Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2850,2,Mod(1,2850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2850, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2850.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2850.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(22.7573645761\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 570) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.311108\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2850.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 4.42864 | 1.67387 | 0.836934 | − | 0.547304i | \(-0.184346\pi\) | ||||
0.836934 | + | 0.547304i | \(0.184346\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.80642 | −1.75070 | −0.875351 | − | 0.483487i | \(-0.839370\pi\) | ||||
−0.875351 | + | 0.483487i | \(0.839370\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −6.42864 | −1.78298 | −0.891492 | − | 0.453037i | \(-0.850341\pi\) | ||||
−0.891492 | + | 0.453037i | \(0.850341\pi\) | |||||||
\(14\) | −4.42864 | −1.18360 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.37778 | −0.819233 | −0.409617 | − | 0.912258i | \(-0.634337\pi\) | ||||
−0.409617 | + | 0.912258i | \(0.634337\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.42864 | −0.966408 | ||||||||
\(22\) | 5.80642 | 1.23793 | ||||||||
\(23\) | −6.42864 | −1.34046 | −0.670232 | − | 0.742152i | \(-0.733805\pi\) | ||||
−0.670232 | + | 0.742152i | \(0.733805\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.42864 | 1.26076 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 4.42864 | 0.836934 | ||||||||
\(29\) | 7.80642 | 1.44962 | 0.724808 | − | 0.688951i | \(-0.241928\pi\) | ||||
0.724808 | + | 0.688951i | \(0.241928\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.05086 | 1.62558 | 0.812791 | − | 0.582556i | \(-0.197947\pi\) | ||||
0.812791 | + | 0.582556i | \(0.197947\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 5.80642 | 1.01077 | ||||||||
\(34\) | 3.37778 | 0.579285 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 3.67307 | 0.603849 | 0.301925 | − | 0.953332i | \(-0.402371\pi\) | ||||
0.301925 | + | 0.953332i | \(0.402371\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 6.42864 | 1.02941 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.42864 | 0.691637 | 0.345819 | − | 0.938301i | \(-0.387601\pi\) | ||||
0.345819 | + | 0.938301i | \(0.387601\pi\) | |||||||
\(42\) | 4.42864 | 0.683354 | ||||||||
\(43\) | −1.05086 | −0.160254 | −0.0801270 | − | 0.996785i | \(-0.525533\pi\) | ||||
−0.0801270 | + | 0.996785i | \(0.525533\pi\) | |||||||
\(44\) | −5.80642 | −0.875351 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.42864 | 0.947851 | ||||||||
\(47\) | 5.18421 | 0.756194 | 0.378097 | − | 0.925766i | \(-0.376578\pi\) | ||||
0.378097 | + | 0.925766i | \(0.376578\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 12.6128 | 1.80184 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.37778 | 0.472984 | ||||||||
\(52\) | −6.42864 | −0.891492 | ||||||||
\(53\) | −4.75557 | −0.653228 | −0.326614 | − | 0.945158i | \(-0.605908\pi\) | ||||
−0.326614 | + | 0.945158i | \(0.605908\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.42864 | −0.591802 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | −7.80642 | −1.02503 | ||||||||
\(59\) | 4.62222 | 0.601761 | 0.300881 | − | 0.953662i | \(-0.402719\pi\) | ||||
0.300881 | + | 0.953662i | \(0.402719\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | −9.05086 | −1.14946 | ||||||||
\(63\) | 4.42864 | 0.557956 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.80642 | −0.714721 | ||||||||
\(67\) | 2.75557 | 0.336646 | 0.168323 | − | 0.985732i | \(-0.446165\pi\) | ||||
0.168323 | + | 0.985732i | \(0.446165\pi\) | |||||||
\(68\) | −3.37778 | −0.409617 | ||||||||
\(69\) | 6.42864 | 0.773917 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.61285 | 0.903479 | 0.451739 | − | 0.892150i | \(-0.350804\pi\) | ||||
0.451739 | + | 0.892150i | \(0.350804\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 11.6128 | 1.35918 | 0.679591 | − | 0.733592i | \(-0.262157\pi\) | ||||
0.679591 | + | 0.733592i | \(0.262157\pi\) | |||||||
\(74\) | −3.67307 | −0.426986 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −25.7146 | −2.93045 | ||||||||
\(78\) | −6.42864 | −0.727900 | ||||||||
\(79\) | 2.94914 | 0.331805 | 0.165902 | − | 0.986142i | \(-0.446946\pi\) | ||||
0.165902 | + | 0.986142i | \(0.446946\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.42864 | −0.489061 | ||||||||
\(83\) | −0.133353 | −0.0146374 | −0.00731870 | − | 0.999973i | \(-0.502330\pi\) | ||||
−0.00731870 | + | 0.999973i | \(0.502330\pi\) | |||||||
\(84\) | −4.42864 | −0.483204 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.05086 | 0.113317 | ||||||||
\(87\) | −7.80642 | −0.836936 | ||||||||
\(88\) | 5.80642 | 0.618967 | ||||||||
\(89\) | −3.18421 | −0.337525 | −0.168763 | − | 0.985657i | \(-0.553977\pi\) | ||||
−0.168763 | + | 0.985657i | \(0.553977\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −28.4701 | −2.98448 | ||||||||
\(92\) | −6.42864 | −0.670232 | ||||||||
\(93\) | −9.05086 | −0.938530 | ||||||||
\(94\) | −5.18421 | −0.534710 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −11.4193 | −1.15945 | −0.579726 | − | 0.814812i | \(-0.696840\pi\) | ||||
−0.579726 | + | 0.814812i | \(0.696840\pi\) | |||||||
\(98\) | −12.6128 | −1.27409 | ||||||||
\(99\) | −5.80642 | −0.583568 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.86665 | −0.185738 | −0.0928692 | − | 0.995678i | \(-0.529604\pi\) | ||||
−0.0928692 | + | 0.995678i | \(0.529604\pi\) | |||||||
\(102\) | −3.37778 | −0.334450 | ||||||||
\(103\) | 10.6222 | 1.04664 | 0.523319 | − | 0.852137i | \(-0.324694\pi\) | ||||
0.523319 | + | 0.852137i | \(0.324694\pi\) | |||||||
\(104\) | 6.42864 | 0.630380 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.75557 | 0.461902 | ||||||||
\(107\) | 7.61285 | 0.735962 | 0.367981 | − | 0.929833i | \(-0.380049\pi\) | ||||
0.367981 | + | 0.929833i | \(0.380049\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 5.53972 | 0.530609 | 0.265304 | − | 0.964165i | \(-0.414528\pi\) | ||||
0.265304 | + | 0.964165i | \(0.414528\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.67307 | −0.348632 | ||||||||
\(112\) | 4.42864 | 0.418467 | ||||||||
\(113\) | 12.3684 | 1.16352 | 0.581761 | − | 0.813360i | \(-0.302364\pi\) | ||||
0.581761 | + | 0.813360i | \(0.302364\pi\) | |||||||
\(114\) | −1.00000 | −0.0936586 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 7.80642 | 0.724808 | ||||||||
\(117\) | −6.42864 | −0.594328 | ||||||||
\(118\) | −4.62222 | −0.425509 | ||||||||
\(119\) | −14.9590 | −1.37129 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 22.7146 | 2.06496 | ||||||||
\(122\) | −2.00000 | −0.181071 | ||||||||
