Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,4,Mod(13,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.13");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.m (of order \(4\), 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: | \(6.19520055060\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 13.12 | ||
Character | \(\chi\) | \(=\) | 105.13 |
Dual form | 105.4.m.a.97.12 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.811442 | + | 0.811442i | −0.286888 | + | 0.286888i | −0.835848 | − | 0.548960i | \(-0.815024\pi\) |
0.548960 | + | 0.835848i | \(0.315024\pi\) | |||||||
\(3\) | 2.12132 | − | 2.12132i | 0.408248 | − | 0.408248i | ||||
\(4\) | 6.68312i | 0.835391i | ||||||||
\(5\) | 4.54645 | − | 10.2142i | 0.406647 | − | 0.913586i | ||||
\(6\) | 3.44266i | 0.234243i | ||||||||
\(7\) | 10.5095 | + | 15.2496i | 0.567459 | + | 0.823402i | ||||
\(8\) | −11.9145 | − | 11.9145i | −0.526551 | − | 0.526551i | ||||
\(9\) | − | 9.00000i | − | 0.333333i | ||||||
\(10\) | 4.59905 | + | 11.9774i | 0.145435 | + | 0.378759i | ||||
\(11\) | 47.0616 | 1.28996 | 0.644982 | − | 0.764198i | \(-0.276865\pi\) | ||||
0.644982 | + | 0.764198i | \(0.276865\pi\) | |||||||
\(12\) | 14.1770 | + | 14.1770i | 0.341047 | + | 0.341047i | ||||
\(13\) | −6.35598 | + | 6.35598i | −0.135602 | + | 0.135602i | −0.771650 | − | 0.636048i | \(-0.780568\pi\) |
0.636048 | + | 0.771650i | \(0.280568\pi\) | |||||||
\(14\) | −20.9020 | − | 3.84634i | −0.399021 | − | 0.0734270i | ||||
\(15\) | −12.0231 | − | 31.3121i | −0.206957 | − | 0.538982i | ||||
\(16\) | −34.1292 | −0.533268 | ||||||||
\(17\) | 48.7908 | + | 48.7908i | 0.696088 | + | 0.696088i | 0.963564 | − | 0.267476i | \(-0.0861897\pi\) |
−0.267476 | + | 0.963564i | \(0.586190\pi\) | |||||||
\(18\) | 7.30297 | + | 7.30297i | 0.0956293 | + | 0.0956293i | ||||
\(19\) | 122.702 | 1.48157 | 0.740785 | − | 0.671743i | \(-0.234454\pi\) | ||||
0.740785 | + | 0.671743i | \(0.234454\pi\) | |||||||
\(20\) | 68.2628 | + | 30.3845i | 0.763201 | + | 0.339709i | ||||
\(21\) | 54.6433 | + | 10.0553i | 0.567816 | + | 0.104488i | ||||
\(22\) | −38.1877 | + | 38.1877i | −0.370075 | + | 0.370075i | ||||
\(23\) | 32.8029 | + | 32.8029i | 0.297386 | + | 0.297386i | 0.839989 | − | 0.542603i | \(-0.182561\pi\) |
−0.542603 | + | 0.839989i | \(0.682561\pi\) | |||||||
\(24\) | −50.5489 | −0.429927 | ||||||||
\(25\) | −83.6597 | − | 92.8766i | −0.669277 | − | 0.743013i | ||||
\(26\) | − | 10.3150i | − | 0.0778054i | ||||||
\(27\) | −19.0919 | − | 19.0919i | −0.136083 | − | 0.136083i | ||||
\(28\) | −101.915 | + | 70.2362i | −0.687862 | + | 0.474050i | ||||
\(29\) | 111.792i | 0.715836i | 0.933753 | + | 0.357918i | \(0.116513\pi\) | ||||
−0.933753 | + | 0.357918i | \(0.883487\pi\) | |||||||
\(30\) | 35.1640 | + | 15.6518i | 0.214001 | + | 0.0952541i | ||||
\(31\) | − | 69.1953i | − | 0.400898i | −0.979704 | − | 0.200449i | \(-0.935760\pi\) | ||
0.979704 | − | 0.200449i | \(-0.0642401\pi\) | |||||||
\(32\) | 123.010 | − | 123.010i | 0.679540 | − | 0.679540i | ||||
\(33\) | 99.8327 | − | 99.8327i | 0.526626 | − | 0.526626i | ||||
\(34\) | −79.1817 | −0.399399 | ||||||||
\(35\) | 203.543 | − | 38.0144i | 0.983003 | − | 0.183589i | ||||
\(36\) | 60.1481 | 0.278464 | ||||||||
\(37\) | −227.678 | + | 227.678i | −1.01162 | + | 1.01162i | −0.0116924 | + | 0.999932i | \(0.503722\pi\) |
−0.999932 | + | 0.0116924i | \(0.996278\pi\) | |||||||
\(38\) | −99.5657 | + | 99.5657i | −0.425044 | + | 0.425044i | ||||
\(39\) | 26.9661i | 0.110719i | ||||||||
\(40\) | −175.866 | + | 67.5284i | −0.695170 | + | 0.266929i | ||||
\(41\) | − | 258.481i | − | 0.984586i | −0.870430 | − | 0.492293i | \(-0.836159\pi\) | ||
0.870430 | − | 0.492293i | \(-0.163841\pi\) | |||||||
