Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4730,2,Mod(1,4730)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4730, 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("4730.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4730.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: | \(37.7692401561\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 26 x^{10} + 79 x^{9} + 247 x^{8} - 766 x^{7} - 1023 x^{6} + 3281 x^{5} + 1634 x^{4} - 5557 x^{3} - 483 x^{2} + 1648 x + 392 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(2.14541\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4730.1 |
$q$-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 | ||||||||
\(3\) | 2.14541 | 1.23865 | 0.619325 | − | 0.785134i | \(-0.287406\pi\) | ||||
0.619325 | + | 0.785134i | \(0.287406\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 2.14541 | 0.875858 | ||||||||
\(7\) | −4.86538 | −1.83894 | −0.919470 | − | 0.393159i | \(-0.871382\pi\) | ||||
−0.919470 | + | 0.393159i | \(0.871382\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.60277 | 0.534255 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 2.14541 | 0.619325 | ||||||||
\(13\) | 0.772928 | 0.214372 | 0.107186 | − | 0.994239i | \(-0.465816\pi\) | ||||
0.107186 | + | 0.994239i | \(0.465816\pi\) | |||||||
\(14\) | −4.86538 | −1.30033 | ||||||||
\(15\) | 2.14541 | 0.553941 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.64772 | 0.884703 | 0.442351 | − | 0.896842i | \(-0.354144\pi\) | ||||
0.442351 | + | 0.896842i | \(0.354144\pi\) | |||||||
\(18\) | 1.60277 | 0.377776 | ||||||||
\(19\) | 6.17757 | 1.41723 | 0.708616 | − | 0.705594i | \(-0.249320\pi\) | ||||
0.708616 | + | 0.705594i | \(0.249320\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −10.4382 | −2.27781 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 1.22707 | 0.255862 | 0.127931 | − | 0.991783i | \(-0.459166\pi\) | ||||
0.127931 | + | 0.991783i | \(0.459166\pi\) | |||||||
\(24\) | 2.14541 | 0.437929 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.772928 | 0.151584 | ||||||||
\(27\) | −2.99763 | −0.576895 | ||||||||
\(28\) | −4.86538 | −0.919470 | ||||||||
\(29\) | 8.75395 | 1.62557 | 0.812784 | − | 0.582566i | \(-0.197951\pi\) | ||||
0.812784 | + | 0.582566i | \(0.197951\pi\) | |||||||
\(30\) | 2.14541 | 0.391696 | ||||||||
\(31\) | −1.82359 | −0.327526 | −0.163763 | − | 0.986500i | \(-0.552363\pi\) | ||||
−0.163763 | + | 0.986500i | \(0.552363\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −2.14541 | −0.373467 | ||||||||
\(34\) | 3.64772 | 0.625579 | ||||||||
\(35\) | −4.86538 | −0.822399 | ||||||||
\(36\) | 1.60277 | 0.267128 | ||||||||
\(37\) | 10.5210 | 1.72965 | 0.864824 | − | 0.502076i | \(-0.167430\pi\) | ||||
0.864824 | + | 0.502076i | \(0.167430\pi\) | |||||||
\(38\) | 6.17757 | 1.00213 | ||||||||
\(39\) | 1.65824 | 0.265532 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 1.71235 | 0.267425 | 0.133712 | − | 0.991020i | \(-0.457310\pi\) | ||||
0.133712 | + | 0.991020i | \(0.457310\pi\) | |||||||
\(42\) | −10.4382 | −1.61065 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 1.60277 | 0.238926 | ||||||||
\(46\) | 1.22707 | 0.180922 | ||||||||
\(47\) | −0.956221 | −0.139479 | −0.0697396 | − | 0.997565i | \(-0.522217\pi\) | ||||
−0.0697396 | + | 0.997565i | \(0.522217\pi\) | |||||||
\(48\) | 2.14541 | 0.309663 | ||||||||
\(49\) | 16.6719 | 2.38170 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 7.82585 | 1.09584 | ||||||||
\(52\) | 0.772928 | 0.107186 | ||||||||
\(53\) | 12.8969 | 1.77153 | 0.885763 | − | 0.464138i | \(-0.153636\pi\) | ||||
0.885763 | + | 0.464138i | \(0.153636\pi\) | |||||||
\(54\) | −2.99763 | −0.407926 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | −4.86538 | −0.650164 | ||||||||
\(57\) | 13.2534 | 1.75546 | ||||||||
\(58\) | 8.75395 | 1.14945 | ||||||||
\(59\) | −10.8365 | −1.41079 | −0.705396 | − | 0.708813i | \(-0.749231\pi\) | ||||
−0.705396 | + | 0.708813i | \(0.749231\pi\) | |||||||
\(60\) | 2.14541 | 0.276971 | ||||||||
\(61\) | −1.28503 | −0.164531 | −0.0822654 | − | 0.996610i | \(-0.526216\pi\) | ||||
−0.0822654 | + | 0.996610i | \(0.526216\pi\) | |||||||
\(62\) | −1.82359 | −0.231596 | ||||||||
\(63\) | −7.79807 | −0.982464 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.772928 | 0.0958699 | ||||||||
\(66\) | −2.14541 | −0.264081 | ||||||||
\(67\) | −13.6755 | −1.67072 | −0.835362 | − | 0.549700i | \(-0.814742\pi\) | ||||
−0.835362 | + | 0.549700i | \(0.814742\pi\) | |||||||
\(68\) | 3.64772 | 0.442351 | ||||||||
\(69\) | 2.63257 | 0.316924 | ||||||||
\(70\) | −4.86538 | −0.581524 | ||||||||
\(71\) | 6.58014 | 0.780919 | 0.390459 | − | 0.920620i | \(-0.372316\pi\) | ||||
0.390459 | + | 0.920620i | \(0.372316\pi\) | |||||||
\(72\) | 1.60277 | 0.188888 | ||||||||
\(73\) | 12.0544 | 1.41086 | 0.705429 | − | 0.708781i | \(-0.250754\pi\) | ||||
0.705429 | + | 0.708781i | \(0.250754\pi\) | |||||||
\(74\) | 10.5210 | 1.22305 | ||||||||
\(75\) | 2.14541 | 0.247730 | ||||||||
\(76\) | 6.17757 | 0.708616 | ||||||||
\(77\) | 4.86538 | 0.554462 | ||||||||
\(78\) | 1.65824 | 0.187759 | ||||||||
\(79\) | −2.42150 | −0.272440 | −0.136220 | − | 0.990679i | \(-0.543495\pi\) | ||||
−0.136220 | + | 0.990679i | \(0.543495\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −11.2394 | −1.24883 | ||||||||
\(82\) | 1.71235 | 0.189098 | ||||||||
\(83\) | −4.52346 | −0.496515 | −0.248257 | − | 0.968694i | \(-0.579858\pi\) | ||||
−0.248257 | + | 0.968694i | \(0.579858\pi\) | |||||||
\(84\) | −10.4382 | −1.13890 | ||||||||
\(85\) | 3.64772 | 0.395651 | ||||||||
\(86\) | 1.00000 | 0.107833 | ||||||||
\(87\) | 18.7808 | 2.01351 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −3.19651 | −0.338829 | −0.169415 | − | 0.985545i | \(-0.554188\pi\) | ||||
−0.169415 | + | 0.985545i | \(0.554188\pi\) | |||||||
\(90\) | 1.60277 | 0.168946 | ||||||||
\(91\) | −3.76059 | −0.394217 | ||||||||
\(92\) | 1.22707 | 0.127931 | ||||||||
\(93\) | −3.91233 | −0.405690 | ||||||||
\(94\) | −0.956221 | −0.0986267 | ||||||||
\(95\) | 6.17757 | 0.633806 | ||||||||
\(96\) | 2.14541 | 0.218965 | ||||||||
\(97\) | −9.25991 | −0.940201 | −0.470101 | − | 0.882613i | \(-0.655782\pi\) | ||||
−0.470101 | + | 0.882613i | \(0.655782\pi\) | |||||||
\(98\) | 16.6719 | 1.68412 | ||||||||
\(99\) | −1.60277 | −0.161084 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −19.6223 | −1.95249 | −0.976247 | − | 0.216661i | \(-0.930483\pi\) | ||||
−0.976247 | + | 0.216661i | \(0.930483\pi\) | |||||||
\(102\) | 7.82585 | 0.774874 | ||||||||
\(103\) | −1.16390 | −0.114682 | −0.0573410 | − | 0.998355i | \(-0.518262\pi\) | ||||
−0.0573410 | + | 0.998355i | \(0.518262\pi\) | |||||||
\(104\) | 0.772928 | 0.0757918 | ||||||||
\(105\) | −10.4382 | −1.01867 | ||||||||
\(106\) | 12.8969 | 1.25266 | ||||||||
\(107\) | 10.5763 | 1.02245 | 0.511227 | − | 0.859446i | \(-0.329191\pi\) | ||||
0.511227 | + | 0.859446i | \(0.329191\pi\) | |||||||
\(108\) | −2.99763 | −0.288447 | ||||||||
\(109\) | 14.6577 | 1.40395 | 0.701977 | − | 0.712199i | \(-0.252301\pi\) | ||||
0.701977 | + | 0.712199i | \(0.252301\pi\) | |||||||
