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: | \(1\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 100 x^{16} + 4066 x^{14} - 86197 x^{12} + 1016064 x^{10} - 6594119 x^{8} + 22251817 x^{6} - 37096332 x^{4} + 27824160 x^{2} - 6889792 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3}\cdot 7\cdot 13^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-4.80856\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.80856 | −1.70008 | −0.850042 | − | 0.526715i | \(-0.823423\pi\) | ||||
−0.850042 | + | 0.526715i | \(0.823423\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 15.1223 | 1.89028 | ||||||||
\(5\) | −1.59043 | −0.142252 | −0.0711262 | − | 0.997467i | \(-0.522659\pi\) | ||||
−0.0711262 | + | 0.997467i | \(0.522659\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −34.5272 | −1.86429 | −0.932146 | − | 0.362083i | \(-0.882066\pi\) | ||||
−0.932146 | + | 0.362083i | \(0.882066\pi\) | |||||||
\(8\) | −34.2479 | −1.51356 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 7.64769 | 0.241841 | ||||||||
\(11\) | −42.6836 | −1.16996 | −0.584981 | − | 0.811047i | \(-0.698898\pi\) | ||||
−0.584981 | + | 0.811047i | \(0.698898\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 166.026 | 3.16945 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 43.7049 | 0.682888 | ||||||||
\(17\) | −45.4494 | −0.648418 | −0.324209 | − | 0.945985i | \(-0.605098\pi\) | ||||
−0.324209 | + | 0.945985i | \(0.605098\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −41.0910 | −0.496153 | −0.248077 | − | 0.968740i | \(-0.579798\pi\) | ||||
−0.248077 | + | 0.968740i | \(0.579798\pi\) | |||||||
\(20\) | −24.0509 | −0.268897 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 205.247 | 1.98903 | ||||||||
\(23\) | 171.733 | 1.55690 | 0.778450 | − | 0.627706i | \(-0.216006\pi\) | ||||
0.778450 | + | 0.627706i | \(0.216006\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −122.471 | −0.979764 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −522.129 | −3.52404 | ||||||||
\(29\) | 178.040 | 1.14004 | 0.570019 | − | 0.821631i | \(-0.306936\pi\) | ||||
0.570019 | + | 0.821631i | \(0.306936\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −18.5736 | −0.107610 | −0.0538051 | − | 0.998551i | \(-0.517135\pi\) | ||||
−0.0538051 | + | 0.998551i | \(0.517135\pi\) | |||||||
\(32\) | 63.8255 | 0.352589 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 218.546 | 1.10236 | ||||||||
\(35\) | 54.9131 | 0.265200 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 331.269 | 1.47190 | 0.735949 | − | 0.677037i | \(-0.236736\pi\) | ||||
0.735949 | + | 0.677037i | \(0.236736\pi\) | |||||||
\(38\) | 197.588 | 0.843502 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 54.4689 | 0.215307 | ||||||||
\(41\) | 411.934 | 1.56911 | 0.784553 | − | 0.620062i | \(-0.212893\pi\) | ||||
0.784553 | + | 0.620062i | \(0.212893\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.3363 | 0.0402040 | 0.0201020 | − | 0.999798i | \(-0.493601\pi\) | ||||
0.0201020 | + | 0.999798i | \(0.493601\pi\) | |||||||
\(44\) | −645.473 | −2.21156 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −825.787 | −2.64686 | ||||||||
\(47\) | 494.592 | 1.53497 | 0.767486 | − | 0.641065i | \(-0.221507\pi\) | ||||
0.767486 | + | 0.641065i | \(0.221507\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 849.125 | 2.47558 | ||||||||
\(50\) | 588.907 | 1.66568 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −217.808 | −0.564495 | −0.282248 | − | 0.959342i | \(-0.591080\pi\) | ||||
−0.282248 | + | 0.959342i | \(0.591080\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 67.8853 | 0.166430 | ||||||||
\(56\) | 1182.48 | 2.82171 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −856.115 | −1.93816 | ||||||||
\(59\) | −775.414 | −1.71102 | −0.855511 | − | 0.517785i | \(-0.826757\pi\) | ||||
−0.855511 | + | 0.517785i | \(0.826757\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 340.831 | 0.715392 | 0.357696 | − | 0.933838i | \(-0.383562\pi\) | ||||
0.357696 | + | 0.933838i | \(0.383562\pi\) | |||||||
\(62\) | 89.3123 | 0.182946 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −656.547 | −1.28232 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −676.191 | −1.23298 | −0.616492 | − | 0.787361i | \(-0.711447\pi\) | ||||
−0.616492 | + | 0.787361i | \(0.711447\pi\) | |||||||
\(68\) | −687.298 | −1.22569 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −264.053 | −0.450862 | ||||||||
\(71\) | 449.604 | 0.751524 | 0.375762 | − | 0.926716i | \(-0.377381\pi\) | ||||
0.375762 | + | 0.926716i | \(0.377381\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −645.014 | −1.03415 | −0.517076 | − | 0.855939i | \(-0.672980\pi\) | ||||
−0.517076 | + | 0.855939i | \(0.672980\pi\) | |||||||
\(74\) | −1592.93 | −2.50235 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −621.389 | −0.937870 | ||||||||
\(77\) | 1473.74 | 2.18115 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −778.289 | −1.10841 | −0.554205 | − | 0.832380i | \(-0.686978\pi\) | ||||
−0.554205 | + | 0.832380i | \(0.686978\pi\) | |||||||
\(80\) | −69.5095 | −0.0971425 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1980.81 | −2.66761 | ||||||||
\(83\) | 1056.50 | 1.39718 | 0.698591 | − | 0.715521i | \(-0.253811\pi\) | ||||
0.698591 | + | 0.715521i | \(0.253811\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 72.2842 | 0.0922391 | ||||||||
\(86\) | −54.5114 | −0.0683501 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1461.82 | 1.77080 | ||||||||
\(89\) | −160.228 | −0.190833 | −0.0954166 | − | 0.995437i | \(-0.530418\pi\) | ||||
−0.0954166 | + | 0.995437i | \(0.530418\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2596.99 | 2.94298 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2378.28 | −2.60958 | ||||||||
\(95\) | 65.3523 | 0.0705790 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.23476 | −0.00757297 | −0.00378649 | − | 0.999993i | \(-0.501205\pi\) | ||||
−0.00378649 | + | 0.999993i | \(0.501205\pi\) | |||||||
\(98\) | −4083.07 | −4.20870 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1852.03 | −1.85203 | ||||||||
\(101\) | 1125.70 | 1.10902 | 0.554511 | − | 0.832176i | \(-0.312905\pi\) | ||||
0.554511 | + | 0.832176i | \(0.312905\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1204.03 | 1.15181 | 0.575907 | − | 0.817515i | \(-0.304649\pi\) | ||||
0.575907 | + | 0.817515i | \(0.304649\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1047.34 | 0.959689 | ||||||||
\(107\) | −1491.74 | −1.34778 | −0.673889 | − | 0.738833i | \(-0.735377\pi\) | ||||
