Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8013,2,Mod(1,8013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8013, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8013 = 3 \cdot 2671 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8013.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: | \(63.9841271397\) |
Analytic rank: | \(0\) |
Dimension: | \(129\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 8013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.58900 | −1.83070 | −0.915348 | − | 0.402663i | \(-0.868085\pi\) | ||||
−0.915348 | + | 0.402663i | \(0.868085\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 4.70290 | 2.35145 | ||||||||
\(5\) | −3.13677 | −1.40281 | −0.701404 | − | 0.712764i | \(-0.747443\pi\) | ||||
−0.701404 | + | 0.712764i | \(0.747443\pi\) | |||||||
\(6\) | −2.58900 | −1.05695 | ||||||||
\(7\) | 5.18243 | 1.95878 | 0.979388 | − | 0.201990i | \(-0.0647407\pi\) | ||||
0.979388 | + | 0.201990i | \(0.0647407\pi\) | |||||||
\(8\) | −6.99780 | −2.47410 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 8.12109 | 2.56811 | ||||||||
\(11\) | 3.07795 | 0.928036 | 0.464018 | − | 0.885826i | \(-0.346407\pi\) | ||||
0.464018 | + | 0.885826i | \(0.346407\pi\) | |||||||
\(12\) | 4.70290 | 1.35761 | ||||||||
\(13\) | 1.01286 | 0.280916 | 0.140458 | − | 0.990087i | \(-0.455142\pi\) | ||||
0.140458 | + | 0.990087i | \(0.455142\pi\) | |||||||
\(14\) | −13.4173 | −3.58592 | ||||||||
\(15\) | −3.13677 | −0.809911 | ||||||||
\(16\) | 8.71148 | 2.17787 | ||||||||
\(17\) | 7.25364 | 1.75927 | 0.879633 | − | 0.475654i | \(-0.157788\pi\) | ||||
0.879633 | + | 0.475654i | \(0.157788\pi\) | |||||||
\(18\) | −2.58900 | −0.610232 | ||||||||
\(19\) | 5.96116 | 1.36758 | 0.683792 | − | 0.729677i | \(-0.260329\pi\) | ||||
0.683792 | + | 0.729677i | \(0.260329\pi\) | |||||||
\(20\) | −14.7519 | −3.29863 | ||||||||
\(21\) | 5.18243 | 1.13090 | ||||||||
\(22\) | −7.96880 | −1.69895 | ||||||||
\(23\) | −7.91632 | −1.65067 | −0.825333 | − | 0.564646i | \(-0.809013\pi\) | ||||
−0.825333 | + | 0.564646i | \(0.809013\pi\) | |||||||
\(24\) | −6.99780 | −1.42842 | ||||||||
\(25\) | 4.83934 | 0.967869 | ||||||||
\(26\) | −2.62228 | −0.514272 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 24.3725 | 4.60596 | ||||||||
\(29\) | −8.81122 | −1.63620 | −0.818101 | − | 0.575074i | \(-0.804973\pi\) | ||||
−0.818101 | + | 0.575074i | \(0.804973\pi\) | |||||||
\(30\) | 8.12109 | 1.48270 | ||||||||
\(31\) | −6.72996 | −1.20874 | −0.604368 | − | 0.796705i | \(-0.706575\pi\) | ||||
−0.604368 | + | 0.796705i | \(0.706575\pi\) | |||||||
\(32\) | −8.55838 | −1.51292 | ||||||||
\(33\) | 3.07795 | 0.535802 | ||||||||
\(34\) | −18.7796 | −3.22068 | ||||||||
\(35\) | −16.2561 | −2.74778 | ||||||||
\(36\) | 4.70290 | 0.783817 | ||||||||
\(37\) | −2.27457 | −0.373936 | −0.186968 | − | 0.982366i | \(-0.559866\pi\) | ||||
−0.186968 | + | 0.982366i | \(0.559866\pi\) | |||||||
\(38\) | −15.4334 | −2.50363 | ||||||||
\(39\) | 1.01286 | 0.162187 | ||||||||
\(40\) | 21.9505 | 3.47068 | ||||||||
\(41\) | −2.30062 | −0.359297 | −0.179648 | − | 0.983731i | \(-0.557496\pi\) | ||||
−0.179648 | + | 0.983731i | \(0.557496\pi\) | |||||||
\(42\) | −13.4173 | −2.07033 | ||||||||
\(43\) | 1.33463 | 0.203529 | 0.101764 | − | 0.994809i | \(-0.467551\pi\) | ||||
0.101764 | + | 0.994809i | \(0.467551\pi\) | |||||||
\(44\) | 14.4753 | 2.18223 | ||||||||
\(45\) | −3.13677 | −0.467602 | ||||||||
\(46\) | 20.4953 | 3.02187 | ||||||||
\(47\) | 5.80601 | 0.846894 | 0.423447 | − | 0.905921i | \(-0.360820\pi\) | ||||
0.423447 | + | 0.905921i | \(0.360820\pi\) | |||||||
\(48\) | 8.71148 | 1.25739 | ||||||||
\(49\) | 19.8576 | 2.83680 | ||||||||
\(50\) | −12.5290 | −1.77187 | ||||||||
\(51\) | 7.25364 | 1.01571 | ||||||||
\(52\) | 4.76337 | 0.660560 | ||||||||
\(53\) | 2.49814 | 0.343146 | 0.171573 | − | 0.985171i | \(-0.445115\pi\) | ||||
0.171573 | + | 0.985171i | \(0.445115\pi\) | |||||||
\(54\) | −2.58900 | −0.352318 | ||||||||
\(55\) | −9.65482 | −1.30186 | ||||||||
\(56\) | −36.2656 | −4.84620 | ||||||||
\(57\) | 5.96116 | 0.789575 | ||||||||
\(58\) | 22.8122 | 2.99539 | ||||||||
\(59\) | 6.15954 | 0.801904 | 0.400952 | − | 0.916099i | \(-0.368679\pi\) | ||||
0.400952 | + | 0.916099i | \(0.368679\pi\) | |||||||
\(60\) | −14.7519 | −1.90447 | ||||||||
\(61\) | 11.0981 | 1.42096 | 0.710481 | − | 0.703717i | \(-0.248478\pi\) | ||||
0.710481 | + | 0.703717i | \(0.248478\pi\) | |||||||
\(62\) | 17.4238 | 2.21283 | ||||||||
\(63\) | 5.18243 | 0.652925 | ||||||||
\(64\) | 4.73466 | 0.591833 | ||||||||
\(65\) | −3.17710 | −0.394071 | ||||||||
\(66\) | −7.96880 | −0.980891 | ||||||||
\(67\) | −7.41039 | −0.905323 | −0.452662 | − | 0.891682i | \(-0.649525\pi\) | ||||
−0.452662 | + | 0.891682i | \(0.649525\pi\) | |||||||
\(68\) | 34.1131 | 4.13683 | ||||||||
\(69\) | −7.91632 | −0.953013 | ||||||||
\(70\) | 42.0870 | 5.03036 | ||||||||
\(71\) | 10.6743 | 1.26681 | 0.633405 | − | 0.773820i | \(-0.281657\pi\) | ||||
0.633405 | + | 0.773820i | \(0.281657\pi\) | |||||||
\(72\) | −6.99780 | −0.824699 | ||||||||
\(73\) | −0.487453 | −0.0570520 | −0.0285260 | − | 0.999593i | \(-0.509081\pi\) | ||||
−0.0285260 | + | 0.999593i | \(0.509081\pi\) | |||||||
\(74\) | 5.88884 | 0.684564 | ||||||||
\(75\) | 4.83934 | 0.558799 | ||||||||
\(76\) | 28.0348 | 3.21581 | ||||||||
\(77\) | 15.9513 | 1.81781 | ||||||||
\(78\) | −2.62228 | −0.296915 | ||||||||
\(79\) | 2.07524 | 0.233483 | 0.116742 | − | 0.993162i | \(-0.462755\pi\) | ||||
0.116742 | + | 0.993162i | \(0.462755\pi\) | |||||||
\(80\) | −27.3259 | −3.05513 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 5.95630 | 0.657763 | ||||||||
\(83\) | 11.9859 | 1.31562 | 0.657809 | − | 0.753184i | \(-0.271483\pi\) | ||||
0.657809 | + | 0.753184i | \(0.271483\pi\) | |||||||
\(84\) | 24.3725 | 2.65925 | ||||||||
\(85\) | −22.7530 | −2.46791 | ||||||||
\(86\) | −3.45534 | −0.372599 | ||||||||
\(87\) | −8.81122 | −0.944662 | ||||||||
\(88\) | −21.5389 | −2.29605 | ||||||||
\(89\) | 2.15121 | 0.228028 | 0.114014 | − | 0.993479i | \(-0.463629\pi\) | ||||
0.114014 | + | 0.993479i | \(0.463629\pi\) | |||||||
\(90\) | 8.12109 | 0.856038 | ||||||||
\(91\) | 5.24906 | 0.550251 | ||||||||
\(92\) | −37.2297 | −3.88146 | ||||||||
\(93\) | −6.72996 | −0.697865 | ||||||||
\(94\) | −15.0317 | −1.55041 | ||||||||
\(95\) | −18.6988 | −1.91846 | ||||||||
\(96\) | −8.55838 | −0.873486 | ||||||||
\(97\) | 1.02023 | 0.103589 | 0.0517945 | − | 0.998658i | \(-0.483506\pi\) | ||||
0.0517945 | + | 0.998658i | \(0.483506\pi\) | |||||||
\(98\) | −51.4113 | −5.19332 | ||||||||
\(99\) | 3.07795 | 0.309345 | ||||||||
\(100\) | 22.7590 | 2.27590 | ||||||||
\(101\) | 8.44534 | 0.840342 | 0.420171 | − | 0.907445i | \(-0.361970\pi\) | ||||
0.420171 | + | 0.907445i | \(0.361970\pi\) | |||||||
\(102\) | −18.7796 | −1.85946 | ||||||||
\(103\) | −7.02341 | −0.692037 | −0.346019 | − | 0.938228i | \(-0.612467\pi\) | ||||
−0.346019 | + | 0.938228i | \(0.612467\pi\) | |||||||
\(104\) | −7.08777 | −0.695013 | ||||||||
\(105\) | −16.2561 | −1.58643 | ||||||||
\(106\) | −6.46768 | −0.628197 | ||||||||
