Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,4,Mod(199,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.199");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.c (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(48.6765757547\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 54x^{6} + 913x^{4} + 5292x^{2} + 8464 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.8 | ||
Root | \(4.17080i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.199 |
Dual form | 825.4.c.p.199.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.17080i | 1.82815i | 0.405540 | + | 0.914077i | \(0.367083\pi\) | ||||
−0.405540 | + | 0.914077i | \(0.632917\pi\) | |||||||
\(3\) | − 3.00000i | − 0.577350i | ||||||||
\(4\) | −18.7372 | −2.34215 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 15.5124 | 1.05549 | ||||||||
\(7\) | − 11.1745i | − 0.603368i | −0.953408 | − | 0.301684i | \(-0.902451\pi\) | ||||
0.953408 | − | 0.301684i | \(-0.0975487\pi\) | |||||||
\(8\) | − 55.5199i | − 2.45365i | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 56.2116i | 1.35224i | ||||||||
\(13\) | 89.5310i | 1.91011i | 0.296427 | + | 0.955056i | \(0.404205\pi\) | ||||
−0.296427 | + | 0.955056i | \(0.595795\pi\) | |||||||
\(14\) | 57.7813 | 1.10305 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 137.185 | 2.14351 | ||||||||
\(17\) | 58.3242i | 0.832100i | 0.909342 | + | 0.416050i | \(0.136586\pi\) | ||||
−0.909342 | + | 0.416050i | \(0.863414\pi\) | |||||||
\(18\) | − 46.5372i | − 0.609385i | ||||||||
\(19\) | −24.5575 | −0.296520 | −0.148260 | − | 0.988948i | \(-0.547367\pi\) | ||||
−0.148260 | + | 0.988948i | \(0.547367\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −33.5236 | −0.348355 | ||||||||
\(22\) | − 56.8788i | − 0.551209i | ||||||||
\(23\) | 111.696i | 1.01262i | 0.862353 | + | 0.506308i | \(0.168990\pi\) | ||||
−0.862353 | + | 0.506308i | \(0.831010\pi\) | |||||||
\(24\) | −166.560 | −1.41662 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −462.947 | −3.49198 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | 209.379i | 1.41318i | ||||||||
\(29\) | −109.954 | −0.704066 | −0.352033 | − | 0.935988i | \(-0.614510\pi\) | ||||
−0.352033 | + | 0.935988i | \(0.614510\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 119.547 | 0.692621 | 0.346310 | − | 0.938120i | \(-0.387434\pi\) | ||||
0.346310 | + | 0.938120i | \(0.387434\pi\) | |||||||
\(32\) | 265.196i | 1.46501i | ||||||||
\(33\) | 33.0000i | 0.174078i | ||||||||
\(34\) | −301.583 | −1.52121 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 168.635 | 0.780716 | ||||||||
\(37\) | − 356.544i | − 1.58420i | −0.610391 | − | 0.792100i | \(-0.708988\pi\) | ||||
0.610391 | − | 0.792100i | \(-0.291012\pi\) | |||||||
\(38\) | − 126.982i | − 0.542085i | ||||||||
\(39\) | 268.593 | 1.10280 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 268.798 | 1.02388 | 0.511941 | − | 0.859021i | \(-0.328927\pi\) | ||||
0.511941 | + | 0.859021i | \(0.328927\pi\) | |||||||
\(42\) | − 173.344i | − 0.636846i | ||||||||
\(43\) | − 263.371i | − 0.934038i | −0.884247 | − | 0.467019i | \(-0.845328\pi\) | ||||
0.884247 | − | 0.467019i | \(-0.154672\pi\) | |||||||
\(44\) | 206.109 | 0.706184 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −577.557 | −1.85122 | ||||||||
\(47\) | − 206.732i | − 0.641594i | −0.947148 | − | 0.320797i | \(-0.896049\pi\) | ||||
0.947148 | − | 0.320797i | \(-0.103951\pi\) | |||||||
\(48\) | − 411.554i | − 1.23756i | ||||||||
\(49\) | 218.130 | 0.635947 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 174.973 | 0.480413 | ||||||||
\(52\) | − 1677.56i | − 4.47376i | ||||||||
\(53\) | − 223.749i | − 0.579891i | −0.957043 | − | 0.289946i | \(-0.906363\pi\) | ||||
0.957043 | − | 0.289946i | \(-0.0936372\pi\) | |||||||
\(54\) | −139.612 | −0.351828 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −620.408 | −1.48046 | ||||||||
\(57\) | 73.6726i | 0.171196i | ||||||||
\(58\) | − 568.549i | − 1.28714i | ||||||||
\(59\) | −475.000 | −1.04813 | −0.524066 | − | 0.851678i | \(-0.675585\pi\) | ||||
−0.524066 | + | 0.851678i | \(0.675585\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −513.204 | −1.07720 | −0.538598 | − | 0.842563i | \(-0.681046\pi\) | ||||
−0.538598 | + | 0.842563i | \(0.681046\pi\) | |||||||
\(62\) | 618.153i | 1.26622i | ||||||||
\(63\) | 100.571i | 0.201123i | ||||||||
\(64\) | −273.798 | −0.534761 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −170.636 | −0.318241 | ||||||||
\(67\) | − 264.533i | − 0.482355i | −0.970481 | − | 0.241178i | \(-0.922466\pi\) | ||||
0.970481 | − | 0.241178i | \(-0.0775337\pi\) | |||||||
\(68\) | − 1092.83i | − 1.94890i | ||||||||
\(69\) | 335.087 | 0.584634 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1110.33 | −1.85595 | −0.927973 | − | 0.372648i | \(-0.878450\pi\) | ||||
−0.927973 | + | 0.372648i | \(0.878450\pi\) | |||||||
\(72\) | 499.679i | 0.817885i | ||||||||
\(73\) | − 893.608i | − 1.43273i | −0.697728 | − | 0.716363i | \(-0.745806\pi\) | ||||
0.697728 | − | 0.716363i | \(-0.254194\pi\) | |||||||
\(74\) | 1843.62 | 2.89616 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 460.139 | 0.694494 | ||||||||
\(77\) | 122.920i | 0.181922i | ||||||||
\(78\) | 1388.84i | 2.01609i | ||||||||
\(79\) | −1303.66 | −1.85663 | −0.928314 | − | 0.371797i | \(-0.878742\pi\) | ||||
−0.928314 | + | 0.371797i | \(0.878742\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 1389.90i | 1.87181i | ||||||||
\(83\) | − 1049.37i | − 1.38775i | −0.720098 | − | 0.693873i | \(-0.755903\pi\) | ||||
0.720098 | − | 0.693873i | \(-0.244097\pi\) | |||||||
\(84\) | 628.138 | 0.815898 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1361.84 | 1.70757 | ||||||||
\(87\) | 329.862i | 0.406493i | ||||||||
\(88\) | 610.718i | 0.739805i | ||||||||
\(89\) | 1417.91 | 1.68875 | 0.844374 | − | 0.535754i | \(-0.179972\pi\) | ||||
0.844374 | + | 0.535754i | \(0.179972\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1000.47 | 1.15250 | ||||||||
\(92\) | − 2092.86i | − 2.37170i | ||||||||
\(93\) | − 358.640i | − 0.399885i | ||||||||
\(94\) | 1068.97 | 1.17293 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 795.587 | 0.845826 | ||||||||
\(97\) | 85.8091i | 0.0898206i | 0.998991 | + | 0.0449103i | \(0.0143002\pi\) | ||||
−0.998991 | + | 0.0449103i | \(0.985700\pi\) | |||||||
\(98\) | 1127.91i | 1.16261i | ||||||||
\(99\) | 99.0000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 137.761 | 0.135721 | 0.0678603 | − | 0.997695i | \(-0.478383\pi\) | ||||
0.0678603 | + | 0.997695i | \(0.478383\pi\) | |||||||
\(102\) | 904.749i | 0.878269i | ||||||||
\(103\) | − 419.397i | − 0.401208i | −0.979672 | − | 0.200604i | \(-0.935710\pi\) | ||||
0.979672 | − | 0.200604i | \(-0.0642905\pi\) | |||||||
\(104\) | 4970.75 | 4.68675 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1156.96 | 1.06013 | ||||||||
\(107\) | − 1190.45i | − 1.07557i | −0.843083 | − | 0.537783i | \(-0.819262\pi\) | ||||
0.843083 | − | 0.537783i | \(-0.180738\pi\) | |||||||
\(108\) | − 505.904i | − 0.450747i | ||||||||
\(109\) | −1033.37 | −0.908066 | −0.454033 | − | 0.890985i | \(-0.650015\pi\) | ||||
