Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [187,2,Mod(1,187)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(187, 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("187.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 187 = 11 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 187.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: | \(1.49320251780\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.311108\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 187.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.688892 | −0.487120 | −0.243560 | − | 0.969886i | \(-0.578315\pi\) | ||||
−0.243560 | + | 0.969886i | \(0.578315\pi\) | |||||||
\(3\) | 1.21432 | 0.701088 | 0.350544 | − | 0.936546i | \(-0.385997\pi\) | ||||
0.350544 | + | 0.936546i | \(0.385997\pi\) | |||||||
\(4\) | −1.52543 | −0.762714 | ||||||||
\(5\) | −2.31111 | −1.03356 | −0.516779 | − | 0.856119i | \(-0.672869\pi\) | ||||
−0.516779 | + | 0.856119i | \(0.672869\pi\) | |||||||
\(6\) | −0.836535 | −0.341514 | ||||||||
\(7\) | −4.42864 | −1.67387 | −0.836934 | − | 0.547304i | \(-0.815654\pi\) | ||||
−0.836934 | + | 0.547304i | \(0.815654\pi\) | |||||||
\(8\) | 2.42864 | 0.858654 | ||||||||
\(9\) | −1.52543 | −0.508476 | ||||||||
\(10\) | 1.59210 | 0.503468 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −1.85236 | −0.534729 | ||||||||
\(13\) | −0.0666765 | −0.0184927 | −0.00924637 | − | 0.999957i | \(-0.502943\pi\) | ||||
−0.00924637 | + | 0.999957i | \(0.502943\pi\) | |||||||
\(14\) | 3.05086 | 0.815375 | ||||||||
\(15\) | −2.80642 | −0.724616 | ||||||||
\(16\) | 1.37778 | 0.344446 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 1.05086 | 0.247689 | ||||||||
\(19\) | 6.49532 | 1.49013 | 0.745064 | − | 0.666993i | \(-0.232419\pi\) | ||||
0.745064 | + | 0.666993i | \(0.232419\pi\) | |||||||
\(20\) | 3.52543 | 0.788310 | ||||||||
\(21\) | −5.37778 | −1.17353 | ||||||||
\(22\) | 0.688892 | 0.146872 | ||||||||
\(23\) | −2.78568 | −0.580854 | −0.290427 | − | 0.956897i | \(-0.593797\pi\) | ||||
−0.290427 | + | 0.956897i | \(0.593797\pi\) | |||||||
\(24\) | 2.94914 | 0.601992 | ||||||||
\(25\) | 0.341219 | 0.0682439 | ||||||||
\(26\) | 0.0459330 | 0.00900819 | ||||||||
\(27\) | −5.49532 | −1.05757 | ||||||||
\(28\) | 6.75557 | 1.27668 | ||||||||
\(29\) | −2.40790 | −0.447135 | −0.223568 | − | 0.974688i | \(-0.571770\pi\) | ||||
−0.223568 | + | 0.974688i | \(0.571770\pi\) | |||||||
\(30\) | 1.93332 | 0.352975 | ||||||||
\(31\) | −7.49532 | −1.34620 | −0.673099 | − | 0.739552i | \(-0.735037\pi\) | ||||
−0.673099 | + | 0.739552i | \(0.735037\pi\) | |||||||
\(32\) | −5.80642 | −1.02644 | ||||||||
\(33\) | −1.21432 | −0.211386 | ||||||||
\(34\) | 0.688892 | 0.118144 | ||||||||
\(35\) | 10.2351 | 1.73004 | ||||||||
\(36\) | 2.32693 | 0.387822 | ||||||||
\(37\) | 7.44938 | 1.22467 | 0.612336 | − | 0.790598i | \(-0.290230\pi\) | ||||
0.612336 | + | 0.790598i | \(0.290230\pi\) | |||||||
\(38\) | −4.47457 | −0.725872 | ||||||||
\(39\) | −0.0809666 | −0.0129650 | ||||||||
\(40\) | −5.61285 | −0.887469 | ||||||||
\(41\) | −4.42864 | −0.691637 | −0.345819 | − | 0.938301i | \(-0.612399\pi\) | ||||
−0.345819 | + | 0.938301i | \(0.612399\pi\) | |||||||
\(42\) | 3.70471 | 0.571650 | ||||||||
\(43\) | 11.6128 | 1.77094 | 0.885471 | − | 0.464694i | \(-0.153836\pi\) | ||||
0.885471 | + | 0.464694i | \(0.153836\pi\) | |||||||
\(44\) | 1.52543 | 0.229967 | ||||||||
\(45\) | 3.52543 | 0.525540 | ||||||||
\(46\) | 1.91903 | 0.282946 | ||||||||
\(47\) | −1.33185 | −0.194270 | −0.0971352 | − | 0.995271i | \(-0.530968\pi\) | ||||
−0.0971352 | + | 0.995271i | \(0.530968\pi\) | |||||||
\(48\) | 1.67307 | 0.241487 | ||||||||
\(49\) | 12.6128 | 1.80184 | ||||||||
\(50\) | −0.235063 | −0.0332430 | ||||||||
\(51\) | −1.21432 | −0.170039 | ||||||||
\(52\) | 0.101710 | 0.0141047 | ||||||||
\(53\) | −12.2810 | −1.68692 | −0.843462 | − | 0.537188i | \(-0.819486\pi\) | ||||
−0.843462 | + | 0.537188i | \(0.819486\pi\) | |||||||
\(54\) | 3.78568 | 0.515166 | ||||||||
\(55\) | 2.31111 | 0.311630 | ||||||||
\(56\) | −10.7556 | −1.43727 | ||||||||
\(57\) | 7.88739 | 1.04471 | ||||||||
\(58\) | 1.65878 | 0.217809 | ||||||||
\(59\) | 1.76986 | 0.230416 | 0.115208 | − | 0.993341i | \(-0.463247\pi\) | ||||
0.115208 | + | 0.993341i | \(0.463247\pi\) | |||||||
\(60\) | 4.28100 | 0.552674 | ||||||||
\(61\) | 2.42864 | 0.310955 | 0.155478 | − | 0.987839i | \(-0.450308\pi\) | ||||
0.155478 | + | 0.987839i | \(0.450308\pi\) | |||||||
\(62\) | 5.16346 | 0.655761 | ||||||||
\(63\) | 6.75557 | 0.851122 | ||||||||
\(64\) | 1.24443 | 0.155554 | ||||||||
\(65\) | 0.154097 | 0.0191133 | ||||||||
\(66\) | 0.836535 | 0.102970 | ||||||||
\(67\) | −13.2351 | −1.61692 | −0.808460 | − | 0.588551i | \(-0.799699\pi\) | ||||
−0.808460 | + | 0.588551i | \(0.799699\pi\) | |||||||
\(68\) | 1.52543 | 0.184985 | ||||||||
\(69\) | −3.38271 | −0.407230 | ||||||||
\(70\) | −7.05086 | −0.842738 | ||||||||
\(71\) | −1.06668 | −0.126591 | −0.0632956 | − | 0.997995i | \(-0.520161\pi\) | ||||
−0.0632956 | + | 0.997995i | \(0.520161\pi\) | |||||||
\(72\) | −3.70471 | −0.436605 | ||||||||
\(73\) | −1.78568 | −0.208998 | −0.104499 | − | 0.994525i | \(-0.533324\pi\) | ||||
−0.104499 | + | 0.994525i | \(0.533324\pi\) | |||||||
\(74\) | −5.13182 | −0.596562 | ||||||||
\(75\) | 0.414349 | 0.0478449 | ||||||||
\(76\) | −9.90813 | −1.13654 | ||||||||
\(77\) | 4.42864 | 0.504690 | ||||||||
\(78\) | 0.0557773 | 0.00631553 | ||||||||
\(79\) | 6.83654 | 0.769170 | 0.384585 | − | 0.923090i | \(-0.374345\pi\) | ||||
0.384585 | + | 0.923090i | \(0.374345\pi\) | |||||||
\(80\) | −3.18421 | −0.356005 | ||||||||
\(81\) | −2.09679 | −0.232976 | ||||||||
\(82\) | 3.05086 | 0.336911 | ||||||||
\(83\) | 2.75557 | 0.302463 | 0.151231 | − | 0.988498i | \(-0.451676\pi\) | ||||
0.151231 | + | 0.988498i | \(0.451676\pi\) | |||||||
\(84\) | 8.20342 | 0.895067 | ||||||||
\(85\) | 2.31111 | 0.250675 | ||||||||
\(86\) | −8.00000 | −0.862662 | ||||||||
\(87\) | −2.92396 | −0.313481 | ||||||||
\(88\) | −2.42864 | −0.258894 | ||||||||
\(89\) | −8.47949 | −0.898825 | −0.449412 | − | 0.893324i | \(-0.648367\pi\) | ||||
−0.449412 | + | 0.893324i | \(0.648367\pi\) | |||||||
\(90\) | −2.42864 | −0.256001 | ||||||||
\(91\) | 0.295286 | 0.0309544 | ||||||||
\(92\) | 4.24935 | 0.443026 | ||||||||
\(93\) | −9.10171 | −0.943803 | ||||||||
\(94\) | 0.917502 | 0.0946331 | ||||||||
\(95\) | −15.0114 | −1.54013 | ||||||||
\(96\) | −7.05086 | −0.719625 | ||||||||
\(97\) | −7.83654 | −0.795680 | −0.397840 | − | 0.917455i | \(-0.630240\pi\) | ||||
−0.397840 | + | 0.917455i | \(0.630240\pi\) | |||||||
\(98\) | −8.68889 | −0.877711 | ||||||||
\(99\) | 1.52543 | 0.153311 | ||||||||
\(100\) | −0.520505 | −0.0520505 | ||||||||
\(101\) | −4.36196 | −0.434032 | −0.217016 | − | 0.976168i | \(-0.569632\pi\) | ||||
−0.217016 | + | 0.976168i | \(0.569632\pi\) | |||||||
\(102\) | 0.836535 | 0.0828293 | ||||||||
\(103\) | −12.2494 | −1.20696 | −0.603482 | − | 0.797376i | \(-0.706221\pi\) | ||||
−0.603482 | + | 0.797376i | \(0.706221\pi\) | |||||||
\(104\) | −0.161933 | −0.0158789 | ||||||||
\(105\) | 12.4286 | 1.21291 | ||||||||
\(106\) | 8.46028 | 0.821735 | ||||||||
\(107\) | −12.0207 | −1.16209 | −0.581045 | − | 0.813872i | \(-0.697356\pi\) | ||||
