Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,4,Mod(1,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("966.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.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: | \(56.9958450655\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.65101.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 28x - 29 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.08080\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 966.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −13.6703 | −1.22270 | −0.611352 | − | 0.791359i | \(-0.709374\pi\) | ||||
−0.611352 | + | 0.791359i | \(0.709374\pi\) | |||||||
\(6\) | −6.00000 | −0.408248 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −27.3405 | −0.864583 | ||||||||
\(11\) | −2.24894 | −0.0616438 | −0.0308219 | − | 0.999525i | \(-0.509812\pi\) | ||||
−0.0308219 | + | 0.999525i | \(0.509812\pi\) | |||||||
\(12\) | −12.0000 | −0.288675 | ||||||||
\(13\) | 45.7445 | 0.975942 | 0.487971 | − | 0.872860i | \(-0.337737\pi\) | ||||
0.487971 | + | 0.872860i | \(0.337737\pi\) | |||||||
\(14\) | −14.0000 | −0.267261 | ||||||||
\(15\) | 41.0108 | 0.705929 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 4.13496 | 0.0589927 | 0.0294964 | − | 0.999565i | \(-0.490610\pi\) | ||||
0.0294964 | + | 0.999565i | \(0.490610\pi\) | |||||||
\(18\) | 18.0000 | 0.235702 | ||||||||
\(19\) | 133.113 | 1.60728 | 0.803638 | − | 0.595119i | \(-0.202895\pi\) | ||||
0.803638 | + | 0.595119i | \(0.202895\pi\) | |||||||
\(20\) | −54.6810 | −0.611352 | ||||||||
\(21\) | 21.0000 | 0.218218 | ||||||||
\(22\) | −4.49789 | −0.0435888 | ||||||||
\(23\) | −23.0000 | −0.208514 | ||||||||
\(24\) | −24.0000 | −0.204124 | ||||||||
\(25\) | 61.8758 | 0.495006 | ||||||||
\(26\) | 91.4891 | 0.690095 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −28.0000 | −0.188982 | ||||||||
\(29\) | −197.341 | −1.26363 | −0.631816 | − | 0.775119i | \(-0.717690\pi\) | ||||
−0.631816 | + | 0.775119i | \(0.717690\pi\) | |||||||
\(30\) | 82.0215 | 0.499167 | ||||||||
\(31\) | 116.520 | 0.675084 | 0.337542 | − | 0.941311i | \(-0.390405\pi\) | ||||
0.337542 | + | 0.941311i | \(0.390405\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 6.74683 | 0.0355901 | ||||||||
\(34\) | 8.26993 | 0.0417141 | ||||||||
\(35\) | 95.6918 | 0.462139 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | 54.4321 | 0.241853 | 0.120927 | − | 0.992661i | \(-0.461413\pi\) | ||||
0.120927 | + | 0.992661i | \(0.461413\pi\) | |||||||
\(38\) | 266.226 | 1.13652 | ||||||||
\(39\) | −137.234 | −0.563461 | ||||||||
\(40\) | −109.362 | −0.432291 | ||||||||
\(41\) | −234.204 | −0.892111 | −0.446055 | − | 0.895005i | \(-0.647172\pi\) | ||||
−0.446055 | + | 0.895005i | \(0.647172\pi\) | |||||||
\(42\) | 42.0000 | 0.154303 | ||||||||
\(43\) | −266.216 | −0.944130 | −0.472065 | − | 0.881564i | \(-0.656491\pi\) | ||||
−0.472065 | + | 0.881564i | \(0.656491\pi\) | |||||||
\(44\) | −8.99577 | −0.0308219 | ||||||||
\(45\) | −123.032 | −0.407568 | ||||||||
\(46\) | −46.0000 | −0.147442 | ||||||||
\(47\) | −341.707 | −1.06049 | −0.530245 | − | 0.847844i | \(-0.677900\pi\) | ||||
−0.530245 | + | 0.847844i | \(0.677900\pi\) | |||||||
\(48\) | −48.0000 | −0.144338 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 123.752 | 0.350022 | ||||||||
\(51\) | −12.4049 | −0.0340595 | ||||||||
\(52\) | 182.978 | 0.487971 | ||||||||
\(53\) | 114.614 | 0.297046 | 0.148523 | − | 0.988909i | \(-0.452548\pi\) | ||||
0.148523 | + | 0.988909i | \(0.452548\pi\) | |||||||
\(54\) | −54.0000 | −0.136083 | ||||||||
\(55\) | 30.7436 | 0.0753722 | ||||||||
\(56\) | −56.0000 | −0.133631 | ||||||||
\(57\) | −399.339 | −0.927961 | ||||||||
\(58\) | −394.682 | −0.893522 | ||||||||
\(59\) | −292.868 | −0.646240 | −0.323120 | − | 0.946358i | \(-0.604732\pi\) | ||||
−0.323120 | + | 0.946358i | \(0.604732\pi\) | |||||||
\(60\) | 164.043 | 0.352964 | ||||||||
\(61\) | −648.641 | −1.36148 | −0.680738 | − | 0.732527i | \(-0.738341\pi\) | ||||
−0.680738 | + | 0.732527i | \(0.738341\pi\) | |||||||
\(62\) | 233.040 | 0.477356 | ||||||||
\(63\) | −63.0000 | −0.125988 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −625.339 | −1.19329 | ||||||||
\(66\) | 13.4937 | 0.0251660 | ||||||||
\(67\) | −329.305 | −0.600463 | −0.300231 | − | 0.953866i | \(-0.597064\pi\) | ||||
−0.300231 | + | 0.953866i | \(0.597064\pi\) | |||||||
\(68\) | 16.5399 | 0.0294964 | ||||||||
\(69\) | 69.0000 | 0.120386 | ||||||||
\(70\) | 191.384 | 0.326782 | ||||||||
\(71\) | −57.5035 | −0.0961185 | −0.0480592 | − | 0.998844i | \(-0.515304\pi\) | ||||
−0.0480592 | + | 0.998844i | \(0.515304\pi\) | |||||||
\(72\) | 72.0000 | 0.117851 | ||||||||
\(73\) | −536.143 | −0.859599 | −0.429800 | − | 0.902924i | \(-0.641416\pi\) | ||||
−0.429800 | + | 0.902924i | \(0.641416\pi\) | |||||||
\(74\) | 108.864 | 0.171016 | ||||||||
\(75\) | −185.627 | −0.285792 | ||||||||
\(76\) | 532.452 | 0.803638 | ||||||||
\(77\) | 15.7426 | 0.0232992 | ||||||||
\(78\) | −274.467 | −0.398427 | ||||||||
\(79\) | −245.033 | −0.348966 | −0.174483 | − | 0.984660i | \(-0.555825\pi\) | ||||
−0.174483 | + | 0.984660i | \(0.555825\pi\) | |||||||
\(80\) | −218.724 | −0.305676 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −468.408 | −0.630817 | ||||||||
\(83\) | 481.992 | 0.637416 | 0.318708 | − | 0.947853i | \(-0.396751\pi\) | ||||
0.318708 | + | 0.947853i | \(0.396751\pi\) | |||||||
\(84\) | 84.0000 | 0.109109 | ||||||||
\(85\) | −56.5260 | −0.0721307 | ||||||||
\(86\) | −532.433 | −0.667601 | ||||||||
\(87\) | 592.023 | 0.729558 | ||||||||
\(88\) | −17.9915 | −0.0217944 | ||||||||
\(89\) | 750.007 | 0.893265 | 0.446632 | − | 0.894718i | \(-0.352623\pi\) | ||||
0.446632 | + | 0.894718i | \(0.352623\pi\) | |||||||
\(90\) | −246.065 | −0.288194 | ||||||||
\(91\) | −320.212 | −0.368871 | ||||||||
\(92\) | −92.0000 | −0.104257 | ||||||||
\(93\) | −349.560 | −0.389760 | ||||||||
\(94\) | −683.413 | −0.749880 | ||||||||
\(95\) | −1819.69 | −1.96522 | ||||||||
\(96\) | −96.0000 | −0.102062 | ||||||||
\(97\) | 1258.45 | 1.31729 | 0.658643 | − | 0.752456i | \(-0.271131\pi\) | ||||
0.658643 | + | 0.752456i | \(0.271131\pi\) | |||||||
\(98\) | 98.0000 | 0.101015 | ||||||||
\(99\) | −20.2405 | −0.0205479 | ||||||||
\(100\) | 247.503 | 0.247503 | ||||||||
\(101\) | −187.049 | −0.184278 | −0.0921390 | − | 0.995746i | \(-0.529370\pi\) | ||||
−0.0921390 | + | 0.995746i | \(0.529370\pi\) | |||||||
\(102\) | −24.8098 | −0.0240837 | ||||||||
\(103\) | −23.0657 | −0.0220653 | −0.0110327 | − | 0.999939i | \(-0.503512\pi\) | ||||
−0.0110327 | + | 0.999939i | \(0.503512\pi\) | |||||||
\(104\) | 365.956 | 0.345048 | ||||||||
\(105\) | −287.075 | −0.266816 | ||||||||
\(106\) | 229.228 | 0.210043 | ||||||||
\(107\) | −2038.20 | −1.84150 | −0.920748 | − | 0.390158i | \(-0.872420\pi\) | ||||
−0.920748 | + | 0.390158i | \(0.872420\pi\) | |||||||
\(108\) | −108.000 | −0.0962250 | ||||||||
\(109\) | −1090.83 | −0.958559 | −0.479280 | − | 0.877662i | \(-0.659102\pi\) | ||||
−0.479280 | + | 0.877662i | \(0.659102\pi\) | |||||||
\(110\) | 61.4872 | 0.0532962 | ||||||||
\(111\) | −163.296 | −0.139634 | ||||||||
\(112\) | −112.000 | −0.0944911 | ||||||||
