Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8030,2,Mod(1,8030)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8030, 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("8030.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8030 = 2 \cdot 5 \cdot 11 \cdot 73 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8030.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: | \(64.1198728231\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 7 x^{14} - 6 x^{13} + 136 x^{12} - 149 x^{11} - 876 x^{10} + 1631 x^{9} + 2142 x^{8} - 5473 x^{7} - 1914 x^{6} + 7517 x^{5} + 392 x^{4} - 3966 x^{3} - 79 x^{2} + 491 x - 32 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Root | \(3.03129\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8030.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 3.03129 | 1.75012 | 0.875059 | − | 0.484017i | \(-0.160823\pi\) | ||||
0.875059 | + | 0.484017i | \(0.160823\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 3.03129 | 1.23752 | ||||||||
\(7\) | 3.50775 | 1.32580 | 0.662902 | − | 0.748706i | \(-0.269325\pi\) | ||||
0.662902 | + | 0.748706i | \(0.269325\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 6.18873 | 2.06291 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 3.03129 | 0.875059 | ||||||||
\(13\) | −6.77606 | −1.87934 | −0.939671 | − | 0.342080i | \(-0.888869\pi\) | ||||
−0.939671 | + | 0.342080i | \(0.888869\pi\) | |||||||
\(14\) | 3.50775 | 0.937485 | ||||||||
\(15\) | −3.03129 | −0.782676 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.63062 | 0.395483 | 0.197741 | − | 0.980254i | \(-0.436639\pi\) | ||||
0.197741 | + | 0.980254i | \(0.436639\pi\) | |||||||
\(18\) | 6.18873 | 1.45870 | ||||||||
\(19\) | 7.46655 | 1.71294 | 0.856472 | − | 0.516193i | \(-0.172651\pi\) | ||||
0.856472 | + | 0.516193i | \(0.172651\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 10.6330 | 2.32031 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 3.16743 | 0.660454 | 0.330227 | − | 0.943902i | \(-0.392875\pi\) | ||||
0.330227 | + | 0.943902i | \(0.392875\pi\) | |||||||
\(24\) | 3.03129 | 0.618760 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −6.77606 | −1.32890 | ||||||||
\(27\) | 9.66598 | 1.86022 | ||||||||
\(28\) | 3.50775 | 0.662902 | ||||||||
\(29\) | 5.19277 | 0.964273 | 0.482137 | − | 0.876096i | \(-0.339861\pi\) | ||||
0.482137 | + | 0.876096i | \(0.339861\pi\) | |||||||
\(30\) | −3.03129 | −0.553436 | ||||||||
\(31\) | −3.03853 | −0.545737 | −0.272868 | − | 0.962051i | \(-0.587972\pi\) | ||||
−0.272868 | + | 0.962051i | \(0.587972\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −3.03129 | −0.527680 | ||||||||
\(34\) | 1.63062 | 0.279649 | ||||||||
\(35\) | −3.50775 | −0.592917 | ||||||||
\(36\) | 6.18873 | 1.03146 | ||||||||
\(37\) | 11.5416 | 1.89743 | 0.948714 | − | 0.316135i | \(-0.102385\pi\) | ||||
0.948714 | + | 0.316135i | \(0.102385\pi\) | |||||||
\(38\) | 7.46655 | 1.21123 | ||||||||
\(39\) | −20.5402 | −3.28907 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −2.42690 | −0.379018 | −0.189509 | − | 0.981879i | \(-0.560690\pi\) | ||||
−0.189509 | + | 0.981879i | \(0.560690\pi\) | |||||||
\(42\) | 10.6330 | 1.64071 | ||||||||
\(43\) | −10.5318 | −1.60609 | −0.803046 | − | 0.595917i | \(-0.796789\pi\) | ||||
−0.803046 | + | 0.595917i | \(0.796789\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | −6.18873 | −0.922562 | ||||||||
\(46\) | 3.16743 | 0.467011 | ||||||||
\(47\) | 2.77614 | 0.404941 | 0.202470 | − | 0.979288i | \(-0.435103\pi\) | ||||
0.202470 | + | 0.979288i | \(0.435103\pi\) | |||||||
\(48\) | 3.03129 | 0.437529 | ||||||||
\(49\) | 5.30428 | 0.757754 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 4.94288 | 0.692141 | ||||||||
\(52\) | −6.77606 | −0.939671 | ||||||||
\(53\) | −12.7598 | −1.75270 | −0.876348 | − | 0.481679i | \(-0.840027\pi\) | ||||
−0.876348 | + | 0.481679i | \(0.840027\pi\) | |||||||
\(54\) | 9.66598 | 1.31537 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 3.50775 | 0.468742 | ||||||||
\(57\) | 22.6333 | 2.99785 | ||||||||
\(58\) | 5.19277 | 0.681844 | ||||||||
\(59\) | 4.64925 | 0.605281 | 0.302641 | − | 0.953105i | \(-0.402132\pi\) | ||||
0.302641 | + | 0.953105i | \(0.402132\pi\) | |||||||
\(60\) | −3.03129 | −0.391338 | ||||||||
\(61\) | −6.19293 | −0.792923 | −0.396462 | − | 0.918051i | \(-0.629762\pi\) | ||||
−0.396462 | + | 0.918051i | \(0.629762\pi\) | |||||||
\(62\) | −3.03853 | −0.385894 | ||||||||
\(63\) | 21.7085 | 2.73501 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.77606 | 0.840467 | ||||||||
\(66\) | −3.03129 | −0.373126 | ||||||||
\(67\) | 6.25363 | 0.764003 | 0.382001 | − | 0.924162i | \(-0.375235\pi\) | ||||
0.382001 | + | 0.924162i | \(0.375235\pi\) | |||||||
\(68\) | 1.63062 | 0.197741 | ||||||||
\(69\) | 9.60139 | 1.15587 | ||||||||
\(70\) | −3.50775 | −0.419256 | ||||||||
\(71\) | −6.63711 | −0.787680 | −0.393840 | − | 0.919179i | \(-0.628854\pi\) | ||||
−0.393840 | + | 0.919179i | \(0.628854\pi\) | |||||||
\(72\) | 6.18873 | 0.729349 | ||||||||
\(73\) | −1.00000 | −0.117041 | ||||||||
\(74\) | 11.5416 | 1.34168 | ||||||||
\(75\) | 3.03129 | 0.350023 | ||||||||
\(76\) | 7.46655 | 0.856472 | ||||||||
\(77\) | −3.50775 | −0.399745 | ||||||||
\(78\) | −20.5402 | −2.32572 | ||||||||
\(79\) | 10.3469 | 1.16412 | 0.582060 | − | 0.813146i | \(-0.302247\pi\) | ||||
0.582060 | + | 0.813146i | \(0.302247\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 10.7342 | 1.19269 | ||||||||
\(82\) | −2.42690 | −0.268006 | ||||||||
\(83\) | 9.45862 | 1.03822 | 0.519109 | − | 0.854708i | \(-0.326264\pi\) | ||||
0.519109 | + | 0.854708i | \(0.326264\pi\) | |||||||
\(84\) | 10.6330 | 1.16016 | ||||||||
\(85\) | −1.63062 | −0.176865 | ||||||||
\(86\) | −10.5318 | −1.13568 | ||||||||
\(87\) | 15.7408 | 1.68759 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −5.49478 | −0.582445 | −0.291223 | − | 0.956655i | \(-0.594062\pi\) | ||||
−0.291223 | + | 0.956655i | \(0.594062\pi\) | |||||||
\(90\) | −6.18873 | −0.652350 | ||||||||
\(91\) | −23.7687 | −2.49164 | ||||||||
\(92\) | 3.16743 | 0.330227 | ||||||||
\(93\) | −9.21069 | −0.955104 | ||||||||
\(94\) | 2.77614 | 0.286336 | ||||||||
\(95\) | −7.46655 | −0.766052 | ||||||||
\(96\) | 3.03129 | 0.309380 | ||||||||
\(97\) | −6.93289 | −0.703928 | −0.351964 | − | 0.936014i | \(-0.614486\pi\) | ||||
−0.351964 | + | 0.936014i | \(0.614486\pi\) | |||||||
\(98\) | 5.30428 | 0.535813 | ||||||||
\(99\) | −6.18873 | −0.621991 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −5.27322 | −0.524705 | −0.262353 | − | 0.964972i | \(-0.584498\pi\) | ||||
−0.262353 | + | 0.964972i | \(0.584498\pi\) | |||||||
\(102\) | 4.94288 | 0.489418 | ||||||||
\(103\) | 0.506930 | 0.0499493 | 0.0249746 | − | 0.999688i | \(-0.492049\pi\) | ||||
0.0249746 | + | 0.999688i | \(0.492049\pi\) | |||||||
\(104\) | −6.77606 | −0.664448 | ||||||||
\(105\) | −10.6330 | −1.03767 | ||||||||
\(106\) | −12.7598 | −1.23934 | ||||||||
\(107\) | 1.78929 | 0.172977 | 0.0864884 | − | 0.996253i | \(-0.472435\pi\) | ||||
0.0864884 | + | 0.996253i | \(0.472435\pi\) | |||||||
\(108\) | 9.66598 | 0.930109 | ||||||||
