Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3525,2,Mod(1,3525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3525, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3525.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3525 = 3 \cdot 5^{2} \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3525.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: | \(28.1472667125\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 9x^{5} + 10x^{4} + 16x^{3} - 15x^{2} - 6x + 5 \) |
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 | 1.7 | ||
Root | \(2.30790\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3525.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.30790 | 1.63193 | 0.815966 | − | 0.578100i | \(-0.196206\pi\) | ||||
0.815966 | + | 0.578100i | \(0.196206\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.32640 | 1.66320 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.30790 | −0.942196 | ||||||||
\(7\) | −0.860272 | −0.325152 | −0.162576 | − | 0.986696i | \(-0.551980\pi\) | ||||
−0.162576 | + | 0.986696i | \(0.551980\pi\) | |||||||
\(8\) | 3.06120 | 1.08230 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.86972 | 0.865253 | 0.432626 | − | 0.901573i | \(-0.357587\pi\) | ||||
0.432626 | + | 0.901573i | \(0.357587\pi\) | |||||||
\(12\) | −3.32640 | −0.960250 | ||||||||
\(13\) | −4.01667 | −1.11402 | −0.557012 | − | 0.830505i | \(-0.688052\pi\) | ||||
−0.557012 | + | 0.830505i | \(0.688052\pi\) | |||||||
\(14\) | −1.98542 | −0.530626 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.412149 | 0.103037 | ||||||||
\(17\) | −6.25340 | −1.51667 | −0.758336 | − | 0.651864i | \(-0.773987\pi\) | ||||
−0.758336 | + | 0.651864i | \(0.773987\pi\) | |||||||
\(18\) | 2.30790 | 0.543977 | ||||||||
\(19\) | −7.86109 | −1.80346 | −0.901729 | − | 0.432301i | \(-0.857702\pi\) | ||||
−0.901729 | + | 0.432301i | \(0.857702\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.860272 | 0.187727 | ||||||||
\(22\) | 6.62302 | 1.41203 | ||||||||
\(23\) | −1.67752 | −0.349787 | −0.174894 | − | 0.984587i | \(-0.555958\pi\) | ||||
−0.174894 | + | 0.984587i | \(0.555958\pi\) | |||||||
\(24\) | −3.06120 | −0.624866 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −9.27007 | −1.81801 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −2.86161 | −0.540794 | ||||||||
\(29\) | −1.38052 | −0.256356 | −0.128178 | − | 0.991751i | \(-0.540913\pi\) | ||||
−0.128178 | + | 0.991751i | \(0.540913\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.32196 | 1.31506 | 0.657532 | − | 0.753427i | \(-0.271601\pi\) | ||||
0.657532 | + | 0.753427i | \(0.271601\pi\) | |||||||
\(32\) | −5.17121 | −0.914150 | ||||||||
\(33\) | −2.86972 | −0.499554 | ||||||||
\(34\) | −14.4322 | −2.47511 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.32640 | 0.554400 | ||||||||
\(37\) | −7.22336 | −1.18751 | −0.593756 | − | 0.804645i | \(-0.702356\pi\) | ||||
−0.593756 | + | 0.804645i | \(0.702356\pi\) | |||||||
\(38\) | −18.1426 | −2.94312 | ||||||||
\(39\) | 4.01667 | 0.643182 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.55591 | 1.18004 | 0.590018 | − | 0.807390i | \(-0.299121\pi\) | ||||
0.590018 | + | 0.807390i | \(0.299121\pi\) | |||||||
\(42\) | 1.98542 | 0.306357 | ||||||||
\(43\) | 6.88207 | 1.04951 | 0.524753 | − | 0.851255i | \(-0.324158\pi\) | ||||
0.524753 | + | 0.851255i | \(0.324158\pi\) | |||||||
\(44\) | 9.54584 | 1.43909 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.87155 | −0.570829 | ||||||||
\(47\) | −1.00000 | −0.145865 | ||||||||
\(48\) | −0.412149 | −0.0594885 | ||||||||
\(49\) | −6.25993 | −0.894276 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.25340 | 0.875651 | ||||||||
\(52\) | −13.3611 | −1.85285 | ||||||||
\(53\) | −10.3790 | −1.42567 | −0.712836 | − | 0.701331i | \(-0.752590\pi\) | ||||
−0.712836 | + | 0.701331i | \(0.752590\pi\) | |||||||
\(54\) | −2.30790 | −0.314065 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.63347 | −0.351912 | ||||||||
\(57\) | 7.86109 | 1.04123 | ||||||||
\(58\) | −3.18610 | −0.418355 | ||||||||
\(59\) | −8.17819 | −1.06471 | −0.532355 | − | 0.846521i | \(-0.678693\pi\) | ||||
−0.532355 | + | 0.846521i | \(0.678693\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.18776 | −0.920298 | −0.460149 | − | 0.887842i | \(-0.652204\pi\) | ||||
−0.460149 | + | 0.887842i | \(0.652204\pi\) | |||||||
\(62\) | 16.8984 | 2.14609 | ||||||||
\(63\) | −0.860272 | −0.108384 | ||||||||
\(64\) | −12.7589 | −1.59487 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.62302 | −0.815238 | ||||||||
\(67\) | 5.56732 | 0.680156 | 0.340078 | − | 0.940397i | \(-0.389546\pi\) | ||||
0.340078 | + | 0.940397i | \(0.389546\pi\) | |||||||
\(68\) | −20.8013 | −2.52253 | ||||||||
\(69\) | 1.67752 | 0.201950 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.3542 | 1.34750 | 0.673749 | − | 0.738960i | \(-0.264683\pi\) | ||||
0.673749 | + | 0.738960i | \(0.264683\pi\) | |||||||
\(72\) | 3.06120 | 0.360766 | ||||||||
\(73\) | 3.97123 | 0.464797 | 0.232398 | − | 0.972621i | \(-0.425343\pi\) | ||||
0.232398 | + | 0.972621i | \(0.425343\pi\) | |||||||
\(74\) | −16.6708 | −1.93794 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −26.1492 | −2.99951 | ||||||||
\(77\) | −2.46874 | −0.281339 | ||||||||
\(78\) | 9.27007 | 1.04963 | ||||||||
\(79\) | 16.6332 | 1.87138 | 0.935688 | − | 0.352828i | \(-0.114780\pi\) | ||||
0.935688 | + | 0.352828i | \(0.114780\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 17.4383 | 1.92574 | ||||||||
\(83\) | −6.31404 | −0.693056 | −0.346528 | − | 0.938040i | \(-0.612639\pi\) | ||||
−0.346528 | + | 0.938040i | \(0.612639\pi\) | |||||||
\(84\) | 2.86161 | 0.312227 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 15.8831 | 1.71272 | ||||||||
\(87\) | 1.38052 | 0.148007 | ||||||||
\(88\) | 8.78479 | 0.936462 | ||||||||
\(89\) | −8.21367 | −0.870648 | −0.435324 | − | 0.900274i | \(-0.643366\pi\) | ||||
−0.435324 | + | 0.900274i | \(0.643366\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.45543 | 0.362227 | ||||||||
\(92\) | −5.58011 | −0.581767 | ||||||||
\(93\) | −7.32196 | −0.759252 | ||||||||
\(94\) | −2.30790 | −0.238042 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 5.17121 | 0.527785 | ||||||||
\(97\) | 13.1992 | 1.34018 | 0.670088 | − | 0.742282i | \(-0.266256\pi\) | ||||
0.670088 | + | 0.742282i | \(0.266256\pi\) | |||||||
\(98\) | −14.4473 | −1.45940 | ||||||||
\(99\) | 2.86972 | 0.288418 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −18.7067 | −1.86139 | −0.930695 | − | 0.365797i | \(-0.880797\pi\) | ||||
−0.930695 | + | 0.365797i | \(0.880797\pi\) | |||||||
\(102\) | 14.4322 | 1.42900 | ||||||||
\(103\) | −6.78830 | −0.668871 | −0.334436 | − | 0.942419i | \(-0.608546\pi\) | ||||
−0.334436 | + | 0.942419i | \(0.608546\pi\) | |||||||
\(104\) | −12.2958 | −1.20571 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −23.9538 | −2.32660 | ||||||||
