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: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 4 x^{12} - 41 x^{11} + 179 x^{10} + 540 x^{9} - 2773 x^{8} - 2260 x^{7} + 17621 x^{6} - 838 x^{5} - 44478 x^{4} + 16472 x^{3} + 29944 x^{2} - 6856 x + 128 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(0.197152\) 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 | ||||||||
\(5\) | 0.197152 | 0.0881692 | 0.0440846 | − | 0.999028i | \(-0.485963\pi\) | ||||
0.0440846 | + | 0.999028i | \(0.485963\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 1.50880 | 0.570272 | 0.285136 | − | 0.958487i | \(-0.407961\pi\) | ||||
0.285136 | + | 0.958487i | \(0.407961\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.197152 | 0.0623450 | ||||||||
\(11\) | −1.06748 | −0.321857 | −0.160928 | − | 0.986966i | \(-0.551449\pi\) | ||||
−0.160928 | + | 0.986966i | \(0.551449\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −3.56974 | −0.990068 | −0.495034 | − | 0.868874i | \(-0.664844\pi\) | ||||
−0.495034 | + | 0.868874i | \(0.664844\pi\) | |||||||
\(14\) | 1.50880 | 0.403243 | ||||||||
\(15\) | 0.197152 | 0.0509045 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −3.08651 | −0.708094 | −0.354047 | − | 0.935228i | \(-0.615195\pi\) | ||||
−0.354047 | + | 0.935228i | \(0.615195\pi\) | |||||||
\(20\) | 0.197152 | 0.0440846 | ||||||||
\(21\) | 1.50880 | 0.329247 | ||||||||
\(22\) | −1.06748 | −0.227587 | ||||||||
\(23\) | 2.60504 | 0.543189 | 0.271594 | − | 0.962412i | \(-0.412449\pi\) | ||||
0.271594 | + | 0.962412i | \(0.412449\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.96113 | −0.992226 | ||||||||
\(26\) | −3.56974 | −0.700084 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.50880 | 0.285136 | ||||||||
\(29\) | 1.69549 | 0.314845 | 0.157423 | − | 0.987531i | \(-0.449682\pi\) | ||||
0.157423 | + | 0.987531i | \(0.449682\pi\) | |||||||
\(30\) | 0.197152 | 0.0359949 | ||||||||
\(31\) | 8.35472 | 1.50055 | 0.750276 | − | 0.661124i | \(-0.229920\pi\) | ||||
0.750276 | + | 0.661124i | \(0.229920\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.06748 | −0.185824 | ||||||||
\(34\) | 1.00000 | 0.171499 | ||||||||
\(35\) | 0.297463 | 0.0502804 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 10.5779 | 1.73900 | 0.869498 | − | 0.493936i | \(-0.164442\pi\) | ||||
0.869498 | + | 0.493936i | \(0.164442\pi\) | |||||||
\(38\) | −3.08651 | −0.500698 | ||||||||
\(39\) | −3.56974 | −0.571616 | ||||||||
\(40\) | 0.197152 | 0.0311725 | ||||||||
\(41\) | 10.3617 | 1.61823 | 0.809114 | − | 0.587651i | \(-0.199947\pi\) | ||||
0.809114 | + | 0.587651i | \(0.199947\pi\) | |||||||
\(42\) | 1.50880 | 0.232812 | ||||||||
\(43\) | 3.49884 | 0.533568 | 0.266784 | − | 0.963756i | \(-0.414039\pi\) | ||||
0.266784 | + | 0.963756i | \(0.414039\pi\) | |||||||
\(44\) | −1.06748 | −0.160928 | ||||||||
\(45\) | 0.197152 | 0.0293897 | ||||||||
\(46\) | 2.60504 | 0.384093 | ||||||||
\(47\) | 8.36241 | 1.21978 | 0.609892 | − | 0.792485i | \(-0.291213\pi\) | ||||
0.609892 | + | 0.792485i | \(0.291213\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −4.72353 | −0.674790 | ||||||||
\(50\) | −4.96113 | −0.701610 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −3.56974 | −0.495034 | ||||||||
\(53\) | −9.48041 | −1.30223 | −0.651117 | − | 0.758977i | \(-0.725699\pi\) | ||||
−0.651117 | + | 0.758977i | \(0.725699\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −0.210456 | −0.0283778 | ||||||||
\(56\) | 1.50880 | 0.201622 | ||||||||
\(57\) | −3.08651 | −0.408818 | ||||||||
\(58\) | 1.69549 | 0.222629 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | 0.197152 | 0.0254522 | ||||||||
\(61\) | 13.8381 | 1.77179 | 0.885894 | − | 0.463887i | \(-0.153546\pi\) | ||||
0.885894 | + | 0.463887i | \(0.153546\pi\) | |||||||
\(62\) | 8.35472 | 1.06105 | ||||||||
\(63\) | 1.50880 | 0.190091 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.703783 | −0.0872935 | ||||||||
\(66\) | −1.06748 | −0.131397 | ||||||||
\(67\) | 13.1934 | 1.61183 | 0.805914 | − | 0.592033i | \(-0.201674\pi\) | ||||
0.805914 | + | 0.592033i | \(0.201674\pi\) | |||||||
\(68\) | 1.00000 | 0.121268 | ||||||||
\(69\) | 2.60504 | 0.313610 | ||||||||
\(70\) | 0.297463 | 0.0355536 | ||||||||
\(71\) | 0.742176 | 0.0880801 | 0.0440401 | − | 0.999030i | \(-0.485977\pi\) | ||||
0.0440401 | + | 0.999030i | \(0.485977\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −7.50498 | −0.878391 | −0.439196 | − | 0.898391i | \(-0.644736\pi\) | ||||
−0.439196 | + | 0.898391i | \(0.644736\pi\) | |||||||
\(74\) | 10.5779 | 1.22966 | ||||||||
\(75\) | −4.96113 | −0.572862 | ||||||||
\(76\) | −3.08651 | −0.354047 | ||||||||
\(77\) | −1.61061 | −0.183546 | ||||||||
\(78\) | −3.56974 | −0.404194 | ||||||||
\(79\) | 10.8576 | 1.22157 | 0.610786 | − | 0.791795i | \(-0.290853\pi\) | ||||
0.610786 | + | 0.791795i | \(0.290853\pi\) | |||||||
\(80\) | 0.197152 | 0.0220423 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 10.3617 | 1.14426 | ||||||||
\(83\) | −1.77582 | −0.194921 | −0.0974607 | − | 0.995239i | \(-0.531072\pi\) | ||||
−0.0974607 | + | 0.995239i | \(0.531072\pi\) | |||||||
\(84\) | 1.50880 | 0.164623 | ||||||||
\(85\) | 0.197152 | 0.0213842 | ||||||||
\(86\) | 3.49884 | 0.377290 | ||||||||
\(87\) | 1.69549 | 0.181776 | ||||||||
\(88\) | −1.06748 | −0.113794 | ||||||||
\(89\) | 4.46785 | 0.473592 | 0.236796 | − | 0.971559i | \(-0.423903\pi\) | ||||
0.236796 | + | 0.971559i | \(0.423903\pi\) | |||||||
\(90\) | 0.197152 | 0.0207817 | ||||||||
\(91\) | −5.38602 | −0.564608 | ||||||||
\(92\) | 2.60504 | 0.271594 | ||||||||
\(93\) | 8.35472 | 0.866345 | ||||||||
\(94\) | 8.36241 | 0.862517 | ||||||||
\(95\) | −0.608512 | −0.0624320 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 15.6563 | 1.58966 | 0.794830 | − | 0.606832i | \(-0.207560\pi\) | ||||
0.794830 | + | 0.606832i | \(0.207560\pi\) | |||||||
\(98\) | −4.72353 | −0.477149 | ||||||||
\(99\) | −1.06748 | −0.107286 | ||||||||
\(100\) | −4.96113 | −0.496113 | ||||||||
\(101\) | 9.50176 | 0.945460 | 0.472730 | − | 0.881207i | \(-0.343269\pi\) | ||||
0.472730 | + | 0.881207i | \(0.343269\pi\) | |||||||
\(102\) | 1.00000 | 0.0990148 | ||||||||
\(103\) | −3.93030 | −0.387264 | −0.193632 | − | 0.981074i | \(-0.562027\pi\) | ||||
−0.193632 | + | 0.981074i | \(0.562027\pi\) | |||||||
\(104\) | −3.56974 | −0.350042 | ||||||||
\(105\) | 0.297463 | 0.0290294 | ||||||||
\(106\) | −9.48041 | −0.920819 | ||||||||
\(107\) | 6.77958 | 0.655407 | 0.327703 | − | 0.944781i | \(-0.393725\pi\) | ||||
0.327703 | + | 0.944781i | \(0.393725\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 7.32838 | 0.701932 | 0.350966 | − | 0.936388i | \(-0.385853\pi\) | ||||
0.350966 | + | 0.936388i | \(0.385853\pi\) | |||||||
\(110\) | −0.210456 | −0.0200662 | ||||||||
\(111\) | 10.5779 | 1.00401 | ||||||||
\(112\) | 1.50880 | 0.142568 | ||||||||
\(113\) | −15.0982 | −1.42032 | −0.710161 | − | 0.704039i | \(-0.751378\pi\) | ||||
−0.710161 | + | 0.704039i | \(0.751378\pi\) | |||||||
\(114\) | −3.08651 | −0.289078 | ||||||||
\(115\) | 0.513590 | 0.0478925 | ||||||||
\(116\) | 1.69549 | 0.157423 | ||||||||