\(42\) | −52.4992 | + | 36.1805i | −0.192876 | + | 0.132923i | ||||
\(43\) | −331.574 | − | 331.574i | −1.17592 | − | 1.17592i | −0.980774 | − | 0.195147i | \(-0.937481\pi\) |
−0.195147 | − | 0.980774i | \(-0.562519\pi\) | |||||||
\(44\) | 314.518i | 1.07762i | ||||||||
\(45\) | −91.9278 | − | 40.9180i | −0.304529 | − | 0.135549i | ||||
\(46\) | −53.2353 | −0.170633 | ||||||||
\(47\) | −332.722 | − | 332.722i | −1.03261 | − | 1.03261i | −0.999450 | − | 0.0331550i | \(-0.989444\pi\) |
−0.0331550 | − | 0.999450i | \(-0.510556\pi\) | |||||||
\(48\) | −72.3989 | + | 72.3989i | −0.217706 | + | 0.217706i | ||||
\(49\) | −122.101 | + | 320.531i | −0.355981 | + | 0.934493i | ||||
\(50\) | 143.249 | + | 7.47901i | 0.405169 | + | 0.0211538i | ||||
\(51\) | 207.002 | 0.568354 | ||||||||
\(52\) | −42.4778 | − | 42.4778i | −0.113281 | − | 0.113281i | ||||
\(53\) | −397.103 | − | 397.103i | −1.02917 | − | 1.02917i | −0.999561 | − | 0.0296135i | \(-0.990572\pi\) |
−0.0296135 | − | 0.999561i | \(-0.509428\pi\) | |||||||
\(54\) | 30.9839 | 0.0780810 | ||||||||
\(55\) | 213.963 | − | 480.696i | 0.524559 | − | 1.17849i | ||||
\(56\) | 56.4763 | − | 306.907i | 0.134767 | − | 0.732360i | ||||
\(57\) | 260.291 | − | 260.291i | 0.604848 | − | 0.604848i | ||||
\(58\) | −90.7126 | − | 90.7126i | −0.205365 | − | 0.205365i | ||||
\(59\) | −124.410 | −0.274522 | −0.137261 | − | 0.990535i | \(-0.543830\pi\) | ||||
−0.137261 | + | 0.990535i | \(0.543830\pi\) | |||||||
\(60\) | 209.262 | − | 80.3520i | 0.450261 | − | 0.172890i | ||||
\(61\) | 390.333i | 0.819296i | 0.912244 | + | 0.409648i | \(0.134349\pi\) | ||||
−0.912244 | + | 0.409648i | \(0.865651\pi\) | |||||||
\(62\) | 56.1479 | + | 56.1479i | 0.115013 | + | 0.115013i | ||||
\(63\) | 137.247 | − | 94.5854i | 0.274467 | − | 0.189153i | ||||
\(64\) | − | 73.4027i | − | 0.143365i | ||||||
\(65\) | 36.0241 | + | 93.8183i | 0.0687421 | + | 0.179027i | ||||
\(66\) | 162.017i | 0.302165i | ||||||||
\(67\) | −172.872 | + | 172.872i | −0.315219 | + | 0.315219i | −0.846928 | − | 0.531708i | \(-0.821550\pi\) |
0.531708 | + | 0.846928i | \(0.321550\pi\) | |||||||
\(68\) | −326.075 | + | 326.075i | −0.581506 | + | 0.581506i | ||||
\(69\) | 139.171 | 0.242815 | ||||||||
\(70\) | −134.317 | + | 196.010i | −0.229342 | + | 0.334681i | ||||
\(71\) | 146.934 | 0.245604 | 0.122802 | − | 0.992431i | \(-0.460812\pi\) | ||||
0.122802 | + | 0.992431i | \(0.460812\pi\) | |||||||
\(72\) | −107.230 | + | 107.230i | −0.175517 | + | 0.175517i | ||||
\(73\) | 360.078 | − | 360.078i | 0.577314 | − | 0.577314i | −0.356849 | − | 0.934162i | \(-0.616149\pi\) |
0.934162 | + | 0.356849i | \(0.116149\pi\) | |||||||
\(74\) | − | 369.495i | − | 0.580445i | ||||||
\(75\) | −374.490 | − | 19.5521i | −0.576565 | − | 0.0301024i | ||||
\(76\) | 820.034i | 1.23769i | ||||||||
\(77\) | 494.593 | + | 717.671i | 0.732001 | + | 1.06216i | ||||
\(78\) | −21.8814 | − | 21.8814i | −0.0317639 | − | 0.0317639i | ||||
\(79\) | 1191.77i | 1.69728i | 0.528973 | + | 0.848639i | \(0.322577\pi\) | ||||
−0.528973 | + | 0.848639i | \(0.677423\pi\) | |||||||
\(80\) | −155.166 | + | 348.602i | −0.216852 | + | 0.487186i | ||||
\(81\) | −81.0000 | −0.111111 | ||||||||
\(82\) | 209.743 | + | 209.743i | 0.282466 | + | 0.282466i | ||||
\(83\) | 33.8129 | − | 33.8129i | 0.0447163 | − | 0.0447163i | −0.684395 | − | 0.729111i | \(-0.739934\pi\) |
0.729111 | + | 0.684395i | \(0.239934\pi\) | |||||||
\(84\) | −67.2011 | + | 365.188i | −0.0872885 | + | 0.474349i | ||||
\(85\) | 720.183 | − | 276.534i | 0.918998 | − | 0.352874i | ||||
\(86\) | 538.106 | 0.674715 | ||||||||
\(87\) | 237.147 | + | 237.147i | 0.292239 | + | 0.292239i | ||||
\(88\) | −560.715 | − | 560.715i | −0.679232 | − | 0.679232i | ||||
\(89\) | 1283.38 | 1.52852 | 0.764261 | − | 0.644908i | \(-0.223104\pi\) | ||||
