Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3675,2,Mod(1,3675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3675, 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("3675.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3675 = 3 \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3675.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: | \(29.3450227428\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.88404.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 7x^{2} + 5x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 525) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-2.43736\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3675.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.43736 | 1.72347 | 0.861737 | − | 0.507356i | \(-0.169377\pi\) | ||||
0.861737 | + | 0.507356i | \(0.169377\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.94072 | 1.97036 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.43736 | −0.995048 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 4.73024 | 1.67239 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.58184 | 1.38148 | 0.690739 | − | 0.723104i | \(-0.257286\pi\) | ||||
0.690739 | + | 0.723104i | \(0.257286\pi\) | |||||||
\(12\) | −3.94072 | −1.13759 | ||||||||
\(13\) | −1.35888 | −0.376885 | −0.188443 | − | 0.982084i | \(-0.560344\pi\) | ||||
−0.188443 | + | 0.982084i | \(0.560344\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.64784 | 0.911961 | ||||||||
\(17\) | −4.29288 | −1.04118 | −0.520588 | − | 0.853808i | \(-0.674287\pi\) | ||||
−0.520588 | + | 0.853808i | \(0.674287\pi\) | |||||||
\(18\) | 2.43736 | 0.574491 | ||||||||
\(19\) | 6.81544 | 1.56357 | 0.781785 | − | 0.623548i | \(-0.214310\pi\) | ||||
0.781785 | + | 0.623548i | \(0.214310\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 11.1676 | 2.38094 | ||||||||
\(23\) | 3.88144 | 0.809337 | 0.404668 | − | 0.914463i | \(-0.367387\pi\) | ||||
0.404668 | + | 0.914463i | \(0.367387\pi\) | |||||||
\(24\) | −4.73024 | −0.965556 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.31208 | −0.649552 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.00000 | 0.742781 | 0.371391 | − | 0.928477i | \(-0.378881\pi\) | ||||
0.371391 | + | 0.928477i | \(0.378881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.10832 | 1.45630 | 0.728148 | − | 0.685419i | \(-0.240381\pi\) | ||||
0.728148 | + | 0.685419i | \(0.240381\pi\) | |||||||
\(32\) | −0.569365 | −0.100650 | ||||||||
\(33\) | −4.58184 | −0.797596 | ||||||||
\(34\) | −10.4633 | −1.79444 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.94072 | 0.656787 | ||||||||
\(37\) | −11.7562 | −1.93270 | −0.966351 | − | 0.257228i | \(-0.917191\pi\) | ||||
−0.966351 | + | 0.257228i | \(0.917191\pi\) | |||||||
\(38\) | 16.6117 | 2.69477 | ||||||||
\(39\) | 1.35888 | 0.217595 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.17432 | −1.27661 | −0.638307 | − | 0.769782i | \(-0.720365\pi\) | ||||
−0.638307 | + | 0.769782i | \(0.720365\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.52256 | 0.537186 | 0.268593 | − | 0.963254i | \(-0.413441\pi\) | ||||
0.268593 | + | 0.963254i | \(0.413441\pi\) | |||||||
\(44\) | 18.0558 | 2.72201 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 9.46047 | 1.39487 | ||||||||
\(47\) | 3.29960 | 0.481296 | 0.240648 | − | 0.970612i | \(-0.422640\pi\) | ||||
0.240648 | + | 0.970612i | \(0.422640\pi\) | |||||||
\(48\) | −3.64784 | −0.526521 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.29288 | 0.601123 | ||||||||
\(52\) | −5.35497 | −0.742600 | ||||||||
\(53\) | 9.45656 | 1.29896 | 0.649479 | − | 0.760379i | \(-0.274987\pi\) | ||||
0.649479 | + | 0.760379i | \(0.274987\pi\) | |||||||
\(54\) | −2.43736 | −0.331683 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.81544 | −0.902727 | ||||||||
\(58\) | 9.74944 | 1.28016 | ||||||||
\(59\) | −0.700398 | −0.0911841 | −0.0455921 | − | 0.998960i | \(-0.514517\pi\) | ||||
−0.0455921 | + | 0.998960i | \(0.514517\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.00000 | 0.640184 | 0.320092 | − | 0.947386i | \(-0.396286\pi\) | ||||
0.320092 | + | 0.947386i | \(0.396286\pi\) | |||||||
\(62\) | 19.7629 | 2.50989 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.68344 | −1.08543 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −11.1676 | −1.37464 | ||||||||
\(67\) | 1.94072 | 0.237097 | 0.118548 | − | 0.992948i | \(-0.462176\pi\) | ||||
0.118548 | + | 0.992948i | \(0.462176\pi\) | |||||||
\(68\) | −16.9170 | −2.05149 | ||||||||
\(69\) | −3.88144 | −0.467271 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.8680 | 1.40847 | 0.704236 | − | 0.709966i | \(-0.251290\pi\) | ||||
0.704236 | + | 0.709966i | \(0.251290\pi\) | |||||||
\(72\) | 4.73024 | 0.557464 | ||||||||
\(73\) | 6.16368 | 0.721405 | 0.360702 | − | 0.932681i | \(-0.382537\pi\) | ||||
0.360702 | + | 0.932681i | \(0.382537\pi\) | |||||||
\(74\) | −28.6540 | −3.33096 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 26.8578 | 3.08080 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.31208 | 0.375019 | ||||||||
\(79\) | −6.16760 | −0.693909 | −0.346954 | − | 0.937882i | \(-0.612784\pi\) | ||||
−0.346954 | + | 0.937882i | \(0.612784\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −19.9238 | −2.20021 | ||||||||
\(83\) | 13.0490 | 1.43232 | 0.716159 | − | 0.697937i | \(-0.245898\pi\) | ||||
0.716159 | + | 0.697937i | \(0.245898\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.58575 | 0.925826 | ||||||||
\(87\) | −4.00000 | −0.428845 | ||||||||
\(88\) | 21.6732 | 2.31037 | ||||||||
\(89\) | −0.292877 | −0.0310449 | −0.0155225 | − | 0.999880i | \(-0.504941\pi\) | ||||
−0.0155225 | + | 0.999880i | \(0.504941\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 15.2957 | 1.59469 | ||||||||
\(93\) | −8.10832 | −0.840793 | ||||||||
\(94\) | 8.04232 | 0.829502 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.569365 | 0.0581105 | ||||||||
\(97\) | −2.00672 | −0.203752 | −0.101876 | − | 0.994797i | \(-0.532484\pi\) | ||||
−0.101876 | + | 0.994797i | \(0.532484\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.58184 | 0.460492 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.29288 | −0.626165 | −0.313082 | − | 0.949726i | \(-0.601362\pi\) | ||||
−0.313082 | + | 0.949726i | \(0.601362\pi\) | |||||||
\(102\) | 10.4633 | 1.03602 | ||||||||
\(103\) | −3.41143 | −0.336139 | −0.168069 | − | 0.985775i | \(-0.553753\pi\) | ||||
−0.168069 | + | 0.985775i | \(0.553753\pi\) | |||||||
\(104\) | −6.42782 | −0.630300 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 23.0490 | 2.23872 | ||||||||
\(107\) | −3.16760 | −0.306223 | −0.153112 | − | 0.988209i | \(-0.548929\pi\) | ||||
