Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1859,2,Mod(1,1859)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1859, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1859.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1859 = 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1859.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: | \(14.8441897358\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 8x^{6} + 18x^{5} + 7x^{4} - 22x^{3} - 3x^{2} + 6x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 143) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(2.20621\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1859.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.20621 | 1.56003 | 0.780014 | − | 0.625762i | \(-0.215212\pi\) | ||||
0.780014 | + | 0.625762i | \(0.215212\pi\) | |||||||
\(3\) | 2.48500 | 1.43471 | 0.717357 | − | 0.696706i | \(-0.245352\pi\) | ||||
0.717357 | + | 0.696706i | \(0.245352\pi\) | |||||||
\(4\) | 2.86737 | 1.43369 | ||||||||
\(5\) | 1.68345 | 0.752862 | 0.376431 | − | 0.926445i | \(-0.377151\pi\) | ||||
0.376431 | + | 0.926445i | \(0.377151\pi\) | |||||||
\(6\) | 5.48243 | 2.23819 | ||||||||
\(7\) | −0.336274 | −0.127100 | −0.0635499 | − | 0.997979i | \(-0.520242\pi\) | ||||
−0.0635499 | + | 0.997979i | \(0.520242\pi\) | |||||||
\(8\) | 1.91361 | 0.676563 | ||||||||
\(9\) | 3.17521 | 1.05840 | ||||||||
\(10\) | 3.71405 | 1.17449 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 7.12541 | 2.05693 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −0.741892 | −0.198279 | ||||||||
\(15\) | 4.18337 | 1.08014 | ||||||||
\(16\) | −1.51292 | −0.378230 | ||||||||
\(17\) | 0.144194 | 0.0349721 | 0.0174861 | − | 0.999847i | \(-0.494434\pi\) | ||||
0.0174861 | + | 0.999847i | \(0.494434\pi\) | |||||||
\(18\) | 7.00519 | 1.65114 | ||||||||
\(19\) | 5.22231 | 1.19808 | 0.599040 | − | 0.800719i | \(-0.295549\pi\) | ||||
0.599040 | + | 0.800719i | \(0.295549\pi\) | |||||||
\(20\) | 4.82708 | 1.07937 | ||||||||
\(21\) | −0.835641 | −0.182352 | ||||||||
\(22\) | −2.20621 | −0.470366 | ||||||||
\(23\) | −4.38689 | −0.914729 | −0.457365 | − | 0.889279i | \(-0.651207\pi\) | ||||
−0.457365 | + | 0.889279i | \(0.651207\pi\) | |||||||
\(24\) | 4.75531 | 0.970674 | ||||||||
\(25\) | −2.16599 | −0.433199 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.435403 | 0.0837934 | ||||||||
\(28\) | −0.964223 | −0.182221 | ||||||||
\(29\) | −2.44316 | −0.453684 | −0.226842 | − | 0.973932i | \(-0.572840\pi\) | ||||
−0.226842 | + | 0.973932i | \(0.572840\pi\) | |||||||
\(30\) | 9.22941 | 1.68505 | ||||||||
\(31\) | 10.1942 | 1.83093 | 0.915467 | − | 0.402393i | \(-0.131822\pi\) | ||||
0.915467 | + | 0.402393i | \(0.131822\pi\) | |||||||
\(32\) | −7.16504 | −1.26661 | ||||||||
\(33\) | −2.48500 | −0.432583 | ||||||||
\(34\) | 0.318122 | 0.0545575 | ||||||||
\(35\) | −0.566101 | −0.0956886 | ||||||||
\(36\) | 9.10452 | 1.51742 | ||||||||
\(37\) | 4.55644 | 0.749074 | 0.374537 | − | 0.927212i | \(-0.377802\pi\) | ||||
0.374537 | + | 0.927212i | \(0.377802\pi\) | |||||||
\(38\) | 11.5215 | 1.86904 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.22147 | 0.509358 | ||||||||
\(41\) | −11.1758 | −1.74537 | −0.872685 | − | 0.488283i | \(-0.837623\pi\) | ||||
−0.872685 | + | 0.488283i | \(0.837623\pi\) | |||||||
\(42\) | −1.84360 | −0.284474 | ||||||||
\(43\) | 8.04583 | 1.22698 | 0.613489 | − | 0.789703i | \(-0.289766\pi\) | ||||
0.613489 | + | 0.789703i | \(0.289766\pi\) | |||||||
\(44\) | −2.86737 | −0.432273 | ||||||||
\(45\) | 5.34532 | 0.796833 | ||||||||
\(46\) | −9.67840 | −1.42700 | ||||||||
\(47\) | 0.887789 | 0.129497 | 0.0647487 | − | 0.997902i | \(-0.479375\pi\) | ||||
0.0647487 | + | 0.997902i | \(0.479375\pi\) | |||||||
\(48\) | −3.75960 | −0.542652 | ||||||||
\(49\) | −6.88692 | −0.983846 | ||||||||
\(50\) | −4.77864 | −0.675802 | ||||||||
\(51\) | 0.358321 | 0.0501750 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.33873 | −0.733331 | −0.366666 | − | 0.930353i | \(-0.619501\pi\) | ||||
−0.366666 | + | 0.930353i | \(0.619501\pi\) | |||||||
\(54\) | 0.960592 | 0.130720 | ||||||||
\(55\) | −1.68345 | −0.226996 | ||||||||
\(56\) | −0.643497 | −0.0859909 | ||||||||
\(57\) | 12.9774 | 1.71890 | ||||||||
\(58\) | −5.39013 | −0.707759 | ||||||||
\(59\) | −11.8665 | −1.54488 | −0.772441 | − | 0.635086i | \(-0.780964\pi\) | ||||
−0.772441 | + | 0.635086i | \(0.780964\pi\) | |||||||
\(60\) | 11.9953 | 1.54858 | ||||||||
\(61\) | −2.40749 | −0.308248 | −0.154124 | − | 0.988052i | \(-0.549255\pi\) | ||||
−0.154124 | + | 0.988052i | \(0.549255\pi\) | |||||||
\(62\) | 22.4906 | 2.85631 | ||||||||
\(63\) | −1.06774 | −0.134523 | ||||||||
\(64\) | −12.7818 | −1.59772 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.48243 | −0.674841 | ||||||||
\(67\) | 6.42376 | 0.784788 | 0.392394 | − | 0.919797i | \(-0.371647\pi\) | ||||
0.392394 | + | 0.919797i | \(0.371647\pi\) | |||||||
\(68\) | 0.413457 | 0.0501390 | ||||||||
\(69\) | −10.9014 | −1.31237 | ||||||||
\(70\) | −1.24894 | −0.149277 | ||||||||
\(71\) | −5.30052 | −0.629056 | −0.314528 | − | 0.949248i | \(-0.601846\pi\) | ||||
−0.314528 | + | 0.949248i | \(0.601846\pi\) | |||||||
\(72\) | 6.07611 | 0.716077 | ||||||||
\(73\) | 14.9244 | 1.74677 | 0.873387 | − | 0.487027i | \(-0.161919\pi\) | ||||
0.873387 | + | 0.487027i | \(0.161919\pi\) | |||||||
\(74\) | 10.0525 | 1.16858 | ||||||||
\(75\) | −5.38249 | −0.621516 | ||||||||
\(76\) | 14.9743 | 1.71767 | ||||||||
\(77\) | 0.336274 | 0.0383220 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.95553 | 0.670049 | 0.335025 | − | 0.942209i | \(-0.391255\pi\) | ||||
0.335025 | + | 0.942209i | \(0.391255\pi\) | |||||||
\(80\) | −2.54693 | −0.284755 | ||||||||
\(81\) | −8.44366 | −0.938185 | ||||||||
\(82\) | −24.6562 | −2.72283 | ||||||||
\(83\) | 11.5950 | 1.27271 | 0.636357 | − | 0.771395i | \(-0.280440\pi\) | ||||
0.636357 | + | 0.771395i | \(0.280440\pi\) | |||||||
\(84\) | −2.39609 | −0.261435 | ||||||||
\(85\) | 0.242743 | 0.0263292 | ||||||||
\(86\) | 17.7508 | 1.91412 | ||||||||
\(87\) | −6.07125 | −0.650906 | ||||||||
\(88\) | −1.91361 | −0.203991 | ||||||||
\(89\) | −7.37352 | −0.781591 | −0.390796 | − | 0.920477i | \(-0.627800\pi\) | ||||
−0.390796 | + | 0.920477i | \(0.627800\pi\) | |||||||
\(90\) | 11.7929 | 1.24308 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −12.5788 | −1.31143 | ||||||||
\(93\) | 25.3326 | 2.62687 | ||||||||
\(94\) | 1.95865 | 0.202019 | ||||||||
\(95\) | 8.79150 | 0.901989 | ||||||||
\(96\) | −17.8051 | −1.81723 | ||||||||
\(97\) | −7.38121 | −0.749448 | −0.374724 | − | 0.927136i | \(-0.622263\pi\) | ||||
−0.374724 | + | 0.927136i | \(0.622263\pi\) | |||||||
\(98\) | −15.1940 | −1.53483 | ||||||||
\(99\) | −3.17521 | −0.319121 | ||||||||
\(100\) | −6.21071 | −0.621071 | ||||||||
\(101\) | −14.0876 | −1.40177 | −0.700886 | − | 0.713273i | \(-0.747212\pi\) | ||||
−0.700886 | + | 0.713273i | \(0.747212\pi\) | |||||||
\(102\) | 0.790532 | 0.0782744 | ||||||||
\(103\) | −9.81986 | −0.967579 | −0.483790 | − | 0.875184i | \(-0.660740\pi\) | ||||
−0.483790 | + | 0.875184i | \(0.660740\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.40676 | −0.137286 | ||||||||
