Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2070,2,Mod(829,2070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2070, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2070.829");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2070.d (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(16.5290332184\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 230) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 829.2 | ||
Root | \(0.618034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2070.829 |
Dual form | 2070.2.d.c.829.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(1891\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 2.23607 | 1.00000 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.85410i | 0.700785i | 0.936603 | + | 0.350392i | \(0.113952\pi\) | ||||
−0.936603 | + | 0.350392i | \(0.886048\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 2.23607i | − 0.707107i | ||||||||
\(11\) | 5.61803 | 1.69390 | 0.846950 | − | 0.531672i | \(-0.178436\pi\) | ||||
0.846950 | + | 0.531672i | \(0.178436\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.61803i | 0.726112i | 0.931767 | + | 0.363056i | \(0.118267\pi\) | ||||
−0.931767 | + | 0.363056i | \(0.881733\pi\) | |||||||
\(14\) | 1.85410 | 0.495530 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.854102i | 0.207150i | 0.994622 | + | 0.103575i | \(0.0330282\pi\) | ||||
−0.994622 | + | 0.103575i | \(0.966972\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.145898 | 0.0334713 | 0.0167357 | − | 0.999860i | \(-0.494673\pi\) | ||||
0.0167357 | + | 0.999860i | \(0.494673\pi\) | |||||||
\(20\) | −2.23607 | −0.500000 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − 5.61803i | − 1.19777i | ||||||||
\(23\) | − 1.00000i | − 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000 | 1.00000 | ||||||||
\(26\) | 2.61803 | 0.513439 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 1.85410i | − 0.350392i | ||||||||
\(29\) | −9.70820 | −1.80277 | −0.901384 | − | 0.433020i | \(-0.857448\pi\) | ||||
−0.901384 | + | 0.433020i | \(0.857448\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.14590 | −0.385415 | −0.192707 | − | 0.981256i | \(-0.561727\pi\) | ||||
−0.192707 | + | 0.981256i | \(0.561727\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.854102 | 0.146477 | ||||||||
\(35\) | 4.14590i | 0.700785i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.70820i | 1.59602i | 0.602645 | + | 0.798009i | \(0.294114\pi\) | ||||
−0.602645 | + | 0.798009i | \(0.705886\pi\) | |||||||
\(38\) | − 0.145898i | − 0.0236678i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.23607i | 0.353553i | ||||||||
\(41\) | 5.61803 | 0.877390 | 0.438695 | − | 0.898636i | \(-0.355441\pi\) | ||||
0.438695 | + | 0.898636i | \(0.355441\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.2361i | 1.71348i | 0.515745 | + | 0.856742i | \(0.327515\pi\) | ||||
−0.515745 | + | 0.856742i | \(0.672485\pi\) | |||||||
\(44\) | −5.61803 | −0.846950 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | 1.70820i | 0.249167i | 0.992209 | + | 0.124584i | \(0.0397595\pi\) | ||||
−0.992209 | + | 0.124584i | \(0.960241\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.56231 | 0.508901 | ||||||||
\(50\) | − 5.00000i | − 0.707107i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 2.61803i | − 0.363056i | ||||||||
\(53\) | 2.00000i | 0.274721i | 0.990521 | + | 0.137361i | \(0.0438619\pi\) | ||||
−0.990521 | + | 0.137361i | \(0.956138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 12.5623 | 1.69390 | ||||||||
\(56\) | −1.85410 | −0.247765 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.70820i | 1.27475i | ||||||||
\(59\) | −6.00000 | −0.781133 | −0.390567 | − | 0.920575i | \(-0.627721\pi\) | ||||
−0.390567 | + | 0.920575i | \(0.627721\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.85410 | 0.365430 | 0.182715 | − | 0.983166i | \(-0.441511\pi\) | ||||
0.182715 | + | 0.983166i | \(0.441511\pi\) | |||||||
\(62\) | 2.14590i | 0.272529i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 5.85410i | 0.726112i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 5.23607i | − 0.639688i | −0.947470 | − | 0.319844i | \(-0.896370\pi\) | ||||
0.947470 | − | 0.319844i | \(-0.103630\pi\) | |||||||
\(68\) | − 0.854102i | − 0.103575i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.14590 | 0.495530 | ||||||||
\(71\) | −0.381966 | −0.0453310 | −0.0226655 | − | 0.999743i | \(-0.507215\pi\) | ||||
−0.0226655 | + | 0.999743i | \(0.507215\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 16.4721i | − 1.92792i | −0.266051 | − | 0.963959i | \(-0.585719\pi\) | ||||
0.266051 | − | 0.963959i | \(-0.414281\pi\) | |||||||
\(74\) | 9.70820 | 1.12856 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.145898 | −0.0167357 | ||||||||
\(77\) | 10.4164i | 1.18706i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.70820 | 0.867241 | 0.433620 | − | 0.901096i | \(-0.357236\pi\) | ||||
0.433620 | + | 0.901096i | \(0.357236\pi\) | |||||||
\(80\) | 2.23607 | 0.250000 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 5.61803i | − 0.620408i | ||||||||
\(83\) | − 7.70820i | − 0.846085i | −0.906110 | − | 0.423043i | \(-0.860962\pi\) | ||||
0.906110 | − | 0.423043i | \(-0.139038\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.90983i | 0.207150i | ||||||||
\(86\) | 11.2361 | 1.21162 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.61803i | 0.598884i | ||||||||
\(89\) | 3.70820 | 0.393069 | 0.196534 | − | 0.980497i | \(-0.437031\pi\) | ||||
0.196534 | + | 0.980497i | \(0.437031\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.85410 | −0.508848 | ||||||||
\(92\) | 1.00000i | 0.104257i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.70820 | 0.176188 | ||||||||
\(95\) | 0.326238 | 0.0334713 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 13.0344i | − 1.32345i | −0.749748 | − | 0.661724i | \(-0.769825\pi\) | ||||
0.749748 | − | 0.661724i | \(-0.230175\pi\) | |||||||
\(98\) | − 3.56231i | − 0.359847i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.00000 | −0.500000 | ||||||||
\(101\) | 1.52786 | 0.152028 | 0.0760141 | − | 0.997107i | \(-0.475781\pi\) | ||||
0.0760141 | + | 0.997107i | \(0.475781\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.8541i | 1.06949i | 0.845015 | + | 0.534743i | \(0.179592\pi\) | ||||
−0.845015 | + | 0.534743i | \(0.820408\pi\) | |||||||
\(104\) | −2.61803 | −0.256719 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.00000 | 0.194257 | ||||||||
\(107\) | 11.7082i | 1.13187i | 0.824448 | + | 0.565937i | \(0.191486\pi\) | ||||
−0.824448 | + | 0.565937i | \(0.808514\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.56231 | −0.724338 | −0.362169 | − | 0.932113i | \(-0.617964\pi\) | ||||
−0.362169 | + | 0.932113i | \(0.617964\pi\) | |||||||
\(110\) | − 12.5623i | − 1.19777i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.85410i | 0.175196i | ||||||||
