Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5625,2,Mod(1,5625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5625, 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("5625.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5625 = 3^{2} \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5625.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: | \(44.9158511370\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.46840000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 11x^{4} + 8x^{3} + 31x^{2} - 15x - 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1875) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(2.78712\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5625.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.78712 | 1.97079 | 0.985395 | − | 0.170281i | \(-0.0544677\pi\) | ||||
0.985395 | + | 0.170281i | \(0.0544677\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.76803 | 2.88402 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.15000 | 1.19059 | 0.595294 | − | 0.803508i | \(-0.297036\pi\) | ||||
0.595294 | + | 0.803508i | \(0.297036\pi\) | |||||||
\(8\) | 10.5020 | 3.71300 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.94681 | −0.888496 | −0.444248 | − | 0.895904i | \(-0.646529\pi\) | ||||
−0.444248 | + | 0.895904i | \(0.646529\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.188171 | −0.0521891 | −0.0260946 | − | 0.999659i | \(-0.508307\pi\) | ||||
−0.0260946 | + | 0.999659i | \(0.508307\pi\) | |||||||
\(14\) | 8.77943 | 2.34640 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 17.7341 | 4.43354 | ||||||||
\(17\) | 2.62743 | 0.637246 | 0.318623 | − | 0.947882i | \(-0.396780\pi\) | ||||
0.318623 | + | 0.947882i | \(0.396780\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.94100 | 0.445296 | 0.222648 | − | 0.974899i | \(-0.428530\pi\) | ||||
0.222648 | + | 0.974899i | \(0.428530\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8.21310 | −1.75104 | ||||||||
\(23\) | −1.30447 | −0.272000 | −0.136000 | − | 0.990709i | \(-0.543425\pi\) | ||||
−0.136000 | + | 0.990709i | \(0.543425\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.524454 | −0.102854 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 18.1693 | 3.43368 | ||||||||
\(29\) | −1.23197 | −0.228770 | −0.114385 | − | 0.993436i | \(-0.536490\pi\) | ||||
−0.114385 | + | 0.993436i | \(0.536490\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.65174 | 0.476266 | 0.238133 | − | 0.971233i | \(-0.423465\pi\) | ||||
0.238133 | + | 0.971233i | \(0.423465\pi\) | |||||||
\(32\) | 28.4233 | 5.02457 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.32297 | 1.25588 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.1161 | −1.66308 | −0.831540 | − | 0.555466i | \(-0.812540\pi\) | ||||
−0.831540 | + | 0.555466i | \(0.812540\pi\) | |||||||
\(38\) | 5.40980 | 0.877585 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.85940 | −0.602737 | −0.301368 | − | 0.953508i | \(-0.597443\pi\) | ||||
−0.301368 | + | 0.953508i | \(0.597443\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.63734 | 1.46968 | 0.734840 | − | 0.678240i | \(-0.237257\pi\) | ||||
0.734840 | + | 0.678240i | \(0.237257\pi\) | |||||||
\(44\) | −16.9973 | −2.56244 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.63570 | −0.536055 | ||||||||
\(47\) | −11.9846 | −1.74814 | −0.874068 | − | 0.485804i | \(-0.838527\pi\) | ||||
−0.874068 | + | 0.485804i | \(0.838527\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.92250 | 0.417500 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.08537 | −0.150514 | ||||||||
\(53\) | 0.369521 | 0.0507576 | 0.0253788 | − | 0.999678i | \(-0.491921\pi\) | ||||
0.0253788 | + | 0.999678i | \(0.491921\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 33.0812 | 4.42066 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.43364 | −0.450859 | ||||||||
\(59\) | 6.90864 | 0.899428 | 0.449714 | − | 0.893173i | \(-0.351526\pi\) | ||||
0.449714 | + | 0.893173i | \(0.351526\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.68643 | 0.728073 | 0.364037 | − | 0.931385i | \(-0.381398\pi\) | ||||
0.364037 | + | 0.931385i | \(0.381398\pi\) | |||||||
\(62\) | 7.39071 | 0.938621 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 43.7507 | 5.46884 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.24188 | −0.396058 | −0.198029 | − | 0.980196i | \(-0.563454\pi\) | ||||
−0.198029 | + | 0.980196i | \(0.563454\pi\) | |||||||
\(68\) | 15.1551 | 1.83783 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.69982 | −0.795122 | −0.397561 | − | 0.917576i | \(-0.630143\pi\) | ||||
−0.397561 | + | 0.917576i | \(0.630143\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.46938 | 1.10831 | 0.554153 | − | 0.832415i | \(-0.313042\pi\) | ||||
0.554153 | + | 0.832415i | \(0.313042\pi\) | |||||||
\(74\) | −28.1948 | −3.27758 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 11.1957 | 1.28424 | ||||||||
\(77\) | −9.28244 | −1.05783 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.420137 | 0.0472691 | 0.0236345 | − | 0.999721i | \(-0.492476\pi\) | ||||
0.0236345 | + | 0.999721i | \(0.492476\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −10.7566 | −1.18787 | ||||||||
\(83\) | −12.1635 | −1.33512 | −0.667559 | − | 0.744557i | \(-0.732661\pi\) | ||||
−0.667559 | + | 0.744557i | \(0.732661\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 26.8604 | 2.89643 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −30.9473 | −3.29899 | ||||||||
\(89\) | 15.1828 | 1.60937 | 0.804687 | − | 0.593699i | \(-0.202333\pi\) | ||||
0.804687 | + | 0.593699i | \(0.202333\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.592737 | −0.0621358 | ||||||||
\(92\) | −7.52421 | −0.784453 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −33.4025 | −3.44521 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.9035 | −1.41169 | −0.705845 | − | 0.708367i | \(-0.749432\pi\) | ||||
−0.705845 | + | 0.708367i | \(0.749432\pi\) | |||||||
\(98\) | 8.14536 | 0.822805 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.67188 | 0.962388 | 0.481194 | − | 0.876614i | \(-0.340203\pi\) | ||||
