Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,4,Mod(1,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, 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("1323.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.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: | \(78.0595269376\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 42x^{4} + 369x^{2} - 112 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-5.45019\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1323.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.45019 | −1.92693 | −0.963467 | − | 0.267826i | \(-0.913695\pi\) | ||||
−0.963467 | + | 0.267826i | \(0.913695\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 21.7046 | 2.71308 | ||||||||
\(5\) | 19.3432 | 1.73011 | 0.865053 | − | 0.501681i | \(-0.167285\pi\) | ||||
0.865053 | + | 0.501681i | \(0.167285\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −74.6929 | −3.30099 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −105.424 | −3.33380 | ||||||||
\(11\) | 11.2132 | 0.307354 | 0.153677 | − | 0.988121i | \(-0.450888\pi\) | ||||
0.153677 | + | 0.988121i | \(0.450888\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −46.3102 | −0.988010 | −0.494005 | − | 0.869459i | \(-0.664468\pi\) | ||||
−0.494005 | + | 0.869459i | \(0.664468\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 233.454 | 3.64771 | ||||||||
\(17\) | −97.6541 | −1.39321 | −0.696606 | − | 0.717454i | \(-0.745307\pi\) | ||||
−0.696606 | + | 0.717454i | \(0.745307\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −98.9176 | −1.19438 | −0.597191 | − | 0.802099i | \(-0.703716\pi\) | ||||
−0.597191 | + | 0.802099i | \(0.703716\pi\) | |||||||
\(20\) | 419.836 | 4.69391 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −61.1139 | −0.592251 | ||||||||
\(23\) | 138.173 | 1.25265 | 0.626325 | − | 0.779562i | \(-0.284558\pi\) | ||||
0.626325 | + | 0.779562i | \(0.284558\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 249.158 | 1.99327 | ||||||||
\(26\) | 252.400 | 1.90383 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 180.123 | 1.15338 | 0.576690 | − | 0.816963i | \(-0.304344\pi\) | ||||
0.576690 | + | 0.816963i | \(0.304344\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −31.9046 | −0.184846 | −0.0924230 | − | 0.995720i | \(-0.529461\pi\) | ||||
−0.0924230 | + | 0.995720i | \(0.529461\pi\) | |||||||
\(32\) | −674.825 | −3.72792 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 532.234 | 2.68463 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −205.452 | −0.912867 | −0.456433 | − | 0.889758i | \(-0.650873\pi\) | ||||
−0.456433 | + | 0.889758i | \(0.650873\pi\) | |||||||
\(38\) | 539.120 | 2.30149 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1444.80 | −5.71106 | ||||||||
\(41\) | 234.404 | 0.892874 | 0.446437 | − | 0.894815i | \(-0.352693\pi\) | ||||
0.446437 | + | 0.894815i | \(0.352693\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −320.568 | −1.13689 | −0.568443 | − | 0.822723i | \(-0.692454\pi\) | ||||
−0.568443 | + | 0.822723i | \(0.692454\pi\) | |||||||
\(44\) | 243.377 | 0.833875 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −753.067 | −2.41378 | ||||||||
\(47\) | −312.715 | −0.970516 | −0.485258 | − | 0.874371i | \(-0.661274\pi\) | ||||
−0.485258 | + | 0.874371i | \(0.661274\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1357.96 | −3.84089 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1005.15 | −2.68055 | ||||||||
\(53\) | 53.7942 | 0.139419 | 0.0697094 | − | 0.997567i | \(-0.477793\pi\) | ||||
0.0697094 | + | 0.997567i | \(0.477793\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 216.898 | 0.531755 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −981.706 | −2.22249 | ||||||||
\(59\) | 400.291 | 0.883278 | 0.441639 | − | 0.897193i | \(-0.354397\pi\) | ||||
0.441639 | + | 0.897193i | \(0.354397\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −97.3536 | −0.204342 | −0.102171 | − | 0.994767i | \(-0.532579\pi\) | ||||
−0.102171 | + | 0.994767i | \(0.532579\pi\) | |||||||
\(62\) | 173.886 | 0.356186 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1810.30 | 3.53574 | ||||||||
\(65\) | −895.786 | −1.70936 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 257.525 | 0.469577 | 0.234789 | − | 0.972046i | \(-0.424560\pi\) | ||||
0.234789 | + | 0.972046i | \(0.424560\pi\) | |||||||
\(68\) | −2119.55 | −3.77989 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 253.601 | 0.423900 | 0.211950 | − | 0.977280i | \(-0.432019\pi\) | ||||
0.211950 | + | 0.977280i | \(0.432019\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1161.99 | −1.86303 | −0.931514 | − | 0.363706i | \(-0.881511\pi\) | ||||
−0.931514 | + | 0.363706i | \(0.881511\pi\) | |||||||
\(74\) | 1119.75 | 1.75904 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2146.97 | −3.24045 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1070.16 | −1.52408 | −0.762039 | − | 0.647531i | \(-0.775802\pi\) | ||||
−0.762039 | + | 0.647531i | \(0.775802\pi\) | |||||||
\(80\) | 4515.73 | 6.31093 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1277.55 | −1.72051 | ||||||||
\(83\) | −889.495 | −1.17632 | −0.588161 | − | 0.808744i | \(-0.700148\pi\) | ||||
−0.588161 | + | 0.808744i | \(0.700148\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1888.94 | −2.41040 | ||||||||
\(86\) | 1747.16 | 2.19070 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −837.543 | −1.01457 | ||||||||
\(89\) | −647.303 | −0.770943 | −0.385472 | − | 0.922720i | \(-0.625961\pi\) | ||||
−0.385472 | + | 0.922720i | \(0.625961\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2998.98 | 3.39854 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1704.36 | 1.87012 | ||||||||
\(95\) | −1913.38 | −2.06641 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 673.379 | 0.704859 | 0.352429 | − | 0.935838i | \(-0.385356\pi\) | ||||
0.352429 | + | 0.935838i | \(0.385356\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5407.89 | 5.40789 | ||||||||
\(101\) | −243.254 | −0.239650 | −0.119825 | − | 0.992795i | \(-0.538233\pi\) | ||||
−0.119825 | + | 0.992795i | \(0.538233\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 486.156 | 0.465072 | 0.232536 | − | 0.972588i | \(-0.425298\pi\) | ||||
0.232536 | + | 0.972588i | \(0.425298\pi\) | |||||||
