Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8004,2,Mod(1,8004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8004, 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("8004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8004.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: | \(63.9122617778\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 13x^{7} + 32x^{6} + 40x^{5} - 79x^{4} - 39x^{3} + 58x^{2} + 9x - 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-0.553378\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8004.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.29187 | 1.47217 | 0.736085 | − | 0.676889i | \(-0.236672\pi\) | ||||
0.736085 | + | 0.676889i | \(0.236672\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.02028 | −0.385630 | −0.192815 | − | 0.981235i | \(-0.561762\pi\) | ||||
−0.192815 | + | 0.981235i | \(0.561762\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.88720 | −0.569013 | −0.284506 | − | 0.958674i | \(-0.591830\pi\) | ||||
−0.284506 | + | 0.958674i | \(0.591830\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.64262 | −1.01028 | −0.505141 | − | 0.863037i | \(-0.668560\pi\) | ||||
−0.505141 | + | 0.863037i | \(0.668560\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.29187 | −0.849958 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.28578 | −0.311848 | −0.155924 | − | 0.987769i | \(-0.549835\pi\) | ||||
−0.155924 | + | 0.987769i | \(0.549835\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.72913 | 1.31435 | 0.657177 | − | 0.753737i | \(-0.271751\pi\) | ||||
0.657177 | + | 0.753737i | \(0.271751\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.02028 | 0.222644 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.83643 | 1.16729 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.90835 | −1.42038 | −0.710191 | − | 0.704009i | \(-0.751391\pi\) | ||||
−0.710191 | + | 0.704009i | \(0.751391\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.88720 | 0.328520 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.35864 | −0.567714 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.37633 | −0.719464 | −0.359732 | − | 0.933056i | \(-0.617132\pi\) | ||||
−0.359732 | + | 0.933056i | \(0.617132\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.64262 | 0.583287 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.79282 | −0.748512 | −0.374256 | − | 0.927325i | \(-0.622102\pi\) | ||||
−0.374256 | + | 0.927325i | \(0.622102\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.68133 | 1.47639 | 0.738195 | − | 0.674588i | \(-0.235678\pi\) | ||||
0.738195 | + | 0.674588i | \(0.235678\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.29187 | 0.490723 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.33639 | 0.924257 | 0.462129 | − | 0.886813i | \(-0.347086\pi\) | ||||
0.462129 | + | 0.886813i | \(0.347086\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.95902 | −0.851289 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.28578 | 0.180045 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.39752 | −0.466685 | −0.233343 | − | 0.972395i | \(-0.574966\pi\) | ||||
−0.233343 | + | 0.972395i | \(0.574966\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.21243 | −0.837683 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.72913 | −0.758842 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.11544 | 0.535784 | 0.267892 | − | 0.963449i | \(-0.413673\pi\) | ||||
0.267892 | + | 0.963449i | \(0.413673\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.134655 | −0.0172408 | −0.00862042 | − | 0.999963i | \(-0.502744\pi\) | ||||
−0.00862042 | + | 0.999963i | \(0.502744\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.02028 | −0.128543 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −11.9911 | −1.48731 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.1554 | 1.48502 | 0.742510 | − | 0.669835i | \(-0.233635\pi\) | ||||
0.742510 | + | 0.669835i | \(0.233635\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.67588 | −0.198890 | −0.0994450 | − | 0.995043i | \(-0.531707\pi\) | ||||
−0.0994450 | + | 0.995043i | \(0.531707\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.127917 | −0.0149715 | −0.00748577 | − | 0.999972i | \(-0.502383\pi\) | ||||
−0.00748577 | + | 0.999972i | \(0.502383\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.83643 | −0.673933 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.92548 | 0.219429 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.342687 | −0.0385553 | −0.0192777 | − | 0.999814i | \(-0.506137\pi\) | ||||
−0.0192777 | + | 0.999814i | \(0.506137\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.0974823 | 0.0107001 | 0.00535004 | − | 0.999986i | \(-0.498297\pi\) | ||||
0.00535004 | + | 0.999986i | \(0.498297\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.23263 | −0.459093 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.4602 | −1.53278 | −0.766390 | − | 0.642375i | \(-0.777949\pi\) | ||||
−0.766390 | + | 0.642375i | \(0.777949\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.71650 | 0.389596 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.90835 | 0.820058 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 18.8596 | 1.93495 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −18.0506 | −1.83276 | −0.916382 | − | 0.400305i | \(-0.868904\pi\) | ||||
−0.916382 | + | 0.400305i | \(0.868904\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.88720 | −0.189671 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.307106 | −0.0305582 | −0.0152791 | − | 0.999883i | \(-0.504864\pi\) | ||||
−0.0152791 | + | 0.999883i | \(0.504864\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.96209 | −0.981594 | −0.490797 | − | 0.871274i | \(-0.663294\pi\) | ||||
−0.490797 | + | 0.871274i | \(0.663294\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.35864 | 0.327770 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.95885 | −0.479390 | −0.239695 | − | 0.970848i | \(-0.577047\pi\) | ||||
−0.239695 | + | 0.970848i | \(0.577047\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.9944 | −1.14886 | −0.574428 | − | 0.818555i | \(-0.694776\pi\) | ||||
−0.574428 | + | 0.818555i | \(0.694776\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.37633 | 0.415383 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.20091 | 0.112972 | 0.0564862 | − | 0.998403i | \(-0.482010\pi\) | ||||
