Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7623,2,Mod(1,7623)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7623, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7623.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7623.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: | \(60.8699614608\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 8x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.16372\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7623.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.64575 | 1.18322 | 0.591608 | − | 0.806226i | \(-0.298493\pi\) | ||||
0.591608 | + | 0.806226i | \(0.298493\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.82843 | 1.00000 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.74166 | −1.18322 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.74166 | −1.59245 | −0.796225 | − | 0.605001i | \(-0.793173\pi\) | ||||
−0.796225 | + | 0.605001i | \(0.793173\pi\) | |||||||
\(14\) | −1.41421 | −0.377964 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | −5.47418 | −1.32768 | −0.663842 | − | 0.747873i | \(-0.731075\pi\) | ||||
−0.663842 | + | 0.747873i | \(0.731075\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.74166 | 1.31723 | 0.658613 | − | 0.752482i | \(-0.271143\pi\) | ||||
0.658613 | + | 0.752482i | \(0.271143\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.87729 | −0.808471 | −0.404235 | − | 0.914655i | \(-0.632462\pi\) | ||||
−0.404235 | + | 0.914655i | \(0.632462\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | 0.400000 | ||||||||
\(26\) | 8.11993 | 1.59245 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.87729 | −0.719995 | −0.359997 | − | 0.932953i | \(-0.617222\pi\) | ||||
−0.359997 | + | 0.932953i | \(0.617222\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.48331 | 0.984832 | 0.492416 | − | 0.870360i | \(-0.336114\pi\) | ||||
0.492416 | + | 0.870360i | \(0.336114\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.74166 | 1.32768 | ||||||||
\(35\) | 2.64575 | 0.447214 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.48331 | 0.572653 | 0.286327 | − | 0.958132i | \(-0.407566\pi\) | ||||
0.286327 | + | 0.958132i | \(0.407566\pi\) | |||||||
\(38\) | −8.11993 | −1.31723 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 7.48331 | 1.18322 | ||||||||
\(41\) | 5.65685 | 0.883452 | 0.441726 | − | 0.897150i | \(-0.354366\pi\) | ||||
0.441726 | + | 0.897150i | \(0.354366\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.00000 | −0.152499 | −0.0762493 | − | 0.997089i | \(-0.524294\pi\) | ||||
−0.0762493 | + | 0.997089i | \(0.524294\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.48331 | 0.808471 | ||||||||
\(47\) | −5.47418 | −0.798491 | −0.399245 | − | 0.916844i | \(-0.630728\pi\) | ||||
−0.399245 | + | 0.916844i | \(0.630728\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.82843 | −0.400000 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.4114 | 1.84220 | 0.921101 | − | 0.389324i | \(-0.127291\pi\) | ||||
0.921101 | + | 0.389324i | \(0.127291\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.82843 | 0.377964 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.48331 | 0.719995 | ||||||||
\(59\) | 8.30261 | 1.08091 | 0.540454 | − | 0.841374i | \(-0.318253\pi\) | ||||
0.540454 | + | 0.841374i | \(0.318253\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.74166 | 0.222996 | 0.111498 | − | 0.993765i | \(-0.464435\pi\) | ||||
0.111498 | + | 0.993765i | \(0.464435\pi\) | |||||||
\(62\) | −7.75458 | −0.984832 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | −15.1910 | −1.88421 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.48331 | −0.792063 | −0.396031 | − | 0.918237i | \(-0.629613\pi\) | ||||
−0.396031 | + | 0.918237i | \(0.629613\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.74166 | −0.447214 | ||||||||
\(71\) | −1.41421 | −0.167836 | −0.0839181 | − | 0.996473i | \(-0.526743\pi\) | ||||
−0.0839181 | + | 0.996473i | \(0.526743\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.7417 | −1.84242 | −0.921211 | − | 0.389064i | \(-0.872799\pi\) | ||||
−0.921211 | + | 0.389064i | \(0.872799\pi\) | |||||||
\(74\) | −4.92615 | −0.572653 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.4833 | −1.51699 | −0.758496 | − | 0.651678i | \(-0.774065\pi\) | ||||
−0.758496 | + | 0.651678i | \(0.774065\pi\) | |||||||
\(80\) | −10.5830 | −1.18322 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8.00000 | −0.883452 | ||||||||
\(83\) | −11.1310 | −1.22179 | −0.610895 | − | 0.791712i | \(-0.709190\pi\) | ||||
−0.610895 | + | 0.791712i | \(0.709190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −14.4833 | −1.57094 | ||||||||
\(86\) | 1.41421 | 0.152499 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.83953 | 0.618989 | 0.309494 | − | 0.950901i | \(-0.399840\pi\) | ||||
0.309494 | + | 0.950901i | \(0.399840\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.74166 | −0.601889 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.74166 | 0.798491 | ||||||||
\(95\) | 15.1910 | 1.55856 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.22497 | −0.733585 | −0.366792 | − | 0.930303i | \(-0.619544\pi\) | ||||
−0.366792 | + | 0.930303i | \(0.619544\pi\) | |||||||
\(98\) | −1.41421 | −0.142857 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.66796 | 0.862494 | 0.431247 | − | 0.902234i | \(-0.358074\pi\) | ||||
0.431247 | + | 0.902234i | \(0.358074\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.2250 | −1.30310 | −0.651548 | − | 0.758608i | \(-0.725880\pi\) | ||||
−0.651548 | + | 0.758608i | \(0.725880\pi\) | |||||||
\(104\) | −16.2399 | −1.59245 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −18.9666 | −1.84220 | ||||||||
\(107\) | 9.53414 | 0.921700 | 0.460850 | − | 0.887478i | \(-0.347545\pi\) | ||||