\(113\) | 13.4164i | 1.26211i | 0.775738 | + | 0.631055i | \(0.217378\pi\) | ||||
−0.775738 | + | 0.631055i | \(0.782622\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 2.23607i | − 0.208514i | ||||||||
\(116\) | 9.70820 | 0.901384 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.00000i | 0.552345i | ||||||||
\(119\) | −1.58359 | −0.145168 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.5623 | 1.86930 | ||||||||
\(122\) | − 2.85410i | − 0.258398i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.14590 | 0.192707 | ||||||||
\(125\) | 11.1803 | 1.00000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.70820i | 0.861464i | 0.902480 | + | 0.430732i | \(0.141745\pi\) | ||||
−0.902480 | + | 0.430732i | \(0.858255\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.85410 | 0.513439 | ||||||||
\(131\) | 14.1803 | 1.23894 | 0.619471 | − | 0.785020i | \(-0.287347\pi\) | ||||
0.619471 | + | 0.785020i | \(0.287347\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.270510i | 0.0234562i | ||||||||
\(134\) | −5.23607 | −0.452327 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.854102 | −0.0732386 | ||||||||
\(137\) | − 13.8541i | − 1.18364i | −0.806072 | − | 0.591818i | \(-0.798410\pi\) | ||||
0.806072 | − | 0.591818i | \(-0.201590\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.29180 | −0.364025 | −0.182013 | − | 0.983296i | \(-0.558261\pi\) | ||||
−0.182013 | + | 0.983296i | \(0.558261\pi\) | |||||||
\(140\) | − 4.14590i | − 0.350392i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.381966i | 0.0320539i | ||||||||
\(143\) | 14.7082i | 1.22996i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −21.7082 | −1.80277 | ||||||||
\(146\) | −16.4721 | −1.36324 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − 9.70820i | − 0.798009i | ||||||||
\(149\) | −2.61803 | −0.214478 | −0.107239 | − | 0.994233i | \(-0.534201\pi\) | ||||
−0.107239 | + | 0.994233i | \(0.534201\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.2705 | 1.16132 | 0.580659 | − | 0.814147i | \(-0.302795\pi\) | ||||
0.580659 | + | 0.814147i | \(0.302795\pi\) | |||||||
\(152\) | 0.145898i | 0.0118339i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 10.4164 | 0.839378 | ||||||||
\(155\) | −4.79837 | −0.385415 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 2.29180i | − 0.182905i | −0.995809 | − | 0.0914526i | \(-0.970849\pi\) | ||||
0.995809 | − | 0.0914526i | \(-0.0291510\pi\) | |||||||
\(158\) | − 7.70820i | − 0.613232i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − 2.23607i | − 0.176777i | ||||||||
\(161\) | 1.85410 | 0.146124 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 22.0344i | − 1.72587i | −0.505314 | − | 0.862935i | \(-0.668623\pi\) | ||||
0.505314 | − | 0.862935i | \(-0.331377\pi\) | |||||||
\(164\) | −5.61803 | −0.438695 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.70820 | −0.598273 | ||||||||
\(167\) | − 9.70820i | − 0.751243i | −0.926773 | − | 0.375622i | \(-0.877429\pi\) | ||||
0.926773 | − | 0.375622i | \(-0.122571\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.14590 | 0.472761 | ||||||||
\(170\) | 1.90983 | 0.146477 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 11.2361i | − 0.856742i | ||||||||
\(173\) | − 16.5623i | − 1.25921i | −0.776916 | − | 0.629604i | \(-0.783217\pi\) | ||||
0.776916 | − | 0.629604i | \(-0.216783\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.27051i | 0.700785i | ||||||||
\(176\) | 5.61803 | 0.423475 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 3.70820i | − 0.277942i | ||||||||
\(179\) | 7.52786 | 0.562659 | 0.281329 | − | 0.959611i | \(-0.409225\pi\) | ||||
0.281329 | + | 0.959611i | \(0.409225\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.5623 | 1.15674 | 0.578369 | − | 0.815776i | \(-0.303690\pi\) | ||||
0.578369 | + | 0.815776i | \(0.303690\pi\) | |||||||
\(182\) | 4.85410i | 0.359810i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 21.7082i | 1.59602i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.79837i | 0.350892i | ||||||||
\(188\) | − 1.70820i | − 0.124584i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − 0.326238i | − 0.0236678i | ||||||||
\(191\) | −25.4164 | −1.83907 | −0.919533 | − | 0.393012i | \(-0.871433\pi\) | ||||
−0.919533 | + | 0.393012i | \(0.871433\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 15.7082i | − 1.13070i | −0.824851 | − | 0.565351i | \(-0.808741\pi\) | ||||
0.824851 | − | 0.565351i | \(-0.191259\pi\) | |||||||
\(194\) | −13.0344 | −0.935818 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.56231 | −0.254450 | ||||||||
\(197\) | − 20.5623i | − 1.46500i | −0.680765 | − | 0.732502i | \(-0.738353\pi\) | ||||
0.680765 | − | 0.732502i | \(-0.261647\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.4164 | −0.809288 | −0.404644 | − | 0.914474i | \(-0.632605\pi\) | ||||
−0.404644 | + | 0.914474i | \(0.632605\pi\) | |||||||
\(200\) | 5.00000i | 0.353553i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 1.52786i | − 0.107500i | ||||||||
\(203\) | − 18.0000i | − 1.26335i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.5623 | 0.877390 | ||||||||
\(206\) | 10.8541 | 0.756241 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.61803i | 0.181528i | ||||||||
\(209\) | 0.819660 | 0.0566971 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.70820 | −0.530655 | −0.265327 | − | 0.964158i | \(-0.585480\pi\) | ||||
−0.265327 | + | 0.964158i | \(0.585480\pi\) | |||||||
\(212\) | − 2.00000i | − 0.137361i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 11.7082 | 0.800356 | ||||||||
\(215\) | 25.1246i | 1.71348i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 3.97871i | − 0.270093i | ||||||||
\(218\) | 7.56231i | 0.512184i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −12.5623 | −0.846950 | ||||||||
\(221\) | −2.23607 | −0.150414 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.3607i | 1.49738i | 0.662919 | + | 0.748691i | \(0.269317\pi\) | ||||
−0.662919 | + | 0.748691i | \(0.730683\pi\) | |||||||
\(224\) | 1.85410 | 0.123882 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13.4164 | 0.892446 | ||||||||
\(227\) | 10.2918i | 0.683090i | 0.939865 | + | 0.341545i | \(0.110950\pi\) | ||||
−0.939865 | + | 0.341545i | \(0.889050\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.0000 | 0.660819 | 0.330409 | − | 0.943838i | \(-0.392813\pi\) | ||||
0.330409 | + | 0.943838i | \(0.392813\pi\) | |||||||
\(230\) | −2.23607 | −0.147442 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 9.70820i | − 0.637375i | ||||||||
\(233\) | − 21.1246i | − 1.38392i | −0.721936 | − | 0.691960i | \(-0.756748\pi\) | ||||
0.721936 | − | 0.691960i | \(-0.243252\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.81966i | 0.249167i | ||||||||
\(236\) | 6.00000 | 0.390567 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.58359i | 0.102649i | ||||||||
