Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6015,2,Mod(1,6015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6015 = 3 \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6015.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: | \(48.0300168158\) |
Analytic rank: | \(0\) |
Dimension: | \(43\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 6015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.15381 | −0.815865 | −0.407932 | − | 0.913012i | \(-0.633750\pi\) | ||||
−0.407932 | + | 0.913012i | \(0.633750\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −0.668729 | −0.334364 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.15381 | −0.471040 | ||||||||
\(7\) | −0.585541 | −0.221314 | −0.110657 | − | 0.993859i | \(-0.535295\pi\) | ||||
−0.110657 | + | 0.993859i | \(0.535295\pi\) | |||||||
\(8\) | 3.07920 | 1.08866 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.15381 | −0.364866 | ||||||||
\(11\) | −4.52853 | −1.36540 | −0.682702 | − | 0.730697i | \(-0.739195\pi\) | ||||
−0.682702 | + | 0.730697i | \(0.739195\pi\) | |||||||
\(12\) | −0.668729 | −0.193045 | ||||||||
\(13\) | 2.29360 | 0.636131 | 0.318066 | − | 0.948069i | \(-0.396967\pi\) | ||||
0.318066 | + | 0.948069i | \(0.396967\pi\) | |||||||
\(14\) | 0.675601 | 0.180562 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | −2.21534 | −0.553836 | ||||||||
\(17\) | −5.75017 | −1.39462 | −0.697311 | − | 0.716769i | \(-0.745620\pi\) | ||||
−0.697311 | + | 0.716769i | \(0.745620\pi\) | |||||||
\(18\) | −1.15381 | −0.271955 | ||||||||
\(19\) | 8.01713 | 1.83925 | 0.919627 | − | 0.392792i | \(-0.128491\pi\) | ||||
0.919627 | + | 0.392792i | \(0.128491\pi\) | |||||||
\(20\) | −0.668729 | −0.149532 | ||||||||
\(21\) | −0.585541 | −0.127775 | ||||||||
\(22\) | 5.22505 | 1.11398 | ||||||||
\(23\) | −0.111184 | −0.0231835 | −0.0115917 | − | 0.999933i | \(-0.503690\pi\) | ||||
−0.0115917 | + | 0.999933i | \(0.503690\pi\) | |||||||
\(24\) | 3.07920 | 0.628539 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −2.64638 | −0.518997 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.391568 | 0.0739994 | ||||||||
\(29\) | 0.451788 | 0.0838948 | 0.0419474 | − | 0.999120i | \(-0.486644\pi\) | ||||
0.0419474 | + | 0.999120i | \(0.486644\pi\) | |||||||
\(30\) | −1.15381 | −0.210655 | ||||||||
\(31\) | 6.58928 | 1.18347 | 0.591735 | − | 0.806133i | \(-0.298443\pi\) | ||||
0.591735 | + | 0.806133i | \(0.298443\pi\) | |||||||
\(32\) | −3.60232 | −0.636806 | ||||||||
\(33\) | −4.52853 | −0.788316 | ||||||||
\(34\) | 6.63459 | 1.13782 | ||||||||
\(35\) | −0.585541 | −0.0989744 | ||||||||
\(36\) | −0.668729 | −0.111455 | ||||||||
\(37\) | 4.27095 | 0.702140 | 0.351070 | − | 0.936349i | \(-0.385818\pi\) | ||||
0.351070 | + | 0.936349i | \(0.385818\pi\) | |||||||
\(38\) | −9.25022 | −1.50058 | ||||||||
\(39\) | 2.29360 | 0.367270 | ||||||||
\(40\) | 3.07920 | 0.486864 | ||||||||
\(41\) | −5.70975 | −0.891714 | −0.445857 | − | 0.895104i | \(-0.647101\pi\) | ||||
−0.445857 | + | 0.895104i | \(0.647101\pi\) | |||||||
\(42\) | 0.675601 | 0.104248 | ||||||||
\(43\) | −4.41525 | −0.673319 | −0.336660 | − | 0.941626i | \(-0.609297\pi\) | ||||
−0.336660 | + | 0.941626i | \(0.609297\pi\) | |||||||
\(44\) | 3.02836 | 0.456542 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0.128285 | 0.0189146 | ||||||||
\(47\) | 11.5549 | 1.68546 | 0.842728 | − | 0.538339i | \(-0.180948\pi\) | ||||
0.842728 | + | 0.538339i | \(0.180948\pi\) | |||||||
\(48\) | −2.21534 | −0.319757 | ||||||||
\(49\) | −6.65714 | −0.951020 | ||||||||
\(50\) | −1.15381 | −0.163173 | ||||||||
\(51\) | −5.75017 | −0.805185 | ||||||||
\(52\) | −1.53380 | −0.212700 | ||||||||
\(53\) | −7.63198 | −1.04833 | −0.524167 | − | 0.851616i | \(-0.675623\pi\) | ||||
−0.524167 | + | 0.851616i | \(0.675623\pi\) | |||||||
\(54\) | −1.15381 | −0.157013 | ||||||||
\(55\) | −4.52853 | −0.610627 | ||||||||
\(56\) | −1.80300 | −0.240936 | ||||||||
\(57\) | 8.01713 | 1.06189 | ||||||||
\(58\) | −0.521276 | −0.0684469 | ||||||||
\(59\) | −2.30187 | −0.299678 | −0.149839 | − | 0.988710i | \(-0.547876\pi\) | ||||
−0.149839 | + | 0.988710i | \(0.547876\pi\) | |||||||
\(60\) | −0.668729 | −0.0863325 | ||||||||
\(61\) | −0.380836 | −0.0487611 | −0.0243806 | − | 0.999703i | \(-0.507761\pi\) | ||||
−0.0243806 | + | 0.999703i | \(0.507761\pi\) | |||||||
\(62\) | −7.60276 | −0.965551 | ||||||||
\(63\) | −0.585541 | −0.0737712 | ||||||||
\(64\) | 8.58707 | 1.07338 | ||||||||
\(65\) | 2.29360 | 0.284486 | ||||||||
\(66\) | 5.22505 | 0.643159 | ||||||||
\(67\) | −5.22423 | −0.638241 | −0.319121 | − | 0.947714i | \(-0.603388\pi\) | ||||
−0.319121 | + | 0.947714i | \(0.603388\pi\) | |||||||
\(68\) | 3.84531 | 0.466312 | ||||||||
\(69\) | −0.111184 | −0.0133850 | ||||||||
\(70\) | 0.675601 | 0.0807498 | ||||||||
\(71\) | −4.94094 | −0.586381 | −0.293191 | − | 0.956054i | \(-0.594717\pi\) | ||||
−0.293191 | + | 0.956054i | \(0.594717\pi\) | |||||||
\(72\) | 3.07920 | 0.362887 | ||||||||
\(73\) | 2.47973 | 0.290231 | 0.145115 | − | 0.989415i | \(-0.453645\pi\) | ||||
0.145115 | + | 0.989415i | \(0.453645\pi\) | |||||||
\(74\) | −4.92785 | −0.572851 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | −5.36128 | −0.614981 | ||||||||
\(77\) | 2.65164 | 0.302182 | ||||||||
\(78\) | −2.64638 | −0.299643 | ||||||||
\(79\) | 9.89835 | 1.11365 | 0.556826 | − | 0.830629i | \(-0.312019\pi\) | ||||
0.556826 | + | 0.830629i | \(0.312019\pi\) | |||||||
\(80\) | −2.21534 | −0.247683 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 6.58795 | 0.727518 | ||||||||
\(83\) | −0.690336 | −0.0757742 | −0.0378871 | − | 0.999282i | \(-0.512063\pi\) | ||||
−0.0378871 | + | 0.999282i | \(0.512063\pi\) | |||||||
\(84\) | 0.391568 | 0.0427236 | ||||||||
\(85\) | −5.75017 | −0.623694 | ||||||||
\(86\) | 5.09435 | 0.549337 | ||||||||
\(87\) | 0.451788 | 0.0484367 | ||||||||
\(88\) | −13.9442 | −1.48646 | ||||||||
\(89\) | 10.0852 | 1.06903 | 0.534514 | − | 0.845160i | \(-0.320495\pi\) | ||||
0.534514 | + | 0.845160i | \(0.320495\pi\) | |||||||
\(90\) | −1.15381 | −0.121622 | ||||||||
\(91\) | −1.34300 | −0.140784 | ||||||||
\(92\) | 0.0743520 | 0.00775173 | ||||||||
\(93\) | 6.58928 | 0.683276 | ||||||||
\(94\) | −13.3321 | −1.37510 | ||||||||
\(95\) | 8.01713 | 0.822540 | ||||||||
\(96\) | −3.60232 | −0.367660 | ||||||||
\(97\) | 6.21880 | 0.631424 | 0.315712 | − | 0.948855i | \(-0.397757\pi\) | ||||
0.315712 | + | 0.948855i | \(0.397757\pi\) | |||||||
\(98\) | 7.68106 | 0.775904 | ||||||||
\(99\) | −4.52853 | −0.455134 | ||||||||
\(100\) | −0.668729 | −0.0668729 | ||||||||
\(101\) | 14.0429 | 1.39732 | 0.698661 | − | 0.715453i | \(-0.253780\pi\) | ||||
0.698661 | + | 0.715453i | \(0.253780\pi\) | |||||||
\(102\) | 6.63459 | 0.656922 | ||||||||
\(103\) | 2.65147 | 0.261257 | 0.130628 | − | 0.991431i | \(-0.458301\pi\) | ||||
0.130628 | + | 0.991431i | \(0.458301\pi\) | |||||||
\(104\) | 7.06246 | 0.692531 | ||||||||
\(105\) | −0.585541 | −0.0571429 | ||||||||
\(106\) | 8.80584 | 0.855298 | ||||||||
\(107\) | 17.7198 | 1.71304 | 0.856518 | − | 0.516117i | \(-0.172623\pi\) | ||||
0.856518 | + | 0.516117i | \(0.172623\pi\) | |||||||
\(108\) | −0.668729 | −0.0643485 | ||||||||