0.481194 | + | 0.876614i | \(0.340203\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.69434 | −0.856679 | −0.428339 | − | 0.903618i | \(-0.640901\pi\) | ||||
−0.428339 | + | 0.903618i | \(0.640901\pi\) | |||||||
\(104\) | −1.97616 | −0.193778 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.02990 | 0.100033 | ||||||||
\(107\) | −2.56585 | −0.248050 | −0.124025 | − | 0.992279i | \(-0.539580\pi\) | ||||
−0.124025 | + | 0.992279i | \(0.539580\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.2352 | −1.45926 | −0.729632 | − | 0.683840i | \(-0.760309\pi\) | ||||
−0.729632 | + | 0.683840i | \(0.760309\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 55.8626 | 5.27852 | ||||||||
\(113\) | 2.20391 | 0.207326 | 0.103663 | − | 0.994612i | \(-0.466944\pi\) | ||||
0.103663 | + | 0.994612i | \(0.466944\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.10602 | −0.659778 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 19.2552 | 1.77258 | ||||||||
\(119\) | 8.27641 | 0.758697 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.31633 | −0.210575 | ||||||||
\(122\) | 15.8488 | 1.43488 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 15.2953 | 1.37356 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.9689 | 1.32827 | 0.664136 | − | 0.747611i | \(-0.268799\pi\) | ||||
0.664136 | + | 0.747611i | \(0.268799\pi\) | |||||||
\(128\) | 65.0920 | 5.75337 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.2957 | −0.986911 | −0.493456 | − | 0.869771i | \(-0.664266\pi\) | ||||
−0.493456 | + | 0.869771i | \(0.664266\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.11415 | 0.530164 | ||||||||
\(134\) | −9.03550 | −0.780548 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 27.5932 | 2.36610 | ||||||||
\(137\) | 4.17877 | 0.357017 | 0.178508 | − | 0.983938i | \(-0.442873\pi\) | ||||
0.178508 | + | 0.983938i | \(0.442873\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.3552 | −1.30241 | −0.651207 | − | 0.758900i | \(-0.725737\pi\) | ||||
−0.651207 | + | 0.758900i | \(0.725737\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −18.6732 | −1.56702 | ||||||||
\(143\) | 0.554502 | 0.0463698 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 26.3923 | 2.18424 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −58.3501 | −4.79635 | ||||||||
\(149\) | −3.43364 | −0.281294 | −0.140647 | − | 0.990060i | \(-0.544918\pi\) | ||||
−0.140647 | + | 0.990060i | \(0.544918\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.7716 | 0.876581 | 0.438290 | − | 0.898833i | \(-0.355584\pi\) | ||||
0.438290 | + | 0.898833i | \(0.355584\pi\) | |||||||
\(152\) | 20.3843 | 1.65338 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −25.8713 | −2.08477 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.4045 | 1.06980 | 0.534900 | − | 0.844916i | \(-0.320349\pi\) | ||||
0.534900 | + | 0.844916i | \(0.320349\pi\) | |||||||
\(158\) | 1.17097 | 0.0931574 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.10907 | −0.323840 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.4178 | 1.20762 | 0.603808 | − | 0.797129i | \(-0.293649\pi\) | ||||
0.603808 | + | 0.797129i | \(0.293649\pi\) | |||||||
\(164\) | −22.2611 | −1.73830 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −33.9011 | −2.63124 | ||||||||
\(167\) | 17.4045 | 1.34680 | 0.673402 | − | 0.739276i | \(-0.264832\pi\) | ||||
0.673402 | + | 0.739276i | \(0.264832\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9646 | −0.997276 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 55.5885 | 4.23858 | ||||||||
\(173\) | −19.2737 | −1.46535 | −0.732676 | − | 0.680578i | \(-0.761729\pi\) | ||||
−0.732676 | + | 0.680578i | \(0.761729\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −52.2591 | −3.93918 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 42.3163 | 3.17174 | ||||||||
\(179\) | −23.7940 | −1.77845 | −0.889223 | − | 0.457475i | \(-0.848754\pi\) | ||||
−0.889223 | + | 0.457475i | \(0.848754\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.6891 | −0.794516 | −0.397258 | − | 0.917707i | \(-0.630038\pi\) | ||||
−0.397258 | + | 0.917707i | \(0.630038\pi\) | |||||||
\(182\) | −1.65203 | −0.122457 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −13.6995 | −1.00994 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.74253 | −0.566190 | ||||||||
\(188\) | −69.1277 | −5.04165 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.3581 | 1.03892 | 0.519458 | − | 0.854496i | \(-0.326134\pi\) | ||||
0.519458 | + | 0.854496i | \(0.326134\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.95508 | −0.140730 | −0.0703648 | − | 0.997521i | \(-0.522416\pi\) | ||||
−0.0703648 | + | 0.997521i | \(0.522416\pi\) | |||||||
\(194\) | −38.7508 | −2.78214 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 16.8571 | 1.20408 | ||||||||
\(197\) | −1.17958 | −0.0840417 | −0.0420209 | − | 0.999117i | \(-0.513380\pi\) | ||||
−0.0420209 | + | 0.999117i | \(0.513380\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.55820 | −0.464899 | −0.232449 | − | 0.972608i | \(-0.574674\pi\) | ||||
−0.232449 | + | 0.972608i | \(0.574674\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 26.9567 | 1.89666 | ||||||||
\(203\) | −3.88069 | −0.272371 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −24.2322 | −1.68833 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.33705 | −0.231382 | ||||||||
\(209\) | −5.71975 | −0.395643 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.3573 | 0.850715 | 0.425357 | − | 0.905026i | \(-0.360148\pi\) | ||||
0.425357 | + | 0.905026i | \(0.360148\pi\) | |||||||
\(212\) | 2.13141 | 0.146386 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7.15134 | −0.488856 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.35298 | 0.567037 | ||||||||
\(218\) | −42.4622 | −2.87591 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.494405 | −0.0332573 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.30693 | 0.489308 | 0.244654 | − | 0.969610i | \(-0.421326\pi\) | ||||
0.244654 | + | 0.969610i | \(0.421326\pi\) | |||||||
\(224\) | 89.5333 | 5.98219 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.14256 | 0.408597 | ||||||||
