Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,4,Mod(337,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.337");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.b (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: | \(29.9139683729\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{18} + 112 x^{16} + 5026 x^{14} + 114847 x^{12} + 1397921 x^{10} + 8545747 x^{8} + 21033277 x^{6} + 6703200 x^{4} + 137781 x^{2} + 729 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 13^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.7 | ||
Root | \(-0.100291i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.337 |
Dual form | 507.4.b.k.337.12 |
$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.34727i | − 0.829886i | −0.909848 | − | 0.414943i | \(-0.863802\pi\) | ||||
0.909848 | − | 0.414943i | \(-0.136198\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 2.49032 | 0.311290 | ||||||||
\(5\) | − 15.3991i | − 1.37734i | −0.725077 | − | 0.688668i | \(-0.758196\pi\) | ||||
0.725077 | − | 0.688668i | \(-0.241804\pi\) | |||||||
\(6\) | − 7.04181i | − 0.479135i | ||||||||
\(7\) | − 10.1317i | − 0.547062i | −0.961863 | − | 0.273531i | \(-0.911808\pi\) | ||||
0.961863 | − | 0.273531i | \(-0.0881917\pi\) | |||||||
\(8\) | − 24.6236i | − 1.08822i | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −36.1458 | −1.14303 | ||||||||
\(11\) | 15.0669i | 0.412985i | 0.978448 | + | 0.206493i | \(0.0662050\pi\) | ||||
−0.978448 | + | 0.206493i | \(0.933795\pi\) | |||||||
\(12\) | 7.47096 | 0.179723 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −23.7819 | −0.453999 | ||||||||
\(15\) | − 46.1972i | − 0.795205i | ||||||||
\(16\) | −37.8757 | −0.591809 | ||||||||
\(17\) | −90.8352 | −1.29593 | −0.647964 | − | 0.761671i | \(-0.724379\pi\) | ||||
−0.647964 | + | 0.761671i | \(0.724379\pi\) | |||||||
\(18\) | − 21.1254i | − 0.276629i | ||||||||
\(19\) | − 114.640i | − 1.38422i | −0.721792 | − | 0.692110i | \(-0.756681\pi\) | ||||
0.721792 | − | 0.692110i | \(-0.243319\pi\) | |||||||
\(20\) | − 38.3486i | − 0.428751i | ||||||||
\(21\) | − 30.3952i | − 0.315847i | ||||||||
\(22\) | 35.3661 | 0.342731 | ||||||||
\(23\) | −75.7635 | −0.686860 | −0.343430 | − | 0.939178i | \(-0.611589\pi\) | ||||
−0.343430 | + | 0.939178i | \(0.611589\pi\) | |||||||
\(24\) | − 73.8709i | − 0.628284i | ||||||||
\(25\) | −112.132 | −0.897052 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | − 25.2313i | − 0.170295i | ||||||||
\(29\) | 214.817 | 1.37553 | 0.687767 | − | 0.725931i | \(-0.258591\pi\) | ||||
0.687767 | + | 0.725931i | \(0.258591\pi\) | |||||||
\(30\) | −108.437 | −0.659929 | ||||||||
\(31\) | 284.476i | 1.64817i | 0.566463 | + | 0.824087i | \(0.308311\pi\) | ||||
−0.566463 | + | 0.824087i | \(0.691689\pi\) | |||||||
\(32\) | − 108.084i | − 0.597087i | ||||||||
\(33\) | 45.2007i | 0.238437i | ||||||||
\(34\) | 213.215i | 1.07547i | ||||||||
\(35\) | −156.019 | −0.753488 | ||||||||
\(36\) | 22.4129 | 0.103763 | ||||||||
\(37\) | 358.878i | 1.59457i | 0.603602 | + | 0.797286i | \(0.293732\pi\) | ||||
−0.603602 | + | 0.797286i | \(0.706268\pi\) | |||||||
\(38\) | −269.091 | −1.14874 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −379.181 | −1.49884 | ||||||||
\(41\) | − 313.154i | − 1.19284i | −0.802672 | − | 0.596421i | \(-0.796589\pi\) | ||||
0.802672 | − | 0.596421i | \(-0.203411\pi\) | |||||||
\(42\) | −71.3458 | −0.262116 | ||||||||
\(43\) | 296.702 | 1.05225 | 0.526123 | − | 0.850409i | \(-0.323645\pi\) | ||||
0.526123 | + | 0.850409i | \(0.323645\pi\) | |||||||
\(44\) | 37.5214i | 0.128558i | ||||||||
\(45\) | − 138.592i | − 0.459112i | ||||||||
\(46\) | 177.837i | 0.570015i | ||||||||
\(47\) | − 316.691i | − 0.982854i | −0.870919 | − | 0.491427i | \(-0.836475\pi\) | ||||
0.870919 | − | 0.491427i | \(-0.163525\pi\) | |||||||
\(48\) | −113.627 | −0.341681 | ||||||||
\(49\) | 240.348 | 0.700723 | ||||||||
\(50\) | 263.203i | 0.744451i | ||||||||
\(51\) | −272.506 | −0.748204 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 163.911 | 0.424810 | 0.212405 | − | 0.977182i | \(-0.431870\pi\) | ||||
0.212405 | + | 0.977182i | \(0.431870\pi\) | |||||||
\(54\) | − 63.3763i | − 0.159712i | ||||||||
\(55\) | 232.016 | 0.568819 | ||||||||
\(56\) | −249.480 | −0.595324 | ||||||||
\(57\) | − 343.920i | − 0.799180i | ||||||||
\(58\) | − 504.233i | − 1.14154i | ||||||||
\(59\) | 254.149i | 0.560803i | 0.959883 | + | 0.280401i | \(0.0904675\pi\) | ||||
−0.959883 | + | 0.280401i | \(0.909532\pi\) | |||||||
\(60\) | − 115.046i | − 0.247539i | ||||||||
\(61\) | −935.247 | −1.96305 | −0.981526 | − | 0.191330i | \(-0.938720\pi\) | ||||
−0.981526 | + | 0.191330i | \(0.938720\pi\) | |||||||
\(62\) | 667.742 | 1.36780 | ||||||||
\(63\) | − 91.1856i | − 0.182354i | ||||||||
\(64\) | −556.709 | −1.08732 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 106.098 | 0.197876 | ||||||||
\(67\) | 240.494i | 0.438522i | 0.975666 | + | 0.219261i | \(0.0703646\pi\) | ||||
−0.975666 | + | 0.219261i | \(0.929635\pi\) | |||||||
\(68\) | −226.209 | −0.403409 | ||||||||
\(69\) | −227.291 | −0.396559 | ||||||||
\(70\) | 366.220i | 0.625309i | ||||||||
\(71\) | − 947.455i | − 1.58369i | −0.610720 | − | 0.791847i | \(-0.709120\pi\) | ||||
0.610720 | − | 0.791847i | \(-0.290880\pi\) | |||||||
\(72\) | − 221.613i | − 0.362740i | ||||||||
\(73\) | − 430.712i | − 0.690562i | −0.938499 | − | 0.345281i | \(-0.887784\pi\) | ||||
0.938499 | − | 0.345281i | \(-0.112216\pi\) | |||||||
\(74\) | 842.384 | 1.32331 | ||||||||
\(75\) | −336.395 | −0.517913 | ||||||||
\(76\) | − 285.490i | − 0.430894i | ||||||||
\(77\) | 152.654 | 0.225929 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −496.620 | −0.707268 | −0.353634 | − | 0.935384i | \(-0.615054\pi\) | ||||
−0.353634 | + | 0.935384i | \(0.615054\pi\) | |||||||
\(80\) | 583.251i | 0.815119i | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −735.058 | −0.989922 | ||||||||
\(83\) | − 392.527i | − 0.519102i | −0.965729 | − | 0.259551i | \(-0.916425\pi\) | ||||
0.965729 | − | 0.259551i | \(-0.0835746\pi\) | |||||||
\(84\) | − 75.6938i | − 0.0983199i | ||||||||
\(85\) | 1398.78i | 1.78493i | ||||||||
\(86\) | − 696.439i | − 0.873244i | ||||||||
\(87\) | 644.451 | 0.794165 | ||||||||
\(88\) | 371.002 | 0.449419 | ||||||||
\(89\) | 979.895i | 1.16706i | 0.812090 | + | 0.583532i | \(0.198330\pi\) | ||||
−0.812090 | + | 0.583532i | \(0.801670\pi\) | |||||||
\(90\) | −325.312 | −0.381010 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −188.675 | −0.213813 | ||||||||
\(93\) | 853.428i | 0.951574i | ||||||||
\(94\) | −743.360 | −0.815656 | ||||||||
\(95\) | −1765.35 | −1.90654 | ||||||||
\(96\) | − 324.253i | − 0.344729i | ||||||||
\(97\) | 553.356i | 0.579225i | 0.957144 | + | 0.289613i | \(0.0935265\pi\) | ||||
−0.957144 | + | 0.289613i | \(0.906474\pi\) | |||||||
\(98\) | − 564.162i | − 0.581520i | ||||||||
\(99\) | 135.602i | 0.137662i | ||||||||
\(100\) | −279.243 | −0.279243 | ||||||||
\(101\) | 763.951 | 0.752633 | 0.376317 | − | 0.926491i | \(-0.377190\pi\) | ||||
0.376317 | + | 0.926491i | \(0.377190\pi\) | |||||||
\(102\) | 639.645i | 0.620924i | ||||||||
\(103\) | −182.518 | −0.174602 | −0.0873010 | − | 0.996182i | \(-0.527824\pi\) | ||||
−0.0873010 | + | 0.996182i | \(0.527824\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −468.058 | −0.435027 | ||||||||
