Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6018,2,Mod(1,6018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6018, 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("6018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6018.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: | \(48.0539719364\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{13} - 49 x^{12} + 79 x^{11} + 956 x^{10} - 1179 x^{9} - 9396 x^{8} + 8315 x^{7} + 48570 x^{6} - 28124 x^{5} - 125592 x^{4} + 40576 x^{3} + 138096 x^{2} + \cdots - 43744 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(2.33625\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6018.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.33625 | 1.04480 | 0.522401 | − | 0.852700i | \(-0.325036\pi\) | ||||
0.522401 | + | 0.852700i | \(0.325036\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −0.683869 | −0.258478 | −0.129239 | − | 0.991613i | \(-0.541253\pi\) | ||||
−0.129239 | + | 0.991613i | \(0.541253\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.33625 | 0.738787 | ||||||||
\(11\) | 1.93698 | 0.584020 | 0.292010 | − | 0.956415i | \(-0.405676\pi\) | ||||
0.292010 | + | 0.956415i | \(0.405676\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0.480780 | 0.133344 | 0.0666721 | − | 0.997775i | \(-0.478762\pi\) | ||||
0.0666721 | + | 0.997775i | \(0.478762\pi\) | |||||||
\(14\) | −0.683869 | −0.182772 | ||||||||
\(15\) | −2.33625 | −0.603217 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −0.134424 | −0.0308390 | −0.0154195 | − | 0.999881i | \(-0.504908\pi\) | ||||
−0.0154195 | + | 0.999881i | \(0.504908\pi\) | |||||||
\(20\) | 2.33625 | 0.522401 | ||||||||
\(21\) | 0.683869 | 0.149232 | ||||||||
\(22\) | 1.93698 | 0.412965 | ||||||||
\(23\) | 6.84029 | 1.42630 | 0.713150 | − | 0.701012i | \(-0.247268\pi\) | ||||
0.713150 | + | 0.701012i | \(0.247268\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0.458066 | 0.0916132 | ||||||||
\(26\) | 0.480780 | 0.0942886 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.683869 | −0.129239 | ||||||||
\(29\) | 7.79476 | 1.44745 | 0.723725 | − | 0.690088i | \(-0.242428\pi\) | ||||
0.723725 | + | 0.690088i | \(0.242428\pi\) | |||||||
\(30\) | −2.33625 | −0.426539 | ||||||||
\(31\) | 2.80957 | 0.504614 | 0.252307 | − | 0.967647i | \(-0.418811\pi\) | ||||
0.252307 | + | 0.967647i | \(0.418811\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.93698 | −0.337184 | ||||||||
\(34\) | 1.00000 | 0.171499 | ||||||||
\(35\) | −1.59769 | −0.270059 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −0.709000 | −0.116559 | −0.0582795 | − | 0.998300i | \(-0.518561\pi\) | ||||
−0.0582795 | + | 0.998300i | \(0.518561\pi\) | |||||||
\(38\) | −0.134424 | −0.0218064 | ||||||||
\(39\) | −0.480780 | −0.0769863 | ||||||||
\(40\) | 2.33625 | 0.369394 | ||||||||
\(41\) | −2.73813 | −0.427624 | −0.213812 | − | 0.976875i | \(-0.568588\pi\) | ||||
−0.213812 | + | 0.976875i | \(0.568588\pi\) | |||||||
\(42\) | 0.683869 | 0.105523 | ||||||||
\(43\) | −6.44381 | −0.982672 | −0.491336 | − | 0.870970i | \(-0.663491\pi\) | ||||
−0.491336 | + | 0.870970i | \(0.663491\pi\) | |||||||
\(44\) | 1.93698 | 0.292010 | ||||||||
\(45\) | 2.33625 | 0.348268 | ||||||||
\(46\) | 6.84029 | 1.00855 | ||||||||
\(47\) | −8.90316 | −1.29866 | −0.649329 | − | 0.760507i | \(-0.724950\pi\) | ||||
−0.649329 | + | 0.760507i | \(0.724950\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −6.53232 | −0.933189 | ||||||||
\(50\) | 0.458066 | 0.0647803 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | 0.480780 | 0.0666721 | ||||||||
\(53\) | 13.4888 | 1.85283 | 0.926413 | − | 0.376508i | \(-0.122875\pi\) | ||||
0.926413 | + | 0.376508i | \(0.122875\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 4.52526 | 0.610186 | ||||||||
\(56\) | −0.683869 | −0.0913858 | ||||||||
\(57\) | 0.134424 | 0.0178049 | ||||||||
\(58\) | 7.79476 | 1.02350 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | −2.33625 | −0.301609 | ||||||||
\(61\) | −11.1555 | −1.42831 | −0.714157 | − | 0.699986i | \(-0.753190\pi\) | ||||
−0.714157 | + | 0.699986i | \(0.753190\pi\) | |||||||
\(62\) | 2.80957 | 0.356816 | ||||||||
\(63\) | −0.683869 | −0.0861594 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.12322 | 0.139318 | ||||||||
\(66\) | −1.93698 | −0.238425 | ||||||||
\(67\) | 8.92916 | 1.09087 | 0.545435 | − | 0.838153i | \(-0.316364\pi\) | ||||
0.545435 | + | 0.838153i | \(0.316364\pi\) | |||||||
\(68\) | 1.00000 | 0.121268 | ||||||||
\(69\) | −6.84029 | −0.823474 | ||||||||
\(70\) | −1.59769 | −0.190960 | ||||||||
\(71\) | 5.82347 | 0.691119 | 0.345559 | − | 0.938397i | \(-0.387689\pi\) | ||||
0.345559 | + | 0.938397i | \(0.387689\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −2.58810 | −0.302915 | −0.151457 | − | 0.988464i | \(-0.548397\pi\) | ||||
−0.151457 | + | 0.988464i | \(0.548397\pi\) | |||||||
\(74\) | −0.709000 | −0.0824196 | ||||||||
\(75\) | −0.458066 | −0.0528929 | ||||||||
\(76\) | −0.134424 | −0.0154195 | ||||||||
\(77\) | −1.32464 | −0.150956 | ||||||||
\(78\) | −0.480780 | −0.0544376 | ||||||||
\(79\) | 12.0018 | 1.35030 | 0.675151 | − | 0.737679i | \(-0.264078\pi\) | ||||
0.675151 | + | 0.737679i | \(0.264078\pi\) | |||||||
\(80\) | 2.33625 | 0.261201 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.73813 | −0.302376 | ||||||||
\(83\) | −5.79142 | −0.635691 | −0.317846 | − | 0.948142i | \(-0.602959\pi\) | ||||
−0.317846 | + | 0.948142i | \(0.602959\pi\) | |||||||
\(84\) | 0.683869 | 0.0746162 | ||||||||
\(85\) | 2.33625 | 0.253402 | ||||||||
\(86\) | −6.44381 | −0.694854 | ||||||||
\(87\) | −7.79476 | −0.835686 | ||||||||
\(88\) | 1.93698 | 0.206482 | ||||||||
\(89\) | 13.5600 | 1.43736 | 0.718678 | − | 0.695343i | \(-0.244748\pi\) | ||||
0.718678 | + | 0.695343i | \(0.244748\pi\) | |||||||
\(90\) | 2.33625 | 0.246262 | ||||||||
\(91\) | −0.328790 | −0.0344666 | ||||||||
\(92\) | 6.84029 | 0.713150 | ||||||||
\(93\) | −2.80957 | −0.291339 | ||||||||
\(94\) | −8.90316 | −0.918290 | ||||||||
\(95\) | −0.314048 | −0.0322206 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 3.01760 | 0.306390 | 0.153195 | − | 0.988196i | \(-0.451044\pi\) | ||||
0.153195 | + | 0.988196i | \(0.451044\pi\) | |||||||
\(98\) | −6.53232 | −0.659864 | ||||||||
\(99\) | 1.93698 | 0.194673 | ||||||||
\(100\) | 0.458066 | 0.0458066 | ||||||||
\(101\) | 1.42039 | 0.141334 | 0.0706671 | − | 0.997500i | \(-0.477487\pi\) | ||||
0.0706671 | + | 0.997500i | \(0.477487\pi\) | |||||||
\(102\) | −1.00000 | −0.0990148 | ||||||||
\(103\) | −14.5482 | −1.43348 | −0.716740 | − | 0.697340i | \(-0.754367\pi\) | ||||
−0.716740 | + | 0.697340i | \(0.754367\pi\) | |||||||
\(104\) | 0.480780 | 0.0471443 | ||||||||
\(105\) | 1.59769 | 0.155918 | ||||||||
\(106\) | 13.4888 | 1.31015 | ||||||||
\(107\) | 6.16423 | 0.595919 | 0.297959 | − | 0.954579i | \(-0.403694\pi\) | ||||
0.297959 | + | 0.954579i | \(0.403694\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 12.1410 | 1.16290 | 0.581450 | − | 0.813582i | \(-0.302485\pi\) | ||||
0.581450 | + | 0.813582i | \(0.302485\pi\) | |||||||
\(110\) | 4.52526 | 0.431467 | ||||||||
\(111\) | 0.709000 | 0.0672953 | ||||||||
