Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6029,2,Mod(1,6029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6029, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6029 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6029.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: | \(48.1418073786\) |
Analytic rank: | \(1\) |
Dimension: | \(234\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 6029.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.59814 | −1.83716 | −0.918581 | − | 0.395232i | \(-0.870664\pi\) | ||||
−0.918581 | + | 0.395232i | \(0.870664\pi\) | |||||||
\(3\) | 1.65321 | 0.954483 | 0.477241 | − | 0.878772i | \(-0.341637\pi\) | ||||
0.477241 | + | 0.878772i | \(0.341637\pi\) | |||||||
\(4\) | 4.75033 | 2.37517 | ||||||||
\(5\) | 2.01329 | 0.900369 | 0.450184 | − | 0.892936i | \(-0.351358\pi\) | ||||
0.450184 | + | 0.892936i | \(0.351358\pi\) | |||||||
\(6\) | −4.29528 | −1.75354 | ||||||||
\(7\) | 1.44236 | 0.545162 | 0.272581 | − | 0.962133i | \(-0.412123\pi\) | ||||
0.272581 | + | 0.962133i | \(0.412123\pi\) | |||||||
\(8\) | −7.14575 | −2.52640 | ||||||||
\(9\) | −0.266887 | −0.0889624 | ||||||||
\(10\) | −5.23080 | −1.65412 | ||||||||
\(11\) | −3.73074 | −1.12486 | −0.562430 | − | 0.826845i | \(-0.690133\pi\) | ||||
−0.562430 | + | 0.826845i | \(0.690133\pi\) | |||||||
\(12\) | 7.85331 | 2.26706 | ||||||||
\(13\) | 3.40621 | 0.944712 | 0.472356 | − | 0.881408i | \(-0.343404\pi\) | ||||
0.472356 | + | 0.881408i | \(0.343404\pi\) | |||||||
\(14\) | −3.74746 | −1.00155 | ||||||||
\(15\) | 3.32839 | 0.859387 | ||||||||
\(16\) | 9.06499 | 2.26625 | ||||||||
\(17\) | 5.43724 | 1.31872 | 0.659362 | − | 0.751826i | \(-0.270827\pi\) | ||||
0.659362 | + | 0.751826i | \(0.270827\pi\) | |||||||
\(18\) | 0.693410 | 0.163438 | ||||||||
\(19\) | −4.75327 | −1.09047 | −0.545237 | − | 0.838282i | \(-0.683560\pi\) | ||||
−0.545237 | + | 0.838282i | \(0.683560\pi\) | |||||||
\(20\) | 9.56378 | 2.13853 | ||||||||
\(21\) | 2.38453 | 0.520348 | ||||||||
\(22\) | 9.69297 | 2.06655 | ||||||||
\(23\) | −8.10231 | −1.68945 | −0.844724 | − | 0.535202i | \(-0.820235\pi\) | ||||
−0.844724 | + | 0.535202i | \(0.820235\pi\) | |||||||
\(24\) | −11.8134 | −2.41141 | ||||||||
\(25\) | −0.946681 | −0.189336 | ||||||||
\(26\) | −8.84981 | −1.73559 | ||||||||
\(27\) | −5.40086 | −1.03940 | ||||||||
\(28\) | 6.85170 | 1.29485 | ||||||||
\(29\) | 9.42502 | 1.75018 | 0.875092 | − | 0.483957i | \(-0.160801\pi\) | ||||
0.875092 | + | 0.483957i | \(0.160801\pi\) | |||||||
\(30\) | −8.64762 | −1.57883 | ||||||||
\(31\) | 0.0440374 | 0.00790936 | 0.00395468 | − | 0.999992i | \(-0.498741\pi\) | ||||
0.00395468 | + | 0.999992i | \(0.498741\pi\) | |||||||
\(32\) | −9.26062 | −1.63706 | ||||||||
\(33\) | −6.16770 | −1.07366 | ||||||||
\(34\) | −14.1267 | −2.42271 | ||||||||
\(35\) | 2.90389 | 0.490847 | ||||||||
\(36\) | −1.26780 | −0.211300 | ||||||||
\(37\) | −5.74024 | −0.943690 | −0.471845 | − | 0.881681i | \(-0.656412\pi\) | ||||
−0.471845 | + | 0.881681i | \(0.656412\pi\) | |||||||
\(38\) | 12.3497 | 2.00338 | ||||||||
\(39\) | 5.63119 | 0.901712 | ||||||||
\(40\) | −14.3864 | −2.27469 | ||||||||
\(41\) | −9.87971 | −1.54295 | −0.771476 | − | 0.636258i | \(-0.780481\pi\) | ||||
−0.771476 | + | 0.636258i | \(0.780481\pi\) | |||||||
\(42\) | −6.19535 | −0.955963 | ||||||||
\(43\) | −11.2891 | −1.72157 | −0.860786 | − | 0.508968i | \(-0.830027\pi\) | ||||
−0.860786 | + | 0.508968i | \(0.830027\pi\) | |||||||
\(44\) | −17.7222 | −2.67173 | ||||||||
\(45\) | −0.537320 | −0.0800989 | ||||||||
\(46\) | 21.0509 | 3.10379 | ||||||||
\(47\) | −1.87232 | −0.273106 | −0.136553 | − | 0.990633i | \(-0.543602\pi\) | ||||
−0.136553 | + | 0.990633i | \(0.543602\pi\) | |||||||
\(48\) | 14.9864 | 2.16309 | ||||||||
\(49\) | −4.91959 | −0.702799 | ||||||||
\(50\) | 2.45961 | 0.347841 | ||||||||
\(51\) | 8.98891 | 1.25870 | ||||||||
\(52\) | 16.1806 | 2.24385 | ||||||||
\(53\) | 6.24789 | 0.858214 | 0.429107 | − | 0.903254i | \(-0.358828\pi\) | ||||
0.429107 | + | 0.903254i | \(0.358828\pi\) | |||||||
\(54\) | 14.0322 | 1.90954 | ||||||||
\(55\) | −7.51104 | −1.01279 | ||||||||
\(56\) | −10.3068 | −1.37730 | ||||||||
\(57\) | −7.85816 | −1.04084 | ||||||||
\(58\) | −24.4875 | −3.21537 | ||||||||
\(59\) | 7.29466 | 0.949684 | 0.474842 | − | 0.880071i | \(-0.342505\pi\) | ||||
0.474842 | + | 0.880071i | \(0.342505\pi\) | |||||||
\(60\) | 15.8110 | 2.04119 | ||||||||
\(61\) | −11.4330 | −1.46385 | −0.731925 | − | 0.681385i | \(-0.761378\pi\) | ||||
−0.731925 | + | 0.681385i | \(0.761378\pi\) | |||||||
\(62\) | −0.114415 | −0.0145308 | ||||||||
\(63\) | −0.384948 | −0.0484989 | ||||||||
\(64\) | 5.93040 | 0.741300 | ||||||||
\(65\) | 6.85767 | 0.850589 | ||||||||
\(66\) | 16.0246 | 1.97249 | ||||||||
\(67\) | −4.92399 | −0.601561 | −0.300780 | − | 0.953693i | \(-0.597247\pi\) | ||||
−0.300780 | + | 0.953693i | \(0.597247\pi\) | |||||||
\(68\) | 25.8287 | 3.13219 | ||||||||
\(69\) | −13.3948 | −1.61255 | ||||||||
\(70\) | −7.54471 | −0.901765 | ||||||||
\(71\) | −5.63361 | −0.668587 | −0.334293 | − | 0.942469i | \(-0.608498\pi\) | ||||
−0.334293 | + | 0.942469i | \(0.608498\pi\) | |||||||
\(72\) | 1.90711 | 0.224755 | ||||||||
\(73\) | 5.71738 | 0.669168 | 0.334584 | − | 0.942366i | \(-0.391404\pi\) | ||||
0.334584 | + | 0.942366i | \(0.391404\pi\) | |||||||
\(74\) | 14.9140 | 1.73371 | ||||||||
\(75\) | −1.56506 | −0.180718 | ||||||||
\(76\) | −22.5796 | −2.59006 | ||||||||
\(77\) | −5.38107 | −0.613230 | ||||||||
\(78\) | −14.6306 | −1.65659 | ||||||||
\(79\) | −11.6224 | −1.30762 | −0.653812 | − | 0.756657i | \(-0.726831\pi\) | ||||
−0.653812 | + | 0.756657i | \(0.726831\pi\) | |||||||
\(80\) | 18.2504 | 2.04046 | ||||||||
\(81\) | −8.12811 | −0.903123 | ||||||||
\(82\) | 25.6689 | 2.83465 | ||||||||
\(83\) | −6.88507 | −0.755735 | −0.377867 | − | 0.925860i | \(-0.623343\pi\) | ||||
−0.377867 | + | 0.925860i | \(0.623343\pi\) | |||||||
\(84\) | 11.3273 | 1.23591 | ||||||||
\(85\) | 10.9467 | 1.18734 | ||||||||
\(86\) | 29.3307 | 3.16281 | ||||||||
\(87\) | 15.5816 | 1.67052 | ||||||||
\(88\) | 26.6589 | 2.84185 | ||||||||
\(89\) | 12.0708 | 1.27950 | 0.639752 | − | 0.768581i | \(-0.279037\pi\) | ||||
0.639752 | + | 0.768581i | \(0.279037\pi\) | |||||||
\(90\) | 1.39603 | 0.147155 | ||||||||
\(91\) | 4.91299 | 0.515021 | ||||||||
\(92\) | −38.4887 | −4.01272 | ||||||||
\(93\) | 0.0728033 | 0.00754935 | ||||||||
\(94\) | 4.86456 | 0.501741 | ||||||||
\(95\) | −9.56968 | −0.981829 | ||||||||
\(96\) | −15.3098 | −1.56255 | ||||||||
\(97\) | −4.48974 | −0.455864 | −0.227932 | − | 0.973677i | \(-0.573196\pi\) | ||||
−0.227932 | + | 0.973677i | \(0.573196\pi\) | |||||||
\(98\) | 12.7818 | 1.29116 | ||||||||
\(99\) | 0.995685 | 0.100070 | ||||||||
\(100\) | −4.49705 | −0.449705 | ||||||||
\(101\) | 15.7960 | 1.57176 | 0.785879 | − | 0.618380i | \(-0.212211\pi\) | ||||
0.785879 | + | 0.618380i | \(0.212211\pi\) | |||||||
\(102\) | −23.3544 | −2.31243 | ||||||||
\(103\) | 5.34126 | 0.526290 | 0.263145 | − | 0.964756i | \(-0.415240\pi\) | ||||
0.263145 | + | 0.964756i | \(0.415240\pi\) | |||||||
\(104\) | −24.3399 | −2.38672 | ||||||||
