Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4003,2,Mod(1,4003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4003, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4003.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: | \(31.9641159291\) |
Analytic rank: | \(0\) |
Dimension: | \(179\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 4003.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.45370 | −1.73503 | −0.867515 | − | 0.497410i | \(-0.834284\pi\) | ||||
−0.867515 | + | 0.497410i | \(0.834284\pi\) | |||||||
\(3\) | −0.415301 | −0.239774 | −0.119887 | − | 0.992788i | \(-0.538253\pi\) | ||||
−0.119887 | + | 0.992788i | \(0.538253\pi\) | |||||||
\(4\) | 4.02066 | 2.01033 | ||||||||
\(5\) | −3.18084 | −1.42252 | −0.711258 | − | 0.702931i | \(-0.751874\pi\) | ||||
−0.711258 | + | 0.702931i | \(0.751874\pi\) | |||||||
\(6\) | 1.01903 | 0.416016 | ||||||||
\(7\) | −2.85630 | −1.07958 | −0.539790 | − | 0.841800i | \(-0.681496\pi\) | ||||
−0.539790 | + | 0.841800i | \(0.681496\pi\) | |||||||
\(8\) | −4.95811 | −1.75296 | ||||||||
\(9\) | −2.82752 | −0.942508 | ||||||||
\(10\) | 7.80484 | 2.46811 | ||||||||
\(11\) | 1.47266 | 0.444024 | 0.222012 | − | 0.975044i | \(-0.428738\pi\) | ||||
0.222012 | + | 0.975044i | \(0.428738\pi\) | |||||||
\(12\) | −1.66979 | −0.482026 | ||||||||
\(13\) | 3.83328 | 1.06316 | 0.531581 | − | 0.847008i | \(-0.321598\pi\) | ||||
0.531581 | + | 0.847008i | \(0.321598\pi\) | |||||||
\(14\) | 7.00851 | 1.87310 | ||||||||
\(15\) | 1.32101 | 0.341083 | ||||||||
\(16\) | 4.12441 | 1.03110 | ||||||||
\(17\) | 3.98568 | 0.966669 | 0.483335 | − | 0.875436i | \(-0.339425\pi\) | ||||
0.483335 | + | 0.875436i | \(0.339425\pi\) | |||||||
\(18\) | 6.93791 | 1.63528 | ||||||||
\(19\) | −4.57320 | −1.04917 | −0.524583 | − | 0.851360i | \(-0.675779\pi\) | ||||
−0.524583 | + | 0.851360i | \(0.675779\pi\) | |||||||
\(20\) | −12.7891 | −2.85973 | ||||||||
\(21\) | 1.18622 | 0.258855 | ||||||||
\(22\) | −3.61347 | −0.770395 | ||||||||
\(23\) | 0.0487036 | 0.0101554 | 0.00507770 | − | 0.999987i | \(-0.498384\pi\) | ||||
0.00507770 | + | 0.999987i | \(0.498384\pi\) | |||||||
\(24\) | 2.05911 | 0.420314 | ||||||||
\(25\) | 5.11776 | 1.02355 | ||||||||
\(26\) | −9.40574 | −1.84462 | ||||||||
\(27\) | 2.42018 | 0.465763 | ||||||||
\(28\) | −11.4842 | −2.17031 | ||||||||
\(29\) | 7.06083 | 1.31116 | 0.655582 | − | 0.755124i | \(-0.272423\pi\) | ||||
0.655582 | + | 0.755124i | \(0.272423\pi\) | |||||||
\(30\) | −3.24136 | −0.591789 | ||||||||
\(31\) | −1.88706 | −0.338925 | −0.169463 | − | 0.985537i | \(-0.554203\pi\) | ||||
−0.169463 | + | 0.985537i | \(0.554203\pi\) | |||||||
\(32\) | −0.203855 | −0.0360368 | ||||||||
\(33\) | −0.611598 | −0.106465 | ||||||||
\(34\) | −9.77968 | −1.67720 | ||||||||
\(35\) | 9.08543 | 1.53572 | ||||||||
\(36\) | −11.3685 | −1.89475 | ||||||||
\(37\) | −3.06475 | −0.503841 | −0.251921 | − | 0.967748i | \(-0.581062\pi\) | ||||
−0.251921 | + | 0.967748i | \(0.581062\pi\) | |||||||
\(38\) | 11.2213 | 1.82033 | ||||||||
\(39\) | −1.59197 | −0.254919 | ||||||||
\(40\) | 15.7710 | 2.49361 | ||||||||
\(41\) | 1.59606 | 0.249263 | 0.124631 | − | 0.992203i | \(-0.460225\pi\) | ||||
0.124631 | + | 0.992203i | \(0.460225\pi\) | |||||||
\(42\) | −2.91064 | −0.449122 | ||||||||
\(43\) | −9.79157 | −1.49320 | −0.746601 | − | 0.665273i | \(-0.768315\pi\) | ||||
−0.746601 | + | 0.665273i | \(0.768315\pi\) | |||||||
\(44\) | 5.92107 | 0.892635 | ||||||||
\(45\) | 8.99391 | 1.34073 | ||||||||
\(46\) | −0.119504 | −0.0176199 | ||||||||
\(47\) | −12.2176 | −1.78212 | −0.891059 | − | 0.453887i | \(-0.850037\pi\) | ||||
−0.891059 | + | 0.453887i | \(0.850037\pi\) | |||||||
\(48\) | −1.71287 | −0.247232 | ||||||||
\(49\) | 1.15844 | 0.165491 | ||||||||
\(50\) | −12.5575 | −1.77589 | ||||||||
\(51\) | −1.65526 | −0.231782 | ||||||||
\(52\) | 15.4123 | 2.13731 | ||||||||
\(53\) | 1.66410 | 0.228581 | 0.114291 | − | 0.993447i | \(-0.463541\pi\) | ||||
0.114291 | + | 0.993447i | \(0.463541\pi\) | |||||||
\(54\) | −5.93840 | −0.808114 | ||||||||
\(55\) | −4.68430 | −0.631631 | ||||||||
\(56\) | 14.1618 | 1.89246 | ||||||||
\(57\) | 1.89926 | 0.251563 | ||||||||
\(58\) | −17.3252 | −2.27491 | ||||||||
\(59\) | −9.23933 | −1.20286 | −0.601429 | − | 0.798926i | \(-0.705402\pi\) | ||||
−0.601429 | + | 0.798926i | \(0.705402\pi\) | |||||||
\(60\) | 5.31133 | 0.685689 | ||||||||
\(61\) | −1.01299 | −0.129701 | −0.0648503 | − | 0.997895i | \(-0.520657\pi\) | ||||
−0.0648503 | + | 0.997895i | \(0.520657\pi\) | |||||||
\(62\) | 4.63028 | 0.588046 | ||||||||
\(63\) | 8.07625 | 1.01751 | ||||||||
\(64\) | −7.74862 | −0.968577 | ||||||||
\(65\) | −12.1931 | −1.51236 | ||||||||
\(66\) | 1.50068 | 0.184721 | ||||||||
\(67\) | −10.5900 | −1.29377 | −0.646887 | − | 0.762586i | \(-0.723929\pi\) | ||||
−0.646887 | + | 0.762586i | \(0.723929\pi\) | |||||||
\(68\) | 16.0251 | 1.94333 | ||||||||
\(69\) | −0.0202267 | −0.00243500 | ||||||||
\(70\) | −22.2930 | −2.66452 | ||||||||
\(71\) | −11.1767 | −1.32644 | −0.663218 | − | 0.748427i | \(-0.730810\pi\) | ||||
−0.663218 | + | 0.748427i | \(0.730810\pi\) | |||||||
\(72\) | 14.0192 | 1.65218 | ||||||||
\(73\) | 3.38359 | 0.396020 | 0.198010 | − | 0.980200i | \(-0.436552\pi\) | ||||
0.198010 | + | 0.980200i | \(0.436552\pi\) | |||||||
\(74\) | 7.51998 | 0.874180 | ||||||||
\(75\) | −2.12541 | −0.245421 | ||||||||
\(76\) | −18.3873 | −2.10917 | ||||||||
\(77\) | −4.20636 | −0.479359 | ||||||||
\(78\) | 3.90621 | 0.442292 | ||||||||
\(79\) | −5.99683 | −0.674696 | −0.337348 | − | 0.941380i | \(-0.609530\pi\) | ||||
−0.337348 | + | 0.941380i | \(0.609530\pi\) | |||||||
\(80\) | −13.1191 | −1.46676 | ||||||||
\(81\) | 7.47747 | 0.830830 | ||||||||
\(82\) | −3.91626 | −0.432478 | ||||||||
\(83\) | −17.3073 | −1.89972 | −0.949862 | − | 0.312669i | \(-0.898777\pi\) | ||||
−0.949862 | + | 0.312669i | \(0.898777\pi\) | |||||||
\(84\) | 4.76941 | 0.520385 | ||||||||
\(85\) | −12.6778 | −1.37510 | ||||||||
\(86\) | 24.0256 | 2.59075 | ||||||||
\(87\) | −2.93237 | −0.314383 | ||||||||
\(88\) | −7.30161 | −0.778355 | ||||||||
\(89\) | −6.21452 | −0.658737 | −0.329369 | − | 0.944201i | \(-0.606836\pi\) | ||||
−0.329369 | + | 0.944201i | \(0.606836\pi\) | |||||||
\(90\) | −22.0684 | −2.32621 | ||||||||
\(91\) | −10.9490 | −1.14777 | ||||||||
\(92\) | 0.195821 | 0.0204157 | ||||||||
\(93\) | 0.783696 | 0.0812655 | ||||||||
\(94\) | 29.9783 | 3.09203 | ||||||||
\(95\) | 14.5466 | 1.49245 | ||||||||
\(96\) | 0.0846611 | 0.00864069 | ||||||||
\(97\) | −3.11759 | −0.316543 | −0.158271 | − | 0.987396i | \(-0.550592\pi\) | ||||
−0.158271 | + | 0.987396i | \(0.550592\pi\) | |||||||
\(98\) | −2.84247 | −0.287133 | ||||||||
\(99\) | −4.16398 | −0.418496 | ||||||||
\(100\) | 20.5768 | 2.05768 | ||||||||
\(101\) | 11.4905 | 1.14334 | 0.571672 | − | 0.820482i | \(-0.306295\pi\) | ||||
0.571672 | + | 0.820482i | \(0.306295\pi\) | |||||||
\(102\) | 4.06151 | 0.402149 | ||||||||
\(103\) | 1.42647 | 0.140554 | 0.0702772 | − | 0.997528i | \(-0.477612\pi\) | ||||
0.0702772 | + | 0.997528i | \(0.477612\pi\) | |||||||
\(104\) | −19.0058 | −1.86368 | ||||||||
\(105\) | −3.77319 | −0.368226 | ||||||||
