Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8046,2,Mod(1,8046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8046, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8046 = 2 \cdot 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8046.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: | \(64.2476334663\) |
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: | \( x^{9} - 3x^{8} - 9x^{7} + 25x^{6} + 29x^{5} - 58x^{4} - 43x^{3} + 34x^{2} + 25x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-1.55687\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8046.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.71034 | 1.21210 | 0.606050 | − | 0.795426i | \(-0.292753\pi\) | ||||
0.606050 | + | 0.795426i | \(0.292753\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.67819 | 0.634297 | 0.317148 | − | 0.948376i | \(-0.397275\pi\) | ||||
0.317148 | + | 0.948376i | \(0.397275\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.71034 | 0.857084 | ||||||||
\(11\) | −4.37358 | −1.31869 | −0.659343 | − | 0.751843i | \(-0.729165\pi\) | ||||
−0.659343 | + | 0.751843i | \(0.729165\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.34775 | −0.651148 | −0.325574 | − | 0.945517i | \(-0.605557\pi\) | ||||
−0.325574 | + | 0.945517i | \(0.605557\pi\) | |||||||
\(14\) | 1.67819 | 0.448515 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.09598 | −0.993420 | −0.496710 | − | 0.867916i | \(-0.665459\pi\) | ||||
−0.496710 | + | 0.867916i | \(0.665459\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.26207 | −1.66603 | −0.833016 | − | 0.553249i | \(-0.813388\pi\) | ||||
−0.833016 | + | 0.553249i | \(0.813388\pi\) | |||||||
\(20\) | 2.71034 | 0.606050 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.37358 | −0.932451 | ||||||||
\(23\) | 0.0981648 | 0.0204688 | 0.0102344 | − | 0.999948i | \(-0.496742\pi\) | ||||
0.0102344 | + | 0.999948i | \(0.496742\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.34593 | 0.469187 | ||||||||
\(26\) | −2.34775 | −0.460431 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.67819 | 0.317148 | ||||||||
\(29\) | −5.89425 | −1.09454 | −0.547268 | − | 0.836958i | \(-0.684332\pi\) | ||||
−0.547268 | + | 0.836958i | \(0.684332\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.88042 | −0.337734 | −0.168867 | − | 0.985639i | \(-0.554011\pi\) | ||||
−0.168867 | + | 0.985639i | \(0.554011\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.09598 | −0.702454 | ||||||||
\(35\) | 4.54847 | 0.768831 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.13510 | −0.515407 | −0.257704 | − | 0.966224i | \(-0.582966\pi\) | ||||
−0.257704 | + | 0.966224i | \(0.582966\pi\) | |||||||
\(38\) | −7.26207 | −1.17806 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.71034 | 0.428542 | ||||||||
\(41\) | −0.419725 | −0.0655501 | −0.0327750 | − | 0.999463i | \(-0.510434\pi\) | ||||
−0.0327750 | + | 0.999463i | \(0.510434\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.0900380 | −0.0137307 | −0.00686534 | − | 0.999976i | \(-0.502185\pi\) | ||||
−0.00686534 | + | 0.999976i | \(0.502185\pi\) | |||||||
\(44\) | −4.37358 | −0.659343 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.0981648 | 0.0144736 | ||||||||
\(47\) | −1.12980 | −0.164799 | −0.0823993 | − | 0.996599i | \(-0.526258\pi\) | ||||
−0.0823993 | + | 0.996599i | \(0.526258\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.18367 | −0.597668 | ||||||||
\(50\) | 2.34593 | 0.331765 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.34775 | −0.325574 | ||||||||
\(53\) | 12.5105 | 1.71845 | 0.859227 | − | 0.511595i | \(-0.170945\pi\) | ||||
0.859227 | + | 0.511595i | \(0.170945\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.8539 | −1.59838 | ||||||||
\(56\) | 1.67819 | 0.224258 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.89425 | −0.773953 | ||||||||
\(59\) | −7.63266 | −0.993687 | −0.496844 | − | 0.867840i | \(-0.665508\pi\) | ||||
−0.496844 | + | 0.867840i | \(0.665508\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.77438 | 0.483260 | 0.241630 | − | 0.970368i | \(-0.422318\pi\) | ||||
0.241630 | + | 0.970368i | \(0.422318\pi\) | |||||||
\(62\) | −1.88042 | −0.238814 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −6.36319 | −0.789256 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.12705 | 0.382030 | 0.191015 | − | 0.981587i | \(-0.438822\pi\) | ||||
0.191015 | + | 0.981587i | \(0.438822\pi\) | |||||||
\(68\) | −4.09598 | −0.496710 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.54847 | 0.543646 | ||||||||
\(71\) | −3.20185 | −0.379990 | −0.189995 | − | 0.981785i | \(-0.560847\pi\) | ||||
−0.189995 | + | 0.981785i | \(0.560847\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.15506 | 0.135190 | 0.0675951 | − | 0.997713i | \(-0.478467\pi\) | ||||
0.0675951 | + | 0.997713i | \(0.478467\pi\) | |||||||
\(74\) | −3.13510 | −0.364448 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.26207 | −0.833016 | ||||||||
\(77\) | −7.33971 | −0.836437 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.5113 | −1.74516 | −0.872578 | − | 0.488475i | \(-0.837553\pi\) | ||||
−0.872578 | + | 0.488475i | \(0.837553\pi\) | |||||||
\(80\) | 2.71034 | 0.303025 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.419725 | −0.0463509 | ||||||||
\(83\) | −14.9118 | −1.63678 | −0.818389 | − | 0.574665i | \(-0.805132\pi\) | ||||
−0.818389 | + | 0.574665i | \(0.805132\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.1015 | −1.20412 | ||||||||
\(86\) | −0.0900380 | −0.00970905 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.37358 | −0.466226 | ||||||||
\(89\) | 7.11363 | 0.754043 | 0.377022 | − | 0.926204i | \(-0.376948\pi\) | ||||
0.377022 | + | 0.926204i | \(0.376948\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.93997 | −0.413021 | ||||||||
\(92\) | 0.0981648 | 0.0102344 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.12980 | −0.116530 | ||||||||
\(95\) | −19.6827 | −2.01940 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.78642 | −0.485987 | −0.242994 | − | 0.970028i | \(-0.578129\pi\) | ||||
−0.242994 | + | 0.970028i | \(0.578129\pi\) | |||||||
\(98\) | −4.18367 | −0.422615 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.34593 | 0.234593 | ||||||||
\(101\) | −3.25163 | −0.323550 | −0.161775 | − | 0.986828i | \(-0.551722\pi\) | ||||
−0.161775 | + | 0.986828i | \(0.551722\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.91855 | −0.681705 | −0.340852 | − | 0.940117i | \(-0.610716\pi\) | ||||
−0.340852 | + | 0.940117i | \(0.610716\pi\) | |||||||
\(104\) | −2.34775 | −0.230216 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.5105 | 1.21513 | ||||||||
\(107\) | 2.61340 | 0.252647 | 0.126323 | − | 0.991989i | \(-0.459682\pi\) | ||||
