Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [387,2,Mod(1,387)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(387, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("387.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 387 = 3^{2} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 387.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: | \(3.09021055822\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{5}, \sqrt{13})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 9x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.684742\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 387.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.23607 | −1.58114 | −0.790569 | − | 0.612372i | \(-0.790215\pi\) | ||||
−0.790569 | + | 0.612372i | \(0.790215\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.00000 | 1.50000 | ||||||||
\(5\) | 0.684742 | 0.306226 | 0.153113 | − | 0.988209i | \(-0.451070\pi\) | ||||
0.153113 | + | 0.988209i | \(0.451070\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.53113 | 1.33464 | 0.667321 | − | 0.744771i | \(-0.267441\pi\) | ||||
0.667321 | + | 0.744771i | \(0.267441\pi\) | |||||||
\(8\) | −2.23607 | −0.790569 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.53113 | −0.484185 | ||||||||
\(11\) | 0.684742 | 0.206457 | 0.103229 | − | 0.994658i | \(-0.467083\pi\) | ||||
0.103229 | + | 0.994658i | \(0.467083\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.53113 | −0.424659 | −0.212329 | − | 0.977198i | \(-0.568105\pi\) | ||||
−0.212329 | + | 0.977198i | \(0.568105\pi\) | |||||||
\(14\) | −7.89584 | −2.11025 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −1.36948 | −0.332148 | −0.166074 | − | 0.986113i | \(-0.553109\pi\) | ||||
−0.166074 | + | 0.986113i | \(0.553109\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.53113 | 0.810097 | 0.405048 | − | 0.914295i | \(-0.367255\pi\) | ||||
0.405048 | + | 0.914295i | \(0.367255\pi\) | |||||||
\(20\) | 2.05422 | 0.459339 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.53113 | −0.326438 | ||||||||
\(23\) | 5.84162 | 1.21806 | 0.609031 | − | 0.793146i | \(-0.291559\pi\) | ||||
0.609031 | + | 0.793146i | \(0.291559\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.53113 | −0.906226 | ||||||||
\(26\) | 3.42371 | 0.671444 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 10.5934 | 2.00196 | ||||||||
\(29\) | −2.05422 | −0.381460 | −0.190730 | − | 0.981643i | \(-0.561085\pi\) | ||||
−0.190730 | + | 0.981643i | \(0.561085\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 6.70820 | 1.18585 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.06226 | 0.525173 | ||||||||
\(35\) | 2.41791 | 0.408702 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.00000 | 0.986394 | 0.493197 | − | 0.869918i | \(-0.335828\pi\) | ||||
0.493197 | + | 0.869918i | \(0.335828\pi\) | |||||||
\(38\) | −7.89584 | −1.28088 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.53113 | −0.242093 | ||||||||
\(41\) | 11.6832 | 1.82462 | 0.912308 | − | 0.409505i | \(-0.134299\pi\) | ||||
0.912308 | + | 0.409505i | \(0.134299\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | 2.05422 | 0.309686 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −13.0623 | −1.92592 | ||||||||
\(47\) | −2.05422 | −0.299640 | −0.149820 | − | 0.988713i | \(-0.547869\pi\) | ||||
−0.149820 | + | 0.988713i | \(0.547869\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.46887 | 0.781267 | ||||||||
\(50\) | 10.1319 | 1.43287 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.59339 | −0.636988 | ||||||||
\(53\) | 11.6832 | 1.60482 | 0.802408 | − | 0.596776i | \(-0.203552\pi\) | ||||
0.802408 | + | 0.596776i | \(0.203552\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.468871 | 0.0632226 | ||||||||
\(56\) | −7.89584 | −1.05513 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.59339 | 0.603141 | ||||||||
\(59\) | 5.84162 | 0.760514 | 0.380257 | − | 0.924881i | \(-0.375836\pi\) | ||||
0.380257 | + | 0.924881i | \(0.375836\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −13.0000 | −1.62500 | ||||||||
\(65\) | −1.04843 | −0.130041 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000 | 0.488678 | 0.244339 | − | 0.969690i | \(-0.421429\pi\) | ||||
0.244339 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(68\) | −4.10845 | −0.498223 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.40661 | −0.646214 | ||||||||
\(71\) | −13.0527 | −1.54907 | −0.774537 | − | 0.632529i | \(-0.782017\pi\) | ||||
−0.774537 | + | 0.632529i | \(0.782017\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.00000 | 0.702247 | 0.351123 | − | 0.936329i | \(-0.385800\pi\) | ||||
0.351123 | + | 0.936329i | \(0.385800\pi\) | |||||||
\(74\) | −13.4164 | −1.55963 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 10.5934 | 1.21514 | ||||||||
\(77\) | 2.41791 | 0.275547 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.0623 | −1.69464 | −0.847318 | − | 0.531086i | \(-0.821784\pi\) | ||||
−0.847318 | + | 0.531086i | \(0.821784\pi\) | |||||||
\(80\) | −0.684742 | −0.0765564 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −26.1245 | −2.88497 | ||||||||
\(83\) | −10.9985 | −1.20724 | −0.603621 | − | 0.797271i | \(-0.706276\pi\) | ||||
−0.603621 | + | 0.797271i | \(0.706276\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.937742 | −0.101712 | ||||||||
\(86\) | −2.23607 | −0.241121 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.53113 | −0.163219 | ||||||||
\(89\) | −13.4164 | −1.42214 | −0.711068 | − | 0.703123i | \(-0.751788\pi\) | ||||
−0.711068 | + | 0.703123i | \(0.751788\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.40661 | −0.566767 | ||||||||
\(92\) | 17.5249 | 1.82709 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.59339 | 0.473772 | ||||||||
\(95\) | 2.41791 | 0.248072 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.5311 | 1.37388 | 0.686939 | − | 0.726715i | \(-0.258954\pi\) | ||||
0.686939 | + | 0.726715i | \(0.258954\pi\) | |||||||
\(98\) | −12.2288 | −1.23529 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −13.5934 | −1.35934 | ||||||||
\(101\) | −8.94427 | −0.889988 | −0.444994 | − | 0.895533i | \(-0.646794\pi\) | ||||
−0.444994 | + | 0.895533i | \(0.646794\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 3.42371 | 0.335722 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −26.1245 | −2.53744 | ||||||||
\(107\) | 10.9985 | 1.06326 | 0.531632 | − | 0.846975i | \(-0.321579\pi\) | ||||
0.531632 | + | 0.846975i | \(0.321579\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.5934 | 1.58936 | 0.794679 | − | 0.607030i | \(-0.207639\pi\) | ||||