\(109\) | −0.422225 | −0.0404418 | −0.0202209 | − | 0.999796i | \(-0.506437\pi\) | ||||
−0.0202209 | + | 0.999796i | \(0.506437\pi\) | |||||||
\(110\) | 5.22505 | 0.498189 | ||||||||
\(111\) | 4.27095 | 0.405381 | ||||||||
\(112\) | 1.29717 | 0.122571 | ||||||||
\(113\) | −4.02962 | −0.379075 | −0.189538 | − | 0.981873i | \(-0.560699\pi\) | ||||
−0.189538 | + | 0.981873i | \(0.560699\pi\) | |||||||
\(114\) | −9.25022 | −0.866362 | ||||||||
\(115\) | −0.111184 | −0.0103680 | ||||||||
\(116\) | −0.302123 | −0.0280515 | ||||||||
\(117\) | 2.29360 | 0.212044 | ||||||||
\(118\) | 2.65592 | 0.244497 | ||||||||
\(119\) | 3.36696 | 0.308649 | ||||||||
\(120\) | 3.07920 | 0.281091 | ||||||||
\(121\) | 9.50758 | 0.864325 | ||||||||
\(122\) | 0.439412 | 0.0397825 | ||||||||
\(123\) | −5.70975 | −0.514831 | ||||||||
\(124\) | −4.40644 | −0.395710 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0.675601 | 0.0601873 | ||||||||
\(127\) | −5.17311 | −0.459039 | −0.229520 | − | 0.973304i | \(-0.573716\pi\) | ||||
−0.229520 | + | 0.973304i | \(0.573716\pi\) | |||||||
\(128\) | −2.70318 | −0.238930 | ||||||||
\(129\) | −4.41525 | −0.388741 | ||||||||
\(130\) | −2.64638 | −0.232103 | ||||||||
\(131\) | −20.4426 | −1.78608 | −0.893039 | − | 0.449979i | \(-0.851432\pi\) | ||||
−0.893039 | + | 0.449979i | \(0.851432\pi\) | |||||||
\(132\) | 3.02836 | 0.263585 | ||||||||
\(133\) | −4.69435 | −0.407052 | ||||||||
\(134\) | 6.02776 | 0.520719 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | −17.7059 | −1.51827 | ||||||||
\(137\) | 0.511628 | 0.0437114 | 0.0218557 | − | 0.999761i | \(-0.493043\pi\) | ||||
0.0218557 | + | 0.999761i | \(0.493043\pi\) | |||||||
\(138\) | 0.128285 | 0.0109203 | ||||||||
\(139\) | 2.48764 | 0.210999 | 0.105499 | − | 0.994419i | \(-0.466356\pi\) | ||||
0.105499 | + | 0.994419i | \(0.466356\pi\) | |||||||
\(140\) | 0.391568 | 0.0330935 | ||||||||
\(141\) | 11.5549 | 0.973099 | ||||||||
\(142\) | 5.70089 | 0.478408 | ||||||||
\(143\) | −10.3867 | −0.868575 | ||||||||
\(144\) | −2.21534 | −0.184612 | ||||||||
\(145\) | 0.451788 | 0.0375189 | ||||||||
\(146\) | −2.86114 | −0.236789 | ||||||||
\(147\) | −6.65714 | −0.549072 | ||||||||
\(148\) | −2.85611 | −0.234771 | ||||||||
\(149\) | −0.965363 | −0.0790856 | −0.0395428 | − | 0.999218i | \(-0.512590\pi\) | ||||
−0.0395428 | + | 0.999218i | \(0.512590\pi\) | |||||||
\(150\) | −1.15381 | −0.0942080 | ||||||||
\(151\) | 12.9020 | 1.04995 | 0.524976 | − | 0.851117i | \(-0.324074\pi\) | ||||
0.524976 | + | 0.851117i | \(0.324074\pi\) | |||||||
\(152\) | 24.6863 | 2.00233 | ||||||||
\(153\) | −5.75017 | −0.464874 | ||||||||
\(154\) | −3.05948 | −0.246540 | ||||||||
\(155\) | 6.58928 | 0.529264 | ||||||||
\(156\) | −1.53380 | −0.122802 | ||||||||
\(157\) | 6.36673 | 0.508120 | 0.254060 | − | 0.967188i | \(-0.418234\pi\) | ||||
0.254060 | + | 0.967188i | \(0.418234\pi\) | |||||||
\(158\) | −11.4208 | −0.908589 | ||||||||
\(159\) | −7.63198 | −0.605256 | ||||||||
\(160\) | −3.60232 | −0.284788 | ||||||||
\(161\) | 0.0651028 | 0.00513082 | ||||||||
\(162\) | −1.15381 | −0.0906517 | ||||||||
\(163\) | 11.0789 | 0.867767 | 0.433884 | − | 0.900969i | \(-0.357143\pi\) | ||||
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(164\) | 3.81828 | 0.298157 | ||||||||
\(165\) | −4.52853 | −0.352546 | ||||||||
\(166\) | 0.796514 | 0.0618215 | ||||||||
\(167\) | 20.0478 | 1.55134 | 0.775672 | − | 0.631136i | \(-0.217411\pi\) | ||||
0.775672 | + | 0.631136i | \(0.217411\pi\) | |||||||
\(168\) | −1.80300 | −0.139104 | ||||||||
\(169\) | −7.73938 | −0.595337 | ||||||||
\(170\) | 6.63459 | 0.508850 | ||||||||
\(171\) | 8.01713 | 0.613085 | ||||||||
\(172\) | 2.95260 | 0.225134 | ||||||||
\(173\) | 12.7976 | 0.972987 | 0.486494 | − | 0.873684i | \(-0.338276\pi\) | ||||
0.486494 | + | 0.873684i | \(0.338276\pi\) | |||||||
\(174\) | −0.521276 | −0.0395178 | ||||||||
\(175\) | −0.585541 | −0.0442627 | ||||||||
\(176\) | 10.0322 | 0.756209 | ||||||||
\(177\) | −2.30187 | −0.173019 | ||||||||
\(178\) | −11.6364 | −0.872182 | ||||||||
\(179\) | −3.54972 | −0.265318 | −0.132659 | − | 0.991162i | \(-0.542352\pi\) | ||||
−0.132659 | + | 0.991162i | \(0.542352\pi\) | |||||||
\(180\) | −0.668729 | −0.0498441 | ||||||||
\(181\) | 11.8102 | 0.877842 | 0.438921 | − | 0.898526i | \(-0.355361\pi\) | ||||
0.438921 | + | 0.898526i | \(0.355361\pi\) | |||||||
\(182\) | 1.54956 | 0.114861 | ||||||||
\(183\) | −0.380836 | −0.0281522 | ||||||||
\(184\) | −0.342358 | −0.0252390 | ||||||||
\(185\) | 4.27095 | 0.314007 | ||||||||
\(186\) | −7.60276 | −0.557461 | ||||||||
\(187\) | 26.0398 | 1.90422 | ||||||||
\(188\) | −7.72710 | −0.563557 | ||||||||
\(189\) | −0.585541 | −0.0425918 | ||||||||
\(190\) | −9.25022 | −0.671081 | ||||||||
\(191\) | 3.70330 | 0.267961 | 0.133981 | − | 0.990984i | \(-0.457224\pi\) | ||||
0.133981 | + | 0.990984i | \(0.457224\pi\) | |||||||
\(192\) | 8.58707 | 0.619718 | ||||||||
\(193\) | −8.30005 | −0.597451 | −0.298725 | − | 0.954339i | \(-0.596561\pi\) | ||||
−0.298725 | + | 0.954339i | \(0.596561\pi\) | |||||||
\(194\) | −7.17530 | −0.515156 | ||||||||
\(195\) | 2.29360 | 0.164248 | ||||||||
\(196\) | 4.45182 | 0.317987 | ||||||||
\(197\) | −7.12634 | −0.507730 | −0.253865 | − | 0.967240i | \(-0.581702\pi\) | ||||
−0.253865 | + | 0.967240i | \(0.581702\pi\) | |||||||
\(198\) | 5.22505 | 0.371328 | ||||||||
\(199\) | −4.93258 | −0.349661 | −0.174831 | − | 0.984599i | \(-0.555938\pi\) | ||||
−0.174831 | + | 0.984599i | \(0.555938\pi\) | |||||||
\(200\) | 3.07920 | 0.217732 | ||||||||
\(201\) | −5.22423 | −0.368489 | ||||||||
\(202\) | −16.2028 | −1.14003 | ||||||||
\(203\) | −0.264540 | −0.0185671 | ||||||||
\(204\) | 3.84531 | 0.269225 | ||||||||
\(205\) | −5.70975 | −0.398786 | ||||||||
\(206\) | −3.05928 | −0.213150 | ||||||||
\(207\) | −0.111184 | −0.00772783 | ||||||||
\(208\) | −5.08112 | −0.352312 | ||||||||
\(209\) | −36.3058 | −2.51132 | ||||||||
\(210\) | 0.675601 | 0.0466209 | ||||||||
\(211\) | 0.813652 | 0.0560141 | 0.0280070 | − | 0.999608i | \(-0.491084\pi\) | ||||
0.0280070 | + | 0.999608i | \(0.491084\pi\) | |||||||
\(212\) | 5.10373 | 0.350525 | ||||||||
\(213\) | −4.94094 | −0.338547 | ||||||||
\(214\) | −20.4452 | −1.39761 | ||||||||
\(215\) | −4.41525 | −0.301117 | ||||||||
\(216\) | 3.07920 | 0.209513 | ||||||||
\(217\) | −3.85829 | −0.261918 | ||||||||
\(218\) | 0.487166 | 0.0329951 | ||||||||
\(219\) | 2.47973 | 0.167565 | ||||||||
\(220\) | 3.02836 | 0.204172 | ||||||||
\(221\) | −13.1886 | −0.887162 | ||||||||
\(222\) | −4.92785 | −0.330736 | ||||||||
\(223\) | 5.73449 | 0.384010 | 0.192005 | − | 0.981394i | \(-0.438501\pi\) | ||||
0.192005 | + | 0.981394i | \(0.438501\pi\) | |||||||
\(224\) | 2.10930 | 0.140934 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 4.64941 | 0.309274 | ||||||||
\(227\) | 1.59161 | 0.105639 | 0.0528195 | − | 0.998604i | \(-0.483179\pi\) | ||||
0.0528195 | + | 0.998604i | \(0.483179\pi\) | |||||||
\(228\) | −5.36128 | −0.355060 | ||||||||
\(229\) | −9.32150 | −0.615982 | −0.307991 | − | 0.951389i | \(-0.599657\pi\) | ||||
−0.307991 | + | 0.951389i | \(0.599657\pi\) | |||||||
\(230\) | 0.128285 | 0.00845886 | ||||||||
\(231\) | 2.65164 | 0.174465 | ||||||||
