Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1904,2,Mod(1,1904)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1904, 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("1904.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1904 = 2^{4} \cdot 7 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1904.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: | \(15.2035165449\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.229.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - 4x - 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 952) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.11491\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1904.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.47283 | 0.850341 | 0.425171 | − | 0.905113i | \(-0.360214\pi\) | ||||
0.425171 | + | 0.905113i | \(0.360214\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.11491 | −0.498602 | −0.249301 | − | 0.968426i | \(-0.580201\pi\) | ||||
−0.249301 | + | 0.968426i | \(0.580201\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.830760 | −0.276920 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.22982 | 0.672315 | 0.336157 | − | 0.941806i | \(-0.390873\pi\) | ||||
0.336157 | + | 0.941806i | \(0.390873\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.64207 | −0.423982 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.94567 | −1.13461 | −0.567307 | − | 0.823506i | \(-0.692015\pi\) | ||||
−0.567307 | + | 0.823506i | \(0.692015\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.47283 | −0.321399 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −9.17548 | −1.91322 | −0.956610 | − | 0.291371i | \(-0.905889\pi\) | ||||
−0.956610 | + | 0.291371i | \(0.905889\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.75698 | −0.751396 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.64207 | −1.08582 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.945668 | 0.175606 | 0.0878031 | − | 0.996138i | \(-0.472015\pi\) | ||||
0.0878031 | + | 0.996138i | \(0.472015\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.11491 | 0.200243 | 0.100122 | − | 0.994975i | \(-0.468077\pi\) | ||||
0.100122 | + | 0.994975i | \(0.468077\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.28415 | 0.571697 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.11491 | 0.188454 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.94567 | −0.813063 | −0.406531 | − | 0.913637i | \(-0.633262\pi\) | ||||
−0.406531 | + | 0.913637i | \(0.633262\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.2709 | 1.60405 | 0.802026 | − | 0.597289i | \(-0.203756\pi\) | ||||
0.802026 | + | 0.597289i | \(0.203756\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.2166 | 1.71052 | 0.855259 | − | 0.518201i | \(-0.173398\pi\) | ||||
0.855259 | + | 0.518201i | \(0.173398\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.926221 | 0.138073 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.89134 | −1.44280 | −0.721400 | − | 0.692519i | \(-0.756501\pi\) | ||||
−0.721400 | + | 0.692519i | \(0.756501\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.47283 | −0.206238 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.83076 | 1.07564 | 0.537819 | − | 0.843060i | \(-0.319248\pi\) | ||||
0.537819 | + | 0.843060i | \(0.319248\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.48604 | −0.335217 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.28415 | −0.964809 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.7438 | −1.78929 | −0.894644 | − | 0.446780i | \(-0.852571\pi\) | ||||
−0.894644 | + | 0.446780i | \(0.852571\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.904539 | 0.115814 | 0.0579072 | − | 0.998322i | \(-0.481557\pi\) | ||||
0.0579072 | + | 0.998322i | \(0.481557\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.830760 | 0.104666 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.91302 | −1.21107 | −0.605534 | − | 0.795820i | \(-0.707040\pi\) | ||||
−0.605534 | + | 0.795820i | \(0.707040\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −13.5140 | −1.62689 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.6894 | −1.74332 | −0.871658 | − | 0.490114i | \(-0.836955\pi\) | ||||
−0.871658 | + | 0.490114i | \(0.836955\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.756981 | 0.0885979 | 0.0442990 | − | 0.999018i | \(-0.485895\pi\) | ||||
0.0442990 | + | 0.999018i | \(0.485895\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.53341 | −0.638943 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.22982 | −0.254111 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.00000 | −0.900070 | −0.450035 | − | 0.893011i | \(-0.648589\pi\) | ||||
−0.450035 | + | 0.893011i | \(0.648589\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.81756 | −0.646395 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.9736 | 1.31427 | 0.657136 | − | 0.753772i | \(-0.271768\pi\) | ||||
0.657136 | + | 0.753772i | \(0.271768\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.11491 | 0.120929 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.39281 | 0.149325 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.1755 | 1.18460 | 0.592299 | − | 0.805718i | \(-0.298220\pi\) | ||||
0.592299 | + | 0.805718i | \(0.298220\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.64207 | 0.170275 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.51396 | 0.565721 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.0606 | 1.02150 | 0.510748 | − | 0.859730i | \(-0.329368\pi\) | ||||
0.510748 | + | 0.859730i | \(0.329368\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.85244 | −0.186177 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −18.6894 | −1.85967 | −0.929835 | − | 0.367978i | \(-0.880050\pi\) | ||||
−0.929835 | + | 0.367978i | \(0.880050\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.1212 | −1.19433 | −0.597166 | − | 0.802118i | \(-0.703707\pi\) | ||||
−0.597166 | + | 0.802118i | \(0.703707\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.64207 | 0.160250 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.89134 | 0.182842 | 0.0914212 | − | 0.995812i | \(-0.470859\pi\) | ||||
