Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,2,Mod(139,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("230.139");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.b (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: | \(1.83655924649\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 139.4 | ||
Root | \(1.61803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 230.139 |
Dual form | 230.2.b.a.139.1 |
$q$-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 \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 1.61803i | 0.934172i | 0.884212 | + | 0.467086i | \(0.154696\pi\) | ||||
−0.884212 | + | 0.467086i | \(0.845304\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −2.23607 | −1.00000 | ||||||||
\(6\) | −1.61803 | −0.660560 | ||||||||
\(7\) | 1.85410i | 0.700785i | 0.936603 | + | 0.350392i | \(0.113952\pi\) | ||||
−0.936603 | + | 0.350392i | \(0.886048\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | 0.381966 | 0.127322 | ||||||||
\(10\) | − 2.23607i | − 0.707107i | ||||||||
\(11\) | −5.61803 | −1.69390 | −0.846950 | − | 0.531672i | \(-0.821564\pi\) | ||||
−0.846950 | + | 0.531672i | \(0.821564\pi\) | |||||||
\(12\) | − 1.61803i | − 0.467086i | ||||||||
\(13\) | 2.61803i | 0.726112i | 0.931767 | + | 0.363056i | \(0.118267\pi\) | ||||
−0.931767 | + | 0.363056i | \(0.881733\pi\) | |||||||
\(14\) | −1.85410 | −0.495530 | ||||||||
\(15\) | − 3.61803i | − 0.934172i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − 0.854102i | − 0.207150i | −0.994622 | − | 0.103575i | \(-0.966972\pi\) | ||||
0.994622 | − | 0.103575i | \(-0.0330282\pi\) | |||||||
\(18\) | 0.381966i | 0.0900303i | ||||||||
\(19\) | 0.145898 | 0.0334713 | 0.0167357 | − | 0.999860i | \(-0.494673\pi\) | ||||
0.0167357 | + | 0.999860i | \(0.494673\pi\) | |||||||
\(20\) | 2.23607 | 0.500000 | ||||||||
\(21\) | −3.00000 | −0.654654 | ||||||||
\(22\) | − 5.61803i | − 1.19777i | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | 1.61803 | 0.330280 | ||||||||
\(25\) | 5.00000 | 1.00000 | ||||||||
\(26\) | −2.61803 | −0.513439 | ||||||||
\(27\) | 5.47214i | 1.05311i | ||||||||
\(28\) | − 1.85410i | − 0.350392i | ||||||||
\(29\) | 9.70820 | 1.80277 | 0.901384 | − | 0.433020i | \(-0.142552\pi\) | ||||
0.901384 | + | 0.433020i | \(0.142552\pi\) | |||||||
\(30\) | 3.61803 | 0.660560 | ||||||||
\(31\) | −2.14590 | −0.385415 | −0.192707 | − | 0.981256i | \(-0.561727\pi\) | ||||
−0.192707 | + | 0.981256i | \(0.561727\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | − 9.09017i | − 1.58240i | ||||||||
\(34\) | 0.854102 | 0.146477 | ||||||||
\(35\) | − 4.14590i | − 0.700785i | ||||||||
\(36\) | −0.381966 | −0.0636610 | ||||||||
\(37\) | 9.70820i | 1.59602i | 0.602645 | + | 0.798009i | \(0.294114\pi\) | ||||
−0.602645 | + | 0.798009i | \(0.705886\pi\) | |||||||
\(38\) | 0.145898i | 0.0236678i | ||||||||
\(39\) | −4.23607 | −0.678314 | ||||||||
\(40\) | 2.23607i | 0.353553i | ||||||||
\(41\) | −5.61803 | −0.877390 | −0.438695 | − | 0.898636i | \(-0.644559\pi\) | ||||
−0.438695 | + | 0.898636i | \(0.644559\pi\) | |||||||
\(42\) | − 3.00000i | − 0.462910i | ||||||||
\(43\) | 11.2361i | 1.71348i | 0.515745 | + | 0.856742i | \(0.327515\pi\) | ||||
−0.515745 | + | 0.856742i | \(0.672485\pi\) | |||||||
\(44\) | 5.61803 | 0.846950 | ||||||||
\(45\) | −0.854102 | −0.127322 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | − 1.70820i | − 0.249167i | −0.992209 | − | 0.124584i | \(-0.960241\pi\) | ||||
0.992209 | − | 0.124584i | \(-0.0397595\pi\) | |||||||
\(48\) | 1.61803i | 0.233543i | ||||||||
\(49\) | 3.56231 | 0.508901 | ||||||||
\(50\) | 5.00000i | 0.707107i | ||||||||
\(51\) | 1.38197 | 0.193514 | ||||||||
\(52\) | − 2.61803i | − 0.363056i | ||||||||
\(53\) | − 2.00000i | − 0.274721i | −0.990521 | − | 0.137361i | \(-0.956138\pi\) | ||||
0.990521 | − | 0.137361i | \(-0.0438619\pi\) | |||||||
\(54\) | −5.47214 | −0.744663 | ||||||||
\(55\) | 12.5623 | 1.69390 | ||||||||
\(56\) | 1.85410 | 0.247765 | ||||||||
\(57\) | 0.236068i | 0.0312680i | ||||||||
\(58\) | 9.70820i | 1.27475i | ||||||||
\(59\) | 6.00000 | 0.781133 | 0.390567 | − | 0.920575i | \(-0.372279\pi\) | ||||
0.390567 | + | 0.920575i | \(0.372279\pi\) | |||||||
\(60\) | 3.61803i | 0.467086i | ||||||||
\(61\) | 2.85410 | 0.365430 | 0.182715 | − | 0.983166i | \(-0.441511\pi\) | ||||
0.182715 | + | 0.983166i | \(0.441511\pi\) | |||||||
\(62\) | − 2.14590i | − 0.272529i | ||||||||
\(63\) | 0.708204i | 0.0892253i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − 5.85410i | − 0.726112i | ||||||||
\(66\) | 9.09017 | 1.11892 | ||||||||
\(67\) | − 5.23607i | − 0.639688i | −0.947470 | − | 0.319844i | \(-0.896370\pi\) | ||||
0.947470 | − | 0.319844i | \(-0.103630\pi\) | |||||||
\(68\) | 0.854102i | 0.103575i | ||||||||
\(69\) | −1.61803 | −0.194788 | ||||||||
\(70\) | 4.14590 | 0.495530 | ||||||||
\(71\) | 0.381966 | 0.0453310 | 0.0226655 | − | 0.999743i | \(-0.492785\pi\) | ||||
0.0226655 | + | 0.999743i | \(0.492785\pi\) | |||||||
\(72\) | − 0.381966i | − 0.0450151i | ||||||||
\(73\) | − 16.4721i | − 1.92792i | −0.266051 | − | 0.963959i | \(-0.585719\pi\) | ||||
0.266051 | − | 0.963959i | \(-0.414281\pi\) | |||||||
\(74\) | −9.70820 | −1.12856 | ||||||||
\(75\) | 8.09017i | 0.934172i | ||||||||
\(76\) | −0.145898 | −0.0167357 | ||||||||
\(77\) | − 10.4164i | − 1.18706i | ||||||||
\(78\) | − 4.23607i | − 0.479640i | ||||||||
\(79\) | 7.70820 | 0.867241 | 0.433620 | − | 0.901096i | \(-0.357236\pi\) | ||||
0.433620 | + | 0.901096i | \(0.357236\pi\) | |||||||
\(80\) | −2.23607 | −0.250000 | ||||||||
\(81\) | −7.70820 | −0.856467 | ||||||||
\(82\) | − 5.61803i | − 0.620408i | ||||||||
\(83\) | 7.70820i | 0.846085i | 0.906110 | + | 0.423043i | \(0.139038\pi\) | ||||
−0.906110 | + | 0.423043i | \(0.860962\pi\) | |||||||
\(84\) | 3.00000 | 0.327327 | ||||||||
\(85\) | 1.90983i | 0.207150i | ||||||||
\(86\) | −11.2361 | −1.21162 | ||||||||
\(87\) | 15.7082i | 1.68410i | ||||||||
\(88\) | 5.61803i | 0.598884i | ||||||||
\(89\) | −3.70820 | −0.393069 | −0.196534 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196534 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(90\) | − 0.854102i | − 0.0900303i | ||||||||
\(91\) | −4.85410 | −0.508848 | ||||||||
\(92\) | − 1.00000i | − 0.104257i | ||||||||
\(93\) | − 3.47214i | − 0.360044i | ||||||||
\(94\) | 1.70820 | 0.176188 | ||||||||
\(95\) | −0.326238 | −0.0334713 | ||||||||
\(96\) | −1.61803 | −0.165140 | ||||||||
\(97\) | − 13.0344i | − 1.32345i | −0.749748 | − | 0.661724i | \(-0.769825\pi\) | ||||
0.749748 | − | 0.661724i | \(-0.230175\pi\) | |||||||
\(98\) | 3.56231i | 0.359847i | ||||||||
\(99\) | −2.14590 | −0.215671 | ||||||||
\(100\) | −5.00000 | −0.500000 | ||||||||
\(101\) | −1.52786 | −0.152028 | −0.0760141 | − | 0.997107i | \(-0.524219\pi\) | ||||
−0.0760141 | + | 0.997107i | \(0.524219\pi\) | |||||||
\(102\) | 1.38197i | 0.136835i | ||||||||
\(103\) | 10.8541i | 1.06949i | 0.845015 | + | 0.534743i | \(0.179592\pi\) | ||||
−0.845015 | + | 0.534743i | \(0.820408\pi\) | |||||||
\(104\) | 2.61803 | 0.256719 | ||||||||
\(105\) | 6.70820 | 0.654654 | ||||||||
\(106\) | 2.00000 | 0.194257 | ||||||||
\(107\) | − 11.7082i | − 1.13187i | −0.824448 | − | 0.565937i | \(-0.808514\pi\) | ||||
0.824448 | − | 0.565937i | \(-0.191486\pi\) | |||||||
\(108\) | − 5.47214i | − 0.526557i | ||||||||
\(109\) | −7.56231 | −0.724338 | −0.362169 | − | 0.932113i | \(-0.617964\pi\) | ||||
−0.362169 | + | 0.932113i | \(0.617964\pi\) | |||||||