0.794679 | + | 0.607030i | \(0.207639\pi\) | |||||||
\(110\) | −1.04843 | −0.0999637 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.53113 | −0.333660 | ||||||||
\(113\) | 0.684742 | 0.0644151 | 0.0322075 | − | 0.999481i | \(-0.489746\pi\) | ||||
0.0322075 | + | 0.999481i | \(0.489746\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.00000 | 0.373002 | ||||||||
\(116\) | −6.16267 | −0.572190 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −13.0623 | −1.20248 | ||||||||
\(119\) | −4.83582 | −0.443299 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.5311 | −0.957375 | ||||||||
\(122\) | 4.47214 | 0.404888 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.52636 | −0.583735 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.06226 | −0.626674 | −0.313337 | − | 0.949642i | \(-0.601447\pi\) | ||||
−0.313337 | + | 0.949642i | \(0.601447\pi\) | |||||||
\(128\) | 15.6525 | 1.38350 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.34436 | 0.205614 | ||||||||
\(131\) | −11.6832 | −1.02077 | −0.510385 | − | 0.859946i | \(-0.670497\pi\) | ||||
−0.510385 | + | 0.859946i | \(0.670497\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.4689 | 1.08119 | ||||||||
\(134\) | −8.94427 | −0.772667 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.06226 | 0.262586 | ||||||||
\(137\) | 2.05422 | 0.175504 | 0.0877521 | − | 0.996142i | \(-0.472032\pi\) | ||||
0.0877521 | + | 0.996142i | \(0.472032\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.0000 | 1.01783 | 0.508913 | − | 0.860818i | \(-0.330047\pi\) | ||||
0.508913 | + | 0.860818i | \(0.330047\pi\) | |||||||
\(140\) | 7.25373 | 0.613052 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 29.1868 | 2.44930 | ||||||||
\(143\) | −1.04843 | −0.0876739 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.40661 | −0.116813 | ||||||||
\(146\) | −13.4164 | −1.11035 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 18.0000 | 1.47959 | ||||||||
\(149\) | −21.6333 | −1.77227 | −0.886135 | − | 0.463428i | \(-0.846619\pi\) | ||||
−0.886135 | + | 0.463428i | \(0.846619\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | 0.651031 | 0.325515 | − | 0.945537i | \(-0.394462\pi\) | ||||
0.325515 | + | 0.945537i | \(0.394462\pi\) | |||||||
\(152\) | −7.89584 | −0.640438 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −5.40661 | −0.435677 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.0000 | 1.11732 | 0.558661 | − | 0.829396i | \(-0.311315\pi\) | ||||
0.558661 | + | 0.829396i | \(0.311315\pi\) | |||||||
\(158\) | 33.6802 | 2.67946 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.59339 | 0.363139 | ||||||||
\(161\) | 20.6275 | 1.62568 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.5934 | −1.14304 | −0.571521 | − | 0.820587i | \(-0.693646\pi\) | ||||
−0.571521 | + | 0.820587i | \(0.693646\pi\) | |||||||
\(164\) | 35.0497 | 2.73692 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 24.5934 | 1.90882 | ||||||||
\(167\) | 15.1069 | 1.16901 | 0.584505 | − | 0.811390i | \(-0.301289\pi\) | ||||
0.584505 | + | 0.811390i | \(0.301289\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.6556 | −0.819665 | ||||||||
\(170\) | 2.09686 | 0.160821 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.00000 | 0.228748 | ||||||||
\(173\) | −17.8885 | −1.36004 | −0.680020 | − | 0.733193i | \(-0.738029\pi\) | ||||
−0.680020 | + | 0.733193i | \(0.738029\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −16.0000 | −1.20949 | ||||||||
\(176\) | −0.684742 | −0.0516143 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 30.0000 | 2.24860 | ||||||||
\(179\) | 4.83582 | 0.361446 | 0.180723 | − | 0.983534i | \(-0.442156\pi\) | ||||
0.180723 | + | 0.983534i | \(0.442156\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.5311 | 1.00576 | 0.502880 | − | 0.864356i | \(-0.332274\pi\) | ||||
0.502880 | + | 0.864356i | \(0.332274\pi\) | |||||||
\(182\) | 12.0896 | 0.896137 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −13.0623 | −0.962962 | ||||||||
\(185\) | 4.10845 | 0.302059 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.937742 | −0.0685745 | ||||||||
\(188\) | −6.16267 | −0.449459 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.40661 | −0.392237 | ||||||||
\(191\) | 11.6832 | 0.845369 | 0.422685 | − | 0.906277i | \(-0.361088\pi\) | ||||
0.422685 | + | 0.906277i | \(0.361088\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.0000 | −0.719816 | −0.359908 | − | 0.932988i | \(-0.617192\pi\) | ||||
−0.359908 | + | 0.932988i | \(0.617192\pi\) | |||||||
\(194\) | −30.2565 | −2.17229 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 16.4066 | 1.17190 | ||||||||
\(197\) | 21.9970 | 1.56722 | 0.783610 | − | 0.621252i | \(-0.213376\pi\) | ||||
0.783610 | + | 0.621252i | \(0.213376\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −26.1245 | −1.85192 | −0.925959 | − | 0.377624i | \(-0.876741\pi\) | ||||
−0.925959 | + | 0.377624i | \(0.876741\pi\) | |||||||
\(200\) | 10.1319 | 0.716434 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 20.0000 | 1.40720 | ||||||||
\(203\) | −7.25373 | −0.509112 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.00000 | 0.558744 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.53113 | 0.106165 | ||||||||
\(209\) | 2.41791 | 0.167250 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.4689 | −1.13376 | −0.566882 | − | 0.823799i | \(-0.691850\pi\) | ||||
−0.566882 | + | 0.823799i | \(0.691850\pi\) | |||||||
\(212\) | 35.0497 | 2.40722 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −24.5934 | −1.68117 | ||||||||
\(215\) | 0.684742 | 0.0466990 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −37.1039 | −2.51300 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.40661 | 0.0948339 | ||||||||
\(221\) | 2.09686 | 0.141050 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.6556 | −0.914450 | −0.457225 | − | 0.889351i | \(-0.651157\pi\) | ||||
−0.457225 | + | 0.889351i | \(0.651157\pi\) | |||||||
\(224\) | 23.6875 | 1.58269 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.53113 | −0.101849 | ||||||||
\(227\) | −26.1054 | −1.73268 | −0.866340 | − | 0.499455i | \(-0.833533\pi\) | ||||
−0.866340 | + | 0.499455i | \(0.833533\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.00000 | 0.396491 | 0.198246 | − | 0.980152i | \(-0.436476\pi\) | ||||
0.198246 | + | 0.980152i | \(0.436476\pi\) | |||||||
\(230\) | −8.94427 | −0.589768 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.59339 | 0.301571 | ||||||||
\(233\) | −21.3123 | −1.39621 | −0.698106 | − | 0.715994i | \(-0.745974\pi\) | ||||