\(107\) | 17.6121 | 1.70263 | 0.851315 | − | 0.524655i | \(-0.175806\pi\) | ||||
0.851315 | + | 0.524655i | \(0.175806\pi\) | |||||||
\(108\) | 4.70290 | 0.452537 | ||||||||
\(109\) | 1.14771 | 0.109931 | 0.0549653 | − | 0.998488i | \(-0.482495\pi\) | ||||
0.0549653 | + | 0.998488i | \(0.482495\pi\) | |||||||
\(110\) | 24.9963 | 2.38330 | ||||||||
\(111\) | −2.27457 | −0.215892 | ||||||||
\(112\) | 45.1466 | 4.26596 | ||||||||
\(113\) | 5.52424 | 0.519677 | 0.259838 | − | 0.965652i | \(-0.416331\pi\) | ||||
0.259838 | + | 0.965652i | \(0.416331\pi\) | |||||||
\(114\) | −15.4334 | −1.44547 | ||||||||
\(115\) | 24.8317 | 2.31557 | ||||||||
\(116\) | −41.4383 | −3.84745 | ||||||||
\(117\) | 1.01286 | 0.0936387 | ||||||||
\(118\) | −15.9470 | −1.46804 | ||||||||
\(119\) | 37.5915 | 3.44601 | ||||||||
\(120\) | 21.9505 | 2.00380 | ||||||||
\(121\) | −1.52623 | −0.138749 | ||||||||
\(122\) | −28.7328 | −2.60135 | ||||||||
\(123\) | −2.30062 | −0.207440 | ||||||||
\(124\) | −31.6503 | −2.84229 | ||||||||
\(125\) | 0.503945 | 0.0450742 | ||||||||
\(126\) | −13.4173 | −1.19531 | ||||||||
\(127\) | 5.47321 | 0.485669 | 0.242834 | − | 0.970068i | \(-0.421923\pi\) | ||||
0.242834 | + | 0.970068i | \(0.421923\pi\) | |||||||
\(128\) | 4.85874 | 0.429456 | ||||||||
\(129\) | 1.33463 | 0.117507 | ||||||||
\(130\) | 8.22551 | 0.721425 | ||||||||
\(131\) | 11.4817 | 1.00316 | 0.501582 | − | 0.865110i | \(-0.332752\pi\) | ||||
0.501582 | + | 0.865110i | \(0.332752\pi\) | |||||||
\(132\) | 14.4753 | 1.25991 | ||||||||
\(133\) | 30.8933 | 2.67879 | ||||||||
\(134\) | 19.1855 | 1.65737 | ||||||||
\(135\) | −3.13677 | −0.269970 | ||||||||
\(136\) | −50.7595 | −4.35259 | ||||||||
\(137\) | −11.4893 | −0.981594 | −0.490797 | − | 0.871274i | \(-0.663294\pi\) | ||||
−0.490797 | + | 0.871274i | \(0.663294\pi\) | |||||||
\(138\) | 20.4953 | 1.74468 | ||||||||
\(139\) | −6.86691 | −0.582444 | −0.291222 | − | 0.956655i | \(-0.594062\pi\) | ||||
−0.291222 | + | 0.956655i | \(0.594062\pi\) | |||||||
\(140\) | −76.4509 | −6.46128 | ||||||||
\(141\) | 5.80601 | 0.488954 | ||||||||
\(142\) | −27.6358 | −2.31915 | ||||||||
\(143\) | 3.11752 | 0.260700 | ||||||||
\(144\) | 8.71148 | 0.725957 | ||||||||
\(145\) | 27.6388 | 2.29528 | ||||||||
\(146\) | 1.26201 | 0.104445 | ||||||||
\(147\) | 19.8576 | 1.63783 | ||||||||
\(148\) | −10.6971 | −0.879293 | ||||||||
\(149\) | −10.5530 | −0.864539 | −0.432269 | − | 0.901745i | \(-0.642287\pi\) | ||||
−0.432269 | + | 0.901745i | \(0.642287\pi\) | |||||||
\(150\) | −12.5290 | −1.02299 | ||||||||
\(151\) | −12.2609 | −0.997775 | −0.498888 | − | 0.866667i | \(-0.666258\pi\) | ||||
−0.498888 | + | 0.866667i | \(0.666258\pi\) | |||||||
\(152\) | −41.7150 | −3.38354 | ||||||||
\(153\) | 7.25364 | 0.586422 | ||||||||
\(154\) | −41.2977 | −3.32787 | ||||||||
\(155\) | 21.1104 | 1.69563 | ||||||||
\(156\) | 4.76337 | 0.381375 | ||||||||
\(157\) | −4.99350 | −0.398525 | −0.199263 | − | 0.979946i | \(-0.563855\pi\) | ||||
−0.199263 | + | 0.979946i | \(0.563855\pi\) | |||||||
\(158\) | −5.37280 | −0.427437 | ||||||||
\(159\) | 2.49814 | 0.198116 | ||||||||
\(160\) | 26.8457 | 2.12234 | ||||||||
\(161\) | −41.0258 | −3.23329 | ||||||||
\(162\) | −2.58900 | −0.203411 | ||||||||
\(163\) | −1.57054 | −0.123014 | −0.0615071 | − | 0.998107i | \(-0.519591\pi\) | ||||
−0.0615071 | + | 0.998107i | \(0.519591\pi\) | |||||||
\(164\) | −10.8196 | −0.844868 | ||||||||
\(165\) | −9.65482 | −0.751627 | ||||||||
\(166\) | −31.0313 | −2.40850 | ||||||||
\(167\) | −18.3862 | −1.42277 | −0.711383 | − | 0.702804i | \(-0.751931\pi\) | ||||
−0.711383 | + | 0.702804i | \(0.751931\pi\) | |||||||
\(168\) | −36.2656 | −2.79795 | ||||||||
\(169\) | −11.9741 | −0.921086 | ||||||||
\(170\) | 58.9075 | 4.51800 | ||||||||
\(171\) | 5.96116 | 0.455862 | ||||||||
\(172\) | 6.27661 | 0.478587 | ||||||||
\(173\) | −18.4161 | −1.40015 | −0.700077 | − | 0.714068i | \(-0.746851\pi\) | ||||
−0.700077 | + | 0.714068i | \(0.746851\pi\) | |||||||
\(174\) | 22.8122 | 1.72939 | ||||||||
\(175\) | 25.0796 | 1.89584 | ||||||||
\(176\) | 26.8135 | 2.02114 | ||||||||
\(177\) | 6.15954 | 0.462980 | ||||||||
\(178\) | −5.56947 | −0.417449 | ||||||||
\(179\) | 2.59883 | 0.194245 | 0.0971227 | − | 0.995272i | \(-0.469036\pi\) | ||||
0.0971227 | + | 0.995272i | \(0.469036\pi\) | |||||||
\(180\) | −14.7519 | −1.09954 | ||||||||
\(181\) | −25.7664 | −1.91520 | −0.957602 | − | 0.288094i | \(-0.906978\pi\) | ||||
−0.957602 | + | 0.288094i | \(0.906978\pi\) | |||||||
\(182\) | −13.5898 | −1.00734 | ||||||||
\(183\) | 11.0981 | 0.820392 | ||||||||
\(184\) | 55.3968 | 4.08391 | ||||||||
\(185\) | 7.13480 | 0.524561 | ||||||||
\(186\) | 17.4238 | 1.27758 | ||||||||
\(187\) | 22.3263 | 1.63266 | ||||||||
\(188\) | 27.3051 | 1.99143 | ||||||||
\(189\) | 5.18243 | 0.376966 | ||||||||
\(190\) | 48.4112 | 3.51211 | ||||||||
\(191\) | 13.0262 | 0.942540 | 0.471270 | − | 0.881989i | \(-0.343796\pi\) | ||||
0.471270 | + | 0.881989i | \(0.343796\pi\) | |||||||
\(192\) | 4.73466 | 0.341695 | ||||||||
\(193\) | −12.0347 | −0.866277 | −0.433138 | − | 0.901327i | \(-0.642594\pi\) | ||||
−0.433138 | + | 0.901327i | \(0.642594\pi\) | |||||||
\(194\) | −2.64138 | −0.189640 | ||||||||
\(195\) | −3.17710 | −0.227517 | ||||||||
\(196\) | 93.3884 | 6.67060 | ||||||||
\(197\) | 7.54398 | 0.537486 | 0.268743 | − | 0.963212i | \(-0.413392\pi\) | ||||
0.268743 | + | 0.963212i | \(0.413392\pi\) | |||||||
\(198\) | −7.96880 | −0.566318 | ||||||||
\(199\) | 19.0235 | 1.34854 | 0.674272 | − | 0.738483i | \(-0.264458\pi\) | ||||
0.674272 | + | 0.738483i | \(0.264458\pi\) | |||||||
\(200\) | −33.8648 | −2.39460 | ||||||||
\(201\) | −7.41039 | −0.522689 | ||||||||
\(202\) | −21.8649 | −1.53841 | ||||||||
\(203\) | −45.6636 | −3.20495 | ||||||||
\(204\) | 34.1131 | 2.38840 | ||||||||
\(205\) | 7.21652 | 0.504024 | ||||||||
\(206\) | 18.1836 | 1.26691 | ||||||||
\(207\) | −7.91632 | −0.550222 | ||||||||
\(208\) | 8.82348 | 0.611799 | ||||||||
\(209\) | 18.3482 | 1.26917 | ||||||||
\(210\) | 42.0870 | 2.90428 | ||||||||
\(211\) | 0.338456 | 0.0233003 | 0.0116501 | − | 0.999932i | \(-0.496292\pi\) | ||||
0.0116501 | + | 0.999932i | \(0.496292\pi\) | |||||||
\(212\) | 11.7485 | 0.806891 | ||||||||
\(213\) | 10.6743 | 0.731394 | ||||||||
\(214\) | −45.5978 | −3.11700 | ||||||||
\(215\) | −4.18642 | −0.285511 | ||||||||
\(216\) | −6.99780 | −0.476140 | ||||||||
\(217\) | −34.8776 | −2.36764 | ||||||||
\(218\) | −2.97142 | −0.201250 | ||||||||
\(219\) | −0.487453 | −0.0329390 | ||||||||
\(220\) | −45.4057 | −3.06125 | ||||||||
\(221\) | 7.34690 | 0.494206 | ||||||||
\(222\) | 5.88884 | 0.395233 | ||||||||
\(223\) | 9.83348 | 0.658498 | 0.329249 | − | 0.944243i | \(-0.393204\pi\) | ||||
0.329249 | + | 0.944243i | \(0.393204\pi\) | |||||||
\(224\) | −44.3532 | −2.96348 | ||||||||
\(225\) | 4.83934 | 0.322623 | ||||||||
\(226\) | −14.3022 | −0.951370 | ||||||||
\(227\) | −14.4122 | −0.956570 | −0.478285 | − | 0.878205i | \(-0.658741\pi\) | ||||
−0.478285 | + | 0.878205i | \(0.658741\pi\) | |||||||
\(228\) | 28.0348 | 1.85665 | ||||||||
\(229\) | 25.5377 | 1.68758 | 0.843788 | − | 0.536676i | \(-0.180320\pi\) | ||||
