Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,4,Mod(1,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, 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("245.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.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: | \(14.4554679514\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 37x^{3} + 21x^{2} + 288x + 64 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 35) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.79706\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.79706 | −0.988911 | −0.494455 | − | 0.869203i | \(-0.664632\pi\) | ||||
−0.494455 | + | 0.869203i | \(0.664632\pi\) | |||||||
\(3\) | 6.21383 | 1.19585 | 0.597926 | − | 0.801551i | \(-0.295992\pi\) | ||||
0.597926 | + | 0.801551i | \(0.295992\pi\) | |||||||
\(4\) | −0.176445 | −0.0220557 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | −17.3805 | −1.18259 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 22.8700 | 1.01072 | ||||||||
\(9\) | 11.6117 | 0.430064 | ||||||||
\(10\) | 13.9853 | 0.442254 | ||||||||
\(11\) | −49.6023 | −1.35961 | −0.679803 | − | 0.733395i | \(-0.737935\pi\) | ||||
−0.679803 | + | 0.733395i | \(0.737935\pi\) | |||||||
\(12\) | −1.09640 | −0.0263753 | ||||||||
\(13\) | 71.6575 | 1.52879 | 0.764393 | − | 0.644751i | \(-0.223039\pi\) | ||||
0.764393 | + | 0.644751i | \(0.223039\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −31.0692 | −0.534802 | ||||||||
\(16\) | −62.5573 | −0.977458 | ||||||||
\(17\) | 46.2981 | 0.660526 | 0.330263 | − | 0.943889i | \(-0.392863\pi\) | ||||
0.330263 | + | 0.943889i | \(0.392863\pi\) | |||||||
\(18\) | −32.4787 | −0.425295 | ||||||||
\(19\) | 54.1893 | 0.654309 | 0.327155 | − | 0.944971i | \(-0.393910\pi\) | ||||
0.327155 | + | 0.944971i | \(0.393910\pi\) | |||||||
\(20\) | 0.882227 | 0.00986359 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 138.741 | 1.34453 | ||||||||
\(23\) | 152.906 | 1.38623 | 0.693113 | − | 0.720829i | \(-0.256239\pi\) | ||||
0.693113 | + | 0.720829i | \(0.256239\pi\) | |||||||
\(24\) | 142.111 | 1.20867 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −200.430 | −1.51183 | ||||||||
\(27\) | −95.6202 | −0.681560 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −38.5268 | −0.246698 | −0.123349 | − | 0.992363i | \(-0.539363\pi\) | ||||
−0.123349 | + | 0.992363i | \(0.539363\pi\) | |||||||
\(30\) | 86.9024 | 0.528871 | ||||||||
\(31\) | 103.405 | 0.599102 | 0.299551 | − | 0.954080i | \(-0.403163\pi\) | ||||
0.299551 | + | 0.954080i | \(0.403163\pi\) | |||||||
\(32\) | −7.98354 | −0.0441032 | ||||||||
\(33\) | −308.220 | −1.62589 | ||||||||
\(34\) | −129.499 | −0.653201 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.04883 | −0.00948534 | ||||||||
\(37\) | 53.4830 | 0.237637 | 0.118818 | − | 0.992916i | \(-0.462089\pi\) | ||||
0.118818 | + | 0.992916i | \(0.462089\pi\) | |||||||
\(38\) | −151.571 | −0.647054 | ||||||||
\(39\) | 445.268 | 1.82820 | ||||||||
\(40\) | −114.350 | −0.452009 | ||||||||
\(41\) | 40.4953 | 0.154251 | 0.0771256 | − | 0.997021i | \(-0.475426\pi\) | ||||
0.0771256 | + | 0.997021i | \(0.475426\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 377.195 | 1.33771 | 0.668856 | − | 0.743392i | \(-0.266784\pi\) | ||||
0.668856 | + | 0.743392i | \(0.266784\pi\) | |||||||
\(44\) | 8.75210 | 0.0299870 | ||||||||
\(45\) | −58.0586 | −0.192330 | ||||||||
\(46\) | −427.689 | −1.37085 | ||||||||
\(47\) | 389.568 | 1.20903 | 0.604514 | − | 0.796595i | \(-0.293367\pi\) | ||||
0.604514 | + | 0.796595i | \(0.293367\pi\) | |||||||
\(48\) | −388.721 | −1.16890 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −69.9265 | −0.197782 | ||||||||
\(51\) | 287.689 | 0.789891 | ||||||||
\(52\) | −12.6436 | −0.0337184 | ||||||||
\(53\) | 328.820 | 0.852205 | 0.426102 | − | 0.904675i | \(-0.359886\pi\) | ||||
0.426102 | + | 0.904675i | \(0.359886\pi\) | |||||||
\(54\) | 267.456 | 0.674002 | ||||||||
\(55\) | 248.012 | 0.608034 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 336.723 | 0.782458 | ||||||||
\(58\) | 107.762 | 0.243962 | ||||||||
\(59\) | −39.6843 | −0.0875671 | −0.0437836 | − | 0.999041i | \(-0.513941\pi\) | ||||
−0.0437836 | + | 0.999041i | \(0.513941\pi\) | |||||||
\(60\) | 5.48201 | 0.0117954 | ||||||||
\(61\) | 197.460 | 0.414462 | 0.207231 | − | 0.978292i | \(-0.433555\pi\) | ||||
0.207231 | + | 0.978292i | \(0.433555\pi\) | |||||||
\(62\) | −289.231 | −0.592458 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 522.789 | 1.02107 | ||||||||
\(65\) | −358.287 | −0.683694 | ||||||||
\(66\) | 862.112 | 1.60786 | ||||||||
\(67\) | 972.226 | 1.77278 | 0.886390 | − | 0.462939i | \(-0.153205\pi\) | ||||
0.886390 | + | 0.462939i | \(0.153205\pi\) | |||||||
\(68\) | −8.16908 | −0.0145683 | ||||||||
\(69\) | 950.135 | 1.65772 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 386.897 | 0.646708 | 0.323354 | − | 0.946278i | \(-0.395190\pi\) | ||||
0.323354 | + | 0.946278i | \(0.395190\pi\) | |||||||
\(72\) | 265.560 | 0.434675 | ||||||||
\(73\) | −219.720 | −0.352278 | −0.176139 | − | 0.984365i | \(-0.556361\pi\) | ||||
−0.176139 | + | 0.984365i | \(0.556361\pi\) | |||||||
\(74\) | −149.595 | −0.235001 | ||||||||
\(75\) | 155.346 | 0.239171 | ||||||||
\(76\) | −9.56145 | −0.0144312 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1245.44 | −1.80793 | ||||||||
\(79\) | −386.474 | −0.550402 | −0.275201 | − | 0.961387i | \(-0.588744\pi\) | ||||
−0.275201 | + | 0.961387i | \(0.588744\pi\) | |||||||
\(80\) | 312.787 | 0.437132 | ||||||||
\(81\) | −907.684 | −1.24511 | ||||||||
\(82\) | −113.268 | −0.152541 | ||||||||
\(83\) | −1376.83 | −1.82081 | −0.910404 | − | 0.413721i | \(-0.864229\pi\) | ||||
−0.910404 | + | 0.413721i | \(0.864229\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −231.490 | −0.295396 | ||||||||
\(86\) | −1055.04 | −1.32288 | ||||||||
\(87\) | −239.399 | −0.295014 | ||||||||
\(88\) | −1134.41 | −1.37418 | ||||||||
\(89\) | 750.054 | 0.893321 | 0.446661 | − | 0.894703i | \(-0.352613\pi\) | ||||
0.446661 | + | 0.894703i | \(0.352613\pi\) | |||||||
\(90\) | 162.393 | 0.190198 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −26.9796 | −0.0305741 | ||||||||
\(93\) | 642.544 | 0.716437 | ||||||||
\(94\) | −1089.64 | −1.19562 | ||||||||
\(95\) | −270.947 | −0.292616 | ||||||||
\(96\) | −49.6084 | −0.0527410 | ||||||||
\(97\) | 533.467 | 0.558406 | 0.279203 | − | 0.960232i | \(-0.409930\pi\) | ||||
0.279203 | + | 0.960232i | \(0.409930\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −575.968 | −0.584717 | ||||||||
\(100\) | −4.41113 | −0.00441113 | ||||||||
\(101\) | −1321.49 | −1.30191 | −0.650956 | − | 0.759115i | \(-0.725632\pi\) | ||||
−0.650956 | + | 0.759115i | \(0.725632\pi\) | |||||||
\(102\) | −804.683 | −0.781132 | ||||||||
\(103\) | −1491.29 | −1.42662 | −0.713308 | − | 0.700851i | \(-0.752804\pi\) | ||||
−0.713308 | + | 0.700851i | \(0.752804\pi\) | |||||||
\(104\) | 1638.81 | 1.54518 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −919.729 | −0.842754 | ||||||||
\(107\) | −439.516 | −0.397099 | −0.198550 | − | 0.980091i | \(-0.563623\pi\) | ||||
−0.198550 | + | 0.980091i | \(0.563623\pi\) | |||||||
\(108\) | 16.8717 | 0.0150323 | ||||||||