−0.454033 | + | 0.890985i | \(0.650015\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1069.63 | −0.914638 | ||||||||
\(112\) | − 1532.97i | − 1.29333i | ||||||||
\(113\) | 930.760i | 0.774854i | 0.921900 | + | 0.387427i | \(0.126636\pi\) | ||||
−0.921900 | + | 0.387427i | \(0.873364\pi\) | |||||||
\(114\) | −380.946 | −0.312973 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2060.23 | 1.64903 | ||||||||
\(117\) | − 805.779i | − 0.636704i | ||||||||
\(118\) | − 2456.13i | − 1.91615i | ||||||||
\(119\) | 651.746 | 0.502062 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | − 2653.68i | − 1.96928i | ||||||||
\(123\) | − 806.393i | − 0.591138i | ||||||||
\(124\) | −2239.97 | −1.62222 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −520.031 | −0.367683 | ||||||||
\(127\) | 94.4315i | 0.0659799i | 0.999456 | + | 0.0329899i | \(0.0105029\pi\) | ||||
−0.999456 | + | 0.0329899i | \(0.989497\pi\) | |||||||
\(128\) | 705.814i | 0.487389i | ||||||||
\(129\) | −790.112 | −0.539267 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1318.12 | 0.879122 | 0.439561 | − | 0.898213i | \(-0.355134\pi\) | ||||
0.439561 | + | 0.898213i | \(0.355134\pi\) | |||||||
\(132\) | − 618.327i | − 0.407716i | ||||||||
\(133\) | 274.419i | 0.178911i | ||||||||
\(134\) | 1367.85 | 0.881820 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3238.15 | 2.04169 | ||||||||
\(137\) | 2008.43i | 1.25249i | 0.779624 | + | 0.626247i | \(0.215410\pi\) | ||||
−0.779624 | + | 0.626247i | \(0.784590\pi\) | |||||||
\(138\) | 1732.67i | 1.06880i | ||||||||
\(139\) | −2956.76 | −1.80424 | −0.902120 | − | 0.431486i | \(-0.857989\pi\) | ||||
−0.902120 | + | 0.431486i | \(0.857989\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −620.196 | −0.370425 | ||||||||
\(142\) | − 5741.30i | − 3.39295i | ||||||||
\(143\) | − 984.841i | − 0.575920i | ||||||||
\(144\) | −1234.66 | −0.714504 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4620.67 | 2.61924 | ||||||||
\(147\) | − 654.390i | − 0.367164i | ||||||||
\(148\) | 6680.62i | 3.71043i | ||||||||
\(149\) | −878.768 | −0.483164 | −0.241582 | − | 0.970380i | \(-0.577666\pi\) | ||||
−0.241582 | + | 0.970380i | \(0.577666\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1679.35 | −0.905058 | −0.452529 | − | 0.891750i | \(-0.649478\pi\) | ||||
−0.452529 | + | 0.891750i | \(0.649478\pi\) | |||||||
\(152\) | 1363.43i | 0.727558i | ||||||||
\(153\) | − 524.918i | − 0.277367i | ||||||||
\(154\) | −635.594 | −0.332582 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −5032.68 | −2.58293 | ||||||||
\(157\) | 703.051i | 0.357386i | 0.983905 | + | 0.178693i | \(0.0571869\pi\) | ||||
−0.983905 | + | 0.178693i | \(0.942813\pi\) | |||||||
\(158\) | − 6740.99i | − 3.39420i | ||||||||
\(159\) | −671.246 | −0.334800 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1248.15 | 0.610980 | ||||||||
\(162\) | 418.835i | 0.203128i | ||||||||
\(163\) | − 2934.66i | − 1.41019i | −0.709114 | − | 0.705093i | \(-0.750905\pi\) | ||||
0.709114 | − | 0.705093i | \(-0.249095\pi\) | |||||||
\(164\) | −5036.51 | −2.39808 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5426.06 | 2.53701 | ||||||||
\(167\) | − 2146.05i | − 0.994407i | −0.867634 | − | 0.497204i | \(-0.834360\pi\) | ||||
0.867634 | − | 0.497204i | \(-0.165640\pi\) | |||||||
\(168\) | 1861.22i | 0.854742i | ||||||||
\(169\) | −5818.81 | −2.64852 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 221.018 | 0.0988401 | ||||||||
\(172\) | 4934.82i | 2.18766i | ||||||||
\(173\) | − 321.356i | − 0.141227i | −0.997504 | − | 0.0706134i | \(-0.977504\pi\) | ||||
0.997504 | − | 0.0706134i | \(-0.0224957\pi\) | |||||||
\(174\) | −1705.65 | −0.743131 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1509.03 | −0.646293 | ||||||||
\(177\) | 1425.00i | 0.605139i | ||||||||
\(178\) | 7331.75i | 3.08729i | ||||||||
\(179\) | 2662.08 | 1.11158 | 0.555791 | − | 0.831322i | \(-0.312415\pi\) | ||||
0.555791 | + | 0.831322i | \(0.312415\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3306.02 | 1.35765 | 0.678825 | − | 0.734300i | \(-0.262490\pi\) | ||||
0.678825 | + | 0.734300i | \(0.262490\pi\) | |||||||
\(182\) | 5173.22i | 2.10695i | ||||||||
\(183\) | 1539.61i | 0.621920i | ||||||||
\(184\) | 6201.33 | 2.48461 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1854.46 | 0.731051 | ||||||||
\(187\) | − 641.566i | − 0.250888i | ||||||||
\(188\) | 3873.57i | 1.50271i | ||||||||
\(189\) | 301.712 | 0.116118 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 946.068 | 0.358404 | 0.179202 | − | 0.983812i | \(-0.442648\pi\) | ||||
0.179202 | + | 0.983812i | \(0.442648\pi\) | |||||||
\(192\) | 821.393i | 0.308744i | ||||||||
\(193\) | 3692.54i | 1.37717i | 0.725154 | + | 0.688587i | \(0.241769\pi\) | ||||
−0.725154 | + | 0.688587i | \(0.758231\pi\) | |||||||
\(194\) | −443.702 | −0.164206 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4087.14 | −1.48948 | ||||||||
\(197\) | − 411.503i | − 0.148824i | −0.997228 | − | 0.0744122i | \(-0.976292\pi\) | ||||
0.997228 | − | 0.0744122i | \(-0.0237080\pi\) | |||||||
\(198\) | 511.909i | 0.183736i | ||||||||
\(199\) | −1491.28 | −0.531226 | −0.265613 | − | 0.964080i | \(-0.585574\pi\) | ||||
−0.265613 | + | 0.964080i | \(0.585574\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −793.598 | −0.278488 | ||||||||
\(202\) | 712.337i | 0.248118i | ||||||||
\(203\) | 1228.68i | 0.424811i | ||||||||
\(204\) | −3278.49 | −1.12520 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2168.62 | 0.733470 | ||||||||
\(207\) | − 1005.26i | − 0.337539i | ||||||||
\(208\) | 12282.3i | 4.09434i | ||||||||
\(209\) | 270.133 | 0.0894042 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −899.947 | −0.293625 | −0.146813 | − | 0.989164i | \(-0.546901\pi\) | ||||
−0.146813 | + | 0.989164i | \(0.546901\pi\) | |||||||
\(212\) | 4192.42i | 1.35819i | ||||||||
\(213\) | 3330.99i | 1.07153i | ||||||||
\(214\) | 6155.61 | 1.96630 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1499.04 | 0.472206 | ||||||||
\(217\) | − 1335.88i | − 0.417905i | ||||||||
\(218\) | − 5343.37i | − 1.66009i | ||||||||
\(219\) | −2680.82 | −0.827184 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5221.83 | −1.58940 | ||||||||
\(222\) | − 5530.85i | − 1.67210i | ||||||||
\(223\) | − 1935.29i | − 0.581152i | −0.956852 | − | 0.290576i | \(-0.906153\pi\) | ||||
0.956852 | − | 0.290576i | \(-0.0938469\pi\) | |||||||
\(224\) | 2963.44 | 0.883942 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4812.77 | −1.41655 | ||||||||
\(227\) | − 2906.26i | − 0.849758i | −0.905250 | − | 0.424879i | \(-0.860317\pi\) | ||||
0.905250 | − | 0.424879i | \(-0.139683\pi\) | |||||||
\(228\) | − 1380.42i | − 0.400966i | ||||||||
\(229\) | 5411.89 | 1.56169 | 0.780846 | − | 0.624724i | \(-0.214788\pi\) | ||||
0.780846 | + | 0.624724i | \(0.214788\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 368.759 | 0.105033 | ||||||||
\(232\) | 6104.62i | 1.72753i | ||||||||
\(233\) | 4778.90i | 1.34368i | 0.740699 | + | 0.671838i | \(0.234495\pi\) | ||||
−0.740699 | + | 0.671838i | \(0.765505\pi\) | |||||||
