Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2401,4,Mod(1,2401)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2401, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2401.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2401 = 7^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2401.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: | \(141.663585924\) |
Analytic rank: | \(1\) |
Dimension: | \(39\) |
Twist minimal: | no (minimal twist has level 49) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 2401.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.34611 | −1.53658 | −0.768292 | − | 0.640100i | \(-0.778893\pi\) | ||||
−0.768292 | + | 0.640100i | \(0.778893\pi\) | |||||||
\(3\) | 2.32971 | 0.448352 | 0.224176 | − | 0.974549i | \(-0.428031\pi\) | ||||
0.224176 | + | 0.974549i | \(0.428031\pi\) | |||||||
\(4\) | 10.8887 | 1.36109 | ||||||||
\(5\) | 2.24811 | 0.201077 | 0.100539 | − | 0.994933i | \(-0.467943\pi\) | ||||
0.100539 | + | 0.994933i | \(0.467943\pi\) | |||||||
\(6\) | −10.1252 | −0.688931 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −12.5546 | −0.554842 | ||||||||
\(9\) | −21.5725 | −0.798980 | ||||||||
\(10\) | −9.77055 | −0.308972 | ||||||||
\(11\) | −17.9888 | −0.493075 | −0.246538 | − | 0.969133i | \(-0.579293\pi\) | ||||
−0.246538 | + | 0.969133i | \(0.579293\pi\) | |||||||
\(12\) | 25.3675 | 0.610247 | ||||||||
\(13\) | −16.6689 | −0.355624 | −0.177812 | − | 0.984064i | \(-0.556902\pi\) | ||||
−0.177812 | + | 0.984064i | \(0.556902\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.23744 | 0.0901535 | ||||||||
\(16\) | −32.5457 | −0.508527 | ||||||||
\(17\) | 21.0084 | 0.299722 | 0.149861 | − | 0.988707i | \(-0.452117\pi\) | ||||
0.149861 | + | 0.988707i | \(0.452117\pi\) | |||||||
\(18\) | 93.7564 | 1.22770 | ||||||||
\(19\) | 74.5252 | 0.899856 | 0.449928 | − | 0.893065i | \(-0.351450\pi\) | ||||
0.449928 | + | 0.893065i | \(0.351450\pi\) | |||||||
\(20\) | 24.4790 | 0.273684 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 78.1814 | 0.757651 | ||||||||
\(23\) | −9.45614 | −0.0857278 | −0.0428639 | − | 0.999081i | \(-0.513648\pi\) | ||||
−0.0428639 | + | 0.999081i | \(0.513648\pi\) | |||||||
\(24\) | −29.2486 | −0.248765 | ||||||||
\(25\) | −119.946 | −0.959568 | ||||||||
\(26\) | 72.4448 | 0.546446 | ||||||||
\(27\) | −113.160 | −0.806577 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −146.445 | −0.937731 | −0.468866 | − | 0.883269i | \(-0.655337\pi\) | ||||
−0.468866 | + | 0.883269i | \(0.655337\pi\) | |||||||
\(30\) | −22.7625 | −0.138528 | ||||||||
\(31\) | 249.890 | 1.44779 | 0.723896 | − | 0.689909i | \(-0.242350\pi\) | ||||
0.723896 | + | 0.689909i | \(0.242350\pi\) | |||||||
\(32\) | 241.885 | 1.33624 | ||||||||
\(33\) | −41.9086 | −0.221071 | ||||||||
\(34\) | −91.3048 | −0.460548 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −234.896 | −1.08748 | ||||||||
\(37\) | −111.969 | −0.497501 | −0.248750 | − | 0.968568i | \(-0.580020\pi\) | ||||
−0.248750 | + | 0.968568i | \(0.580020\pi\) | |||||||
\(38\) | −323.895 | −1.38270 | ||||||||
\(39\) | −38.8336 | −0.159445 | ||||||||
\(40\) | −28.2243 | −0.111566 | ||||||||
\(41\) | 121.866 | 0.464200 | 0.232100 | − | 0.972692i | \(-0.425440\pi\) | ||||
0.232100 | + | 0.972692i | \(0.425440\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 325.998 | 1.15615 | 0.578073 | − | 0.815985i | \(-0.303805\pi\) | ||||
0.578073 | + | 0.815985i | \(0.303805\pi\) | |||||||
\(44\) | −195.875 | −0.671119 | ||||||||
\(45\) | −48.4973 | −0.160657 | ||||||||
\(46\) | 41.0974 | 0.131728 | ||||||||
\(47\) | 434.775 | 1.34933 | 0.674664 | − | 0.738125i | \(-0.264288\pi\) | ||||
0.674664 | + | 0.738125i | \(0.264288\pi\) | |||||||
\(48\) | −75.8220 | −0.227999 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 521.299 | 1.47446 | ||||||||
\(51\) | 48.9434 | 0.134381 | ||||||||
\(52\) | −181.502 | −0.484036 | ||||||||
\(53\) | 86.4205 | 0.223977 | 0.111988 | − | 0.993710i | \(-0.464278\pi\) | ||||
0.111988 | + | 0.993710i | \(0.464278\pi\) | |||||||
\(54\) | 491.804 | 1.23937 | ||||||||
\(55\) | −40.4409 | −0.0991463 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 173.622 | 0.403452 | ||||||||
\(58\) | 636.468 | 1.44090 | ||||||||
\(59\) | 572.886 | 1.26412 | 0.632062 | − | 0.774917i | \(-0.282209\pi\) | ||||
0.632062 | + | 0.774917i | \(0.282209\pi\) | |||||||
\(60\) | 57.0290 | 0.122707 | ||||||||
\(61\) | 84.8298 | 0.178055 | 0.0890274 | − | 0.996029i | \(-0.471624\pi\) | ||||
0.0890274 | + | 0.996029i | \(0.471624\pi\) | |||||||
\(62\) | −1086.05 | −2.22465 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −790.892 | −1.54471 | ||||||||
\(65\) | −37.4735 | −0.0715080 | ||||||||
\(66\) | 182.140 | 0.339695 | ||||||||
\(67\) | −25.3988 | −0.0463127 | −0.0231564 | − | 0.999732i | \(-0.507372\pi\) | ||||
−0.0231564 | + | 0.999732i | \(0.507372\pi\) | |||||||
\(68\) | 228.754 | 0.407949 | ||||||||
\(69\) | −22.0300 | −0.0384363 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1172.76 | −1.96030 | −0.980150 | − | 0.198255i | \(-0.936472\pi\) | ||||
−0.980150 | + | 0.198255i | \(0.936472\pi\) | |||||||
\(72\) | 270.835 | 0.443308 | ||||||||
\(73\) | 957.095 | 1.53451 | 0.767257 | − | 0.641340i | \(-0.221621\pi\) | ||||
0.767257 | + | 0.641340i | \(0.221621\pi\) | |||||||
\(74\) | 486.629 | 0.764452 | ||||||||
\(75\) | −279.439 | −0.430224 | ||||||||
\(76\) | 811.483 | 1.22478 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 168.775 | 0.245000 | ||||||||
\(79\) | 352.495 | 0.502010 | 0.251005 | − | 0.967986i | \(-0.419239\pi\) | ||||
0.251005 | + | 0.967986i | \(0.419239\pi\) | |||||||
\(80\) | −73.1665 | −0.102253 | ||||||||
\(81\) | 318.828 | 0.437350 | ||||||||
\(82\) | −529.641 | −0.713282 | ||||||||
\(83\) | −1307.72 | −1.72941 | −0.864707 | − | 0.502277i | \(-0.832496\pi\) | ||||
−0.864707 | + | 0.502277i | \(0.832496\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 47.2292 | 0.0602674 | ||||||||
\(86\) | −1416.83 | −1.77652 | ||||||||
\(87\) | −341.175 | −0.420434 | ||||||||
\(88\) | 225.843 | 0.273579 | ||||||||
\(89\) | 1201.77 | 1.43132 | 0.715660 | − | 0.698449i | \(-0.246126\pi\) | ||||
0.715660 | + | 0.698449i | \(0.246126\pi\) | |||||||
\(90\) | 210.775 | 0.246863 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −102.965 | −0.116683 | ||||||||
\(93\) | 582.170 | 0.649121 | ||||||||
\(94\) | −1889.58 | −2.07336 | ||||||||
\(95\) | 167.541 | 0.180941 | ||||||||
\(96\) | 563.520 | 0.599105 | ||||||||
\(97\) | −1434.34 | −1.50139 | −0.750697 | − | 0.660647i | \(-0.770282\pi\) | ||||
−0.750697 | + | 0.660647i | \(0.770282\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 388.063 | 0.393957 | ||||||||
\(100\) | −1306.06 | −1.30606 | ||||||||
\(101\) | −1609.75 | −1.58590 | −0.792949 | − | 0.609288i | \(-0.791455\pi\) | ||||
−0.792949 | + | 0.609288i | \(0.791455\pi\) | |||||||
\(102\) | −212.713 | −0.206488 | ||||||||
\(103\) | 41.4991 | 0.0396993 | 0.0198496 | − | 0.999803i | \(-0.493681\pi\) | ||||
0.0198496 | + | 0.999803i | \(0.493681\pi\) | |||||||