\(239\) | −10.4721 | −0.677386 | −0.338693 | − | 0.940897i | \(-0.609985\pi\) | ||||
−0.338693 | + | 0.940897i | \(0.609985\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.00000 | −0.128831 | −0.0644157 | − | 0.997923i | \(-0.520518\pi\) | ||||
−0.0644157 | + | 0.997923i | \(0.520518\pi\) | |||||||
\(242\) | − 20.5623i | − 1.32180i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.85410 | −0.182715 | ||||||||
\(245\) | 7.96556 | 0.508901 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.381966i | 0.0243039i | ||||||||
\(248\) | − 2.14590i | − 0.136265i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − 11.1803i | − 0.707107i | ||||||||
\(251\) | 16.7984 | 1.06030 | 0.530152 | − | 0.847903i | \(-0.322135\pi\) | ||||
0.530152 | + | 0.847903i | \(0.322135\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 5.61803i | − 0.353203i | ||||||||
\(254\) | 9.70820 | 0.609147 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − 11.4164i | − 0.712136i | −0.934460 | − | 0.356068i | \(-0.884117\pi\) | ||||
0.934460 | − | 0.356068i | \(-0.115883\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −18.0000 | −1.11847 | ||||||||
\(260\) | − 5.85410i | − 0.363056i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 14.1803i | − 0.876064i | ||||||||
\(263\) | 18.2705i | 1.12661i | 0.826250 | + | 0.563304i | \(0.190470\pi\) | ||||
−0.826250 | + | 0.563304i | \(0.809530\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.47214i | 0.274721i | ||||||||
\(266\) | 0.270510 | 0.0165860 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.23607i | 0.319844i | ||||||||
\(269\) | −1.52786 | −0.0931555 | −0.0465778 | − | 0.998915i | \(-0.514832\pi\) | ||||
−0.0465778 | + | 0.998915i | \(0.514832\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.8541 | 1.57052 | 0.785262 | − | 0.619163i | \(-0.212528\pi\) | ||||
0.785262 | + | 0.619163i | \(0.212528\pi\) | |||||||
\(272\) | 0.854102i | 0.0517875i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −13.8541 | −0.836957 | ||||||||
\(275\) | 28.0902 | 1.69390 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 7.52786i | − 0.452306i | −0.974092 | − | 0.226153i | \(-0.927385\pi\) | ||||
0.974092 | − | 0.226153i | \(-0.0726149\pi\) | |||||||
\(278\) | 4.29180i | 0.257405i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.14590 | −0.247765 | ||||||||
\(281\) | −30.6525 | −1.82857 | −0.914287 | − | 0.405068i | \(-0.867248\pi\) | ||||
−0.914287 | + | 0.405068i | \(0.867248\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.9443i | 1.24501i | 0.782617 | + | 0.622504i | \(0.213885\pi\) | ||||
−0.782617 | + | 0.622504i | \(0.786115\pi\) | |||||||
\(284\) | 0.381966 | 0.0226655 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 14.7082 | 0.869714 | ||||||||
\(287\) | 10.4164i | 0.614861i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.2705 | 0.957089 | ||||||||
\(290\) | 21.7082i | 1.27475i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 16.4721i | 0.963959i | ||||||||
\(293\) | 14.2918i | 0.834936i | 0.908692 | + | 0.417468i | \(0.137082\pi\) | ||||
−0.908692 | + | 0.417468i | \(0.862918\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.4164 | −0.781133 | ||||||||
\(296\) | −9.70820 | −0.564278 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.61803i | 0.151659i | ||||||||
\(299\) | 2.61803 | 0.151405 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.8328 | −1.20078 | ||||||||
\(302\) | − 14.2705i | − 0.821176i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.145898 | 0.00836783 | ||||||||
\(305\) | 6.38197 | 0.365430 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 16.8541i | − 0.961914i | −0.876744 | − | 0.480957i | \(-0.840289\pi\) | ||||
0.876744 | − | 0.480957i | \(-0.159711\pi\) | |||||||
\(308\) | − 10.4164i | − 0.593530i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.79837i | 0.272529i | ||||||||
\(311\) | 22.4721 | 1.27428 | 0.637139 | − | 0.770749i | \(-0.280118\pi\) | ||||
0.637139 | + | 0.770749i | \(0.280118\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.8541i | 1.46136i | 0.682720 | + | 0.730680i | \(0.260797\pi\) | ||||
−0.682720 | + | 0.730680i | \(0.739203\pi\) | |||||||
\(314\) | −2.29180 | −0.129334 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.70820 | −0.433620 | ||||||||
\(317\) | − 7.27051i | − 0.408353i | −0.978934 | − | 0.204176i | \(-0.934548\pi\) | ||||
0.978934 | − | 0.204176i | \(-0.0654516\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −54.5410 | −3.05371 | ||||||||
\(320\) | −2.23607 | −0.125000 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − 1.85410i | − 0.103325i | ||||||||
\(323\) | 0.124612i | 0.00693359i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.0902i | 0.726112i | ||||||||
\(326\) | −22.0344 | −1.22037 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.61803i | 0.310204i | ||||||||
\(329\) | −3.16718 | −0.174613 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.1246 | −1.38097 | −0.690487 | − | 0.723345i | \(-0.742604\pi\) | ||||
−0.690487 | + | 0.723345i | \(0.742604\pi\) | |||||||
\(332\) | 7.70820i | 0.423043i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −9.70820 | −0.531209 | ||||||||
\(335\) | − 11.7082i | − 0.639688i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.38197i | 0.184227i | 0.995748 | + | 0.0921137i | \(0.0293623\pi\) | ||||
−0.995748 | + | 0.0921137i | \(0.970638\pi\) | |||||||
\(338\) | − 6.14590i | − 0.334293i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − 1.90983i | − 0.103575i | ||||||||
\(341\) | −12.0557 | −0.652854 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.5836i | 1.05741i | ||||||||
\(344\) | −11.2361 | −0.605808 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −16.5623 | −0.890395 | ||||||||
\(347\) | 14.5623i | 0.781746i | 0.920445 | + | 0.390873i | \(0.127827\pi\) | ||||
−0.920445 | + | 0.390873i | \(0.872173\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −27.7082 | −1.48319 | −0.741593 | − | 0.670850i | \(-0.765929\pi\) | ||||
−0.741593 | + | 0.670850i | \(0.765929\pi\) | |||||||
\(350\) | 9.27051 | 0.495530 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − 5.61803i | − 0.299442i | ||||||||
\(353\) | − 8.00000i | − 0.425797i | −0.977074 | − | 0.212899i | \(-0.931710\pi\) | ||||
0.977074 | − | 0.212899i | \(-0.0682904\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.854102 | −0.0453310 | ||||||||
\(356\) | −3.70820 | −0.196534 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 7.52786i | − 0.397860i | ||||||||
\(359\) | −13.4164 | −0.708091 | −0.354045 | − | 0.935228i | \(-0.615194\pi\) | ||||
−0.354045 | + | 0.935228i | \(0.615194\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9787 | −0.998880 | ||||||||
\(362\) | − 15.5623i | − 0.817937i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.85410 | 0.254424 | ||||||||
\(365\) | − 36.8328i | − 1.92792i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 12.0000i | − 0.626395i | −0.949688 | − | 0.313197i | \(-0.898600\pi\) | ||||