0.843788 | + | 0.536676i | \(0.180320\pi\) | |||||||
\(230\) | −64.2892 | −4.23910 | ||||||||
\(231\) | 15.9513 | 1.04952 | ||||||||
\(232\) | 61.6592 | 4.04812 | ||||||||
\(233\) | 25.4905 | 1.66994 | 0.834968 | − | 0.550299i | \(-0.185486\pi\) | ||||
0.834968 | + | 0.550299i | \(0.185486\pi\) | |||||||
\(234\) | −2.62228 | −0.171424 | ||||||||
\(235\) | −18.2121 | −1.18803 | ||||||||
\(236\) | 28.9677 | 1.88564 | ||||||||
\(237\) | 2.07524 | 0.134802 | ||||||||
\(238\) | −97.3242 | −6.30859 | ||||||||
\(239\) | −8.14532 | −0.526877 | −0.263439 | − | 0.964676i | \(-0.584857\pi\) | ||||
−0.263439 | + | 0.964676i | \(0.584857\pi\) | |||||||
\(240\) | −27.3259 | −1.76388 | ||||||||
\(241\) | −9.03631 | −0.582080 | −0.291040 | − | 0.956711i | \(-0.594001\pi\) | ||||
−0.291040 | + | 0.956711i | \(0.594001\pi\) | |||||||
\(242\) | 3.95141 | 0.254007 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 52.1931 | 3.34132 | ||||||||
\(245\) | −62.2888 | −3.97949 | ||||||||
\(246\) | 5.95630 | 0.379760 | ||||||||
\(247\) | 6.03781 | 0.384176 | ||||||||
\(248\) | 47.0949 | 2.99053 | ||||||||
\(249\) | 11.9859 | 0.759573 | ||||||||
\(250\) | −1.30471 | −0.0825172 | ||||||||
\(251\) | 6.27854 | 0.396298 | 0.198149 | − | 0.980172i | \(-0.436507\pi\) | ||||
0.198149 | + | 0.980172i | \(0.436507\pi\) | |||||||
\(252\) | 24.3725 | 1.53532 | ||||||||
\(253\) | −24.3660 | −1.53188 | ||||||||
\(254\) | −14.1701 | −0.889113 | ||||||||
\(255\) | −22.7530 | −1.42485 | ||||||||
\(256\) | −22.0486 | −1.37804 | ||||||||
\(257\) | −17.3431 | −1.08184 | −0.540918 | − | 0.841075i | \(-0.681923\pi\) | ||||
−0.540918 | + | 0.841075i | \(0.681923\pi\) | |||||||
\(258\) | −3.45534 | −0.215120 | ||||||||
\(259\) | −11.7878 | −0.732457 | ||||||||
\(260\) | −14.9416 | −0.926639 | ||||||||
\(261\) | −8.81122 | −0.545401 | ||||||||
\(262\) | −29.7262 | −1.83649 | ||||||||
\(263\) | −1.50004 | −0.0924963 | −0.0462481 | − | 0.998930i | \(-0.514726\pi\) | ||||
−0.0462481 | + | 0.998930i | \(0.514726\pi\) | |||||||
\(264\) | −21.5389 | −1.32563 | ||||||||
\(265\) | −7.83610 | −0.481368 | ||||||||
\(266\) | −79.9827 | −4.90405 | ||||||||
\(267\) | 2.15121 | 0.131652 | ||||||||
\(268\) | −34.8503 | −2.12882 | ||||||||
\(269\) | 15.7426 | 0.959844 | 0.479922 | − | 0.877311i | \(-0.340665\pi\) | ||||
0.479922 | + | 0.877311i | \(0.340665\pi\) | |||||||
\(270\) | 8.12109 | 0.494234 | ||||||||
\(271\) | 9.29233 | 0.564469 | 0.282234 | − | 0.959345i | \(-0.408924\pi\) | ||||
0.282234 | + | 0.959345i | \(0.408924\pi\) | |||||||
\(272\) | 63.1899 | 3.83145 | ||||||||
\(273\) | 5.24906 | 0.317688 | ||||||||
\(274\) | 29.7457 | 1.79700 | ||||||||
\(275\) | 14.8952 | 0.898217 | ||||||||
\(276\) | −37.2297 | −2.24096 | ||||||||
\(277\) | 7.05145 | 0.423681 | 0.211840 | − | 0.977304i | \(-0.432054\pi\) | ||||
0.211840 | + | 0.977304i | \(0.432054\pi\) | |||||||
\(278\) | 17.7784 | 1.06628 | ||||||||
\(279\) | −6.72996 | −0.402912 | ||||||||
\(280\) | 113.757 | 6.79828 | ||||||||
\(281\) | −25.5843 | −1.52623 | −0.763117 | − | 0.646261i | \(-0.776332\pi\) | ||||
−0.763117 | + | 0.646261i | \(0.776332\pi\) | |||||||
\(282\) | −15.0317 | −0.895127 | ||||||||
\(283\) | 0.286131 | 0.0170087 | 0.00850435 | − | 0.999964i | \(-0.497293\pi\) | ||||
0.00850435 | + | 0.999964i | \(0.497293\pi\) | |||||||
\(284\) | 50.2004 | 2.97884 | ||||||||
\(285\) | −18.6988 | −1.10762 | ||||||||
\(286\) | −8.07125 | −0.477263 | ||||||||
\(287\) | −11.9228 | −0.703781 | ||||||||
\(288\) | −8.55838 | −0.504307 | ||||||||
\(289\) | 35.6153 | 2.09501 | ||||||||
\(290\) | −71.5568 | −4.20196 | ||||||||
\(291\) | 1.02023 | 0.0598072 | ||||||||
\(292\) | −2.29244 | −0.134155 | ||||||||
\(293\) | −7.58655 | −0.443211 | −0.221605 | − | 0.975136i | \(-0.571130\pi\) | ||||
−0.221605 | + | 0.975136i | \(0.571130\pi\) | |||||||
\(294\) | −51.4113 | −2.99837 | ||||||||
\(295\) | −19.3211 | −1.12492 | ||||||||
\(296\) | 15.9170 | 0.925154 | ||||||||
\(297\) | 3.07795 | 0.178601 | ||||||||
\(298\) | 27.3218 | 1.58271 | ||||||||
\(299\) | −8.01810 | −0.463699 | ||||||||
\(300\) | 22.7590 | 1.31399 | ||||||||
\(301\) | 6.91661 | 0.398667 | ||||||||
\(302\) | 31.7433 | 1.82662 | ||||||||
\(303\) | 8.44534 | 0.485172 | ||||||||
\(304\) | 51.9305 | 2.97842 | ||||||||
\(305\) | −34.8121 | −1.99334 | ||||||||
\(306\) | −18.7796 | −1.07356 | ||||||||
\(307\) | 12.8976 | 0.736105 | 0.368052 | − | 0.929805i | \(-0.380025\pi\) | ||||
0.368052 | + | 0.929805i | \(0.380025\pi\) | |||||||
\(308\) | 75.0172 | 4.27450 | ||||||||
\(309\) | −7.02341 | −0.399548 | ||||||||
\(310\) | −54.6546 | −3.10418 | ||||||||
\(311\) | −15.8834 | −0.900667 | −0.450334 | − | 0.892860i | \(-0.648695\pi\) | ||||
−0.450334 | + | 0.892860i | \(0.648695\pi\) | |||||||
\(312\) | −7.08777 | −0.401266 | ||||||||
\(313\) | 27.7054 | 1.56600 | 0.783002 | − | 0.622020i | \(-0.213688\pi\) | ||||
0.783002 | + | 0.622020i | \(0.213688\pi\) | |||||||
\(314\) | 12.9282 | 0.729579 | ||||||||
\(315\) | −16.2561 | −0.915928 | ||||||||
\(316\) | 9.75967 | 0.549024 | ||||||||
\(317\) | −14.6549 | −0.823101 | −0.411551 | − | 0.911387i | \(-0.635013\pi\) | ||||
−0.411551 | + | 0.911387i | \(0.635013\pi\) | |||||||
\(318\) | −6.46768 | −0.362689 | ||||||||
\(319\) | −27.1205 | −1.51846 | ||||||||
\(320\) | −14.8516 | −0.830227 | ||||||||
\(321\) | 17.6121 | 0.983014 | ||||||||
\(322\) | 106.216 | 5.91916 | ||||||||
\(323\) | 43.2401 | 2.40594 | ||||||||
\(324\) | 4.70290 | 0.261272 | ||||||||
\(325\) | 4.90156 | 0.271890 | ||||||||
\(326\) | 4.06612 | 0.225202 | ||||||||
\(327\) | 1.14771 | 0.0634685 | ||||||||
\(328\) | 16.0993 | 0.888934 | ||||||||
\(329\) | 30.0893 | 1.65888 | ||||||||
\(330\) | 24.9963 | 1.37600 | ||||||||
\(331\) | 0.242102 | 0.0133071 | 0.00665355 | − | 0.999978i | \(-0.497882\pi\) | ||||
0.00665355 | + | 0.999978i | \(0.497882\pi\) | |||||||
\(332\) | 56.3683 | 3.09361 | ||||||||
\(333\) | −2.27457 | −0.124645 | ||||||||
\(334\) | 47.6018 | 2.60465 | ||||||||
\(335\) | 23.2447 | 1.26999 | ||||||||
\(336\) | 45.1466 | 2.46295 | ||||||||
\(337\) | 34.0579 | 1.85525 | 0.927626 | − | 0.373511i | \(-0.121846\pi\) | ||||
0.927626 | + | 0.373511i | \(0.121846\pi\) | |||||||
\(338\) | 31.0010 | 1.68623 | ||||||||
\(339\) | 5.52424 | 0.300035 | ||||||||
\(340\) | −107.005 | −5.80317 | ||||||||
\(341\) | −20.7145 | −1.12175 | ||||||||
\(342\) | −15.4334 | −0.834544 | ||||||||
\(343\) | 66.6337 | 3.59788 | ||||||||
\(344\) | −9.33945 | −0.503549 | ||||||||
\(345\) | 24.8317 | 1.33689 | ||||||||
\(346\) | 47.6793 | 2.56326 | ||||||||
\(347\) | −27.1169 | −1.45571 | −0.727855 | − | 0.685731i | \(-0.759483\pi\) | ||||
−0.727855 | + | 0.685731i | \(0.759483\pi\) | |||||||
\(348\) | −41.4383 | −2.22133 | ||||||||
\(349\) | −10.5112 | −0.562654 | −0.281327 | − | 0.959612i | \(-0.590775\pi\) | ||||
−0.281327 | + | 0.959612i | \(0.590775\pi\) | |||||||
\(350\) | −64.9309 | −3.47070 | ||||||||
\(351\) | 1.01286 | 0.0540623 | ||||||||
\(352\) | −26.3423 | −1.40405 | ||||||||
\(353\) | 28.3923 | 1.51117 | 0.755586 | − | 0.655049i | \(-0.227352\pi\) | ||||
0.755586 | + | 0.655049i | \(0.227352\pi\) | |||||||
\(354\) | −15.9470 | −0.847575 | ||||||||
