Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2671,2,Mod(1,2671)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2671, 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("2671.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2671 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2671.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: | \(21.3280423799\) |
Analytic rank: | \(0\) |
Dimension: | \(122\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 2671.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.66332 | −1.88325 | −0.941625 | − | 0.336665i | \(-0.890701\pi\) | ||||
−0.941625 | + | 0.336665i | \(0.890701\pi\) | |||||||
\(3\) | −2.18729 | −1.26283 | −0.631416 | − | 0.775444i | \(-0.717526\pi\) | ||||
−0.631416 | + | 0.775444i | \(0.717526\pi\) | |||||||
\(4\) | 5.09325 | 2.54663 | ||||||||
\(5\) | 2.00666 | 0.897407 | 0.448703 | − | 0.893681i | \(-0.351886\pi\) | ||||
0.448703 | + | 0.893681i | \(0.351886\pi\) | |||||||
\(6\) | 5.82544 | 2.37823 | ||||||||
\(7\) | −4.67426 | −1.76671 | −0.883353 | − | 0.468709i | \(-0.844719\pi\) | ||||
−0.883353 | + | 0.468709i | \(0.844719\pi\) | |||||||
\(8\) | −8.23831 | −2.91268 | ||||||||
\(9\) | 1.78423 | 0.594745 | ||||||||
\(10\) | −5.34438 | −1.69004 | ||||||||
\(11\) | −1.28646 | −0.387883 | −0.193942 | − | 0.981013i | \(-0.562127\pi\) | ||||
−0.193942 | + | 0.981013i | \(0.562127\pi\) | |||||||
\(12\) | −11.1404 | −3.21596 | ||||||||
\(13\) | 0.837420 | 0.232258 | 0.116129 | − | 0.993234i | \(-0.462951\pi\) | ||||
0.116129 | + | 0.993234i | \(0.462951\pi\) | |||||||
\(14\) | 12.4490 | 3.32715 | ||||||||
\(15\) | −4.38915 | −1.13327 | ||||||||
\(16\) | 11.7547 | 2.93868 | ||||||||
\(17\) | −3.72116 | −0.902515 | −0.451257 | − | 0.892394i | \(-0.649024\pi\) | ||||
−0.451257 | + | 0.892394i | \(0.649024\pi\) | |||||||
\(18\) | −4.75198 | −1.12005 | ||||||||
\(19\) | −6.63400 | −1.52194 | −0.760972 | − | 0.648785i | \(-0.775277\pi\) | ||||
−0.760972 | + | 0.648785i | \(0.775277\pi\) | |||||||
\(20\) | 10.2204 | 2.28536 | ||||||||
\(21\) | 10.2240 | 2.23105 | ||||||||
\(22\) | 3.42626 | 0.730480 | ||||||||
\(23\) | −8.18713 | −1.70714 | −0.853568 | − | 0.520982i | \(-0.825566\pi\) | ||||
−0.853568 | + | 0.520982i | \(0.825566\pi\) | |||||||
\(24\) | 18.0196 | 3.67823 | ||||||||
\(25\) | −0.973304 | −0.194661 | ||||||||
\(26\) | −2.23031 | −0.437401 | ||||||||
\(27\) | 2.65923 | 0.511769 | ||||||||
\(28\) | −23.8072 | −4.49914 | ||||||||
\(29\) | −6.01804 | −1.11752 | −0.558761 | − | 0.829329i | \(-0.688723\pi\) | ||||
−0.558761 | + | 0.829329i | \(0.688723\pi\) | |||||||
\(30\) | 11.6897 | 2.13424 | ||||||||
\(31\) | −7.83177 | −1.40663 | −0.703314 | − | 0.710879i | \(-0.748297\pi\) | ||||
−0.703314 | + | 0.710879i | \(0.748297\pi\) | |||||||
\(32\) | −14.8299 | −2.62159 | ||||||||
\(33\) | 2.81387 | 0.489831 | ||||||||
\(34\) | 9.91064 | 1.69966 | ||||||||
\(35\) | −9.37967 | −1.58545 | ||||||||
\(36\) | 9.08756 | 1.51459 | ||||||||
\(37\) | −4.64698 | −0.763959 | −0.381980 | − | 0.924171i | \(-0.624758\pi\) | ||||
−0.381980 | + | 0.924171i | \(0.624758\pi\) | |||||||
\(38\) | 17.6684 | 2.86620 | ||||||||
\(39\) | −1.83168 | −0.293303 | ||||||||
\(40\) | −16.5315 | −2.61386 | ||||||||
\(41\) | 10.7890 | 1.68497 | 0.842483 | − | 0.538723i | \(-0.181093\pi\) | ||||
0.842483 | + | 0.538723i | \(0.181093\pi\) | |||||||
\(42\) | −27.2297 | −4.20163 | ||||||||
\(43\) | 2.02891 | 0.309406 | 0.154703 | − | 0.987961i | \(-0.450558\pi\) | ||||
0.154703 | + | 0.987961i | \(0.450558\pi\) | |||||||
\(44\) | −6.55228 | −0.987793 | ||||||||
\(45\) | 3.58036 | 0.533728 | ||||||||
\(46\) | 21.8049 | 3.21496 | ||||||||
\(47\) | −8.20429 | −1.19672 | −0.598359 | − | 0.801228i | \(-0.704180\pi\) | ||||
−0.598359 | + | 0.801228i | \(0.704180\pi\) | |||||||
\(48\) | −25.7110 | −3.71106 | ||||||||
\(49\) | 14.8487 | 2.12125 | ||||||||
\(50\) | 2.59222 | 0.366595 | ||||||||
\(51\) | 8.13926 | 1.13972 | ||||||||
\(52\) | 4.26519 | 0.591476 | ||||||||
\(53\) | −1.63209 | −0.224185 | −0.112093 | − | 0.993698i | \(-0.535755\pi\) | ||||
−0.112093 | + | 0.993698i | \(0.535755\pi\) | |||||||
\(54\) | −7.08238 | −0.963789 | ||||||||
\(55\) | −2.58150 | −0.348089 | ||||||||
\(56\) | 38.5081 | 5.14585 | ||||||||
\(57\) | 14.5105 | 1.92196 | ||||||||
\(58\) | 16.0279 | 2.10457 | ||||||||
\(59\) | −7.28117 | −0.947928 | −0.473964 | − | 0.880544i | \(-0.657177\pi\) | ||||
−0.473964 | + | 0.880544i | \(0.657177\pi\) | |||||||
\(60\) | −22.3551 | −2.88603 | ||||||||
\(61\) | 10.1621 | 1.30112 | 0.650560 | − | 0.759455i | \(-0.274534\pi\) | ||||
0.650560 | + | 0.759455i | \(0.274534\pi\) | |||||||
\(62\) | 20.8585 | 2.64903 | ||||||||
\(63\) | −8.33998 | −1.05074 | ||||||||
\(64\) | 15.9873 | 1.99842 | ||||||||
\(65\) | 1.68042 | 0.208430 | ||||||||
\(66\) | −7.49421 | −0.922474 | ||||||||
\(67\) | −9.39520 | −1.14781 | −0.573903 | − | 0.818923i | \(-0.694572\pi\) | ||||
−0.573903 | + | 0.818923i | \(0.694572\pi\) | |||||||
\(68\) | −18.9528 | −2.29837 | ||||||||
\(69\) | 17.9076 | 2.15583 | ||||||||
\(70\) | 24.9810 | 2.98580 | ||||||||
\(71\) | 8.18081 | 0.970883 | 0.485442 | − | 0.874269i | \(-0.338659\pi\) | ||||
0.485442 | + | 0.874269i | \(0.338659\pi\) | |||||||
\(72\) | −14.6991 | −1.73230 | ||||||||
\(73\) | −7.41648 | −0.868034 | −0.434017 | − | 0.900905i | \(-0.642904\pi\) | ||||
−0.434017 | + | 0.900905i | \(0.642904\pi\) | |||||||
\(74\) | 12.3764 | 1.43873 | ||||||||
\(75\) | 2.12890 | 0.245824 | ||||||||
\(76\) | −33.7886 | −3.87582 | ||||||||
\(77\) | 6.01327 | 0.685275 | ||||||||
\(78\) | 4.87834 | 0.552363 | ||||||||
\(79\) | −4.96542 | −0.558653 | −0.279326 | − | 0.960196i | \(-0.590111\pi\) | ||||
−0.279326 | + | 0.960196i | \(0.590111\pi\) | |||||||
\(80\) | 23.5878 | 2.63719 | ||||||||
\(81\) | −11.1692 | −1.24102 | ||||||||
\(82\) | −28.7346 | −3.17321 | ||||||||
\(83\) | 11.9648 | 1.31331 | 0.656654 | − | 0.754192i | \(-0.271971\pi\) | ||||
0.656654 | + | 0.754192i | \(0.271971\pi\) | |||||||
\(84\) | 52.0733 | 5.68166 | ||||||||
\(85\) | −7.46712 | −0.809923 | ||||||||
\(86\) | −5.40364 | −0.582689 | ||||||||
\(87\) | 13.1632 | 1.41124 | ||||||||
\(88\) | 10.5983 | 1.12978 | ||||||||
\(89\) | −6.85860 | −0.727010 | −0.363505 | − | 0.931592i | \(-0.618420\pi\) | ||||
−0.363505 | + | 0.931592i | \(0.618420\pi\) | |||||||
\(90\) | −9.53562 | −1.00514 | ||||||||
\(91\) | −3.91432 | −0.410332 | ||||||||
\(92\) | −41.6992 | −4.34744 | ||||||||
\(93\) | 17.1304 | 1.77634 | ||||||||
\(94\) | 21.8506 | 2.25372 | ||||||||
\(95\) | −13.3122 | −1.36580 | ||||||||
\(96\) | 32.4374 | 3.31062 | ||||||||
\(97\) | −7.93820 | −0.806002 | −0.403001 | − | 0.915199i | \(-0.632033\pi\) | ||||
−0.403001 | + | 0.915199i | \(0.632033\pi\) | |||||||
\(98\) | −39.5469 | −3.99484 | ||||||||
\(99\) | −2.29535 | −0.230691 | ||||||||
\(100\) | −4.95728 | −0.495728 | ||||||||
\(101\) | 6.48990 | 0.645769 | 0.322884 | − | 0.946438i | \(-0.395347\pi\) | ||||
0.322884 | + | 0.946438i | \(0.395347\pi\) | |||||||
\(102\) | −21.6774 | −2.14639 | ||||||||
\(103\) | −10.3847 | −1.02324 | −0.511618 | − | 0.859213i | \(-0.670954\pi\) | ||||
−0.511618 | + | 0.859213i | \(0.670954\pi\) | |||||||