\(123\) | −4.42864 | −0.399317 | ||||||||
\(124\) | 9.05086 | 0.812791 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.42864 | −0.394535 | ||||||||
\(127\) | 1.76494 | 0.156613 | 0.0783064 | − | 0.996929i | \(-0.475049\pi\) | ||||
0.0783064 | + | 0.996929i | \(0.475049\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 1.05086 | 0.0925226 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.80642 | 0.856791 | 0.428396 | − | 0.903591i | \(-0.359079\pi\) | ||||
0.428396 | + | 0.903591i | \(0.359079\pi\) | |||||||
\(132\) | 5.80642 | 0.505384 | ||||||||
\(133\) | −4.42864 | −0.384012 | ||||||||
\(134\) | −2.75557 | −0.238045 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.37778 | 0.289643 | ||||||||
\(137\) | 1.47949 | 0.126402 | 0.0632009 | − | 0.998001i | \(-0.479869\pi\) | ||||
0.0632009 | + | 0.998001i | \(0.479869\pi\) | |||||||
\(138\) | −6.42864 | −0.547242 | ||||||||
\(139\) | −4.85728 | −0.411989 | −0.205995 | − | 0.978553i | \(-0.566043\pi\) | ||||
−0.205995 | + | 0.978553i | \(0.566043\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.18421 | −0.436589 | ||||||||
\(142\) | −7.61285 | −0.638856 | ||||||||
\(143\) | 37.3274 | 3.12147 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −11.6128 | −0.961086 | ||||||||
\(147\) | −12.6128 | −1.04029 | ||||||||
\(148\) | 3.67307 | 0.301925 | ||||||||
\(149\) | 4.62222 | 0.378667 | 0.189333 | − | 0.981913i | \(-0.439367\pi\) | ||||
0.189333 | + | 0.981913i | \(0.439367\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.4193 | −0.929287 | −0.464644 | − | 0.885498i | \(-0.653818\pi\) | ||||
−0.464644 | + | 0.885498i | \(0.653818\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | −3.37778 | −0.273078 | ||||||||
\(154\) | 25.7146 | 2.07214 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.42864 | 0.514703 | ||||||||
\(157\) | 7.37778 | 0.588811 | 0.294406 | − | 0.955681i | \(-0.404878\pi\) | ||||
0.294406 | + | 0.955681i | \(0.404878\pi\) | |||||||
\(158\) | −2.94914 | −0.234621 | ||||||||
\(159\) | 4.75557 | 0.377141 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −28.4701 | −2.24376 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −5.90813 | −0.462761 | −0.231380 | − | 0.972863i | \(-0.574324\pi\) | ||||
−0.231380 | + | 0.972863i | \(0.574324\pi\) | |||||||
\(164\) | 4.42864 | 0.345819 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.133353 | 0.0103502 | ||||||||
\(167\) | 2.75557 | 0.213232 | 0.106616 | − | 0.994300i | \(-0.465998\pi\) | ||||
0.106616 | + | 0.994300i | \(0.465998\pi\) | |||||||
\(168\) | 4.42864 | 0.341677 | ||||||||
\(169\) | 28.3274 | 2.17903 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | −1.05086 | −0.0801270 | ||||||||
\(173\) | −8.10171 | −0.615962 | −0.307981 | − | 0.951393i | \(-0.599653\pi\) | ||||
−0.307981 | + | 0.951393i | \(0.599653\pi\) | |||||||
\(174\) | 7.80642 | 0.591803 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.80642 | −0.437676 | ||||||||
\(177\) | −4.62222 | −0.347427 | ||||||||
\(178\) | 3.18421 | 0.238666 | ||||||||
\(179\) | −0.235063 | −0.0175695 | −0.00878473 | − | 0.999961i | \(-0.502796\pi\) | ||||
−0.00878473 | + | 0.999961i | \(0.502796\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.3176 | 0.841228 | 0.420614 | − | 0.907240i | \(-0.361815\pi\) | ||||
0.420614 | + | 0.907240i | \(0.361815\pi\) | |||||||
\(182\) | 28.4701 | 2.11035 | ||||||||
\(183\) | −2.00000 | −0.147844 | ||||||||
\(184\) | 6.42864 | 0.473926 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 9.05086 | 0.663641 | ||||||||
\(187\) | 19.6128 | 1.43423 | ||||||||
\(188\) | 5.18421 | 0.378097 | ||||||||
\(189\) | −4.42864 | −0.322136 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.32693 | −0.457801 | −0.228900 | − | 0.973450i | \(-0.573513\pi\) | ||||
−0.228900 | + | 0.973450i | \(0.573513\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 11.5397 | 0.830647 | 0.415324 | − | 0.909674i | \(-0.363668\pi\) | ||||
0.415324 | + | 0.909674i | \(0.363668\pi\) | |||||||
\(194\) | 11.4193 | 0.819856 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.6128 | 0.900918 | ||||||||
\(197\) | 20.0415 | 1.42790 | 0.713948 | − | 0.700198i | \(-0.246905\pi\) | ||||
0.713948 | + | 0.700198i | \(0.246905\pi\) | |||||||
\(198\) | 5.80642 | 0.412645 | ||||||||
\(199\) | −20.4701 | −1.45109 | −0.725544 | − | 0.688175i | \(-0.758412\pi\) | ||||
−0.725544 | + | 0.688175i | \(0.758412\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.75557 | −0.194363 | ||||||||
\(202\) | 1.86665 | 0.131337 | ||||||||
\(203\) | 34.5718 | 2.42647 | ||||||||
\(204\) | 3.37778 | 0.236492 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −10.6222 | −0.740085 | ||||||||
\(207\) | −6.42864 | −0.446821 | ||||||||
\(208\) | −6.42864 | −0.445746 | ||||||||
\(209\) | 5.80642 | 0.401639 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.75557 | 0.189701 | 0.0948506 | − | 0.995492i | \(-0.469763\pi\) | ||||
0.0948506 | + | 0.995492i | \(0.469763\pi\) | |||||||
\(212\) | −4.75557 | −0.326614 | ||||||||
\(213\) | −7.61285 | −0.521624 | ||||||||
\(214\) | −7.61285 | −0.520404 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 40.0830 | 2.72101 | ||||||||
\(218\) | −5.53972 | −0.375197 | ||||||||
\(219\) | −11.6128 | −0.784724 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 21.7146 | 1.46068 | ||||||||
\(222\) | 3.67307 | 0.246520 | ||||||||
\(223\) | 10.6222 | 0.711316 | 0.355658 | − | 0.934616i | \(-0.384257\pi\) | ||||
0.355658 | + | 0.934616i | \(0.384257\pi\) | |||||||
\(224\) | −4.42864 | −0.295901 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.3684 | −0.822735 | ||||||||
\(227\) | 15.3461 | 1.01856 | 0.509280 | − | 0.860601i | \(-0.329912\pi\) | ||||
0.509280 | + | 0.860601i | \(0.329912\pi\) | |||||||
\(228\) | 1.00000 | 0.0662266 | ||||||||
\(229\) | −19.7146 | −1.30277 | −0.651387 | − | 0.758745i | \(-0.725813\pi\) | ||||
−0.651387 | + | 0.758745i | \(0.725813\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 25.7146 | 1.69189 | ||||||||
\(232\) | −7.80642 | −0.512517 | ||||||||
\(233\) | −29.5625 | −1.93670 | −0.968351 | − | 0.249593i | \(-0.919703\pi\) | ||||
−0.968351 | + | 0.249593i | \(0.919703\pi\) | |||||||
\(234\) | 6.42864 | 0.420253 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.62222 | 0.300881 | ||||||||
\(237\) | −2.94914 | −0.191568 | ||||||||
\(238\) | 14.9590 | 0.969647 | ||||||||
\(239\) | 1.67307 | 0.108222 | 0.0541110 | − | 0.998535i | \(-0.482768\pi\) | ||||
0.0541110 | + | 0.998535i | \(0.482768\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.9590 | −1.09242 | −0.546212 | − | 0.837647i | \(-0.683931\pi\) | ||||
−0.546212 | + | 0.837647i | \(0.683931\pi\) | |||||||
\(242\) | −22.7146 | −1.46015 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 2.00000 | 0.128037 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.42864 | 0.282360 | ||||||||