0.126323 | + | 0.991989i | \(0.459682\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.13251 | −0.778953 | −0.389477 | − | 0.921036i | \(-0.627344\pi\) | ||||
−0.389477 | + | 0.921036i | \(0.627344\pi\) | |||||||
\(110\) | −11.8539 | −1.13022 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.67819 | 0.158574 | ||||||||
\(113\) | 6.09305 | 0.573186 | 0.286593 | − | 0.958052i | \(-0.407477\pi\) | ||||
0.286593 | + | 0.958052i | \(0.407477\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.266060 | 0.0248102 | ||||||||
\(116\) | −5.89425 | −0.547268 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.63266 | −0.702643 | ||||||||
\(119\) | −6.87383 | −0.630123 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.12823 | 0.738930 | ||||||||
\(122\) | 3.77438 | 0.341717 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.88042 | −0.168867 | ||||||||
\(125\) | −7.19342 | −0.643399 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.03062 | 0.268924 | 0.134462 | − | 0.990919i | \(-0.457069\pi\) | ||||
0.134462 | + | 0.990919i | \(0.457069\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.36319 | −0.558089 | ||||||||
\(131\) | 22.8099 | 1.99291 | 0.996454 | − | 0.0841386i | \(-0.0268138\pi\) | ||||
0.996454 | + | 0.0841386i | \(0.0268138\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.1871 | −1.05676 | ||||||||
\(134\) | 3.12705 | 0.270136 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.09598 | −0.351227 | ||||||||
\(137\) | 12.4026 | 1.05962 | 0.529812 | − | 0.848115i | \(-0.322262\pi\) | ||||
0.529812 | + | 0.848115i | \(0.322262\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.1737 | 1.37184 | 0.685918 | − | 0.727679i | \(-0.259401\pi\) | ||||
0.685918 | + | 0.727679i | \(0.259401\pi\) | |||||||
\(140\) | 4.54847 | 0.384415 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.20185 | −0.268693 | ||||||||
\(143\) | 10.2681 | 0.858659 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −15.9754 | −1.32669 | ||||||||
\(146\) | 1.15506 | 0.0955938 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.13510 | −0.257704 | ||||||||
\(149\) | −1.00000 | −0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.5180 | 0.855946 | 0.427973 | − | 0.903791i | \(-0.359228\pi\) | ||||
0.427973 | + | 0.903791i | \(0.359228\pi\) | |||||||
\(152\) | −7.26207 | −0.589031 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −7.33971 | −0.591451 | ||||||||
\(155\) | −5.09658 | −0.409367 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.1463 | 1.52804 | 0.764020 | − | 0.645193i | \(-0.223223\pi\) | ||||
0.764020 | + | 0.645193i | \(0.223223\pi\) | |||||||
\(158\) | −15.5113 | −1.23401 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.71034 | 0.214271 | ||||||||
\(161\) | 0.164739 | 0.0129833 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.53078 | −0.511530 | −0.255765 | − | 0.966739i | \(-0.582327\pi\) | ||||
−0.255765 | + | 0.966739i | \(0.582327\pi\) | |||||||
\(164\) | −0.419725 | −0.0327750 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.9118 | −1.15738 | ||||||||
\(167\) | −11.7228 | −0.907134 | −0.453567 | − | 0.891222i | \(-0.649849\pi\) | ||||
−0.453567 | + | 0.891222i | \(0.649849\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.48808 | −0.576006 | ||||||||
\(170\) | −11.1015 | −0.851445 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.0900380 | −0.00686534 | ||||||||
\(173\) | −1.93624 | −0.147210 | −0.0736049 | − | 0.997287i | \(-0.523450\pi\) | ||||
−0.0736049 | + | 0.997287i | \(0.523450\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.93692 | 0.297604 | ||||||||
\(176\) | −4.37358 | −0.329671 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.11363 | 0.533189 | ||||||||
\(179\) | 13.5559 | 1.01321 | 0.506606 | − | 0.862178i | \(-0.330900\pi\) | ||||
0.506606 | + | 0.862178i | \(0.330900\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.9431 | 1.11071 | 0.555354 | − | 0.831614i | \(-0.312583\pi\) | ||||
0.555354 | + | 0.831614i | \(0.312583\pi\) | |||||||
\(182\) | −3.93997 | −0.292050 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.0981648 | 0.00723681 | ||||||||
\(185\) | −8.49718 | −0.624725 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.9141 | 1.31001 | ||||||||
\(188\) | −1.12980 | −0.0823993 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −19.6827 | −1.42793 | ||||||||
\(191\) | −3.69535 | −0.267386 | −0.133693 | − | 0.991023i | \(-0.542684\pi\) | ||||
−0.133693 | + | 0.991023i | \(0.542684\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.65239 | 0.550831 | 0.275416 | − | 0.961325i | \(-0.411185\pi\) | ||||
0.275416 | + | 0.961325i | \(0.411185\pi\) | |||||||
\(194\) | −4.78642 | −0.343645 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.18367 | −0.298834 | ||||||||
\(197\) | −18.2992 | −1.30376 | −0.651882 | − | 0.758321i | \(-0.726020\pi\) | ||||
−0.651882 | + | 0.758321i | \(0.726020\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.9256 | 0.916269 | 0.458134 | − | 0.888883i | \(-0.348518\pi\) | ||||
0.458134 | + | 0.888883i | \(0.348518\pi\) | |||||||
\(200\) | 2.34593 | 0.165883 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.25163 | −0.228784 | ||||||||
\(203\) | −9.89168 | −0.694260 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.13760 | −0.0794532 | ||||||||
\(206\) | −6.91855 | −0.482038 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.34775 | −0.162787 | ||||||||
\(209\) | 31.7613 | 2.19697 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.7410 | −0.877126 | −0.438563 | − | 0.898700i | \(-0.644512\pi\) | ||||
−0.438563 | + | 0.898700i | \(0.644512\pi\) | |||||||
\(212\) | 12.5105 | 0.859227 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.61340 | 0.178648 | ||||||||
\(215\) | −0.244034 | −0.0166429 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.15571 | −0.214223 | ||||||||
\(218\) | −8.13251 | −0.550803 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −11.8539 | −0.799189 | ||||||||
\(221\) | 9.61632 | 0.646864 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.0497 | −0.672980 | −0.336490 | − | 0.941687i | \(-0.609240\pi\) | ||||
−0.336490 | + | 0.941687i | \(0.609240\pi\) | |||||||
\(224\) | 1.67819 | 0.112129 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.09305 | 0.405303 | ||||||||
\(227\) | 9.51471 | 0.631514 | 0.315757 | − | 0.948840i | \(-0.397742\pi\) | ||||
0.315757 | + | 0.948840i | \(0.397742\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.3081 | 1.14375 | 0.571875 | − | 0.820341i | \(-0.306216\pi\) | ||||
0.571875 | + | 0.820341i | \(0.306216\pi\) | |||||||
\(230\) | 0.266060 | 0.0175435 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.89425 | −0.386977 | ||||||||