\(104\) | 209.272 | 0.197315 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −375.593 | −0.344159 | ||||||||
\(107\) | 1025.00 | 0.926083 | 0.463041 | − | 0.886337i | \(-0.346758\pi\) | ||||
0.463041 | + | 0.886337i | \(0.346758\pi\) | |||||||
\(108\) | −1232.16 | −1.09782 | ||||||||
\(109\) | −1031.80 | −0.906685 | −0.453342 | − | 0.891336i | \(-0.649769\pi\) | ||||
−0.453342 | + | 0.891336i | \(0.649769\pi\) | |||||||
\(110\) | 175.761 | 0.152346 | ||||||||
\(111\) | −260.854 | −0.223056 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 764.600 | 0.636527 | 0.318264 | − | 0.948002i | \(-0.396900\pi\) | ||||
0.318264 | + | 0.948002i | \(0.396900\pi\) | |||||||
\(114\) | −754.580 | −0.619938 | ||||||||
\(115\) | −21.2585 | −0.0172379 | ||||||||
\(116\) | −1594.60 | −1.27634 | ||||||||
\(117\) | 359.589 | 0.284137 | ||||||||
\(118\) | −2489.83 | −1.94243 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −65.7542 | −0.0500210 | ||||||||
\(121\) | −1007.40 | −0.756877 | ||||||||
\(122\) | −368.680 | −0.273596 | ||||||||
\(123\) | 283.911 | 0.208125 | ||||||||
\(124\) | 2720.98 | 1.97057 | ||||||||
\(125\) | −550.666 | −0.394025 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2381.49 | −1.66396 | −0.831980 | − | 0.554806i | \(-0.812792\pi\) | ||||
−0.831980 | + | 0.554806i | \(0.812792\pi\) | |||||||
\(128\) | 1502.23 | 1.03734 | ||||||||
\(129\) | 759.481 | 0.518361 | ||||||||
\(130\) | 162.864 | 0.109878 | ||||||||
\(131\) | 1771.25 | 1.18134 | 0.590668 | − | 0.806915i | \(-0.298864\pi\) | ||||
0.590668 | + | 0.806915i | \(0.298864\pi\) | |||||||
\(132\) | −456.331 | −0.300898 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 110.386 | 0.0711633 | ||||||||
\(135\) | −254.396 | −0.162184 | ||||||||
\(136\) | −263.753 | −0.166299 | ||||||||
\(137\) | −744.084 | −0.464025 | −0.232012 | − | 0.972713i | \(-0.574531\pi\) | ||||
−0.232012 | + | 0.972713i | \(0.574531\pi\) | |||||||
\(138\) | 95.7450 | 0.0590605 | ||||||||
\(139\) | 2853.92 | 1.74148 | 0.870742 | − | 0.491741i | \(-0.163639\pi\) | ||||
0.870742 | + | 0.491741i | \(0.163639\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1012.90 | 0.604975 | ||||||||
\(142\) | 5096.96 | 3.01217 | ||||||||
\(143\) | 299.853 | 0.175349 | ||||||||
\(144\) | 702.092 | 0.406303 | ||||||||
\(145\) | −329.226 | −0.188557 | ||||||||
\(146\) | −4159.64 | −2.35791 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1219.19 | −0.677143 | ||||||||
\(149\) | −3344.16 | −1.83869 | −0.919343 | − | 0.393457i | \(-0.871279\pi\) | ||||
−0.919343 | + | 0.393457i | \(0.871279\pi\) | |||||||
\(150\) | 1214.47 | 0.661076 | ||||||||
\(151\) | 1872.86 | 1.00934 | 0.504672 | − | 0.863311i | \(-0.331613\pi\) | ||||
0.504672 | + | 0.863311i | \(0.331613\pi\) | |||||||
\(152\) | −935.638 | −0.499278 | ||||||||
\(153\) | −453.203 | −0.239472 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 561.781 | 0.291118 | ||||||||
\(156\) | −422.847 | −0.217019 | ||||||||
\(157\) | −1498.57 | −0.761779 | −0.380889 | − | 0.924621i | \(-0.624382\pi\) | ||||
−0.380889 | + | 0.924621i | \(0.624382\pi\) | |||||||
\(158\) | −1531.98 | −0.771380 | ||||||||
\(159\) | 201.334 | 0.100420 | ||||||||
\(160\) | 543.784 | 0.268687 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1385.66 | −0.672024 | ||||||||
\(163\) | −2429.98 | −1.16767 | −0.583835 | − | 0.811872i | \(-0.698449\pi\) | ||||
−0.583835 | + | 0.811872i | \(0.698449\pi\) | |||||||
\(164\) | 1326.96 | 0.631817 | ||||||||
\(165\) | −94.2153 | −0.0444524 | ||||||||
\(166\) | 5683.52 | 2.65739 | ||||||||
\(167\) | 1097.74 | 0.508658 | 0.254329 | − | 0.967118i | \(-0.418145\pi\) | ||||
0.254329 | + | 0.967118i | \(0.418145\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1919.15 | −0.873531 | ||||||||
\(170\) | −205.264 | −0.0926059 | ||||||||
\(171\) | −1607.69 | −0.718967 | ||||||||
\(172\) | 3549.70 | 1.57362 | ||||||||
\(173\) | 893.115 | 0.392499 | 0.196249 | − | 0.980554i | \(-0.437124\pi\) | ||||
0.196249 | + | 0.980554i | \(0.437124\pi\) | |||||||
\(174\) | 1482.78 | 0.646032 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 585.459 | 0.250742 | ||||||||
\(177\) | 1334.66 | 0.566773 | ||||||||
\(178\) | −5223.04 | −2.19934 | ||||||||
\(179\) | −196.938 | −0.0822337 | −0.0411169 | − | 0.999154i | \(-0.513092\pi\) | ||||
−0.0411169 | + | 0.999154i | \(0.513092\pi\) | |||||||
\(180\) | −528.073 | −0.218668 | ||||||||
\(181\) | −798.131 | −0.327760 | −0.163880 | − | 0.986480i | \(-0.552401\pi\) | ||||
−0.163880 | + | 0.986480i | \(0.552401\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 197.629 | 0.0798313 | ||||||||
\(184\) | 118.718 | 0.0475654 | ||||||||
\(185\) | −251.718 | −0.100036 | ||||||||
\(186\) | −2530.18 | −0.997428 | ||||||||
\(187\) | −377.916 | −0.147786 | ||||||||
\(188\) | 4734.14 | 1.83656 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −728.153 | −0.278030 | ||||||||
\(191\) | 1707.50 | 0.646861 | 0.323431 | − | 0.946252i | \(-0.395164\pi\) | ||||
0.323431 | + | 0.946252i | \(0.395164\pi\) | |||||||
\(192\) | −1842.55 | −0.692575 | ||||||||
\(193\) | −3539.06 | −1.31993 | −0.659967 | − | 0.751294i | \(-0.729430\pi\) | ||||
−0.659967 | + | 0.751294i | \(0.729430\pi\) | |||||||
\(194\) | 6233.80 | 2.30702 | ||||||||
\(195\) | −87.3023 | −0.0320608 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −805.236 | −0.291222 | −0.145611 | − | 0.989342i | \(-0.546515\pi\) | ||||
−0.145611 | + | 0.989342i | \(0.546515\pi\) | |||||||
\(198\) | −1686.57 | −0.605348 | ||||||||
\(199\) | −143.693 | −0.0511867 | −0.0255933 | − | 0.999672i | \(-0.508148\pi\) | ||||
−0.0255933 | + | 0.999672i | \(0.508148\pi\) | |||||||
\(200\) | 1505.88 | 0.532409 | ||||||||
\(201\) | −59.1716 | −0.0207644 | ||||||||
\(202\) | 6996.14 | 2.43686 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 532.930 | 0.182905 | ||||||||
\(205\) | 273.967 | 0.0933401 | ||||||||
\(206\) | −180.360 | −0.0610012 | ||||||||
\(207\) | 203.992 | 0.0684949 | ||||||||
\(208\) | 542.501 | 0.180844 | ||||||||
\(209\) | −1340.62 | −0.443697 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2762.56 | 0.901340 | 0.450670 | − | 0.892691i | \(-0.351185\pi\) | ||||
0.450670 | + | 0.892691i | \(0.351185\pi\) | |||||||
\(212\) | 941.007 | 0.304852 | ||||||||
\(213\) | −2732.19 | −0.878905 | ||||||||
\(214\) | −4454.78 | −1.42300 | ||||||||
\(215\) | 732.881 | 0.232475 | ||||||||
\(216\) | 1420.68 | 0.447523 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4484.33 | 1.39320 | ||||||||
\(219\) | 2229.75 | 0.688003 | ||||||||
\(220\) | −440.349 | −0.134947 | ||||||||
\(221\) | −350.186 | −0.106589 | ||||||||
\(222\) | 1133.70 | 0.342744 | ||||||||
\(223\) | 4232.25 | 1.27091 | 0.635454 | − | 0.772138i | \(-0.280813\pi\) | ||||
0.635454 | + | 0.772138i | \(0.280813\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2587.53 | 0.766676 | ||||||||
\(226\) | −3323.04 | −0.978077 | ||||||||
\(227\) | −880.898 | −0.257565 | −0.128783 | − | 0.991673i | \(-0.541107\pi\) | ||||
−0.128783 | + | 0.991673i | \(0.541107\pi\) | |||||||
\(228\) | 1890.52 | 0.549134 | ||||||||