\(110\) | −1.00000 | −0.0953463 | ||||||||
\(111\) | 22.5719 | 2.14243 | ||||||||
\(112\) | −4.86538 | −0.459735 | ||||||||
\(113\) | −5.58684 | −0.525565 | −0.262783 | − | 0.964855i | \(-0.584640\pi\) | ||||
−0.262783 | + | 0.964855i | \(0.584640\pi\) | |||||||
\(114\) | 13.2534 | 1.24130 | ||||||||
\(115\) | 1.22707 | 0.114425 | ||||||||
\(116\) | 8.75395 | 0.812784 | ||||||||
\(117\) | 1.23882 | 0.114529 | ||||||||
\(118\) | −10.8365 | −0.997581 | ||||||||
\(119\) | −17.7476 | −1.62692 | ||||||||
\(120\) | 2.14541 | 0.195848 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −1.28503 | −0.116341 | ||||||||
\(123\) | 3.67370 | 0.331246 | ||||||||
\(124\) | −1.82359 | −0.163763 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −7.79807 | −0.694707 | ||||||||
\(127\) | −10.6963 | −0.949147 | −0.474574 | − | 0.880216i | \(-0.657398\pi\) | ||||
−0.474574 | + | 0.880216i | \(0.657398\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 2.14541 | 0.188892 | ||||||||
\(130\) | 0.772928 | 0.0677903 | ||||||||
\(131\) | 2.05074 | 0.179174 | 0.0895871 | − | 0.995979i | \(-0.471445\pi\) | ||||
0.0895871 | + | 0.995979i | \(0.471445\pi\) | |||||||
\(132\) | −2.14541 | −0.186734 | ||||||||
\(133\) | −30.0562 | −2.60621 | ||||||||
\(134\) | −13.6755 | −1.18138 | ||||||||
\(135\) | −2.99763 | −0.257995 | ||||||||
\(136\) | 3.64772 | 0.312790 | ||||||||
\(137\) | 18.6621 | 1.59441 | 0.797207 | − | 0.603706i | \(-0.206310\pi\) | ||||
0.797207 | + | 0.603706i | \(0.206310\pi\) | |||||||
\(138\) | 2.63257 | 0.224099 | ||||||||
\(139\) | 16.5332 | 1.40233 | 0.701163 | − | 0.713001i | \(-0.252664\pi\) | ||||
0.701163 | + | 0.713001i | \(0.252664\pi\) | |||||||
\(140\) | −4.86538 | −0.411200 | ||||||||
\(141\) | −2.05148 | −0.172766 | ||||||||
\(142\) | 6.58014 | 0.552193 | ||||||||
\(143\) | −0.772928 | −0.0646355 | ||||||||
\(144\) | 1.60277 | 0.133564 | ||||||||
\(145\) | 8.75395 | 0.726976 | ||||||||
\(146\) | 12.0544 | 0.997627 | ||||||||
\(147\) | 35.7680 | 2.95010 | ||||||||
\(148\) | 10.5210 | 0.864824 | ||||||||
\(149\) | 14.4421 | 1.18315 | 0.591573 | − | 0.806252i | \(-0.298507\pi\) | ||||
0.591573 | + | 0.806252i | \(0.298507\pi\) | |||||||
\(150\) | 2.14541 | 0.175172 | ||||||||
\(151\) | 5.43320 | 0.442147 | 0.221074 | − | 0.975257i | \(-0.429044\pi\) | ||||
0.221074 | + | 0.975257i | \(0.429044\pi\) | |||||||
\(152\) | 6.17757 | 0.501067 | ||||||||
\(153\) | 5.84645 | 0.472657 | ||||||||
\(154\) | 4.86538 | 0.392063 | ||||||||
\(155\) | −1.82359 | −0.146474 | ||||||||
\(156\) | 1.65824 | 0.132766 | ||||||||
\(157\) | 2.32998 | 0.185953 | 0.0929765 | − | 0.995668i | \(-0.470362\pi\) | ||||
0.0929765 | + | 0.995668i | \(0.470362\pi\) | |||||||
\(158\) | −2.42150 | −0.192644 | ||||||||
\(159\) | 27.6691 | 2.19430 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −5.97017 | −0.470515 | ||||||||
\(162\) | −11.2394 | −0.883054 | ||||||||
\(163\) | −1.87279 | −0.146688 | −0.0733441 | − | 0.997307i | \(-0.523367\pi\) | ||||
−0.0733441 | + | 0.997307i | \(0.523367\pi\) | |||||||
\(164\) | 1.71235 | 0.133712 | ||||||||
\(165\) | −2.14541 | −0.167020 | ||||||||
\(166\) | −4.52346 | −0.351089 | ||||||||
\(167\) | 12.7269 | 0.984834 | 0.492417 | − | 0.870359i | \(-0.336113\pi\) | ||||
0.492417 | + | 0.870359i | \(0.336113\pi\) | |||||||
\(168\) | −10.4382 | −0.805326 | ||||||||
\(169\) | −12.4026 | −0.954045 | ||||||||
\(170\) | 3.64772 | 0.279768 | ||||||||
\(171\) | 9.90121 | 0.757164 | ||||||||
\(172\) | 1.00000 | 0.0762493 | ||||||||
\(173\) | −18.8851 | −1.43580 | −0.717902 | − | 0.696144i | \(-0.754898\pi\) | ||||
−0.717902 | + | 0.696144i | \(0.754898\pi\) | |||||||
\(174\) | 18.7808 | 1.42377 | ||||||||
\(175\) | −4.86538 | −0.367788 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | −23.2487 | −1.74748 | ||||||||
\(178\) | −3.19651 | −0.239589 | ||||||||
\(179\) | −5.52325 | −0.412827 | −0.206414 | − | 0.978465i | \(-0.566179\pi\) | ||||
−0.206414 | + | 0.978465i | \(0.566179\pi\) | |||||||
\(180\) | 1.60277 | 0.119463 | ||||||||
\(181\) | −12.7201 | −0.945479 | −0.472740 | − | 0.881202i | \(-0.656735\pi\) | ||||
−0.472740 | + | 0.881202i | \(0.656735\pi\) | |||||||
\(182\) | −3.76059 | −0.278753 | ||||||||
\(183\) | −2.75690 | −0.203796 | ||||||||
\(184\) | 1.22707 | 0.0904609 | ||||||||
\(185\) | 10.5210 | 0.773522 | ||||||||
\(186\) | −3.91233 | −0.286866 | ||||||||
\(187\) | −3.64772 | −0.266748 | ||||||||
\(188\) | −0.956221 | −0.0697396 | ||||||||
\(189\) | 14.5846 | 1.06088 | ||||||||
\(190\) | 6.17757 | 0.448168 | ||||||||
\(191\) | 1.51319 | 0.109491 | 0.0547453 | − | 0.998500i | \(-0.482565\pi\) | ||||
0.0547453 | + | 0.998500i | \(0.482565\pi\) | |||||||
\(192\) | 2.14541 | 0.154831 | ||||||||
\(193\) | −0.480458 | −0.0345842 | −0.0172921 | − | 0.999850i | \(-0.505505\pi\) | ||||
−0.0172921 | + | 0.999850i | \(0.505505\pi\) | |||||||
\(194\) | −9.25991 | −0.664823 | ||||||||
\(195\) | 1.65824 | 0.118749 | ||||||||
\(196\) | 16.6719 | 1.19085 | ||||||||
\(197\) | 25.3554 | 1.80650 | 0.903248 | − | 0.429118i | \(-0.141176\pi\) | ||||
0.903248 | + | 0.429118i | \(0.141176\pi\) | |||||||
\(198\) | −1.60277 | −0.113904 | ||||||||
\(199\) | −22.0088 | −1.56017 | −0.780083 | − | 0.625676i | \(-0.784823\pi\) | ||||
−0.780083 | + | 0.625676i | \(0.784823\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −29.3394 | −2.06944 | ||||||||
\(202\) | −19.6223 | −1.38062 | ||||||||
\(203\) | −42.5913 | −2.98932 | ||||||||
\(204\) | 7.82585 | 0.547919 | ||||||||
\(205\) | 1.71235 | 0.119596 | ||||||||
\(206\) | −1.16390 | −0.0810924 | ||||||||
\(207\) | 1.96671 | 0.136696 | ||||||||
\(208\) | 0.772928 | 0.0535929 | ||||||||
\(209\) | −6.17757 | −0.427312 | ||||||||
\(210\) | −10.4382 | −0.720305 | ||||||||
\(211\) | −16.1348 | −1.11076 | −0.555382 | − | 0.831595i | \(-0.687428\pi\) | ||||
−0.555382 | + | 0.831595i | \(0.687428\pi\) | |||||||
\(212\) | 12.8969 | 0.885763 | ||||||||
\(213\) | 14.1171 | 0.967286 | ||||||||
\(214\) | 10.5763 | 0.722984 | ||||||||
\(215\) | 1.00000 | 0.0681994 | ||||||||
\(216\) | −2.99763 | −0.203963 | ||||||||
\(217\) | 8.87244 | 0.602301 | ||||||||
\(218\) | 14.6577 | 0.992746 | ||||||||
\(219\) | 25.8615 | 1.74756 | ||||||||
\(220\) | −1.00000 | −0.0674200 | ||||||||
\(221\) | 2.81943 | 0.189655 | ||||||||
\(222\) | 22.5719 | 1.51493 | ||||||||
\(223\) | 19.6717 | 1.31732 | 0.658658 | − | 0.752443i | \(-0.271124\pi\) | ||||
0.658658 | + | 0.752443i | \(0.271124\pi\) | |||||||
\(224\) | −4.86538 | −0.325082 | ||||||||
\(225\) | 1.60277 | 0.106851 | ||||||||
\(226\) | −5.58684 | −0.371631 | ||||||||
\(227\) | 7.76226 | 0.515200 | 0.257600 | − | 0.966252i | \(-0.417068\pi\) | ||||
0.257600 | + | 0.966252i | \(0.417068\pi\) | |||||||
\(228\) | 13.2534 | 0.877728 | ||||||||
\(229\) | −14.9929 | −0.990759 | −0.495380 | − | 0.868677i | \(-0.664971\pi\) | ||||
−0.495380 | + | 0.868677i | \(0.664971\pi\) | |||||||
\(230\) | 1.22707 | 0.0809107 | ||||||||
\(231\) | 10.4382 | 0.686784 | ||||||||
\(232\) | 8.75395 | 0.574725 | ||||||||
\(233\) | 7.01617 | 0.459644 | 0.229822 | − | 0.973233i | \(-0.426186\pi\) | ||||
0.229822 | + | 0.973233i | \(0.426186\pi\) | |||||||
