Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,4,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, 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("177.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(10.4433380710\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 34x^{5} + 25x^{4} + 315x^{3} - 146x^{2} - 736x + 512 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.58179\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.58179 | −1.61991 | −0.809954 | − | 0.586494i | \(-0.800508\pi\) | ||||
−0.809954 | + | 0.586494i | \(0.800508\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 12.9928 | 1.62410 | ||||||||
\(5\) | −12.2965 | −1.09983 | −0.549917 | − | 0.835219i | \(-0.685341\pi\) | ||||
−0.549917 | + | 0.835219i | \(0.685341\pi\) | |||||||
\(6\) | −13.7454 | −0.935254 | ||||||||
\(7\) | 15.3493 | 0.828784 | 0.414392 | − | 0.910098i | \(-0.363994\pi\) | ||||
0.414392 | + | 0.910098i | \(0.363994\pi\) | |||||||
\(8\) | −22.8759 | −1.01098 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 56.3401 | 1.78163 | ||||||||
\(11\) | −41.7826 | −1.14527 | −0.572633 | − | 0.819812i | \(-0.694078\pi\) | ||||
−0.572633 | + | 0.819812i | \(0.694078\pi\) | |||||||
\(12\) | 38.9784 | 0.937674 | ||||||||
\(13\) | −23.4975 | −0.501310 | −0.250655 | − | 0.968077i | \(-0.580646\pi\) | ||||
−0.250655 | + | 0.968077i | \(0.580646\pi\) | |||||||
\(14\) | −70.3273 | −1.34255 | ||||||||
\(15\) | −36.8896 | −0.634990 | ||||||||
\(16\) | 0.870331 | 0.0135989 | ||||||||
\(17\) | 123.900 | 1.76766 | 0.883832 | − | 0.467805i | \(-0.154955\pi\) | ||||
0.883832 | + | 0.467805i | \(0.154955\pi\) | |||||||
\(18\) | −41.2361 | −0.539969 | ||||||||
\(19\) | 106.282 | 1.28330 | 0.641651 | − | 0.766996i | \(-0.278250\pi\) | ||||
0.641651 | + | 0.766996i | \(0.278250\pi\) | |||||||
\(20\) | −159.766 | −1.78624 | ||||||||
\(21\) | 46.0479 | 0.478499 | ||||||||
\(22\) | 191.439 | 1.85523 | ||||||||
\(23\) | −207.156 | −1.87804 | −0.939021 | − | 0.343860i | \(-0.888265\pi\) | ||||
−0.939021 | + | 0.343860i | \(0.888265\pi\) | |||||||
\(24\) | −68.6278 | −0.583691 | ||||||||
\(25\) | 26.2045 | 0.209636 | ||||||||
\(26\) | 107.660 | 0.812075 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 199.430 | 1.34603 | ||||||||
\(29\) | −53.4048 | −0.341966 | −0.170983 | − | 0.985274i | \(-0.554694\pi\) | ||||
−0.170983 | + | 0.985274i | \(0.554694\pi\) | |||||||
\(30\) | 169.020 | 1.02862 | ||||||||
\(31\) | −252.361 | −1.46211 | −0.731054 | − | 0.682319i | \(-0.760971\pi\) | ||||
−0.731054 | + | 0.682319i | \(0.760971\pi\) | |||||||
\(32\) | 179.020 | 0.988954 | ||||||||
\(33\) | −125.348 | −0.661220 | ||||||||
\(34\) | −567.686 | −2.86345 | ||||||||
\(35\) | −188.743 | −0.911525 | ||||||||
\(36\) | 116.935 | 0.541366 | ||||||||
\(37\) | −357.560 | −1.58872 | −0.794359 | − | 0.607449i | \(-0.792193\pi\) | ||||
−0.794359 | + | 0.607449i | \(0.792193\pi\) | |||||||
\(38\) | −486.962 | −2.07883 | ||||||||
\(39\) | −70.4924 | −0.289431 | ||||||||
\(40\) | 281.294 | 1.11191 | ||||||||
\(41\) | −353.220 | −1.34545 | −0.672727 | − | 0.739891i | \(-0.734877\pi\) | ||||
−0.672727 | + | 0.739891i | \(0.734877\pi\) | |||||||
\(42\) | −210.982 | −0.775124 | ||||||||
\(43\) | −80.6872 | −0.286155 | −0.143078 | − | 0.989711i | \(-0.545700\pi\) | ||||
−0.143078 | + | 0.989711i | \(0.545700\pi\) | |||||||
\(44\) | −542.873 | −1.86003 | ||||||||
\(45\) | −110.669 | −0.366611 | ||||||||
\(46\) | 949.144 | 3.04225 | ||||||||
\(47\) | −5.12471 | −0.0159046 | −0.00795229 | − | 0.999968i | \(-0.502531\pi\) | ||||
−0.00795229 | + | 0.999968i | \(0.502531\pi\) | |||||||
\(48\) | 2.61099 | 0.00785134 | ||||||||
\(49\) | −107.399 | −0.313117 | ||||||||
\(50\) | −120.063 | −0.339591 | ||||||||
\(51\) | 371.701 | 1.02056 | ||||||||
\(52\) | −305.298 | −0.814176 | ||||||||
\(53\) | −260.709 | −0.675681 | −0.337841 | − | 0.941203i | \(-0.609697\pi\) | ||||
−0.337841 | + | 0.941203i | \(0.609697\pi\) | |||||||
\(54\) | −123.708 | −0.311751 | ||||||||
\(55\) | 513.781 | 1.25960 | ||||||||
\(56\) | −351.129 | −0.837887 | ||||||||
\(57\) | 318.846 | 0.740915 | ||||||||
\(58\) | 244.689 | 0.553953 | ||||||||
\(59\) | −59.0000 | −0.130189 | ||||||||
\(60\) | −479.299 | −1.03129 | ||||||||
\(61\) | 35.7406 | 0.0750182 | 0.0375091 | − | 0.999296i | \(-0.488058\pi\) | ||||
0.0375091 | + | 0.999296i | \(0.488058\pi\) | |||||||
\(62\) | 1156.26 | 2.36848 | ||||||||
\(63\) | 138.144 | 0.276261 | ||||||||
\(64\) | −827.193 | −1.61561 | ||||||||
\(65\) | 288.937 | 0.551358 | ||||||||
\(66\) | 574.318 | 1.07112 | ||||||||
\(67\) | 635.590 | 1.15895 | 0.579475 | − | 0.814990i | \(-0.303258\pi\) | ||||
0.579475 | + | 0.814990i | \(0.303258\pi\) | |||||||
\(68\) | 1609.81 | 2.87086 | ||||||||
\(69\) | −621.467 | −1.08429 | ||||||||
\(70\) | 864.781 | 1.47659 | ||||||||
\(71\) | −644.029 | −1.07651 | −0.538255 | − | 0.842782i | \(-0.680916\pi\) | ||||
−0.538255 | + | 0.842782i | \(0.680916\pi\) | |||||||
\(72\) | −205.883 | −0.336994 | ||||||||
\(73\) | −531.586 | −0.852293 | −0.426147 | − | 0.904654i | \(-0.640129\pi\) | ||||
−0.426147 | + | 0.904654i | \(0.640129\pi\) | |||||||
\(74\) | 1638.27 | 2.57357 | ||||||||
\(75\) | 78.6134 | 0.121033 | ||||||||
\(76\) | 1380.90 | 2.08421 | ||||||||
\(77\) | −641.334 | −0.949179 | ||||||||
\(78\) | 322.981 | 0.468852 | ||||||||
\(79\) | 594.860 | 0.847176 | 0.423588 | − | 0.905855i | \(-0.360770\pi\) | ||||
0.423588 | + | 0.905855i | \(0.360770\pi\) | |||||||
\(80\) | −10.7020 | −0.0149566 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 1618.38 | 2.17951 | ||||||||
\(83\) | −95.7821 | −0.126668 | −0.0633340 | − | 0.997992i | \(-0.520173\pi\) | ||||
−0.0633340 | + | 0.997992i | \(0.520173\pi\) | |||||||
\(84\) | 598.291 | 0.777129 | ||||||||
\(85\) | −1523.54 | −1.94414 | ||||||||
\(86\) | 369.692 | 0.463545 | ||||||||
\(87\) | −160.214 | −0.197434 | ||||||||
\(88\) | 955.816 | 1.15784 | ||||||||
\(89\) | 1002.86 | 1.19442 | 0.597208 | − | 0.802086i | \(-0.296277\pi\) | ||||
0.597208 | + | 0.802086i | \(0.296277\pi\) | |||||||
\(90\) | 507.061 | 0.593877 | ||||||||
\(91\) | −360.670 | −0.415477 | ||||||||
\(92\) | −2691.53 | −3.05013 | ||||||||
\(93\) | −757.083 | −0.844149 | ||||||||
\(94\) | 23.4803 | 0.0257639 | ||||||||
\(95\) | −1306.90 | −1.41142 | ||||||||
\(96\) | 537.059 | 0.570973 | ||||||||
\(97\) | −964.276 | −1.00935 | −0.504677 | − | 0.863308i | \(-0.668388\pi\) | ||||
−0.504677 | + | 0.863308i | \(0.668388\pi\) | |||||||
\(98\) | 492.080 | 0.507220 | ||||||||
\(99\) | −376.044 | −0.381756 | ||||||||
\(100\) | 340.469 | 0.340469 | ||||||||
\(101\) | 1294.85 | 1.27567 | 0.637835 | − | 0.770173i | \(-0.279830\pi\) | ||||
0.637835 | + | 0.770173i | \(0.279830\pi\) | |||||||
\(102\) | −1703.06 | −1.65321 | ||||||||
\(103\) | 17.3037 | 0.0165533 | 0.00827663 | − | 0.999966i | \(-0.497365\pi\) | ||||
0.00827663 | + | 0.999966i | \(0.497365\pi\) | |||||||
\(104\) | 537.526 | 0.506815 | ||||||||
\(105\) | −566.229 | −0.526269 | ||||||||
\(106\) | 1194.51 | 1.09454 | ||||||||
\(107\) | 267.634 | 0.241805 | 0.120903 | − | 0.992664i | \(-0.461421\pi\) | ||||
0.120903 | + | 0.992664i | \(0.461421\pi\) | |||||||