\(234\) | 4166.53 | 1.16399 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 8900.17 | 2.45488 | ||||||||
\(237\) | 3910.99i | 1.07192i | ||||||||
\(238\) | 3370.05i | 0.917848i | ||||||||
\(239\) | −5883.88 | −1.59245 | −0.796227 | − | 0.604998i | \(-0.793174\pi\) | ||||
−0.796227 | + | 0.604998i | \(0.793174\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1806.96 | 0.482974 | 0.241487 | − | 0.970404i | \(-0.422365\pi\) | ||||
0.241487 | + | 0.970404i | \(0.422365\pi\) | |||||||
\(242\) | 625.667i | 0.166196i | ||||||||
\(243\) | − 243.000i | − 0.0641500i | ||||||||
\(244\) | 9616.00 | 2.52296 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4169.70 | 1.08069 | ||||||||
\(247\) | − 2198.66i | − 0.566386i | ||||||||
\(248\) | − 6637.22i | − 1.69945i | ||||||||
\(249\) | −3148.10 | −0.801215 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1265.10 | 0.318137 | 0.159069 | − | 0.987268i | \(-0.449151\pi\) | ||||
0.159069 | + | 0.987268i | \(0.449151\pi\) | |||||||
\(252\) | − 1884.41i | − 0.471059i | ||||||||
\(253\) | − 1228.65i | − 0.305315i | ||||||||
\(254\) | −488.287 | −0.120621 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5840.00 | −1.42578 | ||||||||
\(257\) | − 4366.53i | − 1.05983i | −0.848050 | − | 0.529916i | \(-0.822223\pi\) | ||||
0.848050 | − | 0.529916i | \(-0.177777\pi\) | |||||||
\(258\) | − 4085.51i | − 0.985864i | ||||||||
\(259\) | −3984.21 | −0.955855 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 989.585 | 0.234689 | ||||||||
\(262\) | 6815.76i | 1.60717i | ||||||||
\(263\) | 2950.96i | 0.691878i | 0.938257 | + | 0.345939i | \(0.112440\pi\) | ||||
−0.938257 | + | 0.345939i | \(0.887560\pi\) | |||||||
\(264\) | 1832.16 | 0.427126 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1418.97 | −0.327076 | ||||||||
\(267\) | − 4253.74i | − 0.974999i | ||||||||
\(268\) | 4956.60i | 1.12975i | ||||||||
\(269\) | 6048.65 | 1.37098 | 0.685488 | − | 0.728084i | \(-0.259589\pi\) | ||||
0.685488 | + | 0.728084i | \(0.259589\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2922.90 | −0.655180 | −0.327590 | − | 0.944820i | \(-0.606236\pi\) | ||||
−0.327590 | + | 0.944820i | \(0.606236\pi\) | |||||||
\(272\) | 8001.19i | 1.78362i | ||||||||
\(273\) | − 3001.40i | − 0.665396i | ||||||||
\(274\) | −10385.2 | −2.28975 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6278.59 | −1.36930 | ||||||||
\(277\) | − 5433.48i | − 1.17858i | −0.807922 | − | 0.589289i | \(-0.799408\pi\) | ||||
0.807922 | − | 0.589289i | \(-0.200592\pi\) | |||||||
\(278\) | − 15288.8i | − 3.29843i | ||||||||
\(279\) | −1075.92 | −0.230874 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7981.02 | −1.69433 | −0.847167 | − | 0.531327i | \(-0.821693\pi\) | ||||
−0.847167 | + | 0.531327i | \(0.821693\pi\) | |||||||
\(282\) | − 3206.91i | − 0.677194i | ||||||||
\(283\) | 2705.71i | 0.568332i | 0.958775 | + | 0.284166i | \(0.0917167\pi\) | ||||
−0.958775 | + | 0.284166i | \(0.908283\pi\) | |||||||
\(284\) | 20804.5 | 4.34690 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5092.42 | 1.05287 | ||||||||
\(287\) | − 3003.69i | − 0.617777i | ||||||||
\(288\) | − 2386.76i | − 0.488338i | ||||||||
\(289\) | 1511.29 | 0.307610 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 257.427 | 0.0518579 | ||||||||
\(292\) | 16743.7i | 3.35565i | ||||||||
\(293\) | − 2207.71i | − 0.440190i | −0.975478 | − | 0.220095i | \(-0.929363\pi\) | ||||
0.975478 | − | 0.220095i | \(-0.0706367\pi\) | |||||||
\(294\) | 3383.72 | 0.671233 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −19795.2 | −3.88708 | ||||||||
\(297\) | − 297.000i | − 0.0580259i | ||||||||
\(298\) | − 4543.94i | − 0.883299i | ||||||||
\(299\) | −10000.2 | −1.93421 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2943.04 | −0.563569 | ||||||||
\(302\) | − 8683.60i | − 1.65459i | ||||||||
\(303\) | − 413.284i | − 0.0783583i | ||||||||
\(304\) | −3368.92 | −0.635594 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2714.25 | 0.507069 | ||||||||
\(307\) | − 3918.45i | − 0.728462i | −0.931309 | − | 0.364231i | \(-0.881332\pi\) | ||||
0.931309 | − | 0.364231i | \(-0.118668\pi\) | |||||||
\(308\) | − 2303.17i | − 0.426089i | ||||||||
\(309\) | −1258.19 | −0.231638 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8769.03 | 1.59886 | 0.799431 | − | 0.600758i | \(-0.205134\pi\) | ||||
0.799431 | + | 0.600758i | \(0.205134\pi\) | |||||||
\(312\) | − 14912.3i | − 2.70590i | ||||||||
\(313\) | 5058.92i | 0.913569i | 0.889577 | + | 0.456785i | \(0.150999\pi\) | ||||
−0.889577 | + | 0.456785i | \(0.849001\pi\) | |||||||
\(314\) | −3635.34 | −0.653357 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 24427.0 | 4.34850 | ||||||||
\(317\) | − 8329.52i | − 1.47581i | −0.674904 | − | 0.737906i | \(-0.735815\pi\) | ||||
0.674904 | − | 0.737906i | \(-0.264185\pi\) | |||||||
\(318\) | − 3470.88i | − 0.612067i | ||||||||
\(319\) | 1209.49 | 0.212284 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3571.36 | −0.620979 | ||||||||
\(322\) | 6453.92i | 1.11697i | ||||||||
\(323\) | − 1432.30i | − 0.246734i | ||||||||
\(324\) | −1517.71 | −0.260239 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 15174.6 | 2.57804 | ||||||||
\(327\) | 3100.12i | 0.524272i | ||||||||
\(328\) | − 14923.6i | − 2.51225i | ||||||||
\(329\) | −2310.13 | −0.387118 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2901.85 | 0.481874 | 0.240937 | − | 0.970541i | \(-0.422545\pi\) | ||||
0.240937 | + | 0.970541i | \(0.422545\pi\) | |||||||
\(332\) | 19662.2i | 3.25030i | ||||||||
\(333\) | 3208.89i | 0.528067i | ||||||||
\(334\) | 11096.8 | 1.81793 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4598.92 | −0.746702 | ||||||||
\(337\) | 6000.75i | 0.969976i | 0.874521 | + | 0.484988i | \(0.161176\pi\) | ||||
−0.874521 | + | 0.484988i | \(0.838824\pi\) | |||||||
\(338\) | − 30087.9i | − 4.84191i | ||||||||
\(339\) | 2792.28 | 0.447362 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1315.02 | −0.208833 | ||||||||
\(342\) | 1142.84i | 0.180695i | ||||||||
\(343\) | − 6270.36i | − 0.987078i | ||||||||
\(344\) | −14622.3 | −2.29181 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1661.67 | 0.258185 | ||||||||
\(347\) | − 9059.04i | − 1.40148i | −0.713415 | − | 0.700742i | \(-0.752852\pi\) | ||||
0.713415 | − | 0.700742i | \(-0.247148\pi\) | |||||||
\(348\) | − 6180.68i | − 0.952066i | ||||||||
\(349\) | 9362.35 | 1.43597 | 0.717987 | − | 0.696057i | \(-0.245064\pi\) | ||||
0.717987 | + | 0.696057i | \(0.245064\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2417.34 | −0.367601 | ||||||||
\(352\) | − 2917.15i | − 0.441718i | ||||||||
\(353\) | 274.260i | 0.0413524i | 0.999786 | + | 0.0206762i | \(0.00658190\pi\) | ||||
−0.999786 | + | 0.0206762i | \(0.993418\pi\) | |||||||
\(354\) | −7368.39 | −1.10629 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −26567.7 | −3.95530 | ||||||||
\(357\) | − 1955.24i | − 0.289866i | ||||||||
\(358\) | 13765.1i | 2.03214i | ||||||||
\(359\) | 1394.51 | 0.205013 | 0.102506 | − | 0.994732i | \(-0.467314\pi\) | ||||