\(234\) | 1.23882 | 0.0809844 | ||||||||
\(235\) | −0.956221 | −0.0623770 | ||||||||
\(236\) | −10.8365 | −0.705396 | ||||||||
\(237\) | −5.19510 | −0.337458 | ||||||||
\(238\) | −17.7476 | −1.15040 | ||||||||
\(239\) | −6.58603 | −0.426015 | −0.213007 | − | 0.977051i | \(-0.568326\pi\) | ||||
−0.213007 | + | 0.977051i | \(0.568326\pi\) | |||||||
\(240\) | 2.14541 | 0.138485 | ||||||||
\(241\) | −20.3260 | −1.30931 | −0.654656 | − | 0.755927i | \(-0.727187\pi\) | ||||
−0.654656 | + | 0.755927i | \(0.727187\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | −15.1203 | −0.969965 | ||||||||
\(244\) | −1.28503 | −0.0822654 | ||||||||
\(245\) | 16.6719 | 1.06513 | ||||||||
\(246\) | 3.67370 | 0.234226 | ||||||||
\(247\) | 4.77482 | 0.303815 | ||||||||
\(248\) | −1.82359 | −0.115798 | ||||||||
\(249\) | −9.70466 | −0.615008 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −3.62591 | −0.228866 | −0.114433 | − | 0.993431i | \(-0.536505\pi\) | ||||
−0.114433 | + | 0.993431i | \(0.536505\pi\) | |||||||
\(252\) | −7.79807 | −0.491232 | ||||||||
\(253\) | −1.22707 | −0.0771453 | ||||||||
\(254\) | −10.6963 | −0.671148 | ||||||||
\(255\) | 7.82585 | 0.490074 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 7.21242 | 0.449899 | 0.224949 | − | 0.974370i | \(-0.427778\pi\) | ||||
0.224949 | + | 0.974370i | \(0.427778\pi\) | |||||||
\(258\) | 2.14541 | 0.133567 | ||||||||
\(259\) | −51.1888 | −3.18072 | ||||||||
\(260\) | 0.772928 | 0.0479350 | ||||||||
\(261\) | 14.0305 | 0.868468 | ||||||||
\(262\) | 2.05074 | 0.126695 | ||||||||
\(263\) | −18.5653 | −1.14479 | −0.572393 | − | 0.819979i | \(-0.693985\pi\) | ||||
−0.572393 | + | 0.819979i | \(0.693985\pi\) | |||||||
\(264\) | −2.14541 | −0.132041 | ||||||||
\(265\) | 12.8969 | 0.792250 | ||||||||
\(266\) | −30.0562 | −1.84287 | ||||||||
\(267\) | −6.85781 | −0.419691 | ||||||||
\(268\) | −13.6755 | −0.835362 | ||||||||
\(269\) | −23.5234 | −1.43425 | −0.717123 | − | 0.696947i | \(-0.754541\pi\) | ||||
−0.717123 | + | 0.696947i | \(0.754541\pi\) | |||||||
\(270\) | −2.99763 | −0.182430 | ||||||||
\(271\) | 10.8571 | 0.659522 | 0.329761 | − | 0.944064i | \(-0.393032\pi\) | ||||
0.329761 | + | 0.944064i | \(0.393032\pi\) | |||||||
\(272\) | 3.64772 | 0.221176 | ||||||||
\(273\) | −8.06799 | −0.488297 | ||||||||
\(274\) | 18.6621 | 1.12742 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | 2.63257 | 0.158462 | ||||||||
\(277\) | 11.1316 | 0.668832 | 0.334416 | − | 0.942426i | \(-0.391461\pi\) | ||||
0.334416 | + | 0.942426i | \(0.391461\pi\) | |||||||
\(278\) | 16.5332 | 0.991595 | ||||||||
\(279\) | −2.92278 | −0.174982 | ||||||||
\(280\) | −4.86538 | −0.290762 | ||||||||
\(281\) | −7.18944 | −0.428886 | −0.214443 | − | 0.976737i | \(-0.568794\pi\) | ||||
−0.214443 | + | 0.976737i | \(0.568794\pi\) | |||||||
\(282\) | −2.05148 | −0.122164 | ||||||||
\(283\) | −15.0195 | −0.892817 | −0.446408 | − | 0.894829i | \(-0.647297\pi\) | ||||
−0.446408 | + | 0.894829i | \(0.647297\pi\) | |||||||
\(284\) | 6.58014 | 0.390459 | ||||||||
\(285\) | 13.2534 | 0.785064 | ||||||||
\(286\) | −0.772928 | −0.0457042 | ||||||||
\(287\) | −8.33126 | −0.491779 | ||||||||
\(288\) | 1.60277 | 0.0944439 | ||||||||
\(289\) | −3.69411 | −0.217301 | ||||||||
\(290\) | 8.75395 | 0.514050 | ||||||||
\(291\) | −19.8663 | −1.16458 | ||||||||
\(292\) | 12.0544 | 0.705429 | ||||||||
\(293\) | −19.1081 | −1.11631 | −0.558154 | − | 0.829737i | \(-0.688490\pi\) | ||||
−0.558154 | + | 0.829737i | \(0.688490\pi\) | |||||||
\(294\) | 35.7680 | 2.08603 | ||||||||
\(295\) | −10.8365 | −0.630926 | ||||||||
\(296\) | 10.5210 | 0.611523 | ||||||||
\(297\) | 2.99763 | 0.173940 | ||||||||
\(298\) | 14.4421 | 0.836610 | ||||||||
\(299\) | 0.948438 | 0.0548496 | ||||||||
\(300\) | 2.14541 | 0.123865 | ||||||||
\(301\) | −4.86538 | −0.280436 | ||||||||
\(302\) | 5.43320 | 0.312645 | ||||||||
\(303\) | −42.0978 | −2.41846 | ||||||||
\(304\) | 6.17757 | 0.354308 | ||||||||
\(305\) | −1.28503 | −0.0735804 | ||||||||
\(306\) | 5.84645 | 0.334219 | ||||||||
\(307\) | −15.6944 | −0.895729 | −0.447865 | − | 0.894101i | \(-0.647815\pi\) | ||||
−0.447865 | + | 0.894101i | \(0.647815\pi\) | |||||||
\(308\) | 4.86538 | 0.277231 | ||||||||
\(309\) | −2.49703 | −0.142051 | ||||||||
\(310\) | −1.82359 | −0.103573 | ||||||||
\(311\) | −17.4073 | −0.987077 | −0.493538 | − | 0.869724i | \(-0.664297\pi\) | ||||
−0.493538 | + | 0.869724i | \(0.664297\pi\) | |||||||
\(312\) | 1.65824 | 0.0938796 | ||||||||
\(313\) | −5.94600 | −0.336088 | −0.168044 | − | 0.985780i | \(-0.553745\pi\) | ||||
−0.168044 | + | 0.985780i | \(0.553745\pi\) | |||||||
\(314\) | 2.32998 | 0.131489 | ||||||||
\(315\) | −7.79807 | −0.439371 | ||||||||
\(316\) | −2.42150 | −0.136220 | ||||||||
\(317\) | 10.1749 | 0.571477 | 0.285739 | − | 0.958308i | \(-0.407761\pi\) | ||||
0.285739 | + | 0.958308i | \(0.407761\pi\) | |||||||
\(318\) | 27.6691 | 1.55161 | ||||||||
\(319\) | −8.75395 | −0.490127 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 22.6906 | 1.26646 | ||||||||
\(322\) | −5.97017 | −0.332705 | ||||||||
\(323\) | 22.5341 | 1.25383 | ||||||||
\(324\) | −11.2394 | −0.624413 | ||||||||
\(325\) | 0.772928 | 0.0428743 | ||||||||
\(326\) | −1.87279 | −0.103724 | ||||||||
\(327\) | 31.4467 | 1.73901 | ||||||||
\(328\) | 1.71235 | 0.0945490 | ||||||||
\(329\) | 4.65238 | 0.256494 | ||||||||
\(330\) | −2.14541 | −0.118101 | ||||||||
\(331\) | 21.5396 | 1.18392 | 0.591961 | − | 0.805967i | \(-0.298354\pi\) | ||||
0.591961 | + | 0.805967i | \(0.298354\pi\) | |||||||
\(332\) | −4.52346 | −0.248257 | ||||||||
\(333\) | 16.8628 | 0.924073 | ||||||||
\(334\) | 12.7269 | 0.696383 | ||||||||
\(335\) | −13.6755 | −0.747171 | ||||||||
\(336\) | −10.4382 | −0.569451 | ||||||||
\(337\) | −7.28531 | −0.396856 | −0.198428 | − | 0.980115i | \(-0.563584\pi\) | ||||
−0.198428 | + | 0.980115i | \(0.563584\pi\) | |||||||
\(338\) | −12.4026 | −0.674612 | ||||||||
\(339\) | −11.9860 | −0.650992 | ||||||||
\(340\) | 3.64772 | 0.197826 | ||||||||
\(341\) | 1.82359 | 0.0987527 | ||||||||
\(342\) | 9.90121 | 0.535396 | ||||||||
\(343\) | −47.0576 | −2.54087 | ||||||||
\(344\) | 1.00000 | 0.0539164 | ||||||||
\(345\) | 2.63257 | 0.141733 | ||||||||
\(346\) | −18.8851 | −1.01527 | ||||||||
\(347\) | −8.13671 | −0.436802 | −0.218401 | − | 0.975859i | \(-0.570084\pi\) | ||||
−0.218401 | + | 0.975859i | \(0.570084\pi\) | |||||||
\(348\) | 18.7808 | 1.00676 | ||||||||
\(349\) | −29.8617 | −1.59846 | −0.799229 | − | 0.601026i | \(-0.794759\pi\) | ||||
−0.799229 | + | 0.601026i | \(0.794759\pi\) | |||||||
\(350\) | −4.86538 | −0.260065 | ||||||||
\(351\) | −2.31695 | −0.123670 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | 6.05373 | 0.322207 | 0.161104 | − | 0.986937i | \(-0.448495\pi\) | ||||
0.161104 | + | 0.986937i | \(0.448495\pi\) | |||||||
\(354\) | −23.2487 | −1.23565 | ||||||||
\(355\) | 6.58014 | 0.349238 | ||||||||
\(356\) | −3.19651 | −0.169415 | ||||||||
\(357\) | −38.0757 | −2.01518 | ||||||||
\(358\) | −5.52325 | −0.291913 | ||||||||
\(359\) | 20.3069 | 1.07176 | 0.535878 | − | 0.844296i | \(-0.319981\pi\) | ||||
0.535878 | + | 0.844296i | \(0.319981\pi\) | |||||||