−0.673889 | + | 0.738833i | \(0.735377\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −375.430 | −0.329905 | −0.164953 | − | 0.986301i | \(-0.552747\pi\) | ||||
−0.164953 | + | 0.986301i | \(0.552747\pi\) | |||||||
\(110\) | −326.431 | −0.282945 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1509.00 | −1.27310 | ||||||||
\(113\) | −810.999 | −0.675154 | −0.337577 | − | 0.941298i | \(-0.609607\pi\) | ||||
−0.337577 | + | 0.941298i | \(0.609607\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −273.129 | −0.221473 | ||||||||
\(116\) | 2692.36 | 2.15500 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3728.62 | 2.90888 | ||||||||
\(119\) | 1569.24 | 1.20884 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 490.889 | 0.368812 | ||||||||
\(122\) | −1638.91 | −1.21623 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −280.875 | −0.203414 | ||||||||
\(125\) | 393.585 | 0.281626 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −584.796 | −0.408600 | −0.204300 | − | 0.978908i | \(-0.565492\pi\) | ||||
−0.204300 | + | 0.978908i | \(0.565492\pi\) | |||||||
\(128\) | 2646.45 | 1.82746 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1521.40 | 1.01470 | 0.507350 | − | 0.861740i | \(-0.330625\pi\) | ||||
0.507350 | + | 0.861740i | \(0.330625\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1418.75 | 0.924975 | ||||||||
\(134\) | 3251.51 | 2.09618 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1556.55 | 0.981417 | ||||||||
\(137\) | 583.044 | 0.363597 | 0.181799 | − | 0.983336i | \(-0.441808\pi\) | ||||
0.181799 | + | 0.983336i | \(0.441808\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2008.49 | −1.22560 | −0.612798 | − | 0.790240i | \(-0.709956\pi\) | ||||
−0.612798 | + | 0.790240i | \(0.709956\pi\) | |||||||
\(140\) | 830.410 | 0.501303 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2161.95 | −1.27765 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −283.160 | −0.162173 | ||||||||
\(146\) | 3101.59 | 1.75815 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5009.54 | 2.78231 | ||||||||
\(149\) | −1357.74 | −0.746515 | −0.373257 | − | 0.927728i | \(-0.621759\pi\) | ||||
−0.373257 | + | 0.927728i | \(0.621759\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2305.46 | −1.24249 | −0.621243 | − | 0.783618i | \(-0.713372\pi\) | ||||
−0.621243 | + | 0.783618i | \(0.713372\pi\) | |||||||
\(152\) | 1407.28 | 0.750956 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −7086.59 | −3.70814 | ||||||||
\(155\) | 29.5400 | 0.0153078 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1254.03 | 0.637470 | 0.318735 | − | 0.947844i | \(-0.396742\pi\) | ||||
0.318735 | + | 0.947844i | \(0.396742\pi\) | |||||||
\(158\) | 3742.45 | 1.88439 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −101.510 | −0.0501567 | ||||||||
\(161\) | −5929.44 | −2.90252 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2792.83 | 1.34203 | 0.671017 | − | 0.741442i | \(-0.265858\pi\) | ||||
0.671017 | + | 0.741442i | \(0.265858\pi\) | |||||||
\(164\) | 6229.38 | 2.96605 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5080.25 | −2.37533 | ||||||||
\(167\) | 1218.71 | 0.564712 | 0.282356 | − | 0.959310i | \(-0.408884\pi\) | ||||
0.282356 | + | 0.959310i | \(0.408884\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −347.583 | −0.156814 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 171.431 | 0.0759969 | ||||||||
\(173\) | 1526.65 | 0.670922 | 0.335461 | − | 0.942054i | \(-0.391108\pi\) | ||||
0.335461 | + | 0.942054i | \(0.391108\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4228.56 | 1.82657 | ||||||||
\(176\) | −1865.48 | −0.798954 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 770.468 | 0.324433 | ||||||||
\(179\) | 1067.26 | 0.445647 | 0.222823 | − | 0.974859i | \(-0.428473\pi\) | ||||
0.222823 | + | 0.974859i | \(0.428473\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3579.98 | 1.47015 | 0.735076 | − | 0.677984i | \(-0.237146\pi\) | ||||
0.735076 | + | 0.677984i | \(0.237146\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5881.47 | −2.35646 | ||||||||
\(185\) | −526.860 | −0.209381 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1939.94 | 0.758625 | ||||||||
\(188\) | 7479.36 | 2.90153 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −314.251 | −0.119990 | ||||||||
\(191\) | −3087.19 | −1.16953 | −0.584767 | − | 0.811201i | \(-0.698814\pi\) | ||||
−0.584767 | + | 0.811201i | \(0.698814\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 897.457 | 0.334717 | 0.167358 | − | 0.985896i | \(-0.446476\pi\) | ||||
0.167358 | + | 0.985896i | \(0.446476\pi\) | |||||||
\(194\) | 34.7888 | 0.0128747 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12840.7 | 4.67956 | ||||||||
\(197\) | 23.3043 | 0.00842825 | 0.00421412 | − | 0.999991i | \(-0.498659\pi\) | ||||
0.00421412 | + | 0.999991i | \(0.498659\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3910.89 | 1.39314 | 0.696571 | − | 0.717487i | \(-0.254708\pi\) | ||||
0.696571 | + | 0.717487i | \(0.254708\pi\) | |||||||
\(200\) | 4194.35 | 1.48293 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5412.99 | −1.88543 | ||||||||
\(203\) | −6147.20 | −2.12537 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −655.153 | −0.223209 | ||||||||
\(206\) | −5789.67 | −1.95818 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1753.91 | 0.580481 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −191.920 | −0.0626177 | −0.0313088 | − | 0.999510i | \(-0.509968\pi\) | ||||
−0.0313088 | + | 0.999510i | \(0.509968\pi\) | |||||||
\(212\) | −3293.75 | −1.06706 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7173.14 | 2.29133 | ||||||||
\(215\) | −18.0296 | −0.00571912 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 641.294 | 0.200617 | ||||||||
\(218\) | 1805.28 | 0.560866 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1026.58 | 0.314600 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1444.23 | 0.433688 | 0.216844 | − | 0.976206i | \(-0.430424\pi\) | ||||
0.216844 | + | 0.976206i | \(0.430424\pi\) | |||||||
\(224\) | −2203.71 | −0.657329 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3899.74 | 1.14782 | ||||||||
\(227\) | −4307.34 | −1.25942 | −0.629710 | − | 0.776830i | \(-0.716826\pi\) | ||||
−0.629710 | + | 0.776830i | \(0.716826\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1864.12 | −0.537924 | −0.268962 | − | 0.963151i | \(-0.586681\pi\) | ||||
−0.268962 | + | 0.963151i | \(0.586681\pi\) | |||||||