0.764261 | + | 0.644908i | \(0.223104\pi\) | |||||||
\(90\) | 107.797 | − | 41.3914i | 0.126253 | − | 0.0484782i | ||||
\(91\) | −163.724 | − | 30.1282i | −0.188604 | − | 0.0347065i | ||||
\(92\) | −219.226 | + | 219.226i | −0.248434 | + | 0.248434i | ||||
\(93\) | −146.785 | − | 146.785i | −0.163666 | − | 0.163666i | ||||
\(94\) | 539.968 | 0.592484 | ||||||||
\(95\) | 557.859 | − | 1253.30i | 0.602475 | − | 1.35354i | ||||
\(96\) | − | 521.886i | − | 0.554842i | ||||||
\(97\) | −212.490 | − | 212.490i | −0.222423 | − | 0.222423i | 0.587095 | − | 0.809518i | \(-0.300272\pi\) |
−0.809518 | + | 0.587095i | \(0.800272\pi\) | |||||||
\(98\) | −161.014 | − | 359.171i | −0.165968 | − | 0.370221i | ||||
\(99\) | − | 423.554i | − | 0.429988i | ||||||
\(100\) | 620.706 | − | 559.108i | 0.620706 | − | 0.559108i | ||||
\(101\) | − | 111.213i | − | 0.109566i | −0.998498 | − | 0.0547828i | \(-0.982553\pi\) | ||
0.998498 | − | 0.0547828i | \(-0.0174466\pi\) | |||||||
\(102\) | −167.970 | + | 167.970i | −0.163054 | + | 0.163054i | ||||
\(103\) | −345.690 | + | 345.690i | −0.330698 | + | 0.330698i | −0.852851 | − | 0.522154i | \(-0.825129\pi\) |
0.522154 | + | 0.852851i | \(0.325129\pi\) | |||||||
\(104\) | 151.457 | 0.142803 | ||||||||
\(105\) | 351.140 | − | 512.421i | 0.326360 | − | 0.476259i | ||||
\(106\) | 644.452 | 0.590516 | ||||||||
\(107\) | −1377.95 | + | 1377.95i | −1.24496 | + | 1.24496i | −0.287046 | + | 0.957917i | \(0.592673\pi\) |
−0.957917 | + | 0.287046i | \(0.907327\pi\) | |||||||
\(108\) | 127.593 | − | 127.593i | 0.113682 | − | 0.113682i | ||||
\(109\) | − | 1711.62i | − | 1.50407i | −0.659124 | − | 0.752034i | \(-0.729073\pi\) | ||
0.659124 | − | 0.752034i | \(-0.270927\pi\) | |||||||
\(110\) | 216.439 | + | 563.675i | 0.187606 | + | 0.488585i | ||||
\(111\) | 965.957i | 0.825988i | ||||||||
\(112\) | −358.680 | − | 520.457i | −0.302608 | − | 0.439094i | ||||
\(113\) | −227.921 | − | 227.921i | −0.189743 | − | 0.189743i | 0.605842 | − | 0.795585i | \(-0.292836\pi\) |
−0.795585 | + | 0.605842i | \(0.792836\pi\) | |||||||
\(114\) | 422.421i | 0.347047i | ||||||||
\(115\) | 484.192 | − | 185.919i | 0.392619 | − | 0.150757i | ||||
\(116\) | −747.120 | −0.598003 | ||||||||
\(117\) | 57.2038 | + | 57.2038i | 0.0452008 | + | 0.0452008i | ||||
\(118\) | 100.952 | − | 100.952i | 0.0787572 | − | 0.0787572i | ||||
\(119\) | −231.275 | + | 1256.81i | −0.178159 | + | 0.968162i | ||||
\(120\) | −229.818 | + | 516.317i | −0.174828 | + | 0.392776i | ||||
\(121\) | 883.793 | 0.664007 | ||||||||
\(122\) | −316.733 | − | 316.733i | −0.235046 | − | 0.235046i | ||||
\(123\) | −548.322 | − | 548.322i | −0.401955 | − | 0.401955i | ||||
\(124\) | 462.441 | 0.334906 | ||||||||
\(125\) | −1329.01 | + | 432.258i | −0.950965 | + | 0.309298i | ||||
\(126\) | −34.6171 | + | 188.118i | −0.0244757 | + | 0.133007i | ||||
\(127\) | −67.2228 | + | 67.2228i | −0.0469689 | + | 0.0469689i | −0.730201 | − | 0.683232i | \(-0.760574\pi\) |
0.683232 | + | 0.730201i | \(0.260574\pi\) | |||||||
\(128\) | 1043.64 | + | 1043.64i | 0.720669 | + | 0.720669i | ||||
\(129\) | −1406.75 | −0.960136 | ||||||||
\(130\) | −105.360 | − | 46.8966i | −0.0710818 | − | 0.0316393i | ||||
\(131\) | − | 2233.09i | − | 1.48936i | −0.667424 | − | 0.744678i | \(-0.732603\pi\) | ||
0.667424 | − | 0.744678i | \(-0.267397\pi\) | |||||||
\(132\) | 667.194 | + | 667.194i | 0.439938 | + | 0.439938i | ||||
\(133\) | 1289.54 | + | 1871.16i | 0.840729 | + | 1.21993i | ||||
\(134\) | − | 280.551i | − | 0.180865i | ||||||
\(135\) | −281.808 | + | 108.208i | −0.179661 | + | 0.0689857i | ||||
\(136\) | − | 1162.64i | − | 0.733052i | ||||||
\(137\) | 221.734 | − | 221.734i | 0.138277 | − | 0.138277i | −0.634580 | − | 0.772857i | \(-0.718827\pi\) |