\(106\) | −4.08320 | −0.396595 | ||||||||
\(107\) | 9.89389 | 0.956479 | 0.478239 | − | 0.878230i | \(-0.341275\pi\) | ||||
0.478239 | + | 0.878230i | \(0.341275\pi\) | |||||||
\(108\) | 9.73072 | 0.936339 | ||||||||
\(109\) | 15.9376 | 1.52655 | 0.763273 | − | 0.646076i | \(-0.223591\pi\) | ||||
0.763273 | + | 0.646076i | \(0.223591\pi\) | |||||||
\(110\) | 11.4939 | 1.09590 | ||||||||
\(111\) | 1.27279 | 0.120808 | ||||||||
\(112\) | −11.7805 | −1.11316 | ||||||||
\(113\) | 12.7238 | 1.19695 | 0.598477 | − | 0.801140i | \(-0.295773\pi\) | ||||
0.598477 | + | 0.801140i | \(0.295773\pi\) | |||||||
\(114\) | −4.66021 | −0.436469 | ||||||||
\(115\) | −0.154918 | −0.0144462 | ||||||||
\(116\) | 28.3892 | 2.63587 | ||||||||
\(117\) | −10.8387 | −1.00204 | ||||||||
\(118\) | 22.6706 | 2.08700 | ||||||||
\(119\) | −11.3843 | −1.04360 | ||||||||
\(120\) | −6.54970 | −0.597903 | ||||||||
\(121\) | −8.83127 | −0.802843 | ||||||||
\(122\) | 2.48559 | 0.225034 | ||||||||
\(123\) | −0.662846 | −0.0597668 | ||||||||
\(124\) | −7.58722 | −0.681352 | ||||||||
\(125\) | −0.374563 | −0.0335019 | ||||||||
\(126\) | −19.8167 | −1.76542 | ||||||||
\(127\) | 8.13664 | 0.722010 | 0.361005 | − | 0.932564i | \(-0.382434\pi\) | ||||
0.361005 | + | 0.932564i | \(0.382434\pi\) | |||||||
\(128\) | 19.4205 | 1.71655 | ||||||||
\(129\) | 4.06645 | 0.358031 | ||||||||
\(130\) | 29.9182 | 2.62400 | ||||||||
\(131\) | 9.25580 | 0.808683 | 0.404342 | − | 0.914608i | \(-0.367501\pi\) | ||||
0.404342 | + | 0.914608i | \(0.367501\pi\) | |||||||
\(132\) | −2.45903 | −0.214031 | ||||||||
\(133\) | 13.0624 | 1.13266 | ||||||||
\(134\) | 25.9847 | 2.24474 | ||||||||
\(135\) | −7.69820 | −0.662556 | ||||||||
\(136\) | −19.7614 | −1.69453 | ||||||||
\(137\) | 12.3617 | 1.05613 | 0.528065 | − | 0.849204i | \(-0.322918\pi\) | ||||
0.528065 | + | 0.849204i | \(0.322918\pi\) | |||||||
\(138\) | 0.0496302 | 0.00422480 | ||||||||
\(139\) | −16.8653 | −1.43050 | −0.715250 | − | 0.698869i | \(-0.753687\pi\) | ||||
−0.715250 | + | 0.698869i | \(0.753687\pi\) | |||||||
\(140\) | 36.5295 | 3.08730 | ||||||||
\(141\) | 5.07398 | 0.427306 | ||||||||
\(142\) | 27.4244 | 2.30141 | ||||||||
\(143\) | 5.64512 | 0.472069 | ||||||||
\(144\) | −11.6619 | −0.971822 | ||||||||
\(145\) | −22.4594 | −1.86515 | ||||||||
\(146\) | −8.30234 | −0.687106 | ||||||||
\(147\) | −0.481101 | −0.0396806 | ||||||||
\(148\) | −12.3223 | −1.01289 | ||||||||
\(149\) | −16.4659 | −1.34894 | −0.674469 | − | 0.738303i | \(-0.735627\pi\) | ||||
−0.674469 | + | 0.738303i | \(0.735627\pi\) | |||||||
\(150\) | 5.21513 | 0.425813 | ||||||||
\(151\) | −14.5433 | −1.18352 | −0.591758 | − | 0.806116i | \(-0.701566\pi\) | ||||
−0.591758 | + | 0.806116i | \(0.701566\pi\) | |||||||
\(152\) | 22.6745 | 1.83914 | ||||||||
\(153\) | −11.2696 | −0.911094 | ||||||||
\(154\) | 10.3212 | 0.831703 | ||||||||
\(155\) | 6.00243 | 0.482126 | ||||||||
\(156\) | −6.40076 | −0.512471 | ||||||||
\(157\) | −16.4117 | −1.30980 | −0.654900 | − | 0.755716i | \(-0.727289\pi\) | ||||
−0.654900 | + | 0.755716i | \(0.727289\pi\) | |||||||
\(158\) | 14.7144 | 1.17062 | ||||||||
\(159\) | −0.691101 | −0.0548078 | ||||||||
\(160\) | 0.648430 | 0.0512629 | ||||||||
\(161\) | −0.139112 | −0.0109636 | ||||||||
\(162\) | −18.3475 | −1.44152 | ||||||||
\(163\) | 22.9306 | 1.79606 | 0.898032 | − | 0.439931i | \(-0.144997\pi\) | ||||
0.898032 | + | 0.439931i | \(0.144997\pi\) | |||||||
\(164\) | 6.41722 | 0.501101 | ||||||||
\(165\) | 1.94540 | 0.151449 | ||||||||
\(166\) | 42.4670 | 3.29608 | ||||||||
\(167\) | 9.95056 | 0.769997 | 0.384999 | − | 0.922917i | \(-0.374202\pi\) | ||||
0.384999 | + | 0.922917i | \(0.374202\pi\) | |||||||
\(168\) | −5.88143 | −0.453762 | ||||||||
\(169\) | 1.69405 | 0.130312 | ||||||||
\(170\) | 31.1076 | 2.38584 | ||||||||
\(171\) | 12.9309 | 0.988847 | ||||||||
\(172\) | −39.3686 | −3.00183 | ||||||||
\(173\) | −1.17203 | −0.0891079 | −0.0445540 | − | 0.999007i | \(-0.514187\pi\) | ||||
−0.0445540 | + | 0.999007i | \(0.514187\pi\) | |||||||
\(174\) | 7.19517 | 0.545464 | ||||||||
\(175\) | −14.6178 | −1.10500 | ||||||||
\(176\) | 6.07385 | 0.457834 | ||||||||
\(177\) | 3.83710 | 0.288414 | ||||||||
\(178\) | 15.2486 | 1.14293 | ||||||||
\(179\) | −11.0931 | −0.829137 | −0.414569 | − | 0.910018i | \(-0.636068\pi\) | ||||
−0.414569 | + | 0.910018i | \(0.636068\pi\) | |||||||
\(180\) | 36.1615 | 2.69532 | ||||||||
\(181\) | −14.6027 | −1.08541 | −0.542706 | − | 0.839922i | \(-0.682600\pi\) | ||||
−0.542706 | + | 0.839922i | \(0.682600\pi\) | |||||||
\(182\) | 26.8656 | 1.99141 | ||||||||
\(183\) | 0.420697 | 0.0310989 | ||||||||
\(184\) | −0.241478 | −0.0178020 | ||||||||
\(185\) | 9.74848 | 0.716722 | ||||||||
\(186\) | −1.92296 | −0.140998 | ||||||||
\(187\) | 5.86955 | 0.429224 | ||||||||
\(188\) | −49.1228 | −3.58265 | ||||||||
\(189\) | −6.91275 | −0.502829 | ||||||||
\(190\) | −35.6932 | −2.58945 | ||||||||
\(191\) | 26.1706 | 1.89364 | 0.946818 | − | 0.321769i | \(-0.104277\pi\) | ||||
0.946818 | + | 0.321769i | \(0.104277\pi\) | |||||||
\(192\) | 3.21801 | 0.232240 | ||||||||
\(193\) | 12.7562 | 0.918210 | 0.459105 | − | 0.888382i | \(-0.348170\pi\) | ||||
0.459105 | + | 0.888382i | \(0.348170\pi\) | |||||||
\(194\) | 7.64963 | 0.549212 | ||||||||
\(195\) | 5.06379 | 0.362626 | ||||||||
\(196\) | 4.65770 | 0.332693 | ||||||||
\(197\) | 7.48480 | 0.533270 | 0.266635 | − | 0.963798i | \(-0.414088\pi\) | ||||
0.266635 | + | 0.963798i | \(0.414088\pi\) | |||||||
\(198\) | 10.2172 | 0.726104 | ||||||||
\(199\) | −12.7764 | −0.905692 | −0.452846 | − | 0.891589i | \(-0.649591\pi\) | ||||
−0.452846 | + | 0.891589i | \(0.649591\pi\) | |||||||
\(200\) | −25.3744 | −1.79424 | ||||||||
\(201\) | 4.39804 | 0.310214 | ||||||||
\(202\) | −28.1942 | −1.98374 | ||||||||
\(203\) | −20.1678 | −1.41550 | ||||||||
\(204\) | −6.65523 | −0.465959 | ||||||||
\(205\) | −5.07682 | −0.354580 | ||||||||
\(206\) | −3.50014 | −0.243866 | ||||||||
\(207\) | −0.137711 | −0.00957155 | ||||||||
\(208\) | 15.8100 | 1.09623 | ||||||||
\(209\) | −6.73478 | −0.465854 | ||||||||
\(210\) | 9.25829 | 0.638883 | ||||||||
\(211\) | 8.56374 | 0.589552 | 0.294776 | − | 0.955566i | \(-0.404755\pi\) | ||||
0.294776 | + | 0.955566i | \(0.404755\pi\) | |||||||
\(212\) | 6.69077 | 0.459524 | ||||||||
\(213\) | 4.64171 | 0.318045 | ||||||||
\(214\) | −24.2767 | −1.65952 | ||||||||
\(215\) | 31.1455 | 2.12410 | ||||||||
\(216\) | −11.9995 | −0.816463 | ||||||||
\(217\) | 5.38999 | 0.365897 | ||||||||
\(218\) | −39.1062 | −2.64861 | ||||||||
\(219\) | −1.40521 | −0.0949553 | ||||||||
\(220\) | −18.8340 | −1.26979 | ||||||||
\(221\) | 15.2782 | 1.02773 | ||||||||
\(222\) | −3.12306 | −0.209606 | ||||||||
\(223\) | −17.4201 | −1.16654 | −0.583268 | − | 0.812279i | \(-0.698226\pi\) | ||||
−0.583268 | + | 0.812279i | \(0.698226\pi\) | |||||||
\(224\) | 0.582270 | 0.0389045 | ||||||||
\(225\) | −14.4706 | −0.964706 | ||||||||
\(226\) | −31.2204 | −2.07675 | ||||||||
\(227\) | 9.44268 | 0.626732 | 0.313366 | − | 0.949632i | \(-0.398543\pi\) | ||||
0.313366 | + | 0.949632i | \(0.398543\pi\) | |||||||
\(228\) | 7.63627 | 0.505725 | ||||||||
\(229\) | −26.6402 | −1.76043 | −0.880215 | − | 0.474574i | \(-0.842602\pi\) | ||||
