Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,4,Mod(1,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, 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("507.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.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: | \(29.9139683729\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 56x^{7} - 27x^{6} + 945x^{5} + 763x^{4} - 4139x^{3} - 2478x^{2} + 63x + 27 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 13^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-3.27560\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.52257 | 1.95253 | 0.976263 | − | 0.216591i | \(-0.0694937\pi\) | ||||
0.976263 | + | 0.216591i | \(0.0694937\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 22.4988 | 2.81235 | ||||||||
\(5\) | −6.08065 | −0.543870 | −0.271935 | − | 0.962316i | \(-0.587664\pi\) | ||||
−0.271935 | + | 0.962316i | \(0.587664\pi\) | |||||||
\(6\) | 16.5677 | 1.12729 | ||||||||
\(7\) | 20.2718 | 1.09458 | 0.547288 | − | 0.836944i | \(-0.315660\pi\) | ||||
0.547288 | + | 0.836944i | \(0.315660\pi\) | |||||||
\(8\) | 80.0709 | 3.53867 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −33.5808 | −1.06192 | ||||||||
\(11\) | −48.8284 | −1.33839 | −0.669196 | − | 0.743086i | \(-0.733361\pi\) | ||||
−0.669196 | + | 0.743086i | \(0.733361\pi\) | |||||||
\(12\) | 67.4965 | 1.62371 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 111.953 | 2.13719 | ||||||||
\(15\) | −18.2419 | −0.314003 | ||||||||
\(16\) | 262.207 | 4.09698 | ||||||||
\(17\) | −37.7513 | −0.538591 | −0.269295 | − | 0.963058i | \(-0.586791\pi\) | ||||
−0.269295 | + | 0.963058i | \(0.586791\pi\) | |||||||
\(18\) | 49.7032 | 0.650842 | ||||||||
\(19\) | 120.837 | 1.45905 | 0.729524 | − | 0.683955i | \(-0.239742\pi\) | ||||
0.729524 | + | 0.683955i | \(0.239742\pi\) | |||||||
\(20\) | −136.807 | −1.52955 | ||||||||
\(21\) | 60.8155 | 0.631954 | ||||||||
\(22\) | −269.658 | −2.61324 | ||||||||
\(23\) | 74.8543 | 0.678617 | 0.339309 | − | 0.940675i | \(-0.389807\pi\) | ||||
0.339309 | + | 0.940675i | \(0.389807\pi\) | |||||||
\(24\) | 240.213 | 2.04305 | ||||||||
\(25\) | −88.0257 | −0.704206 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 456.092 | 3.07834 | ||||||||
\(29\) | −112.710 | −0.721715 | −0.360858 | − | 0.932621i | \(-0.617516\pi\) | ||||
−0.360858 | + | 0.932621i | \(0.617516\pi\) | |||||||
\(30\) | −100.742 | −0.613099 | ||||||||
\(31\) | 113.134 | 0.655465 | 0.327733 | − | 0.944770i | \(-0.393715\pi\) | ||||
0.327733 | + | 0.944770i | \(0.393715\pi\) | |||||||
\(32\) | 807.490 | 4.46079 | ||||||||
\(33\) | −146.485 | −0.772721 | ||||||||
\(34\) | −208.485 | −1.05161 | ||||||||
\(35\) | −123.266 | −0.595307 | ||||||||
\(36\) | 202.489 | 0.937451 | ||||||||
\(37\) | −85.7704 | −0.381096 | −0.190548 | − | 0.981678i | \(-0.561027\pi\) | ||||
−0.190548 | + | 0.981678i | \(0.561027\pi\) | |||||||
\(38\) | 667.331 | 2.84883 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −486.883 | −1.92457 | ||||||||
\(41\) | −133.993 | −0.510395 | −0.255197 | − | 0.966889i | \(-0.582140\pi\) | ||||
−0.255197 | + | 0.966889i | \(0.582140\pi\) | |||||||
\(42\) | 335.858 | 1.23391 | ||||||||
\(43\) | −319.135 | −1.13181 | −0.565903 | − | 0.824472i | \(-0.691472\pi\) | ||||
−0.565903 | + | 0.824472i | \(0.691472\pi\) | |||||||
\(44\) | −1098.58 | −3.76403 | ||||||||
\(45\) | −54.7258 | −0.181290 | ||||||||
\(46\) | 413.388 | 1.32502 | ||||||||
\(47\) | −401.982 | −1.24755 | −0.623777 | − | 0.781602i | \(-0.714403\pi\) | ||||
−0.623777 | + | 0.781602i | \(0.714403\pi\) | |||||||
\(48\) | 786.620 | 2.36539 | ||||||||
\(49\) | 67.9471 | 0.198096 | ||||||||
\(50\) | −486.129 | −1.37498 | ||||||||
\(51\) | −113.254 | −0.310955 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −384.493 | −0.996494 | −0.498247 | − | 0.867035i | \(-0.666023\pi\) | ||||
−0.498247 | + | 0.867035i | \(0.666023\pi\) | |||||||
\(54\) | 149.110 | 0.375764 | ||||||||
\(55\) | 296.908 | 0.727911 | ||||||||
\(56\) | 1623.18 | 3.87334 | ||||||||
\(57\) | 362.511 | 0.842382 | ||||||||
\(58\) | −622.450 | −1.40917 | ||||||||
\(59\) | −121.629 | −0.268385 | −0.134192 | − | 0.990955i | \(-0.542844\pi\) | ||||
−0.134192 | + | 0.990955i | \(0.542844\pi\) | |||||||
\(60\) | −410.422 | −0.883088 | ||||||||
\(61\) | 220.043 | 0.461864 | 0.230932 | − | 0.972970i | \(-0.425823\pi\) | ||||
0.230932 | + | 0.972970i | \(0.425823\pi\) | |||||||
\(62\) | 624.790 | 1.27981 | ||||||||
\(63\) | 182.446 | 0.364859 | ||||||||
\(64\) | 2361.77 | 4.61283 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −808.975 | −1.50876 | ||||||||
\(67\) | 975.363 | 1.77850 | 0.889250 | − | 0.457421i | \(-0.151227\pi\) | ||||
0.889250 | + | 0.457421i | \(0.151227\pi\) | |||||||
\(68\) | −849.361 | −1.51471 | ||||||||
\(69\) | 224.563 | 0.391800 | ||||||||
\(70\) | −680.745 | −1.16235 | ||||||||
\(71\) | 106.725 | 0.178394 | 0.0891969 | − | 0.996014i | \(-0.471570\pi\) | ||||
0.0891969 | + | 0.996014i | \(0.471570\pi\) | |||||||
\(72\) | 720.638 | 1.17956 | ||||||||
\(73\) | 43.2566 | 0.0693535 | 0.0346767 | − | 0.999399i | \(-0.488960\pi\) | ||||
0.0346767 | + | 0.999399i | \(0.488960\pi\) | |||||||
\(74\) | −473.673 | −0.744100 | ||||||||
\(75\) | −264.077 | −0.406573 | ||||||||
\(76\) | 2718.69 | 4.10336 | ||||||||
\(77\) | −989.841 | −1.46497 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 539.339 | 0.768106 | 0.384053 | − | 0.923311i | \(-0.374528\pi\) | ||||
0.384053 | + | 0.923311i | \(0.374528\pi\) | |||||||
\(80\) | −1594.39 | −2.22822 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −739.986 | −0.996558 | ||||||||
\(83\) | 811.183 | 1.07276 | 0.536379 | − | 0.843977i | \(-0.319792\pi\) | ||||
0.536379 | + | 0.843977i | \(0.319792\pi\) | |||||||
\(84\) | 1368.28 | 1.77728 | ||||||||
\(85\) | 229.553 | 0.292923 | ||||||||
\(86\) | −1762.45 | −2.20988 | ||||||||
\(87\) | −338.130 | −0.416683 | ||||||||
\(88\) | −3909.73 | −4.73612 | ||||||||
\(89\) | −1130.64 | −1.34661 | −0.673304 | − | 0.739366i | \(-0.735125\pi\) | ||||
−0.673304 | + | 0.739366i | \(0.735125\pi\) | |||||||
\(90\) | −302.227 | −0.353973 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1684.13 | 1.90851 | ||||||||
\(93\) | 339.401 | 0.378433 | ||||||||
\(94\) | −2219.98 | −2.43588 | ||||||||
\(95\) | −734.767 | −0.793532 | ||||||||
\(96\) | 2422.47 | 2.57544 | ||||||||
\(97\) | −229.088 | −0.239797 | −0.119899 | − | 0.992786i | \(-0.538257\pi\) | ||||
−0.119899 | + | 0.992786i | \(0.538257\pi\) | |||||||
\(98\) | 375.243 | 0.386788 | ||||||||
\(99\) | −439.456 | −0.446131 | ||||||||
\(100\) | −1980.48 | −1.98048 | ||||||||
\(101\) | −845.077 | −0.832557 | −0.416279 | − | 0.909237i | \(-0.636666\pi\) | ||||
−0.416279 | + | 0.909237i | \(0.636666\pi\) | |||||||
\(102\) | −625.454 | −0.607148 | ||||||||
\(103\) | −1095.09 | −1.04760 | −0.523800 | − | 0.851841i | \(-0.675486\pi\) | ||||
−0.523800 | + | 0.851841i | \(0.675486\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −369.798 | −0.343700 | ||||||||
\(106\) | −2123.39 | −1.94568 | ||||||||
\(107\) | 1183.33 | 1.06913 | 0.534563 | − | 0.845129i | \(-0.320476\pi\) | ||||