0.0564862 | + | 0.998403i | \(0.482010\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.29187 | −0.306969 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.64262 | −0.336761 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.31186 | 0.120258 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.43847 | −0.676225 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.79282 | 0.432154 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.75342 | 0.246273 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.85660 | −0.253483 | −0.126741 | − | 0.991936i | \(-0.540452\pi\) | ||||
−0.126741 | + | 0.991936i | \(0.540452\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.68133 | −0.852394 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.5796 | 1.09908 | 0.549542 | − | 0.835466i | \(-0.314802\pi\) | ||||
0.549542 | + | 0.835466i | \(0.314802\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.84533 | −0.506855 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.29187 | −0.283319 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.28529 | −0.109810 | −0.0549048 | − | 0.998492i | \(-0.517486\pi\) | ||||
−0.0549048 | + | 0.998492i | \(0.517486\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.27614 | −0.447516 | −0.223758 | − | 0.974645i | \(-0.571833\pi\) | ||||
−0.223758 | + | 0.974645i | \(0.571833\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.33639 | −0.533620 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.87436 | 0.574863 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.29187 | 0.273375 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.95902 | 0.491492 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.0902 | −1.23624 | −0.618119 | − | 0.786084i | \(-0.712105\pi\) | ||||
−0.618119 | + | 0.786084i | \(0.712105\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.0808502 | −0.00657950 | −0.00328975 | − | 0.999995i | \(-0.501047\pi\) | ||||
−0.00328975 | + | 0.999995i | \(0.501047\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.28578 | −0.103949 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −26.0333 | −2.09104 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.2238 | 1.05538 | 0.527688 | − | 0.849438i | \(-0.323059\pi\) | ||||
0.527688 | + | 0.849438i | \(0.323059\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.39752 | 0.269441 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.02028 | 0.0804095 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.32641 | −0.730501 | −0.365250 | − | 0.930909i | \(-0.619017\pi\) | ||||
−0.365250 | + | 0.930909i | \(0.619017\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.21243 | 0.483637 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.65640 | −0.205559 | −0.102779 | − | 0.994704i | \(-0.532774\pi\) | ||||
−0.102779 | + | 0.994704i | \(0.532774\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.268711 | 0.0206701 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.72913 | 0.438118 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −20.8900 | −1.58824 | −0.794120 | − | 0.607761i | \(-0.792068\pi\) | ||||
−0.794120 | + | 0.607761i | \(0.792068\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.95480 | −0.450141 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.11544 | −0.309335 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.03363 | 0.525718 | 0.262859 | − | 0.964834i | \(-0.415335\pi\) | ||||
0.262859 | + | 0.964834i | \(0.415335\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.4995 | 0.780420 | 0.390210 | − | 0.920726i | \(-0.372402\pi\) | ||||
0.390210 | + | 0.920726i | \(0.372402\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.134655 | 0.00995400 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −14.4063 | −1.05917 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.42653 | 0.177445 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.02028 | 0.0742146 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.9567 | 0.937513 | 0.468757 | − | 0.883327i | \(-0.344702\pi\) | ||||
0.468757 | + | 0.883327i | \(0.344702\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −27.1033 | −1.95094 | −0.975470 | − | 0.220134i | \(-0.929351\pi\) | ||||
−0.975470 | + | 0.220134i | \(0.929351\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 11.9911 | 0.858697 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.7303 | 1.04949 | 0.524744 | − | 0.851260i | \(-0.324161\pi\) | ||||
0.524744 | + | 0.851260i | \(0.324161\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.88160 | 0.133383 | 0.0666915 | − | 0.997774i | \(-0.478756\pi\) | ||||
0.0666915 | + | 0.997774i | \(0.478756\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.1554 | −0.857376 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.02028 | −0.0716098 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.7773 | −1.10194 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.8120 | −0.747883 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.5394 | −1.55167 | −0.775837 | − | 0.630933i | \(-0.782672\pi\) | ||||
−0.775837 | + | 0.630933i | \(0.782672\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.67588 | 0.114829 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 31.8697 | 2.17350 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.06875 | 0.547743 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.127917 | 0.00864382 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.68362 | 0.315054 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.0899811 | 0.00602558 | 0.00301279 | − | 0.999995i | \(-0.499041\pi\) | ||||
0.00301279 | + | 0.999995i | \(0.499041\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.83643 | 0.389095 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −24.3526 | −1.61634 | −0.808168 | − | 0.588951i | \(-0.799541\pi\) | ||||
−0.808168 | + | 0.588951i | \(0.799541\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.3336 | 0.881112 | 0.440556 | − | 0.897725i | \(-0.354781\pi\) | ||||
0.440556 | + | 0.897725i | \(0.354781\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.92548 | −0.126687 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.28577 | −0.411794 | −0.205897 | − | 0.978574i | \(-0.566011\pi\) | ||||