\(355\) | −33.4830 | −1.77709 | ||||||||
\(356\) | 10.1169 | 0.536195 | ||||||||
\(357\) | 37.5915 | 1.98955 | ||||||||
\(358\) | −6.72835 | −0.355605 | ||||||||
\(359\) | 16.4215 | 0.866691 | 0.433346 | − | 0.901228i | \(-0.357333\pi\) | ||||
0.433346 | + | 0.901228i | \(0.357333\pi\) | |||||||
\(360\) | 21.9505 | 1.15689 | ||||||||
\(361\) | 16.5355 | 0.870288 | ||||||||
\(362\) | 66.7092 | 3.50616 | ||||||||
\(363\) | −1.52623 | −0.0801065 | ||||||||
\(364\) | 24.6858 | 1.29389 | ||||||||
\(365\) | 1.52903 | 0.0800330 | ||||||||
\(366\) | −28.7328 | −1.50189 | ||||||||
\(367\) | 28.1337 | 1.46857 | 0.734283 | − | 0.678843i | \(-0.237518\pi\) | ||||
0.734283 | + | 0.678843i | \(0.237518\pi\) | |||||||
\(368\) | −68.9628 | −3.59494 | ||||||||
\(369\) | −2.30062 | −0.119766 | ||||||||
\(370\) | −18.4720 | −0.960311 | ||||||||
\(371\) | 12.9465 | 0.672146 | ||||||||
\(372\) | −31.6503 | −1.64099 | ||||||||
\(373\) | −31.0784 | −1.60918 | −0.804590 | − | 0.593831i | \(-0.797615\pi\) | ||||
−0.804590 | + | 0.593831i | \(0.797615\pi\) | |||||||
\(374\) | −57.8028 | −2.98891 | ||||||||
\(375\) | 0.503945 | 0.0260236 | ||||||||
\(376\) | −40.6293 | −2.09530 | ||||||||
\(377\) | −8.92451 | −0.459636 | ||||||||
\(378\) | −13.4173 | −0.690111 | ||||||||
\(379\) | 15.3729 | 0.789653 | 0.394827 | − | 0.918756i | \(-0.370805\pi\) | ||||
0.394827 | + | 0.918756i | \(0.370805\pi\) | |||||||
\(380\) | −87.9387 | −4.51116 | ||||||||
\(381\) | 5.47321 | 0.280401 | ||||||||
\(382\) | −33.7247 | −1.72550 | ||||||||
\(383\) | 13.8558 | 0.708001 | 0.354000 | − | 0.935245i | \(-0.384821\pi\) | ||||
0.354000 | + | 0.935245i | \(0.384821\pi\) | |||||||
\(384\) | 4.85874 | 0.247947 | ||||||||
\(385\) | −50.0355 | −2.55004 | ||||||||
\(386\) | 31.1578 | 1.58589 | ||||||||
\(387\) | 1.33463 | 0.0678428 | ||||||||
\(388\) | 4.79806 | 0.243585 | ||||||||
\(389\) | −20.1130 | −1.01977 | −0.509884 | − | 0.860243i | \(-0.670312\pi\) | ||||
−0.509884 | + | 0.860243i | \(0.670312\pi\) | |||||||
\(390\) | 8.22551 | 0.416515 | ||||||||
\(391\) | −57.4221 | −2.90396 | ||||||||
\(392\) | −138.960 | −7.01852 | ||||||||
\(393\) | 11.4817 | 0.579177 | ||||||||
\(394\) | −19.5313 | −0.983974 | ||||||||
\(395\) | −6.50957 | −0.327532 | ||||||||
\(396\) | 14.4753 | 0.727411 | ||||||||
\(397\) | 31.6025 | 1.58608 | 0.793042 | − | 0.609168i | \(-0.208496\pi\) | ||||
0.793042 | + | 0.609168i | \(0.208496\pi\) | |||||||
\(398\) | −49.2519 | −2.46877 | ||||||||
\(399\) | 30.8933 | 1.54660 | ||||||||
\(400\) | 42.1578 | 2.10789 | ||||||||
\(401\) | −4.71867 | −0.235639 | −0.117820 | − | 0.993035i | \(-0.537590\pi\) | ||||
−0.117820 | + | 0.993035i | \(0.537590\pi\) | |||||||
\(402\) | 19.1855 | 0.956884 | ||||||||
\(403\) | −6.81649 | −0.339554 | ||||||||
\(404\) | 39.7176 | 1.97602 | ||||||||
\(405\) | −3.13677 | −0.155867 | ||||||||
\(406\) | 118.223 | 5.86730 | ||||||||
\(407\) | −7.00100 | −0.347026 | ||||||||
\(408\) | −50.7595 | −2.51297 | ||||||||
\(409\) | 15.6575 | 0.774214 | 0.387107 | − | 0.922035i | \(-0.373474\pi\) | ||||
0.387107 | + | 0.922035i | \(0.373474\pi\) | |||||||
\(410\) | −18.6836 | −0.922715 | ||||||||
\(411\) | −11.4893 | −0.566724 | ||||||||
\(412\) | −33.0304 | −1.62729 | ||||||||
\(413\) | 31.9214 | 1.57075 | ||||||||
\(414\) | 20.4953 | 1.00729 | ||||||||
\(415\) | −37.5969 | −1.84556 | ||||||||
\(416\) | −8.66842 | −0.425004 | ||||||||
\(417\) | −6.86691 | −0.336274 | ||||||||
\(418\) | −47.5033 | −2.32346 | ||||||||
\(419\) | 31.2654 | 1.52741 | 0.763707 | − | 0.645563i | \(-0.223377\pi\) | ||||
0.763707 | + | 0.645563i | \(0.223377\pi\) | |||||||
\(420\) | −76.4509 | −3.73042 | ||||||||
\(421\) | 17.8954 | 0.872168 | 0.436084 | − | 0.899906i | \(-0.356365\pi\) | ||||
0.436084 | + | 0.899906i | \(0.356365\pi\) | |||||||
\(422\) | −0.876261 | −0.0426557 | ||||||||
\(423\) | 5.80601 | 0.282298 | ||||||||
\(424\) | −17.4815 | −0.848977 | ||||||||
\(425\) | 35.1028 | 1.70274 | ||||||||
\(426\) | −27.6358 | −1.33896 | ||||||||
\(427\) | 57.5150 | 2.78334 | ||||||||
\(428\) | 82.8281 | 4.00365 | ||||||||
\(429\) | 3.11752 | 0.150515 | ||||||||
\(430\) | 10.8386 | 0.522685 | ||||||||
\(431\) | −25.7198 | −1.23888 | −0.619440 | − | 0.785044i | \(-0.712640\pi\) | ||||
−0.619440 | + | 0.785044i | \(0.712640\pi\) | |||||||
\(432\) | 8.71148 | 0.419131 | ||||||||
\(433\) | 2.43206 | 0.116877 | 0.0584387 | − | 0.998291i | \(-0.481388\pi\) | ||||
0.0584387 | + | 0.998291i | \(0.481388\pi\) | |||||||
\(434\) | 90.2979 | 4.33444 | ||||||||
\(435\) | 27.6388 | 1.32518 | ||||||||
\(436\) | 5.39756 | 0.258496 | ||||||||
\(437\) | −47.1905 | −2.25743 | ||||||||
\(438\) | 1.26201 | 0.0603013 | ||||||||
\(439\) | −15.5075 | −0.740133 | −0.370066 | − | 0.929005i | \(-0.620665\pi\) | ||||
−0.370066 | + | 0.929005i | \(0.620665\pi\) | |||||||
\(440\) | 67.5625 | 3.22092 | ||||||||
\(441\) | 19.8576 | 0.945600 | ||||||||
\(442\) | −19.0211 | −0.904741 | ||||||||
\(443\) | −25.3601 | −1.20489 | −0.602447 | − | 0.798159i | \(-0.705808\pi\) | ||||
−0.602447 | + | 0.798159i | \(0.705808\pi\) | |||||||
\(444\) | −10.6971 | −0.507660 | ||||||||
\(445\) | −6.74785 | −0.319879 | ||||||||
\(446\) | −25.4588 | −1.20551 | ||||||||
\(447\) | −10.5530 | −0.499142 | ||||||||
\(448\) | 24.5371 | 1.15927 | ||||||||
\(449\) | −3.64164 | −0.171860 | −0.0859298 | − | 0.996301i | \(-0.527386\pi\) | ||||
−0.0859298 | + | 0.996301i | \(0.527386\pi\) | |||||||
\(450\) | −12.5290 | −0.590625 | ||||||||
\(451\) | −7.08119 | −0.333440 | ||||||||
\(452\) | 25.9799 | 1.22199 | ||||||||
\(453\) | −12.2609 | −0.576066 | ||||||||
\(454\) | 37.3131 | 1.75119 | ||||||||
\(455\) | −16.4651 | −0.771897 | ||||||||
\(456\) | −41.7150 | −1.95349 | ||||||||
\(457\) | −7.26109 | −0.339659 | −0.169830 | − | 0.985473i | \(-0.554322\pi\) | ||||
−0.169830 | + | 0.985473i | \(0.554322\pi\) | |||||||
\(458\) | −66.1169 | −3.08944 | ||||||||
\(459\) | 7.25364 | 0.338571 | ||||||||
\(460\) | 116.781 | 5.44494 | ||||||||
\(461\) | 18.5499 | 0.863956 | 0.431978 | − | 0.901884i | \(-0.357816\pi\) | ||||
0.431978 | + | 0.901884i | \(0.357816\pi\) | |||||||
\(462\) | −41.2977 | −1.92135 | ||||||||
\(463\) | −24.8013 | −1.15261 | −0.576306 | − | 0.817234i | \(-0.695506\pi\) | ||||
−0.576306 | + | 0.817234i | \(0.695506\pi\) | |||||||
\(464\) | −76.7588 | −3.56344 | ||||||||
\(465\) | 21.1104 | 0.978970 | ||||||||
\(466\) | −65.9947 | −3.05715 | ||||||||
\(467\) | −21.8676 | −1.01191 | −0.505957 | − | 0.862559i | \(-0.668861\pi\) | ||||
−0.505957 | + | 0.862559i | \(0.668861\pi\) | |||||||
\(468\) | 4.76337 | 0.220187 | ||||||||
\(469\) | −38.4038 | −1.77332 | ||||||||
\(470\) | 47.1512 | 2.17492 | ||||||||
\(471\) | −4.99350 | −0.230089 | ||||||||
\(472\) | −43.1033 | −1.98399 | ||||||||
\(473\) | 4.10791 | 0.188882 | ||||||||
\(474\) | −5.37280 | −0.246781 | ||||||||
\(475\) | 28.8481 | 1.32364 | ||||||||
\(476\) | 176.789 | 8.10311 | ||||||||
\(477\) | 2.49814 | 0.114382 | ||||||||
\(478\) | 21.0882 | 0.964552 | ||||||||
\(479\) | 15.0290 | 0.686695 | 0.343347 | − | 0.939209i | \(-0.388439\pi\) | ||||
0.343347 | + | 0.939209i | \(0.388439\pi\) | |||||||
\(480\) | 26.8457 | 1.22533 | ||||||||