−0.153112 | + | 0.988209i | \(0.548929\pi\) | |||||||
\(108\) | −3.94072 | −0.379196 | ||||||||
\(109\) | 10.2336 | 0.980201 | 0.490101 | − | 0.871666i | \(-0.336960\pi\) | ||||
0.490101 | + | 0.871666i | \(0.336960\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.7562 | 1.11585 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.16368 | 0.297614 | 0.148807 | − | 0.988866i | \(-0.452457\pi\) | ||||
0.148807 | + | 0.988866i | \(0.452457\pi\) | |||||||
\(114\) | −16.6117 | −1.55583 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 15.7629 | 1.46355 | ||||||||
\(117\) | −1.35888 | −0.125628 | ||||||||
\(118\) | −1.70712 | −0.157153 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.99328 | 0.908480 | ||||||||
\(122\) | 12.1868 | 1.10334 | ||||||||
\(123\) | 8.17432 | 0.737054 | ||||||||
\(124\) | 31.9526 | 2.86943 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.0106369 | −0.000943870 0 | −0.000471935 | − | 1.00000i | \(-0.500150\pi\) | ||||
−0.000471935 | 1.00000i | \(0.500150\pi\) | ||||||||
\(128\) | −20.0259 | −1.77006 | ||||||||
\(129\) | −3.52256 | −0.310144 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.7629 | −1.20247 | −0.601235 | − | 0.799073i | \(-0.705324\pi\) | ||||
−0.601235 | + | 0.799073i | \(0.705324\pi\) | |||||||
\(132\) | −18.0558 | −1.57155 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4.73024 | 0.408630 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −20.3063 | −1.74125 | ||||||||
\(137\) | −9.04513 | −0.772777 | −0.386389 | − | 0.922336i | \(-0.626278\pi\) | ||||
−0.386389 | + | 0.922336i | \(0.626278\pi\) | |||||||
\(138\) | −9.46047 | −0.805329 | ||||||||
\(139\) | 21.3313 | 1.80930 | 0.904648 | − | 0.426160i | \(-0.140134\pi\) | ||||
0.904648 | + | 0.426160i | \(0.140134\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.29960 | −0.277877 | ||||||||
\(142\) | 28.9266 | 2.42746 | ||||||||
\(143\) | −6.22617 | −0.520659 | ||||||||
\(144\) | 3.64784 | 0.303987 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 15.0231 | 1.24332 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −46.3278 | −3.80812 | ||||||||
\(149\) | −15.8052 | −1.29481 | −0.647406 | − | 0.762145i | \(-0.724146\pi\) | ||||
−0.647406 | + | 0.762145i | \(0.724146\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.86408 | 0.395833 | 0.197917 | − | 0.980219i | \(-0.436582\pi\) | ||||
0.197917 | + | 0.980219i | \(0.436582\pi\) | |||||||
\(152\) | 32.2386 | 2.61490 | ||||||||
\(153\) | −4.29288 | −0.347059 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 5.35497 | 0.428741 | ||||||||
\(157\) | −6.57903 | −0.525064 | −0.262532 | − | 0.964923i | \(-0.584557\pi\) | ||||
−0.262532 | + | 0.964923i | \(0.584557\pi\) | |||||||
\(158\) | −15.0327 | −1.19593 | ||||||||
\(159\) | −9.45656 | −0.749954 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.43736 | 0.191497 | ||||||||
\(163\) | −11.4633 | −0.897874 | −0.448937 | − | 0.893563i | \(-0.648197\pi\) | ||||
−0.448937 | + | 0.893563i | \(0.648197\pi\) | |||||||
\(164\) | −32.2127 | −2.51539 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 31.8052 | 2.46856 | ||||||||
\(167\) | 20.9170 | 1.61861 | 0.809304 | − | 0.587390i | \(-0.199844\pi\) | ||||
0.809304 | + | 0.587390i | \(0.199844\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.1534 | −0.857957 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.81544 | 0.521190 | ||||||||
\(172\) | 13.8814 | 1.05845 | ||||||||
\(173\) | −11.1637 | −0.848759 | −0.424380 | − | 0.905484i | \(-0.639508\pi\) | ||||
−0.424380 | + | 0.905484i | \(0.639508\pi\) | |||||||
\(174\) | −9.74944 | −0.739103 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 16.7138 | 1.25985 | ||||||||
\(177\) | 0.700398 | 0.0526452 | ||||||||
\(178\) | −0.713847 | −0.0535051 | ||||||||
\(179\) | −17.5123 | −1.30893 | −0.654466 | − | 0.756091i | \(-0.727107\pi\) | ||||
−0.654466 | + | 0.756091i | \(0.727107\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.2653 | −1.50631 | −0.753153 | − | 0.657845i | \(-0.771468\pi\) | ||||
−0.753153 | + | 0.657845i | \(0.771468\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.00000 | −0.369611 | ||||||||
\(184\) | 18.3601 | 1.35353 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −19.7629 | −1.44909 | ||||||||
\(187\) | −19.6693 | −1.43836 | ||||||||
\(188\) | 13.0028 | 0.948328 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.13592 | −0.299265 | −0.149632 | − | 0.988742i | \(-0.547809\pi\) | ||||
−0.149632 | + | 0.988742i | \(0.547809\pi\) | |||||||
\(192\) | 8.68344 | 0.626673 | ||||||||
\(193\) | 4.76640 | 0.343093 | 0.171547 | − | 0.985176i | \(-0.445124\pi\) | ||||
0.171547 | + | 0.985176i | \(0.445124\pi\) | |||||||
\(194\) | −4.89111 | −0.351161 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.30351 | 0.377860 | 0.188930 | − | 0.981991i | \(-0.439498\pi\) | ||||
0.188930 | + | 0.981991i | \(0.439498\pi\) | |||||||
\(198\) | 11.1676 | 0.793647 | ||||||||
\(199\) | 2.27833 | 0.161506 | 0.0807532 | − | 0.996734i | \(-0.474267\pi\) | ||||
0.0807532 | + | 0.996734i | \(0.474267\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.94072 | −0.136888 | ||||||||
\(202\) | −15.3380 | −1.07918 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 16.9170 | 1.18443 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −8.31489 | −0.579326 | ||||||||
\(207\) | 3.88144 | 0.269779 | ||||||||
\(208\) | −4.95698 | −0.343705 | ||||||||
\(209\) | 31.2273 | 2.16004 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.8052 | −1.01923 | −0.509616 | − | 0.860402i | \(-0.670213\pi\) | ||||
−0.509616 | + | 0.860402i | \(0.670213\pi\) | |||||||
\(212\) | 37.2657 | 2.55942 | ||||||||
\(213\) | −11.8680 | −0.813182 | ||||||||
\(214\) | −7.72057 | −0.527767 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4.73024 | −0.321852 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 24.9430 | 1.68935 | ||||||||
\(219\) | −6.16368 | −0.416503 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.83350 | 0.392404 | ||||||||
\(222\) | 28.6540 | 1.92313 | ||||||||
\(223\) | 6.63479 | 0.444299 | 0.222149 | − | 0.975013i | \(-0.428693\pi\) | ||||
0.222149 | + | 0.975013i | \(0.428693\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.71104 | 0.512930 | ||||||||
\(227\) | −9.03168 | −0.599454 | −0.299727 | − | 0.954025i | \(-0.596896\pi\) | ||||
−0.299727 | + | 0.954025i | \(0.596896\pi\) | |||||||
\(228\) | −26.8578 | −1.77870 | ||||||||
\(229\) | −16.8328 | −1.11234 | −0.556171 | − | 0.831068i | \(-0.687730\pi\) | ||||
−0.556171 | + | 0.831068i | \(0.687730\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 18.9209 | 1.24222 | ||||||||