\(230\) | 1313.36 | 0.376522 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6097.48 | −1.72551 | ||||||||
\(233\) | −3541.27 | −0.995691 | −0.497846 | − | 0.867266i | \(-0.665875\pi\) | ||||
−0.497846 | + | 0.867266i | \(0.665875\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −786.615 | −0.218354 | ||||||||
\(236\) | −11726.0 | −3.23432 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −7545.79 | −2.05513 | ||||||||
\(239\) | 2043.01 | 0.552935 | 0.276467 | − | 0.961023i | \(-0.410836\pi\) | ||||
0.276467 | + | 0.961023i | \(0.410836\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 228.833 | 0.0611636 | 0.0305818 | − | 0.999532i | \(-0.490264\pi\) | ||||
0.0305818 | + | 0.999532i | \(0.490264\pi\) | |||||||
\(242\) | −2360.47 | −0.627011 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5154.13 | 1.35229 | ||||||||
\(245\) | −1350.48 | −0.352158 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 636.106 | 0.162874 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1892.58 | −0.478788 | ||||||||
\(251\) | −3409.06 | −0.857282 | −0.428641 | − | 0.903475i | \(-0.641007\pi\) | ||||
−0.428641 | + | 0.903475i | \(0.641007\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7330.16 | −1.82151 | ||||||||
\(254\) | 2812.03 | 0.694654 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7473.22 | −1.82452 | ||||||||
\(257\) | −3963.28 | −0.961955 | −0.480978 | − | 0.876733i | \(-0.659718\pi\) | ||||
−0.480978 | + | 0.876733i | \(0.659718\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11437.8 | −2.74405 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7315.76 | −1.72507 | ||||||||
\(263\) | −4890.12 | −1.14653 | −0.573266 | − | 0.819370i | \(-0.694324\pi\) | ||||
−0.573266 | + | 0.819370i | \(0.694324\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 346.409 | 0.0803008 | ||||||||
\(266\) | −6822.17 | −1.57253 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −10225.5 | −2.33069 | ||||||||
\(269\) | −3946.47 | −0.894500 | −0.447250 | − | 0.894409i | \(-0.647597\pi\) | ||||
−0.447250 | + | 0.894409i | \(0.647597\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2692.66 | −0.603570 | −0.301785 | − | 0.953376i | \(-0.597582\pi\) | ||||
−0.301785 | + | 0.953376i | \(0.597582\pi\) | |||||||
\(272\) | −1986.36 | −0.442797 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2803.60 | −0.618146 | ||||||||
\(275\) | 5227.48 | 1.14629 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2638.62 | −0.572344 | −0.286172 | − | 0.958178i | \(-0.592383\pi\) | ||||
−0.286172 | + | 0.958178i | \(0.592383\pi\) | |||||||
\(278\) | 9657.94 | 2.08361 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1880.66 | −0.401395 | ||||||||
\(281\) | −3345.23 | −0.710176 | −0.355088 | − | 0.934833i | \(-0.615549\pi\) | ||||
−0.355088 | + | 0.934833i | \(0.615549\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2799.71 | 0.588076 | 0.294038 | − | 0.955794i | \(-0.405001\pi\) | ||||
0.294038 | + | 0.955794i | \(0.405001\pi\) | |||||||
\(284\) | 6799.04 | 1.42059 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −14222.9 | −2.92527 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2847.35 | −0.579554 | ||||||||
\(290\) | 1361.59 | 0.275708 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −9754.07 | −1.95484 | ||||||||
\(293\) | 8050.62 | 1.60520 | 0.802598 | − | 0.596521i | \(-0.203451\pi\) | ||||
0.802598 | + | 0.596521i | \(0.203451\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1233.24 | 0.243397 | ||||||||
\(296\) | −11345.2 | −2.22780 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6528.79 | 1.26914 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −391.411 | −0.0749520 | ||||||||
\(302\) | 11085.9 | 2.11233 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1795.87 | −0.338817 | ||||||||
\(305\) | −542.068 | −0.101766 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5378.68 | 0.999926 | 0.499963 | − | 0.866047i | \(-0.333347\pi\) | ||||
0.499963 | + | 0.866047i | \(0.333347\pi\) | |||||||
\(308\) | 22286.3 | 4.12299 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −142.045 | −0.0260246 | ||||||||
\(311\) | 3727.50 | 0.679636 | 0.339818 | − | 0.940491i | \(-0.389634\pi\) | ||||
0.339818 | + | 0.940491i | \(0.389634\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5336.69 | 0.963730 | 0.481865 | − | 0.876245i | \(-0.339960\pi\) | ||||
0.481865 | + | 0.876245i | \(0.339960\pi\) | |||||||
\(314\) | −6030.10 | −1.08375 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11769.5 | −2.09521 | ||||||||
\(317\) | −338.871 | −0.0600408 | −0.0300204 | − | 0.999549i | \(-0.509557\pi\) | ||||
−0.0300204 | + | 0.999549i | \(0.509557\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7599.37 | −1.33380 | ||||||||
\(320\) | 1044.19 | 0.182413 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 28512.1 | 4.93452 | ||||||||
\(323\) | 1867.56 | 0.321715 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −13429.5 | −2.28157 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −14107.9 | −2.37493 | ||||||||
\(329\) | −17076.9 | −2.86164 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2076.44 | −0.344807 | −0.172404 | − | 0.985026i | \(-0.555153\pi\) | ||||
−0.172404 | + | 0.985026i | \(0.555153\pi\) | |||||||
\(332\) | 15976.7 | 2.64107 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5860.26 | −0.960057 | ||||||||
\(335\) | 1075.44 | 0.175395 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2584.64 | 0.417787 | 0.208893 | − | 0.977938i | \(-0.433014\pi\) | ||||
0.208893 | + | 0.977938i | \(0.433014\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1093.10 | 0.174358 | ||||||||
\(341\) | 792.788 | 0.125900 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17475.1 | −2.75092 | ||||||||
\(344\) | −388.244 | −0.0608510 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7341.02 | −1.14062 | ||||||||
\(347\) | −4191.32 | −0.648420 | −0.324210 | − | 0.945985i | \(-0.605098\pi\) | ||||
−0.324210 | + | 0.945985i | \(0.605098\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7431.29 | 1.13979 | 0.569897 | − | 0.821716i | \(-0.306983\pi\) | ||||
0.569897 | + | 0.821716i | \(0.306983\pi\) | |||||||
\(350\) | −20333.3 | −3.10532 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2724.30 | −0.412516 | ||||||||
\(353\) | 12249.5 | 1.84695 | 0.923474 | − | 0.383661i | \(-0.125337\pi\) | ||||
0.923474 | + | 0.383661i | \(0.125337\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −715.065 | −0.106906 | ||||||||