−0.698106 | + | 0.715994i | \(0.745974\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.40661 | −0.0917573 | ||||||||
\(236\) | 17.5249 | 1.14077 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 10.8132 | 0.700917 | ||||||||
\(239\) | −28.8870 | −1.86855 | −0.934274 | − | 0.356557i | \(-0.883951\pi\) | ||||
−0.934274 | + | 0.356557i | \(0.883951\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.1868 | 1.23593 | 0.617964 | − | 0.786206i | \(-0.287958\pi\) | ||||
0.617964 | + | 0.786206i | \(0.287958\pi\) | |||||||
\(242\) | 23.5483 | 1.51374 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.00000 | −0.384111 | ||||||||
\(245\) | 3.74476 | 0.239244 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.40661 | −0.344015 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 14.5934 | 0.922967 | ||||||||
\(251\) | 10.9985 | 0.694219 | 0.347109 | − | 0.937825i | \(-0.387163\pi\) | ||||
0.347109 | + | 0.937825i | \(0.387163\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.00000 | 0.251478 | ||||||||
\(254\) | 15.7917 | 0.990859 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.00000 | −0.562500 | ||||||||
\(257\) | −2.05422 | −0.128139 | −0.0640695 | − | 0.997945i | \(-0.520408\pi\) | ||||
−0.0640695 | + | 0.997945i | \(0.520408\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 21.1868 | 1.31648 | ||||||||
\(260\) | −3.14528 | −0.195062 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 26.1245 | 1.61398 | ||||||||
\(263\) | −15.7917 | −0.973757 | −0.486879 | − | 0.873470i | \(-0.661865\pi\) | ||||
−0.486879 | + | 0.873470i | \(0.661865\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.00000 | 0.491436 | ||||||||
\(266\) | −27.8812 | −1.70951 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 12.0000 | 0.733017 | ||||||||
\(269\) | −4.10845 | −0.250497 | −0.125248 | − | 0.992125i | \(-0.539973\pi\) | ||||
−0.125248 | + | 0.992125i | \(0.539973\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.1868 | −1.28700 | −0.643502 | − | 0.765444i | \(-0.722519\pi\) | ||||
−0.643502 | + | 0.765444i | \(0.722519\pi\) | |||||||
\(272\) | 1.36948 | 0.0830371 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.59339 | −0.277497 | ||||||||
\(275\) | −3.10265 | −0.187097 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.06226 | 0.544498 | 0.272249 | − | 0.962227i | \(-0.412233\pi\) | ||||
0.272249 | + | 0.962227i | \(0.412233\pi\) | |||||||
\(278\) | −26.8328 | −1.60933 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.40661 | −0.323107 | ||||||||
\(281\) | −13.0527 | −0.778660 | −0.389330 | − | 0.921098i | \(-0.627293\pi\) | ||||
−0.389330 | + | 0.921098i | \(0.627293\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.0623 | −1.13313 | −0.566567 | − | 0.824016i | \(-0.691729\pi\) | ||||
−0.566567 | + | 0.824016i | \(0.691729\pi\) | |||||||
\(284\) | −39.1582 | −2.32361 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.34436 | 0.138625 | ||||||||
\(287\) | 41.2550 | 2.43521 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.1245 | −0.889677 | ||||||||
\(290\) | 3.14528 | 0.184697 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 18.0000 | 1.05337 | ||||||||
\(293\) | −6.84742 | −0.400030 | −0.200015 | − | 0.979793i | \(-0.564099\pi\) | ||||
−0.200015 | + | 0.979793i | \(0.564099\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.00000 | 0.232889 | ||||||||
\(296\) | −13.4164 | −0.779813 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 48.3735 | 2.80220 | ||||||||
\(299\) | −8.94427 | −0.517261 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.53113 | 0.203531 | ||||||||
\(302\) | −17.8885 | −1.02937 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.53113 | −0.202524 | ||||||||
\(305\) | −1.36948 | −0.0784164 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.93774 | 0.281812 | 0.140906 | − | 0.990023i | \(-0.454998\pi\) | ||||
0.140906 | + | 0.990023i | \(0.454998\pi\) | |||||||
\(308\) | 7.25373 | 0.413320 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.8870 | 1.63803 | 0.819017 | − | 0.573769i | \(-0.194519\pi\) | ||||
0.819017 | + | 0.573769i | \(0.194519\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.00000 | 0.113047 | 0.0565233 | − | 0.998401i | \(-0.481998\pi\) | ||||
0.0565233 | + | 0.998401i | \(0.481998\pi\) | |||||||
\(314\) | −31.3050 | −1.76664 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −45.1868 | −2.54195 | ||||||||
\(317\) | 7.57479 | 0.425443 | 0.212721 | − | 0.977113i | \(-0.431767\pi\) | ||||
0.212721 | + | 0.977113i | \(0.431767\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.40661 | −0.0787552 | ||||||||
\(320\) | −8.90164 | −0.497617 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −46.1245 | −2.57042 | ||||||||
\(323\) | −4.83582 | −0.269072 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.93774 | 0.384837 | ||||||||
\(326\) | 32.6318 | 1.80731 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −26.1245 | −1.44249 | ||||||||
\(329\) | −7.25373 | −0.399911 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.53113 | −0.194088 | −0.0970442 | − | 0.995280i | \(-0.530939\pi\) | ||||
−0.0970442 | + | 0.995280i | \(0.530939\pi\) | |||||||
\(332\) | −32.9955 | −1.81086 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −33.7802 | −1.84837 | ||||||||
\(335\) | 2.73897 | 0.149646 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.40661 | −0.185570 | −0.0927850 | − | 0.995686i | \(-0.529577\pi\) | ||||
−0.0927850 | + | 0.995686i | \(0.529577\pi\) | |||||||
\(338\) | 23.8267 | 1.29600 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.81323 | −0.152569 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.40661 | −0.291930 | ||||||||
\(344\) | −2.23607 | −0.120561 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 40.0000 | 2.15041 | ||||||||
\(347\) | 13.0527 | 0.700707 | 0.350353 | − | 0.936618i | \(-0.386061\pi\) | ||||
0.350353 | + | 0.936618i | \(0.386061\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −31.1868 | −1.66939 | −0.834695 | − | 0.550713i | \(-0.814356\pi\) | ||||
−0.834695 | + | 0.550713i | \(0.814356\pi\) | |||||||
\(350\) | 35.7771 | 1.91237 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.59339 | 0.244828 | ||||||||
\(353\) | 21.9970 | 1.17078 | 0.585391 | − | 0.810751i | \(-0.300941\pi\) | ||||
0.585391 | + | 0.810751i | \(0.300941\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.93774 | −0.474366 | ||||||||
\(356\) | −40.2492 | −2.13320 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.8132 | −0.571497 | ||||||||
\(359\) | −8.58059 | −0.452866 | −0.226433 | − | 0.974027i | \(-0.572706\pi\) | ||||