\(117\) | −3.56974 | −0.330023 | ||||||||
\(118\) | −1.00000 | −0.0920575 | ||||||||
\(119\) | 1.50880 | 0.138311 | ||||||||
\(120\) | 0.197152 | 0.0179975 | ||||||||
\(121\) | −9.86049 | −0.896408 | ||||||||
\(122\) | 13.8381 | 1.25284 | ||||||||
\(123\) | 10.3617 | 0.934285 | ||||||||
\(124\) | 8.35472 | 0.750276 | ||||||||
\(125\) | −1.96386 | −0.175653 | ||||||||
\(126\) | 1.50880 | 0.134414 | ||||||||
\(127\) | −3.70663 | −0.328910 | −0.164455 | − | 0.986385i | \(-0.552587\pi\) | ||||
−0.164455 | + | 0.986385i | \(0.552587\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 3.49884 | 0.308056 | ||||||||
\(130\) | −0.703783 | −0.0617258 | ||||||||
\(131\) | 5.11961 | 0.447302 | 0.223651 | − | 0.974669i | \(-0.428202\pi\) | ||||
0.223651 | + | 0.974669i | \(0.428202\pi\) | |||||||
\(132\) | −1.06748 | −0.0929120 | ||||||||
\(133\) | −4.65692 | −0.403806 | ||||||||
\(134\) | 13.1934 | 1.13973 | ||||||||
\(135\) | 0.197152 | 0.0169682 | ||||||||
\(136\) | 1.00000 | 0.0857493 | ||||||||
\(137\) | −3.58744 | −0.306495 | −0.153248 | − | 0.988188i | \(-0.548973\pi\) | ||||
−0.153248 | + | 0.988188i | \(0.548973\pi\) | |||||||
\(138\) | 2.60504 | 0.221756 | ||||||||
\(139\) | −14.0373 | −1.19063 | −0.595313 | − | 0.803494i | \(-0.702972\pi\) | ||||
−0.595313 | + | 0.803494i | \(0.702972\pi\) | |||||||
\(140\) | 0.297463 | 0.0251402 | ||||||||
\(141\) | 8.36241 | 0.704242 | ||||||||
\(142\) | 0.742176 | 0.0622821 | ||||||||
\(143\) | 3.81062 | 0.318660 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0.334270 | 0.0277596 | ||||||||
\(146\) | −7.50498 | −0.621116 | ||||||||
\(147\) | −4.72353 | −0.389590 | ||||||||
\(148\) | 10.5779 | 0.869498 | ||||||||
\(149\) | −15.8542 | −1.29883 | −0.649413 | − | 0.760436i | \(-0.724985\pi\) | ||||
−0.649413 | + | 0.760436i | \(0.724985\pi\) | |||||||
\(150\) | −4.96113 | −0.405075 | ||||||||
\(151\) | −12.8033 | −1.04192 | −0.520958 | − | 0.853582i | \(-0.674425\pi\) | ||||
−0.520958 | + | 0.853582i | \(0.674425\pi\) | |||||||
\(152\) | −3.08651 | −0.250349 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | −1.61061 | −0.129786 | ||||||||
\(155\) | 1.64715 | 0.132302 | ||||||||
\(156\) | −3.56974 | −0.285808 | ||||||||
\(157\) | −5.34695 | −0.426733 | −0.213367 | − | 0.976972i | \(-0.568443\pi\) | ||||
−0.213367 | + | 0.976972i | \(0.568443\pi\) | |||||||
\(158\) | 10.8576 | 0.863782 | ||||||||
\(159\) | −9.48041 | −0.751845 | ||||||||
\(160\) | 0.197152 | 0.0155863 | ||||||||
\(161\) | 3.93048 | 0.309765 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 1.99629 | 0.156362 | 0.0781808 | − | 0.996939i | \(-0.475089\pi\) | ||||
0.0781808 | + | 0.996939i | \(0.475089\pi\) | |||||||
\(164\) | 10.3617 | 0.809114 | ||||||||
\(165\) | −0.210456 | −0.0163840 | ||||||||
\(166\) | −1.77582 | −0.137830 | ||||||||
\(167\) | 12.1067 | 0.936846 | 0.468423 | − | 0.883504i | \(-0.344822\pi\) | ||||
0.468423 | + | 0.883504i | \(0.344822\pi\) | |||||||
\(168\) | 1.50880 | 0.116406 | ||||||||
\(169\) | −0.256942 | −0.0197648 | ||||||||
\(170\) | 0.197152 | 0.0151209 | ||||||||
\(171\) | −3.08651 | −0.236031 | ||||||||
\(172\) | 3.49884 | 0.266784 | ||||||||
\(173\) | −9.44184 | −0.717849 | −0.358925 | − | 0.933367i | \(-0.616857\pi\) | ||||
−0.358925 | + | 0.933367i | \(0.616857\pi\) | |||||||
\(174\) | 1.69549 | 0.128535 | ||||||||
\(175\) | −7.48534 | −0.565839 | ||||||||
\(176\) | −1.06748 | −0.0804642 | ||||||||
\(177\) | −1.00000 | −0.0751646 | ||||||||
\(178\) | 4.46785 | 0.334880 | ||||||||
\(179\) | −25.1291 | −1.87823 | −0.939117 | − | 0.343597i | \(-0.888355\pi\) | ||||
−0.939117 | + | 0.343597i | \(0.888355\pi\) | |||||||
\(180\) | 0.197152 | 0.0146949 | ||||||||
\(181\) | −0.499522 | −0.0371292 | −0.0185646 | − | 0.999828i | \(-0.505910\pi\) | ||||
−0.0185646 | + | 0.999828i | \(0.505910\pi\) | |||||||
\(182\) | −5.38602 | −0.399238 | ||||||||
\(183\) | 13.8381 | 1.02294 | ||||||||
\(184\) | 2.60504 | 0.192046 | ||||||||
\(185\) | 2.08546 | 0.153326 | ||||||||
\(186\) | 8.35472 | 0.612598 | ||||||||
\(187\) | −1.06748 | −0.0780617 | ||||||||
\(188\) | 8.36241 | 0.609892 | ||||||||
\(189\) | 1.50880 | 0.109749 | ||||||||
\(190\) | −0.608512 | −0.0441461 | ||||||||
\(191\) | −23.2793 | −1.68443 | −0.842217 | − | 0.539139i | \(-0.818750\pi\) | ||||
−0.842217 | + | 0.539139i | \(0.818750\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −24.5273 | −1.76551 | −0.882755 | − | 0.469833i | \(-0.844314\pi\) | ||||
−0.882755 | + | 0.469833i | \(0.844314\pi\) | |||||||
\(194\) | 15.6563 | 1.12406 | ||||||||
\(195\) | −0.703783 | −0.0503989 | ||||||||
\(196\) | −4.72353 | −0.337395 | ||||||||
\(197\) | 21.4206 | 1.52615 | 0.763077 | − | 0.646308i | \(-0.223688\pi\) | ||||
0.763077 | + | 0.646308i | \(0.223688\pi\) | |||||||
\(198\) | −1.06748 | −0.0758624 | ||||||||
\(199\) | −3.94881 | −0.279924 | −0.139962 | − | 0.990157i | \(-0.544698\pi\) | ||||
−0.139962 | + | 0.990157i | \(0.544698\pi\) | |||||||
\(200\) | −4.96113 | −0.350805 | ||||||||
\(201\) | 13.1934 | 0.930589 | ||||||||
\(202\) | 9.50176 | 0.668541 | ||||||||
\(203\) | 2.55815 | 0.179547 | ||||||||
\(204\) | 1.00000 | 0.0700140 | ||||||||
\(205\) | 2.04284 | 0.142678 | ||||||||
\(206\) | −3.93030 | −0.273837 | ||||||||
\(207\) | 2.60504 | 0.181063 | ||||||||
\(208\) | −3.56974 | −0.247517 | ||||||||
\(209\) | 3.29478 | 0.227905 | ||||||||
\(210\) | 0.297463 | 0.0205269 | ||||||||
\(211\) | −1.28881 | −0.0887251 | −0.0443626 | − | 0.999015i | \(-0.514126\pi\) | ||||
−0.0443626 | + | 0.999015i | \(0.514126\pi\) | |||||||
\(212\) | −9.48041 | −0.651117 | ||||||||
\(213\) | 0.742176 | 0.0508531 | ||||||||
\(214\) | 6.77958 | 0.463442 | ||||||||
\(215\) | 0.689804 | 0.0470443 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 12.6056 | 0.855723 | ||||||||
\(218\) | 7.32838 | 0.496341 | ||||||||
\(219\) | −7.50498 | −0.507139 | ||||||||
\(220\) | −0.210456 | −0.0141889 | ||||||||
\(221\) | −3.56974 | −0.240127 | ||||||||
\(222\) | 10.5779 | 0.709942 | ||||||||
\(223\) | −15.7214 | −1.05278 | −0.526392 | − | 0.850242i | \(-0.676455\pi\) | ||||
−0.526392 | + | 0.850242i | \(0.676455\pi\) | |||||||
\(224\) | 1.50880 | 0.100811 | ||||||||
\(225\) | −4.96113 | −0.330742 | ||||||||
\(226\) | −15.0982 | −1.00432 | ||||||||
\(227\) | 18.9667 | 1.25886 | 0.629432 | − | 0.777055i | \(-0.283287\pi\) | ||||
0.629432 | + | 0.777055i | \(0.283287\pi\) | |||||||
\(228\) | −3.08651 | −0.204409 | ||||||||
\(229\) | −7.27448 | −0.480711 | −0.240355 | − | 0.970685i | \(-0.577264\pi\) | ||||
−0.240355 | + | 0.970685i | \(0.577264\pi\) | |||||||
\(230\) | 0.513590 | 0.0338651 | ||||||||
\(231\) | −1.61061 | −0.105970 | ||||||||
\(232\) | 1.69549 | 0.111315 | ||||||||
\(233\) | 4.19965 | 0.275128 | 0.137564 | − | 0.990493i | \(-0.456073\pi\) | ||||
0.137564 | + | 0.990493i | \(0.456073\pi\) | |||||||
\(234\) | −3.56974 | −0.233361 | ||||||||
\(235\) | 1.64867 | 0.107547 | ||||||||
\(236\) | −1.00000 | −0.0650945 | ||||||||
\(237\) | 10.8576 | 0.705275 | ||||||||
\(238\) | 1.50880 | 0.0978008 | ||||||||
\(239\) | 16.3762 | 1.05929 | 0.529645 | − | 0.848219i | \(-0.322325\pi\) | ||||
