Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(1,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1155.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.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: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 6 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.44949\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1155.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.44949 | 1.73205 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 4.00000 | 2.00000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 2.44949 | 1.00000 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 4.89898 | 1.73205 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.44949 | 0.774597 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 4.00000 | 1.15470 | ||||||||
\(13\) | −0.449490 | −0.124666 | −0.0623330 | − | 0.998055i | \(-0.519854\pi\) | ||||
−0.0623330 | + | 0.998055i | \(0.519854\pi\) | |||||||
\(14\) | 2.44949 | 0.654654 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 4.00000 | 1.00000 | ||||||||
\(17\) | −3.00000 | −0.727607 | −0.363803 | − | 0.931476i | \(-0.618522\pi\) | ||||
−0.363803 | + | 0.931476i | \(0.618522\pi\) | |||||||
\(18\) | 2.44949 | 0.577350 | ||||||||
\(19\) | −1.00000 | −0.229416 | −0.114708 | − | 0.993399i | \(-0.536593\pi\) | ||||
−0.114708 | + | 0.993399i | \(0.536593\pi\) | |||||||
\(20\) | 4.00000 | 0.894427 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −2.44949 | −0.522233 | ||||||||
\(23\) | −1.89898 | −0.395965 | −0.197982 | − | 0.980206i | \(-0.563439\pi\) | ||||
−0.197982 | + | 0.980206i | \(0.563439\pi\) | |||||||
\(24\) | 4.89898 | 1.00000 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.10102 | −0.215928 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 4.00000 | 0.755929 | ||||||||
\(29\) | −0.550510 | −0.102227 | −0.0511136 | − | 0.998693i | \(-0.516277\pi\) | ||||
−0.0511136 | + | 0.998693i | \(0.516277\pi\) | |||||||
\(30\) | 2.44949 | 0.447214 | ||||||||
\(31\) | −5.34847 | −0.960613 | −0.480307 | − | 0.877101i | \(-0.659475\pi\) | ||||
−0.480307 | + | 0.877101i | \(0.659475\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | −7.34847 | −1.26025 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 4.00000 | 0.666667 | ||||||||
\(37\) | 4.44949 | 0.731492 | 0.365746 | − | 0.930715i | \(-0.380814\pi\) | ||||
0.365746 | + | 0.930715i | \(0.380814\pi\) | |||||||
\(38\) | −2.44949 | −0.397360 | ||||||||
\(39\) | −0.449490 | −0.0719760 | ||||||||
\(40\) | 4.89898 | 0.774597 | ||||||||
\(41\) | 2.44949 | 0.382546 | 0.191273 | − | 0.981537i | \(-0.438738\pi\) | ||||
0.191273 | + | 0.981537i | \(0.438738\pi\) | |||||||
\(42\) | 2.44949 | 0.377964 | ||||||||
\(43\) | 2.55051 | 0.388949 | 0.194475 | − | 0.980908i | \(-0.437700\pi\) | ||||
0.194475 | + | 0.980908i | \(0.437700\pi\) | |||||||
\(44\) | −4.00000 | −0.603023 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −4.65153 | −0.685831 | ||||||||
\(47\) | −8.44949 | −1.23248 | −0.616242 | − | 0.787557i | \(-0.711346\pi\) | ||||
−0.616242 | + | 0.787557i | \(0.711346\pi\) | |||||||
\(48\) | 4.00000 | 0.577350 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 2.44949 | 0.346410 | ||||||||
\(51\) | −3.00000 | −0.420084 | ||||||||
\(52\) | −1.79796 | −0.249332 | ||||||||
\(53\) | 3.00000 | 0.412082 | 0.206041 | − | 0.978543i | \(-0.433942\pi\) | ||||
0.206041 | + | 0.978543i | \(0.433942\pi\) | |||||||
\(54\) | 2.44949 | 0.333333 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 4.89898 | 0.654654 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | −1.34847 | −0.177063 | ||||||||
\(59\) | 0.550510 | 0.0716703 | 0.0358352 | − | 0.999358i | \(-0.488591\pi\) | ||||
0.0358352 | + | 0.999358i | \(0.488591\pi\) | |||||||
\(60\) | 4.00000 | 0.516398 | ||||||||
\(61\) | −2.10102 | −0.269008 | −0.134504 | − | 0.990913i | \(-0.542944\pi\) | ||||
−0.134504 | + | 0.990913i | \(0.542944\pi\) | |||||||
\(62\) | −13.1010 | −1.66383 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | −0.449490 | −0.0557523 | ||||||||
\(66\) | −2.44949 | −0.301511 | ||||||||
\(67\) | 2.00000 | 0.244339 | 0.122169 | − | 0.992509i | \(-0.461015\pi\) | ||||
0.122169 | + | 0.992509i | \(0.461015\pi\) | |||||||
\(68\) | −12.0000 | −1.45521 | ||||||||
\(69\) | −1.89898 | −0.228610 | ||||||||
\(70\) | 2.44949 | 0.292770 | ||||||||
\(71\) | 12.2474 | 1.45350 | 0.726752 | − | 0.686900i | \(-0.241029\pi\) | ||||
0.726752 | + | 0.686900i | \(0.241029\pi\) | |||||||
\(72\) | 4.89898 | 0.577350 | ||||||||
\(73\) | 3.10102 | 0.362947 | 0.181473 | − | 0.983396i | \(-0.441913\pi\) | ||||
0.181473 | + | 0.983396i | \(0.441913\pi\) | |||||||
\(74\) | 10.8990 | 1.26698 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | −4.00000 | −0.458831 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | −1.10102 | −0.124666 | ||||||||
\(79\) | 3.34847 | 0.376732 | 0.188366 | − | 0.982099i | \(-0.439681\pi\) | ||||
0.188366 | + | 0.982099i | \(0.439681\pi\) | |||||||
\(80\) | 4.00000 | 0.447214 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 6.00000 | 0.662589 | ||||||||
\(83\) | −9.00000 | −0.987878 | −0.493939 | − | 0.869496i | \(-0.664443\pi\) | ||||
−0.493939 | + | 0.869496i | \(0.664443\pi\) | |||||||
\(84\) | 4.00000 | 0.436436 | ||||||||
\(85\) | −3.00000 | −0.325396 | ||||||||
\(86\) | 6.24745 | 0.673680 | ||||||||
\(87\) | −0.550510 | −0.0590209 | ||||||||
\(88\) | −4.89898 | −0.522233 | ||||||||
\(89\) | −10.3485 | −1.09694 | −0.548468 | − | 0.836172i | \(-0.684789\pi\) | ||||
−0.548468 | + | 0.836172i | \(0.684789\pi\) | |||||||
\(90\) | 2.44949 | 0.258199 | ||||||||
\(91\) | −0.449490 | −0.0471193 | ||||||||
\(92\) | −7.59592 | −0.791929 | ||||||||
\(93\) | −5.34847 | −0.554610 | ||||||||
\(94\) | −20.6969 | −2.13473 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.44949 | −0.350243 | −0.175121 | − | 0.984547i | \(-0.556032\pi\) | ||||
−0.175121 | + | 0.984547i | \(0.556032\pi\) | |||||||
\(98\) | 2.44949 | 0.247436 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 4.00000 | 0.400000 | ||||||||
\(101\) | −3.79796 | −0.377911 | −0.188956 | − | 0.981986i | \(-0.560510\pi\) | ||||
−0.188956 | + | 0.981986i | \(0.560510\pi\) | |||||||
\(102\) | −7.34847 | −0.727607 | ||||||||
\(103\) | 18.3485 | 1.80793 | 0.903964 | − | 0.427608i | \(-0.140644\pi\) | ||||
0.903964 | + | 0.427608i | \(0.140644\pi\) | |||||||
\(104\) | −2.20204 | −0.215928 | ||||||||
\(105\) | 1.00000 | 0.0975900 | ||||||||
\(106\) | 7.34847 | 0.713746 | ||||||||
\(107\) | −1.34847 | −0.130361 | −0.0651807 | − | 0.997873i | \(-0.520762\pi\) | ||||
−0.0651807 | + | 0.997873i | \(0.520762\pi\) | |||||||
\(108\) | 4.00000 | 0.384900 | ||||||||
\(109\) | −0.449490 | −0.0430533 | −0.0215267 | − | 0.999768i | \(-0.506853\pi\) | ||||
−0.0215267 | + | 0.999768i | \(0.506853\pi\) | |||||||
\(110\) | −2.44949 | −0.233550 | ||||||||
\(111\) | 4.44949 | 0.422327 | ||||||||
\(112\) | 4.00000 | 0.377964 | ||||||||
\(113\) | 9.00000 | 0.846649 | 0.423324 | − | 0.905978i | \(-0.360863\pi\) | ||||
0.423324 | + | 0.905978i | \(0.360863\pi\) | |||||||