\(233\) | −18.2929 | −1.19841 | −0.599203 | − | 0.800597i | \(-0.704516\pi\) | ||||
−0.599203 | + | 0.800597i | \(0.704516\pi\) | |||||||
\(234\) | −3.31208 | −0.216517 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.76008 | −0.179666 | ||||||||
\(237\) | 6.16760 | 0.400628 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.6309 | 0.752339 | 0.376170 | − | 0.926551i | \(-0.377241\pi\) | ||||
0.376170 | + | 0.926551i | \(0.377241\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.76961 | 0.113991 | 0.0569953 | − | 0.998374i | \(-0.481848\pi\) | ||||
0.0569953 | + | 0.998374i | \(0.481848\pi\) | |||||||
\(242\) | 24.3572 | 1.56574 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 19.7036 | 1.26139 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 19.9238 | 1.27029 | ||||||||
\(247\) | −9.26137 | −0.589287 | ||||||||
\(248\) | 38.3543 | 2.43550 | ||||||||
\(249\) | −13.0490 | −0.826949 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.7004 | 0.675403 | 0.337702 | − | 0.941253i | \(-0.390351\pi\) | ||||
0.337702 | + | 0.941253i | \(0.390351\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 17.7842 | 1.11808 | ||||||||
\(254\) | −0.0259259 | −0.00162674 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −31.4435 | −1.96522 | ||||||||
\(257\) | 26.1609 | 1.63187 | 0.815935 | − | 0.578143i | \(-0.196223\pi\) | ||||
0.815935 | + | 0.578143i | \(0.196223\pi\) | |||||||
\(258\) | −8.58575 | −0.534526 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.00000 | 0.247594 | ||||||||
\(262\) | −33.5451 | −2.07242 | ||||||||
\(263\) | −13.3803 | −0.825066 | −0.412533 | − | 0.910943i | \(-0.635356\pi\) | ||||
−0.412533 | + | 0.910943i | \(0.635356\pi\) | |||||||
\(264\) | −21.6732 | −1.33389 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.292877 | 0.0179238 | ||||||||
\(268\) | 7.64784 | 0.467166 | ||||||||
\(269\) | 2.87081 | 0.175036 | 0.0875181 | − | 0.996163i | \(-0.472106\pi\) | ||||
0.0875181 | + | 0.996163i | \(0.472106\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −29.3419 | −1.78239 | −0.891197 | − | 0.453616i | \(-0.850134\pi\) | ||||
−0.891197 | + | 0.453616i | \(0.850134\pi\) | |||||||
\(272\) | −15.6597 | −0.949512 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −22.0462 | −1.33186 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −15.2957 | −0.920692 | ||||||||
\(277\) | −19.9830 | −1.20066 | −0.600332 | − | 0.799751i | \(-0.704965\pi\) | ||||
−0.600332 | + | 0.799751i | \(0.704965\pi\) | |||||||
\(278\) | 51.9920 | 3.11827 | ||||||||
\(279\) | 8.10832 | 0.485432 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.12919 | 0.425292 | 0.212646 | − | 0.977129i | \(-0.431792\pi\) | ||||
0.212646 | + | 0.977129i | \(0.431792\pi\) | |||||||
\(282\) | −8.04232 | −0.478913 | ||||||||
\(283\) | 22.8751 | 1.35978 | 0.679892 | − | 0.733312i | \(-0.262027\pi\) | ||||
0.679892 | + | 0.733312i | \(0.262027\pi\) | |||||||
\(284\) | 46.7685 | 2.77520 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −15.1754 | −0.897341 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.569365 | −0.0335501 | ||||||||
\(289\) | 1.42879 | 0.0840468 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.00672 | 0.117636 | ||||||||
\(292\) | 24.2894 | 1.42143 | ||||||||
\(293\) | −3.63088 | −0.212118 | −0.106059 | − | 0.994360i | \(-0.533823\pi\) | ||||
−0.106059 | + | 0.994360i | \(0.533823\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −55.6094 | −3.23223 | ||||||||
\(297\) | −4.58184 | −0.265865 | ||||||||
\(298\) | −38.5230 | −2.23158 | ||||||||
\(299\) | −5.27442 | −0.305027 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 11.8555 | 0.682208 | ||||||||
\(303\) | 6.29288 | 0.361516 | ||||||||
\(304\) | 24.8617 | 1.42591 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −10.4633 | −0.598146 | ||||||||
\(307\) | −6.22687 | −0.355387 | −0.177693 | − | 0.984086i | \(-0.556863\pi\) | ||||
−0.177693 | + | 0.984086i | \(0.556863\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.41143 | 0.194070 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.6309 | 1.22657 | 0.613287 | − | 0.789860i | \(-0.289847\pi\) | ||||
0.613287 | + | 0.789860i | \(0.289847\pi\) | |||||||
\(312\) | 6.42782 | 0.363904 | ||||||||
\(313\) | 23.8962 | 1.35069 | 0.675345 | − | 0.737502i | \(-0.263995\pi\) | ||||
0.675345 | + | 0.737502i | \(0.263995\pi\) | |||||||
\(314\) | −16.0355 | −0.904933 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −24.3048 | −1.36725 | ||||||||
\(317\) | −8.57231 | −0.481469 | −0.240734 | − | 0.970591i | \(-0.577388\pi\) | ||||
−0.240734 | + | 0.970591i | \(0.577388\pi\) | |||||||
\(318\) | −23.0490 | −1.29253 | ||||||||
\(319\) | 18.3274 | 1.02614 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.16760 | 0.176798 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −29.2579 | −1.62795 | ||||||||
\(324\) | 3.94072 | 0.218929 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −27.9401 | −1.54746 | ||||||||
\(327\) | −10.2336 | −0.565919 | ||||||||
\(328\) | −38.6665 | −2.13500 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.5095 | 0.742550 | 0.371275 | − | 0.928523i | \(-0.378921\pi\) | ||||
0.371275 | + | 0.928523i | \(0.378921\pi\) | |||||||
\(332\) | 51.4226 | 2.82218 | ||||||||
\(333\) | −11.7562 | −0.644234 | ||||||||
\(334\) | 50.9823 | 2.78963 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.1016 | −0.604742 | −0.302371 | − | 0.953190i | \(-0.597778\pi\) | ||||
−0.302371 | + | 0.953190i | \(0.597778\pi\) | |||||||
\(338\) | −27.1850 | −1.47867 | ||||||||
\(339\) | −3.16368 | −0.171828 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 37.1510 | 2.01184 | ||||||||
\(342\) | 16.6117 | 0.898257 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 16.6626 | 0.898385 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −27.2099 | −1.46281 | ||||||||
\(347\) | −27.3842 | −1.47006 | −0.735031 | − | 0.678033i | \(-0.762833\pi\) | ||||
−0.735031 | + | 0.678033i | \(0.762833\pi\) | |||||||
\(348\) | −15.7629 | −0.844979 | ||||||||
\(349\) | −6.17823 | −0.330713 | −0.165357 | − | 0.986234i | \(-0.552878\pi\) | ||||
−0.165357 | + | 0.986234i | \(0.552878\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.35888 | 0.0725316 | ||||||||
\(352\) | −2.60874 | −0.139046 | ||||||||
\(353\) | −7.80520 | −0.415429 | −0.207715 | − | 0.978189i | \(-0.566603\pi\) | ||||
−0.207715 | + | 0.978189i | \(0.566603\pi\) | |||||||
\(354\) | 1.70712 | 0.0907326 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.15415 | −0.0611697 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −42.6838 | −2.25591 | ||||||||
\(359\) | 4.11464 | 0.217163 | 0.108581 | − | 0.994088i | \(-0.465369\pi\) | ||||
