Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [81,4,Mod(28,81)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(81, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("81.28");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 81 = 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 81.c (of order \(3\), degree \(2\), not 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: | \(4.77915471046\) |
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: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 27) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 28.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 81.28 |
Dual form | 81.4.c.a.55.1 |
$q$-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 \(\left(\mathbb{Z}/81\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.50000 | − | 2.59808i | −0.530330 | − | 0.918559i | −0.999374 | − | 0.0353837i | \(-0.988735\pi\) |
0.469044 | − | 0.883175i | \(-0.344599\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.0625000 | + | 0.108253i | ||||
\(5\) | −7.50000 | + | 12.9904i | −0.670820 | + | 1.16190i | 0.306851 | + | 0.951757i | \(0.400725\pi\) |
−0.977672 | + | 0.210138i | \(0.932609\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 12.5000 | + | 21.6506i | 0.674937 | + | 1.16902i | 0.976487 | + | 0.215574i | \(0.0691624\pi\) |
−0.301551 | + | 0.953450i | \(0.597504\pi\) | |||||||
\(8\) | −21.0000 | −0.928078 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 45.0000 | 1.42302 | ||||||||
\(11\) | 7.50000 | + | 12.9904i | 0.205576 | + | 0.356068i | 0.950316 | − | 0.311287i | \(-0.100760\pi\) |
−0.744740 | + | 0.667355i | \(0.767427\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −10.0000 | + | 17.3205i | −0.213346 | + | 0.369527i | −0.952760 | − | 0.303725i | \(-0.901770\pi\) |
0.739413 | + | 0.673252i | \(0.235103\pi\) | |||||||
\(14\) | 37.5000 | − | 64.9519i | 0.715878 | − | 1.23994i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 35.5000 | + | 61.4878i | 0.554688 | + | 0.960747i | ||||
\(17\) | 72.0000 | 1.02721 | 0.513605 | − | 0.858027i | \(-0.328310\pi\) | ||||
0.513605 | + | 0.858027i | \(0.328310\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | 0.0241490 | 0.0120745 | − | 0.999927i | \(-0.496156\pi\) | ||||
0.0120745 | + | 0.999927i | \(0.496156\pi\) | |||||||
\(20\) | −7.50000 | − | 12.9904i | −0.0838525 | − | 0.145237i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 22.5000 | − | 38.9711i | 0.218046 | − | 0.377667i | ||||
\(23\) | −57.0000 | + | 98.7269i | −0.516753 | + | 0.895043i | 0.483058 | + | 0.875589i | \(0.339526\pi\) |
−0.999811 | + | 0.0194541i | \(0.993807\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −50.0000 | − | 86.6025i | −0.400000 | − | 0.692820i | ||||
\(26\) | 60.0000 | 0.452576 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −25.0000 | −0.168734 | ||||||||
\(29\) | −15.0000 | − | 25.9808i | −0.0960493 | − | 0.166362i | 0.813997 | − | 0.580869i | \(-0.197287\pi\) |
−0.910046 | + | 0.414507i | \(0.863954\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −50.5000 | + | 87.4686i | −0.292583 | + | 0.506768i | −0.974420 | − | 0.224736i | \(-0.927848\pi\) |
0.681837 | + | 0.731504i | \(0.261181\pi\) | |||||||
\(32\) | 22.5000 | − | 38.9711i | 0.124296 | − | 0.215287i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −108.000 | − | 187.061i | −0.544760 | − | 0.943552i | ||||
\(35\) | −375.000 | −1.81104 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −430.000 | −1.91058 | −0.955291 | − | 0.295666i | \(-0.904458\pi\) | ||||
−0.955291 | + | 0.295666i | \(0.904458\pi\) | |||||||
\(38\) | −3.00000 | − | 5.19615i | −0.0128070 | − | 0.0221823i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 157.500 | − | 272.798i | 0.622573 | − | 1.07833i | ||||
\(41\) | 15.0000 | − | 25.9808i | 0.0571367 | − | 0.0989637i | −0.836042 | − | 0.548665i | \(-0.815136\pi\) |
0.893179 | + | 0.449701i | \(0.148470\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −55.0000 | − | 95.2628i | −0.195056 | − | 0.337847i | 0.751863 | − | 0.659320i | \(-0.229156\pi\) |
−0.946919 | + | 0.321472i | \(0.895822\pi\) | |||||||
\(44\) | −15.0000 | −0.0513940 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 342.000 | 1.09620 | ||||||||
\(47\) | 165.000 | + | 285.788i | 0.512079 | + | 0.886947i | 0.999902 | + | 0.0140045i | \(0.00445792\pi\) |
−0.487823 | + | 0.872943i | \(0.662209\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −141.000 | + | 244.219i | −0.411079 | + | 0.712009i | ||||
\(50\) | −150.000 | + | 259.808i | −0.424264 | + | 0.734847i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −10.0000 | − | 17.3205i | −0.0266683 | − | 0.0461908i | ||||
\(53\) | 621.000 | 1.60945 | 0.804726 | − | 0.593647i | \(-0.202312\pi\) | ||||
0.804726 | + | 0.593647i | \(0.202312\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −225.000 | −0.551618 | ||||||||
\(56\) | −262.500 | − | 454.663i | −0.626394 | − | 1.08495i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −45.0000 | + | 77.9423i | −0.101876 | + | 0.176454i | ||||
\(59\) | 330.000 | − | 571.577i | 0.728175 | − | 1.26124i | −0.229478 | − | 0.973314i | \(-0.573702\pi\) |
0.957654 | − | 0.287923i | \(-0.0929647\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 188.000 | + | 325.626i | 0.394605 | + | 0.683477i | 0.993051 | − | 0.117687i | \(-0.0375479\pi\) |
−0.598445 | + | 0.801164i | \(0.704215\pi\) | |||||||
\(62\) | 303.000 | 0.620662 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 433.000 | 0.845703 | ||||||||
\(65\) | −150.000 | − | 259.808i | −0.286234 | − | 0.495772i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 125.000 | − | 216.506i | 0.227928 | − | 0.394783i | −0.729266 | − | 0.684230i | \(-0.760138\pi\) |
0.957194 | + | 0.289447i | \(0.0934716\pi\) | |||||||
\(68\) | −36.0000 | + | 62.3538i | −0.0642006 | + | 0.111199i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 562.500 | + | 974.279i | 0.960452 | + | 1.66355i | ||||
\(71\) | −360.000 | −0.601748 | −0.300874 | − | 0.953664i | \(-0.597278\pi\) | ||||
−0.300874 | + | 0.953664i | \(0.597278\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 785.000 | 1.25859 | 0.629297 | − | 0.777165i | \(-0.283343\pi\) | ||||
0.629297 | + | 0.777165i | \(0.283343\pi\) | |||||||
\(74\) | 645.000 | + | 1117.17i | 1.01324 | + | 1.75498i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | + | 1.73205i | −0.00150931 | + | 0.00261421i | ||||
\(77\) | −187.500 | + | 324.760i | −0.277501 | + | 0.480647i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −244.000 | − | 422.620i | −0.347496 | − | 0.601880i | 0.638308 | − | 0.769781i | \(-0.279634\pi\) |
−0.985804 | + | 0.167901i | \(0.946301\pi\) | |||||||
\(80\) | −1065.00 | −1.48838 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −90.0000 | −0.121205 | ||||||||
\(83\) | −244.500 | − | 423.486i | −0.323342 | − | 0.560044i | 0.657834 | − | 0.753163i | \(-0.271473\pi\) |
−0.981175 | + | 0.193119i | \(0.938140\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −540.000 | + | 935.307i | −0.689073 | + | 1.19351i | ||||
\(86\) | −165.000 | + | 285.788i | −0.206888 | + | 0.358341i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −157.500 | − | 272.798i | −0.190790 | − | 0.330459i | ||||
\(89\) | −450.000 | −0.535954 | −0.267977 | − | 0.963425i | \(-0.586355\pi\) | ||||
−0.267977 | + | 0.963425i | \(0.586355\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −500.000 | −0.575981 | ||||||||
\(92\) | −57.0000 | − | 98.7269i | −0.0645941 | − | 0.111880i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 495.000 | − | 857.365i | 0.543142 | − | 0.940750i | ||||
\(95\) | −15.0000 | + | 25.9808i | −0.0161997 | + | 0.0280586i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 552.500 | + | 956.958i | 0.578329 | + | 1.00169i | 0.995671 | + | 0.0929453i | \(0.0296282\pi\) |
−0.417343 | + | 0.908749i | \(0.637038\pi\) | |||||||
\(98\) | 846.000 | 0.872030 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 100.000 | 0.100000 | ||||||||
\(101\) | −712.500 | − | 1234.09i | −0.701945 | − | 1.21580i | −0.967783 | − | 0.251786i | \(-0.918982\pi\) |
0.265838 | − | 0.964018i | \(-0.414351\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 530.000 | − | 917.987i | 0.507014 | − | 0.878174i | −0.492953 | − | 0.870056i | \(-0.664083\pi\) |
0.999967 | − | 0.00811820i | \(-0.00258413\pi\) | |||||||
\(104\) | 210.000 | − | 363.731i | 0.198002 | − | 0.342949i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −931.500 | − | 1613.41i | −0.853540 | − | 1.47838i | ||||
\(107\) | 1485.00 | 1.34169 | 0.670843 | − | 0.741600i | \(-0.265933\pi\) | ||||