0.0914212 | + | 0.995812i | \(0.470859\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.0000 | −1.34096 | −0.670478 | − | 0.741929i | \(-0.733911\pi\) | ||||
−0.670478 | + | 0.741929i | \(0.733911\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.28415 | −0.691381 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.85244 | −0.362407 | −0.181204 | − | 0.983446i | \(-0.557999\pi\) | ||||
−0.181204 | + | 0.983446i | \(0.557999\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.2298 | 0.953935 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.00000 | 0.0916698 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.02792 | −0.547993 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 15.1274 | 1.36399 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.76322 | 0.873249 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.2361 | 1.88440 | 0.942198 | − | 0.335057i | \(-0.108756\pi\) | ||||
0.942198 | + | 0.335057i | \(0.108756\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 16.5202 | 1.45452 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.60719 | 0.402532 | 0.201266 | − | 0.979537i | \(-0.435494\pi\) | ||||
0.201266 | + | 0.979537i | \(0.435494\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.94567 | 0.428844 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.29039 | 0.541391 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.379608 | 0.0324321 | 0.0162160 | − | 0.999869i | \(-0.494838\pi\) | ||||
0.0162160 | + | 0.999869i | \(0.494838\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.06058 | −0.514051 | −0.257026 | − | 0.966405i | \(-0.582742\pi\) | ||||
−0.257026 | + | 0.966405i | \(0.582742\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −14.5683 | −1.22687 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.05433 | −0.0875575 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.47283 | 0.121477 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.1887 | −0.834690 | −0.417345 | − | 0.908748i | \(-0.637039\pi\) | ||||
−0.417345 | + | 0.908748i | \(0.637039\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.18869 | 0.666386 | 0.333193 | − | 0.942859i | \(-0.391874\pi\) | ||||
0.333193 | + | 0.942859i | \(0.391874\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.830760 | 0.0671630 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.24302 | −0.0998417 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.2687 | −1.13877 | −0.569383 | − | 0.822072i | \(-0.692818\pi\) | ||||
−0.569383 | + | 0.822072i | \(0.692818\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.5334 | 0.914659 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.17548 | 0.723129 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.7438 | −1.23315 | −0.616574 | − | 0.787297i | \(-0.711480\pi\) | ||||
−0.616574 | + | 0.787297i | \(0.711480\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.66152 | −0.285049 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.648317 | 0.0501683 | 0.0250841 | − | 0.999685i | \(-0.492015\pi\) | ||||
0.0250841 | + | 0.999685i | \(0.492015\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.10866 | 0.314197 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.9325 | 1.21132 | 0.605661 | − | 0.795722i | \(-0.292909\pi\) | ||||
0.605661 | + | 0.795722i | \(0.292909\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.75698 | 0.284001 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −20.2423 | −1.52150 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.0257 | 1.27256 | 0.636280 | − | 0.771458i | \(-0.280472\pi\) | ||||
0.636280 | + | 0.771458i | \(0.280472\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.63511 | 0.418855 | 0.209427 | − | 0.977824i | \(-0.432840\pi\) | ||||
0.209427 | + | 0.977824i | \(0.432840\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.33224 | 0.0984817 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.51396 | 0.405395 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.22982 | −0.163060 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.64207 | 0.410400 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.88509 | −0.208758 | −0.104379 | − | 0.994538i | \(-0.533285\pi\) | ||||
−0.104379 | + | 0.994538i | \(0.533285\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.5264 | 1.26158 | 0.630791 | − | 0.775953i | \(-0.282731\pi\) | ||||
0.630791 | + | 0.775953i | \(0.282731\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.9193 | 1.06295 | 0.531477 | − | 0.847073i | \(-0.321637\pi\) | ||||
0.531477 | + | 0.847073i | \(0.321637\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.6483 | 1.18017 | 0.590084 | − | 0.807342i | \(-0.299095\pi\) | ||||
0.590084 | + | 0.807342i | \(0.299095\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.6002 | −1.02982 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.945668 | −0.0663729 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.4512 | −0.799783 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.62263 | 0.529809 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.0279 | −0.762818 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.40530 | −0.509802 | −0.254901 | − | 0.966967i | \(-0.582043\pi\) | ||||
−0.254901 | + | 0.966967i | \(0.582043\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −21.6351 | −1.48241 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.5055 | −0.852867 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.11491 | −0.0756849 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.11491 | 0.0753385 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −27.1491 | −1.81804 | −0.909018 | − | 0.416756i | \(-0.863167\pi\) | ||||
−0.909018 | + | 0.416756i | \(0.863167\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.12115 | 0.208077 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.50772 | 0.299188 | 0.149594 | − | 0.988748i | \(-0.452203\pi\) | ||||
0.149594 | + | 0.988748i | \(0.452203\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.2298 | 0.676005 | 0.338003 | − | 0.941145i | \(-0.390249\pi\) | ||||
0.338003 | + | 0.941145i | \(0.390249\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.28415 | −0.216081 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.5529 | 0.756853 | 0.378426 | − | 0.925631i | \(-0.376465\pi\) | ||||