\(360\) | 1.60277 | 0.0844732 | ||||||||
\(361\) | 19.1624 | 1.00855 | ||||||||
\(362\) | −12.7201 | −0.668555 | ||||||||
\(363\) | 2.14541 | 0.112605 | ||||||||
\(364\) | −3.76059 | −0.197108 | ||||||||
\(365\) | 12.0544 | 0.630955 | ||||||||
\(366\) | −2.75690 | −0.144106 | ||||||||
\(367\) | −5.38172 | −0.280924 | −0.140462 | − | 0.990086i | \(-0.544859\pi\) | ||||
−0.140462 | + | 0.990086i | \(0.544859\pi\) | |||||||
\(368\) | 1.22707 | 0.0639655 | ||||||||
\(369\) | 2.74451 | 0.142873 | ||||||||
\(370\) | 10.5210 | 0.546962 | ||||||||
\(371\) | −62.7483 | −3.25773 | ||||||||
\(372\) | −3.91233 | −0.202845 | ||||||||
\(373\) | 32.0733 | 1.66069 | 0.830346 | − | 0.557248i | \(-0.188143\pi\) | ||||
0.830346 | + | 0.557248i | \(0.188143\pi\) | |||||||
\(374\) | −3.64772 | −0.188619 | ||||||||
\(375\) | 2.14541 | 0.110788 | ||||||||
\(376\) | −0.956221 | −0.0493134 | ||||||||
\(377\) | 6.76617 | 0.348476 | ||||||||
\(378\) | 14.5846 | 0.750152 | ||||||||
\(379\) | −25.8241 | −1.32649 | −0.663247 | − | 0.748400i | \(-0.730822\pi\) | ||||
−0.663247 | + | 0.748400i | \(0.730822\pi\) | |||||||
\(380\) | 6.17757 | 0.316903 | ||||||||
\(381\) | −22.9480 | −1.17566 | ||||||||
\(382\) | 1.51319 | 0.0774215 | ||||||||
\(383\) | −19.1585 | −0.978953 | −0.489476 | − | 0.872017i | \(-0.662812\pi\) | ||||
−0.489476 | + | 0.872017i | \(0.662812\pi\) | |||||||
\(384\) | 2.14541 | 0.109482 | ||||||||
\(385\) | 4.86538 | 0.247963 | ||||||||
\(386\) | −0.480458 | −0.0244547 | ||||||||
\(387\) | 1.60277 | 0.0814732 | ||||||||
\(388\) | −9.25991 | −0.470101 | ||||||||
\(389\) | 19.0935 | 0.968077 | 0.484039 | − | 0.875047i | \(-0.339169\pi\) | ||||
0.484039 | + | 0.875047i | \(0.339169\pi\) | |||||||
\(390\) | 1.65824 | 0.0839685 | ||||||||
\(391\) | 4.47602 | 0.226362 | ||||||||
\(392\) | 16.6719 | 0.842059 | ||||||||
\(393\) | 4.39968 | 0.221934 | ||||||||
\(394\) | 25.3554 | 1.27739 | ||||||||
\(395\) | −2.42150 | −0.121839 | ||||||||
\(396\) | −1.60277 | −0.0805420 | ||||||||
\(397\) | 4.23712 | 0.212655 | 0.106327 | − | 0.994331i | \(-0.466091\pi\) | ||||
0.106327 | + | 0.994331i | \(0.466091\pi\) | |||||||
\(398\) | −22.0088 | −1.10320 | ||||||||
\(399\) | −64.4829 | −3.22818 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −22.0131 | −1.09928 | −0.549642 | − | 0.835400i | \(-0.685236\pi\) | ||||
−0.549642 | + | 0.835400i | \(0.685236\pi\) | |||||||
\(402\) | −29.3394 | −1.46332 | ||||||||
\(403\) | −1.40950 | −0.0702123 | ||||||||
\(404\) | −19.6223 | −0.976247 | ||||||||
\(405\) | −11.2394 | −0.558492 | ||||||||
\(406\) | −42.5913 | −2.11377 | ||||||||
\(407\) | −10.5210 | −0.521508 | ||||||||
\(408\) | 7.82585 | 0.387437 | ||||||||
\(409\) | −16.4216 | −0.811995 | −0.405998 | − | 0.913874i | \(-0.633076\pi\) | ||||
−0.405998 | + | 0.913874i | \(0.633076\pi\) | |||||||
\(410\) | 1.71235 | 0.0845672 | ||||||||
\(411\) | 40.0379 | 1.97492 | ||||||||
\(412\) | −1.16390 | −0.0573410 | ||||||||
\(413\) | 52.7237 | 2.59436 | ||||||||
\(414\) | 1.96671 | 0.0966585 | ||||||||
\(415\) | −4.52346 | −0.222048 | ||||||||
\(416\) | 0.772928 | 0.0378959 | ||||||||
\(417\) | 35.4704 | 1.73699 | ||||||||
\(418\) | −6.17757 | −0.302155 | ||||||||
\(419\) | 21.6506 | 1.05770 | 0.528851 | − | 0.848715i | \(-0.322623\pi\) | ||||
0.528851 | + | 0.848715i | \(0.322623\pi\) | |||||||
\(420\) | −10.4382 | −0.509333 | ||||||||
\(421\) | −1.30156 | −0.0634340 | −0.0317170 | − | 0.999497i | \(-0.510098\pi\) | ||||
−0.0317170 | + | 0.999497i | \(0.510098\pi\) | |||||||
\(422\) | −16.1348 | −0.785429 | ||||||||
\(423\) | −1.53260 | −0.0745175 | ||||||||
\(424\) | 12.8969 | 0.626329 | ||||||||
\(425\) | 3.64772 | 0.176941 | ||||||||
\(426\) | 14.1171 | 0.683974 | ||||||||
\(427\) | 6.25214 | 0.302562 | ||||||||
\(428\) | 10.5763 | 0.511227 | ||||||||
\(429\) | −1.65824 | −0.0800608 | ||||||||
\(430\) | 1.00000 | 0.0482243 | ||||||||
\(431\) | 24.6994 | 1.18973 | 0.594864 | − | 0.803827i | \(-0.297206\pi\) | ||||
0.594864 | + | 0.803827i | \(0.297206\pi\) | |||||||
\(432\) | −2.99763 | −0.144224 | ||||||||
\(433\) | 2.38419 | 0.114577 | 0.0572885 | − | 0.998358i | \(-0.481755\pi\) | ||||
0.0572885 | + | 0.998358i | \(0.481755\pi\) | |||||||
\(434\) | 8.87244 | 0.425891 | ||||||||
\(435\) | 18.7808 | 0.900469 | ||||||||
\(436\) | 14.6577 | 0.701977 | ||||||||
\(437\) | 7.58033 | 0.362616 | ||||||||
\(438\) | 25.8615 | 1.23571 | ||||||||
\(439\) | 18.0871 | 0.863252 | 0.431626 | − | 0.902053i | \(-0.357940\pi\) | ||||
0.431626 | + | 0.902053i | \(0.357940\pi\) | |||||||
\(440\) | −1.00000 | −0.0476731 | ||||||||
\(441\) | 26.7212 | 1.27244 | ||||||||
\(442\) | 2.81943 | 0.134107 | ||||||||
\(443\) | −18.9713 | −0.901352 | −0.450676 | − | 0.892687i | \(-0.648817\pi\) | ||||
−0.450676 | + | 0.892687i | \(0.648817\pi\) | |||||||
\(444\) | 22.5719 | 1.07121 | ||||||||
\(445\) | −3.19651 | −0.151529 | ||||||||
\(446\) | 19.6717 | 0.931483 | ||||||||
\(447\) | 30.9842 | 1.46550 | ||||||||
\(448\) | −4.86538 | −0.229868 | ||||||||
\(449\) | −36.1825 | −1.70756 | −0.853779 | − | 0.520636i | \(-0.825695\pi\) | ||||
−0.853779 | + | 0.520636i | \(0.825695\pi\) | |||||||
\(450\) | 1.60277 | 0.0755551 | ||||||||
\(451\) | −1.71235 | −0.0806316 | ||||||||
\(452\) | −5.58684 | −0.262783 | ||||||||
\(453\) | 11.6564 | 0.547666 | ||||||||
\(454\) | 7.76226 | 0.364301 | ||||||||
\(455\) | −3.76059 | −0.176299 | ||||||||
\(456\) | 13.2534 | 0.620648 | ||||||||
\(457\) | −40.0930 | −1.87547 | −0.937736 | − | 0.347349i | \(-0.887082\pi\) | ||||
−0.937736 | + | 0.347349i | \(0.887082\pi\) | |||||||
\(458\) | −14.9929 | −0.700573 | ||||||||
\(459\) | −10.9345 | −0.510381 | ||||||||
\(460\) | 1.22707 | 0.0572125 | ||||||||
\(461\) | 35.4116 | 1.64928 | 0.824641 | − | 0.565656i | \(-0.191377\pi\) | ||||
0.824641 | + | 0.565656i | \(0.191377\pi\) | |||||||
\(462\) | 10.4382 | 0.485630 | ||||||||
\(463\) | 26.9926 | 1.25445 | 0.627225 | − | 0.778838i | \(-0.284191\pi\) | ||||
0.627225 | + | 0.778838i | \(0.284191\pi\) | |||||||
\(464\) | 8.75395 | 0.406392 | ||||||||
\(465\) | −3.91233 | −0.181430 | ||||||||
\(466\) | 7.01617 | 0.325018 | ||||||||
\(467\) | −24.0272 | −1.11185 | −0.555923 | − | 0.831234i | \(-0.687635\pi\) | ||||
−0.555923 | + | 0.831234i | \(0.687635\pi\) | |||||||
\(468\) | 1.23882 | 0.0572646 | ||||||||
\(469\) | 66.5363 | 3.07236 | ||||||||
\(470\) | −0.956221 | −0.0441072 | ||||||||
\(471\) | 4.99876 | 0.230331 | ||||||||
\(472\) | −10.8365 | −0.498791 | ||||||||
\(473\) | −1.00000 | −0.0459800 | ||||||||
\(474\) | −5.19510 | −0.238619 | ||||||||
\(475\) | 6.17757 | 0.283447 | ||||||||
\(476\) | −17.7476 | −0.813458 | ||||||||
\(477\) | 20.6707 | 0.946447 | ||||||||
\(478\) | −6.58603 | −0.301238 | ||||||||
\(479\) | −10.9421 | −0.499960 | −0.249980 | − | 0.968251i | \(-0.580424\pi\) | ||||
−0.249980 | + | 0.968251i | \(0.580424\pi\) | |||||||
\(480\) | 2.14541 | 0.0979239 | ||||||||
\(481\) | 8.13200 | 0.370787 | ||||||||
\(482\) | −20.3260 | −0.925824 | ||||||||
\(483\) | −12.8084 | −0.582804 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −9.25991 | −0.420471 | ||||||||
\(486\) | −15.1203 | −0.685869 | ||||||||