\(247\) | 6.42864 | 0.409045 | ||||||||
\(248\) | −9.05086 | −0.574730 | ||||||||
\(249\) | 0.133353 | 0.00845091 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.94914 | 0.312387 | 0.156194 | − | 0.987726i | \(-0.450078\pi\) | ||||
0.156194 | + | 0.987726i | \(0.450078\pi\) | |||||||
\(252\) | 4.42864 | 0.278978 | ||||||||
\(253\) | 37.3274 | 2.34675 | ||||||||
\(254\) | −1.76494 | −0.110742 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 5.34614 | 0.333483 | 0.166742 | − | 0.986001i | \(-0.446675\pi\) | ||||
0.166742 | + | 0.986001i | \(0.446675\pi\) | |||||||
\(258\) | −1.05086 | −0.0654234 | ||||||||
\(259\) | 16.2667 | 1.01076 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.80642 | 0.483206 | ||||||||
\(262\) | −9.80642 | −0.605843 | ||||||||
\(263\) | −9.45091 | −0.582768 | −0.291384 | − | 0.956606i | \(-0.594116\pi\) | ||||
−0.291384 | + | 0.956606i | \(0.594116\pi\) | |||||||
\(264\) | −5.80642 | −0.357361 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.42864 | 0.271537 | ||||||||
\(267\) | 3.18421 | 0.194870 | ||||||||
\(268\) | 2.75557 | 0.168323 | ||||||||
\(269\) | 2.94914 | 0.179813 | 0.0899063 | − | 0.995950i | \(-0.471343\pi\) | ||||
0.0899063 | + | 0.995950i | \(0.471343\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.9590 | 1.88062 | 0.940312 | − | 0.340313i | \(-0.110533\pi\) | ||||
0.940312 | + | 0.340313i | \(0.110533\pi\) | |||||||
\(272\) | −3.37778 | −0.204808 | ||||||||
\(273\) | 28.4701 | 1.72309 | ||||||||
\(274\) | −1.47949 | −0.0893795 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.42864 | 0.386959 | ||||||||
\(277\) | −13.0923 | −0.786643 | −0.393321 | − | 0.919401i | \(-0.628674\pi\) | ||||
−0.393321 | + | 0.919401i | \(0.628674\pi\) | |||||||
\(278\) | 4.85728 | 0.291320 | ||||||||
\(279\) | 9.05086 | 0.541861 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.5303 | 1.10543 | 0.552714 | − | 0.833371i | \(-0.313592\pi\) | ||||
0.552714 | + | 0.833371i | \(0.313592\pi\) | |||||||
\(282\) | 5.18421 | 0.308715 | ||||||||
\(283\) | −26.3783 | −1.56802 | −0.784012 | − | 0.620745i | \(-0.786830\pi\) | ||||
−0.784012 | + | 0.620745i | \(0.786830\pi\) | |||||||
\(284\) | 7.61285 | 0.451739 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −37.3274 | −2.20722 | ||||||||
\(287\) | 19.6128 | 1.15771 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −5.59057 | −0.328857 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.4193 | 0.669410 | ||||||||
\(292\) | 11.6128 | 0.679591 | ||||||||
\(293\) | −28.5718 | −1.66918 | −0.834592 | − | 0.550868i | \(-0.814297\pi\) | ||||
−0.834592 | + | 0.550868i | \(0.814297\pi\) | |||||||
\(294\) | 12.6128 | 0.735596 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.67307 | −0.213493 | ||||||||
\(297\) | 5.80642 | 0.336923 | ||||||||
\(298\) | −4.62222 | −0.267758 | ||||||||
\(299\) | 41.3274 | 2.39003 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.65386 | −0.268244 | ||||||||
\(302\) | 11.4193 | 0.657105 | ||||||||
\(303\) | 1.86665 | 0.107236 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.37778 | 0.193095 | ||||||||
\(307\) | 22.7556 | 1.29873 | 0.649364 | − | 0.760477i | \(-0.275035\pi\) | ||||
0.649364 | + | 0.760477i | \(0.275035\pi\) | |||||||
\(308\) | −25.7146 | −1.46522 | ||||||||
\(309\) | −10.6222 | −0.604277 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.32693 | −0.358767 | −0.179384 | − | 0.983779i | \(-0.557410\pi\) | ||||
−0.179384 | + | 0.983779i | \(0.557410\pi\) | |||||||
\(312\) | −6.42864 | −0.363950 | ||||||||
\(313\) | −13.7146 | −0.775193 | −0.387596 | − | 0.921829i | \(-0.626695\pi\) | ||||
−0.387596 | + | 0.921829i | \(0.626695\pi\) | |||||||
\(314\) | −7.37778 | −0.416352 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.94914 | 0.165902 | ||||||||
\(317\) | −32.5718 | −1.82942 | −0.914708 | − | 0.404115i | \(-0.867580\pi\) | ||||
−0.914708 | + | 0.404115i | \(0.867580\pi\) | |||||||
\(318\) | −4.75557 | −0.266679 | ||||||||
\(319\) | −45.3274 | −2.53785 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.61285 | −0.424908 | ||||||||
\(322\) | 28.4701 | 1.58658 | ||||||||
\(323\) | 3.37778 | 0.187945 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.90813 | 0.327221 | ||||||||
\(327\) | −5.53972 | −0.306347 | ||||||||
\(328\) | −4.42864 | −0.244531 | ||||||||
\(329\) | 22.9590 | 1.26577 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.63158 | 0.309540 | 0.154770 | − | 0.987951i | \(-0.450536\pi\) | ||||
0.154770 | + | 0.987951i | \(0.450536\pi\) | |||||||
\(332\) | −0.133353 | −0.00731870 | ||||||||
\(333\) | 3.67307 | 0.201283 | ||||||||
\(334\) | −2.75557 | −0.150778 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.42864 | −0.241602 | ||||||||
\(337\) | 5.70471 | 0.310756 | 0.155378 | − | 0.987855i | \(-0.450341\pi\) | ||||
0.155378 | + | 0.987855i | \(0.450341\pi\) | |||||||
\(338\) | −28.3274 | −1.54081 | ||||||||
\(339\) | −12.3684 | −0.671760 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −52.5531 | −2.84591 | ||||||||
\(342\) | 1.00000 | 0.0540738 | ||||||||
\(343\) | 24.8573 | 1.34217 | ||||||||
\(344\) | 1.05086 | 0.0566583 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.10171 | 0.435551 | ||||||||
\(347\) | −2.62222 | −0.140768 | −0.0703840 | − | 0.997520i | \(-0.522422\pi\) | ||||
−0.0703840 | + | 0.997520i | \(0.522422\pi\) | |||||||
\(348\) | −7.80642 | −0.418468 | ||||||||
\(349\) | −24.1017 | −1.29013 | −0.645067 | − | 0.764126i | \(-0.723171\pi\) | ||||
−0.645067 | + | 0.764126i | \(0.723171\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.42864 | 0.343135 | ||||||||
\(352\) | 5.80642 | 0.309483 | ||||||||
\(353\) | 3.64449 | 0.193977 | 0.0969883 | − | 0.995286i | \(-0.469079\pi\) | ||||
0.0969883 | + | 0.995286i | \(0.469079\pi\) | |||||||
\(354\) | 4.62222 | 0.245668 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3.18421 | −0.168763 | ||||||||
\(357\) | 14.9590 | 0.791714 | ||||||||
\(358\) | 0.235063 | 0.0124235 | ||||||||
\(359\) | 9.08250 | 0.479356 | 0.239678 | − | 0.970852i | \(-0.422958\pi\) | ||||
0.239678 | + | 0.970852i | \(0.422958\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −11.3176 | −0.594838 | ||||||||
\(363\) | −22.7146 | −1.19221 | ||||||||
\(364\) | −28.4701 | −1.49224 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.00000 | 0.104542 | ||||||||
\(367\) | 3.95851 | 0.206633 | 0.103316 | − | 0.994649i | \(-0.467055\pi\) | ||||
0.103316 | + | 0.994649i | \(0.467055\pi\) | |||||||
\(368\) | −6.42864 | −0.335116 | ||||||||
\(369\) | 4.42864 | 0.230546 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −21.0607 | −1.09342 | ||||||||
\(372\) | −9.05086 | −0.469265 | ||||||||