0.460850 | + | 0.887478i | \(0.347545\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.4833 | 1.57882 | 0.789408 | − | 0.613869i | \(-0.210388\pi\) | ||||
0.789408 | + | 0.613869i | \(0.210388\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.00000 | −0.377964 | ||||||||
\(113\) | 5.29150 | 0.497783 | 0.248891 | − | 0.968531i | \(-0.419934\pi\) | ||||
0.248891 | + | 0.968531i | \(0.419934\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.2583 | −0.956595 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −11.7417 | −1.08091 | ||||||||
\(119\) | −5.47418 | −0.501817 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −2.46308 | −0.222996 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.93725 | −0.709930 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.4833 | −1.46266 | −0.731329 | − | 0.682025i | \(-0.761100\pi\) | ||||
−0.731329 | + | 0.682025i | \(0.761100\pi\) | |||||||
\(128\) | −11.3137 | −1.00000 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 21.4833 | 1.88421 | ||||||||
\(131\) | −8.66796 | −0.757323 | −0.378661 | − | 0.925535i | \(-0.623616\pi\) | ||||
−0.378661 | + | 0.925535i | \(0.623616\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.74166 | 0.497865 | ||||||||
\(134\) | 9.16879 | 0.792063 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −15.4833 | −1.32768 | ||||||||
\(137\) | 8.80344 | 0.752129 | 0.376064 | − | 0.926594i | \(-0.377277\pi\) | ||||
0.376064 | + | 0.926594i | \(0.377277\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.74166 | 0.317363 | 0.158682 | − | 0.987330i | \(-0.449276\pi\) | ||||
0.158682 | + | 0.987330i | \(0.449276\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.00000 | 0.167836 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.2583 | −0.851909 | ||||||||
\(146\) | 22.2621 | 1.84242 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −23.3109 | −1.90971 | −0.954853 | − | 0.297079i | \(-0.903987\pi\) | ||||
−0.954853 | + | 0.297079i | \(0.903987\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.51669 | −0.611699 | −0.305850 | − | 0.952080i | \(-0.598940\pi\) | ||||
−0.305850 | + | 0.952080i | \(0.598940\pi\) | |||||||
\(152\) | 16.2399 | 1.31723 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 14.5075 | 1.16527 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.9666 | −1.03485 | −0.517425 | − | 0.855729i | \(-0.673109\pi\) | ||||
−0.517425 | + | 0.855729i | \(0.673109\pi\) | |||||||
\(158\) | 19.0683 | 1.51699 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.87729 | −0.305573 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −24.4499 | −1.91507 | −0.957534 | − | 0.288321i | \(-0.906903\pi\) | ||||
−0.957534 | + | 0.288321i | \(0.906903\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.7417 | 1.22179 | ||||||||
\(167\) | 8.66796 | 0.670747 | 0.335373 | − | 0.942085i | \(-0.391138\pi\) | ||||
0.335373 | + | 0.942085i | \(0.391138\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.9666 | 1.53589 | ||||||||
\(170\) | 20.4825 | 1.57094 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.10883 | −0.388417 | −0.194208 | − | 0.980960i | \(-0.562214\pi\) | ||||
−0.194208 | + | 0.980960i | \(0.562214\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.00000 | 0.151186 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −8.25834 | −0.618989 | ||||||||
\(179\) | 14.1421 | 1.05703 | 0.528516 | − | 0.848923i | \(-0.322748\pi\) | ||||
0.528516 | + | 0.848923i | \(0.322748\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | 8.11993 | 0.601889 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −10.9666 | −0.808471 | ||||||||
\(185\) | 9.21598 | 0.677573 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −21.4833 | −1.55856 | ||||||||
\(191\) | −1.41421 | −0.102329 | −0.0511645 | − | 0.998690i | \(-0.516293\pi\) | ||||
−0.0511645 | + | 0.998690i | \(0.516293\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.4833 | −1.18649 | −0.593247 | − | 0.805020i | \(-0.702154\pi\) | ||||
−0.593247 | + | 0.805020i | \(0.702154\pi\) | |||||||
\(194\) | 10.2177 | 0.733585 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.2621 | −1.58611 | −0.793053 | − | 0.609152i | \(-0.791510\pi\) | ||||
−0.793053 | + | 0.609152i | \(0.791510\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.25834 | 0.160090 | 0.0800448 | − | 0.996791i | \(-0.474494\pi\) | ||||
0.0800448 | + | 0.996791i | \(0.474494\pi\) | |||||||
\(200\) | 5.65685 | 0.400000 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −12.2583 | −0.862494 | ||||||||
\(203\) | −3.87729 | −0.272132 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.9666 | 1.04531 | ||||||||
\(206\) | 18.7029 | 1.30310 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 22.9666 | 1.59245 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.51669 | −0.655156 | −0.327578 | − | 0.944824i | \(-0.606232\pi\) | ||||
−0.327578 | + | 0.944824i | \(0.606232\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −13.4833 | −0.921700 | ||||||||
\(215\) | −2.64575 | −0.180439 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.48331 | 0.372232 | ||||||||
\(218\) | −23.3109 | −1.57882 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 31.4309 | 2.11427 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.4833 | 1.17077 | 0.585385 | − | 0.810756i | \(-0.300943\pi\) | ||||
0.585385 | + | 0.810756i | \(0.300943\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.48331 | −0.497783 | ||||||||
\(227\) | −27.7362 | −1.84092 | −0.920460 | − | 0.390838i | \(-0.872185\pi\) | ||||
−0.920460 | + | 0.390838i | \(0.872185\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.4833 | 0.891003 | 0.445501 | − | 0.895281i | \(-0.353025\pi\) | ||||
0.445501 | + | 0.895281i | \(0.353025\pi\) | |||||||
\(230\) | 14.5075 | 0.956595 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.9666 | −0.719995 | ||||||||
\(233\) | −6.34036 | −0.415371 | −0.207686 | − | 0.978196i | \(-0.566593\pi\) | ||||