\(487\) | −5.20402 | −0.235817 | −0.117908 | − | 0.993024i | \(-0.537619\pi\) | ||||
−0.117908 | + | 0.993024i | \(0.537619\pi\) | |||||||
\(488\) | −1.28503 | −0.0581704 | ||||||||
\(489\) | −4.01789 | −0.181695 | ||||||||
\(490\) | 16.6719 | 0.753161 | ||||||||
\(491\) | 13.6038 | 0.613931 | 0.306966 | − | 0.951721i | \(-0.400686\pi\) | ||||
0.306966 | + | 0.951721i | \(0.400686\pi\) | |||||||
\(492\) | 3.67370 | 0.165623 | ||||||||
\(493\) | 31.9320 | 1.43814 | ||||||||
\(494\) | 4.77482 | 0.214829 | ||||||||
\(495\) | −1.60277 | −0.0720390 | ||||||||
\(496\) | −1.82359 | −0.0818814 | ||||||||
\(497\) | −32.0149 | −1.43606 | ||||||||
\(498\) | −9.70466 | −0.434876 | ||||||||
\(499\) | 29.2689 | 1.31026 | 0.655129 | − | 0.755517i | \(-0.272614\pi\) | ||||
0.655129 | + | 0.755517i | \(0.272614\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 27.3043 | 1.21987 | ||||||||
\(502\) | −3.62591 | −0.161832 | ||||||||
\(503\) | 34.2338 | 1.52641 | 0.763204 | − | 0.646157i | \(-0.223625\pi\) | ||||
0.763204 | + | 0.646157i | \(0.223625\pi\) | |||||||
\(504\) | −7.79807 | −0.347354 | ||||||||
\(505\) | −19.6223 | −0.873182 | ||||||||
\(506\) | −1.22707 | −0.0545500 | ||||||||
\(507\) | −26.6086 | −1.18173 | ||||||||
\(508\) | −10.6963 | −0.474574 | ||||||||
\(509\) | −42.7379 | −1.89432 | −0.947162 | − | 0.320756i | \(-0.896063\pi\) | ||||
−0.947162 | + | 0.320756i | \(0.896063\pi\) | |||||||
\(510\) | 7.82585 | 0.346534 | ||||||||
\(511\) | −58.6491 | −2.59448 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −18.5181 | −0.817594 | ||||||||
\(514\) | 7.21242 | 0.318126 | ||||||||
\(515\) | −1.16390 | −0.0512874 | ||||||||
\(516\) | 2.14541 | 0.0944462 | ||||||||
\(517\) | 0.956221 | 0.0420546 | ||||||||
\(518\) | −51.1888 | −2.24911 | ||||||||
\(519\) | −40.5161 | −1.77846 | ||||||||
\(520\) | 0.772928 | 0.0338951 | ||||||||
\(521\) | −18.1284 | −0.794219 | −0.397109 | − | 0.917771i | \(-0.629987\pi\) | ||||
−0.397109 | + | 0.917771i | \(0.629987\pi\) | |||||||
\(522\) | 14.0305 | 0.614100 | ||||||||
\(523\) | −24.2328 | −1.05963 | −0.529813 | − | 0.848114i | \(-0.677738\pi\) | ||||
−0.529813 | + | 0.848114i | \(0.677738\pi\) | |||||||
\(524\) | 2.05074 | 0.0895871 | ||||||||
\(525\) | −10.4382 | −0.455561 | ||||||||
\(526\) | −18.5653 | −0.809486 | ||||||||
\(527\) | −6.65194 | −0.289763 | ||||||||
\(528\) | −2.14541 | −0.0933668 | ||||||||
\(529\) | −21.4943 | −0.934535 | ||||||||
\(530\) | 12.8969 | 0.560205 | ||||||||
\(531\) | −17.3684 | −0.753724 | ||||||||
\(532\) | −30.0562 | −1.30310 | ||||||||
\(533\) | 1.32353 | 0.0573283 | ||||||||
\(534\) | −6.85781 | −0.296767 | ||||||||
\(535\) | 10.5763 | 0.457255 | ||||||||
\(536\) | −13.6755 | −0.590690 | ||||||||
\(537\) | −11.8496 | −0.511349 | ||||||||
\(538\) | −23.5234 | −1.01416 | ||||||||
\(539\) | −16.6719 | −0.718111 | ||||||||
\(540\) | −2.99763 | −0.128998 | ||||||||
\(541\) | −8.36896 | −0.359810 | −0.179905 | − | 0.983684i | \(-0.557579\pi\) | ||||
−0.179905 | + | 0.983684i | \(0.557579\pi\) | |||||||
\(542\) | 10.8571 | 0.466352 | ||||||||
\(543\) | −27.2898 | −1.17112 | ||||||||
\(544\) | 3.64772 | 0.156395 | ||||||||
\(545\) | 14.6577 | 0.627867 | ||||||||
\(546\) | −8.06799 | −0.345278 | ||||||||
\(547\) | 16.7353 | 0.715550 | 0.357775 | − | 0.933808i | \(-0.383536\pi\) | ||||
0.357775 | + | 0.933808i | \(0.383536\pi\) | |||||||
\(548\) | 18.6621 | 0.797207 | ||||||||
\(549\) | −2.05960 | −0.0879014 | ||||||||
\(550\) | −1.00000 | −0.0426401 | ||||||||
\(551\) | 54.0782 | 2.30381 | ||||||||
\(552\) | 2.63257 | 0.112050 | ||||||||
\(553\) | 11.7815 | 0.501001 | ||||||||
\(554\) | 11.1316 | 0.472935 | ||||||||
\(555\) | 22.5719 | 0.958123 | ||||||||
\(556\) | 16.5332 | 0.701163 | ||||||||
\(557\) | 7.35292 | 0.311553 | 0.155777 | − | 0.987792i | \(-0.450212\pi\) | ||||
0.155777 | + | 0.987792i | \(0.450212\pi\) | |||||||
\(558\) | −2.92278 | −0.123731 | ||||||||
\(559\) | 0.772928 | 0.0326914 | ||||||||
\(560\) | −4.86538 | −0.205600 | ||||||||
\(561\) | −7.82585 | −0.330408 | ||||||||
\(562\) | −7.18944 | −0.303268 | ||||||||
\(563\) | −9.88663 | −0.416672 | −0.208336 | − | 0.978057i | \(-0.566805\pi\) | ||||
−0.208336 | + | 0.978057i | \(0.566805\pi\) | |||||||
\(564\) | −2.05148 | −0.0863830 | ||||||||
\(565\) | −5.58684 | −0.235040 | ||||||||
\(566\) | −15.0195 | −0.631317 | ||||||||
\(567\) | 54.6841 | 2.29652 | ||||||||
\(568\) | 6.58014 | 0.276097 | ||||||||
\(569\) | 46.3023 | 1.94110 | 0.970548 | − | 0.240909i | \(-0.0774457\pi\) | ||||
0.970548 | + | 0.240909i | \(0.0774457\pi\) | |||||||
\(570\) | 13.2534 | 0.555124 | ||||||||
\(571\) | −1.12415 | −0.0470444 | −0.0235222 | − | 0.999723i | \(-0.507488\pi\) | ||||
−0.0235222 | + | 0.999723i | \(0.507488\pi\) | |||||||
\(572\) | −0.772928 | −0.0323177 | ||||||||
\(573\) | 3.24641 | 0.135621 | ||||||||
\(574\) | −8.33126 | −0.347740 | ||||||||
\(575\) | 1.22707 | 0.0511724 | ||||||||
\(576\) | 1.60277 | 0.0667819 | ||||||||
\(577\) | −3.80465 | −0.158390 | −0.0791948 | − | 0.996859i | \(-0.525235\pi\) | ||||
−0.0791948 | + | 0.996859i | \(0.525235\pi\) | |||||||
\(578\) | −3.69411 | −0.153655 | ||||||||
\(579\) | −1.03078 | −0.0428377 | ||||||||
\(580\) | 8.75395 | 0.363488 | ||||||||
\(581\) | 22.0084 | 0.913061 | ||||||||
\(582\) | −19.8663 | −0.823483 | ||||||||
\(583\) | −12.8969 | −0.534135 | ||||||||
\(584\) | 12.0544 | 0.498814 | ||||||||
\(585\) | 1.23882 | 0.0512190 | ||||||||
\(586\) | −19.1081 | −0.789349 | ||||||||
\(587\) | 13.2532 | 0.547019 | 0.273510 | − | 0.961869i | \(-0.411815\pi\) | ||||
0.273510 | + | 0.961869i | \(0.411815\pi\) | |||||||
\(588\) | 35.7680 | 1.47505 | ||||||||
\(589\) | −11.2653 | −0.464180 | ||||||||
\(590\) | −10.8365 | −0.446132 | ||||||||
\(591\) | 54.3976 | 2.23762 | ||||||||
\(592\) | 10.5210 | 0.432412 | ||||||||
\(593\) | 24.5509 | 1.00819 | 0.504093 | − | 0.863650i | \(-0.331827\pi\) | ||||
0.504093 | + | 0.863650i | \(0.331827\pi\) | |||||||
\(594\) | 2.99763 | 0.122994 | ||||||||
\(595\) | −17.7476 | −0.727579 | ||||||||
\(596\) | 14.4421 | 0.591573 | ||||||||
\(597\) | −47.2179 | −1.93250 | ||||||||
\(598\) | 0.948438 | 0.0387845 | ||||||||
\(599\) | −12.6605 | −0.517295 | −0.258648 | − | 0.965972i | \(-0.583277\pi\) | ||||
−0.258648 | + | 0.965972i | \(0.583277\pi\) | |||||||
\(600\) | 2.14541 | 0.0875858 | ||||||||
\(601\) | 7.39922 | 0.301820 | 0.150910 | − | 0.988547i | \(-0.451780\pi\) | ||||
0.150910 | + | 0.988547i | \(0.451780\pi\) | |||||||
\(602\) | −4.86538 | −0.198298 | ||||||||
\(603\) | −21.9186 | −0.892594 | ||||||||
\(604\) | 5.43320 | 0.221074 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | −42.0978 | −1.71011 | ||||||||
\(607\) | −11.2387 | −0.456163 | −0.228081 | − | 0.973642i | \(-0.573245\pi\) | ||||
−0.228081 | + | 0.973642i | \(0.573245\pi\) | |||||||
\(608\) | 6.17757 | 0.250534 | ||||||||
\(609\) | −91.3756 | −3.70273 | ||||||||
\(610\) | −1.28503 | −0.0520292 | ||||||||
\(611\) | −0.739090 | −0.0299004 | ||||||||
\(612\) | 5.84645 | 0.236329 | ||||||||
\(613\) | −5.91644 | −0.238963 | −0.119481 | − | 0.992836i | \(-0.538123\pi\) | ||||
−0.119481 | + | 0.992836i | \(0.538123\pi\) | |||||||