\(109\) | 8.93951 | 0.856250 | 0.428125 | − | 0.903720i | \(-0.359174\pi\) | ||||
0.428125 | + | 0.903720i | \(0.359174\pi\) | |||||||
\(110\) | 1.00000 | 0.0953463 | ||||||||
\(111\) | 34.9860 | 3.32072 | ||||||||
\(112\) | 3.50775 | 0.331451 | ||||||||
\(113\) | −17.5669 | −1.65256 | −0.826278 | − | 0.563263i | \(-0.809546\pi\) | ||||
−0.826278 | + | 0.563263i | \(0.809546\pi\) | |||||||
\(114\) | 22.6333 | 2.11980 | ||||||||
\(115\) | −3.16743 | −0.295364 | ||||||||
\(116\) | 5.19277 | 0.482137 | ||||||||
\(117\) | −41.9352 | −3.87691 | ||||||||
\(118\) | 4.64925 | 0.427998 | ||||||||
\(119\) | 5.71979 | 0.524332 | ||||||||
\(120\) | −3.03129 | −0.276718 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −6.19293 | −0.560681 | ||||||||
\(123\) | −7.35665 | −0.663327 | ||||||||
\(124\) | −3.03853 | −0.272868 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 21.7085 | 1.93395 | ||||||||
\(127\) | 8.76750 | 0.777990 | 0.388995 | − | 0.921240i | \(-0.372822\pi\) | ||||
0.388995 | + | 0.921240i | \(0.372822\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −31.9251 | −2.81085 | ||||||||
\(130\) | 6.77606 | 0.594300 | ||||||||
\(131\) | 10.0699 | 0.879813 | 0.439907 | − | 0.898044i | \(-0.355012\pi\) | ||||
0.439907 | + | 0.898044i | \(0.355012\pi\) | |||||||
\(132\) | −3.03129 | −0.263840 | ||||||||
\(133\) | 26.1908 | 2.27103 | ||||||||
\(134\) | 6.25363 | 0.540232 | ||||||||
\(135\) | −9.66598 | −0.831915 | ||||||||
\(136\) | 1.63062 | 0.139824 | ||||||||
\(137\) | −21.8423 | −1.86611 | −0.933055 | − | 0.359734i | \(-0.882868\pi\) | ||||
−0.933055 | + | 0.359734i | \(0.882868\pi\) | |||||||
\(138\) | 9.60139 | 0.817325 | ||||||||
\(139\) | −14.4697 | −1.22730 | −0.613652 | − | 0.789576i | \(-0.710300\pi\) | ||||
−0.613652 | + | 0.789576i | \(0.710300\pi\) | |||||||
\(140\) | −3.50775 | −0.296459 | ||||||||
\(141\) | 8.41528 | 0.708694 | ||||||||
\(142\) | −6.63711 | −0.556974 | ||||||||
\(143\) | 6.77606 | 0.566643 | ||||||||
\(144\) | 6.18873 | 0.515728 | ||||||||
\(145\) | −5.19277 | −0.431236 | ||||||||
\(146\) | −1.00000 | −0.0827606 | ||||||||
\(147\) | 16.0788 | 1.32616 | ||||||||
\(148\) | 11.5416 | 0.948714 | ||||||||
\(149\) | 22.4097 | 1.83588 | 0.917938 | − | 0.396724i | \(-0.129853\pi\) | ||||
0.917938 | + | 0.396724i | \(0.129853\pi\) | |||||||
\(150\) | 3.03129 | 0.247504 | ||||||||
\(151\) | −2.42552 | −0.197386 | −0.0986930 | − | 0.995118i | \(-0.531466\pi\) | ||||
−0.0986930 | + | 0.995118i | \(0.531466\pi\) | |||||||
\(152\) | 7.46655 | 0.605617 | ||||||||
\(153\) | 10.0915 | 0.815846 | ||||||||
\(154\) | −3.50775 | −0.282662 | ||||||||
\(155\) | 3.03853 | 0.244061 | ||||||||
\(156\) | −20.5402 | −1.64453 | ||||||||
\(157\) | 12.2085 | 0.974344 | 0.487172 | − | 0.873306i | \(-0.338028\pi\) | ||||
0.487172 | + | 0.873306i | \(0.338028\pi\) | |||||||
\(158\) | 10.3469 | 0.823158 | ||||||||
\(159\) | −38.6787 | −3.06742 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 11.1105 | 0.875632 | ||||||||
\(162\) | 10.7342 | 0.843359 | ||||||||
\(163\) | −16.8631 | −1.32082 | −0.660408 | − | 0.750907i | \(-0.729617\pi\) | ||||
−0.660408 | + | 0.750907i | \(0.729617\pi\) | |||||||
\(164\) | −2.42690 | −0.189509 | ||||||||
\(165\) | 3.03129 | 0.235986 | ||||||||
\(166\) | 9.45862 | 0.734132 | ||||||||
\(167\) | 15.2813 | 1.18250 | 0.591252 | − | 0.806487i | \(-0.298634\pi\) | ||||
0.591252 | + | 0.806487i | \(0.298634\pi\) | |||||||
\(168\) | 10.6330 | 0.820354 | ||||||||
\(169\) | 32.9150 | 2.53193 | ||||||||
\(170\) | −1.63062 | −0.125063 | ||||||||
\(171\) | 46.2085 | 3.53365 | ||||||||
\(172\) | −10.5318 | −0.803046 | ||||||||
\(173\) | −1.38794 | −0.105523 | −0.0527617 | − | 0.998607i | \(-0.516802\pi\) | ||||
−0.0527617 | + | 0.998607i | \(0.516802\pi\) | |||||||
\(174\) | 15.7408 | 1.19331 | ||||||||
\(175\) | 3.50775 | 0.265161 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 14.0932 | 1.05931 | ||||||||
\(178\) | −5.49478 | −0.411851 | ||||||||
\(179\) | −5.85001 | −0.437250 | −0.218625 | − | 0.975809i | \(-0.570157\pi\) | ||||
−0.218625 | + | 0.975809i | \(0.570157\pi\) | |||||||
\(180\) | −6.18873 | −0.461281 | ||||||||
\(181\) | 25.5379 | 1.89822 | 0.949110 | − | 0.314946i | \(-0.101986\pi\) | ||||
0.949110 | + | 0.314946i | \(0.101986\pi\) | |||||||
\(182\) | −23.7687 | −1.76185 | ||||||||
\(183\) | −18.7726 | −1.38771 | ||||||||
\(184\) | 3.16743 | 0.233506 | ||||||||
\(185\) | −11.5416 | −0.848556 | ||||||||
\(186\) | −9.21069 | −0.675360 | ||||||||
\(187\) | −1.63062 | −0.119243 | ||||||||
\(188\) | 2.77614 | 0.202470 | ||||||||
\(189\) | 33.9058 | 2.46628 | ||||||||
\(190\) | −7.46655 | −0.541680 | ||||||||
\(191\) | 17.5333 | 1.26867 | 0.634333 | − | 0.773060i | \(-0.281275\pi\) | ||||
0.634333 | + | 0.773060i | \(0.281275\pi\) | |||||||
\(192\) | 3.03129 | 0.218765 | ||||||||
\(193\) | −6.62499 | −0.476877 | −0.238439 | − | 0.971158i | \(-0.576636\pi\) | ||||
−0.238439 | + | 0.971158i | \(0.576636\pi\) | |||||||
\(194\) | −6.93289 | −0.497752 | ||||||||
\(195\) | 20.5402 | 1.47092 | ||||||||
\(196\) | 5.30428 | 0.378877 | ||||||||
\(197\) | 4.55572 | 0.324582 | 0.162291 | − | 0.986743i | \(-0.448112\pi\) | ||||
0.162291 | + | 0.986743i | \(0.448112\pi\) | |||||||
\(198\) | −6.18873 | −0.439814 | ||||||||
\(199\) | 4.04141 | 0.286488 | 0.143244 | − | 0.989687i | \(-0.454247\pi\) | ||||
0.143244 | + | 0.989687i | \(0.454247\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 18.9566 | 1.33709 | ||||||||
\(202\) | −5.27322 | −0.371023 | ||||||||
\(203\) | 18.2149 | 1.27844 | ||||||||
\(204\) | 4.94288 | 0.346071 | ||||||||
\(205\) | 2.42690 | 0.169502 | ||||||||
\(206\) | 0.506930 | 0.0353195 | ||||||||
\(207\) | 19.6023 | 1.36246 | ||||||||
\(208\) | −6.77606 | −0.469835 | ||||||||
\(209\) | −7.46655 | −0.516472 | ||||||||
\(210\) | −10.6330 | −0.733747 | ||||||||
\(211\) | −17.5194 | −1.20609 | −0.603043 | − | 0.797708i | \(-0.706045\pi\) | ||||
−0.603043 | + | 0.797708i | \(0.706045\pi\) | |||||||
\(212\) | −12.7598 | −0.876348 | ||||||||
\(213\) | −20.1190 | −1.37853 | ||||||||
\(214\) | 1.78929 | 0.122313 | ||||||||
\(215\) | 10.5318 | 0.718266 | ||||||||
\(216\) | 9.66598 | 0.657686 | ||||||||
\(217\) | −10.6584 | −0.723540 | ||||||||
\(218\) | 8.93951 | 0.605460 | ||||||||
\(219\) | −3.03129 | −0.204836 | ||||||||
\(220\) | 1.00000 | 0.0674200 | ||||||||
\(221\) | −11.0492 | −0.743247 | ||||||||
\(222\) | 34.9860 | 2.34811 | ||||||||
\(223\) | 8.38259 | 0.561340 | 0.280670 | − | 0.959804i | \(-0.409443\pi\) | ||||
0.280670 | + | 0.959804i | \(0.409443\pi\) | |||||||
\(224\) | 3.50775 | 0.234371 | ||||||||
\(225\) | 6.18873 | 0.412582 | ||||||||
\(226\) | −17.5669 | −1.16853 | ||||||||
\(227\) | −0.352740 | −0.0234122 | −0.0117061 | − | 0.999931i | \(-0.503726\pi\) | ||||
−0.0117061 | + | 0.999931i | \(0.503726\pi\) | |||||||
\(228\) | 22.6333 | 1.49893 | ||||||||
\(229\) | −3.80347 | −0.251340 | −0.125670 | − | 0.992072i | \(-0.540108\pi\) | ||||
−0.125670 | + | 0.992072i | \(0.540108\pi\) | |||||||
\(230\) | −3.16743 | −0.208854 | ||||||||
\(231\) | −10.6330 | −0.699600 | ||||||||
\(232\) | 5.19277 | 0.340922 | ||||||||