\(105\) | 4.80074 | 0.468505 | ||||||||
\(106\) | −16.2329 | −1.57668 | ||||||||
\(107\) | 0.216064 | 0.0208876 | 0.0104438 | − | 0.999945i | \(-0.496676\pi\) | ||||
0.0104438 | + | 0.999945i | \(0.496676\pi\) | |||||||
\(108\) | −25.6559 | −2.46874 | ||||||||
\(109\) | 15.4582 | 1.48063 | 0.740316 | − | 0.672259i | \(-0.234676\pi\) | ||||
0.740316 | + | 0.672259i | \(0.234676\pi\) | |||||||
\(110\) | 19.5147 | 1.86066 | ||||||||
\(111\) | −9.48985 | −0.900736 | ||||||||
\(112\) | 13.0750 | 1.23547 | ||||||||
\(113\) | 9.77920 | 0.919950 | 0.459975 | − | 0.887932i | \(-0.347858\pi\) | ||||
0.459975 | + | 0.887932i | \(0.347858\pi\) | |||||||
\(114\) | 20.4166 | 1.91219 | ||||||||
\(115\) | −16.3123 | −1.52113 | ||||||||
\(116\) | 44.7720 | 4.15698 | ||||||||
\(117\) | −0.909073 | −0.0840438 | ||||||||
\(118\) | −18.9525 | −1.74472 | ||||||||
\(119\) | 7.84247 | 0.718918 | ||||||||
\(120\) | −23.7838 | −2.17116 | ||||||||
\(121\) | 2.91839 | 0.265308 | ||||||||
\(122\) | 29.7046 | 2.68933 | ||||||||
\(123\) | −16.3333 | −1.47272 | ||||||||
\(124\) | 0.209192 | 0.0187860 | ||||||||
\(125\) | −11.9724 | −1.07084 | ||||||||
\(126\) | 1.00015 | 0.0891003 | ||||||||
\(127\) | −20.6491 | −1.83231 | −0.916156 | − | 0.400822i | \(-0.868725\pi\) | ||||
−0.916156 | + | 0.400822i | \(0.868725\pi\) | |||||||
\(128\) | 3.11322 | 0.275172 | ||||||||
\(129\) | −18.6633 | −1.64321 | ||||||||
\(130\) | −17.8172 | −1.56267 | ||||||||
\(131\) | −7.97819 | −0.697058 | −0.348529 | − | 0.937298i | \(-0.613319\pi\) | ||||
−0.348529 | + | 0.937298i | \(0.613319\pi\) | |||||||
\(132\) | −29.2986 | −2.55012 | ||||||||
\(133\) | −6.85593 | −0.594485 | ||||||||
\(134\) | 12.7932 | 1.10516 | ||||||||
\(135\) | −10.8735 | −0.935840 | ||||||||
\(136\) | −38.8531 | −3.33163 | ||||||||
\(137\) | −12.9898 | −1.10979 | −0.554896 | − | 0.831920i | \(-0.687242\pi\) | ||||
−0.554896 | + | 0.831920i | \(0.687242\pi\) | |||||||
\(138\) | 34.8017 | 2.96252 | ||||||||
\(139\) | −14.2125 | −1.20549 | −0.602746 | − | 0.797933i | \(-0.705927\pi\) | ||||
−0.602746 | + | 0.797933i | \(0.705927\pi\) | |||||||
\(140\) | 13.7944 | 1.16584 | ||||||||
\(141\) | −3.09535 | −0.260675 | ||||||||
\(142\) | 14.6369 | 1.22830 | ||||||||
\(143\) | −12.7077 | −1.06267 | ||||||||
\(144\) | −2.41933 | −0.201611 | ||||||||
\(145\) | 18.9753 | 1.57581 | ||||||||
\(146\) | −14.8545 | −1.22937 | ||||||||
\(147\) | −8.13313 | −0.670809 | ||||||||
\(148\) | −27.2681 | −2.24142 | ||||||||
\(149\) | −4.89879 | −0.401324 | −0.200662 | − | 0.979661i | \(-0.564309\pi\) | ||||
−0.200662 | + | 0.979661i | \(0.564309\pi\) | |||||||
\(150\) | 4.06626 | 0.332009 | ||||||||
\(151\) | 24.1129 | 1.96228 | 0.981142 | − | 0.193290i | \(-0.0619160\pi\) | ||||
0.981142 | + | 0.193290i | \(0.0619160\pi\) | |||||||
\(152\) | 33.9656 | 2.75498 | ||||||||
\(153\) | −1.45113 | −0.117317 | ||||||||
\(154\) | 13.9808 | 1.12660 | ||||||||
\(155\) | 0.0886600 | 0.00712134 | ||||||||
\(156\) | 26.7500 | 2.14172 | ||||||||
\(157\) | −11.2949 | −0.901432 | −0.450716 | − | 0.892667i | \(-0.648831\pi\) | ||||
−0.450716 | + | 0.892667i | \(0.648831\pi\) | |||||||
\(158\) | 30.1967 | 2.40232 | ||||||||
\(159\) | 10.3291 | 0.819151 | ||||||||
\(160\) | −18.6443 | −1.47396 | ||||||||
\(161\) | −11.6865 | −0.921023 | ||||||||
\(162\) | 21.1180 | 1.65918 | ||||||||
\(163\) | −9.78659 | −0.766545 | −0.383273 | − | 0.923635i | \(-0.625203\pi\) | ||||
−0.383273 | + | 0.923635i | \(0.625203\pi\) | |||||||
\(164\) | −46.9319 | −3.66477 | ||||||||
\(165\) | −12.4173 | −0.966689 | ||||||||
\(166\) | 17.8884 | 1.38841 | ||||||||
\(167\) | −7.34958 | −0.568728 | −0.284364 | − | 0.958716i | \(-0.591782\pi\) | ||||
−0.284364 | + | 0.958716i | \(0.591782\pi\) | |||||||
\(168\) | −17.0393 | −1.31461 | ||||||||
\(169\) | −1.39774 | −0.107519 | ||||||||
\(170\) | −28.4411 | −2.18133 | ||||||||
\(171\) | 1.26859 | 0.0970112 | ||||||||
\(172\) | −53.6270 | −4.08902 | ||||||||
\(173\) | −23.2959 | −1.77116 | −0.885579 | − | 0.464489i | \(-0.846238\pi\) | ||||
−0.885579 | + | 0.464489i | \(0.846238\pi\) | |||||||
\(174\) | −40.4831 | −3.06902 | ||||||||
\(175\) | −1.36546 | −0.103219 | ||||||||
\(176\) | −33.8191 | −2.54921 | ||||||||
\(177\) | 12.0596 | 0.906457 | ||||||||
\(178\) | −31.3617 | −2.35066 | ||||||||
\(179\) | 6.31476 | 0.471987 | 0.235994 | − | 0.971755i | \(-0.424166\pi\) | ||||
0.235994 | + | 0.971755i | \(0.424166\pi\) | |||||||
\(180\) | −2.55245 | −0.190248 | ||||||||
\(181\) | −10.5959 | −0.787588 | −0.393794 | − | 0.919199i | \(-0.628838\pi\) | ||||
−0.393794 | + | 0.919199i | \(0.628838\pi\) | |||||||
\(182\) | −12.7646 | −0.946177 | ||||||||
\(183\) | −18.9012 | −1.39722 | ||||||||
\(184\) | 57.8970 | 4.26823 | ||||||||
\(185\) | −11.5568 | −0.849669 | ||||||||
\(186\) | −0.189153 | −0.0138694 | ||||||||
\(187\) | −20.2849 | −1.48338 | ||||||||
\(188\) | −8.89415 | −0.648673 | ||||||||
\(189\) | −7.79000 | −0.566639 | ||||||||
\(190\) | 24.8634 | 1.80378 | ||||||||
\(191\) | 7.65742 | 0.554071 | 0.277036 | − | 0.960860i | \(-0.410648\pi\) | ||||
0.277036 | + | 0.960860i | \(0.410648\pi\) | |||||||
\(192\) | 9.80422 | 0.707558 | ||||||||
\(193\) | 26.6124 | 1.91560 | 0.957800 | − | 0.287435i | \(-0.0928025\pi\) | ||||
0.957800 | + | 0.287435i | \(0.0928025\pi\) | |||||||
\(194\) | 11.6650 | 0.837497 | ||||||||
\(195\) | 11.3372 | 0.811873 | ||||||||
\(196\) | −23.3697 | −1.66926 | ||||||||
\(197\) | 5.71918 | 0.407475 | 0.203738 | − | 0.979026i | \(-0.434691\pi\) | ||||
0.203738 | + | 0.979026i | \(0.434691\pi\) | |||||||
\(198\) | −2.58693 | −0.183845 | ||||||||
\(199\) | −1.80996 | −0.128305 | −0.0641523 | − | 0.997940i | \(-0.520434\pi\) | ||||
−0.0641523 | + | 0.997940i | \(0.520434\pi\) | |||||||
\(200\) | 6.76474 | 0.478339 | ||||||||
\(201\) | −8.14040 | −0.574179 | ||||||||
\(202\) | −41.0401 | −2.88757 | ||||||||
\(203\) | 13.5943 | 0.954133 | ||||||||
\(204\) | 42.7003 | 2.98962 | ||||||||
\(205\) | −19.8907 | −1.38923 | ||||||||
\(206\) | −13.8773 | −0.966880 | ||||||||
\(207\) | 2.16240 | 0.150297 | ||||||||
\(208\) | 30.8772 | 2.14095 | ||||||||
\(209\) | 17.7332 | 1.22663 | ||||||||
\(210\) | −12.4730 | −0.860719 | ||||||||
\(211\) | −11.1067 | −0.764615 | −0.382307 | − | 0.924035i | \(-0.624870\pi\) | ||||
−0.382307 | + | 0.924035i | \(0.624870\pi\) | |||||||
\(212\) | 29.6796 | 2.03840 | ||||||||
\(213\) | −9.31356 | −0.638155 | ||||||||
\(214\) | −0.561363 | −0.0383740 | ||||||||
\(215\) | −22.7282 | −1.55005 | ||||||||
\(216\) | 38.5932 | 2.62593 | ||||||||
\(217\) | 0.0635180 | 0.00431188 | ||||||||
\(218\) | −40.1627 | −2.72016 | ||||||||
\(219\) | 9.45204 | 0.638710 | ||||||||
\(220\) | −35.6799 | −2.40554 | ||||||||
\(221\) | 18.5204 | 1.24581 | ||||||||
\(222\) | 24.6559 | 1.65480 | ||||||||
\(223\) | 0.644839 | 0.0431816 | 0.0215908 | − | 0.999767i | \(-0.493127\pi\) | ||||
0.0215908 | + | 0.999767i | \(0.493127\pi\) | |||||||
\(224\) | −13.3572 | −0.892463 | ||||||||
\(225\) | 0.252657 | 0.0168438 | ||||||||
\(226\) | −25.4077 | −1.69010 | ||||||||
\(227\) | −3.40110 | −0.225739 | −0.112869 | − | 0.993610i | \(-0.536004\pi\) | ||||
−0.112869 | + | 0.993610i | \(0.536004\pi\) | |||||||
\(228\) | −37.3289 | −2.47217 | ||||||||