0.108581 | + | 0.994088i | \(0.465369\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 27.4502 | 1.44475 | ||||||||
\(362\) | −49.3938 | −2.59608 | ||||||||
\(363\) | −9.99328 | −0.524511 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −12.1868 | −0.637014 | ||||||||
\(367\) | −21.8115 | −1.13855 | −0.569276 | − | 0.822146i | \(-0.692777\pi\) | ||||
−0.569276 | + | 0.822146i | \(0.692777\pi\) | |||||||
\(368\) | 14.1589 | 0.738084 | ||||||||
\(369\) | −8.17432 | −0.425538 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −31.9526 | −1.65667 | ||||||||
\(373\) | −2.93791 | −0.152119 | −0.0760596 | − | 0.997103i | \(-0.524234\pi\) | ||||
−0.0760596 | + | 0.997103i | \(0.524234\pi\) | |||||||
\(374\) | −47.9411 | −2.47898 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 15.6079 | 0.804916 | ||||||||
\(377\) | −5.43552 | −0.279943 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.85384 | −0.454791 | −0.227396 | − | 0.973802i | \(-0.573021\pi\) | ||||
−0.227396 | + | 0.973802i | \(0.573021\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.0106369 | 0.000544944 0 | ||||||||
\(382\) | −10.0807 | −0.515774 | ||||||||
\(383\) | −17.6387 | −0.901296 | −0.450648 | − | 0.892702i | \(-0.648807\pi\) | ||||
−0.450648 | + | 0.892702i | \(0.648807\pi\) | |||||||
\(384\) | 20.0259 | 1.02194 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 11.6174 | 0.591312 | ||||||||
\(387\) | 3.52256 | 0.179062 | ||||||||
\(388\) | −7.90794 | −0.401465 | ||||||||
\(389\) | 18.1878 | 0.922157 | 0.461078 | − | 0.887359i | \(-0.347463\pi\) | ||||
0.461078 | + | 0.887359i | \(0.347463\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.6626 | −0.842662 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.7629 | 0.694246 | ||||||||
\(394\) | 12.9266 | 0.651231 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 18.0558 | 0.907336 | ||||||||
\(397\) | −10.5237 | −0.528168 | −0.264084 | − | 0.964500i | \(-0.585070\pi\) | ||||
−0.264084 | + | 0.964500i | \(0.585070\pi\) | |||||||
\(398\) | 5.55310 | 0.278352 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.58857 | 0.179204 | 0.0896022 | − | 0.995978i | \(-0.471440\pi\) | ||||
0.0896022 | + | 0.995978i | \(0.471440\pi\) | |||||||
\(402\) | −4.73024 | −0.235923 | ||||||||
\(403\) | −11.0182 | −0.548857 | ||||||||
\(404\) | −24.7985 | −1.23377 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −53.8649 | −2.66998 | ||||||||
\(408\) | 20.3063 | 1.00531 | ||||||||
\(409\) | 22.5304 | 1.11406 | 0.557028 | − | 0.830494i | \(-0.311942\pi\) | ||||
0.557028 | + | 0.830494i | \(0.311942\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.04513 | 0.446163 | ||||||||
\(412\) | −13.4435 | −0.662314 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 9.46047 | 0.464957 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.773698 | 0.0379337 | ||||||||
\(417\) | −21.3313 | −1.04460 | ||||||||
\(418\) | 76.1121 | 3.72276 | ||||||||
\(419\) | −39.4055 | −1.92508 | −0.962542 | − | 0.271131i | \(-0.912602\pi\) | ||||
−0.962542 | + | 0.271131i | \(0.912602\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.57121 | −0.417735 | −0.208867 | − | 0.977944i | \(-0.566978\pi\) | ||||
−0.208867 | + | 0.977944i | \(0.566978\pi\) | |||||||
\(422\) | −36.0856 | −1.75662 | ||||||||
\(423\) | 3.29960 | 0.160432 | ||||||||
\(424\) | 44.7318 | 2.17237 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −28.9266 | −1.40150 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −12.4826 | −0.603370 | ||||||||
\(429\) | 6.22617 | 0.300602 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.28224 | 0.0617633 | 0.0308817 | − | 0.999523i | \(-0.490168\pi\) | ||||
0.0308817 | + | 0.999523i | \(0.490168\pi\) | |||||||
\(432\) | −3.64784 | −0.175507 | ||||||||
\(433\) | 5.21233 | 0.250488 | 0.125244 | − | 0.992126i | \(-0.460029\pi\) | ||||
0.125244 | + | 0.992126i | \(0.460029\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 40.3278 | 1.93135 | ||||||||
\(437\) | 26.4537 | 1.26545 | ||||||||
\(438\) | −15.0231 | −0.717832 | ||||||||
\(439\) | −19.6281 | −0.936797 | −0.468398 | − | 0.883517i | \(-0.655169\pi\) | ||||
−0.468398 | + | 0.883517i | \(0.655169\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 14.2183 | 0.676298 | ||||||||
\(443\) | 18.0347 | 0.856856 | 0.428428 | − | 0.903576i | \(-0.359068\pi\) | ||||
0.428428 | + | 0.903576i | \(0.359068\pi\) | |||||||
\(444\) | 46.3278 | 2.19862 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 16.1714 | 0.765737 | ||||||||
\(447\) | 15.8052 | 0.747560 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.99719 | −0.330218 | −0.165109 | − | 0.986275i | \(-0.552798\pi\) | ||||
−0.165109 | + | 0.986275i | \(0.552798\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −37.4534 | −1.76361 | ||||||||
\(452\) | 12.4672 | 0.586408 | ||||||||
\(453\) | −4.86408 | −0.228535 | ||||||||
\(454\) | −22.0134 | −1.03314 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −32.2386 | −1.50971 | ||||||||
\(457\) | −37.8408 | −1.77012 | −0.885059 | − | 0.465479i | \(-0.845882\pi\) | ||||
−0.885059 | + | 0.465479i | \(0.845882\pi\) | |||||||
\(458\) | −41.0276 | −1.91709 | ||||||||
\(459\) | 4.29288 | 0.200374 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.0903 | −1.12200 | −0.560998 | − | 0.827817i | \(-0.689582\pi\) | ||||
−0.560998 | + | 0.827817i | \(0.689582\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.1154 | −1.07427 | −0.537133 | − | 0.843498i | \(-0.680493\pi\) | ||||
−0.537133 | + | 0.843498i | \(0.680493\pi\) | |||||||
\(464\) | 14.5914 | 0.677388 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −44.5863 | −2.06542 | ||||||||
\(467\) | 12.5645 | 0.581415 | 0.290707 | − | 0.956812i | \(-0.406109\pi\) | ||||
0.290707 | + | 0.956812i | \(0.406109\pi\) | |||||||
\(468\) | −5.35497 | −0.247533 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.57903 | 0.303146 | ||||||||
\(472\) | −3.31305 | −0.152496 | ||||||||
\(473\) | 16.1398 | 0.742110 | ||||||||
\(474\) | 15.0327 | 0.690472 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.45656 | 0.432986 | ||||||||
\(478\) | 28.3486 | 1.29664 | ||||||||
\(479\) | 2.03081 | 0.0927901 | 0.0463950 | − | 0.998923i | \(-0.485227\pi\) | ||||
0.0463950 | + | 0.998923i | \(0.485227\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.9752 | 0.728407 | ||||||||
\(482\) | 4.31318 | 0.196460 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 39.3807 | 1.79003 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.43736 | −0.110561 | ||||||||
\(487\) | −27.5226 | −1.24717 | −0.623583 | − | 0.781757i | \(-0.714324\pi\) | ||||
−0.623583 | + | 0.781757i | \(0.714324\pi\) | |||||||
\(488\) | 23.6512 | 1.07064 | ||||||||