\(233\) | −21.8741 | −1.43302 | −0.716511 | − | 0.697576i | \(-0.754262\pi\) | ||||
−0.716511 | + | 0.697576i | \(0.754262\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.06215 | −0.199752 | ||||||||
\(236\) | −7.63266 | −0.496844 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −6.87383 | −0.445564 | ||||||||
\(239\) | 25.8220 | 1.67029 | 0.835143 | − | 0.550032i | \(-0.185385\pi\) | ||||
0.835143 | + | 0.550032i | \(0.185385\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.3157 | −0.793327 | −0.396663 | − | 0.917964i | \(-0.629832\pi\) | ||||
−0.396663 | + | 0.917964i | \(0.629832\pi\) | |||||||
\(242\) | 8.12823 | 0.522503 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.77438 | 0.241630 | ||||||||
\(245\) | −11.3392 | −0.724433 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17.0495 | 1.08483 | ||||||||
\(248\) | −1.88042 | −0.119407 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −7.19342 | −0.454952 | ||||||||
\(251\) | 24.1336 | 1.52330 | 0.761649 | − | 0.647990i | \(-0.224390\pi\) | ||||
0.761649 | + | 0.647990i | \(0.224390\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.429332 | −0.0269919 | ||||||||
\(254\) | 3.03062 | 0.190158 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −1.94139 | −0.121101 | −0.0605504 | − | 0.998165i | \(-0.519286\pi\) | ||||
−0.0605504 | + | 0.998165i | \(0.519286\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.26129 | −0.326921 | ||||||||
\(260\) | −6.36319 | −0.394628 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 22.8099 | 1.40920 | ||||||||
\(263\) | −12.2957 | −0.758187 | −0.379093 | − | 0.925358i | \(-0.623764\pi\) | ||||
−0.379093 | + | 0.925358i | \(0.623764\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 33.9078 | 2.08294 | ||||||||
\(266\) | −12.1871 | −0.747241 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.12705 | 0.191015 | ||||||||
\(269\) | −5.20845 | −0.317565 | −0.158782 | − | 0.987314i | \(-0.550757\pi\) | ||||
−0.158782 | + | 0.987314i | \(0.550757\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.53266 | 0.579068 | 0.289534 | − | 0.957168i | \(-0.406500\pi\) | ||||
0.289534 | + | 0.957168i | \(0.406500\pi\) | |||||||
\(272\) | −4.09598 | −0.248355 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.4026 | 0.749268 | ||||||||
\(275\) | −10.2601 | −0.618710 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.2562 | 0.736404 | 0.368202 | − | 0.929746i | \(-0.379973\pi\) | ||||
0.368202 | + | 0.929746i | \(0.379973\pi\) | |||||||
\(278\) | 16.1737 | 0.970034 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.54847 | 0.271823 | ||||||||
\(281\) | 1.20525 | 0.0718992 | 0.0359496 | − | 0.999354i | \(-0.488554\pi\) | ||||
0.0359496 | + | 0.999354i | \(0.488554\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.3087 | −1.44500 | −0.722500 | − | 0.691371i | \(-0.757007\pi\) | ||||
−0.722500 | + | 0.691371i | \(0.757007\pi\) | |||||||
\(284\) | −3.20185 | −0.189995 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.2681 | 0.607164 | ||||||||
\(287\) | −0.704379 | −0.0415782 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.222971 | −0.0131159 | ||||||||
\(290\) | −15.9754 | −0.938109 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.15506 | 0.0675951 | ||||||||
\(293\) | 9.58867 | 0.560176 | 0.280088 | − | 0.959974i | \(-0.409636\pi\) | ||||
0.280088 | + | 0.959974i | \(0.409636\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.6871 | −1.20445 | ||||||||
\(296\) | −3.13510 | −0.182224 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.00000 | −0.0579284 | ||||||||
\(299\) | −0.230466 | −0.0133282 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.151101 | −0.00870932 | ||||||||
\(302\) | 10.5180 | 0.605246 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.26207 | −0.416508 | ||||||||
\(305\) | 10.2299 | 0.585760 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.9118 | −1.19350 | −0.596750 | − | 0.802427i | \(-0.703542\pi\) | ||||
−0.596750 | + | 0.802427i | \(0.703542\pi\) | |||||||
\(308\) | −7.33971 | −0.418219 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.09658 | −0.289466 | ||||||||
\(311\) | 13.7307 | 0.778598 | 0.389299 | − | 0.921111i | \(-0.372717\pi\) | ||||
0.389299 | + | 0.921111i | \(0.372717\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −27.3384 | −1.54526 | −0.772628 | − | 0.634859i | \(-0.781058\pi\) | ||||
−0.772628 | + | 0.634859i | \(0.781058\pi\) | |||||||
\(314\) | 19.1463 | 1.08049 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −15.5113 | −0.872578 | ||||||||
\(317\) | 19.0031 | 1.06732 | 0.533659 | − | 0.845700i | \(-0.320817\pi\) | ||||
0.533659 | + | 0.845700i | \(0.320817\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 25.7790 | 1.44335 | ||||||||
\(320\) | 2.71034 | 0.151513 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.164739 | 0.00918056 | ||||||||
\(323\) | 29.7453 | 1.65507 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.50766 | −0.305510 | ||||||||
\(326\) | −6.53078 | −0.361707 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.419725 | −0.0231754 | ||||||||
\(329\) | −1.89602 | −0.104531 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.2079 | −1.33059 | −0.665294 | − | 0.746581i | \(-0.731694\pi\) | ||||
−0.665294 | + | 0.746581i | \(0.731694\pi\) | |||||||
\(332\) | −14.9118 | −0.818389 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −11.7228 | −0.641440 | ||||||||
\(335\) | 8.47536 | 0.463059 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.7597 | −1.18533 | −0.592663 | − | 0.805450i | \(-0.701924\pi\) | ||||
−0.592663 | + | 0.805450i | \(0.701924\pi\) | |||||||
\(338\) | −7.48808 | −0.407298 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −11.1015 | −0.602062 | ||||||||
\(341\) | 8.22418 | 0.445364 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.7683 | −1.01340 | ||||||||
\(344\) | −0.0900380 | −0.00485453 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.93624 | −0.104093 | ||||||||
\(347\) | −11.4110 | −0.612574 | −0.306287 | − | 0.951939i | \(-0.599087\pi\) | ||||
−0.306287 | + | 0.951939i | \(0.599087\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.2720 | 1.56689 | 0.783446 | − | 0.621460i | \(-0.213460\pi\) | ||||
0.783446 | + | 0.621460i | \(0.213460\pi\) | |||||||
\(350\) | 3.93692 | 0.210437 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.37358 | −0.233113 | ||||||||
\(353\) | 25.2789 | 1.34546 | 0.672730 | − | 0.739888i | \(-0.265121\pi\) | ||||
0.672730 | + | 0.739888i | \(0.265121\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.67810 | −0.460586 | ||||||||
\(356\) | 7.11363 | 0.377022 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13.5559 | 0.716449 | ||||||||