\(233\) | −10.8696 | −0.712089 | −0.356045 | − | 0.934469i | \(-0.615875\pi\) | ||||
−0.356045 | + | 0.934469i | \(0.615875\pi\) | |||||||
\(234\) | −41.9352 | −2.74139 | ||||||||
\(235\) | −2.77614 | −0.181095 | ||||||||
\(236\) | 4.64925 | 0.302641 | ||||||||
\(237\) | 31.3646 | 2.03735 | ||||||||
\(238\) | 5.71979 | 0.370759 | ||||||||
\(239\) | 7.40131 | 0.478751 | 0.239376 | − | 0.970927i | \(-0.423057\pi\) | ||||
0.239376 | + | 0.970927i | \(0.423057\pi\) | |||||||
\(240\) | −3.03129 | −0.195669 | ||||||||
\(241\) | −17.4401 | −1.12342 | −0.561708 | − | 0.827336i | \(-0.689856\pi\) | ||||
−0.561708 | + | 0.827336i | \(0.689856\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 3.54057 | 0.227128 | ||||||||
\(244\) | −6.19293 | −0.396462 | ||||||||
\(245\) | −5.30428 | −0.338878 | ||||||||
\(246\) | −7.35665 | −0.469043 | ||||||||
\(247\) | −50.5938 | −3.21921 | ||||||||
\(248\) | −3.03853 | −0.192947 | ||||||||
\(249\) | 28.6718 | 1.81700 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −7.02700 | −0.443540 | −0.221770 | − | 0.975099i | \(-0.571183\pi\) | ||||
−0.221770 | + | 0.975099i | \(0.571183\pi\) | |||||||
\(252\) | 21.7085 | 1.36751 | ||||||||
\(253\) | −3.16743 | −0.199134 | ||||||||
\(254\) | 8.76750 | 0.550122 | ||||||||
\(255\) | −4.94288 | −0.309535 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −21.1301 | −1.31806 | −0.659029 | − | 0.752118i | \(-0.729032\pi\) | ||||
−0.659029 | + | 0.752118i | \(0.729032\pi\) | |||||||
\(258\) | −31.9251 | −1.98757 | ||||||||
\(259\) | 40.4850 | 2.51562 | ||||||||
\(260\) | 6.77606 | 0.420234 | ||||||||
\(261\) | 32.1367 | 1.98921 | ||||||||
\(262\) | 10.0699 | 0.622122 | ||||||||
\(263\) | −20.7751 | −1.28105 | −0.640524 | − | 0.767938i | \(-0.721283\pi\) | ||||
−0.640524 | + | 0.767938i | \(0.721283\pi\) | |||||||
\(264\) | −3.03129 | −0.186563 | ||||||||
\(265\) | 12.7598 | 0.783829 | ||||||||
\(266\) | 26.1908 | 1.60586 | ||||||||
\(267\) | −16.6563 | −1.01935 | ||||||||
\(268\) | 6.25363 | 0.382001 | ||||||||
\(269\) | −1.24744 | −0.0760578 | −0.0380289 | − | 0.999277i | \(-0.512108\pi\) | ||||
−0.0380289 | + | 0.999277i | \(0.512108\pi\) | |||||||
\(270\) | −9.66598 | −0.588253 | ||||||||
\(271\) | 12.9392 | 0.785999 | 0.392999 | − | 0.919539i | \(-0.371437\pi\) | ||||
0.392999 | + | 0.919539i | \(0.371437\pi\) | |||||||
\(272\) | 1.63062 | 0.0988707 | ||||||||
\(273\) | −72.0499 | −4.36066 | ||||||||
\(274\) | −21.8423 | −1.31954 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | 9.60139 | 0.577936 | ||||||||
\(277\) | 27.8940 | 1.67599 | 0.837993 | − | 0.545681i | \(-0.183729\pi\) | ||||
0.837993 | + | 0.545681i | \(0.183729\pi\) | |||||||
\(278\) | −14.4697 | −0.867835 | ||||||||
\(279\) | −18.8047 | −1.12581 | ||||||||
\(280\) | −3.50775 | −0.209628 | ||||||||
\(281\) | −3.66745 | −0.218782 | −0.109391 | − | 0.993999i | \(-0.534890\pi\) | ||||
−0.109391 | + | 0.993999i | \(0.534890\pi\) | |||||||
\(282\) | 8.41528 | 0.501122 | ||||||||
\(283\) | −29.6089 | −1.76007 | −0.880034 | − | 0.474910i | \(-0.842481\pi\) | ||||
−0.880034 | + | 0.474910i | \(0.842481\pi\) | |||||||
\(284\) | −6.63711 | −0.393840 | ||||||||
\(285\) | −22.6333 | −1.34068 | ||||||||
\(286\) | 6.77606 | 0.400677 | ||||||||
\(287\) | −8.51295 | −0.502504 | ||||||||
\(288\) | 6.18873 | 0.364674 | ||||||||
\(289\) | −14.3411 | −0.843593 | ||||||||
\(290\) | −5.19277 | −0.304930 | ||||||||
\(291\) | −21.0156 | −1.23196 | ||||||||
\(292\) | −1.00000 | −0.0585206 | ||||||||
\(293\) | −24.3264 | −1.42116 | −0.710582 | − | 0.703614i | \(-0.751568\pi\) | ||||
−0.710582 | + | 0.703614i | \(0.751568\pi\) | |||||||
\(294\) | 16.0788 | 0.937736 | ||||||||
\(295\) | −4.64925 | −0.270690 | ||||||||
\(296\) | 11.5416 | 0.670842 | ||||||||
\(297\) | −9.66598 | −0.560877 | ||||||||
\(298\) | 22.4097 | 1.29816 | ||||||||
\(299\) | −21.4627 | −1.24122 | ||||||||
\(300\) | 3.03129 | 0.175012 | ||||||||
\(301\) | −36.9431 | −2.12936 | ||||||||
\(302\) | −2.42552 | −0.139573 | ||||||||
\(303\) | −15.9847 | −0.918296 | ||||||||
\(304\) | 7.46655 | 0.428236 | ||||||||
\(305\) | 6.19293 | 0.354606 | ||||||||
\(306\) | 10.0915 | 0.576890 | ||||||||
\(307\) | 14.3026 | 0.816293 | 0.408147 | − | 0.912916i | \(-0.366175\pi\) | ||||
0.408147 | + | 0.912916i | \(0.366175\pi\) | |||||||
\(308\) | −3.50775 | −0.199872 | ||||||||
\(309\) | 1.53665 | 0.0874171 | ||||||||
\(310\) | 3.03853 | 0.172577 | ||||||||
\(311\) | −0.540885 | −0.0306708 | −0.0153354 | − | 0.999882i | \(-0.504882\pi\) | ||||
−0.0153354 | + | 0.999882i | \(0.504882\pi\) | |||||||
\(312\) | −20.5402 | −1.16286 | ||||||||
\(313\) | 24.8705 | 1.40576 | 0.702881 | − | 0.711307i | \(-0.251897\pi\) | ||||
0.702881 | + | 0.711307i | \(0.251897\pi\) | |||||||
\(314\) | 12.2085 | 0.688965 | ||||||||
\(315\) | −21.7085 | −1.22314 | ||||||||
\(316\) | 10.3469 | 0.582060 | ||||||||
\(317\) | −23.8128 | −1.33746 | −0.668730 | − | 0.743506i | \(-0.733162\pi\) | ||||
−0.668730 | + | 0.743506i | \(0.733162\pi\) | |||||||
\(318\) | −38.6787 | −2.16900 | ||||||||
\(319\) | −5.19277 | −0.290739 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 5.42385 | 0.302730 | ||||||||
\(322\) | 11.1105 | 0.619165 | ||||||||
\(323\) | 12.1751 | 0.677440 | ||||||||
\(324\) | 10.7342 | 0.596345 | ||||||||
\(325\) | −6.77606 | −0.375868 | ||||||||
\(326\) | −16.8631 | −0.933958 | ||||||||
\(327\) | 27.0983 | 1.49854 | ||||||||
\(328\) | −2.42690 | −0.134003 | ||||||||
\(329\) | 9.73798 | 0.536872 | ||||||||
\(330\) | 3.03129 | 0.166867 | ||||||||
\(331\) | −12.1011 | −0.665137 | −0.332569 | − | 0.943079i | \(-0.607915\pi\) | ||||
−0.332569 | + | 0.943079i | \(0.607915\pi\) | |||||||
\(332\) | 9.45862 | 0.519109 | ||||||||
\(333\) | 71.4279 | 3.91422 | ||||||||
\(334\) | 15.2813 | 0.836157 | ||||||||
\(335\) | −6.25363 | −0.341673 | ||||||||
\(336\) | 10.6330 | 0.580078 | ||||||||
\(337\) | −22.6731 | −1.23508 | −0.617541 | − | 0.786539i | \(-0.711871\pi\) | ||||
−0.617541 | + | 0.786539i | \(0.711871\pi\) | |||||||
\(338\) | 32.9150 | 1.79034 | ||||||||
\(339\) | −53.2504 | −2.89217 | ||||||||
\(340\) | −1.63062 | −0.0884326 | ||||||||
\(341\) | 3.03853 | 0.164546 | ||||||||
\(342\) | 46.2085 | 2.49867 | ||||||||
\(343\) | −5.94815 | −0.321170 | ||||||||
\(344\) | −10.5318 | −0.567839 | ||||||||
\(345\) | −9.60139 | −0.516922 | ||||||||
\(346\) | −1.38794 | −0.0746163 | ||||||||
\(347\) | 22.8290 | 1.22552 | 0.612762 | − | 0.790268i | \(-0.290059\pi\) | ||||
0.612762 | + | 0.790268i | \(0.290059\pi\) | |||||||
\(348\) | 15.7408 | 0.843796 | ||||||||
\(349\) | 9.69867 | 0.519158 | 0.259579 | − | 0.965722i | \(-0.416416\pi\) | ||||
0.259579 | + | 0.965722i | \(0.416416\pi\) | |||||||
\(350\) | 3.50775 | 0.187497 | ||||||||
\(351\) | −65.4973 | −3.49599 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | 20.2399 | 1.07726 | 0.538630 | − | 0.842542i | \(-0.318942\pi\) | ||||
0.538630 | + | 0.842542i | \(0.318942\pi\) | |||||||
\(354\) | 14.0932 | 0.749047 | ||||||||
\(355\) | 6.63711 | 0.352261 | ||||||||
\(356\) | −5.49478 | −0.291223 | ||||||||
\(357\) | 17.3384 | 0.917643 | ||||||||
\(358\) | −5.85001 | −0.309183 | ||||||||