\(113\) | −2043.44 | −1.70116 | −0.850580 | − | 0.525846i | \(-0.823749\pi\) | ||||
−0.850580 | + | 0.525846i | \(0.823749\pi\) | |||||||
\(114\) | −798.678 | −0.656167 | ||||||||
\(115\) | 314.416 | 0.254952 | ||||||||
\(116\) | −789.364 | −0.631816 | ||||||||
\(117\) | 411.701 | 0.325314 | ||||||||
\(118\) | −585.736 | −0.456961 | ||||||||
\(119\) | −28.9447 | −0.0222971 | ||||||||
\(120\) | 328.086 | 0.249584 | ||||||||
\(121\) | −1325.94 | −0.996200 | ||||||||
\(122\) | −1297.28 | −0.962709 | ||||||||
\(123\) | 702.612 | 0.515060 | ||||||||
\(124\) | 466.080 | 0.337542 | ||||||||
\(125\) | 862.924 | 0.617458 | ||||||||
\(126\) | −126.000 | −0.0890871 | ||||||||
\(127\) | 2696.86 | 1.88431 | 0.942154 | − | 0.335179i | \(-0.108797\pi\) | ||||
0.942154 | + | 0.335179i | \(0.108797\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 798.649 | 0.545094 | ||||||||
\(130\) | −1250.68 | −0.843783 | ||||||||
\(131\) | −243.606 | −0.162473 | −0.0812366 | − | 0.996695i | \(-0.525887\pi\) | ||||
−0.0812366 | + | 0.996695i | \(0.525887\pi\) | |||||||
\(132\) | 26.9873 | 0.0177950 | ||||||||
\(133\) | −931.792 | −0.607493 | ||||||||
\(134\) | −658.610 | −0.424591 | ||||||||
\(135\) | 369.097 | 0.235310 | ||||||||
\(136\) | 33.0797 | 0.0208571 | ||||||||
\(137\) | 42.4481 | 0.0264714 | 0.0132357 | − | 0.999912i | \(-0.495787\pi\) | ||||
0.0132357 | + | 0.999912i | \(0.495787\pi\) | |||||||
\(138\) | 138.000 | 0.0851257 | ||||||||
\(139\) | −190.134 | −0.116021 | −0.0580106 | − | 0.998316i | \(-0.518476\pi\) | ||||
−0.0580106 | + | 0.998316i | \(0.518476\pi\) | |||||||
\(140\) | 382.767 | 0.231069 | ||||||||
\(141\) | 1025.12 | 0.612274 | ||||||||
\(142\) | −115.007 | −0.0679660 | ||||||||
\(143\) | −102.877 | −0.0601608 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | 2697.70 | 1.54505 | ||||||||
\(146\) | −1072.29 | −0.607829 | ||||||||
\(147\) | −147.000 | −0.0824786 | ||||||||
\(148\) | 217.728 | 0.120927 | ||||||||
\(149\) | −743.917 | −0.409020 | −0.204510 | − | 0.978864i | \(-0.565560\pi\) | ||||
−0.204510 | + | 0.978864i | \(0.565560\pi\) | |||||||
\(150\) | −371.255 | −0.202085 | ||||||||
\(151\) | −843.472 | −0.454575 | −0.227287 | − | 0.973828i | \(-0.572986\pi\) | ||||
−0.227287 | + | 0.973828i | \(0.572986\pi\) | |||||||
\(152\) | 1064.90 | 0.568258 | ||||||||
\(153\) | 37.2147 | 0.0196642 | ||||||||
\(154\) | 31.4852 | 0.0164750 | ||||||||
\(155\) | −1592.86 | −0.825428 | ||||||||
\(156\) | −548.934 | −0.281730 | ||||||||
\(157\) | 800.908 | 0.407130 | 0.203565 | − | 0.979061i | \(-0.434747\pi\) | ||||
0.203565 | + | 0.979061i | \(0.434747\pi\) | |||||||
\(158\) | −490.065 | −0.246756 | ||||||||
\(159\) | −343.841 | −0.171499 | ||||||||
\(160\) | −437.448 | −0.216146 | ||||||||
\(161\) | 161.000 | 0.0788110 | ||||||||
\(162\) | 162.000 | 0.0785674 | ||||||||
\(163\) | −2882.00 | −1.38488 | −0.692442 | − | 0.721474i | \(-0.743465\pi\) | ||||
−0.692442 | + | 0.721474i | \(0.743465\pi\) | |||||||
\(164\) | −936.816 | −0.446055 | ||||||||
\(165\) | −92.2309 | −0.0435161 | ||||||||
\(166\) | 963.985 | 0.450721 | ||||||||
\(167\) | −1920.92 | −0.890092 | −0.445046 | − | 0.895508i | \(-0.646813\pi\) | ||||
−0.445046 | + | 0.895508i | \(0.646813\pi\) | |||||||
\(168\) | 168.000 | 0.0771517 | ||||||||
\(169\) | −104.438 | −0.0475367 | ||||||||
\(170\) | −113.052 | −0.0510041 | ||||||||
\(171\) | 1198.02 | 0.535758 | ||||||||
\(172\) | −1064.87 | −0.472065 | ||||||||
\(173\) | 1054.30 | 0.463336 | 0.231668 | − | 0.972795i | \(-0.425582\pi\) | ||||
0.231668 | + | 0.972795i | \(0.425582\pi\) | |||||||
\(174\) | 1184.05 | 0.515875 | ||||||||
\(175\) | −433.131 | −0.187095 | ||||||||
\(176\) | −35.9831 | −0.0154110 | ||||||||
\(177\) | 878.604 | 0.373107 | ||||||||
\(178\) | 1500.01 | 0.631634 | ||||||||
\(179\) | 1791.12 | 0.747903 | 0.373952 | − | 0.927448i | \(-0.378003\pi\) | ||||
0.373952 | + | 0.927448i | \(0.378003\pi\) | |||||||
\(180\) | −492.129 | −0.203784 | ||||||||
\(181\) | 2257.56 | 0.927088 | 0.463544 | − | 0.886074i | \(-0.346578\pi\) | ||||
0.463544 | + | 0.886074i | \(0.346578\pi\) | |||||||
\(182\) | −640.423 | −0.260832 | ||||||||
\(183\) | 1945.92 | 0.786048 | ||||||||
\(184\) | −184.000 | −0.0737210 | ||||||||
\(185\) | −744.100 | −0.295715 | ||||||||
\(186\) | −699.120 | −0.275602 | ||||||||
\(187\) | −9.29930 | −0.00363654 | ||||||||
\(188\) | −1366.83 | −0.530245 | ||||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | −3639.38 | −1.38962 | ||||||||
\(191\) | −1959.08 | −0.742166 | −0.371083 | − | 0.928600i | \(-0.621014\pi\) | ||||
−0.371083 | + | 0.928600i | \(0.621014\pi\) | |||||||
\(192\) | −192.000 | −0.0721688 | ||||||||
\(193\) | 597.599 | 0.222882 | 0.111441 | − | 0.993771i | \(-0.464453\pi\) | ||||
0.111441 | + | 0.993771i | \(0.464453\pi\) | |||||||
\(194\) | 2516.91 | 0.931461 | ||||||||
\(195\) | 1876.02 | 0.688946 | ||||||||
\(196\) | 196.000 | 0.0714286 | ||||||||
\(197\) | 577.779 | 0.208960 | 0.104480 | − | 0.994527i | \(-0.466682\pi\) | ||||
0.104480 | + | 0.994527i | \(0.466682\pi\) | |||||||
\(198\) | −40.4810 | −0.0145296 | ||||||||
\(199\) | 750.244 | 0.267253 | 0.133627 | − | 0.991032i | \(-0.457338\pi\) | ||||
0.133627 | + | 0.991032i | \(0.457338\pi\) | |||||||
\(200\) | 495.006 | 0.175011 | ||||||||
\(201\) | 987.915 | 0.346677 | ||||||||
\(202\) | −374.098 | −0.130304 | ||||||||
\(203\) | 1381.39 | 0.477608 | ||||||||
\(204\) | −49.6196 | −0.0170297 | ||||||||
\(205\) | 3201.63 | 1.09079 | ||||||||
\(206\) | −46.1313 | −0.0156025 | ||||||||
\(207\) | −207.000 | −0.0695048 | ||||||||
\(208\) | 731.912 | 0.243986 | ||||||||
\(209\) | −299.364 | −0.0990786 | ||||||||
\(210\) | −574.151 | −0.188667 | ||||||||
\(211\) | −2101.72 | −0.685726 | −0.342863 | − | 0.939385i | \(-0.611397\pi\) | ||||
−0.342863 | + | 0.939385i | \(0.611397\pi\) | |||||||
\(212\) | 458.455 | 0.148523 | ||||||||
\(213\) | 172.511 | 0.0554940 | ||||||||
\(214\) | −4076.40 | −1.30213 | ||||||||
\(215\) | 3639.24 | 1.15439 | ||||||||
\(216\) | −216.000 | −0.0680414 | ||||||||
\(217\) | −815.639 | −0.255158 | ||||||||
\(218\) | −2181.67 | −0.677804 | ||||||||
\(219\) | 1608.43 | 0.496290 | ||||||||
\(220\) | 122.974 | 0.0376861 | ||||||||
\(221\) | 189.152 | 0.0575735 | ||||||||
\(222\) | −326.592 | −0.0987362 | ||||||||
\(223\) | 717.403 | 0.215430 | 0.107715 | − | 0.994182i | \(-0.465647\pi\) | ||||
0.107715 | + | 0.994182i | \(0.465647\pi\) | |||||||
\(224\) | −224.000 | −0.0668153 | ||||||||
\(225\) | 556.882 | 0.165002 | ||||||||
\(226\) | −4086.89 | −1.20290 | ||||||||
\(227\) | −2998.37 | −0.876689 | −0.438345 | − | 0.898807i | \(-0.644435\pi\) | ||||
−0.438345 | + | 0.898807i | \(0.644435\pi\) | |||||||
\(228\) | −1597.36 | −0.463980 | ||||||||
\(229\) | −4217.18 | −1.21694 | −0.608470 | − | 0.793577i | \(-0.708217\pi\) | ||||
−0.608470 | + | 0.793577i | \(0.708217\pi\) | |||||||
\(230\) | 628.832 | 0.180278 | ||||||||
\(231\) | −47.2278 | −0.0134518 | ||||||||
\(232\) | −1578.73 | −0.446761 | ||||||||
\(233\) | −5781.45 | −1.62556 | −0.812779 | − | 0.582572i | \(-0.802047\pi\) | ||||
−0.812779 | + | 0.582572i | \(0.802047\pi\) | |||||||
\(234\) | 823.401 | 0.230032 | ||||||||