\(104\) | −6.89893 | −0.676496 | ||||||||
\(105\) | 20.5161 | 2.00216 | ||||||||
\(106\) | 4.34678 | 0.422197 | ||||||||
\(107\) | −3.36124 | −0.324943 | −0.162472 | − | 0.986713i | \(-0.551947\pi\) | ||||
−0.162472 | + | 0.986713i | \(0.551947\pi\) | |||||||
\(108\) | 13.5441 | 1.30329 | ||||||||
\(109\) | −6.77144 | −0.648587 | −0.324293 | − | 0.945957i | \(-0.605127\pi\) | ||||
−0.324293 | + | 0.945957i | \(0.605127\pi\) | |||||||
\(110\) | 6.87534 | 0.655538 | ||||||||
\(111\) | 10.1643 | 0.964752 | ||||||||
\(112\) | −54.9447 | −5.19179 | ||||||||
\(113\) | −11.4522 | −1.07733 | −0.538664 | − | 0.842521i | \(-0.681071\pi\) | ||||
−0.538664 | + | 0.842521i | \(0.681071\pi\) | |||||||
\(114\) | −38.6460 | −3.61953 | ||||||||
\(115\) | −16.4288 | −1.53200 | ||||||||
\(116\) | −30.6514 | −2.84591 | ||||||||
\(117\) | 1.49415 | 0.138134 | ||||||||
\(118\) | 19.3921 | 1.78518 | ||||||||
\(119\) | 17.3937 | 1.59448 | ||||||||
\(120\) | 36.1592 | 3.30087 | ||||||||
\(121\) | −9.34501 | −0.849547 | ||||||||
\(122\) | −27.0648 | −2.45033 | ||||||||
\(123\) | −23.5988 | −2.12783 | ||||||||
\(124\) | −39.8892 | −3.58216 | ||||||||
\(125\) | −11.9864 | −1.07210 | ||||||||
\(126\) | 22.2120 | 1.97880 | ||||||||
\(127\) | 6.37785 | 0.565942 | 0.282971 | − | 0.959128i | \(-0.408680\pi\) | ||||
0.282971 | + | 0.959128i | \(0.408680\pi\) | |||||||
\(128\) | −12.9195 | −1.14193 | ||||||||
\(129\) | −4.43782 | −0.390728 | ||||||||
\(130\) | −4.47549 | −0.392526 | ||||||||
\(131\) | −9.70503 | −0.847932 | −0.423966 | − | 0.905678i | \(-0.639362\pi\) | ||||
−0.423966 | + | 0.905678i | \(0.639362\pi\) | |||||||
\(132\) | 14.3317 | 1.24742 | ||||||||
\(133\) | 31.0091 | 2.68883 | ||||||||
\(134\) | 25.0224 | 2.16161 | ||||||||
\(135\) | 5.33618 | 0.459265 | ||||||||
\(136\) | 30.6561 | 2.62874 | ||||||||
\(137\) | 16.4808 | 1.40805 | 0.704025 | − | 0.710175i | \(-0.251384\pi\) | ||||
0.704025 | + | 0.710175i | \(0.251384\pi\) | |||||||
\(138\) | −47.6937 | −4.05996 | ||||||||
\(139\) | 2.38455 | 0.202255 | 0.101128 | − | 0.994873i | \(-0.467755\pi\) | ||||
0.101128 | + | 0.994873i | \(0.467755\pi\) | |||||||
\(140\) | −47.7730 | −4.03756 | ||||||||
\(141\) | 17.9451 | 1.51125 | ||||||||
\(142\) | −21.7881 | −1.82841 | ||||||||
\(143\) | −1.07731 | −0.0900891 | ||||||||
\(144\) | 20.9732 | 1.74777 | ||||||||
\(145\) | −12.0762 | −1.00287 | ||||||||
\(146\) | 19.7524 | 1.63472 | ||||||||
\(147\) | −32.4785 | −2.67878 | ||||||||
\(148\) | −23.6683 | −1.94552 | ||||||||
\(149\) | 12.3573 | 1.01235 | 0.506174 | − | 0.862431i | \(-0.331059\pi\) | ||||
0.506174 | + | 0.862431i | \(0.331059\pi\) | |||||||
\(150\) | −5.66993 | −0.462948 | ||||||||
\(151\) | −5.65832 | −0.460467 | −0.230234 | − | 0.973135i | \(-0.573949\pi\) | ||||
−0.230234 | + | 0.973135i | \(0.573949\pi\) | |||||||
\(152\) | 54.6530 | 4.43294 | ||||||||
\(153\) | −6.63943 | −0.536766 | ||||||||
\(154\) | −16.0152 | −1.29054 | ||||||||
\(155\) | −15.7157 | −1.26232 | ||||||||
\(156\) | −9.32921 | −0.746935 | ||||||||
\(157\) | −22.2420 | −1.77511 | −0.887553 | − | 0.460706i | \(-0.847596\pi\) | ||||
−0.887553 | + | 0.460706i | \(0.847596\pi\) | |||||||
\(158\) | 13.2245 | 1.05208 | ||||||||
\(159\) | 3.56986 | 0.283109 | ||||||||
\(160\) | −29.7587 | −2.35263 | ||||||||
\(161\) | 38.2688 | 3.01601 | ||||||||
\(162\) | 29.7471 | 2.33716 | ||||||||
\(163\) | 14.8534 | 1.16341 | 0.581703 | − | 0.813401i | \(-0.302386\pi\) | ||||
0.581703 | + | 0.813401i | \(0.302386\pi\) | |||||||
\(164\) | 54.9513 | 4.29098 | ||||||||
\(165\) | 5.64648 | 0.439578 | ||||||||
\(166\) | −31.8661 | −2.47329 | ||||||||
\(167\) | 9.87378 | 0.764056 | 0.382028 | − | 0.924151i | \(-0.375226\pi\) | ||||
0.382028 | + | 0.924151i | \(0.375226\pi\) | |||||||
\(168\) | −84.2282 | −6.49835 | ||||||||
\(169\) | −12.2987 | −0.946056 | ||||||||
\(170\) | 19.8873 | 1.52529 | ||||||||
\(171\) | −11.8366 | −0.905168 | ||||||||
\(172\) | 10.3338 | 0.787942 | ||||||||
\(173\) | −22.6187 | −1.71967 | −0.859834 | − | 0.510574i | \(-0.829433\pi\) | ||||
−0.859834 | + | 0.510574i | \(0.829433\pi\) | |||||||
\(174\) | −35.0577 | −2.65772 | ||||||||
\(175\) | 4.54948 | 0.343908 | ||||||||
\(176\) | −15.1220 | −1.13987 | ||||||||
\(177\) | 15.9260 | 1.19707 | ||||||||
\(178\) | 18.2666 | 1.36914 | ||||||||
\(179\) | 4.78710 | 0.357805 | 0.178902 | − | 0.983867i | \(-0.442745\pi\) | ||||
0.178902 | + | 0.983867i | \(0.442745\pi\) | |||||||
\(180\) | 18.2357 | 1.35921 | ||||||||
\(181\) | −18.3074 | −1.36078 | −0.680389 | − | 0.732851i | \(-0.738189\pi\) | ||||
−0.680389 | + | 0.732851i | \(0.738189\pi\) | |||||||
\(182\) | 10.4251 | 0.772758 | ||||||||
\(183\) | −22.2274 | −1.64310 | ||||||||
\(184\) | 67.4482 | 4.97235 | ||||||||
\(185\) | −9.32493 | −0.685582 | ||||||||
\(186\) | −45.6236 | −3.34528 | ||||||||
\(187\) | 4.78714 | 0.350070 | ||||||||
\(188\) | −41.7865 | −3.04759 | ||||||||
\(189\) | −12.4300 | −0.904146 | ||||||||
\(190\) | 35.4546 | 2.57215 | ||||||||
\(191\) | 10.3998 | 0.752501 | 0.376251 | − | 0.926518i | \(-0.377213\pi\) | ||||
0.376251 | + | 0.926518i | \(0.377213\pi\) | |||||||
\(192\) | −34.9690 | −2.52367 | ||||||||
\(193\) | 7.70248 | 0.554437 | 0.277218 | − | 0.960807i | \(-0.410587\pi\) | ||||
0.277218 | + | 0.960807i | \(0.410587\pi\) | |||||||
\(194\) | 21.1419 | 1.51790 | ||||||||
\(195\) | −3.67556 | −0.263213 | ||||||||
\(196\) | 75.6284 | 5.40203 | ||||||||
\(197\) | 8.15356 | 0.580917 | 0.290459 | − | 0.956888i | \(-0.406192\pi\) | ||||
0.290459 | + | 0.956888i | \(0.406192\pi\) | |||||||
\(198\) | 6.11324 | 0.434449 | ||||||||
\(199\) | −22.1347 | −1.56909 | −0.784545 | − | 0.620072i | \(-0.787103\pi\) | ||||
−0.784545 | + | 0.620072i | \(0.787103\pi\) | |||||||
\(200\) | 8.01838 | 0.566985 | ||||||||
\(201\) | 20.5500 | 1.44949 | ||||||||
\(202\) | −17.2846 | −1.21614 | ||||||||
\(203\) | 28.1299 | 1.97433 | ||||||||
\(204\) | 41.4553 | 2.90245 | ||||||||
\(205\) | 21.6500 | 1.51210 | ||||||||
\(206\) | 27.6577 | 1.92701 | ||||||||
\(207\) | −14.6078 | −1.01531 | ||||||||
\(208\) | 9.84364 | 0.682534 | ||||||||
\(209\) | 8.53439 | 0.590336 | ||||||||
\(210\) | −54.6407 | −3.77057 | ||||||||
\(211\) | 9.37060 | 0.645098 | 0.322549 | − | 0.946553i | \(-0.395460\pi\) | ||||
0.322549 | + | 0.946553i | \(0.395460\pi\) | |||||||
\(212\) | −8.31267 | −0.570917 | ||||||||
\(213\) | −17.8938 | −1.22606 | ||||||||
\(214\) | 8.95205 | 0.611949 | ||||||||
\(215\) | 4.07134 | 0.277663 | ||||||||
\(216\) | −21.9076 | −1.49062 | ||||||||
\(217\) | 36.6078 | 2.48510 | ||||||||
\(218\) | 18.0345 | 1.22145 | ||||||||
\(219\) | 16.2220 | 1.09618 | ||||||||
\(220\) | −13.1482 | −0.886453 | ||||||||
\(221\) | −3.11618 | −0.209617 | ||||||||
\(222\) | −27.0707 | −1.81687 | ||||||||
\(223\) | −8.93203 | −0.598133 | −0.299066 | − | 0.954232i | \(-0.596675\pi\) | ||||
−0.299066 | + | 0.954232i | \(0.596675\pi\) | |||||||
\(224\) | 69.3190 | 4.63157 | ||||||||
\(225\) | −1.73660 | −0.115773 | ||||||||
\(226\) | 30.5007 | 2.02888 | ||||||||
\(227\) | 26.8461 | 1.78184 | 0.890920 | − | 0.454161i | \(-0.150061\pi\) | ||||
0.890920 | + | 0.454161i | \(0.150061\pi\) | |||||||
\(228\) | 73.9055 | 4.89451 | ||||||||