−0.226433 | + | 0.974027i | \(0.572706\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.53113 | −0.343744 | ||||||||
\(362\) | −30.2565 | −1.59025 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −16.2198 | −0.850151 | ||||||||
\(365\) | 4.10845 | 0.215046 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.0623 | −0.786243 | −0.393122 | − | 0.919486i | \(-0.628605\pi\) | ||||
−0.393122 | + | 0.919486i | \(0.628605\pi\) | |||||||
\(368\) | −5.84162 | −0.304515 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −9.18677 | −0.477598 | ||||||||
\(371\) | 41.2550 | 2.14185 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.00000 | 0.310668 | 0.155334 | − | 0.987862i | \(-0.450355\pi\) | ||||
0.155334 | + | 0.987862i | \(0.450355\pi\) | |||||||
\(374\) | 2.09686 | 0.108426 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.59339 | 0.236886 | ||||||||
\(377\) | 3.14528 | 0.161990 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.12452 | 0.109129 | 0.0545645 | − | 0.998510i | \(-0.482623\pi\) | ||||
0.0545645 | + | 0.998510i | \(0.482623\pi\) | |||||||
\(380\) | 7.25373 | 0.372109 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −26.1245 | −1.33665 | ||||||||
\(383\) | −30.9413 | −1.58102 | −0.790512 | − | 0.612446i | \(-0.790186\pi\) | ||||
−0.790512 | + | 0.612446i | \(0.790186\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.65564 | 0.0843795 | ||||||||
\(386\) | 22.3607 | 1.13813 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 40.5934 | 2.06082 | ||||||||
\(389\) | 19.9428 | 1.01114 | 0.505569 | − | 0.862786i | \(-0.331283\pi\) | ||||
0.505569 | + | 0.862786i | \(0.331283\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.00000 | −0.404577 | ||||||||
\(392\) | −12.2288 | −0.617646 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −49.1868 | −2.47799 | ||||||||
\(395\) | −10.3138 | −0.518941 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.593387 | −0.0297812 | −0.0148906 | − | 0.999889i | \(-0.504740\pi\) | ||||
−0.0148906 | + | 0.999889i | \(0.504740\pi\) | |||||||
\(398\) | 58.4162 | 2.92814 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.53113 | 0.226556 | ||||||||
\(401\) | −4.10845 | −0.205166 | −0.102583 | − | 0.994724i | \(-0.532711\pi\) | ||||
−0.102583 | + | 0.994724i | \(0.532711\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −26.8328 | −1.33498 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 16.2198 | 0.804977 | ||||||||
\(407\) | 4.10845 | 0.203648 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.0623 | −1.23925 | −0.619624 | − | 0.784898i | \(-0.712715\pi\) | ||||
−0.619624 | + | 0.784898i | \(0.712715\pi\) | |||||||
\(410\) | −17.8885 | −0.883452 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 20.6275 | 1.01501 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.53113 | −0.369689 | ||||||||
\(416\) | −10.2711 | −0.503583 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5.40661 | −0.264446 | ||||||||
\(419\) | 32.3107 | 1.57848 | 0.789242 | − | 0.614083i | \(-0.210474\pi\) | ||||
0.789242 | + | 0.614083i | \(0.210474\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.93774 | 0.143177 | 0.0715884 | − | 0.997434i | \(-0.477193\pi\) | ||||
0.0715884 | + | 0.997434i | \(0.477193\pi\) | |||||||
\(422\) | 36.8255 | 1.79264 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −26.1245 | −1.26872 | ||||||||
\(425\) | 6.20531 | 0.301002 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.06226 | −0.341767 | ||||||||
\(428\) | 32.9955 | 1.59490 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.53113 | −0.0738376 | ||||||||
\(431\) | −4.79319 | −0.230880 | −0.115440 | − | 0.993314i | \(-0.536828\pi\) | ||||
−0.115440 | + | 0.993314i | \(0.536828\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.1868 | 1.11429 | 0.557143 | − | 0.830417i | \(-0.311898\pi\) | ||||
0.557143 | + | 0.830417i | \(0.311898\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 49.7802 | 2.38404 | ||||||||
\(437\) | 20.6275 | 0.986748 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.1868 | 1.01119 | 0.505595 | − | 0.862771i | \(-0.331273\pi\) | ||||
0.505595 | + | 0.862771i | \(0.331273\pi\) | |||||||
\(440\) | −1.04843 | −0.0499818 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.68871 | −0.223019 | ||||||||
\(443\) | −4.79319 | −0.227731 | −0.113866 | − | 0.993496i | \(-0.536323\pi\) | ||||
−0.113866 | + | 0.993496i | \(0.536323\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.18677 | −0.435495 | ||||||||
\(446\) | 30.5349 | 1.44587 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −45.9047 | −2.16879 | ||||||||
\(449\) | 6.16267 | 0.290835 | 0.145417 | − | 0.989370i | \(-0.453548\pi\) | ||||
0.145417 | + | 0.989370i | \(0.453548\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.00000 | 0.376705 | ||||||||
\(452\) | 2.05422 | 0.0966226 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 58.3735 | 2.73961 | ||||||||
\(455\) | −3.70213 | −0.173559 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.0000 | −0.842004 | −0.421002 | − | 0.907060i | \(-0.638322\pi\) | ||||
−0.421002 | + | 0.907060i | \(0.638322\pi\) | |||||||
\(458\) | −13.4164 | −0.626908 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 12.0000 | 0.559503 | ||||||||
\(461\) | −28.2023 | −1.31351 | −0.656756 | − | 0.754103i | \(-0.728072\pi\) | ||||
−0.656756 | + | 0.754103i | \(0.728072\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.5934 | 1.05000 | 0.525002 | − | 0.851101i | \(-0.324065\pi\) | ||||
0.525002 | + | 0.851101i | \(0.324065\pi\) | |||||||
\(464\) | 2.05422 | 0.0953650 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 47.6556 | 2.20761 | ||||||||
\(467\) | 4.83582 | 0.223775 | 0.111888 | − | 0.993721i | \(-0.464310\pi\) | ||||
0.111888 | + | 0.993721i | \(0.464310\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.1245 | 0.652210 | ||||||||
\(470\) | 3.14528 | 0.145081 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −13.0623 | −0.601239 | ||||||||
\(473\) | 0.684742 | 0.0314845 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.0000 | −0.734130 | ||||||||
\(476\) | −14.5075 | −0.664949 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 64.5934 | 2.95443 | ||||||||
\(479\) | 36.4618 | 1.66598 | 0.832992 | − | 0.553285i | \(-0.186626\pi\) | ||||
0.832992 | + | 0.553285i | \(0.186626\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.18677 | −0.418881 | ||||||||
\(482\) | −42.9029 | −1.95417 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −31.5934 | −1.43606 | ||||||||
\(485\) | 9.26533 | 0.420717 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.06226 | −0.320021 | −0.160011 | − | 0.987115i | \(-0.551153\pi\) | ||||
