Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8002,2,Mod(1,8002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8002, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8002 = 2 \cdot 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8002.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.8962916974\) |
Analytic rank: | \(0\) |
Dimension: | \(77\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 8002.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −3.14624 | −1.81648 | −0.908241 | − | 0.418447i | \(-0.862575\pi\) | ||||
−0.908241 | + | 0.418447i | \(0.862575\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.08369 | 1.37907 | 0.689534 | − | 0.724253i | \(-0.257815\pi\) | ||||
0.689534 | + | 0.724253i | \(0.257815\pi\) | |||||||
\(6\) | 3.14624 | 1.28445 | ||||||||
\(7\) | 2.61077 | 0.986777 | 0.493388 | − | 0.869809i | \(-0.335758\pi\) | ||||
0.493388 | + | 0.869809i | \(0.335758\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 6.89883 | 2.29961 | ||||||||
\(10\) | −3.08369 | −0.975148 | ||||||||
\(11\) | 3.38926 | 1.02190 | 0.510950 | − | 0.859611i | \(-0.329294\pi\) | ||||
0.510950 | + | 0.859611i | \(0.329294\pi\) | |||||||
\(12\) | −3.14624 | −0.908241 | ||||||||
\(13\) | 4.00517 | 1.11084 | 0.555418 | − | 0.831572i | \(-0.312558\pi\) | ||||
0.555418 | + | 0.831572i | \(0.312558\pi\) | |||||||
\(14\) | −2.61077 | −0.697756 | ||||||||
\(15\) | −9.70203 | −2.50505 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.238806 | 0.0579189 | 0.0289595 | − | 0.999581i | \(-0.490781\pi\) | ||||
0.0289595 | + | 0.999581i | \(0.490781\pi\) | |||||||
\(18\) | −6.89883 | −1.62607 | ||||||||
\(19\) | 0.0258865 | 0.00593878 | 0.00296939 | − | 0.999996i | \(-0.499055\pi\) | ||||
0.00296939 | + | 0.999996i | \(0.499055\pi\) | |||||||
\(20\) | 3.08369 | 0.689534 | ||||||||
\(21\) | −8.21409 | −1.79246 | ||||||||
\(22\) | −3.38926 | −0.722592 | ||||||||
\(23\) | 2.40323 | 0.501107 | 0.250554 | − | 0.968103i | \(-0.419387\pi\) | ||||
0.250554 | + | 0.968103i | \(0.419387\pi\) | |||||||
\(24\) | 3.14624 | 0.642224 | ||||||||
\(25\) | 4.50915 | 0.901829 | ||||||||
\(26\) | −4.00517 | −0.785479 | ||||||||
\(27\) | −12.2666 | −2.36072 | ||||||||
\(28\) | 2.61077 | 0.493388 | ||||||||
\(29\) | −7.95586 | −1.47737 | −0.738683 | − | 0.674053i | \(-0.764552\pi\) | ||||
−0.738683 | + | 0.674053i | \(0.764552\pi\) | |||||||
\(30\) | 9.70203 | 1.77134 | ||||||||
\(31\) | 4.55958 | 0.818924 | 0.409462 | − | 0.912327i | \(-0.365716\pi\) | ||||
0.409462 | + | 0.912327i | \(0.365716\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −10.6634 | −1.85626 | ||||||||
\(34\) | −0.238806 | −0.0409548 | ||||||||
\(35\) | 8.05079 | 1.36083 | ||||||||
\(36\) | 6.89883 | 1.14980 | ||||||||
\(37\) | −9.29097 | −1.52743 | −0.763713 | − | 0.645556i | \(-0.776626\pi\) | ||||
−0.763713 | + | 0.645556i | \(0.776626\pi\) | |||||||
\(38\) | −0.0258865 | −0.00419935 | ||||||||
\(39\) | −12.6012 | −2.01781 | ||||||||
\(40\) | −3.08369 | −0.487574 | ||||||||
\(41\) | −0.667693 | −0.104276 | −0.0521380 | − | 0.998640i | \(-0.516604\pi\) | ||||
−0.0521380 | + | 0.998640i | \(0.516604\pi\) | |||||||
\(42\) | 8.21409 | 1.26746 | ||||||||
\(43\) | 11.2716 | 1.71891 | 0.859454 | − | 0.511213i | \(-0.170804\pi\) | ||||
0.859454 | + | 0.511213i | \(0.170804\pi\) | |||||||
\(44\) | 3.38926 | 0.510950 | ||||||||
\(45\) | 21.2738 | 3.17132 | ||||||||
\(46\) | −2.40323 | −0.354336 | ||||||||
\(47\) | 6.01678 | 0.877637 | 0.438818 | − | 0.898576i | \(-0.355397\pi\) | ||||
0.438818 | + | 0.898576i | \(0.355397\pi\) | |||||||
\(48\) | −3.14624 | −0.454121 | ||||||||
\(49\) | −0.183905 | −0.0262721 | ||||||||
\(50\) | −4.50915 | −0.637689 | ||||||||
\(51\) | −0.751340 | −0.105209 | ||||||||
\(52\) | 4.00517 | 0.555418 | ||||||||
\(53\) | 4.53839 | 0.623396 | 0.311698 | − | 0.950181i | \(-0.399102\pi\) | ||||
0.311698 | + | 0.950181i | \(0.399102\pi\) | |||||||
\(54\) | 12.2666 | 1.66928 | ||||||||
\(55\) | 10.4514 | 1.40927 | ||||||||
\(56\) | −2.61077 | −0.348878 | ||||||||
\(57\) | −0.0814452 | −0.0107877 | ||||||||
\(58\) | 7.95586 | 1.04466 | ||||||||
\(59\) | −5.43268 | −0.707275 | −0.353637 | − | 0.935383i | \(-0.615055\pi\) | ||||
−0.353637 | + | 0.935383i | \(0.615055\pi\) | |||||||
\(60\) | −9.70203 | −1.25253 | ||||||||
\(61\) | 5.12334 | 0.655976 | 0.327988 | − | 0.944682i | \(-0.393629\pi\) | ||||
0.327988 | + | 0.944682i | \(0.393629\pi\) | |||||||
\(62\) | −4.55958 | −0.579067 | ||||||||
\(63\) | 18.0112 | 2.26920 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 12.3507 | 1.53192 | ||||||||
\(66\) | 10.6634 | 1.31258 | ||||||||
\(67\) | −10.0561 | −1.22855 | −0.614273 | − | 0.789094i | \(-0.710551\pi\) | ||||
−0.614273 | + | 0.789094i | \(0.710551\pi\) | |||||||
\(68\) | 0.238806 | 0.0289595 | ||||||||
\(69\) | −7.56113 | −0.910252 | ||||||||
\(70\) | −8.05079 | −0.962254 | ||||||||
\(71\) | 9.94308 | 1.18003 | 0.590013 | − | 0.807394i | \(-0.299122\pi\) | ||||
0.590013 | + | 0.807394i | \(0.299122\pi\) | |||||||
\(72\) | −6.89883 | −0.813035 | ||||||||
\(73\) | −0.921882 | −0.107898 | −0.0539491 | − | 0.998544i | \(-0.517181\pi\) | ||||
−0.0539491 | + | 0.998544i | \(0.517181\pi\) | |||||||
\(74\) | 9.29097 | 1.08005 | ||||||||
\(75\) | −14.1869 | −1.63816 | ||||||||
\(76\) | 0.0258865 | 0.00296939 | ||||||||
\(77\) | 8.84856 | 1.00839 | ||||||||
\(78\) | 12.6012 | 1.42681 | ||||||||
\(79\) | −3.59191 | −0.404121 | −0.202061 | − | 0.979373i | \(-0.564764\pi\) | ||||
−0.202061 | + | 0.979373i | \(0.564764\pi\) | |||||||
\(80\) | 3.08369 | 0.344767 | ||||||||
\(81\) | 17.8973 | 1.98859 | ||||||||
\(82\) | 0.667693 | 0.0737343 | ||||||||
\(83\) | −2.35994 | −0.259037 | −0.129519 | − | 0.991577i | \(-0.541343\pi\) | ||||
−0.129519 | + | 0.991577i | \(0.541343\pi\) | |||||||
\(84\) | −8.21409 | −0.896231 | ||||||||
\(85\) | 0.736403 | 0.0798741 | ||||||||
\(86\) | −11.2716 | −1.21545 | ||||||||
\(87\) | 25.0311 | 2.68361 | ||||||||
\(88\) | −3.38926 | −0.361296 | ||||||||
\(89\) | 5.42030 | 0.574551 | 0.287275 | − | 0.957848i | \(-0.407251\pi\) | ||||
0.287275 | + | 0.957848i | \(0.407251\pi\) | |||||||
\(90\) | −21.2738 | −2.24246 | ||||||||
\(91\) | 10.4566 | 1.09615 | ||||||||
\(92\) | 2.40323 | 0.250554 | ||||||||
\(93\) | −14.3455 | −1.48756 | ||||||||
\(94\) | −6.01678 | −0.620583 | ||||||||
\(95\) | 0.0798260 | 0.00818998 | ||||||||
\(96\) | 3.14624 | 0.321112 | ||||||||
\(97\) | 6.57243 | 0.667329 | 0.333665 | − | 0.942692i | \(-0.391715\pi\) | ||||
0.333665 | + | 0.942692i | \(0.391715\pi\) | |||||||
\(98\) | 0.183905 | 0.0185772 | ||||||||
\(99\) | 23.3819 | 2.34997 | ||||||||
\(100\) | 4.50915 | 0.450915 | ||||||||
\(101\) | 15.5393 | 1.54622 | 0.773109 | − | 0.634274i | \(-0.218701\pi\) | ||||
0.773109 | + | 0.634274i | \(0.218701\pi\) | |||||||
\(102\) | 0.751340 | 0.0743938 | ||||||||
\(103\) | 16.6555 | 1.64112 | 0.820558 | − | 0.571563i | \(-0.193663\pi\) | ||||
0.820558 | + | 0.571563i | \(0.193663\pi\) | |||||||
\(104\) | −4.00517 | −0.392740 | ||||||||
\(105\) | −25.3297 | −2.47193 | ||||||||
\(106\) | −4.53839 | −0.440807 | ||||||||
\(107\) | 13.1120 | 1.26759 | 0.633793 | − | 0.773503i | \(-0.281497\pi\) | ||||
0.633793 | + | 0.773503i | \(0.281497\pi\) | |||||||
