Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [126,4,Mod(37,126)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(126, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("126.37");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 126 = 2 \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 126.g (of order \(3\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(7.43424066072\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 14) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 109.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 126.109 |
Dual form | 126.4.g.d.37.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.73205i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | + | 3.46410i | −0.250000 | + | 0.433013i | ||||
\(5\) | −4.50000 | − | 7.79423i | −0.402492 | − | 0.697137i | 0.591534 | − | 0.806280i | \(-0.298523\pi\) |
−0.994026 | + | 0.109143i | \(0.965189\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −14.0000 | + | 12.1244i | −0.755929 | + | 0.654654i | ||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 9.00000 | − | 15.5885i | 0.284605 | − | 0.492950i | ||||
\(11\) | −28.5000 | + | 49.3634i | −0.781188 | + | 1.35306i | 0.150061 | + | 0.988677i | \(0.452053\pi\) |
−0.931250 | + | 0.364381i | \(0.881280\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −70.0000 | −1.49342 | −0.746712 | − | 0.665148i | \(-0.768369\pi\) | ||||
−0.746712 | + | 0.665148i | \(0.768369\pi\) | |||||||
\(14\) | −35.0000 | − | 12.1244i | −0.668153 | − | 0.231455i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | − | 13.8564i | −0.125000 | − | 0.216506i | ||||
\(17\) | 25.5000 | − | 44.1673i | 0.363803 | − | 0.630126i | −0.624780 | − | 0.780801i | \(-0.714811\pi\) |
0.988583 | + | 0.150675i | \(0.0481447\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.50000 | − | 4.33013i | −0.0301863 | − | 0.0522842i | 0.850538 | − | 0.525914i | \(-0.176277\pi\) |
−0.880724 | + | 0.473630i | \(0.842943\pi\) | |||||||
\(20\) | 36.0000 | 0.402492 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −114.000 | −1.10477 | ||||||||
\(23\) | 34.5000 | + | 59.7558i | 0.312772 | + | 0.541736i | 0.978961 | − | 0.204046i | \(-0.0654092\pi\) |
−0.666190 | + | 0.745782i | \(0.732076\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 22.0000 | − | 38.1051i | 0.176000 | − | 0.304841i | ||||
\(26\) | −70.0000 | − | 121.244i | −0.528005 | − | 0.914531i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −14.0000 | − | 72.7461i | −0.0944911 | − | 0.490990i | ||||
\(29\) | −114.000 | −0.729975 | −0.364987 | − | 0.931012i | \(-0.618927\pi\) | ||||
−0.364987 | + | 0.931012i | \(0.618927\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −11.5000 | + | 19.9186i | −0.0666278 | + | 0.115403i | −0.897415 | − | 0.441188i | \(-0.854557\pi\) |
0.830787 | + | 0.556590i | \(0.187891\pi\) | |||||||
\(32\) | 16.0000 | − | 27.7128i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 102.000 | 0.514496 | ||||||||
\(35\) | 157.500 | + | 54.5596i | 0.760639 | + | 0.263493i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 126.500 | + | 219.104i | 0.562067 | + | 0.973528i | 0.997316 | + | 0.0732182i | \(0.0233270\pi\) |
−0.435249 | + | 0.900310i | \(0.643340\pi\) | |||||||
\(38\) | 5.00000 | − | 8.66025i | 0.0213449 | − | 0.0369705i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 36.0000 | + | 62.3538i | 0.142302 | + | 0.246475i | ||||
\(41\) | 42.0000 | 0.159983 | 0.0799914 | − | 0.996796i | \(-0.474511\pi\) | ||||
0.0799914 | + | 0.996796i | \(0.474511\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −124.000 | −0.439763 | −0.219882 | − | 0.975527i | \(-0.570567\pi\) | ||||
−0.219882 | + | 0.975527i | \(0.570567\pi\) | |||||||
\(44\) | −114.000 | − | 197.454i | −0.390594 | − | 0.676529i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −69.0000 | + | 119.512i | −0.221163 | + | 0.383065i | ||||
\(47\) | 100.500 | + | 174.071i | 0.311903 | + | 0.540231i | 0.978774 | − | 0.204941i | \(-0.0657003\pi\) |
−0.666871 | + | 0.745173i | \(0.732367\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | − | 339.482i | 0.142857 | − | 0.989743i | ||||
\(50\) | 88.0000 | 0.248902 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 140.000 | − | 242.487i | 0.373356 | − | 0.646671i | ||||
\(53\) | −196.500 | + | 340.348i | −0.509271 | + | 0.882083i | 0.490672 | + | 0.871345i | \(0.336751\pi\) |
−0.999942 | + | 0.0107383i | \(0.996582\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 513.000 | 1.25769 | ||||||||
\(56\) | 112.000 | − | 96.9948i | 0.267261 | − | 0.231455i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −114.000 | − | 197.454i | −0.258085 | − | 0.447016i | ||||
\(59\) | 109.500 | − | 189.660i | 0.241622 | − | 0.418501i | −0.719555 | − | 0.694436i | \(-0.755654\pi\) |
0.961176 | + | 0.275935i | \(0.0889873\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 354.500 | + | 614.012i | 0.744083 | + | 1.28879i | 0.950622 | + | 0.310351i | \(0.100447\pi\) |
−0.206539 | + | 0.978438i | \(0.566220\pi\) | |||||||
\(62\) | −46.0000 | −0.0942259 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 315.000 | + | 545.596i | 0.601091 | + | 1.04112i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −209.500 | + | 362.865i | −0.382007 | + | 0.661656i | −0.991349 | − | 0.131251i | \(-0.958100\pi\) |
0.609342 | + | 0.792908i | \(0.291434\pi\) | |||||||
\(68\) | 102.000 | + | 176.669i | 0.181902 | + | 0.315063i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 63.0000 | + | 327.358i | 0.107571 | + | 0.558953i | ||||
\(71\) | 96.0000 | 0.160466 | 0.0802331 | − | 0.996776i | \(-0.474434\pi\) | ||||
0.0802331 | + | 0.996776i | \(0.474434\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 156.500 | − | 271.066i | 0.250917 | − | 0.434601i | −0.712862 | − | 0.701305i | \(-0.752601\pi\) |
0.963779 | + | 0.266704i | \(0.0859346\pi\) | |||||||
\(74\) | −253.000 | + | 438.209i | −0.397441 | + | 0.688388i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 20.0000 | 0.0301863 | ||||||||
\(77\) | −199.500 | − | 1036.63i | −0.295261 | − | 1.53422i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −230.500 | − | 399.238i | −0.328269 | − | 0.568579i | 0.653899 | − | 0.756582i | \(-0.273132\pi\) |
−0.982169 | + | 0.188003i | \(0.939799\pi\) | |||||||
\(80\) | −72.0000 | + | 124.708i | −0.100623 | + | 0.174284i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 42.0000 | + | 72.7461i | 0.0565625 | + | 0.0979691i | ||||
\(83\) | 588.000 | 0.777607 | 0.388804 | − | 0.921321i | \(-0.372888\pi\) | ||||
0.388804 | + | 0.921321i | \(0.372888\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −459.000 | −0.585712 | ||||||||
\(86\) | −124.000 | − | 214.774i | −0.155480 | − | 0.269299i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 228.000 | − | 394.908i | 0.276192 | − | 0.478378i | ||||
\(89\) | −508.500 | − | 880.748i | −0.605628 | − | 1.04898i | −0.991952 | − | 0.126615i | \(-0.959589\pi\) |
0.386324 | − | 0.922363i | \(-0.373745\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 980.000 | − | 848.705i | 1.12892 | − | 0.977675i | ||||
\(92\) | −276.000 | −0.312772 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −201.000 | + | 348.142i | −0.220549 | + | 0.382001i | ||||
\(95\) | −22.5000 | + | 38.9711i | −0.0242995 | + | 0.0420879i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1834.00 | −1.91974 | −0.959868 | − | 0.280451i | \(-0.909516\pi\) | ||||
−0.959868 | + | 0.280451i | \(0.909516\pi\) | |||||||
\(98\) | 637.000 | − | 254.611i | 0.656599 | − | 0.262445i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 88.0000 | + | 152.420i | 0.0880000 | + | 0.152420i | ||||
\(101\) | −142.500 | + | 246.817i | −0.140389 | + | 0.243161i | −0.927643 | − | 0.373468i | \(-0.878169\pi\) |
0.787254 | + | 0.616629i | \(0.211502\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 249.500 | + | 432.147i | 0.238679 | + | 0.413405i | 0.960336 | − | 0.278847i | \(-0.0899522\pi\) |
−0.721656 | + | 0.692252i | \(0.756619\pi\) | |||||||
\(104\) | 560.000 | 0.528005 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −786.000 | −0.720218 | ||||||||
\(107\) | −553.500 | − | 958.690i | −0.500083 | − | 0.866169i | −1.00000 | 9.56665e-5i | \(-0.999970\pi\) | |
0.499917 | − | 0.866073i | \(-0.333364\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −461.500 | + | 799.341i | −0.405538 | + | 0.702413i | −0.994384 | − | 0.105832i | \(-0.966249\pi\) |
0.588846 | + | 0.808246i | \(0.299583\pi\) | |||||||
\(110\) | 513.000 | + | 888.542i | 0.444660 | + | 0.770174i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 280.000 | + | 96.9948i | 0.236228 | + | 0.0818317i | ||||
\(113\) | −1542.00 | −1.28371 | −0.641855 | − | 0.766826i | \(-0.721835\pi\) | ||||