\(114\) | −2.44949 | −0.229416 | ||||||||
\(115\) | −1.89898 | −0.177081 | ||||||||
\(116\) | −2.20204 | −0.204454 | ||||||||
\(117\) | −0.449490 | −0.0415553 | ||||||||
\(118\) | 1.34847 | 0.124137 | ||||||||
\(119\) | −3.00000 | −0.275010 | ||||||||
\(120\) | 4.89898 | 0.447214 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −5.14643 | −0.465936 | ||||||||
\(123\) | 2.44949 | 0.220863 | ||||||||
\(124\) | −21.3939 | −1.92123 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 2.44949 | 0.218218 | ||||||||
\(127\) | −10.5505 | −0.936206 | −0.468103 | − | 0.883674i | \(-0.655062\pi\) | ||||
−0.468103 | + | 0.883674i | \(0.655062\pi\) | |||||||
\(128\) | −19.5959 | −1.73205 | ||||||||
\(129\) | 2.55051 | 0.224560 | ||||||||
\(130\) | −1.10102 | −0.0965659 | ||||||||
\(131\) | −3.55051 | −0.310210 | −0.155105 | − | 0.987898i | \(-0.549572\pi\) | ||||
−0.155105 | + | 0.987898i | \(0.549572\pi\) | |||||||
\(132\) | −4.00000 | −0.348155 | ||||||||
\(133\) | −1.00000 | −0.0867110 | ||||||||
\(134\) | 4.89898 | 0.423207 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | −14.6969 | −1.26025 | ||||||||
\(137\) | 12.0000 | 1.02523 | 0.512615 | − | 0.858619i | \(-0.328677\pi\) | ||||
0.512615 | + | 0.858619i | \(0.328677\pi\) | |||||||
\(138\) | −4.65153 | −0.395965 | ||||||||
\(139\) | −7.79796 | −0.661414 | −0.330707 | − | 0.943733i | \(-0.607287\pi\) | ||||
−0.330707 | + | 0.943733i | \(0.607287\pi\) | |||||||
\(140\) | 4.00000 | 0.338062 | ||||||||
\(141\) | −8.44949 | −0.711575 | ||||||||
\(142\) | 30.0000 | 2.51754 | ||||||||
\(143\) | 0.449490 | 0.0375882 | ||||||||
\(144\) | 4.00000 | 0.333333 | ||||||||
\(145\) | −0.550510 | −0.0457174 | ||||||||
\(146\) | 7.59592 | 0.628643 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 17.7980 | 1.46298 | ||||||||
\(149\) | −8.69694 | −0.712481 | −0.356240 | − | 0.934394i | \(-0.615942\pi\) | ||||
−0.356240 | + | 0.934394i | \(0.615942\pi\) | |||||||
\(150\) | 2.44949 | 0.200000 | ||||||||
\(151\) | 14.0000 | 1.13930 | 0.569652 | − | 0.821886i | \(-0.307078\pi\) | ||||
0.569652 | + | 0.821886i | \(0.307078\pi\) | |||||||
\(152\) | −4.89898 | −0.397360 | ||||||||
\(153\) | −3.00000 | −0.242536 | ||||||||
\(154\) | −2.44949 | −0.197386 | ||||||||
\(155\) | −5.34847 | −0.429599 | ||||||||
\(156\) | −1.79796 | −0.143952 | ||||||||
\(157\) | −12.1464 | −0.969391 | −0.484695 | − | 0.874683i | \(-0.661069\pi\) | ||||
−0.484695 | + | 0.874683i | \(0.661069\pi\) | |||||||
\(158\) | 8.20204 | 0.652519 | ||||||||
\(159\) | 3.00000 | 0.237915 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.89898 | −0.149661 | ||||||||
\(162\) | 2.44949 | 0.192450 | ||||||||
\(163\) | −12.4495 | −0.975119 | −0.487560 | − | 0.873090i | \(-0.662113\pi\) | ||||
−0.487560 | + | 0.873090i | \(0.662113\pi\) | |||||||
\(164\) | 9.79796 | 0.765092 | ||||||||
\(165\) | −1.00000 | −0.0778499 | ||||||||
\(166\) | −22.0454 | −1.71106 | ||||||||
\(167\) | −6.00000 | −0.464294 | −0.232147 | − | 0.972681i | \(-0.574575\pi\) | ||||
−0.232147 | + | 0.972681i | \(0.574575\pi\) | |||||||
\(168\) | 4.89898 | 0.377964 | ||||||||
\(169\) | −12.7980 | −0.984458 | ||||||||
\(170\) | −7.34847 | −0.563602 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | 10.2020 | 0.777898 | ||||||||
\(173\) | −2.20204 | −0.167418 | −0.0837090 | − | 0.996490i | \(-0.526677\pi\) | ||||
−0.0837090 | + | 0.996490i | \(0.526677\pi\) | |||||||
\(174\) | −1.34847 | −0.102227 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | −4.00000 | −0.301511 | ||||||||
\(177\) | 0.550510 | 0.0413789 | ||||||||
\(178\) | −25.3485 | −1.89995 | ||||||||
\(179\) | 14.4495 | 1.08001 | 0.540003 | − | 0.841663i | \(-0.318423\pi\) | ||||
0.540003 | + | 0.841663i | \(0.318423\pi\) | |||||||
\(180\) | 4.00000 | 0.298142 | ||||||||
\(181\) | 23.7980 | 1.76889 | 0.884444 | − | 0.466646i | \(-0.154538\pi\) | ||||
0.884444 | + | 0.466646i | \(0.154538\pi\) | |||||||
\(182\) | −1.10102 | −0.0816131 | ||||||||
\(183\) | −2.10102 | −0.155312 | ||||||||
\(184\) | −9.30306 | −0.685831 | ||||||||
\(185\) | 4.44949 | 0.327133 | ||||||||
\(186\) | −13.1010 | −0.960613 | ||||||||
\(187\) | 3.00000 | 0.219382 | ||||||||
\(188\) | −33.7980 | −2.46497 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | −2.44949 | −0.177705 | ||||||||
\(191\) | −2.20204 | −0.159334 | −0.0796670 | − | 0.996822i | \(-0.525386\pi\) | ||||
−0.0796670 | + | 0.996822i | \(0.525386\pi\) | |||||||
\(192\) | −8.00000 | −0.577350 | ||||||||
\(193\) | 26.4949 | 1.90714 | 0.953572 | − | 0.301164i | \(-0.0973753\pi\) | ||||
0.953572 | + | 0.301164i | \(0.0973753\pi\) | |||||||
\(194\) | −8.44949 | −0.606638 | ||||||||
\(195\) | −0.449490 | −0.0321886 | ||||||||
\(196\) | 4.00000 | 0.285714 | ||||||||
\(197\) | 16.8990 | 1.20400 | 0.602001 | − | 0.798495i | \(-0.294370\pi\) | ||||
0.602001 | + | 0.798495i | \(0.294370\pi\) | |||||||
\(198\) | −2.44949 | −0.174078 | ||||||||
\(199\) | −25.7980 | −1.82877 | −0.914384 | − | 0.404847i | \(-0.867325\pi\) | ||||
−0.914384 | + | 0.404847i | \(0.867325\pi\) | |||||||
\(200\) | 4.89898 | 0.346410 | ||||||||
\(201\) | 2.00000 | 0.141069 | ||||||||
\(202\) | −9.30306 | −0.654561 | ||||||||
\(203\) | −0.550510 | −0.0386382 | ||||||||
\(204\) | −12.0000 | −0.840168 | ||||||||
\(205\) | 2.44949 | 0.171080 | ||||||||
\(206\) | 44.9444 | 3.13142 | ||||||||
\(207\) | −1.89898 | −0.131988 | ||||||||
\(208\) | −1.79796 | −0.124666 | ||||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | 2.44949 | 0.169031 | ||||||||
\(211\) | 6.89898 | 0.474945 | 0.237473 | − | 0.971394i | \(-0.423681\pi\) | ||||
0.237473 | + | 0.971394i | \(0.423681\pi\) | |||||||
\(212\) | 12.0000 | 0.824163 | ||||||||
\(213\) | 12.2474 | 0.839181 | ||||||||
\(214\) | −3.30306 | −0.225793 | ||||||||
\(215\) | 2.55051 | 0.173943 | ||||||||
\(216\) | 4.89898 | 0.333333 | ||||||||
\(217\) | −5.34847 | −0.363078 | ||||||||
\(218\) | −1.10102 | −0.0745705 | ||||||||
\(219\) | 3.10102 | 0.209548 | ||||||||
\(220\) | −4.00000 | −0.269680 | ||||||||
\(221\) | 1.34847 | 0.0907079 | ||||||||
\(222\) | 10.8990 | 0.731492 | ||||||||
\(223\) | 24.3485 | 1.63049 | 0.815247 | − | 0.579113i | \(-0.196601\pi\) | ||||
0.815247 | + | 0.579113i | \(0.196601\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 22.0454 | 1.46644 | ||||||||
\(227\) | −27.4949 | −1.82490 | −0.912450 | − | 0.409188i | \(-0.865812\pi\) | ||||
−0.912450 | + | 0.409188i | \(0.865812\pi\) | |||||||
\(228\) | −4.00000 | −0.264906 | ||||||||
\(229\) | −2.65153 | −0.175218 | −0.0876090 | − | 0.996155i | \(-0.527923\pi\) | ||||
−0.0876090 | + | 0.996155i | \(0.527923\pi\) | |||||||
\(230\) | −4.65153 | −0.306713 | ||||||||
\(231\) | −1.00000 | −0.0657952 | ||||||||
\(232\) | −2.69694 | −0.177063 | ||||||||
\(233\) | −22.0454 | −1.44424 | −0.722121 | − | 0.691766i | \(-0.756833\pi\) | ||||
−0.722121 | + | 0.691766i | \(0.756833\pi\) | |||||||
\(234\) | −1.10102 | −0.0719760 | ||||||||
\(235\) | −8.44949 | −0.551184 | ||||||||
\(236\) | 2.20204 | 0.143341 | ||||||||
\(237\) | 3.34847 | 0.217506 | ||||||||
\(238\) | −7.34847 | −0.476331 | ||||||||
\(239\) | −0.550510 | −0.0356095 | −0.0178048 | − | 0.999841i | \(-0.505668\pi\) | ||||
