Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [354,4,Mod(1,354)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(354, 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("354.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 354 = 2 \cdot 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 354.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: | \(20.8866761420\) |
Analytic rank: | \(0\) |
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: | \( x^{6} - 2x^{5} - 492x^{4} + 3376x^{3} + 13255x^{2} - 108942x + 106740 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-23.5704\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 354.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −20.5704 | −1.83988 | −0.919938 | − | 0.392064i | \(-0.871761\pi\) | ||||
−0.919938 | + | 0.392064i | \(0.871761\pi\) | |||||||
\(6\) | 6.00000 | 0.408248 | ||||||||
\(7\) | 10.6977 | 0.577620 | 0.288810 | − | 0.957386i | \(-0.406740\pi\) | ||||
0.288810 | + | 0.957386i | \(0.406740\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −41.1409 | −1.30099 | ||||||||
\(11\) | −2.23495 | −0.0612602 | −0.0306301 | − | 0.999531i | \(-0.509751\pi\) | ||||
−0.0306301 | + | 0.999531i | \(0.509751\pi\) | |||||||
\(12\) | 12.0000 | 0.288675 | ||||||||
\(13\) | 85.5511 | 1.82520 | 0.912601 | − | 0.408852i | \(-0.134071\pi\) | ||||
0.912601 | + | 0.408852i | \(0.134071\pi\) | |||||||
\(14\) | 21.3953 | 0.408439 | ||||||||
\(15\) | −61.7113 | −1.06225 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 60.1629 | 0.858332 | 0.429166 | − | 0.903226i | \(-0.358808\pi\) | ||||
0.429166 | + | 0.903226i | \(0.358808\pi\) | |||||||
\(18\) | 18.0000 | 0.235702 | ||||||||
\(19\) | 0.284714 | 0.00343778 | 0.00171889 | − | 0.999999i | \(-0.499453\pi\) | ||||
0.00171889 | + | 0.999999i | \(0.499453\pi\) | |||||||
\(20\) | −82.2818 | −0.919938 | ||||||||
\(21\) | 32.0930 | 0.333489 | ||||||||
\(22\) | −4.46989 | −0.0433175 | ||||||||
\(23\) | 2.95213 | 0.0267636 | 0.0133818 | − | 0.999910i | \(-0.495740\pi\) | ||||
0.0133818 | + | 0.999910i | \(0.495740\pi\) | |||||||
\(24\) | 24.0000 | 0.204124 | ||||||||
\(25\) | 298.143 | 2.38514 | ||||||||
\(26\) | 171.102 | 1.29061 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 42.7907 | 0.288810 | ||||||||
\(29\) | 66.9477 | 0.428686 | 0.214343 | − | 0.976758i | \(-0.431239\pi\) | ||||
0.214343 | + | 0.976758i | \(0.431239\pi\) | |||||||
\(30\) | −123.423 | −0.751126 | ||||||||
\(31\) | 111.170 | 0.644087 | 0.322043 | − | 0.946725i | \(-0.395630\pi\) | ||||
0.322043 | + | 0.946725i | \(0.395630\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | −6.70484 | −0.0353686 | ||||||||
\(34\) | 120.326 | 0.606932 | ||||||||
\(35\) | −220.056 | −1.06275 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | 153.036 | 0.679970 | 0.339985 | − | 0.940431i | \(-0.389578\pi\) | ||||
0.339985 | + | 0.940431i | \(0.389578\pi\) | |||||||
\(38\) | 0.569428 | 0.00243088 | ||||||||
\(39\) | 256.653 | 1.05378 | ||||||||
\(40\) | −164.564 | −0.650494 | ||||||||
\(41\) | −196.485 | −0.748435 | −0.374218 | − | 0.927341i | \(-0.622089\pi\) | ||||
−0.374218 | + | 0.927341i | \(0.622089\pi\) | |||||||
\(42\) | 64.1860 | 0.235812 | ||||||||
\(43\) | 308.000 | 1.09232 | 0.546158 | − | 0.837682i | \(-0.316090\pi\) | ||||
0.546158 | + | 0.837682i | \(0.316090\pi\) | |||||||
\(44\) | −8.93979 | −0.0306301 | ||||||||
\(45\) | −185.134 | −0.613292 | ||||||||
\(46\) | 5.90427 | 0.0189247 | ||||||||
\(47\) | 130.989 | 0.406526 | 0.203263 | − | 0.979124i | \(-0.434845\pi\) | ||||
0.203263 | + | 0.979124i | \(0.434845\pi\) | |||||||
\(48\) | 48.0000 | 0.144338 | ||||||||
\(49\) | −228.560 | −0.666355 | ||||||||
\(50\) | 596.286 | 1.68655 | ||||||||
\(51\) | 180.489 | 0.495558 | ||||||||
\(52\) | 342.205 | 0.912601 | ||||||||
\(53\) | −297.454 | −0.770915 | −0.385457 | − | 0.922726i | \(-0.625956\pi\) | ||||
−0.385457 | + | 0.922726i | \(0.625956\pi\) | |||||||
\(54\) | 54.0000 | 0.136083 | ||||||||
\(55\) | 45.9738 | 0.112711 | ||||||||
\(56\) | 85.5814 | 0.204220 | ||||||||
\(57\) | 0.854142 | 0.00198480 | ||||||||
\(58\) | 133.895 | 0.303127 | ||||||||
\(59\) | −59.0000 | −0.130189 | ||||||||
\(60\) | −246.845 | −0.531126 | ||||||||
\(61\) | 92.3530 | 0.193846 | 0.0969229 | − | 0.995292i | \(-0.469100\pi\) | ||||
0.0969229 | + | 0.995292i | \(0.469100\pi\) | |||||||
\(62\) | 222.340 | 0.455438 | ||||||||
\(63\) | 96.2791 | 0.192540 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −1759.82 | −3.35814 | ||||||||
\(66\) | −13.4097 | −0.0250094 | ||||||||
\(67\) | −484.184 | −0.882873 | −0.441436 | − | 0.897293i | \(-0.645531\pi\) | ||||
−0.441436 | + | 0.897293i | \(0.645531\pi\) | |||||||
\(68\) | 240.652 | 0.429166 | ||||||||
\(69\) | 8.85640 | 0.0154520 | ||||||||
\(70\) | −440.112 | −0.751477 | ||||||||
\(71\) | −485.984 | −0.812333 | −0.406166 | − | 0.913799i | \(-0.633135\pi\) | ||||
−0.406166 | + | 0.913799i | \(0.633135\pi\) | |||||||
\(72\) | 72.0000 | 0.117851 | ||||||||
\(73\) | −729.508 | −1.16962 | −0.584812 | − | 0.811169i | \(-0.698832\pi\) | ||||
−0.584812 | + | 0.811169i | \(0.698832\pi\) | |||||||
\(74\) | 306.071 | 0.480811 | ||||||||
\(75\) | 894.429 | 1.37706 | ||||||||
\(76\) | 1.13886 | 0.00171889 | ||||||||
\(77\) | −23.9087 | −0.0353851 | ||||||||
\(78\) | 513.307 | 0.745135 | ||||||||
\(79\) | −354.288 | −0.504564 | −0.252282 | − | 0.967654i | \(-0.581181\pi\) | ||||
−0.252282 | + | 0.967654i | \(0.581181\pi\) | |||||||
\(80\) | −329.127 | −0.459969 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −392.970 | −0.529224 | ||||||||
\(83\) | 1254.88 | 1.65953 | 0.829765 | − | 0.558112i | \(-0.188474\pi\) | ||||
0.829765 | + | 0.558112i | \(0.188474\pi\) | |||||||
\(84\) | 128.372 | 0.166745 | ||||||||
\(85\) | −1237.58 | −1.57922 | ||||||||
\(86\) | 616.001 | 0.772384 | ||||||||
\(87\) | 200.843 | 0.247502 | ||||||||
\(88\) | −17.8796 | −0.0216587 | ||||||||
\(89\) | 873.062 | 1.03982 | 0.519912 | − | 0.854220i | \(-0.325965\pi\) | ||||
0.519912 | + | 0.854220i | \(0.325965\pi\) | |||||||
\(90\) | −370.268 | −0.433663 | ||||||||
\(91\) | 915.198 | 1.05427 | ||||||||
\(92\) | 11.8085 | 0.0133818 | ||||||||
\(93\) | 333.510 | 0.371864 | ||||||||
\(94\) | 261.978 | 0.287457 | ||||||||
\(95\) | −5.85669 | −0.00632509 | ||||||||
\(96\) | 96.0000 | 0.102062 | ||||||||
\(97\) | 1214.61 | 1.27139 | 0.635695 | − | 0.771940i | \(-0.280713\pi\) | ||||
0.635695 | + | 0.771940i | \(0.280713\pi\) | |||||||
\(98\) | −457.120 | −0.471184 | ||||||||
\(99\) | −20.1145 | −0.0204201 | ||||||||
\(100\) | 1192.57 | 1.19257 | ||||||||
\(101\) | −1493.51 | −1.47139 | −0.735694 | − | 0.677314i | \(-0.763144\pi\) | ||||
−0.735694 | + | 0.677314i | \(0.763144\pi\) | |||||||
\(102\) | 360.977 | 0.350413 | ||||||||
\(103\) | −1251.38 | −1.19711 | −0.598555 | − | 0.801082i | \(-0.704258\pi\) | ||||
−0.598555 | + | 0.801082i | \(0.704258\pi\) | |||||||
\(104\) | 684.409 | 0.645306 | ||||||||
\(105\) | −660.168 | −0.613579 | ||||||||
\(106\) | −594.909 | −0.545119 | ||||||||
\(107\) | 1533.68 | 1.38567 | 0.692834 | − | 0.721097i | \(-0.256362\pi\) | ||||
0.692834 | + | 0.721097i | \(0.256362\pi\) | |||||||
\(108\) | 108.000 | 0.0962250 | ||||||||