−0.207686 | + | 0.978196i | \(0.566593\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.4833 | −0.944787 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.74166 | 0.501817 | ||||||||
\(239\) | 8.11993 | 0.525235 | 0.262617 | − | 0.964900i | \(-0.415414\pi\) | ||||
0.262617 | + | 0.964900i | \(0.415414\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.22497 | 0.207739 | 0.103869 | − | 0.994591i | \(-0.466878\pi\) | ||||
0.103869 | + | 0.994591i | \(0.466878\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.64575 | 0.169031 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −32.9666 | −2.09762 | ||||||||
\(248\) | 15.5092 | 0.984832 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 11.2250 | 0.709930 | ||||||||
\(251\) | −2.09772 | −0.132407 | −0.0662036 | − | 0.997806i | \(-0.521089\pi\) | ||||
−0.0662036 | + | 0.997806i | \(0.521089\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 23.3109 | 1.46266 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.548027 | 0.0341850 | 0.0170925 | − | 0.999854i | \(-0.494559\pi\) | ||||
0.0170925 | + | 0.999854i | \(0.494559\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.48331 | 0.216443 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12.2583 | 0.757323 | ||||||||
\(263\) | 20.1171 | 1.24048 | 0.620238 | − | 0.784413i | \(-0.287036\pi\) | ||||
0.620238 | + | 0.784413i | \(0.287036\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 35.4833 | 2.17972 | ||||||||
\(266\) | −8.11993 | −0.497865 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −24.3598 | −1.48524 | −0.742621 | − | 0.669712i | \(-0.766418\pi\) | ||||
−0.742621 | + | 0.669712i | \(0.766418\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.96663 | −0.544684 | −0.272342 | − | 0.962201i | \(-0.587798\pi\) | ||||
−0.272342 | + | 0.962201i | \(0.587798\pi\) | |||||||
\(272\) | 21.8967 | 1.32768 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.4499 | −0.752129 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.9666 | −1.19968 | −0.599839 | − | 0.800121i | \(-0.704769\pi\) | ||||
−0.599839 | + | 0.800121i | \(0.704769\pi\) | |||||||
\(278\) | −5.29150 | −0.317363 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 7.48331 | 0.447214 | ||||||||
\(281\) | 16.2399 | 0.968789 | 0.484394 | − | 0.874850i | \(-0.339040\pi\) | ||||
0.484394 | + | 0.874850i | \(0.339040\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.96663 | 0.533011 | 0.266505 | − | 0.963833i | \(-0.414131\pi\) | ||||
0.266505 | + | 0.963833i | \(0.414131\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.65685 | 0.333914 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.9666 | 0.762743 | ||||||||
\(290\) | 14.5075 | 0.851909 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 28.1016 | 1.64171 | 0.820856 | − | 0.571135i | \(-0.193497\pi\) | ||||
0.820856 | + | 0.571135i | \(0.193497\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 21.9666 | 1.27895 | ||||||||
\(296\) | 9.85230 | 0.572653 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 32.9666 | 1.90971 | ||||||||
\(299\) | 22.2621 | 1.28745 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.00000 | −0.0576390 | ||||||||
\(302\) | 10.6302 | 0.611699 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −22.9666 | −1.31723 | ||||||||
\(305\) | 4.60799 | 0.263853 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.70829 | −0.382862 | −0.191431 | − | 0.981506i | \(-0.561313\pi\) | ||||
−0.191431 | + | 0.981506i | \(0.561313\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −20.5167 | −1.16527 | ||||||||
\(311\) | 15.3265 | 0.869085 | 0.434542 | − | 0.900651i | \(-0.356910\pi\) | ||||
0.434542 | + | 0.900651i | \(0.356910\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.51669 | −0.255298 | −0.127649 | − | 0.991819i | \(-0.540743\pi\) | ||||
−0.127649 | + | 0.991819i | \(0.540743\pi\) | |||||||
\(314\) | 18.3376 | 1.03485 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.53414 | 0.535491 | 0.267745 | − | 0.963490i | \(-0.413721\pi\) | ||||
0.267745 | + | 0.963490i | \(0.413721\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 21.1660 | 1.18322 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.48331 | 0.305573 | ||||||||
\(323\) | −31.4309 | −1.74886 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.4833 | −0.636980 | ||||||||
\(326\) | 34.5774 | 1.91507 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 16.0000 | 0.883452 | ||||||||
\(329\) | −5.47418 | −0.301801 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.4833 | 1.12586 | 0.562932 | − | 0.826503i | \(-0.309673\pi\) | ||||
0.562932 | + | 0.826503i | \(0.309673\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −12.2583 | −0.670747 | ||||||||
\(335\) | −17.1532 | −0.937182 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.9666 | 1.25107 | 0.625536 | − | 0.780195i | \(-0.284880\pi\) | ||||
0.625536 | + | 0.780195i | \(0.284880\pi\) | |||||||
\(338\) | −28.2371 | −1.53589 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −2.82843 | −0.152499 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.22497 | 0.388417 | ||||||||
\(347\) | −33.1632 | −1.78030 | −0.890148 | − | 0.455672i | \(-0.849399\pi\) | ||||
−0.890148 | + | 0.455672i | \(0.849399\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −33.4833 | −1.79232 | −0.896160 | − | 0.443730i | \(-0.853655\pi\) | ||||
−0.896160 | + | 0.443730i | \(0.853655\pi\) | |||||||
\(350\) | −2.82843 | −0.151186 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.9928 | −1.22378 | −0.611891 | − | 0.790942i | \(-0.709591\pi\) | ||||
−0.611891 | + | 0.790942i | \(0.709591\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.74166 | −0.198587 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −20.0000 | −1.05703 | ||||||||
\(359\) | 14.0949 | 0.743903 | 0.371951 | − | 0.928252i | \(-0.378689\pi\) | ||||
