Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7938,2,Mod(1,7938)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7938, 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("7938.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7938 = 2 \cdot 3^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7938.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: | \(63.3852491245\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 1134) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7938.1 |
$q$-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 | ||||||||
\(5\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.24264 | 1.27920 | 0.639602 | − | 0.768706i | \(-0.279099\pi\) | ||||
0.639602 | + | 0.768706i | \(0.279099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.24264 | 0.621997 | 0.310998 | − | 0.950410i | \(-0.399337\pi\) | ||||
0.310998 | + | 0.950410i | \(0.399337\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.24264 | 0.514497 | 0.257249 | − | 0.966345i | \(-0.417184\pi\) | ||||
0.257249 | + | 0.966345i | \(0.417184\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.24264 | −0.904534 | ||||||||
\(23\) | 1.24264 | 0.259108 | 0.129554 | − | 0.991572i | \(-0.458645\pi\) | ||||
0.129554 | + | 0.991572i | \(0.458645\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −1.00000 | ||||||||
\(26\) | −2.24264 | −0.439818 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.24264 | −0.787839 | −0.393919 | − | 0.919145i | \(-0.628881\pi\) | ||||
−0.393919 | + | 0.919145i | \(0.628881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.24264 | −1.66003 | −0.830014 | − | 0.557743i | \(-0.811667\pi\) | ||||
−0.830014 | + | 0.557743i | \(0.811667\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | −0.657596 | −0.328798 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328798 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(38\) | −2.24264 | −0.363804 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.4853 | 1.79370 | 0.896850 | − | 0.442335i | \(-0.145850\pi\) | ||||
0.896850 | + | 0.442335i | \(0.145850\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.4853 | 1.59899 | 0.799495 | − | 0.600672i | \(-0.205100\pi\) | ||||
0.799495 | + | 0.600672i | \(0.205100\pi\) | |||||||
\(44\) | 4.24264 | 0.639602 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.24264 | −0.183217 | ||||||||
\(47\) | 4.75736 | 0.693932 | 0.346966 | − | 0.937878i | \(-0.387212\pi\) | ||||
0.346966 | + | 0.937878i | \(0.387212\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 5.00000 | 0.707107 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.24264 | 0.310998 | ||||||||
\(53\) | 4.24264 | 0.582772 | 0.291386 | − | 0.956606i | \(-0.405884\pi\) | ||||
0.291386 | + | 0.956606i | \(0.405884\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.24264 | 0.557086 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.24264 | 0.287141 | 0.143570 | − | 0.989640i | \(-0.454142\pi\) | ||||
0.143570 | + | 0.989640i | \(0.454142\pi\) | |||||||
\(62\) | 9.24264 | 1.17382 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.242641 | 0.0296433 | 0.0148216 | − | 0.999890i | \(-0.495282\pi\) | ||||
0.0148216 | + | 0.999890i | \(0.495282\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.24264 | −0.147474 | −0.0737372 | − | 0.997278i | \(-0.523493\pi\) | ||||
−0.0737372 | + | 0.997278i | \(0.523493\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.00000 | 0.819288 | 0.409644 | − | 0.912245i | \(-0.365653\pi\) | ||||
0.409644 | + | 0.912245i | \(0.365653\pi\) | |||||||
\(74\) | 4.00000 | 0.464991 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.24264 | 0.257249 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.757359 | 0.0852096 | 0.0426048 | − | 0.999092i | \(-0.486434\pi\) | ||||
0.0426048 | + | 0.999092i | \(0.486434\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −11.4853 | −1.26834 | ||||||||
\(83\) | 16.2426 | 1.78286 | 0.891431 | − | 0.453157i | \(-0.149702\pi\) | ||||
0.891431 | + | 0.453157i | \(0.149702\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −10.4853 | −1.13066 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.24264 | −0.452267 | ||||||||
\(89\) | 11.4853 | 1.21744 | 0.608719 | − | 0.793386i | \(-0.291684\pi\) | ||||
0.608719 | + | 0.793386i | \(0.291684\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.24264 | 0.129554 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.75736 | −0.490684 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.48528 | −0.455411 | −0.227706 | − | 0.973730i | \(-0.573122\pi\) | ||||
−0.227706 | + | 0.973730i | \(0.573122\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.00000 | −0.500000 | ||||||||
\(101\) | 16.2426 | 1.61620 | 0.808102 | − | 0.589043i | \(-0.200495\pi\) | ||||
0.808102 | + | 0.589043i | \(0.200495\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.24264 | −0.910704 | −0.455352 | − | 0.890311i | \(-0.650487\pi\) | ||||
−0.455352 | + | 0.890311i | \(0.650487\pi\) | |||||||
\(104\) | −2.24264 | −0.219909 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.24264 | −0.412082 | ||||||||
\(107\) | −14.4853 | −1.40035 | −0.700173 | − | 0.713974i | \(-0.746894\pi\) | ||||
−0.700173 | + | 0.713974i | \(0.746894\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.24264 | 0.597937 | 0.298968 | − | 0.954263i | \(-0.403358\pi\) | ||||
0.298968 | + | 0.954263i | \(0.403358\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.51472 | 0.330637 | 0.165318 | − | 0.986240i | \(-0.447135\pi\) | ||||
