Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1521,4,Mod(1,1521)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1521, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1521.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1521 = 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1521.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(89.7419051187\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 70x^{8} + 1645x^{6} - 14700x^{4} + 44100x^{2} - 27648 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 39) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(2.04224\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1521.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.04224 | 0.722042 | 0.361021 | − | 0.932558i | \(-0.382428\pi\) | ||||
0.361021 | + | 0.932558i | \(0.382428\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.82924 | −0.478656 | ||||||||
\(5\) | 12.0825 | 1.08069 | 0.540344 | − | 0.841444i | \(-0.318294\pi\) | ||||
0.540344 | + | 0.841444i | \(0.318294\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −29.7373 | −1.60566 | −0.802832 | − | 0.596206i | \(-0.796674\pi\) | ||||
−0.802832 | + | 0.596206i | \(0.796674\pi\) | |||||||
\(8\) | −24.1582 | −1.06765 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 24.6753 | 0.780302 | ||||||||
\(11\) | 28.0636 | 0.769226 | 0.384613 | − | 0.923078i | \(-0.374335\pi\) | ||||
0.384613 | + | 0.923078i | \(0.374335\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −60.7308 | −1.15936 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −18.7029 | −0.292233 | ||||||||
\(17\) | 50.6556 | 0.722693 | 0.361347 | − | 0.932432i | \(-0.382317\pi\) | ||||
0.361347 | + | 0.932432i | \(0.382317\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −105.148 | −1.26962 | −0.634808 | − | 0.772670i | \(-0.718921\pi\) | ||||
−0.634808 | + | 0.772670i | \(0.718921\pi\) | |||||||
\(20\) | −46.2667 | −0.517277 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 57.3126 | 0.555413 | ||||||||
\(23\) | 160.592 | 1.45590 | 0.727951 | − | 0.685629i | \(-0.240473\pi\) | ||||
0.727951 | + | 0.685629i | \(0.240473\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 20.9857 | 0.167886 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 113.871 | 0.768560 | ||||||||
\(29\) | −140.105 | −0.897132 | −0.448566 | − | 0.893750i | \(-0.648065\pi\) | ||||
−0.448566 | + | 0.893750i | \(0.648065\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −223.593 | −1.29544 | −0.647718 | − | 0.761880i | \(-0.724276\pi\) | ||||
−0.647718 | + | 0.761880i | \(0.724276\pi\) | |||||||
\(32\) | 155.070 | 0.856647 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 103.451 | 0.521815 | ||||||||
\(35\) | −359.300 | −1.73522 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 228.352 | 1.01462 | 0.507308 | − | 0.861765i | \(-0.330641\pi\) | ||||
0.507308 | + | 0.861765i | \(0.330641\pi\) | |||||||
\(38\) | −214.739 | −0.916716 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −291.890 | −1.15380 | ||||||||
\(41\) | −295.902 | −1.12713 | −0.563563 | − | 0.826073i | \(-0.690570\pi\) | ||||
−0.563563 | + | 0.826073i | \(0.690570\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 192.103 | 0.681291 | 0.340645 | − | 0.940192i | \(-0.389354\pi\) | ||||
0.340645 | + | 0.940192i | \(0.389354\pi\) | |||||||
\(44\) | −107.462 | −0.368194 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 327.968 | 1.05122 | ||||||||
\(47\) | 36.9300 | 0.114613 | 0.0573063 | − | 0.998357i | \(-0.481749\pi\) | ||||
0.0573063 | + | 0.998357i | \(0.481749\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 541.307 | 1.57815 | ||||||||
\(50\) | 42.8579 | 0.121220 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −149.102 | −0.386429 | −0.193214 | − | 0.981157i | \(-0.561891\pi\) | ||||
−0.193214 | + | 0.981157i | \(0.561891\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 339.077 | 0.831293 | ||||||||
\(56\) | 718.399 | 1.71429 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −286.128 | −0.647767 | ||||||||
\(59\) | 438.867 | 0.968400 | 0.484200 | − | 0.874957i | \(-0.339111\pi\) | ||||
0.484200 | + | 0.874957i | \(0.339111\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 286.146 | 0.600610 | 0.300305 | − | 0.953843i | \(-0.402912\pi\) | ||||
0.300305 | + | 0.953843i | \(0.402912\pi\) | |||||||
\(62\) | −456.631 | −0.935358 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 466.313 | 0.910768 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 537.128 | 0.979412 | 0.489706 | − | 0.871888i | \(-0.337104\pi\) | ||||
0.489706 | + | 0.871888i | \(0.337104\pi\) | |||||||
\(68\) | −193.973 | −0.345921 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −733.777 | −1.25290 | ||||||||
\(71\) | 102.729 | 0.171713 | 0.0858567 | − | 0.996307i | \(-0.472637\pi\) | ||||
0.0858567 | + | 0.996307i | \(0.472637\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 75.5209 | 0.121083 | 0.0605414 | − | 0.998166i | \(-0.480717\pi\) | ||||
0.0605414 | + | 0.998166i | \(0.480717\pi\) | |||||||
\(74\) | 466.350 | 0.732596 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 402.639 | 0.607709 | ||||||||
\(77\) | −834.535 | −1.23512 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 17.5526 | 0.0249978 | 0.0124989 | − | 0.999922i | \(-0.496021\pi\) | ||||
0.0124989 | + | 0.999922i | \(0.496021\pi\) | |||||||
\(80\) | −225.977 | −0.315813 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −604.304 | −0.813831 | ||||||||
\(83\) | 1463.08 | 1.93487 | 0.967434 | − | 0.253122i | \(-0.0814573\pi\) | ||||
0.967434 | + | 0.253122i | \(0.0814573\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 612.044 | 0.781005 | ||||||||
\(86\) | 392.322 | 0.491920 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −677.965 | −0.821265 | ||||||||
\(89\) | −334.905 | −0.398875 | −0.199438 | − | 0.979911i | \(-0.563911\pi\) | ||||
−0.199438 | + | 0.979911i | \(0.563911\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −614.946 | −0.696876 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 75.4200 | 0.0827551 | ||||||||
\(95\) | −1270.45 | −1.37206 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 748.756 | 0.783760 | 0.391880 | − | 0.920016i | \(-0.371825\pi\) | ||||
0.391880 | + | 0.920016i | \(0.371825\pi\) | |||||||
\(98\) | 1105.48 | 1.13949 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −80.3594 | −0.0803594 | ||||||||
\(101\) | 784.002 | 0.772387 | 0.386194 | − | 0.922418i | \(-0.373790\pi\) | ||||
0.386194 | + | 0.922418i | \(0.373790\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 396.040 | 0.378864 | 0.189432 | − | 0.981894i | \(-0.439335\pi\) | ||||