\(108\) | 350.805 | 0.312558 | ||||||||
\(109\) | −179.027 | −0.157318 | −0.0786591 | − | 0.996902i | \(-0.525064\pi\) | ||||
−0.0786591 | + | 0.996902i | \(0.525064\pi\) | |||||||
\(110\) | −2354.04 | −2.04044 | ||||||||
\(111\) | −1072.68 | −0.917246 | ||||||||
\(112\) | 13.3590 | 0.0112706 | ||||||||
\(113\) | −694.415 | −0.578098 | −0.289049 | − | 0.957314i | \(-0.593339\pi\) | ||||
−0.289049 | + | 0.957314i | \(0.593339\pi\) | |||||||
\(114\) | −1460.88 | −1.20021 | ||||||||
\(115\) | 2547.30 | 2.06553 | ||||||||
\(116\) | −693.877 | −0.555387 | ||||||||
\(117\) | −211.477 | −0.167103 | ||||||||
\(118\) | 270.326 | 0.210894 | ||||||||
\(119\) | 1901.78 | 1.46501 | ||||||||
\(120\) | 843.883 | 0.641964 | ||||||||
\(121\) | 414.788 | 0.311636 | ||||||||
\(122\) | −163.756 | −0.121523 | ||||||||
\(123\) | −1059.66 | −0.776799 | ||||||||
\(124\) | −3278.87 | −2.37461 | ||||||||
\(125\) | 1214.84 | 0.869270 | ||||||||
\(126\) | −632.945 | −0.447518 | ||||||||
\(127\) | −1929.31 | −1.34802 | −0.674010 | − | 0.738722i | \(-0.735430\pi\) | ||||
−0.674010 | + | 0.738722i | \(0.735430\pi\) | |||||||
\(128\) | 2357.87 | 1.62819 | ||||||||
\(129\) | −242.062 | −0.165212 | ||||||||
\(130\) | −1323.85 | −0.893148 | ||||||||
\(131\) | 2118.62 | 1.41301 | 0.706506 | − | 0.707707i | \(-0.250270\pi\) | ||||
0.706506 | + | 0.707707i | \(0.250270\pi\) | |||||||
\(132\) | −1628.62 | −1.07389 | ||||||||
\(133\) | 1631.35 | 1.06358 | ||||||||
\(134\) | −2912.14 | −1.87739 | ||||||||
\(135\) | −332.006 | −0.211663 | ||||||||
\(136\) | −2834.34 | −1.78708 | ||||||||
\(137\) | 318.864 | 0.198850 | 0.0994249 | − | 0.995045i | \(-0.468300\pi\) | ||||
0.0994249 | + | 0.995045i | \(0.468300\pi\) | |||||||
\(138\) | 2847.43 | 1.75645 | ||||||||
\(139\) | 2310.92 | 1.41014 | 0.705070 | − | 0.709138i | \(-0.250916\pi\) | ||||
0.705070 | + | 0.709138i | \(0.250916\pi\) | |||||||
\(140\) | −2452.30 | −1.48041 | ||||||||
\(141\) | −15.3741 | −0.00918251 | ||||||||
\(142\) | 2950.81 | 1.74385 | ||||||||
\(143\) | 981.786 | 0.574133 | ||||||||
\(144\) | 7.83298 | 0.00453297 | ||||||||
\(145\) | 656.693 | 0.376106 | ||||||||
\(146\) | 2435.61 | 1.38064 | ||||||||
\(147\) | −322.197 | −0.180778 | ||||||||
\(148\) | −4645.71 | −2.58023 | ||||||||
\(149\) | −1168.54 | −0.642485 | −0.321243 | − | 0.946997i | \(-0.604101\pi\) | ||||
−0.321243 | + | 0.946997i | \(0.604101\pi\) | |||||||
\(150\) | −360.190 | −0.196063 | ||||||||
\(151\) | −1537.12 | −0.828402 | −0.414201 | − | 0.910186i | \(-0.635939\pi\) | ||||
−0.414201 | + | 0.910186i | \(0.635939\pi\) | |||||||
\(152\) | −2431.30 | −1.29740 | ||||||||
\(153\) | 1115.10 | 0.589221 | ||||||||
\(154\) | 2938.46 | 1.53758 | ||||||||
\(155\) | 3103.16 | 1.60808 | ||||||||
\(156\) | −915.893 | −0.470065 | ||||||||
\(157\) | −2351.07 | −1.19513 | −0.597565 | − | 0.801820i | \(-0.703865\pi\) | ||||
−0.597565 | + | 0.801820i | \(0.703865\pi\) | |||||||
\(158\) | −2725.52 | −1.37235 | ||||||||
\(159\) | −782.127 | −0.390105 | ||||||||
\(160\) | −2201.32 | −1.08769 | ||||||||
\(161\) | −3179.70 | −1.55649 | ||||||||
\(162\) | −371.125 | −0.179990 | ||||||||
\(163\) | −2755.11 | −1.32391 | −0.661954 | − | 0.749545i | \(-0.730272\pi\) | ||||
−0.661954 | + | 0.749545i | \(0.730272\pi\) | |||||||
\(164\) | −4589.31 | −2.18515 | ||||||||
\(165\) | 1541.34 | 0.727233 | ||||||||
\(166\) | 438.853 | 0.205190 | ||||||||
\(167\) | −3741.97 | −1.73390 | −0.866952 | − | 0.498391i | \(-0.833924\pi\) | ||||
−0.866952 | + | 0.498391i | \(0.833924\pi\) | |||||||
\(168\) | −1053.39 | −0.483754 | ||||||||
\(169\) | −1644.87 | −0.748689 | ||||||||
\(170\) | 6980.56 | 3.14932 | ||||||||
\(171\) | 956.538 | 0.427768 | ||||||||
\(172\) | −1048.35 | −0.464745 | ||||||||
\(173\) | 3970.75 | 1.74503 | 0.872515 | − | 0.488587i | \(-0.162487\pi\) | ||||
0.872515 | + | 0.488587i | \(0.162487\pi\) | |||||||
\(174\) | 734.068 | 0.319825 | ||||||||
\(175\) | 402.220 | 0.173743 | ||||||||
\(176\) | −36.3647 | −0.0155744 | ||||||||
\(177\) | −177.000 | −0.0751646 | ||||||||
\(178\) | −4594.90 | −1.93484 | ||||||||
\(179\) | 1322.29 | 0.552139 | 0.276070 | − | 0.961138i | \(-0.410968\pi\) | ||||
0.276070 | + | 0.961138i | \(0.410968\pi\) | |||||||
\(180\) | −1437.90 | −0.595413 | ||||||||
\(181\) | 3244.93 | 1.33256 | 0.666280 | − | 0.745701i | \(-0.267885\pi\) | ||||
0.666280 | + | 0.745701i | \(0.267885\pi\) | |||||||
\(182\) | 1652.51 | 0.673035 | ||||||||
\(183\) | 107.222 | 0.0433118 | ||||||||
\(184\) | 4738.88 | 1.89867 | ||||||||
\(185\) | 4396.75 | 1.74733 | ||||||||
\(186\) | 3468.79 | 1.36744 | ||||||||
\(187\) | −5176.89 | −2.02445 | ||||||||
\(188\) | −66.5842 | −0.0258306 | ||||||||
\(189\) | 414.431 | 0.159500 | ||||||||
\(190\) | 5987.93 | 2.28637 | ||||||||
\(191\) | 1496.99 | 0.567110 | 0.283555 | − | 0.958956i | \(-0.408486\pi\) | ||||
0.283555 | + | 0.958956i | \(0.408486\pi\) | |||||||
\(192\) | −2481.58 | −0.932774 | ||||||||
\(193\) | 219.504 | 0.0818665 | 0.0409333 | − | 0.999162i | \(-0.486967\pi\) | ||||
0.0409333 | + | 0.999162i | \(0.486967\pi\) | |||||||
\(194\) | 4418.11 | 1.63506 | ||||||||
\(195\) | 866.811 | 0.318326 | ||||||||
\(196\) | −1395.41 | −0.508533 | ||||||||
\(197\) | 740.027 | 0.267638 | 0.133819 | − | 0.991006i | \(-0.457276\pi\) | ||||
0.133819 | + | 0.991006i | \(0.457276\pi\) | |||||||
\(198\) | 1722.95 | 0.618409 | ||||||||
\(199\) | 2138.04 | 0.761617 | 0.380808 | − | 0.924654i | \(-0.375646\pi\) | ||||
0.380808 | + | 0.924654i | \(0.375646\pi\) | |||||||
\(200\) | −599.452 | −0.211938 | ||||||||
\(201\) | 1906.77 | 0.669120 | ||||||||
\(202\) | −5932.74 | −2.06647 | ||||||||
\(203\) | −819.726 | −0.283416 | ||||||||
\(204\) | 4829.44 | 1.65749 | ||||||||
\(205\) | 4343.37 | 1.47978 | ||||||||
\(206\) | −79.2820 | −0.0268147 | ||||||||
\(207\) | −1864.40 | −0.626014 | ||||||||
\(208\) | −20.4506 | −0.00681727 | ||||||||
\(209\) | −4440.74 | −1.46972 | ||||||||
\(210\) | 2594.34 | 0.852508 | ||||||||
\(211\) | −510.304 | −0.166497 | −0.0832483 | − | 0.996529i | \(-0.526529\pi\) | ||||
−0.0832483 | + | 0.996529i | \(0.526529\pi\) | |||||||
\(212\) | −3387.34 | −1.09737 | ||||||||
\(213\) | −1932.09 | −0.621524 | ||||||||
\(214\) | −1226.24 | −0.391702 | ||||||||
\(215\) | 992.172 | 0.314723 | ||||||||
\(216\) | −617.650 | −0.194564 | ||||||||
\(217\) | −3873.56 | −1.21177 | ||||||||
\(218\) | 820.264 | 0.254841 | ||||||||
\(219\) | −1594.76 | −0.492072 | ||||||||
\(220\) | 6675.45 | 2.04572 | ||||||||
\(221\) | −2911.35 | −0.886146 | ||||||||
\(222\) | 4914.80 | 1.48585 | ||||||||
\(223\) | −2449.19 | −0.735469 | −0.367735 | − | 0.929931i | \(-0.619867\pi\) | ||||
−0.367735 | + | 0.929931i | \(0.619867\pi\) | |||||||
\(224\) | 2747.83 | 0.819629 | ||||||||
\(225\) | 235.840 | 0.0698786 | ||||||||
\(226\) | 3181.66 | 0.936465 | ||||||||
\(227\) | −185.296 | −0.0541786 | −0.0270893 | − | 0.999633i | \(-0.508624\pi\) | ||||
−0.0270893 | + | 0.999633i | \(0.508624\pi\) | |||||||
\(228\) | 4142.70 | 1.20332 | ||||||||
\(229\) | 6185.66 | 1.78498 | 0.892488 | − | 0.451071i | \(-0.148958\pi\) | ||||
0.892488 | + | 0.451071i | \(0.148958\pi\) | |||||||
\(230\) | −11671.2 | −3.34597 | ||||||||
\(231\) | −1924.00 | −0.548009 | ||||||||