\(229\) | 1622.26 | 0.468131 | 0.234065 | − | 0.972221i | \(-0.424797\pi\) | ||||
0.234065 | + | 0.972221i | \(0.424797\pi\) | |||||||
\(230\) | 92.3917 | 0.0264875 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1838.57 | 0.520293 | ||||||||
\(233\) | −3926.05 | −1.10388 | −0.551940 | − | 0.833884i | \(-0.686112\pi\) | ||||
−0.551940 | + | 0.833884i | \(0.686112\pi\) | |||||||
\(234\) | −1562.81 | −0.436600 | ||||||||
\(235\) | 977.423 | 0.271319 | ||||||||
\(236\) | 6237.98 | 1.72059 | ||||||||
\(237\) | 821.209 | 0.225077 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3458.66 | −0.936077 | −0.468038 | − | 0.883708i | \(-0.655039\pi\) | ||||
−0.468038 | + | 0.883708i | \(0.655039\pi\) | |||||||
\(240\) | −170.456 | −0.0458455 | ||||||||
\(241\) | 4466.02 | 1.19370 | 0.596850 | − | 0.802353i | \(-0.296419\pi\) | ||||
0.596850 | + | 0.802353i | \(0.296419\pi\) | |||||||
\(242\) | 4378.29 | 1.16300 | ||||||||
\(243\) | 3798.08 | 1.00266 | ||||||||
\(244\) | 923.687 | 0.242348 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1233.91 | −0.319802 | ||||||||
\(247\) | −1242.25 | −0.320010 | ||||||||
\(248\) | −3137.28 | −0.803296 | ||||||||
\(249\) | −3046.61 | −0.775387 | ||||||||
\(250\) | 2393.26 | 0.605452 | ||||||||
\(251\) | 2978.25 | 0.748947 | 0.374473 | − | 0.927238i | \(-0.377824\pi\) | ||||
0.374473 | + | 0.927238i | \(0.377824\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 170.105 | 0.0422703 | ||||||||
\(254\) | 10350.2 | 2.55681 | ||||||||
\(255\) | 110.030 | 0.0270210 | ||||||||
\(256\) | −201.729 | −0.0492502 | ||||||||
\(257\) | −4278.07 | −1.03836 | −0.519180 | − | 0.854665i | \(-0.673763\pi\) | ||||
−0.519180 | + | 0.854665i | \(0.673763\pi\) | |||||||
\(258\) | −3300.79 | −0.796505 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −408.038 | −0.0973286 | ||||||||
\(261\) | 3159.19 | 0.749229 | ||||||||
\(262\) | −7698.06 | −1.81522 | ||||||||
\(263\) | −601.979 | −0.141139 | −0.0705696 | − | 0.997507i | \(-0.522482\pi\) | ||||
−0.0705696 | + | 0.997507i | \(0.522482\pi\) | |||||||
\(264\) | 526.148 | 0.122660 | ||||||||
\(265\) | 194.283 | 0.0450366 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2799.77 | 0.641736 | ||||||||
\(268\) | −276.560 | −0.0630357 | ||||||||
\(269\) | −7920.85 | −1.79533 | −0.897663 | − | 0.440682i | \(-0.854737\pi\) | ||||
−0.897663 | + | 0.440682i | \(0.854737\pi\) | |||||||
\(270\) | 1105.63 | 0.249210 | ||||||||
\(271\) | 4473.92 | 1.00285 | 0.501423 | − | 0.865202i | \(-0.332810\pi\) | ||||
0.501423 | + | 0.865202i | \(0.332810\pi\) | |||||||
\(272\) | −683.733 | −0.152417 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3233.87 | 0.713013 | ||||||||
\(275\) | 2157.68 | 0.473139 | ||||||||
\(276\) | −239.878 | −0.0523152 | ||||||||
\(277\) | −1656.22 | −0.359251 | −0.179625 | − | 0.983735i | \(-0.557489\pi\) | ||||
−0.179625 | + | 0.983735i | \(0.557489\pi\) | |||||||
\(278\) | −12403.5 | −2.67593 | ||||||||
\(279\) | −5390.74 | −1.15676 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3481.30 | −0.739063 | −0.369532 | − | 0.929218i | \(-0.620482\pi\) | ||||
−0.369532 | + | 0.929218i | \(0.620482\pi\) | |||||||
\(282\) | −4402.17 | −0.929594 | ||||||||
\(283\) | 7363.19 | 1.54663 | 0.773314 | − | 0.634023i | \(-0.218597\pi\) | ||||
0.773314 | + | 0.634023i | \(0.218597\pi\) | |||||||
\(284\) | −12769.9 | −2.66814 | ||||||||
\(285\) | 390.322 | 0.0811251 | ||||||||
\(286\) | −1303.20 | −0.269439 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −5218.05 | −1.06763 | ||||||||
\(289\) | −4471.65 | −0.910166 | ||||||||
\(290\) | 1430.85 | 0.289733 | ||||||||
\(291\) | −3341.59 | −0.673153 | ||||||||
\(292\) | 10421.5 | 2.08861 | ||||||||
\(293\) | −1440.22 | −0.287162 | −0.143581 | − | 0.989639i | \(-0.545862\pi\) | ||||
−0.143581 | + | 0.989639i | \(0.545862\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1287.91 | 0.254187 | ||||||||
\(296\) | 1405.73 | 0.276035 | ||||||||
\(297\) | 2035.61 | 0.397703 | ||||||||
\(298\) | 14534.1 | 2.82529 | ||||||||
\(299\) | 157.623 | 0.0304869 | ||||||||
\(300\) | −3042.73 | −0.585573 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −8139.65 | −1.55094 | ||||||||
\(303\) | −3750.24 | −0.711041 | ||||||||
\(304\) | −2425.48 | −0.457601 | ||||||||
\(305\) | 190.707 | 0.0358028 | ||||||||
\(306\) | 1969.67 | 0.367969 | ||||||||
\(307\) | 561.058 | 0.104304 | 0.0521519 | − | 0.998639i | \(-0.483392\pi\) | ||||
0.0521519 | + | 0.998639i | \(0.483392\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 96.6806 | 0.0177993 | ||||||||
\(310\) | −2441.56 | −0.447327 | ||||||||
\(311\) | −3641.23 | −0.663908 | −0.331954 | − | 0.943296i | \(-0.607708\pi\) | ||||
−0.331954 | + | 0.943296i | \(0.607708\pi\) | |||||||
\(312\) | 487.542 | 0.0884668 | ||||||||
\(313\) | 8474.44 | 1.53036 | 0.765182 | − | 0.643815i | \(-0.222649\pi\) | ||||
0.765182 | + | 0.643815i | \(0.222649\pi\) | |||||||
\(314\) | 6512.98 | 1.17054 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3838.21 | 0.683279 | ||||||||
\(317\) | −661.990 | −0.117290 | −0.0586452 | − | 0.998279i | \(-0.518678\pi\) | ||||
−0.0586452 | + | 0.998279i | \(0.518678\pi\) | |||||||
\(318\) | −875.022 | −0.154304 | ||||||||
\(319\) | 2634.38 | 0.462372 | ||||||||
\(320\) | −1778.02 | −0.310606 | ||||||||
\(321\) | 2387.96 | 0.415211 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1565.65 | 0.269707 | ||||||||
\(324\) | 3471.62 | 0.595272 | ||||||||
\(325\) | 1999.36 | 0.341246 | ||||||||
\(326\) | 10560.9 | 1.79422 | ||||||||
\(327\) | −2403.79 | −0.406514 | ||||||||
\(328\) | −1529.98 | −0.257558 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 409.471 | 0.0683049 | ||||||||
\(331\) | 2857.55 | 0.474517 | 0.237258 | − | 0.971447i | \(-0.423751\pi\) | ||||
0.237258 | + | 0.971447i | \(0.423751\pi\) | |||||||
\(332\) | −14239.4 | −2.35389 | ||||||||
\(333\) | 2415.44 | 0.397493 | ||||||||
\(334\) | −4770.91 | −0.781595 | ||||||||
\(335\) | −57.0993 | −0.00931244 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2053.91 | 0.331998 | 0.165999 | − | 0.986126i | \(-0.446915\pi\) | ||||
0.165999 | + | 0.986126i | \(0.446915\pi\) | |||||||
\(338\) | 8340.84 | 1.34225 | ||||||||
\(339\) | 1781.29 | 0.285388 | ||||||||
\(340\) | 514.265 | 0.0820292 | ||||||||
\(341\) | −4495.22 | −0.713870 | ||||||||
\(342\) | 6987.22 | 1.10475 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −4092.79 | −0.641479 | ||||||||
\(345\) | −49.5260 | −0.00772866 | ||||||||
\(346\) | −3881.58 | −0.603107 | ||||||||
\(347\) | 4806.99 | 0.743669 | 0.371834 | − | 0.928299i | \(-0.378729\pi\) | ||||
0.371834 | + | 0.928299i | \(0.378729\pi\) | |||||||
\(348\) | −3714.95 | −0.572248 | ||||||||
\(349\) | −785.561 | −0.120487 | −0.0602437 | − | 0.998184i | \(-0.519188\pi\) | ||||
−0.0602437 | + | 0.998184i | \(0.519188\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1886.24 | 0.286838 | ||||||||
\(352\) | −4351.21 | −0.658865 | ||||||||
\(353\) | −4340.98 | −0.654524 | −0.327262 | − | 0.944934i | \(-0.606126\pi\) | ||||
−0.327262 | + | 0.944934i | \(0.606126\pi\) | |||||||
\(354\) | −5800.57 | −0.870894 | ||||||||
