Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2667,2,Mod(1,2667)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2667, 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("2667.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2667 = 3 \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2667.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: | \(21.2961022191\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 4 x^{12} - 10 x^{11} + 53 x^{10} + 19 x^{9} - 242 x^{8} + 61 x^{7} + 467 x^{6} - 211 x^{5} + \cdots - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(0.307326\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2667.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.307326 | 0.217312 | 0.108656 | − | 0.994079i | \(-0.465345\pi\) | ||||
0.108656 | + | 0.994079i | \(0.465345\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.90555 | −0.952775 | ||||||||
\(5\) | −0.988649 | −0.442137 | −0.221069 | − | 0.975258i | \(-0.570954\pi\) | ||||
−0.221069 | + | 0.975258i | \(0.570954\pi\) | |||||||
\(6\) | −0.307326 | −0.125465 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.20028 | −0.424362 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.303838 | −0.0960819 | ||||||||
\(11\) | 2.00682 | 0.605081 | 0.302540 | − | 0.953137i | \(-0.402165\pi\) | ||||
0.302540 | + | 0.953137i | \(0.402165\pi\) | |||||||
\(12\) | 1.90555 | 0.550085 | ||||||||
\(13\) | −0.289737 | −0.0803585 | −0.0401792 | − | 0.999192i | \(-0.512793\pi\) | ||||
−0.0401792 | + | 0.999192i | \(0.512793\pi\) | |||||||
\(14\) | 0.307326 | 0.0821364 | ||||||||
\(15\) | 0.988649 | 0.255268 | ||||||||
\(16\) | 3.44222 | 0.860556 | ||||||||
\(17\) | 0.186210 | 0.0451625 | 0.0225813 | − | 0.999745i | \(-0.492812\pi\) | ||||
0.0225813 | + | 0.999745i | \(0.492812\pi\) | |||||||
\(18\) | 0.307326 | 0.0724375 | ||||||||
\(19\) | 0.852422 | 0.195559 | 0.0977795 | − | 0.995208i | \(-0.468826\pi\) | ||||
0.0977795 | + | 0.995208i | \(0.468826\pi\) | |||||||
\(20\) | 1.88392 | 0.421257 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0.616750 | 0.131491 | ||||||||
\(23\) | −3.33599 | −0.695601 | −0.347801 | − | 0.937569i | \(-0.613071\pi\) | ||||
−0.347801 | + | 0.937569i | \(0.613071\pi\) | |||||||
\(24\) | 1.20028 | 0.245006 | ||||||||
\(25\) | −4.02257 | −0.804515 | ||||||||
\(26\) | −0.0890436 | −0.0174629 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.90555 | −0.360115 | ||||||||
\(29\) | −4.37763 | −0.812905 | −0.406452 | − | 0.913672i | \(-0.633234\pi\) | ||||
−0.406452 | + | 0.913672i | \(0.633234\pi\) | |||||||
\(30\) | 0.303838 | 0.0554729 | ||||||||
\(31\) | −5.73898 | −1.03075 | −0.515376 | − | 0.856964i | \(-0.672348\pi\) | ||||
−0.515376 | + | 0.856964i | \(0.672348\pi\) | |||||||
\(32\) | 3.45844 | 0.611372 | ||||||||
\(33\) | −2.00682 | −0.349343 | ||||||||
\(34\) | 0.0572272 | 0.00981438 | ||||||||
\(35\) | −0.988649 | −0.167112 | ||||||||
\(36\) | −1.90555 | −0.317592 | ||||||||
\(37\) | −7.05580 | −1.15997 | −0.579983 | − | 0.814629i | \(-0.696941\pi\) | ||||
−0.579983 | + | 0.814629i | \(0.696941\pi\) | |||||||
\(38\) | 0.261972 | 0.0424974 | ||||||||
\(39\) | 0.289737 | 0.0463950 | ||||||||
\(40\) | 1.18665 | 0.187626 | ||||||||
\(41\) | 3.81974 | 0.596544 | 0.298272 | − | 0.954481i | \(-0.403590\pi\) | ||||
0.298272 | + | 0.954481i | \(0.403590\pi\) | |||||||
\(42\) | −0.307326 | −0.0474214 | ||||||||
\(43\) | 9.06384 | 1.38222 | 0.691112 | − | 0.722748i | \(-0.257121\pi\) | ||||
0.691112 | + | 0.722748i | \(0.257121\pi\) | |||||||
\(44\) | −3.82411 | −0.576506 | ||||||||
\(45\) | −0.988649 | −0.147379 | ||||||||
\(46\) | −1.02524 | −0.151163 | ||||||||
\(47\) | 1.34856 | 0.196708 | 0.0983540 | − | 0.995151i | \(-0.468642\pi\) | ||||
0.0983540 | + | 0.995151i | \(0.468642\pi\) | |||||||
\(48\) | −3.44222 | −0.496842 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.23624 | −0.174831 | ||||||||
\(51\) | −0.186210 | −0.0260746 | ||||||||
\(52\) | 0.552108 | 0.0765636 | ||||||||
\(53\) | 3.75486 | 0.515770 | 0.257885 | − | 0.966176i | \(-0.416974\pi\) | ||||
0.257885 | + | 0.966176i | \(0.416974\pi\) | |||||||
\(54\) | −0.307326 | −0.0418218 | ||||||||
\(55\) | −1.98405 | −0.267529 | ||||||||
\(56\) | −1.20028 | −0.160394 | ||||||||
\(57\) | −0.852422 | −0.112906 | ||||||||
\(58\) | −1.34536 | −0.176654 | ||||||||
\(59\) | −4.26624 | −0.555418 | −0.277709 | − | 0.960665i | \(-0.589575\pi\) | ||||
−0.277709 | + | 0.960665i | \(0.589575\pi\) | |||||||
\(60\) | −1.88392 | −0.243213 | ||||||||
\(61\) | 3.08411 | 0.394880 | 0.197440 | − | 0.980315i | \(-0.436737\pi\) | ||||
0.197440 | + | 0.980315i | \(0.436737\pi\) | |||||||
\(62\) | −1.76374 | −0.223995 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −5.82158 | −0.727698 | ||||||||
\(65\) | 0.286448 | 0.0355295 | ||||||||
\(66\) | −0.616750 | −0.0759166 | ||||||||
\(67\) | −10.8349 | −1.32370 | −0.661850 | − | 0.749636i | \(-0.730228\pi\) | ||||
−0.661850 | + | 0.749636i | \(0.730228\pi\) | |||||||
\(68\) | −0.354832 | −0.0430297 | ||||||||
\(69\) | 3.33599 | 0.401606 | ||||||||
\(70\) | −0.303838 | −0.0363155 | ||||||||
\(71\) | 13.0932 | 1.55387 | 0.776937 | − | 0.629579i | \(-0.216773\pi\) | ||||
0.776937 | + | 0.629579i | \(0.216773\pi\) | |||||||
\(72\) | −1.20028 | −0.141454 | ||||||||
\(73\) | 14.9066 | 1.74469 | 0.872343 | − | 0.488894i | \(-0.162600\pi\) | ||||
0.872343 | + | 0.488894i | \(0.162600\pi\) | |||||||
\(74\) | −2.16843 | −0.252075 | ||||||||
\(75\) | 4.02257 | 0.464487 | ||||||||
\(76\) | −1.62433 | −0.186324 | ||||||||
\(77\) | 2.00682 | 0.228699 | ||||||||
\(78\) | 0.0890436 | 0.0100822 | ||||||||
\(79\) | 16.7593 | 1.88557 | 0.942785 | − | 0.333400i | \(-0.108196\pi\) | ||||
0.942785 | + | 0.333400i | \(0.108196\pi\) | |||||||
\(80\) | −3.40315 | −0.380484 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.17391 | 0.129636 | ||||||||
\(83\) | 15.1974 | 1.66813 | 0.834067 | − | 0.551663i | \(-0.186007\pi\) | ||||
0.834067 | + | 0.551663i | \(0.186007\pi\) | |||||||
\(84\) | 1.90555 | 0.207913 | ||||||||
\(85\) | −0.184096 | −0.0199680 | ||||||||
\(86\) | 2.78556 | 0.300374 | ||||||||
\(87\) | 4.37763 | 0.469331 | ||||||||
\(88\) | −2.40875 | −0.256773 | ||||||||
\(89\) | −0.526198 | −0.0557769 | −0.0278884 | − | 0.999611i | \(-0.508878\pi\) | ||||
−0.0278884 | + | 0.999611i | \(0.508878\pi\) | |||||||
\(90\) | −0.303838 | −0.0320273 | ||||||||
\(91\) | −0.289737 | −0.0303726 | ||||||||
\(92\) | 6.35689 | 0.662752 | ||||||||
\(93\) | 5.73898 | 0.595105 | ||||||||
\(94\) | 0.414448 | 0.0427471 | ||||||||
\(95\) | −0.842746 | −0.0864639 | ||||||||
\(96\) | −3.45844 | −0.352976 | ||||||||
\(97\) | 6.83150 | 0.693634 | 0.346817 | − | 0.937933i | \(-0.387262\pi\) | ||||
0.346817 | + | 0.937933i | \(0.387262\pi\) | |||||||
\(98\) | 0.307326 | 0.0310446 | ||||||||
\(99\) | 2.00682 | 0.201694 | ||||||||
\(100\) | 7.66522 | 0.766522 | ||||||||
\(101\) | 13.4337 | 1.33670 | 0.668350 | − | 0.743847i | \(-0.267001\pi\) | ||||
0.668350 | + | 0.743847i | \(0.267001\pi\) | |||||||
\(102\) | −0.0572272 | −0.00566633 | ||||||||
\(103\) | −2.29311 | −0.225947 | −0.112973 | − | 0.993598i | \(-0.536037\pi\) | ||||
−0.112973 | + | 0.993598i | \(0.536037\pi\) | |||||||
\(104\) | 0.347764 | 0.0341011 | ||||||||
\(105\) | 0.988649 | 0.0964823 | ||||||||
