Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2013,4,Mod(1,2013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2013, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2013.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2013 = 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2013.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: | \(118.770844842\) |
Analytic rank: | \(1\) |
Dimension: | \(37\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 2013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.94841 | −0.688867 | −0.344434 | − | 0.938811i | \(-0.611929\pi\) | ||||
−0.344434 | + | 0.938811i | \(0.611929\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | −4.20370 | −0.525462 | ||||||||
\(5\) | 15.7553 | 1.40920 | 0.704599 | − | 0.709606i | \(-0.251127\pi\) | ||||
0.704599 | + | 0.709606i | \(0.251127\pi\) | |||||||
\(6\) | 5.84523 | 0.397718 | ||||||||
\(7\) | 3.79858 | 0.205104 | 0.102552 | − | 0.994728i | \(-0.467299\pi\) | ||||
0.102552 | + | 0.994728i | \(0.467299\pi\) | |||||||
\(8\) | 23.7778 | 1.05084 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −30.6978 | −0.970750 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | 12.6111 | 0.303376 | ||||||||
\(13\) | 55.4159 | 1.18228 | 0.591138 | − | 0.806570i | \(-0.298679\pi\) | ||||
0.591138 | + | 0.806570i | \(0.298679\pi\) | |||||||
\(14\) | −7.40119 | −0.141289 | ||||||||
\(15\) | −47.2659 | −0.813601 | ||||||||
\(16\) | −12.6993 | −0.198427 | ||||||||
\(17\) | 20.7761 | 0.296408 | 0.148204 | − | 0.988957i | \(-0.452651\pi\) | ||||
0.148204 | + | 0.988957i | \(0.452651\pi\) | |||||||
\(18\) | −17.5357 | −0.229622 | ||||||||
\(19\) | −32.9745 | −0.398150 | −0.199075 | − | 0.979984i | \(-0.563794\pi\) | ||||
−0.199075 | + | 0.979984i | \(0.563794\pi\) | |||||||
\(20\) | −66.2306 | −0.740480 | ||||||||
\(21\) | −11.3957 | −0.118417 | ||||||||
\(22\) | −21.4325 | −0.207701 | ||||||||
\(23\) | −38.9042 | −0.352700 | −0.176350 | − | 0.984328i | \(-0.556429\pi\) | ||||
−0.176350 | + | 0.984328i | \(0.556429\pi\) | |||||||
\(24\) | −71.3334 | −0.606703 | ||||||||
\(25\) | 123.230 | 0.985838 | ||||||||
\(26\) | −107.973 | −0.814432 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −15.9681 | −0.107774 | ||||||||
\(29\) | 129.231 | 0.827504 | 0.413752 | − | 0.910390i | \(-0.364218\pi\) | ||||
0.413752 | + | 0.910390i | \(0.364218\pi\) | |||||||
\(30\) | 92.0934 | 0.560463 | ||||||||
\(31\) | −249.275 | −1.44423 | −0.722116 | − | 0.691772i | \(-0.756830\pi\) | ||||
−0.722116 | + | 0.691772i | \(0.756830\pi\) | |||||||
\(32\) | −165.479 | −0.914151 | ||||||||
\(33\) | −33.0000 | −0.174078 | ||||||||
\(34\) | −40.4803 | −0.204186 | ||||||||
\(35\) | 59.8478 | 0.289032 | ||||||||
\(36\) | −37.8333 | −0.175154 | ||||||||
\(37\) | −388.149 | −1.72463 | −0.862314 | − | 0.506374i | \(-0.830986\pi\) | ||||
−0.862314 | + | 0.506374i | \(0.830986\pi\) | |||||||
\(38\) | 64.2478 | 0.274273 | ||||||||
\(39\) | −166.248 | −0.682588 | ||||||||
\(40\) | 374.627 | 1.48084 | ||||||||
\(41\) | −109.584 | −0.417417 | −0.208709 | − | 0.977978i | \(-0.566926\pi\) | ||||
−0.208709 | + | 0.977978i | \(0.566926\pi\) | |||||||
\(42\) | 22.2036 | 0.0815734 | ||||||||
\(43\) | 309.284 | 1.09687 | 0.548434 | − | 0.836194i | \(-0.315224\pi\) | ||||
0.548434 | + | 0.836194i | \(0.315224\pi\) | |||||||
\(44\) | −46.2407 | −0.158433 | ||||||||
\(45\) | 141.798 | 0.469733 | ||||||||
\(46\) | 75.8014 | 0.242963 | ||||||||
\(47\) | −137.846 | −0.427805 | −0.213903 | − | 0.976855i | \(-0.568618\pi\) | ||||
−0.213903 | + | 0.976855i | \(0.568618\pi\) | |||||||
\(48\) | 38.0980 | 0.114562 | ||||||||
\(49\) | −328.571 | −0.957932 | ||||||||
\(50\) | −240.102 | −0.679111 | ||||||||
\(51\) | −62.3282 | −0.171131 | ||||||||
\(52\) | −232.952 | −0.621242 | ||||||||
\(53\) | −648.460 | −1.68062 | −0.840309 | − | 0.542107i | \(-0.817627\pi\) | ||||
−0.840309 | + | 0.542107i | \(0.817627\pi\) | |||||||
\(54\) | 52.6071 | 0.132573 | ||||||||
\(55\) | 173.308 | 0.424889 | ||||||||
\(56\) | 90.3219 | 0.215532 | ||||||||
\(57\) | 98.9234 | 0.229872 | ||||||||
\(58\) | −251.795 | −0.570040 | ||||||||
\(59\) | −715.504 | −1.57883 | −0.789413 | − | 0.613863i | \(-0.789615\pi\) | ||||
−0.789413 | + | 0.613863i | \(0.789615\pi\) | |||||||
\(60\) | 198.692 | 0.427516 | ||||||||
\(61\) | −61.0000 | −0.128037 | ||||||||
\(62\) | 485.691 | 0.994883 | ||||||||
\(63\) | 34.1872 | 0.0683680 | ||||||||
\(64\) | 424.016 | 0.828156 | ||||||||
\(65\) | 873.094 | 1.66606 | ||||||||
\(66\) | 64.2975 | 0.119916 | ||||||||
\(67\) | −655.093 | −1.19451 | −0.597256 | − | 0.802050i | \(-0.703743\pi\) | ||||
−0.597256 | + | 0.802050i | \(0.703743\pi\) | |||||||
\(68\) | −87.3363 | −0.155751 | ||||||||
\(69\) | 116.713 | 0.203631 | ||||||||
\(70\) | −116.608 | −0.199105 | ||||||||
\(71\) | −308.934 | −0.516390 | −0.258195 | − | 0.966093i | \(-0.583128\pi\) | ||||
−0.258195 | + | 0.966093i | \(0.583128\pi\) | |||||||
\(72\) | 214.000 | 0.350280 | ||||||||
\(73\) | 442.021 | 0.708694 | 0.354347 | − | 0.935114i | \(-0.384703\pi\) | ||||
0.354347 | + | 0.935114i | \(0.384703\pi\) | |||||||
\(74\) | 756.273 | 1.18804 | ||||||||
\(75\) | −369.689 | −0.569174 | ||||||||
\(76\) | 138.615 | 0.209213 | ||||||||
\(77\) | 41.7844 | 0.0618412 | ||||||||
\(78\) | 323.919 | 0.470212 | ||||||||
\(79\) | 694.672 | 0.989325 | 0.494662 | − | 0.869085i | \(-0.335292\pi\) | ||||
0.494662 | + | 0.869085i | \(0.335292\pi\) | |||||||
\(80\) | −200.082 | −0.279623 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 213.514 | 0.287545 | ||||||||
\(83\) | −957.704 | −1.26653 | −0.633263 | − | 0.773937i | \(-0.718285\pi\) | ||||
−0.633263 | + | 0.773937i | \(0.718285\pi\) | |||||||
\(84\) | 47.9042 | 0.0622236 | ||||||||
\(85\) | 327.333 | 0.417698 | ||||||||
\(86\) | −602.612 | −0.755597 | ||||||||
\(87\) | −387.693 | −0.477760 | ||||||||
\(88\) | 261.556 | 0.316840 | ||||||||
\(89\) | 460.404 | 0.548346 | 0.274173 | − | 0.961680i | \(-0.411596\pi\) | ||||
0.274173 | + | 0.961680i | \(0.411596\pi\) | |||||||
\(90\) | −276.280 | −0.323583 | ||||||||
\(91\) | 210.502 | 0.242490 | ||||||||
\(92\) | 163.542 | 0.185330 | ||||||||
\(93\) | 747.826 | 0.833827 | ||||||||
\(94\) | 268.580 | 0.294701 | ||||||||
\(95\) | −519.523 | −0.561073 | ||||||||
\(96\) | 496.437 | 0.527785 | ||||||||
\(97\) | 1222.33 | 1.27947 | 0.639736 | − | 0.768595i | \(-0.279044\pi\) | ||||
0.639736 | + | 0.768595i | \(0.279044\pi\) | |||||||
\(98\) | 640.191 | 0.659888 | ||||||||
\(99\) | 99.0000 | 0.100504 | ||||||||
\(100\) | −518.021 | −0.518021 | ||||||||
\(101\) | −1232.26 | −1.21401 | −0.607003 | − | 0.794699i | \(-0.707628\pi\) | ||||
−0.607003 | + | 0.794699i | \(0.707628\pi\) | |||||||
\(102\) | 121.441 | 0.117887 | ||||||||
\(103\) | −1152.90 | −1.10290 | −0.551449 | − | 0.834209i | \(-0.685925\pi\) | ||||
−0.551449 | + | 0.834209i | \(0.685925\pi\) | |||||||
\(104\) | 1317.67 | 1.24238 | ||||||||
\(105\) | −179.543 | −0.166873 | ||||||||
\(106\) | 1263.47 | 1.15772 | ||||||||
\(107\) | 484.448 | 0.437695 | 0.218847 | − | 0.975759i | \(-0.429770\pi\) | ||||
0.218847 | + | 0.975759i | \(0.429770\pi\) | |||||||
\(108\) | 113.500 | 0.101125 | ||||||||