0.670843 | + | 0.741600i | \(0.265933\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −862.000 | −0.757474 | −0.378737 | − | 0.925504i | \(-0.623641\pi\) | ||||
−0.378737 | + | 0.925504i | \(0.623641\pi\) | |||||||
\(110\) | 337.500 | + | 584.567i | 0.292540 | + | 0.506694i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −887.500 | + | 1537.20i | −0.748758 | + | 1.29689i | ||||
\(113\) | −345.000 | + | 597.558i | −0.287211 | + | 0.497464i | −0.973143 | − | 0.230201i | \(-0.926062\pi\) |
0.685932 | + | 0.727666i | \(0.259395\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −855.000 | − | 1480.90i | −0.693297 | − | 1.20083i | ||||
\(116\) | 30.0000 | 0.0240123 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1980.00 | −1.54469 | ||||||||
\(119\) | 900.000 | + | 1558.85i | 0.693301 | + | 1.20083i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 553.000 | − | 957.824i | 0.415477 | − | 0.719627i | ||||
\(122\) | 564.000 | − | 976.877i | 0.418542 | − | 0.724937i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −50.5000 | − | 87.4686i | −0.0365729 | − | 0.0633460i | ||||
\(125\) | −375.000 | −0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1865.00 | 1.30309 | 0.651543 | − | 0.758611i | \(-0.274122\pi\) | ||||
0.651543 | + | 0.758611i | \(0.274122\pi\) | |||||||
\(128\) | −829.500 | − | 1436.74i | −0.572798 | − | 0.992115i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −450.000 | + | 779.423i | −0.303597 | + | 0.525845i | ||||
\(131\) | 577.500 | − | 1000.26i | 0.385163 | − | 0.667123i | −0.606628 | − | 0.794986i | \(-0.707478\pi\) |
0.991792 | + | 0.127863i | \(0.0408117\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 25.0000 | + | 43.3013i | 0.0162991 | + | 0.0282308i | ||||
\(134\) | −750.000 | −0.483508 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1512.00 | −0.953330 | ||||||||
\(137\) | 1389.00 | + | 2405.82i | 0.866206 | + | 1.50031i | 0.865844 | + | 0.500314i | \(0.166782\pi\) |
0.000362133 | 1.00000i | \(0.499885\pi\) | ||||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 962.000 | − | 1666.23i | 0.587020 | − | 1.01675i | −0.407600 | − | 0.913160i | \(-0.633634\pi\) |
0.994620 | − | 0.103588i | \(-0.0330323\pi\) | |||||||
\(140\) | 187.500 | − | 324.760i | 0.113190 | − | 0.196051i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 540.000 | + | 935.307i | 0.319125 | + | 0.552741i | ||||
\(143\) | −300.000 | −0.175435 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 450.000 | 0.257727 | ||||||||
\(146\) | −1177.50 | − | 2039.49i | −0.667470 | − | 1.15609i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 215.000 | − | 372.391i | 0.119411 | − | 0.206827i | ||||
\(149\) | −727.500 | + | 1260.07i | −0.399994 | + | 0.692810i | −0.993725 | − | 0.111854i | \(-0.964321\pi\) |
0.593731 | + | 0.804664i | \(0.297655\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 363.500 | + | 629.600i | 0.195902 | + | 0.339312i | 0.947196 | − | 0.320656i | \(-0.103903\pi\) |
−0.751294 | + | 0.659968i | \(0.770570\pi\) | |||||||
\(152\) | −42.0000 | −0.0224122 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1125.00 | 0.588669 | ||||||||
\(155\) | −757.500 | − | 1312.03i | −0.392541 | − | 0.679901i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1630.00 | + | 2823.24i | −0.828587 | + | 1.43515i | 0.0705597 | + | 0.997508i | \(0.477521\pi\) |
−0.899147 | + | 0.437647i | \(0.855812\pi\) | |||||||
\(158\) | −732.000 | + | 1267.86i | −0.368575 | + | 0.638390i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 337.500 | + | 584.567i | 0.166761 | + | 0.288838i | ||||
\(161\) | −2850.00 | −1.39510 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2540.00 | 1.22054 | 0.610270 | − | 0.792193i | \(-0.291061\pi\) | ||||
0.610270 | + | 0.792193i | \(0.291061\pi\) | |||||||
\(164\) | 15.0000 | + | 25.9808i | 0.00714209 | + | 0.0123705i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −733.500 | + | 1270.46i | −0.342956 | + | 0.594017i | ||||
\(167\) | −1749.00 | + | 3029.36i | −0.810429 | + | 1.40370i | 0.102135 | + | 0.994771i | \(0.467433\pi\) |
−0.912564 | + | 0.408934i | \(0.865901\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 898.500 | + | 1556.25i | 0.408967 | + | 0.708351i | ||||
\(170\) | 3240.00 | 1.46175 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 110.000 | 0.0487641 | ||||||||
\(173\) | 574.500 | + | 995.063i | 0.252476 | + | 0.437302i | 0.964207 | − | 0.265150i | \(-0.0854216\pi\) |
−0.711731 | + | 0.702453i | \(0.752088\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1250.00 | − | 2165.06i | 0.539949 | − | 0.935220i | ||||
\(176\) | −532.500 | + | 922.317i | −0.228061 | + | 0.395013i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 675.000 | + | 1169.13i | 0.284233 | + | 0.492305i | ||||
\(179\) | 315.000 | 0.131532 | 0.0657659 | − | 0.997835i | \(-0.479051\pi\) | ||||
0.0657659 | + | 0.997835i | \(0.479051\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1136.00 | 0.466509 | 0.233255 | − | 0.972416i | \(-0.425062\pi\) | ||||
0.233255 | + | 0.972416i | \(0.425062\pi\) | |||||||
\(182\) | 750.000 | + | 1299.04i | 0.305460 | + | 0.529072i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1197.00 | − | 2073.26i | 0.479587 | − | 0.830669i | ||||
\(185\) | 3225.00 | − | 5585.86i | 1.28166 | − | 2.21990i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 540.000 | + | 935.307i | 0.211170 | + | 0.365756i | ||||
\(188\) | −330.000 | −0.128020 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 90.0000 | 0.0343647 | ||||||||
\(191\) | −1230.00 | − | 2130.42i | −0.465967 | − | 0.807078i | 0.533278 | − | 0.845940i | \(-0.320960\pi\) |
−0.999245 | + | 0.0388619i | \(0.987627\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −482.500 | + | 835.715i | −0.179954 | + | 0.311689i | −0.941865 | − | 0.335993i | \(-0.890928\pi\) |
0.761911 | + | 0.647682i | \(0.224262\pi\) | |||||||
\(194\) | 1657.50 | − | 2870.87i | 0.613410 | − | 1.06246i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −141.000 | − | 244.219i | −0.0513848 | − | 0.0890012i | ||||
\(197\) | 2493.00 | 0.901619 | 0.450809 | − | 0.892620i | \(-0.351135\pi\) | ||||
0.450809 | + | 0.892620i | \(0.351135\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −511.000 | −0.182029 | −0.0910146 | − | 0.995850i | \(-0.529011\pi\) | ||||
−0.0910146 | + | 0.995850i | \(0.529011\pi\) | |||||||
\(200\) | 1050.00 | + | 1818.65i | 0.371231 | + | 0.642991i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2137.50 | + | 3702.26i | −0.744525 | + | 1.28955i | ||||
\(203\) | 375.000 | − | 649.519i | 0.129654 | − | 0.224568i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 225.000 | + | 389.711i | 0.0766570 | + | 0.132774i | ||||
\(206\) | −3180.00 | −1.07554 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1420.00 | −0.473362 | ||||||||
\(209\) | 15.0000 | + | 25.9808i | 0.00496446 | + | 0.00859869i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1043.00 | − | 1806.53i | 0.340299 | − | 0.589415i | −0.644189 | − | 0.764866i | \(-0.722805\pi\) |
0.984488 | + | 0.175451i | \(0.0561384\pi\) | |||||||
\(212\) | −310.500 | + | 537.802i | −0.100591 | + | 0.174228i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2227.50 | − | 3858.14i | −0.711536 | − | 1.23242i | ||||
\(215\) | 1650.00 | 0.523391 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2525.00 | −0.789899 | ||||||||
\(218\) | 1293.00 | + | 2239.54i | 0.401711 | + | 0.695784i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 112.500 | − | 194.856i | 0.0344761 | − | 0.0597144i | ||||
\(221\) | −720.000 | + | 1247.08i | −0.219151 | + | 0.379581i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2620.00 | − | 4537.97i | −0.786763 | − | 1.36271i | −0.927940 | − | 0.372729i | \(-0.878422\pi\) |
0.141177 | − | 0.989984i | \(-0.454911\pi\) | |||||||
\(224\) | 1125.00 | 0.335568 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2070.00 | 0.609267 | ||||||||
\(227\) | −1194.00 | − | 2068.07i | −0.349113 | − | 0.604681i | 0.636979 | − | 0.770881i | \(-0.280184\pi\) |
−0.986092 | + | 0.166200i | \(0.946850\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −91.0000 | + | 157.617i | −0.0262596 | + | 0.0454830i | −0.878857 | − | 0.477086i | \(-0.841693\pi\) |
0.852597 | + | 0.522569i | \(0.175026\pi\) | |||||||
\(230\) | −2565.00 | + | 4442.71i | −0.735353 | + | 1.27367i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 315.000 | + | 545.596i | 0.0891412 | + | 0.154397i | ||||
\(233\) | 450.000 | 0.126526 | 0.0632628 | − | 0.997997i | \(-0.479849\pi\) | ||||