\(359\) | 3.38548 | 0.178679 | 0.0893393 | − | 0.996001i | \(-0.471524\pi\) | ||||
0.0893393 | + | 0.996001i | \(0.471524\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 33.7376 | 1.77566 | ||||||||
\(362\) | 14.9431 | 0.785389 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.93997 | −0.206510 | ||||||||
\(365\) | 3.13062 | 0.163864 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.07969 | 0.369557 | 0.184778 | − | 0.982780i | \(-0.440843\pi\) | ||||
0.184778 | + | 0.982780i | \(0.440843\pi\) | |||||||
\(368\) | 0.0981648 | 0.00511719 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −8.49718 | −0.441747 | ||||||||
\(371\) | 20.9951 | 1.09001 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.58277 | 0.392621 | 0.196311 | − | 0.980542i | \(-0.437104\pi\) | ||||
0.196311 | + | 0.980542i | \(0.437104\pi\) | |||||||
\(374\) | 17.9141 | 0.926316 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.12980 | −0.0582651 | ||||||||
\(377\) | 13.8382 | 0.712704 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −37.0298 | −1.90210 | −0.951048 | − | 0.309044i | \(-0.899991\pi\) | ||||
−0.951048 | + | 0.309044i | \(0.899991\pi\) | |||||||
\(380\) | −19.6827 | −1.00970 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.69535 | −0.189071 | ||||||||
\(383\) | 9.47515 | 0.484158 | 0.242079 | − | 0.970257i | \(-0.422171\pi\) | ||||
0.242079 | + | 0.970257i | \(0.422171\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −19.8931 | −1.01385 | ||||||||
\(386\) | 7.65239 | 0.389496 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.78642 | −0.242994 | ||||||||
\(389\) | 8.01018 | 0.406132 | 0.203066 | − | 0.979165i | \(-0.434909\pi\) | ||||
0.203066 | + | 0.979165i | \(0.434909\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.402081 | −0.0203341 | ||||||||
\(392\) | −4.18367 | −0.211307 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −18.2992 | −0.921900 | ||||||||
\(395\) | −42.0408 | −2.11530 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.4377 | −0.824984 | −0.412492 | − | 0.910961i | \(-0.635342\pi\) | ||||
−0.412492 | + | 0.910961i | \(0.635342\pi\) | |||||||
\(398\) | 12.9256 | 0.647900 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.34593 | 0.117297 | ||||||||
\(401\) | 17.7661 | 0.887199 | 0.443599 | − | 0.896225i | \(-0.353701\pi\) | ||||
0.443599 | + | 0.896225i | \(0.353701\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.41475 | 0.219914 | ||||||||
\(404\) | −3.25163 | −0.161775 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.89168 | −0.490916 | ||||||||
\(407\) | 13.7116 | 0.679660 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.3199 | −1.20254 | −0.601270 | − | 0.799046i | \(-0.705338\pi\) | ||||
−0.601270 | + | 0.799046i | \(0.705338\pi\) | |||||||
\(410\) | −1.13760 | −0.0561819 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.91855 | −0.340852 | ||||||||
\(413\) | −12.8091 | −0.630293 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −40.4159 | −1.98394 | ||||||||
\(416\) | −2.34775 | −0.115108 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 31.7613 | 1.55349 | ||||||||
\(419\) | −23.5738 | −1.15166 | −0.575829 | − | 0.817570i | \(-0.695321\pi\) | ||||
−0.575829 | + | 0.817570i | \(0.695321\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.218135 | −0.0106312 | −0.00531562 | − | 0.999986i | \(-0.501692\pi\) | ||||
−0.00531562 | + | 0.999986i | \(0.501692\pi\) | |||||||
\(422\) | −12.7410 | −0.620222 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 12.5105 | 0.607565 | ||||||||
\(425\) | −9.60889 | −0.466100 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.33414 | 0.306530 | ||||||||
\(428\) | 2.61340 | 0.126323 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.244034 | −0.0117683 | ||||||||
\(431\) | 16.3041 | 0.785339 | 0.392670 | − | 0.919680i | \(-0.371552\pi\) | ||||
0.392670 | + | 0.919680i | \(0.371552\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.4350 | 0.789815 | 0.394908 | − | 0.918721i | \(-0.370777\pi\) | ||||
0.394908 | + | 0.918721i | \(0.370777\pi\) | |||||||
\(434\) | −3.15571 | −0.151479 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.13251 | −0.389477 | ||||||||
\(437\) | −0.712879 | −0.0341016 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.1285 | −1.19932 | −0.599660 | − | 0.800255i | \(-0.704697\pi\) | ||||
−0.599660 | + | 0.800255i | \(0.704697\pi\) | |||||||
\(440\) | −11.8539 | −0.565112 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.61632 | 0.457402 | ||||||||
\(443\) | 26.4593 | 1.25712 | 0.628560 | − | 0.777761i | \(-0.283645\pi\) | ||||
0.628560 | + | 0.777761i | \(0.283645\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19.2803 | 0.913976 | ||||||||
\(446\) | −10.0497 | −0.475869 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.67819 | 0.0792871 | ||||||||
\(449\) | 11.6779 | 0.551112 | 0.275556 | − | 0.961285i | \(-0.411138\pi\) | ||||
0.275556 | + | 0.961285i | \(0.411138\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.83570 | 0.0864399 | ||||||||
\(452\) | 6.09305 | 0.286593 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9.51471 | 0.446548 | ||||||||
\(455\) | −10.6786 | −0.500623 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.2598 | 0.526709 | 0.263355 | − | 0.964699i | \(-0.415171\pi\) | ||||
0.263355 | + | 0.964699i | \(0.415171\pi\) | |||||||
\(458\) | 17.3081 | 0.808753 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.266060 | 0.0124051 | ||||||||
\(461\) | −14.7144 | −0.685318 | −0.342659 | − | 0.939460i | \(-0.611328\pi\) | ||||
−0.342659 | + | 0.939460i | \(0.611328\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.2474 | 0.708607 | 0.354303 | − | 0.935131i | \(-0.384718\pi\) | ||||
0.354303 | + | 0.935131i | \(0.384718\pi\) | |||||||
\(464\) | −5.89425 | −0.273634 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −21.8741 | −1.01330 | ||||||||
\(467\) | −31.9586 | −1.47887 | −0.739433 | − | 0.673230i | \(-0.764906\pi\) | ||||
−0.739433 | + | 0.673230i | \(0.764906\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.24779 | 0.242320 | ||||||||
\(470\) | −3.06215 | −0.141246 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7.63266 | −0.351322 | ||||||||
\(473\) | 0.393789 | 0.0181064 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −17.0363 | −0.781680 | ||||||||
\(476\) | −6.87383 | −0.315062 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 25.8220 | 1.18107 | ||||||||
\(479\) | 10.9302 | 0.499413 | 0.249706 | − | 0.968322i | \(-0.419666\pi\) | ||||
0.249706 | + | 0.968322i | \(0.419666\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.36042 | 0.335606 | ||||||||
\(482\) | −12.3157 | −0.560967 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.12823 | 0.369465 | ||||||||
