Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4033,2,Mod(1,4033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4033, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4033 = 37 \cdot 109 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4033.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: | \(32.2036671352\) |
Analytic rank: | \(0\) |
Dimension: | \(85\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 4033.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.92648 | −1.36223 | −0.681115 | − | 0.732176i | \(-0.738505\pi\) | ||||
−0.681115 | + | 0.732176i | \(0.738505\pi\) | |||||||
\(3\) | −3.23973 | −1.87046 | −0.935230 | − | 0.354040i | \(-0.884808\pi\) | ||||
−0.935230 | + | 0.354040i | \(0.884808\pi\) | |||||||
\(4\) | 1.71134 | 0.855671 | ||||||||
\(5\) | 1.34988 | 0.603685 | 0.301842 | − | 0.953358i | \(-0.402398\pi\) | ||||
0.301842 | + | 0.953358i | \(0.402398\pi\) | |||||||
\(6\) | 6.24129 | 2.54800 | ||||||||
\(7\) | 3.96616 | 1.49907 | 0.749534 | − | 0.661966i | \(-0.230278\pi\) | ||||
0.749534 | + | 0.661966i | \(0.230278\pi\) | |||||||
\(8\) | 0.556094 | 0.196609 | ||||||||
\(9\) | 7.49587 | 2.49862 | ||||||||
\(10\) | −2.60052 | −0.822358 | ||||||||
\(11\) | −2.26646 | −0.683363 | −0.341682 | − | 0.939816i | \(-0.610996\pi\) | ||||
−0.341682 | + | 0.939816i | \(0.610996\pi\) | |||||||
\(12\) | −5.54429 | −1.60050 | ||||||||
\(13\) | −1.74141 | −0.482980 | −0.241490 | − | 0.970403i | \(-0.577636\pi\) | ||||
−0.241490 | + | 0.970403i | \(0.577636\pi\) | |||||||
\(14\) | −7.64075 | −2.04208 | ||||||||
\(15\) | −4.37325 | −1.12917 | ||||||||
\(16\) | −4.49399 | −1.12350 | ||||||||
\(17\) | 2.07799 | 0.503986 | 0.251993 | − | 0.967729i | \(-0.418914\pi\) | ||||
0.251993 | + | 0.967729i | \(0.418914\pi\) | |||||||
\(18\) | −14.4407 | −3.40370 | ||||||||
\(19\) | −0.0556045 | −0.0127565 | −0.00637827 | − | 0.999980i | \(-0.502030\pi\) | ||||
−0.00637827 | + | 0.999980i | \(0.502030\pi\) | |||||||
\(20\) | 2.31011 | 0.516556 | ||||||||
\(21\) | −12.8493 | −2.80395 | ||||||||
\(22\) | 4.36630 | 0.930898 | ||||||||
\(23\) | 2.13566 | 0.445316 | 0.222658 | − | 0.974897i | \(-0.428527\pi\) | ||||
0.222658 | + | 0.974897i | \(0.428527\pi\) | |||||||
\(24\) | −1.80160 | −0.367749 | ||||||||
\(25\) | −3.17782 | −0.635565 | ||||||||
\(26\) | 3.35480 | 0.657931 | ||||||||
\(27\) | −14.5654 | −2.80311 | ||||||||
\(28\) | 6.78746 | 1.28271 | ||||||||
\(29\) | −1.24737 | −0.231632 | −0.115816 | − | 0.993271i | \(-0.536948\pi\) | ||||
−0.115816 | + | 0.993271i | \(0.536948\pi\) | |||||||
\(30\) | 8.42500 | 1.53819 | ||||||||
\(31\) | 6.48541 | 1.16481 | 0.582407 | − | 0.812897i | \(-0.302111\pi\) | ||||
0.582407 | + | 0.812897i | \(0.302111\pi\) | |||||||
\(32\) | 7.54542 | 1.33385 | ||||||||
\(33\) | 7.34272 | 1.27820 | ||||||||
\(34\) | −4.00321 | −0.686545 | ||||||||
\(35\) | 5.35384 | 0.904964 | ||||||||
\(36\) | 12.8280 | 2.13800 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | 0.107121 | 0.0173773 | ||||||||
\(39\) | 5.64170 | 0.903396 | ||||||||
\(40\) | 0.750660 | 0.118690 | ||||||||
\(41\) | 9.82822 | 1.53491 | 0.767455 | − | 0.641103i | \(-0.221523\pi\) | ||||
0.767455 | + | 0.641103i | \(0.221523\pi\) | |||||||
\(42\) | 24.7540 | 3.81962 | ||||||||
\(43\) | 5.56260 | 0.848288 | 0.424144 | − | 0.905595i | \(-0.360575\pi\) | ||||
0.424144 | + | 0.905595i | \(0.360575\pi\) | |||||||
\(44\) | −3.87869 | −0.584734 | ||||||||
\(45\) | 10.1185 | 1.50838 | ||||||||
\(46\) | −4.11431 | −0.606622 | ||||||||
\(47\) | −4.31048 | −0.628748 | −0.314374 | − | 0.949299i | \(-0.601795\pi\) | ||||
−0.314374 | + | 0.949299i | \(0.601795\pi\) | |||||||
\(48\) | 14.5593 | 2.10146 | ||||||||
\(49\) | 8.73042 | 1.24720 | ||||||||
\(50\) | 6.12203 | 0.865785 | ||||||||
\(51\) | −6.73212 | −0.942685 | ||||||||
\(52\) | −2.98015 | −0.413272 | ||||||||
\(53\) | −3.11563 | −0.427964 | −0.213982 | − | 0.976838i | \(-0.568643\pi\) | ||||
−0.213982 | + | 0.976838i | \(0.568643\pi\) | |||||||
\(54\) | 28.0600 | 3.81849 | ||||||||
\(55\) | −3.05945 | −0.412536 | ||||||||
\(56\) | 2.20556 | 0.294730 | ||||||||
\(57\) | 0.180144 | 0.0238606 | ||||||||
\(58\) | 2.40305 | 0.315536 | ||||||||
\(59\) | 4.26046 | 0.554664 | 0.277332 | − | 0.960774i | \(-0.410550\pi\) | ||||
0.277332 | + | 0.960774i | \(0.410550\pi\) | |||||||
\(60\) | −7.48413 | −0.966197 | ||||||||
\(61\) | −5.43610 | −0.696022 | −0.348011 | − | 0.937491i | \(-0.613143\pi\) | ||||
−0.348011 | + | 0.937491i | \(0.613143\pi\) | |||||||
\(62\) | −12.4941 | −1.58675 | ||||||||
\(63\) | 29.7298 | 3.74560 | ||||||||
\(64\) | −5.54815 | −0.693518 | ||||||||
\(65\) | −2.35070 | −0.291568 | ||||||||
\(66\) | −14.1456 | −1.74121 | ||||||||
\(67\) | 0.851420 | 0.104018 | 0.0520088 | − | 0.998647i | \(-0.483438\pi\) | ||||
0.0520088 | + | 0.998647i | \(0.483438\pi\) | |||||||
\(68\) | 3.55615 | 0.431246 | ||||||||
\(69\) | −6.91896 | −0.832945 | ||||||||
\(70\) | −10.3141 | −1.23277 | ||||||||
\(71\) | 13.0363 | 1.54712 | 0.773560 | − | 0.633723i | \(-0.218474\pi\) | ||||
0.773560 | + | 0.633723i | \(0.218474\pi\) | |||||||
\(72\) | 4.16841 | 0.491251 | ||||||||
\(73\) | −1.26557 | −0.148123 | −0.0740616 | − | 0.997254i | \(-0.523596\pi\) | ||||
−0.0740616 | + | 0.997254i | \(0.523596\pi\) | |||||||
\(74\) | −1.92648 | −0.223949 | ||||||||
\(75\) | 10.2953 | 1.18880 | ||||||||
\(76\) | −0.0951583 | −0.0109154 | ||||||||
\(77\) | −8.98914 | −1.02441 | ||||||||
\(78\) | −10.8687 | −1.23063 | ||||||||
\(79\) | −2.32278 | −0.261334 | −0.130667 | − | 0.991426i | \(-0.541712\pi\) | ||||
−0.130667 | + | 0.991426i | \(0.541712\pi\) | |||||||
\(80\) | −6.06635 | −0.678239 | ||||||||
\(81\) | 24.7004 | 2.74449 | ||||||||
\(82\) | −18.9339 | −2.09090 | ||||||||
\(83\) | −0.341132 | −0.0374441 | −0.0187220 | − | 0.999825i | \(-0.505960\pi\) | ||||
−0.0187220 | + | 0.999825i | \(0.505960\pi\) | |||||||
\(84\) | −21.9896 | −2.39926 | ||||||||
\(85\) | 2.80503 | 0.304249 | ||||||||
\(86\) | −10.7163 | −1.15556 | ||||||||
\(87\) | 4.04116 | 0.433258 | ||||||||
\(88\) | −1.26036 | −0.134355 | ||||||||
\(89\) | −10.6367 | −1.12748 | −0.563742 | − | 0.825951i | \(-0.690639\pi\) | ||||
−0.563742 | + | 0.825951i | \(0.690639\pi\) | |||||||
\(90\) | −19.4932 | −2.05476 | ||||||||
\(91\) | −6.90671 | −0.724020 | ||||||||
\(92\) | 3.65484 | 0.381044 | ||||||||
\(93\) | −21.0110 | −2.17874 | ||||||||
\(94\) | 8.30407 | 0.856499 | ||||||||
\(95\) | −0.0750594 | −0.00770093 | ||||||||
\(96\) | −24.4451 | −2.49492 | ||||||||
\(97\) | 0.0238378 | 0.00242036 | 0.00121018 | − | 0.999999i | \(-0.499615\pi\) | ||||
0.00121018 | + | 0.999999i | \(0.499615\pi\) | |||||||
\(98\) | −16.8190 | −1.69898 | ||||||||
\(99\) | −16.9891 | −1.70747 | ||||||||
\(100\) | −5.43834 | −0.543834 | ||||||||
\(101\) | −2.07023 | −0.205995 | −0.102998 | − | 0.994682i | \(-0.532843\pi\) | ||||
−0.102998 | + | 0.994682i | \(0.532843\pi\) | |||||||
\(102\) | 12.9693 | 1.28415 | ||||||||
\(103\) | 6.35658 | 0.626332 | 0.313166 | − | 0.949698i | \(-0.398610\pi\) | ||||
0.313166 | + | 0.949698i | \(0.398610\pi\) | |||||||
\(104\) | −0.968388 | −0.0949582 | ||||||||
\(105\) | −17.3450 | −1.69270 | ||||||||
\(106\) | 6.00220 | 0.582986 | ||||||||