0.189432 | + | 0.981894i | \(0.439335\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −304.502 | −0.279018 | ||||||||
\(107\) | 1436.59 | 1.29795 | 0.648974 | − | 0.760810i | \(-0.275198\pi\) | ||||
0.648974 | + | 0.760810i | \(0.275198\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1977.92 | 1.73807 | 0.869037 | − | 0.494746i | \(-0.164739\pi\) | ||||
0.869037 | + | 0.494746i | \(0.164739\pi\) | |||||||
\(110\) | 692.477 | 0.600228 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 556.175 | 0.469228 | ||||||||
\(113\) | −122.405 | −0.101902 | −0.0509509 | − | 0.998701i | \(-0.516225\pi\) | ||||
−0.0509509 | + | 0.998701i | \(0.516225\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1940.35 | 1.57338 | ||||||||
\(116\) | 536.496 | 0.429417 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 896.273 | 0.699225 | ||||||||
\(119\) | −1506.36 | −1.16040 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −543.436 | −0.408291 | ||||||||
\(122\) | 584.379 | 0.433665 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 856.192 | 0.620067 | ||||||||
\(125\) | −1256.75 | −0.899256 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2309.61 | 1.61374 | 0.806868 | − | 0.590731i | \(-0.201161\pi\) | ||||
0.806868 | + | 0.590731i | \(0.201161\pi\) | |||||||
\(128\) | −288.232 | −0.199034 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1444.26 | 0.963250 | 0.481625 | − | 0.876377i | \(-0.340047\pi\) | ||||
0.481625 | + | 0.876377i | \(0.340047\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3126.83 | 2.03858 | ||||||||
\(134\) | 1096.94 | 0.707176 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1223.75 | −0.771584 | ||||||||
\(137\) | −735.918 | −0.458932 | −0.229466 | − | 0.973317i | \(-0.573698\pi\) | ||||
−0.229466 | + | 0.973317i | \(0.573698\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1505.14 | −0.918449 | −0.459225 | − | 0.888320i | \(-0.651873\pi\) | ||||
−0.459225 | + | 0.888320i | \(0.651873\pi\) | |||||||
\(140\) | 1375.85 | 0.830573 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 209.797 | 0.123984 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1692.81 | −0.969520 | ||||||||
\(146\) | 154.232 | 0.0874269 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −874.415 | −0.485652 | ||||||||
\(149\) | 427.843 | 0.235237 | 0.117618 | − | 0.993059i | \(-0.462474\pi\) | ||||
0.117618 | + | 0.993059i | \(0.462474\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1601.83 | 0.863278 | 0.431639 | − | 0.902046i | \(-0.357935\pi\) | ||||
0.431639 | + | 0.902046i | \(0.357935\pi\) | |||||||
\(152\) | 2540.20 | 1.35551 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1704.32 | −0.891807 | ||||||||
\(155\) | −2701.55 | −1.39996 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −730.346 | −0.371261 | −0.185631 | − | 0.982620i | \(-0.559433\pi\) | ||||
−0.185631 | + | 0.982620i | \(0.559433\pi\) | |||||||
\(158\) | 35.8467 | 0.0180495 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1873.62 | 0.925767 | ||||||||
\(161\) | −4775.58 | −2.33769 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1898.36 | −0.912215 | −0.456107 | − | 0.889925i | \(-0.650757\pi\) | ||||
−0.456107 | + | 0.889925i | \(0.650757\pi\) | |||||||
\(164\) | 1133.08 | 0.539505 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2987.97 | 1.39706 | ||||||||
\(167\) | 1427.50 | 0.661457 | 0.330729 | − | 0.943726i | \(-0.392706\pi\) | ||||
0.330729 | + | 0.943726i | \(0.392706\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 1249.94 | 0.563919 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −735.611 | −0.326104 | ||||||||
\(173\) | 2044.40 | 0.898454 | 0.449227 | − | 0.893418i | \(-0.351699\pi\) | ||||
0.449227 | + | 0.893418i | \(0.351699\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −624.058 | −0.269568 | ||||||||
\(176\) | −524.871 | −0.224793 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −683.958 | −0.288004 | ||||||||
\(179\) | 3889.72 | 1.62420 | 0.812098 | − | 0.583521i | \(-0.198325\pi\) | ||||
0.812098 | + | 0.583521i | \(0.198325\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2477.02 | −1.01721 | −0.508606 | − | 0.861000i | \(-0.669839\pi\) | ||||
−0.508606 | + | 0.861000i | \(0.669839\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3879.61 | −1.55440 | ||||||||
\(185\) | 2759.05 | 1.09648 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1421.58 | 0.555914 | ||||||||
\(188\) | −141.414 | −0.0548600 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2594.57 | −0.990683 | ||||||||
\(191\) | −2276.81 | −0.862535 | −0.431267 | − | 0.902224i | \(-0.641933\pi\) | ||||
−0.431267 | + | 0.902224i | \(0.641933\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3922.42 | −1.46291 | −0.731456 | − | 0.681888i | \(-0.761159\pi\) | ||||
−0.731456 | + | 0.681888i | \(0.761159\pi\) | |||||||
\(194\) | 1529.14 | 0.565907 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2072.80 | −0.755392 | ||||||||
\(197\) | −5063.23 | −1.83117 | −0.915584 | − | 0.402128i | \(-0.868271\pi\) | ||||
−0.915584 | + | 0.402128i | \(0.868271\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3270.06 | 1.16487 | 0.582433 | − | 0.812879i | \(-0.302101\pi\) | ||||
0.582433 | + | 0.812879i | \(0.302101\pi\) | |||||||
\(200\) | −506.977 | −0.179243 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1601.12 | 0.557696 | ||||||||
\(203\) | 4166.34 | 1.44049 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3575.22 | −1.21807 | ||||||||
\(206\) | 808.810 | 0.273555 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2950.84 | −0.976622 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2812.18 | −0.917527 | −0.458764 | − | 0.888558i | \(-0.651708\pi\) | ||||
−0.458764 | + | 0.888558i | \(0.651708\pi\) | |||||||
\(212\) | 570.948 | 0.184966 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2933.87 | 0.937173 | ||||||||
\(215\) | 2321.08 | 0.736262 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6649.05 | 2.08003 | ||||||||
\(218\) | 4039.39 | 1.25496 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1298.41 | −0.397903 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 917.736 | 0.275588 | 0.137794 | − | 0.990461i | \(-0.455999\pi\) | ||||
0.137794 | + | 0.990461i | \(0.455999\pi\) | |||||||
\(224\) | −4611.35 | −1.37549 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −249.981 | −0.0735774 | ||||||||
\(227\) | −1336.39 | −0.390746 | −0.195373 | − | 0.980729i | \(-0.562592\pi\) | ||||
−0.195373 | + | 0.980729i | \(0.562592\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −164.820 | −0.0475617 | −0.0237808 | − | 0.999717i | \(-0.507570\pi\) | ||||