0.371951 | + | 0.928252i | \(0.378689\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.9666 | 0.735086 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −41.6485 | −2.17998 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.2250 | 0.899136 | 0.449568 | − | 0.893246i | \(-0.351578\pi\) | ||||
0.449568 | + | 0.893246i | \(0.351578\pi\) | |||||||
\(368\) | 15.5092 | 0.808471 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −13.0334 | −0.677573 | ||||||||
\(371\) | 13.4114 | 0.696287 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.4499 | −1.00708 | −0.503540 | − | 0.863972i | \(-0.667969\pi\) | ||||
−0.503540 | + | 0.863972i | \(0.667969\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −15.4833 | −0.798491 | ||||||||
\(377\) | 22.2621 | 1.14655 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −34.4833 | −1.77129 | −0.885644 | − | 0.464364i | \(-0.846283\pi\) | ||||
−0.885644 | + | 0.464364i | \(0.846283\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.00000 | 0.102329 | ||||||||
\(383\) | −21.3487 | −1.09087 | −0.545433 | − | 0.838154i | \(-0.683635\pi\) | ||||
−0.545433 | + | 0.838154i | \(0.683635\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 23.3109 | 1.18649 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −33.5758 | −1.70236 | −0.851180 | − | 0.524874i | \(-0.824112\pi\) | ||||
−0.851180 | + | 0.524874i | \(0.824112\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.2250 | 1.07339 | ||||||||
\(392\) | 2.82843 | 0.142857 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 31.4833 | 1.58611 | ||||||||
\(395\) | −35.6735 | −1.79493 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.48331 | 0.0744454 | 0.0372227 | − | 0.999307i | \(-0.488149\pi\) | ||||
0.0372227 | + | 0.999307i | \(0.488149\pi\) | |||||||
\(398\) | −3.19378 | −0.160090 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8.00000 | −0.400000 | ||||||||
\(401\) | 8.11993 | 0.405490 | 0.202745 | − | 0.979232i | \(-0.435014\pi\) | ||||
0.202745 | + | 0.979232i | \(0.435014\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −31.4833 | −1.56830 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.48331 | 0.272132 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.22497 | 0.456146 | 0.228073 | − | 0.973644i | \(-0.426758\pi\) | ||||
0.228073 | + | 0.973644i | \(0.426758\pi\) | |||||||
\(410\) | −21.1660 | −1.04531 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.30261 | 0.408545 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −29.4499 | −1.44564 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −29.4686 | −1.43964 | −0.719818 | − | 0.694163i | \(-0.755775\pi\) | ||||
−0.719818 | + | 0.694163i | \(0.755775\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.51669 | −0.366341 | −0.183170 | − | 0.983081i | \(-0.558636\pi\) | ||||
−0.183170 | + | 0.983081i | \(0.558636\pi\) | |||||||
\(422\) | 13.4586 | 0.655156 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 37.9333 | 1.84220 | ||||||||
\(425\) | −10.9484 | −0.531073 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.74166 | 0.0842847 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.74166 | 0.180439 | ||||||||
\(431\) | 15.8745 | 0.764648 | 0.382324 | − | 0.924028i | \(-0.375124\pi\) | ||||
0.382324 | + | 0.924028i | \(0.375124\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.74166 | −0.0836987 | −0.0418494 | − | 0.999124i | \(-0.513325\pi\) | ||||
−0.0418494 | + | 0.999124i | \(0.513325\pi\) | |||||||
\(434\) | −7.75458 | −0.372232 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −22.2621 | −1.06494 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.4833 | −0.929888 | −0.464944 | − | 0.885340i | \(-0.653926\pi\) | ||||
−0.464944 | + | 0.885340i | \(0.653926\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −44.4499 | −2.11427 | ||||||||
\(443\) | −27.2354 | −1.29399 | −0.646997 | − | 0.762493i | \(-0.723975\pi\) | ||||
−0.646997 | + | 0.762493i | \(0.723975\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.4499 | 0.732398 | ||||||||
\(446\) | −24.7251 | −1.17077 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.00000 | 0.377964 | ||||||||
\(449\) | 10.2177 | 0.482201 | 0.241100 | − | 0.970500i | \(-0.422492\pi\) | ||||
0.241100 | + | 0.970500i | \(0.422492\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 39.2250 | 1.84092 | ||||||||
\(455\) | −15.1910 | −0.712165 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.0000 | −1.07589 | −0.537947 | − | 0.842978i | \(-0.680800\pi\) | ||||
−0.537947 | + | 0.842978i | \(0.680800\pi\) | |||||||
\(458\) | −19.0683 | −0.891003 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.20655 | −0.335643 | −0.167821 | − | 0.985817i | \(-0.553673\pi\) | ||||
−0.167821 | + | 0.985817i | \(0.553673\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.4833 | −0.812519 | −0.406259 | − | 0.913758i | \(-0.633167\pi\) | ||||
−0.406259 | + | 0.913758i | \(0.633167\pi\) | |||||||
\(464\) | 15.5092 | 0.719995 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.96663 | 0.415371 | ||||||||
\(467\) | 20.8007 | 0.962540 | 0.481270 | − | 0.876572i | \(-0.340176\pi\) | ||||
0.481270 | + | 0.876572i | \(0.340176\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.48331 | −0.299372 | ||||||||
\(470\) | 20.4825 | 0.944787 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 23.4833 | 1.08091 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.4833 | 0.526891 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −11.4833 | −0.525235 | ||||||||
\(479\) | −23.1754 | −1.05891 | −0.529457 | − | 0.848337i | \(-0.677604\pi\) | ||||
−0.529457 | + | 0.848337i | \(0.677604\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.0000 | −0.911922 | ||||||||
\(482\) | −4.56080 | −0.207739 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −19.1155 | −0.867989 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.51669 | 0.249985 | 0.124992 | − | 0.992158i | \(-0.460109\pi\) | ||||