0.949688 | − | 0.313197i | \(-0.101400\pi\) | |||||||
\(368\) | − 1.00000i | − 0.0521286i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 21.7082 | 1.12856 | ||||||||
\(371\) | −3.70820 | −0.192520 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 20.9443i | − 1.08445i | −0.840232 | − | 0.542227i | \(-0.817581\pi\) | ||||
0.840232 | − | 0.542227i | \(-0.182419\pi\) | |||||||
\(374\) | 4.79837 | 0.248118 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.70820 | −0.0880939 | ||||||||
\(377\) | − 25.4164i | − 1.30901i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.2705 | 1.24669 | 0.623346 | − | 0.781946i | \(-0.285773\pi\) | ||||
0.623346 | + | 0.781946i | \(0.285773\pi\) | |||||||
\(380\) | −0.326238 | −0.0167357 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 25.4164i | 1.30042i | ||||||||
\(383\) | − 0.583592i | − 0.0298202i | −0.999889 | − | 0.0149101i | \(-0.995254\pi\) | ||||
0.999889 | − | 0.0149101i | \(-0.00474620\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 23.2918i | 1.18706i | ||||||||
\(386\) | −15.7082 | −0.799527 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13.0344i | 0.661724i | ||||||||
\(389\) | −21.3262 | −1.08128 | −0.540642 | − | 0.841253i | \(-0.681818\pi\) | ||||
−0.540642 | + | 0.841253i | \(0.681818\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.854102 | 0.0431938 | ||||||||
\(392\) | 3.56231i | 0.179924i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −20.5623 | −1.03591 | ||||||||
\(395\) | 17.2361 | 0.867241 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 15.4377i | − 0.774796i | −0.921913 | − | 0.387398i | \(-0.873374\pi\) | ||||
0.921913 | − | 0.387398i | \(-0.126626\pi\) | |||||||
\(398\) | 11.4164i | 0.572253i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.00000 | 0.250000 | ||||||||
\(401\) | 25.5279 | 1.27480 | 0.637400 | − | 0.770533i | \(-0.280010\pi\) | ||||
0.637400 | + | 0.770533i | \(0.280010\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 5.61803i | − 0.279854i | ||||||||
\(404\) | −1.52786 | −0.0760141 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −18.0000 | −0.893325 | ||||||||
\(407\) | 54.5410i | 2.70350i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.5623 | −0.670613 | −0.335306 | − | 0.942109i | \(-0.608840\pi\) | ||||
−0.335306 | + | 0.942109i | \(0.608840\pi\) | |||||||
\(410\) | − 12.5623i | − 0.620408i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 10.8541i | − 0.534743i | ||||||||
\(413\) | − 11.1246i | − 0.547406i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 17.2361i | − 0.846085i | ||||||||
\(416\) | 2.61803 | 0.128360 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 0.819660i | − 0.0400909i | ||||||||
\(419\) | −29.8885 | −1.46015 | −0.730075 | − | 0.683367i | \(-0.760515\pi\) | ||||
−0.730075 | + | 0.683367i | \(0.760515\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.145898 | 0.00711064 | 0.00355532 | − | 0.999994i | \(-0.498868\pi\) | ||||
0.00355532 | + | 0.999994i | \(0.498868\pi\) | |||||||
\(422\) | 7.70820i | 0.375229i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.00000 | −0.0971286 | ||||||||
\(425\) | 4.27051i | 0.207150i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.29180i | 0.256088i | ||||||||
\(428\) | − 11.7082i | − 0.565937i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 25.1246 | 1.21162 | ||||||||
\(431\) | 11.2361 | 0.541222 | 0.270611 | − | 0.962689i | \(-0.412774\pi\) | ||||
0.270611 | + | 0.962689i | \(0.412774\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 27.3820i | − 1.31589i | −0.753065 | − | 0.657947i | \(-0.771425\pi\) | ||||
0.753065 | − | 0.657947i | \(-0.228575\pi\) | |||||||
\(434\) | −3.97871 | −0.190984 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.56231 | 0.362169 | ||||||||
\(437\) | − 0.145898i | − 0.00697925i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −33.2705 | −1.58791 | −0.793957 | − | 0.607973i | \(-0.791983\pi\) | ||||
−0.793957 | + | 0.607973i | \(0.791983\pi\) | |||||||
\(440\) | 12.5623i | 0.598884i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.23607i | 0.106359i | ||||||||
\(443\) | − 0.145898i | − 0.00693182i | −0.999994 | − | 0.00346591i | \(-0.998897\pi\) | ||||
0.999994 | − | 0.00346591i | \(-0.00110324\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.29180 | 0.393069 | ||||||||
\(446\) | 22.3607 | 1.05881 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 1.85410i | − 0.0875981i | ||||||||
\(449\) | −17.5623 | −0.828816 | −0.414408 | − | 0.910091i | \(-0.636011\pi\) | ||||
−0.414408 | + | 0.910091i | \(0.636011\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 31.5623 | 1.48621 | ||||||||
\(452\) | − 13.4164i | − 0.631055i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 10.2918 | 0.483018 | ||||||||
\(455\) | −10.8541 | −0.508848 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 1.41641i | − 0.0662568i | −0.999451 | − | 0.0331284i | \(-0.989453\pi\) | ||||
0.999451 | − | 0.0331284i | \(-0.0105470\pi\) | |||||||
\(458\) | − 10.0000i | − 0.467269i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.23607i | 0.104257i | ||||||||
\(461\) | −37.3050 | −1.73746 | −0.868732 | − | 0.495282i | \(-0.835065\pi\) | ||||
−0.868732 | + | 0.495282i | \(0.835065\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 15.7082i | − 0.730022i | −0.931003 | − | 0.365011i | \(-0.881065\pi\) | ||||
0.931003 | − | 0.365011i | \(-0.118935\pi\) | |||||||
\(464\) | −9.70820 | −0.450692 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −21.1246 | −0.978579 | ||||||||
\(467\) | 23.1246i | 1.07008i | 0.844827 | + | 0.535040i | \(0.179703\pi\) | ||||
−0.844827 | + | 0.535040i | \(0.820297\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.70820 | 0.448283 | ||||||||
\(470\) | 3.81966 | 0.176188 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 6.00000i | − 0.276172i | ||||||||
\(473\) | 63.1246i | 2.90247i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.729490 | 0.0334713 | ||||||||
\(476\) | 1.58359 | 0.0725838 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 10.4721i | 0.478984i | ||||||||
\(479\) | −28.4721 | −1.30093 | −0.650463 | − | 0.759538i | \(-0.725425\pi\) | ||||
−0.650463 | + | 0.759538i | \(0.725425\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −25.4164 | −1.15889 | ||||||||
\(482\) | 2.00000i | 0.0910975i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −20.5623 | −0.934650 | ||||||||
\(485\) | − 29.1459i | − 1.32345i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.29180i | 0.375737i | 0.982194 | + | 0.187869i | \(0.0601579\pi\) | ||||
−0.982194 | + | 0.187869i | \(0.939842\pi\) | |||||||
\(488\) | 2.85410i | 0.129199i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | − 7.96556i | − 0.359847i | ||||||||
\(491\) | −26.8328 | −1.21095 | −0.605474 | − | 0.795865i | \(-0.707016\pi\) | ||||