\(355\) | −2636.50 | −0.394172 | ||||||||
\(356\) | 13085.7 | 1.94815 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 855.915 | 0.126359 | ||||||||
\(359\) | −3640.84 | −0.535254 | −0.267627 | − | 0.963523i | \(-0.586239\pi\) | ||||
−0.267627 | + | 0.963523i | \(0.586239\pi\) | |||||||
\(360\) | 608.867 | 0.0891392 | ||||||||
\(361\) | −1304.99 | −0.190260 | ||||||||
\(362\) | 3468.77 | 0.503631 | ||||||||
\(363\) | −2346.95 | −0.339347 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2151.66 | 0.308556 | ||||||||
\(366\) | −858.916 | −0.122667 | ||||||||
\(367\) | −4305.91 | −0.612444 | −0.306222 | − | 0.951960i | \(-0.599065\pi\) | ||||
−0.306222 | + | 0.951960i | \(0.599065\pi\) | |||||||
\(368\) | 307.757 | 0.0435949 | ||||||||
\(369\) | −2628.94 | −0.370887 | ||||||||
\(370\) | 1094.00 | 0.153714 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 6339.08 | 0.883510 | ||||||||
\(373\) | 4904.40 | 0.680805 | 0.340403 | − | 0.940280i | \(-0.389437\pi\) | ||||
0.340403 | + | 0.940280i | \(0.389437\pi\) | |||||||
\(374\) | 1642.46 | 0.227085 | ||||||||
\(375\) | −1282.89 | −0.176662 | ||||||||
\(376\) | −5458.45 | −0.748665 | ||||||||
\(377\) | 2441.08 | 0.333480 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4748.66 | −0.643594 | −0.321797 | − | 0.946809i | \(-0.604287\pi\) | ||||
−0.321797 | + | 0.946809i | \(0.604287\pi\) | |||||||
\(380\) | 1824.31 | 0.246276 | ||||||||
\(381\) | −5548.17 | −0.746040 | ||||||||
\(382\) | −7421.00 | −0.993956 | ||||||||
\(383\) | −5520.26 | −0.736481 | −0.368240 | − | 0.929731i | \(-0.620040\pi\) | ||||
−0.368240 | + | 0.929731i | \(0.620040\pi\) | |||||||
\(384\) | 3499.76 | 0.465094 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 15381.2 | 2.02819 | ||||||||
\(387\) | −7032.59 | −0.923738 | ||||||||
\(388\) | −15618.1 | −2.04353 | ||||||||
\(389\) | 11831.2 | 1.54207 | 0.771034 | − | 0.636794i | \(-0.219740\pi\) | ||||
0.771034 | + | 0.636794i | \(0.219740\pi\) | |||||||
\(390\) | 379.426 | 0.0492640 | ||||||||
\(391\) | −198.658 | −0.0256946 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4126.50 | 0.529654 | ||||||||
\(394\) | 3499.65 | 0.447487 | ||||||||
\(395\) | 792.448 | 0.100943 | ||||||||
\(396\) | 4225.50 | 0.536211 | ||||||||
\(397\) | −5923.53 | −0.748849 | −0.374425 | − | 0.927257i | \(-0.622160\pi\) | ||||
−0.374425 | + | 0.927257i | \(0.622160\pi\) | |||||||
\(398\) | 624.508 | 0.0786526 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3903.73 | 0.487966 | ||||||||
\(401\) | 3689.81 | 0.459502 | 0.229751 | − | 0.973249i | \(-0.426209\pi\) | ||||
0.229751 | + | 0.973249i | \(0.426209\pi\) | |||||||
\(402\) | 257.167 | 0.0319062 | ||||||||
\(403\) | −4165.38 | −0.514870 | ||||||||
\(404\) | −17528.1 | −2.15855 | ||||||||
\(405\) | 716.761 | 0.0879411 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2014.18 | 0.245305 | ||||||||
\(408\) | −614.467 | −0.0745604 | ||||||||
\(409\) | 551.712 | 0.0667002 | 0.0333501 | − | 0.999444i | \(-0.489382\pi\) | ||||
0.0333501 | + | 0.999444i | \(0.489382\pi\) | |||||||
\(410\) | −1190.69 | −0.143425 | ||||||||
\(411\) | −1733.50 | −0.208047 | ||||||||
\(412\) | 451.871 | 0.0540342 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −886.573 | −0.105248 | ||||||||
\(415\) | −2939.91 | −0.347746 | ||||||||
\(416\) | −4031.94 | −0.475198 | ||||||||
\(417\) | 6648.79 | 0.780798 | ||||||||
\(418\) | 5826.48 | 0.681777 | ||||||||
\(419\) | −13584.8 | −1.58391 | −0.791955 | − | 0.610579i | \(-0.790937\pi\) | ||||
−0.791955 | + | 0.610579i | \(0.790937\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14750.9 | −1.70764 | −0.853820 | − | 0.520569i | \(-0.825720\pi\) | ||||
−0.853820 | + | 0.520569i | \(0.825720\pi\) | |||||||
\(422\) | −12006.4 | −1.38498 | ||||||||
\(423\) | −9379.17 | −1.07809 | ||||||||
\(424\) | −1084.98 | −0.124272 | ||||||||
\(425\) | −2519.87 | −0.287604 | ||||||||
\(426\) | 11874.4 | 1.35051 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 11161.0 | 1.26048 | ||||||||
\(429\) | 698.570 | 0.0786183 | ||||||||
\(430\) | −3185.19 | −0.357217 | ||||||||
\(431\) | −8917.00 | −0.996559 | −0.498280 | − | 0.867016i | \(-0.666035\pi\) | ||||
−0.498280 | + | 0.867016i | \(0.666035\pi\) | |||||||
\(432\) | 3682.86 | 0.410166 | ||||||||
\(433\) | −13038.4 | −1.44708 | −0.723541 | − | 0.690281i | \(-0.757487\pi\) | ||||
−0.723541 | + | 0.690281i | \(0.757487\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −766.999 | −0.0845397 | ||||||||
\(436\) | −11235.0 | −1.23408 | ||||||||
\(437\) | −704.721 | −0.0771427 | ||||||||
\(438\) | −9690.75 | −1.05717 | ||||||||
\(439\) | −407.776 | −0.0443328 | −0.0221664 | − | 0.999754i | \(-0.507056\pi\) | ||||
−0.0221664 | + | 0.999754i | \(0.507056\pi\) | |||||||
\(440\) | 507.721 | 0.0550105 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1521.95 | 0.163782 | ||||||||
\(443\) | 6603.65 | 0.708237 | 0.354119 | − | 0.935201i | \(-0.384781\pi\) | ||||
0.354119 | + | 0.935201i | \(0.384781\pi\) | |||||||
\(444\) | −2840.36 | −0.303598 | ||||||||
\(445\) | 2701.72 | 0.287806 | ||||||||
\(446\) | −18393.9 | −1.95286 | ||||||||
\(447\) | −7790.91 | −0.824379 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3047.11 | 0.320272 | 0.160136 | − | 0.987095i | \(-0.448807\pi\) | ||||
0.160136 | + | 0.987095i | \(0.448807\pi\) | |||||||
\(450\) | −11245.7 | −1.17806 | ||||||||
\(451\) | −2192.21 | −0.228886 | ||||||||
\(452\) | 8325.51 | 0.866369 | ||||||||
\(453\) | 4363.21 | 0.452542 | ||||||||
\(454\) | 3828.48 | 0.395770 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2179.76 | −0.223852 | ||||||||
\(457\) | 8839.77 | 0.904829 | 0.452415 | − | 0.891808i | \(-0.350563\pi\) | ||||
0.452415 | + | 0.891808i | \(0.350563\pi\) | |||||||
\(458\) | −7050.53 | −0.719322 | ||||||||
\(459\) | −2377.30 | −0.241749 | ||||||||
\(460\) | −231.477 | −0.0234623 | ||||||||
\(461\) | −9929.15 | −1.00314 | −0.501569 | − | 0.865118i | \(-0.667244\pi\) | ||||
−0.501569 | + | 0.865118i | \(0.667244\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15165.6 | −1.52225 | −0.761127 | − | 0.648603i | \(-0.775354\pi\) | ||||
−0.761127 | + | 0.648603i | \(0.775354\pi\) | |||||||
\(464\) | 4766.17 | 0.476862 | ||||||||
\(465\) | 1308.78 | 0.130523 | ||||||||
\(466\) | 17063.1 | 1.69620 | ||||||||
\(467\) | −13652.8 | −1.35284 | −0.676421 | − | 0.736515i | \(-0.736470\pi\) | ||||
−0.676421 | + | 0.736515i | \(0.736470\pi\) | |||||||
\(468\) | 3915.46 | 0.386735 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −4247.99 | −0.416905 | ||||||||
\(471\) | −3491.24 | −0.341545 | ||||||||
\(472\) | −7192.38 | −0.701390 | ||||||||
\(473\) | −5864.32 | −0.570067 | ||||||||
\(474\) | −3569.07 | −0.345850 | ||||||||
\(475\) | −8939.00 | −0.863473 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1864.30 | −0.178953 | ||||||||
\(478\) | 15031.7 | 1.43836 | ||||||||
\(479\) | 9267.83 | 0.884046 | 0.442023 | − | 0.897004i | \(-0.354261\pi\) | ||||
0.442023 | + | 0.897004i | \(0.354261\pi\) | |||||||
\(480\) | 1266.86 | 0.120466 | ||||||||
\(481\) | 1866.39 | 0.176923 | ||||||||