\(106\) | −11.7784 | −1.14402 | ||||||||
\(107\) | 6.95718 | 0.672576 | 0.336288 | − | 0.941759i | \(-0.390828\pi\) | ||||
0.336288 | + | 0.941759i | \(0.390828\pi\) | |||||||
\(108\) | 1.24846 | 0.120133 | ||||||||
\(109\) | −6.92594 | −0.663385 | −0.331692 | − | 0.943388i | \(-0.607620\pi\) | ||||
−0.331692 | + | 0.943388i | \(0.607620\pi\) | |||||||
\(110\) | −3.71405 | −0.354121 | ||||||||
\(111\) | 11.3227 | 1.07471 | ||||||||
\(112\) | 0.508756 | 0.0480729 | ||||||||
\(113\) | 4.06846 | 0.382728 | 0.191364 | − | 0.981519i | \(-0.438709\pi\) | ||||
0.191364 | + | 0.981519i | \(0.438709\pi\) | |||||||
\(114\) | 28.6309 | 2.68153 | ||||||||
\(115\) | −7.38511 | −0.688665 | ||||||||
\(116\) | −7.00546 | −0.650440 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −26.1799 | −2.41006 | ||||||||
\(119\) | −0.0484886 | −0.00444495 | ||||||||
\(120\) | 8.00533 | 0.730784 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −5.31144 | −0.480875 | ||||||||
\(123\) | −27.7719 | −2.50411 | ||||||||
\(124\) | 29.2306 | 2.62498 | ||||||||
\(125\) | −12.0636 | −1.07900 | ||||||||
\(126\) | −2.35567 | −0.209859 | ||||||||
\(127\) | 3.76899 | 0.334444 | 0.167222 | − | 0.985919i | \(-0.446520\pi\) | ||||
0.167222 | + | 0.985919i | \(0.446520\pi\) | |||||||
\(128\) | −13.8692 | −1.22587 | ||||||||
\(129\) | 19.9939 | 1.76036 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.7278 | −1.19940 | −0.599701 | − | 0.800224i | \(-0.704714\pi\) | ||||
−0.599701 | + | 0.800224i | \(0.704714\pi\) | |||||||
\(132\) | −7.12541 | −0.620188 | ||||||||
\(133\) | −1.75613 | −0.152276 | ||||||||
\(134\) | 14.1722 | 1.22429 | ||||||||
\(135\) | 0.732980 | 0.0630849 | ||||||||
\(136\) | 0.275930 | 0.0236608 | ||||||||
\(137\) | 19.1145 | 1.63306 | 0.816530 | − | 0.577303i | \(-0.195895\pi\) | ||||
0.816530 | + | 0.577303i | \(0.195895\pi\) | |||||||
\(138\) | −24.0508 | −2.04734 | ||||||||
\(139\) | 7.50407 | 0.636487 | 0.318243 | − | 0.948009i | \(-0.396907\pi\) | ||||
0.318243 | + | 0.948009i | \(0.396907\pi\) | |||||||
\(140\) | −1.62322 | −0.137187 | ||||||||
\(141\) | 2.20615 | 0.185792 | ||||||||
\(142\) | −11.6941 | −0.981344 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.80384 | −0.400320 | ||||||||
\(145\) | −4.11294 | −0.341561 | ||||||||
\(146\) | 32.9265 | 2.72502 | ||||||||
\(147\) | −17.1140 | −1.41154 | ||||||||
\(148\) | 13.0650 | 1.07394 | ||||||||
\(149\) | 18.7218 | 1.53375 | 0.766876 | − | 0.641796i | \(-0.221810\pi\) | ||||
0.766876 | + | 0.641796i | \(0.221810\pi\) | |||||||
\(150\) | −11.8749 | −0.969582 | ||||||||
\(151\) | −2.67555 | −0.217733 | −0.108866 | − | 0.994056i | \(-0.534722\pi\) | ||||
−0.108866 | + | 0.994056i | \(0.534722\pi\) | |||||||
\(152\) | 9.99345 | 0.810576 | ||||||||
\(153\) | 0.457846 | 0.0370146 | ||||||||
\(154\) | 0.741892 | 0.0597834 | ||||||||
\(155\) | 17.1614 | 1.37844 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.2945 | 1.38025 | 0.690126 | − | 0.723689i | \(-0.257555\pi\) | ||||
0.690126 | + | 0.723689i | \(0.257555\pi\) | |||||||
\(158\) | 13.1392 | 1.04530 | ||||||||
\(159\) | −13.2667 | −1.05212 | ||||||||
\(160\) | −12.0620 | −0.953584 | ||||||||
\(161\) | 1.47520 | 0.116262 | ||||||||
\(162\) | −18.6285 | −1.46359 | ||||||||
\(163\) | 3.68040 | 0.288271 | 0.144135 | − | 0.989558i | \(-0.453960\pi\) | ||||
0.144135 | + | 0.989558i | \(0.453960\pi\) | |||||||
\(164\) | −32.0453 | −2.50231 | ||||||||
\(165\) | −4.18337 | −0.325675 | ||||||||
\(166\) | 25.5810 | 1.98547 | ||||||||
\(167\) | −6.70452 | −0.518811 | −0.259406 | − | 0.965768i | \(-0.583527\pi\) | ||||
−0.259406 | + | 0.965768i | \(0.583527\pi\) | |||||||
\(168\) | −1.59909 | −0.123372 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0.535543 | 0.0410743 | ||||||||
\(171\) | 16.5819 | 1.26805 | ||||||||
\(172\) | 23.0704 | 1.75910 | ||||||||
\(173\) | 9.98689 | 0.759289 | 0.379645 | − | 0.925132i | \(-0.376046\pi\) | ||||
0.379645 | + | 0.925132i | \(0.376046\pi\) | |||||||
\(174\) | −13.3945 | −1.01543 | ||||||||
\(175\) | 0.728367 | 0.0550594 | ||||||||
\(176\) | 1.51292 | 0.114041 | ||||||||
\(177\) | −29.4881 | −2.21646 | ||||||||
\(178\) | −16.2675 | −1.21930 | ||||||||
\(179\) | −13.3089 | −0.994758 | −0.497379 | − | 0.867533i | \(-0.665704\pi\) | ||||
−0.497379 | + | 0.867533i | \(0.665704\pi\) | |||||||
\(180\) | 15.3270 | 1.14241 | ||||||||
\(181\) | −12.5134 | −0.930113 | −0.465056 | − | 0.885281i | \(-0.653966\pi\) | ||||
−0.465056 | + | 0.885281i | \(0.653966\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.98261 | −0.442247 | ||||||||
\(184\) | −8.39478 | −0.618871 | ||||||||
\(185\) | 7.67054 | 0.563949 | ||||||||
\(186\) | 55.8891 | 4.09798 | ||||||||
\(187\) | −0.144194 | −0.0105445 | ||||||||
\(188\) | 2.54562 | 0.185659 | ||||||||
\(189\) | −0.146415 | −0.0106501 | ||||||||
\(190\) | 19.3959 | 1.40713 | ||||||||
\(191\) | −1.34878 | −0.0975943 | −0.0487971 | − | 0.998809i | \(-0.515539\pi\) | ||||
−0.0487971 | + | 0.998809i | \(0.515539\pi\) | |||||||
\(192\) | −31.7626 | −2.29227 | ||||||||
\(193\) | 4.74532 | 0.341576 | 0.170788 | − | 0.985308i | \(-0.445369\pi\) | ||||
0.170788 | + | 0.985308i | \(0.445369\pi\) | |||||||
\(194\) | −16.2845 | −1.16916 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −19.7474 | −1.41053 | ||||||||
\(197\) | −4.17222 | −0.297259 | −0.148629 | − | 0.988893i | \(-0.547486\pi\) | ||||
−0.148629 | + | 0.988893i | \(0.547486\pi\) | |||||||
\(198\) | −7.00519 | −0.497837 | ||||||||
\(199\) | −21.3154 | −1.51101 | −0.755503 | − | 0.655145i | \(-0.772608\pi\) | ||||
−0.755503 | + | 0.655145i | \(0.772608\pi\) | |||||||
\(200\) | −4.14486 | −0.293086 | ||||||||
\(201\) | 15.9630 | 1.12595 | ||||||||
\(202\) | −31.0803 | −2.18680 | ||||||||
\(203\) | 0.821572 | 0.0576631 | ||||||||
\(204\) | 1.02744 | 0.0719352 | ||||||||
\(205\) | −18.8140 | −1.31402 | ||||||||
\(206\) | −21.6647 | −1.50945 | ||||||||
\(207\) | −13.9293 | −0.968153 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.22231 | −0.361235 | ||||||||
\(210\) | −3.10361 | −0.214170 | ||||||||
\(211\) | 20.5228 | 1.41284 | 0.706422 | − | 0.707791i | \(-0.250308\pi\) | ||||
0.706422 | + | 0.707791i | \(0.250308\pi\) | |||||||
\(212\) | −15.3081 | −1.05137 | ||||||||
\(213\) | −13.1718 | −0.902515 | ||||||||
\(214\) | 15.3490 | 1.04924 | ||||||||
\(215\) | 13.5448 | 0.923745 | ||||||||
\(216\) | 0.833191 | 0.0566915 | ||||||||
\(217\) | −3.42805 | −0.232711 | ||||||||
\(218\) | −15.2801 | −1.03490 | ||||||||
\(219\) | 37.0872 | 2.50612 | ||||||||
\(220\) | −4.82708 | −0.325442 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 24.9804 | 1.67657 | ||||||||
\(223\) | 19.6456 | 1.31557 | 0.657783 | − | 0.753208i | \(-0.271495\pi\) | ||||
0.657783 | + | 0.753208i | \(0.271495\pi\) | |||||||
\(224\) | 2.40942 | 0.160986 | ||||||||
\(225\) | −6.87749 | −0.458499 | ||||||||
\(226\) | 8.97588 | 0.597066 | ||||||||
\(227\) | −8.67982 | −0.576100 | −0.288050 | − | 0.957615i | \(-0.593007\pi\) | ||||
−0.288050 | + | 0.957615i | \(0.593007\pi\) | |||||||
\(228\) | 37.2111 | 2.46437 | ||||||||
\(229\) | 20.5716 | 1.35941 | 0.679705 | − | 0.733486i | \(-0.262108\pi\) | ||||