\(229\) | −16.8934 | −1.11635 | −0.558175 | − | 0.829723i | \(-0.688498\pi\) | ||||
−0.558175 | + | 0.829723i | \(0.688498\pi\) | |||||||
\(230\) | 42.3815 | 2.79456 | ||||||||
\(231\) | −8.89606 | −0.585318 | ||||||||
\(232\) | −67.3488 | −4.42167 | ||||||||
\(233\) | 14.6392 | 0.959048 | 0.479524 | − | 0.877529i | \(-0.340809\pi\) | ||||
0.479524 | + | 0.877529i | \(0.340809\pi\) | |||||||
\(234\) | 2.36190 | 0.154402 | ||||||||
\(235\) | −3.76952 | −0.245896 | ||||||||
\(236\) | 34.6521 | 2.25566 | ||||||||
\(237\) | −19.2143 | −1.24811 | ||||||||
\(238\) | −20.3758 | −1.32077 | ||||||||
\(239\) | 19.5254 | 1.26299 | 0.631496 | − | 0.775379i | \(-0.282441\pi\) | ||||
0.631496 | + | 0.775379i | \(0.282441\pi\) | |||||||
\(240\) | 30.1718 | 1.94758 | ||||||||
\(241\) | −20.4738 | −1.31883 | −0.659417 | − | 0.751778i | \(-0.729197\pi\) | ||||
−0.659417 | + | 0.751778i | \(0.729197\pi\) | |||||||
\(242\) | −7.58239 | −0.487414 | ||||||||
\(243\) | 2.76508 | 0.177380 | ||||||||
\(244\) | −54.3107 | −3.47689 | ||||||||
\(245\) | −9.90454 | −0.632778 | ||||||||
\(246\) | 42.4361 | 2.70563 | ||||||||
\(247\) | −16.1906 | −1.03018 | ||||||||
\(248\) | −0.314680 | −0.0199822 | ||||||||
\(249\) | −11.3825 | −0.721336 | ||||||||
\(250\) | 31.1059 | 1.96731 | ||||||||
\(251\) | 19.9618 | 1.25998 | 0.629989 | − | 0.776604i | \(-0.283059\pi\) | ||||
0.629989 | + | 0.776604i | \(0.283059\pi\) | |||||||
\(252\) | −1.82863 | −0.115193 | ||||||||
\(253\) | 30.2276 | 1.90039 | ||||||||
\(254\) | 53.6493 | 3.36626 | ||||||||
\(255\) | 18.0972 | 1.13329 | ||||||||
\(256\) | −19.9494 | −1.24684 | ||||||||
\(257\) | 6.07861 | 0.379173 | 0.189587 | − | 0.981864i | \(-0.439285\pi\) | ||||
0.189587 | + | 0.981864i | \(0.439285\pi\) | |||||||
\(258\) | 48.4898 | 3.01884 | ||||||||
\(259\) | −8.27951 | −0.514464 | ||||||||
\(260\) | 32.5762 | 2.02029 | ||||||||
\(261\) | −2.51542 | −0.155700 | ||||||||
\(262\) | 20.7285 | 1.28061 | ||||||||
\(263\) | −12.1575 | −0.749663 | −0.374832 | − | 0.927093i | \(-0.622299\pi\) | ||||
−0.374832 | + | 0.927093i | \(0.622299\pi\) | |||||||
\(264\) | 44.0728 | 2.71250 | ||||||||
\(265\) | 12.5788 | 0.772709 | ||||||||
\(266\) | 17.8127 | 1.09217 | ||||||||
\(267\) | 19.9556 | 1.22127 | ||||||||
\(268\) | −23.3906 | −1.42881 | ||||||||
\(269\) | 27.5734 | 1.68118 | 0.840588 | − | 0.541674i | \(-0.182209\pi\) | ||||
0.840588 | + | 0.541674i | \(0.182209\pi\) | |||||||
\(270\) | 28.2508 | 1.71929 | ||||||||
\(271\) | −15.1120 | −0.917986 | −0.458993 | − | 0.888440i | \(-0.651790\pi\) | ||||
−0.458993 | + | 0.888440i | \(0.651790\pi\) | |||||||
\(272\) | 49.2885 | 2.98855 | ||||||||
\(273\) | 8.12222 | 0.491579 | ||||||||
\(274\) | 33.7493 | 2.03887 | ||||||||
\(275\) | 3.53182 | 0.212977 | ||||||||
\(276\) | −63.6299 | −3.83007 | ||||||||
\(277\) | 27.7426 | 1.66689 | 0.833446 | − | 0.552600i | \(-0.186364\pi\) | ||||
0.833446 | + | 0.552600i | \(0.186364\pi\) | |||||||
\(278\) | 36.9261 | 2.21468 | ||||||||
\(279\) | −0.0117530 | −0.000703635 0 | ||||||||
\(280\) | −20.7504 | −1.24008 | ||||||||
\(281\) | 4.26997 | 0.254725 | 0.127362 | − | 0.991856i | \(-0.459349\pi\) | ||||
0.127362 | + | 0.991856i | \(0.459349\pi\) | |||||||
\(282\) | 8.04215 | 0.478903 | ||||||||
\(283\) | 26.9329 | 1.60100 | 0.800498 | − | 0.599335i | \(-0.204568\pi\) | ||||
0.800498 | + | 0.599335i | \(0.204568\pi\) | |||||||
\(284\) | −26.7615 | −1.58800 | ||||||||
\(285\) | −15.8207 | −0.937139 | ||||||||
\(286\) | 33.0163 | 1.95229 | ||||||||
\(287\) | −14.2501 | −0.841159 | ||||||||
\(288\) | 2.47154 | 0.145637 | ||||||||
\(289\) | 12.5635 | 0.739031 | ||||||||
\(290\) | −49.3004 | −2.89502 | ||||||||
\(291\) | −7.42250 | −0.435115 | ||||||||
\(292\) | 27.1594 | 1.58939 | ||||||||
\(293\) | 5.84367 | 0.341391 | 0.170695 | − | 0.985324i | \(-0.445399\pi\) | ||||
0.170695 | + | 0.985324i | \(0.445399\pi\) | |||||||
\(294\) | 21.1310 | 1.23239 | ||||||||
\(295\) | 14.6862 | 0.855066 | ||||||||
\(296\) | 41.0183 | 2.38414 | ||||||||
\(297\) | 20.1492 | 1.16917 | ||||||||
\(298\) | 12.7277 | 0.737298 | ||||||||
\(299\) | −27.5982 | −1.59604 | ||||||||
\(300\) | −7.43458 | −0.429236 | ||||||||
\(301\) | −16.2830 | −0.938535 | ||||||||
\(302\) | −62.6488 | −3.60503 | ||||||||
\(303\) | 26.1141 | 1.50022 | ||||||||
\(304\) | −43.0883 | −2.47128 | ||||||||
\(305\) | −23.0180 | −1.31801 | ||||||||
\(306\) | 3.77023 | 0.215530 | ||||||||
\(307\) | −12.6475 | −0.721830 | −0.360915 | − | 0.932599i | \(-0.617536\pi\) | ||||
−0.360915 | + | 0.932599i | \(0.617536\pi\) | |||||||
\(308\) | −25.5619 | −1.45652 | ||||||||
\(309\) | 8.83024 | 0.502335 | ||||||||
\(310\) | −0.230351 | −0.0130831 | ||||||||
\(311\) | −16.5795 | −0.940138 | −0.470069 | − | 0.882630i | \(-0.655771\pi\) | ||||
−0.470069 | + | 0.882630i | \(0.655771\pi\) | |||||||
\(312\) | −40.2391 | −2.27809 | ||||||||
\(313\) | 18.9024 | 1.06842 | 0.534212 | − | 0.845350i | \(-0.320608\pi\) | ||||
0.534212 | + | 0.845350i | \(0.320608\pi\) | |||||||
\(314\) | 29.3458 | 1.65608 | ||||||||
\(315\) | −0.775010 | −0.0436669 | ||||||||
\(316\) | −55.2104 | −3.10583 | ||||||||
\(317\) | 5.05382 | 0.283851 | 0.141925 | − | 0.989877i | \(-0.454671\pi\) | ||||
0.141925 | + | 0.989877i | \(0.454671\pi\) | |||||||
\(318\) | −26.8364 | −1.50491 | ||||||||
\(319\) | −35.1623 | −1.96871 | ||||||||
\(320\) | 11.9396 | 0.667443 | ||||||||
\(321\) | 0.357199 | 0.0199369 | ||||||||
\(322\) | 30.3631 | 1.69207 | ||||||||
\(323\) | −25.8446 | −1.43803 | ||||||||
\(324\) | −38.6112 | −2.14507 | ||||||||
\(325\) | −3.22459 | −0.178868 | ||||||||
\(326\) | 25.4269 | 1.40827 | ||||||||
\(327\) | 25.5558 | 1.41324 | ||||||||
\(328\) | 70.5979 | 3.89812 | ||||||||
\(329\) | −2.70057 | −0.148887 | ||||||||
\(330\) | 32.2620 | 1.77596 | ||||||||
\(331\) | 27.3204 | 1.50167 | 0.750833 | − | 0.660492i | \(-0.229652\pi\) | ||||
0.750833 | + | 0.660492i | \(0.229652\pi\) | |||||||
\(332\) | −32.7064 | −1.79500 | ||||||||
\(333\) | 1.53200 | 0.0839529 | ||||||||
\(334\) | 19.0953 | 1.04485 | ||||||||
\(335\) | −9.91339 | −0.541627 | ||||||||
\(336\) | 21.6158 | 1.17924 | ||||||||
\(337\) | −0.593491 | −0.0323295 | −0.0161648 | − | 0.999869i | \(-0.505146\pi\) | ||||
−0.0161648 | + | 0.999869i | \(0.505146\pi\) | |||||||
\(338\) | 3.63153 | 0.197529 | ||||||||
\(339\) | 16.1671 | 0.878076 | ||||||||
\(340\) | 52.0005 | 2.82012 | ||||||||
\(341\) | −0.164292 | −0.00889692 | ||||||||
\(342\) | −3.29596 | −0.178225 | ||||||||
\(343\) | −17.1924 | −0.928301 | ||||||||
\(344\) | 80.6690 | 4.34938 | ||||||||
\(345\) | −26.9676 | −1.45189 | ||||||||
\(346\) | 60.5261 | 3.25390 | ||||||||
\(347\) | −30.2804 | −1.62554 | −0.812769 | − | 0.582586i | \(-0.802041\pi\) | ||||
−0.812769 | + | 0.582586i | \(0.802041\pi\) | |||||||
\(348\) | 74.0176 | 3.96776 | ||||||||
\(349\) | 19.4498 | 1.04113 | 0.520563 | − | 0.853823i | \(-0.325722\pi\) | ||||
0.520563 | + | 0.853823i | \(0.325722\pi\) | |||||||
\(350\) | 3.54765 | 0.189630 | ||||||||
\(351\) | −18.3965 | −0.981930 | ||||||||
\(352\) | 34.5489 | 1.84146 | ||||||||
\(353\) | 3.44548 | 0.183385 | 0.0916923 | − | 0.995787i | \(-0.470772\pi\) | ||||
0.0916923 | + | 0.995787i | \(0.470772\pi\) | |||||||