\(482\) | −19409.8 | −1.83422 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10969.3 | −1.03018 | ||||||||
\(485\) | −3224.56 | −0.301896 | ||||||||
\(486\) | −16506.9 | −1.54068 | ||||||||
\(487\) | −4135.09 | −0.384762 | −0.192381 | − | 0.981320i | \(-0.561621\pi\) | ||||
−0.192381 | + | 0.981320i | \(0.561621\pi\) | |||||||
\(488\) | −1065.01 | −0.0987924 | ||||||||
\(489\) | −5661.13 | −0.523528 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4511.68 | 0.414683 | 0.207342 | − | 0.978269i | \(-0.433519\pi\) | ||||
0.207342 | + | 0.978269i | \(0.433519\pi\) | |||||||
\(492\) | 3091.42 | 0.283277 | ||||||||
\(493\) | −3076.58 | −0.281059 | ||||||||
\(494\) | 5398.97 | 0.491723 | ||||||||
\(495\) | 872.409 | 0.0792159 | ||||||||
\(496\) | −8132.85 | −0.736241 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 13240.9 | 1.19145 | ||||||||
\(499\) | −14416.5 | −1.29332 | −0.646662 | − | 0.762776i | \(-0.723836\pi\) | ||||
−0.646662 | + | 0.762776i | \(0.723836\pi\) | |||||||
\(500\) | −5996.04 | −0.536302 | ||||||||
\(501\) | 2557.42 | 0.228058 | ||||||||
\(502\) | −12943.8 | −1.15082 | ||||||||
\(503\) | −16181.4 | −1.43438 | −0.717188 | − | 0.696880i | \(-0.754571\pi\) | ||||
−0.717188 | + | 0.696880i | \(0.754571\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3618.89 | −0.318888 | ||||||||
\(506\) | −739.294 | −0.0649518 | ||||||||
\(507\) | −4471.05 | −0.391650 | ||||||||
\(508\) | −25931.3 | −2.26480 | ||||||||
\(509\) | −15301.3 | −1.33245 | −0.666227 | − | 0.745749i | \(-0.732092\pi\) | ||||
−0.666227 | + | 0.745749i | \(0.732092\pi\) | |||||||
\(510\) | −478.204 | −0.0415200 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −11141.1 | −0.961664 | ||||||||
\(513\) | −8433.24 | −0.725803 | ||||||||
\(514\) | 18593.0 | 1.59553 | ||||||||
\(515\) | 93.2946 | 0.00798262 | ||||||||
\(516\) | 8269.76 | 0.705535 | ||||||||
\(517\) | −7821.08 | −0.665321 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2080.70 | 0.175978 | ||||||||
\(520\) | 470.467 | 0.0396756 | ||||||||
\(521\) | −3639.78 | −0.306069 | −0.153034 | − | 0.988221i | \(-0.548905\pi\) | ||||
−0.153034 | + | 0.988221i | \(0.548905\pi\) | |||||||
\(522\) | −13730.2 | −1.15125 | ||||||||
\(523\) | −21163.1 | −1.76940 | −0.884700 | − | 0.466160i | \(-0.845637\pi\) | ||||
−0.884700 | + | 0.466160i | \(0.845637\pi\) | |||||||
\(524\) | 19286.6 | 1.60790 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2616.27 | 0.216872 | ||||||||
\(527\) | 5249.78 | 0.433936 | ||||||||
\(528\) | 1363.95 | 0.112421 | ||||||||
\(529\) | −12077.6 | −0.992651 | ||||||||
\(530\) | −844.376 | −0.0692026 | ||||||||
\(531\) | −12358.6 | −1.01001 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2031.36 | −0.165081 | ||||||||
\(534\) | −12168.1 | −0.986080 | ||||||||
\(535\) | 2304.32 | 0.186214 | ||||||||
\(536\) | 318.872 | 0.0256962 | ||||||||
\(537\) | −458.808 | −0.0368697 | ||||||||
\(538\) | 34424.9 | 2.75867 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2770.04 | −0.220747 | ||||||||
\(541\) | 20129.7 | 1.59971 | 0.799855 | − | 0.600193i | \(-0.204910\pi\) | ||||
0.799855 | + | 0.600193i | \(0.204910\pi\) | |||||||
\(542\) | −19444.2 | −1.54096 | ||||||||
\(543\) | −1859.41 | −0.146952 | ||||||||
\(544\) | 5081.60 | 0.400500 | ||||||||
\(545\) | −2319.61 | −0.182314 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15914.9 | 1.24401 | 0.622003 | − | 0.783015i | \(-0.286319\pi\) | ||||
0.622003 | + | 0.783015i | \(0.286319\pi\) | |||||||
\(548\) | −8102.11 | −0.631579 | ||||||||
\(549\) | −1829.99 | −0.142262 | ||||||||
\(550\) | −9377.54 | −0.727018 | ||||||||
\(551\) | −10913.9 | −0.843823 | ||||||||
\(552\) | 276.579 | 0.0213261 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 7198.11 | 0.552019 | ||||||||
\(555\) | −586.430 | −0.0448514 | ||||||||
\(556\) | 31075.5 | 2.37031 | ||||||||
\(557\) | −5577.43 | −0.424279 | −0.212139 | − | 0.977239i | \(-0.568043\pi\) | ||||
−0.212139 | + | 0.977239i | \(0.568043\pi\) | |||||||
\(558\) | 23428.8 | 1.77745 | ||||||||
\(559\) | −5434.03 | −0.411154 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −880.433 | −0.0662601 | ||||||||
\(562\) | 15130.1 | 1.13563 | ||||||||
\(563\) | 11272.1 | 0.843809 | 0.421904 | − | 0.906640i | \(-0.361362\pi\) | ||||
0.421904 | + | 0.906640i | \(0.361362\pi\) | |||||||
\(564\) | 11029.2 | 0.823424 | ||||||||
\(565\) | 1718.91 | 0.127991 | ||||||||
\(566\) | −32001.2 | −2.37652 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 14723.6 | 1.08766 | ||||||||
\(569\) | −15667.9 | −1.15437 | −0.577183 | − | 0.816615i | \(-0.695848\pi\) | ||||
−0.577183 | + | 0.816615i | \(0.695848\pi\) | |||||||
\(570\) | −1696.38 | −0.124655 | ||||||||
\(571\) | 15747.6 | 1.15415 | 0.577073 | − | 0.816692i | \(-0.304195\pi\) | ||||
0.577073 | + | 0.816692i | \(0.304195\pi\) | |||||||
\(572\) | 3265.01 | 0.238666 | ||||||||
\(573\) | 3977.98 | 0.290022 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1134.23 | 0.0822617 | ||||||||
\(576\) | 17061.5 | 1.23419 | ||||||||
\(577\) | 5393.16 | 0.389116 | 0.194558 | − | 0.980891i | \(-0.437673\pi\) | ||||
0.194558 | + | 0.980891i | \(0.437673\pi\) | |||||||
\(578\) | 19434.3 | 1.39855 | ||||||||
\(579\) | −8244.98 | −0.591796 | ||||||||
\(580\) | −3584.84 | −0.256642 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 14522.9 | 1.03436 | ||||||||
\(583\) | −1554.60 | −0.110437 | ||||||||
\(584\) | −12016.0 | −0.851413 | ||||||||
\(585\) | 808.396 | 0.0571334 | ||||||||
\(586\) | 6259.35 | 0.441248 | ||||||||
\(587\) | −12745.0 | −0.896157 | −0.448078 | − | 0.893994i | \(-0.647891\pi\) | ||||
−0.448078 | + | 0.893994i | \(0.647891\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18623.1 | 1.30280 | ||||||||
\(590\) | −5597.41 | −0.390579 | ||||||||
\(591\) | −1875.96 | −0.130570 | ||||||||
\(592\) | 3644.10 | 0.252993 | ||||||||
\(593\) | −12151.4 | −0.841483 | −0.420741 | − | 0.907181i | \(-0.638230\pi\) | ||||
−0.420741 | + | 0.907181i | \(0.638230\pi\) | |||||||
\(594\) | −8846.97 | −0.611104 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −36413.6 | −2.50261 | ||||||||
\(597\) | −334.763 | −0.0229497 | ||||||||
\(598\) | −685.048 | −0.0468457 | ||||||||
\(599\) | −4620.70 | −0.315186 | −0.157593 | − | 0.987504i | \(-0.550373\pi\) | ||||
−0.157593 | + | 0.987504i | \(0.550373\pi\) | |||||||
\(600\) | 3508.26 | 0.238707 | ||||||||
\(601\) | 19257.6 | 1.30704 | 0.653522 | − | 0.756908i | \(-0.273291\pi\) | ||||
0.653522 | + | 0.756908i | \(0.273291\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 547.914 | 0.0370029 | ||||||||
\(604\) | 20393.0 | 1.37381 | ||||||||
\(605\) | −2264.76 | −0.152191 | ||||||||
\(606\) | 16299.0 | 1.09257 | ||||||||
\(607\) | −10802.5 | −0.722342 | −0.361171 | − | 0.932500i | \(-0.617623\pi\) | ||||
−0.361171 | + | 0.932500i | \(0.617623\pi\) | |||||||
\(608\) | 18026.5 | 1.20242 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −828.834 | −0.0550140 | ||||||||
\(611\) | −7247.21 | −0.479854 | ||||||||
\(612\) | −4934.79 | −0.325943 | ||||||||
\(613\) | −23434.5 | −1.54406 | −0.772030 | − | 0.635586i | \(-0.780759\pi\) | ||||