0.679705 | + | 0.733486i | \(0.262108\pi\) | |||||||
\(230\) | −16.2931 | −1.07434 | ||||||||
\(231\) | 0.835641 | 0.0549811 | ||||||||
\(232\) | −4.67525 | −0.306945 | ||||||||
\(233\) | 14.1716 | 0.928414 | 0.464207 | − | 0.885727i | \(-0.346339\pi\) | ||||
0.464207 | + | 0.885727i | \(0.346339\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.49455 | 0.0974936 | ||||||||
\(236\) | −34.0256 | −2.21488 | ||||||||
\(237\) | 14.7995 | 0.961329 | ||||||||
\(238\) | −0.106976 | −0.00693424 | ||||||||
\(239\) | 5.16781 | 0.334278 | 0.167139 | − | 0.985933i | \(-0.446547\pi\) | ||||
0.167139 | + | 0.985933i | \(0.446547\pi\) | |||||||
\(240\) | −6.32911 | −0.408542 | ||||||||
\(241\) | 8.40947 | 0.541701 | 0.270851 | − | 0.962621i | \(-0.412695\pi\) | ||||
0.270851 | + | 0.962621i | \(0.412695\pi\) | |||||||
\(242\) | 2.20621 | 0.141821 | ||||||||
\(243\) | −22.2887 | −1.42982 | ||||||||
\(244\) | −6.90318 | −0.441931 | ||||||||
\(245\) | −11.5938 | −0.740700 | ||||||||
\(246\) | −61.2707 | −3.90648 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 19.5077 | 1.23874 | ||||||||
\(249\) | 28.8135 | 1.82598 | ||||||||
\(250\) | −26.6149 | −1.68327 | ||||||||
\(251\) | −7.17578 | −0.452931 | −0.226466 | − | 0.974019i | \(-0.572717\pi\) | ||||
−0.226466 | + | 0.974019i | \(0.572717\pi\) | |||||||
\(252\) | −3.06161 | −0.192864 | ||||||||
\(253\) | 4.38689 | 0.275801 | ||||||||
\(254\) | 8.31520 | 0.521742 | ||||||||
\(255\) | 0.603216 | 0.0377748 | ||||||||
\(256\) | −5.03486 | −0.314679 | ||||||||
\(257\) | 13.3333 | 0.831708 | 0.415854 | − | 0.909431i | \(-0.363483\pi\) | ||||
0.415854 | + | 0.909431i | \(0.363483\pi\) | |||||||
\(258\) | 44.1107 | 2.74621 | ||||||||
\(259\) | −1.53221 | −0.0952071 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.75756 | −0.480181 | ||||||||
\(262\) | −30.2864 | −1.87110 | ||||||||
\(263\) | −4.02733 | −0.248336 | −0.124168 | − | 0.992261i | \(-0.539626\pi\) | ||||
−0.124168 | + | 0.992261i | \(0.539626\pi\) | |||||||
\(264\) | −4.75531 | −0.292669 | ||||||||
\(265\) | −8.98749 | −0.552097 | ||||||||
\(266\) | −3.87439 | −0.237554 | ||||||||
\(267\) | −18.3232 | −1.12136 | ||||||||
\(268\) | 18.4193 | 1.12514 | ||||||||
\(269\) | 24.7893 | 1.51143 | 0.755716 | − | 0.654899i | \(-0.227289\pi\) | ||||
0.755716 | + | 0.654899i | \(0.227289\pi\) | |||||||
\(270\) | 1.61711 | 0.0984141 | ||||||||
\(271\) | 26.0809 | 1.58430 | 0.792151 | − | 0.610326i | \(-0.208961\pi\) | ||||
0.792151 | + | 0.610326i | \(0.208961\pi\) | |||||||
\(272\) | −0.218154 | −0.0132275 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 42.1706 | 2.54762 | ||||||||
\(275\) | 2.16599 | 0.130614 | ||||||||
\(276\) | −31.2584 | −1.88153 | ||||||||
\(277\) | 0.904447 | 0.0543429 | 0.0271715 | − | 0.999631i | \(-0.491350\pi\) | ||||
0.0271715 | + | 0.999631i | \(0.491350\pi\) | |||||||
\(278\) | 16.5556 | 0.992937 | ||||||||
\(279\) | 32.3688 | 1.93787 | ||||||||
\(280\) | −1.08330 | −0.0647393 | ||||||||
\(281\) | −4.92210 | −0.293628 | −0.146814 | − | 0.989164i | \(-0.546902\pi\) | ||||
−0.146814 | + | 0.989164i | \(0.546902\pi\) | |||||||
\(282\) | 4.86724 | 0.289840 | ||||||||
\(283\) | −29.9388 | −1.77968 | −0.889840 | − | 0.456273i | \(-0.849184\pi\) | ||||
−0.889840 | + | 0.456273i | \(0.849184\pi\) | |||||||
\(284\) | −15.1986 | −0.901868 | ||||||||
\(285\) | 21.8469 | 1.29410 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.75814 | 0.221836 | ||||||||
\(288\) | −22.7505 | −1.34059 | ||||||||
\(289\) | −16.9792 | −0.998777 | ||||||||
\(290\) | −9.07403 | −0.532845 | ||||||||
\(291\) | −18.3423 | −1.07524 | ||||||||
\(292\) | 42.7939 | 2.50433 | ||||||||
\(293\) | 15.4613 | 0.903257 | 0.451629 | − | 0.892206i | \(-0.350843\pi\) | ||||
0.451629 | + | 0.892206i | \(0.350843\pi\) | |||||||
\(294\) | −37.7571 | −2.20204 | ||||||||
\(295\) | −19.9766 | −1.16308 | ||||||||
\(296\) | 8.71924 | 0.506795 | ||||||||
\(297\) | −0.435403 | −0.0252647 | ||||||||
\(298\) | 41.3043 | 2.39269 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −15.4336 | −0.891059 | ||||||||
\(301\) | −2.70561 | −0.155949 | ||||||||
\(302\) | −5.90282 | −0.339669 | ||||||||
\(303\) | −35.0077 | −2.01114 | ||||||||
\(304\) | −7.90093 | −0.453150 | ||||||||
\(305\) | −4.05290 | −0.232068 | ||||||||
\(306\) | 1.01010 | 0.0577439 | ||||||||
\(307\) | −6.05444 | −0.345545 | −0.172773 | − | 0.984962i | \(-0.555273\pi\) | ||||
−0.172773 | + | 0.984962i | \(0.555273\pi\) | |||||||
\(308\) | 0.964223 | 0.0549417 | ||||||||
\(309\) | −24.4023 | −1.38820 | ||||||||
\(310\) | 37.8618 | 2.15041 | ||||||||
\(311\) | 5.91438 | 0.335374 | 0.167687 | − | 0.985840i | \(-0.446370\pi\) | ||||
0.167687 | + | 0.985840i | \(0.446370\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.7018 | 0.944043 | 0.472022 | − | 0.881587i | \(-0.343524\pi\) | ||||
0.472022 | + | 0.881587i | \(0.343524\pi\) | |||||||
\(314\) | 38.1554 | 2.15323 | ||||||||
\(315\) | −1.79749 | −0.101277 | ||||||||
\(316\) | 17.0767 | 0.960641 | ||||||||
\(317\) | 10.8342 | 0.608508 | 0.304254 | − | 0.952591i | \(-0.401593\pi\) | ||||
0.304254 | + | 0.952591i | \(0.401593\pi\) | |||||||
\(318\) | −29.2692 | −1.64134 | ||||||||
\(319\) | 2.44316 | 0.136791 | ||||||||
\(320\) | −21.5175 | −1.20286 | ||||||||
\(321\) | 17.2886 | 0.964955 | ||||||||
\(322\) | 3.25460 | 0.181372 | ||||||||
\(323\) | 0.753024 | 0.0418994 | ||||||||
\(324\) | −24.2111 | −1.34506 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8.11974 | 0.449711 | ||||||||
\(327\) | −17.2109 | −0.951767 | ||||||||
\(328\) | −21.3861 | −1.18085 | ||||||||
\(329\) | −0.298541 | −0.0164591 | ||||||||
\(330\) | −9.22941 | −0.508062 | ||||||||
\(331\) | −28.8701 | −1.58684 | −0.793421 | − | 0.608673i | \(-0.791702\pi\) | ||||
−0.793421 | + | 0.608673i | \(0.791702\pi\) | |||||||
\(332\) | 33.2471 | 1.82467 | ||||||||
\(333\) | 14.4677 | 0.792823 | ||||||||
\(334\) | −14.7916 | −0.809360 | ||||||||
\(335\) | 10.8141 | 0.590837 | ||||||||
\(336\) | 1.26426 | 0.0689709 | ||||||||
\(337\) | 22.2421 | 1.21160 | 0.605801 | − | 0.795616i | \(-0.292853\pi\) | ||||
0.605801 | + | 0.795616i | \(0.292853\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.1101 | 0.549105 | ||||||||
\(340\) | 0.696035 | 0.0377478 | ||||||||
\(341\) | −10.1942 | −0.552047 | ||||||||
\(342\) | 36.5833 | 1.97820 | ||||||||
\(343\) | 4.66981 | 0.252146 | ||||||||
\(344\) | 15.3966 | 0.830127 | ||||||||
\(345\) | −18.3520 | −0.988037 | ||||||||
\(346\) | 22.0332 | 1.18451 | ||||||||
\(347\) | 2.29240 | 0.123062 | 0.0615312 | − | 0.998105i | \(-0.480402\pi\) | ||||
0.0615312 | + | 0.998105i | \(0.480402\pi\) | |||||||
\(348\) | −17.4085 | −0.933196 | ||||||||
\(349\) | −25.3366 | −1.35624 | −0.678118 | − | 0.734953i | \(-0.737204\pi\) | ||||
−0.678118 | + | 0.734953i | \(0.737204\pi\) | |||||||
\(350\) | 1.60693 | 0.0858942 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.16504 | 0.381898 | ||||||||
\(353\) | −0.552385 | −0.0294005 | −0.0147002 | − | 0.999892i | \(-0.504679\pi\) | ||||
−0.0147002 | + | 0.999892i | \(0.504679\pi\) | |||||||
\(354\) | −65.0571 | −3.45775 | ||||||||
\(355\) | −8.92316 | −0.473592 | ||||||||