\(108\) | −12.2666 | −1.18036 | ||||||||
\(109\) | −7.46706 | −0.715215 | −0.357608 | − | 0.933872i | \(-0.616407\pi\) | ||||
−0.357608 | + | 0.933872i | \(0.616407\pi\) | |||||||
\(110\) | −10.4514 | −0.996504 | ||||||||
\(111\) | 29.2316 | 2.77454 | ||||||||
\(112\) | 2.61077 | 0.246694 | ||||||||
\(113\) | 0.107346 | 0.0100983 | 0.00504913 | − | 0.999987i | \(-0.498393\pi\) | ||||
0.00504913 | + | 0.999987i | \(0.498393\pi\) | |||||||
\(114\) | 0.0814452 | 0.00762805 | ||||||||
\(115\) | 7.41080 | 0.691061 | ||||||||
\(116\) | −7.95586 | −0.738683 | ||||||||
\(117\) | 27.6310 | 2.55449 | ||||||||
\(118\) | 5.43268 | 0.500119 | ||||||||
\(119\) | 0.623466 | 0.0571530 | ||||||||
\(120\) | 9.70203 | 0.885670 | ||||||||
\(121\) | 0.487066 | 0.0442788 | ||||||||
\(122\) | −5.12334 | −0.463845 | ||||||||
\(123\) | 2.10072 | 0.189416 | ||||||||
\(124\) | 4.55958 | 0.409462 | ||||||||
\(125\) | −1.51364 | −0.135384 | ||||||||
\(126\) | −18.0112 | −1.60457 | ||||||||
\(127\) | −2.97087 | −0.263622 | −0.131811 | − | 0.991275i | \(-0.542079\pi\) | ||||
−0.131811 | + | 0.991275i | \(0.542079\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −35.4633 | −3.12237 | ||||||||
\(130\) | −12.3507 | −1.08323 | ||||||||
\(131\) | 10.6464 | 0.930178 | 0.465089 | − | 0.885264i | \(-0.346022\pi\) | ||||
0.465089 | + | 0.885264i | \(0.346022\pi\) | |||||||
\(132\) | −10.6634 | −0.928131 | ||||||||
\(133\) | 0.0675836 | 0.00586025 | ||||||||
\(134\) | 10.0561 | 0.868713 | ||||||||
\(135\) | −37.8265 | −3.25559 | ||||||||
\(136\) | −0.238806 | −0.0204774 | ||||||||
\(137\) | 18.7855 | 1.60495 | 0.802477 | − | 0.596683i | \(-0.203515\pi\) | ||||
0.802477 | + | 0.596683i | \(0.203515\pi\) | |||||||
\(138\) | 7.56113 | 0.643646 | ||||||||
\(139\) | −4.48551 | −0.380456 | −0.190228 | − | 0.981740i | \(-0.560923\pi\) | ||||
−0.190228 | + | 0.981740i | \(0.560923\pi\) | |||||||
\(140\) | 8.05079 | 0.680416 | ||||||||
\(141\) | −18.9302 | −1.59421 | ||||||||
\(142\) | −9.94308 | −0.834405 | ||||||||
\(143\) | 13.5746 | 1.13516 | ||||||||
\(144\) | 6.89883 | 0.574902 | ||||||||
\(145\) | −24.5334 | −2.03739 | ||||||||
\(146\) | 0.921882 | 0.0762955 | ||||||||
\(147\) | 0.578609 | 0.0477229 | ||||||||
\(148\) | −9.29097 | −0.763713 | ||||||||
\(149\) | −15.2436 | −1.24881 | −0.624403 | − | 0.781103i | \(-0.714657\pi\) | ||||
−0.624403 | + | 0.781103i | \(0.714657\pi\) | |||||||
\(150\) | 14.1869 | 1.15835 | ||||||||
\(151\) | −1.68603 | −0.137207 | −0.0686037 | − | 0.997644i | \(-0.521854\pi\) | ||||
−0.0686037 | + | 0.997644i | \(0.521854\pi\) | |||||||
\(152\) | −0.0258865 | −0.00209967 | ||||||||
\(153\) | 1.64748 | 0.133191 | ||||||||
\(154\) | −8.84856 | −0.713037 | ||||||||
\(155\) | 14.0603 | 1.12935 | ||||||||
\(156\) | −12.6012 | −1.00891 | ||||||||
\(157\) | −11.9385 | −0.952796 | −0.476398 | − | 0.879230i | \(-0.658058\pi\) | ||||
−0.476398 | + | 0.879230i | \(0.658058\pi\) | |||||||
\(158\) | 3.59191 | 0.285757 | ||||||||
\(159\) | −14.2789 | −1.13239 | ||||||||
\(160\) | −3.08369 | −0.243787 | ||||||||
\(161\) | 6.27426 | 0.494481 | ||||||||
\(162\) | −17.8973 | −1.40615 | ||||||||
\(163\) | 3.33451 | 0.261179 | 0.130589 | − | 0.991437i | \(-0.458313\pi\) | ||||
0.130589 | + | 0.991437i | \(0.458313\pi\) | |||||||
\(164\) | −0.667693 | −0.0521380 | ||||||||
\(165\) | −32.8827 | −2.55991 | ||||||||
\(166\) | 2.35994 | 0.183167 | ||||||||
\(167\) | −20.8102 | −1.61034 | −0.805170 | − | 0.593044i | \(-0.797926\pi\) | ||||
−0.805170 | + | 0.593044i | \(0.797926\pi\) | |||||||
\(168\) | 8.21409 | 0.633731 | ||||||||
\(169\) | 3.04142 | 0.233955 | ||||||||
\(170\) | −0.736403 | −0.0564795 | ||||||||
\(171\) | 0.178587 | 0.0136569 | ||||||||
\(172\) | 11.2716 | 0.859454 | ||||||||
\(173\) | −14.2446 | −1.08300 | −0.541499 | − | 0.840701i | \(-0.682143\pi\) | ||||
−0.541499 | + | 0.840701i | \(0.682143\pi\) | |||||||
\(174\) | −25.0311 | −1.89760 | ||||||||
\(175\) | 11.7723 | 0.889904 | ||||||||
\(176\) | 3.38926 | 0.255475 | ||||||||
\(177\) | 17.0925 | 1.28475 | ||||||||
\(178\) | −5.42030 | −0.406269 | ||||||||
\(179\) | 17.0388 | 1.27354 | 0.636770 | − | 0.771054i | \(-0.280270\pi\) | ||||
0.636770 | + | 0.771054i | \(0.280270\pi\) | |||||||
\(180\) | 21.2738 | 1.58566 | ||||||||
\(181\) | −6.88283 | −0.511597 | −0.255798 | − | 0.966730i | \(-0.582338\pi\) | ||||
−0.255798 | + | 0.966730i | \(0.582338\pi\) | |||||||
\(182\) | −10.4566 | −0.775092 | ||||||||
\(183\) | −16.1193 | −1.19157 | ||||||||
\(184\) | −2.40323 | −0.177168 | ||||||||
\(185\) | −28.6505 | −2.10643 | ||||||||
\(186\) | 14.3455 | 1.05187 | ||||||||
\(187\) | 0.809374 | 0.0591873 | ||||||||
\(188\) | 6.01678 | 0.438818 | ||||||||
\(189\) | −32.0253 | −2.32950 | ||||||||
\(190\) | −0.0798260 | −0.00579119 | ||||||||
\(191\) | 13.6450 | 0.987316 | 0.493658 | − | 0.869656i | \(-0.335659\pi\) | ||||
0.493658 | + | 0.869656i | \(0.335659\pi\) | |||||||
\(192\) | −3.14624 | −0.227060 | ||||||||
\(193\) | 24.0091 | 1.72821 | 0.864106 | − | 0.503310i | \(-0.167885\pi\) | ||||
0.864106 | + | 0.503310i | \(0.167885\pi\) | |||||||
\(194\) | −6.57243 | −0.471873 | ||||||||
\(195\) | −38.8583 | −2.78270 | ||||||||
\(196\) | −0.183905 | −0.0131361 | ||||||||
\(197\) | 2.45319 | 0.174783 | 0.0873914 | − | 0.996174i | \(-0.472147\pi\) | ||||
0.0873914 | + | 0.996174i | \(0.472147\pi\) | |||||||
\(198\) | −23.3819 | −1.66168 | ||||||||
\(199\) | 9.03508 | 0.640480 | 0.320240 | − | 0.947336i | \(-0.396236\pi\) | ||||
0.320240 | + | 0.947336i | \(0.396236\pi\) | |||||||
\(200\) | −4.50915 | −0.318845 | ||||||||
\(201\) | 31.6388 | 2.23163 | ||||||||
\(202\) | −15.5393 | −1.09334 | ||||||||
\(203\) | −20.7709 | −1.45783 | ||||||||
\(204\) | −0.751340 | −0.0526043 | ||||||||
\(205\) | −2.05896 | −0.143804 | ||||||||
\(206\) | −16.6555 | −1.16044 | ||||||||
\(207\) | 16.5794 | 1.15235 | ||||||||
\(208\) | 4.00517 | 0.277709 | ||||||||
\(209\) | 0.0877361 | 0.00606883 | ||||||||
\(210\) | 25.3297 | 1.74792 | ||||||||
\(211\) | −5.91599 | −0.407274 | −0.203637 | − | 0.979047i | \(-0.565276\pi\) | ||||
−0.203637 | + | 0.979047i | \(0.565276\pi\) | |||||||
\(212\) | 4.53839 | 0.311698 | ||||||||
\(213\) | −31.2833 | −2.14350 | ||||||||
\(214\) | −13.1120 | −0.896319 | ||||||||
\(215\) | 34.7582 | 2.37049 | ||||||||
\(216\) | 12.2666 | 0.834640 | ||||||||
\(217\) | 11.9040 | 0.808095 | ||||||||
\(218\) | 7.46706 | 0.505733 | ||||||||
\(219\) | 2.90046 | 0.195995 | ||||||||
\(220\) | 10.4514 | 0.704635 | ||||||||
\(221\) | 0.956459 | 0.0643384 | ||||||||
\(222\) | −29.2316 | −1.96190 | ||||||||
\(223\) | 0.856135 | 0.0573311 | 0.0286655 | − | 0.999589i | \(-0.490874\pi\) | ||||
0.0286655 | + | 0.999589i | \(0.490874\pi\) | |||||||
\(224\) | −2.61077 | −0.174439 | ||||||||
\(225\) | 31.1078 | 2.07385 | ||||||||
\(226\) | −0.107346 | −0.00714055 | ||||||||
\(227\) | −13.6768 | −0.907761 | −0.453881 | − | 0.891063i | \(-0.649961\pi\) | ||||
−0.453881 | + | 0.891063i | \(0.649961\pi\) | |||||||
\(228\) | −0.0814452 | −0.00539384 | ||||||||
\(229\) | −11.4129 | −0.754188 | −0.377094 | − | 0.926175i | \(-0.623077\pi\) | ||||
−0.377094 | + | 0.926175i | \(0.623077\pi\) | |||||||
\(230\) | −7.41080 | −0.488654 | ||||||||