\(485\) | −12.9728 | −0.589065 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −34.7186 | −1.57325 | −0.786626 | − | 0.617430i | \(-0.788174\pi\) | ||||
−0.786626 | + | 0.617430i | \(0.788174\pi\) | |||||||
\(488\) | 3.77438 | 0.170858 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −11.3392 | −0.512252 | ||||||||
\(491\) | −33.3466 | −1.50491 | −0.752456 | − | 0.658642i | \(-0.771131\pi\) | ||||
−0.752456 | + | 0.658642i | \(0.771131\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 24.1427 | 1.08733 | ||||||||
\(494\) | 17.0495 | 0.767093 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.88042 | −0.0844334 | ||||||||
\(497\) | −5.37332 | −0.241026 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.1107 | −1.03458 | −0.517289 | − | 0.855811i | \(-0.673059\pi\) | ||||
−0.517289 | + | 0.855811i | \(0.673059\pi\) | |||||||
\(500\) | −7.19342 | −0.321699 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 24.1336 | 1.07713 | ||||||||
\(503\) | 31.7411 | 1.41527 | 0.707633 | − | 0.706580i | \(-0.249763\pi\) | ||||
0.707633 | + | 0.706580i | \(0.249763\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.81303 | −0.392175 | ||||||||
\(506\) | −0.429332 | −0.0190861 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.03062 | 0.134462 | ||||||||
\(509\) | 15.5438 | 0.688965 | 0.344483 | − | 0.938793i | \(-0.388054\pi\) | ||||
0.344483 | + | 0.938793i | \(0.388054\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.93842 | 0.0857506 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.94139 | −0.0856311 | ||||||||
\(515\) | −18.7516 | −0.826294 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.94129 | 0.217318 | ||||||||
\(518\) | −5.26129 | −0.231168 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.36319 | −0.279044 | ||||||||
\(521\) | 18.6011 | 0.814929 | 0.407465 | − | 0.913221i | \(-0.366413\pi\) | ||||
0.407465 | + | 0.913221i | \(0.366413\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.4760 | −0.720444 | −0.360222 | − | 0.932867i | \(-0.617299\pi\) | ||||
−0.360222 | + | 0.932867i | \(0.617299\pi\) | |||||||
\(524\) | 22.8099 | 0.996454 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.2957 | −0.536119 | ||||||||
\(527\) | 7.70216 | 0.335511 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9904 | −0.999581 | ||||||||
\(530\) | 33.9078 | 1.47286 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −12.1871 | −0.528379 | ||||||||
\(533\) | 0.985408 | 0.0426828 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.08319 | 0.306233 | ||||||||
\(536\) | 3.12705 | 0.135068 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5.20845 | −0.224552 | ||||||||
\(539\) | 18.2977 | 0.788136 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.8765 | 0.768573 | 0.384286 | − | 0.923214i | \(-0.374448\pi\) | ||||
0.384286 | + | 0.923214i | \(0.374448\pi\) | |||||||
\(542\) | 9.53266 | 0.409463 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.09598 | −0.175614 | ||||||||
\(545\) | −22.0419 | −0.944169 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.9324 | −1.19430 | −0.597152 | − | 0.802128i | \(-0.703701\pi\) | ||||
−0.597152 | + | 0.802128i | \(0.703701\pi\) | |||||||
\(548\) | 12.4026 | 0.529812 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −10.2601 | −0.437494 | ||||||||
\(551\) | 42.8044 | 1.82353 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −26.0309 | −1.10695 | ||||||||
\(554\) | 12.2562 | 0.520716 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.1737 | 0.685918 | ||||||||
\(557\) | −17.0091 | −0.720700 | −0.360350 | − | 0.932817i | \(-0.617343\pi\) | ||||
−0.360350 | + | 0.932817i | \(0.617343\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.211387 | 0.00894070 | ||||||||
\(560\) | 4.54847 | 0.192208 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.20525 | 0.0508404 | ||||||||
\(563\) | −36.1048 | −1.52164 | −0.760818 | − | 0.648965i | \(-0.775202\pi\) | ||||
−0.760818 | + | 0.648965i | \(0.775202\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.5142 | 0.694758 | ||||||||
\(566\) | −24.3087 | −1.02177 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.20185 | −0.134347 | ||||||||
\(569\) | −6.41843 | −0.269074 | −0.134537 | − | 0.990909i | \(-0.542955\pi\) | ||||
−0.134537 | + | 0.990909i | \(0.542955\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.2900 | 0.681716 | 0.340858 | − | 0.940115i | \(-0.389282\pi\) | ||||
0.340858 | + | 0.940115i | \(0.389282\pi\) | |||||||
\(572\) | 10.2681 | 0.429329 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.704379 | −0.0294002 | ||||||||
\(575\) | 0.230288 | 0.00960368 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.1764 | 0.590170 | 0.295085 | − | 0.955471i | \(-0.404652\pi\) | ||||
0.295085 | + | 0.955471i | \(0.404652\pi\) | |||||||
\(578\) | −0.222971 | −0.00927438 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −15.9754 | −0.663343 | ||||||||
\(581\) | −25.0248 | −1.03820 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −54.7159 | −2.26610 | ||||||||
\(584\) | 1.15506 | 0.0477969 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.58867 | 0.396104 | ||||||||
\(587\) | −16.5294 | −0.682242 | −0.341121 | − | 0.940019i | \(-0.610807\pi\) | ||||
−0.341121 | + | 0.940019i | \(0.610807\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.6557 | 0.562675 | ||||||||
\(590\) | −20.6871 | −0.851674 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.13510 | −0.128852 | ||||||||
\(593\) | 32.0924 | 1.31788 | 0.658939 | − | 0.752196i | \(-0.271005\pi\) | ||||
0.658939 | + | 0.752196i | \(0.271005\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.6304 | −0.763772 | ||||||||
\(596\) | −1.00000 | −0.0409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.230466 | −0.00942446 | ||||||||
\(599\) | −22.1189 | −0.903754 | −0.451877 | − | 0.892080i | \(-0.649245\pi\) | ||||
−0.451877 | + | 0.892080i | \(0.649245\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.2111 | −0.906009 | −0.453004 | − | 0.891508i | \(-0.649648\pi\) | ||||
−0.453004 | + | 0.891508i | \(0.649648\pi\) | |||||||
\(602\) | −0.151101 | −0.00615842 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10.5180 | 0.427973 | ||||||||
\(605\) | 22.0303 | 0.895658 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.78678 | −0.234878 | −0.117439 | − | 0.993080i | \(-0.537468\pi\) | ||||
−0.117439 | + | 0.993080i | \(0.537468\pi\) | |||||||
\(608\) | −7.26207 | −0.294516 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 10.2299 | 0.414195 | ||||||||
\(611\) | 2.65249 | 0.107308 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.4581 | −1.14941 | −0.574706 | − | 0.818360i | \(-0.694884\pi\) | ||||
−0.574706 | + | 0.818360i | \(0.694884\pi\) | |||||||