−0.581045 | + | 0.813872i | \(0.697356\pi\) | |||||||
\(108\) | 8.38271 | 0.806626 | ||||||||
\(109\) | −14.1541 | −1.35572 | −0.677858 | − | 0.735193i | \(-0.737092\pi\) | ||||
−0.677858 | + | 0.735193i | \(0.737092\pi\) | |||||||
\(110\) | −1.59210 | −0.151801 | ||||||||
\(111\) | 9.04593 | 0.858602 | ||||||||
\(112\) | −6.10171 | −0.576557 | ||||||||
\(113\) | 4.44446 | 0.418100 | 0.209050 | − | 0.977905i | \(-0.432963\pi\) | ||||
0.209050 | + | 0.977905i | \(0.432963\pi\) | |||||||
\(114\) | −5.43356 | −0.508900 | ||||||||
\(115\) | 6.43801 | 0.600347 | ||||||||
\(116\) | 3.67307 | 0.341036 | ||||||||
\(117\) | 0.101710 | 0.00940312 | ||||||||
\(118\) | −1.21924 | −0.112240 | ||||||||
\(119\) | 4.42864 | 0.405973 | ||||||||
\(120\) | −6.81579 | −0.622194 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −1.67307 | −0.151473 | ||||||||
\(123\) | −5.37778 | −0.484898 | ||||||||
\(124\) | 11.4336 | 1.02676 | ||||||||
\(125\) | 10.7669 | 0.963025 | ||||||||
\(126\) | −4.65386 | −0.414599 | ||||||||
\(127\) | 13.6128 | 1.20794 | 0.603972 | − | 0.797005i | \(-0.293584\pi\) | ||||
0.603972 | + | 0.797005i | \(0.293584\pi\) | |||||||
\(128\) | 10.7556 | 0.950667 | ||||||||
\(129\) | 14.1017 | 1.24159 | ||||||||
\(130\) | −0.106156 | −0.00931050 | ||||||||
\(131\) | 20.9590 | 1.83120 | 0.915598 | − | 0.402096i | \(-0.131718\pi\) | ||||
0.915598 | + | 0.402096i | \(0.131718\pi\) | |||||||
\(132\) | 1.85236 | 0.161227 | ||||||||
\(133\) | −28.7654 | −2.49428 | ||||||||
\(134\) | 9.11753 | 0.787635 | ||||||||
\(135\) | 12.7003 | 1.09307 | ||||||||
\(136\) | −2.42864 | −0.208254 | ||||||||
\(137\) | −17.2351 | −1.47249 | −0.736245 | − | 0.676715i | \(-0.763403\pi\) | ||||
−0.736245 | + | 0.676715i | \(0.763403\pi\) | |||||||
\(138\) | 2.33032 | 0.198370 | ||||||||
\(139\) | 6.96989 | 0.591178 | 0.295589 | − | 0.955315i | \(-0.404484\pi\) | ||||
0.295589 | + | 0.955315i | \(0.404484\pi\) | |||||||
\(140\) | −15.6128 | −1.31953 | ||||||||
\(141\) | −1.61729 | −0.136201 | ||||||||
\(142\) | 0.734825 | 0.0616652 | ||||||||
\(143\) | 0.0666765 | 0.00557577 | ||||||||
\(144\) | −2.10171 | −0.175143 | ||||||||
\(145\) | 5.56491 | 0.462140 | ||||||||
\(146\) | 1.23014 | 0.101807 | ||||||||
\(147\) | 15.3160 | 1.26324 | ||||||||
\(148\) | −11.3635 | −0.934073 | ||||||||
\(149\) | −12.3620 | −1.01273 | −0.506366 | − | 0.862319i | \(-0.669011\pi\) | ||||
−0.506366 | + | 0.862319i | \(0.669011\pi\) | |||||||
\(150\) | −0.285442 | −0.0233062 | ||||||||
\(151\) | 14.4953 | 1.17961 | 0.589806 | − | 0.807545i | \(-0.299204\pi\) | ||||
0.589806 | + | 0.807545i | \(0.299204\pi\) | |||||||
\(152\) | 15.7748 | 1.27950 | ||||||||
\(153\) | 1.52543 | 0.123324 | ||||||||
\(154\) | −3.05086 | −0.245845 | ||||||||
\(155\) | 17.3225 | 1.39138 | ||||||||
\(156\) | 0.123509 | 0.00988861 | ||||||||
\(157\) | 14.2859 | 1.14014 | 0.570070 | − | 0.821596i | \(-0.306916\pi\) | ||||
0.570070 | + | 0.821596i | \(0.306916\pi\) | |||||||
\(158\) | −4.70964 | −0.374679 | ||||||||
\(159\) | −14.9131 | −1.18268 | ||||||||
\(160\) | 13.4193 | 1.06089 | ||||||||
\(161\) | 12.3368 | 0.972274 | ||||||||
\(162\) | 1.44446 | 0.113488 | ||||||||
\(163\) | 8.29529 | 0.649737 | 0.324868 | − | 0.945759i | \(-0.394680\pi\) | ||||
0.324868 | + | 0.945759i | \(0.394680\pi\) | |||||||
\(164\) | 6.75557 | 0.527521 | ||||||||
\(165\) | 2.80642 | 0.218480 | ||||||||
\(166\) | −1.89829 | −0.147336 | ||||||||
\(167\) | −11.2050 | −0.867065 | −0.433533 | − | 0.901138i | \(-0.642733\pi\) | ||||
−0.433533 | + | 0.901138i | \(0.642733\pi\) | |||||||
\(168\) | −13.0607 | −1.00765 | ||||||||
\(169\) | −12.9956 | −0.999658 | ||||||||
\(170\) | −1.59210 | −0.122109 | ||||||||
\(171\) | −9.90813 | −0.757694 | ||||||||
\(172\) | −17.7146 | −1.35072 | ||||||||
\(173\) | −19.0923 | −1.45156 | −0.725782 | − | 0.687925i | \(-0.758522\pi\) | ||||
−0.725782 | + | 0.687925i | \(0.758522\pi\) | |||||||
\(174\) | 2.01429 | 0.152703 | ||||||||
\(175\) | −1.51114 | −0.114231 | ||||||||
\(176\) | −1.37778 | −0.103854 | ||||||||
\(177\) | 2.14917 | 0.161542 | ||||||||
\(178\) | 5.84146 | 0.437836 | ||||||||
\(179\) | 23.6637 | 1.76871 | 0.884354 | − | 0.466817i | \(-0.154599\pi\) | ||||
0.884354 | + | 0.466817i | \(0.154599\pi\) | |||||||
\(180\) | −5.37778 | −0.400836 | ||||||||
\(181\) | −3.21432 | −0.238919 | −0.119459 | − | 0.992839i | \(-0.538116\pi\) | ||||
−0.119459 | + | 0.992839i | \(0.538116\pi\) | |||||||
\(182\) | −0.203420 | −0.0150785 | ||||||||
\(183\) | 2.94914 | 0.218007 | ||||||||
\(184\) | −6.76541 | −0.498753 | ||||||||
\(185\) | −17.2163 | −1.26577 | ||||||||
\(186\) | 6.27010 | 0.459746 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | 2.03164 | 0.148173 | ||||||||
\(189\) | 24.3368 | 1.77024 | ||||||||
\(190\) | 10.3412 | 0.750231 | ||||||||
\(191\) | 12.6128 | 0.912634 | 0.456317 | − | 0.889817i | \(-0.349168\pi\) | ||||
0.456317 | + | 0.889817i | \(0.349168\pi\) | |||||||
\(192\) | 1.51114 | 0.109057 | ||||||||
\(193\) | 5.03011 | 0.362075 | 0.181038 | − | 0.983476i | \(-0.442054\pi\) | ||||
0.181038 | + | 0.983476i | \(0.442054\pi\) | |||||||
\(194\) | 5.39853 | 0.387592 | ||||||||
\(195\) | 0.187123 | 0.0134001 | ||||||||
\(196\) | −19.2400 | −1.37428 | ||||||||
\(197\) | −21.8874 | −1.55941 | −0.779706 | − | 0.626146i | \(-0.784631\pi\) | ||||
−0.779706 | + | 0.626146i | \(0.784631\pi\) | |||||||
\(198\) | −1.05086 | −0.0746810 | ||||||||
\(199\) | 15.7748 | 1.11824 | 0.559122 | − | 0.829085i | \(-0.311138\pi\) | ||||
0.559122 | + | 0.829085i | \(0.311138\pi\) | |||||||
\(200\) | 0.828699 | 0.0585979 | ||||||||
\(201\) | −16.0716 | −1.13360 | ||||||||
\(202\) | 3.00492 | 0.211426 | ||||||||
\(203\) | 10.6637 | 0.748445 | ||||||||
\(204\) | 1.85236 | 0.129691 | ||||||||
\(205\) | 10.2351 | 0.714848 | ||||||||
\(206\) | 8.43848 | 0.587937 | ||||||||
\(207\) | 4.24935 | 0.295350 | ||||||||
\(208\) | −0.0918659 | −0.00636975 | ||||||||
\(209\) | −6.49532 | −0.449290 | ||||||||
\(210\) | −8.56199 | −0.590834 | ||||||||
\(211\) | −7.51114 | −0.517088 | −0.258544 | − | 0.965999i | \(-0.583243\pi\) | ||||
−0.258544 | + | 0.965999i | \(0.583243\pi\) | |||||||
\(212\) | 18.7338 | 1.28664 | ||||||||
\(213\) | −1.29529 | −0.0887516 | ||||||||
\(214\) | 8.28100 | 0.566077 | ||||||||
\(215\) | −26.8385 | −1.83037 | ||||||||
\(216\) | −13.3461 | −0.908090 | ||||||||
\(217\) | 33.1941 | 2.25336 | ||||||||
\(218\) | 9.75065 | 0.660397 | ||||||||
\(219\) | −2.16839 | −0.146526 | ||||||||
\(220\) | −3.52543 | −0.237684 | ||||||||
\(221\) | 0.0666765 | 0.00448515 | ||||||||
\(222\) | −6.23167 | −0.418242 | ||||||||
\(223\) | −19.1476 | −1.28222 | −0.641111 | − | 0.767449i | \(-0.721526\pi\) | ||||
−0.641111 | + | 0.767449i | \(0.721526\pi\) | |||||||
\(224\) | 25.7146 | 1.71813 | ||||||||
\(225\) | −0.520505 | −0.0347004 | ||||||||
\(226\) | −3.06175 | −0.203665 | ||||||||
\(227\) | −15.1318 | −1.00433 | −0.502167 | − | 0.864771i | \(-0.667464\pi\) | ||||
−0.502167 | + | 0.864771i | \(0.667464\pi\) | |||||||
\(228\) | −12.0316 | −0.796815 | ||||||||
\(229\) | 2.79213 | 0.184509 | 0.0922547 | − | 0.995735i | \(-0.470593\pi\) | ||||
0.0922547 | + | 0.995735i | \(0.470593\pi\) | |||||||
\(230\) | −4.43509 | −0.292441 | ||||||||
\(231\) | 5.37778 | 0.353832 | ||||||||
\(232\) | −5.84791 | −0.383934 | ||||||||