−0.772030 | + | 0.635586i | \(0.780759\pi\) | |||||||
\(614\) | −2438.42 | −0.160271 | ||||||||
\(615\) | 638.264 | 0.0418492 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25636.7 | −1.67276 | −0.836380 | − | 0.548149i | \(-0.815333\pi\) | ||||
−0.836380 | + | 0.548149i | \(0.815333\pi\) | |||||||
\(618\) | −420.185 | −0.0273500 | ||||||||
\(619\) | 9673.75 | 0.628144 | 0.314072 | − | 0.949399i | \(-0.398307\pi\) | ||||
0.314072 | + | 0.949399i | \(0.398307\pi\) | |||||||
\(620\) | 6117.06 | 0.396237 | ||||||||
\(621\) | 1070.05 | 0.0691461 | ||||||||
\(622\) | 15825.2 | 1.02015 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1263.87 | 0.0810820 | ||||||||
\(625\) | 13755.3 | 0.880338 | ||||||||
\(626\) | −36830.9 | −2.35153 | ||||||||
\(627\) | −3123.25 | −0.198932 | ||||||||
\(628\) | −16317.5 | −1.03685 | ||||||||
\(629\) | −2352.28 | −0.149112 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14878.8 | 0.938694 | 0.469347 | − | 0.883014i | \(-0.344489\pi\) | ||||
0.469347 | + | 0.883014i | \(0.344489\pi\) | |||||||
\(632\) | −4425.45 | −0.278536 | ||||||||
\(633\) | 6435.96 | 0.404118 | ||||||||
\(634\) | 2877.08 | 0.180227 | ||||||||
\(635\) | −5353.85 | −0.334585 | ||||||||
\(636\) | 2192.27 | 0.136681 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −11449.3 | −0.710473 | ||||||||
\(639\) | 25299.4 | 1.56624 | ||||||||
\(640\) | 3377.18 | 0.208586 | ||||||||
\(641\) | −21274.3 | −1.31089 | −0.655447 | − | 0.755241i | \(-0.727520\pi\) | ||||
−0.655447 | + | 0.755241i | \(0.727520\pi\) | |||||||
\(642\) | −10378.3 | −0.638007 | ||||||||
\(643\) | −30347.4 | −1.86125 | −0.930627 | − | 0.365969i | \(-0.880738\pi\) | ||||
−0.930627 | + | 0.365969i | \(0.880738\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1707.40 | 0.104231 | ||||||||
\(646\) | −6804.51 | −0.414427 | ||||||||
\(647\) | 3556.80 | 0.216124 | 0.108062 | − | 0.994144i | \(-0.465536\pi\) | ||||
0.108062 | + | 0.994144i | \(0.465536\pi\) | |||||||
\(648\) | −4002.77 | −0.242660 | ||||||||
\(649\) | −10305.5 | −0.623309 | ||||||||
\(650\) | −8689.47 | −0.524352 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −26459.3 | −1.58930 | ||||||||
\(653\) | 3633.28 | 0.217736 | 0.108868 | − | 0.994056i | \(-0.465277\pi\) | ||||
0.108868 | + | 0.994056i | \(0.465277\pi\) | |||||||
\(654\) | 10447.2 | 0.624643 | ||||||||
\(655\) | 3981.97 | 0.237540 | ||||||||
\(656\) | −3966.20 | −0.236058 | ||||||||
\(657\) | −20646.9 | −1.22605 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5559.27 | −0.328617 | −0.164308 | − | 0.986409i | \(-0.552539\pi\) | ||||
−0.164308 | + | 0.986409i | \(0.552539\pi\) | |||||||
\(660\) | −1025.88 | −0.0605037 | ||||||||
\(661\) | −29787.5 | −1.75280 | −0.876399 | − | 0.481586i | \(-0.840061\pi\) | ||||
−0.876399 | + | 0.481586i | \(0.840061\pi\) | |||||||
\(662\) | −12419.2 | −0.729135 | ||||||||
\(663\) | −815.831 | −0.0477892 | ||||||||
\(664\) | 16418.0 | 0.959552 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −10497.8 | −0.610782 | ||||||||
\(667\) | 1384.81 | 0.0803897 | ||||||||
\(668\) | 11953.0 | 0.692328 | ||||||||
\(669\) | 9859.91 | 0.569815 | ||||||||
\(670\) | 248.160 | 0.0143093 | ||||||||
\(671\) | −1525.99 | −0.0877944 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19124.8 | −1.09540 | −0.547702 | − | 0.836673i | \(-0.684497\pi\) | ||||
−0.547702 | + | 0.836673i | \(0.684497\pi\) | |||||||
\(674\) | −8926.51 | −0.510143 | ||||||||
\(675\) | 13573.0 | 0.773965 | ||||||||
\(676\) | −20897.0 | −1.18895 | ||||||||
\(677\) | 2966.75 | 0.168421 | 0.0842107 | − | 0.996448i | \(-0.473163\pi\) | ||||
0.0842107 | + | 0.996448i | \(0.473163\pi\) | |||||||
\(678\) | −7741.71 | −0.438523 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −592.946 | −0.0334389 | ||||||||
\(681\) | −2052.23 | −0.115480 | ||||||||
\(682\) | 19536.7 | 1.09692 | ||||||||
\(683\) | −11936.7 | −0.668736 | −0.334368 | − | 0.942443i | \(-0.608523\pi\) | ||||
−0.334368 | + | 0.942443i | \(0.608523\pi\) | |||||||
\(684\) | −17505.7 | −0.978577 | ||||||||
\(685\) | −1672.78 | −0.0933049 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3779.39 | 0.209887 | ||||||||
\(688\) | −10609.9 | −0.587932 | ||||||||
\(689\) | −1440.53 | −0.0796515 | ||||||||
\(690\) | 215.246 | 0.0118757 | ||||||||
\(691\) | 10447.6 | 0.575174 | 0.287587 | − | 0.957754i | \(-0.407147\pi\) | ||||
0.287587 | + | 0.957754i | \(0.407147\pi\) | |||||||
\(692\) | 9724.86 | 0.534225 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −20891.7 | −1.14271 | ||||||||
\(695\) | 6415.93 | 0.350173 | ||||||||
\(696\) | 4283.33 | 0.233275 | ||||||||
\(697\) | 2560.20 | 0.139131 | ||||||||
\(698\) | 3414.14 | 0.185139 | ||||||||
\(699\) | −9146.55 | −0.494927 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1573.42 | 0.0847748 | 0.0423874 | − | 0.999101i | \(-0.486504\pi\) | ||||
0.0423874 | + | 0.999101i | \(0.486504\pi\) | |||||||
\(702\) | −8197.83 | −0.440751 | ||||||||
\(703\) | −8344.49 | −0.447679 | ||||||||
\(704\) | 14227.2 | 0.761659 | ||||||||
\(705\) | 2277.11 | 0.121647 | ||||||||
\(706\) | 18866.4 | 1.00573 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 14532.7 | 0.771428 | ||||||||
\(709\) | 595.641 | 0.0315511 | 0.0157756 | − | 0.999876i | \(-0.494978\pi\) | ||||
0.0157756 | + | 0.999876i | \(0.494978\pi\) | |||||||
\(710\) | 11458.5 | 0.605678 | ||||||||
\(711\) | −7604.18 | −0.401096 | ||||||||
\(712\) | −15087.8 | −0.794157 | ||||||||
\(713\) | −2362.99 | −0.124116 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 674.104 | 0.0352588 | ||||||||
\(716\) | −2144.40 | −0.111927 | ||||||||
\(717\) | −8057.67 | −0.419692 | ||||||||
\(718\) | 15823.5 | 0.822462 | ||||||||
\(719\) | −21498.1 | −1.11508 | −0.557542 | − | 0.830149i | \(-0.688255\pi\) | ||||
−0.557542 | + | 0.830149i | \(0.688255\pi\) | |||||||
\(720\) | 1578.38 | 0.0816983 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 5671.64 | 0.292350 | ||||||||
\(723\) | 10404.5 | 0.535198 | ||||||||
\(724\) | −8690.61 | −0.446111 | ||||||||
\(725\) | 17565.5 | 0.899817 | ||||||||
\(726\) | 10200.1 | 0.521436 | ||||||||
\(727\) | 15331.0 | 0.782110 | 0.391055 | − | 0.920367i | \(-0.372110\pi\) | ||||
0.391055 | + | 0.920367i | \(0.372110\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 240.067 | 0.0121967 | ||||||||
\(730\) | −9351.35 | −0.474122 | ||||||||
\(731\) | 6848.70 | 0.346523 | ||||||||
\(732\) | 2151.92 | 0.108657 | ||||||||
\(733\) | 12319.8 | 0.620794 | 0.310397 | − | 0.950607i | \(-0.399538\pi\) | ||||
0.310397 | + | 0.950607i | \(0.399538\pi\) | |||||||
\(734\) | 18714.0 | 0.941071 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2287.29 | −0.114553 | ||||||||
\(737\) | 456.893 | 0.0228357 | ||||||||
\(738\) | 11425.7 | 0.569898 | ||||||||
\(739\) | 19796.5 | 0.985421 | 0.492711 | − | 0.870193i | \(-0.336006\pi\) | ||||
0.492711 | + | 0.870193i | \(0.336006\pi\) | |||||||
\(740\) | −2740.89 | −0.136158 | ||||||||
\(741\) | −2894.08 | −0.143477 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25309.1 | 1.24967 | 0.624833 | − | 0.780759i | \(-0.285167\pi\) | ||||