\(481\) | −2.30381 | −0.105045 | ||||||||
\(482\) | 23.3950 | 1.06561 | ||||||||
\(483\) | −41.0258 | −1.86674 | ||||||||
\(484\) | −7.17773 | −0.326260 | ||||||||
\(485\) | −3.20024 | −0.145315 | ||||||||
\(486\) | −2.58900 | −0.117439 | ||||||||
\(487\) | −31.3745 | −1.42172 | −0.710858 | − | 0.703336i | \(-0.751693\pi\) | ||||
−0.710858 | + | 0.703336i | \(0.751693\pi\) | |||||||
\(488\) | −77.6620 | −3.51560 | ||||||||
\(489\) | −1.57054 | −0.0710222 | ||||||||
\(490\) | 161.265 | 7.28523 | ||||||||
\(491\) | −33.6092 | −1.51676 | −0.758380 | − | 0.651812i | \(-0.774009\pi\) | ||||
−0.758380 | + | 0.651812i | \(0.774009\pi\) | |||||||
\(492\) | −10.8196 | −0.487785 | ||||||||
\(493\) | −63.9134 | −2.87852 | ||||||||
\(494\) | −15.6319 | −0.703311 | ||||||||
\(495\) | −9.65482 | −0.433952 | ||||||||
\(496\) | −58.6279 | −2.63247 | ||||||||
\(497\) | 55.3190 | 2.48140 | ||||||||
\(498\) | −31.0313 | −1.39055 | ||||||||
\(499\) | −5.69371 | −0.254886 | −0.127443 | − | 0.991846i | \(-0.540677\pi\) | ||||
−0.127443 | + | 0.991846i | \(0.540677\pi\) | |||||||
\(500\) | 2.37000 | 0.105990 | ||||||||
\(501\) | −18.3862 | −0.821435 | ||||||||
\(502\) | −16.2551 | −0.725501 | ||||||||
\(503\) | 43.3295 | 1.93197 | 0.965983 | − | 0.258605i | \(-0.0832628\pi\) | ||||
0.965983 | + | 0.258605i | \(0.0832628\pi\) | |||||||
\(504\) | −36.2656 | −1.61540 | ||||||||
\(505\) | −26.4911 | −1.17884 | ||||||||
\(506\) | 63.0835 | 2.80441 | ||||||||
\(507\) | −11.9741 | −0.531789 | ||||||||
\(508\) | 25.7400 | 1.14203 | ||||||||
\(509\) | 22.3110 | 0.988918 | 0.494459 | − | 0.869201i | \(-0.335366\pi\) | ||||
0.494459 | + | 0.869201i | \(0.335366\pi\) | |||||||
\(510\) | 58.9075 | 2.60847 | ||||||||
\(511\) | −2.52619 | −0.111752 | ||||||||
\(512\) | 47.3662 | 2.09331 | ||||||||
\(513\) | 5.96116 | 0.263192 | ||||||||
\(514\) | 44.9013 | 1.98051 | ||||||||
\(515\) | 22.0308 | 0.970795 | ||||||||
\(516\) | 6.27661 | 0.276313 | ||||||||
\(517\) | 17.8706 | 0.785948 | ||||||||
\(518\) | 30.5185 | 1.34091 | ||||||||
\(519\) | −18.4161 | −0.808379 | ||||||||
\(520\) | 22.2327 | 0.974970 | ||||||||
\(521\) | 26.9276 | 1.17972 | 0.589860 | − | 0.807506i | \(-0.299183\pi\) | ||||
0.589860 | + | 0.807506i | \(0.299183\pi\) | |||||||
\(522\) | 22.8122 | 0.998464 | ||||||||
\(523\) | 12.2573 | 0.535975 | 0.267987 | − | 0.963422i | \(-0.413641\pi\) | ||||
0.267987 | + | 0.963422i | \(0.413641\pi\) | |||||||
\(524\) | 53.9975 | 2.35889 | ||||||||
\(525\) | 25.0796 | 1.09456 | ||||||||
\(526\) | 3.88359 | 0.169333 | ||||||||
\(527\) | −48.8167 | −2.12649 | ||||||||
\(528\) | 26.8135 | 1.16691 | ||||||||
\(529\) | 39.6681 | 1.72470 | ||||||||
\(530\) | 20.2876 | 0.881239 | ||||||||
\(531\) | 6.15954 | 0.267301 | ||||||||
\(532\) | 145.288 | 6.29904 | ||||||||
\(533\) | −2.33020 | −0.100932 | ||||||||
\(534\) | −5.56947 | −0.241014 | ||||||||
\(535\) | −55.2453 | −2.38846 | ||||||||
\(536\) | 51.8564 | 2.23986 | ||||||||
\(537\) | 2.59883 | 0.112148 | ||||||||
\(538\) | −40.7575 | −1.75718 | ||||||||
\(539\) | 61.1207 | 2.63265 | ||||||||
\(540\) | −14.7519 | −0.634822 | ||||||||
\(541\) | −41.5884 | −1.78803 | −0.894013 | − | 0.448042i | \(-0.852122\pi\) | ||||
−0.894013 | + | 0.448042i | \(0.852122\pi\) | |||||||
\(542\) | −24.0578 | −1.03337 | ||||||||
\(543\) | −25.7664 | −1.10574 | ||||||||
\(544\) | −62.0794 | −2.66163 | ||||||||
\(545\) | −3.60010 | −0.154211 | ||||||||
\(546\) | −13.5898 | −0.581590 | ||||||||
\(547\) | −15.5817 | −0.666227 | −0.333114 | − | 0.942887i | \(-0.608099\pi\) | ||||
−0.333114 | + | 0.942887i | \(0.608099\pi\) | |||||||
\(548\) | −54.0329 | −2.30817 | ||||||||
\(549\) | 11.0981 | 0.473654 | ||||||||
\(550\) | −38.5637 | −1.64436 | ||||||||
\(551\) | −52.5251 | −2.23765 | ||||||||
\(552\) | 55.3968 | 2.35785 | ||||||||
\(553\) | 10.7548 | 0.457341 | ||||||||
\(554\) | −18.2562 | −0.775631 | ||||||||
\(555\) | 7.13480 | 0.302855 | ||||||||
\(556\) | −32.2944 | −1.36959 | ||||||||
\(557\) | 39.4222 | 1.67037 | 0.835185 | − | 0.549968i | \(-0.185360\pi\) | ||||
0.835185 | + | 0.549968i | \(0.185360\pi\) | |||||||
\(558\) | 17.4238 | 0.737610 | ||||||||
\(559\) | 1.35179 | 0.0571744 | ||||||||
\(560\) | −141.615 | −5.98432 | ||||||||
\(561\) | 22.3263 | 0.942618 | ||||||||
\(562\) | 66.2377 | 2.79407 | ||||||||
\(563\) | −1.50615 | −0.0634766 | −0.0317383 | − | 0.999496i | \(-0.510104\pi\) | ||||
−0.0317383 | + | 0.999496i | \(0.510104\pi\) | |||||||
\(564\) | 27.3051 | 1.14975 | ||||||||
\(565\) | −17.3283 | −0.729006 | ||||||||
\(566\) | −0.740792 | −0.0311378 | ||||||||
\(567\) | 5.18243 | 0.217642 | ||||||||
\(568\) | −74.6969 | −3.13421 | ||||||||
\(569\) | −1.10393 | −0.0462790 | −0.0231395 | − | 0.999732i | \(-0.507366\pi\) | ||||
−0.0231395 | + | 0.999732i | \(0.507366\pi\) | |||||||
\(570\) | 48.4112 | 2.02772 | ||||||||
\(571\) | −20.8711 | −0.873428 | −0.436714 | − | 0.899601i | \(-0.643858\pi\) | ||||
−0.436714 | + | 0.899601i | \(0.643858\pi\) | |||||||
\(572\) | 14.6614 | 0.613024 | ||||||||
\(573\) | 13.0262 | 0.544176 | ||||||||
\(574\) | 30.8681 | 1.28841 | ||||||||
\(575\) | −38.3098 | −1.59763 | ||||||||
\(576\) | 4.73466 | 0.197278 | ||||||||
\(577\) | 0.893001 | 0.0371761 | 0.0185880 | − | 0.999827i | \(-0.494083\pi\) | ||||
0.0185880 | + | 0.999827i | \(0.494083\pi\) | |||||||
\(578\) | −92.2078 | −3.83534 | ||||||||
\(579\) | −12.0347 | −0.500145 | ||||||||
\(580\) | 129.983 | 5.39723 | ||||||||
\(581\) | 62.1159 | 2.57700 | ||||||||
\(582\) | −2.64138 | −0.109489 | ||||||||
\(583\) | 7.68915 | 0.318452 | ||||||||
\(584\) | 3.41110 | 0.141152 | ||||||||
\(585\) | −3.17710 | −0.131357 | ||||||||
\(586\) | 19.6415 | 0.811385 | ||||||||
\(587\) | −11.6045 | −0.478971 | −0.239485 | − | 0.970900i | \(-0.576979\pi\) | ||||
−0.239485 | + | 0.970900i | \(0.576979\pi\) | |||||||
\(588\) | 93.3884 | 3.85127 | ||||||||
\(589\) | −40.1184 | −1.65305 | ||||||||
\(590\) | 50.0222 | 2.05938 | ||||||||
\(591\) | 7.54398 | 0.310318 | ||||||||
\(592\) | −19.8148 | −0.814384 | ||||||||
\(593\) | −15.2866 | −0.627745 | −0.313872 | − | 0.949465i | \(-0.601626\pi\) | ||||
−0.313872 | + | 0.949465i | \(0.601626\pi\) | |||||||
\(594\) | −7.96880 | −0.326964 | ||||||||
\(595\) | −117.916 | −4.83408 | ||||||||
\(596\) | −49.6299 | −2.03292 | ||||||||
\(597\) | 19.0235 | 0.778582 | ||||||||
\(598\) | 20.7588 | 0.848892 | ||||||||
\(599\) | −24.2869 | −0.992338 | −0.496169 | − | 0.868226i | \(-0.665260\pi\) | ||||
−0.496169 | + | 0.868226i | \(0.665260\pi\) | |||||||
\(600\) | −33.8648 | −1.38252 | ||||||||
\(601\) | 2.18062 | 0.0889495 | 0.0444748 | − | 0.999011i | \(-0.485839\pi\) | ||||
0.0444748 | + | 0.999011i | \(0.485839\pi\) | |||||||
\(602\) | −17.9071 | −0.729838 | ||||||||
\(603\) | −7.41039 | −0.301774 | ||||||||
\(604\) | −57.6617 | −2.34622 | ||||||||
\(605\) | 4.78745 | 0.194638 | ||||||||
\(606\) | −21.8649 | −0.888203 | ||||||||
\(607\) | 25.1637 | 1.02136 | 0.510682 | − | 0.859769i | \(-0.329393\pi\) | ||||
0.510682 | + | 0.859769i | \(0.329393\pi\) | |||||||
\(608\) | −51.0179 | −2.06905 | ||||||||
\(609\) | −45.6636 | −1.85038 | ||||||||
\(610\) | 90.1284 | 3.64919 | ||||||||