\(107\) | −12.4206 | −1.20075 | −0.600373 | − | 0.799720i | \(-0.704981\pi\) | ||||
−0.600373 | + | 0.799720i | \(0.704981\pi\) | |||||||
\(108\) | −3.32640 | −0.320083 | ||||||||
\(109\) | 4.30272 | 0.412126 | 0.206063 | − | 0.978539i | \(-0.433935\pi\) | ||||
0.206063 | + | 0.978539i | \(0.433935\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.22336 | 0.685611 | ||||||||
\(112\) | −0.354560 | −0.0335028 | ||||||||
\(113\) | 9.47563 | 0.891392 | 0.445696 | − | 0.895184i | \(-0.352956\pi\) | ||||
0.445696 | + | 0.895184i | \(0.352956\pi\) | |||||||
\(114\) | 18.1426 | 1.69921 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.59216 | −0.426371 | ||||||||
\(117\) | −4.01667 | −0.371341 | ||||||||
\(118\) | −18.8745 | −1.73753 | ||||||||
\(119\) | 5.37963 | 0.493149 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.76472 | −0.251338 | ||||||||
\(122\) | −16.5886 | −1.50186 | ||||||||
\(123\) | −7.55591 | −0.681294 | ||||||||
\(124\) | 24.3558 | 2.18721 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.98542 | −0.176875 | ||||||||
\(127\) | −12.4618 | −1.10581 | −0.552903 | − | 0.833246i | \(-0.686480\pi\) | ||||
−0.552903 | + | 0.833246i | \(0.686480\pi\) | |||||||
\(128\) | −19.1039 | −1.68856 | ||||||||
\(129\) | −6.88207 | −0.605932 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.3498 | 1.25375 | 0.626873 | − | 0.779122i | \(-0.284335\pi\) | ||||
0.626873 | + | 0.779122i | \(0.284335\pi\) | |||||||
\(132\) | −9.54584 | −0.830859 | ||||||||
\(133\) | 6.76268 | 0.586399 | ||||||||
\(134\) | 12.8488 | 1.10997 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −19.1429 | −1.64149 | ||||||||
\(137\) | 3.74430 | 0.319897 | 0.159948 | − | 0.987125i | \(-0.448867\pi\) | ||||
0.159948 | + | 0.987125i | \(0.448867\pi\) | |||||||
\(138\) | 3.87155 | 0.329568 | ||||||||
\(139\) | 0.537864 | 0.0456210 | 0.0228105 | − | 0.999740i | \(-0.492739\pi\) | ||||
0.0228105 | + | 0.999740i | \(0.492739\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.00000 | 0.0842152 | ||||||||
\(142\) | 26.2044 | 2.19902 | ||||||||
\(143\) | −11.5267 | −0.963912 | ||||||||
\(144\) | 0.412149 | 0.0343457 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 9.16519 | 0.758517 | ||||||||
\(147\) | 6.25993 | 0.516311 | ||||||||
\(148\) | −24.0278 | −1.97507 | ||||||||
\(149\) | 13.9660 | 1.14414 | 0.572068 | − | 0.820206i | \(-0.306141\pi\) | ||||
0.572068 | + | 0.820206i | \(0.306141\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.5462 | −1.50926 | −0.754632 | − | 0.656148i | \(-0.772185\pi\) | ||||
−0.754632 | + | 0.656148i | \(0.772185\pi\) | |||||||
\(152\) | −24.0644 | −1.95188 | ||||||||
\(153\) | −6.25340 | −0.505558 | ||||||||
\(154\) | −5.69760 | −0.459126 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 13.3611 | 1.06974 | ||||||||
\(157\) | 10.6512 | 0.850060 | 0.425030 | − | 0.905179i | \(-0.360263\pi\) | ||||
0.425030 | + | 0.905179i | \(0.360263\pi\) | |||||||
\(158\) | 38.3877 | 3.05396 | ||||||||
\(159\) | 10.3790 | 0.823112 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.44312 | 0.113734 | ||||||||
\(162\) | 2.30790 | 0.181326 | ||||||||
\(163\) | −9.61416 | −0.753039 | −0.376520 | − | 0.926409i | \(-0.622879\pi\) | ||||
−0.376520 | + | 0.926409i | \(0.622879\pi\) | |||||||
\(164\) | 25.1340 | 1.96264 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.5722 | −1.13102 | ||||||||
\(167\) | 5.59100 | 0.432644 | 0.216322 | − | 0.976322i | \(-0.430594\pi\) | ||||
0.216322 | + | 0.976322i | \(0.430594\pi\) | |||||||
\(168\) | 2.63347 | 0.203176 | ||||||||
\(169\) | 3.13363 | 0.241048 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.86109 | −0.601153 | ||||||||
\(172\) | 22.8925 | 1.74554 | ||||||||
\(173\) | −12.2528 | −0.931562 | −0.465781 | − | 0.884900i | \(-0.654226\pi\) | ||||
−0.465781 | + | 0.884900i | \(0.654226\pi\) | |||||||
\(174\) | 3.18610 | 0.241537 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.18275 | 0.0891532 | ||||||||
\(177\) | 8.17819 | 0.614711 | ||||||||
\(178\) | −18.9563 | −1.42084 | ||||||||
\(179\) | −26.0992 | −1.95075 | −0.975373 | − | 0.220562i | \(-0.929211\pi\) | ||||
−0.975373 | + | 0.220562i | \(0.929211\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.0691 | 0.822761 | 0.411380 | − | 0.911464i | \(-0.365047\pi\) | ||||
0.411380 | + | 0.911464i | \(0.365047\pi\) | |||||||
\(182\) | 7.97478 | 0.591130 | ||||||||
\(183\) | 7.18776 | 0.531334 | ||||||||
\(184\) | −5.13524 | −0.378575 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −16.8984 | −1.23905 | ||||||||
\(187\) | −17.9455 | −1.31230 | ||||||||
\(188\) | −3.32640 | −0.242603 | ||||||||
\(189\) | 0.860272 | 0.0625756 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.50035 | −0.108561 | −0.0542806 | − | 0.998526i | \(-0.517287\pi\) | ||||
−0.0542806 | + | 0.998526i | \(0.517287\pi\) | |||||||
\(192\) | 12.7589 | 0.920797 | ||||||||
\(193\) | 17.4657 | 1.25721 | 0.628606 | − | 0.777724i | \(-0.283626\pi\) | ||||
0.628606 | + | 0.777724i | \(0.283626\pi\) | |||||||
\(194\) | 30.4624 | 2.18708 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −20.8231 | −1.48736 | ||||||||
\(197\) | 21.9598 | 1.56457 | 0.782285 | − | 0.622920i | \(-0.214054\pi\) | ||||
0.782285 | + | 0.622920i | \(0.214054\pi\) | |||||||
\(198\) | 6.62302 | 0.470678 | ||||||||
\(199\) | −10.8996 | −0.772652 | −0.386326 | − | 0.922362i | \(-0.626256\pi\) | ||||
−0.386326 | + | 0.922362i | \(0.626256\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.56732 | −0.392688 | ||||||||
\(202\) | −43.1733 | −3.03766 | ||||||||
\(203\) | 1.18762 | 0.0833546 | ||||||||
\(204\) | 20.8013 | 1.45638 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −15.6667 | −1.09155 | ||||||||
\(207\) | −1.67752 | −0.116596 | ||||||||
\(208\) | −1.65546 | −0.114786 | ||||||||
\(209\) | −22.5591 | −1.56045 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.5183 | −0.930640 | −0.465320 | − | 0.885142i | \(-0.654061\pi\) | ||||
−0.465320 | + | 0.885142i | \(0.654061\pi\) | |||||||
\(212\) | −34.5249 | −2.37118 | ||||||||
\(213\) | −11.3542 | −0.777978 | ||||||||
\(214\) | −28.6655 | −1.95954 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.06120 | −0.208289 | ||||||||
\(217\) | −6.29888 | −0.427596 | ||||||||
\(218\) | 9.93024 | 0.672561 | ||||||||
\(219\) | −3.97123 | −0.268351 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 25.1178 | 1.68961 | ||||||||
\(222\) | 16.6708 | 1.11887 | ||||||||
\(223\) | −3.42274 | −0.229204 | −0.114602 | − | 0.993412i | \(-0.536559\pi\) | ||||
−0.114602 | + | 0.993412i | \(0.536559\pi\) | |||||||
\(224\) | 4.44865 | 0.297238 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 21.8688 | 1.45469 | ||||||||
\(227\) | −26.8967 | −1.78519 | −0.892597 | − | 0.450856i | \(-0.851119\pi\) | ||||
−0.892597 | + | 0.450856i | \(0.851119\pi\) | |||||||
\(228\) | 26.1492 | 1.73177 | ||||||||
\(229\) | 10.5653 | 0.698173 | 0.349086 | − | 0.937091i | \(-0.386492\pi\) | ||||