\(107\) | 6.15416 | 0.594945 | 0.297473 | − | 0.954730i | \(-0.403856\pi\) | ||||
0.297473 | + | 0.954730i | \(0.403856\pi\) | |||||||
\(108\) | −24.9264 | −2.39854 | ||||||||
\(109\) | −1.00000 | −0.0957826 | ||||||||
\(110\) | 5.89398 | 0.561969 | ||||||||
\(111\) | −3.23973 | −0.307502 | ||||||||
\(112\) | −17.8239 | −1.68420 | ||||||||
\(113\) | 16.6497 | 1.56627 | 0.783134 | − | 0.621853i | \(-0.213620\pi\) | ||||
0.783134 | + | 0.621853i | \(0.213620\pi\) | |||||||
\(114\) | −0.347044 | −0.0325036 | ||||||||
\(115\) | 2.88288 | 0.268830 | ||||||||
\(116\) | −2.13468 | −0.198201 | ||||||||
\(117\) | −13.0534 | −1.20679 | ||||||||
\(118\) | −8.20771 | −0.755581 | ||||||||
\(119\) | 8.24163 | 0.755509 | ||||||||
\(120\) | −2.43194 | −0.222005 | ||||||||
\(121\) | −5.86316 | −0.533015 | ||||||||
\(122\) | 10.4726 | 0.948142 | ||||||||
\(123\) | −31.8408 | −2.87099 | ||||||||
\(124\) | 11.0988 | 0.996699 | ||||||||
\(125\) | −11.0391 | −0.987366 | ||||||||
\(126\) | −57.2740 | −5.10237 | ||||||||
\(127\) | 5.64587 | 0.500990 | 0.250495 | − | 0.968118i | \(-0.419407\pi\) | ||||
0.250495 | + | 0.968118i | \(0.419407\pi\) | |||||||
\(128\) | −4.40242 | −0.389122 | ||||||||
\(129\) | −18.0213 | −1.58669 | ||||||||
\(130\) | 4.52858 | 0.397183 | ||||||||
\(131\) | 13.1502 | 1.14894 | 0.574469 | − | 0.818526i | \(-0.305208\pi\) | ||||
0.574469 | + | 0.818526i | \(0.305208\pi\) | |||||||
\(132\) | 12.5659 | 1.09372 | ||||||||
\(133\) | −0.220536 | −0.0191229 | ||||||||
\(134\) | −1.64025 | −0.141696 | ||||||||
\(135\) | −19.6616 | −1.69220 | ||||||||
\(136\) | 1.15556 | 0.0990881 | ||||||||
\(137\) | −4.51177 | −0.385467 | −0.192733 | − | 0.981251i | \(-0.561735\pi\) | ||||
−0.192733 | + | 0.981251i | \(0.561735\pi\) | |||||||
\(138\) | 13.3293 | 1.13466 | ||||||||
\(139\) | −1.93497 | −0.164122 | −0.0820610 | − | 0.996627i | \(-0.526150\pi\) | ||||
−0.0820610 | + | 0.996627i | \(0.526150\pi\) | |||||||
\(140\) | 9.16226 | 0.774352 | ||||||||
\(141\) | 13.9648 | 1.17605 | ||||||||
\(142\) | −25.1142 | −2.10753 | ||||||||
\(143\) | 3.94684 | 0.330051 | ||||||||
\(144\) | −33.6864 | −2.80720 | ||||||||
\(145\) | −1.68381 | −0.139832 | ||||||||
\(146\) | 2.43809 | 0.201778 | ||||||||
\(147\) | −28.2842 | −2.33284 | ||||||||
\(148\) | 1.71134 | 0.140671 | ||||||||
\(149\) | 13.5228 | 1.10783 | 0.553917 | − | 0.832572i | \(-0.313132\pi\) | ||||
0.553917 | + | 0.832572i | \(0.313132\pi\) | |||||||
\(150\) | −19.8337 | −1.61942 | ||||||||
\(151\) | −8.03719 | −0.654058 | −0.327029 | − | 0.945014i | \(-0.606047\pi\) | ||||
−0.327029 | + | 0.945014i | \(0.606047\pi\) | |||||||
\(152\) | −0.0309213 | −0.00250805 | ||||||||
\(153\) | 15.5763 | 1.25927 | ||||||||
\(154\) | 17.3174 | 1.39548 | ||||||||
\(155\) | 8.75453 | 0.703181 | ||||||||
\(156\) | 9.65489 | 0.773010 | ||||||||
\(157\) | 5.49841 | 0.438821 | 0.219410 | − | 0.975633i | \(-0.429587\pi\) | ||||
0.219410 | + | 0.975633i | \(0.429587\pi\) | |||||||
\(158\) | 4.47481 | 0.355997 | ||||||||
\(159\) | 10.0938 | 0.800490 | ||||||||
\(160\) | 10.1854 | 0.805227 | ||||||||
\(161\) | 8.47036 | 0.667558 | ||||||||
\(162\) | −47.5850 | −3.73863 | ||||||||
\(163\) | 3.77403 | 0.295605 | 0.147802 | − | 0.989017i | \(-0.452780\pi\) | ||||
0.147802 | + | 0.989017i | \(0.452780\pi\) | |||||||
\(164\) | 16.8194 | 1.31338 | ||||||||
\(165\) | 9.91180 | 0.771632 | ||||||||
\(166\) | 0.657185 | 0.0510075 | ||||||||
\(167\) | 22.0558 | 1.70673 | 0.853366 | − | 0.521313i | \(-0.174558\pi\) | ||||
0.853366 | + | 0.521313i | \(0.174558\pi\) | |||||||
\(168\) | −7.14542 | −0.551281 | ||||||||
\(169\) | −9.96749 | −0.766730 | ||||||||
\(170\) | −5.40385 | −0.414457 | ||||||||
\(171\) | −0.416804 | −0.0318738 | ||||||||
\(172\) | 9.51951 | 0.725856 | ||||||||
\(173\) | −18.6692 | −1.41939 | −0.709696 | − | 0.704508i | \(-0.751168\pi\) | ||||
−0.709696 | + | 0.704508i | \(0.751168\pi\) | |||||||
\(174\) | −7.78523 | −0.590197 | ||||||||
\(175\) | −12.6038 | −0.952754 | ||||||||
\(176\) | 10.1855 | 0.767757 | ||||||||
\(177\) | −13.8027 | −1.03748 | ||||||||
\(178\) | 20.4914 | 1.53589 | ||||||||
\(179\) | −12.9707 | −0.969474 | −0.484737 | − | 0.874660i | \(-0.661085\pi\) | ||||
−0.484737 | + | 0.874660i | \(0.661085\pi\) | |||||||
\(180\) | 17.3163 | 1.29068 | ||||||||
\(181\) | −20.5983 | −1.53106 | −0.765531 | − | 0.643399i | \(-0.777523\pi\) | ||||
−0.765531 | + | 0.643399i | \(0.777523\pi\) | |||||||
\(182\) | 13.3057 | 0.986282 | ||||||||
\(183\) | 17.6115 | 1.30188 | ||||||||
\(184\) | 1.18763 | 0.0875530 | ||||||||
\(185\) | 1.34988 | 0.0992452 | ||||||||
\(186\) | 40.4774 | 2.96795 | ||||||||
\(187\) | −4.70967 | −0.344405 | ||||||||
\(188\) | −7.37670 | −0.538001 | ||||||||
\(189\) | −57.7687 | −4.20206 | ||||||||
\(190\) | 0.144601 | 0.0104904 | ||||||||
\(191\) | 5.17869 | 0.374717 | 0.187358 | − | 0.982292i | \(-0.440007\pi\) | ||||
0.187358 | + | 0.982292i | \(0.440007\pi\) | |||||||
\(192\) | 17.9745 | 1.29720 | ||||||||
\(193\) | 14.4871 | 1.04280 | 0.521401 | − | 0.853312i | \(-0.325410\pi\) | ||||
0.521401 | + | 0.853312i | \(0.325410\pi\) | |||||||
\(194\) | −0.0459231 | −0.00329709 | ||||||||
\(195\) | 7.61563 | 0.545366 | ||||||||
\(196\) | 14.9407 | 1.06720 | ||||||||
\(197\) | 0.161692 | 0.0115201 | 0.00576005 | − | 0.999983i | \(-0.498167\pi\) | ||||
0.00576005 | + | 0.999983i | \(0.498167\pi\) | |||||||
\(198\) | 32.7292 | 2.32596 | ||||||||
\(199\) | −3.85590 | −0.273337 | −0.136669 | − | 0.990617i | \(-0.543640\pi\) | ||||
−0.136669 | + | 0.990617i | \(0.543640\pi\) | |||||||
\(200\) | −1.76717 | −0.124958 | ||||||||
\(201\) | −2.75837 | −0.194561 | ||||||||
\(202\) | 3.98826 | 0.280613 | ||||||||
\(203\) | −4.94729 | −0.347231 | ||||||||
\(204\) | −11.5210 | −0.806629 | ||||||||
\(205\) | 13.2669 | 0.926602 | ||||||||
\(206\) | −12.2458 | −0.853209 | ||||||||
\(207\) | 16.0086 | 1.11268 | ||||||||
\(208\) | 7.82588 | 0.542627 | ||||||||
\(209\) | 0.126025 | 0.00871735 | ||||||||
\(210\) | 33.4149 | 2.30585 | ||||||||
\(211\) | −4.80857 | −0.331036 | −0.165518 | − | 0.986207i | \(-0.552930\pi\) | ||||
−0.165518 | + | 0.986207i | \(0.552930\pi\) | |||||||
\(212\) | −5.33190 | −0.366197 | ||||||||
\(213\) | −42.2340 | −2.89383 | ||||||||
\(214\) | −11.8559 | −0.810453 | ||||||||
\(215\) | 7.50884 | 0.512099 | ||||||||
\(216\) | −8.09974 | −0.551117 | ||||||||
\(217\) | 25.7222 | 1.74614 | ||||||||
\(218\) | 1.92648 | 0.130478 | ||||||||
\(219\) | 4.10009 | 0.277059 | ||||||||
\(220\) | −5.23577 | −0.352995 | ||||||||
\(221\) | −3.61863 | −0.243415 | ||||||||
\(222\) | 6.24129 | 0.418888 | ||||||||
\(223\) | 12.8924 | 0.863337 | 0.431669 | − | 0.902032i | \(-0.357925\pi\) | ||||
0.431669 | + | 0.902032i | \(0.357925\pi\) | |||||||
\(224\) | 29.9263 | 1.99954 | ||||||||
\(225\) | −23.8205 | −1.58804 | ||||||||
\(226\) | −32.0753 | −2.13362 | ||||||||
\(227\) | 25.3867 | 1.68497 | 0.842487 | − | 0.538717i | \(-0.181091\pi\) | ||||
0.842487 | + | 0.538717i | \(0.181091\pi\) | |||||||
\(228\) | 0.308288 | 0.0204168 | ||||||||
\(229\) | −11.8144 | −0.780720 | −0.390360 | − | 0.920662i | \(-0.627650\pi\) | ||||
−0.390360 | + | 0.920662i | \(0.627650\pi\) | |||||||
\(230\) | −5.55383 | −0.366209 | ||||||||
