Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(1,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1155.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.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: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.13448.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 7x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.546295\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1155.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.546295 | 0.386289 | 0.193144 | − | 0.981170i | \(-0.438131\pi\) | ||||
0.193144 | + | 0.981170i | \(0.438131\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.70156 | −0.850781 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0.546295 | 0.223024 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.02214 | −0.714936 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.546295 | −0.172754 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −1.70156 | −0.491199 | ||||||||
\(13\) | −0.568438 | −0.157656 | −0.0788282 | − | 0.996888i | \(-0.525118\pi\) | ||||
−0.0788282 | + | 0.996888i | \(0.525118\pi\) | |||||||
\(14\) | −0.546295 | −0.146003 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 2.29844 | 0.574609 | ||||||||
\(17\) | 2.70156 | 0.655225 | 0.327613 | − | 0.944812i | \(-0.393756\pi\) | ||||
0.327613 | + | 0.944812i | \(0.393756\pi\) | |||||||
\(18\) | 0.546295 | 0.128763 | ||||||||
\(19\) | 6.62049 | 1.51885 | 0.759423 | − | 0.650598i | \(-0.225482\pi\) | ||||
0.759423 | + | 0.650598i | \(0.225482\pi\) | |||||||
\(20\) | 1.70156 | 0.380481 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −0.546295 | −0.116470 | ||||||||
\(23\) | 8.93103 | 1.86225 | 0.931124 | − | 0.364703i | \(-0.118829\pi\) | ||||
0.931124 | + | 0.364703i | \(0.118829\pi\) | |||||||
\(24\) | −2.02214 | −0.412768 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.310535 | −0.0609009 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.70156 | 0.321565 | ||||||||
\(29\) | 5.27000 | 0.978615 | 0.489307 | − | 0.872111i | \(-0.337250\pi\) | ||||
0.489307 | + | 0.872111i | \(0.337250\pi\) | |||||||
\(30\) | −0.546295 | −0.0997393 | ||||||||
\(31\) | 9.66103 | 1.73517 | 0.867586 | − | 0.497287i | \(-0.165671\pi\) | ||||
0.867586 | + | 0.497287i | \(0.165671\pi\) | |||||||
\(32\) | 5.29991 | 0.936901 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 1.47585 | 0.253106 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −1.70156 | −0.283594 | ||||||||
\(37\) | −2.75362 | −0.452692 | −0.226346 | − | 0.974047i | \(-0.572678\pi\) | ||||
−0.226346 | + | 0.974047i | \(0.572678\pi\) | |||||||
\(38\) | 3.61674 | 0.586713 | ||||||||
\(39\) | −0.568438 | −0.0910230 | ||||||||
\(40\) | 2.02214 | 0.319729 | ||||||||
\(41\) | −10.9831 | −1.71527 | −0.857635 | − | 0.514259i | \(-0.828067\pi\) | ||||
−0.857635 | + | 0.514259i | \(0.828067\pi\) | |||||||
\(42\) | −0.546295 | −0.0842951 | ||||||||
\(43\) | −0.0520550 | −0.00793831 | −0.00396916 | − | 0.999992i | \(-0.501263\pi\) | ||||
−0.00396916 | + | 0.999992i | \(0.501263\pi\) | |||||||
\(44\) | 1.70156 | 0.256520 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 4.87897 | 0.719365 | ||||||||
\(47\) | −10.1567 | −1.48151 | −0.740756 | − | 0.671774i | \(-0.765533\pi\) | ||||
−0.740756 | + | 0.671774i | \(0.765533\pi\) | |||||||
\(48\) | 2.29844 | 0.331751 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0.546295 | 0.0772577 | ||||||||
\(51\) | 2.70156 | 0.378294 | ||||||||
\(52\) | 0.967233 | 0.134131 | ||||||||
\(53\) | 1.56469 | 0.214926 | 0.107463 | − | 0.994209i | \(-0.465727\pi\) | ||||
0.107463 | + | 0.994209i | \(0.465727\pi\) | |||||||
\(54\) | 0.546295 | 0.0743413 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 2.02214 | 0.270220 | ||||||||
\(57\) | 6.62049 | 0.876906 | ||||||||
\(58\) | 2.87897 | 0.378028 | ||||||||
\(59\) | 6.36259 | 0.828339 | 0.414169 | − | 0.910200i | \(-0.364072\pi\) | ||||
0.414169 | + | 0.910200i | \(0.364072\pi\) | |||||||
\(60\) | 1.70156 | 0.219671 | ||||||||
\(61\) | −3.71308 | −0.475412 | −0.237706 | − | 0.971337i | \(-0.576395\pi\) | ||||
−0.237706 | + | 0.971337i | \(0.576395\pi\) | |||||||
\(62\) | 5.27777 | 0.670277 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | −1.70156 | −0.212695 | ||||||||
\(65\) | 0.568438 | 0.0705061 | ||||||||
\(66\) | −0.546295 | −0.0672442 | ||||||||
\(67\) | −10.4146 | −1.27235 | −0.636176 | − | 0.771544i | \(-0.719485\pi\) | ||||
−0.636176 | + | 0.771544i | \(0.719485\pi\) | |||||||
\(68\) | −4.59688 | −0.557453 | ||||||||
\(69\) | 8.93103 | 1.07517 | ||||||||
\(70\) | 0.546295 | 0.0652947 | ||||||||
\(71\) | 2.56844 | 0.304818 | 0.152409 | − | 0.988318i | \(-0.451297\pi\) | ||||
0.152409 | + | 0.988318i | \(0.451297\pi\) | |||||||
\(72\) | −2.02214 | −0.238312 | ||||||||
\(73\) | 2.26625 | 0.265244 | 0.132622 | − | 0.991167i | \(-0.457660\pi\) | ||||
0.132622 | + | 0.991167i | \(0.457660\pi\) | |||||||
\(74\) | −1.50429 | −0.174870 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | −11.2652 | −1.29220 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | −0.310535 | −0.0351612 | ||||||||
\(79\) | −2.56844 | −0.288972 | −0.144486 | − | 0.989507i | \(-0.546153\pi\) | ||||
−0.144486 | + | 0.989507i | \(0.546153\pi\) | |||||||
\(80\) | −2.29844 | −0.256973 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −6.00000 | −0.662589 | ||||||||
\(83\) | 17.1605 | 1.88361 | 0.941804 | − | 0.336161i | \(-0.109129\pi\) | ||||
0.941804 | + | 0.336161i | \(0.109129\pi\) | |||||||
\(84\) | 1.70156 | 0.185656 | ||||||||
\(85\) | −2.70156 | −0.293026 | ||||||||
\(86\) | −0.0284374 | −0.00306648 | ||||||||
\(87\) | 5.27000 | 0.565003 | ||||||||
\(88\) | 2.02214 | 0.215561 | ||||||||
\(89\) | −10.7772 | −1.14238 | −0.571192 | − | 0.820816i | \(-0.693519\pi\) | ||||
−0.571192 | + | 0.820816i | \(0.693519\pi\) | |||||||
\(90\) | −0.546295 | −0.0575845 | ||||||||
\(91\) | 0.568438 | 0.0595885 | ||||||||
\(92\) | −15.1967 | −1.58437 | ||||||||
\(93\) | 9.66103 | 1.00180 | ||||||||
\(94\) | −5.54857 | −0.572292 | ||||||||
\(95\) | −6.62049 | −0.679248 | ||||||||
\(96\) | 5.29991 | 0.540920 | ||||||||
\(97\) | 17.9952 | 1.82713 | 0.913567 | − | 0.406689i | \(-0.133317\pi\) | ||||
0.913567 | + | 0.406689i | \(0.133317\pi\) | |||||||
\(98\) | 0.546295 | 0.0551841 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | −1.70156 | −0.170156 | ||||||||
\(101\) | 0.826342 | 0.0822241 | 0.0411120 | − | 0.999155i | \(-0.486910\pi\) | ||||
0.0411120 | + | 0.999155i | \(0.486910\pi\) | |||||||
\(102\) | 1.47585 | 0.146131 | ||||||||
\(103\) | 10.5921 | 1.04367 | 0.521833 | − | 0.853048i | \(-0.325248\pi\) | ||||
0.521833 | + | 0.853048i | \(0.325248\pi\) | |||||||
\(104\) | 1.14946 | 0.112714 | ||||||||
\(105\) | 1.00000 | 0.0975900 | ||||||||
\(106\) | 0.854779 | 0.0830235 | ||||||||
\(107\) | −13.7864 | −1.33278 | −0.666390 | − | 0.745603i | \(-0.732161\pi\) | ||||
−0.666390 | + | 0.745603i | \(0.732161\pi\) | |||||||
\(108\) | −1.70156 | −0.163733 | ||||||||
\(109\) | 19.8905 | 1.90516 | 0.952582 | − | 0.304282i | \(-0.0984166\pi\) | ||||
0.952582 | + | 0.304282i | \(0.0984166\pi\) | |||||||
\(110\) | 0.546295 | 0.0520872 | ||||||||
\(111\) | −2.75362 | −0.261362 | ||||||||