0.772857 | + | 0.634580i | \(0.218827\pi\) | |||||||
\(138\) | −112.929 | + | 112.929i | −0.0696606 | + | 0.0696606i | ||||
\(139\) | −1884.04 | −1.14966 | −0.574829 | − | 0.818274i | \(-0.694931\pi\) | ||||
−0.574829 | + | 0.818274i | \(0.694931\pi\) | |||||||
\(140\) | 254.055 | + | 1360.31i | 0.153368 | + | 0.821192i | ||||
\(141\) | −1411.62 | −0.843119 | ||||||||
\(142\) | −119.229 | + | 119.229i | −0.0704609 | + | 0.0704609i | ||||
\(143\) | −299.122 | + | 299.122i | −0.174922 | + | 0.174922i | ||||
\(144\) | 307.162i | 0.177756i | ||||||||
\(145\) | 1141.86 | + | 508.256i | 0.653977 | + | 0.291092i | ||||
\(146\) | 584.364i | 0.331249i | ||||||||
\(147\) | 420.933 | + | 938.966i | 0.236177 | + | 0.526834i | ||||
\(148\) | −1521.60 | − | 1521.60i | −0.845101 | − | 0.845101i | ||||
\(149\) | − | 1940.65i | − | 1.06701i | −0.845798 | − | 0.533504i | \(-0.820875\pi\) | ||
0.845798 | − | 0.533504i | \(-0.179125\pi\) | |||||||
\(150\) | 319.742 | − | 288.011i | 0.174046 | − | 0.156774i | ||||
\(151\) | 1479.51 | 0.797358 | 0.398679 | − | 0.917091i | \(-0.369469\pi\) | ||||
0.398679 | + | 0.917091i | \(0.369469\pi\) | |||||||
\(152\) | −1461.94 | − | 1461.94i | −0.780122 | − | 0.780122i | ||||
\(153\) | 439.117 | − | 439.117i | 0.232029 | − | 0.232029i | ||||
\(154\) | −983.682 | − | 181.015i | −0.514723 | − | 0.0947181i | ||||
\(155\) | −706.774 | − | 314.593i | −0.366255 | − | 0.163024i | ||||
\(156\) | −180.218 | −0.0924935 | ||||||||
\(157\) | −151.871 | − | 151.871i | −0.0772017 | − | 0.0772017i | 0.667452 | − | 0.744653i | \(-0.267385\pi\) |
−0.744653 | + | 0.667452i | \(0.767385\pi\) | |||||||
\(158\) | −967.054 | − | 967.054i | −0.486929 | − | 0.486929i | ||||
\(159\) | −1684.76 | −0.840318 | ||||||||
\(160\) | −697.189 | − | 1815.70i | −0.344485 | − | 0.897150i | ||||
\(161\) | −155.490 | + | 844.974i | −0.0761139 | + | 0.413623i | ||||
\(162\) | 65.7268 | − | 65.7268i | 0.0318764 | − | 0.0318764i | ||||
\(163\) | 1578.51 | + | 1578.51i | 0.758516 | + | 0.758516i | 0.976052 | − | 0.217536i | \(-0.0698020\pi\) |
−0.217536 | + | 0.976052i | \(0.569802\pi\) | |||||||
\(164\) | 1727.46 | 0.822514 | ||||||||
\(165\) | −565.827 | − | 1473.59i | −0.266967 | − | 0.695268i | ||||
\(166\) | 54.8744i | 0.0256571i | ||||||||
\(167\) | −995.566 | − | 995.566i | −0.461312 | − | 0.461312i | 0.437773 | − | 0.899085i | \(-0.355767\pi\) |
−0.899085 | + | 0.437773i | \(0.855767\pi\) | |||||||
\(168\) | −531.243 | − | 770.852i | −0.243966 | − | 0.354003i | ||||
\(169\) | 2116.20i | 0.963224i | ||||||||
\(170\) | −359.995 | + | 808.778i | −0.162414 | + | 0.364885i | ||||
\(171\) | − | 1104.32i | − | 0.493856i | ||||||
\(172\) | 2215.95 | − | 2215.95i | 0.982354 | − | 0.982354i | ||||
\(173\) | −1095.42 | + | 1095.42i | −0.481407 | + | 0.481407i | −0.905581 | − | 0.424174i | \(-0.860565\pi\) |
0.424174 | + | 0.905581i | \(0.360565\pi\) | |||||||
\(174\) | −384.861 | −0.167680 | ||||||||
\(175\) | 537.113 | − | 2251.86i | 0.232011 | − | 0.972713i | ||||
\(176\) | −1606.17 | −0.687897 | ||||||||
\(177\) | −263.914 | + | 263.914i | −0.112073 | + | 0.112073i | ||||
\(178\) | −1041.39 | + | 1041.39i | −0.438514 | + | 0.438514i | ||||
\(179\) | 579.722i | 0.242070i | 0.992648 | + | 0.121035i | \(0.0386213\pi\) | ||||
−0.992648 | + | 0.121035i | \(0.961379\pi\) | |||||||
\(180\) | 273.460 | − | 614.365i | 0.113236 | − | 0.254400i | ||||
\(181\) | 1187.74i | 0.487755i | 0.969806 | + | 0.243878i | \(0.0784195\pi\) | ||||
−0.969806 | + | 0.243878i | \(0.921580\pi\) | |||||||
\(182\) | 157.300 | − | 108.405i | 0.0640651 | − | 0.0441513i | ||||
\(183\) | 828.022 | + | 828.022i | 0.334476 | + | 0.334476i | ||||
\(184\) | − | 781.661i | − | 0.313178i | ||||||
\(185\) | 1290.42 | + | 3360.68i | 0.512832 | + | 1.33558i | ||||