−0.205897 | + | 0.978574i | \(0.566011\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 20.8586 | 1.36066 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.342687 | 0.0222599 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.2321 | −0.855916 | −0.427958 | − | 0.903799i | \(-0.640767\pi\) | ||||
−0.427958 | + | 0.903799i | \(0.640767\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.0873 | 1.22952 | 0.614760 | − | 0.788714i | \(-0.289253\pi\) | ||||
0.614760 | + | 0.788714i | \(0.289253\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −19.6164 | −1.25324 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20.8691 | −1.32787 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.0974823 | −0.00617769 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.09378 | 0.510875 | 0.255438 | − | 0.966826i | \(-0.417780\pi\) | ||||
0.255438 | + | 0.966826i | \(0.417780\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.88720 | 0.118647 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.23263 | 0.265058 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.6298 | 0.725446 | 0.362723 | − | 0.931897i | \(-0.381847\pi\) | ||||
0.362723 | + | 0.931897i | \(0.381847\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.46509 | 0.277447 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.51527 | −0.463411 | −0.231706 | − | 0.972786i | \(-0.574431\pi\) | ||||
−0.231706 | + | 0.972786i | \(0.574431\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.1842 | −0.687040 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.4602 | 0.884951 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.14454 | 0.0697836 | 0.0348918 | − | 0.999391i | \(-0.488891\pi\) | ||||
0.0348918 | + | 0.999391i | \(0.488891\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.5549 | −0.762654 | −0.381327 | − | 0.924440i | \(-0.624533\pi\) | ||||
−0.381327 | + | 0.924440i | \(0.624533\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.71650 | −0.224933 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −11.0145 | −0.664200 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.89067 | −0.173683 | −0.0868417 | − | 0.996222i | \(-0.527677\pi\) | ||||
−0.0868417 | + | 0.996222i | \(0.527677\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.90835 | −0.473461 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.1332 | 0.664150 | 0.332075 | − | 0.943253i | \(-0.392251\pi\) | ||||
0.332075 | + | 0.943253i | \(0.392251\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.153847 | −0.00914527 | −0.00457264 | − | 0.999990i | \(-0.501456\pi\) | ||||
−0.00457264 | + | 0.999990i | \(0.501456\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −18.8596 | −1.11715 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.89002 | 0.288649 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.3468 | −0.902751 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 18.0506 | 1.05815 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 32.7574 | 1.91371 | 0.956855 | − | 0.290567i | \(-0.0938440\pi\) | ||||
0.956855 | + | 0.290567i | \(0.0938440\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.5475 | 0.788766 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.88720 | 0.109507 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.64262 | 0.210658 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.87769 | −0.569341 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.307106 | 0.0176428 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.443268 | −0.0253815 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.3644 | 0.591527 | 0.295764 | − | 0.955261i | \(-0.404426\pi\) | ||||
0.295764 | + | 0.955261i | \(0.404426\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.96209 | 0.566724 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.192809 | −0.0109332 | −0.00546661 | − | 0.999985i | \(-0.501740\pi\) | ||||
−0.00546661 | + | 0.999985i | \(0.501740\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.5661 | −1.04942 | −0.524709 | − | 0.851282i | \(-0.675826\pi\) | ||||
−0.524709 | + | 0.851282i | \(0.675826\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.35864 | −0.189238 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.1487 | 0.907004 | 0.453502 | − | 0.891255i | \(-0.350175\pi\) | ||||
0.453502 | + | 0.891255i | \(0.350175\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.88720 | −0.105663 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.95885 | 0.276776 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.36642 | −0.409878 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −21.2599 | −1.17929 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.9944 | 0.663293 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.46491 | −0.356422 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.9714 | −1.04277 | −0.521383 | − | 0.853323i | \(-0.674584\pi\) | ||||
−0.521383 | + | 0.853323i | \(0.674584\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.37633 | −0.239821 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 40.0141 | 2.18620 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.9061 | 1.08436 | 0.542178 | − | 0.840264i | \(-0.317600\pi\) | ||||
0.542178 | + | 0.840264i | \(0.317600\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.20091 | −0.0652247 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.9247 | 0.808215 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.2219 | 0.713913 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.29187 | 0.177228 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.225778 | 0.0121204 | 0.00606020 | − | 0.999982i | \(-0.498071\pi\) | ||||
0.00606020 | + | 0.999982i | \(0.498071\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.5780 | 0.619756 | 0.309878 | − | 0.950776i | \(-0.399712\pi\) | ||||
0.309878 | + | 0.950776i | \(0.399712\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.64262 | 0.194429 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −30.4567 | −1.62105 | −0.810523 | − | 0.585706i | \(-0.800817\pi\) | ||||
−0.810523 | + | 0.585706i | \(0.800817\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.51677 | −0.292800 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.31186 | −0.0694310 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.9315 | 0.682499 | 0.341249 | − | 0.939973i | \(-0.389150\pi\) | ||||