\(106\) | 1.15397 | 0.112083 | ||||||||
\(107\) | 4.90083 | 0.473781 | 0.236890 | − | 0.971536i | \(-0.423872\pi\) | ||||
0.236890 | + | 0.971536i | \(0.423872\pi\) | |||||||
\(108\) | 1.90555 | 0.183362 | ||||||||
\(109\) | 2.58229 | 0.247339 | 0.123669 | − | 0.992323i | \(-0.460534\pi\) | ||||
0.123669 | + | 0.992323i | \(0.460534\pi\) | |||||||
\(110\) | −0.609749 | −0.0581373 | ||||||||
\(111\) | 7.05580 | 0.669707 | ||||||||
\(112\) | 3.44222 | 0.325260 | ||||||||
\(113\) | −1.77268 | −0.166760 | −0.0833799 | − | 0.996518i | \(-0.526572\pi\) | ||||
−0.0833799 | + | 0.996518i | \(0.526572\pi\) | |||||||
\(114\) | −0.261972 | −0.0245359 | ||||||||
\(115\) | 3.29812 | 0.307551 | ||||||||
\(116\) | 8.34179 | 0.774516 | ||||||||
\(117\) | −0.289737 | −0.0267862 | ||||||||
\(118\) | −1.31113 | −0.120699 | ||||||||
\(119\) | 0.186210 | 0.0170698 | ||||||||
\(120\) | −1.18665 | −0.108326 | ||||||||
\(121\) | −6.97265 | −0.633878 | ||||||||
\(122\) | 0.947829 | 0.0858124 | ||||||||
\(123\) | −3.81974 | −0.344415 | ||||||||
\(124\) | 10.9359 | 0.982075 | ||||||||
\(125\) | 8.92016 | 0.797843 | ||||||||
\(126\) | 0.307326 | 0.0273788 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | −8.70601 | −0.769509 | ||||||||
\(129\) | −9.06384 | −0.798027 | ||||||||
\(130\) | 0.0880329 | 0.00772099 | ||||||||
\(131\) | −11.9789 | −1.04661 | −0.523303 | − | 0.852147i | \(-0.675300\pi\) | ||||
−0.523303 | + | 0.852147i | \(0.675300\pi\) | |||||||
\(132\) | 3.82411 | 0.332846 | ||||||||
\(133\) | 0.852422 | 0.0739144 | ||||||||
\(134\) | −3.32986 | −0.287656 | ||||||||
\(135\) | 0.988649 | 0.0850894 | ||||||||
\(136\) | −0.223504 | −0.0191653 | ||||||||
\(137\) | −13.4775 | −1.15146 | −0.575731 | − | 0.817639i | \(-0.695282\pi\) | ||||
−0.575731 | + | 0.817639i | \(0.695282\pi\) | |||||||
\(138\) | 1.02524 | 0.0872738 | ||||||||
\(139\) | 6.28920 | 0.533443 | 0.266721 | − | 0.963774i | \(-0.414060\pi\) | ||||
0.266721 | + | 0.963774i | \(0.414060\pi\) | |||||||
\(140\) | 1.88392 | 0.159220 | ||||||||
\(141\) | −1.34856 | −0.113569 | ||||||||
\(142\) | 4.02387 | 0.337676 | ||||||||
\(143\) | −0.581451 | −0.0486233 | ||||||||
\(144\) | 3.44222 | 0.286852 | ||||||||
\(145\) | 4.32794 | 0.359416 | ||||||||
\(146\) | 4.58119 | 0.379142 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 13.4452 | 1.10519 | ||||||||
\(149\) | 2.21608 | 0.181548 | 0.0907740 | − | 0.995872i | \(-0.471066\pi\) | ||||
0.0907740 | + | 0.995872i | \(0.471066\pi\) | |||||||
\(150\) | 1.23624 | 0.100939 | ||||||||
\(151\) | −11.7145 | −0.953316 | −0.476658 | − | 0.879089i | \(-0.658152\pi\) | ||||
−0.476658 | + | 0.879089i | \(0.658152\pi\) | |||||||
\(152\) | −1.02314 | −0.0829879 | ||||||||
\(153\) | 0.186210 | 0.0150542 | ||||||||
\(154\) | 0.616750 | 0.0496991 | ||||||||
\(155\) | 5.67384 | 0.455734 | ||||||||
\(156\) | −0.552108 | −0.0442040 | ||||||||
\(157\) | −3.95965 | −0.316014 | −0.158007 | − | 0.987438i | \(-0.550507\pi\) | ||||
−0.158007 | + | 0.987438i | \(0.550507\pi\) | |||||||
\(158\) | 5.15058 | 0.409758 | ||||||||
\(159\) | −3.75486 | −0.297780 | ||||||||
\(160\) | −3.41918 | −0.270310 | ||||||||
\(161\) | −3.33599 | −0.262913 | ||||||||
\(162\) | 0.307326 | 0.0241458 | ||||||||
\(163\) | 22.5680 | 1.76766 | 0.883832 | − | 0.467805i | \(-0.154955\pi\) | ||||
0.883832 | + | 0.467805i | \(0.154955\pi\) | |||||||
\(164\) | −7.27872 | −0.568372 | ||||||||
\(165\) | 1.98405 | 0.154458 | ||||||||
\(166\) | 4.67056 | 0.362506 | ||||||||
\(167\) | 15.6225 | 1.20891 | 0.604453 | − | 0.796641i | \(-0.293392\pi\) | ||||
0.604453 | + | 0.796641i | \(0.293392\pi\) | |||||||
\(168\) | 1.20028 | 0.0926034 | ||||||||
\(169\) | −12.9161 | −0.993543 | ||||||||
\(170\) | −0.0565776 | −0.00433930 | ||||||||
\(171\) | 0.852422 | 0.0651863 | ||||||||
\(172\) | −17.2716 | −1.31695 | ||||||||
\(173\) | 16.8019 | 1.27743 | 0.638713 | − | 0.769445i | \(-0.279467\pi\) | ||||
0.638713 | + | 0.769445i | \(0.279467\pi\) | |||||||
\(174\) | 1.34536 | 0.101991 | ||||||||
\(175\) | −4.02257 | −0.304078 | ||||||||
\(176\) | 6.90794 | 0.520706 | ||||||||
\(177\) | 4.26624 | 0.320671 | ||||||||
\(178\) | −0.161714 | −0.0121210 | ||||||||
\(179\) | 18.5086 | 1.38340 | 0.691699 | − | 0.722186i | \(-0.256862\pi\) | ||||
0.691699 | + | 0.722186i | \(0.256862\pi\) | |||||||
\(180\) | 1.88392 | 0.140419 | ||||||||
\(181\) | 5.16665 | 0.384034 | 0.192017 | − | 0.981392i | \(-0.438497\pi\) | ||||
0.192017 | + | 0.981392i | \(0.438497\pi\) | |||||||
\(182\) | −0.0890436 | −0.00660035 | ||||||||
\(183\) | −3.08411 | −0.227984 | ||||||||
\(184\) | 4.00411 | 0.295187 | ||||||||
\(185\) | 6.97571 | 0.512864 | ||||||||
\(186\) | 1.76374 | 0.129324 | ||||||||
\(187\) | 0.373691 | 0.0273270 | ||||||||
\(188\) | −2.56975 | −0.187418 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −0.258998 | −0.0187897 | ||||||||
\(191\) | −1.27980 | −0.0926027 | −0.0463014 | − | 0.998928i | \(-0.514743\pi\) | ||||
−0.0463014 | + | 0.998928i | \(0.514743\pi\) | |||||||
\(192\) | 5.82158 | 0.420136 | ||||||||
\(193\) | 5.02979 | 0.362052 | 0.181026 | − | 0.983478i | \(-0.442058\pi\) | ||||
0.181026 | + | 0.983478i | \(0.442058\pi\) | |||||||
\(194\) | 2.09950 | 0.150735 | ||||||||
\(195\) | −0.286448 | −0.0205130 | ||||||||
\(196\) | −1.90555 | −0.136111 | ||||||||
\(197\) | −5.69293 | −0.405604 | −0.202802 | − | 0.979220i | \(-0.565005\pi\) | ||||
−0.202802 | + | 0.979220i | \(0.565005\pi\) | |||||||
\(198\) | 0.616750 | 0.0438305 | ||||||||
\(199\) | 0.823780 | 0.0583962 | 0.0291981 | − | 0.999574i | \(-0.490705\pi\) | ||||
0.0291981 | + | 0.999574i | \(0.490705\pi\) | |||||||
\(200\) | 4.82820 | 0.341406 | ||||||||
\(201\) | 10.8349 | 0.764238 | ||||||||
\(202\) | 4.12852 | 0.290482 | ||||||||
\(203\) | −4.37763 | −0.307249 | ||||||||
\(204\) | 0.354832 | 0.0248432 | ||||||||
\(205\) | −3.77639 | −0.263754 | ||||||||
\(206\) | −0.704732 | −0.0491010 | ||||||||
\(207\) | −3.33599 | −0.231867 | ||||||||
\(208\) | −0.997338 | −0.0691530 | ||||||||
\(209\) | 1.71066 | 0.118329 | ||||||||
\(210\) | 0.303838 | 0.0209668 | ||||||||
\(211\) | −15.1264 | −1.04135 | −0.520674 | − | 0.853756i | \(-0.674319\pi\) | ||||
−0.520674 | + | 0.853756i | \(0.674319\pi\) | |||||||
\(212\) | −7.15508 | −0.491413 | ||||||||
\(213\) | −13.0932 | −0.897129 | ||||||||
\(214\) | 1.50615 | 0.102958 | ||||||||
\(215\) | −8.96096 | −0.611132 | ||||||||
\(216\) | 1.20028 | 0.0816685 | ||||||||
\(217\) | −5.73898 | −0.389587 | ||||||||
\(218\) | 0.793606 | 0.0537498 | ||||||||
\(219\) | −14.9066 | −1.00729 | ||||||||
\(220\) | 3.78070 | 0.254895 | ||||||||
\(221\) | −0.0539518 | −0.00362919 | ||||||||
\(222\) | 2.16843 | 0.145536 | ||||||||
\(223\) | 4.14354 | 0.277472 | 0.138736 | − | 0.990329i | \(-0.455696\pi\) | ||||
0.138736 | + | 0.990329i | \(0.455696\pi\) | |||||||
\(224\) | 3.45844 | 0.231077 | ||||||||
\(225\) | −4.02257 | −0.268172 | ||||||||
\(226\) | −0.544791 | −0.0362390 | ||||||||
\(227\) | −17.7163 | −1.17587 | −0.587935 | − | 0.808908i | \(-0.700059\pi\) | ||||
−0.587935 | + | 0.808908i | \(0.700059\pi\) | |||||||
\(228\) | 1.62433 | 0.107574 | ||||||||
\(229\) | 27.6285 | 1.82574 | 0.912871 | − | 0.408249i | \(-0.133860\pi\) | ||||
0.912871 | + | 0.408249i | \(0.133860\pi\) | |||||||
