||
\(61\) | 2.24895 | 0.287948 | 0.143974 | − | 0.989581i | \(-0.454012\pi\) | ||||
0.143974 | + | 0.989581i | \(0.454012\pi\) | |||||||
\(62\) | 21.2583 | 2.69980 | ||||||||
\(63\) | 1.33825 | 0.168603 | ||||||||
\(64\) | 23.7076 | 2.96345 | ||||||||
\(65\) | 1.17856 | 0.146183 | ||||||||
\(66\) | 3.43983 | 0.423414 | ||||||||
\(67\) | −10.7576 | −1.31425 | −0.657126 | − | 0.753781i | \(-0.728228\pi\) | ||||
−0.657126 | + | 0.753781i | \(0.728228\pi\) | |||||||
\(68\) | −6.33436 | −0.768154 | ||||||||
\(69\) | −3.98397 | −0.479613 | ||||||||
\(70\) | 2.61930 | 0.313066 | ||||||||
\(71\) | 9.15992 | 1.08708 | 0.543541 | − | 0.839382i | \(-0.317083\pi\) | ||||
0.543541 | + | 0.839382i | \(0.317083\pi\) | |||||||
\(72\) | 12.3637 | 1.45708 | ||||||||
\(73\) | 1.00000 | 0.117041 | ||||||||
\(74\) | 11.2797 | 1.31124 | ||||||||
\(75\) | −1.27224 | −0.146906 | ||||||||
\(76\) | 24.5925 | 2.82096 | ||||||||
\(77\) | −0.968765 | −0.110401 | ||||||||
\(78\) | 4.05406 | 0.459032 | ||||||||
\(79\) | 5.23984 | 0.589528 | 0.294764 | − | 0.955570i | \(-0.404759\pi\) | ||||
0.294764 | + | 0.955570i | \(0.404759\pi\) | |||||||
\(80\) | 13.5785 | 1.51813 | ||||||||
\(81\) | −2.94756 | −0.327507 | ||||||||
\(82\) | −6.32667 | −0.698664 | ||||||||
\(83\) | 6.06424 | 0.665637 | 0.332818 | − | 0.942991i | \(-0.392000\pi\) | ||||
0.332818 | + | 0.942991i | \(0.392000\pi\) | |||||||
\(84\) | 6.54495 | 0.714112 | ||||||||
\(85\) | −1.19285 | −0.129383 | ||||||||
\(86\) | 15.6628 | 1.68897 | ||||||||
\(87\) | −12.1206 | −1.29947 | ||||||||
\(88\) | −8.95019 | −0.954093 | ||||||||
\(89\) | −14.1945 | −1.50461 | −0.752306 | − | 0.658814i | \(-0.771058\pi\) | ||||
−0.752306 | + | 0.658814i | \(0.771058\pi\) | |||||||
\(90\) | 3.73495 | 0.393699 | ||||||||
\(91\) | −1.14175 | −0.119688 | ||||||||
\(92\) | 16.6289 | 1.73368 | ||||||||
\(93\) | 10.0030 | 1.03727 | ||||||||
\(94\) | −8.60624 | −0.887666 | ||||||||
\(95\) | 4.63111 | 0.475142 | ||||||||
\(96\) | 23.9342 | 2.44278 | ||||||||
\(97\) | −2.72029 | −0.276204 | −0.138102 | − | 0.990418i | \(-0.544100\pi\) | ||||
−0.138102 | + | 0.990418i | \(0.544100\pi\) | |||||||
\(98\) | 16.3888 | 1.65552 | ||||||||
\(99\) | −1.38140 | −0.138835 | ||||||||
\(100\) | 5.31028 | 0.531028 | ||||||||
\(101\) | 17.5380 | 1.74509 | 0.872547 | − | 0.488531i | \(-0.162467\pi\) | ||||
0.872547 | + | 0.488531i | \(0.162467\pi\) | |||||||
\(102\) | −4.10320 | −0.406277 | ||||||||
\(103\) | 3.49675 | 0.344545 | 0.172273 | − | 0.985049i | \(-0.444889\pi\) | ||||
0.172273 | + | 0.985049i | \(0.444889\pi\) | |||||||
\(104\) | −10.5484 | −1.03435 | ||||||||
\(105\) | 1.23250 | 0.120280 | ||||||||
\(106\) | 5.86276 | 0.569441 | ||||||||
\(107\) | −15.6762 | −1.51548 | −0.757739 | − | 0.652558i | \(-0.773696\pi\) | ||||
−0.757739 | + | 0.652558i | \(0.773696\pi\) | |||||||
\(108\) | 29.6006 | 2.84832 | ||||||||
\(109\) | 8.59662 | 0.823407 | 0.411703 | − | 0.911318i | \(-0.364934\pi\) | ||||
0.411703 | + | 0.911318i | \(0.364934\pi\) | |||||||
\(110\) | −2.70375 | −0.257793 | ||||||||
\(111\) | 5.30763 | 0.503778 | ||||||||
\(112\) | −13.1544 | −1.24297 | ||||||||
\(113\) | −8.64672 | −0.813415 | −0.406708 | − | 0.913558i | \(-0.633323\pi\) | ||||
−0.406708 | + | 0.913558i | \(0.633323\pi\) | |||||||
\(114\) | 15.9303 | 1.49201 | ||||||||
\(115\) | 3.13145 | 0.292009 | ||||||||
\(116\) | 50.5909 | 4.69725 | ||||||||
\(117\) | −1.62806 | −0.150514 | ||||||||
\(118\) | −25.8062 | −2.37566 | ||||||||
\(119\) | 1.15559 | 0.105933 | ||||||||
\(120\) | 11.3868 | 1.03947 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −6.08060 | −0.550512 | ||||||||
\(123\) | −2.97700 | −0.268427 | ||||||||
\(124\) | −41.7521 | −3.74945 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −3.61829 | −0.322343 | ||||||||
\(127\) | 16.7348 | 1.48497 | 0.742487 | − | 0.669861i | \(-0.233646\pi\) | ||||
0.742487 | + | 0.669861i | \(0.233646\pi\) | |||||||
\(128\) | −26.4743 | −2.34002 | ||||||||
\(129\) | 7.37011 | 0.648902 | ||||||||
\(130\) | −3.18655 | −0.279479 | ||||||||
\(131\) | −21.5488 | −1.88273 | −0.941365 | − | 0.337389i | \(-0.890456\pi\) | ||||
−0.941365 | + | 0.337389i | \(0.890456\pi\) | |||||||
\(132\) | −6.75597 | −0.588032 | ||||||||
\(133\) | −4.48646 | −0.389025 | ||||||||
\(134\) | 29.0859 | 2.51264 | ||||||||
\(135\) | 5.57420 | 0.479751 | ||||||||
\(136\) | 10.6762 | 0.915477 | ||||||||
\(137\) | −8.20987 | −0.701417 | −0.350708 | − | 0.936485i | \(-0.614059\pi\) | ||||
−0.350708 | + | 0.936485i | \(0.614059\pi\) | |||||||
\(138\) | 10.7717 | 0.916945 | ||||||||
\(139\) | −15.2511 | −1.29358 | −0.646789 | − | 0.762669i | \(-0.723888\pi\) | ||||
−0.646789 | + | 0.762669i | \(0.723888\pi\) | |||||||
\(140\) | −5.14441 | −0.434782 | ||||||||
\(141\) | −4.04964 | −0.341041 | ||||||||
\(142\) | −24.7662 | −2.07833 | ||||||||
\(143\) | 1.17856 | 0.0985565 | ||||||||
\(144\) | −18.7573 | −1.56311 | ||||||||
\(145\) | 9.52697 | 0.791172 | ||||||||
\(146\) | −2.70375 | −0.223764 | ||||||||
\(147\) | 7.71170 | 0.636050 | ||||||||
\(148\) | −22.1538 | −1.82103 | ||||||||
\(149\) | 18.5819 | 1.52229 | 0.761144 | − | 0.648583i | \(-0.224638\pi\) | ||||
0.761144 | + | 0.648583i | \(0.224638\pi\) | |||||||
\(150\) | 3.43983 | 0.280861 | ||||||||
\(151\) | −5.47867 | −0.445848 | −0.222924 | − | 0.974836i | \(-0.571560\pi\) | ||||
−0.222924 | + | 0.974836i | \(0.571560\pi\) | |||||||
\(152\) | −41.4493 | −3.36198 | ||||||||
\(153\) | 1.64779 | 0.133216 | ||||||||
\(154\) | 2.61930 | 0.211069 | ||||||||
\(155\) | −7.86250 | −0.631532 | ||||||||
\(156\) | −7.96235 | −0.637498 | ||||||||
\(157\) | 8.18386 | 0.653143 | 0.326571 | − | 0.945173i | \(-0.394107\pi\) | ||||
0.326571 | + | 0.945173i | \(0.394107\pi\) | |||||||
\(158\) | −14.1672 | −1.12708 | ||||||||
\(159\) | 2.75871 | 0.218780 | ||||||||
\(160\) | −18.8126 | −1.48727 | ||||||||
\(161\) | −3.03364 | −0.239084 | ||||||||
\(162\) | 7.96947 | 0.626141 | ||||||||
\(163\) | 2.24631 | 0.175945 | 0.0879724 | − | 0.996123i | \(-0.471961\pi\) | ||||
0.0879724 | + | 0.996123i | \(0.471961\pi\) | |||||||
\(164\) | 12.4258 | 0.970295 | ||||||||
\(165\) | −1.27224 | −0.0990440 | ||||||||
\(166\) | −16.3962 | −1.27259 | ||||||||
\(167\) | 9.48520 | 0.733987 | 0.366993 | − | 0.930224i | \(-0.380387\pi\) | ||||
0.366993 | + | 0.930224i | \(0.380387\pi\) | |||||||
\(168\) | −11.0311 | −0.851071 | ||||||||
\(169\) | −11.6110 | −0.893153 | ||||||||
\(170\) | 3.22517 | 0.247359 | ||||||||
\(171\) | −6.39740 | −0.489221 | ||||||||
\(172\) | −30.7625 | −2.34562 | ||||||||
\(173\) | 3.11794 | 0.237053 | 0.118526 | − | 0.992951i | \(-0.462183\pi\) | ||||