0.165318 | + | 0.986240i | \(0.447135\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.24264 | −0.393919 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | −2.24264 | −0.203039 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.24264 | −0.830014 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.2426 | 1.35257 | 0.676283 | − | 0.736642i | \(-0.263590\pi\) | ||||
0.676283 | + | 0.736642i | \(0.263590\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.2426 | −1.41913 | −0.709563 | − | 0.704642i | \(-0.751108\pi\) | ||||
−0.709563 | + | 0.704642i | \(0.751108\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.242641 | −0.0209610 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.9706 | −1.19359 | −0.596793 | − | 0.802395i | \(-0.703559\pi\) | ||||
−0.596793 | + | 0.802395i | \(0.703559\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.7279 | −1.75812 | −0.879060 | − | 0.476712i | \(-0.841829\pi\) | ||||
−0.879060 | + | 0.476712i | \(0.841829\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.24264 | 0.104280 | ||||||||
\(143\) | 9.51472 | 0.795661 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −7.00000 | −0.579324 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.00000 | −0.328798 | ||||||||
\(149\) | −7.75736 | −0.635508 | −0.317754 | − | 0.948173i | \(-0.602929\pi\) | ||||
−0.317754 | + | 0.948173i | \(0.602929\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.2426 | −0.914913 | −0.457457 | − | 0.889232i | \(-0.651239\pi\) | ||||
−0.457457 | + | 0.889232i | \(0.651239\pi\) | |||||||
\(152\) | −2.24264 | −0.181902 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.0000 | −1.11732 | −0.558661 | − | 0.829396i | \(-0.688685\pi\) | ||||
−0.558661 | + | 0.829396i | \(0.688685\pi\) | |||||||
\(158\) | −0.757359 | −0.0602523 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.2426 | −1.58553 | −0.792763 | − | 0.609530i | \(-0.791358\pi\) | ||||
−0.792763 | + | 0.609530i | \(0.791358\pi\) | |||||||
\(164\) | 11.4853 | 0.896850 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −16.2426 | −1.26067 | ||||||||
\(167\) | −18.2132 | −1.40938 | −0.704690 | − | 0.709515i | \(-0.748914\pi\) | ||||
−0.704690 | + | 0.709515i | \(0.748914\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.97056 | −0.613120 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 10.4853 | 0.799495 | ||||||||
\(173\) | 22.9706 | 1.74642 | 0.873210 | − | 0.487345i | \(-0.162034\pi\) | ||||
0.873210 | + | 0.487345i | \(0.162034\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.24264 | 0.319801 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −11.4853 | −0.860858 | ||||||||
\(179\) | 7.75736 | 0.579812 | 0.289906 | − | 0.957055i | \(-0.406376\pi\) | ||||
0.289906 | + | 0.957055i | \(0.406376\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.7574 | 0.873918 | 0.436959 | − | 0.899482i | \(-0.356056\pi\) | ||||
0.436959 | + | 0.899482i | \(0.356056\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.24264 | −0.0916087 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 4.75736 | 0.346966 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.48528 | 0.613973 | 0.306987 | − | 0.951714i | \(-0.400679\pi\) | ||||
0.306987 | + | 0.951714i | \(0.400679\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.4853 | −1.54654 | −0.773272 | − | 0.634074i | \(-0.781381\pi\) | ||||
−0.773272 | + | 0.634074i | \(0.781381\pi\) | |||||||
\(194\) | 4.48528 | 0.322024 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.9706 | 1.20910 | 0.604551 | − | 0.796566i | \(-0.293352\pi\) | ||||
0.604551 | + | 0.796566i | \(0.293352\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.2426 | 1.64763 | 0.823814 | − | 0.566861i | \(-0.191842\pi\) | ||||
0.823814 | + | 0.566861i | \(0.191842\pi\) | |||||||
\(200\) | 5.00000 | 0.353553 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −16.2426 | −1.14283 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 9.24264 | 0.643965 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.24264 | 0.155499 | ||||||||
\(209\) | 9.51472 | 0.658147 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.4853 | 0.721837 | 0.360918 | − | 0.932597i | \(-0.382463\pi\) | ||||
0.360918 | + | 0.932597i | \(0.382463\pi\) | |||||||
\(212\) | 4.24264 | 0.291386 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 14.4853 | 0.990193 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −6.24264 | −0.422805 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.7279 | 0.919290 | 0.459645 | − | 0.888103i | \(-0.347977\pi\) | ||||
0.459645 | + | 0.888103i | \(0.347977\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.51472 | −0.233796 | ||||||||
\(227\) | 9.51472 | 0.631514 | 0.315757 | − | 0.948840i | \(-0.397742\pi\) | ||||
0.315757 | + | 0.948840i | \(0.397742\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.97056 | 0.592791 | 0.296396 | − | 0.955065i | \(-0.404215\pi\) | ||||
0.296396 | + | 0.955065i | \(0.404215\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.24264 | 0.278543 | ||||||||
\(233\) | −3.51472 | −0.230257 | −0.115128 | − | 0.993351i | \(-0.536728\pi\) | ||||
−0.115128 | + | 0.993351i | \(0.536728\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.7279 | 1.40546 | 0.702731 | − | 0.711455i | \(-0.251964\pi\) | ||||
0.702731 | + | 0.711455i | \(0.251964\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.4853 | −1.64165 | −0.820826 | − | 0.571179i | \(-0.806486\pi\) | ||||