0.529645 | + | 0.848219i | \(0.322325\pi\) | |||||||
\(240\) | 0.197152 | 0.0127261 | ||||||||
\(241\) | −1.50349 | −0.0968480 | −0.0484240 | − | 0.998827i | \(-0.515420\pi\) | ||||
−0.0484240 | + | 0.998827i | \(0.515420\pi\) | |||||||
\(242\) | −9.86049 | −0.633856 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 13.8381 | 0.885894 | ||||||||
\(245\) | −0.931255 | −0.0594957 | ||||||||
\(246\) | 10.3617 | 0.660639 | ||||||||
\(247\) | 11.0180 | 0.701061 | ||||||||
\(248\) | 8.35472 | 0.530526 | ||||||||
\(249\) | −1.77582 | −0.112538 | ||||||||
\(250\) | −1.96386 | −0.124205 | ||||||||
\(251\) | 4.65482 | 0.293810 | 0.146905 | − | 0.989151i | \(-0.453069\pi\) | ||||
0.146905 | + | 0.989151i | \(0.453069\pi\) | |||||||
\(252\) | 1.50880 | 0.0950453 | ||||||||
\(253\) | −2.78083 | −0.174829 | ||||||||
\(254\) | −3.70663 | −0.232575 | ||||||||
\(255\) | 0.197152 | 0.0123462 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −6.74375 | −0.420664 | −0.210332 | − | 0.977630i | \(-0.567454\pi\) | ||||
−0.210332 | + | 0.977630i | \(0.567454\pi\) | |||||||
\(258\) | 3.49884 | 0.217828 | ||||||||
\(259\) | 15.9599 | 0.991701 | ||||||||
\(260\) | −0.703783 | −0.0436467 | ||||||||
\(261\) | 1.69549 | 0.104948 | ||||||||
\(262\) | 5.11961 | 0.316291 | ||||||||
\(263\) | 27.3944 | 1.68921 | 0.844606 | − | 0.535388i | \(-0.179835\pi\) | ||||
0.844606 | + | 0.535388i | \(0.179835\pi\) | |||||||
\(264\) | −1.06748 | −0.0656987 | ||||||||
\(265\) | −1.86908 | −0.114817 | ||||||||
\(266\) | −4.65692 | −0.285534 | ||||||||
\(267\) | 4.46785 | 0.273428 | ||||||||
\(268\) | 13.1934 | 0.805914 | ||||||||
\(269\) | 4.62812 | 0.282181 | 0.141091 | − | 0.989997i | \(-0.454939\pi\) | ||||
0.141091 | + | 0.989997i | \(0.454939\pi\) | |||||||
\(270\) | 0.197152 | 0.0119983 | ||||||||
\(271\) | −14.6545 | −0.890196 | −0.445098 | − | 0.895482i | \(-0.646831\pi\) | ||||
−0.445098 | + | 0.895482i | \(0.646831\pi\) | |||||||
\(272\) | 1.00000 | 0.0606339 | ||||||||
\(273\) | −5.38602 | −0.325977 | ||||||||
\(274\) | −3.58744 | −0.216725 | ||||||||
\(275\) | 5.29590 | 0.319355 | ||||||||
\(276\) | 2.60504 | 0.156805 | ||||||||
\(277\) | −15.0346 | −0.903340 | −0.451670 | − | 0.892185i | \(-0.649172\pi\) | ||||
−0.451670 | + | 0.892185i | \(0.649172\pi\) | |||||||
\(278\) | −14.0373 | −0.841900 | ||||||||
\(279\) | 8.35472 | 0.500184 | ||||||||
\(280\) | 0.297463 | 0.0177768 | ||||||||
\(281\) | −17.4883 | −1.04326 | −0.521632 | − | 0.853170i | \(-0.674677\pi\) | ||||
−0.521632 | + | 0.853170i | \(0.674677\pi\) | |||||||
\(282\) | 8.36241 | 0.497974 | ||||||||
\(283\) | −33.2804 | −1.97832 | −0.989158 | − | 0.146855i | \(-0.953085\pi\) | ||||
−0.989158 | + | 0.146855i | \(0.953085\pi\) | |||||||
\(284\) | 0.742176 | 0.0440401 | ||||||||
\(285\) | −0.608512 | −0.0360451 | ||||||||
\(286\) | 3.81062 | 0.225327 | ||||||||
\(287\) | 15.6337 | 0.922830 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0.334270 | 0.0196290 | ||||||||
\(291\) | 15.6563 | 0.917790 | ||||||||
\(292\) | −7.50498 | −0.439196 | ||||||||
\(293\) | −1.05772 | −0.0617928 | −0.0308964 | − | 0.999523i | \(-0.509836\pi\) | ||||
−0.0308964 | + | 0.999523i | \(0.509836\pi\) | |||||||
\(294\) | −4.72353 | −0.275482 | ||||||||
\(295\) | −0.197152 | −0.0114786 | ||||||||
\(296\) | 10.5779 | 0.614828 | ||||||||
\(297\) | −1.06748 | −0.0619414 | ||||||||
\(298\) | −15.8542 | −0.918409 | ||||||||
\(299\) | −9.29933 | −0.537794 | ||||||||
\(300\) | −4.96113 | −0.286431 | ||||||||
\(301\) | 5.27904 | 0.304279 | ||||||||
\(302\) | −12.8033 | −0.736746 | ||||||||
\(303\) | 9.50176 | 0.545862 | ||||||||
\(304\) | −3.08651 | −0.177023 | ||||||||
\(305\) | 2.72821 | 0.156217 | ||||||||
\(306\) | 1.00000 | 0.0571662 | ||||||||
\(307\) | −20.8598 | −1.19053 | −0.595266 | − | 0.803529i | \(-0.702953\pi\) | ||||
−0.595266 | + | 0.803529i | \(0.702953\pi\) | |||||||
\(308\) | −1.61061 | −0.0917729 | ||||||||
\(309\) | −3.93030 | −0.223587 | ||||||||
\(310\) | 1.64715 | 0.0935520 | ||||||||
\(311\) | −2.33820 | −0.132587 | −0.0662935 | − | 0.997800i | \(-0.521117\pi\) | ||||
−0.0662935 | + | 0.997800i | \(0.521117\pi\) | |||||||
\(312\) | −3.56974 | −0.202097 | ||||||||
\(313\) | −2.49236 | −0.140877 | −0.0704384 | − | 0.997516i | \(-0.522440\pi\) | ||||
−0.0704384 | + | 0.997516i | \(0.522440\pi\) | |||||||
\(314\) | −5.34695 | −0.301746 | ||||||||
\(315\) | 0.297463 | 0.0167601 | ||||||||
\(316\) | 10.8576 | 0.610786 | ||||||||
\(317\) | 23.3541 | 1.31170 | 0.655850 | − | 0.754891i | \(-0.272310\pi\) | ||||
0.655850 | + | 0.754891i | \(0.272310\pi\) | |||||||
\(318\) | −9.48041 | −0.531635 | ||||||||
\(319\) | −1.80990 | −0.101335 | ||||||||
\(320\) | 0.197152 | 0.0110211 | ||||||||
\(321\) | 6.77958 | 0.378399 | ||||||||
\(322\) | 3.93048 | 0.219037 | ||||||||
\(323\) | −3.08651 | −0.171738 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 17.7100 | 0.982372 | ||||||||
\(326\) | 1.99629 | 0.110564 | ||||||||
\(327\) | 7.32838 | 0.405260 | ||||||||
\(328\) | 10.3617 | 0.572130 | ||||||||
\(329\) | 12.6172 | 0.695608 | ||||||||
\(330\) | −0.210456 | −0.0115852 | ||||||||
\(331\) | 15.3552 | 0.843999 | 0.422000 | − | 0.906596i | \(-0.361328\pi\) | ||||
0.422000 | + | 0.906596i | \(0.361328\pi\) | |||||||
\(332\) | −1.77582 | −0.0974607 | ||||||||
\(333\) | 10.5779 | 0.579665 | ||||||||
\(334\) | 12.1067 | 0.662450 | ||||||||
\(335\) | 2.60110 | 0.142114 | ||||||||
\(336\) | 1.50880 | 0.0823116 | ||||||||
\(337\) | −27.4294 | −1.49418 | −0.747088 | − | 0.664725i | \(-0.768549\pi\) | ||||
−0.747088 | + | 0.664725i | \(0.768549\pi\) | |||||||
\(338\) | −0.256942 | −0.0139758 | ||||||||
\(339\) | −15.0982 | −0.820023 | ||||||||
\(340\) | 0.197152 | 0.0106921 | ||||||||
\(341\) | −8.91848 | −0.482963 | ||||||||
\(342\) | −3.08651 | −0.166899 | ||||||||
\(343\) | −17.6884 | −0.955086 | ||||||||
\(344\) | 3.49884 | 0.188645 | ||||||||
\(345\) | 0.513590 | 0.0276507 | ||||||||
\(346\) | −9.44184 | −0.507596 | ||||||||
\(347\) | −4.95564 | −0.266033 | −0.133016 | − | 0.991114i | \(-0.542466\pi\) | ||||
−0.133016 | + | 0.991114i | \(0.542466\pi\) | |||||||
\(348\) | 1.69549 | 0.0908879 | ||||||||
\(349\) | −4.68176 | −0.250609 | −0.125304 | − | 0.992118i | \(-0.539991\pi\) | ||||
−0.125304 | + | 0.992118i | \(0.539991\pi\) | |||||||
\(350\) | −7.48534 | −0.400108 | ||||||||
\(351\) | −3.56974 | −0.190539 | ||||||||
\(352\) | −1.06748 | −0.0568968 | ||||||||
\(353\) | −7.74350 | −0.412145 | −0.206073 | − | 0.978537i | \(-0.566068\pi\) | ||||
−0.206073 | + | 0.978537i | \(0.566068\pi\) | |||||||
\(354\) | −1.00000 | −0.0531494 | ||||||||
\(355\) | 0.146322 | 0.00776595 | ||||||||
\(356\) | 4.46785 | 0.236796 | ||||||||
\(357\) | 1.50880 | 0.0798540 | ||||||||
\(358\) | −25.1291 | −1.32811 | ||||||||
\(359\) | 20.8428 | 1.10004 | 0.550022 | − | 0.835150i | \(-0.314619\pi\) | ||||
0.550022 | + | 0.835150i | \(0.314619\pi\) | |||||||
\(360\) | 0.197152 | 0.0103908 | ||||||||
\(361\) | −9.47346 | −0.498603 | ||||||||
\(362\) | −0.499522 | −0.0262543 | ||||||||
\(363\) | −9.86049 | −0.517542 | ||||||||
\(364\) | −5.38602 | −0.282304 | ||||||||
\(365\) | −1.47962 | −0.0774470 | ||||||||