\(233\) | 4.32693 | 0.283467 | 0.141733 | − | 0.989905i | \(-0.454732\pi\) | ||||
0.141733 | + | 0.989905i | \(0.454732\pi\) | |||||||
\(234\) | −0.0700674 | −0.00458045 | ||||||||
\(235\) | 3.07805 | 0.200790 | ||||||||
\(236\) | −2.69979 | −0.175741 | ||||||||
\(237\) | 8.30174 | 0.539256 | ||||||||
\(238\) | −3.05086 | −0.197758 | ||||||||
\(239\) | 11.9748 | 0.774586 | 0.387293 | − | 0.921957i | \(-0.373410\pi\) | ||||
0.387293 | + | 0.921957i | \(0.373410\pi\) | |||||||
\(240\) | −3.86665 | −0.249591 | ||||||||
\(241\) | −7.31756 | −0.471366 | −0.235683 | − | 0.971830i | \(-0.575733\pi\) | ||||
−0.235683 | + | 0.971830i | \(0.575733\pi\) | |||||||
\(242\) | −0.688892 | −0.0442837 | ||||||||
\(243\) | 13.9398 | 0.894237 | ||||||||
\(244\) | −3.70471 | −0.237170 | ||||||||
\(245\) | −29.1497 | −1.86230 | ||||||||
\(246\) | 3.70471 | 0.236204 | ||||||||
\(247\) | −0.433085 | −0.0275566 | ||||||||
\(248\) | −18.2034 | −1.15592 | ||||||||
\(249\) | 3.34614 | 0.212053 | ||||||||
\(250\) | −7.41726 | −0.469109 | ||||||||
\(251\) | 22.6731 | 1.43111 | 0.715556 | − | 0.698556i | \(-0.246174\pi\) | ||||
0.715556 | + | 0.698556i | \(0.246174\pi\) | |||||||
\(252\) | −10.3051 | −0.649162 | ||||||||
\(253\) | 2.78568 | 0.175134 | ||||||||
\(254\) | −9.37778 | −0.588415 | ||||||||
\(255\) | 2.80642 | 0.175745 | ||||||||
\(256\) | −9.89829 | −0.618643 | ||||||||
\(257\) | −6.22077 | −0.388041 | −0.194021 | − | 0.980997i | \(-0.562153\pi\) | ||||
−0.194021 | + | 0.980997i | \(0.562153\pi\) | |||||||
\(258\) | −9.71456 | −0.604802 | ||||||||
\(259\) | −32.9906 | −2.04994 | ||||||||
\(260\) | −0.235063 | −0.0145780 | ||||||||
\(261\) | 3.67307 | 0.227357 | ||||||||
\(262\) | −14.4385 | −0.892013 | ||||||||
\(263\) | 9.78123 | 0.603137 | 0.301568 | − | 0.953445i | \(-0.402490\pi\) | ||||
0.301568 | + | 0.953445i | \(0.402490\pi\) | |||||||
\(264\) | −2.94914 | −0.181507 | ||||||||
\(265\) | 28.3827 | 1.74354 | ||||||||
\(266\) | 19.8163 | 1.21501 | ||||||||
\(267\) | −10.2968 | −0.630155 | ||||||||
\(268\) | 20.1891 | 1.23325 | ||||||||
\(269\) | 13.5714 | 0.827460 | 0.413730 | − | 0.910400i | \(-0.364226\pi\) | ||||
0.413730 | + | 0.910400i | \(0.364226\pi\) | |||||||
\(270\) | −8.74912 | −0.532454 | ||||||||
\(271\) | 7.41927 | 0.450689 | 0.225344 | − | 0.974279i | \(-0.427649\pi\) | ||||
0.225344 | + | 0.974279i | \(0.427649\pi\) | |||||||
\(272\) | −1.37778 | −0.0835404 | ||||||||
\(273\) | 0.358572 | 0.0217018 | ||||||||
\(274\) | 11.8731 | 0.717280 | ||||||||
\(275\) | −0.341219 | −0.0205763 | ||||||||
\(276\) | 5.16007 | 0.310600 | ||||||||
\(277\) | −20.8256 | −1.25129 | −0.625646 | − | 0.780107i | \(-0.715164\pi\) | ||||
−0.625646 | + | 0.780107i | \(0.715164\pi\) | |||||||
\(278\) | −4.80150 | −0.287975 | ||||||||
\(279\) | 11.4336 | 0.684509 | ||||||||
\(280\) | 24.8573 | 1.48551 | ||||||||
\(281\) | 11.5462 | 0.688787 | 0.344393 | − | 0.938825i | \(-0.388085\pi\) | ||||
0.344393 | + | 0.938825i | \(0.388085\pi\) | |||||||
\(282\) | 1.11414 | 0.0663461 | ||||||||
\(283\) | −23.6938 | −1.40845 | −0.704226 | − | 0.709976i | \(-0.748706\pi\) | ||||
−0.704226 | + | 0.709976i | \(0.748706\pi\) | |||||||
\(284\) | 1.62714 | 0.0965529 | ||||||||
\(285\) | −18.2286 | −1.07977 | ||||||||
\(286\) | −0.0459330 | −0.00271607 | ||||||||
\(287\) | 19.6128 | 1.15771 | ||||||||
\(288\) | 8.85728 | 0.521920 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −3.83362 | −0.225118 | ||||||||
\(291\) | −9.51606 | −0.557841 | ||||||||
\(292\) | 2.72393 | 0.159406 | ||||||||
\(293\) | −4.94914 | −0.289132 | −0.144566 | − | 0.989495i | \(-0.546179\pi\) | ||||
−0.144566 | + | 0.989495i | \(0.546179\pi\) | |||||||
\(294\) | −10.5511 | −0.615352 | ||||||||
\(295\) | −4.09033 | −0.238148 | ||||||||
\(296\) | 18.0919 | 1.05157 | ||||||||
\(297\) | 5.49532 | 0.318871 | ||||||||
\(298\) | 8.51606 | 0.493322 | ||||||||
\(299\) | 0.185740 | 0.0107416 | ||||||||
\(300\) | −0.632060 | −0.0364920 | ||||||||
\(301\) | −51.4291 | −2.96432 | ||||||||
\(302\) | −9.98571 | −0.574613 | ||||||||
\(303\) | −5.29682 | −0.304294 | ||||||||
\(304\) | 8.94914 | 0.513269 | ||||||||
\(305\) | −5.61285 | −0.321391 | ||||||||
\(306\) | −1.05086 | −0.0600734 | ||||||||
\(307\) | 6.45383 | 0.368339 | 0.184170 | − | 0.982894i | \(-0.441040\pi\) | ||||
0.184170 | + | 0.982894i | \(0.441040\pi\) | |||||||
\(308\) | −6.75557 | −0.384934 | ||||||||
\(309\) | −14.8746 | −0.846188 | ||||||||
\(310\) | −11.9333 | −0.677767 | ||||||||
\(311\) | 9.41927 | 0.534118 | 0.267059 | − | 0.963680i | \(-0.413948\pi\) | ||||
0.267059 | + | 0.963680i | \(0.413948\pi\) | |||||||
\(312\) | −0.196639 | −0.0111325 | ||||||||
\(313\) | 14.7812 | 0.835485 | 0.417742 | − | 0.908566i | \(-0.362821\pi\) | ||||
0.417742 | + | 0.908566i | \(0.362821\pi\) | |||||||
\(314\) | −9.84146 | −0.555386 | ||||||||
\(315\) | −15.6128 | −0.879684 | ||||||||
\(316\) | −10.4286 | −0.586657 | ||||||||
\(317\) | −13.8825 | −0.779717 | −0.389859 | − | 0.920875i | \(-0.627476\pi\) | ||||
−0.389859 | + | 0.920875i | \(0.627476\pi\) | |||||||
\(318\) | 10.2735 | 0.576109 | ||||||||
\(319\) | 2.40790 | 0.134816 | ||||||||
\(320\) | −2.87601 | −0.160774 | ||||||||
\(321\) | −14.5970 | −0.814727 | ||||||||
\(322\) | −8.49871 | −0.473614 | ||||||||
\(323\) | −6.49532 | −0.361409 | ||||||||
\(324\) | 3.19850 | 0.177694 | ||||||||
\(325\) | −0.0227513 | −0.00126202 | ||||||||
\(326\) | −5.71456 | −0.316500 | ||||||||
\(327\) | −17.1876 | −0.950476 | ||||||||
\(328\) | −10.7556 | −0.593877 | ||||||||
\(329\) | 5.89829 | 0.325183 | ||||||||
\(330\) | −1.93332 | −0.106426 | ||||||||
\(331\) | −26.5812 | −1.46104 | −0.730518 | − | 0.682894i | \(-0.760721\pi\) | ||||
−0.730518 | + | 0.682894i | \(0.760721\pi\) | |||||||
\(332\) | −4.20342 | −0.230693 | ||||||||
\(333\) | −11.3635 | −0.622716 | ||||||||
\(334\) | 7.71900 | 0.422365 | ||||||||
\(335\) | 30.5877 | 1.67118 | ||||||||
\(336\) | −7.40943 | −0.404217 | ||||||||
\(337\) | −10.6637 | −0.580889 | −0.290444 | − | 0.956892i | \(-0.593803\pi\) | ||||
−0.290444 | + | 0.956892i | \(0.593803\pi\) | |||||||
\(338\) | 8.95254 | 0.486954 | ||||||||
\(339\) | 5.39700 | 0.293125 | ||||||||
\(340\) | −3.52543 | −0.191193 | ||||||||
\(341\) | 7.49532 | 0.405894 | ||||||||
\(342\) | 6.82564 | 0.369088 | ||||||||
\(343\) | −24.8573 | −1.34217 | ||||||||
\(344\) | 28.2034 | 1.52063 | ||||||||
\(345\) | 7.81780 | 0.420896 | ||||||||
\(346\) | 13.1526 | 0.707086 | ||||||||
\(347\) | 27.0321 | 1.45116 | 0.725580 | − | 0.688138i | \(-0.241572\pi\) | ||||
0.725580 | + | 0.688138i | \(0.241572\pi\) | |||||||
\(348\) | 4.46028 | 0.239096 | ||||||||
\(349\) | 2.79706 | 0.149723 | 0.0748615 | − | 0.997194i | \(-0.476149\pi\) | ||||
0.0748615 | + | 0.997194i | \(0.476149\pi\) | |||||||
\(350\) | 1.04101 | 0.0556444 | ||||||||
\(351\) | 0.366409 | 0.0195574 | ||||||||
\(352\) | 5.80642 | 0.309483 | ||||||||
\(353\) | 18.7003 | 0.995315 | 0.497657 | − | 0.867374i | \(-0.334194\pi\) | ||||
0.497657 | + | 0.867374i | \(0.334194\pi\) | |||||||
\(354\) | −1.48055 | −0.0786903 | ||||||||
\(355\) | 2.46520 | 0.130839 | ||||||||
\(356\) | 12.9349 | 0.685546 | ||||||||
\(357\) | 5.37778 | 0.284623 | ||||||||
\(358\) | −16.3017 | −0.861574 | ||||||||
\(359\) | −26.0163 | −1.37309 | −0.686544 | − | 0.727088i | \(-0.740873\pi\) | ||||