−0.605474 | + | 0.795865i | \(0.707016\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 8.29180i | − 0.373444i | ||||||||
\(494\) | 0.381966 | 0.0171855 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.14590 | −0.0963537 | ||||||||
\(497\) | − 0.708204i | − 0.0317673i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.4164 | 0.690133 | 0.345067 | − | 0.938578i | \(-0.387856\pi\) | ||||
0.345067 | + | 0.938578i | \(0.387856\pi\) | |||||||
\(500\) | −11.1803 | −0.500000 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 16.7984i | − 0.749748i | ||||||||
\(503\) | − 10.1459i | − 0.452383i | −0.974083 | − | 0.226192i | \(-0.927372\pi\) | ||||
0.974083 | − | 0.226192i | \(-0.0726276\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.41641 | 0.152028 | ||||||||
\(506\) | −5.61803 | −0.249752 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − 9.70820i | − 0.430732i | ||||||||
\(509\) | 6.65248 | 0.294866 | 0.147433 | − | 0.989072i | \(-0.452899\pi\) | ||||
0.147433 | + | 0.989072i | \(0.452899\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 30.5410 | 1.35106 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −11.4164 | −0.503556 | ||||||||
\(515\) | 24.2705i | 1.06949i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.59675i | 0.422064i | ||||||||
\(518\) | 18.0000i | 0.790875i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.85410 | −0.256719 | ||||||||
\(521\) | 38.0689 | 1.66783 | 0.833914 | − | 0.551894i | \(-0.186095\pi\) | ||||
0.833914 | + | 0.551894i | \(0.186095\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.36068i | 0.190679i | 0.995445 | + | 0.0953396i | \(0.0303937\pi\) | ||||
−0.995445 | + | 0.0953396i | \(0.969606\pi\) | |||||||
\(524\) | −14.1803 | −0.619471 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18.2705 | 0.796632 | ||||||||
\(527\) | − 1.83282i | − 0.0798387i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 4.47214 | 0.194257 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − 0.270510i | − 0.0117281i | ||||||||
\(533\) | 14.7082i | 0.637083i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 26.1803i | 1.13187i | ||||||||
\(536\) | 5.23607 | 0.226164 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.52786i | 0.0658709i | ||||||||
\(539\) | 20.0132 | 0.862028 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.583592 | −0.0250906 | −0.0125453 | − | 0.999921i | \(-0.503993\pi\) | ||||
−0.0125453 | + | 0.999921i | \(0.503993\pi\) | |||||||
\(542\) | − 25.8541i | − 1.11053i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.854102 | 0.0366193 | ||||||||
\(545\) | −16.9098 | −0.724338 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.85410i | 0.335817i | 0.985803 | + | 0.167909i | \(0.0537013\pi\) | ||||
−0.985803 | + | 0.167909i | \(0.946299\pi\) | |||||||
\(548\) | 13.8541i | 0.591818i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | − 28.0902i | − 1.19777i | ||||||||
\(551\) | −1.41641 | −0.0603410 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.2918i | 0.607749i | ||||||||
\(554\) | −7.52786 | −0.319828 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.29180 | 0.182013 | ||||||||
\(557\) | − 30.0000i | − 1.27114i | −0.772043 | − | 0.635570i | \(-0.780765\pi\) | ||||
0.772043 | − | 0.635570i | \(-0.219235\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −29.4164 | −1.24418 | ||||||||
\(560\) | 4.14590i | 0.175196i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 30.6525i | 1.29300i | ||||||||
\(563\) | 15.7082i | 0.662022i | 0.943627 | + | 0.331011i | \(0.107390\pi\) | ||||
−0.943627 | + | 0.331011i | \(0.892610\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 30.0000i | 1.26211i | ||||||||
\(566\) | 20.9443 | 0.880353 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − 0.381966i | − 0.0160269i | ||||||||
\(569\) | −16.3607 | −0.685875 | −0.342938 | − | 0.939358i | \(-0.611422\pi\) | ||||
−0.342938 | + | 0.939358i | \(0.611422\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.27051 | 0.346110 | 0.173055 | − | 0.984912i | \(-0.444636\pi\) | ||||
0.173055 | + | 0.984912i | \(0.444636\pi\) | |||||||
\(572\) | − 14.7082i | − 0.614981i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 10.4164 | 0.434772 | ||||||||
\(575\) | − 5.00000i | − 0.208514i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 39.7082i | 1.65307i | 0.562882 | + | 0.826537i | \(0.309692\pi\) | ||||
−0.562882 | + | 0.826537i | \(0.690308\pi\) | |||||||
\(578\) | − 16.2705i | − 0.676764i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 21.7082 | 0.901384 | ||||||||
\(581\) | 14.2918 | 0.592924 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.2361i | 0.465350i | ||||||||
\(584\) | 16.4721 | 0.681622 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.2918 | 0.590389 | ||||||||
\(587\) | − 8.85410i | − 0.365448i | −0.983164 | − | 0.182724i | \(-0.941509\pi\) | ||||
0.983164 | − | 0.182724i | \(-0.0584915\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.313082 | −0.0129003 | ||||||||
\(590\) | 13.4164i | 0.552345i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9.70820i | 0.399005i | ||||||||
\(593\) | − 6.58359i | − 0.270356i | −0.990821 | − | 0.135178i | \(-0.956839\pi\) | ||||
0.990821 | − | 0.135178i | \(-0.0431606\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.54102 | −0.145168 | ||||||||
\(596\) | 2.61803 | 0.107239 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 2.61803i | − 0.107059i | ||||||||
\(599\) | 23.6180 | 0.965007 | 0.482503 | − | 0.875894i | \(-0.339728\pi\) | ||||
0.482503 | + | 0.875894i | \(0.339728\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.85410 | −0.401957 | −0.200979 | − | 0.979596i | \(-0.564412\pi\) | ||||
−0.200979 | + | 0.979596i | \(0.564412\pi\) | |||||||
\(602\) | 20.8328i | 0.849082i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −14.2705 | −0.580659 | ||||||||
\(605\) | 45.9787 | 1.86930 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 21.0557i | − 0.854626i | −0.904104 | − | 0.427313i | \(-0.859460\pi\) | ||||
0.904104 | − | 0.427313i | \(-0.140540\pi\) | |||||||
\(608\) | − 0.145898i | − 0.00591695i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − 6.38197i | − 0.258398i | ||||||||
\(611\) | −4.47214 | −0.180923 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 0.763932i | − 0.0308549i | −0.999881 | − | 0.0154275i | \(-0.995089\pi\) | ||||
0.999881 | − | 0.0154275i | \(-0.00491091\pi\) | |||||||
\(614\) | −16.8541 | −0.680176 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10.4164 | −0.419689 | ||||||||
\(617\) | − 2.56231i | − 0.103155i | −0.998669 | − | 0.0515773i | \(-0.983575\pi\) | ||||
0.998669 | − | 0.0515773i | \(-0.0164248\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.8541 | 1.11955 | 0.559775 | − | 0.828644i | \(-0.310887\pi\) | ||||
0.559775 | + | 0.828644i | \(0.310887\pi\) | |||||||