0.349086 | + | 0.937091i | \(0.386492\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.46874 | 0.162431 | ||||||||
\(232\) | −4.22605 | −0.277454 | ||||||||
\(233\) | 5.05163 | 0.330944 | 0.165472 | − | 0.986215i | \(-0.447085\pi\) | ||||
0.165472 | + | 0.986215i | \(0.447085\pi\) | |||||||
\(234\) | −9.27007 | −0.606003 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −27.2040 | −1.77083 | ||||||||
\(237\) | −16.6332 | −1.08044 | ||||||||
\(238\) | 12.4156 | 0.804786 | ||||||||
\(239\) | 6.73903 | 0.435912 | 0.217956 | − | 0.975959i | \(-0.430061\pi\) | ||||
0.217956 | + | 0.975959i | \(0.430061\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.3842 | −1.37748 | −0.688740 | − | 0.725009i | \(-0.741836\pi\) | ||||
−0.688740 | + | 0.725009i | \(0.741836\pi\) | |||||||
\(242\) | −6.38069 | −0.410166 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −23.9094 | −1.53064 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −17.4383 | −1.11182 | ||||||||
\(247\) | 31.5754 | 2.00910 | ||||||||
\(248\) | 22.4140 | 1.42329 | ||||||||
\(249\) | 6.31404 | 0.400136 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.7999 | 0.997281 | 0.498641 | − | 0.866809i | \(-0.333833\pi\) | ||||
0.498641 | + | 0.866809i | \(0.333833\pi\) | |||||||
\(252\) | −2.86161 | −0.180265 | ||||||||
\(253\) | −4.81401 | −0.302654 | ||||||||
\(254\) | −28.7606 | −1.80460 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −18.5721 | −1.16075 | ||||||||
\(257\) | 8.34387 | 0.520477 | 0.260238 | − | 0.965544i | \(-0.416199\pi\) | ||||
0.260238 | + | 0.965544i | \(0.416199\pi\) | |||||||
\(258\) | −15.8831 | −0.988840 | ||||||||
\(259\) | 6.21405 | 0.386122 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.38052 | −0.0854519 | ||||||||
\(262\) | 33.1178 | 2.04603 | ||||||||
\(263\) | 10.0710 | 0.621003 | 0.310502 | − | 0.950573i | \(-0.399503\pi\) | ||||
0.310502 | + | 0.950573i | \(0.399503\pi\) | |||||||
\(264\) | −8.78479 | −0.540667 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 15.6076 | 0.956962 | ||||||||
\(267\) | 8.21367 | 0.502669 | ||||||||
\(268\) | 18.5191 | 1.13124 | ||||||||
\(269\) | 13.1491 | 0.801717 | 0.400859 | − | 0.916140i | \(-0.368712\pi\) | ||||
0.400859 | + | 0.916140i | \(0.368712\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.77052 | 0.472026 | 0.236013 | − | 0.971750i | \(-0.424159\pi\) | ||||
0.236013 | + | 0.971750i | \(0.424159\pi\) | |||||||
\(272\) | −2.57733 | −0.156274 | ||||||||
\(273\) | −3.45543 | −0.209132 | ||||||||
\(274\) | 8.64146 | 0.522050 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.58011 | 0.335883 | ||||||||
\(277\) | −3.34256 | −0.200835 | −0.100417 | − | 0.994945i | \(-0.532018\pi\) | ||||
−0.100417 | + | 0.994945i | \(0.532018\pi\) | |||||||
\(278\) | 1.24134 | 0.0744504 | ||||||||
\(279\) | 7.32196 | 0.438354 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.1042 | 0.781729 | 0.390864 | − | 0.920448i | \(-0.372176\pi\) | ||||
0.390864 | + | 0.920448i | \(0.372176\pi\) | |||||||
\(282\) | 2.30790 | 0.137433 | ||||||||
\(283\) | −31.3949 | −1.86623 | −0.933115 | − | 0.359578i | \(-0.882921\pi\) | ||||
−0.933115 | + | 0.359578i | \(0.882921\pi\) | |||||||
\(284\) | 37.7687 | 2.24116 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −26.6025 | −1.57304 | ||||||||
\(287\) | −6.50014 | −0.383691 | ||||||||
\(288\) | −5.17121 | −0.304717 | ||||||||
\(289\) | 22.1050 | 1.30030 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.1992 | −0.773751 | ||||||||
\(292\) | 13.2099 | 0.773051 | ||||||||
\(293\) | −16.1948 | −0.946110 | −0.473055 | − | 0.881033i | \(-0.656849\pi\) | ||||
−0.473055 | + | 0.881033i | \(0.656849\pi\) | |||||||
\(294\) | 14.4473 | 0.842584 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −22.1122 | −1.28524 | ||||||||
\(297\) | −2.86972 | −0.166518 | ||||||||
\(298\) | 32.2321 | 1.86715 | ||||||||
\(299\) | 6.73805 | 0.389671 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.92045 | −0.341249 | ||||||||
\(302\) | −42.8027 | −2.46302 | ||||||||
\(303\) | 18.7067 | 1.07467 | ||||||||
\(304\) | −3.23994 | −0.185823 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −14.4322 | −0.825035 | ||||||||
\(307\) | −25.8625 | −1.47605 | −0.738026 | − | 0.674772i | \(-0.764242\pi\) | ||||
−0.738026 | + | 0.674772i | \(0.764242\pi\) | |||||||
\(308\) | −8.21202 | −0.467923 | ||||||||
\(309\) | 6.78830 | 0.386173 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.5509 | 0.598288 | 0.299144 | − | 0.954208i | \(-0.403299\pi\) | ||||
0.299144 | + | 0.954208i | \(0.403299\pi\) | |||||||
\(312\) | 12.2958 | 0.696115 | ||||||||
\(313\) | −13.3525 | −0.754728 | −0.377364 | − | 0.926065i | \(-0.623169\pi\) | ||||
−0.377364 | + | 0.926065i | \(0.623169\pi\) | |||||||
\(314\) | 24.5820 | 1.38724 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 55.3286 | 3.11248 | ||||||||
\(317\) | −2.87288 | −0.161357 | −0.0806786 | − | 0.996740i | \(-0.525709\pi\) | ||||
−0.0806786 | + | 0.996740i | \(0.525709\pi\) | |||||||
\(318\) | 23.9538 | 1.34326 | ||||||||
\(319\) | −3.96170 | −0.221812 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.4206 | 0.693251 | ||||||||
\(322\) | 3.33059 | 0.185606 | ||||||||
\(323\) | 49.1586 | 2.73526 | ||||||||
\(324\) | 3.32640 | 0.184800 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −22.1885 | −1.22891 | ||||||||
\(327\) | −4.30272 | −0.237941 | ||||||||
\(328\) | 23.1302 | 1.27715 | ||||||||
\(329\) | 0.860272 | 0.0474283 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.8952 | 1.47829 | 0.739147 | − | 0.673544i | \(-0.235229\pi\) | ||||
0.739147 | + | 0.673544i | \(0.235229\pi\) | |||||||
\(332\) | −21.0030 | −1.15269 | ||||||||
\(333\) | −7.22336 | −0.395838 | ||||||||
\(334\) | 12.9035 | 0.706046 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.354560 | 0.0193428 | ||||||||
\(337\) | −5.56374 | −0.303076 | −0.151538 | − | 0.988451i | \(-0.548423\pi\) | ||||
−0.151538 | + | 0.988451i | \(0.548423\pi\) | |||||||
\(338\) | 7.23210 | 0.393374 | ||||||||
\(339\) | −9.47563 | −0.514646 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 21.0120 | 1.13786 | ||||||||
\(342\) | −18.1426 | −0.981040 | ||||||||
\(343\) | 11.4071 | 0.615928 | ||||||||
\(344\) | 21.0674 | 1.13588 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −28.2782 | −1.52024 | ||||||||
\(347\) | 23.1678 | 1.24371 | 0.621855 | − | 0.783132i | \(-0.286379\pi\) | ||||
0.621855 | + | 0.783132i | \(0.286379\pi\) | |||||||
\(348\) | 4.59216 | 0.246166 | ||||||||
\(349\) | 0.135140 | 0.00723388 | 0.00361694 | − | 0.999993i | \(-0.498849\pi\) | ||||
0.00361694 | + | 0.999993i | \(0.498849\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.01667 | 0.214394 | ||||||||
\(352\) | −14.8399 | −0.790970 | ||||||||
\(353\) | 28.9889 | 1.54293 | 0.771463 | − | 0.636274i | \(-0.219525\pi\) | ||||
0.771463 | + | 0.636274i | \(0.219525\pi\) | |||||||
\(354\) | 18.8745 | 1.00317 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −27.3220 | −1.44806 | ||||||||