0.534563 | + | 0.845129i | \(0.320476\pi\) | |||||||
\(108\) | 607.468 | 0.541238 | ||||||||
\(109\) | −239.968 | −0.210870 | −0.105435 | − | 0.994426i | \(-0.533623\pi\) | ||||
−0.105435 | + | 0.994426i | \(0.533623\pi\) | |||||||
\(110\) | 1639.70 | 1.42126 | ||||||||
\(111\) | −257.311 | −0.220026 | ||||||||
\(112\) | 5315.41 | 4.48446 | ||||||||
\(113\) | −1031.22 | −0.858490 | −0.429245 | − | 0.903188i | \(-0.641220\pi\) | ||||
−0.429245 | + | 0.903188i | \(0.641220\pi\) | |||||||
\(114\) | 2001.99 | 1.64477 | ||||||||
\(115\) | −455.162 | −0.369079 | ||||||||
\(116\) | −2535.85 | −2.02972 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −671.703 | −0.524028 | ||||||||
\(119\) | −765.288 | −0.589528 | ||||||||
\(120\) | −1460.65 | −1.11115 | ||||||||
\(121\) | 1053.21 | 0.791294 | ||||||||
\(122\) | 1215.21 | 0.901800 | ||||||||
\(123\) | −401.979 | −0.294676 | ||||||||
\(124\) | 2545.38 | 1.84340 | ||||||||
\(125\) | 1295.33 | 0.926866 | ||||||||
\(126\) | 1007.57 | 0.712396 | ||||||||
\(127\) | −18.0201 | −0.0125908 | −0.00629539 | − | 0.999980i | \(-0.502004\pi\) | ||||
−0.00629539 | + | 0.999980i | \(0.502004\pi\) | |||||||
\(128\) | 6583.12 | 4.54587 | ||||||||
\(129\) | −957.406 | −0.653449 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1282.52 | −0.855378 | −0.427689 | − | 0.903926i | \(-0.640672\pi\) | ||||
−0.427689 | + | 0.903926i | \(0.640672\pi\) | |||||||
\(132\) | −3295.75 | −2.17317 | ||||||||
\(133\) | 2449.59 | 1.59704 | ||||||||
\(134\) | 5386.51 | 3.47257 | ||||||||
\(135\) | −164.177 | −0.104668 | ||||||||
\(136\) | −3022.78 | −1.90589 | ||||||||
\(137\) | 1547.36 | 0.964965 | 0.482482 | − | 0.875906i | \(-0.339735\pi\) | ||||
0.482482 | + | 0.875906i | \(0.339735\pi\) | |||||||
\(138\) | 1240.16 | 0.764999 | ||||||||
\(139\) | −3096.87 | −1.88973 | −0.944867 | − | 0.327455i | \(-0.893809\pi\) | ||||
−0.944867 | + | 0.327455i | \(0.893809\pi\) | |||||||
\(140\) | −2773.34 | −1.67421 | ||||||||
\(141\) | −1205.95 | −0.720276 | ||||||||
\(142\) | 589.398 | 0.348318 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2359.86 | 1.36566 | ||||||||
\(145\) | 685.351 | 0.392519 | ||||||||
\(146\) | 238.888 | 0.135414 | ||||||||
\(147\) | 203.841 | 0.114371 | ||||||||
\(148\) | −1929.73 | −1.07178 | ||||||||
\(149\) | 420.879 | 0.231408 | 0.115704 | − | 0.993284i | \(-0.463088\pi\) | ||||
0.115704 | + | 0.993284i | \(0.463088\pi\) | |||||||
\(150\) | −1458.39 | −0.793845 | ||||||||
\(151\) | −2801.17 | −1.50964 | −0.754821 | − | 0.655931i | \(-0.772276\pi\) | ||||
−0.754821 | + | 0.655931i | \(0.772276\pi\) | |||||||
\(152\) | 9675.52 | 5.16308 | ||||||||
\(153\) | −339.762 | −0.179530 | ||||||||
\(154\) | −5466.47 | −2.86039 | ||||||||
\(155\) | −687.927 | −0.356488 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2344.20 | −1.19164 | −0.595820 | − | 0.803118i | \(-0.703173\pi\) | ||||
−0.595820 | + | 0.803118i | \(0.703173\pi\) | |||||||
\(158\) | 2978.54 | 1.49975 | ||||||||
\(159\) | −1153.48 | −0.575326 | ||||||||
\(160\) | −4910.06 | −2.42609 | ||||||||
\(161\) | 1517.43 | 0.742798 | ||||||||
\(162\) | 447.329 | 0.216947 | ||||||||
\(163\) | 3658.41 | 1.75797 | 0.878984 | − | 0.476851i | \(-0.158222\pi\) | ||||
0.878984 | + | 0.476851i | \(0.158222\pi\) | |||||||
\(164\) | −3014.68 | −1.43541 | ||||||||
\(165\) | 890.725 | 0.420260 | ||||||||
\(166\) | 4479.82 | 2.09459 | ||||||||
\(167\) | 1987.85 | 0.921105 | 0.460552 | − | 0.887632i | \(-0.347651\pi\) | ||||
0.460552 | + | 0.887632i | \(0.347651\pi\) | |||||||
\(168\) | 4869.55 | 2.23627 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 1267.72 | 0.571940 | ||||||||
\(171\) | 1087.53 | 0.486349 | ||||||||
\(172\) | −7180.17 | −3.18304 | ||||||||
\(173\) | −3577.11 | −1.57204 | −0.786019 | − | 0.618202i | \(-0.787861\pi\) | ||||
−0.786019 | + | 0.618202i | \(0.787861\pi\) | |||||||
\(174\) | −1867.35 | −0.813583 | ||||||||
\(175\) | −1784.44 | −0.770807 | ||||||||
\(176\) | −12803.1 | −5.48337 | ||||||||
\(177\) | −364.886 | −0.154952 | ||||||||
\(178\) | −6244.07 | −2.62928 | ||||||||
\(179\) | 770.144 | 0.321582 | 0.160791 | − | 0.986988i | \(-0.448595\pi\) | ||||
0.160791 | + | 0.986988i | \(0.448595\pi\) | |||||||
\(180\) | −1231.27 | −0.509851 | ||||||||
\(181\) | −1895.69 | −0.778482 | −0.389241 | − | 0.921136i | \(-0.627263\pi\) | ||||
−0.389241 | + | 0.921136i | \(0.627263\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 660.130 | 0.266657 | ||||||||
\(184\) | 5993.65 | 2.40140 | ||||||||
\(185\) | 521.539 | 0.207267 | ||||||||
\(186\) | 1874.37 | 0.738900 | ||||||||
\(187\) | 1843.34 | 0.720846 | ||||||||
\(188\) | −9044.12 | −3.50857 | ||||||||
\(189\) | 547.339 | 0.210651 | ||||||||
\(190\) | −4057.81 | −1.54939 | ||||||||
\(191\) | 2203.83 | 0.834887 | 0.417443 | − | 0.908703i | \(-0.362926\pi\) | ||||
0.417443 | + | 0.908703i | \(0.362926\pi\) | |||||||
\(192\) | 7085.30 | 2.66322 | ||||||||
\(193\) | 1016.38 | 0.379069 | 0.189534 | − | 0.981874i | \(-0.439302\pi\) | ||||
0.189534 | + | 0.981874i | \(0.439302\pi\) | |||||||
\(194\) | −1265.15 | −0.468210 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1528.73 | 0.557117 | ||||||||
\(197\) | 4318.58 | 1.56186 | 0.780930 | − | 0.624619i | \(-0.214746\pi\) | ||||
0.780930 | + | 0.624619i | \(0.214746\pi\) | |||||||
\(198\) | −2426.93 | −0.871082 | ||||||||
\(199\) | 1363.40 | 0.485672 | 0.242836 | − | 0.970067i | \(-0.421922\pi\) | ||||
0.242836 | + | 0.970067i | \(0.421922\pi\) | |||||||
\(200\) | −7048.30 | −2.49195 | ||||||||
\(201\) | 2926.09 | 1.02682 | ||||||||
\(202\) | −4667.00 | −1.62559 | ||||||||
\(203\) | −2284.84 | −0.789972 | ||||||||
\(204\) | −2548.08 | −0.874517 | ||||||||
\(205\) | 814.764 | 0.277588 | ||||||||
\(206\) | −6047.74 | −2.04546 | ||||||||
\(207\) | 673.688 | 0.226206 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5900.28 | −1.95278 | ||||||||
\(210\) | −2042.23 | −0.671084 | ||||||||
\(211\) | 5288.34 | 1.72542 | 0.862711 | − | 0.505697i | \(-0.168765\pi\) | ||||
0.862711 | + | 0.505697i | \(0.168765\pi\) | |||||||
\(212\) | −8650.64 | −2.80249 | ||||||||
\(213\) | 320.176 | 0.102996 | ||||||||
\(214\) | 6535.00 | 2.08749 | ||||||||
\(215\) | 1940.55 | 0.615555 | ||||||||
\(216\) | 2161.91 | 0.681017 | ||||||||
\(217\) | 2293.43 | 0.717457 | ||||||||
\(218\) | −1325.24 | −0.411728 | ||||||||
\(219\) | 129.770 | 0.0400412 | ||||||||
\(220\) | 6680.09 | 2.04714 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1421.02 | −0.429606 | ||||||||
\(223\) | −1258.01 | −0.377769 | −0.188884 | − | 0.981999i | \(-0.560487\pi\) | ||||
−0.188884 | + | 0.981999i | \(0.560487\pi\) | |||||||
\(224\) | 16369.3 | 4.88268 | ||||||||
\(225\) | −792.232 | −0.234735 | ||||||||
\(226\) | −5695.01 | −1.67622 | ||||||||
\(227\) | 1135.21 | 0.331922 | 0.165961 | − | 0.986132i | \(-0.446927\pi\) | ||||
0.165961 | + | 0.986132i | \(0.446927\pi\) | |||||||
\(228\) | 8156.07 | 2.36908 | ||||||||
\(229\) | −218.002 | −0.0629083 | −0.0314541 | − | 0.999505i | \(-0.510014\pi\) | ||||
−0.0314541 | + | 0.999505i | \(0.510014\pi\) | |||||||
\(230\) | −2513.67 | −0.720636 | ||||||||