\(235\) | 4671.22 | 1.29667 | ||||||||
\(236\) | −1171.47 | −0.323120 | ||||||||
\(237\) | 735.098 | 0.201476 | ||||||||
\(238\) | −57.8895 | −0.0157665 | ||||||||
\(239\) | −1880.38 | −0.508920 | −0.254460 | − | 0.967083i | \(-0.581898\pi\) | ||||
−0.254460 | + | 0.967083i | \(0.581898\pi\) | |||||||
\(240\) | 656.172 | 0.176482 | ||||||||
\(241\) | −3640.87 | −0.973149 | −0.486575 | − | 0.873639i | \(-0.661754\pi\) | ||||
−0.486575 | + | 0.873639i | \(0.661754\pi\) | |||||||
\(242\) | −2651.88 | −0.704420 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −2594.57 | −0.680738 | ||||||||
\(245\) | −669.842 | −0.174672 | ||||||||
\(246\) | 1405.22 | 0.364203 | ||||||||
\(247\) | 6089.19 | 1.56861 | ||||||||
\(248\) | 932.159 | 0.238678 | ||||||||
\(249\) | −1445.98 | −0.368012 | ||||||||
\(250\) | 1725.85 | 0.436609 | ||||||||
\(251\) | 3732.87 | 0.938711 | 0.469355 | − | 0.883009i | \(-0.344486\pi\) | ||||
0.469355 | + | 0.883009i | \(0.344486\pi\) | |||||||
\(252\) | −252.000 | −0.0629941 | ||||||||
\(253\) | 51.7257 | 0.0128536 | ||||||||
\(254\) | 5393.71 | 1.33241 | ||||||||
\(255\) | 169.578 | 0.0416447 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 5136.35 | 1.24668 | 0.623339 | − | 0.781951i | \(-0.285776\pi\) | ||||
0.623339 | + | 0.781951i | \(0.285776\pi\) | |||||||
\(258\) | 1597.30 | 0.385440 | ||||||||
\(259\) | −381.024 | −0.0914120 | ||||||||
\(260\) | −2501.36 | −0.596644 | ||||||||
\(261\) | −1776.07 | −0.421210 | ||||||||
\(262\) | −487.213 | −0.114886 | ||||||||
\(263\) | 2813.09 | 0.659554 | 0.329777 | − | 0.944059i | \(-0.393026\pi\) | ||||
0.329777 | + | 0.944059i | \(0.393026\pi\) | |||||||
\(264\) | 53.9746 | 0.0125830 | ||||||||
\(265\) | −1566.80 | −0.363199 | ||||||||
\(266\) | −1863.58 | −0.429562 | ||||||||
\(267\) | −2250.02 | −0.515727 | ||||||||
\(268\) | −1317.22 | −0.300231 | ||||||||
\(269\) | 4514.17 | 1.02317 | 0.511587 | − | 0.859232i | \(-0.329058\pi\) | ||||
0.511587 | + | 0.859232i | \(0.329058\pi\) | |||||||
\(270\) | 738.194 | 0.166389 | ||||||||
\(271\) | −7839.12 | −1.75717 | −0.878584 | − | 0.477588i | \(-0.841511\pi\) | ||||
−0.878584 | + | 0.477588i | \(0.841511\pi\) | |||||||
\(272\) | 66.1594 | 0.0147482 | ||||||||
\(273\) | 960.635 | 0.212968 | ||||||||
\(274\) | 84.8961 | 0.0187181 | ||||||||
\(275\) | −139.155 | −0.0305141 | ||||||||
\(276\) | 276.000 | 0.0601929 | ||||||||
\(277\) | −4158.00 | −0.901912 | −0.450956 | − | 0.892546i | \(-0.648917\pi\) | ||||
−0.450956 | + | 0.892546i | \(0.648917\pi\) | |||||||
\(278\) | −380.268 | −0.0820394 | ||||||||
\(279\) | 1048.68 | 0.225028 | ||||||||
\(280\) | 765.534 | 0.163391 | ||||||||
\(281\) | −4081.76 | −0.866539 | −0.433270 | − | 0.901264i | \(-0.642640\pi\) | ||||
−0.433270 | + | 0.901264i | \(0.642640\pi\) | |||||||
\(282\) | 2050.24 | 0.432943 | ||||||||
\(283\) | 3452.60 | 0.725216 | 0.362608 | − | 0.931942i | \(-0.381886\pi\) | ||||
0.362608 | + | 0.931942i | \(0.381886\pi\) | |||||||
\(284\) | −230.014 | −0.0480592 | ||||||||
\(285\) | 5459.07 | 1.13462 | ||||||||
\(286\) | −205.754 | −0.0425401 | ||||||||
\(287\) | 1639.43 | 0.337186 | ||||||||
\(288\) | 288.000 | 0.0589256 | ||||||||
\(289\) | −4895.90 | −0.996520 | ||||||||
\(290\) | 5395.40 | 1.09251 | ||||||||
\(291\) | −3775.36 | −0.760535 | ||||||||
\(292\) | −2144.57 | −0.429800 | ||||||||
\(293\) | −71.6634 | −0.0142888 | −0.00714440 | − | 0.999974i | \(-0.502274\pi\) | ||||
−0.00714440 | + | 0.999974i | \(0.502274\pi\) | |||||||
\(294\) | −294.000 | −0.0583212 | ||||||||
\(295\) | 4003.58 | 0.790160 | ||||||||
\(296\) | 435.457 | 0.0855081 | ||||||||
\(297\) | 60.7215 | 0.0118634 | ||||||||
\(298\) | −1487.83 | −0.289221 | ||||||||
\(299\) | −1052.12 | −0.203498 | ||||||||
\(300\) | −742.510 | −0.142896 | ||||||||
\(301\) | 1863.51 | 0.356848 | ||||||||
\(302\) | −1686.94 | −0.321433 | ||||||||
\(303\) | 561.147 | 0.106393 | ||||||||
\(304\) | 2129.81 | 0.401819 | ||||||||
\(305\) | 8867.09 | 1.66468 | ||||||||
\(306\) | 74.4294 | 0.0139047 | ||||||||
\(307\) | −4057.18 | −0.754252 | −0.377126 | − | 0.926162i | \(-0.623088\pi\) | ||||
−0.377126 | + | 0.926162i | \(0.623088\pi\) | |||||||
\(308\) | 62.9704 | 0.0116496 | ||||||||
\(309\) | 69.1970 | 0.0127394 | ||||||||
\(310\) | −3185.71 | −0.583666 | ||||||||
\(311\) | −2894.69 | −0.527790 | −0.263895 | − | 0.964551i | \(-0.585007\pi\) | ||||
−0.263895 | + | 0.964551i | \(0.585007\pi\) | |||||||
\(312\) | −1097.87 | −0.199213 | ||||||||
\(313\) | 6860.31 | 1.23887 | 0.619437 | − | 0.785046i | \(-0.287361\pi\) | ||||
0.619437 | + | 0.785046i | \(0.287361\pi\) | |||||||
\(314\) | 1601.82 | 0.287884 | ||||||||
\(315\) | 861.226 | 0.154046 | ||||||||
\(316\) | −980.131 | −0.174483 | ||||||||
\(317\) | −649.300 | −0.115042 | −0.0575210 | − | 0.998344i | \(-0.518320\pi\) | ||||
−0.0575210 | + | 0.998344i | \(0.518320\pi\) | |||||||
\(318\) | −687.683 | −0.121268 | ||||||||
\(319\) | 443.809 | 0.0778951 | ||||||||
\(320\) | −874.896 | −0.152838 | ||||||||
\(321\) | 6114.59 | 1.06319 | ||||||||
\(322\) | 322.000 | 0.0557278 | ||||||||
\(323\) | 550.418 | 0.0948175 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | 2830.48 | 0.483098 | ||||||||
\(326\) | −5764.01 | −0.979260 | ||||||||
\(327\) | 3272.50 | 0.553425 | ||||||||
\(328\) | −1873.63 | −0.315409 | ||||||||
\(329\) | 2391.95 | 0.400828 | ||||||||
\(330\) | −184.462 | −0.0307706 | ||||||||
\(331\) | 357.326 | 0.0593365 | 0.0296683 | − | 0.999560i | \(-0.490555\pi\) | ||||
0.0296683 | + | 0.999560i | \(0.490555\pi\) | |||||||
\(332\) | 1927.97 | 0.318708 | ||||||||
\(333\) | 489.889 | 0.0806178 | ||||||||
\(334\) | −3841.84 | −0.629390 | ||||||||
\(335\) | 4501.68 | 0.734189 | ||||||||
\(336\) | 336.000 | 0.0545545 | ||||||||
\(337\) | 1082.26 | 0.174940 | 0.0874698 | − | 0.996167i | \(-0.472122\pi\) | ||||
0.0874698 | + | 0.996167i | \(0.472122\pi\) | |||||||
\(338\) | −208.876 | −0.0336136 | ||||||||
\(339\) | 6130.33 | 0.982165 | ||||||||
\(340\) | −226.104 | −0.0360653 | ||||||||
\(341\) | −262.047 | −0.0416147 | ||||||||
\(342\) | 2396.04 | 0.378838 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | −2129.73 | −0.333800 | ||||||||
\(345\) | −943.247 | −0.147196 | ||||||||
\(346\) | 2108.60 | 0.327628 | ||||||||
\(347\) | −8970.38 | −1.38777 | −0.693883 | − | 0.720087i | \(-0.744102\pi\) | ||||
−0.693883 | + | 0.720087i | \(0.744102\pi\) | |||||||
\(348\) | 2368.09 | 0.364779 | ||||||||
\(349\) | 4741.49 | 0.727238 | 0.363619 | − | 0.931548i | \(-0.381541\pi\) | ||||
0.363619 | + | 0.931548i | \(0.381541\pi\) | |||||||
\(350\) | −866.261 | −0.132296 | ||||||||
\(351\) | −1235.10 | −0.187820 | ||||||||
\(352\) | −71.9662 | −0.0108972 | ||||||||
\(353\) | −3746.71 | −0.564921 | −0.282460 | − | 0.959279i | \(-0.591151\pi\) | ||||
−0.282460 | + | 0.959279i | \(0.591151\pi\) | |||||||
\(354\) | 1757.21 | 0.263826 | ||||||||
\(355\) | 786.087 | 0.117524 | ||||||||
\(356\) | 3000.03 | 0.446632 | ||||||||
\(357\) | 86.8342 | 0.0128733 | ||||||||
\(358\) | 3582.24 | 0.528847 | ||||||||
\(359\) | 3071.00 | 0.451480 | 0.225740 | − | 0.974188i | \(-0.427520\pi\) | ||||
0.225740 | + | 0.974188i | \(0.427520\pi\) | |||||||
\(360\) | −984.258 | −0.144097 | ||||||||