−0.160011 | + | 0.987115i | \(0.551153\pi\) | |||||||
\(488\) | 4.47214 | 0.202444 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −8.37355 | −0.378278 | ||||||||
\(491\) | −13.7801 | −0.621887 | −0.310943 | − | 0.950428i | \(-0.600645\pi\) | ||||
−0.310943 | + | 0.950428i | \(0.600645\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.81323 | 0.126701 | ||||||||
\(494\) | 12.0896 | 0.543935 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −46.0908 | −2.06746 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.5934 | −0.474225 | −0.237113 | − | 0.971482i | \(-0.576201\pi\) | ||||
−0.237113 | + | 0.971482i | \(0.576201\pi\) | |||||||
\(500\) | −19.5791 | −0.875603 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −24.5934 | −1.09766 | ||||||||
\(503\) | −13.7801 | −0.614424 | −0.307212 | − | 0.951641i | \(-0.599396\pi\) | ||||
−0.307212 | + | 0.951641i | \(0.599396\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.12452 | −0.272537 | ||||||||
\(506\) | −8.94427 | −0.397621 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −21.1868 | −0.940011 | ||||||||
\(509\) | 8.21690 | 0.364208 | 0.182104 | − | 0.983279i | \(-0.441709\pi\) | ||||
0.182104 | + | 0.983279i | \(0.441709\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21.1868 | 0.937248 | ||||||||
\(512\) | −11.1803 | −0.494106 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.59339 | 0.202606 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.40661 | −0.0618628 | ||||||||
\(518\) | −47.3751 | −2.08154 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.34436 | 0.102807 | ||||||||
\(521\) | 41.9398 | 1.83741 | 0.918707 | − | 0.394939i | \(-0.129234\pi\) | ||||
0.918707 | + | 0.394939i | \(0.129234\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.5934 | −0.463216 | −0.231608 | − | 0.972809i | \(-0.574399\pi\) | ||||
−0.231608 | + | 0.972809i | \(0.574399\pi\) | |||||||
\(524\) | −35.0497 | −1.53115 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 35.3113 | 1.53965 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.1245 | 0.483675 | ||||||||
\(530\) | −17.8885 | −0.777029 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 37.4066 | 1.62178 | ||||||||
\(533\) | −17.8885 | −0.774839 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.53113 | 0.325599 | ||||||||
\(536\) | −8.94427 | −0.386334 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 9.18677 | 0.396070 | ||||||||
\(539\) | 3.74476 | 0.161298 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 32.1245 | 1.38114 | 0.690570 | − | 0.723265i | \(-0.257360\pi\) | ||||
0.690570 | + | 0.723265i | \(0.257360\pi\) | |||||||
\(542\) | 47.3751 | 2.03493 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −9.18677 | −0.393880 | ||||||||
\(545\) | 11.3622 | 0.486702 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.0000 | 0.513083 | 0.256541 | − | 0.966533i | \(-0.417417\pi\) | ||||
0.256541 | + | 0.966533i | \(0.417417\pi\) | |||||||
\(548\) | 6.16267 | 0.263256 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.93774 | 0.295826 | ||||||||
\(551\) | −7.25373 | −0.309019 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −53.1868 | −2.26173 | ||||||||
\(554\) | −20.2638 | −0.860927 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 36.0000 | 1.52674 | ||||||||
\(557\) | 8.21690 | 0.348161 | 0.174081 | − | 0.984731i | \(-0.444305\pi\) | ||||
0.174081 | + | 0.984731i | \(0.444305\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.53113 | −0.0647599 | ||||||||
\(560\) | −2.41791 | −0.102175 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 29.1868 | 1.23117 | ||||||||
\(563\) | 20.2638 | 0.854018 | 0.427009 | − | 0.904247i | \(-0.359567\pi\) | ||||
0.427009 | + | 0.904247i | \(0.359567\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.468871 | 0.0197256 | ||||||||
\(566\) | 42.6245 | 1.79164 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 29.1868 | 1.22465 | ||||||||
\(569\) | 28.2023 | 1.18230 | 0.591151 | − | 0.806561i | \(-0.298674\pi\) | ||||
0.591151 | + | 0.806561i | \(0.298674\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.5311 | −1.31954 | −0.659768 | − | 0.751469i | \(-0.729346\pi\) | ||||
−0.659768 | + | 0.751469i | \(0.729346\pi\) | |||||||
\(572\) | −3.14528 | −0.131511 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −92.2490 | −3.85040 | ||||||||
\(575\) | −26.4691 | −1.10384 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.1245 | 1.00432 | 0.502158 | − | 0.864776i | \(-0.332539\pi\) | ||||
0.502158 | + | 0.864776i | \(0.332539\pi\) | |||||||
\(578\) | 33.8194 | 1.40670 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.21984 | −0.175219 | ||||||||
\(581\) | −38.8371 | −1.61123 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.00000 | 0.331326 | ||||||||
\(584\) | −13.4164 | −0.555175 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15.3113 | 0.632504 | ||||||||
\(587\) | −27.4749 | −1.13401 | −0.567006 | − | 0.823714i | \(-0.691898\pi\) | ||||
−0.567006 | + | 0.823714i | \(0.691898\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −8.94427 | −0.368230 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.00000 | −0.246598 | ||||||||
\(593\) | −33.3165 | −1.36815 | −0.684073 | − | 0.729413i | \(-0.739793\pi\) | ||||
−0.684073 | + | 0.729413i | \(0.739793\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.31129 | −0.135750 | ||||||||
\(596\) | −64.8999 | −2.65840 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 20.0000 | 0.817861 | ||||||||
\(599\) | −5.52056 | −0.225564 | −0.112782 | − | 0.993620i | \(-0.535976\pi\) | ||||
−0.112782 | + | 0.993620i | \(0.535976\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.0000 | 0.407909 | 0.203954 | − | 0.978980i | \(-0.434621\pi\) | ||||
0.203954 | + | 0.978980i | \(0.434621\pi\) | |||||||
\(602\) | −7.89584 | −0.321811 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 24.0000 | 0.976546 | ||||||||
\(605\) | −7.21110 | −0.293173 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.5934 | 1.24175 | 0.620874 | − | 0.783911i | \(-0.286778\pi\) | ||||
0.620874 | + | 0.783911i | \(0.286778\pi\) | |||||||
\(608\) | 23.6875 | 0.960656 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.06226 | 0.123987 | ||||||||
\(611\) | 3.14528 | 0.127245 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.12452 | 0.328146 | 0.164073 | − | 0.986448i | \(-0.447537\pi\) | ||||
0.164073 | + | 0.986448i | \(0.447537\pi\) | |||||||
\(614\) | −11.0411 | −0.445584 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.40661 | −0.217839 | ||||||||