−0.686544 | + | 0.727088i | \(0.740873\pi\) | |||||||
\(360\) | 8.56199 | 0.451257 | ||||||||
\(361\) | 23.1891 | 1.22048 | ||||||||
\(362\) | 2.21432 | 0.116382 | ||||||||
\(363\) | 1.21432 | 0.0637353 | ||||||||
\(364\) | −0.450438 | −0.0236094 | ||||||||
\(365\) | 4.12690 | 0.216012 | ||||||||
\(366\) | −2.03164 | −0.106196 | ||||||||
\(367\) | −16.6479 | −0.869012 | −0.434506 | − | 0.900669i | \(-0.643077\pi\) | ||||
−0.434506 | + | 0.900669i | \(0.643077\pi\) | |||||||
\(368\) | −3.83807 | −0.200073 | ||||||||
\(369\) | 6.75557 | 0.351681 | ||||||||
\(370\) | 11.8602 | 0.616582 | ||||||||
\(371\) | 54.3881 | 2.82369 | ||||||||
\(372\) | 13.8840 | 0.719852 | ||||||||
\(373\) | 5.77139 | 0.298831 | 0.149416 | − | 0.988774i | \(-0.452261\pi\) | ||||
0.149416 | + | 0.988774i | \(0.452261\pi\) | |||||||
\(374\) | −0.688892 | −0.0356218 | ||||||||
\(375\) | 13.0745 | 0.675165 | ||||||||
\(376\) | −3.23459 | −0.166811 | ||||||||
\(377\) | 0.160550 | 0.00826876 | ||||||||
\(378\) | −16.7654 | −0.862320 | ||||||||
\(379\) | −17.2099 | −0.884012 | −0.442006 | − | 0.897012i | \(-0.645733\pi\) | ||||
−0.442006 | + | 0.897012i | \(0.645733\pi\) | |||||||
\(380\) | 22.8988 | 1.17468 | ||||||||
\(381\) | 16.5303 | 0.846875 | ||||||||
\(382\) | −8.68889 | −0.444562 | ||||||||
\(383\) | −18.5526 | −0.947995 | −0.473997 | − | 0.880526i | \(-0.657189\pi\) | ||||
−0.473997 | + | 0.880526i | \(0.657189\pi\) | |||||||
\(384\) | 13.0607 | 0.666501 | ||||||||
\(385\) | −10.2351 | −0.521627 | ||||||||
\(386\) | −3.46520 | −0.176374 | ||||||||
\(387\) | −17.7146 | −0.900482 | ||||||||
\(388\) | 11.9541 | 0.606876 | ||||||||
\(389\) | 2.03657 | 0.103258 | 0.0516290 | − | 0.998666i | \(-0.483559\pi\) | ||||
0.0516290 | + | 0.998666i | \(0.483559\pi\) | |||||||
\(390\) | −0.128907 | −0.00652748 | ||||||||
\(391\) | 2.78568 | 0.140878 | ||||||||
\(392\) | 30.6321 | 1.54715 | ||||||||
\(393\) | 25.4509 | 1.28383 | ||||||||
\(394\) | 15.0781 | 0.759621 | ||||||||
\(395\) | −15.8000 | −0.794983 | ||||||||
\(396\) | −2.32693 | −0.116933 | ||||||||
\(397\) | 25.9353 | 1.30166 | 0.650828 | − | 0.759225i | \(-0.274422\pi\) | ||||
0.650828 | + | 0.759225i | \(0.274422\pi\) | |||||||
\(398\) | −10.8671 | −0.544720 | ||||||||
\(399\) | −34.9304 | −1.74871 | ||||||||
\(400\) | 0.470127 | 0.0235063 | ||||||||
\(401\) | −1.55707 | −0.0777564 | −0.0388782 | − | 0.999244i | \(-0.512378\pi\) | ||||
−0.0388782 | + | 0.999244i | \(0.512378\pi\) | |||||||
\(402\) | 11.0716 | 0.552201 | ||||||||
\(403\) | 0.499762 | 0.0248949 | ||||||||
\(404\) | 6.65386 | 0.331042 | ||||||||
\(405\) | 4.84590 | 0.240795 | ||||||||
\(406\) | −7.34614 | −0.364583 | ||||||||
\(407\) | −7.44938 | −0.369252 | ||||||||
\(408\) | −2.94914 | −0.146004 | ||||||||
\(409\) | 12.4351 | 0.614876 | 0.307438 | − | 0.951568i | \(-0.400528\pi\) | ||||
0.307438 | + | 0.951568i | \(0.400528\pi\) | |||||||
\(410\) | −7.05086 | −0.348217 | ||||||||
\(411\) | −20.9289 | −1.03235 | ||||||||
\(412\) | 18.6855 | 0.920569 | ||||||||
\(413\) | −7.83807 | −0.385686 | ||||||||
\(414\) | −2.92735 | −0.143871 | ||||||||
\(415\) | −6.36842 | −0.312613 | ||||||||
\(416\) | 0.387152 | 0.0189817 | ||||||||
\(417\) | 8.46367 | 0.414468 | ||||||||
\(418\) | 4.47457 | 0.218858 | ||||||||
\(419\) | 23.8666 | 1.16596 | 0.582981 | − | 0.812486i | \(-0.301886\pi\) | ||||
0.582981 | + | 0.812486i | \(0.301886\pi\) | |||||||
\(420\) | −18.9590 | −0.925104 | ||||||||
\(421\) | 4.54770 | 0.221641 | 0.110821 | − | 0.993840i | \(-0.464652\pi\) | ||||
0.110821 | + | 0.993840i | \(0.464652\pi\) | |||||||
\(422\) | 5.17436 | 0.251884 | ||||||||
\(423\) | 2.03164 | 0.0987819 | ||||||||
\(424\) | −29.8261 | −1.44848 | ||||||||
\(425\) | −0.341219 | −0.0165516 | ||||||||
\(426\) | 0.892313 | 0.0432327 | ||||||||
\(427\) | −10.7556 | −0.520498 | ||||||||
\(428\) | 18.3368 | 0.886341 | ||||||||
\(429\) | 0.0809666 | 0.00390911 | ||||||||
\(430\) | 18.4889 | 0.891612 | ||||||||
\(431\) | −28.1225 | −1.35461 | −0.677305 | − | 0.735702i | \(-0.736852\pi\) | ||||
−0.677305 | + | 0.735702i | \(0.736852\pi\) | |||||||
\(432\) | −7.57136 | −0.364277 | ||||||||
\(433\) | −23.2623 | −1.11791 | −0.558956 | − | 0.829197i | \(-0.688798\pi\) | ||||
−0.558956 | + | 0.829197i | \(0.688798\pi\) | |||||||
\(434\) | −22.8671 | −1.09766 | ||||||||
\(435\) | 6.75758 | 0.324001 | ||||||||
\(436\) | 21.5910 | 1.03402 | ||||||||
\(437\) | −18.0939 | −0.865547 | ||||||||
\(438\) | 1.49378 | 0.0713758 | ||||||||
\(439\) | 25.8557 | 1.23403 | 0.617014 | − | 0.786952i | \(-0.288342\pi\) | ||||
0.617014 | + | 0.786952i | \(0.288342\pi\) | |||||||
\(440\) | 5.61285 | 0.267582 | ||||||||
\(441\) | −19.2400 | −0.916190 | ||||||||
\(442\) | −0.0459330 | −0.00218481 | ||||||||
\(443\) | −36.7101 | −1.74415 | −0.872075 | − | 0.489372i | \(-0.837226\pi\) | ||||
−0.872075 | + | 0.489372i | \(0.837226\pi\) | |||||||
\(444\) | −13.7989 | −0.654868 | ||||||||
\(445\) | 19.5970 | 0.928988 | ||||||||
\(446\) | 13.1907 | 0.624596 | ||||||||
\(447\) | −15.0114 | −0.710014 | ||||||||
\(448\) | −5.51114 | −0.260377 | ||||||||
\(449\) | −25.1541 | −1.18710 | −0.593548 | − | 0.804799i | \(-0.702273\pi\) | ||||
−0.593548 | + | 0.804799i | \(0.702273\pi\) | |||||||
\(450\) | 0.358572 | 0.0169033 | ||||||||
\(451\) | 4.42864 | 0.208536 | ||||||||
\(452\) | −6.77970 | −0.318890 | ||||||||
\(453\) | 17.6019 | 0.827012 | ||||||||
\(454\) | 10.4242 | 0.489232 | ||||||||
\(455\) | −0.682439 | −0.0319932 | ||||||||
\(456\) | 19.1556 | 0.897044 | ||||||||
\(457\) | 12.2701 | 0.573971 | 0.286985 | − | 0.957935i | \(-0.407347\pi\) | ||||
0.286985 | + | 0.957935i | \(0.407347\pi\) | |||||||
\(458\) | −1.92348 | −0.0898783 | ||||||||
\(459\) | 5.49532 | 0.256499 | ||||||||
\(460\) | −9.82071 | −0.457893 | ||||||||
\(461\) | 26.1017 | 1.21568 | 0.607839 | − | 0.794060i | \(-0.292037\pi\) | ||||
0.607839 | + | 0.794060i | \(0.292037\pi\) | |||||||
\(462\) | −3.70471 | −0.172359 | ||||||||
\(463\) | 20.4336 | 0.949628 | 0.474814 | − | 0.880086i | \(-0.342515\pi\) | ||||
0.474814 | + | 0.880086i | \(0.342515\pi\) | |||||||
\(464\) | −3.31756 | −0.154014 | ||||||||
\(465\) | 21.0350 | 0.975476 | ||||||||
\(466\) | −2.98079 | −0.138082 | ||||||||
\(467\) | −41.5259 | −1.92159 | −0.960795 | − | 0.277260i | \(-0.910574\pi\) | ||||
−0.960795 | + | 0.277260i | \(0.910574\pi\) | |||||||
\(468\) | −0.155152 | −0.00717189 | ||||||||
\(469\) | 58.6133 | 2.70651 | ||||||||
\(470\) | −2.12045 | −0.0978089 | ||||||||
\(471\) | 17.3477 | 0.799339 | ||||||||
\(472\) | 4.29835 | 0.197848 | ||||||||
\(473\) | −11.6128 | −0.533959 | ||||||||
\(474\) | −5.71900 | −0.262683 | ||||||||
\(475\) | 2.21633 | 0.101692 | ||||||||
\(476\) | −6.75557 | −0.309641 | ||||||||
\(477\) | 18.7338 | 0.857760 | ||||||||
\(478\) | −8.24935 | −0.377317 | ||||||||
\(479\) | 14.9304 | 0.682188 | 0.341094 | − | 0.940029i | \(-0.389203\pi\) | ||||
0.341094 | + | 0.940029i | \(0.389203\pi\) | |||||||
\(480\) | 16.2953 | 0.743775 | ||||||||
\(481\) | −0.496699 | −0.0226475 | ||||||||
\(482\) | 5.04101 | 0.229612 | ||||||||
\(483\) | 14.9808 | 0.681649 | ||||||||
\(484\) | −1.52543 | −0.0693376 | ||||||||
\(485\) | 18.1111 | 0.822382 | ||||||||
\(486\) | −9.60300 | −0.435601 | ||||||||
\(487\) | −22.9476 | −1.03986 | −0.519928 | − | 0.854210i | \(-0.674041\pi\) | ||||