\(112\) | −2.29844 | −0.217182 | ||||||||
\(113\) | 6.43531 | 0.605383 | 0.302692 | − | 0.953089i | \(-0.402115\pi\) | ||||
0.302692 | + | 0.953089i | \(0.402115\pi\) | |||||||
\(114\) | 3.61674 | 0.338739 | ||||||||
\(115\) | −8.93103 | −0.832823 | ||||||||
\(116\) | −8.96723 | −0.832587 | ||||||||
\(117\) | −0.568438 | −0.0525521 | ||||||||
\(118\) | 3.47585 | 0.319978 | ||||||||
\(119\) | −2.70156 | −0.247652 | ||||||||
\(120\) | 2.02214 | 0.184596 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −2.02844 | −0.183646 | ||||||||
\(123\) | −10.9831 | −0.990311 | ||||||||
\(124\) | −16.4388 | −1.47625 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −0.546295 | −0.0486678 | ||||||||
\(127\) | 4.05206 | 0.359562 | 0.179781 | − | 0.983707i | \(-0.442461\pi\) | ||||
0.179781 | + | 0.983707i | \(0.442461\pi\) | |||||||
\(128\) | −11.5294 | −1.01906 | ||||||||
\(129\) | −0.0520550 | −0.00458319 | ||||||||
\(130\) | 0.310535 | 0.0272357 | ||||||||
\(131\) | −5.69781 | −0.497820 | −0.248910 | − | 0.968527i | \(-0.580072\pi\) | ||||
−0.248910 | + | 0.968527i | \(0.580072\pi\) | |||||||
\(132\) | 1.70156 | 0.148102 | ||||||||
\(133\) | −6.62049 | −0.574070 | ||||||||
\(134\) | −5.68947 | −0.491495 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −5.46295 | −0.468444 | ||||||||
\(137\) | −3.40312 | −0.290749 | −0.145374 | − | 0.989377i | \(-0.546439\pi\) | ||||
−0.145374 | + | 0.989377i | \(0.546439\pi\) | |||||||
\(138\) | 4.87897 | 0.415326 | ||||||||
\(139\) | −8.04724 | −0.682558 | −0.341279 | − | 0.939962i | \(-0.610860\pi\) | ||||
−0.341279 | + | 0.939962i | \(0.610860\pi\) | |||||||
\(140\) | −1.70156 | −0.143808 | ||||||||
\(141\) | −10.1567 | −0.855352 | ||||||||
\(142\) | 1.40312 | 0.117748 | ||||||||
\(143\) | 0.568438 | 0.0475352 | ||||||||
\(144\) | 2.29844 | 0.191536 | ||||||||
\(145\) | −5.27000 | −0.437650 | ||||||||
\(146\) | 1.23804 | 0.102461 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 4.68545 | 0.385142 | ||||||||
\(149\) | 7.50723 | 0.615017 | 0.307508 | − | 0.951545i | \(-0.400505\pi\) | ||||
0.307508 | + | 0.951545i | \(0.400505\pi\) | |||||||
\(150\) | 0.546295 | 0.0446048 | ||||||||
\(151\) | 3.21795 | 0.261873 | 0.130936 | − | 0.991391i | \(-0.458202\pi\) | ||||
0.130936 | + | 0.991391i | \(0.458202\pi\) | |||||||
\(152\) | −13.3876 | −1.08588 | ||||||||
\(153\) | 2.70156 | 0.218408 | ||||||||
\(154\) | 0.546295 | 0.0440217 | ||||||||
\(155\) | −9.66103 | −0.775992 | ||||||||
\(156\) | 0.967233 | 0.0774406 | ||||||||
\(157\) | −3.35107 | −0.267444 | −0.133722 | − | 0.991019i | \(-0.542693\pi\) | ||||
−0.133722 | + | 0.991019i | \(0.542693\pi\) | |||||||
\(158\) | −1.40312 | −0.111627 | ||||||||
\(159\) | 1.56469 | 0.124088 | ||||||||
\(160\) | −5.29991 | −0.418995 | ||||||||
\(161\) | −8.93103 | −0.703864 | ||||||||
\(162\) | 0.546295 | 0.0429210 | ||||||||
\(163\) | 10.9600 | 0.858457 | 0.429228 | − | 0.903196i | \(-0.358786\pi\) | ||||
0.429228 | + | 0.903196i | \(0.358786\pi\) | |||||||
\(164\) | 18.6884 | 1.45932 | ||||||||
\(165\) | 1.00000 | 0.0778499 | ||||||||
\(166\) | 9.37469 | 0.727617 | ||||||||
\(167\) | −7.58830 | −0.587201 | −0.293600 | − | 0.955928i | \(-0.594853\pi\) | ||||
−0.293600 | + | 0.955928i | \(0.594853\pi\) | |||||||
\(168\) | 2.02214 | 0.156012 | ||||||||
\(169\) | −12.6769 | −0.975144 | ||||||||
\(170\) | −1.47585 | −0.113192 | ||||||||
\(171\) | 6.62049 | 0.506282 | ||||||||
\(172\) | 0.0885748 | 0.00675377 | ||||||||
\(173\) | −18.2094 | −1.38443 | −0.692216 | − | 0.721690i | \(-0.743366\pi\) | ||||
−0.692216 | + | 0.721690i | \(0.743366\pi\) | |||||||
\(174\) | 2.87897 | 0.218254 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | −2.29844 | −0.173251 | ||||||||
\(177\) | 6.36259 | 0.478242 | ||||||||
\(178\) | −5.88755 | −0.441290 | ||||||||
\(179\) | 4.75362 | 0.355302 | 0.177651 | − | 0.984094i | \(-0.443150\pi\) | ||||
0.177651 | + | 0.984094i | \(0.443150\pi\) | |||||||
\(180\) | 1.70156 | 0.126827 | ||||||||
\(181\) | 25.2652 | 1.87795 | 0.938973 | − | 0.343991i | \(-0.111779\pi\) | ||||
0.938973 | + | 0.343991i | \(0.111779\pi\) | |||||||
\(182\) | 0.310535 | 0.0230184 | ||||||||
\(183\) | −3.71308 | −0.274479 | ||||||||
\(184\) | −18.0598 | −1.33139 | ||||||||
\(185\) | 2.75362 | 0.202450 | ||||||||
\(186\) | 5.27777 | 0.386985 | ||||||||
\(187\) | −2.70156 | −0.197558 | ||||||||
\(188\) | 17.2823 | 1.26044 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −3.61674 | −0.262386 | ||||||||
\(191\) | −17.4504 | −1.26266 | −0.631332 | − | 0.775513i | \(-0.717491\pi\) | ||||
−0.631332 | + | 0.775513i | \(0.717491\pi\) | |||||||
\(192\) | −1.70156 | −0.122800 | ||||||||
\(193\) | 22.9546 | 1.65231 | 0.826156 | − | 0.563442i | \(-0.190523\pi\) | ||||
0.826156 | + | 0.563442i | \(0.190523\pi\) | |||||||
\(194\) | 9.83067 | 0.705801 | ||||||||
\(195\) | 0.568438 | 0.0407067 | ||||||||
\(196\) | −1.70156 | −0.121540 | ||||||||
\(197\) | −3.36634 | −0.239842 | −0.119921 | − | 0.992783i | \(-0.538264\pi\) | ||||
−0.119921 | + | 0.992783i | \(0.538264\pi\) | |||||||
\(198\) | −0.546295 | −0.0388235 | ||||||||
\(199\) | 9.54402 | 0.676557 | 0.338279 | − | 0.941046i | \(-0.390155\pi\) | ||||
0.338279 | + | 0.941046i | \(0.390155\pi\) | |||||||
\(200\) | −2.02214 | −0.142987 | ||||||||
\(201\) | −10.4146 | −0.734592 | ||||||||
\(202\) | 0.451426 | 0.0317622 | ||||||||
\(203\) | −5.27000 | −0.369882 | ||||||||
\(204\) | −4.59688 | −0.321846 | ||||||||
\(205\) | 10.9831 | 0.767092 | ||||||||
\(206\) | 5.78638 | 0.403156 | ||||||||
\(207\) | 8.93103 | 0.620749 | ||||||||
\(208\) | −1.30652 | −0.0905909 | ||||||||
\(209\) | −6.62049 | −0.457949 | ||||||||
\(210\) | 0.546295 | 0.0376979 | ||||||||
\(211\) | −7.73375 | −0.532413 | −0.266207 | − | 0.963916i | \(-0.585770\pi\) | ||||
−0.266207 | + | 0.963916i | \(0.585770\pi\) | |||||||
\(212\) | −2.66241 | −0.182855 | ||||||||
\(213\) | 2.56844 | 0.175986 | ||||||||
\(214\) | −7.53143 | −0.514838 | ||||||||
\(215\) | 0.0520550 | 0.00355012 | ||||||||
\(216\) | −2.02214 | −0.137589 | ||||||||
\(217\) | −9.66103 | −0.655833 | ||||||||
\(218\) | 10.8661 | 0.735943 | ||||||||
\(219\) | 2.26625 | 0.153139 | ||||||||
\(220\) | −1.70156 | −0.114719 | ||||||||
\(221\) | −1.53567 | −0.103300 | ||||||||
\(222\) | −1.50429 | −0.100961 | ||||||||
\(223\) | −13.9141 | −0.931758 | −0.465879 | − | 0.884848i | \(-0.654262\pi\) | ||||
−0.465879 | + | 0.884848i | \(0.654262\pi\) | |||||||
\(224\) | −5.29991 | −0.354115 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 3.51558 | 0.233853 | ||||||||
\(227\) | 0.597452 | 0.0396543 | 0.0198271 | − | 0.999803i | \(-0.493688\pi\) | ||||
0.0198271 | + | 0.999803i | \(0.493688\pi\) | |||||||
\(228\) | −11.2652 | −0.746055 | ||||||||
\(229\) | 21.1895 | 1.40024 | 0.700121 | − | 0.714024i | \(-0.253129\pi\) | ||||
0.700121 | + | 0.714024i | \(0.253129\pi\) | |||||||
\(230\) | −4.87897 | −0.321710 | ||||||||
\(231\) | 1.00000 | 0.0657952 | ||||||||
\(232\) | −10.6567 | −0.699647 | ||||||||
\(233\) | −20.2821 | −1.32872 | −0.664362 | − | 0.747411i | \(-0.731297\pi\) | ||||
−0.664362 | + | 0.747411i | \(0.731297\pi\) | |||||||
\(234\) | −0.310535 | −0.0203003 | ||||||||
\(235\) | 10.1567 | 0.662553 | ||||||||