0.102506 | + | 0.994732i | \(0.467314\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6255.93 | −0.912076 | ||||||||
\(362\) | 17094.8i | 2.48199i | ||||||||
\(363\) | − 363.000i | − 0.0524864i | ||||||||
\(364\) | −18745.9 | −2.69933 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −7961.03 | −1.13697 | ||||||||
\(367\) | 11610.1i | 1.65134i | 0.564155 | + | 0.825669i | \(0.309202\pi\) | ||||
−0.564155 | + | 0.825669i | \(0.690798\pi\) | |||||||
\(368\) | 15322.9i | 2.17055i | ||||||||
\(369\) | −2419.18 | −0.341294 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2500.29 | −0.349888 | ||||||||
\(372\) | 6719.91i | 0.936590i | ||||||||
\(373\) | − 5068.89i | − 0.703639i | −0.936068 | − | 0.351819i | \(-0.885563\pi\) | ||||
0.936068 | − | 0.351819i | \(-0.114437\pi\) | |||||||
\(374\) | 3317.41 | 0.458661 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −11477.7 | −1.57425 | ||||||||
\(377\) | − 9844.28i | − 1.34484i | ||||||||
\(378\) | 1560.09i | 0.212282i | ||||||||
\(379\) | −1623.62 | −0.220052 | −0.110026 | − | 0.993929i | \(-0.535093\pi\) | ||||
−0.110026 | + | 0.993929i | \(0.535093\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 283.295 | 0.0380935 | ||||||||
\(382\) | 4891.93i | 0.655217i | ||||||||
\(383\) | − 5513.47i | − 0.735575i | −0.929910 | − | 0.367787i | \(-0.880115\pi\) | ||||
0.929910 | − | 0.367787i | \(-0.119885\pi\) | |||||||
\(384\) | 2117.44 | 0.281394 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −19093.4 | −2.51769 | ||||||||
\(387\) | 2370.34i | 0.311346i | ||||||||
\(388\) | − 1607.82i | − 0.210373i | ||||||||
\(389\) | −1591.80 | −0.207474 | −0.103737 | − | 0.994605i | \(-0.533080\pi\) | ||||
−0.103737 | + | 0.994605i | \(0.533080\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6514.57 | −0.842598 | ||||||||
\(392\) | − 12110.5i | − 1.56039i | ||||||||
\(393\) | − 3954.37i | − 0.507561i | ||||||||
\(394\) | 2127.80 | 0.272074 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1854.98 | −0.235395 | ||||||||
\(397\) | − 8032.19i | − 1.01543i | −0.861526 | − | 0.507713i | \(-0.830491\pi\) | ||||
0.861526 | − | 0.507713i | \(-0.169509\pi\) | |||||||
\(398\) | − 7711.11i | − 0.971164i | ||||||||
\(399\) | 823.256 | 0.103294 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 588.148 | 0.0732436 | 0.0366218 | − | 0.999329i | \(-0.488340\pi\) | ||||
0.0366218 | + | 0.999329i | \(0.488340\pi\) | |||||||
\(402\) | − 4103.54i | − 0.509119i | ||||||||
\(403\) | 10703.2i | 1.32298i | ||||||||
\(404\) | −2581.26 | −0.317878 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6353.27 | −0.776620 | ||||||||
\(407\) | 3921.98i | 0.477654i | ||||||||
\(408\) | − 9714.46i | − 1.17877i | ||||||||
\(409\) | −6945.63 | −0.839705 | −0.419853 | − | 0.907592i | \(-0.637918\pi\) | ||||
−0.419853 | + | 0.907592i | \(0.637918\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6025.29 | 0.723128 | ||||||||
\(412\) | 7858.33i | 0.939689i | ||||||||
\(413\) | 5307.90i | 0.632409i | ||||||||
\(414\) | 5198.01 | 0.617073 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −23743.3 | −2.79834 | ||||||||
\(417\) | 8870.28i | 1.04168i | ||||||||
\(418\) | 1396.80i | 0.163445i | ||||||||
\(419\) | 3310.93 | 0.386037 | 0.193018 | − | 0.981195i | \(-0.438172\pi\) | ||||
0.193018 | + | 0.981195i | \(0.438172\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13906.6 | −1.60989 | −0.804946 | − | 0.593348i | \(-0.797806\pi\) | ||||
−0.804946 | + | 0.593348i | \(0.797806\pi\) | |||||||
\(422\) | − 4653.45i | − 0.536792i | ||||||||
\(423\) | 1860.59i | 0.213865i | ||||||||
\(424\) | −12422.5 | −1.42285 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −17223.9 | −1.95892 | ||||||||
\(427\) | 5734.81i | 0.649946i | ||||||||
\(428\) | 22305.8i | 2.51914i | ||||||||
\(429\) | −2954.52 | −0.332508 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2713.07 | 0.303211 | 0.151606 | − | 0.988441i | \(-0.451556\pi\) | ||||
0.151606 | + | 0.988441i | \(0.451556\pi\) | |||||||
\(432\) | 3703.99i | 0.412519i | ||||||||
\(433\) | − 668.058i | − 0.0741451i | −0.999313 | − | 0.0370725i | \(-0.988197\pi\) | ||||
0.999313 | − | 0.0370725i | \(-0.0118033\pi\) | |||||||
\(434\) | 6907.57 | 0.763995 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 19362.5 | 2.12683 | ||||||||
\(437\) | − 2742.97i | − 0.300261i | ||||||||
\(438\) | − 13862.0i | − 1.51222i | ||||||||
\(439\) | −16512.6 | −1.79522 | −0.897611 | − | 0.440788i | \(-0.854699\pi\) | ||||
−0.897611 | + | 0.440788i | \(0.854699\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1963.17 | −0.211982 | ||||||||
\(442\) | − 27001.0i | − 2.90567i | ||||||||
\(443\) | 11305.6i | 1.21252i | 0.795268 | + | 0.606258i | \(0.207330\pi\) | ||||
−0.795268 | + | 0.606258i | \(0.792670\pi\) | |||||||
\(444\) | 20041.9 | 2.14222 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10007.0 | 1.06244 | ||||||||
\(447\) | 2636.31i | 0.278955i | ||||||||
\(448\) | 3059.56i | 0.322657i | ||||||||
\(449\) | −2103.65 | −0.221108 | −0.110554 | − | 0.993870i | \(-0.535262\pi\) | ||||
−0.110554 | + | 0.993870i | \(0.535262\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2956.77 | −0.308712 | ||||||||
\(452\) | − 17439.8i | − 1.81482i | ||||||||
\(453\) | 5038.06i | 0.522536i | ||||||||
\(454\) | 15027.7 | 1.55349 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4090.29 | 0.420056 | ||||||||
\(457\) | − 16013.6i | − 1.63914i | −0.572979 | − | 0.819570i | \(-0.694212\pi\) | ||||
0.572979 | − | 0.819570i | \(-0.305788\pi\) | |||||||
\(458\) | 27983.8i | 2.85501i | ||||||||
\(459\) | −1574.75 | −0.160138 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13332.9 | 1.34702 | 0.673509 | − | 0.739179i | \(-0.264786\pi\) | ||||
0.673509 | + | 0.739179i | \(0.264786\pi\) | |||||||
\(462\) | 1906.78i | 0.192016i | ||||||||
\(463\) | − 2453.48i | − 0.246270i | −0.992390 | − | 0.123135i | \(-0.960705\pi\) | ||||
0.992390 | − | 0.123135i | \(-0.0392948\pi\) | |||||||
\(464\) | −15084.0 | −1.50917 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −24710.8 | −2.45645 | ||||||||
\(467\) | − 771.767i | − 0.0764735i | −0.999269 | − | 0.0382367i | \(-0.987826\pi\) | ||||
0.999269 | − | 0.0382367i | \(-0.0121741\pi\) | |||||||
\(468\) | 15098.0i | 1.49125i | ||||||||
\(469\) | −2956.03 | −0.291038 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2109.15 | 0.206337 | ||||||||
\(472\) | 26371.9i | 2.57175i | ||||||||
\(473\) | 2897.08i | 0.281623i | ||||||||
\(474\) | −20223.0 | −1.95964 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −12211.9 | −1.17590 | ||||||||
\(477\) | 2013.74i | 0.193297i | ||||||||
\(478\) | − 30424.4i | − 2.91125i | ||||||||
\(479\) | −2782.55 | −0.265423 | −0.132712 | − | 0.991155i | \(-0.542368\pi\) | ||||
−0.132712 | + | 0.991155i | \(0.542368\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 31921.7 | 3.02600 | ||||||||
\(482\) | 9343.44i | 0.882950i | ||||||||
\(483\) | − 3744.44i | − 0.352750i | ||||||||
\(484\) | −2267.20 | −0.212923 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1256.50 | 0.117276 | ||||||||
\(487\) | − 9716.69i | − 0.904118i | −0.891988 | − | 0.452059i | \(-0.850690\pi\) | ||||