\(112\) | −0.683869 | −0.0646195 | ||||||||
\(113\) | 10.7865 | 1.01471 | 0.507353 | − | 0.861738i | \(-0.330624\pi\) | ||||
0.507353 | + | 0.861738i | \(0.330624\pi\) | |||||||
\(114\) | 0.134424 | 0.0125900 | ||||||||
\(115\) | 15.9806 | 1.49020 | ||||||||
\(116\) | 7.79476 | 0.723725 | ||||||||
\(117\) | 0.480780 | 0.0444481 | ||||||||
\(118\) | 1.00000 | 0.0920575 | ||||||||
\(119\) | −0.683869 | −0.0626902 | ||||||||
\(120\) | −2.33625 | −0.213270 | ||||||||
\(121\) | −7.24813 | −0.658921 | ||||||||
\(122\) | −11.1555 | −1.00997 | ||||||||
\(123\) | 2.73813 | 0.246889 | ||||||||
\(124\) | 2.80957 | 0.252307 | ||||||||
\(125\) | −10.6111 | −0.949085 | ||||||||
\(126\) | −0.683869 | −0.0609239 | ||||||||
\(127\) | −3.99253 | −0.354280 | −0.177140 | − | 0.984186i | \(-0.556685\pi\) | ||||
−0.177140 | + | 0.984186i | \(0.556685\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 6.44381 | 0.567346 | ||||||||
\(130\) | 1.12322 | 0.0985130 | ||||||||
\(131\) | −9.37785 | −0.819347 | −0.409673 | − | 0.912232i | \(-0.634357\pi\) | ||||
−0.409673 | + | 0.912232i | \(0.634357\pi\) | |||||||
\(132\) | −1.93698 | −0.168592 | ||||||||
\(133\) | 0.0919283 | 0.00797120 | ||||||||
\(134\) | 8.92916 | 0.771362 | ||||||||
\(135\) | −2.33625 | −0.201072 | ||||||||
\(136\) | 1.00000 | 0.0857493 | ||||||||
\(137\) | 17.3272 | 1.48036 | 0.740181 | − | 0.672407i | \(-0.234740\pi\) | ||||
0.740181 | + | 0.672407i | \(0.234740\pi\) | |||||||
\(138\) | −6.84029 | −0.582284 | ||||||||
\(139\) | −18.9097 | −1.60390 | −0.801949 | − | 0.597392i | \(-0.796204\pi\) | ||||
−0.801949 | + | 0.597392i | \(0.796204\pi\) | |||||||
\(140\) | −1.59769 | −0.135029 | ||||||||
\(141\) | 8.90316 | 0.749781 | ||||||||
\(142\) | 5.82347 | 0.488695 | ||||||||
\(143\) | 0.931258 | 0.0778757 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 18.2105 | 1.51230 | ||||||||
\(146\) | −2.58810 | −0.214193 | ||||||||
\(147\) | 6.53232 | 0.538777 | ||||||||
\(148\) | −0.709000 | −0.0582795 | ||||||||
\(149\) | 0.845331 | 0.0692522 | 0.0346261 | − | 0.999400i | \(-0.488976\pi\) | ||||
0.0346261 | + | 0.999400i | \(0.488976\pi\) | |||||||
\(150\) | −0.458066 | −0.0374009 | ||||||||
\(151\) | 20.7691 | 1.69017 | 0.845085 | − | 0.534633i | \(-0.179550\pi\) | ||||
0.845085 | + | 0.534633i | \(0.179550\pi\) | |||||||
\(152\) | −0.134424 | −0.0109032 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | −1.32464 | −0.106742 | ||||||||
\(155\) | 6.56386 | 0.527222 | ||||||||
\(156\) | −0.480780 | −0.0384932 | ||||||||
\(157\) | 4.90486 | 0.391451 | 0.195725 | − | 0.980659i | \(-0.437294\pi\) | ||||
0.195725 | + | 0.980659i | \(0.437294\pi\) | |||||||
\(158\) | 12.0018 | 0.954808 | ||||||||
\(159\) | −13.4888 | −1.06973 | ||||||||
\(160\) | 2.33625 | 0.184697 | ||||||||
\(161\) | −4.67786 | −0.368667 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −0.793255 | −0.0621325 | −0.0310663 | − | 0.999517i | \(-0.509890\pi\) | ||||
−0.0310663 | + | 0.999517i | \(0.509890\pi\) | |||||||
\(164\) | −2.73813 | −0.213812 | ||||||||
\(165\) | −4.52526 | −0.352291 | ||||||||
\(166\) | −5.79142 | −0.449502 | ||||||||
\(167\) | −1.71195 | −0.132475 | −0.0662374 | − | 0.997804i | \(-0.521099\pi\) | ||||
−0.0662374 | + | 0.997804i | \(0.521099\pi\) | |||||||
\(168\) | 0.683869 | 0.0527616 | ||||||||
\(169\) | −12.7689 | −0.982219 | ||||||||
\(170\) | 2.33625 | 0.179182 | ||||||||
\(171\) | −0.134424 | −0.0102797 | ||||||||
\(172\) | −6.44381 | −0.491336 | ||||||||
\(173\) | 23.6118 | 1.79517 | 0.897585 | − | 0.440842i | \(-0.145320\pi\) | ||||
0.897585 | + | 0.440842i | \(0.145320\pi\) | |||||||
\(174\) | −7.79476 | −0.590919 | ||||||||
\(175\) | −0.313257 | −0.0236800 | ||||||||
\(176\) | 1.93698 | 0.146005 | ||||||||
\(177\) | −1.00000 | −0.0751646 | ||||||||
\(178\) | 13.5600 | 1.01636 | ||||||||
\(179\) | −21.7180 | −1.62328 | −0.811640 | − | 0.584157i | \(-0.801425\pi\) | ||||
−0.811640 | + | 0.584157i | \(0.801425\pi\) | |||||||
\(180\) | 2.33625 | 0.174134 | ||||||||
\(181\) | 14.4439 | 1.07361 | 0.536805 | − | 0.843707i | \(-0.319631\pi\) | ||||
0.536805 | + | 0.843707i | \(0.319631\pi\) | |||||||
\(182\) | −0.328790 | −0.0243715 | ||||||||
\(183\) | 11.1555 | 0.824637 | ||||||||
\(184\) | 6.84029 | 0.504273 | ||||||||
\(185\) | −1.65640 | −0.121781 | ||||||||
\(186\) | −2.80957 | −0.206008 | ||||||||
\(187\) | 1.93698 | 0.141646 | ||||||||
\(188\) | −8.90316 | −0.649329 | ||||||||
\(189\) | 0.683869 | 0.0497441 | ||||||||
\(190\) | −0.314048 | −0.0227834 | ||||||||
\(191\) | 0.474135 | 0.0343072 | 0.0171536 | − | 0.999853i | \(-0.494540\pi\) | ||||
0.0171536 | + | 0.999853i | \(0.494540\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 7.01099 | 0.504662 | 0.252331 | − | 0.967641i | \(-0.418803\pi\) | ||||
0.252331 | + | 0.967641i | \(0.418803\pi\) | |||||||
\(194\) | 3.01760 | 0.216651 | ||||||||
\(195\) | −1.12322 | −0.0804356 | ||||||||
\(196\) | −6.53232 | −0.466595 | ||||||||
\(197\) | −1.46125 | −0.104110 | −0.0520550 | − | 0.998644i | \(-0.516577\pi\) | ||||
−0.0520550 | + | 0.998644i | \(0.516577\pi\) | |||||||
\(198\) | 1.93698 | 0.137655 | ||||||||
\(199\) | −12.2073 | −0.865354 | −0.432677 | − | 0.901549i | \(-0.642431\pi\) | ||||
−0.432677 | + | 0.901549i | \(0.642431\pi\) | |||||||
\(200\) | 0.458066 | 0.0323902 | ||||||||
\(201\) | −8.92916 | −0.629815 | ||||||||
\(202\) | 1.42039 | 0.0999384 | ||||||||
\(203\) | −5.33059 | −0.374134 | ||||||||
\(204\) | −1.00000 | −0.0700140 | ||||||||
\(205\) | −6.39696 | −0.446783 | ||||||||
\(206\) | −14.5482 | −1.01362 | ||||||||
\(207\) | 6.84029 | 0.475433 | ||||||||
\(208\) | 0.480780 | 0.0333361 | ||||||||
\(209\) | −0.260376 | −0.0180106 | ||||||||
\(210\) | 1.59769 | 0.110251 | ||||||||
\(211\) | −12.4282 | −0.855596 | −0.427798 | − | 0.903874i | \(-0.640710\pi\) | ||||
−0.427798 | + | 0.903874i | \(0.640710\pi\) | |||||||
\(212\) | 13.4888 | 0.926413 | ||||||||
\(213\) | −5.82347 | −0.399017 | ||||||||
\(214\) | 6.16423 | 0.421378 | ||||||||
\(215\) | −15.0544 | −1.02670 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −1.92138 | −0.130432 | ||||||||
\(218\) | 12.1410 | 0.822295 | ||||||||
\(219\) | 2.58810 | 0.174888 | ||||||||
\(220\) | 4.52526 | 0.305093 | ||||||||
\(221\) | 0.480780 | 0.0323407 | ||||||||
\(222\) | 0.709000 | 0.0475850 | ||||||||
\(223\) | 5.55345 | 0.371886 | 0.185943 | − | 0.982561i | \(-0.440466\pi\) | ||||
0.185943 | + | 0.982561i | \(0.440466\pi\) | |||||||
\(224\) | −0.683869 | −0.0456929 | ||||||||
\(225\) | 0.458066 | 0.0305377 | ||||||||
\(226\) | 10.7865 | 0.717506 | ||||||||
\(227\) | 12.3784 | 0.821580 | 0.410790 | − | 0.911730i | \(-0.365253\pi\) | ||||
0.410790 | + | 0.911730i | \(0.365253\pi\) | |||||||
\(228\) | 0.134424 | 0.00890244 | ||||||||
\(229\) | −2.70403 | −0.178687 | −0.0893435 | − | 0.996001i | \(-0.528477\pi\) | ||||
−0.0893435 | + | 0.996001i | \(0.528477\pi\) | |||||||
\(230\) | 15.9806 | 1.05373 | ||||||||
\(231\) | 1.32464 | 0.0871547 | ||||||||
\(232\) | 7.79476 | 0.511751 | ||||||||
\(233\) | −9.87308 | −0.646807 | −0.323404 | − | 0.946261i | \(-0.604827\pi\) | ||||
−0.323404 | + | 0.946261i | \(0.604827\pi\) | |||||||
\(234\) | 0.480780 | 0.0314295 | ||||||||