−0.880215 | + | 0.474574i | \(0.842602\pi\) | |||||||
\(230\) | 0.380124 | 0.0250646 | ||||||||
\(231\) | 1.74691 | 0.114938 | ||||||||
\(232\) | −35.0084 | −2.29841 | ||||||||
\(233\) | 20.0451 | 1.31320 | 0.656600 | − | 0.754239i | \(-0.271994\pi\) | ||||
0.656600 | + | 0.754239i | \(0.271994\pi\) | |||||||
\(234\) | 26.5950 | 1.73857 | ||||||||
\(235\) | 38.8622 | 2.53509 | ||||||||
\(236\) | −37.1482 | −2.41814 | ||||||||
\(237\) | 2.49049 | 0.161775 | ||||||||
\(238\) | 27.9337 | 1.81067 | ||||||||
\(239\) | 5.83490 | 0.377429 | 0.188714 | − | 0.982032i | \(-0.439568\pi\) | ||||
0.188714 | + | 0.982032i | \(0.439568\pi\) | |||||||
\(240\) | 5.44837 | 0.351691 | ||||||||
\(241\) | −1.21367 | −0.0781797 | −0.0390898 | − | 0.999236i | \(-0.512446\pi\) | ||||
−0.0390898 | + | 0.999236i | \(0.512446\pi\) | |||||||
\(242\) | 21.6693 | 1.39296 | ||||||||
\(243\) | −10.3659 | −0.664975 | ||||||||
\(244\) | −4.07291 | −0.260741 | ||||||||
\(245\) | −3.68481 | −0.235414 | ||||||||
\(246\) | 1.62643 | 0.103697 | ||||||||
\(247\) | −17.5304 | −1.11543 | ||||||||
\(248\) | 9.35623 | 0.594121 | ||||||||
\(249\) | 7.18775 | 0.455505 | ||||||||
\(250\) | 0.919067 | 0.0581269 | ||||||||
\(251\) | 14.5934 | 0.921128 | 0.460564 | − | 0.887626i | \(-0.347647\pi\) | ||||
0.460564 | + | 0.887626i | \(0.347647\pi\) | |||||||
\(252\) | 32.4719 | 2.04554 | ||||||||
\(253\) | 0.0717238 | 0.00450924 | ||||||||
\(254\) | −19.9649 | −1.25271 | ||||||||
\(255\) | 5.26511 | 0.329714 | ||||||||
\(256\) | −32.1550 | −2.00969 | ||||||||
\(257\) | −3.11554 | −0.194342 | −0.0971709 | − | 0.995268i | \(-0.530979\pi\) | ||||
−0.0971709 | + | 0.995268i | \(0.530979\pi\) | |||||||
\(258\) | −9.97787 | −0.621195 | ||||||||
\(259\) | 8.75383 | 0.543937 | ||||||||
\(260\) | −49.0242 | −3.04035 | ||||||||
\(261\) | −19.9647 | −1.23578 | ||||||||
\(262\) | −22.7110 | −1.40309 | ||||||||
\(263\) | −21.5673 | −1.32990 | −0.664950 | − | 0.746888i | \(-0.731547\pi\) | ||||
−0.664950 | + | 0.746888i | \(0.731547\pi\) | |||||||
\(264\) | 3.03237 | 0.186629 | ||||||||
\(265\) | −5.29322 | −0.325160 | ||||||||
\(266\) | −32.0514 | −1.96519 | ||||||||
\(267\) | 2.58090 | 0.157948 | ||||||||
\(268\) | −42.5788 | −2.60091 | ||||||||
\(269\) | −3.82904 | −0.233461 | −0.116730 | − | 0.993164i | \(-0.537241\pi\) | ||||
−0.116730 | + | 0.993164i | \(0.537241\pi\) | |||||||
\(270\) | 18.8891 | 1.14955 | ||||||||
\(271\) | −12.5093 | −0.759888 | −0.379944 | − | 0.925009i | \(-0.624057\pi\) | ||||
−0.379944 | + | 0.925009i | \(0.624057\pi\) | |||||||
\(272\) | 16.4386 | 0.996734 | ||||||||
\(273\) | 4.54713 | 0.275205 | ||||||||
\(274\) | −30.3319 | −1.83242 | ||||||||
\(275\) | 7.53672 | 0.454481 | ||||||||
\(276\) | −0.0813246 | −0.00489516 | ||||||||
\(277\) | −8.80554 | −0.529073 | −0.264537 | − | 0.964376i | \(-0.585219\pi\) | ||||
−0.264537 | + | 0.964376i | \(0.585219\pi\) | |||||||
\(278\) | 41.3826 | 2.48196 | ||||||||
\(279\) | 5.33570 | 0.319440 | ||||||||
\(280\) | −45.0466 | −2.69205 | ||||||||
\(281\) | 20.5445 | 1.22558 | 0.612790 | − | 0.790246i | \(-0.290047\pi\) | ||||
0.612790 | + | 0.790246i | \(0.290047\pi\) | |||||||
\(282\) | −12.4500 | −0.741389 | ||||||||
\(283\) | 11.8855 | 0.706522 | 0.353261 | − | 0.935525i | \(-0.385073\pi\) | ||||
0.353261 | + | 0.935525i | \(0.385073\pi\) | |||||||
\(284\) | −44.9379 | −2.66658 | ||||||||
\(285\) | −6.04124 | −0.357852 | ||||||||
\(286\) | −13.8515 | −0.819054 | ||||||||
\(287\) | −4.55882 | −0.269099 | ||||||||
\(288\) | 0.576404 | 0.0339650 | ||||||||
\(289\) | −1.11436 | −0.0655507 | ||||||||
\(290\) | 55.1087 | 3.23609 | ||||||||
\(291\) | 1.29474 | 0.0758988 | ||||||||
\(292\) | 13.6043 | 0.796131 | ||||||||
\(293\) | 14.4312 | 0.843078 | 0.421539 | − | 0.906810i | \(-0.361490\pi\) | ||||
0.421539 | + | 0.906810i | \(0.361490\pi\) | |||||||
\(294\) | 1.18048 | 0.0688470 | ||||||||
\(295\) | 29.3888 | 1.71108 | ||||||||
\(296\) | 15.1954 | 0.883212 | ||||||||
\(297\) | 3.56410 | 0.206810 | ||||||||
\(298\) | 40.4024 | 2.34045 | ||||||||
\(299\) | 0.186695 | 0.0107968 | ||||||||
\(300\) | −8.54556 | −0.493378 | ||||||||
\(301\) | 27.9677 | 1.61203 | ||||||||
\(302\) | 35.6849 | 2.05344 | ||||||||
\(303\) | −4.77200 | −0.274144 | ||||||||
\(304\) | −18.8618 | −1.08180 | ||||||||
\(305\) | 3.22217 | 0.184501 | ||||||||
\(306\) | 27.6523 | 1.58078 | ||||||||
\(307\) | 17.1739 | 0.980165 | 0.490082 | − | 0.871676i | \(-0.336967\pi\) | ||||
0.490082 | + | 0.871676i | \(0.336967\pi\) | |||||||
\(308\) | −16.9124 | −0.963671 | ||||||||
\(309\) | −0.592415 | −0.0337013 | ||||||||
\(310\) | −14.7282 | −0.836504 | ||||||||
\(311\) | −23.7296 | −1.34558 | −0.672791 | − | 0.739832i | \(-0.734905\pi\) | ||||
−0.672791 | + | 0.739832i | \(0.734905\pi\) | |||||||
\(312\) | 7.89314 | 0.446861 | ||||||||
\(313\) | −25.7050 | −1.45293 | −0.726467 | − | 0.687202i | \(-0.758839\pi\) | ||||
−0.726467 | + | 0.687202i | \(0.758839\pi\) | |||||||
\(314\) | 40.2696 | 2.27254 | ||||||||
\(315\) | −25.6893 | −1.44743 | ||||||||
\(316\) | −24.1112 | −1.35636 | ||||||||
\(317\) | −8.02788 | −0.450891 | −0.225445 | − | 0.974256i | \(-0.572384\pi\) | ||||
−0.225445 | + | 0.974256i | \(0.572384\pi\) | |||||||
\(318\) | 1.69576 | 0.0950933 | ||||||||
\(319\) | 10.3982 | 0.582188 | ||||||||
\(320\) | 24.6471 | 1.37782 | ||||||||
\(321\) | −4.10895 | −0.229339 | ||||||||
\(322\) | 0.341340 | 0.0190221 | ||||||||
\(323\) | −18.2273 | −1.01420 | ||||||||
\(324\) | 30.0644 | 1.67024 | ||||||||
\(325\) | 19.6178 | 1.08820 | ||||||||
\(326\) | −56.2649 | −3.11622 | ||||||||
\(327\) | −6.61891 | −0.366027 | ||||||||
\(328\) | −7.91344 | −0.436947 | ||||||||
\(329\) | 34.8971 | 1.92394 | ||||||||
\(330\) | −4.77342 | −0.262768 | ||||||||
\(331\) | 5.24402 | 0.288237 | 0.144119 | − | 0.989560i | \(-0.453965\pi\) | ||||
0.144119 | + | 0.989560i | \(0.453965\pi\) | |||||||
\(332\) | −69.5869 | −3.81908 | ||||||||
\(333\) | 8.66565 | 0.474875 | ||||||||
\(334\) | −24.4157 | −1.33597 | ||||||||
\(335\) | 33.6851 | 1.84041 | ||||||||
\(336\) | 4.89247 | 0.266906 | ||||||||
\(337\) | 17.6574 | 0.961861 | 0.480930 | − | 0.876759i | \(-0.340299\pi\) | ||||
0.480930 | + | 0.876759i | \(0.340299\pi\) | |||||||
\(338\) | −4.15670 | −0.226095 | ||||||||
\(339\) | −5.28421 | −0.286999 | ||||||||
\(340\) | −50.9732 | −2.76441 | ||||||||
\(341\) | −2.77899 | −0.150491 | ||||||||
\(342\) | −31.7285 | −1.71568 | ||||||||
\(343\) | 16.6852 | 0.900918 | ||||||||
\(344\) | 48.5477 | 2.61752 | ||||||||
\(345\) | 0.0643378 | 0.00346383 | ||||||||
\(346\) | 2.87582 | 0.154605 | ||||||||
\(347\) | −12.9881 | −0.697238 | −0.348619 | − | 0.937265i | \(-0.613349\pi\) | ||||
−0.348619 | + | 0.937265i | \(0.613349\pi\) | |||||||
\(348\) | −11.7901 | −0.632014 | ||||||||
\(349\) | 16.4846 | 0.882401 | 0.441201 | − | 0.897408i | \(-0.354553\pi\) | ||||
0.441201 | + | 0.897408i | \(0.354553\pi\) | |||||||
\(350\) | 35.8678 | 1.91722 | ||||||||
\(351\) | 9.27722 | 0.495182 | ||||||||
\(352\) | −0.300209 | −0.0160012 | ||||||||
\(353\) | 13.8669 | 0.738063 | 0.369032 | − | 0.929417i | \(-0.379689\pi\) | ||||
0.369032 | + | 0.929417i | \(0.379689\pi\) | |||||||
\(354\) | −9.41512 | −0.500408 | ||||||||