0.0632628 | + | 0.997997i | \(0.479849\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4950.00 | −1.37405 | ||||||||
\(236\) | 330.000 | + | 571.577i | 0.0910219 | + | 0.157655i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2700.00 | − | 4676.54i | 0.735357 | − | 1.27368i | ||||
\(239\) | −2595.00 | + | 4494.67i | −0.702329 | + | 1.21647i | 0.265318 | + | 0.964161i | \(0.414523\pi\) |
−0.967647 | + | 0.252308i | \(0.918810\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1133.00 | + | 1962.41i | 0.302834 | + | 0.524524i | 0.976777 | − | 0.214260i | \(-0.0687340\pi\) |
−0.673943 | + | 0.738783i | \(0.735401\pi\) | |||||||
\(242\) | −3318.00 | −0.881360 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −376.000 | −0.0986514 | ||||||||
\(245\) | −2115.00 | − | 3663.29i | −0.551520 | − | 0.955261i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20.0000 | + | 34.6410i | −0.00515210 | + | 0.00892370i | ||||
\(248\) | 1060.50 | − | 1836.84i | 0.271540 | − | 0.470320i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 562.500 | + | 974.279i | 0.142302 | + | 0.246475i | ||||
\(251\) | −2880.00 | −0.724239 | −0.362119 | − | 0.932132i | \(-0.617947\pi\) | ||||
−0.362119 | + | 0.932132i | \(0.617947\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1710.00 | −0.424928 | ||||||||
\(254\) | −2797.50 | − | 4845.41i | −0.691066 | − | 1.19696i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −756.500 | + | 1310.30i | −0.184692 | + | 0.319897i | ||||
\(257\) | 2094.00 | − | 3626.91i | 0.508250 | − | 0.880314i | −0.491705 | − | 0.870762i | \(-0.663626\pi\) |
0.999954 | − | 0.00955209i | \(-0.00304057\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5375.00 | − | 9309.77i | −1.28952 | − | 2.23352i | ||||
\(260\) | 300.000 | 0.0715585 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3465.00 | −0.817055 | ||||||||
\(263\) | 1515.00 | + | 2624.06i | 0.355205 | + | 0.615233i | 0.987153 | − | 0.159778i | \(-0.0510777\pi\) |
−0.631948 | + | 0.775011i | \(0.717744\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4657.50 | + | 8067.03i | −1.07965 | + | 1.87001i | ||||
\(266\) | 75.0000 | − | 129.904i | 0.0172878 | − | 0.0299433i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 125.000 | + | 216.506i | 0.0284910 | + | 0.0493479i | ||||
\(269\) | 3510.00 | 0.795571 | 0.397785 | − | 0.917479i | \(-0.369779\pi\) | ||||
0.397785 | + | 0.917479i | \(0.369779\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2999.00 | 0.672237 | 0.336119 | − | 0.941820i | \(-0.390886\pi\) | ||||
0.336119 | + | 0.941820i | \(0.390886\pi\) | |||||||
\(272\) | 2556.00 | + | 4427.12i | 0.569780 | + | 0.986889i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4167.00 | − | 7217.46i | 0.918751 | − | 1.59132i | ||||
\(275\) | 750.000 | − | 1299.04i | 0.164461 | − | 0.284854i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3860.00 | + | 6685.72i | 0.837274 | + | 1.45020i | 0.892165 | + | 0.451709i | \(0.149185\pi\) |
−0.0548913 | + | 0.998492i | \(0.517481\pi\) | |||||||
\(278\) | −5772.00 | −1.24526 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 7875.00 | 1.68079 | ||||||||
\(281\) | 3720.00 | + | 6443.23i | 0.789739 | + | 1.36787i | 0.926127 | + | 0.377212i | \(0.123117\pi\) |
−0.136388 | + | 0.990655i | \(0.543549\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −415.000 | + | 718.801i | −0.0871703 | + | 0.150983i | −0.906314 | − | 0.422605i | \(-0.861116\pi\) |
0.819144 | + | 0.573588i | \(0.194449\pi\) | |||||||
\(284\) | 180.000 | − | 311.769i | 0.0376093 | − | 0.0651412i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 450.000 | + | 779.423i | 0.0930387 | + | 0.161148i | ||||
\(287\) | 750.000 | 0.154255 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 271.000 | 0.0551598 | ||||||||
\(290\) | −675.000 | − | 1169.13i | −0.136681 | − | 0.236738i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −392.500 | + | 679.830i | −0.0786621 | + | 0.136247i | ||||
\(293\) | −273.000 | + | 472.850i | −0.0544329 | + | 0.0942805i | −0.891958 | − | 0.452118i | \(-0.850668\pi\) |
0.837525 | + | 0.546399i | \(0.184002\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4950.00 | + | 8573.65i | 0.976950 | + | 1.69213i | ||||
\(296\) | 9030.00 | 1.77317 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4365.00 | 0.848516 | ||||||||
\(299\) | −1140.00 | − | 1974.54i | −0.220495 | − | 0.381908i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1375.00 | − | 2381.57i | 0.263301 | − | 0.456051i | ||||
\(302\) | 1090.50 | − | 1888.80i | 0.207786 | − | 0.359895i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 71.0000 | + | 122.976i | 0.0133952 | + | 0.0232011i | ||||
\(305\) | −5640.00 | −1.05884 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5560.00 | −1.03364 | −0.516818 | − | 0.856096i | \(-0.672883\pi\) | ||||
−0.516818 | + | 0.856096i | \(0.672883\pi\) | |||||||
\(308\) | −187.500 | − | 324.760i | −0.0346877 | − | 0.0600808i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2272.50 | + | 3936.09i | −0.416353 | + | 0.721144i | ||||
\(311\) | 4335.00 | − | 7508.44i | 0.790403 | − | 1.36902i | −0.135315 | − | 0.990803i | \(-0.543205\pi\) |
0.925718 | − | 0.378215i | \(-0.123462\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2282.50 | − | 3953.41i | −0.412187 | − | 0.713929i | 0.582942 | − | 0.812514i | \(-0.301902\pi\) |
−0.995129 | + | 0.0985852i | \(0.968568\pi\) | |||||||
\(314\) | 9780.00 | 1.75770 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 488.000 | 0.0868739 | ||||||||
\(317\) | −2116.50 | − | 3665.89i | −0.374998 | − | 0.649516i | 0.615328 | − | 0.788271i | \(-0.289023\pi\) |
−0.990327 | + | 0.138755i | \(0.955690\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 225.000 | − | 389.711i | 0.0394909 | − | 0.0684002i | ||||
\(320\) | −3247.50 | + | 5624.83i | −0.567315 | + | 0.982618i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4275.00 | + | 7404.52i | 0.739865 | + | 1.28148i | ||||
\(323\) | 144.000 | 0.0248061 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2000.00 | 0.341354 | ||||||||
\(326\) | −3810.00 | − | 6599.11i | −0.647290 | − | 1.12114i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −315.000 | + | 545.596i | −0.0530273 | + | 0.0918460i | ||||
\(329\) | −4125.00 | + | 7144.71i | −0.691242 | + | 1.19727i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −271.000 | − | 469.386i | −0.0450015 | − | 0.0779449i | 0.842647 | − | 0.538466i | \(-0.180996\pi\) |
−0.887649 | + | 0.460521i | \(0.847663\pi\) | |||||||
\(332\) | 489.000 | 0.0808354 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10494.0 | 1.71918 | ||||||||
\(335\) | 1875.00 | + | 3247.60i | 0.305798 | + | 0.529657i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2845.00 | + | 4927.68i | −0.459872 | + | 0.796522i | −0.998954 | − | 0.0457312i | \(-0.985438\pi\) |
0.539081 | + | 0.842254i | \(0.318772\pi\) | |||||||
\(338\) | 2695.50 | − | 4668.74i | 0.433775 | − | 0.751320i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −540.000 | − | 935.307i | −0.0861342 | − | 0.149189i | ||||
\(341\) | −1515.00 | −0.240592 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1525.00 | 0.240065 | ||||||||
\(344\) | 1155.00 | + | 2000.52i | 0.181027 | + | 0.313549i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1723.50 | − | 2985.19i | 0.267792 | − | 0.463829i | ||||
\(347\) | −2527.50 | + | 4377.76i | −0.391018 | + | 0.677263i | −0.992584 | − | 0.121560i | \(-0.961210\pi\) |
0.601566 | + | 0.798823i | \(0.294544\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −811.000 | − | 1404.69i | −0.124389 | − | 0.215448i | 0.797105 | − | 0.603841i | \(-0.206364\pi\) |
−0.921494 | + | 0.388393i | \(0.873030\pi\) | |||||||
\(350\) | −7500.00 | −1.14541 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 675.000 | 0.102209 | ||||||||
\(353\) | −15.0000 | − | 25.9808i | −0.00226167 | − | 0.00391733i | 0.864892 | − | 0.501957i | \(-0.167387\pi\) |
−0.867154 | + | 0.498040i | \(0.834053\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2700.00 | − | 4676.54i | 0.403665 | − | 0.699169i | ||||
\(356\) | 225.000 | − | 389.711i | 0.0334971 | − | 0.0580187i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −472.500 | − | 818.394i | −0.0697553 | − | 0.120820i | ||||
\(359\) | −7470.00 | −1.09819 | −0.549097 | − | 0.835759i | \(-0.685028\pi\) | ||||
−0.549097 | + | 0.835759i | \(0.685028\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6855.00 | −0.999417 | ||||||||
\(362\) | −1704.00 | − | 2951.41i | −0.247404 | − | 0.428516i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 250.000 | − | 433.013i | 0.0359988 | − | 0.0623517i | ||||