0.891988 | − | 0.452059i | \(-0.149310\pi\) | |||||||
\(488\) | 28493.0i | 2.64307i | ||||||||
\(489\) | −8803.99 | −0.814172 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13582.7 | 1.24843 | 0.624213 | − | 0.781254i | \(-0.285420\pi\) | ||||
0.624213 | + | 0.781254i | \(0.285420\pi\) | |||||||
\(492\) | 15109.5i | 1.38453i | ||||||||
\(493\) | − 6412.97i | − 0.585853i | ||||||||
\(494\) | 11368.8 | 1.03544 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 16400.0 | 1.48464 | ||||||||
\(497\) | 12407.4i | 1.11982i | ||||||||
\(498\) | − 16278.2i | − 1.46474i | ||||||||
\(499\) | −12177.8 | −1.09249 | −0.546244 | − | 0.837626i | \(-0.683943\pi\) | ||||
−0.546244 | + | 0.837626i | \(0.683943\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6438.14 | −0.574121 | ||||||||
\(502\) | 6541.59i | 0.581604i | ||||||||
\(503\) | − 5799.88i | − 0.514123i | −0.966395 | − | 0.257061i | \(-0.917246\pi\) | ||||
0.966395 | − | 0.257061i | \(-0.0827543\pi\) | |||||||
\(504\) | 5583.67 | 0.493485 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6353.12 | 0.558164 | ||||||||
\(507\) | 17456.4i | 1.52913i | ||||||||
\(508\) | − 1769.38i | − 0.154535i | ||||||||
\(509\) | −19516.8 | −1.69954 | −0.849772 | − | 0.527151i | \(-0.823260\pi\) | ||||
−0.849772 | + | 0.527151i | \(0.823260\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9985.65 | −0.864460 | ||||||||
\(512\) | − 24551.0i | − 2.11916i | ||||||||
\(513\) | − 663.053i | − 0.0570653i | ||||||||
\(514\) | 22578.5 | 1.93754 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 14804.5 | 1.26304 | ||||||||
\(517\) | 2274.05i | 0.193448i | ||||||||
\(518\) | − 20601.5i | − 1.74745i | ||||||||
\(519\) | −964.068 | −0.0815374 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9489.76 | 0.797993 | 0.398996 | − | 0.916953i | \(-0.369359\pi\) | ||||
0.398996 | + | 0.916953i | \(0.369359\pi\) | |||||||
\(522\) | 5116.95i | 0.429047i | ||||||||
\(523\) | − 5714.17i | − 0.477750i | −0.971050 | − | 0.238875i | \(-0.923221\pi\) | ||||
0.971050 | − | 0.238875i | \(-0.0767786\pi\) | |||||||
\(524\) | −24697.9 | −2.05903 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15258.8 | −1.26486 | ||||||||
\(527\) | 6972.47i | 0.576330i | ||||||||
\(528\) | 4527.09i | 0.373137i | ||||||||
\(529\) | −308.942 | −0.0253918 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4275.00 | 0.349377 | ||||||||
\(532\) | − 5141.84i | − 0.419036i | ||||||||
\(533\) | 24065.7i | 1.95573i | ||||||||
\(534\) | 21995.3 | 1.78245 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −14686.8 | −1.18353 | ||||||||
\(537\) | − 7986.24i | − 0.641772i | ||||||||
\(538\) | 31276.4i | 2.50636i | ||||||||
\(539\) | −2399.43 | −0.191745 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2530.63 | −0.201110 | −0.100555 | − | 0.994932i | \(-0.532062\pi\) | ||||
−0.100555 | + | 0.994932i | \(0.532062\pi\) | |||||||
\(542\) | − 15113.8i | − 1.19777i | ||||||||
\(543\) | − 9918.06i | − 0.783839i | ||||||||
\(544\) | −15467.3 | −1.21904 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 15519.7 | 1.21645 | ||||||||
\(547\) | 18910.4i | 1.47816i | 0.673619 | + | 0.739079i | \(0.264739\pi\) | ||||
−0.673619 | + | 0.739079i | \(0.735261\pi\) | |||||||
\(548\) | − 37632.3i | − 2.93353i | ||||||||
\(549\) | 4618.83 | 0.359066 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2700.19 | 0.208770 | ||||||||
\(552\) | − 18604.0i | − 1.43449i | ||||||||
\(553\) | 14567.8i | 1.12023i | ||||||||
\(554\) | 28095.4 | 2.15462 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 55401.4 | 4.22580 | ||||||||
\(557\) | 4480.34i | 0.340823i | 0.985373 | + | 0.170411i | \(0.0545096\pi\) | ||||
−0.985373 | + | 0.170411i | \(0.945490\pi\) | |||||||
\(558\) | − 5563.38i | − 0.422073i | ||||||||
\(559\) | 23579.8 | 1.78412 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1924.70 | −0.144850 | ||||||||
\(562\) | − 41268.3i | − 3.09750i | ||||||||
\(563\) | − 1726.52i | − 0.129244i | −0.997910 | − | 0.0646218i | \(-0.979416\pi\) | ||||
0.997910 | − | 0.0646218i | \(-0.0205841\pi\) | |||||||
\(564\) | 11620.7 | 0.867590 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −13990.7 | −1.03900 | ||||||||
\(567\) | − 905.137i | − 0.0670409i | ||||||||
\(568\) | 61645.5i | 4.55385i | ||||||||
\(569\) | 10862.7 | 0.800327 | 0.400164 | − | 0.916444i | \(-0.368953\pi\) | ||||
0.400164 | + | 0.916444i | \(0.368953\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14448.8 | 1.05895 | 0.529477 | − | 0.848324i | \(-0.322388\pi\) | ||||
0.529477 | + | 0.848324i | \(0.322388\pi\) | |||||||
\(572\) | 18453.2i | 1.34889i | ||||||||
\(573\) | − 2838.20i | − 0.206924i | ||||||||
\(574\) | 15531.5 | 1.12939 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2464.18 | 0.178254 | ||||||||
\(577\) | − 5335.95i | − 0.384988i | −0.981298 | − | 0.192494i | \(-0.938342\pi\) | ||||
0.981298 | − | 0.192494i | \(-0.0616577\pi\) | |||||||
\(578\) | 7814.56i | 0.562358i | ||||||||
\(579\) | 11077.6 | 0.795112 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11726.2 | −0.837321 | ||||||||
\(582\) | 1331.11i | 0.0948043i | ||||||||
\(583\) | 2461.23i | 0.174844i | ||||||||
\(584\) | −49613.0 | −3.51541 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11415.6 | 0.804735 | ||||||||
\(587\) | 25633.8i | 1.80242i | 0.433386 | + | 0.901208i | \(0.357319\pi\) | ||||
−0.433386 | + | 0.901208i | \(0.642681\pi\) | |||||||
\(588\) | 12261.4i | 0.859953i | ||||||||
\(589\) | −2935.77 | −0.205376 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1234.51 | −0.0859238 | ||||||||
\(592\) | − 48912.3i | − 3.39575i | ||||||||
\(593\) | 16094.8i | 1.11456i | 0.830324 | + | 0.557282i | \(0.188156\pi\) | ||||
−0.830324 | + | 0.557282i | \(0.811844\pi\) | |||||||
\(594\) | 1535.73 | 0.106080 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16465.6 | 1.13164 | ||||||||
\(597\) | 4473.84i | 0.306704i | ||||||||
\(598\) | − 51709.2i | − 3.53603i | ||||||||
\(599\) | 17160.5 | 1.17055 | 0.585275 | − | 0.810835i | \(-0.300986\pi\) | ||||
0.585275 | + | 0.810835i | \(0.300986\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14563.2 | −0.988426 | −0.494213 | − | 0.869341i | \(-0.664544\pi\) | ||||
−0.494213 | + | 0.869341i | \(0.664544\pi\) | |||||||
\(602\) | − 15217.9i | − 1.03029i | ||||||||
\(603\) | 2380.79i | 0.160785i | ||||||||
\(604\) | 31466.3 | 2.11978 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2137.01 | 0.143251 | ||||||||
\(607\) | − 12834.7i | − 0.858230i | −0.903250 | − | 0.429115i | \(-0.858825\pi\) | ||||
0.903250 | − | 0.429115i | \(-0.141175\pi\) | |||||||
\(608\) | − 6512.55i | − 0.434406i | ||||||||
\(609\) | 3686.05 | 0.245265 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18508.9 | 1.22552 | ||||||||
\(612\) | 9835.48i | 0.649634i | ||||||||
\(613\) | 10814.5i | 0.712548i | 0.934381 | + | 0.356274i | \(0.115953\pi\) | ||||
−0.934381 | + | 0.356274i | \(0.884047\pi\) | |||||||
\(614\) | 20261.5 | 1.33174 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6824.49 | 0.446374 | ||||||||
\(617\) | 5118.52i | 0.333977i | 0.985959 | + | 0.166988i | \(0.0534042\pi\) | ||||