\(236\) | −10.8263 | −0.704735 | ||||||||
\(237\) | −2.56844 | −0.166838 | ||||||||
\(238\) | −1.47585 | −0.0956651 | ||||||||
\(239\) | 2.23723 | 0.144715 | 0.0723573 | − | 0.997379i | \(-0.476948\pi\) | ||||
0.0723573 | + | 0.997379i | \(0.476948\pi\) | |||||||
\(240\) | −2.29844 | −0.148364 | ||||||||
\(241\) | 8.93045 | 0.575261 | 0.287630 | − | 0.957741i | \(-0.407133\pi\) | ||||
0.287630 | + | 0.957741i | \(0.407133\pi\) | |||||||
\(242\) | 0.546295 | 0.0351172 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 6.31804 | 0.404471 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −6.00000 | −0.382546 | ||||||||
\(247\) | −3.76334 | −0.239456 | ||||||||
\(248\) | −19.5360 | −1.24054 | ||||||||
\(249\) | 17.1605 | 1.08750 | ||||||||
\(250\) | −0.546295 | −0.0345507 | ||||||||
\(251\) | 3.35884 | 0.212008 | 0.106004 | − | 0.994366i | \(-0.466194\pi\) | ||||
0.106004 | + | 0.994366i | \(0.466194\pi\) | |||||||
\(252\) | 1.70156 | 0.107188 | ||||||||
\(253\) | −8.93103 | −0.561489 | ||||||||
\(254\) | 2.21362 | 0.138895 | ||||||||
\(255\) | −2.70156 | −0.169178 | ||||||||
\(256\) | −2.89531 | −0.180957 | ||||||||
\(257\) | 5.80943 | 0.362382 | 0.181191 | − | 0.983448i | \(-0.442005\pi\) | ||||
0.181191 | + | 0.983448i | \(0.442005\pi\) | |||||||
\(258\) | −0.0284374 | −0.00177043 | ||||||||
\(259\) | 2.75362 | 0.171101 | ||||||||
\(260\) | −0.967233 | −0.0599853 | ||||||||
\(261\) | 5.27000 | 0.326205 | ||||||||
\(262\) | −3.11268 | −0.192302 | ||||||||
\(263\) | −23.3221 | −1.43810 | −0.719050 | − | 0.694959i | \(-0.755423\pi\) | ||||
−0.719050 | + | 0.694959i | \(0.755423\pi\) | |||||||
\(264\) | 2.02214 | 0.124454 | ||||||||
\(265\) | −1.56469 | −0.0961179 | ||||||||
\(266\) | −3.61674 | −0.221757 | ||||||||
\(267\) | −10.7772 | −0.659556 | ||||||||
\(268\) | 17.7212 | 1.08249 | ||||||||
\(269\) | 29.1246 | 1.77576 | 0.887878 | − | 0.460080i | \(-0.152179\pi\) | ||||
0.887878 | + | 0.460080i | \(0.152179\pi\) | |||||||
\(270\) | −0.546295 | −0.0332464 | ||||||||
\(271\) | 31.2416 | 1.89779 | 0.948895 | − | 0.315592i | \(-0.102203\pi\) | ||||
0.948895 | + | 0.315592i | \(0.102203\pi\) | |||||||
\(272\) | 6.20937 | 0.376499 | ||||||||
\(273\) | 0.568438 | 0.0344035 | ||||||||
\(274\) | −1.85911 | −0.112313 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | −15.1967 | −0.914734 | ||||||||
\(277\) | −15.8988 | −0.955269 | −0.477634 | − | 0.878559i | \(-0.658506\pi\) | ||||
−0.477634 | + | 0.878559i | \(0.658506\pi\) | |||||||
\(278\) | −4.39616 | −0.263664 | ||||||||
\(279\) | 9.66103 | 0.578391 | ||||||||
\(280\) | −2.02214 | −0.120846 | ||||||||
\(281\) | −14.1041 | −0.841381 | −0.420690 | − | 0.907204i | \(-0.638212\pi\) | ||||
−0.420690 | + | 0.907204i | \(0.638212\pi\) | |||||||
\(282\) | −5.54857 | −0.330413 | ||||||||
\(283\) | −1.32745 | −0.0789088 | −0.0394544 | − | 0.999221i | \(-0.512562\pi\) | ||||
−0.0394544 | + | 0.999221i | \(0.512562\pi\) | |||||||
\(284\) | −4.37036 | −0.259333 | ||||||||
\(285\) | −6.62049 | −0.392164 | ||||||||
\(286\) | 0.310535 | 0.0183623 | ||||||||
\(287\) | 10.9831 | 0.648311 | ||||||||
\(288\) | 5.29991 | 0.312300 | ||||||||
\(289\) | −9.70156 | −0.570680 | ||||||||
\(290\) | −2.87897 | −0.169059 | ||||||||
\(291\) | 17.9952 | 1.05490 | ||||||||
\(292\) | −3.85616 | −0.225665 | ||||||||
\(293\) | 18.3784 | 1.07368 | 0.536840 | − | 0.843684i | \(-0.319618\pi\) | ||||
0.536840 | + | 0.843684i | \(0.319618\pi\) | |||||||
\(294\) | 0.546295 | 0.0318606 | ||||||||
\(295\) | −6.36259 | −0.370444 | ||||||||
\(296\) | 5.56821 | 0.323646 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 4.10116 | 0.237574 | ||||||||
\(299\) | −5.07674 | −0.293595 | ||||||||
\(300\) | −1.70156 | −0.0982397 | ||||||||
\(301\) | 0.0520550 | 0.00300040 | ||||||||
\(302\) | 1.75795 | 0.101158 | ||||||||
\(303\) | 0.826342 | 0.0474721 | ||||||||
\(304\) | 15.2168 | 0.872743 | ||||||||
\(305\) | 3.71308 | 0.212611 | ||||||||
\(306\) | 1.47585 | 0.0843687 | ||||||||
\(307\) | 6.45143 | 0.368202 | 0.184101 | − | 0.982907i | \(-0.441063\pi\) | ||||
0.184101 | + | 0.982907i | \(0.441063\pi\) | |||||||
\(308\) | −1.70156 | −0.0969555 | ||||||||
\(309\) | 10.5921 | 0.602561 | ||||||||
\(310\) | −5.27777 | −0.299757 | ||||||||
\(311\) | −29.4136 | −1.66789 | −0.833946 | − | 0.551847i | \(-0.813923\pi\) | ||||
−0.833946 | + | 0.551847i | \(0.813923\pi\) | |||||||
\(312\) | 1.14946 | 0.0650756 | ||||||||
\(313\) | −24.7542 | −1.39919 | −0.699595 | − | 0.714540i | \(-0.746636\pi\) | ||||
−0.699595 | + | 0.714540i | \(0.746636\pi\) | |||||||
\(314\) | −1.83067 | −0.103311 | ||||||||
\(315\) | 1.00000 | 0.0563436 | ||||||||
\(316\) | 4.37036 | 0.245852 | ||||||||
\(317\) | −15.0955 | −0.847850 | −0.423925 | − | 0.905697i | \(-0.639348\pi\) | ||||
−0.423925 | + | 0.905697i | \(0.639348\pi\) | |||||||
\(318\) | 0.854779 | 0.0479336 | ||||||||
\(319\) | −5.27000 | −0.295063 | ||||||||
\(320\) | 1.70156 | 0.0951202 | ||||||||
\(321\) | −13.7864 | −0.769481 | ||||||||
\(322\) | −4.87897 | −0.271895 | ||||||||
\(323\) | 17.8857 | 0.995186 | ||||||||
\(324\) | −1.70156 | −0.0945312 | ||||||||
\(325\) | −0.568438 | −0.0315313 | ||||||||
\(326\) | 5.98741 | 0.331612 | ||||||||
\(327\) | 19.8905 | 1.09995 | ||||||||
\(328\) | 22.2094 | 1.22631 | ||||||||
\(329\) | 10.1567 | 0.559959 | ||||||||
\(330\) | 0.546295 | 0.0300725 | ||||||||
\(331\) | 6.78263 | 0.372807 | 0.186404 | − | 0.982473i | \(-0.440317\pi\) | ||||
0.186404 | + | 0.982473i | \(0.440317\pi\) | |||||||
\(332\) | −29.1996 | −1.60254 | ||||||||
\(333\) | −2.75362 | −0.150897 | ||||||||
\(334\) | −4.14545 | −0.226829 | ||||||||
\(335\) | 10.4146 | 0.569013 | ||||||||
\(336\) | −2.29844 | −0.125390 | ||||||||
\(337\) | −31.9509 | −1.74048 | −0.870238 | − | 0.492631i | \(-0.836035\pi\) | ||||
−0.870238 | + | 0.492631i | \(0.836035\pi\) | |||||||
\(338\) | −6.92531 | −0.376687 | ||||||||
\(339\) | 6.43531 | 0.349518 | ||||||||
\(340\) | 4.59688 | 0.249301 | ||||||||
\(341\) | −9.66103 | −0.523174 | ||||||||
\(342\) | 3.61674 | 0.195571 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0.105263 | 0.00567538 | ||||||||
\(345\) | −8.93103 | −0.480830 | ||||||||
\(346\) | −9.94768 | −0.534791 | ||||||||
\(347\) | −13.6694 | −0.733810 | −0.366905 | − | 0.930258i | \(-0.619583\pi\) | ||||
−0.366905 | + | 0.930258i | \(0.619583\pi\) | |||||||
\(348\) | −8.96723 | −0.480694 | ||||||||
\(349\) | 16.1720 | 0.865668 | 0.432834 | − | 0.901474i | \(-0.357514\pi\) | ||||
0.432834 | + | 0.901474i | \(0.357514\pi\) | |||||||
\(350\) | −0.546295 | −0.0292007 | ||||||||
\(351\) | −0.568438 | −0.0303410 | ||||||||
\(352\) | −5.29991 | −0.282486 | ||||||||
\(353\) | −9.94313 | −0.529219 | −0.264610 | − | 0.964356i | \(-0.585243\pi\) | ||||
−0.264610 | + | 0.964356i | \(0.585243\pi\) | |||||||
\(354\) | 3.47585 | 0.184739 | ||||||||
\(355\) | −2.56844 | −0.136319 | ||||||||
\(356\) | 18.3381 | 0.971919 | ||||||||
\(357\) | −2.70156 | −0.142982 | ||||||||
\(358\) | 2.59688 | 0.137249 | ||||||||
\(359\) | −12.5845 | −0.664187 | −0.332094 | − | 0.943246i | \(-0.607755\pi\) | ||||
−0.332094 | + | 0.943246i | \(0.607755\pi\) | |||||||
\(360\) | 2.02214 | 0.106576 | ||||||||
\(361\) | 24.8309 | 1.30689 | ||||||||