\(365\) | −5887.50 | + | 10197.4i | −0.844290 | + | 1.46235i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 687.500 | + | 1190.78i | 0.0977853 | + | 0.169369i | 0.910768 | − | 0.412919i | \(-0.135491\pi\) |
−0.812982 | + | 0.582288i | \(0.802157\pi\) | |||||||
\(368\) | −8094.00 | −1.14655 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −19350.0 | −2.71881 | ||||||||
\(371\) | 7762.50 | + | 13445.0i | 1.08628 | + | 1.88149i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2420.00 | − | 4191.56i | 0.335933 | − | 0.581852i | −0.647731 | − | 0.761869i | \(-0.724282\pi\) |
0.983664 | + | 0.180017i | \(0.0576152\pi\) | |||||||
\(374\) | 1620.00 | − | 2805.92i | 0.223979 | − | 0.387943i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3465.00 | − | 6001.56i | −0.475249 | − | 0.823156i | ||||
\(377\) | 600.000 | 0.0819670 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1892.00 | 0.256426 | 0.128213 | − | 0.991747i | \(-0.459076\pi\) | ||||
0.128213 | + | 0.991747i | \(0.459076\pi\) | |||||||
\(380\) | −15.0000 | − | 25.9808i | −0.00202496 | − | 0.00350733i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3690.00 | + | 6391.27i | −0.494233 | + | 0.856036i | ||||
\(383\) | 5352.00 | − | 9269.94i | 0.714032 | − | 1.23674i | −0.249299 | − | 0.968427i | \(-0.580200\pi\) |
0.963332 | − | 0.268314i | \(-0.0864664\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2812.50 | − | 4871.39i | −0.372307 | − | 0.644855i | ||||
\(386\) | 2895.00 | 0.381740 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1105.00 | −0.144582 | ||||||||
\(389\) | −3907.50 | − | 6767.99i | −0.509301 | − | 0.882135i | −0.999942 | − | 0.0107735i | \(-0.996571\pi\) |
0.490641 | − | 0.871362i | \(-0.336763\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4104.00 | + | 7108.34i | −0.530814 | + | 0.919396i | ||||
\(392\) | 2961.00 | − | 5128.60i | 0.381513 | − | 0.660800i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3739.50 | − | 6477.00i | −0.478156 | − | 0.828190i | ||||
\(395\) | 7320.00 | 0.932428 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4700.00 | 0.594172 | 0.297086 | − | 0.954851i | \(-0.403985\pi\) | ||||
0.297086 | + | 0.954851i | \(0.403985\pi\) | |||||||
\(398\) | 766.500 | + | 1327.62i | 0.0965356 | + | 0.167205i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3550.00 | − | 6148.78i | 0.443750 | − | 0.768598i | ||||
\(401\) | 1050.00 | − | 1818.65i | 0.130759 | − | 0.226482i | −0.793210 | − | 0.608948i | \(-0.791592\pi\) |
0.923970 | + | 0.382466i | \(0.124925\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1010.00 | − | 1749.37i | −0.124843 | − | 0.216234i | ||||
\(404\) | 1425.00 | 0.175486 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2250.00 | −0.275038 | ||||||||
\(407\) | −3225.00 | − | 5585.86i | −0.392770 | − | 0.680297i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5376.50 | − | 9312.37i | 0.650002 | − | 1.12584i | −0.333120 | − | 0.942884i | \(-0.608101\pi\) |
0.983122 | − | 0.182952i | \(-0.0585653\pi\) | |||||||
\(410\) | 675.000 | − | 1169.13i | 0.0813070 | − | 0.140828i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 530.000 | + | 917.987i | 0.0633768 | + | 0.109772i | ||||
\(413\) | 16500.0 | 1.96589 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7335.00 | 0.867617 | ||||||||
\(416\) | 450.000 | + | 779.423i | 0.0530362 | + | 0.0918614i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 45.0000 | − | 77.9423i | 0.00526560 | − | 0.00912029i | ||||
\(419\) | −1470.00 | + | 2546.11i | −0.171394 | + | 0.296864i | −0.938908 | − | 0.344169i | \(-0.888161\pi\) |
0.767513 | + | 0.641033i | \(0.221494\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4348.00 | − | 7530.96i | −0.503346 | − | 0.871820i | −0.999993 | − | 0.00386764i | \(-0.998769\pi\) |
0.496647 | − | 0.867953i | \(-0.334564\pi\) | |||||||
\(422\) | −6258.00 | −0.721883 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −13041.0 | −1.49370 | ||||||||
\(425\) | −3600.00 | − | 6235.38i | −0.410884 | − | 0.711672i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4700.00 | + | 8140.64i | −0.532667 | + | 0.922607i | ||||
\(428\) | −742.500 | + | 1286.05i | −0.0838554 | + | 0.145242i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2475.00 | − | 4286.83i | −0.277570 | − | 0.480765i | ||||
\(431\) | 8370.00 | 0.935426 | 0.467713 | − | 0.883880i | \(-0.345078\pi\) | ||||
0.467713 | + | 0.883880i | \(0.345078\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5155.00 | −0.572133 | −0.286066 | − | 0.958210i | \(-0.592348\pi\) | ||||
−0.286066 | + | 0.958210i | \(0.592348\pi\) | |||||||
\(434\) | 3787.50 | + | 6560.14i | 0.418907 | + | 0.725569i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 431.000 | − | 746.514i | 0.0473421 | − | 0.0819989i | ||||
\(437\) | −114.000 | + | 197.454i | −0.0124791 | + | 0.0216144i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5493.50 | + | 9515.02i | 0.597245 | + | 1.03446i | 0.993226 | + | 0.116200i | \(0.0370712\pi\) |
−0.395981 | + | 0.918259i | \(0.629595\pi\) | |||||||
\(440\) | 4725.00 | 0.511944 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4320.00 | 0.464890 | ||||||||
\(443\) | −978.000 | − | 1693.95i | −0.104890 | − | 0.181674i | 0.808803 | − | 0.588079i | \(-0.200116\pi\) |
−0.913693 | + | 0.406405i | \(0.866782\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3375.00 | − | 5845.67i | 0.359529 | − | 0.622722i | ||||
\(446\) | −7860.00 | + | 13613.9i | −0.834488 | + | 1.44538i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 5412.50 | + | 9374.72i | 0.570796 | + | 0.988648i | ||||
\(449\) | −8730.00 | −0.917582 | −0.458791 | − | 0.888544i | \(-0.651717\pi\) | ||||
−0.458791 | + | 0.888544i | \(0.651717\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 450.000 | 0.0469838 | ||||||||
\(452\) | −345.000 | − | 597.558i | −0.0359014 | − | 0.0621831i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3582.00 | + | 6204.21i | −0.370290 | + | 0.641361i | ||||
\(455\) | 3750.00 | − | 6495.19i | 0.386380 | − | 0.669229i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4332.50 | + | 7504.11i | 0.443470 | + | 0.768113i | 0.997944 | − | 0.0640883i | \(-0.0204139\pi\) |
−0.554474 | + | 0.832201i | \(0.687081\pi\) | |||||||
\(458\) | 546.000 | 0.0557050 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1710.00 | 0.173324 | ||||||||
\(461\) | 4912.50 | + | 8508.70i | 0.496308 | + | 0.859630i | 0.999991 | − | 0.00425805i | \(-0.00135538\pi\) |
−0.503683 | + | 0.863889i | \(0.668022\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2622.50 | − | 4542.30i | 0.263235 | − | 0.455937i | −0.703865 | − | 0.710334i | \(-0.748544\pi\) |
0.967100 | + | 0.254397i | \(0.0818771\pi\) | |||||||
\(464\) | 1065.00 | − | 1844.63i | 0.106555 | − | 0.184558i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −675.000 | − | 1169.13i | −0.0671004 | − | 0.116221i | ||||
\(467\) | −11007.0 | −1.09067 | −0.545335 | − | 0.838218i | \(-0.683598\pi\) | ||||
−0.545335 | + | 0.838218i | \(0.683598\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6250.00 | 0.615348 | ||||||||
\(470\) | 7425.00 | + | 12860.5i | 0.728702 | + | 1.26215i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6930.00 | + | 12003.1i | −0.675803 | + | 1.17053i | ||||
\(473\) | 825.000 | − | 1428.94i | 0.0801978 | − | 0.138907i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −100.000 | − | 173.205i | −0.00965961 | − | 0.0167309i | ||||
\(476\) | −1800.00 | −0.173325 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 15570.0 | 1.48986 | ||||||||
\(479\) | −8475.00 | − | 14679.1i | −0.808419 | − | 1.40022i | −0.913959 | − | 0.405807i | \(-0.866990\pi\) |
0.105540 | − | 0.994415i | \(-0.466343\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4300.00 | − | 7447.82i | 0.407616 | − | 0.706011i | ||||
\(482\) | 3399.00 | − | 5887.24i | 0.321204 | − | 0.556341i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 553.000 | + | 957.824i | 0.0519346 | + | 0.0899534i | ||||
\(485\) | −16575.0 | −1.55182 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10640.0 | 0.990030 | 0.495015 | − | 0.868885i | \(-0.335163\pi\) | ||||
0.495015 | + | 0.868885i | \(0.335163\pi\) | |||||||
\(488\) | −3948.00 | − | 6838.14i | −0.366225 | − | 0.634319i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6345.00 | + | 10989.9i | −0.584975 | + | 1.01321i | ||||
\(491\) | −817.500 | + | 1415.95i | −0.0751390 | + | 0.130145i | −0.901147 | − | 0.433514i | \(-0.857273\pi\) |
0.826008 | + | 0.563659i | \(0.190607\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1080.00 | − | 1870.61i | −0.0986628 | − | 0.170889i | ||||