\(106\) | − 384.744i | − 0.352544i | ||||||||
\(107\) | 183.699 | 0.165971 | 0.0829855 | − | 0.996551i | \(-0.473554\pi\) | ||||
0.0829855 | + | 0.996551i | \(0.473554\pi\) | |||||||
\(108\) | 67.2386 | 0.0599078 | ||||||||
\(109\) | − 1774.42i | − 1.55925i | −0.626244 | − | 0.779627i | \(-0.715408\pi\) | ||||
0.626244 | − | 0.779627i | \(-0.284592\pi\) | |||||||
\(110\) | − 544.605i | − 0.472055i | ||||||||
\(111\) | 1076.63i | 0.920627i | ||||||||
\(112\) | 383.747i | 0.323756i | ||||||||
\(113\) | 417.288 | 0.347391 | 0.173695 | − | 0.984799i | \(-0.444429\pi\) | ||||
0.173695 | + | 0.984799i | \(0.444429\pi\) | |||||||
\(114\) | −807.273 | −0.663228 | ||||||||
\(115\) | 1166.69i | 0.946037i | ||||||||
\(116\) | 534.963 | 0.428190 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 596.556 | 0.465402 | ||||||||
\(119\) | 920.318i | 0.708953i | ||||||||
\(120\) | −1137.54 | −0.865358 | ||||||||
\(121\) | 1103.99 | 0.829443 | ||||||||
\(122\) | 2195.28i | 1.62911i | ||||||||
\(123\) | − 939.463i | − 0.688687i | ||||||||
\(124\) | 708.436i | 0.513060i | ||||||||
\(125\) | − 198.162i | − 0.141793i | ||||||||
\(126\) | −214.037 | −0.151333 | ||||||||
\(127\) | 1951.69 | 1.36366 | 0.681828 | − | 0.731513i | \(-0.261185\pi\) | ||||
0.681828 | + | 0.731513i | \(0.261185\pi\) | |||||||
\(128\) | 442.072i | 0.305266i | ||||||||
\(129\) | 890.105 | 0.607514 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1475.61 | −0.984159 | −0.492080 | − | 0.870550i | \(-0.663763\pi\) | ||||
−0.492080 | + | 0.870550i | \(0.663763\pi\) | |||||||
\(132\) | 112.564i | 0.0742231i | ||||||||
\(133\) | −1161.50 | −0.757255 | ||||||||
\(134\) | 564.503 | 0.363923 | ||||||||
\(135\) | − 415.775i | − 0.265068i | ||||||||
\(136\) | 2236.69i | 1.41026i | ||||||||
\(137\) | − 1900.71i | − 1.18532i | −0.805453 | − | 0.592660i | \(-0.798078\pi\) | ||||
0.805453 | − | 0.592660i | \(-0.201922\pi\) | |||||||
\(138\) | 533.512i | 0.329099i | ||||||||
\(139\) | −2326.76 | −1.41981 | −0.709903 | − | 0.704299i | \(-0.751261\pi\) | ||||
−0.709903 | + | 0.704299i | \(0.751261\pi\) | |||||||
\(140\) | −388.538 | −0.234553 | ||||||||
\(141\) | − 950.073i | − 0.567451i | ||||||||
\(142\) | −2223.93 | −1.31428 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −340.882 | −0.197270 | ||||||||
\(145\) | − 3307.98i | − 1.89457i | ||||||||
\(146\) | −1011.00 | −0.573088 | ||||||||
\(147\) | 721.044 | 0.404563 | ||||||||
\(148\) | 893.721i | 0.496374i | ||||||||
\(149\) | 1370.92i | 0.753761i | 0.926262 | + | 0.376881i | \(0.123003\pi\) | ||||
−0.926262 | + | 0.376881i | \(0.876997\pi\) | |||||||
\(150\) | 789.609i | 0.429809i | ||||||||
\(151\) | 1177.57i | 0.634628i | 0.948320 | + | 0.317314i | \(0.102781\pi\) | ||||
−0.948320 | + | 0.317314i | \(0.897219\pi\) | |||||||
\(152\) | −2822.85 | −1.50634 | ||||||||
\(153\) | −817.517 | −0.431976 | ||||||||
\(154\) | − 358.320i | − 0.187495i | ||||||||
\(155\) | 4380.67 | 2.27009 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1621.57 | 0.824302 | 0.412151 | − | 0.911116i | \(-0.364778\pi\) | ||||
0.412151 | + | 0.911116i | \(0.364778\pi\) | |||||||
\(158\) | 1165.70i | 0.586951i | ||||||||
\(159\) | 491.734 | 0.245264 | ||||||||
\(160\) | −1664.40 | −0.822389 | ||||||||
\(161\) | 767.616i | 0.375755i | ||||||||
\(162\) | − 190.129i | − 0.0922095i | ||||||||
\(163\) | − 133.130i | − 0.0639727i | −0.999488 | − | 0.0319864i | \(-0.989817\pi\) | ||||
0.999488 | − | 0.0319864i | \(-0.0101833\pi\) | |||||||
\(164\) | − 779.854i | − 0.371320i | ||||||||
\(165\) | 696.049 | 0.328408 | ||||||||
\(166\) | −921.368 | −0.430795 | ||||||||
\(167\) | − 490.724i | − 0.227385i | −0.993516 | − | 0.113693i | \(-0.963732\pi\) | ||||
0.993516 | − | 0.113693i | \(-0.0362679\pi\) | |||||||
\(168\) | −748.440 | −0.343711 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 3283.31 | 1.48129 | ||||||||
\(171\) | − 1031.76i | − 0.461407i | ||||||||
\(172\) | 738.882 | 0.327554 | ||||||||
\(173\) | −2008.13 | −0.882518 | −0.441259 | − | 0.897380i | \(-0.645468\pi\) | ||||
−0.441259 | + | 0.897380i | \(0.645468\pi\) | |||||||
\(174\) | − 1512.70i | − 0.659066i | ||||||||
\(175\) | 1136.09i | 0.490743i | ||||||||
\(176\) | − 570.670i | − 0.244408i | ||||||||
\(177\) | 762.446i | 0.323779i | ||||||||
\(178\) | 2300.08 | 0.968529 | ||||||||
\(179\) | 2152.60 | 0.898843 | 0.449421 | − | 0.893320i | \(-0.351630\pi\) | ||||
0.449421 | + | 0.893320i | \(0.351630\pi\) | |||||||
\(180\) | − 345.138i | − 0.142917i | ||||||||
\(181\) | −834.690 | −0.342774 | −0.171387 | − | 0.985204i | \(-0.554825\pi\) | ||||
−0.171387 | + | 0.985204i | \(0.554825\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2805.74 | −1.13337 | ||||||||
\(184\) | 1865.57i | 0.747455i | ||||||||
\(185\) | 5526.39 | 2.19626 | ||||||||
\(186\) | 2003.23 | 0.789697 | ||||||||
\(187\) | − 1368.60i | − 0.535200i | ||||||||
\(188\) | − 788.662i | − 0.305953i | ||||||||
\(189\) | − 273.557i | − 0.105282i | ||||||||
\(190\) | 4143.75i | 1.58221i | ||||||||
\(191\) | 4464.71 | 1.69139 | 0.845695 | − | 0.533667i | \(-0.179186\pi\) | ||||
0.845695 | + | 0.533667i | \(0.179186\pi\) | |||||||
\(192\) | −1670.13 | −0.627766 | ||||||||
\(193\) | − 3299.84i | − 1.23071i | −0.788248 | − | 0.615357i | \(-0.789012\pi\) | ||||
0.788248 | − | 0.615357i | \(-0.210988\pi\) | |||||||
\(194\) | 1298.88 | 0.480691 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 598.543 | 0.218128 | ||||||||
\(197\) | − 2973.59i | − 1.07543i | −0.843127 | − | 0.537714i | \(-0.819288\pi\) | ||||
0.843127 | − | 0.537714i | \(-0.180712\pi\) | |||||||
\(198\) | 318.295 | 0.114244 | ||||||||
\(199\) | 5430.82 | 1.93457 | 0.967287 | − | 0.253684i | \(-0.0816422\pi\) | ||||
0.967287 | + | 0.253684i | \(0.0816422\pi\) | |||||||
\(200\) | 2761.08i | 0.976191i | ||||||||
\(201\) | 721.481i | 0.253181i | ||||||||
\(202\) | − 1793.20i | − 0.624600i | ||||||||
\(203\) | − 2176.47i | − 0.752503i | ||||||||
\(204\) | −678.626 | −0.232909 | ||||||||
\(205\) | −4822.29 | −1.64294 | ||||||||
\(206\) | 428.419i | 0.144900i | ||||||||
\(207\) | −681.872 | −0.228953 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1727.27 | 0.571663 | ||||||||
\(210\) | 1098.66i | 0.361022i | ||||||||
\(211\) | 1228.25 | 0.400742 | 0.200371 | − | 0.979720i | \(-0.435785\pi\) | ||||
0.200371 | + | 0.979720i | \(0.435785\pi\) | |||||||
\(212\) | 408.192 | 0.132239 | ||||||||
\(213\) | − 2842.37i | − 0.914346i | ||||||||
\(214\) | − 431.192i | − 0.137737i | ||||||||
\(215\) | − 4568.93i | − 1.44930i | ||||||||
\(216\) | − 664.838i | − 0.209428i | ||||||||
\(217\) | 2882.24 | 0.901654 | ||||||||
\(218\) | −4165.05 | −1.29400 | ||||||||
\(219\) | − 1292.14i | − 0.398696i | ||||||||
\(220\) | 577.795 | 0.177068 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 2527.15 | 0.764015 | ||||||||
\(223\) | 685.256i | 0.205776i | 0.994693 | + | 0.102888i | \(0.0328084\pi\) | ||||
−0.994693 | + | 0.102888i | \(0.967192\pi\) | |||||||
\(224\) | −1095.08 | −0.326644 | ||||||||
\(225\) | −1009.18 | −0.299017 | ||||||||
\(226\) | − 979.487i | − 0.288294i | ||||||||
\(227\) | − 287.067i | − 0.0839354i | −0.999119 | − | 0.0419677i | \(-0.986637\pi\) | ||||
0.999119 | − | 0.0419677i | \(-0.0133627\pi\) | |||||||
\(228\) | − 856.470i | − 0.248777i | ||||||||
\(229\) | − 2302.23i | − 0.664347i | −0.943218 | − | 0.332174i | \(-0.892218\pi\) | ||||