\(373\) | 12.5303 | 0.648797 | 0.324398 | − | 0.945921i | \(-0.394838\pi\) | ||||
0.324398 | + | 0.945921i | \(0.394838\pi\) | |||||||
\(374\) | −19.6128 | −1.01416 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.18421 | −0.267355 | ||||||||
\(377\) | −50.1847 | −2.58464 | ||||||||
\(378\) | 4.42864 | 0.227785 | ||||||||
\(379\) | 26.8385 | 1.37860 | 0.689302 | − | 0.724474i | \(-0.257917\pi\) | ||||
0.689302 | + | 0.724474i | \(0.257917\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.76494 | −0.0904204 | ||||||||
\(382\) | 6.32693 | 0.323714 | ||||||||
\(383\) | 17.5111 | 0.894777 | 0.447389 | − | 0.894340i | \(-0.352354\pi\) | ||||
0.447389 | + | 0.894340i | \(0.352354\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −11.5397 | −0.587356 | ||||||||
\(387\) | −1.05086 | −0.0534180 | ||||||||
\(388\) | −11.4193 | −0.579726 | ||||||||
\(389\) | −29.4795 | −1.49467 | −0.747335 | − | 0.664448i | \(-0.768667\pi\) | ||||
−0.747335 | + | 0.664448i | \(0.768667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.7146 | 1.09815 | ||||||||
\(392\) | −12.6128 | −0.637045 | ||||||||
\(393\) | −9.80642 | −0.494669 | ||||||||
\(394\) | −20.0415 | −1.00968 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −5.80642 | −0.291784 | ||||||||
\(397\) | 9.21279 | 0.462377 | 0.231188 | − | 0.972909i | \(-0.425739\pi\) | ||||
0.231188 | + | 0.972909i | \(0.425739\pi\) | |||||||
\(398\) | 20.4701 | 1.02607 | ||||||||
\(399\) | 4.42864 | 0.221709 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 29.2859 | 1.46247 | 0.731234 | − | 0.682126i | \(-0.238945\pi\) | ||||
0.731234 | + | 0.682126i | \(0.238945\pi\) | |||||||
\(402\) | 2.75557 | 0.137435 | ||||||||
\(403\) | −58.1847 | −2.89839 | ||||||||
\(404\) | −1.86665 | −0.0928692 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −34.5718 | −1.71577 | ||||||||
\(407\) | −21.3274 | −1.05716 | ||||||||
\(408\) | −3.37778 | −0.167225 | ||||||||
\(409\) | −17.8796 | −0.884087 | −0.442044 | − | 0.896994i | \(-0.645746\pi\) | ||||
−0.442044 | + | 0.896994i | \(0.645746\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.47949 | −0.0729781 | ||||||||
\(412\) | 10.6222 | 0.523319 | ||||||||
\(413\) | 20.4701 | 1.00727 | ||||||||
\(414\) | 6.42864 | 0.315950 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 6.42864 | 0.315190 | ||||||||
\(417\) | 4.85728 | 0.237862 | ||||||||
\(418\) | −5.80642 | −0.284001 | ||||||||
\(419\) | 30.8671 | 1.50796 | 0.753979 | − | 0.656899i | \(-0.228132\pi\) | ||||
0.753979 | + | 0.656899i | \(0.228132\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.3970 | −0.896615 | −0.448307 | − | 0.893879i | \(-0.647973\pi\) | ||||
−0.448307 | + | 0.893879i | \(0.647973\pi\) | |||||||
\(422\) | −2.75557 | −0.134139 | ||||||||
\(423\) | 5.18421 | 0.252065 | ||||||||
\(424\) | 4.75557 | 0.230951 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.61285 | 0.368844 | ||||||||
\(427\) | 8.85728 | 0.428634 | ||||||||
\(428\) | 7.61285 | 0.367981 | ||||||||
\(429\) | −37.3274 | −1.80218 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.5941 | 1.42550 | 0.712749 | − | 0.701419i | \(-0.247450\pi\) | ||||
0.712749 | + | 0.701419i | \(0.247450\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 27.2988 | 1.31190 | 0.655949 | − | 0.754805i | \(-0.272269\pi\) | ||||
0.655949 | + | 0.754805i | \(0.272269\pi\) | |||||||
\(434\) | −40.0830 | −1.92404 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.53972 | 0.265304 | ||||||||
\(437\) | 6.42864 | 0.307524 | ||||||||
\(438\) | 11.6128 | 0.554883 | ||||||||
\(439\) | 9.64143 | 0.460160 | 0.230080 | − | 0.973172i | \(-0.426101\pi\) | ||||
0.230080 | + | 0.973172i | \(0.426101\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.6128 | 0.600612 | ||||||||
\(442\) | −21.7146 | −1.03286 | ||||||||
\(443\) | 6.70519 | 0.318573 | 0.159287 | − | 0.987232i | \(-0.449081\pi\) | ||||
0.159287 | + | 0.987232i | \(0.449081\pi\) | |||||||
\(444\) | −3.67307 | −0.174316 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −10.6222 | −0.502976 | ||||||||
\(447\) | −4.62222 | −0.218623 | ||||||||
\(448\) | 4.42864 | 0.209234 | ||||||||
\(449\) | −13.9398 | −0.657859 | −0.328929 | − | 0.944355i | \(-0.606688\pi\) | ||||
−0.328929 | + | 0.944355i | \(0.606688\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25.7146 | −1.21085 | ||||||||
\(452\) | 12.3684 | 0.581761 | ||||||||
\(453\) | 11.4193 | 0.536524 | ||||||||
\(454\) | −15.3461 | −0.720230 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.00000 | −0.0468293 | ||||||||
\(457\) | 23.2257 | 1.08645 | 0.543226 | − | 0.839586i | \(-0.317203\pi\) | ||||
0.543226 | + | 0.839586i | \(0.317203\pi\) | |||||||
\(458\) | 19.7146 | 0.921201 | ||||||||
\(459\) | 3.37778 | 0.157661 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.9684 | 0.930019 | 0.465010 | − | 0.885306i | \(-0.346051\pi\) | ||||
0.465010 | + | 0.885306i | \(0.346051\pi\) | |||||||
\(462\) | −25.7146 | −1.19635 | ||||||||
\(463\) | −2.79706 | −0.129990 | −0.0649951 | − | 0.997886i | \(-0.520703\pi\) | ||||
−0.0649951 | + | 0.997886i | \(0.520703\pi\) | |||||||
\(464\) | 7.80642 | 0.362404 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 29.5625 | 1.36945 | ||||||||
\(467\) | −30.9719 | −1.43321 | −0.716604 | − | 0.697480i | \(-0.754305\pi\) | ||||
−0.716604 | + | 0.697480i | \(0.754305\pi\) | |||||||
\(468\) | −6.42864 | −0.297164 | ||||||||
\(469\) | 12.2034 | 0.563502 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.37778 | −0.339950 | ||||||||
\(472\) | −4.62222 | −0.212755 | ||||||||
\(473\) | 6.10171 | 0.280557 | ||||||||
\(474\) | 2.94914 | 0.135459 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −14.9590 | −0.685644 | ||||||||
\(477\) | −4.75557 | −0.217743 | ||||||||
\(478\) | −1.67307 | −0.0765245 | ||||||||
\(479\) | 29.8765 | 1.36509 | 0.682546 | − | 0.730843i | \(-0.260873\pi\) | ||||
0.682546 | + | 0.730843i | \(0.260873\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −23.6128 | −1.07665 | ||||||||
\(482\) | 16.9590 | 0.772461 | ||||||||
\(483\) | 28.4701 | 1.29544 | ||||||||
\(484\) | 22.7146 | 1.03248 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 17.8479 | 0.808766 | 0.404383 | − | 0.914590i | \(-0.367486\pi\) | ||||
0.404383 | + | 0.914590i | \(0.367486\pi\) | |||||||
\(488\) | −2.00000 | −0.0905357 | ||||||||
\(489\) | 5.90813 | 0.267175 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.68244 | −0.391833 | −0.195916 | − | 0.980621i | \(-0.562768\pi\) | ||||
−0.195916 | + | 0.980621i | \(0.562768\pi\) | |||||||
\(492\) | −4.42864 | −0.199658 | ||||||||
\(493\) | −26.3684 | −1.18757 | ||||||||
\(494\) | −6.42864 | −0.289238 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.05086 | 0.406395 | ||||||||
\(497\) | 33.7146 | 1.51230 | ||||||||
\(498\) | −0.133353 | −0.00597570 | ||||||||