\(494\) | 120.000 | 0.0109293 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7171.00 | −0.649168 | ||||||||
\(497\) | −4500.00 | − | 7794.23i | −0.406142 | − | 0.703459i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7901.00 | − | 13684.9i | 0.708812 | − | 1.22770i | −0.256486 | − | 0.966548i | \(-0.582565\pi\) |
0.965298 | − | 0.261151i | \(-0.0841020\pi\) | |||||||
\(500\) | 187.500 | − | 324.760i | 0.0167705 | − | 0.0290474i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4320.00 | + | 7482.46i | 0.384086 | + | 0.665256i | ||||
\(503\) | −7866.00 | −0.697272 | −0.348636 | − | 0.937258i | \(-0.613355\pi\) | ||||
−0.348636 | + | 0.937258i | \(0.613355\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 21375.0 | 1.88351 | ||||||||
\(506\) | 2565.00 | + | 4442.71i | 0.225352 | + | 0.390321i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −932.500 | + | 1615.14i | −0.0814429 | + | 0.141063i | ||||
\(509\) | 5977.50 | − | 10353.3i | 0.520527 | − | 0.901578i | −0.479189 | − | 0.877712i | \(-0.659069\pi\) |
0.999715 | − | 0.0238665i | \(-0.00759767\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9812.50 | + | 16995.7i | 0.849471 | + | 1.47133i | ||||
\(512\) | −8733.00 | −0.753804 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −12564.0 | −1.07816 | ||||||||
\(515\) | 7950.00 | + | 13769.8i | 0.680231 | + | 1.17819i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2475.00 | + | 4286.83i | −0.210542 | + | 0.364670i | ||||
\(518\) | −16125.0 | + | 27929.3i | −1.36774 | + | 2.36900i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3150.00 | + | 5455.96i | 0.265647 | + | 0.460115i | ||||
\(521\) | 19260.0 | 1.61957 | 0.809785 | − | 0.586727i | \(-0.199584\pi\) | ||||
0.809785 | + | 0.586727i | \(0.199584\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18520.0 | −1.54842 | −0.774209 | − | 0.632930i | \(-0.781852\pi\) | ||||
−0.774209 | + | 0.632930i | \(0.781852\pi\) | |||||||
\(524\) | 577.500 | + | 1000.26i | 0.0481454 | + | 0.0833903i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4545.00 | − | 7872.17i | 0.376752 | − | 0.652553i | ||||
\(527\) | −3636.00 | + | 6297.74i | −0.300544 | + | 0.520557i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −414.500 | − | 717.935i | −0.0340676 | − | 0.0590067i | ||||
\(530\) | 27945.0 | 2.29029 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −50.0000 | −0.00407476 | ||||||||
\(533\) | 300.000 | + | 519.615i | 0.0243798 | + | 0.0422271i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11137.5 | + | 19290.7i | −0.900030 | + | 1.55890i | ||||
\(536\) | −2625.00 | + | 4546.63i | −0.211535 | + | 0.366389i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5265.00 | − | 9119.25i | −0.421915 | − | 0.730778i | ||||
\(539\) | −4230.00 | −0.338032 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8372.00 | 0.665324 | 0.332662 | − | 0.943046i | \(-0.392053\pi\) | ||||
0.332662 | + | 0.943046i | \(0.392053\pi\) | |||||||
\(542\) | −4498.50 | − | 7791.63i | −0.356508 | − | 0.617489i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1620.00 | − | 2805.92i | 0.127678 | − | 0.221145i | ||||
\(545\) | 6465.00 | − | 11197.7i | 0.508129 | − | 0.880105i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8560.00 | − | 14826.4i | −0.669103 | − | 1.15892i | −0.978155 | − | 0.207875i | \(-0.933345\pi\) |
0.309053 | − | 0.951045i | \(-0.399988\pi\) | |||||||
\(548\) | −2778.00 | −0.216552 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4500.00 | −0.348874 | ||||||||
\(551\) | −30.0000 | − | 51.9615i | −0.00231950 | − | 0.00401749i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6100.00 | − | 10565.5i | 0.469075 | − | 0.812461i | ||||
\(554\) | 11580.0 | − | 20057.1i | 0.888063 | − | 1.53817i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 962.000 | + | 1666.23i | 0.0733775 | + | 0.127094i | ||||
\(557\) | 10575.0 | 0.804447 | 0.402224 | − | 0.915541i | \(-0.368237\pi\) | ||||
0.402224 | + | 0.915541i | \(0.368237\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2200.00 | 0.166458 | ||||||||
\(560\) | −13312.5 | − | 23057.9i | −1.00456 | − | 1.73996i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 11160.0 | − | 19329.7i | 0.837644 | − | 1.45084i | ||||
\(563\) | −5227.50 | + | 9054.30i | −0.391319 | + | 0.677785i | −0.992624 | − | 0.121235i | \(-0.961315\pi\) |
0.601304 | + | 0.799020i | \(0.294648\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5175.00 | − | 8963.36i | −0.385334 | − | 0.667419i | ||||
\(566\) | 2490.00 | 0.184916 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7560.00 | 0.558469 | ||||||||
\(569\) | 12270.0 | + | 21252.3i | 0.904016 | + | 1.56580i | 0.822233 | + | 0.569152i | \(0.192728\pi\) |
0.0817836 | + | 0.996650i | \(0.473938\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12322.0 | + | 21342.3i | −0.903082 | + | 1.56418i | −0.0796100 | + | 0.996826i | \(0.525367\pi\) |
−0.823472 | + | 0.567357i | \(0.807966\pi\) | |||||||
\(572\) | 150.000 | − | 259.808i | 0.0109647 | − | 0.0189914i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1125.00 | − | 1948.56i | −0.0818059 | − | 0.141692i | ||||
\(575\) | 11400.0 | 0.826805 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9610.00 | −0.693361 | −0.346681 | − | 0.937983i | \(-0.612691\pi\) | ||||
−0.346681 | + | 0.937983i | \(0.612691\pi\) | |||||||
\(578\) | −406.500 | − | 704.079i | −0.0292529 | − | 0.0506675i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −225.000 | + | 389.711i | −0.0161080 | + | 0.0278998i | ||||
\(581\) | 6112.50 | − | 10587.2i | 0.436470 | − | 0.755989i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4657.50 | + | 8067.03i | 0.330864 | + | 0.573074i | ||||
\(584\) | −16485.0 | −1.16807 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1638.00 | 0.115470 | ||||||||
\(587\) | −2008.50 | − | 3478.82i | −0.141226 | − | 0.244611i | 0.786733 | − | 0.617294i | \(-0.211771\pi\) |
−0.927959 | + | 0.372683i | \(0.878438\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −101.000 | + | 174.937i | −0.00706559 | + | 0.0122380i | ||||
\(590\) | 14850.0 | − | 25721.0i | 1.03621 | − | 1.79477i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −15265.0 | − | 26439.8i | −1.05978 | − | 1.83559i | ||||
\(593\) | 594.000 | 0.0411343 | 0.0205672 | − | 0.999788i | \(-0.493453\pi\) | ||||
0.0205672 | + | 0.999788i | \(0.493453\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −27000.0 | −1.86032 | ||||||||
\(596\) | −727.500 | − | 1260.07i | −0.0499993 | − | 0.0866013i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3420.00 | + | 5923.61i | −0.233870 | + | 0.405075i | ||||
\(599\) | −4395.00 | + | 7612.36i | −0.299791 | + | 0.519253i | −0.976088 | − | 0.217376i | \(-0.930250\pi\) |
0.676297 | + | 0.736629i | \(0.263584\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4685.50 | − | 8115.52i | −0.318013 | − | 0.550814i | 0.662061 | − | 0.749450i | \(-0.269682\pi\) |
−0.980073 | + | 0.198636i | \(0.936349\pi\) | |||||||
\(602\) | −8250.00 | −0.558546 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −727.000 | −0.0489755 | ||||||||
\(605\) | 8295.00 | + | 14367.4i | 0.557421 | + | 0.965481i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7280.00 | − | 12609.3i | 0.486798 | − | 0.843158i | −0.513087 | − | 0.858336i | \(-0.671498\pi\) |
0.999885 | + | 0.0151784i | \(0.00483163\pi\) | |||||||
\(608\) | 45.0000 | − | 77.9423i | 0.00300163 | − | 0.00519898i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8460.00 | + | 14653.1i | 0.561533 | + | 0.972604i | ||||
\(611\) | −6600.00 | −0.437001 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18250.0 | −1.20246 | −0.601232 | − | 0.799074i | \(-0.705323\pi\) | ||||
−0.601232 | + | 0.799074i | \(0.705323\pi\) | |||||||
\(614\) | 8340.00 | + | 14445.3i | 0.548168 | + | 0.949454i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3937.50 | − | 6819.95i | 0.257543 | − | 0.446077i | ||||
\(617\) | −9831.00 | + | 17027.8i | −0.641461 | + | 1.11104i | 0.343646 | + | 0.939099i | \(0.388338\pi\) |
−0.985107 | + | 0.171943i | \(0.944995\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6022.00 | − | 10430.4i | −0.391025 | − | 0.677276i | 0.601560 | − | 0.798828i | \(-0.294546\pi\) |
−0.992585 | + | 0.121552i | \(0.961213\pi\) | |||||||
\(620\) | 1515.00 | 0.0981353 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −26010.0 | −1.67670 | ||||||||
\(623\) | −5625.00 | − | 9742.79i | −0.361735 | − | 0.626543i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9062.50 | − | 15696.7i | 0.580000 | − | 1.00459i | ||||