\(362\) | 13.8022 | 0.725429 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | −0.967233 | −0.0506968 | ||||||||
\(365\) | −2.26625 | −0.118621 | ||||||||
\(366\) | −2.02844 | −0.106028 | ||||||||
\(367\) | 36.9699 | 1.92981 | 0.964907 | − | 0.262592i | \(-0.0845772\pi\) | ||||
0.964907 | + | 0.262592i | \(0.0845772\pi\) | |||||||
\(368\) | 20.5274 | 1.07007 | ||||||||
\(369\) | −10.9831 | −0.571756 | ||||||||
\(370\) | 1.50429 | 0.0782041 | ||||||||
\(371\) | −1.56469 | −0.0812344 | ||||||||
\(372\) | −16.4388 | −0.852314 | ||||||||
\(373\) | −13.4109 | −0.694390 | −0.347195 | − | 0.937793i | \(-0.612866\pi\) | ||||
−0.347195 | + | 0.937793i | \(0.612866\pi\) | |||||||
\(374\) | −1.47585 | −0.0763143 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 20.5384 | 1.05919 | ||||||||
\(377\) | −2.99567 | −0.154285 | ||||||||
\(378\) | −0.546295 | −0.0280984 | ||||||||
\(379\) | −0.805672 | −0.0413846 | −0.0206923 | − | 0.999786i | \(-0.506587\pi\) | ||||
−0.0206923 | + | 0.999786i | \(0.506587\pi\) | |||||||
\(380\) | 11.2652 | 0.577892 | ||||||||
\(381\) | 4.05206 | 0.207593 | ||||||||
\(382\) | −9.53304 | −0.487753 | ||||||||
\(383\) | −22.3494 | −1.14200 | −0.571001 | − | 0.820949i | \(-0.693445\pi\) | ||||
−0.571001 | + | 0.820949i | \(0.693445\pi\) | |||||||
\(384\) | −11.5294 | −0.588356 | ||||||||
\(385\) | −1.00000 | −0.0509647 | ||||||||
\(386\) | 12.5400 | 0.638269 | ||||||||
\(387\) | −0.0520550 | −0.00264610 | ||||||||
\(388\) | −30.6199 | −1.55449 | ||||||||
\(389\) | −29.4863 | −1.49501 | −0.747507 | − | 0.664253i | \(-0.768750\pi\) | ||||
−0.747507 | + | 0.664253i | \(0.768750\pi\) | |||||||
\(390\) | 0.310535 | 0.0157245 | ||||||||
\(391\) | 24.1277 | 1.22019 | ||||||||
\(392\) | −2.02214 | −0.102134 | ||||||||
\(393\) | −5.69781 | −0.287416 | ||||||||
\(394\) | −1.83902 | −0.0926482 | ||||||||
\(395\) | 2.56844 | 0.129232 | ||||||||
\(396\) | 1.70156 | 0.0855067 | ||||||||
\(397\) | 4.45143 | 0.223411 | 0.111705 | − | 0.993741i | \(-0.464369\pi\) | ||||
0.111705 | + | 0.993741i | \(0.464369\pi\) | |||||||
\(398\) | 5.21384 | 0.261346 | ||||||||
\(399\) | −6.62049 | −0.331439 | ||||||||
\(400\) | 2.29844 | 0.114922 | ||||||||
\(401\) | 22.7123 | 1.13420 | 0.567099 | − | 0.823650i | \(-0.308066\pi\) | ||||
0.567099 | + | 0.823650i | \(0.308066\pi\) | |||||||
\(402\) | −5.68947 | −0.283765 | ||||||||
\(403\) | −5.49170 | −0.273561 | ||||||||
\(404\) | −1.40607 | −0.0699547 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | −2.87897 | −0.142881 | ||||||||
\(407\) | 2.75362 | 0.136492 | ||||||||
\(408\) | −5.46295 | −0.270456 | ||||||||
\(409\) | 5.09259 | 0.251812 | 0.125906 | − | 0.992042i | \(-0.459816\pi\) | ||||
0.125906 | + | 0.992042i | \(0.459816\pi\) | |||||||
\(410\) | 6.00000 | 0.296319 | ||||||||
\(411\) | −3.40312 | −0.167864 | ||||||||
\(412\) | −18.0230 | −0.887932 | ||||||||
\(413\) | −6.36259 | −0.313083 | ||||||||
\(414\) | 4.87897 | 0.239788 | ||||||||
\(415\) | −17.1605 | −0.842376 | ||||||||
\(416\) | −3.01267 | −0.147708 | ||||||||
\(417\) | −8.04724 | −0.394075 | ||||||||
\(418\) | −3.61674 | −0.176901 | ||||||||
\(419\) | −2.86286 | −0.139860 | −0.0699300 | − | 0.997552i | \(-0.522278\pi\) | ||||
−0.0699300 | + | 0.997552i | \(0.522278\pi\) | |||||||
\(420\) | −1.70156 | −0.0830277 | ||||||||
\(421\) | −16.1047 | −0.784894 | −0.392447 | − | 0.919775i | \(-0.628371\pi\) | ||||
−0.392447 | + | 0.919775i | \(0.628371\pi\) | |||||||
\(422\) | −4.22491 | −0.205665 | ||||||||
\(423\) | −10.1567 | −0.493838 | ||||||||
\(424\) | −3.16402 | −0.153658 | ||||||||
\(425\) | 2.70156 | 0.131045 | ||||||||
\(426\) | 1.40312 | 0.0679816 | ||||||||
\(427\) | 3.71308 | 0.179689 | ||||||||
\(428\) | 23.4584 | 1.13390 | ||||||||
\(429\) | 0.568438 | 0.0274445 | ||||||||
\(430\) | 0.0284374 | 0.00137137 | ||||||||
\(431\) | −4.67794 | −0.225329 | −0.112664 | − | 0.993633i | \(-0.535938\pi\) | ||||
−0.112664 | + | 0.993633i | \(0.535938\pi\) | |||||||
\(432\) | 2.29844 | 0.110584 | ||||||||
\(433\) | −27.4337 | −1.31838 | −0.659189 | − | 0.751977i | \(-0.729100\pi\) | ||||
−0.659189 | + | 0.751977i | \(0.729100\pi\) | |||||||
\(434\) | −5.27777 | −0.253341 | ||||||||
\(435\) | −5.27000 | −0.252677 | ||||||||
\(436\) | −33.8449 | −1.62088 | ||||||||
\(437\) | 59.1278 | 2.82847 | ||||||||
\(438\) | 1.23804 | 0.0591558 | ||||||||
\(439\) | 5.73433 | 0.273685 | 0.136842 | − | 0.990593i | \(-0.456305\pi\) | ||||
0.136842 | + | 0.990593i | \(0.456305\pi\) | |||||||
\(440\) | −2.02214 | −0.0964019 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −0.838929 | −0.0399038 | ||||||||
\(443\) | −9.58536 | −0.455414 | −0.227707 | − | 0.973730i | \(-0.573123\pi\) | ||||
−0.227707 | + | 0.973730i | \(0.573123\pi\) | |||||||
\(444\) | 4.68545 | 0.222362 | ||||||||
\(445\) | 10.7772 | 0.510890 | ||||||||
\(446\) | −7.60121 | −0.359927 | ||||||||
\(447\) | 7.50723 | 0.355080 | ||||||||
\(448\) | 1.70156 | 0.0803913 | ||||||||
\(449\) | 30.9463 | 1.46045 | 0.730223 | − | 0.683209i | \(-0.239416\pi\) | ||||
0.730223 | + | 0.683209i | \(0.239416\pi\) | |||||||
\(450\) | 0.546295 | 0.0257526 | ||||||||
\(451\) | 10.9831 | 0.517173 | ||||||||
\(452\) | −10.9501 | −0.515049 | ||||||||
\(453\) | 3.21795 | 0.151192 | ||||||||
\(454\) | 0.326385 | 0.0153180 | ||||||||
\(455\) | −0.568438 | −0.0266488 | ||||||||
\(456\) | −13.3876 | −0.626931 | ||||||||
\(457\) | −42.2246 | −1.97519 | −0.987593 | − | 0.157036i | \(-0.949806\pi\) | ||||
−0.987593 | + | 0.157036i | \(0.949806\pi\) | |||||||
\(458\) | 11.5757 | 0.540898 | ||||||||
\(459\) | 2.70156 | 0.126098 | ||||||||
\(460\) | 15.1967 | 0.708550 | ||||||||
\(461\) | 9.87464 | 0.459908 | 0.229954 | − | 0.973201i | \(-0.426142\pi\) | ||||
0.229954 | + | 0.973201i | \(0.426142\pi\) | |||||||
\(462\) | 0.546295 | 0.0254159 | ||||||||
\(463\) | 2.56009 | 0.118978 | 0.0594888 | − | 0.998229i | \(-0.481053\pi\) | ||||
0.0594888 | + | 0.998229i | \(0.481053\pi\) | |||||||
\(464\) | 12.1128 | 0.562321 | ||||||||
\(465\) | −9.66103 | −0.448019 | ||||||||
\(466\) | −11.0800 | −0.513271 | ||||||||
\(467\) | −19.6924 | −0.911256 | −0.455628 | − | 0.890170i | \(-0.650585\pi\) | ||||
−0.455628 | + | 0.890170i | \(0.650585\pi\) | |||||||
\(468\) | 0.967233 | 0.0447104 | ||||||||
\(469\) | 10.4146 | 0.480904 | ||||||||
\(470\) | 5.54857 | 0.255937 | ||||||||
\(471\) | −3.35107 | −0.154409 | ||||||||
\(472\) | −12.8661 | −0.592209 | ||||||||
\(473\) | 0.0520550 | 0.00239349 | ||||||||
\(474\) | −1.40312 | −0.0644476 | ||||||||
\(475\) | 6.62049 | 0.303769 | ||||||||
\(476\) | 4.59688 | 0.210697 | ||||||||
\(477\) | 1.56469 | 0.0716420 | ||||||||
\(478\) | 1.22219 | 0.0559016 | ||||||||
\(479\) | 15.3672 | 0.702144 | 0.351072 | − | 0.936348i | \(-0.385817\pi\) | ||||
0.351072 | + | 0.936348i | \(0.385817\pi\) | |||||||
\(480\) | −5.29991 | −0.241907 | ||||||||
\(481\) | 1.56526 | 0.0713698 | ||||||||
\(482\) | 4.87866 | 0.222217 | ||||||||
\(483\) | −8.93103 | −0.406376 | ||||||||
\(484\) | −1.70156 | −0.0773437 | ||||||||
\(485\) | −17.9952 | −0.817119 | ||||||||
\(486\) | 0.546295 | 0.0247804 | ||||||||
\(487\) | −1.52848 | −0.0692621 | −0.0346310 | − | 0.999400i | \(-0.511026\pi\) | ||||