\(227\) | −21.0202 | −1.39516 | −0.697579 | − | 0.716508i | \(-0.745739\pi\) | ||||
−0.697579 | + | 0.716508i | \(0.745739\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.5544 | 1.29219 | 0.646094 | − | 0.763258i | \(-0.276401\pi\) | ||||
0.646094 | + | 0.763258i | \(0.276401\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −12.9381 | −0.849425 | ||||||||
\(233\) | 12.1472 | 0.795792 | 0.397896 | − | 0.917430i | \(-0.369740\pi\) | ||||
0.397896 | + | 0.917430i | \(0.369740\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 39.8493 | 2.59397 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 23.0673 | 1.49523 | ||||||||
\(239\) | −13.4517 | −0.870119 | −0.435059 | − | 0.900402i | \(-0.643273\pi\) | ||||
−0.435059 | + | 0.900402i | \(0.643273\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.9370 | 1.28426 | 0.642129 | − | 0.766597i | \(-0.278051\pi\) | ||||
0.642129 | + | 0.766597i | \(0.278051\pi\) | |||||||
\(242\) | −6.45588 | −0.415000 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 32.7995 | 2.09978 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.365239 | −0.0232396 | ||||||||
\(248\) | 27.8485 | 1.76838 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.76013 | 0.174218 | 0.0871088 | − | 0.996199i | \(-0.472237\pi\) | ||||
0.0871088 | + | 0.996199i | \(0.472237\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.84401 | 0.241671 | ||||||||
\(254\) | 41.7200 | 2.61775 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 93.9177 | 5.86986 | ||||||||
\(257\) | −17.2848 | −1.07820 | −0.539098 | − | 0.842243i | \(-0.681235\pi\) | ||||
−0.539098 | + | 0.842243i | \(0.681235\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −31.8658 | −1.98004 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −31.4825 | −1.94500 | ||||||||
\(263\) | −3.96578 | −0.244541 | −0.122270 | − | 0.992497i | \(-0.539017\pi\) | ||||
−0.122270 | + | 0.992497i | \(0.539017\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 17.0409 | 1.04484 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −18.6993 | −1.14224 | ||||||||
\(269\) | −1.19564 | −0.0728993 | −0.0364496 | − | 0.999335i | \(-0.511605\pi\) | ||||
−0.0364496 | + | 0.999335i | \(0.511605\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.18295 | −0.132605 | −0.0663023 | − | 0.997800i | \(-0.521120\pi\) | ||||
−0.0663023 | + | 0.997800i | \(0.521120\pi\) | |||||||
\(272\) | 46.5953 | 2.82525 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.6467 | 0.703605 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.95174 | −0.117268 | −0.0586342 | − | 0.998280i | \(-0.518675\pi\) | ||||
−0.0586342 | + | 0.998280i | \(0.518675\pi\) | |||||||
\(278\) | −42.7969 | −2.56679 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.30131 | −0.137284 | −0.0686422 | − | 0.997641i | \(-0.521867\pi\) | ||||
−0.0686422 | + | 0.997641i | \(0.521867\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.6459 | 0.632835 | 0.316417 | − | 0.948620i | \(-0.397520\pi\) | ||||
0.316417 | + | 0.948620i | \(0.397520\pi\) | |||||||
\(284\) | −38.6448 | −2.29315 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.54546 | 0.0913852 | ||||||||
\(287\) | −12.1571 | −0.717611 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.0966 | −0.593918 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 54.6197 | 3.19638 | ||||||||
\(293\) | 14.9591 | 0.873921 | 0.436960 | − | 0.899481i | \(-0.356055\pi\) | ||||
0.436960 | + | 0.899481i | \(0.356055\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −106.239 | −6.17502 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.56995 | −0.554373 | ||||||||
\(299\) | 0.245462 | 0.0141954 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 30.3576 | 1.74978 | ||||||||
\(302\) | 30.0217 | 1.72756 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 34.4220 | 1.97424 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.07333 | 0.175404 | 0.0877021 | − | 0.996147i | \(-0.472048\pi\) | ||||
0.0877021 | + | 0.996147i | \(0.472048\pi\) | |||||||
\(308\) | −53.5414 | −3.05081 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.9095 | −1.41249 | −0.706244 | − | 0.707968i | \(-0.749612\pi\) | ||||
−0.706244 | + | 0.707968i | \(0.749612\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.28562 | −0.524854 | −0.262427 | − | 0.964952i | \(-0.584523\pi\) | ||||
−0.262427 | + | 0.964952i | \(0.584523\pi\) | |||||||
\(314\) | 37.3601 | 2.10835 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.42336 | 0.136325 | ||||||||
\(317\) | 20.7685 | 1.16647 | 0.583237 | − | 0.812302i | \(-0.301786\pi\) | ||||
0.583237 | + | 0.812302i | \(0.301786\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.63037 | 0.203261 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −11.4525 | −0.638221 | ||||||||
\(323\) | 5.09984 | 0.283763 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 42.9713 | 2.37996 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −40.5312 | −2.23796 | ||||||||
\(329\) | −37.7515 | −2.08131 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −33.9172 | −1.86426 | −0.932128 | − | 0.362129i | \(-0.882050\pi\) | ||||
−0.932128 | + | 0.362129i | \(0.882050\pi\) | |||||||
\(332\) | −70.1595 | −3.85050 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 48.5085 | 2.65427 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.7792 | −0.968494 | −0.484247 | − | 0.874931i | \(-0.660906\pi\) | ||||
−0.484247 | + | 0.874931i | \(0.660906\pi\) | |||||||
\(338\) | −36.1339 | −1.96542 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.81416 | −0.423161 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.8441 | −0.693518 | ||||||||
\(344\) | 101.211 | 5.45693 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −53.7181 | −2.88790 | ||||||||
\(347\) | −12.2251 | −0.656277 | −0.328138 | − | 0.944630i | \(-0.606421\pi\) | ||||
−0.328138 | + | 0.944630i | \(0.606421\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.8425 | 0.687441 | 0.343720 | − | 0.939072i | \(-0.388313\pi\) | ||||
0.343720 | + | 0.939072i | \(0.388313\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −83.7579 | −4.46431 | ||||||||