−0.0237808 | + | 0.999717i | \(0.507570\pi\) | |||||||
\(230\) | 3962.66 | 1.13604 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3384.68 | 0.957824 | ||||||||
\(233\) | 4243.42 | 1.19312 | 0.596558 | − | 0.802570i | \(-0.296535\pi\) | ||||
0.596558 | + | 0.802570i | \(0.296535\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 446.205 | 0.123860 | ||||||||
\(236\) | −1680.53 | −0.463530 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3076.35 | −0.837859 | ||||||||
\(239\) | −2491.07 | −0.674200 | −0.337100 | − | 0.941469i | \(-0.609446\pi\) | ||||
−0.337100 | + | 0.941469i | \(0.609446\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2917.40 | −0.779776 | −0.389888 | − | 0.920862i | \(-0.627486\pi\) | ||||
−0.389888 | + | 0.920862i | \(0.627486\pi\) | |||||||
\(242\) | −1109.83 | −0.294803 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1095.72 | −0.287485 | ||||||||
\(245\) | 6540.32 | 1.70549 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 5401.60 | 1.38307 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2566.58 | −0.649300 | ||||||||
\(251\) | 1313.88 | 0.330403 | 0.165202 | − | 0.986260i | \(-0.447173\pi\) | ||||
0.165202 | + | 0.986260i | \(0.447173\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4506.79 | 1.11992 | ||||||||
\(254\) | 4716.78 | 1.16519 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4319.15 | −1.05448 | ||||||||
\(257\) | 987.582 | 0.239703 | 0.119851 | − | 0.992792i | \(-0.461758\pi\) | ||||
0.119851 | + | 0.992792i | \(0.461758\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6790.57 | −1.62913 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2949.53 | 0.695507 | ||||||||
\(263\) | 6986.45 | 1.63803 | 0.819017 | − | 0.573769i | \(-0.194519\pi\) | ||||
0.819017 | + | 0.573769i | \(0.194519\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1801.52 | −0.417609 | ||||||||
\(266\) | 6385.74 | 1.47194 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2056.79 | −0.468801 | ||||||||
\(269\) | 5904.34 | 1.33827 | 0.669134 | − | 0.743142i | \(-0.266665\pi\) | ||||
0.669134 | + | 0.743142i | \(0.266665\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2131.54 | 0.477793 | 0.238897 | − | 0.971045i | \(-0.423214\pi\) | ||||
0.238897 | + | 0.971045i | \(0.423214\pi\) | |||||||
\(272\) | −947.408 | −0.211195 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1502.92 | −0.331368 | ||||||||
\(275\) | 588.934 | 0.129142 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4032.41 | 0.874673 | 0.437336 | − | 0.899298i | \(-0.355922\pi\) | ||||
0.437336 | + | 0.899298i | \(0.355922\pi\) | |||||||
\(278\) | −3073.86 | −0.663159 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 8680.03 | 1.85261 | ||||||||
\(281\) | −2298.29 | −0.487916 | −0.243958 | − | 0.969786i | \(-0.578446\pi\) | ||||
−0.243958 | + | 0.969786i | \(0.578446\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6656.80 | 1.39825 | 0.699127 | − | 0.714998i | \(-0.253572\pi\) | ||||
0.699127 | + | 0.714998i | \(0.253572\pi\) | |||||||
\(284\) | −393.373 | −0.0821916 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8799.33 | 1.80978 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2347.01 | −0.477715 | ||||||||
\(290\) | −3457.13 | −0.700034 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −289.188 | −0.0579570 | ||||||||
\(293\) | 7466.99 | 1.48883 | 0.744413 | − | 0.667719i | \(-0.232729\pi\) | ||||
0.744413 | + | 0.667719i | \(0.232729\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5302.59 | 1.04654 | ||||||||
\(296\) | −5516.57 | −1.08326 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 873.759 | 0.169851 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5712.64 | −1.09392 | ||||||||
\(302\) | 3271.32 | 0.623323 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1966.58 | 0.371024 | ||||||||
\(305\) | 3457.34 | 0.649071 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3965.99 | 0.737299 | 0.368650 | − | 0.929568i | \(-0.379820\pi\) | ||||
0.368650 | + | 0.929568i | \(0.379820\pi\) | |||||||
\(308\) | 3195.64 | 0.591196 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5517.23 | −1.01083 | ||||||||
\(311\) | −7372.29 | −1.34419 | −0.672097 | − | 0.740463i | \(-0.734606\pi\) | ||||
−0.672097 | + | 0.740463i | \(0.734606\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8249.55 | 1.48975 | 0.744875 | − | 0.667204i | \(-0.232509\pi\) | ||||
0.744875 | + | 0.667204i | \(0.232509\pi\) | |||||||
\(314\) | −1491.54 | −0.268066 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −67.2133 | −0.0119653 | ||||||||
\(317\) | −5575.26 | −0.987817 | −0.493909 | − | 0.869514i | \(-0.664432\pi\) | ||||
−0.493909 | + | 0.869514i | \(0.664432\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3931.85 | −0.690098 | ||||||||
\(320\) | 5634.21 | 0.984256 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −9752.88 | −1.68791 | ||||||||
\(323\) | −5326.35 | −0.917543 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3876.91 | −0.658657 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7148.46 | 1.20338 | ||||||||
\(329\) | −1098.20 | −0.184029 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4157.36 | 0.690361 | 0.345180 | − | 0.938536i | \(-0.387818\pi\) | ||||
0.345180 | + | 0.938536i | \(0.387818\pi\) | |||||||
\(332\) | −5602.50 | −0.926136 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2915.30 | 0.477600 | ||||||||
\(335\) | 6489.82 | 1.05844 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3225.18 | 0.521326 | 0.260663 | − | 0.965430i | \(-0.416059\pi\) | ||||
0.260663 | + | 0.965430i | \(0.416059\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2343.67 | −0.373833 | ||||||||
\(341\) | −6274.82 | −0.996483 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5897.11 | −0.928321 | ||||||||
\(344\) | −4640.87 | −0.727381 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4175.15 | 0.648721 | ||||||||
\(347\) | −3290.49 | −0.509057 | −0.254529 | − | 0.967065i | \(-0.581920\pi\) | ||||
−0.254529 | + | 0.967065i | \(0.581920\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4491.52 | 0.688899 | 0.344449 | − | 0.938805i | \(-0.388066\pi\) | ||||
0.344449 | + | 0.938805i | \(0.388066\pi\) | |||||||
\(350\) | −1274.48 | −0.194639 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4351.81 | 0.658955 | ||||||||
\(353\) | 5897.88 | 0.889270 | 0.444635 | − | 0.895712i | \(-0.353333\pi\) | ||||
0.444635 | + | 0.895712i | \(0.353333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1241.21 | 0.185569 | ||||||||
\(356\) | 1282.43 | 0.190924 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7943.75 | 1.17274 | ||||||||