\(104\) | 3459.04 | 3.26141 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −293.189 | −0.268651 | ||||||||
\(107\) | −384.679 | −0.347555 | −0.173777 | − | 0.984785i | \(-0.555597\pi\) | ||||
−0.173777 | + | 0.984785i | \(0.555597\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 994.781 | 0.874153 | 0.437077 | − | 0.899424i | \(-0.356014\pi\) | ||||
0.437077 | + | 0.899424i | \(0.356014\pi\) | |||||||
\(110\) | −1182.14 | −1.02466 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 189.932 | 0.158118 | 0.0790589 | − | 0.996870i | \(-0.474808\pi\) | ||||
0.0790589 | + | 0.996870i | \(0.474808\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2672.70 | 2.16722 | ||||||||
\(116\) | 3909.50 | 3.12921 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2181.66 | −1.70202 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1205.27 | −0.905534 | ||||||||
\(122\) | 530.596 | 0.393754 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −692.476 | −0.501502 | ||||||||
\(125\) | 2401.62 | 1.71846 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1679.82 | 1.17370 | 0.586851 | − | 0.809695i | \(-0.300367\pi\) | ||||
0.586851 | + | 0.809695i | \(0.300367\pi\) | |||||||
\(128\) | −4467.88 | −3.08522 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4882.21 | 3.29383 | ||||||||
\(131\) | 237.457 | 0.158372 | 0.0791859 | − | 0.996860i | \(-0.474768\pi\) | ||||
0.0791859 | + | 0.996860i | \(0.474768\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1403.56 | −0.904845 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7294.07 | 4.59898 | ||||||||
\(137\) | −526.657 | −0.328433 | −0.164217 | − | 0.986424i | \(-0.552510\pi\) | ||||
−0.164217 | + | 0.986424i | \(0.552510\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 580.607 | 0.354291 | 0.177145 | − | 0.984185i | \(-0.443314\pi\) | ||||
0.177145 | + | 0.984185i | \(0.443314\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1382.18 | −0.816828 | ||||||||
\(143\) | −519.283 | −0.303669 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3484.15 | 1.99547 | ||||||||
\(146\) | 6333.09 | 3.58993 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4459.26 | −2.47668 | ||||||||
\(149\) | −2781.48 | −1.52931 | −0.764657 | − | 0.644438i | \(-0.777091\pi\) | ||||
−0.764657 | + | 0.644438i | \(0.777091\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1413.35 | −0.761702 | −0.380851 | − | 0.924636i | \(-0.624369\pi\) | ||||
−0.380851 | + | 0.924636i | \(0.624369\pi\) | |||||||
\(152\) | 7388.44 | 3.94264 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −617.135 | −0.319803 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2356.59 | −1.19794 | −0.598970 | − | 0.800772i | \(-0.704423\pi\) | ||||
−0.598970 | + | 0.800772i | \(0.704423\pi\) | |||||||
\(158\) | 5832.57 | 2.93680 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −13053.3 | −6.44969 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1309.51 | 0.629255 | 0.314627 | − | 0.949215i | \(-0.398120\pi\) | ||||
0.314627 | + | 0.949215i | \(0.398120\pi\) | |||||||
\(164\) | 5087.66 | 2.42244 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4847.92 | 2.26670 | ||||||||
\(167\) | 1623.77 | 0.752401 | 0.376201 | − | 0.926538i | \(-0.377230\pi\) | ||||
0.376201 | + | 0.926538i | \(0.377230\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −52.3668 | −0.0238356 | ||||||||
\(170\) | 10295.1 | 4.64469 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6957.80 | −3.08446 | ||||||||
\(173\) | −2219.78 | −0.975529 | −0.487765 | − | 0.872975i | \(-0.662188\pi\) | ||||
−0.487765 | + | 0.872975i | \(0.662188\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2617.75 | 1.12114 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3527.92 | 1.48556 | ||||||||
\(179\) | −1124.59 | −0.469584 | −0.234792 | − | 0.972046i | \(-0.575441\pi\) | ||||
−0.234792 | + | 0.972046i | \(0.575441\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3951.04 | −1.62253 | −0.811267 | − | 0.584676i | \(-0.801222\pi\) | ||||
−0.811267 | + | 0.584676i | \(0.801222\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −10320.5 | −4.13499 | ||||||||
\(185\) | −3974.09 | −1.57936 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1095.01 | −0.428209 | ||||||||
\(188\) | −6787.37 | −2.63308 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10428.3 | 3.98183 | ||||||||
\(191\) | −1177.40 | −0.446039 | −0.223019 | − | 0.974814i | \(-0.571591\pi\) | ||||
−0.223019 | + | 0.974814i | \(0.571591\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1772.08 | −0.660917 | −0.330458 | − | 0.943821i | \(-0.607203\pi\) | ||||
−0.330458 | + | 0.943821i | \(0.607203\pi\) | |||||||
\(194\) | −3670.05 | −1.35822 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 794.274 | 0.287257 | 0.143629 | − | 0.989632i | \(-0.454123\pi\) | ||||
0.143629 | + | 0.989632i | \(0.454123\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3662.14 | −1.30453 | −0.652267 | − | 0.757990i | \(-0.726182\pi\) | ||||
−0.652267 | + | 0.757990i | \(0.726182\pi\) | |||||||
\(200\) | −18610.3 | −6.57975 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1325.78 | 0.461791 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4534.12 | 1.54477 | ||||||||
\(206\) | −2649.64 | −0.896162 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −10811.3 | −3.60398 | ||||||||
\(209\) | −1109.18 | −0.367098 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2063.69 | 0.673318 | 0.336659 | − | 0.941627i | \(-0.390703\pi\) | ||||
0.336659 | + | 0.941627i | \(0.390703\pi\) | |||||||
\(212\) | 1167.58 | 0.378254 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2096.58 | 0.669715 | ||||||||
\(215\) | −6200.79 | −1.96693 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −5421.75 | −1.68444 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4707.69 | 1.44269 | ||||||||
\(221\) | 4522.38 | 1.37651 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3728.28 | 1.11957 | 0.559784 | − | 0.828638i | \(-0.310884\pi\) | ||||
0.559784 | + | 0.828638i | \(0.310884\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1035.17 | −0.304683 | ||||||||
\(227\) | −4558.22 | −1.33277 | −0.666387 | − | 0.745606i | \(-0.732160\pi\) | ||||