\(614\) | −15.6944 | −0.633376 | ||||||||
\(615\) | 3.67370 | 0.148138 | ||||||||
\(616\) | 4.86538 | 0.196032 | ||||||||
\(617\) | −41.8120 | −1.68329 | −0.841644 | − | 0.540033i | \(-0.818412\pi\) | ||||
−0.841644 | + | 0.540033i | \(0.818412\pi\) | |||||||
\(618\) | −2.49703 | −0.100445 | ||||||||
\(619\) | 17.9307 | 0.720697 | 0.360349 | − | 0.932818i | \(-0.382658\pi\) | ||||
0.360349 | + | 0.932818i | \(0.382658\pi\) | |||||||
\(620\) | −1.82359 | −0.0732370 | ||||||||
\(621\) | −3.67831 | −0.147606 | ||||||||
\(622\) | −17.4073 | −0.697969 | ||||||||
\(623\) | 15.5522 | 0.623087 | ||||||||
\(624\) | 1.65824 | 0.0663829 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −5.94600 | −0.237650 | ||||||||
\(627\) | −13.2534 | −0.529290 | ||||||||
\(628\) | 2.32998 | 0.0929765 | ||||||||
\(629\) | 38.3778 | 1.53022 | ||||||||
\(630\) | −7.79807 | −0.310682 | ||||||||
\(631\) | −5.71163 | −0.227377 | −0.113688 | − | 0.993516i | \(-0.536267\pi\) | ||||
−0.113688 | + | 0.993516i | \(0.536267\pi\) | |||||||
\(632\) | −2.42150 | −0.0963221 | ||||||||
\(633\) | −34.6156 | −1.37585 | ||||||||
\(634\) | 10.1749 | 0.404096 | ||||||||
\(635\) | −10.6963 | −0.424471 | ||||||||
\(636\) | 27.6691 | 1.09715 | ||||||||
\(637\) | 12.8862 | 0.510570 | ||||||||
\(638\) | −8.75395 | −0.346572 | ||||||||
\(639\) | 10.5464 | 0.417210 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −21.7733 | −0.859994 | −0.429997 | − | 0.902830i | \(-0.641485\pi\) | ||||
−0.429997 | + | 0.902830i | \(0.641485\pi\) | |||||||
\(642\) | 22.6906 | 0.895525 | ||||||||
\(643\) | 31.6164 | 1.24683 | 0.623414 | − | 0.781892i | \(-0.285745\pi\) | ||||
0.623414 | + | 0.781892i | \(0.285745\pi\) | |||||||
\(644\) | −5.97017 | −0.235258 | ||||||||
\(645\) | 2.14541 | 0.0844753 | ||||||||
\(646\) | 22.5341 | 0.886592 | ||||||||
\(647\) | 33.3862 | 1.31255 | 0.656273 | − | 0.754523i | \(-0.272132\pi\) | ||||
0.656273 | + | 0.754523i | \(0.272132\pi\) | |||||||
\(648\) | −11.2394 | −0.441527 | ||||||||
\(649\) | 10.8365 | 0.425370 | ||||||||
\(650\) | 0.772928 | 0.0303167 | ||||||||
\(651\) | 19.0350 | 0.746040 | ||||||||
\(652\) | −1.87279 | −0.0733441 | ||||||||
\(653\) | 8.49962 | 0.332616 | 0.166308 | − | 0.986074i | \(-0.446815\pi\) | ||||
0.166308 | + | 0.986074i | \(0.446815\pi\) | |||||||
\(654\) | 31.4467 | 1.22967 | ||||||||
\(655\) | 2.05074 | 0.0801292 | ||||||||
\(656\) | 1.71235 | 0.0668562 | ||||||||
\(657\) | 19.3204 | 0.753759 | ||||||||
\(658\) | 4.65238 | 0.181369 | ||||||||
\(659\) | −31.0343 | −1.20892 | −0.604462 | − | 0.796634i | \(-0.706612\pi\) | ||||
−0.604462 | + | 0.796634i | \(0.706612\pi\) | |||||||
\(660\) | −2.14541 | −0.0835098 | ||||||||
\(661\) | 3.33299 | 0.129638 | 0.0648191 | − | 0.997897i | \(-0.479353\pi\) | ||||
0.0648191 | + | 0.997897i | \(0.479353\pi\) | |||||||
\(662\) | 21.5396 | 0.837159 | ||||||||
\(663\) | 6.04882 | 0.234917 | ||||||||
\(664\) | −4.52346 | −0.175544 | ||||||||
\(665\) | −30.0562 | −1.16553 | ||||||||
\(666\) | 16.8628 | 0.653419 | ||||||||
\(667\) | 10.7417 | 0.415921 | ||||||||
\(668\) | 12.7269 | 0.492417 | ||||||||
\(669\) | 42.2038 | 1.63169 | ||||||||
\(670\) | −13.6755 | −0.528329 | ||||||||
\(671\) | 1.28503 | 0.0496079 | ||||||||
\(672\) | −10.4382 | −0.402663 | ||||||||
\(673\) | −34.9119 | −1.34575 | −0.672877 | − | 0.739755i | \(-0.734942\pi\) | ||||
−0.672877 | + | 0.739755i | \(0.734942\pi\) | |||||||
\(674\) | −7.28531 | −0.280620 | ||||||||
\(675\) | −2.99763 | −0.115379 | ||||||||
\(676\) | −12.4026 | −0.477022 | ||||||||
\(677\) | 18.6517 | 0.716842 | 0.358421 | − | 0.933560i | \(-0.383315\pi\) | ||||
0.358421 | + | 0.933560i | \(0.383315\pi\) | |||||||
\(678\) | −11.9860 | −0.460321 | ||||||||
\(679\) | 45.0530 | 1.72897 | ||||||||
\(680\) | 3.64772 | 0.139884 | ||||||||
\(681\) | 16.6532 | 0.638152 | ||||||||
\(682\) | 1.82359 | 0.0698287 | ||||||||
\(683\) | −10.8277 | −0.414310 | −0.207155 | − | 0.978308i | \(-0.566421\pi\) | ||||
−0.207155 | + | 0.978308i | \(0.566421\pi\) | |||||||
\(684\) | 9.90121 | 0.378582 | ||||||||
\(685\) | 18.6621 | 0.713044 | ||||||||
\(686\) | −47.0576 | −1.79667 | ||||||||
\(687\) | −32.1659 | −1.22720 | ||||||||
\(688\) | 1.00000 | 0.0381246 | ||||||||
\(689\) | 9.96838 | 0.379765 | ||||||||
\(690\) | 2.63257 | 0.100220 | ||||||||
\(691\) | 11.5977 | 0.441197 | 0.220598 | − | 0.975365i | \(-0.429199\pi\) | ||||
0.220598 | + | 0.975365i | \(0.429199\pi\) | |||||||
\(692\) | −18.8851 | −0.717902 | ||||||||
\(693\) | 7.79807 | 0.296224 | ||||||||
\(694\) | −8.13671 | −0.308865 | ||||||||
\(695\) | 16.5332 | 0.627140 | ||||||||
\(696\) | 18.7808 | 0.711883 | ||||||||
\(697\) | 6.24620 | 0.236592 | ||||||||
\(698\) | −29.8617 | −1.13028 | ||||||||
\(699\) | 15.0525 | 0.569339 | ||||||||
\(700\) | −4.86538 | −0.183894 | ||||||||
\(701\) | 44.7904 | 1.69171 | 0.845855 | − | 0.533412i | \(-0.179091\pi\) | ||||
0.845855 | + | 0.533412i | \(0.179091\pi\) | |||||||
\(702\) | −2.31695 | −0.0874478 | ||||||||
\(703\) | 64.9945 | 2.45131 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | −2.05148 | −0.0772633 | ||||||||
\(706\) | 6.05373 | 0.227835 | ||||||||
\(707\) | 95.4700 | 3.59052 | ||||||||
\(708\) | −23.2487 | −0.873740 | ||||||||
\(709\) | 12.7391 | 0.478426 | 0.239213 | − | 0.970967i | \(-0.423110\pi\) | ||||
0.239213 | + | 0.970967i | \(0.423110\pi\) | |||||||
\(710\) | 6.58014 | 0.246948 | ||||||||
\(711\) | −3.88110 | −0.145553 | ||||||||
\(712\) | −3.19651 | −0.119794 | ||||||||
\(713\) | −2.23767 | −0.0838015 | ||||||||
\(714\) | −38.0757 | −1.42495 | ||||||||
\(715\) | −0.772928 | −0.0289059 | ||||||||
\(716\) | −5.52325 | −0.206414 | ||||||||
\(717\) | −14.1297 | −0.527684 | ||||||||
\(718\) | 20.3069 | 0.757846 | ||||||||
\(719\) | 13.8359 | 0.515992 | 0.257996 | − | 0.966146i | \(-0.416938\pi\) | ||||
0.257996 | + | 0.966146i | \(0.416938\pi\) | |||||||
\(720\) | 1.60277 | 0.0597316 | ||||||||
\(721\) | 5.66279 | 0.210893 | ||||||||
\(722\) | 19.1624 | 0.713152 | ||||||||
\(723\) | −43.6075 | −1.62178 | ||||||||
\(724\) | −12.7201 | −0.472740 | ||||||||
\(725\) | 8.75395 | 0.325113 | ||||||||
\(726\) | 2.14541 | 0.0796235 | ||||||||
\(727\) | −0.669168 | −0.0248181 | −0.0124090 | − | 0.999923i | \(-0.503950\pi\) | ||||
−0.0124090 | + | 0.999923i | \(0.503950\pi\) | |||||||
\(728\) | −3.76059 | −0.139377 | ||||||||
\(729\) | 1.27922 | 0.0473786 | ||||||||
\(730\) | 12.0544 | 0.446153 | ||||||||
\(731\) | 3.64772 | 0.134916 | ||||||||
\(732\) | −2.75690 | −0.101898 | ||||||||
\(733\) | −48.5314 | −1.79255 | −0.896273 | − | 0.443502i | \(-0.853736\pi\) | ||||
−0.896273 | + | 0.443502i | \(0.853736\pi\) | |||||||
\(734\) | −5.38172 | −0.198643 | ||||||||
\(735\) | 35.7680 | 1.31932 | ||||||||
\(736\) | 1.22707 | 0.0452305 | ||||||||
\(737\) | 13.6755 | 0.503742 | ||||||||
\(738\) | 2.74451 | 0.101027 | ||||||||
\(739\) | −10.9944 | −0.404434 | −0.202217 | − | 0.979341i | \(-0.564815\pi\) | ||||
−0.202217 | + | 0.979341i | \(0.564815\pi\) | |||||||
\(740\) | 10.5210 | 0.386761 | ||||||||
\(741\) | 10.2439 | 0.376320 | ||||||||
\(742\) | −62.7483 | −2.30356 | ||||||||