\(355\) | 35.5515 | 1.88688 | ||||||||
\(356\) | −24.9865 | −1.32428 | ||||||||
\(357\) | 4.72791 | 0.250227 | ||||||||
\(358\) | 27.2192 | 1.43858 | ||||||||
\(359\) | −32.4774 | −1.71409 | −0.857047 | − | 0.515238i | \(-0.827703\pi\) | ||||
−0.857047 | + | 0.515238i | \(0.827703\pi\) | |||||||
\(360\) | −44.5928 | −2.35025 | ||||||||
\(361\) | 1.91420 | 0.100747 | ||||||||
\(362\) | 35.8308 | 1.88322 | ||||||||
\(363\) | 3.66764 | 0.192501 | ||||||||
\(364\) | −44.0222 | −2.30739 | ||||||||
\(365\) | −10.7627 | −0.563344 | ||||||||
\(366\) | −1.03227 | −0.0539575 | ||||||||
\(367\) | 8.16012 | 0.425955 | 0.212978 | − | 0.977057i | \(-0.431684\pi\) | ||||
0.212978 | + | 0.977057i | \(0.431684\pi\) | |||||||
\(368\) | 0.200873 | 0.0104712 | ||||||||
\(369\) | −4.51290 | −0.234932 | ||||||||
\(370\) | −23.9199 | −1.24354 | ||||||||
\(371\) | −4.75315 | −0.246771 | ||||||||
\(372\) | 3.15098 | 0.163371 | ||||||||
\(373\) | 24.1101 | 1.24837 | 0.624187 | − | 0.781275i | \(-0.285430\pi\) | ||||
0.624187 | + | 0.781275i | \(0.285430\pi\) | |||||||
\(374\) | −14.4021 | −0.744717 | ||||||||
\(375\) | 0.155556 | 0.00803290 | ||||||||
\(376\) | 60.5761 | 3.12398 | ||||||||
\(377\) | 27.0662 | 1.39398 | ||||||||
\(378\) | 16.9618 | 0.872423 | ||||||||
\(379\) | 11.5728 | 0.594454 | 0.297227 | − | 0.954807i | \(-0.403938\pi\) | ||||
0.297227 | + | 0.954807i | \(0.403938\pi\) | |||||||
\(380\) | 58.4871 | 3.00033 | ||||||||
\(381\) | −3.37916 | −0.173119 | ||||||||
\(382\) | −64.2148 | −3.28552 | ||||||||
\(383\) | 16.0663 | 0.820951 | 0.410476 | − | 0.911872i | \(-0.365363\pi\) | ||||
0.410476 | + | 0.911872i | \(0.365363\pi\) | |||||||
\(384\) | −8.06536 | −0.411584 | ||||||||
\(385\) | 13.3798 | 0.681896 | ||||||||
\(386\) | −31.2999 | −1.59312 | ||||||||
\(387\) | 27.6859 | 1.40735 | ||||||||
\(388\) | −12.5348 | −0.636356 | ||||||||
\(389\) | 21.8451 | 1.10759 | 0.553796 | − | 0.832652i | \(-0.313179\pi\) | ||||
0.553796 | + | 0.832652i | \(0.313179\pi\) | |||||||
\(390\) | −12.4251 | −0.629167 | ||||||||
\(391\) | 0.194117 | 0.00981691 | ||||||||
\(392\) | −5.74367 | −0.290099 | ||||||||
\(393\) | −3.84394 | −0.193901 | ||||||||
\(394\) | −18.3655 | −0.925240 | ||||||||
\(395\) | 19.0750 | 0.959765 | ||||||||
\(396\) | −16.7420 | −0.841316 | ||||||||
\(397\) | −9.07170 | −0.455295 | −0.227648 | − | 0.973744i | \(-0.573103\pi\) | ||||
−0.227648 | + | 0.973744i | \(0.573103\pi\) | |||||||
\(398\) | 31.3494 | 1.57140 | ||||||||
\(399\) | −5.42484 | −0.271582 | ||||||||
\(400\) | 21.1077 | 1.05539 | ||||||||
\(401\) | −25.5092 | −1.27387 | −0.636934 | − | 0.770918i | \(-0.719798\pi\) | ||||
−0.636934 | + | 0.770918i | \(0.719798\pi\) | |||||||
\(402\) | −10.7915 | −0.538230 | ||||||||
\(403\) | −7.23362 | −0.360332 | ||||||||
\(404\) | 46.1993 | 2.29850 | ||||||||
\(405\) | −23.7847 | −1.18187 | ||||||||
\(406\) | 49.4859 | 2.45594 | ||||||||
\(407\) | −4.51333 | −0.223718 | ||||||||
\(408\) | 8.20695 | 0.406304 | ||||||||
\(409\) | −7.55183 | −0.373414 | −0.186707 | − | 0.982416i | \(-0.559782\pi\) | ||||
−0.186707 | + | 0.982416i | \(0.559782\pi\) | |||||||
\(410\) | 12.4570 | 0.615207 | ||||||||
\(411\) | −5.13382 | −0.253233 | ||||||||
\(412\) | 5.73536 | 0.282561 | ||||||||
\(413\) | 26.3903 | 1.29858 | ||||||||
\(414\) | 0.337901 | 0.0166069 | ||||||||
\(415\) | 55.0518 | 2.70239 | ||||||||
\(416\) | −0.781433 | −0.0383129 | ||||||||
\(417\) | 7.00420 | 0.342997 | ||||||||
\(418\) | 16.5252 | 0.808272 | ||||||||
\(419\) | 1.89237 | 0.0924485 | 0.0462243 | − | 0.998931i | \(-0.485281\pi\) | ||||
0.0462243 | + | 0.998931i | \(0.485281\pi\) | |||||||
\(420\) | −15.1707 | −0.740256 | ||||||||
\(421\) | −9.42961 | −0.459571 | −0.229786 | − | 0.973241i | \(-0.573803\pi\) | ||||
−0.229786 | + | 0.973241i | \(0.573803\pi\) | |||||||
\(422\) | −21.0129 | −1.02289 | ||||||||
\(423\) | 34.5455 | 1.67966 | ||||||||
\(424\) | −8.25077 | −0.400693 | ||||||||
\(425\) | 20.3977 | 0.989435 | ||||||||
\(426\) | −11.3894 | −0.551818 | ||||||||
\(427\) | 2.89341 | 0.140022 | ||||||||
\(428\) | 39.7800 | 1.92284 | ||||||||
\(429\) | −2.34443 | −0.113190 | ||||||||
\(430\) | −76.4217 | −3.68538 | ||||||||
\(431\) | 3.05460 | 0.147135 | 0.0735674 | − | 0.997290i | \(-0.476562\pi\) | ||||
0.0735674 | + | 0.997290i | \(0.476562\pi\) | |||||||
\(432\) | 9.98180 | 0.480249 | ||||||||
\(433\) | 14.5869 | 0.701001 | 0.350501 | − | 0.936563i | \(-0.386011\pi\) | ||||
0.350501 | + | 0.936563i | \(0.386011\pi\) | |||||||
\(434\) | −13.2255 | −0.634842 | ||||||||
\(435\) | 9.32741 | 0.447215 | ||||||||
\(436\) | 64.0798 | 3.06887 | ||||||||
\(437\) | −0.222731 | −0.0106547 | ||||||||
\(438\) | 3.44797 | 0.164750 | ||||||||
\(439\) | 37.0215 | 1.76694 | 0.883471 | − | 0.468486i | \(-0.155200\pi\) | ||||
0.883471 | + | 0.468486i | \(0.155200\pi\) | |||||||
\(440\) | 23.2253 | 1.10722 | ||||||||
\(441\) | −3.27552 | −0.155977 | ||||||||
\(442\) | −37.4883 | −1.78313 | ||||||||
\(443\) | −28.9365 | −1.37481 | −0.687407 | − | 0.726272i | \(-0.741251\pi\) | ||||
−0.687407 | + | 0.726272i | \(0.741251\pi\) | |||||||
\(444\) | 5.11747 | 0.242865 | ||||||||
\(445\) | 19.7674 | 0.937064 | ||||||||
\(446\) | 42.7438 | 2.02398 | ||||||||
\(447\) | 6.83830 | 0.323441 | ||||||||
\(448\) | 22.1324 | 1.04566 | ||||||||
\(449\) | −29.4580 | −1.39021 | −0.695104 | − | 0.718909i | \(-0.744642\pi\) | ||||
−0.695104 | + | 0.718909i | \(0.744642\pi\) | |||||||
\(450\) | 35.5065 | 1.67379 | ||||||||
\(451\) | 2.35046 | 0.110679 | ||||||||
\(452\) | 51.1581 | 2.40628 | ||||||||
\(453\) | 6.03984 | 0.283776 | ||||||||
\(454\) | −23.1695 | −1.08740 | ||||||||
\(455\) | 34.8270 | 1.63272 | ||||||||
\(456\) | −9.41672 | −0.440979 | ||||||||
\(457\) | 22.4801 | 1.05157 | 0.525787 | − | 0.850616i | \(-0.323771\pi\) | ||||
0.525787 | + | 0.850616i | \(0.323771\pi\) | |||||||
\(458\) | 65.3671 | 3.05440 | ||||||||
\(459\) | 9.64605 | 0.450239 | ||||||||
\(460\) | −0.622875 | −0.0290417 | ||||||||
\(461\) | 6.96743 | 0.324505 | 0.162253 | − | 0.986749i | \(-0.448124\pi\) | ||||
0.162253 | + | 0.986749i | \(0.448124\pi\) | |||||||
\(462\) | −4.28639 | −0.199421 | ||||||||
\(463\) | −10.2555 | −0.476615 | −0.238308 | − | 0.971190i | \(-0.576593\pi\) | ||||
−0.238308 | + | 0.971190i | \(0.576593\pi\) | |||||||
\(464\) | 29.1217 | 1.35194 | ||||||||
\(465\) | −2.49281 | −0.115601 | ||||||||
\(466\) | −49.1848 | −2.27844 | ||||||||
\(467\) | 4.05232 | 0.187519 | 0.0937595 | − | 0.995595i | \(-0.470112\pi\) | ||||
0.0937595 | + | 0.995595i | \(0.470112\pi\) | |||||||
\(468\) | −43.5788 | −2.01443 | ||||||||
\(469\) | 30.2482 | 1.39673 | ||||||||
\(470\) | −95.3564 | −4.39846 | ||||||||
\(471\) | 6.81581 | 0.314056 | ||||||||
\(472\) | 45.8096 | 2.10856 | ||||||||
\(473\) | −14.4197 | −0.663017 | ||||||||
\(474\) | −6.11092 | −0.280684 | ||||||||
\(475\) | −23.4045 | −1.07387 | ||||||||
\(476\) | −45.7724 | −2.09797 | ||||||||
\(477\) | −4.70527 | −0.215440 | ||||||||
\(478\) | −14.3171 | −0.654850 | ||||||||
\(479\) | 36.2095 | 1.65446 | 0.827228 | − | 0.561867i | \(-0.189917\pi\) | ||||
0.827228 | + | 0.561867i | \(0.189917\pi\) | |||||||
\(480\) | −0.269294 | −0.0122915 | ||||||||