\(229\) | −5.70574 | −0.377046 | −0.188523 | − | 0.982069i | \(-0.560370\pi\) | ||||
−0.188523 | + | 0.982069i | \(0.560370\pi\) | |||||||
\(230\) | 43.7551 | 2.88513 | ||||||||
\(231\) | −13.1527 | −0.865387 | ||||||||
\(232\) | 49.5785 | 3.25499 | ||||||||
\(233\) | −25.1291 | −1.64626 | −0.823132 | − | 0.567850i | \(-0.807775\pi\) | ||||
−0.823132 | + | 0.567850i | \(0.807775\pi\) | |||||||
\(234\) | −3.97940 | −0.260142 | ||||||||
\(235\) | −16.4632 | −1.07394 | ||||||||
\(236\) | −37.0849 | −2.41402 | ||||||||
\(237\) | 10.8608 | 0.705485 | ||||||||
\(238\) | −46.3249 | −3.00280 | ||||||||
\(239\) | −14.2166 | −0.919597 | −0.459798 | − | 0.888023i | \(-0.652078\pi\) | ||||
−0.459798 | + | 0.888023i | \(0.652078\pi\) | |||||||
\(240\) | −51.5933 | −3.33033 | ||||||||
\(241\) | −13.9784 | −0.900428 | −0.450214 | − | 0.892921i | \(-0.648652\pi\) | ||||
−0.450214 | + | 0.892921i | \(0.648652\pi\) | |||||||
\(242\) | 24.8887 | 1.59991 | ||||||||
\(243\) | 16.4526 | 1.05543 | ||||||||
\(244\) | 51.7580 | 3.31347 | ||||||||
\(245\) | 29.7964 | 1.90362 | ||||||||
\(246\) | 62.8510 | 4.00723 | ||||||||
\(247\) | −5.55544 | −0.353484 | ||||||||
\(248\) | 64.5206 | 4.09706 | ||||||||
\(249\) | −26.1705 | −1.65849 | ||||||||
\(250\) | 31.9236 | 2.01903 | ||||||||
\(251\) | 16.2604 | 1.02635 | 0.513175 | − | 0.858284i | \(-0.328469\pi\) | ||||
0.513175 | + | 0.858284i | \(0.328469\pi\) | |||||||
\(252\) | −42.4776 | −2.67584 | ||||||||
\(253\) | 10.5324 | 0.662169 | ||||||||
\(254\) | −16.9862 | −1.06581 | ||||||||
\(255\) | 16.3328 | 1.02280 | ||||||||
\(256\) | 2.43401 | 0.152126 | ||||||||
\(257\) | −2.07375 | −0.129357 | −0.0646785 | − | 0.997906i | \(-0.520602\pi\) | ||||
−0.0646785 | + | 0.997906i | \(0.520602\pi\) | |||||||
\(258\) | 11.8193 | 0.735838 | ||||||||
\(259\) | 21.7212 | 1.34969 | ||||||||
\(260\) | 8.55880 | 0.530794 | ||||||||
\(261\) | −10.7376 | −0.664640 | ||||||||
\(262\) | 25.8476 | 1.59687 | ||||||||
\(263\) | −0.346995 | −0.0213966 | −0.0106983 | − | 0.999943i | \(-0.503405\pi\) | ||||
−0.0106983 | + | 0.999943i | \(0.503405\pi\) | |||||||
\(264\) | −23.1815 | −1.42672 | ||||||||
\(265\) | −3.27506 | −0.201186 | ||||||||
\(266\) | −82.5869 | −5.06373 | ||||||||
\(267\) | 15.0017 | 0.918092 | ||||||||
\(268\) | −47.8522 | −2.92304 | ||||||||
\(269\) | 30.8745 | 1.88245 | 0.941226 | − | 0.337776i | \(-0.109675\pi\) | ||||
0.941226 | + | 0.337776i | \(0.109675\pi\) | |||||||
\(270\) | −14.2119 | −0.864911 | ||||||||
\(271\) | 15.4027 | 0.935647 | 0.467823 | − | 0.883822i | \(-0.345038\pi\) | ||||
0.467823 | + | 0.883822i | \(0.345038\pi\) | |||||||
\(272\) | −43.7413 | −2.65220 | ||||||||
\(273\) | 8.56175 | 0.518181 | ||||||||
\(274\) | −43.8936 | −2.65171 | ||||||||
\(275\) | 1.25212 | 0.0755056 | ||||||||
\(276\) | 91.2081 | 5.49008 | ||||||||
\(277\) | −26.0543 | −1.56545 | −0.782727 | − | 0.622365i | \(-0.786172\pi\) | ||||
−0.782727 | + | 0.622365i | \(0.786172\pi\) | |||||||
\(278\) | −6.35082 | −0.380897 | ||||||||
\(279\) | −13.9737 | −0.836585 | ||||||||
\(280\) | 77.2727 | 4.61793 | ||||||||
\(281\) | 12.6198 | 0.752835 | 0.376418 | − | 0.926450i | \(-0.377156\pi\) | ||||
0.376418 | + | 0.926450i | \(0.377156\pi\) | |||||||
\(282\) | −47.7936 | −2.84607 | ||||||||
\(283\) | 22.8594 | 1.35885 | 0.679426 | − | 0.733744i | \(-0.262229\pi\) | ||||
0.679426 | + | 0.733744i | \(0.262229\pi\) | |||||||
\(284\) | 41.6669 | 2.47248 | ||||||||
\(285\) | 29.1176 | 1.72478 | ||||||||
\(286\) | 2.86922 | 0.169660 | ||||||||
\(287\) | −50.4308 | −2.97684 | ||||||||
\(288\) | −26.4601 | −1.55917 | ||||||||
\(289\) | −3.15294 | −0.185467 | ||||||||
\(290\) | 32.1627 | 1.88866 | ||||||||
\(291\) | 17.3631 | 1.01785 | ||||||||
\(292\) | −37.7740 | −2.21056 | ||||||||
\(293\) | 5.75528 | 0.336227 | 0.168114 | − | 0.985768i | \(-0.446232\pi\) | ||||
0.168114 | + | 0.985768i | \(0.446232\pi\) | |||||||
\(294\) | 86.5005 | 5.04481 | ||||||||
\(295\) | −14.6109 | −0.850677 | ||||||||
\(296\) | 38.2833 | 2.22517 | ||||||||
\(297\) | −3.42100 | −0.198507 | ||||||||
\(298\) | −32.9114 | −1.90650 | ||||||||
\(299\) | −6.85607 | −0.396497 | ||||||||
\(300\) | 10.8430 | 0.626022 | ||||||||
\(301\) | −9.48367 | −0.546630 | ||||||||
\(302\) | 15.0699 | 0.867175 | ||||||||
\(303\) | −14.1953 | −0.815498 | ||||||||
\(304\) | −77.9808 | −4.47251 | ||||||||
\(305\) | 20.3919 | 1.16763 | ||||||||
\(306\) | 17.6829 | 1.01086 | ||||||||
\(307\) | −0.529976 | −0.0302473 | −0.0151237 | − | 0.999886i | \(-0.504814\pi\) | ||||
−0.0151237 | + | 0.999886i | \(0.504814\pi\) | |||||||
\(308\) | 30.6271 | 1.74514 | ||||||||
\(309\) | 22.7143 | 1.29217 | ||||||||
\(310\) | 41.8560 | 2.37726 | ||||||||
\(311\) | −10.4676 | −0.593565 | −0.296782 | − | 0.954945i | \(-0.595914\pi\) | ||||
−0.296782 | + | 0.954945i | \(0.595914\pi\) | |||||||
\(312\) | 15.0900 | 0.854300 | ||||||||
\(313\) | 0.601656 | 0.0340076 | 0.0170038 | − | 0.999855i | \(-0.494587\pi\) | ||||
0.0170038 | + | 0.999855i | \(0.494587\pi\) | |||||||
\(314\) | 59.2375 | 3.34297 | ||||||||
\(315\) | −16.7355 | −0.942940 | ||||||||
\(316\) | −25.2901 | −1.42268 | ||||||||
\(317\) | 32.8675 | 1.84602 | 0.923012 | − | 0.384770i | \(-0.125719\pi\) | ||||
0.923012 | + | 0.384770i | \(0.125719\pi\) | |||||||
\(318\) | −9.50767 | −0.533164 | ||||||||
\(319\) | 7.74198 | 0.433467 | ||||||||
\(320\) | 32.0812 | 1.79339 | ||||||||
\(321\) | 7.35200 | 0.410349 | ||||||||
\(322\) | −101.922 | −5.67989 | ||||||||
\(323\) | 24.6862 | 1.37358 | ||||||||
\(324\) | −56.8876 | −3.16042 | ||||||||
\(325\) | −0.815064 | −0.0452116 | ||||||||
\(326\) | −39.5593 | −2.19098 | ||||||||
\(327\) | 14.8111 | 0.819056 | ||||||||
\(328\) | −88.8835 | −4.90777 | ||||||||
\(329\) | 38.3490 | 2.11425 | ||||||||
\(330\) | −15.0384 | −0.827835 | ||||||||
\(331\) | 30.0571 | 1.65209 | 0.826044 | − | 0.563605i | \(-0.190586\pi\) | ||||
0.826044 | + | 0.563605i | \(0.190586\pi\) | |||||||
\(332\) | 60.9398 | 3.34451 | ||||||||
\(333\) | −8.29131 | −0.454361 | ||||||||
\(334\) | −26.2970 | −1.43891 | ||||||||
\(335\) | −18.8530 | −1.03005 | ||||||||
\(336\) | 120.180 | 6.55635 | ||||||||
\(337\) | 0.969105 | 0.0527905 | 0.0263953 | − | 0.999652i | \(-0.491597\pi\) | ||||
0.0263953 | + | 0.999652i | \(0.491597\pi\) | |||||||
\(338\) | 32.7554 | 1.78166 | ||||||||
\(339\) | 25.0492 | 1.36048 | ||||||||
\(340\) | −38.0319 | −2.06257 | ||||||||
\(341\) | 10.0753 | 0.545607 | ||||||||
\(342\) | 31.5246 | 1.70466 | ||||||||
\(343\) | −36.6871 | −1.98092 | ||||||||
\(344\) | −16.7148 | −0.901203 | ||||||||
\(345\) | 35.9346 | 1.93465 | ||||||||
\(346\) | 60.2407 | 3.23856 | ||||||||
\(347\) | 35.9887 | 1.93198 | 0.965988 | − | 0.258588i | \(-0.0832570\pi\) | ||||
0.965988 | + | 0.258588i | \(0.0832570\pi\) | |||||||
\(348\) | 67.0434 | 3.59391 | ||||||||
\(349\) | −16.1972 | −0.867015 | −0.433507 | − | 0.901150i | \(-0.642724\pi\) | ||||
−0.433507 | + | 0.901150i | \(0.642724\pi\) | |||||||
\(350\) | −12.1167 | −0.647665 | ||||||||
\(351\) | 2.22689 | 0.118863 | ||||||||
\(352\) | 19.0782 | 1.01687 | ||||||||
\(353\) | 5.73632 | 0.305313 | 0.152657 | − | 0.988279i | \(-0.451217\pi\) | ||||