\(231\) | 29.1224 | 1.91611 | ||||||||
\(232\) | −0.693657 | −0.0455408 | ||||||||
\(233\) | −28.9936 | −1.89943 | −0.949716 | − | 0.313112i | \(-0.898628\pi\) | ||||
−0.949716 | + | 0.313112i | \(0.898628\pi\) | |||||||
\(234\) | 25.1471 | 1.64392 | ||||||||
\(235\) | −5.81863 | −0.379565 | ||||||||
\(236\) | 7.29110 | 0.474610 | ||||||||
\(237\) | 7.52520 | 0.488814 | ||||||||
\(238\) | −15.8774 | −1.02918 | ||||||||
\(239\) | −1.92586 | −0.124573 | −0.0622867 | − | 0.998058i | \(-0.519839\pi\) | ||||
−0.0622867 | + | 0.998058i | \(0.519839\pi\) | |||||||
\(240\) | 19.6534 | 1.26862 | ||||||||
\(241\) | 2.04690 | 0.131852 | 0.0659261 | − | 0.997825i | \(-0.479000\pi\) | ||||
0.0659261 | + | 0.997825i | \(0.479000\pi\) | |||||||
\(242\) | 11.2953 | 0.726089 | ||||||||
\(243\) | −36.3266 | −2.33035 | ||||||||
\(244\) | −9.30303 | −0.595566 | ||||||||
\(245\) | 11.7850 | 0.752918 | ||||||||
\(246\) | 61.3408 | 3.91095 | ||||||||
\(247\) | 0.0968302 | 0.00616116 | ||||||||
\(248\) | 3.60650 | 0.229013 | ||||||||
\(249\) | 1.10518 | 0.0700377 | ||||||||
\(250\) | 21.2666 | 1.34502 | ||||||||
\(251\) | 8.84677 | 0.558403 | 0.279202 | − | 0.960232i | \(-0.409930\pi\) | ||||
0.279202 | + | 0.960232i | \(0.409930\pi\) | |||||||
\(252\) | 50.8779 | 3.20501 | ||||||||
\(253\) | −4.84038 | −0.304312 | ||||||||
\(254\) | −10.8767 | −0.682464 | ||||||||
\(255\) | −9.08756 | −0.569085 | ||||||||
\(256\) | 19.5775 | 1.22359 | ||||||||
\(257\) | 25.9731 | 1.62016 | 0.810079 | − | 0.586321i | \(-0.199424\pi\) | ||||
0.810079 | + | 0.586321i | \(0.199424\pi\) | |||||||
\(258\) | 34.7178 | 2.16144 | ||||||||
\(259\) | 3.96616 | 0.246445 | ||||||||
\(260\) | −4.02285 | −0.249486 | ||||||||
\(261\) | −9.35015 | −0.578760 | ||||||||
\(262\) | −25.3337 | −1.56512 | ||||||||
\(263\) | 0.803203 | 0.0495276 | 0.0247638 | − | 0.999693i | \(-0.492117\pi\) | ||||
0.0247638 | + | 0.999693i | \(0.492117\pi\) | |||||||
\(264\) | 4.08324 | 0.251306 | ||||||||
\(265\) | −4.20572 | −0.258355 | ||||||||
\(266\) | 0.424860 | 0.0260498 | ||||||||
\(267\) | 34.4599 | 2.10891 | ||||||||
\(268\) | 1.45707 | 0.0890048 | ||||||||
\(269\) | 22.4963 | 1.37162 | 0.685812 | − | 0.727779i | \(-0.259447\pi\) | ||||
0.685812 | + | 0.727779i | \(0.259447\pi\) | |||||||
\(270\) | 37.8777 | 2.30516 | ||||||||
\(271\) | −23.2444 | −1.41200 | −0.706000 | − | 0.708212i | \(-0.749502\pi\) | ||||
−0.706000 | + | 0.708212i | \(0.749502\pi\) | |||||||
\(272\) | −9.33845 | −0.566227 | ||||||||
\(273\) | 22.3759 | 1.35425 | ||||||||
\(274\) | 8.69186 | 0.525094 | ||||||||
\(275\) | 7.20241 | 0.434322 | ||||||||
\(276\) | −11.8407 | −0.712727 | ||||||||
\(277\) | −23.4400 | −1.40838 | −0.704188 | − | 0.710014i | \(-0.748689\pi\) | ||||
−0.704188 | + | 0.710014i | \(0.748689\pi\) | |||||||
\(278\) | 3.72769 | 0.223572 | ||||||||
\(279\) | 48.6138 | 2.91043 | ||||||||
\(280\) | 2.97724 | 0.177924 | ||||||||
\(281\) | −0.318088 | −0.0189755 | −0.00948777 | − | 0.999955i | \(-0.503020\pi\) | ||||
−0.00948777 | + | 0.999955i | \(0.503020\pi\) | |||||||
\(282\) | −26.9030 | −1.60205 | ||||||||
\(283\) | −23.9981 | −1.42654 | −0.713270 | − | 0.700889i | \(-0.752787\pi\) | ||||
−0.713270 | + | 0.700889i | \(0.752787\pi\) | |||||||
\(284\) | 22.3095 | 1.32383 | ||||||||
\(285\) | 0.243172 | 0.0144043 | ||||||||
\(286\) | −7.60352 | −0.449606 | ||||||||
\(287\) | 38.9803 | 2.30093 | ||||||||
\(288\) | 56.5595 | 3.33280 | ||||||||
\(289\) | −12.6820 | −0.745998 | ||||||||
\(290\) | 3.24383 | 0.190484 | ||||||||
\(291\) | −0.0772280 | −0.00452718 | ||||||||
\(292\) | −2.16582 | −0.126745 | ||||||||
\(293\) | 11.7660 | 0.687376 | 0.343688 | − | 0.939084i | \(-0.388324\pi\) | ||||
0.343688 | + | 0.939084i | \(0.388324\pi\) | |||||||
\(294\) | 54.4891 | 3.17787 | ||||||||
\(295\) | 5.75111 | 0.334842 | ||||||||
\(296\) | 0.556094 | 0.0323223 | ||||||||
\(297\) | 33.0119 | 1.91555 | ||||||||
\(298\) | −26.0515 | −1.50913 | ||||||||
\(299\) | −3.71906 | −0.215079 | ||||||||
\(300\) | 17.6188 | 1.01722 | ||||||||
\(301\) | 22.0621 | 1.27164 | ||||||||
\(302\) | 15.4835 | 0.890977 | ||||||||
\(303\) | 6.70699 | 0.385306 | ||||||||
\(304\) | 0.249886 | 0.0143319 | ||||||||
\(305\) | −7.33809 | −0.420178 | ||||||||
\(306\) | −30.0075 | −1.71542 | ||||||||
\(307\) | 33.1856 | 1.89400 | 0.947002 | − | 0.321227i | \(-0.104095\pi\) | ||||
0.947002 | + | 0.321227i | \(0.104095\pi\) | |||||||
\(308\) | −15.3835 | −0.876556 | ||||||||
\(309\) | −20.5936 | −1.17153 | ||||||||
\(310\) | −16.8655 | −0.957894 | ||||||||
\(311\) | −19.9194 | −1.12952 | −0.564761 | − | 0.825254i | \(-0.691032\pi\) | ||||
−0.564761 | + | 0.825254i | \(0.691032\pi\) | |||||||
\(312\) | 3.13732 | 0.177616 | ||||||||
\(313\) | 12.6244 | 0.713573 | 0.356786 | − | 0.934186i | \(-0.383872\pi\) | ||||
0.356786 | + | 0.934186i | \(0.383872\pi\) | |||||||
\(314\) | −10.5926 | −0.597775 | ||||||||
\(315\) | 40.1317 | 2.26116 | ||||||||
\(316\) | −3.97508 | −0.223616 | ||||||||
\(317\) | 31.4879 | 1.76854 | 0.884268 | − | 0.466979i | \(-0.154658\pi\) | ||||
0.884268 | + | 0.466979i | \(0.154658\pi\) | |||||||
\(318\) | −19.4455 | −1.09045 | ||||||||
\(319\) | 2.82712 | 0.158289 | ||||||||
\(320\) | −7.48933 | −0.418666 | ||||||||
\(321\) | −19.9378 | −1.11282 | ||||||||
\(322\) | −16.3180 | −0.909368 | ||||||||
\(323\) | −0.115545 | −0.00642912 | ||||||||
\(324\) | 42.2709 | 2.34838 | ||||||||
\(325\) | 5.53390 | 0.306965 | ||||||||
\(326\) | −7.27061 | −0.402682 | ||||||||
\(327\) | 3.23973 | 0.179158 | ||||||||
\(328\) | 5.46541 | 0.301777 | ||||||||
\(329\) | −17.0960 | −0.942535 | ||||||||
\(330\) | −19.0949 | −1.05114 | ||||||||
\(331\) | −19.0817 | −1.04882 | −0.524412 | − | 0.851465i | \(-0.675715\pi\) | ||||
−0.524412 | + | 0.851465i | \(0.675715\pi\) | |||||||
\(332\) | −0.583794 | −0.0320398 | ||||||||
\(333\) | 7.49587 | 0.410771 | ||||||||
\(334\) | −42.4902 | −2.32496 | ||||||||
\(335\) | 1.14932 | 0.0627938 | ||||||||
\(336\) | 57.7446 | 3.15023 | ||||||||
\(337\) | 29.6681 | 1.61612 | 0.808062 | − | 0.589097i | \(-0.200517\pi\) | ||||
0.808062 | + | 0.589097i | \(0.200517\pi\) | |||||||
\(338\) | 19.2022 | 1.04446 | ||||||||
\(339\) | −53.9404 | −2.92964 | ||||||||
\(340\) | 4.80037 | 0.260337 | ||||||||
\(341\) | −14.6989 | −0.795992 | ||||||||
\(342\) | 0.802966 | 0.0434194 | ||||||||
\(343\) | 6.86313 | 0.370574 | ||||||||
\(344\) | 3.09333 | 0.166781 | ||||||||
\(345\) | −9.33977 | −0.502836 | ||||||||
\(346\) | 35.9659 | 1.93354 | ||||||||
\(347\) | −9.89584 | −0.531237 | −0.265618 | − | 0.964078i | \(-0.585576\pi\) | ||||
−0.265618 | + | 0.964078i | \(0.585576\pi\) | |||||||
\(348\) | 6.91581 | 0.370726 | ||||||||
\(349\) | 3.30139 | 0.176719 | 0.0883597 | − | 0.996089i | \(-0.471837\pi\) | ||||
0.0883597 | + | 0.996089i | \(0.471837\pi\) | |||||||
\(350\) | 24.2809 | 1.29787 | ||||||||
\(351\) | 25.3644 | 1.35385 | ||||||||
\(352\) | −17.1014 | −0.911507 | ||||||||
\(353\) | 11.0858 | 0.590036 | 0.295018 | − | 0.955492i | \(-0.404674\pi\) | ||||
0.295018 | + | 0.955492i | \(0.404674\pi\) | |||||||
\(354\) | 26.5908 | 1.41328 | ||||||||
\(355\) | 17.5974 | 0.933973 | ||||||||
\(356\) | −18.2030 | −0.964755 | ||||||||