0.341249 | + | 0.939973i | \(0.389150\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.8230 | 0.727525 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.43847 | 0.390419 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.421086 | −0.0220407 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.6009 | 1.07536 | 0.537678 | − | 0.843150i | \(-0.319302\pi\) | ||||
0.537678 | + | 0.843150i | \(0.319302\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.79282 | −0.249504 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.46643 | 0.179968 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −31.6195 | −1.63720 | −0.818599 | − | 0.574365i | \(-0.805249\pi\) | ||||
−0.818599 | + | 0.574365i | \(0.805249\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.75342 | −0.142186 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.64262 | −0.187605 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −33.8695 | −1.73976 | −0.869878 | − | 0.493266i | \(-0.835803\pi\) | ||||
−0.869878 | + | 0.493266i | \(0.835803\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.85660 | 0.146348 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.3113 | 1.24225 | 0.621125 | − | 0.783712i | \(-0.286676\pi\) | ||||
0.621125 | + | 0.783712i | \(0.286676\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.33843 | 0.323036 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.68133 | 0.492130 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 30.3825 | 1.54046 | 0.770228 | − | 0.637769i | \(-0.220143\pi\) | ||||
0.770228 | + | 0.637769i | \(0.220143\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.28578 | 0.0650248 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.5796 | −0.634556 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.12808 | −0.0567600 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.9430 | 1.45261 | 0.726304 | − | 0.687373i | \(-0.241236\pi\) | ||||
0.726304 | + | 0.687373i | \(0.241236\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.84533 | 0.292633 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −32.0873 | −1.60236 | −0.801182 | − | 0.598421i | \(-0.795795\pi\) | ||||
−0.801182 | + | 0.598421i | \(0.795795\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 28.8072 | 1.43499 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.29187 | 0.163574 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.25902 | 0.409384 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.8190 | 0.831646 | 0.415823 | − | 0.909445i | \(-0.363494\pi\) | ||||
0.415823 | + | 0.909445i | \(0.363494\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.28529 | 0.0633987 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.19891 | −0.206615 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.320899 | 0.0157523 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.27614 | 0.258374 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.5339 | −1.14971 | −0.574853 | − | 0.818257i | \(-0.694941\pi\) | ||||
−0.574853 | + | 0.818257i | \(0.694941\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.05228 | −0.197496 | −0.0987481 | − | 0.995112i | \(-0.531484\pi\) | ||||
−0.0987481 | + | 0.995112i | \(0.531484\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.33639 | 0.308086 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.50437 | −0.364016 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.137386 | 0.00664859 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.87436 | −0.331897 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.17887 | 0.201289 | 0.100644 | − | 0.994922i | \(-0.467910\pi\) | ||||
0.100644 | + | 0.994922i | \(0.467910\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.8989 | 1.00434 | 0.502168 | − | 0.864770i | \(-0.332536\pi\) | ||||
0.502168 | + | 0.864770i | \(0.332536\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.29187 | −0.157833 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.72913 | −0.274062 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −35.9387 | −1.71526 | −0.857631 | − | 0.514266i | \(-0.828064\pi\) | ||||
−0.857631 | + | 0.514266i | \(0.828064\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.95902 | −0.283763 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.911071 | −0.0432863 | −0.0216432 | − | 0.999766i | \(-0.506890\pi\) | ||||
−0.0216432 | + | 0.999766i | \(0.506890\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −47.6012 | −2.25651 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 15.0902 | 0.713743 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.5377 | −0.969235 | −0.484617 | − | 0.874726i | \(-0.661041\pi\) | ||||
−0.484617 | + | 0.874726i | \(0.661041\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.04501 | 0.425913 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.0808502 | 0.00379867 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12.2343 | 0.573551 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 38.8892 | 1.81916 | 0.909581 | − | 0.415527i | \(-0.136403\pi\) | ||||
0.909581 | + | 0.415527i | \(0.136403\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.28578 | 0.0600152 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −36.7804 | −1.71304 | −0.856518 | − | 0.516118i | \(-0.827377\pi\) | ||||
−0.856518 | + | 0.516118i | \(0.827377\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.42298 | −0.344975 | −0.172488 | − | 0.985012i | \(-0.555180\pi\) | ||||
−0.172488 | + | 0.985012i | \(0.555180\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 26.0333 | 1.20727 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −27.8689 | −1.28962 | −0.644808 | − | 0.764344i | \(-0.723063\pi\) | ||||
−0.644808 | + | 0.764344i | \(0.723063\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.4019 | −0.572669 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.2238 | −0.609322 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −18.2706 | −0.840084 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 33.4377 | 1.53423 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.39752 | −0.155562 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.8615 | −0.496277 | −0.248138 | − | 0.968725i | \(-0.579819\pi\) | ||||
−0.248138 | + | 0.968725i | \(0.579819\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.9413 | 0.726862 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.02028 | −0.0464244 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −59.4204 | −2.69814 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.1469 | 0.686374 | 0.343187 | − | 0.939267i | \(-0.388494\pi\) | ||||