\(361\) | 10860.1 | 1.58333 | ||||||||
\(362\) | 4515.11 | 0.655550 | ||||||||
\(363\) | 3977.83 | 0.575156 | ||||||||
\(364\) | −1280.85 | −0.184436 | ||||||||
\(365\) | 7329.21 | 1.05104 | ||||||||
\(366\) | 3891.85 | 0.555820 | ||||||||
\(367\) | 10815.2 | 1.53827 | 0.769137 | − | 0.639084i | \(-0.220686\pi\) | ||||
0.769137 | + | 0.639084i | \(0.220686\pi\) | |||||||
\(368\) | −368.000 | −0.0521286 | ||||||||
\(369\) | −2107.84 | −0.297370 | ||||||||
\(370\) | −1488.20 | −0.209102 | ||||||||
\(371\) | −802.297 | −0.112273 | ||||||||
\(372\) | −1398.24 | −0.194880 | ||||||||
\(373\) | 6306.89 | 0.875491 | 0.437746 | − | 0.899099i | \(-0.355777\pi\) | ||||
0.437746 | + | 0.899099i | \(0.355777\pi\) | |||||||
\(374\) | −18.5986 | −0.00257142 | ||||||||
\(375\) | −2588.77 | −0.356490 | ||||||||
\(376\) | −2733.65 | −0.374940 | ||||||||
\(377\) | −9027.27 | −1.23323 | ||||||||
\(378\) | 378.000 | 0.0514344 | ||||||||
\(379\) | 10326.7 | 1.39960 | 0.699798 | − | 0.714341i | \(-0.253273\pi\) | ||||
0.699798 | + | 0.714341i | \(0.253273\pi\) | |||||||
\(380\) | −7278.76 | −0.982611 | ||||||||
\(381\) | −8090.57 | −1.08791 | ||||||||
\(382\) | −3918.15 | −0.524791 | ||||||||
\(383\) | −2.17159 | −0.000289721 0 | −0.000144860 | − | 1.00000i | \(-0.500046\pi\) | ||||
−0.000144860 | 1.00000i | \(0.500046\pi\) | ||||||||
\(384\) | −384.000 | −0.0510310 | ||||||||
\(385\) | −215.205 | −0.0284880 | ||||||||
\(386\) | 1195.20 | 0.157601 | ||||||||
\(387\) | −2395.95 | −0.314710 | ||||||||
\(388\) | 5033.82 | 0.658643 | ||||||||
\(389\) | 5237.25 | 0.682620 | 0.341310 | − | 0.939951i | \(-0.389129\pi\) | ||||
0.341310 | + | 0.939951i | \(0.389129\pi\) | |||||||
\(390\) | 3752.04 | 0.487158 | ||||||||
\(391\) | −95.1042 | −0.0123008 | ||||||||
\(392\) | 392.000 | 0.0505076 | ||||||||
\(393\) | 730.819 | 0.0938040 | ||||||||
\(394\) | 1155.56 | 0.147757 | ||||||||
\(395\) | 3349.66 | 0.426683 | ||||||||
\(396\) | −80.9620 | −0.0102740 | ||||||||
\(397\) | −4123.42 | −0.521281 | −0.260641 | − | 0.965436i | \(-0.583934\pi\) | ||||
−0.260641 | + | 0.965436i | \(0.583934\pi\) | |||||||
\(398\) | 1500.49 | 0.188977 | ||||||||
\(399\) | 2795.37 | 0.350736 | ||||||||
\(400\) | 990.013 | 0.123752 | ||||||||
\(401\) | −3775.05 | −0.470117 | −0.235059 | − | 0.971981i | \(-0.575528\pi\) | ||||
−0.235059 | + | 0.971981i | \(0.575528\pi\) | |||||||
\(402\) | 1975.83 | 0.245138 | ||||||||
\(403\) | 5330.15 | 0.658843 | ||||||||
\(404\) | −748.196 | −0.0921390 | ||||||||
\(405\) | −1107.29 | −0.135856 | ||||||||
\(406\) | 2762.77 | 0.337720 | ||||||||
\(407\) | −122.415 | −0.0149088 | ||||||||
\(408\) | −99.2391 | −0.0120418 | ||||||||
\(409\) | −7150.35 | −0.864455 | −0.432227 | − | 0.901765i | \(-0.642272\pi\) | ||||
−0.432227 | + | 0.901765i | \(0.642272\pi\) | |||||||
\(410\) | 6403.26 | 0.771303 | ||||||||
\(411\) | −127.344 | −0.0152833 | ||||||||
\(412\) | −92.2627 | −0.0110327 | ||||||||
\(413\) | 2050.08 | 0.244256 | ||||||||
\(414\) | −414.000 | −0.0491473 | ||||||||
\(415\) | −6588.96 | −0.779372 | ||||||||
\(416\) | 1463.82 | 0.172524 | ||||||||
\(417\) | 570.402 | 0.0669849 | ||||||||
\(418\) | −598.728 | −0.0700591 | ||||||||
\(419\) | 4943.81 | 0.576423 | 0.288211 | − | 0.957567i | \(-0.406939\pi\) | ||||
0.288211 | + | 0.957567i | \(0.406939\pi\) | |||||||
\(420\) | −1148.30 | −0.133408 | ||||||||
\(421\) | 8461.47 | 0.979541 | 0.489771 | − | 0.871851i | \(-0.337081\pi\) | ||||
0.489771 | + | 0.871851i | \(0.337081\pi\) | |||||||
\(422\) | −4203.44 | −0.484882 | ||||||||
\(423\) | −3075.36 | −0.353497 | ||||||||
\(424\) | 916.910 | 0.105021 | ||||||||
\(425\) | 255.854 | 0.0292018 | ||||||||
\(426\) | 345.021 | 0.0392402 | ||||||||
\(427\) | 4540.49 | 0.514589 | ||||||||
\(428\) | −8152.79 | −0.920748 | ||||||||
\(429\) | 308.631 | 0.0347339 | ||||||||
\(430\) | 7278.49 | 0.816279 | ||||||||
\(431\) | −4753.05 | −0.531199 | −0.265599 | − | 0.964084i | \(-0.585570\pi\) | ||||
−0.265599 | + | 0.964084i | \(0.585570\pi\) | |||||||
\(432\) | −432.000 | −0.0481125 | ||||||||
\(433\) | 7712.94 | 0.856029 | 0.428014 | − | 0.903772i | \(-0.359213\pi\) | ||||
0.428014 | + | 0.903772i | \(0.359213\pi\) | |||||||
\(434\) | −1631.28 | −0.180424 | ||||||||
\(435\) | −8093.10 | −0.892034 | ||||||||
\(436\) | −4363.34 | −0.479280 | ||||||||
\(437\) | −3061.60 | −0.335140 | ||||||||
\(438\) | 3216.86 | 0.350930 | ||||||||
\(439\) | −7571.77 | −0.823191 | −0.411595 | − | 0.911367i | \(-0.635028\pi\) | ||||
−0.411595 | + | 0.911367i | \(0.635028\pi\) | |||||||
\(440\) | 245.949 | 0.0266481 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 378.304 | 0.0407106 | ||||||||
\(443\) | −12543.0 | −1.34523 | −0.672615 | − | 0.739992i | \(-0.734829\pi\) | ||||
−0.672615 | + | 0.739992i | \(0.734829\pi\) | |||||||
\(444\) | −653.185 | −0.0698171 | ||||||||
\(445\) | −10252.8 | −1.09220 | ||||||||
\(446\) | 1434.81 | 0.152332 | ||||||||
\(447\) | 2231.75 | 0.236148 | ||||||||
\(448\) | −448.000 | −0.0472456 | ||||||||
\(449\) | 8755.46 | 0.920258 | 0.460129 | − | 0.887852i | \(-0.347803\pi\) | ||||
0.460129 | + | 0.887852i | \(0.347803\pi\) | |||||||
\(450\) | 1113.76 | 0.116674 | ||||||||
\(451\) | 526.712 | 0.0549931 | ||||||||
\(452\) | −8173.78 | −0.850580 | ||||||||
\(453\) | 2530.42 | 0.262449 | ||||||||
\(454\) | −5996.73 | −0.619913 | ||||||||
\(455\) | 4377.37 | 0.451021 | ||||||||
\(456\) | −3194.71 | −0.328084 | ||||||||
\(457\) | −2061.64 | −0.211027 | −0.105514 | − | 0.994418i | \(-0.533649\pi\) | ||||
−0.105514 | + | 0.994418i | \(0.533649\pi\) | |||||||
\(458\) | −8434.37 | −0.860507 | ||||||||
\(459\) | −111.644 | −0.0113532 | ||||||||
\(460\) | 1257.66 | 0.127476 | ||||||||
\(461\) | −4924.04 | −0.497473 | −0.248737 | − | 0.968571i | \(-0.580015\pi\) | ||||
−0.248737 | + | 0.968571i | \(0.580015\pi\) | |||||||
\(462\) | −94.4556 | −0.00951185 | ||||||||
\(463\) | 4482.52 | 0.449936 | 0.224968 | − | 0.974366i | \(-0.427772\pi\) | ||||
0.224968 | + | 0.974366i | \(0.427772\pi\) | |||||||
\(464\) | −3157.46 | −0.315908 | ||||||||
\(465\) | 4778.57 | 0.476561 | ||||||||
\(466\) | −11562.9 | −1.14944 | ||||||||
\(467\) | −9387.29 | −0.930175 | −0.465088 | − | 0.885265i | \(-0.653977\pi\) | ||||
−0.465088 | + | 0.885265i | \(0.653977\pi\) | |||||||
\(468\) | 1646.80 | 0.162657 | ||||||||
\(469\) | 2305.13 | 0.226954 | ||||||||
\(470\) | 9342.43 | 0.916882 | ||||||||
\(471\) | −2402.72 | −0.235057 | ||||||||
\(472\) | −2342.94 | −0.228480 | ||||||||
\(473\) | 598.705 | 0.0581998 | ||||||||
\(474\) | 1470.20 | 0.142465 | ||||||||
\(475\) | 8236.48 | 0.795612 | ||||||||
\(476\) | −115.779 | −0.0111486 | ||||||||
\(477\) | 1031.52 | 0.0990152 | ||||||||
\(478\) | −3760.76 | −0.359861 | ||||||||
\(479\) | −20437.4 | −1.94949 | −0.974747 | − | 0.223313i | \(-0.928313\pi\) | ||||
−0.974747 | + | 0.223313i | \(0.928313\pi\) | |||||||
\(480\) | 1312.34 | 0.124792 | ||||||||
\(481\) | 2489.97 | 0.236035 | ||||||||
\(482\) | −7281.74 | −0.688120 | ||||||||
\(483\) | −483.000 | −0.0455016 | ||||||||
\(484\) | −5303.77 | −0.498100 | ||||||||
\(485\) | −17203.4 | −1.61065 | ||||||||
\(486\) | −486.000 | −0.0453609 | ||||||||