\(614\) | −20.9118 | −0.843932 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.33971 | −0.295725 | ||||||||
\(617\) | −13.5829 | −0.546826 | −0.273413 | − | 0.961897i | \(-0.588153\pi\) | ||||
−0.273413 | + | 0.961897i | \(0.588153\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.0851 | 0.927870 | 0.463935 | − | 0.885869i | \(-0.346437\pi\) | ||||
0.463935 | + | 0.885869i | \(0.346437\pi\) | |||||||
\(620\) | −5.09658 | −0.204683 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 13.7307 | 0.550552 | ||||||||
\(623\) | 11.9380 | 0.478287 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2263 | −1.24905 | ||||||||
\(626\) | −27.3384 | −1.09266 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 19.1463 | 0.764020 | ||||||||
\(629\) | 12.8413 | 0.512016 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.5613 | −1.17682 | −0.588409 | − | 0.808563i | \(-0.700246\pi\) | ||||
−0.588409 | + | 0.808563i | \(0.700246\pi\) | |||||||
\(632\) | −15.5113 | −0.617006 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 19.0031 | 0.754708 | ||||||||
\(635\) | 8.21400 | 0.325963 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.82221 | 0.389170 | ||||||||
\(638\) | 25.7790 | 1.02060 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.71034 | 0.107136 | ||||||||
\(641\) | 3.36162 | 0.132776 | 0.0663881 | − | 0.997794i | \(-0.478852\pi\) | ||||
0.0663881 | + | 0.997794i | \(0.478852\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −37.2776 | −1.47009 | −0.735043 | − | 0.678020i | \(-0.762838\pi\) | ||||
−0.735043 | + | 0.678020i | \(0.762838\pi\) | |||||||
\(644\) | 0.164739 | 0.00649164 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 29.7453 | 1.17031 | ||||||||
\(647\) | 17.7157 | 0.696478 | 0.348239 | − | 0.937406i | \(-0.386780\pi\) | ||||
0.348239 | + | 0.937406i | \(0.386780\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 33.3821 | 1.31036 | ||||||||
\(650\) | −5.50766 | −0.216028 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.53078 | −0.255765 | ||||||||
\(653\) | 31.2042 | 1.22111 | 0.610557 | − | 0.791972i | \(-0.290946\pi\) | ||||
0.610557 | + | 0.791972i | \(0.290946\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 61.8225 | 2.41560 | ||||||||
\(656\) | −0.419725 | −0.0163875 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.89602 | −0.0739147 | ||||||||
\(659\) | 42.2097 | 1.64426 | 0.822128 | − | 0.569303i | \(-0.192787\pi\) | ||||
0.822128 | + | 0.569303i | \(0.192787\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.0759 | −0.430801 | −0.215401 | − | 0.976526i | \(-0.569106\pi\) | ||||
−0.215401 | + | 0.976526i | \(0.569106\pi\) | |||||||
\(662\) | −24.2079 | −0.940868 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −14.9118 | −0.578688 | ||||||||
\(665\) | −33.0313 | −1.28090 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.578608 | −0.0224038 | ||||||||
\(668\) | −11.7228 | −0.453567 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8.47536 | 0.327432 | ||||||||
\(671\) | −16.5076 | −0.637268 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.6065 | 0.678680 | 0.339340 | − | 0.940664i | \(-0.389796\pi\) | ||||
0.339340 | + | 0.940664i | \(0.389796\pi\) | |||||||
\(674\) | −21.7597 | −0.838152 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.48808 | −0.288003 | ||||||||
\(677\) | 21.4160 | 0.823083 | 0.411542 | − | 0.911391i | \(-0.364990\pi\) | ||||
0.411542 | + | 0.911391i | \(0.364990\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.03253 | −0.308260 | ||||||||
\(680\) | −11.1015 | −0.425722 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.22418 | 0.314920 | ||||||||
\(683\) | −41.4123 | −1.58460 | −0.792298 | − | 0.610134i | \(-0.791116\pi\) | ||||
−0.792298 | + | 0.610134i | \(0.791116\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 33.6152 | 1.28437 | ||||||||
\(686\) | −18.7683 | −0.716579 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.0900380 | −0.00343267 | ||||||||
\(689\) | −29.3716 | −1.11897 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.2709 | 0.580932 | 0.290466 | − | 0.956885i | \(-0.406190\pi\) | ||||
0.290466 | + | 0.956885i | \(0.406190\pi\) | |||||||
\(692\) | −1.93624 | −0.0736049 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −11.4110 | −0.433155 | ||||||||
\(695\) | 43.8362 | 1.66280 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.71918 | 0.0651188 | ||||||||
\(698\) | 29.2720 | 1.10796 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.93692 | 0.148802 | ||||||||
\(701\) | −37.9423 | −1.43306 | −0.716531 | − | 0.697555i | \(-0.754271\pi\) | ||||
−0.716531 | + | 0.697555i | \(0.754271\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22.7673 | 0.858685 | ||||||||
\(704\) | −4.37358 | −0.164836 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 25.2789 | 0.951384 | ||||||||
\(707\) | −5.45686 | −0.205226 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26.1329 | −0.981441 | −0.490721 | − | 0.871317i | \(-0.663266\pi\) | ||||
−0.490721 | + | 0.871317i | \(0.663266\pi\) | |||||||
\(710\) | −8.67810 | −0.325683 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.11363 | 0.266595 | ||||||||
\(713\) | −0.184591 | −0.00691299 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 27.8299 | 1.04078 | ||||||||
\(716\) | 13.5559 | 0.506606 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.38548 | 0.126345 | ||||||||
\(719\) | −2.05961 | −0.0768107 | −0.0384053 | − | 0.999262i | \(-0.512228\pi\) | ||||
−0.0384053 | + | 0.999262i | \(0.512228\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.6106 | −0.432403 | ||||||||
\(722\) | 33.7376 | 1.25558 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 14.9431 | 0.555354 | ||||||||
\(725\) | −13.8275 | −0.513541 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.4096 | −0.386073 | −0.193036 | − | 0.981192i | \(-0.561833\pi\) | ||||
−0.193036 | + | 0.981192i | \(0.561833\pi\) | |||||||
\(728\) | −3.93997 | −0.146025 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.13062 | 0.115869 | ||||||||
\(731\) | 0.368794 | 0.0136403 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.8723 | −0.697065 | −0.348533 | − | 0.937297i | \(-0.613320\pi\) | ||||
−0.348533 | + | 0.937297i | \(0.613320\pi\) | |||||||
\(734\) | 7.07969 | 0.261316 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.0981648 | 0.00361840 | ||||||||
\(737\) | −13.6764 | −0.503777 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.8498 | −0.840544 | −0.420272 | − | 0.907398i | \(-0.638065\pi\) | ||||
−0.420272 | + | 0.907398i | \(0.638065\pi\) | |||||||
\(740\) | −8.49718 | −0.312362 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 20.9951 | 0.770753 | ||||||||