\(617\) | 8.21690 | 0.330800 | 0.165400 | − | 0.986227i | \(-0.447108\pi\) | ||||
0.165400 | + | 0.986227i | \(0.447108\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.18677 | 0.369248 | 0.184624 | − | 0.982809i | \(-0.440893\pi\) | ||||
0.184624 | + | 0.982809i | \(0.440893\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −64.5934 | −2.58996 | ||||||||
\(623\) | −47.3751 | −1.89804 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.1868 | 0.727471 | ||||||||
\(626\) | −4.47214 | −0.178743 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 42.0000 | 1.67598 | ||||||||
\(629\) | −8.21690 | −0.327629 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.87548 | −0.393137 | −0.196568 | − | 0.980490i | \(-0.562980\pi\) | ||||
−0.196568 | + | 0.980490i | \(0.562980\pi\) | |||||||
\(632\) | 33.6802 | 1.33973 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −16.9377 | −0.672684 | ||||||||
\(635\) | −4.83582 | −0.191904 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.37355 | −0.331772 | ||||||||
\(638\) | 3.14528 | 0.124523 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 10.7179 | 0.423662 | ||||||||
\(641\) | 9.95007 | 0.393004 | 0.196502 | − | 0.980503i | \(-0.437042\pi\) | ||||
0.196502 | + | 0.980503i | \(0.437042\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −33.1868 | −1.30876 | −0.654379 | − | 0.756166i | \(-0.727070\pi\) | ||||
−0.654379 | + | 0.756166i | \(0.727070\pi\) | |||||||
\(644\) | 61.8825 | 2.43851 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 10.8132 | 0.425441 | ||||||||
\(647\) | 15.7917 | 0.620835 | 0.310418 | − | 0.950600i | \(-0.399531\pi\) | ||||
0.310418 | + | 0.950600i | \(0.399531\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.00000 | 0.157014 | ||||||||
\(650\) | −15.5133 | −0.608480 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −43.7802 | −1.71456 | ||||||||
\(653\) | −24.0512 | −0.941197 | −0.470598 | − | 0.882347i | \(-0.655962\pi\) | ||||
−0.470598 | + | 0.882347i | \(0.655962\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.00000 | −0.312586 | ||||||||
\(656\) | −11.6832 | −0.456154 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 16.2198 | 0.632315 | ||||||||
\(659\) | −32.6744 | −1.27282 | −0.636408 | − | 0.771353i | \(-0.719580\pi\) | ||||
−0.636408 | + | 0.771353i | \(0.719580\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.4066 | 0.910412 | 0.455206 | − | 0.890386i | \(-0.349566\pi\) | ||||
0.455206 | + | 0.890386i | \(0.349566\pi\) | |||||||
\(662\) | 7.89584 | 0.306881 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 24.5934 | 0.954408 | ||||||||
\(665\) | 8.53796 | 0.331088 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.0000 | −0.464642 | ||||||||
\(668\) | 45.3208 | 1.75352 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6.12452 | −0.236611 | ||||||||
\(671\) | −1.36948 | −0.0528683 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.0000 | −0.848038 | −0.424019 | − | 0.905653i | \(-0.639381\pi\) | ||||
−0.424019 | + | 0.905653i | \(0.639381\pi\) | |||||||
\(674\) | 7.61742 | 0.293412 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −31.9669 | −1.22950 | ||||||||
\(677\) | 16.1554 | 0.620901 | 0.310451 | − | 0.950589i | \(-0.399520\pi\) | ||||
0.310451 | + | 0.950589i | \(0.399520\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 47.7802 | 1.83363 | ||||||||
\(680\) | 2.09686 | 0.0804107 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.30796 | 0.356159 | 0.178080 | − | 0.984016i | \(-0.443012\pi\) | ||||
0.178080 | + | 0.984016i | \(0.443012\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.40661 | 0.0537439 | ||||||||
\(686\) | 12.0896 | 0.461581 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.00000 | −0.0381246 | ||||||||
\(689\) | −17.8885 | −0.681499 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 40.0000 | 1.52167 | 0.760836 | − | 0.648944i | \(-0.224789\pi\) | ||||
0.760836 | + | 0.648944i | \(0.224789\pi\) | |||||||
\(692\) | −53.6656 | −2.04006 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −29.1868 | −1.10791 | ||||||||
\(695\) | 8.21690 | 0.311685 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.0000 | −0.606043 | ||||||||
\(698\) | 69.7357 | 2.63954 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −48.0000 | −1.81423 | ||||||||
\(701\) | −17.1612 | −0.648169 | −0.324084 | − | 0.946028i | \(-0.605056\pi\) | ||||
−0.324084 | + | 0.946028i | \(0.605056\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21.1868 | 0.799074 | ||||||||
\(704\) | −8.90164 | −0.335493 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −49.1868 | −1.85117 | ||||||||
\(707\) | −31.5834 | −1.18782 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34.7179 | 1.30386 | 0.651929 | − | 0.758280i | \(-0.273960\pi\) | ||||
0.651929 | + | 0.758280i | \(0.273960\pi\) | |||||||
\(710\) | 19.9854 | 0.750039 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 30.0000 | 1.12430 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.717902 | −0.0268480 | ||||||||
\(716\) | 14.5075 | 0.542169 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 19.1868 | 0.716044 | ||||||||
\(719\) | 0.363686 | 0.0135632 | 0.00678160 | − | 0.999977i | \(-0.497841\pi\) | ||||
0.00678160 | + | 0.999977i | \(0.497841\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 14.6040 | 0.543506 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 40.5934 | 1.50864 | ||||||||
\(725\) | 9.30796 | 0.345689 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.40661 | 0.200520 | 0.100260 | − | 0.994961i | \(-0.468033\pi\) | ||||
0.100260 | + | 0.994961i | \(0.468033\pi\) | |||||||
\(728\) | 12.0896 | 0.448069 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −9.18677 | −0.340018 | ||||||||
\(731\) | −1.36948 | −0.0506522 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 39.1868 | 1.44740 | 0.723698 | − | 0.690117i | \(-0.242441\pi\) | ||||
0.723698 | + | 0.690117i | \(0.242441\pi\) | |||||||
\(734\) | 33.6802 | 1.24316 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 39.1868 | 1.44444 | ||||||||
\(737\) | 2.73897 | 0.100891 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.5934 | 0.536826 | 0.268413 | − | 0.963304i | \(-0.413501\pi\) | ||||
0.268413 | + | 0.963304i | \(0.413501\pi\) | |||||||
\(740\) | 12.3253 | 0.453089 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −92.2490 | −3.38657 | ||||||||
\(743\) | 33.6802 | 1.23561 | 0.617804 | − | 0.786332i | \(-0.288023\pi\) | ||||
0.617804 | + | 0.786332i | \(0.288023\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.8132 | −0.542715 | ||||||||
\(746\) | −13.4164 | −0.491210 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.81323 | −0.102862 | ||||||||