\(487\) | 5380.22 | 0.500618 | 0.250309 | − | 0.968166i | \(-0.419468\pi\) | ||||
0.250309 | + | 0.968166i | \(0.419468\pi\) | |||||||
\(488\) | −5189.13 | −0.481354 | ||||||||
\(489\) | 8646.01 | 0.799563 | ||||||||
\(490\) | −1339.68 | −0.123512 | ||||||||
\(491\) | −11763.2 | −1.08120 | −0.540598 | − | 0.841281i | \(-0.681802\pi\) | ||||
−0.540598 | + | 0.841281i | \(0.681802\pi\) | |||||||
\(492\) | 2810.45 | 0.257530 | ||||||||
\(493\) | −815.998 | −0.0745450 | ||||||||
\(494\) | 12178.4 | 1.10917 | ||||||||
\(495\) | 276.693 | 0.0251241 | ||||||||
\(496\) | 1864.32 | 0.168771 | ||||||||
\(497\) | 402.525 | 0.0363294 | ||||||||
\(498\) | −2891.95 | −0.260224 | ||||||||
\(499\) | 19677.6 | 1.76531 | 0.882655 | − | 0.470021i | \(-0.155754\pi\) | ||||
0.882655 | + | 0.470021i | \(0.155754\pi\) | |||||||
\(500\) | 3451.70 | 0.308729 | ||||||||
\(501\) | 5762.76 | 0.513895 | ||||||||
\(502\) | 7465.73 | 0.663769 | ||||||||
\(503\) | −1256.89 | −0.111415 | −0.0557075 | − | 0.998447i | \(-0.517741\pi\) | ||||
−0.0557075 | + | 0.998447i | \(0.517741\pi\) | |||||||
\(504\) | −504.000 | −0.0445435 | ||||||||
\(505\) | 2557.01 | 0.225318 | ||||||||
\(506\) | 103.451 | 0.00908888 | ||||||||
\(507\) | 313.315 | 0.0274454 | ||||||||
\(508\) | 10787.4 | 0.942154 | ||||||||
\(509\) | 7115.85 | 0.619655 | 0.309828 | − | 0.950793i | \(-0.399729\pi\) | ||||
0.309828 | + | 0.950793i | \(0.399729\pi\) | |||||||
\(510\) | 339.156 | 0.0294472 | ||||||||
\(511\) | 3753.00 | 0.324898 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | −3594.05 | −0.309320 | ||||||||
\(514\) | 10272.7 | 0.881535 | ||||||||
\(515\) | 315.314 | 0.0269794 | ||||||||
\(516\) | 3194.60 | 0.272547 | ||||||||
\(517\) | 768.479 | 0.0653727 | ||||||||
\(518\) | −762.049 | −0.0646380 | ||||||||
\(519\) | −3162.91 | −0.267507 | ||||||||
\(520\) | −5002.71 | −0.421891 | ||||||||
\(521\) | 2680.13 | 0.225372 | 0.112686 | − | 0.993631i | \(-0.464055\pi\) | ||||
0.112686 | + | 0.993631i | \(0.464055\pi\) | |||||||
\(522\) | −3552.14 | −0.297841 | ||||||||
\(523\) | −6097.07 | −0.509763 | −0.254882 | − | 0.966972i | \(-0.582037\pi\) | ||||
−0.254882 | + | 0.966972i | \(0.582037\pi\) | |||||||
\(524\) | −974.426 | −0.0812366 | ||||||||
\(525\) | 1299.39 | 0.108019 | ||||||||
\(526\) | 5626.18 | 0.466375 | ||||||||
\(527\) | 481.806 | 0.0398250 | ||||||||
\(528\) | 107.949 | 0.00889752 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | −3133.60 | −0.256820 | ||||||||
\(531\) | −2635.81 | −0.215413 | ||||||||
\(532\) | −3727.17 | −0.303747 | ||||||||
\(533\) | −10713.6 | −0.870648 | ||||||||
\(534\) | −4500.04 | −0.364674 | ||||||||
\(535\) | 27862.7 | 2.25160 | ||||||||
\(536\) | −2634.44 | −0.212296 | ||||||||
\(537\) | −5373.36 | −0.431802 | ||||||||
\(538\) | 9028.34 | 0.723493 | ||||||||
\(539\) | −110.198 | −0.00880626 | ||||||||
\(540\) | 1476.39 | 0.117655 | ||||||||
\(541\) | −8998.60 | −0.715120 | −0.357560 | − | 0.933890i | \(-0.616391\pi\) | ||||
−0.357560 | + | 0.933890i | \(0.616391\pi\) | |||||||
\(542\) | −15678.2 | −1.24251 | ||||||||
\(543\) | −6772.67 | −0.535254 | ||||||||
\(544\) | 132.319 | 0.0104285 | ||||||||
\(545\) | 14912.0 | 1.17203 | ||||||||
\(546\) | 1921.27 | 0.150591 | ||||||||
\(547\) | 2587.96 | 0.202291 | 0.101145 | − | 0.994872i | \(-0.467749\pi\) | ||||
0.101145 | + | 0.994872i | \(0.467749\pi\) | |||||||
\(548\) | 169.792 | 0.0132357 | ||||||||
\(549\) | −5837.77 | −0.453825 | ||||||||
\(550\) | −278.310 | −0.0215767 | ||||||||
\(551\) | −26268.7 | −2.03100 | ||||||||
\(552\) | 552.000 | 0.0425628 | ||||||||
\(553\) | 1715.23 | 0.131897 | ||||||||
\(554\) | −8315.99 | −0.637748 | ||||||||
\(555\) | 2232.30 | 0.170731 | ||||||||
\(556\) | −760.536 | −0.0580106 | ||||||||
\(557\) | 21691.8 | 1.65011 | 0.825054 | − | 0.565053i | \(-0.191144\pi\) | ||||
0.825054 | + | 0.565053i | \(0.191144\pi\) | |||||||
\(558\) | 2097.36 | 0.159119 | ||||||||
\(559\) | −12177.9 | −0.921417 | ||||||||
\(560\) | 1531.07 | 0.115535 | ||||||||
\(561\) | 27.8979 | 0.00209955 | ||||||||
\(562\) | −8163.52 | −0.612736 | ||||||||
\(563\) | 9737.57 | 0.728934 | 0.364467 | − | 0.931216i | \(-0.381251\pi\) | ||||
0.364467 | + | 0.931216i | \(0.381251\pi\) | |||||||
\(564\) | 4100.48 | 0.306137 | ||||||||
\(565\) | 27934.4 | 2.08002 | ||||||||
\(566\) | 6905.21 | 0.512805 | ||||||||
\(567\) | −567.000 | −0.0419961 | ||||||||
\(568\) | −460.028 | −0.0339830 | ||||||||
\(569\) | −7487.90 | −0.551685 | −0.275843 | − | 0.961203i | \(-0.588957\pi\) | ||||
−0.275843 | + | 0.961203i | \(0.588957\pi\) | |||||||
\(570\) | 10918.1 | 0.802299 | ||||||||
\(571\) | 21995.9 | 1.61208 | 0.806041 | − | 0.591859i | \(-0.201606\pi\) | ||||
0.806041 | + | 0.591859i | \(0.201606\pi\) | |||||||
\(572\) | −411.507 | −0.0300804 | ||||||||
\(573\) | 5877.23 | 0.428490 | ||||||||
\(574\) | 3278.86 | 0.238427 | ||||||||
\(575\) | −1423.14 | −0.103216 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | −290.397 | −0.0209521 | −0.0104761 | − | 0.999945i | \(-0.503335\pi\) | ||||
−0.0104761 | + | 0.999945i | \(0.503335\pi\) | |||||||
\(578\) | −9791.80 | −0.704646 | ||||||||
\(579\) | −1792.80 | −0.128681 | ||||||||
\(580\) | 10790.8 | 0.772524 | ||||||||
\(581\) | −3373.95 | −0.240921 | ||||||||
\(582\) | −7550.73 | −0.537779 | ||||||||
\(583\) | −257.760 | −0.0183110 | ||||||||
\(584\) | −4289.14 | −0.303914 | ||||||||
\(585\) | −5628.05 | −0.397763 | ||||||||
\(586\) | −143.327 | −0.0101037 | ||||||||
\(587\) | −7867.97 | −0.553230 | −0.276615 | − | 0.960981i | \(-0.589213\pi\) | ||||
−0.276615 | + | 0.960981i | \(0.589213\pi\) | |||||||
\(588\) | −588.000 | −0.0412393 | ||||||||
\(589\) | 15510.3 | 1.08505 | ||||||||
\(590\) | 8007.16 | 0.558728 | ||||||||
\(591\) | −1733.34 | −0.120643 | ||||||||
\(592\) | 870.913 | 0.0604634 | ||||||||
\(593\) | −11265.5 | −0.780132 | −0.390066 | − | 0.920787i | \(-0.627548\pi\) | ||||
−0.390066 | + | 0.920787i | \(0.627548\pi\) | |||||||
\(594\) | 121.443 | 0.00838866 | ||||||||
\(595\) | 395.682 | 0.0272628 | ||||||||
\(596\) | −2975.67 | −0.204510 | ||||||||
\(597\) | −2250.73 | −0.154299 | ||||||||
\(598\) | −2104.25 | −0.143895 | ||||||||
\(599\) | −19215.6 | −1.31073 | −0.655364 | − | 0.755313i | \(-0.727485\pi\) | ||||
−0.655364 | + | 0.755313i | \(0.727485\pi\) | |||||||
\(600\) | −1485.02 | −0.101043 | ||||||||
\(601\) | 19551.2 | 1.32697 | 0.663486 | − | 0.748189i | \(-0.269076\pi\) | ||||
0.663486 | + | 0.748189i | \(0.269076\pi\) | |||||||
\(602\) | 3727.03 | 0.252329 | ||||||||
\(603\) | −2963.74 | −0.200154 | ||||||||
\(604\) | −3373.89 | −0.227287 | ||||||||
\(605\) | 18126.0 | 1.21806 | ||||||||
\(606\) | 1122.29 | 0.0752312 | ||||||||
\(607\) | −13803.0 | −0.922979 | −0.461490 | − | 0.887146i | \(-0.652685\pi\) | ||||
−0.461490 | + | 0.887146i | \(0.652685\pi\) | |||||||
\(608\) | 4259.62 | 0.284129 | ||||||||
\(609\) | −4144.16 | −0.275747 | ||||||||
\(610\) | 17734.2 | 1.17711 | ||||||||
\(611\) | −15631.2 | −1.03498 | ||||||||
\(612\) | 148.859 | 0.00983212 | ||||||||
\(613\) | −12878.1 | −0.848519 | −0.424260 | − | 0.905541i | \(-0.639466\pi\) | ||||
−0.424260 | + | 0.905541i | \(0.639466\pi\) | |||||||
\(614\) | −8114.35 | −0.533336 | ||||||||