\(354\) | −31.3326 | −1.66531 | ||||||||
\(355\) | −11.3421 | −0.601975 | ||||||||
\(356\) | 57.3404 | 3.03904 | ||||||||
\(357\) | 12.9653 | 0.686195 | ||||||||
\(358\) | −16.4066 | −0.867118 | ||||||||
\(359\) | −34.9173 | −1.84286 | −0.921431 | − | 0.388541i | \(-0.872979\pi\) | ||||
−0.921431 | + | 0.388541i | \(0.872979\pi\) | |||||||
\(360\) | 3.83955 | 0.202362 | ||||||||
\(361\) | 3.59355 | 0.189134 | ||||||||
\(362\) | 27.5297 | 1.44693 | ||||||||
\(363\) | 4.82472 | 0.253232 | ||||||||
\(364\) | 23.3383 | 1.22326 | ||||||||
\(365\) | 11.5107 | 0.602498 | ||||||||
\(366\) | 49.1081 | 2.56692 | ||||||||
\(367\) | −6.84534 | −0.357324 | −0.178662 | − | 0.983911i | \(-0.557177\pi\) | ||||
−0.178662 | + | 0.983911i | \(0.557177\pi\) | |||||||
\(368\) | −73.4473 | −3.82871 | ||||||||
\(369\) | 2.63677 | 0.137265 | ||||||||
\(370\) | 30.0261 | 1.56098 | ||||||||
\(371\) | 9.01173 | 0.467866 | ||||||||
\(372\) | 0.345840 | 0.0179310 | ||||||||
\(373\) | −15.6257 | −0.809066 | −0.404533 | − | 0.914523i | \(-0.632566\pi\) | ||||
−0.404533 | + | 0.914523i | \(0.632566\pi\) | |||||||
\(374\) | 52.7030 | 2.72521 | ||||||||
\(375\) | −19.7929 | −1.02210 | ||||||||
\(376\) | 13.3791 | 0.689977 | ||||||||
\(377\) | 32.1036 | 1.65342 | ||||||||
\(378\) | 20.2395 | 1.04101 | ||||||||
\(379\) | 35.1845 | 1.80731 | 0.903654 | − | 0.428264i | \(-0.140875\pi\) | ||||
0.903654 | + | 0.428264i | \(0.140875\pi\) | |||||||
\(380\) | −45.4592 | −2.33201 | ||||||||
\(381\) | −34.1374 | −1.74891 | ||||||||
\(382\) | −19.8950 | −1.01792 | ||||||||
\(383\) | −7.91595 | −0.404486 | −0.202243 | − | 0.979335i | \(-0.564823\pi\) | ||||
−0.202243 | + | 0.979335i | \(0.564823\pi\) | |||||||
\(384\) | 5.14682 | 0.262647 | ||||||||
\(385\) | −10.8336 | −0.552133 | ||||||||
\(386\) | −69.1427 | −3.51927 | ||||||||
\(387\) | 3.01291 | 0.153155 | ||||||||
\(388\) | −21.3278 | −1.08275 | ||||||||
\(389\) | −0.603547 | −0.0306010 | −0.0153005 | − | 0.999883i | \(-0.504870\pi\) | ||||
−0.0153005 | + | 0.999883i | \(0.504870\pi\) | |||||||
\(390\) | −29.4556 | −1.49154 | ||||||||
\(391\) | −44.0542 | −2.22791 | ||||||||
\(392\) | 35.1541 | 1.77555 | ||||||||
\(393\) | −13.1896 | −0.665330 | ||||||||
\(394\) | −14.8592 | −0.748598 | ||||||||
\(395\) | −23.3993 | −1.17734 | ||||||||
\(396\) | 4.72983 | 0.237683 | ||||||||
\(397\) | 6.97307 | 0.349968 | 0.174984 | − | 0.984571i | \(-0.444013\pi\) | ||||
0.174984 | + | 0.984571i | \(0.444013\pi\) | |||||||
\(398\) | 4.70253 | 0.235716 | ||||||||
\(399\) | −11.3343 | −0.567426 | ||||||||
\(400\) | −8.58165 | −0.429083 | ||||||||
\(401\) | −12.9048 | −0.644437 | −0.322219 | − | 0.946665i | \(-0.604429\pi\) | ||||
−0.322219 | + | 0.946665i | \(0.604429\pi\) | |||||||
\(402\) | 21.1499 | 1.05486 | ||||||||
\(403\) | 0.150001 | 0.00747207 | ||||||||
\(404\) | 75.0361 | 3.73319 | ||||||||
\(405\) | −16.3642 | −0.813144 | ||||||||
\(406\) | −35.3199 | −1.75290 | ||||||||
\(407\) | 21.4153 | 1.06152 | ||||||||
\(408\) | −64.2325 | −3.17998 | ||||||||
\(409\) | 10.0890 | 0.498870 | 0.249435 | − | 0.968392i | \(-0.419755\pi\) | ||||
0.249435 | + | 0.968392i | \(0.419755\pi\) | |||||||
\(410\) | 51.6788 | 2.55223 | ||||||||
\(411\) | −21.4749 | −1.05928 | ||||||||
\(412\) | 25.3727 | 1.25003 | ||||||||
\(413\) | 10.5215 | 0.517731 | ||||||||
\(414\) | −5.61822 | −0.276121 | ||||||||
\(415\) | −13.8616 | −0.680440 | ||||||||
\(416\) | −31.5436 | −1.54655 | ||||||||
\(417\) | −23.4963 | −1.15062 | ||||||||
\(418\) | −46.0733 | −2.25352 | ||||||||
\(419\) | −4.22807 | −0.206555 | −0.103277 | − | 0.994653i | \(-0.532933\pi\) | ||||
−0.103277 | + | 0.994653i | \(0.532933\pi\) | |||||||
\(420\) | 22.8051 | 1.11278 | ||||||||
\(421\) | 13.8674 | 0.675857 | 0.337929 | − | 0.941172i | \(-0.390274\pi\) | ||||
0.337929 | + | 0.941172i | \(0.390274\pi\) | |||||||
\(422\) | 28.8567 | 1.40472 | ||||||||
\(423\) | 0.499699 | 0.0242962 | ||||||||
\(424\) | −44.6459 | −2.16820 | ||||||||
\(425\) | −5.14733 | −0.249682 | ||||||||
\(426\) | 24.1979 | 1.17239 | ||||||||
\(427\) | −16.4906 | −0.798035 | ||||||||
\(428\) | 1.02637 | 0.0496116 | ||||||||
\(429\) | −21.0085 | −1.01430 | ||||||||
\(430\) | 59.0510 | 2.84769 | ||||||||
\(431\) | −8.73912 | −0.420948 | −0.210474 | − | 0.977599i | \(-0.567501\pi\) | ||||
−0.210474 | + | 0.977599i | \(0.567501\pi\) | |||||||
\(432\) | −48.9587 | −2.35553 | ||||||||
\(433\) | −15.7443 | −0.756625 | −0.378312 | − | 0.925678i | \(-0.623495\pi\) | ||||
−0.378312 | + | 0.925678i | \(0.623495\pi\) | |||||||
\(434\) | −0.165029 | −0.00792163 | ||||||||
\(435\) | 31.3702 | 1.50408 | ||||||||
\(436\) | 73.4318 | 3.51675 | ||||||||
\(437\) | 38.5124 | 1.84230 | ||||||||
\(438\) | −24.5577 | −1.17341 | ||||||||
\(439\) | 29.7230 | 1.41860 | 0.709300 | − | 0.704907i | \(-0.249011\pi\) | ||||
0.709300 | + | 0.704907i | \(0.249011\pi\) | |||||||
\(440\) | 53.6720 | 2.55871 | ||||||||
\(441\) | 1.31297 | 0.0625226 | ||||||||
\(442\) | −48.1185 | −2.28876 | ||||||||
\(443\) | 21.6471 | 1.02849 | 0.514243 | − | 0.857645i | \(-0.328073\pi\) | ||||
0.514243 | + | 0.857645i | \(0.328073\pi\) | |||||||
\(444\) | −45.0799 | −2.13940 | ||||||||
\(445\) | 24.3020 | 1.15203 | ||||||||
\(446\) | −1.67538 | −0.0793317 | ||||||||
\(447\) | −8.09874 | −0.383057 | ||||||||
\(448\) | 8.55379 | 0.404128 | ||||||||
\(449\) | 11.2403 | 0.530463 | 0.265232 | − | 0.964185i | \(-0.414552\pi\) | ||||
0.265232 | + | 0.964185i | \(0.414552\pi\) | |||||||
\(450\) | −0.656438 | −0.0309448 | ||||||||
\(451\) | 36.8586 | 1.73560 | ||||||||
\(452\) | 46.4544 | 2.18503 | ||||||||
\(453\) | 39.8638 | 1.87297 | ||||||||
\(454\) | 8.83653 | 0.414719 | ||||||||
\(455\) | 9.89125 | 0.463709 | ||||||||
\(456\) | 56.1524 | 2.62958 | ||||||||
\(457\) | 27.7369 | 1.29748 | 0.648740 | − | 0.761010i | \(-0.275296\pi\) | ||||
0.648740 | + | 0.761010i | \(0.275296\pi\) | |||||||
\(458\) | 43.8915 | 2.05092 | ||||||||
\(459\) | −29.3657 | −1.37068 | ||||||||
\(460\) | −77.4887 | −3.61293 | ||||||||
\(461\) | 6.30503 | 0.293655 | 0.146827 | − | 0.989162i | \(-0.453094\pi\) | ||||
0.146827 | + | 0.989162i | \(0.453094\pi\) | |||||||
\(462\) | 23.1132 | 1.07532 | ||||||||
\(463\) | −4.82972 | −0.224456 | −0.112228 | − | 0.993682i | \(-0.535799\pi\) | ||||
−0.112228 | + | 0.993682i | \(0.535799\pi\) | |||||||
\(464\) | 85.4377 | 3.96635 | ||||||||
\(465\) | 0.146574 | 0.00679720 | ||||||||
\(466\) | −38.0348 | −1.76193 | ||||||||
\(467\) | −34.0684 | −1.57650 | −0.788248 | − | 0.615358i | \(-0.789012\pi\) | ||||
−0.788248 | + | 0.615358i | \(0.789012\pi\) | |||||||
\(468\) | −4.31840 | −0.199618 | ||||||||
\(469\) | −7.10217 | −0.327948 | ||||||||
\(470\) | 9.79374 | 0.451752 | ||||||||
\(471\) | −18.6729 | −0.860402 | ||||||||
\(472\) | −52.1258 | −2.39928 | ||||||||
\(473\) | 42.1166 | 1.93653 | ||||||||
\(474\) | 49.9215 | 2.29297 | ||||||||
\(475\) | 4.49983 | 0.206466 | ||||||||
\(476\) | 37.2543 | 1.70755 | ||||||||
\(477\) | −1.66748 | −0.0763488 | ||||||||
\(478\) | −50.7297 | −2.32032 | ||||||||
\(479\) | −9.65667 | −0.441225 | −0.220612 | − | 0.975362i | \(-0.570806\pi\) | ||||
−0.220612 | + | 0.975362i | \(0.570806\pi\) | |||||||