\(356\) | −21.1426 | −1.12056 | ||||||||
\(357\) | −0.120494 | −0.00637723 | ||||||||
\(358\) | −29.3624 | −1.55185 | ||||||||
\(359\) | 18.2421 | 0.962784 | 0.481392 | − | 0.876506i | \(-0.340131\pi\) | ||||
0.481392 | + | 0.876506i | \(0.340131\pi\) | |||||||
\(360\) | 10.2288 | 0.539107 | ||||||||
\(361\) | 8.27250 | 0.435395 | ||||||||
\(362\) | −27.6072 | −1.45100 | ||||||||
\(363\) | 2.48500 | 0.130429 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 25.1246 | 1.31508 | ||||||||
\(366\) | −13.1989 | −0.689918 | ||||||||
\(367\) | 28.8039 | 1.50355 | 0.751776 | − | 0.659418i | \(-0.229197\pi\) | ||||
0.751776 | + | 0.659418i | \(0.229197\pi\) | |||||||
\(368\) | 6.63701 | 0.345978 | ||||||||
\(369\) | −35.4856 | −1.84731 | ||||||||
\(370\) | 16.9228 | 0.879777 | ||||||||
\(371\) | 1.79528 | 0.0932062 | ||||||||
\(372\) | 72.6379 | 3.76610 | ||||||||
\(373\) | 3.76201 | 0.194789 | 0.0973946 | − | 0.995246i | \(-0.468949\pi\) | ||||
0.0973946 | + | 0.995246i | \(0.468949\pi\) | |||||||
\(374\) | −0.318122 | −0.0164497 | ||||||||
\(375\) | −29.9780 | −1.54806 | ||||||||
\(376\) | 1.69888 | 0.0876130 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.323022 | −0.0166145 | ||||||||
\(379\) | −21.3722 | −1.09781 | −0.548907 | − | 0.835883i | \(-0.684956\pi\) | ||||
−0.548907 | + | 0.835883i | \(0.684956\pi\) | |||||||
\(380\) | 25.2085 | 1.29317 | ||||||||
\(381\) | 9.36594 | 0.479832 | ||||||||
\(382\) | −2.97569 | −0.152250 | ||||||||
\(383\) | −6.34011 | −0.323964 | −0.161982 | − | 0.986794i | \(-0.551789\pi\) | ||||
−0.161982 | + | 0.986794i | \(0.551789\pi\) | |||||||
\(384\) | −34.4649 | −1.75878 | ||||||||
\(385\) | 0.566101 | 0.0288512 | ||||||||
\(386\) | 10.4692 | 0.532867 | ||||||||
\(387\) | 25.5472 | 1.29864 | ||||||||
\(388\) | −21.1647 | −1.07447 | ||||||||
\(389\) | −7.02161 | −0.356010 | −0.178005 | − | 0.984030i | \(-0.556964\pi\) | ||||
−0.178005 | + | 0.984030i | \(0.556964\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.632561 | −0.0319900 | ||||||||
\(392\) | −13.1789 | −0.665633 | ||||||||
\(393\) | −34.1135 | −1.72080 | ||||||||
\(394\) | −9.20481 | −0.463732 | ||||||||
\(395\) | 10.0258 | 0.504455 | ||||||||
\(396\) | −9.10452 | −0.457519 | ||||||||
\(397\) | −16.5239 | −0.829311 | −0.414656 | − | 0.909978i | \(-0.636098\pi\) | ||||
−0.414656 | + | 0.909978i | \(0.636098\pi\) | |||||||
\(398\) | −47.0262 | −2.35721 | ||||||||
\(399\) | −4.36397 | −0.218472 | ||||||||
\(400\) | 3.27697 | 0.163849 | ||||||||
\(401\) | −13.8349 | −0.690880 | −0.345440 | − | 0.938441i | \(-0.612270\pi\) | ||||
−0.345440 | + | 0.938441i | \(0.612270\pi\) | |||||||
\(402\) | 35.2178 | 1.75651 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −40.3945 | −2.00970 | ||||||||
\(405\) | −14.2145 | −0.706324 | ||||||||
\(406\) | 1.81256 | 0.0899560 | ||||||||
\(407\) | −4.55644 | −0.225854 | ||||||||
\(408\) | 0.685686 | 0.0339465 | ||||||||
\(409\) | −15.9129 | −0.786843 | −0.393421 | − | 0.919358i | \(-0.628709\pi\) | ||||
−0.393421 | + | 0.919358i | \(0.628709\pi\) | |||||||
\(410\) | −41.5076 | −2.04991 | ||||||||
\(411\) | 47.4994 | 2.34297 | ||||||||
\(412\) | −28.1572 | −1.38720 | ||||||||
\(413\) | 3.99039 | 0.196354 | ||||||||
\(414\) | −30.7310 | −1.51035 | ||||||||
\(415\) | 19.5196 | 0.958179 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 18.6476 | 0.913177 | ||||||||
\(418\) | −11.5215 | −0.563536 | ||||||||
\(419\) | 11.8796 | 0.580358 | 0.290179 | − | 0.956972i | \(-0.406285\pi\) | ||||
0.290179 | + | 0.956972i | \(0.406285\pi\) | |||||||
\(420\) | −4.03370 | −0.196825 | ||||||||
\(421\) | 12.3932 | 0.604006 | 0.302003 | − | 0.953307i | \(-0.402345\pi\) | ||||
0.302003 | + | 0.953307i | \(0.402345\pi\) | |||||||
\(422\) | 45.2775 | 2.20408 | ||||||||
\(423\) | 2.81892 | 0.137061 | ||||||||
\(424\) | −10.2162 | −0.496145 | ||||||||
\(425\) | −0.312323 | −0.0151499 | ||||||||
\(426\) | −29.0597 | −1.40795 | ||||||||
\(427\) | 0.809578 | 0.0391782 | ||||||||
\(428\) | 19.9488 | 0.964264 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 29.8826 | 1.44107 | ||||||||
\(431\) | −16.1247 | −0.776702 | −0.388351 | − | 0.921512i | \(-0.626955\pi\) | ||||
−0.388351 | + | 0.921512i | \(0.626955\pi\) | |||||||
\(432\) | −0.658730 | −0.0316932 | ||||||||
\(433\) | −17.3833 | −0.835386 | −0.417693 | − | 0.908588i | \(-0.637161\pi\) | ||||
−0.417693 | + | 0.908588i | \(0.637161\pi\) | |||||||
\(434\) | −7.56300 | −0.363036 | ||||||||
\(435\) | −10.2207 | −0.490043 | ||||||||
\(436\) | −19.8592 | −0.951085 | ||||||||
\(437\) | −22.9097 | −1.09592 | ||||||||
\(438\) | 81.8222 | 3.90962 | ||||||||
\(439\) | 12.4698 | 0.595150 | 0.297575 | − | 0.954698i | \(-0.403822\pi\) | ||||
0.297575 | + | 0.954698i | \(0.403822\pi\) | |||||||
\(440\) | −3.22147 | −0.153577 | ||||||||
\(441\) | −21.8674 | −1.04131 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −31.8864 | −1.51497 | −0.757485 | − | 0.652852i | \(-0.773572\pi\) | ||||
−0.757485 | + | 0.652852i | \(0.773572\pi\) | |||||||
\(444\) | 32.4665 | 1.54079 | ||||||||
\(445\) | −12.4130 | −0.588431 | ||||||||
\(446\) | 43.3423 | 2.05232 | ||||||||
\(447\) | 46.5237 | 2.20049 | ||||||||
\(448\) | 4.29817 | 0.203070 | ||||||||
\(449\) | −6.02668 | −0.284416 | −0.142208 | − | 0.989837i | \(-0.545420\pi\) | ||||
−0.142208 | + | 0.989837i | \(0.545420\pi\) | |||||||
\(450\) | −15.1732 | −0.715271 | ||||||||
\(451\) | 11.1758 | 0.526249 | ||||||||
\(452\) | 11.6658 | 0.548712 | ||||||||
\(453\) | −6.64873 | −0.312384 | ||||||||
\(454\) | −19.1495 | −0.898732 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 24.8337 | 1.16294 | ||||||||
\(457\) | 16.6738 | 0.779968 | 0.389984 | − | 0.920822i | \(-0.372480\pi\) | ||||
0.389984 | + | 0.920822i | \(0.372480\pi\) | |||||||
\(458\) | 45.3853 | 2.12072 | ||||||||
\(459\) | 0.0627824 | 0.00293043 | ||||||||
\(460\) | −21.1759 | −0.987329 | ||||||||
\(461\) | 36.6737 | 1.70806 | 0.854032 | − | 0.520220i | \(-0.174150\pi\) | ||||
0.854032 | + | 0.520220i | \(0.174150\pi\) | |||||||
\(462\) | 1.84360 | 0.0857721 | ||||||||
\(463\) | −12.1287 | −0.563668 | −0.281834 | − | 0.959463i | \(-0.590943\pi\) | ||||
−0.281834 | + | 0.959463i | \(0.590943\pi\) | |||||||
\(464\) | 3.69631 | 0.171597 | ||||||||
\(465\) | 42.6462 | 1.97767 | ||||||||
\(466\) | 31.2656 | 1.44835 | ||||||||
\(467\) | −13.7912 | −0.638179 | −0.319089 | − | 0.947725i | \(-0.603377\pi\) | ||||
−0.319089 | + | 0.947725i | \(0.603377\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.16015 | −0.0997463 | ||||||||
\(470\) | 3.29729 | 0.152093 | ||||||||
\(471\) | 42.9768 | 1.98027 | ||||||||
\(472\) | −22.7078 | −1.04521 | ||||||||
\(473\) | −8.04583 | −0.369948 | ||||||||
\(474\) | 32.6508 | 1.49970 | ||||||||
\(475\) | −11.3115 | −0.519006 | ||||||||
\(476\) | −0.139035 | −0.00637266 | ||||||||
\(477\) | −16.9516 | −0.776161 | ||||||||
\(478\) | 11.4013 | 0.521483 | ||||||||
\(479\) | −29.7342 | −1.35859 | −0.679295 | − | 0.733865i | \(-0.737714\pi\) | ||||
−0.679295 | + | 0.733865i | \(0.737714\pi\) | |||||||
\(480\) | −29.9740 | −1.36812 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 18.5531 | 0.845069 | ||||||||