\(357\) | −5.37963 | −0.284720 | ||||||||
\(358\) | −60.2344 | −3.18348 | ||||||||
\(359\) | −13.1094 | −0.691885 | −0.345943 | − | 0.938256i | \(-0.612441\pi\) | ||||
−0.345943 | + | 0.938256i | \(0.612441\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 42.7968 | 2.25246 | ||||||||
\(362\) | 25.5464 | 1.34269 | ||||||||
\(363\) | 2.76472 | 0.145110 | ||||||||
\(364\) | 11.4941 | 0.602457 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 16.5886 | 0.867101 | ||||||||
\(367\) | 6.48436 | 0.338481 | 0.169240 | − | 0.985575i | \(-0.445869\pi\) | ||||
0.169240 | + | 0.985575i | \(0.445869\pi\) | |||||||
\(368\) | −0.691388 | −0.0360411 | ||||||||
\(369\) | 7.55591 | 0.393345 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.92880 | 0.463560 | ||||||||
\(372\) | −24.3558 | −1.26279 | ||||||||
\(373\) | 23.6810 | 1.22616 | 0.613078 | − | 0.790022i | \(-0.289931\pi\) | ||||
0.613078 | + | 0.790022i | \(0.289931\pi\) | |||||||
\(374\) | −41.4164 | −2.14159 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.06120 | −0.157870 | ||||||||
\(377\) | 5.54508 | 0.285586 | ||||||||
\(378\) | 1.98542 | 0.102119 | ||||||||
\(379\) | 7.41124 | 0.380690 | 0.190345 | − | 0.981717i | \(-0.439039\pi\) | ||||
0.190345 | + | 0.981717i | \(0.439039\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.4618 | 0.638437 | ||||||||
\(382\) | −3.46265 | −0.177165 | ||||||||
\(383\) | 8.40592 | 0.429523 | 0.214761 | − | 0.976667i | \(-0.431103\pi\) | ||||
0.214761 | + | 0.976667i | \(0.431103\pi\) | |||||||
\(384\) | 19.1039 | 0.974893 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 40.3092 | 2.05168 | ||||||||
\(387\) | 6.88207 | 0.349835 | ||||||||
\(388\) | 43.9059 | 2.22898 | ||||||||
\(389\) | −15.2122 | −0.771291 | −0.385646 | − | 0.922647i | \(-0.626021\pi\) | ||||
−0.385646 | + | 0.922647i | \(0.626021\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.4902 | 0.530513 | ||||||||
\(392\) | −19.1629 | −0.967874 | ||||||||
\(393\) | −14.3498 | −0.723850 | ||||||||
\(394\) | 50.6810 | 2.55327 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 9.54584 | 0.479696 | ||||||||
\(397\) | −15.8445 | −0.795211 | −0.397605 | − | 0.917557i | \(-0.630159\pi\) | ||||
−0.397605 | + | 0.917557i | \(0.630159\pi\) | |||||||
\(398\) | −25.1552 | −1.26092 | ||||||||
\(399\) | −6.76268 | −0.338557 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.4884 | 1.32277 | 0.661385 | − | 0.750047i | \(-0.269969\pi\) | ||||
0.661385 | + | 0.750047i | \(0.269969\pi\) | |||||||
\(402\) | −12.8488 | −0.640841 | ||||||||
\(403\) | −29.4099 | −1.46501 | ||||||||
\(404\) | −62.2261 | −3.09587 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.74091 | 0.136029 | ||||||||
\(407\) | −20.7290 | −1.02750 | ||||||||
\(408\) | 19.1429 | 0.947717 | ||||||||
\(409\) | −14.7515 | −0.729415 | −0.364707 | − | 0.931122i | \(-0.618831\pi\) | ||||
−0.364707 | + | 0.931122i | \(0.618831\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.74430 | −0.184693 | ||||||||
\(412\) | −22.5806 | −1.11247 | ||||||||
\(413\) | 7.03547 | 0.346193 | ||||||||
\(414\) | −3.87155 | −0.190276 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 20.7710 | 1.01838 | ||||||||
\(417\) | −0.537864 | −0.0263393 | ||||||||
\(418\) | −52.0642 | −2.54654 | ||||||||
\(419\) | 7.31296 | 0.357261 | 0.178631 | − | 0.983916i | \(-0.442833\pi\) | ||||
0.178631 | + | 0.983916i | \(0.442833\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.65488 | −0.0806541 | −0.0403271 | − | 0.999187i | \(-0.512840\pi\) | ||||
−0.0403271 | + | 0.999187i | \(0.512840\pi\) | |||||||
\(422\) | −31.1990 | −1.51874 | ||||||||
\(423\) | −1.00000 | −0.0486217 | ||||||||
\(424\) | −31.7724 | −1.54300 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −26.2044 | −1.26961 | ||||||||
\(427\) | 6.18342 | 0.299237 | ||||||||
\(428\) | −41.3160 | −1.99708 | ||||||||
\(429\) | 11.5267 | 0.556515 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.61351 | 0.414898 | 0.207449 | − | 0.978246i | \(-0.433484\pi\) | ||||
0.207449 | + | 0.978246i | \(0.433484\pi\) | |||||||
\(432\) | −0.412149 | −0.0198295 | ||||||||
\(433\) | −0.474268 | −0.0227919 | −0.0113959 | − | 0.999935i | \(-0.503628\pi\) | ||||
−0.0113959 | + | 0.999935i | \(0.503628\pi\) | |||||||
\(434\) | −14.5372 | −0.697807 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.3126 | 0.685448 | ||||||||
\(437\) | 13.1872 | 0.630827 | ||||||||
\(438\) | −9.16519 | −0.437930 | ||||||||
\(439\) | 21.7771 | 1.03936 | 0.519682 | − | 0.854360i | \(-0.326050\pi\) | ||||
0.519682 | + | 0.854360i | \(0.326050\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.25993 | −0.298092 | ||||||||
\(442\) | 57.9695 | 2.75733 | ||||||||
\(443\) | −30.9632 | −1.47111 | −0.735553 | − | 0.677468i | \(-0.763077\pi\) | ||||
−0.735553 | + | 0.677468i | \(0.763077\pi\) | |||||||
\(444\) | 24.0278 | 1.14031 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7.89934 | −0.374045 | ||||||||
\(447\) | −13.9660 | −0.660568 | ||||||||
\(448\) | 10.9762 | 0.518575 | ||||||||
\(449\) | 19.3567 | 0.913501 | 0.456751 | − | 0.889595i | \(-0.349013\pi\) | ||||
0.456751 | + | 0.889595i | \(0.349013\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.6833 | 1.02103 | ||||||||
\(452\) | 31.5198 | 1.48256 | ||||||||
\(453\) | 18.5462 | 0.871374 | ||||||||
\(454\) | −62.0748 | −2.91331 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 24.0644 | 1.12692 | ||||||||
\(457\) | 13.4013 | 0.626888 | 0.313444 | − | 0.949607i | \(-0.398517\pi\) | ||||
0.313444 | + | 0.949607i | \(0.398517\pi\) | |||||||
\(458\) | 24.3836 | 1.13937 | ||||||||
\(459\) | 6.25340 | 0.291884 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.6488 | 0.775413 | 0.387707 | − | 0.921783i | \(-0.373267\pi\) | ||||
0.387707 | + | 0.921783i | \(0.373267\pi\) | |||||||
\(462\) | 5.69760 | 0.265076 | ||||||||
\(463\) | 6.09512 | 0.283264 | 0.141632 | − | 0.989919i | \(-0.454765\pi\) | ||||
0.141632 | + | 0.989919i | \(0.454765\pi\) | |||||||
\(464\) | −0.568979 | −0.0264142 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.6587 | 0.540077 | ||||||||
\(467\) | 11.0692 | 0.512223 | 0.256112 | − | 0.966647i | \(-0.417559\pi\) | ||||
0.256112 | + | 0.966647i | \(0.417559\pi\) | |||||||
\(468\) | −13.3611 | −0.617615 | ||||||||
\(469\) | −4.78941 | −0.221154 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.6512 | −0.490783 | ||||||||
\(472\) | −25.0351 | −1.15234 | ||||||||
\(473\) | 19.7496 | 0.908088 | ||||||||
\(474\) | −38.3877 | −1.76320 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 17.8948 | 0.820207 | ||||||||
\(477\) | −10.3790 | −0.475224 | ||||||||
\(478\) | 15.5530 | 0.711378 | ||||||||
\(479\) | −9.72149 | −0.444186 | −0.222093 | − | 0.975025i | \(-0.571289\pi\) | ||||
−0.222093 | + | 0.975025i | \(0.571289\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 29.0138 | 1.32292 | ||||||||