\(499\) | 11.2257 | 0.502531 | 0.251266 | − | 0.967918i | \(-0.419153\pi\) | ||||
0.251266 | + | 0.967918i | \(0.419153\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.75557 | −0.123110 | ||||||||
\(502\) | −4.94914 | −0.220891 | ||||||||
\(503\) | −17.6543 | −0.787168 | −0.393584 | − | 0.919289i | \(-0.628765\pi\) | ||||
−0.393584 | + | 0.919289i | \(0.628765\pi\) | |||||||
\(504\) | −4.42864 | −0.197267 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −37.3274 | −1.65941 | ||||||||
\(507\) | −28.3274 | −1.25806 | ||||||||
\(508\) | 1.76494 | 0.0783064 | ||||||||
\(509\) | 14.1748 | 0.628289 | 0.314144 | − | 0.949375i | \(-0.398282\pi\) | ||||
0.314144 | + | 0.949375i | \(0.398282\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 51.4291 | 2.27509 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | −5.34614 | −0.235808 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.05086 | 0.0462613 | ||||||||
\(517\) | −30.1017 | −1.32387 | ||||||||
\(518\) | −16.2667 | −0.714718 | ||||||||
\(519\) | 8.10171 | 0.355626 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.0005 | −0.657183 | −0.328591 | − | 0.944472i | \(-0.606574\pi\) | ||||
−0.328591 | + | 0.944472i | \(0.606574\pi\) | |||||||
\(522\) | −7.80642 | −0.341678 | ||||||||
\(523\) | 40.2864 | 1.76160 | 0.880801 | − | 0.473488i | \(-0.157005\pi\) | ||||
0.880801 | + | 0.473488i | \(0.157005\pi\) | |||||||
\(524\) | 9.80642 | 0.428396 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.45091 | 0.412079 | ||||||||
\(527\) | −30.5718 | −1.33173 | ||||||||
\(528\) | 5.80642 | 0.252692 | ||||||||
\(529\) | 18.3274 | 0.796844 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.62222 | 0.200587 | ||||||||
\(532\) | −4.42864 | −0.192006 | ||||||||
\(533\) | −28.4701 | −1.23318 | ||||||||
\(534\) | −3.18421 | −0.137794 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.75557 | −0.119022 | ||||||||
\(537\) | 0.235063 | 0.0101437 | ||||||||
\(538\) | −2.94914 | −0.127147 | ||||||||
\(539\) | −73.2355 | −3.15448 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.3872 | −0.962499 | −0.481249 | − | 0.876584i | \(-0.659817\pi\) | ||||
−0.481249 | + | 0.876584i | \(0.659817\pi\) | |||||||
\(542\) | −30.9590 | −1.32980 | ||||||||
\(543\) | −11.3176 | −0.485683 | ||||||||
\(544\) | 3.37778 | 0.144821 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −28.4701 | −1.21841 | ||||||||
\(547\) | 19.7333 | 0.843735 | 0.421867 | − | 0.906658i | \(-0.361375\pi\) | ||||
0.421867 | + | 0.906658i | \(0.361375\pi\) | |||||||
\(548\) | 1.47949 | 0.0632009 | ||||||||
\(549\) | 2.00000 | 0.0853579 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.80642 | −0.332565 | ||||||||
\(552\) | −6.42864 | −0.273621 | ||||||||
\(553\) | 13.0607 | 0.555397 | ||||||||
\(554\) | 13.0923 | 0.556240 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.85728 | −0.205995 | ||||||||
\(557\) | 15.6543 | 0.663295 | 0.331648 | − | 0.943403i | \(-0.392395\pi\) | ||||
0.331648 | + | 0.943403i | \(0.392395\pi\) | |||||||
\(558\) | −9.05086 | −0.383153 | ||||||||
\(559\) | 6.75557 | 0.285730 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −19.6128 | −0.828055 | ||||||||
\(562\) | −18.5303 | −0.781656 | ||||||||
\(563\) | 36.9403 | 1.55685 | 0.778423 | − | 0.627740i | \(-0.216020\pi\) | ||||
0.778423 | + | 0.627740i | \(0.216020\pi\) | |||||||
\(564\) | −5.18421 | −0.218295 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 26.3783 | 1.10876 | ||||||||
\(567\) | 4.42864 | 0.185985 | ||||||||
\(568\) | −7.61285 | −0.319428 | ||||||||
\(569\) | −1.20294 | −0.0504300 | −0.0252150 | − | 0.999682i | \(-0.508027\pi\) | ||||
−0.0252150 | + | 0.999682i | \(0.508027\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 37.7975 | 1.58178 | 0.790889 | − | 0.611960i | \(-0.209619\pi\) | ||||
0.790889 | + | 0.611960i | \(0.209619\pi\) | |||||||
\(572\) | 37.3274 | 1.56074 | ||||||||
\(573\) | 6.32693 | 0.264311 | ||||||||
\(574\) | −19.6128 | −0.818624 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 23.2257 | 0.966898 | 0.483449 | − | 0.875372i | \(-0.339384\pi\) | ||||
0.483449 | + | 0.875372i | \(0.339384\pi\) | |||||||
\(578\) | 5.59057 | 0.232537 | ||||||||
\(579\) | −11.5397 | −0.479574 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.590573 | −0.0245011 | ||||||||
\(582\) | −11.4193 | −0.473344 | ||||||||
\(583\) | 27.6128 | 1.14361 | ||||||||
\(584\) | −11.6128 | −0.480543 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 28.5718 | 1.18029 | ||||||||
\(587\) | 16.8069 | 0.693695 | 0.346848 | − | 0.937922i | \(-0.387252\pi\) | ||||
0.346848 | + | 0.937922i | \(0.387252\pi\) | |||||||
\(588\) | −12.6128 | −0.520145 | ||||||||
\(589\) | −9.05086 | −0.372934 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.0415 | −0.824397 | ||||||||
\(592\) | 3.67307 | 0.150962 | ||||||||
\(593\) | −16.3555 | −0.671640 | −0.335820 | − | 0.941926i | \(-0.609013\pi\) | ||||
−0.335820 | + | 0.941926i | \(0.609013\pi\) | |||||||
\(594\) | −5.80642 | −0.238240 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.62222 | 0.189333 | ||||||||
\(597\) | 20.4701 | 0.837787 | ||||||||
\(598\) | −41.3274 | −1.69000 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.89829 | 0.322178 | 0.161089 | − | 0.986940i | \(-0.448499\pi\) | ||||
0.161089 | + | 0.986940i | \(0.448499\pi\) | |||||||
\(602\) | 4.65386 | 0.189677 | ||||||||
\(603\) | 2.75557 | 0.112215 | ||||||||
\(604\) | −11.4193 | −0.464644 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.86665 | −0.0758273 | ||||||||
\(607\) | 17.8479 | 0.724424 | 0.362212 | − | 0.932096i | \(-0.382022\pi\) | ||||
0.362212 | + | 0.932096i | \(0.382022\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | −34.5718 | −1.40092 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −33.3274 | −1.34828 | ||||||||
\(612\) | −3.37778 | −0.136539 | ||||||||
\(613\) | 0.622216 | 0.0251311 | 0.0125655 | − | 0.999921i | \(-0.496000\pi\) | ||||
0.0125655 | + | 0.999921i | \(0.496000\pi\) | |||||||
\(614\) | −22.7556 | −0.918340 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 25.7146 | 1.03607 | ||||||||
\(617\) | −37.4795 | −1.50887 | −0.754434 | − | 0.656376i | \(-0.772088\pi\) | ||||
−0.754434 | + | 0.656376i | \(0.772088\pi\) | |||||||
\(618\) | 10.6222 | 0.427288 | ||||||||
\(619\) | 28.6735 | 1.15249 | 0.576244 | − | 0.817278i | \(-0.304518\pi\) | ||||
0.576244 | + | 0.817278i | \(0.304518\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.42864 | 0.257972 | ||||||||
\(622\) | 6.32693 | 0.253687 | ||||||||
\(623\) | −14.1017 | −0.564973 | ||||||||
\(624\) | 6.42864 | 0.257352 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 13.7146 | 0.548144 | ||||||||
\(627\) | −5.80642 | −0.231886 | ||||||||
\(628\) | 7.37778 | 0.294406 | ||||||||
