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: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.2624.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 3x^{2} + 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.360409\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.36041 | −0.961955 | −0.480977 | − | 0.876733i | \(-0.659718\pi\) | ||||
−0.480977 | + | 0.876733i | \(0.659718\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −0.149286 | −0.0746432 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.36041 | −0.555385 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.92391 | 1.03376 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.625336 | 0.188546 | 0.0942730 | − | 0.995546i | \(-0.469947\pi\) | ||||
0.0942730 | + | 0.995546i | \(0.469947\pi\) | |||||||
\(12\) | −0.149286 | −0.0430953 | ||||||||
\(13\) | 0.211123 | 0.0585550 | 0.0292775 | − | 0.999571i | \(-0.490679\pi\) | ||||
0.0292775 | + | 0.999571i | \(0.490679\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.67914 | −0.919785 | ||||||||
\(17\) | −0.904518 | −0.219378 | −0.109689 | − | 0.993966i | \(-0.534985\pi\) | ||||
−0.109689 | + | 0.993966i | \(0.534985\pi\) | |||||||
\(18\) | −1.36041 | −0.320652 | ||||||||
\(19\) | 0.808269 | 0.185430 | 0.0927148 | − | 0.995693i | \(-0.470446\pi\) | ||||
0.0927148 | + | 0.995693i | \(0.470446\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.850714 | −0.181373 | ||||||||
\(23\) | −5.75234 | −1.19945 | −0.599723 | − | 0.800208i | \(-0.704722\pi\) | ||||
−0.599723 | + | 0.800208i | \(0.704722\pi\) | |||||||
\(24\) | 2.92391 | 0.596840 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.287214 | −0.0563272 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.22248 | 0.598400 | 0.299200 | − | 0.954190i | \(-0.403280\pi\) | ||||
0.299200 | + | 0.954190i | \(0.403280\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.68428 | −1.73935 | −0.869674 | − | 0.493627i | \(-0.835671\pi\) | ||||
−0.869674 | + | 0.493627i | \(0.835671\pi\) | |||||||
\(32\) | −0.842681 | −0.148966 | ||||||||
\(33\) | 0.625336 | 0.108857 | ||||||||
\(34\) | 1.23051 | 0.211031 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.149286 | −0.0248811 | ||||||||
\(37\) | −2.89239 | −0.475506 | −0.237753 | − | 0.971326i | \(-0.576411\pi\) | ||||
−0.237753 | + | 0.971326i | \(0.576411\pi\) | |||||||
\(38\) | −1.09958 | −0.178375 | ||||||||
\(39\) | 0.211123 | 0.0338067 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.8478 | −1.85032 | −0.925159 | − | 0.379579i | \(-0.876069\pi\) | ||||
−0.925159 | + | 0.379579i | \(0.876069\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.94631 | 1.51680 | 0.758399 | − | 0.651791i | \(-0.225982\pi\) | ||||
0.758399 | + | 0.651791i | \(0.225982\pi\) | |||||||
\(44\) | −0.0933543 | −0.0140737 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.82553 | 1.15381 | ||||||||
\(47\) | 1.36663 | 0.199344 | 0.0996718 | − | 0.995020i | \(-0.468221\pi\) | ||||
0.0996718 | + | 0.995020i | \(0.468221\pi\) | |||||||
\(48\) | −3.67914 | −0.531038 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.904518 | −0.126658 | ||||||||
\(52\) | −0.0315178 | −0.00437073 | ||||||||
\(53\) | −2.56864 | −0.352829 | −0.176415 | − | 0.984316i | \(-0.556450\pi\) | ||||
−0.176415 | + | 0.984316i | \(0.556450\pi\) | |||||||
\(54\) | −1.36041 | −0.185128 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.808269 | 0.107058 | ||||||||
\(58\) | −4.38389 | −0.575634 | ||||||||
\(59\) | 7.07833 | 0.921520 | 0.460760 | − | 0.887525i | \(-0.347577\pi\) | ||||
0.460760 | + | 0.887525i | \(0.347577\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.17157 | −0.662152 | −0.331076 | − | 0.943604i | \(-0.607412\pi\) | ||||
−0.331076 | + | 0.943604i | \(0.607412\pi\) | |||||||
\(62\) | 13.1746 | 1.67317 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.50467 | 1.06308 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.850714 | −0.104716 | ||||||||
\(67\) | −14.6956 | −1.79536 | −0.897679 | − | 0.440650i | \(-0.854748\pi\) | ||||
−0.897679 | + | 0.440650i | \(0.854748\pi\) | |||||||
\(68\) | 0.135032 | 0.0163751 | ||||||||
\(69\) | −5.75234 | −0.692500 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.41345 | −0.405102 | −0.202551 | − | 0.979272i | \(-0.564923\pi\) | ||||
−0.202551 | + | 0.979272i | \(0.564923\pi\) | |||||||
\(72\) | 2.92391 | 0.344586 | ||||||||
\(73\) | 10.9148 | 1.27748 | 0.638740 | − | 0.769423i | \(-0.279456\pi\) | ||||
0.638740 | + | 0.769423i | \(0.279456\pi\) | |||||||
\(74\) | 3.93484 | 0.457415 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.120664 | −0.0138411 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.287214 | −0.0325205 | ||||||||
\(79\) | −13.8387 | −1.55698 | −0.778488 | − | 0.627660i | \(-0.784013\pi\) | ||||
−0.778488 | + | 0.627660i | \(0.784013\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 16.1179 | 1.77992 | ||||||||
\(83\) | 10.0620 | 1.10444 | 0.552221 | − | 0.833698i | \(-0.313780\pi\) | ||||
0.552221 | + | 0.833698i | \(0.313780\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −13.5311 | −1.45909 | ||||||||
\(87\) | 3.22248 | 0.345486 | ||||||||
\(88\) | 1.82843 | 0.194911 | ||||||||
\(89\) | −7.02349 | −0.744488 | −0.372244 | − | 0.928135i | \(-0.621412\pi\) | ||||
−0.372244 | + | 0.928135i | \(0.621412\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.858746 | 0.0895304 | ||||||||
\(93\) | −9.68428 | −1.00421 | ||||||||
\(94\) | −1.85918 | −0.191760 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.842681 | −0.0860058 | ||||||||
\(97\) | 10.0114 | 1.01650 | 0.508250 | − | 0.861210i | \(-0.330293\pi\) | ||||
0.508250 | + | 0.861210i | \(0.330293\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.625336 | 0.0628487 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.26706 | −0.424588 | −0.212294 | − | 0.977206i | \(-0.568093\pi\) | ||||
−0.212294 | + | 0.977206i | \(0.568093\pi\) | |||||||
\(102\) | 1.23051 | 0.121839 | ||||||||
\(103\) | −7.63670 | −0.752466 | −0.376233 | − | 0.926525i | \(-0.622781\pi\) | ||||
−0.376233 | + | 0.926525i | \(0.622781\pi\) | |||||||
\(104\) | 0.617304 | 0.0605317 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.49440 | 0.339406 | ||||||||
\(107\) | 16.8790 | 1.63176 | 0.815878 | − | 0.578224i | \(-0.196254\pi\) | ||||
0.815878 | + | 0.578224i | \(0.196254\pi\) | |||||||
\(108\) | −0.149286 | −0.0143651 | ||||||||
\(109\) | −6.33403 | −0.606690 | −0.303345 | − | 0.952881i | \(-0.598103\pi\) | ||||