−0.666387 | + | 0.745606i | \(0.732160\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2068.22 | −0.596819 | −0.298410 | − | 0.954438i | \(-0.596456\pi\) | ||||
−0.298410 | + | 0.954438i | \(0.596456\pi\) | |||||||
\(230\) | −14566.7 | −4.17609 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −13453.9 | −3.80730 | ||||||||
\(233\) | −1459.56 | −0.410383 | −0.205191 | − | 0.978722i | \(-0.565782\pi\) | ||||
−0.205191 | + | 0.978722i | \(0.565782\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6048.91 | −1.67909 | ||||||||
\(236\) | 8688.16 | 2.39640 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2220.74 | 0.601035 | 0.300518 | − | 0.953776i | \(-0.402841\pi\) | ||||
0.300518 | + | 0.953776i | \(0.402841\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5064.37 | 1.35363 | 0.676815 | − | 0.736153i | \(-0.263360\pi\) | ||||
0.676815 | + | 0.736153i | \(0.263360\pi\) | |||||||
\(242\) | 6568.93 | 1.74490 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2113.02 | −0.554395 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4580.89 | 1.18006 | ||||||||
\(248\) | 2383.04 | 0.610175 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −13089.3 | −3.31135 | ||||||||
\(251\) | −1797.86 | −0.452112 | −0.226056 | − | 0.974114i | \(-0.572583\pi\) | ||||
−0.226056 | + | 0.974114i | \(0.572583\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1549.35 | 0.385007 | ||||||||
\(254\) | −9155.37 | −2.26165 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 9868.42 | 2.40928 | ||||||||
\(257\) | −2734.28 | −0.663656 | −0.331828 | − | 0.943340i | \(-0.607665\pi\) | ||||
−0.331828 | + | 0.943340i | \(0.607665\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −19442.7 | −4.63763 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1294.19 | −0.305172 | ||||||||
\(263\) | −8197.71 | −1.92203 | −0.961013 | − | 0.276504i | \(-0.910824\pi\) | ||||
−0.961013 | + | 0.276504i | \(0.910824\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1040.55 | 0.241209 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5589.48 | 1.27400 | ||||||||
\(269\) | 237.512 | 0.0538342 | 0.0269171 | − | 0.999638i | \(-0.491431\pi\) | ||||
0.0269171 | + | 0.999638i | \(0.491431\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4349.95 | 0.975057 | 0.487528 | − | 0.873107i | \(-0.337899\pi\) | ||||
0.487528 | + | 0.873107i | \(0.337899\pi\) | |||||||
\(272\) | −22797.7 | −5.08204 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2870.38 | 0.632869 | ||||||||
\(275\) | 2793.85 | 0.612638 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6228.51 | 1.35103 | 0.675515 | − | 0.737347i | \(-0.263921\pi\) | ||||
0.675515 | + | 0.737347i | \(0.263921\pi\) | |||||||
\(278\) | −3164.42 | −0.682695 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3360.95 | 0.713515 | 0.356757 | − | 0.934197i | \(-0.383882\pi\) | ||||
0.356757 | + | 0.934197i | \(0.383882\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8009.37 | −1.68236 | −0.841180 | − | 0.540755i | \(-0.818138\pi\) | ||||
−0.841180 | + | 0.540755i | \(0.818138\pi\) | |||||||
\(284\) | 5504.32 | 1.15007 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2830.19 | 0.585150 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4623.33 | 0.941041 | ||||||||
\(290\) | −18989.3 | −3.84514 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −25220.6 | −5.05454 | ||||||||
\(293\) | 9247.12 | 1.84376 | 0.921881 | − | 0.387472i | \(-0.126652\pi\) | ||||
0.921881 | + | 0.387472i | \(0.126652\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7742.89 | 1.52816 | ||||||||
\(296\) | 15345.8 | 3.01336 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 15159.6 | 2.94689 | ||||||||
\(299\) | −6398.80 | −1.23763 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 7703.04 | 1.46775 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −23092.7 | −4.35676 | ||||||||
\(305\) | −1883.13 | −0.353533 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3367.11 | −0.625965 | −0.312983 | − | 0.949759i | \(-0.601328\pi\) | ||||
−0.312983 | + | 0.949759i | \(0.601328\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3363.51 | 0.616240 | ||||||||
\(311\) | −6555.92 | −1.19534 | −0.597672 | − | 0.801740i | \(-0.703908\pi\) | ||||
−0.597672 | + | 0.801740i | \(0.703908\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 616.028 | 0.111246 | 0.0556229 | − | 0.998452i | \(-0.482286\pi\) | ||||
0.0556229 | + | 0.998452i | \(0.482286\pi\) | |||||||
\(314\) | 12843.9 | 2.30835 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −23227.4 | −4.13494 | ||||||||
\(317\) | −3481.49 | −0.616845 | −0.308422 | − | 0.951250i | \(-0.599801\pi\) | ||||
−0.308422 | + | 0.951250i | \(0.599801\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2019.75 | 0.354496 | ||||||||
\(320\) | 35016.9 | 6.11720 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9659.71 | 1.66403 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11538.6 | −1.96937 | ||||||||
\(326\) | −7137.07 | −1.21253 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −17508.3 | −2.94737 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7187.44 | −1.19353 | −0.596763 | − | 0.802417i | \(-0.703547\pi\) | ||||
−0.596763 | + | 0.802417i | \(0.703547\pi\) | |||||||
\(332\) | −19306.2 | −3.19145 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8849.86 | −1.44983 | ||||||||
\(335\) | 4981.35 | 0.812418 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3575.89 | 0.578015 | 0.289007 | − | 0.957327i | \(-0.406675\pi\) | ||||
0.289007 | + | 0.957327i | \(0.406675\pi\) | |||||||
\(338\) | 285.410 | 0.0459297 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −40998.8 | −6.53962 | ||||||||
\(341\) | −357.751 | −0.0568131 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 23944.1 | 3.75285 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12098.2 | 1.87978 | ||||||||
\(347\) | 574.458 | 0.0888719 | 0.0444359 | − | 0.999012i | \(-0.485851\pi\) | ||||
0.0444359 | + | 0.999012i | \(0.485851\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11491.0 | 1.76246 | 0.881229 | − | 0.472689i | \(-0.156717\pi\) | ||||
0.881229 | + | 0.472689i | \(0.156717\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −7566.92 | −1.14579 | ||||||||
\(353\) | −1369.32 | −0.206464 | −0.103232 | − | 0.994657i | \(-0.532918\pi\) | ||||