\(359\) | −9277.20 | −1.36388 | −0.681938 | − | 0.731410i | \(-0.738863\pi\) | ||||
−0.681938 | + | 0.731410i | \(0.738863\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4197.19 | 0.611924 | ||||||||
\(362\) | −5058.67 | −0.734469 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 912.477 | 0.130853 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6574.36 | −0.935092 | −0.467546 | − | 0.883969i | \(-0.654862\pi\) | ||||
−0.467546 | + | 0.883969i | \(0.654862\pi\) | |||||||
\(368\) | −3003.54 | −0.425463 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5634.65 | 0.791707 | ||||||||
\(371\) | 4433.89 | 0.620474 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5345.55 | −0.742043 | −0.371021 | − | 0.928624i | \(-0.620992\pi\) | ||||
−0.371021 | + | 0.928624i | \(0.620992\pi\) | |||||||
\(374\) | 2903.20 | 0.401393 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −892.162 | −0.122366 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1038.51 | 0.140751 | 0.0703757 | − | 0.997521i | \(-0.477580\pi\) | ||||
0.0703757 | + | 0.997521i | \(0.477580\pi\) | |||||||
\(380\) | 4864.87 | 0.656743 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4649.80 | −0.622786 | ||||||||
\(383\) | 6749.19 | 0.900437 | 0.450219 | − | 0.892918i | \(-0.351346\pi\) | ||||
0.450219 | + | 0.892918i | \(0.351346\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10083.2 | −1.33478 | ||||||||
\(386\) | −8010.54 | −1.05628 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2867.17 | −0.375151 | ||||||||
\(389\) | 1246.11 | 0.162417 | 0.0812083 | − | 0.996697i | \(-0.474122\pi\) | ||||
0.0812083 | + | 0.996697i | \(0.474122\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8134.89 | 1.05217 | ||||||||
\(392\) | −13077.0 | −1.68492 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −10340.3 | −1.32218 | ||||||||
\(395\) | 212.079 | 0.0270148 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8355.69 | −1.05632 | −0.528161 | − | 0.849144i | \(-0.677118\pi\) | ||||
−0.528161 | + | 0.849144i | \(0.677118\pi\) | |||||||
\(398\) | 6678.25 | 0.841082 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −392.494 | −0.0490618 | ||||||||
\(401\) | 3283.66 | 0.408923 | 0.204461 | − | 0.978875i | \(-0.434456\pi\) | ||||
0.204461 | + | 0.978875i | \(0.434456\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −3002.14 | −0.369708 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8508.68 | 1.04010 | ||||||||
\(407\) | 6408.37 | 0.780470 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10928.9 | −1.32127 | −0.660636 | − | 0.750706i | \(-0.729713\pi\) | ||||
−0.660636 | + | 0.750706i | \(0.729713\pi\) | |||||||
\(410\) | −7301.47 | −0.879497 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1516.53 | −0.181345 | ||||||||
\(413\) | −13050.7 | −1.55492 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17677.6 | 2.09099 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6026.33 | −0.705162 | ||||||||
\(419\) | −7302.94 | −0.851485 | −0.425742 | − | 0.904844i | \(-0.639987\pi\) | ||||
−0.425742 | + | 0.904844i | \(0.639987\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7580.99 | −0.877612 | −0.438806 | − | 0.898582i | \(-0.644599\pi\) | ||||
−0.438806 | + | 0.898582i | \(0.644599\pi\) | |||||||
\(422\) | −5743.15 | −0.662493 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3602.03 | 0.412571 | ||||||||
\(425\) | 1063.04 | 0.121330 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8509.19 | −0.964377 | ||||||||
\(428\) | −5501.06 | −0.621270 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4740.21 | 0.531612 | ||||||||
\(431\) | −10056.7 | −1.12394 | −0.561968 | − | 0.827159i | \(-0.689956\pi\) | ||||
−0.561968 | + | 0.827159i | \(0.689956\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2733.38 | 0.303367 | 0.151683 | − | 0.988429i | \(-0.451531\pi\) | ||||
0.151683 | + | 0.988429i | \(0.451531\pi\) | |||||||
\(434\) | 13579.0 | 1.50187 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7573.93 | −0.831939 | ||||||||
\(437\) | −16886.0 | −1.84844 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6744.23 | 0.733223 | 0.366611 | − | 0.930374i | \(-0.380518\pi\) | ||||
0.366611 | + | 0.930374i | \(0.380518\pi\) | |||||||
\(440\) | −8191.48 | −0.887531 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8655.69 | −0.928317 | −0.464158 | − | 0.885752i | \(-0.653643\pi\) | ||||
−0.464158 | + | 0.885752i | \(0.653643\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4046.48 | −0.431059 | ||||||||
\(446\) | 1874.24 | 0.198986 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −13866.9 | −1.46239 | ||||||||
\(449\) | −6522.46 | −0.685555 | −0.342777 | − | 0.939417i | \(-0.611368\pi\) | ||||
−0.342777 | + | 0.939417i | \(0.611368\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8304.07 | −0.867014 | ||||||||
\(452\) | 468.719 | 0.0487759 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2729.23 | −0.282135 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1551.23 | −0.158782 | −0.0793909 | − | 0.996844i | \(-0.525298\pi\) | ||||
−0.0793909 | + | 0.996844i | \(0.525298\pi\) | |||||||
\(458\) | −336.603 | −0.0343415 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7430.06 | −0.753105 | ||||||||
\(461\) | −7766.25 | −0.784621 | −0.392310 | − | 0.919833i | \(-0.628324\pi\) | ||||
−0.392310 | + | 0.919833i | \(0.628324\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2004.52 | −0.201205 | −0.100603 | − | 0.994927i | \(-0.532077\pi\) | ||||
−0.100603 | + | 0.994927i | \(0.532077\pi\) | |||||||
\(464\) | 2620.37 | 0.262172 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8666.10 | 0.861479 | ||||||||
\(467\) | −18674.3 | −1.85042 | −0.925209 | − | 0.379458i | \(-0.876111\pi\) | ||||
−0.925209 | + | 0.379458i | \(0.876111\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15972.7 | −1.57261 | ||||||||
\(470\) | 911.259 | 0.0894324 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −10602.2 | −1.03391 | ||||||||
\(473\) | 5391.11 | 0.524067 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2206.61 | −0.213150 | ||||||||
\(476\) | 5768.22 | 0.555433 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5087.36 | −0.486800 | ||||||||
\(479\) | 9313.02 | 0.888357 | 0.444178 | − | 0.895938i | \(-0.353496\pi\) | ||||
0.444178 | + | 0.895938i | \(0.353496\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −5958.03 | −0.563031 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2080.95 | 0.195431 | ||||||||
\(485\) | 9046.81 | 0.846999 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3536.80 | −0.329092 | −0.164546 | − | 0.986369i | \(-0.552616\pi\) | ||||