\(366\) | 13.8381 | 0.723330 | ||||||||
\(367\) | −26.4124 | −1.37872 | −0.689358 | − | 0.724421i | \(-0.742107\pi\) | ||||
−0.689358 | + | 0.724421i | \(0.742107\pi\) | |||||||
\(368\) | 2.60504 | 0.135797 | ||||||||
\(369\) | 10.3617 | 0.539410 | ||||||||
\(370\) | 2.08546 | 0.108418 | ||||||||
\(371\) | −14.3040 | −0.742627 | ||||||||
\(372\) | 8.35472 | 0.433172 | ||||||||
\(373\) | 27.4940 | 1.42358 | 0.711792 | − | 0.702390i | \(-0.247884\pi\) | ||||
0.711792 | + | 0.702390i | \(0.247884\pi\) | |||||||
\(374\) | −1.06748 | −0.0551980 | ||||||||
\(375\) | −1.96386 | −0.101413 | ||||||||
\(376\) | 8.36241 | 0.431258 | ||||||||
\(377\) | −6.05247 | −0.311718 | ||||||||
\(378\) | 1.50880 | 0.0776042 | ||||||||
\(379\) | 18.5566 | 0.953187 | 0.476593 | − | 0.879124i | \(-0.341871\pi\) | ||||
0.476593 | + | 0.879124i | \(0.341871\pi\) | |||||||
\(380\) | −0.608512 | −0.0312160 | ||||||||
\(381\) | −3.70663 | −0.189896 | ||||||||
\(382\) | −23.2793 | −1.19107 | ||||||||
\(383\) | −30.7392 | −1.57070 | −0.785349 | − | 0.619054i | \(-0.787516\pi\) | ||||
−0.785349 | + | 0.619054i | \(0.787516\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −0.317535 | −0.0161831 | ||||||||
\(386\) | −24.5273 | −1.24840 | ||||||||
\(387\) | 3.49884 | 0.177856 | ||||||||
\(388\) | 15.6563 | 0.794830 | ||||||||
\(389\) | −20.5958 | −1.04425 | −0.522125 | − | 0.852869i | \(-0.674861\pi\) | ||||
−0.522125 | + | 0.852869i | \(0.674861\pi\) | |||||||
\(390\) | −0.703783 | −0.0356374 | ||||||||
\(391\) | 2.60504 | 0.131743 | ||||||||
\(392\) | −4.72353 | −0.238574 | ||||||||
\(393\) | 5.11961 | 0.258250 | ||||||||
\(394\) | 21.4206 | 1.07915 | ||||||||
\(395\) | 2.14060 | 0.107705 | ||||||||
\(396\) | −1.06748 | −0.0536428 | ||||||||
\(397\) | −0.324755 | −0.0162990 | −0.00814949 | − | 0.999967i | \(-0.502594\pi\) | ||||
−0.00814949 | + | 0.999967i | \(0.502594\pi\) | |||||||
\(398\) | −3.94881 | −0.197936 | ||||||||
\(399\) | −4.65692 | −0.233137 | ||||||||
\(400\) | −4.96113 | −0.248057 | ||||||||
\(401\) | 33.6158 | 1.67869 | 0.839347 | − | 0.543596i | \(-0.182937\pi\) | ||||
0.839347 | + | 0.543596i | \(0.182937\pi\) | |||||||
\(402\) | 13.1934 | 0.658026 | ||||||||
\(403\) | −29.8242 | −1.48565 | ||||||||
\(404\) | 9.50176 | 0.472730 | ||||||||
\(405\) | 0.197152 | 0.00979657 | ||||||||
\(406\) | 2.55815 | 0.126959 | ||||||||
\(407\) | −11.2917 | −0.559708 | ||||||||
\(408\) | 1.00000 | 0.0495074 | ||||||||
\(409\) | −12.5737 | −0.621728 | −0.310864 | − | 0.950454i | \(-0.600618\pi\) | ||||
−0.310864 | + | 0.950454i | \(0.600618\pi\) | |||||||
\(410\) | 2.04284 | 0.100888 | ||||||||
\(411\) | −3.58744 | −0.176955 | ||||||||
\(412\) | −3.93030 | −0.193632 | ||||||||
\(413\) | −1.50880 | −0.0742431 | ||||||||
\(414\) | 2.60504 | 0.128031 | ||||||||
\(415\) | −0.350107 | −0.0171861 | ||||||||
\(416\) | −3.56974 | −0.175021 | ||||||||
\(417\) | −14.0373 | −0.687408 | ||||||||
\(418\) | 3.29478 | 0.161153 | ||||||||
\(419\) | 37.5244 | 1.83319 | 0.916594 | − | 0.399819i | \(-0.130927\pi\) | ||||
0.916594 | + | 0.399819i | \(0.130927\pi\) | |||||||
\(420\) | 0.297463 | 0.0145147 | ||||||||
\(421\) | 29.0179 | 1.41424 | 0.707122 | − | 0.707091i | \(-0.249993\pi\) | ||||
0.707122 | + | 0.707091i | \(0.249993\pi\) | |||||||
\(422\) | −1.28881 | −0.0627381 | ||||||||
\(423\) | 8.36241 | 0.406594 | ||||||||
\(424\) | −9.48041 | −0.460409 | ||||||||
\(425\) | −4.96113 | −0.240650 | ||||||||
\(426\) | 0.742176 | 0.0359586 | ||||||||
\(427\) | 20.8789 | 1.01040 | ||||||||
\(428\) | 6.77958 | 0.327703 | ||||||||
\(429\) | 3.81062 | 0.183979 | ||||||||
\(430\) | 0.689804 | 0.0332653 | ||||||||
\(431\) | −14.4178 | −0.694482 | −0.347241 | − | 0.937776i | \(-0.612881\pi\) | ||||
−0.347241 | + | 0.937776i | \(0.612881\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 35.7355 | 1.71734 | 0.858670 | − | 0.512528i | \(-0.171291\pi\) | ||||
0.858670 | + | 0.512528i | \(0.171291\pi\) | |||||||
\(434\) | 12.6056 | 0.605087 | ||||||||
\(435\) | 0.334270 | 0.0160270 | ||||||||
\(436\) | 7.32838 | 0.350966 | ||||||||
\(437\) | −8.04049 | −0.384629 | ||||||||
\(438\) | −7.50498 | −0.358602 | ||||||||
\(439\) | −9.07090 | −0.432930 | −0.216465 | − | 0.976290i | \(-0.569453\pi\) | ||||
−0.216465 | + | 0.976290i | \(0.569453\pi\) | |||||||
\(440\) | −0.210456 | −0.0100331 | ||||||||
\(441\) | −4.72353 | −0.224930 | ||||||||
\(442\) | −3.56974 | −0.169795 | ||||||||
\(443\) | 20.7004 | 0.983507 | 0.491753 | − | 0.870735i | \(-0.336356\pi\) | ||||
0.491753 | + | 0.870735i | \(0.336356\pi\) | |||||||
\(444\) | 10.5779 | 0.502005 | ||||||||
\(445\) | 0.880847 | 0.0417562 | ||||||||
\(446\) | −15.7214 | −0.744430 | ||||||||
\(447\) | −15.8542 | −0.749878 | ||||||||
\(448\) | 1.50880 | 0.0712840 | ||||||||
\(449\) | −1.92736 | −0.0909577 | −0.0454788 | − | 0.998965i | \(-0.514481\pi\) | ||||
−0.0454788 | + | 0.998965i | \(0.514481\pi\) | |||||||
\(450\) | −4.96113 | −0.233870 | ||||||||
\(451\) | −11.0609 | −0.520838 | ||||||||
\(452\) | −15.0982 | −0.710161 | ||||||||
\(453\) | −12.8033 | −0.601551 | ||||||||
\(454\) | 18.9667 | 0.890152 | ||||||||
\(455\) | −1.06187 | −0.0497810 | ||||||||
\(456\) | −3.08651 | −0.144539 | ||||||||
\(457\) | −20.5877 | −0.963053 | −0.481527 | − | 0.876431i | \(-0.659918\pi\) | ||||
−0.481527 | + | 0.876431i | \(0.659918\pi\) | |||||||
\(458\) | −7.27448 | −0.339914 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 0.513590 | 0.0239463 | ||||||||
\(461\) | 21.2081 | 0.987758 | 0.493879 | − | 0.869531i | \(-0.335579\pi\) | ||||
0.493879 | + | 0.869531i | \(0.335579\pi\) | |||||||
\(462\) | −1.61061 | −0.0749323 | ||||||||
\(463\) | 33.2158 | 1.54367 | 0.771835 | − | 0.635823i | \(-0.219339\pi\) | ||||
0.771835 | + | 0.635823i | \(0.219339\pi\) | |||||||
\(464\) | 1.69549 | 0.0787113 | ||||||||
\(465\) | 1.64715 | 0.0763849 | ||||||||
\(466\) | 4.19965 | 0.194545 | ||||||||
\(467\) | 36.7332 | 1.69981 | 0.849905 | − | 0.526936i | \(-0.176659\pi\) | ||||
0.849905 | + | 0.526936i | \(0.176659\pi\) | |||||||
\(468\) | −3.56974 | −0.165011 | ||||||||
\(469\) | 19.9061 | 0.919180 | ||||||||
\(470\) | 1.64867 | 0.0760474 | ||||||||
\(471\) | −5.34695 | −0.246375 | ||||||||
\(472\) | −1.00000 | −0.0460287 | ||||||||
\(473\) | −3.73494 | −0.171733 | ||||||||
\(474\) | 10.8576 | 0.498705 | ||||||||
\(475\) | 15.3126 | 0.702589 | ||||||||
\(476\) | 1.50880 | 0.0691556 | ||||||||
\(477\) | −9.48041 | −0.434078 | ||||||||
\(478\) | 16.3762 | 0.749031 | ||||||||
\(479\) | −28.4509 | −1.29995 | −0.649977 | − | 0.759954i | \(-0.725222\pi\) | ||||
−0.649977 | + | 0.759954i | \(0.725222\pi\) | |||||||
\(480\) | 0.197152 | 0.00899873 | ||||||||
\(481\) | −37.7604 | −1.72173 | ||||||||
\(482\) | −1.50349 | −0.0684819 | ||||||||
\(483\) | 3.93048 | 0.178843 | ||||||||
\(484\) | −9.86049 | −0.448204 | ||||||||
\(485\) | 3.08668 | 0.140159 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 35.4163 | 1.60487 | 0.802433 | − | 0.596743i | \(-0.203539\pi\) | ||||
0.802433 | + | 0.596743i | \(0.203539\pi\) | |||||||
\(488\) | 13.8381 | 0.626422 | ||||||||
\(489\) | 1.99629 | 0.0902754 | ||||||||