\(353\) | 17.4163 | 0.926976 | 0.463488 | − | 0.886103i | \(-0.346598\pi\) | ||||
0.463488 | + | 0.886103i | \(0.346598\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 87.5749 | 4.64146 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −66.3167 | −3.50494 | ||||||||
\(359\) | 3.82947 | 0.202111 | 0.101056 | − | 0.994881i | \(-0.467778\pi\) | ||||
0.101056 | + | 0.994881i | \(0.467778\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.2325 | −0.801712 | ||||||||
\(362\) | −29.7918 | −1.56582 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.41893 | −0.179201 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.6282 | 1.54658 | 0.773289 | − | 0.634054i | \(-0.218610\pi\) | ||||
0.773289 | + | 0.634054i | \(0.218610\pi\) | |||||||
\(368\) | −23.1336 | −1.20592 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.16399 | 0.0604314 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.4595 | −0.593350 | −0.296675 | − | 0.954978i | \(-0.595878\pi\) | ||||
−0.296675 | + | 0.954978i | \(0.595878\pi\) | |||||||
\(374\) | −21.5794 | −1.11584 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −125.862 | −6.49083 | ||||||||
\(377\) | 0.231820 | 0.0119393 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.19307 | −0.112650 | −0.0563251 | − | 0.998412i | \(-0.517938\pi\) | ||||
−0.0563251 | + | 0.998412i | \(0.517938\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 40.0177 | 2.04749 | ||||||||
\(383\) | −10.1997 | −0.521181 | −0.260591 | − | 0.965449i | \(-0.583917\pi\) | ||||
−0.260591 | + | 0.965449i | \(0.583917\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.44904 | −0.277349 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −80.1960 | −4.07134 | ||||||||
\(389\) | −28.5482 | −1.44745 | −0.723726 | − | 0.690088i | \(-0.757572\pi\) | ||||
−0.723726 | + | 0.690088i | \(0.757572\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.42740 | −0.173331 | ||||||||
\(392\) | 30.6920 | 1.55018 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.28764 | −0.165629 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −37.1827 | −1.86614 | −0.933072 | − | 0.359688i | \(-0.882883\pi\) | ||||
−0.933072 | + | 0.359688i | \(0.882883\pi\) | |||||||
\(398\) | −18.2785 | −0.916218 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.38648 | −0.368863 | −0.184432 | − | 0.982845i | \(-0.559044\pi\) | ||||
−0.184432 | + | 0.982845i | \(0.559044\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.498979 | −0.0248559 | ||||||||
\(404\) | 55.7877 | 2.77554 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.8160 | −0.536787 | ||||||||
\(407\) | 29.8102 | 1.47764 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.19942 | −0.257095 | −0.128547 | − | 0.991703i | \(-0.541031\pi\) | ||||
−0.128547 | + | 0.991703i | \(0.541031\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −50.1492 | −2.47068 | ||||||||
\(413\) | 21.7622 | 1.07085 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5.34842 | −0.262228 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −15.9416 | −0.779730 | ||||||||
\(419\) | 14.9205 | 0.728914 | 0.364457 | − | 0.931220i | \(-0.381255\pi\) | ||||
0.364457 | + | 0.931220i | \(0.381255\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.0666925 | −0.00325039 | −0.00162520 | − | 0.999999i | \(-0.500517\pi\) | ||||
−0.00162520 | + | 0.999999i | \(0.500517\pi\) | |||||||
\(422\) | 34.4414 | 1.67658 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.88069 | 0.188463 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.9123 | 0.866835 | ||||||||
\(428\) | −14.7999 | −0.715382 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.6996 | −1.33424 | −0.667121 | − | 0.744950i | \(-0.732473\pi\) | ||||
−0.667121 | + | 0.744950i | \(0.732473\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.5626 | 1.46874 | 0.734372 | − | 0.678748i | \(-0.237477\pi\) | ||||
0.734372 | + | 0.678748i | \(0.237477\pi\) | |||||||
\(434\) | 23.2807 | 1.11751 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −87.8770 | −4.20854 | ||||||||
\(437\) | −2.53197 | −0.121120 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.0968 | 0.529623 | 0.264812 | − | 0.964300i | \(-0.414690\pi\) | ||||
0.264812 | + | 0.964300i | \(0.414690\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.37797 | −0.0655432 | ||||||||
\(443\) | −9.82831 | −0.466957 | −0.233479 | − | 0.972362i | \(-0.575011\pi\) | ||||
−0.233479 | + | 0.972362i | \(0.575011\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 20.3653 | 0.964324 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 137.815 | 6.51114 | ||||||||
\(449\) | 19.1301 | 0.902805 | 0.451402 | − | 0.892320i | \(-0.350924\pi\) | ||||
0.451402 | + | 0.892320i | \(0.350924\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.3729 | 0.535529 | ||||||||
\(452\) | 12.7122 | 0.597933 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −58.5858 | −2.74957 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.7578 | −0.877452 | −0.438726 | − | 0.898621i | \(-0.644570\pi\) | ||||
−0.438726 | + | 0.898621i | \(0.644570\pi\) | |||||||
\(458\) | 54.5003 | 2.54663 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 37.6208 | 1.75217 | 0.876087 | − | 0.482153i | \(-0.160145\pi\) | ||||
0.876087 | + | 0.482153i | \(0.160145\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.9275 | 0.926111 | 0.463056 | − | 0.886329i | \(-0.346753\pi\) | ||||
0.463056 | + | 0.886329i | \(0.346753\pi\) | |||||||
\(464\) | −21.8479 | −1.01426 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 33.8558 | 1.56834 | ||||||||
\(467\) | 27.3667 | 1.26638 | 0.633190 | − | 0.773997i | \(-0.281745\pi\) | ||||
0.633190 | + | 0.773997i | \(0.281745\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.2119 | −0.471542 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 72.5542 | 3.33958 | ||||||||
\(473\) | −28.3994 | −1.30581 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 47.7386 | 2.18810 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −37.4915 | −1.71482 | ||||||||
\(479\) | 38.5742 | 1.76250 | 0.881250 | − | 0.472650i | \(-0.156703\pi\) | ||||