\(231\) | −27.8397 | −1.83172 | ||||||||
\(232\) | 7.95586 | 0.522328 | ||||||||
\(233\) | 6.64772 | 0.435507 | 0.217753 | − | 0.976004i | \(-0.430127\pi\) | ||||
0.217753 | + | 0.976004i | \(0.430127\pi\) | |||||||
\(234\) | −27.6310 | −1.80630 | ||||||||
\(235\) | 18.5539 | 1.21032 | ||||||||
\(236\) | −5.43268 | −0.353637 | ||||||||
\(237\) | 11.3010 | 0.734079 | ||||||||
\(238\) | −0.623466 | −0.0404133 | ||||||||
\(239\) | 10.3920 | 0.672205 | 0.336103 | − | 0.941825i | \(-0.390891\pi\) | ||||
0.336103 | + | 0.941825i | \(0.390891\pi\) | |||||||
\(240\) | −9.70203 | −0.626263 | ||||||||
\(241\) | −0.616335 | −0.0397016 | −0.0198508 | − | 0.999803i | \(-0.506319\pi\) | ||||
−0.0198508 | + | 0.999803i | \(0.506319\pi\) | |||||||
\(242\) | −0.487066 | −0.0313098 | ||||||||
\(243\) | −19.5094 | −1.25153 | ||||||||
\(244\) | 5.12334 | 0.327988 | ||||||||
\(245\) | −0.567106 | −0.0362311 | ||||||||
\(246\) | −2.10072 | −0.133937 | ||||||||
\(247\) | 0.103680 | 0.00659700 | ||||||||
\(248\) | −4.55958 | −0.289533 | ||||||||
\(249\) | 7.42494 | 0.470537 | ||||||||
\(250\) | 1.51364 | 0.0957312 | ||||||||
\(251\) | −11.8217 | −0.746177 | −0.373089 | − | 0.927796i | \(-0.621701\pi\) | ||||
−0.373089 | + | 0.927796i | \(0.621701\pi\) | |||||||
\(252\) | 18.0112 | 1.13460 | ||||||||
\(253\) | 8.14515 | 0.512081 | ||||||||
\(254\) | 2.97087 | 0.186409 | ||||||||
\(255\) | −2.31690 | −0.145090 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −24.0463 | −1.49997 | −0.749985 | − | 0.661455i | \(-0.769939\pi\) | ||||
−0.749985 | + | 0.661455i | \(0.769939\pi\) | |||||||
\(258\) | 35.4633 | 2.20785 | ||||||||
\(259\) | −24.2565 | −1.50723 | ||||||||
\(260\) | 12.3507 | 0.765959 | ||||||||
\(261\) | −54.8861 | −3.39737 | ||||||||
\(262\) | −10.6464 | −0.657735 | ||||||||
\(263\) | −0.539361 | −0.0332584 | −0.0166292 | − | 0.999862i | \(-0.505293\pi\) | ||||
−0.0166292 | + | 0.999862i | \(0.505293\pi\) | |||||||
\(264\) | 10.6634 | 0.656288 | ||||||||
\(265\) | 13.9950 | 0.859705 | ||||||||
\(266\) | −0.0675836 | −0.00414382 | ||||||||
\(267\) | −17.0536 | −1.04366 | ||||||||
\(268\) | −10.0561 | −0.614273 | ||||||||
\(269\) | 9.13670 | 0.557074 | 0.278537 | − | 0.960425i | \(-0.410150\pi\) | ||||
0.278537 | + | 0.960425i | \(0.410150\pi\) | |||||||
\(270\) | 37.8265 | 2.30205 | ||||||||
\(271\) | −18.0046 | −1.09370 | −0.546852 | − | 0.837229i | \(-0.684174\pi\) | ||||
−0.546852 | + | 0.837229i | \(0.684174\pi\) | |||||||
\(272\) | 0.238806 | 0.0144797 | ||||||||
\(273\) | −32.8989 | −1.99113 | ||||||||
\(274\) | −18.7855 | −1.13487 | ||||||||
\(275\) | 15.2827 | 0.921579 | ||||||||
\(276\) | −7.56113 | −0.455126 | ||||||||
\(277\) | 16.5401 | 0.993799 | 0.496899 | − | 0.867808i | \(-0.334472\pi\) | ||||
0.496899 | + | 0.867808i | \(0.334472\pi\) | |||||||
\(278\) | 4.48551 | 0.269023 | ||||||||
\(279\) | 31.4557 | 1.88321 | ||||||||
\(280\) | −8.05079 | −0.481127 | ||||||||
\(281\) | −25.0769 | −1.49597 | −0.747983 | − | 0.663718i | \(-0.768977\pi\) | ||||
−0.747983 | + | 0.663718i | \(0.768977\pi\) | |||||||
\(282\) | 18.9302 | 1.12728 | ||||||||
\(283\) | −6.26724 | −0.372549 | −0.186274 | − | 0.982498i | \(-0.559641\pi\) | ||||
−0.186274 | + | 0.982498i | \(0.559641\pi\) | |||||||
\(284\) | 9.94308 | 0.590013 | ||||||||
\(285\) | −0.251152 | −0.0148770 | ||||||||
\(286\) | −13.5746 | −0.802681 | ||||||||
\(287\) | −1.74319 | −0.102897 | ||||||||
\(288\) | −6.89883 | −0.406517 | ||||||||
\(289\) | −16.9430 | −0.996645 | ||||||||
\(290\) | 24.5334 | 1.44065 | ||||||||
\(291\) | −20.6784 | −1.21219 | ||||||||
\(292\) | −0.921882 | −0.0539491 | ||||||||
\(293\) | −3.99615 | −0.233458 | −0.116729 | − | 0.993164i | \(-0.537241\pi\) | ||||
−0.116729 | + | 0.993164i | \(0.537241\pi\) | |||||||
\(294\) | −0.578609 | −0.0337452 | ||||||||
\(295\) | −16.7527 | −0.975380 | ||||||||
\(296\) | 9.29097 | 0.540027 | ||||||||
\(297\) | −41.5748 | −2.41242 | ||||||||
\(298\) | 15.2436 | 0.883039 | ||||||||
\(299\) | 9.62534 | 0.556648 | ||||||||
\(300\) | −14.1869 | −0.819078 | ||||||||
\(301\) | 29.4276 | 1.69618 | ||||||||
\(302\) | 1.68603 | 0.0970203 | ||||||||
\(303\) | −48.8903 | −2.80868 | ||||||||
\(304\) | 0.0258865 | 0.00148469 | ||||||||
\(305\) | 15.7988 | 0.904636 | ||||||||
\(306\) | −1.64748 | −0.0941801 | ||||||||
\(307\) | 30.0684 | 1.71610 | 0.858048 | − | 0.513569i | \(-0.171677\pi\) | ||||
0.858048 | + | 0.513569i | \(0.171677\pi\) | |||||||
\(308\) | 8.84856 | 0.504193 | ||||||||
\(309\) | −52.4022 | −2.98106 | ||||||||
\(310\) | −14.0603 | −0.798573 | ||||||||
\(311\) | −32.5024 | −1.84304 | −0.921521 | − | 0.388330i | \(-0.873052\pi\) | ||||
−0.921521 | + | 0.388330i | \(0.873052\pi\) | |||||||
\(312\) | 12.6012 | 0.713405 | ||||||||
\(313\) | −6.14448 | −0.347307 | −0.173653 | − | 0.984807i | \(-0.555557\pi\) | ||||
−0.173653 | + | 0.984807i | \(0.555557\pi\) | |||||||
\(314\) | 11.9385 | 0.673729 | ||||||||
\(315\) | 55.5410 | 3.12938 | ||||||||
\(316\) | −3.59191 | −0.202061 | ||||||||
\(317\) | 2.16699 | 0.121710 | 0.0608550 | − | 0.998147i | \(-0.480617\pi\) | ||||
0.0608550 | + | 0.998147i | \(0.480617\pi\) | |||||||
\(318\) | 14.2789 | 0.800719 | ||||||||
\(319\) | −26.9645 | −1.50972 | ||||||||
\(320\) | 3.08369 | 0.172384 | ||||||||
\(321\) | −41.2535 | −2.30255 | ||||||||
\(322\) | −6.27426 | −0.349651 | ||||||||
\(323\) | 0.00618185 | 0.000343967 0 | ||||||||
\(324\) | 17.8973 | 0.994297 | ||||||||
\(325\) | 18.0599 | 1.00178 | ||||||||
\(326\) | −3.33451 | −0.184681 | ||||||||
\(327\) | 23.4932 | 1.29918 | ||||||||
\(328\) | 0.667693 | 0.0368672 | ||||||||
\(329\) | 15.7084 | 0.866031 | ||||||||
\(330\) | 32.8827 | 1.81013 | ||||||||
\(331\) | 9.82271 | 0.539905 | 0.269952 | − | 0.962874i | \(-0.412992\pi\) | ||||
0.269952 | + | 0.962874i | \(0.412992\pi\) | |||||||
\(332\) | −2.35994 | −0.129519 | ||||||||
\(333\) | −64.0968 | −3.51248 | ||||||||
\(334\) | 20.8102 | 1.13868 | ||||||||
\(335\) | −31.0098 | −1.69425 | ||||||||
\(336\) | −8.21409 | −0.448116 | ||||||||
\(337\) | 21.0002 | 1.14395 | 0.571976 | − | 0.820271i | \(-0.306177\pi\) | ||||
0.571976 | + | 0.820271i | \(0.306177\pi\) | |||||||
\(338\) | −3.04142 | −0.165431 | ||||||||
\(339\) | −0.337736 | −0.0183433 | ||||||||
\(340\) | 0.736403 | 0.0399371 | ||||||||
\(341\) | 15.4536 | 0.836858 | ||||||||
\(342\) | −0.178587 | −0.00965686 | ||||||||
\(343\) | −18.7555 | −1.01270 | ||||||||
\(344\) | −11.2716 | −0.607726 | ||||||||
\(345\) | −23.3162 | −1.25530 | ||||||||
\(346\) | 14.2446 | 0.765796 | ||||||||
\(347\) | 27.4959 | 1.47606 | 0.738029 | − | 0.674769i | \(-0.235757\pi\) | ||||
0.738029 | + | 0.674769i | \(0.235757\pi\) | |||||||
\(348\) | 25.0311 | 1.34181 | ||||||||
\(349\) | 9.78992 | 0.524042 | 0.262021 | − | 0.965062i | \(-0.415611\pi\) | ||||
0.262021 | + | 0.965062i | \(0.415611\pi\) | |||||||
\(350\) | −11.7723 | −0.629257 | ||||||||
\(351\) | −49.1301 | −2.62237 | ||||||||
\(352\) | −3.38926 | −0.180648 | ||||||||
\(353\) | −23.9154 | −1.27289 | −0.636445 | − | 0.771322i | \(-0.719596\pi\) | ||||
−0.636445 | + | 0.771322i | \(0.719596\pi\) | |||||||
\(354\) | −17.0925 | −0.908457 | ||||||||
\(355\) | 30.6614 | 1.62734 | ||||||||
\(356\) | 5.42030 | 0.287275 | ||||||||