\(615\) | −9604.89 | −0.629767 | ||||||||
\(616\) | 125.941 | 0.00823750 | ||||||||
\(617\) | 20412.1 | 1.33187 | 0.665933 | − | 0.746012i | \(-0.268034\pi\) | ||||
0.665933 | + | 0.746012i | \(0.268034\pi\) | |||||||
\(618\) | 138.394 | 0.00900813 | ||||||||
\(619\) | 5190.18 | 0.337013 | 0.168507 | − | 0.985701i | \(-0.446106\pi\) | ||||
0.168507 | + | 0.985701i | \(0.446106\pi\) | |||||||
\(620\) | −6371.43 | −0.412714 | ||||||||
\(621\) | 621.000 | 0.0401286 | ||||||||
\(622\) | −5789.38 | −0.373204 | ||||||||
\(623\) | −5250.05 | −0.337622 | ||||||||
\(624\) | −2195.74 | −0.140865 | ||||||||
\(625\) | −19530.9 | −1.24998 | ||||||||
\(626\) | 13720.6 | 0.876016 | ||||||||
\(627\) | 898.091 | 0.0572030 | ||||||||
\(628\) | 3203.63 | 0.203565 | ||||||||
\(629\) | 225.075 | 0.0142676 | ||||||||
\(630\) | 1722.45 | 0.108927 | ||||||||
\(631\) | 10103.1 | 0.637401 | 0.318700 | − | 0.947856i | \(-0.396754\pi\) | ||||
0.318700 | + | 0.947856i | \(0.396754\pi\) | |||||||
\(632\) | −1960.26 | −0.123378 | ||||||||
\(633\) | 6305.15 | 0.395904 | ||||||||
\(634\) | −1298.60 | −0.0813470 | ||||||||
\(635\) | −36866.7 | −2.30395 | ||||||||
\(636\) | −1375.37 | −0.0857497 | ||||||||
\(637\) | 2241.48 | 0.139420 | ||||||||
\(638\) | 887.618 | 0.0550801 | ||||||||
\(639\) | −517.532 | −0.0320395 | ||||||||
\(640\) | −1749.79 | −0.108073 | ||||||||
\(641\) | 17138.8 | 1.05607 | 0.528037 | − | 0.849221i | \(-0.322928\pi\) | ||||
0.528037 | + | 0.849221i | \(0.322928\pi\) | |||||||
\(642\) | 12229.2 | 0.751787 | ||||||||
\(643\) | −16302.6 | −0.999860 | −0.499930 | − | 0.866066i | \(-0.666641\pi\) | ||||
−0.499930 | + | 0.866066i | \(0.666641\pi\) | |||||||
\(644\) | 644.000 | 0.0394055 | ||||||||
\(645\) | −10917.7 | −0.666489 | ||||||||
\(646\) | 1100.84 | 0.0670461 | ||||||||
\(647\) | 26719.6 | 1.62358 | 0.811791 | − | 0.583949i | \(-0.198493\pi\) | ||||
0.811791 | + | 0.583949i | \(0.198493\pi\) | |||||||
\(648\) | 648.000 | 0.0392837 | ||||||||
\(649\) | 658.643 | 0.0398367 | ||||||||
\(650\) | 5660.96 | 0.341602 | ||||||||
\(651\) | 2446.92 | 0.147315 | ||||||||
\(652\) | −11528.0 | −0.692442 | ||||||||
\(653\) | 27974.5 | 1.67646 | 0.838229 | − | 0.545319i | \(-0.183591\pi\) | ||||
0.838229 | + | 0.545319i | \(0.183591\pi\) | |||||||
\(654\) | 6545.01 | 0.391330 | ||||||||
\(655\) | 3330.16 | 0.198657 | ||||||||
\(656\) | −3747.27 | −0.223028 | ||||||||
\(657\) | −4825.28 | −0.286533 | ||||||||
\(658\) | 4783.89 | 0.283428 | ||||||||
\(659\) | −28367.4 | −1.67684 | −0.838421 | − | 0.545023i | \(-0.816521\pi\) | ||||
−0.838421 | + | 0.545023i | \(0.816521\pi\) | |||||||
\(660\) | −368.923 | −0.0217581 | ||||||||
\(661\) | 22702.1 | 1.33587 | 0.667935 | − | 0.744219i | \(-0.267178\pi\) | ||||
0.667935 | + | 0.744219i | \(0.267178\pi\) | |||||||
\(662\) | 714.651 | 0.0419573 | ||||||||
\(663\) | −567.456 | −0.0332401 | ||||||||
\(664\) | 3855.94 | 0.225361 | ||||||||
\(665\) | 12737.8 | 0.742784 | ||||||||
\(666\) | 979.777 | 0.0570054 | ||||||||
\(667\) | 4538.84 | 0.263485 | ||||||||
\(668\) | −7683.68 | −0.445046 | ||||||||
\(669\) | −2152.21 | −0.124378 | ||||||||
\(670\) | 9003.36 | 0.519150 | ||||||||
\(671\) | 1458.76 | 0.0839266 | ||||||||
\(672\) | 672.000 | 0.0385758 | ||||||||
\(673\) | 114.075 | 0.00653382 | 0.00326691 | − | 0.999995i | \(-0.498960\pi\) | ||||
0.00326691 | + | 0.999995i | \(0.498960\pi\) | |||||||
\(674\) | 2164.53 | 0.123701 | ||||||||
\(675\) | −1670.65 | −0.0952640 | ||||||||
\(676\) | −417.753 | −0.0237684 | ||||||||
\(677\) | −15152.5 | −0.860201 | −0.430101 | − | 0.902781i | \(-0.641522\pi\) | ||||
−0.430101 | + | 0.902781i | \(0.641522\pi\) | |||||||
\(678\) | 12260.7 | 0.694496 | ||||||||
\(679\) | −8809.18 | −0.497887 | ||||||||
\(680\) | −452.208 | −0.0255020 | ||||||||
\(681\) | 8995.10 | 0.506157 | ||||||||
\(682\) | −524.093 | −0.0294261 | ||||||||
\(683\) | −15093.7 | −0.845600 | −0.422800 | − | 0.906223i | \(-0.638953\pi\) | ||||
−0.422800 | + | 0.906223i | \(0.638953\pi\) | |||||||
\(684\) | 4792.07 | 0.267879 | ||||||||
\(685\) | −580.276 | −0.0323667 | ||||||||
\(686\) | −686.000 | −0.0381802 | ||||||||
\(687\) | 12651.6 | 0.702601 | ||||||||
\(688\) | −4259.46 | −0.236033 | ||||||||
\(689\) | 5242.95 | 0.289899 | ||||||||
\(690\) | −1886.49 | −0.104084 | ||||||||
\(691\) | −21282.9 | −1.17169 | −0.585847 | − | 0.810422i | \(-0.699238\pi\) | ||||
−0.585847 | + | 0.810422i | \(0.699238\pi\) | |||||||
\(692\) | 4217.21 | 0.231668 | ||||||||
\(693\) | 141.683 | 0.00776639 | ||||||||
\(694\) | −17940.8 | −0.981299 | ||||||||
\(695\) | 2599.18 | 0.141860 | ||||||||
\(696\) | 4736.18 | 0.257938 | ||||||||
\(697\) | −968.426 | −0.0526280 | ||||||||
\(698\) | 9482.98 | 0.514235 | ||||||||
\(699\) | 17344.3 | 0.938517 | ||||||||
\(700\) | −1732.52 | −0.0935474 | ||||||||
\(701\) | 34984.4 | 1.88494 | 0.942471 | − | 0.334288i | \(-0.108496\pi\) | ||||
0.942471 | + | 0.334288i | \(0.108496\pi\) | |||||||
\(702\) | −2470.20 | −0.132809 | ||||||||
\(703\) | 7245.62 | 0.388725 | ||||||||
\(704\) | −143.932 | −0.00770548 | ||||||||
\(705\) | −14013.7 | −0.748631 | ||||||||
\(706\) | −7493.41 | −0.399459 | ||||||||
\(707\) | 1309.34 | 0.0696505 | ||||||||
\(708\) | 3514.41 | 0.186553 | ||||||||
\(709\) | 28316.7 | 1.49994 | 0.749968 | − | 0.661474i | \(-0.230069\pi\) | ||||
0.749968 | + | 0.661474i | \(0.230069\pi\) | |||||||
\(710\) | 1572.17 | 0.0831024 | ||||||||
\(711\) | −2205.29 | −0.116322 | ||||||||
\(712\) | 6000.06 | 0.315817 | ||||||||
\(713\) | −2679.96 | −0.140765 | ||||||||
\(714\) | 173.668 | 0.00910277 | ||||||||
\(715\) | 1406.35 | 0.0735589 | ||||||||
\(716\) | 7164.48 | 0.373952 | ||||||||
\(717\) | 5641.15 | 0.293825 | ||||||||
\(718\) | 6142.00 | 0.319244 | ||||||||
\(719\) | −12607.4 | −0.653930 | −0.326965 | − | 0.945036i | \(-0.606026\pi\) | ||||
−0.326965 | + | 0.945036i | \(0.606026\pi\) | |||||||
\(720\) | −1968.52 | −0.101892 | ||||||||
\(721\) | 161.460 | 0.00833991 | ||||||||
\(722\) | 21720.2 | 1.11959 | ||||||||
\(723\) | 10922.6 | 0.561848 | ||||||||
\(724\) | 9030.23 | 0.463544 | ||||||||
\(725\) | −12210.6 | −0.625506 | ||||||||
\(726\) | 7955.65 | 0.406697 | ||||||||
\(727\) | −29247.4 | −1.49206 | −0.746029 | − | 0.665914i | \(-0.768042\pi\) | ||||
−0.746029 | + | 0.665914i | \(0.768042\pi\) | |||||||
\(728\) | −2561.69 | −0.130416 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 14658.4 | 0.743195 | ||||||||
\(731\) | −1100.79 | −0.0556968 | ||||||||
\(732\) | 7783.70 | 0.393024 | ||||||||
\(733\) | 22731.4 | 1.14543 | 0.572717 | − | 0.819753i | \(-0.305890\pi\) | ||||
0.572717 | + | 0.819753i | \(0.305890\pi\) | |||||||
\(734\) | 21630.3 | 1.08772 | ||||||||
\(735\) | 2009.53 | 0.100847 | ||||||||
\(736\) | −736.000 | −0.0368605 | ||||||||
\(737\) | 740.588 | 0.0370148 | ||||||||
\(738\) | −4215.67 | −0.210272 | ||||||||
\(739\) | −12055.5 | −0.600095 | −0.300047 | − | 0.953924i | \(-0.597002\pi\) | ||||
−0.300047 | + | 0.953924i | \(0.597002\pi\) | |||||||
\(740\) | −2976.40 | −0.147858 | ||||||||
\(741\) | −18267.6 | −0.905636 | ||||||||
\(742\) | −1604.59 | −0.0793888 | ||||||||
\(743\) | −37806.7 | −1.86675 | −0.933375 | − | 0.358903i | \(-0.883151\pi\) | ||||