\(230\) | 1.01360 | 0.0668347 | ||||||||
\(231\) | −2.00682 | −0.132039 | ||||||||
\(232\) | 5.25437 | 0.344966 | ||||||||
\(233\) | 21.6658 | 1.41937 | 0.709687 | − | 0.704517i | \(-0.248836\pi\) | ||||
0.709687 | + | 0.704517i | \(0.248836\pi\) | |||||||
\(234\) | −0.0890436 | −0.00582096 | ||||||||
\(235\) | −1.33325 | −0.0869719 | ||||||||
\(236\) | 8.12954 | 0.529188 | ||||||||
\(237\) | −16.7593 | −1.08863 | ||||||||
\(238\) | 0.0572272 | 0.00370949 | ||||||||
\(239\) | 3.33796 | 0.215915 | 0.107957 | − | 0.994156i | \(-0.465569\pi\) | ||||
0.107957 | + | 0.994156i | \(0.465569\pi\) | |||||||
\(240\) | 3.40315 | 0.219673 | ||||||||
\(241\) | −13.4703 | −0.867701 | −0.433851 | − | 0.900985i | \(-0.642845\pi\) | ||||
−0.433851 | + | 0.900985i | \(0.642845\pi\) | |||||||
\(242\) | −2.14288 | −0.137749 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −5.87693 | −0.376232 | ||||||||
\(245\) | −0.988649 | −0.0631625 | ||||||||
\(246\) | −1.17391 | −0.0748456 | ||||||||
\(247\) | −0.246978 | −0.0157148 | ||||||||
\(248\) | 6.88837 | 0.437412 | ||||||||
\(249\) | −15.1974 | −0.963097 | ||||||||
\(250\) | 2.74140 | 0.173381 | ||||||||
\(251\) | 3.19071 | 0.201396 | 0.100698 | − | 0.994917i | \(-0.467892\pi\) | ||||
0.100698 | + | 0.994917i | \(0.467892\pi\) | |||||||
\(252\) | −1.90555 | −0.120038 | ||||||||
\(253\) | −6.69474 | −0.420895 | ||||||||
\(254\) | −0.307326 | −0.0192834 | ||||||||
\(255\) | 0.184096 | 0.0115286 | ||||||||
\(256\) | 8.96758 | 0.560474 | ||||||||
\(257\) | 9.04475 | 0.564196 | 0.282098 | − | 0.959386i | \(-0.408970\pi\) | ||||
0.282098 | + | 0.959386i | \(0.408970\pi\) | |||||||
\(258\) | −2.78556 | −0.173421 | ||||||||
\(259\) | −7.05580 | −0.438426 | ||||||||
\(260\) | −0.545841 | −0.0338516 | ||||||||
\(261\) | −4.37763 | −0.270968 | ||||||||
\(262\) | −3.68144 | −0.227440 | ||||||||
\(263\) | 28.1759 | 1.73740 | 0.868700 | − | 0.495339i | \(-0.164956\pi\) | ||||
0.868700 | + | 0.495339i | \(0.164956\pi\) | |||||||
\(264\) | 2.40875 | 0.148248 | ||||||||
\(265\) | −3.71224 | −0.228041 | ||||||||
\(266\) | 0.261972 | 0.0160625 | ||||||||
\(267\) | 0.526198 | 0.0322028 | ||||||||
\(268\) | 20.6465 | 1.26119 | ||||||||
\(269\) | 28.9671 | 1.76616 | 0.883078 | − | 0.469226i | \(-0.155467\pi\) | ||||
0.883078 | + | 0.469226i | \(0.155467\pi\) | |||||||
\(270\) | 0.303838 | 0.0184910 | ||||||||
\(271\) | −2.61077 | −0.158593 | −0.0792964 | − | 0.996851i | \(-0.525267\pi\) | ||||
−0.0792964 | + | 0.996851i | \(0.525267\pi\) | |||||||
\(272\) | 0.640976 | 0.0388649 | ||||||||
\(273\) | 0.289737 | 0.0175357 | ||||||||
\(274\) | −4.14199 | −0.250227 | ||||||||
\(275\) | −8.07260 | −0.486796 | ||||||||
\(276\) | −6.35689 | −0.382640 | ||||||||
\(277\) | −15.2284 | −0.914988 | −0.457494 | − | 0.889213i | \(-0.651253\pi\) | ||||
−0.457494 | + | 0.889213i | \(0.651253\pi\) | |||||||
\(278\) | 1.93283 | 0.115924 | ||||||||
\(279\) | −5.73898 | −0.343584 | ||||||||
\(280\) | 1.18665 | 0.0709161 | ||||||||
\(281\) | −16.7836 | −1.00122 | −0.500612 | − | 0.865672i | \(-0.666892\pi\) | ||||
−0.500612 | + | 0.865672i | \(0.666892\pi\) | |||||||
\(282\) | −0.414448 | −0.0246800 | ||||||||
\(283\) | −5.84420 | −0.347401 | −0.173701 | − | 0.984798i | \(-0.555573\pi\) | ||||
−0.173701 | + | 0.984798i | \(0.555573\pi\) | |||||||
\(284\) | −24.9497 | −1.48049 | ||||||||
\(285\) | 0.842746 | 0.0499200 | ||||||||
\(286\) | −0.178695 | −0.0105665 | ||||||||
\(287\) | 3.81974 | 0.225472 | ||||||||
\(288\) | 3.45844 | 0.203791 | ||||||||
\(289\) | −16.9653 | −0.997960 | ||||||||
\(290\) | 1.33009 | 0.0781054 | ||||||||
\(291\) | −6.83150 | −0.400470 | ||||||||
\(292\) | −28.4053 | −1.66229 | ||||||||
\(293\) | 2.88058 | 0.168285 | 0.0841427 | − | 0.996454i | \(-0.473185\pi\) | ||||
0.0841427 | + | 0.996454i | \(0.473185\pi\) | |||||||
\(294\) | −0.307326 | −0.0179236 | ||||||||
\(295\) | 4.21782 | 0.245571 | ||||||||
\(296\) | 8.46892 | 0.492246 | ||||||||
\(297\) | −2.00682 | −0.116448 | ||||||||
\(298\) | 0.681058 | 0.0394526 | ||||||||
\(299\) | 0.966557 | 0.0558974 | ||||||||
\(300\) | −7.66522 | −0.442552 | ||||||||
\(301\) | 9.06384 | 0.522431 | ||||||||
\(302\) | −3.60018 | −0.207167 | ||||||||
\(303\) | −13.4337 | −0.771744 | ||||||||
\(304\) | 2.93423 | 0.168290 | ||||||||
\(305\) | −3.04911 | −0.174591 | ||||||||
\(306\) | 0.0572272 | 0.00327146 | ||||||||
\(307\) | 2.95818 | 0.168832 | 0.0844161 | − | 0.996431i | \(-0.473098\pi\) | ||||
0.0844161 | + | 0.996431i | \(0.473098\pi\) | |||||||
\(308\) | −3.82411 | −0.217899 | ||||||||
\(309\) | 2.29311 | 0.130450 | ||||||||
\(310\) | 1.74372 | 0.0990366 | ||||||||
\(311\) | −7.79466 | −0.441995 | −0.220997 | − | 0.975274i | \(-0.570931\pi\) | ||||
−0.220997 | + | 0.975274i | \(0.570931\pi\) | |||||||
\(312\) | −0.347764 | −0.0196883 | ||||||||
\(313\) | 7.56008 | 0.427321 | 0.213660 | − | 0.976908i | \(-0.431461\pi\) | ||||
0.213660 | + | 0.976908i | \(0.431461\pi\) | |||||||
\(314\) | −1.21690 | −0.0686738 | ||||||||
\(315\) | −0.988649 | −0.0557041 | ||||||||
\(316\) | −31.9357 | −1.79653 | ||||||||
\(317\) | 31.2502 | 1.75519 | 0.877593 | − | 0.479406i | \(-0.159148\pi\) | ||||
0.877593 | + | 0.479406i | \(0.159148\pi\) | |||||||
\(318\) | −1.15397 | −0.0647112 | ||||||||
\(319\) | −8.78513 | −0.491873 | ||||||||
\(320\) | 5.75550 | 0.321742 | ||||||||
\(321\) | −4.90083 | −0.273538 | ||||||||
\(322\) | −1.02524 | −0.0571341 | ||||||||
\(323\) | 0.158729 | 0.00883194 | ||||||||
\(324\) | −1.90555 | −0.105864 | ||||||||
\(325\) | 1.16549 | 0.0646496 | ||||||||
\(326\) | 6.93574 | 0.384135 | ||||||||
\(327\) | −2.58229 | −0.142801 | ||||||||
\(328\) | −4.58475 | −0.253151 | ||||||||
\(329\) | 1.34856 | 0.0743486 | ||||||||
\(330\) | 0.609749 | 0.0335656 | ||||||||
\(331\) | 12.3799 | 0.680461 | 0.340230 | − | 0.940342i | \(-0.389495\pi\) | ||||
0.340230 | + | 0.940342i | \(0.389495\pi\) | |||||||
\(332\) | −28.9595 | −1.58936 | ||||||||
\(333\) | −7.05580 | −0.386655 | ||||||||
\(334\) | 4.80120 | 0.262710 | ||||||||
\(335\) | 10.7120 | 0.585257 | ||||||||
\(336\) | −3.44222 | −0.187789 | ||||||||
\(337\) | 24.7975 | 1.35081 | 0.675403 | − | 0.737448i | \(-0.263970\pi\) | ||||
0.675403 | + | 0.737448i | \(0.263970\pi\) | |||||||
\(338\) | −3.96944 | −0.215909 | ||||||||
\(339\) | 1.77268 | 0.0962788 | ||||||||
\(340\) | 0.350805 | 0.0190251 | ||||||||
\(341\) | −11.5171 | −0.623688 | ||||||||
\(342\) | 0.261972 | 0.0141658 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −10.8791 | −0.586563 | ||||||||
\(345\) | −3.29812 | −0.177565 | ||||||||
\(346\) | 5.16367 | 0.277601 | ||||||||
\(347\) | −36.3026 | −1.94883 | −0.974413 | − | 0.224763i | \(-0.927839\pi\) | ||||
−0.974413 | + | 0.224763i | \(0.927839\pi\) | |||||||
\(348\) | −8.34179 | −0.447167 | ||||||||
\(349\) | 11.0963 | 0.593973 | 0.296986 | − | 0.954882i | \(-0.404018\pi\) | ||||
0.296986 | + | 0.954882i | \(0.404018\pi\) | |||||||
\(350\) | −1.23624 | −0.0660799 | ||||||||
\(351\) | 0.289737 | 0.0154650 | ||||||||
\(352\) | 6.94049 | 0.369929 | ||||||||
\(353\) | 10.7528 | 0.572312 | 0.286156 | − | 0.958183i | \(-0.407622\pi\) | ||||
0.286156 | + | 0.958183i | \(0.407622\pi\) | |||||||
\(354\) | 1.31113 | 0.0696857 | ||||||||
\(355\) | −12.9445 | −0.687025 | ||||||||
\(356\) | 1.00270 | 0.0531428 | ||||||||