\(232\) | 1221.68 | 0.345722 | ||||||||
\(233\) | −4695.37 | −1.32019 | −0.660094 | − | 0.751183i | \(-0.729484\pi\) | ||||
−0.660094 | + | 0.751183i | \(0.729484\pi\) | |||||||
\(234\) | 968.944 | 0.270692 | ||||||||
\(235\) | 63.0161 | 0.0174924 | ||||||||
\(236\) | −766.575 | −0.211440 | ||||||||
\(237\) | 1784.58 | 0.489117 | ||||||||
\(238\) | −8713.58 | −2.37318 | ||||||||
\(239\) | −3690.23 | −0.998748 | −0.499374 | − | 0.866386i | \(-0.666437\pi\) | ||||
−0.499374 | + | 0.866386i | \(0.666437\pi\) | |||||||
\(240\) | −32.1061 | −0.00863518 | ||||||||
\(241\) | −129.939 | −0.0347307 | −0.0173654 | − | 0.999849i | \(-0.505528\pi\) | ||||
−0.0173654 | + | 0.999849i | \(0.505528\pi\) | |||||||
\(242\) | −1900.47 | −0.504822 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 464.370 | 0.121837 | ||||||||
\(245\) | 1320.63 | 0.344377 | ||||||||
\(246\) | 4855.13 | 1.25834 | ||||||||
\(247\) | −2497.36 | −0.643332 | ||||||||
\(248\) | 5772.99 | 1.47817 | ||||||||
\(249\) | −287.346 | −0.0731318 | ||||||||
\(250\) | −5566.15 | −1.40814 | ||||||||
\(251\) | −921.958 | −0.231846 | −0.115923 | − | 0.993258i | \(-0.536983\pi\) | ||||
−0.115923 | + | 0.993258i | \(0.536983\pi\) | |||||||
\(252\) | 1794.87 | 0.448676 | ||||||||
\(253\) | 8655.51 | 2.15086 | ||||||||
\(254\) | 8839.69 | 2.18367 | ||||||||
\(255\) | −4570.63 | −1.12245 | ||||||||
\(256\) | −4185.71 | −1.02190 | ||||||||
\(257\) | 2067.03 | 0.501704 | 0.250852 | − | 0.968026i | \(-0.419289\pi\) | ||||
0.250852 | + | 0.968026i | \(0.419289\pi\) | |||||||
\(258\) | 1109.07 | 0.267628 | ||||||||
\(259\) | −5488.30 | −1.31670 | ||||||||
\(260\) | 3754.10 | 0.895459 | ||||||||
\(261\) | −480.643 | −0.113989 | ||||||||
\(262\) | −9707.07 | −2.28895 | ||||||||
\(263\) | 4434.33 | 1.03967 | 0.519833 | − | 0.854268i | \(-0.325994\pi\) | ||||
0.519833 | + | 0.854268i | \(0.325994\pi\) | |||||||
\(264\) | 2867.45 | 0.668482 | ||||||||
\(265\) | 3205.81 | 0.743138 | ||||||||
\(266\) | −7474.52 | −1.72290 | ||||||||
\(267\) | 3008.58 | 0.689596 | ||||||||
\(268\) | 8258.09 | 1.88225 | ||||||||
\(269\) | 2401.90 | 0.544410 | 0.272205 | − | 0.962239i | \(-0.412247\pi\) | ||||
0.272205 | + | 0.962239i | \(0.412247\pi\) | |||||||
\(270\) | 1521.18 | 0.342875 | ||||||||
\(271\) | 3740.90 | 0.838537 | 0.419268 | − | 0.907862i | \(-0.362287\pi\) | ||||
0.419268 | + | 0.907862i | \(0.362287\pi\) | |||||||
\(272\) | 107.834 | 0.0240383 | ||||||||
\(273\) | −1082.01 | −0.239876 | ||||||||
\(274\) | −1460.97 | −0.322118 | ||||||||
\(275\) | −1094.89 | −0.240089 | ||||||||
\(276\) | −8074.59 | −1.76099 | ||||||||
\(277\) | −1443.22 | −0.313049 | −0.156525 | − | 0.987674i | \(-0.550029\pi\) | ||||
−0.156525 | + | 0.987674i | \(0.550029\pi\) | |||||||
\(278\) | −10588.1 | −2.28430 | ||||||||
\(279\) | −2271.25 | −0.487370 | ||||||||
\(280\) | 4317.67 | 0.921536 | ||||||||
\(281\) | −3497.86 | −0.742580 | −0.371290 | − | 0.928517i | \(-0.621084\pi\) | ||||
−0.371290 | + | 0.928517i | \(0.621084\pi\) | |||||||
\(282\) | 70.4410 | 0.0148748 | ||||||||
\(283\) | −396.792 | −0.0833457 | −0.0416728 | − | 0.999131i | \(-0.513269\pi\) | ||||
−0.0416728 | + | 0.999131i | \(0.513269\pi\) | |||||||
\(284\) | −8367.74 | −1.74836 | ||||||||
\(285\) | −3920.70 | −0.814884 | ||||||||
\(286\) | −4498.34 | −0.930043 | ||||||||
\(287\) | −5421.67 | −1.11509 | ||||||||
\(288\) | 1611.18 | 0.329651 | ||||||||
\(289\) | 10438.3 | 2.12463 | ||||||||
\(290\) | −3008.83 | −0.609257 | ||||||||
\(291\) | −2892.83 | −0.582751 | ||||||||
\(292\) | −6906.79 | −1.38421 | ||||||||
\(293\) | 9247.65 | 1.84387 | 0.921934 | − | 0.387347i | \(-0.126609\pi\) | ||||
0.921934 | + | 0.387347i | \(0.126609\pi\) | |||||||
\(294\) | 1476.24 | 0.292844 | ||||||||
\(295\) | 725.495 | 0.143186 | ||||||||
\(296\) | 8179.52 | 1.60617 | ||||||||
\(297\) | −1128.13 | −0.220407 | ||||||||
\(298\) | 5353.99 | 1.04077 | ||||||||
\(299\) | 4867.63 | 0.941480 | ||||||||
\(300\) | 1021.41 | 0.196570 | ||||||||
\(301\) | −1238.49 | −0.237161 | ||||||||
\(302\) | 7042.74 | 1.34193 | ||||||||
\(303\) | 3884.56 | 0.736508 | ||||||||
\(304\) | 92.5005 | 0.0174515 | ||||||||
\(305\) | −439.485 | −0.0825076 | ||||||||
\(306\) | −5109.17 | −0.954483 | ||||||||
\(307\) | 5013.01 | 0.931946 | 0.465973 | − | 0.884799i | \(-0.345704\pi\) | ||||
0.465973 | + | 0.884799i | \(0.345704\pi\) | |||||||
\(308\) | −8332.72 | −1.54156 | ||||||||
\(309\) | 51.9112 | 0.00955703 | ||||||||
\(310\) | −14218.0 | −2.60494 | ||||||||
\(311\) | −6356.34 | −1.15896 | −0.579478 | − | 0.814988i | \(-0.696743\pi\) | ||||
−0.579478 | + | 0.814988i | \(0.696743\pi\) | |||||||
\(312\) | 1612.58 | 0.292610 | ||||||||
\(313\) | 1664.15 | 0.300521 | 0.150261 | − | 0.988646i | \(-0.451989\pi\) | ||||
0.150261 | + | 0.988646i | \(0.451989\pi\) | |||||||
\(314\) | 10772.1 | 1.93600 | ||||||||
\(315\) | −1698.69 | −0.303842 | ||||||||
\(316\) | 7728.89 | 1.37590 | ||||||||
\(317\) | −9467.95 | −1.67752 | −0.838759 | − | 0.544503i | \(-0.816718\pi\) | ||||
−0.838759 | + | 0.544503i | \(0.816718\pi\) | |||||||
\(318\) | 3583.54 | 0.631934 | ||||||||
\(319\) | 2231.39 | 0.391642 | ||||||||
\(320\) | 10171.6 | 1.77691 | ||||||||
\(321\) | 802.901 | 0.139606 | ||||||||
\(322\) | 14568.7 | 2.52137 | ||||||||
\(323\) | 13168.4 | 2.26845 | ||||||||
\(324\) | 1052.42 | 0.180455 | ||||||||
\(325\) | −615.739 | −0.105092 | ||||||||
\(326\) | 12623.3 | 2.14461 | ||||||||
\(327\) | −537.081 | −0.0908277 | ||||||||
\(328\) | 8080.23 | 1.36023 | ||||||||
\(329\) | −78.6606 | −0.0131815 | ||||||||
\(330\) | −7062.11 | −1.17805 | ||||||||
\(331\) | −5398.35 | −0.896436 | −0.448218 | − | 0.893924i | \(-0.647941\pi\) | ||||
−0.448218 | + | 0.893924i | \(0.647941\pi\) | |||||||
\(332\) | −1244.48 | −0.205721 | ||||||||
\(333\) | −3218.04 | −0.529572 | ||||||||
\(334\) | 17144.9 | 2.80876 | ||||||||
\(335\) | −7815.54 | −1.27465 | ||||||||
\(336\) | 40.0769 | 0.00650707 | ||||||||
\(337\) | 4793.04 | 0.774759 | 0.387379 | − | 0.921920i | \(-0.373380\pi\) | ||||
0.387379 | + | 0.921920i | \(0.373380\pi\) | |||||||
\(338\) | 7536.44 | 1.21281 | ||||||||
\(339\) | −2083.25 | −0.333765 | ||||||||
\(340\) | −19795.1 | −3.15747 | ||||||||
\(341\) | 10544.3 | 1.67450 | ||||||||
\(342\) | −4382.65 | −0.692944 | ||||||||
\(343\) | −6913.31 | −1.08829 | ||||||||
\(344\) | 1845.79 | 0.289298 | ||||||||
\(345\) | 7641.89 | 1.19254 | ||||||||
\(346\) | −18193.1 | −2.82679 | ||||||||
\(347\) | −10721.0 | −1.65860 | −0.829298 | − | 0.558806i | \(-0.811260\pi\) | ||||
−0.829298 | + | 0.558806i | \(0.811260\pi\) | |||||||
\(348\) | −2081.63 | −0.320653 | ||||||||
\(349\) | 1043.92 | 0.160114 | 0.0800571 | − | 0.996790i | \(-0.474490\pi\) | ||||
0.0800571 | + | 0.996790i | \(0.474490\pi\) | |||||||
\(350\) | −1842.89 | −0.281447 | ||||||||
\(351\) | −634.432 | −0.0964771 | ||||||||
\(352\) | −7479.91 | −1.13262 | ||||||||
\(353\) | −9834.72 | −1.48286 | −0.741429 | − | 0.671031i | \(-0.765852\pi\) | ||||
−0.741429 | + | 0.671031i | \(0.765852\pi\) | |||||||
\(354\) | 810.977 | 0.121760 | ||||||||
\(355\) | 7919.32 | 1.18398 | ||||||||
\(356\) | 13030.0 | 1.93985 | ||||||||
\(357\) | 5705.35 | 0.845825 | ||||||||