\(235\) | −20.8000 | −1.35684 | ||||||||
\(236\) | 1.00000 | 0.0650945 | ||||||||
\(237\) | −12.0018 | −0.779597 | ||||||||
\(238\) | −0.683869 | −0.0443286 | ||||||||
\(239\) | 3.27930 | 0.212120 | 0.106060 | − | 0.994360i | \(-0.466176\pi\) | ||||
0.106060 | + | 0.994360i | \(0.466176\pi\) | |||||||
\(240\) | −2.33625 | −0.150804 | ||||||||
\(241\) | −6.96482 | −0.448644 | −0.224322 | − | 0.974515i | \(-0.572017\pi\) | ||||
−0.224322 | + | 0.974515i | \(0.572017\pi\) | |||||||
\(242\) | −7.24813 | −0.465927 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −11.1555 | −0.714157 | ||||||||
\(245\) | −15.2611 | −0.974999 | ||||||||
\(246\) | 2.73813 | 0.174577 | ||||||||
\(247\) | −0.0646283 | −0.00411220 | ||||||||
\(248\) | 2.80957 | 0.178408 | ||||||||
\(249\) | 5.79142 | 0.367017 | ||||||||
\(250\) | −10.6111 | −0.671105 | ||||||||
\(251\) | −20.2352 | −1.27723 | −0.638616 | − | 0.769525i | \(-0.720493\pi\) | ||||
−0.638616 | + | 0.769525i | \(0.720493\pi\) | |||||||
\(252\) | −0.683869 | −0.0430797 | ||||||||
\(253\) | 13.2495 | 0.832987 | ||||||||
\(254\) | −3.99253 | −0.250514 | ||||||||
\(255\) | −2.33625 | −0.146302 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −0.910524 | −0.0567969 | −0.0283985 | − | 0.999597i | \(-0.509041\pi\) | ||||
−0.0283985 | + | 0.999597i | \(0.509041\pi\) | |||||||
\(258\) | 6.44381 | 0.401174 | ||||||||
\(259\) | 0.484863 | 0.0301279 | ||||||||
\(260\) | 1.12322 | 0.0696592 | ||||||||
\(261\) | 7.79476 | 0.482483 | ||||||||
\(262\) | −9.37785 | −0.579365 | ||||||||
\(263\) | 15.6632 | 0.965834 | 0.482917 | − | 0.875666i | \(-0.339577\pi\) | ||||
0.482917 | + | 0.875666i | \(0.339577\pi\) | |||||||
\(264\) | −1.93698 | −0.119213 | ||||||||
\(265\) | 31.5132 | 1.93584 | ||||||||
\(266\) | 0.0919283 | 0.00563649 | ||||||||
\(267\) | −13.5600 | −0.829858 | ||||||||
\(268\) | 8.92916 | 0.545435 | ||||||||
\(269\) | 15.6658 | 0.955158 | 0.477579 | − | 0.878589i | \(-0.341514\pi\) | ||||
0.477579 | + | 0.878589i | \(0.341514\pi\) | |||||||
\(270\) | −2.33625 | −0.142180 | ||||||||
\(271\) | 0.951602 | 0.0578057 | 0.0289028 | − | 0.999582i | \(-0.490799\pi\) | ||||
0.0289028 | + | 0.999582i | \(0.490799\pi\) | |||||||
\(272\) | 1.00000 | 0.0606339 | ||||||||
\(273\) | 0.328790 | 0.0198993 | ||||||||
\(274\) | 17.3272 | 1.04677 | ||||||||
\(275\) | 0.887263 | 0.0535040 | ||||||||
\(276\) | −6.84029 | −0.411737 | ||||||||
\(277\) | −8.23112 | −0.494560 | −0.247280 | − | 0.968944i | \(-0.579537\pi\) | ||||
−0.247280 | + | 0.968944i | \(0.579537\pi\) | |||||||
\(278\) | −18.9097 | −1.13413 | ||||||||
\(279\) | 2.80957 | 0.168205 | ||||||||
\(280\) | −1.59769 | −0.0954802 | ||||||||
\(281\) | 12.9741 | 0.773972 | 0.386986 | − | 0.922086i | \(-0.373516\pi\) | ||||
0.386986 | + | 0.922086i | \(0.373516\pi\) | |||||||
\(282\) | 8.90316 | 0.530175 | ||||||||
\(283\) | −3.83895 | −0.228202 | −0.114101 | − | 0.993469i | \(-0.536399\pi\) | ||||
−0.114101 | + | 0.993469i | \(0.536399\pi\) | |||||||
\(284\) | 5.82347 | 0.345559 | ||||||||
\(285\) | 0.314048 | 0.0186026 | ||||||||
\(286\) | 0.931258 | 0.0550665 | ||||||||
\(287\) | 1.87252 | 0.110532 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 18.2105 | 1.06936 | ||||||||
\(291\) | −3.01760 | −0.176895 | ||||||||
\(292\) | −2.58810 | −0.151457 | ||||||||
\(293\) | 20.7091 | 1.20984 | 0.604920 | − | 0.796286i | \(-0.293205\pi\) | ||||
0.604920 | + | 0.796286i | \(0.293205\pi\) | |||||||
\(294\) | 6.53232 | 0.380973 | ||||||||
\(295\) | 2.33625 | 0.136022 | ||||||||
\(296\) | −0.709000 | −0.0412098 | ||||||||
\(297\) | −1.93698 | −0.112395 | ||||||||
\(298\) | 0.845331 | 0.0489687 | ||||||||
\(299\) | 3.28867 | 0.190189 | ||||||||
\(300\) | −0.458066 | −0.0264465 | ||||||||
\(301\) | 4.40672 | 0.253999 | ||||||||
\(302\) | 20.7691 | 1.19513 | ||||||||
\(303\) | −1.42039 | −0.0815993 | ||||||||
\(304\) | −0.134424 | −0.00770974 | ||||||||
\(305\) | −26.0620 | −1.49231 | ||||||||
\(306\) | 1.00000 | 0.0571662 | ||||||||
\(307\) | 6.93896 | 0.396027 | 0.198014 | − | 0.980199i | \(-0.436551\pi\) | ||||
0.198014 | + | 0.980199i | \(0.436551\pi\) | |||||||
\(308\) | −1.32464 | −0.0754782 | ||||||||
\(309\) | 14.5482 | 0.827621 | ||||||||
\(310\) | 6.56386 | 0.372802 | ||||||||
\(311\) | 3.79474 | 0.215180 | 0.107590 | − | 0.994195i | \(-0.465687\pi\) | ||||
0.107590 | + | 0.994195i | \(0.465687\pi\) | |||||||
\(312\) | −0.480780 | −0.0272188 | ||||||||
\(313\) | −5.69740 | −0.322036 | −0.161018 | − | 0.986951i | \(-0.551478\pi\) | ||||
−0.161018 | + | 0.986951i | \(0.551478\pi\) | |||||||
\(314\) | 4.90486 | 0.276797 | ||||||||
\(315\) | −1.59769 | −0.0900196 | ||||||||
\(316\) | 12.0018 | 0.675151 | ||||||||
\(317\) | −19.0607 | −1.07056 | −0.535278 | − | 0.844676i | \(-0.679793\pi\) | ||||
−0.535278 | + | 0.844676i | \(0.679793\pi\) | |||||||
\(318\) | −13.4888 | −0.756413 | ||||||||
\(319\) | 15.0983 | 0.845340 | ||||||||
\(320\) | 2.33625 | 0.130600 | ||||||||
\(321\) | −6.16423 | −0.344054 | ||||||||
\(322\) | −4.67786 | −0.260687 | ||||||||
\(323\) | −0.134424 | −0.00747955 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0.220229 | 0.0122161 | ||||||||
\(326\) | −0.793255 | −0.0439343 | ||||||||
\(327\) | −12.1410 | −0.671401 | ||||||||
\(328\) | −2.73813 | −0.151188 | ||||||||
\(329\) | 6.08859 | 0.335675 | ||||||||
\(330\) | −4.52526 | −0.249107 | ||||||||
\(331\) | 7.10042 | 0.390274 | 0.195137 | − | 0.980776i | \(-0.437485\pi\) | ||||
0.195137 | + | 0.980776i | \(0.437485\pi\) | |||||||
\(332\) | −5.79142 | −0.317846 | ||||||||
\(333\) | −0.709000 | −0.0388530 | ||||||||
\(334\) | −1.71195 | −0.0936738 | ||||||||
\(335\) | 20.8608 | 1.13974 | ||||||||
\(336\) | 0.683869 | 0.0373081 | ||||||||
\(337\) | −2.63257 | −0.143405 | −0.0717025 | − | 0.997426i | \(-0.522843\pi\) | ||||
−0.0717025 | + | 0.997426i | \(0.522843\pi\) | |||||||
\(338\) | −12.7689 | −0.694534 | ||||||||
\(339\) | −10.7865 | −0.585841 | ||||||||
\(340\) | 2.33625 | 0.126701 | ||||||||
\(341\) | 5.44207 | 0.294704 | ||||||||
\(342\) | −0.134424 | −0.00726881 | ||||||||
\(343\) | 9.25433 | 0.499687 | ||||||||
\(344\) | −6.44381 | −0.347427 | ||||||||
\(345\) | −15.9806 | −0.860368 | ||||||||
\(346\) | 23.6118 | 1.26938 | ||||||||
\(347\) | −15.7899 | −0.847645 | −0.423823 | − | 0.905745i | \(-0.639312\pi\) | ||||
−0.423823 | + | 0.905745i | \(0.639312\pi\) | |||||||
\(348\) | −7.79476 | −0.417843 | ||||||||
\(349\) | −11.5109 | −0.616164 | −0.308082 | − | 0.951360i | \(-0.599687\pi\) | ||||
−0.308082 | + | 0.951360i | \(0.599687\pi\) | |||||||
\(350\) | −0.313257 | −0.0167443 | ||||||||
\(351\) | −0.480780 | −0.0256621 | ||||||||
\(352\) | 1.93698 | 0.103241 | ||||||||
\(353\) | 31.0633 | 1.65333 | 0.826666 | − | 0.562694i | \(-0.190235\pi\) | ||||
0.826666 | + | 0.562694i | \(0.190235\pi\) | |||||||
\(354\) | −1.00000 | −0.0531494 | ||||||||
\(355\) | 13.6051 | 0.722083 | ||||||||
\(356\) | 13.5600 | 0.718678 | ||||||||
\(357\) | 0.683869 | 0.0361942 | ||||||||
\(358\) | −21.7180 | −1.14783 | ||||||||
\(359\) | 23.5865 | 1.24485 | 0.622425 | − | 0.782680i | \(-0.286148\pi\) | ||||
0.622425 | + | 0.782680i | \(0.286148\pi\) | |||||||
\(360\) | 2.33625 | 0.123131 | ||||||||