−0.0346310 | + | 0.999400i | \(0.511026\pi\) | |||||||
\(488\) | 7.50839 | 0.339889 | ||||||||
\(489\) | 10.9600 | 0.495630 | ||||||||
\(490\) | −0.546295 | −0.0246791 | ||||||||
\(491\) | −40.7359 | −1.83839 | −0.919193 | − | 0.393808i | \(-0.871157\pi\) | ||||
−0.919193 | + | 0.393808i | \(0.871157\pi\) | |||||||
\(492\) | 18.6884 | 0.842538 | ||||||||
\(493\) | 14.2372 | 0.641213 | ||||||||
\(494\) | −2.05589 | −0.0924990 | ||||||||
\(495\) | 1.00000 | 0.0449467 | ||||||||
\(496\) | 22.2053 | 0.997046 | ||||||||
\(497\) | −2.56844 | −0.115210 | ||||||||
\(498\) | 9.37469 | 0.420090 | ||||||||
\(499\) | −20.3312 | −0.910150 | −0.455075 | − | 0.890453i | \(-0.650388\pi\) | ||||
−0.455075 | + | 0.890453i | \(0.650388\pi\) | |||||||
\(500\) | 1.70156 | 0.0760962 | ||||||||
\(501\) | −7.58830 | −0.339020 | ||||||||
\(502\) | 1.83491 | 0.0818963 | ||||||||
\(503\) | −23.5952 | −1.05206 | −0.526030 | − | 0.850466i | \(-0.676320\pi\) | ||||
−0.526030 | + | 0.850466i | \(0.676320\pi\) | |||||||
\(504\) | 2.02214 | 0.0900734 | ||||||||
\(505\) | −0.826342 | −0.0367717 | ||||||||
\(506\) | −4.87897 | −0.216897 | ||||||||
\(507\) | −12.6769 | −0.563000 | ||||||||
\(508\) | −6.89482 | −0.305908 | ||||||||
\(509\) | 38.0993 | 1.68872 | 0.844361 | − | 0.535775i | \(-0.179981\pi\) | ||||
0.844361 | + | 0.535775i | \(0.179981\pi\) | |||||||
\(510\) | −1.47585 | −0.0653517 | ||||||||
\(511\) | −2.26625 | −0.100253 | ||||||||
\(512\) | 21.4771 | 0.949161 | ||||||||
\(513\) | 6.62049 | 0.292302 | ||||||||
\(514\) | 3.17366 | 0.139984 | ||||||||
\(515\) | −10.5921 | −0.466742 | ||||||||
\(516\) | 0.0885748 | 0.00389929 | ||||||||
\(517\) | 10.1567 | 0.446693 | ||||||||
\(518\) | 1.50429 | 0.0660945 | ||||||||
\(519\) | −18.2094 | −0.799303 | ||||||||
\(520\) | −1.14946 | −0.0504073 | ||||||||
\(521\) | 33.9952 | 1.48936 | 0.744678 | − | 0.667424i | \(-0.232603\pi\) | ||||
0.744678 | + | 0.667424i | \(0.232603\pi\) | |||||||
\(522\) | 2.87897 | 0.126009 | ||||||||
\(523\) | 10.9517 | 0.478884 | 0.239442 | − | 0.970911i | \(-0.423035\pi\) | ||||
0.239442 | + | 0.970911i | \(0.423035\pi\) | |||||||
\(524\) | 9.69518 | 0.423536 | ||||||||
\(525\) | −1.00000 | −0.0436436 | ||||||||
\(526\) | −12.7407 | −0.555522 | ||||||||
\(527\) | 26.0999 | 1.13693 | ||||||||
\(528\) | −2.29844 | −0.100027 | ||||||||
\(529\) | 56.7633 | 2.46797 | ||||||||
\(530\) | −0.854779 | −0.0371292 | ||||||||
\(531\) | 6.36259 | 0.276113 | ||||||||
\(532\) | 11.2652 | 0.488408 | ||||||||
\(533\) | 6.24321 | 0.270423 | ||||||||
\(534\) | −5.88755 | −0.254779 | ||||||||
\(535\) | 13.7864 | 0.596037 | ||||||||
\(536\) | 21.0599 | 0.909650 | ||||||||
\(537\) | 4.75362 | 0.205134 | ||||||||
\(538\) | 15.9106 | 0.685954 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 1.70156 | 0.0732236 | ||||||||
\(541\) | 13.4971 | 0.580285 | 0.290143 | − | 0.956983i | \(-0.406297\pi\) | ||||
0.290143 | + | 0.956983i | \(0.406297\pi\) | |||||||
\(542\) | 17.0671 | 0.733095 | ||||||||
\(543\) | 25.2652 | 1.08423 | ||||||||
\(544\) | 14.3180 | 0.613881 | ||||||||
\(545\) | −19.8905 | −0.852015 | ||||||||
\(546\) | 0.310535 | 0.0132897 | ||||||||
\(547\) | −42.0182 | −1.79657 | −0.898285 | − | 0.439414i | \(-0.855186\pi\) | ||||
−0.898285 | + | 0.439414i | \(0.855186\pi\) | |||||||
\(548\) | 5.79063 | 0.247363 | ||||||||
\(549\) | −3.71308 | −0.158471 | ||||||||
\(550\) | −0.546295 | −0.0232941 | ||||||||
\(551\) | 34.8900 | 1.48636 | ||||||||
\(552\) | −18.0598 | −0.768677 | ||||||||
\(553\) | 2.56844 | 0.109221 | ||||||||
\(554\) | −8.68545 | −0.369009 | ||||||||
\(555\) | 2.75362 | 0.116885 | ||||||||
\(556\) | 13.6929 | 0.580707 | ||||||||
\(557\) | −27.9461 | −1.18411 | −0.592057 | − | 0.805896i | \(-0.701684\pi\) | ||||
−0.592057 | + | 0.805896i | \(0.701684\pi\) | |||||||
\(558\) | 5.27777 | 0.223426 | ||||||||
\(559\) | 0.0295901 | 0.00125153 | ||||||||
\(560\) | 2.29844 | 0.0971267 | ||||||||
\(561\) | −2.70156 | −0.114060 | ||||||||
\(562\) | −7.70500 | −0.325016 | ||||||||
\(563\) | −0.266247 | −0.0112210 | −0.00561050 | − | 0.999984i | \(-0.501786\pi\) | ||||
−0.00561050 | + | 0.999984i | \(0.501786\pi\) | |||||||
\(564\) | 17.2823 | 0.727717 | ||||||||
\(565\) | −6.43531 | −0.270736 | ||||||||
\(566\) | −0.725180 | −0.0304816 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −5.19375 | −0.217925 | ||||||||
\(569\) | −35.3983 | −1.48397 | −0.741987 | − | 0.670414i | \(-0.766116\pi\) | ||||
−0.741987 | + | 0.670414i | \(0.766116\pi\) | |||||||
\(570\) | −3.61674 | −0.151489 | ||||||||
\(571\) | −0.440134 | −0.0184191 | −0.00920953 | − | 0.999958i | \(-0.502932\pi\) | ||||
−0.00920953 | + | 0.999958i | \(0.502932\pi\) | |||||||
\(572\) | −0.967233 | −0.0404421 | ||||||||
\(573\) | −17.4504 | −0.728999 | ||||||||
\(574\) | 6.00000 | 0.250435 | ||||||||
\(575\) | 8.93103 | 0.372450 | ||||||||
\(576\) | −1.70156 | −0.0708984 | ||||||||
\(577\) | −25.1030 | −1.04505 | −0.522527 | − | 0.852623i | \(-0.675010\pi\) | ||||
−0.522527 | + | 0.852623i | \(0.675010\pi\) | |||||||
\(578\) | −5.29991 | −0.220447 | ||||||||
\(579\) | 22.9546 | 0.953963 | ||||||||
\(580\) | 8.96723 | 0.372344 | ||||||||
\(581\) | −17.1605 | −0.711937 | ||||||||
\(582\) | 9.83067 | 0.407494 | ||||||||
\(583\) | −1.56469 | −0.0648026 | ||||||||
\(584\) | −4.58268 | −0.189633 | ||||||||
\(585\) | 0.568438 | 0.0235020 | ||||||||
\(586\) | 10.0400 | 0.414750 | ||||||||
\(587\) | 3.24638 | 0.133993 | 0.0669963 | − | 0.997753i | \(-0.478658\pi\) | ||||
0.0669963 | + | 0.997753i | \(0.478658\pi\) | |||||||
\(588\) | −1.70156 | −0.0701712 | ||||||||
\(589\) | 63.9608 | 2.63546 | ||||||||
\(590\) | −3.47585 | −0.143098 | ||||||||
\(591\) | −3.36634 | −0.138473 | ||||||||
\(592\) | −6.32902 | −0.260121 | ||||||||
\(593\) | 10.7252 | 0.440430 | 0.220215 | − | 0.975451i | \(-0.429324\pi\) | ||||
0.220215 | + | 0.975451i | \(0.429324\pi\) | |||||||
\(594\) | −0.546295 | −0.0224147 | ||||||||
\(595\) | 2.70156 | 0.110753 | ||||||||
\(596\) | −12.7740 | −0.523244 | ||||||||
\(597\) | 9.54402 | 0.390611 | ||||||||
\(598\) | −2.77340 | −0.113413 | ||||||||
\(599\) | 36.3607 | 1.48566 | 0.742829 | − | 0.669481i | \(-0.233483\pi\) | ||||
0.742829 | + | 0.669481i | \(0.233483\pi\) | |||||||
\(600\) | −2.02214 | −0.0825537 | ||||||||
\(601\) | −39.7034 | −1.61954 | −0.809769 | − | 0.586749i | \(-0.800407\pi\) | ||||
−0.809769 | + | 0.586749i | \(0.800407\pi\) | |||||||
\(602\) | 0.0284374 | 0.00115902 | ||||||||
\(603\) | −10.4146 | −0.424117 | ||||||||
\(604\) | −5.47553 | −0.222796 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | 0.451426 | 0.0183379 | ||||||||
\(607\) | −9.91893 | −0.402597 | −0.201299 | − | 0.979530i | \(-0.564516\pi\) | ||||
−0.201299 | + | 0.979530i | \(0.564516\pi\) | |||||||
\(608\) | 35.0880 | 1.42301 | ||||||||
\(609\) | −5.27000 | −0.213551 | ||||||||
\(610\) | 2.02844 | 0.0821290 | ||||||||
\(611\) | 5.77348 | 0.233570 | ||||||||
\(612\) | −4.59688 | −0.185818 | ||||||||
\(613\) | 39.2681 | 1.58602 | 0.793012 | − | 0.609206i | \(-0.208512\pi\) | ||||
0.793012 | + | 0.609206i | \(0.208512\pi\) | |||||||
\(614\) | 3.52438 | 0.142232 | ||||||||
\(615\) | 10.9831 | 0.442881 | ||||||||
\(616\) | −2.02214 | −0.0814745 | ||||||||