0.124992 | + | 0.992158i | \(0.460109\pi\) | |||||||
\(488\) | 4.92615 | 0.222996 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.74166 | −0.169031 | ||||||||
\(491\) | 29.6985 | 1.34027 | 0.670137 | − | 0.742237i | \(-0.266235\pi\) | ||||
0.670137 | + | 0.742237i | \(0.266235\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 21.2250 | 0.955925 | ||||||||
\(494\) | 46.6219 | 2.09762 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −21.9333 | −0.984832 | ||||||||
\(497\) | −1.41421 | −0.0634361 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.9666 | −0.804297 | −0.402148 | − | 0.915574i | \(-0.631736\pi\) | ||||
−0.402148 | + | 0.915574i | \(0.631736\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.96663 | 0.132407 | ||||||||
\(503\) | 34.3948 | 1.53359 | 0.766793 | − | 0.641894i | \(-0.221851\pi\) | ||||
0.766793 | + | 0.641894i | \(0.221851\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.9333 | 1.02052 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.8617 | −0.525762 | −0.262881 | − | 0.964828i | \(-0.584673\pi\) | ||||
−0.262881 | + | 0.964828i | \(0.584673\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.7417 | −0.696370 | ||||||||
\(512\) | 22.6274 | 1.00000 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.775028 | −0.0341850 | ||||||||
\(515\) | −34.9900 | −1.54184 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −4.92615 | −0.216443 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −42.9666 | −1.88421 | ||||||||
\(521\) | −7.20655 | −0.315725 | −0.157862 | − | 0.987461i | \(-0.550460\pi\) | ||||
−0.157862 | + | 0.987461i | \(0.550460\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.22497 | 0.315926 | 0.157963 | − | 0.987445i | \(-0.449507\pi\) | ||||
0.157963 | + | 0.987445i | \(0.449507\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −28.4499 | −1.24048 | ||||||||
\(527\) | −30.0166 | −1.30755 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.96663 | −0.346375 | ||||||||
\(530\) | −50.1810 | −2.17972 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −32.4797 | −1.40685 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 25.2250 | 1.09057 | ||||||||
\(536\) | −18.3376 | −0.792063 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 34.4499 | 1.48524 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.0000 | −0.644900 | −0.322450 | − | 0.946586i | \(-0.604506\pi\) | ||||
−0.322450 | + | 0.946586i | \(0.604506\pi\) | |||||||
\(542\) | 12.6807 | 0.544684 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 43.6108 | 1.86808 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.0000 | 0.427569 | 0.213785 | − | 0.976881i | \(-0.431421\pi\) | ||||
0.213785 | + | 0.976881i | \(0.431421\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.2621 | −0.948396 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.4833 | −0.573369 | ||||||||
\(554\) | 28.2371 | 1.19968 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 46.9872 | 1.99091 | 0.995456 | − | 0.0952236i | \(-0.0303566\pi\) | ||||
0.995456 | + | 0.0952236i | \(0.0303566\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.74166 | 0.242846 | ||||||||
\(560\) | −10.5830 | −0.447214 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −22.9666 | −0.968789 | ||||||||
\(563\) | 13.2288 | 0.557526 | 0.278763 | − | 0.960360i | \(-0.410076\pi\) | ||||
0.278763 | + | 0.960360i | \(0.410076\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.0000 | 0.588984 | ||||||||
\(566\) | −12.6807 | −0.533011 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.00000 | −0.167836 | ||||||||
\(569\) | −18.3848 | −0.770730 | −0.385365 | − | 0.922764i | \(-0.625924\pi\) | ||||
−0.385365 | + | 0.922764i | \(0.625924\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.9666 | −1.12852 | −0.564259 | − | 0.825598i | \(-0.690838\pi\) | ||||
−0.564259 | + | 0.825598i | \(0.690838\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8.00000 | −0.333914 | ||||||||
\(575\) | −7.75458 | −0.323388 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.7083 | −0.778836 | −0.389418 | − | 0.921061i | \(-0.627324\pi\) | ||||
−0.389418 | + | 0.921061i | \(0.627324\pi\) | |||||||
\(578\) | −18.3376 | −0.762743 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.1310 | −0.461793 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −44.5241 | −1.84242 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −39.7417 | −1.64171 | ||||||||
\(587\) | 1.54970 | 0.0639628 | 0.0319814 | − | 0.999488i | \(-0.489818\pi\) | ||||
0.0319814 | + | 0.999488i | \(0.489818\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 31.4833 | 1.29725 | ||||||||
\(590\) | −31.0655 | −1.27895 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −13.9333 | −0.572653 | ||||||||
\(593\) | 39.6863 | 1.62972 | 0.814860 | − | 0.579658i | \(-0.196814\pi\) | ||||
0.814860 | + | 0.579658i | \(0.196814\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14.4833 | −0.593758 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −31.4833 | −1.28745 | ||||||||
\(599\) | 29.6513 | 1.21152 | 0.605759 | − | 0.795648i | \(-0.292869\pi\) | ||||
0.605759 | + | 0.795648i | \(0.292869\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −37.2250 | −1.51844 | −0.759219 | − | 0.650835i | \(-0.774419\pi\) | ||||
−0.759219 | + | 0.650835i | \(0.774419\pi\) | |||||||
\(602\) | 1.41421 | 0.0576390 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −35.7417 | −1.45071 | −0.725355 | − | 0.688375i | \(-0.758324\pi\) | ||||
−0.725355 | + | 0.688375i | \(0.758324\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.51669 | −0.263853 | ||||||||
\(611\) | 31.4309 | 1.27156 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.4833 | −1.06965 | −0.534826 | − | 0.844963i | \(-0.679623\pi\) | ||||
−0.534826 | + | 0.844963i | \(0.679623\pi\) | |||||||
\(614\) | 9.48695 | 0.382862 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.09772 | −0.0844512 | −0.0422256 | − | 0.999108i | \(-0.513445\pi\) | ||||