\(109\) | 1463.10 | 1.28568 | 0.642840 | − | 0.766000i | \(-0.277756\pi\) | ||||
0.642840 | + | 0.766000i | \(0.277756\pi\) | |||||||
\(110\) | −693.704 | −0.601291 | ||||||||
\(111\) | 332.334 | 0.284178 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1270.15 | −1.05740 | −0.528699 | − | 0.848809i | \(-0.677320\pi\) | ||||
−0.528699 | + | 0.848809i | \(0.677320\pi\) | |||||||
\(114\) | −941.836 | −0.773781 | ||||||||
\(115\) | −764.532 | −0.619939 | ||||||||
\(116\) | 6.79787 | 0.00544109 | ||||||||
\(117\) | 832.067 | 0.657475 | ||||||||
\(118\) | 111.000 | 0.0865960 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −710.553 | −0.540536 | ||||||||
\(121\) | 1129.39 | 0.848527 | ||||||||
\(122\) | −552.308 | −0.409866 | ||||||||
\(123\) | 251.631 | 0.184462 | ||||||||
\(124\) | −18.2454 | −0.0132136 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −675.261 | −0.471809 | −0.235904 | − | 0.971776i | \(-0.575805\pi\) | ||||
−0.235904 | + | 0.971776i | \(0.575805\pi\) | |||||||
\(128\) | −1398.40 | −0.965646 | ||||||||
\(129\) | 2343.82 | 1.59971 | ||||||||
\(130\) | 1002.15 | 0.676112 | ||||||||
\(131\) | 694.929 | 0.463483 | 0.231741 | − | 0.972777i | \(-0.425558\pi\) | ||||
0.231741 | + | 0.972777i | \(0.425558\pi\) | |||||||
\(132\) | 54.3841 | 0.0358600 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2719.38 | −1.75312 | ||||||||
\(135\) | 478.101 | 0.304803 | ||||||||
\(136\) | 1058.84 | 0.667608 | ||||||||
\(137\) | −2519.10 | −1.57096 | −0.785478 | − | 0.618890i | \(-0.787583\pi\) | ||||
−0.785478 | + | 0.618890i | \(0.787583\pi\) | |||||||
\(138\) | −2657.59 | −1.63934 | ||||||||
\(139\) | −1711.61 | −1.04444 | −0.522219 | − | 0.852812i | \(-0.674896\pi\) | ||||
−0.522219 | + | 0.852812i | \(0.674896\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2420.71 | 1.44582 | ||||||||
\(142\) | −1082.18 | −0.639536 | ||||||||
\(143\) | −3554.38 | −2.07854 | ||||||||
\(144\) | −726.398 | −0.420369 | ||||||||
\(145\) | 192.634 | 0.110327 | ||||||||
\(146\) | 614.571 | 0.348372 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.43683 | −0.00524123 | ||||||||
\(149\) | −721.377 | −0.396628 | −0.198314 | − | 0.980139i | \(-0.563546\pi\) | ||||
−0.198314 | + | 0.980139i | \(0.563546\pi\) | |||||||
\(150\) | −434.512 | −0.236518 | ||||||||
\(151\) | 930.692 | 0.501580 | 0.250790 | − | 0.968041i | \(-0.419310\pi\) | ||||
0.250790 | + | 0.968041i | \(0.419310\pi\) | |||||||
\(152\) | 1239.31 | 0.661325 | ||||||||
\(153\) | 537.600 | 0.284068 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −517.027 | −0.267926 | ||||||||
\(156\) | −78.5654 | −0.0403222 | ||||||||
\(157\) | 2266.66 | 1.15222 | 0.576111 | − | 0.817371i | \(-0.304570\pi\) | ||||
0.576111 | + | 0.817371i | \(0.304570\pi\) | |||||||
\(158\) | 1080.99 | 0.544298 | ||||||||
\(159\) | 2043.23 | 1.01911 | ||||||||
\(160\) | 39.9177 | 0.0197236 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2538.85 | 1.23130 | ||||||||
\(163\) | 3194.30 | 1.53495 | 0.767474 | − | 0.641080i | \(-0.221513\pi\) | ||||
0.767474 | + | 0.641080i | \(0.221513\pi\) | |||||||
\(164\) | −7.14521 | −0.00340212 | ||||||||
\(165\) | 1541.10 | 0.727119 | ||||||||
\(166\) | 3851.09 | 1.80062 | ||||||||
\(167\) | −611.079 | −0.283154 | −0.141577 | − | 0.989927i | \(-0.545217\pi\) | ||||
−0.141577 | + | 0.989927i | \(0.545217\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2937.79 | 1.33718 | ||||||||
\(170\) | 647.493 | 0.292120 | ||||||||
\(171\) | 629.231 | 0.281395 | ||||||||
\(172\) | −66.5542 | −0.0295041 | ||||||||
\(173\) | 8.81121 | 0.00387228 | 0.00193614 | − | 0.999998i | \(-0.499384\pi\) | ||||
0.00193614 | + | 0.999998i | \(0.499384\pi\) | |||||||
\(174\) | 669.613 | 0.291743 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3102.99 | 1.32896 | ||||||||
\(177\) | −246.592 | −0.104717 | ||||||||
\(178\) | −2097.95 | −0.883415 | ||||||||
\(179\) | −1250.16 | −0.522018 | −0.261009 | − | 0.965336i | \(-0.584055\pi\) | ||||
−0.261009 | + | 0.965336i | \(0.584055\pi\) | |||||||
\(180\) | 10.2442 | 0.00424197 | ||||||||
\(181\) | −2448.02 | −1.00531 | −0.502653 | − | 0.864488i | \(-0.667643\pi\) | ||||
−0.502653 | + | 0.864488i | \(0.667643\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1226.98 | 0.495635 | ||||||||
\(184\) | 3496.97 | 1.40109 | ||||||||
\(185\) | −267.415 | −0.106274 | ||||||||
\(186\) | −1797.23 | −0.708493 | ||||||||
\(187\) | −2296.49 | −0.898054 | ||||||||
\(188\) | −68.7374 | −0.0266659 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 757.854 | 0.289371 | ||||||||
\(191\) | −5068.33 | −1.92006 | −0.960030 | − | 0.279898i | \(-0.909699\pi\) | ||||
−0.960030 | + | 0.279898i | \(0.909699\pi\) | |||||||
\(192\) | 3248.52 | 1.22105 | ||||||||
\(193\) | 3444.56 | 1.28469 | 0.642345 | − | 0.766416i | \(-0.277962\pi\) | ||||
0.642345 | + | 0.766416i | \(0.277962\pi\) | |||||||
\(194\) | −1492.14 | −0.552214 | ||||||||
\(195\) | −2226.34 | −0.817597 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1769.61 | −0.639998 | −0.319999 | − | 0.947418i | \(-0.603683\pi\) | ||||
−0.319999 | + | 0.947418i | \(0.603683\pi\) | |||||||
\(198\) | 1611.02 | 0.578233 | ||||||||
\(199\) | 205.971 | 0.0733715 | 0.0366858 | − | 0.999327i | \(-0.488320\pi\) | ||||
0.0366858 | + | 0.999327i | \(0.488320\pi\) | |||||||
\(200\) | 571.751 | 0.202144 | ||||||||
\(201\) | 6041.25 | 2.11998 | ||||||||
\(202\) | 3696.29 | 1.28748 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −50.7613 | −0.0174216 | ||||||||
\(205\) | −202.476 | −0.0689833 | ||||||||
\(206\) | 4171.24 | 1.41080 | ||||||||
\(207\) | 1775.51 | 0.596165 | ||||||||
\(208\) | −4482.70 | −1.49432 | ||||||||
\(209\) | −2687.91 | −0.889603 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4973.82 | 1.62281 | 0.811403 | − | 0.584488i | \(-0.198704\pi\) | ||||
0.811403 | + | 0.584488i | \(0.198704\pi\) | |||||||
\(212\) | −58.0187 | −0.0187959 | ||||||||
\(213\) | 2404.11 | 0.773367 | ||||||||
\(214\) | 1229.35 | 0.392696 | ||||||||
\(215\) | −1885.97 | −0.598243 | ||||||||
\(216\) | −2186.84 | −0.688867 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −4092.37 | −1.27142 | ||||||||
\(219\) | −1365.31 | −0.421273 | ||||||||
\(220\) | −43.7605 | −0.0134106 | ||||||||
\(221\) | 3317.60 | 1.00980 | ||||||||
\(222\) | −929.560 | −0.281027 | ||||||||
\(223\) | 3355.68 | 1.00768 | 0.503841 | − | 0.863796i | \(-0.331920\pi\) | ||||
0.503841 | + | 0.863796i | \(0.331920\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 290.293 | 0.0860127 | ||||||||
\(226\) | 3552.70 | 1.04567 | ||||||||
\(227\) | −2083.10 | −0.609074 | −0.304537 | − | 0.952500i | \(-0.598502\pi\) | ||||
−0.304537 | + | 0.952500i | \(0.598502\pi\) | |||||||
\(228\) | −59.4133 | −0.0172576 | ||||||||
\(229\) | −5011.75 | −1.44623 | −0.723114 | − | 0.690729i | \(-0.757290\pi\) | ||||
−0.723114 | + | 0.690729i | \(0.757290\pi\) | |||||||
\(230\) | 2138.44 | 0.613064 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −881.108 | −0.249343 | ||||||||
\(233\) | 1150.64 | 0.323525 | 0.161762 | − | 0.986830i | \(-0.448282\pi\) | ||||
0.161762 | + | 0.986830i | \(0.448282\pi\) | |||||||
\(234\) | −2327.34 | −0.650184 | ||||||||
\(235\) | −1947.84 | −0.540693 | ||||||||
\(236\) | 7.00211 | 0.00193135 | ||||||||