\(489\) | 11.4633 | 0.518388 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.459373 | 0.0207312 | 0.0103656 | − | 0.999946i | \(-0.496700\pi\) | ||||
0.0103656 | + | 0.999946i | \(0.496700\pi\) | |||||||
\(492\) | 32.2127 | 1.45226 | ||||||||
\(493\) | −17.1715 | −0.773366 | ||||||||
\(494\) | −22.5733 | −1.01562 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 29.5779 | 1.32809 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −31.8052 | −1.42523 | ||||||||
\(499\) | −11.6383 | −0.521002 | −0.260501 | − | 0.965474i | \(-0.583888\pi\) | ||||
−0.260501 | + | 0.965474i | \(0.583888\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.9170 | −0.934504 | ||||||||
\(502\) | 26.0807 | 1.16404 | ||||||||
\(503\) | −32.4254 | −1.44578 | −0.722890 | − | 0.690964i | \(-0.757187\pi\) | ||||
−0.722890 | + | 0.690964i | \(0.757187\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 43.3464 | 1.92698 | ||||||||
\(507\) | 11.1534 | 0.495342 | ||||||||
\(508\) | −0.0419170 | −0.00185977 | ||||||||
\(509\) | −17.0395 | −0.755263 | −0.377631 | − | 0.925956i | \(-0.623261\pi\) | ||||
−0.377631 | + | 0.925956i | \(0.623261\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −36.5873 | −1.61695 | ||||||||
\(513\) | −6.81544 | −0.300909 | ||||||||
\(514\) | 63.7635 | 2.81249 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −13.8814 | −0.611096 | ||||||||
\(517\) | 15.1183 | 0.664900 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.1637 | 0.490031 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.61265 | −0.114462 | −0.0572312 | − | 0.998361i | \(-0.518227\pi\) | ||||
−0.0572312 | + | 0.998361i | \(0.518227\pi\) | |||||||
\(522\) | 9.74944 | 0.426721 | ||||||||
\(523\) | −28.0032 | −1.22449 | −0.612247 | − | 0.790666i | \(-0.709734\pi\) | ||||
−0.612247 | + | 0.790666i | \(0.709734\pi\) | |||||||
\(524\) | −54.2357 | −2.36930 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −32.6127 | −1.42198 | ||||||||
\(527\) | −34.8080 | −1.51626 | ||||||||
\(528\) | −16.7138 | −0.727377 | ||||||||
\(529\) | −7.93440 | −0.344974 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.700398 | −0.0303947 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.1079 | 0.481137 | ||||||||
\(534\) | 0.713847 | 0.0308912 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 9.18007 | 0.396519 | ||||||||
\(537\) | 17.5123 | 0.755713 | ||||||||
\(538\) | 6.99719 | 0.301670 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.45696 | −0.320600 | −0.160300 | − | 0.987068i | \(-0.551246\pi\) | ||||
−0.160300 | + | 0.987068i | \(0.551246\pi\) | |||||||
\(542\) | −71.5168 | −3.07191 | ||||||||
\(543\) | 20.2653 | 0.869666 | ||||||||
\(544\) | 2.44421 | 0.104795 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.7640 | 0.716776 | 0.358388 | − | 0.933573i | \(-0.383326\pi\) | ||||
0.358388 | + | 0.933573i | \(0.383326\pi\) | |||||||
\(548\) | −35.6443 | −1.52265 | ||||||||
\(549\) | 5.00000 | 0.213395 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 27.2618 | 1.16139 | ||||||||
\(552\) | −18.3601 | −0.781460 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −48.7058 | −2.06931 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 84.0606 | 3.56497 | ||||||||
\(557\) | 15.0451 | 0.637483 | 0.318741 | − | 0.947842i | \(-0.396740\pi\) | ||||
0.318741 | + | 0.947842i | \(0.396740\pi\) | |||||||
\(558\) | 19.7629 | 0.836630 | ||||||||
\(559\) | −4.78674 | −0.202458 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 19.6693 | 0.830438 | ||||||||
\(562\) | 17.3764 | 0.732980 | ||||||||
\(563\) | 21.1676 | 0.892108 | 0.446054 | − | 0.895006i | \(-0.352829\pi\) | ||||
0.446054 | + | 0.895006i | \(0.352829\pi\) | |||||||
\(564\) | −13.0028 | −0.547517 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 55.7549 | 2.34355 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 56.1384 | 2.35552 | ||||||||
\(569\) | 44.9767 | 1.88552 | 0.942761 | − | 0.333469i | \(-0.108219\pi\) | ||||
0.942761 | + | 0.333469i | \(0.108219\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 39.2238 | 1.64146 | 0.820732 | − | 0.571314i | \(-0.193566\pi\) | ||||
0.820732 | + | 0.571314i | \(0.193566\pi\) | |||||||
\(572\) | −24.5356 | −1.02589 | ||||||||
\(573\) | 4.13592 | 0.172780 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −8.68344 | −0.361810 | ||||||||
\(577\) | 7.06319 | 0.294044 | 0.147022 | − | 0.989133i | \(-0.453031\pi\) | ||||
0.147022 | + | 0.989133i | \(0.453031\pi\) | |||||||
\(578\) | 3.48249 | 0.144852 | ||||||||
\(579\) | −4.76640 | −0.198085 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 4.89111 | 0.202743 | ||||||||
\(583\) | 43.3285 | 1.79448 | ||||||||
\(584\) | 29.1557 | 1.20647 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.84976 | −0.365580 | ||||||||
\(587\) | −13.7629 | −0.568055 | −0.284028 | − | 0.958816i | \(-0.591671\pi\) | ||||
−0.284028 | + | 0.958816i | \(0.591671\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 55.2618 | 2.27702 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.30351 | −0.218157 | ||||||||
\(592\) | −42.8847 | −1.76255 | ||||||||
\(593\) | −29.6309 | −1.21679 | −0.608397 | − | 0.793633i | \(-0.708187\pi\) | ||||
−0.608397 | + | 0.793633i | \(0.708187\pi\) | |||||||
\(594\) | −11.1676 | −0.458212 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −62.2839 | −2.55125 | ||||||||
\(597\) | −2.27833 | −0.0932458 | ||||||||
\(598\) | −12.8556 | −0.525706 | ||||||||
\(599\) | 33.1810 | 1.35574 | 0.677870 | − | 0.735181i | \(-0.262903\pi\) | ||||
0.677870 | + | 0.735181i | \(0.262903\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27.1161 | −1.10609 | −0.553045 | − | 0.833151i | \(-0.686534\pi\) | ||||
−0.553045 | + | 0.833151i | \(0.686534\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.94072 | 0.0790323 | ||||||||
\(604\) | 19.1680 | 0.779935 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 15.3380 | 0.623064 | ||||||||
\(607\) | −23.5684 | −0.956612 | −0.478306 | − | 0.878193i | \(-0.658749\pi\) | ||||
−0.478306 | + | 0.878193i | \(0.658749\pi\) | |||||||
\(608\) | −3.88047 | −0.157374 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.48376 | −0.181394 | ||||||||
\(612\) | −16.9170 | −0.683831 | ||||||||
\(613\) | −18.5190 | −0.747977 | −0.373989 | − | 0.927433i | \(-0.622010\pi\) | ||||
−0.373989 | + | 0.927433i | \(0.622010\pi\) | |||||||
\(614\) | −15.1771 | −0.612499 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.5653 | 0.988961 | 0.494480 | − | 0.869189i | \(-0.335358\pi\) | ||||
0.494480 | + | 0.869189i | \(0.335358\pi\) | |||||||
\(618\) | 8.31489 | 0.334474 | ||||||||
\(619\) | −21.2720 | −0.854994 | −0.427497 | − | 0.904017i | \(-0.640605\pi\) | ||||