−0.985959 | + | 0.166988i | \(0.946596\pi\) | |||||||
\(618\) | − 6505.86i | − 0.423469i | ||||||||
\(619\) | −26144.1 | −1.69761 | −0.848804 | − | 0.528708i | \(-0.822677\pi\) | ||||
−0.848804 | + | 0.528708i | \(0.822677\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3015.79 | −0.194878 | ||||||||
\(622\) | 45342.9i | 2.92297i | ||||||||
\(623\) | − 15844.5i | − 1.01894i | ||||||||
\(624\) | 36846.9 | 2.36387 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −26158.7 | −1.67015 | ||||||||
\(627\) | − 810.398i | − 0.0516175i | ||||||||
\(628\) | − 13173.2i | − 0.837051i | ||||||||
\(629\) | 20795.1 | 1.31821 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15147.2 | −0.955626 | −0.477813 | − | 0.878462i | \(-0.658570\pi\) | ||||
−0.477813 | + | 0.878462i | \(0.658570\pi\) | |||||||
\(632\) | 72379.2i | 4.55552i | ||||||||
\(633\) | 2699.84i | 0.169525i | ||||||||
\(634\) | 43070.3 | 2.69801 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 12577.3 | 0.784152 | ||||||||
\(637\) | 19529.4i | 1.21473i | ||||||||
\(638\) | 6254.04i | 0.388088i | ||||||||
\(639\) | 9992.98 | 0.618648 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6959.04 | 0.428807 | 0.214404 | − | 0.976745i | \(-0.431219\pi\) | ||||
0.214404 | + | 0.976745i | \(0.431219\pi\) | |||||||
\(642\) | − 18466.8i | − 1.13524i | ||||||||
\(643\) | − 50.7662i | − 0.00311357i | −0.999999 | − | 0.00155678i | \(-0.999504\pi\) | ||||
0.999999 | − | 0.00155678i | \(-0.000495540\pi\) | |||||||
\(644\) | −23386.8 | −1.43101 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7406.13 | 0.451069 | ||||||||
\(647\) | − 14853.2i | − 0.902537i | −0.892388 | − | 0.451268i | \(-0.850972\pi\) | ||||
0.892388 | − | 0.451268i | \(-0.149028\pi\) | |||||||
\(648\) | − 4497.11i | − 0.272628i | ||||||||
\(649\) | 5225.00 | 0.316023 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4007.64 | −0.241278 | ||||||||
\(652\) | 54987.3i | 3.30287i | ||||||||
\(653\) | − 18366.0i | − 1.10064i | −0.834953 | − | 0.550321i | \(-0.814505\pi\) | ||||
0.834953 | − | 0.550321i | \(-0.185495\pi\) | |||||||
\(654\) | −16030.1 | −0.958451 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 36874.9 | 2.19470 | ||||||||
\(657\) | 8042.47i | 0.477575i | ||||||||
\(658\) | − 11945.2i | − 0.707711i | ||||||||
\(659\) | 8660.13 | 0.511913 | 0.255957 | − | 0.966688i | \(-0.417610\pi\) | ||||
0.255957 | + | 0.966688i | \(0.417610\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11057.5 | −0.650661 | −0.325331 | − | 0.945600i | \(-0.605476\pi\) | ||||
−0.325331 | + | 0.945600i | \(0.605476\pi\) | |||||||
\(662\) | 15004.9i | 0.880940i | ||||||||
\(663\) | 15665.5i | 0.917642i | ||||||||
\(664\) | −58260.6 | −3.40505 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −16592.5 | −0.965387 | ||||||||
\(667\) | − 12281.4i | − 0.712949i | ||||||||
\(668\) | 40210.9i | 2.32905i | ||||||||
\(669\) | −5805.88 | −0.335528 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5645.24 | 0.324787 | ||||||||
\(672\) | − 8890.32i | − 0.510344i | ||||||||
\(673\) | − 1921.35i | − 0.110048i | −0.998485 | − | 0.0550241i | \(-0.982476\pi\) | ||||
0.998485 | − | 0.0550241i | \(-0.0175236\pi\) | |||||||
\(674\) | −31028.7 | −1.77327 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 109028. | 6.20324 | ||||||||
\(677\) | 25838.8i | 1.46686i | 0.679764 | + | 0.733431i | \(0.262082\pi\) | ||||
−0.679764 | + | 0.733431i | \(0.737918\pi\) | |||||||
\(678\) | 14438.3i | 0.817847i | ||||||||
\(679\) | 958.877 | 0.0541948 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8718.78 | −0.490608 | ||||||||
\(682\) | − 6799.68i | − 0.381779i | ||||||||
\(683\) | 33038.7i | 1.85094i | 0.378823 | + | 0.925469i | \(0.376329\pi\) | ||||
−0.378823 | + | 0.925469i | \(0.623671\pi\) | |||||||
\(684\) | −4141.25 | −0.231498 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 32422.8 | 1.80453 | ||||||||
\(687\) | − 16235.7i | − 0.901643i | ||||||||
\(688\) | − 36130.4i | − 2.00212i | ||||||||
\(689\) | 20032.4 | 1.10766 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2065.11 | −0.113691 | −0.0568454 | − | 0.998383i | \(-0.518104\pi\) | ||||
−0.0568454 | + | 0.998383i | \(0.518104\pi\) | |||||||
\(692\) | 6021.31i | 0.330774i | ||||||||
\(693\) | − 1106.28i | − 0.0606408i | ||||||||
\(694\) | 46842.5 | 2.56213 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 18313.9 | 0.997393 | ||||||||
\(697\) | 15677.4i | 0.851972i | ||||||||
\(698\) | 48410.8i | 2.62518i | ||||||||
\(699\) | 14336.7 | 0.775771 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23504.1 | −1.26639 | −0.633194 | − | 0.773993i | \(-0.718257\pi\) | ||||
−0.633194 | + | 0.773993i | \(0.718257\pi\) | |||||||
\(702\) | − 12499.6i | − 0.672031i | ||||||||
\(703\) | 8755.83i | 0.469747i | ||||||||
\(704\) | 3011.77 | 0.161236 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1418.14 | −0.0755985 | ||||||||
\(707\) | − 1539.42i | − 0.0818894i | ||||||||
\(708\) | − 26700.5i | − 1.41732i | ||||||||
\(709\) | 135.537 | 0.00717943 | 0.00358971 | − | 0.999994i | \(-0.498857\pi\) | ||||
0.00358971 | + | 0.999994i | \(0.498857\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11733.0 | 0.618876 | ||||||||
\(712\) | − 78722.4i | − 4.14361i | ||||||||
\(713\) | 13352.9i | 0.701359i | ||||||||
\(714\) | 10110.1 | 0.529920 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −49879.9 | −2.60349 | ||||||||
\(717\) | 17651.6i | 0.919404i | ||||||||
\(718\) | 7210.75i | 0.374795i | ||||||||
\(719\) | −10752.3 | −0.557711 | −0.278856 | − | 0.960333i | \(-0.589955\pi\) | ||||
−0.278856 | + | 0.960333i | \(0.589955\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4686.57 | −0.242076 | ||||||||
\(722\) | − 32348.2i | − 1.66742i | ||||||||
\(723\) | − 5420.88i | − 0.278845i | ||||||||
\(724\) | −61945.5 | −3.17982 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1877.00 | 0.0959532 | ||||||||
\(727\) | − 7521.06i | − 0.383687i | −0.981425 | − | 0.191844i | \(-0.938553\pi\) | ||||
0.981425 | − | 0.191844i | \(-0.0614467\pi\) | |||||||
\(728\) | − 55545.8i | − 2.82784i | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15360.9 | 0.777213 | ||||||||
\(732\) | − 28848.0i | − 1.45663i | ||||||||
\(733\) | 5330.33i | 0.268595i | 0.990941 | + | 0.134298i | \(0.0428778\pi\) | ||||
−0.990941 | + | 0.134298i | \(0.957122\pi\) | |||||||
\(734\) | −60033.4 | −3.01890 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −29621.2 | −1.48350 | ||||||||
\(737\) | 2909.86i | 0.145436i | ||||||||
\(738\) | − 12509.1i | − 0.623938i | ||||||||
\(739\) | −29328.0 | −1.45988 | −0.729938 | − | 0.683513i | \(-0.760451\pi\) | ||||
−0.729938 | + | 0.683513i | \(0.760451\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6595.98 | −0.327003 | ||||||||
\(742\) | − 12928.5i | − 0.639649i | ||||||||
\(743\) | 1378.56i | 0.0680679i | 0.999421 | + | 0.0340340i | \(0.0108354\pi\) | ||||
−0.999421 | + | 0.0340340i | \(0.989165\pi\) | |||||||
\(744\) | −19911.7 | −0.981179 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 26210.2 | 1.28636 | ||||||||
\(747\) | 9444.29i | 0.462582i | ||||||||
\(748\) | 12021.1i | 0.587616i | ||||||||