\(358\) | −6058.48 | −0.894414 | ||||||||
\(359\) | 9944.23 | 1.46194 | 0.730970 | − | 0.682409i | \(-0.239068\pi\) | ||||
0.730970 | + | 0.682409i | \(0.239068\pi\) | |||||||
\(360\) | 2531.65 | 0.370638 | ||||||||
\(361\) | 4436.85 | 0.646866 | ||||||||
\(362\) | −14867.6 | −2.15862 | ||||||||
\(363\) | 1244.36 | 0.179923 | ||||||||
\(364\) | −4686.11 | −0.674777 | ||||||||
\(365\) | 6536.66 | 0.937382 | ||||||||
\(366\) | −491.267 | −0.0701611 | ||||||||
\(367\) | 8177.88 | 1.16317 | 0.581583 | − | 0.813487i | \(-0.302433\pi\) | ||||
0.581583 | + | 0.813487i | \(0.302433\pi\) | |||||||
\(368\) | −180.294 | −0.0255393 | ||||||||
\(369\) | −3178.98 | −0.448485 | ||||||||
\(370\) | −20145.0 | −2.83051 | ||||||||
\(371\) | −4001.70 | −0.559994 | ||||||||
\(372\) | −9836.62 | −1.37098 | ||||||||
\(373\) | −5263.36 | −0.730633 | −0.365317 | − | 0.930883i | \(-0.619039\pi\) | ||||
−0.365317 | + | 0.930883i | \(0.619039\pi\) | |||||||
\(374\) | 23719.4 | 3.27941 | ||||||||
\(375\) | 3644.52 | 0.501873 | ||||||||
\(376\) | 117.232 | 0.0160793 | ||||||||
\(377\) | 1254.88 | 0.171431 | ||||||||
\(378\) | −1898.84 | −0.258375 | ||||||||
\(379\) | −1581.26 | −0.214310 | −0.107155 | − | 0.994242i | \(-0.534174\pi\) | ||||
−0.107155 | + | 0.994242i | \(0.534174\pi\) | |||||||
\(380\) | −16980.3 | −2.29229 | ||||||||
\(381\) | −5787.93 | −0.778280 | ||||||||
\(382\) | −6858.87 | −0.918666 | ||||||||
\(383\) | 18.1202 | 0.00241749 | 0.00120875 | − | 0.999999i | \(-0.499615\pi\) | ||||
0.00120875 | + | 0.999999i | \(0.499615\pi\) | |||||||
\(384\) | 7073.60 | 0.940035 | ||||||||
\(385\) | 7886.18 | 1.04394 | ||||||||
\(386\) | −1005.72 | −0.132616 | ||||||||
\(387\) | −726.185 | −0.0953851 | ||||||||
\(388\) | −12528.6 | −1.63929 | ||||||||
\(389\) | −7475.52 | −0.974354 | −0.487177 | − | 0.873303i | \(-0.661973\pi\) | ||||
−0.487177 | + | 0.873303i | \(0.661973\pi\) | |||||||
\(390\) | −3971.55 | −0.515659 | ||||||||
\(391\) | −25666.7 | −3.31974 | ||||||||
\(392\) | 2456.85 | 0.316556 | ||||||||
\(393\) | 6355.86 | 0.815803 | ||||||||
\(394\) | −3390.65 | −0.433549 | ||||||||
\(395\) | −7314.70 | −0.931754 | ||||||||
\(396\) | −4885.86 | −0.620009 | ||||||||
\(397\) | −8078.60 | −1.02129 | −0.510647 | − | 0.859791i | \(-0.670594\pi\) | ||||
−0.510647 | + | 0.859791i | \(0.670594\pi\) | |||||||
\(398\) | −9796.06 | −1.23375 | ||||||||
\(399\) | 4894.06 | 0.614059 | ||||||||
\(400\) | 22.8066 | 0.00285082 | ||||||||
\(401\) | 1634.60 | 0.203561 | 0.101781 | − | 0.994807i | \(-0.467546\pi\) | ||||
0.101781 | + | 0.994807i | \(0.467546\pi\) | |||||||
\(402\) | −8736.42 | −1.08391 | ||||||||
\(403\) | 5929.84 | 0.732969 | ||||||||
\(404\) | 16823.7 | 2.07181 | ||||||||
\(405\) | −996.018 | −0.122204 | ||||||||
\(406\) | 3755.81 | 0.459108 | ||||||||
\(407\) | 14939.8 | 1.81951 | ||||||||
\(408\) | −8503.01 | −1.03177 | ||||||||
\(409\) | −2121.07 | −0.256430 | −0.128215 | − | 0.991746i | \(-0.540925\pi\) | ||||
−0.128215 | + | 0.991746i | \(0.540925\pi\) | |||||||
\(410\) | −19900.4 | −2.39710 | ||||||||
\(411\) | 956.593 | 0.114806 | ||||||||
\(412\) | 224.824 | 0.0268841 | ||||||||
\(413\) | −905.609 | −0.107899 | ||||||||
\(414\) | 8542.30 | 1.01408 | ||||||||
\(415\) | 1177.79 | 0.139314 | ||||||||
\(416\) | −4206.51 | −0.495772 | ||||||||
\(417\) | 6932.75 | 0.814145 | ||||||||
\(418\) | 20346.5 | 2.38082 | ||||||||
\(419\) | −14819.7 | −1.72790 | −0.863950 | − | 0.503577i | \(-0.832017\pi\) | ||||
−0.863950 | + | 0.503577i | \(0.832017\pi\) | |||||||
\(420\) | −7356.90 | −0.854714 | ||||||||
\(421\) | 5226.64 | 0.605061 | 0.302531 | − | 0.953140i | \(-0.402169\pi\) | ||||
0.302531 | + | 0.953140i | \(0.402169\pi\) | |||||||
\(422\) | 2338.10 | 0.269709 | ||||||||
\(423\) | −46.1223 | −0.00530153 | ||||||||
\(424\) | 5963.96 | 0.683102 | ||||||||
\(425\) | 3246.75 | 0.370565 | ||||||||
\(426\) | 8852.42 | 1.00681 | ||||||||
\(427\) | 548.593 | 0.0621739 | ||||||||
\(428\) | 3477.31 | 0.392715 | ||||||||
\(429\) | 2945.36 | 0.331476 | ||||||||
\(430\) | −4545.92 | −0.509823 | ||||||||
\(431\) | −10926.6 | −1.22115 | −0.610577 | − | 0.791957i | \(-0.709063\pi\) | ||||
−0.610577 | + | 0.791957i | \(0.709063\pi\) | |||||||
\(432\) | 23.4989 | 0.00261711 | ||||||||
\(433\) | 3172.98 | 0.352157 | 0.176078 | − | 0.984376i | \(-0.443659\pi\) | ||||
0.176078 | + | 0.984376i | \(0.443659\pi\) | |||||||
\(434\) | 17747.9 | 1.96296 | ||||||||
\(435\) | 1970.08 | 0.217145 | ||||||||
\(436\) | −2326.06 | −0.255500 | ||||||||
\(437\) | −22016.9 | −2.41010 | ||||||||
\(438\) | 7306.84 | 0.797111 | ||||||||
\(439\) | 2162.68 | 0.235123 | 0.117562 | − | 0.993066i | \(-0.462492\pi\) | ||||
0.117562 | + | 0.993066i | \(0.462492\pi\) | |||||||
\(440\) | −11753.2 | −1.27344 | ||||||||
\(441\) | −966.591 | −0.104372 | ||||||||
\(442\) | 13339.2 | 1.43547 | ||||||||
\(443\) | −10270.6 | −1.10152 | −0.550760 | − | 0.834664i | \(-0.685662\pi\) | ||||
−0.550760 | + | 0.834664i | \(0.685662\pi\) | |||||||
\(444\) | −13937.1 | −1.48970 | ||||||||
\(445\) | −12331.7 | −1.31366 | ||||||||
\(446\) | 11221.7 | 1.19139 | ||||||||
\(447\) | −3505.61 | −0.370939 | ||||||||
\(448\) | −12696.8 | −1.33899 | ||||||||
\(449\) | −3822.43 | −0.401763 | −0.200882 | − | 0.979616i | \(-0.564381\pi\) | ||||
−0.200882 | + | 0.979616i | \(0.564381\pi\) | |||||||
\(450\) | −1080.57 | −0.113197 | ||||||||
\(451\) | 14758.4 | 1.54090 | ||||||||
\(452\) | −9022.39 | −0.938889 | ||||||||
\(453\) | −4611.35 | −0.478278 | ||||||||
\(454\) | 848.989 | 0.0877644 | ||||||||
\(455\) | 4434.98 | 0.456956 | ||||||||
\(456\) | −7293.89 | −0.749052 | ||||||||
\(457\) | 16654.3 | 1.70471 | 0.852357 | − | 0.522961i | \(-0.175173\pi\) | ||||
0.852357 | + | 0.522961i | \(0.175173\pi\) | |||||||
\(458\) | −28341.4 | −2.89150 | ||||||||
\(459\) | 3345.31 | 0.340187 | ||||||||
\(460\) | 33096.5 | 3.35463 | ||||||||
\(461\) | 14478.5 | 1.46276 | 0.731378 | − | 0.681972i | \(-0.238878\pi\) | ||||
0.731378 | + | 0.681972i | \(0.238878\pi\) | |||||||
\(462\) | 8815.37 | 0.887723 | ||||||||
\(463\) | −11106.8 | −1.11485 | −0.557425 | − | 0.830227i | \(-0.688211\pi\) | ||||
−0.557425 | + | 0.830227i | \(0.688211\pi\) | |||||||
\(464\) | −46.4798 | −0.00465037 | ||||||||
\(465\) | 9309.49 | 0.928424 | ||||||||
\(466\) | 21513.2 | 2.13858 | ||||||||
\(467\) | 18099.7 | 1.79347 | 0.896737 | − | 0.442563i | \(-0.145931\pi\) | ||||
0.896737 | + | 0.442563i | \(0.145931\pi\) | |||||||
\(468\) | −2747.68 | −0.271392 | ||||||||
\(469\) | 9755.86 | 0.960519 | ||||||||
\(470\) | −288.726 | −0.0283361 | ||||||||
\(471\) | −7053.20 | −0.690009 | ||||||||
\(472\) | 1349.68 | 0.131619 | ||||||||
\(473\) | 3371.32 | 0.327724 | ||||||||
\(474\) | −8176.56 | −0.792325 | ||||||||
\(475\) | 2785.06 | 0.269026 | ||||||||
\(476\) | 24709.5 | 2.37932 | ||||||||
\(477\) | −2346.38 | −0.225227 | ||||||||
\(478\) | 16907.8 | 1.61788 | ||||||||
\(479\) | −15597.9 | −1.48787 | −0.743933 | − | 0.668255i | \(-0.767042\pi\) | ||||
−0.743933 | + | 0.668255i | \(0.767042\pi\) | |||||||
\(480\) | −6603.96 | −0.627975 | ||||||||
\(481\) | 8401.76 | 0.796439 | ||||||||
\(482\) | 595.353 | 0.0562606 | ||||||||
\(483\) | −9539.09 | −0.898641 | ||||||||