0.943218 | − | 0.332174i | \(-0.107782\pi\) | |||||||
\(230\) | 2738.53 | 0.785102 | ||||||||
\(231\) | 457.961 | 0.130440 | ||||||||
\(232\) | − 5289.57i | − 1.49688i | ||||||||
\(233\) | 970.620 | 0.272908 | 0.136454 | − | 0.990646i | \(-0.456429\pi\) | ||||
0.136454 | + | 0.990646i | \(0.456429\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4876.75 | −1.35372 | ||||||||
\(236\) | 632.912i | 0.174572i | ||||||||
\(237\) | −1489.86 | −0.408341 | ||||||||
\(238\) | 2160.24 | 0.588350 | ||||||||
\(239\) | 5007.40i | 1.35524i | 0.735413 | + | 0.677619i | \(0.236988\pi\) | ||||
−0.735413 | + | 0.677619i | \(0.763012\pi\) | |||||||
\(240\) | 1749.75i | 0.470609i | ||||||||
\(241\) | − 540.092i | − 0.144358i | −0.997392 | − | 0.0721792i | \(-0.977005\pi\) | ||||
0.997392 | − | 0.0721792i | \(-0.0229953\pi\) | |||||||
\(242\) | − 2591.36i | − 0.688343i | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −2329.07 | −0.611078 | ||||||||
\(245\) | − 3701.14i | − 0.965130i | ||||||||
\(246\) | −2205.17 | −0.571531 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 7004.83 | 1.79358 | ||||||||
\(249\) | − 1177.58i | − 0.299704i | ||||||||
\(250\) | −465.141 | −0.117672 | ||||||||
\(251\) | 6087.80 | 1.53091 | 0.765455 | − | 0.643489i | \(-0.222514\pi\) | ||||
0.765455 | + | 0.643489i | \(0.222514\pi\) | |||||||
\(252\) | − 227.081i | − 0.0567650i | ||||||||
\(253\) | − 1141.52i | − 0.283663i | ||||||||
\(254\) | − 4581.14i | − 1.13168i | ||||||||
\(255\) | 4196.34i | 1.03053i | ||||||||
\(256\) | −3416.01 | −0.833987 | ||||||||
\(257\) | 5096.34 | 1.23697 | 0.618484 | − | 0.785797i | \(-0.287747\pi\) | ||||
0.618484 | + | 0.785797i | \(0.287747\pi\) | |||||||
\(258\) | − 2089.32i | − 0.504167i | ||||||||
\(259\) | 3636.06 | 0.872330 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1933.35 | 0.458511 | ||||||||
\(262\) | 3463.66i | 0.816739i | ||||||||
\(263\) | 3405.50 | 0.798450 | 0.399225 | − | 0.916853i | \(-0.369279\pi\) | ||||
0.399225 | + | 0.916853i | \(0.369279\pi\) | |||||||
\(264\) | 1113.00 | 0.259472 | ||||||||
\(265\) | − 2524.08i | − 0.585106i | ||||||||
\(266\) | 2726.36i | 0.628435i | ||||||||
\(267\) | 2939.68i | 0.673804i | ||||||||
\(268\) | 598.906i | 0.136507i | ||||||||
\(269\) | −2720.44 | −0.616611 | −0.308306 | − | 0.951287i | \(-0.599762\pi\) | ||||
−0.308306 | + | 0.951287i | \(0.599762\pi\) | |||||||
\(270\) | −975.937 | −0.219976 | ||||||||
\(271\) | 6954.27i | 1.55883i | 0.626511 | + | 0.779413i | \(0.284482\pi\) | ||||
−0.626511 | + | 0.779413i | \(0.715518\pi\) | |||||||
\(272\) | 3440.45 | 0.766941 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4461.49 | −0.983680 | ||||||||
\(275\) | − 1689.47i | − 0.370470i | ||||||||
\(276\) | −566.026 | −0.123445 | ||||||||
\(277\) | 6563.96 | 1.42379 | 0.711895 | − | 0.702286i | \(-0.247837\pi\) | ||||
0.711895 | + | 0.702286i | \(0.247837\pi\) | |||||||
\(278\) | 5461.53i | 1.17828i | ||||||||
\(279\) | 2560.28i | 0.549392i | ||||||||
\(280\) | 3841.76i | 0.819961i | ||||||||
\(281\) | − 652.800i | − 0.138586i | −0.997596 | − | 0.0692932i | \(-0.977926\pi\) | ||||
0.997596 | − | 0.0692932i | \(-0.0220744\pi\) | |||||||
\(282\) | −2230.08 | −0.470919 | ||||||||
\(283\) | −6010.62 | −1.26252 | −0.631262 | − | 0.775570i | \(-0.717463\pi\) | ||||
−0.631262 | + | 0.775570i | \(0.717463\pi\) | |||||||
\(284\) | − 2359.47i | − 0.492988i | ||||||||
\(285\) | −5296.05 | −1.10074 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3172.80 | −0.652558 | ||||||||
\(288\) | − 972.759i | − 0.199029i | ||||||||
\(289\) | 3338.04 | 0.679430 | ||||||||
\(290\) | −7764.73 | −1.57228 | ||||||||
\(291\) | 1660.07i | 0.334416i | ||||||||
\(292\) | − 1072.61i | − 0.214965i | ||||||||
\(293\) | − 1912.72i | − 0.381372i | −0.981651 | − | 0.190686i | \(-0.938929\pi\) | ||||
0.981651 | − | 0.190686i | \(-0.0610713\pi\) | |||||||
\(294\) | − 1692.49i | − 0.335741i | ||||||||
\(295\) | 3913.66 | 0.772413 | ||||||||
\(296\) | 8836.87 | 1.73525 | ||||||||
\(297\) | 406.806i | 0.0794791i | ||||||||
\(298\) | 3217.93 | 0.625535 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −837.730 | −0.161221 | ||||||||
\(301\) | − 3006.10i | − 0.575644i | ||||||||
\(302\) | 2764.06 | 0.526669 | ||||||||
\(303\) | 2291.85 | 0.434533 | ||||||||
\(304\) | 4342.07i | 0.819194i | ||||||||
\(305\) | 14401.9i | 2.70378i | ||||||||
\(306\) | 1918.93i | 0.358491i | ||||||||
\(307\) | − 1983.07i | − 0.368665i | −0.982864 | − | 0.184332i | \(-0.940988\pi\) | ||||
0.982864 | − | 0.184332i | \(-0.0590123\pi\) | |||||||
\(308\) | 380.157 | 0.0703294 | ||||||||
\(309\) | −547.553 | −0.100807 | ||||||||
\(310\) | − 10282.6i | − 1.88391i | ||||||||
\(311\) | −1893.76 | −0.345291 | −0.172645 | − | 0.984984i | \(-0.555231\pi\) | ||||
−0.172645 | + | 0.984984i | \(0.555231\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4574.19 | 0.826034 | 0.413017 | − | 0.910723i | \(-0.364475\pi\) | ||||
0.413017 | + | 0.910723i | \(0.364475\pi\) | |||||||
\(314\) | − 3806.26i | − 0.684076i | ||||||||
\(315\) | −1404.17 | −0.251163 | ||||||||
\(316\) | −1236.74 | −0.220165 | ||||||||
\(317\) | − 7594.53i | − 1.34559i | −0.739830 | − | 0.672794i | \(-0.765094\pi\) | ||||
0.739830 | − | 0.672794i | \(-0.234906\pi\) | |||||||
\(318\) | − 1154.23i | − 0.203541i | ||||||||
\(319\) | 3236.62i | 0.568076i | ||||||||
\(320\) | 8572.81i | 1.49761i | ||||||||
\(321\) | 551.098 | 0.0958234 | ||||||||
\(322\) | 1801.80 | 0.311834 | ||||||||
\(323\) | 10413.3i | 1.79385i | ||||||||
\(324\) | 201.716 | 0.0345878 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −312.492 | −0.0530901 | ||||||||
\(327\) | − 5323.27i | − 0.900236i | ||||||||
\(328\) | −7710.99 | −1.29807 | ||||||||
\(329\) | −3208.63 | −0.537682 | ||||||||
\(330\) | − 1633.82i | − 0.272541i | ||||||||
\(331\) | 1738.58i | 0.288705i | 0.989526 | + | 0.144352i | \(0.0461099\pi\) | ||||
−0.989526 | + | 0.144352i | \(0.953890\pi\) | |||||||
\(332\) | − 977.519i | − 0.161591i | ||||||||
\(333\) | 3229.90i | 0.531524i | ||||||||
\(334\) | −1151.86 | −0.188704 | ||||||||
\(335\) | 3703.38 | 0.603992 | ||||||||
\(336\) | 1151.24i | 0.186921i | ||||||||
\(337\) | 2710.61 | 0.438149 | 0.219074 | − | 0.975708i | \(-0.429696\pi\) | ||||
0.219074 | + | 0.975708i | \(0.429696\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1251.86 | 0.200566 | ||||||||
\(340\) | 3483.41i | 0.555630i | ||||||||
\(341\) | −4286.17 | −0.680672 | ||||||||
\(342\) | −2421.82 | −0.382915 | ||||||||
\(343\) | − 5910.33i | − 0.930401i | ||||||||
\(344\) | − 7305.87i | − 1.14508i | ||||||||
\(345\) | 3500.06i | 0.546195i | ||||||||
\(346\) | 4713.63i | 0.732389i | ||||||||
\(347\) | −2506.81 | −0.387817 | −0.193908 | − | 0.981020i | \(-0.562116\pi\) | ||||
−0.193908 | + | 0.981020i | \(0.562116\pi\) | |||||||
\(348\) | 1604.89 | 0.247216 | ||||||||
\(349\) | 7536.48i | 1.15593i | 0.816063 | + | 0.577963i | \(0.196152\pi\) | ||||
−0.816063 | + | 0.577963i | \(0.803848\pi\) | |||||||
\(350\) | 2666.70 | 0.407261 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1628.50 | 0.246588 | ||||||||
\(353\) | 8992.88i | 1.35593i | 0.735095 | + | 0.677964i | \(0.237138\pi\) | ||||
−0.735095 | + | 0.677964i | \(0.762862\pi\) | |||||||
\(354\) | 1789.67 | 0.268700 | ||||||||
\(355\) | −14589.9 | −2.18128 | ||||||||
\(356\) | 2440.25i | 0.363295i | ||||||||
\(357\) | 2760.96i | 0.409314i | ||||||||