−0.303345 | + | 0.952881i | \(0.598103\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.89239 | −0.274534 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.2570 | 1.62340 | 0.811701 | − | 0.584073i | \(-0.198542\pi\) | ||||
0.811701 | + | 0.584073i | \(0.198542\pi\) | |||||||
\(114\) | −1.09958 | −0.102985 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.481073 | −0.0446665 | ||||||||
\(117\) | 0.211123 | 0.0195183 | ||||||||
\(118\) | −9.62943 | −0.886461 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6090 | −0.964450 | ||||||||
\(122\) | 7.03546 | 0.636960 | ||||||||
\(123\) | −11.8478 | −1.06828 | ||||||||
\(124\) | 1.44573 | 0.129831 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.0597 | −0.892655 | −0.446327 | − | 0.894870i | \(-0.647268\pi\) | ||||
−0.446327 | + | 0.894870i | \(0.647268\pi\) | |||||||
\(128\) | −9.88447 | −0.873672 | ||||||||
\(129\) | 9.94631 | 0.875724 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.55651 | −0.834956 | −0.417478 | − | 0.908687i | \(-0.637086\pi\) | ||||
−0.417478 | + | 0.908687i | \(0.637086\pi\) | |||||||
\(132\) | −0.0933543 | −0.00812544 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 19.9921 | 1.72705 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.64473 | −0.226784 | ||||||||
\(137\) | 0.180690 | 0.0154374 | 0.00771868 | − | 0.999970i | \(-0.497543\pi\) | ||||
0.00771868 | + | 0.999970i | \(0.497543\pi\) | |||||||
\(138\) | 7.82553 | 0.666154 | ||||||||
\(139\) | −0.933026 | −0.0791382 | −0.0395691 | − | 0.999217i | \(-0.512599\pi\) | ||||
−0.0395691 | + | 0.999217i | \(0.512599\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.36663 | 0.115091 | ||||||||
\(142\) | 4.64368 | 0.389689 | ||||||||
\(143\) | 0.132023 | 0.0110403 | ||||||||
\(144\) | −3.67914 | −0.306595 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −14.8486 | −1.22888 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.431795 | 0.0354933 | ||||||||
\(149\) | −2.31070 | −0.189300 | −0.0946499 | − | 0.995511i | \(-0.530173\pi\) | ||||
−0.0946499 | + | 0.995511i | \(0.530173\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.46589 | 0.688944 | 0.344472 | − | 0.938797i | \(-0.388058\pi\) | ||||
0.344472 | + | 0.938797i | \(0.388058\pi\) | |||||||
\(152\) | 2.36330 | 0.191689 | ||||||||
\(153\) | −0.904518 | −0.0731259 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.0315178 | −0.00252344 | ||||||||
\(157\) | −10.3088 | −0.822736 | −0.411368 | − | 0.911469i | \(-0.634949\pi\) | ||||
−0.411368 | + | 0.911469i | \(0.634949\pi\) | |||||||
\(158\) | 18.8263 | 1.49774 | ||||||||
\(159\) | −2.56864 | −0.203706 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.36041 | −0.106884 | ||||||||
\(163\) | −4.97635 | −0.389778 | −0.194889 | − | 0.980825i | \(-0.562435\pi\) | ||||
−0.194889 | + | 0.980825i | \(0.562435\pi\) | |||||||
\(164\) | 1.76872 | 0.138114 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13.6884 | −1.06242 | ||||||||
\(167\) | 1.61398 | 0.124893 | 0.0624467 | − | 0.998048i | \(-0.480110\pi\) | ||||
0.0624467 | + | 0.998048i | \(0.480110\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9554 | −0.996571 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.808269 | 0.0618098 | ||||||||
\(172\) | −1.48485 | −0.113219 | ||||||||
\(173\) | −21.1978 | −1.61164 | −0.805818 | − | 0.592164i | \(-0.798274\pi\) | ||||
−0.805818 | + | 0.592164i | \(0.798274\pi\) | |||||||
\(174\) | −4.38389 | −0.332342 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.30070 | −0.173422 | ||||||||
\(177\) | 7.07833 | 0.532040 | ||||||||
\(178\) | 9.55482 | 0.716164 | ||||||||
\(179\) | 21.2288 | 1.58672 | 0.793358 | − | 0.608755i | \(-0.208331\pi\) | ||||
0.793358 | + | 0.608755i | \(0.208331\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.3941 | −1.14423 | −0.572116 | − | 0.820173i | \(-0.693877\pi\) | ||||
−0.572116 | + | 0.820173i | \(0.693877\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.17157 | −0.382294 | ||||||||
\(184\) | −16.8193 | −1.23994 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 13.1746 | 0.966007 | ||||||||
\(187\) | −0.565628 | −0.0413628 | ||||||||
\(188\) | −0.204020 | −0.0148797 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.71656 | −0.341279 | −0.170639 | − | 0.985334i | \(-0.554583\pi\) | ||||
−0.170639 | + | 0.985334i | \(0.554583\pi\) | |||||||
\(192\) | 8.50467 | 0.613772 | ||||||||
\(193\) | −4.56169 | −0.328358 | −0.164179 | − | 0.986431i | \(-0.552497\pi\) | ||||
−0.164179 | + | 0.986431i | \(0.552497\pi\) | |||||||
\(194\) | −13.6195 | −0.977826 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.41012 | 0.314208 | 0.157104 | − | 0.987582i | \(-0.449784\pi\) | ||||
0.157104 | + | 0.987582i | \(0.449784\pi\) | |||||||
\(198\) | −0.850714 | −0.0604576 | ||||||||
\(199\) | −22.9690 | −1.62823 | −0.814116 | − | 0.580703i | \(-0.802778\pi\) | ||||
−0.814116 | + | 0.580703i | \(0.802778\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.6956 | −1.03655 | ||||||||
\(202\) | 5.80494 | 0.408434 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.135032 | 0.00945415 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 10.3890 | 0.723838 | ||||||||
\(207\) | −5.75234 | −0.399815 | ||||||||
\(208\) | −0.776751 | −0.0538580 | ||||||||
\(209\) | 0.505440 | 0.0349620 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.5401 | 0.725612 | 0.362806 | − | 0.931865i | \(-0.381819\pi\) | ||||
0.362806 | + | 0.931865i | \(0.381819\pi\) | |||||||
\(212\) | 0.383463 | 0.0263363 | ||||||||
\(213\) | −3.41345 | −0.233886 | ||||||||
\(214\) | −22.9624 | −1.56968 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.92391 | 0.198947 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 8.61687 | 0.583608 | ||||||||
\(219\) | 10.9148 | 0.737553 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.190964 | −0.0128457 | ||||||||
\(222\) | 3.93484 | 0.264089 | ||||||||
\(223\) | −22.6507 | −1.51681 | −0.758403 | − | 0.651786i | \(-0.774020\pi\) | ||||
−0.758403 | + | 0.651786i | \(0.774020\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −23.4766 | −1.56164 | ||||||||
\(227\) | 4.35326 | 0.288936 | 0.144468 | − | 0.989509i | \(-0.453853\pi\) | ||||
0.144468 | + | 0.989509i | \(0.453853\pi\) | |||||||
\(228\) | −0.120664 | −0.00799114 | ||||||||
\(229\) | 19.8813 | 1.31379 | 0.656895 | − | 0.753982i | \(-0.271869\pi\) | ||||
0.656895 | + | 0.753982i | \(0.271869\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.42225 | 0.618601 | ||||||||
\(233\) | −5.87601 | −0.384950 | −0.192475 | − | 0.981302i | \(-0.561651\pi\) | ||||
−0.192475 | + | 0.981302i | \(0.561651\pi\) | |||||||