0.378426 | + | 0.925631i | \(0.376465\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.0279 | 0.719382 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.7827 | −0.765367 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 30.7570 | 1.98950 | 0.994752 | − | 0.102317i | \(-0.0326256\pi\) | ||||
0.994752 | + | 0.102317i | \(0.0326256\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.967349 | −0.0623124 | −0.0311562 | − | 0.999515i | \(-0.509919\pi\) | ||||
−0.0311562 | + | 0.999515i | \(0.509919\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.35793 | 0.536161 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.11491 | −0.0712288 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 17.6351 | 1.11758 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.0264075 | −0.00166683 | −0.000833413 | − | 1.00000i | \(-0.500265\pi\) | ||||
−0.000833413 | 1.00000i | \(0.500265\pi\) | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20.4596 | −1.28629 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.64207 | 0.102831 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.7159 | 0.917950 | 0.458975 | − | 0.888449i | \(-0.348217\pi\) | ||||
0.458975 | + | 0.888449i | \(0.348217\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.94567 | 0.307309 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.785623 | −0.0486289 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −24.9193 | −1.53659 | −0.768294 | − | 0.640097i | \(-0.778894\pi\) | ||||
−0.768294 | + | 0.640097i | \(0.778894\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.73057 | −0.536315 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16.4596 | 1.00731 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −23.9861 | −1.46246 | −0.731229 | − | 0.682133i | \(-0.761053\pi\) | ||||
−0.731229 | + | 0.682133i | \(0.761053\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.0668 | 0.915244 | 0.457622 | − | 0.889147i | \(-0.348701\pi\) | ||||
0.457622 | + | 0.889147i | \(0.348701\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.37737 | −0.505175 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.350966 | 0.0210875 | 0.0105437 | − | 0.999944i | \(-0.496644\pi\) | ||||
0.0105437 | + | 0.999944i | \(0.496644\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.926221 | −0.0554514 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.30583 | 0.316519 | 0.158260 | − | 0.987398i | \(-0.449412\pi\) | ||||
0.158260 | + | 0.987398i | \(0.449412\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.6134 | −0.690347 | −0.345173 | − | 0.938539i | \(-0.612180\pi\) | ||||
−0.345173 | + | 0.938539i | \(0.612180\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.12115 | 0.481055 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.2709 | −0.606275 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.8176 | 0.868621 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.2423 | 1.18257 | 0.591284 | − | 0.806463i | \(-0.298621\pi\) | ||||
0.591284 | + | 0.806463i | \(0.298621\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.3230 | 0.892142 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −12.5808 | −0.730011 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.2166 | −0.646515 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −27.5264 | −1.58135 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.00848 | −0.0577453 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.20189 | 0.0685955 | 0.0342978 | − | 0.999412i | \(-0.489081\pi\) | ||||
0.0342978 | + | 0.999412i | \(0.489081\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.8524 | −1.01559 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.2081 | 0.578850 | 0.289425 | − | 0.957201i | \(-0.406536\pi\) | ||||
0.289425 | + | 0.957201i | \(0.406536\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.7375 | 1.05911 | 0.529554 | − | 0.848276i | \(-0.322359\pi\) | ||||
0.529554 | + | 0.848276i | \(0.322359\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.926221 | −0.0521866 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.4985 | −0.589656 | −0.294828 | − | 0.955550i | \(-0.595262\pi\) | ||||
−0.294828 | + | 0.955550i | \(0.595262\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.10866 | 0.118063 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.78562 | 0.155478 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.94567 | 0.275184 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −20.6197 | −1.14027 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.89134 | 0.545327 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.0062 | −1.48440 | −0.742199 | − | 0.670180i | \(-0.766217\pi\) | ||||
−0.742199 | + | 0.670180i | \(0.766217\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.10866 | 0.225153 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.0521 | 0.603841 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.4985 | −0.571891 | −0.285946 | − | 0.958246i | \(-0.592308\pi\) | ||||
−0.285946 | + | 0.958246i | \(0.592308\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.67401 | −0.308170 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.48604 | 0.134626 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 15.0668 | 0.811170 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.0668 | −0.808829 | −0.404415 | − | 0.914576i | \(-0.632525\pi\) | ||||
−0.404415 | + | 0.914576i | \(0.632525\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.86493 | 0.421000 | 0.210500 | − | 0.977594i | \(-0.432491\pi\) | ||||
0.210500 | + | 0.977594i | \(0.432491\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 29.4053 | 1.56509 | 0.782543 | − | 0.622596i | \(-0.213922\pi\) | ||||
0.782543 | + | 0.622596i | \(0.213922\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.3774 | 0.869221 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.47283 | 0.0779506 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.91302 | 0.312077 | 0.156039 | − | 0.987751i | \(-0.450128\pi\) | ||||