\(231\) | −2969.52 | −0.845802 | ||||||||
\(232\) | −9024.80 | −2.55391 | ||||||||
\(233\) | −2.56367 | −0.000720823 0 | −0.000360412 | − | 1.00000i | \(-0.500115\pi\) | ||||
−0.000360412 | 1.00000i | \(0.500115\pi\) | ||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2444.31 | 0.678507 | ||||||||
\(236\) | −2736.50 | −0.754793 | ||||||||
\(237\) | 1618.02 | 0.443466 | ||||||||
\(238\) | −4226.36 | −1.15107 | ||||||||
\(239\) | 3971.13 | 1.07477 | 0.537387 | − | 0.843336i | \(-0.319411\pi\) | ||||
0.537387 | + | 0.843336i | \(0.319411\pi\) | |||||||
\(240\) | −4783.16 | −1.28647 | ||||||||
\(241\) | −658.032 | −0.175882 | −0.0879411 | − | 0.996126i | \(-0.528029\pi\) | ||||
−0.0879411 | + | 0.996126i | \(0.528029\pi\) | |||||||
\(242\) | 5816.44 | 1.54502 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 4950.72 | 1.29892 | ||||||||
\(245\) | −413.162 | −0.107739 | ||||||||
\(246\) | −2219.96 | −0.575363 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 9058.72 | 2.31947 | ||||||||
\(249\) | 2433.55 | 0.619357 | ||||||||
\(250\) | 7153.58 | 1.80973 | ||||||||
\(251\) | 7091.01 | 1.78319 | 0.891595 | − | 0.452833i | \(-0.149587\pi\) | ||||
0.891595 | + | 0.452833i | \(0.149587\pi\) | |||||||
\(252\) | 4104.83 | 1.02611 | ||||||||
\(253\) | −3655.01 | −0.908256 | ||||||||
\(254\) | −99.5176 | −0.0245838 | ||||||||
\(255\) | 688.658 | 0.169119 | ||||||||
\(256\) | 17461.6 | 4.26309 | ||||||||
\(257\) | 792.530 | 0.192361 | 0.0961803 | − | 0.995364i | \(-0.469337\pi\) | ||||
0.0961803 | + | 0.995364i | \(0.469337\pi\) | |||||||
\(258\) | −5287.35 | −1.27588 | ||||||||
\(259\) | −1738.72 | −0.417139 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1014.39 | −0.240572 | ||||||||
\(262\) | −7082.83 | −1.67015 | ||||||||
\(263\) | −337.467 | −0.0791221 | −0.0395610 | − | 0.999217i | \(-0.512596\pi\) | ||||
−0.0395610 | + | 0.999217i | \(0.512596\pi\) | |||||||
\(264\) | −11729.2 | −2.73440 | ||||||||
\(265\) | 2337.97 | 0.541963 | ||||||||
\(266\) | 13528.0 | 3.11826 | ||||||||
\(267\) | −3391.93 | −0.777464 | ||||||||
\(268\) | 21944.5 | 5.00177 | ||||||||
\(269\) | −3523.93 | −0.798728 | −0.399364 | − | 0.916792i | \(-0.630769\pi\) | ||||
−0.399364 | + | 0.916792i | \(0.630769\pi\) | |||||||
\(270\) | −906.682 | −0.204366 | ||||||||
\(271\) | 8313.62 | 1.86353 | 0.931765 | − | 0.363063i | \(-0.118269\pi\) | ||||
0.931765 | + | 0.363063i | \(0.118269\pi\) | |||||||
\(272\) | −9898.65 | −2.20660 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8545.43 | 1.88412 | ||||||||
\(275\) | 4298.16 | 0.942504 | ||||||||
\(276\) | 5052.40 | 1.10188 | ||||||||
\(277\) | −2500.33 | −0.542347 | −0.271174 | − | 0.962530i | \(-0.587412\pi\) | ||||
−0.271174 | + | 0.962530i | \(0.587412\pi\) | |||||||
\(278\) | −17102.7 | −3.68975 | ||||||||
\(279\) | 1018.20 | 0.218488 | ||||||||
\(280\) | −9870.01 | −2.10659 | ||||||||
\(281\) | −3053.13 | −0.648165 | −0.324083 | − | 0.946029i | \(-0.605056\pi\) | ||||
−0.324083 | + | 0.946029i | \(0.605056\pi\) | |||||||
\(282\) | −6659.93 | −1.40636 | ||||||||
\(283\) | 1158.80 | 0.243404 | 0.121702 | − | 0.992567i | \(-0.461165\pi\) | ||||
0.121702 | + | 0.992567i | \(0.461165\pi\) | |||||||
\(284\) | 2401.19 | 0.501706 | ||||||||
\(285\) | −2204.30 | −0.458146 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2716.28 | −0.558666 | ||||||||
\(288\) | 7267.41 | 1.48693 | ||||||||
\(289\) | −3487.84 | −0.709920 | ||||||||
\(290\) | 3784.90 | 0.766403 | ||||||||
\(291\) | −687.263 | −0.138447 | ||||||||
\(292\) | 973.223 | 0.195046 | ||||||||
\(293\) | −8357.45 | −1.66637 | −0.833187 | − | 0.552991i | \(-0.813486\pi\) | ||||
−0.833187 | + | 0.552991i | \(0.813486\pi\) | |||||||
\(294\) | 1125.73 | 0.223312 | ||||||||
\(295\) | 739.581 | 0.145966 | ||||||||
\(296\) | −6867.71 | −1.34857 | ||||||||
\(297\) | −1318.37 | −0.257574 | ||||||||
\(298\) | 2324.33 | 0.451829 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −5941.43 | −1.14343 | ||||||||
\(301\) | −6469.46 | −1.23885 | ||||||||
\(302\) | −15469.7 | −2.94761 | ||||||||
\(303\) | −2535.23 | −0.480677 | ||||||||
\(304\) | 31684.3 | 5.97769 | ||||||||
\(305\) | −1338.01 | −0.251194 | ||||||||
\(306\) | −1876.36 | −0.350537 | ||||||||
\(307\) | −8429.30 | −1.56705 | −0.783527 | − | 0.621357i | \(-0.786582\pi\) | ||||
−0.783527 | + | 0.621357i | \(0.786582\pi\) | |||||||
\(308\) | −22270.3 | −4.12002 | ||||||||
\(309\) | −3285.28 | −0.604832 | ||||||||
\(310\) | −3799.13 | −0.696051 | ||||||||
\(311\) | 3602.87 | 0.656914 | 0.328457 | − | 0.944519i | \(-0.393471\pi\) | ||||
0.328457 | + | 0.944519i | \(0.393471\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6626.98 | 1.19674 | 0.598369 | − | 0.801220i | \(-0.295816\pi\) | ||||
0.598369 | + | 0.801220i | \(0.295816\pi\) | |||||||
\(314\) | −12946.0 | −2.32671 | ||||||||
\(315\) | −1109.39 | −0.198436 | ||||||||
\(316\) | 12134.5 | 2.16019 | ||||||||
\(317\) | 3983.87 | 0.705857 | 0.352928 | − | 0.935650i | \(-0.385186\pi\) | ||||
0.352928 | + | 0.935650i | \(0.385186\pi\) | |||||||
\(318\) | −6370.17 | −1.12334 | ||||||||
\(319\) | 5503.46 | 0.965938 | ||||||||
\(320\) | −14361.1 | −2.50878 | ||||||||
\(321\) | 3549.98 | 0.617260 | ||||||||
\(322\) | 8380.14 | 1.45033 | ||||||||
\(323\) | −4561.76 | −0.785829 | ||||||||
\(324\) | 1822.41 | 0.312484 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 20203.8 | 3.43248 | ||||||||
\(327\) | −719.905 | −0.121746 | ||||||||
\(328\) | −10728.9 | −1.80612 | ||||||||
\(329\) | −8148.91 | −1.36554 | ||||||||
\(330\) | 4919.09 | 0.820567 | ||||||||
\(331\) | 4172.82 | 0.692927 | 0.346464 | − | 0.938063i | \(-0.387382\pi\) | ||||
0.346464 | + | 0.938063i | \(0.387382\pi\) | |||||||
\(332\) | 18250.7 | 3.01697 | ||||||||
\(333\) | −771.933 | −0.127032 | ||||||||
\(334\) | 10978.1 | 1.79848 | ||||||||
\(335\) | −5930.84 | −0.967272 | ||||||||
\(336\) | 15946.2 | 2.58910 | ||||||||
\(337\) | 4157.51 | 0.672030 | 0.336015 | − | 0.941857i | \(-0.390921\pi\) | ||||
0.336015 | + | 0.941857i | \(0.390921\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3093.67 | −0.495649 | ||||||||
\(340\) | 5164.66 | 0.823804 | ||||||||
\(341\) | −5524.14 | −0.877270 | ||||||||
\(342\) | 6005.98 | 0.949609 | ||||||||
\(343\) | −5575.83 | −0.877744 | ||||||||
\(344\) | −25553.4 | −4.00509 | ||||||||
\(345\) | −1365.49 | −0.213088 | ||||||||
\(346\) | −19754.9 | −3.06944 | ||||||||
\(347\) | 4667.98 | 0.722162 | 0.361081 | − | 0.932535i | \(-0.382408\pi\) | ||||
0.361081 | + | 0.932535i | \(0.382408\pi\) | |||||||
\(348\) | −7607.54 | −1.17186 | ||||||||
\(349\) | 11905.6 | 1.82606 | 0.913028 | − | 0.407896i | \(-0.133737\pi\) | ||||
0.913028 | + | 0.407896i | \(0.133737\pi\) | |||||||
\(350\) | −9854.72 | −1.50502 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −39428.4 | −5.97029 | ||||||||
\(353\) | −1662.12 | −0.250610 | −0.125305 | − | 0.992118i | \(-0.539991\pi\) | ||||
−0.125305 | + | 0.992118i | \(0.539991\pi\) | |||||||
\(354\) | −2015.11 | −0.302548 | ||||||||
\(355\) | −648.959 | −0.0970229 | ||||||||
\(356\) | −25438.2 | −3.78714 | ||||||||
\(357\) | −2295.87 | −0.340364 | ||||||||
\(358\) | 4253.18 | 0.627898 | ||||||||