\(109\) | −203.333 | −0.178677 | −0.0893383 | − | 0.996001i | \(-0.528475\pi\) | ||||
−0.0893383 | + | 0.996001i | \(0.528475\pi\) | |||||||
\(110\) | −337.676 | −0.292692 | ||||||||
\(111\) | 1164.45 | 0.995714 | ||||||||
\(112\) | −48.2395 | −0.0406982 | ||||||||
\(113\) | −2222.56 | −1.85027 | −0.925136 | − | 0.379636i | \(-0.876049\pi\) | ||||
−0.925136 | + | 0.379636i | \(0.876049\pi\) | |||||||
\(114\) | −192.743 | −0.158351 | ||||||||
\(115\) | −612.948 | −0.497024 | ||||||||
\(116\) | −543.249 | −0.434822 | ||||||||
\(117\) | 498.743 | 0.394092 | ||||||||
\(118\) | 1394.10 | 1.08760 | ||||||||
\(119\) | 78.9195 | 0.0607945 | ||||||||
\(120\) | −1123.88 | −0.854965 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 118.853 | 0.0882004 | ||||||||
\(123\) | 328.751 | 0.240996 | ||||||||
\(124\) | 1047.88 | 0.758889 | ||||||||
\(125\) | −27.8906 | −0.0199569 | ||||||||
\(126\) | −66.6107 | −0.0470964 | ||||||||
\(127\) | 1539.47 | 1.07564 | 0.537819 | − | 0.843061i | \(-0.319249\pi\) | ||||
0.537819 | + | 0.843061i | \(0.319249\pi\) | |||||||
\(128\) | 497.675 | 0.343662 | ||||||||
\(129\) | −927.852 | −0.633277 | ||||||||
\(130\) | −1701.15 | −1.14770 | ||||||||
\(131\) | 646.766 | 0.431361 | 0.215680 | − | 0.976464i | \(-0.430803\pi\) | ||||
0.215680 | + | 0.976464i | \(0.430803\pi\) | |||||||
\(132\) | 138.722 | 0.0914712 | ||||||||
\(133\) | −125.256 | −0.0816622 | ||||||||
\(134\) | 1276.39 | 0.822861 | ||||||||
\(135\) | −425.393 | −0.271200 | ||||||||
\(136\) | 494.009 | 0.311478 | ||||||||
\(137\) | 2631.38 | 1.64098 | 0.820488 | − | 0.571663i | \(-0.193702\pi\) | ||||
0.820488 | + | 0.571663i | \(0.193702\pi\) | |||||||
\(138\) | −227.404 | −0.140275 | ||||||||
\(139\) | −1109.12 | −0.676793 | −0.338397 | − | 0.941004i | \(-0.609885\pi\) | ||||
−0.338397 | + | 0.941004i | \(0.609885\pi\) | |||||||
\(140\) | −251.582 | −0.151875 | ||||||||
\(141\) | 413.537 | 0.246994 | ||||||||
\(142\) | 601.930 | 0.355724 | ||||||||
\(143\) | 609.575 | 0.356470 | ||||||||
\(144\) | −114.294 | −0.0661424 | ||||||||
\(145\) | 2036.08 | 1.16612 | ||||||||
\(146\) | −861.238 | −0.488196 | ||||||||
\(147\) | 985.712 | 0.553063 | ||||||||
\(148\) | 1631.66 | 0.906227 | ||||||||
\(149\) | 1251.92 | 0.688333 | 0.344167 | − | 0.938909i | \(-0.388161\pi\) | ||||
0.344167 | + | 0.938909i | \(0.388161\pi\) | |||||||
\(150\) | 720.306 | 0.392085 | ||||||||
\(151\) | −654.318 | −0.352633 | −0.176317 | − | 0.984334i | \(-0.556418\pi\) | ||||
−0.176317 | + | 0.984334i | \(0.556418\pi\) | |||||||
\(152\) | −784.060 | −0.418393 | ||||||||
\(153\) | 186.985 | 0.0988027 | ||||||||
\(154\) | −81.4131 | −0.0426003 | ||||||||
\(155\) | −3927.41 | −2.03521 | ||||||||
\(156\) | 698.855 | 0.358674 | ||||||||
\(157\) | −223.625 | −0.113677 | −0.0568383 | − | 0.998383i | \(-0.518102\pi\) | ||||
−0.0568383 | + | 0.998383i | \(0.518102\pi\) | |||||||
\(158\) | −1353.51 | −0.681513 | ||||||||
\(159\) | 1945.38 | 0.970306 | ||||||||
\(160\) | −2607.17 | −1.28822 | ||||||||
\(161\) | −147.781 | −0.0723401 | ||||||||
\(162\) | −157.821 | −0.0765408 | ||||||||
\(163\) | 2084.70 | 1.00175 | 0.500877 | − | 0.865518i | \(-0.333011\pi\) | ||||
0.500877 | + | 0.865518i | \(0.333011\pi\) | |||||||
\(164\) | 460.657 | 0.219337 | ||||||||
\(165\) | −519.925 | −0.245310 | ||||||||
\(166\) | 1866.00 | 0.872468 | ||||||||
\(167\) | 606.255 | 0.280919 | 0.140459 | − | 0.990086i | \(-0.455142\pi\) | ||||
0.140459 | + | 0.990086i | \(0.455142\pi\) | |||||||
\(168\) | −270.966 | −0.124437 | ||||||||
\(169\) | 873.919 | 0.397778 | ||||||||
\(170\) | −637.780 | −0.287738 | ||||||||
\(171\) | −296.770 | −0.132717 | ||||||||
\(172\) | −1300.14 | −0.576363 | ||||||||
\(173\) | −4141.92 | −1.82026 | −0.910128 | − | 0.414327i | \(-0.864017\pi\) | ||||
−0.910128 | + | 0.414327i | \(0.864017\pi\) | |||||||
\(174\) | 755.386 | 0.329113 | ||||||||
\(175\) | 468.098 | 0.202199 | ||||||||
\(176\) | −139.693 | −0.0598281 | ||||||||
\(177\) | 2146.51 | 0.911535 | ||||||||
\(178\) | −897.057 | −0.377737 | ||||||||
\(179\) | −2828.55 | −1.18110 | −0.590548 | − | 0.807003i | \(-0.701088\pi\) | ||||
−0.590548 | + | 0.807003i | \(0.701088\pi\) | |||||||
\(180\) | −596.075 | −0.246827 | ||||||||
\(181\) | 1992.62 | 0.818291 | 0.409145 | − | 0.912469i | \(-0.365827\pi\) | ||||
0.409145 | + | 0.912469i | \(0.365827\pi\) | |||||||
\(182\) | −410.143 | −0.167043 | ||||||||
\(183\) | 183.000 | 0.0739221 | ||||||||
\(184\) | −925.057 | −0.370631 | ||||||||
\(185\) | −6115.40 | −2.43034 | ||||||||
\(186\) | −1457.07 | −0.574396 | ||||||||
\(187\) | 228.537 | 0.0893704 | ||||||||
\(188\) | 579.461 | 0.224796 | ||||||||
\(189\) | −102.562 | −0.0394723 | ||||||||
\(190\) | 1012.24 | 0.386505 | ||||||||
\(191\) | −1027.76 | −0.389350 | −0.194675 | − | 0.980868i | \(-0.562365\pi\) | ||||
−0.194675 | + | 0.980868i | \(0.562365\pi\) | |||||||
\(192\) | −1272.05 | −0.478136 | ||||||||
\(193\) | 1403.94 | 0.523615 | 0.261808 | − | 0.965120i | \(-0.415681\pi\) | ||||
0.261808 | + | 0.965120i | \(0.415681\pi\) | |||||||
\(194\) | −2381.60 | −0.881386 | ||||||||
\(195\) | −2619.28 | −0.961901 | ||||||||
\(196\) | 1381.21 | 0.503357 | ||||||||
\(197\) | 3160.58 | 1.14306 | 0.571529 | − | 0.820582i | \(-0.306351\pi\) | ||||
0.571529 | + | 0.820582i | \(0.306351\pi\) | |||||||
\(198\) | −192.893 | −0.0692337 | ||||||||
\(199\) | −899.836 | −0.320541 | −0.160270 | − | 0.987073i | \(-0.551237\pi\) | ||||
−0.160270 | + | 0.987073i | \(0.551237\pi\) | |||||||
\(200\) | 2930.13 | 1.03596 | ||||||||
\(201\) | 1965.28 | 0.689652 | ||||||||
\(202\) | 2400.95 | 0.836289 | ||||||||
\(203\) | 490.895 | 0.169724 | ||||||||
\(204\) | 262.009 | 0.0899230 | ||||||||
\(205\) | −1726.53 | −0.588224 | ||||||||
\(206\) | 2246.32 | 0.759750 | ||||||||
\(207\) | −350.138 | −0.117567 | ||||||||
\(208\) | −703.745 | −0.234596 | ||||||||
\(209\) | −362.719 | −0.120047 | ||||||||
\(210\) | 349.824 | 0.114953 | ||||||||
\(211\) | −2932.17 | −0.956677 | −0.478338 | − | 0.878176i | \(-0.658761\pi\) | ||||
−0.478338 | + | 0.878176i | \(0.658761\pi\) | |||||||
\(212\) | 2725.93 | 0.883102 | ||||||||
\(213\) | 926.801 | 0.298138 | ||||||||
\(214\) | −943.903 | −0.301514 | ||||||||
\(215\) | 4872.86 | 1.54570 | ||||||||
\(216\) | −642.001 | −0.202234 | ||||||||
\(217\) | −946.892 | −0.296218 | ||||||||
\(218\) | 396.176 | 0.123084 | ||||||||
\(219\) | −1326.06 | −0.409165 | ||||||||
\(220\) | −728.536 | −0.223263 | ||||||||
\(221\) | 1151.32 | 0.350436 | ||||||||
\(222\) | −2268.82 | −0.685915 | ||||||||
\(223\) | 895.070 | 0.268782 | 0.134391 | − | 0.990928i | \(-0.457092\pi\) | ||||
0.134391 | + | 0.990928i | \(0.457092\pi\) | |||||||
\(224\) | −628.585 | −0.187496 | ||||||||
\(225\) | 1109.07 | 0.328613 | ||||||||
\(226\) | 4330.46 | 1.27459 | ||||||||
\(227\) | 1544.96 | 0.451729 | 0.225864 | − | 0.974159i | \(-0.427479\pi\) | ||||
0.225864 | + | 0.974159i | \(0.427479\pi\) | |||||||
\(228\) | −415.844 | −0.120789 | ||||||||
\(229\) | −4066.57 | −1.17348 | −0.586739 | − | 0.809776i | \(-0.699588\pi\) | ||||
−0.586739 | + | 0.809776i | \(0.699588\pi\) | |||||||
\(230\) | 1194.27 | 0.342383 | ||||||||
\(231\) | −125.353 | −0.0357040 | ||||||||