0.156039 | + | 0.987751i | \(0.450128\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.45963 | 0.287349 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.87813 | −0.465981 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.843964 | −0.0441751 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.6762 | 0.818293 | 0.409147 | − | 0.912469i | \(-0.365826\pi\) | ||||
0.409147 | + | 0.912469i | \(0.365826\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.53269 | −0.444194 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.83076 | −0.406553 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.81131 | −0.508011 | −0.254005 | − | 0.967203i | \(-0.581748\pi\) | ||||
−0.254005 | + | 0.967203i | \(0.581748\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 14.3796 | 0.742560 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.6615 | −0.599012 | −0.299506 | − | 0.954094i | \(-0.596822\pi\) | ||||
−0.299506 | + | 0.954094i | \(0.596822\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 31.2772 | 1.60238 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 27.6087 | 1.41074 | 0.705369 | − | 0.708840i | \(-0.250781\pi\) | ||||
0.705369 | + | 0.708840i | \(0.250781\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.48604 | 0.126700 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.31832 | −0.473677 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.8308 | 0.599843 | 0.299922 | − | 0.953964i | \(-0.403039\pi\) | ||||
0.299922 | + | 0.953964i | \(0.403039\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.17548 | 0.464024 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.78562 | 0.342289 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.91926 | 0.448777 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.7111 | −1.13984 | −0.569919 | − | 0.821701i | \(-0.693026\pi\) | ||||
−0.569919 | + | 0.821701i | \(0.693026\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.28415 | 0.364663 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 37.6087 | 1.87809 | 0.939045 | − | 0.343795i | \(-0.111713\pi\) | ||||
0.939045 | + | 0.343795i | \(0.111713\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.48604 | 0.322294 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.0279 | −0.546634 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.5808 | −1.11655 | −0.558274 | − | 0.829657i | \(-0.688536\pi\) | ||||
−0.558274 | + | 0.829657i | \(0.688536\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.559099 | 0.0275783 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.7438 | 0.676287 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.3494 | −0.655299 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.92622 | −0.437119 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.2904 | −1.18666 | −0.593332 | − | 0.804958i | \(-0.702188\pi\) | ||||
−0.593332 | + | 0.804958i | \(0.702188\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.5676 | 0.563769 | 0.281885 | − | 0.959448i | \(-0.409040\pi\) | ||||
0.281885 | + | 0.959448i | \(0.409040\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.21733 | 0.399540 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.75698 | 0.182240 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.904539 | −0.0437737 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.9457 | 1.10525 | 0.552627 | − | 0.833429i | \(-0.313625\pi\) | ||||
0.552627 | + | 0.833429i | \(0.313625\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.8913 | 0.955917 | 0.477958 | − | 0.878383i | \(-0.341377\pi\) | ||||
0.477958 | + | 0.878383i | \(0.341377\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.55286 | −0.0744538 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 45.3789 | 2.17077 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.8936 | −0.949468 | −0.474734 | − | 0.880129i | \(-0.657456\pi\) | ||||
−0.474734 | + | 0.880129i | \(0.657456\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.830760 | −0.0395600 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.7827 | 0.749857 | 0.374929 | − | 0.927054i | \(-0.377667\pi\) | ||||
0.374929 | + | 0.927054i | \(0.377667\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.4596 | −0.590643 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.0062 | −0.709771 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −41.2702 | −1.94766 | −0.973831 | − | 0.227273i | \(-0.927019\pi\) | ||||
−0.973831 | + | 0.227273i | \(0.927019\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.9023 | 1.07843 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.0606 | 0.566655 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −36.9923 | −1.73043 | −0.865214 | − | 0.501403i | \(-0.832817\pi\) | ||||
−0.865214 | + | 0.501403i | \(0.832817\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.64207 | 0.263349 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.3649 | 0.482741 | 0.241370 | − | 0.970433i | \(-0.422403\pi\) | ||||
0.241370 | + | 0.970433i | \(0.422403\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.2709 | −0.570279 | −0.285140 | − | 0.958486i | \(-0.592040\pi\) | ||||
−0.285140 | + | 0.958486i | \(0.592040\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.83076 | −0.0848995 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.86341 | −0.410150 | −0.205075 | − | 0.978746i | \(-0.565744\pi\) | ||||
−0.205075 | + | 0.978746i | \(0.565744\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.91302 | 0.457741 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −21.0154 | −0.968340 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 25.0110 | 1.15001 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.5808 | 0.852545 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.50548 | −0.297866 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.56606 | 0.208629 | 0.104314 | − | 0.994544i | \(-0.466735\pi\) | ||||
0.104314 | + | 0.994544i | \(0.466735\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 13.5140 | 0.614907 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.2166 | −0.509320 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.8649 | −1.08142 | −0.540712 | − | 0.841208i | \(-0.681845\pi\) | ||||
−0.540712 | + | 0.841208i | \(0.681845\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −23.1880 | −1.04860 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.00624 | 0.316187 | 0.158094 | − | 0.987424i | \(-0.449465\pi\) | ||||