0.152657 | + | 0.988279i | \(0.451217\pi\) | |||||||
\(354\) | −42.4161 | −2.25439 | ||||||||
\(355\) | 16.4161 | 0.871277 | ||||||||
\(356\) | −34.9326 | −1.85142 | ||||||||
\(357\) | −38.0451 | −2.01356 | ||||||||
\(358\) | −12.7496 | −0.673835 | ||||||||
\(359\) | −14.1387 | −0.746215 | −0.373107 | − | 0.927788i | \(-0.621708\pi\) | ||||
−0.373107 | + | 0.927788i | \(0.621708\pi\) | |||||||
\(360\) | −29.4961 | −1.55458 | ||||||||
\(361\) | 25.0099 | 1.31631 | ||||||||
\(362\) | 48.7584 | 2.56268 | ||||||||
\(363\) | 20.4402 | 1.07283 | ||||||||
\(364\) | −19.9366 | −1.04496 | ||||||||
\(365\) | −14.8824 | −0.778979 | ||||||||
\(366\) | 59.1986 | 3.09436 | ||||||||
\(367\) | −8.05407 | −0.420419 | −0.210210 | − | 0.977656i | \(-0.567415\pi\) | ||||
−0.210210 | + | 0.977656i | \(0.567415\pi\) | |||||||
\(368\) | −96.2375 | −5.01673 | ||||||||
\(369\) | 19.2502 | 1.00212 | ||||||||
\(370\) | 24.8352 | 1.29112 | ||||||||
\(371\) | 7.62884 | 0.396070 | ||||||||
\(372\) | 87.2493 | 4.52366 | ||||||||
\(373\) | 3.41546 | 0.176846 | 0.0884228 | − | 0.996083i | \(-0.471817\pi\) | ||||
0.0884228 | + | 0.996083i | \(0.471817\pi\) | |||||||
\(374\) | −12.7497 | −0.659269 | ||||||||
\(375\) | 26.2177 | 1.35388 | ||||||||
\(376\) | 67.5895 | 3.48566 | ||||||||
\(377\) | −5.03962 | −0.259554 | ||||||||
\(378\) | 33.1049 | 1.70273 | ||||||||
\(379\) | 14.1907 | 0.728925 | 0.364463 | − | 0.931218i | \(-0.381253\pi\) | ||||
0.364463 | + | 0.931218i | \(0.381253\pi\) | |||||||
\(380\) | −67.8024 | −3.47819 | ||||||||
\(381\) | −13.9502 | −0.714690 | ||||||||
\(382\) | −27.6979 | −1.41715 | ||||||||
\(383\) | −2.11868 | −0.108259 | −0.0541297 | − | 0.998534i | \(-0.517238\pi\) | ||||
−0.0541297 | + | 0.998534i | \(0.517238\pi\) | |||||||
\(384\) | 28.2587 | 1.44207 | ||||||||
\(385\) | 12.0666 | 0.614971 | ||||||||
\(386\) | −20.5141 | −1.04414 | ||||||||
\(387\) | 3.62005 | 0.184018 | ||||||||
\(388\) | −40.4313 | −2.05259 | ||||||||
\(389\) | −17.2805 | −0.876158 | −0.438079 | − | 0.898936i | \(-0.644341\pi\) | ||||
−0.438079 | + | 0.898936i | \(0.644341\pi\) | |||||||
\(390\) | 9.78919 | 0.495695 | ||||||||
\(391\) | 30.4657 | 1.54072 | ||||||||
\(392\) | −122.329 | −6.17853 | ||||||||
\(393\) | 21.2277 | 1.07080 | ||||||||
\(394\) | −21.7155 | −1.09401 | ||||||||
\(395\) | −9.96391 | −0.501339 | ||||||||
\(396\) | −11.6908 | −0.587485 | ||||||||
\(397\) | 18.0286 | 0.904830 | 0.452415 | − | 0.891807i | \(-0.350563\pi\) | ||||
0.452415 | + | 0.891807i | \(0.350563\pi\) | |||||||
\(398\) | 58.9518 | 2.95499 | ||||||||
\(399\) | −67.8258 | −3.39554 | ||||||||
\(400\) | −11.4409 | −0.572046 | ||||||||
\(401\) | −7.89119 | −0.394067 | −0.197034 | − | 0.980397i | \(-0.563131\pi\) | ||||
−0.197034 | + | 0.980397i | \(0.563131\pi\) | |||||||
\(402\) | −54.7312 | −2.72975 | ||||||||
\(403\) | −6.55848 | −0.326701 | ||||||||
\(404\) | 33.0547 | 1.64453 | ||||||||
\(405\) | −22.4128 | −1.11370 | ||||||||
\(406\) | −74.9188 | −3.71816 | ||||||||
\(407\) | 5.97817 | 0.296327 | ||||||||
\(408\) | −67.0538 | −3.31966 | ||||||||
\(409\) | 7.63751 | 0.377651 | 0.188825 | − | 0.982011i | \(-0.439532\pi\) | ||||
0.188825 | + | 0.982011i | \(0.439532\pi\) | |||||||
\(410\) | −57.6607 | −2.84766 | ||||||||
\(411\) | −36.0483 | −1.77813 | ||||||||
\(412\) | −52.8919 | −2.60580 | ||||||||
\(413\) | 34.0341 | 1.67471 | ||||||||
\(414\) | 38.9051 | 1.91208 | ||||||||
\(415\) | 24.0093 | 1.17857 | ||||||||
\(416\) | −12.4189 | −0.608886 | ||||||||
\(417\) | −5.21571 | −0.255414 | ||||||||
\(418\) | −22.7298 | −1.11175 | ||||||||
\(419\) | −35.2617 | −1.72265 | −0.861323 | − | 0.508057i | \(-0.830364\pi\) | ||||
−0.861323 | + | 0.508057i | \(0.830364\pi\) | |||||||
\(420\) | 104.493 | 5.09876 | ||||||||
\(421\) | 18.3743 | 0.895511 | 0.447755 | − | 0.894156i | \(-0.352224\pi\) | ||||
0.447755 | + | 0.894156i | \(0.352224\pi\) | |||||||
\(422\) | −24.9569 | −1.21488 | ||||||||
\(423\) | −14.6384 | −0.711742 | ||||||||
\(424\) | 13.4457 | 0.652981 | ||||||||
\(425\) | 3.62182 | 0.175684 | ||||||||
\(426\) | 47.6568 | 2.30898 | ||||||||
\(427\) | −47.5002 | −2.29870 | ||||||||
\(428\) | −17.1196 | −0.827509 | ||||||||
\(429\) | 2.35639 | 0.113767 | ||||||||
\(430\) | −10.8433 | −0.522909 | ||||||||
\(431\) | −5.93338 | −0.285801 | −0.142900 | − | 0.989737i | \(-0.545643\pi\) | ||||
−0.142900 | + | 0.989737i | \(0.545643\pi\) | |||||||
\(432\) | 31.2586 | 1.50393 | ||||||||
\(433\) | −26.6012 | −1.27837 | −0.639187 | − | 0.769051i | \(-0.720729\pi\) | ||||
−0.639187 | + | 0.769051i | \(0.720729\pi\) | |||||||
\(434\) | −97.4981 | −4.68006 | ||||||||
\(435\) | 26.4141 | 1.26646 | ||||||||
\(436\) | −34.4887 | −1.65171 | ||||||||
\(437\) | 54.3134 | 2.59816 | ||||||||
\(438\) | −43.2043 | −2.06438 | ||||||||
\(439\) | −9.42551 | −0.449855 | −0.224927 | − | 0.974376i | \(-0.572215\pi\) | ||||
−0.224927 | + | 0.974376i | \(0.572215\pi\) | |||||||
\(440\) | 21.2672 | 1.01387 | ||||||||
\(441\) | 26.4936 | 1.26160 | ||||||||
\(442\) | 8.29936 | 0.394761 | ||||||||
\(443\) | −9.78308 | −0.464808 | −0.232404 | − | 0.972619i | \(-0.574659\pi\) | ||||
−0.232404 | + | 0.972619i | \(0.574659\pi\) | |||||||
\(444\) | 51.7693 | 2.45686 | ||||||||
\(445\) | −13.7629 | −0.652424 | ||||||||
\(446\) | 23.7888 | 1.12643 | ||||||||
\(447\) | −27.0290 | −1.27843 | ||||||||
\(448\) | −74.7291 | −3.53062 | ||||||||
\(449\) | −9.56221 | −0.451269 | −0.225634 | − | 0.974212i | \(-0.572445\pi\) | ||||
−0.225634 | + | 0.974212i | \(0.572445\pi\) | |||||||
\(450\) | 4.62512 | 0.218030 | ||||||||
\(451\) | −13.8797 | −0.653570 | ||||||||
\(452\) | −58.3288 | −2.74355 | ||||||||
\(453\) | 12.3764 | 0.581493 | ||||||||
\(454\) | −71.4997 | −3.35565 | ||||||||
\(455\) | −7.85472 | −0.368235 | ||||||||
\(456\) | −119.542 | −5.59806 | ||||||||
\(457\) | −8.30614 | −0.388545 | −0.194272 | − | 0.980948i | \(-0.562235\pi\) | ||||
−0.194272 | + | 0.980948i | \(0.562235\pi\) | |||||||
\(458\) | 15.1962 | 0.710071 | ||||||||
\(459\) | −9.89544 | −0.461879 | ||||||||
\(460\) | −83.6761 | −3.90142 | ||||||||
\(461\) | 5.81176 | 0.270681 | 0.135340 | − | 0.990799i | \(-0.456787\pi\) | ||||
0.135340 | + | 0.990799i | \(0.456787\pi\) | |||||||
\(462\) | 35.0299 | 1.62974 | ||||||||
\(463\) | −38.7694 | −1.80176 | −0.900882 | − | 0.434063i | \(-0.857079\pi\) | ||||
−0.900882 | + | 0.434063i | \(0.857079\pi\) | |||||||
\(464\) | −70.7404 | −3.28404 | ||||||||
\(465\) | 34.3748 | 1.59410 | ||||||||
\(466\) | 66.9268 | 3.10033 | ||||||||
\(467\) | 15.2641 | 0.706340 | 0.353170 | − | 0.935559i | \(-0.385104\pi\) | ||||
0.353170 | + | 0.935559i | \(0.385104\pi\) | |||||||
\(468\) | 7.61010 | 0.351777 | ||||||||
\(469\) | 43.9157 | 2.02784 | ||||||||
\(470\) | 43.8468 | 2.02250 | ||||||||
\(471\) | 48.6497 | 2.24166 | ||||||||
\(472\) | 59.9846 | 2.76101 | ||||||||
\(473\) | −2.61012 | −0.120013 | ||||||||
\(474\) | −28.9257 | −1.32860 | ||||||||
\(475\) | 6.45690 | 0.296263 | ||||||||
\(476\) | 88.5905 | 4.06054 | ||||||||
\(477\) | −2.91204 | −0.133333 | ||||||||
\(478\) | 37.8634 | 1.73183 | ||||||||
\(479\) | −30.0271 | −1.37197 | −0.685987 | − | 0.727614i | \(-0.740629\pi\) | ||||