\(358\) | − 5052.74i | − 0.745937i | ||||||||
\(359\) | − 4566.64i | − 0.671359i | −0.941976 | − | 0.335679i | \(-0.891034\pi\) | ||||
0.941976 | − | 0.335679i | \(-0.108966\pi\) | |||||||
\(360\) | −3412.63 | −0.499615 | ||||||||
\(361\) | −6283.31 | −0.916068 | ||||||||
\(362\) | 1959.24i | 0.284463i | ||||||||
\(363\) | 3311.97 | 0.478879 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6632.57 | −0.951136 | ||||||||
\(366\) | 6585.84i | 0.940566i | ||||||||
\(367\) | −6449.50 | −0.917332 | −0.458666 | − | 0.888609i | \(-0.651673\pi\) | ||||
−0.458666 | + | 0.888609i | \(0.651673\pi\) | |||||||
\(368\) | 2869.60 | 0.406490 | ||||||||
\(369\) | − 2818.39i | − 0.397614i | ||||||||
\(370\) | − 12971.9i | − 1.82264i | ||||||||
\(371\) | − 1660.71i | − 0.232398i | ||||||||
\(372\) | 2125.31i | 0.296215i | ||||||||
\(373\) | 7648.89 | 1.06178 | 0.530891 | − | 0.847440i | \(-0.321857\pi\) | ||||
0.530891 | + | 0.847440i | \(0.321857\pi\) | |||||||
\(374\) | −3212.49 | −0.444154 | ||||||||
\(375\) | − 594.487i | − 0.0818645i | ||||||||
\(376\) | −7798.08 | −1.06956 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −642.112 | −0.0873722 | ||||||||
\(379\) | 10297.8i | 1.39567i | 0.716256 | + | 0.697837i | \(0.245854\pi\) | ||||
−0.716256 | + | 0.697837i | \(0.754146\pi\) | |||||||
\(380\) | −4396.28 | −0.593486 | ||||||||
\(381\) | 5855.06 | 0.787307 | ||||||||
\(382\) | − 10479.9i | − 1.40366i | ||||||||
\(383\) | − 10258.0i | − 1.36856i | −0.729217 | − | 0.684282i | \(-0.760116\pi\) | ||||
0.729217 | − | 0.684282i | \(-0.239884\pi\) | |||||||
\(384\) | 1326.22i | 0.176245i | ||||||||
\(385\) | − 2350.73i | − 0.311180i | ||||||||
\(386\) | −7745.63 | −1.02135 | ||||||||
\(387\) | 2670.31 | 0.350749 | ||||||||
\(388\) | 1378.03i | 0.180307i | ||||||||
\(389\) | 4771.57 | 0.621924 | 0.310962 | − | 0.950422i | \(-0.399349\pi\) | ||||
0.310962 | + | 0.950422i | \(0.399349\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6882.00 | 0.890122 | ||||||||
\(392\) | − 5918.24i | − 0.762541i | ||||||||
\(393\) | −4426.84 | −0.568205 | ||||||||
\(394\) | −6979.82 | −0.892483 | ||||||||
\(395\) | 7647.50i | 0.974145i | ||||||||
\(396\) | 337.693i | 0.0428528i | ||||||||
\(397\) | 2291.22i | 0.289655i | 0.989457 | + | 0.144827i | \(0.0462627\pi\) | ||||
−0.989457 | + | 0.144827i | \(0.953737\pi\) | |||||||
\(398\) | − 12747.6i | − 1.60548i | ||||||||
\(399\) | −3484.50 | −0.437201 | ||||||||
\(400\) | 4247.07 | 0.530883 | ||||||||
\(401\) | 7534.63i | 0.938308i | 0.883116 | + | 0.469154i | \(0.155441\pi\) | ||||
−0.883116 | + | 0.469154i | \(0.844559\pi\) | |||||||
\(402\) | 1693.51 | 0.210111 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 1902.48 | 0.234287 | ||||||||
\(405\) | − 1247.33i | − 0.153037i | ||||||||
\(406\) | −5108.76 | −0.624491 | ||||||||
\(407\) | −5407.18 | −0.658535 | ||||||||
\(408\) | 6710.08i | 0.814211i | ||||||||
\(409\) | 1517.97i | 0.183517i | 0.995781 | + | 0.0917587i | \(0.0292488\pi\) | ||||
−0.995781 | + | 0.0917587i | \(0.970751\pi\) | |||||||
\(410\) | 11319.2i | 1.36345i | ||||||||
\(411\) | − 5702.14i | − 0.684345i | ||||||||
\(412\) | −454.528 | −0.0543519 | ||||||||
\(413\) | 2574.97 | 0.306794 | ||||||||
\(414\) | 1600.54i | 0.190005i | ||||||||
\(415\) | −6044.56 | −0.714978 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6980.28 | −0.819726 | ||||||||
\(418\) | − 4054.36i | − 0.474415i | ||||||||
\(419\) | 8080.97 | 0.942199 | 0.471100 | − | 0.882080i | \(-0.343857\pi\) | ||||
0.471100 | + | 0.882080i | \(0.343857\pi\) | |||||||
\(420\) | −1165.61 | −0.135419 | ||||||||
\(421\) | − 8073.13i | − 0.934585i | −0.884103 | − | 0.467293i | \(-0.845229\pi\) | ||||
0.884103 | − | 0.467293i | \(-0.154771\pi\) | |||||||
\(422\) | − 2883.05i | − 0.332570i | ||||||||
\(423\) | − 2850.22i | − 0.327618i | ||||||||
\(424\) | − 4036.09i | − 0.462287i | ||||||||
\(425\) | 10185.5 | 1.16252 | ||||||||
\(426\) | −6671.80 | −0.758803 | ||||||||
\(427\) | 9475.68i | 1.07391i | ||||||||
\(428\) | 457.470 | 0.0516651 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −10724.5 | −1.20275 | ||||||||
\(431\) | − 2241.39i | − 0.250496i | −0.992125 | − | 0.125248i | \(-0.960027\pi\) | ||||
0.992125 | − | 0.125248i | \(-0.0399726\pi\) | |||||||
\(432\) | −1022.65 | −0.113894 | ||||||||
\(433\) | −10237.9 | −1.13626 | −0.568130 | − | 0.822939i | \(-0.692333\pi\) | ||||
−0.568130 | + | 0.822939i | \(0.692333\pi\) | |||||||
\(434\) | − 6765.39i | − 0.748270i | ||||||||
\(435\) | − 9923.94i | − 1.09383i | ||||||||
\(436\) | − 4418.88i | − 0.485380i | ||||||||
\(437\) | 8685.52i | 0.950766i | ||||||||
\(438\) | −3033.00 | −0.330872 | ||||||||
\(439\) | 5416.69 | 0.588894 | 0.294447 | − | 0.955668i | \(-0.404865\pi\) | ||||
0.294447 | + | 0.955668i | \(0.404865\pi\) | |||||||
\(440\) | − 5713.08i | − 0.619001i | ||||||||
\(441\) | 2163.13 | 0.233574 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2537.44 | −0.272138 | −0.136069 | − | 0.990699i | \(-0.543447\pi\) | ||||
−0.136069 | + | 0.990699i | \(0.543447\pi\) | |||||||
\(444\) | 2681.16i | 0.286582i | ||||||||
\(445\) | 15089.5 | 1.60744 | ||||||||
\(446\) | 1608.48 | 0.170771 | ||||||||
\(447\) | 4112.77i | 0.435184i | ||||||||
\(448\) | 5640.43i | 0.594833i | ||||||||
\(449\) | 7790.61i | 0.818846i | 0.912345 | + | 0.409423i | \(0.134270\pi\) | ||||
−0.912345 | + | 0.409423i | \(0.865730\pi\) | |||||||
\(450\) | 2368.83i | 0.248150i | ||||||||
\(451\) | 4718.26 | 0.492626 | ||||||||
\(452\) | 1039.18 | 0.108139 | ||||||||
\(453\) | 3532.70i | 0.366403i | ||||||||
\(454\) | −673.825 | −0.0696568 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8468.55 | −0.869685 | ||||||||
\(457\) | − 6599.71i | − 0.675539i | −0.941229 | − | 0.337770i | \(-0.890328\pi\) | ||||
0.941229 | − | 0.337770i | \(-0.109672\pi\) | |||||||
\(458\) | −5403.95 | −0.551332 | ||||||||
\(459\) | −2452.55 | −0.249401 | ||||||||
\(460\) | 2905.43i | 0.294492i | ||||||||
\(461\) | − 4482.57i | − 0.452872i | −0.974026 | − | 0.226436i | \(-0.927293\pi\) | ||||
0.974026 | − | 0.226436i | \(-0.0727074\pi\) | |||||||
\(462\) | − 1074.96i | − 0.108250i | ||||||||
\(463\) | − 3805.86i | − 0.382016i | −0.981589 | − | 0.191008i | \(-0.938824\pi\) | ||||
0.981589 | − | 0.191008i | \(-0.0611756\pi\) | |||||||
\(464\) | −8136.35 | −0.814053 | ||||||||
\(465\) | 13142.0 | 1.31064 | ||||||||
\(466\) | − 2278.31i | − 0.226482i | ||||||||
\(467\) | −14778.8 | −1.46441 | −0.732207 | − | 0.681082i | \(-0.761510\pi\) | ||||
−0.732207 | + | 0.681082i | \(0.761510\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2436.62 | 0.239899 | ||||||||
\(470\) | 11447.0i | 1.12343i | ||||||||
\(471\) | 4864.71 | 0.475911 | ||||||||
\(472\) | 6258.06 | 0.610277 | ||||||||
\(473\) | 4470.37i | 0.434562i | ||||||||
\(474\) | 3497.11i | 0.338877i | ||||||||
\(475\) | 12854.8i | 1.24172i | ||||||||
\(476\) | 2291.89i | 0.220690i | ||||||||
\(477\) | 1475.20 | 0.141603 | ||||||||
\(478\) | 11753.7 | 1.12469 | ||||||||
\(479\) | 11171.2i | 1.06560i | 0.846240 | + | 0.532801i | \(0.178861\pi\) | ||||
−0.846240 | + | 0.532801i | \(0.821139\pi\) | |||||||
\(480\) | −4993.20 | −0.474807 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −1267.74 | −0.119801 | ||||||||
\(483\) | 2302.85i | 0.216942i | ||||||||
\(484\) | 2749.29 | 0.258197 | ||||||||
\(485\) | 8521.18 | 0.797787 | ||||||||