\(617\) | 31.3462 | 1.26195 | 0.630976 | − | 0.775802i | \(-0.282655\pi\) | ||||
0.630976 | + | 0.775802i | \(0.282655\pi\) | |||||||
\(618\) | 5.78638 | 0.232762 | ||||||||
\(619\) | −12.3916 | −0.498061 | −0.249030 | − | 0.968496i | \(-0.580112\pi\) | ||||
−0.249030 | + | 0.968496i | \(0.580112\pi\) | |||||||
\(620\) | 16.4388 | 0.660200 | ||||||||
\(621\) | 8.93103 | 0.358390 | ||||||||
\(622\) | −16.0685 | −0.644287 | ||||||||
\(623\) | 10.7772 | 0.431781 | ||||||||
\(624\) | −1.30652 | −0.0523027 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −13.5231 | −0.540491 | ||||||||
\(627\) | −6.62049 | −0.264397 | ||||||||
\(628\) | 5.70205 | 0.227537 | ||||||||
\(629\) | −7.43907 | −0.296615 | ||||||||
\(630\) | 0.546295 | 0.0217649 | ||||||||
\(631\) | 33.2233 | 1.32260 | 0.661299 | − | 0.750123i | \(-0.270006\pi\) | ||||
0.661299 | + | 0.750123i | \(0.270006\pi\) | |||||||
\(632\) | 5.19375 | 0.206596 | ||||||||
\(633\) | −7.73375 | −0.307389 | ||||||||
\(634\) | −8.24661 | −0.327515 | ||||||||
\(635\) | −4.05206 | −0.160801 | ||||||||
\(636\) | −2.66241 | −0.105571 | ||||||||
\(637\) | −0.568438 | −0.0225223 | ||||||||
\(638\) | −2.87897 | −0.113980 | ||||||||
\(639\) | 2.56844 | 0.101606 | ||||||||
\(640\) | 11.5294 | 0.455739 | ||||||||
\(641\) | 18.9179 | 0.747211 | 0.373605 | − | 0.927588i | \(-0.378121\pi\) | ||||
0.373605 | + | 0.927588i | \(0.378121\pi\) | |||||||
\(642\) | −7.53143 | −0.297242 | ||||||||
\(643\) | −5.82554 | −0.229737 | −0.114868 | − | 0.993381i | \(-0.536645\pi\) | ||||
−0.114868 | + | 0.993381i | \(0.536645\pi\) | |||||||
\(644\) | 15.1967 | 0.598834 | ||||||||
\(645\) | 0.0520550 | 0.00204966 | ||||||||
\(646\) | 9.77085 | 0.384429 | ||||||||
\(647\) | 8.30759 | 0.326605 | 0.163302 | − | 0.986576i | \(-0.447785\pi\) | ||||
0.163302 | + | 0.986576i | \(0.447785\pi\) | |||||||
\(648\) | −2.02214 | −0.0794373 | ||||||||
\(649\) | −6.36259 | −0.249753 | ||||||||
\(650\) | −0.310535 | −0.0121802 | ||||||||
\(651\) | −9.66103 | −0.378646 | ||||||||
\(652\) | −18.6492 | −0.730359 | ||||||||
\(653\) | 44.4182 | 1.73822 | 0.869109 | − | 0.494621i | \(-0.164693\pi\) | ||||
0.869109 | + | 0.494621i | \(0.164693\pi\) | |||||||
\(654\) | 10.8661 | 0.424897 | ||||||||
\(655\) | 5.69781 | 0.222632 | ||||||||
\(656\) | −25.2439 | −0.985610 | ||||||||
\(657\) | 2.26625 | 0.0884147 | ||||||||
\(658\) | 5.54857 | 0.216306 | ||||||||
\(659\) | −13.4965 | −0.525750 | −0.262875 | − | 0.964830i | \(-0.584671\pi\) | ||||
−0.262875 | + | 0.964830i | \(0.584671\pi\) | |||||||
\(660\) | −1.70156 | −0.0662332 | ||||||||
\(661\) | 31.7450 | 1.23474 | 0.617370 | − | 0.786673i | \(-0.288198\pi\) | ||||
0.617370 | + | 0.786673i | \(0.288198\pi\) | |||||||
\(662\) | 3.70532 | 0.144011 | ||||||||
\(663\) | −1.53567 | −0.0596405 | ||||||||
\(664\) | −34.7010 | −1.34666 | ||||||||
\(665\) | 6.62049 | 0.256732 | ||||||||
\(666\) | −1.50429 | −0.0582899 | ||||||||
\(667\) | 47.0665 | 1.82242 | ||||||||
\(668\) | 12.9120 | 0.499579 | ||||||||
\(669\) | −13.9141 | −0.537951 | ||||||||
\(670\) | 5.68947 | 0.219803 | ||||||||
\(671\) | 3.71308 | 0.143342 | ||||||||
\(672\) | −5.29991 | −0.204449 | ||||||||
\(673\) | 5.81295 | 0.224073 | 0.112036 | − | 0.993704i | \(-0.464263\pi\) | ||||
0.112036 | + | 0.993704i | \(0.464263\pi\) | |||||||
\(674\) | −17.4546 | −0.672326 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 21.5705 | 0.829634 | ||||||||
\(677\) | −23.3699 | −0.898177 | −0.449088 | − | 0.893487i | \(-0.648251\pi\) | ||||
−0.449088 | + | 0.893487i | \(0.648251\pi\) | |||||||
\(678\) | 3.51558 | 0.135015 | ||||||||
\(679\) | −17.9952 | −0.690592 | ||||||||
\(680\) | 5.46295 | 0.209494 | ||||||||
\(681\) | 0.597452 | 0.0228944 | ||||||||
\(682\) | −5.27777 | −0.202096 | ||||||||
\(683\) | 13.4705 | 0.515433 | 0.257716 | − | 0.966221i | \(-0.417030\pi\) | ||||
0.257716 | + | 0.966221i | \(0.417030\pi\) | |||||||
\(684\) | −11.2652 | −0.430735 | ||||||||
\(685\) | 3.40312 | 0.130027 | ||||||||
\(686\) | −0.546295 | −0.0208576 | ||||||||
\(687\) | 21.1895 | 0.808430 | ||||||||
\(688\) | −0.119645 | −0.00456143 | ||||||||
\(689\) | −0.889427 | −0.0338845 | ||||||||
\(690\) | −4.87897 | −0.185739 | ||||||||
\(691\) | 9.79358 | 0.372565 | 0.186283 | − | 0.982496i | \(-0.440356\pi\) | ||||
0.186283 | + | 0.982496i | \(0.440356\pi\) | |||||||
\(692\) | 30.9844 | 1.17785 | ||||||||
\(693\) | 1.00000 | 0.0379869 | ||||||||
\(694\) | −7.46751 | −0.283463 | ||||||||
\(695\) | 8.04724 | 0.305249 | ||||||||
\(696\) | −10.6567 | −0.403941 | ||||||||
\(697\) | −29.6715 | −1.12389 | ||||||||
\(698\) | 8.83469 | 0.334398 | ||||||||
\(699\) | −20.2821 | −0.767139 | ||||||||
\(700\) | 1.70156 | 0.0643130 | ||||||||
\(701\) | −9.27000 | −0.350123 | −0.175062 | − | 0.984557i | \(-0.556012\pi\) | ||||
−0.175062 | + | 0.984557i | \(0.556012\pi\) | |||||||
\(702\) | −0.310535 | −0.0117204 | ||||||||
\(703\) | −18.2303 | −0.687569 | ||||||||
\(704\) | 1.70156 | 0.0641300 | ||||||||
\(705\) | 10.1567 | 0.382525 | ||||||||
\(706\) | −5.43188 | −0.204431 | ||||||||
\(707\) | −0.826342 | −0.0310778 | ||||||||
\(708\) | −10.8263 | −0.406879 | ||||||||
\(709\) | −19.9898 | −0.750732 | −0.375366 | − | 0.926877i | \(-0.622483\pi\) | ||||
−0.375366 | + | 0.926877i | \(0.622483\pi\) | |||||||
\(710\) | −1.40312 | −0.0526583 | ||||||||
\(711\) | −2.56844 | −0.0963240 | ||||||||
\(712\) | 21.7931 | 0.816732 | ||||||||
\(713\) | 86.2829 | 3.23132 | ||||||||
\(714\) | −1.47585 | −0.0552323 | ||||||||
\(715\) | −0.568438 | −0.0212584 | ||||||||
\(716\) | −8.08857 | −0.302284 | ||||||||
\(717\) | 2.23723 | 0.0835510 | ||||||||
\(718\) | −6.87487 | −0.256568 | ||||||||
\(719\) | −26.7174 | −0.996391 | −0.498196 | − | 0.867065i | \(-0.666004\pi\) | ||||
−0.498196 | + | 0.867065i | \(0.666004\pi\) | |||||||
\(720\) | −2.29844 | −0.0856577 | ||||||||
\(721\) | −10.5921 | −0.394469 | ||||||||
\(722\) | 13.5650 | 0.504837 | ||||||||
\(723\) | 8.93045 | 0.332127 | ||||||||
\(724\) | −42.9903 | −1.59772 | ||||||||
\(725\) | 5.27000 | 0.195723 | ||||||||
\(726\) | 0.546295 | 0.0202749 | ||||||||
\(727\) | 16.4955 | 0.611782 | 0.305891 | − | 0.952066i | \(-0.401046\pi\) | ||||
0.305891 | + | 0.952066i | \(0.401046\pi\) | |||||||
\(728\) | −1.14946 | −0.0426020 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.23804 | −0.0458219 | ||||||||
\(731\) | −0.140630 | −0.00520138 | ||||||||
\(732\) | 6.31804 | 0.233522 | ||||||||
\(733\) | −22.6838 | −0.837847 | −0.418923 | − | 0.908022i | \(-0.637592\pi\) | ||||
−0.418923 | + | 0.908022i | \(0.637592\pi\) | |||||||
\(734\) | 20.1965 | 0.745465 | ||||||||
\(735\) | −1.00000 | −0.0368856 | ||||||||
\(736\) | 47.3337 | 1.74474 | ||||||||
\(737\) | 10.4146 | 0.383628 | ||||||||
\(738\) | −6.00000 | −0.220863 | ||||||||
\(739\) | −41.7166 | −1.53457 | −0.767285 | − | 0.641306i | \(-0.778393\pi\) | ||||
−0.767285 | + | 0.641306i | \(0.778393\pi\) | |||||||
\(740\) | −4.68545 | −0.172241 | ||||||||
\(741\) | −3.76334 | −0.138250 | ||||||||
\(742\) | −0.854779 | −0.0313799 | ||||||||
\(743\) | −26.4664 | −0.970959 | −0.485480 | − | 0.874248i | \(-0.661355\pi\) | ||||
−0.485480 | + | 0.874248i | \(0.661355\pi\) | |||||||
\(744\) | −19.5360 | −0.716224 | ||||||||