\(480\) | −30.8229 | −1.40687 | ||||||||
\(481\) | −19.5525 | −0.891516 | ||||||||
\(482\) | 53.1938 | 2.42291 | ||||||||
\(483\) | −19.3202 | −0.879100 | ||||||||
\(484\) | 13.8633 | 0.630151 | ||||||||
\(485\) | −9.03914 | −0.410446 | ||||||||
\(486\) | −7.18407 | −0.325876 | ||||||||
\(487\) | 14.6484 | 0.663784 | 0.331892 | − | 0.943317i | \(-0.392313\pi\) | ||||
0.331892 | + | 0.943317i | \(0.392313\pi\) | |||||||
\(488\) | 81.6976 | 3.69828 | ||||||||
\(489\) | −16.1793 | −0.731654 | ||||||||
\(490\) | 25.7334 | 1.16252 | ||||||||
\(491\) | −9.90530 | −0.447020 | −0.223510 | − | 0.974702i | \(-0.571751\pi\) | ||||
−0.223510 | + | 0.974702i | \(0.571751\pi\) | |||||||
\(492\) | −77.5885 | −3.49796 | ||||||||
\(493\) | 51.2461 | 2.30801 | ||||||||
\(494\) | 42.0655 | 1.89262 | ||||||||
\(495\) | 2.00460 | 0.0901000 | ||||||||
\(496\) | 0.399199 | 0.0179246 | ||||||||
\(497\) | −8.12571 | −0.364488 | ||||||||
\(498\) | 29.5733 | 1.32521 | ||||||||
\(499\) | 24.2703 | 1.08649 | 0.543243 | − | 0.839575i | \(-0.317196\pi\) | ||||
0.543243 | + | 0.839575i | \(0.317196\pi\) | |||||||
\(500\) | −56.8727 | −2.54343 | ||||||||
\(501\) | −12.1504 | −0.542841 | ||||||||
\(502\) | −51.8636 | −2.31479 | ||||||||
\(503\) | 4.80596 | 0.214287 | 0.107144 | − | 0.994244i | \(-0.465830\pi\) | ||||
0.107144 | + | 0.994244i | \(0.465830\pi\) | |||||||
\(504\) | 2.75074 | 0.122528 | ||||||||
\(505\) | 31.8018 | 1.41516 | ||||||||
\(506\) | −78.5355 | −3.49133 | ||||||||
\(507\) | −2.31076 | −0.102625 | ||||||||
\(508\) | −98.0901 | −4.35205 | ||||||||
\(509\) | 12.3833 | 0.548881 | 0.274441 | − | 0.961604i | \(-0.411507\pi\) | ||||
0.274441 | + | 0.961604i | \(0.411507\pi\) | |||||||
\(510\) | −47.0192 | −2.08204 | ||||||||
\(511\) | 8.24653 | 0.364805 | ||||||||
\(512\) | 45.6049 | 2.01547 | ||||||||
\(513\) | 25.6717 | 1.13343 | ||||||||
\(514\) | −15.7931 | −0.696603 | ||||||||
\(515\) | 10.7535 | 0.473855 | ||||||||
\(516\) | −88.6568 | −3.90290 | ||||||||
\(517\) | 6.98514 | 0.307206 | ||||||||
\(518\) | 21.5113 | 0.945154 | ||||||||
\(519\) | −38.5131 | −1.69054 | ||||||||
\(520\) | −49.0032 | −2.14893 | ||||||||
\(521\) | −22.6313 | −0.991497 | −0.495749 | − | 0.868466i | \(-0.665106\pi\) | ||||
−0.495749 | + | 0.868466i | \(0.665106\pi\) | |||||||
\(522\) | 6.53541 | 0.286047 | ||||||||
\(523\) | −24.4574 | −1.06945 | −0.534723 | − | 0.845027i | \(-0.679584\pi\) | ||||
−0.534723 | + | 0.845027i | \(0.679584\pi\) | |||||||
\(524\) | −37.8990 | −1.65563 | ||||||||
\(525\) | −2.25739 | −0.0985206 | ||||||||
\(526\) | 31.5869 | 1.37725 | ||||||||
\(527\) | 0.239442 | 0.0104303 | ||||||||
\(528\) | −55.9101 | −2.43318 | ||||||||
\(529\) | 42.6474 | 1.85423 | ||||||||
\(530\) | −32.6815 | −1.41959 | ||||||||
\(531\) | −1.94685 | −0.0844861 | ||||||||
\(532\) | −32.5680 | −1.41200 | ||||||||
\(533\) | −33.6524 | −1.45765 | ||||||||
\(534\) | −51.8475 | −2.24366 | ||||||||
\(535\) | 0.434998 | 0.0188066 | ||||||||
\(536\) | 35.1856 | 1.51979 | ||||||||
\(537\) | 10.4396 | 0.450504 | ||||||||
\(538\) | −71.6394 | −3.08860 | ||||||||
\(539\) | 18.3537 | 0.790549 | ||||||||
\(540\) | −51.6526 | −2.22277 | ||||||||
\(541\) | 7.63310 | 0.328172 | 0.164086 | − | 0.986446i | \(-0.447532\pi\) | ||||
0.164086 | + | 0.986446i | \(0.447532\pi\) | |||||||
\(542\) | 39.2630 | 1.68649 | ||||||||
\(543\) | −17.5173 | −0.751739 | ||||||||
\(544\) | −50.3522 | −2.15883 | ||||||||
\(545\) | 31.1219 | 1.33311 | ||||||||
\(546\) | −21.1027 | −0.903110 | ||||||||
\(547\) | 26.3335 | 1.12594 | 0.562970 | − | 0.826478i | \(-0.309659\pi\) | ||||
0.562970 | + | 0.826478i | \(0.309659\pi\) | |||||||
\(548\) | −61.7058 | −2.63594 | ||||||||
\(549\) | 3.05133 | 0.130228 | ||||||||
\(550\) | −9.17615 | −0.391272 | ||||||||
\(551\) | −44.7997 | −1.90853 | ||||||||
\(552\) | 95.7161 | 4.07395 | ||||||||
\(553\) | −16.7637 | −0.712867 | ||||||||
\(554\) | −72.0792 | −3.06235 | ||||||||
\(555\) | −19.1058 | −0.810995 | ||||||||
\(556\) | −67.5142 | −2.86324 | ||||||||
\(557\) | −29.0926 | −1.23269 | −0.616347 | − | 0.787475i | \(-0.711388\pi\) | ||||
−0.616347 | + | 0.787475i | \(0.711388\pi\) | |||||||
\(558\) | 0.0305360 | 0.00129269 | ||||||||
\(559\) | −38.4530 | −1.62639 | ||||||||
\(560\) | 26.3237 | 1.11238 | ||||||||
\(561\) | −33.5352 | −1.41586 | ||||||||
\(562\) | −11.0940 | −0.467971 | ||||||||
\(563\) | −5.25239 | −0.221362 | −0.110681 | − | 0.993856i | \(-0.535303\pi\) | ||||
−0.110681 | + | 0.993856i | \(0.535303\pi\) | |||||||
\(564\) | −14.7039 | −0.619147 | ||||||||
\(565\) | 19.6883 | 0.828294 | ||||||||
\(566\) | −69.9755 | −2.94129 | ||||||||
\(567\) | −11.7237 | −0.492348 | ||||||||
\(568\) | 40.2564 | 1.68912 | ||||||||
\(569\) | −28.7723 | −1.20620 | −0.603099 | − | 0.797666i | \(-0.706068\pi\) | ||||
−0.603099 | + | 0.797666i | \(0.706068\pi\) | |||||||
\(570\) | 41.1045 | 1.72168 | ||||||||
\(571\) | −11.0364 | −0.461859 | −0.230930 | − | 0.972970i | \(-0.574177\pi\) | ||||
−0.230930 | + | 0.972970i | \(0.574177\pi\) | |||||||
\(572\) | −60.3656 | −2.52401 | ||||||||
\(573\) | 12.6593 | 0.528852 | ||||||||
\(574\) | 37.0238 | 1.54534 | ||||||||
\(575\) | 7.67030 | 0.319874 | ||||||||
\(576\) | −1.58275 | −0.0659478 | ||||||||
\(577\) | 3.05554 | 0.127204 | 0.0636019 | − | 0.997975i | \(-0.479741\pi\) | ||||
0.0636019 | + | 0.997975i | \(0.479741\pi\) | |||||||
\(578\) | −32.6418 | −1.35772 | ||||||||
\(579\) | 43.9959 | 1.82841 | ||||||||
\(580\) | 90.1388 | 3.74281 | ||||||||
\(581\) | −9.93077 | −0.411998 | ||||||||
\(582\) | 19.2847 | 0.799376 | ||||||||
\(583\) | −23.3092 | −0.965370 | ||||||||
\(584\) | −40.8549 | −1.69059 | ||||||||
\(585\) | −1.83022 | −0.0756704 | ||||||||
\(586\) | −15.1827 | −0.627190 | ||||||||
\(587\) | 26.1743 | 1.08033 | 0.540164 | − | 0.841560i | \(-0.318362\pi\) | ||||
0.540164 | + | 0.841560i | \(0.318362\pi\) | |||||||
\(588\) | −38.6351 | −1.59328 | ||||||||
\(589\) | −0.209322 | −0.00862495 | ||||||||
\(590\) | −38.1569 | −1.57089 | ||||||||
\(591\) | 9.45503 | 0.388928 | ||||||||
\(592\) | −52.0352 | −2.13864 | ||||||||
\(593\) | −22.7743 | −0.935229 | −0.467615 | − | 0.883932i | \(-0.654887\pi\) | ||||
−0.467615 | + | 0.883932i | \(0.654887\pi\) | |||||||
\(594\) | −52.3504 | −2.14796 | ||||||||
\(595\) | 15.7891 | 0.647291 | ||||||||
\(596\) | −23.2709 | −0.953212 | ||||||||
\(597\) | −2.99225 | −0.122465 | ||||||||
\(598\) | 71.7039 | 2.93219 | ||||||||
\(599\) | −37.8063 | −1.54472 | −0.772361 | − | 0.635183i | \(-0.780925\pi\) | ||||
−0.772361 | + | 0.635183i | \(0.780925\pi\) | |||||||
\(600\) | 11.1836 | 0.456567 | ||||||||
\(601\) | −34.3589 | −1.40153 | −0.700764 | − | 0.713393i | \(-0.747157\pi\) | ||||
−0.700764 | + | 0.713393i | \(0.747157\pi\) | |||||||
\(602\) | 42.3054 | 1.72424 | ||||||||
\(603\) | 1.31415 | 0.0535163 | ||||||||
\(604\) | 114.544 | 4.66075 | ||||||||
\(605\) | 5.87555 | 0.238875 | ||||||||
\(606\) | −67.8481 | −2.75614 | ||||||||
\(607\) | −44.5187 | −1.80696 | −0.903480 | − | 0.428630i | \(-0.858996\pi\) | ||||
−0.903480 | + | 0.428630i | \(0.858996\pi\) | |||||||
\(608\) | 44.0182 | 1.78517 | ||||||||
\(609\) | 22.4743 | 0.910704 | ||||||||
\(610\) | 59.8039 | 2.42139 | ||||||||