\(237\) | −2401.49 | −0.658199 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1919.63 | 0.519543 | 0.259771 | − | 0.965670i | \(-0.416353\pi\) | ||||
0.259771 | + | 0.965670i | \(0.416353\pi\) | |||||||
\(240\) | 1943.60 | 0.522746 | ||||||||
\(241\) | −250.169 | −0.0668664 | −0.0334332 | − | 0.999441i | \(-0.510644\pi\) | ||||
−0.0334332 | + | 0.999441i | \(0.510644\pi\) | |||||||
\(242\) | −3158.97 | −0.839117 | ||||||||
\(243\) | −3058.45 | −0.807407 | ||||||||
\(244\) | −34.8409 | −0.00914123 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −703.828 | −0.182416 | ||||||||
\(247\) | 3883.07 | 1.00030 | ||||||||
\(248\) | 2364.88 | 0.605525 | ||||||||
\(249\) | −8555.41 | −2.17742 | ||||||||
\(250\) | 349.633 | 0.0884509 | ||||||||
\(251\) | 2905.43 | 0.730634 | 0.365317 | − | 0.930883i | \(-0.380961\pi\) | ||||
0.365317 | + | 0.930883i | \(0.380961\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7584.51 | −1.88472 | ||||||||
\(254\) | 1888.75 | 0.466577 | ||||||||
\(255\) | −1438.44 | −0.353250 | ||||||||
\(256\) | −270.887 | −0.0661346 | ||||||||
\(257\) | 1489.30 | 0.361478 | 0.180739 | − | 0.983531i | \(-0.442151\pi\) | ||||
0.180739 | + | 0.983531i | \(0.442151\pi\) | |||||||
\(258\) | −6555.82 | −1.58197 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 63.2181 | 0.0150793 | ||||||||
\(261\) | −447.362 | −0.106096 | ||||||||
\(262\) | −1943.76 | −0.458343 | ||||||||
\(263\) | 3309.86 | 0.776025 | 0.388013 | − | 0.921654i | \(-0.373162\pi\) | ||||
0.388013 | + | 0.921654i | \(0.373162\pi\) | |||||||
\(264\) | −7049.01 | −1.64332 | ||||||||
\(265\) | −1644.10 | −0.381118 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4660.71 | 1.06828 | ||||||||
\(268\) | −171.545 | −0.0390999 | ||||||||
\(269\) | 4110.05 | 0.931577 | 0.465789 | − | 0.884896i | \(-0.345771\pi\) | ||||
0.465789 | + | 0.884896i | \(0.345771\pi\) | |||||||
\(270\) | −1337.28 | −0.301423 | ||||||||
\(271\) | −1728.27 | −0.387399 | −0.193700 | − | 0.981061i | \(-0.562049\pi\) | ||||
−0.193700 | + | 0.981061i | \(0.562049\pi\) | |||||||
\(272\) | −2896.28 | −0.645636 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7046.07 | 1.55353 | ||||||||
\(275\) | −1240.06 | −0.271921 | ||||||||
\(276\) | −167.647 | −0.0365622 | ||||||||
\(277\) | −4548.14 | −0.986540 | −0.493270 | − | 0.869876i | \(-0.664198\pi\) | ||||
−0.493270 | + | 0.869876i | \(0.664198\pi\) | |||||||
\(278\) | 4787.48 | 1.03286 | ||||||||
\(279\) | 1200.71 | 0.257652 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3781.62 | −0.802821 | −0.401410 | − | 0.915898i | \(-0.631480\pi\) | ||||
−0.401410 | + | 0.915898i | \(0.631480\pi\) | |||||||
\(282\) | −6770.87 | −1.42979 | ||||||||
\(283\) | 953.988 | 0.200384 | 0.100192 | − | 0.994968i | \(-0.468054\pi\) | ||||
0.100192 | + | 0.994968i | \(0.468054\pi\) | |||||||
\(284\) | −68.2662 | −0.0142636 | ||||||||
\(285\) | −1683.62 | −0.349926 | ||||||||
\(286\) | 9941.81 | 2.05550 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −92.7026 | −0.0189672 | ||||||||
\(289\) | −2769.49 | −0.563706 | ||||||||
\(290\) | −538.809 | −0.109103 | ||||||||
\(291\) | 3314.88 | 0.667772 | ||||||||
\(292\) | 38.7686 | 0.00776973 | ||||||||
\(293\) | 4463.04 | 0.889875 | 0.444938 | − | 0.895562i | \(-0.353226\pi\) | ||||
0.444938 | + | 0.895562i | \(0.353226\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 198.422 | 0.0391612 | ||||||||
\(296\) | 1223.16 | 0.240184 | ||||||||
\(297\) | 4742.98 | 0.926653 | ||||||||
\(298\) | 2017.74 | 0.392229 | ||||||||
\(299\) | 10956.9 | 2.11924 | ||||||||
\(300\) | −27.4100 | −0.00527507 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2603.20 | −0.496018 | ||||||||
\(303\) | −8211.52 | −1.55690 | ||||||||
\(304\) | −3389.94 | −0.639560 | ||||||||
\(305\) | −987.300 | −0.185353 | ||||||||
\(306\) | −1503.70 | −0.280918 | ||||||||
\(307\) | 6617.48 | 1.23023 | 0.615113 | − | 0.788439i | \(-0.289110\pi\) | ||||
0.615113 | + | 0.788439i | \(0.289110\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9266.64 | −1.70602 | ||||||||
\(310\) | 1446.16 | 0.264955 | ||||||||
\(311\) | 168.563 | 0.0307342 | 0.0153671 | − | 0.999882i | \(-0.495108\pi\) | ||||
0.0153671 | + | 0.999882i | \(0.495108\pi\) | |||||||
\(312\) | 10183.3 | 1.84780 | ||||||||
\(313\) | 7501.86 | 1.35473 | 0.677364 | − | 0.735648i | \(-0.263122\pi\) | ||||
0.677364 | + | 0.735648i | \(0.263122\pi\) | |||||||
\(314\) | −6339.98 | −1.13944 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 68.1915 | 0.0121395 | ||||||||
\(317\) | 3425.16 | 0.606864 | 0.303432 | − | 0.952853i | \(-0.401867\pi\) | ||||
0.303432 | + | 0.952853i | \(0.401867\pi\) | |||||||
\(318\) | −5715.04 | −1.00781 | ||||||||
\(319\) | 1911.02 | 0.335412 | ||||||||
\(320\) | −2613.94 | −0.456637 | ||||||||
\(321\) | −2731.08 | −0.474872 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2508.86 | 0.432188 | ||||||||
\(324\) | 160.157 | 0.0274617 | ||||||||
\(325\) | 1791.44 | 0.305757 | ||||||||
\(326\) | −8934.65 | −1.51793 | ||||||||
\(327\) | 9091.43 | 1.53748 | ||||||||
\(328\) | 926.128 | 0.155905 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −4310.56 | −0.719056 | ||||||||
\(331\) | 1095.47 | 0.181911 | 0.0909557 | − | 0.995855i | \(-0.471008\pi\) | ||||
0.0909557 | + | 0.995855i | \(0.471008\pi\) | |||||||
\(332\) | 242.936 | 0.0401591 | ||||||||
\(333\) | 621.030 | 0.102199 | ||||||||
\(334\) | 1709.23 | 0.280014 | ||||||||
\(335\) | −4861.13 | −0.792812 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4241.92 | 0.685673 | 0.342837 | − | 0.939395i | \(-0.388612\pi\) | ||||
0.342837 | + | 0.939395i | \(0.388612\pi\) | |||||||
\(338\) | −8217.19 | −1.32236 | ||||||||
\(339\) | −7892.52 | −1.26449 | ||||||||
\(340\) | 40.8454 | 0.00651516 | ||||||||
\(341\) | −5129.14 | −0.814542 | ||||||||
\(342\) | −1760.00 | −0.278274 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 8626.45 | 1.35206 | ||||||||
\(345\) | −4750.67 | −0.741356 | ||||||||
\(346\) | −24.6455 | −0.00382934 | ||||||||
\(347\) | 78.1669 | 0.0120929 | 0.00604643 | − | 0.999982i | \(-0.498075\pi\) | ||||
0.00604643 | + | 0.999982i | \(0.498075\pi\) | |||||||
\(348\) | 42.2408 | 0.00650674 | ||||||||
\(349\) | −167.845 | −0.0257436 | −0.0128718 | − | 0.999917i | \(-0.504097\pi\) | ||||
−0.0128718 | + | 0.999917i | \(0.504097\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6851.90 | −1.04196 | ||||||||
\(352\) | 396.002 | 0.0599630 | ||||||||
\(353\) | −4872.81 | −0.734713 | −0.367357 | − | 0.930080i | \(-0.619737\pi\) | ||||
−0.367357 | + | 0.930080i | \(0.619737\pi\) | |||||||
\(354\) | 689.732 | 0.103556 | ||||||||
\(355\) | −1934.49 | −0.289216 | ||||||||
\(356\) | −132.344 | −0.0197028 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3496.77 | 0.516230 | ||||||||
\(359\) | 8449.53 | 1.24220 | 0.621099 | − | 0.783732i | \(-0.286687\pi\) | ||||
0.621099 | + | 0.783732i | \(0.286687\pi\) | |||||||
\(360\) | −1327.80 | −0.194392 | ||||||||
\(361\) | −3922.52 | −0.571879 | ||||||||
\(362\) | 6847.28 | 0.994157 | ||||||||
\(363\) | 7017.84 | 1.01471 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1098.60 | 0.157544 | ||||||||
\(366\) | −3431.95 | −0.490139 | ||||||||
\(367\) | −4801.20 | −0.682890 | −0.341445 | − | 0.939902i | \(-0.610916\pi\) | ||||