\(357\) | −1.96157 | −0.103817 | ||||||||
\(358\) | −17.0388 | −0.900528 | ||||||||
\(359\) | 25.7610 | 1.35961 | 0.679806 | − | 0.733392i | \(-0.262064\pi\) | ||||
0.679806 | + | 0.733392i | \(0.262064\pi\) | |||||||
\(360\) | −21.2738 | −1.12123 | ||||||||
\(361\) | −18.9993 | −0.999965 | ||||||||
\(362\) | 6.88283 | 0.361754 | ||||||||
\(363\) | −1.53243 | −0.0804316 | ||||||||
\(364\) | 10.4566 | 0.548073 | ||||||||
\(365\) | −2.84280 | −0.148799 | ||||||||
\(366\) | 16.1193 | 0.842567 | ||||||||
\(367\) | 17.9719 | 0.938124 | 0.469062 | − | 0.883165i | \(-0.344592\pi\) | ||||
0.469062 | + | 0.883165i | \(0.344592\pi\) | |||||||
\(368\) | 2.40323 | 0.125277 | ||||||||
\(369\) | −4.60630 | −0.239794 | ||||||||
\(370\) | 28.6505 | 1.48947 | ||||||||
\(371\) | 11.8487 | 0.615152 | ||||||||
\(372\) | −14.3455 | −0.743781 | ||||||||
\(373\) | 33.6059 | 1.74005 | 0.870023 | − | 0.493011i | \(-0.164104\pi\) | ||||
0.870023 | + | 0.493011i | \(0.164104\pi\) | |||||||
\(374\) | −0.809374 | −0.0418517 | ||||||||
\(375\) | 4.76228 | 0.245923 | ||||||||
\(376\) | −6.01678 | −0.310291 | ||||||||
\(377\) | −31.8646 | −1.64111 | ||||||||
\(378\) | 32.0253 | 1.64721 | ||||||||
\(379\) | −0.257592 | −0.0132316 | −0.00661581 | − | 0.999978i | \(-0.502106\pi\) | ||||
−0.00661581 | + | 0.999978i | \(0.502106\pi\) | |||||||
\(380\) | 0.0798260 | 0.00409499 | ||||||||
\(381\) | 9.34708 | 0.478865 | ||||||||
\(382\) | −13.6450 | −0.698138 | ||||||||
\(383\) | −0.919190 | −0.0469684 | −0.0234842 | − | 0.999724i | \(-0.507476\pi\) | ||||
−0.0234842 | + | 0.999724i | \(0.507476\pi\) | |||||||
\(384\) | 3.14624 | 0.160556 | ||||||||
\(385\) | 27.2862 | 1.39063 | ||||||||
\(386\) | −24.0091 | −1.22203 | ||||||||
\(387\) | 77.7610 | 3.95282 | ||||||||
\(388\) | 6.57243 | 0.333665 | ||||||||
\(389\) | 28.4290 | 1.44141 | 0.720703 | − | 0.693244i | \(-0.243819\pi\) | ||||
0.720703 | + | 0.693244i | \(0.243819\pi\) | |||||||
\(390\) | 38.8583 | 1.96767 | ||||||||
\(391\) | 0.573904 | 0.0290236 | ||||||||
\(392\) | 0.183905 | 0.00928860 | ||||||||
\(393\) | −33.4960 | −1.68965 | ||||||||
\(394\) | −2.45319 | −0.123590 | ||||||||
\(395\) | −11.0763 | −0.557311 | ||||||||
\(396\) | 23.3819 | 1.17498 | ||||||||
\(397\) | −33.6514 | −1.68892 | −0.844459 | − | 0.535621i | \(-0.820078\pi\) | ||||
−0.844459 | + | 0.535621i | \(0.820078\pi\) | |||||||
\(398\) | −9.03508 | −0.452888 | ||||||||
\(399\) | −0.212634 | −0.0106450 | ||||||||
\(400\) | 4.50915 | 0.225457 | ||||||||
\(401\) | −8.75579 | −0.437243 | −0.218622 | − | 0.975810i | \(-0.570156\pi\) | ||||
−0.218622 | + | 0.975810i | \(0.570156\pi\) | |||||||
\(402\) | −31.6388 | −1.57800 | ||||||||
\(403\) | 18.2619 | 0.909690 | ||||||||
\(404\) | 15.5393 | 0.773109 | ||||||||
\(405\) | 55.1899 | 2.74241 | ||||||||
\(406\) | 20.7709 | 1.03084 | ||||||||
\(407\) | −31.4895 | −1.56088 | ||||||||
\(408\) | 0.751340 | 0.0371969 | ||||||||
\(409\) | −36.8347 | −1.82136 | −0.910681 | − | 0.413111i | \(-0.864442\pi\) | ||||
−0.910681 | + | 0.413111i | \(0.864442\pi\) | |||||||
\(410\) | 2.05896 | 0.101685 | ||||||||
\(411\) | −59.1037 | −2.91537 | ||||||||
\(412\) | 16.6555 | 0.820558 | ||||||||
\(413\) | −14.1835 | −0.697922 | ||||||||
\(414\) | −16.5794 | −0.814835 | ||||||||
\(415\) | −7.27733 | −0.357230 | ||||||||
\(416\) | −4.00517 | −0.196370 | ||||||||
\(417\) | 14.1125 | 0.691092 | ||||||||
\(418\) | −0.0877361 | −0.00429131 | ||||||||
\(419\) | −0.950481 | −0.0464340 | −0.0232170 | − | 0.999730i | \(-0.507391\pi\) | ||||
−0.0232170 | + | 0.999730i | \(0.507391\pi\) | |||||||
\(420\) | −25.3297 | −1.23596 | ||||||||
\(421\) | −10.7725 | −0.525021 | −0.262510 | − | 0.964929i | \(-0.584550\pi\) | ||||
−0.262510 | + | 0.964929i | \(0.584550\pi\) | |||||||
\(422\) | 5.91599 | 0.287986 | ||||||||
\(423\) | 41.5087 | 2.01822 | ||||||||
\(424\) | −4.53839 | −0.220404 | ||||||||
\(425\) | 1.07681 | 0.0522330 | ||||||||
\(426\) | 31.2833 | 1.51568 | ||||||||
\(427\) | 13.3758 | 0.647302 | ||||||||
\(428\) | 13.1120 | 0.633793 | ||||||||
\(429\) | −42.7088 | −2.06200 | ||||||||
\(430\) | −34.7582 | −1.67619 | ||||||||
\(431\) | 27.2947 | 1.31474 | 0.657370 | − | 0.753568i | \(-0.271669\pi\) | ||||
0.657370 | + | 0.753568i | \(0.271669\pi\) | |||||||
\(432\) | −12.2666 | −0.590179 | ||||||||
\(433\) | 32.5271 | 1.56315 | 0.781576 | − | 0.623810i | \(-0.214416\pi\) | ||||
0.781576 | + | 0.623810i | \(0.214416\pi\) | |||||||
\(434\) | −11.9040 | −0.571410 | ||||||||
\(435\) | 77.1880 | 3.70088 | ||||||||
\(436\) | −7.46706 | −0.357608 | ||||||||
\(437\) | 0.0622112 | 0.00297596 | ||||||||
\(438\) | −2.90046 | −0.138589 | ||||||||
\(439\) | −10.2456 | −0.488997 | −0.244498 | − | 0.969650i | \(-0.578623\pi\) | ||||
−0.244498 | + | 0.969650i | \(0.578623\pi\) | |||||||
\(440\) | −10.4514 | −0.498252 | ||||||||
\(441\) | −1.26873 | −0.0604156 | ||||||||
\(442\) | −0.956459 | −0.0454941 | ||||||||
\(443\) | 29.3010 | 1.39213 | 0.696066 | − | 0.717978i | \(-0.254932\pi\) | ||||
0.696066 | + | 0.717978i | \(0.254932\pi\) | |||||||
\(444\) | 29.2316 | 1.38727 | ||||||||
\(445\) | 16.7145 | 0.792345 | ||||||||
\(446\) | −0.856135 | −0.0405392 | ||||||||
\(447\) | 47.9601 | 2.26843 | ||||||||
\(448\) | 2.61077 | 0.123347 | ||||||||
\(449\) | 3.99304 | 0.188443 | 0.0942215 | − | 0.995551i | \(-0.469964\pi\) | ||||
0.0942215 | + | 0.995551i | \(0.469964\pi\) | |||||||
\(450\) | −31.1078 | −1.46644 | ||||||||
\(451\) | −2.26298 | −0.106560 | ||||||||
\(452\) | 0.107346 | 0.00504913 | ||||||||
\(453\) | 5.30467 | 0.249235 | ||||||||
\(454\) | 13.6768 | 0.641884 | ||||||||
\(455\) | 32.2448 | 1.51166 | ||||||||
\(456\) | 0.0814452 | 0.00381402 | ||||||||
\(457\) | −31.1775 | −1.45842 | −0.729211 | − | 0.684289i | \(-0.760113\pi\) | ||||
−0.729211 | + | 0.684289i | \(0.760113\pi\) | |||||||
\(458\) | 11.4129 | 0.533291 | ||||||||
\(459\) | −2.92935 | −0.136730 | ||||||||
\(460\) | 7.41080 | 0.345530 | ||||||||
\(461\) | −14.3164 | −0.666783 | −0.333391 | − | 0.942788i | \(-0.608193\pi\) | ||||
−0.333391 | + | 0.942788i | \(0.608193\pi\) | |||||||
\(462\) | 27.8397 | 1.29522 | ||||||||
\(463\) | 42.6472 | 1.98198 | 0.990992 | − | 0.133919i | \(-0.0427561\pi\) | ||||
0.990992 | + | 0.133919i | \(0.0427561\pi\) | |||||||
\(464\) | −7.95586 | −0.369342 | ||||||||
\(465\) | −44.2372 | −2.05145 | ||||||||
\(466\) | −6.64772 | −0.307950 | ||||||||
\(467\) | −23.4726 | −1.08618 | −0.543092 | − | 0.839673i | \(-0.682746\pi\) | ||||
−0.543092 | + | 0.839673i | \(0.682746\pi\) | |||||||
\(468\) | 27.6310 | 1.27724 | ||||||||
\(469\) | −26.2541 | −1.21230 | ||||||||
\(470\) | −18.5539 | −0.855826 | ||||||||
\(471\) | 37.5614 | 1.73074 | ||||||||
\(472\) | 5.43268 | 0.250059 | ||||||||
\(473\) | 38.2025 | 1.75655 | ||||||||
\(474\) | −11.3010 | −0.519072 | ||||||||
\(475\) | 0.116726 | 0.00535576 | ||||||||
\(476\) | 0.623466 | 0.0285765 | ||||||||
\(477\) | 31.3096 | 1.43357 | ||||||||
\(478\) | −10.3920 | −0.475321 | ||||||||
\(479\) | 9.85431 | 0.450255 | 0.225127 | − | 0.974329i | \(-0.427720\pi\) | ||||
0.225127 | + | 0.974329i | \(0.427720\pi\) | |||||||
\(480\) | 9.70203 | 0.442835 | ||||||||
\(481\) | −37.2120 | −1.69672 | ||||||||