\(359\) | 12754.4 | 1.87507 | 0.937535 | − | 0.347890i | \(-0.113102\pi\) | ||||
0.937535 | + | 0.347890i | \(0.113102\pi\) | |||||||
\(360\) | −4381.95 | −0.641524 | ||||||||
\(361\) | 7742.58 | 1.12882 | ||||||||
\(362\) | −10469.1 | −1.52001 | ||||||||
\(363\) | 3159.64 | 0.456854 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −263.028 | −0.0377192 | ||||||||
\(366\) | 3645.62 | 0.520655 | ||||||||
\(367\) | 4463.81 | 0.634901 | 0.317451 | − | 0.948275i | \(-0.397173\pi\) | ||||
0.317451 | + | 0.948275i | \(0.397173\pi\) | |||||||
\(368\) | 19627.3 | 2.78028 | ||||||||
\(369\) | −1205.94 | −0.170132 | ||||||||
\(370\) | 2880.24 | 0.404693 | ||||||||
\(371\) | −7794.38 | −1.09074 | ||||||||
\(372\) | 7636.13 | 1.06429 | ||||||||
\(373\) | 9454.46 | 1.31242 | 0.656211 | − | 0.754578i | \(-0.272158\pi\) | ||||
0.656211 | + | 0.754578i | \(0.272158\pi\) | |||||||
\(374\) | 10180.0 | 1.40747 | ||||||||
\(375\) | 3886.00 | 0.535126 | ||||||||
\(376\) | −32187.0 | −4.41468 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 3022.72 | 0.411302 | ||||||||
\(379\) | 14085.9 | 1.90908 | 0.954542 | − | 0.298077i | \(-0.0963453\pi\) | ||||
0.954542 | + | 0.298077i | \(0.0963453\pi\) | |||||||
\(380\) | −16531.4 | −2.23169 | ||||||||
\(381\) | −54.0604 | −0.00726929 | ||||||||
\(382\) | 12170.8 | 1.63014 | ||||||||
\(383\) | −8663.84 | −1.15588 | −0.577939 | − | 0.816080i | \(-0.696143\pi\) | ||||
−0.577939 | + | 0.816080i | \(0.696143\pi\) | |||||||
\(384\) | 19749.4 | 2.62456 | ||||||||
\(385\) | 6018.87 | 0.796754 | ||||||||
\(386\) | 5613.01 | 0.740141 | ||||||||
\(387\) | −2872.22 | −0.377269 | ||||||||
\(388\) | −5154.20 | −0.674395 | ||||||||
\(389\) | 5085.58 | 0.662852 | 0.331426 | − | 0.943481i | \(-0.392470\pi\) | ||||
0.331426 | + | 0.943481i | \(0.392470\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2825.85 | −0.365497 | ||||||||
\(392\) | 5440.58 | 0.700997 | ||||||||
\(393\) | −3847.57 | −0.493853 | ||||||||
\(394\) | 23849.7 | 3.04957 | ||||||||
\(395\) | −3279.53 | −0.417750 | ||||||||
\(396\) | −9887.24 | −1.25468 | ||||||||
\(397\) | 12983.7 | 1.64140 | 0.820700 | − | 0.571360i | \(-0.193584\pi\) | ||||
0.820700 | + | 0.571360i | \(0.193584\pi\) | |||||||
\(398\) | 7529.48 | 0.948288 | ||||||||
\(399\) | 7348.76 | 0.922051 | ||||||||
\(400\) | −23080.9 | −2.88512 | ||||||||
\(401\) | 6493.66 | 0.808673 | 0.404337 | − | 0.914610i | \(-0.367502\pi\) | ||||
0.404337 | + | 0.914610i | \(0.367502\pi\) | |||||||
\(402\) | 16159.5 | 2.00489 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −19013.2 | −2.34145 | ||||||||
\(405\) | −492.532 | −0.0604300 | ||||||||
\(406\) | −12618.2 | −1.54244 | ||||||||
\(407\) | 4188.03 | 0.510056 | ||||||||
\(408\) | −9068.35 | −1.10037 | ||||||||
\(409\) | −12546.2 | −1.51680 | −0.758398 | − | 0.651792i | \(-0.774017\pi\) | ||||
−0.758398 | + | 0.651792i | \(0.774017\pi\) | |||||||
\(410\) | 4499.59 | 0.541998 | ||||||||
\(411\) | 4642.09 | 0.557123 | ||||||||
\(412\) | −24638.3 | −2.94622 | ||||||||
\(413\) | −2465.63 | −0.293767 | ||||||||
\(414\) | 3720.49 | 0.441672 | ||||||||
\(415\) | −4932.52 | −0.583440 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9290.61 | −1.09104 | ||||||||
\(418\) | −32584.7 | −3.81285 | ||||||||
\(419\) | 7945.58 | 0.926413 | 0.463206 | − | 0.886250i | \(-0.346699\pi\) | ||||
0.463206 | + | 0.886250i | \(0.346699\pi\) | |||||||
\(420\) | −8320.01 | −0.966607 | ||||||||
\(421\) | −284.758 | −0.0329650 | −0.0164825 | − | 0.999864i | \(-0.505247\pi\) | ||||
−0.0164825 | + | 0.999864i | \(0.505247\pi\) | |||||||
\(422\) | 29205.2 | 3.36893 | ||||||||
\(423\) | −3617.84 | −0.415852 | ||||||||
\(424\) | −30786.7 | −3.52626 | ||||||||
\(425\) | 3323.09 | 0.379279 | ||||||||
\(426\) | 1768.19 | 0.201102 | ||||||||
\(427\) | 4460.68 | 0.505545 | ||||||||
\(428\) | 26623.4 | 3.00676 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 10716.8 | 1.20189 | ||||||||
\(431\) | −12512.1 | −1.39835 | −0.699173 | − | 0.714952i | \(-0.746448\pi\) | ||||
−0.699173 | + | 0.714952i | \(0.746448\pi\) | |||||||
\(432\) | 7079.58 | 0.788464 | ||||||||
\(433\) | −13217.2 | −1.46692 | −0.733460 | − | 0.679732i | \(-0.762096\pi\) | ||||
−0.733460 | + | 0.679732i | \(0.762096\pi\) | |||||||
\(434\) | 12665.6 | 1.40085 | ||||||||
\(435\) | 2056.05 | 0.226621 | ||||||||
\(436\) | −5399.01 | −0.593040 | ||||||||
\(437\) | 9045.16 | 0.990135 | ||||||||
\(438\) | 716.663 | 0.0781815 | ||||||||
\(439\) | 4635.40 | 0.503953 | 0.251977 | − | 0.967733i | \(-0.418919\pi\) | ||||
0.251977 | + | 0.967733i | \(0.418919\pi\) | |||||||
\(440\) | 23773.7 | 2.57583 | ||||||||
\(441\) | 611.524 | 0.0660321 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2945.92 | −0.315947 | −0.157974 | − | 0.987443i | \(-0.550496\pi\) | ||||
−0.157974 | + | 0.987443i | \(0.550496\pi\) | |||||||
\(444\) | −5789.20 | −0.618791 | ||||||||
\(445\) | 6875.05 | 0.732379 | ||||||||
\(446\) | −6947.45 | −0.737603 | ||||||||
\(447\) | 1262.64 | 0.133603 | ||||||||
\(448\) | 47877.3 | 5.04909 | ||||||||
\(449\) | −8668.29 | −0.911095 | −0.455548 | − | 0.890211i | \(-0.650557\pi\) | ||||
−0.455548 | + | 0.890211i | \(0.650557\pi\) | |||||||
\(450\) | −4375.16 | −0.458326 | ||||||||
\(451\) | 6542.66 | 0.683108 | ||||||||
\(452\) | −23201.3 | −2.41438 | ||||||||
\(453\) | −8403.51 | −0.871592 | ||||||||
\(454\) | 6269.27 | 0.648087 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 29026.6 | 2.98091 | ||||||||
\(457\) | −5195.36 | −0.531791 | −0.265896 | − | 0.964002i | \(-0.585668\pi\) | ||||
−0.265896 | + | 0.964002i | \(0.585668\pi\) | |||||||
\(458\) | −1203.93 | −0.122830 | ||||||||
\(459\) | −1019.29 | −0.103652 | ||||||||
\(460\) | −10240.6 | −1.03798 | ||||||||
\(461\) | −2931.19 | −0.296136 | −0.148068 | − | 0.988977i | \(-0.547306\pi\) | ||||
−0.148068 | + | 0.988977i | \(0.547306\pi\) | |||||||
\(462\) | −16399.4 | −1.65145 | ||||||||
\(463\) | −396.589 | −0.0398079 | −0.0199039 | − | 0.999802i | \(-0.506336\pi\) | ||||
−0.0199039 | + | 0.999802i | \(0.506336\pi\) | |||||||
\(464\) | −29553.4 | −2.95685 | ||||||||
\(465\) | −2063.78 | −0.205818 | ||||||||
\(466\) | −14.1581 | −0.00140743 | ||||||||
\(467\) | 16627.5 | 1.64760 | 0.823801 | − | 0.566880i | \(-0.191850\pi\) | ||||
0.823801 | + | 0.566880i | \(0.191850\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19772.4 | 1.94670 | ||||||||
\(470\) | 13498.9 | 1.32480 | ||||||||
\(471\) | −7032.60 | −0.687994 | ||||||||
\(472\) | −9738.91 | −0.949724 | ||||||||
\(473\) | 15582.9 | 1.51480 | ||||||||
\(474\) | 8935.62 | 0.865879 | ||||||||
\(475\) | −10636.8 | −1.02747 | ||||||||
\(476\) | −17218.1 | −1.65796 | ||||||||
\(477\) | −3460.44 | −0.332165 | ||||||||
\(478\) | 21930.9 | 2.09852 | ||||||||
\(479\) | 8903.28 | 0.849272 | 0.424636 | − | 0.905364i | \(-0.360402\pi\) | ||||
0.424636 | + | 0.905364i | \(0.360402\pi\) | |||||||
\(480\) | −14730.2 | −1.40070 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −3634.03 | −0.343414 | ||||||||
\(483\) | 4552.30 | 0.428855 | ||||||||
\(484\) | 23696.1 | 2.22540 | ||||||||
\(485\) | 1393.00 | 0.130418 | ||||||||