\(482\) | −49.3527 | −2.24795 | ||||||||
\(483\) | −1.44312 | −0.0656644 | ||||||||
\(484\) | −9.19657 | −0.418026 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.30790 | −0.104688 | ||||||||
\(487\) | 22.1252 | 1.00259 | 0.501294 | − | 0.865277i | \(-0.332857\pi\) | ||||
0.501294 | + | 0.865277i | \(0.332857\pi\) | |||||||
\(488\) | −22.0032 | −0.996038 | ||||||||
\(489\) | 9.61416 | 0.434767 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.80744 | −0.126698 | −0.0633490 | − | 0.997991i | \(-0.520178\pi\) | ||||
−0.0633490 | + | 0.997991i | \(0.520178\pi\) | |||||||
\(492\) | −25.1340 | −1.13313 | ||||||||
\(493\) | 8.63293 | 0.388808 | ||||||||
\(494\) | 72.8729 | 3.27871 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.01774 | 0.135500 | ||||||||
\(497\) | −9.76771 | −0.438142 | ||||||||
\(498\) | 14.5722 | 0.652995 | ||||||||
\(499\) | 35.0285 | 1.56809 | 0.784045 | − | 0.620703i | \(-0.213153\pi\) | ||||
0.784045 | + | 0.620703i | \(0.213153\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.59100 | −0.249787 | ||||||||
\(502\) | 36.4646 | 1.62749 | ||||||||
\(503\) | −11.5993 | −0.517187 | −0.258593 | − | 0.965986i | \(-0.583259\pi\) | ||||
−0.258593 | + | 0.965986i | \(0.583259\pi\) | |||||||
\(504\) | −2.63347 | −0.117304 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −11.1103 | −0.493911 | ||||||||
\(507\) | −3.13363 | −0.139169 | ||||||||
\(508\) | −41.4530 | −1.83918 | ||||||||
\(509\) | 29.3580 | 1.30127 | 0.650636 | − | 0.759390i | \(-0.274502\pi\) | ||||
0.650636 | + | 0.759390i | \(0.274502\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.41633 | −0.151130 | ||||||||
\(512\) | −4.65465 | −0.205708 | ||||||||
\(513\) | 7.86109 | 0.347076 | ||||||||
\(514\) | 19.2568 | 0.849382 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −22.8925 | −1.00779 | ||||||||
\(517\) | −2.86972 | −0.126210 | ||||||||
\(518\) | 14.3414 | 0.630125 | ||||||||
\(519\) | 12.2528 | 0.537837 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.8903 | −1.00284 | −0.501421 | − | 0.865203i | \(-0.667189\pi\) | ||||
−0.501421 | + | 0.865203i | \(0.667189\pi\) | |||||||
\(522\) | −3.18610 | −0.139452 | ||||||||
\(523\) | −34.8070 | −1.52200 | −0.761001 | − | 0.648751i | \(-0.775292\pi\) | ||||
−0.761001 | + | 0.648751i | \(0.775292\pi\) | |||||||
\(524\) | 47.7331 | 2.08523 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 23.2428 | 1.01343 | ||||||||
\(527\) | −45.7872 | −1.99452 | ||||||||
\(528\) | −1.18275 | −0.0514726 | ||||||||
\(529\) | −20.1859 | −0.877649 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.17819 | −0.354903 | ||||||||
\(532\) | 22.4954 | 0.975299 | ||||||||
\(533\) | −30.3496 | −1.31459 | ||||||||
\(534\) | 18.9563 | 0.820321 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 17.0427 | 0.736132 | ||||||||
\(537\) | 26.0992 | 1.12626 | ||||||||
\(538\) | 30.3469 | 1.30835 | ||||||||
\(539\) | −17.9642 | −0.773775 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.3915 | −1.09167 | −0.545833 | − | 0.837894i | \(-0.683787\pi\) | ||||
−0.545833 | + | 0.837894i | \(0.683787\pi\) | |||||||
\(542\) | 17.9336 | 0.770314 | ||||||||
\(543\) | −11.0691 | −0.475021 | ||||||||
\(544\) | 32.3377 | 1.38647 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −7.97478 | −0.341289 | ||||||||
\(547\) | 16.5226 | 0.706457 | 0.353228 | − | 0.935537i | \(-0.385084\pi\) | ||||
0.353228 | + | 0.935537i | \(0.385084\pi\) | |||||||
\(548\) | 12.4550 | 0.532053 | ||||||||
\(549\) | −7.18776 | −0.306766 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.8524 | 0.462327 | ||||||||
\(552\) | 5.13524 | 0.218570 | ||||||||
\(553\) | −14.3090 | −0.608482 | ||||||||
\(554\) | −7.71429 | −0.327749 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.78915 | 0.0758769 | ||||||||
\(557\) | −44.1449 | −1.87048 | −0.935240 | − | 0.354014i | \(-0.884817\pi\) | ||||
−0.935240 | + | 0.354014i | \(0.884817\pi\) | |||||||
\(558\) | 16.8984 | 0.715364 | ||||||||
\(559\) | −27.6430 | −1.16917 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 17.9455 | 0.757660 | ||||||||
\(562\) | 30.2431 | 1.27573 | ||||||||
\(563\) | −23.5370 | −0.991968 | −0.495984 | − | 0.868332i | \(-0.665193\pi\) | ||||
−0.495984 | + | 0.868332i | \(0.665193\pi\) | |||||||
\(564\) | 3.32640 | 0.140067 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −72.4562 | −3.04556 | ||||||||
\(567\) | −0.860272 | −0.0361280 | ||||||||
\(568\) | 34.7576 | 1.45840 | ||||||||
\(569\) | −20.0449 | −0.840326 | −0.420163 | − | 0.907449i | \(-0.638027\pi\) | ||||
−0.420163 | + | 0.907449i | \(0.638027\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.33472 | −0.223251 | −0.111625 | − | 0.993750i | \(-0.535606\pi\) | ||||
−0.111625 | + | 0.993750i | \(0.535606\pi\) | |||||||
\(572\) | −38.3425 | −1.60318 | ||||||||
\(573\) | 1.50035 | 0.0626779 | ||||||||
\(574\) | −15.0017 | −0.626158 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −12.7589 | −0.531622 | ||||||||
\(577\) | −32.3381 | −1.34625 | −0.673125 | − | 0.739528i | \(-0.735049\pi\) | ||||
−0.673125 | + | 0.739528i | \(0.735049\pi\) | |||||||
\(578\) | 51.0162 | 2.12199 | ||||||||
\(579\) | −17.4657 | −0.725852 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.43179 | 0.225349 | ||||||||
\(582\) | −30.4624 | −1.26271 | ||||||||
\(583\) | −29.7849 | −1.23357 | ||||||||
\(584\) | 12.1567 | 0.503049 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −37.3760 | −1.54399 | ||||||||
\(587\) | 10.7947 | 0.445544 | 0.222772 | − | 0.974871i | \(-0.428489\pi\) | ||||
0.222772 | + | 0.974871i | \(0.428489\pi\) | |||||||
\(588\) | 20.8231 | 0.858728 | ||||||||
\(589\) | −57.5586 | −2.37166 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −21.9598 | −0.903305 | ||||||||
\(592\) | −2.97710 | −0.122358 | ||||||||
\(593\) | −14.7449 | −0.605501 | −0.302751 | − | 0.953070i | \(-0.597905\pi\) | ||||
−0.302751 | + | 0.953070i | \(0.597905\pi\) | |||||||
\(594\) | −6.62302 | −0.271746 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 46.4564 | 1.90293 | ||||||||
\(597\) | 10.8996 | 0.446091 | ||||||||
\(598\) | 15.5507 | 0.635917 | ||||||||
\(599\) | −20.3969 | −0.833395 | −0.416698 | − | 0.909045i | \(-0.636813\pi\) | ||||
−0.416698 | + | 0.909045i | \(0.636813\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.2300 | −1.39627 | −0.698135 | − | 0.715966i | \(-0.745986\pi\) | ||||
−0.698135 | + | 0.715966i | \(0.745986\pi\) | |||||||
\(602\) | −13.6638 | −0.556895 | ||||||||
\(603\) | 5.56732 | 0.226719 | ||||||||
\(604\) | −61.6920 | −2.51021 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 43.1733 | 1.75379 | ||||||||
\(607\) | −48.2028 | −1.95649 | −0.978245 | − | 0.207451i | \(-0.933483\pi\) | ||||
−0.978245 | + | 0.207451i | \(0.933483\pi\) | |||||||
\(608\) | 40.6514 | 1.64863 | ||||||||
\(609\) | −1.18762 | −0.0481248 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.01667 | 0.162497 | ||||||||
\(612\) | −20.8013 | −0.840844 | ||||||||