−0.0178048 | + | 0.999841i | \(0.505668\pi\) | |||||||
\(240\) | 4.00000 | 0.258199 | ||||||||
\(241\) | 10.6969 | 0.689050 | 0.344525 | − | 0.938777i | \(-0.388040\pi\) | ||||
0.344525 | + | 0.938777i | \(0.388040\pi\) | |||||||
\(242\) | 2.44949 | 0.157459 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −8.40408 | −0.538016 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 6.00000 | 0.382546 | ||||||||
\(247\) | 0.449490 | 0.0286003 | ||||||||
\(248\) | −26.2020 | −1.66383 | ||||||||
\(249\) | −9.00000 | −0.570352 | ||||||||
\(250\) | 2.44949 | 0.154919 | ||||||||
\(251\) | 21.7980 | 1.37587 | 0.687937 | − | 0.725770i | \(-0.258516\pi\) | ||||
0.687937 | + | 0.725770i | \(0.258516\pi\) | |||||||
\(252\) | 4.00000 | 0.251976 | ||||||||
\(253\) | 1.89898 | 0.119388 | ||||||||
\(254\) | −25.8434 | −1.62156 | ||||||||
\(255\) | −3.00000 | −0.187867 | ||||||||
\(256\) | −32.0000 | −2.00000 | ||||||||
\(257\) | 14.4495 | 0.901334 | 0.450667 | − | 0.892692i | \(-0.351186\pi\) | ||||
0.450667 | + | 0.892692i | \(0.351186\pi\) | |||||||
\(258\) | 6.24745 | 0.388949 | ||||||||
\(259\) | 4.44949 | 0.276478 | ||||||||
\(260\) | −1.79796 | −0.111505 | ||||||||
\(261\) | −0.550510 | −0.0340757 | ||||||||
\(262\) | −8.69694 | −0.537299 | ||||||||
\(263\) | −16.8990 | −1.04204 | −0.521018 | − | 0.853546i | \(-0.674448\pi\) | ||||
−0.521018 | + | 0.853546i | \(0.674448\pi\) | |||||||
\(264\) | −4.89898 | −0.301511 | ||||||||
\(265\) | 3.00000 | 0.184289 | ||||||||
\(266\) | −2.44949 | −0.150188 | ||||||||
\(267\) | −10.3485 | −0.633316 | ||||||||
\(268\) | 8.00000 | 0.488678 | ||||||||
\(269\) | −11.4495 | −0.698088 | −0.349044 | − | 0.937106i | \(-0.613494\pi\) | ||||
−0.349044 | + | 0.937106i | \(0.613494\pi\) | |||||||
\(270\) | 2.44949 | 0.149071 | ||||||||
\(271\) | −1.00000 | −0.0607457 | −0.0303728 | − | 0.999539i | \(-0.509669\pi\) | ||||
−0.0303728 | + | 0.999539i | \(0.509669\pi\) | |||||||
\(272\) | −12.0000 | −0.727607 | ||||||||
\(273\) | −0.449490 | −0.0272044 | ||||||||
\(274\) | 29.3939 | 1.77575 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | −7.59592 | −0.457221 | ||||||||
\(277\) | 10.6969 | 0.642717 | 0.321358 | − | 0.946958i | \(-0.395861\pi\) | ||||
0.321358 | + | 0.946958i | \(0.395861\pi\) | |||||||
\(278\) | −19.1010 | −1.14560 | ||||||||
\(279\) | −5.34847 | −0.320204 | ||||||||
\(280\) | 4.89898 | 0.292770 | ||||||||
\(281\) | 16.8990 | 1.00811 | 0.504054 | − | 0.863672i | \(-0.331841\pi\) | ||||
0.504054 | + | 0.863672i | \(0.331841\pi\) | |||||||
\(282\) | −20.6969 | −1.23248 | ||||||||
\(283\) | −14.6515 | −0.870943 | −0.435472 | − | 0.900202i | \(-0.643418\pi\) | ||||
−0.435472 | + | 0.900202i | \(0.643418\pi\) | |||||||
\(284\) | 48.9898 | 2.90701 | ||||||||
\(285\) | −1.00000 | −0.0592349 | ||||||||
\(286\) | 1.10102 | 0.0651047 | ||||||||
\(287\) | 2.44949 | 0.144589 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | −1.34847 | −0.0791848 | ||||||||
\(291\) | −3.44949 | −0.202213 | ||||||||
\(292\) | 12.4041 | 0.725894 | ||||||||
\(293\) | −16.5959 | −0.969544 | −0.484772 | − | 0.874641i | \(-0.661097\pi\) | ||||
−0.484772 | + | 0.874641i | \(0.661097\pi\) | |||||||
\(294\) | 2.44949 | 0.142857 | ||||||||
\(295\) | 0.550510 | 0.0320519 | ||||||||
\(296\) | 21.7980 | 1.26698 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | −21.3031 | −1.23405 | ||||||||
\(299\) | 0.853572 | 0.0493633 | ||||||||
\(300\) | 4.00000 | 0.230940 | ||||||||
\(301\) | 2.55051 | 0.147009 | ||||||||
\(302\) | 34.2929 | 1.97333 | ||||||||
\(303\) | −3.79796 | −0.218187 | ||||||||
\(304\) | −4.00000 | −0.229416 | ||||||||
\(305\) | −2.10102 | −0.120304 | ||||||||
\(306\) | −7.34847 | −0.420084 | ||||||||
\(307\) | −5.10102 | −0.291131 | −0.145565 | − | 0.989349i | \(-0.546500\pi\) | ||||
−0.145565 | + | 0.989349i | \(0.546500\pi\) | |||||||
\(308\) | −4.00000 | −0.227921 | ||||||||
\(309\) | 18.3485 | 1.04381 | ||||||||
\(310\) | −13.1010 | −0.744088 | ||||||||
\(311\) | 4.89898 | 0.277796 | 0.138898 | − | 0.990307i | \(-0.455644\pi\) | ||||
0.138898 | + | 0.990307i | \(0.455644\pi\) | |||||||
\(312\) | −2.20204 | −0.124666 | ||||||||
\(313\) | 23.2474 | 1.31402 | 0.657012 | − | 0.753880i | \(-0.271820\pi\) | ||||
0.657012 | + | 0.753880i | \(0.271820\pi\) | |||||||
\(314\) | −29.7526 | −1.67903 | ||||||||
\(315\) | 1.00000 | 0.0563436 | ||||||||
\(316\) | 13.3939 | 0.753464 | ||||||||
\(317\) | 2.69694 | 0.151475 | 0.0757376 | − | 0.997128i | \(-0.475869\pi\) | ||||
0.0757376 | + | 0.997128i | \(0.475869\pi\) | |||||||
\(318\) | 7.34847 | 0.412082 | ||||||||
\(319\) | 0.550510 | 0.0308227 | ||||||||
\(320\) | −8.00000 | −0.447214 | ||||||||
\(321\) | −1.34847 | −0.0752642 | ||||||||
\(322\) | −4.65153 | −0.259220 | ||||||||
\(323\) | 3.00000 | 0.166924 | ||||||||
\(324\) | 4.00000 | 0.222222 | ||||||||
\(325\) | −0.449490 | −0.0249332 | ||||||||
\(326\) | −30.4949 | −1.68896 | ||||||||
\(327\) | −0.449490 | −0.0248568 | ||||||||
\(328\) | 12.0000 | 0.662589 | ||||||||
\(329\) | −8.44949 | −0.465835 | ||||||||
\(330\) | −2.44949 | −0.134840 | ||||||||
\(331\) | 31.6969 | 1.74222 | 0.871111 | − | 0.491087i | \(-0.163400\pi\) | ||||
0.871111 | + | 0.491087i | \(0.163400\pi\) | |||||||
\(332\) | −36.0000 | −1.97576 | ||||||||
\(333\) | 4.44949 | 0.243831 | ||||||||
\(334\) | −14.6969 | −0.804181 | ||||||||
\(335\) | 2.00000 | 0.109272 | ||||||||
\(336\) | 4.00000 | 0.218218 | ||||||||
\(337\) | −2.34847 | −0.127929 | −0.0639646 | − | 0.997952i | \(-0.520374\pi\) | ||||
−0.0639646 | + | 0.997952i | \(0.520374\pi\) | |||||||
\(338\) | −31.3485 | −1.70513 | ||||||||
\(339\) | 9.00000 | 0.488813 | ||||||||
\(340\) | −12.0000 | −0.650791 | ||||||||
\(341\) | 5.34847 | 0.289636 | ||||||||
\(342\) | −2.44949 | −0.132453 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 12.4949 | 0.673680 | ||||||||
\(345\) | −1.89898 | −0.102238 | ||||||||
\(346\) | −5.39388 | −0.289977 | ||||||||
\(347\) | 12.4949 | 0.670761 | 0.335381 | − | 0.942083i | \(-0.391135\pi\) | ||||
0.335381 | + | 0.942083i | \(0.391135\pi\) | |||||||
\(348\) | −2.20204 | −0.118042 | ||||||||
\(349\) | 15.8990 | 0.851053 | 0.425526 | − | 0.904946i | \(-0.360089\pi\) | ||||
0.425526 | + | 0.904946i | \(0.360089\pi\) | |||||||
\(350\) | 2.44949 | 0.130931 | ||||||||
\(351\) | −0.449490 | −0.0239920 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.69694 | −0.462891 | −0.231446 | − | 0.972848i | \(-0.574346\pi\) | ||||
−0.231446 | + | 0.972848i | \(0.574346\pi\) | |||||||
\(354\) | 1.34847 | 0.0716703 | ||||||||
\(355\) | 12.2474 | 0.650027 | ||||||||
\(356\) | −41.3939 | −2.19387 | ||||||||
\(357\) | −3.00000 | −0.158777 | ||||||||
\(358\) | 35.3939 | 1.87062 | ||||||||
\(359\) | −21.2474 | −1.12140 | −0.560699 | − | 0.828020i | \(-0.689467\pi\) | ||||
−0.560699 | + | 0.828020i | \(0.689467\pi\) | |||||||
\(360\) | 4.89898 | 0.258199 | ||||||||
\(361\) | −18.0000 | −0.947368 | ||||||||
\(362\) | 58.2929 | 3.06380 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | −1.79796 | −0.0942387 | ||||||||
\(365\) | 3.10102 | 0.162315 | ||||||||
\(366\) | −5.14643 | −0.269008 | ||||||||