−0.427497 | + | 0.904017i | \(0.640605\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.88144 | −0.155757 | ||||||||
\(622\) | 52.7222 | 2.11397 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.95698 | 0.198438 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 58.2435 | 2.32788 | ||||||||
\(627\) | −31.2273 | −1.24710 | ||||||||
\(628\) | −25.9261 | −1.03457 | ||||||||
\(629\) | 50.4678 | 2.01228 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.3899 | 0.572851 | 0.286426 | − | 0.958102i | \(-0.407533\pi\) | ||||
0.286426 | + | 0.958102i | \(0.407533\pi\) | |||||||
\(632\) | −29.1742 | −1.16049 | ||||||||
\(633\) | 14.8052 | 0.588454 | ||||||||
\(634\) | −20.8938 | −0.829798 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −37.2657 | −1.47768 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 44.6704 | 1.76852 | ||||||||
\(639\) | 11.8680 | 0.469491 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.7155 | −1.09470 | −0.547348 | − | 0.836905i | \(-0.684363\pi\) | ||||
−0.547348 | + | 0.836905i | \(0.684363\pi\) | |||||||
\(642\) | 7.72057 | 0.304707 | ||||||||
\(643\) | 44.6065 | 1.75911 | 0.879554 | − | 0.475799i | \(-0.157841\pi\) | ||||
0.879554 | + | 0.475799i | \(0.157841\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −71.3119 | −2.80573 | ||||||||
\(647\) | −13.2023 | −0.519037 | −0.259518 | − | 0.965738i | \(-0.583564\pi\) | ||||
−0.259518 | + | 0.965738i | \(0.583564\pi\) | |||||||
\(648\) | 4.73024 | 0.185821 | ||||||||
\(649\) | −3.20911 | −0.125969 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −45.1736 | −1.76914 | ||||||||
\(653\) | −12.4114 | −0.485697 | −0.242848 | − | 0.970064i | \(-0.578082\pi\) | ||||
−0.242848 | + | 0.970064i | \(0.578082\pi\) | |||||||
\(654\) | −24.9430 | −0.975347 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −29.8187 | −1.16422 | ||||||||
\(657\) | 6.16368 | 0.240468 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.3391 | 0.714390 | 0.357195 | − | 0.934030i | \(-0.383733\pi\) | ||||
0.357195 | + | 0.934030i | \(0.383733\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 42.9277 | 1.66969 | 0.834846 | − | 0.550483i | \(-0.185556\pi\) | ||||
0.834846 | + | 0.550483i | \(0.185556\pi\) | |||||||
\(662\) | 32.9275 | 1.27977 | ||||||||
\(663\) | −5.83350 | −0.226555 | ||||||||
\(664\) | 61.7250 | 2.39540 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −28.6540 | −1.11032 | ||||||||
\(667\) | 15.5258 | 0.601160 | ||||||||
\(668\) | 82.4282 | 3.18924 | ||||||||
\(669\) | −6.63479 | −0.256516 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 22.9092 | 0.884400 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.9400 | −0.691537 | −0.345768 | − | 0.938320i | \(-0.612382\pi\) | ||||
−0.345768 | + | 0.938320i | \(0.612382\pi\) | |||||||
\(674\) | −27.0586 | −1.04226 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −43.9526 | −1.69049 | ||||||||
\(677\) | −25.7077 | −0.988027 | −0.494013 | − | 0.869454i | \(-0.664471\pi\) | ||||
−0.494013 | + | 0.869454i | \(0.664471\pi\) | |||||||
\(678\) | −7.71104 | −0.296141 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.03168 | 0.346095 | ||||||||
\(682\) | 90.5504 | 3.46735 | ||||||||
\(683\) | 16.3100 | 0.624085 | 0.312043 | − | 0.950068i | \(-0.398987\pi\) | ||||
0.312043 | + | 0.950068i | \(0.398987\pi\) | |||||||
\(684\) | 26.8578 | 1.02693 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.8328 | 0.642211 | ||||||||
\(688\) | 12.8498 | 0.489893 | ||||||||
\(689\) | −12.8503 | −0.489559 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.8890 | −0.642489 | −0.321245 | − | 0.946996i | \(-0.604101\pi\) | ||||
−0.321245 | + | 0.946996i | \(0.604101\pi\) | |||||||
\(692\) | −43.9930 | −1.67236 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −66.7452 | −2.53361 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −18.9209 | −0.717197 | ||||||||
\(697\) | 35.0914 | 1.32918 | ||||||||
\(698\) | −15.0586 | −0.569976 | ||||||||
\(699\) | 18.2929 | 0.691900 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.2329 | 1.17965 | 0.589825 | − | 0.807531i | \(-0.299197\pi\) | ||||
0.589825 | + | 0.807531i | \(0.299197\pi\) | |||||||
\(702\) | 3.31208 | 0.125006 | ||||||||
\(703\) | −80.1234 | −3.02191 | ||||||||
\(704\) | −39.7861 | −1.49950 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −19.0241 | −0.715981 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.76008 | 0.103730 | ||||||||
\(709\) | 16.9064 | 0.634933 | 0.317467 | − | 0.948269i | \(-0.397168\pi\) | ||||
0.317467 | + | 0.948269i | \(0.397168\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.16760 | −0.231303 | ||||||||
\(712\) | −1.38538 | −0.0519193 | ||||||||
\(713\) | 31.4720 | 1.17863 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −69.0112 | −2.57907 | ||||||||
\(717\) | −11.6309 | −0.434363 | ||||||||
\(718\) | 10.0289 | 0.374274 | ||||||||
\(719\) | 12.7638 | 0.476008 | 0.238004 | − | 0.971264i | \(-0.423507\pi\) | ||||
0.238004 | + | 0.971264i | \(0.423507\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 66.9061 | 2.48999 | ||||||||
\(723\) | −1.76961 | −0.0658126 | ||||||||
\(724\) | −79.8598 | −2.96797 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −24.3572 | −0.903981 | ||||||||
\(727\) | 12.5649 | 0.466006 | 0.233003 | − | 0.972476i | \(-0.425145\pi\) | ||||
0.233003 | + | 0.972476i | \(0.425145\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.1219 | −0.559305 | ||||||||
\(732\) | −19.7036 | −0.728266 | ||||||||
\(733\) | 38.5202 | 1.42277 | 0.711387 | − | 0.702800i | \(-0.248067\pi\) | ||||
0.711387 | + | 0.702800i | \(0.248067\pi\) | |||||||
\(734\) | −53.1625 | −1.96227 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.20996 | −0.0814601 | ||||||||
\(737\) | 8.89208 | 0.327544 | ||||||||
\(738\) | −19.9238 | −0.733404 | ||||||||
\(739\) | −4.56729 | −0.168011 | −0.0840053 | − | 0.996465i | \(-0.526771\pi\) | ||||
−0.0840053 | + | 0.996465i | \(0.526771\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.26137 | 0.340225 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36.7043 | 1.34655 | 0.673275 | − | 0.739392i | \(-0.264887\pi\) | ||||
0.673275 | + | 0.739392i | \(0.264887\pi\) | |||||||
\(744\) | −38.3543 | −1.40614 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −7.16074 | −0.262173 | ||||||||
\(747\) | 13.0490 | 0.477439 | ||||||||
\(748\) | −77.5112 | −2.83409 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −54.4092 | −1.98542 | −0.992710 | − | 0.120530i | \(-0.961541\pi\) | ||||
−0.992710 | + | 0.120530i | \(0.961541\pi\) | |||||||
\(752\) | 12.0364 | 0.438924 | ||||||||
\(753\) | −10.7004 | −0.389944 | ||||||||