\(629\) | −12.4068 | −0.494693 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.24443 | 0.0495400 | 0.0247700 | − | 0.999693i | \(-0.492115\pi\) | ||||
0.0247700 | + | 0.999693i | \(0.492115\pi\) | |||||||
\(632\) | −2.94914 | −0.117311 | ||||||||
\(633\) | −2.75557 | −0.109524 | ||||||||
\(634\) | 32.5718 | 1.29359 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 4.75557 | 0.188571 | ||||||||
\(637\) | −81.0835 | −3.21264 | ||||||||
\(638\) | 45.3274 | 1.79453 | ||||||||
\(639\) | 7.61285 | 0.301160 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.4064 | −0.687510 | −0.343755 | − | 0.939059i | \(-0.611699\pi\) | ||||
−0.343755 | + | 0.939059i | \(0.611699\pi\) | |||||||
\(642\) | 7.61285 | 0.300455 | ||||||||
\(643\) | −35.1526 | −1.38628 | −0.693141 | − | 0.720802i | \(-0.743774\pi\) | ||||
−0.693141 | + | 0.720802i | \(0.743774\pi\) | |||||||
\(644\) | −28.4701 | −1.12188 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.37778 | −0.132897 | ||||||||
\(647\) | 34.4286 | 1.35353 | 0.676765 | − | 0.736199i | \(-0.263381\pi\) | ||||
0.676765 | + | 0.736199i | \(0.263381\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −26.8385 | −1.05350 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −40.0830 | −1.57098 | ||||||||
\(652\) | −5.90813 | −0.231380 | ||||||||
\(653\) | −4.30819 | −0.168593 | −0.0842963 | − | 0.996441i | \(-0.526864\pi\) | ||||
−0.0842963 | + | 0.996441i | \(0.526864\pi\) | |||||||
\(654\) | 5.53972 | 0.216620 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.42864 | 0.172909 | ||||||||
\(657\) | 11.6128 | 0.453060 | ||||||||
\(658\) | −22.9590 | −0.895035 | ||||||||
\(659\) | −27.0736 | −1.05464 | −0.527319 | − | 0.849667i | \(-0.676803\pi\) | ||||
−0.527319 | + | 0.849667i | \(0.676803\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −43.2543 | −1.68240 | −0.841198 | − | 0.540727i | \(-0.818149\pi\) | ||||
−0.841198 | + | 0.540727i | \(0.818149\pi\) | |||||||
\(662\) | −5.63158 | −0.218878 | ||||||||
\(663\) | −21.7146 | −0.843324 | ||||||||
\(664\) | 0.133353 | 0.00517510 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.67307 | −0.142329 | ||||||||
\(667\) | −50.1847 | −1.94316 | ||||||||
\(668\) | 2.75557 | 0.106616 | ||||||||
\(669\) | −10.6222 | −0.410679 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.6128 | −0.448309 | ||||||||
\(672\) | 4.42864 | 0.170838 | ||||||||
\(673\) | 15.0321 | 0.579446 | 0.289723 | − | 0.957111i | \(-0.406437\pi\) | ||||
0.289723 | + | 0.957111i | \(0.406437\pi\) | |||||||
\(674\) | −5.70471 | −0.219737 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 28.3274 | 1.08952 | ||||||||
\(677\) | 22.9403 | 0.881666 | 0.440833 | − | 0.897589i | \(-0.354683\pi\) | ||||
0.440833 | + | 0.897589i | \(0.354683\pi\) | |||||||
\(678\) | 12.3684 | 0.475006 | ||||||||
\(679\) | −50.5718 | −1.94077 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.3461 | −0.588065 | ||||||||
\(682\) | 52.5531 | 2.01236 | ||||||||
\(683\) | 9.77784 | 0.374139 | 0.187069 | − | 0.982347i | \(-0.440101\pi\) | ||||
0.187069 | + | 0.982347i | \(0.440101\pi\) | |||||||
\(684\) | −1.00000 | −0.0382360 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −24.8573 | −0.949055 | ||||||||
\(687\) | 19.7146 | 0.752157 | ||||||||
\(688\) | −1.05086 | −0.0400635 | ||||||||
\(689\) | 30.5718 | 1.16469 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −44.0830 | −1.67700 | −0.838498 | − | 0.544905i | \(-0.816566\pi\) | ||||
−0.838498 | + | 0.544905i | \(0.816566\pi\) | |||||||
\(692\) | −8.10171 | −0.307981 | ||||||||
\(693\) | −25.7146 | −0.976815 | ||||||||
\(694\) | 2.62222 | 0.0995379 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 7.80642 | 0.295902 | ||||||||
\(697\) | −14.9590 | −0.566612 | ||||||||
\(698\) | 24.1017 | 0.912263 | ||||||||
\(699\) | 29.5625 | 1.11816 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.7685 | −0.482259 | −0.241129 | − | 0.970493i | \(-0.577518\pi\) | ||||
−0.241129 | + | 0.970493i | \(0.577518\pi\) | |||||||
\(702\) | −6.42864 | −0.242633 | ||||||||
\(703\) | −3.67307 | −0.138532 | ||||||||
\(704\) | −5.80642 | −0.218838 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.64449 | −0.137162 | ||||||||
\(707\) | −8.26671 | −0.310901 | ||||||||
\(708\) | −4.62222 | −0.173714 | ||||||||
\(709\) | −47.5941 | −1.78743 | −0.893717 | − | 0.448631i | \(-0.851912\pi\) | ||||
−0.893717 | + | 0.448631i | \(0.851912\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.94914 | 0.110602 | ||||||||
\(712\) | 3.18421 | 0.119333 | ||||||||
\(713\) | −58.1847 | −2.17903 | ||||||||
\(714\) | −14.9590 | −0.559826 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.235063 | −0.00878473 | ||||||||
\(717\) | −1.67307 | −0.0624820 | ||||||||
\(718\) | −9.08250 | −0.338956 | ||||||||
\(719\) | −47.0005 | −1.75282 | −0.876411 | − | 0.481564i | \(-0.840069\pi\) | ||||
−0.876411 | + | 0.481564i | \(0.840069\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 47.0420 | 1.75193 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 16.9590 | 0.630712 | ||||||||
\(724\) | 11.3176 | 0.420614 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 22.7146 | 0.843016 | ||||||||
\(727\) | 52.6321 | 1.95202 | 0.976008 | − | 0.217737i | \(-0.0698674\pi\) | ||||
0.976008 | + | 0.217737i | \(0.0698674\pi\) | |||||||
\(728\) | 28.4701 | 1.05517 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.54956 | 0.131285 | ||||||||
\(732\) | −2.00000 | −0.0739221 | ||||||||
\(733\) | 27.3145 | 1.00888 | 0.504442 | − | 0.863446i | \(-0.331698\pi\) | ||||
0.504442 | + | 0.863446i | \(0.331698\pi\) | |||||||
\(734\) | −3.95851 | −0.146111 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.42864 | 0.236963 | ||||||||
\(737\) | −16.0000 | −0.589368 | ||||||||
\(738\) | −4.42864 | −0.163020 | ||||||||
\(739\) | 25.3274 | 0.931684 | 0.465842 | − | 0.884868i | \(-0.345752\pi\) | ||||
0.465842 | + | 0.884868i | \(0.345752\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.42864 | −0.236162 | ||||||||
\(742\) | 21.0607 | 0.773163 | ||||||||
\(743\) | −11.8796 | −0.435819 | −0.217909 | − | 0.975969i | \(-0.569924\pi\) | ||||
−0.217909 | + | 0.975969i | \(0.569924\pi\) | |||||||
\(744\) | 9.05086 | 0.331820 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −12.5303 | −0.458769 | ||||||||
\(747\) | −0.133353 | −0.00487913 | ||||||||
\(748\) | 19.6128 | 0.717117 | ||||||||
\(749\) | 33.7146 | 1.23190 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −45.5210 | −1.66108 | −0.830542 | − | 0.556956i | \(-0.811969\pi\) | ||||
−0.830542 | + | 0.556956i | \(0.811969\pi\) | |||||||
\(752\) | 5.18421 | 0.189049 | ||||||||
\(753\) | −4.94914 | −0.180357 | ||||||||
\(754\) | 50.1847 | 1.82762 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.42864 | −0.161068 | ||||||||