\(484\) | 5389.25 | 0.506128 | ||||||||
\(485\) | 11857.2 | 1.11012 | ||||||||
\(486\) | −1113.37 | −0.103917 | ||||||||
\(487\) | 14116.3 | 1.31349 | 0.656745 | − | 0.754113i | \(-0.271933\pi\) | ||||
0.656745 | + | 0.754113i | \(0.271933\pi\) | |||||||
\(488\) | −817.598 | −0.0758421 | ||||||||
\(489\) | −8265.33 | −0.764358 | ||||||||
\(490\) | −6050.87 | −0.557858 | ||||||||
\(491\) | 14694.8 | 1.35064 | 0.675321 | − | 0.737524i | \(-0.264005\pi\) | ||||
0.675321 | + | 0.737524i | \(0.264005\pi\) | |||||||
\(492\) | −13767.9 | −1.26160 | ||||||||
\(493\) | −6616.88 | −0.604481 | ||||||||
\(494\) | 11442.4 | 1.04214 | ||||||||
\(495\) | 4624.03 | 0.419868 | ||||||||
\(496\) | −219.638 | −0.0198831 | ||||||||
\(497\) | −9885.40 | −0.892195 | ||||||||
\(498\) | 1316.56 | 0.118467 | ||||||||
\(499\) | 4395.99 | 0.394372 | 0.197186 | − | 0.980366i | \(-0.436820\pi\) | ||||
0.197186 | + | 0.980366i | \(0.436820\pi\) | |||||||
\(500\) | 15784.2 | 1.41178 | ||||||||
\(501\) | −11225.9 | −1.00107 | ||||||||
\(502\) | 4224.22 | 0.375570 | ||||||||
\(503\) | −2345.33 | −0.207899 | −0.103950 | − | 0.994583i | \(-0.533148\pi\) | ||||
−0.103950 | + | 0.994583i | \(0.533148\pi\) | |||||||
\(504\) | −3160.16 | −0.279296 | ||||||||
\(505\) | −15922.2 | −1.40303 | ||||||||
\(506\) | −39657.7 | −3.48419 | ||||||||
\(507\) | −4934.61 | −0.432256 | ||||||||
\(508\) | −25067.1 | −2.18932 | ||||||||
\(509\) | −7711.84 | −0.671554 | −0.335777 | − | 0.941941i | \(-0.608999\pi\) | ||||
−0.335777 | + | 0.941941i | \(0.608999\pi\) | |||||||
\(510\) | 20941.7 | 1.81826 | ||||||||
\(511\) | −8159.47 | −0.706367 | ||||||||
\(512\) | 315.083 | 0.0271970 | ||||||||
\(513\) | 2869.61 | 0.246972 | ||||||||
\(514\) | −9470.70 | −0.812713 | ||||||||
\(515\) | −212.776 | −0.0182058 | ||||||||
\(516\) | −3145.06 | −0.268320 | ||||||||
\(517\) | 214.124 | 0.0182150 | ||||||||
\(518\) | 25146.2 | 2.13294 | ||||||||
\(519\) | 11912.2 | 1.00749 | ||||||||
\(520\) | −6609.70 | −0.557413 | ||||||||
\(521\) | 5616.57 | 0.472296 | 0.236148 | − | 0.971717i | \(-0.424115\pi\) | ||||
0.236148 | + | 0.971717i | \(0.424115\pi\) | |||||||
\(522\) | 2202.20 | 0.184651 | ||||||||
\(523\) | −14763.5 | −1.23435 | −0.617173 | − | 0.786828i | \(-0.711722\pi\) | ||||
−0.617173 | + | 0.786828i | \(0.711722\pi\) | |||||||
\(524\) | 27526.8 | 2.29487 | ||||||||
\(525\) | 1206.66 | 0.100310 | ||||||||
\(526\) | −20317.1 | −1.68416 | ||||||||
\(527\) | −31267.6 | −2.58452 | ||||||||
\(528\) | −109.094 | −0.00899188 | ||||||||
\(529\) | 30746.5 | 2.52704 | ||||||||
\(530\) | −14688.4 | −1.20381 | ||||||||
\(531\) | −531.000 | −0.0433963 | ||||||||
\(532\) | 21195.8 | 1.72736 | ||||||||
\(533\) | 8299.77 | 0.674489 | ||||||||
\(534\) | −13784.7 | −1.11708 | ||||||||
\(535\) | −3290.97 | −0.265945 | ||||||||
\(536\) | −14539.7 | −1.17168 | ||||||||
\(537\) | 3966.88 | 0.318778 | ||||||||
\(538\) | −11005.0 | −0.881894 | ||||||||
\(539\) | 4487.41 | 0.358602 | ||||||||
\(540\) | −4313.69 | −0.343762 | ||||||||
\(541\) | 15882.7 | 1.26220 | 0.631102 | − | 0.775700i | \(-0.282603\pi\) | ||||
0.631102 | + | 0.775700i | \(0.282603\pi\) | |||||||
\(542\) | −17140.0 | −1.35835 | ||||||||
\(543\) | 9734.78 | 0.769354 | ||||||||
\(544\) | 22180.6 | 1.74814 | ||||||||
\(545\) | 2201.41 | 0.173024 | ||||||||
\(546\) | 4957.54 | 0.388577 | ||||||||
\(547\) | −3258.45 | −0.254701 | −0.127350 | − | 0.991858i | \(-0.540647\pi\) | ||||
−0.127350 | + | 0.991858i | \(0.540647\pi\) | |||||||
\(548\) | 4142.94 | 0.322952 | ||||||||
\(549\) | 321.665 | 0.0250061 | ||||||||
\(550\) | 5016.56 | 0.388922 | ||||||||
\(551\) | −5675.96 | −0.438846 | ||||||||
\(552\) | 14216.6 | 1.09620 | ||||||||
\(553\) | 9130.68 | 0.702126 | ||||||||
\(554\) | 6612.53 | 0.507111 | ||||||||
\(555\) | 13190.2 | 1.00882 | ||||||||
\(556\) | 30025.3 | 2.29021 | ||||||||
\(557\) | −8065.81 | −0.613572 | −0.306786 | − | 0.951779i | \(-0.599254\pi\) | ||||
−0.306786 | + | 0.951779i | \(0.599254\pi\) | |||||||
\(558\) | 10406.4 | 0.789493 | ||||||||
\(559\) | 1895.94 | 0.143452 | ||||||||
\(560\) | −164.269 | −0.0123958 | ||||||||
\(561\) | −15530.7 | −1.16881 | ||||||||
\(562\) | 16026.5 | 1.20291 | ||||||||
\(563\) | 19540.5 | 1.46276 | 0.731379 | − | 0.681971i | \(-0.238877\pi\) | ||||
0.731379 | + | 0.681971i | \(0.238877\pi\) | |||||||
\(564\) | −199.753 | −0.0149133 | ||||||||
\(565\) | 8538.89 | 0.635812 | ||||||||
\(566\) | 1818.02 | 0.135012 | ||||||||
\(567\) | 1243.29 | 0.0920871 | ||||||||
\(568\) | 14732.8 | 1.08833 | ||||||||
\(569\) | 13811.1 | 1.01756 | 0.508780 | − | 0.860897i | \(-0.330097\pi\) | ||||
0.508780 | + | 0.860897i | \(0.330097\pi\) | |||||||
\(570\) | 17963.8 | 1.32004 | ||||||||
\(571\) | 9120.73 | 0.668460 | 0.334230 | − | 0.942492i | \(-0.391524\pi\) | ||||
0.334230 | + | 0.942492i | \(0.391524\pi\) | |||||||
\(572\) | 12756.1 | 0.932449 | ||||||||
\(573\) | 4490.96 | 0.327421 | ||||||||
\(574\) | 24841.0 | 1.80634 | ||||||||
\(575\) | −5428.41 | −0.393705 | ||||||||
\(576\) | −7444.74 | −0.538537 | ||||||||
\(577\) | 19680.3 | 1.41993 | 0.709965 | − | 0.704237i | \(-0.248711\pi\) | ||||
0.709965 | + | 0.704237i | \(0.248711\pi\) | |||||||
\(578\) | −47826.2 | −3.44171 | ||||||||
\(579\) | 658.512 | 0.0472657 | ||||||||
\(580\) | 8532.28 | 0.610834 | ||||||||
\(581\) | −1470.19 | −0.104980 | ||||||||
\(582\) | 13254.3 | 0.944002 | ||||||||
\(583\) | 10893.1 | 0.773835 | ||||||||
\(584\) | 12160.5 | 0.861654 | ||||||||
\(585\) | 2600.43 | 0.183786 | ||||||||
\(586\) | −42370.8 | −2.98689 | ||||||||
\(587\) | −26509.2 | −1.86398 | −0.931988 | − | 0.362489i | \(-0.881927\pi\) | ||||
−0.931988 | + | 0.362489i | \(0.881927\pi\) | |||||||
\(588\) | −4186.24 | −0.293601 | ||||||||
\(589\) | −26821.4 | −1.87633 | ||||||||
\(590\) | −3324.06 | −0.231948 | ||||||||
\(591\) | 2220.08 | 0.154521 | ||||||||
\(592\) | −311.196 | −0.0216048 | ||||||||
\(593\) | −1515.35 | −0.104937 | −0.0524686 | − | 0.998623i | \(-0.516709\pi\) | ||||
−0.0524686 | + | 0.998623i | \(0.516709\pi\) | |||||||
\(594\) | 5168.86 | 0.357038 | ||||||||
\(595\) | −23385.3 | −1.61127 | ||||||||
\(596\) | −15182.6 | −1.04346 | ||||||||
\(597\) | 6414.12 | 0.439720 | ||||||||
\(598\) | −22302.5 | −1.52511 | ||||||||
\(599\) | −4721.57 | −0.322067 | −0.161033 | − | 0.986949i | \(-0.551483\pi\) | ||||
−0.161033 | + | 0.986949i | \(0.551483\pi\) | |||||||
\(600\) | −1798.36 | −0.122363 | ||||||||
\(601\) | 14051.0 | 0.953663 | 0.476831 | − | 0.878995i | \(-0.341785\pi\) | ||||
0.476831 | + | 0.878995i | \(0.341785\pi\) | |||||||
\(602\) | 5674.51 | 0.384179 | ||||||||
\(603\) | 5720.31 | 0.386317 | ||||||||
\(604\) | −19971.4 | −1.34541 | ||||||||
\(605\) | −5100.45 | −0.342748 | ||||||||
\(606\) | −17798.2 | −1.19307 | ||||||||
\(607\) | −8076.32 | −0.540046 | −0.270023 | − | 0.962854i | \(-0.587031\pi\) | ||||
−0.270023 | + | 0.962854i | \(0.587031\pi\) | |||||||
\(608\) | 19026.6 | 1.26913 | ||||||||
\(609\) | −2459.18 | −0.163630 | ||||||||
\(610\) | 2013.63 | 0.133655 | ||||||||
\(611\) | 120.418 | 0.00797312 | ||||||||
\(612\) | 14488.3 | 0.956953 | ||||||||
\(613\) | −3386.14 | −0.223107 | −0.111554 | − | 0.993758i | \(-0.535583\pi\) | ||||