\(357\) | −0.186210 | −0.00985527 | ||||||||
\(358\) | 5.68818 | 0.300630 | ||||||||
\(359\) | −4.97551 | −0.262598 | −0.131299 | − | 0.991343i | \(-0.541915\pi\) | ||||
−0.131299 | + | 0.991343i | \(0.541915\pi\) | |||||||
\(360\) | 1.18665 | 0.0625421 | ||||||||
\(361\) | −18.2734 | −0.961757 | ||||||||
\(362\) | 1.58785 | 0.0834554 | ||||||||
\(363\) | 6.97265 | 0.365969 | ||||||||
\(364\) | 0.552108 | 0.0289383 | ||||||||
\(365\) | −14.7374 | −0.771391 | ||||||||
\(366\) | −0.947829 | −0.0495438 | ||||||||
\(367\) | −21.4750 | −1.12099 | −0.560493 | − | 0.828159i | \(-0.689388\pi\) | ||||
−0.560493 | + | 0.828159i | \(0.689388\pi\) | |||||||
\(368\) | −11.4832 | −0.598604 | ||||||||
\(369\) | 3.81974 | 0.198848 | ||||||||
\(370\) | 2.14382 | 0.111452 | ||||||||
\(371\) | 3.75486 | 0.194943 | ||||||||
\(372\) | −10.9359 | −0.567001 | ||||||||
\(373\) | 19.7237 | 1.02125 | 0.510627 | − | 0.859803i | \(-0.329413\pi\) | ||||
0.510627 | + | 0.859803i | \(0.329413\pi\) | |||||||
\(374\) | 0.114845 | 0.00593849 | ||||||||
\(375\) | −8.92016 | −0.460635 | ||||||||
\(376\) | −1.61865 | −0.0834754 | ||||||||
\(377\) | 1.26836 | 0.0653238 | ||||||||
\(378\) | −0.307326 | −0.0158071 | ||||||||
\(379\) | −0.520876 | −0.0267556 | −0.0133778 | − | 0.999911i | \(-0.504258\pi\) | ||||
−0.0133778 | + | 0.999911i | \(0.504258\pi\) | |||||||
\(380\) | 1.60590 | 0.0823807 | ||||||||
\(381\) | 1.00000 | 0.0512316 | ||||||||
\(382\) | −0.393314 | −0.0201237 | ||||||||
\(383\) | 24.9559 | 1.27519 | 0.637594 | − | 0.770372i | \(-0.279930\pi\) | ||||
0.637594 | + | 0.770372i | \(0.279930\pi\) | |||||||
\(384\) | 8.70601 | 0.444276 | ||||||||
\(385\) | −1.98405 | −0.101116 | ||||||||
\(386\) | 1.54579 | 0.0786785 | ||||||||
\(387\) | 9.06384 | 0.460741 | ||||||||
\(388\) | −13.0178 | −0.660877 | ||||||||
\(389\) | 14.5891 | 0.739696 | 0.369848 | − | 0.929092i | \(-0.379410\pi\) | ||||
0.369848 | + | 0.929092i | \(0.379410\pi\) | |||||||
\(390\) | −0.0880329 | −0.00445772 | ||||||||
\(391\) | −0.621194 | −0.0314151 | ||||||||
\(392\) | −1.20028 | −0.0606232 | ||||||||
\(393\) | 11.9789 | 0.604258 | ||||||||
\(394\) | −1.74959 | −0.0881429 | ||||||||
\(395\) | −16.5691 | −0.833681 | ||||||||
\(396\) | −3.82411 | −0.192169 | ||||||||
\(397\) | −5.87002 | −0.294608 | −0.147304 | − | 0.989091i | \(-0.547060\pi\) | ||||
−0.147304 | + | 0.989091i | \(0.547060\pi\) | |||||||
\(398\) | 0.253169 | 0.0126902 | ||||||||
\(399\) | −0.852422 | −0.0426745 | ||||||||
\(400\) | −13.8466 | −0.692330 | ||||||||
\(401\) | 5.35527 | 0.267429 | 0.133715 | − | 0.991020i | \(-0.457309\pi\) | ||||
0.133715 | + | 0.991020i | \(0.457309\pi\) | |||||||
\(402\) | 3.32986 | 0.166078 | ||||||||
\(403\) | 1.66279 | 0.0828296 | ||||||||
\(404\) | −25.5985 | −1.27358 | ||||||||
\(405\) | −0.988649 | −0.0491264 | ||||||||
\(406\) | −1.34536 | −0.0667690 | ||||||||
\(407\) | −14.1598 | −0.701873 | ||||||||
\(408\) | 0.223504 | 0.0110651 | ||||||||
\(409\) | −35.4278 | −1.75179 | −0.875896 | − | 0.482500i | \(-0.839729\pi\) | ||||
−0.875896 | + | 0.482500i | \(0.839729\pi\) | |||||||
\(410\) | −1.16058 | −0.0573171 | ||||||||
\(411\) | 13.4775 | 0.664797 | ||||||||
\(412\) | 4.36963 | 0.215276 | ||||||||
\(413\) | −4.26624 | −0.209928 | ||||||||
\(414\) | −1.02524 | −0.0503876 | ||||||||
\(415\) | −15.0249 | −0.737544 | ||||||||
\(416\) | −1.00204 | −0.0491289 | ||||||||
\(417\) | −6.28920 | −0.307983 | ||||||||
\(418\) | 0.525731 | 0.0257143 | ||||||||
\(419\) | 15.6038 | 0.762293 | 0.381147 | − | 0.924515i | \(-0.375529\pi\) | ||||
0.381147 | + | 0.924515i | \(0.375529\pi\) | |||||||
\(420\) | −1.88392 | −0.0919259 | ||||||||
\(421\) | 25.4791 | 1.24177 | 0.620887 | − | 0.783900i | \(-0.286773\pi\) | ||||
0.620887 | + | 0.783900i | \(0.286773\pi\) | |||||||
\(422\) | −4.64875 | −0.226298 | ||||||||
\(423\) | 1.34856 | 0.0655693 | ||||||||
\(424\) | −4.50688 | −0.218873 | ||||||||
\(425\) | −0.749043 | −0.0363339 | ||||||||
\(426\) | −4.02387 | −0.194957 | ||||||||
\(427\) | 3.08411 | 0.149251 | ||||||||
\(428\) | −9.33878 | −0.451407 | ||||||||
\(429\) | 0.581451 | 0.0280727 | ||||||||
\(430\) | −2.75394 | −0.132807 | ||||||||
\(431\) | 2.51062 | 0.120932 | 0.0604661 | − | 0.998170i | \(-0.480741\pi\) | ||||
0.0604661 | + | 0.998170i | \(0.480741\pi\) | |||||||
\(432\) | −3.44222 | −0.165614 | ||||||||
\(433\) | −26.5601 | −1.27640 | −0.638198 | − | 0.769872i | \(-0.720320\pi\) | ||||
−0.638198 | + | 0.769872i | \(0.720320\pi\) | |||||||
\(434\) | −1.76374 | −0.0846622 | ||||||||
\(435\) | −4.32794 | −0.207509 | ||||||||
\(436\) | −4.92069 | −0.235658 | ||||||||
\(437\) | −2.84367 | −0.136031 | ||||||||
\(438\) | −4.58119 | −0.218898 | ||||||||
\(439\) | 2.59419 | 0.123814 | 0.0619070 | − | 0.998082i | \(-0.480282\pi\) | ||||
0.0619070 | + | 0.998082i | \(0.480282\pi\) | |||||||
\(440\) | 2.38141 | 0.113529 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −0.0165808 | −0.000788668 0 | ||||||||
\(443\) | 24.0954 | 1.14481 | 0.572404 | − | 0.819972i | \(-0.306011\pi\) | ||||
0.572404 | + | 0.819972i | \(0.306011\pi\) | |||||||
\(444\) | −13.4452 | −0.638080 | ||||||||
\(445\) | 0.520225 | 0.0246610 | ||||||||
\(446\) | 1.27342 | 0.0602981 | ||||||||
\(447\) | −2.21608 | −0.104817 | ||||||||
\(448\) | −5.82158 | −0.275044 | ||||||||
\(449\) | −11.0719 | −0.522514 | −0.261257 | − | 0.965269i | \(-0.584137\pi\) | ||||
−0.261257 | + | 0.965269i | \(0.584137\pi\) | |||||||
\(450\) | −1.23624 | −0.0582770 | ||||||||
\(451\) | 7.66556 | 0.360957 | ||||||||
\(452\) | 3.37793 | 0.158885 | ||||||||
\(453\) | 11.7145 | 0.550397 | ||||||||
\(454\) | −5.44467 | −0.255531 | ||||||||
\(455\) | 0.286448 | 0.0134289 | ||||||||
\(456\) | 1.02314 | 0.0479131 | ||||||||
\(457\) | 7.11118 | 0.332647 | 0.166324 | − | 0.986071i | \(-0.446810\pi\) | ||||
0.166324 | + | 0.986071i | \(0.446810\pi\) | |||||||
\(458\) | 8.49095 | 0.396756 | ||||||||
\(459\) | −0.186210 | −0.00869153 | ||||||||
\(460\) | −6.28473 | −0.293027 | ||||||||
\(461\) | 24.0587 | 1.12052 | 0.560262 | − | 0.828315i | \(-0.310700\pi\) | ||||
0.560262 | + | 0.828315i | \(0.310700\pi\) | |||||||
\(462\) | −0.616750 | −0.0286938 | ||||||||
\(463\) | −18.9750 | −0.881842 | −0.440921 | − | 0.897546i | \(-0.645348\pi\) | ||||
−0.440921 | + | 0.897546i | \(0.645348\pi\) | |||||||
\(464\) | −15.0688 | −0.699550 | ||||||||
\(465\) | −5.67384 | −0.263118 | ||||||||
\(466\) | 6.65847 | 0.308448 | ||||||||
\(467\) | 7.40649 | 0.342732 | 0.171366 | − | 0.985207i | \(-0.445182\pi\) | ||||
0.171366 | + | 0.985207i | \(0.445182\pi\) | |||||||
\(468\) | 0.552108 | 0.0255212 | ||||||||
\(469\) | −10.8349 | −0.500311 | ||||||||
\(470\) | −0.409744 | −0.0189001 | ||||||||
\(471\) | 3.95965 | 0.182451 | ||||||||
\(472\) | 5.12068 | 0.235698 | ||||||||
\(473\) | 18.1895 | 0.836356 | ||||||||
\(474\) | −5.15058 | −0.236574 | ||||||||
\(475\) | −3.42893 | −0.157330 | ||||||||
\(476\) | −0.354832 | −0.0162637 | ||||||||
\(477\) | 3.75486 | 0.171923 | ||||||||
\(478\) | 1.02584 | 0.0469209 | ||||||||
\(479\) | −4.92351 | −0.224961 | −0.112481 | − | 0.993654i | \(-0.535880\pi\) | ||||
−0.112481 | + | 0.993654i | \(0.535880\pi\) | |||||||
\(480\) | 3.41918 | 0.156064 | ||||||||
\(481\) | 2.04432 | 0.0932131 | ||||||||
\(482\) | −4.13979 | −0.188562 | ||||||||