\(486\) | − 570.387i | − 0.0532372i | ||||||||
\(487\) | − 6046.57i | − 0.562621i | −0.959617 | − | 0.281310i | \(-0.909231\pi\) | ||||
0.959617 | − | 0.281310i | \(-0.0907690\pi\) | |||||||
\(488\) | 23029.2i | 2.13623i | ||||||||
\(489\) | − 399.390i | − 0.0369347i | ||||||||
\(490\) | −8687.57 | −0.800948 | ||||||||
\(491\) | 1035.04 | 0.0951338 | 0.0475669 | − | 0.998868i | \(-0.484853\pi\) | ||||
0.0475669 | + | 0.998868i | \(0.484853\pi\) | |||||||
\(492\) | − 2339.56i | − 0.214381i | ||||||||
\(493\) | −19512.9 | −1.78259 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2088.15 | 0.189606 | ||||||||
\(496\) | − 10774.7i | − 0.975404i | ||||||||
\(497\) | −9599.37 | −0.866379 | ||||||||
\(498\) | −2764.10 | −0.248720 | ||||||||
\(499\) | 11698.3i | 1.04947i | 0.851265 | + | 0.524736i | \(0.175836\pi\) | ||||
−0.851265 | + | 0.524736i | \(0.824164\pi\) | |||||||
\(500\) | − 493.488i | − 0.0441389i | ||||||||
\(501\) | − 1472.17i | − 0.131281i | ||||||||
\(502\) | − 14289.7i | − 1.27048i | ||||||||
\(503\) | −13552.0 | −1.20130 | −0.600651 | − | 0.799511i | \(-0.705092\pi\) | ||||
−0.600651 | + | 0.799511i | \(0.705092\pi\) | |||||||
\(504\) | −2245.32 | −0.198441 | ||||||||
\(505\) | − 11764.1i | − 1.03663i | ||||||||
\(506\) | −2679.46 | −0.235408 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4860.33 | 0.424492 | ||||||||
\(509\) | − 5076.46i | − 0.442064i | −0.975267 | − | 0.221032i | \(-0.929058\pi\) | ||||
0.975267 | − | 0.221032i | \(-0.0709425\pi\) | |||||||
\(510\) | 9849.94 | 0.855221 | ||||||||
\(511\) | −4363.86 | −0.377781 | ||||||||
\(512\) | 11554.9i | 0.997380i | ||||||||
\(513\) | − 3095.28i | − 0.266393i | ||||||||
\(514\) | − 11962.5i | − 1.02654i | ||||||||
\(515\) | 2810.60i | 0.240486i | ||||||||
\(516\) | 2216.65 | 0.189113 | ||||||||
\(517\) | 4771.55 | 0.405904 | ||||||||
\(518\) | − 8534.81i | − 0.723934i | ||||||||
\(519\) | −6024.40 | −0.509522 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8493.73 | −0.714236 | −0.357118 | − | 0.934059i | \(-0.616241\pi\) | ||||
−0.357118 | + | 0.934059i | \(0.616241\pi\) | |||||||
\(522\) | − 4538.10i | − 0.380512i | ||||||||
\(523\) | −1384.53 | −0.115758 | −0.0578789 | − | 0.998324i | \(-0.518434\pi\) | ||||
−0.0578789 | + | 0.998324i | \(0.518434\pi\) | |||||||
\(524\) | −3674.75 | −0.306359 | ||||||||
\(525\) | 3408.26i | 0.283331i | ||||||||
\(526\) | − 7993.64i | − 0.662622i | ||||||||
\(527\) | − 25840.4i | − 2.13592i | ||||||||
\(528\) | − 1712.01i | − 0.141109i | ||||||||
\(529\) | −6426.89 | −0.528223 | ||||||||
\(530\) | −5924.71 | −0.485571 | ||||||||
\(531\) | 2287.34i | 0.186934i | ||||||||
\(532\) | −2892.51 | −0.235726 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 6900.24 | 0.559181 | ||||||||
\(535\) | − 2828.80i | − 0.228598i | ||||||||
\(536\) | 5921.82 | 0.477208 | ||||||||
\(537\) | 6457.80 | 0.518947 | ||||||||
\(538\) | 6385.62i | 0.511717i | ||||||||
\(539\) | 3621.30i | 0.289388i | ||||||||
\(540\) | − 1035.41i | − 0.0825131i | ||||||||
\(541\) | 5026.83i | 0.399483i | 0.979849 | + | 0.199742i | \(0.0640103\pi\) | ||||
−0.979849 | + | 0.199742i | \(0.935990\pi\) | |||||||
\(542\) | 16323.6 | 1.29365 | ||||||||
\(543\) | −2504.07 | −0.197900 | ||||||||
\(544\) | 9817.87i | 0.773782i | ||||||||
\(545\) | −27324.5 | −2.14762 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1540.36 | 0.120404 | 0.0602021 | − | 0.998186i | \(-0.480825\pi\) | ||||
0.0602021 | + | 0.998186i | \(0.480825\pi\) | |||||||
\(548\) | − 4733.38i | − 0.368978i | ||||||||
\(549\) | −8417.23 | −0.654351 | ||||||||
\(550\) | −3965.65 | −0.307447 | ||||||||
\(551\) | − 24626.6i | − 1.90404i | ||||||||
\(552\) | 5596.72i | 0.431544i | ||||||||
\(553\) | 5031.63i | 0.386920i | ||||||||
\(554\) | − 15407.4i | − 1.18158i | ||||||||
\(555\) | 16579.2 | 1.26801 | ||||||||
\(556\) | −5794.38 | −0.441972 | ||||||||
\(557\) | − 8550.51i | − 0.650443i | −0.945638 | − | 0.325221i | \(-0.894561\pi\) | ||||
0.945638 | − | 0.325221i | \(-0.105439\pi\) | |||||||
\(558\) | 6009.68 | 0.455932 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 5909.35 | 0.445921 | ||||||||
\(561\) | − 4105.81i | − 0.308998i | ||||||||
\(562\) | −1532.30 | −0.115011 | ||||||||
\(563\) | 6569.35 | 0.491768 | 0.245884 | − | 0.969299i | \(-0.420922\pi\) | ||||
0.245884 | + | 0.969299i | \(0.420922\pi\) | |||||||
\(564\) | − 2365.99i | − 0.176642i | ||||||||
\(565\) | − 6425.85i | − 0.478473i | ||||||||
\(566\) | 14108.5i | 1.04775i | ||||||||
\(567\) | − 820.671i | − 0.0607847i | ||||||||
\(568\) | −23329.8 | −1.72341 | ||||||||
\(569\) | −23766.1 | −1.75102 | −0.875508 | − | 0.483204i | \(-0.839473\pi\) | ||||
−0.875508 | + | 0.483204i | \(0.839473\pi\) | |||||||
\(570\) | 12431.3i | 0.913488i | ||||||||
\(571\) | 24971.7 | 1.83018 | 0.915091 | − | 0.403248i | \(-0.132119\pi\) | ||||
0.915091 | + | 0.403248i | \(0.132119\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13394.1 | 0.976524 | ||||||||
\(574\) | 7447.41i | 0.541549i | ||||||||
\(575\) | 8495.48 | 0.616150 | ||||||||
\(576\) | −5010.38 | −0.362441 | ||||||||
\(577\) | 16643.4i | 1.20082i | 0.799693 | + | 0.600409i | \(0.204996\pi\) | ||||
−0.799693 | + | 0.600409i | \(0.795004\pi\) | |||||||
\(578\) | − 7835.28i | − 0.563849i | ||||||||
\(579\) | − 9899.53i | − 0.710553i | ||||||||
\(580\) | − 8237.93i | − 0.589761i | ||||||||
\(581\) | −3976.98 | −0.283981 | ||||||||
\(582\) | 3896.63 | 0.277527 | ||||||||
\(583\) | 2469.64i | 0.175441i | ||||||||
\(584\) | −10605.7 | −0.751484 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4489.66 | −0.316495 | ||||||||
\(587\) | 6720.67i | 0.472558i | 0.971685 | + | 0.236279i | \(0.0759280\pi\) | ||||
−0.971685 | + | 0.236279i | \(0.924072\pi\) | |||||||
\(588\) | 1795.63 | 0.125936 | ||||||||
\(589\) | 32612.3 | 2.28144 | ||||||||
\(590\) | − 9186.41i | − 0.641014i | ||||||||
\(591\) | − 8920.77i | − 0.620899i | ||||||||
\(592\) | − 13592.8i | − 0.943681i | ||||||||
\(593\) | 26349.8i | 1.82471i | 0.409395 | + | 0.912357i | \(0.365740\pi\) | ||||
−0.409395 | + | 0.912357i | \(0.634260\pi\) | |||||||
\(594\) | 954.884 | 0.0659586 | ||||||||
\(595\) | 14172.1 | 0.976466 | ||||||||
\(596\) | 3414.04i | 0.234638i | ||||||||
\(597\) | 16292.4 | 1.11693 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6136.81 | −0.418603 | −0.209302 | − | 0.977851i | \(-0.567119\pi\) | ||||
−0.209302 | + | 0.977851i | \(0.567119\pi\) | |||||||
\(600\) | 8283.25i | 0.563604i | ||||||||
\(601\) | 12493.7 | 0.847966 | 0.423983 | − | 0.905670i | \(-0.360632\pi\) | ||||
0.423983 | + | 0.905670i | \(0.360632\pi\) | |||||||
\(602\) | −7056.14 | −0.477719 | ||||||||
\(603\) | 2164.44i | 0.146174i | ||||||||
\(604\) | 2932.51i | 0.197553i | ||||||||
\(605\) | − 17000.4i | − 1.14242i | ||||||||
\(606\) | − 5379.60i | − 0.360613i | ||||||||
\(607\) | 18696.6 | 1.25020 | 0.625099 | − | 0.780545i | \(-0.285059\pi\) | ||||
0.625099 | + | 0.780545i | \(0.285059\pi\) | |||||||
\(608\) | −12390.8 | −0.826501 | ||||||||
\(609\) | − 6529.40i | − 0.434458i | ||||||||
\(610\) | 33805.3 | 2.24383 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2035.88 | −0.134470 | ||||||||
\(613\) | − 1238.64i | − 0.0816123i | −0.999167 | − | 0.0408062i | \(-0.987007\pi\) | ||||
0.999167 | − | 0.0408062i | \(-0.0129926\pi\) | |||||||
\(614\) | −4654.81 | −0.305949 | ||||||||
\(615\) | −14466.9 | −0.948553 | ||||||||