\(481\) | −11.7480 | −0.535665 | ||||||||
\(482\) | 2.97800 | 0.135644 | ||||||||
\(483\) | 0.0577733 | 0.00262878 | ||||||||
\(484\) | −35.5076 | −1.61398 | ||||||||
\(485\) | 9.91655 | 0.450287 | ||||||||
\(486\) | 25.4349 | 1.15375 | ||||||||
\(487\) | 7.21245 | 0.326827 | 0.163414 | − | 0.986558i | \(-0.447749\pi\) | ||||
0.163414 | + | 0.986558i | \(0.447749\pi\) | |||||||
\(488\) | 5.02253 | 0.227359 | ||||||||
\(489\) | −9.52310 | −0.430650 | ||||||||
\(490\) | 9.04144 | 0.408451 | ||||||||
\(491\) | −30.7216 | −1.38645 | −0.693223 | − | 0.720723i | \(-0.743810\pi\) | ||||
−0.693223 | + | 0.720723i | \(0.743810\pi\) | |||||||
\(492\) | −2.66508 | −0.120151 | ||||||||
\(493\) | 28.1422 | 1.26746 | ||||||||
\(494\) | 43.0144 | 1.93531 | ||||||||
\(495\) | 13.2450 | 0.595318 | ||||||||
\(496\) | −7.78299 | −0.349466 | ||||||||
\(497\) | 31.9241 | 1.43199 | ||||||||
\(498\) | −17.6366 | −0.790315 | ||||||||
\(499\) | −2.36094 | −0.105690 | −0.0528451 | − | 0.998603i | \(-0.516829\pi\) | ||||
−0.0528451 | + | 0.998603i | \(0.516829\pi\) | |||||||
\(500\) | −1.50599 | −0.0673500 | ||||||||
\(501\) | −4.13248 | −0.184626 | ||||||||
\(502\) | −35.8079 | −1.59819 | ||||||||
\(503\) | 15.9751 | 0.712296 | 0.356148 | − | 0.934430i | \(-0.384090\pi\) | ||||
0.356148 | + | 0.934430i | \(0.384090\pi\) | |||||||
\(504\) | −40.0430 | −1.78366 | ||||||||
\(505\) | −36.5493 | −1.62642 | ||||||||
\(506\) | −0.175989 | −0.00782367 | ||||||||
\(507\) | −0.703542 | −0.0312454 | ||||||||
\(508\) | 32.7147 | 1.45148 | ||||||||
\(509\) | 18.4502 | 0.817792 | 0.408896 | − | 0.912581i | \(-0.365914\pi\) | ||||
0.408896 | + | 0.912581i | \(0.365914\pi\) | |||||||
\(510\) | −12.9190 | −0.572064 | ||||||||
\(511\) | −9.66455 | −0.427535 | ||||||||
\(512\) | 40.0577 | 1.77032 | ||||||||
\(513\) | −11.0680 | −0.488663 | ||||||||
\(514\) | 7.64460 | 0.337189 | ||||||||
\(515\) | −4.53738 | −0.199941 | ||||||||
\(516\) | 16.3498 | 0.719761 | ||||||||
\(517\) | −17.9924 | −0.791303 | ||||||||
\(518\) | −21.4793 | −0.943747 | ||||||||
\(519\) | 0.486746 | 0.0213658 | ||||||||
\(520\) | 60.4546 | 2.65111 | ||||||||
\(521\) | 40.0816 | 1.75601 | 0.878004 | − | 0.478653i | \(-0.158875\pi\) | ||||
0.878004 | + | 0.478653i | \(0.158875\pi\) | |||||||
\(522\) | 48.9874 | 2.14412 | ||||||||
\(523\) | 25.7630 | 1.12654 | 0.563269 | − | 0.826273i | \(-0.309543\pi\) | ||||
0.563269 | + | 0.826273i | \(0.309543\pi\) | |||||||
\(524\) | 37.2145 | 1.62572 | ||||||||
\(525\) | 6.07080 | 0.264952 | ||||||||
\(526\) | 52.9199 | 2.30742 | ||||||||
\(527\) | −7.52120 | −0.327629 | ||||||||
\(528\) | −2.52248 | −0.109777 | ||||||||
\(529\) | −22.9976 | −0.999897 | ||||||||
\(530\) | 12.9880 | 0.564163 | ||||||||
\(531\) | 26.1244 | 1.13370 | ||||||||
\(532\) | 52.5197 | 2.27702 | ||||||||
\(533\) | 6.11815 | 0.265006 | ||||||||
\(534\) | −6.33275 | −0.274045 | ||||||||
\(535\) | −31.4709 | −1.36061 | ||||||||
\(536\) | 52.5064 | 2.26793 | ||||||||
\(537\) | 4.60698 | 0.198806 | ||||||||
\(538\) | 9.39534 | 0.405062 | ||||||||
\(539\) | 1.70599 | 0.0734821 | ||||||||
\(540\) | −30.9519 | −1.33196 | ||||||||
\(541\) | 8.30184 | 0.356924 | 0.178462 | − | 0.983947i | \(-0.442888\pi\) | ||||
0.178462 | + | 0.983947i | \(0.442888\pi\) | |||||||
\(542\) | 30.6942 | 1.31843 | ||||||||
\(543\) | 6.06453 | 0.260254 | ||||||||
\(544\) | −0.812500 | −0.0348356 | ||||||||
\(545\) | −50.6950 | −2.17154 | ||||||||
\(546\) | −11.1573 | −0.477489 | ||||||||
\(547\) | 14.2221 | 0.608094 | 0.304047 | − | 0.952657i | \(-0.401662\pi\) | ||||
0.304047 | + | 0.952657i | \(0.401662\pi\) | |||||||
\(548\) | 49.7021 | 2.12317 | ||||||||
\(549\) | 2.86427 | 0.122244 | ||||||||
\(550\) | −18.4929 | −0.788539 | ||||||||
\(551\) | −32.2906 | −1.37563 | ||||||||
\(552\) | 0.100286 | 0.00426845 | ||||||||
\(553\) | 17.1287 | 0.728387 | ||||||||
\(554\) | 21.6062 | 0.917959 | ||||||||
\(555\) | −4.04855 | −0.171852 | ||||||||
\(556\) | −67.8099 | −2.87578 | ||||||||
\(557\) | −40.0926 | −1.69878 | −0.849388 | − | 0.527768i | \(-0.823029\pi\) | ||||
−0.849388 | + | 0.527768i | \(0.823029\pi\) | |||||||
\(558\) | −13.0922 | −0.554238 | ||||||||
\(559\) | −37.5339 | −1.58751 | ||||||||
\(560\) | 37.4720 | 1.58348 | ||||||||
\(561\) | −2.43763 | −0.102917 | ||||||||
\(562\) | −50.4101 | −2.12642 | ||||||||
\(563\) | 3.96606 | 0.167149 | 0.0835747 | − | 0.996502i | \(-0.473366\pi\) | ||||
0.0835747 | + | 0.996502i | \(0.473366\pi\) | |||||||
\(564\) | 20.4008 | 0.859027 | ||||||||
\(565\) | −40.4724 | −1.70269 | ||||||||
\(566\) | −29.1636 | −1.22584 | ||||||||
\(567\) | −21.3579 | −0.896947 | ||||||||
\(568\) | 55.4155 | 2.32518 | ||||||||
\(569\) | −0.313860 | −0.0131577 | −0.00657884 | − | 0.999978i | \(-0.502094\pi\) | ||||
−0.00657884 | + | 0.999978i | \(0.502094\pi\) | |||||||
\(570\) | 14.8234 | 0.620884 | ||||||||
\(571\) | −27.3508 | −1.14459 | −0.572297 | − | 0.820046i | \(-0.693948\pi\) | ||||
−0.572297 | + | 0.820046i | \(0.693948\pi\) | |||||||
\(572\) | 22.6971 | 0.949015 | ||||||||
\(573\) | −10.8687 | −0.454045 | ||||||||
\(574\) | 11.1860 | 0.466895 | ||||||||
\(575\) | 0.249253 | 0.0103946 | ||||||||
\(576\) | 21.9094 | 0.912892 | ||||||||
\(577\) | 32.3912 | 1.34846 | 0.674232 | − | 0.738520i | \(-0.264475\pi\) | ||||
0.674232 | + | 0.738520i | \(0.264475\pi\) | |||||||
\(578\) | 2.73432 | 0.113733 | ||||||||
\(579\) | −5.29766 | −0.220163 | ||||||||
\(580\) | −90.3016 | −3.74957 | ||||||||
\(581\) | 49.4348 | 2.05090 | ||||||||
\(582\) | −3.17690 | −0.131687 | ||||||||
\(583\) | 2.45065 | 0.101495 | ||||||||
\(584\) | −16.7762 | −0.694205 | ||||||||
\(585\) | 34.4762 | 1.42542 | ||||||||
\(586\) | −35.4098 | −1.46277 | ||||||||
\(587\) | −43.1957 | −1.78288 | −0.891439 | − | 0.453141i | \(-0.850303\pi\) | ||||
−0.891439 | + | 0.453141i | \(0.850303\pi\) | |||||||
\(588\) | −1.93435 | −0.0797711 | ||||||||
\(589\) | 8.62989 | 0.355589 | ||||||||
\(590\) | −72.1115 | −2.96878 | ||||||||
\(591\) | −3.10845 | −0.127864 | ||||||||
\(592\) | −12.6403 | −0.519512 | ||||||||
\(593\) | 17.4547 | 0.716780 | 0.358390 | − | 0.933572i | \(-0.383326\pi\) | ||||
0.358390 | + | 0.933572i | \(0.383326\pi\) | |||||||
\(594\) | −8.74525 | −0.358822 | ||||||||
\(595\) | 36.2116 | 1.48453 | ||||||||
\(596\) | −66.2038 | −2.71181 | ||||||||
\(597\) | 5.30604 | 0.217162 | ||||||||
\(598\) | −0.458093 | −0.0187328 | ||||||||
\(599\) | −3.40234 | −0.139016 | −0.0695079 | − | 0.997581i | \(-0.522143\pi\) | ||||
−0.0695079 | + | 0.997581i | \(0.522143\pi\) | |||||||
\(600\) | 10.5380 | 0.430213 | ||||||||
\(601\) | 7.96270 | 0.324805 | 0.162403 | − | 0.986725i | \(-0.448076\pi\) | ||||
0.162403 | + | 0.986725i | \(0.448076\pi\) | |||||||
\(602\) | −68.6244 | −2.79692 | ||||||||
\(603\) | 29.9435 | 1.21939 | ||||||||
\(604\) | −58.4736 | −2.37926 | ||||||||
\(605\) | 28.0909 | 1.14206 | ||||||||
\(606\) | 11.7091 | 0.475649 | ||||||||
\(607\) | 47.8410 | 1.94181 | 0.970904 | − | 0.239469i | \(-0.0769732\pi\) | ||||
0.970904 | + | 0.239469i | \(0.0769732\pi\) | |||||||
\(608\) | 0.932269 | 0.0378085 | ||||||||
\(609\) | 8.37573 | 0.339402 | ||||||||
\(610\) | −7.90626 | −0.320115 | ||||||||
\(611\) | −46.8335 | −1.89468 | ||||||||