−0.341445 | + | 0.939902i | \(0.610916\pi\) | |||||||
\(368\) | −9565.41 | −1.35498 | ||||||||
\(369\) | 470.220 | 0.0663379 | ||||||||
\(370\) | 747.976 | 0.105096 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −113.374 | −0.0158015 | ||||||||
\(373\) | 6498.62 | 0.902106 | 0.451053 | − | 0.892497i | \(-0.351048\pi\) | ||||
0.451053 | + | 0.892497i | \(0.351048\pi\) | |||||||
\(374\) | 6423.43 | 0.888095 | ||||||||
\(375\) | −776.729 | −0.106960 | ||||||||
\(376\) | 8909.42 | 1.22199 | ||||||||
\(377\) | −2760.73 | −0.377148 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11049.4 | −1.49754 | −0.748770 | − | 0.662830i | \(-0.769355\pi\) | ||||
−0.748770 | + | 0.662830i | \(0.769355\pi\) | |||||||
\(380\) | 47.8073 | 0.00645384 | ||||||||
\(381\) | −4195.96 | −0.564214 | ||||||||
\(382\) | 14176.4 | 1.89877 | ||||||||
\(383\) | −8098.52 | −1.08046 | −0.540229 | − | 0.841518i | \(-0.681662\pi\) | ||||
−0.540229 | + | 0.841518i | \(0.681662\pi\) | |||||||
\(384\) | −8689.45 | −1.15477 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9634.66 | −1.27044 | ||||||||
\(387\) | 4379.88 | 0.575302 | ||||||||
\(388\) | −94.1278 | −0.0123160 | ||||||||
\(389\) | 5897.42 | 0.768666 | 0.384333 | − | 0.923194i | \(-0.374431\pi\) | ||||
0.384333 | + | 0.923194i | \(0.374431\pi\) | |||||||
\(390\) | 6227.21 | 0.808530 | ||||||||
\(391\) | 7079.27 | 0.915637 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4318.17 | 0.554257 | ||||||||
\(394\) | 4949.71 | 0.632901 | ||||||||
\(395\) | 1932.37 | 0.246147 | ||||||||
\(396\) | 101.627 | 0.0128963 | ||||||||
\(397\) | −11561.4 | −1.46159 | −0.730795 | − | 0.682597i | \(-0.760850\pi\) | ||||
−0.730795 | + | 0.682597i | \(0.760850\pi\) | |||||||
\(398\) | −576.115 | −0.0725579 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1563.93 | −0.195492 | ||||||||
\(401\) | −13069.2 | −1.62754 | −0.813769 | − | 0.581188i | \(-0.802588\pi\) | ||||
−0.813769 | + | 0.581188i | \(0.802588\pi\) | |||||||
\(402\) | −16897.7 | −2.09648 | ||||||||
\(403\) | 7409.77 | 0.915898 | ||||||||
\(404\) | 233.171 | 0.0287146 | ||||||||
\(405\) | 4538.42 | 0.556830 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2652.88 | −0.323092 | ||||||||
\(408\) | 6579.44 | 0.798360 | ||||||||
\(409\) | −439.733 | −0.0531623 | −0.0265812 | − | 0.999647i | \(-0.508462\pi\) | ||||
−0.0265812 | + | 0.999647i | \(0.508462\pi\) | |||||||
\(410\) | 566.339 | 0.0682183 | ||||||||
\(411\) | −15653.2 | −1.87863 | ||||||||
\(412\) | 263.132 | 0.0314650 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −4966.20 | −0.589554 | ||||||||
\(415\) | 6884.16 | 0.814290 | ||||||||
\(416\) | −572.080 | −0.0674244 | ||||||||
\(417\) | −10635.7 | −1.24899 | ||||||||
\(418\) | 7518.26 | 0.879738 | ||||||||
\(419\) | 1673.71 | 0.195146 | 0.0975730 | − | 0.995228i | \(-0.468892\pi\) | ||||
0.0975730 | + | 0.995228i | \(0.468892\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 805.413 | 0.0932385 | 0.0466192 | − | 0.998913i | \(-0.485155\pi\) | ||||
0.0466192 | + | 0.998913i | \(0.485155\pi\) | |||||||
\(422\) | −13912.1 | −1.60481 | ||||||||
\(423\) | 4523.55 | 0.519959 | ||||||||
\(424\) | 7520.11 | 0.861342 | ||||||||
\(425\) | 1157.45 | 0.132105 | ||||||||
\(426\) | −6724.46 | −0.764791 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 77.5506 | 0.00875829 | ||||||||
\(429\) | −22086.3 | −2.48563 | ||||||||
\(430\) | 5275.18 | 0.591609 | ||||||||
\(431\) | 908.315 | 0.101513 | 0.0507564 | − | 0.998711i | \(-0.483837\pi\) | ||||
0.0507564 | + | 0.998711i | \(0.483837\pi\) | |||||||
\(432\) | 5981.74 | 0.666196 | ||||||||
\(433\) | 1464.37 | 0.162524 | 0.0812621 | − | 0.996693i | \(-0.474105\pi\) | ||||
0.0812621 | + | 0.996693i | \(0.474105\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1196.99 | 0.131934 | ||||||||
\(436\) | −258.157 | −0.0283565 | ||||||||
\(437\) | 8285.89 | 0.907020 | ||||||||
\(438\) | 3818.84 | 0.416601 | ||||||||
\(439\) | −7413.86 | −0.806024 | −0.403012 | − | 0.915195i | \(-0.632037\pi\) | ||||
−0.403012 | + | 0.915195i | \(0.632037\pi\) | |||||||
\(440\) | 5672.03 | 0.614553 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9279.54 | −0.998604 | ||||||||
\(443\) | 8656.90 | 0.928447 | 0.464223 | − | 0.885718i | \(-0.346333\pi\) | ||||
0.464223 | + | 0.885718i | \(0.346333\pi\) | |||||||
\(444\) | −58.6389 | −0.00626774 | ||||||||
\(445\) | −3750.27 | −0.399505 | ||||||||
\(446\) | −9386.05 | −0.996507 | ||||||||
\(447\) | −4482.52 | −0.474308 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7138.71 | 0.750326 | 0.375163 | − | 0.926959i | \(-0.377587\pi\) | ||||
0.375163 | + | 0.926959i | \(0.377587\pi\) | |||||||
\(450\) | −811.967 | −0.0850589 | ||||||||
\(451\) | −2008.66 | −0.209721 | ||||||||
\(452\) | 224.113 | 0.0233216 | ||||||||
\(453\) | 5783.16 | 0.599816 | ||||||||
\(454\) | 5826.55 | 0.602320 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7700.87 | 0.790847 | ||||||||
\(457\) | 9955.60 | 1.01904 | 0.509522 | − | 0.860457i | \(-0.329822\pi\) | ||||
0.509522 | + | 0.860457i | \(0.329822\pi\) | |||||||
\(458\) | 14018.2 | 1.43019 | ||||||||
\(459\) | −4427.03 | −0.450188 | ||||||||
\(460\) | 134.898 | 0.0136732 | ||||||||
\(461\) | −10380.2 | −1.04870 | −0.524351 | − | 0.851502i | \(-0.675692\pi\) | ||||
−0.524351 | + | 0.851502i | \(0.675692\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2851.77 | −0.286249 | −0.143124 | − | 0.989705i | \(-0.545715\pi\) | ||||
−0.143124 | + | 0.989705i | \(0.545715\pi\) | |||||||
\(464\) | 2410.13 | 0.241137 | ||||||||
\(465\) | −3212.72 | −0.320401 | ||||||||
\(466\) | −3218.42 | −0.319937 | ||||||||
\(467\) | −12568.5 | −1.24540 | −0.622698 | − | 0.782462i | \(-0.713963\pi\) | ||||
−0.622698 | + | 0.782462i | \(0.713963\pi\) | |||||||
\(468\) | −146.814 | −0.0145011 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 5448.22 | 0.534697 | ||||||||
\(471\) | 14084.6 | 1.37789 | ||||||||
\(472\) | −907.581 | −0.0885060 | ||||||||
\(473\) | −18709.7 | −1.81876 | ||||||||
\(474\) | 6717.10 | 0.650900 | ||||||||
\(475\) | 1354.73 | 0.130862 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3818.16 | 0.366502 | ||||||||
\(478\) | −5369.33 | −0.513781 | ||||||||
\(479\) | 5539.53 | 0.528409 | 0.264204 | − | 0.964467i | \(-0.414891\pi\) | ||||
0.264204 | + | 0.964467i | \(0.414891\pi\) | |||||||
\(480\) | 248.042 | 0.0235865 | ||||||||
\(481\) | 3832.46 | 0.363295 | ||||||||
\(482\) | 699.738 | 0.0661249 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −199.276 | −0.0187148 | ||||||||
\(485\) | −2667.34 | −0.249727 | ||||||||
\(486\) | 8554.68 | 0.798453 | ||||||||
\(487\) | −10949.9 | −1.01886 | −0.509432 | − | 0.860511i | \(-0.670144\pi\) | ||||
−0.509432 | + | 0.860511i | \(0.670144\pi\) | |||||||
\(488\) | 4515.92 | 0.418906 | ||||||||
\(489\) | 19848.8 | 1.83557 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5381.76 | 0.494654 | 0.247327 | − | 0.968932i | \(-0.420448\pi\) | ||||
0.247327 | + | 0.968932i | \(0.420448\pi\) | |||||||
\(492\) | −44.3991 | −0.00406843 | ||||||||
\(493\) | −1783.72 | −0.162950 | ||||||||
\(494\) | −10861.2 | −0.989206 | ||||||||
\(495\) | 2879.84 | 0.261493 | ||||||||
\(496\) | −6468.76 | −0.585597 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 23930.0 | 2.15327 | ||||||||