\(616\) | − 3758.89i | − 0.245860i | ||||||||
\(617\) | − 16549.5i | − 1.07983i | −0.841718 | − | 0.539917i | \(-0.818456\pi\) | ||||
0.841718 | − | 0.539917i | \(-0.181544\pi\) | |||||||
\(618\) | 1285.26i | 0.0836579i | ||||||||
\(619\) | 13945.4i | 0.905513i | 0.891634 | + | 0.452756i | \(0.149559\pi\) | ||||
−0.891634 | + | 0.452756i | \(0.850441\pi\) | |||||||
\(620\) | 10909.3 | 0.706656 | ||||||||
\(621\) | −2045.62 | −0.132186 | ||||||||
\(622\) | 4445.17i | 0.286552i | ||||||||
\(623\) | 9928.03 | 0.638456 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17068.0 | −1.09235 | ||||||||
\(626\) | − 10736.9i | − 0.685513i | ||||||||
\(627\) | 5181.80 | 0.330050 | ||||||||
\(628\) | 4038.23 | 0.256597 | ||||||||
\(629\) | − 32598.8i | − 2.06645i | ||||||||
\(630\) | 3295.98i | 0.208436i | ||||||||
\(631\) | 15343.1i | 0.967987i | 0.875072 | + | 0.483994i | \(0.160814\pi\) | ||||
−0.875072 | + | 0.483994i | \(0.839186\pi\) | |||||||
\(632\) | 12228.6i | 0.769663i | ||||||||
\(633\) | 3684.76 | 0.231368 | ||||||||
\(634\) | −17826.4 | −1.11668 | ||||||||
\(635\) | − 30054.2i | − 1.87821i | ||||||||
\(636\) | 1224.58 | 0.0763484 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 7597.23 | 0.471438 | ||||||||
\(639\) | − 8527.10i | − 0.527898i | ||||||||
\(640\) | 6807.51 | 0.420454 | ||||||||
\(641\) | −11067.7 | −0.681979 | −0.340989 | − | 0.940067i | \(-0.610762\pi\) | ||||
−0.340989 | + | 0.940067i | \(0.610762\pi\) | |||||||
\(642\) | − 1293.58i | − 0.0795224i | ||||||||
\(643\) | 25118.7i | 1.54057i | 0.637701 | + | 0.770284i | \(0.279885\pi\) | ||||
−0.637701 | + | 0.770284i | \(0.720115\pi\) | |||||||
\(644\) | 1911.61i | 0.116969i | ||||||||
\(645\) | − 13706.8i | − 0.836751i | ||||||||
\(646\) | 24442.9 | 1.48869 | ||||||||
\(647\) | 4447.03 | 0.270217 | 0.135109 | − | 0.990831i | \(-0.456862\pi\) | ||||
0.135109 | + | 0.990831i | \(0.456862\pi\) | |||||||
\(648\) | − 1994.51i | − 0.120913i | ||||||||
\(649\) | −3829.23 | −0.231603 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8646.71 | 0.520570 | ||||||||
\(652\) | − 331.537i | − 0.0199141i | ||||||||
\(653\) | −19426.2 | −1.16418 | −0.582088 | − | 0.813126i | \(-0.697764\pi\) | ||||
−0.582088 | + | 0.813126i | \(0.697764\pi\) | |||||||
\(654\) | −12495.1 | −0.747093 | ||||||||
\(655\) | 22723.1i | 1.35552i | ||||||||
\(656\) | 11861.0i | 0.705934i | ||||||||
\(657\) | − 3876.41i | − 0.230187i | ||||||||
\(658\) | 7531.52i | 0.446215i | ||||||||
\(659\) | −14099.4 | −0.833438 | −0.416719 | − | 0.909035i | \(-0.636820\pi\) | ||||
−0.416719 | + | 0.909035i | \(0.636820\pi\) | |||||||
\(660\) | 1733.38 | 0.102230 | ||||||||
\(661\) | 2754.25i | 0.162070i | 0.996711 | + | 0.0810348i | \(0.0258225\pi\) | ||||
−0.996711 | + | 0.0810348i | \(0.974177\pi\) | |||||||
\(662\) | 4080.93 | 0.239592 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9665.44 | −0.564898 | ||||||||
\(665\) | 17886.0i | 1.04299i | ||||||||
\(666\) | 7581.45 | 0.441104 | ||||||||
\(667\) | −16275.3 | −0.944800 | ||||||||
\(668\) | − 1222.06i | − 0.0707828i | ||||||||
\(669\) | 2055.77i | 0.118805i | ||||||||
\(670\) | − 8692.83i | − 0.501244i | ||||||||
\(671\) | − 14091.3i | − 0.810712i | ||||||||
\(672\) | −3285.25 | −0.188588 | ||||||||
\(673\) | −11936.8 | −0.683700 | −0.341850 | − | 0.939754i | \(-0.611054\pi\) | ||||
−0.341850 | + | 0.939754i | \(0.611054\pi\) | |||||||
\(674\) | − 6362.53i | − 0.363613i | ||||||||
\(675\) | −3027.55 | −0.172638 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10255.2 | −0.582186 | −0.291093 | − | 0.956695i | \(-0.594019\pi\) | ||||
−0.291093 | + | 0.956695i | \(0.594019\pi\) | |||||||
\(678\) | − 2938.46i | − 0.166447i | ||||||||
\(679\) | 5606.46 | 0.316872 | ||||||||
\(680\) | 34443.0 | 1.94239 | ||||||||
\(681\) | − 861.202i | − 0.0484601i | ||||||||
\(682\) | 10060.8i | 0.564880i | ||||||||
\(683\) | 10605.7i | 0.594169i | 0.954851 | + | 0.297085i | \(0.0960143\pi\) | ||||
−0.954851 | + | 0.297085i | \(0.903986\pi\) | |||||||
\(684\) | − 2569.41i | − 0.143631i | ||||||||
\(685\) | −29269.2 | −1.63258 | ||||||||
\(686\) | −13873.1 | −0.772127 | ||||||||
\(687\) | − 6906.69i | − 0.383561i | ||||||||
\(688\) | −11237.8 | −0.622728 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 8215.60 | 0.453279 | ||||||||
\(691\) | − 4660.14i | − 0.256556i | −0.991738 | − | 0.128278i | \(-0.959055\pi\) | ||||
0.991738 | − | 0.128278i | \(-0.0409449\pi\) | |||||||
\(692\) | −5000.90 | −0.274719 | ||||||||
\(693\) | 1373.88 | 0.0753096 | ||||||||
\(694\) | 5884.15i | 0.321844i | ||||||||
\(695\) | 35829.9i | 1.95555i | ||||||||
\(696\) | − 15868.7i | − 0.864227i | ||||||||
\(697\) | 28445.4i | 1.54584i | ||||||||
\(698\) | 17690.2 | 0.959287 | ||||||||
\(699\) | 2911.86 | 0.157563 | ||||||||
\(700\) | 2829.22i | 0.152764i | ||||||||
\(701\) | 24016.9 | 1.29402 | 0.647008 | − | 0.762483i | \(-0.276020\pi\) | ||||
0.647008 | + | 0.762483i | \(0.276020\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 41141.7 | 2.20724 | ||||||||
\(704\) | − 8387.88i | − 0.449048i | ||||||||
\(705\) | −14630.2 | −0.781570 | ||||||||
\(706\) | 21108.7 | 1.12527 | ||||||||
\(707\) | − 7740.15i | − 0.411737i | ||||||||
\(708\) | 1898.74i | 0.100789i | ||||||||
\(709\) | − 7252.56i | − 0.384169i | −0.981378 | − | 0.192084i | \(-0.938475\pi\) | ||||
0.981378 | − | 0.192084i | \(-0.0615247\pi\) | |||||||
\(710\) | 34246.5i | 1.81021i | ||||||||
\(711\) | −4469.58 | −0.235756 | ||||||||
\(712\) | 24128.6 | 1.27002 | ||||||||
\(713\) | − 21552.9i | − 1.13207i | ||||||||
\(714\) | 6480.71 | 0.339684 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5360.66 | 0.279801 | ||||||||
\(717\) | 15022.2i | 0.782447i | ||||||||
\(718\) | −10719.1 | −0.557151 | ||||||||
\(719\) | −10951.7 | −0.568050 | −0.284025 | − | 0.958817i | \(-0.591670\pi\) | ||||
−0.284025 | + | 0.958817i | \(0.591670\pi\) | |||||||
\(720\) | 5249.26i | 0.271706i | ||||||||
\(721\) | 1849.22i | 0.0955182i | ||||||||
\(722\) | 14748.6i | 0.760231i | ||||||||
\(723\) | − 1620.28i | − 0.0833454i | ||||||||
\(724\) | −2078.65 | −0.106702 | ||||||||
\(725\) | −24087.7 | −1.23393 | ||||||||
\(726\) | − 7774.08i | − 0.397415i | ||||||||
\(727\) | 27856.0 | 1.42108 | 0.710538 | − | 0.703658i | \(-0.248451\pi\) | ||||
0.710538 | + | 0.703658i | \(0.248451\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 15568.4i | 0.789334i | ||||||||
\(731\) | −26951.0 | −1.36364 | ||||||||
\(732\) | −6987.20 | −0.352806 | ||||||||
\(733\) | 31213.8i | 1.57286i | 0.617678 | + | 0.786431i | \(0.288073\pi\) | ||||
−0.617678 | + | 0.786431i | \(0.711927\pi\) | |||||||
\(734\) | 15138.7i | 0.761281i | ||||||||
\(735\) | − 11103.4i | − 0.557218i | ||||||||
\(736\) | 8188.85i | 0.410116i | ||||||||
\(737\) | −3623.49 | −0.181103 | ||||||||
\(738\) | −6615.52 | −0.329974 | ||||||||
\(739\) | 14423.1i | 0.717946i | 0.933348 | + | 0.358973i | \(0.116873\pi\) | ||||
−0.933348 | + | 0.358973i | \(0.883127\pi\) | |||||||
\(740\) | 13762.5 | 0.683674 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3898.13 | −0.192864 | ||||||||
\(743\) | − 13469.7i | − 0.665079i | −0.943089 | − | 0.332539i | \(-0.892095\pi\) | ||||
0.943089 | − | 0.332539i | \(-0.107905\pi\) | |||||||
\(744\) | 21014.5 | 1.03552 | ||||||||
\(745\) | 21111.0 | 1.03818 | ||||||||
\(746\) | − 17954.0i | − 0.881158i | ||||||||