\(749\) | −13302.8 | −0.648962 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31066.4 | −1.50950 | −0.754748 | − | 0.656015i | \(-0.772241\pi\) | ||||
−0.754748 | + | 0.656015i | \(0.772241\pi\) | |||||||
\(752\) | − 28360.4i | − 1.37526i | ||||||||
\(753\) | − 3795.30i | − 0.183677i | ||||||||
\(754\) | 50902.8 | 2.45858 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −5653.24 | −0.271966 | ||||||||
\(757\) | 21971.1i | 1.05489i | 0.849589 | + | 0.527445i | \(0.176850\pi\) | ||||
−0.849589 | + | 0.527445i | \(0.823150\pi\) | |||||||
\(758\) | − 8395.42i | − 0.402290i | ||||||||
\(759\) | −3685.96 | −0.176274 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −35175.8 | −1.67559 | −0.837794 | − | 0.545987i | \(-0.816155\pi\) | ||||
−0.837794 | + | 0.545987i | \(0.816155\pi\) | |||||||
\(762\) | 1464.86i | 0.0696408i | ||||||||
\(763\) | 11547.5i | 0.547898i | ||||||||
\(764\) | −17726.7 | −0.839435 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 28509.1 | 1.34474 | ||||||||
\(767\) | − 42527.3i | − 2.00205i | ||||||||
\(768\) | 17520.0i | 0.823176i | ||||||||
\(769\) | −32952.5 | −1.54525 | −0.772626 | − | 0.634862i | \(-0.781057\pi\) | ||||
−0.772626 | + | 0.634862i | \(0.781057\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13099.6 | −0.611894 | ||||||||
\(772\) | − 69187.7i | − 3.22554i | ||||||||
\(773\) | 11158.7i | 0.519213i | 0.965714 | + | 0.259607i | \(0.0835929\pi\) | ||||
−0.965714 | + | 0.259607i | \(0.916407\pi\) | |||||||
\(774\) | −12256.5 | −0.569189 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4764.11 | 0.220389 | ||||||||
\(777\) | 11952.6i | 0.551863i | ||||||||
\(778\) | − 8230.86i | − 0.379294i | ||||||||
\(779\) | −6601.00 | −0.303601 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12213.6 | 0.559589 | ||||||||
\(782\) | − 33685.5i | − 1.54040i | ||||||||
\(783\) | − 2968.75i | − 0.135498i | ||||||||
\(784\) | 29924.1 | 1.36316 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 20447.3 | 0.927901 | ||||||||
\(787\) | 17308.9i | 0.783985i | 0.919968 | + | 0.391993i | \(0.128214\pi\) | ||||
−0.919968 | + | 0.391993i | \(0.871786\pi\) | |||||||
\(788\) | 7710.41i | 0.348569i | ||||||||
\(789\) | 8852.87 | 0.399456 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10400.8 | 0.467522 | ||||||||
\(792\) | − 5496.47i | − 0.246602i | ||||||||
\(793\) | − 45947.7i | − 2.05757i | ||||||||
\(794\) | 41532.9 | 1.85636 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 27942.4 | 1.24421 | ||||||||
\(797\) | − 14802.4i | − 0.657876i | −0.944351 | − | 0.328938i | \(-0.893309\pi\) | ||||
0.944351 | − | 0.328938i | \(-0.106691\pi\) | |||||||
\(798\) | 4256.90i | 0.188838i | ||||||||
\(799\) | 12057.5 | 0.533871 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12761.2 | −0.562916 | ||||||||
\(802\) | 3041.19i | 0.133901i | ||||||||
\(803\) | 9829.69i | 0.431983i | ||||||||
\(804\) | 14869.8 | 0.652260 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −55343.9 | −2.41862 | ||||||||
\(807\) | − 18146.0i | − 0.791534i | ||||||||
\(808\) | − 7648.50i | − 0.333011i | ||||||||
\(809\) | 8999.53 | 0.391108 | 0.195554 | − | 0.980693i | \(-0.437349\pi\) | ||||
0.195554 | + | 0.980693i | \(0.437349\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −41368.5 | −1.79117 | −0.895587 | − | 0.444886i | \(-0.853244\pi\) | ||||
−0.895587 | + | 0.444886i | \(0.853244\pi\) | |||||||
\(812\) | − 23022.1i | − 0.994970i | ||||||||
\(813\) | 8768.71i | 0.378268i | ||||||||
\(814\) | −20279.8 | −0.873226 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 24003.6 | 1.02977 | ||||||||
\(817\) | 6467.73i | 0.276961i | ||||||||
\(818\) | − 35914.5i | − 1.53511i | ||||||||
\(819\) | −9004.21 | −0.384167 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27772.2 | 1.18058 | 0.590289 | − | 0.807192i | \(-0.299014\pi\) | ||||
0.590289 | + | 0.807192i | \(0.299014\pi\) | |||||||
\(822\) | 31155.6i | 1.32199i | ||||||||
\(823\) | 9315.89i | 0.394571i | 0.980346 | + | 0.197285i | \(0.0632125\pi\) | ||||
−0.980346 | + | 0.197285i | \(0.936787\pi\) | |||||||
\(824\) | −23284.9 | −0.984426 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −27446.1 | −1.15614 | ||||||||
\(827\) | − 20344.6i | − 0.855443i | −0.903911 | − | 0.427721i | \(-0.859316\pi\) | ||||
0.903911 | − | 0.427721i | \(-0.140684\pi\) | |||||||
\(828\) | 18835.8i | 0.790566i | ||||||||
\(829\) | −16916.7 | −0.708737 | −0.354368 | − | 0.935106i | \(-0.615304\pi\) | ||||
−0.354368 | + | 0.935106i | \(0.615304\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16300.4 | −0.680452 | ||||||||
\(832\) | − 24513.4i | − 1.02145i | ||||||||
\(833\) | 12722.3i | 0.529172i | ||||||||
\(834\) | −45866.5 | −1.90435 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −5061.53 | −0.209398 | ||||||||
\(837\) | 3227.76i | 0.133295i | ||||||||
\(838\) | 17120.2i | 0.705735i | ||||||||
\(839\) | −23690.7 | −0.974844 | −0.487422 | − | 0.873167i | \(-0.662063\pi\) | ||||
−0.487422 | + | 0.873167i | \(0.662063\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12299.2 | −0.504291 | ||||||||
\(842\) | − 71908.1i | − 2.94313i | ||||||||
\(843\) | 23943.1i | 0.978224i | ||||||||
\(844\) | 16862.5 | 0.687714 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −9620.72 | −0.390978 | ||||||||
\(847\) | − 1352.12i | − 0.0548516i | ||||||||
\(848\) | − 30694.9i | − 1.24300i | ||||||||
\(849\) | 8117.14 | 0.328127 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 39824.4 | 1.60419 | ||||||||
\(852\) | − 62413.5i | − 2.50968i | ||||||||
\(853\) | 3804.67i | 0.152719i | 0.997080 | + | 0.0763596i | \(0.0243297\pi\) | ||||
−0.997080 | + | 0.0763596i | \(0.975670\pi\) | |||||||
\(854\) | −29653.6 | −1.18820 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −66093.9 | −2.63907 | ||||||||
\(857\) | − 3125.89i | − 0.124596i | −0.998058 | − | 0.0622978i | \(-0.980157\pi\) | ||||
0.998058 | − | 0.0622978i | \(-0.0198429\pi\) | |||||||
\(858\) | − 15277.3i | − 0.607875i | ||||||||
\(859\) | 38044.2 | 1.51112 | 0.755559 | − | 0.655081i | \(-0.227365\pi\) | ||||
0.755559 | + | 0.655081i | \(0.227365\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9011.06 | −0.356674 | ||||||||
\(862\) | 14028.8i | 0.554317i | ||||||||
\(863\) | − 728.739i | − 0.0287446i | −0.999897 | − | 0.0143723i | \(-0.995425\pi\) | ||||
0.999897 | − | 0.0143723i | \(-0.00457500\pi\) | |||||||
\(864\) | −7160.29 | −0.281942 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3454.39 | 0.135549 | ||||||||
\(867\) | − 4533.86i | − 0.177599i | ||||||||
\(868\) | 25030.6i | 0.978796i | ||||||||
\(869\) | 14340.3 | 0.559795 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23683.9 | 0.921352 | ||||||||
\(872\) | 57372.7i | 2.22808i | ||||||||
\(873\) | − 772.282i | − 0.0299402i | ||||||||
\(874\) | 14183.4 | 0.548924 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 50231.1 | 1.93739 | ||||||||
\(877\) | 18861.7i | 0.726241i | 0.931742 | + | 0.363120i | \(0.118289\pi\) | ||||
−0.931742 | + | 0.363120i | \(0.881711\pi\) | |||||||
\(878\) | − 85383.3i | − 3.28194i | ||||||||