\(110\) | 12.5623i | 1.19777i | ||||||||
\(111\) | −15.7082 | −1.49096 | ||||||||
\(112\) | 1.85410i | 0.175196i | ||||||||
\(113\) | − 13.4164i | − 1.26211i | −0.775738 | − | 0.631055i | \(-0.782622\pi\) | ||||
0.775738 | − | 0.631055i | \(-0.217378\pi\) | |||||||
\(114\) | −0.236068 | −0.0221098 | ||||||||
\(115\) | − 2.23607i | − 0.208514i | ||||||||
\(116\) | −9.70820 | −0.901384 | ||||||||
\(117\) | 1.00000i | 0.0924500i | ||||||||
\(118\) | 6.00000i | 0.552345i | ||||||||
\(119\) | 1.58359 | 0.145168 | ||||||||
\(120\) | −3.61803 | −0.330280 | ||||||||
\(121\) | 20.5623 | 1.86930 | ||||||||
\(122\) | 2.85410i | 0.258398i | ||||||||
\(123\) | − 9.09017i | − 0.819633i | ||||||||
\(124\) | 2.14590 | 0.192707 | ||||||||
\(125\) | −11.1803 | −1.00000 | ||||||||
\(126\) | −0.708204 | −0.0630918 | ||||||||
\(127\) | 9.70820i | 0.861464i | 0.902480 | + | 0.430732i | \(0.141745\pi\) | ||||
−0.902480 | + | 0.430732i | \(0.858255\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | −18.1803 | −1.60069 | ||||||||
\(130\) | 5.85410 | 0.513439 | ||||||||
\(131\) | −14.1803 | −1.23894 | −0.619471 | − | 0.785020i | \(-0.712653\pi\) | ||||
−0.619471 | + | 0.785020i | \(0.712653\pi\) | |||||||
\(132\) | 9.09017i | 0.791198i | ||||||||
\(133\) | 0.270510i | 0.0234562i | ||||||||
\(134\) | 5.23607 | 0.452327 | ||||||||
\(135\) | − 12.2361i | − 1.05311i | ||||||||
\(136\) | −0.854102 | −0.0732386 | ||||||||
\(137\) | 13.8541i | 1.18364i | 0.806072 | + | 0.591818i | \(0.201590\pi\) | ||||
−0.806072 | + | 0.591818i | \(0.798410\pi\) | |||||||
\(138\) | − 1.61803i | − 0.137736i | ||||||||
\(139\) | −4.29180 | −0.364025 | −0.182013 | − | 0.983296i | \(-0.558261\pi\) | ||||
−0.182013 | + | 0.983296i | \(0.558261\pi\) | |||||||
\(140\) | 4.14590i | 0.350392i | ||||||||
\(141\) | 2.76393 | 0.232765 | ||||||||
\(142\) | 0.381966i | 0.0320539i | ||||||||
\(143\) | − 14.7082i | − 1.22996i | ||||||||
\(144\) | 0.381966 | 0.0318305 | ||||||||
\(145\) | −21.7082 | −1.80277 | ||||||||
\(146\) | 16.4721 | 1.36324 | ||||||||
\(147\) | 5.76393i | 0.475401i | ||||||||
\(148\) | − 9.70820i | − 0.798009i | ||||||||
\(149\) | 2.61803 | 0.214478 | 0.107239 | − | 0.994233i | \(-0.465799\pi\) | ||||
0.107239 | + | 0.994233i | \(0.465799\pi\) | |||||||
\(150\) | −8.09017 | −0.660560 | ||||||||
\(151\) | 14.2705 | 1.16132 | 0.580659 | − | 0.814147i | \(-0.302795\pi\) | ||||
0.580659 | + | 0.814147i | \(0.302795\pi\) | |||||||
\(152\) | − 0.145898i | − 0.0118339i | ||||||||
\(153\) | − 0.326238i | − 0.0263748i | ||||||||
\(154\) | 10.4164 | 0.839378 | ||||||||
\(155\) | 4.79837 | 0.385415 | ||||||||
\(156\) | 4.23607 | 0.339157 | ||||||||
\(157\) | − 2.29180i | − 0.182905i | −0.995809 | − | 0.0914526i | \(-0.970849\pi\) | ||||
0.995809 | − | 0.0914526i | \(-0.0291510\pi\) | |||||||
\(158\) | 7.70820i | 0.613232i | ||||||||
\(159\) | 3.23607 | 0.256637 | ||||||||
\(160\) | − 2.23607i | − 0.176777i | ||||||||
\(161\) | −1.85410 | −0.146124 | ||||||||
\(162\) | − 7.70820i | − 0.605614i | ||||||||
\(163\) | − 22.0344i | − 1.72587i | −0.505314 | − | 0.862935i | \(-0.668623\pi\) | ||||
0.505314 | − | 0.862935i | \(-0.331377\pi\) | |||||||
\(164\) | 5.61803 | 0.438695 | ||||||||
\(165\) | 20.3262i | 1.58240i | ||||||||
\(166\) | −7.70820 | −0.598273 | ||||||||
\(167\) | 9.70820i | 0.751243i | 0.926773 | + | 0.375622i | \(0.122571\pi\) | ||||
−0.926773 | + | 0.375622i | \(0.877429\pi\) | |||||||
\(168\) | 3.00000i | 0.231455i | ||||||||
\(169\) | 6.14590 | 0.472761 | ||||||||
\(170\) | −1.90983 | −0.146477 | ||||||||
\(171\) | 0.0557281 | 0.00426163 | ||||||||
\(172\) | − 11.2361i | − 0.856742i | ||||||||
\(173\) | 16.5623i | 1.25921i | 0.776916 | + | 0.629604i | \(0.216783\pi\) | ||||
−0.776916 | + | 0.629604i | \(0.783217\pi\) | |||||||
\(174\) | −15.7082 | −1.19084 | ||||||||
\(175\) | 9.27051i | 0.700785i | ||||||||
\(176\) | −5.61803 | −0.423475 | ||||||||
\(177\) | 9.70820i | 0.729713i | ||||||||
\(178\) | − 3.70820i | − 0.277942i | ||||||||
\(179\) | −7.52786 | −0.562659 | −0.281329 | − | 0.959611i | \(-0.590775\pi\) | ||||
−0.281329 | + | 0.959611i | \(0.590775\pi\) | |||||||
\(180\) | 0.854102 | 0.0636610 | ||||||||
\(181\) | 15.5623 | 1.15674 | 0.578369 | − | 0.815776i | \(-0.303690\pi\) | ||||
0.578369 | + | 0.815776i | \(0.303690\pi\) | |||||||
\(182\) | − 4.85410i | − 0.359810i | ||||||||
\(183\) | 4.61803i | 0.341375i | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | − 21.7082i | − 1.59602i | ||||||||
\(186\) | 3.47214 | 0.254589 | ||||||||
\(187\) | 4.79837i | 0.350892i | ||||||||
\(188\) | 1.70820i | 0.124584i | ||||||||
\(189\) | −10.1459 | −0.738005 | ||||||||
\(190\) | − 0.326238i | − 0.0236678i | ||||||||
\(191\) | 25.4164 | 1.83907 | 0.919533 | − | 0.393012i | \(-0.128567\pi\) | ||||
0.919533 | + | 0.393012i | \(0.128567\pi\) | |||||||
\(192\) | − 1.61803i | − 0.116772i | ||||||||
\(193\) | − 15.7082i | − 1.13070i | −0.824851 | − | 0.565351i | \(-0.808741\pi\) | ||||
0.824851 | − | 0.565351i | \(-0.191259\pi\) | |||||||
\(194\) | 13.0344 | 0.935818 | ||||||||
\(195\) | 9.47214 | 0.678314 | ||||||||
\(196\) | −3.56231 | −0.254450 | ||||||||
\(197\) | 20.5623i | 1.46500i | 0.680765 | + | 0.732502i | \(0.261647\pi\) | ||||
−0.680765 | + | 0.732502i | \(0.738353\pi\) | |||||||
\(198\) | − 2.14590i | − 0.152502i | ||||||||
\(199\) | −11.4164 | −0.809288 | −0.404644 | − | 0.914474i | \(-0.632605\pi\) | ||||
−0.404644 | + | 0.914474i | \(0.632605\pi\) | |||||||
\(200\) | − 5.00000i | − 0.353553i | ||||||||
\(201\) | 8.47214 | 0.597578 | ||||||||
\(202\) | − 1.52786i | − 0.107500i | ||||||||
\(203\) | 18.0000i | 1.26335i | ||||||||
\(204\) | −1.38197 | −0.0967570 | ||||||||
\(205\) | 12.5623 | 0.877390 | ||||||||
\(206\) | −10.8541 | −0.756241 | ||||||||
\(207\) | 0.381966i | 0.0265485i | ||||||||
\(208\) | 2.61803i | 0.181528i | ||||||||
\(209\) | −0.819660 | −0.0566971 | ||||||||
\(210\) | 6.70820i | 0.462910i | ||||||||
\(211\) | −7.70820 | −0.530655 | −0.265327 | − | 0.964158i | \(-0.585480\pi\) | ||||
−0.265327 | + | 0.964158i | \(0.585480\pi\) | |||||||
\(212\) | 2.00000i | 0.137361i | ||||||||
\(213\) | 0.618034i | 0.0423470i | ||||||||
\(214\) | 11.7082 | 0.800356 | ||||||||
\(215\) | − 25.1246i | − 1.71348i | ||||||||
\(216\) | 5.47214 | 0.372332 | ||||||||
\(217\) | − 3.97871i | − 0.270093i | ||||||||
\(218\) | − 7.56231i | − 0.512184i | ||||||||
\(219\) | 26.6525 | 1.80101 | ||||||||
\(220\) | −12.5623 | −0.846950 | ||||||||
\(221\) | 2.23607 | 0.150414 | ||||||||
\(222\) | − 15.7082i | − 1.05427i | ||||||||
\(223\) | 22.3607i | 1.49738i | 0.662919 | + | 0.748691i | \(0.269317\pi\) | ||||
−0.662919 | + | 0.748691i | \(0.730683\pi\) | |||||||
\(224\) | −1.85410 | −0.123882 | ||||||||
\(225\) | 1.90983 | 0.127322 | ||||||||
\(226\) | 13.4164 | 0.892446 | ||||||||
\(227\) | − 10.2918i | − 0.683090i | −0.939865 | − | 0.341545i | \(-0.889050\pi\) | ||||
0.939865 | − | 0.341545i | \(-0.110950\pi\) | |||||||
\(228\) | − 0.236068i | − 0.0156340i | ||||||||
\(229\) | 10.0000 | 0.660819 | 0.330409 | − | 0.943838i | \(-0.392813\pi\) | ||||
0.330409 | + | 0.943838i | \(0.392813\pi\) | |||||||
\(230\) | 2.23607 | 0.147442 | ||||||||
\(231\) | 16.8541 | 1.10892 | ||||||||
\(232\) | − 9.70820i | − 0.637375i | ||||||||
\(233\) | 21.1246i | 1.38392i | 0.721936 | + | 0.691960i | \(0.243252\pi\) | ||||
−0.721936 | + | 0.691960i | \(0.756748\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | 3.81966i | 0.249167i | ||||||||