0.881250 | + | 0.472650i | \(0.156703\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.90356 | 0.0867946 | ||||||||
\(482\) | 55.5669 | 2.53100 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13.3607 | −0.607303 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.4995 | 0.838294 | 0.419147 | − | 0.907918i | \(-0.362329\pi\) | ||||
0.419147 | + | 0.907918i | \(0.362329\pi\) | |||||||
\(488\) | 59.7187 | 2.70334 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.7211 | −0.890000 | −0.445000 | − | 0.895531i | \(-0.646796\pi\) | ||||
−0.445000 | + | 0.895531i | \(0.646796\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.23691 | −0.145783 | ||||||||
\(494\) | −1.01796 | −0.0458004 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 47.0263 | 2.11154 | ||||||||
\(497\) | −21.1044 | −0.946663 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −36.2906 | −1.62459 | −0.812296 | − | 0.583245i | \(-0.801783\pi\) | ||||
−0.812296 | + | 0.583245i | \(0.801783\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7.69280 | 0.343347 | ||||||||
\(503\) | 2.66163 | 0.118676 | 0.0593382 | − | 0.998238i | \(-0.481101\pi\) | ||||
0.0593382 | + | 0.998238i | \(0.481101\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 10.7137 | 0.476283 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 86.3410 | 3.83076 | ||||||||
\(509\) | −22.8322 | −1.01202 | −0.506010 | − | 0.862528i | \(-0.668880\pi\) | ||||
−0.506010 | + | 0.862528i | \(0.668880\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 29.8285 | 1.31954 | ||||||||
\(512\) | 131.576 | 5.81488 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −48.1748 | −2.12490 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 35.3163 | 1.55321 | ||||||||
\(518\) | −88.8137 | −3.90225 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.3029 | 0.539001 | 0.269501 | − | 0.963000i | \(-0.413141\pi\) | ||||
0.269501 | + | 0.963000i | \(0.413141\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.3902 | 1.46005 | 0.730025 | − | 0.683420i | \(-0.239508\pi\) | ||||
0.730025 | + | 0.683420i | \(0.239508\pi\) | |||||||
\(524\) | −65.1541 | −2.84627 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.0531 | −0.481939 | ||||||||
\(527\) | 6.96726 | 0.303499 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.2984 | −0.926016 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 35.2666 | 1.52900 | ||||||||
\(533\) | 0.726225 | 0.0314563 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −34.0461 | −1.47057 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.33238 | −0.143669 | ||||||||
\(539\) | −8.61204 | −0.370947 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.98673 | 0.257389 | 0.128695 | − | 0.991684i | \(-0.458921\pi\) | ||||
0.128695 | + | 0.991684i | \(0.458921\pi\) | |||||||
\(542\) | −6.08413 | −0.261336 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 74.6802 | 3.20189 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.47889 | −0.191503 | −0.0957516 | − | 0.995405i | \(-0.530525\pi\) | ||||
−0.0957516 | + | 0.995405i | \(0.530525\pi\) | |||||||
\(548\) | 24.1033 | 1.02964 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.39124 | −0.101870 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.32343 | 0.0562780 | ||||||||
\(554\) | −5.43972 | −0.231112 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −88.5695 | −3.75618 | ||||||||
\(557\) | −14.4278 | −0.611326 | −0.305663 | − | 0.952140i | \(-0.598878\pi\) | ||||
−0.305663 | + | 0.952140i | \(0.598878\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.81346 | −0.0767014 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.41401 | −0.270559 | ||||||||
\(563\) | 27.6973 | 1.16730 | 0.583652 | − | 0.812004i | \(-0.301623\pi\) | ||||
0.583652 | + | 0.812004i | \(0.301623\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 29.6715 | 1.24719 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −70.3612 | −2.95229 | ||||||||
\(569\) | −35.6179 | −1.49318 | −0.746590 | − | 0.665285i | \(-0.768310\pi\) | ||||
−0.746590 | + | 0.665285i | \(0.768310\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.85044 | 0.244833 | 0.122417 | − | 0.992479i | \(-0.460936\pi\) | ||||
0.122417 | + | 0.992479i | \(0.460936\pi\) | |||||||
\(572\) | 3.19839 | 0.133731 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −33.8833 | −1.41426 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.0524 | −0.501746 | −0.250873 | − | 0.968020i | \(-0.580718\pi\) | ||||
−0.250873 | + | 0.968020i | \(0.580718\pi\) | |||||||
\(578\) | −28.1404 | −1.17049 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −38.3150 | −1.58958 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.08891 | −0.0450979 | ||||||||
\(584\) | 99.4470 | 4.11515 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 41.6928 | 1.72232 | ||||||||
\(587\) | 40.2350 | 1.66068 | 0.830339 | − | 0.557259i | \(-0.188147\pi\) | ||||
0.830339 | + | 0.557259i | \(0.188147\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.14702 | 0.212079 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −179.401 | −7.37332 | ||||||||
\(593\) | 33.4086 | 1.37193 | 0.685964 | − | 0.727636i | \(-0.259381\pi\) | ||||
0.685964 | + | 0.727636i | \(0.259381\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −19.8053 | −0.811258 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.684132 | 0.0279763 | ||||||||
\(599\) | 24.6421 | 1.00685 | 0.503424 | − | 0.864040i | \(-0.332073\pi\) | ||||
0.503424 | + | 0.864040i | \(0.332073\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.6327 | 0.678461 | 0.339230 | − | 0.940703i | \(-0.389833\pi\) | ||||
0.339230 | + | 0.940703i | \(0.389833\pi\) | |||||||
\(602\) | 84.6103 | 3.44846 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 62.1310 | 2.52807 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −29.4057 | −1.19354 | −0.596770 | − | 0.802412i | \(-0.703550\pi\) | ||||
−0.596770 | + | 0.802412i | \(0.703550\pi\) | |||||||
\(608\) | 55.1695 | 2.23742 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.25515 | 0.0912337 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.1702 | −0.491549 | −0.245775 | − | 0.969327i | \(-0.579042\pi\) | ||||