0.158094 | + | 0.987424i | \(0.449465\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.945668 | −0.0425907 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.06530 | 0.0928284 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14.6894 | 0.658912 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.2687 | −0.459691 | −0.229845 | − | 0.973227i | \(-0.573822\pi\) | ||||
−0.229845 | + | 0.973227i | \(0.573822\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.954863 | 0.0426601 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.53413 | −0.380518 | −0.190259 | − | 0.981734i | \(-0.560933\pi\) | ||||
−0.190259 | + | 0.981734i | \(0.560933\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.8370 | 0.927234 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −19.1468 | −0.850341 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −23.8216 | −1.05587 | −0.527936 | − | 0.849284i | \(-0.677034\pi\) | ||||
−0.527936 | + | 0.849284i | \(0.677034\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.756981 | −0.0334869 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 27.9038 | 1.23198 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13.5140 | 0.595496 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22.0558 | −0.970015 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.4659 | 1.03004 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.48532 | −0.152695 | −0.0763473 | − | 0.997081i | \(-0.524326\pi\) | ||||
−0.0763473 | + | 0.997081i | \(0.524326\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.2144 | 1.01509 | 0.507547 | − | 0.861624i | \(-0.330552\pi\) | ||||
0.507547 | + | 0.861624i | \(0.330552\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.53341 | 0.241498 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.11491 | −0.0485661 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 61.1895 | 2.66041 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.4178 | 0.495490 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.10866 | −0.0911655 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 25.0760 | 1.08211 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.22982 | 0.0960449 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.08074 | −0.390411 | −0.195206 | − | 0.980762i | \(-0.562537\pi\) | ||||
−0.195206 | + | 0.980762i | \(0.562537\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.29959 | 0.356169 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 15.6087 | 0.668603 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.34945 | −0.228726 | −0.114363 | − | 0.993439i | \(-0.536483\pi\) | ||||
−0.114363 | + | 0.993439i | \(0.536483\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.751455 | −0.0320713 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.67696 | −0.199245 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.00000 | 0.340195 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.12115 | 0.344724 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.9472 | −0.590961 | −0.295481 | − | 0.955349i | \(-0.595480\pi\) | ||||
−0.295481 | + | 0.955349i | \(0.595480\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.28415 | −0.138657 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.43322 | −0.355418 | −0.177709 | − | 0.984083i | \(-0.556869\pi\) | ||||
−0.177709 | + | 0.984083i | \(0.556869\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.29512 | 0.180697 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.81756 | 0.244314 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.89357 | −0.247071 | −0.123536 | − | 0.992340i | \(-0.539423\pi\) | ||||
−0.123536 | + | 0.992340i | \(0.539423\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −40.2857 | −1.68590 | −0.842951 | − | 0.537990i | \(-0.819184\pi\) | ||||
−0.842951 | + | 0.537990i | \(0.819184\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.24926 | −0.177515 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 34.4721 | 1.43759 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.1616 | 1.13075 | 0.565375 | − | 0.824834i | \(-0.308731\pi\) | ||||
0.565375 | + | 0.824834i | \(0.308731\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 25.8135 | 1.07277 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.9736 | −0.496748 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.4611 | 0.723167 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.2423 | −0.422745 | −0.211373 | − | 0.977406i | \(-0.567793\pi\) | ||||
−0.211373 | + | 0.977406i | \(0.567793\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.51396 | −0.227199 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 21.9736 | 0.903873 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 27.9736 | 1.14874 | 0.574369 | − | 0.818597i | \(-0.305248\pi\) | ||||
0.574369 | + | 0.818597i | \(0.305248\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.11491 | −0.0457068 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 24.5202 | 1.00355 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.00223 | −0.245245 | −0.122622 | − | 0.992453i | \(-0.539130\pi\) | ||||
−0.122622 | + | 0.992453i | \(0.539130\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.8913 | −0.811385 | −0.405692 | − | 0.914010i | \(-0.632970\pi\) | ||||
−0.405692 | + | 0.914010i | \(0.632970\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.23534 | 0.335369 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.72058 | 0.273230 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.4784 | 1.19649 | 0.598245 | − | 0.801313i | \(-0.295865\pi\) | ||||
0.598245 | + | 0.801313i | \(0.295865\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.39281 | −0.0564396 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −36.4115 | −1.47065 | −0.735324 | − | 0.677716i | \(-0.762970\pi\) | ||||
−0.735324 | + | 0.677716i | \(0.762970\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −16.8656 | −0.680088 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.51396 | −0.302501 | −0.151250 | − | 0.988495i | \(-0.548330\pi\) | ||||