\(499\) | 13142.8 | 1.17906 | 0.589530 | − | 0.807747i | \(-0.299313\pi\) | ||||
0.589530 | + | 0.807747i | \(0.299313\pi\) | |||||||
\(500\) | 22.0557 | 0.00197272 | ||||||||
\(501\) | −3797.14 | −0.338611 | ||||||||
\(502\) | −8126.67 | −0.722532 | ||||||||
\(503\) | −5172.75 | −0.458532 | −0.229266 | − | 0.973364i | \(-0.573633\pi\) | ||||
−0.229266 | + | 0.973364i | \(0.573633\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6607.45 | 0.582233 | ||||||||
\(506\) | 21214.3 | 1.86382 | ||||||||
\(507\) | 18255.0 | 1.59908 | ||||||||
\(508\) | 119.147 | 0.0104061 | ||||||||
\(509\) | −5487.45 | −0.477852 | −0.238926 | − | 0.971038i | \(-0.576795\pi\) | ||||
−0.238926 | + | 0.971038i | \(0.576795\pi\) | |||||||
\(510\) | 4023.41 | 0.349333 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 11944.9 | 1.03105 | ||||||||
\(513\) | −5181.59 | −0.445951 | ||||||||
\(514\) | −4165.65 | −0.357469 | ||||||||
\(515\) | 7456.46 | 0.638002 | ||||||||
\(516\) | −413.557 | −0.0352826 | ||||||||
\(517\) | −19323.5 | −1.64380 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 54.7514 | 0.00463067 | ||||||||
\(520\) | −8194.04 | −0.691024 | ||||||||
\(521\) | −9911.27 | −0.833437 | −0.416719 | − | 0.909036i | \(-0.636820\pi\) | ||||
−0.416719 | + | 0.909036i | \(0.636820\pi\) | |||||||
\(522\) | 1251.30 | 0.104919 | ||||||||
\(523\) | 328.966 | 0.0275042 | 0.0137521 | − | 0.999905i | \(-0.495622\pi\) | ||||
0.0137521 | + | 0.999905i | \(0.495622\pi\) | |||||||
\(524\) | −122.617 | −0.0102224 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9257.88 | −0.767420 | ||||||||
\(527\) | 4787.47 | 0.395722 | ||||||||
\(528\) | 19281.4 | 1.58924 | ||||||||
\(529\) | 11213.4 | 0.921621 | ||||||||
\(530\) | 4598.64 | 0.376891 | ||||||||
\(531\) | −460.803 | −0.0376594 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2901.79 | 0.235817 | ||||||||
\(534\) | −13036.3 | −1.05643 | ||||||||
\(535\) | 2197.58 | 0.177588 | ||||||||
\(536\) | 22234.8 | 1.79179 | ||||||||
\(537\) | −7768.28 | −0.624257 | ||||||||
\(538\) | −11496.1 | −0.921247 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −84.3587 | −0.00672263 | ||||||||
\(541\) | −11235.5 | −0.892884 | −0.446442 | − | 0.894813i | \(-0.647309\pi\) | ||||
−0.446442 | + | 0.894813i | \(0.647309\pi\) | |||||||
\(542\) | 4834.09 | 0.383103 | ||||||||
\(543\) | −15211.6 | −1.20220 | ||||||||
\(544\) | −369.623 | −0.0291313 | ||||||||
\(545\) | −7315.48 | −0.574974 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19423.1 | −1.51823 | −0.759115 | − | 0.650957i | \(-0.774368\pi\) | ||||
−0.759115 | + | 0.650957i | \(0.774368\pi\) | |||||||
\(548\) | 444.483 | 0.0346485 | ||||||||
\(549\) | 2292.85 | 0.178245 | ||||||||
\(550\) | 3468.52 | 0.268906 | ||||||||
\(551\) | −2087.74 | −0.161417 | ||||||||
\(552\) | 21729.6 | 1.67550 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 12721.4 | 0.975600 | ||||||||
\(555\) | −1661.67 | −0.127088 | ||||||||
\(556\) | 302.006 | 0.0230358 | ||||||||
\(557\) | 12912.4 | 0.982254 | 0.491127 | − | 0.871088i | \(-0.336585\pi\) | ||||
0.491127 | + | 0.871088i | \(0.336585\pi\) | |||||||
\(558\) | −3358.47 | −0.254795 | ||||||||
\(559\) | 27028.8 | 2.04508 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14270.0 | −1.07394 | ||||||||
\(562\) | 10577.4 | 0.793918 | ||||||||
\(563\) | 5883.84 | 0.440452 | 0.220226 | − | 0.975449i | \(-0.429321\pi\) | ||||
0.220226 | + | 0.975449i | \(0.429321\pi\) | |||||||
\(564\) | −427.123 | −0.0318885 | ||||||||
\(565\) | 6350.77 | 0.472883 | ||||||||
\(566\) | −2668.36 | −0.198162 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8848.35 | 0.653642 | ||||||||
\(569\) | 3037.55 | 0.223797 | 0.111899 | − | 0.993720i | \(-0.464307\pi\) | ||||
0.111899 | + | 0.993720i | \(0.464307\pi\) | |||||||
\(570\) | 4709.18 | 0.346045 | ||||||||
\(571\) | 15684.7 | 1.14953 | 0.574766 | − | 0.818318i | \(-0.305093\pi\) | ||||
0.574766 | + | 0.818318i | \(0.305093\pi\) | |||||||
\(572\) | 627.153 | 0.0458437 | ||||||||
\(573\) | −31493.7 | −2.29611 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3822.66 | 0.277245 | ||||||||
\(576\) | 6070.48 | 0.439126 | ||||||||
\(577\) | −16184.0 | −1.16767 | −0.583837 | − | 0.811871i | \(-0.698449\pi\) | ||||
−0.583837 | + | 0.811871i | \(0.698449\pi\) | |||||||
\(578\) | 7746.43 | 0.557455 | ||||||||
\(579\) | 21403.9 | 1.53630 | ||||||||
\(580\) | −33.9893 | −0.00243333 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −9271.92 | −0.660366 | ||||||||
\(583\) | −16310.2 | −1.15866 | ||||||||
\(584\) | −5025.01 | −0.356055 | ||||||||
\(585\) | −4160.33 | −0.294032 | ||||||||
\(586\) | −12483.4 | −0.880007 | ||||||||
\(587\) | 9256.04 | 0.650831 | 0.325415 | − | 0.945571i | \(-0.394496\pi\) | ||||
0.325415 | + | 0.945571i | \(0.394496\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5603.46 | 0.391998 | ||||||||
\(590\) | −554.998 | −0.0387269 | ||||||||
\(591\) | −10996.1 | −0.765344 | ||||||||
\(592\) | −3345.75 | −0.232280 | ||||||||
\(593\) | 19154.5 | 1.32645 | 0.663223 | − | 0.748422i | \(-0.269188\pi\) | ||||
0.663223 | + | 0.748422i | \(0.269188\pi\) | |||||||
\(594\) | −13266.4 | −0.916377 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 127.284 | 0.00874788 | ||||||||
\(597\) | 1279.87 | 0.0877415 | ||||||||
\(598\) | −30647.1 | −2.09574 | ||||||||
\(599\) | 20884.5 | 1.42457 | 0.712285 | − | 0.701891i | \(-0.247660\pi\) | ||||
0.712285 | + | 0.701891i | \(0.247660\pi\) | |||||||
\(600\) | 3552.76 | 0.241735 | ||||||||
\(601\) | −8569.93 | −0.581655 | −0.290828 | − | 0.956775i | \(-0.593931\pi\) | ||||
−0.290828 | + | 0.956775i | \(0.593931\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11289.2 | 0.762409 | ||||||||
\(604\) | −164.216 | −0.0110627 | ||||||||
\(605\) | −5646.95 | −0.379473 | ||||||||
\(606\) | 22968.1 | 1.53963 | ||||||||
\(607\) | −19361.0 | −1.29463 | −0.647313 | − | 0.762225i | \(-0.724107\pi\) | ||||
−0.647313 | + | 0.762225i | \(0.724107\pi\) | |||||||
\(608\) | −432.622 | −0.0288572 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2761.54 | 0.183298 | ||||||||
\(611\) | 27915.4 | 1.84834 | ||||||||
\(612\) | −94.8571 | −0.00626531 | ||||||||
\(613\) | −15907.2 | −1.04810 | −0.524050 | − | 0.851688i | \(-0.675579\pi\) | ||||
−0.524050 | + | 0.851688i | \(0.675579\pi\) | |||||||
\(614\) | −18509.5 | −1.21658 | ||||||||
\(615\) | −1258.16 | −0.0824938 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17496.4 | 1.14162 | 0.570810 | − | 0.821082i | \(-0.306629\pi\) | ||||
0.570810 | + | 0.821082i | \(0.306629\pi\) | |||||||
\(618\) | 25919.4 | 1.68710 | ||||||||
\(619\) | 22908.6 | 1.48752 | 0.743758 | − | 0.668449i | \(-0.233041\pi\) | ||||
0.743758 | + | 0.668449i | \(0.233041\pi\) | |||||||
\(620\) | 91.2270 | 0.00590930 | ||||||||
\(621\) | −14620.9 | −0.944796 | ||||||||
\(622\) | −471.482 | −0.0303934 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −27854.7 | −1.78699 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −20983.2 | −1.33971 | ||||||||
\(627\) | −16702.3 | −1.06383 | ||||||||
\(628\) | −399.941 | −0.0254130 | ||||||||
\(629\) | 2476.16 | 0.156965 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27379.1 | 1.72733 | 0.863665 | − | 0.504066i | \(-0.168163\pi\) | ||||