−0.245775 | + | 0.969327i | \(0.579042\pi\) | |||||||
\(614\) | 8.56574 | 0.345685 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −97.4838 | −3.92774 | ||||||||
\(617\) | −39.1024 | −1.57420 | −0.787102 | − | 0.616823i | \(-0.788419\pi\) | ||||
−0.787102 | + | 0.616823i | \(0.788419\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.72717 | −0.190001 | −0.0950006 | − | 0.995477i | \(-0.530285\pi\) | ||||
−0.0950006 | + | 0.995477i | \(0.530285\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −69.4258 | −2.78372 | ||||||||
\(623\) | 47.8258 | 1.91610 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −25.8801 | −1.03438 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 77.3179 | 3.08532 | ||||||||
\(629\) | −26.5794 | −1.05979 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.8710 | −1.34838 | −0.674191 | − | 0.738557i | \(-0.735508\pi\) | ||||
−0.674191 | + | 0.738557i | \(0.735508\pi\) | |||||||
\(632\) | 4.41226 | 0.175510 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 57.8842 | 2.29888 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.549929 | −0.0217890 | ||||||||
\(638\) | 10.1183 | 0.400586 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.9571 | −0.630269 | −0.315135 | − | 0.949047i | \(-0.602050\pi\) | ||||
−0.315135 | + | 0.949047i | \(0.602050\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.2436 | 0.403968 | 0.201984 | − | 0.979389i | \(-0.435261\pi\) | ||||
0.201984 | + | 0.979389i | \(0.435261\pi\) | |||||||
\(644\) | −23.7013 | −0.933960 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 14.2139 | 0.559237 | ||||||||
\(647\) | −6.00244 | −0.235980 | −0.117990 | − | 0.993015i | \(-0.537645\pi\) | ||||
−0.117990 | + | 0.993015i | \(0.537645\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.3584 | −0.799138 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 88.9305 | 3.48279 | ||||||||
\(653\) | 33.1069 | 1.29557 | 0.647787 | − | 0.761822i | \(-0.275695\pi\) | ||||
0.647787 | + | 0.761822i | \(0.275695\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −68.4431 | −2.67226 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −105.218 | −4.10183 | ||||||||
\(659\) | −19.5593 | −0.761922 | −0.380961 | − | 0.924591i | \(-0.624407\pi\) | ||||
−0.380961 | + | 0.924591i | \(0.624407\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.5290 | 1.18744 | 0.593721 | − | 0.804671i | \(-0.297658\pi\) | ||||
0.593721 | + | 0.804671i | \(0.297658\pi\) | |||||||
\(662\) | −94.5312 | −3.67406 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −127.741 | −4.95730 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.60706 | 0.0622255 | ||||||||
\(668\) | 100.390 | 3.88421 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.7568 | −0.646890 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.19687 | −0.161778 | −0.0808888 | − | 0.996723i | \(-0.525776\pi\) | ||||
−0.0808888 | + | 0.996723i | \(0.525776\pi\) | |||||||
\(674\) | −49.5527 | −1.90870 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −74.7802 | −2.87616 | ||||||||
\(677\) | 9.66481 | 0.371449 | 0.185724 | − | 0.982602i | \(-0.440537\pi\) | ||||
0.185724 | + | 0.982602i | \(0.440537\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −43.7961 | −1.68074 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −21.7790 | −0.833961 | ||||||||
\(683\) | 9.03781 | 0.345822 | 0.172911 | − | 0.984937i | \(-0.444683\pi\) | ||||
0.172911 | + | 0.984937i | \(0.444683\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −35.7981 | −1.36678 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 170.910 | 6.51588 | ||||||||
\(689\) | −0.0695329 | −0.00264899 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32.1359 | −1.22251 | −0.611254 | − | 0.791435i | \(-0.709334\pi\) | ||||
−0.611254 | + | 0.791435i | \(0.709334\pi\) | |||||||
\(692\) | −111.171 | −4.22610 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −34.0728 | −1.29338 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.1403 | −0.384091 | ||||||||
\(698\) | 35.7935 | 1.35480 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.54116 | 0.322595 | 0.161298 | − | 0.986906i | \(-0.448432\pi\) | ||||
0.161298 | + | 0.986906i | \(0.448432\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19.6354 | −0.740562 | ||||||||
\(704\) | −128.925 | −4.85904 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 48.5413 | 1.82688 | ||||||||
\(707\) | 30.4664 | 1.14581 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.04613 | 0.189511 | 0.0947556 | − | 0.995501i | \(-0.469793\pi\) | ||||
0.0947556 | + | 0.995501i | \(0.469793\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 159.449 | 5.97561 | ||||||||
\(713\) | −3.45910 | −0.129544 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −137.244 | −5.12907 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10.6732 | 0.398319 | ||||||||
\(719\) | 19.5253 | 0.728170 | 0.364085 | − | 0.931366i | \(-0.381382\pi\) | ||||
0.364085 | + | 0.931366i | \(0.381382\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −27.3872 | −1.01995 | ||||||||
\(722\) | −42.4549 | −1.58001 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −61.6552 | −2.29140 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.4464 | −1.50007 | −0.750037 | − | 0.661395i | \(-0.769965\pi\) | ||||
−0.750037 | + | 0.661395i | \(0.769965\pi\) | |||||||
\(728\) | −6.22490 | −0.230710 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 25.3215 | 0.936548 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.3862 | −1.08540 | −0.542702 | − | 0.839926i | \(-0.682599\pi\) | ||||
−0.542702 | + | 0.839926i | \(0.682599\pi\) | |||||||
\(734\) | 82.5772 | 3.04798 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −37.0772 | −1.36668 | ||||||||
\(737\) | 9.55318 | 0.351896 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30.7254 | −1.13025 | −0.565126 | − | 0.825005i | \(-0.691172\pi\) | ||||
−0.565126 | + | 0.825005i | \(0.691172\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.24418 | 0.119098 | ||||||||
\(743\) | 41.4841 | 1.52190 | 0.760952 | − | 0.648808i | \(-0.224732\pi\) | ||||