\(359\) | −24.6263 | −1.29973 | −0.649864 | − | 0.760050i | \(-0.725174\pi\) | ||||
−0.649864 | + | 0.760050i | \(0.725174\pi\) | |||||||
\(360\) | −6.18873 | −0.326175 | ||||||||
\(361\) | 36.7494 | 1.93418 | ||||||||
\(362\) | 25.5379 | 1.34224 | ||||||||
\(363\) | 3.03129 | 0.159102 | ||||||||
\(364\) | −23.7687 | −1.24582 | ||||||||
\(365\) | 1.00000 | 0.0523424 | ||||||||
\(366\) | −18.7726 | −0.981258 | ||||||||
\(367\) | −31.0873 | −1.62274 | −0.811372 | − | 0.584530i | \(-0.801279\pi\) | ||||
−0.811372 | + | 0.584530i | \(0.801279\pi\) | |||||||
\(368\) | 3.16743 | 0.165113 | ||||||||
\(369\) | −15.0194 | −0.781881 | ||||||||
\(370\) | −11.5416 | −0.600020 | ||||||||
\(371\) | −44.7582 | −2.32373 | ||||||||
\(372\) | −9.21069 | −0.477552 | ||||||||
\(373\) | 8.77686 | 0.454449 | 0.227224 | − | 0.973842i | \(-0.427035\pi\) | ||||
0.227224 | + | 0.973842i | \(0.427035\pi\) | |||||||
\(374\) | −1.63062 | −0.0843172 | ||||||||
\(375\) | −3.03129 | −0.156535 | ||||||||
\(376\) | 2.77614 | 0.143168 | ||||||||
\(377\) | −35.1866 | −1.81220 | ||||||||
\(378\) | 33.9058 | 1.74393 | ||||||||
\(379\) | −24.9480 | −1.28149 | −0.640747 | − | 0.767752i | \(-0.721375\pi\) | ||||
−0.640747 | + | 0.767752i | \(0.721375\pi\) | |||||||
\(380\) | −7.46655 | −0.383026 | ||||||||
\(381\) | 26.5768 | 1.36157 | ||||||||
\(382\) | 17.5333 | 0.897082 | ||||||||
\(383\) | −26.0631 | −1.33176 | −0.665880 | − | 0.746059i | \(-0.731944\pi\) | ||||
−0.665880 | + | 0.746059i | \(0.731944\pi\) | |||||||
\(384\) | 3.03129 | 0.154690 | ||||||||
\(385\) | 3.50775 | 0.178771 | ||||||||
\(386\) | −6.62499 | −0.337203 | ||||||||
\(387\) | −65.1788 | −3.31322 | ||||||||
\(388\) | −6.93289 | −0.351964 | ||||||||
\(389\) | 4.33744 | 0.219917 | 0.109958 | − | 0.993936i | \(-0.464928\pi\) | ||||
0.109958 | + | 0.993936i | \(0.464928\pi\) | |||||||
\(390\) | 20.5402 | 1.04009 | ||||||||
\(391\) | 5.16486 | 0.261198 | ||||||||
\(392\) | 5.30428 | 0.267907 | ||||||||
\(393\) | 30.5249 | 1.53978 | ||||||||
\(394\) | 4.55572 | 0.229514 | ||||||||
\(395\) | −10.3469 | −0.520611 | ||||||||
\(396\) | −6.18873 | −0.310995 | ||||||||
\(397\) | 10.0832 | 0.506061 | 0.253031 | − | 0.967458i | \(-0.418573\pi\) | ||||
0.253031 | + | 0.967458i | \(0.418573\pi\) | |||||||
\(398\) | 4.04141 | 0.202577 | ||||||||
\(399\) | 79.3918 | 3.97456 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 26.7837 | 1.33752 | 0.668758 | − | 0.743480i | \(-0.266826\pi\) | ||||
0.668758 | + | 0.743480i | \(0.266826\pi\) | |||||||
\(402\) | 18.9566 | 0.945469 | ||||||||
\(403\) | 20.5893 | 1.02563 | ||||||||
\(404\) | −5.27322 | −0.262353 | ||||||||
\(405\) | −10.7342 | −0.533387 | ||||||||
\(406\) | 18.2149 | 0.903991 | ||||||||
\(407\) | −11.5416 | −0.572096 | ||||||||
\(408\) | 4.94288 | 0.244709 | ||||||||
\(409\) | 7.19999 | 0.356017 | 0.178008 | − | 0.984029i | \(-0.443035\pi\) | ||||
0.178008 | + | 0.984029i | \(0.443035\pi\) | |||||||
\(410\) | 2.42690 | 0.119856 | ||||||||
\(411\) | −66.2103 | −3.26591 | ||||||||
\(412\) | 0.506930 | 0.0249746 | ||||||||
\(413\) | 16.3084 | 0.802484 | ||||||||
\(414\) | 19.6023 | 0.963403 | ||||||||
\(415\) | −9.45862 | −0.464306 | ||||||||
\(416\) | −6.77606 | −0.332224 | ||||||||
\(417\) | −43.8619 | −2.14793 | ||||||||
\(418\) | −7.46655 | −0.365201 | ||||||||
\(419\) | 0.832557 | 0.0406731 | 0.0203365 | − | 0.999793i | \(-0.493526\pi\) | ||||
0.0203365 | + | 0.999793i | \(0.493526\pi\) | |||||||
\(420\) | −10.6330 | −0.518837 | ||||||||
\(421\) | −32.8737 | −1.60216 | −0.801082 | − | 0.598555i | \(-0.795742\pi\) | ||||
−0.801082 | + | 0.598555i | \(0.795742\pi\) | |||||||
\(422\) | −17.5194 | −0.852832 | ||||||||
\(423\) | 17.1808 | 0.835357 | ||||||||
\(424\) | −12.7598 | −0.619671 | ||||||||
\(425\) | 1.63062 | 0.0790966 | ||||||||
\(426\) | −20.1190 | −0.974770 | ||||||||
\(427\) | −21.7232 | −1.05126 | ||||||||
\(428\) | 1.78929 | 0.0864884 | ||||||||
\(429\) | 20.5402 | 0.991692 | ||||||||
\(430\) | 10.5318 | 0.507891 | ||||||||
\(431\) | 10.8956 | 0.524821 | 0.262411 | − | 0.964956i | \(-0.415482\pi\) | ||||
0.262411 | + | 0.964956i | \(0.415482\pi\) | |||||||
\(432\) | 9.66598 | 0.465055 | ||||||||
\(433\) | 2.05905 | 0.0989515 | 0.0494757 | − | 0.998775i | \(-0.484245\pi\) | ||||
0.0494757 | + | 0.998775i | \(0.484245\pi\) | |||||||
\(434\) | −10.6584 | −0.511620 | ||||||||
\(435\) | −15.7408 | −0.754714 | ||||||||
\(436\) | 8.93951 | 0.428125 | ||||||||
\(437\) | 23.6497 | 1.13132 | ||||||||
\(438\) | −3.03129 | −0.144841 | ||||||||
\(439\) | −17.5600 | −0.838092 | −0.419046 | − | 0.907965i | \(-0.637635\pi\) | ||||
−0.419046 | + | 0.907965i | \(0.637635\pi\) | |||||||
\(440\) | 1.00000 | 0.0476731 | ||||||||
\(441\) | 32.8268 | 1.56318 | ||||||||
\(442\) | −11.0492 | −0.525555 | ||||||||
\(443\) | −30.6787 | −1.45759 | −0.728794 | − | 0.684733i | \(-0.759919\pi\) | ||||
−0.728794 | + | 0.684733i | \(0.759919\pi\) | |||||||
\(444\) | 34.9860 | 1.66036 | ||||||||
\(445\) | 5.49478 | 0.260478 | ||||||||
\(446\) | 8.38259 | 0.396927 | ||||||||
\(447\) | 67.9304 | 3.21300 | ||||||||
\(448\) | 3.50775 | 0.165725 | ||||||||
\(449\) | 24.7126 | 1.16626 | 0.583130 | − | 0.812379i | \(-0.301828\pi\) | ||||
0.583130 | + | 0.812379i | \(0.301828\pi\) | |||||||
\(450\) | 6.18873 | 0.291740 | ||||||||
\(451\) | 2.42690 | 0.114278 | ||||||||
\(452\) | −17.5669 | −0.826278 | ||||||||
\(453\) | −7.35246 | −0.345449 | ||||||||
\(454\) | −0.352740 | −0.0165549 | ||||||||
\(455\) | 23.7687 | 1.11429 | ||||||||
\(456\) | 22.6333 | 1.05990 | ||||||||
\(457\) | −25.9039 | −1.21173 | −0.605867 | − | 0.795566i | \(-0.707174\pi\) | ||||
−0.605867 | + | 0.795566i | \(0.707174\pi\) | |||||||
\(458\) | −3.80347 | −0.177724 | ||||||||
\(459\) | 15.7615 | 0.735684 | ||||||||
\(460\) | −3.16743 | −0.147682 | ||||||||
\(461\) | 12.1699 | 0.566811 | 0.283405 | − | 0.959000i | \(-0.408536\pi\) | ||||
0.283405 | + | 0.959000i | \(0.408536\pi\) | |||||||
\(462\) | −10.6330 | −0.494692 | ||||||||
\(463\) | −3.82987 | −0.177989 | −0.0889945 | − | 0.996032i | \(-0.528365\pi\) | ||||
−0.0889945 | + | 0.996032i | \(0.528365\pi\) | |||||||
\(464\) | 5.19277 | 0.241068 | ||||||||
\(465\) | 9.21069 | 0.427135 | ||||||||
\(466\) | −10.8696 | −0.503523 | ||||||||
\(467\) | −23.8515 | −1.10371 | −0.551857 | − | 0.833939i | \(-0.686081\pi\) | ||||
−0.551857 | + | 0.833939i | \(0.686081\pi\) | |||||||
\(468\) | −41.9352 | −1.93846 | ||||||||
\(469\) | 21.9362 | 1.01292 | ||||||||
\(470\) | −2.77614 | −0.128054 | ||||||||
\(471\) | 37.0075 | 1.70522 | ||||||||
\(472\) | 4.64925 | 0.213999 | ||||||||
\(473\) | 10.5318 | 0.484255 | ||||||||
\(474\) | 31.3646 | 1.44062 | ||||||||
\(475\) | 7.46655 | 0.342589 | ||||||||
\(476\) | 5.71979 | 0.262166 | ||||||||
\(477\) | −78.9671 | −3.61565 | ||||||||
\(478\) | 7.40131 | 0.338528 | ||||||||
\(479\) | −16.3428 | −0.746721 | −0.373360 | − | 0.927686i | \(-0.621795\pi\) | ||||
−0.373360 | + | 0.927686i | \(0.621795\pi\) | |||||||
\(480\) | −3.03129 | −0.138359 | ||||||||
\(481\) | −78.2067 | −3.56592 | ||||||||
\(482\) | −17.4401 | −0.794375 | ||||||||
\(483\) | 33.6792 | 1.53246 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 6.93289 | 0.314806 | ||||||||