−0.111554 | + | 0.993758i | \(0.535583\pi\) | |||||||
\(614\) | −22968.6 | −1.50967 | ||||||||
\(615\) | 13030.1 | 0.854350 | ||||||||
\(616\) | 14671.1 | 0.959604 | ||||||||
\(617\) | 26131.0 | 1.70502 | 0.852508 | − | 0.522714i | \(-0.175080\pi\) | ||||
0.852508 | + | 0.522714i | \(0.175080\pi\) | |||||||
\(618\) | −237.846 | −0.0154815 | ||||||||
\(619\) | 7409.73 | 0.481134 | 0.240567 | − | 0.970633i | \(-0.422667\pi\) | ||||
0.240567 | + | 0.970633i | \(0.422667\pi\) | |||||||
\(620\) | 40318.7 | 2.61168 | ||||||||
\(621\) | −5593.20 | −0.361429 | ||||||||
\(622\) | 29123.4 | 1.87740 | ||||||||
\(623\) | 15393.2 | 0.989913 | ||||||||
\(624\) | −61.3517 | −0.00393595 | ||||||||
\(625\) | −18213.9 | −1.16569 | ||||||||
\(626\) | −7624.77 | −0.486816 | ||||||||
\(627\) | −13322.2 | −0.848546 | ||||||||
\(628\) | −30546.9 | −1.94101 | ||||||||
\(629\) | −44301.9 | −2.80832 | ||||||||
\(630\) | 7783.03 | 0.492196 | ||||||||
\(631\) | −18236.5 | −1.15053 | −0.575264 | − | 0.817968i | \(-0.695101\pi\) | ||||
−0.575264 | + | 0.817968i | \(0.695101\pi\) | |||||||
\(632\) | −13608.0 | −0.856481 | ||||||||
\(633\) | −1530.91 | −0.0961268 | ||||||||
\(634\) | 43380.2 | 2.71742 | ||||||||
\(635\) | 23723.8 | 1.48260 | ||||||||
\(636\) | −10162.0 | −0.633569 | ||||||||
\(637\) | 2523.61 | 0.156968 | ||||||||
\(638\) | −10223.8 | −0.634424 | ||||||||
\(639\) | −5796.27 | −0.358837 | ||||||||
\(640\) | −28993.6 | −1.79074 | ||||||||
\(641\) | −27792.6 | −1.71255 | −0.856273 | − | 0.516524i | \(-0.827226\pi\) | ||||
−0.856273 | + | 0.516524i | \(0.827226\pi\) | |||||||
\(642\) | −3678.73 | −0.226149 | ||||||||
\(643\) | −19061.5 | −1.16907 | −0.584534 | − | 0.811369i | \(-0.698723\pi\) | ||||
−0.584534 | + | 0.811369i | \(0.698723\pi\) | |||||||
\(644\) | −41313.1 | −2.52790 | ||||||||
\(645\) | 2976.52 | 0.181706 | ||||||||
\(646\) | −60334.7 | −3.67467 | ||||||||
\(647\) | −6267.83 | −0.380856 | −0.190428 | − | 0.981701i | \(-0.560988\pi\) | ||||
−0.190428 | + | 0.981701i | \(0.560988\pi\) | |||||||
\(648\) | −1852.95 | −0.112331 | ||||||||
\(649\) | 2465.17 | 0.149101 | ||||||||
\(650\) | 2821.19 | 0.170240 | ||||||||
\(651\) | −11620.7 | −0.699617 | ||||||||
\(652\) | −35796.6 | −2.15016 | ||||||||
\(653\) | 21401.4 | 1.28254 | 0.641271 | − | 0.767314i | \(-0.278407\pi\) | ||||
0.641271 | + | 0.767314i | \(0.278407\pi\) | |||||||
\(654\) | 2460.79 | 0.147132 | ||||||||
\(655\) | −26051.7 | −1.55408 | ||||||||
\(656\) | −307.418 | −0.0182967 | ||||||||
\(657\) | −4784.27 | −0.284098 | ||||||||
\(658\) | 360.406 | 0.0213527 | ||||||||
\(659\) | 17027.7 | 1.00653 | 0.503267 | − | 0.864131i | \(-0.332131\pi\) | ||||
0.503267 | + | 0.864131i | \(0.332131\pi\) | |||||||
\(660\) | 20026.4 | 1.18110 | ||||||||
\(661\) | 26007.0 | 1.53034 | 0.765170 | − | 0.643828i | \(-0.222655\pi\) | ||||
0.765170 | + | 0.643828i | \(0.222655\pi\) | |||||||
\(662\) | 24734.1 | 1.45214 | ||||||||
\(663\) | −8734.04 | −0.511617 | ||||||||
\(664\) | 2191.10 | 0.128059 | ||||||||
\(665\) | −20060.0 | −1.16976 | ||||||||
\(666\) | 14744.4 | 0.857858 | ||||||||
\(667\) | 11063.1 | 0.642227 | ||||||||
\(668\) | −48618.6 | −2.81603 | ||||||||
\(669\) | −7347.56 | −0.424623 | ||||||||
\(670\) | 35809.2 | 2.06482 | ||||||||
\(671\) | −1493.33 | −0.0859159 | ||||||||
\(672\) | 8243.48 | 0.473213 | ||||||||
\(673\) | 11947.8 | 0.684329 | 0.342164 | − | 0.939640i | \(-0.388840\pi\) | ||||
0.342164 | + | 0.939640i | \(0.388840\pi\) | |||||||
\(674\) | −21960.7 | −1.25504 | ||||||||
\(675\) | 707.521 | 0.0403444 | ||||||||
\(676\) | −21371.4 | −1.21594 | ||||||||
\(677\) | −6173.05 | −0.350442 | −0.175221 | − | 0.984529i | \(-0.556064\pi\) | ||||
−0.175221 | + | 0.984529i | \(0.556064\pi\) | |||||||
\(678\) | 9544.99 | 0.540669 | ||||||||
\(679\) | −14801.0 | −0.836537 | ||||||||
\(680\) | 34852.5 | 1.96549 | ||||||||
\(681\) | −555.889 | −0.0312801 | ||||||||
\(682\) | −48311.8 | −2.71254 | ||||||||
\(683\) | −31454.6 | −1.76219 | −0.881097 | − | 0.472936i | \(-0.843194\pi\) | ||||
−0.881097 | + | 0.472936i | \(0.843194\pi\) | |||||||
\(684\) | 12428.1 | 0.694737 | ||||||||
\(685\) | −3920.92 | −0.218702 | ||||||||
\(686\) | 31675.3 | 1.76293 | ||||||||
\(687\) | 18557.0 | 1.03056 | ||||||||
\(688\) | −70.2246 | −0.00389140 | ||||||||
\(689\) | 6126.00 | 0.338726 | ||||||||
\(690\) | −35013.5 | −1.93180 | ||||||||
\(691\) | 5719.61 | 0.314883 | 0.157441 | − | 0.987528i | \(-0.449675\pi\) | ||||
0.157441 | + | 0.987528i | \(0.449675\pi\) | |||||||
\(692\) | 51591.1 | 2.83410 | ||||||||
\(693\) | −5772.01 | −0.316393 | ||||||||
\(694\) | 49121.3 | 2.68677 | ||||||||
\(695\) | −28416.3 | −1.55092 | ||||||||
\(696\) | 3665.05 | 0.199603 | ||||||||
\(697\) | −43764.1 | −2.37831 | ||||||||
\(698\) | −4783.03 | −0.259370 | ||||||||
\(699\) | −14086.1 | −0.762211 | ||||||||
\(700\) | 5225.97 | 0.282176 | ||||||||
\(701\) | −1237.43 | −0.0666719 | −0.0333360 | − | 0.999444i | \(-0.510613\pi\) | ||||
−0.0333360 | + | 0.999444i | \(0.510613\pi\) | |||||||
\(702\) | 2906.83 | 0.156284 | ||||||||
\(703\) | −38002.2 | −2.03881 | ||||||||
\(704\) | 34562.3 | 1.85031 | ||||||||
\(705\) | 189.048 | 0.0100992 | ||||||||
\(706\) | 45060.6 | 2.40209 | ||||||||
\(707\) | 19875.1 | 1.05725 | ||||||||
\(708\) | −2299.72 | −0.122075 | ||||||||
\(709\) | −14978.1 | −0.793393 | −0.396697 | − | 0.917950i | \(-0.629844\pi\) | ||||
−0.396697 | + | 0.917950i | \(0.629844\pi\) | |||||||
\(710\) | −36284.7 | −1.91794 | ||||||||
\(711\) | 5353.74 | 0.282392 | ||||||||
\(712\) | −22941.4 | −1.20753 | ||||||||
\(713\) | 52278.0 | 2.74590 | ||||||||
\(714\) | −26140.7 | −1.37016 | ||||||||
\(715\) | −12072.6 | −0.631452 | ||||||||
\(716\) | 17180.3 | 0.896729 | ||||||||
\(717\) | −11070.7 | −0.576628 | ||||||||
\(718\) | −45562.4 | −2.36821 | ||||||||
\(719\) | 1416.69 | 0.0734822 | 0.0367411 | − | 0.999325i | \(-0.488302\pi\) | ||||
0.0367411 | + | 0.999325i | \(0.488302\pi\) | |||||||
\(720\) | −96.3184 | −0.00498552 | ||||||||
\(721\) | 265.600 | 0.0137191 | ||||||||
\(722\) | −20328.7 | −1.04786 | ||||||||
\(723\) | −389.817 | −0.0200518 | ||||||||
\(724\) | 42160.7 | 2.16421 | ||||||||
\(725\) | −1399.44 | −0.0716884 | ||||||||
\(726\) | −5701.41 | −0.291459 | ||||||||
\(727\) | −15069.5 | −0.768773 | −0.384387 | − | 0.923172i | \(-0.625587\pi\) | ||||
−0.384387 | + | 0.923172i | \(0.625587\pi\) | |||||||
\(728\) | 8250.65 | 0.420041 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −29949.6 | −1.51847 | ||||||||
\(731\) | −9997.18 | −0.505826 | ||||||||
\(732\) | 1393.11 | 0.0703426 | ||||||||
\(733\) | 17103.5 | 0.861844 | 0.430922 | − | 0.902389i | \(-0.358188\pi\) | ||||
0.430922 | + | 0.902389i | \(0.358188\pi\) | |||||||
\(734\) | −37469.3 | −1.88422 | ||||||||
\(735\) | 3961.90 | 0.198826 | ||||||||
\(736\) | −37085.0 | −1.85730 | ||||||||
\(737\) | −26556.6 | −1.32731 | ||||||||
\(738\) | 14565.4 | 0.726504 | ||||||||
\(739\) | 9749.49 | 0.485306 | 0.242653 | − | 0.970113i | \(-0.421982\pi\) | ||||
0.242653 | + | 0.970113i | \(0.421982\pi\) | |||||||
\(740\) | 57126.0 | 2.83783 | ||||||||
\(741\) | −7492.07 | −0.371428 | ||||||||
\(742\) | 18334.9 | 0.907138 | ||||||||