\(232\) | 3072.83 | 0.869575 | ||||||||
\(233\) | 236.307 | 0.0664420 | 0.0332210 | − | 0.999448i | \(-0.489423\pi\) | ||||
0.0332210 | + | 0.999448i | \(0.489423\pi\) | |||||||
\(234\) | −971.756 | −0.271477 | ||||||||
\(235\) | −2171.80 | −0.602862 | ||||||||
\(236\) | 3007.76 | 0.829613 | ||||||||
\(237\) | −2084.02 | −0.571187 | ||||||||
\(238\) | −153.768 | −0.0418793 | ||||||||
\(239\) | −2593.17 | −0.701832 | −0.350916 | − | 0.936407i | \(-0.614130\pi\) | ||||
−0.350916 | + | 0.936407i | \(0.614130\pi\) | |||||||
\(240\) | 600.246 | 0.161441 | ||||||||
\(241\) | 3758.93 | 1.00471 | 0.502353 | − | 0.864663i | \(-0.332468\pi\) | ||||
0.502353 | + | 0.864663i | \(0.332468\pi\) | |||||||
\(242\) | −235.758 | −0.0626243 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 256.426 | 0.0672785 | ||||||||
\(245\) | −5176.73 | −1.34992 | ||||||||
\(246\) | −640.543 | −0.166014 | ||||||||
\(247\) | −1827.31 | −0.470724 | ||||||||
\(248\) | −5927.22 | −1.51766 | ||||||||
\(249\) | 2873.11 | 0.731229 | ||||||||
\(250\) | 54.3423 | 0.0137476 | ||||||||
\(251\) | 260.668 | 0.0655506 | 0.0327753 | − | 0.999463i | \(-0.489565\pi\) | ||||
0.0327753 | + | 0.999463i | \(0.489565\pi\) | |||||||
\(252\) | −143.713 | −0.0359248 | ||||||||
\(253\) | −427.946 | −0.106343 | ||||||||
\(254\) | −2999.52 | −0.740971 | ||||||||
\(255\) | −982.000 | −0.241158 | ||||||||
\(256\) | −4361.80 | −1.06489 | ||||||||
\(257\) | 6902.88 | 1.67545 | 0.837723 | − | 0.546095i | \(-0.183886\pi\) | ||||
0.837723 | + | 0.546095i | \(0.183886\pi\) | |||||||
\(258\) | 1807.84 | 0.436244 | ||||||||
\(259\) | −1474.41 | −0.353728 | ||||||||
\(260\) | −3670.22 | −0.875452 | ||||||||
\(261\) | 1163.08 | 0.275835 | ||||||||
\(262\) | −1260.17 | −0.297150 | ||||||||
\(263\) | −793.192 | −0.185971 | −0.0929854 | − | 0.995667i | \(-0.529641\pi\) | ||||
−0.0929854 | + | 0.995667i | \(0.529641\pi\) | |||||||
\(264\) | −784.668 | −0.182928 | ||||||||
\(265\) | −10216.7 | −2.36832 | ||||||||
\(266\) | 244.050 | 0.0562544 | ||||||||
\(267\) | −1381.21 | −0.316588 | ||||||||
\(268\) | 2753.81 | 0.627671 | ||||||||
\(269\) | 1382.27 | 0.313303 | 0.156651 | − | 0.987654i | \(-0.449930\pi\) | ||||
0.156651 | + | 0.987654i | \(0.449930\pi\) | |||||||
\(270\) | 828.841 | 0.186821 | ||||||||
\(271\) | −6038.49 | −1.35355 | −0.676775 | − | 0.736190i | \(-0.736623\pi\) | ||||
−0.676775 | + | 0.736190i | \(0.736623\pi\) | |||||||
\(272\) | −263.843 | −0.0588155 | ||||||||
\(273\) | −631.505 | −0.140001 | ||||||||
\(274\) | −5127.00 | −1.13041 | ||||||||
\(275\) | 1355.53 | 0.297241 | ||||||||
\(276\) | −490.625 | −0.107001 | ||||||||
\(277\) | −1413.83 | −0.306675 | −0.153337 | − | 0.988174i | \(-0.549002\pi\) | ||||
−0.153337 | + | 0.988174i | \(0.549002\pi\) | |||||||
\(278\) | 2161.02 | 0.466220 | ||||||||
\(279\) | −2243.48 | −0.481410 | ||||||||
\(280\) | 1423.05 | 0.303727 | ||||||||
\(281\) | −949.955 | −0.201671 | −0.100836 | − | 0.994903i | \(-0.532152\pi\) | ||||
−0.100836 | + | 0.994903i | \(0.532152\pi\) | |||||||
\(282\) | −805.739 | −0.170146 | ||||||||
\(283\) | −3728.05 | −0.783072 | −0.391536 | − | 0.920163i | \(-0.628056\pi\) | ||||
−0.391536 | + | 0.920163i | \(0.628056\pi\) | |||||||
\(284\) | 1298.66 | 0.271343 | ||||||||
\(285\) | 1558.57 | 0.323935 | ||||||||
\(286\) | −1187.70 | −0.245560 | ||||||||
\(287\) | −416.263 | −0.0856140 | ||||||||
\(288\) | −1489.31 | −0.304717 | ||||||||
\(289\) | −4481.35 | −0.912142 | ||||||||
\(290\) | −3967.11 | −0.803300 | ||||||||
\(291\) | −3666.99 | −0.738703 | ||||||||
\(292\) | −1858.12 | −0.372392 | ||||||||
\(293\) | 4418.33 | 0.880960 | 0.440480 | − | 0.897762i | \(-0.354808\pi\) | ||||
0.440480 | + | 0.897762i | \(0.354808\pi\) | |||||||
\(294\) | −1920.57 | −0.380987 | ||||||||
\(295\) | −11273.0 | −2.22488 | ||||||||
\(296\) | −9229.32 | −1.81231 | ||||||||
\(297\) | −297.000 | −0.0580259 | ||||||||
\(298\) | −2439.26 | −0.474170 | ||||||||
\(299\) | −2155.91 | −0.416989 | ||||||||
\(300\) | 1554.06 | 0.299079 | ||||||||
\(301\) | 1174.84 | 0.224972 | ||||||||
\(302\) | 1274.88 | 0.242917 | ||||||||
\(303\) | 3696.79 | 0.700907 | ||||||||
\(304\) | 418.754 | 0.0790039 | ||||||||
\(305\) | −961.074 | −0.180429 | ||||||||
\(306\) | −364.323 | −0.0680619 | ||||||||
\(307\) | −10642.1 | −1.97843 | −0.989217 | − | 0.146458i | \(-0.953213\pi\) | ||||
−0.989217 | + | 0.146458i | \(0.953213\pi\) | |||||||
\(308\) | −175.649 | −0.0324952 | ||||||||
\(309\) | 3458.69 | 0.636758 | ||||||||
\(310\) | 7652.21 | 1.40199 | ||||||||
\(311\) | −364.170 | −0.0663993 | −0.0331996 | − | 0.999449i | \(-0.510570\pi\) | ||||
−0.0331996 | + | 0.999449i | \(0.510570\pi\) | |||||||
\(312\) | −3953.00 | −0.717291 | ||||||||
\(313\) | −8381.95 | −1.51366 | −0.756831 | − | 0.653611i | \(-0.773253\pi\) | ||||
−0.756831 | + | 0.653611i | \(0.773253\pi\) | |||||||
\(314\) | 435.713 | 0.0783080 | ||||||||
\(315\) | 538.630 | 0.0963440 | ||||||||
\(316\) | −2920.19 | −0.519853 | ||||||||
\(317\) | 2005.50 | 0.355331 | 0.177665 | − | 0.984091i | \(-0.443146\pi\) | ||||
0.177665 | + | 0.984091i | \(0.443146\pi\) | |||||||
\(318\) | −3790.40 | −0.668412 | ||||||||
\(319\) | 1421.54 | 0.249502 | ||||||||
\(320\) | 6680.50 | 1.16703 | ||||||||
\(321\) | −1453.34 | −0.252703 | ||||||||
\(322\) | 287.937 | 0.0498327 | ||||||||
\(323\) | −685.080 | −0.118015 | ||||||||
\(324\) | −340.500 | −0.0583847 | ||||||||
\(325\) | 6828.89 | 1.16553 | ||||||||
\(326\) | −4061.84 | −0.690075 | ||||||||
\(327\) | 609.998 | 0.103159 | ||||||||
\(328\) | −2605.66 | −0.438639 | ||||||||
\(329\) | −523.617 | −0.0877446 | ||||||||
\(330\) | 1013.03 | 0.168986 | ||||||||
\(331\) | −6018.67 | −0.999443 | −0.499722 | − | 0.866186i | \(-0.666564\pi\) | ||||
−0.499722 | + | 0.866186i | \(0.666564\pi\) | |||||||
\(332\) | 4025.90 | 0.665511 | ||||||||
\(333\) | −3493.34 | −0.574876 | ||||||||
\(334\) | −1181.23 | −0.193516 | ||||||||
\(335\) | −10321.2 | −1.68330 | ||||||||
\(336\) | 144.718 | 0.0234971 | ||||||||
\(337\) | 9165.98 | 1.48161 | 0.740805 | − | 0.671720i | \(-0.234444\pi\) | ||||
0.740805 | + | 0.671720i | \(0.234444\pi\) | |||||||
\(338\) | −1702.75 | −0.274016 | ||||||||
\(339\) | 6667.67 | 1.06825 | ||||||||
\(340\) | −1376.01 | −0.219484 | ||||||||
\(341\) | −2742.03 | −0.435452 | ||||||||
\(342\) | 578.230 | 0.0914242 | ||||||||
\(343\) | −2551.01 | −0.401580 | ||||||||
\(344\) | 7354.09 | 1.15263 | ||||||||
\(345\) | 1838.84 | 0.286957 | ||||||||
\(346\) | 8070.16 | 1.25391 | ||||||||
\(347\) | −518.469 | −0.0802100 | −0.0401050 | − | 0.999195i | \(-0.512769\pi\) | ||||
−0.0401050 | + | 0.999195i | \(0.512769\pi\) | |||||||
\(348\) | 1629.75 | 0.251045 | ||||||||
\(349\) | 2667.51 | 0.409136 | 0.204568 | − | 0.978852i | \(-0.434421\pi\) | ||||
0.204568 | + | 0.978852i | \(0.434421\pi\) | |||||||
\(350\) | −912.047 | −0.139288 | ||||||||
\(351\) | −1496.23 | −0.227529 | ||||||||
\(352\) | −1820.27 | −0.275627 | ||||||||
\(353\) | −9043.64 | −1.36358 | −0.681791 | − | 0.731547i | \(-0.738799\pi\) | ||||
−0.681791 | + | 0.731547i | \(0.738799\pi\) | |||||||
\(354\) | −4182.29 | −0.627926 | ||||||||
\(355\) | −4867.35 | −0.727695 | ||||||||
\(356\) | −1935.40 | −0.288135 | ||||||||