\(747\) | − 3532.75i | − 0.173034i | ||||||||
\(748\) | − 3408.26i | − 0.166602i | ||||||||
\(749\) | − 1861.19i | − 0.0907965i | ||||||||
\(750\) | −1395.42 | −0.0679381 | ||||||||
\(751\) | 32033.6 | 1.55649 | 0.778245 | − | 0.627961i | \(-0.216110\pi\) | ||||
0.778245 | + | 0.627961i | \(0.216110\pi\) | |||||||
\(752\) | 11994.9i | 0.581661i | ||||||||
\(753\) | 18263.4 | 0.883871 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18133.4 | 0.874096 | ||||||||
\(756\) | − 681.244i | − 0.0327733i | ||||||||
\(757\) | −26097.2 | −1.25300 | −0.626498 | − | 0.779423i | \(-0.715512\pi\) | ||||
−0.626498 | + | 0.779423i | \(0.715512\pi\) | |||||||
\(758\) | 24171.6 | 1.15825 | ||||||||
\(759\) | − 3424.56i | − 0.163773i | ||||||||
\(760\) | 43469.3i | 2.07473i | ||||||||
\(761\) | 18238.2i | 0.868772i | 0.900727 | + | 0.434386i | \(0.143035\pi\) | ||||
−0.900727 | + | 0.434386i | \(0.856965\pi\) | |||||||
\(762\) | − 13743.4i | − 0.653375i | ||||||||
\(763\) | −17978.0 | −0.853009 | ||||||||
\(764\) | 11118.6 | 0.526513 | ||||||||
\(765\) | 12589.0i | 0.594976i | ||||||||
\(766\) | −24078.4 | −1.13575 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −10248.0 | −0.481502 | ||||||||
\(769\) | 18817.0i | 0.882390i | 0.897411 | + | 0.441195i | \(0.145445\pi\) | ||||
−0.897411 | + | 0.441195i | \(0.854555\pi\) | |||||||
\(770\) | −5517.79 | −0.258243 | ||||||||
\(771\) | 15289.0 | 0.714164 | ||||||||
\(772\) | − 8217.67i | − 0.383109i | ||||||||
\(773\) | 13795.6i | 0.641904i | 0.947095 | + | 0.320952i | \(0.104003\pi\) | ||||
−0.947095 | + | 0.320952i | \(0.895997\pi\) | |||||||
\(774\) | − 6267.95i | − 0.291081i | ||||||||
\(775\) | − 31898.7i | − 1.47850i | ||||||||
\(776\) | 13625.6 | 0.630325 | ||||||||
\(777\) | 10908.2 | 0.503640 | ||||||||
\(778\) | − 11200.2i | − 0.516126i | ||||||||
\(779\) | −35900.0 | −1.65116 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14275.2 | 0.654043 | ||||||||
\(782\) | − 16153.9i | − 0.738699i | ||||||||
\(783\) | 5800.05 | 0.264722 | ||||||||
\(784\) | −9103.36 | −0.414694 | ||||||||
\(785\) | − 24970.7i | − 1.13534i | ||||||||
\(786\) | 10391.0i | 0.471545i | ||||||||
\(787\) | − 40545.4i | − 1.83645i | −0.396055 | − | 0.918227i | \(-0.629621\pi\) | ||||
0.396055 | − | 0.918227i | \(-0.370379\pi\) | |||||||
\(788\) | − 7405.19i | − 0.334770i | ||||||||
\(789\) | 10216.5 | 0.460985 | ||||||||
\(790\) | 17950.7 | 0.808429 | ||||||||
\(791\) | − 4227.85i | − 0.190044i | ||||||||
\(792\) | 3339.01 | 0.149806 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 5378.11 | 0.240380 | ||||||||
\(795\) | − 7572.25i | − 0.337811i | ||||||||
\(796\) | 13524.5 | 0.602214 | ||||||||
\(797\) | 31576.4 | 1.40338 | 0.701690 | − | 0.712482i | \(-0.252429\pi\) | ||||
0.701690 | + | 0.712482i | \(0.252429\pi\) | |||||||
\(798\) | 8179.07i | 0.362827i | ||||||||
\(799\) | 28766.7i | 1.27371i | ||||||||
\(800\) | 12119.7i | 0.535619i | ||||||||
\(801\) | 8819.05i | 0.389021i | ||||||||
\(802\) | 17685.8 | 0.778688 | ||||||||
\(803\) | 6489.50 | 0.285192 | ||||||||
\(804\) | 1796.72i | 0.0788126i | ||||||||
\(805\) | 11820.6 | 0.517541 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8161.33 | −0.356001 | ||||||||
\(808\) | − 18811.2i | − 0.819031i | ||||||||
\(809\) | 31130.1 | 1.35287 | 0.676437 | − | 0.736501i | \(-0.263523\pi\) | ||||
0.676437 | + | 0.736501i | \(0.263523\pi\) | |||||||
\(810\) | −2927.81 | −0.127003 | ||||||||
\(811\) | 8733.71i | 0.378153i | 0.981962 | + | 0.189076i | \(0.0605494\pi\) | ||||
−0.981962 | + | 0.189076i | \(0.939451\pi\) | |||||||
\(812\) | − 5420.10i | − 0.234247i | ||||||||
\(813\) | 20862.8i | 0.899988i | ||||||||
\(814\) | 12692.1i | 0.546509i | ||||||||
\(815\) | −2050.08 | −0.0881119 | ||||||||
\(816\) | 10321.4 | 0.442794 | ||||||||
\(817\) | − 34013.8i | − 1.45654i | ||||||||
\(818\) | 3563.08 | 0.152298 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12009.0 | −0.511431 | ||||||||
\(821\) | 36960.1i | 1.57115i | 0.618765 | + | 0.785576i | \(0.287633\pi\) | ||||
−0.618765 | + | 0.785576i | \(0.712367\pi\) | |||||||
\(822\) | −13384.5 | −0.567928 | ||||||||
\(823\) | −20509.7 | −0.868679 | −0.434340 | − | 0.900749i | \(-0.643018\pi\) | ||||
−0.434340 | + | 0.900749i | \(0.643018\pi\) | |||||||
\(824\) | 4494.25i | 0.190006i | ||||||||
\(825\) | − 5068.42i | − 0.213891i | ||||||||
\(826\) | − 6044.15i | − 0.254604i | ||||||||
\(827\) | − 11533.4i | − 0.484952i | −0.970157 | − | 0.242476i | \(-0.922040\pi\) | ||||
0.970157 | − | 0.242476i | \(-0.0779596\pi\) | |||||||
\(828\) | −1698.08 | −0.0712709 | ||||||||
\(829\) | −34096.4 | −1.42849 | −0.714244 | − | 0.699897i | \(-0.753229\pi\) | ||||
−0.714244 | + | 0.699897i | \(0.753229\pi\) | |||||||
\(830\) | 14188.2i | 0.593350i | ||||||||
\(831\) | 19691.9 | 0.822026 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −21832.1 | −0.908087 | ||||||||
\(834\) | 16384.6i | 0.680279i | ||||||||
\(835\) | −7556.69 | −0.313186 | ||||||||
\(836\) | 4301.45 | 0.177953 | ||||||||
\(837\) | 7680.85i | 0.317191i | ||||||||
\(838\) | − 18968.2i | − 0.781917i | ||||||||
\(839\) | − 1855.42i | − 0.0763484i | −0.999271 | − | 0.0381742i | \(-0.987846\pi\) | ||||
0.999271 | − | 0.0381742i | \(-0.0121542\pi\) | |||||||
\(840\) | 11525.3i | 0.473405i | ||||||||
\(841\) | 21757.3 | 0.892094 | ||||||||
\(842\) | −18949.8 | −0.775599 | ||||||||
\(843\) | − 1958.40i | − 0.0800129i | ||||||||
\(844\) | 3058.75 | 0.124747 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6690.24 | −0.271885 | ||||||||
\(847\) | − 11185.3i | − 0.453757i | ||||||||
\(848\) | −6208.26 | −0.251406 | ||||||||
\(849\) | −18031.9 | −0.728918 | ||||||||
\(850\) | − 23908.1i | − 0.964755i | ||||||||
\(851\) | − 27189.9i | − 1.09525i | ||||||||
\(852\) | − 7078.40i | − 0.284627i | ||||||||
\(853\) | − 28668.7i | − 1.15076i | −0.817886 | − | 0.575380i | \(-0.804854\pi\) | ||||
0.817886 | − | 0.575380i | \(-0.195146\pi\) | |||||||
\(854\) | 22242.0 | 0.891224 | ||||||||
\(855\) | −15888.1 | −0.635512 | ||||||||
\(856\) | − 4523.35i | − 0.180613i | ||||||||
\(857\) | −449.310 | −0.0179091 | −0.00895457 | − | 0.999960i | \(-0.502850\pi\) | ||||
−0.00895457 | + | 0.999960i | \(0.502850\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33466.9 | 1.32931 | 0.664654 | − | 0.747151i | \(-0.268579\pi\) | ||||
0.664654 | + | 0.747151i | \(0.268579\pi\) | |||||||
\(860\) | − 11378.1i | − 0.451151i | ||||||||
\(861\) | −9518.39 | −0.376755 | ||||||||
\(862\) | −5261.14 | −0.207883 | ||||||||
\(863\) | 25097.5i | 0.989953i | 0.868906 | + | 0.494976i | \(0.164823\pi\) | ||||
−0.868906 | + | 0.494976i | \(0.835177\pi\) | |||||||
\(864\) | − 2918.28i | − 0.114910i | ||||||||
\(865\) | 30923.4i | 1.21552i | ||||||||
\(866\) | 24031.0i | 0.942965i | ||||||||
\(867\) | 10014.1 | 0.392269 | ||||||||
\(868\) | 7177.69 | 0.280676 | ||||||||
\(869\) | − 7482.53i | − 0.292091i | ||||||||
\(870\) | −23294.2 | −0.907755 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −43692.7 | −1.69681 | ||||||||
\(873\) | 4980.21i | 0.193075i | ||||||||
\(874\) | 20387.3 | 0.789027 | ||||||||
\(875\) | −2007.73 | −0.0775698 | ||||||||
\(876\) | − 3217.83i | − 0.124110i | ||||||||
\(877\) | − 27015.2i | − 1.04018i | −0.854112 | − | 0.520090i | \(-0.825899\pi\) | ||||
0.854112 | − | 0.520090i | \(-0.174101\pi\) | |||||||
\(878\) | − 12714.4i | − 0.488715i | ||||||||