0.118526 | + | 0.992951i | \(0.462183\pi\) | |||||||
\(174\) | 32.7712 | 2.48438 | ||||||||
\(175\) | −0.968765 | −0.0732317 | ||||||||
\(176\) | 13.5785 | 1.02352 | ||||||||
\(177\) | −12.1431 | −0.912728 | ||||||||
\(178\) | 38.3784 | 2.87658 | ||||||||
\(179\) | 13.6553 | 1.02064 | 0.510321 | − | 0.859984i | \(-0.329527\pi\) | ||||
0.510321 | + | 0.859984i | \(0.329527\pi\) | |||||||
\(180\) | −7.33560 | −0.546763 | ||||||||
\(181\) | 2.15937 | 0.160505 | 0.0802525 | − | 0.996775i | \(-0.474427\pi\) | ||||
0.0802525 | + | 0.996775i | \(0.474427\pi\) | |||||||
\(182\) | 3.08701 | 0.228825 | ||||||||
\(183\) | −2.86121 | −0.211507 | ||||||||
\(184\) | −28.0270 | −2.06618 | ||||||||
\(185\) | −4.17187 | −0.306722 | ||||||||
\(186\) | −27.0457 | −1.98309 | ||||||||
\(187\) | −1.19285 | −0.0872297 | ||||||||
\(188\) | 16.9030 | 1.23278 | ||||||||
\(189\) | −5.40009 | −0.392799 | ||||||||
\(190\) | −12.5214 | −0.908397 | ||||||||
\(191\) | 9.47771 | 0.685783 | 0.342892 | − | 0.939375i | \(-0.388594\pi\) | ||||
0.342892 | + | 0.939375i | \(0.388594\pi\) | |||||||
\(192\) | −30.1619 | −2.17675 | ||||||||
\(193\) | −13.6330 | −0.981323 | −0.490661 | − | 0.871350i | \(-0.663245\pi\) | ||||
−0.490661 | + | 0.871350i | \(0.663245\pi\) | |||||||
\(194\) | 7.35501 | 0.528059 | ||||||||
\(195\) | −1.49942 | −0.107376 | ||||||||
\(196\) | −32.1882 | −2.29916 | ||||||||
\(197\) | 21.7011 | 1.54614 | 0.773069 | − | 0.634322i | \(-0.218721\pi\) | ||||
0.773069 | + | 0.634322i | \(0.218721\pi\) | |||||||
\(198\) | 3.73495 | 0.265432 | ||||||||
\(199\) | −20.2297 | −1.43404 | −0.717022 | − | 0.697051i | \(-0.754495\pi\) | ||||
−0.717022 | + | 0.697051i | \(0.754495\pi\) | |||||||
\(200\) | −8.95019 | −0.632874 | ||||||||
\(201\) | 13.6863 | 0.965358 | ||||||||
\(202\) | −47.4184 | −3.33634 | ||||||||
\(203\) | −9.22939 | −0.647776 | ||||||||
\(204\) | 8.05885 | 0.564232 | ||||||||
\(205\) | 2.33996 | 0.163430 | ||||||||
\(206\) | −9.45436 | −0.658716 | ||||||||
\(207\) | −4.32577 | −0.300662 | ||||||||
\(208\) | 16.0032 | 1.10962 | ||||||||
\(209\) | 4.63111 | 0.320341 | ||||||||
\(210\) | −3.33239 | −0.229957 | ||||||||
\(211\) | −9.81658 | −0.675801 | −0.337901 | − | 0.941182i | \(-0.609717\pi\) | ||||
−0.337901 | + | 0.941182i | \(0.609717\pi\) | |||||||
\(212\) | −11.5147 | −0.790833 | ||||||||
\(213\) | −11.6537 | −0.798495 | ||||||||
\(214\) | 42.3846 | 2.89735 | ||||||||
\(215\) | −5.79300 | −0.395079 | ||||||||
\(216\) | −49.8902 | −3.39460 | ||||||||
\(217\) | 7.61692 | 0.517070 | ||||||||
\(218\) | −23.2431 | −1.57422 | ||||||||
\(219\) | −1.27224 | −0.0859703 | ||||||||
\(220\) | 5.31028 | 0.358019 | ||||||||
\(221\) | −1.40585 | −0.0945675 | ||||||||
\(222\) | −14.3505 | −0.963144 | ||||||||
\(223\) | −3.61113 | −0.241819 | −0.120910 | − | 0.992664i | \(-0.538581\pi\) | ||||
−0.120910 | + | 0.992664i | \(0.538581\pi\) | |||||||
\(224\) | 18.2250 | 1.21771 | ||||||||
\(225\) | −1.38140 | −0.0920930 | ||||||||
\(226\) | 23.3786 | 1.55512 | ||||||||
\(227\) | 14.9233 | 0.990495 | 0.495247 | − | 0.868752i | \(-0.335077\pi\) | ||||
0.495247 | + | 0.868752i | \(0.335077\pi\) | |||||||
\(228\) | −31.2877 | −2.07208 | ||||||||
\(229\) | 23.6020 | 1.55966 | 0.779832 | − | 0.625989i | \(-0.215305\pi\) | ||||
0.779832 | + | 0.625989i | \(0.215305\pi\) | |||||||
\(230\) | −8.46666 | −0.558275 | ||||||||
\(231\) | 1.23250 | 0.0810929 | ||||||||
\(232\) | −85.2681 | −5.59813 | ||||||||
\(233\) | 10.9690 | 0.718604 | 0.359302 | − | 0.933221i | \(-0.383015\pi\) | ||||
0.359302 | + | 0.933221i | \(0.383015\pi\) | |||||||
\(234\) | 4.40188 | 0.287760 | ||||||||
\(235\) | 3.18307 | 0.207641 | ||||||||
\(236\) | 50.6845 | 3.29928 | ||||||||
\(237\) | −6.66635 | −0.433026 | ||||||||
\(238\) | −3.12443 | −0.202527 | ||||||||
\(239\) | −23.1920 | −1.50016 | −0.750082 | − | 0.661345i | \(-0.769986\pi\) | ||||
−0.750082 | + | 0.661345i | \(0.769986\pi\) | |||||||
\(240\) | −17.2752 | −1.11511 | ||||||||
\(241\) | 4.16361 | 0.268202 | 0.134101 | − | 0.990968i | \(-0.457185\pi\) | ||||
0.134101 | + | 0.990968i | \(0.457185\pi\) | |||||||
\(242\) | −2.70375 | −0.173804 | ||||||||
\(243\) | −12.9726 | −0.832192 | ||||||||
\(244\) | 11.9425 | 0.764543 | ||||||||
\(245\) | −6.06150 | −0.387255 | ||||||||
\(246\) | 8.04907 | 0.513190 | ||||||||
\(247\) | 5.45806 | 0.347288 | ||||||||
\(248\) | 70.3709 | 4.46855 | ||||||||
\(249\) | −7.71519 | −0.488930 | ||||||||
\(250\) | −2.70375 | −0.171000 | ||||||||
\(251\) | −18.2743 | −1.15347 | −0.576733 | − | 0.816933i | \(-0.695673\pi\) | ||||
−0.576733 | + | 0.816933i | \(0.695673\pi\) | |||||||
\(252\) | 7.10647 | 0.447666 | ||||||||
\(253\) | 3.13145 | 0.196872 | ||||||||
\(254\) | −45.2468 | −2.83903 | ||||||||
\(255\) | 1.51759 | 0.0950354 | ||||||||
\(256\) | 24.1648 | 1.51030 | ||||||||
\(257\) | 14.5172 | 0.905561 | 0.452780 | − | 0.891622i | \(-0.350432\pi\) | ||||
0.452780 | + | 0.891622i | \(0.350432\pi\) | |||||||
\(258\) | −19.9269 | −1.24060 | ||||||||
\(259\) | 4.04156 | 0.251130 | ||||||||
\(260\) | 6.25851 | 0.388136 | ||||||||
\(261\) | −13.1605 | −0.814615 | ||||||||
\(262\) | 58.2627 | 3.59948 | ||||||||
\(263\) | −12.2954 | −0.758168 | −0.379084 | − | 0.925362i | \(-0.623761\pi\) | ||||
−0.379084 | + | 0.925362i | \(0.623761\pi\) | |||||||
\(264\) | 11.3868 | 0.700810 | ||||||||
\(265\) | −2.16838 | −0.133202 | ||||||||
\(266\) | 12.1303 | 0.743755 | ||||||||
\(267\) | 18.0588 | 1.10518 | ||||||||
\(268\) | −57.1260 | −3.48952 | ||||||||
\(269\) | −5.35815 | −0.326692 | −0.163346 | − | 0.986569i | \(-0.552229\pi\) | ||||
−0.163346 | + | 0.986569i | \(0.552229\pi\) | |||||||
\(270\) | −15.0713 | −0.917208 | ||||||||
\(271\) | −14.2061 | −0.862957 | −0.431478 | − | 0.902123i | \(-0.642008\pi\) | ||||
−0.431478 | + | 0.902123i | \(0.642008\pi\) | |||||||
\(272\) | −16.1971 | −0.982095 | ||||||||
\(273\) | 1.45259 | 0.0879145 | ||||||||
\(274\) | 22.1975 | 1.34100 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | −21.1560 | −1.27344 | ||||||||
\(277\) | 20.3216 | 1.22101 | 0.610504 | − | 0.792013i | \(-0.290967\pi\) | ||||
0.610504 | + | 0.792013i | \(0.290967\pi\) | |||||||
\(278\) | 41.2351 | 2.47312 | ||||||||
\(279\) | 10.8612 | 0.650245 | ||||||||
\(280\) | 8.67062 | 0.518169 | ||||||||
\(281\) | 10.0021 | 0.596674 | 0.298337 | − | 0.954461i | \(-0.403568\pi\) | ||||
0.298337 | + | 0.954461i | \(0.403568\pi\) | |||||||
\(282\) | 10.9492 | 0.652018 | ||||||||
\(283\) | 15.4115 | 0.916120 | 0.458060 | − | 0.888921i | \(-0.348544\pi\) | ||||
0.458060 | + | 0.888921i | \(0.348544\pi\) | |||||||
\(284\) | 48.6418 | 2.88636 | ||||||||