−0.933375 | + | 0.358903i | \(0.883151\pi\) | |||||||
\(744\) | −2796.48 | −0.137801 | ||||||||
\(745\) | 10169.5 | 0.500111 | ||||||||
\(746\) | 12613.8 | 0.619066 | ||||||||
\(747\) | 4337.93 | 0.212472 | ||||||||
\(748\) | −37.1972 | −0.00181827 | ||||||||
\(749\) | 14267.4 | 0.696020 | ||||||||
\(750\) | −5177.54 | −0.252076 | ||||||||
\(751\) | −32936.0 | −1.60033 | −0.800167 | − | 0.599777i | \(-0.795256\pi\) | ||||
−0.800167 | + | 0.599777i | \(0.795256\pi\) | |||||||
\(752\) | −5467.31 | −0.265123 | ||||||||
\(753\) | −11198.6 | −0.541965 | ||||||||
\(754\) | −18054.5 | −0.872026 | ||||||||
\(755\) | 11530.5 | 0.555811 | ||||||||
\(756\) | 756.000 | 0.0363696 | ||||||||
\(757\) | 9916.45 | 0.476116 | 0.238058 | − | 0.971251i | \(-0.423489\pi\) | ||||
0.238058 | + | 0.971251i | \(0.423489\pi\) | |||||||
\(758\) | 20653.4 | 0.989664 | ||||||||
\(759\) | −155.177 | −0.00742104 | ||||||||
\(760\) | −14557.5 | −0.694811 | ||||||||
\(761\) | −22886.3 | −1.09018 | −0.545092 | − | 0.838377i | \(-0.683505\pi\) | ||||
−0.545092 | + | 0.838377i | \(0.683505\pi\) | |||||||
\(762\) | −16181.1 | −0.769266 | ||||||||
\(763\) | 7635.84 | 0.362301 | ||||||||
\(764\) | −7836.30 | −0.371083 | ||||||||
\(765\) | −508.734 | −0.0240436 | ||||||||
\(766\) | −4.34318 | −0.000204864 0 | ||||||||
\(767\) | −13397.1 | −0.630693 | ||||||||
\(768\) | −768.000 | −0.0360844 | ||||||||
\(769\) | −26115.9 | −1.22466 | −0.612329 | − | 0.790603i | \(-0.709767\pi\) | ||||
−0.612329 | + | 0.790603i | \(0.709767\pi\) | |||||||
\(770\) | −430.411 | −0.0201441 | ||||||||
\(771\) | −15409.0 | −0.719770 | ||||||||
\(772\) | 2390.40 | 0.111441 | ||||||||
\(773\) | 4051.95 | 0.188536 | 0.0942681 | − | 0.995547i | \(-0.469949\pi\) | ||||
0.0942681 | + | 0.995547i | \(0.469949\pi\) | |||||||
\(774\) | −4791.89 | −0.222534 | ||||||||
\(775\) | 7209.76 | 0.334171 | ||||||||
\(776\) | 10067.6 | 0.465731 | ||||||||
\(777\) | 1143.07 | 0.0527767 | ||||||||
\(778\) | 10474.5 | 0.482685 | ||||||||
\(779\) | −31175.6 | −1.43387 | ||||||||
\(780\) | 7504.07 | 0.344473 | ||||||||
\(781\) | 129.322 | 0.00592511 | ||||||||
\(782\) | −190.208 | −0.00869800 | ||||||||
\(783\) | 5328.21 | 0.243186 | ||||||||
\(784\) | 784.000 | 0.0357143 | ||||||||
\(785\) | −10948.6 | −0.497800 | ||||||||
\(786\) | 1461.64 | 0.0663294 | ||||||||
\(787\) | 14327.0 | 0.648921 | 0.324461 | − | 0.945899i | \(-0.394817\pi\) | ||||
0.324461 | + | 0.945899i | \(0.394817\pi\) | |||||||
\(788\) | 2311.12 | 0.104480 | ||||||||
\(789\) | −8439.27 | −0.380793 | ||||||||
\(790\) | 6699.32 | 0.301710 | ||||||||
\(791\) | 14304.1 | 0.642978 | ||||||||
\(792\) | −161.924 | −0.00726479 | ||||||||
\(793\) | −29671.8 | −1.32872 | ||||||||
\(794\) | −8246.85 | −0.368602 | ||||||||
\(795\) | 4700.40 | 0.209693 | ||||||||
\(796\) | 3000.98 | 0.133627 | ||||||||
\(797\) | 6604.16 | 0.293515 | 0.146757 | − | 0.989173i | \(-0.453116\pi\) | ||||
0.146757 | + | 0.989173i | \(0.453116\pi\) | |||||||
\(798\) | 5590.75 | 0.248008 | ||||||||
\(799\) | −1412.95 | −0.0625612 | ||||||||
\(800\) | 1980.03 | 0.0875056 | ||||||||
\(801\) | 6750.06 | 0.297755 | ||||||||
\(802\) | −7550.10 | −0.332423 | ||||||||
\(803\) | 1205.75 | 0.0529890 | ||||||||
\(804\) | 3951.66 | 0.173339 | ||||||||
\(805\) | −2200.91 | −0.0963626 | ||||||||
\(806\) | 10660.3 | 0.465872 | ||||||||
\(807\) | −13542.5 | −0.590730 | ||||||||
\(808\) | −1496.39 | −0.0651521 | ||||||||
\(809\) | −19434.3 | −0.844592 | −0.422296 | − | 0.906458i | \(-0.638776\pi\) | ||||
−0.422296 | + | 0.906458i | \(0.638776\pi\) | |||||||
\(810\) | −2214.58 | −0.0960647 | ||||||||
\(811\) | −12521.9 | −0.542174 | −0.271087 | − | 0.962555i | \(-0.587383\pi\) | ||||
−0.271087 | + | 0.962555i | \(0.587383\pi\) | |||||||
\(812\) | 5525.55 | 0.238804 | ||||||||
\(813\) | 23517.4 | 1.01450 | ||||||||
\(814\) | −244.829 | −0.0105421 | ||||||||
\(815\) | 39397.7 | 1.69330 | ||||||||
\(816\) | −198.478 | −0.00851486 | ||||||||
\(817\) | −35436.9 | −1.51748 | ||||||||
\(818\) | −14300.7 | −0.611262 | ||||||||
\(819\) | −2881.91 | −0.122957 | ||||||||
\(820\) | 12806.5 | 0.545394 | ||||||||
\(821\) | −22995.9 | −0.977542 | −0.488771 | − | 0.872412i | \(-0.662555\pi\) | ||||
−0.488771 | + | 0.872412i | \(0.662555\pi\) | |||||||
\(822\) | −254.688 | −0.0108069 | ||||||||
\(823\) | 10120.8 | 0.428664 | 0.214332 | − | 0.976761i | \(-0.431243\pi\) | ||||
0.214332 | + | 0.976761i | \(0.431243\pi\) | |||||||
\(824\) | −184.525 | −0.00780127 | ||||||||
\(825\) | 417.465 | 0.0176173 | ||||||||
\(826\) | 4100.15 | 0.172715 | ||||||||
\(827\) | 5060.60 | 0.212786 | 0.106393 | − | 0.994324i | \(-0.466070\pi\) | ||||
0.106393 | + | 0.994324i | \(0.466070\pi\) | |||||||
\(828\) | −828.000 | −0.0347524 | ||||||||
\(829\) | 33161.5 | 1.38932 | 0.694661 | − | 0.719337i | \(-0.255554\pi\) | ||||
0.694661 | + | 0.719337i | \(0.255554\pi\) | |||||||
\(830\) | −13177.9 | −0.551099 | ||||||||
\(831\) | 12474.0 | 0.520719 | ||||||||
\(832\) | 2927.65 | 0.121993 | ||||||||
\(833\) | 202.613 | 0.00842753 | ||||||||
\(834\) | 1140.80 | 0.0473655 | ||||||||
\(835\) | 26259.5 | 1.08832 | ||||||||
\(836\) | −1197.46 | −0.0495393 | ||||||||
\(837\) | −3146.04 | −0.129920 | ||||||||
\(838\) | 9887.63 | 0.407592 | ||||||||
\(839\) | −21458.6 | −0.882997 | −0.441498 | − | 0.897262i | \(-0.645553\pi\) | ||||
−0.441498 | + | 0.897262i | \(0.645553\pi\) | |||||||
\(840\) | −2296.60 | −0.0943337 | ||||||||
\(841\) | 14554.5 | 0.596764 | ||||||||
\(842\) | 16922.9 | 0.692640 | ||||||||
\(843\) | 12245.3 | 0.500297 | ||||||||
\(844\) | −8406.87 | −0.342863 | ||||||||
\(845\) | 1427.70 | 0.0581234 | ||||||||
\(846\) | −6150.72 | −0.249960 | ||||||||
\(847\) | 9281.60 | 0.376528 | ||||||||
\(848\) | 1833.82 | 0.0742614 | ||||||||
\(849\) | −10357.8 | −0.418703 | ||||||||
\(850\) | 511.708 | 0.0206488 | ||||||||
\(851\) | −1251.94 | −0.0504299 | ||||||||
\(852\) | 690.042 | 0.0277470 | ||||||||
\(853\) | −3125.48 | −0.125456 | −0.0627282 | − | 0.998031i | \(-0.519980\pi\) | ||||
−0.0627282 | + | 0.998031i | \(0.519980\pi\) | |||||||
\(854\) | 9080.98 | 0.363870 | ||||||||
\(855\) | −16377.2 | −0.655074 | ||||||||
\(856\) | −16305.6 | −0.651067 | ||||||||
\(857\) | −7942.86 | −0.316596 | −0.158298 | − | 0.987391i | \(-0.550601\pi\) | ||||
−0.158298 | + | 0.987391i | \(0.550601\pi\) | |||||||
\(858\) | 617.261 | 0.0245605 | ||||||||
\(859\) | −46688.0 | −1.85445 | −0.927227 | − | 0.374500i | \(-0.877814\pi\) | ||||
−0.927227 | + | 0.374500i | \(0.877814\pi\) | |||||||
\(860\) | 14557.0 | 0.577196 | ||||||||
\(861\) | −4918.29 | −0.194675 | ||||||||
\(862\) | −9506.11 | −0.375614 | ||||||||
\(863\) | −17044.1 | −0.672293 | −0.336147 | − | 0.941810i | \(-0.609124\pi\) | ||||
−0.336147 | + | 0.941810i | \(0.609124\pi\) | |||||||
\(864\) | −864.000 | −0.0340207 | ||||||||
\(865\) | −14412.6 | −0.566523 | ||||||||
\(866\) | 15425.9 | 0.605304 | ||||||||
\(867\) | 14687.7 | 0.575341 | ||||||||
\(868\) | −3262.56 | −0.127579 | ||||||||
\(869\) | 551.065 | 0.0215116 | ||||||||
\(870\) | −16186.2 | −0.630763 | ||||||||
\(871\) | −15063.9 | −0.586017 | ||||||||
\(872\) | −8726.67 | −0.338902 | ||||||||
\(873\) | 11326.1 | 0.439095 | ||||||||