\(490\) | −0.931255 | −0.0420698 | ||||||||
\(491\) | 26.6887 | 1.20444 | 0.602221 | − | 0.798329i | \(-0.294283\pi\) | ||||
0.602221 | + | 0.798329i | \(0.294283\pi\) | |||||||
\(492\) | 10.3617 | 0.467142 | ||||||||
\(493\) | 1.69549 | 0.0763611 | ||||||||
\(494\) | 11.0180 | 0.495725 | ||||||||
\(495\) | −0.210456 | −0.00945928 | ||||||||
\(496\) | 8.35472 | 0.375138 | ||||||||
\(497\) | 1.11979 | 0.0502296 | ||||||||
\(498\) | −1.77582 | −0.0795764 | ||||||||
\(499\) | −0.942608 | −0.0421969 | −0.0210985 | − | 0.999777i | \(-0.506716\pi\) | ||||
−0.0210985 | + | 0.999777i | \(0.506716\pi\) | |||||||
\(500\) | −1.96386 | −0.0878264 | ||||||||
\(501\) | 12.1067 | 0.540888 | ||||||||
\(502\) | 4.65482 | 0.207755 | ||||||||
\(503\) | −8.62835 | −0.384719 | −0.192360 | − | 0.981325i | \(-0.561614\pi\) | ||||
−0.192360 | + | 0.981325i | \(0.561614\pi\) | |||||||
\(504\) | 1.50880 | 0.0672072 | ||||||||
\(505\) | 1.87329 | 0.0833604 | ||||||||
\(506\) | −2.78083 | −0.123623 | ||||||||
\(507\) | −0.256942 | −0.0114112 | ||||||||
\(508\) | −3.70663 | −0.164455 | ||||||||
\(509\) | −1.60098 | −0.0709622 | −0.0354811 | − | 0.999370i | \(-0.511296\pi\) | ||||
−0.0354811 | + | 0.999370i | \(0.511296\pi\) | |||||||
\(510\) | 0.197152 | 0.00873005 | ||||||||
\(511\) | −11.3235 | −0.500922 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −3.08651 | −0.136273 | ||||||||
\(514\) | −6.74375 | −0.297454 | ||||||||
\(515\) | −0.774867 | −0.0341447 | ||||||||
\(516\) | 3.49884 | 0.154028 | ||||||||
\(517\) | −8.92669 | −0.392595 | ||||||||
\(518\) | 15.9599 | 0.701238 | ||||||||
\(519\) | −9.44184 | −0.414451 | ||||||||
\(520\) | −0.703783 | −0.0308629 | ||||||||
\(521\) | 18.4489 | 0.808263 | 0.404131 | − | 0.914701i | \(-0.367574\pi\) | ||||
0.404131 | + | 0.914701i | \(0.367574\pi\) | |||||||
\(522\) | 1.69549 | 0.0742097 | ||||||||
\(523\) | 21.0391 | 0.919976 | 0.459988 | − | 0.887925i | \(-0.347854\pi\) | ||||
0.459988 | + | 0.887925i | \(0.347854\pi\) | |||||||
\(524\) | 5.11961 | 0.223651 | ||||||||
\(525\) | −7.48534 | −0.326687 | ||||||||
\(526\) | 27.3944 | 1.19445 | ||||||||
\(527\) | 8.35472 | 0.363938 | ||||||||
\(528\) | −1.06748 | −0.0464560 | ||||||||
\(529\) | −16.2138 | −0.704946 | ||||||||
\(530\) | −1.86908 | −0.0811878 | ||||||||
\(531\) | −1.00000 | −0.0433963 | ||||||||
\(532\) | −4.65692 | −0.201903 | ||||||||
\(533\) | −36.9887 | −1.60216 | ||||||||
\(534\) | 4.46785 | 0.193343 | ||||||||
\(535\) | 1.33661 | 0.0577866 | ||||||||
\(536\) | 13.1934 | 0.569867 | ||||||||
\(537\) | −25.1291 | −1.08440 | ||||||||
\(538\) | 4.62812 | 0.199532 | ||||||||
\(539\) | 5.04226 | 0.217186 | ||||||||
\(540\) | 0.197152 | 0.00848408 | ||||||||
\(541\) | 19.0472 | 0.818903 | 0.409452 | − | 0.912332i | \(-0.365720\pi\) | ||||
0.409452 | + | 0.912332i | \(0.365720\pi\) | |||||||
\(542\) | −14.6545 | −0.629464 | ||||||||
\(543\) | −0.499522 | −0.0214365 | ||||||||
\(544\) | 1.00000 | 0.0428746 | ||||||||
\(545\) | 1.44481 | 0.0618887 | ||||||||
\(546\) | −5.38602 | −0.230500 | ||||||||
\(547\) | −31.5093 | −1.34724 | −0.673621 | − | 0.739077i | \(-0.735262\pi\) | ||||
−0.673621 | + | 0.739077i | \(0.735262\pi\) | |||||||
\(548\) | −3.58744 | −0.153248 | ||||||||
\(549\) | 13.8381 | 0.590596 | ||||||||
\(550\) | 5.29590 | 0.225818 | ||||||||
\(551\) | −5.23315 | −0.222940 | ||||||||
\(552\) | 2.60504 | 0.110878 | ||||||||
\(553\) | 16.3819 | 0.696629 | ||||||||
\(554\) | −15.0346 | −0.638758 | ||||||||
\(555\) | 2.08546 | 0.0885227 | ||||||||
\(556\) | −14.0373 | −0.595313 | ||||||||
\(557\) | −23.7863 | −1.00786 | −0.503929 | − | 0.863745i | \(-0.668113\pi\) | ||||
−0.503929 | + | 0.863745i | \(0.668113\pi\) | |||||||
\(558\) | 8.35472 | 0.353684 | ||||||||
\(559\) | −12.4900 | −0.528269 | ||||||||
\(560\) | 0.297463 | 0.0125701 | ||||||||
\(561\) | −1.06748 | −0.0450690 | ||||||||
\(562\) | −17.4883 | −0.737699 | ||||||||
\(563\) | −10.4358 | −0.439816 | −0.219908 | − | 0.975521i | \(-0.570576\pi\) | ||||
−0.219908 | + | 0.975521i | \(0.570576\pi\) | |||||||
\(564\) | 8.36241 | 0.352121 | ||||||||
\(565\) | −2.97665 | −0.125229 | ||||||||
\(566\) | −33.2804 | −1.39888 | ||||||||
\(567\) | 1.50880 | 0.0633635 | ||||||||
\(568\) | 0.742176 | 0.0311410 | ||||||||
\(569\) | −4.85639 | −0.203590 | −0.101795 | − | 0.994805i | \(-0.532459\pi\) | ||||
−0.101795 | + | 0.994805i | \(0.532459\pi\) | |||||||
\(570\) | −0.608512 | −0.0254878 | ||||||||
\(571\) | −10.7132 | −0.448333 | −0.224166 | − | 0.974551i | \(-0.571966\pi\) | ||||
−0.224166 | + | 0.974551i | \(0.571966\pi\) | |||||||
\(572\) | 3.81062 | 0.159330 | ||||||||
\(573\) | −23.2793 | −0.972508 | ||||||||
\(574\) | 15.6337 | 0.652539 | ||||||||
\(575\) | −12.9240 | −0.538966 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −37.1189 | −1.54528 | −0.772640 | − | 0.634844i | \(-0.781064\pi\) | ||||
−0.772640 | + | 0.634844i | \(0.781064\pi\) | |||||||
\(578\) | 1.00000 | 0.0415945 | ||||||||
\(579\) | −24.5273 | −1.01932 | ||||||||
\(580\) | 0.334270 | 0.0138798 | ||||||||
\(581\) | −2.67935 | −0.111158 | ||||||||
\(582\) | 15.6563 | 0.648976 | ||||||||
\(583\) | 10.1201 | 0.419133 | ||||||||
\(584\) | −7.50498 | −0.310558 | ||||||||
\(585\) | −0.703783 | −0.0290978 | ||||||||
\(586\) | −1.05772 | −0.0436941 | ||||||||
\(587\) | −4.23721 | −0.174889 | −0.0874443 | − | 0.996169i | \(-0.527870\pi\) | ||||
−0.0874443 | + | 0.996169i | \(0.527870\pi\) | |||||||
\(588\) | −4.72353 | −0.194795 | ||||||||
\(589\) | −25.7869 | −1.06253 | ||||||||
\(590\) | −0.197152 | −0.00811663 | ||||||||
\(591\) | 21.4206 | 0.881125 | ||||||||
\(592\) | 10.5779 | 0.434749 | ||||||||
\(593\) | 17.0811 | 0.701437 | 0.350719 | − | 0.936481i | \(-0.385937\pi\) | ||||
0.350719 | + | 0.936481i | \(0.385937\pi\) | |||||||
\(594\) | −1.06748 | −0.0437992 | ||||||||
\(595\) | 0.297463 | 0.0121948 | ||||||||
\(596\) | −15.8542 | −0.649413 | ||||||||
\(597\) | −3.94881 | −0.161614 | ||||||||
\(598\) | −9.29933 | −0.380278 | ||||||||
\(599\) | 1.37562 | 0.0562065 | 0.0281032 | − | 0.999605i | \(-0.491053\pi\) | ||||
0.0281032 | + | 0.999605i | \(0.491053\pi\) | |||||||
\(600\) | −4.96113 | −0.202537 | ||||||||
\(601\) | −12.1746 | −0.496614 | −0.248307 | − | 0.968681i | \(-0.579874\pi\) | ||||
−0.248307 | + | 0.968681i | \(0.579874\pi\) | |||||||
\(602\) | 5.27904 | 0.215158 | ||||||||
\(603\) | 13.1934 | 0.537276 | ||||||||
\(604\) | −12.8033 | −0.520958 | ||||||||
\(605\) | −1.94402 | −0.0790356 | ||||||||
\(606\) | 9.50176 | 0.385983 | ||||||||
\(607\) | −19.7047 | −0.799787 | −0.399894 | − | 0.916562i | \(-0.630953\pi\) | ||||
−0.399894 | + | 0.916562i | \(0.630953\pi\) | |||||||
\(608\) | −3.08651 | −0.125174 | ||||||||
\(609\) | 2.55815 | 0.103662 | ||||||||
\(610\) | 2.72821 | 0.110462 | ||||||||
\(611\) | −29.8517 | −1.20767 | ||||||||
\(612\) | 1.00000 | 0.0404226 | ||||||||
\(613\) | 19.9816 | 0.807047 | 0.403524 | − | 0.914969i | \(-0.367785\pi\) | ||||
0.403524 | + | 0.914969i | \(0.367785\pi\) | |||||||
\(614\) | −20.8598 | −0.841833 | ||||||||
\(615\) | 2.04284 | 0.0823751 | ||||||||
\(616\) | −1.61061 | −0.0648932 | ||||||||