\(234\) | −0.287214 | −0.0187757 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.05670 | −0.0687853 | ||||||||
\(237\) | −13.8387 | −0.898920 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.7587 | −1.01934 | −0.509672 | − | 0.860369i | \(-0.670233\pi\) | ||||
−0.509672 | + | 0.860369i | \(0.670233\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.9101 | −1.21811 | −0.609053 | − | 0.793130i | \(-0.708450\pi\) | ||||
−0.609053 | + | 0.793130i | \(0.708450\pi\) | |||||||
\(242\) | 14.4325 | 0.927758 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0.772046 | 0.0494252 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 16.1179 | 1.02764 | ||||||||
\(247\) | 0.170644 | 0.0108578 | ||||||||
\(248\) | −28.3160 | −1.79806 | ||||||||
\(249\) | 10.0620 | 0.637650 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.4916 | −1.73526 | −0.867628 | − | 0.497214i | \(-0.834356\pi\) | ||||
−0.867628 | + | 0.497214i | \(0.834356\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.59715 | −0.226151 | ||||||||
\(254\) | 13.6853 | 0.858693 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.56242 | −0.222651 | ||||||||
\(257\) | −20.1411 | −1.25636 | −0.628182 | − | 0.778066i | \(-0.716201\pi\) | ||||
−0.628182 | + | 0.778066i | \(0.716201\pi\) | |||||||
\(258\) | −13.5311 | −0.842407 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.22248 | 0.199467 | ||||||||
\(262\) | 13.0008 | 0.803190 | ||||||||
\(263\) | 22.6641 | 1.39753 | 0.698765 | − | 0.715352i | \(-0.253733\pi\) | ||||
0.698765 | + | 0.715352i | \(0.253733\pi\) | |||||||
\(264\) | 1.82843 | 0.112532 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.02349 | −0.429830 | ||||||||
\(268\) | 2.19386 | 0.134011 | ||||||||
\(269\) | −17.5218 | −1.06832 | −0.534162 | − | 0.845382i | \(-0.679373\pi\) | ||||
−0.534162 | + | 0.845382i | \(0.679373\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.5830 | 0.885855 | 0.442927 | − | 0.896558i | \(-0.353940\pi\) | ||||
0.442927 | + | 0.896558i | \(0.353940\pi\) | |||||||
\(272\) | 3.32785 | 0.201780 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.245812 | −0.0148500 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.858746 | 0.0516904 | ||||||||
\(277\) | 0.176434 | 0.0106009 | 0.00530044 | − | 0.999986i | \(-0.498313\pi\) | ||||
0.00530044 | + | 0.999986i | \(0.498313\pi\) | |||||||
\(278\) | 1.26930 | 0.0761274 | ||||||||
\(279\) | −9.68428 | −0.579783 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.8896 | 1.12686 | 0.563430 | − | 0.826164i | \(-0.309482\pi\) | ||||
0.563430 | + | 0.826164i | \(0.309482\pi\) | |||||||
\(282\) | −1.85918 | −0.110712 | ||||||||
\(283\) | 13.6925 | 0.813933 | 0.406966 | − | 0.913443i | \(-0.366587\pi\) | ||||
0.406966 | + | 0.913443i | \(0.366587\pi\) | |||||||
\(284\) | 0.509581 | 0.0302381 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.179605 | −0.0106203 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.842681 | −0.0496555 | ||||||||
\(289\) | −16.1818 | −0.951873 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.0114 | 0.586876 | ||||||||
\(292\) | −1.62943 | −0.0953552 | ||||||||
\(293\) | 19.8191 | 1.15785 | 0.578924 | − | 0.815382i | \(-0.303473\pi\) | ||||
0.578924 | + | 0.815382i | \(0.303473\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8.45709 | −0.491558 | ||||||||
\(297\) | 0.625336 | 0.0362857 | ||||||||
\(298\) | 3.14350 | 0.182098 | ||||||||
\(299\) | −1.21445 | −0.0702335 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −11.5171 | −0.662733 | ||||||||
\(303\) | −4.26706 | −0.245136 | ||||||||
\(304\) | −2.97373 | −0.170555 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.23051 | 0.0703438 | ||||||||
\(307\) | −2.98941 | −0.170615 | −0.0853073 | − | 0.996355i | \(-0.527187\pi\) | ||||
−0.0853073 | + | 0.996355i | \(0.527187\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.63670 | −0.434436 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.3361 | 1.37997 | 0.689987 | − | 0.723822i | \(-0.257616\pi\) | ||||
0.689987 | + | 0.723822i | \(0.257616\pi\) | |||||||
\(312\) | 0.617304 | 0.0349480 | ||||||||
\(313\) | −3.15141 | −0.178128 | −0.0890642 | − | 0.996026i | \(-0.528388\pi\) | ||||
−0.0890642 | + | 0.996026i | \(0.528388\pi\) | |||||||
\(314\) | 14.0243 | 0.791434 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.06593 | 0.116218 | ||||||||
\(317\) | 26.7944 | 1.50493 | 0.752463 | − | 0.658634i | \(-0.228866\pi\) | ||||
0.752463 | + | 0.658634i | \(0.228866\pi\) | |||||||
\(318\) | 3.49440 | 0.195956 | ||||||||
\(319\) | 2.01514 | 0.112826 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.8790 | 0.942095 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.731093 | −0.0406791 | ||||||||
\(324\) | −0.149286 | −0.00829369 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.76988 | 0.374949 | ||||||||
\(327\) | −6.33403 | −0.350273 | ||||||||
\(328\) | −34.6419 | −1.91278 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.89239 | 0.158980 | 0.0794901 | − | 0.996836i | \(-0.474671\pi\) | ||||
0.0794901 | + | 0.996836i | \(0.474671\pi\) | |||||||
\(332\) | −1.50211 | −0.0824391 | ||||||||
\(333\) | −2.89239 | −0.158502 | ||||||||
\(334\) | −2.19567 | −0.120142 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.8387 | −1.24410 | −0.622052 | − | 0.782976i | \(-0.713701\pi\) | ||||
−0.622052 | + | 0.782976i | \(0.713701\pi\) | |||||||
\(338\) | 17.6247 | 0.958656 | ||||||||
\(339\) | 17.2570 | 0.937272 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.05593 | −0.327947 | ||||||||
\(342\) | −1.09958 | −0.0594583 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 29.0821 | 1.56800 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 28.8376 | 1.55032 | ||||||||
\(347\) | 4.56230 | 0.244917 | 0.122459 | − | 0.992474i | \(-0.460922\pi\) | ||||
0.122459 | + | 0.992474i | \(0.460922\pi\) | |||||||
\(348\) | −0.481073 | −0.0257882 | ||||||||
\(349\) | −21.8680 | −1.17057 | −0.585283 | − | 0.810829i | \(-0.699017\pi\) | ||||
−0.585283 | + | 0.810829i | \(0.699017\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.211123 | 0.0112689 | ||||||||
\(352\) | −0.526959 | −0.0280870 | ||||||||
\(353\) | −29.5424 | −1.57238 | −0.786191 | − | 0.617984i | \(-0.787950\pi\) | ||||
−0.786191 | + | 0.617984i | \(0.787950\pi\) | |||||||
\(354\) | −9.62943 | −0.511798 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.04851 | 0.0555710 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −28.8799 | −1.52635 | ||||||||
\(359\) | 6.34948 | 0.335113 | 0.167556 | − | 0.985862i | \(-0.446412\pi\) | ||||