\(483\) | 3.33599 | 0.151793 | ||||||||
\(484\) | 13.2867 | 0.603943 | ||||||||
\(485\) | −6.75396 | −0.306681 | ||||||||
\(486\) | −0.307326 | −0.0139406 | ||||||||
\(487\) | 9.85082 | 0.446383 | 0.223192 | − | 0.974775i | \(-0.428352\pi\) | ||||
0.223192 | + | 0.974775i | \(0.428352\pi\) | |||||||
\(488\) | −3.70179 | −0.167572 | ||||||||
\(489\) | −22.5680 | −1.02056 | ||||||||
\(490\) | −0.303838 | −0.0137260 | ||||||||
\(491\) | −31.4542 | −1.41951 | −0.709755 | − | 0.704449i | \(-0.751194\pi\) | ||||
−0.709755 | + | 0.704449i | \(0.751194\pi\) | |||||||
\(492\) | 7.27872 | 0.328150 | ||||||||
\(493\) | −0.815157 | −0.0367128 | ||||||||
\(494\) | −0.0759027 | −0.00341503 | ||||||||
\(495\) | −1.98405 | −0.0891762 | ||||||||
\(496\) | −19.7549 | −0.887020 | ||||||||
\(497\) | 13.0932 | 0.587309 | ||||||||
\(498\) | −4.67056 | −0.209293 | ||||||||
\(499\) | −15.4537 | −0.691801 | −0.345900 | − | 0.938271i | \(-0.612426\pi\) | ||||
−0.345900 | + | 0.938271i | \(0.612426\pi\) | |||||||
\(500\) | −16.9978 | −0.760165 | ||||||||
\(501\) | −15.6225 | −0.697962 | ||||||||
\(502\) | 0.980590 | 0.0437659 | ||||||||
\(503\) | 34.8449 | 1.55366 | 0.776829 | − | 0.629712i | \(-0.216827\pi\) | ||||
0.776829 | + | 0.629712i | \(0.216827\pi\) | |||||||
\(504\) | −1.20028 | −0.0534646 | ||||||||
\(505\) | −13.2812 | −0.591005 | ||||||||
\(506\) | −2.05747 | −0.0914656 | ||||||||
\(507\) | 12.9161 | 0.573622 | ||||||||
\(508\) | 1.90555 | 0.0845451 | ||||||||
\(509\) | 22.9563 | 1.01752 | 0.508761 | − | 0.860908i | \(-0.330104\pi\) | ||||
0.508761 | + | 0.860908i | \(0.330104\pi\) | |||||||
\(510\) | 0.0565776 | 0.00250530 | ||||||||
\(511\) | 14.9066 | 0.659429 | ||||||||
\(512\) | 20.1680 | 0.891307 | ||||||||
\(513\) | −0.852422 | −0.0376354 | ||||||||
\(514\) | 2.77969 | 0.122607 | ||||||||
\(515\) | 2.26708 | 0.0998994 | ||||||||
\(516\) | 17.2716 | 0.760340 | ||||||||
\(517\) | 2.70633 | 0.119024 | ||||||||
\(518\) | −2.16843 | −0.0952754 | ||||||||
\(519\) | −16.8019 | −0.737522 | ||||||||
\(520\) | −0.343817 | −0.0150774 | ||||||||
\(521\) | 23.8812 | 1.04625 | 0.523127 | − | 0.852255i | \(-0.324765\pi\) | ||||
0.523127 | + | 0.852255i | \(0.324765\pi\) | |||||||
\(522\) | −1.34536 | −0.0588848 | ||||||||
\(523\) | −42.3363 | −1.85124 | −0.925620 | − | 0.378455i | \(-0.876455\pi\) | ||||
−0.925620 | + | 0.378455i | \(0.876455\pi\) | |||||||
\(524\) | 22.8265 | 0.997180 | ||||||||
\(525\) | 4.02257 | 0.175559 | ||||||||
\(526\) | 8.65919 | 0.377558 | ||||||||
\(527\) | −1.06866 | −0.0465514 | ||||||||
\(528\) | −6.90794 | −0.300630 | ||||||||
\(529\) | −11.8712 | −0.516139 | ||||||||
\(530\) | −1.14087 | −0.0495561 | ||||||||
\(531\) | −4.26624 | −0.185139 | ||||||||
\(532\) | −1.62433 | −0.0704238 | ||||||||
\(533\) | −1.10672 | −0.0479373 | ||||||||
\(534\) | 0.161714 | 0.00699807 | ||||||||
\(535\) | −4.84520 | −0.209476 | ||||||||
\(536\) | 13.0049 | 0.561728 | ||||||||
\(537\) | −18.5086 | −0.798705 | ||||||||
\(538\) | 8.90235 | 0.383808 | ||||||||
\(539\) | 2.00682 | 0.0864401 | ||||||||
\(540\) | −1.88392 | −0.0810710 | ||||||||
\(541\) | −10.0291 | −0.431186 | −0.215593 | − | 0.976483i | \(-0.569168\pi\) | ||||
−0.215593 | + | 0.976483i | \(0.569168\pi\) | |||||||
\(542\) | −0.802357 | −0.0344642 | ||||||||
\(543\) | −5.16665 | −0.221722 | ||||||||
\(544\) | 0.643996 | 0.0276111 | ||||||||
\(545\) | −2.55298 | −0.109358 | ||||||||
\(546\) | 0.0890436 | 0.00381071 | ||||||||
\(547\) | −38.5584 | −1.64864 | −0.824318 | − | 0.566127i | \(-0.808441\pi\) | ||||
−0.824318 | + | 0.566127i | \(0.808441\pi\) | |||||||
\(548\) | 25.6821 | 1.09708 | ||||||||
\(549\) | 3.08411 | 0.131627 | ||||||||
\(550\) | −2.48092 | −0.105787 | ||||||||
\(551\) | −3.73159 | −0.158971 | ||||||||
\(552\) | −4.00411 | −0.170426 | ||||||||
\(553\) | 16.7593 | 0.712679 | ||||||||
\(554\) | −4.68010 | −0.198838 | ||||||||
\(555\) | −6.97571 | −0.296102 | ||||||||
\(556\) | −11.9844 | −0.508251 | ||||||||
\(557\) | −27.3968 | −1.16084 | −0.580420 | − | 0.814317i | \(-0.697112\pi\) | ||||
−0.580420 | + | 0.814317i | \(0.697112\pi\) | |||||||
\(558\) | −1.76374 | −0.0746650 | ||||||||
\(559\) | −2.62613 | −0.111073 | ||||||||
\(560\) | −3.40315 | −0.143809 | ||||||||
\(561\) | −0.373691 | −0.0157772 | ||||||||
\(562\) | −5.15803 | −0.217578 | ||||||||
\(563\) | −39.9956 | −1.68561 | −0.842807 | − | 0.538216i | \(-0.819098\pi\) | ||||
−0.842807 | + | 0.538216i | \(0.819098\pi\) | |||||||
\(564\) | 2.56975 | 0.108206 | ||||||||
\(565\) | 1.75256 | 0.0737307 | ||||||||
\(566\) | −1.79607 | −0.0754946 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −15.7154 | −0.659405 | ||||||||
\(569\) | −39.2508 | −1.64548 | −0.822740 | − | 0.568418i | \(-0.807556\pi\) | ||||
−0.822740 | + | 0.568418i | \(0.807556\pi\) | |||||||
\(570\) | 0.258998 | 0.0108482 | ||||||||
\(571\) | −14.5997 | −0.610978 | −0.305489 | − | 0.952196i | \(-0.598820\pi\) | ||||
−0.305489 | + | 0.952196i | \(0.598820\pi\) | |||||||
\(572\) | 1.10798 | 0.0463271 | ||||||||
\(573\) | 1.27980 | 0.0534642 | ||||||||
\(574\) | 1.17391 | 0.0489979 | ||||||||
\(575\) | 13.4192 | 0.559621 | ||||||||
\(576\) | −5.82158 | −0.242566 | ||||||||
\(577\) | 22.3677 | 0.931181 | 0.465591 | − | 0.885000i | \(-0.345842\pi\) | ||||
0.465591 | + | 0.885000i | \(0.345842\pi\) | |||||||
\(578\) | −5.21389 | −0.216869 | ||||||||
\(579\) | −5.02979 | −0.209031 | ||||||||
\(580\) | −8.24710 | −0.342442 | ||||||||
\(581\) | 15.1974 | 0.630495 | ||||||||
\(582\) | −2.09950 | −0.0870270 | ||||||||
\(583\) | 7.53535 | 0.312082 | ||||||||
\(584\) | −17.8921 | −0.740379 | ||||||||
\(585\) | 0.286448 | 0.0118432 | ||||||||
\(586\) | 0.885278 | 0.0365705 | ||||||||
\(587\) | 37.4645 | 1.54633 | 0.773164 | − | 0.634207i | \(-0.218673\pi\) | ||||
0.773164 | + | 0.634207i | \(0.218673\pi\) | |||||||
\(588\) | 1.90555 | 0.0785836 | ||||||||
\(589\) | −4.89204 | −0.201573 | ||||||||
\(590\) | 1.29625 | 0.0533656 | ||||||||
\(591\) | 5.69293 | 0.234176 | ||||||||
\(592\) | −24.2876 | −0.998216 | ||||||||
\(593\) | 48.5027 | 1.99177 | 0.995883 | − | 0.0906456i | \(-0.0288930\pi\) | ||||
0.995883 | + | 0.0906456i | \(0.0288930\pi\) | |||||||
\(594\) | −0.616750 | −0.0253055 | ||||||||
\(595\) | −0.184096 | −0.00754721 | ||||||||
\(596\) | −4.22284 | −0.172974 | ||||||||
\(597\) | −0.823780 | −0.0337151 | ||||||||
\(598\) | 0.297048 | 0.0121472 | ||||||||
\(599\) | 26.4798 | 1.08194 | 0.540968 | − | 0.841043i | \(-0.318058\pi\) | ||||
0.540968 | + | 0.841043i | \(0.318058\pi\) | |||||||
\(600\) | −4.82820 | −0.197111 | ||||||||
\(601\) | 44.0904 | 1.79849 | 0.899243 | − | 0.437449i | \(-0.144118\pi\) | ||||
0.899243 | + | 0.437449i | \(0.144118\pi\) | |||||||
\(602\) | 2.78556 | 0.113531 | ||||||||
\(603\) | −10.8349 | −0.441233 | ||||||||
\(604\) | 22.3227 | 0.908296 | ||||||||
\(605\) | 6.89351 | 0.280261 | ||||||||
\(606\) | −4.12852 | −0.167710 | ||||||||
\(607\) | 36.8393 | 1.49526 | 0.747630 | − | 0.664116i | \(-0.231192\pi\) | ||||
0.747630 | + | 0.664116i | \(0.231192\pi\) | |||||||
\(608\) | 2.94805 | 0.119559 | ||||||||
\(609\) | 4.37763 | 0.177390 | ||||||||
\(610\) | −0.937070 | −0.0379408 | ||||||||
\(611\) | −0.390728 | −0.0158071 | ||||||||
\(612\) | −0.354832 | −0.0143432 | ||||||||