−0.641855 | + | 0.766826i | \(0.721835\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 310.500 | − | 537.802i | 0.251776 | − | 0.436089i | ||||
\(116\) | 228.000 | − | 394.908i | 0.182494 | − | 0.316088i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 438.000 | 0.341705 | ||||||||
\(119\) | 178.500 | + | 927.513i | 0.137505 | + | 0.714496i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −959.000 | − | 1661.04i | −0.720511 | − | 1.24796i | ||||
\(122\) | −709.000 | + | 1228.02i | −0.526146 | + | 0.911312i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −46.0000 | − | 79.6743i | −0.0333139 | − | 0.0577013i | ||||
\(125\) | −1521.00 | −1.08834 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2056.00 | −1.43654 | −0.718270 | − | 0.695765i | \(-0.755066\pi\) | ||||
−0.718270 | + | 0.695765i | \(0.755066\pi\) | |||||||
\(128\) | 64.0000 | + | 110.851i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −630.000 | + | 1091.19i | −0.425036 | + | 0.736184i | ||||
\(131\) | 1024.50 | + | 1774.49i | 0.683290 | + | 1.18349i | 0.973971 | + | 0.226673i | \(0.0727848\pi\) |
−0.290681 | + | 0.956820i | \(0.593882\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 87.5000 | + | 30.3109i | 0.0570467 | + | 0.0197616i | ||||
\(134\) | −838.000 | −0.540240 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −204.000 | + | 353.338i | −0.128624 | + | 0.222783i | ||||
\(137\) | −70.5000 | + | 122.110i | −0.0439651 | + | 0.0761498i | −0.887171 | − | 0.461442i | \(-0.847332\pi\) |
0.843205 | + | 0.537591i | \(0.180666\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1484.00 | 0.905548 | 0.452774 | − | 0.891625i | \(-0.350434\pi\) | ||||
0.452774 | + | 0.891625i | \(0.350434\pi\) | |||||||
\(140\) | −504.000 | + | 436.477i | −0.304256 | + | 0.263493i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 96.0000 | + | 166.277i | 0.0567334 | + | 0.0982651i | ||||
\(143\) | 1995.00 | − | 3455.44i | 1.16665 | − | 2.02069i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 513.000 | + | 888.542i | 0.293809 | + | 0.508892i | ||||
\(146\) | 626.000 | 0.354850 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1012.00 | −0.562067 | ||||||||
\(149\) | −28.5000 | − | 49.3634i | −0.0156699 | − | 0.0271410i | 0.858084 | − | 0.513509i | \(-0.171655\pi\) |
−0.873754 | + | 0.486368i | \(0.838321\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −419.500 | + | 726.595i | −0.226082 | + | 0.391586i | −0.956644 | − | 0.291261i | \(-0.905925\pi\) |
0.730561 | + | 0.682847i | \(0.239258\pi\) | |||||||
\(152\) | 20.0000 | + | 34.6410i | 0.0106725 | + | 0.0184852i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1596.00 | − | 1382.18i | 0.835126 | − | 0.723240i | ||||
\(155\) | 207.000 | 0.107269 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1416.50 | − | 2453.45i | 0.720057 | − | 1.24718i | −0.240919 | − | 0.970545i | \(-0.577449\pi\) |
0.960976 | − | 0.276631i | \(-0.0892179\pi\) | |||||||
\(158\) | 461.000 | − | 798.475i | 0.232121 | − | 0.402046i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −288.000 | −0.142302 | ||||||||
\(161\) | −1207.50 | − | 418.290i | −0.591083 | − | 0.204757i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1155.50 | + | 2001.38i | 0.555250 | + | 0.961721i | 0.997884 | + | 0.0650188i | \(0.0207107\pi\) |
−0.442634 | + | 0.896702i | \(0.645956\pi\) | |||||||
\(164\) | −84.0000 | + | 145.492i | −0.0399957 | + | 0.0692746i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 588.000 | + | 1018.45i | 0.274926 | + | 0.476185i | ||||
\(167\) | −1260.00 | −0.583843 | −0.291921 | − | 0.956442i | \(-0.594295\pi\) | ||||
−0.291921 | + | 0.956442i | \(0.594295\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2703.00 | 1.23031 | ||||||||
\(170\) | −459.000 | − | 795.011i | −0.207081 | − | 0.358674i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 248.000 | − | 429.549i | 0.109941 | − | 0.190423i | ||||
\(173\) | 1633.50 | + | 2829.30i | 0.717877 | + | 1.24340i | 0.961839 | + | 0.273615i | \(0.0882193\pi\) |
−0.243962 | + | 0.969785i | \(0.578447\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 154.000 | + | 800.207i | 0.0665217 | + | 0.345657i | ||||
\(176\) | 912.000 | 0.390594 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1017.00 | − | 1761.50i | 0.428244 | − | 0.741740i | ||||
\(179\) | 643.500 | − | 1114.57i | 0.268701 | − | 0.465403i | −0.699826 | − | 0.714314i | \(-0.746739\pi\) |
0.968527 | + | 0.248910i | \(0.0800724\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2674.00 | −1.09810 | −0.549052 | − | 0.835788i | \(-0.685011\pi\) | ||||
−0.549052 | + | 0.835788i | \(0.685011\pi\) | |||||||
\(182\) | 2450.00 | + | 848.705i | 0.997836 | + | 0.345660i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −276.000 | − | 478.046i | −0.110581 | − | 0.191533i | ||||
\(185\) | 1138.50 | − | 1971.94i | 0.452455 | − | 0.783675i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1453.50 | + | 2517.54i | 0.568398 | + | 0.984494i | ||||
\(188\) | −804.000 | −0.311903 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −90.0000 | −0.0343647 | ||||||||
\(191\) | 2092.50 | + | 3624.32i | 0.792712 | + | 1.37302i | 0.924282 | + | 0.381711i | \(0.124665\pi\) |
−0.131570 | + | 0.991307i | \(0.542002\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 42.5000 | − | 73.6122i | 0.0158509 | − | 0.0274545i | −0.857991 | − | 0.513664i | \(-0.828288\pi\) |
0.873842 | + | 0.486210i | \(0.161621\pi\) | |||||||
\(194\) | −1834.00 | − | 3176.58i | −0.678730 | − | 1.17559i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1078.00 | + | 848.705i | 0.392857 | + | 0.309295i | ||||
\(197\) | 390.000 | 0.141047 | 0.0705237 | − | 0.997510i | \(-0.477533\pi\) | ||||
0.0705237 | + | 0.997510i | \(0.477533\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1416.50 | − | 2453.45i | 0.504588 | − | 0.873972i | −0.495398 | − | 0.868666i | \(-0.664978\pi\) |
0.999986 | − | 0.00530596i | \(-0.00168895\pi\) | |||||||
\(200\) | −176.000 | + | 304.841i | −0.0622254 | + | 0.107778i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −570.000 | −0.198540 | ||||||||
\(203\) | 1596.00 | − | 1382.18i | 0.551809 | − | 0.477881i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −189.000 | − | 327.358i | −0.0643919 | − | 0.111530i | ||||
\(206\) | −499.000 | + | 864.293i | −0.168772 | + | 0.292321i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 560.000 | + | 969.948i | 0.186678 | + | 0.323336i | ||||
\(209\) | 285.000 | 0.0943247 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −124.000 | −0.0404574 | −0.0202287 | − | 0.999795i | \(-0.506439\pi\) | ||||
−0.0202287 | + | 0.999795i | \(0.506439\pi\) | |||||||
\(212\) | −786.000 | − | 1361.39i | −0.254635 | − | 0.441041i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1107.00 | − | 1917.38i | 0.353612 | − | 0.612474i | ||||
\(215\) | 558.000 | + | 966.484i | 0.177001 | + | 0.306575i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −80.5000 | − | 418.290i | −0.0251829 | − | 0.130854i | ||||
\(218\) | −1846.00 | −0.573518 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1026.00 | + | 1777.08i | −0.314422 | + | 0.544595i | ||||
\(221\) | −1785.00 | + | 3091.71i | −0.543313 | + | 0.941045i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 56.0000 | 0.0168163 | 0.00840816 | − | 0.999965i | \(-0.497324\pi\) | ||||
0.00840816 | + | 0.999965i | \(0.497324\pi\) | |||||||
\(224\) | 112.000 | + | 581.969i | 0.0334077 | + | 0.173591i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1542.00 | − | 2670.82i | −0.453860 | − | 0.786108i | ||||
\(227\) | −1528.50 | + | 2647.44i | −0.446917 | + | 0.774083i | −0.998184 | − | 0.0602465i | \(-0.980811\pi\) |
0.551267 | + | 0.834329i | \(0.314145\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 480.500 | + | 832.250i | 0.138656 | + | 0.240160i | 0.926988 | − | 0.375090i | \(-0.122388\pi\) |
−0.788332 | + | 0.615250i | \(0.789055\pi\) | |||||||
\(230\) | 1242.00 | 0.356065 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 912.000 | 0.258085 | ||||||||
\(233\) | −1414.50 | − | 2449.99i | −0.397712 | − | 0.688858i | 0.595731 | − | 0.803184i | \(-0.296862\pi\) |
−0.993443 | + | 0.114326i | \(0.963529\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 904.500 | − | 1566.64i | 0.251077 | − | 0.434878i | ||||
\(236\) | 438.000 | + | 758.638i | 0.120811 | + | 0.209251i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1428.00 | + | 1236.68i | −0.388922 | + | 0.336817i | ||||
\(239\) | 3540.00 | 0.958090 | 0.479045 | − | 0.877790i | \(-0.340983\pi\) | ||||
0.479045 | + | 0.877790i | \(0.340983\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2615.50 | + | 4530.18i | −0.699084 | + | 1.21085i | 0.269701 | + | 0.962944i | \(0.413075\pi\) |