\(626\) | −6847.50 | + | 11860.2i | −0.437190 | + | 0.757236i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1630.00 | − | 2823.24i | −0.103573 | − | 0.179394i | ||||
\(629\) | −30960.0 | −1.96257 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14879.0 | 0.938706 | 0.469353 | − | 0.883011i | \(-0.344487\pi\) | ||||
0.469353 | + | 0.883011i | \(0.344487\pi\) | |||||||
\(632\) | 5124.00 | + | 8875.03i | 0.322503 | + | 0.558591i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6349.50 | + | 10997.7i | −0.397746 | + | 0.688916i | ||||
\(635\) | −13987.5 | + | 24227.1i | −0.874137 | + | 1.51405i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2820.00 | − | 4884.38i | −0.175404 | − | 0.303809i | ||||
\(638\) | −1350.00 | −0.0837727 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 24885.0 | 1.53698 | ||||||||
\(641\) | −4425.00 | − | 7664.32i | −0.272663 | − | 0.472266i | 0.696880 | − | 0.717188i | \(-0.254571\pi\) |
−0.969543 | + | 0.244922i | \(0.921238\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9190.00 | + | 15917.5i | −0.563636 | + | 0.976247i | 0.433539 | + | 0.901135i | \(0.357265\pi\) |
−0.997175 | + | 0.0751120i | \(0.976069\pi\) | |||||||
\(644\) | 1425.00 | − | 2468.17i | 0.0871939 | − | 0.151024i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −216.000 | − | 374.123i | −0.0131554 | − | 0.0227859i | ||||
\(647\) | 3888.00 | 0.236249 | 0.118124 | − | 0.992999i | \(-0.462312\pi\) | ||||
0.118124 | + | 0.992999i | \(0.462312\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9900.00 | 0.598781 | ||||||||
\(650\) | −3000.00 | − | 5196.15i | −0.181030 | − | 0.313554i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1270.00 | + | 2199.70i | −0.0762838 | + | 0.132127i | ||||
\(653\) | 3394.50 | − | 5879.45i | 0.203426 | − | 0.352344i | −0.746204 | − | 0.665717i | \(-0.768126\pi\) |
0.949630 | + | 0.313373i | \(0.101459\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8662.50 | + | 15003.9i | 0.516751 | + | 0.895039i | ||||
\(656\) | 2130.00 | 0.126772 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 24750.0 | 1.46635 | ||||||||
\(659\) | −14167.5 | − | 24538.8i | −0.837462 | − | 1.45053i | −0.892010 | − | 0.452016i | \(-0.850705\pi\) |
0.0545481 | − | 0.998511i | \(-0.482628\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3041.00 | − | 5267.17i | 0.178943 | − | 0.309938i | −0.762576 | − | 0.646899i | \(-0.776066\pi\) |
0.941519 | + | 0.336961i | \(0.109399\pi\) | |||||||
\(662\) | −813.000 | + | 1408.16i | −0.0477313 | + | 0.0826731i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5134.50 | + | 8893.21i | 0.300086 | + | 0.519765i | ||||
\(665\) | −750.000 | −0.0437350 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3420.00 | 0.198535 | ||||||||
\(668\) | −1749.00 | − | 3029.36i | −0.101304 | − | 0.175463i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5625.00 | − | 9742.79i | 0.324347 | − | 0.561786i | ||||
\(671\) | −2820.00 | + | 4884.38i | −0.162243 | + | 0.281013i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4982.50 | − | 8629.94i | −0.285381 | − | 0.494294i | 0.687321 | − | 0.726354i | \(-0.258787\pi\) |
−0.972701 | + | 0.232060i | \(0.925453\pi\) | |||||||
\(674\) | 17070.0 | 0.975537 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1797.00 | −0.102242 | ||||||||
\(677\) | −4065.00 | − | 7040.79i | −0.230769 | − | 0.399704i | 0.727266 | − | 0.686356i | \(-0.240791\pi\) |
−0.958035 | + | 0.286652i | \(0.907458\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13812.5 | + | 23924.0i | −0.780670 | + | 1.35216i | ||||
\(680\) | 11340.0 | − | 19641.5i | 0.639513 | − | 1.10767i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2272.50 | + | 3936.09i | 0.127593 | + | 0.220998i | ||||
\(683\) | 33516.0 | 1.87768 | 0.938839 | − | 0.344356i | \(-0.111903\pi\) | ||||
0.938839 | + | 0.344356i | \(0.111903\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −41670.0 | −2.32428 | ||||||||
\(686\) | −2287.50 | − | 3962.07i | −0.127314 | − | 0.220514i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3905.00 | − | 6763.66i | 0.216391 | − | 0.374800i | ||||
\(689\) | −6210.00 | + | 10756.0i | −0.343370 | + | 0.594735i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11042.0 | + | 19125.3i | 0.607898 | + | 1.05291i | 0.991586 | + | 0.129447i | \(0.0413204\pi\) |
−0.383688 | + | 0.923463i | \(0.625346\pi\) | |||||||
\(692\) | −1149.00 | −0.0631191 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15165.0 | 0.829475 | ||||||||
\(695\) | 14430.0 | + | 24993.5i | 0.787570 | + | 1.36411i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1080.00 | − | 1870.61i | 0.0586914 | − | 0.101657i | ||||
\(698\) | −2433.00 | + | 4214.08i | −0.131935 | + | 0.228518i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1250.00 | + | 2165.06i | 0.0674937 | + | 0.116902i | ||||
\(701\) | −10395.0 | −0.560077 | −0.280038 | − | 0.959989i | \(-0.590347\pi\) | ||||
−0.280038 | + | 0.959989i | \(0.590347\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −860.000 | −0.0461387 | ||||||||
\(704\) | 3247.50 | + | 5624.83i | 0.173856 | + | 0.301128i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −45.0000 | + | 77.9423i | −0.00239886 | + | 0.00415495i | ||||
\(707\) | 17812.5 | − | 30852.2i | 0.947536 | − | 1.64118i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2402.00 | + | 4160.39i | 0.127234 | + | 0.220376i | 0.922604 | − | 0.385748i | \(-0.126057\pi\) |
−0.795370 | + | 0.606124i | \(0.792723\pi\) | |||||||
\(710\) | −16200.0 | −0.856303 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9450.00 | 0.497407 | ||||||||
\(713\) | −5757.00 | − | 9971.42i | −0.302386 | − | 0.523748i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2250.00 | − | 3897.11i | 0.117686 | − | 0.203837i | ||||
\(716\) | −157.500 | + | 272.798i | −0.00822074 | + | 0.0142387i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 11205.0 | + | 19407.6i | 0.582405 | + | 1.00876i | ||||
\(719\) | 10980.0 | 0.569520 | 0.284760 | − | 0.958599i | \(-0.408086\pi\) | ||||
0.284760 | + | 0.958599i | \(0.408086\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 26500.0 | 1.36881 | ||||||||
\(722\) | 10282.5 | + | 17809.8i | 0.530021 | + | 0.918023i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −568.000 | + | 983.805i | −0.0291568 | + | 0.0505011i | ||||
\(725\) | −1500.00 | + | 2598.08i | −0.0768395 | + | 0.133090i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12972.5 | + | 22469.0i | 0.661793 | + | 1.14626i | 0.980144 | + | 0.198286i | \(0.0635375\pi\) |
−0.318351 | + | 0.947973i | \(0.603129\pi\) | |||||||
\(728\) | 10500.0 | 0.534555 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 35325.0 | 1.79101 | ||||||||
\(731\) | −3960.00 | − | 6858.92i | −0.200364 | − | 0.347040i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9325.00 | + | 16151.4i | −0.469886 | + | 0.813867i | −0.999407 | − | 0.0344299i | \(-0.989038\pi\) |
0.529521 | + | 0.848297i | \(0.322372\pi\) | |||||||
\(734\) | 2062.50 | − | 3572.35i | 0.103717 | − | 0.179643i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2565.00 | + | 4442.71i | 0.128461 | + | 0.222501i | ||||
\(737\) | 3750.00 | 0.187426 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5128.00 | −0.255259 | −0.127630 | − | 0.991822i | \(-0.540737\pi\) | ||||
−0.127630 | + | 0.991822i | \(0.540737\pi\) | |||||||
\(740\) | 3225.00 | + | 5585.86i | 0.160207 | + | 0.277487i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 23287.5 | − | 40335.1i | 1.15217 | − | 1.99562i | ||||
\(743\) | 16350.0 | − | 28319.0i | 0.807299 | − | 1.39828i | −0.107429 | − | 0.994213i | \(-0.534262\pi\) |
0.914728 | − | 0.404070i | \(-0.132405\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10912.5 | − | 18901.0i | −0.536648 | − | 0.929502i | ||||
\(746\) | −14520.0 | −0.712621 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1080.00 | −0.0527924 | ||||||||
\(749\) | 18562.5 | + | 32151.2i | 0.905553 | + | 1.56846i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10580.5 | + | 18326.0i | −0.514098 | + | 0.890445i | 0.485768 | + | 0.874088i | \(0.338540\pi\) |
−0.999866 | + | 0.0163567i | \(0.994793\pi\) | |||||||
\(752\) | −11715.0 | + | 20291.0i | −0.568088 | + | 0.983957i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −900.000 | − | 1558.85i | −0.0434696 | − | 0.0752915i | ||||
\(755\) | −10905.0 | −0.525660 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7130.00 | 0.342331 | 0.171165 | − | 0.985242i | \(-0.445247\pi\) | ||||
0.171165 | + | 0.985242i | \(0.445247\pi\) | |||||||