\(356\) | −2423.01 | −0.360729 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5131.98 | −0.757636 | ||||||||
\(359\) | 5485.46 | 0.806439 | 0.403219 | − | 0.915103i | \(-0.367891\pi\) | ||||
0.403219 | + | 0.915103i | \(0.367891\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5170.53 | −0.753832 | ||||||||
\(362\) | −17214.5 | −2.49938 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1025.85 | 0.147111 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8752.18 | −1.24485 | −0.622425 | − | 0.782680i | \(-0.713852\pi\) | ||||
−0.622425 | + | 0.782680i | \(0.713852\pi\) | |||||||
\(368\) | 7505.54 | 1.06319 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2533.44 | 0.355966 | ||||||||
\(371\) | 7520.30 | 1.05238 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5987.30 | 0.831128 | 0.415564 | − | 0.909564i | \(-0.363584\pi\) | ||||
0.415564 | + | 0.909564i | \(0.363584\pi\) | |||||||
\(374\) | −9328.34 | −1.28973 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −16938.7 | −2.32327 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13603.0 | −1.84364 | −0.921819 | − | 0.387620i | \(-0.873297\pi\) | ||||
−0.921819 | + | 0.387620i | \(0.873297\pi\) | |||||||
\(380\) | 988.276 | 0.133414 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 14844.9 | 1.98831 | ||||||||
\(383\) | 6648.90 | 0.887057 | 0.443528 | − | 0.896260i | \(-0.353727\pi\) | ||||
0.443528 | + | 0.896260i | \(0.353727\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2343.89 | −0.310274 | ||||||||
\(386\) | −4315.48 | −0.569047 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −109.406 | −0.0143151 | ||||||||
\(389\) | −4923.40 | −0.641713 | −0.320856 | − | 0.947128i | \(-0.603971\pi\) | ||||
−0.320856 | + | 0.947128i | \(0.603971\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7805.15 | −1.00952 | ||||||||
\(392\) | −29080.7 | −3.74694 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −112.060 | −0.0143287 | ||||||||
\(395\) | 1237.82 | 0.157674 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 576.103 | 0.0728307 | 0.0364153 | − | 0.999337i | \(-0.488406\pi\) | ||||
0.0364153 | + | 0.999337i | \(0.488406\pi\) | |||||||
\(398\) | −18805.7 | −2.36846 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5352.56 | −0.669070 | ||||||||
\(401\) | −9053.52 | −1.12746 | −0.563730 | − | 0.825959i | \(-0.690634\pi\) | ||||
−0.563730 | + | 0.825959i | \(0.690634\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 17023.1 | 2.09637 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 29559.2 | 3.61330 | ||||||||
\(407\) | −14139.7 | −1.72207 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15789.9 | −1.90895 | −0.954474 | − | 0.298293i | \(-0.903583\pi\) | ||||
−0.954474 | + | 0.298293i | \(0.903583\pi\) | |||||||
\(410\) | 3150.34 | 0.379474 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 18207.7 | 2.17726 | ||||||||
\(413\) | 26772.8 | 3.18984 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1680.29 | −0.198753 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8433.78 | −0.986866 | ||||||||
\(419\) | −4091.45 | −0.477041 | −0.238521 | − | 0.971137i | \(-0.576662\pi\) | ||||
−0.238521 | + | 0.971137i | \(0.576662\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5540.81 | 0.641431 | 0.320715 | − | 0.947176i | \(-0.396077\pi\) | ||||
0.320715 | + | 0.947176i | \(0.396077\pi\) | |||||||
\(422\) | 922.860 | 0.106455 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7459.46 | 0.854395 | ||||||||
\(425\) | 5566.22 | 0.635297 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11767.9 | −1.33370 | ||||||||
\(428\) | −22558.5 | −2.54768 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 86.6965 | 0.00972297 | ||||||||
\(431\) | −40.7848 | −0.00455808 | −0.00227904 | − | 0.999997i | \(-0.500725\pi\) | ||||
−0.00227904 | + | 0.999997i | \(0.500725\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 766.330 | 0.0850519 | 0.0425259 | − | 0.999095i | \(-0.486459\pi\) | ||||
0.0425259 | + | 0.999095i | \(0.486459\pi\) | |||||||
\(434\) | −3083.70 | −0.341066 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5677.35 | −0.623614 | ||||||||
\(437\) | −7056.65 | −0.772461 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6054.63 | −0.658250 | −0.329125 | − | 0.944286i | \(-0.606754\pi\) | ||||
−0.329125 | + | 0.944286i | \(0.606754\pi\) | |||||||
\(440\) | −2324.93 | −0.251901 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7422.44 | −0.796051 | −0.398025 | − | 0.917374i | \(-0.630304\pi\) | ||||
−0.398025 | + | 0.917374i | \(0.630304\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 254.832 | 0.0271465 | ||||||||
\(446\) | −6944.65 | −0.737306 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 22668.7 | 2.39062 | ||||||||
\(449\) | 1050.84 | 0.110451 | 0.0552253 | − | 0.998474i | \(-0.482412\pi\) | ||||
0.0552253 | + | 0.998474i | \(0.482412\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17582.8 | −1.83579 | ||||||||
\(452\) | −12264.1 | −1.27623 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 20712.1 | 2.14112 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14462.4 | 1.48036 | 0.740179 | − | 0.672409i | \(-0.234741\pi\) | ||||
0.740179 | + | 0.672409i | \(0.234741\pi\) | |||||||
\(458\) | 8963.74 | 0.914516 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4130.33 | −0.418647 | ||||||||
\(461\) | −1400.23 | −0.141465 | −0.0707323 | − | 0.997495i | \(-0.522534\pi\) | ||||
−0.0707323 | + | 0.997495i | \(0.522534\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11922.3 | 1.19671 | 0.598353 | − | 0.801232i | \(-0.295822\pi\) | ||||
0.598353 | + | 0.801232i | \(0.295822\pi\) | |||||||
\(464\) | 7781.20 | 0.778519 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 17028.4 | 1.69276 | ||||||||
\(467\) | 8048.13 | 0.797479 | 0.398740 | − | 0.917064i | \(-0.369448\pi\) | ||||
0.398740 | + | 0.917064i | \(0.369448\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23347.0 | 2.29864 | ||||||||
\(470\) | 3782.49 | 0.371219 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 26556.3 | 2.58973 | ||||||||
\(473\) | −483.874 | −0.0470371 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5032.43 | 0.486113 | ||||||||
\(476\) | 23730.5 | 2.28505 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −9823.95 | −0.940035 | ||||||||
\(479\) | −15262.5 | −1.45587 | −0.727933 | − | 0.685648i | \(-0.759519\pi\) | ||||
−0.727933 | + | 0.685648i | \(0.759519\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −1100.36 | −0.103983 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7423.35 | 0.697159 | ||||||||