−0.151250 | + | 0.988495i | \(0.548330\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.7438 | −0.873956 | −0.436978 | − | 0.899472i | \(-0.643951\pi\) | ||||
−0.436978 | + | 0.899472i | \(0.643951\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 51.7688 | 2.07741 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.1755 | −0.447736 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.89981 | 0.315993 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.2423 | −0.648655 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.94567 | 0.197197 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.57454 | 0.381156 | 0.190578 | − | 0.981672i | \(-0.438964\pi\) | ||||
0.190578 | + | 0.981672i | \(0.438964\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.9068 | −0.433505 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −23.6762 | −0.939563 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.2034 | 0.482759 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.8759 | 0.903544 | 0.451772 | − | 0.892134i | \(-0.350792\pi\) | ||||
0.451772 | + | 0.892134i | \(0.350792\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.2834 | −1.11539 | −0.557695 | − | 0.830046i | \(-0.688314\pi\) | ||||
−0.557695 | + | 0.830046i | \(0.688314\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −18.4185 | −0.725228 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.0125 | 0.393631 | 0.196816 | − | 0.980440i | \(-0.436940\pi\) | ||||
0.196816 | + | 0.980440i | \(0.436940\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −30.6461 | −1.20296 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.64207 | −0.0643579 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.45963 | −0.0962528 | −0.0481264 | − | 0.998841i | \(-0.515325\pi\) | ||||
−0.0481264 | + | 0.998841i | \(0.515325\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.13659 | −0.200703 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.628870 | −0.0245346 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.0187 | −1.28623 | −0.643114 | − | 0.765771i | \(-0.722358\pi\) | ||||
−0.643114 | + | 0.765771i | \(0.722358\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.97359 | 0.232346 | 0.116173 | − | 0.993229i | \(-0.462937\pi\) | ||||
0.116173 | + | 0.993229i | \(0.462937\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.51396 | −0.213822 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.67696 | −0.335973 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −39.9861 | −1.54595 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.01696 | 0.0778637 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.29512 | 0.242659 | 0.121329 | − | 0.992612i | \(-0.461284\pi\) | ||||
0.121329 | + | 0.992612i | \(0.461284\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 21.1972 | 0.815879 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 46.5544 | 1.78923 | 0.894615 | − | 0.446838i | \(-0.147450\pi\) | ||||
0.894615 | + | 0.446838i | \(0.147450\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.0606 | −0.386089 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.63912 | 0.254412 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −43.9861 | −1.68308 | −0.841540 | − | 0.540194i | \(-0.818351\pi\) | ||||
−0.841540 | + | 0.540194i | \(0.818351\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.423228 | −0.0161707 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15.0668 | 0.574835 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.17772 | 0.349137 | 0.174568 | − | 0.984645i | \(-0.444147\pi\) | ||||
0.174568 | + | 0.984645i | \(0.444147\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.85244 | 0.0703684 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.75698 | 0.256307 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.2709 | −0.389040 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 17.0154 | 0.643583 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.59622 | −0.286905 | −0.143453 | − | 0.989657i | \(-0.545820\pi\) | ||||
−0.143453 | + | 0.989657i | \(0.545820\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.4596 | 0.922512 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16.2423 | 0.611720 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18.6894 | 0.702889 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.63511 | 0.286743 | 0.143371 | − | 0.989669i | \(-0.454206\pi\) | ||||
0.143371 | + | 0.989669i | \(0.454206\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.64608 | 0.249248 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10.2298 | −0.383110 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 45.2999 | 1.69176 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.6204 | 0.507955 | 0.253977 | − | 0.967210i | \(-0.418261\pi\) | ||||
0.253977 | + | 0.967210i | \(0.418261\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.1212 | 0.451415 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.42474 | −0.0529868 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.55286 | −0.131950 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.9457 | −0.405952 | −0.202976 | − | 0.979184i | \(-0.565061\pi\) | ||||
−0.202976 | + | 0.979184i | \(0.565061\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.7625 | 1.10232 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.2166 | −0.414861 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.28415 | 0.269046 | 0.134523 | − | 0.990910i | \(-0.457050\pi\) | ||||
0.134523 | + | 0.990910i | \(0.457050\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.64207 | −0.0605688 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −22.1042 | −0.814218 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 50.3268 | 1.85130 | 0.925651 | − | 0.378380i | \(-0.123519\pi\) | ||||
0.925651 | + | 0.378380i | \(0.123519\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.9317 | −0.547793 | −0.273896 | − | 0.961759i | \(-0.588313\pi\) | ||||
−0.273896 | + | 0.961759i | \(0.588313\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.3594 | 0.416178 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.94719 | −0.363948 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.89134 | −0.0691079 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.9347 | −1.09233 | −0.546166 | − | 0.837677i | \(-0.683913\pi\) | ||||