\(482\) | 0.616335 | 0.0280733 | ||||||||
\(483\) | −19.7403 | −0.898216 | ||||||||
\(484\) | 0.487066 | 0.0221394 | ||||||||
\(485\) | 20.2673 | 0.920292 | ||||||||
\(486\) | 19.5094 | 0.884964 | ||||||||
\(487\) | −11.1216 | −0.503967 | −0.251984 | − | 0.967732i | \(-0.581083\pi\) | ||||
−0.251984 | + | 0.967732i | \(0.581083\pi\) | |||||||
\(488\) | −5.12334 | −0.231923 | ||||||||
\(489\) | −10.4912 | −0.474427 | ||||||||
\(490\) | 0.567106 | 0.0256192 | ||||||||
\(491\) | −13.1409 | −0.593042 | −0.296521 | − | 0.955026i | \(-0.595826\pi\) | ||||
−0.296521 | + | 0.955026i | \(0.595826\pi\) | |||||||
\(492\) | 2.10072 | 0.0947078 | ||||||||
\(493\) | −1.89991 | −0.0855675 | ||||||||
\(494\) | −0.103680 | −0.00466479 | ||||||||
\(495\) | 72.1025 | 3.24077 | ||||||||
\(496\) | 4.55958 | 0.204731 | ||||||||
\(497\) | 25.9591 | 1.16442 | ||||||||
\(498\) | −7.42494 | −0.332720 | ||||||||
\(499\) | −35.3049 | −1.58046 | −0.790232 | − | 0.612807i | \(-0.790040\pi\) | ||||
−0.790232 | + | 0.612807i | \(0.790040\pi\) | |||||||
\(500\) | −1.51364 | −0.0676922 | ||||||||
\(501\) | 65.4738 | 2.92515 | ||||||||
\(502\) | 11.8217 | 0.527627 | ||||||||
\(503\) | 20.1758 | 0.899596 | 0.449798 | − | 0.893130i | \(-0.351496\pi\) | ||||
0.449798 | + | 0.893130i | \(0.351496\pi\) | |||||||
\(504\) | −18.0112 | −0.802283 | ||||||||
\(505\) | 47.9184 | 2.13234 | ||||||||
\(506\) | −8.14515 | −0.362096 | ||||||||
\(507\) | −9.56903 | −0.424975 | ||||||||
\(508\) | −2.97087 | −0.131811 | ||||||||
\(509\) | 23.3159 | 1.03346 | 0.516730 | − | 0.856149i | \(-0.327149\pi\) | ||||
0.516730 | + | 0.856149i | \(0.327149\pi\) | |||||||
\(510\) | 2.31690 | 0.102594 | ||||||||
\(511\) | −2.40682 | −0.106471 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −0.317541 | −0.0140198 | ||||||||
\(514\) | 24.0463 | 1.06064 | ||||||||
\(515\) | 51.3604 | 2.26321 | ||||||||
\(516\) | −35.4633 | −1.56118 | ||||||||
\(517\) | 20.3924 | 0.896857 | ||||||||
\(518\) | 24.2565 | 1.06577 | ||||||||
\(519\) | 44.8170 | 1.96725 | ||||||||
\(520\) | −12.3507 | −0.541615 | ||||||||
\(521\) | 3.72546 | 0.163215 | 0.0816077 | − | 0.996665i | \(-0.473995\pi\) | ||||
0.0816077 | + | 0.996665i | \(0.473995\pi\) | |||||||
\(522\) | 54.8861 | 2.40230 | ||||||||
\(523\) | 16.5874 | 0.725317 | 0.362659 | − | 0.931922i | \(-0.381869\pi\) | ||||
0.362659 | + | 0.931922i | \(0.381869\pi\) | |||||||
\(524\) | 10.6464 | 0.465089 | ||||||||
\(525\) | −37.0385 | −1.61649 | ||||||||
\(526\) | 0.539361 | 0.0235172 | ||||||||
\(527\) | 1.08885 | 0.0474312 | ||||||||
\(528\) | −10.6634 | −0.464066 | ||||||||
\(529\) | −17.2245 | −0.748892 | ||||||||
\(530\) | −13.9950 | −0.607904 | ||||||||
\(531\) | −37.4791 | −1.62646 | ||||||||
\(532\) | 0.0675836 | 0.00293012 | ||||||||
\(533\) | −2.67422 | −0.115834 | ||||||||
\(534\) | 17.0536 | 0.737980 | ||||||||
\(535\) | 40.4334 | 1.74809 | ||||||||
\(536\) | 10.0561 | 0.434357 | ||||||||
\(537\) | −53.6081 | −2.31336 | ||||||||
\(538\) | −9.13670 | −0.393911 | ||||||||
\(539\) | −0.623301 | −0.0268475 | ||||||||
\(540\) | −37.8265 | −1.62780 | ||||||||
\(541\) | −4.65675 | −0.200209 | −0.100105 | − | 0.994977i | \(-0.531918\pi\) | ||||
−0.100105 | + | 0.994977i | \(0.531918\pi\) | |||||||
\(542\) | 18.0046 | 0.773365 | ||||||||
\(543\) | 21.6550 | 0.929307 | ||||||||
\(544\) | −0.238806 | −0.0102387 | ||||||||
\(545\) | −23.0261 | −0.986330 | ||||||||
\(546\) | 32.8989 | 1.40794 | ||||||||
\(547\) | −16.8673 | −0.721195 | −0.360598 | − | 0.932721i | \(-0.617427\pi\) | ||||
−0.360598 | + | 0.932721i | \(0.617427\pi\) | |||||||
\(548\) | 18.7855 | 0.802477 | ||||||||
\(549\) | 35.3450 | 1.50849 | ||||||||
\(550\) | −15.2827 | −0.651655 | ||||||||
\(551\) | −0.205950 | −0.00877375 | ||||||||
\(552\) | 7.56113 | 0.321823 | ||||||||
\(553\) | −9.37763 | −0.398777 | ||||||||
\(554\) | −16.5401 | −0.702722 | ||||||||
\(555\) | 90.1413 | 3.82629 | ||||||||
\(556\) | −4.48551 | −0.190228 | ||||||||
\(557\) | −0.750506 | −0.0317999 | −0.0159000 | − | 0.999874i | \(-0.505061\pi\) | ||||
−0.0159000 | + | 0.999874i | \(0.505061\pi\) | |||||||
\(558\) | −31.4557 | −1.33163 | ||||||||
\(559\) | 45.1448 | 1.90942 | ||||||||
\(560\) | 8.05079 | 0.340208 | ||||||||
\(561\) | −2.54649 | −0.107513 | ||||||||
\(562\) | 25.0769 | 1.05781 | ||||||||
\(563\) | 23.2228 | 0.978726 | 0.489363 | − | 0.872080i | \(-0.337229\pi\) | ||||
0.489363 | + | 0.872080i | \(0.337229\pi\) | |||||||
\(564\) | −18.9302 | −0.797106 | ||||||||
\(565\) | 0.331022 | 0.0139262 | ||||||||
\(566\) | 6.26724 | 0.263432 | ||||||||
\(567\) | 46.7258 | 1.96230 | ||||||||
\(568\) | −9.94308 | −0.417202 | ||||||||
\(569\) | −33.3465 | −1.39796 | −0.698978 | − | 0.715143i | \(-0.746362\pi\) | ||||
−0.698978 | + | 0.715143i | \(0.746362\pi\) | |||||||
\(570\) | 0.251152 | 0.0105196 | ||||||||
\(571\) | −15.2711 | −0.639074 | −0.319537 | − | 0.947574i | \(-0.603527\pi\) | ||||
−0.319537 | + | 0.947574i | \(0.603527\pi\) | |||||||
\(572\) | 13.5746 | 0.567581 | ||||||||
\(573\) | −42.9304 | −1.79344 | ||||||||
\(574\) | 1.74319 | 0.0727593 | ||||||||
\(575\) | 10.8365 | 0.451913 | ||||||||
\(576\) | 6.89883 | 0.287451 | ||||||||
\(577\) | 22.2326 | 0.925555 | 0.462777 | − | 0.886475i | \(-0.346853\pi\) | ||||
0.462777 | + | 0.886475i | \(0.346853\pi\) | |||||||
\(578\) | 16.9430 | 0.704735 | ||||||||
\(579\) | −75.5383 | −3.13927 | ||||||||
\(580\) | −24.5334 | −1.01869 | ||||||||
\(581\) | −6.16125 | −0.255612 | ||||||||
\(582\) | 20.6784 | 0.857149 | ||||||||
\(583\) | 15.3818 | 0.637048 | ||||||||
\(584\) | 0.921882 | 0.0381478 | ||||||||
\(585\) | 85.2055 | 3.52281 | ||||||||
\(586\) | 3.99615 | 0.165079 | ||||||||
\(587\) | −11.4075 | −0.470836 | −0.235418 | − | 0.971894i | \(-0.575646\pi\) | ||||
−0.235418 | + | 0.971894i | \(0.575646\pi\) | |||||||
\(588\) | 0.578609 | 0.0238614 | ||||||||
\(589\) | 0.118032 | 0.00486341 | ||||||||
\(590\) | 16.7527 | 0.689698 | ||||||||
\(591\) | −7.71833 | −0.317490 | ||||||||
\(592\) | −9.29097 | −0.381857 | ||||||||
\(593\) | 30.6077 | 1.25691 | 0.628454 | − | 0.777846i | \(-0.283688\pi\) | ||||
0.628454 | + | 0.777846i | \(0.283688\pi\) | |||||||
\(594\) | 41.5748 | 1.70584 | ||||||||
\(595\) | 1.92258 | 0.0788179 | ||||||||
\(596\) | −15.2436 | −0.624403 | ||||||||
\(597\) | −28.4265 | −1.16342 | ||||||||
\(598\) | −9.62534 | −0.393609 | ||||||||
\(599\) | −25.6496 | −1.04801 | −0.524006 | − | 0.851714i | \(-0.675563\pi\) | ||||
−0.524006 | + | 0.851714i | \(0.675563\pi\) | |||||||
\(600\) | 14.1869 | 0.579176 | ||||||||
\(601\) | 8.68896 | 0.354430 | 0.177215 | − | 0.984172i | \(-0.443291\pi\) | ||||
0.177215 | + | 0.984172i | \(0.443291\pi\) | |||||||
\(602\) | −29.4276 | −1.19938 | ||||||||
\(603\) | −69.3752 | −2.82518 | ||||||||
\(604\) | −1.68603 | −0.0686037 | ||||||||
\(605\) | 1.50196 | 0.0610634 | ||||||||
\(606\) | 48.8903 | 1.98603 | ||||||||
\(607\) | 5.94745 | 0.241399 | 0.120700 | − | 0.992689i | \(-0.461486\pi\) | ||||
0.120700 | + | 0.992689i | \(0.461486\pi\) | |||||||
\(608\) | −0.0258865 | −0.00104984 | ||||||||
\(609\) | 65.3502 | 2.64812 | ||||||||
\(610\) | −15.7988 | −0.639674 | ||||||||
\(611\) | 24.0982 | 0.974910 | ||||||||
\(612\) | 1.64748 | 0.0665954 | ||||||||