\(743\) | −40.5510 | −1.48767 | −0.743837 | − | 0.668362i | \(-0.766996\pi\) | ||||
−0.743837 | + | 0.668362i | \(0.766996\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.71034 | −0.0992991 | ||||||||
\(746\) | 7.58277 | 0.277625 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 17.9141 | 0.655004 | ||||||||
\(749\) | 4.38578 | 0.160253 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.7741 | 0.685078 | 0.342539 | − | 0.939504i | \(-0.388713\pi\) | ||||
0.342539 | + | 0.939504i | \(0.388713\pi\) | |||||||
\(752\) | −1.12980 | −0.0411997 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 13.8382 | 0.503958 | ||||||||
\(755\) | 28.5075 | 1.03749 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.1211 | −0.367857 | −0.183928 | − | 0.982940i | \(-0.558881\pi\) | ||||
−0.183928 | + | 0.982940i | \(0.558881\pi\) | |||||||
\(758\) | −37.0298 | −1.34498 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −19.6827 | −0.713965 | ||||||||
\(761\) | 20.0772 | 0.727799 | 0.363899 | − | 0.931438i | \(-0.381445\pi\) | ||||
0.363899 | + | 0.931438i | \(0.381445\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.6479 | −0.494087 | ||||||||
\(764\) | −3.69535 | −0.133693 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.47515 | 0.342351 | ||||||||
\(767\) | 17.9195 | 0.647037 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.24889 | 0.225341 | 0.112670 | − | 0.993632i | \(-0.464060\pi\) | ||||
0.112670 | + | 0.993632i | \(0.464060\pi\) | |||||||
\(770\) | −19.8931 | −0.716897 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.65239 | 0.275416 | ||||||||
\(773\) | −1.11866 | −0.0402353 | −0.0201176 | − | 0.999798i | \(-0.506404\pi\) | ||||
−0.0201176 | + | 0.999798i | \(0.506404\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.41134 | −0.158460 | ||||||||
\(776\) | −4.78642 | −0.171822 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.01018 | 0.287179 | ||||||||
\(779\) | 3.04807 | 0.109209 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.0036 | 0.501087 | ||||||||
\(782\) | −0.402081 | −0.0143784 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.18367 | −0.149417 | ||||||||
\(785\) | 51.8929 | 1.85214 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37.0689 | 1.32136 | 0.660682 | − | 0.750666i | \(-0.270267\pi\) | ||||
0.660682 | + | 0.750666i | \(0.270267\pi\) | |||||||
\(788\) | −18.2992 | −0.651882 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −42.0408 | −1.49575 | ||||||||
\(791\) | 10.2253 | 0.363570 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.86130 | −0.314674 | ||||||||
\(794\) | −16.4377 | −0.583352 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12.9256 | 0.458134 | ||||||||
\(797\) | −32.5071 | −1.15146 | −0.575730 | − | 0.817640i | \(-0.695282\pi\) | ||||
−0.575730 | + | 0.817640i | \(0.695282\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.62765 | 0.163714 | ||||||||
\(800\) | 2.34593 | 0.0829413 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 17.7661 | 0.627344 | ||||||||
\(803\) | −5.05177 | −0.178273 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.446499 | 0.0157370 | ||||||||
\(806\) | 4.41475 | 0.155503 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.25163 | −0.114392 | ||||||||
\(809\) | 2.43628 | 0.0856552 | 0.0428276 | − | 0.999082i | \(-0.486363\pi\) | ||||
0.0428276 | + | 0.999082i | \(0.486363\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.2685 | −1.34379 | −0.671894 | − | 0.740647i | \(-0.734519\pi\) | ||||
−0.671894 | + | 0.740647i | \(0.734519\pi\) | |||||||
\(812\) | −9.89168 | −0.347130 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 13.7116 | 0.480592 | ||||||||
\(815\) | −17.7006 | −0.620026 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.653862 | 0.0228757 | ||||||||
\(818\) | −24.3199 | −0.850325 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.13760 | −0.0397266 | ||||||||
\(821\) | 0.603988 | 0.0210793 | 0.0105397 | − | 0.999944i | \(-0.496645\pi\) | ||||
0.0105397 | + | 0.999944i | \(0.496645\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.46449 | −0.329911 | −0.164956 | − | 0.986301i | \(-0.552748\pi\) | ||||
−0.164956 | + | 0.986301i | \(0.552748\pi\) | |||||||
\(824\) | −6.91855 | −0.241019 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12.8091 | −0.445684 | ||||||||
\(827\) | −9.04512 | −0.314530 | −0.157265 | − | 0.987556i | \(-0.550268\pi\) | ||||
−0.157265 | + | 0.987556i | \(0.550268\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.2814 | −0.773864 | −0.386932 | − | 0.922108i | \(-0.626465\pi\) | ||||
−0.386932 | + | 0.922108i | \(0.626465\pi\) | |||||||
\(830\) | −40.4159 | −1.40286 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.34775 | −0.0813935 | ||||||||
\(833\) | 17.1362 | 0.593735 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −31.7726 | −1.09954 | ||||||||
\(836\) | 31.7613 | 1.09849 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −23.5738 | −0.814345 | ||||||||
\(839\) | 3.95317 | 0.136479 | 0.0682393 | − | 0.997669i | \(-0.478262\pi\) | ||||
0.0682393 | + | 0.997669i | \(0.478262\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.74221 | 0.198007 | ||||||||
\(842\) | −0.218135 | −0.00751742 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −12.7410 | −0.438563 | ||||||||
\(845\) | −20.2952 | −0.698178 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.6407 | 0.468701 | ||||||||
\(848\) | 12.5105 | 0.429613 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −9.60889 | −0.329582 | ||||||||
\(851\) | −0.307756 | −0.0105498 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.31219 | 0.216125 | 0.108063 | − | 0.994144i | \(-0.465535\pi\) | ||||
0.108063 | + | 0.994144i | \(0.465535\pi\) | |||||||
\(854\) | 6.33414 | 0.216750 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.61340 | 0.0893241 | ||||||||
\(857\) | −22.0163 | −0.752064 | −0.376032 | − | 0.926607i | \(-0.622712\pi\) | ||||
−0.376032 | + | 0.926607i | \(0.622712\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −48.1678 | −1.64346 | −0.821732 | − | 0.569875i | \(-0.806992\pi\) | ||||
−0.821732 | + | 0.569875i | \(0.806992\pi\) | |||||||
\(860\) | −0.244034 | −0.00832147 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 16.3041 | 0.555319 | ||||||||
\(863\) | 23.0500 | 0.784631 | 0.392315 | − | 0.919831i | \(-0.371674\pi\) | ||||
0.392315 | + | 0.919831i | \(0.371674\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.24787 | −0.178433 | ||||||||
\(866\) | 16.4350 | 0.558484 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.15571 | −0.107112 | ||||||||
\(869\) | 67.8399 | 2.30131 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.34152 | −0.248758 | ||||||||
\(872\) | −8.13251 | −0.275402 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.712879 | −0.0241135 | ||||||||