−0.685987 | + | 0.727614i | \(0.740629\pi\) | |||||||
\(480\) | 65.0908 | 2.97098 | ||||||||
\(481\) | −3.89148 | −0.177436 | ||||||||
\(482\) | 37.2289 | 1.69573 | ||||||||
\(483\) | −83.7050 | −3.80871 | ||||||||
\(484\) | −47.5965 | −2.16348 | ||||||||
\(485\) | −15.9293 | −0.723312 | ||||||||
\(486\) | −43.8185 | −1.98765 | ||||||||
\(487\) | 23.4168 | 1.06112 | 0.530559 | − | 0.847648i | \(-0.321982\pi\) | ||||
0.530559 | + | 0.847648i | \(0.321982\pi\) | |||||||
\(488\) | −83.7183 | −3.78975 | ||||||||
\(489\) | −32.4886 | −1.46919 | ||||||||
\(490\) | −79.3573 | −3.58500 | ||||||||
\(491\) | −25.0575 | −1.13083 | −0.565415 | − | 0.824807i | \(-0.691284\pi\) | ||||
−0.565415 | + | 0.824807i | \(0.691284\pi\) | |||||||
\(492\) | −120.194 | −5.41879 | ||||||||
\(493\) | 22.3941 | 1.00858 | ||||||||
\(494\) | 14.7959 | 0.665699 | ||||||||
\(495\) | −4.60599 | −0.207024 | ||||||||
\(496\) | −92.0604 | −4.13363 | ||||||||
\(497\) | −38.2392 | −1.71526 | ||||||||
\(498\) | 69.7003 | 3.12335 | ||||||||
\(499\) | −8.85100 | −0.396225 | −0.198112 | − | 0.980179i | \(-0.563481\pi\) | ||||
−0.198112 | + | 0.980179i | \(0.563481\pi\) | |||||||
\(500\) | −61.0498 | −2.73023 | ||||||||
\(501\) | −21.5968 | −0.964874 | ||||||||
\(502\) | −43.3067 | −1.93287 | ||||||||
\(503\) | −13.8848 | −0.619092 | −0.309546 | − | 0.950884i | \(-0.600177\pi\) | ||||
−0.309546 | + | 0.950884i | \(0.600177\pi\) | |||||||
\(504\) | 68.7074 | 3.06047 | ||||||||
\(505\) | 13.0230 | 0.579517 | ||||||||
\(506\) | −28.0512 | −1.24703 | ||||||||
\(507\) | 26.9009 | 1.19471 | ||||||||
\(508\) | 32.4840 | 1.44124 | ||||||||
\(509\) | −15.3759 | −0.681523 | −0.340762 | − | 0.940150i | \(-0.610685\pi\) | ||||
−0.340762 | + | 0.940150i | \(0.610685\pi\) | |||||||
\(510\) | −43.4993 | −1.92618 | ||||||||
\(511\) | 34.6666 | 1.53356 | ||||||||
\(512\) | 19.3564 | 0.855442 | ||||||||
\(513\) | −17.6413 | −0.778884 | ||||||||
\(514\) | 5.52305 | 0.243611 | ||||||||
\(515\) | −20.8386 | −0.918258 | ||||||||
\(516\) | −22.6029 | −0.995039 | ||||||||
\(517\) | 10.5545 | 0.464187 | ||||||||
\(518\) | −57.8505 | −2.54180 | ||||||||
\(519\) | 49.4736 | 2.17165 | ||||||||
\(520\) | −13.8438 | −0.607092 | ||||||||
\(521\) | 29.3976 | 1.28793 | 0.643967 | − | 0.765053i | \(-0.277287\pi\) | ||||
0.643967 | + | 0.765053i | \(0.277287\pi\) | |||||||
\(522\) | 28.5976 | 1.25168 | ||||||||
\(523\) | −25.8707 | −1.13125 | −0.565624 | − | 0.824663i | \(-0.691365\pi\) | ||||
−0.565624 | + | 0.824663i | \(0.691365\pi\) | |||||||
\(524\) | −49.4302 | −2.15937 | ||||||||
\(525\) | −9.95103 | −0.434298 | ||||||||
\(526\) | 0.924158 | 0.0402952 | ||||||||
\(527\) | 29.1433 | 1.26950 | ||||||||
\(528\) | 33.0762 | 1.43946 | ||||||||
\(529\) | 44.0292 | 1.91431 | ||||||||
\(530\) | 8.72253 | 0.378883 | ||||||||
\(531\) | −12.9913 | −0.563775 | ||||||||
\(532\) | 157.937 | 6.84744 | ||||||||
\(533\) | 9.03496 | 0.391348 | ||||||||
\(534\) | −39.9544 | −1.72899 | ||||||||
\(535\) | −6.74488 | −0.291606 | ||||||||
\(536\) | 77.4006 | 3.34320 | ||||||||
\(537\) | −10.4708 | −0.451847 | ||||||||
\(538\) | −82.2286 | −3.54513 | ||||||||
\(539\) | −19.1023 | −0.822796 | ||||||||
\(540\) | 27.1785 | 1.16958 | ||||||||
\(541\) | 23.3694 | 1.00473 | 0.502365 | − | 0.864656i | \(-0.332463\pi\) | ||||
0.502365 | + | 0.864656i | \(0.332463\pi\) | |||||||
\(542\) | −41.0222 | −1.76206 | ||||||||
\(543\) | 40.0436 | 1.71843 | ||||||||
\(544\) | 55.1846 | 2.36602 | ||||||||
\(545\) | −13.5880 | −0.582046 | ||||||||
\(546\) | −22.8027 | −0.975864 | ||||||||
\(547\) | 34.3858 | 1.47023 | 0.735116 | − | 0.677942i | \(-0.237128\pi\) | ||||
0.735116 | + | 0.677942i | \(0.237128\pi\) | |||||||
\(548\) | 83.9409 | 3.58578 | ||||||||
\(549\) | 18.1315 | 0.773834 | ||||||||
\(550\) | −3.33479 | −0.142196 | ||||||||
\(551\) | 39.9236 | 1.70080 | ||||||||
\(552\) | −147.529 | −6.27924 | ||||||||
\(553\) | 23.2097 | 0.986975 | ||||||||
\(554\) | 69.3910 | 2.94814 | ||||||||
\(555\) | 20.3963 | 0.865775 | ||||||||
\(556\) | 12.1451 | 0.515069 | ||||||||
\(557\) | 14.8010 | 0.627137 | 0.313569 | − | 0.949566i | \(-0.398475\pi\) | ||||
0.313569 | + | 0.949566i | \(0.398475\pi\) | |||||||
\(558\) | 37.2164 | 1.57550 | ||||||||
\(559\) | 1.69905 | 0.0718622 | ||||||||
\(560\) | −110.255 | −4.65914 | ||||||||
\(561\) | −10.4709 | −0.442080 | ||||||||
\(562\) | −33.6106 | −1.41778 | ||||||||
\(563\) | 15.6915 | 0.661317 | 0.330659 | − | 0.943750i | \(-0.392729\pi\) | ||||
0.330659 | + | 0.943750i | \(0.392729\pi\) | |||||||
\(564\) | 91.3992 | 3.84860 | ||||||||
\(565\) | −22.9806 | −0.966802 | ||||||||
\(566\) | −60.8819 | −2.55906 | ||||||||
\(567\) | 52.2078 | 2.19252 | ||||||||
\(568\) | −67.3961 | −2.82788 | ||||||||
\(569\) | 17.6535 | 0.740074 | 0.370037 | − | 0.929017i | \(-0.379345\pi\) | ||||
0.370037 | + | 0.929017i | \(0.379345\pi\) | |||||||
\(570\) | −77.5494 | −3.24819 | ||||||||
\(571\) | −27.1355 | −1.13558 | −0.567792 | − | 0.823172i | \(-0.692202\pi\) | ||||
−0.567792 | + | 0.823172i | \(0.692202\pi\) | |||||||
\(572\) | −5.48701 | −0.229423 | ||||||||
\(573\) | −22.7473 | −0.950283 | ||||||||
\(574\) | 134.313 | 5.60613 | ||||||||
\(575\) | 7.96857 | 0.332312 | ||||||||
\(576\) | 28.5252 | 1.18855 | ||||||||
\(577\) | 18.8841 | 0.786155 | 0.393078 | − | 0.919505i | \(-0.371410\pi\) | ||||
0.393078 | + | 0.919505i | \(0.371410\pi\) | |||||||
\(578\) | 8.39727 | 0.349281 | ||||||||
\(579\) | −16.8475 | −0.700160 | ||||||||
\(580\) | −61.5070 | −2.55394 | ||||||||
\(581\) | −55.9267 | −2.32023 | ||||||||
\(582\) | −46.2436 | −1.91686 | ||||||||
\(583\) | 2.09963 | 0.0869577 | ||||||||
\(584\) | 61.0993 | 2.52831 | ||||||||
\(585\) | 2.99826 | 0.123963 | ||||||||
\(586\) | −15.3281 | −0.633199 | ||||||||
\(587\) | 18.9962 | 0.784057 | 0.392029 | − | 0.919953i | \(-0.371773\pi\) | ||||
0.392029 | + | 0.919953i | \(0.371773\pi\) | |||||||
\(588\) | −165.421 | −6.82185 | ||||||||
\(589\) | 51.9560 | 2.14081 | ||||||||
\(590\) | 38.9133 | 1.60204 | ||||||||
\(591\) | −17.8342 | −0.733601 | ||||||||
\(592\) | −54.6240 | −2.24503 | ||||||||
\(593\) | 5.71365 | 0.234631 | 0.117316 | − | 0.993095i | \(-0.462571\pi\) | ||||
0.117316 | + | 0.993095i | \(0.462571\pi\) | |||||||
\(594\) | 9.11121 | 0.373838 | ||||||||
\(595\) | 34.9033 | 1.43090 | ||||||||
\(596\) | 62.9388 | 2.57807 | ||||||||
\(597\) | 48.4151 | 1.98150 | ||||||||
\(598\) | 18.2599 | 0.746702 | ||||||||
\(599\) | 20.0897 | 0.820841 | 0.410421 | − | 0.911896i | \(-0.365382\pi\) | ||||
0.410421 | + | 0.911896i | \(0.365382\pi\) | |||||||
\(600\) | −17.5385 | −0.716007 | ||||||||
\(601\) | 22.1512 | 0.903566 | 0.451783 | − | 0.892128i | \(-0.350788\pi\) | ||||
0.451783 | + | 0.892128i | \(0.350788\pi\) | |||||||
\(602\) | 25.2580 | 1.02944 | ||||||||
\(603\) | −16.7632 | −0.682652 | ||||||||
\(604\) | −28.8192 | −1.17264 | ||||||||
\(605\) | −18.7523 | −0.762389 | ||||||||
\(606\) | 37.8065 | 1.53578 | ||||||||
\(607\) | −26.8138 | −1.08834 | −0.544169 | − | 0.838975i | \(-0.683155\pi\) | ||||
−0.544169 | + | 0.838975i | \(0.683155\pi\) | |||||||
\(608\) | 98.3817 | 3.98991 | ||||||||
\(609\) | −61.5282 | −2.49325 | ||||||||
\(610\) | −54.3100 | −2.19895 | ||||||||