\(620\) | 4.79837 | 0.192707 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 22.4721i | − 0.901051i | ||||||||
\(623\) | 6.87539i | 0.275457i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 25.8541 | 1.03334 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.29180i | 0.0914526i | ||||||||
\(629\) | −8.29180 | −0.330616 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.4164 | −0.932192 | −0.466096 | − | 0.884734i | \(-0.654340\pi\) | ||||
−0.466096 | + | 0.884734i | \(0.654340\pi\) | |||||||
\(632\) | 7.70820i | 0.306616i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −7.27051 | −0.288749 | ||||||||
\(635\) | 21.7082i | 0.861464i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.32624i | 0.369519i | ||||||||
\(638\) | 54.5410i | 2.15930i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.23607i | 0.0883883i | ||||||||
\(641\) | 0.652476 | 0.0257712 | 0.0128856 | − | 0.999917i | \(-0.495898\pi\) | ||||
0.0128856 | + | 0.999917i | \(0.495898\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 41.0132i | − 1.61740i | −0.588221 | − | 0.808700i | \(-0.700171\pi\) | ||||
0.588221 | − | 0.808700i | \(-0.299829\pi\) | |||||||
\(644\) | −1.85410 | −0.0730619 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.124612 | 0.00490279 | ||||||||
\(647\) | − 13.7082i | − 0.538925i | −0.963011 | − | 0.269463i | \(-0.913154\pi\) | ||||
0.963011 | − | 0.269463i | \(-0.0868460\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −33.7082 | −1.32316 | ||||||||
\(650\) | 13.0902 | 0.513439 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 22.0344i | 0.862935i | ||||||||
\(653\) | − 34.9787i | − 1.36882i | −0.729096 | − | 0.684411i | \(-0.760059\pi\) | ||||
0.729096 | − | 0.684411i | \(-0.239941\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 31.7082 | 1.23894 | ||||||||
\(656\) | 5.61803 | 0.219347 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.16718i | 0.123470i | ||||||||
\(659\) | −17.8885 | −0.696839 | −0.348419 | − | 0.937339i | \(-0.613281\pi\) | ||||
−0.348419 | + | 0.937339i | \(0.613281\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −39.3951 | −1.53229 | −0.766146 | − | 0.642666i | \(-0.777828\pi\) | ||||
−0.766146 | + | 0.642666i | \(0.777828\pi\) | |||||||
\(662\) | 25.1246i | 0.976496i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7.70820 | 0.299136 | ||||||||
\(665\) | 0.604878i | 0.0234562i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.70820i | 0.375903i | ||||||||
\(668\) | 9.70820i | 0.375622i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −11.7082 | −0.452327 | ||||||||
\(671\) | 16.0344 | 0.619003 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 27.7082i | − 1.06807i | −0.845461 | − | 0.534036i | \(-0.820675\pi\) | ||||
0.845461 | − | 0.534036i | \(-0.179325\pi\) | |||||||
\(674\) | 3.38197 | 0.130268 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.14590 | −0.236381 | ||||||||
\(677\) | 42.0000i | 1.61419i | 0.590421 | + | 0.807096i | \(0.298962\pi\) | ||||
−0.590421 | + | 0.807096i | \(0.701038\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24.1672 | 0.927451 | ||||||||
\(680\) | −1.90983 | −0.0732386 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 12.0557i | 0.461638i | ||||||||
\(683\) | 10.9787i | 0.420089i | 0.977692 | + | 0.210044i | \(0.0673609\pi\) | ||||
−0.977692 | + | 0.210044i | \(0.932639\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 30.9787i | − 1.18364i | ||||||||
\(686\) | 19.5836 | 0.747705 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 11.2361i | 0.428371i | ||||||||
\(689\) | −5.23607 | −0.199478 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.1246 | −0.803618 | −0.401809 | − | 0.915723i | \(-0.631618\pi\) | ||||
−0.401809 | + | 0.915723i | \(0.631618\pi\) | |||||||
\(692\) | 16.5623i | 0.629604i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.5623 | 0.552778 | ||||||||
\(695\) | −9.59675 | −0.364025 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.79837i | 0.181751i | ||||||||
\(698\) | 27.7082i | 1.04877i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | − 9.27051i | − 0.350392i | ||||||||
\(701\) | 27.9230 | 1.05464 | 0.527318 | − | 0.849668i | \(-0.323198\pi\) | ||||
0.527318 | + | 0.849668i | \(0.323198\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.41641i | 0.0534208i | ||||||||
\(704\) | −5.61803 | −0.211738 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.00000 | −0.301084 | ||||||||
\(707\) | 2.83282i | 0.106539i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.56231 | −0.321564 | −0.160782 | − | 0.986990i | \(-0.551402\pi\) | ||||
−0.160782 | + | 0.986990i | \(0.551402\pi\) | |||||||
\(710\) | 0.854102i | 0.0320539i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.70820i | 0.138971i | ||||||||
\(713\) | 2.14590i | 0.0803645i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 32.8885i | 1.22996i | ||||||||
\(716\) | −7.52786 | −0.281329 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 13.4164i | 0.500696i | ||||||||
\(719\) | 23.4508 | 0.874569 | 0.437285 | − | 0.899323i | \(-0.355940\pi\) | ||||
0.437285 | + | 0.899323i | \(0.355940\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.1246 | −0.749480 | ||||||||
\(722\) | 18.9787i | 0.706315i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −15.5623 | −0.578369 | ||||||||
\(725\) | −48.5410 | −1.80277 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 40.7426i | − 1.51106i | −0.655113 | − | 0.755531i | \(-0.727379\pi\) | ||||
0.655113 | − | 0.755531i | \(-0.272621\pi\) | |||||||
\(728\) | − 4.85410i | − 0.179905i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −36.8328 | −1.36324 | ||||||||
\(731\) | −9.59675 | −0.354949 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.111456i | 0.00411673i | 0.999998 | + | 0.00205836i | \(0.000655198\pi\) | ||||
−0.999998 | + | 0.00205836i | \(0.999345\pi\) | |||||||
\(734\) | −12.0000 | −0.442928 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | − 29.4164i | − 1.08357i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −34.5410 | −1.27061 | −0.635306 | − | 0.772261i | \(-0.719126\pi\) | ||||
−0.635306 | + | 0.772261i | \(0.719126\pi\) | |||||||
\(740\) | − 21.7082i | − 0.798009i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.70820i | 0.136132i | ||||||||
\(743\) | − 36.9787i | − 1.35662i | −0.734777 | − | 0.678309i | \(-0.762713\pi\) | ||||
0.734777 | − | 0.678309i | \(-0.237287\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.85410 | −0.214478 | ||||||||
\(746\) | −20.9443 | −0.766824 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 4.79837i | − 0.175446i | ||||||||
\(749\) | −21.7082 | −0.793201 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.875388 | −0.0319434 | −0.0159717 | − | 0.999872i | \(-0.505084\pi\) | ||||
−0.0159717 | + | 0.999872i | \(0.505084\pi\) | |||||||
\(752\) | 1.70820i | 0.0622918i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −25.4164 | −0.925611 | ||||||||