−0.0422256 | + | 0.999108i | \(0.513445\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 34.4499 | 1.38466 | 0.692330 | − | 0.721581i | \(-0.256584\pi\) | ||||
0.692330 | + | 0.721581i | \(0.256584\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −21.6749 | −0.869085 | ||||||||
\(623\) | 5.83953 | 0.233956 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.0000 | −1.24000 | ||||||||
\(626\) | 6.38756 | 0.255298 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −19.0683 | −0.760302 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.4499 | −1.01315 | −0.506573 | − | 0.862197i | \(-0.669088\pi\) | ||||
−0.506573 | + | 0.862197i | \(0.669088\pi\) | |||||||
\(632\) | −38.1366 | −1.51699 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −13.4833 | −0.535491 | ||||||||
\(635\) | −43.6108 | −1.73064 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.74166 | −0.227493 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −29.9333 | −1.18322 | ||||||||
\(641\) | −11.2665 | −0.445001 | −0.222500 | − | 0.974933i | \(-0.571422\pi\) | ||||
−0.222500 | + | 0.974933i | \(0.571422\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −40.4499 | −1.59519 | −0.797595 | − | 0.603193i | \(-0.793895\pi\) | ||||
−0.797595 | + | 0.603193i | \(0.793895\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 44.4499 | 1.74886 | ||||||||
\(647\) | 47.9006 | 1.88317 | 0.941583 | − | 0.336781i | \(-0.109338\pi\) | ||||
0.941583 | + | 0.336781i | \(0.109338\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 16.2399 | 0.636980 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.8717 | 1.09070 | 0.545352 | − | 0.838207i | \(-0.316396\pi\) | ||||
0.545352 | + | 0.838207i | \(0.316396\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −22.9333 | −0.896077 | ||||||||
\(656\) | −22.6274 | −0.883452 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 7.74166 | 0.301801 | ||||||||
\(659\) | 32.5269 | 1.26707 | 0.633534 | − | 0.773715i | \(-0.281604\pi\) | ||||
0.633534 | + | 0.773715i | \(0.281604\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.0000 | 1.55582 | 0.777910 | − | 0.628376i | \(-0.216280\pi\) | ||||
0.777910 | + | 0.628376i | \(0.216280\pi\) | |||||||
\(662\) | −28.9678 | −1.12586 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −31.4833 | −1.22179 | ||||||||
\(665\) | 15.1910 | 0.589082 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.0334 | 0.582094 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 24.2583 | 0.937182 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.44994 | 0.210080 | 0.105040 | − | 0.994468i | \(-0.466503\pi\) | ||||
0.105040 | + | 0.994468i | \(0.466503\pi\) | |||||||
\(674\) | −32.4797 | −1.25107 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.3265 | −0.589044 | −0.294522 | − | 0.955645i | \(-0.595161\pi\) | ||||
−0.294522 | + | 0.955645i | \(0.595161\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.22497 | −0.277269 | ||||||||
\(680\) | −40.9650 | −1.57094 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.1421 | −0.541134 | −0.270567 | − | 0.962701i | \(-0.587211\pi\) | ||||
−0.270567 | + | 0.962701i | \(0.587211\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 23.2917 | 0.889931 | ||||||||
\(686\) | −1.41421 | −0.0539949 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.00000 | 0.152499 | ||||||||
\(689\) | −77.0038 | −2.93361 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.4499 | −0.397535 | −0.198767 | − | 0.980047i | \(-0.563694\pi\) | ||||
−0.198767 | + | 0.980047i | \(0.563694\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 46.8999 | 1.78030 | ||||||||
\(695\) | 9.89949 | 0.375509 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −30.9666 | −1.17294 | ||||||||
\(698\) | 47.3526 | 1.79232 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.97334 | −0.187841 | −0.0939203 | − | 0.995580i | \(-0.529940\pi\) | ||||
−0.0939203 | + | 0.995580i | \(0.529940\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.0000 | 0.754314 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 32.5167 | 1.22378 | ||||||||
\(707\) | 8.66796 | 0.325992 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.4166 | 1.51788 | 0.758938 | − | 0.651163i | \(-0.225718\pi\) | ||||
0.758938 | + | 0.651163i | \(0.225718\pi\) | |||||||
\(710\) | 5.29150 | 0.198587 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 16.5167 | 0.618989 | ||||||||
\(713\) | −21.2604 | −0.796208 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −19.9333 | −0.743903 | ||||||||
\(719\) | −2.82843 | −0.105483 | −0.0527413 | − | 0.998608i | \(-0.516796\pi\) | ||||
−0.0527413 | + | 0.998608i | \(0.516796\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.2250 | −0.492524 | ||||||||
\(722\) | −19.7518 | −0.735086 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.75458 | −0.287998 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.1916 | 0.377986 | 0.188993 | − | 0.981978i | \(-0.439478\pi\) | ||||
0.188993 | + | 0.981978i | \(0.439478\pi\) | |||||||
\(728\) | −16.2399 | −0.601889 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 58.8999 | 2.17998 | ||||||||
\(731\) | 5.47418 | 0.202470 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.29171 | 0.0477105 | 0.0238553 | − | 0.999715i | \(-0.492406\pi\) | ||||
0.0238553 | + | 0.999715i | \(0.492406\pi\) | |||||||
\(734\) | −24.3598 | −0.899136 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.9333 | 1.02754 | 0.513771 | − | 0.857927i | \(-0.328248\pi\) | ||||
0.513771 | + | 0.857927i | \(0.328248\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −18.9666 | −0.696287 | ||||||||
\(743\) | 32.1616 | 1.17989 | 0.589947 | − | 0.807442i | \(-0.299149\pi\) | ||||
0.589947 | + | 0.807442i | \(0.299149\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −61.6749 | −2.25959 | ||||||||