\(612\) | −45.3113 | −1.83160 | ||||||||
\(613\) | 17.1970 | 0.694582 | 0.347291 | − | 0.937757i | \(-0.387102\pi\) | ||||
0.347291 | + | 0.937757i | \(0.387102\pi\) | |||||||
\(614\) | −42.1396 | −1.70062 | ||||||||
\(615\) | 2.10841 | 0.0850192 | ||||||||
\(616\) | 20.8556 | 0.840295 | ||||||||
\(617\) | −25.6380 | −1.03215 | −0.516073 | − | 0.856545i | \(-0.672607\pi\) | ||||
−0.516073 | + | 0.856545i | \(0.672607\pi\) | |||||||
\(618\) | 1.45361 | 0.0584728 | ||||||||
\(619\) | −27.3832 | −1.10063 | −0.550313 | − | 0.834959i | \(-0.685492\pi\) | ||||
−0.550313 | + | 0.834959i | \(0.685492\pi\) | |||||||
\(620\) | 24.1337 | 0.969234 | ||||||||
\(621\) | 0.117871 | 0.00473001 | ||||||||
\(622\) | 58.2254 | 2.33463 | ||||||||
\(623\) | 17.7505 | 0.711159 | ||||||||
\(624\) | −6.56592 | −0.262847 | ||||||||
\(625\) | −24.3974 | −0.975894 | ||||||||
\(626\) | 63.0725 | 2.52088 | ||||||||
\(627\) | 2.79696 | 0.111700 | ||||||||
\(628\) | −65.9861 | −2.63313 | ||||||||
\(629\) | −12.2151 | −0.487048 | ||||||||
\(630\) | 63.0339 | 2.51133 | ||||||||
\(631\) | 3.42616 | 0.136393 | 0.0681967 | − | 0.997672i | \(-0.478275\pi\) | ||||
0.0681967 | + | 0.997672i | \(0.478275\pi\) | |||||||
\(632\) | 29.7329 | 1.18271 | ||||||||
\(633\) | −3.55653 | −0.141359 | ||||||||
\(634\) | 19.6980 | 0.782309 | ||||||||
\(635\) | −25.8814 | −1.02707 | ||||||||
\(636\) | −2.77868 | −0.110182 | ||||||||
\(637\) | 4.44063 | 0.175944 | ||||||||
\(638\) | −25.5141 | −1.01011 | ||||||||
\(639\) | 31.6025 | 1.25018 | ||||||||
\(640\) | −61.7736 | −2.44182 | ||||||||
\(641\) | 0.940539 | 0.0371491 | 0.0185745 | − | 0.999827i | \(-0.494087\pi\) | ||||
0.0185745 | + | 0.999827i | \(0.494087\pi\) | |||||||
\(642\) | 10.0821 | 0.397910 | ||||||||
\(643\) | −21.0572 | −0.830415 | −0.415207 | − | 0.909727i | \(-0.636291\pi\) | ||||
−0.415207 | + | 0.909727i | \(0.636291\pi\) | |||||||
\(644\) | −0.559322 | −0.0220404 | ||||||||
\(645\) | −12.9347 | −0.509305 | ||||||||
\(646\) | 44.7245 | 1.75966 | ||||||||
\(647\) | 39.4010 | 1.54902 | 0.774508 | − | 0.632565i | \(-0.217998\pi\) | ||||
0.774508 | + | 0.632565i | \(0.217998\pi\) | |||||||
\(648\) | −37.0741 | −1.45641 | ||||||||
\(649\) | −13.6064 | −0.534098 | ||||||||
\(650\) | −48.1363 | −1.88806 | ||||||||
\(651\) | −2.23847 | −0.0877326 | ||||||||
\(652\) | 92.1962 | 3.61068 | ||||||||
\(653\) | 15.6535 | 0.612571 | 0.306285 | − | 0.951940i | \(-0.400914\pi\) | ||||
0.306285 | + | 0.951940i | \(0.400914\pi\) | |||||||
\(654\) | 16.2408 | 0.635067 | ||||||||
\(655\) | −29.4412 | −1.15036 | ||||||||
\(656\) | 6.58280 | 0.257015 | ||||||||
\(657\) | −9.56720 | −0.373252 | ||||||||
\(658\) | −85.6271 | −3.33809 | ||||||||
\(659\) | −30.4412 | −1.18582 | −0.592911 | − | 0.805268i | \(-0.702021\pi\) | ||||
−0.592911 | + | 0.805268i | \(0.702021\pi\) | |||||||
\(660\) | 7.82178 | 0.304462 | ||||||||
\(661\) | −11.9942 | −0.466522 | −0.233261 | − | 0.972414i | \(-0.574940\pi\) | ||||
−0.233261 | + | 0.972414i | \(0.574940\pi\) | |||||||
\(662\) | −12.8673 | −0.500100 | ||||||||
\(663\) | −6.34507 | −0.246422 | ||||||||
\(664\) | 85.8116 | 3.33013 | ||||||||
\(665\) | −41.5495 | −1.61122 | ||||||||
\(666\) | −21.2629 | −0.823922 | ||||||||
\(667\) | 0.343888 | 0.0133154 | ||||||||
\(668\) | 40.0079 | 1.54795 | ||||||||
\(669\) | 7.23459 | 0.279705 | ||||||||
\(670\) | −82.6533 | −3.19317 | ||||||||
\(671\) | −1.49180 | −0.0575902 | ||||||||
\(672\) | −0.241817 | −0.00932831 | ||||||||
\(673\) | 15.7547 | 0.607297 | 0.303649 | − | 0.952784i | \(-0.401795\pi\) | ||||
0.303649 | + | 0.952784i | \(0.401795\pi\) | |||||||
\(674\) | −43.3261 | −1.66886 | ||||||||
\(675\) | 12.3859 | 0.476733 | ||||||||
\(676\) | 6.81121 | 0.261970 | ||||||||
\(677\) | −6.69488 | −0.257305 | −0.128653 | − | 0.991690i | \(-0.541065\pi\) | ||||
−0.128653 | + | 0.991690i | \(0.541065\pi\) | |||||||
\(678\) | 12.9659 | 0.497952 | ||||||||
\(679\) | 8.90476 | 0.341733 | ||||||||
\(680\) | 62.8580 | 2.41049 | ||||||||
\(681\) | −3.92155 | −0.150274 | ||||||||
\(682\) | 6.81883 | 0.261106 | ||||||||
\(683\) | 30.9121 | 1.18282 | 0.591410 | − | 0.806371i | \(-0.298571\pi\) | ||||
0.591410 | + | 0.806371i | \(0.298571\pi\) | |||||||
\(684\) | 51.9906 | 1.98791 | ||||||||
\(685\) | −39.3205 | −1.50236 | ||||||||
\(686\) | −40.9406 | −1.56312 | ||||||||
\(687\) | 11.0637 | 0.422106 | ||||||||
\(688\) | −40.3844 | −1.53964 | ||||||||
\(689\) | 6.37895 | 0.243018 | ||||||||
\(690\) | −0.157866 | −0.00600985 | ||||||||
\(691\) | 19.9693 | 0.759670 | 0.379835 | − | 0.925054i | \(-0.375981\pi\) | ||||
0.379835 | + | 0.925054i | \(0.375981\pi\) | |||||||
\(692\) | −4.71235 | −0.179137 | ||||||||
\(693\) | 11.8936 | 0.451800 | ||||||||
\(694\) | 31.8689 | 1.20973 | ||||||||
\(695\) | 53.6460 | 2.03491 | ||||||||
\(696\) | 14.5390 | 0.551100 | ||||||||
\(697\) | 6.36138 | 0.240955 | ||||||||
\(698\) | −40.4484 | −1.53099 | ||||||||
\(699\) | −8.32476 | −0.314871 | ||||||||
\(700\) | −58.7734 | −2.22143 | ||||||||
\(701\) | −28.7748 | −1.08681 | −0.543405 | − | 0.839471i | \(-0.682865\pi\) | ||||
−0.543405 | + | 0.839471i | \(0.682865\pi\) | |||||||
\(702\) | −22.7636 | −0.859155 | ||||||||
\(703\) | 14.0157 | 0.528613 | ||||||||
\(704\) | −11.4111 | −0.430071 | ||||||||
\(705\) | −16.1395 | −0.607849 | ||||||||
\(706\) | −34.0254 | −1.28056 | ||||||||
\(707\) | −32.8202 | −1.23433 | ||||||||
\(708\) | 15.4277 | 0.579809 | ||||||||
\(709\) | 10.0280 | 0.376609 | 0.188305 | − | 0.982111i | \(-0.439701\pi\) | ||||
0.188305 | + | 0.982111i | \(0.439701\pi\) | |||||||
\(710\) | −87.2327 | −3.27379 | ||||||||
\(711\) | 16.9562 | 0.635906 | ||||||||
\(712\) | 30.8122 | 1.15474 | ||||||||
\(713\) | −0.0919064 | −0.00344192 | ||||||||
\(714\) | −11.6009 | −0.434152 | ||||||||
\(715\) | −17.9562 | −0.671526 | ||||||||
\(716\) | −44.6016 | −1.66684 | ||||||||
\(717\) | −2.42324 | −0.0904976 | ||||||||
\(718\) | 79.6900 | 2.97401 | ||||||||
\(719\) | −16.6360 | −0.620419 | −0.310210 | − | 0.950668i | \(-0.600399\pi\) | ||||
−0.310210 | + | 0.950668i | \(0.600399\pi\) | |||||||
\(720\) | 37.0945 | 1.38243 | ||||||||
\(721\) | −4.07443 | −0.151740 | ||||||||
\(722\) | −4.69688 | −0.174800 | ||||||||
\(723\) | 0.504040 | 0.0187455 | ||||||||
\(724\) | −58.7127 | −2.18204 | ||||||||
\(725\) | 36.1356 | 1.34204 | ||||||||
\(726\) | −8.99929 | −0.333995 | ||||||||
\(727\) | 29.3994 | 1.09036 | 0.545182 | − | 0.838318i | \(-0.316461\pi\) | ||||
0.545182 | + | 0.838318i | \(0.316461\pi\) | |||||||
\(728\) | 54.2863 | 2.01199 | ||||||||
\(729\) | −18.1274 | −0.671386 | ||||||||
\(730\) | 26.4084 | 0.977420 | ||||||||
\(731\) | −39.0261 | −1.44343 | ||||||||
\(732\) | 1.69148 | 0.0625190 | ||||||||
\(733\) | 22.8461 | 0.843840 | 0.421920 | − | 0.906633i | \(-0.361356\pi\) | ||||
0.421920 | + | 0.906633i | \(0.361356\pi\) | |||||||
\(734\) | −20.0225 | −0.739045 | ||||||||
\(735\) | 1.53031 | 0.0564462 | ||||||||
\(736\) | −0.00992846 | −0.000365968 0 | ||||||||
\(737\) | −15.5955 | −0.574467 | ||||||||
\(738\) | 11.0733 | 0.407615 | ||||||||
\(739\) | 38.3670 | 1.41135 | 0.705677 | − | 0.708533i | \(-0.250643\pi\) | ||||
0.705677 | + | 0.708533i | \(0.250643\pi\) | |||||||
\(740\) | 39.1954 | 1.44085 | ||||||||