\(611\) | −6.37752 | −0.258007 | ||||||||
\(612\) | −6.89334 | −0.278647 | ||||||||
\(613\) | −16.9501 | −0.684609 | −0.342305 | − | 0.939589i | \(-0.611207\pi\) | ||||
−0.342305 | + | 0.939589i | \(0.611207\pi\) | |||||||
\(614\) | 32.8599 | 1.32612 | ||||||||
\(615\) | −32.8835 | −1.32599 | ||||||||
\(616\) | 38.4518 | 1.54927 | ||||||||
\(617\) | 17.8366 | 0.718073 | 0.359036 | − | 0.933324i | \(-0.383105\pi\) | ||||
0.359036 | + | 0.933324i | \(0.383105\pi\) | |||||||
\(618\) | −22.9422 | −0.922870 | ||||||||
\(619\) | 15.2259 | 0.611982 | 0.305991 | − | 0.952034i | \(-0.401012\pi\) | ||||
0.305991 | + | 0.952034i | \(0.401012\pi\) | |||||||
\(620\) | 0.421164 | 0.0169144 | ||||||||
\(621\) | 43.7594 | 1.75601 | ||||||||
\(622\) | 43.0759 | 1.72719 | ||||||||
\(623\) | 17.4105 | 0.697537 | ||||||||
\(624\) | 51.0467 | 2.04350 | ||||||||
\(625\) | −19.3704 | −0.774816 | ||||||||
\(626\) | −49.1110 | −1.96287 | ||||||||
\(627\) | 29.3167 | 1.17080 | ||||||||
\(628\) | −53.6546 | −2.14105 | ||||||||
\(629\) | −31.2111 | −1.24447 | ||||||||
\(630\) | 2.01358 | 0.0802231 | ||||||||
\(631\) | 31.5181 | 1.25472 | 0.627359 | − | 0.778731i | \(-0.284136\pi\) | ||||
0.627359 | + | 0.778731i | \(0.284136\pi\) | |||||||
\(632\) | 83.0509 | 3.30359 | ||||||||
\(633\) | −18.3617 | −0.729812 | ||||||||
\(634\) | −13.1305 | −0.521480 | ||||||||
\(635\) | −41.5726 | −1.64976 | ||||||||
\(636\) | 49.0666 | 1.94562 | ||||||||
\(637\) | −16.7572 | −0.663943 | ||||||||
\(638\) | 91.3565 | 3.61684 | ||||||||
\(639\) | 1.50354 | 0.0594790 | ||||||||
\(640\) | 6.26780 | 0.247757 | ||||||||
\(641\) | 24.8029 | 0.979655 | 0.489828 | − | 0.871819i | \(-0.337060\pi\) | ||||
0.489828 | + | 0.871819i | \(0.337060\pi\) | |||||||
\(642\) | −0.928053 | −0.0366273 | ||||||||
\(643\) | −1.70507 | −0.0672412 | −0.0336206 | − | 0.999435i | \(-0.510704\pi\) | ||||
−0.0336206 | + | 0.999435i | \(0.510704\pi\) | |||||||
\(644\) | −55.5146 | −2.18758 | ||||||||
\(645\) | −37.5745 | −1.47950 | ||||||||
\(646\) | 67.1480 | 2.64190 | ||||||||
\(647\) | 20.8917 | 0.821339 | 0.410669 | − | 0.911784i | \(-0.365295\pi\) | ||||
0.410669 | + | 0.911784i | \(0.365295\pi\) | |||||||
\(648\) | 58.0814 | 2.28165 | ||||||||
\(649\) | −27.2145 | −1.06826 | ||||||||
\(650\) | 8.37794 | 0.328610 | ||||||||
\(651\) | 0.105009 | 0.00411562 | ||||||||
\(652\) | −46.4896 | −1.82067 | ||||||||
\(653\) | −30.2909 | −1.18538 | −0.592688 | − | 0.805432i | \(-0.701933\pi\) | ||||
−0.592688 | + | 0.805432i | \(0.701933\pi\) | |||||||
\(654\) | −66.3975 | −2.59635 | ||||||||
\(655\) | −16.0624 | −0.627609 | ||||||||
\(656\) | −89.5595 | −3.49671 | ||||||||
\(657\) | −1.52589 | −0.0595308 | ||||||||
\(658\) | 7.01645 | 0.273530 | ||||||||
\(659\) | 33.6408 | 1.31046 | 0.655229 | − | 0.755430i | \(-0.272572\pi\) | ||||
0.655229 | + | 0.755430i | \(0.272572\pi\) | |||||||
\(660\) | −58.9865 | −2.29605 | ||||||||
\(661\) | −19.7038 | −0.766389 | −0.383195 | − | 0.923668i | \(-0.625176\pi\) | ||||
−0.383195 | + | 0.923668i | \(0.625176\pi\) | |||||||
\(662\) | −70.9823 | −2.75881 | ||||||||
\(663\) | 30.6181 | 1.18911 | ||||||||
\(664\) | 49.1990 | 1.90929 | ||||||||
\(665\) | −13.8030 | −0.535256 | ||||||||
\(666\) | −3.98034 | −0.154235 | ||||||||
\(667\) | −76.3645 | −2.95684 | ||||||||
\(668\) | −34.9130 | −1.35082 | ||||||||
\(669\) | 1.06606 | 0.0412161 | ||||||||
\(670\) | 25.7564 | 0.995056 | ||||||||
\(671\) | 42.6536 | 1.64663 | ||||||||
\(672\) | −22.0822 | −0.851841 | ||||||||
\(673\) | 42.6013 | 1.64216 | 0.821080 | − | 0.570813i | \(-0.193372\pi\) | ||||
0.821080 | + | 0.570813i | \(0.193372\pi\) | |||||||
\(674\) | 1.54197 | 0.0593946 | ||||||||
\(675\) | 5.11289 | 0.196795 | ||||||||
\(676\) | −6.63973 | −0.255374 | ||||||||
\(677\) | 5.88371 | 0.226129 | 0.113065 | − | 0.993588i | \(-0.463933\pi\) | ||||
0.113065 | + | 0.993588i | \(0.463933\pi\) | |||||||
\(678\) | −42.0044 | −1.61317 | ||||||||
\(679\) | −6.47584 | −0.248520 | ||||||||
\(680\) | −78.2224 | −2.99969 | ||||||||
\(681\) | −5.62274 | −0.215464 | ||||||||
\(682\) | 0.426854 | 0.0163451 | ||||||||
\(683\) | 30.9349 | 1.18369 | 0.591846 | − | 0.806051i | \(-0.298399\pi\) | ||||
0.591846 | + | 0.806051i | \(0.298399\pi\) | |||||||
\(684\) | 6.02620 | 0.230418 | ||||||||
\(685\) | −26.1522 | −0.999222 | ||||||||
\(686\) | 44.6682 | 1.70544 | ||||||||
\(687\) | −27.9284 | −1.06554 | ||||||||
\(688\) | −102.336 | −3.90151 | ||||||||
\(689\) | 21.2816 | 0.810766 | ||||||||
\(690\) | 70.0657 | 2.66736 | ||||||||
\(691\) | 25.4504 | 0.968180 | 0.484090 | − | 0.875018i | \(-0.339151\pi\) | ||||
0.484090 | + | 0.875018i | \(0.339151\pi\) | |||||||
\(692\) | −110.663 | −4.20679 | ||||||||
\(693\) | 1.43614 | 0.0545544 | ||||||||
\(694\) | 78.6728 | 2.98638 | ||||||||
\(695\) | −28.6139 | −1.08539 | ||||||||
\(696\) | −111.342 | −4.22041 | ||||||||
\(697\) | −53.7183 | −2.03473 | ||||||||
\(698\) | −50.5334 | −1.91272 | ||||||||
\(699\) | 24.2018 | 0.915395 | ||||||||
\(700\) | −6.48637 | −0.245162 | ||||||||
\(701\) | −39.6667 | −1.49819 | −0.749094 | − | 0.662463i | \(-0.769511\pi\) | ||||
−0.749094 | + | 0.662463i | \(0.769511\pi\) | |||||||
\(702\) | 47.7966 | 1.80397 | ||||||||
\(703\) | 27.2849 | 1.02907 | ||||||||
\(704\) | −22.1248 | −0.833858 | ||||||||
\(705\) | −6.23182 | −0.234704 | ||||||||
\(706\) | −8.95185 | −0.336907 | ||||||||
\(707\) | 22.7835 | 0.856862 | ||||||||
\(708\) | 57.2872 | 2.15299 | ||||||||
\(709\) | −13.9802 | −0.525037 | −0.262519 | − | 0.964927i | \(-0.584553\pi\) | ||||
−0.262519 | + | 0.964927i | \(0.584553\pi\) | |||||||
\(710\) | 29.4683 | 1.10593 | ||||||||
\(711\) | 3.10187 | 0.116329 | ||||||||
\(712\) | −86.2550 | −3.23254 | ||||||||
\(713\) | −0.356805 | −0.0133625 | ||||||||
\(714\) | −33.6856 | −1.26065 | ||||||||
\(715\) | −25.5842 | −0.956793 | ||||||||
\(716\) | 29.9972 | 1.12105 | ||||||||
\(717\) | 32.2796 | 1.20550 | ||||||||
\(718\) | 90.7199 | 3.38564 | ||||||||
\(719\) | −16.6240 | −0.619972 | −0.309986 | − | 0.950741i | \(-0.600324\pi\) | ||||
−0.309986 | + | 0.950741i | \(0.600324\pi\) | |||||||
\(720\) | −4.87080 | −0.181524 | ||||||||
\(721\) | 7.70403 | 0.286913 | ||||||||
\(722\) | −9.33654 | −0.347470 | ||||||||
\(723\) | −33.8475 | −1.25880 | ||||||||
\(724\) | −50.3341 | −1.87065 | ||||||||
\(725\) | −8.92249 | −0.331373 | ||||||||
\(726\) | −12.5353 | −0.465229 | ||||||||
\(727\) | −9.36085 | −0.347175 | −0.173587 | − | 0.984818i | \(-0.555536\pi\) | ||||
−0.173587 | + | 0.984818i | \(0.555536\pi\) | |||||||
\(728\) | −35.1070 | −1.30115 | ||||||||
\(729\) | 28.9556 | 1.07243 | ||||||||
\(730\) | −29.9064 | −1.10689 | ||||||||
\(731\) | −61.3815 | −2.27028 | ||||||||
\(732\) | −89.7872 | −3.31863 | ||||||||
\(733\) | −37.8108 | −1.39657 | −0.698286 | − | 0.715819i | \(-0.746054\pi\) | ||||
−0.698286 | + | 0.715819i | \(0.746054\pi\) | |||||||
\(734\) | 17.7851 | 0.656462 | ||||||||
\(735\) | −16.3743 | −0.603976 | ||||||||
\(736\) | 75.0324 | 2.76573 | ||||||||
\(737\) | 18.3701 | 0.676671 | ||||||||
\(738\) | −6.85069 | −0.252177 | ||||||||
\(739\) | 7.41914 | 0.272917 | 0.136459 | − | 0.990646i | \(-0.456428\pi\) | ||||
0.136459 | + | 0.990646i | \(0.456428\pi\) | |||||||