\(617\) | −0.388897 | −0.0156564 | −0.00782821 | − | 0.999969i | \(-0.502492\pi\) | ||||
−0.00782821 | + | 0.999969i | \(0.502492\pi\) | |||||||
\(618\) | −3.93030 | −0.158100 | ||||||||
\(619\) | 5.29120 | 0.212671 | 0.106336 | − | 0.994330i | \(-0.466088\pi\) | ||||
0.106336 | + | 0.994330i | \(0.466088\pi\) | |||||||
\(620\) | 1.64715 | 0.0661512 | ||||||||
\(621\) | 2.60504 | 0.104537 | ||||||||
\(622\) | −2.33820 | −0.0937531 | ||||||||
\(623\) | 6.74109 | 0.270076 | ||||||||
\(624\) | −3.56974 | −0.142904 | ||||||||
\(625\) | 24.4185 | 0.976739 | ||||||||
\(626\) | −2.49236 | −0.0996149 | ||||||||
\(627\) | 3.29478 | 0.131581 | ||||||||
\(628\) | −5.34695 | −0.213367 | ||||||||
\(629\) | 10.5779 | 0.421769 | ||||||||
\(630\) | 0.297463 | 0.0118512 | ||||||||
\(631\) | −24.1983 | −0.963318 | −0.481659 | − | 0.876359i | \(-0.659966\pi\) | ||||
−0.481659 | + | 0.876359i | \(0.659966\pi\) | |||||||
\(632\) | 10.8576 | 0.431891 | ||||||||
\(633\) | −1.28881 | −0.0512255 | ||||||||
\(634\) | 23.3541 | 0.927512 | ||||||||
\(635\) | −0.730770 | −0.0289997 | ||||||||
\(636\) | −9.48041 | −0.375923 | ||||||||
\(637\) | 16.8618 | 0.668088 | ||||||||
\(638\) | −1.80990 | −0.0716547 | ||||||||
\(639\) | 0.742176 | 0.0293600 | ||||||||
\(640\) | 0.197152 | 0.00779313 | ||||||||
\(641\) | 25.0424 | 0.989117 | 0.494558 | − | 0.869144i | \(-0.335330\pi\) | ||||
0.494558 | + | 0.869144i | \(0.335330\pi\) | |||||||
\(642\) | 6.77958 | 0.267569 | ||||||||
\(643\) | 20.5535 | 0.810550 | 0.405275 | − | 0.914195i | \(-0.367176\pi\) | ||||
0.405275 | + | 0.914195i | \(0.367176\pi\) | |||||||
\(644\) | 3.93048 | 0.154883 | ||||||||
\(645\) | 0.689804 | 0.0271610 | ||||||||
\(646\) | −3.08651 | −0.121437 | ||||||||
\(647\) | 4.98493 | 0.195978 | 0.0979889 | − | 0.995188i | \(-0.468759\pi\) | ||||
0.0979889 | + | 0.995188i | \(0.468759\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 1.06748 | 0.0419022 | ||||||||
\(650\) | 17.7100 | 0.694642 | ||||||||
\(651\) | 12.6056 | 0.494052 | ||||||||
\(652\) | 1.99629 | 0.0781808 | ||||||||
\(653\) | −39.8724 | −1.56033 | −0.780163 | − | 0.625576i | \(-0.784864\pi\) | ||||
−0.780163 | + | 0.625576i | \(0.784864\pi\) | |||||||
\(654\) | 7.32838 | 0.286562 | ||||||||
\(655\) | 1.00934 | 0.0394383 | ||||||||
\(656\) | 10.3617 | 0.404557 | ||||||||
\(657\) | −7.50498 | −0.292797 | ||||||||
\(658\) | 12.6172 | 0.491869 | ||||||||
\(659\) | −28.3875 | −1.10582 | −0.552909 | − | 0.833242i | \(-0.686482\pi\) | ||||
−0.552909 | + | 0.833242i | \(0.686482\pi\) | |||||||
\(660\) | −0.210456 | −0.00819198 | ||||||||
\(661\) | 1.44575 | 0.0562331 | 0.0281166 | − | 0.999605i | \(-0.491049\pi\) | ||||
0.0281166 | + | 0.999605i | \(0.491049\pi\) | |||||||
\(662\) | 15.3552 | 0.596798 | ||||||||
\(663\) | −3.56974 | −0.138637 | ||||||||
\(664\) | −1.77582 | −0.0689152 | ||||||||
\(665\) | −0.918121 | −0.0356032 | ||||||||
\(666\) | 10.5779 | 0.409885 | ||||||||
\(667\) | 4.41683 | 0.171020 | ||||||||
\(668\) | 12.1067 | 0.468423 | ||||||||
\(669\) | −15.7214 | −0.607825 | ||||||||
\(670\) | 2.60110 | 0.100489 | ||||||||
\(671\) | −14.7719 | −0.570262 | ||||||||
\(672\) | 1.50880 | 0.0582031 | ||||||||
\(673\) | 10.9909 | 0.423668 | 0.211834 | − | 0.977306i | \(-0.432056\pi\) | ||||
0.211834 | + | 0.977306i | \(0.432056\pi\) | |||||||
\(674\) | −27.4294 | −1.05654 | ||||||||
\(675\) | −4.96113 | −0.190954 | ||||||||
\(676\) | −0.256942 | −0.00988240 | ||||||||
\(677\) | 3.92845 | 0.150983 | 0.0754913 | − | 0.997146i | \(-0.475947\pi\) | ||||
0.0754913 | + | 0.997146i | \(0.475947\pi\) | |||||||
\(678\) | −15.0982 | −0.579844 | ||||||||
\(679\) | 23.6222 | 0.906538 | ||||||||
\(680\) | 0.197152 | 0.00756044 | ||||||||
\(681\) | 18.9667 | 0.726806 | ||||||||
\(682\) | −8.91848 | −0.341506 | ||||||||
\(683\) | 20.3112 | 0.777186 | 0.388593 | − | 0.921409i | \(-0.372961\pi\) | ||||
0.388593 | + | 0.921409i | \(0.372961\pi\) | |||||||
\(684\) | −3.08651 | −0.118016 | ||||||||
\(685\) | −0.707271 | −0.0270234 | ||||||||
\(686\) | −17.6884 | −0.675347 | ||||||||
\(687\) | −7.27448 | −0.277539 | ||||||||
\(688\) | 3.49884 | 0.133392 | ||||||||
\(689\) | 33.8426 | 1.28930 | ||||||||
\(690\) | 0.513590 | 0.0195520 | ||||||||
\(691\) | −39.0453 | −1.48535 | −0.742677 | − | 0.669649i | \(-0.766444\pi\) | ||||
−0.742677 | + | 0.669649i | \(0.766444\pi\) | |||||||
\(692\) | −9.44184 | −0.358925 | ||||||||
\(693\) | −1.61061 | −0.0611819 | ||||||||
\(694\) | −4.95564 | −0.188114 | ||||||||
\(695\) | −2.76748 | −0.104976 | ||||||||
\(696\) | 1.69549 | 0.0642675 | ||||||||
\(697\) | 10.3617 | 0.392478 | ||||||||
\(698\) | −4.68176 | −0.177207 | ||||||||
\(699\) | 4.19965 | 0.158845 | ||||||||
\(700\) | −7.48534 | −0.282919 | ||||||||
\(701\) | 40.3399 | 1.52362 | 0.761808 | − | 0.647803i | \(-0.224312\pi\) | ||||
0.761808 | + | 0.647803i | \(0.224312\pi\) | |||||||
\(702\) | −3.56974 | −0.134731 | ||||||||
\(703\) | −32.6488 | −1.23137 | ||||||||
\(704\) | −1.06748 | −0.0402321 | ||||||||
\(705\) | 1.64867 | 0.0620924 | ||||||||
\(706\) | −7.74350 | −0.291431 | ||||||||
\(707\) | 14.3362 | 0.539169 | ||||||||
\(708\) | −1.00000 | −0.0375823 | ||||||||
\(709\) | −15.6377 | −0.587288 | −0.293644 | − | 0.955915i | \(-0.594868\pi\) | ||||
−0.293644 | + | 0.955915i | \(0.594868\pi\) | |||||||
\(710\) | 0.146322 | 0.00549136 | ||||||||
\(711\) | 10.8576 | 0.407191 | ||||||||
\(712\) | 4.46785 | 0.167440 | ||||||||
\(713\) | 21.7644 | 0.815084 | ||||||||
\(714\) | 1.50880 | 0.0564653 | ||||||||
\(715\) | 0.751272 | 0.0280960 | ||||||||
\(716\) | −25.1291 | −0.939117 | ||||||||
\(717\) | 16.3762 | 0.611581 | ||||||||
\(718\) | 20.8428 | 0.777848 | ||||||||
\(719\) | −37.4057 | −1.39500 | −0.697499 | − | 0.716586i | \(-0.745704\pi\) | ||||
−0.697499 | + | 0.716586i | \(0.745704\pi\) | |||||||
\(720\) | 0.197152 | 0.00734743 | ||||||||
\(721\) | −5.93003 | −0.220846 | ||||||||
\(722\) | −9.47346 | −0.352566 | ||||||||
\(723\) | −1.50349 | −0.0559152 | ||||||||
\(724\) | −0.499522 | −0.0185646 | ||||||||
\(725\) | −8.41156 | −0.312397 | ||||||||
\(726\) | −9.86049 | −0.365957 | ||||||||
\(727\) | −26.0435 | −0.965901 | −0.482951 | − | 0.875648i | \(-0.660435\pi\) | ||||
−0.482951 | + | 0.875648i | \(0.660435\pi\) | |||||||
\(728\) | −5.38602 | −0.199619 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.47962 | −0.0547633 | ||||||||
\(731\) | 3.49884 | 0.129409 | ||||||||
\(732\) | 13.8381 | 0.511471 | ||||||||
\(733\) | 10.3141 | 0.380959 | 0.190480 | − | 0.981691i | \(-0.438996\pi\) | ||||
0.190480 | + | 0.981691i | \(0.438996\pi\) | |||||||
\(734\) | −26.4124 | −0.974899 | ||||||||
\(735\) | −0.931255 | −0.0343498 | ||||||||
\(736\) | 2.60504 | 0.0960231 | ||||||||
\(737\) | −14.0836 | −0.518778 | ||||||||
\(738\) | 10.3617 | 0.381420 | ||||||||
\(739\) | −5.75525 | −0.211710 | −0.105855 | − | 0.994382i | \(-0.533758\pi\) | ||||
−0.105855 | + | 0.994382i | \(0.533758\pi\) | |||||||
\(740\) | 2.08546 | 0.0766629 | ||||||||
\(741\) | 11.0180 | 0.404758 | ||||||||
\(742\) | −14.3040 | −0.525117 | ||||||||
\(743\) | −27.4435 | −1.00681 | −0.503403 | − | 0.864052i | \(-0.667919\pi\) | ||||
−0.503403 | + | 0.864052i | \(0.667919\pi\) | |||||||