0.624833 | + | 0.780759i | \(0.285167\pi\) | |||||||
\(744\) | −7308.94 | −0.360159 | ||||||||
\(745\) | −7518.05 | −0.369718 | ||||||||
\(746\) | −21315.1 | −1.04611 | ||||||||
\(747\) | 28210.8 | 1.38177 | ||||||||
\(748\) | −4115.01 | −0.201149 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 5575.59 | 0.271456 | ||||||||
\(751\) | 15125.9 | 0.734957 | 0.367479 | − | 0.930032i | \(-0.380221\pi\) | ||||
0.367479 | + | 0.930032i | \(0.380221\pi\) | |||||||
\(752\) | −14150.1 | −0.686170 | ||||||||
\(753\) | 6938.45 | 0.335792 | ||||||||
\(754\) | −10609.2 | −0.512420 | ||||||||
\(755\) | 4210.40 | 0.202956 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23598.6 | 1.13303 | 0.566517 | − | 0.824050i | \(-0.308290\pi\) | ||||
0.566517 | + | 0.824050i | \(0.308290\pi\) | |||||||
\(758\) | 20638.2 | 0.988937 | ||||||||
\(759\) | 396.294 | 0.0189520 | ||||||||
\(760\) | −2103.42 | −0.100393 | ||||||||
\(761\) | −19827.3 | −0.944468 | −0.472234 | − | 0.881473i | \(-0.656552\pi\) | ||||
−0.472234 | + | 0.881473i | \(0.656552\pi\) | |||||||
\(762\) | 24113.0 | 1.14635 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 18592.5 | 0.880435 | ||||||||
\(765\) | −1018.85 | −0.0481525 | ||||||||
\(766\) | 23991.7 | 1.13166 | ||||||||
\(767\) | −9549.36 | −0.449553 | ||||||||
\(768\) | −469.969 | −0.0220814 | ||||||||
\(769\) | −14670.9 | −0.687968 | −0.343984 | − | 0.938976i | \(-0.611777\pi\) | ||||
−0.343984 | + | 0.938976i | \(0.611777\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9966.64 | −0.465551 | ||||||||
\(772\) | −38535.8 | −1.79655 | ||||||||
\(773\) | 32441.5 | 1.50949 | 0.754747 | − | 0.656016i | \(-0.227760\pi\) | ||||
0.754747 | + | 0.656016i | \(0.227760\pi\) | |||||||
\(774\) | 30564.4 | 1.41940 | ||||||||
\(775\) | −29973.3 | −1.38925 | ||||||||
\(776\) | 18007.6 | 0.833036 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −51419.7 | −2.36952 | ||||||||
\(779\) | 9082.05 | 0.417713 | ||||||||
\(780\) | −950.609 | −0.0436375 | ||||||||
\(781\) | 21096.6 | 0.966576 | ||||||||
\(782\) | 863.391 | 0.0394818 | ||||||||
\(783\) | 16571.7 | 0.756352 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3368.97 | −0.153176 | ||||||||
\(786\) | −17934.2 | −0.813858 | ||||||||
\(787\) | 26331.4 | 1.19265 | 0.596324 | − | 0.802744i | \(-0.296627\pi\) | ||||
0.596324 | + | 0.802744i | \(0.296627\pi\) | |||||||
\(788\) | −8767.98 | −0.396379 | ||||||||
\(789\) | −1402.43 | −0.0632801 | ||||||||
\(790\) | −3444.07 | −0.155107 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −4871.99 | −0.218584 | ||||||||
\(793\) | −1414.02 | −0.0633206 | ||||||||
\(794\) | 25744.3 | 1.15067 | ||||||||
\(795\) | 452.622 | 0.0201923 | ||||||||
\(796\) | −1564.63 | −0.0696696 | ||||||||
\(797\) | −18317.9 | −0.814121 | −0.407061 | − | 0.913401i | \(-0.633446\pi\) | ||||
−0.407061 | + | 0.913401i | \(0.633446\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9133.92 | 0.404424 | ||||||||
\(800\) | −29013.1 | −1.28221 | ||||||||
\(801\) | −25925.2 | −1.14360 | ||||||||
\(802\) | −16036.3 | −0.706064 | ||||||||
\(803\) | −17217.0 | −0.756631 | ||||||||
\(804\) | −644.303 | −0.0282622 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 18103.2 | 0.791140 | ||||||||
\(807\) | −18453.3 | −0.804939 | ||||||||
\(808\) | 20209.8 | 0.879923 | ||||||||
\(809\) | 19252.0 | 0.836666 | 0.418333 | − | 0.908294i | \(-0.362615\pi\) | ||||
0.418333 | + | 0.908294i | \(0.362615\pi\) | |||||||
\(810\) | −3115.13 | −0.135129 | ||||||||
\(811\) | 15983.0 | 0.692033 | 0.346017 | − | 0.938228i | \(-0.387534\pi\) | ||||
0.346017 | + | 0.938228i | \(0.387534\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10422.9 | 0.449628 | ||||||||
\(814\) | −8753.86 | −0.376932 | ||||||||
\(815\) | −5462.86 | −0.234792 | ||||||||
\(816\) | −1592.90 | −0.0683365 | ||||||||
\(817\) | 24295.1 | 1.04036 | ||||||||
\(818\) | −2397.80 | −0.102490 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2983.15 | 0.127044 | ||||||||
\(821\) | −37248.2 | −1.58340 | −0.791700 | − | 0.610910i | \(-0.790804\pi\) | ||||
−0.791700 | + | 0.610910i | \(0.790804\pi\) | |||||||
\(822\) | 7533.98 | 0.319681 | ||||||||
\(823\) | −1197.09 | −0.0507023 | −0.0253512 | − | 0.999679i | \(-0.508070\pi\) | ||||
−0.0253512 | + | 0.999679i | \(0.508070\pi\) | |||||||
\(824\) | −521.006 | −0.0220268 | ||||||||
\(825\) | 5026.77 | 0.212133 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36095.2 | −1.51772 | −0.758859 | − | 0.651255i | \(-0.774243\pi\) | ||||
−0.758859 | + | 0.651255i | \(0.774243\pi\) | |||||||
\(828\) | 2221.21 | 0.0932276 | ||||||||
\(829\) | 39715.1 | 1.66389 | 0.831943 | − | 0.554861i | \(-0.187229\pi\) | ||||
0.831943 | + | 0.554861i | \(0.187229\pi\) | |||||||
\(830\) | 12777.2 | 0.534341 | ||||||||
\(831\) | −3858.50 | −0.161071 | ||||||||
\(832\) | 13183.3 | 0.549337 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −28896.4 | −1.19976 | ||||||||
\(835\) | 2467.85 | 0.102280 | ||||||||
\(836\) | −14597.6 | −0.603910 | ||||||||
\(837\) | −28277.4 | −1.16776 | ||||||||
\(838\) | 59040.9 | 2.43381 | ||||||||
\(839\) | 44254.4 | 1.82102 | 0.910508 | − | 0.413492i | \(-0.135691\pi\) | ||||
0.910508 | + | 0.413492i | \(0.135691\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2942.77 | −0.120660 | ||||||||
\(842\) | 64109.2 | 2.62393 | ||||||||
\(843\) | −8110.40 | −0.331361 | ||||||||
\(844\) | 30080.7 | 1.22680 | ||||||||
\(845\) | −4314.46 | −0.175647 | ||||||||
\(846\) | 40762.9 | 1.65657 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2812.62 | −0.113898 | ||||||||
\(849\) | 17154.1 | 0.693434 | ||||||||
\(850\) | 10951.6 | 0.441928 | ||||||||
\(851\) | 1058.79 | 0.0426497 | ||||||||
\(852\) | −29750.1 | −1.19627 | ||||||||
\(853\) | −12595.8 | −0.505593 | −0.252797 | − | 0.967519i | \(-0.581350\pi\) | ||||
−0.252797 | + | 0.967519i | \(0.581350\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3614.27 | −0.144568 | ||||||||
\(856\) | −12868.6 | −0.513830 | ||||||||
\(857\) | −31318.6 | −1.24833 | −0.624167 | − | 0.781291i | \(-0.714561\pi\) | ||||
−0.624167 | + | 0.781291i | \(0.714561\pi\) | |||||||
\(858\) | −3036.06 | −0.120804 | ||||||||
\(859\) | 12280.8 | 0.487795 | 0.243898 | − | 0.969801i | \(-0.421574\pi\) | ||||
0.243898 | + | 0.969801i | \(0.421574\pi\) | |||||||
\(860\) | 7980.13 | 0.316419 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 38754.3 | 1.53130 | ||||||||
\(863\) | 43670.3 | 1.72254 | 0.861272 | − | 0.508144i | \(-0.169668\pi\) | ||||
0.861272 | + | 0.508144i | \(0.169668\pi\) | |||||||
\(864\) | −27371.6 | −1.07778 | ||||||||
\(865\) | 2007.82 | 0.0789226 | ||||||||
\(866\) | 56666.5 | 2.22356 | ||||||||
\(867\) | −10417.6 | −0.408075 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6340.96 | −0.247529 | ||||||||
\(870\) | 3333.47 | 0.129902 | ||||||||
\(871\) | 423.369 | 0.0164699 | ||||||||
\(872\) | 12953.9 | 0.503067 | ||||||||
\(873\) | 30942.2 | 1.19958 | ||||||||
\(874\) | 3062.80 | 0.118536 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 24279.1 | 0.936432 | ||||||||