\(109\) | 257.128 | 0.225949 | 0.112974 | − | 0.993598i | \(-0.463962\pi\) | ||||
0.112974 | + | 0.993598i | \(0.463962\pi\) | |||||||
\(110\) | 91.9477 | 0.0796988 | ||||||||
\(111\) | 459.107 | 0.392581 | ||||||||
\(112\) | 171.163 | 0.144405 | ||||||||
\(113\) | 2128.87 | 1.77227 | 0.886137 | − | 0.463423i | \(-0.153379\pi\) | ||||
0.886137 | + | 0.463423i | \(0.153379\pi\) | |||||||
\(114\) | 1.70828 | 0.00140347 | ||||||||
\(115\) | −60.7267 | −0.0492417 | ||||||||
\(116\) | 267.791 | 0.214343 | ||||||||
\(117\) | 769.960 | 0.608400 | ||||||||
\(118\) | −118.000 | −0.0920575 | ||||||||
\(119\) | 643.603 | 0.495790 | ||||||||
\(120\) | −493.691 | −0.375563 | ||||||||
\(121\) | −1326.01 | −0.996247 | ||||||||
\(122\) | 184.706 | 0.137070 | ||||||||
\(123\) | −589.456 | −0.432109 | ||||||||
\(124\) | 444.679 | 0.322043 | ||||||||
\(125\) | −3561.63 | −2.54849 | ||||||||
\(126\) | 192.558 | 0.136146 | ||||||||
\(127\) | 1861.39 | 1.30056 | 0.650282 | − | 0.759693i | \(-0.274651\pi\) | ||||
0.650282 | + | 0.759693i | \(0.274651\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 924.001 | 0.630649 | ||||||||
\(130\) | −3519.65 | −2.37457 | ||||||||
\(131\) | −254.823 | −0.169954 | −0.0849771 | − | 0.996383i | \(-0.527082\pi\) | ||||
−0.0849771 | + | 0.996383i | \(0.527082\pi\) | |||||||
\(132\) | −26.8194 | −0.0176843 | ||||||||
\(133\) | 3.04578 | 0.00198573 | ||||||||
\(134\) | −968.368 | −0.624285 | ||||||||
\(135\) | −555.402 | −0.354084 | ||||||||
\(136\) | 481.303 | 0.303466 | ||||||||
\(137\) | −2391.69 | −1.49150 | −0.745751 | − | 0.666225i | \(-0.767909\pi\) | ||||
−0.745751 | + | 0.666225i | \(0.767909\pi\) | |||||||
\(138\) | 17.7128 | 0.0109262 | ||||||||
\(139\) | −1981.83 | −1.20933 | −0.604663 | − | 0.796481i | \(-0.706692\pi\) | ||||
−0.604663 | + | 0.796481i | \(0.706692\pi\) | |||||||
\(140\) | −880.223 | −0.531375 | ||||||||
\(141\) | 392.967 | 0.234708 | ||||||||
\(142\) | −971.967 | −0.574406 | ||||||||
\(143\) | −191.202 | −0.111812 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | −1377.14 | −0.788728 | ||||||||
\(146\) | −1459.02 | −0.827049 | ||||||||
\(147\) | −685.679 | −0.384720 | ||||||||
\(148\) | 612.142 | 0.339985 | ||||||||
\(149\) | −3117.67 | −1.71416 | −0.857079 | − | 0.515184i | \(-0.827723\pi\) | ||||
−0.857079 | + | 0.515184i | \(0.827723\pi\) | |||||||
\(150\) | 1788.86 | 0.973731 | ||||||||
\(151\) | −1691.78 | −0.911758 | −0.455879 | − | 0.890042i | \(-0.650675\pi\) | ||||
−0.455879 | + | 0.890042i | \(0.650675\pi\) | |||||||
\(152\) | 2.27771 | 0.00121544 | ||||||||
\(153\) | 541.466 | 0.286111 | ||||||||
\(154\) | −47.8175 | −0.0250210 | ||||||||
\(155\) | −2286.81 | −1.18504 | ||||||||
\(156\) | 1026.61 | 0.526890 | ||||||||
\(157\) | 1600.30 | 0.813489 | 0.406744 | − | 0.913542i | \(-0.366664\pi\) | ||||
0.406744 | + | 0.913542i | \(0.366664\pi\) | |||||||
\(158\) | −708.576 | −0.356780 | ||||||||
\(159\) | −892.363 | −0.445088 | ||||||||
\(160\) | −658.254 | −0.325247 | ||||||||
\(161\) | 31.5810 | 0.0154592 | ||||||||
\(162\) | 162.000 | 0.0785674 | ||||||||
\(163\) | 1610.34 | 0.773812 | 0.386906 | − | 0.922119i | \(-0.373544\pi\) | ||||
0.386906 | + | 0.922119i | \(0.373544\pi\) | |||||||
\(164\) | −785.941 | −0.374218 | ||||||||
\(165\) | 137.921 | 0.0650738 | ||||||||
\(166\) | 2509.76 | 1.17347 | ||||||||
\(167\) | −1983.03 | −0.918869 | −0.459435 | − | 0.888212i | \(-0.651948\pi\) | ||||
−0.459435 | + | 0.888212i | \(0.651948\pi\) | |||||||
\(168\) | 256.744 | 0.117906 | ||||||||
\(169\) | 5122.00 | 2.33136 | ||||||||
\(170\) | −2475.15 | −1.11668 | ||||||||
\(171\) | 2.56243 | 0.00114593 | ||||||||
\(172\) | 1232.00 | 0.546158 | ||||||||
\(173\) | 3462.71 | 1.52176 | 0.760882 | − | 0.648890i | \(-0.224766\pi\) | ||||
0.760882 | + | 0.648890i | \(0.224766\pi\) | |||||||
\(174\) | 401.686 | 0.175010 | ||||||||
\(175\) | 3189.44 | 1.37771 | ||||||||
\(176\) | −35.7591 | −0.0153150 | ||||||||
\(177\) | −177.000 | −0.0751646 | ||||||||
\(178\) | 1746.12 | 0.735267 | ||||||||
\(179\) | −3713.11 | −1.55045 | −0.775226 | − | 0.631684i | \(-0.782364\pi\) | ||||
−0.775226 | + | 0.631684i | \(0.782364\pi\) | |||||||
\(180\) | −740.536 | −0.306646 | ||||||||
\(181\) | 219.945 | 0.0903224 | 0.0451612 | − | 0.998980i | \(-0.485620\pi\) | ||||
0.0451612 | + | 0.998980i | \(0.485620\pi\) | |||||||
\(182\) | 1830.40 | 0.745484 | ||||||||
\(183\) | 277.059 | 0.111917 | ||||||||
\(184\) | 23.6171 | 0.00946236 | ||||||||
\(185\) | −3148.01 | −1.25106 | ||||||||
\(186\) | 667.019 | 0.262947 | ||||||||
\(187\) | −134.461 | −0.0525815 | ||||||||
\(188\) | 523.956 | 0.203263 | ||||||||
\(189\) | 288.837 | 0.111163 | ||||||||
\(190\) | −11.7134 | −0.00447252 | ||||||||
\(191\) | −3454.10 | −1.30853 | −0.654267 | − | 0.756263i | \(-0.727023\pi\) | ||||
−0.654267 | + | 0.756263i | \(0.727023\pi\) | |||||||
\(192\) | 192.000 | 0.0721688 | ||||||||
\(193\) | 564.088 | 0.210383 | 0.105192 | − | 0.994452i | \(-0.466454\pi\) | ||||
0.105192 | + | 0.994452i | \(0.466454\pi\) | |||||||
\(194\) | 2429.22 | 0.899009 | ||||||||
\(195\) | −5279.47 | −1.93883 | ||||||||
\(196\) | −914.239 | −0.333178 | ||||||||
\(197\) | −748.278 | −0.270623 | −0.135311 | − | 0.990803i | \(-0.543203\pi\) | ||||
−0.135311 | + | 0.990803i | \(0.543203\pi\) | |||||||
\(198\) | −40.2290 | −0.0144392 | ||||||||
\(199\) | −338.672 | −0.120642 | −0.0603212 | − | 0.998179i | \(-0.519213\pi\) | ||||
−0.0603212 | + | 0.998179i | \(0.519213\pi\) | |||||||
\(200\) | 2385.14 | 0.843276 | ||||||||
\(201\) | −1452.55 | −0.509727 | ||||||||
\(202\) | −2987.03 | −1.04043 | ||||||||
\(203\) | 716.185 | 0.247617 | ||||||||
\(204\) | 721.955 | 0.247779 | ||||||||
\(205\) | 4041.79 | 1.37703 | ||||||||
\(206\) | −2502.76 | −0.846484 | ||||||||
\(207\) | 26.5692 | 0.00892119 | ||||||||
\(208\) | 1368.82 | 0.456300 | ||||||||
\(209\) | −0.636320 | −0.000210599 0 | ||||||||
\(210\) | −1320.34 | −0.433866 | ||||||||
\(211\) | 1962.10 | 0.640172 | 0.320086 | − | 0.947388i | \(-0.396288\pi\) | ||||
0.320086 | + | 0.947388i | \(0.396288\pi\) | |||||||
\(212\) | −1189.82 | −0.385457 | ||||||||
\(213\) | −1457.95 | −0.469001 | ||||||||
\(214\) | 3067.36 | 0.979815 | ||||||||
\(215\) | −6335.70 | −2.00973 | ||||||||
\(216\) | 216.000 | 0.0680414 | ||||||||
\(217\) | 1189.26 | 0.372038 | ||||||||
\(218\) | 514.256 | 0.159770 | ||||||||
\(219\) | −2188.53 | −0.675282 | ||||||||
\(220\) | 183.895 | 0.0563555 | ||||||||
\(221\) | 5147.00 | 1.56663 | ||||||||
\(222\) | 918.213 | 0.277597 | ||||||||
\(223\) | −5094.92 | −1.52996 | −0.764980 | − | 0.644055i | \(-0.777251\pi\) | ||||
−0.764980 | + | 0.644055i | \(0.777251\pi\) | |||||||
\(224\) | 342.326 | 0.102110 | ||||||||
\(225\) | 2683.29 | 0.795048 | ||||||||
\(226\) | 4257.74 | 1.25319 | ||||||||
\(227\) | 5673.58 | 1.65889 | 0.829447 | − | 0.558586i | \(-0.188656\pi\) | ||||
0.829447 | + | 0.558586i | \(0.188656\pi\) | |||||||
\(228\) | 3.41657 | 0.000992402 0 | ||||||||
\(229\) | −3447.28 | −0.994772 | −0.497386 | − | 0.867529i | \(-0.665707\pi\) | ||||
−0.497386 | + | 0.867529i | \(0.665707\pi\) | |||||||
\(230\) | −121.453 | −0.0348191 | ||||||||
\(231\) | −71.7262 | −0.0204296 | ||||||||
\(232\) | 535.582 | 0.151563 | ||||||||