\(236\) | −6.00000 | −0.390567 | ||||||||
\(237\) | 12.4721i | 0.810152i | ||||||||
\(238\) | 1.58359i | 0.102649i | ||||||||
\(239\) | 10.4721 | 0.677386 | 0.338693 | − | 0.940897i | \(-0.390015\pi\) | ||||
0.338693 | + | 0.940897i | \(0.390015\pi\) | |||||||
\(240\) | − 3.61803i | − 0.233543i | ||||||||
\(241\) | −2.00000 | −0.128831 | −0.0644157 | − | 0.997923i | \(-0.520518\pi\) | ||||
−0.0644157 | + | 0.997923i | \(0.520518\pi\) | |||||||
\(242\) | 20.5623i | 1.32180i | ||||||||
\(243\) | 3.94427i | 0.253025i | ||||||||
\(244\) | −2.85410 | −0.182715 | ||||||||
\(245\) | −7.96556 | −0.508901 | ||||||||
\(246\) | 9.09017 | 0.579568 | ||||||||
\(247\) | 0.381966i | 0.0243039i | ||||||||
\(248\) | 2.14590i | 0.136265i | ||||||||
\(249\) | −12.4721 | −0.790390 | ||||||||
\(250\) | − 11.1803i | − 0.707107i | ||||||||
\(251\) | −16.7984 | −1.06030 | −0.530152 | − | 0.847903i | \(-0.677865\pi\) | ||||
−0.530152 | + | 0.847903i | \(0.677865\pi\) | |||||||
\(252\) | − 0.708204i | − 0.0446127i | ||||||||
\(253\) | − 5.61803i | − 0.353203i | ||||||||
\(254\) | −9.70820 | −0.609147 | ||||||||
\(255\) | −3.09017 | −0.193514 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.4164i | 0.712136i | 0.934460 | + | 0.356068i | \(0.115883\pi\) | ||||
−0.934460 | + | 0.356068i | \(0.884117\pi\) | |||||||
\(258\) | − 18.1803i | − 1.13186i | ||||||||
\(259\) | −18.0000 | −1.11847 | ||||||||
\(260\) | 5.85410i | 0.363056i | ||||||||
\(261\) | 3.70820 | 0.229532 | ||||||||
\(262\) | − 14.1803i | − 0.876064i | ||||||||
\(263\) | − 18.2705i | − 1.12661i | −0.826250 | − | 0.563304i | \(-0.809530\pi\) | ||||
0.826250 | − | 0.563304i | \(-0.190470\pi\) | |||||||
\(264\) | −9.09017 | −0.559461 | ||||||||
\(265\) | 4.47214i | 0.274721i | ||||||||
\(266\) | −0.270510 | −0.0165860 | ||||||||
\(267\) | − 6.00000i | − 0.367194i | ||||||||
\(268\) | 5.23607i | 0.319844i | ||||||||
\(269\) | 1.52786 | 0.0931555 | 0.0465778 | − | 0.998915i | \(-0.485168\pi\) | ||||
0.0465778 | + | 0.998915i | \(0.485168\pi\) | |||||||
\(270\) | 12.2361 | 0.744663 | ||||||||
\(271\) | 25.8541 | 1.57052 | 0.785262 | − | 0.619163i | \(-0.212528\pi\) | ||||
0.785262 | + | 0.619163i | \(0.212528\pi\) | |||||||
\(272\) | − 0.854102i | − 0.0517875i | ||||||||
\(273\) | − 7.85410i | − 0.475352i | ||||||||
\(274\) | −13.8541 | −0.836957 | ||||||||
\(275\) | −28.0902 | −1.69390 | ||||||||
\(276\) | 1.61803 | 0.0973942 | ||||||||
\(277\) | − 7.52786i | − 0.452306i | −0.974092 | − | 0.226153i | \(-0.927385\pi\) | ||||
0.974092 | − | 0.226153i | \(-0.0726149\pi\) | |||||||
\(278\) | − 4.29180i | − 0.257405i | ||||||||
\(279\) | −0.819660 | −0.0490718 | ||||||||
\(280\) | −4.14590 | −0.247765 | ||||||||
\(281\) | 30.6525 | 1.82857 | 0.914287 | − | 0.405068i | \(-0.132752\pi\) | ||||
0.914287 | + | 0.405068i | \(0.132752\pi\) | |||||||
\(282\) | 2.76393i | 0.164590i | ||||||||
\(283\) | 20.9443i | 1.24501i | 0.782617 | + | 0.622504i | \(0.213885\pi\) | ||||
−0.782617 | + | 0.622504i | \(0.786115\pi\) | |||||||
\(284\) | −0.381966 | −0.0226655 | ||||||||
\(285\) | − 0.527864i | − 0.0312680i | ||||||||
\(286\) | 14.7082 | 0.869714 | ||||||||
\(287\) | − 10.4164i | − 0.614861i | ||||||||
\(288\) | 0.381966i | 0.0225076i | ||||||||
\(289\) | 16.2705 | 0.957089 | ||||||||
\(290\) | − 21.7082i | − 1.27475i | ||||||||
\(291\) | 21.0902 | 1.23633 | ||||||||
\(292\) | 16.4721i | 0.963959i | ||||||||
\(293\) | − 14.2918i | − 0.834936i | −0.908692 | − | 0.417468i | \(-0.862918\pi\) | ||||
0.908692 | − | 0.417468i | \(-0.137082\pi\) | |||||||
\(294\) | −5.76393 | −0.336159 | ||||||||
\(295\) | −13.4164 | −0.781133 | ||||||||
\(296\) | 9.70820 | 0.564278 | ||||||||
\(297\) | − 30.7426i | − 1.78387i | ||||||||
\(298\) | 2.61803i | 0.151659i | ||||||||
\(299\) | −2.61803 | −0.151405 | ||||||||
\(300\) | − 8.09017i | − 0.467086i | ||||||||
\(301\) | −20.8328 | −1.20078 | ||||||||
\(302\) | 14.2705i | 0.821176i | ||||||||
\(303\) | − 2.47214i | − 0.142020i | ||||||||
\(304\) | 0.145898 | 0.00836783 | ||||||||
\(305\) | −6.38197 | −0.365430 | ||||||||
\(306\) | 0.326238 | 0.0186498 | ||||||||
\(307\) | − 16.8541i | − 0.961914i | −0.876744 | − | 0.480957i | \(-0.840289\pi\) | ||||
0.876744 | − | 0.480957i | \(-0.159711\pi\) | |||||||
\(308\) | 10.4164i | 0.593530i | ||||||||
\(309\) | −17.5623 | −0.999085 | ||||||||
\(310\) | 4.79837i | 0.272529i | ||||||||
\(311\) | −22.4721 | −1.27428 | −0.637139 | − | 0.770749i | \(-0.719882\pi\) | ||||
−0.637139 | + | 0.770749i | \(0.719882\pi\) | |||||||
\(312\) | 4.23607i | 0.239820i | ||||||||
\(313\) | 25.8541i | 1.46136i | 0.682720 | + | 0.730680i | \(0.260797\pi\) | ||||
−0.682720 | + | 0.730680i | \(0.739203\pi\) | |||||||
\(314\) | 2.29180 | 0.129334 | ||||||||
\(315\) | − 1.58359i | − 0.0892253i | ||||||||
\(316\) | −7.70820 | −0.433620 | ||||||||
\(317\) | 7.27051i | 0.408353i | 0.978934 | + | 0.204176i | \(0.0654516\pi\) | ||||
−0.978934 | + | 0.204176i | \(0.934548\pi\) | |||||||
\(318\) | 3.23607i | 0.181470i | ||||||||
\(319\) | −54.5410 | −3.05371 | ||||||||
\(320\) | 2.23607 | 0.125000 | ||||||||
\(321\) | 18.9443 | 1.05737 | ||||||||
\(322\) | − 1.85410i | − 0.103325i | ||||||||
\(323\) | − 0.124612i | − 0.00693359i | ||||||||
\(324\) | 7.70820 | 0.428234 | ||||||||
\(325\) | 13.0902i | 0.726112i | ||||||||
\(326\) | 22.0344 | 1.22037 | ||||||||
\(327\) | − 12.2361i | − 0.676656i | ||||||||
\(328\) | 5.61803i | 0.310204i | ||||||||
\(329\) | 3.16718 | 0.174613 | ||||||||
\(330\) | −20.3262 | −1.11892 | ||||||||
\(331\) | −25.1246 | −1.38097 | −0.690487 | − | 0.723345i | \(-0.742604\pi\) | ||||
−0.690487 | + | 0.723345i | \(0.742604\pi\) | |||||||
\(332\) | − 7.70820i | − 0.423043i | ||||||||
\(333\) | 3.70820i | 0.203208i | ||||||||
\(334\) | −9.70820 | −0.531209 | ||||||||
\(335\) | 11.7082i | 0.639688i | ||||||||
\(336\) | −3.00000 | −0.163663 | ||||||||
\(337\) | 3.38197i | 0.184227i | 0.995748 | + | 0.0921137i | \(0.0293623\pi\) | ||||
−0.995748 | + | 0.0921137i | \(0.970638\pi\) | |||||||
\(338\) | 6.14590i | 0.334293i | ||||||||
\(339\) | 21.7082 | 1.17903 | ||||||||
\(340\) | − 1.90983i | − 0.103575i | ||||||||
\(341\) | 12.0557 | 0.652854 | ||||||||
\(342\) | 0.0557281i | 0.00301343i | ||||||||
\(343\) | 19.5836i | 1.05741i | ||||||||
\(344\) | 11.2361 | 0.605808 | ||||||||
\(345\) | 3.61803 | 0.194788 | ||||||||
\(346\) | −16.5623 | −0.890395 | ||||||||
\(347\) | − 14.5623i | − 0.781746i | −0.920445 | − | 0.390873i | \(-0.872173\pi\) | ||||
0.920445 | − | 0.390873i | \(-0.127827\pi\) | |||||||
\(348\) | − 15.7082i | − 0.842048i | ||||||||
\(349\) | −27.7082 | −1.48319 | −0.741593 | − | 0.670850i | \(-0.765929\pi\) | ||||
−0.741593 | + | 0.670850i | \(0.765929\pi\) | |||||||
\(350\) | −9.27051 | −0.495530 | ||||||||
\(351\) | −14.3262 | −0.764678 | ||||||||
\(352\) | − 5.61803i | − 0.299442i | ||||||||
\(353\) | 8.00000i | 0.425797i | 0.977074 | + | 0.212899i | \(0.0682904\pi\) | ||||
−0.977074 | + | 0.212899i | \(0.931710\pi\) | |||||||
\(354\) | −9.70820 | −0.515985 | ||||||||
\(355\) | −0.854102 | −0.0453310 | ||||||||
\(356\) | 3.70820 | 0.196534 | ||||||||
\(357\) | 2.56231i | 0.135612i | ||||||||
\(358\) | − 7.52786i | − 0.397860i | ||||||||
\(359\) | 13.4164 | 0.708091 | 0.354045 | − | 0.935228i | \(-0.384806\pi\) | ||||
0.354045 | + | 0.935228i | \(0.384806\pi\) | |||||||
\(360\) | 0.854102i | 0.0450151i | ||||||||
\(361\) | −18.9787 | −0.998880 | ||||||||
\(362\) | 15.5623i | 0.817937i | ||||||||
\(363\) | 33.2705i | 1.74625i | ||||||||