\(285\) | −5.89191 | −0.349006 | ||||||||
\(286\) | −3.18655 | −0.188424 | ||||||||
\(287\) | −2.26687 | −0.133809 | ||||||||
\(288\) | 25.9877 | 1.53134 | ||||||||
\(289\) | −15.5771 | −0.916301 | ||||||||
\(290\) | −25.7586 | −1.51260 | ||||||||
\(291\) | 3.46088 | 0.202880 | ||||||||
\(292\) | 5.31028 | 0.310761 | ||||||||
\(293\) | 0.927528 | 0.0541868 | 0.0270934 | − | 0.999633i | \(-0.491375\pi\) | ||||
0.0270934 | + | 0.999633i | \(0.491375\pi\) | |||||||
\(294\) | −20.8505 | −1.21603 | ||||||||
\(295\) | 9.54460 | 0.555708 | ||||||||
\(296\) | 37.3390 | 2.17028 | ||||||||
\(297\) | 5.57420 | 0.323448 | ||||||||
\(298\) | −50.2409 | −2.91037 | ||||||||
\(299\) | 3.69061 | 0.213434 | ||||||||
\(300\) | −6.75597 | −0.390056 | ||||||||
\(301\) | 5.61205 | 0.323473 | ||||||||
\(302\) | 14.8130 | 0.852391 | ||||||||
\(303\) | −22.3126 | −1.28182 | ||||||||
\(304\) | 62.8837 | 3.60663 | ||||||||
\(305\) | 2.24895 | 0.128774 | ||||||||
\(306\) | −4.45523 | −0.254689 | ||||||||
\(307\) | 14.4001 | 0.821857 | 0.410929 | − | 0.911668i | \(-0.365205\pi\) | ||||
0.410929 | + | 0.911668i | \(0.365205\pi\) | |||||||
\(308\) | −5.14441 | −0.293130 | ||||||||
\(309\) | −4.44872 | −0.253079 | ||||||||
\(310\) | 21.2583 | 1.20739 | ||||||||
\(311\) | −11.4706 | −0.650440 | −0.325220 | − | 0.945638i | \(-0.605438\pi\) | ||||
−0.325220 | + | 0.945638i | \(0.605438\pi\) | |||||||
\(312\) | 13.4201 | 0.759763 | ||||||||
\(313\) | −27.3078 | −1.54353 | −0.771763 | − | 0.635910i | \(-0.780625\pi\) | ||||
−0.771763 | + | 0.635910i | \(0.780625\pi\) | |||||||
\(314\) | −22.1271 | −1.24871 | ||||||||
\(315\) | 1.33825 | 0.0754017 | ||||||||
\(316\) | 27.8250 | 1.56528 | ||||||||
\(317\) | 3.27303 | 0.183832 | 0.0919158 | − | 0.995767i | \(-0.470701\pi\) | ||||
0.0919158 | + | 0.995767i | \(0.470701\pi\) | |||||||
\(318\) | −7.45886 | −0.418272 | ||||||||
\(319\) | 9.52697 | 0.533408 | ||||||||
\(320\) | 23.7076 | 1.32530 | ||||||||
\(321\) | 19.9440 | 1.11316 | ||||||||
\(322\) | 8.20221 | 0.457091 | ||||||||
\(323\) | −5.52422 | −0.307376 | ||||||||
\(324\) | −15.6524 | −0.869576 | ||||||||
\(325\) | 1.17856 | 0.0653750 | ||||||||
\(326\) | −6.07347 | −0.336379 | ||||||||
\(327\) | −10.9370 | −0.604817 | ||||||||
\(328\) | −20.9431 | −1.15639 | ||||||||
\(329\) | −3.08365 | −0.170007 | ||||||||
\(330\) | 3.43983 | 0.189357 | ||||||||
\(331\) | 31.4299 | 1.72754 | 0.863771 | − | 0.503884i | \(-0.168096\pi\) | ||||
0.863771 | + | 0.503884i | \(0.168096\pi\) | |||||||
\(332\) | 32.2028 | 1.76736 | ||||||||
\(333\) | 5.76300 | 0.315810 | ||||||||
\(334\) | −25.6456 | −1.40327 | ||||||||
\(335\) | −10.7576 | −0.587751 | ||||||||
\(336\) | 16.7356 | 0.913002 | ||||||||
\(337\) | 18.6135 | 1.01394 | 0.506970 | − | 0.861964i | \(-0.330765\pi\) | ||||
0.506970 | + | 0.861964i | \(0.330765\pi\) | |||||||
\(338\) | 31.3932 | 1.70757 | ||||||||
\(339\) | 11.0007 | 0.597478 | ||||||||
\(340\) | −6.33436 | −0.343529 | ||||||||
\(341\) | −7.86250 | −0.425778 | ||||||||
\(342\) | 17.2970 | 0.935314 | ||||||||
\(343\) | 12.6535 | 0.683226 | ||||||||
\(344\) | 51.8484 | 2.79548 | ||||||||
\(345\) | −3.98397 | −0.214490 | ||||||||
\(346\) | −8.43015 | −0.453208 | ||||||||
\(347\) | 19.6533 | 1.05504 | 0.527521 | − | 0.849542i | \(-0.323122\pi\) | ||||
0.527521 | + | 0.849542i | \(0.323122\pi\) | |||||||
\(348\) | −64.3640 | −3.45027 | ||||||||
\(349\) | −2.60085 | −0.139221 | −0.0696103 | − | 0.997574i | \(-0.522176\pi\) | ||||
−0.0696103 | + | 0.997574i | \(0.522176\pi\) | |||||||
\(350\) | 2.61930 | 0.140008 | ||||||||
\(351\) | 6.56956 | 0.350657 | ||||||||
\(352\) | −18.8126 | −1.00272 | ||||||||
\(353\) | −4.56840 | −0.243152 | −0.121576 | − | 0.992582i | \(-0.538795\pi\) | ||||
−0.121576 | + | 0.992582i | \(0.538795\pi\) | |||||||
\(354\) | 32.8318 | 1.74499 | ||||||||
\(355\) | 9.15992 | 0.486158 | ||||||||
\(356\) | −75.3767 | −3.99496 | ||||||||
\(357\) | −1.47019 | −0.0778108 | ||||||||
\(358\) | −36.9205 | −1.95131 | ||||||||
\(359\) | −15.8842 | −0.838336 | −0.419168 | − | 0.907909i | \(-0.637678\pi\) | ||||
−0.419168 | + | 0.907909i | \(0.637678\pi\) | |||||||
\(360\) | 12.3637 | 0.651627 | ||||||||
\(361\) | 2.44722 | 0.128801 | ||||||||
\(362\) | −5.83841 | −0.306860 | ||||||||
\(363\) | −1.27224 | −0.0667755 | ||||||||
\(364\) | −6.06302 | −0.317789 | ||||||||
\(365\) | 1.00000 | 0.0523424 | ||||||||
\(366\) | 7.73600 | 0.404367 | ||||||||
\(367\) | 1.58307 | 0.0826354 | 0.0413177 | − | 0.999146i | \(-0.486844\pi\) | ||||
0.0413177 | + | 0.999146i | \(0.486844\pi\) | |||||||
\(368\) | 42.5205 | 2.21653 | ||||||||
\(369\) | −3.23241 | −0.168272 | ||||||||
\(370\) | 11.2797 | 0.586404 | ||||||||
\(371\) | 2.10065 | 0.109060 | ||||||||
\(372\) | 53.1189 | 2.75409 | ||||||||
\(373\) | 32.1045 | 1.66231 | 0.831154 | − | 0.556042i | \(-0.187681\pi\) | ||||
0.831154 | + | 0.556042i | \(0.187681\pi\) | |||||||
\(374\) | 3.22517 | 0.166769 | ||||||||
\(375\) | −1.27224 | −0.0656984 | ||||||||
\(376\) | −28.4891 | −1.46921 | ||||||||
\(377\) | 11.2281 | 0.578279 | ||||||||
\(378\) | 14.6005 | 0.750969 | ||||||||
\(379\) | 26.9082 | 1.38218 | 0.691092 | − | 0.722767i | \(-0.257130\pi\) | ||||
0.691092 | + | 0.722767i | \(0.257130\pi\) | |||||||
\(380\) | 24.5925 | 1.26157 | ||||||||
\(381\) | −21.2907 | −1.09076 | ||||||||
\(382\) | −25.6254 | −1.31111 | ||||||||
\(383\) | −13.2905 | −0.679114 | −0.339557 | − | 0.940586i | \(-0.610277\pi\) | ||||
−0.339557 | + | 0.940586i | \(0.610277\pi\) | |||||||
\(384\) | 33.6818 | 1.71882 | ||||||||
\(385\) | −0.968765 | −0.0493728 | ||||||||
\(386\) | 36.8602 | 1.87613 | ||||||||
\(387\) | 8.00242 | 0.406786 | ||||||||
\(388\) | −14.4455 | −0.733361 | ||||||||
\(389\) | −1.28597 | −0.0652011 | −0.0326006 | − | 0.999468i | \(-0.510379\pi\) | ||||
−0.0326006 | + | 0.999468i | \(0.510379\pi\) | |||||||
\(390\) | 4.05406 | 0.205286 | ||||||||
\(391\) | −3.73534 | −0.188904 | ||||||||
\(392\) | 54.2515 | 2.74011 | ||||||||
\(393\) | 27.4154 | 1.38292 | ||||||||
\(394\) | −58.6743 | −2.95597 | ||||||||
\(395\) | 5.23984 | 0.263645 | ||||||||
\(396\) | −7.33560 | −0.368628 | ||||||||
\(397\) | 31.9071 | 1.60137 | 0.800685 | − | 0.599086i | \(-0.204469\pi\) | ||||
0.800685 | + | 0.599086i | \(0.204469\pi\) | |||||||
\(398\) | 54.6961 | 2.74167 | ||||||||
\(399\) | 5.70787 | 0.285751 | ||||||||
\(400\) | 13.5785 | 0.678926 | ||||||||
\(401\) | 38.1822 | 1.90673 | 0.953364 | − | 0.301823i | \(-0.0975952\pi\) | ||||
0.953364 | + | 0.301823i | \(0.0975952\pi\) | |||||||
\(402\) | −37.0044 | −1.84561 | ||||||||
\(403\) | −9.26646 | −0.461595 | ||||||||
\(404\) | 93.1316 | 4.63347 | ||||||||