\(357\) | −236.759 | −0.0350997 | ||||||||
\(358\) | 5511.18 | 0.813617 | ||||||||
\(359\) | −7367.14 | −1.08307 | −0.541536 | − | 0.840678i | \(-0.682157\pi\) | ||||
−0.541536 | + | 0.840678i | \(0.682157\pi\) | |||||||
\(360\) | 3371.64 | 0.493614 | ||||||||
\(361\) | −5771.69 | −0.841476 | ||||||||
\(362\) | −3882.45 | −0.563693 | ||||||||
\(363\) | −363.000 | −0.0524864 | ||||||||
\(364\) | −884.885 | −0.127419 | ||||||||
\(365\) | 6964.18 | 0.998690 | ||||||||
\(366\) | −356.559 | −0.0509225 | ||||||||
\(367\) | −2312.64 | −0.328935 | −0.164467 | − | 0.986383i | \(-0.552591\pi\) | ||||
−0.164467 | + | 0.986383i | \(0.552591\pi\) | |||||||
\(368\) | 494.058 | 0.0699852 | ||||||||
\(369\) | −986.254 | −0.139139 | ||||||||
\(370\) | 11915.3 | 1.67418 | ||||||||
\(371\) | −2463.23 | −0.344702 | ||||||||
\(372\) | −3143.63 | −0.438145 | ||||||||
\(373\) | 6689.84 | 0.928650 | 0.464325 | − | 0.885665i | \(-0.346297\pi\) | ||||
0.464325 | + | 0.885665i | \(0.346297\pi\) | |||||||
\(374\) | −445.283 | −0.0615643 | ||||||||
\(375\) | 83.6718 | 0.0115221 | ||||||||
\(376\) | −3277.67 | −0.449555 | ||||||||
\(377\) | 7161.46 | 0.978339 | ||||||||
\(378\) | 199.832 | 0.0271911 | ||||||||
\(379\) | −2487.15 | −0.337088 | −0.168544 | − | 0.985694i | \(-0.553907\pi\) | ||||
−0.168544 | + | 0.985694i | \(0.553907\pi\) | |||||||
\(380\) | 2183.92 | 0.294823 | ||||||||
\(381\) | −4618.41 | −0.621019 | ||||||||
\(382\) | 2002.49 | 0.268211 | ||||||||
\(383\) | −4747.65 | −0.633404 | −0.316702 | − | 0.948525i | \(-0.602575\pi\) | ||||
−0.316702 | + | 0.948525i | \(0.602575\pi\) | |||||||
\(384\) | −1493.03 | −0.198413 | ||||||||
\(385\) | 658.325 | 0.0871464 | ||||||||
\(386\) | −2735.45 | −0.360701 | ||||||||
\(387\) | 2783.55 | 0.365623 | ||||||||
\(388\) | −5138.30 | −0.672314 | ||||||||
\(389\) | 2948.01 | 0.384242 | 0.192121 | − | 0.981371i | \(-0.438463\pi\) | ||||
0.192121 | + | 0.981371i | \(0.438463\pi\) | |||||||
\(390\) | 5103.44 | 0.662622 | ||||||||
\(391\) | −808.277 | −0.104543 | ||||||||
\(392\) | −7812.69 | −1.00663 | ||||||||
\(393\) | −1940.30 | −0.249046 | ||||||||
\(394\) | −6158.11 | −0.787414 | ||||||||
\(395\) | 10944.8 | 1.39415 | ||||||||
\(396\) | −416.166 | −0.0528109 | ||||||||
\(397\) | −1848.91 | −0.233738 | −0.116869 | − | 0.993147i | \(-0.537286\pi\) | ||||
−0.116869 | + | 0.993147i | \(0.537286\pi\) | |||||||
\(398\) | 1753.25 | 0.220810 | ||||||||
\(399\) | 375.768 | 0.0471477 | ||||||||
\(400\) | −1564.94 | −0.195617 | ||||||||
\(401\) | 6395.55 | 0.796455 | 0.398227 | − | 0.917287i | \(-0.369625\pi\) | ||||
0.398227 | + | 0.917287i | \(0.369625\pi\) | |||||||
\(402\) | −3829.17 | −0.475079 | ||||||||
\(403\) | −13813.8 | −1.70748 | ||||||||
\(404\) | 5180.06 | 0.637914 | ||||||||
\(405\) | 1276.18 | 0.156578 | ||||||||
\(406\) | −956.464 | −0.116918 | ||||||||
\(407\) | −4269.63 | −0.519995 | ||||||||
\(408\) | −1482.03 | −0.179832 | ||||||||
\(409\) | −6387.30 | −0.772205 | −0.386103 | − | 0.922456i | \(-0.626179\pi\) | ||||
−0.386103 | + | 0.922456i | \(0.626179\pi\) | |||||||
\(410\) | 3363.98 | 0.405208 | ||||||||
\(411\) | −7894.13 | −0.947418 | ||||||||
\(412\) | 4846.43 | 0.579531 | ||||||||
\(413\) | −2717.90 | −0.323823 | ||||||||
\(414\) | 682.213 | 0.0809877 | ||||||||
\(415\) | −15088.9 | −1.78479 | ||||||||
\(416\) | −9170.16 | −1.08078 | ||||||||
\(417\) | 3327.36 | 0.390747 | ||||||||
\(418\) | 706.725 | 0.0826963 | ||||||||
\(419\) | −14385.9 | −1.67732 | −0.838661 | − | 0.544654i | \(-0.816661\pi\) | ||||
−0.838661 | + | 0.544654i | \(0.816661\pi\) | |||||||
\(420\) | 754.746 | 0.0876853 | ||||||||
\(421\) | 9475.99 | 1.09699 | 0.548494 | − | 0.836155i | \(-0.315201\pi\) | ||||
0.548494 | + | 0.836155i | \(0.315201\pi\) | |||||||
\(422\) | 5713.07 | 0.659023 | ||||||||
\(423\) | −1240.61 | −0.142602 | ||||||||
\(424\) | −15419.0 | −1.76606 | ||||||||
\(425\) | 2560.23 | 0.292210 | ||||||||
\(426\) | −1805.79 | −0.205377 | ||||||||
\(427\) | −231.713 | −0.0262609 | ||||||||
\(428\) | −2036.47 | −0.229992 | ||||||||
\(429\) | −1828.72 | −0.205808 | ||||||||
\(430\) | −9494.34 | −1.06479 | ||||||||
\(431\) | 16387.1 | 1.83141 | 0.915707 | − | 0.401847i | \(-0.131632\pi\) | ||||
0.915707 | + | 0.401847i | \(0.131632\pi\) | |||||||
\(432\) | 342.882 | 0.0381873 | ||||||||
\(433\) | 7229.00 | 0.802317 | 0.401159 | − | 0.916009i | \(-0.368608\pi\) | ||||
0.401159 | + | 0.916009i | \(0.368608\pi\) | |||||||
\(434\) | 1844.93 | 0.204055 | ||||||||
\(435\) | −6108.23 | −0.673258 | ||||||||
\(436\) | 854.749 | 0.0938878 | ||||||||
\(437\) | 1282.85 | 0.140428 | ||||||||
\(438\) | 2583.72 | 0.281860 | ||||||||
\(439\) | 2073.13 | 0.225387 | 0.112694 | − | 0.993630i | \(-0.464052\pi\) | ||||
0.112694 | + | 0.993630i | \(0.464052\pi\) | |||||||
\(440\) | 4120.89 | 0.446491 | ||||||||
\(441\) | −2957.14 | −0.319311 | ||||||||
\(442\) | −2243.25 | −0.241404 | ||||||||
\(443\) | 9208.90 | 0.987648 | 0.493824 | − | 0.869562i | \(-0.335599\pi\) | ||||
0.493824 | + | 0.869562i | \(0.335599\pi\) | |||||||
\(444\) | −4894.98 | −0.523210 | ||||||||
\(445\) | 7253.81 | 0.772727 | ||||||||
\(446\) | −1743.96 | −0.185155 | ||||||||
\(447\) | −3755.77 | −0.397409 | ||||||||
\(448\) | 1610.66 | 0.169858 | ||||||||
\(449\) | 142.052 | 0.0149306 | 0.00746532 | − | 0.999972i | \(-0.497624\pi\) | ||||
0.00746532 | + | 0.999972i | \(0.497624\pi\) | |||||||
\(450\) | −2160.92 | −0.226370 | ||||||||
\(451\) | −1205.42 | −0.125856 | ||||||||
\(452\) | 9342.96 | 0.972248 | ||||||||
\(453\) | 1962.95 | 0.203593 | ||||||||
\(454\) | −3010.21 | −0.311181 | ||||||||
\(455\) | 3316.52 | 0.341716 | ||||||||
\(456\) | 2352.18 | 0.241559 | ||||||||
\(457\) | 4968.52 | 0.508572 | 0.254286 | − | 0.967129i | \(-0.418159\pi\) | ||||
0.254286 | + | 0.967129i | \(0.418159\pi\) | |||||||
\(458\) | 7923.34 | 0.808370 | ||||||||
\(459\) | −560.954 | −0.0570438 | ||||||||
\(460\) | 2576.65 | 0.261167 | ||||||||
\(461\) | 2953.91 | 0.298432 | 0.149216 | − | 0.988805i | \(-0.452325\pi\) | ||||
0.149216 | + | 0.988805i | \(0.452325\pi\) | |||||||
\(462\) | 244.239 | 0.0245953 | ||||||||
\(463\) | 9071.55 | 0.910563 | 0.455281 | − | 0.890348i | \(-0.349539\pi\) | ||||
0.455281 | + | 0.890348i | \(0.349539\pi\) | |||||||
\(464\) | −1641.15 | −0.164199 | ||||||||
\(465\) | 11782.2 | 1.17503 | ||||||||
\(466\) | −460.423 | −0.0457697 | ||||||||
\(467\) | 3299.17 | 0.326911 | 0.163456 | − | 0.986551i | \(-0.447736\pi\) | ||||
0.163456 | + | 0.986551i | \(0.447736\pi\) | |||||||
\(468\) | −2096.56 | −0.207081 | ||||||||
\(469\) | −2488.42 | −0.244999 | ||||||||
\(470\) | 4231.56 | 0.415292 | ||||||||
\(471\) | 670.875 | 0.0656312 | ||||||||
\(472\) | −17013.1 | −1.65909 | ||||||||
\(473\) | 3402.12 | 0.330718 | ||||||||
\(474\) | 4060.52 | 0.393472 | ||||||||
\(475\) | −4063.43 | −0.392512 | ||||||||
\(476\) | −331.754 | −0.0319452 | ||||||||
\(477\) | −5836.14 | −0.560206 | ||||||||
\(478\) | 5052.55 | 0.483469 | ||||||||
\(479\) | 12938.1 | 1.23415 | 0.617076 | − | 0.786904i | \(-0.288317\pi\) | ||||
0.617076 | + | 0.786904i | \(0.288317\pi\) | |||||||
\(480\) | 7821.52 | 0.743754 | ||||||||
\(481\) | −21509.6 | −2.03899 | ||||||||
\(482\) | −7323.94 | −0.692109 | ||||||||