\(364\) | 4.85410 | 0.254424 | ||||||||
\(365\) | 36.8328i | 1.92792i | ||||||||
\(366\) | −4.61803 | −0.241389 | ||||||||
\(367\) | − 12.0000i | − 0.626395i | −0.949688 | − | 0.313197i | \(-0.898600\pi\) | ||||
0.949688 | − | 0.313197i | \(-0.101400\pi\) | |||||||
\(368\) | 1.00000i | 0.0521286i | ||||||||
\(369\) | −2.14590 | −0.111711 | ||||||||
\(370\) | 21.7082 | 1.12856 | ||||||||
\(371\) | 3.70820 | 0.192520 | ||||||||
\(372\) | 3.47214i | 0.180022i | ||||||||
\(373\) | − 20.9443i | − 1.08445i | −0.840232 | − | 0.542227i | \(-0.817581\pi\) | ||||
0.840232 | − | 0.542227i | \(-0.182419\pi\) | |||||||
\(374\) | −4.79837 | −0.248118 | ||||||||
\(375\) | − 18.0902i | − 0.934172i | ||||||||
\(376\) | −1.70820 | −0.0880939 | ||||||||
\(377\) | 25.4164i | 1.30901i | ||||||||
\(378\) | − 10.1459i | − 0.521849i | ||||||||
\(379\) | 24.2705 | 1.24669 | 0.623346 | − | 0.781946i | \(-0.285773\pi\) | ||||
0.623346 | + | 0.781946i | \(0.285773\pi\) | |||||||
\(380\) | 0.326238 | 0.0167357 | ||||||||
\(381\) | −15.7082 | −0.804756 | ||||||||
\(382\) | 25.4164i | 1.30042i | ||||||||
\(383\) | 0.583592i | 0.0298202i | 0.999889 | + | 0.0149101i | \(0.00474620\pi\) | ||||
−0.999889 | + | 0.0149101i | \(0.995254\pi\) | |||||||
\(384\) | 1.61803 | 0.0825700 | ||||||||
\(385\) | 23.2918i | 1.18706i | ||||||||
\(386\) | 15.7082 | 0.799527 | ||||||||
\(387\) | 4.29180i | 0.218164i | ||||||||
\(388\) | 13.0344i | 0.661724i | ||||||||
\(389\) | 21.3262 | 1.08128 | 0.540642 | − | 0.841253i | \(-0.318182\pi\) | ||||
0.540642 | + | 0.841253i | \(0.318182\pi\) | |||||||
\(390\) | 9.47214i | 0.479640i | ||||||||
\(391\) | 0.854102 | 0.0431938 | ||||||||
\(392\) | − 3.56231i | − 0.179924i | ||||||||
\(393\) | − 22.9443i | − 1.15739i | ||||||||
\(394\) | −20.5623 | −1.03591 | ||||||||
\(395\) | −17.2361 | −0.867241 | ||||||||
\(396\) | 2.14590 | 0.107835 | ||||||||
\(397\) | − 15.4377i | − 0.774796i | −0.921913 | − | 0.387398i | \(-0.873374\pi\) | ||||
0.921913 | − | 0.387398i | \(-0.126626\pi\) | |||||||
\(398\) | − 11.4164i | − 0.572253i | ||||||||
\(399\) | −0.437694 | −0.0219121 | ||||||||
\(400\) | 5.00000 | 0.250000 | ||||||||
\(401\) | −25.5279 | −1.27480 | −0.637400 | − | 0.770533i | \(-0.719990\pi\) | ||||
−0.637400 | + | 0.770533i | \(0.719990\pi\) | |||||||
\(402\) | 8.47214i | 0.422552i | ||||||||
\(403\) | − 5.61803i | − 0.279854i | ||||||||
\(404\) | 1.52786 | 0.0760141 | ||||||||
\(405\) | 17.2361 | 0.856467 | ||||||||
\(406\) | −18.0000 | −0.893325 | ||||||||
\(407\) | − 54.5410i | − 2.70350i | ||||||||
\(408\) | − 1.38197i | − 0.0684175i | ||||||||
\(409\) | −13.5623 | −0.670613 | −0.335306 | − | 0.942109i | \(-0.608840\pi\) | ||||
−0.335306 | + | 0.942109i | \(0.608840\pi\) | |||||||
\(410\) | 12.5623i | 0.620408i | ||||||||
\(411\) | −22.4164 | −1.10572 | ||||||||
\(412\) | − 10.8541i | − 0.534743i | ||||||||
\(413\) | 11.1246i | 0.547406i | ||||||||
\(414\) | −0.381966 | −0.0187726 | ||||||||
\(415\) | − 17.2361i | − 0.846085i | ||||||||
\(416\) | −2.61803 | −0.128360 | ||||||||
\(417\) | − 6.94427i | − 0.340062i | ||||||||
\(418\) | − 0.819660i | − 0.0400909i | ||||||||
\(419\) | 29.8885 | 1.46015 | 0.730075 | − | 0.683367i | \(-0.239485\pi\) | ||||
0.730075 | + | 0.683367i | \(0.239485\pi\) | |||||||
\(420\) | −6.70820 | −0.327327 | ||||||||
\(421\) | 0.145898 | 0.00711064 | 0.00355532 | − | 0.999994i | \(-0.498868\pi\) | ||||
0.00355532 | + | 0.999994i | \(0.498868\pi\) | |||||||
\(422\) | − 7.70820i | − 0.375229i | ||||||||
\(423\) | − 0.652476i | − 0.0317245i | ||||||||
\(424\) | −2.00000 | −0.0971286 | ||||||||
\(425\) | − 4.27051i | − 0.207150i | ||||||||
\(426\) | −0.618034 | −0.0299438 | ||||||||
\(427\) | 5.29180i | 0.256088i | ||||||||
\(428\) | 11.7082i | 0.565937i | ||||||||
\(429\) | 23.7984 | 1.14900 | ||||||||
\(430\) | 25.1246 | 1.21162 | ||||||||
\(431\) | −11.2361 | −0.541222 | −0.270611 | − | 0.962689i | \(-0.587226\pi\) | ||||
−0.270611 | + | 0.962689i | \(0.587226\pi\) | |||||||
\(432\) | 5.47214i | 0.263278i | ||||||||
\(433\) | − 27.3820i | − 1.31589i | −0.753065 | − | 0.657947i | \(-0.771425\pi\) | ||||
0.753065 | − | 0.657947i | \(-0.228575\pi\) | |||||||
\(434\) | 3.97871 | 0.190984 | ||||||||
\(435\) | − 35.1246i | − 1.68410i | ||||||||
\(436\) | 7.56231 | 0.362169 | ||||||||
\(437\) | 0.145898i | 0.00697925i | ||||||||
\(438\) | 26.6525i | 1.27350i | ||||||||
\(439\) | −33.2705 | −1.58791 | −0.793957 | − | 0.607973i | \(-0.791983\pi\) | ||||
−0.793957 | + | 0.607973i | \(0.791983\pi\) | |||||||
\(440\) | − 12.5623i | − 0.598884i | ||||||||
\(441\) | 1.36068 | 0.0647943 | ||||||||
\(442\) | 2.23607i | 0.106359i | ||||||||
\(443\) | 0.145898i | 0.00693182i | 0.999994 | + | 0.00346591i | \(0.00110324\pi\) | ||||
−0.999994 | + | 0.00346591i | \(0.998897\pi\) | |||||||
\(444\) | 15.7082 | 0.745478 | ||||||||
\(445\) | 8.29180 | 0.393069 | ||||||||
\(446\) | −22.3607 | −1.05881 | ||||||||
\(447\) | 4.23607i | 0.200359i | ||||||||
\(448\) | − 1.85410i | − 0.0875981i | ||||||||
\(449\) | 17.5623 | 0.828816 | 0.414408 | − | 0.910091i | \(-0.363989\pi\) | ||||
0.414408 | + | 0.910091i | \(0.363989\pi\) | |||||||
\(450\) | 1.90983i | 0.0900303i | ||||||||
\(451\) | 31.5623 | 1.48621 | ||||||||
\(452\) | 13.4164i | 0.631055i | ||||||||
\(453\) | 23.0902i | 1.08487i | ||||||||
\(454\) | 10.2918 | 0.483018 | ||||||||
\(455\) | 10.8541 | 0.508848 | ||||||||
\(456\) | 0.236068 | 0.0110549 | ||||||||
\(457\) | − 1.41641i | − 0.0662568i | −0.999451 | − | 0.0331284i | \(-0.989453\pi\) | ||||
0.999451 | − | 0.0331284i | \(-0.0105470\pi\) | |||||||
\(458\) | 10.0000i | 0.467269i | ||||||||
\(459\) | 4.67376 | 0.218153 | ||||||||
\(460\) | 2.23607i | 0.104257i | ||||||||
\(461\) | 37.3050 | 1.73746 | 0.868732 | − | 0.495282i | \(-0.164935\pi\) | ||||
0.868732 | + | 0.495282i | \(0.164935\pi\) | |||||||
\(462\) | 16.8541i | 0.784124i | ||||||||
\(463\) | − 15.7082i | − 0.730022i | −0.931003 | − | 0.365011i | \(-0.881065\pi\) | ||||
0.931003 | − | 0.365011i | \(-0.118935\pi\) | |||||||
\(464\) | 9.70820 | 0.450692 | ||||||||
\(465\) | 7.76393i | 0.360044i | ||||||||
\(466\) | −21.1246 | −0.978579 | ||||||||
\(467\) | − 23.1246i | − 1.07008i | −0.844827 | − | 0.535040i | \(-0.820297\pi\) | ||||
0.844827 | − | 0.535040i | \(-0.179703\pi\) | |||||||
\(468\) | − 1.00000i | − 0.0462250i | ||||||||
\(469\) | 9.70820 | 0.448283 | ||||||||
\(470\) | −3.81966 | −0.176188 | ||||||||
\(471\) | 3.70820 | 0.170865 | ||||||||
\(472\) | − 6.00000i | − 0.276172i | ||||||||
\(473\) | − 63.1246i | − 2.90247i | ||||||||
\(474\) | −12.4721 | −0.572864 | ||||||||
\(475\) | 0.729490 | 0.0334713 | ||||||||
\(476\) | −1.58359 | −0.0725838 | ||||||||
\(477\) | − 0.763932i | − 0.0349780i | ||||||||
\(478\) | 10.4721i | 0.478984i | ||||||||
\(479\) | 28.4721 | 1.30093 | 0.650463 | − | 0.759538i | \(-0.274575\pi\) | ||||
0.650463 | + | 0.759538i | \(0.274575\pi\) | |||||||
\(480\) | 3.61803 | 0.165140 | ||||||||
\(481\) | −25.4164 | −1.15889 | ||||||||
\(482\) | − 2.00000i | − 0.0910975i | ||||||||
\(483\) | − 3.00000i | − 0.136505i | ||||||||
\(484\) | −20.5623 | −0.934650 | ||||||||
\(485\) | 29.1459i | 1.32345i | ||||||||
\(486\) | −3.94427 | −0.178916 | ||||||||
\(487\) | 8.29180i | 0.375737i | 0.982194 | + | 0.187869i | \(0.0601579\pi\) | ||||
−0.982194 | + | 0.187869i | \(0.939842\pi\) | |||||||
\(488\) | − 2.85410i | − 0.129199i | ||||||||
\(489\) | 35.6525 | 1.61226 | ||||||||
\(490\) | − 7.96556i | − 0.359847i | ||||||||