\(485\) | 11.5064 | 0.00107727 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5277.64 | 0.491073 | 0.245537 | − | 0.969387i | \(-0.421036\pi\) | ||||
0.245537 | + | 0.969387i | \(0.421036\pi\) | |||||||
\(488\) | −11672.7 | −1.08279 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6493.84 | 0.598698 | ||||||||
\(491\) | −11058.1 | −1.01638 | −0.508192 | − | 0.861244i | \(-0.669686\pi\) | ||||
−0.508192 | + | 0.861244i | \(0.669686\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8091.80 | −0.739222 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −811.757 | −0.0734858 | ||||||||
\(497\) | −15523.6 | −1.40106 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −112.405 | −0.0100840 | −0.00504201 | − | 0.999987i | \(-0.501605\pi\) | ||||
−0.00504201 | + | 0.999987i | \(0.501605\pi\) | |||||||
\(500\) | 5951.89 | 0.532354 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 16392.7 | 1.45745 | ||||||||
\(503\) | −10080.5 | −0.893570 | −0.446785 | − | 0.894641i | \(-0.647431\pi\) | ||||
−0.446785 | + | 0.894641i | \(0.647431\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1790.35 | −0.157761 | ||||||||
\(506\) | 35247.5 | 3.09673 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8843.44 | −0.772370 | ||||||||
\(509\) | 19683.5 | 1.71406 | 0.857031 | − | 0.515265i | \(-0.172306\pi\) | ||||
0.857031 | + | 0.515265i | \(0.172306\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22270.5 | 1.92796 | ||||||||
\(512\) | 14763.9 | 1.27437 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 19057.7 | 1.63540 | ||||||||
\(515\) | −1914.93 | −0.163849 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −21111.0 | −1.79586 | ||||||||
\(518\) | 54999.2 | 4.66511 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14722.3 | −1.23800 | −0.618998 | − | 0.785393i | \(-0.712461\pi\) | ||||
−0.618998 | + | 0.785393i | \(0.712461\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11311.6 | −0.945738 | −0.472869 | − | 0.881133i | \(-0.656782\pi\) | ||||
−0.472869 | + | 0.881133i | \(0.656782\pi\) | |||||||
\(524\) | 23007.1 | 1.91807 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 23514.4 | 1.94920 | ||||||||
\(527\) | 844.160 | 0.0697764 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17325.1 | 1.42394 | ||||||||
\(530\) | −1665.73 | −0.136518 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 21454.8 | 1.74846 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2372.51 | 0.191725 | ||||||||
\(536\) | 23158.1 | 1.86619 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 18976.8 | 1.52073 | ||||||||
\(539\) | −36243.7 | −2.89634 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12705.1 | −1.00967 | −0.504837 | − | 0.863215i | \(-0.668447\pi\) | ||||
−0.504837 | + | 0.863215i | \(0.668447\pi\) | |||||||
\(542\) | 12947.8 | 1.02612 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2900.83 | −0.228625 | ||||||||
\(545\) | 597.095 | 0.0469298 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6624.52 | −0.517814 | −0.258907 | − | 0.965902i | \(-0.583362\pi\) | ||||
−0.258907 | + | 0.965902i | \(0.583362\pi\) | |||||||
\(548\) | 8816.95 | 0.687302 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −25136.7 | −1.94878 | ||||||||
\(551\) | −7315.82 | −0.565634 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 26872.1 | 2.06640 | ||||||||
\(554\) | 12688.0 | 0.973032 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −30372.9 | −2.31672 | ||||||||
\(557\) | 14637.9 | 1.11351 | 0.556757 | − | 0.830676i | \(-0.312046\pi\) | ||||
0.556757 | + | 0.830676i | \(0.312046\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 2399.97 | 0.181102 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 16085.7 | 1.20736 | ||||||||
\(563\) | 18465.4 | 1.38228 | 0.691139 | − | 0.722722i | \(-0.257109\pi\) | ||||
0.691139 | + | 0.722722i | \(0.257109\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1289.84 | 0.0960423 | ||||||||
\(566\) | −13462.6 | −0.999778 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −15398.0 | −1.13747 | ||||||||
\(569\) | −195.327 | −0.0143911 | −0.00719557 | − | 0.999974i | \(-0.502290\pi\) | ||||
−0.00719557 | + | 0.999974i | \(0.502290\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12479.1 | −0.914592 | −0.457296 | − | 0.889314i | \(-0.651182\pi\) | ||||
−0.457296 | + | 0.889314i | \(0.651182\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 68391.8 | 4.97320 | ||||||||
\(575\) | −21032.2 | −1.52540 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5511.41 | −0.397648 | −0.198824 | − | 0.980035i | \(-0.563712\pi\) | ||||
−0.198824 | + | 0.980035i | \(0.563712\pi\) | |||||||
\(578\) | 13691.7 | 0.985290 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4282.02 | −0.306554 | ||||||||
\(581\) | −36478.0 | −2.60476 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9296.83 | 0.660438 | ||||||||
\(584\) | 22090.4 | 1.56525 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −38711.9 | −2.72897 | ||||||||
\(587\) | 11511.5 | 0.809420 | 0.404710 | − | 0.914445i | \(-0.367372\pi\) | ||||
0.404710 | + | 0.914445i | \(0.367372\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 763.207 | 0.0533912 | ||||||||
\(590\) | −5930.12 | −0.413795 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 14478.1 | 1.00514 | ||||||||
\(593\) | −22211.3 | −1.53812 | −0.769062 | − | 0.639174i | \(-0.779276\pi\) | ||||
−0.769062 | + | 0.639174i | \(0.779276\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2495.77 | −0.171961 | ||||||||
\(596\) | −20532.2 | −1.41112 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18477.3 | 1.26037 | 0.630184 | − | 0.776446i | \(-0.282979\pi\) | ||||
0.630184 | + | 0.776446i | \(0.282979\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1530.40 | 0.103871 | 0.0519355 | − | 0.998650i | \(-0.483461\pi\) | ||||
0.0519355 | + | 0.998650i | \(0.483461\pi\) | |||||||
\(602\) | 1882.12 | 0.127425 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −34863.7 | −2.34865 | ||||||||
\(605\) | −780.725 | −0.0524644 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18934.8 | −1.26613 | −0.633063 | − | 0.774101i | \(-0.718202\pi\) | ||||
−0.633063 | + | 0.774101i | \(0.718202\pi\) | |||||||
\(608\) | −2622.65 | −0.174938 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2606.57 | 0.173011 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3888.26 | −0.256191 | −0.128096 | − | 0.991762i | \(-0.540886\pi\) | ||||
−0.128096 | + | 0.991762i | \(0.540886\pi\) | |||||||