\(232\) | 1.39114 | 0.0913331 | ||||||||
\(233\) | −9.45607 | −0.619488 | −0.309744 | − | 0.950820i | \(-0.600243\pi\) | ||||
−0.309744 | + | 0.950820i | \(0.600243\pi\) | |||||||
\(234\) | −2.64638 | −0.172999 | ||||||||
\(235\) | 11.5549 | 0.753759 | ||||||||
\(236\) | 1.53933 | 0.100202 | ||||||||
\(237\) | 9.89835 | 0.642967 | ||||||||
\(238\) | −3.88482 | −0.251816 | ||||||||
\(239\) | 20.1533 | 1.30361 | 0.651804 | − | 0.758387i | \(-0.274012\pi\) | ||||
0.651804 | + | 0.758387i | \(0.274012\pi\) | |||||||
\(240\) | −2.21534 | −0.143000 | ||||||||
\(241\) | 4.62092 | 0.297659 | 0.148830 | − | 0.988863i | \(-0.452449\pi\) | ||||
0.148830 | + | 0.988863i | \(0.452449\pi\) | |||||||
\(242\) | −10.9699 | −0.705173 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0.254676 | 0.0163040 | ||||||||
\(245\) | −6.65714 | −0.425309 | ||||||||
\(246\) | 6.58795 | 0.420033 | ||||||||
\(247\) | 18.3881 | 1.17001 | ||||||||
\(248\) | 20.2897 | 1.28840 | ||||||||
\(249\) | −0.690336 | −0.0437482 | ||||||||
\(250\) | −1.15381 | −0.0729732 | ||||||||
\(251\) | −5.53993 | −0.349677 | −0.174839 | − | 0.984597i | \(-0.555940\pi\) | ||||
−0.174839 | + | 0.984597i | \(0.555940\pi\) | |||||||
\(252\) | 0.391568 | 0.0246665 | ||||||||
\(253\) | 0.503500 | 0.0316548 | ||||||||
\(254\) | 5.96877 | 0.374514 | ||||||||
\(255\) | −5.75017 | −0.360090 | ||||||||
\(256\) | −14.0552 | −0.878449 | ||||||||
\(257\) | −14.5839 | −0.909722 | −0.454861 | − | 0.890563i | \(-0.650311\pi\) | ||||
−0.454861 | + | 0.890563i | \(0.650311\pi\) | |||||||
\(258\) | 5.09435 | 0.317160 | ||||||||
\(259\) | −2.50082 | −0.155393 | ||||||||
\(260\) | −1.53380 | −0.0951222 | ||||||||
\(261\) | 0.451788 | 0.0279649 | ||||||||
\(262\) | 23.5868 | 1.45720 | ||||||||
\(263\) | 10.6443 | 0.656353 | 0.328177 | − | 0.944616i | \(-0.393566\pi\) | ||||
0.328177 | + | 0.944616i | \(0.393566\pi\) | |||||||
\(264\) | −13.9442 | −0.858209 | ||||||||
\(265\) | −7.63198 | −0.468829 | ||||||||
\(266\) | 5.41638 | 0.332100 | ||||||||
\(267\) | 10.0852 | 0.617203 | ||||||||
\(268\) | 3.49359 | 0.213405 | ||||||||
\(269\) | −2.56660 | −0.156488 | −0.0782441 | − | 0.996934i | \(-0.524931\pi\) | ||||
−0.0782441 | + | 0.996934i | \(0.524931\pi\) | |||||||
\(270\) | −1.15381 | −0.0702185 | ||||||||
\(271\) | 8.13957 | 0.494444 | 0.247222 | − | 0.968959i | \(-0.420482\pi\) | ||||
0.247222 | + | 0.968959i | \(0.420482\pi\) | |||||||
\(272\) | 12.7386 | 0.772392 | ||||||||
\(273\) | −1.34300 | −0.0812819 | ||||||||
\(274\) | −0.590320 | −0.0356626 | ||||||||
\(275\) | −4.52853 | −0.273081 | ||||||||
\(276\) | 0.0743520 | 0.00447547 | ||||||||
\(277\) | −11.4444 | −0.687629 | −0.343815 | − | 0.939038i | \(-0.611719\pi\) | ||||
−0.343815 | + | 0.939038i | \(0.611719\pi\) | |||||||
\(278\) | −2.87026 | −0.172147 | ||||||||
\(279\) | 6.58928 | 0.394490 | ||||||||
\(280\) | −1.80300 | −0.107750 | ||||||||
\(281\) | 4.68281 | 0.279353 | 0.139677 | − | 0.990197i | \(-0.455394\pi\) | ||||
0.139677 | + | 0.990197i | \(0.455394\pi\) | |||||||
\(282\) | −13.3321 | −0.793917 | ||||||||
\(283\) | 10.0859 | 0.599547 | 0.299774 | − | 0.954010i | \(-0.403089\pi\) | ||||
0.299774 | + | 0.954010i | \(0.403089\pi\) | |||||||
\(284\) | 3.30415 | 0.196065 | ||||||||
\(285\) | 8.01713 | 0.474894 | ||||||||
\(286\) | 11.9842 | 0.708640 | ||||||||
\(287\) | 3.34329 | 0.197348 | ||||||||
\(288\) | −3.60232 | −0.212269 | ||||||||
\(289\) | 16.0645 | 0.944970 | ||||||||
\(290\) | −0.521276 | −0.0306104 | ||||||||
\(291\) | 6.21880 | 0.364553 | ||||||||
\(292\) | −1.65827 | −0.0970429 | ||||||||
\(293\) | 3.65301 | 0.213411 | 0.106706 | − | 0.994291i | \(-0.465970\pi\) | ||||
0.106706 | + | 0.994291i | \(0.465970\pi\) | |||||||
\(294\) | 7.68106 | 0.447968 | ||||||||
\(295\) | −2.30187 | −0.134020 | ||||||||
\(296\) | 13.1511 | 0.764392 | ||||||||
\(297\) | −4.52853 | −0.262772 | ||||||||
\(298\) | 1.11384 | 0.0645232 | ||||||||
\(299\) | −0.255012 | −0.0147477 | ||||||||
\(300\) | −0.668729 | −0.0386091 | ||||||||
\(301\) | 2.58531 | 0.149015 | ||||||||
\(302\) | −14.8865 | −0.856619 | ||||||||
\(303\) | 14.0429 | 0.806744 | ||||||||
\(304\) | −17.7607 | −1.01865 | ||||||||
\(305\) | −0.380836 | −0.0218066 | ||||||||
\(306\) | 6.63459 | 0.379274 | ||||||||
\(307\) | −29.5411 | −1.68600 | −0.843001 | − | 0.537913i | \(-0.819213\pi\) | ||||
−0.843001 | + | 0.537913i | \(0.819213\pi\) | |||||||
\(308\) | −1.77323 | −0.101039 | ||||||||
\(309\) | 2.65147 | 0.150837 | ||||||||
\(310\) | −7.60276 | −0.431808 | ||||||||
\(311\) | −17.3304 | −0.982719 | −0.491360 | − | 0.870957i | \(-0.663500\pi\) | ||||
−0.491360 | + | 0.870957i | \(0.663500\pi\) | |||||||
\(312\) | 7.06246 | 0.399833 | ||||||||
\(313\) | 18.5118 | 1.04635 | 0.523175 | − | 0.852225i | \(-0.324748\pi\) | ||||
0.523175 | + | 0.852225i | \(0.324748\pi\) | |||||||
\(314\) | −7.34597 | −0.414557 | ||||||||
\(315\) | −0.585541 | −0.0329915 | ||||||||
\(316\) | −6.61931 | −0.372365 | ||||||||
\(317\) | 30.3195 | 1.70291 | 0.851456 | − | 0.524426i | \(-0.175720\pi\) | ||||
0.851456 | + | 0.524426i | \(0.175720\pi\) | |||||||
\(318\) | 8.80584 | 0.493807 | ||||||||
\(319\) | −2.04593 | −0.114550 | ||||||||
\(320\) | 8.58707 | 0.480032 | ||||||||
\(321\) | 17.7198 | 0.989022 | ||||||||
\(322\) | −0.0751161 | −0.00418606 | ||||||||
\(323\) | −46.0999 | −2.56507 | ||||||||
\(324\) | −0.668729 | −0.0371516 | ||||||||
\(325\) | 2.29360 | 0.127226 | ||||||||
\(326\) | −12.7829 | −0.707981 | ||||||||
\(327\) | −0.422225 | −0.0233491 | ||||||||
\(328\) | −17.5815 | −0.970774 | ||||||||
\(329\) | −6.76587 | −0.373014 | ||||||||
\(330\) | 5.22505 | 0.287630 | ||||||||
\(331\) | 11.2666 | 0.619270 | 0.309635 | − | 0.950855i | \(-0.399793\pi\) | ||||
0.309635 | + | 0.950855i | \(0.399793\pi\) | |||||||
\(332\) | 0.461647 | 0.0253362 | ||||||||
\(333\) | 4.27095 | 0.234047 | ||||||||
\(334\) | −23.1313 | −1.26569 | ||||||||
\(335\) | −5.22423 | −0.285430 | ||||||||
\(336\) | 1.29717 | 0.0707666 | ||||||||
\(337\) | 8.60499 | 0.468744 | 0.234372 | − | 0.972147i | \(-0.424697\pi\) | ||||
0.234372 | + | 0.972147i | \(0.424697\pi\) | |||||||
\(338\) | 8.92976 | 0.485715 | ||||||||
\(339\) | −4.02962 | −0.218859 | ||||||||
\(340\) | 3.84531 | 0.208541 | ||||||||
\(341\) | −29.8397 | −1.61591 | ||||||||
\(342\) | −9.25022 | −0.500194 | ||||||||
\(343\) | 7.99681 | 0.431787 | ||||||||
\(344\) | −13.5954 | −0.733016 | ||||||||
\(345\) | −0.111184 | −0.00598595 | ||||||||
\(346\) | −14.7660 | −0.793826 | ||||||||
\(347\) | −25.4085 | −1.36400 | −0.681999 | − | 0.731353i | \(-0.738889\pi\) | ||||
−0.681999 | + | 0.731353i | \(0.738889\pi\) | |||||||
\(348\) | −0.302123 | −0.0161955 | ||||||||
\(349\) | 35.5541 | 1.90317 | 0.951584 | − | 0.307388i | \(-0.0994549\pi\) | ||||
0.951584 | + | 0.307388i | \(0.0994549\pi\) | |||||||
\(350\) | 0.675601 | 0.0361124 | ||||||||
\(351\) | 2.29360 | 0.122423 | ||||||||
\(352\) | 16.3132 | 0.869497 | ||||||||
\(353\) | 24.6714 | 1.31312 | 0.656562 | − | 0.754272i | \(-0.272010\pi\) | ||||
0.656562 | + | 0.754272i | \(0.272010\pi\) | |||||||
\(354\) | 2.65592 | 0.141160 | ||||||||
\(355\) | −4.94094 | −0.262238 | ||||||||
\(356\) | −6.74425 | −0.357445 | ||||||||