\(486\) | 1341.99 | 0.125255 | ||||||||
\(487\) | −469.526 | −0.0436884 | −0.0218442 | − | 0.999761i | \(-0.506954\pi\) | ||||
−0.0218442 | + | 0.999761i | \(0.506954\pi\) | |||||||
\(488\) | 17619.1 | 1.63438 | ||||||||
\(489\) | 10975.2 | 1.01496 | ||||||||
\(490\) | −2281.72 | −0.210362 | ||||||||
\(491\) | −18823.8 | −1.73015 | −0.865077 | − | 0.501639i | \(-0.832731\pi\) | ||||
−0.865077 | + | 0.501639i | \(0.832731\pi\) | |||||||
\(492\) | −9044.05 | −0.828734 | ||||||||
\(493\) | 4254.96 | 0.388709 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2672.17 | 0.242637 | ||||||||
\(496\) | 29664.4 | 2.68543 | ||||||||
\(497\) | 2163.52 | 0.195265 | ||||||||
\(498\) | 13439.5 | 1.20931 | ||||||||
\(499\) | −5651.95 | −0.507046 | −0.253523 | − | 0.967329i | \(-0.581589\pi\) | ||||
−0.253523 | + | 0.967329i | \(0.581589\pi\) | |||||||
\(500\) | 29143.5 | 2.60667 | ||||||||
\(501\) | 5963.55 | 0.531800 | ||||||||
\(502\) | 39160.7 | 3.48172 | ||||||||
\(503\) | 8022.35 | 0.711131 | 0.355565 | − | 0.934651i | \(-0.384288\pi\) | ||||
0.355565 | + | 0.934651i | \(0.384288\pi\) | |||||||
\(504\) | 14608.7 | 1.29111 | ||||||||
\(505\) | 5138.62 | 0.452803 | ||||||||
\(506\) | −20185.1 | −1.77339 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −405.432 | −0.0354097 | ||||||||
\(509\) | 3940.56 | 0.343148 | 0.171574 | − | 0.985171i | \(-0.445115\pi\) | ||||
0.171574 | + | 0.985171i | \(0.445115\pi\) | |||||||
\(510\) | 3803.16 | 0.330210 | ||||||||
\(511\) | 876.890 | 0.0759126 | ||||||||
\(512\) | 43768.2 | 3.77793 | ||||||||
\(513\) | 3262.60 | 0.280794 | ||||||||
\(514\) | 4376.81 | 0.375589 | ||||||||
\(515\) | 6658.88 | 0.569758 | ||||||||
\(516\) | −21540.5 | −1.83773 | ||||||||
\(517\) | 19628.1 | 1.66972 | ||||||||
\(518\) | −9602.22 | −0.814474 | ||||||||
\(519\) | −10731.3 | −0.907617 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8644.84 | 0.726943 | 0.363472 | − | 0.931605i | \(-0.381591\pi\) | ||||
0.363472 | + | 0.931605i | \(0.381591\pi\) | |||||||
\(522\) | −5602.05 | −0.469722 | ||||||||
\(523\) | 1956.76 | 0.163600 | 0.0818001 | − | 0.996649i | \(-0.473933\pi\) | ||||
0.0818001 | + | 0.996649i | \(0.473933\pi\) | |||||||
\(524\) | −28855.3 | −2.40563 | ||||||||
\(525\) | −5353.33 | −0.445025 | ||||||||
\(526\) | −1863.69 | −0.154488 | ||||||||
\(527\) | −4270.95 | −0.353028 | ||||||||
\(528\) | −38409.4 | −3.16582 | ||||||||
\(529\) | −6563.84 | −0.539479 | ||||||||
\(530\) | 12911.6 | 1.05820 | ||||||||
\(531\) | −1094.66 | −0.0894615 | ||||||||
\(532\) | 55112.8 | 4.49144 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −18732.2 | −1.51802 | ||||||||
\(535\) | −7195.39 | −0.581465 | ||||||||
\(536\) | 78098.2 | 6.29352 | ||||||||
\(537\) | 2310.43 | 0.185666 | ||||||||
\(538\) | −19461.2 | −1.55954 | ||||||||
\(539\) | −3317.75 | −0.265131 | ||||||||
\(540\) | −3693.80 | −0.294363 | ||||||||
\(541\) | 7005.37 | 0.556718 | 0.278359 | − | 0.960477i | \(-0.410210\pi\) | ||||
0.278359 | + | 0.960477i | \(0.410210\pi\) | |||||||
\(542\) | 45912.6 | 3.63859 | ||||||||
\(543\) | −5687.06 | −0.449457 | ||||||||
\(544\) | −30483.8 | −2.40254 | ||||||||
\(545\) | 1459.16 | 0.114686 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23216.7 | 1.81476 | 0.907382 | − | 0.420307i | \(-0.138077\pi\) | ||||
0.907382 | + | 0.420307i | \(0.138077\pi\) | |||||||
\(548\) | 34813.9 | 2.71382 | ||||||||
\(549\) | 1980.39 | 0.153955 | ||||||||
\(550\) | 23736.9 | 1.84026 | ||||||||
\(551\) | −13619.6 | −1.05302 | ||||||||
\(552\) | 17980.9 | 1.38645 | ||||||||
\(553\) | 10933.4 | 0.840751 | ||||||||
\(554\) | −13808.2 | −1.05895 | ||||||||
\(555\) | 1564.62 | 0.119665 | ||||||||
\(556\) | −69675.9 | −5.31460 | ||||||||
\(557\) | −14912.9 | −1.13443 | −0.567217 | − | 0.823568i | \(-0.691980\pi\) | ||||
−0.567217 | + | 0.823568i | \(0.691980\pi\) | |||||||
\(558\) | 5623.11 | 0.426604 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −32321.1 | −2.43896 | ||||||||
\(561\) | 5530.01 | 0.416180 | ||||||||
\(562\) | −16861.1 | −1.26556 | ||||||||
\(563\) | 10854.3 | 0.812531 | 0.406266 | − | 0.913755i | \(-0.366831\pi\) | ||||
0.406266 | + | 0.913755i | \(0.366831\pi\) | |||||||
\(564\) | −27132.4 | −2.02567 | ||||||||
\(565\) | 6270.50 | 0.466906 | ||||||||
\(566\) | 6399.55 | 0.475253 | ||||||||
\(567\) | 1642.02 | 0.121620 | ||||||||
\(568\) | 8545.58 | 0.631276 | ||||||||
\(569\) | 17892.5 | 1.31827 | 0.659134 | − | 0.752026i | \(-0.270923\pi\) | ||||
0.659134 | + | 0.752026i | \(0.270923\pi\) | |||||||
\(570\) | −12173.4 | −0.894541 | ||||||||
\(571\) | 17319.8 | 1.26937 | 0.634686 | − | 0.772770i | \(-0.281130\pi\) | ||||
0.634686 | + | 0.772770i | \(0.281130\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6611.48 | 0.482022 | ||||||||
\(574\) | −15000.9 | −1.09081 | ||||||||
\(575\) | −6589.10 | −0.477886 | ||||||||
\(576\) | 21255.9 | 1.53761 | ||||||||
\(577\) | −9738.48 | −0.702632 | −0.351316 | − | 0.936257i | \(-0.614266\pi\) | ||||
−0.351316 | + | 0.936257i | \(0.614266\pi\) | |||||||
\(578\) | −19261.8 | −1.38614 | ||||||||
\(579\) | 3049.13 | 0.218855 | ||||||||
\(580\) | 15419.6 | 1.10390 | ||||||||
\(581\) | 16444.2 | 1.17421 | ||||||||
\(582\) | −3795.46 | −0.270321 | ||||||||
\(583\) | 18774.2 | 1.33370 | ||||||||
\(584\) | 3463.59 | 0.245419 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −46154.7 | −3.25364 | ||||||||
\(587\) | −5960.31 | −0.419095 | −0.209547 | − | 0.977799i | \(-0.567199\pi\) | ||||
−0.209547 | + | 0.977799i | \(0.567199\pi\) | |||||||
\(588\) | 4586.19 | 0.321652 | ||||||||
\(589\) | 13670.7 | 0.956355 | ||||||||
\(590\) | 4084.39 | 0.285003 | ||||||||
\(591\) | 12955.7 | 0.901740 | ||||||||
\(592\) | −22489.6 | −1.56134 | ||||||||
\(593\) | −17870.2 | −1.23751 | −0.618753 | − | 0.785586i | \(-0.712362\pi\) | ||||
−0.618753 | + | 0.785586i | \(0.712362\pi\) | |||||||
\(594\) | −7280.78 | −0.502919 | ||||||||
\(595\) | 4653.45 | 0.320627 | ||||||||
\(596\) | 9469.28 | 0.650800 | ||||||||
\(597\) | 4090.20 | 0.280403 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17943.7 | −1.22397 | −0.611987 | − | 0.790868i | \(-0.709629\pi\) | ||||
−0.611987 | + | 0.790868i | \(0.709629\pi\) | |||||||
\(600\) | −21144.9 | −1.43873 | ||||||||
\(601\) | 6548.20 | 0.444437 | 0.222219 | − | 0.974997i | \(-0.428670\pi\) | ||||
0.222219 | + | 0.974997i | \(0.428670\pi\) | |||||||
\(602\) | −35728.1 | −2.41888 | ||||||||
\(603\) | 8778.27 | 0.592834 | ||||||||
\(604\) | −63023.0 | −4.24565 | ||||||||
\(605\) | −6404.21 | −0.430361 | ||||||||
\(606\) | −14001.0 | −0.938534 | ||||||||
\(607\) | −14886.0 | −0.995391 | −0.497696 | − | 0.867352i | \(-0.665820\pi\) | ||||
−0.497696 | + | 0.867352i | \(0.665820\pi\) | |||||||
\(608\) | 97574.6 | 6.50851 | ||||||||
\(609\) | −6854.52 | −0.456091 | ||||||||
\(610\) | −7389.24 | −0.490462 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −7644.25 | −0.504903 | ||||||||
\(613\) | −8774.65 | −0.578148 | −0.289074 | − | 0.957307i | \(-0.593347\pi\) | ||||
−0.289074 | + | 0.957307i | \(0.593347\pi\) | |||||||
\(614\) | −46551.5 | −3.05971 | ||||||||
\(615\) | 2444.29 | 0.160266 | ||||||||