\(613\) | −43.1987 | −1.74478 | −0.872389 | − | 0.488812i | \(-0.837430\pi\) | ||||
−0.872389 | + | 0.488812i | \(0.837430\pi\) | |||||||
\(614\) | 0.909125 | 0.0366893 | ||||||||
\(615\) | 3.77639 | 0.152279 | ||||||||
\(616\) | −2.40875 | −0.0970512 | ||||||||
\(617\) | 8.35601 | 0.336400 | 0.168200 | − | 0.985753i | \(-0.446205\pi\) | ||||
0.168200 | + | 0.985753i | \(0.446205\pi\) | |||||||
\(618\) | 0.704732 | 0.0283485 | ||||||||
\(619\) | −33.1859 | −1.33385 | −0.666927 | − | 0.745123i | \(-0.732391\pi\) | ||||
−0.666927 | + | 0.745123i | \(0.732391\pi\) | |||||||
\(620\) | −10.8118 | −0.434212 | ||||||||
\(621\) | 3.33599 | 0.133869 | ||||||||
\(622\) | −2.39550 | −0.0960509 | ||||||||
\(623\) | −0.526198 | −0.0210817 | ||||||||
\(624\) | 0.997338 | 0.0399255 | ||||||||
\(625\) | 11.2940 | 0.451758 | ||||||||
\(626\) | 2.32341 | 0.0928621 | ||||||||
\(627\) | −1.71066 | −0.0683173 | ||||||||
\(628\) | 7.54531 | 0.301091 | ||||||||
\(629\) | −1.31386 | −0.0523870 | ||||||||
\(630\) | −0.303838 | −0.0121052 | ||||||||
\(631\) | −33.3707 | −1.32847 | −0.664234 | − | 0.747525i | \(-0.731242\pi\) | ||||
−0.664234 | + | 0.747525i | \(0.731242\pi\) | |||||||
\(632\) | −20.1158 | −0.800165 | ||||||||
\(633\) | 15.1264 | 0.601222 | ||||||||
\(634\) | 9.60400 | 0.381424 | ||||||||
\(635\) | 0.988649 | 0.0392333 | ||||||||
\(636\) | 7.15508 | 0.283717 | ||||||||
\(637\) | −0.289737 | −0.0114798 | ||||||||
\(638\) | −2.69990 | −0.106890 | ||||||||
\(639\) | 13.0932 | 0.517958 | ||||||||
\(640\) | 8.60718 | 0.340229 | ||||||||
\(641\) | 11.9243 | 0.470982 | 0.235491 | − | 0.971877i | \(-0.424330\pi\) | ||||
0.235491 | + | 0.971877i | \(0.424330\pi\) | |||||||
\(642\) | −1.50615 | −0.0594431 | ||||||||
\(643\) | −28.5011 | −1.12397 | −0.561987 | − | 0.827146i | \(-0.689963\pi\) | ||||
−0.561987 | + | 0.827146i | \(0.689963\pi\) | |||||||
\(644\) | 6.35689 | 0.250497 | ||||||||
\(645\) | 8.96096 | 0.352837 | ||||||||
\(646\) | 0.0487817 | 0.00191929 | ||||||||
\(647\) | −13.0053 | −0.511291 | −0.255645 | − | 0.966771i | \(-0.582288\pi\) | ||||
−0.255645 | + | 0.966771i | \(0.582288\pi\) | |||||||
\(648\) | −1.20028 | −0.0471514 | ||||||||
\(649\) | −8.56161 | −0.336072 | ||||||||
\(650\) | 0.358184 | 0.0140491 | ||||||||
\(651\) | 5.73898 | 0.224928 | ||||||||
\(652\) | −43.0045 | −1.68419 | ||||||||
\(653\) | −25.3698 | −0.992797 | −0.496398 | − | 0.868095i | \(-0.665344\pi\) | ||||
−0.496398 | + | 0.868095i | \(0.665344\pi\) | |||||||
\(654\) | −0.793606 | −0.0310325 | ||||||||
\(655\) | 11.8430 | 0.462743 | ||||||||
\(656\) | 13.1484 | 0.513359 | ||||||||
\(657\) | 14.9066 | 0.581562 | ||||||||
\(658\) | 0.414448 | 0.0161569 | ||||||||
\(659\) | 38.0906 | 1.48380 | 0.741899 | − | 0.670511i | \(-0.233925\pi\) | ||||
0.741899 | + | 0.670511i | \(0.233925\pi\) | |||||||
\(660\) | −3.78070 | −0.147164 | ||||||||
\(661\) | 29.6423 | 1.15295 | 0.576477 | − | 0.817114i | \(-0.304427\pi\) | ||||
0.576477 | + | 0.817114i | \(0.304427\pi\) | |||||||
\(662\) | 3.80467 | 0.147873 | ||||||||
\(663\) | 0.0539518 | 0.00209531 | ||||||||
\(664\) | −18.2411 | −0.707893 | ||||||||
\(665\) | −0.842746 | −0.0326803 | ||||||||
\(666\) | −2.16843 | −0.0840250 | ||||||||
\(667\) | 14.6037 | 0.565458 | ||||||||
\(668\) | −29.7695 | −1.15182 | ||||||||
\(669\) | −4.14354 | −0.160198 | ||||||||
\(670\) | 3.29207 | 0.127184 | ||||||||
\(671\) | 6.18928 | 0.238934 | ||||||||
\(672\) | −3.45844 | −0.133412 | ||||||||
\(673\) | 13.5428 | 0.522038 | 0.261019 | − | 0.965334i | \(-0.415941\pi\) | ||||
0.261019 | + | 0.965334i | \(0.415941\pi\) | |||||||
\(674\) | 7.62092 | 0.293547 | ||||||||
\(675\) | 4.02257 | 0.154829 | ||||||||
\(676\) | 24.6122 | 0.946623 | ||||||||
\(677\) | 15.8075 | 0.607533 | 0.303767 | − | 0.952746i | \(-0.401756\pi\) | ||||
0.303767 | + | 0.952746i | \(0.401756\pi\) | |||||||
\(678\) | 0.544791 | 0.0209226 | ||||||||
\(679\) | 6.83150 | 0.262169 | ||||||||
\(680\) | 0.220967 | 0.00847368 | ||||||||
\(681\) | 17.7163 | 0.678889 | ||||||||
\(682\) | −3.53952 | −0.135535 | ||||||||
\(683\) | −3.33700 | −0.127687 | −0.0638433 | − | 0.997960i | \(-0.520336\pi\) | ||||
−0.0638433 | + | 0.997960i | \(0.520336\pi\) | |||||||
\(684\) | −1.62433 | −0.0621079 | ||||||||
\(685\) | 13.3245 | 0.509104 | ||||||||
\(686\) | 0.307326 | 0.0117338 | ||||||||
\(687\) | −27.6285 | −1.05409 | ||||||||
\(688\) | 31.1998 | 1.18948 | ||||||||
\(689\) | −1.08792 | −0.0414465 | ||||||||
\(690\) | −1.01360 | −0.0385870 | ||||||||
\(691\) | 18.9842 | 0.722191 | 0.361096 | − | 0.932529i | \(-0.382403\pi\) | ||||
0.361096 | + | 0.932529i | \(0.382403\pi\) | |||||||
\(692\) | −32.0169 | −1.21710 | ||||||||
\(693\) | 2.00682 | 0.0762330 | ||||||||
\(694\) | −11.1567 | −0.423504 | ||||||||
\(695\) | −6.21781 | −0.235855 | ||||||||
\(696\) | −5.25437 | −0.199166 | ||||||||
\(697\) | 0.711274 | 0.0269414 | ||||||||
\(698\) | 3.41019 | 0.129078 | ||||||||
\(699\) | −21.6658 | −0.819476 | ||||||||
\(700\) | 7.66522 | 0.289718 | ||||||||
\(701\) | 6.87293 | 0.259587 | 0.129793 | − | 0.991541i | \(-0.458569\pi\) | ||||
0.129793 | + | 0.991541i | \(0.458569\pi\) | |||||||
\(702\) | 0.0890436 | 0.00336073 | ||||||||
\(703\) | −6.01452 | −0.226842 | ||||||||
\(704\) | −11.6829 | −0.440316 | ||||||||
\(705\) | 1.33325 | 0.0502133 | ||||||||
\(706\) | 3.30461 | 0.124371 | ||||||||
\(707\) | 13.4337 | 0.505225 | ||||||||
\(708\) | −8.12954 | −0.305527 | ||||||||
\(709\) | 15.3156 | 0.575188 | 0.287594 | − | 0.957752i | \(-0.407145\pi\) | ||||
0.287594 | + | 0.957752i | \(0.407145\pi\) | |||||||
\(710\) | −3.97820 | −0.149299 | ||||||||
\(711\) | 16.7593 | 0.628524 | ||||||||
\(712\) | 0.631584 | 0.0236696 | ||||||||
\(713\) | 19.1452 | 0.716992 | ||||||||
\(714\) | −0.0572272 | −0.00214167 | ||||||||
\(715\) | 0.574851 | 0.0214982 | ||||||||
\(716\) | −35.2691 | −1.31807 | ||||||||
\(717\) | −3.33796 | −0.124658 | ||||||||
\(718\) | −1.52911 | −0.0570657 | ||||||||
\(719\) | 28.3904 | 1.05878 | 0.529391 | − | 0.848378i | \(-0.322421\pi\) | ||||
0.529391 | + | 0.848378i | \(0.322421\pi\) | |||||||
\(720\) | −3.40315 | −0.126828 | ||||||||
\(721\) | −2.29311 | −0.0853998 | ||||||||
\(722\) | −5.61589 | −0.209002 | ||||||||
\(723\) | 13.4703 | 0.500967 | ||||||||
\(724\) | −9.84532 | −0.365898 | ||||||||
\(725\) | 17.6093 | 0.653994 | ||||||||
\(726\) | 2.14288 | 0.0795297 | ||||||||
\(727\) | 3.08701 | 0.114491 | 0.0572454 | − | 0.998360i | \(-0.481768\pi\) | ||||
0.0572454 | + | 0.998360i | \(0.481768\pi\) | |||||||
\(728\) | 0.347764 | 0.0128890 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −4.52919 | −0.167633 | ||||||||
\(731\) | 1.68778 | 0.0624247 | ||||||||
\(732\) | 5.87693 | 0.217218 | ||||||||
\(733\) | −35.7181 | −1.31928 | −0.659638 | − | 0.751583i | \(-0.729291\pi\) | ||||
−0.659638 | + | 0.751583i | \(0.729291\pi\) | |||||||
\(734\) | −6.59983 | −0.243604 | ||||||||
\(735\) | 0.988649 | 0.0364669 | ||||||||
\(736\) | −11.5373 | −0.425271 | ||||||||
\(737\) | −21.7438 | −0.800945 | ||||||||
\(738\) | 1.17391 | 0.0432121 | ||||||||
\(739\) | −19.6678 | −0.723490 | −0.361745 | − | 0.932277i | \(-0.617819\pi\) | ||||
−0.361745 | + | 0.932277i | \(0.617819\pi\) | |||||||
\(740\) | −13.2926 | −0.488644 | ||||||||
\(741\) | 0.246978 | 0.00907296 | ||||||||
\(742\) | 1.15397 | 0.0423634 | ||||||||