\(361\) | −18.9819 | −0.999049 | ||||||||
\(362\) | 14.4439 | 0.759156 | ||||||||
\(363\) | 7.24813 | 0.380428 | ||||||||
\(364\) | −0.328790 | −0.0172333 | ||||||||
\(365\) | −6.04646 | −0.316486 | ||||||||
\(366\) | 11.1555 | 0.583107 | ||||||||
\(367\) | −7.13232 | −0.372304 | −0.186152 | − | 0.982521i | \(-0.559602\pi\) | ||||
−0.186152 | + | 0.982521i | \(0.559602\pi\) | |||||||
\(368\) | 6.84029 | 0.356575 | ||||||||
\(369\) | −2.73813 | −0.142541 | ||||||||
\(370\) | −1.65640 | −0.0861122 | ||||||||
\(371\) | −9.22456 | −0.478915 | ||||||||
\(372\) | −2.80957 | −0.145669 | ||||||||
\(373\) | 28.1071 | 1.45533 | 0.727665 | − | 0.685933i | \(-0.240606\pi\) | ||||
0.727665 | + | 0.685933i | \(0.240606\pi\) | |||||||
\(374\) | 1.93698 | 0.100159 | ||||||||
\(375\) | 10.6111 | 0.547955 | ||||||||
\(376\) | −8.90316 | −0.459145 | ||||||||
\(377\) | 3.74756 | 0.193009 | ||||||||
\(378\) | 0.683869 | 0.0351744 | ||||||||
\(379\) | −3.21621 | −0.165206 | −0.0826028 | − | 0.996583i | \(-0.526323\pi\) | ||||
−0.0826028 | + | 0.996583i | \(0.526323\pi\) | |||||||
\(380\) | −0.314048 | −0.0161103 | ||||||||
\(381\) | 3.99253 | 0.204544 | ||||||||
\(382\) | 0.474135 | 0.0242589 | ||||||||
\(383\) | −17.9314 | −0.916252 | −0.458126 | − | 0.888887i | \(-0.651479\pi\) | ||||
−0.458126 | + | 0.888887i | \(0.651479\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −3.09468 | −0.157720 | ||||||||
\(386\) | 7.01099 | 0.356850 | ||||||||
\(387\) | −6.44381 | −0.327557 | ||||||||
\(388\) | 3.01760 | 0.153195 | ||||||||
\(389\) | 24.8722 | 1.26107 | 0.630536 | − | 0.776160i | \(-0.282835\pi\) | ||||
0.630536 | + | 0.776160i | \(0.282835\pi\) | |||||||
\(390\) | −1.12322 | −0.0568765 | ||||||||
\(391\) | 6.84029 | 0.345928 | ||||||||
\(392\) | −6.53232 | −0.329932 | ||||||||
\(393\) | 9.37785 | 0.473050 | ||||||||
\(394\) | −1.46125 | −0.0736169 | ||||||||
\(395\) | 28.0391 | 1.41080 | ||||||||
\(396\) | 1.93698 | 0.0973367 | ||||||||
\(397\) | 22.0814 | 1.10823 | 0.554116 | − | 0.832439i | \(-0.313056\pi\) | ||||
0.554116 | + | 0.832439i | \(0.313056\pi\) | |||||||
\(398\) | −12.2073 | −0.611898 | ||||||||
\(399\) | −0.0919283 | −0.00460217 | ||||||||
\(400\) | 0.458066 | 0.0229033 | ||||||||
\(401\) | −20.6434 | −1.03088 | −0.515441 | − | 0.856925i | \(-0.672372\pi\) | ||||
−0.515441 | + | 0.856925i | \(0.672372\pi\) | |||||||
\(402\) | −8.92916 | −0.445346 | ||||||||
\(403\) | 1.35078 | 0.0672873 | ||||||||
\(404\) | 1.42039 | 0.0706671 | ||||||||
\(405\) | 2.33625 | 0.116089 | ||||||||
\(406\) | −5.33059 | −0.264553 | ||||||||
\(407\) | −1.37332 | −0.0680727 | ||||||||
\(408\) | −1.00000 | −0.0495074 | ||||||||
\(409\) | 31.1858 | 1.54204 | 0.771020 | − | 0.636811i | \(-0.219747\pi\) | ||||
0.771020 | + | 0.636811i | \(0.219747\pi\) | |||||||
\(410\) | −6.39696 | −0.315923 | ||||||||
\(411\) | −17.3272 | −0.854688 | ||||||||
\(412\) | −14.5482 | −0.716740 | ||||||||
\(413\) | −0.683869 | −0.0336510 | ||||||||
\(414\) | 6.84029 | 0.336182 | ||||||||
\(415\) | −13.5302 | −0.664172 | ||||||||
\(416\) | 0.480780 | 0.0235722 | ||||||||
\(417\) | 18.9097 | 0.926011 | ||||||||
\(418\) | −0.260376 | −0.0127354 | ||||||||
\(419\) | 32.5126 | 1.58835 | 0.794173 | − | 0.607691i | \(-0.207904\pi\) | ||||
0.794173 | + | 0.607691i | \(0.207904\pi\) | |||||||
\(420\) | 1.59769 | 0.0779592 | ||||||||
\(421\) | 10.5978 | 0.516505 | 0.258253 | − | 0.966077i | \(-0.416853\pi\) | ||||
0.258253 | + | 0.966077i | \(0.416853\pi\) | |||||||
\(422\) | −12.4282 | −0.604998 | ||||||||
\(423\) | −8.90316 | −0.432886 | ||||||||
\(424\) | 13.4888 | 0.655073 | ||||||||
\(425\) | 0.458066 | 0.0222195 | ||||||||
\(426\) | −5.82347 | −0.282148 | ||||||||
\(427\) | 7.62889 | 0.369188 | ||||||||
\(428\) | 6.16423 | 0.297959 | ||||||||
\(429\) | −0.931258 | −0.0449616 | ||||||||
\(430\) | −15.0544 | −0.725985 | ||||||||
\(431\) | 10.0321 | 0.483227 | 0.241614 | − | 0.970373i | \(-0.422323\pi\) | ||||
0.241614 | + | 0.970373i | \(0.422323\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −18.5634 | −0.892099 | −0.446050 | − | 0.895008i | \(-0.647170\pi\) | ||||
−0.446050 | + | 0.895008i | \(0.647170\pi\) | |||||||
\(434\) | −1.92138 | −0.0922290 | ||||||||
\(435\) | −18.2105 | −0.873127 | ||||||||
\(436\) | 12.1410 | 0.581450 | ||||||||
\(437\) | −0.919499 | −0.0439856 | ||||||||
\(438\) | 2.58810 | 0.123664 | ||||||||
\(439\) | −24.9087 | −1.18883 | −0.594415 | − | 0.804159i | \(-0.702616\pi\) | ||||
−0.594415 | + | 0.804159i | \(0.702616\pi\) | |||||||
\(440\) | 4.52526 | 0.215733 | ||||||||
\(441\) | −6.53232 | −0.311063 | ||||||||
\(442\) | 0.480780 | 0.0228684 | ||||||||
\(443\) | −10.3404 | −0.491285 | −0.245642 | − | 0.969361i | \(-0.578999\pi\) | ||||
−0.245642 | + | 0.969361i | \(0.578999\pi\) | |||||||
\(444\) | 0.709000 | 0.0336477 | ||||||||
\(445\) | 31.6795 | 1.50175 | ||||||||
\(446\) | 5.55345 | 0.262963 | ||||||||
\(447\) | −0.845331 | −0.0399828 | ||||||||
\(448\) | −0.683869 | −0.0323098 | ||||||||
\(449\) | −22.0314 | −1.03973 | −0.519864 | − | 0.854249i | \(-0.674017\pi\) | ||||
−0.519864 | + | 0.854249i | \(0.674017\pi\) | |||||||
\(450\) | 0.458066 | 0.0215934 | ||||||||
\(451\) | −5.30369 | −0.249741 | ||||||||
\(452\) | 10.7865 | 0.507353 | ||||||||
\(453\) | −20.7691 | −0.975820 | ||||||||
\(454\) | 12.3784 | 0.580945 | ||||||||
\(455\) | −0.768136 | −0.0360108 | ||||||||
\(456\) | 0.134424 | 0.00629498 | ||||||||
\(457\) | 21.8148 | 1.02045 | 0.510227 | − | 0.860040i | \(-0.329561\pi\) | ||||
0.510227 | + | 0.860040i | \(0.329561\pi\) | |||||||
\(458\) | −2.70403 | −0.126351 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | 15.9806 | 0.745101 | ||||||||
\(461\) | −23.1270 | −1.07713 | −0.538566 | − | 0.842583i | \(-0.681034\pi\) | ||||
−0.538566 | + | 0.842583i | \(0.681034\pi\) | |||||||
\(462\) | 1.32464 | 0.0616277 | ||||||||
\(463\) | −2.30556 | −0.107149 | −0.0535743 | − | 0.998564i | \(-0.517061\pi\) | ||||
−0.0535743 | + | 0.998564i | \(0.517061\pi\) | |||||||
\(464\) | 7.79476 | 0.361863 | ||||||||
\(465\) | −6.56386 | −0.304392 | ||||||||
\(466\) | −9.87308 | −0.457362 | ||||||||
\(467\) | 18.8292 | 0.871310 | 0.435655 | − | 0.900114i | \(-0.356517\pi\) | ||||
0.435655 | + | 0.900114i | \(0.356517\pi\) | |||||||
\(468\) | 0.480780 | 0.0222240 | ||||||||
\(469\) | −6.10638 | −0.281966 | ||||||||
\(470\) | −20.8000 | −0.959433 | ||||||||
\(471\) | −4.90486 | −0.226004 | ||||||||
\(472\) | 1.00000 | 0.0460287 | ||||||||
\(473\) | −12.4815 | −0.573900 | ||||||||
\(474\) | −12.0018 | −0.551259 | ||||||||
\(475\) | −0.0615750 | −0.00282526 | ||||||||
\(476\) | −0.683869 | −0.0313451 | ||||||||
\(477\) | 13.4888 | 0.617609 | ||||||||
\(478\) | 3.27930 | 0.149992 | ||||||||
\(479\) | 40.4771 | 1.84945 | 0.924724 | − | 0.380639i | \(-0.124296\pi\) | ||||
0.924724 | + | 0.380639i | \(0.124296\pi\) | |||||||
\(480\) | −2.33625 | −0.106635 | ||||||||
\(481\) | −0.340873 | −0.0155425 | ||||||||
\(482\) | −6.96482 | −0.317239 | ||||||||
\(483\) | 4.67786 | 0.212850 | ||||||||
\(484\) | −7.24813 | −0.329460 | ||||||||
\(485\) | 7.04986 | 0.320118 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −11.7648 | −0.533112 | −0.266556 | − | 0.963819i | \(-0.585886\pi\) | ||||