\(233\) | −3411.20 | −0.959122 | −0.479561 | − | 0.877509i | \(-0.659204\pi\) | ||||
−0.479561 | + | 0.877509i | \(0.659204\pi\) | |||||||
\(234\) | 1539.92 | 0.430204 | ||||||||
\(235\) | −2694.50 | −0.747957 | ||||||||
\(236\) | −236.000 | −0.0650945 | ||||||||
\(237\) | −1062.86 | −0.291310 | ||||||||
\(238\) | 1287.21 | 0.350576 | ||||||||
\(239\) | 4885.08 | 1.32213 | 0.661066 | − | 0.750328i | \(-0.270104\pi\) | ||||
0.661066 | + | 0.750328i | \(0.270104\pi\) | |||||||
\(240\) | −987.381 | −0.265563 | ||||||||
\(241\) | 2885.77 | 0.771322 | 0.385661 | − | 0.922641i | \(-0.373973\pi\) | ||||
0.385661 | + | 0.922641i | \(0.373973\pi\) | |||||||
\(242\) | −2652.01 | −0.704453 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 369.412 | 0.0969229 | ||||||||
\(245\) | 4701.57 | 1.22601 | ||||||||
\(246\) | −1178.91 | −0.305547 | ||||||||
\(247\) | 24.3576 | 0.00627465 | ||||||||
\(248\) | 889.359 | 0.227719 | ||||||||
\(249\) | 3764.64 | 0.958131 | ||||||||
\(250\) | −7123.25 | −1.80206 | ||||||||
\(251\) | 2011.37 | 0.505803 | 0.252901 | − | 0.967492i | \(-0.418615\pi\) | ||||
0.252901 | + | 0.967492i | \(0.418615\pi\) | |||||||
\(252\) | 385.116 | 0.0962700 | ||||||||
\(253\) | −6.59786 | −0.00163954 | ||||||||
\(254\) | 3722.78 | 0.919637 | ||||||||
\(255\) | −3712.73 | −0.911765 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −3671.61 | −0.891163 | −0.445581 | − | 0.895241i | \(-0.647003\pi\) | ||||
−0.445581 | + | 0.895241i | \(0.647003\pi\) | |||||||
\(258\) | 1848.00 | 0.445936 | ||||||||
\(259\) | 1637.12 | 0.392764 | ||||||||
\(260\) | −7039.30 | −1.67907 | ||||||||
\(261\) | 602.530 | 0.142895 | ||||||||
\(262\) | −509.647 | −0.120176 | ||||||||
\(263\) | −3963.12 | −0.929188 | −0.464594 | − | 0.885524i | \(-0.653800\pi\) | ||||
−0.464594 | + | 0.885524i | \(0.653800\pi\) | |||||||
\(264\) | −53.6387 | −0.0125047 | ||||||||
\(265\) | 6118.77 | 1.41839 | ||||||||
\(266\) | 6.09155 | 0.00140412 | ||||||||
\(267\) | 2619.18 | 0.600343 | ||||||||
\(268\) | −1936.74 | −0.441436 | ||||||||
\(269\) | −407.113 | −0.0922755 | −0.0461378 | − | 0.998935i | \(-0.514691\pi\) | ||||
−0.0461378 | + | 0.998935i | \(0.514691\pi\) | |||||||
\(270\) | −1110.80 | −0.250375 | ||||||||
\(271\) | −5324.46 | −1.19350 | −0.596749 | − | 0.802428i | \(-0.703541\pi\) | ||||
−0.596749 | + | 0.802428i | \(0.703541\pi\) | |||||||
\(272\) | 962.606 | 0.214583 | ||||||||
\(273\) | 2745.59 | 0.608685 | ||||||||
\(274\) | −4783.38 | −1.05465 | ||||||||
\(275\) | −666.333 | −0.146114 | ||||||||
\(276\) | 35.4256 | 0.00772598 | ||||||||
\(277\) | 1794.59 | 0.389266 | 0.194633 | − | 0.980876i | \(-0.437648\pi\) | ||||
0.194633 | + | 0.980876i | \(0.437648\pi\) | |||||||
\(278\) | −3963.65 | −0.855123 | ||||||||
\(279\) | 1000.53 | 0.214696 | ||||||||
\(280\) | −1760.45 | −0.375739 | ||||||||
\(281\) | −1375.35 | −0.291981 | −0.145990 | − | 0.989286i | \(-0.546637\pi\) | ||||
−0.145990 | + | 0.989286i | \(0.546637\pi\) | |||||||
\(282\) | 785.934 | 0.165963 | ||||||||
\(283\) | 5607.66 | 1.17788 | 0.588941 | − | 0.808176i | \(-0.299545\pi\) | ||||
0.588941 | + | 0.808176i | \(0.299545\pi\) | |||||||
\(284\) | −1943.93 | −0.406166 | ||||||||
\(285\) | −17.5701 | −0.00365179 | ||||||||
\(286\) | −382.404 | −0.0790631 | ||||||||
\(287\) | −2101.93 | −0.432311 | ||||||||
\(288\) | 288.000 | 0.0589256 | ||||||||
\(289\) | −1293.43 | −0.263266 | ||||||||
\(290\) | −2754.29 | −0.557715 | ||||||||
\(291\) | 3643.83 | 0.734038 | ||||||||
\(292\) | −2918.03 | −0.584812 | ||||||||
\(293\) | 4607.07 | 0.918593 | 0.459297 | − | 0.888283i | \(-0.348101\pi\) | ||||
0.459297 | + | 0.888283i | \(0.348101\pi\) | |||||||
\(294\) | −1371.36 | −0.272038 | ||||||||
\(295\) | 1213.66 | 0.239531 | ||||||||
\(296\) | 1224.28 | 0.240406 | ||||||||
\(297\) | −60.3436 | −0.0117895 | ||||||||
\(298\) | −6235.34 | −1.21209 | ||||||||
\(299\) | 252.558 | 0.0488489 | ||||||||
\(300\) | 3577.72 | 0.688532 | ||||||||
\(301\) | 3294.89 | 0.630944 | ||||||||
\(302\) | −3383.57 | −0.644710 | ||||||||
\(303\) | −4480.54 | −0.849506 | ||||||||
\(304\) | 4.55542 | 0.000859446 0 | ||||||||
\(305\) | −1899.74 | −0.356652 | ||||||||
\(306\) | 1082.93 | 0.202311 | ||||||||
\(307\) | −1501.61 | −0.279158 | −0.139579 | − | 0.990211i | \(-0.544575\pi\) | ||||
−0.139579 | + | 0.990211i | \(0.544575\pi\) | |||||||
\(308\) | −95.6349 | −0.0176925 | ||||||||
\(309\) | −3754.14 | −0.691152 | ||||||||
\(310\) | −4573.62 | −0.837950 | ||||||||
\(311\) | 7757.92 | 1.41450 | 0.707252 | − | 0.706961i | \(-0.249934\pi\) | ||||
0.707252 | + | 0.706961i | \(0.249934\pi\) | |||||||
\(312\) | 2053.23 | 0.372568 | ||||||||
\(313\) | 7752.37 | 1.39997 | 0.699984 | − | 0.714158i | \(-0.253190\pi\) | ||||
0.699984 | + | 0.714158i | \(0.253190\pi\) | |||||||
\(314\) | 3200.60 | 0.575223 | ||||||||
\(315\) | −1980.50 | −0.354250 | ||||||||
\(316\) | −1417.15 | −0.252282 | ||||||||
\(317\) | −3065.47 | −0.543135 | −0.271568 | − | 0.962419i | \(-0.587542\pi\) | ||||
−0.271568 | + | 0.962419i | \(0.587542\pi\) | |||||||
\(318\) | −1784.73 | −0.314725 | ||||||||
\(319\) | −149.625 | −0.0262614 | ||||||||
\(320\) | −1316.51 | −0.229984 | ||||||||
\(321\) | 4601.04 | 0.800016 | ||||||||
\(322\) | 63.1619 | 0.0109313 | ||||||||
\(323\) | 17.1292 | 0.00295076 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | 25506.5 | 4.35337 | ||||||||
\(326\) | 3220.67 | 0.547168 | ||||||||
\(327\) | 771.384 | 0.130452 | ||||||||
\(328\) | −1571.88 | −0.264612 | ||||||||
\(329\) | 1401.28 | 0.234817 | ||||||||
\(330\) | 275.843 | 0.0460141 | ||||||||
\(331\) | 4787.75 | 0.795041 | 0.397521 | − | 0.917593i | \(-0.369871\pi\) | ||||
0.397521 | + | 0.917593i | \(0.369871\pi\) | |||||||
\(332\) | 5019.52 | 0.829765 | ||||||||
\(333\) | 1377.32 | 0.226657 | ||||||||
\(334\) | −3966.05 | −0.649739 | ||||||||
\(335\) | 9959.87 | 1.62438 | ||||||||
\(336\) | 513.488 | 0.0833723 | ||||||||
\(337\) | 4927.46 | 0.796486 | 0.398243 | − | 0.917280i | \(-0.369620\pi\) | ||||
0.398243 | + | 0.917280i | \(0.369620\pi\) | |||||||
\(338\) | 10244.0 | 1.64852 | ||||||||
\(339\) | 6386.60 | 1.02322 | ||||||||
\(340\) | −4950.31 | −0.789612 | ||||||||
\(341\) | −248.459 | −0.0394569 | ||||||||
\(342\) | 5.12485 | 0.000810293 0 | ||||||||
\(343\) | −6114.36 | −0.962520 | ||||||||
\(344\) | 2464.00 | 0.386192 | ||||||||
\(345\) | −182.180 | −0.0284297 | ||||||||
\(346\) | 6925.43 | 1.07605 | ||||||||
\(347\) | 2074.22 | 0.320893 | 0.160446 | − | 0.987045i | \(-0.448707\pi\) | ||||
0.160446 | + | 0.987045i | \(0.448707\pi\) | |||||||
\(348\) | 803.373 | 0.123751 | ||||||||
\(349\) | −4556.88 | −0.698923 | −0.349461 | − | 0.936951i | \(-0.613635\pi\) | ||||
−0.349461 | + | 0.936951i | \(0.613635\pi\) | |||||||
\(350\) | 6378.87 | 0.974186 | ||||||||
\(351\) | 2309.88 | 0.351260 | ||||||||
\(352\) | −71.5183 | −0.0108294 | ||||||||
\(353\) | −5680.79 | −0.856539 | −0.428269 | − | 0.903651i | \(-0.640877\pi\) | ||||
−0.428269 | + | 0.903651i | \(0.640877\pi\) | |||||||
\(354\) | −354.000 | −0.0531494 | ||||||||
\(355\) | 9996.89 | 1.49459 | ||||||||
\(356\) | 3492.25 | 0.519912 | ||||||||
\(357\) | 1930.81 | 0.286244 | ||||||||
\(358\) | −7426.22 | −1.09634 | ||||||||