−0.164546 | + | 0.986369i | \(0.552616\pi\) | |||||||
\(488\) | −6912.76 | −0.641241 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 13356.9 | 1.23144 | ||||||||
\(491\) | 3361.78 | 0.308992 | 0.154496 | − | 0.987993i | \(-0.450625\pi\) | ||||
0.154496 | + | 0.987993i | \(0.450625\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7097.10 | −0.648351 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4181.84 | 0.378569 | ||||||||
\(497\) | −3054.87 | −0.275714 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4027.43 | 0.361308 | 0.180654 | − | 0.983547i | \(-0.442179\pi\) | ||||
0.180654 | + | 0.983547i | \(0.442179\pi\) | |||||||
\(500\) | 4812.40 | 0.430434 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2683.26 | 0.238565 | ||||||||
\(503\) | −1766.67 | −0.156604 | −0.0783022 | − | 0.996930i | \(-0.524950\pi\) | ||||
−0.0783022 | + | 0.996930i | \(0.524950\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9472.67 | 0.834709 | ||||||||
\(506\) | 9203.96 | 0.808628 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8844.05 | −0.772424 | ||||||||
\(509\) | 6816.27 | 0.593567 | 0.296784 | − | 0.954945i | \(-0.404086\pi\) | ||||
0.296784 | + | 0.954945i | \(0.404086\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2245.79 | −0.194418 | ||||||||
\(512\) | −6514.89 | −0.562344 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2016.88 | 0.173076 | ||||||||
\(515\) | 4785.13 | 0.409433 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1036.39 | 0.0881630 | ||||||||
\(518\) | −13868.0 | −1.17630 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5442.27 | 0.457640 | 0.228820 | − | 0.973469i | \(-0.426513\pi\) | ||||
0.228820 | + | 0.973469i | \(0.426513\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20728.5 | 1.73307 | 0.866535 | − | 0.499117i | \(-0.166342\pi\) | ||||
0.866535 | + | 0.499117i | \(0.166342\pi\) | |||||||
\(524\) | −5530.43 | −0.461065 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14268.0 | 1.18273 | ||||||||
\(527\) | −11326.2 | −0.936202 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13622.8 | 1.11965 | ||||||||
\(530\) | −3679.13 | −0.301531 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −11973.4 | −0.975775 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17357.5 | 1.40268 | ||||||||
\(536\) | −12976.0 | −1.04567 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 12058.1 | 0.966285 | ||||||||
\(539\) | 15191.0 | 1.21396 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8577.44 | −0.681651 | −0.340825 | − | 0.940127i | \(-0.610706\pi\) | ||||
−0.340825 | + | 0.940127i | \(0.610706\pi\) | |||||||
\(542\) | 4353.13 | 0.344987 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7855.14 | 0.619093 | ||||||||
\(545\) | 23898.1 | 1.87832 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8723.99 | 0.681921 | 0.340961 | − | 0.940078i | \(-0.389248\pi\) | ||||
0.340961 | + | 0.940078i | \(0.389248\pi\) | |||||||
\(548\) | 2818.01 | 0.219671 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1202.75 | 0.0932459 | ||||||||
\(551\) | 14731.8 | 1.13901 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −521.968 | −0.0401380 | ||||||||
\(554\) | 8235.17 | 0.631550 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5763.56 | 0.439621 | ||||||||
\(557\) | −965.006 | −0.0734087 | −0.0367043 | − | 0.999326i | \(-0.511686\pi\) | ||||
−0.0367043 | + | 0.999326i | \(0.511686\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 6719.95 | 0.507089 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4693.66 | −0.352296 | ||||||||
\(563\) | 14605.2 | 1.09331 | 0.546657 | − | 0.837357i | \(-0.315900\pi\) | ||||
0.546657 | + | 0.837357i | \(0.315900\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1478.95 | −0.110124 | ||||||||
\(566\) | 13594.8 | 1.00960 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2481.74 | −0.183330 | ||||||||
\(569\) | −7802.48 | −0.574863 | −0.287432 | − | 0.957801i | \(-0.592801\pi\) | ||||
−0.287432 | + | 0.957801i | \(0.592801\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11988.2 | 0.878618 | 0.439309 | − | 0.898336i | \(-0.355223\pi\) | ||||
0.439309 | + | 0.898336i | \(0.355223\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 17970.4 | 1.30674 | ||||||||
\(575\) | 3370.14 | 0.244425 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5576.90 | −0.402374 | −0.201187 | − | 0.979553i | \(-0.564480\pi\) | ||||
−0.201187 | + | 0.979553i | \(0.564480\pi\) | |||||||
\(578\) | −4793.17 | −0.344930 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6482.19 | 0.464066 | ||||||||
\(581\) | −43508.1 | −3.10675 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4184.33 | −0.297251 | ||||||||
\(584\) | −1824.45 | −0.129274 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15249.4 | 1.07499 | ||||||||
\(587\) | 26754.0 | 1.88119 | 0.940593 | − | 0.339535i | \(-0.110270\pi\) | ||||
0.940593 | + | 0.339535i | \(0.110270\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23510.5 | 1.64471 | ||||||||
\(590\) | 10829.2 | 0.755644 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4270.85 | −0.296505 | ||||||||
\(593\) | −3589.40 | −0.248565 | −0.124283 | − | 0.992247i | \(-0.539663\pi\) | ||||
−0.124283 | + | 0.992247i | \(0.539663\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18200.5 | −1.25403 | ||||||||
\(596\) | −1638.32 | −0.112597 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7462.78 | 0.509050 | 0.254525 | − | 0.967066i | \(-0.418081\pi\) | ||||
0.254525 | + | 0.967066i | \(0.418081\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16511.0 | −1.12063 | −0.560316 | − | 0.828279i | \(-0.689320\pi\) | ||||
−0.560316 | + | 0.828279i | \(0.689320\pi\) | |||||||
\(602\) | −11666.6 | −0.789858 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6133.80 | −0.413213 | ||||||||
\(605\) | −6566.04 | −0.441235 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11953.6 | −0.799309 | −0.399654 | − | 0.916666i | \(-0.630870\pi\) | ||||
−0.399654 | + | 0.916666i | \(0.630870\pi\) | |||||||
\(608\) | −16305.3 | −1.08761 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7060.73 | 0.468657 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4575.65 | 0.301482 | 0.150741 | − | 0.988573i | \(-0.451834\pi\) | ||||
0.150741 | + | 0.988573i | \(0.451834\pi\) | |||||||
\(614\) | 8099.51 | 0.532361 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 20160.9 | 1.31868 | ||||||||
\(617\) | −19231.0 | −1.25480 | −0.627400 | − | 0.778697i | \(-0.715881\pi\) | ||||
−0.627400 | + | 0.778697i | \(0.715881\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11715.6 | 0.760727 | 0.380363 | − | 0.924837i | \(-0.375799\pi\) | ||||