−0.266556 | + | 0.963819i | \(0.585886\pi\) | |||||||
\(488\) | −11.1555 | −0.504985 | ||||||||
\(489\) | 0.793255 | 0.0358722 | ||||||||
\(490\) | −15.2611 | −0.689428 | ||||||||
\(491\) | −26.3139 | −1.18753 | −0.593765 | − | 0.804638i | \(-0.702359\pi\) | ||||
−0.593765 | + | 0.804638i | \(0.702359\pi\) | |||||||
\(492\) | 2.73813 | 0.123444 | ||||||||
\(493\) | 7.79476 | 0.351058 | ||||||||
\(494\) | −0.0646283 | −0.00290776 | ||||||||
\(495\) | 4.52526 | 0.203395 | ||||||||
\(496\) | 2.80957 | 0.126153 | ||||||||
\(497\) | −3.98249 | −0.178639 | ||||||||
\(498\) | 5.79142 | 0.259520 | ||||||||
\(499\) | −3.10849 | −0.139155 | −0.0695775 | − | 0.997577i | \(-0.522165\pi\) | ||||
−0.0695775 | + | 0.997577i | \(0.522165\pi\) | |||||||
\(500\) | −10.6111 | −0.474543 | ||||||||
\(501\) | 1.71195 | 0.0764843 | ||||||||
\(502\) | −20.2352 | −0.903140 | ||||||||
\(503\) | 1.13272 | 0.0505055 | 0.0252528 | − | 0.999681i | \(-0.491961\pi\) | ||||
0.0252528 | + | 0.999681i | \(0.491961\pi\) | |||||||
\(504\) | −0.683869 | −0.0304619 | ||||||||
\(505\) | 3.31839 | 0.147666 | ||||||||
\(506\) | 13.2495 | 0.589011 | ||||||||
\(507\) | 12.7689 | 0.567085 | ||||||||
\(508\) | −3.99253 | −0.177140 | ||||||||
\(509\) | 11.7618 | 0.521334 | 0.260667 | − | 0.965429i | \(-0.416058\pi\) | ||||
0.260667 | + | 0.965429i | \(0.416058\pi\) | |||||||
\(510\) | −2.33625 | −0.103451 | ||||||||
\(511\) | 1.76992 | 0.0782968 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0.134424 | 0.00593496 | ||||||||
\(514\) | −0.910524 | −0.0401615 | ||||||||
\(515\) | −33.9883 | −1.49771 | ||||||||
\(516\) | 6.44381 | 0.283673 | ||||||||
\(517\) | −17.2452 | −0.758443 | ||||||||
\(518\) | 0.484863 | 0.0213037 | ||||||||
\(519\) | −23.6118 | −1.03644 | ||||||||
\(520\) | 1.12322 | 0.0492565 | ||||||||
\(521\) | −15.5802 | −0.682580 | −0.341290 | − | 0.939958i | \(-0.610864\pi\) | ||||
−0.341290 | + | 0.939958i | \(0.610864\pi\) | |||||||
\(522\) | 7.79476 | 0.341167 | ||||||||
\(523\) | −39.8744 | −1.74359 | −0.871793 | − | 0.489875i | \(-0.837043\pi\) | ||||
−0.871793 | + | 0.489875i | \(0.837043\pi\) | |||||||
\(524\) | −9.37785 | −0.409673 | ||||||||
\(525\) | 0.313257 | 0.0136717 | ||||||||
\(526\) | 15.6632 | 0.682948 | ||||||||
\(527\) | 2.80957 | 0.122387 | ||||||||
\(528\) | −1.93698 | −0.0842960 | ||||||||
\(529\) | 23.7896 | 1.03433 | ||||||||
\(530\) | 31.5132 | 1.36884 | ||||||||
\(531\) | 1.00000 | 0.0433963 | ||||||||
\(532\) | 0.0919283 | 0.00398560 | ||||||||
\(533\) | −1.31644 | −0.0570212 | ||||||||
\(534\) | −13.5600 | −0.586798 | ||||||||
\(535\) | 14.4012 | 0.622618 | ||||||||
\(536\) | 8.92916 | 0.385681 | ||||||||
\(537\) | 21.7180 | 0.937202 | ||||||||
\(538\) | 15.6658 | 0.675399 | ||||||||
\(539\) | −12.6530 | −0.545001 | ||||||||
\(540\) | −2.33625 | −0.100536 | ||||||||
\(541\) | 27.4040 | 1.17819 | 0.589094 | − | 0.808064i | \(-0.299485\pi\) | ||||
0.589094 | + | 0.808064i | \(0.299485\pi\) | |||||||
\(542\) | 0.951602 | 0.0408748 | ||||||||
\(543\) | −14.4439 | −0.619849 | ||||||||
\(544\) | 1.00000 | 0.0428746 | ||||||||
\(545\) | 28.3645 | 1.21500 | ||||||||
\(546\) | 0.328790 | 0.0140709 | ||||||||
\(547\) | −25.6204 | −1.09545 | −0.547724 | − | 0.836659i | \(-0.684505\pi\) | ||||
−0.547724 | + | 0.836659i | \(0.684505\pi\) | |||||||
\(548\) | 17.3272 | 0.740181 | ||||||||
\(549\) | −11.1555 | −0.476105 | ||||||||
\(550\) | 0.887263 | 0.0378330 | ||||||||
\(551\) | −1.04780 | −0.0446379 | ||||||||
\(552\) | −6.84029 | −0.291142 | ||||||||
\(553\) | −8.20762 | −0.349024 | ||||||||
\(554\) | −8.23112 | −0.349707 | ||||||||
\(555\) | 1.65640 | 0.0703103 | ||||||||
\(556\) | −18.9097 | −0.801949 | ||||||||
\(557\) | −10.5851 | −0.448503 | −0.224252 | − | 0.974531i | \(-0.571994\pi\) | ||||
−0.224252 | + | 0.974531i | \(0.571994\pi\) | |||||||
\(558\) | 2.80957 | 0.118939 | ||||||||
\(559\) | −3.09805 | −0.131034 | ||||||||
\(560\) | −1.59769 | −0.0675147 | ||||||||
\(561\) | −1.93698 | −0.0817792 | ||||||||
\(562\) | 12.9741 | 0.547281 | ||||||||
\(563\) | −18.0402 | −0.760303 | −0.380151 | − | 0.924924i | \(-0.624128\pi\) | ||||
−0.380151 | + | 0.924924i | \(0.624128\pi\) | |||||||
\(564\) | 8.90316 | 0.374891 | ||||||||
\(565\) | 25.1999 | 1.06017 | ||||||||
\(566\) | −3.83895 | −0.161363 | ||||||||
\(567\) | −0.683869 | −0.0287198 | ||||||||
\(568\) | 5.82347 | 0.244347 | ||||||||
\(569\) | −10.5867 | −0.443820 | −0.221910 | − | 0.975067i | \(-0.571229\pi\) | ||||
−0.221910 | + | 0.975067i | \(0.571229\pi\) | |||||||
\(570\) | 0.314048 | 0.0131540 | ||||||||
\(571\) | 8.89154 | 0.372099 | 0.186050 | − | 0.982540i | \(-0.440431\pi\) | ||||
0.186050 | + | 0.982540i | \(0.440431\pi\) | |||||||
\(572\) | 0.931258 | 0.0389379 | ||||||||
\(573\) | −0.474135 | −0.0198073 | ||||||||
\(574\) | 1.87252 | 0.0781576 | ||||||||
\(575\) | 3.13330 | 0.130668 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 34.1238 | 1.42059 | 0.710296 | − | 0.703903i | \(-0.248561\pi\) | ||||
0.710296 | + | 0.703903i | \(0.248561\pi\) | |||||||
\(578\) | 1.00000 | 0.0415945 | ||||||||
\(579\) | −7.01099 | −0.291367 | ||||||||
\(580\) | 18.2105 | 0.756150 | ||||||||
\(581\) | 3.96057 | 0.164312 | ||||||||
\(582\) | −3.01760 | −0.125083 | ||||||||
\(583\) | 26.1274 | 1.08209 | ||||||||
\(584\) | −2.58810 | −0.107097 | ||||||||
\(585\) | 1.12322 | 0.0464395 | ||||||||
\(586\) | 20.7091 | 0.855486 | ||||||||
\(587\) | −11.2691 | −0.465125 | −0.232563 | − | 0.972581i | \(-0.574711\pi\) | ||||
−0.232563 | + | 0.972581i | \(0.574711\pi\) | |||||||
\(588\) | 6.53232 | 0.269388 | ||||||||
\(589\) | −0.377673 | −0.0155618 | ||||||||
\(590\) | 2.33625 | 0.0961819 | ||||||||
\(591\) | 1.46125 | 0.0601079 | ||||||||
\(592\) | −0.709000 | −0.0291397 | ||||||||
\(593\) | 10.9643 | 0.450252 | 0.225126 | − | 0.974330i | \(-0.427721\pi\) | ||||
0.225126 | + | 0.974330i | \(0.427721\pi\) | |||||||
\(594\) | −1.93698 | −0.0794751 | ||||||||
\(595\) | −1.59769 | −0.0654989 | ||||||||
\(596\) | 0.845331 | 0.0346261 | ||||||||
\(597\) | 12.2073 | 0.499613 | ||||||||
\(598\) | 3.28867 | 0.134484 | ||||||||
\(599\) | −40.7716 | −1.66588 | −0.832941 | − | 0.553362i | \(-0.813345\pi\) | ||||
−0.832941 | + | 0.553362i | \(0.813345\pi\) | |||||||
\(600\) | −0.458066 | −0.0187005 | ||||||||
\(601\) | −26.7629 | −1.09168 | −0.545841 | − | 0.837889i | \(-0.683790\pi\) | ||||
−0.545841 | + | 0.837889i | \(0.683790\pi\) | |||||||
\(602\) | 4.40672 | 0.179605 | ||||||||
\(603\) | 8.92916 | 0.363624 | ||||||||
\(604\) | 20.7691 | 0.845085 | ||||||||
\(605\) | −16.9334 | −0.688442 | ||||||||
\(606\) | −1.42039 | −0.0576994 | ||||||||
\(607\) | −21.8331 | −0.886176 | −0.443088 | − | 0.896478i | \(-0.646117\pi\) | ||||
−0.443088 | + | 0.896478i | \(0.646117\pi\) | |||||||
\(608\) | −0.134424 | −0.00545161 | ||||||||
\(609\) | 5.33059 | 0.216007 | ||||||||
\(610\) | −26.0620 | −1.05522 | ||||||||
\(611\) | −4.28046 | −0.173169 | ||||||||
\(612\) | 1.00000 | 0.0404226 | ||||||||
\(613\) | 21.7308 | 0.877698 | 0.438849 | − | 0.898561i | \(-0.355386\pi\) | ||||
0.438849 | + | 0.898561i | \(0.355386\pi\) | |||||||
\(614\) | 6.93896 | 0.280034 | ||||||||