\(613\) | −9.24727 | −0.373494 | −0.186747 | − | 0.982408i | \(-0.559794\pi\) | ||||
−0.186747 | + | 0.982408i | \(0.559794\pi\) | |||||||
\(614\) | −30.0684 | −1.21346 | ||||||||
\(615\) | 6.47797 | 0.261217 | ||||||||
\(616\) | −8.84856 | −0.356518 | ||||||||
\(617\) | −9.12218 | −0.367245 | −0.183622 | − | 0.982997i | \(-0.558782\pi\) | ||||
−0.183622 | + | 0.982997i | \(0.558782\pi\) | |||||||
\(618\) | 52.4022 | 2.10793 | ||||||||
\(619\) | 12.1582 | 0.488680 | 0.244340 | − | 0.969690i | \(-0.421429\pi\) | ||||
0.244340 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(620\) | 14.0603 | 0.564676 | ||||||||
\(621\) | −29.4795 | −1.18297 | ||||||||
\(622\) | 32.5024 | 1.30323 | ||||||||
\(623\) | 14.1511 | 0.566953 | ||||||||
\(624\) | −12.6012 | −0.504453 | ||||||||
\(625\) | −27.2133 | −1.08853 | ||||||||
\(626\) | 6.14448 | 0.245583 | ||||||||
\(627\) | −0.276039 | −0.0110239 | ||||||||
\(628\) | −11.9385 | −0.476398 | ||||||||
\(629\) | −2.21874 | −0.0884669 | ||||||||
\(630\) | −55.5410 | −2.21281 | ||||||||
\(631\) | −38.6267 | −1.53771 | −0.768853 | − | 0.639426i | \(-0.779172\pi\) | ||||
−0.768853 | + | 0.639426i | \(0.779172\pi\) | |||||||
\(632\) | 3.59191 | 0.142878 | ||||||||
\(633\) | 18.6131 | 0.739805 | ||||||||
\(634\) | −2.16699 | −0.0860620 | ||||||||
\(635\) | −9.16125 | −0.363553 | ||||||||
\(636\) | −14.2789 | −0.566194 | ||||||||
\(637\) | −0.736571 | −0.0291840 | ||||||||
\(638\) | 26.9645 | 1.06753 | ||||||||
\(639\) | 68.5956 | 2.71360 | ||||||||
\(640\) | −3.08369 | −0.121894 | ||||||||
\(641\) | 23.7027 | 0.936198 | 0.468099 | − | 0.883676i | \(-0.344939\pi\) | ||||
0.468099 | + | 0.883676i | \(0.344939\pi\) | |||||||
\(642\) | 41.2535 | 1.62815 | ||||||||
\(643\) | −9.69181 | −0.382208 | −0.191104 | − | 0.981570i | \(-0.561207\pi\) | ||||
−0.191104 | + | 0.981570i | \(0.561207\pi\) | |||||||
\(644\) | 6.27426 | 0.247240 | ||||||||
\(645\) | −109.358 | −4.30596 | ||||||||
\(646\) | −0.00618185 | −0.000243222 0 | ||||||||
\(647\) | 15.5086 | 0.609706 | 0.304853 | − | 0.952399i | \(-0.401393\pi\) | ||||
0.304853 | + | 0.952399i | \(0.401393\pi\) | |||||||
\(648\) | −17.8973 | −0.703074 | ||||||||
\(649\) | −18.4128 | −0.722764 | ||||||||
\(650\) | −18.0599 | −0.708368 | ||||||||
\(651\) | −37.4528 | −1.46789 | ||||||||
\(652\) | 3.33451 | 0.130589 | ||||||||
\(653\) | −8.73305 | −0.341751 | −0.170875 | − | 0.985293i | \(-0.554660\pi\) | ||||
−0.170875 | + | 0.985293i | \(0.554660\pi\) | |||||||
\(654\) | −23.4932 | −0.918656 | ||||||||
\(655\) | 32.8301 | 1.28278 | ||||||||
\(656\) | −0.667693 | −0.0260690 | ||||||||
\(657\) | −6.35991 | −0.248124 | ||||||||
\(658\) | −15.7084 | −0.612377 | ||||||||
\(659\) | 18.7596 | 0.730770 | 0.365385 | − | 0.930857i | \(-0.380937\pi\) | ||||
0.365385 | + | 0.930857i | \(0.380937\pi\) | |||||||
\(660\) | −32.8827 | −1.27996 | ||||||||
\(661\) | 32.6408 | 1.26958 | 0.634790 | − | 0.772685i | \(-0.281087\pi\) | ||||
0.634790 | + | 0.772685i | \(0.281087\pi\) | |||||||
\(662\) | −9.82271 | −0.381770 | ||||||||
\(663\) | −3.00925 | −0.116870 | ||||||||
\(664\) | 2.35994 | 0.0915835 | ||||||||
\(665\) | 0.208407 | 0.00808168 | ||||||||
\(666\) | 64.0968 | 2.48370 | ||||||||
\(667\) | −19.1197 | −0.740319 | ||||||||
\(668\) | −20.8102 | −0.805170 | ||||||||
\(669\) | −2.69361 | −0.104141 | ||||||||
\(670\) | 31.0098 | 1.19801 | ||||||||
\(671\) | 17.3643 | 0.670342 | ||||||||
\(672\) | 8.21409 | 0.316866 | ||||||||
\(673\) | 5.60520 | 0.216064 | 0.108032 | − | 0.994147i | \(-0.465545\pi\) | ||||
0.108032 | + | 0.994147i | \(0.465545\pi\) | |||||||
\(674\) | −21.0002 | −0.808896 | ||||||||
\(675\) | −55.3121 | −2.12896 | ||||||||
\(676\) | 3.04142 | 0.116978 | ||||||||
\(677\) | −4.24856 | −0.163285 | −0.0816427 | − | 0.996662i | \(-0.526017\pi\) | ||||
−0.0816427 | + | 0.996662i | \(0.526017\pi\) | |||||||
\(678\) | 0.337736 | 0.0129707 | ||||||||
\(679\) | 17.1591 | 0.658505 | ||||||||
\(680\) | −0.736403 | −0.0282398 | ||||||||
\(681\) | 43.0305 | 1.64893 | ||||||||
\(682\) | −15.4536 | −0.591748 | ||||||||
\(683\) | 21.8681 | 0.836760 | 0.418380 | − | 0.908272i | \(-0.362598\pi\) | ||||
0.418380 | + | 0.908272i | \(0.362598\pi\) | |||||||
\(684\) | 0.178587 | 0.00682843 | ||||||||
\(685\) | 57.9287 | 2.21334 | ||||||||
\(686\) | 18.7555 | 0.716088 | ||||||||
\(687\) | 35.9078 | 1.36997 | ||||||||
\(688\) | 11.2716 | 0.429727 | ||||||||
\(689\) | 18.1770 | 0.692490 | ||||||||
\(690\) | 23.3162 | 0.887631 | ||||||||
\(691\) | −1.27015 | −0.0483188 | −0.0241594 | − | 0.999708i | \(-0.507691\pi\) | ||||
−0.0241594 | + | 0.999708i | \(0.507691\pi\) | |||||||
\(692\) | −14.2446 | −0.541499 | ||||||||
\(693\) | 61.0447 | 2.31889 | ||||||||
\(694\) | −27.4959 | −1.04373 | ||||||||
\(695\) | −13.8319 | −0.524675 | ||||||||
\(696\) | −25.0311 | −0.948800 | ||||||||
\(697\) | −0.159449 | −0.00603956 | ||||||||
\(698\) | −9.78992 | −0.370554 | ||||||||
\(699\) | −20.9153 | −0.791090 | ||||||||
\(700\) | 11.7723 | 0.444952 | ||||||||
\(701\) | −25.2956 | −0.955401 | −0.477700 | − | 0.878523i | \(-0.658530\pi\) | ||||
−0.477700 | + | 0.878523i | \(0.658530\pi\) | |||||||
\(702\) | 49.1301 | 1.85429 | ||||||||
\(703\) | −0.240511 | −0.00907105 | ||||||||
\(704\) | 3.38926 | 0.127737 | ||||||||
\(705\) | −58.3749 | −2.19853 | ||||||||
\(706\) | 23.9154 | 0.900069 | ||||||||
\(707\) | 40.5694 | 1.52577 | ||||||||
\(708\) | 17.0925 | 0.642376 | ||||||||
\(709\) | 25.8575 | 0.971100 | 0.485550 | − | 0.874209i | \(-0.338619\pi\) | ||||
0.485550 | + | 0.874209i | \(0.338619\pi\) | |||||||
\(710\) | −30.6614 | −1.15070 | ||||||||
\(711\) | −24.7800 | −0.929321 | ||||||||
\(712\) | −5.42030 | −0.203134 | ||||||||
\(713\) | 10.9577 | 0.410369 | ||||||||
\(714\) | 1.96157 | 0.0734100 | ||||||||
\(715\) | 41.8598 | 1.56547 | ||||||||
\(716\) | 17.0388 | 0.636770 | ||||||||
\(717\) | −32.6958 | −1.22105 | ||||||||
\(718\) | −25.7610 | −0.961391 | ||||||||
\(719\) | −6.73270 | −0.251087 | −0.125544 | − | 0.992088i | \(-0.540068\pi\) | ||||
−0.125544 | + | 0.992088i | \(0.540068\pi\) | |||||||
\(720\) | 21.2738 | 0.792829 | ||||||||
\(721\) | 43.4836 | 1.61941 | ||||||||
\(722\) | 18.9993 | 0.707082 | ||||||||
\(723\) | 1.93914 | 0.0721173 | ||||||||
\(724\) | −6.88283 | −0.255798 | ||||||||
\(725\) | −35.8741 | −1.33233 | ||||||||
\(726\) | 1.53243 | 0.0568737 | ||||||||
\(727\) | 39.7352 | 1.47370 | 0.736849 | − | 0.676057i | \(-0.236313\pi\) | ||||
0.736849 | + | 0.676057i | \(0.236313\pi\) | |||||||
\(728\) | −10.4566 | −0.387546 | ||||||||
\(729\) | 7.68920 | 0.284785 | ||||||||
\(730\) | 2.84280 | 0.105217 | ||||||||
\(731\) | 2.69173 | 0.0995572 | ||||||||
\(732\) | −16.1193 | −0.595785 | ||||||||
\(733\) | −36.7125 | −1.35601 | −0.678003 | − | 0.735059i | \(-0.737154\pi\) | ||||
−0.678003 | + | 0.735059i | \(0.737154\pi\) | |||||||
\(734\) | −17.9719 | −0.663353 | ||||||||
\(735\) | 1.78425 | 0.0658131 | ||||||||
\(736\) | −2.40323 | −0.0885841 | ||||||||
\(737\) | −34.0826 | −1.25545 | ||||||||
\(738\) | 4.60630 | 0.169560 | ||||||||
\(739\) | −27.6405 | −1.01677 | −0.508386 | − | 0.861130i | \(-0.669758\pi\) | ||||
−0.508386 | + | 0.861130i | \(0.669758\pi\) | |||||||
\(740\) | −28.6505 | −1.05321 | ||||||||