\(405\) | −2.94756 | −0.146465 | ||||||||
\(406\) | 24.9540 | 1.23845 | ||||||||
\(407\) | −4.17187 | −0.206792 | ||||||||
\(408\) | −13.5827 | −0.672446 | ||||||||
\(409\) | 0.912283 | 0.0451095 | 0.0225547 | − | 0.999746i | \(-0.492820\pi\) | ||||
0.0225547 | + | 0.999746i | \(0.492820\pi\) | |||||||
\(410\) | −6.32667 | −0.312452 | ||||||||
\(411\) | 10.4450 | 0.515212 | ||||||||
\(412\) | 18.5687 | 0.914816 | ||||||||
\(413\) | −9.24647 | −0.454989 | ||||||||
\(414\) | 11.6958 | 0.574818 | ||||||||
\(415\) | 6.06424 | 0.297682 | ||||||||
\(416\) | −22.1719 | −1.08707 | ||||||||
\(417\) | 19.4031 | 0.950172 | ||||||||
\(418\) | −12.5214 | −0.612441 | ||||||||
\(419\) | 5.50500 | 0.268937 | 0.134469 | − | 0.990918i | \(-0.457067\pi\) | ||||
0.134469 | + | 0.990918i | \(0.457067\pi\) | |||||||
\(420\) | 6.54495 | 0.319361 | ||||||||
\(421\) | −8.04720 | −0.392197 | −0.196098 | − | 0.980584i | \(-0.562827\pi\) | ||||
−0.196098 | + | 0.980584i | \(0.562827\pi\) | |||||||
\(422\) | 26.5416 | 1.29203 | ||||||||
\(423\) | −4.39708 | −0.213793 | ||||||||
\(424\) | 19.4074 | 0.942506 | ||||||||
\(425\) | −1.19285 | −0.0578616 | ||||||||
\(426\) | 31.5086 | 1.52660 | ||||||||
\(427\) | −2.17870 | −0.105435 | ||||||||
\(428\) | −83.2451 | −4.02381 | ||||||||
\(429\) | −1.49942 | −0.0723927 | ||||||||
\(430\) | 15.6628 | 0.755329 | ||||||||
\(431\) | −11.9665 | −0.576408 | −0.288204 | − | 0.957569i | \(-0.593058\pi\) | ||||
−0.288204 | + | 0.957569i | \(0.593058\pi\) | |||||||
\(432\) | 75.6895 | 3.64161 | ||||||||
\(433\) | 29.5566 | 1.42040 | 0.710201 | − | 0.703999i | \(-0.248604\pi\) | ||||
0.710201 | + | 0.703999i | \(0.248604\pi\) | |||||||
\(434\) | −20.5943 | −0.988556 | ||||||||
\(435\) | −12.1206 | −0.581140 | ||||||||
\(436\) | 45.6505 | 2.18626 | ||||||||
\(437\) | 14.5021 | 0.693729 | ||||||||
\(438\) | 3.43983 | 0.164362 | ||||||||
\(439\) | 17.3711 | 0.829075 | 0.414538 | − | 0.910032i | \(-0.363943\pi\) | ||||
0.414538 | + | 0.910032i | \(0.363943\pi\) | |||||||
\(440\) | −8.95019 | −0.426683 | ||||||||
\(441\) | 8.37332 | 0.398730 | ||||||||
\(442\) | 3.80107 | 0.180798 | ||||||||
\(443\) | 19.2798 | 0.916012 | 0.458006 | − | 0.888949i | \(-0.348564\pi\) | ||||
0.458006 | + | 0.888949i | \(0.348564\pi\) | |||||||
\(444\) | 28.1850 | 1.33760 | ||||||||
\(445\) | −14.1945 | −0.672883 | ||||||||
\(446\) | 9.76361 | 0.462320 | ||||||||
\(447\) | −23.6407 | −1.11817 | ||||||||
\(448\) | −22.9671 | −1.08509 | ||||||||
\(449\) | 6.51781 | 0.307595 | 0.153797 | − | 0.988102i | \(-0.450850\pi\) | ||||
0.153797 | + | 0.988102i | \(0.450850\pi\) | |||||||
\(450\) | 3.73495 | 0.176067 | ||||||||
\(451\) | 2.33996 | 0.110184 | ||||||||
\(452\) | −45.9165 | −2.15973 | ||||||||
\(453\) | 6.97020 | 0.327489 | ||||||||
\(454\) | −40.3489 | −1.89367 | ||||||||
\(455\) | −1.14175 | −0.0535261 | ||||||||
\(456\) | 52.7337 | 2.46948 | ||||||||
\(457\) | −12.7406 | −0.595981 | −0.297991 | − | 0.954569i | \(-0.596316\pi\) | ||||
−0.297991 | + | 0.954569i | \(0.596316\pi\) | |||||||
\(458\) | −63.8140 | −2.98183 | ||||||||
\(459\) | −6.64918 | −0.310357 | ||||||||
\(460\) | 16.6289 | 0.775325 | ||||||||
\(461\) | 31.1508 | 1.45084 | 0.725419 | − | 0.688308i | \(-0.241646\pi\) | ||||
0.725419 | + | 0.688308i | \(0.241646\pi\) | |||||||
\(462\) | −3.33239 | −0.155037 | ||||||||
\(463\) | 9.72995 | 0.452189 | 0.226095 | − | 0.974105i | \(-0.427404\pi\) | ||||
0.226095 | + | 0.974105i | \(0.427404\pi\) | |||||||
\(464\) | 129.362 | 6.00549 | ||||||||
\(465\) | 10.0030 | 0.463879 | ||||||||
\(466\) | −29.6575 | −1.37386 | ||||||||
\(467\) | 4.23935 | 0.196174 | 0.0980868 | − | 0.995178i | \(-0.468728\pi\) | ||||
0.0980868 | + | 0.995178i | \(0.468728\pi\) | |||||||
\(468\) | −8.64547 | −0.399637 | ||||||||
\(469\) | 10.4216 | 0.481225 | ||||||||
\(470\) | −8.60624 | −0.396976 | ||||||||
\(471\) | −10.4119 | −0.479753 | ||||||||
\(472\) | −85.4259 | −3.93205 | ||||||||
\(473\) | −5.79300 | −0.266362 | ||||||||
\(474\) | 18.0242 | 0.827877 | ||||||||
\(475\) | 4.63111 | 0.212490 | ||||||||
\(476\) | 6.13650 | 0.281266 | ||||||||
\(477\) | 2.99539 | 0.137149 | ||||||||
\(478\) | 62.7054 | 2.86808 | ||||||||
\(479\) | 31.7379 | 1.45014 | 0.725071 | − | 0.688674i | \(-0.241807\pi\) | ||||
0.725071 | + | 0.688674i | \(0.241807\pi\) | |||||||
\(480\) | 23.9342 | 1.09244 | ||||||||
\(481\) | −4.91681 | −0.224187 | ||||||||
\(482\) | −11.2574 | −0.512760 | ||||||||
\(483\) | 3.85953 | 0.175614 | ||||||||
\(484\) | 5.31028 | 0.241376 | ||||||||
\(485\) | −2.72029 | −0.123522 | ||||||||
\(486\) | 35.0747 | 1.59102 | ||||||||
\(487\) | −6.48491 | −0.293859 | −0.146930 | − | 0.989147i | \(-0.546939\pi\) | ||||
−0.146930 | + | 0.989147i | \(0.546939\pi\) | |||||||
\(488\) | −20.1285 | −0.911174 | ||||||||
\(489\) | −2.85786 | −0.129237 | ||||||||
\(490\) | 16.3888 | 0.740370 | ||||||||
\(491\) | 21.3615 | 0.964031 | 0.482016 | − | 0.876163i | \(-0.339905\pi\) | ||||
0.482016 | + | 0.876163i | \(0.339905\pi\) | |||||||
\(492\) | −15.8087 | −0.712711 | ||||||||
\(493\) | −11.3642 | −0.511819 | ||||||||
\(494\) | −14.7573 | −0.663961 | ||||||||
\(495\) | −1.38140 | −0.0620891 | ||||||||
\(496\) | −106.761 | −4.79372 | ||||||||
\(497\) | −8.87381 | −0.398045 | ||||||||
\(498\) | 20.8600 | 0.934758 | ||||||||
\(499\) | 15.1949 | 0.680218 | 0.340109 | − | 0.940386i | \(-0.389536\pi\) | ||||
0.340109 | + | 0.940386i | \(0.389536\pi\) | |||||||
\(500\) | 5.31028 | 0.237483 | ||||||||
\(501\) | −12.0675 | −0.539135 | ||||||||
\(502\) | 49.4093 | 2.20524 | ||||||||
\(503\) | −16.8224 | −0.750076 | −0.375038 | − | 0.927010i | \(-0.622370\pi\) | ||||
−0.375038 | + | 0.927010i | \(0.622370\pi\) | |||||||
\(504\) | −11.9776 | −0.533523 | ||||||||
\(505\) | 17.5380 | 0.780430 | ||||||||
\(506\) | −8.46666 | −0.376389 | ||||||||
\(507\) | 14.7720 | 0.656048 | ||||||||
\(508\) | 88.8665 | 3.94281 | ||||||||
\(509\) | 2.31853 | 0.102767 | 0.0513835 | − | 0.998679i | \(-0.483637\pi\) | ||||
0.0513835 | + | 0.998679i | \(0.483637\pi\) | |||||||
\(510\) | −4.10320 | −0.181693 | ||||||||
\(511\) | −0.968765 | −0.0428556 | ||||||||
\(512\) | −12.3870 | −0.547435 | ||||||||
\(513\) | 25.8148 | 1.13975 | ||||||||
\(514\) | −39.2510 | −1.73129 | ||||||||
\(515\) | 3.49675 | 0.154085 | ||||||||
\(516\) | 39.1373 | 1.72293 | ||||||||
\(517\) | 3.18307 | 0.139991 | ||||||||
\(518\) | −10.9274 | −0.480121 | ||||||||
\(519\) | −3.96679 | −0.174123 | ||||||||
\(520\) | −10.5484 | −0.462576 | ||||||||
\(521\) | 4.39367 | 0.192490 | 0.0962450 | − | 0.995358i | \(-0.469317\pi\) | ||||
0.0962450 | + | 0.995358i | \(0.469317\pi\) | |||||||