0.380363 | + | 0.924837i | \(0.375799\pi\) | |||||||
\(620\) | 10344.9 | 0.670099 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −15056.0 | −0.970564 | ||||||||
\(623\) | 9959.17 | 0.640459 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17807.8 | −1.13970 | ||||||||
\(626\) | 16847.6 | 1.07566 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2796.68 | 0.177706 | ||||||||
\(629\) | 11567.3 | 0.733256 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8780.09 | 0.553930 | 0.276965 | − | 0.960880i | \(-0.410671\pi\) | ||||
0.276965 | + | 0.960880i | \(0.410671\pi\) | |||||||
\(632\) | −424.040 | −0.0266889 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −11386.0 | −0.713245 | ||||||||
\(635\) | 27905.7 | 1.74395 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −8029.78 | −0.498279 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3482.55 | −0.215094 | ||||||||
\(641\) | −24991.7 | −1.53996 | −0.769980 | − | 0.638068i | \(-0.779734\pi\) | ||||
−0.769980 | + | 0.638068i | \(0.779734\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2353.86 | 0.144365 | 0.0721827 | − | 0.997391i | \(-0.477004\pi\) | ||||
0.0721827 | + | 0.997391i | \(0.477004\pi\) | |||||||
\(644\) | 18286.8 | 1.11895 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10877.7 | −0.662504 | ||||||||
\(647\) | 5910.80 | 0.359162 | 0.179581 | − | 0.983743i | \(-0.442526\pi\) | ||||
0.179581 | + | 0.983743i | \(0.442526\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12316.2 | 0.744918 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7269.28 | 0.436637 | ||||||||
\(653\) | −5924.34 | −0.355034 | −0.177517 | − | 0.984118i | \(-0.556806\pi\) | ||||
−0.177517 | + | 0.984118i | \(0.556806\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17450.2 | 1.04097 | ||||||||
\(656\) | 5534.23 | 0.329383 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2242.79 | −0.132877 | ||||||||
\(659\) | 12839.5 | 0.758964 | 0.379482 | − | 0.925199i | \(-0.376102\pi\) | ||||
0.379482 | + | 0.925199i | \(0.376102\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10265.5 | −0.604057 | −0.302028 | − | 0.953299i | \(-0.597664\pi\) | ||||
−0.302028 | + | 0.953299i | \(0.597664\pi\) | |||||||
\(662\) | 8490.35 | 0.498469 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −35345.4 | −2.06577 | ||||||||
\(665\) | 37779.8 | 2.20306 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22499.7 | −1.30614 | ||||||||
\(668\) | −5466.25 | −0.316610 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 13253.8 | 0.764236 | ||||||||
\(671\) | 8030.27 | 0.462004 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9862.82 | 0.564909 | 0.282454 | − | 0.959281i | \(-0.408851\pi\) | ||||
0.282454 | + | 0.959281i | \(0.408851\pi\) | |||||||
\(674\) | 6586.61 | 0.376419 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −32615.5 | −1.85158 | −0.925788 | − | 0.378043i | \(-0.876597\pi\) | ||||
−0.925788 | + | 0.378043i | \(0.876597\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22266.0 | −1.25845 | ||||||||
\(680\) | −14785.9 | −0.833841 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −12814.7 | −0.719502 | ||||||||
\(683\) | −21627.4 | −1.21164 | −0.605820 | − | 0.795602i | \(-0.707155\pi\) | ||||
−0.605820 | + | 0.795602i | \(0.707155\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8891.70 | −0.495962 | ||||||||
\(686\) | −12043.3 | −0.670286 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3592.90 | −0.199096 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14233.1 | −0.783580 | −0.391790 | − | 0.920055i | \(-0.628144\pi\) | ||||
−0.391790 | + | 0.920055i | \(0.628144\pi\) | |||||||
\(692\) | −7828.49 | −0.430050 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6719.98 | −0.367561 | ||||||||
\(695\) | −18185.8 | −0.992557 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14989.1 | −0.814566 | ||||||||
\(698\) | 9172.78 | 0.497414 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2389.67 | 0.129030 | ||||||||
\(701\) | 28747.0 | 1.54887 | 0.774437 | − | 0.632651i | \(-0.218033\pi\) | ||||
0.774437 | + | 0.632651i | \(0.218033\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24010.8 | −1.28817 | ||||||||
\(704\) | 13086.4 | 0.700586 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12044.9 | 0.642090 | ||||||||
\(707\) | −23314.1 | −1.24019 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1818.65 | 0.0963339 | 0.0481670 | − | 0.998839i | \(-0.484662\pi\) | ||||
0.0481670 | + | 0.998839i | \(0.484662\pi\) | |||||||
\(710\) | 2534.86 | 0.133988 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8090.70 | 0.425859 | ||||||||
\(713\) | −35907.3 | −1.88603 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −14894.7 | −0.777431 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −18946.3 | −0.984776 | ||||||||
\(719\) | −26141.8 | −1.35595 | −0.677973 | − | 0.735087i | \(-0.737141\pi\) | ||||
−0.677973 | + | 0.735087i | \(0.737141\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11777.2 | −0.608328 | ||||||||
\(722\) | 8571.68 | 0.441835 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9485.10 | 0.486894 | ||||||||
\(725\) | −2940.20 | −0.150616 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1340.10 | −0.0683652 | −0.0341826 | − | 0.999416i | \(-0.510883\pi\) | ||||
−0.0341826 | + | 0.999416i | \(0.510883\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1863.50 | 0.0944811 | ||||||||
\(731\) | 9731.11 | 0.492364 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32517.1 | 1.63854 | 0.819269 | − | 0.573409i | \(-0.194380\pi\) | ||||
0.819269 | + | 0.573409i | \(0.194380\pi\) | |||||||
\(734\) | −13426.4 | −0.675176 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 24903.0 | 1.24719 | ||||||||
\(737\) | 15073.7 | 0.753389 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22170.5 | 1.10359 | 0.551797 | − | 0.833978i | \(-0.313942\pi\) | ||||
0.551797 | + | 0.833978i | \(0.313942\pi\) | |||||||
\(740\) | −10565.1 | −0.524838 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9055.07 | 0.448008 | ||||||||
\(743\) | −30387.8 | −1.50043 | −0.750216 | − | 0.661193i | \(-0.770051\pi\) | ||||
−0.750216 | + | 0.661193i | \(0.770051\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5169.39 | 0.254217 | ||||||||
\(746\) | −10916.9 | −0.535786 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5443.57 | −0.266092 | ||||||||
\(749\) | −42720.3 | −2.08407 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16898.3 | −0.821077 | −0.410539 | − | 0.911843i | \(-0.634659\pi\) | ||||
−0.410539 | + | 0.911843i | \(0.634659\pi\) | |||||||