\(613\) | −20.9737 | −0.847119 | −0.423559 | − | 0.905868i | \(-0.639219\pi\) | ||||
−0.423559 | + | 0.905868i | \(0.639219\pi\) | |||||||
\(614\) | −59.6881 | −2.40882 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.55731 | −0.304493 | ||||||||
\(617\) | −22.6650 | −0.912458 | −0.456229 | − | 0.889862i | \(-0.650800\pi\) | ||||
−0.456229 | + | 0.889862i | \(0.650800\pi\) | |||||||
\(618\) | 15.6667 | 0.630208 | ||||||||
\(619\) | 21.2811 | 0.855360 | 0.427680 | − | 0.903930i | \(-0.359331\pi\) | ||||
0.427680 | + | 0.903930i | \(0.359331\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.67752 | 0.0673166 | ||||||||
\(622\) | 24.3505 | 0.976366 | ||||||||
\(623\) | 7.06599 | 0.283093 | ||||||||
\(624\) | 1.65546 | 0.0662716 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −30.8162 | −1.23166 | ||||||||
\(627\) | 22.5591 | 0.900925 | ||||||||
\(628\) | 35.4303 | 1.41382 | ||||||||
\(629\) | 45.1706 | 1.80107 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −39.3678 | −1.56721 | −0.783603 | − | 0.621261i | \(-0.786621\pi\) | ||||
−0.783603 | + | 0.621261i | \(0.786621\pi\) | |||||||
\(632\) | 50.9175 | 2.02539 | ||||||||
\(633\) | 13.5183 | 0.537305 | ||||||||
\(634\) | −6.63033 | −0.263324 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 34.5249 | 1.36900 | ||||||||
\(637\) | 25.1441 | 0.996244 | ||||||||
\(638\) | −9.14320 | −0.361983 | ||||||||
\(639\) | 11.3542 | 0.449166 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.7640 | 1.01762 | 0.508808 | − | 0.860880i | \(-0.330086\pi\) | ||||
0.508808 | + | 0.860880i | \(0.330086\pi\) | |||||||
\(642\) | 28.6655 | 1.13134 | ||||||||
\(643\) | 18.9260 | 0.746368 | 0.373184 | − | 0.927757i | \(-0.378266\pi\) | ||||
0.373184 | + | 0.927757i | \(0.378266\pi\) | |||||||
\(644\) | 4.80041 | 0.189163 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 113.453 | 4.46375 | ||||||||
\(647\) | −25.3575 | −0.996908 | −0.498454 | − | 0.866916i | \(-0.666099\pi\) | ||||
−0.498454 | + | 0.866916i | \(0.666099\pi\) | |||||||
\(648\) | 3.06120 | 0.120255 | ||||||||
\(649\) | −23.4691 | −0.921243 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.29888 | 0.246872 | ||||||||
\(652\) | −31.9806 | −1.25246 | ||||||||
\(653\) | 4.84804 | 0.189718 | 0.0948592 | − | 0.995491i | \(-0.469760\pi\) | ||||
0.0948592 | + | 0.995491i | \(0.469760\pi\) | |||||||
\(654\) | −9.93024 | −0.388303 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.11416 | 0.121587 | ||||||||
\(657\) | 3.97123 | 0.154932 | ||||||||
\(658\) | 1.98542 | 0.0773998 | ||||||||
\(659\) | 19.1497 | 0.745966 | 0.372983 | − | 0.927838i | \(-0.378335\pi\) | ||||
0.372983 | + | 0.927838i | \(0.378335\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.6815 | 0.843313 | 0.421656 | − | 0.906756i | \(-0.361449\pi\) | ||||
0.421656 | + | 0.906756i | \(0.361449\pi\) | |||||||
\(662\) | 62.0715 | 2.41248 | ||||||||
\(663\) | −25.1178 | −0.975496 | ||||||||
\(664\) | −19.3286 | −0.750094 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −16.6708 | −0.645980 | ||||||||
\(667\) | 2.31585 | 0.0896700 | ||||||||
\(668\) | 18.5979 | 0.719575 | ||||||||
\(669\) | 3.42274 | 0.132331 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20.6268 | −0.796290 | ||||||||
\(672\) | −4.44865 | −0.171610 | ||||||||
\(673\) | 3.54925 | 0.136813 | 0.0684067 | − | 0.997658i | \(-0.478208\pi\) | ||||
0.0684067 | + | 0.997658i | \(0.478208\pi\) | |||||||
\(674\) | −12.8406 | −0.494600 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.4237 | 0.400912 | ||||||||
\(677\) | −3.34037 | −0.128381 | −0.0641905 | − | 0.997938i | \(-0.520447\pi\) | ||||
−0.0641905 | + | 0.997938i | \(0.520447\pi\) | |||||||
\(678\) | −21.8688 | −0.839866 | ||||||||
\(679\) | −11.3549 | −0.435761 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 26.8967 | 1.03068 | ||||||||
\(682\) | 48.4935 | 1.85691 | ||||||||
\(683\) | −27.5303 | −1.05342 | −0.526708 | − | 0.850046i | \(-0.676574\pi\) | ||||
−0.526708 | + | 0.850046i | \(0.676574\pi\) | |||||||
\(684\) | −26.1492 | −0.999838 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 26.3266 | 1.00515 | ||||||||
\(687\) | −10.5653 | −0.403090 | ||||||||
\(688\) | 2.83644 | 0.108138 | ||||||||
\(689\) | 41.6892 | 1.58823 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.9214 | −1.10022 | −0.550111 | − | 0.835092i | \(-0.685414\pi\) | ||||
−0.550111 | + | 0.835092i | \(0.685414\pi\) | |||||||
\(692\) | −40.7577 | −1.54937 | ||||||||
\(693\) | −2.46874 | −0.0937796 | ||||||||
\(694\) | 53.4689 | 2.02965 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4.22605 | 0.160188 | ||||||||
\(697\) | −47.2501 | −1.78973 | ||||||||
\(698\) | 0.311890 | 0.0118052 | ||||||||
\(699\) | −5.05163 | −0.191070 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.5099 | −0.963496 | −0.481748 | − | 0.876310i | \(-0.659998\pi\) | ||||
−0.481748 | + | 0.876310i | \(0.659998\pi\) | |||||||
\(702\) | 9.27007 | 0.349876 | ||||||||
\(703\) | 56.7835 | 2.14163 | ||||||||
\(704\) | −36.6145 | −1.37996 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 66.9036 | 2.51795 | ||||||||
\(707\) | 16.0929 | 0.605235 | ||||||||
\(708\) | 27.2040 | 1.02239 | ||||||||
\(709\) | −21.7987 | −0.818667 | −0.409334 | − | 0.912385i | \(-0.634239\pi\) | ||||
−0.409334 | + | 0.912385i | \(0.634239\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 16.6332 | 0.623792 | ||||||||
\(712\) | −25.1437 | −0.942301 | ||||||||
\(713\) | −12.2827 | −0.459993 | ||||||||
\(714\) | −12.4156 | −0.464644 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −86.8165 | −3.24448 | ||||||||
\(717\) | −6.73903 | −0.251674 | ||||||||
\(718\) | −30.2551 | −1.12911 | ||||||||
\(719\) | −5.07665 | −0.189327 | −0.0946636 | − | 0.995509i | \(-0.530178\pi\) | ||||
−0.0946636 | + | 0.995509i | \(0.530178\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.83979 | 0.217485 | ||||||||
\(722\) | 98.7707 | 3.67587 | ||||||||
\(723\) | 21.3842 | 0.795288 | ||||||||
\(724\) | 36.8203 | 1.36842 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 6.38069 | 0.236810 | ||||||||
\(727\) | 46.8976 | 1.73934 | 0.869668 | − | 0.493638i | \(-0.164333\pi\) | ||||
0.869668 | + | 0.493638i | \(0.164333\pi\) | |||||||
\(728\) | 10.5778 | 0.392038 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −43.0363 | −1.59176 | ||||||||
\(732\) | 23.9094 | 0.883716 | ||||||||
\(733\) | −8.55200 | −0.315875 | −0.157938 | − | 0.987449i | \(-0.550484\pi\) | ||||
−0.157938 | + | 0.987449i | \(0.550484\pi\) | |||||||
\(734\) | 14.9653 | 0.552378 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.67482 | 0.319758 | ||||||||
\(737\) | 15.9766 | 0.588507 | ||||||||
\(738\) | 17.4383 | 0.641912 | ||||||||
\(739\) | 33.0654 | 1.21633 | 0.608166 | − | 0.793810i | \(-0.291906\pi\) | ||||
0.608166 | + | 0.793810i | \(0.291906\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −31.5754 | −1.15995 | ||||||||
\(742\) | 20.6068 | 0.756499 | ||||||||