\(186\) | 238.216 | 0.0939076 | ||||||||
\(187\) | 2296.17 | + | 2296.17i | 0.897929 | + | 0.897929i | ||||
\(188\) | 2223.62 | − | 2223.62i | 0.862629 | − | 0.862629i | ||||
\(189\) | 90.4980 | − | 491.790i | 0.0348294 | − | 0.189272i | ||||
\(190\) | 564.313 | + | 1469.65i | 0.215472 | + | 0.561157i | ||||
\(191\) | −972.125 | −0.368275 | −0.184137 | − | 0.982900i | \(-0.558949\pi\) | ||||
−0.184137 | + | 0.982900i | \(0.558949\pi\) | |||||||
\(192\) | −155.711 | − | 155.711i | −0.0585284 | − | 0.0585284i | ||||
\(193\) | 1277.75 | + | 1277.75i | 0.476552 | + | 0.476552i | 0.904027 | − | 0.427475i | \(-0.140597\pi\) |
−0.427475 | + | 0.904027i | \(0.640597\pi\) | |||||||
\(194\) | 344.846 | 0.127621 | ||||||||
\(195\) | 275.437 | + | 122.600i | 0.101151 | + | 0.0450234i | ||||
\(196\) | −2142.15 | − | 816.020i | −0.780667 | − | 0.297383i | ||||
\(197\) | 959.936 | − | 959.936i | 0.347170 | − | 0.347170i | −0.511884 | − | 0.859055i | \(-0.671052\pi\) |
0.859055 | + | 0.511884i | \(0.171052\pi\) | |||||||
\(198\) | 343.690 | + | 343.690i | 0.123358 | + | 0.123358i | ||||
\(199\) | −3154.27 | −1.12362 | −0.561809 | − | 0.827267i | \(-0.689894\pi\) | ||||
−0.561809 | + | 0.827267i | \(0.689894\pi\) | |||||||
\(200\) | −109.815 | + | 2103.34i | −0.0388256 | + | 0.743643i | ||||
\(201\) | 733.434i | 0.257375i | ||||||||
\(202\) | 90.2430 | + | 90.2430i | 0.0314330 | + | 0.0314330i | ||||
\(203\) | −1704.78 | + | 1174.88i | −0.589421 | + | 0.406207i | ||||
\(204\) | 1383.42i | 0.474797i | ||||||||
\(205\) | −2640.18 | − | 1175.17i | −0.899503 | − | 0.400378i | ||||
\(206\) | − | 561.015i | − | 0.189746i | ||||||
\(207\) | 295.226 | − | 295.226i | 0.0991287 | − | 0.0991287i | ||||
\(208\) | 216.924 | − | 216.924i | 0.0723124 | − | 0.0723124i | ||||
\(209\) | 5774.56 | 1.91117 | ||||||||
\(210\) | 130.870 | + | 700.730i | 0.0430044 | + | 0.230262i | ||||
\(211\) | −991.755 | −0.323579 | −0.161790 | − | 0.986825i | \(-0.551727\pi\) | ||||
−0.161790 | + | 0.986825i | \(0.551727\pi\) | |||||||
\(212\) | 2653.89 | − | 2653.89i | 0.859763 | − | 0.859763i | ||||
\(213\) | 311.695 | − | 311.695i | 0.100268 | − | 0.100268i | ||||
\(214\) | − | 2236.24i | − | 0.714329i | ||||||
\(215\) | −4894.25 | + | 1879.28i | −1.55249 | + | 0.596120i | ||||
\(216\) | 454.940i | 0.143309i | ||||||||
\(217\) | 1055.20 | − | 727.207i | 0.330100 | − | 0.227493i | ||||
\(218\) | 1388.88 | + | 1388.88i | 0.431499 | + | 0.431499i | ||||
\(219\) | − | 1527.68i | − | 0.471375i | ||||||
\(220\) | 3212.55 | + | 1429.94i | 0.984501 | + | 0.438212i | ||||
\(221\) | −620.226 | −0.188782 | ||||||||
\(222\) | −783.818 | − | 783.818i | −0.236966 | − | 0.236966i | ||||
\(223\) | 2748.98 | − | 2748.98i | 0.825496 | − | 0.825496i | −0.161394 | − | 0.986890i | \(-0.551599\pi\) |
0.986890 | + | 0.161394i | \(0.0515990\pi\) | |||||||
\(224\) | 3168.62 | + | 583.083i | 0.945145 | + | 0.173923i | ||||
\(225\) | −835.889 | + | 752.937i | −0.247671 | + | 0.223092i | ||||
\(226\) | 369.889 | 0.108870 | ||||||||
\(227\) | −2447.76 | − | 2447.76i | −0.715699 | − | 0.715699i | 0.252022 | − | 0.967721i | \(-0.418904\pi\) |
−0.967721 | + | 0.252022i | \(0.918904\pi\) | |||||||
\(228\) | 1739.55 | + | 1739.55i | 0.505284 | + | 0.505284i | ||||
\(229\) | 6394.63 | 1.84528 | 0.922639 | − | 0.385664i | \(-0.126028\pi\) | ||||
0.922639 | + | 0.385664i | \(0.126028\pi\) | |||||||
\(230\) | −242.032 | + | 543.756i | −0.0693873 | + | 0.155888i | ||||
\(231\) | 2571.60 | + | 473.220i | 0.732463 | + | 0.134786i | ||||
\(232\) | 1331.94 | − | 1331.94i | 0.376924 | − | 0.376924i | ||||
\(233\) | 641.078 | + | 641.078i | 0.180251 | + | 0.180251i | 0.791465 | − | 0.611214i | \(-0.209319\pi\) |
−0.611214 | + | 0.791465i | \(0.709319\pi\) | |||||||
\(234\) | −92.8351 | −0.0259351 | ||||||||
\(235\) | −4911.19 | + | 1885.78i | −1.36328 | + | 0.523468i | ||||
\(236\) | − | 831.448i | − | 0.229333i | ||||||
\(237\) | 2528.13 | + | 2528.13i | 0.692911 | + | 0.692911i | ||||
\(238\) | −832.159 | − | 1207.49i | −0.226642 | − | 0.328866i | ||||
\(239\) | − | 5704.10i | − | 1.54380i | −0.635745 | − | 0.771899i | \(-0.719307\pi\) | ||
0.635745 | − | 0.771899i | \(-0.280693\pi\) | |||||||
\(240\) | 410.339 | + | 1068.65i | 0.110364 | + | 0.287422i | ||||
\(241\) | 4745.28i | 1.26834i | 0.773193 | + | 0.634171i | \(0.218658\pi\) | ||||
−0.773193 | + | 0.634171i | \(0.781342\pi\) | |||||||
\(242\) | −717.146 | + | 717.146i | −0.190496 | + | 0.190496i | ||||
\(243\) | −171.827 | + | 171.827i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | −2608.65 | −0.684432 | ||||||||
\(245\) | 2718.84 | + | 2704.45i | 0.708981 | + | 0.705228i | ||||
\(246\) | 889.862 | 0.230632 | ||||||||
\(247\) | −779.892 | + | 779.892i | −0.200904 | + | 0.200904i | ||||
\(248\) | −824.427 | + | 824.427i | −0.211093 | + | 0.211093i | ||||
\(249\) | − | 143.456i | − | 0.0365107i | ||||||
\(250\) | 727.665 | − | 1429.17i | 0.184086 | − | 0.361554i | ||||
\(251\) | 100.815i | 0.0253521i | 0.999920 | + | 0.0126760i | \(0.00403502\pi\) | ||||
−0.999920 | + | 0.0126760i | \(0.995965\pi\) | |||||||
\(252\) | 632.126 | + | 917.236i | 0.158017 | + | 0.229287i | ||||
\(253\) | 1543.76 | + | 1543.76i | 0.383617 | + | 0.383617i | ||||
\(254\) | − | 109.095i | − | 0.0269496i | ||||||
\(255\) | 941.122 | − | 2114.36i | 0.231119 | − | 0.519240i | ||||
\(256\) | −1106.48 | −0.270138 | ||||||||
\(257\) | −1554.62 | − | 1554.62i | −0.377332 | − | 0.377332i | 0.492807 | − | 0.870139i | \(-0.335971\pi\) |
−0.870139 | + | 0.492807i | \(0.835971\pi\) | |||||||
\(258\) | 1141.50 | − | 1141.50i | 0.275451 | − | 0.275451i | ||||
\(259\) | −5864.79 | − | 1079.23i | −1.40703 | − | 0.258918i | ||||
\(260\) | −626.999 | + | 240.753i | −0.149557 | + | 0.0574265i | ||||
\(261\) | 1006.13 | 0.238612 | ||||||||
\(262\) | 1812.02 | + | 1812.02i | 0.427278 | + | 0.427278i | ||||
\(263\) | 3703.36 | + | 3703.36i | 0.868285 | + | 0.868285i | 0.992282 | − | 0.123998i | \(-0.0395716\pi\) |
−0.123998 | + | 0.992282i | \(0.539572\pi\) | |||||||
\(264\) | −2378.91 | −0.554591 | ||||||||
\(265\) | −5861.49 | + | 2250.68i | −1.35875 | + | 0.521729i | ||||
\(266\) | −2564.72 | − | 471.954i | −0.591177 | − | 0.108787i | ||||
\(267\) | 2722.47 | − | 2722.47i | 0.624016 | − | 0.624016i | ||||
\(268\) | −1155.33 | − | 1155.33i | −0.263331 | − | 0.263331i | ||||
\(269\) | −730.510 | −0.165576 | −0.0827881 | − | 0.996567i | \(-0.526382\pi\) | ||||
−0.0827881 | + | 0.996567i | \(0.526382\pi\) | |||||||
\(270\) | 140.867 | − | 316.476i | 0.0317514 | − | 0.0713337i | ||||
\(271\) | 5669.88i | 1.27092i | 0.772132 | + | 0.635462i | \(0.219190\pi\) | ||||
−0.772132 | + | 0.635462i | \(0.780810\pi\) | |||||||
\(272\) | −1665.19 | − | 1665.19i | −0.371202 | − | 0.371202i | ||||
\(273\) | −411.223 | + | 283.400i | −0.0911661 | + | 0.0628284i | ||||
\(274\) | 359.848i | 0.0793401i | ||||||||
\(275\) | −3937.16 | − | 4370.92i | −0.863343 | − | 0.958460i | ||||
\(276\) | 930.097i | 0.202845i | ||||||||
\(277\) | −5980.25 | + | 5980.25i | −1.29718 | + | 1.29718i | −0.366931 | + | 0.930248i | \(0.619591\pi\) |
−0.930248 | + | 0.366931i | \(0.880409\pi\) | |||||||
\(278\) | 1528.79 | − | 1528.79i | 0.329823 | − | 0.329823i | ||||
\(279\) | −622.758 | −0.133633 | ||||||||
\(280\) | −2878.04 | − | 1972.19i | −0.614271 | − | 0.420933i | ||||
\(281\) | 4582.79 | 0.972905 | 0.486452 | − | 0.873707i | \(-0.338291\pi\) | ||||
0.486452 | + | 0.873707i | \(0.338291\pi\) | |||||||
\(282\) | 1145.45 | − | 1145.45i | 0.241881 | − | 0.241881i | ||||