\(758\) | −2838.00 | − | 4915.56i | −0.135991 | − | 0.235542i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 315.000 | − | 545.596i | 0.0150345 | − | 0.0260406i | ||||
\(761\) | 1680.00 | − | 2909.85i | 0.0800262 | − | 0.138609i | −0.823235 | − | 0.567701i | \(-0.807833\pi\) |
0.903261 | + | 0.429092i | \(0.141166\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10775.0 | − | 18662.8i | −0.511247 | − | 0.885505i | ||||
\(764\) | 2460.00 | 0.116492 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −32112.0 | −1.51469 | ||||||||
\(767\) | 6600.00 | + | 11431.5i | 0.310707 | + | 0.538160i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16736.5 | + | 28988.5i | −0.784829 | + | 1.35936i | 0.144272 | + | 0.989538i | \(0.453916\pi\) |
−0.929101 | + | 0.369826i | \(0.879417\pi\) | |||||||
\(770\) | −8437.50 | + | 14614.2i | −0.394891 | + | 0.683972i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −482.500 | − | 835.715i | −0.0224942 | − | 0.0389612i | ||||
\(773\) | −3546.00 | −0.164995 | −0.0824973 | − | 0.996591i | \(-0.526290\pi\) | ||||
−0.0824973 | + | 0.996591i | \(0.526290\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10100.0 | 0.468133 | ||||||||
\(776\) | −11602.5 | − | 20096.1i | −0.536734 | − | 0.929650i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −11722.5 | + | 20304.0i | −0.540195 | + | 0.935646i | ||||
\(779\) | 30.0000 | − | 51.9615i | 0.00137980 | − | 0.00238988i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2700.00 | − | 4676.54i | −0.123705 | − | 0.214263i | ||||
\(782\) | 24624.0 | 1.12603 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −20022.0 | −0.912081 | ||||||||
\(785\) | −24450.0 | − | 42348.6i | −1.11167 | − | 1.92546i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15920.0 | − | 27574.2i | 0.721076 | − | 1.24894i | −0.239493 | − | 0.970898i | \(-0.576981\pi\) |
0.960569 | − | 0.278042i | \(-0.0896854\pi\) | |||||||
\(788\) | −1246.50 | + | 2159.00i | −0.0563512 | + | 0.0976031i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −10980.0 | − | 19017.9i | −0.494495 | − | 0.856490i | ||||
\(791\) | −17250.0 | −0.775397 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7520.00 | −0.336750 | ||||||||
\(794\) | −7050.00 | − | 12211.0i | −0.315107 | − | 0.545782i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 255.500 | − | 442.539i | 0.0113768 | − | 0.0197052i | ||||
\(797\) | 7858.50 | − | 13611.3i | 0.349263 | − | 0.604941i | −0.636856 | − | 0.770983i | \(-0.719765\pi\) |
0.986119 | + | 0.166042i | \(0.0530988\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11880.0 | + | 20576.8i | 0.526013 | + | 0.911081i | ||||
\(800\) | −4500.00 | −0.198874 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6300.00 | −0.277382 | ||||||||
\(803\) | 5887.50 | + | 10197.4i | 0.258736 | + | 0.448145i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21375.0 | − | 37022.6i | 0.935863 | − | 1.62096i | ||||
\(806\) | −3030.00 | + | 5248.11i | −0.132416 | + | 0.229351i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 14962.5 | + | 25915.8i | 0.651459 | + | 1.12836i | ||||
\(809\) | 10530.0 | 0.457621 | 0.228810 | − | 0.973471i | \(-0.426516\pi\) | ||||
0.228810 | + | 0.973471i | \(0.426516\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26782.0 | −1.15961 | −0.579805 | − | 0.814755i | \(-0.696871\pi\) | ||||
−0.579805 | + | 0.814755i | \(0.696871\pi\) | |||||||
\(812\) | 375.000 | + | 649.519i | 0.0162068 | + | 0.0280710i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −9675.00 | + | 16757.6i | −0.416595 | + | 0.721564i | ||||
\(815\) | −19050.0 | + | 32995.6i | −0.818764 | + | 1.41814i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −110.000 | − | 190.526i | −0.00471042 | − | 0.00815869i | ||||
\(818\) | −32259.0 | −1.37886 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −450.000 | −0.0191642 | ||||||||
\(821\) | −5055.00 | − | 8755.52i | −0.214885 | − | 0.372192i | 0.738352 | − | 0.674416i | \(-0.235604\pi\) |
−0.953237 | + | 0.302224i | \(0.902271\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6267.50 | − | 10855.6i | 0.265457 | − | 0.459785i | −0.702226 | − | 0.711954i | \(-0.747810\pi\) |
0.967683 | + | 0.252169i | \(0.0811438\pi\) | |||||||
\(824\) | −11130.0 | + | 19277.7i | −0.470548 | + | 0.815014i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −24750.0 | − | 42868.3i | −1.04257 | − | 1.80578i | ||||
\(827\) | 9792.00 | 0.411731 | 0.205865 | − | 0.978580i | \(-0.433999\pi\) | ||||
0.205865 | + | 0.978580i | \(0.433999\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4534.00 | −0.189955 | −0.0949773 | − | 0.995479i | \(-0.530278\pi\) | ||||
−0.0949773 | + | 0.995479i | \(0.530278\pi\) | |||||||
\(830\) | −11002.5 | − | 19056.9i | −0.460123 | − | 0.796957i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4330.00 | + | 7499.78i | −0.180428 | + | 0.312510i | ||||
\(833\) | −10152.0 | + | 17583.8i | −0.422264 | + | 0.731383i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −26235.0 | − | 45440.4i | −1.08730 | − | 1.88327i | ||||
\(836\) | −30.0000 | −0.00124111 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8820.00 | 0.363582 | ||||||||
\(839\) | 4440.00 | + | 7690.31i | 0.182701 | + | 0.316447i | 0.942799 | − | 0.333361i | \(-0.108183\pi\) |
−0.760099 | + | 0.649808i | \(0.774849\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11744.5 | − | 20342.1i | 0.481549 | − | 0.834067i | ||||
\(842\) | −13044.0 | + | 22592.9i | −0.533879 | + | 0.924705i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1043.00 | + | 1806.53i | 0.0425374 | + | 0.0736769i | ||||
\(845\) | −26955.0 | −1.09737 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27650.0 | 1.12168 | ||||||||
\(848\) | 22045.5 | + | 38183.9i | 0.892742 | + | 1.54628i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −10800.0 | + | 18706.1i | −0.435808 | + | 0.754842i | ||||
\(851\) | 24510.0 | − | 42452.6i | 0.987300 | − | 1.71005i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1135.00 | − | 1965.88i | −0.0455588 | − | 0.0789102i | 0.842347 | − | 0.538936i | \(-0.181174\pi\) |
−0.887906 | + | 0.460026i | \(0.847840\pi\) | |||||||
\(854\) | 28200.0 | 1.12996 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −31185.0 | −1.24519 | ||||||||
\(857\) | 9804.00 | + | 16981.0i | 0.390780 | + | 0.676850i | 0.992553 | − | 0.121817i | \(-0.0388721\pi\) |
−0.601773 | + | 0.798667i | \(0.705539\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 476.000 | − | 824.456i | 0.0189068 | − | 0.0327475i | −0.856417 | − | 0.516284i | \(-0.827315\pi\) |
0.875324 | + | 0.483537i | \(0.160648\pi\) | |||||||
\(860\) | −825.000 | + | 1428.94i | −0.0327119 | + | 0.0566587i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −12555.0 | − | 21745.9i | −0.496085 | − | 0.859244i | ||||
\(863\) | −17604.0 | −0.694377 | −0.347188 | − | 0.937795i | \(-0.612864\pi\) | ||||
−0.347188 | + | 0.937795i | \(0.612864\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17235.0 | −0.677465 | ||||||||
\(866\) | 7732.50 | + | 13393.1i | 0.303419 | + | 0.525538i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1262.50 | − | 2186.71i | 0.0493687 | − | 0.0855091i | ||||
\(869\) | 3660.00 | − | 6339.31i | 0.142873 | − | 0.247464i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2500.00 | + | 4330.13i | 0.0972552 | + | 0.168451i | ||||
\(872\) | 18102.0 | 0.702994 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 684.000 | 0.0264721 | ||||||||
\(875\) | −4687.50 | − | 8118.99i | −0.181104 | − | 0.313682i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10945.0 | + | 18957.3i | −0.421421 | + | 0.729923i | −0.996079 | − | 0.0884711i | \(-0.971802\pi\) |
0.574658 | + | 0.818394i | \(0.305135\pi\) | |||||||
\(878\) | 16480.5 | − | 28545.1i | 0.633474 | − | 1.09721i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −7987.50 | − | 13834.8i | −0.305976 | − | 0.529965i | ||||
\(881\) | 23940.0 | 0.915504 | 0.457752 | − | 0.889080i | \(-0.348655\pi\) | ||||
0.457752 | + | 0.889080i | \(0.348655\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34990.0 | −1.33353 | −0.666765 | − | 0.745268i | \(-0.732322\pi\) | ||||
−0.666765 | + | 0.745268i | \(0.732322\pi\) | |||||||
\(884\) | −720.000 | − | 1247.08i | −0.0273939 | − | 0.0474477i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2934.00 | + | 5081.84i | −0.111252 | + | 0.192695i | ||||
\(887\) | 11094.0 | − | 19215.4i | 0.419955 | − | 0.727383i | −0.575979 | − | 0.817464i | \(-0.695379\pi\) |
0.995934 | + | 0.0900808i | \(0.0287125\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23312.5 | + | 40378.4i | 0.879501 | + | 1.52334i | ||||