\(522\) | 35.5828 | 1.55742 | ||||||||
\(523\) | 8.83180 | 0.386188 | 0.193094 | − | 0.981180i | \(-0.438148\pi\) | ||||
0.193094 | + | 0.981180i | \(0.438148\pi\) | |||||||
\(524\) | −114.430 | −4.99892 | ||||||||
\(525\) | 1.23250 | 0.0537909 | ||||||||
\(526\) | 33.2438 | 1.44950 | ||||||||
\(527\) | 9.37877 | 0.408546 | ||||||||
\(528\) | −17.2752 | −0.751807 | ||||||||
\(529\) | −13.1940 | −0.573653 | ||||||||
\(530\) | 5.86276 | 0.254662 | ||||||||
\(531\) | −13.1849 | −0.572174 | ||||||||
\(532\) | −23.8244 | −1.03292 | ||||||||
\(533\) | 2.75779 | 0.119453 | ||||||||
\(534\) | −48.8266 | −2.11293 | ||||||||
\(535\) | −15.6762 | −0.677742 | ||||||||
\(536\) | 96.2826 | 4.15878 | ||||||||
\(537\) | −17.3728 | −0.749693 | ||||||||
\(538\) | 14.4871 | 0.624584 | ||||||||
\(539\) | −6.06150 | −0.261087 | ||||||||
\(540\) | 29.6006 | 1.27381 | ||||||||
\(541\) | 25.4462 | 1.09402 | 0.547009 | − | 0.837127i | \(-0.315766\pi\) | ||||
0.547009 | + | 0.837127i | \(0.315766\pi\) | |||||||
\(542\) | 38.4097 | 1.64984 | ||||||||
\(543\) | −2.74725 | −0.117896 | ||||||||
\(544\) | 22.4406 | 0.962133 | ||||||||
\(545\) | 8.59662 | 0.368239 | ||||||||
\(546\) | −3.92743 | −0.168079 | ||||||||
\(547\) | 20.8447 | 0.891255 | 0.445627 | − | 0.895219i | \(-0.352981\pi\) | ||||
0.445627 | + | 0.895219i | \(0.352981\pi\) | |||||||
\(548\) | −43.5967 | −1.86236 | ||||||||
\(549\) | −3.10669 | −0.132590 | ||||||||
\(550\) | −2.70375 | −0.115288 | ||||||||
\(551\) | 44.1205 | 1.87960 | ||||||||
\(552\) | 35.6572 | 1.51767 | ||||||||
\(553\) | −5.07617 | −0.215861 | ||||||||
\(554\) | −54.9447 | −2.33437 | ||||||||
\(555\) | 5.30763 | 0.225296 | ||||||||
\(556\) | −80.9874 | −3.43463 | ||||||||
\(557\) | 18.1884 | 0.770666 | 0.385333 | − | 0.922778i | \(-0.374087\pi\) | ||||
0.385333 | + | 0.922778i | \(0.374087\pi\) | |||||||
\(558\) | −29.3661 | −1.24317 | ||||||||
\(559\) | −6.82742 | −0.288769 | ||||||||
\(560\) | −13.1544 | −0.555875 | ||||||||
\(561\) | 1.51759 | 0.0640728 | ||||||||
\(562\) | −27.0431 | −1.14075 | ||||||||
\(563\) | 41.9655 | 1.76864 | 0.884318 | − | 0.466886i | \(-0.154624\pi\) | ||||
0.884318 | + | 0.466886i | \(0.154624\pi\) | |||||||
\(564\) | −21.5047 | −0.905513 | ||||||||
\(565\) | −8.64672 | −0.363770 | ||||||||
\(566\) | −41.6690 | −1.75148 | ||||||||
\(567\) | 2.85549 | 0.119919 | ||||||||
\(568\) | −81.9830 | −3.43993 | ||||||||
\(569\) | −4.03365 | −0.169099 | −0.0845496 | − | 0.996419i | \(-0.526945\pi\) | ||||
−0.0845496 | + | 0.996419i | \(0.526945\pi\) | |||||||
\(570\) | 15.9303 | 0.667245 | ||||||||
\(571\) | −39.9132 | −1.67032 | −0.835158 | − | 0.550010i | \(-0.814624\pi\) | ||||
−0.835158 | + | 0.550010i | \(0.814624\pi\) | |||||||
\(572\) | 6.25851 | 0.261681 | ||||||||
\(573\) | −12.0580 | −0.503728 | ||||||||
\(574\) | 6.12906 | 0.255822 | ||||||||
\(575\) | 3.13145 | 0.130590 | ||||||||
\(576\) | −32.7496 | −1.36457 | ||||||||
\(577\) | −21.4729 | −0.893929 | −0.446965 | − | 0.894552i | \(-0.647495\pi\) | ||||
−0.446965 | + | 0.894552i | \(0.647495\pi\) | |||||||
\(578\) | 42.1167 | 1.75182 | ||||||||
\(579\) | 17.3445 | 0.720811 | ||||||||
\(580\) | 50.5909 | 2.10067 | ||||||||
\(581\) | −5.87482 | −0.243729 | ||||||||
\(582\) | −9.35736 | −0.387875 | ||||||||
\(583\) | −2.16838 | −0.0898050 | ||||||||
\(584\) | −8.95019 | −0.370361 | ||||||||
\(585\) | −1.62806 | −0.0673121 | ||||||||
\(586\) | −2.50781 | −0.103597 | ||||||||
\(587\) | 8.50628 | 0.351092 | 0.175546 | − | 0.984471i | \(-0.443831\pi\) | ||||
0.175546 | + | 0.984471i | \(0.443831\pi\) | |||||||
\(588\) | 40.9513 | 1.68880 | ||||||||
\(589\) | −36.4122 | −1.50034 | ||||||||
\(590\) | −25.8062 | −1.06243 | ||||||||
\(591\) | −27.6091 | −1.13568 | ||||||||
\(592\) | −56.6478 | −2.32821 | ||||||||
\(593\) | −31.7932 | −1.30559 | −0.652795 | − | 0.757535i | \(-0.726404\pi\) | ||||
−0.652795 | + | 0.757535i | \(0.726404\pi\) | |||||||
\(594\) | −15.0713 | −0.618382 | ||||||||
\(595\) | 1.15559 | 0.0473745 | ||||||||
\(596\) | 98.6751 | 4.04189 | ||||||||
\(597\) | 25.7371 | 1.05335 | ||||||||
\(598\) | −9.97851 | −0.408051 | ||||||||
\(599\) | −48.4679 | −1.98034 | −0.990172 | − | 0.139852i | \(-0.955337\pi\) | ||||
−0.990172 | + | 0.139852i | \(0.955337\pi\) | |||||||
\(600\) | 11.3868 | 0.464865 | ||||||||
\(601\) | −33.4695 | −1.36525 | −0.682625 | − | 0.730769i | \(-0.739162\pi\) | ||||
−0.682625 | + | 0.730769i | \(0.739162\pi\) | |||||||
\(602\) | −15.1736 | −0.618430 | ||||||||
\(603\) | 14.8605 | 0.605167 | ||||||||
\(604\) | −29.0933 | −1.18379 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 60.3277 | 2.45065 | ||||||||
\(607\) | 2.67486 | 0.108569 | 0.0542845 | − | 0.998526i | \(-0.482712\pi\) | ||||
0.0542845 | + | 0.998526i | \(0.482712\pi\) | |||||||
\(608\) | −87.1234 | −3.53332 | ||||||||
\(609\) | 11.7420 | 0.475811 | ||||||||
\(610\) | −6.08060 | −0.246196 | ||||||||
\(611\) | 3.75145 | 0.151768 | ||||||||
\(612\) | 8.75026 | 0.353708 | ||||||||
\(613\) | −47.9182 | −1.93540 | −0.967699 | − | 0.252107i | \(-0.918877\pi\) | ||||
−0.967699 | + | 0.252107i | \(0.918877\pi\) | |||||||
\(614\) | −38.9343 | −1.57126 | ||||||||
\(615\) | −2.97700 | −0.120044 | ||||||||
\(616\) | 8.67062 | 0.349349 | ||||||||
\(617\) | 26.8831 | 1.08227 | 0.541137 | − | 0.840935i | \(-0.317994\pi\) | ||||
0.541137 | + | 0.840935i | \(0.317994\pi\) | |||||||
\(618\) | 12.0282 | 0.483847 | ||||||||
\(619\) | 23.1893 | 0.932056 | 0.466028 | − | 0.884770i | \(-0.345685\pi\) | ||||
0.466028 | + | 0.884770i | \(0.345685\pi\) | |||||||
\(620\) | −41.7521 | −1.67681 | ||||||||
\(621\) | 17.4553 | 0.700458 | ||||||||
\(622\) | 31.0138 | 1.24354 | ||||||||
\(623\) | 13.7511 | 0.550926 | ||||||||
\(624\) | −20.3599 | −0.815049 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 73.8334 | 2.95098 | ||||||||
\(627\) | −5.89191 | −0.235300 | ||||||||
\(628\) | 43.4586 | 1.73419 | ||||||||
\(629\) | 4.97640 | 0.198422 | ||||||||
\(630\) | −3.61829 | −0.144156 | ||||||||
\(631\) | 23.5589 | 0.937865 | 0.468932 | − | 0.883234i | \(-0.344639\pi\) | ||||
0.468932 | + | 0.883234i | \(0.344639\pi\) | |||||||
\(632\) | −46.8975 | −1.86548 | ||||||||
\(633\) | 12.4891 | 0.496396 | ||||||||
\(634\) | −8.84946 | −0.351457 | ||||||||
\(635\) | 16.7348 | 0.664100 | ||||||||
\(636\) | 14.6495 | 0.580891 | ||||||||
\(637\) | −7.14386 | −0.283050 | ||||||||
\(638\) | −25.7586 | −1.01979 | ||||||||
\(639\) | −12.6535 | −0.500564 | ||||||||
\(640\) | −26.4743 | −1.04649 | ||||||||
\(641\) | −4.55225 | −0.179803 | −0.0899016 | − | 0.995951i | \(-0.528655\pi\) | ||||
−0.0899016 | + | 0.995951i | \(0.528655\pi\) | |||||||