\(486\) | 3.54057 | 0.160604 | ||||||||
\(487\) | −4.84862 | −0.219712 | −0.109856 | − | 0.993948i | \(-0.535039\pi\) | ||||
−0.109856 | + | 0.993948i | \(0.535039\pi\) | |||||||
\(488\) | −6.19293 | −0.280341 | ||||||||
\(489\) | −51.1168 | −2.31158 | ||||||||
\(490\) | −5.30428 | −0.239623 | ||||||||
\(491\) | −9.77007 | −0.440917 | −0.220458 | − | 0.975396i | \(-0.570755\pi\) | ||||
−0.220458 | + | 0.975396i | \(0.570755\pi\) | |||||||
\(492\) | −7.35665 | −0.331663 | ||||||||
\(493\) | 8.46742 | 0.381354 | ||||||||
\(494\) | −50.5938 | −2.27632 | ||||||||
\(495\) | 6.18873 | 0.278163 | ||||||||
\(496\) | −3.03853 | −0.136434 | ||||||||
\(497\) | −23.2813 | −1.04431 | ||||||||
\(498\) | 28.6718 | 1.28482 | ||||||||
\(499\) | −9.92500 | −0.444304 | −0.222152 | − | 0.975012i | \(-0.571308\pi\) | ||||
−0.222152 | + | 0.975012i | \(0.571308\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 46.3222 | 2.06952 | ||||||||
\(502\) | −7.02700 | −0.313630 | ||||||||
\(503\) | 26.0555 | 1.16176 | 0.580879 | − | 0.813990i | \(-0.302709\pi\) | ||||
0.580879 | + | 0.813990i | \(0.302709\pi\) | |||||||
\(504\) | 21.7085 | 0.966973 | ||||||||
\(505\) | 5.27322 | 0.234655 | ||||||||
\(506\) | −3.16743 | −0.140809 | ||||||||
\(507\) | 99.7751 | 4.43117 | ||||||||
\(508\) | 8.76750 | 0.388995 | ||||||||
\(509\) | −27.9509 | −1.23890 | −0.619451 | − | 0.785035i | \(-0.712645\pi\) | ||||
−0.619451 | + | 0.785035i | \(0.712645\pi\) | |||||||
\(510\) | −4.94288 | −0.218874 | ||||||||
\(511\) | −3.50775 | −0.155174 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 72.1715 | 3.18645 | ||||||||
\(514\) | −21.1301 | −0.932007 | ||||||||
\(515\) | −0.506930 | −0.0223380 | ||||||||
\(516\) | −31.9251 | −1.40542 | ||||||||
\(517\) | −2.77614 | −0.122094 | ||||||||
\(518\) | 40.4850 | 1.77881 | ||||||||
\(519\) | −4.20726 | −0.184678 | ||||||||
\(520\) | 6.77606 | 0.297150 | ||||||||
\(521\) | 28.8879 | 1.26560 | 0.632800 | − | 0.774315i | \(-0.281906\pi\) | ||||
0.632800 | + | 0.774315i | \(0.281906\pi\) | |||||||
\(522\) | 32.1367 | 1.40658 | ||||||||
\(523\) | 19.9488 | 0.872299 | 0.436150 | − | 0.899874i | \(-0.356342\pi\) | ||||
0.436150 | + | 0.899874i | \(0.356342\pi\) | |||||||
\(524\) | 10.0699 | 0.439907 | ||||||||
\(525\) | 10.6330 | 0.464062 | ||||||||
\(526\) | −20.7751 | −0.905837 | ||||||||
\(527\) | −4.95469 | −0.215830 | ||||||||
\(528\) | −3.03129 | −0.131920 | ||||||||
\(529\) | −12.9674 | −0.563801 | ||||||||
\(530\) | 12.7598 | 0.554251 | ||||||||
\(531\) | 28.7730 | 1.24864 | ||||||||
\(532\) | 26.1908 | 1.13551 | ||||||||
\(533\) | 16.4448 | 0.712305 | ||||||||
\(534\) | −16.6563 | −0.720788 | ||||||||
\(535\) | −1.78929 | −0.0773576 | ||||||||
\(536\) | 6.25363 | 0.270116 | ||||||||
\(537\) | −17.7331 | −0.765239 | ||||||||
\(538\) | −1.24744 | −0.0537810 | ||||||||
\(539\) | −5.30428 | −0.228472 | ||||||||
\(540\) | −9.66598 | −0.415957 | ||||||||
\(541\) | −29.9581 | −1.28800 | −0.643999 | − | 0.765026i | \(-0.722726\pi\) | ||||
−0.643999 | + | 0.765026i | \(0.722726\pi\) | |||||||
\(542\) | 12.9392 | 0.555785 | ||||||||
\(543\) | 77.4129 | 3.32211 | ||||||||
\(544\) | 1.63062 | 0.0699121 | ||||||||
\(545\) | −8.93951 | −0.382926 | ||||||||
\(546\) | −72.0499 | −3.08345 | ||||||||
\(547\) | 28.0606 | 1.19979 | 0.599893 | − | 0.800080i | \(-0.295210\pi\) | ||||
0.599893 | + | 0.800080i | \(0.295210\pi\) | |||||||
\(548\) | −21.8423 | −0.933055 | ||||||||
\(549\) | −38.3264 | −1.63573 | ||||||||
\(550\) | −1.00000 | −0.0426401 | ||||||||
\(551\) | 38.7721 | 1.65175 | ||||||||
\(552\) | 9.60139 | 0.408662 | ||||||||
\(553\) | 36.2944 | 1.54339 | ||||||||
\(554\) | 27.8940 | 1.18510 | ||||||||
\(555\) | −34.9860 | −1.48507 | ||||||||
\(556\) | −14.4697 | −0.613652 | ||||||||
\(557\) | −33.7799 | −1.43130 | −0.715649 | − | 0.698460i | \(-0.753869\pi\) | ||||
−0.715649 | + | 0.698460i | \(0.753869\pi\) | |||||||
\(558\) | −18.8047 | −0.796065 | ||||||||
\(559\) | 71.3645 | 3.01840 | ||||||||
\(560\) | −3.50775 | −0.148229 | ||||||||
\(561\) | −4.94288 | −0.208688 | ||||||||
\(562\) | −3.66745 | −0.154702 | ||||||||
\(563\) | −31.1193 | −1.31152 | −0.655760 | − | 0.754969i | \(-0.727652\pi\) | ||||
−0.655760 | + | 0.754969i | \(0.727652\pi\) | |||||||
\(564\) | 8.41528 | 0.354347 | ||||||||
\(565\) | 17.5669 | 0.739045 | ||||||||
\(566\) | −29.6089 | −1.24456 | ||||||||
\(567\) | 37.6529 | 1.58127 | ||||||||
\(568\) | −6.63711 | −0.278487 | ||||||||
\(569\) | −14.2008 | −0.595330 | −0.297665 | − | 0.954670i | \(-0.596208\pi\) | ||||
−0.297665 | + | 0.954670i | \(0.596208\pi\) | |||||||
\(570\) | −22.6333 | −0.948004 | ||||||||
\(571\) | −16.1552 | −0.676073 | −0.338037 | − | 0.941133i | \(-0.609763\pi\) | ||||
−0.338037 | + | 0.941133i | \(0.609763\pi\) | |||||||
\(572\) | 6.77606 | 0.283321 | ||||||||
\(573\) | 53.1486 | 2.22031 | ||||||||
\(574\) | −8.51295 | −0.355324 | ||||||||
\(575\) | 3.16743 | 0.132091 | ||||||||
\(576\) | 6.18873 | 0.257864 | ||||||||
\(577\) | 24.9530 | 1.03881 | 0.519403 | − | 0.854529i | \(-0.326154\pi\) | ||||
0.519403 | + | 0.854529i | \(0.326154\pi\) | |||||||
\(578\) | −14.3411 | −0.596511 | ||||||||
\(579\) | −20.0823 | −0.834591 | ||||||||
\(580\) | −5.19277 | −0.215618 | ||||||||
\(581\) | 33.1784 | 1.37647 | ||||||||
\(582\) | −21.0156 | −0.871125 | ||||||||
\(583\) | 12.7598 | 0.528458 | ||||||||
\(584\) | −1.00000 | −0.0413803 | ||||||||
\(585\) | 41.9352 | 1.73381 | ||||||||
\(586\) | −24.3264 | −1.00491 | ||||||||
\(587\) | −4.49910 | −0.185698 | −0.0928488 | − | 0.995680i | \(-0.529597\pi\) | ||||
−0.0928488 | + | 0.995680i | \(0.529597\pi\) | |||||||
\(588\) | 16.0788 | 0.663080 | ||||||||
\(589\) | −22.6874 | −0.934817 | ||||||||
\(590\) | −4.64925 | −0.191407 | ||||||||
\(591\) | 13.8097 | 0.568056 | ||||||||
\(592\) | 11.5416 | 0.474357 | ||||||||
\(593\) | 2.32311 | 0.0953987 | 0.0476993 | − | 0.998862i | \(-0.484811\pi\) | ||||
0.0476993 | + | 0.998862i | \(0.484811\pi\) | |||||||
\(594\) | −9.66598 | −0.396600 | ||||||||
\(595\) | −5.71979 | −0.234489 | ||||||||
\(596\) | 22.4097 | 0.917938 | ||||||||
\(597\) | 12.2507 | 0.501387 | ||||||||
\(598\) | −21.4627 | −0.877674 | ||||||||
\(599\) | −25.2752 | −1.03272 | −0.516359 | − | 0.856372i | \(-0.672713\pi\) | ||||
−0.516359 | + | 0.856372i | \(0.672713\pi\) | |||||||
\(600\) | 3.03129 | 0.123752 | ||||||||
\(601\) | −16.7537 | −0.683400 | −0.341700 | − | 0.939809i | \(-0.611003\pi\) | ||||
−0.341700 | + | 0.939809i | \(0.611003\pi\) | |||||||
\(602\) | −36.9431 | −1.50569 | ||||||||
\(603\) | 38.7021 | 1.57607 | ||||||||
\(604\) | −2.42552 | −0.0986930 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | −15.9847 | −0.649333 | ||||||||
\(607\) | −7.15814 | −0.290540 | −0.145270 | − | 0.989392i | \(-0.546405\pi\) | ||||
−0.145270 | + | 0.989392i | \(0.546405\pi\) | |||||||
\(608\) | 7.46655 | 0.302809 | ||||||||
\(609\) | 55.2148 | 2.23741 | ||||||||
\(610\) | 6.19293 | 0.250744 | ||||||||
\(611\) | −18.8113 | −0.761023 | ||||||||
\(612\) | 10.0915 | 0.407923 | ||||||||
\(613\) | −5.30177 | −0.214137 | −0.107068 | − | 0.994252i | \(-0.534146\pi\) | ||||