\(746\) | 27.5064 | 1.00708 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.53414 | 0.348370 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.9666 | −1.16648 | −0.583239 | − | 0.812300i | \(-0.698215\pi\) | ||||
−0.583239 | + | 0.812300i | \(0.698215\pi\) | |||||||
\(752\) | 21.8967 | 0.798491 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −31.4833 | −1.14655 | ||||||||
\(755\) | −19.8873 | −0.723772 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.4833 | −0.889861 | −0.444931 | − | 0.895565i | \(-0.646772\pi\) | ||||
−0.444931 | + | 0.895565i | \(0.646772\pi\) | |||||||
\(758\) | 48.7668 | 1.77129 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 42.9666 | 1.55856 | ||||||||
\(761\) | 41.5130 | 1.50485 | 0.752423 | − | 0.658680i | \(-0.228885\pi\) | ||||
0.752423 | + | 0.658680i | \(0.228885\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.4833 | 0.596736 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 30.1916 | 1.09087 | ||||||||
\(767\) | −47.6707 | −1.72129 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.55006 | −0.128018 | −0.0640091 | − | 0.997949i | \(-0.520389\pi\) | ||||
−0.0640091 | + | 0.997949i | \(0.520389\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −46.8045 | −1.68344 | −0.841721 | − | 0.539913i | \(-0.818457\pi\) | ||||
−0.841721 | + | 0.539913i | \(0.818457\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.9666 | 0.393933 | ||||||||
\(776\) | −20.4353 | −0.733585 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 47.4833 | 1.70236 | ||||||||
\(779\) | 32.4797 | 1.16371 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −30.0166 | −1.07339 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.00000 | −0.142857 | ||||||||
\(785\) | −34.3065 | −1.22445 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.55006 | −0.269130 | −0.134565 | − | 0.990905i | \(-0.542964\pi\) | ||||
−0.134565 | + | 0.990905i | \(0.542964\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 50.4499 | 1.79493 | ||||||||
\(791\) | 5.29150 | 0.188144 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.0000 | −0.355110 | ||||||||
\(794\) | −2.09772 | −0.0744454 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −25.5441 | −0.904820 | −0.452410 | − | 0.891810i | \(-0.649436\pi\) | ||||
−0.452410 | + | 0.891810i | \(0.649436\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 29.9666 | 1.06014 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −11.4833 | −0.405490 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.2583 | −0.361559 | ||||||||
\(806\) | 44.5241 | 1.56830 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 24.5167 | 0.862494 | ||||||||
\(809\) | 10.9955 | 0.386583 | 0.193291 | − | 0.981141i | \(-0.438084\pi\) | ||||
0.193291 | + | 0.981141i | \(0.438084\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26.7750 | −0.940198 | −0.470099 | − | 0.882614i | \(-0.655782\pi\) | ||||
−0.470099 | + | 0.882614i | \(0.655782\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −64.6885 | −2.26594 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.74166 | −0.200875 | ||||||||
\(818\) | −13.0461 | −0.456146 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −33.9411 | −1.18455 | −0.592277 | − | 0.805735i | \(-0.701771\pi\) | ||||
−0.592277 | + | 0.805735i | \(0.701771\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −55.9333 | −1.94971 | −0.974855 | − | 0.222838i | \(-0.928468\pi\) | ||||
−0.974855 | + | 0.222838i | \(0.928468\pi\) | |||||||
\(824\) | −37.4059 | −1.30310 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −11.7417 | −0.408545 | ||||||||
\(827\) | 21.4842 | 0.747078 | 0.373539 | − | 0.927615i | \(-0.378144\pi\) | ||||
0.373539 | + | 0.927615i | \(0.378144\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.77503 | 0.165844 | 0.0829218 | − | 0.996556i | \(-0.473575\pi\) | ||||
0.0829218 | + | 0.996556i | \(0.473575\pi\) | |||||||
\(830\) | 41.6485 | 1.44564 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −45.9333 | −1.59245 | ||||||||
\(833\) | −5.47418 | −0.189669 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22.9333 | 0.793638 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 41.6749 | 1.43964 | ||||||||
\(839\) | −22.0794 | −0.762265 | −0.381133 | − | 0.924520i | \(-0.624466\pi\) | ||||
−0.381133 | + | 0.924520i | \(0.624466\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.9666 | −0.481608 | ||||||||
\(842\) | 10.6302 | 0.366341 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 52.8267 | 1.81729 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −53.6457 | −1.84220 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 15.4833 | 0.531073 | ||||||||
\(851\) | −13.5058 | −0.462973 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.9666 | 1.33419 | 0.667096 | − | 0.744972i | \(-0.267537\pi\) | ||||
0.667096 | + | 0.744972i | \(0.267537\pi\) | |||||||
\(854\) | −2.46308 | −0.0842847 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 26.9666 | 0.921700 | ||||||||
\(857\) | 12.8634 | 0.439406 | 0.219703 | − | 0.975567i | \(-0.429491\pi\) | ||||
0.219703 | + | 0.975567i | \(0.429491\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.4499 | −1.03894 | −0.519469 | − | 0.854489i | \(-0.673870\pi\) | ||||
−0.519469 | + | 0.854489i | \(0.673870\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −22.4499 | −0.764648 | ||||||||
\(863\) | 18.7029 | 0.636655 | 0.318328 | − | 0.947981i | \(-0.396879\pi\) | ||||
0.318328 | + | 0.947981i | \(0.396879\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.5167 | −0.459581 | ||||||||
\(866\) | 2.46308 | 0.0836987 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 37.2250 | 1.26132 | ||||||||
\(872\) | 46.6219 | 1.57882 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 31.4833 | 1.06494 | ||||||||
\(875\) | −7.93725 | −0.268328 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 48.8999 | 1.65123 | 0.825616 | − | 0.564232i | \(-0.190828\pi\) | ||||