\(357\) | −26.7007 | −1.41315 | ||||||||
\(358\) | 24.9878 | 1.32065 | ||||||||
\(359\) | 6.34740 | 0.335003 | 0.167502 | − | 0.985872i | \(-0.446430\pi\) | ||||
0.167502 | + | 0.985872i | \(0.446430\pi\) | |||||||
\(360\) | 5.62685 | 0.296561 | ||||||||
\(361\) | −18.9969 | −0.999837 | ||||||||
\(362\) | 39.6824 | 2.08566 | ||||||||
\(363\) | 18.9951 | 0.996983 | ||||||||
\(364\) | −11.8198 | −0.619523 | ||||||||
\(365\) | −1.70836 | −0.0894197 | ||||||||
\(366\) | −33.9283 | −1.77346 | ||||||||
\(367\) | 32.5563 | 1.69942 | 0.849712 | − | 0.527247i | \(-0.176776\pi\) | ||||
0.849712 | + | 0.527247i | \(0.176776\pi\) | |||||||
\(368\) | −9.59763 | −0.500311 | ||||||||
\(369\) | 73.6710 | 3.83516 | ||||||||
\(370\) | −2.60052 | −0.135195 | ||||||||
\(371\) | −12.3571 | −0.641547 | ||||||||
\(372\) | −35.9570 | −1.86429 | ||||||||
\(373\) | 3.47387 | 0.179870 | 0.0899350 | − | 0.995948i | \(-0.471334\pi\) | ||||
0.0899350 | + | 0.995948i | \(0.471334\pi\) | |||||||
\(374\) | 9.07311 | 0.469159 | ||||||||
\(375\) | 35.7637 | 1.84683 | ||||||||
\(376\) | −2.39703 | −0.123617 | ||||||||
\(377\) | 2.17219 | 0.111874 | ||||||||
\(378\) | 111.291 | 5.72417 | ||||||||
\(379\) | −9.28610 | −0.476995 | −0.238497 | − | 0.971143i | \(-0.576655\pi\) | ||||
−0.238497 | + | 0.971143i | \(0.576655\pi\) | |||||||
\(380\) | −0.128452 | −0.00658947 | ||||||||
\(381\) | −18.2911 | −0.937083 | ||||||||
\(382\) | −9.97667 | −0.510451 | ||||||||
\(383\) | −28.2878 | −1.44544 | −0.722720 | − | 0.691141i | \(-0.757108\pi\) | ||||
−0.722720 | + | 0.691141i | \(0.757108\pi\) | |||||||
\(384\) | 14.2627 | 0.727838 | ||||||||
\(385\) | −12.1343 | −0.618419 | ||||||||
\(386\) | −27.9091 | −1.42054 | ||||||||
\(387\) | 41.6965 | 2.11955 | ||||||||
\(388\) | 0.0407946 | 0.00207103 | ||||||||
\(389\) | −1.02205 | −0.0518202 | −0.0259101 | − | 0.999664i | \(-0.508248\pi\) | ||||
−0.0259101 | + | 0.999664i | \(0.508248\pi\) | |||||||
\(390\) | −14.6714 | −0.742914 | ||||||||
\(391\) | 4.43787 | 0.224433 | ||||||||
\(392\) | 4.85493 | 0.245211 | ||||||||
\(393\) | −42.6032 | −2.14904 | ||||||||
\(394\) | −0.311498 | −0.0156930 | ||||||||
\(395\) | −3.13548 | −0.157763 | ||||||||
\(396\) | −29.0741 | −1.46103 | ||||||||
\(397\) | −8.22353 | −0.412727 | −0.206364 | − | 0.978475i | \(-0.566163\pi\) | ||||
−0.206364 | + | 0.978475i | \(0.566163\pi\) | |||||||
\(398\) | 7.42833 | 0.372348 | ||||||||
\(399\) | 0.714478 | 0.0357687 | ||||||||
\(400\) | 14.2811 | 0.714056 | ||||||||
\(401\) | −11.1475 | −0.556681 | −0.278341 | − | 0.960482i | \(-0.589784\pi\) | ||||
−0.278341 | + | 0.960482i | \(0.589784\pi\) | |||||||
\(402\) | 5.31397 | 0.265037 | ||||||||
\(403\) | −11.2938 | −0.562583 | ||||||||
\(404\) | −3.54287 | −0.176264 | ||||||||
\(405\) | 33.3426 | 1.65681 | ||||||||
\(406\) | 9.53087 | 0.473009 | ||||||||
\(407\) | −2.26646 | −0.112344 | ||||||||
\(408\) | −3.74369 | −0.185340 | ||||||||
\(409\) | −22.8940 | −1.13204 | −0.566018 | − | 0.824393i | \(-0.691517\pi\) | ||||
−0.566018 | + | 0.824393i | \(0.691517\pi\) | |||||||
\(410\) | −25.5585 | −1.26224 | ||||||||
\(411\) | 14.6169 | 0.721000 | ||||||||
\(412\) | 10.8783 | 0.535934 | ||||||||
\(413\) | 16.8977 | 0.831479 | ||||||||
\(414\) | −30.8403 | −1.51572 | ||||||||
\(415\) | −0.460487 | −0.0226044 | ||||||||
\(416\) | −13.1397 | −0.644225 | ||||||||
\(417\) | 6.26878 | 0.306984 | ||||||||
\(418\) | −0.242786 | −0.0118750 | ||||||||
\(419\) | −0.628840 | −0.0307208 | −0.0153604 | − | 0.999882i | \(-0.504890\pi\) | ||||
−0.0153604 | + | 0.999882i | \(0.504890\pi\) | |||||||
\(420\) | −29.6833 | −1.44839 | ||||||||
\(421\) | 9.90182 | 0.482585 | 0.241293 | − | 0.970452i | \(-0.422429\pi\) | ||||
0.241293 | + | 0.970452i | \(0.422429\pi\) | |||||||
\(422\) | 9.26364 | 0.450947 | ||||||||
\(423\) | −32.3108 | −1.57100 | ||||||||
\(424\) | −1.73258 | −0.0841415 | ||||||||
\(425\) | −6.60347 | −0.320316 | ||||||||
\(426\) | 81.3632 | 3.94206 | ||||||||
\(427\) | −21.5604 | −1.04338 | ||||||||
\(428\) | 10.5319 | 0.509078 | ||||||||
\(429\) | −12.7867 | −0.617347 | ||||||||
\(430\) | −14.4657 | −0.697596 | ||||||||
\(431\) | 13.9722 | 0.673015 | 0.336507 | − | 0.941681i | \(-0.390754\pi\) | ||||
0.336507 | + | 0.941681i | \(0.390754\pi\) | |||||||
\(432\) | 65.4568 | 3.14929 | ||||||||
\(433\) | −8.97314 | −0.431222 | −0.215611 | − | 0.976479i | \(-0.569174\pi\) | ||||
−0.215611 | + | 0.976479i | \(0.569174\pi\) | |||||||
\(434\) | −49.5534 | −2.37864 | ||||||||
\(435\) | 5.45508 | 0.261551 | ||||||||
\(436\) | −1.71134 | −0.0819584 | ||||||||
\(437\) | −0.118752 | −0.00568069 | ||||||||
\(438\) | −7.89877 | −0.377418 | ||||||||
\(439\) | −35.1841 | −1.67925 | −0.839623 | − | 0.543169i | \(-0.817224\pi\) | ||||
−0.839623 | + | 0.543169i | \(0.817224\pi\) | |||||||
\(440\) | −1.70134 | −0.0811083 | ||||||||
\(441\) | 65.4421 | 3.11629 | ||||||||
\(442\) | 6.97123 | 0.331588 | ||||||||
\(443\) | −1.42393 | −0.0676531 | −0.0338266 | − | 0.999428i | \(-0.510769\pi\) | ||||
−0.0338266 | + | 0.999428i | \(0.510769\pi\) | |||||||
\(444\) | −5.54429 | −0.263120 | ||||||||
\(445\) | −14.3582 | −0.680645 | ||||||||
\(446\) | −24.8370 | −1.17606 | ||||||||
\(447\) | −43.8104 | −2.07216 | ||||||||
\(448\) | −22.0048 | −1.03963 | ||||||||
\(449\) | −17.0025 | −0.802398 | −0.401199 | − | 0.915991i | \(-0.631406\pi\) | ||||
−0.401199 | + | 0.915991i | \(0.631406\pi\) | |||||||
\(450\) | 45.8899 | 2.16327 | ||||||||
\(451\) | −22.2753 | −1.04890 | ||||||||
\(452\) | 28.4933 | 1.34021 | ||||||||
\(453\) | 26.0384 | 1.22339 | ||||||||
\(454\) | −48.9071 | −2.29532 | ||||||||
\(455\) | −9.32323 | −0.437080 | ||||||||
\(456\) | 0.100177 | 0.00469121 | ||||||||
\(457\) | 3.03418 | 0.141933 | 0.0709665 | − | 0.997479i | \(-0.477392\pi\) | ||||
0.0709665 | + | 0.997479i | \(0.477392\pi\) | |||||||
\(458\) | 22.7603 | 1.06352 | ||||||||
\(459\) | −30.2667 | −1.41273 | ||||||||
\(460\) | 4.93360 | 0.230030 | ||||||||
\(461\) | 33.7244 | 1.57070 | 0.785350 | − | 0.619051i | \(-0.212483\pi\) | ||||
0.785350 | + | 0.619051i | \(0.212483\pi\) | |||||||
\(462\) | −56.1039 | −2.61019 | ||||||||
\(463\) | 17.8786 | 0.830891 | 0.415446 | − | 0.909618i | \(-0.363626\pi\) | ||||
0.415446 | + | 0.909618i | \(0.363626\pi\) | |||||||
\(464\) | 5.60569 | 0.260238 | ||||||||
\(465\) | −28.3623 | −1.31527 | ||||||||
\(466\) | 55.8557 | 2.58746 | ||||||||
\(467\) | −17.1965 | −0.795758 | −0.397879 | − | 0.917438i | \(-0.630254\pi\) | ||||
−0.397879 | + | 0.917438i | \(0.630254\pi\) | |||||||
\(468\) | −22.3388 | −1.03261 | ||||||||
\(469\) | 3.37687 | 0.155929 | ||||||||
\(470\) | 11.2095 | 0.517055 | ||||||||
\(471\) | −17.8134 | −0.820797 | ||||||||
\(472\) | 2.36921 | 0.109052 | ||||||||
\(473\) | −12.6074 | −0.579689 | ||||||||
\(474\) | −14.4972 | −0.665878 | ||||||||
\(475\) | 0.176701 | 0.00810761 | ||||||||
\(476\) | 14.1042 | 0.646467 | ||||||||
\(477\) | −23.3543 | −1.06932 | ||||||||
\(478\) | 3.71013 | 0.169698 | ||||||||
\(479\) | 4.32679 | 0.197696 | 0.0988480 | − | 0.995103i | \(-0.468484\pi\) | ||||
0.0988480 | + | 0.995103i | \(0.468484\pi\) | |||||||
\(480\) | −32.9980 | −1.50615 | ||||||||
\(481\) | −1.74141 | −0.0794015 | ||||||||