\(615\) | 6.39696 | 0.257950 | ||||||||
\(616\) | −1.32464 | −0.0533712 | ||||||||
\(617\) | 4.18038 | 0.168296 | 0.0841478 | − | 0.996453i | \(-0.473183\pi\) | ||||
0.0841478 | + | 0.996453i | \(0.473183\pi\) | |||||||
\(618\) | 14.5482 | 0.585216 | ||||||||
\(619\) | −19.2345 | −0.773100 | −0.386550 | − | 0.922268i | \(-0.626333\pi\) | ||||
−0.386550 | + | 0.922268i | \(0.626333\pi\) | |||||||
\(620\) | 6.56386 | 0.263611 | ||||||||
\(621\) | −6.84029 | −0.274491 | ||||||||
\(622\) | 3.79474 | 0.152155 | ||||||||
\(623\) | −9.27325 | −0.371525 | ||||||||
\(624\) | −0.480780 | −0.0192466 | ||||||||
\(625\) | −27.0805 | −1.08322 | ||||||||
\(626\) | −5.69740 | −0.227714 | ||||||||
\(627\) | 0.260376 | 0.0103984 | ||||||||
\(628\) | 4.90486 | 0.195725 | ||||||||
\(629\) | −0.709000 | −0.0282697 | ||||||||
\(630\) | −1.59769 | −0.0636534 | ||||||||
\(631\) | −18.9098 | −0.752785 | −0.376393 | − | 0.926460i | \(-0.622836\pi\) | ||||
−0.376393 | + | 0.926460i | \(0.622836\pi\) | |||||||
\(632\) | 12.0018 | 0.477404 | ||||||||
\(633\) | 12.4282 | 0.493978 | ||||||||
\(634\) | −19.0607 | −0.756998 | ||||||||
\(635\) | −9.32756 | −0.370153 | ||||||||
\(636\) | −13.4888 | −0.534865 | ||||||||
\(637\) | −3.14061 | −0.124435 | ||||||||
\(638\) | 15.0983 | 0.597746 | ||||||||
\(639\) | 5.82347 | 0.230373 | ||||||||
\(640\) | 2.33625 | 0.0923484 | ||||||||
\(641\) | −30.7190 | −1.21333 | −0.606664 | − | 0.794958i | \(-0.707493\pi\) | ||||
−0.606664 | + | 0.794958i | \(0.707493\pi\) | |||||||
\(642\) | −6.16423 | −0.243283 | ||||||||
\(643\) | −38.4980 | −1.51821 | −0.759106 | − | 0.650967i | \(-0.774364\pi\) | ||||
−0.759106 | + | 0.650967i | \(0.774364\pi\) | |||||||
\(644\) | −4.67786 | −0.184334 | ||||||||
\(645\) | 15.0544 | 0.592765 | ||||||||
\(646\) | −0.134424 | −0.00528884 | ||||||||
\(647\) | −42.8012 | −1.68269 | −0.841345 | − | 0.540498i | \(-0.818236\pi\) | ||||
−0.841345 | + | 0.540498i | \(0.818236\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 1.93698 | 0.0760329 | ||||||||
\(650\) | 0.220229 | 0.00863808 | ||||||||
\(651\) | 1.92138 | 0.0753047 | ||||||||
\(652\) | −0.793255 | −0.0310663 | ||||||||
\(653\) | −45.9452 | −1.79797 | −0.898987 | − | 0.437976i | \(-0.855695\pi\) | ||||
−0.898987 | + | 0.437976i | \(0.855695\pi\) | |||||||
\(654\) | −12.1410 | −0.474752 | ||||||||
\(655\) | −21.9090 | −0.856056 | ||||||||
\(656\) | −2.73813 | −0.106906 | ||||||||
\(657\) | −2.58810 | −0.100972 | ||||||||
\(658\) | 6.08859 | 0.237358 | ||||||||
\(659\) | −13.1101 | −0.510696 | −0.255348 | − | 0.966849i | \(-0.582190\pi\) | ||||
−0.255348 | + | 0.966849i | \(0.582190\pi\) | |||||||
\(660\) | −4.52526 | −0.176145 | ||||||||
\(661\) | −16.0578 | −0.624576 | −0.312288 | − | 0.949987i | \(-0.601095\pi\) | ||||
−0.312288 | + | 0.949987i | \(0.601095\pi\) | |||||||
\(662\) | 7.10042 | 0.275966 | ||||||||
\(663\) | −0.480780 | −0.0186719 | ||||||||
\(664\) | −5.79142 | −0.224751 | ||||||||
\(665\) | 0.214768 | 0.00832833 | ||||||||
\(666\) | −0.709000 | −0.0274732 | ||||||||
\(667\) | 53.3184 | 2.06450 | ||||||||
\(668\) | −1.71195 | −0.0662374 | ||||||||
\(669\) | −5.55345 | −0.214709 | ||||||||
\(670\) | 20.8608 | 0.805921 | ||||||||
\(671\) | −21.6079 | −0.834164 | ||||||||
\(672\) | 0.683869 | 0.0263808 | ||||||||
\(673\) | −14.6881 | −0.566184 | −0.283092 | − | 0.959093i | \(-0.591360\pi\) | ||||
−0.283092 | + | 0.959093i | \(0.591360\pi\) | |||||||
\(674\) | −2.63257 | −0.101403 | ||||||||
\(675\) | −0.458066 | −0.0176310 | ||||||||
\(676\) | −12.7689 | −0.491110 | ||||||||
\(677\) | 3.08551 | 0.118586 | 0.0592930 | − | 0.998241i | \(-0.481115\pi\) | ||||
0.0592930 | + | 0.998241i | \(0.481115\pi\) | |||||||
\(678\) | −10.7865 | −0.414252 | ||||||||
\(679\) | −2.06364 | −0.0791952 | ||||||||
\(680\) | 2.33625 | 0.0895911 | ||||||||
\(681\) | −12.3784 | −0.474340 | ||||||||
\(682\) | 5.44207 | 0.208388 | ||||||||
\(683\) | −31.0309 | −1.18736 | −0.593682 | − | 0.804700i | \(-0.702326\pi\) | ||||
−0.593682 | + | 0.804700i | \(0.702326\pi\) | |||||||
\(684\) | −0.134424 | −0.00513983 | ||||||||
\(685\) | 40.4807 | 1.54669 | ||||||||
\(686\) | 9.25433 | 0.353332 | ||||||||
\(687\) | 2.70403 | 0.103165 | ||||||||
\(688\) | −6.44381 | −0.245668 | ||||||||
\(689\) | 6.48513 | 0.247064 | ||||||||
\(690\) | −15.9806 | −0.608372 | ||||||||
\(691\) | 1.91114 | 0.0727032 | 0.0363516 | − | 0.999339i | \(-0.488426\pi\) | ||||
0.0363516 | + | 0.999339i | \(0.488426\pi\) | |||||||
\(692\) | 23.6118 | 0.897585 | ||||||||
\(693\) | −1.32464 | −0.0503188 | ||||||||
\(694\) | −15.7899 | −0.599376 | ||||||||
\(695\) | −44.1778 | −1.67576 | ||||||||
\(696\) | −7.79476 | −0.295460 | ||||||||
\(697\) | −2.73813 | −0.103714 | ||||||||
\(698\) | −11.5109 | −0.435694 | ||||||||
\(699\) | 9.87308 | 0.373434 | ||||||||
\(700\) | −0.313257 | −0.0118400 | ||||||||
\(701\) | −32.7563 | −1.23719 | −0.618593 | − | 0.785711i | \(-0.712297\pi\) | ||||
−0.618593 | + | 0.785711i | \(0.712297\pi\) | |||||||
\(702\) | −0.480780 | −0.0181459 | ||||||||
\(703\) | 0.0953066 | 0.00359456 | ||||||||
\(704\) | 1.93698 | 0.0730025 | ||||||||
\(705\) | 20.8000 | 0.783373 | ||||||||
\(706\) | 31.0633 | 1.16908 | ||||||||
\(707\) | −0.971361 | −0.0365318 | ||||||||
\(708\) | −1.00000 | −0.0375823 | ||||||||
\(709\) | −18.9454 | −0.711510 | −0.355755 | − | 0.934579i | \(-0.615776\pi\) | ||||
−0.355755 | + | 0.934579i | \(0.615776\pi\) | |||||||
\(710\) | 13.6051 | 0.510590 | ||||||||
\(711\) | 12.0018 | 0.450101 | ||||||||
\(712\) | 13.5600 | 0.508182 | ||||||||
\(713\) | 19.2183 | 0.719730 | ||||||||
\(714\) | 0.683869 | 0.0255931 | ||||||||
\(715\) | 2.17565 | 0.0813648 | ||||||||
\(716\) | −21.7180 | −0.811640 | ||||||||
\(717\) | −3.27930 | −0.122468 | ||||||||
\(718\) | 23.5865 | 0.880242 | ||||||||
\(719\) | −24.1272 | −0.899791 | −0.449896 | − | 0.893081i | \(-0.648539\pi\) | ||||
−0.449896 | + | 0.893081i | \(0.648539\pi\) | |||||||
\(720\) | 2.33625 | 0.0870669 | ||||||||
\(721\) | 9.94909 | 0.370523 | ||||||||
\(722\) | −18.9819 | −0.706434 | ||||||||
\(723\) | 6.96482 | 0.259025 | ||||||||
\(724\) | 14.4439 | 0.536805 | ||||||||
\(725\) | 3.57051 | 0.132606 | ||||||||
\(726\) | 7.24813 | 0.269003 | ||||||||
\(727\) | 50.8356 | 1.88539 | 0.942694 | − | 0.333659i | \(-0.108283\pi\) | ||||
0.942694 | + | 0.333659i | \(0.108283\pi\) | |||||||
\(728\) | −0.328790 | −0.0121858 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −6.04646 | −0.223789 | ||||||||
\(731\) | −6.44381 | −0.238333 | ||||||||
\(732\) | 11.1555 | 0.412319 | ||||||||
\(733\) | 39.5771 | 1.46181 | 0.730906 | − | 0.682478i | \(-0.239098\pi\) | ||||
0.730906 | + | 0.682478i | \(0.239098\pi\) | |||||||
\(734\) | −7.13232 | −0.263259 | ||||||||
\(735\) | 15.2611 | 0.562916 | ||||||||
\(736\) | 6.84029 | 0.252136 | ||||||||
\(737\) | 17.2956 | 0.637090 | ||||||||
\(738\) | −2.73813 | −0.100792 | ||||||||
\(739\) | −2.39046 | −0.0879346 | −0.0439673 | − | 0.999033i | \(-0.514000\pi\) | ||||
−0.0439673 | + | 0.999033i | \(0.514000\pi\) | |||||||
\(740\) | −1.65640 | −0.0608905 | ||||||||
\(741\) | 0.0646283 | 0.00237418 | ||||||||
\(742\) | −9.22456 | −0.338644 | ||||||||