−0.820826 | + | 0.571179i | \(0.806486\pi\) | |||||||
\(242\) | −7.00000 | −0.449977 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.24264 | 0.143570 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.02944 | 0.320015 | ||||||||
\(248\) | 9.24264 | 0.586908 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.72792 | −0.424663 | −0.212331 | − | 0.977198i | \(-0.568106\pi\) | ||||
−0.212331 | + | 0.977198i | \(0.568106\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.27208 | 0.331453 | ||||||||
\(254\) | −15.2426 | −0.956408 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −11.4853 | −0.716432 | −0.358216 | − | 0.933639i | \(-0.616615\pi\) | ||||
−0.358216 | + | 0.933639i | \(0.616615\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 16.2426 | 1.00347 | ||||||||
\(263\) | 10.9706 | 0.676474 | 0.338237 | − | 0.941061i | \(-0.390169\pi\) | ||||
0.338237 | + | 0.941061i | \(0.390169\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.242641 | 0.0148216 | ||||||||
\(269\) | 22.9706 | 1.40054 | 0.700270 | − | 0.713878i | \(-0.253063\pi\) | ||||
0.700270 | + | 0.713878i | \(0.253063\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.48528 | −0.272461 | −0.136231 | − | 0.990677i | \(-0.543499\pi\) | ||||
−0.136231 | + | 0.990677i | \(0.543499\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.9706 | 0.843993 | ||||||||
\(275\) | −21.2132 | −1.27920 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.2132 | 1.39475 | 0.697373 | − | 0.716708i | \(-0.254352\pi\) | ||||
0.697373 | + | 0.716708i | \(0.254352\pi\) | |||||||
\(278\) | 20.7279 | 1.24318 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.4558 | 1.69753 | 0.848767 | − | 0.528768i | \(-0.177346\pi\) | ||||
0.848767 | + | 0.528768i | \(0.177346\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.97056 | 0.533245 | 0.266622 | − | 0.963801i | \(-0.414092\pi\) | ||||
0.266622 | + | 0.963801i | \(0.414092\pi\) | |||||||
\(284\) | −1.24264 | −0.0737372 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.51472 | −0.562617 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.00000 | 0.409644 | ||||||||
\(293\) | 22.9706 | 1.34195 | 0.670977 | − | 0.741478i | \(-0.265875\pi\) | ||||
0.670977 | + | 0.741478i | \(0.265875\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.00000 | 0.232495 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.75736 | 0.449372 | ||||||||
\(299\) | 2.78680 | 0.161165 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 11.2426 | 0.646941 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.24264 | 0.128624 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.0000 | 1.59804 | 0.799022 | − | 0.601302i | \(-0.205351\pi\) | ||||
0.799022 | + | 0.601302i | \(0.205351\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.9706 | 1.30254 | 0.651271 | − | 0.758846i | \(-0.274236\pi\) | ||||
0.651271 | + | 0.758846i | \(0.274236\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.9706 | −0.902710 | −0.451355 | − | 0.892345i | \(-0.649059\pi\) | ||||
−0.451355 | + | 0.892345i | \(0.649059\pi\) | |||||||
\(314\) | 14.0000 | 0.790066 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.757359 | 0.0426048 | ||||||||
\(317\) | −16.9706 | −0.953162 | −0.476581 | − | 0.879131i | \(-0.658124\pi\) | ||||
−0.476581 | + | 0.879131i | \(0.658124\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.0000 | −1.00781 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.2132 | −0.621997 | ||||||||
\(326\) | 20.2426 | 1.12114 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −11.4853 | −0.634169 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.51472 | −0.0832565 | −0.0416282 | − | 0.999133i | \(-0.513255\pi\) | ||||
−0.0416282 | + | 0.999133i | \(0.513255\pi\) | |||||||
\(332\) | 16.2426 | 0.891431 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 18.2132 | 0.996582 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.4853 | −0.680117 | −0.340058 | − | 0.940404i | \(-0.610447\pi\) | ||||
−0.340058 | + | 0.940404i | \(0.610447\pi\) | |||||||
\(338\) | 7.97056 | 0.433541 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −39.2132 | −2.12351 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −10.4853 | −0.565328 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −22.9706 | −1.23491 | ||||||||
\(347\) | −18.7279 | −1.00537 | −0.502684 | − | 0.864470i | \(-0.667654\pi\) | ||||
−0.502684 | + | 0.864470i | \(0.667654\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.97056 | 0.480183 | 0.240092 | − | 0.970750i | \(-0.422823\pi\) | ||||
0.240092 | + | 0.970750i | \(0.422823\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.24264 | −0.226134 | ||||||||
\(353\) | 21.0000 | 1.11772 | 0.558859 | − | 0.829263i | \(-0.311239\pi\) | ||||
0.558859 | + | 0.829263i | \(0.311239\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 11.4853 | 0.608719 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7.75736 | −0.409989 | ||||||||
\(359\) | −19.2426 | −1.01559 | −0.507794 | − | 0.861479i | \(-0.669539\pi\) | ||||
−0.507794 | + | 0.861479i | \(0.669539\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.9706 | −0.735293 | ||||||||
\(362\) | −11.7574 | −0.617953 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.7279 | 0.716592 | 0.358296 | − | 0.933608i | \(-0.383358\pi\) | ||||
0.358296 | + | 0.933608i | \(0.383358\pi\) | |||||||
\(368\) | 1.24264 | 0.0647771 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 35.2132 | 1.82327 | 0.911635 | − | 0.411000i | \(-0.134820\pi\) | ||||