\(283\) | 1702.34 | − | 1702.34i | 0.357574 | − | 0.357574i | −0.505344 | − | 0.862918i | \(-0.668634\pi\) |
0.862918 | + | 0.505344i | \(0.168634\pi\) | |||||||
\(284\) | 981.981i | 0.205176i | ||||||||
\(285\) | −1475.26 | − | 3842.06i | −0.306621 | − | 0.798540i | ||||
\(286\) | − | 485.441i | − | 0.100366i | ||||||
\(287\) | 3941.74 | − | 2716.51i | 0.810710 | − | 0.558712i | ||||
\(288\) | −1107.09 | − | 1107.09i | −0.226513 | − | 0.226513i | ||||
\(289\) | − | 151.922i | − | 0.0309224i | ||||||
\(290\) | −1338.98 | + | 514.137i | −0.271129 | + | 0.104107i | ||||
\(291\) | −901.518 | −0.181608 | ||||||||
\(292\) | 2406.44 | + | 2406.44i | 0.482282 | + | 0.482282i | ||||
\(293\) | −1568.34 | + | 1568.34i | −0.312708 | + | 0.312708i | −0.845958 | − | 0.533250i | \(-0.820971\pi\) |
0.533250 | + | 0.845958i | \(0.320971\pi\) | |||||||
\(294\) | −1103.48 | − | 420.353i | −0.218899 | − | 0.0833861i | ||||
\(295\) | −565.624 | + | 1270.75i | −0.111634 | + | 0.250800i | ||||
\(296\) | 5425.35 | 1.06534 | ||||||||
\(297\) | −898.494 | − | 898.494i | −0.175542 | − | 0.175542i | ||||
\(298\) | 1574.72 | + | 1574.72i | 0.306111 | + | 0.306111i | ||||
\(299\) | −416.989 | −0.0806525 | ||||||||
\(300\) | 130.669 | − | 2502.76i | 0.0251473 | − | 0.481657i | ||||
\(301\) | 1571.71 | − | 8541.06i | 0.300969 | − | 1.63554i | ||||
\(302\) | −1200.54 | + | 1200.54i | −0.228752 | + | 0.228752i | ||||
\(303\) | −235.919 | − | 235.919i | −0.0447300 | − | 0.0447300i | ||||
\(304\) | −4187.72 | −0.790074 | ||||||||
\(305\) | 3986.94 | + | 1774.63i | 0.748497 | + | 0.333164i | ||||
\(306\) | 712.635i | 0.133133i | ||||||||
\(307\) | −6468.95 | − | 6468.95i | −1.20261 | − | 1.20261i | −0.973368 | − | 0.229246i | \(-0.926374\pi\) |
−0.229246 | − | 0.973368i | \(-0.573626\pi\) | |||||||
\(308\) | −4796.29 | + | 3305.43i | −0.887317 | + | 0.611507i | ||||
\(309\) | 1466.64i | 0.270013i | ||||||||
\(310\) | 828.780 | − | 318.233i | 0.151844 | − | 0.0583045i | ||||
\(311\) | − | 10432.5i | − | 1.90217i | −0.308936 | − | 0.951083i | \(-0.599973\pi\) | ||
0.308936 | − | 0.951083i | \(-0.400027\pi\) | |||||||
\(312\) | 321.288 | − | 321.288i | 0.0582992 | − | 0.0582992i | ||||
\(313\) | 5223.03 | − | 5223.03i | 0.943206 | − | 0.943206i | −0.0552660 | − | 0.998472i | \(-0.517601\pi\) |
0.998472 | + | 0.0552660i | \(0.0176007\pi\) | |||||||
\(314\) | 246.470 | 0.0442965 | ||||||||
\(315\) | −342.129 | − | 1831.89i | −0.0611962 | − | 0.327668i | ||||
\(316\) | −7964.77 | −1.41789 | ||||||||
\(317\) | −5323.08 | + | 5323.08i | −0.943136 | + | 0.943136i | −0.998468 | − | 0.0553322i | \(-0.982378\pi\) |
0.0553322 | + | 0.998468i | \(0.482378\pi\) | |||||||
\(318\) | 1367.09 | − | 1367.09i | 0.241077 | − | 0.241077i | ||||
\(319\) | 5261.11i | 0.923403i | ||||||||
\(320\) | −749.750 | − | 333.721i | −0.130976 | − | 0.0582987i | ||||
\(321\) | 5846.13i | 1.01651i | ||||||||
\(322\) | −559.476 | − | 811.818i | −0.0968272 | − | 0.140500i | ||||
\(323\) | 5986.73 | + | 5986.73i | 1.03130 | + | 1.03130i | ||||
\(324\) | − | 541.333i | − | 0.0928212i | ||||||
\(325\) | 1122.06 | + | 58.5827i | 0.191510 | + | 0.00999872i | ||||
\(326\) | −2561.73 | −0.435218 | ||||||||
\(327\) | −3630.89 | − | 3630.89i | −0.614033 | − | 0.614033i | ||||
\(328\) | −3079.68 | + | 3079.68i | −0.518435 | + | 0.518435i | ||||
\(329\) | 1577.14 | − | 8570.61i | 0.264288 | − | 1.43621i | ||||
\(330\) | 1654.87 | + | 736.601i | 0.276054 | + | 0.122874i | ||||
\(331\) | −8385.42 | −1.39246 | −0.696230 | − | 0.717818i | \(-0.745141\pi\) | ||||
−0.696230 | + | 0.717818i | \(0.745141\pi\) | |||||||
\(332\) | 225.976 | + | 225.976i | 0.0373556 | + | 0.0373556i | ||||
\(333\) | 2049.11 | + | 2049.11i | 0.337208 | + | 0.337208i | ||||