\(357\) | 3.36696 | 0.178198 | ||||||||
\(358\) | 4.09569 | 0.216464 | ||||||||
\(359\) | 12.4951 | 0.659467 | 0.329734 | − | 0.944074i | \(-0.393041\pi\) | ||||
0.329734 | + | 0.944074i | \(0.393041\pi\) | |||||||
\(360\) | 3.07920 | 0.162288 | ||||||||
\(361\) | 45.2743 | 2.38286 | ||||||||
\(362\) | −13.6266 | −0.716201 | ||||||||
\(363\) | 9.50758 | 0.499019 | ||||||||
\(364\) | 0.898102 | 0.0470733 | ||||||||
\(365\) | 2.47973 | 0.129795 | ||||||||
\(366\) | 0.439412 | 0.0229684 | ||||||||
\(367\) | 19.2503 | 1.00486 | 0.502429 | − | 0.864618i | \(-0.332440\pi\) | ||||
0.502429 | + | 0.864618i | \(0.332440\pi\) | |||||||
\(368\) | 0.246311 | 0.0128398 | ||||||||
\(369\) | −5.70975 | −0.297238 | ||||||||
\(370\) | −4.92785 | −0.256187 | ||||||||
\(371\) | 4.46884 | 0.232010 | ||||||||
\(372\) | −4.40644 | −0.228463 | ||||||||
\(373\) | 8.52274 | 0.441291 | 0.220645 | − | 0.975354i | \(-0.429184\pi\) | ||||
0.220645 | + | 0.975354i | \(0.429184\pi\) | |||||||
\(374\) | −30.0449 | −1.55359 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 35.5798 | 1.83489 | ||||||||
\(377\) | 1.03622 | 0.0533681 | ||||||||
\(378\) | 0.675601 | 0.0347492 | ||||||||
\(379\) | 15.1043 | 0.775857 | 0.387928 | − | 0.921690i | \(-0.373191\pi\) | ||||
0.387928 | + | 0.921690i | \(0.373191\pi\) | |||||||
\(380\) | −5.36128 | −0.275028 | ||||||||
\(381\) | −5.17311 | −0.265027 | ||||||||
\(382\) | −4.27290 | −0.218620 | ||||||||
\(383\) | 0.392713 | 0.0200667 | 0.0100334 | − | 0.999950i | \(-0.496806\pi\) | ||||
0.0100334 | + | 0.999950i | \(0.496806\pi\) | |||||||
\(384\) | −2.70318 | −0.137946 | ||||||||
\(385\) | 2.65164 | 0.135140 | ||||||||
\(386\) | 9.57666 | 0.487439 | ||||||||
\(387\) | −4.41525 | −0.224440 | ||||||||
\(388\) | −4.15869 | −0.211126 | ||||||||
\(389\) | 16.2969 | 0.826285 | 0.413142 | − | 0.910666i | \(-0.364431\pi\) | ||||
0.413142 | + | 0.910666i | \(0.364431\pi\) | |||||||
\(390\) | −2.64638 | −0.134004 | ||||||||
\(391\) | 0.639328 | 0.0323322 | ||||||||
\(392\) | −20.4987 | −1.03534 | ||||||||
\(393\) | −20.4426 | −1.03119 | ||||||||
\(394\) | 8.22242 | 0.414239 | ||||||||
\(395\) | 9.89835 | 0.498040 | ||||||||
\(396\) | 3.02836 | 0.152181 | ||||||||
\(397\) | 5.91260 | 0.296745 | 0.148372 | − | 0.988932i | \(-0.452597\pi\) | ||||
0.148372 | + | 0.988932i | \(0.452597\pi\) | |||||||
\(398\) | 5.69125 | 0.285276 | ||||||||
\(399\) | −4.69435 | −0.235012 | ||||||||
\(400\) | −2.21534 | −0.110767 | ||||||||
\(401\) | 1.00000 | 0.0499376 | ||||||||
\(402\) | 6.02776 | 0.300637 | ||||||||
\(403\) | 15.1132 | 0.752842 | ||||||||
\(404\) | −9.39090 | −0.467215 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0.305228 | 0.0151482 | ||||||||
\(407\) | −19.3411 | −0.958704 | ||||||||
\(408\) | −17.7059 | −0.876574 | ||||||||
\(409\) | 23.4879 | 1.16140 | 0.580701 | − | 0.814117i | \(-0.302779\pi\) | ||||
0.580701 | + | 0.814117i | \(0.302779\pi\) | |||||||
\(410\) | 6.58795 | 0.325356 | ||||||||
\(411\) | 0.511628 | 0.0252368 | ||||||||
\(412\) | −1.77311 | −0.0873550 | ||||||||
\(413\) | 1.34784 | 0.0663229 | ||||||||
\(414\) | 0.128285 | 0.00630486 | ||||||||
\(415\) | −0.690336 | −0.0338872 | ||||||||
\(416\) | −8.26229 | −0.405092 | ||||||||
\(417\) | 2.48764 | 0.121820 | ||||||||
\(418\) | 41.8899 | 2.04890 | ||||||||
\(419\) | 15.6109 | 0.762644 | 0.381322 | − | 0.924442i | \(-0.375469\pi\) | ||||
0.381322 | + | 0.924442i | \(0.375469\pi\) | |||||||
\(420\) | 0.391568 | 0.0191066 | ||||||||
\(421\) | 24.1760 | 1.17826 | 0.589132 | − | 0.808037i | \(-0.299470\pi\) | ||||
0.589132 | + | 0.808037i | \(0.299470\pi\) | |||||||
\(422\) | −0.938797 | −0.0456999 | ||||||||
\(423\) | 11.5549 | 0.561819 | ||||||||
\(424\) | −23.5004 | −1.14128 | ||||||||
\(425\) | −5.75017 | −0.278924 | ||||||||
\(426\) | 5.70089 | 0.276209 | ||||||||
\(427\) | 0.222995 | 0.0107915 | ||||||||
\(428\) | −11.8497 | −0.572779 | ||||||||
\(429\) | −10.3867 | −0.501472 | ||||||||
\(430\) | 5.09435 | 0.245671 | ||||||||
\(431\) | 20.3572 | 0.980574 | 0.490287 | − | 0.871561i | \(-0.336892\pi\) | ||||
0.490287 | + | 0.871561i | \(0.336892\pi\) | |||||||
\(432\) | −2.21534 | −0.106586 | ||||||||
\(433\) | 23.9356 | 1.15027 | 0.575137 | − | 0.818057i | \(-0.304949\pi\) | ||||
0.575137 | + | 0.818057i | \(0.304949\pi\) | |||||||
\(434\) | 4.45172 | 0.213690 | ||||||||
\(435\) | 0.451788 | 0.0216616 | ||||||||
\(436\) | 0.282354 | 0.0135223 | ||||||||
\(437\) | −0.891377 | −0.0426403 | ||||||||
\(438\) | −2.86114 | −0.136710 | ||||||||
\(439\) | 7.73444 | 0.369145 | 0.184572 | − | 0.982819i | \(-0.440910\pi\) | ||||
0.184572 | + | 0.982819i | \(0.440910\pi\) | |||||||
\(440\) | −13.9442 | −0.664766 | ||||||||
\(441\) | −6.65714 | −0.317007 | ||||||||
\(442\) | 15.2171 | 0.723805 | ||||||||
\(443\) | 16.6113 | 0.789228 | 0.394614 | − | 0.918847i | \(-0.370878\pi\) | ||||
0.394614 | + | 0.918847i | \(0.370878\pi\) | |||||||
\(444\) | −2.85611 | −0.135545 | ||||||||
\(445\) | 10.0852 | 0.478083 | ||||||||
\(446\) | −6.61650 | −0.313300 | ||||||||
\(447\) | −0.965363 | −0.0456601 | ||||||||
\(448\) | −5.02808 | −0.237554 | ||||||||
\(449\) | 13.2741 | 0.626444 | 0.313222 | − | 0.949680i | \(-0.398592\pi\) | ||||
0.313222 | + | 0.949680i | \(0.398592\pi\) | |||||||
\(450\) | −1.15381 | −0.0543910 | ||||||||
\(451\) | 25.8568 | 1.21755 | ||||||||
\(452\) | 2.69473 | 0.126749 | ||||||||
\(453\) | 12.9020 | 0.606190 | ||||||||
\(454\) | −1.83641 | −0.0861872 | ||||||||
\(455\) | −1.34300 | −0.0629607 | ||||||||
\(456\) | 24.6863 | 1.15604 | ||||||||
\(457\) | 8.89548 | 0.416113 | 0.208057 | − | 0.978117i | \(-0.433286\pi\) | ||||
0.208057 | + | 0.978117i | \(0.433286\pi\) | |||||||
\(458\) | 10.7552 | 0.502558 | ||||||||
\(459\) | −5.75017 | −0.268395 | ||||||||
\(460\) | 0.0743520 | 0.00346668 | ||||||||
\(461\) | 34.3555 | 1.60009 | 0.800047 | − | 0.599937i | \(-0.204808\pi\) | ||||
0.800047 | + | 0.599937i | \(0.204808\pi\) | |||||||
\(462\) | −3.05948 | −0.142340 | ||||||||
\(463\) | 0.0155481 | 0.000722584 0 | 0.000361292 | − | 1.00000i | \(-0.499885\pi\) | ||||
0.000361292 | 1.00000i | \(0.499885\pi\) | ||||||||
\(464\) | −1.00086 | −0.0464640 | ||||||||
\(465\) | 6.58928 | 0.305570 | ||||||||
\(466\) | 10.9105 | 0.505418 | ||||||||
\(467\) | −30.5186 | −1.41223 | −0.706117 | − | 0.708095i | \(-0.749555\pi\) | ||||
−0.706117 | + | 0.708095i | \(0.749555\pi\) | |||||||
\(468\) | −1.53380 | −0.0708999 | ||||||||
\(469\) | 3.05900 | 0.141251 | ||||||||
\(470\) | −13.3321 | −0.614965 | ||||||||
\(471\) | 6.36673 | 0.293363 | ||||||||
\(472\) | −7.08792 | −0.326248 | ||||||||
\(473\) | 19.9946 | 0.919352 | ||||||||
\(474\) | −11.4208 | −0.524574 | ||||||||
\(475\) | 8.01713 | 0.367851 | ||||||||
\(476\) | −2.25158 | −0.103201 | ||||||||
\(477\) | −7.63198 | −0.349444 | ||||||||
\(478\) | −23.2530 | −1.06357 | ||||||||
\(479\) | −11.7810 | −0.538289 | −0.269144 | − | 0.963100i | \(-0.586741\pi\) | ||||
−0.269144 | + | 0.963100i | \(0.586741\pi\) | |||||||
\(480\) | −3.60232 | −0.164423 | ||||||||
\(481\) | 9.79587 | 0.446653 | ||||||||
\(482\) | −5.33165 | −0.242850 | ||||||||
\(483\) | 0.0651028 | 0.00296228 | ||||||||
\(484\) | −6.35799 | −0.289000 | ||||||||