0.343187 | + | 0.939267i | \(0.388494\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.32641 | 0.421755 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.1888 | −0.911107 | −0.455553 | − | 0.890208i | \(-0.650559\pi\) | ||||
−0.455553 | + | 0.890208i | \(0.650559\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.28578 | −0.0579087 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.21243 | −0.279228 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.70987 | 0.0766980 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.12975 | −0.0953406 | −0.0476703 | − | 0.998863i | \(-0.515180\pi\) | ||||
−0.0476703 | + | 0.998863i | \(0.515180\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.65640 | 0.118679 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −33.5893 | −1.49767 | −0.748835 | − | 0.662756i | \(-0.769387\pi\) | ||||
−0.748835 | + | 0.662756i | \(0.769387\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.01096 | −0.0449869 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.268711 | −0.0119339 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −29.0969 | −1.28970 | −0.644848 | − | 0.764311i | \(-0.723079\pi\) | ||||
−0.644848 | + | 0.764311i | \(0.723079\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.130511 | 0.00577348 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.72913 | −0.252947 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −32.7939 | −1.44507 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.9580 | −0.525914 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.8900 | 0.916971 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −39.7968 | −1.74353 | −0.871764 | − | 0.489925i | \(-0.837024\pi\) | ||||
−0.871764 | + | 0.489925i | \(0.837024\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.3933 | 0.454469 | 0.227235 | − | 0.973840i | \(-0.427032\pi\) | ||||
0.227235 | + | 0.973840i | \(0.427032\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.95480 | 0.259889 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.1684 | 0.442943 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.11544 | 0.178595 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.4584 | 0.756208 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.3239 | −0.705743 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.03363 | −0.303523 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.2459 | 0.484394 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.986445 | −0.0424106 | −0.0212053 | − | 0.999775i | \(-0.506750\pi\) | ||||
−0.0212053 | + | 0.999775i | \(0.506750\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.4995 | −0.450576 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −39.4841 | −1.69131 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.0767 | −0.473607 | −0.236804 | − | 0.971558i | \(-0.576100\pi\) | ||||
−0.236804 | + | 0.971558i | \(0.576100\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.134655 | −0.00574695 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.72913 | 0.244069 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.349638 | 0.0148681 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 14.4063 | 0.611515 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.81205 | 0.0767789 | 0.0383895 | − | 0.999263i | \(-0.487777\pi\) | ||||
0.0383895 | + | 0.999263i | \(0.487777\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −35.2655 | −1.49157 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.42653 | −0.102448 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.19519 | 0.0925163 | 0.0462581 | − | 0.998930i | \(-0.485270\pi\) | ||||
0.0462581 | + | 0.998930i | \(0.485270\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.95326 | 0.166315 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.02028 | −0.0428478 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.4169 | −0.855921 | −0.427961 | − | 0.903797i | \(-0.640768\pi\) | ||||
−0.427961 | + | 0.903797i | \(0.640768\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.1651 | −0.969429 | −0.484714 | − | 0.874672i | \(-0.661076\pi\) | ||||
−0.484714 | + | 0.874672i | \(0.661076\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.9567 | −0.541273 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.83643 | −0.243396 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29.6341 | −1.23368 | −0.616842 | − | 0.787087i | \(-0.711588\pi\) | ||||
−0.616842 | + | 0.787087i | \(0.711588\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 27.1033 | 1.12638 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.0994595 | −0.00412627 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.41181 | 0.265550 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −11.9911 | −0.495769 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.0958 | 0.870717 | 0.435359 | − | 0.900257i | \(-0.356622\pi\) | ||||
0.435359 | + | 0.900257i | \(0.356622\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −45.3080 | −1.86688 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.7303 | −0.605922 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.5799 | −1.00938 | −0.504688 | − | 0.863302i | \(-0.668392\pi\) | ||||
−0.504688 | + | 0.863302i | \(0.668392\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.31848 | 0.177040 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.88160 | −0.0770087 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 33.2567 | 1.35883 | 0.679415 | − | 0.733754i | \(-0.262234\pi\) | ||||
0.679415 | + | 0.733754i | \(0.262234\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.74958 | 0.275321 | 0.137660 | − | 0.990479i | \(-0.456042\pi\) | ||||
0.137660 | + | 0.990479i | \(0.456042\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.1554 | 0.495006 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −24.4865 | −0.995518 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.7679 | −0.558821 | −0.279410 | − | 0.960172i | \(-0.590139\pi\) | ||||
−0.279410 | + | 0.960172i | \(0.590139\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.02028 | 0.0413439 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −23.0811 | −0.933761 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −38.6304 | −1.56027 | −0.780134 | − | 0.625612i | \(-0.784849\pi\) | ||||