\(749\) | 38.8371 | 1.41908 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.59339 | 0.240596 | 0.120298 | − | 0.992738i | \(-0.461615\pi\) | ||||
0.120298 | + | 0.992738i | \(0.461615\pi\) | |||||||
\(752\) | 2.05422 | 0.0749099 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7.03307 | −0.256129 | ||||||||
\(755\) | 5.47793 | 0.199362 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.1868 | 1.42427 | 0.712134 | − | 0.702044i | \(-0.247729\pi\) | ||||
0.712134 | + | 0.702044i | \(0.247729\pi\) | |||||||
\(758\) | −4.75056 | −0.172548 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.40661 | −0.196118 | ||||||||
\(761\) | −39.5219 | −1.43267 | −0.716333 | − | 0.697759i | \(-0.754181\pi\) | ||||
−0.716333 | + | 0.697759i | \(0.754181\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 58.5934 | 2.12122 | ||||||||
\(764\) | 35.0497 | 1.26805 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 69.1868 | 2.49982 | ||||||||
\(767\) | −8.94427 | −0.322959 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −43.6556 | −1.57426 | −0.787131 | − | 0.616785i | \(-0.788435\pi\) | ||||
−0.787131 | + | 0.616785i | \(0.788435\pi\) | |||||||
\(770\) | −3.70213 | −0.133416 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −30.0000 | −1.07972 | ||||||||
\(773\) | −37.8313 | −1.36070 | −0.680349 | − | 0.732888i | \(-0.738172\pi\) | ||||
−0.680349 | + | 0.732888i | \(0.738172\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −30.2565 | −1.08615 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −44.5934 | −1.59875 | ||||||||
\(779\) | 41.2550 | 1.47811 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.93774 | −0.319818 | ||||||||
\(782\) | 17.8885 | 0.639693 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.46887 | −0.195317 | ||||||||
\(785\) | 9.58638 | 0.342153 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −48.2490 | −1.71989 | −0.859946 | − | 0.510385i | \(-0.829503\pi\) | ||||
−0.859946 | + | 0.510385i | \(0.829503\pi\) | |||||||
\(788\) | 65.9910 | 2.35083 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 23.0623 | 0.820518 | ||||||||
\(791\) | 2.41791 | 0.0859710 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.06226 | 0.108744 | ||||||||
\(794\) | 1.32685 | 0.0470882 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −78.3735 | −2.77788 | ||||||||
\(797\) | 9.67164 | 0.342587 | 0.171294 | − | 0.985220i | \(-0.445205\pi\) | ||||
0.171294 | + | 0.985220i | \(0.445205\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.81323 | 0.0995248 | ||||||||
\(800\) | −30.3957 | −1.07465 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.18677 | 0.324396 | ||||||||
\(803\) | 4.10845 | 0.144984 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14.1245 | 0.497824 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 20.0000 | 0.703598 | ||||||||
\(809\) | 30.2139 | 1.06226 | 0.531132 | − | 0.847289i | \(-0.321767\pi\) | ||||
0.531132 | + | 0.847289i | \(0.321767\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.0000 | −1.26413 | −0.632065 | − | 0.774915i | \(-0.717793\pi\) | ||||
−0.632065 | + | 0.774915i | \(0.717793\pi\) | |||||||
\(812\) | −21.7612 | −0.763668 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −9.18677 | −0.321996 | ||||||||
\(815\) | −9.99270 | −0.350029 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.53113 | 0.123539 | ||||||||
\(818\) | 56.0409 | 1.95942 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 24.0000 | 0.838116 | ||||||||
\(821\) | 26.1054 | 0.911086 | 0.455543 | − | 0.890214i | \(-0.349445\pi\) | ||||
0.455543 | + | 0.890214i | \(0.349445\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.8755 | −0.623100 | −0.311550 | − | 0.950230i | \(-0.600848\pi\) | ||||
−0.311550 | + | 0.950230i | \(0.600848\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −46.1245 | −1.60488 | ||||||||
\(827\) | −8.90164 | −0.309540 | −0.154770 | − | 0.987950i | \(-0.549464\pi\) | ||||
−0.154770 | + | 0.987950i | \(0.549464\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.0623 | −0.453671 | −0.226835 | − | 0.973933i | \(-0.572838\pi\) | ||||
−0.226835 | + | 0.973933i | \(0.572838\pi\) | |||||||
\(830\) | 16.8401 | 0.584529 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 19.9047 | 0.690070 | ||||||||
\(833\) | −7.48953 | −0.259497 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.3444 | 0.357981 | ||||||||
\(836\) | 7.25373 | 0.250876 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −72.2490 | −2.49580 | ||||||||
\(839\) | −19.2580 | −0.664861 | −0.332430 | − | 0.943128i | \(-0.607869\pi\) | ||||
−0.332430 | + | 0.943128i | \(0.607869\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.7802 | −0.854488 | ||||||||
\(842\) | −6.56899 | −0.226382 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −49.4066 | −1.70065 | ||||||||
\(845\) | −7.29636 | −0.251003 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −37.1868 | −1.27775 | ||||||||
\(848\) | −11.6832 | −0.401204 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −13.8755 | −0.475925 | ||||||||
\(851\) | 35.0497 | 1.20149 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 55.6556 | 1.90561 | 0.952806 | − | 0.303578i | \(-0.0981814\pi\) | ||||
0.952806 | + | 0.303578i | \(0.0981814\pi\) | |||||||
\(854\) | 15.7917 | 0.540380 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −24.5934 | −0.840585 | ||||||||
\(857\) | −36.4192 | −1.24406 | −0.622028 | − | 0.782995i | \(-0.713691\pi\) | ||||
−0.622028 | + | 0.782995i | \(0.713691\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.7802 | −0.674890 | −0.337445 | − | 0.941345i | \(-0.609563\pi\) | ||||
−0.337445 | + | 0.941345i | \(0.609563\pi\) | |||||||
\(860\) | 2.05422 | 0.0700485 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10.7179 | 0.365053 | ||||||||
\(863\) | −34.4076 | −1.17125 | −0.585624 | − | 0.810583i | \(-0.699151\pi\) | ||||
−0.585624 | + | 0.810583i | \(0.699151\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.2490 | −0.416480 | ||||||||
\(866\) | −51.8472 | −1.76184 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.3138 | −0.349870 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.12452 | −0.207521 | ||||||||
\(872\) | −37.1039 | −1.25650 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −46.1245 | −1.56019 | ||||||||
\(875\) | −23.0454 | −0.779077 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.1245 | 0.409416 | 0.204708 | − | 0.978823i | \(-0.434376\pi\) | ||||
0.204708 | + | 0.978823i | \(0.434376\pi\) | |||||||