\(483\) | 443.342 | 0.0417656 | ||||||||
\(484\) | −508.647 | −0.0477693 | ||||||||
\(485\) | 19258.2 | 1.80303 | ||||||||
\(486\) | 473.464 | 0.0441908 | ||||||||
\(487\) | −4480.51 | −0.416902 | −0.208451 | − | 0.978033i | \(-0.566842\pi\) | ||||
−0.208451 | + | 0.978033i | \(0.566842\pi\) | |||||||
\(488\) | −1450.45 | −0.134546 | ||||||||
\(489\) | −6254.09 | −0.578363 | ||||||||
\(490\) | 10086.4 | 0.929913 | ||||||||
\(491\) | 4382.73 | 0.402831 | 0.201415 | − | 0.979506i | \(-0.435446\pi\) | ||||
0.201415 | + | 0.979506i | \(0.435446\pi\) | |||||||
\(492\) | −1381.97 | −0.126634 | ||||||||
\(493\) | 2684.92 | 0.245279 | ||||||||
\(494\) | 3560.35 | 0.324266 | ||||||||
\(495\) | 1559.78 | 0.141630 | ||||||||
\(496\) | 3165.63 | 0.286575 | ||||||||
\(497\) | −1173.51 | −0.105914 | ||||||||
\(498\) | −5598.00 | −0.503720 | ||||||||
\(499\) | −4611.26 | −0.413684 | −0.206842 | − | 0.978374i | \(-0.566319\pi\) | ||||
−0.206842 | + | 0.978374i | \(0.566319\pi\) | |||||||
\(500\) | 117.244 | 0.0104866 | ||||||||
\(501\) | −1818.77 | −0.162189 | ||||||||
\(502\) | −507.888 | −0.0451557 | ||||||||
\(503\) | 948.320 | 0.0840626 | 0.0420313 | − | 0.999116i | \(-0.486617\pi\) | ||||
0.0420313 | + | 0.999116i | \(0.486617\pi\) | |||||||
\(504\) | 812.897 | 0.0718439 | ||||||||
\(505\) | −19414.7 | −1.71077 | ||||||||
\(506\) | 833.815 | 0.0732561 | ||||||||
\(507\) | −2621.76 | −0.229657 | ||||||||
\(508\) | −6471.47 | −0.565207 | ||||||||
\(509\) | 16954.1 | 1.47638 | 0.738190 | − | 0.674593i | \(-0.235681\pi\) | ||||
0.738190 | + | 0.674593i | \(0.235681\pi\) | |||||||
\(510\) | 1913.34 | 0.166126 | ||||||||
\(511\) | 1679.05 | 0.145356 | ||||||||
\(512\) | 4517.18 | 0.389908 | ||||||||
\(513\) | 890.310 | 0.0766241 | ||||||||
\(514\) | −13449.6 | −1.15416 | ||||||||
\(515\) | −18164.3 | −1.55420 | ||||||||
\(516\) | 3900.41 | 0.332763 | ||||||||
\(517\) | −1516.30 | −0.128988 | ||||||||
\(518\) | 2872.76 | 0.243672 | ||||||||
\(519\) | 12425.8 | 1.05093 | ||||||||
\(520\) | 20760.3 | 1.75077 | ||||||||
\(521\) | 6839.25 | 0.575111 | 0.287556 | − | 0.957764i | \(-0.407157\pi\) | ||||
0.287556 | + | 0.957764i | \(0.407157\pi\) | |||||||
\(522\) | −2266.16 | −0.190013 | ||||||||
\(523\) | −7500.51 | −0.627102 | −0.313551 | − | 0.949571i | \(-0.601519\pi\) | ||||
−0.313551 | + | 0.949571i | \(0.601519\pi\) | |||||||
\(524\) | −2718.81 | −0.226664 | ||||||||
\(525\) | −1404.29 | −0.116740 | ||||||||
\(526\) | 1545.46 | 0.128109 | ||||||||
\(527\) | −5178.96 | −0.428082 | ||||||||
\(528\) | 419.078 | 0.0345418 | ||||||||
\(529\) | −10653.5 | −0.875603 | ||||||||
\(530\) | 19906.3 | 1.63146 | ||||||||
\(531\) | −6439.54 | −0.526275 | ||||||||
\(532\) | 526.539 | 0.0429104 | ||||||||
\(533\) | −6072.68 | −0.493503 | ||||||||
\(534\) | 2691.17 | 0.218087 | ||||||||
\(535\) | 7632.63 | 0.616799 | ||||||||
\(536\) | −15576.7 | −1.25524 | ||||||||
\(537\) | 8485.66 | 0.681906 | ||||||||
\(538\) | −2693.23 | −0.215824 | ||||||||
\(539\) | −3614.28 | −0.288827 | ||||||||
\(540\) | 1788.22 | 0.142505 | ||||||||
\(541\) | −2316.11 | −0.184062 | −0.0920309 | − | 0.995756i | \(-0.529336\pi\) | ||||
−0.0920309 | + | 0.995756i | \(0.529336\pi\) | |||||||
\(542\) | 11765.4 | 0.932416 | ||||||||
\(543\) | −5977.87 | −0.472440 | ||||||||
\(544\) | −3438.00 | −0.270962 | ||||||||
\(545\) | −3203.57 | −0.251791 | ||||||||
\(546\) | 1230.43 | 0.0964424 | ||||||||
\(547\) | 17507.2 | 1.36847 | 0.684237 | − | 0.729259i | \(-0.260135\pi\) | ||||
0.684237 | + | 0.729259i | \(0.260135\pi\) | |||||||
\(548\) | −11061.5 | −0.862271 | ||||||||
\(549\) | −549.000 | −0.0426790 | ||||||||
\(550\) | −2641.12 | −0.204760 | ||||||||
\(551\) | −4261.33 | −0.329471 | ||||||||
\(552\) | 2775.17 | 0.213984 | ||||||||
\(553\) | 2638.76 | 0.202914 | ||||||||
\(554\) | 2754.72 | 0.211258 | ||||||||
\(555\) | 18346.2 | 1.40316 | ||||||||
\(556\) | 4662.40 | 0.355629 | ||||||||
\(557\) | −23914.5 | −1.81919 | −0.909594 | − | 0.415498i | \(-0.863607\pi\) | ||||
−0.909594 | + | 0.415498i | \(0.863607\pi\) | |||||||
\(558\) | 4371.22 | 0.331628 | ||||||||
\(559\) | 17139.2 | 1.29680 | ||||||||
\(560\) | −760.028 | −0.0573518 | ||||||||
\(561\) | −685.610 | −0.0515980 | ||||||||
\(562\) | 1850.90 | 0.138925 | ||||||||
\(563\) | 13115.2 | 0.981773 | 0.490887 | − | 0.871223i | \(-0.336673\pi\) | ||||
0.490887 | + | 0.871223i | \(0.336673\pi\) | |||||||
\(564\) | −1738.38 | −0.129786 | ||||||||
\(565\) | −35017.1 | −2.60740 | ||||||||
\(566\) | 7263.77 | 0.539433 | ||||||||
\(567\) | 307.685 | 0.0227893 | ||||||||
\(568\) | −7345.77 | −0.542643 | ||||||||
\(569\) | −12675.6 | −0.933900 | −0.466950 | − | 0.884284i | \(-0.654647\pi\) | ||||
−0.466950 | + | 0.884284i | \(0.654647\pi\) | |||||||
\(570\) | −3036.73 | −0.223148 | ||||||||
\(571\) | 9557.59 | 0.700478 | 0.350239 | − | 0.936660i | \(-0.386100\pi\) | ||||
0.350239 | + | 0.936660i | \(0.386100\pi\) | |||||||
\(572\) | −2562.47 | −0.187311 | ||||||||
\(573\) | 3083.27 | 0.224792 | ||||||||
\(574\) | 811.050 | 0.0589766 | ||||||||
\(575\) | −4794.16 | −0.347705 | ||||||||
\(576\) | 3816.14 | 0.276052 | ||||||||
\(577\) | −11716.0 | −0.845306 | −0.422653 | − | 0.906292i | \(-0.638901\pi\) | ||||
−0.422653 | + | 0.906292i | \(0.638901\pi\) | |||||||
\(578\) | 8731.52 | 0.628345 | ||||||||
\(579\) | −4211.82 | −0.302309 | ||||||||
\(580\) | −8559.05 | −0.612750 | ||||||||
\(581\) | −3637.91 | −0.259769 | ||||||||
\(582\) | 7144.80 | 0.508868 | ||||||||
\(583\) | −7133.06 | −0.506726 | ||||||||
\(584\) | 10510.3 | 0.744724 | ||||||||
\(585\) | 7857.85 | 0.555354 | ||||||||
\(586\) | −8608.71 | −0.606864 | ||||||||
\(587\) | −15552.2 | −1.09354 | −0.546772 | − | 0.837282i | \(-0.684143\pi\) | ||||
−0.546772 | + | 0.837282i | \(0.684143\pi\) | |||||||
\(588\) | −4143.64 | −0.290613 | ||||||||
\(589\) | 8219.72 | 0.575021 | ||||||||
\(590\) | 21964.4 | 1.53264 | ||||||||
\(591\) | −9481.75 | −0.659944 | ||||||||
\(592\) | 4929.23 | 0.342213 | ||||||||
\(593\) | 1156.23 | 0.0800688 | 0.0400344 | − | 0.999198i | \(-0.487253\pi\) | ||||
0.0400344 | + | 0.999198i | \(0.487253\pi\) | |||||||
\(594\) | 578.678 | 0.0399721 | ||||||||
\(595\) | 1243.40 | 0.0856714 | ||||||||
\(596\) | −5262.71 | −0.361693 | ||||||||
\(597\) | 2699.51 | 0.185064 | ||||||||
\(598\) | 4200.60 | 0.287250 | ||||||||
\(599\) | 21400.2 | 1.45975 | 0.729874 | − | 0.683582i | \(-0.239579\pi\) | ||||
0.729874 | + | 0.683582i | \(0.239579\pi\) | |||||||
\(600\) | −8790.40 | −0.598111 | ||||||||
\(601\) | 16937.0 | 1.14954 | 0.574772 | − | 0.818314i | \(-0.305091\pi\) | ||||
0.574772 | + | 0.818314i | \(0.305091\pi\) | |||||||
\(602\) | −2289.07 | −0.154976 | ||||||||
\(603\) | −5895.84 | −0.398171 | ||||||||
\(604\) | 2750.55 | 0.185295 | ||||||||
\(605\) | 1906.39 | 0.128109 | ||||||||
\(606\) | −7202.85 | −0.482832 | ||||||||
\(607\) | −4910.54 | −0.328357 | −0.164178 | − | 0.986431i | \(-0.552497\pi\) | ||||
−0.164178 | + | 0.986431i | \(0.552497\pi\) | |||||||
\(608\) | 5456.58 | 0.363970 | ||||||||
\(609\) | −1472.68 | −0.0979904 | ||||||||
\(610\) | 1872.57 | 0.124292 | ||||||||
\(611\) | −7638.84 | −0.505784 | ||||||||
\(612\) | −786.027 | −0.0519171 | ||||||||