\(879\) | − 5738.15i | − 0.220185i | ||||||||
\(880\) | −8787.79 | −0.336632 | ||||||||
\(881\) | −48638.7 | −1.86002 | −0.930010 | − | 0.367534i | \(-0.880202\pi\) | ||||
−0.930010 | + | 0.367534i | \(0.880202\pi\) | |||||||
\(882\) | − 5077.46i | − 0.193840i | ||||||||
\(883\) | 25479.0 | 0.971048 | 0.485524 | − | 0.874223i | \(-0.338629\pi\) | ||||
0.485524 | + | 0.874223i | \(0.338629\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11741.0 | 0.445953 | ||||||||
\(886\) | 5956.05i | 0.225843i | ||||||||
\(887\) | 42359.7 | 1.60350 | 0.801748 | − | 0.597663i | \(-0.203904\pi\) | ||||
0.801748 | + | 0.597663i | \(0.203904\pi\) | |||||||
\(888\) | 26510.6 | 1.00184 | ||||||||
\(889\) | − 19774.0i | − 0.746005i | ||||||||
\(890\) | − 35419.1i | − 1.33399i | ||||||||
\(891\) | 1220.42i | 0.0458873i | ||||||||
\(892\) | 1706.51i | 0.0640561i | ||||||||
\(893\) | −36305.4 | −1.36049 | ||||||||
\(894\) | 9653.78 | 0.361153 | ||||||||
\(895\) | − 33148.1i | − 1.23801i | ||||||||
\(896\) | 4478.96 | 0.167000 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 18286.7 | 0.679548 | ||||||||
\(899\) | 61110.3i | 2.26712i | ||||||||
\(900\) | −2513.19 | −0.0930811 | ||||||||
\(901\) | −14888.9 | −0.550524 | ||||||||
\(902\) | − 11075.0i | − 0.408823i | ||||||||
\(903\) | − 9018.31i | − 0.332348i | ||||||||
\(904\) | − 10275.1i | − 0.378038i | ||||||||
\(905\) | 12853.5i | 0.472114i | ||||||||
\(906\) | 8292.19 | 0.304072 | ||||||||
\(907\) | 5314.91 | 0.194574 | 0.0972871 | − | 0.995256i | \(-0.468984\pi\) | ||||
0.0972871 | + | 0.995256i | \(0.468984\pi\) | |||||||
\(908\) | − 714.890i | − 0.0261283i | ||||||||
\(909\) | 6875.56 | 0.250878 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2471.71 | 0.0898919 | 0.0449459 | − | 0.998989i | \(-0.485688\pi\) | ||||
0.0449459 | + | 0.998989i | \(0.485688\pi\) | |||||||
\(912\) | 13026.2i | 0.472962i | ||||||||
\(913\) | 5914.17 | 0.214382 | ||||||||
\(914\) | −15491.3 | −0.560620 | ||||||||
\(915\) | 43205.8i | 1.56103i | ||||||||
\(916\) | − 5733.29i | − 0.206805i | ||||||||
\(917\) | 14950.5i | 0.538396i | ||||||||
\(918\) | 5756.80i | 0.206975i | ||||||||
\(919\) | −9636.13 | −0.345883 | −0.172942 | − | 0.984932i | \(-0.555327\pi\) | ||||
−0.172942 | + | 0.984932i | \(0.555327\pi\) | |||||||
\(920\) | 28728.1 | 1.02950 | ||||||||
\(921\) | − 5949.22i | − 0.212849i | ||||||||
\(922\) | −10521.8 | −0.375832 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 1140.47 | 0.0406047 | ||||||||
\(925\) | − 40241.5i | − 1.43041i | ||||||||
\(926\) | −8933.38 | −0.317029 | ||||||||
\(927\) | −1642.66 | −0.0582007 | ||||||||
\(928\) | − 23218.3i | − 0.821314i | ||||||||
\(929\) | 53249.1i | 1.88057i | 0.340394 | + | 0.940283i | \(0.389439\pi\) | ||||
−0.340394 | + | 0.940283i | \(0.610561\pi\) | |||||||
\(930\) | − 30847.8i | − 1.08768i | ||||||||
\(931\) | − 27553.5i | − 0.969955i | ||||||||
\(932\) | 2417.16 | 0.0849534 | ||||||||
\(933\) | −5681.28 | −0.199354 | ||||||||
\(934\) | 34689.8i | 1.21530i | ||||||||
\(935\) | −21075.3 | −0.737149 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41122.6 | −1.43374 | −0.716871 | − | 0.697205i | \(-0.754427\pi\) | ||||
−0.716871 | + | 0.697205i | \(0.754427\pi\) | |||||||
\(938\) | − 5719.40i | − 0.199088i | ||||||||
\(939\) | 13722.6 | 0.476911 | ||||||||
\(940\) | −12144.7 | −0.421399 | ||||||||
\(941\) | 8005.71i | 0.277342i | 0.990339 | + | 0.138671i | \(0.0442831\pi\) | ||||
−0.990339 | + | 0.138671i | \(0.955717\pi\) | |||||||
\(942\) | − 11418.8i | − 0.394952i | ||||||||
\(943\) | 23725.7i | 0.819315i | ||||||||
\(944\) | − 9626.07i | − 0.331888i | ||||||||
\(945\) | −4212.52 | −0.145009 | ||||||||
\(946\) | 10493.2 | 0.360637 | ||||||||
\(947\) | − 17468.6i | − 0.599424i | −0.954030 | − | 0.299712i | \(-0.903109\pi\) | ||||
0.954030 | − | 0.299712i | \(-0.0968905\pi\) | |||||||
\(948\) | −3710.23 | −0.127113 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 30173.6 | 1.03048 | ||||||||
\(951\) | − 22783.6i | − 0.776875i | ||||||||
\(952\) | 22661.6 | 0.771498 | ||||||||
\(953\) | −30681.4 | −1.04288 | −0.521442 | − | 0.853287i | \(-0.674606\pi\) | ||||
−0.521442 | + | 0.853287i | \(0.674606\pi\) | |||||||
\(954\) | − 3462.70i | − 0.117515i | ||||||||
\(955\) | − 68752.5i | − 2.32961i | ||||||||
\(956\) | 12470.0i | 0.421872i | ||||||||
\(957\) | 9709.87i | 0.327979i | ||||||||
\(958\) | 26221.8 | 0.884328 | ||||||||
\(959\) | −19257.5 | −0.648444 | ||||||||
\(960\) | 25718.4i | 0.864644i | ||||||||
\(961\) | −51135.6 | −1.71648 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1653.29 | 0.0553237 | ||||||||
\(964\) | − 1345.00i | − 0.0449373i | ||||||||
\(965\) | −50814.5 | −1.69511 | ||||||||
\(966\) | 5405.41 | 0.180037 | ||||||||
\(967\) | − 15616.0i | − 0.519313i | −0.965701 | − | 0.259656i | \(-0.916391\pi\) | ||||
0.965701 | − | 0.259656i | \(-0.0836093\pi\) | |||||||
\(968\) | − 27184.2i | − 0.902617i | ||||||||
\(969\) | 31240.0i | 1.03568i | ||||||||
\(970\) | − 20001.5i | − 0.662072i | ||||||||
\(971\) | 7185.98 | 0.237496 | 0.118748 | − | 0.992924i | \(-0.462112\pi\) | ||||
0.118748 | + | 0.992924i | \(0.462112\pi\) | |||||||
\(972\) | 605.148 | 0.0199693 | ||||||||
\(973\) | 23574.1i | 0.776723i | ||||||||
\(974\) | −14192.9 | −0.466911 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 35423.2 | 1.16175 | ||||||||
\(977\) | − 33165.3i | − 1.08603i | −0.839723 | − | 0.543015i | \(-0.817283\pi\) | ||||
0.839723 | − | 0.543015i | \(-0.182717\pi\) | |||||||
\(978\) | −937.477 | −0.0306516 | ||||||||
\(979\) | −14764.0 | −0.481980 | ||||||||
\(980\) | − 9217.01i | − 0.300435i | ||||||||
\(981\) | − 15969.8i | − 0.519752i | ||||||||
\(982\) | − 2429.52i | − 0.0789502i | ||||||||
\(983\) | − 11658.7i | − 0.378287i | −0.981949 | − | 0.189143i | \(-0.939429\pi\) | ||||
0.981949 | − | 0.189143i | \(-0.0605711\pi\) | |||||||
\(984\) | −23133.0 | −0.749444 | ||||||||
\(985\) | −45790.5 | −1.48123 | ||||||||
\(986\) | 45802.1i | 1.47935i | ||||||||
\(987\) | −9625.89 | −0.310431 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −22479.2 | −0.722746 | ||||||||
\(990\) | − 4901.45i | − 0.157352i | ||||||||
\(991\) | −1957.32 | −0.0627409 | −0.0313704 | − | 0.999508i | \(-0.509987\pi\) | ||||
−0.0313704 | + | 0.999508i | \(0.509987\pi\) | |||||||
\(992\) | 30747.4 | 0.984104 | ||||||||
\(993\) | 5215.75i | 0.166684i | ||||||||
\(994\) | 22532.3i | 0.718996i | ||||||||
\(995\) | − 83629.5i | − 2.66456i | ||||||||
\(996\) | − 2932.56i | − 0.0932948i | ||||||||
\(997\) | −11434.8 | −0.363233 | −0.181617 | − | 0.983369i | \(-0.558133\pi\) | ||||
−0.181617 | + | 0.983369i | \(0.558133\pi\) | |||||||
\(998\) | 27459.0 | 0.870942 | ||||||||
\(999\) | 9689.70i | 0.306876i |
(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 | 507.4.b.k.337.7 | 18 | ||
13.5 | odd | 4 | 507.4.a.o.1.4 | ✓ | 9 | ||
13.8 | odd | 4 | 507.4.a.p.1.6 | yes | 9 | ||
13.12 | even | 2 | inner | 507.4.b.k.337.12 | 18 | ||
39.5 | even | 4 | 1521.4.a.bi.1.6 | 9 | |||
39.8 | even | 4 | 1521.4.a.bf.1.4 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.4.a.o.1.4 | ✓ | 9 | 13.5 | odd | 4 | ||
507.4.a.p.1.6 | yes | 9 | 13.8 | odd | 4 | ||
507.4.b.k.337.7 | 18 | 1.1 | even | 1 | trivial | ||
507.4.b.k.337.12 | 18 | 13.12 | even | 2 | inner | ||
1521.4.a.bf.1.4 | 9 | 39.8 | even | 4 | |||
1521.4.a.bi.1.6 | 9 | 39.5 | even | 4 |