\(743\) | 42.3391 | 1.55327 | 0.776635 | − | 0.629951i | \(-0.216925\pi\) | ||||
0.776635 | + | 0.629951i | \(0.216925\pi\) | |||||||
\(744\) | −3.91233 | −0.143433 | ||||||||
\(745\) | 14.4421 | 0.529119 | ||||||||
\(746\) | 32.0733 | 1.17429 | ||||||||
\(747\) | −7.25006 | −0.265266 | ||||||||
\(748\) | −3.64772 | −0.133374 | ||||||||
\(749\) | −51.4579 | −1.88023 | ||||||||
\(750\) | 2.14541 | 0.0783391 | ||||||||
\(751\) | 8.53646 | 0.311500 | 0.155750 | − | 0.987797i | \(-0.450221\pi\) | ||||
0.155750 | + | 0.987797i | \(0.450221\pi\) | |||||||
\(752\) | −0.956221 | −0.0348698 | ||||||||
\(753\) | −7.77906 | −0.283485 | ||||||||
\(754\) | 6.76617 | 0.246409 | ||||||||
\(755\) | 5.43320 | 0.197734 | ||||||||
\(756\) | 14.5846 | 0.530438 | ||||||||
\(757\) | 11.3872 | 0.413876 | 0.206938 | − | 0.978354i | \(-0.433650\pi\) | ||||
0.206938 | + | 0.978354i | \(0.433650\pi\) | |||||||
\(758\) | −25.8241 | −0.937973 | ||||||||
\(759\) | −2.63257 | −0.0955561 | ||||||||
\(760\) | 6.17757 | 0.224084 | ||||||||
\(761\) | 41.8331 | 1.51645 | 0.758225 | − | 0.651993i | \(-0.226067\pi\) | ||||
0.758225 | + | 0.651993i | \(0.226067\pi\) | |||||||
\(762\) | −22.9480 | −0.831318 | ||||||||
\(763\) | −71.3153 | −2.58179 | ||||||||
\(764\) | 1.51319 | 0.0547453 | ||||||||
\(765\) | 5.84645 | 0.211379 | ||||||||
\(766\) | −19.1585 | −0.692224 | ||||||||
\(767\) | −8.37584 | −0.302434 | ||||||||
\(768\) | 2.14541 | 0.0774157 | ||||||||
\(769\) | 44.4811 | 1.60403 | 0.802015 | − | 0.597303i | \(-0.203761\pi\) | ||||
0.802015 | + | 0.597303i | \(0.203761\pi\) | |||||||
\(770\) | 4.86538 | 0.175336 | ||||||||
\(771\) | 15.4736 | 0.557267 | ||||||||
\(772\) | −0.480458 | −0.0172921 | ||||||||
\(773\) | 6.19609 | 0.222858 | 0.111429 | − | 0.993772i | \(-0.464457\pi\) | ||||
0.111429 | + | 0.993772i | \(0.464457\pi\) | |||||||
\(774\) | 1.60277 | 0.0576103 | ||||||||
\(775\) | −1.82359 | −0.0655052 | ||||||||
\(776\) | −9.25991 | −0.332411 | ||||||||
\(777\) | −109.821 | −3.93980 | ||||||||
\(778\) | 19.0935 | 0.684534 | ||||||||
\(779\) | 10.5782 | 0.379003 | ||||||||
\(780\) | 1.65824 | 0.0593747 | ||||||||
\(781\) | −6.58014 | −0.235456 | ||||||||
\(782\) | 4.47602 | 0.160062 | ||||||||
\(783\) | −26.2411 | −0.937781 | ||||||||
\(784\) | 16.6719 | 0.595426 | ||||||||
\(785\) | 2.32998 | 0.0831607 | ||||||||
\(786\) | 4.39968 | 0.156931 | ||||||||
\(787\) | −29.7402 | −1.06012 | −0.530062 | − | 0.847959i | \(-0.677831\pi\) | ||||
−0.530062 | + | 0.847959i | \(0.677831\pi\) | |||||||
\(788\) | 25.3554 | 0.903248 | ||||||||
\(789\) | −39.8301 | −1.41799 | ||||||||
\(790\) | −2.42150 | −0.0861531 | ||||||||
\(791\) | 27.1821 | 0.966484 | ||||||||
\(792\) | −1.60277 | −0.0569518 | ||||||||
\(793\) | −0.993233 | −0.0352707 | ||||||||
\(794\) | 4.23712 | 0.150370 | ||||||||
\(795\) | 27.6691 | 0.981321 | ||||||||
\(796\) | −22.0088 | −0.780083 | ||||||||
\(797\) | 1.14408 | 0.0405254 | 0.0202627 | − | 0.999795i | \(-0.493550\pi\) | ||||
0.0202627 | + | 0.999795i | \(0.493550\pi\) | |||||||
\(798\) | −64.4829 | −2.28267 | ||||||||
\(799\) | −3.48803 | −0.123398 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −5.12326 | −0.181021 | ||||||||
\(802\) | −22.0131 | −0.777311 | ||||||||
\(803\) | −12.0544 | −0.425390 | ||||||||
\(804\) | −29.3394 | −1.03472 | ||||||||
\(805\) | −5.97017 | −0.210421 | ||||||||
\(806\) | −1.40950 | −0.0496476 | ||||||||
\(807\) | −50.4672 | −1.77653 | ||||||||
\(808\) | −19.6223 | −0.690311 | ||||||||
\(809\) | −15.6089 | −0.548781 | −0.274390 | − | 0.961618i | \(-0.588476\pi\) | ||||
−0.274390 | + | 0.961618i | \(0.588476\pi\) | |||||||
\(810\) | −11.2394 | −0.394914 | ||||||||
\(811\) | −28.4191 | −0.997928 | −0.498964 | − | 0.866623i | \(-0.666286\pi\) | ||||
−0.498964 | + | 0.866623i | \(0.666286\pi\) | |||||||
\(812\) | −42.5913 | −1.49466 | ||||||||
\(813\) | 23.2929 | 0.816917 | ||||||||
\(814\) | −10.5210 | −0.368762 | ||||||||
\(815\) | −1.87279 | −0.0656009 | ||||||||
\(816\) | 7.82585 | 0.273959 | ||||||||
\(817\) | 6.17757 | 0.216126 | ||||||||
\(818\) | −16.4216 | −0.574167 | ||||||||
\(819\) | −6.02735 | −0.210613 | ||||||||
\(820\) | 1.71235 | 0.0597980 | ||||||||
\(821\) | 22.0333 | 0.768966 | 0.384483 | − | 0.923132i | \(-0.374380\pi\) | ||||
0.384483 | + | 0.923132i | \(0.374380\pi\) | |||||||
\(822\) | 40.0379 | 1.39648 | ||||||||
\(823\) | −3.16142 | −0.110200 | −0.0551002 | − | 0.998481i | \(-0.517548\pi\) | ||||
−0.0551002 | + | 0.998481i | \(0.517548\pi\) | |||||||
\(824\) | −1.16390 | −0.0405462 | ||||||||
\(825\) | −2.14541 | −0.0746934 | ||||||||
\(826\) | 52.7237 | 1.83449 | ||||||||
\(827\) | 31.7908 | 1.10547 | 0.552737 | − | 0.833355i | \(-0.313583\pi\) | ||||
0.552737 | + | 0.833355i | \(0.313583\pi\) | |||||||
\(828\) | 1.96671 | 0.0683479 | ||||||||
\(829\) | 10.0201 | 0.348014 | 0.174007 | − | 0.984744i | \(-0.444328\pi\) | ||||
0.174007 | + | 0.984744i | \(0.444328\pi\) | |||||||
\(830\) | −4.52346 | −0.157012 | ||||||||
\(831\) | 23.8817 | 0.828449 | ||||||||
\(832\) | 0.772928 | 0.0267965 | ||||||||
\(833\) | 60.8146 | 2.10710 | ||||||||
\(834\) | 35.4704 | 1.22824 | ||||||||
\(835\) | 12.7269 | 0.440431 | ||||||||
\(836\) | −6.17757 | −0.213656 | ||||||||
\(837\) | 5.46644 | 0.188948 | ||||||||
\(838\) | 21.6506 | 0.747908 | ||||||||
\(839\) | 1.53509 | 0.0529973 | 0.0264986 | − | 0.999649i | \(-0.491564\pi\) | ||||
0.0264986 | + | 0.999649i | \(0.491564\pi\) | |||||||
\(840\) | −10.4382 | −0.360153 | ||||||||
\(841\) | 47.6316 | 1.64247 | ||||||||
\(842\) | −1.30156 | −0.0448546 | ||||||||
\(843\) | −15.4243 | −0.531240 | ||||||||
\(844\) | −16.1348 | −0.555382 | ||||||||
\(845\) | −12.4026 | −0.426662 | ||||||||
\(846\) | −1.53260 | −0.0526919 | ||||||||
\(847\) | −4.86538 | −0.167176 | ||||||||
\(848\) | 12.8969 | 0.442881 | ||||||||
\(849\) | −32.2229 | −1.10589 | ||||||||
\(850\) | 3.64772 | 0.125116 | ||||||||
\(851\) | 12.9101 | 0.442551 | ||||||||
\(852\) | 14.1171 | 0.483643 | ||||||||
\(853\) | −20.2927 | −0.694808 | −0.347404 | − | 0.937716i | \(-0.612937\pi\) | ||||
−0.347404 | + | 0.937716i | \(0.612937\pi\) | |||||||
\(854\) | 6.25214 | 0.213944 | ||||||||
\(855\) | 9.90121 | 0.338614 | ||||||||
\(856\) | 10.5763 | 0.361492 | ||||||||
\(857\) | −54.4394 | −1.85961 | −0.929807 | − | 0.368048i | \(-0.880026\pi\) | ||||
−0.929807 | + | 0.368048i | \(0.880026\pi\) | |||||||
\(858\) | −1.65824 | −0.0566115 | ||||||||
\(859\) | 33.0740 | 1.12847 | 0.564236 | − | 0.825614i | \(-0.309171\pi\) | ||||
0.564236 | + | 0.825614i | \(0.309171\pi\) | |||||||
\(860\) | 1.00000 | 0.0340997 | ||||||||
\(861\) | −17.8739 | −0.609142 | ||||||||
\(862\) | 24.6994 | 0.841264 | ||||||||
\(863\) | 11.0252 | 0.375304 | 0.187652 | − | 0.982236i | \(-0.439912\pi\) | ||||
0.187652 | + | 0.982236i | \(0.439912\pi\) | |||||||
\(864\) | −2.99763 | −0.101982 | ||||||||
\(865\) | −18.8851 | −0.642111 | ||||||||
\(866\) | 2.38419 | 0.0810182 | ||||||||
\(867\) | −7.92537 | −0.269160 | ||||||||
\(868\) | 8.87244 | 0.301150 | ||||||||
\(869\) | 2.42150 | 0.0821438 | ||||||||
\(870\) | 18.7808 | 0.636728 | ||||||||
\(871\) | −10.5702 | −0.358156 | ||||||||