\(359\) | −11834.3 | −1.73980 | −0.869900 | − | 0.493228i | \(-0.835817\pi\) | ||||
−0.869900 | + | 0.493228i | \(0.835817\pi\) | |||||||
\(360\) | −1481.07 | −0.216831 | ||||||||
\(361\) | −6858.92 | −0.999988 | ||||||||
\(362\) | 439.889 | 0.0638676 | ||||||||
\(363\) | −3978.02 | −0.575184 | ||||||||
\(364\) | 3660.79 | 0.527136 | ||||||||
\(365\) | 15006.3 | 2.15196 | ||||||||
\(366\) | 554.118 | 0.0791372 | ||||||||
\(367\) | 5218.71 | 0.742273 | 0.371137 | − | 0.928578i | \(-0.378968\pi\) | ||||
0.371137 | + | 0.928578i | \(0.378968\pi\) | |||||||
\(368\) | 47.2341 | 0.00669090 | ||||||||
\(369\) | −1768.37 | −0.249478 | ||||||||
\(370\) | −6296.02 | −0.884633 | ||||||||
\(371\) | −3182.07 | −0.445296 | ||||||||
\(372\) | 1334.04 | 0.185932 | ||||||||
\(373\) | −9115.29 | −1.26534 | −0.632670 | − | 0.774421i | \(-0.718041\pi\) | ||||
−0.632670 | + | 0.774421i | \(0.718041\pi\) | |||||||
\(374\) | −268.922 | −0.0371808 | ||||||||
\(375\) | −10684.9 | −1.47137 | ||||||||
\(376\) | 1047.91 | 0.143728 | ||||||||
\(377\) | 5727.46 | 0.782438 | ||||||||
\(378\) | 577.674 | 0.0786041 | ||||||||
\(379\) | −5005.47 | −0.678400 | −0.339200 | − | 0.940714i | \(-0.610156\pi\) | ||||
−0.339200 | + | 0.940714i | \(0.610156\pi\) | |||||||
\(380\) | −23.4268 | −0.00316255 | ||||||||
\(381\) | 5584.17 | 0.750880 | ||||||||
\(382\) | −6908.21 | −0.925274 | ||||||||
\(383\) | 4486.35 | 0.598542 | 0.299271 | − | 0.954168i | \(-0.403257\pi\) | ||||
0.299271 | + | 0.954168i | \(0.403257\pi\) | |||||||
\(384\) | 384.000 | 0.0510310 | ||||||||
\(385\) | 491.813 | 0.0651042 | ||||||||
\(386\) | 1128.18 | 0.148763 | ||||||||
\(387\) | 2772.00 | 0.364105 | ||||||||
\(388\) | 4858.44 | 0.635695 | ||||||||
\(389\) | −1874.92 | −0.244376 | −0.122188 | − | 0.992507i | \(-0.538991\pi\) | ||||
−0.122188 | + | 0.992507i | \(0.538991\pi\) | |||||||
\(390\) | −10558.9 | −1.37096 | ||||||||
\(391\) | 177.609 | 0.0229720 | ||||||||
\(392\) | −1828.48 | −0.235592 | ||||||||
\(393\) | −764.470 | −0.0981232 | ||||||||
\(394\) | −1496.56 | −0.191359 | ||||||||
\(395\) | 7287.86 | 0.928335 | ||||||||
\(396\) | −80.4581 | −0.0102100 | ||||||||
\(397\) | 4124.57 | 0.521427 | 0.260713 | − | 0.965416i | \(-0.416042\pi\) | ||||
0.260713 | + | 0.965416i | \(0.416042\pi\) | |||||||
\(398\) | −677.345 | −0.0853071 | ||||||||
\(399\) | 9.13733 | 0.00114646 | ||||||||
\(400\) | 4770.29 | 0.596286 | ||||||||
\(401\) | −5543.46 | −0.690342 | −0.345171 | − | 0.938540i | \(-0.612179\pi\) | ||||
−0.345171 | + | 0.938540i | \(0.612179\pi\) | |||||||
\(402\) | −2905.10 | −0.360431 | ||||||||
\(403\) | 9510.71 | 1.17559 | ||||||||
\(404\) | −5974.05 | −0.735694 | ||||||||
\(405\) | −1666.21 | −0.204431 | ||||||||
\(406\) | 1432.37 | 0.175092 | ||||||||
\(407\) | −342.026 | −0.0416551 | ||||||||
\(408\) | 1443.91 | 0.175206 | ||||||||
\(409\) | 14156.7 | 1.71150 | 0.855748 | − | 0.517393i | \(-0.173097\pi\) | ||||
0.855748 | + | 0.517393i | \(0.173097\pi\) | |||||||
\(410\) | 8083.58 | 0.973706 | ||||||||
\(411\) | −7175.07 | −0.861119 | ||||||||
\(412\) | −5005.53 | −0.598555 | ||||||||
\(413\) | −631.163 | −0.0751997 | ||||||||
\(414\) | 53.1384 | 0.00630824 | ||||||||
\(415\) | −25813.4 | −3.05333 | ||||||||
\(416\) | 2737.64 | 0.322653 | ||||||||
\(417\) | −5945.48 | −0.698205 | ||||||||
\(418\) | −1.27264 | −0.000148916 0 | ||||||||
\(419\) | 10128.0 | 1.18088 | 0.590438 | − | 0.807083i | \(-0.298955\pi\) | ||||
0.590438 | + | 0.807083i | \(0.298955\pi\) | |||||||
\(420\) | −2640.67 | −0.306789 | ||||||||
\(421\) | −5141.33 | −0.595185 | −0.297593 | − | 0.954693i | \(-0.596184\pi\) | ||||
−0.297593 | + | 0.954693i | \(0.596184\pi\) | |||||||
\(422\) | 3924.19 | 0.452670 | ||||||||
\(423\) | 1178.90 | 0.135509 | ||||||||
\(424\) | −2379.63 | −0.272560 | ||||||||
\(425\) | 17937.1 | 2.04724 | ||||||||
\(426\) | −2915.90 | −0.331634 | ||||||||
\(427\) | 987.963 | 0.111969 | ||||||||
\(428\) | 6134.72 | 0.692834 | ||||||||
\(429\) | −573.607 | −0.0645548 | ||||||||
\(430\) | −12671.4 | −1.42109 | ||||||||
\(431\) | −14321.7 | −1.60059 | −0.800293 | − | 0.599609i | \(-0.795323\pi\) | ||||
−0.800293 | + | 0.599609i | \(0.795323\pi\) | |||||||
\(432\) | 432.000 | 0.0481125 | ||||||||
\(433\) | −9152.49 | −1.01580 | −0.507899 | − | 0.861417i | \(-0.669578\pi\) | ||||
−0.507899 | + | 0.861417i | \(0.669578\pi\) | |||||||
\(434\) | 2378.52 | 0.263070 | ||||||||
\(435\) | −4131.43 | −0.455373 | ||||||||
\(436\) | 1028.51 | 0.112974 | ||||||||
\(437\) | 0.840514 | 9.20074e−5 0 | ||||||||
\(438\) | −4377.05 | −0.477497 | ||||||||
\(439\) | −13370.0 | −1.45356 | −0.726781 | − | 0.686869i | \(-0.758985\pi\) | ||||
−0.726781 | + | 0.686869i | \(0.758985\pi\) | |||||||
\(440\) | 367.791 | 0.0398494 | ||||||||
\(441\) | −2057.04 | −0.222118 | ||||||||
\(442\) | 10294.0 | 1.10777 | ||||||||
\(443\) | 9301.03 | 0.997529 | 0.498764 | − | 0.866738i | \(-0.333787\pi\) | ||||
0.498764 | + | 0.866738i | \(0.333787\pi\) | |||||||
\(444\) | 1836.43 | 0.196290 | ||||||||
\(445\) | −17959.3 | −1.91315 | ||||||||
\(446\) | −10189.8 | −1.08184 | ||||||||
\(447\) | −9353.02 | −0.989670 | ||||||||
\(448\) | 684.651 | 0.0722025 | ||||||||
\(449\) | −173.955 | −0.0182838 | −0.00914192 | − | 0.999958i | \(-0.502910\pi\) | ||||
−0.00914192 | + | 0.999958i | \(0.502910\pi\) | |||||||
\(450\) | 5366.57 | 0.562184 | ||||||||
\(451\) | 439.134 | 0.0458492 | ||||||||
\(452\) | 8515.47 | 0.886137 | ||||||||
\(453\) | −5075.35 | −0.526404 | ||||||||
\(454\) | 11347.2 | 1.17301 | ||||||||
\(455\) | −18826.0 | −1.93973 | ||||||||
\(456\) | 6.83314 | 0.000701734 0 | ||||||||
\(457\) | 6334.55 | 0.648397 | 0.324199 | − | 0.945989i | \(-0.394905\pi\) | ||||
0.324199 | + | 0.945989i | \(0.394905\pi\) | |||||||
\(458\) | −6894.56 | −0.703410 | ||||||||
\(459\) | 1624.40 | 0.165186 | ||||||||
\(460\) | −242.907 | −0.0246208 | ||||||||
\(461\) | 16961.2 | 1.71358 | 0.856792 | − | 0.515661i | \(-0.172454\pi\) | ||||
0.856792 | + | 0.515661i | \(0.172454\pi\) | |||||||
\(462\) | −143.452 | −0.0144459 | ||||||||
\(463\) | −3211.30 | −0.322336 | −0.161168 | − | 0.986927i | \(-0.551526\pi\) | ||||
−0.161168 | + | 0.986927i | \(0.551526\pi\) | |||||||
\(464\) | 1071.16 | 0.107171 | ||||||||
\(465\) | −6860.44 | −0.684183 | ||||||||
\(466\) | −6822.41 | −0.678201 | ||||||||
\(467\) | −6991.32 | −0.692762 | −0.346381 | − | 0.938094i | \(-0.612590\pi\) | ||||
−0.346381 | + | 0.938094i | \(0.612590\pi\) | |||||||
\(468\) | 3079.84 | 0.304200 | ||||||||
\(469\) | −5179.64 | −0.509965 | ||||||||
\(470\) | −5389.00 | −0.528885 | ||||||||
\(471\) | 4800.89 | 0.469668 | ||||||||
\(472\) | −472.000 | −0.0460287 | ||||||||
\(473\) | −688.364 | −0.0669155 | ||||||||
\(474\) | −2125.73 | −0.205987 | ||||||||
\(475\) | 84.8855 | 0.00819960 | ||||||||
\(476\) | 2574.41 | 0.247895 | ||||||||
\(477\) | −2677.09 | −0.256972 | ||||||||
\(478\) | 9770.16 | 0.934889 | ||||||||
\(479\) | −14165.5 | −1.35123 | −0.675614 | − | 0.737255i | \(-0.736122\pi\) | ||||
−0.675614 | + | 0.737255i | \(0.736122\pi\) | |||||||
\(480\) | −1974.76 | −0.187782 | ||||||||
\(481\) | 13092.4 | 1.24108 | ||||||||
\(482\) | 5771.53 | 0.545407 | ||||||||
\(483\) | 94.7429 | 0.00892536 | ||||||||
\(484\) | −5304.02 | −0.498124 | ||||||||