\(752\) | −690.699 | −0.0334936 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 19354.0 | 0.932934 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32925.8 | 1.58086 | 0.790428 | − | 0.612555i | \(-0.209858\pi\) | ||||
0.790428 | + | 0.612555i | \(0.209858\pi\) | |||||||
\(758\) | 2120.89 | 0.101628 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 30691.8 | 1.46488 | ||||||||
\(761\) | −16792.0 | −0.799882 | −0.399941 | − | 0.916541i | \(-0.630969\pi\) | ||||
−0.399941 | + | 0.916541i | \(0.630969\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −58817.9 | −2.79076 | ||||||||
\(764\) | 8718.46 | 0.412857 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13783.5 | 0.650153 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1541.57 | 0.0722891 | 0.0361445 | − | 0.999347i | \(-0.488492\pi\) | ||||
0.0361445 | + | 0.999347i | \(0.488492\pi\) | |||||||
\(770\) | −20592.4 | −0.963765 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 15019.9 | 0.700231 | ||||||||
\(773\) | −38071.2 | −1.77144 | −0.885721 | − | 0.464218i | \(-0.846335\pi\) | ||||
−0.885721 | + | 0.464218i | \(0.846335\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4692.26 | −0.217485 | ||||||||
\(776\) | −18088.6 | −0.836782 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2544.85 | 0.117272 | ||||||||
\(779\) | 31113.6 | 1.43102 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2882.93 | 0.132086 | ||||||||
\(782\) | 16613.4 | 0.759712 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −10124.0 | −0.461189 | ||||||||
\(785\) | −8824.38 | −0.401217 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20049.8 | −0.908129 | −0.454065 | − | 0.890969i | \(-0.650027\pi\) | ||||
−0.454065 | + | 0.890969i | \(0.650027\pi\) | |||||||
\(788\) | 19388.3 | 0.876498 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 433.117 | 0.0195058 | ||||||||
\(791\) | 3640.00 | 0.163620 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −17064.4 | −0.762709 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −12521.9 | −0.557570 | ||||||||
\(797\) | 22401.9 | 0.995627 | 0.497813 | − | 0.867284i | \(-0.334136\pi\) | ||||
0.497813 | + | 0.867284i | \(0.334136\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1870.71 | 0.0828298 | ||||||||
\(800\) | 3254.24 | 0.143819 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6706.02 | 0.295259 | ||||||||
\(803\) | 2119.39 | 0.0931401 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −57700.7 | −2.52631 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −18940.1 | −0.824640 | ||||||||
\(809\) | 41966.4 | 1.82381 | 0.911903 | − | 0.410406i | \(-0.134613\pi\) | ||||
0.911903 | + | 0.410406i | \(0.134613\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13029.1 | 0.564133 | 0.282067 | − | 0.959395i | \(-0.408980\pi\) | ||||
0.282067 | + | 0.959395i | \(0.408980\pi\) | |||||||
\(812\) | −15953.9 | −0.689500 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 13087.4 | 0.563532 | ||||||||
\(815\) | −22936.8 | −0.985819 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20199.4 | −0.864977 | ||||||||
\(818\) | −22319.5 | −0.954014 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13690.4 | 0.583036 | ||||||||
\(821\) | 8898.14 | 0.378255 | 0.189127 | − | 0.981953i | \(-0.439434\pi\) | ||||
0.189127 | + | 0.981953i | \(0.439434\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22723.6 | 0.962448 | 0.481224 | − | 0.876598i | \(-0.340192\pi\) | ||||
0.481224 | + | 0.876598i | \(0.340192\pi\) | |||||||
\(824\) | −9567.61 | −0.404494 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −26652.7 | −1.12272 | ||||||||
\(827\) | 19073.3 | 0.801989 | 0.400994 | − | 0.916081i | \(-0.368665\pi\) | ||||
0.400994 | + | 0.916081i | \(0.368665\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 42503.8 | 1.78072 | 0.890361 | − | 0.455255i | \(-0.150452\pi\) | ||||
0.890361 | + | 0.455255i | \(0.150452\pi\) | |||||||
\(830\) | 36102.0 | 1.50978 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 27420.2 | 1.14052 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17247.7 | 0.714829 | ||||||||
\(836\) | 11299.5 | 0.467465 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −14914.4 | −0.614808 | ||||||||
\(839\) | −19427.2 | −0.799408 | −0.399704 | − | 0.916644i | \(-0.630887\pi\) | ||||
−0.399704 | + | 0.916644i | \(0.630887\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4759.60 | −0.195154 | ||||||||
\(842\) | −15482.2 | −0.633673 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 10768.5 | 0.439180 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16160.3 | 0.655578 | ||||||||
\(848\) | 2788.64 | 0.112927 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2170.99 | 0.0876052 | ||||||||
\(851\) | 36671.5 | 1.47718 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26851.8 | −1.07783 | −0.538914 | − | 0.842361i | \(-0.681165\pi\) | ||||
−0.538914 | + | 0.842361i | \(0.681165\pi\) | |||||||
\(854\) | −17377.8 | −0.696320 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −34705.4 | −1.38576 | ||||||||
\(857\) | −41539.4 | −1.65573 | −0.827864 | − | 0.560929i | \(-0.810444\pi\) | ||||
−0.827864 | + | 0.560929i | \(0.810444\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11936.2 | −0.474107 | −0.237054 | − | 0.971497i | \(-0.576182\pi\) | ||||
−0.237054 | + | 0.971497i | \(0.576182\pi\) | |||||||
\(860\) | −8887.99 | −0.352416 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −20538.3 | −0.811529 | ||||||||
\(863\) | 41128.6 | 1.62229 | 0.811143 | − | 0.584848i | \(-0.198846\pi\) | ||||
0.811143 | + | 0.584848i | \(0.198846\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24701.3 | 0.970948 | ||||||||
\(866\) | 5582.22 | 0.219043 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −25460.8 | −0.995619 | ||||||||
\(869\) | 492.590 | 0.0192290 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −47782.9 | −1.85566 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −34485.3 | −1.33465 | ||||||||
\(875\) | 37372.3 | 1.44390 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6406.86 | 0.246687 | 0.123343 | − | 0.992364i | \(-0.460638\pi\) | ||||
0.123343 | + | 0.992364i | \(0.460638\pi\) | |||||||
\(878\) | 13773.4 | 0.529417 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6341.73 | −0.242931 | ||||||||
\(881\) | 2938.07 | 0.112357 | 0.0561783 | − | 0.998421i | \(-0.482108\pi\) | ||||
0.0561783 | + | 0.998421i | \(0.482108\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3022.06 | 0.115176 | 0.0575881 | − | 0.998340i | \(-0.481659\pi\) | ||||
0.0575881 | + | 0.998340i | \(0.481659\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −17677.0 | −0.670284 | ||||||||