\(743\) | −13906.1 | −0.686630 | −0.343315 | − | 0.939220i | \(-0.611550\pi\) | ||||
−0.343315 | + | 0.939220i | \(0.611550\pi\) | |||||||
\(744\) | 17319.0 | 0.853420 | ||||||||
\(745\) | 14369.0 | 0.706628 | ||||||||
\(746\) | 24115.6 | 1.18356 | ||||||||
\(747\) | −862.038 | −0.0422227 | ||||||||
\(748\) | −67262.2 | −3.28790 | ||||||||
\(749\) | 4107.99 | 0.200404 | ||||||||
\(750\) | −16698.4 | −0.812988 | ||||||||
\(751\) | −11178.8 | −0.543170 | −0.271585 | − | 0.962415i | \(-0.587548\pi\) | ||||
−0.271585 | + | 0.962415i | \(0.587548\pi\) | |||||||
\(752\) | −4.46019 | −0.000216285 0 | ||||||||
\(753\) | −2765.87 | −0.133857 | ||||||||
\(754\) | −5749.58 | −0.277702 | ||||||||
\(755\) | 18901.2 | 0.911105 | ||||||||
\(756\) | 5384.62 | 0.259043 | ||||||||
\(757\) | 4697.99 | 0.225563 | 0.112782 | − | 0.993620i | \(-0.464024\pi\) | ||||
0.112782 | + | 0.993620i | \(0.464024\pi\) | |||||||
\(758\) | 7244.98 | 0.347163 | ||||||||
\(759\) | 25966.5 | 1.24180 | ||||||||
\(760\) | 29896.5 | 1.42692 | ||||||||
\(761\) | 15776.9 | 0.751526 | 0.375763 | − | 0.926716i | \(-0.377381\pi\) | ||||
0.375763 | + | 0.926716i | \(0.377381\pi\) | |||||||
\(762\) | 26519.1 | 1.26074 | ||||||||
\(763\) | −2747.94 | −0.130383 | ||||||||
\(764\) | 19450.0 | 0.921044 | ||||||||
\(765\) | −13711.9 | −0.648046 | ||||||||
\(766\) | −83.0230 | −0.00391611 | ||||||||
\(767\) | 1386.35 | 0.0652649 | ||||||||
\(768\) | −12557.1 | −0.589995 | ||||||||
\(769\) | −25079.3 | −1.17605 | −0.588024 | − | 0.808843i | \(-0.700094\pi\) | ||||
−0.588024 | + | 0.808843i | \(0.700094\pi\) | |||||||
\(770\) | −36132.8 | −1.69109 | ||||||||
\(771\) | 6201.09 | 0.289659 | ||||||||
\(772\) | 2851.97 | 0.132959 | ||||||||
\(773\) | 15991.3 | 0.744071 | 0.372036 | − | 0.928218i | \(-0.378660\pi\) | ||||
0.372036 | + | 0.928218i | \(0.378660\pi\) | |||||||
\(774\) | 3327.22 | 0.154515 | ||||||||
\(775\) | −6612.99 | −0.306510 | ||||||||
\(776\) | 22058.7 | 1.02044 | ||||||||
\(777\) | −16464.9 | −0.760199 | ||||||||
\(778\) | 34251.2 | 1.57836 | ||||||||
\(779\) | −37540.9 | −1.72663 | ||||||||
\(780\) | 11262.3 | 0.516994 | ||||||||
\(781\) | 26909.2 | 1.23289 | ||||||||
\(782\) | 117599. | 5.37768 | ||||||||
\(783\) | −1441.93 | −0.0658114 | ||||||||
\(784\) | −93.4727 | −0.00425805 | ||||||||
\(785\) | 28909.9 | 1.31445 | ||||||||
\(786\) | −29121.2 | −1.32153 | ||||||||
\(787\) | 32468.4 | 1.47061 | 0.735307 | − | 0.677734i | \(-0.237038\pi\) | ||||
0.735307 | + | 0.677734i | \(0.237038\pi\) | |||||||
\(788\) | 9615.02 | 0.434671 | ||||||||
\(789\) | 13303.0 | 0.600252 | ||||||||
\(790\) | 33514.4 | 1.50935 | ||||||||
\(791\) | −10658.8 | −0.479119 | ||||||||
\(792\) | 8602.35 | 0.385948 | ||||||||
\(793\) | −839.813 | −0.0376073 | ||||||||
\(794\) | 37014.4 | 1.65440 | ||||||||
\(795\) | 9617.44 | 0.429051 | ||||||||
\(796\) | 27779.1 | 1.23694 | ||||||||
\(797\) | 16858.3 | 0.749248 | 0.374624 | − | 0.927177i | \(-0.377772\pi\) | ||||
0.374624 | + | 0.927177i | \(0.377772\pi\) | |||||||
\(798\) | −22423.6 | −0.994718 | ||||||||
\(799\) | −634.953 | −0.0281139 | ||||||||
\(800\) | 4691.12 | 0.207320 | ||||||||
\(801\) | 9025.75 | 0.398139 | ||||||||
\(802\) | −7489.40 | −0.329751 | ||||||||
\(803\) | 22211.1 | 0.976103 | ||||||||
\(804\) | 24774.3 | 1.08672 | ||||||||
\(805\) | 39099.2 | 1.71188 | ||||||||
\(806\) | −27169.3 | −1.18734 | ||||||||
\(807\) | 7205.70 | 0.314315 | ||||||||
\(808\) | −29620.9 | −1.28968 | ||||||||
\(809\) | −9132.42 | −0.396884 | −0.198442 | − | 0.980113i | \(-0.563588\pi\) | ||||
−0.198442 | + | 0.980113i | \(0.563588\pi\) | |||||||
\(810\) | 4563.55 | 0.197959 | ||||||||
\(811\) | −10235.5 | −0.443179 | −0.221589 | − | 0.975140i | \(-0.571124\pi\) | ||||
−0.221589 | + | 0.975140i | \(0.571124\pi\) | |||||||
\(812\) | −10650.5 | −0.460296 | ||||||||
\(813\) | 11222.7 | 0.484129 | ||||||||
\(814\) | −68451.0 | −2.94743 | ||||||||
\(815\) | 33878.3 | 1.45608 | ||||||||
\(816\) | 323.503 | 0.0138785 | ||||||||
\(817\) | −8575.59 | −0.367224 | ||||||||
\(818\) | 9718.28 | 0.415393 | ||||||||
\(819\) | −3246.03 | −0.138492 | ||||||||
\(820\) | 56432.5 | 2.40330 | ||||||||
\(821\) | −32830.2 | −1.39559 | −0.697797 | − | 0.716295i | \(-0.745836\pi\) | ||||
−0.697797 | + | 0.716295i | \(0.745836\pi\) | |||||||
\(822\) | −4382.91 | −0.185975 | ||||||||
\(823\) | 27497.4 | 1.16464 | 0.582320 | − | 0.812960i | \(-0.302145\pi\) | ||||
0.582320 | + | 0.812960i | \(0.302145\pi\) | |||||||
\(824\) | −395.839 | −0.0167351 | ||||||||
\(825\) | −3284.68 | −0.138615 | ||||||||
\(826\) | 4149.31 | 0.174786 | ||||||||
\(827\) | −39886.2 | −1.67712 | −0.838560 | − | 0.544809i | \(-0.816602\pi\) | ||||
−0.838560 | + | 0.544809i | \(0.816602\pi\) | |||||||
\(828\) | −24223.8 | −1.01671 | ||||||||
\(829\) | −42518.9 | −1.78135 | −0.890676 | − | 0.454638i | \(-0.849769\pi\) | ||||
−0.890676 | + | 0.454638i | \(0.849769\pi\) | |||||||
\(830\) | −5396.37 | −0.225676 | ||||||||
\(831\) | −4329.66 | −0.180739 | ||||||||
\(832\) | 19436.9 | 0.809922 | ||||||||
\(833\) | −13306.8 | −0.553485 | ||||||||
\(834\) | −31764.4 | −1.31884 | ||||||||
\(835\) | 46013.2 | 1.90701 | ||||||||
\(836\) | −57697.6 | −2.38698 | ||||||||
\(837\) | −6813.75 | −0.281383 | ||||||||
\(838\) | 67900.8 | 2.79904 | ||||||||
\(839\) | 22032.0 | 0.906592 | 0.453296 | − | 0.891360i | \(-0.350248\pi\) | ||||
0.453296 | + | 0.891360i | \(0.350248\pi\) | |||||||
\(840\) | 12953.0 | 0.532049 | ||||||||
\(841\) | −21536.9 | −0.883059 | ||||||||
\(842\) | −23947.4 | −0.980143 | ||||||||
\(843\) | −10493.6 | −0.428729 | ||||||||
\(844\) | −6630.27 | −0.270407 | ||||||||
\(845\) | 20226.2 | 0.823434 | ||||||||
\(846\) | 211.323 | 0.00858798 | ||||||||
\(847\) | 6366.70 | 0.258279 | ||||||||
\(848\) | −226.903 | −0.00918854 | ||||||||
\(849\) | −1190.38 | −0.0481196 | ||||||||
\(850\) | −14875.9 | −0.600282 | ||||||||
\(851\) | 74070.7 | 2.98368 | ||||||||
\(852\) | −25103.2 | −1.00942 | ||||||||
\(853\) | −43140.4 | −1.73165 | −0.865825 | − | 0.500346i | \(-0.833206\pi\) | ||||
−0.865825 | + | 0.500346i | \(0.833206\pi\) | |||||||
\(854\) | −2513.54 | −0.100716 | ||||||||
\(855\) | −11762.1 | −0.470474 | ||||||||
\(856\) | −6122.37 | −0.244461 | ||||||||
\(857\) | 8131.01 | 0.324096 | 0.162048 | − | 0.986783i | \(-0.448190\pi\) | ||||
0.162048 | + | 0.986783i | \(0.448190\pi\) | |||||||
\(858\) | −13495.0 | −0.536960 | ||||||||
\(859\) | −25210.4 | −1.00136 | −0.500680 | − | 0.865632i | \(-0.666917\pi\) | ||||
−0.500680 | + | 0.865632i | \(0.666917\pi\) | |||||||
\(860\) | 12891.1 | 0.511142 | ||||||||
\(861\) | −16265.0 | −0.643798 | ||||||||
\(862\) | 50063.6 | 1.97816 | ||||||||
\(863\) | 23.0095 | 0.000907593 0 | 0.000453797 | − | 1.00000i | \(-0.499856\pi\) | ||||
0.000453797 | 1.00000i | \(0.499856\pi\) | ||||||||
\(864\) | 4833.53 | 0.190324 | ||||||||
\(865\) | −48826.4 | −1.91924 | ||||||||
\(866\) | −14537.9 | −0.570461 | ||||||||
\(867\) | 31315.0 | 1.22666 | ||||||||
\(868\) | −50328.4 | −1.96804 | ||||||||
\(869\) | −24854.8 | −0.970243 | ||||||||
\(870\) | −9026.49 | −0.351755 | ||||||||
\(871\) | −14934.7 | −0.580993 | ||||||||
\(872\) | 4095.41 | 0.159046 | ||||||||