−0.968785 | + | 0.247904i | \(0.920258\pi\) | |||||||
\(242\) | 1918.00 | − | 3322.07i | 0.509478 | − | 0.882442i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2836.00 | −0.744083 | ||||||||
\(245\) | −2866.50 | + | 1145.75i | −0.747486 | + | 0.298773i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 175.000 | + | 303.109i | 0.0450809 | + | 0.0780824i | ||||
\(248\) | 92.0000 | − | 159.349i | 0.0235565 | − | 0.0408010i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1521.00 | − | 2634.45i | −0.384786 | − | 0.666469i | ||||
\(251\) | −5040.00 | −1.26742 | −0.633709 | − | 0.773571i | \(-0.718468\pi\) | ||||
−0.633709 | + | 0.773571i | \(0.718468\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3933.00 | −0.977334 | ||||||||
\(254\) | −2056.00 | − | 3561.10i | −0.507893 | − | 0.879697i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | + | 221.703i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −718.500 | − | 1244.48i | −0.174392 | − | 0.302056i | 0.765559 | − | 0.643366i | \(-0.222463\pi\) |
−0.939951 | + | 0.341310i | \(0.889129\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4427.50 | − | 1533.73i | −1.06221 | − | 0.367959i | ||||
\(260\) | −2520.00 | −0.601091 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2049.00 | + | 3548.97i | −0.483159 | + | 0.836856i | ||||
\(263\) | −1162.50 | + | 2013.51i | −0.272558 | + | 0.472085i | −0.969516 | − | 0.245027i | \(-0.921203\pi\) |
0.696958 | + | 0.717112i | \(0.254536\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3537.00 | 0.819910 | ||||||||
\(266\) | 35.0000 | + | 181.865i | 0.00806762 | + | 0.0419206i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −838.000 | − | 1451.46i | −0.191004 | − | 0.330828i | ||||
\(269\) | −1192.50 | + | 2065.47i | −0.270290 | + | 0.468156i | −0.968936 | − | 0.247311i | \(-0.920453\pi\) |
0.698646 | + | 0.715467i | \(0.253786\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 165.500 | + | 286.654i | 0.0370975 | + | 0.0642547i | 0.883978 | − | 0.467528i | \(-0.154855\pi\) |
−0.846881 | + | 0.531783i | \(0.821522\pi\) | |||||||
\(272\) | −816.000 | −0.181902 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −282.000 | −0.0621761 | ||||||||
\(275\) | 1254.00 | + | 2171.99i | 0.274978 | + | 0.476276i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2435.50 | + | 4218.41i | −0.528285 | + | 0.915017i | 0.471171 | + | 0.882042i | \(0.343831\pi\) |
−0.999456 | + | 0.0329750i | \(0.989502\pi\) | |||||||
\(278\) | 1484.00 | + | 2570.36i | 0.320160 | + | 0.554533i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1260.00 | − | 436.477i | −0.268926 | − | 0.0931589i | ||||
\(281\) | 7026.00 | 1.49159 | 0.745794 | − | 0.666177i | \(-0.232070\pi\) | ||||
0.745794 | + | 0.666177i | \(0.232070\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2676.50 | − | 4635.83i | 0.562196 | − | 0.973752i | −0.435109 | − | 0.900378i | \(-0.643290\pi\) |
0.997305 | − | 0.0733738i | \(-0.0233766\pi\) | |||||||
\(284\) | −192.000 | + | 332.554i | −0.0401166 | + | 0.0694839i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7980.00 | 1.64989 | ||||||||
\(287\) | −588.000 | + | 509.223i | −0.120936 | + | 0.104733i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1156.00 | + | 2002.25i | 0.235294 | + | 0.407541i | ||||
\(290\) | −1026.00 | + | 1777.08i | −0.207754 | + | 0.359841i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 626.000 | + | 1084.26i | 0.125458 | + | 0.217300i | ||||
\(293\) | −4158.00 | −0.829054 | −0.414527 | − | 0.910037i | \(-0.636053\pi\) | ||||
−0.414527 | + | 0.910037i | \(0.636053\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1971.00 | −0.389004 | ||||||||
\(296\) | −1012.00 | − | 1752.84i | −0.198721 | − | 0.344194i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 57.0000 | − | 98.7269i | 0.0110803 | − | 0.0191916i | ||||
\(299\) | −2415.00 | − | 4182.90i | −0.467101 | − | 0.809042i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1736.00 | − | 1503.42i | 0.332430 | − | 0.287893i | ||||
\(302\) | −1678.00 | −0.319729 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −40.0000 | + | 69.2820i | −0.00754657 | + | 0.0130710i | ||||
\(305\) | 3190.50 | − | 5526.11i | 0.598975 | − | 1.03746i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9604.00 | −1.78544 | −0.892719 | − | 0.450615i | \(-0.851205\pi\) | ||||
−0.892719 | + | 0.450615i | \(0.851205\pi\) | |||||||
\(308\) | 3990.00 | + | 1382.18i | 0.738154 | + | 0.255704i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 207.000 | + | 358.535i | 0.0379252 | + | 0.0656884i | ||||
\(311\) | 5065.50 | − | 8773.70i | 0.923595 | − | 1.59971i | 0.129791 | − | 0.991541i | \(-0.458570\pi\) |
0.793805 | − | 0.608173i | \(-0.208097\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5399.50 | − | 9352.21i | −0.975073 | − | 1.68888i | −0.679695 | − | 0.733495i | \(-0.737888\pi\) |
−0.295378 | − | 0.955380i | \(-0.595446\pi\) | |||||||
\(314\) | 5666.00 | 1.01831 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1844.00 | 0.328269 | ||||||||
\(317\) | 265.500 | + | 459.859i | 0.0470409 | + | 0.0814772i | 0.888587 | − | 0.458708i | \(-0.151688\pi\) |
−0.841546 | + | 0.540185i | \(0.818354\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3249.00 | − | 5627.43i | 0.570248 | − | 0.987698i | ||||
\(320\) | −288.000 | − | 498.831i | −0.0503115 | − | 0.0871421i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −483.000 | − | 2509.74i | −0.0835917 | − | 0.434355i | ||||
\(323\) | −255.000 | −0.0439275 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1540.00 | + | 2667.36i | −0.262843 | + | 0.455257i | ||||
\(326\) | −2311.00 | + | 4002.77i | −0.392621 | + | 0.680040i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −336.000 | −0.0565625 | ||||||||
\(329\) | −3517.50 | − | 1218.50i | −0.589441 | − | 0.204188i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3507.50 | + | 6075.17i | 0.582446 | + | 1.00883i | 0.995189 | + | 0.0979784i | \(0.0312376\pi\) |
−0.412743 | + | 0.910848i | \(0.635429\pi\) | |||||||
\(332\) | −1176.00 | + | 2036.89i | −0.194402 | + | 0.336714i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1260.00 | − | 2182.38i | −0.206420 | − | 0.357529i | ||||
\(335\) | 3771.00 | 0.615020 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8990.00 | 1.45316 | 0.726582 | − | 0.687079i | \(-0.241108\pi\) | ||||
0.726582 | + | 0.687079i | \(0.241108\pi\) | |||||||
\(338\) | 2703.00 | + | 4681.73i | 0.434982 | + | 0.753410i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 918.000 | − | 1590.02i | 0.146428 | − | 0.253621i | ||||
\(341\) | −655.500 | − | 1135.36i | −0.104098 | − | 0.180303i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3430.00 | + | 5346.84i | 0.539949 | + | 0.841698i | ||||
\(344\) | 992.000 | 0.155480 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3267.00 | + | 5658.61i | −0.507616 | + | 0.879216i | ||||
\(347\) | −4354.50 | + | 7542.22i | −0.673665 | + | 1.16682i | 0.303192 | + | 0.952929i | \(0.401948\pi\) |
−0.976857 | + | 0.213893i | \(0.931386\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6482.00 | 0.994193 | 0.497097 | − | 0.867695i | \(-0.334399\pi\) | ||||
0.497097 | + | 0.867695i | \(0.334399\pi\) | |||||||
\(350\) | −1232.00 | + | 1066.94i | −0.188152 | + | 0.162944i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 912.000 | + | 1579.63i | 0.138096 | + | 0.239189i | ||||
\(353\) | −1066.50 | + | 1847.23i | −0.160805 | + | 0.278522i | −0.935158 | − | 0.354232i | \(-0.884742\pi\) |
0.774353 | + | 0.632754i | \(0.218076\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −432.000 | − | 748.246i | −0.0645864 | − | 0.111867i | ||||
\(356\) | 4068.00 | 0.605628 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2574.00 | 0.380000 | ||||||||
\(359\) | 1924.50 | + | 3333.33i | 0.282928 | + | 0.490046i | 0.972105 | − | 0.234548i | \(-0.0753608\pi\) |
−0.689176 | + | 0.724594i | \(0.742028\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3417.00 | − | 5918.42i | 0.498178 | − | 0.862869i | ||||
\(362\) | −2674.00 | − | 4631.50i | −0.388238 | − | 0.672449i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 980.000 | + | 5092.23i | 0.141115 | + | 0.733256i | ||||
\(365\) | −2817.00 | −0.403969 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3245.50 | + | 5621.37i | −0.461618 | + | 0.799545i | −0.999042 | − | 0.0437668i | \(-0.986064\pi\) |
0.537424 | + | 0.843312i | \(0.319397\pi\) | |||||||
\(368\) | 552.000 | − | 956.092i | 0.0781929 | − | 0.135434i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4554.00 | 0.639868 | ||||||||
\(371\) | −1375.50 | − | 7147.31i | −0.192486 | − | 1.00019i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −461.500 | − | 799.341i | −0.0640632 | − | 0.110961i | 0.832215 | − | 0.554453i | \(-0.187073\pi\) |