\(483\) | 3.66586 | 0.166802 | ||||||||
\(484\) | 2.86737 | 0.130335 | ||||||||
\(485\) | −12.4259 | −0.564231 | ||||||||
\(486\) | −49.1736 | −2.23056 | ||||||||
\(487\) | 14.5106 | 0.657537 | 0.328769 | − | 0.944410i | \(-0.393366\pi\) | ||||
0.328769 | + | 0.944410i | \(0.393366\pi\) | |||||||
\(488\) | −4.60700 | −0.208549 | ||||||||
\(489\) | 9.14578 | 0.413586 | ||||||||
\(490\) | −25.5784 | −1.15551 | ||||||||
\(491\) | 42.5048 | 1.91822 | 0.959108 | − | 0.283041i | \(-0.0913431\pi\) | ||||
0.959108 | + | 0.283041i | \(0.0913431\pi\) | |||||||
\(492\) | −79.6324 | −3.59010 | ||||||||
\(493\) | −0.352289 | −0.0158663 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.34532 | −0.240254 | ||||||||
\(496\) | −15.4230 | −0.692514 | ||||||||
\(497\) | 1.78243 | 0.0799528 | ||||||||
\(498\) | 63.5687 | 2.84858 | ||||||||
\(499\) | 34.3952 | 1.53974 | 0.769869 | − | 0.638201i | \(-0.220321\pi\) | ||||
0.769869 | + | 0.638201i | \(0.220321\pi\) | |||||||
\(500\) | −34.5908 | −1.54695 | ||||||||
\(501\) | −16.6607 | −0.744346 | ||||||||
\(502\) | −15.8313 | −0.706585 | ||||||||
\(503\) | −3.66673 | −0.163491 | −0.0817456 | − | 0.996653i | \(-0.526050\pi\) | ||||
−0.0817456 | + | 0.996653i | \(0.526050\pi\) | |||||||
\(504\) | −2.04324 | −0.0910131 | ||||||||
\(505\) | −23.7159 | −1.05534 | ||||||||
\(506\) | 9.67840 | 0.430257 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10.8071 | 0.479488 | ||||||||
\(509\) | 34.8590 | 1.54510 | 0.772549 | − | 0.634955i | \(-0.218982\pi\) | ||||
0.772549 | + | 0.634955i | \(0.218982\pi\) | |||||||
\(510\) | 1.33082 | 0.0589298 | ||||||||
\(511\) | −5.01870 | −0.222014 | ||||||||
\(512\) | 16.6304 | 0.734967 | ||||||||
\(513\) | 2.27381 | 0.100391 | ||||||||
\(514\) | 29.4161 | 1.29749 | ||||||||
\(515\) | −16.5312 | −0.728454 | ||||||||
\(516\) | 57.3299 | 2.52381 | ||||||||
\(517\) | −0.887789 | −0.0390449 | ||||||||
\(518\) | −3.38039 | −0.148526 | ||||||||
\(519\) | 24.8174 | 1.08936 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.8987 | 1.26607 | 0.633037 | − | 0.774121i | \(-0.281808\pi\) | ||||
0.633037 | + | 0.774121i | \(0.281808\pi\) | |||||||
\(522\) | −17.1148 | −0.749095 | ||||||||
\(523\) | −35.5037 | −1.55247 | −0.776234 | − | 0.630444i | \(-0.782873\pi\) | ||||
−0.776234 | + | 0.630444i | \(0.782873\pi\) | |||||||
\(524\) | −39.3627 | −1.71957 | ||||||||
\(525\) | 1.80999 | 0.0789945 | ||||||||
\(526\) | −8.88515 | −0.387411 | ||||||||
\(527\) | 1.46994 | 0.0640316 | ||||||||
\(528\) | 3.75960 | 0.163616 | ||||||||
\(529\) | −3.75523 | −0.163271 | ||||||||
\(530\) | −19.8283 | −0.861287 | ||||||||
\(531\) | −37.6786 | −1.63511 | ||||||||
\(532\) | −5.03547 | −0.218315 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −40.4248 | −1.74935 | ||||||||
\(535\) | 11.7121 | 0.506357 | ||||||||
\(536\) | 12.2926 | 0.530958 | ||||||||
\(537\) | −33.0727 | −1.42719 | ||||||||
\(538\) | 54.6905 | 2.35788 | ||||||||
\(539\) | 6.88692 | 0.296641 | ||||||||
\(540\) | 2.10173 | 0.0904439 | ||||||||
\(541\) | 10.6399 | 0.457443 | 0.228721 | − | 0.973492i | \(-0.426545\pi\) | ||||
0.228721 | + | 0.973492i | \(0.426545\pi\) | |||||||
\(542\) | 57.5400 | 2.47155 | ||||||||
\(543\) | −31.0957 | −1.33445 | ||||||||
\(544\) | −1.03315 | −0.0442961 | ||||||||
\(545\) | −11.6595 | −0.499437 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.5162 | 1.04824 | 0.524119 | − | 0.851645i | \(-0.324395\pi\) | ||||
0.524119 | + | 0.851645i | \(0.324395\pi\) | |||||||
\(548\) | 54.8083 | 2.34129 | ||||||||
\(549\) | −7.64430 | −0.326251 | ||||||||
\(550\) | 4.77864 | 0.203762 | ||||||||
\(551\) | −12.7589 | −0.543549 | ||||||||
\(552\) | −20.8610 | −0.887904 | ||||||||
\(553\) | −2.00269 | −0.0851631 | ||||||||
\(554\) | 1.99540 | 0.0847765 | ||||||||
\(555\) | 19.0613 | 0.809106 | ||||||||
\(556\) | 21.5170 | 0.912523 | ||||||||
\(557\) | −4.63250 | −0.196285 | −0.0981426 | − | 0.995172i | \(-0.531290\pi\) | ||||
−0.0981426 | + | 0.995172i | \(0.531290\pi\) | |||||||
\(558\) | 71.4124 | 3.02313 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0.856466 | 0.0361923 | ||||||||
\(561\) | −0.358321 | −0.0151283 | ||||||||
\(562\) | −10.8592 | −0.458068 | ||||||||
\(563\) | 44.9000 | 1.89231 | 0.946156 | − | 0.323712i | \(-0.104931\pi\) | ||||
0.946156 | + | 0.323712i | \(0.104931\pi\) | |||||||
\(564\) | 6.32586 | 0.266367 | ||||||||
\(565\) | 6.84905 | 0.288141 | ||||||||
\(566\) | −66.0515 | −2.77635 | ||||||||
\(567\) | 2.83939 | 0.119243 | ||||||||
\(568\) | −10.1431 | −0.425595 | ||||||||
\(569\) | 3.18675 | 0.133596 | 0.0667978 | − | 0.997767i | \(-0.478722\pi\) | ||||
0.0667978 | + | 0.997767i | \(0.478722\pi\) | |||||||
\(570\) | 48.1988 | 2.01883 | ||||||||
\(571\) | 9.63072 | 0.403033 | 0.201517 | − | 0.979485i | \(-0.435413\pi\) | ||||
0.201517 | + | 0.979485i | \(0.435413\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.35171 | −0.140020 | ||||||||
\(574\) | 8.29126 | 0.346070 | ||||||||
\(575\) | 9.50196 | 0.396259 | ||||||||
\(576\) | −40.5848 | −1.69103 | ||||||||
\(577\) | −27.6544 | −1.15127 | −0.575634 | − | 0.817708i | \(-0.695245\pi\) | ||||
−0.575634 | + | 0.817708i | \(0.695245\pi\) | |||||||
\(578\) | −37.4597 | −1.55812 | ||||||||
\(579\) | 11.7921 | 0.490063 | ||||||||
\(580\) | −11.7933 | −0.489692 | ||||||||
\(581\) | −3.89909 | −0.161762 | ||||||||
\(582\) | −40.4670 | −1.67741 | ||||||||
\(583\) | 5.33873 | 0.221108 | ||||||||
\(584\) | 28.5595 | 1.18180 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 34.1108 | 1.40911 | ||||||||
\(587\) | −29.1153 | −1.20172 | −0.600858 | − | 0.799356i | \(-0.705174\pi\) | ||||
−0.600858 | + | 0.799356i | \(0.705174\pi\) | |||||||
\(588\) | −49.0722 | −2.02370 | ||||||||
\(589\) | 53.2373 | 2.19360 | ||||||||
\(590\) | −44.0726 | −1.81444 | ||||||||
\(591\) | −10.3680 | −0.426481 | ||||||||
\(592\) | −6.89352 | −0.283322 | ||||||||
\(593\) | 6.27876 | 0.257838 | 0.128919 | − | 0.991655i | \(-0.458849\pi\) | ||||
0.128919 | + | 0.991655i | \(0.458849\pi\) | |||||||
\(594\) | −0.960592 | −0.0394136 | ||||||||
\(595\) | −0.0816282 | −0.00334643 | ||||||||
\(596\) | 53.6824 | 2.19892 | ||||||||
\(597\) | −52.9686 | −2.16786 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −42.9316 | −1.75414 | −0.877068 | − | 0.480366i | \(-0.840504\pi\) | ||||
−0.877068 | + | 0.480366i | \(0.840504\pi\) | |||||||
\(600\) | −10.3000 | −0.420494 | ||||||||
\(601\) | −21.3284 | −0.870005 | −0.435002 | − | 0.900429i | \(-0.643252\pi\) | ||||
−0.435002 | + | 0.900429i | \(0.643252\pi\) | |||||||
\(602\) | −5.96914 | −0.243284 | ||||||||
\(603\) | 20.3968 | 0.830623 | ||||||||
\(604\) | −7.67179 | −0.312161 | ||||||||
\(605\) | 1.68345 | 0.0684420 | ||||||||
\(606\) | −77.2345 | −3.13744 | ||||||||
\(607\) | −13.4656 | −0.546551 | −0.273275 | − | 0.961936i | \(-0.588107\pi\) | ||||
−0.273275 | + | 0.961936i | \(0.588107\pi\) | |||||||
\(608\) | −37.4180 | −1.51750 | ||||||||
\(609\) | 2.04161 | 0.0827300 | ||||||||
\(610\) | −8.94155 | −0.362033 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 1.31281 | 0.0530674 | ||||||||
\(613\) | −26.3116 | −1.06272 | −0.531358 | − | 0.847147i | \(-0.678318\pi\) | ||||