\(743\) | 11.2795 | 0.413804 | 0.206902 | − | 0.978362i | \(-0.433662\pi\) | ||||
0.206902 | + | 0.978362i | \(0.433662\pi\) | |||||||
\(744\) | −2.80957 | −0.103004 | ||||||||
\(745\) | 1.97491 | 0.0723549 | ||||||||
\(746\) | 28.1071 | 1.02907 | ||||||||
\(747\) | −5.79142 | −0.211897 | ||||||||
\(748\) | 1.93698 | 0.0708228 | ||||||||
\(749\) | −4.21553 | −0.154032 | ||||||||
\(750\) | 10.6111 | 0.387462 | ||||||||
\(751\) | 15.3530 | 0.560238 | 0.280119 | − | 0.959965i | \(-0.409626\pi\) | ||||
0.280119 | + | 0.959965i | \(0.409626\pi\) | |||||||
\(752\) | −8.90316 | −0.324665 | ||||||||
\(753\) | 20.2352 | 0.737411 | ||||||||
\(754\) | 3.74756 | 0.136478 | ||||||||
\(755\) | 48.5219 | 1.76589 | ||||||||
\(756\) | 0.683869 | 0.0248721 | ||||||||
\(757\) | −15.6544 | −0.568969 | −0.284484 | − | 0.958681i | \(-0.591822\pi\) | ||||
−0.284484 | + | 0.958681i | \(0.591822\pi\) | |||||||
\(758\) | −3.21621 | −0.116818 | ||||||||
\(759\) | −13.2495 | −0.480926 | ||||||||
\(760\) | −0.314048 | −0.0113917 | ||||||||
\(761\) | 2.16738 | 0.0785674 | 0.0392837 | − | 0.999228i | \(-0.487492\pi\) | ||||
0.0392837 | + | 0.999228i | \(0.487492\pi\) | |||||||
\(762\) | 3.99253 | 0.144634 | ||||||||
\(763\) | −8.30288 | −0.300584 | ||||||||
\(764\) | 0.474135 | 0.0171536 | ||||||||
\(765\) | 2.33625 | 0.0844673 | ||||||||
\(766\) | −17.9314 | −0.647888 | ||||||||
\(767\) | 0.480780 | 0.0173599 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 34.5419 | 1.24561 | 0.622806 | − | 0.782376i | \(-0.285993\pi\) | ||||
0.622806 | + | 0.782376i | \(0.285993\pi\) | |||||||
\(770\) | −3.09468 | −0.111525 | ||||||||
\(771\) | 0.910524 | 0.0327917 | ||||||||
\(772\) | 7.01099 | 0.252331 | ||||||||
\(773\) | −3.30022 | −0.118701 | −0.0593503 | − | 0.998237i | \(-0.518903\pi\) | ||||
−0.0593503 | + | 0.998237i | \(0.518903\pi\) | |||||||
\(774\) | −6.44381 | −0.231618 | ||||||||
\(775\) | 1.28697 | 0.0462293 | ||||||||
\(776\) | 3.01760 | 0.108325 | ||||||||
\(777\) | −0.484863 | −0.0173944 | ||||||||
\(778\) | 24.8722 | 0.891713 | ||||||||
\(779\) | 0.368070 | 0.0131875 | ||||||||
\(780\) | −1.12322 | −0.0402178 | ||||||||
\(781\) | 11.2799 | 0.403627 | ||||||||
\(782\) | 6.84029 | 0.244608 | ||||||||
\(783\) | −7.79476 | −0.278562 | ||||||||
\(784\) | −6.53232 | −0.233297 | ||||||||
\(785\) | 11.4590 | 0.408989 | ||||||||
\(786\) | 9.37785 | 0.334497 | ||||||||
\(787\) | 12.5418 | 0.447067 | 0.223533 | − | 0.974696i | \(-0.428241\pi\) | ||||
0.223533 | + | 0.974696i | \(0.428241\pi\) | |||||||
\(788\) | −1.46125 | −0.0520550 | ||||||||
\(789\) | −15.6632 | −0.557625 | ||||||||
\(790\) | 28.0391 | 0.997586 | ||||||||
\(791\) | −7.37654 | −0.262280 | ||||||||
\(792\) | 1.93698 | 0.0688274 | ||||||||
\(793\) | −5.36333 | −0.190457 | ||||||||
\(794\) | 22.0814 | 0.783639 | ||||||||
\(795\) | −31.5132 | −1.11766 | ||||||||
\(796\) | −12.2073 | −0.432677 | ||||||||
\(797\) | −54.6473 | −1.93571 | −0.967853 | − | 0.251517i | \(-0.919070\pi\) | ||||
−0.967853 | + | 0.251517i | \(0.919070\pi\) | |||||||
\(798\) | −0.0919283 | −0.00325423 | ||||||||
\(799\) | −8.90316 | −0.314971 | ||||||||
\(800\) | 0.458066 | 0.0161951 | ||||||||
\(801\) | 13.5600 | 0.479119 | ||||||||
\(802\) | −20.6434 | −0.728944 | ||||||||
\(803\) | −5.01309 | −0.176908 | ||||||||
\(804\) | −8.92916 | −0.314907 | ||||||||
\(805\) | −10.9287 | −0.385185 | ||||||||
\(806\) | 1.35078 | 0.0475793 | ||||||||
\(807\) | −15.6658 | −0.551461 | ||||||||
\(808\) | 1.42039 | 0.0499692 | ||||||||
\(809\) | −47.6421 | −1.67501 | −0.837504 | − | 0.546431i | \(-0.815986\pi\) | ||||
−0.837504 | + | 0.546431i | \(0.815986\pi\) | |||||||
\(810\) | 2.33625 | 0.0820875 | ||||||||
\(811\) | −18.9398 | −0.665067 | −0.332533 | − | 0.943092i | \(-0.607903\pi\) | ||||
−0.332533 | + | 0.943092i | \(0.607903\pi\) | |||||||
\(812\) | −5.33059 | −0.187067 | ||||||||
\(813\) | −0.951602 | −0.0333741 | ||||||||
\(814\) | −1.37332 | −0.0481347 | ||||||||
\(815\) | −1.85324 | −0.0649163 | ||||||||
\(816\) | −1.00000 | −0.0350070 | ||||||||
\(817\) | 0.866202 | 0.0303046 | ||||||||
\(818\) | 31.1858 | 1.09039 | ||||||||
\(819\) | −0.328790 | −0.0114889 | ||||||||
\(820\) | −6.39696 | −0.223392 | ||||||||
\(821\) | 9.34226 | 0.326047 | 0.163024 | − | 0.986622i | \(-0.447875\pi\) | ||||
0.163024 | + | 0.986622i | \(0.447875\pi\) | |||||||
\(822\) | −17.3272 | −0.604356 | ||||||||
\(823\) | −39.9866 | −1.39385 | −0.696923 | − | 0.717146i | \(-0.745448\pi\) | ||||
−0.696923 | + | 0.717146i | \(0.745448\pi\) | |||||||
\(824\) | −14.5482 | −0.506812 | ||||||||
\(825\) | −0.887263 | −0.0308905 | ||||||||
\(826\) | −0.683869 | −0.0237948 | ||||||||
\(827\) | 42.0276 | 1.46144 | 0.730722 | − | 0.682675i | \(-0.239184\pi\) | ||||
0.730722 | + | 0.682675i | \(0.239184\pi\) | |||||||
\(828\) | 6.84029 | 0.237717 | ||||||||
\(829\) | −29.0685 | −1.00959 | −0.504796 | − | 0.863239i | \(-0.668432\pi\) | ||||
−0.504796 | + | 0.863239i | \(0.668432\pi\) | |||||||
\(830\) | −13.5302 | −0.469641 | ||||||||
\(831\) | 8.23112 | 0.285534 | ||||||||
\(832\) | 0.480780 | 0.0166680 | ||||||||
\(833\) | −6.53232 | −0.226332 | ||||||||
\(834\) | 18.9097 | 0.654789 | ||||||||
\(835\) | −3.99955 | −0.138410 | ||||||||
\(836\) | −0.260376 | −0.00900529 | ||||||||
\(837\) | −2.80957 | −0.0971129 | ||||||||
\(838\) | 32.5126 | 1.12313 | ||||||||
\(839\) | −41.3546 | −1.42772 | −0.713860 | − | 0.700289i | \(-0.753055\pi\) | ||||
−0.713860 | + | 0.700289i | \(0.753055\pi\) | |||||||
\(840\) | 1.59769 | 0.0551255 | ||||||||
\(841\) | 31.7583 | 1.09511 | ||||||||
\(842\) | 10.5978 | 0.365224 | ||||||||
\(843\) | −12.9741 | −0.446853 | ||||||||
\(844\) | −12.4282 | −0.427798 | ||||||||
\(845\) | −29.8312 | −1.02623 | ||||||||
\(846\) | −8.90316 | −0.306097 | ||||||||
\(847\) | 4.95677 | 0.170317 | ||||||||
\(848\) | 13.4888 | 0.463207 | ||||||||
\(849\) | 3.83895 | 0.131752 | ||||||||
\(850\) | 0.458066 | 0.0157115 | ||||||||
\(851\) | −4.84977 | −0.166248 | ||||||||
\(852\) | −5.82347 | −0.199509 | ||||||||
\(853\) | 5.71145 | 0.195556 | 0.0977781 | − | 0.995208i | \(-0.468826\pi\) | ||||
0.0977781 | + | 0.995208i | \(0.468826\pi\) | |||||||
\(854\) | 7.62889 | 0.261055 | ||||||||
\(855\) | −0.314048 | −0.0107402 | ||||||||
\(856\) | 6.16423 | 0.210689 | ||||||||
\(857\) | 40.9247 | 1.39796 | 0.698981 | − | 0.715141i | \(-0.253637\pi\) | ||||
0.698981 | + | 0.715141i | \(0.253637\pi\) | |||||||
\(858\) | −0.931258 | −0.0317926 | ||||||||
\(859\) | −31.5340 | −1.07593 | −0.537963 | − | 0.842968i | \(-0.680806\pi\) | ||||
−0.537963 | + | 0.842968i | \(0.680806\pi\) | |||||||
\(860\) | −15.0544 | −0.513349 | ||||||||
\(861\) | −1.87252 | −0.0638154 | ||||||||
\(862\) | 10.0321 | 0.341693 | ||||||||
\(863\) | 13.3177 | 0.453338 | 0.226669 | − | 0.973972i | \(-0.427216\pi\) | ||||
0.226669 | + | 0.973972i | \(0.427216\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 55.1630 | 1.87560 | ||||||||
\(866\) | −18.5634 | −0.630809 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −1.92138 | −0.0652158 | ||||||||
\(869\) | 23.2471 | 0.788604 | ||||||||
\(870\) | −18.2105 | −0.617394 | ||||||||
\(871\) | 4.29296 | 0.145461 | ||||||||
\(872\) | 12.1410 | 0.411148 | ||||||||