−0.896278 | + | 0.443493i | \(0.853739\pi\) | |||||||
\(374\) | −2907.00 | + | 5035.07i | −0.401918 | + | 0.696143i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −804.000 | − | 1392.57i | −0.110274 | − | 0.191001i | ||||
\(377\) | 7980.00 | 1.09016 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6344.00 | 0.859814 | 0.429907 | − | 0.902873i | \(-0.358546\pi\) | ||||
0.429907 | + | 0.902873i | \(0.358546\pi\) | |||||||
\(380\) | −90.0000 | − | 155.885i | −0.0121497 | − | 0.0210440i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4185.00 | + | 7248.63i | −0.560532 | + | 0.970870i | ||||
\(383\) | −2503.50 | − | 4336.19i | −0.334002 | − | 0.578509i | 0.649290 | − | 0.760541i | \(-0.275066\pi\) |
−0.983293 | + | 0.182032i | \(0.941733\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7182.00 | + | 6219.79i | −0.950724 | + | 0.823351i | ||||
\(386\) | 170.000 | 0.0224165 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3668.00 | − | 6353.16i | 0.479934 | − | 0.831270i | ||||
\(389\) | 6145.50 | − | 10644.3i | 0.801001 | − | 1.38737i | −0.117958 | − | 0.993019i | \(-0.537635\pi\) |
0.918958 | − | 0.394355i | \(-0.129032\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3519.00 | 0.455150 | ||||||||
\(392\) | −392.000 | + | 2715.86i | −0.0505076 | + | 0.349927i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 390.000 | + | 675.500i | 0.0498678 | + | 0.0863736i | ||||
\(395\) | −2074.50 | + | 3593.14i | −0.264252 | + | 0.457697i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −443.500 | − | 768.165i | −0.0560671 | − | 0.0971110i | 0.836630 | − | 0.547769i | \(-0.184523\pi\) |
−0.892697 | + | 0.450658i | \(0.851189\pi\) | |||||||
\(398\) | 5666.00 | 0.713595 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −704.000 | −0.0880000 | ||||||||
\(401\) | 5977.50 | + | 10353.3i | 0.744394 | + | 1.28933i | 0.950477 | + | 0.310794i | \(0.100595\pi\) |
−0.206083 | + | 0.978535i | \(0.566072\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 805.000 | − | 1394.30i | 0.0995035 | − | 0.172345i | ||||
\(404\) | −570.000 | − | 987.269i | −0.0701945 | − | 0.121580i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3990.00 | + | 1382.18i | 0.487735 | + | 0.168956i | ||||
\(407\) | −14421.0 | −1.75632 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1710.50 | − | 2962.67i | 0.206794 | − | 0.358178i | −0.743909 | − | 0.668281i | \(-0.767030\pi\) |
0.950703 | + | 0.310103i | \(0.100364\pi\) | |||||||
\(410\) | 378.000 | − | 654.715i | 0.0455319 | − | 0.0788636i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1996.00 | −0.238679 | ||||||||
\(413\) | 766.500 | + | 3982.85i | 0.0913245 | + | 0.474536i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2646.00 | − | 4583.01i | −0.312981 | − | 0.542099i | ||||
\(416\) | −1120.00 | + | 1939.90i | −0.132001 | + | 0.228633i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 285.000 | + | 493.634i | 0.0333488 | + | 0.0577618i | ||||
\(419\) | 5460.00 | 0.636607 | 0.318304 | − | 0.947989i | \(-0.396887\pi\) | ||||
0.318304 | + | 0.947989i | \(0.396887\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7730.00 | 0.894863 | 0.447431 | − | 0.894318i | \(-0.352339\pi\) | ||||
0.447431 | + | 0.894318i | \(0.352339\pi\) | |||||||
\(422\) | −124.000 | − | 214.774i | −0.0143039 | − | 0.0247750i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1572.00 | − | 2722.78i | 0.180054 | − | 0.311863i | ||||
\(425\) | −1122.00 | − | 1943.36i | −0.128059 | − | 0.221804i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12407.5 | − | 4298.08i | −1.40619 | − | 0.487117i | ||||
\(428\) | 4428.00 | 0.500083 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1116.00 | + | 1932.97i | −0.125159 | + | 0.216781i | ||||
\(431\) | −5656.50 | + | 9797.35i | −0.632167 | + | 1.09495i | 0.354941 | + | 0.934889i | \(0.384501\pi\) |
−0.987108 | + | 0.160057i | \(0.948832\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4214.00 | 0.467695 | 0.233847 | − | 0.972273i | \(-0.424868\pi\) | ||||
0.233847 | + | 0.972273i | \(0.424868\pi\) | |||||||
\(434\) | 644.000 | − | 557.720i | 0.0712281 | − | 0.0616853i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1846.00 | − | 3197.37i | −0.202769 | − | 0.351207i | ||||
\(437\) | 172.500 | − | 298.779i | 0.0188828 | − | 0.0327060i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8276.50 | − | 14335.3i | −0.899808 | − | 1.55851i | −0.827739 | − | 0.561114i | \(-0.810373\pi\) |
−0.0720696 | − | 0.997400i | \(-0.522960\pi\) | |||||||
\(440\) | −4104.00 | −0.444660 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7140.00 | −0.768360 | ||||||||
\(443\) | −8197.50 | − | 14198.5i | −0.879176 | − | 1.52278i | −0.852247 | − | 0.523140i | \(-0.824760\pi\) |
−0.0269294 | − | 0.999637i | \(-0.508573\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4576.50 | + | 7926.73i | −0.487521 | + | 0.844411i | ||||
\(446\) | 56.0000 | + | 96.9948i | 0.00594546 | + | 0.0102978i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −896.000 | + | 775.959i | −0.0944911 | + | 0.0818317i | ||||
\(449\) | 15090.0 | 1.58606 | 0.793030 | − | 0.609182i | \(-0.208502\pi\) | ||||
0.793030 | + | 0.609182i | \(0.208502\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1197.00 | + | 2073.26i | −0.124977 | + | 0.216466i | ||||
\(452\) | 3084.00 | − | 5341.64i | 0.320927 | − | 0.555862i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6114.00 | −0.632036 | ||||||||
\(455\) | −11025.0 | − | 3819.17i | −1.13596 | − | 0.393507i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7392.50 | + | 12804.2i | 0.756688 | + | 1.31062i | 0.944531 | + | 0.328423i | \(0.106517\pi\) |
−0.187842 | + | 0.982199i | \(0.560149\pi\) | |||||||
\(458\) | −961.000 | + | 1664.50i | −0.0980449 | + | 0.169819i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1242.00 | + | 2151.21i | 0.125888 | + | 0.218045i | ||||
\(461\) | −2898.00 | −0.292784 | −0.146392 | − | 0.989227i | \(-0.546766\pi\) | ||||
−0.146392 | + | 0.989227i | \(0.546766\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 464.000 | 0.0465743 | 0.0232872 | − | 0.999729i | \(-0.492587\pi\) | ||||
0.0232872 | + | 0.999729i | \(0.492587\pi\) | |||||||
\(464\) | 912.000 | + | 1579.63i | 0.0912468 | + | 0.158044i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2829.00 | − | 4899.97i | 0.281225 | − | 0.487096i | ||||
\(467\) | 2116.50 | + | 3665.89i | 0.209721 | + | 0.363248i | 0.951627 | − | 0.307256i | \(-0.0994109\pi\) |
−0.741905 | + | 0.670505i | \(0.766078\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1466.50 | − | 7620.16i | −0.144385 | − | 0.750248i | ||||
\(470\) | 3618.00 | 0.355076 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −876.000 | + | 1517.28i | −0.0854262 | + | 0.147963i | ||||
\(473\) | 3534.00 | − | 6121.07i | 0.343538 | − | 0.595025i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −220.000 | −0.0212511 | ||||||||
\(476\) | −3570.00 | − | 1236.68i | −0.343762 | − | 0.119083i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3540.00 | + | 6131.46i | 0.338736 | + | 0.586708i | ||||
\(479\) | 1369.50 | − | 2372.04i | 0.130635 | − | 0.226266i | −0.793287 | − | 0.608848i | \(-0.791632\pi\) |
0.923921 | + | 0.382582i | \(0.124965\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8855.00 | − | 15337.3i | −0.839404 | − | 1.45389i | ||||
\(482\) | −10462.0 | −0.988654 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7672.00 | 0.720511 | ||||||||
\(485\) | 8253.00 | + | 14294.6i | 0.772679 | + | 1.33832i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8525.50 | + | 14766.6i | −0.793280 | + | 1.37400i | 0.130646 | + | 0.991429i | \(0.458295\pi\) |
−0.923926 | + | 0.382572i | \(0.875038\pi\) | |||||||
\(488\) | −2836.00 | − | 4912.10i | −0.263073 | − | 0.455656i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4851.00 | − | 3819.17i | −0.447236 | − | 0.352107i | ||||
\(491\) | 4296.00 | 0.394859 | 0.197429 | − | 0.980317i | \(-0.436741\pi\) | ||||
0.197429 | + | 0.980317i | \(0.436741\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2907.00 | + | 5035.07i | −0.265567 | + | 0.459976i | ||||
\(494\) | −350.000 | + | 606.218i | −0.0318770 | + | 0.0552126i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 368.000 | 0.0333139 | ||||||||
\(497\) | −1344.00 | + | 1163.94i | −0.121301 | + | 0.105050i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1700.50 | − | 2945.35i | −0.152555 | − | 0.264233i | 0.779611 | − | 0.626264i | \(-0.215417\pi\) |
−0.932166 | + | 0.362031i | \(0.882083\pi\) | |||||||
\(500\) | 3042.00 | − | 5268.90i | 0.272085 | − | 0.471265i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5040.00 | − | 8729.54i | −0.448100 | − | 0.776132i | ||||