−0.519928 | + | 0.854210i | \(0.674041\pi\) | |||||||
\(488\) | 5.89829 | 0.267003 | ||||||||
\(489\) | 10.0731 | 0.455523 | ||||||||
\(490\) | 20.0810 | 0.907166 | ||||||||
\(491\) | −19.7527 | −0.891425 | −0.445712 | − | 0.895176i | \(-0.647050\pi\) | ||||
−0.445712 | + | 0.895176i | \(0.647050\pi\) | |||||||
\(492\) | 8.20342 | 0.369839 | ||||||||
\(493\) | 2.40790 | 0.108446 | ||||||||
\(494\) | 0.298349 | 0.0134234 | ||||||||
\(495\) | −3.52543 | −0.158456 | ||||||||
\(496\) | −10.3269 | −0.463693 | ||||||||
\(497\) | 4.72393 | 0.211897 | ||||||||
\(498\) | −2.30513 | −0.103295 | ||||||||
\(499\) | −9.43356 | −0.422304 | −0.211152 | − | 0.977453i | \(-0.567722\pi\) | ||||
−0.211152 | + | 0.977453i | \(0.567722\pi\) | |||||||
\(500\) | −16.4242 | −0.734512 | ||||||||
\(501\) | −13.6064 | −0.607889 | ||||||||
\(502\) | −15.6193 | −0.697124 | ||||||||
\(503\) | 14.3763 | 0.641005 | 0.320503 | − | 0.947248i | \(-0.396148\pi\) | ||||
0.320503 | + | 0.947248i | \(0.396148\pi\) | |||||||
\(504\) | 16.4068 | 0.730819 | ||||||||
\(505\) | 10.0810 | 0.448597 | ||||||||
\(506\) | −1.91903 | −0.0853114 | ||||||||
\(507\) | −15.7808 | −0.700848 | ||||||||
\(508\) | −20.7654 | −0.921316 | ||||||||
\(509\) | −31.6766 | −1.40404 | −0.702021 | − | 0.712157i | \(-0.747719\pi\) | ||||
−0.702021 | + | 0.712157i | \(0.747719\pi\) | |||||||
\(510\) | −1.93332 | −0.0856090 | ||||||||
\(511\) | 7.90813 | 0.349835 | ||||||||
\(512\) | −14.6923 | −0.649313 | ||||||||
\(513\) | −35.6938 | −1.57592 | ||||||||
\(514\) | 4.28544 | 0.189023 | ||||||||
\(515\) | 28.3096 | 1.24747 | ||||||||
\(516\) | −21.5111 | −0.946975 | ||||||||
\(517\) | 1.33185 | 0.0585748 | ||||||||
\(518\) | 22.7270 | 0.998567 | ||||||||
\(519\) | −23.1842 | −1.01767 | ||||||||
\(520\) | 0.374245 | 0.0164117 | ||||||||
\(521\) | −20.9748 | −0.918923 | −0.459462 | − | 0.888198i | \(-0.651958\pi\) | ||||
−0.459462 | + | 0.888198i | \(0.651958\pi\) | |||||||
\(522\) | −2.53035 | −0.110750 | ||||||||
\(523\) | −6.91750 | −0.302481 | −0.151241 | − | 0.988497i | \(-0.548327\pi\) | ||||
−0.151241 | + | 0.988497i | \(0.548327\pi\) | |||||||
\(524\) | −31.9714 | −1.39668 | ||||||||
\(525\) | −1.83500 | −0.0800861 | ||||||||
\(526\) | −6.73822 | −0.293800 | ||||||||
\(527\) | 7.49532 | 0.326501 | ||||||||
\(528\) | −1.67307 | −0.0728111 | ||||||||
\(529\) | −15.2400 | −0.662608 | ||||||||
\(530\) | −19.5526 | −0.849312 | ||||||||
\(531\) | −2.69979 | −0.117161 | ||||||||
\(532\) | 43.8796 | 1.90242 | ||||||||
\(533\) | 0.295286 | 0.0127903 | ||||||||
\(534\) | 7.09340 | 0.306961 | ||||||||
\(535\) | 27.7812 | 1.20109 | ||||||||
\(536\) | −32.1432 | −1.38837 | ||||||||
\(537\) | 28.7353 | 1.24002 | ||||||||
\(538\) | −9.34920 | −0.403073 | ||||||||
\(539\) | −12.6128 | −0.543274 | ||||||||
\(540\) | −19.3733 | −0.833696 | ||||||||
\(541\) | 12.5096 | 0.537830 | 0.268915 | − | 0.963164i | \(-0.413335\pi\) | ||||
0.268915 | + | 0.963164i | \(0.413335\pi\) | |||||||
\(542\) | −5.11108 | −0.219540 | ||||||||
\(543\) | −3.90321 | −0.167503 | ||||||||
\(544\) | 5.80642 | 0.248948 | ||||||||
\(545\) | 32.7116 | 1.40121 | ||||||||
\(546\) | −0.247018 | −0.0105714 | ||||||||
\(547\) | −8.35752 | −0.357342 | −0.178671 | − | 0.983909i | \(-0.557180\pi\) | ||||
−0.178671 | + | 0.983909i | \(0.557180\pi\) | |||||||
\(548\) | 26.2908 | 1.12309 | ||||||||
\(549\) | −3.70471 | −0.158113 | ||||||||
\(550\) | 0.235063 | 0.0100231 | ||||||||
\(551\) | −15.6400 | −0.666288 | ||||||||
\(552\) | −8.21537 | −0.349670 | ||||||||
\(553\) | −30.2766 | −1.28749 | ||||||||
\(554\) | 14.3466 | 0.609529 | ||||||||
\(555\) | −20.9061 | −0.887416 | ||||||||
\(556\) | −10.6321 | −0.450900 | ||||||||
\(557\) | −27.1427 | −1.15007 | −0.575037 | − | 0.818127i | \(-0.695012\pi\) | ||||
−0.575037 | + | 0.818127i | \(0.695012\pi\) | |||||||
\(558\) | −7.87649 | −0.333438 | ||||||||
\(559\) | −0.774305 | −0.0327496 | ||||||||
\(560\) | 14.1017 | 0.595906 | ||||||||
\(561\) | 1.21432 | 0.0512686 | ||||||||
\(562\) | −7.95407 | −0.335522 | ||||||||
\(563\) | 12.5239 | 0.527819 | 0.263910 | − | 0.964547i | \(-0.414988\pi\) | ||||
0.263910 | + | 0.964547i | \(0.414988\pi\) | |||||||
\(564\) | 2.46706 | 0.103882 | ||||||||
\(565\) | −10.2716 | −0.432131 | ||||||||
\(566\) | 16.3225 | 0.686085 | ||||||||
\(567\) | 9.28592 | 0.389972 | ||||||||
\(568\) | −2.59057 | −0.108698 | ||||||||
\(569\) | −3.14272 | −0.131750 | −0.0658749 | − | 0.997828i | \(-0.520984\pi\) | ||||
−0.0658749 | + | 0.997828i | \(0.520984\pi\) | |||||||
\(570\) | 12.5575 | 0.525978 | ||||||||
\(571\) | −26.9195 | −1.12655 | −0.563273 | − | 0.826271i | \(-0.690458\pi\) | ||||
−0.563273 | + | 0.826271i | \(0.690458\pi\) | |||||||
\(572\) | −0.101710 | −0.00425272 | ||||||||
\(573\) | 15.3160 | 0.639836 | ||||||||
\(574\) | −13.5111 | −0.563944 | ||||||||
\(575\) | −0.950528 | −0.0396398 | ||||||||
\(576\) | −1.89829 | −0.0790954 | ||||||||
\(577\) | 34.0607 | 1.41797 | 0.708983 | − | 0.705226i | \(-0.249154\pi\) | ||||
0.708983 | + | 0.705226i | \(0.249154\pi\) | |||||||
\(578\) | −0.688892 | −0.0286541 | ||||||||
\(579\) | 6.10816 | 0.253847 | ||||||||
\(580\) | −8.48886 | −0.352481 | ||||||||
\(581\) | −12.2034 | −0.506283 | ||||||||
\(582\) | 6.55554 | 0.271736 | ||||||||
\(583\) | 12.2810 | 0.508627 | ||||||||
\(584\) | −4.33677 | −0.179457 | ||||||||
\(585\) | −0.235063 | −0.00971867 | ||||||||
\(586\) | 3.40943 | 0.140842 | ||||||||
\(587\) | 23.0464 | 0.951227 | 0.475614 | − | 0.879654i | \(-0.342226\pi\) | ||||
0.475614 | + | 0.879654i | \(0.342226\pi\) | |||||||
\(588\) | −23.3635 | −0.963494 | ||||||||
\(589\) | −48.6844 | −2.00601 | ||||||||
\(590\) | 2.81780 | 0.116007 | ||||||||
\(591\) | −26.5783 | −1.09328 | ||||||||
\(592\) | 10.2636 | 0.421833 | ||||||||
\(593\) | −16.9427 | −0.695753 | −0.347876 | − | 0.937540i | \(-0.613097\pi\) | ||||
−0.347876 | + | 0.937540i | \(0.613097\pi\) | |||||||
\(594\) | −3.78568 | −0.155328 | ||||||||
\(595\) | −10.2351 | −0.419597 | ||||||||
\(596\) | 18.8573 | 0.772424 | ||||||||
\(597\) | 19.1556 | 0.783988 | ||||||||
\(598\) | −0.127955 | −0.00523245 | ||||||||
\(599\) | −32.8528 | −1.34233 | −0.671165 | − | 0.741308i | \(-0.734206\pi\) | ||||
−0.671165 | + | 0.741308i | \(0.734206\pi\) | |||||||
\(600\) | 1.00631 | 0.0410822 | ||||||||
\(601\) | −13.9496 | −0.569017 | −0.284508 | − | 0.958674i | \(-0.591830\pi\) | ||||
−0.284508 | + | 0.958674i | \(0.591830\pi\) | |||||||
\(602\) | 35.4291 | 1.44398 | ||||||||
\(603\) | 20.1891 | 0.822165 | ||||||||
\(604\) | −22.1116 | −0.899706 | ||||||||
\(605\) | −2.31111 | −0.0939599 | ||||||||
\(606\) | 3.64894 | 0.148228 | ||||||||
\(607\) | 31.3274 | 1.27154 | 0.635770 | − | 0.771878i | \(-0.280683\pi\) | ||||
0.635770 | + | 0.771878i | \(0.280683\pi\) | |||||||
\(608\) | −37.7146 | −1.52953 | ||||||||
\(609\) | 12.9491 | 0.524726 | ||||||||
\(610\) | 3.86665 | 0.156556 | ||||||||
\(611\) | 0.0888033 | 0.00359260 | ||||||||
\(612\) | −2.32693 | −0.0940605 | ||||||||
\(613\) | −39.2355 | −1.58471 | −0.792354 | − | 0.610061i | \(-0.791145\pi\) | ||||
−0.792354 | + | 0.610061i | \(0.791145\pi\) | |||||||
\(614\) | −4.44599 | −0.179426 | ||||||||
\(615\) | 12.4286 | 0.501171 | ||||||||
\(616\) | 10.7556 | 0.433354 | ||||||||
\(617\) | −10.1748 | −0.409624 | −0.204812 | − | 0.978801i | \(-0.565658\pi\) | ||||