−0.103232 | + | 0.994657i | \(0.532918\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4905.45 | 0.733392 | ||||||||
\(356\) | −14049.5 | −2.09163 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6129.21 | 0.904857 | ||||||||
\(359\) | 12915.0 | 1.89868 | 0.949339 | − | 0.314254i | \(-0.101754\pi\) | ||||
0.949339 | + | 0.314254i | \(0.101754\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2925.68 | 0.426546 | ||||||||
\(362\) | 21533.9 | 3.12652 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −22476.6 | −3.22323 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1186.30 | −0.168731 | −0.0843653 | − | 0.996435i | \(-0.526886\pi\) | ||||
−0.0843653 | + | 0.996435i | \(0.526886\pi\) | |||||||
\(368\) | 32256.9 | 4.56931 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 21659.6 | 3.04332 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6462.68 | −0.897117 | −0.448559 | − | 0.893753i | \(-0.648062\pi\) | ||||
−0.448559 | + | 0.893753i | \(0.648062\pi\) | |||||||
\(374\) | 5968.02 | 0.825131 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 23357.6 | 3.20366 | ||||||||
\(377\) | −8341.54 | −1.13955 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8555.31 | −1.15952 | −0.579758 | − | 0.814789i | \(-0.696853\pi\) | ||||
−0.579758 | + | 0.814789i | \(0.696853\pi\) | |||||||
\(380\) | −41529.2 | −5.60632 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6417.04 | 0.859488 | ||||||||
\(383\) | 570.982 | 0.0761770 | 0.0380885 | − | 0.999274i | \(-0.487873\pi\) | ||||
0.0380885 | + | 0.999274i | \(0.487873\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9658.17 | 1.27354 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 14615.4 | 1.91234 | ||||||||
\(389\) | 14437.2 | 1.88174 | 0.940869 | − | 0.338771i | \(-0.110011\pi\) | ||||
0.940869 | + | 0.338771i | \(0.110011\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13493.1 | −1.74521 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4328.95 | −0.553526 | ||||||||
\(395\) | −20700.3 | −2.63682 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9384.81 | −1.18642 | −0.593212 | − | 0.805047i | \(-0.702140\pi\) | ||||
−0.593212 | + | 0.805047i | \(0.702140\pi\) | |||||||
\(398\) | 19959.4 | 2.51375 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 58166.9 | 7.27086 | ||||||||
\(401\) | −8167.50 | −1.01712 | −0.508560 | − | 0.861026i | \(-0.669822\pi\) | ||||
−0.508560 | + | 0.861026i | \(0.669822\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1477.51 | 0.182630 | ||||||||
\(404\) | −5279.74 | −0.650190 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2303.76 | −0.280573 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11655.7 | 1.40913 | 0.704567 | − | 0.709637i | \(-0.251141\pi\) | ||||
0.704567 | + | 0.709637i | \(0.251141\pi\) | |||||||
\(410\) | −24711.9 | −2.97666 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 10551.8 | 1.26178 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −17205.7 | −2.03516 | ||||||||
\(416\) | 31251.3 | 3.68322 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6045.23 | 0.707373 | ||||||||
\(419\) | 10257.6 | 1.19598 | 0.597992 | − | 0.801502i | \(-0.295965\pi\) | ||||
0.597992 | + | 0.801502i | \(0.295965\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8160.70 | −0.944723 | −0.472361 | − | 0.881405i | \(-0.656598\pi\) | ||||
−0.472361 | + | 0.881405i | \(0.656598\pi\) | |||||||
\(422\) | −11247.5 | −1.29744 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4018.04 | −0.460220 | ||||||||
\(425\) | −24331.3 | −2.77704 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −8349.32 | −0.942943 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 33795.5 | 3.79015 | ||||||||
\(431\) | 8722.62 | 0.974835 | 0.487417 | − | 0.873169i | \(-0.337939\pi\) | ||||
0.487417 | + | 0.873169i | \(0.337939\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12628.4 | −1.40157 | −0.700787 | − | 0.713371i | \(-0.747168\pi\) | ||||
−0.700787 | + | 0.713371i | \(0.747168\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 21591.3 | 2.37165 | ||||||||
\(437\) | −13667.7 | −1.49614 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3487.47 | 0.379153 | 0.189576 | − | 0.981866i | \(-0.439289\pi\) | ||||
0.189576 | + | 0.981866i | \(0.439289\pi\) | |||||||
\(440\) | −16200.7 | −1.75532 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −24647.9 | −2.65244 | ||||||||
\(443\) | 14138.0 | 1.51629 | 0.758144 | − | 0.652087i | \(-0.226106\pi\) | ||||
0.758144 | + | 0.652087i | \(0.226106\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12520.9 | −1.33381 | ||||||||
\(446\) | −20319.8 | −2.15734 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14007.0 | −1.47223 | −0.736114 | − | 0.676858i | \(-0.763341\pi\) | ||||
−0.736114 | + | 0.676858i | \(0.763341\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2628.41 | 0.274428 | ||||||||
\(452\) | 4122.40 | 0.428986 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 24843.2 | 2.56817 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4837.29 | 0.495140 | 0.247570 | − | 0.968870i | \(-0.420368\pi\) | ||||
0.247570 | + | 0.968870i | \(0.420368\pi\) | |||||||
\(458\) | 11272.2 | 1.15003 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 58009.9 | 5.87983 | ||||||||
\(461\) | −10034.5 | −1.01378 | −0.506890 | − | 0.862011i | \(-0.669205\pi\) | ||||
−0.506890 | + | 0.862011i | \(0.669205\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15501.9 | −1.55602 | −0.778008 | − | 0.628254i | \(-0.783770\pi\) | ||||
−0.778008 | + | 0.628254i | \(0.783770\pi\) | |||||||
\(464\) | 42050.4 | 4.20720 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7954.91 | 0.790781 | ||||||||
\(467\) | −9616.13 | −0.952851 | −0.476426 | − | 0.879215i | \(-0.658068\pi\) | ||||
−0.476426 | + | 0.879215i | \(0.658068\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 32967.7 | 3.23551 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −29898.8 | −2.91569 | ||||||||
\(473\) | −3594.57 | −0.349426 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −24646.1 | −2.38072 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12103.4 | −1.15816 | ||||||||
\(479\) | 14159.7 | 1.35067 | 0.675337 | − | 0.737509i | \(-0.263998\pi\) | ||||
0.675337 | + | 0.737509i | \(0.263998\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9514.51 | 0.901922 | ||||||||