\(616\) | −79257.4 | −5.18405 | ||||||||
\(617\) | −3810.41 | −0.248625 | −0.124312 | − | 0.992243i | \(-0.539673\pi\) | ||||
−0.124312 | + | 0.992243i | \(0.539673\pi\) | |||||||
\(618\) | −18143.2 | −1.18095 | ||||||||
\(619\) | −16392.6 | −1.06441 | −0.532207 | − | 0.846614i | \(-0.678637\pi\) | ||||
−0.532207 | + | 0.846614i | \(0.678637\pi\) | |||||||
\(620\) | −15477.5 | −1.00257 | ||||||||
\(621\) | 2021.07 | 0.130600 | ||||||||
\(622\) | 19897.1 | 1.28264 | ||||||||
\(623\) | −22920.2 | −1.47396 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3126.74 | 0.200112 | ||||||||
\(626\) | 36598.0 | 2.33666 | ||||||||
\(627\) | −17700.8 | −1.12744 | ||||||||
\(628\) | −52741.8 | −3.35131 | ||||||||
\(629\) | 3237.95 | 0.205255 | ||||||||
\(630\) | −6126.70 | −0.387450 | ||||||||
\(631\) | −11077.3 | −0.698858 | −0.349429 | − | 0.936963i | \(-0.613624\pi\) | ||||
−0.349429 | + | 0.936963i | \(0.613624\pi\) | |||||||
\(632\) | 43185.4 | 2.71807 | ||||||||
\(633\) | 15865.0 | 0.996173 | ||||||||
\(634\) | 22001.2 | 1.37820 | ||||||||
\(635\) | 109.574 | 0.00684775 | ||||||||
\(636\) | −25951.9 | −1.61802 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 30393.2 | 1.88602 | ||||||||
\(639\) | 960.527 | 0.0594646 | ||||||||
\(640\) | −40029.6 | −2.47236 | ||||||||
\(641\) | −2143.45 | −0.132077 | −0.0660383 | − | 0.997817i | \(-0.521036\pi\) | ||||
−0.0660383 | + | 0.997817i | \(0.521036\pi\) | |||||||
\(642\) | 19605.0 | 1.20522 | ||||||||
\(643\) | 9774.93 | 0.599511 | 0.299755 | − | 0.954016i | \(-0.403095\pi\) | ||||
0.299755 | + | 0.954016i | \(0.403095\pi\) | |||||||
\(644\) | 34140.5 | 2.08901 | ||||||||
\(645\) | 5821.65 | 0.355391 | ||||||||
\(646\) | −25192.6 | −1.53435 | ||||||||
\(647\) | −22447.6 | −1.36400 | −0.681999 | − | 0.731353i | \(-0.738889\pi\) | ||||
−0.681999 | + | 0.731353i | \(0.738889\pi\) | |||||||
\(648\) | 6485.74 | 0.393185 | ||||||||
\(649\) | 5938.93 | 0.359204 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6880.29 | 0.414224 | ||||||||
\(652\) | 82310.0 | 4.94403 | ||||||||
\(653\) | 10582.0 | 0.634157 | 0.317079 | − | 0.948399i | \(-0.397298\pi\) | ||||
0.317079 | + | 0.948399i | \(0.397298\pi\) | |||||||
\(654\) | −3975.73 | −0.237711 | ||||||||
\(655\) | 7798.57 | 0.465214 | ||||||||
\(656\) | −35133.9 | −2.09108 | ||||||||
\(657\) | 389.309 | 0.0231178 | ||||||||
\(658\) | −45003.0 | −2.66626 | ||||||||
\(659\) | −15114.6 | −0.893445 | −0.446722 | − | 0.894673i | \(-0.647409\pi\) | ||||
−0.446722 | + | 0.894673i | \(0.647409\pi\) | |||||||
\(660\) | 20040.3 | 1.18192 | ||||||||
\(661\) | 2229.61 | 0.131198 | 0.0655990 | − | 0.997846i | \(-0.479104\pi\) | ||||
0.0655990 | + | 0.997846i | \(0.479104\pi\) | |||||||
\(662\) | 23044.7 | 1.35296 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 64952.1 | 3.79613 | ||||||||
\(665\) | −14895.1 | −0.868581 | ||||||||
\(666\) | −4263.06 | −0.248033 | ||||||||
\(667\) | −8436.83 | −0.489768 | ||||||||
\(668\) | 44724.3 | 2.59047 | ||||||||
\(669\) | −3774.03 | −0.218105 | ||||||||
\(670\) | −32753.5 | −1.88862 | ||||||||
\(671\) | −10744.4 | −0.618155 | ||||||||
\(672\) | 49107.9 | 2.81901 | ||||||||
\(673\) | −3588.22 | −0.205521 | −0.102761 | − | 0.994706i | \(-0.532768\pi\) | ||||
−0.102761 | + | 0.994706i | \(0.532768\pi\) | |||||||
\(674\) | 22960.2 | 1.31216 | ||||||||
\(675\) | −2376.69 | −0.135524 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −26458.4 | −1.50204 | −0.751019 | − | 0.660280i | \(-0.770438\pi\) | ||||
−0.751019 | + | 0.660280i | \(0.770438\pi\) | |||||||
\(678\) | −17085.0 | −0.967767 | ||||||||
\(679\) | −4644.03 | −0.262476 | ||||||||
\(680\) | 18380.5 | 1.03656 | ||||||||
\(681\) | 3405.62 | 0.191635 | ||||||||
\(682\) | −30507.5 | −1.71289 | ||||||||
\(683\) | −23598.4 | −1.32206 | −0.661031 | − | 0.750358i | \(-0.729881\pi\) | ||||
−0.661031 | + | 0.750358i | \(0.729881\pi\) | |||||||
\(684\) | 24468.2 | 1.36779 | ||||||||
\(685\) | −9408.97 | −0.524815 | ||||||||
\(686\) | −30792.9 | −1.71382 | ||||||||
\(687\) | −654.007 | −0.0363201 | ||||||||
\(688\) | −83679.4 | −4.63699 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −7541.01 | −0.416060 | ||||||||
\(691\) | −16433.6 | −0.904722 | −0.452361 | − | 0.891835i | \(-0.649418\pi\) | ||||
−0.452361 | + | 0.891835i | \(0.649418\pi\) | |||||||
\(692\) | −80480.8 | −4.42113 | ||||||||
\(693\) | −8908.57 | −0.488324 | ||||||||
\(694\) | 25779.2 | 1.41004 | ||||||||
\(695\) | 18831.0 | 1.02777 | ||||||||
\(696\) | −27074.4 | −1.47450 | ||||||||
\(697\) | 5058.41 | 0.274894 | ||||||||
\(698\) | 65749.7 | 3.56542 | ||||||||
\(699\) | −7.69102 | −0.000416167 0 | ||||||||
\(700\) | −40147.9 | −2.16778 | ||||||||
\(701\) | 13899.4 | 0.748892 | 0.374446 | − | 0.927249i | \(-0.377833\pi\) | ||||
0.374446 | + | 0.927249i | \(0.377833\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10364.2 | −0.556038 | ||||||||
\(704\) | −115321. | −6.17377 | ||||||||
\(705\) | 7332.93 | 0.391736 | ||||||||
\(706\) | −9179.16 | −0.489323 | ||||||||
\(707\) | −17131.3 | −0.911297 | ||||||||
\(708\) | −8209.50 | −0.435780 | ||||||||
\(709\) | 32829.6 | 1.73899 | 0.869494 | − | 0.493944i | \(-0.164445\pi\) | ||||
0.869494 | + | 0.493944i | \(0.164445\pi\) | |||||||
\(710\) | −3583.92 | −0.189440 | ||||||||
\(711\) | 4854.05 | 0.256035 | ||||||||
\(712\) | −90531.7 | −4.76519 | ||||||||
\(713\) | 8468.55 | 0.444810 | ||||||||
\(714\) | −12679.1 | −0.664570 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 17327.3 | 0.904403 | ||||||||
\(717\) | 11913.4 | 0.620521 | ||||||||
\(718\) | 70437.0 | 3.66112 | ||||||||
\(719\) | −4683.94 | −0.242951 | −0.121475 | − | 0.992594i | \(-0.538763\pi\) | ||||
−0.121475 | + | 0.992594i | \(0.538763\pi\) | |||||||
\(720\) | −14349.5 | −0.742741 | ||||||||
\(721\) | −22199.5 | −1.14668 | ||||||||
\(722\) | 42759.0 | 2.20405 | ||||||||
\(723\) | −1974.10 | −0.101546 | ||||||||
\(724\) | −42650.7 | −2.18937 | ||||||||
\(725\) | 9921.39 | 0.508236 | ||||||||
\(726\) | 17449.3 | 0.892019 | ||||||||
\(727\) | −35368.3 | −1.80432 | −0.902159 | − | 0.431405i | \(-0.858018\pi\) | ||||
−0.902159 | + | 0.431405i | \(0.858018\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −1452.59 | −0.0736478 | ||||||||
\(731\) | 12047.8 | 0.609580 | ||||||||
\(732\) | 14852.2 | 0.749934 | ||||||||
\(733\) | 33988.4 | 1.71268 | 0.856338 | − | 0.516416i | \(-0.172734\pi\) | ||||
0.856338 | + | 0.516416i | \(0.172734\pi\) | |||||||
\(734\) | 24651.7 | 1.23966 | ||||||||
\(735\) | −1239.49 | −0.0622029 | ||||||||
\(736\) | 60444.0 | 3.02717 | ||||||||
\(737\) | −47625.4 | −2.38033 | ||||||||
\(738\) | −6659.87 | −0.332186 | ||||||||
\(739\) | −7777.31 | −0.387135 | −0.193568 | − | 0.981087i | \(-0.562006\pi\) | ||||
−0.193568 | + | 0.981087i | \(0.562006\pi\) | |||||||
\(740\) | 11734.0 | 0.582907 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −43045.0 | −2.12969 | ||||||||
\(743\) | −7022.08 | −0.346723 | −0.173361 | − | 0.984858i | \(-0.555463\pi\) | ||||
−0.173361 | + | 0.984858i | \(0.555463\pi\) | |||||||
\(744\) | 27176.2 | 1.33915 | ||||||||
\(745\) | −2559.22 | −0.125856 | ||||||||
\(746\) | 52212.9 | 2.56254 | ||||||||