\(741\) | 7.28039 | 0.267452 | ||||||||
\(742\) | 11.6628 | 0.428156 | ||||||||
\(743\) | 40.3801 | 1.48140 | 0.740701 | − | 0.671834i | \(-0.234493\pi\) | ||||
0.740701 | + | 0.671834i | \(0.234493\pi\) | |||||||
\(744\) | −3.88565 | −0.142455 | ||||||||
\(745\) | 52.3754 | 1.91889 | ||||||||
\(746\) | −59.1590 | −2.16597 | ||||||||
\(747\) | 48.9369 | 1.79051 | ||||||||
\(748\) | 23.5995 | 0.862883 | ||||||||
\(749\) | −28.2599 | −1.03259 | ||||||||
\(750\) | −0.381689 | −0.0139373 | ||||||||
\(751\) | 29.2280 | 1.06655 | 0.533273 | − | 0.845943i | \(-0.320962\pi\) | ||||
0.533273 | + | 0.845943i | \(0.320962\pi\) | |||||||
\(752\) | −50.3903 | −1.83755 | ||||||||
\(753\) | −6.06066 | −0.220863 | ||||||||
\(754\) | −66.4123 | −2.41859 | ||||||||
\(755\) | 46.2599 | 1.68357 | ||||||||
\(756\) | −27.7938 | −1.01085 | ||||||||
\(757\) | 31.2717 | 1.13659 | 0.568294 | − | 0.822826i | \(-0.307604\pi\) | ||||
0.568294 | + | 0.822826i | \(0.307604\pi\) | |||||||
\(758\) | −28.3962 | −1.03140 | ||||||||
\(759\) | −0.0297870 | −0.00108120 | ||||||||
\(760\) | −72.1238 | −2.61621 | ||||||||
\(761\) | −11.5473 | −0.418588 | −0.209294 | − | 0.977853i | \(-0.567117\pi\) | ||||
−0.209294 | + | 0.977853i | \(0.567117\pi\) | |||||||
\(762\) | 8.29145 | 0.300368 | ||||||||
\(763\) | −45.5226 | −1.64803 | ||||||||
\(764\) | 105.223 | 3.80684 | ||||||||
\(765\) | 35.8468 | 1.29605 | ||||||||
\(766\) | −39.4220 | −1.42438 | ||||||||
\(767\) | −35.4170 | −1.27883 | ||||||||
\(768\) | 13.3540 | 0.481871 | ||||||||
\(769\) | −25.3576 | −0.914418 | −0.457209 | − | 0.889359i | \(-0.651151\pi\) | ||||
−0.457209 | + | 0.889359i | \(0.651151\pi\) | |||||||
\(770\) | −32.8300 | −1.18311 | ||||||||
\(771\) | 1.29389 | 0.0465982 | ||||||||
\(772\) | 51.2883 | 1.84591 | ||||||||
\(773\) | −4.45434 | −0.160211 | −0.0801057 | − | 0.996786i | \(-0.525526\pi\) | ||||
−0.0801057 | + | 0.996786i | \(0.525526\pi\) | |||||||
\(774\) | −67.9331 | −2.44180 | ||||||||
\(775\) | −9.65749 | −0.346907 | ||||||||
\(776\) | 15.4573 | 0.554886 | ||||||||
\(777\) | −3.63548 | −0.130422 | ||||||||
\(778\) | −53.6015 | −1.92171 | ||||||||
\(779\) | −7.29911 | −0.261518 | ||||||||
\(780\) | 20.3598 | 0.728998 | ||||||||
\(781\) | −16.4596 | −0.588969 | ||||||||
\(782\) | −0.476305 | −0.0170326 | ||||||||
\(783\) | 17.0885 | 0.610692 | ||||||||
\(784\) | 4.77788 | 0.170638 | ||||||||
\(785\) | 52.2032 | 1.86321 | ||||||||
\(786\) | 9.43190 | 0.336425 | ||||||||
\(787\) | 29.7128 | 1.05915 | 0.529573 | − | 0.848264i | \(-0.322352\pi\) | ||||
0.529573 | + | 0.848264i | \(0.322352\pi\) | |||||||
\(788\) | 30.0939 | 1.07205 | ||||||||
\(789\) | 8.95694 | 0.318876 | ||||||||
\(790\) | −46.8043 | −1.66522 | ||||||||
\(791\) | −36.3430 | −1.29221 | ||||||||
\(792\) | 20.6455 | 0.733606 | ||||||||
\(793\) | −3.88309 | −0.137893 | ||||||||
\(794\) | 22.2593 | 0.789952 | ||||||||
\(795\) | 2.19828 | 0.0779650 | ||||||||
\(796\) | −51.3694 | −1.82074 | ||||||||
\(797\) | 36.7236 | 1.30082 | 0.650408 | − | 0.759585i | \(-0.274598\pi\) | ||||
0.650408 | + | 0.759585i | \(0.274598\pi\) | |||||||
\(798\) | 13.3110 | 0.471203 | ||||||||
\(799\) | −48.6954 | −1.72272 | ||||||||
\(800\) | −1.04328 | −0.0368855 | ||||||||
\(801\) | 17.5717 | 0.620865 | ||||||||
\(802\) | 62.5920 | 2.21020 | ||||||||
\(803\) | 4.98289 | 0.175842 | ||||||||
\(804\) | 17.6830 | 0.623632 | ||||||||
\(805\) | 0.442493 | 0.0155958 | ||||||||
\(806\) | 17.7492 | 0.625187 | ||||||||
\(807\) | 1.59021 | 0.0559779 | ||||||||
\(808\) | −56.9710 | −2.00423 | ||||||||
\(809\) | 2.17184 | 0.0763578 | 0.0381789 | − | 0.999271i | \(-0.487844\pi\) | ||||
0.0381789 | + | 0.999271i | \(0.487844\pi\) | |||||||
\(810\) | 58.3605 | 2.05058 | ||||||||
\(811\) | 11.9110 | 0.418254 | 0.209127 | − | 0.977889i | \(-0.432938\pi\) | ||||
0.209127 | + | 0.977889i | \(0.432938\pi\) | |||||||
\(812\) | −81.0881 | −2.84563 | ||||||||
\(813\) | 5.19514 | 0.182202 | ||||||||
\(814\) | 11.0744 | 0.388157 | ||||||||
\(815\) | −72.9386 | −2.55493 | ||||||||
\(816\) | −6.82695 | −0.238991 | ||||||||
\(817\) | 44.7789 | 1.56661 | ||||||||
\(818\) | 18.5300 | 0.647885 | ||||||||
\(819\) | 30.9586 | 1.08178 | ||||||||
\(820\) | −20.4122 | −0.712824 | ||||||||
\(821\) | −13.6014 | −0.474693 | −0.237347 | − | 0.971425i | \(-0.576278\pi\) | ||||
−0.237347 | + | 0.971425i | \(0.576278\pi\) | |||||||
\(822\) | 12.5969 | 0.439366 | ||||||||
\(823\) | 27.5095 | 0.958922 | 0.479461 | − | 0.877563i | \(-0.340832\pi\) | ||||
0.479461 | + | 0.877563i | \(0.340832\pi\) | |||||||
\(824\) | −7.07260 | −0.246386 | ||||||||
\(825\) | −3.13001 | −0.108973 | ||||||||
\(826\) | −64.7539 | −2.25308 | ||||||||
\(827\) | 35.5469 | 1.23609 | 0.618043 | − | 0.786144i | \(-0.287926\pi\) | ||||
0.618043 | + | 0.786144i | \(0.287926\pi\) | |||||||
\(828\) | −0.553688 | −0.0192420 | ||||||||
\(829\) | −29.5771 | −1.02726 | −0.513628 | − | 0.858013i | \(-0.671699\pi\) | ||||
−0.513628 | + | 0.858013i | \(0.671699\pi\) | |||||||
\(830\) | −135.081 | −4.68873 | ||||||||
\(831\) | 3.65695 | 0.126858 | ||||||||
\(832\) | −29.7026 | −1.02975 | ||||||||
\(833\) | 4.61717 | 0.159975 | ||||||||
\(834\) | −17.1862 | −0.595110 | ||||||||
\(835\) | −31.6512 | −1.09533 | ||||||||
\(836\) | −27.0783 | −0.936522 | ||||||||
\(837\) | −4.56701 | −0.157859 | ||||||||
\(838\) | −4.64333 | −0.160401 | ||||||||
\(839\) | 4.37288 | 0.150969 | 0.0754844 | − | 0.997147i | \(-0.475950\pi\) | ||||
0.0754844 | + | 0.997147i | \(0.475950\pi\) | |||||||
\(840\) | 18.7079 | 0.645484 | ||||||||
\(841\) | 20.8553 | 0.719150 | ||||||||
\(842\) | 23.1375 | 0.797370 | ||||||||
\(843\) | −8.53214 | −0.293863 | ||||||||
\(844\) | 34.4319 | 1.18520 | ||||||||
\(845\) | −5.38851 | −0.185370 | ||||||||
\(846\) | −84.7645 | −2.91426 | ||||||||
\(847\) | 25.2247 | 0.866732 | ||||||||
\(848\) | 6.86341 | 0.235690 | ||||||||
\(849\) | −4.93608 | −0.169406 | ||||||||
\(850\) | −50.0500 | −1.71670 | ||||||||
\(851\) | −0.149264 | −0.00511671 | ||||||||
\(852\) | 18.6628 | 0.639376 | ||||||||
\(853\) | −4.06987 | −0.139350 | −0.0696749 | − | 0.997570i | \(-0.522196\pi\) | ||||
−0.0696749 | + | 0.997570i | \(0.522196\pi\) | |||||||
\(854\) | −7.09958 | −0.242943 | ||||||||
\(855\) | −41.1310 | −1.40665 | ||||||||
\(856\) | −49.0550 | −1.67667 | ||||||||
\(857\) | −52.4420 | −1.79139 | −0.895693 | − | 0.444673i | \(-0.853320\pi\) | ||||
−0.895693 | + | 0.444673i | \(0.853320\pi\) | |||||||
\(858\) | 5.75253 | 0.196388 | ||||||||
\(859\) | 18.9272 | 0.645788 | 0.322894 | − | 0.946435i | \(-0.395344\pi\) | ||||
0.322894 | + | 0.946435i | \(0.395344\pi\) | |||||||
\(860\) | 125.225 | 4.27015 | ||||||||
\(861\) | 1.89328 | 0.0645230 | ||||||||
\(862\) | −7.49508 | −0.255283 | ||||||||
\(863\) | 16.3931 | 0.558027 | 0.279014 | − | 0.960287i | \(-0.409993\pi\) | ||||
0.279014 | + | 0.960287i | \(0.409993\pi\) | |||||||
\(864\) | −0.493365 | −0.0167846 | ||||||||
\(865\) | 3.72805 | 0.126757 | ||||||||
\(866\) | −35.7919 | −1.21626 | ||||||||
\(867\) | 0.462796 | 0.0157174 | ||||||||
\(868\) | 21.6714 | 0.735574 | ||||||||
\(869\) | −8.83129 | −0.299581 | ||||||||
\(870\) | −22.8867 | −0.775932 | ||||||||
\(871\) | −40.5944 | −1.37549 | ||||||||