\(754\) | −13.2483 | −0.482475 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.1704 | −0.478687 | −0.239343 | − | 0.970935i | \(-0.576932\pi\) | ||||
−0.239343 | + | 0.970935i | \(0.576932\pi\) | |||||||
\(758\) | −21.5800 | −0.783821 | ||||||||
\(759\) | −17.7842 | −0.645524 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −48.2724 | −1.74987 | −0.874937 | − | 0.484238i | \(-0.839097\pi\) | ||||
−0.874937 | + | 0.484238i | \(0.839097\pi\) | |||||||
\(762\) | 0.0259259 | 0.000939196 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −16.2985 | −0.589659 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −42.9919 | −1.55336 | ||||||||
\(767\) | 0.951757 | 0.0343660 | ||||||||
\(768\) | 31.4435 | 1.13462 | ||||||||
\(769\) | −19.7846 | −0.713452 | −0.356726 | − | 0.934209i | \(-0.616107\pi\) | ||||
−0.356726 | + | 0.934209i | \(0.616107\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −26.1609 | −0.942161 | ||||||||
\(772\) | 18.7831 | 0.676017 | ||||||||
\(773\) | 15.7707 | 0.567233 | 0.283617 | − | 0.958938i | \(-0.408466\pi\) | ||||
0.283617 | + | 0.958938i | \(0.408466\pi\) | |||||||
\(774\) | 8.58575 | 0.308609 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −9.49228 | −0.340753 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 44.3301 | 1.58931 | ||||||||
\(779\) | −55.7116 | −1.99608 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 54.3773 | 1.94577 | ||||||||
\(782\) | −40.6127 | −1.45231 | ||||||||
\(783\) | −4.00000 | −0.142948 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 33.5451 | 1.19651 | ||||||||
\(787\) | −14.6937 | −0.523773 | −0.261886 | − | 0.965099i | \(-0.584345\pi\) | ||||
−0.261886 | + | 0.965099i | \(0.584345\pi\) | |||||||
\(788\) | 20.8997 | 0.744520 | ||||||||
\(789\) | 13.3803 | 0.476352 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 21.6732 | 0.770124 | ||||||||
\(793\) | −6.79440 | −0.241276 | ||||||||
\(794\) | −25.6500 | −0.910283 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.97826 | 0.318226 | ||||||||
\(797\) | −25.3938 | −0.899493 | −0.449747 | − | 0.893156i | \(-0.648486\pi\) | ||||
−0.449747 | + | 0.893156i | \(0.648486\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.1648 | −0.501114 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.292877 | −0.0103483 | ||||||||
\(802\) | 8.74663 | 0.308854 | ||||||||
\(803\) | 28.2410 | 0.996604 | ||||||||
\(804\) | −7.64784 | −0.269719 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −26.8554 | −0.945941 | ||||||||
\(807\) | −2.87081 | −0.101057 | ||||||||
\(808\) | −29.7668 | −1.04719 | ||||||||
\(809\) | 33.3938 | 1.17406 | 0.587031 | − | 0.809564i | \(-0.300297\pi\) | ||||
0.587031 | + | 0.809564i | \(0.300297\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33.3276 | 1.17029 | 0.585145 | − | 0.810929i | \(-0.301038\pi\) | ||||
0.585145 | + | 0.810929i | \(0.301038\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 29.3419 | 1.02907 | ||||||||
\(814\) | −131.288 | −4.60164 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 15.6597 | 0.548201 | ||||||||
\(817\) | 24.0078 | 0.839927 | ||||||||
\(818\) | 54.9147 | 1.92005 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 52.1538 | 1.82018 | 0.910091 | − | 0.414409i | \(-0.136012\pi\) | ||||
0.910091 | + | 0.414409i | \(0.136012\pi\) | |||||||
\(822\) | 22.0462 | 0.768951 | ||||||||
\(823\) | 17.0345 | 0.593785 | 0.296893 | − | 0.954911i | \(-0.404050\pi\) | ||||
0.296893 | + | 0.954911i | \(0.404050\pi\) | |||||||
\(824\) | −16.1369 | −0.562155 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.2054 | −0.389651 | −0.194826 | − | 0.980838i | \(-0.562414\pi\) | ||||
−0.194826 | + | 0.980838i | \(0.562414\pi\) | |||||||
\(828\) | 15.2957 | 0.531562 | ||||||||
\(829\) | −20.6693 | −0.717874 | −0.358937 | − | 0.933362i | \(-0.616861\pi\) | ||||
−0.358937 | + | 0.933362i | \(0.616861\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19.9830 | 0.693204 | ||||||||
\(832\) | 11.7997 | 0.409083 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −51.9920 | −1.80034 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 123.058 | 4.25605 | ||||||||
\(837\) | −8.10832 | −0.280264 | ||||||||
\(838\) | −96.0454 | −3.31783 | ||||||||
\(839\) | 10.3486 | 0.357275 | 0.178637 | − | 0.983915i | \(-0.442831\pi\) | ||||
0.178637 | + | 0.983915i | \(0.442831\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0000 | −0.448276 | ||||||||
\(842\) | −20.8911 | −0.719955 | ||||||||
\(843\) | −7.12919 | −0.245542 | ||||||||
\(844\) | −58.3432 | −2.00826 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 8.04232 | 0.276501 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 34.4961 | 1.18460 | ||||||||
\(849\) | −22.8751 | −0.785072 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −45.6309 | −1.56421 | ||||||||
\(852\) | −46.7685 | −1.60226 | ||||||||
\(853\) | 50.5890 | 1.73213 | 0.866067 | − | 0.499929i | \(-0.166640\pi\) | ||||
0.866067 | + | 0.499929i | \(0.166640\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −14.9835 | −0.512125 | ||||||||
\(857\) | 35.8814 | 1.22569 | 0.612843 | − | 0.790204i | \(-0.290026\pi\) | ||||
0.612843 | + | 0.790204i | \(0.290026\pi\) | |||||||
\(858\) | 15.1754 | 0.518080 | ||||||||
\(859\) | −43.1850 | −1.47345 | −0.736726 | − | 0.676192i | \(-0.763629\pi\) | ||||
−0.736726 | + | 0.676192i | \(0.763629\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.12528 | 0.106447 | ||||||||
\(863\) | 23.6135 | 0.803814 | 0.401907 | − | 0.915681i | \(-0.368348\pi\) | ||||
0.401907 | + | 0.915681i | \(0.368348\pi\) | |||||||
\(864\) | 0.569365 | 0.0193702 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 12.7043 | 0.431710 | ||||||||
\(867\) | −1.42879 | −0.0485244 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −28.2590 | −0.958619 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.63721 | −0.0893584 | ||||||||
\(872\) | 48.4073 | 1.63928 | ||||||||
\(873\) | −2.00672 | −0.0679173 | ||||||||
\(874\) | 64.4773 | 2.18098 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −24.2894 | −0.820662 | ||||||||
\(877\) | 32.8397 | 1.10892 | 0.554459 | − | 0.832211i | \(-0.312925\pi\) | ||||
0.554459 | + | 0.832211i | \(0.312925\pi\) | |||||||
\(878\) | −47.8407 | −1.61454 | ||||||||
\(879\) | 3.63088 | 0.122467 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.72896 | 0.327777 | 0.163889 | − | 0.986479i | \(-0.447596\pi\) | ||||
0.163889 | + | 0.986479i | \(0.447596\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 54.5366 | 1.83530 | 0.917651 | − | 0.397387i | \(-0.130083\pi\) | ||||
0.917651 | + | 0.397387i | \(0.130083\pi\) | |||||||
\(884\) | 22.9882 | 0.773177 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 43.9571 | 1.47677 | ||||||||