\(613\) | −18252.4 | −1.20262 | −0.601311 | − | 0.799015i | \(-0.705355\pi\) | ||||
−0.601311 | + | 0.799015i | \(0.705355\pi\) | |||||||
\(614\) | 20735.3 | 1.36288 | ||||||||
\(615\) | 5179.58 | 0.339611 | ||||||||
\(616\) | 993.541 | 0.0649852 | ||||||||
\(617\) | 12841.7 | 0.837908 | 0.418954 | − | 0.908007i | \(-0.362397\pi\) | ||||
0.418954 | + | 0.908007i | \(0.362397\pi\) | |||||||
\(618\) | −6738.95 | −0.438642 | ||||||||
\(619\) | −3240.98 | −0.210446 | −0.105223 | − | 0.994449i | \(-0.533556\pi\) | ||||
−0.105223 | + | 0.994449i | \(0.533556\pi\) | |||||||
\(620\) | 16509.6 | 1.06942 | ||||||||
\(621\) | 1050.41 | 0.0678771 | ||||||||
\(622\) | 709.552 | 0.0457403 | ||||||||
\(623\) | 1748.88 | 0.112468 | ||||||||
\(624\) | 2111.24 | 0.135444 | ||||||||
\(625\) | −15843.1 | −1.01396 | ||||||||
\(626\) | 16331.5 | 1.04271 | ||||||||
\(627\) | 1088.16 | 0.0693091 | ||||||||
\(628\) | 940.052 | 0.0597327 | ||||||||
\(629\) | −8064.20 | −0.511194 | ||||||||
\(630\) | −1049.47 | −0.0663682 | ||||||||
\(631\) | −11396.2 | −0.718977 | −0.359489 | − | 0.933149i | \(-0.617049\pi\) | ||||
−0.359489 | + | 0.933149i | \(0.617049\pi\) | |||||||
\(632\) | 16517.8 | 1.03962 | ||||||||
\(633\) | 8796.50 | 0.552337 | ||||||||
\(634\) | −3907.53 | −0.244776 | ||||||||
\(635\) | 24254.8 | 1.51579 | ||||||||
\(636\) | −8177.79 | −0.509859 | ||||||||
\(637\) | −18208.0 | −1.13254 | ||||||||
\(638\) | −2769.75 | −0.171874 | ||||||||
\(639\) | −2780.40 | −0.172130 | ||||||||
\(640\) | 7841.03 | 0.484287 | ||||||||
\(641\) | −23594.8 | −1.45388 | −0.726941 | − | 0.686700i | \(-0.759059\pi\) | ||||
−0.726941 | + | 0.686700i | \(0.759059\pi\) | |||||||
\(642\) | 2831.71 | 0.174079 | ||||||||
\(643\) | 3093.23 | 0.189712 | 0.0948562 | − | 0.995491i | \(-0.469761\pi\) | ||||
0.0948562 | + | 0.995491i | \(0.469761\pi\) | |||||||
\(644\) | 621.226 | 0.0380120 | ||||||||
\(645\) | −14618.6 | −0.892413 | ||||||||
\(646\) | 1334.82 | 0.0812967 | ||||||||
\(647\) | −17755.5 | −1.07889 | −0.539443 | − | 0.842022i | \(-0.681365\pi\) | ||||
−0.539443 | + | 0.842022i | \(0.681365\pi\) | |||||||
\(648\) | 1926.00 | 0.116760 | ||||||||
\(649\) | −7870.54 | −0.476034 | ||||||||
\(650\) | −13305.5 | −0.802898 | ||||||||
\(651\) | 2840.68 | 0.171021 | ||||||||
\(652\) | −8763.43 | −0.526384 | ||||||||
\(653\) | 3167.79 | 0.189839 | 0.0949197 | − | 0.995485i | \(-0.469741\pi\) | ||||
0.0949197 | + | 0.995485i | \(0.469741\pi\) | |||||||
\(654\) | −1188.53 | −0.0710628 | ||||||||
\(655\) | 10190.0 | 0.607872 | ||||||||
\(656\) | 1391.64 | 0.0828270 | ||||||||
\(657\) | 3978.19 | 0.236231 | ||||||||
\(658\) | 1020.22 | 0.0604443 | ||||||||
\(659\) | 2160.76 | 0.127726 | 0.0638629 | − | 0.997959i | \(-0.479658\pi\) | ||||
0.0638629 | + | 0.997959i | \(0.479658\pi\) | |||||||
\(660\) | 2185.61 | 0.128901 | ||||||||
\(661\) | 11806.4 | 0.694731 | 0.347366 | − | 0.937730i | \(-0.387076\pi\) | ||||
0.347366 | + | 0.937730i | \(0.387076\pi\) | |||||||
\(662\) | 11726.8 | 0.688484 | ||||||||
\(663\) | −3453.97 | −0.202325 | ||||||||
\(664\) | −22772.1 | −1.33092 | ||||||||
\(665\) | −1973.45 | −0.115078 | ||||||||
\(666\) | 6806.45 | 0.396013 | ||||||||
\(667\) | −5027.64 | −0.291860 | ||||||||
\(668\) | −2548.51 | −0.147612 | ||||||||
\(669\) | −2685.21 | −0.155181 | ||||||||
\(670\) | 20109.9 | 1.15957 | ||||||||
\(671\) | −671.000 | −0.0386046 | ||||||||
\(672\) | 1885.75 | 0.108251 | ||||||||
\(673\) | −784.015 | −0.0449057 | −0.0224529 | − | 0.999748i | \(-0.507148\pi\) | ||||
−0.0224529 | + | 0.999748i | \(0.507148\pi\) | |||||||
\(674\) | −17859.1 | −1.02063 | ||||||||
\(675\) | −3327.20 | −0.189725 | ||||||||
\(676\) | −3673.69 | −0.209018 | ||||||||
\(677\) | 16496.4 | 0.936496 | 0.468248 | − | 0.883597i | \(-0.344885\pi\) | ||||
0.468248 | + | 0.883597i | \(0.344885\pi\) | |||||||
\(678\) | −12991.4 | −0.735886 | ||||||||
\(679\) | 4643.11 | 0.262425 | ||||||||
\(680\) | 7783.27 | 0.438934 | ||||||||
\(681\) | −4634.87 | −0.260806 | ||||||||
\(682\) | 5342.60 | 0.299969 | ||||||||
\(683\) | 20139.7 | 1.12829 | 0.564145 | − | 0.825675i | \(-0.309206\pi\) | ||||
0.564145 | + | 0.825675i | \(0.309206\pi\) | |||||||
\(684\) | 1247.53 | 0.0697377 | ||||||||
\(685\) | 41458.2 | 2.31246 | ||||||||
\(686\) | 4970.42 | 0.276635 | ||||||||
\(687\) | 12199.7 | 0.677508 | ||||||||
\(688\) | −3927.70 | −0.217649 | ||||||||
\(689\) | −35935.0 | −1.98696 | ||||||||
\(690\) | −3582.82 | −0.197675 | ||||||||
\(691\) | 13577.4 | 0.747481 | 0.373740 | − | 0.927533i | \(-0.378075\pi\) | ||||
0.373740 | + | 0.927533i | \(0.378075\pi\) | |||||||
\(692\) | 17411.4 | 0.956476 | ||||||||
\(693\) | 376.059 | 0.0206137 | ||||||||
\(694\) | 1010.19 | 0.0552540 | ||||||||
\(695\) | −17474.5 | −0.953735 | ||||||||
\(696\) | −9218.50 | −0.502049 | ||||||||
\(697\) | −2276.72 | −0.123726 | ||||||||
\(698\) | −5197.40 | −0.281840 | ||||||||
\(699\) | −708.921 | −0.0383603 | ||||||||
\(700\) | −1967.74 | −0.106248 | ||||||||
\(701\) | −16056.2 | −0.865099 | −0.432550 | − | 0.901610i | \(-0.642386\pi\) | ||||
−0.432550 | + | 0.901610i | \(0.642386\pi\) | |||||||
\(702\) | 2915.27 | 0.156737 | ||||||||
\(703\) | 12799.0 | 0.686661 | ||||||||
\(704\) | 4664.17 | 0.249698 | ||||||||
\(705\) | 6515.40 | 0.348063 | ||||||||
\(706\) | 17620.7 | 0.939326 | ||||||||
\(707\) | −4680.84 | −0.248997 | ||||||||
\(708\) | −9023.29 | −0.478977 | ||||||||
\(709\) | 6595.03 | 0.349339 | 0.174670 | − | 0.984627i | \(-0.444114\pi\) | ||||
0.174670 | + | 0.984627i | \(0.444114\pi\) | |||||||
\(710\) | 9483.59 | 0.501285 | ||||||||
\(711\) | 6252.05 | 0.329775 | ||||||||
\(712\) | 10947.4 | 0.576224 | ||||||||
\(713\) | 9697.86 | 0.509380 | ||||||||
\(714\) | 461.303 | 0.0241790 | ||||||||
\(715\) | 9604.04 | 0.502337 | ||||||||
\(716\) | 11890.4 | 0.620621 | ||||||||
\(717\) | 7779.50 | 0.405203 | ||||||||
\(718\) | 14354.2 | 0.746093 | ||||||||
\(719\) | −33575.6 | −1.74153 | −0.870765 | − | 0.491700i | \(-0.836376\pi\) | ||||
−0.870765 | + | 0.491700i | \(0.836376\pi\) | |||||||
\(720\) | −1800.74 | −0.0932078 | ||||||||
\(721\) | −4379.37 | −0.226209 | ||||||||
\(722\) | 11245.6 | 0.579665 | ||||||||
\(723\) | −11276.8 | −0.580067 | ||||||||
\(724\) | −8376.39 | −0.429981 | ||||||||
\(725\) | 15925.1 | 0.815785 | ||||||||
\(726\) | 707.273 | 0.0361561 | ||||||||
\(727\) | −17204.7 | −0.877699 | −0.438849 | − | 0.898561i | \(-0.644614\pi\) | ||||
−0.438849 | + | 0.898561i | \(0.644614\pi\) | |||||||
\(728\) | 5005.27 | 0.254818 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −13569.1 | −0.687965 | ||||||||
\(731\) | 6425.70 | 0.325121 | ||||||||
\(732\) | −769.277 | −0.0388433 | ||||||||
\(733\) | 2317.28 | 0.116768 | 0.0583839 | − | 0.998294i | \(-0.481405\pi\) | ||||
0.0583839 | + | 0.998294i | \(0.481405\pi\) | |||||||
\(734\) | 4505.98 | 0.226592 | ||||||||
\(735\) | 15530.2 | 0.779374 | ||||||||
\(736\) | 6437.83 | 0.322421 | ||||||||
\(737\) | −7206.02 | −0.360159 | ||||||||
\(738\) | 1921.63 | 0.0958484 | ||||||||
\(739\) | 14058.3 | 0.699789 | 0.349894 | − | 0.936789i | \(-0.386217\pi\) | ||||
0.349894 | + | 0.936789i | \(0.386217\pi\) | |||||||
\(740\) | 25707.3 | 1.27705 | ||||||||