\(485\) | −24985.0 | −2.33920 | ||||||||
\(486\) | 486.000 | 0.0453609 | ||||||||
\(487\) | −16442.6 | −1.52995 | −0.764975 | − | 0.644060i | \(-0.777249\pi\) | ||||
−0.764975 | + | 0.644060i | \(0.777249\pi\) | |||||||
\(488\) | 738.824 | 0.0685348 | ||||||||
\(489\) | 4831.01 | 0.446760 | ||||||||
\(490\) | 9403.15 | 0.866920 | ||||||||
\(491\) | −12860.4 | −1.18204 | −0.591018 | − | 0.806658i | \(-0.701274\pi\) | ||||
−0.591018 | + | 0.806658i | \(0.701274\pi\) | |||||||
\(492\) | −2357.82 | −0.216055 | ||||||||
\(493\) | 4027.77 | 0.367955 | ||||||||
\(494\) | 48.7152 | 0.00443684 | ||||||||
\(495\) | 413.764 | 0.0375704 | ||||||||
\(496\) | 1778.72 | 0.161022 | ||||||||
\(497\) | −5198.89 | −0.469220 | ||||||||
\(498\) | 7529.28 | 0.677501 | ||||||||
\(499\) | −3243.78 | −0.291005 | −0.145502 | − | 0.989358i | \(-0.546480\pi\) | ||||
−0.145502 | + | 0.989358i | \(0.546480\pi\) | |||||||
\(500\) | −14246.5 | −1.27425 | ||||||||
\(501\) | −5949.08 | −0.530509 | ||||||||
\(502\) | 4022.74 | 0.357657 | ||||||||
\(503\) | 18521.3 | 1.64179 | 0.820897 | − | 0.571077i | \(-0.193474\pi\) | ||||
0.820897 | + | 0.571077i | \(0.193474\pi\) | |||||||
\(504\) | 770.233 | 0.0680732 | ||||||||
\(505\) | 30722.2 | 2.70717 | ||||||||
\(506\) | −13.1957 | −0.00115933 | ||||||||
\(507\) | 15366.0 | 1.34601 | ||||||||
\(508\) | 7445.55 | 0.650282 | ||||||||
\(509\) | 6048.84 | 0.526739 | 0.263369 | − | 0.964695i | \(-0.415166\pi\) | ||||
0.263369 | + | 0.964695i | \(0.415166\pi\) | |||||||
\(510\) | −7425.46 | −0.644716 | ||||||||
\(511\) | −7804.04 | −0.675598 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 7.68728 | 0.000661602 0 | ||||||||
\(514\) | −7343.22 | −0.630147 | ||||||||
\(515\) | 25741.5 | 2.20253 | ||||||||
\(516\) | 3696.00 | 0.315325 | ||||||||
\(517\) | −292.753 | −0.0249038 | ||||||||
\(518\) | 3274.25 | 0.277726 | ||||||||
\(519\) | 10388.1 | 0.878591 | ||||||||
\(520\) | −14078.6 | −1.18728 | ||||||||
\(521\) | −4489.66 | −0.377535 | −0.188767 | − | 0.982022i | \(-0.560449\pi\) | ||||
−0.188767 | + | 0.982022i | \(0.560449\pi\) | |||||||
\(522\) | 1205.06 | 0.101042 | ||||||||
\(523\) | 12017.2 | 1.00473 | 0.502365 | − | 0.864656i | \(-0.332463\pi\) | ||||
0.502365 | + | 0.864656i | \(0.332463\pi\) | |||||||
\(524\) | −1019.29 | −0.0849771 | ||||||||
\(525\) | 9568.31 | 0.795419 | ||||||||
\(526\) | −7926.24 | −0.657035 | ||||||||
\(527\) | 6688.30 | 0.552840 | ||||||||
\(528\) | −107.277 | −0.00884214 | ||||||||
\(529\) | −12158.3 | −0.999284 | ||||||||
\(530\) | 12237.5 | 1.00295 | ||||||||
\(531\) | −531.000 | −0.0433963 | ||||||||
\(532\) | 12.1831 | 0.000992866 0 | ||||||||
\(533\) | −16809.5 | −1.36604 | ||||||||
\(534\) | 5238.37 | 0.424506 | ||||||||
\(535\) | −31548.5 | −2.54946 | ||||||||
\(536\) | −3873.47 | −0.312143 | ||||||||
\(537\) | −11139.3 | −0.895154 | ||||||||
\(538\) | −814.226 | −0.0652487 | ||||||||
\(539\) | 510.819 | 0.0408210 | ||||||||
\(540\) | −2221.61 | −0.177042 | ||||||||
\(541\) | −4726.84 | −0.375642 | −0.187821 | − | 0.982203i | \(-0.560143\pi\) | ||||
−0.187821 | + | 0.982203i | \(0.560143\pi\) | |||||||
\(542\) | −10648.9 | −0.843930 | ||||||||
\(543\) | 659.834 | 0.0521477 | ||||||||
\(544\) | 1925.21 | 0.151733 | ||||||||
\(545\) | −5289.24 | −0.415718 | ||||||||
\(546\) | 5491.19 | 0.430405 | ||||||||
\(547\) | −8146.35 | −0.636769 | −0.318385 | − | 0.947962i | \(-0.603140\pi\) | ||||
−0.318385 | + | 0.947962i | \(0.603140\pi\) | |||||||
\(548\) | −9566.76 | −0.745751 | ||||||||
\(549\) | 831.177 | 0.0646153 | ||||||||
\(550\) | −1332.67 | −0.103318 | ||||||||
\(551\) | 19.0610 | 0.00147373 | ||||||||
\(552\) | 70.8512 | 0.00546309 | ||||||||
\(553\) | −3790.06 | −0.291446 | ||||||||
\(554\) | 3589.18 | 0.275252 | ||||||||
\(555\) | −9444.02 | −0.722300 | ||||||||
\(556\) | −7927.31 | −0.604663 | ||||||||
\(557\) | 16255.2 | 1.23654 | 0.618270 | − | 0.785965i | \(-0.287834\pi\) | ||||
0.618270 | + | 0.785965i | \(0.287834\pi\) | |||||||
\(558\) | 2001.06 | 0.151813 | ||||||||
\(559\) | 26349.8 | 1.99370 | ||||||||
\(560\) | −3520.89 | −0.265687 | ||||||||
\(561\) | −403.382 | −0.0303580 | ||||||||
\(562\) | −2750.70 | −0.206462 | ||||||||
\(563\) | 8289.78 | 0.620555 | 0.310278 | − | 0.950646i | \(-0.399578\pi\) | ||||
0.310278 | + | 0.950646i | \(0.399578\pi\) | |||||||
\(564\) | 1571.87 | 0.117354 | ||||||||
\(565\) | −43791.7 | −3.26077 | ||||||||
\(566\) | 11215.3 | 0.832888 | ||||||||
\(567\) | 866.512 | 0.0641800 | ||||||||
\(568\) | −3887.87 | −0.287203 | ||||||||
\(569\) | −4884.07 | −0.359843 | −0.179922 | − | 0.983681i | \(-0.557584\pi\) | ||||
−0.179922 | + | 0.983681i | \(0.557584\pi\) | |||||||
\(570\) | −35.1401 | −0.00258221 | ||||||||
\(571\) | 5925.23 | 0.434262 | 0.217131 | − | 0.976143i | \(-0.430330\pi\) | ||||
0.217131 | + | 0.976143i | \(0.430330\pi\) | |||||||
\(572\) | −764.809 | −0.0559061 | ||||||||
\(573\) | −10362.3 | −0.755483 | ||||||||
\(574\) | −4203.87 | −0.305690 | ||||||||
\(575\) | 880.158 | 0.0638350 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | 7156.64 | 0.516352 | 0.258176 | − | 0.966098i | \(-0.416879\pi\) | ||||
0.258176 | + | 0.966098i | \(0.416879\pi\) | |||||||
\(578\) | −2586.86 | −0.186158 | ||||||||
\(579\) | 1692.26 | 0.121465 | ||||||||
\(580\) | −5508.58 | −0.394364 | ||||||||
\(581\) | 13424.3 | 0.958578 | ||||||||
\(582\) | 7287.66 | 0.519043 | ||||||||
\(583\) | 664.794 | 0.0472264 | ||||||||
\(584\) | −5836.07 | −0.413524 | ||||||||
\(585\) | −15838.4 | −1.11938 | ||||||||
\(586\) | 9214.14 | 0.649544 | ||||||||
\(587\) | −18003.9 | −1.26593 | −0.632964 | − | 0.774181i | \(-0.718162\pi\) | ||||
−0.632964 | + | 0.774181i | \(0.718162\pi\) | |||||||
\(588\) | −2742.72 | −0.192360 | ||||||||
\(589\) | 31.6516 | 0.00221423 | ||||||||
\(590\) | 2427.31 | 0.169374 | ||||||||
\(591\) | −2244.84 | −0.156244 | ||||||||
\(592\) | 2448.57 | 0.169992 | ||||||||
\(593\) | −8897.47 | −0.616147 | −0.308074 | − | 0.951363i | \(-0.599684\pi\) | ||||
−0.308074 | + | 0.951363i | \(0.599684\pi\) | |||||||
\(594\) | −120.687 | −0.00833645 | ||||||||
\(595\) | −13239.2 | −0.912192 | ||||||||
\(596\) | −12470.7 | −0.857079 | ||||||||
\(597\) | −1016.02 | −0.0696530 | ||||||||
\(598\) | 505.117 | 0.0345414 | ||||||||
\(599\) | −12124.1 | −0.827009 | −0.413505 | − | 0.910502i | \(-0.635695\pi\) | ||||
−0.413505 | + | 0.910502i | \(0.635695\pi\) | |||||||
\(600\) | 7155.43 | 0.486865 | ||||||||
\(601\) | 5354.06 | 0.363389 | 0.181694 | − | 0.983355i | \(-0.441842\pi\) | ||||
0.181694 | + | 0.983355i | \(0.441842\pi\) | |||||||
\(602\) | 6589.77 | 0.446145 | ||||||||
\(603\) | −4357.65 | −0.294291 | ||||||||
\(604\) | −6767.14 | −0.455879 | ||||||||
\(605\) | 27276.5 | 1.83297 | ||||||||
\(606\) | −8961.08 | −0.600692 | ||||||||
\(607\) | 3932.68 | 0.262969 | 0.131485 | − | 0.991318i | \(-0.458026\pi\) | ||||
0.131485 | + | 0.991318i | \(0.458026\pi\) | |||||||
\(608\) | 9.11085 | 0.000607720 0 | ||||||||
\(609\) | 2148.56 | 0.142962 | ||||||||
\(610\) | −3799.49 | −0.252191 | ||||||||
\(611\) | 11206.3 | 0.741991 | ||||||||
\(612\) | 2165.86 | 0.143055 | ||||||||
\(613\) | −22292.0 | −1.46878 | −0.734392 | − | 0.678726i | \(-0.762532\pi\) | ||||