0.911635 | + | 0.411000i | \(0.134820\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.75736 | −0.245342 | ||||||||
\(377\) | −9.51472 | −0.490033 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.7279 | 1.37292 | 0.686461 | − | 0.727167i | \(-0.259163\pi\) | ||||
0.686461 | + | 0.727167i | \(0.259163\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8.48528 | −0.434145 | ||||||||
\(383\) | 18.2132 | 0.930651 | 0.465326 | − | 0.885140i | \(-0.345937\pi\) | ||||
0.465326 | + | 0.885140i | \(0.345937\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 21.4853 | 1.09357 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.48528 | −0.227706 | ||||||||
\(389\) | −1.75736 | −0.0891017 | −0.0445508 | − | 0.999007i | \(-0.514186\pi\) | ||||
−0.0445508 | + | 0.999007i | \(0.514186\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −16.9706 | −0.854965 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.7574 | 0.590085 | 0.295042 | − | 0.955484i | \(-0.404666\pi\) | ||||
0.295042 | + | 0.955484i | \(0.404666\pi\) | |||||||
\(398\) | −23.2426 | −1.16505 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.00000 | −0.250000 | ||||||||
\(401\) | −12.5147 | −0.624955 | −0.312478 | − | 0.949925i | \(-0.601159\pi\) | ||||
−0.312478 | + | 0.949925i | \(0.601159\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.7279 | −1.03253 | ||||||||
\(404\) | 16.2426 | 0.808102 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16.9706 | −0.841200 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −35.0000 | −1.73064 | −0.865319 | − | 0.501221i | \(-0.832884\pi\) | ||||
−0.865319 | + | 0.501221i | \(0.832884\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9.24264 | −0.455352 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.24264 | −0.109955 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −9.51472 | −0.465380 | ||||||||
\(419\) | −16.2426 | −0.793505 | −0.396752 | − | 0.917926i | \(-0.629863\pi\) | ||||
−0.396752 | + | 0.917926i | \(0.629863\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.75736 | −0.280597 | −0.140298 | − | 0.990109i | \(-0.544806\pi\) | ||||
−0.140298 | + | 0.990109i | \(0.544806\pi\) | |||||||
\(422\) | −10.4853 | −0.510416 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.24264 | −0.206041 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −14.4853 | −0.700173 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.7574 | 1.38519 | 0.692597 | − | 0.721325i | \(-0.256467\pi\) | ||||
0.692597 | + | 0.721325i | \(0.256467\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.9706 | 1.44029 | 0.720147 | − | 0.693822i | \(-0.244074\pi\) | ||||
0.720147 | + | 0.693822i | \(0.244074\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.24264 | 0.298968 | ||||||||
\(437\) | 2.78680 | 0.133311 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.7279 | 0.655198 | 0.327599 | − | 0.944817i | \(-0.393761\pi\) | ||||
0.327599 | + | 0.944817i | \(0.393761\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.4853 | −1.25835 | −0.629177 | − | 0.777262i | \(-0.716608\pi\) | ||||
−0.629177 | + | 0.777262i | \(0.716608\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −13.7279 | −0.650036 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.9706 | −1.36721 | −0.683603 | − | 0.729854i | \(-0.739588\pi\) | ||||
−0.683603 | + | 0.729854i | \(0.739588\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 48.7279 | 2.29451 | ||||||||
\(452\) | 3.51472 | 0.165318 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −9.51472 | −0.446548 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.4853 | 1.33249 | 0.666243 | − | 0.745735i | \(-0.267902\pi\) | ||||
0.666243 | + | 0.745735i | \(0.267902\pi\) | |||||||
\(458\) | −8.97056 | −0.419167 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.7574 | 1.19964 | 0.599820 | − | 0.800135i | \(-0.295239\pi\) | ||||
0.599820 | + | 0.800135i | \(0.295239\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.2426 | −0.801333 | −0.400667 | − | 0.916224i | \(-0.631221\pi\) | ||||
−0.400667 | + | 0.916224i | \(0.631221\pi\) | |||||||
\(464\) | −4.24264 | −0.196960 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.51472 | 0.162816 | ||||||||
\(467\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 44.4853 | 2.04544 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.2132 | −0.514497 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −21.7279 | −0.993812 | ||||||||
\(479\) | −4.75736 | −0.217369 | −0.108685 | − | 0.994076i | \(-0.534664\pi\) | ||||
−0.108685 | + | 0.994076i | \(0.534664\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.97056 | −0.409022 | ||||||||
\(482\) | 25.4853 | 1.16082 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.00000 | 0.318182 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.2426 | −0.509453 | −0.254726 | − | 0.967013i | \(-0.581985\pi\) | ||||
−0.254726 | + | 0.967013i | \(0.581985\pi\) | |||||||
\(488\) | −2.24264 | −0.101520 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.7279 | 0.845179 | 0.422590 | − | 0.906321i | \(-0.361121\pi\) | ||||
0.422590 | + | 0.906321i | \(0.361121\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −5.02944 | −0.226285 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9.24264 | −0.415007 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.7279 | 0.659312 | 0.329656 | − | 0.944101i | \(-0.393067\pi\) | ||||
0.329656 | + | 0.944101i | \(0.393067\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.72792 | 0.300282 | ||||||||