\(873\) | −8678.48 | −0.336451 | ||||||||
\(874\) | 100877. | 3.90413 | ||||||||
\(875\) | 18647.0 | 0.720437 | ||||||||
\(876\) | −20720.4 | −0.799174 | ||||||||
\(877\) | −3988.93 | −0.153588 | −0.0767939 | − | 0.997047i | \(-0.524468\pi\) | ||||
−0.0767939 | + | 0.997047i | \(0.524468\pi\) | |||||||
\(878\) | −9908.94 | −0.380877 | ||||||||
\(879\) | 27742.9 | 1.06456 | ||||||||
\(880\) | 447.160 | 0.0171293 | ||||||||
\(881\) | 42436.5 | 1.62284 | 0.811420 | − | 0.584464i | \(-0.198695\pi\) | ||||
0.811420 | + | 0.584464i | \(0.198695\pi\) | |||||||
\(882\) | 4428.72 | 0.169073 | ||||||||
\(883\) | −9854.79 | −0.375583 | −0.187792 | − | 0.982209i | \(-0.560133\pi\) | ||||
−0.187792 | + | 0.982209i | \(0.560133\pi\) | |||||||
\(884\) | −37826.5 | −1.43919 | ||||||||
\(885\) | 2176.48 | 0.0826686 | ||||||||
\(886\) | 47057.9 | 1.78436 | ||||||||
\(887\) | 631.042 | 0.0238876 | 0.0119438 | − | 0.999929i | \(-0.496198\pi\) | ||||
0.0119438 | + | 0.999929i | \(0.496198\pi\) | |||||||
\(888\) | 24538.6 | 0.927320 | ||||||||
\(889\) | −29613.6 | −1.11722 | ||||||||
\(890\) | 56501.2 | 2.12801 | ||||||||
\(891\) | −3384.39 | −0.127252 | ||||||||
\(892\) | −31821.8 | −1.19447 | ||||||||
\(893\) | −544.664 | −0.0204104 | ||||||||
\(894\) | 16062.0 | 0.600887 | ||||||||
\(895\) | −16259.6 | −0.607262 | ||||||||
\(896\) | 36191.6 | 1.34942 | ||||||||
\(897\) | 14602.9 | 0.543564 | ||||||||
\(898\) | 17513.6 | 0.650819 | ||||||||
\(899\) | 13477.3 | 0.499992 | ||||||||
\(900\) | 3064.22 | 0.113490 | ||||||||
\(901\) | −32301.9 | −1.19438 | ||||||||
\(902\) | −67620.1 | −2.49612 | ||||||||
\(903\) | −3715.47 | −0.136925 | ||||||||
\(904\) | 15885.4 | 0.584447 | ||||||||
\(905\) | −39901.3 | −1.46560 | ||||||||
\(906\) | 21128.2 | 0.774766 | ||||||||
\(907\) | 18816.6 | 0.688858 | 0.344429 | − | 0.938812i | \(-0.388072\pi\) | ||||
0.344429 | + | 0.938812i | \(0.388072\pi\) | |||||||
\(908\) | −2407.52 | −0.0879915 | ||||||||
\(909\) | 11653.7 | 0.425223 | ||||||||
\(910\) | −20320.2 | −0.740227 | ||||||||
\(911\) | 3772.72 | 0.137207 | 0.0686036 | − | 0.997644i | \(-0.478146\pi\) | ||||
0.0686036 | + | 0.997644i | \(0.478146\pi\) | |||||||
\(912\) | 277.501 | 0.0100756 | ||||||||
\(913\) | 4002.03 | 0.145069 | ||||||||
\(914\) | −76306.4 | −2.76148 | ||||||||
\(915\) | −1318.45 | −0.0476358 | ||||||||
\(916\) | 80368.9 | 2.89898 | ||||||||
\(917\) | 32519.3 | 1.17108 | ||||||||
\(918\) | −15327.5 | −0.551071 | ||||||||
\(919\) | −28498.4 | −1.02293 | −0.511467 | − | 0.859303i | \(-0.670898\pi\) | ||||
−0.511467 | + | 0.859303i | \(0.670898\pi\) | |||||||
\(920\) | −58271.7 | −2.08822 | ||||||||
\(921\) | 15039.0 | 0.538059 | ||||||||
\(922\) | −66337.4 | −2.36953 | ||||||||
\(923\) | 15133.1 | 0.539665 | ||||||||
\(924\) | −24998.2 | −0.890021 | ||||||||
\(925\) | −9369.68 | −0.333052 | ||||||||
\(926\) | 50888.9 | 1.80595 | ||||||||
\(927\) | 155.733 | 0.00551775 | ||||||||
\(928\) | −9560.51 | −0.338189 | ||||||||
\(929\) | −15966.5 | −0.563879 | −0.281940 | − | 0.959432i | \(-0.590978\pi\) | ||||
−0.281940 | + | 0.959432i | \(0.590978\pi\) | |||||||
\(930\) | −42654.1 | −1.50396 | ||||||||
\(931\) | −11414.6 | −0.401824 | ||||||||
\(932\) | −61006.0 | −2.14412 | ||||||||
\(933\) | −19069.0 | −0.669123 | ||||||||
\(934\) | −82928.9 | −2.90526 | ||||||||
\(935\) | 63657.7 | 2.22656 | ||||||||
\(936\) | 4837.74 | 0.168938 | ||||||||
\(937\) | 3986.01 | 0.138973 | 0.0694863 | − | 0.997583i | \(-0.477864\pi\) | ||||
0.0694863 | + | 0.997583i | \(0.477864\pi\) | |||||||
\(938\) | −44699.3 | −1.55595 | ||||||||
\(939\) | 4992.44 | 0.173506 | ||||||||
\(940\) | 818.755 | 0.0284094 | ||||||||
\(941\) | 30284.1 | 1.04913 | 0.524566 | − | 0.851370i | \(-0.324227\pi\) | ||||
0.524566 | + | 0.851370i | \(0.324227\pi\) | |||||||
\(942\) | 32316.3 | 1.11775 | ||||||||
\(943\) | 73171.5 | 2.52682 | ||||||||
\(944\) | −51.3495 | −0.00177043 | ||||||||
\(945\) | −5096.06 | −0.175423 | ||||||||
\(946\) | −15446.7 | −0.530883 | ||||||||
\(947\) | −30270.4 | −1.03871 | −0.519354 | − | 0.854559i | \(-0.673827\pi\) | ||||
−0.519354 | + | 0.854559i | \(0.673827\pi\) | |||||||
\(948\) | 23186.7 | 0.794375 | ||||||||
\(949\) | 12490.9 | 0.427263 | ||||||||
\(950\) | −12760.6 | −0.435798 | ||||||||
\(951\) | −28403.9 | −0.968515 | ||||||||
\(952\) | −43505.1 | −1.48110 | ||||||||
\(953\) | 19399.4 | 0.659401 | 0.329700 | − | 0.944086i | \(-0.393052\pi\) | ||||
0.329700 | + | 0.944086i | \(0.393052\pi\) | |||||||
\(954\) | 10750.6 | 0.364847 | ||||||||
\(955\) | −18407.7 | −0.623728 | ||||||||
\(956\) | −47946.3 | −1.62207 | ||||||||
\(957\) | 6694.18 | 0.226115 | ||||||||
\(958\) | 71466.4 | 2.41020 | ||||||||
\(959\) | 4894.35 | 0.164804 | ||||||||
\(960\) | 30514.8 | 1.02590 | ||||||||
\(961\) | 33895.0 | 1.13776 | ||||||||
\(962\) | −38495.1 | −1.29016 | ||||||||
\(963\) | 2408.70 | 0.0806017 | ||||||||
\(964\) | −1688.27 | −0.0564062 | ||||||||
\(965\) | −2699.14 | −0.0900396 | ||||||||
\(966\) | 43706.1 | 1.45571 | ||||||||
\(967\) | 20800.3 | 0.691720 | 0.345860 | − | 0.938286i | \(-0.387587\pi\) | ||||
0.345860 | + | 0.938286i | \(0.387587\pi\) | |||||||
\(968\) | −9488.65 | −0.315059 | ||||||||
\(969\) | 39505.1 | 1.30969 | ||||||||
\(970\) | −54327.4 | −1.79830 | ||||||||
\(971\) | −27717.3 | −0.916055 | −0.458028 | − | 0.888938i | \(-0.651444\pi\) | ||||
−0.458028 | + | 0.888938i | \(0.651444\pi\) | |||||||
\(972\) | 3157.25 | 0.104186 | ||||||||
\(973\) | 35471.0 | 1.16870 | ||||||||
\(974\) | −64677.8 | −2.12773 | ||||||||
\(975\) | −1847.22 | −0.0606752 | ||||||||
\(976\) | 31.1061 | 0.00102017 | ||||||||
\(977\) | −19576.1 | −0.641039 | −0.320519 | − | 0.947242i | \(-0.603857\pi\) | ||||
−0.320519 | + | 0.947242i | \(0.603857\pi\) | |||||||
\(978\) | 37870.0 | 1.23819 | ||||||||
\(979\) | −41902.1 | −1.36792 | ||||||||
\(980\) | 17158.7 | 0.559302 | ||||||||
\(981\) | −1611.24 | −0.0524394 | ||||||||
\(982\) | −67328.3 | −2.18792 | ||||||||
\(983\) | −11769.7 | −0.381888 | −0.190944 | − | 0.981601i | \(-0.561155\pi\) | ||||
−0.190944 | + | 0.981601i | \(0.561155\pi\) | |||||||
\(984\) | 24240.7 | 0.785330 | ||||||||
\(985\) | −9099.76 | −0.294358 | ||||||||
\(986\) | 30317.1 | 0.979203 | ||||||||
\(987\) | −235.982 | −0.00761032 | ||||||||
\(988\) | −32447.6 | −1.04483 | ||||||||
\(989\) | 16714.8 | 0.537412 | ||||||||
\(990\) | −21186.3 | −0.680147 | ||||||||
\(991\) | 52861.1 | 1.69444 | 0.847219 | − | 0.531245i | \(-0.178275\pi\) | ||||
0.847219 | + | 0.531245i | \(0.178275\pi\) | |||||||
\(992\) | −45177.6 | −1.44596 | ||||||||
\(993\) | −16195.1 | −0.517558 | ||||||||
\(994\) | 45292.8 | 1.44527 | ||||||||
\(995\) | −26290.5 | −0.837652 | ||||||||
\(996\) | −3733.43 | −0.118773 | ||||||||
\(997\) | −38949.2 | −1.23725 | −0.618623 | − | 0.785688i | \(-0.712309\pi\) | ||||
−0.618623 | + | 0.785688i | \(0.712309\pi\) | |||||||
\(998\) | −20141.5 | −0.638846 | ||||||||
\(999\) | −9654.13 | −0.305749 |
(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 | 177.4.a.a.1.2 | ✓ | 7 | |
3.2 | odd | 2 | 531.4.a.d.1.6 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.4.a.a.1.2 | ✓ | 7 | 1.1 | even | 1 | trivial | |
531.4.a.d.1.6 | 7 | 3.2 | odd | 2 |