\(757\) | −51.7275 | −1.88007 | −0.940033 | − | 0.341083i | \(-0.889206\pi\) | ||||
−0.940033 | + | 0.341083i | \(0.889206\pi\) | |||||||
\(758\) | −26.8385 | −0.974820 | ||||||||
\(759\) | −37.3274 | −1.35490 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.3684 | 1.02835 | 0.514177 | − | 0.857684i | \(-0.328097\pi\) | ||||
0.514177 | + | 0.857684i | \(0.328097\pi\) | |||||||
\(762\) | 1.76494 | 0.0639369 | ||||||||
\(763\) | 24.5334 | 0.888169 | ||||||||
\(764\) | −6.32693 | −0.228900 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −17.5111 | −0.632703 | ||||||||
\(767\) | −29.7146 | −1.07293 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −0.285442 | −0.0102933 | −0.00514665 | − | 0.999987i | \(-0.501638\pi\) | ||||
−0.00514665 | + | 0.999987i | \(0.501638\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.34614 | −0.192537 | ||||||||
\(772\) | 11.5397 | 0.415324 | ||||||||
\(773\) | 49.8163 | 1.79177 | 0.895883 | − | 0.444289i | \(-0.146544\pi\) | ||||
0.895883 | + | 0.444289i | \(0.146544\pi\) | |||||||
\(774\) | 1.05086 | 0.0377722 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 11.4193 | 0.409928 | ||||||||
\(777\) | −16.2667 | −0.583565 | ||||||||
\(778\) | 29.4795 | 1.05689 | ||||||||
\(779\) | −4.42864 | −0.158672 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −44.2034 | −1.58172 | ||||||||
\(782\) | −21.7146 | −0.776511 | ||||||||
\(783\) | −7.80642 | −0.278979 | ||||||||
\(784\) | 12.6128 | 0.450459 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 9.80642 | 0.349784 | ||||||||
\(787\) | −20.7368 | −0.739188 | −0.369594 | − | 0.929193i | \(-0.620503\pi\) | ||||
−0.369594 | + | 0.929193i | \(0.620503\pi\) | |||||||
\(788\) | 20.0415 | 0.713948 | ||||||||
\(789\) | 9.45091 | 0.336461 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 54.7753 | 1.94758 | ||||||||
\(792\) | 5.80642 | 0.206322 | ||||||||
\(793\) | −12.8573 | −0.456575 | ||||||||
\(794\) | −9.21279 | −0.326950 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −20.4701 | −0.725544 | ||||||||
\(797\) | −21.3461 | −0.756119 | −0.378060 | − | 0.925781i | \(-0.623409\pi\) | ||||
−0.378060 | + | 0.925781i | \(0.623409\pi\) | |||||||
\(798\) | −4.42864 | −0.156772 | ||||||||
\(799\) | −17.5111 | −0.619500 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.18421 | −0.112508 | ||||||||
\(802\) | −29.2859 | −1.03412 | ||||||||
\(803\) | −67.4291 | −2.37952 | ||||||||
\(804\) | −2.75557 | −0.0971814 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 58.1847 | 2.04947 | ||||||||
\(807\) | −2.94914 | −0.103815 | ||||||||
\(808\) | 1.86665 | 0.0656684 | ||||||||
\(809\) | −18.6735 | −0.656527 | −0.328263 | − | 0.944586i | \(-0.606463\pi\) | ||||
−0.328263 | + | 0.944586i | \(0.606463\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.8385 | −0.521052 | −0.260526 | − | 0.965467i | \(-0.583896\pi\) | ||||
−0.260526 | + | 0.965467i | \(0.583896\pi\) | |||||||
\(812\) | 34.5718 | 1.21323 | ||||||||
\(813\) | −30.9590 | −1.08578 | ||||||||
\(814\) | 21.3274 | 0.747525 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.37778 | 0.118246 | ||||||||
\(817\) | 1.05086 | 0.0367648 | ||||||||
\(818\) | 17.8796 | 0.625144 | ||||||||
\(819\) | −28.4701 | −0.994827 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.1521 | 0.563712 | 0.281856 | − | 0.959457i | \(-0.409050\pi\) | ||||
0.281856 | + | 0.959457i | \(0.409050\pi\) | |||||||
\(822\) | 1.47949 | 0.0516033 | ||||||||
\(823\) | −47.6543 | −1.66113 | −0.830563 | − | 0.556925i | \(-0.811981\pi\) | ||||
−0.830563 | + | 0.556925i | \(0.811981\pi\) | |||||||
\(824\) | −10.6222 | −0.370042 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −20.4701 | −0.712247 | ||||||||
\(827\) | 26.1017 | 0.907645 | 0.453823 | − | 0.891092i | \(-0.350060\pi\) | ||||
0.453823 | + | 0.891092i | \(0.350060\pi\) | |||||||
\(828\) | −6.42864 | −0.223411 | ||||||||
\(829\) | −13.8894 | −0.482399 | −0.241199 | − | 0.970476i | \(-0.577541\pi\) | ||||
−0.241199 | + | 0.970476i | \(0.577541\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.0923 | 0.454168 | ||||||||
\(832\) | −6.42864 | −0.222873 | ||||||||
\(833\) | −42.6035 | −1.47612 | ||||||||
\(834\) | −4.85728 | −0.168194 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 5.80642 | 0.200819 | ||||||||
\(837\) | −9.05086 | −0.312843 | ||||||||
\(838\) | −30.8671 | −1.06629 | ||||||||
\(839\) | 31.6958 | 1.09426 | 0.547131 | − | 0.837047i | \(-0.315720\pi\) | ||||
0.547131 | + | 0.837047i | \(0.315720\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 31.9403 | 1.10139 | ||||||||
\(842\) | 18.3970 | 0.634002 | ||||||||
\(843\) | −18.5303 | −0.638219 | ||||||||
\(844\) | 2.75557 | 0.0948506 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5.18421 | −0.178237 | ||||||||
\(847\) | 100.595 | 3.45647 | ||||||||
\(848\) | −4.75557 | −0.163307 | ||||||||
\(849\) | 26.3783 | 0.905300 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −23.6128 | −0.809438 | ||||||||
\(852\) | −7.61285 | −0.260812 | ||||||||
\(853\) | 34.8702 | 1.19393 | 0.596966 | − | 0.802266i | \(-0.296373\pi\) | ||||
0.596966 | + | 0.802266i | \(0.296373\pi\) | |||||||
\(854\) | −8.85728 | −0.303090 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.61285 | −0.260202 | ||||||||
\(857\) | −33.9367 | −1.15926 | −0.579628 | − | 0.814881i | \(-0.696802\pi\) | ||||
−0.579628 | + | 0.814881i | \(0.696802\pi\) | |||||||
\(858\) | 37.3274 | 1.27434 | ||||||||
\(859\) | −37.4479 | −1.27770 | −0.638852 | − | 0.769330i | \(-0.720590\pi\) | ||||
−0.638852 | + | 0.769330i | \(0.720590\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −19.6128 | −0.668404 | ||||||||
\(862\) | −29.5941 | −1.00798 | ||||||||
\(863\) | 15.5299 | 0.528643 | 0.264322 | − | 0.964435i | \(-0.414852\pi\) | ||||
0.264322 | + | 0.964435i | \(0.414852\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −27.2988 | −0.927652 | ||||||||
\(867\) | 5.59057 | 0.189866 | ||||||||
\(868\) | 40.0830 | 1.36050 | ||||||||
\(869\) | −17.1240 | −0.580891 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.7146 | −0.600235 | ||||||||
\(872\) | −5.53972 | −0.187599 | ||||||||
\(873\) | −11.4193 | −0.386484 | ||||||||
\(874\) | −6.42864 | −0.217452 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −11.6128 | −0.392362 | ||||||||
\(877\) | −7.87649 | −0.265970 | −0.132985 | − | 0.991118i | \(-0.542456\pi\) | ||||
−0.132985 | + | 0.991118i | \(0.542456\pi\) | |||||||
\(878\) | −9.64143 | −0.325382 | ||||||||
\(879\) | 28.5718 | 0.963704 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.5496 | 1.13031 | 0.565157 | − | 0.824984i | \(-0.308816\pi\) | ||||
0.565157 | + | 0.824984i | \(0.308816\pi\) | |||||||
\(882\) | −12.6128 | −0.424697 | ||||||||
\(883\) | 50.9688 | 1.71524 | 0.857619 | − | 0.514286i | \(-0.171943\pi\) | ||||