\(503\) | 18.2132 | 0.812087 | 0.406043 | − | 0.913854i | \(-0.366908\pi\) | ||||
0.406043 | + | 0.913854i | \(0.366908\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.27208 | −0.234372 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 15.2426 | 0.676283 | ||||||||
\(509\) | 16.2426 | 0.719942 | 0.359971 | − | 0.932963i | \(-0.382787\pi\) | ||||
0.359971 | + | 0.932963i | \(0.382787\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 11.4853 | 0.506594 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.1838 | 0.887681 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −34.4558 | −1.50954 | −0.754769 | − | 0.655991i | \(-0.772251\pi\) | ||||
−0.754769 | + | 0.655991i | \(0.772251\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.7574 | 0.514113 | 0.257057 | − | 0.966396i | \(-0.417247\pi\) | ||||
0.257057 | + | 0.966396i | \(0.417247\pi\) | |||||||
\(524\) | −16.2426 | −0.709563 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.9706 | −0.478339 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.4558 | −0.932863 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 25.7574 | 1.11568 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.242641 | −0.0104805 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −22.9706 | −0.990331 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.9706 | 0.815608 | 0.407804 | − | 0.913069i | \(-0.366295\pi\) | ||||
0.407804 | + | 0.913069i | \(0.366295\pi\) | |||||||
\(542\) | 4.48528 | 0.192659 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.4853 | 0.448318 | 0.224159 | − | 0.974553i | \(-0.428036\pi\) | ||||
0.224159 | + | 0.974553i | \(0.428036\pi\) | |||||||
\(548\) | −13.9706 | −0.596793 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 21.2132 | 0.904534 | ||||||||
\(551\) | −9.51472 | −0.405341 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −23.2132 | −0.986235 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −20.7279 | −0.879060 | ||||||||
\(557\) | 7.02944 | 0.297847 | 0.148923 | − | 0.988849i | \(-0.452419\pi\) | ||||
0.148923 | + | 0.988849i | \(0.452419\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23.5147 | 0.994567 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −28.4558 | −1.20034 | ||||||||
\(563\) | −6.72792 | −0.283548 | −0.141774 | − | 0.989899i | \(-0.545281\pi\) | ||||
−0.141774 | + | 0.989899i | \(0.545281\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −8.97056 | −0.377061 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.24264 | 0.0521400 | ||||||||
\(569\) | 42.9411 | 1.80019 | 0.900093 | − | 0.435698i | \(-0.143499\pi\) | ||||
0.900093 | + | 0.435698i | \(0.143499\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.9706 | 0.542801 | 0.271401 | − | 0.962466i | \(-0.412513\pi\) | ||||
0.271401 | + | 0.962466i | \(0.412513\pi\) | |||||||
\(572\) | 9.51472 | 0.397830 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.21320 | −0.259108 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.9411 | 1.32973 | 0.664863 | − | 0.746965i | \(-0.268490\pi\) | ||||
0.664863 | + | 0.746965i | \(0.268490\pi\) | |||||||
\(578\) | 17.0000 | 0.707107 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.0000 | 0.745484 | ||||||||
\(584\) | −7.00000 | −0.289662 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −22.9706 | −0.948905 | ||||||||
\(587\) | 39.2132 | 1.61850 | 0.809251 | − | 0.587463i | \(-0.199873\pi\) | ||||
0.809251 | + | 0.587463i | \(0.199873\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.7279 | −0.854079 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.00000 | −0.164399 | ||||||||
\(593\) | 11.4853 | 0.471644 | 0.235822 | − | 0.971796i | \(-0.424222\pi\) | ||||
0.235822 | + | 0.971796i | \(0.424222\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.75736 | −0.317754 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.78680 | −0.113961 | ||||||||
\(599\) | 10.9706 | 0.448245 | 0.224123 | − | 0.974561i | \(-0.428048\pi\) | ||||
0.224123 | + | 0.974561i | \(0.428048\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.9706 | −0.651453 | −0.325726 | − | 0.945464i | \(-0.605609\pi\) | ||||
−0.325726 | + | 0.945464i | \(0.605609\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −11.2426 | −0.457457 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.02944 | 0.204139 | 0.102069 | − | 0.994777i | \(-0.467454\pi\) | ||||
0.102069 | + | 0.994777i | \(0.467454\pi\) | |||||||
\(608\) | −2.24264 | −0.0909511 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.6690 | 0.431623 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.9411 | 1.20931 | 0.604655 | − | 0.796487i | \(-0.293311\pi\) | ||||
0.604655 | + | 0.796487i | \(0.293311\pi\) | |||||||
\(614\) | −28.0000 | −1.12999 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.4558 | −0.904038 | −0.452019 | − | 0.892008i | \(-0.649296\pi\) | ||||
−0.452019 | + | 0.892008i | \(0.649296\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.4853 | 0.742986 | 0.371493 | − | 0.928436i | \(-0.378846\pi\) | ||||
0.371493 | + | 0.928436i | \(0.378846\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −22.9706 | −0.921036 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 15.9706 | 0.638312 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −14.0000 | −0.558661 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.51472 | −0.299156 | −0.149578 | − | 0.988750i | \(-0.547792\pi\) | ||||
−0.149578 | + | 0.988750i | \(0.547792\pi\) | |||||||