0.167556 | + | 0.985862i | \(0.446412\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.3467 | −0.965616 | ||||||||
\(362\) | 20.9422 | 1.10070 | ||||||||
\(363\) | −10.6090 | −0.556826 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 7.03546 | 0.367749 | ||||||||
\(367\) | −33.5595 | −1.75179 | −0.875896 | − | 0.482499i | \(-0.839729\pi\) | ||||
−0.875896 | + | 0.482499i | \(0.839729\pi\) | |||||||
\(368\) | 21.1637 | 1.10323 | ||||||||
\(369\) | −11.8478 | −0.616773 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.44573 | 0.0749577 | ||||||||
\(373\) | 19.1845 | 0.993338 | 0.496669 | − | 0.867940i | \(-0.334556\pi\) | ||||
0.496669 | + | 0.867940i | \(0.334556\pi\) | |||||||
\(374\) | 0.769486 | 0.0397892 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.99591 | 0.206073 | ||||||||
\(377\) | 0.680340 | 0.0350393 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.5586 | −1.21012 | −0.605062 | − | 0.796179i | \(-0.706852\pi\) | ||||
−0.605062 | + | 0.796179i | \(0.706852\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.0597 | −0.515374 | ||||||||
\(382\) | 6.41646 | 0.328294 | ||||||||
\(383\) | −0.465123 | −0.0237667 | −0.0118833 | − | 0.999929i | \(-0.503783\pi\) | ||||
−0.0118833 | + | 0.999929i | \(0.503783\pi\) | |||||||
\(384\) | −9.88447 | −0.504415 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.20577 | 0.315865 | ||||||||
\(387\) | 9.94631 | 0.505599 | ||||||||
\(388\) | −1.49456 | −0.0758748 | ||||||||
\(389\) | 32.1506 | 1.63010 | 0.815049 | − | 0.579392i | \(-0.196710\pi\) | ||||
0.815049 | + | 0.579392i | \(0.196710\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.20309 | 0.263132 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.55651 | −0.482062 | ||||||||
\(394\) | −5.99957 | −0.302254 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.0933543 | −0.00469123 | ||||||||
\(397\) | −6.31355 | −0.316868 | −0.158434 | − | 0.987370i | \(-0.550645\pi\) | ||||
−0.158434 | + | 0.987370i | \(0.550645\pi\) | |||||||
\(398\) | 31.2473 | 1.56628 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.0912 | 0.603807 | 0.301904 | − | 0.953338i | \(-0.402378\pi\) | ||||
0.301904 | + | 0.953338i | \(0.402378\pi\) | |||||||
\(402\) | 19.9921 | 0.997114 | ||||||||
\(403\) | −2.04457 | −0.101847 | ||||||||
\(404\) | 0.637013 | 0.0316926 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.80872 | −0.0896548 | ||||||||
\(408\) | −2.64473 | −0.130934 | ||||||||
\(409\) | −24.3839 | −1.20570 | −0.602852 | − | 0.797853i | \(-0.705969\pi\) | ||||
−0.602852 | + | 0.797853i | \(0.705969\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.180690 | 0.00891277 | ||||||||
\(412\) | 1.14006 | 0.0561665 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 7.82553 | 0.384604 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.177909 | −0.00872272 | ||||||||
\(417\) | −0.933026 | −0.0456905 | ||||||||
\(418\) | −0.687605 | −0.0336319 | ||||||||
\(419\) | 12.5084 | 0.611078 | 0.305539 | − | 0.952180i | \(-0.401163\pi\) | ||||
0.305539 | + | 0.952180i | \(0.401163\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.4804 | 1.09563 | 0.547814 | − | 0.836600i | \(-0.315460\pi\) | ||||
0.547814 | + | 0.836600i | \(0.315460\pi\) | |||||||
\(422\) | −14.3389 | −0.698006 | ||||||||
\(423\) | 1.36663 | 0.0664479 | ||||||||
\(424\) | −7.51046 | −0.364740 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.64368 | 0.224987 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2.51981 | −0.121800 | ||||||||
\(429\) | 0.132023 | 0.00637412 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.2433 | −1.31227 | −0.656133 | − | 0.754645i | \(-0.727809\pi\) | ||||
−0.656133 | + | 0.754645i | \(0.727809\pi\) | |||||||
\(432\) | −3.67914 | −0.177013 | ||||||||
\(433\) | −20.2358 | −0.972469 | −0.486234 | − | 0.873828i | \(-0.661630\pi\) | ||||
−0.486234 | + | 0.873828i | \(0.661630\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.945585 | 0.0452853 | ||||||||
\(437\) | −4.64943 | −0.222413 | ||||||||
\(438\) | −14.8486 | −0.709493 | ||||||||
\(439\) | 8.82280 | 0.421089 | 0.210545 | − | 0.977584i | \(-0.432476\pi\) | ||||
0.210545 | + | 0.977584i | \(0.432476\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.259790 | 0.0123569 | ||||||||
\(443\) | 1.34647 | 0.0639729 | 0.0319864 | − | 0.999488i | \(-0.489817\pi\) | ||||
0.0319864 | + | 0.999488i | \(0.489817\pi\) | |||||||
\(444\) | 0.431795 | 0.0204921 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 30.8143 | 1.45910 | ||||||||
\(447\) | −2.31070 | −0.109292 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.3270 | −1.05368 | −0.526838 | − | 0.849966i | \(-0.676623\pi\) | ||||
−0.526838 | + | 0.849966i | \(0.676623\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.40887 | −0.348870 | ||||||||
\(452\) | −2.57624 | −0.121176 | ||||||||
\(453\) | 8.46589 | 0.397762 | ||||||||
\(454\) | −5.92221 | −0.277943 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.36330 | 0.110672 | ||||||||
\(457\) | −1.74933 | −0.0818301 | −0.0409150 | − | 0.999163i | \(-0.513027\pi\) | ||||
−0.0409150 | + | 0.999163i | \(0.513027\pi\) | |||||||
\(458\) | −27.0467 | −1.26381 | ||||||||
\(459\) | −0.904518 | −0.0422193 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.9086 | 0.880659 | 0.440330 | − | 0.897836i | \(-0.354862\pi\) | ||||
0.440330 | + | 0.897836i | \(0.354862\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.9345 | −0.787013 | −0.393507 | − | 0.919322i | \(-0.628738\pi\) | ||||
−0.393507 | + | 0.919322i | \(0.628738\pi\) | |||||||
\(464\) | −11.8560 | −0.550399 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.99378 | 0.370305 | ||||||||
\(467\) | −25.3293 | −1.17210 | −0.586051 | − | 0.810274i | \(-0.699318\pi\) | ||||
−0.586051 | + | 0.810274i | \(0.699318\pi\) | |||||||
\(468\) | −0.0315178 | −0.00145691 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.3088 | −0.475007 | ||||||||
\(472\) | 20.6964 | 0.952629 | ||||||||
\(473\) | 6.21979 | 0.285986 | ||||||||
\(474\) | 18.8263 | 0.864721 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.56864 | −0.117610 | ||||||||
\(478\) | 21.4382 | 0.980563 | ||||||||
\(479\) | −32.6636 | −1.49244 | −0.746220 | − | 0.665700i | \(-0.768133\pi\) | ||||
−0.746220 | + | 0.665700i | \(0.768133\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.610650 | −0.0278432 | ||||||||
\(482\) | 25.7255 | 1.17176 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.58377 | 0.0719897 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.36041 | −0.0617094 | ||||||||