\(485\) | 6.21880 | 0.282381 | ||||||||
\(486\) | −1.15381 | −0.0523378 | ||||||||
\(487\) | −22.6242 | −1.02520 | −0.512600 | − | 0.858627i | \(-0.671318\pi\) | ||||
−0.512600 | + | 0.858627i | \(0.671318\pi\) | |||||||
\(488\) | −1.17267 | −0.0530843 | ||||||||
\(489\) | 11.0789 | 0.501006 | ||||||||
\(490\) | 7.68106 | 0.346995 | ||||||||
\(491\) | −33.6142 | −1.51699 | −0.758493 | − | 0.651681i | \(-0.774064\pi\) | ||||
−0.758493 | + | 0.651681i | \(0.774064\pi\) | |||||||
\(492\) | 3.81828 | 0.172141 | ||||||||
\(493\) | −2.59786 | −0.117002 | ||||||||
\(494\) | −21.2163 | −0.954568 | ||||||||
\(495\) | −4.52853 | −0.203542 | ||||||||
\(496\) | −14.5975 | −0.655448 | ||||||||
\(497\) | 2.89312 | 0.129774 | ||||||||
\(498\) | 0.796514 | 0.0356927 | ||||||||
\(499\) | −37.7163 | −1.68841 | −0.844206 | − | 0.536018i | \(-0.819928\pi\) | ||||
−0.844206 | + | 0.536018i | \(0.819928\pi\) | |||||||
\(500\) | −0.668729 | −0.0299065 | ||||||||
\(501\) | 20.0478 | 0.895669 | ||||||||
\(502\) | 6.39201 | 0.285290 | ||||||||
\(503\) | −42.2420 | −1.88348 | −0.941739 | − | 0.336345i | \(-0.890809\pi\) | ||||
−0.941739 | + | 0.336345i | \(0.890809\pi\) | |||||||
\(504\) | −1.80300 | −0.0803118 | ||||||||
\(505\) | 14.0429 | 0.624901 | ||||||||
\(506\) | −0.580942 | −0.0258260 | ||||||||
\(507\) | −7.73938 | −0.343718 | ||||||||
\(508\) | 3.45941 | 0.153486 | ||||||||
\(509\) | −4.17164 | −0.184905 | −0.0924524 | − | 0.995717i | \(-0.529471\pi\) | ||||
−0.0924524 | + | 0.995717i | \(0.529471\pi\) | |||||||
\(510\) | 6.63459 | 0.293785 | ||||||||
\(511\) | −1.45199 | −0.0642321 | ||||||||
\(512\) | 21.6233 | 0.955626 | ||||||||
\(513\) | 8.01713 | 0.353965 | ||||||||
\(514\) | 16.8271 | 0.742210 | ||||||||
\(515\) | 2.65147 | 0.116838 | ||||||||
\(516\) | 2.95260 | 0.129981 | ||||||||
\(517\) | −52.3267 | −2.30133 | ||||||||
\(518\) | 2.88546 | 0.126780 | ||||||||
\(519\) | 12.7976 | 0.561754 | ||||||||
\(520\) | 7.06246 | 0.309709 | ||||||||
\(521\) | 40.3841 | 1.76926 | 0.884629 | − | 0.466296i | \(-0.154412\pi\) | ||||
0.884629 | + | 0.466296i | \(0.154412\pi\) | |||||||
\(522\) | −0.521276 | −0.0228156 | ||||||||
\(523\) | −29.7150 | −1.29934 | −0.649672 | − | 0.760215i | \(-0.725094\pi\) | ||||
−0.649672 | + | 0.760215i | \(0.725094\pi\) | |||||||
\(524\) | 13.6706 | 0.597201 | ||||||||
\(525\) | −0.585541 | −0.0255551 | ||||||||
\(526\) | −12.2814 | −0.535495 | ||||||||
\(527\) | −37.8895 | −1.65049 | ||||||||
\(528\) | 10.0322 | 0.436598 | ||||||||
\(529\) | −22.9876 | −0.999463 | ||||||||
\(530\) | 8.80584 | 0.382501 | ||||||||
\(531\) | −2.30187 | −0.0998928 | ||||||||
\(532\) | 3.13925 | 0.136104 | ||||||||
\(533\) | −13.0959 | −0.567247 | ||||||||
\(534\) | −11.6364 | −0.503554 | ||||||||
\(535\) | 17.7198 | 0.766093 | ||||||||
\(536\) | −16.0864 | −0.694829 | ||||||||
\(537\) | −3.54972 | −0.153182 | ||||||||
\(538\) | 2.96136 | 0.127673 | ||||||||
\(539\) | 30.1471 | 1.29853 | ||||||||
\(540\) | −0.668729 | −0.0287775 | ||||||||
\(541\) | 9.61051 | 0.413188 | 0.206594 | − | 0.978427i | \(-0.433762\pi\) | ||||
0.206594 | + | 0.978427i | \(0.433762\pi\) | |||||||
\(542\) | −9.39149 | −0.403399 | ||||||||
\(543\) | 11.8102 | 0.506822 | ||||||||
\(544\) | 20.7140 | 0.888103 | ||||||||
\(545\) | −0.422225 | −0.0180861 | ||||||||
\(546\) | 1.54956 | 0.0663151 | ||||||||
\(547\) | 19.6757 | 0.841273 | 0.420637 | − | 0.907229i | \(-0.361807\pi\) | ||||
0.420637 | + | 0.907229i | \(0.361807\pi\) | |||||||
\(548\) | −0.342141 | −0.0146155 | ||||||||
\(549\) | −0.380836 | −0.0162537 | ||||||||
\(550\) | 5.22505 | 0.222797 | ||||||||
\(551\) | 3.62204 | 0.154304 | ||||||||
\(552\) | −0.342358 | −0.0145717 | ||||||||
\(553\) | −5.79589 | −0.246466 | ||||||||
\(554\) | 13.2047 | 0.561013 | ||||||||
\(555\) | 4.27095 | 0.181292 | ||||||||
\(556\) | −1.66356 | −0.0705506 | ||||||||
\(557\) | 25.0002 | 1.05929 | 0.529647 | − | 0.848218i | \(-0.322324\pi\) | ||||
0.529647 | + | 0.848218i | \(0.322324\pi\) | |||||||
\(558\) | −7.60276 | −0.321850 | ||||||||
\(559\) | −10.1268 | −0.428319 | ||||||||
\(560\) | 1.29717 | 0.0548156 | ||||||||
\(561\) | 26.0398 | 1.09940 | ||||||||
\(562\) | −5.40306 | −0.227915 | ||||||||
\(563\) | −38.8731 | −1.63831 | −0.819153 | − | 0.573576i | \(-0.805556\pi\) | ||||
−0.819153 | + | 0.573576i | \(0.805556\pi\) | |||||||
\(564\) | −7.72710 | −0.325370 | ||||||||
\(565\) | −4.02962 | −0.169528 | ||||||||
\(566\) | −11.6372 | −0.489150 | ||||||||
\(567\) | −0.585541 | −0.0245904 | ||||||||
\(568\) | −15.2141 | −0.638371 | ||||||||
\(569\) | −20.2483 | −0.848854 | −0.424427 | − | 0.905462i | \(-0.639524\pi\) | ||||
−0.424427 | + | 0.905462i | \(0.639524\pi\) | |||||||
\(570\) | −9.25022 | −0.387449 | ||||||||
\(571\) | 27.5922 | 1.15470 | 0.577349 | − | 0.816498i | \(-0.304087\pi\) | ||||
0.577349 | + | 0.816498i | \(0.304087\pi\) | |||||||
\(572\) | 6.94585 | 0.290421 | ||||||||
\(573\) | 3.70330 | 0.154708 | ||||||||
\(574\) | −3.85752 | −0.161010 | ||||||||
\(575\) | −0.111184 | −0.00463670 | ||||||||
\(576\) | 8.58707 | 0.357794 | ||||||||
\(577\) | −37.9292 | −1.57901 | −0.789506 | − | 0.613742i | \(-0.789663\pi\) | ||||
−0.789506 | + | 0.613742i | \(0.789663\pi\) | |||||||
\(578\) | −18.5353 | −0.770968 | ||||||||
\(579\) | −8.30005 | −0.344938 | ||||||||
\(580\) | −0.302123 | −0.0125450 | ||||||||
\(581\) | 0.404220 | 0.0167699 | ||||||||
\(582\) | −7.17530 | −0.297426 | ||||||||
\(583\) | 34.5617 | 1.43140 | ||||||||
\(584\) | 7.63559 | 0.315963 | ||||||||
\(585\) | 2.29360 | 0.0948288 | ||||||||
\(586\) | −4.21487 | −0.174115 | ||||||||
\(587\) | 14.7558 | 0.609037 | 0.304519 | − | 0.952506i | \(-0.401504\pi\) | ||||
0.304519 | + | 0.952506i | \(0.401504\pi\) | |||||||
\(588\) | 4.45182 | 0.183590 | ||||||||
\(589\) | 52.8271 | 2.17670 | ||||||||
\(590\) | 2.65592 | 0.109342 | ||||||||
\(591\) | −7.12634 | −0.293138 | ||||||||
\(592\) | −9.46162 | −0.388870 | ||||||||
\(593\) | −1.34965 | −0.0554233 | −0.0277117 | − | 0.999616i | \(-0.508822\pi\) | ||||
−0.0277117 | + | 0.999616i | \(0.508822\pi\) | |||||||
\(594\) | 5.22505 | 0.214386 | ||||||||
\(595\) | 3.36696 | 0.138032 | ||||||||
\(596\) | 0.645566 | 0.0264434 | ||||||||
\(597\) | −4.93258 | −0.201877 | ||||||||
\(598\) | 0.294235 | 0.0120322 | ||||||||
\(599\) | 25.4987 | 1.04185 | 0.520924 | − | 0.853603i | \(-0.325588\pi\) | ||||
0.520924 | + | 0.853603i | \(0.325588\pi\) | |||||||
\(600\) | 3.07920 | 0.125708 | ||||||||
\(601\) | −4.09437 | −0.167013 | −0.0835065 | − | 0.996507i | \(-0.526612\pi\) | ||||
−0.0835065 | + | 0.996507i | \(0.526612\pi\) | |||||||
\(602\) | −2.98295 | −0.121576 | ||||||||
\(603\) | −5.22423 | −0.212747 | ||||||||
\(604\) | −8.62796 | −0.351067 | ||||||||
\(605\) | 9.50758 | 0.386538 | ||||||||
\(606\) | −16.2028 | −0.658194 | ||||||||
\(607\) | 32.2467 | 1.30885 | 0.654427 | − | 0.756125i | \(-0.272910\pi\) | ||||
0.654427 | + | 0.756125i | \(0.272910\pi\) | |||||||
\(608\) | −28.8802 | −1.17125 | ||||||||
\(609\) | −0.264540 | −0.0107197 | ||||||||
\(610\) | 0.439412 | 0.0177913 | ||||||||
\(611\) | 26.5024 | 1.07217 | ||||||||
\(612\) | 3.84531 | 0.155437 | ||||||||
\(613\) | −2.55559 | −0.103219 | −0.0516097 | − | 0.998667i | \(-0.516435\pi\) | ||||