\(741\) | −0.326202 | −0.0119833 | ||||||||
\(742\) | −11.8487 | −0.434978 | ||||||||
\(743\) | 40.6209 | 1.49024 | 0.745118 | − | 0.666933i | \(-0.232393\pi\) | ||||
0.745118 | + | 0.666933i | \(0.232393\pi\) | |||||||
\(744\) | 14.3455 | 0.525933 | ||||||||
\(745\) | −47.0066 | −1.72219 | ||||||||
\(746\) | −33.6059 | −1.23040 | ||||||||
\(747\) | −16.2808 | −0.595684 | ||||||||
\(748\) | 0.809374 | 0.0295937 | ||||||||
\(749\) | 34.2324 | 1.25082 | ||||||||
\(750\) | −4.76228 | −0.173894 | ||||||||
\(751\) | −38.3572 | −1.39968 | −0.699838 | − | 0.714302i | \(-0.746744\pi\) | ||||
−0.699838 | + | 0.714302i | \(0.746744\pi\) | |||||||
\(752\) | 6.01678 | 0.219409 | ||||||||
\(753\) | 37.1938 | 1.35542 | ||||||||
\(754\) | 31.8646 | 1.16044 | ||||||||
\(755\) | −5.19921 | −0.189218 | ||||||||
\(756\) | −32.0253 | −1.16475 | ||||||||
\(757\) | 30.2585 | 1.09976 | 0.549882 | − | 0.835243i | \(-0.314673\pi\) | ||||
0.549882 | + | 0.835243i | \(0.314673\pi\) | |||||||
\(758\) | 0.257592 | 0.00935616 | ||||||||
\(759\) | −25.6266 | −0.930187 | ||||||||
\(760\) | −0.0798260 | −0.00289559 | ||||||||
\(761\) | 26.0598 | 0.944666 | 0.472333 | − | 0.881420i | \(-0.343412\pi\) | ||||
0.472333 | + | 0.881420i | \(0.343412\pi\) | |||||||
\(762\) | −9.34708 | −0.338609 | ||||||||
\(763\) | −19.4948 | −0.705757 | ||||||||
\(764\) | 13.6450 | 0.493658 | ||||||||
\(765\) | 5.08032 | 0.183679 | ||||||||
\(766\) | 0.919190 | 0.0332117 | ||||||||
\(767\) | −21.7588 | −0.785666 | ||||||||
\(768\) | −3.14624 | −0.113530 | ||||||||
\(769\) | −27.1532 | −0.979169 | −0.489585 | − | 0.871956i | \(-0.662852\pi\) | ||||
−0.489585 | + | 0.871956i | \(0.662852\pi\) | |||||||
\(770\) | −27.2862 | −0.983327 | ||||||||
\(771\) | 75.6556 | 2.72467 | ||||||||
\(772\) | 24.0091 | 0.864106 | ||||||||
\(773\) | 12.5518 | 0.451456 | 0.225728 | − | 0.974190i | \(-0.427524\pi\) | ||||
0.225728 | + | 0.974190i | \(0.427524\pi\) | |||||||
\(774\) | −77.7610 | −2.79506 | ||||||||
\(775\) | 20.5598 | 0.738530 | ||||||||
\(776\) | −6.57243 | −0.235936 | ||||||||
\(777\) | 76.3169 | 2.73785 | ||||||||
\(778\) | −28.4290 | −1.01923 | ||||||||
\(779\) | −0.0172842 | −0.000619272 0 | ||||||||
\(780\) | −38.8583 | −1.39135 | ||||||||
\(781\) | 33.6997 | 1.20587 | ||||||||
\(782\) | −0.573904 | −0.0205228 | ||||||||
\(783\) | 97.5918 | 3.48765 | ||||||||
\(784\) | −0.183905 | −0.00656803 | ||||||||
\(785\) | −36.8147 | −1.31397 | ||||||||
\(786\) | 33.4960 | 1.19476 | ||||||||
\(787\) | 27.8035 | 0.991086 | 0.495543 | − | 0.868583i | \(-0.334969\pi\) | ||||
0.495543 | + | 0.868583i | \(0.334969\pi\) | |||||||
\(788\) | 2.45319 | 0.0873914 | ||||||||
\(789\) | 1.69696 | 0.0604133 | ||||||||
\(790\) | 11.0763 | 0.394078 | ||||||||
\(791\) | 0.280255 | 0.00996472 | ||||||||
\(792\) | −23.3819 | −0.830840 | ||||||||
\(793\) | 20.5199 | 0.728682 | ||||||||
\(794\) | 33.6514 | 1.19424 | ||||||||
\(795\) | −44.0316 | −1.56164 | ||||||||
\(796\) | 9.03508 | 0.320240 | ||||||||
\(797\) | −31.9823 | −1.13287 | −0.566435 | − | 0.824106i | \(-0.691678\pi\) | ||||
−0.566435 | + | 0.824106i | \(0.691678\pi\) | |||||||
\(798\) | 0.212634 | 0.00752718 | ||||||||
\(799\) | 1.43684 | 0.0508318 | ||||||||
\(800\) | −4.50915 | −0.159422 | ||||||||
\(801\) | 37.3937 | 1.32124 | ||||||||
\(802\) | 8.75579 | 0.309178 | ||||||||
\(803\) | −3.12450 | −0.110261 | ||||||||
\(804\) | 31.6388 | 1.11582 | ||||||||
\(805\) | 19.3479 | 0.681923 | ||||||||
\(806\) | −18.2619 | −0.643248 | ||||||||
\(807\) | −28.7463 | −1.01192 | ||||||||
\(808\) | −15.5393 | −0.546670 | ||||||||
\(809\) | 7.98539 | 0.280751 | 0.140376 | − | 0.990098i | \(-0.455169\pi\) | ||||
0.140376 | + | 0.990098i | \(0.455169\pi\) | |||||||
\(810\) | −55.1899 | −1.93917 | ||||||||
\(811\) | 48.9140 | 1.71760 | 0.858801 | − | 0.512309i | \(-0.171210\pi\) | ||||
0.858801 | + | 0.512309i | \(0.171210\pi\) | |||||||
\(812\) | −20.7709 | −0.728915 | ||||||||
\(813\) | 56.6469 | 1.98669 | ||||||||
\(814\) | 31.4895 | 1.10371 | ||||||||
\(815\) | 10.2826 | 0.360183 | ||||||||
\(816\) | −0.751340 | −0.0263022 | ||||||||
\(817\) | 0.291783 | 0.0102082 | ||||||||
\(818\) | 36.8347 | 1.28790 | ||||||||
\(819\) | 72.1381 | 2.52071 | ||||||||
\(820\) | −2.05896 | −0.0719019 | ||||||||
\(821\) | −8.37063 | −0.292137 | −0.146068 | − | 0.989274i | \(-0.546662\pi\) | ||||
−0.146068 | + | 0.989274i | \(0.546662\pi\) | |||||||
\(822\) | 59.1037 | 2.06148 | ||||||||
\(823\) | 22.8868 | 0.797785 | 0.398892 | − | 0.916998i | \(-0.369395\pi\) | ||||
0.398892 | + | 0.916998i | \(0.369395\pi\) | |||||||
\(824\) | −16.6555 | −0.580222 | ||||||||
\(825\) | −48.0829 | −1.67403 | ||||||||
\(826\) | 14.1835 | 0.493505 | ||||||||
\(827\) | −28.4787 | −0.990301 | −0.495151 | − | 0.868807i | \(-0.664887\pi\) | ||||
−0.495151 | + | 0.868807i | \(0.664887\pi\) | |||||||
\(828\) | 16.5794 | 0.576175 | ||||||||
\(829\) | −40.6456 | −1.41168 | −0.705841 | − | 0.708371i | \(-0.749431\pi\) | ||||
−0.705841 | + | 0.708371i | \(0.749431\pi\) | |||||||
\(830\) | 7.27733 | 0.252600 | ||||||||
\(831\) | −52.0392 | −1.80522 | ||||||||
\(832\) | 4.00517 | 0.138854 | ||||||||
\(833\) | −0.0439176 | −0.00152165 | ||||||||
\(834\) | −14.1125 | −0.488676 | ||||||||
\(835\) | −64.1721 | −2.22077 | ||||||||
\(836\) | 0.0877361 | 0.00303442 | ||||||||
\(837\) | −55.9307 | −1.93325 | ||||||||
\(838\) | 0.950481 | 0.0328338 | ||||||||
\(839\) | 1.27190 | 0.0439108 | 0.0219554 | − | 0.999759i | \(-0.493011\pi\) | ||||
0.0219554 | + | 0.999759i | \(0.493011\pi\) | |||||||
\(840\) | 25.3297 | 0.873958 | ||||||||
\(841\) | 34.2958 | 1.18261 | ||||||||
\(842\) | 10.7725 | 0.371246 | ||||||||
\(843\) | 78.8981 | 2.71740 | ||||||||
\(844\) | −5.91599 | −0.203637 | ||||||||
\(845\) | 9.37879 | 0.322640 | ||||||||
\(846\) | −41.5087 | −1.42710 | ||||||||
\(847\) | 1.27162 | 0.0436932 | ||||||||
\(848\) | 4.53839 | 0.155849 | ||||||||
\(849\) | 19.7182 | 0.676728 | ||||||||
\(850\) | −1.07681 | −0.0369343 | ||||||||
\(851\) | −22.3283 | −0.765404 | ||||||||
\(852\) | −31.2833 | −1.07175 | ||||||||
\(853\) | 45.6111 | 1.56169 | 0.780847 | − | 0.624723i | \(-0.214788\pi\) | ||||
0.780847 | + | 0.624723i | \(0.214788\pi\) | |||||||
\(854\) | −13.3758 | −0.457712 | ||||||||
\(855\) | 0.550706 | 0.0188337 | ||||||||
\(856\) | −13.1120 | −0.448159 | ||||||||
\(857\) | 14.4680 | 0.494218 | 0.247109 | − | 0.968988i | \(-0.420519\pi\) | ||||
0.247109 | + | 0.968988i | \(0.420519\pi\) | |||||||
\(858\) | 42.7088 | 1.45806 | ||||||||
\(859\) | −43.8964 | −1.49773 | −0.748863 | − | 0.662725i | \(-0.769400\pi\) | ||||
−0.748863 | + | 0.662725i | \(0.769400\pi\) | |||||||
\(860\) | 34.7582 | 1.18525 | ||||||||
\(861\) | 5.48449 | 0.186911 | ||||||||
\(862\) | −27.2947 | −0.929662 | ||||||||
\(863\) | −23.0416 | −0.784346 | −0.392173 | − | 0.919891i | \(-0.628277\pi\) | ||||
−0.392173 | + | 0.919891i | \(0.628277\pi\) | |||||||
\(864\) | 12.2666 | 0.417320 | ||||||||
\(865\) | −43.9260 | −1.49353 | ||||||||
\(866\) | −32.5271 | −1.10532 | ||||||||
\(867\) | 53.3067 | 1.81039 | ||||||||
\(868\) | 11.9040 | 0.404048 | ||||||||
\(869\) | −12.1739 | −0.412971 | ||||||||
\(870\) | −77.1880 | −2.61692 | ||||||||
\(871\) | −40.2763 | −1.36471 | ||||||||