\(755\) | 31.9098 | 1.16132 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 29.0132i | − 1.05450i | −0.849710 | − | 0.527251i | \(-0.823223\pi\) | ||||
0.849710 | − | 0.527251i | \(-0.176777\pi\) | |||||||
\(758\) | − 24.2705i | − 0.881545i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.326238i | 0.0118339i | ||||||||
\(761\) | −26.5066 | −0.960863 | −0.480431 | − | 0.877032i | \(-0.659520\pi\) | ||||
−0.480431 | + | 0.877032i | \(0.659520\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 14.0213i | − 0.507605i | ||||||||
\(764\) | 25.4164 | 0.919533 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.583592 | −0.0210860 | ||||||||
\(767\) | − 15.7082i | − 0.567190i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 47.7082 | 1.72040 | 0.860201 | − | 0.509955i | \(-0.170338\pi\) | ||||
0.860201 | + | 0.509955i | \(0.170338\pi\) | |||||||
\(770\) | 23.2918 | 0.839378 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 15.7082i | 0.565351i | ||||||||
\(773\) | − 14.0000i | − 0.503545i | −0.967786 | − | 0.251773i | \(-0.918987\pi\) | ||||
0.967786 | − | 0.251773i | \(-0.0810135\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.7295 | −0.385415 | ||||||||
\(776\) | 13.0344 | 0.467909 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 21.3262i | 0.764583i | ||||||||
\(779\) | 0.819660 | 0.0293674 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.14590 | −0.0767863 | ||||||||
\(782\) | − 0.854102i | − 0.0305426i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.56231 | 0.127225 | ||||||||
\(785\) | − 5.12461i | − 0.182905i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 4.58359i | − 0.163387i | −0.996657 | − | 0.0816937i | \(-0.973967\pi\) | ||||
0.996657 | − | 0.0816937i | \(-0.0260329\pi\) | |||||||
\(788\) | 20.5623i | 0.732502i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − 17.2361i | − 0.613232i | ||||||||
\(791\) | −24.8754 | −0.884467 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.47214i | 0.265343i | ||||||||
\(794\) | −15.4377 | −0.547863 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.4164 | 0.404644 | ||||||||
\(797\) | 45.4164i | 1.60873i | 0.594134 | + | 0.804366i | \(0.297495\pi\) | ||||
−0.594134 | + | 0.804366i | \(0.702505\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.45898 | −0.0516150 | ||||||||
\(800\) | − 5.00000i | − 0.176777i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − 25.5279i | − 0.901420i | ||||||||
\(803\) | − 92.5410i | − 3.26570i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.14590 | 0.146124 | ||||||||
\(806\) | −5.61803 | −0.197887 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.52786i | 0.0537501i | ||||||||
\(809\) | −42.1591 | −1.48223 | −0.741117 | − | 0.671376i | \(-0.765703\pi\) | ||||
−0.741117 | + | 0.671376i | \(0.765703\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.70820 | 0.200442 | 0.100221 | − | 0.994965i | \(-0.468045\pi\) | ||||
0.100221 | + | 0.994965i | \(0.468045\pi\) | |||||||
\(812\) | 18.0000i | 0.631676i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 54.5410 | 1.91166 | ||||||||
\(815\) | − 49.2705i | − 1.72587i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.63932i | 0.0573526i | ||||||||
\(818\) | 13.5623i | 0.474195i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.5623 | −0.438695 | ||||||||
\(821\) | −14.9443 | −0.521559 | −0.260779 | − | 0.965398i | \(-0.583980\pi\) | ||||
−0.260779 | + | 0.965398i | \(0.583980\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 32.8328i | − 1.14448i | −0.820086 | − | 0.572240i | \(-0.806075\pi\) | ||||
0.820086 | − | 0.572240i | \(-0.193925\pi\) | |||||||
\(824\) | −10.8541 | −0.378121 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −11.1246 | −0.387075 | ||||||||
\(827\) | − 32.2492i | − 1.12142i | −0.828014 | − | 0.560708i | \(-0.810529\pi\) | ||||
0.828014 | − | 0.560708i | \(-0.189471\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.5410 | 1.19966 | 0.599830 | − | 0.800128i | \(-0.295235\pi\) | ||||
0.599830 | + | 0.800128i | \(0.295235\pi\) | |||||||
\(830\) | −17.2361 | −0.598273 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 2.61803i | − 0.0907640i | ||||||||
\(833\) | 3.04257i | 0.105419i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 21.7082i | − 0.751243i | ||||||||
\(836\) | −0.819660 | −0.0283485 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 29.8885i | 1.03248i | ||||||||
\(839\) | −11.2361 | −0.387912 | −0.193956 | − | 0.981010i | \(-0.562132\pi\) | ||||
−0.193956 | + | 0.981010i | \(0.562132\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 65.2492 | 2.24997 | ||||||||
\(842\) | − 0.145898i | − 0.00502798i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7.70820 | 0.265327 | ||||||||
\(845\) | 13.7426 | 0.472761 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 38.1246i | 1.30998i | ||||||||
\(848\) | 2.00000i | 0.0686803i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.27051 | 0.146477 | ||||||||
\(851\) | 9.70820 | 0.332793 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.214782i | 0.00735399i | 0.999993 | + | 0.00367699i | \(0.00117043\pi\) | ||||
−0.999993 | + | 0.00367699i | \(0.998830\pi\) | |||||||
\(854\) | 5.29180 | 0.181082 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −11.7082 | −0.400178 | ||||||||
\(857\) | − 36.0000i | − 1.22974i | −0.788630 | − | 0.614868i | \(-0.789209\pi\) | ||||
0.788630 | − | 0.614868i | \(-0.210791\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.00000 | −0.136478 | −0.0682391 | − | 0.997669i | \(-0.521738\pi\) | ||||
−0.0682391 | + | 0.997669i | \(0.521738\pi\) | |||||||
\(860\) | − 25.1246i | − 0.856742i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − 11.2361i | − 0.382702i | ||||||||
\(863\) | − 24.0000i | − 0.816970i | −0.912765 | − | 0.408485i | \(-0.866057\pi\) | ||||
0.912765 | − | 0.408485i | \(-0.133943\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − 37.0344i | − 1.25921i | ||||||||
\(866\) | −27.3820 | −0.930477 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.97871i | 0.135046i | ||||||||
\(869\) | 43.3050 | 1.46902 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.7082 | 0.464485 | ||||||||
\(872\) | − 7.56231i | − 0.256092i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.145898 | −0.00493507 | ||||||||
\(875\) | 20.7295i | 0.700785i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 25.6869i | − 0.867386i | −0.901061 | − | 0.433693i | \(-0.857210\pi\) | ||||
0.901061 | − | 0.433693i | \(-0.142790\pi\) | |||||||
\(878\) | 33.2705i | 1.12283i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 12.5623 | 0.423475 | ||||||||
\(881\) | 51.7082 | 1.74209 | 0.871047 | − | 0.491200i | \(-0.163442\pi\) | ||||
0.871047 | + | 0.491200i | \(0.163442\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 51.2705i | − 1.72539i | −0.505725 | − | 0.862695i | \(-0.668775\pi\) | ||||
0.505725 | − | 0.862695i | \(-0.331225\pi\) | |||||||