−0.546166 | + | 0.837677i | \(0.683913\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.0388938 | −0.00141737 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.12963 | −0.332261 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.48827 | −0.235820 | −0.117910 | − | 0.993024i | \(-0.537619\pi\) | ||||
−0.117910 | + | 0.993024i | \(0.537619\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −30.1336 | −1.09378 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28.2159 | −1.02283 | −0.511413 | − | 0.859335i | \(-0.670878\pi\) | ||||
−0.511413 | + | 0.859335i | \(0.670878\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.0000 | 0.506834 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.926221 | −0.0334876 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.8260 | −0.787067 | −0.393533 | − | 0.919310i | \(-0.628747\pi\) | ||||
−0.393533 | + | 0.919310i | \(0.628747\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.6740 | 0.780570 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26.5683 | 0.955595 | 0.477798 | − | 0.878470i | \(-0.341435\pi\) | ||||
0.477798 | + | 0.878470i | \(0.341435\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.18869 | −0.150462 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.28415 | 0.261317 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −50.7967 | −1.81998 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.7547 | −1.17206 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.33553 | −0.190676 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.9083 | 0.567791 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.98903 | −0.177840 | −0.0889199 | − | 0.996039i | \(-0.528342\pi\) | ||||
−0.0889199 | + | 0.996039i | \(0.528342\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −36.7019 | −1.30662 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.85244 | 0.136977 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −12.8587 | −0.456051 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −47.0963 | −1.66824 | −0.834118 | − | 0.551587i | \(-0.814023\pi\) | ||||
−0.834118 | + | 0.551587i | \(0.814023\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.89134 | 0.349930 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.28415 | −0.328039 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.68793 | 0.0595657 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.2298 | −0.360554 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −35.3275 | −1.24359 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.2423 | −0.360100 | −0.180050 | − | 0.983657i | \(-0.557626\pi\) | ||||
−0.180050 | + | 0.983657i | \(0.557626\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.98680 | 0.104881 | 0.0524403 | − | 0.998624i | \(-0.483300\pi\) | ||||
0.0524403 | + | 0.998624i | \(0.483300\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 22.1909 | 0.778270 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.5529 | 0.614850 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −55.4736 | −1.94078 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −52.7283 | −1.84023 | −0.920116 | − | 0.391646i | \(-0.871906\pi\) | ||||
−0.920116 | + | 0.391646i | \(0.871906\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.68945 | 0.233179 | 0.116590 | − | 0.993180i | \(-0.462804\pi\) | ||||
0.116590 | + | 0.993180i | \(0.462804\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12.3385 | −0.429571 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −41.5140 | −1.44358 | −0.721791 | − | 0.692111i | \(-0.756681\pi\) | ||||
−0.721791 | + | 0.692111i | \(0.756681\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −48.4596 | −1.68307 | −0.841536 | − | 0.540201i | \(-0.818348\pi\) | ||||
−0.841536 | + | 0.540201i | \(0.818348\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.516914 | 0.0179316 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.00000 | −0.0346479 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.722813 | −0.0250140 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.29039 | −0.217428 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.64903 | 0.333122 | 0.166561 | − | 0.986031i | \(-0.446734\pi\) | ||||
0.166561 | + | 0.986031i | \(0.446734\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.1057 | −0.969162 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.81460 | 0.269149 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14.4938 | 0.498602 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.02792 | 0.207122 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.1047 | −0.587030 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 45.3789 | 1.55557 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35.3619 | −1.21077 | −0.605385 | − | 0.795933i | \(-0.706981\pi\) | ||||
−0.605385 | + | 0.795933i | \(0.706981\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.58078 | −0.156659 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 29.0451 | 0.992163 | 0.496081 | − | 0.868276i | \(-0.334772\pi\) | ||||
0.496081 | + | 0.868276i | \(0.334772\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43.7996 | 1.49442 | 0.747212 | − | 0.664586i | \(-0.231392\pi\) | ||||
0.747212 | + | 0.664586i | \(0.231392\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.1274 | −0.515540 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.39754 | 0.115654 | 0.0578268 | − | 0.998327i | \(-0.481583\pi\) | ||||
0.0578268 | + | 0.998327i | \(0.481583\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17.7632 | −0.603968 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.47283 | 0.0500201 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17.8385 | −0.605130 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.35793 | −0.282873 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.76322 | −0.330057 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −29.0529 | −0.981047 | −0.490523 | − | 0.871428i | \(-0.663194\pi\) | ||||
−0.490523 | + | 0.871428i | \(0.663194\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 29.8135 | 1.00559 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.4923 | −0.387185 | −0.193592 | − | 0.981082i | \(-0.562014\pi\) | ||||