\(503\) | −16800.0 | −1.48921 | −0.744607 | − | 0.667503i | \(-0.767363\pi\) | ||||
−0.744607 | + | 0.667503i | \(0.767363\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2565.00 | 0.226022 | ||||||||
\(506\) | −3933.00 | − | 6812.16i | −0.345540 | − | 0.598493i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4112.00 | − | 7122.19i | 0.359135 | − | 0.622040i | ||||
\(509\) | 919.500 | + | 1592.62i | 0.0800710 | + | 0.138687i | 0.903280 | − | 0.429051i | \(-0.141152\pi\) |
−0.823209 | + | 0.567738i | \(0.807819\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1095.50 | + | 5692.38i | 0.0948377 | + | 0.492791i | ||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1437.00 | − | 2488.96i | 0.123314 | − | 0.213586i | ||||
\(515\) | 2245.50 | − | 3889.32i | 0.192133 | − | 0.332784i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11457.0 | −0.974620 | ||||||||
\(518\) | −1771.00 | − | 9202.39i | −0.150219 | − | 0.780559i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2520.00 | − | 4364.77i | −0.212518 | − | 0.368092i | ||||
\(521\) | 151.500 | − | 262.406i | 0.0127396 | − | 0.0220656i | −0.859585 | − | 0.510992i | \(-0.829278\pi\) |
0.872325 | + | 0.488927i | \(0.162611\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10833.5 | + | 18764.2i | 0.905767 | + | 1.56883i | 0.819885 | + | 0.572528i | \(0.194037\pi\) |
0.0858815 | + | 0.996305i | \(0.472629\pi\) | |||||||
\(524\) | −8196.00 | −0.683290 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4650.00 | −0.385456 | ||||||||
\(527\) | 586.500 | + | 1015.85i | 0.0484788 | + | 0.0839678i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3703.00 | − | 6413.78i | 0.304348 | − | 0.527146i | ||||
\(530\) | 3537.00 | + | 6126.26i | 0.289882 | + | 0.502090i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −280.000 | + | 242.487i | −0.0228187 | + | 0.0197616i | ||||
\(533\) | −2940.00 | −0.238922 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4981.50 | + | 8628.21i | −0.402559 | + | 0.697253i | ||||
\(536\) | 1676.00 | − | 2902.92i | 0.135060 | − | 0.233931i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4770.00 | −0.382248 | ||||||||
\(539\) | 15361.5 | + | 12094.0i | 1.22758 | + | 0.966470i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2519.50 | − | 4363.90i | −0.200225 | − | 0.346800i | 0.748376 | − | 0.663275i | \(-0.230834\pi\) |
−0.948601 | + | 0.316475i | \(0.897501\pi\) | |||||||
\(542\) | −331.000 | + | 573.309i | −0.0262319 | + | 0.0454349i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −816.000 | − | 1413.35i | −0.0643120 | − | 0.111392i | ||||
\(545\) | 8307.00 | 0.652904 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2392.00 | −0.186974 | −0.0934868 | − | 0.995621i | \(-0.529801\pi\) | ||||
−0.0934868 | + | 0.995621i | \(0.529801\pi\) | |||||||
\(548\) | −282.000 | − | 488.438i | −0.0219826 | − | 0.0380749i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2508.00 | + | 4343.98i | −0.194439 | + | 0.336778i | ||||
\(551\) | 285.000 | + | 493.634i | 0.0220352 | + | 0.0381661i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8067.50 | + | 2794.66i | 0.620371 | + | 0.214903i | ||||
\(554\) | −9742.00 | −0.747108 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2968.00 | + | 5140.73i | −0.226387 | + | 0.392114i | ||||
\(557\) | −11074.5 | + | 19181.6i | −0.842445 | + | 1.45916i | 0.0453775 | + | 0.998970i | \(0.485551\pi\) |
−0.887822 | + | 0.460187i | \(0.847782\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8680.00 | 0.656753 | ||||||||
\(560\) | −504.000 | − | 2618.86i | −0.0380319 | − | 0.197620i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7026.00 | + | 12169.4i | 0.527356 | + | 0.913407i | ||||
\(563\) | −4174.50 | + | 7230.45i | −0.312494 | + | 0.541256i | −0.978902 | − | 0.204332i | \(-0.934498\pi\) |
0.666408 | + | 0.745588i | \(0.267831\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6939.00 | + | 12018.7i | 0.516683 | + | 0.894921i | ||||
\(566\) | 10706.0 | 0.795065 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −768.000 | −0.0567334 | ||||||||
\(569\) | −7672.50 | − | 13289.2i | −0.565286 | − | 0.979105i | −0.997023 | − | 0.0771050i | \(-0.975432\pi\) |
0.431737 | − | 0.902000i | \(-0.357901\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5796.50 | − | 10039.8i | 0.424827 | − | 0.735821i | −0.571578 | − | 0.820548i | \(-0.693668\pi\) |
0.996404 | + | 0.0847268i | \(0.0270017\pi\) | |||||||
\(572\) | 7980.00 | + | 13821.8i | 0.583323 | + | 1.01034i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1470.00 | − | 509.223i | −0.106893 | − | 0.0370288i | ||||
\(575\) | 3036.00 | 0.220191 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7296.50 | − | 12637.9i | 0.526442 | − | 0.911825i | −0.473083 | − | 0.881018i | \(-0.656859\pi\) |
0.999525 | − | 0.0308071i | \(-0.00980776\pi\) | |||||||
\(578\) | −2312.00 | + | 4004.50i | −0.166378 | + | 0.288175i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4104.00 | −0.293809 | ||||||||
\(581\) | −8232.00 | + | 7129.12i | −0.587816 | + | 0.509063i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11200.5 | − | 19399.8i | −0.795673 | − | 1.37815i | ||||
\(584\) | −1252.00 | + | 2168.53i | −0.0887125 | + | 0.153655i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4158.00 | − | 7201.87i | −0.293115 | − | 0.507690i | ||||
\(587\) | 15372.0 | 1.08087 | 0.540435 | − | 0.841386i | \(-0.318260\pi\) | ||||
0.540435 | + | 0.841386i | \(0.318260\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 115.000 | 0.00804498 | ||||||||
\(590\) | −1971.00 | − | 3413.87i | −0.137534 | − | 0.238215i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2024.00 | − | 3505.67i | 0.140517 | − | 0.243382i | ||||
\(593\) | −7186.50 | − | 12447.4i | −0.497663 | − | 0.861978i | 0.502333 | − | 0.864674i | \(-0.332475\pi\) |
−0.999996 | + | 0.00269639i | \(0.999142\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6426.00 | − | 5565.08i | 0.442757 | − | 0.383439i | ||||
\(596\) | 228.000 | 0.0156699 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4830.00 | − | 8365.81i | 0.330290 | − | 0.572079i | ||||
\(599\) | 1273.50 | − | 2205.77i | 0.0868678 | − | 0.150459i | −0.819318 | − | 0.573340i | \(-0.805648\pi\) |
0.906186 | + | 0.422880i | \(0.138981\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7042.00 | −0.477952 | −0.238976 | − | 0.971025i | \(-0.576812\pi\) | ||||
−0.238976 | + | 0.971025i | \(0.576812\pi\) | |||||||
\(602\) | 4340.00 | + | 1503.42i | 0.293829 | + | 0.101785i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1678.00 | − | 2906.38i | −0.113041 | − | 0.195793i | ||||
\(605\) | −8631.00 | + | 14949.3i | −0.580000 | + | 1.00459i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11295.5 | + | 19564.4i | 0.755305 | + | 1.30823i | 0.945223 | + | 0.326427i | \(0.105845\pi\) |
−0.189917 | + | 0.981800i | \(0.560822\pi\) | |||||||
\(608\) | −160.000 | −0.0106725 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 12762.0 | 0.847079 | ||||||||
\(611\) | −7035.00 | − | 12185.0i | −0.465803 | − | 0.806794i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4242.50 | − | 7348.23i | 0.279532 | − | 0.484163i | −0.691737 | − | 0.722150i | \(-0.743154\pi\) |
0.971268 | + | 0.237987i | \(0.0764874\pi\) | |||||||
\(614\) | −9604.00 | − | 16634.6i | −0.631247 | − | 1.09335i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1596.00 | + | 8293.06i | 0.104391 | + | 0.542430i | ||||
\(617\) | 18282.0 | 1.19288 | 0.596439 | − | 0.802658i | \(-0.296582\pi\) | ||||
0.596439 | + | 0.802658i | \(0.296582\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1145.50 | + | 1984.06i | −0.0743805 | + | 0.128831i | −0.900817 | − | 0.434200i | \(-0.857031\pi\) |
0.826436 | + | 0.563030i | \(0.190365\pi\) | |||||||
\(620\) | −414.000 | + | 717.069i | −0.0268172 | + | 0.0464487i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 20262.0 | 1.30616 | ||||||||
\(623\) | 17797.5 | + | 6165.23i | 1.14453 | + | 0.396477i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4094.50 | + | 7091.88i | 0.262048 | + | 0.453880i | ||||
\(626\) | 10799.0 | − | 18704.4i | 0.689481 | − | 1.19422i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5666.00 | + | 9813.80i | 0.360029 | + | 0.623588i | ||||
\(629\) | 12903.0 | 0.817927 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6928.00 | −0.437083 | −0.218541 | − | 0.975828i | \(-0.570130\pi\) | ||||
−0.218541 | + | 0.975828i | \(0.570130\pi\) | |||||||
\(632\) | 1844.00 | + | 3193.90i | 0.116061 | + | 0.201023i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −531.000 | + | 919.719i | −0.0332629 | + | 0.0576131i | ||||
\(635\) | 9252.00 | + | 16024.9i | 0.578196 | + | 1.00146i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3430.00 | + | 23763.7i | −0.213346 | + | 1.47811i | ||||