\(873\) | 3.01760 | 0.102130 | ||||||||
\(874\) | −0.919499 | −0.0311025 | ||||||||
\(875\) | 7.25660 | 0.245318 | ||||||||
\(876\) | 2.58810 | 0.0874439 | ||||||||
\(877\) | 45.2580 | 1.52825 | 0.764127 | − | 0.645066i | \(-0.223170\pi\) | ||||
0.764127 | + | 0.645066i | \(0.223170\pi\) | |||||||
\(878\) | −24.9087 | −0.840629 | ||||||||
\(879\) | −20.7091 | −0.698501 | ||||||||
\(880\) | 4.52526 | 0.152546 | ||||||||
\(881\) | −1.92725 | −0.0649306 | −0.0324653 | − | 0.999473i | \(-0.510336\pi\) | ||||
−0.0324653 | + | 0.999473i | \(0.510336\pi\) | |||||||
\(882\) | −6.53232 | −0.219955 | ||||||||
\(883\) | 11.8267 | 0.398001 | 0.199000 | − | 0.979999i | \(-0.436231\pi\) | ||||
0.199000 | + | 0.979999i | \(0.436231\pi\) | |||||||
\(884\) | 0.480780 | 0.0161704 | ||||||||
\(885\) | −2.33625 | −0.0785322 | ||||||||
\(886\) | −10.3404 | −0.347391 | ||||||||
\(887\) | 19.3000 | 0.648032 | 0.324016 | − | 0.946052i | \(-0.394967\pi\) | ||||
0.324016 | + | 0.946052i | \(0.394967\pi\) | |||||||
\(888\) | 0.709000 | 0.0237925 | ||||||||
\(889\) | 2.73037 | 0.0915737 | ||||||||
\(890\) | 31.6795 | 1.06190 | ||||||||
\(891\) | 1.93698 | 0.0648911 | ||||||||
\(892\) | 5.55345 | 0.185943 | ||||||||
\(893\) | 1.19680 | 0.0400493 | ||||||||
\(894\) | −0.845331 | −0.0282721 | ||||||||
\(895\) | −50.7387 | −1.69601 | ||||||||
\(896\) | −0.683869 | −0.0228465 | ||||||||
\(897\) | −3.28867 | −0.109806 | ||||||||
\(898\) | −22.0314 | −0.735198 | ||||||||
\(899\) | 21.8999 | 0.730403 | ||||||||
\(900\) | 0.458066 | 0.0152689 | ||||||||
\(901\) | 13.4888 | 0.449377 | ||||||||
\(902\) | −5.30369 | −0.176594 | ||||||||
\(903\) | −4.40672 | −0.146646 | ||||||||
\(904\) | 10.7865 | 0.358753 | ||||||||
\(905\) | 33.7447 | 1.12171 | ||||||||
\(906\) | −20.7691 | −0.690009 | ||||||||
\(907\) | 29.5964 | 0.982733 | 0.491367 | − | 0.870953i | \(-0.336497\pi\) | ||||
0.491367 | + | 0.870953i | \(0.336497\pi\) | |||||||
\(908\) | 12.3784 | 0.410790 | ||||||||
\(909\) | 1.42039 | 0.0471114 | ||||||||
\(910\) | −0.768136 | −0.0254635 | ||||||||
\(911\) | 47.5967 | 1.57695 | 0.788474 | − | 0.615068i | \(-0.210871\pi\) | ||||
0.788474 | + | 0.615068i | \(0.210871\pi\) | |||||||
\(912\) | 0.134424 | 0.00445122 | ||||||||
\(913\) | −11.2178 | −0.371256 | ||||||||
\(914\) | 21.8148 | 0.721570 | ||||||||
\(915\) | 26.0620 | 0.861583 | ||||||||
\(916\) | −2.70403 | −0.0893435 | ||||||||
\(917\) | 6.41322 | 0.211783 | ||||||||
\(918\) | −1.00000 | −0.0330049 | ||||||||
\(919\) | −33.8497 | −1.11660 | −0.558300 | − | 0.829639i | \(-0.688546\pi\) | ||||
−0.558300 | + | 0.829639i | \(0.688546\pi\) | |||||||
\(920\) | 15.9806 | 0.526866 | ||||||||
\(921\) | −6.93896 | −0.228646 | ||||||||
\(922\) | −23.1270 | −0.761648 | ||||||||
\(923\) | 2.79980 | 0.0921567 | ||||||||
\(924\) | 1.32464 | 0.0435774 | ||||||||
\(925\) | −0.324769 | −0.0106783 | ||||||||
\(926\) | −2.30556 | −0.0757655 | ||||||||
\(927\) | −14.5482 | −0.477827 | ||||||||
\(928\) | 7.79476 | 0.255875 | ||||||||
\(929\) | −21.3804 | −0.701467 | −0.350734 | − | 0.936475i | \(-0.614068\pi\) | ||||
−0.350734 | + | 0.936475i | \(0.614068\pi\) | |||||||
\(930\) | −6.56386 | −0.215237 | ||||||||
\(931\) | 0.878100 | 0.0287786 | ||||||||
\(932\) | −9.87308 | −0.323404 | ||||||||
\(933\) | −3.79474 | −0.124234 | ||||||||
\(934\) | 18.8292 | 0.616109 | ||||||||
\(935\) | 4.52526 | 0.147992 | ||||||||
\(936\) | 0.480780 | 0.0157148 | ||||||||
\(937\) | −13.6256 | −0.445128 | −0.222564 | − | 0.974918i | \(-0.571443\pi\) | ||||
−0.222564 | + | 0.974918i | \(0.571443\pi\) | |||||||
\(938\) | −6.10638 | −0.199380 | ||||||||
\(939\) | 5.69740 | 0.185928 | ||||||||
\(940\) | −20.8000 | −0.678421 | ||||||||
\(941\) | −1.26926 | −0.0413767 | −0.0206883 | − | 0.999786i | \(-0.506586\pi\) | ||||
−0.0206883 | + | 0.999786i | \(0.506586\pi\) | |||||||
\(942\) | −4.90486 | −0.159809 | ||||||||
\(943\) | −18.7296 | −0.609920 | ||||||||
\(944\) | 1.00000 | 0.0325472 | ||||||||
\(945\) | 1.59769 | 0.0519728 | ||||||||
\(946\) | −12.4815 | −0.405809 | ||||||||
\(947\) | −51.7861 | −1.68282 | −0.841412 | − | 0.540395i | \(-0.818275\pi\) | ||||
−0.841412 | + | 0.540395i | \(0.818275\pi\) | |||||||
\(948\) | −12.0018 | −0.389799 | ||||||||
\(949\) | −1.24431 | −0.0403919 | ||||||||
\(950\) | −0.0615750 | −0.00199776 | ||||||||
\(951\) | 19.0607 | 0.618086 | ||||||||
\(952\) | −0.683869 | −0.0221643 | ||||||||
\(953\) | −13.7380 | −0.445017 | −0.222509 | − | 0.974931i | \(-0.571425\pi\) | ||||
−0.222509 | + | 0.974931i | \(0.571425\pi\) | |||||||
\(954\) | 13.4888 | 0.436716 | ||||||||
\(955\) | 1.10770 | 0.0358443 | ||||||||
\(956\) | 3.27930 | 0.106060 | ||||||||
\(957\) | −15.0983 | −0.488057 | ||||||||
\(958\) | 40.4771 | 1.30776 | ||||||||
\(959\) | −11.8495 | −0.382641 | ||||||||
\(960\) | −2.33625 | −0.0754022 | ||||||||
\(961\) | −23.1063 | −0.745365 | ||||||||
\(962\) | −0.340873 | −0.0109902 | ||||||||
\(963\) | 6.16423 | 0.198640 | ||||||||
\(964\) | −6.96482 | −0.224322 | ||||||||
\(965\) | 16.3794 | 0.527272 | ||||||||
\(966\) | 4.67786 | 0.150508 | ||||||||
\(967\) | 42.7342 | 1.37424 | 0.687120 | − | 0.726544i | \(-0.258875\pi\) | ||||
0.687120 | + | 0.726544i | \(0.258875\pi\) | |||||||
\(968\) | −7.24813 | −0.232964 | ||||||||
\(969\) | 0.134424 | 0.00431832 | ||||||||
\(970\) | 7.04986 | 0.226357 | ||||||||
\(971\) | −29.9598 | −0.961454 | −0.480727 | − | 0.876870i | \(-0.659627\pi\) | ||||
−0.480727 | + | 0.876870i | \(0.659627\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 12.9317 | 0.414573 | ||||||||
\(974\) | −11.7648 | −0.376967 | ||||||||
\(975\) | −0.220229 | −0.00705297 | ||||||||
\(976\) | −11.1555 | −0.357078 | ||||||||
\(977\) | 24.9595 | 0.798524 | 0.399262 | − | 0.916837i | \(-0.369266\pi\) | ||||
0.399262 | + | 0.916837i | \(0.369266\pi\) | |||||||
\(978\) | 0.793255 | 0.0253655 | ||||||||
\(979\) | 26.2654 | 0.839445 | ||||||||
\(980\) | −15.2611 | −0.487499 | ||||||||
\(981\) | 12.1410 | 0.387634 | ||||||||
\(982\) | −26.3139 | −0.839711 | ||||||||
\(983\) | −48.3918 | −1.54346 | −0.771730 | − | 0.635951i | \(-0.780608\pi\) | ||||
−0.771730 | + | 0.635951i | \(0.780608\pi\) | |||||||
\(984\) | 2.73813 | 0.0872884 | ||||||||
\(985\) | −3.41385 | −0.108774 | ||||||||
\(986\) | 7.79476 | 0.248236 | ||||||||
\(987\) | −6.08859 | −0.193802 | ||||||||
\(988\) | −0.0646283 | −0.00205610 | ||||||||
\(989\) | −44.0775 | −1.40158 | ||||||||
\(990\) | 4.52526 | 0.143822 | ||||||||
\(991\) | 21.7193 | 0.689938 | 0.344969 | − | 0.938614i | \(-0.387890\pi\) | ||||
0.344969 | + | 0.938614i | \(0.387890\pi\) | |||||||
\(992\) | 2.80957 | 0.0892039 | ||||||||
\(993\) | −7.10042 | −0.225325 | ||||||||
\(994\) | −3.98249 | −0.126317 | ||||||||
\(995\) | −28.5194 | −0.904125 | ||||||||
\(996\) | 5.79142 | 0.183508 | ||||||||
\(997\) | −49.4539 | −1.56622 | −0.783110 | − | 0.621884i | \(-0.786368\pi\) | ||||
−0.783110 | + | 0.621884i | \(0.786368\pi\) | |||||||
\(998\) | −3.10849 | −0.0983975 | ||||||||
\(999\) | 0.709000 | 0.0224318 |
(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 | 6018.2.a.bc.1.10 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6018.2.a.bc.1.10 | ✓ | 14 | 1.1 | even | 1 | trivial |