−0.0516097 | + | 0.998667i | \(0.516435\pi\) | |||||||
\(614\) | 34.0848 | 1.37555 | ||||||||
\(615\) | −5.70975 | −0.230239 | ||||||||
\(616\) | 8.16492 | 0.328974 | ||||||||
\(617\) | −12.8155 | −0.515932 | −0.257966 | − | 0.966154i | \(-0.583052\pi\) | ||||
−0.257966 | + | 0.966154i | \(0.583052\pi\) | |||||||
\(618\) | −3.05928 | −0.123062 | ||||||||
\(619\) | −11.6120 | −0.466724 | −0.233362 | − | 0.972390i | \(-0.574973\pi\) | ||||
−0.233362 | + | 0.972390i | \(0.574973\pi\) | |||||||
\(620\) | −4.40644 | −0.176967 | ||||||||
\(621\) | −0.111184 | −0.00446166 | ||||||||
\(622\) | 19.9960 | 0.801766 | ||||||||
\(623\) | −5.90528 | −0.236590 | ||||||||
\(624\) | −5.08112 | −0.203408 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −21.3591 | −0.853680 | ||||||||
\(627\) | −36.3058 | −1.44991 | ||||||||
\(628\) | −4.25761 | −0.169897 | ||||||||
\(629\) | −24.5587 | −0.979220 | ||||||||
\(630\) | 0.675601 | 0.0269166 | ||||||||
\(631\) | −4.69142 | −0.186762 | −0.0933812 | − | 0.995630i | \(-0.529768\pi\) | ||||
−0.0933812 | + | 0.995630i | \(0.529768\pi\) | |||||||
\(632\) | 30.4790 | 1.21239 | ||||||||
\(633\) | 0.813652 | 0.0323398 | ||||||||
\(634\) | −34.9829 | −1.38935 | ||||||||
\(635\) | −5.17311 | −0.205289 | ||||||||
\(636\) | 5.10373 | 0.202376 | ||||||||
\(637\) | −15.2688 | −0.604974 | ||||||||
\(638\) | 2.36061 | 0.0934576 | ||||||||
\(639\) | −4.94094 | −0.195460 | ||||||||
\(640\) | −2.70318 | −0.106853 | ||||||||
\(641\) | −50.1953 | −1.98259 | −0.991297 | − | 0.131641i | \(-0.957975\pi\) | ||||
−0.991297 | + | 0.131641i | \(0.957975\pi\) | |||||||
\(642\) | −20.4452 | −0.806908 | ||||||||
\(643\) | −32.1702 | −1.26867 | −0.634335 | − | 0.773059i | \(-0.718726\pi\) | ||||
−0.634335 | + | 0.773059i | \(0.718726\pi\) | |||||||
\(644\) | −0.0435361 | −0.00171556 | ||||||||
\(645\) | −4.41525 | −0.173850 | ||||||||
\(646\) | 53.1904 | 2.09275 | ||||||||
\(647\) | 16.7150 | 0.657134 | 0.328567 | − | 0.944481i | \(-0.393434\pi\) | ||||
0.328567 | + | 0.944481i | \(0.393434\pi\) | |||||||
\(648\) | 3.07920 | 0.120962 | ||||||||
\(649\) | 10.4241 | 0.409182 | ||||||||
\(650\) | −2.64638 | −0.103799 | ||||||||
\(651\) | −3.85829 | −0.151218 | ||||||||
\(652\) | −7.40879 | −0.290150 | ||||||||
\(653\) | 22.7786 | 0.891397 | 0.445699 | − | 0.895183i | \(-0.352955\pi\) | ||||
0.445699 | + | 0.895183i | \(0.352955\pi\) | |||||||
\(654\) | 0.487166 | 0.0190497 | ||||||||
\(655\) | −20.4426 | −0.798759 | ||||||||
\(656\) | 12.6491 | 0.493863 | ||||||||
\(657\) | 2.47973 | 0.0967437 | ||||||||
\(658\) | 7.80651 | 0.304329 | ||||||||
\(659\) | 29.4504 | 1.14722 | 0.573612 | − | 0.819127i | \(-0.305542\pi\) | ||||
0.573612 | + | 0.819127i | \(0.305542\pi\) | |||||||
\(660\) | 3.02836 | 0.117879 | ||||||||
\(661\) | 47.1516 | 1.83398 | 0.916992 | − | 0.398905i | \(-0.130610\pi\) | ||||
0.916992 | + | 0.398905i | \(0.130610\pi\) | |||||||
\(662\) | −12.9995 | −0.505241 | ||||||||
\(663\) | −13.1886 | −0.512203 | ||||||||
\(664\) | −2.12568 | −0.0824924 | ||||||||
\(665\) | −4.69435 | −0.182039 | ||||||||
\(666\) | −4.92785 | −0.190950 | ||||||||
\(667\) | −0.0502316 | −0.00194497 | ||||||||
\(668\) | −13.4065 | −0.518715 | ||||||||
\(669\) | 5.73449 | 0.221708 | ||||||||
\(670\) | 6.02776 | 0.232872 | ||||||||
\(671\) | 1.72463 | 0.0665786 | ||||||||
\(672\) | 2.10930 | 0.0813682 | ||||||||
\(673\) | 0.871872 | 0.0336082 | 0.0168041 | − | 0.999859i | \(-0.494651\pi\) | ||||
0.0168041 | + | 0.999859i | \(0.494651\pi\) | |||||||
\(674\) | −9.92850 | −0.382432 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 5.17555 | 0.199060 | ||||||||
\(677\) | 10.0481 | 0.386178 | 0.193089 | − | 0.981181i | \(-0.438149\pi\) | ||||
0.193089 | + | 0.981181i | \(0.438149\pi\) | |||||||
\(678\) | 4.64941 | 0.178560 | ||||||||
\(679\) | −3.64136 | −0.139743 | ||||||||
\(680\) | −17.7059 | −0.678991 | ||||||||
\(681\) | 1.59161 | 0.0609908 | ||||||||
\(682\) | 34.4293 | 1.31837 | ||||||||
\(683\) | −29.1797 | −1.11653 | −0.558266 | − | 0.829662i | \(-0.688533\pi\) | ||||
−0.558266 | + | 0.829662i | \(0.688533\pi\) | |||||||
\(684\) | −5.36128 | −0.204994 | ||||||||
\(685\) | 0.511628 | 0.0195483 | ||||||||
\(686\) | −9.22678 | −0.352280 | ||||||||
\(687\) | −9.32150 | −0.355637 | ||||||||
\(688\) | 9.78129 | 0.372908 | ||||||||
\(689\) | −17.5047 | −0.666877 | ||||||||
\(690\) | 0.128285 | 0.00488373 | ||||||||
\(691\) | 45.0891 | 1.71527 | 0.857636 | − | 0.514257i | \(-0.171932\pi\) | ||||
0.857636 | + | 0.514257i | \(0.171932\pi\) | |||||||
\(692\) | −8.55816 | −0.325332 | ||||||||
\(693\) | 2.65164 | 0.100727 | ||||||||
\(694\) | 29.3165 | 1.11284 | ||||||||
\(695\) | 2.48764 | 0.0943616 | ||||||||
\(696\) | 1.39114 | 0.0527312 | ||||||||
\(697\) | 32.8321 | 1.24360 | ||||||||
\(698\) | −41.0226 | −1.55273 | ||||||||
\(699\) | −9.45607 | −0.357661 | ||||||||
\(700\) | 0.391568 | 0.0147999 | ||||||||
\(701\) | −13.8257 | −0.522191 | −0.261096 | − | 0.965313i | \(-0.584084\pi\) | ||||
−0.261096 | + | 0.965313i | \(0.584084\pi\) | |||||||
\(702\) | −2.64638 | −0.0998810 | ||||||||
\(703\) | 34.2407 | 1.29141 | ||||||||
\(704\) | −38.8868 | −1.46560 | ||||||||
\(705\) | 11.5549 | 0.435183 | ||||||||
\(706\) | −28.4660 | −1.07133 | ||||||||
\(707\) | −8.22269 | −0.309246 | ||||||||
\(708\) | 1.53933 | 0.0578515 | ||||||||
\(709\) | 20.2589 | 0.760840 | 0.380420 | − | 0.924814i | \(-0.375779\pi\) | ||||
0.380420 | + | 0.924814i | \(0.375779\pi\) | |||||||
\(710\) | 5.70089 | 0.213951 | ||||||||
\(711\) | 9.89835 | 0.371217 | ||||||||
\(712\) | 31.0543 | 1.16381 | ||||||||
\(713\) | −0.732623 | −0.0274369 | ||||||||
\(714\) | −3.88482 | −0.145386 | ||||||||
\(715\) | −10.3867 | −0.388439 | ||||||||
\(716\) | 2.37380 | 0.0887130 | ||||||||
\(717\) | 20.1533 | 0.752638 | ||||||||
\(718\) | −14.4170 | −0.538036 | ||||||||
\(719\) | 5.36666 | 0.200143 | 0.100071 | − | 0.994980i | \(-0.468093\pi\) | ||||
0.100071 | + | 0.994980i | \(0.468093\pi\) | |||||||
\(720\) | −2.21534 | −0.0825610 | ||||||||
\(721\) | −1.55254 | −0.0578197 | ||||||||
\(722\) | −52.2378 | −1.94409 | ||||||||
\(723\) | 4.62092 | 0.171854 | ||||||||
\(724\) | −7.89780 | −0.293519 | ||||||||
\(725\) | 0.451788 | 0.0167790 | ||||||||
\(726\) | −10.9699 | −0.407132 | ||||||||
\(727\) | −21.3002 | −0.789980 | −0.394990 | − | 0.918685i | \(-0.629252\pi\) | ||||
−0.394990 | + | 0.918685i | \(0.629252\pi\) | |||||||
\(728\) | −4.13536 | −0.153267 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −2.86114 | −0.105895 | ||||||||
\(731\) | 25.3884 | 0.939025 | ||||||||
\(732\) | 0.254676 | 0.00941311 | ||||||||
\(733\) | −44.5891 | −1.64694 | −0.823468 | − | 0.567363i | \(-0.807964\pi\) | ||||
−0.823468 | + | 0.567363i | \(0.807964\pi\) | |||||||
\(734\) | −22.2111 | −0.819828 | ||||||||
\(735\) | −6.65714 | −0.245552 | ||||||||
\(736\) | 0.400520 | 0.0147634 | ||||||||
\(737\) | 23.6581 | 0.871457 | ||||||||
\(738\) | 6.58795 | 0.242506 | ||||||||
\(739\) | 39.0951 | 1.43814 | 0.719069 | − | 0.694939i | \(-0.244569\pi\) | ||||
0.719069 | + | 0.694939i | \(0.244569\pi\) | |||||||
\(740\) | −2.85611 | −0.104993 | ||||||||
\(741\) | 18.3881 | 0.675504 | ||||||||
\(742\) | −5.15618 | −0.189289 | ||||||||