\(745\) | −7.50723 | −0.275044 | ||||||||
\(746\) | −7.32630 | −0.268235 | ||||||||
\(747\) | 17.1605 | 0.627870 | ||||||||
\(748\) | 4.59688 | 0.168078 | ||||||||
\(749\) | 13.7864 | 0.503744 | ||||||||
\(750\) | −0.546295 | −0.0199479 | ||||||||
\(751\) | −36.2802 | −1.32388 | −0.661942 | − | 0.749555i | \(-0.730268\pi\) | ||||
−0.661942 | + | 0.749555i | \(0.730268\pi\) | |||||||
\(752\) | −23.3446 | −0.851291 | ||||||||
\(753\) | 3.35884 | 0.122403 | ||||||||
\(754\) | −1.63652 | −0.0595985 | ||||||||
\(755\) | −3.21795 | −0.117113 | ||||||||
\(756\) | 1.70156 | 0.0618852 | ||||||||
\(757\) | 27.3451 | 0.993874 | 0.496937 | − | 0.867786i | \(-0.334458\pi\) | ||||
0.496937 | + | 0.867786i | \(0.334458\pi\) | |||||||
\(758\) | −0.440134 | −0.0159864 | ||||||||
\(759\) | −8.93103 | −0.324176 | ||||||||
\(760\) | 13.3876 | 0.485619 | ||||||||
\(761\) | −16.2537 | −0.589195 | −0.294597 | − | 0.955621i | \(-0.595186\pi\) | ||||
−0.294597 | + | 0.955621i | \(0.595186\pi\) | |||||||
\(762\) | 2.21362 | 0.0801909 | ||||||||
\(763\) | −19.8905 | −0.720084 | ||||||||
\(764\) | 29.6929 | 1.07425 | ||||||||
\(765\) | −2.70156 | −0.0976752 | ||||||||
\(766\) | −12.2094 | −0.441143 | ||||||||
\(767\) | −3.61674 | −0.130593 | ||||||||
\(768\) | −2.89531 | −0.104476 | ||||||||
\(769\) | −38.2698 | −1.38004 | −0.690022 | − | 0.723789i | \(-0.742399\pi\) | ||||
−0.690022 | + | 0.723789i | \(0.742399\pi\) | |||||||
\(770\) | −0.546295 | −0.0196871 | ||||||||
\(771\) | 5.80943 | 0.209221 | ||||||||
\(772\) | −39.0588 | −1.40576 | ||||||||
\(773\) | 6.60438 | 0.237543 | 0.118772 | − | 0.992922i | \(-0.462104\pi\) | ||||
0.118772 | + | 0.992922i | \(0.462104\pi\) | |||||||
\(774\) | −0.0284374 | −0.00102216 | ||||||||
\(775\) | 9.66103 | 0.347034 | ||||||||
\(776\) | −36.3888 | −1.30628 | ||||||||
\(777\) | 2.75362 | 0.0987855 | ||||||||
\(778\) | −16.1082 | −0.577507 | ||||||||
\(779\) | −72.7134 | −2.60523 | ||||||||
\(780\) | −0.967233 | −0.0346325 | ||||||||
\(781\) | −2.56844 | −0.0919060 | ||||||||
\(782\) | 13.1808 | 0.471346 | ||||||||
\(783\) | 5.27000 | 0.188334 | ||||||||
\(784\) | 2.29844 | 0.0820871 | ||||||||
\(785\) | 3.35107 | 0.119605 | ||||||||
\(786\) | −3.11268 | −0.111026 | ||||||||
\(787\) | −23.1916 | −0.826692 | −0.413346 | − | 0.910574i | \(-0.635640\pi\) | ||||
−0.413346 | + | 0.910574i | \(0.635640\pi\) | |||||||
\(788\) | 5.72804 | 0.204053 | ||||||||
\(789\) | −23.3221 | −0.830287 | ||||||||
\(790\) | 1.40312 | 0.0499209 | ||||||||
\(791\) | −6.43531 | −0.228813 | ||||||||
\(792\) | 2.02214 | 0.0718537 | ||||||||
\(793\) | 2.11066 | 0.0749517 | ||||||||
\(794\) | 2.43179 | 0.0863010 | ||||||||
\(795\) | −1.56469 | −0.0554937 | ||||||||
\(796\) | −16.2397 | −0.575602 | ||||||||
\(797\) | 32.5872 | 1.15430 | 0.577150 | − | 0.816638i | \(-0.304165\pi\) | ||||
0.577150 | + | 0.816638i | \(0.304165\pi\) | |||||||
\(798\) | −3.61674 | −0.128031 | ||||||||
\(799\) | −27.4391 | −0.970724 | ||||||||
\(800\) | 5.29991 | 0.187380 | ||||||||
\(801\) | −10.7772 | −0.380795 | ||||||||
\(802\) | 12.4076 | 0.438127 | ||||||||
\(803\) | −2.26625 | −0.0799741 | ||||||||
\(804\) | 17.7212 | 0.624977 | ||||||||
\(805\) | 8.93103 | 0.314777 | ||||||||
\(806\) | −3.00009 | −0.105674 | ||||||||
\(807\) | 29.1246 | 1.02523 | ||||||||
\(808\) | −1.67098 | −0.0587849 | ||||||||
\(809\) | 13.5303 | 0.475699 | 0.237850 | − | 0.971302i | \(-0.423557\pi\) | ||||
0.237850 | + | 0.971302i | \(0.423557\pi\) | |||||||
\(810\) | −0.546295 | −0.0191948 | ||||||||
\(811\) | 27.7241 | 0.973525 | 0.486763 | − | 0.873534i | \(-0.338178\pi\) | ||||
0.486763 | + | 0.873534i | \(0.338178\pi\) | |||||||
\(812\) | 8.96723 | 0.314688 | ||||||||
\(813\) | 31.2416 | 1.09569 | ||||||||
\(814\) | 1.50429 | 0.0527252 | ||||||||
\(815\) | −10.9600 | −0.383914 | ||||||||
\(816\) | 6.20937 | 0.217372 | ||||||||
\(817\) | −0.344630 | −0.0120571 | ||||||||
\(818\) | 2.78205 | 0.0972723 | ||||||||
\(819\) | 0.568438 | 0.0198628 | ||||||||
\(820\) | −18.6884 | −0.652627 | ||||||||
\(821\) | 40.9774 | 1.43012 | 0.715061 | − | 0.699062i | \(-0.246399\pi\) | ||||
0.715061 | + | 0.699062i | \(0.246399\pi\) | |||||||
\(822\) | −1.85911 | −0.0648439 | ||||||||
\(823\) | 3.27352 | 0.114108 | 0.0570539 | − | 0.998371i | \(-0.481829\pi\) | ||||
0.0570539 | + | 0.998371i | \(0.481829\pi\) | |||||||
\(824\) | −21.4187 | −0.746154 | ||||||||
\(825\) | −1.00000 | −0.0348155 | ||||||||
\(826\) | −3.47585 | −0.120940 | ||||||||
\(827\) | −36.5217 | −1.26998 | −0.634992 | − | 0.772519i | \(-0.718997\pi\) | ||||
−0.634992 | + | 0.772519i | \(0.718997\pi\) | |||||||
\(828\) | −15.1967 | −0.528122 | ||||||||
\(829\) | 21.2335 | 0.737469 | 0.368735 | − | 0.929535i | \(-0.379791\pi\) | ||||
0.368735 | + | 0.929535i | \(0.379791\pi\) | |||||||
\(830\) | −9.37469 | −0.325400 | ||||||||
\(831\) | −15.8988 | −0.551525 | ||||||||
\(832\) | 0.967233 | 0.0335328 | ||||||||
\(833\) | 2.70156 | 0.0936036 | ||||||||
\(834\) | −4.39616 | −0.152227 | ||||||||
\(835\) | 7.58830 | 0.262604 | ||||||||
\(836\) | 11.2652 | 0.389614 | ||||||||
\(837\) | 9.66103 | 0.333934 | ||||||||
\(838\) | −1.56397 | −0.0540263 | ||||||||
\(839\) | 20.7571 | 0.716616 | 0.358308 | − | 0.933603i | \(-0.383354\pi\) | ||||
0.358308 | + | 0.933603i | \(0.383354\pi\) | |||||||
\(840\) | −2.02214 | −0.0697706 | ||||||||
\(841\) | −1.22709 | −0.0423136 | ||||||||
\(842\) | −8.79790 | −0.303196 | ||||||||
\(843\) | −14.1041 | −0.485771 | ||||||||
\(844\) | 13.1595 | 0.452967 | ||||||||
\(845\) | 12.6769 | 0.436098 | ||||||||
\(846\) | −5.54857 | −0.190764 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 3.59633 | 0.123499 | ||||||||
\(849\) | −1.32745 | −0.0455580 | ||||||||
\(850\) | 1.47585 | 0.0506212 | ||||||||
\(851\) | −24.5926 | −0.843025 | ||||||||
\(852\) | −4.37036 | −0.149726 | ||||||||
\(853\) | −31.3333 | −1.07283 | −0.536417 | − | 0.843953i | \(-0.680222\pi\) | ||||
−0.536417 | + | 0.843953i | \(0.680222\pi\) | |||||||
\(854\) | 2.02844 | 0.0694117 | ||||||||
\(855\) | −6.62049 | −0.226416 | ||||||||
\(856\) | 27.8780 | 0.952852 | ||||||||
\(857\) | 13.5411 | 0.462554 | 0.231277 | − | 0.972888i | \(-0.425710\pi\) | ||||
0.231277 | + | 0.972888i | \(0.425710\pi\) | |||||||
\(858\) | 0.310535 | 0.0106015 | ||||||||
\(859\) | −19.5644 | −0.667530 | −0.333765 | − | 0.942656i | \(-0.608319\pi\) | ||||
−0.333765 | + | 0.942656i | \(0.608319\pi\) | |||||||
\(860\) | −0.0885748 | −0.00302038 | ||||||||
\(861\) | 10.9831 | 0.374302 | ||||||||
\(862\) | −2.55554 | −0.0870419 | ||||||||
\(863\) | −8.91434 | −0.303448 | −0.151724 | − | 0.988423i | \(-0.548482\pi\) | ||||
−0.151724 | + | 0.988423i | \(0.548482\pi\) | |||||||
\(864\) | 5.29991 | 0.180307 | ||||||||
\(865\) | 18.2094 | 0.619137 | ||||||||
\(866\) | −14.9869 | −0.509275 | ||||||||
\(867\) | −9.70156 | −0.329482 | ||||||||
\(868\) | 16.4388 | 0.557971 | ||||||||
\(869\) | 2.56844 | 0.0871283 | ||||||||
\(870\) | −2.87897 | −0.0976063 | ||||||||
\(871\) | 5.92008 | 0.200594 | ||||||||
\(872\) | −40.2214 | −1.36207 | ||||||||
\(873\) | 17.9952 | 0.609045 | ||||||||
\(874\) | 32.3012 | 1.09260 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −3.85616 | −0.130288 | ||||||||