0.863665 | + | 0.504066i | \(0.168163\pi\) | |||||||
\(632\) | −8838.67 | −0.556303 | ||||||||
\(633\) | 30906.5 | 1.94064 | ||||||||
\(634\) | −9580.37 | −0.600134 | ||||||||
\(635\) | 3376.30 | 0.210999 | ||||||||
\(636\) | −360.519 | −0.0224772 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5345.23 | −0.331692 | ||||||||
\(639\) | 4492.54 | 0.278125 | ||||||||
\(640\) | 6992.02 | 0.431850 | ||||||||
\(641\) | −8816.10 | −0.543237 | −0.271619 | − | 0.962405i | \(-0.587559\pi\) | ||||
−0.271619 | + | 0.962405i | \(0.587559\pi\) | |||||||
\(642\) | 7639.00 | 0.469606 | ||||||||
\(643\) | 25760.8 | 1.57995 | 0.789975 | − | 0.613139i | \(-0.210094\pi\) | ||||
0.789975 | + | 0.613139i | \(0.210094\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11719.1 | −0.715411 | ||||||||
\(646\) | −7017.44 | −0.427395 | ||||||||
\(647\) | −21618.1 | −1.31359 | −0.656797 | − | 0.754067i | \(-0.728089\pi\) | ||||
−0.656797 | + | 0.754067i | \(0.728089\pi\) | |||||||
\(648\) | −20758.8 | −1.25846 | ||||||||
\(649\) | 1968.43 | 0.119057 | ||||||||
\(650\) | −5010.76 | −0.302366 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −563.619 | −0.0338543 | ||||||||
\(653\) | −25008.3 | −1.49870 | −0.749349 | − | 0.662175i | \(-0.769633\pi\) | ||||
−0.749349 | + | 0.662175i | \(0.769633\pi\) | |||||||
\(654\) | −25429.3 | −1.52044 | ||||||||
\(655\) | −3474.64 | −0.207276 | ||||||||
\(656\) | −2533.28 | −0.150774 | ||||||||
\(657\) | −2551.33 | −0.151502 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −29424.3 | −1.73932 | −0.869658 | − | 0.493655i | \(-0.835660\pi\) | ||||
−0.869658 | + | 0.493655i | \(0.835660\pi\) | |||||||
\(660\) | −271.920 | −0.0160371 | ||||||||
\(661\) | −21022.4 | −1.23703 | −0.618513 | − | 0.785774i | \(-0.712265\pi\) | ||||
−0.618513 | + | 0.785774i | \(0.712265\pi\) | |||||||
\(662\) | −3064.11 | −0.179894 | ||||||||
\(663\) | 20615.0 | 1.20757 | ||||||||
\(664\) | −31488.2 | −1.84033 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1737.06 | −0.101066 | ||||||||
\(667\) | −5890.99 | −0.341979 | ||||||||
\(668\) | 107.822 | 0.00624515 | ||||||||
\(669\) | 20851.6 | 1.20504 | ||||||||
\(670\) | 13596.9 | 0.784020 | ||||||||
\(671\) | −9794.48 | −0.563504 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5241.08 | 0.300192 | 0.150096 | − | 0.988671i | \(-0.452042\pi\) | ||||
0.150096 | + | 0.988671i | \(0.452042\pi\) | |||||||
\(674\) | −11864.9 | −0.678069 | ||||||||
\(675\) | −2390.51 | −0.136312 | ||||||||
\(676\) | −518.360 | −0.0294925 | ||||||||
\(677\) | 5348.26 | 0.303620 | 0.151810 | − | 0.988410i | \(-0.451490\pi\) | ||||
0.151810 | + | 0.988410i | \(0.451490\pi\) | |||||||
\(678\) | 22075.9 | 1.25047 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −5294.19 | −0.298563 | ||||||||
\(681\) | −12944.0 | −0.728363 | ||||||||
\(682\) | 14346.5 | 0.805509 | ||||||||
\(683\) | 17974.4 | 1.00699 | 0.503494 | − | 0.863999i | \(-0.332048\pi\) | ||||
0.503494 | + | 0.863999i | \(0.332048\pi\) | |||||||
\(684\) | −111.025 | −0.00620635 | ||||||||
\(685\) | 12595.5 | 0.702553 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −31142.2 | −1.72947 | ||||||||
\(688\) | −23596.3 | −1.30756 | ||||||||
\(689\) | 23562.4 | 1.30284 | ||||||||
\(690\) | 13287.9 | 0.733134 | ||||||||
\(691\) | 23734.1 | 1.30664 | 0.653319 | − | 0.757083i | \(-0.273376\pi\) | ||||
0.653319 | + | 0.757083i | \(0.273376\pi\) | |||||||
\(692\) | −1.55470 | −8.54056e−5 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −218.638 | −0.0119587 | ||||||||
\(695\) | 8558.05 | 0.467087 | ||||||||
\(696\) | −5475.06 | −0.298177 | ||||||||
\(697\) | 1874.85 | 0.101887 | ||||||||
\(698\) | 469.472 | 0.0254581 | ||||||||
\(699\) | 7149.91 | 0.386888 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31094.0 | −1.67533 | −0.837664 | − | 0.546186i | \(-0.816079\pi\) | ||||
−0.837664 | + | 0.546186i | \(0.816079\pi\) | |||||||
\(702\) | 19165.2 | 1.03040 | ||||||||
\(703\) | 2898.21 | 0.155488 | ||||||||
\(704\) | −25931.5 | −1.38826 | ||||||||
\(705\) | −12103.5 | −0.646590 | ||||||||
\(706\) | 13629.6 | 0.726566 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 43.5100 | 0.00230961 | ||||||||
\(709\) | −9053.94 | −0.479588 | −0.239794 | − | 0.970824i | \(-0.577080\pi\) | ||||
−0.239794 | + | 0.970824i | \(0.577080\pi\) | |||||||
\(710\) | 5410.88 | 0.286009 | ||||||||
\(711\) | −4487.63 | −0.236708 | ||||||||
\(712\) | 17153.8 | 0.902899 | ||||||||
\(713\) | 15811.3 | 0.830490 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17771.9 | 0.929554 | ||||||||
\(716\) | 220.585 | 0.0115135 | ||||||||
\(717\) | 11928.3 | 0.621296 | ||||||||
\(718\) | −23633.8 | −1.22842 | ||||||||
\(719\) | −1101.81 | −0.0571498 | −0.0285749 | − | 0.999592i | \(-0.509097\pi\) | ||||
−0.0285749 | + | 0.999592i | \(0.509097\pi\) | |||||||
\(720\) | 3631.99 | 0.187995 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 10971.5 | 0.565537 | ||||||||
\(723\) | −1554.51 | −0.0799624 | ||||||||
\(724\) | 431.943 | 0.0221727 | ||||||||
\(725\) | −963.169 | −0.0493396 | ||||||||
\(726\) | −19629.3 | −1.00346 | ||||||||
\(727\) | −6476.47 | −0.330397 | −0.165199 | − | 0.986260i | \(-0.552827\pi\) | ||||
−0.165199 | + | 0.986260i | \(0.552827\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5502.76 | 0.279569 | ||||||||
\(730\) | −3072.86 | −0.155797 | ||||||||
\(731\) | 17463.4 | 0.883593 | ||||||||
\(732\) | −216.496 | −0.0109316 | ||||||||
\(733\) | −16111.9 | −0.811880 | −0.405940 | − | 0.913900i | \(-0.633056\pi\) | ||||
−0.405940 | + | 0.913900i | \(0.633056\pi\) | |||||||
\(734\) | 13429.3 | 0.675317 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1220.73 | −0.0611370 | ||||||||
\(737\) | −48224.7 | −2.41028 | ||||||||
\(738\) | −1315.23 | −0.0656022 | ||||||||
\(739\) | −9172.27 | −0.456573 | −0.228286 | − | 0.973594i | \(-0.573312\pi\) | ||||
−0.228286 | + | 0.973594i | \(0.573312\pi\) | |||||||
\(740\) | 47.1841 | 0.00234395 | ||||||||
\(741\) | 24128.7 | 1.19621 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3249.07 | 0.160426 | 0.0802131 | − | 0.996778i | \(-0.474440\pi\) | ||||
0.0802131 | + | 0.996778i | \(0.474440\pi\) | |||||||
\(744\) | 14695.0 | 0.724119 | ||||||||
\(745\) | 3606.88 | 0.177377 | ||||||||
\(746\) | −18177.0 | −0.892103 | ||||||||
\(747\) | −15987.4 | −0.783063 | ||||||||
\(748\) | 405.205 | 0.0198072 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2172.56 | 0.105774 | ||||||||
\(751\) | −24191.6 | −1.17545 | −0.587726 | − | 0.809060i | \(-0.699977\pi\) | ||||
−0.587726 | + | 0.809060i | \(0.699977\pi\) | |||||||
\(752\) | −24370.3 | −1.18177 | ||||||||
\(753\) | 18053.9 | 0.873731 | ||||||||
\(754\) | 7721.94 | 0.372966 | ||||||||
\(755\) | −4653.46 | −0.224313 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21282.7 | −1.02184 | −0.510919 | − | 0.859629i | \(-0.670695\pi\) | ||||
−0.510919 | + | 0.859629i | \(0.670695\pi\) | |||||||
\(758\) | 30905.8 | 1.48093 | ||||||||
\(759\) | −47128.9 | −2.25385 | ||||||||
\(760\) | −6196.55 | −0.295753 | ||||||||
\(761\) | 32224.5 | 1.53500 | 0.767501 | − | 0.641047i | \(-0.221500\pi\) | ||||
0.767501 | + | 0.641047i | \(0.221500\pi\) | |||||||
\(762\) | 11736.4 | 0.557957 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 894.283 | 0.0423482 | ||||||||
\(765\) | −2688.00 | −0.127039 | ||||||||
\(766\) | 22652.1 | 1.06848 | ||||||||
\(767\) | −2843.68 | −0.133871 | ||||||||
\(768\) | −1683.25 | −0.0790872 | ||||||||
\(769\) | −25116.5 | −1.17780 | −0.588898 | − | 0.808208i | \(-0.700438\pi\) | ||||
−0.588898 | + | 0.808208i | \(0.700438\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9254.24 | 0.432274 | ||||||||
\(772\) | −607.777 | −0.0283347 | ||||||||
\(773\) | −11824.7 | −0.550202 | −0.275101 | − | 0.961415i | \(-0.588711\pi\) | ||||
−0.275101 | + | 0.961415i | \(0.588711\pi\) | |||||||
\(774\) | −12250.8 | −0.568922 | ||||||||
\(775\) | 2585.13 | 0.119820 | ||||||||
\(776\) | 12200.4 | 0.564393 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −16495.5 | −0.760142 | ||||||||
\(779\) | 2194.41 | 0.100928 | ||||||||
\(780\) | 392.827 | 0.0180326 | ||||||||
\(781\) | −19191.0 | −0.879267 | ||||||||
\(782\) | −19801.2 | −0.905484 | ||||||||
\(783\) | 3683.94 | 0.168139 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11333.3 | −0.515289 | ||||||||
\(786\) | −12078.2 | −0.548111 | ||||||||
\(787\) | −20291.0 | −0.919053 | −0.459527 | − | 0.888164i | \(-0.651981\pi\) | ||||
−0.459527 | + | 0.888164i | \(0.651981\pi\) | |||||||
\(788\) | 312.240 | 0.0141156 | ||||||||
\(789\) | 20566.9 | 0.928012 | ||||||||
\(790\) | −5404.96 | −0.243417 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −13172.4 | −0.590986 | ||||||||
\(793\) | 14149.5 | 0.633623 | ||||||||
\(794\) | 32338.0 | 1.44538 | ||||||||
\(795\) | −10216.2 | −0.455760 | ||||||||
\(796\) | −36.3427 | −0.00161826 | ||||||||
\(797\) | −37140.0 | −1.65065 | −0.825325 | − | 0.564658i | \(-0.809008\pi\) | ||||
−0.825325 | + | 0.564658i | \(0.809008\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18036.2 | 0.798594 | ||||||||
\(800\) | −199.588 | −0.00882065 | ||||||||
\(801\) | 8709.42 | 0.384185 | ||||||||
\(802\) | 36555.3 | 1.60949 | ||||||||
\(803\) | 10898.6 | 0.478959 | ||||||||
\(804\) | −1065.95 | −0.0467577 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −20725.6 | −0.905741 | ||||||||
\(807\) | 25539.2 | 1.11403 | ||||||||
\(808\) | −30222.5 | −1.31587 | ||||||||
\(809\) | −3834.95 | −0.166662 | −0.0833311 | − | 0.996522i | \(-0.526556\pi\) | ||||
−0.0833311 | + | 0.996522i | \(0.526556\pi\) | |||||||
\(810\) | −12694.2 | −0.550655 | ||||||||
\(811\) | −19628.9 | −0.849894 | −0.424947 | − | 0.905218i | \(-0.639707\pi\) | ||||
−0.424947 | + | 0.905218i | \(0.639707\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10739.2 | −0.463272 | ||||||||
\(814\) | 7420.27 | 0.319509 | ||||||||
\(815\) | −15971.5 | −0.686450 | ||||||||
\(816\) | −17997.0 | −0.772086 | ||||||||
\(817\) | 20439.9 | 0.875278 | ||||||||
\(818\) | 1229.96 | 0.0525728 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 35.7260 | 0.00152147 | ||||||||
\(821\) | −12225.4 | −0.519696 | −0.259848 | − | 0.965650i | \(-0.583672\pi\) | ||||
−0.259848 | + | 0.965650i | \(0.583672\pi\) | |||||||
\(822\) | 43783.1 | 1.85780 | ||||||||
\(823\) | 25094.4 | 1.06286 | 0.531431 | − | 0.847102i | \(-0.321655\pi\) | ||||
0.531431 | + | 0.847102i | \(0.321655\pi\) | |||||||
\(824\) | −34105.9 | −1.44191 | ||||||||
\(825\) | −7705.51 | −0.325178 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36846.0 | 1.54929 | 0.774644 | − | 0.632397i | \(-0.217929\pi\) | ||||
0.774644 | + | 0.632397i | \(0.217929\pi\) | |||||||
\(828\) | −313.280 | −0.0131488 | ||||||||
\(829\) | −35126.1 | −1.47163 | −0.735814 | − | 0.677184i | \(-0.763200\pi\) | ||||
−0.735814 | + | 0.677184i | \(0.763200\pi\) | |||||||
\(830\) | −19255.4 | −0.805260 | ||||||||
\(831\) | −28261.4 | −1.17976 | ||||||||
\(832\) | 37461.7 | 1.56100 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 29748.6 | 1.23514 | ||||||||
\(835\) | 3055.40 | 0.126630 | ||||||||
\(836\) | 474.270 | 0.0196208 | ||||||||
\(837\) | −9887.64 | −0.408324 | ||||||||
\(838\) | −4681.48 | −0.192982 | ||||||||
\(839\) | 20946.7 | 0.861931 | 0.430965 | − | 0.902368i | \(-0.358173\pi\) | ||||
0.430965 | + | 0.902368i | \(0.358173\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22904.7 | −0.939140 | ||||||||
\(842\) | −2252.79 | −0.0922045 | ||||||||
\(843\) | −23498.4 | −0.960055 | ||||||||
\(844\) | −877.607 | −0.0357921 | ||||||||
\(845\) | −14689.0 | −0.598007 | ||||||||
\(846\) | −12652.6 | −0.514193 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −20570.1 | −0.832994 | ||||||||
\(849\) | 5927.92 | 0.239630 | ||||||||
\(850\) | −3237.47 | −0.130640 | ||||||||
\(851\) | 8177.89 | 0.329418 | ||||||||
\(852\) | −424.195 | −0.0170571 | ||||||||
\(853\) | −30591.5 | −1.22794 | −0.613969 | − | 0.789330i | \(-0.710428\pi\) | ||||
−0.613969 | + | 0.789330i | \(0.710428\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3146.16 | −0.125844 | ||||||||
\(856\) | −10051.7 | −0.401357 | ||||||||
\(857\) | −6484.50 | −0.258467 | −0.129233 | − | 0.991614i | \(-0.541252\pi\) | ||||
−0.129233 | + | 0.991614i | \(0.541252\pi\) | |||||||
\(858\) | 61776.8 | 2.45807 | ||||||||
\(859\) | −43597.9 | −1.73171 | −0.865857 | − | 0.500292i | \(-0.833226\pi\) | ||||
−0.865857 | + | 0.500292i | \(0.833226\pi\) | |||||||
\(860\) | 332.771 | 0.0131947 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2540.61 | −0.100387 | ||||||||
\(863\) | −5402.94 | −0.213115 | −0.106558 | − | 0.994307i | \(-0.533983\pi\) | ||||
−0.106558 | + | 0.994307i | \(0.533983\pi\) | |||||||
\(864\) | 763.387 | 0.0300590 | ||||||||
\(865\) | −44.0560 | −0.00173173 | ||||||||
\(866\) | −4095.93 | −0.160722 | ||||||||
\(867\) | −17209.1 | −0.674109 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19170.0 | 0.748329 | ||||||||
\(870\) | −3348.07 | −0.130471 | ||||||||
\(871\) | 69667.3 | 2.71020 | ||||||||
\(872\) | 33461.0 | 1.29947 | ||||||||
\(873\) | 6194.47 | 0.240150 | ||||||||
\(874\) | −23176.1 | −0.896962 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 240.902 | 0.00929146 | ||||||||
\(877\) | 48981.8 | 1.88597 | 0.942987 | − | 0.332831i | \(-0.108004\pi\) | ||||
0.942987 | + | 0.332831i | \(0.108004\pi\) | |||||||
\(878\) | 20737.0 | 0.797085 | ||||||||
\(879\) | 27732.6 | 1.06416 | ||||||||
\(880\) | −15514.9 | −0.594328 | ||||||||
\(881\) | 13125.8 | 0.501952 | 0.250976 | − | 0.967993i | \(-0.419248\pi\) | ||||
0.250976 | + | 0.967993i | \(0.419248\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7496.22 | −0.285694 | −0.142847 | − | 0.989745i | \(-0.545626\pi\) | ||||
−0.142847 | + | 0.989745i | \(0.545626\pi\) | |||||||
\(884\) | −585.376 | −0.0222719 | ||||||||
\(885\) | 1232.96 | 0.0468310 | ||||||||
\(886\) | −24213.9 | −0.918151 | ||||||||
\(887\) | 46027.7 | 1.74235 | 0.871173 | − | 0.490977i | \(-0.163360\pi\) | ||||
0.871173 | + | 0.490977i | \(0.163360\pi\) | |||||||
\(888\) | 7600.50 | 0.287225 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 10489.7 | 0.395075 | ||||||||
\(891\) | 45023.2 | 1.69286 | ||||||||
\(892\) | −592.094 | −0.0222251 | ||||||||
\(893\) | 21110.4 | 0.791078 | ||||||||
\(894\) | 12537.9 | 0.469048 | ||||||||
\(895\) | 6250.80 | 0.233454 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 68084.3 | 2.53430 | ||||||||
\(898\) | −19967.4 | −0.742006 | ||||||||
\(899\) | −3983.87 | −0.147797 | ||||||||
\(900\) | −51.2208 | −0.00189707 | ||||||||
\(901\) | 15223.7 | 0.562903 | ||||||||
\(902\) | 5618.35 | 0.207395 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −29048.4 | −1.06874 | ||||||||
\(905\) | 12240.1 | 0.449586 | ||||||||
\(906\) | −16175.9 | −0.593164 | ||||||||
\(907\) | 11769.4 | 0.430866 | 0.215433 | − | 0.976519i | \(-0.430884\pi\) | ||||
0.215433 | + | 0.976519i | \(0.430884\pi\) | |||||||
\(908\) | 367.552 | 0.0134335 | ||||||||
\(909\) | −15344.8 | −0.559905 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4591.84 | 0.166997 | 0.0834986 | − | 0.996508i | \(-0.473391\pi\) | ||||
0.0834986 | + | 0.996508i | \(0.473391\pi\) | |||||||
\(912\) | −21064.5 | −0.764819 | ||||||||
\(913\) | 68294.1 | 2.47558 | ||||||||
\(914\) | −27846.4 | −1.00774 | ||||||||
\(915\) | −6134.92 | −0.221655 | ||||||||
\(916\) | 884.301 | 0.0318975 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 12382.7 | 0.445196 | ||||||||
\(919\) | 5444.40 | 0.195424 | 0.0977118 | − | 0.995215i | \(-0.468848\pi\) | ||||
0.0977118 | + | 0.995215i | \(0.468848\pi\) | |||||||
\(920\) | −17484.9 | −0.626586 | ||||||||
\(921\) | 41119.9 | 1.47117 | ||||||||
\(922\) | 29033.9 | 1.03707 | ||||||||
\(923\) | 27724.1 | 0.988677 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1337.08 | 0.0475273 | ||||||||
\(926\) | 7976.58 | 0.283074 | ||||||||
\(927\) | −17316.5 | −0.613536 | ||||||||
\(928\) | 307.580 | 0.0108802 | ||||||||
\(929\) | 22114.5 | 0.781004 | 0.390502 | − | 0.920602i | \(-0.372302\pi\) | ||||
0.390502 | + | 0.920602i | \(0.372302\pi\) | |||||||
\(930\) | 8986.17 | 0.316847 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −203.026 | −0.00713555 | ||||||||
\(933\) | 1047.42 | 0.0367536 | ||||||||
\(934\) | 35154.8 | 1.23159 | ||||||||
\(935\) | 11482.5 | 0.401622 | ||||||||
\(936\) | 19029.4 | 0.664524 | ||||||||
\(937\) | −38332.7 | −1.33647 | −0.668236 | − | 0.743949i | \(-0.732950\pi\) | ||||
−0.668236 | + | 0.743949i | \(0.732950\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 46615.3 | 1.62006 | ||||||||
\(940\) | 343.687 | 0.0119254 | ||||||||
\(941\) | −41340.7 | −1.43216 | −0.716082 | − | 0.698016i | \(-0.754066\pi\) | ||||
−0.716082 | + | 0.698016i | \(0.754066\pi\) | |||||||
\(942\) | −39395.6 | −1.36261 | ||||||||
\(943\) | 6191.99 | 0.213827 | ||||||||
\(944\) | 2482.54 | 0.0855932 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 52332.3 | 1.79859 | ||||||||
\(947\) | −4417.34 | −0.151578 | −0.0757889 | − | 0.997124i | \(-0.524148\pi\) | ||||
−0.0757889 | + | 0.997124i | \(0.524148\pi\) | |||||||
\(948\) | 423.731 | 0.0145170 | ||||||||
\(949\) | −15744.6 | −0.538558 | ||||||||
\(950\) | −3789.27 | −0.129411 | ||||||||
\(951\) | 21283.3 | 0.725720 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1981.88 | −0.0673656 | −0.0336828 | − | 0.999433i | \(-0.510724\pi\) | ||||
−0.0336828 | + | 0.999433i | \(0.510724\pi\) | |||||||
\(954\) | −10679.6 | −0.362438 | ||||||||
\(955\) | 25341.6 | 0.858677 | ||||||||
\(956\) | −338.710 | −0.0114589 | ||||||||
\(957\) | 11874.7 | 0.401103 | ||||||||
\(958\) | −15494.4 | −0.522549 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −16242.6 | −0.546071 | ||||||||
\(961\) | −19098.3 | −0.641077 | ||||||||
\(962\) | −10719.6 | −0.359267 | ||||||||
\(963\) | −5103.54 | −0.170778 | ||||||||
\(964\) | 44.1412 | 0.00147478 | ||||||||
\(965\) | −17222.8 | −0.574531 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12406.6 | 0.412586 | 0.206293 | − | 0.978490i | \(-0.433860\pi\) | ||||
0.206293 | + | 0.978490i | \(0.433860\pi\) | |||||||
\(968\) | 25829.2 | 0.857625 | ||||||||
\(969\) | 15589.6 | 0.516833 | ||||||||
\(970\) | 7460.71 | 0.246958 | ||||||||
\(971\) | −22191.2 | −0.733418 | −0.366709 | − | 0.930336i | \(-0.619516\pi\) | ||||
−0.366709 | + | 0.930336i | \(0.619516\pi\) | |||||||
\(972\) | 539.650 | 0.0178079 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 30627.5 | 1.00756 | ||||||||
\(975\) | 11131.7 | 0.365640 | ||||||||
\(976\) | −12352.6 | −0.405119 | ||||||||
\(977\) | −1300.82 | −0.0425966 | −0.0212983 | − | 0.999773i | \(-0.506780\pi\) | ||||
−0.0212983 | + | 0.999773i | \(0.506780\pi\) | |||||||
\(978\) | −55518.4 | −1.81522 | ||||||||
\(979\) | −37204.4 | −1.21456 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16989.1 | 0.552925 | ||||||||
\(982\) | −15053.1 | −0.489169 | ||||||||
\(983\) | −38899.7 | −1.26216 | −0.631082 | − | 0.775716i | \(-0.717389\pi\) | ||||
−0.631082 | + | 0.775716i | \(0.717389\pi\) | |||||||
\(984\) | 5754.81 | 0.186440 | ||||||||
\(985\) | 8848.06 | 0.286216 | ||||||||
\(986\) | 4989.16 | 0.161143 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −685.149 | −0.0220623 | ||||||||
\(989\) | 57675.5 | 1.85437 | ||||||||
\(990\) | −8055.09 | −0.258594 | ||||||||
\(991\) | −2713.22 | −0.0869711 | −0.0434856 | − | 0.999054i | \(-0.513846\pi\) | ||||
−0.0434856 | + | 0.999054i | \(0.513846\pi\) | |||||||
\(992\) | −825.541 | −0.0264223 | ||||||||
\(993\) | 6807.09 | 0.217539 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1029.86 | −0.0328127 | ||||||||
\(996\) | 1509.56 | 0.0480244 | ||||||||
\(997\) | 51048.1 | 1.62158 | 0.810788 | − | 0.585340i | \(-0.199039\pi\) | ||||
0.810788 | + | 0.585340i | \(0.199039\pi\) | |||||||
\(998\) | −36761.1 | −1.16598 | ||||||||
\(999\) | −5114.06 | −0.161964 |
(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 | 245.4.a.m.1.2 | 5 | ||
3.2 | odd | 2 | 2205.4.a.bu.1.4 | 5 | |||
5.4 | even | 2 | 1225.4.a.bg.1.4 | 5 | |||
7.2 | even | 3 | 35.4.e.c.11.4 | ✓ | 10 | ||
7.3 | odd | 6 | 245.4.e.o.226.4 | 10 | |||
7.4 | even | 3 | 35.4.e.c.16.4 | yes | 10 | ||
7.5 | odd | 6 | 245.4.e.o.116.4 | 10 | |||
7.6 | odd | 2 | 245.4.a.n.1.2 | 5 | |||
21.2 | odd | 6 | 315.4.j.g.46.2 | 10 | |||
21.11 | odd | 6 | 315.4.j.g.226.2 | 10 | |||
21.20 | even | 2 | 2205.4.a.bt.1.4 | 5 | |||
28.11 | odd | 6 | 560.4.q.n.401.5 | 10 | |||
28.23 | odd | 6 | 560.4.q.n.81.5 | 10 | |||
35.2 | odd | 12 | 175.4.k.d.74.4 | 20 | |||
35.4 | even | 6 | 175.4.e.d.51.2 | 10 | |||
35.9 | even | 6 | 175.4.e.d.151.2 | 10 | |||
35.18 | odd | 12 | 175.4.k.d.149.4 | 20 | |||
35.23 | odd | 12 | 175.4.k.d.74.7 | 20 | |||
35.32 | odd | 12 | 175.4.k.d.149.7 | 20 | |||
35.34 | odd | 2 | 1225.4.a.bf.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.4.e.c.11.4 | ✓ | 10 | 7.2 | even | 3 | ||
35.4.e.c.16.4 | yes | 10 | 7.4 | even | 3 | ||
175.4.e.d.51.2 | 10 | 35.4 | even | 6 | |||
175.4.e.d.151.2 | 10 | 35.9 | even | 6 | |||
175.4.k.d.74.4 | 20 | 35.2 | odd | 12 | |||
175.4.k.d.74.7 | 20 | 35.23 | odd | 12 | |||
175.4.k.d.149.4 | 20 | 35.18 | odd | 12 | |||
175.4.k.d.149.7 | 20 | 35.32 | odd | 12 | |||
245.4.a.m.1.2 | 5 | 1.1 | even | 1 | trivial | ||
245.4.a.n.1.2 | 5 | 7.6 | odd | 2 | |||
245.4.e.o.116.4 | 10 | 7.5 | odd | 6 | |||
245.4.e.o.226.4 | 10 | 7.3 | odd | 6 | |||
315.4.j.g.46.2 | 10 | 21.2 | odd | 6 | |||
315.4.j.g.226.2 | 10 | 21.11 | odd | 6 | |||
560.4.q.n.81.5 | 10 | 28.23 | odd | 6 | |||
560.4.q.n.401.5 | 10 | 28.11 | odd | 6 | |||
1225.4.a.bf.1.4 | 5 | 35.34 | odd | 2 | |||
1225.4.a.bg.1.4 | 5 | 5.4 | even | 2 | |||
2205.4.a.bt.1.4 | 5 | 21.20 | even | 2 | |||
2205.4.a.bu.1.4 | 5 | 3.2 | odd | 2 |