\(642\) | −53.9236 | −2.12819 | ||||||||
\(643\) | −9.85269 | −0.388552 | −0.194276 | − | 0.980947i | \(-0.562236\pi\) | ||||
−0.194276 | + | 0.980947i | \(0.562236\pi\) | |||||||
\(644\) | −16.1095 | −0.634802 | ||||||||
\(645\) | 7.37011 | 0.290198 | ||||||||
\(646\) | 14.9361 | 0.587654 | ||||||||
\(647\) | −2.14227 | −0.0842213 | −0.0421107 | − | 0.999113i | \(-0.513408\pi\) | ||||
−0.0421107 | + | 0.999113i | \(0.513408\pi\) | |||||||
\(648\) | 26.3812 | 1.03635 | ||||||||
\(649\) | 9.54460 | 0.374658 | ||||||||
\(650\) | −3.18655 | −0.124987 | ||||||||
\(651\) | −9.69057 | −0.379804 | ||||||||
\(652\) | 11.9285 | 0.467158 | ||||||||
\(653\) | 30.1085 | 1.17824 | 0.589119 | − | 0.808046i | \(-0.299475\pi\) | ||||
0.589119 | + | 0.808046i | \(0.299475\pi\) | |||||||
\(654\) | 29.5709 | 1.15632 | ||||||||
\(655\) | −21.5488 | −0.841983 | ||||||||
\(656\) | 31.7732 | 1.24054 | ||||||||
\(657\) | −1.38140 | −0.0538934 | ||||||||
\(658\) | 8.33742 | 0.325027 | ||||||||
\(659\) | −15.5244 | −0.604747 | −0.302373 | − | 0.953190i | \(-0.597779\pi\) | ||||
−0.302373 | + | 0.953190i | \(0.597779\pi\) | |||||||
\(660\) | −6.75597 | −0.262976 | ||||||||
\(661\) | 2.42023 | 0.0941358 | 0.0470679 | − | 0.998892i | \(-0.485012\pi\) | ||||
0.0470679 | + | 0.998892i | \(0.485012\pi\) | |||||||
\(662\) | −84.9787 | −3.30279 | ||||||||
\(663\) | 1.78858 | 0.0694627 | ||||||||
\(664\) | −54.2761 | −2.10632 | ||||||||
\(665\) | −4.48646 | −0.173977 | ||||||||
\(666\) | −15.5817 | −0.603780 | ||||||||
\(667\) | 29.8332 | 1.15515 | ||||||||
\(668\) | 50.3691 | 1.94884 | ||||||||
\(669\) | 4.59424 | 0.177624 | ||||||||
\(670\) | 29.0859 | 1.12369 | ||||||||
\(671\) | 2.24895 | 0.0868197 | ||||||||
\(672\) | −23.1866 | −0.894444 | ||||||||
\(673\) | −0.133513 | −0.00514655 | −0.00257327 | − | 0.999997i | \(-0.500819\pi\) | ||||
−0.00257327 | + | 0.999997i | \(0.500819\pi\) | |||||||
\(674\) | −50.3262 | −1.93849 | ||||||||
\(675\) | 5.57420 | 0.214551 | ||||||||
\(676\) | −61.6576 | −2.37145 | ||||||||
\(677\) | 24.7677 | 0.951898 | 0.475949 | − | 0.879473i | \(-0.342105\pi\) | ||||
0.475949 | + | 0.879473i | \(0.342105\pi\) | |||||||
\(678\) | −29.7433 | −1.14228 | ||||||||
\(679\) | 2.63533 | 0.101135 | ||||||||
\(680\) | 10.6762 | 0.409414 | ||||||||
\(681\) | −18.9861 | −0.727548 | ||||||||
\(682\) | 21.2583 | 0.814021 | ||||||||
\(683\) | −0.262116 | −0.0100296 | −0.00501480 | − | 0.999987i | \(-0.501596\pi\) | ||||
−0.00501480 | + | 0.999987i | \(0.501596\pi\) | |||||||
\(684\) | −33.9720 | −1.29895 | ||||||||
\(685\) | −8.20987 | −0.313683 | ||||||||
\(686\) | −34.2120 | −1.30622 | ||||||||
\(687\) | −30.0275 | −1.14562 | ||||||||
\(688\) | −78.6604 | −2.99890 | ||||||||
\(689\) | −2.55557 | −0.0973595 | ||||||||
\(690\) | 10.7717 | 0.410070 | ||||||||
\(691\) | −37.6806 | −1.43344 | −0.716720 | − | 0.697361i | \(-0.754357\pi\) | ||||
−0.716720 | + | 0.697361i | \(0.754357\pi\) | |||||||
\(692\) | 16.5572 | 0.629409 | ||||||||
\(693\) | 1.33825 | 0.0508358 | ||||||||
\(694\) | −53.1376 | −2.01707 | ||||||||
\(695\) | −15.2511 | −0.578505 | ||||||||
\(696\) | 108.482 | 4.11199 | ||||||||
\(697\) | −2.79122 | −0.105725 | ||||||||
\(698\) | 7.03207 | 0.266168 | ||||||||
\(699\) | −13.9553 | −0.527836 | ||||||||
\(700\) | −5.14441 | −0.194441 | ||||||||
\(701\) | 38.7705 | 1.46434 | 0.732172 | − | 0.681120i | \(-0.238507\pi\) | ||||
0.732172 | + | 0.681120i | \(0.238507\pi\) | |||||||
\(702\) | −17.7625 | −0.670401 | ||||||||
\(703\) | −19.3204 | −0.728682 | ||||||||
\(704\) | 23.7076 | 0.893515 | ||||||||
\(705\) | −4.04964 | −0.152518 | ||||||||
\(706\) | 12.3518 | 0.464867 | ||||||||
\(707\) | −16.9902 | −0.638981 | ||||||||
\(708\) | −64.4830 | −2.42342 | ||||||||
\(709\) | 14.4160 | 0.541403 | 0.270702 | − | 0.962663i | \(-0.412744\pi\) | ||||
0.270702 | + | 0.962663i | \(0.412744\pi\) | |||||||
\(710\) | −24.7662 | −0.929458 | ||||||||
\(711\) | −7.23829 | −0.271457 | ||||||||
\(712\) | 127.043 | 4.76114 | ||||||||
\(713\) | −24.6210 | −0.922065 | ||||||||
\(714\) | 3.97503 | 0.148762 | ||||||||
\(715\) | 1.17856 | 0.0440758 | ||||||||
\(716\) | 72.5133 | 2.70995 | ||||||||
\(717\) | 29.5058 | 1.10192 | ||||||||
\(718\) | 42.9470 | 1.60277 | ||||||||
\(719\) | 51.7436 | 1.92971 | 0.964855 | − | 0.262783i | \(-0.0846402\pi\) | ||||
0.964855 | + | 0.262783i | \(0.0846402\pi\) | |||||||
\(720\) | −18.7573 | −0.699044 | ||||||||
\(721\) | −3.38753 | −0.126158 | ||||||||
\(722\) | −6.61668 | −0.246247 | ||||||||
\(723\) | −5.29713 | −0.197002 | ||||||||
\(724\) | 11.4669 | 0.426163 | ||||||||
\(725\) | 9.52697 | 0.353823 | ||||||||
\(726\) | 3.43983 | 0.127664 | ||||||||
\(727\) | −12.5070 | −0.463859 | −0.231930 | − | 0.972733i | \(-0.574504\pi\) | ||||
−0.231930 | + | 0.972733i | \(0.574504\pi\) | |||||||
\(728\) | 10.2189 | 0.378737 | ||||||||
\(729\) | 25.3470 | 0.938777 | ||||||||
\(730\) | −2.70375 | −0.100070 | ||||||||
\(731\) | 6.91017 | 0.255582 | ||||||||
\(732\) | −15.1938 | −0.561580 | ||||||||
\(733\) | −30.8493 | −1.13944 | −0.569722 | − | 0.821837i | \(-0.692949\pi\) | ||||
−0.569722 | + | 0.821837i | \(0.692949\pi\) | |||||||
\(734\) | −4.28022 | −0.157986 | ||||||||
\(735\) | 7.71170 | 0.284450 | ||||||||
\(736\) | −58.9108 | −2.17148 | ||||||||
\(737\) | −10.7576 | −0.396262 | ||||||||
\(738\) | 8.73964 | 0.321710 | ||||||||
\(739\) | −40.7402 | −1.49865 | −0.749327 | − | 0.662201i | \(-0.769623\pi\) | ||||
−0.749327 | + | 0.662201i | \(0.769623\pi\) | |||||||
\(740\) | −22.1538 | −0.814390 | ||||||||
\(741\) | −6.94399 | −0.255094 | ||||||||
\(742\) | −5.67963 | −0.208506 | ||||||||
\(743\) | −4.29466 | −0.157556 | −0.0787780 | − | 0.996892i | \(-0.525102\pi\) | ||||
−0.0787780 | + | 0.996892i | \(0.525102\pi\) | |||||||
\(744\) | −89.5289 | −3.28229 | ||||||||
\(745\) | 18.5819 | 0.680788 | ||||||||
\(746\) | −86.8027 | −3.17807 | ||||||||
\(747\) | −8.37712 | −0.306503 | ||||||||
\(748\) | −6.33436 | −0.231607 | ||||||||
\(749\) | 15.1866 | 0.554905 | ||||||||
\(750\) | 3.43983 | 0.125605 | ||||||||
\(751\) | 14.8650 | 0.542430 | 0.271215 | − | 0.962519i | \(-0.412575\pi\) | ||||
0.271215 | + | 0.962519i | \(0.412575\pi\) | |||||||
\(752\) | 43.2214 | 1.57612 | ||||||||
\(753\) | 23.2494 | 0.847255 | ||||||||
\(754\) | −30.3581 | −1.10558 | ||||||||
\(755\) | −5.47867 | −0.199389 | ||||||||
\(756\) | −28.6760 | −1.04294 | ||||||||
\(757\) | 52.1803 | 1.89652 | 0.948262 | − | 0.317489i | \(-0.102840\pi\) | ||||
0.948262 | + | 0.317489i | \(0.102840\pi\) | |||||||
\(758\) | −72.7532 | −2.64252 | ||||||||
\(759\) | −3.98397 | −0.144609 | ||||||||
\(760\) | −41.4493 | −1.50353 | ||||||||