\(482\) | −27601.8 | −2.60836 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −26159.8 | −2.45678 | ||||||||
\(485\) | 13025.3 | 1.21948 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15584.6 | 1.45012 | 0.725058 | − | 0.688688i | \(-0.241813\pi\) | ||||
0.725058 | + | 0.688688i | \(0.241813\pi\) | |||||||
\(488\) | 7271.62 | 0.674530 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12898.0 | 1.18549 | 0.592747 | − | 0.805389i | \(-0.298043\pi\) | ||||
0.592747 | + | 0.805389i | \(0.298043\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17589.8 | −1.60690 | ||||||||
\(494\) | −24966.7 | −2.27390 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7448.23 | −0.674265 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6707.11 | 0.601707 | 0.300853 | − | 0.953670i | \(-0.402729\pi\) | ||||
0.300853 | + | 0.953670i | \(0.402729\pi\) | |||||||
\(500\) | 52126.1 | 4.66230 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9798.70 | 0.871190 | ||||||||
\(503\) | 14186.3 | 1.25753 | 0.628763 | − | 0.777597i | \(-0.283562\pi\) | ||||
0.628763 | + | 0.777597i | \(0.283562\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4705.31 | −0.414620 | ||||||||
\(506\) | −8444.26 | −0.741884 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 36459.9 | 3.18435 | ||||||||
\(509\) | −12086.8 | −1.05253 | −0.526263 | − | 0.850322i | \(-0.676407\pi\) | ||||
−0.526263 | + | 0.850322i | \(0.676407\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −18041.8 | −1.55731 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 14902.3 | 1.27882 | ||||||||
\(515\) | 9403.80 | 0.804623 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3506.53 | −0.298292 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 66908.8 | 5.64259 | ||||||||
\(521\) | 12142.6 | 1.02107 | 0.510534 | − | 0.859857i | \(-0.329448\pi\) | ||||
0.510534 | + | 0.859857i | \(0.329448\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3408.38 | 0.284967 | 0.142484 | − | 0.989797i | \(-0.454491\pi\) | ||||
0.142484 | + | 0.989797i | \(0.454491\pi\) | |||||||
\(524\) | 5153.91 | 0.429675 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 44679.1 | 3.70362 | ||||||||
\(527\) | 3115.61 | 0.257530 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6924.66 | 0.569135 | ||||||||
\(530\) | −5671.20 | −0.464795 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10855.3 | −0.882168 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7440.92 | −0.601306 | ||||||||
\(536\) | −19235.3 | −1.55007 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1294.49 | −0.103735 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16737.5 | −1.33013 | −0.665066 | − | 0.746785i | \(-0.731597\pi\) | ||||
−0.665066 | + | 0.746785i | \(0.731597\pi\) | |||||||
\(542\) | −23708.1 | −1.87887 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 65899.5 | 5.19378 | ||||||||
\(545\) | 19242.2 | 1.51238 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13940.6 | −1.08968 | −0.544840 | − | 0.838540i | \(-0.683410\pi\) | ||||
−0.544840 | + | 0.838540i | \(0.683410\pi\) | |||||||
\(548\) | −11430.9 | −0.891065 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −15227.0 | −1.18051 | ||||||||
\(551\) | −17817.3 | −1.37758 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −33946.6 | −2.60335 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12601.8 | 0.961218 | ||||||||
\(557\) | −818.376 | −0.0622544 | −0.0311272 | − | 0.999515i | \(-0.509910\pi\) | ||||
−0.0311272 | + | 0.999515i | \(0.509910\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14845.5 | 1.12325 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −18317.9 | −1.37490 | ||||||||
\(563\) | −8957.98 | −0.670575 | −0.335288 | − | 0.942116i | \(-0.608834\pi\) | ||||
−0.335288 | + | 0.942116i | \(0.608834\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3673.89 | 0.273560 | ||||||||
\(566\) | 43652.6 | 3.24180 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −18942.2 | −1.39929 | ||||||||
\(569\) | −19997.8 | −1.47338 | −0.736688 | − | 0.676233i | \(-0.763611\pi\) | ||||
−0.736688 | + | 0.676233i | \(0.763611\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3391.26 | −0.248546 | −0.124273 | − | 0.992248i | \(-0.539660\pi\) | ||||
−0.124273 | + | 0.992248i | \(0.539660\pi\) | |||||||
\(572\) | −11270.8 | −0.823877 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 34426.8 | 2.49687 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3957.72 | 0.285549 | 0.142775 | − | 0.989755i | \(-0.454398\pi\) | ||||
0.142775 | + | 0.989755i | \(0.454398\pi\) | |||||||
\(578\) | −25198.1 | −1.81332 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 75622.2 | 5.41387 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 603.202 | 0.0428509 | ||||||||
\(584\) | 86792.6 | 6.14983 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −50398.6 | −3.55281 | ||||||||
\(587\) | −12647.3 | −0.889283 | −0.444642 | − | 0.895709i | \(-0.646669\pi\) | ||||
−0.444642 | + | 0.895709i | \(0.646669\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3155.92 | 0.220777 | ||||||||
\(590\) | −42200.3 | −2.94467 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −47963.5 | −3.32988 | ||||||||
\(593\) | −3910.60 | −0.270808 | −0.135404 | − | 0.990790i | \(-0.543233\pi\) | ||||
−0.135404 | + | 0.990790i | \(0.543233\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −60371.0 | −4.14915 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 34874.7 | 2.38484 | ||||||||
\(599\) | 13933.9 | 0.950455 | 0.475228 | − | 0.879863i | \(-0.342366\pi\) | ||||
0.475228 | + | 0.879863i | \(0.342366\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16095.1 | −1.09240 | −0.546202 | − | 0.837654i | \(-0.683927\pi\) | ||||
−0.546202 | + | 0.837654i | \(0.683927\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −30676.3 | −2.06656 | ||||||||
\(605\) | −23313.7 | −1.56667 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3050.91 | 0.204008 | 0.102004 | − | 0.994784i | \(-0.467475\pi\) | ||||
0.102004 | + | 0.994784i | \(0.467475\pi\) | |||||||
\(608\) | 66752.0 | 4.45255 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 10263.4 | 0.681235 | ||||||||
\(611\) | 14481.9 | 0.958879 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1512.24 | −0.0996394 | −0.0498197 | − | 0.998758i | \(-0.515865\pi\) | ||||