−0.780134 | + | 0.625612i | \(0.784849\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 15.7773 | 0.636204 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.2750 | 0.614949 | 0.307475 | − | 0.951556i | \(-0.400516\pi\) | ||||
0.307475 | + | 0.951556i | \(0.400516\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.8995 | −0.880213 | −0.440107 | − | 0.897945i | \(-0.645059\pi\) | ||||
−0.440107 | + | 0.897945i | \(0.645059\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14.7535 | 0.591087 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.1182 | −0.804730 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.8120 | 0.431791 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.62701 | 0.224364 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.2070 | 1.40157 | 0.700784 | − | 0.713374i | \(-0.252834\pi\) | ||||
0.700784 | + | 0.713374i | \(0.252834\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 22.5394 | 0.895859 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.40358 | −0.373170 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.7065 | 0.860042 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.67588 | −0.0662966 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −38.4422 | −1.51838 | −0.759188 | − | 0.650872i | \(-0.774403\pi\) | ||||
−0.759188 | + | 0.650872i | \(0.774403\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.4506 | 0.451569 | 0.225785 | − | 0.974177i | \(-0.427505\pi\) | ||||
0.225785 | + | 0.974177i | \(0.427505\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −31.8697 | −1.25487 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29.5280 | −1.16087 | −0.580433 | − | 0.814308i | \(-0.697117\pi\) | ||||
−0.580433 | + | 0.814308i | \(0.697117\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.76666 | −0.304868 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.06875 | −0.316239 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −23.5186 | −0.920353 | −0.460176 | − | 0.887828i | \(-0.652214\pi\) | ||||
−0.460176 | + | 0.887828i | \(0.652214\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 41.4104 | 1.61804 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.127917 | −0.00499051 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.8705 | −0.812999 | −0.406499 | − | 0.913651i | \(-0.633251\pi\) | ||||
−0.406499 | + | 0.913651i | \(0.633251\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −36.2819 | −1.41120 | −0.705602 | − | 0.708608i | \(-0.749323\pi\) | ||||
−0.705602 | + | 0.708608i | \(0.749323\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.68362 | −0.181897 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −19.2421 | −0.746176 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.0899811 | −0.00347887 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.254122 | 0.00981025 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.2490 | 1.05037 | 0.525185 | − | 0.850988i | \(-0.323996\pi\) | ||||
0.525185 | + | 0.850988i | \(0.323996\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.83643 | −0.224644 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 35.3520 | 1.35869 | 0.679344 | − | 0.733820i | \(-0.262264\pi\) | ||||
0.679344 | + | 0.733820i | \(0.262264\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.4167 | 0.706769 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.3526 | 0.933193 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.2266 | 1.11832 | 0.559162 | − | 0.829058i | \(-0.311123\pi\) | ||||
0.559162 | + | 0.829058i | \(0.311123\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.23101 | −0.161659 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13.3336 | −0.508710 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.3759 | 0.471484 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 50.6850 | 1.92815 | 0.964074 | − | 0.265635i | \(-0.0855816\pi\) | ||||
0.964074 | + | 0.265635i | \(0.0855816\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.92548 | 0.0731428 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −17.3684 | −0.658820 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.16251 | 0.233422 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.28577 | 0.237750 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.6090 | −0.665082 | −0.332541 | − | 0.943089i | \(-0.607906\pi\) | ||||
−0.332541 | + | 0.943089i | \(0.607906\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −25.0726 | −0.945631 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −20.8586 | −0.785580 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.313335 | 0.0117842 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.9287 | 0.635771 | 0.317885 | − | 0.948129i | \(-0.397027\pi\) | ||||
0.317885 | + | 0.948129i | \(0.397027\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.342687 | −0.0128518 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.90835 | 0.296170 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22.6295 | 0.846297 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13.2321 | 0.494163 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.578253 | 0.0215652 | 0.0107826 | − | 0.999942i | \(-0.496568\pi\) | ||||
0.0107826 | + | 0.999942i | \(0.496568\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.1641 | 0.378533 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −19.0873 | −0.709864 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.83643 | 0.216760 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33.2629 | 1.23365 | 0.616827 | − | 0.787099i | \(-0.288418\pi\) | ||||
0.616827 | + | 0.787099i | \(0.288418\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.4481 | −0.460409 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 37.4181 | 1.38207 | 0.691035 | − | 0.722821i | \(-0.257155\pi\) | ||||
0.691035 | + | 0.722821i | \(0.257155\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 19.6164 | 0.723560 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −22.9397 | −0.844995 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.7570 | 0.579631 | 0.289815 | − | 0.957083i | \(-0.406406\pi\) | ||||
0.289815 | + | 0.957083i | \(0.406406\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 20.8691 | 0.766645 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.49549 | 0.238296 | 0.119148 | − | 0.992876i | \(-0.461984\pi\) | ||||