−0.734392 | + | 0.678726i | \(0.762532\pi\) | |||||||
\(614\) | −3003.22 | −0.197394 | ||||||||
\(615\) | 12125.4 | 0.795027 | ||||||||
\(616\) | −191.270 | −0.0125105 | ||||||||
\(617\) | 7665.09 | 0.500138 | 0.250069 | − | 0.968228i | \(-0.419547\pi\) | ||||
0.250069 | + | 0.968228i | \(0.419547\pi\) | |||||||
\(618\) | −7508.29 | −0.488718 | ||||||||
\(619\) | −24881.3 | −1.61561 | −0.807807 | − | 0.589446i | \(-0.799346\pi\) | ||||
−0.807807 | + | 0.589446i | \(0.799346\pi\) | |||||||
\(620\) | −9147.25 | −0.592520 | ||||||||
\(621\) | 79.7076 | 0.00515065 | ||||||||
\(622\) | 15515.8 | 1.00021 | ||||||||
\(623\) | 9339.73 | 0.600623 | ||||||||
\(624\) | 4106.45 | 0.263445 | ||||||||
\(625\) | 35996.3 | 2.30377 | ||||||||
\(626\) | 15504.7 | 0.989927 | ||||||||
\(627\) | −1.90896 | −0.000121589 0 | ||||||||
\(628\) | 6401.19 | 0.406744 | ||||||||
\(629\) | 9207.06 | 0.583640 | ||||||||
\(630\) | −3961.01 | −0.250492 | ||||||||
\(631\) | −10193.5 | −0.643099 | −0.321549 | − | 0.946893i | \(-0.604204\pi\) | ||||
−0.321549 | + | 0.946893i | \(0.604204\pi\) | |||||||
\(632\) | −2834.31 | −0.178390 | ||||||||
\(633\) | 5886.29 | 0.369604 | ||||||||
\(634\) | −6130.94 | −0.384055 | ||||||||
\(635\) | −38289.6 | −2.39287 | ||||||||
\(636\) | −3569.45 | −0.222544 | ||||||||
\(637\) | −19553.5 | −1.21623 | ||||||||
\(638\) | −299.249 | −0.0185696 | ||||||||
\(639\) | −4373.85 | −0.270778 | ||||||||
\(640\) | −2633.02 | −0.162624 | ||||||||
\(641\) | 227.166 | 0.0139977 | 0.00699883 | − | 0.999976i | \(-0.497772\pi\) | ||||
0.00699883 | + | 0.999976i | \(0.497772\pi\) | |||||||
\(642\) | 9202.08 | 0.565696 | ||||||||
\(643\) | −26553.3 | −1.62855 | −0.814276 | − | 0.580478i | \(-0.802866\pi\) | ||||
−0.814276 | + | 0.580478i | \(0.802866\pi\) | |||||||
\(644\) | 126.324 | 0.00772959 | ||||||||
\(645\) | −19007.1 | −1.16032 | ||||||||
\(646\) | 34.2584 | 0.00208650 | ||||||||
\(647\) | 8435.80 | 0.512590 | 0.256295 | − | 0.966599i | \(-0.417498\pi\) | ||||
0.256295 | + | 0.966599i | \(0.417498\pi\) | |||||||
\(648\) | 648.000 | 0.0392837 | ||||||||
\(649\) | 131.862 | 0.00797539 | ||||||||
\(650\) | 51012.9 | 3.07830 | ||||||||
\(651\) | 3567.78 | 0.214796 | ||||||||
\(652\) | 6441.35 | 0.386906 | ||||||||
\(653\) | −23909.5 | −1.43285 | −0.716424 | − | 0.697665i | \(-0.754222\pi\) | ||||
−0.716424 | + | 0.697665i | \(0.754222\pi\) | |||||||
\(654\) | 1542.77 | 0.0922432 | ||||||||
\(655\) | 5241.83 | 0.312695 | ||||||||
\(656\) | −3143.76 | −0.187109 | ||||||||
\(657\) | −6565.58 | −0.389874 | ||||||||
\(658\) | 2802.55 | 0.166041 | ||||||||
\(659\) | 27651.8 | 1.63454 | 0.817271 | − | 0.576254i | \(-0.195486\pi\) | ||||
0.817271 | + | 0.576254i | \(0.195486\pi\) | |||||||
\(660\) | 551.686 | 0.0325369 | ||||||||
\(661\) | −26137.9 | −1.53804 | −0.769021 | − | 0.639223i | \(-0.779256\pi\) | ||||
−0.769021 | + | 0.639223i | \(0.779256\pi\) | |||||||
\(662\) | 9575.50 | 0.562179 | ||||||||
\(663\) | 15441.0 | 0.904493 | ||||||||
\(664\) | 10039.0 | 0.586733 | ||||||||
\(665\) | −62.6530 | −0.00365350 | ||||||||
\(666\) | 2754.64 | 0.160270 | ||||||||
\(667\) | 197.639 | 0.0114732 | ||||||||
\(668\) | −7932.10 | −0.459435 | ||||||||
\(669\) | −15284.8 | −0.883322 | ||||||||
\(670\) | 19919.7 | 1.14861 | ||||||||
\(671\) | −206.404 | −0.0118750 | ||||||||
\(672\) | 1026.98 | 0.0589531 | ||||||||
\(673\) | 27608.8 | 1.58134 | 0.790669 | − | 0.612244i | \(-0.209733\pi\) | ||||
0.790669 | + | 0.612244i | \(0.209733\pi\) | |||||||
\(674\) | 9854.92 | 0.563201 | ||||||||
\(675\) | 8049.86 | 0.459021 | ||||||||
\(676\) | 20488.0 | 1.16568 | ||||||||
\(677\) | 32463.5 | 1.84294 | 0.921471 | − | 0.388447i | \(-0.126988\pi\) | ||||
0.921471 | + | 0.388447i | \(0.126988\pi\) | |||||||
\(678\) | 12773.2 | 0.723528 | ||||||||
\(679\) | 12993.5 | 0.734381 | ||||||||
\(680\) | −9900.61 | −0.558340 | ||||||||
\(681\) | 17020.7 | 0.957762 | ||||||||
\(682\) | −496.917 | −0.0279002 | ||||||||
\(683\) | −32825.1 | −1.83897 | −0.919485 | − | 0.393126i | \(-0.871394\pi\) | ||||
−0.919485 | + | 0.393126i | \(0.871394\pi\) | |||||||
\(684\) | 10.2497 | 0.000572964 0 | ||||||||
\(685\) | 49198.1 | 2.74418 | ||||||||
\(686\) | −12228.7 | −0.680605 | ||||||||
\(687\) | −10341.8 | −0.574332 | ||||||||
\(688\) | 4928.01 | 0.273079 | ||||||||
\(689\) | −25447.6 | −1.40707 | ||||||||
\(690\) | −364.360 | −0.0201028 | ||||||||
\(691\) | −9824.85 | −0.540890 | −0.270445 | − | 0.962735i | \(-0.587171\pi\) | ||||
−0.270445 | + | 0.962735i | \(0.587171\pi\) | |||||||
\(692\) | 13850.9 | 0.760882 | ||||||||
\(693\) | −215.179 | −0.0117950 | ||||||||
\(694\) | 4148.43 | 0.226905 | ||||||||
\(695\) | 40767.1 | 2.22501 | ||||||||
\(696\) | 1606.75 | 0.0875051 | ||||||||
\(697\) | −11821.1 | −0.642406 | ||||||||
\(698\) | −9113.75 | −0.494213 | ||||||||
\(699\) | −10233.6 | −0.553749 | ||||||||
\(700\) | 12757.7 | 0.688853 | ||||||||
\(701\) | 8589.00 | 0.462771 | 0.231385 | − | 0.972862i | \(-0.425674\pi\) | ||||
0.231385 | + | 0.972862i | \(0.425674\pi\) | |||||||
\(702\) | 4619.76 | 0.248378 | ||||||||
\(703\) | 43.5714 | 0.00233759 | ||||||||
\(704\) | −143.037 | −0.00765752 | ||||||||
\(705\) | −8083.50 | −0.431833 | ||||||||
\(706\) | −11361.6 | −0.605664 | ||||||||
\(707\) | −15977.1 | −0.849903 | ||||||||
\(708\) | −708.000 | −0.0375823 | ||||||||
\(709\) | 20291.0 | 1.07482 | 0.537409 | − | 0.843322i | \(-0.319403\pi\) | ||||
0.537409 | + | 0.843322i | \(0.319403\pi\) | |||||||
\(710\) | 19993.8 | 1.05684 | ||||||||
\(711\) | −3188.59 | −0.168188 | ||||||||
\(712\) | 6984.49 | 0.367633 | ||||||||
\(713\) | 328.188 | 0.0172381 | ||||||||
\(714\) | 3861.62 | 0.202405 | ||||||||
\(715\) | 3933.11 | 0.205720 | ||||||||
\(716\) | −14852.4 | −0.775226 | ||||||||
\(717\) | 14655.2 | 0.763333 | ||||||||
\(718\) | −23668.5 | −1.23022 | ||||||||
\(719\) | −29601.8 | −1.53541 | −0.767705 | − | 0.640803i | \(-0.778602\pi\) | ||||
−0.767705 | + | 0.640803i | \(0.778602\pi\) | |||||||
\(720\) | −2962.14 | −0.153323 | ||||||||
\(721\) | −13386.9 | −0.691475 | ||||||||
\(722\) | −13717.8 | −0.707098 | ||||||||
\(723\) | 8657.30 | 0.445323 | ||||||||
\(724\) | 879.778 | 0.0451612 | ||||||||
\(725\) | 19960.0 | 1.02248 | ||||||||
\(726\) | −7956.03 | −0.406716 | ||||||||
\(727\) | −13247.0 | −0.675799 | −0.337899 | − | 0.941182i | \(-0.609716\pi\) | ||||
−0.337899 | + | 0.941182i | \(0.609716\pi\) | |||||||
\(728\) | 7321.59 | 0.372742 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 30012.6 | 1.52167 | ||||||||
\(731\) | 18530.2 | 0.937570 | ||||||||
\(732\) | 1108.24 | 0.0559585 | ||||||||
\(733\) | 31066.3 | 1.56543 | 0.782714 | − | 0.622381i | \(-0.213835\pi\) | ||||
0.782714 | + | 0.622381i | \(0.213835\pi\) | |||||||
\(734\) | 10437.4 | 0.524866 | ||||||||
\(735\) | 14104.7 | 0.707838 | ||||||||
\(736\) | 94.4683 | 0.00473118 | ||||||||
\(737\) | 1082.12 | 0.0540849 | ||||||||
\(738\) | −3536.73 | −0.176408 | ||||||||
\(739\) | −37244.1 | −1.85392 | −0.926959 | − | 0.375164i | \(-0.877586\pi\) | ||||
−0.926959 | + | 0.375164i | \(0.877586\pi\) | |||||||
\(740\) | −12592.0 | −0.625530 | ||||||||
\(741\) | 73.0728 | 0.00362267 | ||||||||
\(742\) | −6364.14 | −0.314872 | ||||||||