\(874\) | −6123.20 | −0.236980 | ||||||||
\(875\) | −6040.47 | −0.233377 | ||||||||
\(876\) | 6433.71 | 0.248145 | ||||||||
\(877\) | 47244.8 | 1.81909 | 0.909547 | − | 0.415602i | \(-0.136429\pi\) | ||||
0.909547 | + | 0.415602i | \(0.136429\pi\) | |||||||
\(878\) | −15143.5 | −0.582084 | ||||||||
\(879\) | 214.990 | 0.00824964 | ||||||||
\(880\) | 491.898 | 0.0188430 | ||||||||
\(881\) | 17135.5 | 0.655290 | 0.327645 | − | 0.944801i | \(-0.393745\pi\) | ||||
0.327645 | + | 0.944801i | \(0.393745\pi\) | |||||||
\(882\) | 882.000 | 0.0336718 | ||||||||
\(883\) | 31343.5 | 1.19456 | 0.597278 | − | 0.802034i | \(-0.296249\pi\) | ||||
0.597278 | + | 0.802034i | \(0.296249\pi\) | |||||||
\(884\) | 756.608 | 0.0287867 | ||||||||
\(885\) | −12010.7 | −0.456199 | ||||||||
\(886\) | −25086.0 | −0.951221 | ||||||||
\(887\) | −19459.5 | −0.736625 | −0.368313 | − | 0.929702i | \(-0.620064\pi\) | ||||
−0.368313 | + | 0.929702i | \(0.620064\pi\) | |||||||
\(888\) | −1306.37 | −0.0493681 | ||||||||
\(889\) | −18878.0 | −0.712202 | ||||||||
\(890\) | −20505.6 | −0.772301 | ||||||||
\(891\) | −182.164 | −0.00684931 | ||||||||
\(892\) | 2869.61 | 0.107715 | ||||||||
\(893\) | −45485.6 | −1.70450 | ||||||||
\(894\) | 4463.50 | 0.166982 | ||||||||
\(895\) | −24485.1 | −0.914465 | ||||||||
\(896\) | −896.000 | −0.0334077 | ||||||||
\(897\) | 3156.37 | 0.117490 | ||||||||
\(898\) | 17510.9 | 0.650721 | ||||||||
\(899\) | −22994.2 | −0.853057 | ||||||||
\(900\) | 2227.53 | 0.0825011 | ||||||||
\(901\) | 473.924 | 0.0175235 | ||||||||
\(902\) | 1053.42 | 0.0388860 | ||||||||
\(903\) | −5590.54 | −0.206026 | ||||||||
\(904\) | −16347.6 | −0.601451 | ||||||||
\(905\) | −30861.4 | −1.13355 | ||||||||
\(906\) | 5060.83 | 0.185579 | ||||||||
\(907\) | −9773.95 | −0.357815 | −0.178908 | − | 0.983866i | \(-0.557256\pi\) | ||||
−0.178908 | + | 0.983866i | \(0.557256\pi\) | |||||||
\(908\) | −11993.5 | −0.438345 | ||||||||
\(909\) | −1683.44 | −0.0614260 | ||||||||
\(910\) | 8754.75 | 0.318920 | ||||||||
\(911\) | −3629.19 | −0.131987 | −0.0659936 | − | 0.997820i | \(-0.521022\pi\) | ||||
−0.0659936 | + | 0.997820i | \(0.521022\pi\) | |||||||
\(912\) | −6389.43 | −0.231990 | ||||||||
\(913\) | −1083.97 | −0.0392928 | ||||||||
\(914\) | −4123.28 | −0.149219 | ||||||||
\(915\) | −26601.3 | −0.961105 | ||||||||
\(916\) | −16868.7 | −0.608470 | ||||||||
\(917\) | 1705.24 | 0.0614091 | ||||||||
\(918\) | −223.288 | −0.00802789 | ||||||||
\(919\) | −52390.8 | −1.88054 | −0.940268 | − | 0.340434i | \(-0.889426\pi\) | ||||
−0.940268 | + | 0.340434i | \(0.889426\pi\) | |||||||
\(920\) | 2515.33 | 0.0901390 | ||||||||
\(921\) | 12171.5 | 0.435467 | ||||||||
\(922\) | −9848.07 | −0.351767 | ||||||||
\(923\) | −2630.47 | −0.0938061 | ||||||||
\(924\) | −188.911 | −0.00672589 | ||||||||
\(925\) | 3368.03 | 0.119719 | ||||||||
\(926\) | 8965.04 | 0.318153 | ||||||||
\(927\) | −207.591 | −0.00735511 | ||||||||
\(928\) | −6314.91 | −0.223381 | ||||||||
\(929\) | 1873.27 | 0.0661573 | 0.0330786 | − | 0.999453i | \(-0.489469\pi\) | ||||
0.0330786 | + | 0.999453i | \(0.489469\pi\) | |||||||
\(930\) | 9557.14 | 0.336980 | ||||||||
\(931\) | 6522.54 | 0.229611 | ||||||||
\(932\) | −23125.8 | −0.812779 | ||||||||
\(933\) | 8684.06 | 0.304720 | ||||||||
\(934\) | −18774.6 | −0.657733 | ||||||||
\(935\) | 127.124 | 0.00444641 | ||||||||
\(936\) | 3293.61 | 0.115016 | ||||||||
\(937\) | −44416.3 | −1.54858 | −0.774289 | − | 0.632832i | \(-0.781892\pi\) | ||||
−0.774289 | + | 0.632832i | \(0.781892\pi\) | |||||||
\(938\) | 4610.27 | 0.160480 | ||||||||
\(939\) | −20580.9 | −0.715264 | ||||||||
\(940\) | 18684.9 | 0.648333 | ||||||||
\(941\) | −14295.2 | −0.495227 | −0.247614 | − | 0.968859i | \(-0.579646\pi\) | ||||
−0.247614 | + | 0.968859i | \(0.579646\pi\) | |||||||
\(942\) | −4805.45 | −0.166210 | ||||||||
\(943\) | 5386.69 | 0.186018 | ||||||||
\(944\) | −4685.89 | −0.161560 | ||||||||
\(945\) | −2583.68 | −0.0889387 | ||||||||
\(946\) | 1197.41 | 0.0411535 | ||||||||
\(947\) | 29442.1 | 1.01029 | 0.505143 | − | 0.863036i | \(-0.331440\pi\) | ||||
0.505143 | + | 0.863036i | \(0.331440\pi\) | |||||||
\(948\) | 2940.39 | 0.100738 | ||||||||
\(949\) | −24525.6 | −0.838919 | ||||||||
\(950\) | 16473.0 | 0.562582 | ||||||||
\(951\) | 1947.90 | 0.0664195 | ||||||||
\(952\) | −231.558 | −0.00788323 | ||||||||
\(953\) | 12611.0 | 0.428658 | 0.214329 | − | 0.976762i | \(-0.431244\pi\) | ||||
0.214329 | + | 0.976762i | \(0.431244\pi\) | |||||||
\(954\) | 2063.05 | 0.0700143 | ||||||||
\(955\) | 26781.1 | 0.907450 | ||||||||
\(956\) | −7521.53 | −0.254460 | ||||||||
\(957\) | −1331.43 | −0.0449727 | ||||||||
\(958\) | −40874.7 | −1.37850 | ||||||||
\(959\) | −297.136 | −0.0100053 | ||||||||
\(960\) | 2624.69 | 0.0882411 | ||||||||
\(961\) | −16214.1 | −0.544262 | ||||||||
\(962\) | 4979.94 | 0.166902 | ||||||||
\(963\) | −18343.8 | −0.613832 | ||||||||
\(964\) | −14563.5 | −0.486575 | ||||||||
\(965\) | −8169.33 | −0.272518 | ||||||||
\(966\) | −966.000 | −0.0321745 | ||||||||
\(967\) | 2874.35 | 0.0955871 | 0.0477936 | − | 0.998857i | \(-0.484781\pi\) | ||||
0.0477936 | + | 0.998857i | \(0.484781\pi\) | |||||||
\(968\) | −10607.5 | −0.352210 | ||||||||
\(969\) | −1651.25 | −0.0547429 | ||||||||
\(970\) | −34406.8 | −1.13890 | ||||||||
\(971\) | 701.141 | 0.0231727 | 0.0115863 | − | 0.999933i | \(-0.496312\pi\) | ||||
0.0115863 | + | 0.999933i | \(0.496312\pi\) | |||||||
\(972\) | −972.000 | −0.0320750 | ||||||||
\(973\) | 1330.94 | 0.0438519 | ||||||||
\(974\) | 10760.4 | 0.353991 | ||||||||
\(975\) | −8491.44 | −0.278917 | ||||||||
\(976\) | −10378.3 | −0.340369 | ||||||||
\(977\) | −27477.9 | −0.899790 | −0.449895 | − | 0.893081i | \(-0.648539\pi\) | ||||
−0.449895 | + | 0.893081i | \(0.648539\pi\) | |||||||
\(978\) | 17292.0 | 0.565376 | ||||||||
\(979\) | −1686.72 | −0.0550643 | ||||||||
\(980\) | −2679.37 | −0.0873360 | ||||||||
\(981\) | −9817.51 | −0.319520 | ||||||||
\(982\) | −23526.4 | −0.764521 | ||||||||
\(983\) | −30697.6 | −0.996034 | −0.498017 | − | 0.867167i | \(-0.665938\pi\) | ||||
−0.498017 | + | 0.867167i | \(0.665938\pi\) | |||||||
\(984\) | 5620.90 | 0.182101 | ||||||||
\(985\) | −7898.39 | −0.255496 | ||||||||
\(986\) | −1632.00 | −0.0527113 | ||||||||
\(987\) | −7175.84 | −0.231418 | ||||||||
\(988\) | 24356.8 | 0.784304 | ||||||||
\(989\) | 6122.97 | 0.196865 | ||||||||
\(990\) | 553.385 | 0.0177654 | ||||||||
\(991\) | −34553.8 | −1.10761 | −0.553803 | − | 0.832648i | \(-0.686824\pi\) | ||||
−0.553803 | + | 0.832648i | \(0.686824\pi\) | |||||||
\(992\) | 3728.64 | 0.119339 | ||||||||
\(993\) | −1071.98 | −0.0342580 | ||||||||
\(994\) | 805.049 | 0.0256887 | ||||||||
\(995\) | −10256.0 | −0.326772 | ||||||||
\(996\) | −5783.91 | −0.184006 | ||||||||
\(997\) | −58846.7 | −1.86930 | −0.934651 | − | 0.355566i | \(-0.884288\pi\) | ||||
−0.934651 | + | 0.355566i | \(0.884288\pi\) | |||||||
\(998\) | 39355.2 | 1.24826 | ||||||||
\(999\) | −1469.67 | −0.0465447 |
(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 | 966.4.a.e.1.1 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.4.a.e.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial |