Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [138,4,Mod(1,138)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(138, 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("138.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 138 = 2 \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 138.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: | \(8.14226358079\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{277}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 69 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-7.82166\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 138.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 17.6433 | 1.57807 | 0.789033 | − | 0.614351i | \(-0.210582\pi\) | ||||
0.789033 | + | 0.614351i | \(0.210582\pi\) | |||||||
\(6\) | −6.00000 | −0.408248 | ||||||||
\(7\) | 14.0000 | 0.755929 | 0.377964 | − | 0.925820i | \(-0.376624\pi\) | ||||
0.377964 | + | 0.925820i | \(0.376624\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −35.2866 | −1.11586 | ||||||||
\(11\) | −17.6433 | −0.483605 | −0.241803 | − | 0.970325i | \(-0.577739\pi\) | ||||
−0.241803 | + | 0.970325i | \(0.577739\pi\) | |||||||
\(12\) | 12.0000 | 0.288675 | ||||||||
\(13\) | −9.28663 | −0.198127 | −0.0990634 | − | 0.995081i | \(-0.531585\pi\) | ||||
−0.0990634 | + | 0.995081i | \(0.531585\pi\) | |||||||
\(14\) | −28.0000 | −0.534522 | ||||||||
\(15\) | 52.9300 | 0.911097 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −35.2866 | −0.503427 | −0.251714 | − | 0.967802i | \(-0.580994\pi\) | ||||
−0.251714 | + | 0.967802i | \(0.580994\pi\) | |||||||
\(18\) | −18.0000 | −0.235702 | ||||||||
\(19\) | 55.6433 | 0.671866 | 0.335933 | − | 0.941886i | \(-0.390948\pi\) | ||||
0.335933 | + | 0.941886i | \(0.390948\pi\) | |||||||
\(20\) | 70.5733 | 0.789033 | ||||||||
\(21\) | 42.0000 | 0.436436 | ||||||||
\(22\) | 35.2866 | 0.341961 | ||||||||
\(23\) | 23.0000 | 0.208514 | ||||||||
\(24\) | −24.0000 | −0.204124 | ||||||||
\(25\) | 186.287 | 1.49029 | ||||||||
\(26\) | 18.5733 | 0.140097 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 56.0000 | 0.377964 | ||||||||
\(29\) | −74.4332 | −0.476617 | −0.238308 | − | 0.971190i | \(-0.576593\pi\) | ||||
−0.238308 | + | 0.971190i | \(0.576593\pi\) | |||||||
\(30\) | −105.860 | −0.644243 | ||||||||
\(31\) | 187.287 | 1.08509 | 0.542543 | − | 0.840028i | \(-0.317462\pi\) | ||||
0.542543 | + | 0.840028i | \(0.317462\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | −52.9300 | −0.279210 | ||||||||
\(34\) | 70.5733 | 0.355977 | ||||||||
\(35\) | 247.006 | 1.19291 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | 234.930 | 1.04384 | 0.521922 | − | 0.852993i | \(-0.325215\pi\) | ||||
0.521922 | + | 0.852993i | \(0.325215\pi\) | |||||||
\(38\) | −111.287 | −0.475081 | ||||||||
\(39\) | −27.8599 | −0.114389 | ||||||||
\(40\) | −141.147 | −0.557931 | ||||||||
\(41\) | −393.440 | −1.49866 | −0.749329 | − | 0.662198i | \(-0.769624\pi\) | ||||
−0.749329 | + | 0.662198i | \(0.769624\pi\) | |||||||
\(42\) | −84.0000 | −0.308607 | ||||||||
\(43\) | 209.503 | 0.742999 | 0.371499 | − | 0.928433i | \(-0.378844\pi\) | ||||
0.371499 | + | 0.928433i | \(0.378844\pi\) | |||||||
\(44\) | −70.5733 | −0.241803 | ||||||||
\(45\) | 158.790 | 0.526022 | ||||||||
\(46\) | −46.0000 | −0.147442 | ||||||||
\(47\) | −64.2802 | −0.199494 | −0.0997471 | − | 0.995013i | \(-0.531803\pi\) | ||||
−0.0997471 | + | 0.995013i | \(0.531803\pi\) | |||||||
\(48\) | 48.0000 | 0.144338 | ||||||||
\(49\) | −147.000 | −0.428571 | ||||||||
\(50\) | −372.573 | −1.05380 | ||||||||
\(51\) | −105.860 | −0.290654 | ||||||||
\(52\) | −37.1465 | −0.0990634 | ||||||||
\(53\) | −379.783 | −0.984288 | −0.492144 | − | 0.870514i | \(-0.663787\pi\) | ||||
−0.492144 | + | 0.870514i | \(0.663787\pi\) | |||||||
\(54\) | −54.0000 | −0.136083 | ||||||||
\(55\) | −311.287 | −0.763161 | ||||||||
\(56\) | −112.000 | −0.267261 | ||||||||
\(57\) | 166.930 | 0.387902 | ||||||||
\(58\) | 148.866 | 0.337019 | ||||||||
\(59\) | −396.000 | −0.873810 | −0.436905 | − | 0.899508i | \(-0.643925\pi\) | ||||
−0.436905 | + | 0.899508i | \(0.643925\pi\) | |||||||
\(60\) | 211.720 | 0.455548 | ||||||||
\(61\) | 594.803 | 1.24847 | 0.624235 | − | 0.781237i | \(-0.285411\pi\) | ||||
0.624235 | + | 0.781237i | \(0.285411\pi\) | |||||||
\(62\) | −374.573 | −0.767272 | ||||||||
\(63\) | 126.000 | 0.251976 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −163.847 | −0.312657 | ||||||||
\(66\) | 105.860 | 0.197431 | ||||||||
\(67\) | −1065.81 | −1.94342 | −0.971711 | − | 0.236172i | \(-0.924107\pi\) | ||||
−0.971711 | + | 0.236172i | \(0.924107\pi\) | |||||||
\(68\) | −141.147 | −0.251714 | ||||||||
\(69\) | 69.0000 | 0.120386 | ||||||||
\(70\) | −494.013 | −0.843512 | ||||||||
\(71\) | 911.159 | 1.52302 | 0.761512 | − | 0.648151i | \(-0.224457\pi\) | ||||
0.761512 | + | 0.648151i | \(0.224457\pi\) | |||||||
\(72\) | −72.0000 | −0.117851 | ||||||||
\(73\) | −941.593 | −1.50966 | −0.754829 | − | 0.655921i | \(-0.772280\pi\) | ||||
−0.754829 | + | 0.655921i | \(0.772280\pi\) | |||||||
\(74\) | −469.860 | −0.738110 | ||||||||
\(75\) | 558.860 | 0.860421 | ||||||||
\(76\) | 222.573 | 0.335933 | ||||||||
\(77\) | −247.006 | −0.365571 | ||||||||
\(78\) | 55.7198 | 0.0808849 | ||||||||
\(79\) | −520.293 | −0.740982 | −0.370491 | − | 0.928836i | \(-0.620810\pi\) | ||||
−0.370491 | + | 0.928836i | \(0.620810\pi\) | |||||||
\(80\) | 282.293 | 0.394517 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 786.879 | 1.05971 | ||||||||
\(83\) | −418.382 | −0.553294 | −0.276647 | − | 0.960972i | \(-0.589223\pi\) | ||||
−0.276647 | + | 0.960972i | \(0.589223\pi\) | |||||||
\(84\) | 168.000 | 0.218218 | ||||||||
\(85\) | −622.573 | −0.794442 | ||||||||
\(86\) | −419.006 | −0.525379 | ||||||||
\(87\) | −223.300 | −0.275175 | ||||||||
\(88\) | 141.147 | 0.170980 | ||||||||
\(89\) | 599.159 | 0.713604 | 0.356802 | − | 0.934180i | \(-0.383867\pi\) | ||||
0.356802 | + | 0.934180i | \(0.383867\pi\) | |||||||
\(90\) | −317.580 | −0.371954 | ||||||||
\(91\) | −130.013 | −0.149770 | ||||||||
\(92\) | 92.0000 | 0.104257 | ||||||||
\(93\) | 561.860 | 0.626475 | ||||||||
\(94\) | 128.560 | 0.141064 | ||||||||
\(95\) | 981.733 | 1.06025 | ||||||||
\(96\) | −96.0000 | −0.102062 | ||||||||
\(97\) | 40.7262 | 0.0426301 | 0.0213151 | − | 0.999773i | \(-0.493215\pi\) | ||||
0.0213151 | + | 0.999773i | \(0.493215\pi\) | |||||||
\(98\) | 294.000 | 0.303046 | ||||||||
\(99\) | −158.790 | −0.161202 | ||||||||
\(100\) | 745.147 | 0.745147 | ||||||||
\(101\) | −1461.31 | −1.43966 | −0.719832 | − | 0.694149i | \(-0.755781\pi\) | ||||
−0.719832 | + | 0.694149i | \(0.755781\pi\) | |||||||
\(102\) | 211.720 | 0.205523 | ||||||||
\(103\) | 1573.03 | 1.50481 | 0.752405 | − | 0.658701i | \(-0.228894\pi\) | ||||
0.752405 | + | 0.658701i | \(0.228894\pi\) | |||||||
\(104\) | 74.2931 | 0.0700484 | ||||||||
\(105\) | 741.019 | 0.688725 | ||||||||
\(106\) | 759.567 | 0.695997 | ||||||||
\(107\) | 1698.82 | 1.53487 | 0.767433 | − | 0.641129i | \(-0.221534\pi\) | ||||
0.767433 | + | 0.641129i | \(0.221534\pi\) | |||||||
\(108\) | 108.000 | 0.0962250 | ||||||||
\(109\) | 389.376 | 0.342160 | 0.171080 | − | 0.985257i | \(-0.445274\pi\) | ||||
0.171080 | + | 0.985257i | \(0.445274\pi\) | |||||||
\(110\) | 622.573 | 0.539637 | ||||||||
\(111\) | 704.790 | 0.602664 | ||||||||
\(112\) | 224.000 | 0.188982 | ||||||||
\(113\) | 110.853 | 0.0922851 | 0.0461426 | − | 0.998935i | \(-0.485307\pi\) | ||||
0.0461426 | + | 0.998935i | \(0.485307\pi\) | |||||||
\(114\) | −333.860 | −0.274288 | ||||||||
\(115\) | 405.796 | 0.329050 | ||||||||
\(116\) | −297.733 | −0.238308 | ||||||||
\(117\) | −83.5797 | −0.0660423 | ||||||||
\(118\) | 792.000 | 0.617877 | ||||||||
\(119\) | −494.013 | −0.380555 | ||||||||
\(120\) | −423.440 | −0.322121 | ||||||||
\(121\) | −1019.71 | −0.766126 | ||||||||
\(122\) | −1189.61 | −0.882802 | ||||||||
\(123\) | −1180.32 | −0.865250 | ||||||||
\(124\) | 749.147 | 0.542543 | ||||||||
\(125\) | 1081.30 | 0.773715 | ||||||||
\(126\) | −252.000 | −0.178174 | ||||||||
\(127\) | −437.427 | −0.305633 | −0.152816 | − | 0.988255i | \(-0.548834\pi\) | ||||
−0.152816 | + | 0.988255i | \(0.548834\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 628.510 | 0.428970 | ||||||||
\(130\) | 327.694 | 0.221082 | ||||||||
\(131\) | −2139.06 | −1.42664 | −0.713322 | − | 0.700836i | \(-0.752810\pi\) | ||||
−0.713322 | + | 0.700836i | \(0.752810\pi\) | |||||||
\(132\) | −211.720 | −0.139605 | ||||||||
\(133\) | 779.006 | 0.507883 | ||||||||
\(134\) | 2131.62 | 1.37421 | ||||||||
\(135\) | 476.370 | 0.303699 | ||||||||
\(136\) | 282.293 | 0.177988 | ||||||||
\(137\) | −753.019 | −0.469597 | −0.234798 | − | 0.972044i | \(-0.575443\pi\) | ||||
−0.234798 | + | 0.972044i | \(0.575443\pi\) | |||||||
\(138\) | −138.000 | −0.0851257 | ||||||||
\(139\) | −615.159 | −0.375375 | −0.187688 | − | 0.982229i | \(-0.560099\pi\) | ||||
−0.187688 | + | 0.982229i | \(0.560099\pi\) | |||||||
\(140\) | 988.026 | 0.596453 | ||||||||
\(141\) | −192.841 | −0.115178 | ||||||||
\(142\) | −1822.32 | −1.07694 | ||||||||
\(143\) | 163.847 | 0.0958152 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | −1313.25 | −0.752133 | ||||||||
\(146\) | 1883.19 | 1.06749 | ||||||||
\(147\) | −441.000 | −0.247436 | ||||||||
\(148\) | 939.720 | 0.521922 | ||||||||
\(149\) | −3004.42 | −1.65189 | −0.825946 | − | 0.563750i | \(-0.809358\pi\) | ||||
−0.825946 | + | 0.563750i | \(0.809358\pi\) | |||||||
\(150\) | −1117.72 | −0.608410 | ||||||||
\(151\) | −1863.29 | −1.00419 | −0.502093 | − | 0.864814i | \(-0.667437\pi\) | ||||
−0.502093 | + | 0.864814i | \(0.667437\pi\) | |||||||
\(152\) | −445.147 | −0.237540 | ||||||||
\(153\) | −317.580 | −0.167809 | ||||||||
\(154\) | 494.013 | 0.258498 | ||||||||
\(155\) | 3304.36 | 1.71234 | ||||||||
\(156\) | −111.440 | −0.0571943 | ||||||||
\(157\) | −1471.92 | −0.748231 | −0.374116 | − | 0.927382i | \(-0.622054\pi\) | ||||
−0.374116 | + | 0.927382i | \(0.622054\pi\) | |||||||
\(158\) | 1040.59 | 0.523953 | ||||||||
\(159\) | −1139.35 | −0.568279 | ||||||||
\(160\) | −564.586 | −0.278965 | ||||||||
\(161\) | 322.000 | 0.157622 | ||||||||
\(162\) | −162.000 | −0.0785674 | ||||||||
\(163\) | 467.235 | 0.224520 | 0.112260 | − | 0.993679i | \(-0.464191\pi\) | ||||
0.112260 | + | 0.993679i | \(0.464191\pi\) | |||||||
\(164\) | −1573.76 | −0.749329 | ||||||||
\(165\) | −933.860 | −0.440611 | ||||||||
\(166\) | 836.765 | 0.391238 | ||||||||
\(167\) | 1858.57 | 0.861202 | 0.430601 | − | 0.902542i | \(-0.358302\pi\) | ||||
0.430601 | + | 0.902542i | \(0.358302\pi\) | |||||||
\(168\) | −336.000 | −0.154303 | ||||||||
\(169\) | −2110.76 | −0.960746 | ||||||||
\(170\) | 1245.15 | 0.561755 | ||||||||
\(171\) | 500.790 | 0.223955 | ||||||||
\(172\) | 838.013 | 0.371499 | ||||||||
\(173\) | 2224.78 | 0.977727 | 0.488863 | − | 0.872360i | \(-0.337412\pi\) | ||||
0.488863 | + | 0.872360i | \(0.337412\pi\) | |||||||
\(174\) | 446.599 | 0.194578 | ||||||||
\(175\) | 2608.01 | 1.12656 | ||||||||
\(176\) | −282.293 | −0.120901 | ||||||||
\(177\) | −1188.00 | −0.504495 | ||||||||
\(178\) | −1198.32 | −0.504594 | ||||||||
\(179\) | 3839.29 | 1.60314 | 0.801569 | − | 0.597902i | \(-0.203999\pi\) | ||||
0.801569 | + | 0.597902i | \(0.203999\pi\) | |||||||
\(180\) | 635.159 | 0.263011 | ||||||||
\(181\) | −4215.26 | −1.73104 | −0.865519 | − | 0.500876i | \(-0.833011\pi\) | ||||
−0.865519 | + | 0.500876i | \(0.833011\pi\) | |||||||
\(182\) | 260.026 | 0.105903 | ||||||||
\(183\) | 1784.41 | 0.720805 | ||||||||
\(184\) | −184.000 | −0.0737210 | ||||||||
\(185\) | 4144.94 | 1.64726 | ||||||||
\(186\) | −1123.72 | −0.442985 | ||||||||
\(187\) | 622.573 | 0.243460 | ||||||||
\(188\) | −257.121 | −0.0997471 | ||||||||
\(189\) | 378.000 | 0.145479 | ||||||||
\(190\) | −1963.47 | −0.749709 | ||||||||
\(191\) | −3829.55 | −1.45077 | −0.725384 | − | 0.688344i | \(-0.758338\pi\) | ||||
−0.725384 | + | 0.688344i | \(0.758338\pi\) | |||||||
\(192\) | 192.000 | 0.0721688 | ||||||||
\(193\) | −262.077 | −0.0977447 | −0.0488724 | − | 0.998805i | \(-0.515563\pi\) | ||||
−0.0488724 | + | 0.998805i | \(0.515563\pi\) | |||||||
\(194\) | −81.4525 | −0.0301441 | ||||||||
\(195\) | −491.541 | −0.180513 | ||||||||
\(196\) | −588.000 | −0.214286 | ||||||||
\(197\) | −5380.40 | −1.94587 | −0.972937 | − | 0.231069i | \(-0.925778\pi\) | ||||
−0.972937 | + | 0.231069i | \(0.925778\pi\) | |||||||
\(198\) | 317.580 | 0.113987 | ||||||||
\(199\) | 3908.04 | 1.39213 | 0.696064 | − | 0.717980i | \(-0.254933\pi\) | ||||
0.696064 | + | 0.717980i | \(0.254933\pi\) | |||||||
\(200\) | −1490.29 | −0.526898 | ||||||||
\(201\) | −3197.43 | −1.12204 | ||||||||
\(202\) | 2922.62 | 1.01800 | ||||||||
\(203\) | −1042.06 | −0.360289 | ||||||||
\(204\) | −423.440 | −0.145327 | ||||||||
\(205\) | −6941.58 | −2.36498 | ||||||||
\(206\) | −3146.06 | −1.06406 | ||||||||
\(207\) | 207.000 | 0.0695048 | ||||||||
\(208\) | −148.586 | −0.0495317 | ||||||||
\(209\) | −981.733 | −0.324918 | ||||||||
\(210\) | −1482.04 | −0.487002 | ||||||||
\(211\) | 2113.91 | 0.689705 | 0.344852 | − | 0.938657i | \(-0.387929\pi\) | ||||
0.344852 | + | 0.938657i | \(0.387929\pi\) | |||||||
\(212\) | −1519.13 | −0.492144 | ||||||||
\(213\) | 2733.48 | 0.879319 | ||||||||
\(214\) | −3397.63 | −1.08531 | ||||||||
\(215\) | 3696.33 | 1.17250 | ||||||||
\(216\) | −216.000 | −0.0680414 | ||||||||
\(217\) | 2622.01 | 0.820248 | ||||||||
\(218\) | −778.752 | −0.241944 | ||||||||
\(219\) | −2824.78 | −0.871602 | ||||||||
\(220\) | −1245.15 | −0.381581 | ||||||||
\(221\) | 327.694 | 0.0997425 | ||||||||
\(222\) | −1409.58 | −0.426148 | ||||||||
\(223\) | 4783.70 | 1.43650 | 0.718251 | − | 0.695784i | \(-0.244943\pi\) | ||||
0.718251 | + | 0.695784i | \(0.244943\pi\) | |||||||
\(224\) | −448.000 | −0.133631 | ||||||||
\(225\) | 1676.58 | 0.496764 | ||||||||
\(226\) | −221.707 | −0.0652554 | ||||||||
\(227\) | −663.630 | −0.194038 | −0.0970192 | − | 0.995283i | \(-0.530931\pi\) | ||||
−0.0970192 | + | 0.995283i | \(0.530931\pi\) | |||||||
\(228\) | 667.720 | 0.193951 | ||||||||
\(229\) | 2959.47 | 0.854004 | 0.427002 | − | 0.904251i | \(-0.359570\pi\) | ||||
0.427002 | + | 0.904251i | \(0.359570\pi\) | |||||||
\(230\) | −811.593 | −0.232673 | ||||||||
\(231\) | −741.019 | −0.211063 | ||||||||
\(232\) | 595.465 | 0.168510 | ||||||||
\(233\) | 2503.76 | 0.703977 | 0.351989 | − | 0.936004i | \(-0.385506\pi\) | ||||
0.351989 | + | 0.936004i | \(0.385506\pi\) | |||||||
\(234\) | 167.159 | 0.0466989 | ||||||||
\(235\) | −1134.12 | −0.314815 | ||||||||
\(236\) | −1584.00 | −0.436905 | ||||||||
\(237\) | −1560.88 | −0.427806 | ||||||||
\(238\) | 988.026 | 0.269093 | ||||||||
\(239\) | 6400.36 | 1.73224 | 0.866119 | − | 0.499838i | \(-0.166607\pi\) | ||||
0.866119 | + | 0.499838i | \(0.166607\pi\) | |||||||
\(240\) | 846.879 | 0.227774 | ||||||||
\(241\) | −873.209 | −0.233396 | −0.116698 | − | 0.993167i | \(-0.537231\pi\) | ||||
−0.116698 | + | 0.993167i | \(0.537231\pi\) | |||||||
\(242\) | 2039.43 | 0.541733 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 2379.21 | 0.624235 | ||||||||
\(245\) | −2593.57 | −0.676314 | ||||||||
\(246\) | 2360.64 | 0.611824 | ||||||||
\(247\) | −516.739 | −0.133115 | ||||||||
\(248\) | −1498.29 | −0.383636 | ||||||||
\(249\) | −1255.15 | −0.319445 | ||||||||
\(250\) | −2162.60 | −0.547099 | ||||||||
\(251\) | −1698.87 | −0.427217 | −0.213608 | − | 0.976919i | \(-0.568522\pi\) | ||||
−0.213608 | + | 0.976919i | \(0.568522\pi\) | |||||||
\(252\) | 504.000 | 0.125988 | ||||||||
\(253\) | −405.796 | −0.100839 | ||||||||
\(254\) | 874.853 | 0.216115 | ||||||||
\(255\) | −1867.72 | −0.458671 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 5625.01 | 1.36529 | 0.682643 | − | 0.730752i | \(-0.260831\pi\) | ||||
0.682643 | + | 0.730752i | \(0.260831\pi\) | |||||||
\(258\) | −1257.02 | −0.303328 | ||||||||
\(259\) | 3289.02 | 0.789072 | ||||||||
\(260\) | −655.388 | −0.156329 | ||||||||
\(261\) | −669.899 | −0.158872 | ||||||||
\(262\) | 4278.12 | 1.00879 | ||||||||
\(263\) | −1360.69 | −0.319025 | −0.159513 | − | 0.987196i | \(-0.550992\pi\) | ||||
−0.159513 | + | 0.987196i | \(0.550992\pi\) | |||||||
\(264\) | 423.440 | 0.0987156 | ||||||||
\(265\) | −6700.64 | −1.55327 | ||||||||
\(266\) | −1558.01 | −0.359127 | ||||||||
\(267\) | 1797.48 | 0.412000 | ||||||||
\(268\) | −4263.24 | −0.971711 | ||||||||
\(269\) | 1666.53 | 0.377734 | 0.188867 | − | 0.982003i | \(-0.439519\pi\) | ||||
0.188867 | + | 0.982003i | \(0.439519\pi\) | |||||||
\(270\) | −952.739 | −0.214748 | ||||||||
\(271\) | −3321.20 | −0.744459 | −0.372230 | − | 0.928141i | \(-0.621407\pi\) | ||||
−0.372230 | + | 0.928141i | \(0.621407\pi\) | |||||||
\(272\) | −564.586 | −0.125857 | ||||||||
\(273\) | −390.039 | −0.0864696 | ||||||||
\(274\) | 1506.04 | 0.332055 | ||||||||
\(275\) | −3286.71 | −0.720714 | ||||||||
\(276\) | 276.000 | 0.0601929 | ||||||||
\(277\) | −157.490 | −0.0341611 | −0.0170806 | − | 0.999854i | \(-0.505437\pi\) | ||||
−0.0170806 | + | 0.999854i | \(0.505437\pi\) | |||||||
\(278\) | 1230.32 | 0.265430 | ||||||||
\(279\) | 1685.58 | 0.361695 | ||||||||
\(280\) | −1976.05 | −0.421756 | ||||||||
\(281\) | −150.802 | −0.0320146 | −0.0160073 | − | 0.999872i | \(-0.505095\pi\) | ||||
−0.0160073 | + | 0.999872i | \(0.505095\pi\) | |||||||
\(282\) | 385.681 | 0.0814432 | ||||||||
\(283\) | 6881.58 | 1.44547 | 0.722734 | − | 0.691126i | \(-0.242885\pi\) | ||||
0.722734 | + | 0.691126i | \(0.242885\pi\) | |||||||
\(284\) | 3644.64 | 0.761512 | ||||||||
\(285\) | 2945.20 | 0.612135 | ||||||||
\(286\) | −327.694 | −0.0677516 | ||||||||
\(287\) | −5508.15 | −1.13288 | ||||||||
\(288\) | −288.000 | −0.0589256 | ||||||||
\(289\) | −3667.85 | −0.746561 | ||||||||
\(290\) | 2626.50 | 0.531838 | ||||||||
\(291\) | 122.179 | 0.0246125 | ||||||||
\(292\) | −3766.37 | −0.754829 | ||||||||
\(293\) | 5650.84 | 1.12671 | 0.563354 | − | 0.826215i | \(-0.309511\pi\) | ||||
0.563354 | + | 0.826215i | \(0.309511\pi\) | |||||||
\(294\) | 882.000 | 0.174964 | ||||||||
\(295\) | −6986.75 | −1.37893 | ||||||||
\(296\) | −1879.44 | −0.369055 | ||||||||
\(297\) | −476.370 | −0.0930699 | ||||||||
\(298\) | 6008.84 | 1.16806 | ||||||||
\(299\) | −213.593 | −0.0413123 | ||||||||
\(300\) | 2235.44 | 0.430211 | ||||||||
\(301\) | 2933.05 | 0.561654 | ||||||||
\(302\) | 3726.57 | 0.710067 | ||||||||
\(303\) | −4383.94 | −0.831190 | ||||||||
\(304\) | 890.293 | 0.167966 | ||||||||
\(305\) | 10494.3 | 1.97017 | ||||||||
\(306\) | 635.159 | 0.118659 | ||||||||
\(307\) | 4071.26 | 0.756870 | 0.378435 | − | 0.925628i | \(-0.376462\pi\) | ||||
0.378435 | + | 0.925628i | \(0.376462\pi\) | |||||||
\(308\) | −988.026 | −0.182786 | ||||||||
\(309\) | 4719.10 | 0.868803 | ||||||||
\(310\) | −6608.71 | −1.21081 | ||||||||
\(311\) | −532.535 | −0.0970973 | −0.0485487 | − | 0.998821i | \(-0.515460\pi\) | ||||
−0.0485487 | + | 0.998821i | \(0.515460\pi\) | |||||||
\(312\) | 222.879 | 0.0404425 | ||||||||
\(313\) | 9759.63 | 1.76245 | 0.881225 | − | 0.472697i | \(-0.156719\pi\) | ||||
0.881225 | + | 0.472697i | \(0.156719\pi\) | |||||||
\(314\) | 2943.85 | 0.529079 | ||||||||
\(315\) | 2223.06 | 0.397635 | ||||||||
\(316\) | −2081.17 | −0.370491 | ||||||||
\(317\) | 3997.16 | 0.708211 | 0.354106 | − | 0.935205i | \(-0.384785\pi\) | ||||
0.354106 | + | 0.935205i | \(0.384785\pi\) | |||||||
\(318\) | 2278.70 | 0.401834 | ||||||||
\(319\) | 1313.25 | 0.230495 | ||||||||
\(320\) | 1129.17 | 0.197258 | ||||||||
\(321\) | 5096.45 | 0.886156 | ||||||||
\(322\) | −644.000 | −0.111456 | ||||||||
\(323\) | −1963.47 | −0.338236 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | −1729.98 | −0.295267 | ||||||||
\(326\) | −934.470 | −0.158759 | ||||||||
\(327\) | 1168.13 | 0.197546 | ||||||||
\(328\) | 3147.52 | 0.529855 | ||||||||
\(329\) | −899.923 | −0.150803 | ||||||||
\(330\) | 1867.72 | 0.311559 | ||||||||
\(331\) | 6349.73 | 1.05442 | 0.527210 | − | 0.849735i | \(-0.323238\pi\) | ||||
0.527210 | + | 0.849735i | \(0.323238\pi\) | |||||||
\(332\) | −1673.53 | −0.276647 | ||||||||
\(333\) | 2114.37 | 0.347948 | ||||||||
\(334\) | −3717.15 | −0.608962 | ||||||||
\(335\) | −18804.4 | −3.06685 | ||||||||
\(336\) | 672.000 | 0.109109 | ||||||||
\(337\) | 2530.74 | 0.409074 | 0.204537 | − | 0.978859i | \(-0.434431\pi\) | ||||
0.204537 | + | 0.978859i | \(0.434431\pi\) | |||||||
\(338\) | 4221.52 | 0.679350 | ||||||||
\(339\) | 332.560 | 0.0532808 | ||||||||
\(340\) | −2490.29 | −0.397221 | ||||||||
\(341\) | −3304.36 | −0.524754 | ||||||||
\(342\) | −1001.58 | −0.158360 | ||||||||
\(343\) | −6860.00 | −1.07990 | ||||||||
\(344\) | −1676.03 | −0.262690 | ||||||||
\(345\) | 1217.39 | 0.189977 | ||||||||
\(346\) | −4449.56 | −0.691357 | ||||||||
\(347\) | 4947.72 | 0.765440 | 0.382720 | − | 0.923864i | \(-0.374987\pi\) | ||||
0.382720 | + | 0.923864i | \(0.374987\pi\) | |||||||
\(348\) | −893.198 | −0.137587 | ||||||||
\(349\) | 3314.15 | 0.508317 | 0.254158 | − | 0.967163i | \(-0.418202\pi\) | ||||
0.254158 | + | 0.967163i | \(0.418202\pi\) | |||||||
\(350\) | −5216.03 | −0.796595 | ||||||||
\(351\) | −250.739 | −0.0381295 | ||||||||
\(352\) | 564.586 | 0.0854902 | ||||||||
\(353\) | 4137.26 | 0.623808 | 0.311904 | − | 0.950114i | \(-0.399033\pi\) | ||||
0.311904 | + | 0.950114i | \(0.399033\pi\) | |||||||
\(354\) | 2376.00 | 0.356732 | ||||||||
\(355\) | 16075.9 | 2.40343 | ||||||||
\(356\) | 2396.64 | 0.356802 | ||||||||
\(357\) | −1482.04 | −0.219714 | ||||||||
\(358\) | −7678.57 | −1.13359 | ||||||||
\(359\) | −10388.3 | −1.52723 | −0.763615 | − | 0.645672i | \(-0.776577\pi\) | ||||
−0.763615 | + | 0.645672i | \(0.776577\pi\) | |||||||
\(360\) | −1270.32 | −0.185977 | ||||||||
\(361\) | −3762.82 | −0.548596 | ||||||||
\(362\) | 8430.52 | 1.22403 | ||||||||
\(363\) | −3059.14 | −0.442323 | ||||||||
\(364\) | −520.052 | −0.0748849 | ||||||||
\(365\) | −16612.8 | −2.38234 | ||||||||
\(366\) | −3568.82 | −0.509686 | ||||||||
\(367\) | −6576.09 | −0.935338 | −0.467669 | − | 0.883904i | \(-0.654906\pi\) | ||||
−0.467669 | + | 0.883904i | \(0.654906\pi\) | |||||||
\(368\) | 368.000 | 0.0521286 | ||||||||
\(369\) | −3540.96 | −0.499552 | ||||||||
\(370\) | −8289.89 | −1.16479 | ||||||||
\(371\) | −5316.97 | −0.744052 | ||||||||
\(372\) | 2247.44 | 0.313237 | ||||||||
\(373\) | 6765.53 | 0.939158 | 0.469579 | − | 0.882891i | \(-0.344406\pi\) | ||||
0.469579 | + | 0.882891i | \(0.344406\pi\) | |||||||
\(374\) | −1245.15 | −0.172152 | ||||||||
\(375\) | 3243.90 | 0.446705 | ||||||||
\(376\) | 514.242 | 0.0705319 | ||||||||
\(377\) | 691.234 | 0.0944306 | ||||||||
\(378\) | −756.000 | −0.102869 | ||||||||
\(379\) | −155.159 | −0.0210289 | −0.0105145 | − | 0.999945i | \(-0.503347\pi\) | ||||
−0.0105145 | + | 0.999945i | \(0.503347\pi\) | |||||||
\(380\) | 3926.93 | 0.530124 | ||||||||
\(381\) | −1312.28 | −0.176457 | ||||||||
\(382\) | 7659.11 | 1.02585 | ||||||||
\(383\) | −7842.88 | −1.04635 | −0.523175 | − | 0.852225i | \(-0.675253\pi\) | ||||
−0.523175 | + | 0.852225i | \(0.675253\pi\) | |||||||
\(384\) | −384.000 | −0.0510310 | ||||||||
\(385\) | −4358.01 | −0.576896 | ||||||||
\(386\) | 524.155 | 0.0691160 | ||||||||
\(387\) | 1885.53 | 0.247666 | ||||||||
\(388\) | 162.905 | 0.0213151 | ||||||||
\(389\) | 932.447 | 0.121535 | 0.0607673 | − | 0.998152i | \(-0.480645\pi\) | ||||
0.0607673 | + | 0.998152i | \(0.480645\pi\) | |||||||
\(390\) | 983.082 | 0.127642 | ||||||||
\(391\) | −811.593 | −0.104972 | ||||||||
\(392\) | 1176.00 | 0.151523 | ||||||||
\(393\) | −6417.17 | −0.823673 | ||||||||
\(394\) | 10760.8 | 1.37594 | ||||||||
\(395\) | −9179.70 | −1.16932 | ||||||||
\(396\) | −635.159 | −0.0806009 | ||||||||
\(397\) | 11841.7 | 1.49702 | 0.748512 | − | 0.663121i | \(-0.230768\pi\) | ||||
0.748512 | + | 0.663121i | \(0.230768\pi\) | |||||||
\(398\) | −7816.08 | −0.984383 | ||||||||
\(399\) | 2337.02 | 0.293226 | ||||||||
\(400\) | 2980.59 | 0.372573 | ||||||||
\(401\) | −10096.7 | −1.25737 | −0.628687 | − | 0.777658i | \(-0.716407\pi\) | ||||
−0.628687 | + | 0.777658i | \(0.716407\pi\) | |||||||
\(402\) | 6394.85 | 0.793399 | ||||||||
\(403\) | −1739.26 | −0.214985 | ||||||||
\(404\) | −5845.25 | −0.719832 | ||||||||
\(405\) | 1429.11 | 0.175341 | ||||||||
\(406\) | 2084.13 | 0.254762 | ||||||||
\(407\) | −4144.94 | −0.504809 | ||||||||
\(408\) | 846.879 | 0.102762 | ||||||||
\(409\) | −7527.86 | −0.910095 | −0.455047 | − | 0.890467i | \(-0.650378\pi\) | ||||
−0.455047 | + | 0.890467i | \(0.650378\pi\) | |||||||
\(410\) | 13883.2 | 1.67229 | ||||||||
\(411\) | −2259.06 | −0.271122 | ||||||||
\(412\) | 6292.13 | 0.752405 | ||||||||
\(413\) | −5544.00 | −0.660539 | ||||||||
\(414\) | −414.000 | −0.0491473 | ||||||||
\(415\) | −7381.65 | −0.873135 | ||||||||
\(416\) | 297.172 | 0.0350242 | ||||||||
\(417\) | −1845.48 | −0.216723 | ||||||||
\(418\) | 1963.47 | 0.229752 | ||||||||
\(419\) | −6805.49 | −0.793484 | −0.396742 | − | 0.917930i | \(-0.629859\pi\) | ||||
−0.396742 | + | 0.917930i | \(0.629859\pi\) | |||||||
\(420\) | 2964.08 | 0.344362 | ||||||||
\(421\) | −15768.0 | −1.82538 | −0.912691 | − | 0.408651i | \(-0.865999\pi\) | ||||
−0.912691 | + | 0.408651i | \(0.865999\pi\) | |||||||
\(422\) | −4227.82 | −0.487695 | ||||||||
\(423\) | −578.522 | −0.0664981 | ||||||||
\(424\) | 3038.27 | 0.347998 | ||||||||
\(425\) | −6573.43 | −0.750254 | ||||||||
\(426\) | −5466.96 | −0.621772 | ||||||||
\(427\) | 8327.24 | 0.943755 | ||||||||
\(428\) | 6795.26 | 0.767433 | ||||||||
\(429\) | 491.541 | 0.0553189 | ||||||||
\(430\) | −7392.66 | −0.829083 | ||||||||
\(431\) | −1074.27 | −0.120059 | −0.0600297 | − | 0.998197i | \(-0.519120\pi\) | ||||
−0.0600297 | + | 0.998197i | \(0.519120\pi\) | |||||||
\(432\) | 432.000 | 0.0481125 | ||||||||
\(433\) | 16863.2 | 1.87158 | 0.935788 | − | 0.352563i | \(-0.114690\pi\) | ||||
0.935788 | + | 0.352563i | \(0.114690\pi\) | |||||||
\(434\) | −5244.03 | −0.580003 | ||||||||
\(435\) | −3939.74 | −0.434244 | ||||||||
\(436\) | 1557.50 | 0.171080 | ||||||||
\(437\) | 1279.80 | 0.140094 | ||||||||
\(438\) | 5649.56 | 0.616316 | ||||||||
\(439\) | −1592.20 | −0.173102 | −0.0865509 | − | 0.996247i | \(-0.527585\pi\) | ||||
−0.0865509 | + | 0.996247i | \(0.527585\pi\) | |||||||
\(440\) | 2490.29 | 0.269818 | ||||||||
\(441\) | −1323.00 | −0.142857 | ||||||||
\(442\) | −655.388 | −0.0705286 | ||||||||
\(443\) | 7007.67 | 0.751567 | 0.375784 | − | 0.926707i | \(-0.377374\pi\) | ||||
0.375784 | + | 0.926707i | \(0.377374\pi\) | |||||||
\(444\) | 2819.16 | 0.301332 | ||||||||
\(445\) | 10571.2 | 1.12611 | ||||||||
\(446\) | −9567.39 | −1.01576 | ||||||||
\(447\) | −9013.26 | −0.953720 | ||||||||
\(448\) | 896.000 | 0.0944911 | ||||||||
\(449\) | 15939.5 | 1.67534 | 0.837672 | − | 0.546174i | \(-0.183916\pi\) | ||||
0.837672 | + | 0.546174i | \(0.183916\pi\) | |||||||
\(450\) | −3353.16 | −0.351265 | ||||||||
\(451\) | 6941.58 | 0.724759 | ||||||||
\(452\) | 443.414 | 0.0461426 | ||||||||
\(453\) | −5589.86 | −0.579767 | ||||||||
\(454\) | 1327.26 | 0.137206 | ||||||||
\(455\) | −2293.86 | −0.236347 | ||||||||
\(456\) | −1335.44 | −0.137144 | ||||||||
\(457\) | −7205.18 | −0.737515 | −0.368757 | − | 0.929526i | \(-0.620217\pi\) | ||||
−0.368757 | + | 0.929526i | \(0.620217\pi\) | |||||||
\(458\) | −5918.93 | −0.603872 | ||||||||
\(459\) | −952.739 | −0.0968846 | ||||||||
\(460\) | 1623.19 | 0.164525 | ||||||||
\(461\) | −12480.1 | −1.26086 | −0.630431 | − | 0.776246i | \(-0.717122\pi\) | ||||
−0.630431 | + | 0.776246i | \(0.717122\pi\) | |||||||
\(462\) | 1482.04 | 0.149244 | ||||||||
\(463\) | 62.0613 | 0.00622945 | 0.00311472 | − | 0.999995i | \(-0.499009\pi\) | ||||
0.00311472 | + | 0.999995i | \(0.499009\pi\) | |||||||
\(464\) | −1190.93 | −0.119154 | ||||||||
\(465\) | 9913.07 | 0.988619 | ||||||||
\(466\) | −5007.52 | −0.497787 | ||||||||
\(467\) | 7018.84 | 0.695489 | 0.347744 | − | 0.937589i | \(-0.386948\pi\) | ||||
0.347744 | + | 0.937589i | \(0.386948\pi\) | |||||||
\(468\) | −334.319 | −0.0330211 | ||||||||
\(469\) | −14921.3 | −1.46909 | ||||||||
\(470\) | 2268.23 | 0.222608 | ||||||||
\(471\) | −4415.77 | −0.431991 | ||||||||
\(472\) | 3168.00 | 0.308939 | ||||||||
\(473\) | −3696.33 | −0.359318 | ||||||||
\(474\) | 3121.76 | 0.302504 | ||||||||
\(475\) | 10365.6 | 1.00128 | ||||||||
\(476\) | −1976.05 | −0.190278 | ||||||||
\(477\) | −3418.05 | −0.328096 | ||||||||
\(478\) | −12800.7 | −1.22488 | ||||||||
\(479\) | 18588.6 | 1.77315 | 0.886573 | − | 0.462589i | \(-0.153080\pi\) | ||||
0.886573 | + | 0.462589i | \(0.153080\pi\) | |||||||
\(480\) | −1693.76 | −0.161061 | ||||||||
\(481\) | −2181.71 | −0.206814 | ||||||||
\(482\) | 1746.42 | 0.165036 | ||||||||
\(483\) | 966.000 | 0.0910032 | ||||||||
\(484\) | −4078.85 | −0.383063 | ||||||||
\(485\) | 718.546 | 0.0672732 | ||||||||
\(486\) | −486.000 | −0.0453609 | ||||||||
\(487\) | −2248.82 | −0.209248 | −0.104624 | − | 0.994512i | \(-0.533364\pi\) | ||||
−0.104624 | + | 0.994512i | \(0.533364\pi\) | |||||||
\(488\) | −4758.42 | −0.441401 | ||||||||
\(489\) | 1401.71 | 0.129626 | ||||||||
\(490\) | 5187.14 | 0.478226 | ||||||||
\(491\) | 228.382 | 0.0209913 | 0.0104956 | − | 0.999945i | \(-0.496659\pi\) | ||||
0.0104956 | + | 0.999945i | \(0.496659\pi\) | |||||||
\(492\) | −4721.28 | −0.432625 | ||||||||
\(493\) | 2626.50 | 0.239942 | ||||||||
\(494\) | 1033.48 | 0.0941263 | ||||||||
\(495\) | −2801.58 | −0.254387 | ||||||||
\(496\) | 2996.59 | 0.271272 | ||||||||
\(497\) | 12756.2 | 1.15130 | ||||||||
\(498\) | 2510.29 | 0.225882 | ||||||||
\(499\) | 13676.7 | 1.22696 | 0.613481 | − | 0.789710i | \(-0.289769\pi\) | ||||
0.613481 | + | 0.789710i | \(0.289769\pi\) | |||||||
\(500\) | 4325.20 | 0.386857 | ||||||||
\(501\) | 5575.72 | 0.497215 | ||||||||
\(502\) | 3397.73 | 0.302088 | ||||||||
\(503\) | −3414.19 | −0.302646 | −0.151323 | − | 0.988484i | \(-0.548353\pi\) | ||||
−0.151323 | + | 0.988484i | \(0.548353\pi\) | |||||||
\(504\) | −1008.00 | −0.0890871 | ||||||||
\(505\) | −25782.4 | −2.27188 | ||||||||
\(506\) | 811.593 | 0.0713037 | ||||||||
\(507\) | −6332.28 | −0.554687 | ||||||||
\(508\) | −1749.71 | −0.152816 | ||||||||
\(509\) | 19713.9 | 1.71671 | 0.858353 | − | 0.513060i | \(-0.171488\pi\) | ||||
0.858353 | + | 0.513060i | \(0.171488\pi\) | |||||||
\(510\) | 3735.44 | 0.324330 | ||||||||
\(511\) | −13182.3 | −1.14119 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 1502.37 | 0.129301 | ||||||||
\(514\) | −11250.0 | −0.965403 | ||||||||
\(515\) | 27753.5 | 2.37469 | ||||||||
\(516\) | 2514.04 | 0.214485 | ||||||||
\(517\) | 1134.12 | 0.0964765 | ||||||||
\(518\) | −6578.04 | −0.557958 | ||||||||
\(519\) | 6674.33 | 0.564491 | ||||||||
\(520\) | 1310.78 | 0.110541 | ||||||||
\(521\) | 16581.6 | 1.39434 | 0.697172 | − | 0.716904i | \(-0.254441\pi\) | ||||
0.697172 | + | 0.716904i | \(0.254441\pi\) | |||||||
\(522\) | 1339.80 | 0.112340 | ||||||||
\(523\) | −11603.8 | −0.970170 | −0.485085 | − | 0.874467i | \(-0.661211\pi\) | ||||
−0.485085 | + | 0.874467i | \(0.661211\pi\) | |||||||
\(524\) | −8556.23 | −0.713322 | ||||||||
\(525\) | 7824.04 | 0.650417 | ||||||||
\(526\) | 2721.38 | 0.225585 | ||||||||
\(527\) | −6608.71 | −0.546262 | ||||||||
\(528\) | −846.879 | −0.0698024 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 13401.3 | 1.09833 | ||||||||
\(531\) | −3564.00 | −0.291270 | ||||||||
\(532\) | 3116.03 | 0.253941 | ||||||||
\(533\) | 3653.73 | 0.296924 | ||||||||
\(534\) | −3594.96 | −0.291328 | ||||||||
\(535\) | 29972.7 | 2.42212 | ||||||||
\(536\) | 8526.47 | 0.687104 | ||||||||
\(537\) | 11517.9 | 0.925572 | ||||||||
\(538\) | −3333.07 | −0.267098 | ||||||||
\(539\) | 2593.57 | 0.207259 | ||||||||
\(540\) | 1905.48 | 0.151849 | ||||||||
\(541\) | 22175.8 | 1.76231 | 0.881156 | − | 0.472826i | \(-0.156766\pi\) | ||||
0.881156 | + | 0.472826i | \(0.156766\pi\) | |||||||
\(542\) | 6642.40 | 0.526412 | ||||||||
\(543\) | −12645.8 | −0.999415 | ||||||||
\(544\) | 1129.17 | 0.0889942 | ||||||||
\(545\) | 6869.88 | 0.539951 | ||||||||
\(546\) | 780.077 | 0.0611433 | ||||||||
\(547\) | −7899.03 | −0.617437 | −0.308719 | − | 0.951153i | \(-0.599900\pi\) | ||||
−0.308719 | + | 0.951153i | \(0.599900\pi\) | |||||||
\(548\) | −3012.08 | −0.234798 | ||||||||
\(549\) | 5353.22 | 0.416157 | ||||||||
\(550\) | 6573.43 | 0.509622 | ||||||||
\(551\) | −4141.71 | −0.320223 | ||||||||
\(552\) | −552.000 | −0.0425628 | ||||||||
\(553\) | −7284.10 | −0.560129 | ||||||||
\(554\) | 314.979 | 0.0241556 | ||||||||
\(555\) | 12434.8 | 0.951044 | ||||||||
\(556\) | −2460.64 | −0.187688 | ||||||||
\(557\) | 23535.7 | 1.79037 | 0.895187 | − | 0.445692i | \(-0.147042\pi\) | ||||
0.895187 | + | 0.445692i | \(0.147042\pi\) | |||||||
\(558\) | −3371.16 | −0.255757 | ||||||||
\(559\) | −1945.58 | −0.147208 | ||||||||
\(560\) | 3952.10 | 0.298226 | ||||||||
\(561\) | 1867.72 | 0.140562 | ||||||||
\(562\) | 301.604 | 0.0226377 | ||||||||
\(563\) | 5337.85 | 0.399580 | 0.199790 | − | 0.979839i | \(-0.435974\pi\) | ||||
0.199790 | + | 0.979839i | \(0.435974\pi\) | |||||||
\(564\) | −771.362 | −0.0575890 | ||||||||
\(565\) | 1955.82 | 0.145632 | ||||||||
\(566\) | −13763.2 | −1.02210 | ||||||||
\(567\) | 1134.00 | 0.0839921 | ||||||||
\(568\) | −7289.28 | −0.538470 | ||||||||
\(569\) | −15639.6 | −1.15228 | −0.576140 | − | 0.817351i | \(-0.695442\pi\) | ||||
−0.576140 | + | 0.817351i | \(0.695442\pi\) | |||||||
\(570\) | −5890.40 | −0.432845 | ||||||||
\(571\) | 7640.99 | 0.560010 | 0.280005 | − | 0.959999i | \(-0.409664\pi\) | ||||
0.280005 | + | 0.959999i | \(0.409664\pi\) | |||||||
\(572\) | 655.388 | 0.0479076 | ||||||||
\(573\) | −11488.7 | −0.837602 | ||||||||
\(574\) | 11016.3 | 0.801066 | ||||||||
\(575\) | 4284.59 | 0.310748 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | −7382.08 | −0.532617 | −0.266308 | − | 0.963888i | \(-0.585804\pi\) | ||||
−0.266308 | + | 0.963888i | \(0.585804\pi\) | |||||||
\(578\) | 7335.71 | 0.527898 | ||||||||
\(579\) | −786.232 | −0.0564329 | ||||||||
\(580\) | −5252.99 | −0.376067 | ||||||||
\(581\) | −5857.35 | −0.418251 | ||||||||
\(582\) | −244.357 | −0.0174037 | ||||||||
\(583\) | 6700.64 | 0.476007 | ||||||||
\(584\) | 7532.74 | 0.533745 | ||||||||
\(585\) | −1474.62 | −0.104219 | ||||||||
\(586\) | −11301.7 | −0.796703 | ||||||||
\(587\) | 8046.01 | 0.565749 | 0.282874 | − | 0.959157i | \(-0.408712\pi\) | ||||
0.282874 | + | 0.959157i | \(0.408712\pi\) | |||||||
\(588\) | −1764.00 | −0.123718 | ||||||||
\(589\) | 10421.2 | 0.729032 | ||||||||
\(590\) | 13973.5 | 0.975051 | ||||||||
\(591\) | −16141.2 | −1.12345 | ||||||||
\(592\) | 3758.88 | 0.260961 | ||||||||
\(593\) | −4264.63 | −0.295324 | −0.147662 | − | 0.989038i | \(-0.547175\pi\) | ||||
−0.147662 | + | 0.989038i | \(0.547175\pi\) | |||||||
\(594\) | 952.739 | 0.0658104 | ||||||||
\(595\) | −8716.03 | −0.600542 | ||||||||
\(596\) | −12017.7 | −0.825946 | ||||||||
\(597\) | 11724.1 | 0.803746 | ||||||||
\(598\) | 427.185 | 0.0292122 | ||||||||
\(599\) | −24148.6 | −1.64722 | −0.823612 | − | 0.567154i | \(-0.808044\pi\) | ||||
−0.823612 | + | 0.567154i | \(0.808044\pi\) | |||||||
\(600\) | −4470.88 | −0.304205 | ||||||||
\(601\) | −6389.01 | −0.433632 | −0.216816 | − | 0.976212i | \(-0.569567\pi\) | ||||
−0.216816 | + | 0.976212i | \(0.569567\pi\) | |||||||
\(602\) | −5866.09 | −0.397149 | ||||||||
\(603\) | −9592.28 | −0.647808 | ||||||||
\(604\) | −7453.15 | −0.502093 | ||||||||
\(605\) | −17991.1 | −1.20900 | ||||||||
\(606\) | 8767.87 | 0.587740 | ||||||||
\(607\) | −1666.19 | −0.111414 | −0.0557072 | − | 0.998447i | \(-0.517741\pi\) | ||||
−0.0557072 | + | 0.998447i | \(0.517741\pi\) | |||||||
\(608\) | −1780.59 | −0.118770 | ||||||||
\(609\) | −3126.19 | −0.208013 | ||||||||
\(610\) | −20988.6 | −1.39312 | ||||||||
\(611\) | 596.947 | 0.0395252 | ||||||||
\(612\) | −1270.32 | −0.0839046 | ||||||||
\(613\) | 21040.3 | 1.38631 | 0.693155 | − | 0.720789i | \(-0.256220\pi\) | ||||
0.693155 | + | 0.720789i | \(0.256220\pi\) | |||||||
\(614\) | −8142.52 | −0.535188 | ||||||||
\(615\) | −20824.7 | −1.36542 | ||||||||
\(616\) | 1976.05 | 0.129249 | ||||||||
\(617\) | 13670.0 | 0.891950 | 0.445975 | − | 0.895045i | \(-0.352857\pi\) | ||||
0.445975 | + | 0.895045i | \(0.352857\pi\) | |||||||
\(618\) | −9438.19 | −0.614336 | ||||||||
\(619\) | −22747.0 | −1.47702 | −0.738512 | − | 0.674241i | \(-0.764471\pi\) | ||||
−0.738512 | + | 0.674241i | \(0.764471\pi\) | |||||||
\(620\) | 13217.4 | 0.856169 | ||||||||
\(621\) | 621.000 | 0.0401286 | ||||||||
\(622\) | 1065.07 | 0.0686582 | ||||||||
\(623\) | 8388.23 | 0.539434 | ||||||||
\(624\) | −445.758 | −0.0285971 | ||||||||
\(625\) | −4208.12 | −0.269320 | ||||||||
\(626\) | −19519.3 | −1.24624 | ||||||||
\(627\) | −2945.20 | −0.187592 | ||||||||
\(628\) | −5887.69 | −0.374116 | ||||||||
\(629\) | −8289.89 | −0.525500 | ||||||||
\(630\) | −4446.12 | −0.281171 | ||||||||
\(631\) | −4308.14 | −0.271798 | −0.135899 | − | 0.990723i | \(-0.543392\pi\) | ||||
−0.135899 | + | 0.990723i | \(0.543392\pi\) | |||||||
\(632\) | 4162.34 | 0.261977 | ||||||||
\(633\) | 6341.73 | 0.398201 | ||||||||
\(634\) | −7994.32 | −0.500781 | ||||||||
\(635\) | −7717.66 | −0.482309 | ||||||||
\(636\) | −4557.40 | −0.284139 | ||||||||
\(637\) | 1365.14 | 0.0849115 | ||||||||
\(638\) | −2626.50 | −0.162984 | ||||||||
\(639\) | 8200.43 | 0.507675 | ||||||||
\(640\) | −2258.34 | −0.139483 | ||||||||
\(641\) | 897.151 | 0.0552813 | 0.0276407 | − | 0.999618i | \(-0.491201\pi\) | ||||
0.0276407 | + | 0.999618i | \(0.491201\pi\) | |||||||
\(642\) | −10192.9 | −0.626607 | ||||||||
\(643\) | −19935.4 | −1.22267 | −0.611333 | − | 0.791374i | \(-0.709366\pi\) | ||||
−0.611333 | + | 0.791374i | \(0.709366\pi\) | |||||||
\(644\) | 1288.00 | 0.0788110 | ||||||||
\(645\) | 11089.0 | 0.676944 | ||||||||
\(646\) | 3926.93 | 0.239169 | ||||||||
\(647\) | 4670.58 | 0.283801 | 0.141901 | − | 0.989881i | \(-0.454679\pi\) | ||||
0.141901 | + | 0.989881i | \(0.454679\pi\) | |||||||
\(648\) | −648.000 | −0.0392837 | ||||||||
\(649\) | 6986.75 | 0.422579 | ||||||||
\(650\) | 3459.95 | 0.208785 | ||||||||
\(651\) | 7866.04 | 0.473570 | ||||||||
\(652\) | 1868.94 | 0.112260 | ||||||||
\(653\) | 24406.1 | 1.46261 | 0.731304 | − | 0.682052i | \(-0.238912\pi\) | ||||
0.731304 | + | 0.682052i | \(0.238912\pi\) | |||||||
\(654\) | −2336.26 | −0.139686 | ||||||||
\(655\) | −37740.1 | −2.25134 | ||||||||
\(656\) | −6295.03 | −0.374664 | ||||||||
\(657\) | −8474.33 | −0.503220 | ||||||||
\(658\) | 1799.85 | 0.106634 | ||||||||
\(659\) | 6906.99 | 0.408283 | 0.204141 | − | 0.978941i | \(-0.434560\pi\) | ||||
0.204141 | + | 0.978941i | \(0.434560\pi\) | |||||||
\(660\) | −3735.44 | −0.220306 | ||||||||
\(661\) | 2861.61 | 0.168387 | 0.0841934 | − | 0.996449i | \(-0.473169\pi\) | ||||
0.0841934 | + | 0.996449i | \(0.473169\pi\) | |||||||
\(662\) | −12699.5 | −0.745587 | ||||||||
\(663\) | 983.082 | 0.0575863 | ||||||||
\(664\) | 3347.06 | 0.195619 | ||||||||
\(665\) | 13744.3 | 0.801473 | ||||||||
\(666\) | −4228.74 | −0.246037 | ||||||||
\(667\) | −1711.96 | −0.0993815 | ||||||||
\(668\) | 7434.29 | 0.430601 | ||||||||
\(669\) | 14351.1 | 0.829365 | ||||||||
\(670\) | 37608.8 | 2.16859 | ||||||||
\(671\) | −10494.3 | −0.603767 | ||||||||
\(672\) | −1344.00 | −0.0771517 | ||||||||
\(673\) | −28273.2 | −1.61939 | −0.809696 | − | 0.586849i | \(-0.800368\pi\) | ||||
−0.809696 | + | 0.586849i | \(0.800368\pi\) | |||||||
\(674\) | −5061.48 | −0.289259 | ||||||||
\(675\) | 5029.74 | 0.286807 | ||||||||
\(676\) | −8443.03 | −0.480373 | ||||||||
\(677\) | −22741.0 | −1.29100 | −0.645501 | − | 0.763759i | \(-0.723352\pi\) | ||||
−0.645501 | + | 0.763759i | \(0.723352\pi\) | |||||||
\(678\) | −665.121 | −0.0376752 | ||||||||
\(679\) | 570.167 | 0.0322254 | ||||||||
\(680\) | 4980.59 | 0.280878 | ||||||||
\(681\) | −1990.89 | −0.112028 | ||||||||
\(682\) | 6608.71 | 0.371057 | ||||||||
\(683\) | 31438.8 | 1.76131 | 0.880653 | − | 0.473763i | \(-0.157105\pi\) | ||||
0.880653 | + | 0.473763i | \(0.157105\pi\) | |||||||
\(684\) | 2003.16 | 0.111978 | ||||||||
\(685\) | −13285.8 | −0.741055 | ||||||||
\(686\) | 13720.0 | 0.763604 | ||||||||
\(687\) | 8878.40 | 0.493060 | ||||||||
\(688\) | 3352.05 | 0.185750 | ||||||||
\(689\) | 3526.91 | 0.195014 | ||||||||
\(690\) | −2434.78 | −0.134334 | ||||||||
\(691\) | 2549.94 | 0.140382 | 0.0701912 | − | 0.997534i | \(-0.477639\pi\) | ||||
0.0701912 | + | 0.997534i | \(0.477639\pi\) | |||||||
\(692\) | 8899.11 | 0.488863 | ||||||||
\(693\) | −2223.06 | −0.121857 | ||||||||
\(694\) | −9895.44 | −0.541248 | ||||||||
\(695\) | −10853.5 | −0.592367 | ||||||||
\(696\) | 1786.40 | 0.0972890 | ||||||||
\(697\) | 13883.2 | 0.754465 | ||||||||
\(698\) | −6628.31 | −0.359434 | ||||||||
\(699\) | 7511.28 | 0.406441 | ||||||||
\(700\) | 10432.1 | 0.563278 | ||||||||
\(701\) | −6358.28 | −0.342580 | −0.171290 | − | 0.985221i | \(-0.554794\pi\) | ||||
−0.171290 | + | 0.985221i | \(0.554794\pi\) | |||||||
\(702\) | 501.478 | 0.0269616 | ||||||||
\(703\) | 13072.3 | 0.701324 | ||||||||
\(704\) | −1129.17 | −0.0604507 | ||||||||
\(705\) | −3402.35 | −0.181759 | ||||||||
\(706\) | −8274.52 | −0.441099 | ||||||||
\(707\) | −20458.4 | −1.08828 | ||||||||
\(708\) | −4752.00 | −0.252247 | ||||||||
\(709\) | −11553.3 | −0.611978 | −0.305989 | − | 0.952035i | \(-0.598987\pi\) | ||||
−0.305989 | + | 0.952035i | \(0.598987\pi\) | |||||||
\(710\) | −32151.7 | −1.69948 | ||||||||
\(711\) | −4682.64 | −0.246994 | ||||||||
\(712\) | −4793.28 | −0.252297 | ||||||||
\(713\) | 4307.59 | 0.226256 | ||||||||
\(714\) | 2964.08 | 0.155361 | ||||||||
\(715\) | 2890.81 | 0.151203 | ||||||||
\(716\) | 15357.1 | 0.801569 | ||||||||
\(717\) | 19201.1 | 1.00011 | ||||||||
\(718\) | 20776.7 | 1.07991 | ||||||||
\(719\) | 17141.5 | 0.889110 | 0.444555 | − | 0.895751i | \(-0.353362\pi\) | ||||
0.444555 | + | 0.895751i | \(0.353362\pi\) | |||||||
\(720\) | 2540.64 | 0.131506 | ||||||||
\(721\) | 22022.5 | 1.13753 | ||||||||
\(722\) | 7525.64 | 0.387916 | ||||||||
\(723\) | −2619.63 | −0.134751 | ||||||||
\(724\) | −16861.0 | −0.865519 | ||||||||
\(725\) | −13865.9 | −0.710299 | ||||||||
\(726\) | 6118.28 | 0.312770 | ||||||||
\(727\) | −2741.52 | −0.139859 | −0.0699294 | − | 0.997552i | \(-0.522277\pi\) | ||||
−0.0699294 | + | 0.997552i | \(0.522277\pi\) | |||||||
\(728\) | 1040.10 | 0.0529516 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 33225.6 | 1.68457 | ||||||||
\(731\) | −7392.66 | −0.374046 | ||||||||
\(732\) | 7137.63 | 0.360402 | ||||||||
\(733\) | −9419.32 | −0.474639 | −0.237320 | − | 0.971432i | \(-0.576269\pi\) | ||||
−0.237320 | + | 0.971432i | \(0.576269\pi\) | |||||||
\(734\) | 13152.2 | 0.661384 | ||||||||
\(735\) | −7780.70 | −0.390470 | ||||||||
\(736\) | −736.000 | −0.0368605 | ||||||||
\(737\) | 18804.4 | 0.939850 | ||||||||
\(738\) | 7081.91 | 0.353237 | ||||||||
\(739\) | 14408.2 | 0.717203 | 0.358602 | − | 0.933491i | \(-0.383254\pi\) | ||||
0.358602 | + | 0.933491i | \(0.383254\pi\) | |||||||
\(740\) | 16579.8 | 0.823628 | ||||||||
\(741\) | −1550.22 | −0.0768538 | ||||||||
\(742\) | 10633.9 | 0.526124 | ||||||||
\(743\) | −8023.72 | −0.396180 | −0.198090 | − | 0.980184i | \(-0.563474\pi\) | ||||
−0.198090 | + | 0.980184i | \(0.563474\pi\) | |||||||
\(744\) | −4494.88 | −0.221492 | ||||||||
\(745\) | −53008.0 | −2.60679 | ||||||||
\(746\) | −13531.1 | −0.664085 | ||||||||
\(747\) | −3765.44 | −0.184431 | ||||||||
\(748\) | 2490.29 | 0.121730 | ||||||||
\(749\) | 23783.4 | 1.16025 | ||||||||
\(750\) | −6487.80 | −0.315868 | ||||||||
\(751\) | −16501.1 | −0.801775 | −0.400888 | − | 0.916127i | \(-0.631298\pi\) | ||||
−0.400888 | + | 0.916127i | \(0.631298\pi\) | |||||||
\(752\) | −1028.48 | −0.0498736 | ||||||||
\(753\) | −5096.60 | −0.246654 | ||||||||
\(754\) | −1382.47 | −0.0667725 | ||||||||
\(755\) | −32874.6 | −1.58467 | ||||||||
\(756\) | 1512.00 | 0.0727393 | ||||||||
\(757\) | −17112.3 | −0.821607 | −0.410804 | − | 0.911724i | \(-0.634752\pi\) | ||||
−0.410804 | + | 0.911724i | \(0.634752\pi\) | |||||||
\(758\) | 310.317 | 0.0148697 | ||||||||
\(759\) | −1217.39 | −0.0582193 | ||||||||
\(760\) | −7853.86 | −0.374855 | ||||||||
\(761\) | −21846.4 | −1.04065 | −0.520323 | − | 0.853970i | \(-0.674188\pi\) | ||||
−0.520323 | + | 0.853970i | \(0.674188\pi\) | |||||||
\(762\) | 2624.56 | 0.124774 | ||||||||
\(763\) | 5451.26 | 0.258649 | ||||||||
\(764\) | −15318.2 | −0.725384 | ||||||||
\(765\) | −5603.16 | −0.264814 | ||||||||
\(766\) | 15685.8 | 0.739882 | ||||||||
\(767\) | 3677.51 | 0.173125 | ||||||||
\(768\) | 768.000 | 0.0360844 | ||||||||
\(769\) | −15782.8 | −0.740107 | −0.370053 | − | 0.929010i | \(-0.620661\pi\) | ||||
−0.370053 | + | 0.929010i | \(0.620661\pi\) | |||||||
\(770\) | 8716.03 | 0.407927 | ||||||||
\(771\) | 16875.0 | 0.788248 | ||||||||
\(772\) | −1048.31 | −0.0488724 | ||||||||
\(773\) | 26095.1 | 1.21420 | 0.607100 | − | 0.794625i | \(-0.292333\pi\) | ||||
0.607100 | + | 0.794625i | \(0.292333\pi\) | |||||||
\(774\) | −3771.06 | −0.175126 | ||||||||
\(775\) | 34889.0 | 1.61710 | ||||||||
\(776\) | −325.810 | −0.0150720 | ||||||||
\(777\) | 9867.06 | 0.455571 | ||||||||
\(778\) | −1864.89 | −0.0859379 | ||||||||
\(779\) | −21892.3 | −1.00690 | ||||||||
\(780\) | −1966.16 | −0.0902564 | ||||||||
\(781\) | −16075.9 | −0.736543 | ||||||||
\(782\) | 1623.19 | 0.0742263 | ||||||||
\(783\) | −2009.70 | −0.0917250 | ||||||||
\(784\) | −2352.00 | −0.107143 | ||||||||
\(785\) | −25969.6 | −1.18076 | ||||||||
\(786\) | 12834.3 | 0.582425 | ||||||||
\(787\) | 8756.20 | 0.396601 | 0.198300 | − | 0.980141i | \(-0.436458\pi\) | ||||
0.198300 | + | 0.980141i | \(0.436458\pi\) | |||||||
\(788\) | −21521.6 | −0.972937 | ||||||||
\(789\) | −4082.07 | −0.184189 | ||||||||
\(790\) | 18359.4 | 0.826833 | ||||||||
\(791\) | 1551.95 | 0.0697610 | ||||||||
\(792\) | 1270.32 | 0.0569935 | ||||||||
\(793\) | −5523.72 | −0.247355 | ||||||||
\(794\) | −23683.4 | −1.05856 | ||||||||
\(795\) | −20101.9 | −0.896782 | ||||||||
\(796\) | 15632.2 | 0.696064 | ||||||||
\(797\) | −17161.4 | −0.762719 | −0.381359 | − | 0.924427i | \(-0.624544\pi\) | ||||
−0.381359 | + | 0.924427i | \(0.624544\pi\) | |||||||
\(798\) | −4674.04 | −0.207342 | ||||||||
\(799\) | 2268.23 | 0.100431 | ||||||||
\(800\) | −5961.17 | −0.263449 | ||||||||
\(801\) | 5392.43 | 0.237868 | ||||||||
\(802\) | 20193.5 | 0.889098 | ||||||||
\(803\) | 16612.8 | 0.730079 | ||||||||
\(804\) | −12789.7 | −0.561018 | ||||||||
\(805\) | 5681.15 | 0.248738 | ||||||||
\(806\) | 3478.52 | 0.152017 | ||||||||
\(807\) | 4999.60 | 0.218085 | ||||||||
\(808\) | 11690.5 | 0.508998 | ||||||||
\(809\) | 20060.1 | 0.871785 | 0.435893 | − | 0.899999i | \(-0.356433\pi\) | ||||
0.435893 | + | 0.899999i | \(0.356433\pi\) | |||||||
\(810\) | −2858.22 | −0.123985 | ||||||||
\(811\) | 18329.3 | 0.793622 | 0.396811 | − | 0.917900i | \(-0.370117\pi\) | ||||
0.396811 | + | 0.917900i | \(0.370117\pi\) | |||||||
\(812\) | −4168.26 | −0.180144 | ||||||||
\(813\) | −9963.59 | −0.429814 | ||||||||
\(814\) | 8289.89 | 0.356954 | ||||||||
\(815\) | 8243.58 | 0.354307 | ||||||||
\(816\) | −1693.76 | −0.0726635 | ||||||||
\(817\) | 11657.5 | 0.499195 | ||||||||
\(818\) | 15055.7 | 0.643534 | ||||||||
\(819\) | −1170.12 | −0.0499233 | ||||||||
\(820\) | −27766.3 | −1.18249 | ||||||||
\(821\) | 32619.7 | 1.38665 | 0.693323 | − | 0.720627i | \(-0.256146\pi\) | ||||
0.693323 | + | 0.720627i | \(0.256146\pi\) | |||||||
\(822\) | 4518.12 | 0.191712 | ||||||||
\(823\) | 21374.7 | 0.905316 | 0.452658 | − | 0.891684i | \(-0.350476\pi\) | ||||
0.452658 | + | 0.891684i | \(0.350476\pi\) | |||||||
\(824\) | −12584.3 | −0.532031 | ||||||||
\(825\) | −9860.14 | −0.416104 | ||||||||
\(826\) | 11088.0 | 0.467071 | ||||||||
\(827\) | 3536.45 | 0.148699 | 0.0743497 | − | 0.997232i | \(-0.476312\pi\) | ||||
0.0743497 | + | 0.997232i | \(0.476312\pi\) | |||||||
\(828\) | 828.000 | 0.0347524 | ||||||||
\(829\) | 1345.14 | 0.0563553 | 0.0281776 | − | 0.999603i | \(-0.491030\pi\) | ||||
0.0281776 | + | 0.999603i | \(0.491030\pi\) | |||||||
\(830\) | 14763.3 | 0.617400 | ||||||||
\(831\) | −472.469 | −0.0197229 | ||||||||
\(832\) | −594.345 | −0.0247659 | ||||||||
\(833\) | 5187.14 | 0.215755 | ||||||||
\(834\) | 3690.96 | 0.153246 | ||||||||
\(835\) | 32791.4 | 1.35903 | ||||||||
\(836\) | −3926.93 | −0.162459 | ||||||||
\(837\) | 5056.74 | 0.208825 | ||||||||
\(838\) | 13611.0 | 0.561078 | ||||||||
\(839\) | 14522.5 | 0.597584 | 0.298792 | − | 0.954318i | \(-0.403416\pi\) | ||||
0.298792 | + | 0.954318i | \(0.403416\pi\) | |||||||
\(840\) | −5928.15 | −0.243501 | ||||||||
\(841\) | −18848.7 | −0.772836 | ||||||||
\(842\) | 31536.0 | 1.29074 | ||||||||
\(843\) | −452.406 | −0.0184836 | ||||||||
\(844\) | 8455.65 | 0.344852 | ||||||||
\(845\) | −37240.8 | −1.51612 | ||||||||
\(846\) | 1157.04 | 0.0470212 | ||||||||
\(847\) | −14276.0 | −0.579137 | ||||||||
\(848\) | −6076.53 | −0.246072 | ||||||||
\(849\) | 20644.7 | 0.834541 | ||||||||
\(850\) | 13146.9 | 0.530510 | ||||||||
\(851\) | 5403.39 | 0.217657 | ||||||||
\(852\) | 10933.9 | 0.439659 | ||||||||
\(853\) | −20073.4 | −0.805746 | −0.402873 | − | 0.915256i | \(-0.631988\pi\) | ||||
−0.402873 | + | 0.915256i | \(0.631988\pi\) | |||||||
\(854\) | −16654.5 | −0.667335 | ||||||||
\(855\) | 8835.59 | 0.353416 | ||||||||
\(856\) | −13590.5 | −0.542657 | ||||||||
\(857\) | −16038.0 | −0.639262 | −0.319631 | − | 0.947542i | \(-0.603559\pi\) | ||||
−0.319631 | + | 0.947542i | \(0.603559\pi\) | |||||||
\(858\) | −983.082 | −0.0391164 | ||||||||
\(859\) | 42326.4 | 1.68121 | 0.840605 | − | 0.541648i | \(-0.182200\pi\) | ||||
0.840605 | + | 0.541648i | \(0.182200\pi\) | |||||||
\(860\) | 14785.3 | 0.586251 | ||||||||
\(861\) | −16524.5 | −0.654068 | ||||||||
\(862\) | 2148.53 | 0.0848948 | ||||||||
\(863\) | −14075.7 | −0.555205 | −0.277602 | − | 0.960696i | \(-0.589540\pi\) | ||||
−0.277602 | + | 0.960696i | \(0.589540\pi\) | |||||||
\(864\) | −864.000 | −0.0340207 | ||||||||
\(865\) | 39252.5 | 1.54292 | ||||||||
\(866\) | −33726.4 | −1.32340 | ||||||||
\(867\) | −11003.6 | −0.431027 | ||||||||
\(868\) | 10488.1 | 0.410124 | ||||||||
\(869\) | 9179.70 | 0.358343 | ||||||||
\(870\) | 7879.49 | 0.307057 | ||||||||
\(871\) | 9897.78 | 0.385044 | ||||||||
\(872\) | −3115.01 | −0.120972 | ||||||||
\(873\) | 366.536 | 0.0142100 | ||||||||
\(874\) | −2559.59 | −0.0990612 | ||||||||
\(875\) | 15138.2 | 0.584874 | ||||||||
\(876\) | −11299.1 | −0.435801 | ||||||||
\(877\) | −18552.9 | −0.714351 | −0.357175 | − | 0.934037i | \(-0.616260\pi\) | ||||
−0.357175 | + | 0.934037i | \(0.616260\pi\) | |||||||
\(878\) | 3184.41 | 0.122401 | ||||||||
\(879\) | 16952.5 | 0.650506 | ||||||||
\(880\) | −4980.59 | −0.190790 | ||||||||
\(881\) | −18290.7 | −0.699465 | −0.349732 | − | 0.936850i | \(-0.613728\pi\) | ||||
−0.349732 | + | 0.936850i | \(0.613728\pi\) | |||||||
\(882\) | 2646.00 | 0.101015 | ||||||||
\(883\) | −37336.9 | −1.42298 | −0.711488 | − | 0.702698i | \(-0.751979\pi\) | ||||
−0.711488 | + | 0.702698i | \(0.751979\pi\) | |||||||
\(884\) | 1310.78 | 0.0498712 | ||||||||
\(885\) | −20960.3 | −0.796126 | ||||||||
\(886\) | −14015.3 | −0.531438 | ||||||||
\(887\) | −7792.73 | −0.294988 | −0.147494 | − | 0.989063i | \(-0.547121\pi\) | ||||
−0.147494 | + | 0.989063i | \(0.547121\pi\) | |||||||
\(888\) | −5638.32 | −0.213074 | ||||||||
\(889\) | −6123.97 | −0.231037 | ||||||||
\(890\) | −21142.3 | −0.796283 | ||||||||
\(891\) | −1429.11 | −0.0537339 | ||||||||
\(892\) | 19134.8 | 0.718251 | ||||||||
\(893\) | −3576.76 | −0.134033 | ||||||||
\(894\) | 18026.5 | 0.674382 | ||||||||
\(895\) | 67737.8 | 2.52986 | ||||||||
\(896\) | −1792.00 | −0.0668153 | ||||||||
\(897\) | −640.778 | −0.0238517 | ||||||||
\(898\) | −31878.9 | −1.18465 | ||||||||
\(899\) | −13940.3 | −0.517171 | ||||||||
\(900\) | 6706.32 | 0.248382 | ||||||||
\(901\) | 13401.3 | 0.495518 | ||||||||
\(902\) | −13883.2 | −0.512482 | ||||||||
\(903\) | 8799.14 | 0.324271 | ||||||||
\(904\) | −886.828 | −0.0326277 | ||||||||
\(905\) | −74371.2 | −2.73169 | ||||||||
\(906\) | 11179.7 | 0.409957 | ||||||||
\(907\) | 12764.9 | 0.467313 | 0.233657 | − | 0.972319i | \(-0.424931\pi\) | ||||
0.233657 | + | 0.972319i | \(0.424931\pi\) | |||||||
\(908\) | −2654.52 | −0.0970192 | ||||||||
\(909\) | −13151.8 | −0.479888 | ||||||||
\(910\) | 4587.72 | 0.167122 | ||||||||
\(911\) | −20843.2 | −0.758030 | −0.379015 | − | 0.925390i | \(-0.623737\pi\) | ||||
−0.379015 | + | 0.925390i | \(0.623737\pi\) | |||||||
\(912\) | 2670.88 | 0.0969755 | ||||||||
\(913\) | 7381.65 | 0.267576 | ||||||||
\(914\) | 14410.4 | 0.521502 | ||||||||
\(915\) | 31482.9 | 1.13748 | ||||||||
\(916\) | 11837.9 | 0.427002 | ||||||||
\(917\) | −29946.8 | −1.07844 | ||||||||
\(918\) | 1905.48 | 0.0685078 | ||||||||
\(919\) | −24938.9 | −0.895167 | −0.447583 | − | 0.894242i | \(-0.647715\pi\) | ||||
−0.447583 | + | 0.894242i | \(0.647715\pi\) | |||||||
\(920\) | −3246.37 | −0.116337 | ||||||||
\(921\) | 12213.8 | 0.436979 | ||||||||
\(922\) | 24960.2 | 0.891563 | ||||||||
\(923\) | −8461.60 | −0.301752 | ||||||||
\(924\) | −2964.08 | −0.105531 | ||||||||
\(925\) | 43764.3 | 1.55563 | ||||||||
\(926\) | −124.123 | −0.00440488 | ||||||||
\(927\) | 14157.3 | 0.501603 | ||||||||
\(928\) | 2381.86 | 0.0842548 | ||||||||
\(929\) | 43378.9 | 1.53199 | 0.765993 | − | 0.642849i | \(-0.222248\pi\) | ||||
0.765993 | + | 0.642849i | \(0.222248\pi\) | |||||||
\(930\) | −19826.1 | −0.699059 | ||||||||
\(931\) | −8179.57 | −0.287943 | ||||||||
\(932\) | 10015.0 | 0.351989 | ||||||||
\(933\) | −1597.60 | −0.0560592 | ||||||||
\(934\) | −14037.7 | −0.491785 | ||||||||
\(935\) | 10984.3 | 0.384196 | ||||||||
\(936\) | 668.638 | 0.0233495 | ||||||||
\(937\) | 22043.0 | 0.768530 | 0.384265 | − | 0.923223i | \(-0.374455\pi\) | ||||
0.384265 | + | 0.923223i | \(0.374455\pi\) | |||||||
\(938\) | 29842.7 | 1.03880 | ||||||||
\(939\) | 29278.9 | 1.01755 | ||||||||
\(940\) | −4536.46 | −0.157408 | ||||||||
\(941\) | −11791.8 | −0.408504 | −0.204252 | − | 0.978918i | \(-0.565476\pi\) | ||||
−0.204252 | + | 0.978918i | \(0.565476\pi\) | |||||||
\(942\) | 8831.54 | 0.305464 | ||||||||
\(943\) | −9049.11 | −0.312492 | ||||||||
\(944\) | −6336.00 | −0.218453 | ||||||||
\(945\) | 6669.17 | 0.229575 | ||||||||
\(946\) | 7392.66 | 0.254076 | ||||||||
\(947\) | −34148.3 | −1.17178 | −0.585888 | − | 0.810392i | \(-0.699254\pi\) | ||||
−0.585888 | + | 0.810392i | \(0.699254\pi\) | |||||||
\(948\) | −6243.52 | −0.213903 | ||||||||
\(949\) | 8744.23 | 0.299104 | ||||||||
\(950\) | −20731.2 | −0.708010 | ||||||||
\(951\) | 11991.5 | 0.408886 | ||||||||
\(952\) | 3952.10 | 0.134547 | ||||||||
\(953\) | 24045.9 | 0.817338 | 0.408669 | − | 0.912683i | \(-0.365993\pi\) | ||||
0.408669 | + | 0.912683i | \(0.365993\pi\) | |||||||
\(954\) | 6836.10 | 0.231999 | ||||||||
\(955\) | −67566.0 | −2.28941 | ||||||||
\(956\) | 25601.4 | 0.866119 | ||||||||
\(957\) | 3939.74 | 0.133076 | ||||||||
\(958\) | −37177.3 | −1.25380 | ||||||||
\(959\) | −10542.3 | −0.354982 | ||||||||
\(960\) | 3387.52 | 0.113887 | ||||||||
\(961\) | 5285.28 | 0.177412 | ||||||||
\(962\) | 4363.42 | 0.146239 | ||||||||
\(963\) | 15289.3 | 0.511622 | ||||||||
\(964\) | −3492.84 | −0.116698 | ||||||||
\(965\) | −4623.91 | −0.154248 | ||||||||
\(966\) | −1932.00 | −0.0643489 | ||||||||
\(967\) | −14125.6 | −0.469751 | −0.234876 | − | 0.972025i | \(-0.575468\pi\) | ||||
−0.234876 | + | 0.972025i | \(0.575468\pi\) | |||||||
\(968\) | 8157.71 | 0.270866 | ||||||||
\(969\) | −5890.40 | −0.195280 | ||||||||
\(970\) | −1437.09 | −0.0475693 | ||||||||
\(971\) | 9607.55 | 0.317529 | 0.158765 | − | 0.987316i | \(-0.449249\pi\) | ||||
0.158765 | + | 0.987316i | \(0.449249\pi\) | |||||||
\(972\) | 972.000 | 0.0320750 | ||||||||
\(973\) | −8612.23 | −0.283757 | ||||||||
\(974\) | 4497.64 | 0.147961 | ||||||||
\(975\) | −5189.93 | −0.170473 | ||||||||
\(976\) | 9516.84 | 0.312118 | ||||||||
\(977\) | 35829.9 | 1.17328 | 0.586642 | − | 0.809846i | \(-0.300450\pi\) | ||||
0.586642 | + | 0.809846i | \(0.300450\pi\) | |||||||
\(978\) | −2803.41 | −0.0916597 | ||||||||
\(979\) | −10571.2 | −0.345103 | ||||||||
\(980\) | −10374.3 | −0.338157 | ||||||||
\(981\) | 3504.38 | 0.114053 | ||||||||
\(982\) | −456.763 | −0.0148431 | ||||||||
\(983\) | −32173.8 | −1.04393 | −0.521966 | − | 0.852966i | \(-0.674801\pi\) | ||||
−0.521966 | + | 0.852966i | \(0.674801\pi\) | |||||||
\(984\) | 9442.55 | 0.305912 | ||||||||
\(985\) | −94928.0 | −3.07072 | ||||||||
\(986\) | −5252.99 | −0.169665 | ||||||||
\(987\) | −2699.77 | −0.0870664 | ||||||||
\(988\) | −2066.96 | −0.0665573 | ||||||||
\(989\) | 4818.57 | 0.154926 | ||||||||
\(990\) | 5603.16 | 0.179879 | ||||||||
\(991\) | 7190.75 | 0.230496 | 0.115248 | − | 0.993337i | \(-0.463234\pi\) | ||||
0.115248 | + | 0.993337i | \(0.463234\pi\) | |||||||
\(992\) | −5993.17 | −0.191818 | ||||||||
\(993\) | 19049.2 | 0.608770 | ||||||||
\(994\) | −25512.5 | −0.814091 | ||||||||
\(995\) | 68950.8 | 2.19687 | ||||||||
\(996\) | −5020.59 | −0.159722 | ||||||||
\(997\) | 4706.41 | 0.149502 | 0.0747510 | − | 0.997202i | \(-0.476184\pi\) | ||||
0.0747510 | + | 0.997202i | \(0.476184\pi\) | |||||||
\(998\) | −27353.4 | −0.867593 | ||||||||
\(999\) | 6343.11 | 0.200888 |
(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 | 138.4.a.d.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 414.4.a.k.1.1 | 2 | |||
4.3 | odd | 2 | 1104.4.a.k.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
138.4.a.d.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
414.4.a.k.1.1 | 2 | 3.2 | odd | 2 | |||
1104.4.a.k.1.2 | 2 | 4.3 | odd | 2 |