−0.193592 | + | 0.981082i | \(0.562014\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.1927 | −0.847802 | −0.423901 | − | 0.905709i | \(-0.639340\pi\) | ||||
−0.423901 | + | 0.905709i | \(0.639340\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 22.5683 | 0.758625 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 35.1957 | 1.18176 | 0.590878 | − | 0.806761i | \(-0.298781\pi\) | ||||
0.590878 | + | 0.806761i | \(0.298781\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −21.2361 | −0.712235 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −12.9721 | −0.434581 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 48.9193 | 1.63702 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −18.9821 | −0.634501 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.05433 | 0.0351639 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.83076 | −0.260880 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −16.5202 | −0.549758 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.28263 | −0.208842 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.1227 | 0.834184 | 0.417092 | − | 0.908864i | \(-0.363049\pi\) | ||||
0.417092 | + | 0.908864i | \(0.363049\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.5264 | 0.514980 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.5110 | −0.745823 | −0.372912 | − | 0.927867i | \(-0.621641\pi\) | ||||
−0.372912 | + | 0.927867i | \(0.621641\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 26.6989 | 0.883605 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.48532 | −0.0491032 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.60719 | −0.152143 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.5676 | −0.447553 | −0.223777 | − | 0.974640i | \(-0.571839\pi\) | ||||
−0.223777 | + | 0.974640i | \(0.571839\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.77018 | 0.0583296 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.5808 | 0.610932 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.0698 | 0.330735 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11.9519 | −0.392129 | −0.196065 | − | 0.980591i | \(-0.562816\pi\) | ||||
−0.196065 | + | 0.980591i | \(0.562816\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.94567 | −0.162088 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15.0349 | 0.492220 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.48604 | 0.0813021 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 53.0140 | 1.73189 | 0.865946 | − | 0.500138i | \(-0.166717\pi\) | ||||
0.865946 | + | 0.500138i | \(0.166717\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27.5973 | 0.900603 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.1204 | −0.884101 | −0.442050 | − | 0.896990i | \(-0.645749\pi\) | ||||
−0.442050 | + | 0.896990i | \(0.645749\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −94.2409 | −3.06890 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.29039 | −0.204626 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 44.5808 | 1.44868 | 0.724340 | − | 0.689443i | \(-0.242144\pi\) | ||||
0.724340 | + | 0.689443i | \(0.242144\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.4626 | −0.501409 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −51.8991 | −1.68118 | −0.840588 | − | 0.541675i | \(-0.817791\pi\) | ||||
−0.840588 | + | 0.541675i | \(0.817791\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.21661 | 0.104087 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.10571 | 0.100393 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.379608 | −0.0122582 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.7570 | −0.959903 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.57125 | −0.0506327 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19.5404 | −0.629027 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.2680 | −1.19846 | −0.599229 | − | 0.800578i | \(-0.704526\pi\) | ||||
−0.599229 | + | 0.800578i | \(0.704526\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.28415 | 0.234001 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.05433 | 0.0980182 | 0.0490091 | − | 0.998798i | \(-0.484394\pi\) | ||||
0.0490091 | + | 0.998798i | \(0.484394\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.06058 | 0.194293 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −47.3961 | −1.51634 | −0.758168 | − | 0.652059i | \(-0.773905\pi\) | ||||
−0.758168 | + | 0.652059i | \(0.773905\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.9193 | 0.796423 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.6306 | 0.371338 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 51.1957 | 1.63289 | 0.816445 | − | 0.577423i | \(-0.195942\pi\) | ||||
0.816445 | + | 0.577423i | \(0.195942\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.6336 | −0.529990 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 14.5683 | 0.463714 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −102.918 | −3.27260 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.9332 | −0.537900 | −0.268950 | − | 0.963154i | \(-0.586677\pi\) | ||||
−0.268950 | + | 0.963154i | \(0.586677\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −39.7757 | −1.26224 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18.5613 | −0.588434 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −53.3069 | −1.68825 | −0.844123 | − | 0.536150i | \(-0.819878\pi\) | ||||
−0.844123 | + | 0.536150i | \(0.819878\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 27.9038 | 0.882838 |
(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 | 1904.2.a.m.1.3 | 3 | ||
4.3 | odd | 2 | 952.2.a.f.1.1 | ✓ | 3 | ||
8.3 | odd | 2 | 7616.2.a.bc.1.3 | 3 | |||
8.5 | even | 2 | 7616.2.a.be.1.1 | 3 | |||
12.11 | even | 2 | 8568.2.a.x.1.3 | 3 | |||
28.27 | even | 2 | 6664.2.a.j.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
952.2.a.f.1.1 | ✓ | 3 | 4.3 | odd | 2 | ||
1904.2.a.m.1.3 | 3 | 1.1 | even | 1 | trivial | ||
6664.2.a.j.1.3 | 3 | 28.27 | even | 2 | |||
7616.2.a.bc.1.3 | 3 | 8.3 | odd | 2 | |||
7616.2.a.be.1.1 | 3 | 8.5 | even | 2 | |||
8568.2.a.x.1.3 | 3 | 12.11 | even | 2 |