\(741\) | 5481.92 | 0.271773 | ||||||||
\(742\) | 4799.37 | 0.237454 | ||||||||
\(743\) | 16845.1 | 0.831744 | 0.415872 | − | 0.909423i | \(-0.363476\pi\) | ||||
0.415872 | + | 0.909423i | \(0.363476\pi\) | |||||||
\(744\) | 17781.7 | 0.876220 | ||||||||
\(745\) | 19724.5 | 0.969998 | ||||||||
\(746\) | −13034.5 | −0.639717 | ||||||||
\(747\) | −8619.33 | −0.422175 | ||||||||
\(748\) | −960.700 | −0.0469608 | ||||||||
\(749\) | 1840.21 | 0.0897730 | ||||||||
\(750\) | −163.027 | −0.00793720 | ||||||||
\(751\) | 36184.6 | 1.75818 | 0.879090 | − | 0.476655i | \(-0.158151\pi\) | ||||
0.879090 | + | 0.476655i | \(0.158151\pi\) | |||||||
\(752\) | 1750.55 | 0.0848882 | ||||||||
\(753\) | −782.004 | −0.0378457 | ||||||||
\(754\) | −13953.5 | −0.673946 | ||||||||
\(755\) | −10309.0 | −0.496930 | ||||||||
\(756\) | 431.138 | 0.0207412 | ||||||||
\(757\) | −6259.11 | −0.300517 | −0.150258 | − | 0.988647i | \(-0.548011\pi\) | ||||
−0.150258 | + | 0.988647i | \(0.548011\pi\) | |||||||
\(758\) | 4845.99 | 0.232209 | ||||||||
\(759\) | 1283.84 | 0.0613971 | ||||||||
\(760\) | −12353.1 | −0.589598 | ||||||||
\(761\) | −32306.7 | −1.53892 | −0.769459 | − | 0.638696i | \(-0.779474\pi\) | ||||
−0.769459 | + | 0.638696i | \(0.779474\pi\) | |||||||
\(762\) | 8998.56 | 0.427800 | ||||||||
\(763\) | −772.375 | −0.0366473 | ||||||||
\(764\) | 4320.38 | 0.204589 | ||||||||
\(765\) | 2946.00 | 0.139233 | ||||||||
\(766\) | 9250.37 | 0.436331 | ||||||||
\(767\) | −39650.3 | −1.86661 | ||||||||
\(768\) | 13085.4 | 0.614816 | ||||||||
\(769\) | −11921.2 | −0.559023 | −0.279512 | − | 0.960142i | \(-0.590173\pi\) | ||||
−0.279512 | + | 0.960142i | \(0.590173\pi\) | |||||||
\(770\) | −1282.69 | −0.0600323 | ||||||||
\(771\) | −20708.6 | −0.967319 | ||||||||
\(772\) | −5901.73 | −0.275140 | ||||||||
\(773\) | 15891.4 | 0.739422 | 0.369711 | − | 0.929147i | \(-0.379457\pi\) | ||||
0.369711 | + | 0.929147i | \(0.379457\pi\) | |||||||
\(774\) | −5423.51 | −0.251866 | ||||||||
\(775\) | −30718.1 | −1.42378 | ||||||||
\(776\) | 29064.3 | 1.34452 | ||||||||
\(777\) | 4423.24 | 0.204225 | ||||||||
\(778\) | −5743.94 | −0.264692 | ||||||||
\(779\) | 3613.47 | 0.166195 | ||||||||
\(780\) | 11010.7 | 0.505443 | ||||||||
\(781\) | −3398.27 | −0.155697 | ||||||||
\(782\) | 1574.86 | 0.0720162 | ||||||||
\(783\) | −3489.24 | −0.159253 | ||||||||
\(784\) | 4172.63 | 0.190080 | ||||||||
\(785\) | −3523.28 | −0.160193 | ||||||||
\(786\) | 3780.50 | 0.171560 | ||||||||
\(787\) | −20721.9 | −0.938572 | −0.469286 | − | 0.883046i | \(-0.655489\pi\) | ||||
−0.469286 | + | 0.883046i | \(0.655489\pi\) | |||||||
\(788\) | −13286.1 | −0.600633 | ||||||||
\(789\) | 2379.58 | 0.107370 | ||||||||
\(790\) | −21324.9 | −0.960387 | ||||||||
\(791\) | −8442.56 | −0.379498 | ||||||||
\(792\) | 2354.00 | 0.105613 | ||||||||
\(793\) | −3380.37 | −0.151375 | ||||||||
\(794\) | 3602.43 | 0.161014 | ||||||||
\(795\) | 30650.1 | 1.36735 | ||||||||
\(796\) | 3782.64 | 0.168432 | ||||||||
\(797\) | 27596.9 | 1.22651 | 0.613256 | − | 0.789884i | \(-0.289859\pi\) | ||||
0.613256 | + | 0.789884i | \(0.289859\pi\) | |||||||
\(798\) | −732.150 | −0.0324785 | ||||||||
\(799\) | −2863.89 | −0.126805 | ||||||||
\(800\) | −20391.9 | −0.901205 | ||||||||
\(801\) | 4143.64 | 0.182782 | ||||||||
\(802\) | −12461.1 | −0.548651 | ||||||||
\(803\) | 4862.23 | 0.213679 | ||||||||
\(804\) | −8261.44 | −0.362386 | ||||||||
\(805\) | −2328.33 | −0.101941 | ||||||||
\(806\) | 26915.0 | 1.17623 | ||||||||
\(807\) | −4146.81 | −0.180885 | ||||||||
\(808\) | −29300.5 | −1.27573 | ||||||||
\(809\) | 25973.0 | 1.12876 | 0.564378 | − | 0.825517i | \(-0.309116\pi\) | ||||
0.564378 | + | 0.825517i | \(0.309116\pi\) | |||||||
\(810\) | −2486.52 | −0.107861 | ||||||||
\(811\) | 18039.3 | 0.781069 | 0.390534 | − | 0.920588i | \(-0.372290\pi\) | ||||
0.390534 | + | 0.920588i | \(0.372290\pi\) | |||||||
\(812\) | −2063.57 | −0.0891837 | ||||||||
\(813\) | 18115.5 | 0.781472 | ||||||||
\(814\) | 8319.00 | 0.358207 | ||||||||
\(815\) | 32845.0 | 1.41167 | ||||||||
\(816\) | 791.528 | 0.0339571 | ||||||||
\(817\) | −10198.5 | −0.436719 | ||||||||
\(818\) | 12445.1 | 0.531947 | ||||||||
\(819\) | 1894.51 | 0.0808299 | ||||||||
\(820\) | 7257.80 | 0.309089 | ||||||||
\(821\) | 30848.6 | 1.31136 | 0.655679 | − | 0.755040i | \(-0.272383\pi\) | ||||
0.655679 | + | 0.755040i | \(0.272383\pi\) | |||||||
\(822\) | 15381.0 | 0.652645 | ||||||||
\(823\) | 23673.2 | 1.00267 | 0.501335 | − | 0.865254i | \(-0.332843\pi\) | ||||
0.501335 | + | 0.865254i | \(0.332843\pi\) | |||||||
\(824\) | −27413.4 | −1.15897 | ||||||||
\(825\) | −4066.58 | −0.171612 | ||||||||
\(826\) | 5295.58 | 0.223071 | ||||||||
\(827\) | −24149.8 | −1.01544 | −0.507721 | − | 0.861522i | \(-0.669512\pi\) | ||||
−0.507721 | + | 0.861522i | \(0.669512\pi\) | |||||||
\(828\) | 1471.87 | 0.0617768 | ||||||||
\(829\) | −15376.2 | −0.644193 | −0.322097 | − | 0.946707i | \(-0.604388\pi\) | ||||
−0.322097 | + | 0.946707i | \(0.604388\pi\) | |||||||
\(830\) | 29399.4 | 1.22948 | ||||||||
\(831\) | 4241.49 | 0.177059 | ||||||||
\(832\) | 23497.2 | 0.979109 | ||||||||
\(833\) | −6826.41 | −0.283939 | ||||||||
\(834\) | −6483.06 | −0.269172 | ||||||||
\(835\) | 9551.74 | 0.395870 | ||||||||
\(836\) | 1524.76 | 0.0630801 | ||||||||
\(837\) | 6730.43 | 0.277942 | ||||||||
\(838\) | 28029.6 | 1.15545 | ||||||||
\(839\) | 10677.7 | 0.439376 | 0.219688 | − | 0.975570i | \(-0.429496\pi\) | ||||
0.219688 | + | 0.975570i | \(0.429496\pi\) | |||||||
\(840\) | −4269.15 | −0.175357 | ||||||||
\(841\) | −7688.31 | −0.315237 | ||||||||
\(842\) | −18463.1 | −0.755678 | ||||||||
\(843\) | 2849.87 | 0.116435 | ||||||||
\(844\) | 12325.9 | 0.502697 | ||||||||
\(845\) | 13768.9 | 0.560548 | ||||||||
\(846\) | 2417.22 | 0.0982337 | ||||||||
\(847\) | 459.628 | 0.0186458 | ||||||||
\(848\) | 8235.02 | 0.333481 | ||||||||
\(849\) | 11184.1 | 0.452107 | ||||||||
\(850\) | −4988.38 | −0.201294 | ||||||||
\(851\) | 15100.6 | 0.608276 | ||||||||
\(852\) | −3895.99 | −0.156660 | ||||||||
\(853\) | 22357.1 | 0.897413 | 0.448706 | − | 0.893679i | \(-0.351885\pi\) | ||||
0.448706 | + | 0.893679i | \(0.351885\pi\) | |||||||
\(854\) | 451.472 | 0.0180902 | ||||||||
\(855\) | −4675.70 | −0.187024 | ||||||||
\(856\) | 11519.1 | 0.459948 | ||||||||
\(857\) | 33549.1 | 1.33724 | 0.668620 | − | 0.743604i | \(-0.266885\pi\) | ||||
0.668620 | + | 0.743604i | \(0.266885\pi\) | |||||||
\(858\) | 3563.10 | 0.141774 | ||||||||
\(859\) | −38799.1 | −1.54110 | −0.770552 | − | 0.637377i | \(-0.780019\pi\) | ||||
−0.770552 | + | 0.637377i | \(0.780019\pi\) | |||||||
\(860\) | −20484.0 | −0.812209 | ||||||||
\(861\) | 1248.79 | 0.0494292 | ||||||||
\(862\) | −31928.8 | −1.26160 | ||||||||
\(863\) | 20964.5 | 0.826928 | 0.413464 | − | 0.910520i | \(-0.364319\pi\) | ||||
0.413464 | + | 0.910520i | \(0.364319\pi\) | |||||||
\(864\) | 4467.93 | 0.175928 | ||||||||
\(865\) | −65257.2 | −2.56510 | ||||||||
\(866\) | −14085.0 | −0.552690 | ||||||||
\(867\) | 13444.1 | 0.526626 | ||||||||
\(868\) | 3980.45 | 0.155651 | ||||||||
\(869\) | 7641.39 | 0.298293 | ||||||||
\(870\) | 11901.3 | 0.463785 | ||||||||
\(871\) | −36302.6 | −1.41224 | ||||||||