\(744\) | 8.35472 | 0.306299 | ||||||||
\(745\) | −3.12569 | −0.114516 | ||||||||
\(746\) | 27.4940 | 1.00663 | ||||||||
\(747\) | −1.77582 | −0.0649738 | ||||||||
\(748\) | −1.06748 | −0.0390309 | ||||||||
\(749\) | 10.2290 | 0.373760 | ||||||||
\(750\) | −1.96386 | −0.0717100 | ||||||||
\(751\) | −6.48953 | −0.236806 | −0.118403 | − | 0.992966i | \(-0.537778\pi\) | ||||
−0.118403 | + | 0.992966i | \(0.537778\pi\) | |||||||
\(752\) | 8.36241 | 0.304946 | ||||||||
\(753\) | 4.65482 | 0.169631 | ||||||||
\(754\) | −6.05247 | −0.220418 | ||||||||
\(755\) | −2.52420 | −0.0918649 | ||||||||
\(756\) | 1.50880 | 0.0548744 | ||||||||
\(757\) | −9.12616 | −0.331696 | −0.165848 | − | 0.986151i | \(-0.553036\pi\) | ||||
−0.165848 | + | 0.986151i | \(0.553036\pi\) | |||||||
\(758\) | 18.5566 | 0.674005 | ||||||||
\(759\) | −2.78083 | −0.100938 | ||||||||
\(760\) | −0.608512 | −0.0220731 | ||||||||
\(761\) | 45.1557 | 1.63689 | 0.818446 | − | 0.574583i | \(-0.194836\pi\) | ||||
0.818446 | + | 0.574583i | \(0.194836\pi\) | |||||||
\(762\) | −3.70663 | −0.134277 | ||||||||
\(763\) | 11.0570 | 0.400292 | ||||||||
\(764\) | −23.2793 | −0.842217 | ||||||||
\(765\) | 0.197152 | 0.00712805 | ||||||||
\(766\) | −30.7392 | −1.11065 | ||||||||
\(767\) | 3.56974 | 0.128896 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −36.0909 | −1.30147 | −0.650735 | − | 0.759305i | \(-0.725539\pi\) | ||||
−0.650735 | + | 0.759305i | \(0.725539\pi\) | |||||||
\(770\) | −0.317535 | −0.0114432 | ||||||||
\(771\) | −6.74375 | −0.242870 | ||||||||
\(772\) | −24.5273 | −0.882755 | ||||||||
\(773\) | −31.7772 | −1.14295 | −0.571473 | − | 0.820621i | \(-0.693628\pi\) | ||||
−0.571473 | + | 0.820621i | \(0.693628\pi\) | |||||||
\(774\) | 3.49884 | 0.125763 | ||||||||
\(775\) | −41.4489 | −1.48889 | ||||||||
\(776\) | 15.6563 | 0.562030 | ||||||||
\(777\) | 15.9599 | 0.572559 | ||||||||
\(778\) | −20.5958 | −0.738397 | ||||||||
\(779\) | −31.9815 | −1.14586 | ||||||||
\(780\) | −0.703783 | −0.0251995 | ||||||||
\(781\) | −0.792257 | −0.0283492 | ||||||||
\(782\) | 2.60504 | 0.0931561 | ||||||||
\(783\) | 1.69549 | 0.0605920 | ||||||||
\(784\) | −4.72353 | −0.168698 | ||||||||
\(785\) | −1.05416 | −0.0376247 | ||||||||
\(786\) | 5.11961 | 0.182610 | ||||||||
\(787\) | 21.4904 | 0.766050 | 0.383025 | − | 0.923738i | \(-0.374882\pi\) | ||||
0.383025 | + | 0.923738i | \(0.374882\pi\) | |||||||
\(788\) | 21.4206 | 0.763077 | ||||||||
\(789\) | 27.3944 | 0.975267 | ||||||||
\(790\) | 2.14060 | 0.0761590 | ||||||||
\(791\) | −22.7802 | −0.809970 | ||||||||
\(792\) | −1.06748 | −0.0379312 | ||||||||
\(793\) | −49.3985 | −1.75419 | ||||||||
\(794\) | −0.324755 | −0.0115251 | ||||||||
\(795\) | −1.86908 | −0.0662896 | ||||||||
\(796\) | −3.94881 | −0.139962 | ||||||||
\(797\) | −21.6325 | −0.766262 | −0.383131 | − | 0.923694i | \(-0.625154\pi\) | ||||
−0.383131 | + | 0.923694i | \(0.625154\pi\) | |||||||
\(798\) | −4.65692 | −0.164853 | ||||||||
\(799\) | 8.36241 | 0.295841 | ||||||||
\(800\) | −4.96113 | −0.175402 | ||||||||
\(801\) | 4.46785 | 0.157864 | ||||||||
\(802\) | 33.6158 | 1.18702 | ||||||||
\(803\) | 8.01140 | 0.282716 | ||||||||
\(804\) | 13.1934 | 0.465295 | ||||||||
\(805\) | 0.774903 | 0.0273117 | ||||||||
\(806\) | −29.8242 | −1.05051 | ||||||||
\(807\) | 4.62812 | 0.162917 | ||||||||
\(808\) | 9.50176 | 0.334271 | ||||||||
\(809\) | 4.20447 | 0.147821 | 0.0739107 | − | 0.997265i | \(-0.476452\pi\) | ||||
0.0739107 | + | 0.997265i | \(0.476452\pi\) | |||||||
\(810\) | 0.197152 | 0.00692722 | ||||||||
\(811\) | −6.84292 | −0.240287 | −0.120144 | − | 0.992757i | \(-0.538336\pi\) | ||||
−0.120144 | + | 0.992757i | \(0.538336\pi\) | |||||||
\(812\) | 2.55815 | 0.0897736 | ||||||||
\(813\) | −14.6545 | −0.513955 | ||||||||
\(814\) | −11.2917 | −0.395773 | ||||||||
\(815\) | 0.393573 | 0.0137863 | ||||||||
\(816\) | 1.00000 | 0.0350070 | ||||||||
\(817\) | −10.7992 | −0.377816 | ||||||||
\(818\) | −12.5737 | −0.439628 | ||||||||
\(819\) | −5.38602 | −0.188203 | ||||||||
\(820\) | 2.04284 | 0.0713389 | ||||||||
\(821\) | 29.7525 | 1.03837 | 0.519184 | − | 0.854663i | \(-0.326236\pi\) | ||||
0.519184 | + | 0.854663i | \(0.326236\pi\) | |||||||
\(822\) | −3.58744 | −0.125126 | ||||||||
\(823\) | 15.6663 | 0.546093 | 0.273046 | − | 0.962001i | \(-0.411969\pi\) | ||||
0.273046 | + | 0.962001i | \(0.411969\pi\) | |||||||
\(824\) | −3.93030 | −0.136918 | ||||||||
\(825\) | 5.29590 | 0.184379 | ||||||||
\(826\) | −1.50880 | −0.0524978 | ||||||||
\(827\) | −2.66571 | −0.0926957 | −0.0463479 | − | 0.998925i | \(-0.514758\pi\) | ||||
−0.0463479 | + | 0.998925i | \(0.514758\pi\) | |||||||
\(828\) | 2.60504 | 0.0905315 | ||||||||
\(829\) | −46.8431 | −1.62693 | −0.813465 | − | 0.581614i | \(-0.802421\pi\) | ||||
−0.813465 | + | 0.581614i | \(0.802421\pi\) | |||||||
\(830\) | −0.350107 | −0.0121524 | ||||||||
\(831\) | −15.0346 | −0.521544 | ||||||||
\(832\) | −3.56974 | −0.123759 | ||||||||
\(833\) | −4.72353 | −0.163661 | ||||||||
\(834\) | −14.0373 | −0.486071 | ||||||||
\(835\) | 2.38687 | 0.0826009 | ||||||||
\(836\) | 3.29478 | 0.113952 | ||||||||
\(837\) | 8.35472 | 0.288782 | ||||||||
\(838\) | 37.5244 | 1.29626 | ||||||||
\(839\) | 16.8031 | 0.580107 | 0.290054 | − | 0.957010i | \(-0.406327\pi\) | ||||
0.290054 | + | 0.957010i | \(0.406327\pi\) | |||||||
\(840\) | 0.297463 | 0.0102634 | ||||||||
\(841\) | −26.1253 | −0.900873 | ||||||||
\(842\) | 29.0179 | 1.00002 | ||||||||
\(843\) | −17.4883 | −0.602329 | ||||||||
\(844\) | −1.28881 | −0.0443626 | ||||||||
\(845\) | −0.0506568 | −0.00174265 | ||||||||
\(846\) | 8.36241 | 0.287506 | ||||||||
\(847\) | −14.8775 | −0.511196 | ||||||||
\(848\) | −9.48041 | −0.325559 | ||||||||
\(849\) | −33.2804 | −1.14218 | ||||||||
\(850\) | −4.96113 | −0.170165 | ||||||||
\(851\) | 27.5559 | 0.944603 | ||||||||
\(852\) | 0.742176 | 0.0254265 | ||||||||
\(853\) | 18.3976 | 0.629923 | 0.314961 | − | 0.949104i | \(-0.398008\pi\) | ||||
0.314961 | + | 0.949104i | \(0.398008\pi\) | |||||||
\(854\) | 20.8789 | 0.714462 | ||||||||
\(855\) | −0.608512 | −0.0208107 | ||||||||
\(856\) | 6.77958 | 0.231721 | ||||||||
\(857\) | −13.3510 | −0.456061 | −0.228031 | − | 0.973654i | \(-0.573229\pi\) | ||||
−0.228031 | + | 0.973654i | \(0.573229\pi\) | |||||||
\(858\) | 3.81062 | 0.130092 | ||||||||
\(859\) | −27.1022 | −0.924716 | −0.462358 | − | 0.886693i | \(-0.652996\pi\) | ||||
−0.462358 | + | 0.886693i | \(0.652996\pi\) | |||||||
\(860\) | 0.689804 | 0.0235221 | ||||||||
\(861\) | 15.6337 | 0.532796 | ||||||||
\(862\) | −14.4178 | −0.491073 | ||||||||
\(863\) | −31.7467 | −1.08067 | −0.540336 | − | 0.841449i | \(-0.681703\pi\) | ||||
−0.540336 | + | 0.841449i | \(0.681703\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −1.86148 | −0.0632922 | ||||||||
\(866\) | 35.7355 | 1.21434 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 12.6056 | 0.427861 | ||||||||
\(869\) | −11.5902 | −0.393171 | ||||||||
\(870\) | 0.334270 | 0.0113328 | ||||||||
\(871\) | −47.0970 | −1.59582 | ||||||||
\(872\) | 7.32838 | 0.248170 | ||||||||
\(873\) | 15.6563 | 0.529887 | ||||||||