\(879\) | −6623.12 | −0.254144 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24435.2 | 0.934442 | 0.467221 | − | 0.884141i | \(-0.345255\pi\) | ||||
0.467221 | + | 0.884141i | \(0.345255\pi\) | |||||||
\(882\) | − 10151.2i | − 0.387537i | ||||||||
\(883\) | − 3101.93i | − 0.118220i | −0.998251 | − | 0.0591101i | \(-0.981174\pi\) | ||||
0.998251 | − | 0.0591101i | \(-0.0188263\pi\) | |||||||
\(884\) | 97842.4 | 3.72262 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −58458.9 | −2.21667 | ||||||||
\(887\) | 2129.33i | 0.0806043i | 0.999188 | + | 0.0403021i | \(0.0128320\pi\) | ||||
−0.999188 | + | 0.0403021i | \(0.987168\pi\) | |||||||
\(888\) | 59385.7i | 2.24421i | ||||||||
\(889\) | 1055.23 | 0.0398101 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −891.000 | −0.0335013 | ||||||||
\(892\) | 36262.0i | 1.36114i | ||||||||
\(893\) | 5076.82i | 0.190246i | ||||||||
\(894\) | −13631.8 | −0.509973 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 7887.14 | 0.294075 | ||||||||
\(897\) | 30000.7i | 1.11672i | ||||||||
\(898\) | − 10877.5i | − 0.404219i | ||||||||
\(899\) | −13144.6 | −0.487651 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13050.0 | 0.482527 | ||||||||
\(902\) | − 15288.9i | − 0.564373i | ||||||||
\(903\) | 8829.13i | 0.325376i | ||||||||
\(904\) | 51675.6 | 1.90122 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −26050.8 | −0.955276 | ||||||||
\(907\) | 33678.6i | 1.23294i | 0.787378 | + | 0.616471i | \(0.211438\pi\) | ||||
−0.787378 | + | 0.616471i | \(0.788562\pi\) | |||||||
\(908\) | 54455.1i | 1.99026i | ||||||||
\(909\) | −1239.85 | −0.0452402 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28917.6 | −1.05168 | −0.525841 | − | 0.850583i | \(-0.676249\pi\) | ||||
−0.525841 | + | 0.850583i | \(0.676249\pi\) | |||||||
\(912\) | 10106.7i | 0.366960i | ||||||||
\(913\) | 11543.0i | 0.418421i | ||||||||
\(914\) | 82803.4 | 2.99660 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −101404. | −3.65771 | ||||||||
\(917\) | − 14729.4i | − 0.530434i | ||||||||
\(918\) | − 8142.74i | − 0.292756i | ||||||||
\(919\) | 8611.83 | 0.309117 | 0.154558 | − | 0.987984i | \(-0.450605\pi\) | ||||
0.154558 | + | 0.987984i | \(0.450605\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11755.4 | −0.420578 | ||||||||
\(922\) | 68941.8i | 2.46256i | ||||||||
\(923\) | − 99409.2i | − 3.54506i | ||||||||
\(924\) | −6909.52 | −0.246003 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 12686.5 | 0.450219 | ||||||||
\(927\) | 3774.58i | 0.133736i | ||||||||
\(928\) | − 29159.3i | − 1.03147i | ||||||||
\(929\) | 31195.3 | 1.10171 | 0.550853 | − | 0.834602i | \(-0.314302\pi\) | ||||
0.550853 | + | 0.834602i | \(0.314302\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5356.73 | −0.188571 | ||||||||
\(932\) | − 89543.2i | − 3.14709i | ||||||||
\(933\) | − 26307.1i | − 0.923103i | ||||||||
\(934\) | 3990.65 | 0.139805 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −44736.8 | −1.56225 | ||||||||
\(937\) | 24625.3i | 0.858561i | 0.903171 | + | 0.429281i | \(0.141233\pi\) | ||||
−0.903171 | + | 0.429281i | \(0.858767\pi\) | |||||||
\(938\) | − 15285.0i | − 0.532062i | ||||||||
\(939\) | 15176.8 | 0.527449 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3605.28 | 0.124898 | 0.0624488 | − | 0.998048i | \(-0.480109\pi\) | ||||
0.0624488 | + | 0.998048i | \(0.480109\pi\) | |||||||
\(942\) | 10906.0i | 0.377216i | ||||||||
\(943\) | 30023.6i | 1.03680i | ||||||||
\(944\) | −65162.7 | −2.24668 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −14980.2 | −0.514850 | ||||||||
\(947\) | 11634.6i | 0.399231i | 0.979874 | + | 0.199616i | \(0.0639694\pi\) | ||||
−0.979874 | + | 0.199616i | \(0.936031\pi\) | |||||||
\(948\) | − 73281.0i | − 2.51061i | ||||||||
\(949\) | 80005.7 | 2.73666 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24988.6 | −0.852060 | ||||||||
\(952\) | − 36184.8i | − 1.23189i | ||||||||
\(953\) | − 27302.2i | − 0.928021i | −0.885830 | − | 0.464010i | \(-0.846410\pi\) | ||||
0.885830 | − | 0.464010i | \(-0.153590\pi\) | |||||||
\(954\) | −10412.6 | −0.353377 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 110247. | 3.72976 | ||||||||
\(957\) | − 3628.48i | − 0.122562i | ||||||||
\(958\) | − 14388.0i | − 0.485235i | ||||||||
\(959\) | 22443.3 | 0.755715 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15499.6 | −0.520276 | ||||||||
\(962\) | 165061.i | 5.53199i | ||||||||
\(963\) | 10714.1i | 0.358522i | ||||||||
\(964\) | −33857.4 | −1.13120 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 19361.8 | 0.644881 | ||||||||
\(967\) | − 19429.3i | − 0.646125i | −0.946378 | − | 0.323063i | \(-0.895288\pi\) | ||||
0.946378 | − | 0.323063i | \(-0.104712\pi\) | |||||||
\(968\) | − 6717.90i | − 0.223059i | ||||||||
\(969\) | −4296.90 | −0.142452 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42852.0 | 1.41626 | 0.708129 | − | 0.706083i | \(-0.249539\pi\) | ||||
0.708129 | + | 0.706083i | \(0.249539\pi\) | |||||||
\(972\) | 4553.14i | 0.150249i | ||||||||
\(973\) | 33040.4i | 1.08862i | ||||||||
\(974\) | 50243.1 | 1.65287 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −70403.7 | −2.30898 | ||||||||
\(977\) | 6559.02i | 0.214782i | 0.994217 | + | 0.107391i | \(0.0342496\pi\) | ||||
−0.994217 | + | 0.107391i | \(0.965750\pi\) | |||||||
\(978\) | − 45523.7i | − 1.48843i | ||||||||
\(979\) | −15597.1 | −0.509177 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9300.36 | 0.302689 | ||||||||
\(982\) | 70233.3i | 2.28232i | ||||||||
\(983\) | 15077.3i | 0.489208i | 0.969623 | + | 0.244604i | \(0.0786579\pi\) | ||||
−0.969623 | + | 0.244604i | \(0.921342\pi\) | |||||||
\(984\) | −44770.8 | −1.45045 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 33160.2 | 1.07103 | ||||||||
\(987\) | 6930.39i | 0.223502i | ||||||||
\(988\) | 41196.7i | 1.32656i | ||||||||
\(989\) | 29417.4 | 0.945822 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45239.3 | 1.45013 | 0.725063 | − | 0.688683i | \(-0.241811\pi\) | ||||
0.725063 | + | 0.688683i | \(0.241811\pi\) | |||||||
\(992\) | 31703.3i | 1.01470i | ||||||||
\(993\) | − 8705.56i | − 0.278210i | ||||||||
\(994\) | −64156.4 | −2.04720 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 58986.5 | 1.87656 | ||||||||
\(997\) | 30975.1i | 0.983942i | 0.870612 | + | 0.491971i | \(0.163723\pi\) | ||||
−0.870612 | + | 0.491971i | \(0.836277\pi\) | |||||||
\(998\) | − 62968.8i | − 1.99724i | ||||||||
\(999\) | 9626.68 | 0.304879 |
(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 | 825.4.c.p.199.8 | 8 | ||
5.2 | odd | 4 | 825.4.a.t.1.1 | 4 | |||
5.3 | odd | 4 | 165.4.a.h.1.4 | ✓ | 4 | ||
5.4 | even | 2 | inner | 825.4.c.p.199.1 | 8 | ||
15.2 | even | 4 | 2475.4.a.be.1.4 | 4 | |||
15.8 | even | 4 | 495.4.a.m.1.1 | 4 | |||
55.43 | even | 4 | 1815.4.a.t.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.4.a.h.1.4 | ✓ | 4 | 5.3 | odd | 4 | ||
495.4.a.m.1.1 | 4 | 15.8 | even | 4 | |||
825.4.a.t.1.1 | 4 | 5.2 | odd | 4 | |||
825.4.c.p.199.1 | 8 | 5.4 | even | 2 | inner | ||
825.4.c.p.199.8 | 8 | 1.1 | even | 1 | trivial | ||
1815.4.a.t.1.1 | 4 | 55.43 | even | 4 | |||
2475.4.a.be.1.4 | 4 | 15.2 | even | 4 |