\(611\) | 5.88066 | 0.237906 | ||||||||
\(612\) | 34.1131 | 1.37894 | ||||||||
\(613\) | 33.2060 | 1.34118 | 0.670590 | − | 0.741828i | \(-0.266041\pi\) | ||||
0.670590 | + | 0.741828i | \(0.266041\pi\) | |||||||
\(614\) | −33.3918 | −1.34758 | ||||||||
\(615\) | 7.21652 | 0.290998 | ||||||||
\(616\) | −111.624 | −4.49745 | ||||||||
\(617\) | 40.0478 | 1.61226 | 0.806132 | − | 0.591735i | \(-0.201557\pi\) | ||||
0.806132 | + | 0.591735i | \(0.201557\pi\) | |||||||
\(618\) | 18.1836 | 0.731451 | ||||||||
\(619\) | 32.3170 | 1.29893 | 0.649465 | − | 0.760392i | \(-0.274993\pi\) | ||||
0.649465 | + | 0.760392i | \(0.274993\pi\) | |||||||
\(620\) | 99.2799 | 3.98718 | ||||||||
\(621\) | −7.91632 | −0.317671 | ||||||||
\(622\) | 41.1222 | 1.64885 | ||||||||
\(623\) | 11.1485 | 0.446655 | ||||||||
\(624\) | 8.82348 | 0.353222 | ||||||||
\(625\) | −25.7775 | −1.03110 | ||||||||
\(626\) | −71.7292 | −2.86688 | ||||||||
\(627\) | 18.3482 | 0.732755 | ||||||||
\(628\) | −23.4840 | −0.937112 | ||||||||
\(629\) | −16.4989 | −0.657853 | ||||||||
\(630\) | 42.0870 | 1.67679 | ||||||||
\(631\) | −46.2885 | −1.84272 | −0.921358 | − | 0.388714i | \(-0.872919\pi\) | ||||
−0.921358 | + | 0.388714i | \(0.872919\pi\) | |||||||
\(632\) | −14.5221 | −0.577660 | ||||||||
\(633\) | 0.338456 | 0.0134524 | ||||||||
\(634\) | 37.9415 | 1.50685 | ||||||||
\(635\) | −17.1682 | −0.681300 | ||||||||
\(636\) | 11.7485 | 0.465859 | ||||||||
\(637\) | 20.1129 | 0.796903 | ||||||||
\(638\) | 70.2148 | 2.77983 | ||||||||
\(639\) | 10.6743 | 0.422270 | ||||||||
\(640\) | −15.2408 | −0.602444 | ||||||||
\(641\) | −5.52413 | −0.218190 | −0.109095 | − | 0.994031i | \(-0.534795\pi\) | ||||
−0.109095 | + | 0.994031i | \(0.534795\pi\) | |||||||
\(642\) | −45.5978 | −1.79960 | ||||||||
\(643\) | 26.0076 | 1.02564 | 0.512820 | − | 0.858496i | \(-0.328601\pi\) | ||||
0.512820 | + | 0.858496i | \(0.328601\pi\) | |||||||
\(644\) | −192.940 | −7.60291 | ||||||||
\(645\) | −4.18642 | −0.164840 | ||||||||
\(646\) | −111.948 | −4.40455 | ||||||||
\(647\) | −43.8682 | −1.72464 | −0.862319 | − | 0.506365i | \(-0.830989\pi\) | ||||
−0.862319 | + | 0.506365i | \(0.830989\pi\) | |||||||
\(648\) | −6.99780 | −0.274900 | ||||||||
\(649\) | 18.9588 | 0.744196 | ||||||||
\(650\) | −12.6901 | −0.497748 | ||||||||
\(651\) | −34.8776 | −1.36696 | ||||||||
\(652\) | −7.38609 | −0.289262 | ||||||||
\(653\) | 1.79159 | 0.0701103 | 0.0350552 | − | 0.999385i | \(-0.488839\pi\) | ||||
0.0350552 | + | 0.999385i | \(0.488839\pi\) | |||||||
\(654\) | −2.97142 | −0.116192 | ||||||||
\(655\) | −36.0156 | −1.40725 | ||||||||
\(656\) | −20.0418 | −0.782501 | ||||||||
\(657\) | −0.487453 | −0.0190173 | ||||||||
\(658\) | −77.9010 | −3.03690 | ||||||||
\(659\) | 6.06276 | 0.236171 | 0.118086 | − | 0.993003i | \(-0.462324\pi\) | ||||
0.118086 | + | 0.993003i | \(0.462324\pi\) | |||||||
\(660\) | −45.4057 | −1.76741 | ||||||||
\(661\) | 19.8947 | 0.773814 | 0.386907 | − | 0.922119i | \(-0.373543\pi\) | ||||
0.386907 | + | 0.922119i | \(0.373543\pi\) | |||||||
\(662\) | −0.626800 | −0.0243613 | ||||||||
\(663\) | 7.34690 | 0.285330 | ||||||||
\(664\) | −83.8747 | −3.25497 | ||||||||
\(665\) | −96.9053 | −3.75783 | ||||||||
\(666\) | 5.88884 | 0.228188 | ||||||||
\(667\) | 69.7525 | 2.70083 | ||||||||
\(668\) | −86.4685 | −3.34556 | ||||||||
\(669\) | 9.83348 | 0.380184 | ||||||||
\(670\) | −60.1805 | −2.32497 | ||||||||
\(671\) | 34.1593 | 1.31870 | ||||||||
\(672\) | −44.3532 | −1.71096 | ||||||||
\(673\) | −7.73906 | −0.298319 | −0.149159 | − | 0.988813i | \(-0.547657\pi\) | ||||
−0.149159 | + | 0.988813i | \(0.547657\pi\) | |||||||
\(674\) | −88.1757 | −3.39640 | ||||||||
\(675\) | 4.83934 | 0.186266 | ||||||||
\(676\) | −56.3131 | −2.16589 | ||||||||
\(677\) | −29.4605 | −1.13226 | −0.566130 | − | 0.824316i | \(-0.691560\pi\) | ||||
−0.566130 | + | 0.824316i | \(0.691560\pi\) | |||||||
\(678\) | −14.3022 | −0.549274 | ||||||||
\(679\) | 5.28729 | 0.202908 | ||||||||
\(680\) | 159.221 | 6.10585 | ||||||||
\(681\) | −14.4122 | −0.552276 | ||||||||
\(682\) | 53.6297 | 2.05359 | ||||||||
\(683\) | 34.1778 | 1.30778 | 0.653889 | − | 0.756591i | \(-0.273136\pi\) | ||||
0.653889 | + | 0.756591i | \(0.273136\pi\) | |||||||
\(684\) | 28.0348 | 1.07194 | ||||||||
\(685\) | 36.0392 | 1.37699 | ||||||||
\(686\) | −172.514 | −6.58663 | ||||||||
\(687\) | 25.5377 | 0.974323 | ||||||||
\(688\) | 11.6266 | 0.443259 | ||||||||
\(689\) | 2.53026 | 0.0963953 | ||||||||
\(690\) | −64.2892 | −2.44745 | ||||||||
\(691\) | 43.2751 | 1.64626 | 0.823132 | − | 0.567850i | \(-0.192225\pi\) | ||||
0.823132 | + | 0.567850i | \(0.192225\pi\) | |||||||
\(692\) | −86.6093 | −3.29239 | ||||||||
\(693\) | 15.9513 | 0.605938 | ||||||||
\(694\) | 70.2055 | 2.66497 | ||||||||
\(695\) | 21.5400 | 0.817057 | ||||||||
\(696\) | 61.6592 | 2.33719 | ||||||||
\(697\) | −16.6879 | −0.632098 | ||||||||
\(698\) | 27.2136 | 1.03005 | ||||||||
\(699\) | 25.4905 | 0.964138 | ||||||||
\(700\) | 117.947 | 4.45797 | ||||||||
\(701\) | 9.92122 | 0.374719 | 0.187360 | − | 0.982291i | \(-0.440007\pi\) | ||||
0.187360 | + | 0.982291i | \(0.440007\pi\) | |||||||
\(702\) | −2.62228 | −0.0989717 | ||||||||
\(703\) | −13.5591 | −0.511389 | ||||||||
\(704\) | 14.5730 | 0.549242 | ||||||||
\(705\) | −18.2121 | −0.685909 | ||||||||
\(706\) | −73.5077 | −2.76650 | ||||||||
\(707\) | 43.7674 | 1.64604 | ||||||||
\(708\) | 28.9677 | 1.08867 | ||||||||
\(709\) | −17.9596 | −0.674488 | −0.337244 | − | 0.941417i | \(-0.609495\pi\) | ||||
−0.337244 | + | 0.941417i | \(0.609495\pi\) | |||||||
\(710\) | 86.6873 | 3.25332 | ||||||||
\(711\) | 2.07524 | 0.0778278 | ||||||||
\(712\) | −15.0537 | −0.564162 | ||||||||
\(713\) | 53.2765 | 1.99522 | ||||||||
\(714\) | −97.3242 | −3.64227 | ||||||||
\(715\) | −9.77896 | −0.365712 | ||||||||
\(716\) | 12.2220 | 0.456759 | ||||||||
\(717\) | −8.14532 | −0.304193 | ||||||||
\(718\) | −42.5151 | −1.58665 | ||||||||
\(719\) | −31.0657 | −1.15855 | −0.579277 | − | 0.815130i | \(-0.696665\pi\) | ||||
−0.579277 | + | 0.815130i | \(0.696665\pi\) | |||||||
\(720\) | −27.3259 | −1.01838 | ||||||||
\(721\) | −36.3983 | −1.35555 | ||||||||
\(722\) | −42.8103 | −1.59323 | ||||||||
\(723\) | −9.03631 | −0.336064 | ||||||||
\(724\) | −121.177 | −4.50351 | ||||||||
\(725\) | −42.6405 | −1.58363 | ||||||||
\(726\) | 3.95141 | 0.146651 | ||||||||
\(727\) | −35.3498 | −1.31105 | −0.655525 | − | 0.755174i | \(-0.727553\pi\) | ||||
−0.655525 | + | 0.755174i | \(0.727553\pi\) | |||||||
\(728\) | −36.7319 | −1.36138 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −3.95865 | −0.146516 | ||||||||
\(731\) | 9.68089 | 0.358061 | ||||||||
\(732\) | 52.1931 | 1.92911 | ||||||||
\(733\) | −45.7739 | −1.69070 | −0.845349 | − | 0.534215i | \(-0.820607\pi\) | ||||
−0.845349 | + | 0.534215i | \(0.820607\pi\) | |||||||
\(734\) | −72.8380 | −2.68850 | ||||||||
\(735\) | −62.2888 | −2.29756 | ||||||||
\(736\) | 67.7509 | 2.49733 | ||||||||
\(737\) | −22.8088 | −0.840173 | ||||||||
\(738\) | 5.95630 | 0.219254 | ||||||||
\(739\) | −17.0292 | −0.626430 | −0.313215 | − | 0.949682i | \(-0.601406\pi\) | ||||
−0.313215 | + | 0.949682i | \(0.601406\pi\) | |||||||