\(482\) | −3.94331 | −0.179613 | ||||||||
\(483\) | −27.4417 | −1.24864 | ||||||||
\(484\) | −10.0339 | −0.456085 | ||||||||
\(485\) | 0.0321781 | 0.00146113 | ||||||||
\(486\) | 69.9826 | 3.17447 | ||||||||
\(487\) | 8.43485 | 0.382220 | 0.191110 | − | 0.981569i | \(-0.438791\pi\) | ||||
0.191110 | + | 0.981569i | \(0.438791\pi\) | |||||||
\(488\) | −3.02298 | −0.136844 | ||||||||
\(489\) | −12.2268 | −0.552917 | ||||||||
\(490\) | −22.7037 | −1.02565 | ||||||||
\(491\) | −15.3908 | −0.694577 | −0.347288 | − | 0.937758i | \(-0.612898\pi\) | ||||
−0.347288 | + | 0.937758i | \(0.612898\pi\) | |||||||
\(492\) | −54.4905 | −2.45662 | ||||||||
\(493\) | −2.59203 | −0.116739 | ||||||||
\(494\) | −0.186542 | −0.00839292 | ||||||||
\(495\) | −22.9332 | −1.03077 | ||||||||
\(496\) | −29.1454 | −1.30867 | ||||||||
\(497\) | 51.7039 | 2.31924 | ||||||||
\(498\) | −2.12911 | −0.0954075 | ||||||||
\(499\) | 34.6105 | 1.54938 | 0.774688 | − | 0.632343i | \(-0.217907\pi\) | ||||
0.774688 | + | 0.632343i | \(0.217907\pi\) | |||||||
\(500\) | −18.8917 | −0.844860 | ||||||||
\(501\) | −71.4550 | −3.19237 | ||||||||
\(502\) | −17.0432 | −0.760674 | ||||||||
\(503\) | 33.0545 | 1.47383 | 0.736913 | − | 0.675988i | \(-0.236283\pi\) | ||||
0.736913 | + | 0.675988i | \(0.236283\pi\) | |||||||
\(504\) | 16.5326 | 0.736419 | ||||||||
\(505\) | −2.79456 | −0.124356 | ||||||||
\(506\) | 9.32493 | 0.414543 | ||||||||
\(507\) | 32.2920 | 1.43414 | ||||||||
\(508\) | 9.66203 | 0.428683 | ||||||||
\(509\) | −17.6100 | −0.780550 | −0.390275 | − | 0.920698i | \(-0.627620\pi\) | ||||
−0.390275 | + | 0.920698i | \(0.627620\pi\) | |||||||
\(510\) | 17.5070 | 0.775225 | ||||||||
\(511\) | −5.01943 | −0.222047 | ||||||||
\(512\) | −28.9109 | −1.27769 | ||||||||
\(513\) | 0.809902 | 0.0357580 | ||||||||
\(514\) | −50.0368 | −2.20703 | ||||||||
\(515\) | 8.58062 | 0.378107 | ||||||||
\(516\) | −30.8407 | −1.35768 | ||||||||
\(517\) | 9.76952 | 0.429663 | ||||||||
\(518\) | −7.64075 | −0.335715 | ||||||||
\(519\) | 60.4832 | 2.65492 | ||||||||
\(520\) | −1.30721 | −0.0573248 | ||||||||
\(521\) | 19.9261 | 0.872978 | 0.436489 | − | 0.899710i | \(-0.356222\pi\) | ||||
0.436489 | + | 0.899710i | \(0.356222\pi\) | |||||||
\(522\) | 18.0129 | 0.788404 | ||||||||
\(523\) | 14.0995 | 0.616530 | 0.308265 | − | 0.951301i | \(-0.400252\pi\) | ||||
0.308265 | + | 0.951301i | \(0.400252\pi\) | |||||||
\(524\) | 22.5045 | 0.983114 | ||||||||
\(525\) | 40.8328 | 1.78209 | ||||||||
\(526\) | −1.54736 | −0.0674680 | ||||||||
\(527\) | 13.4766 | 0.587050 | ||||||||
\(528\) | −32.9981 | −1.43606 | ||||||||
\(529\) | −18.4390 | −0.801694 | ||||||||
\(530\) | 8.10226 | 0.351940 | ||||||||
\(531\) | 31.9358 | 1.38590 | ||||||||
\(532\) | −0.377413 | −0.0163629 | ||||||||
\(533\) | −17.1150 | −0.741331 | ||||||||
\(534\) | −66.3865 | −2.87283 | ||||||||
\(535\) | 8.30738 | 0.359159 | ||||||||
\(536\) | 0.473470 | 0.0204508 | ||||||||
\(537\) | 42.0215 | 1.81336 | ||||||||
\(538\) | −43.3388 | −1.86847 | ||||||||
\(539\) | −19.7872 | −0.852293 | ||||||||
\(540\) | −33.6477 | −1.44796 | ||||||||
\(541\) | 0.421224 | 0.0181098 | 0.00905491 | − | 0.999959i | \(-0.497118\pi\) | ||||
0.00905491 | + | 0.999959i | \(0.497118\pi\) | |||||||
\(542\) | 44.7801 | 1.92347 | ||||||||
\(543\) | 66.7331 | 2.86379 | ||||||||
\(544\) | 15.6793 | 0.672243 | ||||||||
\(545\) | −1.34988 | −0.0578225 | ||||||||
\(546\) | −43.1068 | −1.84480 | ||||||||
\(547\) | 3.06417 | 0.131014 | 0.0655072 | − | 0.997852i | \(-0.479133\pi\) | ||||
0.0655072 | + | 0.997852i | \(0.479133\pi\) | |||||||
\(548\) | −7.72118 | −0.329833 | ||||||||
\(549\) | −40.7483 | −1.73910 | ||||||||
\(550\) | −13.8753 | −0.591646 | ||||||||
\(551\) | 0.0693596 | 0.00295482 | ||||||||
\(552\) | −3.84759 | −0.163764 | ||||||||
\(553\) | −9.21253 | −0.391757 | ||||||||
\(554\) | 45.1569 | 1.91853 | ||||||||
\(555\) | −4.37325 | −0.185634 | ||||||||
\(556\) | −3.31140 | −0.140434 | ||||||||
\(557\) | 36.6361 | 1.55232 | 0.776161 | − | 0.630534i | \(-0.217164\pi\) | ||||
0.776161 | + | 0.630534i | \(0.217164\pi\) | |||||||
\(558\) | −93.6537 | −3.96468 | ||||||||
\(559\) | −9.68676 | −0.409706 | ||||||||
\(560\) | −24.0601 | −1.01673 | ||||||||
\(561\) | 15.2581 | 0.644197 | ||||||||
\(562\) | 0.612792 | 0.0258491 | ||||||||
\(563\) | −40.4196 | −1.70348 | −0.851741 | − | 0.523964i | \(-0.824453\pi\) | ||||
−0.851741 | + | 0.523964i | \(0.824453\pi\) | |||||||
\(564\) | 23.8985 | 1.00631 | ||||||||
\(565\) | 22.4750 | 0.945532 | ||||||||
\(566\) | 46.2320 | 1.94328 | ||||||||
\(567\) | 97.9658 | 4.11418 | ||||||||
\(568\) | 7.24939 | 0.304178 | ||||||||
\(569\) | 36.6620 | 1.53695 | 0.768475 | − | 0.639879i | \(-0.221016\pi\) | ||||
0.768475 | + | 0.639879i | \(0.221016\pi\) | |||||||
\(570\) | −0.468468 | −0.0196220 | ||||||||
\(571\) | −6.54264 | −0.273801 | −0.136900 | − | 0.990585i | \(-0.543714\pi\) | ||||
−0.136900 | + | 0.990585i | \(0.543714\pi\) | |||||||
\(572\) | 6.75439 | 0.282415 | ||||||||
\(573\) | −16.7776 | −0.700893 | ||||||||
\(574\) | −75.0949 | −3.13440 | ||||||||
\(575\) | −6.78675 | −0.283027 | ||||||||
\(576\) | −41.5882 | −1.73284 | ||||||||
\(577\) | −9.21807 | −0.383753 | −0.191877 | − | 0.981419i | \(-0.561457\pi\) | ||||
−0.191877 | + | 0.981419i | \(0.561457\pi\) | |||||||
\(578\) | 24.4316 | 1.01622 | ||||||||
\(579\) | −46.9342 | −1.95052 | ||||||||
\(580\) | −2.88157 | −0.119651 | ||||||||
\(581\) | −1.35298 | −0.0561312 | ||||||||
\(582\) | 0.148779 | 0.00616707 | ||||||||
\(583\) | 7.06144 | 0.292455 | ||||||||
\(584\) | −0.703773 | −0.0291223 | ||||||||
\(585\) | −17.6205 | −0.728518 | ||||||||
\(586\) | −22.6670 | −0.936364 | ||||||||
\(587\) | 19.6619 | 0.811535 | 0.405767 | − | 0.913976i | \(-0.367004\pi\) | ||||
0.405767 | + | 0.913976i | \(0.367004\pi\) | |||||||
\(588\) | −48.4040 | −1.99615 | ||||||||
\(589\) | −0.360618 | −0.0148590 | ||||||||
\(590\) | −11.0794 | −0.456132 | ||||||||
\(591\) | −0.523840 | −0.0215479 | ||||||||
\(592\) | −4.49399 | −0.184702 | ||||||||
\(593\) | 3.16157 | 0.129830 | 0.0649151 | − | 0.997891i | \(-0.479322\pi\) | ||||
0.0649151 | + | 0.997891i | \(0.479322\pi\) | |||||||
\(594\) | −63.5969 | −2.60941 | ||||||||
\(595\) | 11.1252 | 0.456089 | ||||||||
\(596\) | 23.1422 | 0.947942 | ||||||||
\(597\) | 12.4921 | 0.511267 | ||||||||
\(598\) | 7.16471 | 0.292987 | ||||||||
\(599\) | 19.3669 | 0.791308 | 0.395654 | − | 0.918400i | \(-0.370518\pi\) | ||||
0.395654 | + | 0.918400i | \(0.370518\pi\) | |||||||
\(600\) | 5.72515 | 0.233728 | ||||||||
\(601\) | 32.6005 | 1.32980 | 0.664901 | − | 0.746932i | \(-0.268474\pi\) | ||||
0.664901 | + | 0.746932i | \(0.268474\pi\) | |||||||
\(602\) | −42.5024 | −1.73227 | ||||||||
\(603\) | 6.38214 | 0.259901 | ||||||||
\(604\) | −13.7544 | −0.559658 | ||||||||
\(605\) | −7.91456 | −0.321773 | ||||||||
\(606\) | −12.9209 | −0.524876 | ||||||||
\(607\) | 37.3475 | 1.51589 | 0.757945 | − | 0.652319i | \(-0.226204\pi\) | ||||
0.757945 | + | 0.652319i | \(0.226204\pi\) | |||||||
\(608\) | −0.419559 | −0.0170154 | ||||||||
\(609\) | 16.0279 | 0.649483 | ||||||||
\(610\) | 14.1367 | 0.572379 | ||||||||
\(611\) | 7.50631 | 0.303673 | ||||||||
\(612\) | 26.6564 | 1.07752 | ||||||||