\(491\) | 26.8328 | 1.21095 | 0.605474 | − | 0.795865i | \(-0.292984\pi\) | ||||
0.605474 | + | 0.795865i | \(0.292984\pi\) | |||||||
\(492\) | 9.09017i | 0.409817i | ||||||||
\(493\) | − 8.29180i | − 0.373444i | ||||||||
\(494\) | −0.381966 | −0.0171855 | ||||||||
\(495\) | 4.79837 | 0.215671 | ||||||||
\(496\) | −2.14590 | −0.0963537 | ||||||||
\(497\) | 0.708204i | 0.0317673i | ||||||||
\(498\) | − 12.4721i | − 0.558890i | ||||||||
\(499\) | 15.4164 | 0.690133 | 0.345067 | − | 0.938578i | \(-0.387856\pi\) | ||||
0.345067 | + | 0.938578i | \(0.387856\pi\) | |||||||
\(500\) | 11.1803 | 0.500000 | ||||||||
\(501\) | −15.7082 | −0.701791 | ||||||||
\(502\) | − 16.7984i | − 0.749748i | ||||||||
\(503\) | 10.1459i | 0.452383i | 0.974083 | + | 0.226192i | \(0.0726276\pi\) | ||||
−0.974083 | + | 0.226192i | \(0.927372\pi\) | |||||||
\(504\) | 0.708204 | 0.0315459 | ||||||||
\(505\) | 3.41641 | 0.152028 | ||||||||
\(506\) | 5.61803 | 0.249752 | ||||||||
\(507\) | 9.94427i | 0.441641i | ||||||||
\(508\) | − 9.70820i | − 0.430732i | ||||||||
\(509\) | −6.65248 | −0.294866 | −0.147433 | − | 0.989072i | \(-0.547101\pi\) | ||||
−0.147433 | + | 0.989072i | \(0.547101\pi\) | |||||||
\(510\) | − 3.09017i | − 0.136835i | ||||||||
\(511\) | 30.5410 | 1.35106 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0.798374i | 0.0352491i | ||||||||
\(514\) | −11.4164 | −0.503556 | ||||||||
\(515\) | − 24.2705i | − 1.06949i | ||||||||
\(516\) | 18.1803 | 0.800345 | ||||||||
\(517\) | 9.59675i | 0.422064i | ||||||||
\(518\) | − 18.0000i | − 0.790875i | ||||||||
\(519\) | −26.7984 | −1.17632 | ||||||||
\(520\) | −5.85410 | −0.256719 | ||||||||
\(521\) | −38.0689 | −1.66783 | −0.833914 | − | 0.551894i | \(-0.813905\pi\) | ||||
−0.833914 | + | 0.551894i | \(0.813905\pi\) | |||||||
\(522\) | 3.70820i | 0.162304i | ||||||||
\(523\) | 4.36068i | 0.190679i | 0.995445 | + | 0.0953396i | \(0.0303937\pi\) | ||||
−0.995445 | + | 0.0953396i | \(0.969606\pi\) | |||||||
\(524\) | 14.1803 | 0.619471 | ||||||||
\(525\) | −15.0000 | −0.654654 | ||||||||
\(526\) | 18.2705 | 0.796632 | ||||||||
\(527\) | 1.83282i | 0.0798387i | ||||||||
\(528\) | − 9.09017i | − 0.395599i | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | −4.47214 | −0.194257 | ||||||||
\(531\) | 2.29180 | 0.0994555 | ||||||||
\(532\) | − 0.270510i | − 0.0117281i | ||||||||
\(533\) | − 14.7082i | − 0.637083i | ||||||||
\(534\) | 6.00000 | 0.259645 | ||||||||
\(535\) | 26.1803i | 1.13187i | ||||||||
\(536\) | −5.23607 | −0.226164 | ||||||||
\(537\) | − 12.1803i | − 0.525620i | ||||||||
\(538\) | 1.52786i | 0.0658709i | ||||||||
\(539\) | −20.0132 | −0.862028 | ||||||||
\(540\) | 12.2361i | 0.526557i | ||||||||
\(541\) | −0.583592 | −0.0250906 | −0.0125453 | − | 0.999921i | \(-0.503993\pi\) | ||||
−0.0125453 | + | 0.999921i | \(0.503993\pi\) | |||||||
\(542\) | 25.8541i | 1.11053i | ||||||||
\(543\) | 25.1803i | 1.08059i | ||||||||
\(544\) | 0.854102 | 0.0366193 | ||||||||
\(545\) | 16.9098 | 0.724338 | ||||||||
\(546\) | 7.85410 | 0.336125 | ||||||||
\(547\) | 7.85410i | 0.335817i | 0.985803 | + | 0.167909i | \(0.0537013\pi\) | ||||
−0.985803 | + | 0.167909i | \(0.946299\pi\) | |||||||
\(548\) | − 13.8541i | − 0.591818i | ||||||||
\(549\) | 1.09017 | 0.0465273 | ||||||||
\(550\) | − 28.0902i | − 1.19777i | ||||||||
\(551\) | 1.41641 | 0.0603410 | ||||||||
\(552\) | 1.61803i | 0.0688681i | ||||||||
\(553\) | 14.2918i | 0.607749i | ||||||||
\(554\) | 7.52786 | 0.319828 | ||||||||
\(555\) | 35.1246 | 1.49096 | ||||||||
\(556\) | 4.29180 | 0.182013 | ||||||||
\(557\) | 30.0000i | 1.27114i | 0.772043 | + | 0.635570i | \(0.219235\pi\) | ||||
−0.772043 | + | 0.635570i | \(0.780765\pi\) | |||||||
\(558\) | − 0.819660i | − 0.0346990i | ||||||||
\(559\) | −29.4164 | −1.24418 | ||||||||
\(560\) | − 4.14590i | − 0.175196i | ||||||||
\(561\) | −7.76393 | −0.327793 | ||||||||
\(562\) | 30.6525i | 1.29300i | ||||||||
\(563\) | − 15.7082i | − 0.662022i | −0.943627 | − | 0.331011i | \(-0.892610\pi\) | ||||
0.943627 | − | 0.331011i | \(-0.107390\pi\) | |||||||
\(564\) | −2.76393 | −0.116383 | ||||||||
\(565\) | 30.0000i | 1.26211i | ||||||||
\(566\) | −20.9443 | −0.880353 | ||||||||
\(567\) | − 14.2918i | − 0.600199i | ||||||||
\(568\) | − 0.381966i | − 0.0160269i | ||||||||
\(569\) | 16.3607 | 0.685875 | 0.342938 | − | 0.939358i | \(-0.388578\pi\) | ||||
0.342938 | + | 0.939358i | \(0.388578\pi\) | |||||||
\(570\) | 0.527864 | 0.0221098 | ||||||||
\(571\) | 8.27051 | 0.346110 | 0.173055 | − | 0.984912i | \(-0.444636\pi\) | ||||
0.173055 | + | 0.984912i | \(0.444636\pi\) | |||||||
\(572\) | 14.7082i | 0.614981i | ||||||||
\(573\) | 41.1246i | 1.71801i | ||||||||
\(574\) | 10.4164 | 0.434772 | ||||||||
\(575\) | 5.00000i | 0.208514i | ||||||||
\(576\) | −0.381966 | −0.0159153 | ||||||||
\(577\) | 39.7082i | 1.65307i | 0.562882 | + | 0.826537i | \(0.309692\pi\) | ||||
−0.562882 | + | 0.826537i | \(0.690308\pi\) | |||||||
\(578\) | 16.2705i | 0.676764i | ||||||||
\(579\) | 25.4164 | 1.05627 | ||||||||
\(580\) | 21.7082 | 0.901384 | ||||||||
\(581\) | −14.2918 | −0.592924 | ||||||||
\(582\) | 21.0902i | 0.874216i | ||||||||
\(583\) | 11.2361i | 0.465350i | ||||||||
\(584\) | −16.4721 | −0.681622 | ||||||||
\(585\) | − 2.23607i | − 0.0924500i | ||||||||
\(586\) | 14.2918 | 0.590389 | ||||||||
\(587\) | 8.85410i | 0.365448i | 0.983164 | + | 0.182724i | \(0.0584915\pi\) | ||||
−0.983164 | + | 0.182724i | \(0.941509\pi\) | |||||||
\(588\) | − 5.76393i | − 0.237701i | ||||||||
\(589\) | −0.313082 | −0.0129003 | ||||||||
\(590\) | − 13.4164i | − 0.552345i | ||||||||
\(591\) | −33.2705 | −1.36857 | ||||||||
\(592\) | 9.70820i | 0.399005i | ||||||||
\(593\) | 6.58359i | 0.270356i | 0.990821 | + | 0.135178i | \(0.0431606\pi\) | ||||
−0.990821 | + | 0.135178i | \(0.956839\pi\) | |||||||
\(594\) | 30.7426 | 1.26139 | ||||||||
\(595\) | −3.54102 | −0.145168 | ||||||||
\(596\) | −2.61803 | −0.107239 | ||||||||
\(597\) | − 18.4721i | − 0.756014i | ||||||||
\(598\) | − 2.61803i | − 0.107059i | ||||||||
\(599\) | −23.6180 | −0.965007 | −0.482503 | − | 0.875894i | \(-0.660272\pi\) | ||||
−0.482503 | + | 0.875894i | \(0.660272\pi\) | |||||||
\(600\) | 8.09017 | 0.330280 | ||||||||
\(601\) | −9.85410 | −0.401957 | −0.200979 | − | 0.979596i | \(-0.564412\pi\) | ||||
−0.200979 | + | 0.979596i | \(0.564412\pi\) | |||||||
\(602\) | − 20.8328i | − 0.849082i | ||||||||
\(603\) | − 2.00000i | − 0.0814463i | ||||||||
\(604\) | −14.2705 | −0.580659 | ||||||||
\(605\) | −45.9787 | −1.86930 | ||||||||
\(606\) | 2.47214 | 0.100424 | ||||||||
\(607\) | − 21.0557i | − 0.854626i | −0.904104 | − | 0.427313i | \(-0.859460\pi\) | ||||
0.904104 | − | 0.427313i | \(-0.140540\pi\) | |||||||
\(608\) | 0.145898i | 0.00591695i | ||||||||
\(609\) | −29.1246 | −1.18019 | ||||||||
\(610\) | − 6.38197i | − 0.258398i | ||||||||
\(611\) | 4.47214 | 0.180923 | ||||||||
\(612\) | 0.326238i | 0.0131874i | ||||||||
\(613\) | − 0.763932i | − 0.0308549i | −0.999881 | − | 0.0154275i | \(-0.995089\pi\) | ||||
0.999881 | − | 0.0154275i | \(-0.00491091\pi\) | |||||||
\(614\) | 16.8541 | 0.680176 | ||||||||
\(615\) | 20.3262i | 0.819633i | ||||||||
\(616\) | −10.4164 | −0.419689 | ||||||||
\(617\) | 2.56231i | 0.103155i | 0.998669 | + | 0.0515773i | \(0.0164248\pi\) | ||||
−0.998669 | + | 0.0515773i | \(0.983575\pi\) | |||||||
\(618\) | − 17.5623i | − 0.706460i | ||||||||
\(619\) | 27.8541 | 1.11955 | 0.559775 | − | 0.828644i | \(-0.310887\pi\) | ||||
0.559775 | + | 0.828644i | \(0.310887\pi\) | |||||||