\(743\) | −26.2210 | −0.00129469 | −0.000647347 | − | 1.00000i | \(-0.500206\pi\) | ||||
−0.000647347 | 1.00000i | \(0.500206\pi\) | ||||||||
\(744\) | 2668.08 | 0.131474 | ||||||||
\(745\) | 64131.9 | 3.15384 | ||||||||
\(746\) | −18230.6 | −0.894731 | ||||||||
\(747\) | 11293.9 | 0.553177 | ||||||||
\(748\) | −537.843 | −0.0262908 | ||||||||
\(749\) | 16406.8 | 0.800389 | ||||||||
\(750\) | −21369.8 | −1.04042 | ||||||||
\(751\) | 13891.3 | 0.674967 | 0.337484 | − | 0.941331i | \(-0.390424\pi\) | ||||
0.337484 | + | 0.941331i | \(0.390424\pi\) | |||||||
\(752\) | 2095.82 | 0.101631 | ||||||||
\(753\) | 6034.11 | 0.292025 | ||||||||
\(754\) | 11454.9 | 0.553267 | ||||||||
\(755\) | 34800.7 | 1.67752 | ||||||||
\(756\) | 1155.35 | 0.0555815 | ||||||||
\(757\) | 28719.9 | 1.37892 | 0.689460 | − | 0.724323i | \(-0.257848\pi\) | ||||
0.689460 | + | 0.724323i | \(0.257848\pi\) | |||||||
\(758\) | −10010.9 | −0.479701 | ||||||||
\(759\) | −19.7936 | −0.000946590 0 | ||||||||
\(760\) | −46.8535 | −0.00223626 | ||||||||
\(761\) | 19474.3 | 0.927653 | 0.463826 | − | 0.885926i | \(-0.346476\pi\) | ||||
0.463826 | + | 0.885926i | \(0.346476\pi\) | |||||||
\(762\) | 11168.3 | 0.530953 | ||||||||
\(763\) | 2750.67 | 0.130512 | ||||||||
\(764\) | −13816.4 | −0.654267 | ||||||||
\(765\) | −11138.2 | −0.526408 | ||||||||
\(766\) | 8972.69 | 0.423233 | ||||||||
\(767\) | −5047.52 | −0.237621 | ||||||||
\(768\) | 768.000 | 0.0360844 | ||||||||
\(769\) | −1759.29 | −0.0824990 | −0.0412495 | − | 0.999149i | \(-0.513134\pi\) | ||||
−0.0412495 | + | 0.999149i | \(0.513134\pi\) | |||||||
\(770\) | 983.626 | 0.0460356 | ||||||||
\(771\) | −11014.8 | −0.514513 | ||||||||
\(772\) | 2256.35 | 0.105192 | ||||||||
\(773\) | −3089.39 | −0.143748 | −0.0718742 | − | 0.997414i | \(-0.522898\pi\) | ||||
−0.0718742 | + | 0.997414i | \(0.522898\pi\) | |||||||
\(774\) | 5544.01 | 0.257461 | ||||||||
\(775\) | 33144.5 | 1.53624 | ||||||||
\(776\) | 9716.87 | 0.449504 | ||||||||
\(777\) | 4911.37 | 0.226763 | ||||||||
\(778\) | −3749.83 | −0.172800 | ||||||||
\(779\) | −55.9421 | −0.00257296 | ||||||||
\(780\) | −21117.9 | −0.969413 | ||||||||
\(781\) | 1086.15 | 0.0497636 | ||||||||
\(782\) | 355.218 | 0.0162437 | ||||||||
\(783\) | 1807.59 | 0.0825006 | ||||||||
\(784\) | −3656.96 | −0.166589 | ||||||||
\(785\) | −32918.8 | −1.49672 | ||||||||
\(786\) | −1528.94 | −0.0693836 | ||||||||
\(787\) | 19285.4 | 0.873506 | 0.436753 | − | 0.899582i | \(-0.356128\pi\) | ||||
0.436753 | + | 0.899582i | \(0.356128\pi\) | |||||||
\(788\) | −2993.11 | −0.135311 | ||||||||
\(789\) | −11889.4 | −0.536467 | ||||||||
\(790\) | 14575.7 | 0.656432 | ||||||||
\(791\) | 22773.9 | 1.02370 | ||||||||
\(792\) | −160.916 | −0.00721958 | ||||||||
\(793\) | 7900.91 | 0.353808 | ||||||||
\(794\) | 8249.15 | 0.368704 | ||||||||
\(795\) | 18356.3 | 0.818907 | ||||||||
\(796\) | −1354.69 | −0.0603212 | ||||||||
\(797\) | −15080.2 | −0.670222 | −0.335111 | − | 0.942179i | \(-0.608774\pi\) | ||||
−0.335111 | + | 0.942179i | \(0.608774\pi\) | |||||||
\(798\) | 18.2747 | 0.000810672 0 | ||||||||
\(799\) | 7880.67 | 0.348934 | ||||||||
\(800\) | 9540.57 | 0.421638 | ||||||||
\(801\) | 7857.55 | 0.346608 | ||||||||
\(802\) | −11086.9 | −0.488145 | ||||||||
\(803\) | 1630.41 | 0.0716513 | ||||||||
\(804\) | −5810.21 | −0.254863 | ||||||||
\(805\) | −649.634 | −0.0284430 | ||||||||
\(806\) | 19021.4 | 0.831266 | ||||||||
\(807\) | −1221.34 | −0.0532753 | ||||||||
\(808\) | −11948.1 | −0.520214 | ||||||||
\(809\) | 27682.3 | 1.20304 | 0.601518 | − | 0.798859i | \(-0.294563\pi\) | ||||
0.601518 | + | 0.798859i | \(0.294563\pi\) | |||||||
\(810\) | −3332.41 | −0.144554 | ||||||||
\(811\) | −3429.01 | −0.148469 | −0.0742347 | − | 0.997241i | \(-0.523651\pi\) | ||||
−0.0742347 | + | 0.997241i | \(0.523651\pi\) | |||||||
\(812\) | 2864.74 | 0.123809 | ||||||||
\(813\) | −15973.4 | −0.689066 | ||||||||
\(814\) | −684.052 | −0.0294546 | ||||||||
\(815\) | −33125.3 | −1.42372 | ||||||||
\(816\) | 2887.82 | 0.123890 | ||||||||
\(817\) | 87.6920 | 0.00375515 | ||||||||
\(818\) | 28313.3 | 1.21021 | ||||||||
\(819\) | 8236.78 | 0.351424 | ||||||||
\(820\) | 16167.2 | 0.688514 | ||||||||
\(821\) | 7419.75 | 0.315409 | 0.157705 | − | 0.987486i | \(-0.449591\pi\) | ||||
0.157705 | + | 0.987486i | \(0.449591\pi\) | |||||||
\(822\) | −14350.1 | −0.608903 | ||||||||
\(823\) | −15195.1 | −0.643583 | −0.321792 | − | 0.946811i | \(-0.604285\pi\) | ||||
−0.321792 | + | 0.946811i | \(0.604285\pi\) | |||||||
\(824\) | −10011.1 | −0.423242 | ||||||||
\(825\) | −1999.00 | −0.0843591 | ||||||||
\(826\) | −1262.33 | −0.0531742 | ||||||||
\(827\) | −2323.17 | −0.0976837 | −0.0488418 | − | 0.998807i | \(-0.515553\pi\) | ||||
−0.0488418 | + | 0.998807i | \(0.515553\pi\) | |||||||
\(828\) | 106.277 | 0.00446060 | ||||||||
\(829\) | −33317.4 | −1.39585 | −0.697927 | − | 0.716169i | \(-0.745894\pi\) | ||||
−0.697927 | + | 0.716169i | \(0.745894\pi\) | |||||||
\(830\) | −51626.9 | −2.15903 | ||||||||
\(831\) | 5383.78 | 0.224743 | ||||||||
\(832\) | 5475.27 | 0.228150 | ||||||||
\(833\) | −13750.8 | −0.571954 | ||||||||
\(834\) | −11891.0 | −0.493706 | ||||||||
\(835\) | 40791.7 | 1.69061 | ||||||||
\(836\) | −2.54528 | −0.000105300 0 | ||||||||
\(837\) | 3001.59 | 0.123955 | ||||||||
\(838\) | 20256.1 | 0.835006 | ||||||||
\(839\) | −46106.5 | −1.89723 | −0.948613 | − | 0.316437i | \(-0.897513\pi\) | ||||
−0.948613 | + | 0.316437i | \(0.897513\pi\) | |||||||
\(840\) | −5281.34 | −0.216933 | ||||||||
\(841\) | −19907.0 | −0.816229 | ||||||||
\(842\) | −10282.7 | −0.420859 | ||||||||
\(843\) | −4126.05 | −0.168575 | ||||||||
\(844\) | 7848.39 | 0.320086 | ||||||||
\(845\) | −105362. | −4.28941 | ||||||||
\(846\) | 2357.80 | 0.0958190 | ||||||||
\(847\) | −14185.2 | −0.575452 | ||||||||
\(848\) | −4759.27 | −0.192729 | ||||||||
\(849\) | 16823.0 | 0.680050 | ||||||||
\(850\) | 35874.3 | 1.44762 | ||||||||
\(851\) | 451.781 | 0.0181984 | ||||||||
\(852\) | −5831.80 | −0.234500 | ||||||||
\(853\) | 1702.35 | 0.0683320 | 0.0341660 | − | 0.999416i | \(-0.489123\pi\) | ||||
0.0341660 | + | 0.999416i | \(0.489123\pi\) | |||||||
\(854\) | 1975.93 | 0.0791742 | ||||||||
\(855\) | −52.7102 | −0.00210836 | ||||||||
\(856\) | 12269.4 | 0.489908 | ||||||||
\(857\) | −2929.81 | −0.116780 | −0.0583901 | − | 0.998294i | \(-0.518597\pi\) | ||||
−0.0583901 | + | 0.998294i | \(0.518597\pi\) | |||||||
\(858\) | −1147.21 | −0.0456471 | ||||||||
\(859\) | 22419.5 | 0.890503 | 0.445252 | − | 0.895405i | \(-0.353114\pi\) | ||||
0.445252 | + | 0.895405i | \(0.353114\pi\) | |||||||
\(860\) | −25342.8 | −1.00486 | ||||||||
\(861\) | −6305.80 | −0.249595 | ||||||||
\(862\) | −28643.4 | −1.13179 | ||||||||
\(863\) | −25151.7 | −0.992088 | −0.496044 | − | 0.868297i | \(-0.665215\pi\) | ||||
−0.496044 | + | 0.868297i | \(0.665215\pi\) | |||||||
\(864\) | 864.000 | 0.0340207 | ||||||||
\(865\) | −71229.5 | −2.79986 | ||||||||
\(866\) | −18305.0 | −0.718277 | ||||||||
\(867\) | −3880.28 | −0.151997 | ||||||||
\(868\) | 4757.03 | 0.186019 | ||||||||
\(869\) | 791.815 | 0.0309097 | ||||||||
\(870\) | −8262.87 | −0.321997 | ||||||||
\(871\) | −41422.5 | −1.61142 | ||||||||
\(872\) | 2057.02 | 0.0798849 | ||||||||