\(743\) | 16.2284 | 0.595362 | 0.297681 | − | 0.954665i | \(-0.403787\pi\) | ||||
0.297681 | + | 0.954665i | \(0.403787\pi\) | |||||||
\(744\) | −22.4140 | −0.821738 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 54.6534 | 2.00100 | ||||||||
\(747\) | −6.31404 | −0.231019 | ||||||||
\(748\) | −59.6939 | −2.18263 | ||||||||
\(749\) | 10.6851 | 0.390425 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.3312 | −1.07031 | −0.535155 | − | 0.844754i | \(-0.679747\pi\) | ||||
−0.535155 | + | 0.844754i | \(0.679747\pi\) | |||||||
\(752\) | −0.412149 | −0.0150295 | ||||||||
\(753\) | −15.7999 | −0.575781 | ||||||||
\(754\) | 12.7975 | 0.466057 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.86161 | 0.104076 | ||||||||
\(757\) | 18.9100 | 0.687295 | 0.343647 | − | 0.939099i | \(-0.388338\pi\) | ||||
0.343647 | + | 0.939099i | \(0.388338\pi\) | |||||||
\(758\) | 17.1044 | 0.621259 | ||||||||
\(759\) | 4.81401 | 0.174738 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 39.2493 | 1.42279 | 0.711393 | − | 0.702794i | \(-0.248065\pi\) | ||||
0.711393 | + | 0.702794i | \(0.248065\pi\) | |||||||
\(762\) | 28.7606 | 1.04189 | ||||||||
\(763\) | −3.70151 | −0.134004 | ||||||||
\(764\) | −4.99076 | −0.180559 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 19.4000 | 0.700952 | ||||||||
\(767\) | 32.8491 | 1.18611 | ||||||||
\(768\) | 18.5721 | 0.670162 | ||||||||
\(769\) | −38.5999 | −1.39195 | −0.695973 | − | 0.718068i | \(-0.745027\pi\) | ||||
−0.695973 | + | 0.718068i | \(0.745027\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.34387 | −0.300497 | ||||||||
\(772\) | 58.0981 | 2.09100 | ||||||||
\(773\) | 51.5701 | 1.85485 | 0.927424 | − | 0.374012i | \(-0.122018\pi\) | ||||
0.927424 | + | 0.374012i | \(0.122018\pi\) | |||||||
\(774\) | 15.8831 | 0.570907 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 40.4055 | 1.45047 | ||||||||
\(777\) | −6.21405 | −0.222928 | ||||||||
\(778\) | −35.1083 | −1.25869 | ||||||||
\(779\) | −59.3977 | −2.12814 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.5834 | 1.16593 | ||||||||
\(782\) | 24.2104 | 0.865761 | ||||||||
\(783\) | 1.38052 | 0.0493357 | ||||||||
\(784\) | −2.58002 | −0.0921437 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −33.1178 | −1.18127 | ||||||||
\(787\) | −5.02336 | −0.179064 | −0.0895318 | − | 0.995984i | \(-0.528537\pi\) | ||||
−0.0895318 | + | 0.995984i | \(0.528537\pi\) | |||||||
\(788\) | 73.0471 | 2.60220 | ||||||||
\(789\) | −10.0710 | −0.358536 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.15162 | −0.289838 | ||||||||
\(792\) | 8.78479 | 0.312154 | ||||||||
\(793\) | 28.8708 | 1.02523 | ||||||||
\(794\) | −36.5674 | −1.29773 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −36.2565 | −1.28508 | ||||||||
\(797\) | 44.4893 | 1.57589 | 0.787945 | − | 0.615745i | \(-0.211145\pi\) | ||||
0.787945 | + | 0.615745i | \(0.211145\pi\) | |||||||
\(798\) | −15.6076 | −0.552503 | ||||||||
\(799\) | 6.25340 | 0.221229 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.21367 | −0.290216 | ||||||||
\(802\) | 61.1327 | 2.15867 | ||||||||
\(803\) | 11.3963 | 0.402167 | ||||||||
\(804\) | −18.5191 | −0.653120 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −67.8751 | −2.39080 | ||||||||
\(807\) | −13.1491 | −0.462872 | ||||||||
\(808\) | −57.2651 | −2.01458 | ||||||||
\(809\) | −52.3087 | −1.83908 | −0.919538 | − | 0.393002i | \(-0.871437\pi\) | ||||
−0.919538 | + | 0.393002i | \(0.871437\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.6701 | 0.725825 | 0.362912 | − | 0.931823i | \(-0.381782\pi\) | ||||
0.362912 | + | 0.931823i | \(0.381782\pi\) | |||||||
\(812\) | 3.95051 | 0.138636 | ||||||||
\(813\) | −7.77052 | −0.272524 | ||||||||
\(814\) | −47.8405 | −1.67681 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.57733 | 0.0902246 | ||||||||
\(817\) | −54.1006 | −1.89274 | ||||||||
\(818\) | −34.0450 | −1.19035 | ||||||||
\(819\) | 3.45543 | 0.120742 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.78712 | 0.0972713 | 0.0486356 | − | 0.998817i | \(-0.484513\pi\) | ||||
0.0486356 | + | 0.998817i | \(0.484513\pi\) | |||||||
\(822\) | −8.64146 | −0.301406 | ||||||||
\(823\) | −32.9272 | −1.14777 | −0.573886 | − | 0.818935i | \(-0.694565\pi\) | ||||
−0.573886 | + | 0.818935i | \(0.694565\pi\) | |||||||
\(824\) | −20.7804 | −0.723919 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 16.2372 | 0.564963 | ||||||||
\(827\) | 15.0311 | 0.522681 | 0.261341 | − | 0.965247i | \(-0.415835\pi\) | ||||
0.261341 | + | 0.965247i | \(0.415835\pi\) | |||||||
\(828\) | −5.58011 | −0.193922 | ||||||||
\(829\) | −42.7779 | −1.48574 | −0.742869 | − | 0.669436i | \(-0.766536\pi\) | ||||
−0.742869 | + | 0.669436i | \(0.766536\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.34256 | 0.115952 | ||||||||
\(832\) | 51.2484 | 1.77672 | ||||||||
\(833\) | 39.1459 | 1.35632 | ||||||||
\(834\) | −1.24134 | −0.0429839 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −75.0407 | −2.59534 | ||||||||
\(837\) | −7.32196 | −0.253084 | ||||||||
\(838\) | 16.8776 | 0.583026 | ||||||||
\(839\) | −40.9986 | −1.41543 | −0.707714 | − | 0.706499i | \(-0.750273\pi\) | ||||
−0.707714 | + | 0.706499i | \(0.750273\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.0942 | −0.934282 | ||||||||
\(842\) | −3.81931 | −0.131622 | ||||||||
\(843\) | −13.1042 | −0.451331 | ||||||||
\(844\) | −44.9674 | −1.54784 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.30790 | −0.0793472 | ||||||||
\(847\) | 2.37841 | 0.0817231 | ||||||||
\(848\) | −4.27771 | −0.146897 | ||||||||
\(849\) | 31.3949 | 1.07747 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.1173 | 0.415377 | ||||||||
\(852\) | −37.7687 | −1.29393 | ||||||||
\(853\) | −3.77117 | −0.129122 | −0.0645611 | − | 0.997914i | \(-0.520565\pi\) | ||||
−0.0645611 | + | 0.997914i | \(0.520565\pi\) | |||||||
\(854\) | 14.2707 | 0.488334 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −38.0220 | −1.29957 | ||||||||
\(857\) | 22.5822 | 0.771395 | 0.385697 | − | 0.922625i | \(-0.373961\pi\) | ||||
0.385697 | + | 0.922625i | \(0.373961\pi\) | |||||||
\(858\) | 26.6025 | 0.908194 | ||||||||
\(859\) | 35.9250 | 1.22574 | 0.612872 | − | 0.790182i | \(-0.290014\pi\) | ||||
0.612872 | + | 0.790182i | \(0.290014\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.50014 | 0.221524 | ||||||||
\(862\) | 19.8791 | 0.677085 | ||||||||
\(863\) | 17.8731 | 0.608409 | 0.304204 | − | 0.952607i | \(-0.401609\pi\) | ||||
0.304204 | + | 0.952607i | \(0.401609\pi\) | |||||||
\(864\) | 5.17121 | 0.175928 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.09456 | −0.0371948 | ||||||||
\(867\) | −22.1050 | −0.750726 | ||||||||
\(868\) | −20.9526 | −0.711178 | ||||||||
\(869\) | 47.7325 | 1.61921 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.3621 | −0.757710 | ||||||||
\(872\) | 13.1715 | 0.446043 | ||||||||
\(873\) | 13.1992 | 0.446725 | ||||||||