−0.107068 | + | 0.994252i | \(0.534146\pi\) | |||||||
\(614\) | 14.3026 | 0.577207 | ||||||||
\(615\) | 7.35665 | 0.296649 | ||||||||
\(616\) | −3.50775 | −0.141331 | ||||||||
\(617\) | 12.8336 | 0.516663 | 0.258331 | − | 0.966056i | \(-0.416827\pi\) | ||||
0.258331 | + | 0.966056i | \(0.416827\pi\) | |||||||
\(618\) | 1.53665 | 0.0618132 | ||||||||
\(619\) | 4.98877 | 0.200516 | 0.100258 | − | 0.994961i | \(-0.468033\pi\) | ||||
0.100258 | + | 0.994961i | \(0.468033\pi\) | |||||||
\(620\) | 3.03853 | 0.122030 | ||||||||
\(621\) | 30.6163 | 1.22859 | ||||||||
\(622\) | −0.540885 | −0.0216875 | ||||||||
\(623\) | −19.2743 | −0.772208 | ||||||||
\(624\) | −20.5402 | −0.822267 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 24.8705 | 0.994024 | ||||||||
\(627\) | −22.6333 | −0.903887 | ||||||||
\(628\) | 12.2085 | 0.487172 | ||||||||
\(629\) | 18.8199 | 0.750400 | ||||||||
\(630\) | −21.7085 | −0.864887 | ||||||||
\(631\) | 25.9597 | 1.03344 | 0.516721 | − | 0.856154i | \(-0.327153\pi\) | ||||
0.516721 | + | 0.856154i | \(0.327153\pi\) | |||||||
\(632\) | 10.3469 | 0.411579 | ||||||||
\(633\) | −53.1065 | −2.11079 | ||||||||
\(634\) | −23.8128 | −0.945726 | ||||||||
\(635\) | −8.76750 | −0.347928 | ||||||||
\(636\) | −38.6787 | −1.53371 | ||||||||
\(637\) | −35.9421 | −1.42408 | ||||||||
\(638\) | −5.19277 | −0.205584 | ||||||||
\(639\) | −41.0753 | −1.62491 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −42.7692 | −1.68928 | −0.844641 | − | 0.535333i | \(-0.820186\pi\) | ||||
−0.844641 | + | 0.535333i | \(0.820186\pi\) | |||||||
\(642\) | 5.42385 | 0.214062 | ||||||||
\(643\) | −2.69662 | −0.106344 | −0.0531722 | − | 0.998585i | \(-0.516933\pi\) | ||||
−0.0531722 | + | 0.998585i | \(0.516933\pi\) | |||||||
\(644\) | 11.1105 | 0.437816 | ||||||||
\(645\) | 31.9251 | 1.25705 | ||||||||
\(646\) | 12.1751 | 0.479022 | ||||||||
\(647\) | 18.3390 | 0.720979 | 0.360489 | − | 0.932763i | \(-0.382610\pi\) | ||||
0.360489 | + | 0.932763i | \(0.382610\pi\) | |||||||
\(648\) | 10.7342 | 0.421679 | ||||||||
\(649\) | −4.64925 | −0.182499 | ||||||||
\(650\) | −6.77606 | −0.265779 | ||||||||
\(651\) | −32.3087 | −1.26628 | ||||||||
\(652\) | −16.8631 | −0.660408 | ||||||||
\(653\) | 40.8513 | 1.59863 | 0.799317 | − | 0.600909i | \(-0.205195\pi\) | ||||
0.799317 | + | 0.600909i | \(0.205195\pi\) | |||||||
\(654\) | 27.0983 | 1.05963 | ||||||||
\(655\) | −10.0699 | −0.393464 | ||||||||
\(656\) | −2.42690 | −0.0947546 | ||||||||
\(657\) | −6.18873 | −0.241445 | ||||||||
\(658\) | 9.73798 | 0.379626 | ||||||||
\(659\) | 22.8207 | 0.888967 | 0.444484 | − | 0.895787i | \(-0.353387\pi\) | ||||
0.444484 | + | 0.895787i | \(0.353387\pi\) | |||||||
\(660\) | 3.03129 | 0.117993 | ||||||||
\(661\) | −25.6995 | −0.999593 | −0.499797 | − | 0.866143i | \(-0.666592\pi\) | ||||
−0.499797 | + | 0.866143i | \(0.666592\pi\) | |||||||
\(662\) | −12.1011 | −0.470323 | ||||||||
\(663\) | −33.4933 | −1.30077 | ||||||||
\(664\) | 9.45862 | 0.367066 | ||||||||
\(665\) | −26.1908 | −1.01563 | ||||||||
\(666\) | 71.4279 | 2.76777 | ||||||||
\(667\) | 16.4477 | 0.636858 | ||||||||
\(668\) | 15.2813 | 0.591252 | ||||||||
\(669\) | 25.4101 | 0.982411 | ||||||||
\(670\) | −6.25363 | −0.241599 | ||||||||
\(671\) | 6.19293 | 0.239075 | ||||||||
\(672\) | 10.6330 | 0.410177 | ||||||||
\(673\) | 35.2433 | 1.35853 | 0.679264 | − | 0.733894i | \(-0.262299\pi\) | ||||
0.679264 | + | 0.733894i | \(0.262299\pi\) | |||||||
\(674\) | −22.6731 | −0.873335 | ||||||||
\(675\) | 9.66598 | 0.372044 | ||||||||
\(676\) | 32.9150 | 1.26596 | ||||||||
\(677\) | 14.5548 | 0.559386 | 0.279693 | − | 0.960089i | \(-0.409767\pi\) | ||||
0.279693 | + | 0.960089i | \(0.409767\pi\) | |||||||
\(678\) | −53.2504 | −2.04507 | ||||||||
\(679\) | −24.3188 | −0.933270 | ||||||||
\(680\) | −1.63062 | −0.0625313 | ||||||||
\(681\) | −1.06926 | −0.0409741 | ||||||||
\(682\) | 3.03853 | 0.116352 | ||||||||
\(683\) | 3.17885 | 0.121635 | 0.0608176 | − | 0.998149i | \(-0.480629\pi\) | ||||
0.0608176 | + | 0.998149i | \(0.480629\pi\) | |||||||
\(684\) | 46.2085 | 1.76683 | ||||||||
\(685\) | 21.8423 | 0.834550 | ||||||||
\(686\) | −5.94815 | −0.227102 | ||||||||
\(687\) | −11.5294 | −0.439875 | ||||||||
\(688\) | −10.5318 | −0.401523 | ||||||||
\(689\) | 86.4613 | 3.29391 | ||||||||
\(690\) | −9.60139 | −0.365519 | ||||||||
\(691\) | 4.23325 | 0.161040 | 0.0805202 | − | 0.996753i | \(-0.474342\pi\) | ||||
0.0805202 | + | 0.996753i | \(0.474342\pi\) | |||||||
\(692\) | −1.38794 | −0.0527617 | ||||||||
\(693\) | −21.7085 | −0.824638 | ||||||||
\(694\) | 22.8290 | 0.866576 | ||||||||
\(695\) | 14.4697 | 0.548867 | ||||||||
\(696\) | 15.7408 | 0.596654 | ||||||||
\(697\) | −3.95735 | −0.149895 | ||||||||
\(698\) | 9.69867 | 0.367100 | ||||||||
\(699\) | −32.9489 | −1.24624 | ||||||||
\(700\) | 3.50775 | 0.132580 | ||||||||
\(701\) | −38.3654 | −1.44904 | −0.724521 | − | 0.689252i | \(-0.757939\pi\) | ||||
−0.724521 | + | 0.689252i | \(0.757939\pi\) | |||||||
\(702\) | −65.4973 | −2.47204 | ||||||||
\(703\) | 86.1760 | 3.25019 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | −8.41528 | −0.316938 | ||||||||
\(706\) | 20.2399 | 0.761738 | ||||||||
\(707\) | −18.4971 | −0.695656 | ||||||||
\(708\) | 14.0932 | 0.529656 | ||||||||
\(709\) | 46.3244 | 1.73975 | 0.869875 | − | 0.493272i | \(-0.164199\pi\) | ||||
0.869875 | + | 0.493272i | \(0.164199\pi\) | |||||||
\(710\) | 6.63711 | 0.249086 | ||||||||
\(711\) | 64.0344 | 2.40148 | ||||||||
\(712\) | −5.49478 | −0.205926 | ||||||||
\(713\) | −9.62433 | −0.360434 | ||||||||
\(714\) | 17.3384 | 0.648872 | ||||||||
\(715\) | −6.77606 | −0.253410 | ||||||||
\(716\) | −5.85001 | −0.218625 | ||||||||
\(717\) | 22.4355 | 0.837871 | ||||||||
\(718\) | −24.6263 | −0.919047 | ||||||||
\(719\) | −37.7562 | −1.40807 | −0.704035 | − | 0.710166i | \(-0.748620\pi\) | ||||
−0.704035 | + | 0.710166i | \(0.748620\pi\) | |||||||
\(720\) | −6.18873 | −0.230640 | ||||||||
\(721\) | 1.77818 | 0.0662229 | ||||||||
\(722\) | 36.7494 | 1.36767 | ||||||||
\(723\) | −52.8660 | −1.96611 | ||||||||
\(724\) | 25.5379 | 0.949110 | ||||||||
\(725\) | 5.19277 | 0.192855 | ||||||||
\(726\) | 3.03129 | 0.112502 | ||||||||
\(727\) | 32.3561 | 1.20002 | 0.600011 | − | 0.799992i | \(-0.295163\pi\) | ||||
0.600011 | + | 0.799992i | \(0.295163\pi\) | |||||||
\(728\) | −23.7687 | −0.880927 | ||||||||
\(729\) | −21.4701 | −0.795189 | ||||||||
\(730\) | 1.00000 | 0.0370117 | ||||||||
\(731\) | −17.1734 | −0.635182 | ||||||||
\(732\) | −18.7726 | −0.693854 | ||||||||
\(733\) | −16.5130 | −0.609923 | −0.304961 | − | 0.952365i | \(-0.598644\pi\) | ||||
−0.304961 | + | 0.952365i | \(0.598644\pi\) | |||||||
\(734\) | −31.0873 | −1.14745 | ||||||||
\(735\) | −16.0788 | −0.593076 | ||||||||
\(736\) | 3.16743 | 0.116753 | ||||||||
\(737\) | −6.25363 | −0.230356 | ||||||||
\(738\) | −15.0194 | −0.552873 | ||||||||
\(739\) | −12.7353 | −0.468474 | −0.234237 | − | 0.972179i | \(-0.575259\pi\) | ||||
−0.234237 | + | 0.972179i | \(0.575259\pi\) | |||||||
\(740\) | −11.5416 | −0.424278 | ||||||||
\(741\) | −153.365 | −5.63399 | ||||||||
\(742\) | −44.7582 | −1.64312 | ||||||||