\(632\) | −0.757359 | −0.0301261 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 16.9706 | 0.673987 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 18.0000 | 0.712627 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −46.4558 | −1.83490 | −0.917448 | − | 0.397856i | \(-0.869754\pi\) | ||||
−0.917448 | + | 0.397856i | \(0.869754\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.2721 | 0.838889 | 0.419444 | − | 0.907781i | \(-0.362225\pi\) | ||||
0.419444 | + | 0.907781i | \(0.362225\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27.7279 | 1.09010 | 0.545049 | − | 0.838404i | \(-0.316511\pi\) | ||||
0.545049 | + | 0.838404i | \(0.316511\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 11.2132 | 0.439818 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −20.2426 | −0.792763 | ||||||||
\(653\) | −24.0000 | −0.939193 | −0.469596 | − | 0.882881i | \(-0.655601\pi\) | ||||
−0.469596 | + | 0.882881i | \(0.655601\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 11.4853 | 0.448425 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.21320 | −0.125169 | −0.0625843 | − | 0.998040i | \(-0.519934\pi\) | ||||
−0.0625843 | + | 0.998040i | \(0.519934\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.1838 | −1.32959 | −0.664797 | − | 0.747024i | \(-0.731482\pi\) | ||||
−0.664797 | + | 0.747024i | \(0.731482\pi\) | |||||||
\(662\) | 1.51472 | 0.0588712 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −16.2426 | −0.630337 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.27208 | −0.204136 | ||||||||
\(668\) | −18.2132 | −0.704690 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.51472 | 0.367312 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.5147 | −0.405313 | −0.202656 | − | 0.979250i | \(-0.564957\pi\) | ||||
−0.202656 | + | 0.979250i | \(0.564957\pi\) | |||||||
\(674\) | 12.4853 | 0.480915 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.97056 | −0.306560 | ||||||||
\(677\) | 25.7574 | 0.989936 | 0.494968 | − | 0.868911i | \(-0.335180\pi\) | ||||
0.494968 | + | 0.868911i | \(0.335180\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 39.2132 | 1.50155 | ||||||||
\(683\) | 17.6985 | 0.677214 | 0.338607 | − | 0.940928i | \(-0.390044\pi\) | ||||
0.338607 | + | 0.940928i | \(0.390044\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 10.4853 | 0.399748 | ||||||||
\(689\) | 9.51472 | 0.362482 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.24264 | 0.0853141 | 0.0426570 | − | 0.999090i | \(-0.486418\pi\) | ||||
0.0426570 | + | 0.999090i | \(0.486418\pi\) | |||||||
\(692\) | 22.9706 | 0.873210 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 18.7279 | 0.710902 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −8.97056 | −0.339541 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.2426 | −0.840093 | −0.420046 | − | 0.907503i | \(-0.637986\pi\) | ||||
−0.420046 | + | 0.907503i | \(0.637986\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.97056 | −0.338331 | ||||||||
\(704\) | 4.24264 | 0.159901 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −21.0000 | −0.790345 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −33.6985 | −1.26557 | −0.632787 | − | 0.774326i | \(-0.718089\pi\) | ||||
−0.632787 | + | 0.774326i | \(0.718089\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11.4853 | −0.430429 | ||||||||
\(713\) | −11.4853 | −0.430127 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.75736 | 0.289906 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 19.2426 | 0.718129 | ||||||||
\(719\) | −27.7279 | −1.03408 | −0.517039 | − | 0.855962i | \(-0.672966\pi\) | ||||
−0.517039 | + | 0.855962i | \(0.672966\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 13.9706 | 0.519931 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 11.7574 | 0.436959 | ||||||||
\(725\) | 21.2132 | 0.787839 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.272078 | 0.0100908 | 0.00504541 | − | 0.999987i | \(-0.498394\pi\) | ||||
0.00504541 | + | 0.999987i | \(0.498394\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.02944 | 0.185767 | 0.0928833 | − | 0.995677i | \(-0.470392\pi\) | ||||
0.0928833 | + | 0.995677i | \(0.470392\pi\) | |||||||
\(734\) | −13.7279 | −0.506707 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.24264 | −0.0458043 | ||||||||
\(737\) | 1.02944 | 0.0379198 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.48528 | −0.238565 | −0.119282 | − | 0.992860i | \(-0.538059\pi\) | ||||
−0.119282 | + | 0.992860i | \(0.538059\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −43.2426 | −1.58642 | −0.793209 | − | 0.608949i | \(-0.791591\pi\) | ||||
−0.793209 | + | 0.608949i | \(0.791591\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −35.2132 | −1.28925 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.75736 | −0.319561 | −0.159780 | − | 0.987153i | \(-0.551079\pi\) | ||||
−0.159780 | + | 0.987153i | \(0.551079\pi\) | |||||||
\(752\) | 4.75736 | 0.173483 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 9.51472 | 0.346506 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.9706 | −0.762188 | −0.381094 | − | 0.924536i | \(-0.624453\pi\) | ||||
−0.381094 | + | 0.924536i | \(0.624453\pi\) | |||||||
\(758\) | −26.7279 | −0.970802 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.0000 | 0.761249 | 0.380625 | − | 0.924730i | \(-0.375709\pi\) | ||||