0.760952 | + | 0.648808i | \(0.224732\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −31.9390 | −1.16937 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −44.6592 | −1.63290 | ||||||||
\(749\) | −8.08244 | −0.295326 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38.6123 | 1.40898 | 0.704491 | − | 0.709713i | \(-0.251175\pi\) | ||||
0.704491 | + | 0.709713i | \(0.251175\pi\) | |||||||
\(752\) | −212.537 | −7.75042 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.646109 | 0.0235299 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.0860 | 0.839074 | 0.419537 | − | 0.907738i | \(-0.362193\pi\) | ||||
0.419537 | + | 0.907738i | \(0.362193\pi\) | |||||||
\(758\) | −6.11234 | −0.222010 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31.7092 | 1.14946 | 0.574728 | − | 0.818344i | \(-0.305108\pi\) | ||||
0.574728 | + | 0.818344i | \(0.305108\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −47.9908 | −1.73738 | ||||||||
\(764\) | 82.8180 | 2.99625 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −28.4278 | −1.02714 | ||||||||
\(767\) | −1.30000 | −0.0469404 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 38.6475 | 1.39366 | 0.696832 | − | 0.717235i | \(-0.254592\pi\) | ||||
0.696832 | + | 0.717235i | \(0.254592\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −11.2770 | −0.405867 | ||||||||
\(773\) | 38.9958 | 1.40258 | 0.701291 | − | 0.712875i | \(-0.252607\pi\) | ||||
0.701291 | + | 0.712875i | \(0.252607\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −146.014 | −5.24161 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −79.5672 | −2.85262 | ||||||||
\(779\) | −7.49109 | −0.268396 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19.7431 | 0.706463 | ||||||||
\(782\) | −9.55256 | −0.341599 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 51.8281 | 1.85100 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.11107 | 0.289128 | 0.144564 | − | 0.989495i | \(-0.453822\pi\) | ||||
0.144564 | + | 0.989495i | \(0.453822\pi\) | |||||||
\(788\) | −6.80387 | −0.242378 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.94231 | 0.246840 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.07002 | −0.0379975 | ||||||||
\(794\) | −103.633 | −3.67778 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −37.8279 | −1.34078 | ||||||||
\(797\) | −19.0152 | −0.673554 | −0.336777 | − | 0.941584i | \(-0.609337\pi\) | ||||
−0.336777 | + | 0.941584i | \(0.609337\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −31.4888 | −1.11399 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −20.5870 | −0.726952 | ||||||||
\(803\) | −27.9044 | −0.984726 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.39071 | −0.0489858 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 101.574 | 3.57335 | ||||||||
\(809\) | −49.9078 | −1.75467 | −0.877333 | − | 0.479882i | \(-0.840679\pi\) | ||||
−0.877333 | + | 0.479882i | \(0.840679\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.9727 | 1.08760 | 0.543799 | − | 0.839215i | \(-0.316985\pi\) | ||||
0.543799 | + | 0.839215i | \(0.316985\pi\) | |||||||
\(812\) | −22.3840 | −0.785523 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 83.0847 | 2.91212 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.7061 | 0.654443 | ||||||||
\(818\) | −14.4914 | −0.506680 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.9246 | −0.660473 | −0.330236 | − | 0.943898i | \(-0.607128\pi\) | ||||
−0.330236 | + | 0.943898i | \(0.607128\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.31122 | 0.324569 | 0.162284 | − | 0.986744i | \(-0.448114\pi\) | ||||
0.162284 | + | 0.986744i | \(0.448114\pi\) | |||||||
\(824\) | −91.3076 | −3.18085 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 60.6539 | 2.11042 | ||||||||
\(827\) | 23.7383 | 0.825461 | 0.412731 | − | 0.910853i | \(-0.364575\pi\) | ||||
0.412731 | + | 0.910853i | \(0.364575\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.91351 | 0.0664590 | 0.0332295 | − | 0.999448i | \(-0.489421\pi\) | ||||
0.0332295 | + | 0.999448i | \(0.489421\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8.23260 | −0.285414 | ||||||||
\(833\) | 7.67867 | 0.266050 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −32.9917 | −1.14104 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 41.5852 | 1.43654 | ||||||||
\(839\) | −40.5105 | −1.39858 | −0.699289 | − | 0.714839i | \(-0.746500\pi\) | ||||
−0.699289 | + | 0.714839i | \(0.746500\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.4823 | −0.947664 | ||||||||
\(842\) | −0.185880 | −0.00640584 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 71.2776 | 2.45348 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.29643 | −0.250708 | ||||||||
\(848\) | 6.55314 | 0.225036 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.1961 | 0.452358 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18.7735 | −0.642792 | −0.321396 | − | 0.946945i | \(-0.604152\pi\) | ||||
−0.321396 | + | 0.946945i | \(0.604152\pi\) | |||||||
\(854\) | 49.9236 | 1.70835 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −26.9465 | −0.921012 | ||||||||
\(857\) | −10.0276 | −0.342536 | −0.171268 | − | 0.985225i | \(-0.554786\pi\) | ||||
−0.171268 | + | 0.985225i | \(0.554786\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.0443 | −0.956858 | −0.478429 | − | 0.878126i | \(-0.658794\pi\) | ||||
−0.478429 | + | 0.878126i | \(0.658794\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −77.2020 | −2.62951 | ||||||||
\(863\) | 9.84666 | 0.335184 | 0.167592 | − | 0.985856i | \(-0.446401\pi\) | ||||
0.167592 | + | 0.985856i | \(0.446401\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 85.1815 | 2.89459 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 48.1802 | 1.63534 | ||||||||
\(869\) | −1.23806 | −0.0419984 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.610026 | 0.0206699 | ||||||||
\(872\) | −159.999 | −5.41826 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −7.05690 | −0.238703 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −36.9671 | −1.24829 | −0.624146 | − | 0.781308i | \(-0.714553\pi\) | ||||
−0.624146 | + | 0.781308i | \(0.714553\pi\) | |||||||