\(620\) | −4.79837 | −0.192707 | ||||||||
\(621\) | −5.47214 | −0.219589 | ||||||||
\(622\) | − 22.4721i | − 0.901051i | ||||||||
\(623\) | − 6.87539i | − 0.275457i | ||||||||
\(624\) | −4.23607 | −0.169578 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | −25.8541 | −1.03334 | ||||||||
\(627\) | − 1.32624i | − 0.0529648i | ||||||||
\(628\) | 2.29180i | 0.0914526i | ||||||||
\(629\) | 8.29180 | 0.330616 | ||||||||
\(630\) | 1.58359 | 0.0630918 | ||||||||
\(631\) | −23.4164 | −0.932192 | −0.466096 | − | 0.884734i | \(-0.654340\pi\) | ||||
−0.466096 | + | 0.884734i | \(0.654340\pi\) | |||||||
\(632\) | − 7.70820i | − 0.306616i | ||||||||
\(633\) | − 12.4721i | − 0.495723i | ||||||||
\(634\) | −7.27051 | −0.288749 | ||||||||
\(635\) | − 21.7082i | − 0.861464i | ||||||||
\(636\) | −3.23607 | −0.128318 | ||||||||
\(637\) | 9.32624i | 0.369519i | ||||||||
\(638\) | − 54.5410i | − 2.15930i | ||||||||
\(639\) | 0.145898 | 0.00577164 | ||||||||
\(640\) | 2.23607i | 0.0883883i | ||||||||
\(641\) | −0.652476 | −0.0257712 | −0.0128856 | − | 0.999917i | \(-0.504102\pi\) | ||||
−0.0128856 | + | 0.999917i | \(0.504102\pi\) | |||||||
\(642\) | 18.9443i | 0.747671i | ||||||||
\(643\) | − 41.0132i | − 1.61740i | −0.588221 | − | 0.808700i | \(-0.700171\pi\) | ||||
0.588221 | − | 0.808700i | \(-0.299829\pi\) | |||||||
\(644\) | 1.85410 | 0.0730619 | ||||||||
\(645\) | 40.6525 | 1.60069 | ||||||||
\(646\) | 0.124612 | 0.00490279 | ||||||||
\(647\) | 13.7082i | 0.538925i | 0.963011 | + | 0.269463i | \(0.0868460\pi\) | ||||
−0.963011 | + | 0.269463i | \(0.913154\pi\) | |||||||
\(648\) | 7.70820i | 0.302807i | ||||||||
\(649\) | −33.7082 | −1.32316 | ||||||||
\(650\) | −13.0902 | −0.513439 | ||||||||
\(651\) | 6.43769 | 0.252313 | ||||||||
\(652\) | 22.0344i | 0.862935i | ||||||||
\(653\) | 34.9787i | 1.36882i | 0.729096 | + | 0.684411i | \(0.239941\pi\) | ||||
−0.729096 | + | 0.684411i | \(0.760059\pi\) | |||||||
\(654\) | 12.2361 | 0.478468 | ||||||||
\(655\) | 31.7082 | 1.23894 | ||||||||
\(656\) | −5.61803 | −0.219347 | ||||||||
\(657\) | − 6.29180i | − 0.245466i | ||||||||
\(658\) | 3.16718i | 0.123470i | ||||||||
\(659\) | 17.8885 | 0.696839 | 0.348419 | − | 0.937339i | \(-0.386719\pi\) | ||||
0.348419 | + | 0.937339i | \(0.386719\pi\) | |||||||
\(660\) | − 20.3262i | − 0.791198i | ||||||||
\(661\) | −39.3951 | −1.53229 | −0.766146 | − | 0.642666i | \(-0.777828\pi\) | ||||
−0.766146 | + | 0.642666i | \(0.777828\pi\) | |||||||
\(662\) | − 25.1246i | − 0.976496i | ||||||||
\(663\) | 3.61803i | 0.140513i | ||||||||
\(664\) | 7.70820 | 0.299136 | ||||||||
\(665\) | − 0.604878i | − 0.0234562i | ||||||||
\(666\) | −3.70820 | −0.143690 | ||||||||
\(667\) | 9.70820i | 0.375903i | ||||||||
\(668\) | − 9.70820i | − 0.375622i | ||||||||
\(669\) | −36.1803 | −1.39881 | ||||||||
\(670\) | −11.7082 | −0.452327 | ||||||||
\(671\) | −16.0344 | −0.619003 | ||||||||
\(672\) | − 3.00000i | − 0.115728i | ||||||||
\(673\) | − 27.7082i | − 1.06807i | −0.845461 | − | 0.534036i | \(-0.820675\pi\) | ||||
0.845461 | − | 0.534036i | \(-0.179325\pi\) | |||||||
\(674\) | −3.38197 | −0.130268 | ||||||||
\(675\) | 27.3607i | 1.05311i | ||||||||
\(676\) | −6.14590 | −0.236381 | ||||||||
\(677\) | − 42.0000i | − 1.61419i | −0.590421 | − | 0.807096i | \(-0.701038\pi\) | ||||
0.590421 | − | 0.807096i | \(-0.298962\pi\) | |||||||
\(678\) | 21.7082i | 0.833699i | ||||||||
\(679\) | 24.1672 | 0.927451 | ||||||||
\(680\) | 1.90983 | 0.0732386 | ||||||||
\(681\) | 16.6525 | 0.638124 | ||||||||
\(682\) | 12.0557i | 0.461638i | ||||||||
\(683\) | − 10.9787i | − 0.420089i | −0.977692 | − | 0.210044i | \(-0.932639\pi\) | ||||
0.977692 | − | 0.210044i | \(-0.0673609\pi\) | |||||||
\(684\) | −0.0557281 | −0.00213082 | ||||||||
\(685\) | − 30.9787i | − 1.18364i | ||||||||
\(686\) | −19.5836 | −0.747705 | ||||||||
\(687\) | 16.1803i | 0.617318i | ||||||||
\(688\) | 11.2361i | 0.428371i | ||||||||
\(689\) | 5.23607 | 0.199478 | ||||||||
\(690\) | 3.61803i | 0.137736i | ||||||||
\(691\) | −21.1246 | −0.803618 | −0.401809 | − | 0.915723i | \(-0.631618\pi\) | ||||
−0.401809 | + | 0.915723i | \(0.631618\pi\) | |||||||
\(692\) | − 16.5623i | − 0.629604i | ||||||||
\(693\) | − 3.97871i | − 0.151139i | ||||||||
\(694\) | 14.5623 | 0.552778 | ||||||||
\(695\) | 9.59675 | 0.364025 | ||||||||
\(696\) | 15.7082 | 0.595418 | ||||||||
\(697\) | 4.79837i | 0.181751i | ||||||||
\(698\) | − 27.7082i | − 1.04877i | ||||||||
\(699\) | −34.1803 | −1.29282 | ||||||||
\(700\) | − 9.27051i | − 0.350392i | ||||||||
\(701\) | −27.9230 | −1.05464 | −0.527318 | − | 0.849668i | \(-0.676802\pi\) | ||||
−0.527318 | + | 0.849668i | \(0.676802\pi\) | |||||||
\(702\) | − 14.3262i | − 0.540709i | ||||||||
\(703\) | 1.41641i | 0.0534208i | ||||||||
\(704\) | 5.61803 | 0.211738 | ||||||||
\(705\) | −6.18034 | −0.232765 | ||||||||
\(706\) | −8.00000 | −0.301084 | ||||||||
\(707\) | − 2.83282i | − 0.106539i | ||||||||
\(708\) | − 9.70820i | − 0.364857i | ||||||||
\(709\) | −8.56231 | −0.321564 | −0.160782 | − | 0.986990i | \(-0.551402\pi\) | ||||
−0.160782 | + | 0.986990i | \(0.551402\pi\) | |||||||
\(710\) | − 0.854102i | − 0.0320539i | ||||||||
\(711\) | 2.94427 | 0.110419 | ||||||||
\(712\) | 3.70820i | 0.138971i | ||||||||
\(713\) | − 2.14590i | − 0.0803645i | ||||||||
\(714\) | −2.56231 | −0.0958919 | ||||||||
\(715\) | 32.8885i | 1.22996i | ||||||||
\(716\) | 7.52786 | 0.281329 | ||||||||
\(717\) | 16.9443i | 0.632795i | ||||||||
\(718\) | 13.4164i | 0.500696i | ||||||||
\(719\) | −23.4508 | −0.874569 | −0.437285 | − | 0.899323i | \(-0.644060\pi\) | ||||
−0.437285 | + | 0.899323i | \(0.644060\pi\) | |||||||
\(720\) | −0.854102 | −0.0318305 | ||||||||
\(721\) | −20.1246 | −0.749480 | ||||||||
\(722\) | − 18.9787i | − 0.706315i | ||||||||
\(723\) | − 3.23607i | − 0.120351i | ||||||||
\(724\) | −15.5623 | −0.578369 | ||||||||
\(725\) | 48.5410 | 1.80277 | ||||||||
\(726\) | −33.2705 | −1.23478 | ||||||||
\(727\) | − 40.7426i | − 1.51106i | −0.655113 | − | 0.755531i | \(-0.727379\pi\) | ||||
0.655113 | − | 0.755531i | \(-0.272621\pi\) | |||||||
\(728\) | 4.85410i | 0.179905i | ||||||||
\(729\) | −29.5066 | −1.09284 | ||||||||
\(730\) | −36.8328 | −1.36324 | ||||||||
\(731\) | 9.59675 | 0.354949 | ||||||||
\(732\) | − 4.61803i | − 0.170687i | ||||||||
\(733\) | 0.111456i | 0.00411673i | 0.999998 | + | 0.00205836i | \(0.000655198\pi\) | ||||
−0.999998 | + | 0.00205836i | \(0.999345\pi\) | |||||||
\(734\) | 12.0000 | 0.442928 | ||||||||
\(735\) | − 12.8885i | − 0.475401i | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 29.4164i | 1.08357i | ||||||||
\(738\) | − 2.14590i | − 0.0789916i | ||||||||
\(739\) | −34.5410 | −1.27061 | −0.635306 | − | 0.772261i | \(-0.719126\pi\) | ||||
−0.635306 | + | 0.772261i | \(0.719126\pi\) | |||||||
\(740\) | 21.7082i | 0.798009i | ||||||||
\(741\) | −0.618034 | −0.0227040 | ||||||||
\(742\) | 3.70820i | 0.136132i | ||||||||
\(743\) | 36.9787i | 1.35662i | 0.734777 | + | 0.678309i | \(0.237287\pi\) | ||||
−0.734777 | + | 0.678309i | \(0.762713\pi\) | |||||||
\(744\) | −3.47214 | −0.127295 | ||||||||
\(745\) | −5.85410 | −0.214478 | ||||||||
\(746\) | 20.9443 | 0.766824 | ||||||||
\(747\) | 2.94427i | 0.107725i | ||||||||
\(748\) | − 4.79837i | − 0.175446i | ||||||||
\(749\) | 21.7082 | 0.793201 | ||||||||
\(750\) | 18.0902 | 0.660560 | ||||||||
\(751\) | −0.875388 | −0.0319434 | −0.0159717 | − | 0.999872i | \(-0.505084\pi\) | ||||