0.380625 | + | 0.924730i | \(0.375709\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 8.48528 | 0.306987 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −18.2132 | −0.658070 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.48528 | −0.161743 | −0.0808717 | − | 0.996725i | \(-0.525770\pi\) | ||||
−0.0808717 | + | 0.996725i | \(0.525770\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −21.4853 | −0.773272 | ||||||||
\(773\) | −2.78680 | −0.100234 | −0.0501171 | − | 0.998743i | \(-0.515959\pi\) | ||||
−0.0501171 | + | 0.998743i | \(0.515959\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 46.2132 | 1.66003 | ||||||||
\(776\) | 4.48528 | 0.161012 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.75736 | 0.0630044 | ||||||||
\(779\) | 25.7574 | 0.922853 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.27208 | −0.188650 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.2132 | −0.399708 | −0.199854 | − | 0.979826i | \(-0.564047\pi\) | ||||
−0.199854 | + | 0.979826i | \(0.564047\pi\) | |||||||
\(788\) | 16.9706 | 0.604551 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.02944 | 0.178601 | ||||||||
\(794\) | −11.7574 | −0.417253 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 23.2426 | 0.823814 | ||||||||
\(797\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 5.00000 | 0.176777 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 12.5147 | 0.441910 | ||||||||
\(803\) | 29.6985 | 1.04804 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 20.7279 | 0.730110 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −16.2426 | −0.571414 | ||||||||
\(809\) | 9.00000 | 0.316423 | 0.158212 | − | 0.987405i | \(-0.449427\pi\) | ||||
0.158212 | + | 0.987405i | \(0.449427\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.4558 | −0.964105 | −0.482053 | − | 0.876142i | \(-0.660109\pi\) | ||||
−0.482053 | + | 0.876142i | \(0.660109\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 16.9706 | 0.594818 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23.5147 | 0.822676 | ||||||||
\(818\) | 35.0000 | 1.22375 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −44.1838 | −1.54202 | −0.771012 | − | 0.636821i | \(-0.780249\pi\) | ||||
−0.771012 | + | 0.636821i | \(0.780249\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.6985 | −0.651788 | −0.325894 | − | 0.945406i | \(-0.605665\pi\) | ||||
−0.325894 | + | 0.945406i | \(0.605665\pi\) | |||||||
\(824\) | 9.24264 | 0.321983 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.9706 | 0.590124 | 0.295062 | − | 0.955478i | \(-0.404660\pi\) | ||||
0.295062 | + | 0.955478i | \(0.404660\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.9411 | −0.623121 | −0.311561 | − | 0.950226i | \(-0.600852\pi\) | ||||
−0.311561 | + | 0.950226i | \(0.600852\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.24264 | 0.0777496 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 9.51472 | 0.329073 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 16.2426 | 0.561093 | ||||||||
\(839\) | 32.4853 | 1.12152 | 0.560758 | − | 0.827980i | \(-0.310510\pi\) | ||||
0.560758 | + | 0.827980i | \(0.310510\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.0000 | −0.379310 | ||||||||
\(842\) | 5.75736 | 0.198412 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 10.4853 | 0.360918 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.24264 | 0.145693 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.97056 | −0.170389 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 48.1838 | 1.64978 | 0.824890 | − | 0.565293i | \(-0.191237\pi\) | ||||
0.824890 | + | 0.565293i | \(0.191237\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 14.4853 | 0.495097 | ||||||||
\(857\) | 11.4853 | 0.392330 | 0.196165 | − | 0.980571i | \(-0.437151\pi\) | ||||
0.196165 | + | 0.980571i | \(0.437151\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.6985 | 0.535625 | 0.267813 | − | 0.963471i | \(-0.413699\pi\) | ||||
0.267813 | + | 0.963471i | \(0.413699\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −28.7574 | −0.979480 | ||||||||
\(863\) | −42.2132 | −1.43695 | −0.718477 | − | 0.695551i | \(-0.755160\pi\) | ||||
−0.718477 | + | 0.695551i | \(0.755160\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −29.9706 | −1.01844 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.21320 | 0.109000 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.544156 | 0.0184380 | ||||||||
\(872\) | −6.24264 | −0.211402 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.78680 | −0.0942648 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33.6985 | −1.13792 | −0.568958 | − | 0.822366i | \(-0.692653\pi\) | ||||
−0.568958 | + | 0.822366i | \(0.692653\pi\) | |||||||
\(878\) | −13.7279 | −0.463295 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −53.4853 | −1.80196 | −0.900982 | − | 0.433856i | \(-0.857153\pi\) | ||||
−0.900982 | + | 0.433856i | \(0.857153\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.69848 | −0.326380 | −0.163190 | − | 0.986595i | \(-0.552178\pi\) | ||||
−0.163190 | + | 0.986595i | \(0.552178\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 26.4853 | 0.889790 | ||||||||
\(887\) | 14.2721 | 0.479209 | 0.239605 | − | 0.970871i | \(-0.422982\pi\) | ||||
0.239605 | + | 0.970871i | \(0.422982\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13.7279 | 0.459645 | ||||||||
\(893\) | 10.6690 | 0.357026 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 28.9706 | 0.966760 | ||||||||
\(899\) | 39.2132 | 1.30783 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −48.7279 | −1.62246 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.51472 | −0.116898 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29.9411 | 0.994179 | 0.497089 | − | 0.867699i | \(-0.334402\pi\) | ||||