−0.531358 | + | 0.847147i | \(0.678318\pi\) | |||||||
\(614\) | −13.3574 | −0.539060 | ||||||||
\(615\) | −46.7526 | −1.88525 | ||||||||
\(616\) | 0.643497 | 0.0259272 | ||||||||
\(617\) | −31.8975 | −1.28415 | −0.642073 | − | 0.766643i | \(-0.721926\pi\) | ||||
−0.642073 | + | 0.766643i | \(0.721926\pi\) | |||||||
\(618\) | −53.8367 | −2.16563 | ||||||||
\(619\) | −17.0725 | −0.686203 | −0.343101 | − | 0.939298i | \(-0.611477\pi\) | ||||
−0.343101 | + | 0.939298i | \(0.611477\pi\) | |||||||
\(620\) | 49.2083 | 1.97625 | ||||||||
\(621\) | −1.91006 | −0.0766482 | ||||||||
\(622\) | 13.0484 | 0.523192 | ||||||||
\(623\) | 2.47952 | 0.0993400 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.47851 | −0.379141 | ||||||||
\(626\) | 36.8478 | 1.47273 | ||||||||
\(627\) | −12.9774 | −0.518268 | ||||||||
\(628\) | 49.5898 | 1.97885 | ||||||||
\(629\) | 0.657010 | 0.0261967 | ||||||||
\(630\) | −3.96565 | −0.157995 | ||||||||
\(631\) | 30.5452 | 1.21599 | 0.607993 | − | 0.793942i | \(-0.291975\pi\) | ||||
0.607993 | + | 0.793942i | \(0.291975\pi\) | |||||||
\(632\) | 11.3965 | 0.453330 | ||||||||
\(633\) | 50.9990 | 2.02703 | ||||||||
\(634\) | 23.9025 | 0.949289 | ||||||||
\(635\) | 6.34492 | 0.251790 | ||||||||
\(636\) | −38.0407 | −1.50841 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5.39013 | 0.213397 | ||||||||
\(639\) | −16.8303 | −0.665795 | ||||||||
\(640\) | −23.3481 | −0.922915 | ||||||||
\(641\) | 13.0260 | 0.514498 | 0.257249 | − | 0.966345i | \(-0.417184\pi\) | ||||
0.257249 | + | 0.966345i | \(0.417184\pi\) | |||||||
\(642\) | 38.1423 | 1.50536 | ||||||||
\(643\) | −19.1962 | −0.757022 | −0.378511 | − | 0.925597i | \(-0.623564\pi\) | ||||
−0.378511 | + | 0.925597i | \(0.623564\pi\) | |||||||
\(644\) | 4.22994 | 0.166683 | ||||||||
\(645\) | 33.6587 | 1.32531 | ||||||||
\(646\) | 1.66133 | 0.0653642 | ||||||||
\(647\) | −17.7730 | −0.698728 | −0.349364 | − | 0.936987i | \(-0.613602\pi\) | ||||
−0.349364 | + | 0.936987i | \(0.613602\pi\) | |||||||
\(648\) | −16.1579 | −0.634741 | ||||||||
\(649\) | 11.8665 | 0.465800 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.51869 | −0.333874 | ||||||||
\(652\) | 10.5531 | 0.413290 | ||||||||
\(653\) | 0.735452 | 0.0287805 | 0.0143902 | − | 0.999896i | \(-0.495419\pi\) | ||||
0.0143902 | + | 0.999896i | \(0.495419\pi\) | |||||||
\(654\) | −37.9710 | −1.48478 | ||||||||
\(655\) | −23.1101 | −0.902985 | ||||||||
\(656\) | 16.9081 | 0.660151 | ||||||||
\(657\) | 47.3883 | 1.84879 | ||||||||
\(658\) | −0.658644 | −0.0256766 | ||||||||
\(659\) | −37.8565 | −1.47468 | −0.737339 | − | 0.675523i | \(-0.763918\pi\) | ||||
−0.737339 | + | 0.675523i | \(0.763918\pi\) | |||||||
\(660\) | −11.9953 | −0.466916 | ||||||||
\(661\) | 30.5721 | 1.18912 | 0.594559 | − | 0.804052i | \(-0.297327\pi\) | ||||
0.594559 | + | 0.804052i | \(0.297327\pi\) | |||||||
\(662\) | −63.6935 | −2.47552 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 22.1882 | 0.861071 | ||||||||
\(665\) | −2.95635 | −0.114643 | ||||||||
\(666\) | 31.9187 | 1.23683 | ||||||||
\(667\) | 10.7179 | 0.414998 | ||||||||
\(668\) | −19.2244 | −0.743812 | ||||||||
\(669\) | 48.8192 | 1.88746 | ||||||||
\(670\) | 23.8582 | 0.921722 | ||||||||
\(671\) | 2.40749 | 0.0929402 | ||||||||
\(672\) | 5.98740 | 0.230969 | ||||||||
\(673\) | −35.0651 | −1.35166 | −0.675830 | − | 0.737057i | \(-0.736215\pi\) | ||||
−0.675830 | + | 0.737057i | \(0.736215\pi\) | |||||||
\(674\) | 49.0707 | 1.89013 | ||||||||
\(675\) | −0.943080 | −0.0362992 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.7474 | 1.10485 | 0.552426 | − | 0.833562i | \(-0.313702\pi\) | ||||
0.552426 | + | 0.833562i | \(0.313702\pi\) | |||||||
\(678\) | 22.3050 | 0.856619 | ||||||||
\(679\) | 2.48211 | 0.0952546 | ||||||||
\(680\) | 0.464515 | 0.0178133 | ||||||||
\(681\) | −21.5693 | −0.826539 | ||||||||
\(682\) | −22.4906 | −0.861209 | ||||||||
\(683\) | −1.37387 | −0.0525698 | −0.0262849 | − | 0.999654i | \(-0.508368\pi\) | ||||
−0.0262849 | + | 0.999654i | \(0.508368\pi\) | |||||||
\(684\) | 47.5466 | 1.81799 | ||||||||
\(685\) | 32.1783 | 1.22947 | ||||||||
\(686\) | 10.3026 | 0.393355 | ||||||||
\(687\) | 51.1204 | 1.95036 | ||||||||
\(688\) | −12.1727 | −0.464080 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −40.4884 | −1.54137 | ||||||||
\(691\) | −19.1956 | −0.730236 | −0.365118 | − | 0.930961i | \(-0.618971\pi\) | ||||
−0.365118 | + | 0.930961i | \(0.618971\pi\) | |||||||
\(692\) | 28.6361 | 1.08858 | ||||||||
\(693\) | 1.06774 | 0.0405602 | ||||||||
\(694\) | 5.05752 | 0.191981 | ||||||||
\(695\) | 12.6327 | 0.479187 | ||||||||
\(696\) | −11.6180 | −0.440379 | ||||||||
\(697\) | −1.61148 | −0.0610393 | ||||||||
\(698\) | −55.8979 | −2.11577 | ||||||||
\(699\) | 35.2165 | 1.33201 | ||||||||
\(700\) | 2.08850 | 0.0789379 | ||||||||
\(701\) | −8.21771 | −0.310378 | −0.155189 | − | 0.987885i | \(-0.549599\pi\) | ||||
−0.155189 | + | 0.987885i | \(0.549599\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 23.7951 | 0.897450 | ||||||||
\(704\) | 12.7818 | 0.481731 | ||||||||
\(705\) | 3.71395 | 0.139875 | ||||||||
\(706\) | −1.21868 | −0.0458656 | ||||||||
\(707\) | 4.73731 | 0.178165 | ||||||||
\(708\) | −84.5535 | −3.17771 | ||||||||
\(709\) | −20.7010 | −0.777443 | −0.388722 | − | 0.921355i | \(-0.627083\pi\) | ||||
−0.388722 | + | 0.921355i | \(0.627083\pi\) | |||||||
\(710\) | −19.6864 | −0.738817 | ||||||||
\(711\) | 18.9101 | 0.709183 | ||||||||
\(712\) | −14.1100 | −0.528796 | ||||||||
\(713\) | −44.7208 | −1.67481 | ||||||||
\(714\) | −0.265836 | −0.00994865 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −38.1617 | −1.42617 | ||||||||
\(717\) | 12.8420 | 0.479593 | ||||||||
\(718\) | 40.2460 | 1.50197 | ||||||||
\(719\) | −10.8361 | −0.404120 | −0.202060 | − | 0.979373i | \(-0.564764\pi\) | ||||
−0.202060 | + | 0.979373i | \(0.564764\pi\) | |||||||
\(720\) | −8.08703 | −0.301386 | ||||||||
\(721\) | 3.30216 | 0.122979 | ||||||||
\(722\) | 18.2509 | 0.679228 | ||||||||
\(723\) | 20.8975 | 0.777186 | ||||||||
\(724\) | −35.8805 | −1.33349 | ||||||||
\(725\) | 5.29187 | 0.196535 | ||||||||
\(726\) | 5.48243 | 0.203472 | ||||||||
\(727\) | 30.6644 | 1.13728 | 0.568639 | − | 0.822587i | \(-0.307470\pi\) | ||||
0.568639 | + | 0.822587i | \(0.307470\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −30.0564 | −1.11320 | ||||||||
\(730\) | 55.4301 | 2.05156 | ||||||||
\(731\) | 1.16016 | 0.0429100 | ||||||||
\(732\) | −17.1544 | −0.634044 | ||||||||
\(733\) | −38.5550 | −1.42406 | −0.712032 | − | 0.702147i | \(-0.752225\pi\) | ||||
−0.712032 | + | 0.702147i | \(0.752225\pi\) | |||||||
\(734\) | 63.5476 | 2.34558 | ||||||||
\(735\) | −28.8105 | −1.06269 | ||||||||
\(736\) | 31.4322 | 1.15861 | ||||||||
\(737\) | −6.42376 | −0.236622 | ||||||||
\(738\) | −78.2888 | −2.88185 | ||||||||
\(739\) | 40.4469 | 1.48786 | 0.743931 | − | 0.668256i | \(-0.232959\pi\) | ||||
0.743931 | + | 0.668256i | \(0.232959\pi\) | |||||||
\(740\) | 21.9943 | 0.808526 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.96076 | 0.145404 | ||||||||
\(743\) | −49.6898 | −1.82294 | −0.911471 | − | 0.411364i | \(-0.865053\pi\) | ||||