\(761\) | 41.7563 | 1.51367 | 0.756833 | − | 0.653608i | \(-0.226746\pi\) | ||||
0.756833 | + | 0.653608i | \(0.226746\pi\) | |||||||
\(762\) | 57.5649 | 2.08536 | ||||||||
\(763\) | −8.32810 | −0.301498 | ||||||||
\(764\) | 50.3293 | 1.82085 | ||||||||
\(765\) | 1.64779 | 0.0595762 | ||||||||
\(766\) | 35.9343 | 1.29836 | ||||||||
\(767\) | 11.2489 | 0.406175 | ||||||||
\(768\) | −30.7435 | −1.10936 | ||||||||
\(769\) | 35.0611 | 1.26434 | 0.632168 | − | 0.774832i | \(-0.282165\pi\) | ||||
0.632168 | + | 0.774832i | \(0.282165\pi\) | |||||||
\(770\) | 2.61930 | 0.0943930 | ||||||||
\(771\) | −18.4695 | −0.665162 | ||||||||
\(772\) | −72.3949 | −2.60555 | ||||||||
\(773\) | 13.8158 | 0.496919 | 0.248459 | − | 0.968642i | \(-0.420076\pi\) | ||||
0.248459 | + | 0.968642i | \(0.420076\pi\) | |||||||
\(774\) | −21.6366 | −0.777711 | ||||||||
\(775\) | −7.86250 | −0.282429 | ||||||||
\(776\) | 24.3471 | 0.874011 | ||||||||
\(777\) | −5.14185 | −0.184463 | ||||||||
\(778\) | 3.47694 | 0.124654 | ||||||||
\(779\) | 10.8366 | 0.388262 | ||||||||
\(780\) | −7.96235 | −0.285098 | ||||||||
\(781\) | 9.15992 | 0.327768 | ||||||||
\(782\) | 10.0994 | 0.361155 | ||||||||
\(783\) | 53.1053 | 1.89783 | ||||||||
\(784\) | −82.3062 | −2.93951 | ||||||||
\(785\) | 8.18386 | 0.292094 | ||||||||
\(786\) | −74.1244 | −2.64393 | ||||||||
\(787\) | −14.1305 | −0.503697 | −0.251849 | − | 0.967767i | \(-0.581038\pi\) | ||||
−0.251849 | + | 0.967767i | \(0.581038\pi\) | |||||||
\(788\) | 115.239 | 4.10521 | ||||||||
\(789\) | 15.6428 | 0.556897 | ||||||||
\(790\) | −14.1672 | −0.504047 | ||||||||
\(791\) | 8.37664 | 0.297839 | ||||||||
\(792\) | 12.3637 | 0.439327 | ||||||||
\(793\) | 2.65053 | 0.0941230 | ||||||||
\(794\) | −86.2688 | −3.06157 | ||||||||
\(795\) | 2.75871 | 0.0978412 | ||||||||
\(796\) | −107.425 | −3.80759 | ||||||||
\(797\) | −30.9703 | −1.09702 | −0.548512 | − | 0.836143i | \(-0.684805\pi\) | ||||
−0.548512 | + | 0.836143i | \(0.684805\pi\) | |||||||
\(798\) | −15.4327 | −0.546311 | ||||||||
\(799\) | −3.79692 | −0.134325 | ||||||||
\(800\) | −18.8126 | −0.665127 | ||||||||
\(801\) | 19.6082 | 0.692821 | ||||||||
\(802\) | −103.235 | −3.64536 | ||||||||
\(803\) | 1.00000 | 0.0352892 | ||||||||
\(804\) | 72.6781 | 2.56316 | ||||||||
\(805\) | −3.03364 | −0.106922 | ||||||||
\(806\) | 25.0542 | 0.882498 | ||||||||
\(807\) | 6.81688 | 0.239965 | ||||||||
\(808\) | −156.968 | −5.52212 | ||||||||
\(809\) | 12.8226 | 0.450818 | 0.225409 | − | 0.974264i | \(-0.427628\pi\) | ||||
0.225409 | + | 0.974264i | \(0.427628\pi\) | |||||||
\(810\) | 7.96947 | 0.280019 | ||||||||
\(811\) | 30.7422 | 1.07950 | 0.539751 | − | 0.841824i | \(-0.318518\pi\) | ||||
0.539751 | + | 0.841824i | \(0.318518\pi\) | |||||||
\(812\) | −49.0107 | −1.71994 | ||||||||
\(813\) | 18.0736 | 0.633868 | ||||||||
\(814\) | 11.2797 | 0.395353 | ||||||||
\(815\) | 2.24631 | 0.0786849 | ||||||||
\(816\) | 20.6067 | 0.721378 | ||||||||
\(817\) | −26.8280 | −0.938594 | ||||||||
\(818\) | −2.46659 | −0.0862422 | ||||||||
\(819\) | 1.57721 | 0.0551122 | ||||||||
\(820\) | 12.4258 | 0.433929 | ||||||||
\(821\) | −6.36417 | −0.222111 | −0.111056 | − | 0.993814i | \(-0.535423\pi\) | ||||
−0.111056 | + | 0.993814i | \(0.535423\pi\) | |||||||
\(822\) | −28.2406 | −0.985004 | ||||||||
\(823\) | −10.9711 | −0.382430 | −0.191215 | − | 0.981548i | \(-0.561243\pi\) | ||||
−0.191215 | + | 0.981548i | \(0.561243\pi\) | |||||||
\(824\) | −31.2966 | −1.09027 | ||||||||
\(825\) | −1.27224 | −0.0442938 | ||||||||
\(826\) | 25.0002 | 0.869867 | ||||||||
\(827\) | 19.4525 | 0.676431 | 0.338216 | − | 0.941069i | \(-0.390177\pi\) | ||||
0.338216 | + | 0.941069i | \(0.390177\pi\) | |||||||
\(828\) | −22.9711 | −0.798299 | ||||||||
\(829\) | 30.2928 | 1.05211 | 0.526057 | − | 0.850449i | \(-0.323670\pi\) | ||||
0.526057 | + | 0.850449i | \(0.323670\pi\) | |||||||
\(830\) | −16.3962 | −0.569121 | ||||||||
\(831\) | −25.8541 | −0.896867 | ||||||||
\(832\) | 27.9410 | 0.968679 | ||||||||
\(833\) | 7.23044 | 0.250520 | ||||||||
\(834\) | −52.4611 | −1.81658 | ||||||||
\(835\) | 9.48520 | 0.328249 | ||||||||
\(836\) | 24.5925 | 0.850550 | ||||||||
\(837\) | −43.8272 | −1.51489 | ||||||||
\(838\) | −14.8842 | −0.514165 | ||||||||
\(839\) | −36.1185 | −1.24695 | −0.623474 | − | 0.781844i | \(-0.714279\pi\) | ||||
−0.623474 | + | 0.781844i | \(0.714279\pi\) | |||||||
\(840\) | −11.0311 | −0.380611 | ||||||||
\(841\) | 61.7632 | 2.12976 | ||||||||
\(842\) | 21.7577 | 0.749818 | ||||||||
\(843\) | −12.7251 | −0.438275 | ||||||||
\(844\) | −52.1288 | −1.79435 | ||||||||
\(845\) | −11.6110 | −0.399430 | ||||||||
\(846\) | 11.8886 | 0.408739 | ||||||||
\(847\) | −0.968765 | −0.0332871 | ||||||||
\(848\) | −29.4434 | −1.01109 | ||||||||
\(849\) | −19.6072 | −0.672918 | ||||||||
\(850\) | 3.22517 | 0.110622 | ||||||||
\(851\) | −13.0640 | −0.447828 | ||||||||
\(852\) | −61.8842 | −2.12012 | ||||||||
\(853\) | 3.33345 | 0.114135 | 0.0570676 | − | 0.998370i | \(-0.481825\pi\) | ||||
0.0570676 | + | 0.998370i | \(0.481825\pi\) | |||||||
\(854\) | 5.89067 | 0.201575 | ||||||||
\(855\) | −6.39740 | −0.218786 | ||||||||
\(856\) | 140.305 | 4.79553 | ||||||||
\(857\) | 17.4481 | 0.596017 | 0.298008 | − | 0.954563i | \(-0.403678\pi\) | ||||
0.298008 | + | 0.954563i | \(0.403678\pi\) | |||||||
\(858\) | 4.05406 | 0.138403 | ||||||||
\(859\) | −26.8695 | −0.916774 | −0.458387 | − | 0.888753i | \(-0.651573\pi\) | ||||
−0.458387 | + | 0.888753i | \(0.651573\pi\) | |||||||
\(860\) | −30.7625 | −1.04899 | ||||||||
\(861\) | 2.88401 | 0.0982868 | ||||||||
\(862\) | 32.3546 | 1.10200 | ||||||||
\(863\) | −39.2400 | −1.33575 | −0.667873 | − | 0.744275i | \(-0.732795\pi\) | ||||
−0.667873 | + | 0.744275i | \(0.732795\pi\) | |||||||
\(864\) | −104.865 | −3.56759 | ||||||||
\(865\) | 3.11794 | 0.106013 | ||||||||
\(866\) | −79.9139 | −2.71558 | ||||||||
\(867\) | 19.8179 | 0.673051 | ||||||||
\(868\) | 40.4480 | 1.37289 | ||||||||
\(869\) | 5.23984 | 0.177749 | ||||||||
\(870\) | 32.7712 | 1.11105 | ||||||||
\(871\) | −12.6785 | −0.429596 | ||||||||
\(872\) | −76.9414 | −2.60556 | ||||||||
\(873\) | 3.75780 | 0.127182 | ||||||||
\(874\) | −39.2101 | −1.32630 | ||||||||
\(875\) | −0.968765 | −0.0327502 | ||||||||
\(876\) | −6.75597 | −0.228263 | ||||||||
\(877\) | 45.1170 | 1.52349 | 0.761747 | − | 0.647875i | \(-0.224342\pi\) | ||||
0.761747 | + | 0.647875i | \(0.224342\pi\) | |||||||
\(878\) | −46.9671 | −1.58506 | ||||||||
\(879\) | −1.18004 | −0.0398018 | ||||||||
\(880\) | 13.5785 | 0.457732 | ||||||||
\(881\) | −12.2355 | −0.412223 | −0.206112 | − | 0.978528i | \(-0.566081\pi\) | ||||