−0.204812 | + | 0.978801i | \(0.565658\pi\) | |||||||
\(618\) | 10.2470 | 0.412195 | ||||||||
\(619\) | −23.6702 | −0.951384 | −0.475692 | − | 0.879612i | \(-0.657802\pi\) | ||||
−0.475692 | + | 0.879612i | \(0.657802\pi\) | |||||||
\(620\) | −26.4242 | −1.06122 | ||||||||
\(621\) | 15.3082 | 0.614297 | ||||||||
\(622\) | −6.48886 | −0.260180 | ||||||||
\(623\) | 37.5526 | 1.50451 | ||||||||
\(624\) | −0.111555 | −0.00446576 | ||||||||
\(625\) | −26.5897 | −1.06359 | ||||||||
\(626\) | −10.1827 | −0.406982 | ||||||||
\(627\) | −7.88739 | −0.314992 | ||||||||
\(628\) | −21.7921 | −0.869601 | ||||||||
\(629\) | −7.44938 | −0.297026 | ||||||||
\(630\) | 10.7556 | 0.428512 | ||||||||
\(631\) | 35.6450 | 1.41900 | 0.709502 | − | 0.704704i | \(-0.248920\pi\) | ||||
0.709502 | + | 0.704704i | \(0.248920\pi\) | |||||||
\(632\) | 16.6035 | 0.660451 | ||||||||
\(633\) | −9.12092 | −0.362524 | ||||||||
\(634\) | 9.56352 | 0.379816 | ||||||||
\(635\) | −31.4608 | −1.24848 | ||||||||
\(636\) | 22.7488 | 0.902048 | ||||||||
\(637\) | −0.840981 | −0.0333209 | ||||||||
\(638\) | −1.65878 | −0.0656718 | ||||||||
\(639\) | 1.62714 | 0.0643686 | ||||||||
\(640\) | −24.8573 | −0.982570 | ||||||||
\(641\) | 32.0114 | 1.26437 | 0.632187 | − | 0.774816i | \(-0.282158\pi\) | ||||
0.632187 | + | 0.774816i | \(0.282158\pi\) | |||||||
\(642\) | 10.0558 | 0.396870 | ||||||||
\(643\) | 14.2652 | 0.562564 | 0.281282 | − | 0.959625i | \(-0.409240\pi\) | ||||
0.281282 | + | 0.959625i | \(0.409240\pi\) | |||||||
\(644\) | −18.8189 | −0.741567 | ||||||||
\(645\) | −32.5906 | −1.28325 | ||||||||
\(646\) | 4.47457 | 0.176050 | ||||||||
\(647\) | 21.1704 | 0.832294 | 0.416147 | − | 0.909297i | \(-0.363380\pi\) | ||||
0.416147 | + | 0.909297i | \(0.363380\pi\) | |||||||
\(648\) | −5.09234 | −0.200046 | ||||||||
\(649\) | −1.76986 | −0.0694730 | ||||||||
\(650\) | 0.0156732 | 0.000614754 0 | ||||||||
\(651\) | 40.3082 | 1.57980 | ||||||||
\(652\) | −12.6539 | −0.495563 | ||||||||
\(653\) | 0.882945 | 0.0345523 | 0.0172761 | − | 0.999851i | \(-0.494501\pi\) | ||||
0.0172761 | + | 0.999851i | \(0.494501\pi\) | |||||||
\(654\) | 11.8404 | 0.462996 | ||||||||
\(655\) | −48.4385 | −1.89265 | ||||||||
\(656\) | −6.10171 | −0.238232 | ||||||||
\(657\) | 2.72393 | 0.106270 | ||||||||
\(658\) | −4.06329 | −0.158403 | ||||||||
\(659\) | −21.4958 | −0.837357 | −0.418679 | − | 0.908134i | \(-0.637507\pi\) | ||||
−0.418679 | + | 0.908134i | \(0.637507\pi\) | |||||||
\(660\) | −4.28100 | −0.166638 | ||||||||
\(661\) | 13.9951 | 0.544345 | 0.272173 | − | 0.962248i | \(-0.412258\pi\) | ||||
0.272173 | + | 0.962248i | \(0.412258\pi\) | |||||||
\(662\) | 18.3116 | 0.711700 | ||||||||
\(663\) | 0.0809666 | 0.00314448 | ||||||||
\(664\) | 6.69228 | 0.259711 | ||||||||
\(665\) | 66.4800 | 2.57798 | ||||||||
\(666\) | 7.82822 | 0.303337 | ||||||||
\(667\) | 6.70763 | 0.259720 | ||||||||
\(668\) | 17.0923 | 0.661323 | ||||||||
\(669\) | −23.2514 | −0.898950 | ||||||||
\(670\) | −21.0716 | −0.814067 | ||||||||
\(671\) | −2.42864 | −0.0937566 | ||||||||
\(672\) | 31.2257 | 1.20456 | ||||||||
\(673\) | −16.2973 | −0.628215 | −0.314107 | − | 0.949388i | \(-0.601705\pi\) | ||||
−0.314107 | + | 0.949388i | \(0.601705\pi\) | |||||||
\(674\) | 7.34614 | 0.282963 | ||||||||
\(675\) | −1.87511 | −0.0721729 | ||||||||
\(676\) | 19.8238 | 0.762453 | ||||||||
\(677\) | 10.4681 | 0.402322 | 0.201161 | − | 0.979558i | \(-0.435528\pi\) | ||||
0.201161 | + | 0.979558i | \(0.435528\pi\) | |||||||
\(678\) | −3.71795 | −0.142787 | ||||||||
\(679\) | 34.7052 | 1.33186 | ||||||||
\(680\) | 5.61285 | 0.215243 | ||||||||
\(681\) | −18.3749 | −0.704127 | ||||||||
\(682\) | −5.16346 | −0.197719 | ||||||||
\(683\) | 15.5625 | 0.595481 | 0.297741 | − | 0.954647i | \(-0.403767\pi\) | ||||
0.297741 | + | 0.954647i | \(0.403767\pi\) | |||||||
\(684\) | 15.1141 | 0.577904 | ||||||||
\(685\) | 39.8321 | 1.52191 | ||||||||
\(686\) | 17.1240 | 0.653797 | ||||||||
\(687\) | 3.39054 | 0.129357 | ||||||||
\(688\) | 16.0000 | 0.609994 | ||||||||
\(689\) | 0.818854 | 0.0311959 | ||||||||
\(690\) | −5.38562 | −0.205027 | ||||||||
\(691\) | −25.9940 | −0.988859 | −0.494430 | − | 0.869218i | \(-0.664623\pi\) | ||||
−0.494430 | + | 0.869218i | \(0.664623\pi\) | |||||||
\(692\) | 29.1240 | 1.10713 | ||||||||
\(693\) | −6.75557 | −0.256623 | ||||||||
\(694\) | −18.6222 | −0.706890 | ||||||||
\(695\) | −16.1082 | −0.611017 | ||||||||
\(696\) | −7.10123 | −0.269172 | ||||||||
\(697\) | 4.42864 | 0.167747 | ||||||||
\(698\) | −1.92687 | −0.0729331 | ||||||||
\(699\) | 5.25428 | 0.198735 | ||||||||
\(700\) | 2.30513 | 0.0871258 | ||||||||
\(701\) | 9.24443 | 0.349157 | 0.174579 | − | 0.984643i | \(-0.444144\pi\) | ||||
0.174579 | + | 0.984643i | \(0.444144\pi\) | |||||||
\(702\) | −0.252416 | −0.00952683 | ||||||||
\(703\) | 48.3861 | 1.82492 | ||||||||
\(704\) | −1.24443 | −0.0469013 | ||||||||
\(705\) | 3.73774 | 0.140771 | ||||||||
\(706\) | −12.8825 | −0.484838 | ||||||||
\(707\) | 19.3176 | 0.726512 | ||||||||
\(708\) | −3.27841 | −0.123210 | ||||||||
\(709\) | −22.0114 | −0.826655 | −0.413327 | − | 0.910583i | \(-0.635633\pi\) | ||||
−0.413327 | + | 0.910583i | \(0.635633\pi\) | |||||||
\(710\) | −1.69826 | −0.0637346 | ||||||||
\(711\) | −10.4286 | −0.391105 | ||||||||
\(712\) | −20.5936 | −0.771779 | ||||||||
\(713\) | 20.8796 | 0.781945 | ||||||||
\(714\) | −3.70471 | −0.138645 | ||||||||
\(715\) | −0.154097 | −0.00576289 | ||||||||
\(716\) | −36.0973 | −1.34902 | ||||||||
\(717\) | 14.5412 | 0.543053 | ||||||||
\(718\) | 17.9224 | 0.668859 | ||||||||
\(719\) | −10.0618 | −0.375240 | −0.187620 | − | 0.982242i | \(-0.560077\pi\) | ||||
−0.187620 | + | 0.982242i | \(0.560077\pi\) | |||||||
\(720\) | 4.85728 | 0.181020 | ||||||||
\(721\) | 54.2480 | 2.02030 | ||||||||
\(722\) | −15.9748 | −0.594521 | ||||||||
\(723\) | −8.88586 | −0.330469 | ||||||||
\(724\) | 4.90321 | 0.182226 | ||||||||
\(725\) | −0.821621 | −0.0305142 | ||||||||
\(726\) | −0.836535 | −0.0310467 | ||||||||
\(727\) | 12.0607 | 0.447307 | 0.223653 | − | 0.974669i | \(-0.428202\pi\) | ||||
0.223653 | + | 0.974669i | \(0.428202\pi\) | |||||||
\(728\) | 0.717144 | 0.0265791 | ||||||||
\(729\) | 23.2177 | 0.859915 | ||||||||
\(730\) | −2.84299 | −0.105224 | ||||||||
\(731\) | −11.6128 | −0.429517 | ||||||||
\(732\) | −4.49871 | −0.166277 | ||||||||
\(733\) | 22.2449 | 0.821634 | 0.410817 | − | 0.911718i | \(-0.365243\pi\) | ||||
0.410817 | + | 0.911718i | \(0.365243\pi\) | |||||||
\(734\) | 11.4686 | 0.423314 | ||||||||
\(735\) | −35.3970 | −1.30564 | ||||||||
\(736\) | 16.1748 | 0.596213 | ||||||||
\(737\) | 13.2351 | 0.487520 | ||||||||
\(738\) | −4.65386 | −0.171311 | ||||||||
\(739\) | 15.2924 | 0.562539 | 0.281269 | − | 0.959629i | \(-0.409245\pi\) | ||||
0.281269 | + | 0.959629i | \(0.409245\pi\) | |||||||
\(740\) | 26.2623 | 0.965420 | ||||||||
\(741\) | −0.525904 | −0.0193196 | ||||||||
\(742\) | −37.4675 | −1.37548 | ||||||||
\(743\) | 49.4893 | 1.81559 | 0.907794 | − | 0.419417i | \(-0.137765\pi\) | ||||
0.907794 | + | 0.419417i | \(0.137765\pi\) | |||||||
\(744\) | −22.1048 | −0.810400 | ||||||||
\(745\) | 28.5698 | 1.04672 | ||||||||
\(746\) | −3.97587 | −0.145567 | ||||||||
\(747\) | −4.20342 | −0.153795 | ||||||||
\(748\) | −1.52543 | −0.0557752 | ||||||||