\(873\) | 10931.5 | 0.423797 | ||||||||
\(874\) | 1.68103 | 6.50590e−5 0 | ||||||||
\(875\) | −38101.1 | −1.47206 | ||||||||
\(876\) | −8754.10 | −0.337641 | ||||||||
\(877\) | −9059.18 | −0.348811 | −0.174405 | − | 0.984674i | \(-0.555800\pi\) | ||||
−0.174405 | + | 0.984674i | \(0.555800\pi\) | |||||||
\(878\) | −26739.9 | −1.02782 | ||||||||
\(879\) | 13821.2 | 0.530350 | ||||||||
\(880\) | 735.581 | 0.0281778 | ||||||||
\(881\) | 41733.0 | 1.59594 | 0.797969 | − | 0.602699i | \(-0.205908\pi\) | ||||
0.797969 | + | 0.602699i | \(0.205908\pi\) | |||||||
\(882\) | −4114.08 | −0.157061 | ||||||||
\(883\) | −40917.8 | −1.55945 | −0.779725 | − | 0.626122i | \(-0.784641\pi\) | ||||
−0.779725 | + | 0.626122i | \(0.784641\pi\) | |||||||
\(884\) | 20588.0 | 0.783314 | ||||||||
\(885\) | 3640.97 | 0.138294 | ||||||||
\(886\) | 18602.1 | 0.705359 | ||||||||
\(887\) | 11039.0 | 0.417874 | 0.208937 | − | 0.977929i | \(-0.433000\pi\) | ||||
0.208937 | + | 0.977929i | \(0.433000\pi\) | |||||||
\(888\) | 3672.85 | 0.138798 | ||||||||
\(889\) | 19912.5 | 0.751231 | ||||||||
\(890\) | −35918.5 | −1.35280 | ||||||||
\(891\) | −181.031 | −0.00680668 | ||||||||
\(892\) | −20379.7 | −0.764980 | ||||||||
\(893\) | 37.2944 | 0.00139755 | ||||||||
\(894\) | −18706.0 | −0.699802 | ||||||||
\(895\) | 76380.3 | 2.85264 | ||||||||
\(896\) | 1369.30 | 0.0510549 | ||||||||
\(897\) | 757.675 | 0.0282029 | ||||||||
\(898\) | −347.910 | −0.0129286 | ||||||||
\(899\) | 7442.57 | 0.276111 | ||||||||
\(900\) | 10733.1 | 0.397524 | ||||||||
\(901\) | −17895.7 | −0.661701 | ||||||||
\(902\) | 878.268 | 0.0324203 | ||||||||
\(903\) | 9884.66 | 0.364276 | ||||||||
\(904\) | 17030.9 | 0.626594 | ||||||||
\(905\) | −4524.36 | −0.166182 | ||||||||
\(906\) | −10150.7 | −0.372224 | ||||||||
\(907\) | 1462.44 | 0.0535387 | 0.0267693 | − | 0.999642i | \(-0.491478\pi\) | ||||
0.0267693 | + | 0.999642i | \(0.491478\pi\) | |||||||
\(908\) | 22694.3 | 0.829447 | ||||||||
\(909\) | −13441.6 | −0.490463 | ||||||||
\(910\) | −37652.1 | −1.37160 | ||||||||
\(911\) | 40422.5 | 1.47010 | 0.735048 | − | 0.678015i | \(-0.237160\pi\) | ||||
0.735048 | + | 0.678015i | \(0.237160\pi\) | |||||||
\(912\) | 13.6663 | 0.000496201 0 | ||||||||
\(913\) | −2804.59 | −0.101663 | ||||||||
\(914\) | 12669.1 | 0.458486 | ||||||||
\(915\) | −5699.23 | −0.205913 | ||||||||
\(916\) | −13789.1 | −0.497386 | ||||||||
\(917\) | −2726.02 | −0.0981690 | ||||||||
\(918\) | 3248.80 | 0.116804 | ||||||||
\(919\) | −55076.9 | −1.97695 | −0.988476 | − | 0.151376i | \(-0.951630\pi\) | ||||
−0.988476 | + | 0.151376i | \(0.951630\pi\) | |||||||
\(920\) | −485.813 | −0.0174096 | ||||||||
\(921\) | −4504.83 | −0.161172 | ||||||||
\(922\) | 33922.4 | 1.21169 | ||||||||
\(923\) | −41576.4 | −1.48267 | ||||||||
\(924\) | −286.905 | −0.0102148 | ||||||||
\(925\) | 45626.5 | 1.62183 | ||||||||
\(926\) | −6422.60 | −0.227926 | ||||||||
\(927\) | −11262.4 | −0.399037 | ||||||||
\(928\) | 2142.33 | 0.0757816 | ||||||||
\(929\) | −22479.1 | −0.793881 | −0.396940 | − | 0.917844i | \(-0.629928\pi\) | ||||
−0.396940 | + | 0.917844i | \(0.629928\pi\) | |||||||
\(930\) | −13720.9 | −0.483791 | ||||||||
\(931\) | −65.0742 | −0.00229078 | ||||||||
\(932\) | −13644.8 | −0.479561 | ||||||||
\(933\) | 23273.7 | 0.816665 | ||||||||
\(934\) | −13982.6 | −0.489857 | ||||||||
\(935\) | 2765.92 | 0.0967435 | ||||||||
\(936\) | 6159.68 | 0.215102 | ||||||||
\(937\) | 46979.2 | 1.63793 | 0.818966 | − | 0.573841i | \(-0.194547\pi\) | ||||
0.818966 | + | 0.573841i | \(0.194547\pi\) | |||||||
\(938\) | −10359.3 | −0.360600 | ||||||||
\(939\) | 23257.1 | 0.808272 | ||||||||
\(940\) | −10778.0 | −0.373978 | ||||||||
\(941\) | 53285.4 | 1.84597 | 0.922983 | − | 0.384841i | \(-0.125744\pi\) | ||||
0.922983 | + | 0.384841i | \(0.125744\pi\) | |||||||
\(942\) | 9601.79 | 0.332105 | ||||||||
\(943\) | −580.051 | −0.0200308 | ||||||||
\(944\) | −944.000 | −0.0325472 | ||||||||
\(945\) | −5941.51 | −0.204526 | ||||||||
\(946\) | −1376.73 | −0.0473164 | ||||||||
\(947\) | −16349.6 | −0.561025 | −0.280513 | − | 0.959850i | \(-0.590504\pi\) | ||||
−0.280513 | + | 0.959850i | \(0.590504\pi\) | |||||||
\(948\) | −4251.46 | −0.145655 | ||||||||
\(949\) | −62410.3 | −2.13480 | ||||||||
\(950\) | 169.771 | 0.00579800 | ||||||||
\(951\) | −9196.40 | −0.313579 | ||||||||
\(952\) | 5148.82 | 0.175288 | ||||||||
\(953\) | 17556.7 | 0.596765 | 0.298383 | − | 0.954446i | \(-0.403553\pi\) | ||||
0.298383 | + | 0.954446i | \(0.403553\pi\) | |||||||
\(954\) | −5354.18 | −0.181706 | ||||||||
\(955\) | 71052.4 | 2.40754 | ||||||||
\(956\) | 19540.3 | 0.661066 | ||||||||
\(957\) | −448.874 | −0.0151620 | ||||||||
\(958\) | −28331.0 | −0.955463 | ||||||||
\(959\) | −25585.5 | −0.861522 | ||||||||
\(960\) | −3949.52 | −0.132782 | ||||||||
\(961\) | −17432.3 | −0.585152 | ||||||||
\(962\) | 26184.7 | 0.877577 | ||||||||
\(963\) | 13803.1 | 0.461889 | ||||||||
\(964\) | 11543.1 | 0.385661 | ||||||||
\(965\) | −11603.5 | −0.387079 | ||||||||
\(966\) | 189.486 | 0.00631119 | ||||||||
\(967\) | 27803.5 | 0.924612 | 0.462306 | − | 0.886720i | \(-0.347022\pi\) | ||||
0.462306 | + | 0.886720i | \(0.347022\pi\) | |||||||
\(968\) | −10608.0 | −0.352227 | ||||||||
\(969\) | 51.3876 | 0.00170362 | ||||||||
\(970\) | −49970.1 | −1.65407 | ||||||||
\(971\) | −11564.0 | −0.382189 | −0.191095 | − | 0.981572i | \(-0.561204\pi\) | ||||
−0.191095 | + | 0.981572i | \(0.561204\pi\) | |||||||
\(972\) | 972.000 | 0.0320750 | ||||||||
\(973\) | −21200.9 | −0.698531 | ||||||||
\(974\) | −32885.2 | −1.08184 | ||||||||
\(975\) | 76519.4 | 2.51342 | ||||||||
\(976\) | 1477.65 | 0.0484615 | ||||||||
\(977\) | 17409.6 | 0.570096 | 0.285048 | − | 0.958513i | \(-0.407990\pi\) | ||||
0.285048 | + | 0.958513i | \(0.407990\pi\) | |||||||
\(978\) | 9662.02 | 0.315907 | ||||||||
\(979\) | −1951.25 | −0.0636998 | ||||||||
\(980\) | 18806.3 | 0.613005 | ||||||||
\(981\) | 2314.15 | 0.0753162 | ||||||||
\(982\) | −25720.7 | −0.835826 | ||||||||
\(983\) | 10174.2 | 0.330120 | 0.165060 | − | 0.986284i | \(-0.447218\pi\) | ||||
0.165060 | + | 0.986284i | \(0.447218\pi\) | |||||||
\(984\) | −4715.65 | −0.152774 | ||||||||
\(985\) | 15392.4 | 0.497912 | ||||||||
\(986\) | 8055.54 | 0.260183 | ||||||||
\(987\) | 4203.83 | 0.135572 | ||||||||
\(988\) | 97.4304 | 0.00313732 | ||||||||
\(989\) | 909.258 | 0.0292343 | ||||||||
\(990\) | 827.529 | 0.0265663 | ||||||||
\(991\) | 22501.5 | 0.721274 | 0.360637 | − | 0.932706i | \(-0.382559\pi\) | ||||
0.360637 | + | 0.932706i | \(0.382559\pi\) | |||||||
\(992\) | 3557.44 | 0.113860 | ||||||||
\(993\) | 14363.3 | 0.459017 | ||||||||
\(994\) | −10397.8 | −0.331788 | ||||||||
\(995\) | 6966.64 | 0.221967 | ||||||||
\(996\) | 15058.6 | 0.479065 | ||||||||
\(997\) | −15746.2 | −0.500187 | −0.250093 | − | 0.968222i | \(-0.580461\pi\) | ||||
−0.250093 | + | 0.968222i | \(0.580461\pi\) | |||||||
\(998\) | −6487.56 | −0.205772 | ||||||||
\(999\) | 4131.96 | 0.130860 |
(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 | 354.4.a.i.1.1 | ✓ | 6 | |
3.2 | odd | 2 | 1062.4.a.s.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
354.4.a.i.1.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
1062.4.a.s.1.6 | 6 | 3.2 | odd | 2 |