\(887\) | 49.0168 | 1.64582 | 0.822912 | − | 0.568169i | \(-0.192348\pi\) | ||||
0.822912 | + | 0.568169i | \(0.192348\pi\) | |||||||
\(888\) | 55.6094 | 1.86613 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.58184 | 0.153497 | ||||||||
\(892\) | 26.1459 | 0.875429 | ||||||||
\(893\) | 22.4882 | 0.752540 | ||||||||
\(894\) | 38.5230 | 1.28840 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.27442 | 0.176108 | ||||||||
\(898\) | −17.0547 | −0.569121 | ||||||||
\(899\) | 32.4333 | 1.08171 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −40.5959 | −1.35244 | ||||||||
\(902\) | −91.2875 | −3.03954 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14.9650 | 0.497728 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −11.8555 | −0.393873 | ||||||||
\(907\) | 3.23768 | 0.107505 | 0.0537527 | − | 0.998554i | \(-0.482882\pi\) | ||||
0.0537527 | + | 0.998554i | \(0.482882\pi\) | |||||||
\(908\) | −35.5913 | −1.18114 | ||||||||
\(909\) | −6.29288 | −0.208722 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.8758 | 0.592252 | 0.296126 | − | 0.955149i | \(-0.404305\pi\) | ||||
0.296126 | + | 0.955149i | \(0.404305\pi\) | |||||||
\(912\) | −24.8617 | −0.823252 | ||||||||
\(913\) | 59.7886 | 1.97872 | ||||||||
\(914\) | −92.2316 | −3.05075 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −66.3334 | −2.19172 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 10.4633 | 0.345340 | ||||||||
\(919\) | −6.26160 | −0.206551 | −0.103276 | − | 0.994653i | \(-0.532932\pi\) | ||||
−0.103276 | + | 0.994653i | \(0.532932\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.22687 | 0.205182 | ||||||||
\(922\) | −58.7166 | −1.93373 | ||||||||
\(923\) | −16.1272 | −0.530833 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −56.3406 | −1.85147 | ||||||||
\(927\) | −3.41143 | −0.112046 | ||||||||
\(928\) | −2.27746 | −0.0747613 | ||||||||
\(929\) | 9.57512 | 0.314149 | 0.157075 | − | 0.987587i | \(-0.449794\pi\) | ||||
0.157075 | + | 0.987587i | \(0.449794\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −72.0871 | −2.36129 | ||||||||
\(933\) | −21.6309 | −0.708163 | ||||||||
\(934\) | 30.6242 | 1.00205 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.42782 | −0.210100 | ||||||||
\(937\) | −55.8679 | −1.82512 | −0.912562 | − | 0.408939i | \(-0.865899\pi\) | ||||
−0.912562 | + | 0.408939i | \(0.865899\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −23.8962 | −0.779822 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.2830 | −0.889402 | −0.444701 | − | 0.895679i | \(-0.646690\pi\) | ||||
−0.444701 | + | 0.895679i | \(0.646690\pi\) | |||||||
\(942\) | 16.0355 | 0.522464 | ||||||||
\(943\) | −31.7282 | −1.03321 | ||||||||
\(944\) | −2.55494 | −0.0831564 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 39.3386 | 1.27901 | ||||||||
\(947\) | 52.1671 | 1.69520 | 0.847601 | − | 0.530634i | \(-0.178046\pi\) | ||||
0.847601 | + | 0.530634i | \(0.178046\pi\) | |||||||
\(948\) | 24.3048 | 0.789383 | ||||||||
\(949\) | −8.37571 | −0.271887 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.57231 | 0.277976 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −27.4644 | −0.889659 | −0.444829 | − | 0.895615i | \(-0.646736\pi\) | ||||
−0.444829 | + | 0.895615i | \(0.646736\pi\) | |||||||
\(954\) | 23.0490 | 0.746240 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 45.8341 | 1.48238 | ||||||||
\(957\) | −18.3274 | −0.592440 | ||||||||
\(958\) | 4.94981 | 0.159921 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 34.7448 | 1.12080 | ||||||||
\(962\) | 38.9373 | 1.25539 | ||||||||
\(963\) | −3.16760 | −0.102074 | ||||||||
\(964\) | 6.97355 | 0.224603 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −45.8901 | −1.47573 | −0.737864 | − | 0.674950i | \(-0.764165\pi\) | ||||
−0.737864 | + | 0.674950i | \(0.764165\pi\) | |||||||
\(968\) | 47.2706 | 1.51933 | ||||||||
\(969\) | 29.2579 | 0.939898 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −39.0569 | −1.25339 | −0.626697 | − | 0.779263i | \(-0.715594\pi\) | ||||
−0.626697 | + | 0.779263i | \(0.715594\pi\) | |||||||
\(972\) | −3.94072 | −0.126399 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −67.0824 | −2.14946 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 18.2392 | 0.583823 | ||||||||
\(977\) | 9.12137 | 0.291818 | 0.145909 | − | 0.989298i | \(-0.453389\pi\) | ||||
0.145909 | + | 0.989298i | \(0.453389\pi\) | |||||||
\(978\) | 27.9401 | 0.893427 | ||||||||
\(979\) | −1.34192 | −0.0428879 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.2336 | 0.326734 | ||||||||
\(982\) | 1.11966 | 0.0357297 | ||||||||
\(983\) | 45.7038 | 1.45772 | 0.728862 | − | 0.684661i | \(-0.240050\pi\) | ||||
0.728862 | + | 0.684661i | \(0.240050\pi\) | |||||||
\(984\) | 38.6665 | 1.23264 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −41.8531 | −1.33288 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −36.4965 | −1.16111 | ||||||||
\(989\) | 13.6726 | 0.434764 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.7798 | −0.405965 | −0.202983 | − | 0.979182i | \(-0.565064\pi\) | ||||
−0.202983 | + | 0.979182i | \(0.565064\pi\) | |||||||
\(992\) | −4.61659 | −0.146577 | ||||||||
\(993\) | −13.5095 | −0.428711 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −51.4226 | −1.62939 | ||||||||
\(997\) | −4.09136 | −0.129575 | −0.0647873 | − | 0.997899i | \(-0.520637\pi\) | ||||
−0.0647873 | + | 0.997899i | \(0.520637\pi\) | |||||||
\(998\) | −28.3667 | −0.897934 | ||||||||
\(999\) | 11.7562 | 0.371949 |
(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 | 3675.2.a.bq.1.4 | 4 | ||
5.4 | even | 2 | 3675.2.a.bx.1.1 | 4 | |||
7.3 | odd | 6 | 525.2.i.j.226.1 | yes | 8 | ||
7.5 | odd | 6 | 525.2.i.j.151.1 | yes | 8 | ||
7.6 | odd | 2 | 3675.2.a.br.1.4 | 4 | |||
35.3 | even | 12 | 525.2.r.h.499.7 | 16 | |||
35.12 | even | 12 | 525.2.r.h.424.7 | 16 | |||
35.17 | even | 12 | 525.2.r.h.499.2 | 16 | |||
35.19 | odd | 6 | 525.2.i.i.151.4 | ✓ | 8 | ||
35.24 | odd | 6 | 525.2.i.i.226.4 | yes | 8 | ||
35.33 | even | 12 | 525.2.r.h.424.2 | 16 | |||
35.34 | odd | 2 | 3675.2.a.bw.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.2.i.i.151.4 | ✓ | 8 | 35.19 | odd | 6 | ||
525.2.i.i.226.4 | yes | 8 | 35.24 | odd | 6 | ||
525.2.i.j.151.1 | yes | 8 | 7.5 | odd | 6 | ||
525.2.i.j.226.1 | yes | 8 | 7.3 | odd | 6 | ||
525.2.r.h.424.2 | 16 | 35.33 | even | 12 | |||
525.2.r.h.424.7 | 16 | 35.12 | even | 12 | |||
525.2.r.h.499.2 | 16 | 35.17 | even | 12 | |||
525.2.r.h.499.7 | 16 | 35.3 | even | 12 | |||
3675.2.a.bq.1.4 | 4 | 1.1 | even | 1 | trivial | ||
3675.2.a.br.1.4 | 4 | 7.6 | odd | 2 | |||
3675.2.a.bw.1.1 | 4 | 35.34 | odd | 2 | |||
3675.2.a.bx.1.1 | 4 | 5.4 | even | 2 |