\(887\) | 10060.4 | 0.380830 | 0.190415 | − | 0.981704i | \(-0.439017\pi\) | ||||
0.190415 | + | 0.981704i | \(0.439017\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −68681.5 | −2.59112 | ||||||||
\(890\) | −8263.89 | −0.311243 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3514.24 | −0.131912 | ||||||||
\(893\) | −3883.13 | −0.145514 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 46997.3 | 1.75525 | ||||||||
\(896\) | 8571.24 | 0.319582 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −13320.5 | −0.494999 | ||||||||
\(899\) | 31326.5 | 1.16218 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7552.84 | −0.279269 | ||||||||
\(902\) | −16958.9 | −0.626020 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2957.09 | 0.108796 | ||||||||
\(905\) | −29928.4 | −1.09929 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −43158.6 | −1.58000 | −0.789999 | − | 0.613108i | \(-0.789919\pi\) | ||||
−0.789999 | + | 0.613108i | \(0.789919\pi\) | |||||||
\(908\) | 5117.36 | 0.187033 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32665.9 | 1.18800 | 0.594001 | − | 0.804464i | \(-0.297547\pi\) | ||||
0.594001 | + | 0.804464i | \(0.297547\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 41059.3 | 1.48835 | ||||||||
\(914\) | −3167.98 | −0.114647 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 631.137 | 0.0227657 | ||||||||
\(917\) | −42948.4 | −1.54665 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18989.9 | 0.681633 | 0.340816 | − | 0.940130i | \(-0.389297\pi\) | ||||
0.340816 | + | 0.940130i | \(0.389297\pi\) | |||||||
\(920\) | −46875.3 | −1.67982 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −15860.6 | −0.566529 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4792.12 | 0.170340 | ||||||||
\(926\) | −4093.72 | −0.145279 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −21726.0 | −0.768525 | ||||||||
\(929\) | −5596.81 | −0.197659 | −0.0988295 | − | 0.995104i | \(-0.531510\pi\) | ||||
−0.0988295 | + | 0.995104i | \(0.531510\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −56917.6 | −2.00365 | ||||||||
\(932\) | −16249.1 | −0.571091 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −38137.5 | −1.33608 | ||||||||
\(935\) | 17176.1 | 0.600770 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40294.4 | 1.40487 | 0.702433 | − | 0.711750i | \(-0.252097\pi\) | ||||
0.702433 | + | 0.711750i | \(0.252097\pi\) | |||||||
\(938\) | −32620.2 | −1.13549 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1708.63 | −0.0592865 | ||||||||
\(941\) | 43648.8 | 1.51213 | 0.756063 | − | 0.654499i | \(-0.227120\pi\) | ||||
0.756063 | + | 0.654499i | \(0.227120\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −47519.5 | −1.64098 | ||||||||
\(944\) | −8208.10 | −0.282999 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11010.0 | 0.378398 | ||||||||
\(947\) | −10486.6 | −0.359839 | −0.179919 | − | 0.983681i | \(-0.557584\pi\) | ||||
−0.179919 | + | 0.983681i | \(0.557584\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −4506.44 | −0.153903 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 36390.9 | 1.23890 | ||||||||
\(953\) | −33058.8 | −1.12369 | −0.561846 | − | 0.827242i | \(-0.689909\pi\) | ||||
−0.561846 | + | 0.827242i | \(0.689909\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −27509.5 | −0.932131 | ||||||||
\(956\) | 9538.90 | 0.322709 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 19019.5 | 0.641431 | ||||||||
\(959\) | 21884.2 | 0.736891 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20202.8 | 0.678152 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 11171.4 | 0.373244 | ||||||||
\(965\) | −47392.5 | −1.58095 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 53634.9 | 1.78364 | 0.891821 | − | 0.452389i | \(-0.149428\pi\) | ||||
0.891821 | + | 0.452389i | \(0.149428\pi\) | |||||||
\(968\) | 13128.4 | 0.435913 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 18475.8 | 0.611569 | ||||||||
\(971\) | 4086.80 | 0.135069 | 0.0675344 | − | 0.997717i | \(-0.478487\pi\) | ||||
0.0675344 | + | 0.997717i | \(0.478487\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 44758.8 | 1.47472 | ||||||||
\(974\) | −7223.00 | −0.237618 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5351.76 | −0.175518 | ||||||||
\(977\) | 14381.0 | 0.470919 | 0.235459 | − | 0.971884i | \(-0.424341\pi\) | ||||
0.235459 | + | 0.971884i | \(0.424341\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9398.64 | −0.306825 | ||||||||
\(980\) | −25044.5 | −0.816343 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6865.57 | 0.223105 | ||||||||
\(983\) | −12916.5 | −0.419099 | −0.209549 | − | 0.977798i | \(-0.567200\pi\) | ||||
−0.209549 | + | 0.977798i | \(0.567200\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −61176.2 | −1.97892 | ||||||||
\(986\) | −14494.0 | −0.468137 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 30850.3 | 0.991893 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5838.98 | −0.187166 | −0.0935829 | − | 0.995611i | \(-0.529832\pi\) | ||||
−0.0935829 | + | 0.995611i | \(0.529832\pi\) | |||||||
\(992\) | −34672.5 | −1.10973 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6238.79 | −0.199077 | ||||||||
\(995\) | 39510.3 | 1.25886 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 44290.1 | 1.40690 | 0.703452 | − | 0.710743i | \(-0.251641\pi\) | ||||
0.703452 | + | 0.710743i | \(0.251641\pi\) | |||||||
\(998\) | 8224.99 | 0.260879 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1521.4.a.bk.1.7 | 10 | ||
3.2 | odd | 2 | 507.4.a.r.1.4 | 10 | |||
13.2 | odd | 12 | 117.4.q.e.82.4 | 10 | |||
13.7 | odd | 12 | 117.4.q.e.10.4 | 10 | |||
13.12 | even | 2 | inner | 1521.4.a.bk.1.4 | 10 | ||
39.2 | even | 12 | 39.4.j.c.4.2 | ✓ | 10 | ||
39.5 | even | 4 | 507.4.b.i.337.7 | 10 | |||
39.8 | even | 4 | 507.4.b.i.337.4 | 10 | |||
39.20 | even | 12 | 39.4.j.c.10.2 | yes | 10 | ||
39.38 | odd | 2 | 507.4.a.r.1.7 | 10 | |||
156.59 | odd | 12 | 624.4.bv.h.49.2 | 10 | |||
156.119 | odd | 12 | 624.4.bv.h.433.4 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.j.c.4.2 | ✓ | 10 | 39.2 | even | 12 | ||
39.4.j.c.10.2 | yes | 10 | 39.20 | even | 12 | ||
117.4.q.e.10.4 | 10 | 13.7 | odd | 12 | |||
117.4.q.e.82.4 | 10 | 13.2 | odd | 12 | |||
507.4.a.r.1.4 | 10 | 3.2 | odd | 2 | |||
507.4.a.r.1.7 | 10 | 39.38 | odd | 2 | |||
507.4.b.i.337.4 | 10 | 39.8 | even | 4 | |||
507.4.b.i.337.7 | 10 | 39.5 | even | 4 | |||
624.4.bv.h.49.2 | 10 | 156.59 | odd | 12 | |||
624.4.bv.h.433.4 | 10 | 156.119 | odd | 12 | |||
1521.4.a.bk.1.4 | 10 | 13.12 | even | 2 | inner | ||
1521.4.a.bk.1.7 | 10 | 1.1 | even | 1 | trivial |