\(638\) | 12996.0 | 0.806452 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 576.000 | − | 997.661i | 0.0355756 | − | 0.0616188i | ||||
\(641\) | 12487.5 | − | 21629.0i | 0.769464 | − | 1.33275i | −0.168390 | − | 0.985721i | \(-0.553857\pi\) |
0.937854 | − | 0.347031i | \(-0.112810\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9548.00 | 0.585593 | 0.292797 | − | 0.956175i | \(-0.405414\pi\) | ||||
0.292797 | + | 0.956175i | \(0.405414\pi\) | |||||||
\(644\) | 3864.00 | − | 3346.32i | 0.236433 | − | 0.204757i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −255.000 | − | 441.673i | −0.0155307 | − | 0.0269000i | ||||
\(647\) | 5065.50 | − | 8773.70i | 0.307798 | − | 0.533122i | −0.670082 | − | 0.742287i | \(-0.733741\pi\) |
0.977880 | + | 0.209165i | \(0.0670745\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6241.50 | + | 10810.6i | 0.377504 | + | 0.653857i | ||||
\(650\) | −6160.00 | −0.371716 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9244.00 | −0.555250 | ||||||||
\(653\) | 8329.50 | + | 14427.1i | 0.499171 | + | 0.864589i | 1.00000 | 0.000957229i | \(-0.000304695\pi\) | |
−0.500829 | + | 0.865546i | \(0.666971\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9220.50 | − | 15970.4i | 0.550038 | − | 0.952693i | ||||
\(656\) | −336.000 | − | 581.969i | −0.0199979 | − | 0.0346373i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1407.00 | − | 7310.99i | −0.0833595 | − | 0.433149i | ||||
\(659\) | −29556.0 | −1.74710 | −0.873550 | − | 0.486735i | \(-0.838188\pi\) | ||||
−0.873550 | + | 0.486735i | \(0.838188\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −95.5000 | + | 165.411i | −0.00561955 | + | 0.00973334i | −0.868822 | − | 0.495125i | \(-0.835122\pi\) |
0.863202 | + | 0.504859i | \(0.168455\pi\) | |||||||
\(662\) | −7015.00 | + | 12150.3i | −0.411852 | + | 0.713348i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4704.00 | −0.274926 | ||||||||
\(665\) | −157.500 | − | 818.394i | −0.00918434 | − | 0.0477232i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3933.00 | − | 6812.16i | −0.228315 | − | 0.395454i | ||||
\(668\) | 2520.00 | − | 4364.77i | 0.145961 | − | 0.252811i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3771.00 | + | 6531.56i | 0.217442 | + | 0.376621i | ||||
\(671\) | −40413.0 | −2.32508 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2606.00 | 0.149263 | 0.0746314 | − | 0.997211i | \(-0.476222\pi\) | ||||
0.0746314 | + | 0.997211i | \(0.476222\pi\) | |||||||
\(674\) | 8990.00 | + | 15571.1i | 0.513771 | + | 0.889878i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5406.00 | + | 9363.47i | −0.307579 | + | 0.532742i | ||||
\(677\) | −2104.50 | − | 3645.10i | −0.119472 | − | 0.206931i | 0.800087 | − | 0.599885i | \(-0.204787\pi\) |
−0.919559 | + | 0.392953i | \(0.871453\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 25676.0 | − | 22236.1i | 1.45118 | − | 1.25676i | ||||
\(680\) | 3672.00 | 0.207081 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1311.00 | − | 2270.72i | 0.0736082 | − | 0.127493i | ||||
\(683\) | 12151.5 | − | 21047.0i | 0.680768 | − | 1.17912i | −0.293979 | − | 0.955812i | \(-0.594980\pi\) |
0.974747 | − | 0.223312i | \(-0.0716869\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1269.00 | 0.0707825 | ||||||||
\(686\) | −5831.00 | + | 11287.8i | −0.324532 | + | 0.628235i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 992.000 | + | 1718.19i | 0.0549704 | + | 0.0952116i | ||||
\(689\) | 13755.0 | − | 23824.4i | 0.760557 | − | 1.31732i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7520.50 | − | 13025.9i | −0.414028 | − | 0.717117i | 0.581298 | − | 0.813691i | \(-0.302545\pi\) |
−0.995326 | + | 0.0965734i | \(0.969212\pi\) | |||||||
\(692\) | −13068.0 | −0.717877 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −17418.0 | −0.952706 | ||||||||
\(695\) | −6678.00 | − | 11566.6i | −0.364476 | − | 0.631291i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1071.00 | − | 1855.03i | 0.0582023 | − | 0.100809i | ||||
\(698\) | 6482.00 | + | 11227.2i | 0.351500 | + | 0.608817i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3080.00 | − | 1066.94i | −0.166304 | − | 0.0576095i | ||||
\(701\) | −24726.0 | −1.33222 | −0.666111 | − | 0.745852i | \(-0.732042\pi\) | ||||
−0.666111 | + | 0.745852i | \(0.732042\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 632.500 | − | 1095.52i | 0.0339334 | − | 0.0587744i | ||||
\(704\) | −1824.00 | + | 3159.26i | −0.0976486 | + | 0.169132i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4266.00 | −0.227412 | ||||||||
\(707\) | −997.500 | − | 5183.16i | −0.0530620 | − | 0.275718i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2478.50 | + | 4292.89i | 0.131286 | + | 0.227395i | 0.924173 | − | 0.381975i | \(-0.124756\pi\) |
−0.792886 | + | 0.609370i | \(0.791423\pi\) | |||||||
\(710\) | 864.000 | − | 1496.49i | 0.0456695 | − | 0.0791019i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4068.00 | + | 7045.98i | 0.214122 | + | 0.370870i | ||||
\(713\) | −1587.00 | −0.0833571 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −35910.0 | −1.87826 | ||||||||
\(716\) | 2574.00 | + | 4458.30i | 0.134350 | + | 0.232702i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3849.00 | + | 6666.66i | −0.200060 | + | 0.346515i | ||||
\(719\) | 13834.5 | + | 23962.1i | 0.717580 | + | 1.24288i | 0.961956 | + | 0.273204i | \(0.0880834\pi\) |
−0.244376 | + | 0.969680i | \(0.578583\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8732.50 | − | 3025.03i | −0.451061 | − | 0.156252i | ||||
\(722\) | 13668.0 | 0.704529 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5348.00 | − | 9263.01i | 0.274526 | − | 0.475493i | ||||
\(725\) | −2508.00 | + | 4343.98i | −0.128476 | + | 0.222526i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13888.0 | −0.708497 | −0.354249 | − | 0.935151i | \(-0.615263\pi\) | ||||
−0.354249 | + | 0.935151i | \(0.615263\pi\) | |||||||
\(728\) | −7840.00 | + | 6789.64i | −0.399134 | + | 0.345660i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2817.00 | − | 4879.19i | −0.142824 | − | 0.247379i | ||||
\(731\) | −3162.00 | + | 5476.74i | −0.159987 | + | 0.277106i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7121.50 | − | 12334.8i | −0.358852 | − | 0.621550i | 0.628917 | − | 0.777472i | \(-0.283498\pi\) |
−0.987769 | + | 0.155922i | \(0.950165\pi\) | |||||||
\(734\) | −12982.0 | −0.652826 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2208.00 | 0.110581 | ||||||||
\(737\) | −11941.5 | − | 20683.3i | −0.596840 | − | 1.03376i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18479.5 | + | 32007.4i | −0.919864 | + | 1.59325i | −0.120244 | + | 0.992744i | \(0.538368\pi\) |
−0.799620 | + | 0.600507i | \(0.794966\pi\) | |||||||
\(740\) | 4554.00 | + | 7887.76i | 0.226228 | + | 0.391838i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 11004.0 | − | 9529.74i | 0.544433 | − | 0.471493i | ||||
\(743\) | 12528.0 | 0.618584 | 0.309292 | − | 0.950967i | \(-0.399908\pi\) | ||||
0.309292 | + | 0.950967i | \(0.399908\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −256.500 | + | 444.271i | −0.0126140 | + | 0.0218481i | ||||
\(746\) | 923.000 | − | 1598.68i | 0.0452995 | − | 0.0784610i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −11628.0 | −0.568398 | ||||||||
\(749\) | 19372.5 | + | 6710.83i | 0.945068 | + | 0.327381i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8883.50 | + | 15386.7i | 0.431643 | + | 0.747627i | 0.997015 | − | 0.0772090i | \(-0.0246009\pi\) |
−0.565372 | + | 0.824836i | \(0.691268\pi\) | |||||||
\(752\) | 1608.00 | − | 2785.14i | 0.0779757 | − | 0.135058i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 7980.00 | + | 13821.8i | 0.385430 | + | 0.667585i | ||||
\(755\) | 7551.00 | 0.363985 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28726.0 | −1.37921 | −0.689606 | − | 0.724184i | \(-0.742216\pi\) | ||||
−0.689606 | + | 0.724184i | \(0.742216\pi\) | |||||||
\(758\) | 6344.00 | + | 10988.1i | 0.303990 | + | 0.526526i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 180.000 | − | 311.769i | 0.00859117 | − | 0.0148803i | ||||
\(761\) | −13234.5 | − | 22922.8i | −0.630421 | − | 1.09192i | −0.987466 | − | 0.157834i | \(-0.949549\pi\) |
0.357045 | − | 0.934087i | \(-0.383784\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3230.50 | − | 16786.2i | −0.153279 | − | 0.796462i | ||||
\(764\) | −16740.0 | −0.792712 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5007.00 | − | 8672.38i | 0.236175 | − | 0.409068i | ||||
\(767\) | −7665.00 | + | 13276.2i | −0.360844 | + | 0.625000i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5054.00 | 0.236999 | 0.118499 | − | 0.992954i | \(-0.462192\pi\) | ||||