0.825616 | + | 0.564232i | \(0.190828\pi\) | |||||||
\(878\) | 27.5536 | 0.929888 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.6791 | 0.393478 | 0.196739 | − | 0.980456i | \(-0.436965\pi\) | ||||
0.196739 | + | 0.980456i | \(0.436965\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 52.4166 | 1.76396 | 0.881979 | − | 0.471289i | \(-0.156211\pi\) | ||||
0.881979 | + | 0.471289i | \(0.156211\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 38.5167 | 1.29399 | ||||||||
\(887\) | 29.4686 | 0.989459 | 0.494730 | − | 0.869047i | \(-0.335267\pi\) | ||||
0.494730 | + | 0.869047i | \(0.335267\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.4833 | −0.552833 | ||||||||
\(890\) | −21.8495 | −0.732398 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −31.4309 | −1.05179 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 37.4166 | 1.25070 | ||||||||
\(896\) | −11.3137 | −0.377964 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −14.4499 | −0.482201 | ||||||||
\(899\) | −21.2604 | −0.709074 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −73.4166 | −2.44586 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14.9666 | 0.497783 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.48331 | −0.0492527 | −0.0246263 | − | 0.999697i | \(-0.507840\pi\) | ||||
−0.0246263 | + | 0.999697i | \(0.507840\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 21.4833 | 0.712165 | ||||||||
\(911\) | −38.8673 | −1.28773 | −0.643865 | − | 0.765139i | \(-0.722670\pi\) | ||||
−0.643865 | + | 0.765139i | \(0.722670\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 32.5269 | 1.07589 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.66796 | −0.286241 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.0334 | −0.891749 | −0.445874 | − | 0.895096i | \(-0.647107\pi\) | ||||
−0.445874 | + | 0.895096i | \(0.647107\pi\) | |||||||
\(920\) | −29.0150 | −0.956595 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 10.1916 | 0.335643 | ||||||||
\(923\) | 8.11993 | 0.267271 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.96663 | 0.229061 | ||||||||
\(926\) | 24.7251 | 0.812519 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16.4225 | −0.538806 | −0.269403 | − | 0.963028i | \(-0.586826\pi\) | ||||
−0.269403 | + | 0.963028i | \(0.586826\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.74166 | 0.188175 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −29.4166 | −0.962540 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.7417 | 1.16763 | 0.583815 | − | 0.811887i | \(-0.301560\pi\) | ||||
0.583815 | + | 0.811887i | \(0.301560\pi\) | |||||||
\(938\) | 9.16879 | 0.299372 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −56.8395 | −1.85292 | −0.926458 | − | 0.376399i | \(-0.877162\pi\) | ||||
−0.926458 | + | 0.376399i | \(0.877162\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21.9333 | −0.714245 | ||||||||
\(944\) | −33.2104 | −1.08091 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −55.1071 | −1.79074 | −0.895371 | − | 0.445322i | \(-0.853089\pi\) | ||||
−0.895371 | + | 0.445322i | \(0.853089\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 90.3832 | 2.93396 | ||||||||
\(950\) | −16.2399 | −0.526891 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −15.4833 | −0.501817 | ||||||||
\(953\) | 50.5463 | 1.63736 | 0.818678 | − | 0.574253i | \(-0.194707\pi\) | ||||
0.818678 | + | 0.574253i | \(0.194707\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.74166 | −0.121077 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 32.7750 | 1.05891 | ||||||||
\(959\) | 8.80344 | 0.284278 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.933259 | −0.0301051 | ||||||||
\(962\) | 28.2843 | 0.911922 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −43.6108 | −1.40388 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.9333 | 0.994747 | 0.497373 | − | 0.867537i | \(-0.334298\pi\) | ||||
0.497373 | + | 0.867537i | \(0.334298\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 27.0334 | 0.867989 | ||||||||
\(971\) | −15.3265 | −0.491850 | −0.245925 | − | 0.969289i | \(-0.579092\pi\) | ||||
−0.245925 | + | 0.969289i | \(0.579092\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.74166 | 0.119952 | ||||||||
\(974\) | −7.80177 | −0.249985 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.96663 | −0.222996 | ||||||||
\(977\) | 19.7518 | 0.631916 | 0.315958 | − | 0.948773i | \(-0.397674\pi\) | ||||
0.315958 | + | 0.948773i | \(0.397674\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −42.0000 | −1.34027 | ||||||||
\(983\) | 2.82843 | 0.0902128 | 0.0451064 | − | 0.998982i | \(-0.485637\pi\) | ||||
0.0451064 | + | 0.998982i | \(0.485637\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −58.8999 | −1.87671 | ||||||||
\(986\) | −30.0166 | −0.955925 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.87729 | 0.123291 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.449944 | 0.0142930 | 0.00714648 | − | 0.999974i | \(-0.497725\pi\) | ||||
0.00714648 | + | 0.999974i | \(0.497725\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.00000 | 0.0634361 | ||||||||
\(995\) | 5.97501 | 0.189421 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.9666 | 0.347317 | 0.173658 | − | 0.984806i | \(-0.444441\pi\) | ||||
0.173658 | + | 0.984806i | \(0.444441\pi\) | |||||||
\(998\) | 25.4087 | 0.804297 | ||||||||
\(999\) | 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 | 7623.2.a.ck.1.2 | yes | 4 | |
3.2 | odd | 2 | inner | 7623.2.a.ck.1.3 | yes | 4 | |
11.10 | odd | 2 | 7623.2.a.cj.1.4 | yes | 4 | ||
33.32 | even | 2 | 7623.2.a.cj.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7623.2.a.cj.1.1 | ✓ | 4 | 33.32 | even | 2 | ||
7623.2.a.cj.1.4 | yes | 4 | 11.10 | odd | 2 | ||
7623.2.a.ck.1.2 | yes | 4 | 1.1 | even | 1 | trivial | |
7623.2.a.ck.1.3 | yes | 4 | 3.2 | odd | 2 | inner |