−0.911471 | + | 0.411364i | \(0.865053\pi\) | |||||||
\(744\) | 48.4766 | 1.77724 | ||||||||
\(745\) | 31.5173 | 1.15470 | ||||||||
\(746\) | 8.29978 | 0.303877 | ||||||||
\(747\) | 36.8165 | 1.34705 | ||||||||
\(748\) | −0.413457 | −0.0151175 | ||||||||
\(749\) | −2.33952 | −0.0854843 | ||||||||
\(750\) | −66.1379 | −2.41501 | ||||||||
\(751\) | 25.2579 | 0.921676 | 0.460838 | − | 0.887484i | \(-0.347549\pi\) | ||||
0.460838 | + | 0.887484i | \(0.347549\pi\) | |||||||
\(752\) | −1.34315 | −0.0489798 | ||||||||
\(753\) | −17.8318 | −0.649827 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.50415 | −0.163923 | ||||||||
\(756\) | −0.419826 | −0.0152689 | ||||||||
\(757\) | 5.77428 | 0.209870 | 0.104935 | − | 0.994479i | \(-0.466537\pi\) | ||||
0.104935 | + | 0.994479i | \(0.466537\pi\) | |||||||
\(758\) | −47.1515 | −1.71262 | ||||||||
\(759\) | 10.9014 | 0.395696 | ||||||||
\(760\) | 16.8235 | 0.610252 | ||||||||
\(761\) | 9.00715 | 0.326509 | 0.163254 | − | 0.986584i | \(-0.447801\pi\) | ||||
0.163254 | + | 0.986584i | \(0.447801\pi\) | |||||||
\(762\) | 20.6633 | 0.748551 | ||||||||
\(763\) | 2.32901 | 0.0843160 | ||||||||
\(764\) | −3.86745 | −0.139920 | ||||||||
\(765\) | 0.770761 | 0.0278669 | ||||||||
\(766\) | −13.9876 | −0.505393 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −12.5116 | −0.451474 | ||||||||
\(769\) | −2.37222 | −0.0855445 | −0.0427723 | − | 0.999085i | \(-0.513619\pi\) | ||||
−0.0427723 | + | 0.999085i | \(0.513619\pi\) | |||||||
\(770\) | 1.24894 | 0.0450086 | ||||||||
\(771\) | 33.1332 | 1.19326 | ||||||||
\(772\) | 13.6066 | 0.489712 | ||||||||
\(773\) | −9.63873 | −0.346681 | −0.173341 | − | 0.984862i | \(-0.555456\pi\) | ||||
−0.173341 | + | 0.984862i | \(0.555456\pi\) | |||||||
\(774\) | 56.3626 | 2.02591 | ||||||||
\(775\) | −22.0806 | −0.793158 | ||||||||
\(776\) | −14.1247 | −0.507048 | ||||||||
\(777\) | −3.80754 | −0.136595 | ||||||||
\(778\) | −15.4912 | −0.555385 | ||||||||
\(779\) | −58.3636 | −2.09109 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.30052 | 0.189667 | ||||||||
\(782\) | −1.39556 | −0.0499053 | ||||||||
\(783\) | −1.06376 | −0.0380157 | ||||||||
\(784\) | 10.4194 | 0.372120 | ||||||||
\(785\) | 29.1145 | 1.03914 | ||||||||
\(786\) | −75.2617 | −2.68450 | ||||||||
\(787\) | −1.65984 | −0.0591671 | −0.0295835 | − | 0.999562i | \(-0.509418\pi\) | ||||
−0.0295835 | + | 0.999562i | \(0.509418\pi\) | |||||||
\(788\) | −11.9633 | −0.426176 | ||||||||
\(789\) | −10.0079 | −0.356291 | ||||||||
\(790\) | 22.1191 | 0.786964 | ||||||||
\(791\) | −1.36812 | −0.0486446 | ||||||||
\(792\) | −6.07611 | −0.215905 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −36.4552 | −1.29375 | ||||||||
\(795\) | −22.3339 | −0.792102 | ||||||||
\(796\) | −61.1191 | −2.16631 | ||||||||
\(797\) | 52.7702 | 1.86922 | 0.934608 | − | 0.355680i | \(-0.115751\pi\) | ||||
0.934608 | + | 0.355680i | \(0.115751\pi\) | |||||||
\(798\) | −9.62785 | −0.340822 | ||||||||
\(799\) | 0.128014 | 0.00452880 | ||||||||
\(800\) | 15.5194 | 0.548694 | ||||||||
\(801\) | −23.4125 | −0.827240 | ||||||||
\(802\) | −30.5227 | −1.07779 | ||||||||
\(803\) | −14.9244 | −0.526672 | ||||||||
\(804\) | 45.7720 | 1.61425 | ||||||||
\(805\) | 2.48342 | 0.0875291 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 61.6014 | 2.16847 | ||||||||
\(808\) | −26.9582 | −0.948387 | ||||||||
\(809\) | 10.5907 | 0.372349 | 0.186175 | − | 0.982517i | \(-0.440391\pi\) | ||||
0.186175 | + | 0.982517i | \(0.440391\pi\) | |||||||
\(810\) | −31.3602 | −1.10188 | ||||||||
\(811\) | 14.7106 | 0.516558 | 0.258279 | − | 0.966070i | \(-0.416845\pi\) | ||||
0.258279 | + | 0.966070i | \(0.416845\pi\) | |||||||
\(812\) | 2.35575 | 0.0826708 | ||||||||
\(813\) | 64.8110 | 2.27302 | ||||||||
\(814\) | −10.0525 | −0.352339 | ||||||||
\(815\) | 6.19577 | 0.217028 | ||||||||
\(816\) | −0.542111 | −0.0189777 | ||||||||
\(817\) | 42.0178 | 1.47002 | ||||||||
\(818\) | −35.1073 | −1.22750 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −53.9466 | −1.88390 | ||||||||
\(821\) | 7.31975 | 0.255461 | 0.127731 | − | 0.991809i | \(-0.459231\pi\) | ||||
0.127731 | + | 0.991809i | \(0.459231\pi\) | |||||||
\(822\) | 104.794 | 3.65510 | ||||||||
\(823\) | 2.08194 | 0.0725718 | 0.0362859 | − | 0.999341i | \(-0.488447\pi\) | ||||
0.0362859 | + | 0.999341i | \(0.488447\pi\) | |||||||
\(824\) | −18.7914 | −0.654628 | ||||||||
\(825\) | 5.38249 | 0.187394 | ||||||||
\(826\) | 8.80364 | 0.306318 | ||||||||
\(827\) | −4.80456 | −0.167071 | −0.0835354 | − | 0.996505i | \(-0.526621\pi\) | ||||
−0.0835354 | + | 0.996505i | \(0.526621\pi\) | |||||||
\(828\) | −39.9405 | −1.38803 | ||||||||
\(829\) | −8.29610 | −0.288135 | −0.144068 | − | 0.989568i | \(-0.546018\pi\) | ||||
−0.144068 | + | 0.989568i | \(0.546018\pi\) | |||||||
\(830\) | 43.0643 | 1.49479 | ||||||||
\(831\) | 2.24755 | 0.0779666 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.993051 | −0.0344072 | ||||||||
\(834\) | 41.1406 | 1.42458 | ||||||||
\(835\) | −11.2867 | −0.390593 | ||||||||
\(836\) | −14.9743 | −0.517897 | ||||||||
\(837\) | 4.43859 | 0.153420 | ||||||||
\(838\) | 26.2090 | 0.905374 | ||||||||
\(839\) | 21.8759 | 0.755239 | 0.377620 | − | 0.925961i | \(-0.376743\pi\) | ||||
0.377620 | + | 0.925961i | \(0.376743\pi\) | |||||||
\(840\) | −2.69199 | −0.0928824 | ||||||||
\(841\) | −23.0310 | −0.794171 | ||||||||
\(842\) | 27.3420 | 0.942266 | ||||||||
\(843\) | −12.2314 | −0.421272 | ||||||||
\(844\) | 58.8464 | 2.02558 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.21913 | 0.213818 | ||||||||
\(847\) | −0.336274 | −0.0115545 | ||||||||
\(848\) | 8.07707 | 0.277368 | ||||||||
\(849\) | −74.3980 | −2.55333 | ||||||||
\(850\) | −0.689050 | −0.0236342 | ||||||||
\(851\) | −19.9886 | −0.685200 | ||||||||
\(852\) | −37.7684 | −1.29392 | ||||||||
\(853\) | −14.9307 | −0.511219 | −0.255610 | − | 0.966780i | \(-0.582276\pi\) | ||||
−0.255610 | + | 0.966780i | \(0.582276\pi\) | |||||||
\(854\) | 1.78610 | 0.0611191 | ||||||||
\(855\) | 27.9149 | 0.954669 | ||||||||
\(856\) | 13.3133 | 0.455040 | ||||||||
\(857\) | 27.3522 | 0.934333 | 0.467167 | − | 0.884169i | \(-0.345275\pi\) | ||||
0.467167 | + | 0.884169i | \(0.345275\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.8367 | −0.915656 | −0.457828 | − | 0.889041i | \(-0.651373\pi\) | ||||
−0.457828 | + | 0.889041i | \(0.651373\pi\) | |||||||
\(860\) | 38.8379 | 1.32436 | ||||||||
\(861\) | 9.33897 | 0.318271 | ||||||||
\(862\) | −35.5746 | −1.21168 | ||||||||
\(863\) | 22.5460 | 0.767476 | 0.383738 | − | 0.923442i | \(-0.374637\pi\) | ||||
0.383738 | + | 0.923442i | \(0.374637\pi\) | |||||||
\(864\) | −3.11968 | −0.106134 | ||||||||
\(865\) | 16.8124 | 0.571640 | ||||||||
\(866\) | −38.3512 | −1.30323 | ||||||||
\(867\) | −42.1933 | −1.43296 | ||||||||
\(868\) | −9.82949 | −0.333635 | ||||||||
\(869\) | −5.95553 | −0.202028 | ||||||||
\(870\) | −22.5489 | −0.764480 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −13.2535 | −0.448821 | ||||||||
\(873\) | −23.4369 | −0.793219 | ||||||||
\(874\) | −50.5436 | −1.70966 | ||||||||
\(875\) | 4.05668 | 0.137141 | ||||||||
\(876\) | 106.343 | 3.59299 | ||||||||