\(367\) | 15.0454 | 0.785364 | 0.392682 | − | 0.919674i | \(-0.371547\pi\) | ||||
0.392682 | + | 0.919674i | \(0.371547\pi\) | |||||||
\(368\) | −7.59592 | −0.395965 | ||||||||
\(369\) | 2.44949 | 0.127515 | ||||||||
\(370\) | 10.8990 | 0.566611 | ||||||||
\(371\) | 3.00000 | 0.155752 | ||||||||
\(372\) | −21.3939 | −1.10922 | ||||||||
\(373\) | 16.1464 | 0.836030 | 0.418015 | − | 0.908440i | \(-0.362726\pi\) | ||||
0.418015 | + | 0.908440i | \(0.362726\pi\) | |||||||
\(374\) | 7.34847 | 0.379980 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | −41.3939 | −2.13473 | ||||||||
\(377\) | 0.247449 | 0.0127443 | ||||||||
\(378\) | 2.44949 | 0.125988 | ||||||||
\(379\) | 35.4949 | 1.82325 | 0.911625 | − | 0.411022i | \(-0.134828\pi\) | ||||
0.911625 | + | 0.411022i | \(0.134828\pi\) | |||||||
\(380\) | −4.00000 | −0.205196 | ||||||||
\(381\) | −10.5505 | −0.540519 | ||||||||
\(382\) | −5.39388 | −0.275975 | ||||||||
\(383\) | 2.44949 | 0.125163 | 0.0625815 | − | 0.998040i | \(-0.480067\pi\) | ||||
0.0625815 | + | 0.998040i | \(0.480067\pi\) | |||||||
\(384\) | −19.5959 | −1.00000 | ||||||||
\(385\) | −1.00000 | −0.0509647 | ||||||||
\(386\) | 64.8990 | 3.30327 | ||||||||
\(387\) | 2.55051 | 0.129650 | ||||||||
\(388\) | −13.7980 | −0.700485 | ||||||||
\(389\) | −6.24745 | −0.316758 | −0.158379 | − | 0.987378i | \(-0.550627\pi\) | ||||
−0.158379 | + | 0.987378i | \(0.550627\pi\) | |||||||
\(390\) | −1.10102 | −0.0557523 | ||||||||
\(391\) | 5.69694 | 0.288107 | ||||||||
\(392\) | 4.89898 | 0.247436 | ||||||||
\(393\) | −3.55051 | −0.179100 | ||||||||
\(394\) | 41.3939 | 2.08539 | ||||||||
\(395\) | 3.34847 | 0.168480 | ||||||||
\(396\) | −4.00000 | −0.201008 | ||||||||
\(397\) | 22.6969 | 1.13913 | 0.569563 | − | 0.821947i | \(-0.307112\pi\) | ||||
0.569563 | + | 0.821947i | \(0.307112\pi\) | |||||||
\(398\) | −63.1918 | −3.16752 | ||||||||
\(399\) | −1.00000 | −0.0500626 | ||||||||
\(400\) | 4.00000 | 0.200000 | ||||||||
\(401\) | −31.3485 | −1.56547 | −0.782734 | − | 0.622356i | \(-0.786175\pi\) | ||||
−0.782734 | + | 0.622356i | \(0.786175\pi\) | |||||||
\(402\) | 4.89898 | 0.244339 | ||||||||
\(403\) | 2.40408 | 0.119756 | ||||||||
\(404\) | −15.1918 | −0.755822 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −1.34847 | −0.0669234 | ||||||||
\(407\) | −4.44949 | −0.220553 | ||||||||
\(408\) | −14.6969 | −0.727607 | ||||||||
\(409\) | 12.8990 | 0.637813 | 0.318907 | − | 0.947786i | \(-0.396684\pi\) | ||||
0.318907 | + | 0.947786i | \(0.396684\pi\) | |||||||
\(410\) | 6.00000 | 0.296319 | ||||||||
\(411\) | 12.0000 | 0.591916 | ||||||||
\(412\) | 73.3939 | 3.61586 | ||||||||
\(413\) | 0.550510 | 0.0270888 | ||||||||
\(414\) | −4.65153 | −0.228610 | ||||||||
\(415\) | −9.00000 | −0.441793 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.79796 | −0.381868 | ||||||||
\(418\) | 2.44949 | 0.119808 | ||||||||
\(419\) | −28.3485 | −1.38491 | −0.692457 | − | 0.721459i | \(-0.743472\pi\) | ||||
−0.692457 | + | 0.721459i | \(0.743472\pi\) | |||||||
\(420\) | 4.00000 | 0.195180 | ||||||||
\(421\) | 14.7980 | 0.721208 | 0.360604 | − | 0.932719i | \(-0.382571\pi\) | ||||
0.360604 | + | 0.932719i | \(0.382571\pi\) | |||||||
\(422\) | 16.8990 | 0.822629 | ||||||||
\(423\) | −8.44949 | −0.410828 | ||||||||
\(424\) | 14.6969 | 0.713746 | ||||||||
\(425\) | −3.00000 | −0.145521 | ||||||||
\(426\) | 30.0000 | 1.45350 | ||||||||
\(427\) | −2.10102 | −0.101676 | ||||||||
\(428\) | −5.39388 | −0.260723 | ||||||||
\(429\) | 0.449490 | 0.0217016 | ||||||||
\(430\) | 6.24745 | 0.301279 | ||||||||
\(431\) | −36.4949 | −1.75790 | −0.878949 | − | 0.476916i | \(-0.841754\pi\) | ||||
−0.878949 | + | 0.476916i | \(0.841754\pi\) | |||||||
\(432\) | 4.00000 | 0.192450 | ||||||||
\(433\) | 38.4949 | 1.84995 | 0.924973 | − | 0.380032i | \(-0.124087\pi\) | ||||
0.924973 | + | 0.380032i | \(0.124087\pi\) | |||||||
\(434\) | −13.1010 | −0.628869 | ||||||||
\(435\) | −0.550510 | −0.0263949 | ||||||||
\(436\) | −1.79796 | −0.0861066 | ||||||||
\(437\) | 1.89898 | 0.0908405 | ||||||||
\(438\) | 7.59592 | 0.362947 | ||||||||
\(439\) | 15.8990 | 0.758817 | 0.379408 | − | 0.925229i | \(-0.376128\pi\) | ||||
0.379408 | + | 0.925229i | \(0.376128\pi\) | |||||||
\(440\) | −4.89898 | −0.233550 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 3.30306 | 0.157111 | ||||||||
\(443\) | 6.00000 | 0.285069 | 0.142534 | − | 0.989790i | \(-0.454475\pi\) | ||||
0.142534 | + | 0.989790i | \(0.454475\pi\) | |||||||
\(444\) | 17.7980 | 0.844654 | ||||||||
\(445\) | −10.3485 | −0.490564 | ||||||||
\(446\) | 59.6413 | 2.82410 | ||||||||
\(447\) | −8.69694 | −0.411351 | ||||||||
\(448\) | −8.00000 | −0.377964 | ||||||||
\(449\) | 7.34847 | 0.346796 | 0.173398 | − | 0.984852i | \(-0.444525\pi\) | ||||
0.173398 | + | 0.984852i | \(0.444525\pi\) | |||||||
\(450\) | 2.44949 | 0.115470 | ||||||||
\(451\) | −2.44949 | −0.115342 | ||||||||
\(452\) | 36.0000 | 1.69330 | ||||||||
\(453\) | 14.0000 | 0.657777 | ||||||||
\(454\) | −67.3485 | −3.16082 | ||||||||
\(455\) | −0.449490 | −0.0210724 | ||||||||
\(456\) | −4.89898 | −0.229416 | ||||||||
\(457\) | 31.4495 | 1.47115 | 0.735573 | − | 0.677446i | \(-0.236913\pi\) | ||||
0.735573 | + | 0.677446i | \(0.236913\pi\) | |||||||
\(458\) | −6.49490 | −0.303487 | ||||||||
\(459\) | −3.00000 | −0.140028 | ||||||||
\(460\) | −7.59592 | −0.354162 | ||||||||
\(461\) | 1.10102 | 0.0512796 | 0.0256398 | − | 0.999671i | \(-0.491838\pi\) | ||||
0.0256398 | + | 0.999671i | \(0.491838\pi\) | |||||||
\(462\) | −2.44949 | −0.113961 | ||||||||
\(463\) | 4.69694 | 0.218285 | 0.109143 | − | 0.994026i | \(-0.465189\pi\) | ||||
0.109143 | + | 0.994026i | \(0.465189\pi\) | |||||||
\(464\) | −2.20204 | −0.102227 | ||||||||
\(465\) | −5.34847 | −0.248029 | ||||||||
\(466\) | −54.0000 | −2.50150 | ||||||||
\(467\) | 12.4949 | 0.578195 | 0.289097 | − | 0.957300i | \(-0.406645\pi\) | ||||
0.289097 | + | 0.957300i | \(0.406645\pi\) | |||||||
\(468\) | −1.79796 | −0.0831107 | ||||||||
\(469\) | 2.00000 | 0.0923514 | ||||||||
\(470\) | −20.6969 | −0.954679 | ||||||||
\(471\) | −12.1464 | −0.559678 | ||||||||
\(472\) | 2.69694 | 0.124137 | ||||||||
\(473\) | −2.55051 | −0.117273 | ||||||||
\(474\) | 8.20204 | 0.376732 | ||||||||
\(475\) | −1.00000 | −0.0458831 | ||||||||
\(476\) | −12.0000 | −0.550019 | ||||||||
\(477\) | 3.00000 | 0.137361 | ||||||||
\(478\) | −1.34847 | −0.0616775 | ||||||||
\(479\) | −11.1464 | −0.509293 | −0.254647 | − | 0.967034i | \(-0.581959\pi\) | ||||
−0.254647 | + | 0.967034i | \(0.581959\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.00000 | −0.0911922 | ||||||||
\(482\) | 26.2020 | 1.19347 | ||||||||
\(483\) | −1.89898 | −0.0864066 | ||||||||
\(484\) | 4.00000 | 0.181818 | ||||||||
\(485\) | −3.44949 | −0.156633 | ||||||||
\(486\) | 2.44949 | 0.111111 | ||||||||
\(487\) | 9.10102 | 0.412407 | 0.206203 | − | 0.978509i | \(-0.433889\pi\) | ||||
0.206203 | + | 0.978509i | \(0.433889\pi\) | |||||||
\(488\) | −10.2929 | −0.465936 | ||||||||
\(489\) | −12.4495 | −0.562985 | ||||||||
\(490\) | 2.44949 | 0.110657 | ||||||||