\(613\) | 19.4375 | 0.785072 | 0.392536 | − | 0.919737i | \(-0.371598\pi\) | ||||
0.392536 | + | 0.919737i | \(0.371598\pi\) | |||||||
\(614\) | −63.9316 | −2.58007 | ||||||||
\(615\) | −42.9813 | −1.73317 | ||||||||
\(616\) | −4.99881 | −0.201408 | ||||||||
\(617\) | −10.5770 | −0.425813 | −0.212906 | − | 0.977073i | \(-0.568293\pi\) | ||||
−0.212906 | + | 0.977073i | \(0.568293\pi\) | |||||||
\(618\) | 39.6733 | 1.59589 | ||||||||
\(619\) | −32.7979 | −1.31826 | −0.659129 | − | 0.752030i | \(-0.729075\pi\) | ||||
−0.659129 | + | 0.752030i | \(0.729075\pi\) | |||||||
\(620\) | 14.9820 | 0.601692 | ||||||||
\(621\) | −31.1067 | −1.24827 | ||||||||
\(622\) | 38.3743 | 1.53867 | ||||||||
\(623\) | −42.1867 | −1.69017 | ||||||||
\(624\) | −25.3538 | −1.01496 | ||||||||
\(625\) | 0.987677 | 0.0395071 | ||||||||
\(626\) | −24.3207 | −0.972050 | ||||||||
\(627\) | −0.408288 | −0.0163055 | ||||||||
\(628\) | 9.40966 | 0.375486 | ||||||||
\(629\) | 2.07799 | 0.0828547 | ||||||||
\(630\) | −77.3131 | −3.08023 | ||||||||
\(631\) | −18.5308 | −0.737699 | −0.368850 | − | 0.929489i | \(-0.620248\pi\) | ||||
−0.368850 | + | 0.929489i | \(0.620248\pi\) | |||||||
\(632\) | −1.29169 | −0.0513805 | ||||||||
\(633\) | 15.5785 | 0.619189 | ||||||||
\(634\) | −60.6609 | −2.40915 | ||||||||
\(635\) | 7.62125 | 0.302440 | ||||||||
\(636\) | 17.2739 | 0.684956 | ||||||||
\(637\) | −15.2033 | −0.602375 | ||||||||
\(638\) | −5.44641 | −0.215625 | ||||||||
\(639\) | 97.7181 | 3.86567 | ||||||||
\(640\) | −5.94273 | −0.234907 | ||||||||
\(641\) | 13.2777 | 0.524437 | 0.262218 | − | 0.965009i | \(-0.415546\pi\) | ||||
0.262218 | + | 0.965009i | \(0.415546\pi\) | |||||||
\(642\) | 38.4099 | 1.51592 | ||||||||
\(643\) | 31.1781 | 1.22954 | 0.614772 | − | 0.788705i | \(-0.289248\pi\) | ||||
0.614772 | + | 0.788705i | \(0.289248\pi\) | |||||||
\(644\) | 14.4957 | 0.571210 | ||||||||
\(645\) | −24.3266 | −0.957860 | ||||||||
\(646\) | 0.222596 | 0.00875794 | ||||||||
\(647\) | 9.16297 | 0.360234 | 0.180117 | − | 0.983645i | \(-0.442352\pi\) | ||||
0.180117 | + | 0.983645i | \(0.442352\pi\) | |||||||
\(648\) | 13.7358 | 0.539592 | ||||||||
\(649\) | −9.65615 | −0.379037 | ||||||||
\(650\) | −10.6610 | −0.418157 | ||||||||
\(651\) | −83.3330 | −3.26608 | ||||||||
\(652\) | 6.45866 | 0.252940 | ||||||||
\(653\) | 12.6327 | 0.494354 | 0.247177 | − | 0.968970i | \(-0.420497\pi\) | ||||
0.247177 | + | 0.968970i | \(0.420497\pi\) | |||||||
\(654\) | −6.24129 | −0.244054 | ||||||||
\(655\) | 17.7512 | 0.693597 | ||||||||
\(656\) | −44.1679 | −1.72447 | ||||||||
\(657\) | −9.48651 | −0.370104 | ||||||||
\(658\) | 32.9353 | 1.28395 | ||||||||
\(659\) | 50.5499 | 1.96914 | 0.984572 | − | 0.174983i | \(-0.0559869\pi\) | ||||
0.984572 | + | 0.174983i | \(0.0559869\pi\) | |||||||
\(660\) | 16.9625 | 0.660264 | ||||||||
\(661\) | −15.2491 | −0.593121 | −0.296561 | − | 0.955014i | \(-0.595840\pi\) | ||||
−0.296561 | + | 0.955014i | \(0.595840\pi\) | |||||||
\(662\) | 36.7605 | 1.42874 | ||||||||
\(663\) | 11.7234 | 0.455299 | ||||||||
\(664\) | −0.189701 | −0.00736184 | ||||||||
\(665\) | −0.297698 | −0.0115442 | ||||||||
\(666\) | −14.4407 | −0.559565 | ||||||||
\(667\) | −2.66397 | −0.103149 | ||||||||
\(668\) | 37.7451 | 1.46040 | ||||||||
\(669\) | −41.7679 | −1.61484 | ||||||||
\(670\) | −2.21414 | −0.0855396 | ||||||||
\(671\) | 12.3207 | 0.475636 | ||||||||
\(672\) | −96.9533 | −3.74006 | ||||||||
\(673\) | −43.3797 | −1.67217 | −0.836083 | − | 0.548603i | \(-0.815160\pi\) | ||||
−0.836083 | + | 0.548603i | \(0.815160\pi\) | |||||||
\(674\) | −57.1551 | −2.20153 | ||||||||
\(675\) | 46.2863 | 1.78156 | ||||||||
\(676\) | −17.0578 | −0.656069 | ||||||||
\(677\) | −33.5075 | −1.28780 | −0.643898 | − | 0.765111i | \(-0.722684\pi\) | ||||
−0.643898 | + | 0.765111i | \(0.722684\pi\) | |||||||
\(678\) | 103.915 | 3.99085 | ||||||||
\(679\) | 0.0945444 | 0.00362828 | ||||||||
\(680\) | 1.55986 | 0.0598180 | ||||||||
\(681\) | −82.2461 | −3.15168 | ||||||||
\(682\) | 28.3173 | 1.08432 | ||||||||
\(683\) | 28.2494 | 1.08093 | 0.540467 | − | 0.841365i | \(-0.318248\pi\) | ||||
0.540467 | + | 0.841365i | \(0.318248\pi\) | |||||||
\(684\) | −0.713294 | −0.0272735 | ||||||||
\(685\) | −6.09035 | −0.232700 | ||||||||
\(686\) | −13.2217 | −0.504808 | ||||||||
\(687\) | 38.2756 | 1.46031 | ||||||||
\(688\) | −24.9983 | −0.953050 | ||||||||
\(689\) | 5.42558 | 0.206698 | ||||||||
\(690\) | 17.9929 | 0.684979 | ||||||||
\(691\) | 25.7424 | 0.979288 | 0.489644 | − | 0.871922i | \(-0.337127\pi\) | ||||
0.489644 | + | 0.871922i | \(0.337127\pi\) | |||||||
\(692\) | −31.9494 | −1.21453 | ||||||||
\(693\) | −67.3814 | −2.55961 | ||||||||
\(694\) | 19.0642 | 0.723666 | ||||||||
\(695\) | −2.61198 | −0.0990779 | ||||||||
\(696\) | 2.24726 | 0.0851823 | ||||||||
\(697\) | 20.4229 | 0.773573 | ||||||||
\(698\) | −6.36008 | −0.240733 | ||||||||
\(699\) | 93.9314 | 3.55281 | ||||||||
\(700\) | −21.5693 | −0.815245 | ||||||||
\(701\) | 12.6667 | 0.478416 | 0.239208 | − | 0.970968i | \(-0.423112\pi\) | ||||
0.239208 | + | 0.970968i | \(0.423112\pi\) | |||||||
\(702\) | −48.8640 | −1.84425 | ||||||||
\(703\) | −0.0556045 | −0.00209716 | ||||||||
\(704\) | 12.5747 | 0.473925 | ||||||||
\(705\) | 18.8508 | 0.709962 | ||||||||
\(706\) | −21.3566 | −0.803765 | ||||||||
\(707\) | −8.21086 | −0.308801 | ||||||||
\(708\) | −23.6212 | −0.887740 | ||||||||
\(709\) | 24.1517 | 0.907035 | 0.453518 | − | 0.891247i | \(-0.350169\pi\) | ||||
0.453518 | + | 0.891247i | \(0.350169\pi\) | |||||||
\(710\) | −33.9011 | −1.27229 | ||||||||
\(711\) | −17.4113 | −0.652974 | ||||||||
\(712\) | −5.91498 | −0.221673 | ||||||||
\(713\) | 13.8506 | 0.518710 | ||||||||
\(714\) | 51.4384 | 1.92503 | ||||||||
\(715\) | 5.32776 | 0.199247 | ||||||||
\(716\) | −22.1973 | −0.829551 | ||||||||
\(717\) | 6.23926 | 0.233010 | ||||||||
\(718\) | −12.2282 | −0.456351 | ||||||||
\(719\) | 21.0475 | 0.784941 | 0.392471 | − | 0.919765i | \(-0.371620\pi\) | ||||
0.392471 | + | 0.919765i | \(0.371620\pi\) | |||||||
\(720\) | −45.4726 | −1.69466 | ||||||||
\(721\) | 25.2112 | 0.938914 | ||||||||
\(722\) | 36.5972 | 1.36201 | ||||||||
\(723\) | −6.63140 | −0.246624 | ||||||||
\(724\) | −35.2508 | −1.31009 | ||||||||
\(725\) | 3.96394 | 0.147217 | ||||||||
\(726\) | −36.5937 | −1.35812 | ||||||||
\(727\) | 47.2143 | 1.75108 | 0.875541 | − | 0.483144i | \(-0.160505\pi\) | ||||
0.875541 | + | 0.483144i | \(0.160505\pi\) | |||||||
\(728\) | −3.84078 | −0.142349 | ||||||||
\(729\) | 43.5871 | 1.61434 | ||||||||
\(730\) | 3.29113 | 0.121810 | ||||||||
\(731\) | 11.5590 | 0.427525 | ||||||||
\(732\) | 30.1393 | 1.11398 | ||||||||
\(733\) | −18.8782 | −0.697282 | −0.348641 | − | 0.937256i | \(-0.613357\pi\) | ||||
−0.348641 | + | 0.937256i | \(0.613357\pi\) | |||||||
\(734\) | −62.7192 | −2.31501 | ||||||||
\(735\) | −38.1803 | −1.40830 | ||||||||
\(736\) | 16.1144 | 0.593986 | ||||||||
\(737\) | −1.92971 | −0.0710818 | ||||||||
\(738\) | −141.926 | −5.22437 | ||||||||
\(739\) | 27.2012 | 1.00061 | 0.500306 | − | 0.865849i | \(-0.333221\pi\) | ||||
0.500306 | + | 0.865849i | \(0.333221\pi\) | |||||||
\(740\) | 2.31011 | 0.0849212 | ||||||||