0.118499 | + | 0.992954i | \(0.462192\pi\) | |||||||
\(770\) | −17955.0 | − | 6219.79i | −0.840329 | − | 0.291098i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 170.000 | + | 294.449i | 0.00792543 | + | 0.0137273i | ||||
\(773\) | −17782.5 | + | 30800.2i | −0.827415 | + | 1.43313i | 0.0726439 | + | 0.997358i | \(0.476856\pi\) |
−0.900059 | + | 0.435767i | \(0.856477\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 506.000 | + | 876.418i | 0.0234530 | + | 0.0406217i | ||||
\(776\) | 14672.0 | 0.678730 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 24582.0 | 1.13279 | ||||||||
\(779\) | −105.000 | − | 181.865i | −0.00482929 | − | 0.00836457i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2736.00 | + | 4738.89i | −0.125354 | + | 0.217120i | ||||
\(782\) | 3519.00 | + | 6095.09i | 0.160920 | + | 0.278721i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5096.00 | + | 2036.89i | −0.232143 | + | 0.0927884i | ||||
\(785\) | −25497.0 | −1.15927 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4314.50 | − | 7472.93i | 0.195420 | − | 0.338477i | −0.751618 | − | 0.659598i | \(-0.770726\pi\) |
0.947038 | + | 0.321121i | \(0.104060\pi\) | |||||||
\(788\) | −780.000 | + | 1351.00i | −0.0352619 | + | 0.0610753i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8298.00 | −0.373708 | ||||||||
\(791\) | 21588.0 | − | 18695.8i | 0.970393 | − | 0.840385i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24815.0 | − | 42980.8i | −1.11123 | − | 1.92471i | ||||
\(794\) | 887.000 | − | 1536.33i | 0.0396454 | − | 0.0686679i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5666.00 | + | 9813.80i | 0.252294 | + | 0.436986i | ||||
\(797\) | −20706.0 | −0.920256 | −0.460128 | − | 0.887853i | \(-0.652197\pi\) | ||||
−0.460128 | + | 0.887853i | \(0.652197\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10251.0 | 0.453885 | ||||||||
\(800\) | −704.000 | − | 1219.36i | −0.0311127 | − | 0.0538888i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −11955.0 | + | 20706.7i | −0.526366 | + | 0.911693i | ||||
\(803\) | 8920.50 | + | 15450.8i | 0.392027 | + | 0.679011i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2173.50 | + | 11293.8i | 0.0951625 | + | 0.494479i | ||||
\(806\) | 3220.00 | 0.140719 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1140.00 | − | 1974.54i | 0.0496350 | − | 0.0859703i | ||||
\(809\) | −8092.50 | + | 14016.6i | −0.351690 | + | 0.609145i | −0.986546 | − | 0.163486i | \(-0.947726\pi\) |
0.634856 | + | 0.772631i | \(0.281060\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11788.0 | −0.510398 | −0.255199 | − | 0.966889i | \(-0.582141\pi\) | ||||
−0.255199 | + | 0.966889i | \(0.582141\pi\) | |||||||
\(812\) | 1596.00 | + | 8293.06i | 0.0689761 | + | 0.358411i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −14421.0 | − | 24977.9i | −0.620953 | − | 1.07552i | ||||
\(815\) | 10399.5 | − | 18012.5i | 0.446968 | − | 0.774171i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 310.000 | + | 536.936i | 0.0132748 | + | 0.0229927i | ||||
\(818\) | 6842.00 | 0.292451 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1512.00 | 0.0643919 | ||||||||
\(821\) | −14896.5 | − | 25801.5i | −0.633242 | − | 1.09681i | −0.986885 | − | 0.161426i | \(-0.948391\pi\) |
0.353643 | − | 0.935380i | \(-0.384943\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15161.5 | + | 26260.5i | −0.642159 | + | 1.11225i | 0.342791 | + | 0.939412i | \(0.388628\pi\) |
−0.984950 | + | 0.172840i | \(0.944706\pi\) | |||||||
\(824\) | −1996.00 | − | 3457.17i | −0.0843859 | − | 0.146161i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6132.00 | + | 5310.47i | −0.258305 | + | 0.223698i | ||||
\(827\) | −21156.0 | −0.889560 | −0.444780 | − | 0.895640i | \(-0.646718\pi\) | ||||
−0.444780 | + | 0.895640i | \(0.646718\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2634.50 | − | 4563.09i | 0.110374 | − | 0.191173i | −0.805547 | − | 0.592532i | \(-0.798129\pi\) |
0.915921 | + | 0.401358i | \(0.131462\pi\) | |||||||
\(830\) | 5292.00 | − | 9166.01i | 0.221311 | − | 0.383322i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4480.00 | −0.186678 | ||||||||
\(833\) | −13744.5 | − | 10821.0i | −0.571691 | − | 0.450090i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5670.00 | + | 9820.73i | 0.234992 | + | 0.407018i | ||||
\(836\) | −570.000 | + | 987.269i | −0.0235812 | + | 0.0408438i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5460.00 | + | 9457.00i | 0.225075 | + | 0.389841i | ||||
\(839\) | 39816.0 | 1.63838 | 0.819190 | − | 0.573522i | \(-0.194423\pi\) | ||||
0.819190 | + | 0.573522i | \(0.194423\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11393.0 | −0.467137 | ||||||||
\(842\) | 7730.00 | + | 13388.8i | 0.316382 | + | 0.547989i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 248.000 | − | 429.549i | 0.0101144 | − | 0.0175186i | ||||
\(845\) | −12163.5 | − | 21067.8i | −0.495192 | − | 0.857697i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 33565.0 | + | 11627.3i | 1.36164 | + | 0.471685i | ||||
\(848\) | 6288.00 | 0.254635 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2244.00 | − | 3886.72i | 0.0905513 | − | 0.156839i | ||||
\(851\) | −8728.50 | + | 15118.2i | −0.351597 | + | 0.608984i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14546.0 | 0.583875 | 0.291938 | − | 0.956437i | \(-0.405700\pi\) | ||||
0.291938 | + | 0.956437i | \(0.405700\pi\) | |||||||
\(854\) | −4963.00 | − | 25788.5i | −0.198865 | − | 1.03333i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4428.00 | + | 7669.52i | 0.176806 | + | 0.306237i | ||||
\(857\) | −15724.5 | + | 27235.6i | −0.626766 | + | 1.08559i | 0.361430 | + | 0.932399i | \(0.382289\pi\) |
−0.988196 | + | 0.153192i | \(0.951045\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12261.5 | + | 21237.5i | 0.487028 | + | 0.843557i | 0.999889 | − | 0.0149147i | \(-0.00474766\pi\) |
−0.512861 | + | 0.858472i | \(0.671414\pi\) | |||||||
\(860\) | −4464.00 | −0.177001 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −22626.0 | −0.894019 | ||||||||
\(863\) | −4081.50 | − | 7069.37i | −0.160992 | − | 0.278846i | 0.774233 | − | 0.632901i | \(-0.218136\pi\) |
−0.935225 | + | 0.354055i | \(0.884803\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14701.5 | − | 25463.7i | 0.577880 | − | 1.00092i | ||||
\(866\) | 4214.00 | + | 7298.86i | 0.165355 | + | 0.286403i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1610.00 | + | 557.720i | 0.0629573 | + | 0.0218091i | ||||
\(869\) | 26277.0 | 1.02576 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14665.0 | − | 25400.5i | 0.570499 | − | 0.988133i | ||||
\(872\) | 3692.00 | − | 6394.73i | 0.143379 | − | 0.248341i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 690.000 | 0.0267043 | ||||||||
\(875\) | 21294.0 | − | 18441.1i | 0.822707 | − | 0.712485i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2183.50 | − | 3781.93i | −0.0840725 | − | 0.145618i | 0.820923 | − | 0.571039i | \(-0.193459\pi\) |
−0.904996 | + | 0.425421i | \(0.860126\pi\) | |||||||
\(878\) | 16553.0 | − | 28670.6i | 0.636260 | − | 1.10204i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4104.00 | − | 7108.34i | −0.157211 | − | 0.272298i | ||||
\(881\) | 50190.0 | 1.91935 | 0.959673 | − | 0.281118i | \(-0.0907053\pi\) | ||||
0.959673 | + | 0.281118i | \(0.0907053\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12308.0 | 0.469079 | 0.234540 | − | 0.972107i | \(-0.424642\pi\) | ||||
0.234540 | + | 0.972107i | \(0.424642\pi\) | |||||||
\(884\) | −7140.00 | − | 12366.8i | −0.271656 | − | 0.470523i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16395.0 | − | 28397.0i | 0.621671 | − | 1.07677i | ||||
\(887\) | 15808.5 | + | 27381.1i | 0.598419 | + | 1.03649i | 0.993055 | + | 0.117654i | \(0.0375374\pi\) |
−0.394636 | + | 0.918838i | \(0.629129\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 28784.0 | − | 24927.7i | 1.08592 | − | 0.940436i | ||||
\(890\) | −18306.0 | −0.689459 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −112.000 | + | 193.990i | −0.00420408 | + | 0.00728168i | ||||
\(893\) | 502.500 | − | 870.356i | 0.0188304 | − | 0.0326152i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11583.0 | −0.432600 | ||||||||
\(896\) | −2240.00 | − | 775.959i | −0.0835191 | − | 0.0289319i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15090.0 | + | 26136.6i | 0.560757 | + | 0.971260i | ||||
\(899\) | 1311.00 | − | 2270.72i | 0.0486366 | − | 0.0842411i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10021.5 | + | 17357.7i | 0.370549 | + | 0.641810i | ||||
\(902\) | −4788.00 | −0.176744 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12336.0 | 0.453860 | ||||||||