\(740\) | −54.8984 | −2.01811 | ||||||||
\(741\) | −26.7665 | −0.983293 | ||||||||
\(742\) | −23.4137 | −0.859545 | ||||||||
\(743\) | 22.9086 | 0.840435 | 0.420217 | − | 0.907424i | \(-0.361954\pi\) | ||||
0.420217 | + | 0.907424i | \(0.361954\pi\) | |||||||
\(744\) | −0.520234 | −0.0190727 | ||||||||
\(745\) | −9.86266 | −0.361340 | ||||||||
\(746\) | 40.5976 | 1.48639 | ||||||||
\(747\) | 1.83754 | 0.0672320 | ||||||||
\(748\) | −96.3600 | −3.52327 | ||||||||
\(749\) | 0.311642 | 0.0113871 | ||||||||
\(750\) | 51.4247 | 1.87776 | ||||||||
\(751\) | 22.8724 | 0.834624 | 0.417312 | − | 0.908763i | \(-0.362972\pi\) | ||||
0.417312 | + | 0.908763i | \(0.362972\pi\) | |||||||
\(752\) | −16.9726 | −0.618927 | ||||||||
\(753\) | 33.0011 | 1.20263 | ||||||||
\(754\) | −83.4097 | −3.03760 | ||||||||
\(755\) | 48.5462 | 1.76678 | ||||||||
\(756\) | −37.0051 | −1.34586 | ||||||||
\(757\) | −15.9748 | −0.580615 | −0.290308 | − | 0.956933i | \(-0.593758\pi\) | ||||
−0.290308 | + | 0.956933i | \(0.593758\pi\) | |||||||
\(758\) | −91.4143 | −3.32032 | ||||||||
\(759\) | 49.9726 | 1.81389 | ||||||||
\(760\) | 68.3825 | 2.48050 | ||||||||
\(761\) | −13.0772 | −0.474047 | −0.237024 | − | 0.971504i | \(-0.576172\pi\) | ||||
−0.237024 | + | 0.971504i | \(0.576172\pi\) | |||||||
\(762\) | 88.6937 | 3.21303 | ||||||||
\(763\) | 22.2964 | 0.807184 | ||||||||
\(764\) | 36.3753 | 1.31601 | ||||||||
\(765\) | −2.92153 | −0.105628 | ||||||||
\(766\) | 20.5667 | 0.743107 | ||||||||
\(767\) | 24.8471 | 0.897178 | ||||||||
\(768\) | −32.9806 | −1.19008 | ||||||||
\(769\) | −50.0321 | −1.80420 | −0.902102 | − | 0.431523i | \(-0.857976\pi\) | ||||
−0.902102 | + | 0.431523i | \(0.857976\pi\) | |||||||
\(770\) | 28.1473 | 1.01436 | ||||||||
\(771\) | 10.0492 | 0.361914 | ||||||||
\(772\) | 126.418 | 4.54987 | ||||||||
\(773\) | 12.5643 | 0.451906 | 0.225953 | − | 0.974138i | \(-0.427450\pi\) | ||||
0.225953 | + | 0.974138i | \(0.427450\pi\) | |||||||
\(774\) | −7.82797 | −0.281371 | ||||||||
\(775\) | −0.0416894 | −0.00149753 | ||||||||
\(776\) | 32.0826 | 1.15170 | ||||||||
\(777\) | −13.6878 | −0.491047 | ||||||||
\(778\) | 1.56810 | 0.0562191 | ||||||||
\(779\) | 46.9609 | 1.68255 | ||||||||
\(780\) | 53.8554 | 1.92833 | ||||||||
\(781\) | 21.0175 | 0.752066 | ||||||||
\(782\) | 114.459 | 4.09304 | ||||||||
\(783\) | −50.9032 | −1.81913 | ||||||||
\(784\) | −44.5960 | −1.59272 | ||||||||
\(785\) | −22.7399 | −0.811621 | ||||||||
\(786\) | 34.2685 | 1.22232 | ||||||||
\(787\) | −9.97149 | −0.355445 | −0.177723 | − | 0.984081i | \(-0.556873\pi\) | ||||
−0.177723 | + | 0.984081i | \(0.556873\pi\) | |||||||
\(788\) | 27.1680 | 0.967821 | ||||||||
\(789\) | −20.0989 | −0.715541 | ||||||||
\(790\) | 60.7945 | 2.16297 | ||||||||
\(791\) | 14.1051 | 0.501521 | ||||||||
\(792\) | −7.11491 | −0.252817 | ||||||||
\(793\) | −38.9433 | −1.38292 | ||||||||
\(794\) | −18.1170 | −0.642949 | ||||||||
\(795\) | 20.7954 | 0.737538 | ||||||||
\(796\) | −8.59791 | −0.304745 | ||||||||
\(797\) | 39.0682 | 1.38387 | 0.691934 | − | 0.721961i | \(-0.256759\pi\) | ||||
0.691934 | + | 0.721961i | \(0.256759\pi\) | |||||||
\(798\) | 29.4481 | 1.04245 | ||||||||
\(799\) | −10.1803 | −0.360152 | ||||||||
\(800\) | 8.76685 | 0.309955 | ||||||||
\(801\) | −3.22155 | −0.113828 | ||||||||
\(802\) | 33.5286 | 1.18394 | ||||||||
\(803\) | −21.3300 | −0.752720 | ||||||||
\(804\) | −38.6696 | −1.36377 | ||||||||
\(805\) | −23.5282 | −0.829260 | ||||||||
\(806\) | −0.389723 | −0.0137274 | ||||||||
\(807\) | 45.5846 | 1.60465 | ||||||||
\(808\) | −112.874 | −3.97089 | ||||||||
\(809\) | −39.8743 | −1.40190 | −0.700952 | − | 0.713208i | \(-0.747242\pi\) | ||||
−0.700952 | + | 0.713208i | \(0.747242\pi\) | |||||||
\(810\) | 42.5165 | 1.49388 | ||||||||
\(811\) | −21.7849 | −0.764970 | −0.382485 | − | 0.923962i | \(-0.624932\pi\) | ||||
−0.382485 | + | 0.923962i | \(0.624932\pi\) | |||||||
\(812\) | 64.5774 | 2.26622 | ||||||||
\(813\) | −24.9833 | −0.876202 | ||||||||
\(814\) | −55.6400 | −1.95018 | ||||||||
\(815\) | −19.7032 | −0.690173 | ||||||||
\(816\) | 81.4844 | 2.85252 | ||||||||
\(817\) | 53.6601 | 1.87733 | ||||||||
\(818\) | −26.2127 | −0.916505 | ||||||||
\(819\) | −1.31121 | −0.0458175 | ||||||||
\(820\) | −94.4874 | −3.29964 | ||||||||
\(821\) | −17.3108 | −0.604150 | −0.302075 | − | 0.953284i | \(-0.597679\pi\) | ||||
−0.302075 | + | 0.953284i | \(0.597679\pi\) | |||||||
\(822\) | 55.7948 | 1.94607 | ||||||||
\(823\) | −26.9088 | −0.937980 | −0.468990 | − | 0.883203i | \(-0.655382\pi\) | ||||
−0.468990 | + | 0.883203i | \(0.655382\pi\) | |||||||
\(824\) | −38.1673 | −1.32962 | ||||||||
\(825\) | 5.83884 | 0.203282 | ||||||||
\(826\) | −27.3364 | −0.951157 | ||||||||
\(827\) | 21.1406 | 0.735130 | 0.367565 | − | 0.929998i | \(-0.380192\pi\) | ||||
0.367565 | + | 0.929998i | \(0.380192\pi\) | |||||||
\(828\) | 10.2721 | 0.356981 | ||||||||
\(829\) | −44.5496 | −1.54727 | −0.773635 | − | 0.633631i | \(-0.781564\pi\) | ||||
−0.773635 | + | 0.633631i | \(0.781564\pi\) | |||||||
\(830\) | 36.0144 | 1.25008 | ||||||||
\(831\) | 45.8645 | 1.59102 | ||||||||
\(832\) | 20.2002 | 0.700315 | ||||||||
\(833\) | −26.7490 | −0.926797 | ||||||||
\(834\) | 61.0468 | 2.11388 | ||||||||
\(835\) | −14.7968 | −0.512065 | ||||||||
\(836\) | 84.2385 | 2.91345 | ||||||||
\(837\) | −0.237840 | −0.00822096 | ||||||||
\(838\) | 10.9851 | 0.379475 | ||||||||
\(839\) | 25.7015 | 0.887315 | 0.443658 | − | 0.896196i | \(-0.353681\pi\) | ||||
0.443658 | + | 0.896196i | \(0.353681\pi\) | |||||||
\(840\) | −34.3049 | −1.18363 | ||||||||
\(841\) | 59.8311 | 2.06314 | ||||||||
\(842\) | −36.0295 | −1.24166 | ||||||||
\(843\) | 7.05917 | 0.243131 | ||||||||
\(844\) | −52.7604 | −1.81609 | ||||||||
\(845\) | −2.81405 | −0.0968063 | ||||||||
\(846\) | −1.29829 | −0.0446360 | ||||||||
\(847\) | 4.20938 | 0.144636 | ||||||||
\(848\) | 56.6371 | 1.94493 | ||||||||
\(849\) | 44.5259 | 1.52812 | ||||||||
\(850\) | 13.3735 | 0.458706 | ||||||||
\(851\) | 46.5092 | 1.59432 | ||||||||
\(852\) | −44.2425 | −1.51572 | ||||||||
\(853\) | 31.3102 | 1.07204 | 0.536021 | − | 0.844205i | \(-0.319927\pi\) | ||||
0.536021 | + | 0.844205i | \(0.319927\pi\) | |||||||
\(854\) | 42.8449 | 1.46612 | ||||||||
\(855\) | 2.55402 | 0.0873458 | ||||||||
\(856\) | −1.54394 | −0.0527706 | ||||||||
\(857\) | 25.5767 | 0.873684 | 0.436842 | − | 0.899538i | \(-0.356097\pi\) | ||||
0.436842 | + | 0.899538i | \(0.356097\pi\) | |||||||
\(858\) | 54.5830 | 1.86343 | ||||||||
\(859\) | −55.5478 | −1.89527 | −0.947633 | − | 0.319361i | \(-0.896532\pi\) | ||||
−0.947633 | + | 0.319361i | \(0.896532\pi\) | |||||||
\(860\) | −107.966 | −3.68162 | ||||||||
\(861\) | −23.5585 | −0.802872 | ||||||||
\(862\) | 22.7055 | 0.773351 | ||||||||
\(863\) | 39.5856 | 1.34751 | 0.673754 | − | 0.738955i | \(-0.264681\pi\) | ||||
0.673754 | + | 0.738955i | \(0.264681\pi\) | |||||||
\(864\) | 50.0153 | 1.70155 | ||||||||
\(865\) | −46.9014 | −1.59469 | ||||||||
\(866\) | 40.9060 | 1.39004 | ||||||||
\(867\) | 20.7702 | 0.705393 | ||||||||
\(868\) | 0.301731 | 0.0102414 | ||||||||
\(869\) | 43.3602 | 1.47089 | ||||||||
\(870\) | −81.5041 | −2.76325 | ||||||||