\(743\) | 51.2621 | 1.88062 | 0.940312 | − | 0.340312i | \(-0.110533\pi\) | ||||
0.940312 | + | 0.340312i | \(0.110533\pi\) | |||||||
\(744\) | 20.2897 | 0.743856 | ||||||||
\(745\) | −0.965363 | −0.0353682 | ||||||||
\(746\) | −9.83360 | −0.360034 | ||||||||
\(747\) | −0.690336 | −0.0252581 | ||||||||
\(748\) | −17.4136 | −0.636704 | ||||||||
\(749\) | −10.3757 | −0.379118 | ||||||||
\(750\) | −1.15381 | −0.0421311 | ||||||||
\(751\) | 47.4027 | 1.72975 | 0.864875 | − | 0.501987i | \(-0.167398\pi\) | ||||
0.864875 | + | 0.501987i | \(0.167398\pi\) | |||||||
\(752\) | −25.5981 | −0.933466 | ||||||||
\(753\) | −5.53993 | −0.201886 | ||||||||
\(754\) | −1.19560 | −0.0435412 | ||||||||
\(755\) | 12.9020 | 0.469553 | ||||||||
\(756\) | 0.391568 | 0.0142412 | ||||||||
\(757\) | 3.94111 | 0.143242 | 0.0716210 | − | 0.997432i | \(-0.477183\pi\) | ||||
0.0716210 | + | 0.997432i | \(0.477183\pi\) | |||||||
\(758\) | −17.4275 | −0.632994 | ||||||||
\(759\) | 0.503500 | 0.0182759 | ||||||||
\(760\) | 24.6863 | 0.895467 | ||||||||
\(761\) | 3.48957 | 0.126497 | 0.0632483 | − | 0.997998i | \(-0.479854\pi\) | ||||
0.0632483 | + | 0.997998i | \(0.479854\pi\) | |||||||
\(762\) | 5.96877 | 0.216226 | ||||||||
\(763\) | 0.247230 | 0.00895032 | ||||||||
\(764\) | −2.47650 | −0.0895968 | ||||||||
\(765\) | −5.75017 | −0.207898 | ||||||||
\(766\) | −0.453115 | −0.0163717 | ||||||||
\(767\) | −5.27958 | −0.190635 | ||||||||
\(768\) | −14.0552 | −0.507173 | ||||||||
\(769\) | 31.9581 | 1.15244 | 0.576220 | − | 0.817295i | \(-0.304527\pi\) | ||||
0.576220 | + | 0.817295i | \(0.304527\pi\) | |||||||
\(770\) | −3.05948 | −0.110256 | ||||||||
\(771\) | −14.5839 | −0.525228 | ||||||||
\(772\) | 5.55048 | 0.199766 | ||||||||
\(773\) | 0.979761 | 0.0352395 | 0.0176198 | − | 0.999845i | \(-0.494391\pi\) | ||||
0.0176198 | + | 0.999845i | \(0.494391\pi\) | |||||||
\(774\) | 5.09435 | 0.183112 | ||||||||
\(775\) | 6.58928 | 0.236694 | ||||||||
\(776\) | 19.1489 | 0.687406 | ||||||||
\(777\) | −2.50082 | −0.0897162 | ||||||||
\(778\) | −18.8035 | −0.674137 | ||||||||
\(779\) | −45.7758 | −1.64009 | ||||||||
\(780\) | −1.53380 | −0.0549188 | ||||||||
\(781\) | 22.3752 | 0.800647 | ||||||||
\(782\) | −0.737661 | −0.0263787 | ||||||||
\(783\) | 0.451788 | 0.0161456 | ||||||||
\(784\) | 14.7479 | 0.526709 | ||||||||
\(785\) | 6.36673 | 0.227238 | ||||||||
\(786\) | 23.5868 | 0.841314 | ||||||||
\(787\) | 6.17071 | 0.219962 | 0.109981 | − | 0.993934i | \(-0.464921\pi\) | ||||
0.109981 | + | 0.993934i | \(0.464921\pi\) | |||||||
\(788\) | 4.76559 | 0.169767 | ||||||||
\(789\) | 10.6443 | 0.378946 | ||||||||
\(790\) | −11.4208 | −0.406333 | ||||||||
\(791\) | 2.35951 | 0.0838945 | ||||||||
\(792\) | −13.9442 | −0.495487 | ||||||||
\(793\) | −0.873488 | −0.0310185 | ||||||||
\(794\) | −6.82200 | −0.242104 | ||||||||
\(795\) | −7.63198 | −0.270679 | ||||||||
\(796\) | 3.29856 | 0.116914 | ||||||||
\(797\) | −30.4071 | −1.07708 | −0.538538 | − | 0.842601i | \(-0.681023\pi\) | ||||
−0.538538 | + | 0.842601i | \(0.681023\pi\) | |||||||
\(798\) | 5.41638 | 0.191738 | ||||||||
\(799\) | −66.4427 | −2.35057 | ||||||||
\(800\) | −3.60232 | −0.127361 | ||||||||
\(801\) | 10.0852 | 0.356342 | ||||||||
\(802\) | −1.15381 | −0.0407423 | ||||||||
\(803\) | −11.2296 | −0.396282 | ||||||||
\(804\) | 3.49359 | 0.123210 | ||||||||
\(805\) | 0.0651028 | 0.00229457 | ||||||||
\(806\) | −17.4377 | −0.614217 | ||||||||
\(807\) | −2.56660 | −0.0903485 | ||||||||
\(808\) | 43.2409 | 1.52121 | ||||||||
\(809\) | −28.5602 | −1.00412 | −0.502061 | − | 0.864832i | \(-0.667425\pi\) | ||||
−0.502061 | + | 0.864832i | \(0.667425\pi\) | |||||||
\(810\) | −1.15381 | −0.0405407 | ||||||||
\(811\) | −32.7101 | −1.14861 | −0.574303 | − | 0.818643i | \(-0.694727\pi\) | ||||
−0.574303 | + | 0.818643i | \(0.694727\pi\) | |||||||
\(812\) | 0.176906 | 0.00620817 | ||||||||
\(813\) | 8.13957 | 0.285467 | ||||||||
\(814\) | 22.3159 | 0.782173 | ||||||||
\(815\) | 11.0789 | 0.388077 | ||||||||
\(816\) | 12.7386 | 0.445941 | ||||||||
\(817\) | −35.3976 | −1.23841 | ||||||||
\(818\) | −27.1005 | −0.947547 | ||||||||
\(819\) | −1.34300 | −0.0469282 | ||||||||
\(820\) | 3.81828 | 0.133340 | ||||||||
\(821\) | 28.3050 | 0.987850 | 0.493925 | − | 0.869504i | \(-0.335562\pi\) | ||||
0.493925 | + | 0.869504i | \(0.335562\pi\) | |||||||
\(822\) | −0.590320 | −0.0205898 | ||||||||
\(823\) | −28.3389 | −0.987831 | −0.493916 | − | 0.869510i | \(-0.664435\pi\) | ||||
−0.493916 | + | 0.869510i | \(0.664435\pi\) | |||||||
\(824\) | 8.16439 | 0.284420 | ||||||||
\(825\) | −4.52853 | −0.157663 | ||||||||
\(826\) | −1.55515 | −0.0541105 | ||||||||
\(827\) | 31.3840 | 1.09133 | 0.545664 | − | 0.838004i | \(-0.316277\pi\) | ||||
0.545664 | + | 0.838004i | \(0.316277\pi\) | |||||||
\(828\) | 0.0743520 | 0.00258391 | ||||||||
\(829\) | −13.7544 | −0.477709 | −0.238855 | − | 0.971055i | \(-0.576772\pi\) | ||||
−0.238855 | + | 0.971055i | \(0.576772\pi\) | |||||||
\(830\) | 0.796514 | 0.0276474 | ||||||||
\(831\) | −11.4444 | −0.397003 | ||||||||
\(832\) | 19.6953 | 0.682813 | ||||||||
\(833\) | 38.2797 | 1.32631 | ||||||||
\(834\) | −2.87026 | −0.0993889 | ||||||||
\(835\) | 20.0478 | 0.693782 | ||||||||
\(836\) | 24.2787 | 0.839698 | ||||||||
\(837\) | 6.58928 | 0.227759 | ||||||||
\(838\) | −18.0120 | −0.622215 | ||||||||
\(839\) | −35.5686 | −1.22796 | −0.613982 | − | 0.789320i | \(-0.710433\pi\) | ||||
−0.613982 | + | 0.789320i | \(0.710433\pi\) | |||||||
\(840\) | −1.80300 | −0.0622093 | ||||||||
\(841\) | −28.7959 | −0.992962 | ||||||||
\(842\) | −27.8944 | −0.961305 | ||||||||
\(843\) | 4.68281 | 0.161285 | ||||||||
\(844\) | −0.544112 | −0.0187291 | ||||||||
\(845\) | −7.73938 | −0.266243 | ||||||||
\(846\) | −13.3321 | −0.458368 | ||||||||
\(847\) | −5.56708 | −0.191287 | ||||||||
\(848\) | 16.9075 | 0.580605 | ||||||||
\(849\) | 10.0859 | 0.346149 | ||||||||
\(850\) | 6.63459 | 0.227565 | ||||||||
\(851\) | −0.474862 | −0.0162780 | ||||||||
\(852\) | 3.30415 | 0.113198 | ||||||||
\(853\) | 27.8730 | 0.954354 | 0.477177 | − | 0.878807i | \(-0.341660\pi\) | ||||
0.477177 | + | 0.878807i | \(0.341660\pi\) | |||||||
\(854\) | −0.257293 | −0.00880440 | ||||||||
\(855\) | 8.01713 | 0.274180 | ||||||||
\(856\) | 54.5627 | 1.86492 | ||||||||
\(857\) | 6.16853 | 0.210713 | 0.105357 | − | 0.994435i | \(-0.466402\pi\) | ||||
0.105357 | + | 0.994435i | \(0.466402\pi\) | |||||||
\(858\) | 11.9842 | 0.409134 | ||||||||
\(859\) | 29.6674 | 1.01224 | 0.506119 | − | 0.862464i | \(-0.331080\pi\) | ||||
0.506119 | + | 0.862464i | \(0.331080\pi\) | |||||||
\(860\) | 2.95260 | 0.100683 | ||||||||
\(861\) | 3.34329 | 0.113939 | ||||||||
\(862\) | −23.4883 | −0.800016 | ||||||||
\(863\) | −41.5697 | −1.41505 | −0.707524 | − | 0.706690i | \(-0.750188\pi\) | ||||
−0.707524 | + | 0.706690i | \(0.750188\pi\) | |||||||
\(864\) | −3.60232 | −0.122553 | ||||||||
\(865\) | 12.7976 | 0.435133 | ||||||||
\(866\) | −27.6171 | −0.938468 | ||||||||
\(867\) | 16.0645 | 0.545579 | ||||||||
\(868\) | 2.58015 | 0.0875760 | ||||||||
\(869\) | −44.8250 | −1.52058 | ||||||||
\(870\) | −0.521276 | −0.0176729 | ||||||||
\(871\) | −11.9823 | −0.406005 | ||||||||
\(872\) | −1.30011 | −0.0440274 | ||||||||