0.857619 | + | 0.514286i | \(0.171943\pi\) | |||||||
\(884\) | 21.7146 | 0.730340 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.70519 | −0.225265 | ||||||||
\(887\) | 17.0035 | 0.570923 | 0.285461 | − | 0.958390i | \(-0.407853\pi\) | ||||
0.285461 | + | 0.958390i | \(0.407853\pi\) | |||||||
\(888\) | 3.67307 | 0.123260 | ||||||||
\(889\) | 7.81627 | 0.262149 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.80642 | −0.194523 | ||||||||
\(892\) | 10.6222 | 0.355658 | ||||||||
\(893\) | −5.18421 | −0.173483 | ||||||||
\(894\) | 4.62222 | 0.154590 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.42864 | −0.147950 | ||||||||
\(897\) | −41.3274 | −1.37988 | ||||||||
\(898\) | 13.9398 | 0.465176 | ||||||||
\(899\) | 70.6548 | 2.35647 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.0633 | 0.535146 | ||||||||
\(902\) | 25.7146 | 0.856201 | ||||||||
\(903\) | 4.65386 | 0.154871 | ||||||||
\(904\) | −12.3684 | −0.411367 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −11.4193 | −0.379380 | ||||||||
\(907\) | −21.7778 | −0.723121 | −0.361561 | − | 0.932349i | \(-0.617756\pi\) | ||||
−0.361561 | + | 0.932349i | \(0.617756\pi\) | |||||||
\(908\) | 15.3461 | 0.509280 | ||||||||
\(909\) | −1.86665 | −0.0619128 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.6351 | 0.352357 | 0.176179 | − | 0.984358i | \(-0.443626\pi\) | ||||
0.176179 | + | 0.984358i | \(0.443626\pi\) | |||||||
\(912\) | 1.00000 | 0.0331133 | ||||||||
\(913\) | 0.774305 | 0.0256257 | ||||||||
\(914\) | −23.2257 | −0.768238 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −19.7146 | −0.651387 | ||||||||
\(917\) | 43.4291 | 1.43416 | ||||||||
\(918\) | −3.37778 | −0.111483 | ||||||||
\(919\) | 12.2667 | 0.404641 | 0.202321 | − | 0.979319i | \(-0.435152\pi\) | ||||
0.202321 | + | 0.979319i | \(0.435152\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22.7556 | −0.749821 | ||||||||
\(922\) | −19.9684 | −0.657623 | ||||||||
\(923\) | −48.9403 | −1.61089 | ||||||||
\(924\) | 25.7146 | 0.845947 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.79706 | 0.0919170 | ||||||||
\(927\) | 10.6222 | 0.348879 | ||||||||
\(928\) | −7.80642 | −0.256258 | ||||||||
\(929\) | −27.9180 | −0.915959 | −0.457980 | − | 0.888963i | \(-0.651427\pi\) | ||||
−0.457980 | + | 0.888963i | \(0.651427\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.6128 | −0.413369 | ||||||||
\(932\) | −29.5625 | −0.968351 | ||||||||
\(933\) | 6.32693 | 0.207134 | ||||||||
\(934\) | 30.9719 | 1.01343 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.42864 | 0.210127 | ||||||||
\(937\) | −3.14272 | −0.102668 | −0.0513341 | − | 0.998682i | \(-0.516347\pi\) | ||||
−0.0513341 | + | 0.998682i | \(0.516347\pi\) | |||||||
\(938\) | −12.2034 | −0.398456 | ||||||||
\(939\) | 13.7146 | 0.447558 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.6227 | −0.639681 | −0.319841 | − | 0.947471i | \(-0.603629\pi\) | ||||
−0.319841 | + | 0.947471i | \(0.603629\pi\) | |||||||
\(942\) | 7.37778 | 0.240381 | ||||||||
\(943\) | −28.4701 | −0.927115 | ||||||||
\(944\) | 4.62222 | 0.150440 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.10171 | −0.198384 | ||||||||
\(947\) | 34.5018 | 1.12116 | 0.560578 | − | 0.828101i | \(-0.310579\pi\) | ||||
0.560578 | + | 0.828101i | \(0.310579\pi\) | |||||||
\(948\) | −2.94914 | −0.0957838 | ||||||||
\(949\) | −74.6548 | −2.42340 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 32.5718 | 1.05621 | ||||||||
\(952\) | 14.9590 | 0.484824 | ||||||||
\(953\) | −19.0035 | −0.615585 | −0.307793 | − | 0.951454i | \(-0.599590\pi\) | ||||
−0.307793 | + | 0.951454i | \(0.599590\pi\) | |||||||
\(954\) | 4.75557 | 0.153967 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.67307 | 0.0541110 | ||||||||
\(957\) | 45.3274 | 1.46523 | ||||||||
\(958\) | −29.8765 | −0.965266 | ||||||||
\(959\) | 6.55215 | 0.211580 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 50.9180 | 1.64252 | ||||||||
\(962\) | 23.6128 | 0.761309 | ||||||||
\(963\) | 7.61285 | 0.245321 | ||||||||
\(964\) | −16.9590 | −0.546212 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −28.4701 | −0.916011 | ||||||||
\(967\) | −17.8765 | −0.574869 | −0.287435 | − | 0.957800i | \(-0.592802\pi\) | ||||
−0.287435 | + | 0.957800i | \(0.592802\pi\) | |||||||
\(968\) | −22.7146 | −0.730074 | ||||||||
\(969\) | −3.37778 | −0.108510 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 34.0701 | 1.09336 | 0.546680 | − | 0.837341i | \(-0.315891\pi\) | ||||
0.546680 | + | 0.837341i | \(0.315891\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −21.5111 | −0.689615 | ||||||||
\(974\) | −17.8479 | −0.571884 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.00000 | 0.0640184 | ||||||||
\(977\) | −54.0830 | −1.73027 | −0.865134 | − | 0.501541i | \(-0.832767\pi\) | ||||
−0.865134 | + | 0.501541i | \(0.832767\pi\) | |||||||
\(978\) | −5.90813 | −0.188921 | ||||||||
\(979\) | 18.4889 | 0.590907 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.53972 | 0.176870 | ||||||||
\(982\) | 8.68244 | 0.277068 | ||||||||
\(983\) | 56.9403 | 1.81611 | 0.908056 | − | 0.418849i | \(-0.137566\pi\) | ||||
0.908056 | + | 0.418849i | \(0.137566\pi\) | |||||||
\(984\) | 4.42864 | 0.141180 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 26.3684 | 0.839741 | ||||||||
\(987\) | −22.9590 | −0.730793 | ||||||||
\(988\) | 6.42864 | 0.204522 | ||||||||
\(989\) | 6.75557 | 0.214815 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47.0321 | −1.49402 | −0.747012 | − | 0.664810i | \(-0.768512\pi\) | ||||
−0.747012 | + | 0.664810i | \(0.768512\pi\) | |||||||
\(992\) | −9.05086 | −0.287365 | ||||||||
\(993\) | −5.63158 | −0.178713 | ||||||||
\(994\) | −33.7146 | −1.06936 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.133353 | 0.00422545 | ||||||||
\(997\) | −20.8256 | −0.659555 | −0.329777 | − | 0.944059i | \(-0.606974\pi\) | ||||
−0.329777 | + | 0.944059i | \(0.606974\pi\) | |||||||
\(998\) | −11.2257 | −0.355343 | ||||||||
\(999\) | −3.67307 | −0.116211 |
(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 | 2850.2.a.bk.1.3 | 3 | ||
3.2 | odd | 2 | 8550.2.a.cr.1.3 | 3 | |||
5.2 | odd | 4 | 570.2.d.d.229.2 | ✓ | 6 | ||
5.3 | odd | 4 | 570.2.d.d.229.5 | yes | 6 | ||
5.4 | even | 2 | 2850.2.a.bn.1.1 | 3 | |||
15.2 | even | 4 | 1710.2.d.e.1369.5 | 6 | |||
15.8 | even | 4 | 1710.2.d.e.1369.2 | 6 | |||
15.14 | odd | 2 | 8550.2.a.cf.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.d.d.229.2 | ✓ | 6 | 5.2 | odd | 4 | ||
570.2.d.d.229.5 | yes | 6 | 5.3 | odd | 4 | ||
1710.2.d.e.1369.2 | 6 | 15.8 | even | 4 | |||
1710.2.d.e.1369.5 | 6 | 15.2 | even | 4 | |||
2850.2.a.bk.1.3 | 3 | 1.1 | even | 1 | trivial | ||
2850.2.a.bn.1.1 | 3 | 5.4 | even | 2 | |||
8550.2.a.cf.1.1 | 3 | 15.14 | odd | 2 | |||
8550.2.a.cr.1.3 | 3 | 3.2 | odd | 2 |