\(749\) | 53.2355 | 1.94518 | ||||||||
\(750\) | −9.00693 | −0.328887 | ||||||||
\(751\) | −48.2005 | −1.75886 | −0.879431 | − | 0.476027i | \(-0.842076\pi\) | ||||
−0.879431 | + | 0.476027i | \(0.842076\pi\) | |||||||
\(752\) | −1.83500 | −0.0669157 | ||||||||
\(753\) | 27.5324 | 1.00333 | ||||||||
\(754\) | −0.110602 | −0.00402788 | ||||||||
\(755\) | −33.5002 | −1.21920 | ||||||||
\(756\) | −37.1240 | −1.35019 | ||||||||
\(757\) | −21.1842 | −0.769953 | −0.384977 | − | 0.922926i | \(-0.625790\pi\) | ||||
−0.384977 | + | 0.922926i | \(0.625790\pi\) | |||||||
\(758\) | 11.8557 | 0.430620 | ||||||||
\(759\) | 3.38271 | 0.122784 | ||||||||
\(760\) | −36.4572 | −1.32244 | ||||||||
\(761\) | 12.0350 | 0.436270 | 0.218135 | − | 0.975919i | \(-0.430003\pi\) | ||||
0.218135 | + | 0.975919i | \(0.430003\pi\) | |||||||
\(762\) | −11.3876 | −0.412530 | ||||||||
\(763\) | 62.6834 | 2.26929 | ||||||||
\(764\) | −19.2400 | −0.696078 | ||||||||
\(765\) | −3.52543 | −0.127462 | ||||||||
\(766\) | 12.7808 | 0.461788 | ||||||||
\(767\) | −0.118008 | −0.00426102 | ||||||||
\(768\) | −12.0197 | −0.433723 | ||||||||
\(769\) | 32.7467 | 1.18088 | 0.590438 | − | 0.807083i | \(-0.298955\pi\) | ||||
0.590438 | + | 0.807083i | \(0.298955\pi\) | |||||||
\(770\) | 7.05086 | 0.254095 | ||||||||
\(771\) | −7.55401 | −0.272051 | ||||||||
\(772\) | −7.67307 | −0.276160 | ||||||||
\(773\) | 6.60793 | 0.237671 | 0.118835 | − | 0.992914i | \(-0.462084\pi\) | ||||
0.118835 | + | 0.992914i | \(0.462084\pi\) | |||||||
\(774\) | 12.2034 | 0.438643 | ||||||||
\(775\) | −2.55755 | −0.0918698 | ||||||||
\(776\) | −19.0321 | −0.683213 | ||||||||
\(777\) | −40.0612 | −1.43719 | ||||||||
\(778\) | −1.40297 | −0.0502990 | ||||||||
\(779\) | −28.7654 | −1.03063 | ||||||||
\(780\) | −0.285442 | −0.0102205 | ||||||||
\(781\) | 1.06668 | 0.0381687 | ||||||||
\(782\) | −1.91903 | −0.0686245 | ||||||||
\(783\) | 13.2321 | 0.472878 | ||||||||
\(784\) | 17.3778 | 0.620635 | ||||||||
\(785\) | −33.0163 | −1.17840 | ||||||||
\(786\) | −17.5329 | −0.625379 | ||||||||
\(787\) | −23.8084 | −0.848679 | −0.424339 | − | 0.905503i | \(-0.639494\pi\) | ||||
−0.424339 | + | 0.905503i | \(0.639494\pi\) | |||||||
\(788\) | 33.3876 | 1.18939 | ||||||||
\(789\) | 11.8775 | 0.422852 | ||||||||
\(790\) | 10.8845 | 0.387252 | ||||||||
\(791\) | −19.6829 | −0.699844 | ||||||||
\(792\) | 3.70471 | 0.131641 | ||||||||
\(793\) | −0.161933 | −0.00575042 | ||||||||
\(794\) | −17.8666 | −0.634064 | ||||||||
\(795\) | 34.4657 | 1.22237 | ||||||||
\(796\) | −24.0633 | −0.852901 | ||||||||
\(797\) | −31.7783 | −1.12565 | −0.562823 | − | 0.826577i | \(-0.690285\pi\) | ||||
−0.562823 | + | 0.826577i | \(0.690285\pi\) | |||||||
\(798\) | 24.0633 | 0.851831 | ||||||||
\(799\) | 1.33185 | 0.0471175 | ||||||||
\(800\) | −1.98126 | −0.0700483 | ||||||||
\(801\) | 12.9349 | 0.457031 | ||||||||
\(802\) | 1.07265 | 0.0378767 | ||||||||
\(803\) | 1.78568 | 0.0630153 | ||||||||
\(804\) | 24.5161 | 0.864615 | ||||||||
\(805\) | −28.5116 | −1.00490 | ||||||||
\(806\) | −0.344282 | −0.0121268 | ||||||||
\(807\) | 16.4800 | 0.580122 | ||||||||
\(808\) | −10.5936 | −0.372683 | ||||||||
\(809\) | −32.2242 | −1.13294 | −0.566471 | − | 0.824082i | \(-0.691692\pi\) | ||||
−0.566471 | + | 0.824082i | \(0.691692\pi\) | |||||||
\(810\) | −3.33830 | −0.117296 | ||||||||
\(811\) | −1.36689 | −0.0479978 | −0.0239989 | − | 0.999712i | \(-0.507640\pi\) | ||||
−0.0239989 | + | 0.999712i | \(0.507640\pi\) | |||||||
\(812\) | −16.2667 | −0.570849 | ||||||||
\(813\) | 9.00937 | 0.315972 | ||||||||
\(814\) | 5.13182 | 0.179870 | ||||||||
\(815\) | −19.1713 | −0.671541 | ||||||||
\(816\) | −1.67307 | −0.0585692 | ||||||||
\(817\) | 75.4291 | 2.63893 | ||||||||
\(818\) | −8.56644 | −0.299518 | ||||||||
\(819\) | −0.450438 | −0.0157396 | ||||||||
\(820\) | −15.6128 | −0.545224 | ||||||||
\(821\) | 20.4780 | 0.714686 | 0.357343 | − | 0.933973i | \(-0.383683\pi\) | ||||
0.357343 | + | 0.933973i | \(0.383683\pi\) | |||||||
\(822\) | 14.4177 | 0.502876 | ||||||||
\(823\) | 52.2835 | 1.82249 | 0.911244 | − | 0.411867i | \(-0.135123\pi\) | ||||
0.911244 | + | 0.411867i | \(0.135123\pi\) | |||||||
\(824\) | −29.7493 | −1.03636 | ||||||||
\(825\) | −0.414349 | −0.0144258 | ||||||||
\(826\) | 5.39958 | 0.187876 | ||||||||
\(827\) | 0.956981 | 0.0332775 | 0.0166388 | − | 0.999862i | \(-0.494703\pi\) | ||||
0.0166388 | + | 0.999862i | \(0.494703\pi\) | |||||||
\(828\) | −6.48208 | −0.225268 | ||||||||
\(829\) | −40.8894 | −1.42015 | −0.710074 | − | 0.704127i | \(-0.751338\pi\) | ||||
−0.710074 | + | 0.704127i | \(0.751338\pi\) | |||||||
\(830\) | 4.38715 | 0.152280 | ||||||||
\(831\) | −25.2890 | −0.877265 | ||||||||
\(832\) | −0.0829744 | −0.00287662 | ||||||||
\(833\) | −12.6128 | −0.437009 | ||||||||
\(834\) | −5.83056 | −0.201896 | ||||||||
\(835\) | 25.8959 | 0.896163 | ||||||||
\(836\) | 9.90813 | 0.342680 | ||||||||
\(837\) | 41.1891 | 1.42370 | ||||||||
\(838\) | −16.4415 | −0.567964 | ||||||||
\(839\) | −22.3067 | −0.770111 | −0.385056 | − | 0.922893i | \(-0.625818\pi\) | ||||
−0.385056 | + | 0.922893i | \(0.625818\pi\) | |||||||
\(840\) | 30.1847 | 1.04147 | ||||||||
\(841\) | −23.2020 | −0.800070 | ||||||||
\(842\) | −3.13288 | −0.107966 | ||||||||
\(843\) | 14.0207 | 0.482900 | ||||||||
\(844\) | 11.4577 | 0.394390 | ||||||||
\(845\) | 30.0341 | 1.03321 | ||||||||
\(846\) | −1.39958 | −0.0481187 | ||||||||
\(847\) | −4.42864 | −0.152170 | ||||||||
\(848\) | −16.9206 | −0.581055 | ||||||||
\(849\) | −28.7719 | −0.987448 | ||||||||
\(850\) | 0.235063 | 0.00806261 | ||||||||
\(851\) | −20.7516 | −0.711356 | ||||||||
\(852\) | 1.97587 | 0.0676920 | ||||||||
\(853\) | 24.6242 | 0.843117 | 0.421559 | − | 0.906801i | \(-0.361483\pi\) | ||||
0.421559 | + | 0.906801i | \(0.361483\pi\) | |||||||
\(854\) | 7.40943 | 0.253545 | ||||||||
\(855\) | 22.8988 | 0.783121 | ||||||||
\(856\) | −29.1941 | −0.997832 | ||||||||
\(857\) | −5.50024 | −0.187885 | −0.0939423 | − | 0.995578i | \(-0.529947\pi\) | ||||
−0.0939423 | + | 0.995578i | \(0.529947\pi\) | |||||||
\(858\) | −0.0557773 | −0.00190421 | ||||||||
\(859\) | −35.2208 | −1.20172 | −0.600859 | − | 0.799355i | \(-0.705175\pi\) | ||||
−0.600859 | + | 0.799355i | \(0.705175\pi\) | |||||||
\(860\) | 40.9403 | 1.39605 | ||||||||
\(861\) | 23.8163 | 0.811656 | ||||||||
\(862\) | 19.3733 | 0.659859 | ||||||||
\(863\) | 3.17976 | 0.108240 | 0.0541202 | − | 0.998534i | \(-0.482765\pi\) | ||||
0.0541202 | + | 0.998534i | \(0.482765\pi\) | |||||||
\(864\) | 31.9081 | 1.08554 | ||||||||
\(865\) | 44.1245 | 1.50028 | ||||||||
\(866\) | 16.0252 | 0.544558 | ||||||||
\(867\) | 1.21432 | 0.0412405 | ||||||||
\(868\) | −50.6351 | −1.71867 | ||||||||
\(869\) | −6.83654 | −0.231914 | ||||||||
\(870\) | −4.65524 | −0.157827 | ||||||||
\(871\) | 0.882468 | 0.0299013 | ||||||||
\(872\) | −34.3752 | −1.16409 | ||||||||
\(873\) | 11.9541 | 0.404584 | ||||||||
\(874\) | 12.4647 | 0.421626 | ||||||||
\(875\) | −47.6829 | −1.61198 | ||||||||
\(876\) | 3.30772 | 0.111757 | ||||||||
\(877\) | −50.4623 | −1.70399 | −0.851995 | − | 0.523550i | \(-0.824607\pi\) | ||||
−0.851995 | + | 0.523550i | \(0.824607\pi\) | |||||||
\(878\) | −17.8118 | −0.601120 | ||||||||
\(879\) | −6.00984 | −0.202707 | ||||||||