\(747\) | 7300.64 | 0.357586 | ||||||||
\(748\) | 41472.9 | 2.02727 | ||||||||
\(749\) | 23988.2 | 1.17024 | ||||||||
\(750\) | 21460.7 | 1.04485 | ||||||||
\(751\) | 8214.69 | 0.399146 | 0.199573 | − | 0.979883i | \(-0.436045\pi\) | ||||
0.199573 | + | 0.979883i | \(0.436045\pi\) | |||||||
\(752\) | −105402. | −5.11121 | ||||||||
\(753\) | 21273.0 | 1.02953 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17032.9 | 0.821048 | ||||||||
\(756\) | 12314.5 | 0.592426 | ||||||||
\(757\) | −20846.9 | −1.00092 | −0.500459 | − | 0.865760i | \(-0.666835\pi\) | ||||
−0.500459 | + | 0.865760i | \(0.666835\pi\) | |||||||
\(758\) | 77790.3 | 3.72753 | ||||||||
\(759\) | −10965.0 | −0.524382 | ||||||||
\(760\) | −58833.5 | −2.80804 | ||||||||
\(761\) | −3563.06 | −0.169725 | −0.0848627 | − | 0.996393i | \(-0.527045\pi\) | ||||
−0.0848627 | + | 0.996393i | \(0.527045\pi\) | |||||||
\(762\) | −298.553 | −0.0141935 | ||||||||
\(763\) | −4864.60 | −0.230813 | ||||||||
\(764\) | 49583.6 | 2.34800 | ||||||||
\(765\) | 2065.97 | 0.0976410 | ||||||||
\(766\) | −47846.7 | −2.25688 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 52384.9 | 2.46130 | ||||||||
\(769\) | 32557.9 | 1.52675 | 0.763373 | − | 0.645958i | \(-0.223542\pi\) | ||||
0.763373 | + | 0.645958i | \(0.223542\pi\) | |||||||
\(770\) | 33239.7 | 1.55568 | ||||||||
\(771\) | 2377.59 | 0.111059 | ||||||||
\(772\) | 22867.3 | 1.06608 | ||||||||
\(773\) | 20126.4 | 0.936477 | 0.468238 | − | 0.883602i | \(-0.344889\pi\) | ||||
0.468238 | + | 0.883602i | \(0.344889\pi\) | |||||||
\(774\) | −15862.0 | −0.736627 | ||||||||
\(775\) | −9958.68 | −0.461583 | ||||||||
\(776\) | −18343.2 | −0.848562 | ||||||||
\(777\) | −5216.17 | −0.240835 | ||||||||
\(778\) | 28085.5 | 1.29423 | ||||||||
\(779\) | −16191.3 | −0.744690 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5211.22 | −0.238761 | ||||||||
\(782\) | −15606.0 | −0.713642 | ||||||||
\(783\) | −3043.17 | −0.138894 | ||||||||
\(784\) | 17816.2 | 0.811597 | ||||||||
\(785\) | 14254.3 | 0.648097 | ||||||||
\(786\) | −21248.5 | −0.964260 | ||||||||
\(787\) | 18828.4 | 0.852806 | 0.426403 | − | 0.904533i | \(-0.359781\pi\) | ||||
0.426403 | + | 0.904533i | \(0.359781\pi\) | |||||||
\(788\) | 97163.1 | 4.39250 | ||||||||
\(789\) | −1012.40 | −0.0456812 | ||||||||
\(790\) | −18111.5 | −0.815667 | ||||||||
\(791\) | −20904.8 | −0.939682 | ||||||||
\(792\) | −35187.6 | −1.57871 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 71703.7 | 3.20487 | ||||||||
\(795\) | 7013.90 | 0.312902 | ||||||||
\(796\) | 30674.9 | 1.36588 | ||||||||
\(797\) | 7288.52 | 0.323930 | 0.161965 | − | 0.986796i | \(-0.448217\pi\) | ||||
0.161965 | + | 0.986796i | \(0.448217\pi\) | |||||||
\(798\) | 40584.1 | 1.80033 | ||||||||
\(799\) | 15175.3 | 0.671921 | ||||||||
\(800\) | −71079.9 | −3.14132 | ||||||||
\(801\) | −10175.8 | −0.448869 | ||||||||
\(802\) | 35861.7 | 1.57896 | ||||||||
\(803\) | −2112.15 | −0.0928221 | ||||||||
\(804\) | 65833.6 | 2.88778 | ||||||||
\(805\) | −9226.97 | −0.403985 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10571.8 | −0.461146 | ||||||||
\(808\) | −67666.1 | −2.94614 | ||||||||
\(809\) | −33799.0 | −1.46886 | −0.734430 | − | 0.678684i | \(-0.762551\pi\) | ||||
−0.734430 | + | 0.678684i | \(0.762551\pi\) | |||||||
\(810\) | −2720.05 | −0.117991 | ||||||||
\(811\) | −29055.3 | −1.25804 | −0.629019 | − | 0.777390i | \(-0.716543\pi\) | ||||
−0.629019 | + | 0.777390i | \(0.716543\pi\) | |||||||
\(812\) | −51406.2 | −2.22168 | ||||||||
\(813\) | 24940.9 | 1.07591 | ||||||||
\(814\) | 23128.7 | 0.995898 | ||||||||
\(815\) | −22245.5 | −0.956106 | ||||||||
\(816\) | −29696.0 | −1.27398 | ||||||||
\(817\) | −38563.3 | −1.65136 | ||||||||
\(818\) | −69287.3 | −2.96158 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 18331.2 | 0.780676 | ||||||||
\(821\) | −8921.98 | −0.379268 | −0.189634 | − | 0.981855i | \(-0.560730\pi\) | ||||
−0.189634 | + | 0.981855i | \(0.560730\pi\) | |||||||
\(822\) | 25636.3 | 1.08780 | ||||||||
\(823\) | −9148.48 | −0.387480 | −0.193740 | − | 0.981053i | \(-0.562062\pi\) | ||||
−0.193740 | + | 0.981053i | \(0.562062\pi\) | |||||||
\(824\) | −87685.1 | −3.70711 | ||||||||
\(825\) | 12894.5 | 0.544155 | ||||||||
\(826\) | −13616.6 | −0.573588 | ||||||||
\(827\) | −20206.0 | −0.849615 | −0.424807 | − | 0.905284i | \(-0.639658\pi\) | ||||
−0.424807 | + | 0.905284i | \(0.639658\pi\) | |||||||
\(828\) | 15157.2 | 0.636170 | ||||||||
\(829\) | −10832.4 | −0.453830 | −0.226915 | − | 0.973915i | \(-0.572864\pi\) | ||||
−0.226915 | + | 0.973915i | \(0.572864\pi\) | |||||||
\(830\) | −27240.2 | −1.13918 | ||||||||
\(831\) | −7500.98 | −0.313124 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2565.09 | −0.106693 | ||||||||
\(834\) | −51308.1 | −2.13028 | ||||||||
\(835\) | −12087.4 | −0.500961 | ||||||||
\(836\) | −132749. | −5.49190 | ||||||||
\(837\) | 3054.61 | 0.126144 | ||||||||
\(838\) | 43880.1 | 1.80884 | ||||||||
\(839\) | 7047.44 | 0.289994 | 0.144997 | − | 0.989432i | \(-0.453683\pi\) | ||||
0.144997 | + | 0.989432i | \(0.453683\pi\) | |||||||
\(840\) | −29610.0 | −1.21624 | ||||||||
\(841\) | −11685.4 | −0.479127 | ||||||||
\(842\) | −1572.60 | −0.0643650 | ||||||||
\(843\) | −9159.39 | −0.374218 | ||||||||
\(844\) | 118981. | 4.85250 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −19979.8 | −0.811961 | ||||||||
\(847\) | 21350.5 | 0.866132 | ||||||||
\(848\) | −100817. | −4.08262 | ||||||||
\(849\) | 3476.40 | 0.140530 | ||||||||
\(850\) | 18352.0 | 0.740551 | ||||||||
\(851\) | −6420.28 | −0.258618 | ||||||||
\(852\) | 7203.58 | 0.289660 | ||||||||
\(853\) | −24085.5 | −0.966790 | −0.483395 | − | 0.875402i | \(-0.660596\pi\) | ||||
−0.483395 | + | 0.875402i | \(0.660596\pi\) | |||||||
\(854\) | 24634.5 | 0.987089 | ||||||||
\(855\) | −6612.90 | −0.264511 | ||||||||
\(856\) | 94749.9 | 3.78328 | ||||||||
\(857\) | −4161.31 | −0.165866 | −0.0829332 | − | 0.996555i | \(-0.526429\pi\) | ||||
−0.0829332 | + | 0.996555i | \(0.526429\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27387.5 | 1.08784 | 0.543918 | − | 0.839139i | \(-0.316940\pi\) | ||||
0.543918 | + | 0.839139i | \(0.316940\pi\) | |||||||
\(860\) | 43660.1 | 1.73116 | ||||||||
\(861\) | −8148.84 | −0.322546 | ||||||||
\(862\) | −69099.1 | −2.73031 | ||||||||
\(863\) | −19420.4 | −0.766022 | −0.383011 | − | 0.923744i | \(-0.625113\pi\) | ||||
−0.383011 | + | 0.923744i | \(0.625113\pi\) | |||||||
\(864\) | 21802.2 | 0.858480 | ||||||||
\(865\) | 21751.1 | 0.854984 | ||||||||
\(866\) | −72992.8 | −2.86420 | ||||||||
\(867\) | −10463.5 | −0.409873 | ||||||||
\(868\) | 51599.5 | 2.01774 | ||||||||
\(869\) | −26335.1 | −1.02803 | ||||||||
\(870\) | 11354.7 | 0.442483 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −19214.5 | −0.746198 | ||||||||
\(873\) | −2061.79 | −0.0799324 | ||||||||
\(874\) | 49952.6 | 1.93326 | ||||||||
\(875\) | 26258.8 | 1.01453 | ||||||||
\(876\) | 2919.67 | 0.112610 | ||||||||
\(877\) | 9908.85 | 0.381526 | 0.190763 | − | 0.981636i | \(-0.438904\pi\) | ||||
0.190763 | + | 0.981636i | \(0.438904\pi\) | |||||||
\(878\) | 25599.3 | 0.983981 | ||||||||