\(614\) | −25863.7 | −1.69996 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −50472.6 | −3.30130 | ||||||||
\(617\) | 13927.8 | 0.908769 | 0.454385 | − | 0.890806i | \(-0.349859\pi\) | ||||
0.454385 | + | 0.890806i | \(0.349859\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29627.9 | −1.92382 | −0.961910 | − | 0.273368i | \(-0.911862\pi\) | ||||
−0.961910 | + | 0.273368i | \(0.911862\pi\) | |||||||
\(620\) | 446.712 | 0.0289361 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −17923.9 | −1.15544 | ||||||||
\(623\) | 5532.23 | 0.355769 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14682.8 | 0.939702 | ||||||||
\(626\) | −25661.8 | −1.63842 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 18963.8 | 1.20500 | ||||||||
\(629\) | −15056.0 | −0.954405 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6066.13 | −0.382708 | −0.191354 | − | 0.981521i | \(-0.561288\pi\) | ||||
−0.191354 | + | 0.981521i | \(0.561288\pi\) | |||||||
\(632\) | 26654.8 | 1.67764 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1629.48 | 0.102074 | ||||||||
\(635\) | 930.077 | 0.0581244 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 36542.0 | 2.26758 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4208.99 | −0.259961 | ||||||||
\(641\) | 16798.4 | 1.03510 | 0.517548 | − | 0.855654i | \(-0.326845\pi\) | ||||
0.517548 | + | 0.855654i | \(0.326845\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20373.2 | 1.24952 | 0.624758 | − | 0.780818i | \(-0.285198\pi\) | ||||
0.624758 | + | 0.780818i | \(0.285198\pi\) | |||||||
\(644\) | −89666.6 | −5.48658 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8980.28 | −0.546942 | ||||||||
\(647\) | 23098.6 | 1.40356 | 0.701778 | − | 0.712396i | \(-0.252390\pi\) | ||||
0.701778 | + | 0.712396i | \(0.252390\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 33097.4 | 2.00183 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 42234.0 | 2.53683 | ||||||||
\(653\) | 1795.81 | 0.107619 | 0.0538097 | − | 0.998551i | \(-0.482864\pi\) | ||||
0.0538097 | + | 0.998551i | \(0.482864\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2419.69 | −0.144344 | ||||||||
\(656\) | 18003.5 | 1.07152 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 82115.2 | 4.86502 | ||||||||
\(659\) | −14640.3 | −0.865412 | −0.432706 | − | 0.901535i | \(-0.642441\pi\) | ||||
−0.432706 | + | 0.901535i | \(0.642441\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20490.3 | 1.20572 | 0.602860 | − | 0.797847i | \(-0.294028\pi\) | ||||
0.602860 | + | 0.797847i | \(0.294028\pi\) | |||||||
\(662\) | 9984.67 | 0.586201 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −36182.9 | −2.11471 | ||||||||
\(665\) | −2256.43 | −0.131580 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 30575.2 | 1.77493 | ||||||||
\(668\) | 18429.7 | 1.06746 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5171.30 | −0.298186 | ||||||||
\(671\) | −14547.9 | −0.836981 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21436.5 | 1.22781 | 0.613904 | − | 0.789380i | \(-0.289598\pi\) | ||||
0.613904 | + | 0.789380i | \(0.289598\pi\) | |||||||
\(674\) | −12428.4 | −0.710273 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20158.0 | 1.14436 | 0.572181 | − | 0.820127i | \(-0.306097\pi\) | ||||
0.572181 | + | 0.820127i | \(0.306097\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 249.796 | 0.0141182 | ||||||||
\(680\) | −2475.58 | −0.139609 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3812.17 | −0.214040 | ||||||||
\(683\) | −4273.98 | −0.239443 | −0.119721 | − | 0.992808i | \(-0.538200\pi\) | ||||
−0.119721 | + | 0.992808i | \(0.538200\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −927.291 | −0.0517226 | ||||||||
\(686\) | 84030.0 | 4.67679 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 495.452 | 0.0274548 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10287.2 | −0.566346 | −0.283173 | − | 0.959069i | \(-0.591387\pi\) | ||||
−0.283173 | + | 0.959069i | \(0.591387\pi\) | |||||||
\(692\) | 23086.5 | 1.26823 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 20154.2 | 1.10237 | ||||||||
\(695\) | 3194.36 | 0.174344 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18722.2 | −1.01744 | ||||||||
\(698\) | −35733.8 | −1.93774 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 63945.4 | 3.45273 | ||||||||
\(701\) | 11726.5 | 0.631815 | 0.315907 | − | 0.948790i | \(-0.397691\pi\) | ||||
0.315907 | + | 0.948790i | \(0.397691\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13612.2 | −0.730287 | ||||||||
\(704\) | 28023.8 | 1.50027 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −58902.3 | −3.13997 | ||||||||
\(707\) | −38867.2 | −2.06754 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11833.0 | 0.626795 | 0.313398 | − | 0.949622i | \(-0.398533\pi\) | ||||
0.313398 | + | 0.949622i | \(0.398533\pi\) | |||||||
\(710\) | 3438.43 | 0.181749 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5487.48 | 0.288837 | ||||||||
\(713\) | −3189.69 | −0.167538 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16139.4 | 0.842398 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −26377.2 | −1.37101 | ||||||||
\(719\) | −5964.80 | −0.309387 | −0.154694 | − | 0.987962i | \(-0.549439\pi\) | ||||
−0.154694 | + | 0.987962i | \(0.549439\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −41571.9 | −2.14732 | ||||||||
\(722\) | 24862.8 | 1.28158 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 54137.4 | 2.77901 | ||||||||
\(725\) | −21804.6 | −1.11697 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25972.8 | −1.32500 | −0.662501 | − | 0.749061i | \(-0.730505\pi\) | ||||
−0.662501 | + | 0.749061i | \(0.730505\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4932.86 | −0.250101 | ||||||||
\(731\) | −515.229 | −0.0260690 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33025.9 | −1.66417 | −0.832087 | − | 0.554646i | \(-0.812854\pi\) | ||||
−0.832087 | + | 0.554646i | \(0.812854\pi\) | |||||||
\(734\) | 42085.4 | 2.11635 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10960.9 | 0.548946 | ||||||||
\(737\) | 28862.3 | 1.44255 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7564.70 | −0.376552 | −0.188276 | − | 0.982116i | \(-0.560290\pi\) | ||||
−0.188276 | + | 0.982116i | \(0.560290\pi\) | |||||||
\(740\) | −7967.32 | −0.395790 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −36161.8 | −1.78914 | ||||||||
\(743\) | 12623.9 | 0.623319 | 0.311660 | − | 0.950194i | \(-0.399115\pi\) | ||||