\(741\) | −0.313704 | −0.0115242 | ||||||||
\(742\) | 23.8057 | 0.873935 | ||||||||
\(743\) | 39.7775 | 1.45929 | 0.729647 | − | 0.683824i | \(-0.239684\pi\) | ||||
0.729647 | + | 0.683824i | \(0.239684\pi\) | |||||||
\(744\) | −11.6841 | −0.428360 | ||||||||
\(745\) | 18.2542 | 0.668783 | ||||||||
\(746\) | −6.69235 | −0.245024 | ||||||||
\(747\) | −2.55708 | −0.0935587 | ||||||||
\(748\) | −8.05986 | −0.294698 | ||||||||
\(749\) | 24.4084 | 0.891863 | ||||||||
\(750\) | −68.8982 | −2.51581 | ||||||||
\(751\) | 43.7727 | 1.59729 | 0.798644 | − | 0.601804i | \(-0.205551\pi\) | ||||
0.798644 | + | 0.601804i | \(0.205551\pi\) | |||||||
\(752\) | 19.3712 | 0.706397 | ||||||||
\(753\) | −28.6612 | −1.04447 | ||||||||
\(754\) | −4.18469 | −0.152397 | ||||||||
\(755\) | −10.8492 | −0.394845 | ||||||||
\(756\) | −98.8621 | −3.59558 | ||||||||
\(757\) | −28.3539 | −1.03054 | −0.515270 | − | 0.857028i | \(-0.672308\pi\) | ||||
−0.515270 | + | 0.857028i | \(0.672308\pi\) | |||||||
\(758\) | 17.8895 | 0.649777 | ||||||||
\(759\) | 15.6816 | 0.569204 | ||||||||
\(760\) | −0.0417401 | −0.00151407 | ||||||||
\(761\) | −21.0154 | −0.761809 | −0.380904 | − | 0.924614i | \(-0.624387\pi\) | ||||
−0.380904 | + | 0.924614i | \(0.624387\pi\) | |||||||
\(762\) | 35.2376 | 1.27652 | ||||||||
\(763\) | −3.96616 | −0.143585 | ||||||||
\(764\) | 8.86251 | 0.320634 | ||||||||
\(765\) | 21.0262 | 0.760202 | ||||||||
\(766\) | 54.4960 | 1.96902 | ||||||||
\(767\) | −7.41921 | −0.267892 | ||||||||
\(768\) | −63.4258 | −2.28868 | ||||||||
\(769\) | −35.5062 | −1.28039 | −0.640193 | − | 0.768214i | \(-0.721146\pi\) | ||||
−0.640193 | + | 0.768214i | \(0.721146\pi\) | |||||||
\(770\) | 23.3765 | 0.842430 | ||||||||
\(771\) | −84.1459 | −3.03044 | ||||||||
\(772\) | 24.7923 | 0.892295 | ||||||||
\(773\) | −8.93550 | −0.321387 | −0.160694 | − | 0.987004i | \(-0.551373\pi\) | ||||
−0.160694 | + | 0.987004i | \(0.551373\pi\) | |||||||
\(774\) | −80.3276 | −2.88732 | ||||||||
\(775\) | −20.6095 | −0.740315 | ||||||||
\(776\) | 0.0132560 | 0.000475864 0 | ||||||||
\(777\) | −12.8493 | −0.460966 | ||||||||
\(778\) | 1.96897 | 0.0705910 | ||||||||
\(779\) | −0.546493 | −0.0195801 | ||||||||
\(780\) | 13.0329 | 0.466654 | ||||||||
\(781\) | −29.5462 | −1.05725 | ||||||||
\(782\) | −8.54949 | −0.305729 | ||||||||
\(783\) | 18.1685 | 0.649290 | ||||||||
\(784\) | −39.2344 | −1.40123 | ||||||||
\(785\) | 7.42219 | 0.264909 | ||||||||
\(786\) | 82.0743 | 2.92749 | ||||||||
\(787\) | −4.74107 | −0.169001 | −0.0845005 | − | 0.996423i | \(-0.526929\pi\) | ||||
−0.0845005 | + | 0.996423i | \(0.526929\pi\) | |||||||
\(788\) | 0.276711 | 0.00985743 | ||||||||
\(789\) | −2.60216 | −0.0926395 | ||||||||
\(790\) | 6.04045 | 0.214910 | ||||||||
\(791\) | 66.0352 | 2.34794 | ||||||||
\(792\) | −9.44752 | −0.335703 | ||||||||
\(793\) | 9.46649 | 0.336165 | ||||||||
\(794\) | 15.8425 | 0.562229 | ||||||||
\(795\) | 13.6254 | 0.483244 | ||||||||
\(796\) | −6.59876 | −0.233887 | ||||||||
\(797\) | −13.3979 | −0.474579 | −0.237290 | − | 0.971439i | \(-0.576259\pi\) | ||||
−0.237290 | + | 0.971439i | \(0.576259\pi\) | |||||||
\(798\) | −1.37643 | −0.0487252 | ||||||||
\(799\) | −8.95711 | −0.316880 | ||||||||
\(800\) | −23.9780 | −0.847750 | ||||||||
\(801\) | −79.7310 | −2.81716 | ||||||||
\(802\) | 21.4755 | 0.758328 | ||||||||
\(803\) | 2.86835 | 0.101222 | ||||||||
\(804\) | −4.72052 | −0.166480 | ||||||||
\(805\) | 11.4340 | 0.402995 | ||||||||
\(806\) | 21.7573 | 0.766367 | ||||||||
\(807\) | −72.8820 | −2.56557 | ||||||||
\(808\) | −1.15124 | −0.0405005 | ||||||||
\(809\) | 44.5045 | 1.56469 | 0.782347 | − | 0.622843i | \(-0.214022\pi\) | ||||
0.782347 | + | 0.622843i | \(0.214022\pi\) | |||||||
\(810\) | −64.2340 | −2.25695 | ||||||||
\(811\) | 52.7827 | 1.85345 | 0.926726 | − | 0.375738i | \(-0.122611\pi\) | ||||
0.926726 | + | 0.375738i | \(0.122611\pi\) | |||||||
\(812\) | −8.46650 | −0.297116 | ||||||||
\(813\) | 75.3058 | 2.64109 | ||||||||
\(814\) | 4.36630 | 0.153039 | ||||||||
\(815\) | 5.09449 | 0.178452 | ||||||||
\(816\) | 30.2541 | 1.05911 | ||||||||
\(817\) | −0.309305 | −0.0108212 | ||||||||
\(818\) | 44.1050 | 1.54209 | ||||||||
\(819\) | −51.7718 | −1.80905 | ||||||||
\(820\) | 22.7042 | 0.792867 | ||||||||
\(821\) | 1.83938 | 0.0641949 | 0.0320974 | − | 0.999485i | \(-0.489781\pi\) | ||||
0.0320974 | + | 0.999485i | \(0.489781\pi\) | |||||||
\(822\) | −28.1593 | −0.982168 | ||||||||
\(823\) | 22.1676 | 0.772714 | 0.386357 | − | 0.922349i | \(-0.373733\pi\) | ||||
0.386357 | + | 0.922349i | \(0.373733\pi\) | |||||||
\(824\) | 3.53485 | 0.123142 | ||||||||
\(825\) | −23.3339 | −0.812381 | ||||||||
\(826\) | −32.5531 | −1.13267 | ||||||||
\(827\) | −1.42069 | −0.0494021 | −0.0247010 | − | 0.999695i | \(-0.507863\pi\) | ||||
−0.0247010 | + | 0.999695i | \(0.507863\pi\) | |||||||
\(828\) | 27.3962 | 0.952085 | ||||||||
\(829\) | −24.1328 | −0.838168 | −0.419084 | − | 0.907948i | \(-0.637649\pi\) | ||||
−0.419084 | + | 0.907948i | \(0.637649\pi\) | |||||||
\(830\) | 0.887122 | 0.0307924 | ||||||||
\(831\) | 75.9395 | 2.63431 | ||||||||
\(832\) | 9.66160 | 0.334956 | ||||||||
\(833\) | 18.1417 | 0.628573 | ||||||||
\(834\) | −12.0767 | −0.418182 | ||||||||
\(835\) | 29.7727 | 1.03033 | ||||||||
\(836\) | 0.215672 | 0.00745919 | ||||||||
\(837\) | −94.4627 | −3.26511 | ||||||||
\(838\) | 1.21145 | 0.0418488 | ||||||||
\(839\) | 5.86000 | 0.202310 | 0.101155 | − | 0.994871i | \(-0.467746\pi\) | ||||
0.101155 | + | 0.994871i | \(0.467746\pi\) | |||||||
\(840\) | −9.64546 | −0.332800 | ||||||||
\(841\) | −27.4441 | −0.946347 | ||||||||
\(842\) | −19.0757 | −0.657392 | ||||||||
\(843\) | 1.03052 | 0.0354930 | ||||||||
\(844\) | −8.22911 | −0.283258 | ||||||||
\(845\) | −13.4549 | −0.462863 | ||||||||
\(846\) | 62.2462 | 2.14007 | ||||||||
\(847\) | −23.2542 | −0.799025 | ||||||||
\(848\) | 14.0016 | 0.480817 | ||||||||
\(849\) | 77.7475 | 2.66829 | ||||||||
\(850\) | 12.7215 | 0.436343 | ||||||||
\(851\) | 2.13566 | 0.0732094 | ||||||||
\(852\) | −72.2769 | −2.47617 | ||||||||
\(853\) | 32.6845 | 1.11909 | 0.559547 | − | 0.828798i | \(-0.310975\pi\) | ||||
0.559547 | + | 0.828798i | \(0.310975\pi\) | |||||||
\(854\) | 41.5359 | 1.42133 | ||||||||
\(855\) | −0.562635 | −0.0192417 | ||||||||
\(856\) | 3.42229 | 0.116972 | ||||||||
\(857\) | −31.8881 | −1.08928 | −0.544639 | − | 0.838671i | \(-0.683333\pi\) | ||||
−0.544639 | + | 0.838671i | \(0.683333\pi\) | |||||||
\(858\) | 24.6334 | 0.840969 | ||||||||
\(859\) | −21.7249 | −0.741244 | −0.370622 | − | 0.928784i | \(-0.620855\pi\) | ||||
−0.370622 | + | 0.928784i | \(0.620855\pi\) | |||||||
\(860\) | 12.8502 | 0.438188 | ||||||||
\(861\) | −126.286 | −4.30381 | ||||||||
\(862\) | −26.9171 | −0.916801 | ||||||||
\(863\) | −39.5074 | −1.34485 | −0.672424 | − | 0.740166i | \(-0.734747\pi\) | ||||
−0.672424 | + | 0.740166i | \(0.734747\pi\) | |||||||
\(864\) | −109.902 | −3.73895 | ||||||||
\(865\) | −25.2012 | −0.856865 | ||||||||
\(866\) | 17.2866 | 0.587423 | ||||||||
\(867\) | 41.0862 | 1.39536 | ||||||||
\(868\) | 44.0195 | 1.49412 | ||||||||
\(869\) | 5.26450 | 0.178586 | ||||||||
\(870\) | −10.5091 | −0.356293 | ||||||||