−0.0159717 | + | 0.999872i | \(0.505084\pi\) | |||||||
\(752\) | − 1.70820i | − 0.0622918i | ||||||||
\(753\) | − 27.1803i | − 0.990507i | ||||||||
\(754\) | −25.4164 | −0.925611 | ||||||||
\(755\) | −31.9098 | −1.16132 | ||||||||
\(756\) | 10.1459 | 0.369003 | ||||||||
\(757\) | − 29.0132i | − 1.05450i | −0.849710 | − | 0.527251i | \(-0.823223\pi\) | ||||
0.849710 | − | 0.527251i | \(-0.176777\pi\) | |||||||
\(758\) | 24.2705i | 0.881545i | ||||||||
\(759\) | 9.09017 | 0.329952 | ||||||||
\(760\) | 0.326238i | 0.0118339i | ||||||||
\(761\) | 26.5066 | 0.960863 | 0.480431 | − | 0.877032i | \(-0.340480\pi\) | ||||
0.480431 | + | 0.877032i | \(0.340480\pi\) | |||||||
\(762\) | − 15.7082i | − 0.569048i | ||||||||
\(763\) | − 14.0213i | − 0.507605i | ||||||||
\(764\) | −25.4164 | −0.919533 | ||||||||
\(765\) | 0.729490i | 0.0263748i | ||||||||
\(766\) | −0.583592 | −0.0210860 | ||||||||
\(767\) | 15.7082i | 0.567190i | ||||||||
\(768\) | 1.61803i | 0.0583858i | ||||||||
\(769\) | 47.7082 | 1.72040 | 0.860201 | − | 0.509955i | \(-0.170338\pi\) | ||||
0.860201 | + | 0.509955i | \(0.170338\pi\) | |||||||
\(770\) | −23.2918 | −0.839378 | ||||||||
\(771\) | −18.4721 | −0.665258 | ||||||||
\(772\) | 15.7082i | 0.565351i | ||||||||
\(773\) | 14.0000i | 0.503545i | 0.967786 | + | 0.251773i | \(0.0810135\pi\) | ||||
−0.967786 | + | 0.251773i | \(0.918987\pi\) | |||||||
\(774\) | −4.29180 | −0.154265 | ||||||||
\(775\) | −10.7295 | −0.385415 | ||||||||
\(776\) | −13.0344 | −0.467909 | ||||||||
\(777\) | − 29.1246i | − 1.04484i | ||||||||
\(778\) | 21.3262i | 0.764583i | ||||||||
\(779\) | −0.819660 | −0.0293674 | ||||||||
\(780\) | −9.47214 | −0.339157 | ||||||||
\(781\) | −2.14590 | −0.0767863 | ||||||||
\(782\) | 0.854102i | 0.0305426i | ||||||||
\(783\) | 53.1246i | 1.89852i | ||||||||
\(784\) | 3.56231 | 0.127225 | ||||||||
\(785\) | 5.12461i | 0.182905i | ||||||||
\(786\) | 22.9443 | 0.818395 | ||||||||
\(787\) | − 4.58359i | − 0.163387i | −0.996657 | − | 0.0816937i | \(-0.973967\pi\) | ||||
0.996657 | − | 0.0816937i | \(-0.0260329\pi\) | |||||||
\(788\) | − 20.5623i | − 0.732502i | ||||||||
\(789\) | 29.5623 | 1.05245 | ||||||||
\(790\) | − 17.2361i | − 0.613232i | ||||||||
\(791\) | 24.8754 | 0.884467 | ||||||||
\(792\) | 2.14590i | 0.0762512i | ||||||||
\(793\) | 7.47214i | 0.265343i | ||||||||
\(794\) | 15.4377 | 0.547863 | ||||||||
\(795\) | −7.23607 | −0.256637 | ||||||||
\(796\) | 11.4164 | 0.404644 | ||||||||
\(797\) | − 45.4164i | − 1.60873i | −0.594134 | − | 0.804366i | \(-0.702505\pi\) | ||||
0.594134 | − | 0.804366i | \(-0.297495\pi\) | |||||||
\(798\) | − 0.437694i | − 0.0154942i | ||||||||
\(799\) | −1.45898 | −0.0516150 | ||||||||
\(800\) | 5.00000i | 0.176777i | ||||||||
\(801\) | −1.41641 | −0.0500463 | ||||||||
\(802\) | − 25.5279i | − 0.901420i | ||||||||
\(803\) | 92.5410i | 3.26570i | ||||||||
\(804\) | −8.47214 | −0.298789 | ||||||||
\(805\) | 4.14590 | 0.146124 | ||||||||
\(806\) | 5.61803 | 0.197887 | ||||||||
\(807\) | 2.47214i | 0.0870233i | ||||||||
\(808\) | 1.52786i | 0.0537501i | ||||||||
\(809\) | 42.1591 | 1.48223 | 0.741117 | − | 0.671376i | \(-0.234297\pi\) | ||||
0.741117 | + | 0.671376i | \(0.234297\pi\) | |||||||
\(810\) | 17.2361i | 0.605614i | ||||||||
\(811\) | 5.70820 | 0.200442 | 0.100221 | − | 0.994965i | \(-0.468045\pi\) | ||||
0.100221 | + | 0.994965i | \(0.468045\pi\) | |||||||
\(812\) | − 18.0000i | − 0.631676i | ||||||||
\(813\) | 41.8328i | 1.46714i | ||||||||
\(814\) | 54.5410 | 1.91166 | ||||||||
\(815\) | 49.2705i | 1.72587i | ||||||||
\(816\) | 1.38197 | 0.0483785 | ||||||||
\(817\) | 1.63932i | 0.0573526i | ||||||||
\(818\) | − 13.5623i | − 0.474195i | ||||||||
\(819\) | −1.85410 | −0.0647876 | ||||||||
\(820\) | −12.5623 | −0.438695 | ||||||||
\(821\) | 14.9443 | 0.521559 | 0.260779 | − | 0.965398i | \(-0.416020\pi\) | ||||
0.260779 | + | 0.965398i | \(0.416020\pi\) | |||||||
\(822\) | − 22.4164i | − 0.781862i | ||||||||
\(823\) | − 32.8328i | − 1.14448i | −0.820086 | − | 0.572240i | \(-0.806075\pi\) | ||||
0.820086 | − | 0.572240i | \(-0.193925\pi\) | |||||||
\(824\) | 10.8541 | 0.378121 | ||||||||
\(825\) | − 45.4508i | − 1.58240i | ||||||||
\(826\) | −11.1246 | −0.387075 | ||||||||
\(827\) | 32.2492i | 1.12142i | 0.828014 | + | 0.560708i | \(0.189471\pi\) | ||||
−0.828014 | + | 0.560708i | \(0.810529\pi\) | |||||||
\(828\) | − 0.381966i | − 0.0132742i | ||||||||
\(829\) | 34.5410 | 1.19966 | 0.599830 | − | 0.800128i | \(-0.295235\pi\) | ||||
0.599830 | + | 0.800128i | \(0.295235\pi\) | |||||||
\(830\) | 17.2361 | 0.598273 | ||||||||
\(831\) | 12.1803 | 0.422531 | ||||||||
\(832\) | − 2.61803i | − 0.0907640i | ||||||||
\(833\) | − 3.04257i | − 0.105419i | ||||||||
\(834\) | 6.94427 | 0.240460 | ||||||||
\(835\) | − 21.7082i | − 0.751243i | ||||||||
\(836\) | 0.819660 | 0.0283485 | ||||||||
\(837\) | − 11.7426i | − 0.405885i | ||||||||
\(838\) | 29.8885i | 1.03248i | ||||||||
\(839\) | 11.2361 | 0.387912 | 0.193956 | − | 0.981010i | \(-0.437868\pi\) | ||||
0.193956 | + | 0.981010i | \(0.437868\pi\) | |||||||
\(840\) | − 6.70820i | − 0.231455i | ||||||||
\(841\) | 65.2492 | 2.24997 | ||||||||
\(842\) | 0.145898i | 0.00502798i | ||||||||
\(843\) | 49.5967i | 1.70820i | ||||||||
\(844\) | 7.70820 | 0.265327 | ||||||||
\(845\) | −13.7426 | −0.472761 | ||||||||
\(846\) | 0.652476 | 0.0224326 | ||||||||
\(847\) | 38.1246i | 1.30998i | ||||||||
\(848\) | − 2.00000i | − 0.0686803i | ||||||||
\(849\) | −33.8885 | −1.16305 | ||||||||
\(850\) | 4.27051 | 0.146477 | ||||||||
\(851\) | −9.70820 | −0.332793 | ||||||||
\(852\) | − 0.618034i | − 0.0211735i | ||||||||
\(853\) | 0.214782i | 0.00735399i | 0.999993 | + | 0.00367699i | \(0.00117043\pi\) | ||||
−0.999993 | + | 0.00367699i | \(0.998830\pi\) | |||||||
\(854\) | −5.29180 | −0.181082 | ||||||||
\(855\) | −0.124612 | −0.00426163 | ||||||||
\(856\) | −11.7082 | −0.400178 | ||||||||
\(857\) | 36.0000i | 1.22974i | 0.788630 | + | 0.614868i | \(0.210791\pi\) | ||||
−0.788630 | + | 0.614868i | \(0.789209\pi\) | |||||||
\(858\) | 23.7984i | 0.812463i | ||||||||
\(859\) | −4.00000 | −0.136478 | −0.0682391 | − | 0.997669i | \(-0.521738\pi\) | ||||
−0.0682391 | + | 0.997669i | \(0.521738\pi\) | |||||||
\(860\) | 25.1246i | 0.856742i | ||||||||
\(861\) | 16.8541 | 0.574386 | ||||||||
\(862\) | − 11.2361i | − 0.382702i | ||||||||
\(863\) | 24.0000i | 0.816970i | 0.912765 | + | 0.408485i | \(0.133943\pi\) | ||||
−0.912765 | + | 0.408485i | \(0.866057\pi\) | |||||||
\(864\) | −5.47214 | −0.186166 | ||||||||
\(865\) | − 37.0344i | − 1.25921i | ||||||||
\(866\) | 27.3820 | 0.930477 | ||||||||
\(867\) | 26.3262i | 0.894086i | ||||||||
\(868\) | 3.97871i | 0.135046i | ||||||||
\(869\) | −43.3050 | −1.46902 | ||||||||
\(870\) | 35.1246 | 1.19084 | ||||||||
\(871\) | 13.7082 | 0.464485 | ||||||||
\(872\) | 7.56231i | 0.256092i | ||||||||
\(873\) | − 4.97871i | − 0.168504i | ||||||||
\(874\) | −0.145898 | −0.00493507 | ||||||||
\(875\) | − 20.7295i | − 0.700785i | ||||||||
\(876\) | −26.6525 | −0.900504 | ||||||||
\(877\) | − 25.6869i | − 0.867386i | −0.901061 | − | 0.433693i | \(-0.857210\pi\) | ||||
0.901061 | − | 0.433693i | \(-0.142790\pi\) | |||||||
\(878\) | − 33.2705i | − 1.12283i | ||||||||
\(879\) | 23.1246 | 0.779974 | ||||||||
\(880\) | 12.5623 | 0.423475 | ||||||||
\(881\) | −51.7082 | −1.74209 | −0.871047 | − | 0.491200i | \(-0.836558\pi\) | ||||
−0.871047 | + | 0.491200i | \(0.836558\pi\) | |||||||
\(882\) | 1.36068i | 0.0458165i | ||||||||