0.497089 | + | 0.867699i | \(0.334402\pi\) | |||||||
\(908\) | 9.51472 | 0.315757 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.7279 | 1.31624 | 0.658122 | − | 0.752911i | \(-0.271351\pi\) | ||||
0.658122 | + | 0.752911i | \(0.271351\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 68.9117 | 2.28064 | ||||||||
\(914\) | −28.4853 | −0.942209 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.97056 | 0.296396 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.4558 | −0.575815 | −0.287908 | − | 0.957658i | \(-0.592960\pi\) | ||||
−0.287908 | + | 0.957658i | \(0.592960\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −25.7574 | −0.848273 | ||||||||
\(923\) | −2.78680 | −0.0917285 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.0000 | 0.657596 | ||||||||
\(926\) | 17.2426 | 0.566628 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.24264 | 0.139272 | ||||||||
\(929\) | −43.9706 | −1.44263 | −0.721314 | − | 0.692609i | \(-0.756461\pi\) | ||||
−0.721314 | + | 0.692609i | \(0.756461\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −3.51472 | −0.115128 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.4558 | 0.668263 | 0.334132 | − | 0.942526i | \(-0.391557\pi\) | ||||
0.334132 | + | 0.942526i | \(0.391557\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 52.6690 | 1.71696 | 0.858481 | − | 0.512845i | \(-0.171409\pi\) | ||||
0.858481 | + | 0.512845i | \(0.171409\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.2721 | 0.464763 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −44.4853 | −1.44634 | ||||||||
\(947\) | 38.4853 | 1.25060 | 0.625302 | − | 0.780383i | \(-0.284976\pi\) | ||||
0.625302 | + | 0.780383i | \(0.284976\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.6985 | 0.509594 | ||||||||
\(950\) | 11.2132 | 0.363804 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23.4853 | 0.760763 | 0.380381 | − | 0.924830i | \(-0.375793\pi\) | ||||
0.380381 | + | 0.924830i | \(0.375793\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 21.7279 | 0.702731 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.75736 | 0.153703 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 54.4264 | 1.75569 | ||||||||
\(962\) | 8.97056 | 0.289223 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −25.4853 | −0.820826 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52.6985 | 1.69467 | 0.847335 | − | 0.531060i | \(-0.178206\pi\) | ||||
0.847335 | + | 0.531060i | \(0.178206\pi\) | |||||||
\(968\) | −7.00000 | −0.224989 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.51472 | −0.305342 | −0.152671 | − | 0.988277i | \(-0.548787\pi\) | ||||
−0.152671 | + | 0.988277i | \(0.548787\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 11.2426 | 0.360237 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.24264 | 0.0717852 | ||||||||
\(977\) | −19.9706 | −0.638915 | −0.319457 | − | 0.947601i | \(-0.603501\pi\) | ||||
−0.319457 | + | 0.947601i | \(0.603501\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 48.7279 | 1.55735 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −18.7279 | −0.597632 | ||||||||
\(983\) | −32.4853 | −1.03612 | −0.518060 | − | 0.855344i | \(-0.673346\pi\) | ||||
−0.518060 | + | 0.855344i | \(0.673346\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.02944 | 0.160008 | ||||||||
\(989\) | 13.0294 | 0.414312 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.78680 | 0.247356 | 0.123678 | − | 0.992322i | \(-0.460531\pi\) | ||||
0.123678 | + | 0.992322i | \(0.460531\pi\) | |||||||
\(992\) | 9.24264 | 0.293454 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.0000 | −0.443384 | −0.221692 | − | 0.975117i | \(-0.571158\pi\) | ||||
−0.221692 | + | 0.975117i | \(0.571158\pi\) | |||||||
\(998\) | −14.7279 | −0.466204 | ||||||||
\(999\) | 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 | 7938.2.a.bj.1.2 | 2 | ||
3.2 | odd | 2 | 7938.2.a.bp.1.1 | 2 | |||
7.3 | odd | 6 | 1134.2.g.j.163.2 | yes | 4 | ||
7.5 | odd | 6 | 1134.2.g.j.487.2 | yes | 4 | ||
7.6 | odd | 2 | 7938.2.a.bk.1.2 | 2 | |||
21.5 | even | 6 | 1134.2.g.i.487.2 | yes | 4 | ||
21.17 | even | 6 | 1134.2.g.i.163.2 | ✓ | 4 | ||
21.20 | even | 2 | 7938.2.a.bq.1.1 | 2 | |||
63.5 | even | 6 | 1134.2.e.s.865.1 | 4 | |||
63.31 | odd | 6 | 1134.2.h.s.541.2 | 4 | |||
63.38 | even | 6 | 1134.2.e.s.919.1 | 4 | |||
63.40 | odd | 6 | 1134.2.e.r.865.1 | 4 | |||
63.47 | even | 6 | 1134.2.h.r.109.1 | 4 | |||
63.52 | odd | 6 | 1134.2.e.r.919.1 | 4 | |||
63.59 | even | 6 | 1134.2.h.r.541.2 | 4 | |||
63.61 | odd | 6 | 1134.2.h.s.109.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1134.2.e.r.865.1 | 4 | 63.40 | odd | 6 | |||
1134.2.e.r.919.1 | 4 | 63.52 | odd | 6 | |||
1134.2.e.s.865.1 | 4 | 63.5 | even | 6 | |||
1134.2.e.s.919.1 | 4 | 63.38 | even | 6 | |||
1134.2.g.i.163.2 | ✓ | 4 | 21.17 | even | 6 | ||
1134.2.g.i.487.2 | yes | 4 | 21.5 | even | 6 | ||
1134.2.g.j.163.2 | yes | 4 | 7.3 | odd | 6 | ||
1134.2.g.j.487.2 | yes | 4 | 7.5 | odd | 6 | ||
1134.2.h.r.109.1 | 4 | 63.47 | even | 6 | |||
1134.2.h.r.541.2 | 4 | 63.59 | even | 6 | |||
1134.2.h.s.109.1 | 4 | 63.61 | odd | 6 | |||
1134.2.h.s.541.2 | 4 | 63.31 | odd | 6 | |||
7938.2.a.bj.1.2 | 2 | 1.1 | even | 1 | trivial | ||
7938.2.a.bk.1.2 | 2 | 7.6 | odd | 2 | |||
7938.2.a.bp.1.1 | 2 | 3.2 | odd | 2 | |||
7938.2.a.bq.1.1 | 2 | 21.20 | even | 2 |