\(871\) | −16.7721 | −0.568302 | ||||||||
\(872\) | −110.461 | −3.74067 | ||||||||
\(873\) | 1.19825 | 0.0405548 | ||||||||
\(874\) | −100.061 | −3.38460 | ||||||||
\(875\) | −17.2685 | −0.583782 | ||||||||
\(876\) | 44.9003 | 1.51704 | ||||||||
\(877\) | −38.2386 | −1.29123 | −0.645613 | − | 0.763665i | \(-0.723398\pi\) | ||||
−0.645613 | + | 0.763665i | \(0.723398\pi\) | |||||||
\(878\) | −77.2244 | −2.60620 | ||||||||
\(879\) | 9.66083 | 0.325852 | ||||||||
\(880\) | −68.0875 | −2.29523 | ||||||||
\(881\) | −25.7037 | −0.865979 | −0.432990 | − | 0.901399i | \(-0.642541\pi\) | ||||
−0.432990 | + | 0.901399i | \(0.642541\pi\) | |||||||
\(882\) | −3.41129 | −0.114864 | ||||||||
\(883\) | −19.9929 | −0.672816 | −0.336408 | − | 0.941716i | \(-0.609212\pi\) | ||||
−0.336408 | + | 0.941716i | \(0.609212\pi\) | |||||||
\(884\) | 87.9779 | 2.95902 | ||||||||
\(885\) | 24.2795 | 0.816146 | ||||||||
\(886\) | −56.2423 | −1.88950 | ||||||||
\(887\) | 23.8844 | 0.801960 | 0.400980 | − | 0.916087i | \(-0.368670\pi\) | ||||
0.400980 | + | 0.916087i | \(0.368670\pi\) | |||||||
\(888\) | 67.8120 | 2.27562 | ||||||||
\(889\) | −29.7835 | −0.998907 | ||||||||
\(890\) | −63.1400 | −2.11646 | ||||||||
\(891\) | 30.3238 | 1.01589 | ||||||||
\(892\) | 3.06320 | 0.102564 | ||||||||
\(893\) | 8.89965 | 0.297815 | ||||||||
\(894\) | 21.0417 | 0.703738 | ||||||||
\(895\) | 12.7134 | 0.424963 | ||||||||
\(896\) | 4.49039 | 0.150014 | ||||||||
\(897\) | −45.6256 | −1.52340 | ||||||||
\(898\) | −29.2039 | −0.974547 | ||||||||
\(899\) | 0.415054 | 0.0138428 | ||||||||
\(900\) | 1.20020 | 0.0400068 | ||||||||
\(901\) | 33.9713 | 1.13175 | ||||||||
\(902\) | −95.7638 | −3.18859 | ||||||||
\(903\) | −26.9192 | −0.895816 | ||||||||
\(904\) | −69.8797 | −2.32416 | ||||||||
\(905\) | −21.3326 | −0.709119 | ||||||||
\(906\) | −103.572 | −3.44094 | ||||||||
\(907\) | 9.87344 | 0.327842 | 0.163921 | − | 0.986473i | \(-0.447586\pi\) | ||||
0.163921 | + | 0.986473i | \(0.447586\pi\) | |||||||
\(908\) | −16.1564 | −0.536167 | ||||||||
\(909\) | −4.21574 | −0.139827 | ||||||||
\(910\) | −25.6988 | −0.851909 | ||||||||
\(911\) | −53.4567 | −1.77110 | −0.885550 | − | 0.464544i | \(-0.846218\pi\) | ||||
−0.885550 | + | 0.464544i | \(0.846218\pi\) | |||||||
\(912\) | −71.2342 | −2.35880 | ||||||||
\(913\) | 25.6864 | 0.850095 | ||||||||
\(914\) | −72.0645 | −2.38368 | ||||||||
\(915\) | −38.0536 | −1.25801 | ||||||||
\(916\) | −80.2494 | −2.65152 | ||||||||
\(917\) | −11.5074 | −0.380009 | ||||||||
\(918\) | 76.2963 | 2.51815 | ||||||||
\(919\) | 17.3223 | 0.571410 | 0.285705 | − | 0.958318i | \(-0.407772\pi\) | ||||
0.285705 | + | 0.958318i | \(0.407772\pi\) | |||||||
\(920\) | 116.563 | 3.84298 | ||||||||
\(921\) | −20.9090 | −0.688974 | ||||||||
\(922\) | −16.3814 | −0.539491 | ||||||||
\(923\) | −19.1893 | −0.631622 | ||||||||
\(924\) | −42.2592 | −1.39023 | ||||||||
\(925\) | 5.43418 | 0.178675 | ||||||||
\(926\) | 12.5483 | 0.412362 | ||||||||
\(927\) | −1.42551 | −0.0468200 | ||||||||
\(928\) | −87.2815 | −2.86516 | ||||||||
\(929\) | 7.81347 | 0.256352 | 0.128176 | − | 0.991751i | \(-0.459088\pi\) | ||||
0.128176 | + | 0.991751i | \(0.459088\pi\) | |||||||
\(930\) | −0.380819 | −0.0124876 | ||||||||
\(931\) | 23.3841 | 0.766384 | ||||||||
\(932\) | 69.5412 | 2.27790 | ||||||||
\(933\) | −27.4095 | −0.897346 | ||||||||
\(934\) | 88.5144 | 2.89628 | ||||||||
\(935\) | −40.8393 | −1.33559 | ||||||||
\(936\) | 6.49601 | 0.212329 | ||||||||
\(937\) | −40.7916 | −1.33260 | −0.666301 | − | 0.745683i | \(-0.732123\pi\) | ||||
−0.666301 | + | 0.745683i | \(0.732123\pi\) | |||||||
\(938\) | 18.4524 | 0.602494 | ||||||||
\(939\) | 31.2496 | 1.01979 | ||||||||
\(940\) | −17.9065 | −0.584045 | ||||||||
\(941\) | −26.1953 | −0.853941 | −0.426971 | − | 0.904266i | \(-0.640419\pi\) | ||||
−0.426971 | + | 0.904266i | \(0.640419\pi\) | |||||||
\(942\) | 48.5148 | 1.58070 | ||||||||
\(943\) | 80.0485 | 2.60674 | ||||||||
\(944\) | 66.1260 | 2.15222 | ||||||||
\(945\) | −15.6835 | −0.510184 | ||||||||
\(946\) | −109.425 | −3.55771 | ||||||||
\(947\) | −45.8628 | −1.49034 | −0.745171 | − | 0.666873i | \(-0.767632\pi\) | ||||
−0.745171 | + | 0.666873i | \(0.767632\pi\) | |||||||
\(948\) | −91.2745 | −2.96446 | ||||||||
\(949\) | 19.4746 | 0.632171 | ||||||||
\(950\) | −11.6912 | −0.379312 | ||||||||
\(951\) | 8.35503 | 0.270931 | ||||||||
\(952\) | −56.0403 | −1.81628 | ||||||||
\(953\) | 24.0684 | 0.779652 | 0.389826 | − | 0.920888i | \(-0.372535\pi\) | ||||
0.389826 | + | 0.920888i | \(0.372535\pi\) | |||||||
\(954\) | 4.33235 | 0.140265 | ||||||||
\(955\) | 15.4166 | 0.498868 | ||||||||
\(956\) | 92.7520 | 2.99982 | ||||||||
\(957\) | −58.1307 | −1.87910 | ||||||||
\(958\) | 25.0894 | 0.810601 | ||||||||
\(959\) | −18.7360 | −0.605016 | ||||||||
\(960\) | 19.7387 | 0.637063 | ||||||||
\(961\) | −30.9981 | −0.999937 | ||||||||
\(962\) | 50.8001 | 1.63786 | ||||||||
\(963\) | −0.0576646 | −0.00185821 | ||||||||
\(964\) | −97.2573 | −3.13245 | ||||||||
\(965\) | 53.5783 | 1.72475 | ||||||||
\(966\) | 50.1966 | 1.61505 | ||||||||
\(967\) | 48.7240 | 1.56686 | 0.783429 | − | 0.621481i | \(-0.213469\pi\) | ||||
0.783429 | + | 0.621481i | \(0.213469\pi\) | |||||||
\(968\) | −20.8541 | −0.670276 | ||||||||
\(969\) | −42.7267 | −1.37258 | ||||||||
\(970\) | 23.4849 | 0.754056 | ||||||||
\(971\) | 13.3886 | 0.429661 | 0.214830 | − | 0.976651i | \(-0.431080\pi\) | ||||
0.214830 | + | 0.976651i | \(0.431080\pi\) | |||||||
\(972\) | 13.1351 | 0.421307 | ||||||||
\(973\) | −20.4996 | −0.657188 | ||||||||
\(974\) | −38.0587 | −1.21948 | ||||||||
\(975\) | −5.33094 | −0.170727 | ||||||||
\(976\) | −103.640 | −3.31745 | ||||||||
\(977\) | 55.7634 | 1.78403 | 0.892015 | − | 0.452006i | \(-0.149291\pi\) | ||||
0.892015 | + | 0.452006i | \(0.149291\pi\) | |||||||
\(978\) | 42.0362 | 1.34417 | ||||||||
\(979\) | −45.0330 | −1.43926 | ||||||||
\(980\) | −47.0499 | −1.50295 | ||||||||
\(981\) | −4.12561 | −0.131720 | ||||||||
\(982\) | 25.7353 | 0.821248 | ||||||||
\(983\) | 26.5135 | 0.845648 | 0.422824 | − | 0.906212i | \(-0.361039\pi\) | ||||
0.422824 | + | 0.906212i | \(0.361039\pi\) | |||||||
\(984\) | 116.713 | 3.72069 | ||||||||
\(985\) | 11.5144 | 0.366878 | ||||||||
\(986\) | −133.145 | −4.24018 | ||||||||
\(987\) | −4.46461 | −0.142110 | ||||||||
\(988\) | −76.9108 | −2.44686 | ||||||||
\(989\) | 91.4677 | 2.90851 | ||||||||
\(990\) | −5.20823 | −0.165528 | ||||||||
\(991\) | 56.1775 | 1.78454 | 0.892268 | − | 0.451506i | \(-0.149113\pi\) | ||||
0.892268 | + | 0.451506i | \(0.149113\pi\) | |||||||
\(992\) | −0.407814 | −0.0129481 | ||||||||
\(993\) | 45.1665 | 1.43332 | ||||||||
\(994\) | 21.1117 | 0.669624 | ||||||||
\(995\) | −3.64397 | −0.115521 | ||||||||
\(996\) | −54.0706 | −1.71329 | ||||||||
\(997\) | −8.72525 | −0.276331 | −0.138166 | − | 0.990409i | \(-0.544121\pi\) | ||||
−0.138166 | + | 0.990409i | \(0.544121\pi\) | |||||||
\(998\) | −63.0576 | −1.99605 | ||||||||
\(999\) | 31.0023 | 0.980868 |
(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 | 6029.2.a.a.1.10 | ✓ | 234 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6029.2.a.a.1.10 | ✓ | 234 | 1.1 | even | 1 | trivial |