−0.206112 | + | 0.978528i | \(0.566081\pi\) | |||||||
\(882\) | −22.6394 | −0.762308 | ||||||||
\(883\) | 17.6401 | 0.593637 | 0.296819 | − | 0.954934i | \(-0.404074\pi\) | ||||
0.296819 | + | 0.954934i | \(0.404074\pi\) | |||||||
\(884\) | −7.46545 | −0.251090 | ||||||||
\(885\) | −12.1431 | −0.408184 | ||||||||
\(886\) | −52.1279 | −1.75127 | ||||||||
\(887\) | 42.8795 | 1.43975 | 0.719876 | − | 0.694103i | \(-0.244199\pi\) | ||||
0.719876 | + | 0.694103i | \(0.244199\pi\) | |||||||
\(888\) | −47.5043 | −1.59414 | ||||||||
\(889\) | −16.2121 | −0.543736 | ||||||||
\(890\) | 38.3784 | 1.28645 | ||||||||
\(891\) | −2.94756 | −0.0987470 | ||||||||
\(892\) | −19.1761 | −0.642064 | ||||||||
\(893\) | 14.7412 | 0.493294 | ||||||||
\(894\) | 63.9186 | 2.13776 | ||||||||
\(895\) | 13.6553 | 0.456445 | ||||||||
\(896\) | 25.6474 | 0.856820 | ||||||||
\(897\) | −4.69536 | −0.156773 | ||||||||
\(898\) | −17.6226 | −0.588072 | ||||||||
\(899\) | −74.9058 | −2.49825 | ||||||||
\(900\) | −7.33560 | −0.244520 | ||||||||
\(901\) | 2.58655 | 0.0861703 | ||||||||
\(902\) | −6.32667 | −0.210655 | ||||||||
\(903\) | −7.13990 | −0.237601 | ||||||||
\(904\) | 77.3898 | 2.57395 | ||||||||
\(905\) | 2.15937 | 0.0717800 | ||||||||
\(906\) | −18.8457 | −0.626107 | ||||||||
\(907\) | −35.6009 | −1.18211 | −0.591054 | − | 0.806632i | \(-0.701288\pi\) | ||||
−0.591054 | + | 0.806632i | \(0.701288\pi\) | |||||||
\(908\) | 79.2470 | 2.62990 | ||||||||
\(909\) | −24.2269 | −0.803555 | ||||||||
\(910\) | 3.08701 | 0.102334 | ||||||||
\(911\) | 2.04185 | 0.0676495 | 0.0338247 | − | 0.999428i | \(-0.489231\pi\) | ||||
0.0338247 | + | 0.999428i | \(0.489231\pi\) | |||||||
\(912\) | −80.0034 | −2.64918 | ||||||||
\(913\) | 6.06424 | 0.200697 | ||||||||
\(914\) | 34.4475 | 1.13942 | ||||||||
\(915\) | −2.86121 | −0.0945887 | ||||||||
\(916\) | 125.333 | 4.14113 | ||||||||
\(917\) | 20.8758 | 0.689378 | ||||||||
\(918\) | 17.9777 | 0.593354 | ||||||||
\(919\) | −20.3660 | −0.671812 | −0.335906 | − | 0.941896i | \(-0.609042\pi\) | ||||
−0.335906 | + | 0.941896i | \(0.609042\pi\) | |||||||
\(920\) | −28.0270 | −0.924024 | ||||||||
\(921\) | −18.3204 | −0.603679 | ||||||||
\(922\) | −84.2241 | −2.77377 | ||||||||
\(923\) | 10.7956 | 0.355340 | ||||||||
\(924\) | 6.54495 | 0.215313 | ||||||||
\(925\) | −4.17187 | −0.137170 | ||||||||
\(926\) | −26.3074 | −0.864515 | ||||||||
\(927\) | −4.83040 | −0.158651 | ||||||||
\(928\) | −179.227 | −5.88342 | ||||||||
\(929\) | 37.9505 | 1.24512 | 0.622558 | − | 0.782574i | \(-0.286094\pi\) | ||||
0.622558 | + | 0.782574i | \(0.286094\pi\) | |||||||
\(930\) | −27.0457 | −0.886864 | ||||||||
\(931\) | −28.0715 | −0.920005 | ||||||||
\(932\) | 58.2486 | 1.90799 | ||||||||
\(933\) | 14.5935 | 0.477768 | ||||||||
\(934\) | −11.4621 | −0.375053 | ||||||||
\(935\) | −1.19285 | −0.0390103 | ||||||||
\(936\) | 14.5715 | 0.476283 | ||||||||
\(937\) | 58.8257 | 1.92175 | 0.960875 | − | 0.276981i | \(-0.0893339\pi\) | ||||
0.960875 | + | 0.276981i | \(0.0893339\pi\) | |||||||
\(938\) | −28.1774 | −0.920025 | ||||||||
\(939\) | 34.7421 | 1.13377 | ||||||||
\(940\) | 16.9030 | 0.551315 | ||||||||
\(941\) | 31.8352 | 1.03780 | 0.518899 | − | 0.854836i | \(-0.326342\pi\) | ||||
0.518899 | + | 0.854836i | \(0.326342\pi\) | |||||||
\(942\) | 28.1511 | 0.917212 | ||||||||
\(943\) | 7.32746 | 0.238615 | ||||||||
\(944\) | 129.602 | 4.21817 | ||||||||
\(945\) | −5.40009 | −0.175665 | ||||||||
\(946\) | 15.6628 | 0.509243 | ||||||||
\(947\) | −0.796045 | −0.0258680 | −0.0129340 | − | 0.999916i | \(-0.504117\pi\) | ||||
−0.0129340 | + | 0.999916i | \(0.504117\pi\) | |||||||
\(948\) | −35.4002 | −1.14975 | ||||||||
\(949\) | 1.17856 | 0.0382578 | ||||||||
\(950\) | −12.5214 | −0.406248 | ||||||||
\(951\) | −4.16409 | −0.135030 | ||||||||
\(952\) | −10.3427 | −0.335210 | ||||||||
\(953\) | −36.0714 | −1.16847 | −0.584233 | − | 0.811586i | \(-0.698605\pi\) | ||||
−0.584233 | + | 0.811586i | \(0.698605\pi\) | |||||||
\(954\) | −8.09879 | −0.262208 | ||||||||
\(955\) | 9.47771 | 0.306692 | ||||||||
\(956\) | −123.156 | −3.98315 | ||||||||
\(957\) | −12.1206 | −0.391804 | ||||||||
\(958\) | −85.8114 | −2.77244 | ||||||||
\(959\) | 7.95343 | 0.256830 | ||||||||
\(960\) | −30.1619 | −0.973471 | ||||||||
\(961\) | 30.8190 | 0.994160 | ||||||||
\(962\) | 13.2938 | 0.428611 | ||||||||
\(963\) | 21.6551 | 0.697825 | ||||||||
\(964\) | 22.1100 | 0.712114 | ||||||||
\(965\) | −13.6330 | −0.438861 | ||||||||
\(966\) | −10.4352 | −0.335747 | ||||||||
\(967\) | 23.9237 | 0.769335 | 0.384668 | − | 0.923055i | \(-0.374316\pi\) | ||||
0.384668 | + | 0.923055i | \(0.374316\pi\) | |||||||
\(968\) | −8.95019 | −0.287670 | ||||||||
\(969\) | 7.02815 | 0.225777 | ||||||||
\(970\) | 7.35501 | 0.236155 | ||||||||
\(971\) | −18.8358 | −0.604469 | −0.302234 | − | 0.953234i | \(-0.597732\pi\) | ||||
−0.302234 | + | 0.953234i | \(0.597732\pi\) | |||||||
\(972\) | −68.8881 | −2.20959 | ||||||||
\(973\) | 14.7747 | 0.473655 | ||||||||
\(974\) | 17.5336 | 0.561813 | ||||||||
\(975\) | −1.49942 | −0.0480199 | ||||||||
\(976\) | 30.5374 | 0.977478 | ||||||||
\(977\) | 35.2631 | 1.12817 | 0.564083 | − | 0.825718i | \(-0.309230\pi\) | ||||
0.564083 | + | 0.825718i | \(0.309230\pi\) | |||||||
\(978\) | 7.72694 | 0.247080 | ||||||||
\(979\) | −14.1945 | −0.453657 | ||||||||
\(980\) | −32.1882 | −1.02822 | ||||||||
\(981\) | −11.8753 | −0.379150 | ||||||||
\(982\) | −57.7563 | −1.84308 | ||||||||
\(983\) | 10.1781 | 0.324631 | 0.162315 | − | 0.986739i | \(-0.448104\pi\) | ||||
0.162315 | + | 0.986739i | \(0.448104\pi\) | |||||||
\(984\) | 26.6447 | 0.849402 | ||||||||
\(985\) | 21.7011 | 0.691454 | ||||||||
\(986\) | 30.7261 | 0.978517 | ||||||||
\(987\) | 3.92315 | 0.124875 | ||||||||
\(988\) | 28.9839 | 0.922099 | ||||||||
\(989\) | −18.1405 | −0.576834 | ||||||||
\(990\) | 3.73495 | 0.118705 | ||||||||
\(991\) | 32.2748 | 1.02524 | 0.512621 | − | 0.858615i | \(-0.328675\pi\) | ||||
0.512621 | + | 0.858615i | \(0.328675\pi\) | |||||||
\(992\) | 147.914 | 4.69628 | ||||||||
\(993\) | −39.9865 | −1.26893 | ||||||||
\(994\) | 23.9926 | 0.760999 | ||||||||
\(995\) | −20.2297 | −0.641324 | ||||||||
\(996\) | −40.9698 | −1.29818 | ||||||||
\(997\) | −22.7855 | −0.721624 | −0.360812 | − | 0.932639i | \(-0.617500\pi\) | ||||
−0.360812 | + | 0.932639i | \(0.617500\pi\) | |||||||
\(998\) | −41.0833 | −1.30047 | ||||||||
\(999\) | −23.2548 | −0.735750 |
(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 | 4015.2.a.h.1.1 | ✓ | 37 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4015.2.a.h.1.1 | ✓ | 37 | 1.1 | even | 1 | trivial |