\(875\) | −12.0719 | −0.408106 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.2938 | −1.15802 | −0.579010 | − | 0.815320i | \(-0.696561\pi\) | ||||
−0.579010 | + | 0.815320i | \(0.696561\pi\) | |||||||
\(878\) | −25.1285 | −0.848047 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −11.8539 | −0.399595 | ||||||||
\(881\) | −30.3973 | −1.02411 | −0.512056 | − | 0.858952i | \(-0.671116\pi\) | ||||
−0.512056 | + | 0.858952i | \(0.671116\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.01379 | −0.0677695 | −0.0338847 | − | 0.999426i | \(-0.510788\pi\) | ||||
−0.0338847 | + | 0.999426i | \(0.510788\pi\) | |||||||
\(884\) | 9.61632 | 0.323432 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 26.4593 | 0.888919 | ||||||||
\(887\) | 22.2434 | 0.746859 | 0.373429 | − | 0.927659i | \(-0.378182\pi\) | ||||
0.373429 | + | 0.927659i | \(0.378182\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.08595 | 0.170577 | ||||||||
\(890\) | 19.2803 | 0.646279 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −10.0497 | −0.336490 | ||||||||
\(893\) | 8.20470 | 0.274560 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 36.7410 | 1.22811 | ||||||||
\(896\) | 1.67819 | 0.0560644 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 11.6779 | 0.389695 | ||||||||
\(899\) | 11.0837 | 0.369661 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −51.2429 | −1.70715 | ||||||||
\(902\) | 1.83570 | 0.0611222 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.09305 | 0.202652 | ||||||||
\(905\) | 40.5007 | 1.34629 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.68674 | −0.0560073 | −0.0280036 | − | 0.999608i | \(-0.508915\pi\) | ||||
−0.0280036 | + | 0.999608i | \(0.508915\pi\) | |||||||
\(908\) | 9.51471 | 0.315757 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −10.6786 | −0.353994 | ||||||||
\(911\) | 54.8311 | 1.81664 | 0.908318 | − | 0.418280i | \(-0.137367\pi\) | ||||
0.908318 | + | 0.418280i | \(0.137367\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 65.2178 | 2.15839 | ||||||||
\(914\) | 11.2598 | 0.372440 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17.3081 | 0.571875 | ||||||||
\(917\) | 38.2793 | 1.26409 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −52.9869 | −1.74788 | −0.873939 | − | 0.486036i | \(-0.838442\pi\) | ||||
−0.873939 | + | 0.486036i | \(0.838442\pi\) | |||||||
\(920\) | 0.266060 | 0.00877173 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −14.7144 | −0.484593 | ||||||||
\(923\) | 7.51714 | 0.247430 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.35473 | −0.241822 | ||||||||
\(926\) | 15.2474 | 0.501061 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.89425 | −0.193488 | ||||||||
\(929\) | 5.24290 | 0.172014 | 0.0860069 | − | 0.996295i | \(-0.472589\pi\) | ||||
0.0860069 | + | 0.996295i | \(0.472589\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 30.3821 | 0.995734 | ||||||||
\(932\) | −21.8741 | −0.716511 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −31.9586 | −1.04572 | ||||||||
\(935\) | 48.5533 | 1.58786 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36.5730 | −1.19479 | −0.597393 | − | 0.801948i | \(-0.703797\pi\) | ||||
−0.597393 | + | 0.801948i | \(0.703797\pi\) | |||||||
\(938\) | 5.24779 | 0.171346 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.06215 | −0.0998762 | ||||||||
\(941\) | −24.6596 | −0.803879 | −0.401940 | − | 0.915666i | \(-0.631664\pi\) | ||||
−0.401940 | + | 0.915666i | \(0.631664\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.0412022 | −0.00134173 | ||||||||
\(944\) | −7.63266 | −0.248422 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.393789 | 0.0128032 | ||||||||
\(947\) | −34.3077 | −1.11485 | −0.557425 | − | 0.830227i | \(-0.688211\pi\) | ||||
−0.557425 | + | 0.830227i | \(0.688211\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.71180 | −0.0880287 | ||||||||
\(950\) | −17.0363 | −0.552731 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −6.87383 | −0.222782 | ||||||||
\(953\) | 31.0422 | 1.00556 | 0.502778 | − | 0.864415i | \(-0.332311\pi\) | ||||
0.502778 | + | 0.864415i | \(0.332311\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.0157 | −0.324099 | ||||||||
\(956\) | 25.8220 | 0.835143 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 10.9302 | 0.353138 | ||||||||
\(959\) | 20.8139 | 0.672116 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.4640 | −0.885936 | ||||||||
\(962\) | 7.36042 | 0.237309 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −12.3157 | −0.396663 | ||||||||
\(965\) | 20.7406 | 0.667662 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 56.2492 | 1.80885 | 0.904426 | − | 0.426631i | \(-0.140300\pi\) | ||||
0.904426 | + | 0.426631i | \(0.140300\pi\) | |||||||
\(968\) | 8.12823 | 0.261251 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −12.9728 | −0.416532 | ||||||||
\(971\) | −26.1008 | −0.837614 | −0.418807 | − | 0.908075i | \(-0.637552\pi\) | ||||
−0.418807 | + | 0.908075i | \(0.637552\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 27.1426 | 0.870151 | ||||||||
\(974\) | −34.7186 | −1.11246 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.77438 | 0.120815 | ||||||||
\(977\) | 13.8161 | 0.442015 | 0.221008 | − | 0.975272i | \(-0.429065\pi\) | ||||
0.221008 | + | 0.975272i | \(0.429065\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −31.1121 | −0.994346 | ||||||||
\(980\) | −11.3392 | −0.362217 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −33.3466 | −1.06413 | ||||||||
\(983\) | −1.02013 | −0.0325370 | −0.0162685 | − | 0.999868i | \(-0.505179\pi\) | ||||
−0.0162685 | + | 0.999868i | \(0.505179\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −49.5970 | −1.58029 | ||||||||
\(986\) | 24.1427 | 0.768861 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 17.0495 | 0.542417 | ||||||||
\(989\) | −0.00883857 | −0.000281050 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30.5516 | −0.970502 | −0.485251 | − | 0.874375i | \(-0.661272\pi\) | ||||
−0.485251 | + | 0.874375i | \(0.661272\pi\) | |||||||
\(992\) | −1.88042 | −0.0597034 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5.37332 | −0.170431 | ||||||||
\(995\) | 35.0326 | 1.11061 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.1051 | 0.446714 | 0.223357 | − | 0.974737i | \(-0.428298\pi\) | ||||
0.223357 | + | 0.974737i | \(0.428298\pi\) | |||||||
\(998\) | −23.1107 | −0.731557 | ||||||||
\(999\) | 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 | 8046.2.a.h.1.9 | yes | 9 | |
3.2 | odd | 2 | 8046.2.a.g.1.1 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.g.1.1 | ✓ | 9 | 3.2 | odd | 2 | ||
8046.2.a.h.1.9 | yes | 9 | 1.1 | even | 1 | trivial |