\(872\) | 7.46706 | 0.252867 | ||||||||
\(873\) | 45.3421 | 1.53460 | ||||||||
\(874\) | −0.0622112 | −0.00210432 | ||||||||
\(875\) | −3.95177 | −0.133594 | ||||||||
\(876\) | 2.90046 | 0.0979976 | ||||||||
\(877\) | −51.1981 | −1.72884 | −0.864419 | − | 0.502772i | \(-0.832314\pi\) | ||||
−0.864419 | + | 0.502772i | \(0.832314\pi\) | |||||||
\(878\) | 10.2456 | 0.345773 | ||||||||
\(879\) | 12.5728 | 0.424072 | ||||||||
\(880\) | 10.4514 | 0.352317 | ||||||||
\(881\) | 5.69895 | 0.192002 | 0.0960012 | − | 0.995381i | \(-0.469395\pi\) | ||||
0.0960012 | + | 0.995381i | \(0.469395\pi\) | |||||||
\(882\) | 1.26873 | 0.0427203 | ||||||||
\(883\) | −58.8062 | −1.97899 | −0.989493 | − | 0.144582i | \(-0.953816\pi\) | ||||
−0.989493 | + | 0.144582i | \(0.953816\pi\) | |||||||
\(884\) | 0.956459 | 0.0321692 | ||||||||
\(885\) | 52.7080 | 1.77176 | ||||||||
\(886\) | −29.3010 | −0.984386 | ||||||||
\(887\) | 24.2030 | 0.812656 | 0.406328 | − | 0.913727i | \(-0.366809\pi\) | ||||
0.406328 | + | 0.913727i | \(0.366809\pi\) | |||||||
\(888\) | −29.2316 | −0.980949 | ||||||||
\(889\) | −7.75625 | −0.260136 | ||||||||
\(890\) | −16.7145 | −0.560272 | ||||||||
\(891\) | 60.6587 | 2.03214 | ||||||||
\(892\) | 0.856135 | 0.0286655 | ||||||||
\(893\) | 0.155753 | 0.00521209 | ||||||||
\(894\) | −47.9601 | −1.60402 | ||||||||
\(895\) | 52.5424 | 1.75630 | ||||||||
\(896\) | −2.61077 | −0.0872195 | ||||||||
\(897\) | −30.2836 | −1.01114 | ||||||||
\(898\) | −3.99304 | −0.133249 | ||||||||
\(899\) | −36.2754 | −1.20985 | ||||||||
\(900\) | 31.1078 | 1.03693 | ||||||||
\(901\) | 1.08379 | 0.0361064 | ||||||||
\(902\) | 2.26298 | 0.0753491 | ||||||||
\(903\) | −92.5862 | −3.08108 | ||||||||
\(904\) | −0.107346 | −0.00357027 | ||||||||
\(905\) | −21.2245 | −0.705527 | ||||||||
\(906\) | −5.30467 | −0.176236 | ||||||||
\(907\) | −28.4278 | −0.943931 | −0.471965 | − | 0.881617i | \(-0.656455\pi\) | ||||
−0.471965 | + | 0.881617i | \(0.656455\pi\) | |||||||
\(908\) | −13.6768 | −0.453881 | ||||||||
\(909\) | 107.203 | 3.55570 | ||||||||
\(910\) | −32.2448 | −1.06891 | ||||||||
\(911\) | −19.3928 | −0.642511 | −0.321256 | − | 0.946993i | \(-0.604105\pi\) | ||||
−0.321256 | + | 0.946993i | \(0.604105\pi\) | |||||||
\(912\) | −0.0814452 | −0.00269692 | ||||||||
\(913\) | −7.99845 | −0.264710 | ||||||||
\(914\) | 31.1775 | 1.03126 | ||||||||
\(915\) | −49.7068 | −1.64326 | ||||||||
\(916\) | −11.4129 | −0.377094 | ||||||||
\(917\) | 27.7952 | 0.917878 | ||||||||
\(918\) | 2.92935 | 0.0966828 | ||||||||
\(919\) | −23.4795 | −0.774517 | −0.387259 | − | 0.921971i | \(-0.626578\pi\) | ||||
−0.387259 | + | 0.921971i | \(0.626578\pi\) | |||||||
\(920\) | −7.41080 | −0.244327 | ||||||||
\(921\) | −94.6026 | −3.11726 | ||||||||
\(922\) | 14.3164 | 0.471487 | ||||||||
\(923\) | 39.8238 | 1.31082 | ||||||||
\(924\) | −27.8397 | −0.915858 | ||||||||
\(925\) | −41.8943 | −1.37748 | ||||||||
\(926\) | −42.6472 | −1.40147 | ||||||||
\(927\) | 114.903 | 3.77393 | ||||||||
\(928\) | 7.95586 | 0.261164 | ||||||||
\(929\) | 59.2756 | 1.94477 | 0.972384 | − | 0.233387i | \(-0.0749808\pi\) | ||||
0.972384 | + | 0.233387i | \(0.0749808\pi\) | |||||||
\(930\) | 44.2372 | 1.45059 | ||||||||
\(931\) | −0.00476066 | −0.000156024 0 | ||||||||
\(932\) | 6.64772 | 0.217753 | ||||||||
\(933\) | 102.260 | 3.34785 | ||||||||
\(934\) | 23.4726 | 0.768048 | ||||||||
\(935\) | 2.49586 | 0.0816233 | ||||||||
\(936\) | −27.6310 | −0.903148 | ||||||||
\(937\) | 8.10621 | 0.264818 | 0.132409 | − | 0.991195i | \(-0.457729\pi\) | ||||
0.132409 | + | 0.991195i | \(0.457729\pi\) | |||||||
\(938\) | 26.2541 | 0.857226 | ||||||||
\(939\) | 19.3320 | 0.630877 | ||||||||
\(940\) | 18.5539 | 0.605161 | ||||||||
\(941\) | 31.3013 | 1.02039 | 0.510196 | − | 0.860058i | \(-0.329573\pi\) | ||||
0.510196 | + | 0.860058i | \(0.329573\pi\) | |||||||
\(942\) | −37.5614 | −1.22382 | ||||||||
\(943\) | −1.60462 | −0.0522535 | ||||||||
\(944\) | −5.43268 | −0.176819 | ||||||||
\(945\) | −98.7562 | −3.21254 | ||||||||
\(946\) | −38.2025 | −1.24207 | ||||||||
\(947\) | −6.28155 | −0.204123 | −0.102061 | − | 0.994778i | \(-0.532544\pi\) | ||||
−0.102061 | + | 0.994778i | \(0.532544\pi\) | |||||||
\(948\) | 11.3010 | 0.367040 | ||||||||
\(949\) | −3.69230 | −0.119857 | ||||||||
\(950\) | −0.116726 | −0.00378710 | ||||||||
\(951\) | −6.81786 | −0.221084 | ||||||||
\(952\) | −0.623466 | −0.0202066 | ||||||||
\(953\) | 26.2252 | 0.849517 | 0.424758 | − | 0.905307i | \(-0.360359\pi\) | ||||
0.424758 | + | 0.905307i | \(0.360359\pi\) | |||||||
\(954\) | −31.3096 | −1.01368 | ||||||||
\(955\) | 42.0769 | 1.36158 | ||||||||
\(956\) | 10.3920 | 0.336103 | ||||||||
\(957\) | 84.8367 | 2.74238 | ||||||||
\(958\) | −9.85431 | −0.318378 | ||||||||
\(959\) | 49.0445 | 1.58373 | ||||||||
\(960\) | −9.70203 | −0.313132 | ||||||||
\(961\) | −10.2103 | −0.329363 | ||||||||
\(962\) | 37.2120 | 1.19976 | ||||||||
\(963\) | 90.4575 | 2.91495 | ||||||||
\(964\) | −0.616335 | −0.0198508 | ||||||||
\(965\) | 74.0366 | 2.38332 | ||||||||
\(966\) | 19.7403 | 0.635134 | ||||||||
\(967\) | 16.1174 | 0.518300 | 0.259150 | − | 0.965837i | \(-0.416558\pi\) | ||||
0.259150 | + | 0.965837i | \(0.416558\pi\) | |||||||
\(968\) | −0.487066 | −0.0156549 | ||||||||
\(969\) | −0.0194496 | −0.000624811 0 | ||||||||
\(970\) | −20.2673 | −0.650745 | ||||||||
\(971\) | −37.4079 | −1.20048 | −0.600238 | − | 0.799822i | \(-0.704927\pi\) | ||||
−0.600238 | + | 0.799822i | \(0.704927\pi\) | |||||||
\(972\) | −19.5094 | −0.625764 | ||||||||
\(973\) | −11.7106 | −0.375425 | ||||||||
\(974\) | 11.1216 | 0.356359 | ||||||||
\(975\) | −56.8208 | −1.81972 | ||||||||
\(976\) | 5.12334 | 0.163994 | ||||||||
\(977\) | −16.3221 | −0.522189 | −0.261094 | − | 0.965313i | \(-0.584083\pi\) | ||||
−0.261094 | + | 0.965313i | \(0.584083\pi\) | |||||||
\(978\) | 10.4912 | 0.335470 | ||||||||
\(979\) | 18.3708 | 0.587133 | ||||||||
\(980\) | −0.567106 | −0.0181155 | ||||||||
\(981\) | −51.5140 | −1.64472 | ||||||||
\(982\) | 13.1409 | 0.419344 | ||||||||
\(983\) | 32.1458 | 1.02529 | 0.512646 | − | 0.858600i | \(-0.328666\pi\) | ||||
0.512646 | + | 0.858600i | \(0.328666\pi\) | |||||||
\(984\) | −2.10072 | −0.0669686 | ||||||||
\(985\) | 7.56489 | 0.241037 | ||||||||
\(986\) | 1.89991 | 0.0605053 | ||||||||
\(987\) | −49.4224 | −1.57313 | ||||||||
\(988\) | 0.103680 | 0.00329850 | ||||||||
\(989\) | 27.0883 | 0.861357 | ||||||||
\(990\) | −72.1025 | −2.29157 | ||||||||
\(991\) | 18.1019 | 0.575025 | 0.287512 | − | 0.957777i | \(-0.407172\pi\) | ||||
0.287512 | + | 0.957777i | \(0.407172\pi\) | |||||||
\(992\) | −4.55958 | −0.144767 | ||||||||
\(993\) | −30.9046 | −0.980728 | ||||||||
\(994\) | −25.9591 | −0.823371 | ||||||||
\(995\) | 27.8614 | 0.883266 | ||||||||
\(996\) | 7.42494 | 0.235268 | ||||||||
\(997\) | −44.8502 | −1.42042 | −0.710210 | − | 0.703990i | \(-0.751400\pi\) | ||||
−0.710210 | + | 0.703990i | \(0.751400\pi\) | |||||||
\(998\) | 35.3049 | 1.11756 | ||||||||
\(999\) | 113.969 | 3.60582 |
(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 | 8002.2.a.e.1.3 | ✓ | 77 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8002.2.a.e.1.3 | ✓ | 77 | 1.1 | even | 1 | trivial |