\(491\) | −6.55051 | −0.295620 | −0.147810 | − | 0.989016i | \(-0.547222\pi\) | ||||
−0.147810 | + | 0.989016i | \(0.547222\pi\) | |||||||
\(492\) | 9.79796 | 0.441726 | ||||||||
\(493\) | 1.65153 | 0.0743812 | ||||||||
\(494\) | 1.10102 | 0.0495373 | ||||||||
\(495\) | −1.00000 | −0.0449467 | ||||||||
\(496\) | −21.3939 | −0.960613 | ||||||||
\(497\) | 12.2474 | 0.549373 | ||||||||
\(498\) | −22.0454 | −0.987878 | ||||||||
\(499\) | −9.20204 | −0.411940 | −0.205970 | − | 0.978558i | \(-0.566035\pi\) | ||||
−0.205970 | + | 0.978558i | \(0.566035\pi\) | |||||||
\(500\) | 4.00000 | 0.178885 | ||||||||
\(501\) | −6.00000 | −0.268060 | ||||||||
\(502\) | 53.3939 | 2.38309 | ||||||||
\(503\) | −26.3939 | −1.17684 | −0.588422 | − | 0.808554i | \(-0.700251\pi\) | ||||
−0.588422 | + | 0.808554i | \(0.700251\pi\) | |||||||
\(504\) | 4.89898 | 0.218218 | ||||||||
\(505\) | −3.79796 | −0.169007 | ||||||||
\(506\) | 4.65153 | 0.206786 | ||||||||
\(507\) | −12.7980 | −0.568377 | ||||||||
\(508\) | −42.2020 | −1.87241 | ||||||||
\(509\) | 7.65153 | 0.339148 | 0.169574 | − | 0.985517i | \(-0.445761\pi\) | ||||
0.169574 | + | 0.985517i | \(0.445761\pi\) | |||||||
\(510\) | −7.34847 | −0.325396 | ||||||||
\(511\) | 3.10102 | 0.137181 | ||||||||
\(512\) | −39.1918 | −1.73205 | ||||||||
\(513\) | −1.00000 | −0.0441511 | ||||||||
\(514\) | 35.3939 | 1.56116 | ||||||||
\(515\) | 18.3485 | 0.808530 | ||||||||
\(516\) | 10.2020 | 0.449120 | ||||||||
\(517\) | 8.44949 | 0.371608 | ||||||||
\(518\) | 10.8990 | 0.478874 | ||||||||
\(519\) | −2.20204 | −0.0966589 | ||||||||
\(520\) | −2.20204 | −0.0965659 | ||||||||
\(521\) | 11.9444 | 0.523293 | 0.261647 | − | 0.965164i | \(-0.415735\pi\) | ||||
0.261647 | + | 0.965164i | \(0.415735\pi\) | |||||||
\(522\) | −1.34847 | −0.0590209 | ||||||||
\(523\) | 44.4949 | 1.94563 | 0.972813 | − | 0.231592i | \(-0.0743934\pi\) | ||||
0.972813 | + | 0.231592i | \(0.0743934\pi\) | |||||||
\(524\) | −14.2020 | −0.620419 | ||||||||
\(525\) | 1.00000 | 0.0436436 | ||||||||
\(526\) | −41.3939 | −1.80486 | ||||||||
\(527\) | 16.0454 | 0.698949 | ||||||||
\(528\) | −4.00000 | −0.174078 | ||||||||
\(529\) | −19.3939 | −0.843212 | ||||||||
\(530\) | 7.34847 | 0.319197 | ||||||||
\(531\) | 0.550510 | 0.0238901 | ||||||||
\(532\) | −4.00000 | −0.173422 | ||||||||
\(533\) | −1.10102 | −0.0476905 | ||||||||
\(534\) | −25.3485 | −1.09694 | ||||||||
\(535\) | −1.34847 | −0.0582994 | ||||||||
\(536\) | 9.79796 | 0.423207 | ||||||||
\(537\) | 14.4495 | 0.623542 | ||||||||
\(538\) | −28.0454 | −1.20912 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 4.00000 | 0.172133 | ||||||||
\(541\) | −8.04541 | −0.345899 | −0.172950 | − | 0.984931i | \(-0.555330\pi\) | ||||
−0.172950 | + | 0.984931i | \(0.555330\pi\) | |||||||
\(542\) | −2.44949 | −0.105215 | ||||||||
\(543\) | 23.7980 | 1.02127 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.449490 | −0.0192540 | ||||||||
\(546\) | −1.10102 | −0.0471193 | ||||||||
\(547\) | −26.3485 | −1.12658 | −0.563290 | − | 0.826260i | \(-0.690464\pi\) | ||||
−0.563290 | + | 0.826260i | \(0.690464\pi\) | |||||||
\(548\) | 48.0000 | 2.05046 | ||||||||
\(549\) | −2.10102 | −0.0896694 | ||||||||
\(550\) | −2.44949 | −0.104447 | ||||||||
\(551\) | 0.550510 | 0.0234525 | ||||||||
\(552\) | −9.30306 | −0.395965 | ||||||||
\(553\) | 3.34847 | 0.142391 | ||||||||
\(554\) | 26.2020 | 1.11322 | ||||||||
\(555\) | 4.44949 | 0.188870 | ||||||||
\(556\) | −31.1918 | −1.32283 | ||||||||
\(557\) | −28.2929 | −1.19881 | −0.599403 | − | 0.800447i | \(-0.704595\pi\) | ||||
−0.599403 | + | 0.800447i | \(0.704595\pi\) | |||||||
\(558\) | −13.1010 | −0.554610 | ||||||||
\(559\) | −1.14643 | −0.0484887 | ||||||||
\(560\) | 4.00000 | 0.169031 | ||||||||
\(561\) | 3.00000 | 0.126660 | ||||||||
\(562\) | 41.3939 | 1.74610 | ||||||||
\(563\) | −15.3031 | −0.644947 | −0.322474 | − | 0.946578i | \(-0.604514\pi\) | ||||
−0.322474 | + | 0.946578i | \(0.604514\pi\) | |||||||
\(564\) | −33.7980 | −1.42315 | ||||||||
\(565\) | 9.00000 | 0.378633 | ||||||||
\(566\) | −35.8888 | −1.50852 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 60.0000 | 2.51754 | ||||||||
\(569\) | −35.9444 | −1.50687 | −0.753434 | − | 0.657524i | \(-0.771604\pi\) | ||||
−0.753434 | + | 0.657524i | \(0.771604\pi\) | |||||||
\(570\) | −2.44949 | −0.102598 | ||||||||
\(571\) | −28.7423 | −1.20283 | −0.601415 | − | 0.798937i | \(-0.705396\pi\) | ||||
−0.601415 | + | 0.798937i | \(0.705396\pi\) | |||||||
\(572\) | 1.79796 | 0.0751764 | ||||||||
\(573\) | −2.20204 | −0.0919916 | ||||||||
\(574\) | 6.00000 | 0.250435 | ||||||||
\(575\) | −1.89898 | −0.0791929 | ||||||||
\(576\) | −8.00000 | −0.333333 | ||||||||
\(577\) | −17.5959 | −0.732528 | −0.366264 | − | 0.930511i | \(-0.619363\pi\) | ||||
−0.366264 | + | 0.930511i | \(0.619363\pi\) | |||||||
\(578\) | −19.5959 | −0.815083 | ||||||||
\(579\) | 26.4949 | 1.10109 | ||||||||
\(580\) | −2.20204 | −0.0914348 | ||||||||
\(581\) | −9.00000 | −0.373383 | ||||||||
\(582\) | −8.44949 | −0.350243 | ||||||||
\(583\) | −3.00000 | −0.124247 | ||||||||
\(584\) | 15.1918 | 0.628643 | ||||||||
\(585\) | −0.449490 | −0.0185841 | ||||||||
\(586\) | −40.6515 | −1.67930 | ||||||||
\(587\) | −6.85357 | −0.282877 | −0.141439 | − | 0.989947i | \(-0.545173\pi\) | ||||
−0.141439 | + | 0.989947i | \(0.545173\pi\) | |||||||
\(588\) | 4.00000 | 0.164957 | ||||||||
\(589\) | 5.34847 | 0.220380 | ||||||||
\(590\) | 1.34847 | 0.0555156 | ||||||||
\(591\) | 16.8990 | 0.695131 | ||||||||
\(592\) | 17.7980 | 0.731492 | ||||||||
\(593\) | 36.4949 | 1.49867 | 0.749333 | − | 0.662193i | \(-0.230374\pi\) | ||||
0.749333 | + | 0.662193i | \(0.230374\pi\) | |||||||
\(594\) | −2.44949 | −0.100504 | ||||||||
\(595\) | −3.00000 | −0.122988 | ||||||||
\(596\) | −34.7878 | −1.42496 | ||||||||
\(597\) | −25.7980 | −1.05584 | ||||||||
\(598\) | 2.09082 | 0.0854998 | ||||||||
\(599\) | 20.6969 | 0.845654 | 0.422827 | − | 0.906210i | \(-0.361038\pi\) | ||||
0.422827 | + | 0.906210i | \(0.361038\pi\) | |||||||
\(600\) | 4.89898 | 0.200000 | ||||||||
\(601\) | 28.3939 | 1.15821 | 0.579105 | − | 0.815253i | \(-0.303402\pi\) | ||||
0.579105 | + | 0.815253i | \(0.303402\pi\) | |||||||
\(602\) | 6.24745 | 0.254627 | ||||||||
\(603\) | 2.00000 | 0.0814463 | ||||||||
\(604\) | 56.0000 | 2.27861 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | −9.30306 | −0.377911 | ||||||||
\(607\) | −14.8990 | −0.604731 | −0.302365 | − | 0.953192i | \(-0.597776\pi\) | ||||
−0.302365 | + | 0.953192i | \(0.597776\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.550510 | −0.0223078 | ||||||||
\(610\) | −5.14643 | −0.208373 | ||||||||
\(611\) | 3.79796 | 0.153649 | ||||||||
\(612\) | −12.0000 | −0.485071 | ||||||||
\(613\) | −7.79796 | −0.314957 | −0.157478 | − | 0.987522i | \(-0.550336\pi\) | ||||
−0.157478 | + | 0.987522i | \(0.550336\pi\) | |||||||
\(614\) | −12.4949 | −0.504253 | ||||||||
\(615\) | 2.44949 | 0.0987730 | ||||||||
\(616\) | −4.89898 | −0.197386 | ||||||||
\(617\) | 12.4949 | 0.503026 | 0.251513 | − | 0.967854i | \(-0.419072\pi\) | ||||
0.251513 | + | 0.967854i | \(0.419072\pi\) | |||||||
\(618\) | 44.9444 | 1.80793 | ||||||||