\(740\) | 33.5542 | 1.23348 | ||||||||
\(741\) | 6.03781 | 0.221804 | ||||||||
\(742\) | −33.5183 | −1.23050 | ||||||||
\(743\) | 39.2325 | 1.43930 | 0.719650 | − | 0.694337i | \(-0.244302\pi\) | ||||
0.719650 | + | 0.694337i | \(0.244302\pi\) | |||||||
\(744\) | 47.0949 | 1.72658 | ||||||||
\(745\) | 33.1025 | 1.21278 | ||||||||
\(746\) | 80.4619 | 2.94592 | ||||||||
\(747\) | 11.9859 | 0.438540 | ||||||||
\(748\) | 104.998 | 3.83912 | ||||||||
\(749\) | 91.2737 | 3.33507 | ||||||||
\(750\) | −1.30471 | −0.0476413 | ||||||||
\(751\) | 27.7034 | 1.01091 | 0.505456 | − | 0.862852i | \(-0.331324\pi\) | ||||
0.505456 | + | 0.862852i | \(0.331324\pi\) | |||||||
\(752\) | 50.5790 | 1.84442 | ||||||||
\(753\) | 6.27854 | 0.228803 | ||||||||
\(754\) | 23.1055 | 0.841454 | ||||||||
\(755\) | 38.4596 | 1.39969 | ||||||||
\(756\) | 24.3725 | 0.886418 | ||||||||
\(757\) | −27.0986 | −0.984916 | −0.492458 | − | 0.870336i | \(-0.663902\pi\) | ||||
−0.492458 | + | 0.870336i | \(0.663902\pi\) | |||||||
\(758\) | −39.8004 | −1.44562 | ||||||||
\(759\) | −24.3660 | −0.884431 | ||||||||
\(760\) | 130.851 | 4.74645 | ||||||||
\(761\) | −6.54814 | −0.237370 | −0.118685 | − | 0.992932i | \(-0.537868\pi\) | ||||
−0.118685 | + | 0.992932i | \(0.537868\pi\) | |||||||
\(762\) | −14.1701 | −0.513329 | ||||||||
\(763\) | 5.94793 | 0.215329 | ||||||||
\(764\) | 61.2607 | 2.21634 | ||||||||
\(765\) | −22.7530 | −0.822637 | ||||||||
\(766\) | −35.8727 | −1.29613 | ||||||||
\(767\) | 6.23874 | 0.225268 | ||||||||
\(768\) | −22.0486 | −0.795610 | ||||||||
\(769\) | 8.93807 | 0.322315 | 0.161157 | − | 0.986929i | \(-0.448477\pi\) | ||||
0.161157 | + | 0.986929i | \(0.448477\pi\) | |||||||
\(770\) | 129.542 | 4.66836 | ||||||||
\(771\) | −17.3431 | −0.624598 | ||||||||
\(772\) | −56.5980 | −2.03701 | ||||||||
\(773\) | 39.5917 | 1.42401 | 0.712006 | − | 0.702173i | \(-0.247787\pi\) | ||||
0.712006 | + | 0.702173i | \(0.247787\pi\) | |||||||
\(774\) | −3.45534 | −0.124200 | ||||||||
\(775\) | −32.5686 | −1.16990 | ||||||||
\(776\) | −7.13939 | −0.256289 | ||||||||
\(777\) | −11.7878 | −0.422884 | ||||||||
\(778\) | 52.0724 | 1.86688 | ||||||||
\(779\) | −13.7144 | −0.491368 | ||||||||
\(780\) | −14.9416 | −0.534995 | ||||||||
\(781\) | 32.8551 | 1.17565 | ||||||||
\(782\) | 148.666 | 5.31627 | ||||||||
\(783\) | −8.81122 | −0.314887 | ||||||||
\(784\) | 172.989 | 6.17818 | ||||||||
\(785\) | 15.6635 | 0.559054 | ||||||||
\(786\) | −29.7262 | −1.06030 | ||||||||
\(787\) | −27.9948 | −0.997909 | −0.498954 | − | 0.866628i | \(-0.666282\pi\) | ||||
−0.498954 | + | 0.866628i | \(0.666282\pi\) | |||||||
\(788\) | 35.4786 | 1.26387 | ||||||||
\(789\) | −1.50004 | −0.0534027 | ||||||||
\(790\) | 16.8533 | 0.599612 | ||||||||
\(791\) | 28.6290 | 1.01793 | ||||||||
\(792\) | −21.5389 | −0.765350 | ||||||||
\(793\) | 11.2408 | 0.399171 | ||||||||
\(794\) | −81.8187 | −2.90364 | ||||||||
\(795\) | −7.83610 | −0.277918 | ||||||||
\(796\) | 89.4659 | 3.17103 | ||||||||
\(797\) | 6.10535 | 0.216263 | 0.108131 | − | 0.994137i | \(-0.465513\pi\) | ||||
0.108131 | + | 0.994137i | \(0.465513\pi\) | |||||||
\(798\) | −79.9827 | −2.83136 | ||||||||
\(799\) | 42.1147 | 1.48991 | ||||||||
\(800\) | −41.4169 | −1.46431 | ||||||||
\(801\) | 2.15121 | 0.0760092 | ||||||||
\(802\) | 12.2166 | 0.431384 | ||||||||
\(803\) | −1.50035 | −0.0529464 | ||||||||
\(804\) | −34.8503 | −1.22908 | ||||||||
\(805\) | 128.689 | 4.53568 | ||||||||
\(806\) | 17.6479 | 0.621620 | ||||||||
\(807\) | 15.7426 | 0.554166 | ||||||||
\(808\) | −59.0988 | −2.07909 | ||||||||
\(809\) | −28.8585 | −1.01461 | −0.507306 | − | 0.861766i | \(-0.669359\pi\) | ||||
−0.507306 | + | 0.861766i | \(0.669359\pi\) | |||||||
\(810\) | 8.12109 | 0.285346 | ||||||||
\(811\) | 34.8022 | 1.22207 | 0.611036 | − | 0.791603i | \(-0.290753\pi\) | ||||
0.611036 | + | 0.791603i | \(0.290753\pi\) | |||||||
\(812\) | −214.751 | −7.53629 | ||||||||
\(813\) | 9.29233 | 0.325896 | ||||||||
\(814\) | 18.1256 | 0.635300 | ||||||||
\(815\) | 4.92642 | 0.172565 | ||||||||
\(816\) | 63.1899 | 2.21209 | ||||||||
\(817\) | 7.95592 | 0.278342 | ||||||||
\(818\) | −40.5372 | −1.41735 | ||||||||
\(819\) | 5.24906 | 0.183417 | ||||||||
\(820\) | 33.9386 | 1.18519 | ||||||||
\(821\) | −54.0615 | −1.88676 | −0.943380 | − | 0.331713i | \(-0.892373\pi\) | ||||
−0.943380 | + | 0.331713i | \(0.892373\pi\) | |||||||
\(822\) | 29.7457 | 1.03750 | ||||||||
\(823\) | −44.7392 | −1.55951 | −0.779756 | − | 0.626084i | \(-0.784657\pi\) | ||||
−0.779756 | + | 0.626084i | \(0.784657\pi\) | |||||||
\(824\) | 49.1484 | 1.71217 | ||||||||
\(825\) | 14.8952 | 0.518586 | ||||||||
\(826\) | −82.6444 | −2.87557 | ||||||||
\(827\) | 17.1697 | 0.597050 | 0.298525 | − | 0.954402i | \(-0.403505\pi\) | ||||
0.298525 | + | 0.954402i | \(0.403505\pi\) | |||||||
\(828\) | −37.2297 | −1.29382 | ||||||||
\(829\) | 21.9088 | 0.760924 | 0.380462 | − | 0.924796i | \(-0.375765\pi\) | ||||
0.380462 | + | 0.924796i | \(0.375765\pi\) | |||||||
\(830\) | 97.3383 | 3.37866 | ||||||||
\(831\) | 7.05145 | 0.244612 | ||||||||
\(832\) | 4.79554 | 0.166255 | ||||||||
\(833\) | 144.040 | 4.99069 | ||||||||
\(834\) | 17.7784 | 0.615616 | ||||||||
\(835\) | 57.6733 | 1.99587 | ||||||||
\(836\) | 86.2895 | 2.98439 | ||||||||
\(837\) | −6.72996 | −0.232622 | ||||||||
\(838\) | −80.9460 | −2.79623 | ||||||||
\(839\) | −12.5103 | −0.431905 | −0.215953 | − | 0.976404i | \(-0.569286\pi\) | ||||
−0.215953 | + | 0.976404i | \(0.569286\pi\) | |||||||
\(840\) | 113.757 | 3.92499 | ||||||||
\(841\) | 48.6376 | 1.67716 | ||||||||
\(842\) | −46.3311 | −1.59668 | ||||||||
\(843\) | −25.5843 | −0.881171 | ||||||||
\(844\) | 1.59172 | 0.0547894 | ||||||||
\(845\) | 37.5601 | 1.29211 | ||||||||
\(846\) | −15.0317 | −0.516802 | ||||||||
\(847\) | −7.90961 | −0.271777 | ||||||||
\(848\) | 21.7625 | 0.747328 | ||||||||
\(849\) | 0.286131 | 0.00981998 | ||||||||
\(850\) | −90.8811 | −3.11720 | ||||||||
\(851\) | 18.0062 | 0.617244 | ||||||||
\(852\) | 50.2004 | 1.71984 | ||||||||
\(853\) | −30.2828 | −1.03686 | −0.518432 | − | 0.855119i | \(-0.673484\pi\) | ||||
−0.518432 | + | 0.855119i | \(0.673484\pi\) | |||||||
\(854\) | −148.906 | −5.09546 | ||||||||
\(855\) | −18.6988 | −0.639486 | ||||||||
\(856\) | −123.246 | −4.21247 | ||||||||
\(857\) | 9.23836 | 0.315576 | 0.157788 | − | 0.987473i | \(-0.449564\pi\) | ||||
0.157788 | + | 0.987473i | \(0.449564\pi\) | |||||||
\(858\) | −8.07125 | −0.275548 | ||||||||
\(859\) | 20.4742 | 0.698571 | 0.349286 | − | 0.937016i | \(-0.386424\pi\) | ||||
0.349286 | + | 0.937016i | \(0.386424\pi\) | |||||||
\(860\) | −19.6883 | −0.671366 | ||||||||
\(861\) | −11.9228 | −0.406328 | ||||||||
\(862\) | 66.5885 | 2.26801 | ||||||||
\(863\) | 35.8291 | 1.21964 | 0.609819 | − | 0.792541i | \(-0.291242\pi\) | ||||
0.609819 | + | 0.792541i | \(0.291242\pi\) | |||||||
\(864\) | −8.55838 | −0.291162 | ||||||||
\(865\) | 57.7673 | 1.96415 | ||||||||
\(866\) | −6.29660 | −0.213967 | ||||||||
\(867\) | 35.6153 | 1.20956 | ||||||||
\(868\) | −164.026 | −5.56740 | ||||||||
\(869\) | 6.38750 | 0.216681 | ||||||||
\(870\) | −71.5568 | −2.42600 | ||||||||