\(879\) | −25072.4 | −0.962081 | ||||||||
\(880\) | 77851.4 | 2.98224 | ||||||||
\(881\) | 20323.3 | 0.777197 | 0.388598 | − | 0.921407i | \(-0.372959\pi\) | ||||
0.388598 | + | 0.921407i | \(0.372959\pi\) | |||||||
\(882\) | 3377.19 | 0.128929 | ||||||||
\(883\) | 12443.3 | 0.474238 | 0.237119 | − | 0.971481i | \(-0.423797\pi\) | ||||
0.237119 | + | 0.971481i | \(0.423797\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2218.74 | 0.0842737 | ||||||||
\(886\) | −16269.0 | −0.616895 | ||||||||
\(887\) | 42313.5 | 1.60174 | 0.800872 | − | 0.598835i | \(-0.204369\pi\) | ||||
0.800872 | + | 0.598835i | \(0.204369\pi\) | |||||||
\(888\) | −20603.1 | −0.778599 | ||||||||
\(889\) | −365.301 | −0.0137816 | ||||||||
\(890\) | 37968.0 | 1.42999 | ||||||||
\(891\) | −3955.10 | −0.148710 | ||||||||
\(892\) | −28303.7 | −1.06242 | ||||||||
\(893\) | −48574.3 | −1.82024 | ||||||||
\(894\) | 6973.00 | 0.260864 | ||||||||
\(895\) | −4682.97 | −0.174899 | ||||||||
\(896\) | 133452. | 4.97580 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −47871.3 | −1.77894 | ||||||||
\(899\) | −12751.3 | −0.473059 | ||||||||
\(900\) | −17824.3 | −0.660159 | ||||||||
\(901\) | 14515.1 | 0.536702 | ||||||||
\(902\) | 36132.3 | 1.33379 | ||||||||
\(903\) | −19408.4 | −0.715249 | ||||||||
\(904\) | −82571.0 | −3.03791 | ||||||||
\(905\) | 11527.0 | 0.423393 | ||||||||
\(906\) | −46409.0 | −1.70181 | ||||||||
\(907\) | −11002.3 | −0.402786 | −0.201393 | − | 0.979511i | \(-0.564547\pi\) | ||||
−0.201393 | + | 0.979511i | \(0.564547\pi\) | |||||||
\(908\) | 25540.8 | 0.933483 | ||||||||
\(909\) | −7605.69 | −0.277519 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40803.4 | −1.48395 | −0.741974 | − | 0.670428i | \(-0.766110\pi\) | ||||
−0.741974 | + | 0.670428i | \(0.766110\pi\) | |||||||
\(912\) | 95052.8 | 3.45122 | ||||||||
\(913\) | −39608.8 | −1.43577 | ||||||||
\(914\) | −28691.8 | −1.03834 | ||||||||
\(915\) | −4014.02 | −0.145027 | ||||||||
\(916\) | −4904.80 | −0.176920 | ||||||||
\(917\) | −25999.1 | −0.936276 | ||||||||
\(918\) | −5629.08 | −0.202383 | ||||||||
\(919\) | 2642.69 | 0.0948579 | 0.0474290 | − | 0.998875i | \(-0.484897\pi\) | ||||
0.0474290 | + | 0.998875i | \(0.484897\pi\) | |||||||
\(920\) | −36445.3 | −1.30605 | ||||||||
\(921\) | −25287.9 | −0.904739 | ||||||||
\(922\) | −16187.7 | −0.578214 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −66810.8 | −2.37869 | ||||||||
\(925\) | 7550.00 | 0.268370 | ||||||||
\(926\) | −2190.19 | −0.0777258 | ||||||||
\(927\) | −9855.84 | −0.349200 | ||||||||
\(928\) | −91012.3 | −3.21942 | ||||||||
\(929\) | −12687.7 | −0.448083 | −0.224042 | − | 0.974580i | \(-0.571925\pi\) | ||||
−0.224042 | + | 0.974580i | \(0.571925\pi\) | |||||||
\(930\) | −11397.4 | −0.401865 | ||||||||
\(931\) | 8210.52 | 0.289032 | ||||||||
\(932\) | −57.6796 | −0.00202721 | ||||||||
\(933\) | 10808.6 | 0.379269 | ||||||||
\(934\) | 91826.7 | 3.21698 | ||||||||
\(935\) | −11208.7 | −0.392046 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23066.2 | −0.804205 | −0.402103 | − | 0.915595i | \(-0.631721\pi\) | ||||
−0.402103 | + | 0.915595i | \(0.631721\pi\) | |||||||
\(938\) | 109195. | 3.80099 | ||||||||
\(939\) | 19880.9 | 0.690937 | ||||||||
\(940\) | 54994.1 | 1.90820 | ||||||||
\(941\) | −12660.7 | −0.438605 | −0.219303 | − | 0.975657i | \(-0.570378\pi\) | ||||
−0.219303 | + | 0.975657i | \(0.570378\pi\) | |||||||
\(942\) | −38838.1 | −1.34332 | ||||||||
\(943\) | −10029.9 | −0.346362 | ||||||||
\(944\) | −31891.8 | −1.09957 | ||||||||
\(945\) | −3328.18 | −0.114567 | ||||||||
\(946\) | 86057.5 | 2.95769 | ||||||||
\(947\) | −21059.1 | −0.722629 | −0.361315 | − | 0.932444i | \(-0.617672\pi\) | ||||
−0.361315 | + | 0.932444i | \(0.617672\pi\) | |||||||
\(948\) | 36403.5 | 1.24718 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −58742.3 | −2.00616 | ||||||||
\(951\) | 11951.6 | 0.407526 | ||||||||
\(952\) | −61277.3 | −2.08614 | ||||||||
\(953\) | 35646.2 | 1.21164 | 0.605820 | − | 0.795602i | \(-0.292845\pi\) | ||||
0.605820 | + | 0.795602i | \(0.292845\pi\) | |||||||
\(954\) | −19110.5 | −0.648560 | ||||||||
\(955\) | −13400.7 | −0.454070 | ||||||||
\(956\) | 89345.8 | 3.02265 | ||||||||
\(957\) | 16510.4 | 0.557685 | ||||||||
\(958\) | 49169.0 | 1.65822 | ||||||||
\(959\) | 31367.9 | 1.05623 | ||||||||
\(960\) | −43083.2 | −1.44844 | ||||||||
\(961\) | −16991.7 | −0.570365 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10649.9 | 0.356375 | ||||||||
\(964\) | −14805.0 | −0.494643 | ||||||||
\(965\) | −6180.22 | −0.206164 | ||||||||
\(966\) | 25140.4 | 0.837349 | ||||||||
\(967\) | −53452.1 | −1.77756 | −0.888782 | − | 0.458329i | \(-0.848448\pi\) | ||||
−0.888782 | + | 0.458329i | \(0.848448\pi\) | |||||||
\(968\) | 84331.7 | 2.80013 | ||||||||
\(969\) | −13685.3 | −0.453699 | ||||||||
\(970\) | 7692.95 | 0.254645 | ||||||||
\(971\) | 6502.60 | 0.214911 | 0.107455 | − | 0.994210i | \(-0.465730\pi\) | ||||
0.107455 | + | 0.994210i | \(0.465730\pi\) | |||||||
\(972\) | 5467.22 | 0.180413 | ||||||||
\(973\) | −62779.2 | −2.06846 | ||||||||
\(974\) | −2592.99 | −0.0853027 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 57696.9 | 1.89225 | ||||||||
\(977\) | 4351.84 | 0.142505 | 0.0712527 | − | 0.997458i | \(-0.477300\pi\) | ||||
0.0712527 | + | 0.997458i | \(0.477300\pi\) | |||||||
\(978\) | 60611.5 | 1.98174 | ||||||||
\(979\) | 55207.5 | 1.80229 | ||||||||
\(980\) | −9295.67 | −0.302999 | ||||||||
\(981\) | −2159.71 | −0.0702899 | ||||||||
\(982\) | −103956. | −3.37817 | ||||||||
\(983\) | −48698.2 | −1.58009 | −0.790047 | − | 0.613046i | \(-0.789944\pi\) | ||||
−0.790047 | + | 0.613046i | \(0.789944\pi\) | |||||||
\(984\) | −32186.8 | −1.04276 | ||||||||
\(985\) | −26259.8 | −0.849448 | ||||||||
\(986\) | 23498.3 | 0.758964 | ||||||||
\(987\) | −24446.7 | −0.788397 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −23888.6 | −0.768063 | ||||||||
\(990\) | 14757.3 | 0.473755 | ||||||||
\(991\) | 46630.0 | 1.49470 | 0.747351 | − | 0.664429i | \(-0.231325\pi\) | ||||
0.747351 | + | 0.664429i | \(0.231325\pi\) | |||||||
\(992\) | 91354.3 | 2.92389 | ||||||||
\(993\) | 12518.5 | 0.400062 | ||||||||
\(994\) | 11948.2 | 0.381261 | ||||||||
\(995\) | −8290.35 | −0.264143 | ||||||||
\(996\) | 54752.0 | 1.74185 | ||||||||
\(997\) | 37175.5 | 1.18090 | 0.590452 | − | 0.807073i | \(-0.298950\pi\) | ||||
0.590452 | + | 0.807073i | \(0.298950\pi\) | |||||||
\(998\) | −31213.3 | −0.990021 | ||||||||
\(999\) | −2315.80 | −0.0733420 |
(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 | 507.4.a.p.1.9 | yes | 9 | |
3.2 | odd | 2 | 1521.4.a.bf.1.1 | 9 | |||
13.5 | odd | 4 | 507.4.b.k.337.1 | 18 | |||
13.8 | odd | 4 | 507.4.b.k.337.18 | 18 | |||
13.12 | even | 2 | 507.4.a.o.1.1 | ✓ | 9 | ||
39.38 | odd | 2 | 1521.4.a.bi.1.9 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.4.a.o.1.1 | ✓ | 9 | 13.12 | even | 2 | ||
507.4.a.p.1.9 | yes | 9 | 1.1 | even | 1 | trivial | |
507.4.b.k.337.1 | 18 | 13.5 | odd | 4 | |||
507.4.b.k.337.18 | 18 | 13.8 | odd | 4 | |||
1521.4.a.bf.1.1 | 9 | 3.2 | odd | 2 | |||
1521.4.a.bi.1.9 | 9 | 39.38 | odd | 2 |