\(619\) | −31.7980 | −1.27807 | −0.639034 | − | 0.769179i | \(-0.720666\pi\) | ||||
−0.639034 | + | 0.769179i | \(0.720666\pi\) | |||||||
\(620\) | −21.3939 | −0.859199 | ||||||||
\(621\) | −1.89898 | −0.0762034 | ||||||||
\(622\) | 12.0000 | 0.481156 | ||||||||
\(623\) | −10.3485 | −0.414603 | ||||||||
\(624\) | −1.79796 | −0.0719760 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 56.9444 | 2.27596 | ||||||||
\(627\) | 1.00000 | 0.0399362 | ||||||||
\(628\) | −48.5857 | −1.93878 | ||||||||
\(629\) | −13.3485 | −0.532238 | ||||||||
\(630\) | 2.44949 | 0.0975900 | ||||||||
\(631\) | −10.3031 | −0.410158 | −0.205079 | − | 0.978745i | \(-0.565745\pi\) | ||||
−0.205079 | + | 0.978745i | \(0.565745\pi\) | |||||||
\(632\) | 16.4041 | 0.652519 | ||||||||
\(633\) | 6.89898 | 0.274210 | ||||||||
\(634\) | 6.60612 | 0.262363 | ||||||||
\(635\) | −10.5505 | −0.418684 | ||||||||
\(636\) | 12.0000 | 0.475831 | ||||||||
\(637\) | −0.449490 | −0.0178094 | ||||||||
\(638\) | 1.34847 | 0.0533864 | ||||||||
\(639\) | 12.2474 | 0.484502 | ||||||||
\(640\) | −19.5959 | −0.774597 | ||||||||
\(641\) | −42.0000 | −1.65890 | −0.829450 | − | 0.558581i | \(-0.811346\pi\) | ||||
−0.829450 | + | 0.558581i | \(0.811346\pi\) | |||||||
\(642\) | −3.30306 | −0.130361 | ||||||||
\(643\) | 41.7423 | 1.64616 | 0.823079 | − | 0.567927i | \(-0.192255\pi\) | ||||
0.823079 | + | 0.567927i | \(0.192255\pi\) | |||||||
\(644\) | −7.59592 | −0.299321 | ||||||||
\(645\) | 2.55051 | 0.100426 | ||||||||
\(646\) | 7.34847 | 0.289122 | ||||||||
\(647\) | −7.10102 | −0.279170 | −0.139585 | − | 0.990210i | \(-0.544577\pi\) | ||||
−0.139585 | + | 0.990210i | \(0.544577\pi\) | |||||||
\(648\) | 4.89898 | 0.192450 | ||||||||
\(649\) | −0.550510 | −0.0216094 | ||||||||
\(650\) | −1.10102 | −0.0431856 | ||||||||
\(651\) | −5.34847 | −0.209623 | ||||||||
\(652\) | −49.7980 | −1.95024 | ||||||||
\(653\) | 48.1918 | 1.88589 | 0.942946 | − | 0.332945i | \(-0.108042\pi\) | ||||
0.942946 | + | 0.332945i | \(0.108042\pi\) | |||||||
\(654\) | −1.10102 | −0.0430533 | ||||||||
\(655\) | −3.55051 | −0.138730 | ||||||||
\(656\) | 9.79796 | 0.382546 | ||||||||
\(657\) | 3.10102 | 0.120982 | ||||||||
\(658\) | −20.6969 | −0.806851 | ||||||||
\(659\) | −31.0454 | −1.20936 | −0.604679 | − | 0.796470i | \(-0.706698\pi\) | ||||
−0.604679 | + | 0.796470i | \(0.706698\pi\) | |||||||
\(660\) | −4.00000 | −0.155700 | ||||||||
\(661\) | −22.2474 | −0.865325 | −0.432663 | − | 0.901556i | \(-0.642426\pi\) | ||||
−0.432663 | + | 0.901556i | \(0.642426\pi\) | |||||||
\(662\) | 77.6413 | 3.01762 | ||||||||
\(663\) | 1.34847 | 0.0523702 | ||||||||
\(664\) | −44.0908 | −1.71106 | ||||||||
\(665\) | −1.00000 | −0.0387783 | ||||||||
\(666\) | 10.8990 | 0.422327 | ||||||||
\(667\) | 1.04541 | 0.0404783 | ||||||||
\(668\) | −24.0000 | −0.928588 | ||||||||
\(669\) | 24.3485 | 0.941366 | ||||||||
\(670\) | 4.89898 | 0.189264 | ||||||||
\(671\) | 2.10102 | 0.0811090 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.3485 | 0.938565 | 0.469282 | − | 0.883048i | \(-0.344513\pi\) | ||||
0.469282 | + | 0.883048i | \(0.344513\pi\) | |||||||
\(674\) | −5.75255 | −0.221580 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | −51.1918 | −1.96892 | ||||||||
\(677\) | 36.1918 | 1.39097 | 0.695483 | − | 0.718543i | \(-0.255191\pi\) | ||||
0.695483 | + | 0.718543i | \(0.255191\pi\) | |||||||
\(678\) | 22.0454 | 0.846649 | ||||||||
\(679\) | −3.44949 | −0.132379 | ||||||||
\(680\) | −14.6969 | −0.563602 | ||||||||
\(681\) | −27.4949 | −1.05361 | ||||||||
\(682\) | 13.1010 | 0.501664 | ||||||||
\(683\) | 31.5959 | 1.20898 | 0.604492 | − | 0.796611i | \(-0.293376\pi\) | ||||
0.604492 | + | 0.796611i | \(0.293376\pi\) | |||||||
\(684\) | −4.00000 | −0.152944 | ||||||||
\(685\) | 12.0000 | 0.458496 | ||||||||
\(686\) | 2.44949 | 0.0935220 | ||||||||
\(687\) | −2.65153 | −0.101162 | ||||||||
\(688\) | 10.2020 | 0.388949 | ||||||||
\(689\) | −1.34847 | −0.0513726 | ||||||||
\(690\) | −4.65153 | −0.177081 | ||||||||
\(691\) | −34.0000 | −1.29342 | −0.646710 | − | 0.762736i | \(-0.723856\pi\) | ||||
−0.646710 | + | 0.762736i | \(0.723856\pi\) | |||||||
\(692\) | −8.80816 | −0.334836 | ||||||||
\(693\) | −1.00000 | −0.0379869 | ||||||||
\(694\) | 30.6061 | 1.16179 | ||||||||
\(695\) | −7.79796 | −0.295793 | ||||||||
\(696\) | −2.69694 | −0.102227 | ||||||||
\(697\) | −7.34847 | −0.278343 | ||||||||
\(698\) | 38.9444 | 1.47407 | ||||||||
\(699\) | −22.0454 | −0.833834 | ||||||||
\(700\) | 4.00000 | 0.151186 | ||||||||
\(701\) | 22.3485 | 0.844090 | 0.422045 | − | 0.906575i | \(-0.361312\pi\) | ||||
0.422045 | + | 0.906575i | \(0.361312\pi\) | |||||||
\(702\) | −1.10102 | −0.0415553 | ||||||||
\(703\) | −4.44949 | −0.167816 | ||||||||
\(704\) | 8.00000 | 0.301511 | ||||||||
\(705\) | −8.44949 | −0.318226 | ||||||||
\(706\) | −21.3031 | −0.801751 | ||||||||
\(707\) | −3.79796 | −0.142837 | ||||||||
\(708\) | 2.20204 | 0.0827578 | ||||||||
\(709\) | −1.00000 | −0.0375558 | −0.0187779 | − | 0.999824i | \(-0.505978\pi\) | ||||
−0.0187779 | + | 0.999824i | \(0.505978\pi\) | |||||||
\(710\) | 30.0000 | 1.12588 | ||||||||
\(711\) | 3.34847 | 0.125577 | ||||||||
\(712\) | −50.6969 | −1.89995 | ||||||||
\(713\) | 10.1566 | 0.380369 | ||||||||
\(714\) | −7.34847 | −0.275010 | ||||||||
\(715\) | 0.449490 | 0.0168100 | ||||||||
\(716\) | 57.7980 | 2.16001 | ||||||||
\(717\) | −0.550510 | −0.0205592 | ||||||||
\(718\) | −52.0454 | −1.94232 | ||||||||
\(719\) | −33.2474 | −1.23992 | −0.619960 | − | 0.784633i | \(-0.712851\pi\) | ||||
−0.619960 | + | 0.784633i | \(0.712851\pi\) | |||||||
\(720\) | 4.00000 | 0.149071 | ||||||||
\(721\) | 18.3485 | 0.683333 | ||||||||
\(722\) | −44.0908 | −1.64089 | ||||||||
\(723\) | 10.6969 | 0.397823 | ||||||||
\(724\) | 95.1918 | 3.53778 | ||||||||
\(725\) | −0.550510 | −0.0204454 | ||||||||
\(726\) | 2.44949 | 0.0909091 | ||||||||
\(727\) | 1.94439 | 0.0721133 | 0.0360567 | − | 0.999350i | \(-0.488520\pi\) | ||||
0.0360567 | + | 0.999350i | \(0.488520\pi\) | |||||||
\(728\) | −2.20204 | −0.0816131 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 7.59592 | 0.281138 | ||||||||
\(731\) | −7.65153 | −0.283002 | ||||||||
\(732\) | −8.40408 | −0.310624 | ||||||||
\(733\) | 42.8990 | 1.58451 | 0.792255 | − | 0.610190i | \(-0.208907\pi\) | ||||
0.792255 | + | 0.610190i | \(0.208907\pi\) | |||||||
\(734\) | 36.8536 | 1.36029 | ||||||||
\(735\) | 1.00000 | 0.0368856 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.00000 | −0.0736709 | ||||||||
\(738\) | 6.00000 | 0.220863 | ||||||||
\(739\) | −48.6969 | −1.79135 | −0.895673 | − | 0.444713i | \(-0.853306\pi\) | ||||
−0.895673 | + | 0.444713i | \(0.853306\pi\) | |||||||
\(740\) | 17.7980 | 0.654266 | ||||||||
\(741\) | 0.449490 | 0.0165124 | ||||||||
\(742\) | 7.34847 | 0.269771 | ||||||||
\(743\) | 52.2929 | 1.91844 | 0.959219 | − | 0.282663i | \(-0.0912177\pi\) | ||||
0.959219 | + | 0.282663i | \(0.0912177\pi\) | |||||||
\(744\) | −26.2020 | −0.960613 | ||||||||
\(745\) | −8.69694 | −0.318631 | ||||||||
\(746\) | 39.5505 | 1.44805 | ||||||||
\(747\) | −9.00000 | −0.329293 | ||||||||