\(611\) | −6.87043 | −0.277948 | ||||||||
\(612\) | −33.8163 | −1.36694 | ||||||||
\(613\) | 14.7552 | 0.595956 | 0.297978 | − | 0.954573i | \(-0.403688\pi\) | ||||
0.297978 | + | 0.954573i | \(0.403688\pi\) | |||||||
\(614\) | 1.41149 | 0.0569632 | ||||||||
\(615\) | −47.3548 | −1.90953 | ||||||||
\(616\) | −49.5392 | −1.99599 | ||||||||
\(617\) | 2.63305 | 0.106003 | 0.0530013 | − | 0.998594i | \(-0.483121\pi\) | ||||
0.0530013 | + | 0.998594i | \(0.483121\pi\) | |||||||
\(618\) | −60.4955 | −2.43349 | ||||||||
\(619\) | 2.49230 | 0.100174 | 0.0500870 | − | 0.998745i | \(-0.484050\pi\) | ||||
0.0500870 | + | 0.998745i | \(0.484050\pi\) | |||||||
\(620\) | −80.0442 | −3.21465 | ||||||||
\(621\) | −21.7715 | −0.873660 | ||||||||
\(622\) | 27.8786 | 1.11783 | ||||||||
\(623\) | 32.0589 | 1.28441 | ||||||||
\(624\) | −21.5309 | −0.861926 | ||||||||
\(625\) | −19.1862 | −0.767446 | ||||||||
\(626\) | −1.60240 | −0.0640448 | ||||||||
\(627\) | −18.6672 | −0.745495 | ||||||||
\(628\) | −113.284 | −4.52053 | ||||||||
\(629\) | 17.2922 | 0.689485 | ||||||||
\(630\) | 44.5720 | 1.77579 | ||||||||
\(631\) | 18.8200 | 0.749213 | 0.374606 | − | 0.927184i | \(-0.377778\pi\) | ||||
0.374606 | + | 0.927184i | \(0.377778\pi\) | |||||||
\(632\) | 40.9067 | 1.62718 | ||||||||
\(633\) | −20.4962 | −0.814651 | ||||||||
\(634\) | −87.5366 | −3.47652 | ||||||||
\(635\) | 12.7982 | 0.507881 | ||||||||
\(636\) | 18.1822 | 0.720972 | ||||||||
\(637\) | 12.4346 | 0.492678 | ||||||||
\(638\) | −20.6193 | −0.816327 | ||||||||
\(639\) | 14.5965 | 0.577428 | ||||||||
\(640\) | −25.9251 | −1.02478 | ||||||||
\(641\) | −36.5787 | −1.44477 | −0.722385 | − | 0.691491i | \(-0.756954\pi\) | ||||
−0.722385 | + | 0.691491i | \(0.756954\pi\) | |||||||
\(642\) | −19.5807 | −0.772789 | ||||||||
\(643\) | 1.98930 | 0.0784502 | 0.0392251 | − | 0.999230i | \(-0.487511\pi\) | ||||
0.0392251 | + | 0.999230i | \(0.487511\pi\) | |||||||
\(644\) | 194.913 | 7.68064 | ||||||||
\(645\) | −8.90520 | −0.350642 | ||||||||
\(646\) | −65.7471 | −2.58679 | ||||||||
\(647\) | −28.5149 | −1.12104 | −0.560518 | − | 0.828142i | \(-0.689398\pi\) | ||||
−0.560518 | + | 0.828142i | \(0.689398\pi\) | |||||||
\(648\) | 92.0155 | 3.61471 | ||||||||
\(649\) | 9.36696 | 0.367685 | ||||||||
\(650\) | 2.17077 | 0.0851448 | ||||||||
\(651\) | −80.0718 | −3.13826 | ||||||||
\(652\) | 75.6521 | 2.96276 | ||||||||
\(653\) | −30.6079 | −1.19778 | −0.598890 | − | 0.800831i | \(-0.704391\pi\) | ||||
−0.598890 | + | 0.800831i | \(0.704391\pi\) | |||||||
\(654\) | −39.4467 | −1.54249 | ||||||||
\(655\) | −19.4747 | −0.760940 | ||||||||
\(656\) | 126.822 | 4.95158 | ||||||||
\(657\) | −13.2327 | −0.516258 | ||||||||
\(658\) | −102.135 | −3.98166 | ||||||||
\(659\) | 19.6933 | 0.767142 | 0.383571 | − | 0.923511i | \(-0.374694\pi\) | ||||
0.383571 | + | 0.923511i | \(0.374694\pi\) | |||||||
\(660\) | 28.7590 | 1.11944 | ||||||||
\(661\) | −2.38827 | −0.0928929 | −0.0464465 | − | 0.998921i | \(-0.514790\pi\) | ||||
−0.0464465 | + | 0.998921i | \(0.514790\pi\) | |||||||
\(662\) | −80.0516 | −3.11129 | ||||||||
\(663\) | 6.81598 | 0.264711 | ||||||||
\(664\) | −98.5699 | −3.82525 | ||||||||
\(665\) | 62.2247 | 2.41297 | ||||||||
\(666\) | 22.0824 | 0.855674 | ||||||||
\(667\) | 49.2705 | 1.90776 | ||||||||
\(668\) | 50.2897 | 1.94577 | ||||||||
\(669\) | 19.5369 | 0.755341 | ||||||||
\(670\) | 50.2115 | 1.93984 | ||||||||
\(671\) | −13.0731 | −0.504682 | ||||||||
\(672\) | −151.621 | −5.84890 | ||||||||
\(673\) | 14.9143 | 0.574902 | 0.287451 | − | 0.957795i | \(-0.407192\pi\) | ||||
0.287451 | + | 0.957795i | \(0.407192\pi\) | |||||||
\(674\) | −2.58103 | −0.0994177 | ||||||||
\(675\) | −2.58824 | −0.0996214 | ||||||||
\(676\) | −62.6405 | −2.40925 | ||||||||
\(677\) | 8.38079 | 0.322100 | 0.161050 | − | 0.986946i | \(-0.448512\pi\) | ||||
0.161050 | + | 0.986946i | \(0.448512\pi\) | |||||||
\(678\) | −66.7139 | −2.56213 | ||||||||
\(679\) | 37.1053 | 1.42397 | ||||||||
\(680\) | 61.5165 | 2.35905 | ||||||||
\(681\) | −58.7202 | −2.25016 | ||||||||
\(682\) | −26.8337 | −1.02751 | ||||||||
\(683\) | 6.69871 | 0.256319 | 0.128159 | − | 0.991754i | \(-0.459093\pi\) | ||||
0.128159 | + | 0.991754i | \(0.459093\pi\) | |||||||
\(684\) | −60.2868 | −2.30512 | ||||||||
\(685\) | 33.0714 | 1.26359 | ||||||||
\(686\) | 97.7093 | 3.73056 | ||||||||
\(687\) | 12.4801 | 0.476145 | ||||||||
\(688\) | 23.8493 | 0.909247 | ||||||||
\(689\) | −1.36675 | −0.0520690 | ||||||||
\(690\) | −95.7051 | −3.64343 | ||||||||
\(691\) | −41.5507 | −1.58066 | −0.790332 | − | 0.612679i | \(-0.790092\pi\) | ||||
−0.790332 | + | 0.612679i | \(0.790092\pi\) | |||||||
\(692\) | −115.203 | −4.37935 | ||||||||
\(693\) | 10.7291 | 0.407564 | ||||||||
\(694\) | −95.8493 | −3.63839 | ||||||||
\(695\) | 4.78500 | 0.181505 | ||||||||
\(696\) | −108.442 | −4.11050 | ||||||||
\(697\) | −40.1478 | −1.52071 | ||||||||
\(698\) | 43.1382 | 1.63280 | ||||||||
\(699\) | 54.9647 | 2.07896 | ||||||||
\(700\) | 23.1717 | 0.875806 | ||||||||
\(701\) | −23.2463 | −0.878001 | −0.439000 | − | 0.898487i | \(-0.644667\pi\) | ||||
−0.439000 | + | 0.898487i | \(0.644667\pi\) | |||||||
\(702\) | −5.93092 | −0.223848 | ||||||||
\(703\) | 30.8281 | 1.16270 | ||||||||
\(704\) | −20.5671 | −0.775153 | ||||||||
\(705\) | 36.0099 | 1.35621 | ||||||||
\(706\) | −15.2776 | −0.574981 | ||||||||
\(707\) | −30.3355 | −1.14088 | ||||||||
\(708\) | 81.1153 | 3.04850 | ||||||||
\(709\) | −47.3562 | −1.77850 | −0.889249 | − | 0.457423i | \(-0.848773\pi\) | ||||
−0.889249 | + | 0.457423i | \(0.848773\pi\) | |||||||
\(710\) | −43.7213 | −1.64083 | ||||||||
\(711\) | −8.85946 | −0.332256 | ||||||||
\(712\) | 56.5033 | 2.11755 | ||||||||
\(713\) | 64.1198 | 2.40130 | ||||||||
\(714\) | 101.326 | 3.79203 | ||||||||
\(715\) | −2.16180 | −0.0808466 | ||||||||
\(716\) | 24.3819 | 0.911195 | ||||||||
\(717\) | 31.0959 | 1.16130 | ||||||||
\(718\) | 37.6560 | 1.40531 | ||||||||
\(719\) | 31.5663 | 1.17723 | 0.588613 | − | 0.808415i | \(-0.299674\pi\) | ||||
0.588613 | + | 0.808415i | \(0.299674\pi\) | |||||||
\(720\) | 42.0861 | 1.56846 | ||||||||
\(721\) | 48.5408 | 1.80776 | ||||||||
\(722\) | −66.6093 | −2.47894 | ||||||||
\(723\) | 30.5748 | 1.13709 | ||||||||
\(724\) | −93.2442 | −3.46539 | ||||||||
\(725\) | 5.85738 | 0.217538 | ||||||||
\(726\) | −54.4388 | −2.02042 | ||||||||
\(727\) | 39.5751 | 1.46776 | 0.733880 | − | 0.679279i | \(-0.237707\pi\) | ||||
0.733880 | + | 0.679279i | \(0.237707\pi\) | |||||||
\(728\) | 32.2474 | 1.19517 | ||||||||
\(729\) | −2.47896 | −0.0918133 | ||||||||
\(730\) | 39.6365 | 1.46701 | ||||||||
\(731\) | −7.54992 | −0.279244 | ||||||||
\(732\) | −113.210 | −4.18435 | ||||||||
\(733\) | −13.2902 | −0.490885 | −0.245443 | − | 0.969411i | \(-0.578933\pi\) | ||||
−0.245443 | + | 0.969411i | \(0.578933\pi\) | |||||||
\(734\) | 21.4505 | 0.791754 | ||||||||
\(735\) | −65.1734 | −2.40396 | ||||||||
\(736\) | 121.415 | 4.47540 | ||||||||
\(737\) | 12.0866 | 0.445215 | ||||||||
\(738\) | −51.2693 | −1.88725 | ||||||||
\(739\) | −33.1110 | −1.21801 | −0.609003 | − | 0.793168i | \(-0.708430\pi\) | ||||
−0.609003 | + | 0.793168i | \(0.708430\pi\) | |||||||