\(743\) | −12.5106 | −0.458969 | −0.229485 | − | 0.973312i | \(-0.573704\pi\) | ||||
−0.229485 | + | 0.973312i | \(0.573704\pi\) | |||||||
\(744\) | −9.21069 | −0.337680 | ||||||||
\(745\) | −22.4097 | −0.821029 | ||||||||
\(746\) | 8.77686 | 0.321344 | ||||||||
\(747\) | 58.5369 | 2.14175 | ||||||||
\(748\) | −1.63062 | −0.0596213 | ||||||||
\(749\) | 6.27636 | 0.229333 | ||||||||
\(750\) | −3.03129 | −0.110687 | ||||||||
\(751\) | 29.5838 | 1.07953 | 0.539764 | − | 0.841817i | \(-0.318514\pi\) | ||||
0.539764 | + | 0.841817i | \(0.318514\pi\) | |||||||
\(752\) | 2.77614 | 0.101235 | ||||||||
\(753\) | −21.3009 | −0.776248 | ||||||||
\(754\) | −35.1866 | −1.28142 | ||||||||
\(755\) | 2.42552 | 0.0882737 | ||||||||
\(756\) | 33.9058 | 1.23314 | ||||||||
\(757\) | 10.8274 | 0.393528 | 0.196764 | − | 0.980451i | \(-0.436957\pi\) | ||||
0.196764 | + | 0.980451i | \(0.436957\pi\) | |||||||
\(758\) | −24.9480 | −0.906153 | ||||||||
\(759\) | −9.60139 | −0.348508 | ||||||||
\(760\) | −7.46655 | −0.270840 | ||||||||
\(761\) | 43.3620 | 1.57187 | 0.785935 | − | 0.618309i | \(-0.212182\pi\) | ||||
0.785935 | + | 0.618309i | \(0.212182\pi\) | |||||||
\(762\) | 26.5768 | 0.962778 | ||||||||
\(763\) | 31.3575 | 1.13522 | ||||||||
\(764\) | 17.5333 | 0.634333 | ||||||||
\(765\) | −10.0915 | −0.364857 | ||||||||
\(766\) | −26.0631 | −0.941697 | ||||||||
\(767\) | −31.5036 | −1.13753 | ||||||||
\(768\) | 3.03129 | 0.109382 | ||||||||
\(769\) | 24.9933 | 0.901282 | 0.450641 | − | 0.892705i | \(-0.351196\pi\) | ||||
0.450641 | + | 0.892705i | \(0.351196\pi\) | |||||||
\(770\) | 3.50775 | 0.126410 | ||||||||
\(771\) | −64.0514 | −2.30675 | ||||||||
\(772\) | −6.62499 | −0.238439 | ||||||||
\(773\) | −27.9458 | −1.00514 | −0.502570 | − | 0.864537i | \(-0.667612\pi\) | ||||
−0.502570 | + | 0.864537i | \(0.667612\pi\) | |||||||
\(774\) | −65.1788 | −2.34280 | ||||||||
\(775\) | −3.03853 | −0.109147 | ||||||||
\(776\) | −6.93289 | −0.248876 | ||||||||
\(777\) | 122.722 | 4.40262 | ||||||||
\(778\) | 4.33744 | 0.155505 | ||||||||
\(779\) | −18.1206 | −0.649237 | ||||||||
\(780\) | 20.5402 | 0.735458 | ||||||||
\(781\) | 6.63711 | 0.237494 | ||||||||
\(782\) | 5.16486 | 0.184695 | ||||||||
\(783\) | 50.1932 | 1.79376 | ||||||||
\(784\) | 5.30428 | 0.189439 | ||||||||
\(785\) | −12.2085 | −0.435740 | ||||||||
\(786\) | 30.5249 | 1.08879 | ||||||||
\(787\) | 45.5560 | 1.62390 | 0.811949 | − | 0.583729i | \(-0.198407\pi\) | ||||
0.811949 | + | 0.583729i | \(0.198407\pi\) | |||||||
\(788\) | 4.55572 | 0.162291 | ||||||||
\(789\) | −62.9754 | −2.24198 | ||||||||
\(790\) | −10.3469 | −0.368127 | ||||||||
\(791\) | −61.6202 | −2.19096 | ||||||||
\(792\) | −6.18873 | −0.219907 | ||||||||
\(793\) | 41.9637 | 1.49017 | ||||||||
\(794\) | 10.0832 | 0.357839 | ||||||||
\(795\) | 38.6787 | 1.37179 | ||||||||
\(796\) | 4.04141 | 0.143244 | ||||||||
\(797\) | −11.2410 | −0.398176 | −0.199088 | − | 0.979982i | \(-0.563798\pi\) | ||||
−0.199088 | + | 0.979982i | \(0.563798\pi\) | |||||||
\(798\) | 79.3918 | 2.81044 | ||||||||
\(799\) | 4.52681 | 0.160147 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −34.0057 | −1.20153 | ||||||||
\(802\) | 26.7837 | 0.945767 | ||||||||
\(803\) | 1.00000 | 0.0352892 | ||||||||
\(804\) | 18.9566 | 0.668547 | ||||||||
\(805\) | −11.1105 | −0.391594 | ||||||||
\(806\) | 20.5893 | 0.725227 | ||||||||
\(807\) | −3.78136 | −0.133110 | ||||||||
\(808\) | −5.27322 | −0.185511 | ||||||||
\(809\) | −5.48510 | −0.192846 | −0.0964229 | − | 0.995340i | \(-0.530740\pi\) | ||||
−0.0964229 | + | 0.995340i | \(0.530740\pi\) | |||||||
\(810\) | −10.7342 | −0.377161 | ||||||||
\(811\) | −29.7573 | −1.04492 | −0.522460 | − | 0.852664i | \(-0.674986\pi\) | ||||
−0.522460 | + | 0.852664i | \(0.674986\pi\) | |||||||
\(812\) | 18.2149 | 0.639218 | ||||||||
\(813\) | 39.2224 | 1.37559 | ||||||||
\(814\) | −11.5416 | −0.404533 | ||||||||
\(815\) | 16.8631 | 0.590687 | ||||||||
\(816\) | 4.94288 | 0.173035 | ||||||||
\(817\) | −78.6366 | −2.75115 | ||||||||
\(818\) | 7.19999 | 0.251742 | ||||||||
\(819\) | −147.098 | −5.14003 | ||||||||
\(820\) | 2.42690 | 0.0847511 | ||||||||
\(821\) | 30.1940 | 1.05378 | 0.526888 | − | 0.849935i | \(-0.323359\pi\) | ||||
0.526888 | + | 0.849935i | \(0.323359\pi\) | |||||||
\(822\) | −66.2103 | −2.30935 | ||||||||
\(823\) | −9.94045 | −0.346502 | −0.173251 | − | 0.984878i | \(-0.555427\pi\) | ||||
−0.173251 | + | 0.984878i | \(0.555427\pi\) | |||||||
\(824\) | 0.506930 | 0.0176597 | ||||||||
\(825\) | −3.03129 | −0.105536 | ||||||||
\(826\) | 16.3084 | 0.567442 | ||||||||
\(827\) | −12.9750 | −0.451185 | −0.225592 | − | 0.974222i | \(-0.572432\pi\) | ||||
−0.225592 | + | 0.974222i | \(0.572432\pi\) | |||||||
\(828\) | 19.6023 | 0.681229 | ||||||||
\(829\) | −31.1035 | −1.08027 | −0.540135 | − | 0.841578i | \(-0.681627\pi\) | ||||
−0.540135 | + | 0.841578i | \(0.681627\pi\) | |||||||
\(830\) | −9.45862 | −0.328314 | ||||||||
\(831\) | 84.5548 | 2.93317 | ||||||||
\(832\) | −6.77606 | −0.234918 | ||||||||
\(833\) | 8.64925 | 0.299679 | ||||||||
\(834\) | −43.8619 | −1.51881 | ||||||||
\(835\) | −15.2813 | −0.528832 | ||||||||
\(836\) | −7.46655 | −0.258236 | ||||||||
\(837\) | −29.3704 | −1.01519 | ||||||||
\(838\) | 0.832557 | 0.0287602 | ||||||||
\(839\) | 24.3203 | 0.839630 | 0.419815 | − | 0.907610i | \(-0.362095\pi\) | ||||
0.419815 | + | 0.907610i | \(0.362095\pi\) | |||||||
\(840\) | −10.6330 | −0.366873 | ||||||||
\(841\) | −2.03512 | −0.0701766 | ||||||||
\(842\) | −32.8737 | −1.13290 | ||||||||
\(843\) | −11.1171 | −0.382894 | ||||||||
\(844\) | −17.5194 | −0.603043 | ||||||||
\(845\) | −32.9150 | −1.13231 | ||||||||
\(846\) | 17.1808 | 0.590687 | ||||||||
\(847\) | 3.50775 | 0.120528 | ||||||||
\(848\) | −12.7598 | −0.438174 | ||||||||
\(849\) | −89.7533 | −3.08033 | ||||||||
\(850\) | 1.63062 | 0.0559297 | ||||||||
\(851\) | 36.5572 | 1.25316 | ||||||||
\(852\) | −20.1190 | −0.689266 | ||||||||
\(853\) | 50.0979 | 1.71532 | 0.857659 | − | 0.514219i | \(-0.171918\pi\) | ||||
0.857659 | + | 0.514219i | \(0.171918\pi\) | |||||||
\(854\) | −21.7232 | −0.743353 | ||||||||
\(855\) | −46.2085 | −1.58030 | ||||||||
\(856\) | 1.78929 | 0.0611565 | ||||||||
\(857\) | −31.1978 | −1.06570 | −0.532849 | − | 0.846210i | \(-0.678879\pi\) | ||||
−0.532849 | + | 0.846210i | \(0.678879\pi\) | |||||||
\(858\) | 20.5402 | 0.701232 | ||||||||
\(859\) | −23.7018 | −0.808693 | −0.404347 | − | 0.914606i | \(-0.632501\pi\) | ||||
−0.404347 | + | 0.914606i | \(0.632501\pi\) | |||||||
\(860\) | 10.5318 | 0.359133 | ||||||||
\(861\) | −25.8053 | −0.879441 | ||||||||
\(862\) | 10.8956 | 0.371105 | ||||||||
\(863\) | −16.9518 | −0.577045 | −0.288523 | − | 0.957473i | \(-0.593164\pi\) | ||||
−0.288523 | + | 0.957473i | \(0.593164\pi\) | |||||||
\(864\) | 9.66598 | 0.328843 | ||||||||
\(865\) | 1.38794 | 0.0471915 | ||||||||
\(866\) | 2.05905 | 0.0699692 | ||||||||
\(867\) | −43.4720 | −1.47639 | ||||||||
\(868\) | −10.6584 | −0.361770 | ||||||||
\(869\) | −10.3469 | −0.350996 | ||||||||
\(870\) | −15.7408 | −0.533663 | ||||||||
\(871\) | −42.3750 | −1.43582 | ||||||||