\(874\) | −8.04049 | −0.271973 | ||||||||
\(875\) | −2.96307 | −0.100170 | ||||||||
\(876\) | −7.50498 | −0.253570 | ||||||||
\(877\) | 32.2350 | 1.08850 | 0.544249 | − | 0.838924i | \(-0.316815\pi\) | ||||
0.544249 | + | 0.838924i | \(0.316815\pi\) | |||||||
\(878\) | −9.07090 | −0.306128 | ||||||||
\(879\) | −1.05772 | −0.0356761 | ||||||||
\(880\) | −0.210456 | −0.00709446 | ||||||||
\(881\) | −18.2954 | −0.616388 | −0.308194 | − | 0.951324i | \(-0.599725\pi\) | ||||
−0.308194 | + | 0.951324i | \(0.599725\pi\) | |||||||
\(882\) | −4.72353 | −0.159050 | ||||||||
\(883\) | −38.7349 | −1.30353 | −0.651766 | − | 0.758420i | \(-0.725972\pi\) | ||||
−0.651766 | + | 0.758420i | \(0.725972\pi\) | |||||||
\(884\) | −3.56974 | −0.120063 | ||||||||
\(885\) | −0.197152 | −0.00662720 | ||||||||
\(886\) | 20.7004 | 0.695444 | ||||||||
\(887\) | −4.45066 | −0.149439 | −0.0747193 | − | 0.997205i | \(-0.523806\pi\) | ||||
−0.0747193 | + | 0.997205i | \(0.523806\pi\) | |||||||
\(888\) | 10.5779 | 0.354971 | ||||||||
\(889\) | −5.59255 | −0.187568 | ||||||||
\(890\) | 0.880847 | 0.0295261 | ||||||||
\(891\) | −1.06748 | −0.0357619 | ||||||||
\(892\) | −15.7214 | −0.526392 | ||||||||
\(893\) | −25.8107 | −0.863721 | ||||||||
\(894\) | −15.8542 | −0.530244 | ||||||||
\(895\) | −4.95425 | −0.165602 | ||||||||
\(896\) | 1.50880 | 0.0504054 | ||||||||
\(897\) | −9.29933 | −0.310496 | ||||||||
\(898\) | −1.92736 | −0.0643168 | ||||||||
\(899\) | 14.1654 | 0.472442 | ||||||||
\(900\) | −4.96113 | −0.165371 | ||||||||
\(901\) | −9.48041 | −0.315838 | ||||||||
\(902\) | −11.0609 | −0.368288 | ||||||||
\(903\) | 5.27904 | 0.175676 | ||||||||
\(904\) | −15.0982 | −0.502160 | ||||||||
\(905\) | −0.0984818 | −0.00327365 | ||||||||
\(906\) | −12.8033 | −0.425361 | ||||||||
\(907\) | −3.99083 | −0.132513 | −0.0662567 | − | 0.997803i | \(-0.521106\pi\) | ||||
−0.0662567 | + | 0.997803i | \(0.521106\pi\) | |||||||
\(908\) | 18.9667 | 0.629432 | ||||||||
\(909\) | 9.50176 | 0.315153 | ||||||||
\(910\) | −1.06187 | −0.0352005 | ||||||||
\(911\) | −2.13351 | −0.0706864 | −0.0353432 | − | 0.999375i | \(-0.511252\pi\) | ||||
−0.0353432 | + | 0.999375i | \(0.511252\pi\) | |||||||
\(912\) | −3.08651 | −0.102205 | ||||||||
\(913\) | 1.89565 | 0.0627368 | ||||||||
\(914\) | −20.5877 | −0.680981 | ||||||||
\(915\) | 2.72821 | 0.0901920 | ||||||||
\(916\) | −7.27448 | −0.240355 | ||||||||
\(917\) | 7.72445 | 0.255084 | ||||||||
\(918\) | 1.00000 | 0.0330049 | ||||||||
\(919\) | −32.1332 | −1.05998 | −0.529988 | − | 0.848005i | \(-0.677804\pi\) | ||||
−0.529988 | + | 0.848005i | \(0.677804\pi\) | |||||||
\(920\) | 0.513590 | 0.0169326 | ||||||||
\(921\) | −20.8598 | −0.687354 | ||||||||
\(922\) | 21.2081 | 0.698450 | ||||||||
\(923\) | −2.64938 | −0.0872053 | ||||||||
\(924\) | −1.61061 | −0.0529851 | ||||||||
\(925\) | −52.4784 | −1.72548 | ||||||||
\(926\) | 33.2158 | 1.09154 | ||||||||
\(927\) | −3.93030 | −0.129088 | ||||||||
\(928\) | 1.69549 | 0.0556573 | ||||||||
\(929\) | −5.96853 | −0.195821 | −0.0979106 | − | 0.995195i | \(-0.531216\pi\) | ||||
−0.0979106 | + | 0.995195i | \(0.531216\pi\) | |||||||
\(930\) | 1.64715 | 0.0540123 | ||||||||
\(931\) | 14.5792 | 0.477815 | ||||||||
\(932\) | 4.19965 | 0.137564 | ||||||||
\(933\) | −2.33820 | −0.0765491 | ||||||||
\(934\) | 36.7332 | 1.20195 | ||||||||
\(935\) | −0.210456 | −0.00688264 | ||||||||
\(936\) | −3.56974 | −0.116681 | ||||||||
\(937\) | 33.3139 | 1.08832 | 0.544158 | − | 0.838982i | \(-0.316849\pi\) | ||||
0.544158 | + | 0.838982i | \(0.316849\pi\) | |||||||
\(938\) | 19.9061 | 0.649958 | ||||||||
\(939\) | −2.49236 | −0.0813352 | ||||||||
\(940\) | 1.64867 | 0.0537736 | ||||||||
\(941\) | 46.8492 | 1.52724 | 0.763621 | − | 0.645665i | \(-0.223420\pi\) | ||||
0.763621 | + | 0.645665i | \(0.223420\pi\) | |||||||
\(942\) | −5.34695 | −0.174213 | ||||||||
\(943\) | 26.9927 | 0.879004 | ||||||||
\(944\) | −1.00000 | −0.0325472 | ||||||||
\(945\) | 0.297463 | 0.00967646 | ||||||||
\(946\) | −3.73494 | −0.121433 | ||||||||
\(947\) | 10.9315 | 0.355226 | 0.177613 | − | 0.984100i | \(-0.443163\pi\) | ||||
0.177613 | + | 0.984100i | \(0.443163\pi\) | |||||||
\(948\) | 10.8576 | 0.352638 | ||||||||
\(949\) | 26.7908 | 0.869667 | ||||||||
\(950\) | 15.3126 | 0.496805 | ||||||||
\(951\) | 23.3541 | 0.757310 | ||||||||
\(952\) | 1.50880 | 0.0489004 | ||||||||
\(953\) | −41.1242 | −1.33214 | −0.666072 | − | 0.745888i | \(-0.732026\pi\) | ||||
−0.666072 | + | 0.745888i | \(0.732026\pi\) | |||||||
\(954\) | −9.48041 | −0.306940 | ||||||||
\(955\) | −4.58957 | −0.148515 | ||||||||
\(956\) | 16.3762 | 0.529645 | ||||||||
\(957\) | −1.80990 | −0.0585058 | ||||||||
\(958\) | −28.4509 | −0.919206 | ||||||||
\(959\) | −5.41271 | −0.174786 | ||||||||
\(960\) | 0.197152 | 0.00636306 | ||||||||
\(961\) | 38.8014 | 1.25166 | ||||||||
\(962\) | −37.7604 | −1.21744 | ||||||||
\(963\) | 6.77958 | 0.218469 | ||||||||
\(964\) | −1.50349 | −0.0484240 | ||||||||
\(965\) | −4.83560 | −0.155664 | ||||||||
\(966\) | 3.93048 | 0.126461 | ||||||||
\(967\) | 11.0062 | 0.353937 | 0.176968 | − | 0.984217i | \(-0.443371\pi\) | ||||
0.176968 | + | 0.984217i | \(0.443371\pi\) | |||||||
\(968\) | −9.86049 | −0.316928 | ||||||||
\(969\) | −3.08651 | −0.0991529 | ||||||||
\(970\) | 3.08668 | 0.0991073 | ||||||||
\(971\) | 48.5171 | 1.55699 | 0.778495 | − | 0.627651i | \(-0.215984\pi\) | ||||
0.778495 | + | 0.627651i | \(0.215984\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −21.1794 | −0.678980 | ||||||||
\(974\) | 35.4163 | 1.13481 | ||||||||
\(975\) | 17.7100 | 0.567173 | ||||||||
\(976\) | 13.8381 | 0.442947 | ||||||||
\(977\) | −2.74376 | −0.0877805 | −0.0438903 | − | 0.999036i | \(-0.513975\pi\) | ||||
−0.0438903 | + | 0.999036i | \(0.513975\pi\) | |||||||
\(978\) | 1.99629 | 0.0638344 | ||||||||
\(979\) | −4.76934 | −0.152429 | ||||||||
\(980\) | −0.931255 | −0.0297478 | ||||||||
\(981\) | 7.32838 | 0.233977 | ||||||||
\(982\) | 26.6887 | 0.851669 | ||||||||
\(983\) | 18.8604 | 0.601552 | 0.300776 | − | 0.953695i | \(-0.402754\pi\) | ||||
0.300776 | + | 0.953695i | \(0.402754\pi\) | |||||||
\(984\) | 10.3617 | 0.330320 | ||||||||
\(985\) | 4.22312 | 0.134560 | ||||||||
\(986\) | 1.69549 | 0.0539955 | ||||||||
\(987\) | 12.6172 | 0.401609 | ||||||||
\(988\) | 11.0180 | 0.350531 | ||||||||
\(989\) | 9.11463 | 0.289828 | ||||||||
\(990\) | −0.210456 | −0.00668872 | ||||||||
\(991\) | −18.6297 | −0.591793 | −0.295897 | − | 0.955220i | \(-0.595618\pi\) | ||||
−0.295897 | + | 0.955220i | \(0.595618\pi\) | |||||||
\(992\) | 8.35472 | 0.265263 | ||||||||
\(993\) | 15.3552 | 0.487283 | ||||||||
\(994\) | 1.11979 | 0.0355177 | ||||||||
\(995\) | −0.778517 | −0.0246807 | ||||||||
\(996\) | −1.77582 | −0.0562690 | ||||||||
\(997\) | −6.25843 | −0.198207 | −0.0991033 | − | 0.995077i | \(-0.531597\pi\) | ||||
−0.0991033 | + | 0.995077i | \(0.531597\pi\) | |||||||
\(998\) | −0.942608 | −0.0298377 | ||||||||
\(999\) | 10.5779 | 0.334670 |
(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.bb.1.7 | ✓ | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6018.2.a.bb.1.7 | ✓ | 13 | 1.1 | even | 1 | trivial |