−0.0498197 | + | 0.998758i | \(0.515865\pi\) | |||||||
\(614\) | 18351.4 | 1.20619 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23466.1 | −1.53114 | −0.765569 | − | 0.643354i | \(-0.777542\pi\) | ||||
−0.765569 | + | 0.643354i | \(0.777542\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20736.1 | −1.34645 | −0.673226 | − | 0.739437i | \(-0.735092\pi\) | ||||
−0.673226 | + | 0.739437i | \(0.735092\pi\) | |||||||
\(620\) | −13394.7 | −0.867651 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 35731.1 | 2.30335 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15310.1 | 0.979844 | ||||||||
\(626\) | −3357.47 | −0.214364 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −51148.9 | −3.25010 | ||||||||
\(629\) | 20063.2 | 1.27182 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15623.5 | 0.985673 | 0.492837 | − | 0.870122i | \(-0.335960\pi\) | ||||
0.492837 | + | 0.870122i | \(0.335960\pi\) | |||||||
\(632\) | 79933.2 | 5.03097 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 18974.8 | 1.18862 | ||||||||
\(635\) | 32493.1 | 2.03063 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −11008.0 | −0.683091 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −86423.0 | −5.33776 | ||||||||
\(641\) | −12284.6 | −0.756961 | −0.378481 | − | 0.925609i | \(-0.623553\pi\) | ||||
−0.378481 | + | 0.925609i | \(0.623553\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 924.041 | 0.0566728 | 0.0283364 | − | 0.999598i | \(-0.490979\pi\) | ||||
0.0283364 | + | 0.999598i | \(0.490979\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −52647.3 | −3.20647 | ||||||||
\(647\) | −10330.2 | −0.627701 | −0.313850 | − | 0.949472i | \(-0.601619\pi\) | ||||
−0.313850 | + | 0.949472i | \(0.601619\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4488.52 | 0.271479 | ||||||||
\(650\) | 62887.4 | 3.79484 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 28422.4 | 1.70722 | ||||||||
\(653\) | −3064.12 | −0.183627 | −0.0918134 | − | 0.995776i | \(-0.529266\pi\) | ||||
−0.0918134 | + | 0.995776i | \(0.529266\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4593.17 | 0.274000 | ||||||||
\(656\) | 54722.6 | 3.25695 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9157.78 | 0.541330 | 0.270665 | − | 0.962674i | \(-0.412756\pi\) | ||||
0.270665 | + | 0.962674i | \(0.412756\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23367.4 | −1.37502 | −0.687508 | − | 0.726177i | \(-0.741295\pi\) | ||||
−0.687508 | + | 0.726177i | \(0.741295\pi\) | |||||||
\(662\) | 39172.9 | 2.29985 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 66438.9 | 3.88303 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 24888.1 | 1.44478 | ||||||||
\(668\) | 35243.3 | 2.04132 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −27149.3 | −1.56548 | ||||||||
\(671\) | −1091.64 | −0.0628053 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34214.8 | 1.95971 | 0.979853 | − | 0.199719i | \(-0.0640029\pi\) | ||||
0.979853 | + | 0.199719i | \(0.0640029\pi\) | |||||||
\(674\) | −19489.3 | −1.11380 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1136.60 | −0.0646679 | ||||||||
\(677\) | 19288.8 | 1.09502 | 0.547511 | − | 0.836799i | \(-0.315576\pi\) | ||||
0.547511 | + | 0.836799i | \(0.315576\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 141090. | 7.95672 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1949.81 | 0.109475 | ||||||||
\(683\) | −31119.7 | −1.74343 | −0.871714 | − | 0.490015i | \(-0.836991\pi\) | ||||
−0.871714 | + | 0.490015i | \(0.836991\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10187.2 | −0.568224 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −74837.7 | −4.14703 | ||||||||
\(689\) | −2491.22 | −0.137747 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12732.5 | −0.700967 | −0.350483 | − | 0.936569i | \(-0.613983\pi\) | ||||
−0.350483 | + | 0.936569i | \(0.613983\pi\) | |||||||
\(692\) | −48179.4 | −2.64669 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3130.91 | −0.171250 | ||||||||
\(695\) | 11230.8 | 0.612961 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −22890.6 | −1.24396 | ||||||||
\(698\) | −62628.1 | −3.39614 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9506.11 | 0.512184 | 0.256092 | − | 0.966652i | \(-0.417565\pi\) | ||||
0.256092 | + | 0.966652i | \(0.417565\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20322.8 | 1.09031 | ||||||||
\(704\) | 20299.2 | 1.08672 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7463.08 | 0.397842 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2500.48 | 0.132450 | 0.0662252 | − | 0.997805i | \(-0.478904\pi\) | ||||
0.0662252 | + | 0.997805i | \(0.478904\pi\) | |||||||
\(710\) | −26735.7 | −1.41320 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 48348.9 | 2.54487 | ||||||||
\(713\) | −4408.33 | −0.231548 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10044.6 | −0.525379 | ||||||||
\(716\) | −24408.7 | −1.27402 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −70389.0 | −3.65863 | ||||||||
\(719\) | −19519.3 | −1.01245 | −0.506223 | − | 0.862403i | \(-0.668959\pi\) | ||||
−0.506223 | + | 0.862403i | \(0.668959\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −15945.5 | −0.821927 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −85755.9 | −4.40206 | ||||||||
\(725\) | 44879.2 | 2.29899 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −35008.3 | −1.78595 | −0.892975 | − | 0.450105i | \(-0.851386\pi\) | ||||
−0.892975 | + | 0.450105i | \(0.851386\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 122502. | 6.21096 | ||||||||
\(731\) | 31304.7 | 1.58392 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33284.0 | −1.67718 | −0.838590 | − | 0.544763i | \(-0.816619\pi\) | ||||
−0.838590 | + | 0.544763i | \(0.816619\pi\) | |||||||
\(734\) | 6465.54 | 0.325133 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −93242.3 | −4.66978 | ||||||||
\(737\) | 2887.67 | 0.144326 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25554.2 | −1.27203 | −0.636013 | − | 0.771678i | \(-0.719418\pi\) | ||||
−0.636013 | + | 0.771678i | \(0.719418\pi\) | |||||||
\(740\) | −86256.1 | −4.28492 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3926.32 | −0.193867 | −0.0969333 | − | 0.995291i | \(-0.530903\pi\) | ||||