\(487\) | −26.8032 | −1.21457 | −0.607286 | − | 0.794484i | \(-0.707742\pi\) | ||||
−0.607286 | + | 0.794484i | \(0.707742\pi\) | |||||||
\(488\) | −15.1212 | −0.684505 | ||||||||
\(489\) | −4.97635 | −0.225038 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −37.3134 | −1.68393 | −0.841965 | − | 0.539532i | \(-0.818601\pi\) | ||||
−0.841965 | + | 0.539532i | \(0.818601\pi\) | |||||||
\(492\) | 1.76872 | 0.0797400 | ||||||||
\(493\) | −2.91479 | −0.131276 | ||||||||
\(494\) | −0.232146 | −0.0104447 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 35.6298 | 1.59983 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −13.6884 | −0.613391 | ||||||||
\(499\) | 23.3137 | 1.04366 | 0.521832 | − | 0.853048i | \(-0.325249\pi\) | ||||
0.521832 | + | 0.853048i | \(0.325249\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.61398 | 0.0721072 | ||||||||
\(502\) | 37.3999 | 1.66924 | ||||||||
\(503\) | 9.11717 | 0.406515 | 0.203257 | − | 0.979125i | \(-0.434847\pi\) | ||||
0.203257 | + | 0.979125i | \(0.434847\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.89359 | 0.217547 | ||||||||
\(507\) | −12.9554 | −0.575371 | ||||||||
\(508\) | 1.50178 | 0.0666306 | ||||||||
\(509\) | −31.7539 | −1.40747 | −0.703734 | − | 0.710463i | \(-0.748485\pi\) | ||||
−0.703734 | + | 0.710463i | \(0.748485\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 24.6153 | 1.08785 | ||||||||
\(513\) | 0.808269 | 0.0356859 | ||||||||
\(514\) | 27.4001 | 1.20857 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.48485 | −0.0653668 | ||||||||
\(517\) | 0.854604 | 0.0375855 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −21.1978 | −0.930478 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.5457 | 0.724880 | 0.362440 | − | 0.932007i | \(-0.381944\pi\) | ||||
0.362440 | + | 0.932007i | \(0.381944\pi\) | |||||||
\(522\) | −4.38389 | −0.191878 | ||||||||
\(523\) | 17.5844 | 0.768912 | 0.384456 | − | 0.923143i | \(-0.374389\pi\) | ||||
0.384456 | + | 0.923143i | \(0.374389\pi\) | |||||||
\(524\) | 1.42666 | 0.0623238 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −30.8325 | −1.34436 | ||||||||
\(527\) | 8.75960 | 0.381574 | ||||||||
\(528\) | −2.30070 | −0.100125 | ||||||||
\(529\) | 10.0894 | 0.438668 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.07833 | 0.307173 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.50135 | −0.108345 | ||||||||
\(534\) | 9.55482 | 0.413477 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −42.9687 | −1.85597 | ||||||||
\(537\) | 21.2288 | 0.916091 | ||||||||
\(538\) | 23.8369 | 1.02768 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.1733 | 1.12528 | 0.562640 | − | 0.826702i | \(-0.309786\pi\) | ||||
0.562640 | + | 0.826702i | \(0.309786\pi\) | |||||||
\(542\) | −19.8389 | −0.852152 | ||||||||
\(543\) | −15.3941 | −0.660622 | ||||||||
\(544\) | 0.762220 | 0.0326799 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.76114 | 0.160815 | 0.0804073 | − | 0.996762i | \(-0.474378\pi\) | ||||
0.0804073 | + | 0.996762i | \(0.474378\pi\) | |||||||
\(548\) | −0.0269745 | −0.00115229 | ||||||||
\(549\) | −5.17157 | −0.220717 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.60463 | 0.110961 | ||||||||
\(552\) | −16.8193 | −0.715877 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −0.240022 | −0.0101976 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.139288 | 0.00590713 | ||||||||
\(557\) | 37.9105 | 1.60632 | 0.803160 | − | 0.595763i | \(-0.203150\pi\) | ||||
0.803160 | + | 0.595763i | \(0.203150\pi\) | |||||||
\(558\) | 13.1746 | 0.557725 | ||||||||
\(559\) | 2.09989 | 0.0888160 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.565628 | −0.0238808 | ||||||||
\(562\) | −25.6976 | −1.08399 | ||||||||
\(563\) | 9.36362 | 0.394630 | 0.197315 | − | 0.980340i | \(-0.436778\pi\) | ||||
0.197315 | + | 0.980340i | \(0.436778\pi\) | |||||||
\(564\) | −0.204020 | −0.00859077 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −18.6274 | −0.782966 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.98061 | −0.418777 | ||||||||
\(569\) | 22.5319 | 0.944588 | 0.472294 | − | 0.881441i | \(-0.343426\pi\) | ||||
0.472294 | + | 0.881441i | \(0.343426\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.6898 | 0.614751 | 0.307375 | − | 0.951588i | \(-0.400549\pi\) | ||||
0.307375 | + | 0.951588i | \(0.400549\pi\) | |||||||
\(572\) | −0.0197092 | −0.000824084 0 | ||||||||
\(573\) | −4.71656 | −0.197037 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 8.50467 | 0.354361 | ||||||||
\(577\) | −27.7400 | −1.15483 | −0.577417 | − | 0.816450i | \(-0.695939\pi\) | ||||
−0.577417 | + | 0.816450i | \(0.695939\pi\) | |||||||
\(578\) | 22.0139 | 0.915659 | ||||||||
\(579\) | −4.56169 | −0.189577 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −13.6195 | −0.564548 | ||||||||
\(583\) | −1.60626 | −0.0665246 | ||||||||
\(584\) | 31.9139 | 1.32061 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −26.9622 | −1.11380 | ||||||||
\(587\) | −36.8359 | −1.52038 | −0.760191 | − | 0.649700i | \(-0.774894\pi\) | ||||
−0.760191 | + | 0.649700i | \(0.774894\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.82750 | −0.322526 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.41012 | 0.181408 | ||||||||
\(592\) | 10.6415 | 0.437364 | ||||||||
\(593\) | −24.2036 | −0.993924 | −0.496962 | − | 0.867772i | \(-0.665551\pi\) | ||||
−0.496962 | + | 0.867772i | \(0.665551\pi\) | |||||||
\(594\) | −0.850714 | −0.0349052 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.344956 | 0.0141299 | ||||||||
\(597\) | −22.9690 | −0.940060 | ||||||||
\(598\) | 1.65215 | 0.0675614 | ||||||||
\(599\) | 22.0912 | 0.902623 | 0.451312 | − | 0.892366i | \(-0.350956\pi\) | ||||
0.451312 | + | 0.892366i | \(0.350956\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.9672 | 1.22239 | 0.611195 | − | 0.791480i | \(-0.290689\pi\) | ||||
0.611195 | + | 0.791480i | \(0.290689\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −14.6956 | −0.598453 | ||||||||
\(604\) | −1.26384 | −0.0514250 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.80494 | 0.235810 | ||||||||
\(607\) | −20.9665 | −0.851003 | −0.425501 | − | 0.904958i | \(-0.639902\pi\) | ||||
−0.425501 | + | 0.904958i | \(0.639902\pi\) | |||||||
\(608\) | −0.681113 | −0.0276228 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.288527 | 0.0116726 | ||||||||
\(612\) | 0.135032 | 0.00545835 | ||||||||
\(613\) | −31.3288 | −1.26536 | −0.632680 | − | 0.774413i | \(-0.718045\pi\) | ||||
−0.632680 | + | 0.774413i | \(0.718045\pi\) | |||||||