\(748\) | 12.0000 | 0.438763 | ||||||||
\(749\) | −1.34847 | −0.0492720 | ||||||||
\(750\) | 2.44949 | 0.0894427 | ||||||||
\(751\) | −31.4949 | −1.14927 | −0.574633 | − | 0.818412i | \(-0.694855\pi\) | ||||
−0.574633 | + | 0.818412i | \(0.694855\pi\) | |||||||
\(752\) | −33.7980 | −1.23248 | ||||||||
\(753\) | 21.7980 | 0.794362 | ||||||||
\(754\) | 0.606123 | 0.0220737 | ||||||||
\(755\) | 14.0000 | 0.509512 | ||||||||
\(756\) | 4.00000 | 0.145479 | ||||||||
\(757\) | −20.2929 | −0.737556 | −0.368778 | − | 0.929517i | \(-0.620224\pi\) | ||||
−0.368778 | + | 0.929517i | \(0.620224\pi\) | |||||||
\(758\) | 86.9444 | 3.15796 | ||||||||
\(759\) | 1.89898 | 0.0689286 | ||||||||
\(760\) | −4.89898 | −0.177705 | ||||||||
\(761\) | 3.79796 | 0.137676 | 0.0688380 | − | 0.997628i | \(-0.478071\pi\) | ||||
0.0688380 | + | 0.997628i | \(0.478071\pi\) | |||||||
\(762\) | −25.8434 | −0.936206 | ||||||||
\(763\) | −0.449490 | −0.0162726 | ||||||||
\(764\) | −8.80816 | −0.318668 | ||||||||
\(765\) | −3.00000 | −0.108465 | ||||||||
\(766\) | 6.00000 | 0.216789 | ||||||||
\(767\) | −0.247449 | −0.00893486 | ||||||||
\(768\) | −32.0000 | −1.15470 | ||||||||
\(769\) | −32.1010 | −1.15759 | −0.578796 | − | 0.815472i | \(-0.696477\pi\) | ||||
−0.578796 | + | 0.815472i | \(0.696477\pi\) | |||||||
\(770\) | −2.44949 | −0.0882735 | ||||||||
\(771\) | 14.4495 | 0.520386 | ||||||||
\(772\) | 105.980 | 3.81429 | ||||||||
\(773\) | 1.10102 | 0.0396010 | 0.0198005 | − | 0.999804i | \(-0.493697\pi\) | ||||
0.0198005 | + | 0.999804i | \(0.493697\pi\) | |||||||
\(774\) | 6.24745 | 0.224560 | ||||||||
\(775\) | −5.34847 | −0.192123 | ||||||||
\(776\) | −16.8990 | −0.606638 | ||||||||
\(777\) | 4.44949 | 0.159625 | ||||||||
\(778\) | −15.3031 | −0.548641 | ||||||||
\(779\) | −2.44949 | −0.0877621 | ||||||||
\(780\) | −1.79796 | −0.0643773 | ||||||||
\(781\) | −12.2474 | −0.438248 | ||||||||
\(782\) | 13.9546 | 0.499015 | ||||||||
\(783\) | −0.550510 | −0.0196736 | ||||||||
\(784\) | 4.00000 | 0.142857 | ||||||||
\(785\) | −12.1464 | −0.433525 | ||||||||
\(786\) | −8.69694 | −0.310210 | ||||||||
\(787\) | −21.3939 | −0.762609 | −0.381305 | − | 0.924449i | \(-0.624525\pi\) | ||||
−0.381305 | + | 0.924449i | \(0.624525\pi\) | |||||||
\(788\) | 67.5959 | 2.40800 | ||||||||
\(789\) | −16.8990 | −0.601620 | ||||||||
\(790\) | 8.20204 | 0.291816 | ||||||||
\(791\) | 9.00000 | 0.320003 | ||||||||
\(792\) | −4.89898 | −0.174078 | ||||||||
\(793\) | 0.944387 | 0.0335362 | ||||||||
\(794\) | 55.5959 | 1.97303 | ||||||||
\(795\) | 3.00000 | 0.106399 | ||||||||
\(796\) | −103.192 | −3.65754 | ||||||||
\(797\) | 40.2929 | 1.42725 | 0.713623 | − | 0.700530i | \(-0.247053\pi\) | ||||
0.713623 | + | 0.700530i | \(0.247053\pi\) | |||||||
\(798\) | −2.44949 | −0.0867110 | ||||||||
\(799\) | 25.3485 | 0.896764 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.3485 | −0.365645 | ||||||||
\(802\) | −76.7878 | −2.71147 | ||||||||
\(803\) | −3.10102 | −0.109433 | ||||||||
\(804\) | 8.00000 | 0.282138 | ||||||||
\(805\) | −1.89898 | −0.0669302 | ||||||||
\(806\) | 5.88877 | 0.207423 | ||||||||
\(807\) | −11.4495 | −0.403041 | ||||||||
\(808\) | −18.6061 | −0.654561 | ||||||||
\(809\) | 8.69694 | 0.305768 | 0.152884 | − | 0.988244i | \(-0.451144\pi\) | ||||
0.152884 | + | 0.988244i | \(0.451144\pi\) | |||||||
\(810\) | 2.44949 | 0.0860663 | ||||||||
\(811\) | 25.3939 | 0.891700 | 0.445850 | − | 0.895108i | \(-0.352902\pi\) | ||||
0.445850 | + | 0.895108i | \(0.352902\pi\) | |||||||
\(812\) | −2.20204 | −0.0772765 | ||||||||
\(813\) | −1.00000 | −0.0350715 | ||||||||
\(814\) | −10.8990 | −0.382009 | ||||||||
\(815\) | −12.4495 | −0.436087 | ||||||||
\(816\) | −12.0000 | −0.420084 | ||||||||
\(817\) | −2.55051 | −0.0892311 | ||||||||
\(818\) | 31.5959 | 1.10473 | ||||||||
\(819\) | −0.449490 | −0.0157064 | ||||||||
\(820\) | 9.79796 | 0.342160 | ||||||||
\(821\) | 30.5505 | 1.06622 | 0.533110 | − | 0.846046i | \(-0.321023\pi\) | ||||
0.533110 | + | 0.846046i | \(0.321023\pi\) | |||||||
\(822\) | 29.3939 | 1.02523 | ||||||||
\(823\) | 38.2474 | 1.33322 | 0.666611 | − | 0.745406i | \(-0.267744\pi\) | ||||
0.666611 | + | 0.745406i | \(0.267744\pi\) | |||||||
\(824\) | 89.8888 | 3.13142 | ||||||||
\(825\) | −1.00000 | −0.0348155 | ||||||||
\(826\) | 1.34847 | 0.0469192 | ||||||||
\(827\) | 2.69694 | 0.0937817 | 0.0468909 | − | 0.998900i | \(-0.485069\pi\) | ||||
0.0468909 | + | 0.998900i | \(0.485069\pi\) | |||||||
\(828\) | −7.59592 | −0.263976 | ||||||||
\(829\) | 46.0908 | 1.60080 | 0.800400 | − | 0.599466i | \(-0.204620\pi\) | ||||
0.800400 | + | 0.599466i | \(0.204620\pi\) | |||||||
\(830\) | −22.0454 | −0.765207 | ||||||||
\(831\) | 10.6969 | 0.371073 | ||||||||
\(832\) | 3.59592 | 0.124666 | ||||||||
\(833\) | −3.00000 | −0.103944 | ||||||||
\(834\) | −19.1010 | −0.661414 | ||||||||
\(835\) | −6.00000 | −0.207639 | ||||||||
\(836\) | 4.00000 | 0.138343 | ||||||||
\(837\) | −5.34847 | −0.184870 | ||||||||
\(838\) | −69.4393 | −2.39874 | ||||||||
\(839\) | 14.1464 | 0.488389 | 0.244194 | − | 0.969726i | \(-0.421476\pi\) | ||||
0.244194 | + | 0.969726i | \(0.421476\pi\) | |||||||
\(840\) | 4.89898 | 0.169031 | ||||||||
\(841\) | −28.6969 | −0.989550 | ||||||||
\(842\) | 36.2474 | 1.24917 | ||||||||
\(843\) | 16.8990 | 0.582032 | ||||||||
\(844\) | 27.5959 | 0.949891 | ||||||||
\(845\) | −12.7980 | −0.440263 | ||||||||
\(846\) | −20.6969 | −0.711575 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 12.0000 | 0.412082 | ||||||||
\(849\) | −14.6515 | −0.502839 | ||||||||
\(850\) | −7.34847 | −0.252050 | ||||||||
\(851\) | −8.44949 | −0.289645 | ||||||||
\(852\) | 48.9898 | 1.67836 | ||||||||
\(853\) | −14.0454 | −0.480906 | −0.240453 | − | 0.970661i | \(-0.577296\pi\) | ||||
−0.240453 | + | 0.970661i | \(0.577296\pi\) | |||||||
\(854\) | −5.14643 | −0.176107 | ||||||||
\(855\) | −1.00000 | −0.0341993 | ||||||||
\(856\) | −6.60612 | −0.225793 | ||||||||
\(857\) | −30.0000 | −1.02478 | −0.512390 | − | 0.858753i | \(-0.671240\pi\) | ||||
−0.512390 | + | 0.858753i | \(0.671240\pi\) | |||||||
\(858\) | 1.10102 | 0.0375882 | ||||||||
\(859\) | 11.5505 | 0.394098 | 0.197049 | − | 0.980394i | \(-0.436864\pi\) | ||||
0.197049 | + | 0.980394i | \(0.436864\pi\) | |||||||
\(860\) | 10.2020 | 0.347887 | ||||||||
\(861\) | 2.44949 | 0.0834784 | ||||||||
\(862\) | −89.3939 | −3.04477 | ||||||||
\(863\) | 1.40408 | 0.0477955 | 0.0238978 | − | 0.999714i | \(-0.492392\pi\) | ||||
0.0238978 | + | 0.999714i | \(0.492392\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.20204 | −0.0748716 | ||||||||
\(866\) | 94.2929 | 3.20420 | ||||||||
\(867\) | −8.00000 | −0.271694 | ||||||||
\(868\) | −21.3939 | −0.726155 | ||||||||
\(869\) | −3.34847 | −0.113589 | ||||||||
\(870\) | −1.34847 | −0.0457174 | ||||||||
\(871\) | −0.898979 | −0.0304608 | ||||||||
\(872\) | −2.20204 | −0.0745705 | ||||||||
\(873\) | −3.44949 | −0.116748 | ||||||||
\(874\) | 4.65153 | 0.157340 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 12.4041 | 0.419095 | ||||||||
\(877\) | −17.6515 | −0.596050 | −0.298025 | − | 0.954558i | \(-0.596328\pi\) | ||||