0.119148 | + | 0.992876i | \(0.461984\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −49.6751 | −1.81995 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.0974823 | 0.00356669 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.05942 | 0.184867 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.7238 | 0.610260 | 0.305130 | − | 0.952311i | \(-0.401300\pi\) | ||||
0.305130 | + | 0.952311i | \(0.401300\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.09378 | −0.294954 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.266149 | −0.00968614 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.2545 | 0.481742 | 0.240871 | − | 0.970557i | \(-0.422567\pi\) | ||||
0.240871 | + | 0.970557i | \(0.422567\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.88720 | −0.0685011 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −35.7001 | −1.29413 | −0.647064 | − | 0.762436i | \(-0.724003\pi\) | ||||
−0.647064 | + | 0.762436i | \(0.724003\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.2377 | 0.443034 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.23263 | −0.153031 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14.9910 | −0.541293 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.0686 | 1.12036 | 0.560182 | − | 0.828370i | \(-0.310731\pi\) | ||||
0.560182 | + | 0.828370i | \(0.310731\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.6298 | −0.418837 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21.8747 | −0.786779 | −0.393390 | − | 0.919372i | \(-0.628698\pi\) | ||||
−0.393390 | + | 0.919372i | \(0.628698\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −46.1565 | −1.65799 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.46509 | −0.160184 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −27.4587 | −0.983809 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.16272 | 0.113171 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 43.5312 | 1.55369 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.97490 | −0.248628 | −0.124314 | − | 0.992243i | \(-0.539673\pi\) | ||||
−0.124314 | + | 0.992243i | \(0.539673\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.51527 | 0.267551 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.22527 | −0.0435656 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.490498 | 0.0174181 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 11.1842 | 0.396663 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.1684 | 0.431025 | 0.215513 | − | 0.976501i | \(-0.430858\pi\) | ||||
0.215513 | + | 0.976501i | \(0.430858\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.14722 | −0.288228 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.4602 | −0.510927 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.241405 | 0.00851900 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.35864 | 0.118376 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.14454 | −0.0402896 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.8416 | 1.04918 | 0.524588 | − | 0.851356i | \(-0.324220\pi\) | ||||
0.524588 | + | 0.851356i | \(0.324220\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.5969 | −0.477451 | −0.238725 | − | 0.971087i | \(-0.576730\pi\) | ||||
−0.238725 | + | 0.971087i | \(0.576730\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.5549 | 0.440319 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −30.7014 | −1.07542 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 55.4657 | 1.94050 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.71650 | 0.129865 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.64965 | −0.162274 | −0.0811369 | − | 0.996703i | \(-0.525855\pi\) | ||||
−0.0811369 | + | 0.996703i | \(0.525855\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.5466 | 0.716210 | 0.358105 | − | 0.933681i | \(-0.383423\pi\) | ||||
0.358105 | + | 0.933681i | \(0.383423\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 11.0145 | 0.383476 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.31525 | −0.115282 | −0.0576412 | − | 0.998337i | \(-0.518358\pi\) | ||||
−0.0576412 | + | 0.998337i | \(0.518358\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.08377 | 0.315492 | 0.157746 | − | 0.987480i | \(-0.449577\pi\) | ||||
0.157746 | + | 0.987480i | \(0.449577\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.89067 | 0.100276 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.66201 | 0.265473 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.74455 | −0.302617 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.90835 | 0.273353 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −36.9667 | −1.27623 | −0.638116 | − | 0.769940i | \(-0.720286\pi\) | ||||
−0.638116 | + | 0.769940i | \(0.720286\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.1332 | −0.383447 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.884563 | 0.0304299 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.58934 | 0.260773 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.153847 | 0.00528002 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.37633 | 0.150019 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.56076 | 0.156158 | 0.0780788 | − | 0.996947i | \(-0.475121\pi\) | ||||
0.0780788 | + | 0.996947i | \(0.475121\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 18.8596 | 0.644984 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −30.9348 | −1.05671 | −0.528356 | − | 0.849023i | \(-0.677191\pi\) | ||||
−0.528356 | + | 0.849023i | \(0.677191\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39.4985 | 1.34767 | 0.673835 | − | 0.738882i | \(-0.264646\pi\) | ||||
0.673835 | + | 0.738882i | \(0.264646\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.89002 | −0.166652 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.03237 | −0.171304 | −0.0856520 | − | 0.996325i | \(-0.527297\pi\) | ||||
−0.0856520 | + | 0.996325i | \(0.527297\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −68.7674 | −2.33816 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15.3468 | 0.521203 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.646719 | 0.0219385 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −44.2776 | −1.50029 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −18.0506 | −0.610921 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.80926 | −0.0949704 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.80048 | −0.0607979 | −0.0303989 | − | 0.999538i | \(-0.509678\pi\) | ||||