\(743\) | 38.7753 | 1.42253 | 0.711264 | − | 0.702925i | \(-0.248123\pi\) | ||||
0.711264 | + | 0.702925i | \(0.248123\pi\) | |||||||
\(744\) | −6.88837 | −0.252540 | ||||||||
\(745\) | −2.19092 | −0.0802691 | ||||||||
\(746\) | 6.06160 | 0.221931 | ||||||||
\(747\) | 15.1974 | 0.556045 | ||||||||
\(748\) | −0.712086 | −0.0260365 | ||||||||
\(749\) | 4.90083 | 0.179072 | ||||||||
\(750\) | −2.74140 | −0.100102 | ||||||||
\(751\) | −14.9648 | −0.546074 | −0.273037 | − | 0.962003i | \(-0.588028\pi\) | ||||
−0.273037 | + | 0.962003i | \(0.588028\pi\) | |||||||
\(752\) | 4.64205 | 0.169278 | ||||||||
\(753\) | −3.19071 | −0.116276 | ||||||||
\(754\) | 0.389800 | 0.0141957 | ||||||||
\(755\) | 11.5816 | 0.421497 | ||||||||
\(756\) | 1.90555 | 0.0693042 | ||||||||
\(757\) | −54.7349 | −1.98937 | −0.994687 | − | 0.102946i | \(-0.967173\pi\) | ||||
−0.994687 | + | 0.102946i | \(0.967173\pi\) | |||||||
\(758\) | −0.160079 | −0.00581432 | ||||||||
\(759\) | 6.69474 | 0.243004 | ||||||||
\(760\) | 1.01153 | 0.0366920 | ||||||||
\(761\) | −16.9679 | −0.615087 | −0.307543 | − | 0.951534i | \(-0.599507\pi\) | ||||
−0.307543 | + | 0.951534i | \(0.599507\pi\) | |||||||
\(762\) | 0.307326 | 0.0111332 | ||||||||
\(763\) | 2.58229 | 0.0934853 | ||||||||
\(764\) | 2.43871 | 0.0882296 | ||||||||
\(765\) | −0.184096 | −0.00665601 | ||||||||
\(766\) | 7.66961 | 0.277114 | ||||||||
\(767\) | 1.23609 | 0.0446325 | ||||||||
\(768\) | −8.96758 | −0.323590 | ||||||||
\(769\) | −12.4821 | −0.450116 | −0.225058 | − | 0.974345i | \(-0.572257\pi\) | ||||
−0.225058 | + | 0.974345i | \(0.572257\pi\) | |||||||
\(770\) | −0.609749 | −0.0219738 | ||||||||
\(771\) | −9.04475 | −0.325739 | ||||||||
\(772\) | −9.58452 | −0.344955 | ||||||||
\(773\) | −7.72207 | −0.277744 | −0.138872 | − | 0.990310i | \(-0.544348\pi\) | ||||
−0.138872 | + | 0.990310i | \(0.544348\pi\) | |||||||
\(774\) | 2.78556 | 0.100125 | ||||||||
\(775\) | 23.0855 | 0.829255 | ||||||||
\(776\) | −8.19970 | −0.294352 | ||||||||
\(777\) | 7.05580 | 0.253125 | ||||||||
\(778\) | 4.48361 | 0.160745 | ||||||||
\(779\) | 3.25603 | 0.116660 | ||||||||
\(780\) | 0.545841 | 0.0195442 | ||||||||
\(781\) | 26.2757 | 0.940218 | ||||||||
\(782\) | −0.190909 | −0.00682689 | ||||||||
\(783\) | 4.37763 | 0.156444 | ||||||||
\(784\) | 3.44222 | 0.122937 | ||||||||
\(785\) | 3.91470 | 0.139722 | ||||||||
\(786\) | 3.68144 | 0.131313 | ||||||||
\(787\) | 4.74326 | 0.169079 | 0.0845396 | − | 0.996420i | \(-0.473058\pi\) | ||||
0.0845396 | + | 0.996420i | \(0.473058\pi\) | |||||||
\(788\) | 10.8482 | 0.386450 | ||||||||
\(789\) | −28.1759 | −1.00309 | ||||||||
\(790\) | −5.09211 | −0.181169 | ||||||||
\(791\) | −1.77268 | −0.0630293 | ||||||||
\(792\) | −2.40875 | −0.0855911 | ||||||||
\(793\) | −0.893580 | −0.0317320 | ||||||||
\(794\) | −1.80401 | −0.0640220 | ||||||||
\(795\) | 3.71224 | 0.131660 | ||||||||
\(796\) | −1.56975 | −0.0556385 | ||||||||
\(797\) | 46.3762 | 1.64273 | 0.821365 | − | 0.570403i | \(-0.193213\pi\) | ||||
0.821365 | + | 0.570403i | \(0.193213\pi\) | |||||||
\(798\) | −0.261972 | −0.00927369 | ||||||||
\(799\) | 0.251116 | 0.00888383 | ||||||||
\(800\) | −13.9118 | −0.491858 | ||||||||
\(801\) | −0.526198 | −0.0185923 | ||||||||
\(802\) | 1.64581 | 0.0581157 | ||||||||
\(803\) | 29.9149 | 1.05568 | ||||||||
\(804\) | −20.6465 | −0.728147 | ||||||||
\(805\) | 3.29812 | 0.116243 | ||||||||
\(806\) | 0.511020 | 0.0179999 | ||||||||
\(807\) | −28.9671 | −1.01969 | ||||||||
\(808\) | −16.1241 | −0.567245 | ||||||||
\(809\) | −38.5949 | −1.35693 | −0.678463 | − | 0.734635i | \(-0.737354\pi\) | ||||
−0.678463 | + | 0.734635i | \(0.737354\pi\) | |||||||
\(810\) | −0.303838 | −0.0106758 | ||||||||
\(811\) | 6.69385 | 0.235053 | 0.117527 | − | 0.993070i | \(-0.462503\pi\) | ||||
0.117527 | + | 0.993070i | \(0.462503\pi\) | |||||||
\(812\) | 8.34179 | 0.292739 | ||||||||
\(813\) | 2.61077 | 0.0915636 | ||||||||
\(814\) | −4.35166 | −0.152526 | ||||||||
\(815\) | −22.3119 | −0.781550 | ||||||||
\(816\) | −0.640976 | −0.0224387 | ||||||||
\(817\) | 7.72622 | 0.270306 | ||||||||
\(818\) | −10.8879 | −0.380686 | ||||||||
\(819\) | −0.289737 | −0.0101242 | ||||||||
\(820\) | 7.19610 | 0.251299 | ||||||||
\(821\) | −27.8784 | −0.972964 | −0.486482 | − | 0.873690i | \(-0.661720\pi\) | ||||
−0.486482 | + | 0.873690i | \(0.661720\pi\) | |||||||
\(822\) | 4.14199 | 0.144469 | ||||||||
\(823\) | −22.7329 | −0.792419 | −0.396209 | − | 0.918160i | \(-0.629675\pi\) | ||||
−0.396209 | + | 0.918160i | \(0.629675\pi\) | |||||||
\(824\) | 2.75237 | 0.0958832 | ||||||||
\(825\) | 8.07260 | 0.281052 | ||||||||
\(826\) | −1.31113 | −0.0456200 | ||||||||
\(827\) | −5.40384 | −0.187910 | −0.0939549 | − | 0.995576i | \(-0.529951\pi\) | ||||
−0.0939549 | + | 0.995576i | \(0.529951\pi\) | |||||||
\(828\) | 6.35689 | 0.220917 | ||||||||
\(829\) | 38.4471 | 1.33532 | 0.667661 | − | 0.744466i | \(-0.267296\pi\) | ||||
0.667661 | + | 0.744466i | \(0.267296\pi\) | |||||||
\(830\) | −4.61755 | −0.160277 | ||||||||
\(831\) | 15.2284 | 0.528269 | ||||||||
\(832\) | 1.68672 | 0.0584767 | ||||||||
\(833\) | 0.186210 | 0.00645179 | ||||||||
\(834\) | −1.93283 | −0.0669286 | ||||||||
\(835\) | −15.4452 | −0.534502 | ||||||||
\(836\) | −3.25975 | −0.112741 | ||||||||
\(837\) | 5.73898 | 0.198368 | ||||||||
\(838\) | 4.79544 | 0.165656 | ||||||||
\(839\) | −22.6601 | −0.782313 | −0.391157 | − | 0.920324i | \(-0.627925\pi\) | ||||
−0.391157 | + | 0.920324i | \(0.627925\pi\) | |||||||
\(840\) | −1.18665 | −0.0409434 | ||||||||
\(841\) | −9.83638 | −0.339186 | ||||||||
\(842\) | 7.83038 | 0.269853 | ||||||||
\(843\) | 16.7836 | 0.578057 | ||||||||
\(844\) | 28.8242 | 0.992170 | ||||||||
\(845\) | 12.7694 | 0.439282 | ||||||||
\(846\) | 0.414448 | 0.0142490 | ||||||||
\(847\) | −6.97265 | −0.239583 | ||||||||
\(848\) | 12.9251 | 0.443849 | ||||||||
\(849\) | 5.84420 | 0.200572 | ||||||||
\(850\) | −0.230200 | −0.00789581 | ||||||||
\(851\) | 23.5380 | 0.806874 | ||||||||
\(852\) | 24.9497 | 0.854762 | ||||||||
\(853\) | 22.6319 | 0.774902 | 0.387451 | − | 0.921890i | \(-0.373356\pi\) | ||||
0.387451 | + | 0.921890i | \(0.373356\pi\) | |||||||
\(854\) | 0.947829 | 0.0324340 | ||||||||
\(855\) | −0.842746 | −0.0288213 | ||||||||
\(856\) | −5.88235 | −0.201055 | ||||||||
\(857\) | −38.6289 | −1.31954 | −0.659770 | − | 0.751468i | \(-0.729346\pi\) | ||||
−0.659770 | + | 0.751468i | \(0.729346\pi\) | |||||||
\(858\) | 0.178695 | 0.00610054 | ||||||||
\(859\) | −2.75056 | −0.0938481 | −0.0469240 | − | 0.998898i | \(-0.514942\pi\) | ||||
−0.0469240 | + | 0.998898i | \(0.514942\pi\) | |||||||
\(860\) | 17.0756 | 0.582272 | ||||||||
\(861\) | −3.81974 | −0.130177 | ||||||||
\(862\) | 0.771579 | 0.0262801 | ||||||||
\(863\) | −18.8268 | −0.640871 | −0.320435 | − | 0.947270i | \(-0.603829\pi\) | ||||
−0.320435 | + | 0.947270i | \(0.603829\pi\) | |||||||
\(864\) | −3.45844 | −0.117659 | ||||||||
\(865\) | −16.6112 | −0.564798 | ||||||||
\(866\) | −8.16261 | −0.277377 | ||||||||
\(867\) | 16.9653 | 0.576173 | ||||||||
\(868\) | 10.9359 | 0.371189 | ||||||||
\(869\) | 33.6330 | 1.14092 | ||||||||
\(870\) | −1.33009 | −0.0450942 | ||||||||
\(871\) | 3.13928 | 0.106370 | ||||||||
\(872\) | −3.09947 | −0.104961 | ||||||||