\(871\) | −7.50567 | −0.254320 | ||||||||
\(872\) | −8.03144 | −0.271979 | ||||||||
\(873\) | 1.02023 | 0.0345297 | ||||||||
\(874\) | 122.176 | 4.13266 | ||||||||
\(875\) | 2.61166 | 0.0882903 | ||||||||
\(876\) | −2.29244 | −0.0774544 | ||||||||
\(877\) | 44.3110 | 1.49628 | 0.748138 | − | 0.663543i | \(-0.230948\pi\) | ||||
0.748138 | + | 0.663543i | \(0.230948\pi\) | |||||||
\(878\) | 40.1489 | 1.35496 | ||||||||
\(879\) | −7.58655 | −0.255888 | ||||||||
\(880\) | −84.1078 | −2.83527 | ||||||||
\(881\) | −52.2531 | −1.76045 | −0.880227 | − | 0.474554i | \(-0.842609\pi\) | ||||
−0.880227 | + | 0.474554i | \(0.842609\pi\) | |||||||
\(882\) | −51.4113 | −1.73111 | ||||||||
\(883\) | −48.0257 | −1.61619 | −0.808097 | − | 0.589050i | \(-0.799502\pi\) | ||||
−0.808097 | + | 0.589050i | \(0.799502\pi\) | |||||||
\(884\) | 34.5517 | 1.16210 | ||||||||
\(885\) | −19.3211 | −0.649471 | ||||||||
\(886\) | 65.6572 | 2.20580 | ||||||||
\(887\) | 1.77558 | 0.0596181 | 0.0298091 | − | 0.999556i | \(-0.490510\pi\) | ||||
0.0298091 | + | 0.999556i | \(0.490510\pi\) | |||||||
\(888\) | 15.9170 | 0.534138 | ||||||||
\(889\) | 28.3645 | 0.951316 | ||||||||
\(890\) | 17.4702 | 0.585601 | ||||||||
\(891\) | 3.07795 | 0.103115 | ||||||||
\(892\) | 46.2459 | 1.54843 | ||||||||
\(893\) | 34.6106 | 1.15820 | ||||||||
\(894\) | 27.3218 | 0.913777 | ||||||||
\(895\) | −8.15193 | −0.272489 | ||||||||
\(896\) | 25.1801 | 0.841208 | ||||||||
\(897\) | −8.01810 | −0.267717 | ||||||||
\(898\) | 9.42819 | 0.314623 | ||||||||
\(899\) | 59.2992 | 1.97774 | ||||||||
\(900\) | 22.7590 | 0.758632 | ||||||||
\(901\) | 18.1206 | 0.603685 | ||||||||
\(902\) | 18.3332 | 0.610428 | ||||||||
\(903\) | 6.91661 | 0.230170 | ||||||||
\(904\) | −38.6575 | −1.28573 | ||||||||
\(905\) | 80.8235 | 2.68666 | ||||||||
\(906\) | 31.7433 | 1.05460 | ||||||||
\(907\) | 14.9102 | 0.495086 | 0.247543 | − | 0.968877i | \(-0.420377\pi\) | ||||
0.247543 | + | 0.968877i | \(0.420377\pi\) | |||||||
\(908\) | −67.7791 | −2.24933 | ||||||||
\(909\) | 8.44534 | 0.280114 | ||||||||
\(910\) | 42.6281 | 1.41311 | ||||||||
\(911\) | −20.3190 | −0.673199 | −0.336600 | − | 0.941648i | \(-0.609277\pi\) | ||||
−0.336600 | + | 0.941648i | \(0.609277\pi\) | |||||||
\(912\) | 51.9305 | 1.71959 | ||||||||
\(913\) | 36.8919 | 1.22094 | ||||||||
\(914\) | 18.7989 | 0.621813 | ||||||||
\(915\) | −34.8121 | −1.15085 | ||||||||
\(916\) | 120.101 | 3.96825 | ||||||||
\(917\) | 59.5033 | 1.96497 | ||||||||
\(918\) | −18.7796 | −0.619820 | ||||||||
\(919\) | −49.4532 | −1.63131 | −0.815655 | − | 0.578538i | \(-0.803623\pi\) | ||||
−0.815655 | + | 0.578538i | \(0.803623\pi\) | |||||||
\(920\) | −173.767 | −5.72894 | ||||||||
\(921\) | 12.8976 | 0.424990 | ||||||||
\(922\) | −48.0257 | −1.58164 | ||||||||
\(923\) | 10.8116 | 0.355868 | ||||||||
\(924\) | 75.0172 | 2.46788 | ||||||||
\(925\) | −11.0074 | −0.361921 | ||||||||
\(926\) | 64.2104 | 2.11008 | ||||||||
\(927\) | −7.02341 | −0.230679 | ||||||||
\(928\) | 75.4098 | 2.47545 | ||||||||
\(929\) | −30.3994 | −0.997371 | −0.498686 | − | 0.866783i | \(-0.666184\pi\) | ||||
−0.498686 | + | 0.866783i | \(0.666184\pi\) | |||||||
\(930\) | −54.6546 | −1.79220 | ||||||||
\(931\) | 118.374 | 3.87956 | ||||||||
\(932\) | 119.879 | 3.92677 | ||||||||
\(933\) | −15.8834 | −0.520000 | ||||||||
\(934\) | 56.6152 | 1.85251 | ||||||||
\(935\) | −70.0326 | −2.29031 | ||||||||
\(936\) | −7.08777 | −0.231671 | ||||||||
\(937\) | 16.3985 | 0.535716 | 0.267858 | − | 0.963458i | \(-0.413684\pi\) | ||||
0.267858 | + | 0.963458i | \(0.413684\pi\) | |||||||
\(938\) | 99.4274 | 3.24642 | ||||||||
\(939\) | 27.7054 | 0.904132 | ||||||||
\(940\) | −85.6499 | −2.79359 | ||||||||
\(941\) | −7.36842 | −0.240204 | −0.120102 | − | 0.992762i | \(-0.538322\pi\) | ||||
−0.120102 | + | 0.992762i | \(0.538322\pi\) | |||||||
\(942\) | 12.9282 | 0.421222 | ||||||||
\(943\) | 18.2124 | 0.593079 | ||||||||
\(944\) | 53.6587 | 1.74644 | ||||||||
\(945\) | −16.2561 | −0.528811 | ||||||||
\(946\) | −10.6354 | −0.345785 | ||||||||
\(947\) | 30.6708 | 0.996668 | 0.498334 | − | 0.866985i | \(-0.333945\pi\) | ||||
0.498334 | + | 0.866985i | \(0.333945\pi\) | |||||||
\(948\) | 9.75967 | 0.316979 | ||||||||
\(949\) | −0.493720 | −0.0160268 | ||||||||
\(950\) | −74.6876 | −2.42319 | ||||||||
\(951\) | −14.6549 | −0.475218 | ||||||||
\(952\) | −263.058 | −8.52575 | ||||||||
\(953\) | 14.4813 | 0.469097 | 0.234548 | − | 0.972104i | \(-0.424639\pi\) | ||||
0.234548 | + | 0.972104i | \(0.424639\pi\) | |||||||
\(954\) | −6.46768 | −0.209399 | ||||||||
\(955\) | −40.8601 | −1.32220 | ||||||||
\(956\) | −38.3067 | −1.23893 | ||||||||
\(957\) | −27.1205 | −0.876681 | ||||||||
\(958\) | −38.9101 | −1.25713 | ||||||||
\(959\) | −59.5423 | −1.92272 | ||||||||
\(960\) | −14.8516 | −0.479332 | ||||||||
\(961\) | 14.2924 | 0.461045 | ||||||||
\(962\) | 5.96456 | 0.192305 | ||||||||
\(963\) | 17.6121 | 0.567543 | ||||||||
\(964\) | −42.4969 | −1.36873 | ||||||||
\(965\) | 37.7501 | 1.21522 | ||||||||
\(966\) | 106.216 | 3.41743 | ||||||||
\(967\) | 13.4446 | 0.432349 | 0.216174 | − | 0.976355i | \(-0.430642\pi\) | ||||
0.216174 | + | 0.976355i | \(0.430642\pi\) | |||||||
\(968\) | 10.6803 | 0.343277 | ||||||||
\(969\) | 43.2401 | 1.38907 | ||||||||
\(970\) | 8.28541 | 0.266029 | ||||||||
\(971\) | −20.3832 | −0.654127 | −0.327064 | − | 0.945002i | \(-0.606059\pi\) | ||||
−0.327064 | + | 0.945002i | \(0.606059\pi\) | |||||||
\(972\) | 4.70290 | 0.150846 | ||||||||
\(973\) | −35.5873 | −1.14088 | ||||||||
\(974\) | 81.2285 | 2.60273 | ||||||||
\(975\) | 4.90156 | 0.156976 | ||||||||
\(976\) | 96.6805 | 3.09467 | ||||||||
\(977\) | 48.3690 | 1.54746 | 0.773731 | − | 0.633514i | \(-0.218388\pi\) | ||||
0.773731 | + | 0.633514i | \(0.218388\pi\) | |||||||
\(978\) | 4.06612 | 0.130020 | ||||||||
\(979\) | 6.62131 | 0.211618 | ||||||||
\(980\) | −292.938 | −9.35756 | ||||||||
\(981\) | 1.14771 | 0.0366435 | ||||||||
\(982\) | 87.0140 | 2.77673 | ||||||||
\(983\) | −38.7186 | −1.23493 | −0.617466 | − | 0.786597i | \(-0.711841\pi\) | ||||
−0.617466 | + | 0.786597i | \(0.711841\pi\) | |||||||
\(984\) | 16.0993 | 0.513227 | ||||||||
\(985\) | −23.6637 | −0.753990 | ||||||||
\(986\) | 165.472 | 5.26969 | ||||||||
\(987\) | 30.0893 | 0.957752 | ||||||||
\(988\) | 28.3952 | 0.903372 | ||||||||
\(989\) | −10.5653 | −0.335958 | ||||||||
\(990\) | 24.9963 | 0.794435 | ||||||||
\(991\) | −35.0461 | −1.11327 | −0.556637 | − | 0.830756i | \(-0.687909\pi\) | ||||
−0.556637 | + | 0.830756i | \(0.687909\pi\) | |||||||
\(992\) | 57.5976 | 1.82873 | ||||||||
\(993\) | 0.242102 | 0.00768286 | ||||||||
\(994\) | −143.221 | −4.54269 | ||||||||
\(995\) | −59.6725 | −1.89175 | ||||||||
\(996\) | 56.3683 | 1.78610 | ||||||||
\(997\) | 49.7947 | 1.57701 | 0.788507 | − | 0.615026i | \(-0.210855\pi\) | ||||
0.788507 | + | 0.615026i | \(0.210855\pi\) | |||||||
\(998\) | 14.7410 | 0.466618 | ||||||||
\(999\) | −2.27457 | −0.0719641 |
(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 | 8013.2.a.d.1.8 | ✓ | 129 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8013.2.a.d.1.8 | ✓ | 129 | 1.1 | even | 1 | trivial |