\(873\) | 6.21880 | 0.210475 | ||||||||
\(874\) | 1.02848 | 0.0347888 | ||||||||
\(875\) | −0.585541 | −0.0197949 | ||||||||
\(876\) | −1.65827 | −0.0560278 | ||||||||
\(877\) | 38.8425 | 1.31162 | 0.655809 | − | 0.754927i | \(-0.272328\pi\) | ||||
0.655809 | + | 0.754927i | \(0.272328\pi\) | |||||||
\(878\) | −8.92405 | −0.301172 | ||||||||
\(879\) | 3.65301 | 0.123213 | ||||||||
\(880\) | 10.0322 | 0.338187 | ||||||||
\(881\) | −0.856594 | −0.0288594 | −0.0144297 | − | 0.999896i | \(-0.504593\pi\) | ||||
−0.0144297 | + | 0.999896i | \(0.504593\pi\) | |||||||
\(882\) | 7.68106 | 0.258635 | ||||||||
\(883\) | −45.1384 | −1.51903 | −0.759514 | − | 0.650491i | \(-0.774563\pi\) | ||||
−0.759514 | + | 0.650491i | \(0.774563\pi\) | |||||||
\(884\) | 8.81961 | 0.296636 | ||||||||
\(885\) | −2.30187 | −0.0773766 | ||||||||
\(886\) | −19.1663 | −0.643903 | ||||||||
\(887\) | −57.5734 | −1.93312 | −0.966562 | − | 0.256431i | \(-0.917453\pi\) | ||||
−0.966562 | + | 0.256431i | \(0.917453\pi\) | |||||||
\(888\) | 13.1511 | 0.441322 | ||||||||
\(889\) | 3.02907 | 0.101592 | ||||||||
\(890\) | −11.6364 | −0.390052 | ||||||||
\(891\) | −4.52853 | −0.151711 | ||||||||
\(892\) | −3.83482 | −0.128399 | ||||||||
\(893\) | 92.6371 | 3.09998 | ||||||||
\(894\) | 1.11384 | 0.0372525 | ||||||||
\(895\) | −3.54972 | −0.118654 | ||||||||
\(896\) | 1.58282 | 0.0528785 | ||||||||
\(897\) | −0.255012 | −0.00851461 | ||||||||
\(898\) | −15.3158 | −0.511094 | ||||||||
\(899\) | 2.97695 | 0.0992870 | ||||||||
\(900\) | −0.668729 | −0.0222910 | ||||||||
\(901\) | 43.8852 | 1.46203 | ||||||||
\(902\) | −29.8337 | −0.993355 | ||||||||
\(903\) | 2.58531 | 0.0860337 | ||||||||
\(904\) | −12.4080 | −0.412684 | ||||||||
\(905\) | 11.8102 | 0.392583 | ||||||||
\(906\) | −14.8865 | −0.494569 | ||||||||
\(907\) | −41.0445 | −1.36286 | −0.681430 | − | 0.731883i | \(-0.738642\pi\) | ||||
−0.681430 | + | 0.731883i | \(0.738642\pi\) | |||||||
\(908\) | −1.06436 | −0.0353220 | ||||||||
\(909\) | 14.0429 | 0.465774 | ||||||||
\(910\) | 1.54956 | 0.0513674 | ||||||||
\(911\) | 23.3628 | 0.774043 | 0.387022 | − | 0.922071i | \(-0.373504\pi\) | ||||
0.387022 | + | 0.922071i | \(0.373504\pi\) | |||||||
\(912\) | −17.7607 | −0.588115 | ||||||||
\(913\) | 3.12620 | 0.103462 | ||||||||
\(914\) | −10.2637 | −0.339492 | ||||||||
\(915\) | −0.380836 | −0.0125901 | ||||||||
\(916\) | 6.23356 | 0.205962 | ||||||||
\(917\) | 11.9700 | 0.395283 | ||||||||
\(918\) | 6.63459 | 0.218974 | ||||||||
\(919\) | −28.4370 | −0.938052 | −0.469026 | − | 0.883184i | \(-0.655395\pi\) | ||||
−0.469026 | + | 0.883184i | \(0.655395\pi\) | |||||||
\(920\) | −0.342358 | −0.0112872 | ||||||||
\(921\) | −29.5411 | −0.973413 | ||||||||
\(922\) | −39.6396 | −1.30546 | ||||||||
\(923\) | −11.3325 | −0.373015 | ||||||||
\(924\) | −1.77323 | −0.0583349 | ||||||||
\(925\) | 4.27095 | 0.140428 | ||||||||
\(926\) | −0.0179396 | −0.000589531 0 | ||||||||
\(927\) | 2.65147 | 0.0870856 | ||||||||
\(928\) | −1.62748 | −0.0534247 | ||||||||
\(929\) | 20.4839 | 0.672053 | 0.336027 | − | 0.941852i | \(-0.390917\pi\) | ||||
0.336027 | + | 0.941852i | \(0.390917\pi\) | |||||||
\(930\) | −7.60276 | −0.249304 | ||||||||
\(931\) | −53.3711 | −1.74917 | ||||||||
\(932\) | 6.32355 | 0.207135 | ||||||||
\(933\) | −17.3304 | −0.567373 | ||||||||
\(934\) | 35.2126 | 1.15219 | ||||||||
\(935\) | 26.0398 | 0.851593 | ||||||||
\(936\) | 7.06246 | 0.230844 | ||||||||
\(937\) | 31.2757 | 1.02173 | 0.510867 | − | 0.859660i | \(-0.329325\pi\) | ||||
0.510867 | + | 0.859660i | \(0.329325\pi\) | |||||||
\(938\) | −3.52950 | −0.115242 | ||||||||
\(939\) | 18.5118 | 0.604110 | ||||||||
\(940\) | −7.72710 | −0.252030 | ||||||||
\(941\) | 18.8485 | 0.614443 | 0.307222 | − | 0.951638i | \(-0.400601\pi\) | ||||
0.307222 | + | 0.951638i | \(0.400601\pi\) | |||||||
\(942\) | −7.34597 | −0.239345 | ||||||||
\(943\) | 0.634834 | 0.0206730 | ||||||||
\(944\) | 5.09944 | 0.165973 | ||||||||
\(945\) | −0.585541 | −0.0190476 | ||||||||
\(946\) | −23.0699 | −0.750067 | ||||||||
\(947\) | 6.73143 | 0.218742 | 0.109371 | − | 0.994001i | \(-0.465116\pi\) | ||||
0.109371 | + | 0.994001i | \(0.465116\pi\) | |||||||
\(948\) | −6.61931 | −0.214985 | ||||||||
\(949\) | 5.68753 | 0.184625 | ||||||||
\(950\) | −9.25022 | −0.300117 | ||||||||
\(951\) | 30.3195 | 0.983177 | ||||||||
\(952\) | 10.3675 | 0.336014 | ||||||||
\(953\) | −35.5943 | −1.15301 | −0.576507 | − | 0.817093i | \(-0.695584\pi\) | ||||
−0.576507 | + | 0.817093i | \(0.695584\pi\) | |||||||
\(954\) | 8.80584 | 0.285099 | ||||||||
\(955\) | 3.70330 | 0.119836 | ||||||||
\(956\) | −13.4771 | −0.435880 | ||||||||
\(957\) | −2.04593 | −0.0661356 | ||||||||
\(958\) | 13.5930 | 0.439171 | ||||||||
\(959\) | −0.299579 | −0.00967392 | ||||||||
\(960\) | 8.58707 | 0.277146 | ||||||||
\(961\) | 12.4186 | 0.400600 | ||||||||
\(962\) | −11.3025 | −0.364409 | ||||||||
\(963\) | 17.7198 | 0.571012 | ||||||||
\(964\) | −3.09014 | −0.0995267 | ||||||||
\(965\) | −8.30005 | −0.267188 | ||||||||
\(966\) | −0.0751161 | −0.00241682 | ||||||||
\(967\) | 6.38906 | 0.205458 | 0.102729 | − | 0.994709i | \(-0.467242\pi\) | ||||
0.102729 | + | 0.994709i | \(0.467242\pi\) | |||||||
\(968\) | 29.2757 | 0.940958 | ||||||||
\(969\) | −46.0999 | −1.48094 | ||||||||
\(970\) | −7.17530 | −0.230385 | ||||||||
\(971\) | −13.1586 | −0.422280 | −0.211140 | − | 0.977456i | \(-0.567718\pi\) | ||||
−0.211140 | + | 0.977456i | \(0.567718\pi\) | |||||||
\(972\) | −0.668729 | −0.0214495 | ||||||||
\(973\) | −1.45662 | −0.0466969 | ||||||||
\(974\) | 26.1040 | 0.836425 | ||||||||
\(975\) | 2.29360 | 0.0734541 | ||||||||
\(976\) | 0.843683 | 0.0270056 | ||||||||
\(977\) | 41.8395 | 1.33857 | 0.669283 | − | 0.743008i | \(-0.266601\pi\) | ||||
0.669283 | + | 0.743008i | \(0.266601\pi\) | |||||||
\(978\) | −12.7829 | −0.408753 | ||||||||
\(979\) | −45.6710 | −1.45965 | ||||||||
\(980\) | 4.45182 | 0.142208 | ||||||||
\(981\) | −0.422225 | −0.0134806 | ||||||||
\(982\) | 38.7843 | 1.23766 | ||||||||
\(983\) | 46.6131 | 1.48673 | 0.743363 | − | 0.668888i | \(-0.233230\pi\) | ||||
0.743363 | + | 0.668888i | \(0.233230\pi\) | |||||||
\(984\) | −17.5815 | −0.560477 | ||||||||
\(985\) | −7.12634 | −0.227064 | ||||||||
\(986\) | 2.99743 | 0.0954575 | ||||||||
\(987\) | −6.76587 | −0.215360 | ||||||||
\(988\) | −12.2967 | −0.391209 | ||||||||
\(989\) | 0.490905 | 0.0156099 | ||||||||
\(990\) | 5.22505 | 0.166063 | ||||||||
\(991\) | −24.1322 | −0.766583 | −0.383292 | − | 0.923627i | \(-0.625210\pi\) | ||||
−0.383292 | + | 0.923627i | \(0.625210\pi\) | |||||||
\(992\) | −23.7367 | −0.753640 | ||||||||
\(993\) | 11.2666 | 0.357536 | ||||||||
\(994\) | −3.33810 | −0.105878 | ||||||||
\(995\) | −4.93258 | −0.156373 | ||||||||
\(996\) | 0.461647 | 0.0146279 | ||||||||
\(997\) | 24.6331 | 0.780137 | 0.390069 | − | 0.920786i | \(-0.372451\pi\) | ||||
0.390069 | + | 0.920786i | \(0.372451\pi\) | |||||||
\(998\) | 43.5173 | 1.37752 | ||||||||
\(999\) | 4.27095 | 0.135127 |
(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 | 6015.2.a.i.1.15 | ✓ | 43 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6015.2.a.i.1.15 | ✓ | 43 | 1.1 | even | 1 | trivial |