−0.0303989 | + | 0.999538i | \(0.509678\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −32.7574 | −1.10488 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −17.4943 | −0.589397 | −0.294698 | − | 0.955590i | \(-0.595219\pi\) | ||||
−0.294698 | + | 0.955590i | \(0.595219\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.9385 | 0.435415 | 0.217708 | − | 0.976014i | \(-0.430142\pi\) | ||||
0.217708 | + | 0.976014i | \(0.430142\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13.5475 | −0.455394 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.9871 | −0.570372 | −0.285186 | − | 0.958472i | \(-0.592055\pi\) | ||||
−0.285186 | + | 0.958472i | \(0.592055\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.91454 | 0.0977506 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.88720 | −0.0632236 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 36.3020 | 1.21480 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23.1538 | 0.773947 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.64262 | −0.121624 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.90835 | −0.263758 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.36847 | 0.145535 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.87769 | 0.328709 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 34.5629 | 1.14891 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −53.7530 | −1.78484 | −0.892419 | − | 0.451207i | \(-0.850994\pi\) | ||||
−0.892419 | + | 0.451207i | \(0.850994\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.307106 | −0.0101861 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.961864 | −0.0318680 | −0.0159340 | − | 0.999873i | \(-0.505072\pi\) | ||||
−0.0159340 | + | 0.999873i | \(0.505072\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.183969 | −0.00608848 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.443268 | 0.0146540 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12.8347 | −0.423840 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.5693 | −0.843454 | −0.421727 | − | 0.906723i | \(-0.638576\pi\) | ||||
−0.421727 | + | 0.906723i | \(0.638576\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.3644 | −0.341518 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.10459 | 0.200935 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.5421 | −0.839821 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.96209 | −0.327198 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20.9124 | −0.686113 | −0.343057 | − | 0.939315i | \(-0.611462\pi\) | ||||
−0.343057 | + | 0.939315i | \(0.611462\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −34.1400 | −1.11889 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.192809 | 0.00631229 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.98783 | 0.261230 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 49.7499 | 1.62526 | 0.812629 | − | 0.582782i | \(-0.198036\pi\) | ||||
0.812629 | + | 0.582782i | \(0.198036\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18.5661 | 0.605882 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.8626 | 0.745300 | 0.372650 | − | 0.927972i | \(-0.378449\pi\) | ||||
0.372650 | + | 0.927972i | \(0.378449\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.79282 | 0.156076 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.35864 | 0.109257 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −44.1781 | −1.43559 | −0.717797 | − | 0.696253i | \(-0.754849\pi\) | ||||
−0.717797 | + | 0.696253i | \(0.754849\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.465953 | 0.0151255 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.1487 | −0.523659 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 43.7614 | 1.41757 | 0.708786 | − | 0.705424i | \(-0.249243\pi\) | ||||
0.708786 | + | 0.705424i | \(0.249243\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 42.6518 | 1.38018 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.88720 | 0.0610045 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.31136 | 0.0423460 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.5421 | 1.01749 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.95885 | −0.159797 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −89.2207 | −2.87212 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.6578 | −0.407048 | −0.203524 | − | 0.979070i | \(-0.565240\pi\) | ||||
−0.203524 | + | 0.979070i | \(0.565240\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.36642 | 0.236643 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.3998 | 0.815118 | 0.407559 | − | 0.913179i | \(-0.366380\pi\) | ||||
0.407559 | + | 0.913179i | \(0.366380\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.38315 | 0.172576 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 21.2599 | 0.680862 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.7723 | 0.984494 | 0.492247 | − | 0.870455i | \(-0.336176\pi\) | ||||
0.492247 | + | 0.870455i | \(0.336176\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27.2893 | 0.872171 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.9944 | −0.382952 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14.3927 | 0.459057 | 0.229528 | − | 0.973302i | \(-0.426282\pi\) | ||||
0.229528 | + | 0.973302i | \(0.426282\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 48.4902 | 1.54502 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.46491 | 0.205780 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.68133 | −0.307849 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.9935 | −0.635116 | −0.317558 | − | 0.948239i | \(-0.602863\pi\) | ||||
−0.317558 | + | 0.948239i | \(0.602863\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.9714 | 0.602041 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.19398 | 0.196362 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.84129 | 0.280006 | 0.140003 | − | 0.990151i | \(-0.455289\pi\) | ||||
0.140003 | + | 0.990151i | \(0.455289\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.37633 | 0.138461 |
(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 | 8004.2.a.e.1.9 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8004.2.a.e.1.9 | ✓ | 9 | 1.1 | even | 1 | trivial |