−0.0969333 | + | 0.995291i | \(0.530903\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −53802.6 | −2.64587 | ||||||||
\(746\) | 35222.8 | 1.72869 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −23766.8 | −1.16177 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2496.80 | 0.121318 | 0.0606589 | − | 0.998159i | \(-0.480680\pi\) | ||||
0.0606589 | + | 0.998159i | \(0.480680\pi\) | |||||||
\(752\) | −73004.6 | −3.54016 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 45463.0 | 2.19584 | ||||||||
\(755\) | −27338.7 | −1.31782 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9014.06 | 0.432789 | 0.216395 | − | 0.976306i | \(-0.430570\pi\) | ||||
0.216395 | + | 0.976306i | \(0.430570\pi\) | |||||||
\(758\) | 46628.1 | 2.23431 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 142916. | 6.82118 | ||||||||
\(761\) | 2393.59 | 0.114018 | 0.0570089 | − | 0.998374i | \(-0.481844\pi\) | ||||
0.0570089 | + | 0.998374i | \(0.481844\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −25554.9 | −1.21014 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3111.96 | −0.146788 | ||||||||
\(767\) | −18537.5 | −0.872688 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9474.06 | −0.444270 | −0.222135 | − | 0.975016i | \(-0.571303\pi\) | ||||
−0.222135 | + | 0.975016i | \(0.571303\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −38462.3 | −1.79312 | ||||||||
\(773\) | 12878.4 | 0.599231 | 0.299615 | − | 0.954060i | \(-0.403142\pi\) | ||||
0.299615 | + | 0.954060i | \(0.403142\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7949.28 | −0.368447 | ||||||||
\(776\) | −50296.6 | −2.32673 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −78685.6 | −3.62599 | ||||||||
\(779\) | −23186.7 | −1.06643 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2843.67 | 0.130287 | ||||||||
\(782\) | 73540.2 | 3.36290 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −45584.0 | −2.07256 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16966.5 | 0.768477 | 0.384239 | − | 0.923234i | \(-0.374464\pi\) | ||||
0.384239 | + | 0.923234i | \(0.374464\pi\) | |||||||
\(788\) | 17239.4 | 0.779351 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 112820. | 5.08097 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4508.46 | 0.201892 | ||||||||
\(794\) | 51149.0 | 2.28616 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −79485.3 | −3.53930 | ||||||||
\(797\) | 21.6935 | 0.000964143 0 | 0.000482072 | − | 1.00000i | \(-0.499847\pi\) | ||||
0.000482072 | 1.00000i | \(0.499847\pi\) | ||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30538.0 | 1.35213 | ||||||||
\(800\) | −168138. | −7.43073 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 44514.5 | 1.95993 | ||||||||
\(803\) | −13029.6 | −0.572609 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8052.69 | −0.351916 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 18169.3 | 0.791083 | ||||||||
\(809\) | −31766.3 | −1.38052 | −0.690262 | − | 0.723560i | \(-0.742505\pi\) | ||||
−0.690262 | + | 0.723560i | \(0.742505\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31081.1 | 1.34575 | 0.672875 | − | 0.739756i | \(-0.265059\pi\) | ||||
0.672875 | + | 0.739756i | \(0.265059\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 12556.0 | 0.540646 | ||||||||
\(815\) | 25330.0 | 1.08868 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 31709.8 | 1.35788 | ||||||||
\(818\) | −63525.7 | −2.71531 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 98411.5 | 4.19107 | ||||||||
\(821\) | −5021.74 | −0.213472 | −0.106736 | − | 0.994287i | \(-0.534040\pi\) | ||||
−0.106736 | + | 0.994287i | \(0.534040\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13443.5 | 0.569394 | 0.284697 | − | 0.958617i | \(-0.408107\pi\) | ||||
0.284697 | + | 0.958617i | \(0.408107\pi\) | |||||||
\(824\) | −36312.4 | −1.53520 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37439.2 | 1.57423 | 0.787116 | − | 0.616805i | \(-0.211573\pi\) | ||||
0.787116 | + | 0.616805i | \(0.211573\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3890.21 | −0.162982 | −0.0814912 | − | 0.996674i | \(-0.525968\pi\) | ||||
−0.0814912 | + | 0.996674i | \(0.525968\pi\) | |||||||
\(830\) | 93774.2 | 3.92162 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −83835.3 | −3.49335 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 31408.9 | 1.30173 | ||||||||
\(836\) | −24074.3 | −0.995965 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −55906.0 | −2.30458 | ||||||||
\(839\) | 15062.0 | 0.619783 | 0.309891 | − | 0.950772i | \(-0.399707\pi\) | ||||
0.309891 | + | 0.950772i | \(0.399707\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8055.35 | 0.330286 | ||||||||
\(842\) | 44477.4 | 1.82042 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 44791.5 | 1.82676 | ||||||||
\(845\) | −1012.94 | −0.0412381 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 12558.4 | 0.508560 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 132611. | 5.35118 | ||||||||
\(851\) | −28387.8 | −1.14350 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −39207.9 | −1.57380 | −0.786900 | − | 0.617081i | \(-0.788315\pi\) | ||||
−0.786900 | + | 0.617081i | \(0.788315\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 28732.8 | 1.14727 | ||||||||
\(857\) | −37029.6 | −1.47597 | −0.737986 | − | 0.674816i | \(-0.764223\pi\) | ||||
−0.737986 | + | 0.674816i | \(0.764223\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37646.3 | 1.49531 | 0.747657 | − | 0.664085i | \(-0.231179\pi\) | ||||
0.747657 | + | 0.664085i | \(0.231179\pi\) | |||||||
\(860\) | −134586. | −5.33644 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −47540.0 | −1.87844 | ||||||||
\(863\) | 26698.1 | 1.05309 | 0.526543 | − | 0.850149i | \(-0.323488\pi\) | ||||
0.526543 | + | 0.850149i | \(0.323488\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −42937.5 | −1.68777 | ||||||||
\(866\) | 68827.2 | 2.70074 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11999.8 | −0.468431 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11926.0 | −0.463947 | ||||||||
\(872\) | −74303.0 | −2.88557 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 74491.6 | 2.88297 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22177.5 | −0.853912 | −0.426956 | − | 0.904272i | \(-0.640414\pi\) | ||||