\(872\) | −4834.81 | −0.187761 | ||||||||
\(873\) | 11001.0 | 0.426491 | ||||||||
\(874\) | −2499.51 | −0.0967359 | ||||||||
\(875\) | −105.945 | −0.00409324 | ||||||||
\(876\) | 5574.37 | 0.215001 | ||||||||
\(877\) | 26833.9 | 1.03320 | 0.516600 | − | 0.856227i | \(-0.327197\pi\) | ||||
0.516600 | + | 0.856227i | \(0.327197\pi\) | |||||||
\(878\) | −4039.31 | −0.155262 | ||||||||
\(879\) | −13255.0 | −0.508623 | ||||||||
\(880\) | −2200.90 | −0.0843096 | ||||||||
\(881\) | 47724.8 | 1.82507 | 0.912536 | − | 0.408997i | \(-0.134121\pi\) | ||||
0.912536 | + | 0.408997i | \(0.134121\pi\) | |||||||
\(882\) | 5761.72 | 0.219963 | ||||||||
\(883\) | 18332.9 | 0.698701 | 0.349350 | − | 0.936992i | \(-0.386402\pi\) | ||||
0.349350 | + | 0.936992i | \(0.386402\pi\) | |||||||
\(884\) | −4839.82 | −0.184141 | ||||||||
\(885\) | 33819.0 | 1.28453 | ||||||||
\(886\) | −17942.7 | −0.680358 | ||||||||
\(887\) | −46861.1 | −1.77389 | −0.886946 | − | 0.461874i | \(-0.847177\pi\) | ||||
−0.886946 | + | 0.461874i | \(0.847177\pi\) | |||||||
\(888\) | 27688.0 | 1.04634 | ||||||||
\(889\) | 5847.80 | 0.220617 | ||||||||
\(890\) | −14133.4 | −0.532307 | ||||||||
\(891\) | 891.000 | 0.0335013 | ||||||||
\(892\) | −3762.60 | −0.141235 | ||||||||
\(893\) | 4545.38 | 0.170331 | ||||||||
\(894\) | 7317.79 | 0.273762 | ||||||||
\(895\) | −44564.7 | −1.66440 | ||||||||
\(896\) | 1890.46 | 0.0704863 | ||||||||
\(897\) | 6467.73 | 0.240748 | ||||||||
\(898\) | −276.776 | −0.0102852 | ||||||||
\(899\) | −32214.1 | −1.19511 | ||||||||
\(900\) | −4662.19 | −0.172674 | ||||||||
\(901\) | −13472.4 | −0.498149 | ||||||||
\(902\) | 2348.66 | 0.0866981 | ||||||||
\(903\) | −3524.52 | −0.129888 | ||||||||
\(904\) | −52847.6 | −1.94434 | ||||||||
\(905\) | 31394.4 | 1.15313 | ||||||||
\(906\) | −3824.64 | −0.140248 | ||||||||
\(907\) | 21170.5 | 0.775032 | 0.387516 | − | 0.921863i | \(-0.373333\pi\) | ||||
0.387516 | + | 0.921863i | \(0.373333\pi\) | |||||||
\(908\) | −6494.54 | −0.237366 | ||||||||
\(909\) | −11090.4 | −0.404669 | ||||||||
\(910\) | −6461.93 | −0.235397 | ||||||||
\(911\) | −14266.8 | −0.518860 | −0.259430 | − | 0.965762i | \(-0.583535\pi\) | ||||
−0.259430 | + | 0.965762i | \(0.583535\pi\) | |||||||
\(912\) | −1256.26 | −0.0456129 | ||||||||
\(913\) | −10534.7 | −0.381872 | ||||||||
\(914\) | −9680.72 | −0.350339 | ||||||||
\(915\) | 2883.22 | 0.104171 | ||||||||
\(916\) | 17094.6 | 0.616618 | ||||||||
\(917\) | 2456.79 | 0.0884738 | ||||||||
\(918\) | 1092.97 | 0.0392956 | ||||||||
\(919\) | 1704.89 | 0.0611959 | 0.0305979 | − | 0.999532i | \(-0.490259\pi\) | ||||
0.0305979 | + | 0.999532i | \(0.490259\pi\) | |||||||
\(920\) | −14574.6 | −0.522293 | ||||||||
\(921\) | 31926.4 | 1.14225 | ||||||||
\(922\) | −5755.42 | −0.205580 | ||||||||
\(923\) | −17119.8 | −0.610516 | ||||||||
\(924\) | 526.946 | 0.0187611 | ||||||||
\(925\) | −47831.5 | −1.70020 | ||||||||
\(926\) | −17675.1 | −0.627257 | ||||||||
\(927\) | −10376.1 | −0.367632 | ||||||||
\(928\) | −21385.0 | −0.756464 | ||||||||
\(929\) | −52560.6 | −1.85625 | −0.928126 | − | 0.372265i | \(-0.878581\pi\) | ||||
−0.928126 | + | 0.372265i | \(0.878581\pi\) | |||||||
\(930\) | −22956.6 | −0.809438 | ||||||||
\(931\) | 10834.4 | 0.381401 | ||||||||
\(932\) | −993.363 | −0.0349128 | ||||||||
\(933\) | 1092.51 | 0.0383357 | ||||||||
\(934\) | −6428.14 | −0.225198 | ||||||||
\(935\) | 3600.67 | 0.125941 | ||||||||
\(936\) | 11859.0 | 0.414128 | ||||||||
\(937\) | −20027.5 | −0.698259 | −0.349130 | − | 0.937074i | \(-0.613523\pi\) | ||||
−0.349130 | + | 0.937074i | \(0.613523\pi\) | |||||||
\(938\) | 4848.47 | 0.168772 | ||||||||
\(939\) | 25145.9 | 0.873913 | ||||||||
\(940\) | 9129.59 | 0.316781 | ||||||||
\(941\) | 40232.8 | 1.39379 | 0.696893 | − | 0.717175i | \(-0.254565\pi\) | ||||
0.696893 | + | 0.717175i | \(0.254565\pi\) | |||||||
\(942\) | −1307.14 | −0.0452112 | ||||||||
\(943\) | 4263.27 | 0.147223 | ||||||||
\(944\) | 9086.43 | 0.313282 | ||||||||
\(945\) | −1615.89 | −0.0556242 | ||||||||
\(946\) | −6628.73 | −0.227821 | ||||||||
\(947\) | 36897.5 | 1.26611 | 0.633056 | − | 0.774106i | \(-0.281800\pi\) | ||||
0.633056 | + | 0.774106i | \(0.281800\pi\) | |||||||
\(948\) | 8760.57 | 0.300137 | ||||||||
\(949\) | 24495.0 | 0.837872 | ||||||||
\(950\) | 7917.24 | 0.270389 | ||||||||
\(951\) | −6016.49 | −0.205150 | ||||||||
\(952\) | 1876.53 | 0.0638853 | ||||||||
\(953\) | −7655.75 | −0.260224 | −0.130112 | − | 0.991499i | \(-0.541534\pi\) | ||||
−0.130112 | + | 0.991499i | \(0.541534\pi\) | |||||||
\(954\) | 11371.2 | 0.385908 | ||||||||
\(955\) | −16192.6 | −0.548672 | ||||||||
\(956\) | 10900.9 | 0.368786 | ||||||||
\(957\) | −4264.63 | −0.144050 | ||||||||
\(958\) | −25208.8 | −0.850166 | ||||||||
\(959\) | 9995.49 | 0.336571 | ||||||||
\(960\) | −20041.5 | −0.673788 | ||||||||
\(961\) | 32347.2 | 1.08580 | ||||||||
\(962\) | 41909.5 | 1.40459 | ||||||||
\(963\) | 4360.03 | 0.145898 | ||||||||
\(964\) | −15801.4 | −0.527935 | ||||||||
\(965\) | 22119.5 | 0.737877 | ||||||||
\(966\) | −863.812 | −0.0287709 | ||||||||
\(967\) | −28874.6 | −0.960232 | −0.480116 | − | 0.877205i | \(-0.659405\pi\) | ||||
−0.480116 | + | 0.877205i | \(0.659405\pi\) | |||||||
\(968\) | 2877.11 | 0.0955310 | ||||||||
\(969\) | 2055.24 | 0.0681360 | ||||||||
\(970\) | −37522.8 | −1.24205 | ||||||||
\(971\) | −40379.7 | −1.33455 | −0.667275 | − | 0.744812i | \(-0.732539\pi\) | ||||
−0.667275 | + | 0.744812i | \(0.732539\pi\) | |||||||
\(972\) | 1021.50 | 0.0337084 | ||||||||
\(973\) | −4213.07 | −0.138813 | ||||||||
\(974\) | 8729.88 | 0.287190 | ||||||||
\(975\) | −20486.7 | −0.672921 | ||||||||
\(976\) | 774.660 | 0.0254060 | ||||||||
\(977\) | −18762.4 | −0.614394 | −0.307197 | − | 0.951646i | \(-0.599391\pi\) | ||||
−0.307197 | + | 0.951646i | \(0.599391\pi\) | |||||||
\(978\) | 12185.5 | 0.398415 | ||||||||
\(979\) | 5064.45 | 0.165332 | ||||||||
\(980\) | 21761.4 | 0.709330 | ||||||||
\(981\) | −1829.99 | −0.0595589 | ||||||||
\(982\) | −8539.36 | −0.277497 | ||||||||
\(983\) | −53978.1 | −1.75141 | −0.875704 | − | 0.482848i | \(-0.839603\pi\) | ||||
−0.875704 | + | 0.482848i | \(0.839603\pi\) | |||||||
\(984\) | 7816.99 | 0.253248 | ||||||||
\(985\) | 49796.0 | 1.61079 | ||||||||
\(986\) | −5231.32 | −0.168965 | ||||||||
\(987\) | 1570.85 | 0.0506593 | ||||||||
\(988\) | 7681.45 | 0.247348 | ||||||||
\(989\) | −12032.4 | −0.386865 | ||||||||
\(990\) | −3039.08 | −0.0975640 | ||||||||
\(991\) | 11175.7 | 0.358233 | 0.179117 | − | 0.983828i | \(-0.442676\pi\) | ||||
0.179117 | + | 0.983828i | \(0.442676\pi\) | |||||||
\(992\) | 41249.8 | 1.32024 | ||||||||
\(993\) | 18056.0 | 0.577029 | ||||||||
\(994\) | 2286.48 | 0.0729604 | ||||||||
\(995\) | −14177.2 | −0.451706 | ||||||||
\(996\) | −12077.7 | −0.384233 | ||||||||
\(997\) | −21697.3 | −0.689228 | −0.344614 | − | 0.938745i | \(-0.611990\pi\) | ||||
−0.344614 | + | 0.938745i | \(0.611990\pi\) | |||||||
\(998\) | 8984.63 | 0.284973 | ||||||||
\(999\) | 10480.0 | 0.331905 |
(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 | 2013.4.a.d.1.14 | ✓ | 37 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.4.a.d.1.14 | ✓ | 37 | 1.1 | even | 1 | trivial |