−0.298025 | + | 0.954558i | \(0.596328\pi\) | |||||||
\(878\) | 38.9444 | 1.31431 | ||||||||
\(879\) | −16.5959 | −0.559766 | ||||||||
\(880\) | −4.00000 | −0.134840 | ||||||||
\(881\) | −1.04541 | −0.0352207 | −0.0176103 | − | 0.999845i | \(-0.505606\pi\) | ||||
−0.0176103 | + | 0.999845i | \(0.505606\pi\) | |||||||
\(882\) | 2.44949 | 0.0824786 | ||||||||
\(883\) | −14.2929 | −0.480993 | −0.240496 | − | 0.970650i | \(-0.577310\pi\) | ||||
−0.240496 | + | 0.970650i | \(0.577310\pi\) | |||||||
\(884\) | 5.39388 | 0.181416 | ||||||||
\(885\) | 0.550510 | 0.0185052 | ||||||||
\(886\) | 14.6969 | 0.493753 | ||||||||
\(887\) | 21.4949 | 0.721728 | 0.360864 | − | 0.932618i | \(-0.382482\pi\) | ||||
0.360864 | + | 0.932618i | \(0.382482\pi\) | |||||||
\(888\) | 21.7980 | 0.731492 | ||||||||
\(889\) | −10.5505 | −0.353853 | ||||||||
\(890\) | −25.3485 | −0.849683 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 97.3939 | 3.26099 | ||||||||
\(893\) | 8.44949 | 0.282751 | ||||||||
\(894\) | −21.3031 | −0.712481 | ||||||||
\(895\) | 14.4495 | 0.482993 | ||||||||
\(896\) | −19.5959 | −0.654654 | ||||||||
\(897\) | 0.853572 | 0.0284999 | ||||||||
\(898\) | 18.0000 | 0.600668 | ||||||||
\(899\) | 2.94439 | 0.0982008 | ||||||||
\(900\) | 4.00000 | 0.133333 | ||||||||
\(901\) | −9.00000 | −0.299833 | ||||||||
\(902\) | −6.00000 | −0.199778 | ||||||||
\(903\) | 2.55051 | 0.0848757 | ||||||||
\(904\) | 44.0908 | 1.46644 | ||||||||
\(905\) | 23.7980 | 0.791071 | ||||||||
\(906\) | 34.2929 | 1.13930 | ||||||||
\(907\) | −20.0454 | −0.665597 | −0.332798 | − | 0.942998i | \(-0.607993\pi\) | ||||
−0.332798 | + | 0.942998i | \(0.607993\pi\) | |||||||
\(908\) | −109.980 | −3.64980 | ||||||||
\(909\) | −3.79796 | −0.125970 | ||||||||
\(910\) | −1.10102 | −0.0364985 | ||||||||
\(911\) | −58.2929 | −1.93133 | −0.965664 | − | 0.259793i | \(-0.916346\pi\) | ||||
−0.965664 | + | 0.259793i | \(0.916346\pi\) | |||||||
\(912\) | −4.00000 | −0.132453 | ||||||||
\(913\) | 9.00000 | 0.297857 | ||||||||
\(914\) | 77.0352 | 2.54810 | ||||||||
\(915\) | −2.10102 | −0.0694576 | ||||||||
\(916\) | −10.6061 | −0.350436 | ||||||||
\(917\) | −3.55051 | −0.117248 | ||||||||
\(918\) | −7.34847 | −0.242536 | ||||||||
\(919\) | 26.0000 | 0.857661 | 0.428830 | − | 0.903385i | \(-0.358926\pi\) | ||||
0.428830 | + | 0.903385i | \(0.358926\pi\) | |||||||
\(920\) | −9.30306 | −0.306713 | ||||||||
\(921\) | −5.10102 | −0.168084 | ||||||||
\(922\) | 2.69694 | 0.0888189 | ||||||||
\(923\) | −5.50510 | −0.181203 | ||||||||
\(924\) | −4.00000 | −0.131590 | ||||||||
\(925\) | 4.44949 | 0.146298 | ||||||||
\(926\) | 11.5051 | 0.378081 | ||||||||
\(927\) | 18.3485 | 0.602643 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.10102 | −0.232977 | −0.116488 | − | 0.993192i | \(-0.537164\pi\) | ||||
−0.116488 | + | 0.993192i | \(0.537164\pi\) | |||||||
\(930\) | −13.1010 | −0.429599 | ||||||||
\(931\) | −1.00000 | −0.0327737 | ||||||||
\(932\) | −88.1816 | −2.88849 | ||||||||
\(933\) | 4.89898 | 0.160385 | ||||||||
\(934\) | 30.6061 | 1.00146 | ||||||||
\(935\) | 3.00000 | 0.0981105 | ||||||||
\(936\) | −2.20204 | −0.0719760 | ||||||||
\(937\) | 0.651531 | 0.0212846 | 0.0106423 | − | 0.999943i | \(-0.496612\pi\) | ||||
0.0106423 | + | 0.999943i | \(0.496612\pi\) | |||||||
\(938\) | 4.89898 | 0.159957 | ||||||||
\(939\) | 23.2474 | 0.758652 | ||||||||
\(940\) | −33.7980 | −1.10237 | ||||||||
\(941\) | 16.0454 | 0.523065 | 0.261533 | − | 0.965195i | \(-0.415772\pi\) | ||||
0.261533 | + | 0.965195i | \(0.415772\pi\) | |||||||
\(942\) | −29.7526 | −0.969391 | ||||||||
\(943\) | −4.65153 | −0.151475 | ||||||||
\(944\) | 2.20204 | 0.0716703 | ||||||||
\(945\) | 1.00000 | 0.0325300 | ||||||||
\(946\) | −6.24745 | −0.203122 | ||||||||
\(947\) | −36.1918 | −1.17608 | −0.588038 | − | 0.808833i | \(-0.700100\pi\) | ||||
−0.588038 | + | 0.808833i | \(0.700100\pi\) | |||||||
\(948\) | 13.3939 | 0.435013 | ||||||||
\(949\) | −1.39388 | −0.0452472 | ||||||||
\(950\) | −2.44949 | −0.0794719 | ||||||||
\(951\) | 2.69694 | 0.0874542 | ||||||||
\(952\) | −14.6969 | −0.476331 | ||||||||
\(953\) | 23.3939 | 0.757802 | 0.378901 | − | 0.925437i | \(-0.376302\pi\) | ||||
0.378901 | + | 0.925437i | \(0.376302\pi\) | |||||||
\(954\) | 7.34847 | 0.237915 | ||||||||
\(955\) | −2.20204 | −0.0712564 | ||||||||
\(956\) | −2.20204 | −0.0712191 | ||||||||
\(957\) | 0.550510 | 0.0177955 | ||||||||
\(958\) | −27.3031 | −0.882122 | ||||||||
\(959\) | 12.0000 | 0.387500 | ||||||||
\(960\) | −8.00000 | −0.258199 | ||||||||
\(961\) | −2.39388 | −0.0772218 | ||||||||
\(962\) | −4.89898 | −0.157949 | ||||||||
\(963\) | −1.34847 | −0.0434538 | ||||||||
\(964\) | 42.7878 | 1.37810 | ||||||||
\(965\) | 26.4949 | 0.852901 | ||||||||
\(966\) | −4.65153 | −0.149661 | ||||||||
\(967\) | −14.8434 | −0.477330 | −0.238665 | − | 0.971102i | \(-0.576710\pi\) | ||||
−0.238665 | + | 0.971102i | \(0.576710\pi\) | |||||||
\(968\) | 4.89898 | 0.157459 | ||||||||
\(969\) | 3.00000 | 0.0963739 | ||||||||
\(970\) | −8.44949 | −0.271297 | ||||||||
\(971\) | −22.3485 | −0.717197 | −0.358598 | − | 0.933492i | \(-0.616745\pi\) | ||||
−0.358598 | + | 0.933492i | \(0.616745\pi\) | |||||||
\(972\) | 4.00000 | 0.128300 | ||||||||
\(973\) | −7.79796 | −0.249991 | ||||||||
\(974\) | 22.2929 | 0.714309 | ||||||||
\(975\) | −0.449490 | −0.0143952 | ||||||||
\(976\) | −8.40408 | −0.269008 | ||||||||
\(977\) | 19.4041 | 0.620792 | 0.310396 | − | 0.950607i | \(-0.399538\pi\) | ||||
0.310396 | + | 0.950607i | \(0.399538\pi\) | |||||||
\(978\) | −30.4949 | −0.975119 | ||||||||
\(979\) | 10.3485 | 0.330739 | ||||||||
\(980\) | 4.00000 | 0.127775 | ||||||||
\(981\) | −0.449490 | −0.0143511 | ||||||||
\(982\) | −16.0454 | −0.512030 | ||||||||
\(983\) | −30.4949 | −0.972636 | −0.486318 | − | 0.873782i | \(-0.661660\pi\) | ||||
−0.486318 | + | 0.873782i | \(0.661660\pi\) | |||||||
\(984\) | 12.0000 | 0.382546 | ||||||||
\(985\) | 16.8990 | 0.538446 | ||||||||
\(986\) | 4.04541 | 0.128832 | ||||||||
\(987\) | −8.44949 | −0.268950 | ||||||||
\(988\) | 1.79796 | 0.0572007 | ||||||||
\(989\) | −4.84337 | −0.154010 | ||||||||
\(990\) | −2.44949 | −0.0778499 | ||||||||
\(991\) | 6.59592 | 0.209526 | 0.104763 | − | 0.994497i | \(-0.466592\pi\) | ||||
0.104763 | + | 0.994497i | \(0.466592\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 31.6969 | 1.00587 | ||||||||
\(994\) | 30.0000 | 0.951542 | ||||||||
\(995\) | −25.7980 | −0.817850 | ||||||||
\(996\) | −36.0000 | −1.14070 | ||||||||
\(997\) | 7.39388 | 0.234166 | 0.117083 | − | 0.993122i | \(-0.462646\pi\) | ||||
0.117083 | + | 0.993122i | \(0.462646\pi\) | |||||||
\(998\) | −22.5403 | −0.713501 | ||||||||
\(999\) | 4.44949 | 0.140776 |
(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 | 1155.2.a.q.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 3465.2.a.y.1.1 | 2 | |||
5.4 | even | 2 | 5775.2.a.bh.1.1 | 2 | |||
7.6 | odd | 2 | 8085.2.a.be.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.a.q.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
3465.2.a.y.1.1 | 2 | 3.2 | odd | 2 | |||
5775.2.a.bh.1.1 | 2 | 5.4 | even | 2 | |||
8085.2.a.be.1.2 | 2 | 7.6 | odd | 2 |