\(878\) | −47.3751 | −1.59883 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.468871 | −0.0158056 | ||||||||
\(881\) | 30.2139 | 1.01793 | 0.508966 | − | 0.860787i | \(-0.330028\pi\) | ||||
0.508966 | + | 0.860787i | \(0.330028\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −46.3735 | −1.56059 | −0.780297 | − | 0.625409i | \(-0.784932\pi\) | ||||
−0.780297 | + | 0.625409i | \(0.784932\pi\) | |||||||
\(884\) | 6.29057 | 0.211575 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10.7179 | 0.360075 | ||||||||
\(887\) | −30.9413 | −1.03891 | −0.519453 | − | 0.854499i | \(-0.673864\pi\) | ||||
−0.519453 | + | 0.854499i | \(0.673864\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −24.9377 | −0.836385 | ||||||||
\(890\) | 20.5422 | 0.688578 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −40.9669 | −1.37167 | ||||||||
\(893\) | −7.25373 | −0.242737 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.31129 | 0.110684 | ||||||||
\(896\) | 55.2709 | 1.84647 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −13.7802 | −0.459850 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.0000 | −0.533037 | ||||||||
\(902\) | −17.8885 | −0.595623 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.53113 | −0.0509246 | ||||||||
\(905\) | 9.26533 | 0.307990 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.18677 | −0.305042 | −0.152521 | − | 0.988300i | \(-0.548739\pi\) | ||||
−0.152521 | + | 0.988300i | \(0.548739\pi\) | |||||||
\(908\) | −78.3163 | −2.59902 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 8.27822 | 0.274420 | ||||||||
\(911\) | 39.1582 | 1.29737 | 0.648684 | − | 0.761058i | \(-0.275320\pi\) | ||||
0.648684 | + | 0.761058i | \(0.275320\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.53113 | −0.249244 | ||||||||
\(914\) | 40.2492 | 1.33133 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18.0000 | 0.594737 | ||||||||
\(917\) | −41.2550 | −1.36236 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 48.0000 | 1.58337 | 0.791687 | − | 0.610927i | \(-0.209203\pi\) | ||||
0.791687 | + | 0.610927i | \(0.209203\pi\) | |||||||
\(920\) | −8.94427 | −0.294884 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 63.0623 | 2.07684 | ||||||||
\(923\) | 19.9854 | 0.657827 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −27.1868 | −0.893896 | ||||||||
\(926\) | −50.5203 | −1.66020 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −13.7802 | −0.452356 | ||||||||
\(929\) | −32.2681 | −1.05868 | −0.529341 | − | 0.848409i | \(-0.677561\pi\) | ||||
−0.529341 | + | 0.848409i | \(0.677561\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.3113 | 0.632902 | ||||||||
\(932\) | −63.9368 | −2.09432 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −10.8132 | −0.353820 | ||||||||
\(935\) | −0.642111 | −0.0209993 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.0623 | 0.818748 | 0.409374 | − | 0.912367i | \(-0.365747\pi\) | ||||
0.409374 | + | 0.912367i | \(0.365747\pi\) | |||||||
\(938\) | −31.5834 | −1.03123 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.21984 | −0.137636 | ||||||||
\(941\) | 48.8298 | 1.59181 | 0.795903 | − | 0.605424i | \(-0.206996\pi\) | ||||
0.795903 | + | 0.605424i | \(0.206996\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 68.2490 | 2.22249 | ||||||||
\(944\) | −5.84162 | −0.190129 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.53113 | −0.0497813 | ||||||||
\(947\) | −50.8840 | −1.65351 | −0.826754 | − | 0.562563i | \(-0.809815\pi\) | ||||
−0.826754 | + | 0.562563i | \(0.809815\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.18677 | −0.298215 | ||||||||
\(950\) | 35.7771 | 1.16076 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 10.8132 | 0.350459 | ||||||||
\(953\) | −19.9428 | −0.646010 | −0.323005 | − | 0.946397i | \(-0.604693\pi\) | ||||
−0.323005 | + | 0.946397i | \(0.604693\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.00000 | 0.258874 | ||||||||
\(956\) | −86.6611 | −2.80282 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −81.5311 | −2.63415 | ||||||||
\(959\) | 7.25373 | 0.234235 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 20.5422 | 0.662309 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 57.5603 | 1.85389 | ||||||||
\(965\) | −6.84742 | −0.220426 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.0000 | 1.02905 | 0.514525 | − | 0.857475i | \(-0.327968\pi\) | ||||
0.514525 | + | 0.857475i | \(0.327968\pi\) | |||||||
\(968\) | 23.5483 | 0.756872 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −20.7179 | −0.665212 | ||||||||
\(971\) | 37.4250 | 1.20103 | 0.600513 | − | 0.799615i | \(-0.294963\pi\) | ||||
0.600513 | + | 0.799615i | \(0.294963\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 42.3735 | 1.35843 | ||||||||
\(974\) | 15.7917 | 0.505998 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.00000 | 0.0640184 | ||||||||
\(977\) | −17.8885 | −0.572305 | −0.286153 | − | 0.958184i | \(-0.592376\pi\) | ||||
−0.286153 | + | 0.958184i | \(0.592376\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.18677 | −0.293611 | ||||||||
\(980\) | 11.2343 | 0.358866 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 30.8132 | 0.983290 | ||||||||
\(983\) | 52.2109 | 1.66527 | 0.832634 | − | 0.553823i | \(-0.186832\pi\) | ||||
0.832634 | + | 0.553823i | \(0.186832\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.0623 | 0.479923 | ||||||||
\(986\) | −6.29057 | −0.200332 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −16.2198 | −0.516022 | ||||||||
\(989\) | 5.84162 | 0.185753 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.4689 | −0.523151 | −0.261575 | − | 0.965183i | \(-0.584242\pi\) | ||||
−0.261575 | + | 0.965183i | \(0.584242\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 103.062 | 3.26894 | ||||||||
\(995\) | −17.8885 | −0.567105 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.2490 | 1.33804 | 0.669020 | − | 0.743244i | \(-0.266714\pi\) | ||||
0.669020 | + | 0.743244i | \(0.266714\pi\) | |||||||
\(998\) | 23.6875 | 0.749816 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 387.2.a.j.1.2 | ✓ | 4 | |
3.2 | odd | 2 | inner | 387.2.a.j.1.3 | yes | 4 | |
4.3 | odd | 2 | 6192.2.a.bz.1.3 | 4 | |||
5.4 | even | 2 | 9675.2.a.bv.1.3 | 4 | |||
12.11 | even | 2 | 6192.2.a.bz.1.2 | 4 | |||
15.14 | odd | 2 | 9675.2.a.bv.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
387.2.a.j.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
387.2.a.j.1.3 | yes | 4 | 3.2 | odd | 2 | inner | |
6192.2.a.bz.1.2 | 4 | 12.11 | even | 2 | |||
6192.2.a.bz.1.3 | 4 | 4.3 | odd | 2 | |||
9675.2.a.bv.1.1 | 4 | 15.14 | odd | 2 | |||
9675.2.a.bv.1.3 | 4 | 5.4 | even | 2 |