0.311660 | + | 0.950194i | \(0.399115\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2159.40 | 0.106194 | ||||||||
\(746\) | −28790.3 | −1.41299 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 29336.4 | 1.43402 | ||||||||
\(749\) | 51505.6 | 2.51265 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15054.7 | 0.731497 | 0.365749 | − | 0.930714i | \(-0.380813\pi\) | ||||
0.365749 | + | 0.930714i | \(0.380813\pi\) | |||||||
\(752\) | 21616.1 | 1.04822 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3666.67 | 0.176747 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17024.5 | 0.817391 | 0.408695 | − | 0.912671i | \(-0.365984\pi\) | ||||
0.408695 | + | 0.912671i | \(0.365984\pi\) | |||||||
\(758\) | 65410.9 | 3.13434 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2238.18 | −0.106825 | ||||||||
\(761\) | −1037.46 | −0.0494191 | −0.0247095 | − | 0.999695i | \(-0.507866\pi\) | ||||
−0.0247095 | + | 0.999695i | \(0.507866\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12962.5 | 0.615040 | ||||||||
\(764\) | −46685.3 | −2.21075 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −31971.6 | −1.50807 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33909.7 | −1.59014 | −0.795068 | − | 0.606520i | \(-0.792565\pi\) | ||||
−0.795068 | + | 0.606520i | \(0.792565\pi\) | |||||||
\(770\) | 11270.7 | 0.527492 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 13571.6 | 0.632710 | ||||||||
\(773\) | −13566.7 | −0.631253 | −0.315626 | − | 0.948884i | \(-0.602215\pi\) | ||||
−0.315626 | + | 0.948884i | \(0.602215\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2274.72 | 0.105433 | ||||||||
\(776\) | 247.775 | 0.0114621 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 23674.5 | 1.09097 | ||||||||
\(779\) | −16926.8 | −0.778517 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19190.7 | −0.879255 | ||||||||
\(782\) | 37531.5 | 1.71627 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 37110.9 | 1.69055 | ||||||||
\(785\) | −1994.46 | −0.0906817 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12545.8 | −0.568246 | −0.284123 | − | 0.958788i | \(-0.591702\pi\) | ||||
−0.284123 | + | 0.958788i | \(0.591702\pi\) | |||||||
\(788\) | 352.414 | 0.0159318 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5952.11 | −0.268059 | ||||||||
\(791\) | 28001.5 | 1.25868 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −2770.23 | −0.123818 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 59141.5 | 2.63344 | ||||||||
\(797\) | −26658.5 | −1.18481 | −0.592403 | − | 0.805642i | \(-0.701821\pi\) | ||||
−0.592403 | + | 0.805642i | \(0.701821\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22478.9 | −0.995304 | ||||||||
\(800\) | −7816.74 | −0.345454 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 43534.4 | 1.91677 | ||||||||
\(803\) | 27531.5 | 1.20992 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9430.36 | 0.412890 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −38552.8 | −1.67857 | ||||||||
\(809\) | 3448.15 | 0.149852 | 0.0749260 | − | 0.997189i | \(-0.476128\pi\) | ||||
0.0749260 | + | 0.997189i | \(0.476128\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33920.4 | −1.46869 | −0.734344 | − | 0.678778i | \(-0.762510\pi\) | ||||
−0.734344 | + | 0.678778i | \(0.762510\pi\) | |||||||
\(812\) | −92959.7 | −4.01754 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 67991.8 | 2.92766 | ||||||||
\(815\) | −4441.81 | −0.190908 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −465.820 | −0.0199473 | ||||||||
\(818\) | 75926.7 | 3.24537 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9907.40 | −0.421928 | ||||||||
\(821\) | 5461.33 | 0.232158 | 0.116079 | − | 0.993240i | \(-0.462967\pi\) | ||||
0.116079 | + | 0.993240i | \(0.462967\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21155.0 | 0.896010 | 0.448005 | − | 0.894031i | \(-0.352135\pi\) | ||||
0.448005 | + | 0.894031i | \(0.352135\pi\) | |||||||
\(824\) | −41235.6 | −1.74334 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −128739. | −5.42300 | ||||||||
\(827\) | −18974.8 | −0.797846 | −0.398923 | − | 0.916984i | \(-0.630616\pi\) | ||||
−0.398923 | + | 0.916984i | \(0.630616\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9497.90 | 0.397920 | 0.198960 | − | 0.980008i | \(-0.436244\pi\) | ||||
0.198960 | + | 0.980008i | \(0.436244\pi\) | |||||||
\(830\) | 8079.79 | 0.337896 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −38592.3 | −1.60521 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1938.28 | −0.0803316 | ||||||||
\(836\) | 26523.1 | 1.09727 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 19674.0 | 0.811010 | ||||||||
\(839\) | 8225.56 | 0.338472 | 0.169236 | − | 0.985576i | \(-0.445870\pi\) | ||||
0.169236 | + | 0.985576i | \(0.445870\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7309.11 | 0.299689 | ||||||||
\(842\) | −26643.3 | −1.09049 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2902.27 | −0.118365 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −16949.0 | −0.687573 | ||||||||
\(848\) | −9519.27 | −0.385487 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −26765.5 | −1.08006 | ||||||||
\(851\) | 56889.6 | 2.29160 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19140.4 | −0.768294 | −0.384147 | − | 0.923272i | \(-0.625504\pi\) | ||||
−0.384147 | + | 0.923272i | \(0.625504\pi\) | |||||||
\(854\) | 56586.8 | 2.26740 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 51089.0 | 2.03994 | ||||||||
\(857\) | 20602.9 | 0.821215 | 0.410608 | − | 0.911812i | \(-0.365317\pi\) | ||||
0.410608 | + | 0.911812i | \(0.365317\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5247.92 | 0.208448 | 0.104224 | − | 0.994554i | \(-0.466764\pi\) | ||||
0.104224 | + | 0.994554i | \(0.466764\pi\) | |||||||
\(860\) | −272.649 | −0.0108107 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 196.116 | 0.00774912 | ||||||||
\(863\) | 38622.5 | 1.52343 | 0.761717 | − | 0.647909i | \(-0.224356\pi\) | ||||
0.761717 | + | 0.647909i | \(0.224356\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2428.04 | −0.0954402 | ||||||||
\(866\) | −3684.95 | −0.144595 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 9697.82 | 0.379223 | ||||||||
\(869\) | 33220.2 | 1.29680 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 12857.7 | 0.499330 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 33932.4 | 1.31325 | ||||||||
\(875\) | −13589.4 | −0.525034 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19963.9 | −0.768682 | −0.384341 | − | 0.923191i | \(-0.625571\pi\) | ||||