\(877\) | −13.0668 | −0.441236 | −0.220618 | − | 0.975360i | \(-0.570807\pi\) | ||||
−0.220618 | + | 0.975360i | \(0.570807\pi\) | |||||||
\(878\) | 27.5110 | 0.928450 | ||||||||
\(879\) | 38.4212 | 1.29592 | ||||||||
\(880\) | 2.54693 | 0.0858569 | ||||||||
\(881\) | 14.0067 | 0.471896 | 0.235948 | − | 0.971766i | \(-0.424180\pi\) | ||||
0.235948 | + | 0.971766i | \(0.424180\pi\) | |||||||
\(882\) | −48.2442 | −1.62447 | ||||||||
\(883\) | −5.69200 | −0.191551 | −0.0957755 | − | 0.995403i | \(-0.530533\pi\) | ||||
−0.0957755 | + | 0.995403i | \(0.530533\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −49.6418 | −1.66869 | ||||||||
\(886\) | −70.3483 | −2.36340 | ||||||||
\(887\) | 26.6418 | 0.894545 | 0.447273 | − | 0.894398i | \(-0.352395\pi\) | ||||
0.447273 | + | 0.894398i | \(0.352395\pi\) | |||||||
\(888\) | 21.6673 | 0.727106 | ||||||||
\(889\) | −1.26742 | −0.0425077 | ||||||||
\(890\) | −27.3856 | −0.917968 | ||||||||
\(891\) | 8.44366 | 0.282873 | ||||||||
\(892\) | 56.3312 | 1.88611 | ||||||||
\(893\) | 4.63631 | 0.155148 | ||||||||
\(894\) | 102.641 | 3.43283 | ||||||||
\(895\) | −22.4050 | −0.748915 | ||||||||
\(896\) | 4.66385 | 0.155808 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −13.2961 | −0.443698 | ||||||||
\(899\) | −24.9061 | −0.830665 | ||||||||
\(900\) | −19.7203 | −0.657344 | ||||||||
\(901\) | −0.769812 | −0.0256461 | ||||||||
\(902\) | 24.6562 | 0.820963 | ||||||||
\(903\) | −6.72342 | −0.223742 | ||||||||
\(904\) | 7.78543 | 0.258939 | ||||||||
\(905\) | −21.0657 | −0.700247 | ||||||||
\(906\) | −14.6685 | −0.487328 | ||||||||
\(907\) | −35.3630 | −1.17421 | −0.587105 | − | 0.809511i | \(-0.699733\pi\) | ||||
−0.587105 | + | 0.809511i | \(0.699733\pi\) | |||||||
\(908\) | −24.8883 | −0.825947 | ||||||||
\(909\) | −44.7312 | −1.48364 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.4640 | 0.379819 | 0.189910 | − | 0.981802i | \(-0.439180\pi\) | ||||
0.189910 | + | 0.981802i | \(0.439180\pi\) | |||||||
\(912\) | −19.6338 | −0.650140 | ||||||||
\(913\) | −11.5950 | −0.383738 | ||||||||
\(914\) | 36.7860 | 1.21677 | ||||||||
\(915\) | −10.0714 | −0.332951 | ||||||||
\(916\) | 58.9865 | 1.94897 | ||||||||
\(917\) | 4.61630 | 0.152444 | ||||||||
\(918\) | 0.138511 | 0.00457155 | ||||||||
\(919\) | 36.7253 | 1.21145 | 0.605727 | − | 0.795672i | \(-0.292882\pi\) | ||||
0.605727 | + | 0.795672i | \(0.292882\pi\) | |||||||
\(920\) | −14.1322 | −0.465925 | ||||||||
\(921\) | −15.0453 | −0.495758 | ||||||||
\(922\) | 80.9100 | 2.66463 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 2.39609 | 0.0788257 | ||||||||
\(925\) | −9.86921 | −0.324498 | ||||||||
\(926\) | −26.7584 | −0.879337 | ||||||||
\(927\) | −31.1801 | −1.02409 | ||||||||
\(928\) | 17.5053 | 0.574641 | ||||||||
\(929\) | −2.34119 | −0.0768120 | −0.0384060 | − | 0.999262i | \(-0.512228\pi\) | ||||
−0.0384060 | + | 0.999262i | \(0.512228\pi\) | |||||||
\(930\) | 94.0865 | 3.08522 | ||||||||
\(931\) | −35.9656 | −1.17873 | ||||||||
\(932\) | 40.6353 | 1.33106 | ||||||||
\(933\) | 14.6972 | 0.481166 | ||||||||
\(934\) | −30.4262 | −0.995577 | ||||||||
\(935\) | −0.242743 | −0.00793855 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −51.2193 | −1.67326 | −0.836631 | − | 0.547767i | \(-0.815478\pi\) | ||||
−0.836631 | + | 0.547767i | \(0.815478\pi\) | |||||||
\(938\) | −4.76574 | −0.155607 | ||||||||
\(939\) | 41.5040 | 1.35443 | ||||||||
\(940\) | 4.28543 | 0.139775 | ||||||||
\(941\) | 20.6159 | 0.672058 | 0.336029 | − | 0.941852i | \(-0.390916\pi\) | ||||
0.336029 | + | 0.941852i | \(0.390916\pi\) | |||||||
\(942\) | 94.8160 | 3.08927 | ||||||||
\(943\) | 49.0271 | 1.59654 | ||||||||
\(944\) | 17.9530 | 0.584321 | ||||||||
\(945\) | −0.246482 | −0.00801807 | ||||||||
\(946\) | −17.7508 | −0.577129 | ||||||||
\(947\) | −23.9223 | −0.777372 | −0.388686 | − | 0.921370i | \(-0.627071\pi\) | ||||
−0.388686 | + | 0.921370i | \(0.627071\pi\) | |||||||
\(948\) | 42.4356 | 1.37824 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −24.9555 | −0.809664 | ||||||||
\(951\) | 26.9229 | 0.873034 | ||||||||
\(952\) | −0.0927882 | −0.00300728 | ||||||||
\(953\) | 39.5009 | 1.27956 | 0.639780 | − | 0.768558i | \(-0.279026\pi\) | ||||
0.639780 | + | 0.768558i | \(0.279026\pi\) | |||||||
\(954\) | −37.3989 | −1.21083 | ||||||||
\(955\) | −2.27060 | −0.0734750 | ||||||||
\(956\) | 14.8180 | 0.479250 | ||||||||
\(957\) | 6.07125 | 0.196256 | ||||||||
\(958\) | −65.6000 | −2.11944 | ||||||||
\(959\) | −6.42770 | −0.207561 | ||||||||
\(960\) | −53.4708 | −1.72576 | ||||||||
\(961\) | 72.9219 | 2.35232 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 22.0905 | 0.711858 | ||||||||
\(964\) | 24.1131 | 0.776630 | ||||||||
\(965\) | 7.98851 | 0.257159 | ||||||||
\(966\) | 8.08767 | 0.260216 | ||||||||
\(967\) | −23.9055 | −0.768750 | −0.384375 | − | 0.923177i | \(-0.625583\pi\) | ||||
−0.384375 | + | 0.923177i | \(0.625583\pi\) | |||||||
\(968\) | 1.91361 | 0.0615057 | ||||||||
\(969\) | 1.87126 | 0.0601136 | ||||||||
\(970\) | −27.4142 | −0.880216 | ||||||||
\(971\) | −43.8547 | −1.40736 | −0.703682 | − | 0.710515i | \(-0.748462\pi\) | ||||
−0.703682 | + | 0.710515i | \(0.748462\pi\) | |||||||
\(972\) | −63.9100 | −2.04991 | ||||||||
\(973\) | −2.52343 | −0.0808973 | ||||||||
\(974\) | 32.0134 | 1.02578 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.64234 | 0.116589 | ||||||||
\(977\) | −33.8398 | −1.08263 | −0.541316 | − | 0.840819i | \(-0.682074\pi\) | ||||
−0.541316 | + | 0.840819i | \(0.682074\pi\) | |||||||
\(978\) | 20.1775 | 0.645206 | ||||||||
\(979\) | 7.37352 | 0.235659 | ||||||||
\(980\) | −33.2437 | −1.06193 | ||||||||
\(981\) | −21.9913 | −0.702129 | ||||||||
\(982\) | 93.7747 | 2.99247 | ||||||||
\(983\) | 43.0887 | 1.37432 | 0.687158 | − | 0.726508i | \(-0.258858\pi\) | ||||
0.687158 | + | 0.726508i | \(0.258858\pi\) | |||||||
\(984\) | −53.1445 | −1.69419 | ||||||||
\(985\) | −7.02373 | −0.223795 | ||||||||
\(986\) | −0.777223 | −0.0247518 | ||||||||
\(987\) | −0.741872 | −0.0236141 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −35.2962 | −1.12235 | ||||||||
\(990\) | −11.7929 | −0.374803 | ||||||||
\(991\) | 39.5491 | 1.25632 | 0.628160 | − | 0.778084i | \(-0.283808\pi\) | ||||
0.628160 | + | 0.778084i | \(0.283808\pi\) | |||||||
\(992\) | −73.0419 | −2.31908 | ||||||||
\(993\) | −71.7421 | −2.27667 | ||||||||
\(994\) | 3.93241 | 0.124729 | ||||||||
\(995\) | −35.8834 | −1.13758 | ||||||||
\(996\) | 82.6190 | 2.61788 | ||||||||
\(997\) | 5.76435 | 0.182559 | 0.0912794 | − | 0.995825i | \(-0.470904\pi\) | ||||
0.0912794 | + | 0.995825i | \(0.470904\pi\) | |||||||
\(998\) | 75.8830 | 2.40204 | ||||||||
\(999\) | 1.98389 | 0.0627674 |
(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 | 1859.2.a.p.1.8 | 8 | ||
13.2 | odd | 12 | 143.2.j.b.56.8 | yes | 16 | ||
13.7 | odd | 12 | 143.2.j.b.23.8 | ✓ | 16 | ||
13.12 | even | 2 | 1859.2.a.o.1.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
143.2.j.b.23.8 | ✓ | 16 | 13.7 | odd | 12 | ||
143.2.j.b.56.8 | yes | 16 | 13.2 | odd | 12 | ||
1859.2.a.o.1.1 | 8 | 13.12 | even | 2 | |||
1859.2.a.p.1.8 | 8 | 1.1 | even | 1 | trivial |