\(614\) | 4.06682 | 0.164123 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.143987 | −0.00579671 | −0.00289835 | − | 0.999996i | \(-0.500923\pi\) | ||||
−0.00289835 | + | 0.999996i | \(0.500923\pi\) | |||||||
\(618\) | 10.3890 | 0.417908 | ||||||||
\(619\) | 4.01011 | 0.161180 | 0.0805900 | − | 0.996747i | \(-0.474320\pi\) | ||||
0.0805900 | + | 0.996747i | \(0.474320\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.75234 | −0.230833 | ||||||||
\(622\) | −33.1071 | −1.32747 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −0.776751 | −0.0310949 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4.28721 | 0.171352 | ||||||||
\(627\) | 0.505440 | 0.0201853 | ||||||||
\(628\) | 1.53897 | 0.0614116 | ||||||||
\(629\) | 2.61622 | 0.104316 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.80843 | 0.231230 | 0.115615 | − | 0.993294i | \(-0.463116\pi\) | ||||
0.115615 | + | 0.993294i | \(0.463116\pi\) | |||||||
\(632\) | −40.4631 | −1.60954 | ||||||||
\(633\) | 10.5401 | 0.418933 | ||||||||
\(634\) | −36.4514 | −1.44767 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.383463 | 0.0152053 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.74141 | −0.108533 | ||||||||
\(639\) | −3.41345 | −0.135034 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.67384 | −0.184606 | −0.0923028 | − | 0.995731i | \(-0.529423\pi\) | ||||
−0.0923028 | + | 0.995731i | \(0.529423\pi\) | |||||||
\(642\) | −22.9624 | −0.906253 | ||||||||
\(643\) | 27.0355 | 1.06617 | 0.533087 | − | 0.846060i | \(-0.321032\pi\) | ||||
0.533087 | + | 0.846060i | \(0.321032\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.994586 | 0.0391315 | ||||||||
\(647\) | −22.9840 | −0.903595 | −0.451797 | − | 0.892121i | \(-0.649217\pi\) | ||||
−0.451797 | + | 0.892121i | \(0.649217\pi\) | |||||||
\(648\) | 2.92391 | 0.114862 | ||||||||
\(649\) | 4.42634 | 0.173749 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.742902 | 0.0290943 | ||||||||
\(653\) | 24.6559 | 0.964861 | 0.482430 | − | 0.875934i | \(-0.339754\pi\) | ||||
0.482430 | + | 0.875934i | \(0.339754\pi\) | |||||||
\(654\) | 8.61687 | 0.336946 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 43.5898 | 1.70190 | ||||||||
\(657\) | 10.9148 | 0.425827 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.7353 | 0.574008 | 0.287004 | − | 0.957929i | \(-0.407341\pi\) | ||||
0.287004 | + | 0.957929i | \(0.407341\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.5233 | −1.14832 | −0.574162 | − | 0.818742i | \(-0.694672\pi\) | ||||
−0.574162 | + | 0.818742i | \(0.694672\pi\) | |||||||
\(662\) | −3.93484 | −0.152932 | ||||||||
\(663\) | −0.190964 | −0.00741644 | ||||||||
\(664\) | 29.4202 | 1.14173 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.93484 | 0.152472 | ||||||||
\(667\) | −18.5368 | −0.717748 | ||||||||
\(668\) | −0.240945 | −0.00932244 | ||||||||
\(669\) | −22.6507 | −0.875728 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.23397 | −0.124846 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33.6065 | 1.29544 | 0.647718 | − | 0.761881i | \(-0.275724\pi\) | ||||
0.647718 | + | 0.761881i | \(0.275724\pi\) | |||||||
\(674\) | 31.0700 | 1.19677 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.93407 | 0.0743873 | ||||||||
\(677\) | −1.19691 | −0.0460010 | −0.0230005 | − | 0.999735i | \(-0.507322\pi\) | ||||
−0.0230005 | + | 0.999735i | \(0.507322\pi\) | |||||||
\(678\) | −23.4766 | −0.901613 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.35326 | 0.166817 | ||||||||
\(682\) | 8.23855 | 0.315470 | ||||||||
\(683\) | −2.10576 | −0.0805745 | −0.0402873 | − | 0.999188i | \(-0.512827\pi\) | ||||
−0.0402873 | + | 0.999188i | \(0.512827\pi\) | |||||||
\(684\) | −0.120664 | −0.00461369 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19.8813 | 0.758517 | ||||||||
\(688\) | −36.5939 | −1.39513 | ||||||||
\(689\) | −0.542298 | −0.0206599 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.3961 | 1.38457 | 0.692287 | − | 0.721622i | \(-0.256603\pi\) | ||||
0.692287 | + | 0.721622i | \(0.256603\pi\) | |||||||
\(692\) | 3.16454 | 0.120298 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.20660 | −0.235599 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 9.42225 | 0.357149 | ||||||||
\(697\) | 10.7166 | 0.405919 | ||||||||
\(698\) | 29.7494 | 1.12603 | ||||||||
\(699\) | −5.87601 | −0.222251 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −44.0551 | −1.66394 | −0.831969 | − | 0.554823i | \(-0.812786\pi\) | ||||
−0.831969 | + | 0.554823i | \(0.812786\pi\) | |||||||
\(702\) | −0.287214 | −0.0108402 | ||||||||
\(703\) | −2.33783 | −0.0881729 | ||||||||
\(704\) | 5.31828 | 0.200440 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 40.1897 | 1.51256 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1.05670 | −0.0397132 | ||||||||
\(709\) | 32.1400 | 1.20704 | 0.603521 | − | 0.797347i | \(-0.293764\pi\) | ||||
0.603521 | + | 0.797347i | \(0.293764\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.8387 | −0.518992 | ||||||||
\(712\) | −20.5360 | −0.769620 | ||||||||
\(713\) | 55.7072 | 2.08625 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.16917 | −0.118438 | ||||||||
\(717\) | −15.7587 | −0.588518 | ||||||||
\(718\) | −8.63789 | −0.322363 | ||||||||
\(719\) | 27.9109 | 1.04090 | 0.520450 | − | 0.853892i | \(-0.325764\pi\) | ||||
0.520450 | + | 0.853892i | \(0.325764\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 24.9590 | 0.928879 | ||||||||
\(723\) | −18.9101 | −0.703274 | ||||||||
\(724\) | 2.29812 | 0.0854091 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 14.4325 | 0.535641 | ||||||||
\(727\) | −44.6347 | −1.65541 | −0.827704 | − | 0.561164i | \(-0.810354\pi\) | ||||
−0.827704 | + | 0.561164i | \(0.810354\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.99661 | −0.332752 | ||||||||
\(732\) | 0.772046 | 0.0285356 | ||||||||
\(733\) | 26.7598 | 0.988397 | 0.494198 | − | 0.869349i | \(-0.335462\pi\) | ||||
0.494198 | + | 0.869349i | \(0.335462\pi\) | |||||||
\(734\) | 45.6547 | 1.68515 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.84739 | 0.178677 | ||||||||
\(737\) | −9.18972 | −0.338508 | ||||||||
\(738\) | 16.1179 | 0.593307 | ||||||||
\(739\) | 31.8841 | 1.17288 | 0.586439 | − | 0.809994i | \(-0.300530\pi\) | ||||
0.586439 | + | 0.809994i | \(0.300530\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.170644 | 0.00626876 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.8572 | 1.27879 | 0.639393 | − | 0.768880i | \(-0.279186\pi\) | ||||
0.639393 | + | 0.768880i | \(0.279186\pi\) | |||||||