\(880\) | 3.18421 | 0.107340 | ||||||||
\(881\) | −18.3526 | −0.618315 | −0.309157 | − | 0.951011i | \(-0.600047\pi\) | ||||
−0.309157 | + | 0.951011i | \(0.600047\pi\) | |||||||
\(882\) | 13.2543 | 0.446295 | ||||||||
\(883\) | 16.8573 | 0.567293 | 0.283646 | − | 0.958929i | \(-0.408456\pi\) | ||||
0.283646 | + | 0.958929i | \(0.408456\pi\) | |||||||
\(884\) | −0.101710 | −0.00342089 | ||||||||
\(885\) | −4.96697 | −0.166963 | ||||||||
\(886\) | 25.2893 | 0.849611 | ||||||||
\(887\) | −39.6829 | −1.33242 | −0.666211 | − | 0.745763i | \(-0.732085\pi\) | ||||
−0.666211 | + | 0.745763i | \(0.732085\pi\) | |||||||
\(888\) | 21.9693 | 0.737242 | ||||||||
\(889\) | −60.2864 | −2.02194 | ||||||||
\(890\) | −13.5002 | −0.452529 | ||||||||
\(891\) | 2.09679 | 0.0702450 | ||||||||
\(892\) | 29.2083 | 0.977968 | ||||||||
\(893\) | −8.65080 | −0.289488 | ||||||||
\(894\) | 10.3412 | 0.345862 | ||||||||
\(895\) | −54.6894 | −1.82806 | ||||||||
\(896\) | −47.6325 | −1.59129 | ||||||||
\(897\) | 0.225547 | 0.00753080 | ||||||||
\(898\) | 17.3285 | 0.578258 | ||||||||
\(899\) | 18.0479 | 0.601933 | ||||||||
\(900\) | 0.793993 | 0.0264664 | ||||||||
\(901\) | 12.2810 | 0.409139 | ||||||||
\(902\) | −3.05086 | −0.101582 | ||||||||
\(903\) | −62.4514 | −2.07825 | ||||||||
\(904\) | 10.7940 | 0.359003 | ||||||||
\(905\) | 7.42864 | 0.246936 | ||||||||
\(906\) | −12.1258 | −0.402854 | ||||||||
\(907\) | 8.94025 | 0.296856 | 0.148428 | − | 0.988923i | \(-0.452579\pi\) | ||||
0.148428 | + | 0.988923i | \(0.452579\pi\) | |||||||
\(908\) | 23.0825 | 0.766020 | ||||||||
\(909\) | 6.65386 | 0.220695 | ||||||||
\(910\) | 0.470127 | 0.0155845 | ||||||||
\(911\) | −50.5861 | −1.67599 | −0.837997 | − | 0.545675i | \(-0.816273\pi\) | ||||
−0.837997 | + | 0.545675i | \(0.816273\pi\) | |||||||
\(912\) | 10.8671 | 0.359846 | ||||||||
\(913\) | −2.75557 | −0.0911960 | ||||||||
\(914\) | −8.45277 | −0.279593 | ||||||||
\(915\) | −6.81579 | −0.225323 | ||||||||
\(916\) | −4.25920 | −0.140728 | ||||||||
\(917\) | −92.8198 | −3.06518 | ||||||||
\(918\) | −3.78568 | −0.124946 | ||||||||
\(919\) | −42.1718 | −1.39112 | −0.695559 | − | 0.718469i | \(-0.744843\pi\) | ||||
−0.695559 | + | 0.718469i | \(0.744843\pi\) | |||||||
\(920\) | 15.6356 | 0.515490 | ||||||||
\(921\) | 7.83701 | 0.258238 | ||||||||
\(922\) | −17.9813 | −0.592181 | ||||||||
\(923\) | 0.0711223 | 0.00234102 | ||||||||
\(924\) | −8.20342 | −0.269873 | ||||||||
\(925\) | 2.54187 | 0.0835763 | ||||||||
\(926\) | −14.0765 | −0.462583 | ||||||||
\(927\) | 18.6855 | 0.613712 | ||||||||
\(928\) | 13.9813 | 0.458957 | ||||||||
\(929\) | 57.6040 | 1.88992 | 0.944962 | − | 0.327179i | \(-0.106098\pi\) | ||||
0.944962 | + | 0.327179i | \(0.106098\pi\) | |||||||
\(930\) | −14.4909 | −0.475174 | ||||||||
\(931\) | 81.9244 | 2.68496 | ||||||||
\(932\) | −6.60042 | −0.216204 | ||||||||
\(933\) | 11.4380 | 0.374464 | ||||||||
\(934\) | 28.6069 | 0.936045 | ||||||||
\(935\) | −2.31111 | −0.0755813 | ||||||||
\(936\) | 0.247018 | 0.00807402 | ||||||||
\(937\) | −32.7273 | −1.06915 | −0.534577 | − | 0.845120i | \(-0.679529\pi\) | ||||
−0.534577 | + | 0.845120i | \(0.679529\pi\) | |||||||
\(938\) | −40.3783 | −1.31840 | ||||||||
\(939\) | 17.9491 | 0.585748 | ||||||||
\(940\) | −4.69535 | −0.153145 | ||||||||
\(941\) | 25.6543 | 0.836307 | 0.418154 | − | 0.908376i | \(-0.362677\pi\) | ||||
0.418154 | + | 0.908376i | \(0.362677\pi\) | |||||||
\(942\) | −11.9507 | −0.389374 | ||||||||
\(943\) | 12.3368 | 0.401741 | ||||||||
\(944\) | 2.43848 | 0.0793659 | ||||||||
\(945\) | −56.2449 | −1.82965 | ||||||||
\(946\) | 8.00000 | 0.260102 | ||||||||
\(947\) | −44.7782 | −1.45510 | −0.727548 | − | 0.686057i | \(-0.759340\pi\) | ||||
−0.727548 | + | 0.686057i | \(0.759340\pi\) | |||||||
\(948\) | −12.6637 | −0.411298 | ||||||||
\(949\) | 0.119063 | 0.00386495 | ||||||||
\(950\) | −1.52681 | −0.0495363 | ||||||||
\(951\) | −16.8578 | −0.546650 | ||||||||
\(952\) | 10.7556 | 0.348590 | ||||||||
\(953\) | −9.22570 | −0.298850 | −0.149425 | − | 0.988773i | \(-0.547742\pi\) | ||||
−0.149425 | + | 0.988773i | \(0.547742\pi\) | |||||||
\(954\) | −12.9055 | −0.417833 | ||||||||
\(955\) | −29.1497 | −0.943261 | ||||||||
\(956\) | −18.2667 | −0.590787 | ||||||||
\(957\) | 2.92396 | 0.0945181 | ||||||||
\(958\) | −10.2854 | −0.332308 | ||||||||
\(959\) | 76.3279 | 2.46476 | ||||||||
\(960\) | −3.49240 | −0.112717 | ||||||||
\(961\) | 25.1798 | 0.812250 | ||||||||
\(962\) | 0.342172 | 0.0110321 | ||||||||
\(963\) | 18.3368 | 0.590894 | ||||||||
\(964\) | 11.1624 | 0.359517 | ||||||||
\(965\) | −11.6251 | −0.374226 | ||||||||
\(966\) | −10.3201 | −0.332045 | ||||||||
\(967\) | −0.0162978 | −0.000524103 0 | −0.000262051 | − | 1.00000i | \(-0.500083\pi\) | ||||
−0.000262051 | 1.00000i | \(0.500083\pi\) | ||||||||
\(968\) | 2.42864 | 0.0780594 | ||||||||
\(969\) | −7.88739 | −0.253379 | ||||||||
\(970\) | −12.4766 | −0.400599 | ||||||||
\(971\) | 29.3225 | 0.941003 | 0.470502 | − | 0.882399i | \(-0.344073\pi\) | ||||
0.470502 | + | 0.882399i | \(0.344073\pi\) | |||||||
\(972\) | −21.2641 | −0.682047 | ||||||||
\(973\) | −30.8671 | −0.989555 | ||||||||
\(974\) | 15.8084 | 0.506535 | ||||||||
\(975\) | −0.0276274 | −0.000884784 0 | ||||||||
\(976\) | 3.34614 | 0.107107 | ||||||||
\(977\) | −7.72837 | −0.247253 | −0.123626 | − | 0.992329i | \(-0.539452\pi\) | ||||
−0.123626 | + | 0.992329i | \(0.539452\pi\) | |||||||
\(978\) | −6.93930 | −0.221894 | ||||||||
\(979\) | 8.47949 | 0.271006 | ||||||||
\(980\) | 44.4657 | 1.42040 | ||||||||
\(981\) | 21.5910 | 0.689349 | ||||||||
\(982\) | 13.6074 | 0.434231 | ||||||||
\(983\) | −7.06668 | −0.225392 | −0.112696 | − | 0.993630i | \(-0.535949\pi\) | ||||
−0.112696 | + | 0.993630i | \(0.535949\pi\) | |||||||
\(984\) | −13.0607 | −0.416360 | ||||||||
\(985\) | 50.5841 | 1.61174 | ||||||||
\(986\) | −1.65878 | −0.0528263 | ||||||||
\(987\) | 7.16241 | 0.227982 | ||||||||
\(988\) | 0.660640 | 0.0210178 | ||||||||
\(989\) | −32.3497 | −1.02866 | ||||||||
\(990\) | 2.42864 | 0.0771872 | ||||||||
\(991\) | −6.06022 | −0.192509 | −0.0962547 | − | 0.995357i | \(-0.530686\pi\) | ||||
−0.0962547 | + | 0.995357i | \(0.530686\pi\) | |||||||
\(992\) | 43.5210 | 1.38179 | ||||||||
\(993\) | −32.2781 | −1.02431 | ||||||||
\(994\) | −3.25428 | −0.103219 | ||||||||
\(995\) | −36.4572 | −1.15577 | ||||||||
\(996\) | −5.10430 | −0.161736 | ||||||||
\(997\) | 30.7447 | 0.973693 | 0.486847 | − | 0.873487i | \(-0.338147\pi\) | ||||
0.486847 | + | 0.873487i | \(0.338147\pi\) | |||||||
\(998\) | 6.49871 | 0.205713 | ||||||||
\(999\) | −40.9367 | −1.29518 |
(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 | 187.2.a.e.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 1683.2.a.v.1.2 | 3 | |||
4.3 | odd | 2 | 2992.2.a.r.1.1 | 3 | |||
5.4 | even | 2 | 4675.2.a.bc.1.2 | 3 | |||
7.6 | odd | 2 | 9163.2.a.j.1.2 | 3 | |||
11.10 | odd | 2 | 2057.2.a.p.1.2 | 3 | |||
17.16 | even | 2 | 3179.2.a.t.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
187.2.a.e.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1683.2.a.v.1.2 | 3 | 3.2 | odd | 2 | |||
2057.2.a.p.1.2 | 3 | 11.10 | odd | 2 | |||
2992.2.a.r.1.1 | 3 | 4.3 | odd | 2 | |||
3179.2.a.t.1.2 | 3 | 17.16 | even | 2 | |||
4675.2.a.bc.1.2 | 3 | 5.4 | even | 2 | |||
9163.2.a.j.1.2 | 3 | 7.6 | odd | 2 |