\(871\) | −1.48267 | −0.0502384 | ||||||||
\(872\) | −0.556094 | −0.0188317 | ||||||||
\(873\) | 0.178685 | 0.00604756 | ||||||||
\(874\) | 0.228774 | 0.00773840 | ||||||||
\(875\) | −43.7828 | −1.48013 | ||||||||
\(876\) | 7.01666 | 0.237071 | ||||||||
\(877\) | −7.82967 | −0.264389 | −0.132195 | − | 0.991224i | \(-0.542202\pi\) | ||||
−0.132195 | + | 0.991224i | \(0.542202\pi\) | |||||||
\(878\) | 67.7817 | 2.28752 | ||||||||
\(879\) | −38.1186 | −1.28571 | ||||||||
\(880\) | 13.7491 | 0.463483 | ||||||||
\(881\) | 4.05232 | 0.136526 | 0.0682631 | − | 0.997667i | \(-0.478254\pi\) | ||||
0.0682631 | + | 0.997667i | \(0.478254\pi\) | |||||||
\(882\) | −126.073 | −4.24510 | ||||||||
\(883\) | −30.9967 | −1.04312 | −0.521562 | − | 0.853214i | \(-0.674650\pi\) | ||||
−0.521562 | + | 0.853214i | \(0.674650\pi\) | |||||||
\(884\) | −6.19271 | −0.208283 | ||||||||
\(885\) | −18.6321 | −0.626310 | ||||||||
\(886\) | 2.74319 | 0.0921592 | ||||||||
\(887\) | −16.4517 | −0.552395 | −0.276197 | − | 0.961101i | \(-0.589074\pi\) | ||||
−0.276197 | + | 0.961101i | \(0.589074\pi\) | |||||||
\(888\) | −1.80160 | −0.0604576 | ||||||||
\(889\) | 22.3924 | 0.751018 | ||||||||
\(890\) | 27.6609 | 0.927195 | ||||||||
\(891\) | −55.9825 | −1.87549 | ||||||||
\(892\) | 22.0633 | 0.738733 | ||||||||
\(893\) | 0.239682 | 0.00802065 | ||||||||
\(894\) | 84.4000 | 2.82276 | ||||||||
\(895\) | −17.5089 | −0.585257 | ||||||||
\(896\) | −17.4607 | −0.583321 | ||||||||
\(897\) | 12.0488 | 0.402296 | ||||||||
\(898\) | 32.7551 | 1.09305 | ||||||||
\(899\) | −8.08974 | −0.269808 | ||||||||
\(900\) | −40.7651 | −1.35884 | ||||||||
\(901\) | −6.47423 | −0.215688 | ||||||||
\(902\) | 42.9129 | 1.42884 | ||||||||
\(903\) | −71.4754 | −2.37855 | ||||||||
\(904\) | 9.25877 | 0.307942 | ||||||||
\(905\) | −27.8053 | −0.924279 | ||||||||
\(906\) | −50.1625 | −1.66654 | ||||||||
\(907\) | 21.4650 | 0.712733 | 0.356366 | − | 0.934346i | \(-0.384015\pi\) | ||||
0.356366 | + | 0.934346i | \(0.384015\pi\) | |||||||
\(908\) | 43.4453 | 1.44178 | ||||||||
\(909\) | −15.5182 | −0.514705 | ||||||||
\(910\) | 17.9611 | 0.595404 | ||||||||
\(911\) | −33.0791 | −1.09596 | −0.547979 | − | 0.836492i | \(-0.684603\pi\) | ||||
−0.547979 | + | 0.836492i | \(0.684603\pi\) | |||||||
\(912\) | −0.809564 | −0.0268073 | ||||||||
\(913\) | 0.773162 | 0.0255879 | ||||||||
\(914\) | −5.84530 | −0.193345 | ||||||||
\(915\) | 23.7734 | 0.785926 | ||||||||
\(916\) | −20.2186 | −0.668040 | ||||||||
\(917\) | 52.1558 | 1.72234 | ||||||||
\(918\) | 58.3084 | 1.92446 | ||||||||
\(919\) | 18.7178 | 0.617442 | 0.308721 | − | 0.951153i | \(-0.400099\pi\) | ||||
0.308721 | + | 0.951153i | \(0.400099\pi\) | |||||||
\(920\) | 1.60315 | 0.0528544 | ||||||||
\(921\) | −107.513 | −3.54266 | ||||||||
\(922\) | −64.9695 | −2.13966 | ||||||||
\(923\) | −22.7015 | −0.747229 | ||||||||
\(924\) | 49.8384 | 1.63956 | ||||||||
\(925\) | −3.17782 | −0.104486 | ||||||||
\(926\) | −34.4429 | −1.13186 | ||||||||
\(927\) | 47.6481 | 1.56497 | ||||||||
\(928\) | −9.41196 | −0.308963 | ||||||||
\(929\) | 50.7241 | 1.66420 | 0.832102 | − | 0.554623i | \(-0.187137\pi\) | ||||
0.832102 | + | 0.554623i | \(0.187137\pi\) | |||||||
\(930\) | 54.6396 | 1.79170 | ||||||||
\(931\) | −0.485451 | −0.0159100 | ||||||||
\(932\) | −49.6179 | −1.62529 | ||||||||
\(933\) | 64.5334 | 2.11273 | ||||||||
\(934\) | 33.1288 | 1.08401 | ||||||||
\(935\) | −6.35749 | −0.207912 | ||||||||
\(936\) | −7.25891 | −0.237265 | ||||||||
\(937\) | −22.8934 | −0.747894 | −0.373947 | − | 0.927450i | \(-0.621996\pi\) | ||||
−0.373947 | + | 0.927450i | \(0.621996\pi\) | |||||||
\(938\) | −6.50549 | −0.212412 | ||||||||
\(939\) | −40.8996 | −1.33471 | ||||||||
\(940\) | −9.95766 | −0.324783 | ||||||||
\(941\) | 35.0799 | 1.14357 | 0.571786 | − | 0.820403i | \(-0.306251\pi\) | ||||
0.571786 | + | 0.820403i | \(0.306251\pi\) | |||||||
\(942\) | 34.3172 | 1.11811 | ||||||||
\(943\) | 20.9897 | 0.683519 | ||||||||
\(944\) | −19.1465 | −0.623164 | ||||||||
\(945\) | −77.9809 | −2.53672 | ||||||||
\(946\) | 24.2880 | 0.789670 | ||||||||
\(947\) | 22.6453 | 0.735872 | 0.367936 | − | 0.929851i | \(-0.380065\pi\) | ||||
0.367936 | + | 0.929851i | \(0.380065\pi\) | |||||||
\(948\) | 12.8782 | 0.418264 | ||||||||
\(949\) | 2.20387 | 0.0715406 | ||||||||
\(950\) | −0.340412 | −0.0110444 | ||||||||
\(951\) | −102.012 | −3.30798 | ||||||||
\(952\) | 4.58312 | 0.148540 | ||||||||
\(953\) | 3.92428 | 0.127120 | 0.0635599 | − | 0.997978i | \(-0.479755\pi\) | ||||
0.0635599 | + | 0.997978i | \(0.479755\pi\) | |||||||
\(954\) | 44.9917 | 1.45666 | ||||||||
\(955\) | 6.99061 | 0.226211 | ||||||||
\(956\) | −3.29580 | −0.106594 | ||||||||
\(957\) | −9.15912 | −0.296072 | ||||||||
\(958\) | −8.33549 | −0.269307 | ||||||||
\(959\) | −17.8944 | −0.577840 | ||||||||
\(960\) | 24.2634 | 0.783099 | ||||||||
\(961\) | 11.0606 | 0.356793 | ||||||||
\(962\) | 3.35480 | 0.108163 | ||||||||
\(963\) | 46.1308 | 1.48654 | ||||||||
\(964\) | 3.50294 | 0.112822 | ||||||||
\(965\) | 19.5558 | 0.629523 | ||||||||
\(966\) | 52.8660 | 1.70094 | ||||||||
\(967\) | −15.2485 | −0.490358 | −0.245179 | − | 0.969478i | \(-0.578847\pi\) | ||||
−0.245179 | + | 0.969478i | \(0.578847\pi\) | |||||||
\(968\) | −3.26047 | −0.104795 | ||||||||
\(969\) | 0.374336 | 0.0120254 | ||||||||
\(970\) | −0.0619907 | −0.00199040 | ||||||||
\(971\) | 40.7839 | 1.30882 | 0.654409 | − | 0.756141i | \(-0.272917\pi\) | ||||
0.654409 | + | 0.756141i | \(0.272917\pi\) | |||||||
\(972\) | −62.1672 | −1.99401 | ||||||||
\(973\) | −7.67440 | −0.246030 | ||||||||
\(974\) | −16.2496 | −0.520671 | ||||||||
\(975\) | −17.9283 | −0.574166 | ||||||||
\(976\) | 24.4298 | 0.781979 | ||||||||
\(977\) | −16.0448 | −0.513318 | −0.256659 | − | 0.966502i | \(-0.582622\pi\) | ||||
−0.256659 | + | 0.966502i | \(0.582622\pi\) | |||||||
\(978\) | 23.5548 | 0.753200 | ||||||||
\(979\) | 24.1076 | 0.770481 | ||||||||
\(980\) | 20.1682 | 0.644250 | ||||||||
\(981\) | −7.49587 | −0.239325 | ||||||||
\(982\) | 29.6501 | 0.946174 | ||||||||
\(983\) | 26.5463 | 0.846694 | 0.423347 | − | 0.905968i | \(-0.360855\pi\) | ||||
0.423347 | + | 0.905968i | \(0.360855\pi\) | |||||||
\(984\) | −17.7065 | −0.564462 | ||||||||
\(985\) | 0.218265 | 0.00695452 | ||||||||
\(986\) | 4.99350 | 0.159025 | ||||||||
\(987\) | 55.3866 | 1.76297 | ||||||||
\(988\) | 0.165710 | 0.00527193 | ||||||||
\(989\) | 11.8798 | 0.377756 | ||||||||
\(990\) | 44.1805 | 1.40415 | ||||||||
\(991\) | −7.26308 | −0.230719 | −0.115360 | − | 0.993324i | \(-0.536802\pi\) | ||||
−0.115360 | + | 0.993324i | \(0.536802\pi\) | |||||||
\(992\) | 48.9352 | 1.55369 | ||||||||
\(993\) | 61.8195 | 1.96178 | ||||||||
\(994\) | −99.6068 | −3.15934 | ||||||||
\(995\) | −5.20500 | −0.165010 | ||||||||
\(996\) | 1.89134 | 0.0599293 | ||||||||
\(997\) | 2.34142 | 0.0741536 | 0.0370768 | − | 0.999312i | \(-0.488195\pi\) | ||||
0.0370768 | + | 0.999312i | \(0.488195\pi\) | |||||||
\(998\) | −66.6765 | −2.11061 | ||||||||
\(999\) | −14.5654 | −0.460829 |
(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 | 4033.2.a.f.1.16 | ✓ | 85 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4033.2.a.f.1.16 | ✓ | 85 | 1.1 | even | 1 | trivial |