\(884\) | 2.23607 | 0.0752071 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.145898 | −0.00490154 | ||||||||
\(887\) | 30.5410i | 1.02547i | 0.858548 | + | 0.512734i | \(0.171367\pi\) | ||||
−0.858548 | + | 0.512734i | \(0.828633\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.0000 | −0.603701 | ||||||||
\(890\) | − 8.29180i | − 0.277942i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 22.3607i | − 0.748691i | ||||||||
\(893\) | 0.249224i | 0.00833995i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.8328 | 0.562659 | ||||||||
\(896\) | −1.85410 | −0.0619412 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 17.5623i | 0.586062i | ||||||||
\(899\) | 20.8328 | 0.694813 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.70820 | −0.0569085 | ||||||||
\(902\) | − 31.5623i | − 1.05091i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13.4164 | −0.446223 | ||||||||
\(905\) | 34.7984 | 1.15674 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36.5410i | 1.21332i | 0.794960 | + | 0.606662i | \(0.207492\pi\) | ||||
−0.794960 | + | 0.606662i | \(0.792508\pi\) | |||||||
\(908\) | − 10.2918i | − 0.341545i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 10.8541i | 0.359810i | ||||||||
\(911\) | 22.3607 | 0.740842 | 0.370421 | − | 0.928864i | \(-0.379213\pi\) | ||||
0.370421 | + | 0.928864i | \(0.379213\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 43.3050i | − 1.43318i | ||||||||
\(914\) | −1.41641 | −0.0468506 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.0000 | −0.330409 | ||||||||
\(917\) | 26.2918i | 0.868232i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 41.4164 | 1.36620 | 0.683101 | − | 0.730324i | \(-0.260631\pi\) | ||||
0.683101 | + | 0.730324i | \(0.260631\pi\) | |||||||
\(920\) | 2.23607 | 0.0737210 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 37.3050i | 1.22857i | ||||||||
\(923\) | − 1.00000i | − 0.0329154i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 48.5410i | 1.59602i | ||||||||
\(926\) | −15.7082 | −0.516204 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9.70820i | 0.318687i | ||||||||
\(929\) | −43.3050 | −1.42079 | −0.710395 | − | 0.703804i | \(-0.751484\pi\) | ||||
−0.710395 | + | 0.703804i | \(0.751484\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.519733 | 0.0170336 | ||||||||
\(932\) | 21.1246i | 0.691960i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 23.1246 | 0.756660 | ||||||||
\(935\) | 10.7295i | 0.350892i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.3262i | 0.794704i | 0.917666 | + | 0.397352i | \(0.130071\pi\) | ||||
−0.917666 | + | 0.397352i | \(0.869929\pi\) | |||||||
\(938\) | − 9.70820i | − 0.316984i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | − 3.81966i | − 0.124584i | ||||||||
\(941\) | −27.2148 | −0.887177 | −0.443588 | − | 0.896231i | \(-0.646295\pi\) | ||||
−0.443588 | + | 0.896231i | \(0.646295\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 5.61803i | − 0.182948i | ||||||||
\(944\) | −6.00000 | −0.195283 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 63.1246 | 2.05236 | ||||||||
\(947\) | 26.3951i | 0.857726i | 0.903369 | + | 0.428863i | \(0.141086\pi\) | ||||
−0.903369 | + | 0.428863i | \(0.858914\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 43.1246 | 1.39988 | ||||||||
\(950\) | − 0.729490i | − 0.0236678i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − 1.58359i | − 0.0513245i | ||||||||
\(953\) | − 37.3951i | − 1.21135i | −0.795713 | − | 0.605673i | \(-0.792904\pi\) | ||||
0.795713 | − | 0.605673i | \(-0.207096\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −56.8328 | −1.83907 | ||||||||
\(956\) | 10.4721 | 0.338693 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 28.4721i | 0.919893i | ||||||||
\(959\) | 25.6869 | 0.829474 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.3951 | −0.851456 | ||||||||
\(962\) | 25.4164i | 0.819458i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.00000 | 0.0644157 | ||||||||
\(965\) | − 35.1246i | − 1.13070i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 29.2361i | − 0.940169i | −0.882622 | − | 0.470084i | \(-0.844224\pi\) | ||||
0.882622 | − | 0.470084i | \(-0.155776\pi\) | |||||||
\(968\) | 20.5623i | 0.660898i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −29.1459 | −0.935818 | ||||||||
\(971\) | −19.1459 | −0.614421 | −0.307211 | − | 0.951642i | \(-0.599396\pi\) | ||||
−0.307211 | + | 0.951642i | \(0.599396\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 7.95743i | − 0.255103i | ||||||||
\(974\) | 8.29180 | 0.265686 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.85410 | 0.0913576 | ||||||||
\(977\) | 1.27051i | 0.0406472i | 0.999793 | + | 0.0203236i | \(0.00646965\pi\) | ||||
−0.999793 | + | 0.0203236i | \(0.993530\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.8328 | 0.665820 | ||||||||
\(980\) | −7.96556 | −0.254450 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 26.8328i | 0.856270i | ||||||||
\(983\) | 47.3951i | 1.51167i | 0.654762 | + | 0.755835i | \(0.272769\pi\) | ||||
−0.654762 | + | 0.755835i | \(0.727231\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 45.9787i | − 1.46500i | ||||||||
\(986\) | −8.29180 | −0.264065 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − 0.381966i | − 0.0121520i | ||||||||
\(989\) | 11.2361 | 0.357286 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.7295 | 0.563196 | 0.281598 | − | 0.959532i | \(-0.409136\pi\) | ||||
0.281598 | + | 0.959532i | \(0.409136\pi\) | |||||||
\(992\) | 2.14590i | 0.0681323i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.708204 | −0.0224629 | ||||||||
\(995\) | −25.5279 | −0.809288 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 62.7214i | 1.98641i | 0.116398 | + | 0.993203i | \(0.462865\pi\) | ||||
−0.116398 | + | 0.993203i | \(0.537135\pi\) | |||||||
\(998\) | − 15.4164i | − 0.487998i | ||||||||
\(999\) | 0 | 0 |
(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 | 2070.2.d.c.829.2 | 4 | ||
3.2 | odd | 2 | 230.2.b.a.139.4 | yes | 4 | ||
5.4 | even | 2 | inner | 2070.2.d.c.829.4 | 4 | ||
12.11 | even | 2 | 1840.2.e.c.369.1 | 4 | |||
15.2 | even | 4 | 1150.2.a.l.1.2 | 2 | |||
15.8 | even | 4 | 1150.2.a.n.1.1 | 2 | |||
15.14 | odd | 2 | 230.2.b.a.139.1 | ✓ | 4 | ||
60.23 | odd | 4 | 9200.2.a.by.1.2 | 2 | |||
60.47 | odd | 4 | 9200.2.a.bo.1.1 | 2 | |||
60.59 | even | 2 | 1840.2.e.c.369.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.2.b.a.139.1 | ✓ | 4 | 15.14 | odd | 2 | ||
230.2.b.a.139.4 | yes | 4 | 3.2 | odd | 2 | ||
1150.2.a.l.1.2 | 2 | 15.2 | even | 4 | |||
1150.2.a.n.1.1 | 2 | 15.8 | even | 4 | |||
1840.2.e.c.369.1 | 4 | 12.11 | even | 2 | |||
1840.2.e.c.369.4 | 4 | 60.59 | even | 2 | |||
2070.2.d.c.829.2 | 4 | 1.1 | even | 1 | trivial | ||
2070.2.d.c.829.4 | 4 | 5.4 | even | 2 | inner | ||
9200.2.a.bo.1.1 | 2 | 60.47 | odd | 4 | |||
9200.2.a.by.1.2 | 2 | 60.23 | odd | 4 |