−0.384341 | + | 0.923191i | \(0.625571\pi\) | |||||||
\(878\) | 29114.1 | 1.11908 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2966.92 | 0.113653 | ||||||||
\(881\) | −13175.8 | −0.503865 | −0.251933 | − | 0.967745i | \(-0.581066\pi\) | ||||
−0.251933 | + | 0.967745i | \(0.581066\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14434.0 | 0.550105 | 0.275052 | − | 0.961429i | \(-0.411305\pi\) | ||||
0.275052 | + | 0.961429i | \(0.411305\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 35691.2 | 1.35335 | ||||||||
\(887\) | 20962.3 | 0.793514 | 0.396757 | − | 0.917924i | \(-0.370136\pi\) | ||||
0.396757 | + | 0.917924i | \(0.370136\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20191.3 | 0.761750 | ||||||||
\(890\) | −1225.38 | −0.0461513 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 21840.0 | 0.819794 | ||||||||
\(893\) | −20323.3 | −0.761582 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1697.40 | −0.0633943 | ||||||||
\(896\) | −91374.3 | −3.40692 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5053.04 | −0.187775 | ||||||||
\(899\) | −3306.84 | −0.122680 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9899.25 | 0.366029 | ||||||||
\(902\) | 84548.1 | 3.12100 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 27775.0 | 1.02188 | ||||||||
\(905\) | −5693.71 | −0.209133 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14079.6 | −0.515441 | −0.257721 | − | 0.966219i | \(-0.582971\pi\) | ||||
−0.257721 | + | 0.966219i | \(0.582971\pi\) | |||||||
\(908\) | −65136.8 | −2.38066 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 622.987 | 0.0226569 | 0.0113285 | − | 0.999936i | \(-0.496394\pi\) | ||||
0.0113285 | + | 0.999936i | \(0.496394\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −45095.3 | −1.63465 | ||||||||
\(914\) | −69543.5 | −2.51673 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −28189.7 | −1.01683 | ||||||||
\(917\) | −52529.8 | −1.89170 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −30293.2 | −1.08735 | −0.543677 | − | 0.839294i | \(-0.682968\pi\) | ||||
−0.543677 | + | 0.839294i | \(0.682968\pi\) | |||||||
\(920\) | 9354.08 | 0.335212 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6733.09 | 0.240502 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −40570.7 | −1.44211 | ||||||||
\(926\) | −57329.0 | −2.03450 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 11363.5 | 0.401965 | ||||||||
\(929\) | −25045.6 | −0.884520 | −0.442260 | − | 0.896887i | \(-0.645823\pi\) | ||||
−0.442260 | + | 0.896887i | \(0.645823\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −34891.4 | −1.22827 | ||||||||
\(932\) | −53552.0 | −1.88214 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −38699.9 | −1.35578 | ||||||||
\(935\) | −3085.35 | −0.107916 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4025.83 | 0.140361 | 0.0701805 | − | 0.997534i | \(-0.477642\pi\) | ||||
0.0701805 | + | 0.997534i | \(0.477642\pi\) | |||||||
\(938\) | −112265. | −3.90788 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −11895.4 | −0.412750 | ||||||||
\(941\) | 50575.8 | 1.75210 | 0.876049 | − | 0.482222i | \(-0.160170\pi\) | ||||
0.876049 | + | 0.482222i | \(0.160170\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 70742.5 | 2.44294 | ||||||||
\(944\) | −33889.3 | −1.16844 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2326.74 | 0.0799671 | ||||||||
\(947\) | −51825.9 | −1.77837 | −0.889185 | − | 0.457547i | \(-0.848728\pi\) | ||||
−0.889185 | + | 0.457547i | \(0.848728\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −24198.8 | −0.826433 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −53743.1 | −1.82965 | ||||||||
\(953\) | −40037.1 | −1.36089 | −0.680446 | − | 0.732798i | \(-0.738214\pi\) | ||||
−0.680446 | + | 0.732798i | \(0.738214\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4909.96 | 0.166369 | ||||||||
\(956\) | 30895.0 | 1.04520 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 73390.5 | 2.47509 | ||||||||
\(959\) | −20130.9 | −0.677851 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29446.0 | −0.988420 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3460.47 | 0.115617 | ||||||||
\(965\) | −1427.34 | −0.0476143 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5557.42 | −0.184813 | −0.0924067 | − | 0.995721i | \(-0.529456\pi\) | ||||
−0.0924067 | + | 0.995721i | \(0.529456\pi\) | |||||||
\(968\) | −16811.9 | −0.558218 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −55.3292 | −0.00183146 | ||||||||
\(971\) | 25730.6 | 0.850396 | 0.425198 | − | 0.905100i | \(-0.360204\pi\) | ||||
0.425198 | + | 0.905100i | \(0.360204\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 69347.4 | 2.28487 | ||||||||
\(974\) | −25377.9 | −0.834865 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 14896.0 | 0.488533 | ||||||||
\(977\) | −39868.8 | −1.30554 | −0.652772 | − | 0.757554i | \(-0.726394\pi\) | ||||
−0.652772 | + | 0.757554i | \(0.726394\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6839.12 | 0.223268 | ||||||||
\(980\) | −20422.2 | −0.665678 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 53173.5 | 1.72794 | ||||||||
\(983\) | 27728.9 | 0.899709 | 0.449854 | − | 0.893102i | \(-0.351476\pi\) | ||||
0.449854 | + | 0.893102i | \(0.351476\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −37.0639 | −0.00119894 | ||||||||
\(986\) | 38909.9 | 1.25674 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1946.81 | 0.0625936 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38088.3 | 1.22090 | 0.610452 | − | 0.792053i | \(-0.290988\pi\) | ||||
0.610452 | + | 0.792053i | \(0.290988\pi\) | |||||||
\(992\) | −1185.47 | −0.0379422 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 74646.0 | 2.38192 | ||||||||
\(995\) | −6220.00 | −0.198178 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18606.0 | −0.591033 | −0.295516 | − | 0.955338i | \(-0.595492\pi\) | ||||
−0.295516 | + | 0.955338i | \(0.595492\pi\) | |||||||
\(998\) | 540.505 | 0.0171437 | ||||||||
\(999\) | 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.bm.1.2 | ✓ | 18 | |
3.2 | odd | 2 | inner | 1521.4.a.bm.1.17 | yes | 18 | |
13.12 | even | 2 | 1521.4.a.bn.1.17 | yes | 18 | ||
39.38 | odd | 2 | 1521.4.a.bn.1.2 | yes | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1521.4.a.bm.1.2 | ✓ | 18 | 1.1 | even | 1 | trivial | |
1521.4.a.bm.1.17 | yes | 18 | 3.2 | odd | 2 | inner | |
1521.4.a.bn.1.2 | yes | 18 | 39.38 | odd | 2 | ||
1521.4.a.bn.1.17 | yes | 18 | 13.12 | even | 2 |