\(878\) | 30.9282 | 1.04378 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.7137 | 0.697863 | 0.348932 | − | 0.937148i | \(-0.386545\pi\) | ||||
0.348932 | + | 0.937148i | \(0.386545\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.7254 | −0.428243 | −0.214121 | − | 0.976807i | \(-0.568689\pi\) | ||||
−0.214121 | + | 0.976807i | \(0.568689\pi\) | |||||||
\(884\) | −2.85175 | −0.0959146 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −27.3927 | −0.920275 | ||||||||
\(887\) | −21.6903 | −0.728287 | −0.364144 | − | 0.931343i | \(-0.618638\pi\) | ||||
−0.364144 | + | 0.931343i | \(0.618638\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 47.1520 | 1.58143 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 42.1466 | 1.41117 | ||||||||
\(893\) | −23.2621 | −0.778437 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 205.040 | 6.84990 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 53.3178 | 1.77924 | ||||||||
\(899\) | −3.26685 | −0.108956 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.970891 | 0.0323451 | ||||||||
\(902\) | 31.6976 | 1.05542 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 23.1454 | 0.769803 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.28462 | 0.109064 | 0.0545320 | − | 0.998512i | \(-0.482633\pi\) | ||||
0.0545320 | + | 0.998512i | \(0.482633\pi\) | |||||||
\(908\) | −121.245 | −4.02366 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.8264 | −0.955060 | −0.477530 | − | 0.878615i | \(-0.658468\pi\) | ||||
−0.477530 | + | 0.878615i | \(0.658468\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 35.8435 | 1.18625 | ||||||||
\(914\) | −52.2802 | −1.72927 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 112.790 | 3.72669 | ||||||||
\(917\) | −35.5815 | −1.17500 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.3985 | −0.573925 | −0.286962 | − | 0.957942i | \(-0.592645\pi\) | ||||
−0.286962 | + | 0.957942i | \(0.592645\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 104.854 | 3.45317 | ||||||||
\(923\) | 1.26071 | 0.0414967 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 55.5404 | 1.82517 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −35.0165 | −1.14947 | ||||||||
\(929\) | 24.3715 | 0.799603 | 0.399801 | − | 0.916602i | \(-0.369079\pi\) | ||||
0.399801 | + | 0.916602i | \(0.369079\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.67257 | 0.185911 | ||||||||
\(932\) | 70.0657 | 2.29508 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 76.2742 | 2.49577 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.5784 | −0.476257 | −0.238129 | − | 0.971234i | \(-0.576534\pi\) | ||||
−0.238129 | + | 0.971234i | \(0.576534\pi\) | |||||||
\(938\) | −28.4618 | −0.929311 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.19686 | 0.136814 | 0.0684068 | − | 0.997658i | \(-0.478208\pi\) | ||||
0.0684068 | + | 0.997658i | \(0.478208\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.03445 | 0.163944 | ||||||||
\(944\) | 122.519 | 3.98765 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −79.1525 | −2.57347 | ||||||||
\(947\) | −5.53251 | −0.179782 | −0.0898912 | − | 0.995952i | \(-0.528652\pi\) | ||||
−0.0898912 | + | 0.995952i | \(0.528652\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.78186 | −0.0578416 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 86.9185 | 2.81705 | ||||||||
\(953\) | 50.4779 | 1.63514 | 0.817570 | − | 0.575830i | \(-0.195321\pi\) | ||||
0.817570 | + | 0.575830i | \(0.195321\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −77.5899 | −2.50944 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 107.511 | 3.47352 | ||||||||
\(959\) | 13.1631 | 0.425060 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.9683 | −0.773170 | ||||||||
\(962\) | 5.30544 | 0.171054 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 114.998 | 3.70382 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.0340 | 0.547777 | 0.273889 | − | 0.961761i | \(-0.411690\pi\) | ||||
0.273889 | + | 0.961761i | \(0.411690\pi\) | |||||||
\(968\) | −24.3260 | −0.781867 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23.4172 | −0.751494 | −0.375747 | − | 0.926722i | \(-0.622614\pi\) | ||||
−0.375747 | + | 0.926722i | \(0.622614\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −48.3690 | −1.55064 | ||||||||
\(974\) | 51.5604 | 1.65210 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 100.844 | 3.22794 | ||||||||
\(977\) | −20.7626 | −0.664253 | −0.332127 | − | 0.943235i | \(-0.607766\pi\) | ||||
−0.332127 | + | 0.943235i | \(0.607766\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −44.7408 | −1.42992 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −54.9650 | −1.75400 | ||||||||
\(983\) | 42.1977 | 1.34590 | 0.672948 | − | 0.739690i | \(-0.265028\pi\) | ||||
0.672948 | + | 0.739690i | \(0.265028\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −9.02164 | −0.287308 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.10671 | −0.0670234 | ||||||||
\(989\) | −12.5716 | −0.399753 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.83926 | −0.121958 | −0.0609791 | − | 0.998139i | \(-0.519422\pi\) | ||||
−0.0609791 | + | 0.998139i | \(0.519422\pi\) | |||||||
\(992\) | 75.3711 | 2.39303 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −58.8206 | −1.86567 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −42.2091 | −1.33678 | −0.668389 | − | 0.743812i | \(-0.733016\pi\) | ||||
−0.668389 | + | 0.743812i | \(0.733016\pi\) | |||||||
\(998\) | −101.146 | −3.20173 | ||||||||
\(999\) | 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 | 5625.2.a.r.1.6 | 6 | ||
3.2 | odd | 2 | 1875.2.a.i.1.1 | ✓ | 6 | ||
5.4 | even | 2 | 5625.2.a.o.1.1 | 6 | |||
15.2 | even | 4 | 1875.2.b.e.1249.1 | 12 | |||
15.8 | even | 4 | 1875.2.b.e.1249.12 | 12 | |||
15.14 | odd | 2 | 1875.2.a.l.1.6 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1875.2.a.i.1.1 | ✓ | 6 | 3.2 | odd | 2 | ||
1875.2.a.l.1.6 | yes | 6 | 15.14 | odd | 2 | ||
1875.2.b.e.1249.1 | 12 | 15.2 | even | 4 | |||
1875.2.b.e.1249.12 | 12 | 15.8 | even | 4 | |||
5625.2.a.o.1.1 | 6 | 5.4 | even | 2 | |||
5625.2.a.r.1.6 | 6 | 1.1 | even | 1 | trivial |