\(740\) | −47.4942 | −1.74592 | ||||||||
\(741\) | 12.1514 | 0.446391 | ||||||||
\(742\) | −20.3180 | −0.745898 | ||||||||
\(743\) | −13.5021 | −0.495345 | −0.247673 | − | 0.968844i | \(-0.579666\pi\) | ||||
−0.247673 | + | 0.968844i | \(0.579666\pi\) | |||||||
\(744\) | −141.125 | −5.17390 | ||||||||
\(745\) | 24.7969 | 0.908489 | ||||||||
\(746\) | −9.09644 | −0.333044 | ||||||||
\(747\) | 21.3480 | 0.781083 | ||||||||
\(748\) | 24.3821 | 0.891498 | ||||||||
\(749\) | 15.7113 | 0.574079 | ||||||||
\(750\) | −69.8261 | −2.54969 | ||||||||
\(751\) | 33.2807 | 1.21443 | 0.607214 | − | 0.794538i | \(-0.292287\pi\) | ||||
0.607214 | + | 0.794538i | \(0.292287\pi\) | |||||||
\(752\) | −96.4392 | −3.51677 | ||||||||
\(753\) | −35.5663 | −1.29611 | ||||||||
\(754\) | 13.4221 | 0.488804 | ||||||||
\(755\) | −11.3543 | −0.413227 | ||||||||
\(756\) | −63.3089 | −2.30252 | ||||||||
\(757\) | −39.1617 | −1.42336 | −0.711678 | − | 0.702506i | \(-0.752064\pi\) | ||||
−0.711678 | + | 0.702506i | \(0.752064\pi\) | |||||||
\(758\) | −37.7942 | −1.37275 | ||||||||
\(759\) | −23.0375 | −0.836208 | ||||||||
\(760\) | 109.670 | 3.97815 | ||||||||
\(761\) | 23.7429 | 0.860681 | 0.430340 | − | 0.902667i | \(-0.358394\pi\) | ||||
0.430340 | + | 0.902667i | \(0.358394\pi\) | |||||||
\(762\) | 37.1538 | 1.34594 | ||||||||
\(763\) | 31.6515 | 1.14586 | ||||||||
\(764\) | 52.9687 | 1.91634 | ||||||||
\(765\) | −13.3231 | −0.481697 | ||||||||
\(766\) | 5.64271 | 0.203879 | ||||||||
\(767\) | −6.09740 | −0.220164 | ||||||||
\(768\) | −5.32389 | −0.192109 | ||||||||
\(769\) | 34.6048 | 1.24788 | 0.623940 | − | 0.781473i | \(-0.285531\pi\) | ||||
0.623940 | + | 0.781473i | \(0.285531\pi\) | |||||||
\(770\) | −32.1372 | −1.15814 | ||||||||
\(771\) | 4.53589 | 0.163356 | ||||||||
\(772\) | 39.2307 | 1.41194 | ||||||||
\(773\) | 50.9737 | 1.83340 | 0.916698 | − | 0.399581i | \(-0.130844\pi\) | ||||
0.916698 | + | 0.399581i | \(0.130844\pi\) | |||||||
\(774\) | −9.64135 | −0.346551 | ||||||||
\(775\) | 7.62270 | 0.273815 | ||||||||
\(776\) | 65.3974 | 2.34763 | ||||||||
\(777\) | −47.5106 | −1.70443 | ||||||||
\(778\) | 46.0236 | 1.65002 | ||||||||
\(779\) | −71.5745 | −2.56442 | ||||||||
\(780\) | −18.7206 | −0.670304 | ||||||||
\(781\) | −10.5243 | −0.376589 | ||||||||
\(782\) | −81.1397 | −2.90155 | ||||||||
\(783\) | −16.0034 | −0.571913 | ||||||||
\(784\) | 174.543 | 6.23368 | ||||||||
\(785\) | −44.6322 | −1.59299 | ||||||||
\(786\) | −56.5361 | −2.01658 | ||||||||
\(787\) | −41.2984 | −1.47213 | −0.736065 | − | 0.676911i | \(-0.763318\pi\) | ||||
−0.736065 | + | 0.676911i | \(0.763318\pi\) | |||||||
\(788\) | 41.5282 | 1.47938 | ||||||||
\(789\) | 0.758979 | 0.0270204 | ||||||||
\(790\) | 26.5371 | 0.944146 | ||||||||
\(791\) | 53.5304 | 1.90332 | ||||||||
\(792\) | 18.9098 | 0.671931 | ||||||||
\(793\) | 8.50992 | 0.302196 | ||||||||
\(794\) | −48.0159 | −1.70402 | ||||||||
\(795\) | 7.16351 | 0.254064 | ||||||||
\(796\) | −112.738 | −3.99589 | ||||||||
\(797\) | −27.6170 | −0.978244 | −0.489122 | − | 0.872215i | \(-0.662683\pi\) | ||||
−0.489122 | + | 0.872215i | \(0.662683\pi\) | |||||||
\(798\) | 180.641 | 6.39464 | ||||||||
\(799\) | 30.5295 | 1.08006 | ||||||||
\(800\) | 14.4340 | 0.510320 | ||||||||
\(801\) | −12.2373 | −0.432385 | ||||||||
\(802\) | 21.0167 | 0.742127 | ||||||||
\(803\) | 9.54103 | 0.336696 | ||||||||
\(804\) | 104.667 | 3.69130 | ||||||||
\(805\) | 76.7926 | 2.70658 | ||||||||
\(806\) | 17.4673 | 0.615260 | ||||||||
\(807\) | −67.5315 | −2.37722 | ||||||||
\(808\) | −53.4658 | −1.88092 | ||||||||
\(809\) | −45.9752 | −1.61640 | −0.808201 | − | 0.588906i | \(-0.799559\pi\) | ||||
−0.808201 | + | 0.588906i | \(0.799559\pi\) | |||||||
\(810\) | 59.6925 | 2.09738 | ||||||||
\(811\) | −16.7481 | −0.588105 | −0.294052 | − | 0.955789i | \(-0.595004\pi\) | ||||
−0.294052 | + | 0.955789i | \(0.595004\pi\) | |||||||
\(812\) | 143.273 | 5.02788 | ||||||||
\(813\) | −33.6901 | −1.18156 | ||||||||
\(814\) | −15.9218 | −0.558057 | ||||||||
\(815\) | 29.8057 | 1.04405 | ||||||||
\(816\) | 95.6748 | 3.34929 | ||||||||
\(817\) | −13.4598 | −0.470899 | ||||||||
\(818\) | −20.3411 | −0.711211 | ||||||||
\(819\) | −6.98406 | −0.244043 | ||||||||
\(820\) | 110.269 | 3.85075 | ||||||||
\(821\) | 16.5734 | 0.578417 | 0.289208 | − | 0.957266i | \(-0.406608\pi\) | ||||
0.289208 | + | 0.957266i | \(0.406608\pi\) | |||||||
\(822\) | 96.0079 | 3.34866 | ||||||||
\(823\) | 7.66199 | 0.267080 | 0.133540 | − | 0.991043i | \(-0.457366\pi\) | ||||
0.133540 | + | 0.991043i | \(0.457366\pi\) | |||||||
\(824\) | 85.5524 | 2.98036 | ||||||||
\(825\) | −2.73875 | −0.0953509 | ||||||||
\(826\) | −90.6436 | −3.15390 | ||||||||
\(827\) | 17.5652 | 0.610803 | 0.305401 | − | 0.952224i | \(-0.401209\pi\) | ||||
0.305401 | + | 0.952224i | \(0.401209\pi\) | |||||||
\(828\) | −74.4010 | −2.58562 | ||||||||
\(829\) | −13.0915 | −0.454688 | −0.227344 | − | 0.973815i | \(-0.573004\pi\) | ||||
−0.227344 | + | 0.973815i | \(0.573004\pi\) | |||||||
\(830\) | −63.9445 | −2.21955 | ||||||||
\(831\) | 56.9884 | 1.97691 | ||||||||
\(832\) | 13.3881 | 0.464150 | ||||||||
\(833\) | −55.2546 | −1.91446 | ||||||||
\(834\) | 13.8911 | 0.481009 | ||||||||
\(835\) | 19.8133 | 0.685669 | ||||||||
\(836\) | 43.4678 | 1.50337 | ||||||||
\(837\) | −20.8265 | −0.719869 | ||||||||
\(838\) | 93.9130 | 3.24417 | ||||||||
\(839\) | −36.3461 | −1.25481 | −0.627404 | − | 0.778694i | \(-0.715883\pi\) | ||||
−0.627404 | + | 0.778694i | \(0.715883\pi\) | |||||||
\(840\) | −169.018 | −5.83166 | ||||||||
\(841\) | 7.21675 | 0.248853 | ||||||||
\(842\) | −48.9367 | −1.68647 | ||||||||
\(843\) | −27.6032 | −0.950705 | ||||||||
\(844\) | 47.7268 | 1.64283 | ||||||||
\(845\) | −24.6794 | −0.848997 | ||||||||
\(846\) | 38.9866 | 1.34039 | ||||||||
\(847\) | 43.6811 | 1.50090 | ||||||||
\(848\) | −19.1848 | −0.658810 | ||||||||
\(849\) | −50.0002 | −1.71600 | ||||||||
\(850\) | −9.64606 | −0.330857 | ||||||||
\(851\) | 38.0455 | 1.30418 | ||||||||
\(852\) | −91.1376 | −3.12232 | ||||||||
\(853\) | −24.6209 | −0.843004 | −0.421502 | − | 0.906828i | \(-0.638497\pi\) | ||||
−0.421502 | + | 0.906828i | \(0.638497\pi\) | |||||||
\(854\) | 126.508 | 4.32902 | ||||||||
\(855\) | −23.7521 | −0.812304 | ||||||||
\(856\) | 27.6910 | 0.946457 | ||||||||
\(857\) | 22.9754 | 0.784825 | 0.392412 | − | 0.919789i | \(-0.371641\pi\) | ||||
0.392412 | + | 0.919789i | \(0.371641\pi\) | |||||||
\(858\) | −6.27580 | −0.214252 | ||||||||
\(859\) | −12.2651 | −0.418480 | −0.209240 | − | 0.977864i | \(-0.567099\pi\) | ||||
−0.209240 | + | 0.977864i | \(0.567099\pi\) | |||||||
\(860\) | 20.7364 | 0.707105 | ||||||||
\(861\) | 110.307 | 3.75925 | ||||||||
\(862\) | 15.8025 | 0.538234 | ||||||||
\(863\) | −47.2349 | −1.60790 | −0.803948 | − | 0.594700i | \(-0.797271\pi\) | ||||
−0.803948 | + | 0.594700i | \(0.797271\pi\) | |||||||
\(864\) | −39.4362 | −1.34165 | ||||||||
\(865\) | −45.3881 | −1.54324 | ||||||||
\(866\) | 70.8475 | 2.40750 | ||||||||
\(867\) | 6.89639 | 0.234214 | ||||||||
\(868\) | 186.453 | 6.32862 | ||||||||
\(869\) | 6.38782 | 0.216692 | ||||||||
\(870\) | −70.3490 | −2.38506 | ||||||||