\(744\) | −28.3160 | −1.03811 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −26.0988 | −0.955546 | ||||||||
\(747\) | 10.0620 | 0.368148 | ||||||||
\(748\) | 0.0844406 | 0.00308745 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.4385 | 0.380908 | 0.190454 | − | 0.981696i | \(-0.439004\pi\) | ||||
0.190454 | + | 0.981696i | \(0.439004\pi\) | |||||||
\(752\) | −5.02803 | −0.183353 | ||||||||
\(753\) | −27.4916 | −1.00185 | ||||||||
\(754\) | −0.925541 | −0.0337062 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.19096 | 0.261360 | 0.130680 | − | 0.991425i | \(-0.458284\pi\) | ||||
0.130680 | + | 0.991425i | \(0.458284\pi\) | |||||||
\(758\) | 32.0493 | 1.16408 | ||||||||
\(759\) | −3.59715 | −0.130568 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28.5401 | −1.03458 | −0.517289 | − | 0.855811i | \(-0.673059\pi\) | ||||
−0.517289 | + | 0.855811i | \(0.673059\pi\) | |||||||
\(762\) | 13.6853 | 0.495767 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.704119 | 0.0254741 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.632758 | 0.0228625 | ||||||||
\(767\) | 1.49440 | 0.0539596 | ||||||||
\(768\) | −3.56242 | −0.128548 | ||||||||
\(769\) | −18.8426 | −0.679483 | −0.339741 | − | 0.940519i | \(-0.610340\pi\) | ||||
−0.339741 | + | 0.940519i | \(0.610340\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.1411 | −0.725362 | ||||||||
\(772\) | 0.680998 | 0.0245097 | ||||||||
\(773\) | 39.6039 | 1.42445 | 0.712226 | − | 0.701950i | \(-0.247687\pi\) | ||||
0.712226 | + | 0.701950i | \(0.247687\pi\) | |||||||
\(774\) | −13.5311 | −0.486364 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 29.2723 | 1.05081 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −43.7379 | −1.56808 | ||||||||
\(779\) | −9.57622 | −0.343104 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.13455 | −0.0763803 | ||||||||
\(782\) | −7.07833 | −0.253121 | ||||||||
\(783\) | 3.22248 | 0.115162 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 13.0008 | 0.463722 | ||||||||
\(787\) | 37.4046 | 1.33333 | 0.666664 | − | 0.745358i | \(-0.267721\pi\) | ||||
0.666664 | + | 0.745358i | \(0.267721\pi\) | |||||||
\(788\) | −0.658371 | −0.0234535 | ||||||||
\(789\) | 22.6641 | 0.806864 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.82843 | 0.0649703 | ||||||||
\(793\) | −1.09184 | −0.0387723 | ||||||||
\(794\) | 8.58902 | 0.304813 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.42896 | 0.121536 | ||||||||
\(797\) | 21.9848 | 0.778741 | 0.389370 | − | 0.921081i | \(-0.372693\pi\) | ||||
0.389370 | + | 0.921081i | \(0.372693\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.23614 | −0.0437316 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.02349 | −0.248163 | ||||||||
\(802\) | −16.4490 | −0.580835 | ||||||||
\(803\) | 6.82542 | 0.240864 | ||||||||
\(804\) | 2.19386 | 0.0773715 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.78146 | 0.0979726 | ||||||||
\(807\) | −17.5218 | −0.616797 | ||||||||
\(808\) | −12.4765 | −0.438921 | ||||||||
\(809\) | −50.0650 | −1.76019 | −0.880096 | − | 0.474795i | \(-0.842522\pi\) | ||||
−0.880096 | + | 0.474795i | \(0.842522\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.52428 | 0.158869 | 0.0794346 | − | 0.996840i | \(-0.474689\pi\) | ||||
0.0794346 | + | 0.996840i | \(0.474689\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.5830 | 0.511448 | ||||||||
\(814\) | 2.46060 | 0.0862439 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.32785 | 0.116498 | ||||||||
\(817\) | 8.03929 | 0.281259 | ||||||||
\(818\) | 33.1720 | 1.15983 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 41.2809 | 1.44071 | 0.720357 | − | 0.693603i | \(-0.243978\pi\) | ||||
0.720357 | + | 0.693603i | \(0.243978\pi\) | |||||||
\(822\) | −0.245812 | −0.00857368 | ||||||||
\(823\) | −20.1761 | −0.703293 | −0.351647 | − | 0.936133i | \(-0.614378\pi\) | ||||
−0.351647 | + | 0.936133i | \(0.614378\pi\) | |||||||
\(824\) | −22.3290 | −0.777868 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.3883 | 0.500329 | 0.250165 | − | 0.968203i | \(-0.419515\pi\) | ||||
0.250165 | + | 0.968203i | \(0.419515\pi\) | |||||||
\(828\) | 0.858746 | 0.0298435 | ||||||||
\(829\) | 31.6680 | 1.09987 | 0.549937 | − | 0.835206i | \(-0.314652\pi\) | ||||
0.549937 | + | 0.835206i | \(0.314652\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.176434 | 0.00612042 | ||||||||
\(832\) | 1.79553 | 0.0622488 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.26930 | 0.0439522 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.0754553 | −0.00260968 | ||||||||
\(837\) | −9.68428 | −0.334738 | ||||||||
\(838\) | −17.0166 | −0.587829 | ||||||||
\(839\) | 30.8602 | 1.06541 | 0.532706 | − | 0.846301i | \(-0.321175\pi\) | ||||
0.532706 | + | 0.846301i | \(0.321175\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.6156 | −0.641918 | ||||||||
\(842\) | −30.5826 | −1.05395 | ||||||||
\(843\) | 18.8896 | 0.650593 | ||||||||
\(844\) | −1.57350 | −0.0541620 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.85918 | −0.0639199 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 9.45038 | 0.324527 | ||||||||
\(849\) | 13.6925 | 0.469924 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.6380 | 0.570344 | ||||||||
\(852\) | 0.509581 | 0.0174580 | ||||||||
\(853\) | 0.143993 | 0.00493024 | 0.00246512 | − | 0.999997i | \(-0.499215\pi\) | ||||
0.00246512 | + | 0.999997i | \(0.499215\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 49.3527 | 1.68684 | ||||||||
\(857\) | 10.4122 | 0.355674 | 0.177837 | − | 0.984060i | \(-0.443090\pi\) | ||||
0.177837 | + | 0.984060i | \(0.443090\pi\) | |||||||
\(858\) | −0.179605 | −0.00613162 | ||||||||
\(859\) | −8.16201 | −0.278484 | −0.139242 | − | 0.990258i | \(-0.544467\pi\) | ||||
−0.139242 | + | 0.990258i | \(0.544467\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 37.0621 | 1.26234 | ||||||||
\(863\) | 15.8130 | 0.538280 | 0.269140 | − | 0.963101i | \(-0.413261\pi\) | ||||
0.269140 | + | 0.963101i | \(0.413261\pi\) | |||||||
\(864\) | −0.842681 | −0.0286686 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 27.5289 | 0.935471 | ||||||||
\(867\) | −16.1818 | −0.549564 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.65384 | −0.293562 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.10259 | −0.105127 | ||||||||
\(872\) | −18.5201 | −0.627171 | ||||||||
\(873\) | 10.0114 | 0.338833 | ||||||||
\(874\) | 6.32513 | 0.213951 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.62943 | −0.0550534 | ||||||||
\(877\) | −31.3204 | −1.05761 | −0.528807 | − | 0.848742i | \(-0.677360\pi\) | ||||