−0.426956 | + | 0.904272i | \(0.640414\pi\) | |||||||
\(878\) | −19007.4 | −0.730602 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 50635.6 | 1.93969 | ||||||||
\(881\) | −11503.1 | −0.439898 | −0.219949 | − | 0.975511i | \(-0.570589\pi\) | ||||
−0.219949 | + | 0.975511i | \(0.570589\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 41751.6 | 1.59123 | 0.795613 | − | 0.605806i | \(-0.207149\pi\) | ||||
0.795613 | + | 0.605806i | \(0.207149\pi\) | |||||||
\(884\) | 98156.6 | 3.73457 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −77054.7 | −2.92179 | ||||||||
\(887\) | −4670.18 | −0.176786 | −0.0883930 | − | 0.996086i | \(-0.528173\pi\) | ||||
−0.0883930 | + | 0.996086i | \(0.528173\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 68241.3 | 2.57017 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 80920.8 | 3.03748 | ||||||||
\(893\) | 30933.0 | 1.15917 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21753.1 | −0.812430 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 76340.8 | 2.83689 | ||||||||
\(899\) | −5746.75 | −0.213198 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5253.22 | −0.194240 | ||||||||
\(902\) | −14325.4 | −0.528805 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14186.6 | −0.521945 | ||||||||
\(905\) | −76425.7 | −2.80715 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33783.8 | 1.23679 | 0.618397 | − | 0.785866i | \(-0.287782\pi\) | ||||
0.618397 | + | 0.785866i | \(0.287782\pi\) | |||||||
\(908\) | −98934.5 | −3.61592 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34880.5 | 1.26854 | 0.634271 | − | 0.773111i | \(-0.281300\pi\) | ||||
0.634271 | + | 0.773111i | \(0.281300\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9974.04 | −0.361547 | ||||||||
\(914\) | −26364.2 | −0.954102 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −44889.9 | −1.61922 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5964.51 | −0.214092 | −0.107046 | − | 0.994254i | \(-0.534139\pi\) | ||||
−0.107046 | + | 0.994254i | \(0.534139\pi\) | |||||||
\(920\) | −199631. | −7.15397 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 54689.9 | 1.95349 | ||||||||
\(923\) | −11744.3 | −0.418818 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −51190.0 | −1.81959 | ||||||||
\(926\) | 84488.5 | 2.99834 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −121552. | −4.29971 | ||||||||
\(929\) | 54065.1 | 1.90939 | 0.954693 | − | 0.297594i | \(-0.0961841\pi\) | ||||
0.954693 | + | 0.297594i | \(0.0961841\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −31679.3 | −1.11340 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 52409.8 | 1.83608 | ||||||||
\(935\) | −21181.0 | −0.740847 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14678.5 | −0.511766 | −0.255883 | − | 0.966708i | \(-0.582366\pi\) | ||||
−0.255883 | + | 0.966708i | \(0.582366\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −131289. | −4.55551 | ||||||||
\(941\) | 22198.8 | 0.769032 | 0.384516 | − | 0.923118i | \(-0.374368\pi\) | ||||
0.384516 | + | 0.923118i | \(0.374368\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32388.3 | 1.11846 | ||||||||
\(944\) | 93449.3 | 3.22194 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 19591.1 | 0.673322 | ||||||||
\(947\) | −3314.30 | −0.113728 | −0.0568639 | − | 0.998382i | \(-0.518110\pi\) | ||||
−0.0568639 | + | 0.998382i | \(0.518110\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 53812.1 | 1.84069 | ||||||||
\(950\) | 134326. | 4.58749 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 45137.3 | 1.53425 | 0.767125 | − | 0.641498i | \(-0.221687\pi\) | ||||
0.767125 | + | 0.641498i | \(0.221687\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −22774.6 | −0.771694 | ||||||||
\(956\) | 48200.2 | 1.63066 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −77173.1 | −2.60266 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28773.1 | −0.965832 | ||||||||
\(962\) | −51856.0 | −1.73794 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 109920. | 3.67250 | ||||||||
\(965\) | −34277.6 | −1.14346 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13423.9 | 0.446416 | 0.223208 | − | 0.974771i | \(-0.428347\pi\) | ||||
0.223208 | + | 0.974771i | \(0.428347\pi\) | |||||||
\(968\) | 90024.7 | 2.98916 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −70990.4 | −2.34986 | ||||||||
\(971\) | 50282.5 | 1.66183 | 0.830917 | − | 0.556396i | \(-0.187816\pi\) | ||||
0.830917 | + | 0.556396i | \(0.187816\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −84939.2 | −2.79428 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −22727.6 | −0.745381 | ||||||||
\(977\) | −24918.5 | −0.815980 | −0.407990 | − | 0.912986i | \(-0.633770\pi\) | ||||
−0.407990 | + | 0.912986i | \(0.633770\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7258.30 | −0.236952 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −70296.5 | −2.28437 | ||||||||
\(983\) | −5830.48 | −0.189179 | −0.0945897 | − | 0.995516i | \(-0.530154\pi\) | ||||
−0.0945897 | + | 0.995516i | \(0.530154\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15363.8 | 0.496986 | ||||||||
\(986\) | 95867.7 | 3.09640 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 99426.5 | 3.20160 | ||||||||
\(989\) | −44293.6 | −1.42412 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15669.9 | 0.502293 | 0.251146 | − | 0.967949i | \(-0.419192\pi\) | ||||
0.251146 | + | 0.967949i | \(0.419192\pi\) | |||||||
\(992\) | 21530.0 | 0.689091 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −70837.4 | −2.25698 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11367.5 | 0.361095 | 0.180548 | − | 0.983566i | \(-0.442213\pi\) | ||||
0.180548 | + | 0.983566i | \(0.442213\pi\) | |||||||
\(998\) | −36555.1 | −1.15945 | ||||||||
\(999\) | 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 | 1323.4.a.bf.1.1 | ✓ | 6 | |
3.2 | odd | 2 | inner | 1323.4.a.bf.1.6 | yes | 6 | |
7.6 | odd | 2 | 1323.4.a.bg.1.1 | yes | 6 | ||
21.20 | even | 2 | 1323.4.a.bg.1.6 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1323.4.a.bf.1.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
1323.4.a.bf.1.6 | yes | 6 | 3.2 | odd | 2 | inner | |
1323.4.a.bg.1.1 | yes | 6 | 7.6 | odd | 2 | ||
1323.4.a.bg.1.6 | yes | 6 | 21.20 | even | 2 |