\(871\) | −7.86773 | −0.266588 | ||||||||
\(872\) | 55.7853 | 1.88913 | ||||||||
\(873\) | −14.1636 | −0.479366 | ||||||||
\(874\) | −144.654 | −4.89299 | ||||||||
\(875\) | 56.0276 | 1.89408 | ||||||||
\(876\) | 82.6227 | 2.79156 | ||||||||
\(877\) | −31.1956 | −1.05340 | −0.526701 | − | 0.850051i | \(-0.676571\pi\) | ||||
−0.526701 | + | 0.850051i | \(0.676571\pi\) | |||||||
\(878\) | 25.1031 | 0.847189 | ||||||||
\(879\) | −12.5885 | −0.424598 | ||||||||
\(880\) | −30.3448 | −1.02292 | ||||||||
\(881\) | −10.2898 | −0.346671 | −0.173336 | − | 0.984863i | \(-0.555455\pi\) | ||||
−0.173336 | + | 0.984863i | \(0.555455\pi\) | |||||||
\(882\) | −70.5609 | −2.37591 | ||||||||
\(883\) | 2.47592 | 0.0833213 | 0.0416607 | − | 0.999132i | \(-0.486735\pi\) | ||||
0.0416607 | + | 0.999132i | \(0.486735\pi\) | |||||||
\(884\) | −15.8715 | −0.533816 | ||||||||
\(885\) | 31.9582 | 1.07426 | ||||||||
\(886\) | 26.0554 | 0.875349 | ||||||||
\(887\) | 39.5772 | 1.32887 | 0.664435 | − | 0.747346i | \(-0.268672\pi\) | ||||
0.664435 | + | 0.747346i | \(0.268672\pi\) | |||||||
\(888\) | −83.7367 | −2.81002 | ||||||||
\(889\) | −29.8117 | −0.999854 | ||||||||
\(890\) | 36.6549 | 1.22868 | ||||||||
\(891\) | 14.3688 | 0.481372 | ||||||||
\(892\) | −45.4931 | −1.52322 | ||||||||
\(893\) | 54.4272 | 1.82134 | ||||||||
\(894\) | 71.9867 | 2.40759 | ||||||||
\(895\) | 9.60609 | 0.321096 | ||||||||
\(896\) | 60.3891 | 2.01746 | ||||||||
\(897\) | 14.9962 | 0.500709 | ||||||||
\(898\) | 25.4672 | 0.849852 | ||||||||
\(899\) | 47.1319 | 1.57194 | ||||||||
\(900\) | −8.84496 | −0.294832 | ||||||||
\(901\) | 6.07329 | 0.202331 | ||||||||
\(902\) | 36.9660 | 1.23083 | ||||||||
\(903\) | 20.7435 | 0.690301 | ||||||||
\(904\) | 94.3465 | 3.13792 | ||||||||
\(905\) | −36.7368 | −1.22117 | ||||||||
\(906\) | −32.9622 | −1.09510 | ||||||||
\(907\) | 26.7368 | 0.887780 | 0.443890 | − | 0.896081i | \(-0.353598\pi\) | ||||
0.443890 | + | 0.896081i | \(0.353598\pi\) | |||||||
\(908\) | 136.734 | 4.53768 | ||||||||
\(909\) | 11.5795 | 0.384068 | ||||||||
\(910\) | 20.9196 | 0.693478 | ||||||||
\(911\) | −39.7030 | −1.31542 | −0.657709 | − | 0.753272i | \(-0.728474\pi\) | ||||
−0.657709 | + | 0.753272i | \(0.728474\pi\) | |||||||
\(912\) | 170.567 | 5.64803 | ||||||||
\(913\) | −15.3923 | −0.509410 | ||||||||
\(914\) | 22.1219 | 0.731727 | ||||||||
\(915\) | −44.6029 | −1.47453 | ||||||||
\(916\) | −29.0608 | −0.960195 | ||||||||
\(917\) | 45.3639 | 1.49805 | ||||||||
\(918\) | 26.3547 | 0.869834 | ||||||||
\(919\) | 24.7787 | 0.817373 | 0.408687 | − | 0.912675i | \(-0.365987\pi\) | ||||
0.408687 | + | 0.912675i | \(0.365987\pi\) | |||||||
\(920\) | 135.346 | 4.46222 | ||||||||
\(921\) | 1.15921 | 0.0381973 | ||||||||
\(922\) | −15.4786 | −0.509759 | ||||||||
\(923\) | 6.85077 | 0.225496 | ||||||||
\(924\) | −66.9903 | −2.20382 | ||||||||
\(925\) | 4.52293 | 0.148713 | ||||||||
\(926\) | 103.255 | 3.39317 | ||||||||
\(927\) | −18.5287 | −0.608564 | ||||||||
\(928\) | 89.2471 | 2.92968 | ||||||||
\(929\) | −47.5142 | −1.55889 | −0.779446 | − | 0.626470i | \(-0.784499\pi\) | ||||
−0.779446 | + | 0.626470i | \(0.784499\pi\) | |||||||
\(930\) | −91.5511 | −3.00208 | ||||||||
\(931\) | −98.5065 | −3.22842 | ||||||||
\(932\) | −127.989 | −4.19242 | ||||||||
\(933\) | 22.8957 | 0.749572 | ||||||||
\(934\) | −40.6532 | −1.33021 | ||||||||
\(935\) | 9.60617 | 0.314155 | ||||||||
\(936\) | −12.3093 | −0.402342 | ||||||||
\(937\) | −53.4347 | −1.74563 | −0.872817 | − | 0.488047i | \(-0.837709\pi\) | ||||
−0.872817 | + | 0.488047i | \(0.837709\pi\) | |||||||
\(938\) | −116.961 | −3.81892 | ||||||||
\(939\) | −1.31600 | −0.0429459 | ||||||||
\(940\) | −83.8514 | −2.73493 | ||||||||
\(941\) | −20.6464 | −0.673053 | −0.336527 | − | 0.941674i | \(-0.609252\pi\) | ||||
−0.336527 | + | 0.941674i | \(0.609252\pi\) | |||||||
\(942\) | −129.570 | −4.22160 | ||||||||
\(943\) | −88.3313 | −2.87646 | ||||||||
\(944\) | −85.5882 | −2.78566 | ||||||||
\(945\) | −24.9427 | −0.811387 | ||||||||
\(946\) | 6.95157 | 0.226015 | ||||||||
\(947\) | −38.4098 | −1.24815 | −0.624075 | − | 0.781364i | \(-0.714524\pi\) | ||||
−0.624075 | + | 0.781364i | \(0.714524\pi\) | |||||||
\(948\) | 55.3168 | 1.79661 | ||||||||
\(949\) | −6.21071 | −0.201608 | ||||||||
\(950\) | −17.1968 | −0.557937 | ||||||||
\(951\) | −71.8908 | −2.33122 | ||||||||
\(952\) | −143.295 | −4.64421 | ||||||||
\(953\) | 13.5699 | 0.439573 | 0.219786 | − | 0.975548i | \(-0.429464\pi\) | ||||
0.219786 | + | 0.975548i | \(0.429464\pi\) | |||||||
\(954\) | 7.75568 | 0.251099 | ||||||||
\(955\) | 20.8688 | 0.675300 | ||||||||
\(956\) | −72.4089 | −2.34187 | ||||||||
\(957\) | −16.9339 | −0.547397 | ||||||||
\(958\) | 79.9717 | 2.58377 | ||||||||
\(959\) | −77.0356 | −2.48761 | ||||||||
\(960\) | −70.1709 | −2.26476 | ||||||||
\(961\) | 30.3367 | 0.978603 | ||||||||
\(962\) | 10.3642 | 0.334156 | ||||||||
\(963\) | −5.99724 | −0.193258 | ||||||||
\(964\) | −71.1955 | −2.29305 | ||||||||
\(965\) | 15.4563 | 0.497555 | ||||||||
\(966\) | 222.933 | 7.17275 | ||||||||
\(967\) | −50.8960 | −1.63671 | −0.818353 | − | 0.574716i | \(-0.805113\pi\) | ||||
−0.818353 | + | 0.574716i | \(0.805113\pi\) | |||||||
\(968\) | 76.9872 | 2.47446 | ||||||||
\(969\) | −53.9958 | −1.73460 | ||||||||
\(970\) | 42.4248 | 1.36218 | ||||||||
\(971\) | −24.3240 | −0.780594 | −0.390297 | − | 0.920689i | \(-0.627628\pi\) | ||||
−0.390297 | + | 0.920689i | \(0.627628\pi\) | |||||||
\(972\) | 83.7973 | 2.68780 | ||||||||
\(973\) | −11.1460 | −0.357326 | ||||||||
\(974\) | −62.3664 | −1.99835 | ||||||||
\(975\) | 1.78278 | 0.0570947 | ||||||||
\(976\) | 119.452 | 3.82358 | ||||||||
\(977\) | 53.5290 | 1.71254 | 0.856272 | − | 0.516525i | \(-0.172775\pi\) | ||||
0.856272 | + | 0.516525i | \(0.172775\pi\) | |||||||
\(978\) | 86.5275 | 2.76685 | ||||||||
\(979\) | 8.82333 | 0.281995 | ||||||||
\(980\) | 151.761 | 4.84782 | ||||||||
\(981\) | −12.0818 | −0.385744 | ||||||||
\(982\) | 66.7361 | 2.12963 | ||||||||
\(983\) | −12.4734 | −0.397839 | −0.198920 | − | 0.980016i | \(-0.563743\pi\) | ||||
−0.198920 | + | 0.980016i | \(0.563743\pi\) | |||||||
\(984\) | 194.414 | 6.19769 | ||||||||
\(985\) | 16.3615 | 0.521319 | ||||||||
\(986\) | −59.6426 | −1.89941 | ||||||||
\(987\) | −83.8803 | −2.66994 | ||||||||
\(988\) | −28.2953 | −0.900193 | ||||||||
\(989\) | −16.6110 | −0.528198 | ||||||||
\(990\) | 12.2672 | 0.389878 | ||||||||
\(991\) | −52.8785 | −1.67974 | −0.839871 | − | 0.542787i | \(-0.817369\pi\) | ||||
−0.839871 | + | 0.542787i | \(0.817369\pi\) | |||||||
\(992\) | 116.145 | 3.68760 | ||||||||
\(993\) | −65.7436 | −2.08631 | ||||||||
\(994\) | 101.843 | 3.23027 | ||||||||
\(995\) | −44.4170 | −1.40811 | ||||||||
\(996\) | −133.293 | −4.22355 | ||||||||
\(997\) | 1.52848 | 0.0484074 | 0.0242037 | − | 0.999707i | \(-0.492295\pi\) | ||||
0.0242037 | + | 0.999707i | \(0.492295\pi\) | |||||||
\(998\) | 23.5730 | 0.746190 | ||||||||
\(999\) | −12.3574 | −0.390971 |
(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 | 2671.2.a.b.1.4 | ✓ | 122 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2671.2.a.b.1.4 | ✓ | 122 | 1.1 | even | 1 | trivial |