\(877\) | −26037.3 | −1.00253 | −0.501265 | − | 0.865294i | \(-0.667132\pi\) | ||||
−0.501265 | + | 0.865294i | \(0.667132\pi\) | |||||||
\(878\) | 1772.24 | 0.0681210 | ||||||||
\(879\) | −3355.29 | −0.128750 | ||||||||
\(880\) | 1316.18 | 0.0504185 | ||||||||
\(881\) | −45357.9 | −1.73456 | −0.867280 | − | 0.497820i | \(-0.834134\pi\) | ||||
−0.867280 | + | 0.497820i | \(0.834134\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3211.59 | 0.122399 | 0.0611996 | − | 0.998126i | \(-0.480507\pi\) | ||||
0.0611996 | + | 0.998126i | \(0.480507\pi\) | |||||||
\(884\) | −3813.07 | −0.145076 | ||||||||
\(885\) | 3000.46 | 0.113965 | ||||||||
\(886\) | −28700.2 | −1.08827 | ||||||||
\(887\) | −4760.50 | −0.180205 | −0.0901025 | − | 0.995932i | \(-0.528719\pi\) | ||||
−0.0901025 | + | 0.995932i | \(0.528719\pi\) | |||||||
\(888\) | 3274.93 | 0.123761 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −11742.0 | −0.442238 | ||||||||
\(891\) | −5735.33 | −0.215646 | ||||||||
\(892\) | 46083.8 | 1.72982 | ||||||||
\(893\) | 32401.7 | 1.21420 | ||||||||
\(894\) | 33860.2 | 1.26673 | ||||||||
\(895\) | −442.739 | −0.0165353 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 367.216 | 0.0136689 | ||||||||
\(898\) | −13243.1 | −0.492125 | ||||||||
\(899\) | −36595.2 | −1.35764 | ||||||||
\(900\) | 28174.9 | 1.04351 | ||||||||
\(901\) | 1815.55 | 0.0671309 | ||||||||
\(902\) | 9527.62 | 0.351702 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9599.29 | −0.353172 | ||||||||
\(905\) | −1794.29 | −0.0659052 | ||||||||
\(906\) | −18963.0 | −0.695368 | ||||||||
\(907\) | 10177.3 | 0.372582 | 0.186291 | − | 0.982495i | \(-0.440353\pi\) | ||||
0.186291 | + | 0.982495i | \(0.440353\pi\) | |||||||
\(908\) | −9591.84 | −0.350569 | ||||||||
\(909\) | 34726.2 | 1.26710 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15584.8 | −0.566792 | −0.283396 | − | 0.959003i | \(-0.591461\pi\) | ||||
−0.283396 | + | 0.959003i | \(0.591461\pi\) | |||||||
\(912\) | −5650.65 | −0.205166 | ||||||||
\(913\) | 23524.4 | 0.852731 | ||||||||
\(914\) | −38418.7 | −1.39035 | ||||||||
\(915\) | 444.291 | 0.0160523 | ||||||||
\(916\) | 17664.3 | 0.637167 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 10332.0 | 0.371468 | ||||||||
\(919\) | 10782.4 | 0.387026 | 0.193513 | − | 0.981098i | \(-0.438012\pi\) | ||||
0.193513 | + | 0.981098i | \(0.438012\pi\) | |||||||
\(920\) | 266.892 | 0.00956433 | ||||||||
\(921\) | 1307.10 | 0.0467648 | ||||||||
\(922\) | 43153.2 | 1.54140 | ||||||||
\(923\) | 19548.6 | 0.697130 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13430.2 | 0.477386 | ||||||||
\(926\) | 65911.3 | 2.33907 | ||||||||
\(927\) | −895.237 | −0.0317189 | ||||||||
\(928\) | −35422.9 | −1.25303 | ||||||||
\(929\) | −53482.3 | −1.88880 | −0.944400 | − | 0.328798i | \(-0.893357\pi\) | ||||
−0.944400 | + | 0.328798i | \(0.893357\pi\) | |||||||
\(930\) | −5688.12 | −0.200560 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −42749.6 | −1.50248 | ||||||||
\(933\) | −8483.01 | −0.297665 | ||||||||
\(934\) | 59336.7 | 2.07876 | ||||||||
\(935\) | −849.597 | −0.0297164 | ||||||||
\(936\) | −4514.51 | −0.157651 | ||||||||
\(937\) | 30490.5 | 1.06305 | 0.531526 | − | 0.847042i | \(-0.321619\pi\) | ||||
0.531526 | + | 0.847042i | \(0.321619\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19743.0 | 0.686142 | ||||||||
\(940\) | 10642.9 | 0.369290 | ||||||||
\(941\) | −36848.7 | −1.27655 | −0.638276 | − | 0.769808i | \(-0.720352\pi\) | ||||
−0.638276 | + | 0.769808i | \(0.720352\pi\) | |||||||
\(942\) | 15173.3 | 0.524813 | ||||||||
\(943\) | −1152.38 | −0.0397949 | ||||||||
\(944\) | −18645.0 | −0.642842 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 25487.0 | 0.875956 | ||||||||
\(947\) | −14328.9 | −0.491687 | −0.245844 | − | 0.969309i | \(-0.579065\pi\) | ||||
−0.245844 | + | 0.969309i | \(0.579065\pi\) | |||||||
\(948\) | 8941.91 | 0.306350 | ||||||||
\(949\) | −15953.7 | −0.545710 | ||||||||
\(950\) | 38849.9 | 1.32680 | ||||||||
\(951\) | −1542.24 | −0.0525874 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1760.96 | 0.0598563 | 0.0299281 | − | 0.999552i | \(-0.490472\pi\) | ||||
0.0299281 | + | 0.999552i | \(0.490472\pi\) | |||||||
\(954\) | 8102.47 | 0.274976 | ||||||||
\(955\) | 3838.66 | 0.130069 | ||||||||
\(956\) | −37660.4 | −1.27408 | ||||||||
\(957\) | 6137.32 | 0.207306 | ||||||||
\(958\) | −40279.1 | −1.35841 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −4142.25 | −0.139261 | ||||||||
\(961\) | 32653.9 | 1.09610 | ||||||||
\(962\) | −8111.55 | −0.271857 | ||||||||
\(963\) | −22111.9 | −0.739922 | ||||||||
\(964\) | 48629.2 | 1.62473 | ||||||||
\(965\) | −7956.21 | −0.265409 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −909.752 | −0.0302540 | −0.0151270 | − | 0.999886i | \(-0.504815\pi\) | ||||
−0.0151270 | + | 0.999886i | \(0.504815\pi\) | |||||||
\(968\) | 12647.6 | 0.419947 | ||||||||
\(969\) | 3647.51 | 0.120924 | ||||||||
\(970\) | 14014.3 | 0.463889 | ||||||||
\(971\) | −4900.51 | −0.161962 | −0.0809809 | − | 0.996716i | \(-0.525805\pi\) | ||||
−0.0809809 | + | 0.996716i | \(0.525805\pi\) | |||||||
\(972\) | 41356.2 | 1.36471 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 17971.6 | 0.591218 | ||||||||
\(975\) | 4657.93 | 0.152998 | ||||||||
\(976\) | −2760.85 | −0.0905457 | ||||||||
\(977\) | 8173.98 | 0.267665 | 0.133833 | − | 0.991004i | \(-0.457272\pi\) | ||||
0.133833 | + | 0.991004i | \(0.457272\pi\) | |||||||
\(978\) | 24603.9 | 0.804444 | ||||||||
\(979\) | −21618.4 | −0.705749 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 22258.5 | 0.724423 | ||||||||
\(982\) | −19608.3 | −0.637195 | ||||||||
\(983\) | 30729.2 | 0.997059 | 0.498530 | − | 0.866873i | \(-0.333874\pi\) | ||||
0.498530 | + | 0.866873i | \(0.333874\pi\) | |||||||
\(984\) | −3564.40 | −0.115477 | ||||||||
\(985\) | −1810.26 | −0.0585581 | ||||||||
\(986\) | 13371.2 | 0.431871 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −13526.5 | −0.435562 | ||||||||
\(989\) | −3082.69 | −0.0991139 | ||||||||
\(990\) | −3791.59 | −0.121722 | ||||||||
\(991\) | −42375.8 | −1.35834 | −0.679169 | − | 0.733982i | \(-0.737660\pi\) | ||||
−0.679169 | + | 0.733982i | \(0.737660\pi\) | |||||||
\(992\) | 60444.5 | 1.93459 | ||||||||
\(993\) | 6657.25 | 0.212751 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −323.039 | −0.0102925 | ||||||||
\(996\) | −33173.7 | −1.05537 | ||||||||
\(997\) | 13594.3 | 0.431831 | 0.215916 | − | 0.976412i | \(-0.430726\pi\) | ||||
0.215916 | + | 0.976412i | \(0.430726\pi\) | |||||||
\(998\) | 62655.6 | 1.98730 | ||||||||
\(999\) | 12670.3 | 0.401273 |
(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 | 2401.4.a.c.1.6 | 39 | ||
7.6 | odd | 2 | 2401.4.a.d.1.6 | 39 | |||
49.13 | odd | 14 | 49.4.e.a.22.12 | ✓ | 78 | ||
49.34 | odd | 14 | 49.4.e.a.29.12 | yes | 78 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
49.4.e.a.22.12 | ✓ | 78 | 49.13 | odd | 14 | ||
49.4.e.a.29.12 | yes | 78 | 49.34 | odd | 14 | ||
2401.4.a.c.1.6 | 39 | 1.1 | even | 1 | trivial | ||
2401.4.a.d.1.6 | 39 | 7.6 | odd | 2 |