\(873\) | 6.83150 | 0.231211 | ||||||||
\(874\) | −0.873933 | −0.0295612 | ||||||||
\(875\) | 8.92016 | 0.301556 | ||||||||
\(876\) | 28.4053 | 0.959726 | ||||||||
\(877\) | 5.91209 | 0.199637 | 0.0998186 | − | 0.995006i | \(-0.468174\pi\) | ||||
0.0998186 | + | 0.995006i | \(0.468174\pi\) | |||||||
\(878\) | 0.797262 | 0.0269063 | ||||||||
\(879\) | −2.88058 | −0.0971596 | ||||||||
\(880\) | −6.82953 | −0.230223 | ||||||||
\(881\) | 23.3170 | 0.785569 | 0.392785 | − | 0.919630i | \(-0.371512\pi\) | ||||
0.392785 | + | 0.919630i | \(0.371512\pi\) | |||||||
\(882\) | 0.307326 | 0.0103482 | ||||||||
\(883\) | −20.2527 | −0.681558 | −0.340779 | − | 0.940143i | \(-0.610691\pi\) | ||||
−0.340779 | + | 0.940143i | \(0.610691\pi\) | |||||||
\(884\) | 0.102808 | 0.00345780 | ||||||||
\(885\) | −4.21782 | −0.141780 | ||||||||
\(886\) | 7.40515 | 0.248781 | ||||||||
\(887\) | −59.2402 | −1.98909 | −0.994545 | − | 0.104309i | \(-0.966737\pi\) | ||||
−0.994545 | + | 0.104309i | \(0.966737\pi\) | |||||||
\(888\) | −8.46892 | −0.284198 | ||||||||
\(889\) | −1.00000 | −0.0335389 | ||||||||
\(890\) | 0.159879 | 0.00535915 | ||||||||
\(891\) | 2.00682 | 0.0672312 | ||||||||
\(892\) | −7.89572 | −0.264368 | ||||||||
\(893\) | 1.14954 | 0.0384680 | ||||||||
\(894\) | −0.681058 | −0.0227780 | ||||||||
\(895\) | −18.2985 | −0.611652 | ||||||||
\(896\) | −8.70601 | −0.290847 | ||||||||
\(897\) | −0.966557 | −0.0322724 | ||||||||
\(898\) | −3.40268 | −0.113549 | ||||||||
\(899\) | 25.1231 | 0.837903 | ||||||||
\(900\) | 7.66522 | 0.255507 | ||||||||
\(901\) | 0.699192 | 0.0232935 | ||||||||
\(902\) | 2.35583 | 0.0784404 | ||||||||
\(903\) | −9.06384 | −0.301626 | ||||||||
\(904\) | 2.12771 | 0.0707666 | ||||||||
\(905\) | −5.10801 | −0.169796 | ||||||||
\(906\) | 3.60018 | 0.119608 | ||||||||
\(907\) | 3.28126 | 0.108953 | 0.0544763 | − | 0.998515i | \(-0.482651\pi\) | ||||
0.0544763 | + | 0.998515i | \(0.482651\pi\) | |||||||
\(908\) | 33.7592 | 1.12034 | ||||||||
\(909\) | 13.4337 | 0.445567 | ||||||||
\(910\) | 0.0880329 | 0.00291826 | ||||||||
\(911\) | −53.0856 | −1.75880 | −0.879402 | − | 0.476080i | \(-0.842057\pi\) | ||||
−0.879402 | + | 0.476080i | \(0.842057\pi\) | |||||||
\(912\) | −2.93423 | −0.0971620 | ||||||||
\(913\) | 30.4986 | 1.00936 | ||||||||
\(914\) | 2.18545 | 0.0722883 | ||||||||
\(915\) | 3.04911 | 0.100800 | ||||||||
\(916\) | −52.6475 | −1.73952 | ||||||||
\(917\) | −11.9789 | −0.395580 | ||||||||
\(918\) | −0.0572272 | −0.00188878 | ||||||||
\(919\) | −10.1491 | −0.334787 | −0.167394 | − | 0.985890i | \(-0.553535\pi\) | ||||
−0.167394 | + | 0.985890i | \(0.553535\pi\) | |||||||
\(920\) | −3.95866 | −0.130513 | ||||||||
\(921\) | −2.95818 | −0.0974753 | ||||||||
\(922\) | 7.39386 | 0.243504 | ||||||||
\(923\) | −3.79357 | −0.124867 | ||||||||
\(924\) | 3.82411 | 0.125804 | ||||||||
\(925\) | 28.3825 | 0.933210 | ||||||||
\(926\) | −5.83151 | −0.191635 | ||||||||
\(927\) | −2.29311 | −0.0753156 | ||||||||
\(928\) | −15.1398 | −0.496987 | ||||||||
\(929\) | −26.8433 | −0.880699 | −0.440350 | − | 0.897826i | \(-0.645145\pi\) | ||||
−0.440350 | + | 0.897826i | \(0.645145\pi\) | |||||||
\(930\) | −1.74372 | −0.0571788 | ||||||||
\(931\) | 0.852422 | 0.0279370 | ||||||||
\(932\) | −41.2853 | −1.35235 | ||||||||
\(933\) | 7.79466 | 0.255186 | ||||||||
\(934\) | 2.27621 | 0.0744798 | ||||||||
\(935\) | −0.369449 | −0.0120823 | ||||||||
\(936\) | 0.347764 | 0.0113670 | ||||||||
\(937\) | 43.6904 | 1.42730 | 0.713651 | − | 0.700501i | \(-0.247040\pi\) | ||||
0.713651 | + | 0.700501i | \(0.247040\pi\) | |||||||
\(938\) | −3.32986 | −0.108724 | ||||||||
\(939\) | −7.56008 | −0.246714 | ||||||||
\(940\) | 2.54058 | 0.0828647 | ||||||||
\(941\) | −9.59031 | −0.312635 | −0.156318 | − | 0.987707i | \(-0.549962\pi\) | ||||
−0.156318 | + | 0.987707i | \(0.549962\pi\) | |||||||
\(942\) | 1.21690 | 0.0396489 | ||||||||
\(943\) | −12.7426 | −0.414957 | ||||||||
\(944\) | −14.6854 | −0.477968 | ||||||||
\(945\) | 0.988649 | 0.0321608 | ||||||||
\(946\) | 5.59012 | 0.181751 | ||||||||
\(947\) | 3.89541 | 0.126584 | 0.0632918 | − | 0.997995i | \(-0.479840\pi\) | ||||
0.0632918 | + | 0.997995i | \(0.479840\pi\) | |||||||
\(948\) | 31.9357 | 1.03722 | ||||||||
\(949\) | −4.31899 | −0.140200 | ||||||||
\(950\) | −1.05380 | −0.0341898 | ||||||||
\(951\) | −31.2502 | −1.01336 | ||||||||
\(952\) | −0.223504 | −0.00724379 | ||||||||
\(953\) | −0.685511 | −0.0222059 | −0.0111029 | − | 0.999938i | \(-0.503534\pi\) | ||||
−0.0111029 | + | 0.999938i | \(0.503534\pi\) | |||||||
\(954\) | 1.15397 | 0.0373610 | ||||||||
\(955\) | 1.26527 | 0.0409431 | ||||||||
\(956\) | −6.36065 | −0.205718 | ||||||||
\(957\) | 8.78513 | 0.283983 | ||||||||
\(958\) | −1.51312 | −0.0488868 | ||||||||
\(959\) | −13.4775 | −0.435212 | ||||||||
\(960\) | −5.75550 | −0.185758 | ||||||||
\(961\) | 1.93592 | 0.0624489 | ||||||||
\(962\) | 0.628274 | 0.0202564 | ||||||||
\(963\) | 4.90083 | 0.157927 | ||||||||
\(964\) | 25.6684 | 0.826724 | ||||||||
\(965\) | −4.97270 | −0.160077 | ||||||||
\(966\) | 1.02524 | 0.0329864 | ||||||||
\(967\) | −38.2729 | −1.23077 | −0.615386 | − | 0.788226i | \(-0.711000\pi\) | ||||
−0.615386 | + | 0.788226i | \(0.711000\pi\) | |||||||
\(968\) | 8.36912 | 0.268994 | ||||||||
\(969\) | −0.158729 | −0.00509912 | ||||||||
\(970\) | −2.07567 | −0.0666457 | ||||||||
\(971\) | 2.76859 | 0.0888482 | 0.0444241 | − | 0.999013i | \(-0.485855\pi\) | ||||
0.0444241 | + | 0.999013i | \(0.485855\pi\) | |||||||
\(972\) | 1.90555 | 0.0611206 | ||||||||
\(973\) | 6.28920 | 0.201622 | ||||||||
\(974\) | 3.02741 | 0.0970046 | ||||||||
\(975\) | −1.16549 | −0.0373254 | ||||||||
\(976\) | 10.6162 | 0.339817 | ||||||||
\(977\) | 25.2322 | 0.807249 | 0.403625 | − | 0.914925i | \(-0.367750\pi\) | ||||
0.403625 | + | 0.914925i | \(0.367750\pi\) | |||||||
\(978\) | −6.93574 | −0.221781 | ||||||||
\(979\) | −1.05599 | −0.0337495 | ||||||||
\(980\) | 1.88392 | 0.0601796 | ||||||||
\(981\) | 2.58229 | 0.0824463 | ||||||||
\(982\) | −9.66671 | −0.308477 | ||||||||
\(983\) | 27.4799 | 0.876472 | 0.438236 | − | 0.898860i | \(-0.355603\pi\) | ||||
0.438236 | + | 0.898860i | \(0.355603\pi\) | |||||||
\(984\) | 4.58475 | 0.146157 | ||||||||
\(985\) | 5.62831 | 0.179333 | ||||||||
\(986\) | −0.250519 | −0.00797816 | ||||||||
\(987\) | −1.34856 | −0.0429252 | ||||||||
\(988\) | 0.470629 | 0.0149727 | ||||||||
\(989\) | −30.2369 | −0.961476 | ||||||||
\(990\) | −0.609749 | −0.0193791 | ||||||||
\(991\) | −26.6965 | −0.848043 | −0.424021 | − | 0.905652i | \(-0.639382\pi\) | ||||
−0.424021 | + | 0.905652i | \(0.639382\pi\) | |||||||
\(992\) | −19.8479 | −0.630172 | ||||||||
\(993\) | −12.3799 | −0.392864 | ||||||||
\(994\) | 4.02387 | 0.127629 | ||||||||
\(995\) | −0.814429 | −0.0258191 | ||||||||
\(996\) | 28.9595 | 0.917615 | ||||||||
\(997\) | −4.92865 | −0.156092 | −0.0780459 | − | 0.996950i | \(-0.524868\pi\) | ||||
−0.0780459 | + | 0.996950i | \(0.524868\pi\) | |||||||
\(998\) | −4.74931 | −0.150337 | ||||||||
\(999\) | 7.05580 | 0.223236 |
(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 | 2667.2.a.l.1.7 | ✓ | 13 | |
3.2 | odd | 2 | 8001.2.a.o.1.7 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.l.1.7 | ✓ | 13 | 1.1 | even | 1 | trivial | |
8001.2.a.o.1.7 | 13 | 3.2 | odd | 2 |