\(872\) | 8.93951 | 0.302730 | ||||||||
\(873\) | −42.9058 | −1.45214 | ||||||||
\(874\) | 23.6497 | 0.799964 | ||||||||
\(875\) | −3.50775 | −0.118583 | ||||||||
\(876\) | −3.03129 | −0.102418 | ||||||||
\(877\) | −2.74306 | −0.0926265 | −0.0463132 | − | 0.998927i | \(-0.514747\pi\) | ||||
−0.0463132 | + | 0.998927i | \(0.514747\pi\) | |||||||
\(878\) | −17.5600 | −0.592620 | ||||||||
\(879\) | −73.7405 | −2.48720 | ||||||||
\(880\) | 1.00000 | 0.0337100 | ||||||||
\(881\) | 53.0362 | 1.78684 | 0.893418 | − | 0.449227i | \(-0.148301\pi\) | ||||
0.893418 | + | 0.449227i | \(0.148301\pi\) | |||||||
\(882\) | 32.8268 | 1.10533 | ||||||||
\(883\) | −11.2374 | −0.378168 | −0.189084 | − | 0.981961i | \(-0.560552\pi\) | ||||
−0.189084 | + | 0.981961i | \(0.560552\pi\) | |||||||
\(884\) | −11.0492 | −0.371624 | ||||||||
\(885\) | −14.0932 | −0.473739 | ||||||||
\(886\) | −30.6787 | −1.03067 | ||||||||
\(887\) | −12.6538 | −0.424873 | −0.212436 | − | 0.977175i | \(-0.568140\pi\) | ||||
−0.212436 | + | 0.977175i | \(0.568140\pi\) | |||||||
\(888\) | 34.9860 | 1.17405 | ||||||||
\(889\) | 30.7542 | 1.03146 | ||||||||
\(890\) | 5.49478 | 0.184185 | ||||||||
\(891\) | −10.7342 | −0.359609 | ||||||||
\(892\) | 8.38259 | 0.280670 | ||||||||
\(893\) | 20.7282 | 0.693641 | ||||||||
\(894\) | 67.9304 | 2.27193 | ||||||||
\(895\) | 5.85001 | 0.195544 | ||||||||
\(896\) | 3.50775 | 0.117186 | ||||||||
\(897\) | −65.0596 | −2.17228 | ||||||||
\(898\) | 24.7126 | 0.824670 | ||||||||
\(899\) | −15.7784 | −0.526240 | ||||||||
\(900\) | 6.18873 | 0.206291 | ||||||||
\(901\) | −20.8064 | −0.693161 | ||||||||
\(902\) | 2.42690 | 0.0808070 | ||||||||
\(903\) | −111.985 | −3.72663 | ||||||||
\(904\) | −17.5669 | −0.584267 | ||||||||
\(905\) | −25.5379 | −0.848909 | ||||||||
\(906\) | −7.35246 | −0.244269 | ||||||||
\(907\) | −49.8822 | −1.65631 | −0.828156 | − | 0.560498i | \(-0.810610\pi\) | ||||
−0.828156 | + | 0.560498i | \(0.810610\pi\) | |||||||
\(908\) | −0.352740 | −0.0117061 | ||||||||
\(909\) | −32.6346 | −1.08242 | ||||||||
\(910\) | 23.7687 | 0.787925 | ||||||||
\(911\) | −34.6748 | −1.14883 | −0.574414 | − | 0.818565i | \(-0.694770\pi\) | ||||
−0.574414 | + | 0.818565i | \(0.694770\pi\) | |||||||
\(912\) | 22.6333 | 0.749463 | ||||||||
\(913\) | −9.45862 | −0.313035 | ||||||||
\(914\) | −25.9039 | −0.856825 | ||||||||
\(915\) | 18.7726 | 0.620602 | ||||||||
\(916\) | −3.80347 | −0.125670 | ||||||||
\(917\) | 35.3227 | 1.16646 | ||||||||
\(918\) | 15.7615 | 0.520207 | ||||||||
\(919\) | 2.00279 | 0.0660659 | 0.0330329 | − | 0.999454i | \(-0.489483\pi\) | ||||
0.0330329 | + | 0.999454i | \(0.489483\pi\) | |||||||
\(920\) | −3.16743 | −0.104427 | ||||||||
\(921\) | 43.3554 | 1.42861 | ||||||||
\(922\) | 12.1699 | 0.400796 | ||||||||
\(923\) | 44.9735 | 1.48032 | ||||||||
\(924\) | −10.6330 | −0.349800 | ||||||||
\(925\) | 11.5416 | 0.379486 | ||||||||
\(926\) | −3.82987 | −0.125857 | ||||||||
\(927\) | 3.13725 | 0.103041 | ||||||||
\(928\) | 5.19277 | 0.170461 | ||||||||
\(929\) | −27.2884 | −0.895303 | −0.447652 | − | 0.894208i | \(-0.647739\pi\) | ||||
−0.447652 | + | 0.894208i | \(0.647739\pi\) | |||||||
\(930\) | 9.21069 | 0.302030 | ||||||||
\(931\) | 39.6047 | 1.29799 | ||||||||
\(932\) | −10.8696 | −0.356045 | ||||||||
\(933\) | −1.63958 | −0.0536775 | ||||||||
\(934\) | −23.8515 | −0.780444 | ||||||||
\(935\) | 1.63062 | 0.0533269 | ||||||||
\(936\) | −41.9352 | −1.37070 | ||||||||
\(937\) | −0.481367 | −0.0157256 | −0.00786279 | − | 0.999969i | \(-0.502503\pi\) | ||||
−0.00786279 | + | 0.999969i | \(0.502503\pi\) | |||||||
\(938\) | 21.9362 | 0.716241 | ||||||||
\(939\) | 75.3897 | 2.46025 | ||||||||
\(940\) | −2.77614 | −0.0905475 | ||||||||
\(941\) | 26.2647 | 0.856204 | 0.428102 | − | 0.903731i | \(-0.359182\pi\) | ||||
0.428102 | + | 0.903731i | \(0.359182\pi\) | |||||||
\(942\) | 37.0075 | 1.20577 | ||||||||
\(943\) | −7.68703 | −0.250324 | ||||||||
\(944\) | 4.64925 | 0.151320 | ||||||||
\(945\) | −33.9058 | −1.10296 | ||||||||
\(946\) | 10.5318 | 0.342420 | ||||||||
\(947\) | −22.5959 | −0.734268 | −0.367134 | − | 0.930168i | \(-0.619661\pi\) | ||||
−0.367134 | + | 0.930168i | \(0.619661\pi\) | |||||||
\(948\) | 31.3646 | 1.01867 | ||||||||
\(949\) | 6.77606 | 0.219960 | ||||||||
\(950\) | 7.46655 | 0.242247 | ||||||||
\(951\) | −72.1835 | −2.34071 | ||||||||
\(952\) | 5.71979 | 0.185379 | ||||||||
\(953\) | 4.78708 | 0.155069 | 0.0775344 | − | 0.996990i | \(-0.475295\pi\) | ||||
0.0775344 | + | 0.996990i | \(0.475295\pi\) | |||||||
\(954\) | −78.9671 | −2.55665 | ||||||||
\(955\) | −17.5333 | −0.567365 | ||||||||
\(956\) | 7.40131 | 0.239376 | ||||||||
\(957\) | −15.7408 | −0.508828 | ||||||||
\(958\) | −16.3428 | −0.528011 | ||||||||
\(959\) | −76.6171 | −2.47409 | ||||||||
\(960\) | −3.03129 | −0.0978345 | ||||||||
\(961\) | −21.7673 | −0.702171 | ||||||||
\(962\) | −78.2067 | −2.52148 | ||||||||
\(963\) | 11.0734 | 0.356836 | ||||||||
\(964\) | −17.4401 | −0.561708 | ||||||||
\(965\) | 6.62499 | 0.213266 | ||||||||
\(966\) | 33.6792 | 1.08361 | ||||||||
\(967\) | 34.2177 | 1.10037 | 0.550184 | − | 0.835044i | \(-0.314558\pi\) | ||||
0.550184 | + | 0.835044i | \(0.314558\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 36.9062 | 1.18560 | ||||||||
\(970\) | 6.93289 | 0.222602 | ||||||||
\(971\) | 18.4858 | 0.593238 | 0.296619 | − | 0.954996i | \(-0.404141\pi\) | ||||
0.296619 | + | 0.954996i | \(0.404141\pi\) | |||||||
\(972\) | 3.54057 | 0.113564 | ||||||||
\(973\) | −50.7560 | −1.62716 | ||||||||
\(974\) | −4.84862 | −0.155360 | ||||||||
\(975\) | −20.5402 | −0.657814 | ||||||||
\(976\) | −6.19293 | −0.198231 | ||||||||
\(977\) | −12.8490 | −0.411075 | −0.205538 | − | 0.978649i | \(-0.565894\pi\) | ||||
−0.205538 | + | 0.978649i | \(0.565894\pi\) | |||||||
\(978\) | −51.1168 | −1.63454 | ||||||||
\(979\) | 5.49478 | 0.175614 | ||||||||
\(980\) | −5.30428 | −0.169439 | ||||||||
\(981\) | 55.3242 | 1.76637 | ||||||||
\(982\) | −9.77007 | −0.311775 | ||||||||
\(983\) | 14.6661 | 0.467776 | 0.233888 | − | 0.972264i | \(-0.424855\pi\) | ||||
0.233888 | + | 0.972264i | \(0.424855\pi\) | |||||||
\(984\) | −7.35665 | −0.234521 | ||||||||
\(985\) | −4.55572 | −0.145157 | ||||||||
\(986\) | 8.46742 | 0.269658 | ||||||||
\(987\) | 29.5187 | 0.939589 | ||||||||
\(988\) | −50.5938 | −1.60960 | ||||||||
\(989\) | −33.3588 | −1.06075 | ||||||||
\(990\) | 6.18873 | 0.196691 | ||||||||
\(991\) | 5.74036 | 0.182348 | 0.0911742 | − | 0.995835i | \(-0.470938\pi\) | ||||
0.0911742 | + | 0.995835i | \(0.470938\pi\) | |||||||
\(992\) | −3.03853 | −0.0964736 | ||||||||
\(993\) | −36.6820 | −1.16407 | ||||||||
\(994\) | −23.2813 | −0.738438 | ||||||||
\(995\) | −4.04141 | −0.128121 | ||||||||
\(996\) | 28.6718 | 0.908502 | ||||||||
\(997\) | 36.8207 | 1.16612 | 0.583062 | − | 0.812428i | \(-0.301855\pi\) | ||||
0.583062 | + | 0.812428i | \(0.301855\pi\) | |||||||
\(998\) | −9.92500 | −0.314170 | ||||||||
\(999\) | 111.561 | 3.52963 |
(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 | 8030.2.a.bg.1.14 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8030.2.a.bg.1.14 | ✓ | 15 | 1.1 | even | 1 | trivial |