\(890\) | −20250.0 | −0.762676 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5240.00 | 0.196691 | ||||||||
\(893\) | 330.000 | + | 571.577i | 0.0123662 | + | 0.0214189i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2362.50 | + | 4091.97i | −0.0882343 | + | 0.152826i | ||||
\(896\) | 20737.5 | − | 35918.4i | 0.773205 | − | 1.33923i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 13095.0 | + | 22681.2i | 0.486621 | + | 0.842853i | ||||
\(899\) | 3030.00 | 0.112410 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 44712.0 | 1.65324 | ||||||||
\(902\) | −675.000 | − | 1169.13i | −0.0249169 | − | 0.0431573i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7245.00 | − | 12548.7i | 0.266554 | − | 0.461686i | ||||
\(905\) | −8520.00 | + | 14757.1i | −0.312944 | + | 0.542035i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18685.0 | − | 32363.4i | −0.684041 | − | 1.18479i | −0.973737 | − | 0.227675i | \(-0.926888\pi\) |
0.289696 | − | 0.957119i | \(-0.406446\pi\) | |||||||
\(908\) | 2388.00 | 0.0872782 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −22500.0 | −0.819635 | ||||||||
\(911\) | −20355.0 | − | 35255.9i | −0.740276 | − | 1.28220i | −0.952370 | − | 0.304946i | \(-0.901362\pi\) |
0.212094 | − | 0.977249i | \(-0.431972\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3667.50 | − | 6352.30i | 0.132943 | − | 0.230263i | ||||
\(914\) | 12997.5 | − | 22512.3i | 0.470371 | − | 0.814706i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −91.0000 | − | 157.617i | −0.00328245 | − | 0.00568537i | ||||
\(917\) | 28875.0 | 1.03984 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20981.0 | 0.753100 | 0.376550 | − | 0.926396i | \(-0.377110\pi\) | ||||
0.376550 | + | 0.926396i | \(0.377110\pi\) | |||||||
\(920\) | 17955.0 | + | 31099.0i | 0.643433 | + | 1.11446i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 14737.5 | − | 25526.1i | 0.526414 | − | 0.911776i | ||||
\(923\) | 3600.00 | − | 6235.38i | 0.128381 | − | 0.222362i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21500.0 | + | 37239.1i | 0.764233 | + | 1.32369i | ||||
\(926\) | −15735.0 | −0.558406 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1350.00 | −0.0477542 | ||||||||
\(929\) | −10050.0 | − | 17407.1i | −0.354930 | − | 0.614756i | 0.632176 | − | 0.774825i | \(-0.282162\pi\) |
−0.987106 | + | 0.160068i | \(0.948829\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −282.000 | + | 488.438i | −0.00992715 | + | 0.0171943i | ||||
\(932\) | −225.000 | + | 389.711i | −0.00790785 | + | 0.0136968i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 16510.5 | + | 28597.0i | 0.578415 | + | 1.00185i | ||||
\(935\) | −16200.0 | −0.566627 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15635.0 | 0.545115 | 0.272558 | − | 0.962139i | \(-0.412130\pi\) | ||||
0.272558 | + | 0.962139i | \(0.412130\pi\) | |||||||
\(938\) | −9375.00 | − | 16238.0i | −0.326338 | − | 0.565233i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2475.00 | − | 4286.83i | 0.0858783 | − | 0.148746i | ||||
\(941\) | −11977.5 | + | 20745.6i | −0.414937 | + | 0.718691i | −0.995422 | − | 0.0955795i | \(-0.969530\pi\) |
0.580485 | + | 0.814271i | \(0.302863\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1710.00 | + | 2961.81i | 0.0590512 | + | 0.102280i | ||||
\(944\) | 46860.0 | 1.61564 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4950.00 | −0.170125 | ||||||||
\(947\) | 18196.5 | + | 31517.3i | 0.624400 | + | 1.08149i | 0.988657 | + | 0.150194i | \(0.0479898\pi\) |
−0.364257 | + | 0.931299i | \(0.618677\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7850.00 | + | 13596.6i | −0.268516 | + | 0.465084i | ||||
\(950\) | −300.000 | + | 519.615i | −0.0102456 | + | 0.0177458i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −18900.0 | − | 32735.8i | −0.643438 | − | 1.11447i | ||||
\(953\) | 43020.0 | 1.46228 | 0.731141 | − | 0.682227i | \(-0.238988\pi\) | ||||
0.731141 | + | 0.682227i | \(0.238988\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 36900.0 | 1.25032 | ||||||||
\(956\) | −2595.00 | − | 4494.67i | −0.0877911 | − | 0.152059i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −25425.0 | + | 44037.4i | −0.857458 | + | 1.48516i | ||||
\(959\) | −34725.0 | + | 60145.5i | −1.16927 | + | 2.02523i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9795.00 | + | 16965.4i | 0.328791 | + | 0.569482i | ||||
\(962\) | −25800.0 | −0.864683 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2266.00 | −0.0757084 | ||||||||
\(965\) | −7237.50 | − | 12535.7i | −0.241434 | − | 0.418175i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21792.5 | − | 37745.7i | 0.724715 | − | 1.25524i | −0.234376 | − | 0.972146i | \(-0.575305\pi\) |
0.959091 | − | 0.283097i | \(-0.0913620\pi\) | |||||||
\(968\) | −11613.0 | + | 20114.3i | −0.385595 | + | 0.667870i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 24862.5 | + | 43063.1i | 0.822976 | + | 1.42544i | ||||
\(971\) | −43335.0 | −1.43222 | −0.716110 | − | 0.697987i | \(-0.754079\pi\) | ||||
−0.716110 | + | 0.697987i | \(0.754079\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 48100.0 | 1.58480 | ||||||||
\(974\) | −15960.0 | − | 27643.5i | −0.525042 | − | 0.909400i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −13348.0 | + | 23119.4i | −0.437765 | + | 0.758232i | ||||
\(977\) | −15195.0 | + | 26318.5i | −0.497575 | + | 0.861826i | −0.999996 | − | 0.00279748i | \(-0.999110\pi\) |
0.502421 | + | 0.864623i | \(0.332443\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3375.00 | − | 5845.67i | −0.110179 | − | 0.190836i | ||||
\(980\) | 4230.00 | 0.137880 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4905.00 | 0.159394 | ||||||||
\(983\) | 29613.0 | + | 51291.2i | 0.960842 | + | 1.66423i | 0.720393 | + | 0.693566i | \(0.243961\pi\) |
0.240449 | + | 0.970662i | \(0.422705\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18697.5 | + | 32385.0i | −0.604824 | + | 1.04759i | ||||
\(986\) | −3240.00 | + | 5611.84i | −0.104648 | + | 0.181255i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −20.0000 | − | 34.6410i | −0.000644013 | − | 0.00111546i | ||||
\(989\) | 12540.0 | 0.403184 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8399.00 | 0.269226 | 0.134613 | − | 0.990898i | \(-0.457021\pi\) | ||||
0.134613 | + | 0.990898i | \(0.457021\pi\) | |||||||
\(992\) | 2272.50 | + | 3936.09i | 0.0727338 | + | 0.125979i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −13500.0 | + | 23382.7i | −0.430779 | + | 0.746131i | ||||
\(995\) | 3832.50 | − | 6638.08i | 0.122109 | − | 0.211499i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6670.00 | − | 11552.8i | −0.211877 | − | 0.366981i | 0.740425 | − | 0.672139i | \(-0.234624\pi\) |
−0.952302 | + | 0.305158i | \(0.901291\pi\) | |||||||
\(998\) | −47406.0 | −1.50362 | ||||||||
\(999\) | 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 | 81.4.c.a.28.1 | 2 | ||
3.2 | odd | 2 | 81.4.c.c.28.1 | 2 | |||
9.2 | odd | 6 | 81.4.c.c.55.1 | 2 | |||
9.4 | even | 3 | 27.4.a.b.1.1 | yes | 1 | ||
9.5 | odd | 6 | 27.4.a.a.1.1 | ✓ | 1 | ||
9.7 | even | 3 | inner | 81.4.c.a.55.1 | 2 | ||
36.23 | even | 6 | 432.4.a.a.1.1 | 1 | |||
36.31 | odd | 6 | 432.4.a.n.1.1 | 1 | |||
45.4 | even | 6 | 675.4.a.a.1.1 | 1 | |||
45.13 | odd | 12 | 675.4.b.a.649.1 | 2 | |||
45.14 | odd | 6 | 675.4.a.j.1.1 | 1 | |||
45.22 | odd | 12 | 675.4.b.a.649.2 | 2 | |||
45.23 | even | 12 | 675.4.b.b.649.2 | 2 | |||
45.32 | even | 12 | 675.4.b.b.649.1 | 2 | |||
63.13 | odd | 6 | 1323.4.a.k.1.1 | 1 | |||
63.41 | even | 6 | 1323.4.a.d.1.1 | 1 | |||
72.5 | odd | 6 | 1728.4.a.bc.1.1 | 1 | |||
72.13 | even | 6 | 1728.4.a.c.1.1 | 1 | |||
72.59 | even | 6 | 1728.4.a.bd.1.1 | 1 | |||
72.67 | odd | 6 | 1728.4.a.d.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.4.a.a.1.1 | ✓ | 1 | 9.5 | odd | 6 | ||
27.4.a.b.1.1 | yes | 1 | 9.4 | even | 3 | ||
81.4.c.a.28.1 | 2 | 1.1 | even | 1 | trivial | ||
81.4.c.a.55.1 | 2 | 9.7 | even | 3 | inner | ||
81.4.c.c.28.1 | 2 | 3.2 | odd | 2 | |||
81.4.c.c.55.1 | 2 | 9.2 | odd | 6 | |||
432.4.a.a.1.1 | 1 | 36.23 | even | 6 | |||
432.4.a.n.1.1 | 1 | 36.31 | odd | 6 | |||
675.4.a.a.1.1 | 1 | 45.4 | even | 6 | |||
675.4.a.j.1.1 | 1 | 45.14 | odd | 6 | |||
675.4.b.a.649.1 | 2 | 45.13 | odd | 12 | |||
675.4.b.a.649.2 | 2 | 45.22 | odd | 12 | |||
675.4.b.b.649.1 | 2 | 45.32 | even | 12 | |||
675.4.b.b.649.2 | 2 | 45.23 | even | 12 | |||
1323.4.a.d.1.1 | 1 | 63.41 | even | 6 | |||
1323.4.a.k.1.1 | 1 | 63.13 | odd | 6 | |||
1728.4.a.c.1.1 | 1 | 72.13 | even | 6 | |||
1728.4.a.d.1.1 | 1 | 72.67 | odd | 6 | |||
1728.4.a.bc.1.1 | 1 | 72.5 | odd | 6 | |||
1728.4.a.bd.1.1 | 1 | 72.59 | even | 6 |