\(883\) | − 51.2705i | − 1.72539i | −0.505725 | − | 0.862695i | \(-0.668775\pi\) | ||||
0.505725 | − | 0.862695i | \(-0.331225\pi\) | |||||||
\(884\) | −2.23607 | −0.0752071 | ||||||||
\(885\) | − 21.7082i | − 0.729713i | ||||||||
\(886\) | −0.145898 | −0.00490154 | ||||||||
\(887\) | − 30.5410i | − 1.02547i | −0.858548 | − | 0.512734i | \(-0.828633\pi\) | ||||
0.858548 | − | 0.512734i | \(-0.171367\pi\) | |||||||
\(888\) | 15.7082i | 0.527133i | ||||||||
\(889\) | −18.0000 | −0.603701 | ||||||||
\(890\) | 8.29180i | 0.277942i | ||||||||
\(891\) | 43.3050 | 1.45077 | ||||||||
\(892\) | − 22.3607i | − 0.748691i | ||||||||
\(893\) | − 0.249224i | − 0.00833995i | ||||||||
\(894\) | −4.23607 | −0.141675 | ||||||||
\(895\) | 16.8328 | 0.562659 | ||||||||
\(896\) | 1.85410 | 0.0619412 | ||||||||
\(897\) | − 4.23607i | − 0.141438i | ||||||||
\(898\) | 17.5623i | 0.586062i | ||||||||
\(899\) | −20.8328 | −0.694813 | ||||||||
\(900\) | −1.90983 | −0.0636610 | ||||||||
\(901\) | −1.70820 | −0.0569085 | ||||||||
\(902\) | 31.5623i | 1.05091i | ||||||||
\(903\) | − 33.7082i | − 1.12174i | ||||||||
\(904\) | −13.4164 | −0.446223 | ||||||||
\(905\) | −34.7984 | −1.15674 | ||||||||
\(906\) | −23.0902 | −0.767120 | ||||||||
\(907\) | 36.5410i | 1.21332i | 0.794960 | + | 0.606662i | \(0.207492\pi\) | ||||
−0.794960 | + | 0.606662i | \(0.792508\pi\) | |||||||
\(908\) | 10.2918i | 0.341545i | ||||||||
\(909\) | −0.583592 | −0.0193565 | ||||||||
\(910\) | 10.8541i | 0.359810i | ||||||||
\(911\) | −22.3607 | −0.740842 | −0.370421 | − | 0.928864i | \(-0.620787\pi\) | ||||
−0.370421 | + | 0.928864i | \(0.620787\pi\) | |||||||
\(912\) | 0.236068i | 0.00781699i | ||||||||
\(913\) | − 43.3050i | − 1.43318i | ||||||||
\(914\) | 1.41641 | 0.0468506 | ||||||||
\(915\) | − 10.3262i | − 0.341375i | ||||||||
\(916\) | −10.0000 | −0.330409 | ||||||||
\(917\) | − 26.2918i | − 0.868232i | ||||||||
\(918\) | 4.67376i | 0.154257i | ||||||||
\(919\) | 41.4164 | 1.36620 | 0.683101 | − | 0.730324i | \(-0.260631\pi\) | ||||
0.683101 | + | 0.730324i | \(0.260631\pi\) | |||||||
\(920\) | −2.23607 | −0.0737210 | ||||||||
\(921\) | 27.2705 | 0.898594 | ||||||||
\(922\) | 37.3050i | 1.22857i | ||||||||
\(923\) | 1.00000i | 0.0329154i | ||||||||
\(924\) | −16.8541 | −0.554459 | ||||||||
\(925\) | 48.5410i | 1.59602i | ||||||||
\(926\) | 15.7082 | 0.516204 | ||||||||
\(927\) | 4.14590i | 0.136169i | ||||||||
\(928\) | 9.70820i | 0.318687i | ||||||||
\(929\) | 43.3050 | 1.42079 | 0.710395 | − | 0.703804i | \(-0.248516\pi\) | ||||
0.710395 | + | 0.703804i | \(0.248516\pi\) | |||||||
\(930\) | −7.76393 | −0.254589 | ||||||||
\(931\) | 0.519733 | 0.0170336 | ||||||||
\(932\) | − 21.1246i | − 0.691960i | ||||||||
\(933\) | − 36.3607i | − 1.19040i | ||||||||
\(934\) | 23.1246 | 0.756660 | ||||||||
\(935\) | − 10.7295i | − 0.350892i | ||||||||
\(936\) | 1.00000 | 0.0326860 | ||||||||
\(937\) | 24.3262i | 0.794704i | 0.917666 | + | 0.397352i | \(0.130071\pi\) | ||||
−0.917666 | + | 0.397352i | \(0.869929\pi\) | |||||||
\(938\) | 9.70820i | 0.316984i | ||||||||
\(939\) | −41.8328 | −1.36516 | ||||||||
\(940\) | − 3.81966i | − 0.124584i | ||||||||
\(941\) | 27.2148 | 0.887177 | 0.443588 | − | 0.896231i | \(-0.353705\pi\) | ||||
0.443588 | + | 0.896231i | \(0.353705\pi\) | |||||||
\(942\) | 3.70820i | 0.120820i | ||||||||
\(943\) | − 5.61803i | − 0.182948i | ||||||||
\(944\) | 6.00000 | 0.195283 | ||||||||
\(945\) | 22.6869 | 0.738005 | ||||||||
\(946\) | 63.1246 | 2.05236 | ||||||||
\(947\) | − 26.3951i | − 0.857726i | −0.903369 | − | 0.428863i | \(-0.858914\pi\) | ||||
0.903369 | − | 0.428863i | \(-0.141086\pi\) | |||||||
\(948\) | − 12.4721i | − 0.405076i | ||||||||
\(949\) | 43.1246 | 1.39988 | ||||||||
\(950\) | 0.729490i | 0.0236678i | ||||||||
\(951\) | −11.7639 | −0.381472 | ||||||||
\(952\) | − 1.58359i | − 0.0513245i | ||||||||
\(953\) | 37.3951i | 1.21135i | 0.795713 | + | 0.605673i | \(0.207096\pi\) | ||||
−0.795713 | + | 0.605673i | \(0.792904\pi\) | |||||||
\(954\) | 0.763932 | 0.0247332 | ||||||||
\(955\) | −56.8328 | −1.83907 | ||||||||
\(956\) | −10.4721 | −0.338693 | ||||||||
\(957\) | − 88.2492i | − 2.85269i | ||||||||
\(958\) | 28.4721i | 0.919893i | ||||||||
\(959\) | −25.6869 | −0.829474 | ||||||||
\(960\) | 3.61803i | 0.116772i | ||||||||
\(961\) | −26.3951 | −0.851456 | ||||||||
\(962\) | − 25.4164i | − 0.819458i | ||||||||
\(963\) | − 4.47214i | − 0.144113i | ||||||||
\(964\) | 2.00000 | 0.0644157 | ||||||||
\(965\) | 35.1246i | 1.13070i | ||||||||
\(966\) | 3.00000 | 0.0965234 | ||||||||
\(967\) | − 29.2361i | − 0.940169i | −0.882622 | − | 0.470084i | \(-0.844224\pi\) | ||||
0.882622 | − | 0.470084i | \(-0.155776\pi\) | |||||||
\(968\) | − 20.5623i | − 0.660898i | ||||||||
\(969\) | 0.201626 | 0.00647716 | ||||||||
\(970\) | −29.1459 | −0.935818 | ||||||||
\(971\) | 19.1459 | 0.614421 | 0.307211 | − | 0.951642i | \(-0.400604\pi\) | ||||
0.307211 | + | 0.951642i | \(0.400604\pi\) | |||||||
\(972\) | − 3.94427i | − 0.126513i | ||||||||
\(973\) | − 7.95743i | − 0.255103i | ||||||||
\(974\) | −8.29180 | −0.265686 | ||||||||
\(975\) | −21.1803 | −0.678314 | ||||||||
\(976\) | 2.85410 | 0.0913576 | ||||||||
\(977\) | − 1.27051i | − 0.0406472i | −0.999793 | − | 0.0203236i | \(-0.993530\pi\) | ||||
0.999793 | − | 0.0203236i | \(-0.00646965\pi\) | |||||||
\(978\) | 35.6525i | 1.14004i | ||||||||
\(979\) | 20.8328 | 0.665820 | ||||||||
\(980\) | 7.96556 | 0.254450 | ||||||||
\(981\) | −2.88854 | −0.0922241 | ||||||||
\(982\) | 26.8328i | 0.856270i | ||||||||
\(983\) | − 47.3951i | − 1.51167i | −0.654762 | − | 0.755835i | \(-0.727231\pi\) | ||||
0.654762 | − | 0.755835i | \(-0.272769\pi\) | |||||||
\(984\) | −9.09017 | −0.289784 | ||||||||
\(985\) | − 45.9787i | − 1.46500i | ||||||||
\(986\) | 8.29180 | 0.264065 | ||||||||
\(987\) | 5.12461i | 0.163118i | ||||||||
\(988\) | − 0.381966i | − 0.0121520i | ||||||||
\(989\) | −11.2361 | −0.357286 | ||||||||
\(990\) | 4.79837i | 0.152502i | ||||||||
\(991\) | 17.7295 | 0.563196 | 0.281598 | − | 0.959532i | \(-0.409136\pi\) | ||||
0.281598 | + | 0.959532i | \(0.409136\pi\) | |||||||
\(992\) | − 2.14590i | − 0.0681323i | ||||||||
\(993\) | − 40.6525i | − 1.29007i | ||||||||
\(994\) | −0.708204 | −0.0224629 | ||||||||
\(995\) | 25.5279 | 0.809288 | ||||||||
\(996\) | 12.4721 | 0.395195 | ||||||||
\(997\) | 62.7214i | 1.98641i | 0.116398 | + | 0.993203i | \(0.462865\pi\) | ||||
−0.116398 | + | 0.993203i | \(0.537135\pi\) | |||||||
\(998\) | 15.4164i | 0.487998i | ||||||||
\(999\) | −53.1246 | −1.68079 |
(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 | 230.2.b.a.139.4 | yes | 4 | |
3.2 | odd | 2 | 2070.2.d.c.829.2 | 4 | |||
4.3 | odd | 2 | 1840.2.e.c.369.1 | 4 | |||
5.2 | odd | 4 | 1150.2.a.l.1.2 | 2 | |||
5.3 | odd | 4 | 1150.2.a.n.1.1 | 2 | |||
5.4 | even | 2 | inner | 230.2.b.a.139.1 | ✓ | 4 | |
15.14 | odd | 2 | 2070.2.d.c.829.4 | 4 | |||
20.3 | even | 4 | 9200.2.a.by.1.2 | 2 | |||
20.7 | even | 4 | 9200.2.a.bo.1.1 | 2 | |||
20.19 | odd | 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 | 5.4 | even | 2 | inner | |
230.2.b.a.139.4 | yes | 4 | 1.1 | even | 1 | trivial | |
1150.2.a.l.1.2 | 2 | 5.2 | odd | 4 | |||
1150.2.a.n.1.1 | 2 | 5.3 | odd | 4 | |||
1840.2.e.c.369.1 | 4 | 4.3 | odd | 2 | |||
1840.2.e.c.369.4 | 4 | 20.19 | odd | 2 | |||
2070.2.d.c.829.2 | 4 | 3.2 | odd | 2 | |||
2070.2.d.c.829.4 | 4 | 15.14 | odd | 2 | |||
9200.2.a.bo.1.1 | 2 | 20.7 | even | 4 | |||
9200.2.a.by.1.2 | 2 | 20.3 | even | 4 |