\(872\) | −79.0205 | −2.67597 | ||||||||
\(873\) | 8.81505 | 0.298344 | ||||||||
\(874\) | 0.546517 | 0.0184862 | ||||||||
\(875\) | 1.06986 | 0.0361680 | ||||||||
\(876\) | −5.64988 | −0.190892 | ||||||||
\(877\) | −31.1690 | −1.05250 | −0.526251 | − | 0.850329i | \(-0.676403\pi\) | ||||
−0.526251 | + | 0.850329i | \(0.676403\pi\) | |||||||
\(878\) | −90.8399 | −3.06570 | ||||||||
\(879\) | −5.99328 | −0.202148 | ||||||||
\(880\) | −19.3200 | −0.651276 | ||||||||
\(881\) | 18.4490 | 0.621563 | 0.310781 | − | 0.950481i | \(-0.399409\pi\) | ||||
0.310781 | + | 0.950481i | \(0.399409\pi\) | |||||||
\(882\) | 8.03715 | 0.270625 | ||||||||
\(883\) | −29.0624 | −0.978029 | −0.489015 | − | 0.872276i | \(-0.662644\pi\) | ||||
−0.489015 | + | 0.872276i | \(0.662644\pi\) | |||||||
\(884\) | 61.4286 | 2.06607 | ||||||||
\(885\) | −12.2052 | −0.410274 | ||||||||
\(886\) | 71.0016 | 2.38535 | ||||||||
\(887\) | −21.9044 | −0.735476 | −0.367738 | − | 0.929929i | \(-0.619868\pi\) | ||||
−0.367738 | + | 0.929929i | \(0.619868\pi\) | |||||||
\(888\) | −6.31065 | −0.211772 | ||||||||
\(889\) | −23.2407 | −0.779467 | ||||||||
\(890\) | −48.5033 | −1.62584 | ||||||||
\(891\) | 11.0118 | 0.368909 | ||||||||
\(892\) | −70.0404 | −2.34513 | ||||||||
\(893\) | 55.8735 | 1.86974 | ||||||||
\(894\) | −16.7792 | −0.561179 | ||||||||
\(895\) | 35.2854 | 1.17946 | ||||||||
\(896\) | −55.4708 | −1.85315 | ||||||||
\(897\) | −0.0775345 | −0.00258880 | ||||||||
\(898\) | 72.2812 | 2.41205 | ||||||||
\(899\) | −13.3242 | −0.444386 | ||||||||
\(900\) | −58.1813 | −1.93938 | ||||||||
\(901\) | 6.63255 | 0.220962 | ||||||||
\(902\) | −5.76732 | −0.192031 | ||||||||
\(903\) | −11.6150 | −0.386523 | ||||||||
\(904\) | −63.0860 | −2.09821 | ||||||||
\(905\) | 46.4490 | 1.54402 | ||||||||
\(906\) | −14.8200 | −0.492361 | ||||||||
\(907\) | −13.1867 | −0.437857 | −0.218928 | − | 0.975741i | \(-0.570256\pi\) | ||||
−0.218928 | + | 0.975741i | \(0.570256\pi\) | |||||||
\(908\) | 37.9658 | 1.25994 | ||||||||
\(909\) | −32.4896 | −1.07761 | ||||||||
\(910\) | −85.4552 | −2.83281 | ||||||||
\(911\) | 18.2306 | 0.604008 | 0.302004 | − | 0.953307i | \(-0.402344\pi\) | ||||
0.302004 | + | 0.953307i | \(0.402344\pi\) | |||||||
\(912\) | 7.83331 | 0.259387 | ||||||||
\(913\) | −25.4878 | −0.843523 | ||||||||
\(914\) | −55.1595 | −1.82451 | ||||||||
\(915\) | −1.33817 | −0.0442386 | ||||||||
\(916\) | −107.111 | −3.53905 | ||||||||
\(917\) | −26.4373 | −0.873038 | ||||||||
\(918\) | −23.6686 | −0.781179 | ||||||||
\(919\) | −3.48482 | −0.114954 | −0.0574768 | − | 0.998347i | \(-0.518306\pi\) | ||||
−0.0574768 | + | 0.998347i | \(0.518306\pi\) | |||||||
\(920\) | 0.768102 | 0.0253236 | ||||||||
\(921\) | −7.13233 | −0.235018 | ||||||||
\(922\) | −17.0960 | −0.563027 | ||||||||
\(923\) | −42.8436 | −1.41021 | ||||||||
\(924\) | 7.02372 | 0.231063 | ||||||||
\(925\) | −15.6846 | −0.515708 | ||||||||
\(926\) | 25.1641 | 0.826942 | ||||||||
\(927\) | −4.03338 | −0.132474 | ||||||||
\(928\) | −1.43938 | −0.0472501 | ||||||||
\(929\) | −36.1583 | −1.18631 | −0.593157 | − | 0.805087i | \(-0.702119\pi\) | ||||
−0.593157 | + | 0.805087i | \(0.702119\pi\) | |||||||
\(930\) | 6.11663 | 0.200572 | ||||||||
\(931\) | −5.29778 | −0.173628 | ||||||||
\(932\) | 80.5947 | 2.63997 | ||||||||
\(933\) | 9.85493 | 0.322636 | ||||||||
\(934\) | −9.94319 | −0.325351 | ||||||||
\(935\) | −18.6701 | −0.610578 | ||||||||
\(936\) | 53.7395 | 1.75653 | ||||||||
\(937\) | −55.7418 | −1.82100 | −0.910502 | − | 0.413504i | \(-0.864305\pi\) | ||||
−0.910502 | + | 0.413504i | \(0.864305\pi\) | |||||||
\(938\) | −74.2201 | −2.42337 | ||||||||
\(939\) | 10.6753 | 0.348376 | ||||||||
\(940\) | 156.252 | 5.09637 | ||||||||
\(941\) | 36.3584 | 1.18525 | 0.592625 | − | 0.805478i | \(-0.298091\pi\) | ||||
0.592625 | + | 0.805478i | \(0.298091\pi\) | |||||||
\(942\) | −16.7240 | −0.544897 | ||||||||
\(943\) | 0.0777338 | 0.00253136 | ||||||||
\(944\) | −38.1068 | −1.24027 | ||||||||
\(945\) | 21.9884 | 0.715281 | ||||||||
\(946\) | 35.3816 | 1.15035 | ||||||||
\(947\) | 5.51942 | 0.179357 | 0.0896785 | − | 0.995971i | \(-0.471416\pi\) | ||||
0.0896785 | + | 0.995971i | \(0.471416\pi\) | |||||||
\(948\) | 10.0134 | 0.325221 | ||||||||
\(949\) | 12.9703 | 0.421033 | ||||||||
\(950\) | 57.4278 | 1.86320 | ||||||||
\(951\) | 3.33399 | 0.108112 | ||||||||
\(952\) | 56.4445 | 1.82938 | ||||||||
\(953\) | 0.837997 | 0.0271454 | 0.0135727 | − | 0.999908i | \(-0.495680\pi\) | ||||
0.0135727 | + | 0.999908i | \(0.495680\pi\) | |||||||
\(954\) | 11.5453 | 0.373794 | ||||||||
\(955\) | −83.2445 | −2.69373 | ||||||||
\(956\) | 23.4602 | 0.758757 | ||||||||
\(957\) | −4.31839 | −0.139594 | ||||||||
\(958\) | −88.8475 | −2.87053 | ||||||||
\(959\) | −35.3086 | −1.14018 | ||||||||
\(960\) | −10.2360 | −0.330365 | ||||||||
\(961\) | −27.4390 | −0.885130 | ||||||||
\(962\) | 28.8262 | 0.929395 | ||||||||
\(963\) | −27.9752 | −0.901489 | ||||||||
\(964\) | −4.87978 | −0.157167 | ||||||||
\(965\) | −40.5754 | −1.30617 | ||||||||
\(966\) | −0.141759 | −0.00456101 | ||||||||
\(967\) | −16.0683 | −0.516720 | −0.258360 | − | 0.966049i | \(-0.583182\pi\) | ||||
−0.258360 | + | 0.966049i | \(0.583182\pi\) | |||||||
\(968\) | 43.7864 | 1.40735 | ||||||||
\(969\) | 7.56983 | 0.243178 | ||||||||
\(970\) | −24.3323 | −0.781262 | ||||||||
\(971\) | 52.6248 | 1.68881 | 0.844406 | − | 0.535704i | \(-0.179954\pi\) | ||||
0.844406 | + | 0.535704i | \(0.179954\pi\) | |||||||
\(972\) | −41.6779 | −1.33682 | ||||||||
\(973\) | 48.1724 | 1.54434 | ||||||||
\(974\) | −17.6972 | −0.567056 | ||||||||
\(975\) | −8.14730 | −0.260922 | ||||||||
\(976\) | −4.17800 | −0.133734 | ||||||||
\(977\) | 45.7366 | 1.46324 | 0.731622 | − | 0.681710i | \(-0.238763\pi\) | ||||
0.731622 | + | 0.681710i | \(0.238763\pi\) | |||||||
\(978\) | 23.3669 | 0.747190 | ||||||||
\(979\) | −9.15187 | −0.292495 | ||||||||
\(980\) | −14.8154 | −0.473260 | ||||||||
\(981\) | −45.0640 | −1.43878 | ||||||||
\(982\) | 75.3817 | 2.40553 | ||||||||
\(983\) | 11.6657 | 0.372079 | 0.186040 | − | 0.982542i | \(-0.440435\pi\) | ||||
0.186040 | + | 0.982542i | \(0.440435\pi\) | |||||||
\(984\) | 3.28646 | 0.104769 | ||||||||
\(985\) | −23.8080 | −0.758585 | ||||||||
\(986\) | −69.0526 | −2.19908 | ||||||||
\(987\) | −14.4928 | −0.461311 | ||||||||
\(988\) | −70.4838 | −2.24239 | ||||||||
\(989\) | −0.476885 | −0.0151641 | ||||||||
\(990\) | −32.4993 | −1.03289 | ||||||||
\(991\) | 29.2300 | 0.928521 | 0.464261 | − | 0.885699i | \(-0.346320\pi\) | ||||
0.464261 | + | 0.885699i | \(0.346320\pi\) | |||||||
\(992\) | 0.384685 | 0.0122138 | ||||||||
\(993\) | −2.17785 | −0.0691119 | ||||||||
\(994\) | −78.3323 | −2.48455 | ||||||||
\(995\) | 40.6396 | 1.28836 | ||||||||
\(996\) | 28.8995 | 0.915716 | ||||||||
\(997\) | 17.1860 | 0.544286 | 0.272143 | − | 0.962257i | \(-0.412268\pi\) | ||||
0.272143 | + | 0.962257i | \(0.412268\pi\) | |||||||
\(998\) | 5.79305 | 0.183376 | ||||||||
\(999\) | −7.41723 | −0.234671 |
(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 | 4003.2.a.c.1.13 | ✓ | 179 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4003.2.a.c.1.13 | ✓ | 179 | 1.1 | even | 1 | trivial |