\(872\) | 14.6577 | 0.496373 | ||||||||
\(873\) | −14.8415 | −0.502308 | ||||||||
\(874\) | 7.58033 | 0.256408 | ||||||||
\(875\) | −4.86538 | −0.164480 | ||||||||
\(876\) | 25.8615 | 0.873780 | ||||||||
\(877\) | −8.09361 | −0.273302 | −0.136651 | − | 0.990619i | \(-0.543634\pi\) | ||||
−0.136651 | + | 0.990619i | \(0.543634\pi\) | |||||||
\(878\) | 18.0871 | 0.610411 | ||||||||
\(879\) | −40.9947 | −1.38272 | ||||||||
\(880\) | −1.00000 | −0.0337100 | ||||||||
\(881\) | −24.5156 | −0.825951 | −0.412975 | − | 0.910742i | \(-0.635510\pi\) | ||||
−0.412975 | + | 0.910742i | \(0.635510\pi\) | |||||||
\(882\) | 26.7212 | 0.899750 | ||||||||
\(883\) | −57.6361 | −1.93961 | −0.969805 | − | 0.243882i | \(-0.921579\pi\) | ||||
−0.969805 | + | 0.243882i | \(0.921579\pi\) | |||||||
\(884\) | 2.81943 | 0.0948276 | ||||||||
\(885\) | −23.2487 | −0.781497 | ||||||||
\(886\) | −18.9713 | −0.637352 | ||||||||
\(887\) | 30.9153 | 1.03804 | 0.519018 | − | 0.854764i | \(-0.326298\pi\) | ||||
0.519018 | + | 0.854764i | \(0.326298\pi\) | |||||||
\(888\) | 22.5719 | 0.757463 | ||||||||
\(889\) | 52.0418 | 1.74543 | ||||||||
\(890\) | −3.19651 | −0.107147 | ||||||||
\(891\) | 11.2394 | 0.376535 | ||||||||
\(892\) | 19.6717 | 0.658658 | ||||||||
\(893\) | −5.90713 | −0.197675 | ||||||||
\(894\) | 30.9842 | 1.03627 | ||||||||
\(895\) | −5.52325 | −0.184622 | ||||||||
\(896\) | −4.86538 | −0.162541 | ||||||||
\(897\) | 2.03479 | 0.0679395 | ||||||||
\(898\) | −36.1825 | −1.20743 | ||||||||
\(899\) | −15.9636 | −0.532415 | ||||||||
\(900\) | 1.60277 | 0.0534255 | ||||||||
\(901\) | 47.0443 | 1.56727 | ||||||||
\(902\) | −1.71235 | −0.0570152 | ||||||||
\(903\) | −10.4382 | −0.347362 | ||||||||
\(904\) | −5.58684 | −0.185815 | ||||||||
\(905\) | −12.7201 | −0.422831 | ||||||||
\(906\) | 11.6564 | 0.387259 | ||||||||
\(907\) | 3.77120 | 0.125221 | 0.0626104 | − | 0.998038i | \(-0.480057\pi\) | ||||
0.0626104 | + | 0.998038i | \(0.480057\pi\) | |||||||
\(908\) | 7.76226 | 0.257600 | ||||||||
\(909\) | −31.4500 | −1.04313 | ||||||||
\(910\) | −3.76059 | −0.124662 | ||||||||
\(911\) | −42.2902 | −1.40114 | −0.700569 | − | 0.713585i | \(-0.747070\pi\) | ||||
−0.700569 | + | 0.713585i | \(0.747070\pi\) | |||||||
\(912\) | 13.2534 | 0.438864 | ||||||||
\(913\) | 4.52346 | 0.149705 | ||||||||
\(914\) | −40.0930 | −1.32616 | ||||||||
\(915\) | −2.75690 | −0.0911404 | ||||||||
\(916\) | −14.9929 | −0.495380 | ||||||||
\(917\) | −9.97764 | −0.329491 | ||||||||
\(918\) | −10.9345 | −0.360894 | ||||||||
\(919\) | −59.6592 | −1.96797 | −0.983987 | − | 0.178241i | \(-0.942959\pi\) | ||||
−0.983987 | + | 0.178241i | \(0.942959\pi\) | |||||||
\(920\) | 1.22707 | 0.0404554 | ||||||||
\(921\) | −33.6709 | −1.10950 | ||||||||
\(922\) | 35.4116 | 1.16622 | ||||||||
\(923\) | 5.08598 | 0.167407 | ||||||||
\(924\) | 10.4382 | 0.343392 | ||||||||
\(925\) | 10.5210 | 0.345929 | ||||||||
\(926\) | 26.9926 | 0.887030 | ||||||||
\(927\) | −1.86545 | −0.0612695 | ||||||||
\(928\) | 8.75395 | 0.287362 | ||||||||
\(929\) | −4.27682 | −0.140318 | −0.0701589 | − | 0.997536i | \(-0.522351\pi\) | ||||
−0.0701589 | + | 0.997536i | \(0.522351\pi\) | |||||||
\(930\) | −3.91233 | −0.128290 | ||||||||
\(931\) | 102.992 | 3.37543 | ||||||||
\(932\) | 7.01617 | 0.229822 | ||||||||
\(933\) | −37.3457 | −1.22264 | ||||||||
\(934\) | −24.0272 | −0.786194 | ||||||||
\(935\) | −3.64772 | −0.119293 | ||||||||
\(936\) | 1.23882 | 0.0404922 | ||||||||
\(937\) | 35.6833 | 1.16572 | 0.582862 | − | 0.812571i | \(-0.301933\pi\) | ||||
0.582862 | + | 0.812571i | \(0.301933\pi\) | |||||||
\(938\) | 66.5363 | 2.17249 | ||||||||
\(939\) | −12.7566 | −0.416295 | ||||||||
\(940\) | −0.956221 | −0.0311885 | ||||||||
\(941\) | 57.1676 | 1.86361 | 0.931805 | − | 0.362959i | \(-0.118233\pi\) | ||||
0.931805 | + | 0.362959i | \(0.118233\pi\) | |||||||
\(942\) | 4.99876 | 0.162868 | ||||||||
\(943\) | 2.10118 | 0.0684239 | ||||||||
\(944\) | −10.8365 | −0.352698 | ||||||||
\(945\) | 14.5846 | 0.474438 | ||||||||
\(946\) | −1.00000 | −0.0325128 | ||||||||
\(947\) | 27.0875 | 0.880225 | 0.440112 | − | 0.897943i | \(-0.354939\pi\) | ||||
0.440112 | + | 0.897943i | \(0.354939\pi\) | |||||||
\(948\) | −5.19510 | −0.168729 | ||||||||
\(949\) | 9.31717 | 0.302448 | ||||||||
\(950\) | 6.17757 | 0.200427 | ||||||||
\(951\) | 21.8292 | 0.707861 | ||||||||
\(952\) | −17.7476 | −0.575202 | ||||||||
\(953\) | −16.3172 | −0.528566 | −0.264283 | − | 0.964445i | \(-0.585135\pi\) | ||||
−0.264283 | + | 0.964445i | \(0.585135\pi\) | |||||||
\(954\) | 20.6707 | 0.669239 | ||||||||
\(955\) | 1.51319 | 0.0489657 | ||||||||
\(956\) | −6.58603 | −0.213007 | ||||||||
\(957\) | −18.7808 | −0.607096 | ||||||||
\(958\) | −10.9421 | −0.353525 | ||||||||
\(959\) | −90.7984 | −2.93203 | ||||||||
\(960\) | 2.14541 | 0.0692427 | ||||||||
\(961\) | −27.6745 | −0.892727 | ||||||||
\(962\) | 8.13200 | 0.262186 | ||||||||
\(963\) | 16.9514 | 0.546252 | ||||||||
\(964\) | −20.3260 | −0.654656 | ||||||||
\(965\) | −0.480458 | −0.0154665 | ||||||||
\(966\) | −12.8084 | −0.412105 | ||||||||
\(967\) | 40.3368 | 1.29714 | 0.648572 | − | 0.761154i | \(-0.275367\pi\) | ||||
0.648572 | + | 0.761154i | \(0.275367\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 48.3448 | 1.55306 | ||||||||
\(970\) | −9.25991 | −0.297318 | ||||||||
\(971\) | −57.4012 | −1.84209 | −0.921046 | − | 0.389453i | \(-0.872664\pi\) | ||||
−0.921046 | + | 0.389453i | \(0.872664\pi\) | |||||||
\(972\) | −15.1203 | −0.484983 | ||||||||
\(973\) | −80.4403 | −2.57880 | ||||||||
\(974\) | −5.20402 | −0.166748 | ||||||||
\(975\) | 1.65824 | 0.0531063 | ||||||||
\(976\) | −1.28503 | −0.0411327 | ||||||||
\(977\) | 10.4168 | 0.333264 | 0.166632 | − | 0.986019i | \(-0.446711\pi\) | ||||
0.166632 | + | 0.986019i | \(0.446711\pi\) | |||||||
\(978\) | −4.01789 | −0.128478 | ||||||||
\(979\) | 3.19651 | 0.102161 | ||||||||
\(980\) | 16.6719 | 0.532565 | ||||||||
\(981\) | 23.4929 | 0.750070 | ||||||||
\(982\) | 13.6038 | 0.434115 | ||||||||
\(983\) | 25.3456 | 0.808398 | 0.404199 | − | 0.914671i | \(-0.367550\pi\) | ||||
0.404199 | + | 0.914671i | \(0.367550\pi\) | |||||||
\(984\) | 3.67370 | 0.117113 | ||||||||
\(985\) | 25.3554 | 0.807890 | ||||||||
\(986\) | 31.9320 | 1.01692 | ||||||||
\(987\) | 9.98124 | 0.317707 | ||||||||
\(988\) | 4.77482 | 0.151907 | ||||||||
\(989\) | 1.22707 | 0.0390186 | ||||||||
\(990\) | −1.60277 | −0.0509393 | ||||||||
\(991\) | −57.8547 | −1.83781 | −0.918907 | − | 0.394474i | \(-0.870927\pi\) | ||||
−0.918907 | + | 0.394474i | \(0.870927\pi\) | |||||||
\(992\) | −1.82359 | −0.0578989 | ||||||||
\(993\) | 46.2111 | 1.46646 | ||||||||
\(994\) | −32.0149 | −1.01545 | ||||||||
\(995\) | −22.0088 | −0.697727 | ||||||||
\(996\) | −9.70466 | −0.307504 | ||||||||
\(997\) | 40.9105 | 1.29565 | 0.647824 | − | 0.761790i | \(-0.275679\pi\) | ||||
0.647824 | + | 0.761790i | \(0.275679\pi\) | |||||||
\(998\) | 29.2689 | 0.926492 | ||||||||
\(999\) | −31.5382 | −0.997824 |
(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 | 4730.2.a.be.1.8 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4730.2.a.be.1.8 | ✓ | 12 | 1.1 | even | 1 | trivial |