\(874\) | 30.4346 | 1.02947 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −13.2099 | −0.446321 | ||||||||
\(877\) | −5.96001 | −0.201255 | −0.100628 | − | 0.994924i | \(-0.532085\pi\) | ||||
−0.100628 | + | 0.994924i | \(0.532085\pi\) | |||||||
\(878\) | 50.2594 | 1.69617 | ||||||||
\(879\) | 16.1948 | 0.546237 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.9463 | 0.436173 | 0.218087 | − | 0.975929i | \(-0.430018\pi\) | ||||
0.218087 | + | 0.975929i | \(0.430018\pi\) | |||||||
\(882\) | −14.4473 | −0.486466 | ||||||||
\(883\) | −42.3233 | −1.42429 | −0.712146 | − | 0.702031i | \(-0.752277\pi\) | ||||
−0.712146 | + | 0.702031i | \(0.752277\pi\) | |||||||
\(884\) | 83.5520 | 2.81016 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −71.4599 | −2.40074 | ||||||||
\(887\) | −7.08289 | −0.237820 | −0.118910 | − | 0.992905i | \(-0.537940\pi\) | ||||
−0.118910 | + | 0.992905i | \(0.537940\pi\) | |||||||
\(888\) | 22.1122 | 0.742036 | ||||||||
\(889\) | 10.7205 | 0.359555 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.86972 | 0.0961392 | ||||||||
\(892\) | −11.3854 | −0.381212 | ||||||||
\(893\) | 7.86109 | 0.263061 | ||||||||
\(894\) | −32.2321 | −1.07800 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 16.4346 | 0.549040 | ||||||||
\(897\) | −6.73805 | −0.224977 | ||||||||
\(898\) | 44.6734 | 1.49077 | ||||||||
\(899\) | −10.1081 | −0.337124 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 64.9043 | 2.16228 | ||||||||
\(902\) | 50.0430 | 1.66625 | ||||||||
\(903\) | 5.92045 | 0.197020 | ||||||||
\(904\) | 29.0068 | 0.964753 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 42.8027 | 1.42202 | ||||||||
\(907\) | 20.5590 | 0.682652 | 0.341326 | − | 0.939945i | \(-0.389124\pi\) | ||||
0.341326 | + | 0.939945i | \(0.389124\pi\) | |||||||
\(908\) | −89.4691 | −2.96914 | ||||||||
\(909\) | −18.7067 | −0.620463 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −55.6550 | −1.84393 | −0.921966 | − | 0.387271i | \(-0.873418\pi\) | ||||
−0.921966 | + | 0.387271i | \(0.873418\pi\) | |||||||
\(912\) | 3.23994 | 0.107285 | ||||||||
\(913\) | −18.1195 | −0.599669 | ||||||||
\(914\) | 30.9289 | 1.02304 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 35.1444 | 1.16120 | ||||||||
\(917\) | −12.3447 | −0.407658 | ||||||||
\(918\) | 14.4322 | 0.476334 | ||||||||
\(919\) | −51.2264 | −1.68980 | −0.844901 | − | 0.534922i | \(-0.820341\pi\) | ||||
−0.844901 | + | 0.534922i | \(0.820341\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 25.8625 | 0.852199 | ||||||||
\(922\) | 38.4238 | 1.26542 | ||||||||
\(923\) | −45.6061 | −1.50114 | ||||||||
\(924\) | 8.21202 | 0.270155 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 14.0669 | 0.462268 | ||||||||
\(927\) | −6.78830 | −0.222957 | ||||||||
\(928\) | 7.13895 | 0.234348 | ||||||||
\(929\) | 5.49756 | 0.180369 | 0.0901846 | − | 0.995925i | \(-0.471254\pi\) | ||||
0.0901846 | + | 0.995925i | \(0.471254\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 49.2099 | 1.61279 | ||||||||
\(932\) | 16.8038 | 0.550426 | ||||||||
\(933\) | −10.5509 | −0.345422 | ||||||||
\(934\) | 25.5467 | 0.835914 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −12.2958 | −0.401902 | ||||||||
\(937\) | 9.57490 | 0.312798 | 0.156399 | − | 0.987694i | \(-0.450011\pi\) | ||||
0.156399 | + | 0.987694i | \(0.450011\pi\) | |||||||
\(938\) | −11.0535 | −0.360909 | ||||||||
\(939\) | 13.3525 | 0.435742 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.6504 | 0.575387 | 0.287694 | − | 0.957722i | \(-0.407111\pi\) | ||||
0.287694 | + | 0.957722i | \(0.407111\pi\) | |||||||
\(942\) | −24.5820 | −0.800924 | ||||||||
\(943\) | −12.6752 | −0.412761 | ||||||||
\(944\) | −3.37063 | −0.109705 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 45.5801 | 1.48194 | ||||||||
\(947\) | −6.29609 | −0.204595 | −0.102298 | − | 0.994754i | \(-0.532619\pi\) | ||||
−0.102298 | + | 0.994754i | \(0.532619\pi\) | |||||||
\(948\) | −55.3286 | −1.79699 | ||||||||
\(949\) | −15.9511 | −0.517795 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.87288 | 0.0931596 | ||||||||
\(952\) | 16.4681 | 0.533735 | ||||||||
\(953\) | 18.1746 | 0.588734 | 0.294367 | − | 0.955692i | \(-0.404891\pi\) | ||||
0.294367 | + | 0.955692i | \(0.404891\pi\) | |||||||
\(954\) | −23.9538 | −0.775533 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 22.4167 | 0.725009 | ||||||||
\(957\) | 3.96170 | 0.128064 | ||||||||
\(958\) | −22.4362 | −0.724881 | ||||||||
\(959\) | −3.22111 | −0.104015 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.6111 | 0.729391 | ||||||||
\(962\) | 66.9610 | 2.15891 | ||||||||
\(963\) | −12.4206 | −0.400249 | ||||||||
\(964\) | −71.1326 | −2.29103 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −3.33059 | −0.107160 | ||||||||
\(967\) | 1.90365 | 0.0612173 | 0.0306086 | − | 0.999531i | \(-0.490255\pi\) | ||||
0.0306086 | + | 0.999531i | \(0.490255\pi\) | |||||||
\(968\) | −8.46337 | −0.272023 | ||||||||
\(969\) | −49.1586 | −1.57920 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −38.9716 | −1.25066 | −0.625328 | − | 0.780362i | \(-0.715035\pi\) | ||||
−0.625328 | + | 0.780362i | \(0.715035\pi\) | |||||||
\(972\) | −3.32640 | −0.106694 | ||||||||
\(973\) | −0.462709 | −0.0148338 | ||||||||
\(974\) | 51.0627 | 1.63616 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.96242 | −0.0948249 | ||||||||
\(977\) | −21.3069 | −0.681669 | −0.340834 | − | 0.940123i | \(-0.610710\pi\) | ||||
−0.340834 | + | 0.940123i | \(0.610710\pi\) | |||||||
\(978\) | 22.1885 | 0.709511 | ||||||||
\(979\) | −23.5709 | −0.753330 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.30272 | 0.137375 | ||||||||
\(982\) | −6.47929 | −0.206763 | ||||||||
\(983\) | 20.2703 | 0.646523 | 0.323262 | − | 0.946310i | \(-0.395221\pi\) | ||||
0.323262 | + | 0.946310i | \(0.395221\pi\) | |||||||
\(984\) | −23.1302 | −0.737364 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 19.9239 | 0.634508 | ||||||||
\(987\) | −0.860272 | −0.0273828 | ||||||||
\(988\) | 105.033 | 3.34153 | ||||||||
\(989\) | −11.5448 | −0.367104 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −35.8010 | −1.13726 | −0.568628 | − | 0.822595i | \(-0.692526\pi\) | ||||
−0.568628 | + | 0.822595i | \(0.692526\pi\) | |||||||
\(992\) | −37.8634 | −1.20216 | ||||||||
\(993\) | −26.8952 | −0.853494 | ||||||||
\(994\) | −22.5429 | −0.715018 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 21.0030 | 0.665507 | ||||||||
\(997\) | 42.5205 | 1.34664 | 0.673319 | − | 0.739352i | \(-0.264868\pi\) | ||||
0.673319 | + | 0.739352i | \(0.264868\pi\) | |||||||
\(998\) | 80.8423 | 2.55902 | ||||||||
\(999\) | 7.22336 | 0.228537 |
(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 | 3525.2.a.ba.1.7 | yes | 7 | |
5.4 | even | 2 | 3525.2.a.z.1.1 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3525.2.a.z.1.1 | ✓ | 7 | 5.4 | even | 2 | ||
3525.2.a.ba.1.7 | yes | 7 | 1.1 | even | 1 | trivial |