−0.528807 | + | 0.848742i | \(0.677360\pi\) | |||||||
\(878\) | −12.0026 | −0.405069 | ||||||||
\(879\) | 19.8191 | 0.668483 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37.0691 | −1.24889 | −0.624445 | − | 0.781069i | \(-0.714675\pi\) | ||||
−0.624445 | + | 0.781069i | \(0.714675\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.2030 | 0.814497 | 0.407248 | − | 0.913317i | \(-0.366488\pi\) | ||||
0.407248 | + | 0.913317i | \(0.366488\pi\) | |||||||
\(884\) | 0.0285084 | 0.000958841 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.83175 | −0.0615390 | ||||||||
\(887\) | −15.4029 | −0.517177 | −0.258589 | − | 0.965988i | \(-0.583257\pi\) | ||||
−0.258589 | + | 0.965988i | \(0.583257\pi\) | |||||||
\(888\) | −8.45709 | −0.283801 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.625336 | 0.0209496 | ||||||||
\(892\) | 3.38145 | 0.113219 | ||||||||
\(893\) | 1.10461 | 0.0369642 | ||||||||
\(894\) | 3.14350 | 0.105134 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.21445 | −0.0405493 | ||||||||
\(898\) | 30.3738 | 1.01359 | ||||||||
\(899\) | −31.2074 | −1.04083 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.32338 | 0.0774029 | ||||||||
\(902\) | 10.0791 | 0.335597 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 50.4579 | 1.67821 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −11.5171 | −0.382629 | ||||||||
\(907\) | −3.00848 | −0.0998950 | −0.0499475 | − | 0.998752i | \(-0.515905\pi\) | ||||
−0.0499475 | + | 0.998752i | \(0.515905\pi\) | |||||||
\(908\) | −0.649882 | −0.0215671 | ||||||||
\(909\) | −4.26706 | −0.141529 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.9381 | −0.958763 | −0.479381 | − | 0.877607i | \(-0.659139\pi\) | ||||
−0.479381 | + | 0.877607i | \(0.659139\pi\) | |||||||
\(912\) | −2.97373 | −0.0984702 | ||||||||
\(913\) | 6.29210 | 0.208238 | ||||||||
\(914\) | 2.37980 | 0.0787168 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.96800 | −0.0980656 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.23051 | 0.0406130 | ||||||||
\(919\) | 28.9517 | 0.955029 | 0.477515 | − | 0.878624i | \(-0.341538\pi\) | ||||
0.477515 | + | 0.878624i | \(0.341538\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.98941 | −0.0985043 | ||||||||
\(922\) | −25.7234 | −0.847154 | ||||||||
\(923\) | −0.720657 | −0.0237207 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 23.0379 | 0.757071 | ||||||||
\(927\) | −7.63670 | −0.250822 | ||||||||
\(928\) | −2.71553 | −0.0891415 | ||||||||
\(929\) | 39.5868 | 1.29880 | 0.649400 | − | 0.760447i | \(-0.275020\pi\) | ||||
0.649400 | + | 0.760447i | \(0.275020\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.877208 | 0.0287339 | ||||||||
\(933\) | 24.3361 | 0.796728 | ||||||||
\(934\) | 34.4582 | 1.12751 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.617304 | 0.0201772 | ||||||||
\(937\) | 12.9075 | 0.421671 | 0.210835 | − | 0.977522i | \(-0.432382\pi\) | ||||
0.210835 | + | 0.977522i | \(0.432382\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.15141 | −0.102843 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.14777 | −0.233011 | −0.116505 | − | 0.993190i | \(-0.537169\pi\) | ||||
−0.116505 | + | 0.993190i | \(0.537169\pi\) | |||||||
\(942\) | 14.0243 | 0.456935 | ||||||||
\(943\) | 68.1526 | 2.21936 | ||||||||
\(944\) | −26.0422 | −0.847601 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.46146 | −0.275106 | ||||||||
\(947\) | 8.89123 | 0.288926 | 0.144463 | − | 0.989510i | \(-0.453854\pi\) | ||||
0.144463 | + | 0.989510i | \(0.453854\pi\) | |||||||
\(948\) | 2.06593 | 0.0670983 | ||||||||
\(949\) | 2.30436 | 0.0748028 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 26.7944 | 0.868869 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.47648 | 0.177401 | 0.0887003 | − | 0.996058i | \(-0.471729\pi\) | ||||
0.0887003 | + | 0.996058i | \(0.471729\pi\) | |||||||
\(954\) | 3.49440 | 0.113135 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2.35256 | 0.0760871 | ||||||||
\(957\) | 2.01514 | 0.0651401 | ||||||||
\(958\) | 44.4359 | 1.43566 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 62.7852 | 2.02533 | ||||||||
\(962\) | 0.830734 | 0.0267839 | ||||||||
\(963\) | 16.8790 | 0.543919 | ||||||||
\(964\) | 2.82302 | 0.0909233 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −52.7941 | −1.69774 | −0.848872 | − | 0.528598i | \(-0.822718\pi\) | ||||
−0.848872 | + | 0.528598i | \(0.822718\pi\) | |||||||
\(968\) | −31.0196 | −0.997008 | ||||||||
\(969\) | −0.731093 | −0.0234861 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 47.6330 | 1.52862 | 0.764308 | − | 0.644852i | \(-0.223081\pi\) | ||||
0.764308 | + | 0.644852i | \(0.223081\pi\) | |||||||
\(972\) | −0.149286 | −0.00478836 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 36.4634 | 1.16836 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 19.0269 | 0.609038 | ||||||||
\(977\) | 44.2561 | 1.41588 | 0.707939 | − | 0.706274i | \(-0.249625\pi\) | ||||
0.707939 | + | 0.706274i | \(0.249625\pi\) | |||||||
\(978\) | 6.76988 | 0.216477 | ||||||||
\(979\) | −4.39204 | −0.140370 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.33403 | −0.202230 | ||||||||
\(982\) | 50.7615 | 1.61986 | ||||||||
\(983\) | 13.6315 | 0.434778 | 0.217389 | − | 0.976085i | \(-0.430246\pi\) | ||||
0.217389 | + | 0.976085i | \(0.430246\pi\) | |||||||
\(984\) | −34.6419 | −1.10434 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.96531 | 0.126281 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.0254748 | −0.000810463 0 | ||||||||
\(989\) | −57.2145 | −1.81932 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31.4182 | 0.998033 | 0.499016 | − | 0.866593i | \(-0.333695\pi\) | ||||
0.499016 | + | 0.866593i | \(0.333695\pi\) | |||||||
\(992\) | 8.16076 | 0.259104 | ||||||||
\(993\) | 2.89239 | 0.0917873 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.50211 | −0.0475963 | ||||||||
\(997\) | 45.2107 | 1.43184 | 0.715919 | − | 0.698183i | \(-0.246008\pi\) | ||||
0.715919 | + | 0.698183i | \(0.246008\pi\) | |||||||
\(998\) | −31.7162 | −1.00396 | ||||||||
\(999\) | −2.89239 | −0.0915112 |
(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.bo.1.2 | yes | 4 | |
5.4 | even | 2 | 3675.2.a.by.1.3 | yes | 4 | ||
7.6 | odd | 2 | 3675.2.a.bm.1.2 | ✓ | 4 | ||
35.34 | odd | 2 | 3675.2.a.ca.1.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3675.2.a.bm.1.2 | ✓ | 4 | 7.6 | odd | 2 | ||
3675.2.a.bo.1.2 | yes | 4 | 1.1 | even | 1 | trivial | |
3675.2.a.by.1.3 | yes | 4 | 5.4 | even | 2 | ||
3675.2.a.ca.1.3 | yes | 4 | 35.34 | odd | 2 |