\(877\) | 6.17626 | 0.208557 | 0.104279 | − | 0.994548i | \(-0.466747\pi\) | ||||
0.104279 | + | 0.994548i | \(0.466747\pi\) | |||||||
\(878\) | 3.13263 | 0.105721 | ||||||||
\(879\) | 18.3784 | 0.619889 | ||||||||
\(880\) | 2.29844 | 0.0774803 | ||||||||
\(881\) | 19.3511 | 0.651954 | 0.325977 | − | 0.945378i | \(-0.394307\pi\) | ||||
0.325977 | + | 0.945378i | \(0.394307\pi\) | |||||||
\(882\) | 0.546295 | 0.0183947 | ||||||||
\(883\) | 28.7925 | 0.968945 | 0.484473 | − | 0.874806i | \(-0.339012\pi\) | ||||
0.484473 | + | 0.874806i | \(0.339012\pi\) | |||||||
\(884\) | 2.61304 | 0.0878861 | ||||||||
\(885\) | −6.36259 | −0.213876 | ||||||||
\(886\) | −5.23643 | −0.175921 | ||||||||
\(887\) | −43.4970 | −1.46049 | −0.730243 | − | 0.683187i | \(-0.760593\pi\) | ||||
−0.730243 | + | 0.683187i | \(0.760593\pi\) | |||||||
\(888\) | 5.56821 | 0.186857 | ||||||||
\(889\) | −4.05206 | −0.135902 | ||||||||
\(890\) | 5.88755 | 0.197351 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 23.6757 | 0.792722 | ||||||||
\(893\) | −67.2426 | −2.25019 | ||||||||
\(894\) | 4.10116 | 0.137163 | ||||||||
\(895\) | −4.75362 | −0.158896 | ||||||||
\(896\) | 11.5294 | 0.385169 | ||||||||
\(897\) | −5.07674 | −0.169507 | ||||||||
\(898\) | 16.9058 | 0.564154 | ||||||||
\(899\) | 50.9136 | 1.69806 | ||||||||
\(900\) | −1.70156 | −0.0567187 | ||||||||
\(901\) | 4.22709 | 0.140825 | ||||||||
\(902\) | 6.00000 | 0.199778 | ||||||||
\(903\) | 0.0520550 | 0.00173228 | ||||||||
\(904\) | −13.0131 | −0.432810 | ||||||||
\(905\) | −25.2652 | −0.839843 | ||||||||
\(906\) | 1.75795 | 0.0584039 | ||||||||
\(907\) | −9.20210 | −0.305551 | −0.152775 | − | 0.988261i | \(-0.548821\pi\) | ||||
−0.152775 | + | 0.988261i | \(0.548821\pi\) | |||||||
\(908\) | −1.01660 | −0.0337371 | ||||||||
\(909\) | 0.826342 | 0.0274080 | ||||||||
\(910\) | −0.310535 | −0.0102941 | ||||||||
\(911\) | 7.98331 | 0.264499 | 0.132249 | − | 0.991216i | \(-0.457780\pi\) | ||||
0.132249 | + | 0.991216i | \(0.457780\pi\) | |||||||
\(912\) | 15.2168 | 0.503878 | ||||||||
\(913\) | −17.1605 | −0.567929 | ||||||||
\(914\) | −23.0671 | −0.762992 | ||||||||
\(915\) | 3.71308 | 0.122751 | ||||||||
\(916\) | −36.0553 | −1.19130 | ||||||||
\(917\) | 5.69781 | 0.188158 | ||||||||
\(918\) | 1.47585 | 0.0487103 | ||||||||
\(919\) | −36.4176 | −1.20131 | −0.600653 | − | 0.799510i | \(-0.705093\pi\) | ||||
−0.600653 | + | 0.799510i | \(0.705093\pi\) | |||||||
\(920\) | 18.0598 | 0.595415 | ||||||||
\(921\) | 6.45143 | 0.212582 | ||||||||
\(922\) | 5.39447 | 0.177657 | ||||||||
\(923\) | −1.46000 | −0.0480565 | ||||||||
\(924\) | −1.70156 | −0.0559773 | ||||||||
\(925\) | −2.75362 | −0.0905384 | ||||||||
\(926\) | 1.39857 | 0.0459597 | ||||||||
\(927\) | 10.5921 | 0.347889 | ||||||||
\(928\) | 27.9305 | 0.916865 | ||||||||
\(929\) | 1.06660 | 0.0349940 | 0.0174970 | − | 0.999847i | \(-0.494430\pi\) | ||||
0.0174970 | + | 0.999847i | \(0.494430\pi\) | |||||||
\(930\) | −5.27777 | −0.173065 | ||||||||
\(931\) | 6.62049 | 0.216978 | ||||||||
\(932\) | 34.5112 | 1.13045 | ||||||||
\(933\) | −29.4136 | −0.962957 | ||||||||
\(934\) | −10.7579 | −0.352008 | ||||||||
\(935\) | 2.70156 | 0.0883505 | ||||||||
\(936\) | 1.14946 | 0.0375714 | ||||||||
\(937\) | −4.74611 | −0.155049 | −0.0775243 | − | 0.996990i | \(-0.524702\pi\) | ||||
−0.0775243 | + | 0.996990i | \(0.524702\pi\) | |||||||
\(938\) | 5.68947 | 0.185768 | ||||||||
\(939\) | −24.7542 | −0.807823 | ||||||||
\(940\) | −17.2823 | −0.563687 | ||||||||
\(941\) | 33.1988 | 1.08225 | 0.541125 | − | 0.840942i | \(-0.317999\pi\) | ||||
0.541125 | + | 0.840942i | \(0.317999\pi\) | |||||||
\(942\) | −1.83067 | −0.0596465 | ||||||||
\(943\) | −98.0902 | −3.19426 | ||||||||
\(944\) | 14.6240 | 0.475971 | ||||||||
\(945\) | 1.00000 | 0.0325300 | ||||||||
\(946\) | 0.0284374 | 0.000924579 0 | ||||||||
\(947\) | 6.30361 | 0.204840 | 0.102420 | − | 0.994741i | \(-0.467341\pi\) | ||||
0.102420 | + | 0.994741i | \(0.467341\pi\) | |||||||
\(948\) | 4.37036 | 0.141943 | ||||||||
\(949\) | −1.28822 | −0.0418175 | ||||||||
\(950\) | 3.61674 | 0.117343 | ||||||||
\(951\) | −15.0955 | −0.489506 | ||||||||
\(952\) | 5.46295 | 0.177055 | ||||||||
\(953\) | −39.4705 | −1.27857 | −0.639287 | − | 0.768968i | \(-0.720770\pi\) | ||||
−0.639287 | + | 0.768968i | \(0.720770\pi\) | |||||||
\(954\) | 0.854779 | 0.0276745 | ||||||||
\(955\) | 17.4504 | 0.564680 | ||||||||
\(956\) | −3.80679 | −0.123120 | ||||||||
\(957\) | −5.27000 | −0.170355 | ||||||||
\(958\) | 8.39501 | 0.271230 | ||||||||
\(959\) | 3.40312 | 0.109893 | ||||||||
\(960\) | 1.70156 | 0.0549177 | ||||||||
\(961\) | 62.3355 | 2.01082 | ||||||||
\(962\) | 0.855094 | 0.0275693 | ||||||||
\(963\) | −13.7864 | −0.444260 | ||||||||
\(964\) | −15.1957 | −0.489421 | ||||||||
\(965\) | −22.9546 | −0.738936 | ||||||||
\(966\) | −4.87897 | −0.156978 | ||||||||
\(967\) | −20.7192 | −0.666285 | −0.333142 | − | 0.942877i | \(-0.608109\pi\) | ||||
−0.333142 | + | 0.942877i | \(0.608109\pi\) | |||||||
\(968\) | −2.02214 | −0.0649942 | ||||||||
\(969\) | 17.8857 | 0.574571 | ||||||||
\(970\) | −9.83067 | −0.315644 | ||||||||
\(971\) | 0.281521 | 0.00903444 | 0.00451722 | − | 0.999990i | \(-0.498562\pi\) | ||||
0.00451722 | + | 0.999990i | \(0.498562\pi\) | |||||||
\(972\) | −1.70156 | −0.0545776 | ||||||||
\(973\) | 8.04724 | 0.257983 | ||||||||
\(974\) | −0.835001 | −0.0267551 | ||||||||
\(975\) | −0.568438 | −0.0182046 | ||||||||
\(976\) | −8.53429 | −0.273176 | ||||||||
\(977\) | 53.1267 | 1.69967 | 0.849836 | − | 0.527047i | \(-0.176701\pi\) | ||||
0.849836 | + | 0.527047i | \(0.176701\pi\) | |||||||
\(978\) | 5.98741 | 0.191456 | ||||||||
\(979\) | 10.7772 | 0.344442 | ||||||||
\(980\) | 1.70156 | 0.0543544 | ||||||||
\(981\) | 19.8905 | 0.635055 | ||||||||
\(982\) | −22.2538 | −0.710147 | ||||||||
\(983\) | −47.2072 | −1.50567 | −0.752837 | − | 0.658207i | \(-0.771315\pi\) | ||||
−0.752837 | + | 0.658207i | \(0.771315\pi\) | |||||||
\(984\) | 22.2094 | 0.708009 | ||||||||
\(985\) | 3.36634 | 0.107261 | ||||||||
\(986\) | 7.77773 | 0.247693 | ||||||||
\(987\) | 10.1567 | 0.323293 | ||||||||
\(988\) | 6.40356 | 0.203724 | ||||||||
\(989\) | −0.464905 | −0.0147831 | ||||||||
\(990\) | 0.546295 | 0.0173624 | ||||||||
\(991\) | −30.4901 | −0.968549 | −0.484274 | − | 0.874916i | \(-0.660916\pi\) | ||||
−0.484274 | + | 0.874916i | \(0.660916\pi\) | |||||||
\(992\) | 51.2026 | 1.62568 | ||||||||
\(993\) | 6.78263 | 0.215240 | ||||||||
\(994\) | −1.40312 | −0.0445044 | ||||||||
\(995\) | −9.54402 | −0.302566 | ||||||||
\(996\) | −29.1996 | −0.925226 | ||||||||
\(997\) | 6.62107 | 0.209691 | 0.104846 | − | 0.994489i | \(-0.466565\pi\) | ||||
0.104846 | + | 0.994489i | \(0.466565\pi\) | |||||||
\(998\) | −11.1068 | −0.351581 | ||||||||
\(999\) | −2.75362 | −0.0871206 |
(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 | 1155.2.a.u.1.3 | ✓ | 4 | |
3.2 | odd | 2 | 3465.2.a.bl.1.2 | 4 | |||
5.4 | even | 2 | 5775.2.a.bz.1.2 | 4 | |||
7.6 | odd | 2 | 8085.2.a.bn.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.a.u.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial | |
3465.2.a.bl.1.2 | 4 | 3.2 | odd | 2 | |||
5775.2.a.bz.1.2 | 4 | 5.4 | even | 2 | |||
8085.2.a.bn.1.3 | 4 | 7.6 | odd | 2 |