\(905\) | 12033.0 | + | 20841.8i | 0.441978 | + | 0.765529i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6762.50 | − | 11713.0i | 0.247569 | − | 0.428802i | −0.715282 | − | 0.698836i | \(-0.753702\pi\) |
0.962851 | + | 0.270034i | \(0.0870350\pi\) | |||||||
\(908\) | −6114.00 | − | 10589.8i | −0.223458 | − | 0.387041i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4410.00 | − | 22915.0i | −0.160648 | − | 0.834754i | ||||
\(911\) | 19248.0 | 0.700016 | 0.350008 | − | 0.936747i | \(-0.386179\pi\) | ||||
0.350008 | + | 0.936747i | \(0.386179\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16758.0 | + | 29025.7i | −0.607458 | + | 1.05215i | ||||
\(914\) | −14785.0 | + | 25608.4i | −0.535059 | + | 0.926750i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3844.00 | −0.138656 | ||||||||
\(917\) | −35857.5 | − | 12421.4i | −1.29130 | − | 0.447318i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4347.50 | + | 7530.09i | 0.156051 | + | 0.270288i | 0.933441 | − | 0.358730i | \(-0.116790\pi\) |
−0.777390 | + | 0.629019i | \(0.783457\pi\) | |||||||
\(920\) | −2484.00 | + | 4302.41i | −0.0890164 | + | 0.154181i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2898.00 | − | 5019.48i | −0.103515 | − | 0.179293i | ||||
\(923\) | −6720.00 | −0.239644 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11132.0 | 0.395695 | ||||||||
\(926\) | 464.000 | + | 803.672i | 0.0164665 | + | 0.0285208i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1824.00 | + | 3159.26i | −0.0645213 | + | 0.111754i | ||||
\(929\) | 9739.50 | + | 16869.3i | 0.343964 | + | 0.595763i | 0.985165 | − | 0.171610i | \(-0.0548968\pi\) |
−0.641201 | + | 0.767373i | \(0.721563\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1592.50 | + | 636.529i | −0.0560602 | + | 0.0224075i | ||||
\(932\) | 11316.0 | 0.397712 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −4233.00 | + | 7331.77i | −0.148295 | + | 0.256855i | ||||
\(935\) | 13081.5 | − | 22657.8i | 0.457552 | − | 0.792503i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12502.0 | −0.435883 | −0.217942 | − | 0.975962i | \(-0.569934\pi\) | ||||
−0.217942 | + | 0.975962i | \(0.569934\pi\) | |||||||
\(938\) | 11732.0 | − | 10160.2i | 0.408383 | − | 0.353670i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3618.00 | + | 6266.56i | 0.125538 | + | 0.217439i | ||||
\(941\) | −7996.50 | + | 13850.3i | −0.277023 | + | 0.479818i | −0.970643 | − | 0.240523i | \(-0.922681\pi\) |
0.693621 | + | 0.720340i | \(0.256014\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1449.00 | + | 2509.74i | 0.0500381 | + | 0.0866685i | ||||
\(944\) | −3504.00 | −0.120811 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 14136.0 | 0.485836 | ||||||||
\(947\) | 22000.5 | + | 38106.0i | 0.754932 | + | 1.30758i | 0.945408 | + | 0.325888i | \(0.105663\pi\) |
−0.190477 | + | 0.981692i | \(0.561003\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10955.0 | + | 18974.6i | −0.374725 | + | 0.649043i | ||||
\(950\) | −220.000 | − | 381.051i | −0.00751341 | − | 0.0130136i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1428.00 | − | 7420.11i | −0.0486153 | − | 0.252612i | ||||
\(953\) | 4002.00 | 0.136031 | 0.0680155 | − | 0.997684i | \(-0.478333\pi\) | ||||
0.0680155 | + | 0.997684i | \(0.478333\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18832.5 | − | 32618.8i | 0.638121 | − | 1.10526i | ||||
\(956\) | −7080.00 | + | 12262.9i | −0.239523 | + | 0.414865i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 5478.00 | 0.184745 | ||||||||
\(959\) | −493.500 | − | 2564.30i | −0.0166173 | − | 0.0863458i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14631.0 | + | 25341.6i | 0.491121 | + | 0.850647i | ||||
\(962\) | 17710.0 | − | 30674.6i | 0.593548 | − | 1.02806i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10462.0 | − | 18120.7i | −0.349542 | − | 0.605424i | ||||
\(965\) | −765.000 | −0.0255194 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10544.0 | 0.350643 | 0.175322 | − | 0.984511i | \(-0.443903\pi\) | ||||
0.175322 | + | 0.984511i | \(0.443903\pi\) | |||||||
\(968\) | 7672.00 | + | 13288.3i | 0.254739 | + | 0.441221i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −16506.0 | + | 28589.2i | −0.546367 | + | 0.946335i | ||||
\(971\) | −3091.50 | − | 5354.64i | −0.102174 | − | 0.176971i | 0.810406 | − | 0.585869i | \(-0.199247\pi\) |
−0.912580 | + | 0.408898i | \(0.865913\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20776.0 | + | 17992.5i | −0.684530 | + | 0.592821i | ||||
\(974\) | −34102.0 | −1.12187 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5672.00 | − | 9824.19i | 0.186021 | − | 0.322197i | ||||
\(977\) | 1861.50 | − | 3224.21i | 0.0609567 | − | 0.105580i | −0.833937 | − | 0.551860i | \(-0.813918\pi\) |
0.894893 | + | 0.446280i | \(0.147252\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 57969.0 | 1.89244 | ||||||||
\(980\) | 1764.00 | − | 12221.4i | 0.0574989 | − | 0.398364i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4296.00 | + | 7440.89i | 0.139604 | + | 0.241801i | ||||
\(983\) | −22948.5 | + | 39748.0i | −0.744602 | + | 1.28969i | 0.205779 | + | 0.978599i | \(0.434027\pi\) |
−0.950381 | + | 0.311089i | \(0.899306\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1755.00 | − | 3039.75i | −0.0567705 | − | 0.0983294i | ||||
\(986\) | −11628.0 | −0.375569 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1400.00 | −0.0450809 | ||||||||
\(989\) | −4278.00 | − | 7409.71i | −0.137545 | − | 0.238236i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3233.50 | + | 5600.59i | −0.103648 | + | 0.179524i | −0.913185 | − | 0.407545i | \(-0.866385\pi\) |
0.809537 | + | 0.587069i | \(0.199718\pi\) | |||||||
\(992\) | 368.000 | + | 637.395i | 0.0117782 | + | 0.0204005i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3360.00 | − | 1163.94i | −0.107216 | − | 0.0371407i | ||||
\(995\) | −25497.0 | −0.812371 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11519.5 | + | 19952.4i | −0.365924 | + | 0.633799i | −0.988924 | − | 0.148423i | \(-0.952580\pi\) |
0.623000 | + | 0.782222i | \(0.285914\pi\) | |||||||
\(998\) | 3401.00 | − | 5890.70i | 0.107873 | − | 0.186841i | ||||
\(999\) | 0 | 0 |
(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 | 126.4.g.d.109.1 | 2 | ||
3.2 | odd | 2 | 14.4.c.a.11.1 | yes | 2 | ||
7.2 | even | 3 | inner | 126.4.g.d.37.1 | 2 | ||
7.3 | odd | 6 | 882.4.a.c.1.1 | 1 | |||
7.4 | even | 3 | 882.4.a.f.1.1 | 1 | |||
7.5 | odd | 6 | 882.4.g.u.667.1 | 2 | |||
7.6 | odd | 2 | 882.4.g.u.361.1 | 2 | |||
12.11 | even | 2 | 112.4.i.a.81.1 | 2 | |||
15.2 | even | 4 | 350.4.j.b.249.2 | 4 | |||
15.8 | even | 4 | 350.4.j.b.249.1 | 4 | |||
15.14 | odd | 2 | 350.4.e.e.151.1 | 2 | |||
21.2 | odd | 6 | 14.4.c.a.9.1 | ✓ | 2 | ||
21.5 | even | 6 | 98.4.c.a.79.1 | 2 | |||
21.11 | odd | 6 | 98.4.a.d.1.1 | 1 | |||
21.17 | even | 6 | 98.4.a.f.1.1 | 1 | |||
21.20 | even | 2 | 98.4.c.a.67.1 | 2 | |||
24.5 | odd | 2 | 448.4.i.b.193.1 | 2 | |||
24.11 | even | 2 | 448.4.i.e.193.1 | 2 | |||
84.11 | even | 6 | 784.4.a.p.1.1 | 1 | |||
84.23 | even | 6 | 112.4.i.a.65.1 | 2 | |||
84.59 | odd | 6 | 784.4.a.c.1.1 | 1 | |||
105.2 | even | 12 | 350.4.j.b.149.1 | 4 | |||
105.23 | even | 12 | 350.4.j.b.149.2 | 4 | |||
105.44 | odd | 6 | 350.4.e.e.51.1 | 2 | |||
105.59 | even | 6 | 2450.4.a.d.1.1 | 1 | |||
105.74 | odd | 6 | 2450.4.a.q.1.1 | 1 | |||
168.107 | even | 6 | 448.4.i.e.65.1 | 2 | |||
168.149 | odd | 6 | 448.4.i.b.65.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.4.c.a.9.1 | ✓ | 2 | 21.2 | odd | 6 | ||
14.4.c.a.11.1 | yes | 2 | 3.2 | odd | 2 | ||
98.4.a.d.1.1 | 1 | 21.11 | odd | 6 | |||
98.4.a.f.1.1 | 1 | 21.17 | even | 6 | |||
98.4.c.a.67.1 | 2 | 21.20 | even | 2 | |||
98.4.c.a.79.1 | 2 | 21.5 | even | 6 | |||
112.4.i.a.65.1 | 2 | 84.23 | even | 6 | |||
112.4.i.a.81.1 | 2 | 12.11 | even | 2 | |||
126.4.g.d.37.1 | 2 | 7.2 | even | 3 | inner | ||
126.4.g.d.109.1 | 2 | 1.1 | even | 1 | trivial | ||
350.4.e.e.51.1 | 2 | 105.44 | odd | 6 | |||
350.4.e.e.151.1 | 2 | 15.14 | odd | 2 | |||
350.4.j.b.149.1 | 4 | 105.2 | even | 12 | |||
350.4.j.b.149.2 | 4 | 105.23 | even | 12 | |||
350.4.j.b.249.1 | 4 | 15.8 | even | 4 | |||
350.4.j.b.249.2 | 4 | 15.2 | even | 4 | |||
448.4.i.b.65.1 | 2 | 168.149 | odd | 6 | |||
448.4.i.b.193.1 | 2 | 24.5 | odd | 2 | |||
448.4.i.e.65.1 | 2 | 168.107 | even | 6 | |||
448.4.i.e.193.1 | 2 | 24.11 | even | 2 | |||
784.4.a.c.1.1 | 1 | 84.59 | odd | 6 | |||
784.4.a.p.1.1 | 1 | 84.11 | even | 6 | |||
882.4.a.c.1.1 | 1 | 7.3 | odd | 6 | |||
882.4.a.f.1.1 | 1 | 7.4 | even | 3 | |||
882.4.g.u.361.1 | 2 | 7.6 | odd | 2 | |||
882.4.g.u.667.1 | 2 | 7.5 | odd | 6 | |||
2450.4.a.d.1.1 | 1 | 105.59 | even | 6 | |||
2450.4.a.q.1.1 | 1 | 105.74 | odd | 6 |