\(334\) | 1615.69 | 0.264690 | ||||||||
\(335\) | 979.796 | + | 2551.70i | 0.159797 | + | 0.416163i | ||||
\(336\) | −1864.93 | − | 343.180i | −0.302798 | − | 0.0557203i | ||||
\(337\) | 593.913 | − | 593.913i | 0.0960015 | − | 0.0960015i | −0.657475 | − | 0.753476i | \(-0.728375\pi\) |
0.753476 | + | 0.657475i | \(0.228375\pi\) | |||||||
\(338\) | −1717.18 | − | 1717.18i | −0.276337 | − | 0.276337i | ||||
\(339\) | −966.987 | −0.154925 | ||||||||
\(340\) | 1848.11 | + | 4813.07i | 0.294788 | + | 0.767722i | ||||
\(341\) | − | 3256.44i | − | 0.517144i | ||||||
\(342\) | 896.091 | + | 896.091i | 0.141681 | + | 0.141681i | ||||
\(343\) | −6171.20 | + | 1506.62i | −0.971468 | + | 0.237171i | ||||
\(344\) | 7901.08i | 1.23837i | ||||||||
\(345\) | 632.734 | − | 1421.52i | 0.0987398 | − | 0.221832i | ||||
\(346\) | − | 1777.74i | − | 0.276220i | ||||||
\(347\) | 1216.59 | − | 1216.59i | 0.188213 | − | 0.188213i | −0.606710 | − | 0.794923i | \(-0.707511\pi\) |
0.794923 | + | 0.606710i | \(0.207511\pi\) | |||||||
\(348\) | −1584.88 | + | 1584.88i | −0.244134 | + | 0.244134i | ||||
\(349\) | 3420.88 | 0.524687 | 0.262343 | − | 0.964975i | \(-0.415505\pi\) | ||||
0.262343 | + | 0.964975i | \(0.415505\pi\) | |||||||
\(350\) | 1391.42 | + | 2263.09i | 0.212499 | + | 0.345621i | ||||
\(351\) | 242.695 | 0.0369063 | ||||||||
\(352\) | 5789.04 | − | 5789.04i | 0.876582 | − | 0.876582i | ||||
\(353\) | −67.8564 | + | 67.8564i | −0.0102313 | + | 0.0102313i | −0.712204 | − | 0.701973i | \(-0.752303\pi\) |
0.701973 | + | 0.712204i | \(0.252303\pi\) | |||||||
\(354\) | − | 428.301i | − | 0.0643049i | ||||||
\(355\) | 668.029 | − | 1500.82i | 0.0998741 | − | 0.224381i | ||||
\(356\) | 8577.01i | 1.27691i | ||||||||
\(357\) | 2175.48 | + | 3156.70i | 0.322517 | + | 0.467983i | ||||
\(358\) | −470.411 | − | 470.411i | −0.0694469 | − | 0.0694469i | ||||
\(359\) | − | 6854.98i | − | 1.00778i | −0.863768 | − | 0.503889i | \(-0.831902\pi\) | ||
0.863768 | − | 0.503889i | \(-0.168098\pi\) | |||||||
\(360\) | 607.756 | + | 1582.79i | 0.0889765 | + | 0.231723i | ||||
\(361\) | 8196.83 | 1.19505 | ||||||||
\(362\) | −963.778 | − | 963.778i | −0.139931 | − | 0.139931i | ||||
\(363\) | 1874.81 | − | 1874.81i | 0.271080 | − | 0.271080i | ||||
\(364\) | 201.350 | − | 1094.19i | 0.0289935 | − | 0.157558i | ||||
\(365\) | −2040.83 | − | 5314.98i | −0.292663 | − | 0.762188i | ||||
\(366\) | −1343.78 | −0.191914 | ||||||||
\(367\) | 5841.95 | + | 5841.95i | 0.830920 | + | 0.830920i | 0.987643 | − | 0.156723i | \(-0.0500929\pi\) |
−0.156723 | + | 0.987643i | \(0.550093\pi\) | |||||||
\(368\) | −1119.54 | − | 1119.54i | −0.158587 | − | 0.158587i | ||||
\(369\) | −2326.33 | −0.328195 | ||||||||
\(370\) | −3774.10 | − | 1679.89i | −0.530287 | − | 0.236036i | ||||
\(371\) | 1882.32 | − | 10229.0i | 0.263410 | − | 1.43144i | ||||
\(372\) | 980.985 | − | 980.985i | 0.136725 | − | 0.136725i | ||||
\(373\) | −5333.16 | − | 5333.16i | −0.740323 | − | 0.740323i | 0.232317 | − | 0.972640i | \(-0.425369\pi\) |
−0.972640 | + | 0.232317i | \(0.925369\pi\) | |||||||
\(374\) | −3726.42 | −0.515210 | ||||||||
\(375\) | −1902.31 | + | 3736.22i | −0.261959 | + | 0.514500i | ||||
\(376\) | 7928.42i | 1.08744i | ||||||||
\(377\) | −710.547 | − | 710.547i | −0.0970690 | − | 0.0970690i | ||||
\(378\) | 325.625 | + | 472.492i | 0.0443078 | + | 0.0642920i | ||||
\(379\) | − | 8939.57i | − | 1.21160i | −0.795618 | − | 0.605798i | \(-0.792854\pi\) | ||
0.795618 | − | 0.605798i | \(-0.207146\pi\) | |||||||
\(380\) | 8375.99 | + | 3728.24i | 1.13073 | + | 0.503302i | ||||
\(381\) | 285.202i | 0.0383500i | ||||||||
\(382\) | 788.823 | − | 788.823i | 0.105654 | − | 0.105654i | ||||
\(383\) | −4901.85 | + | 4901.85i | −0.653976 | + | 0.653976i | −0.953948 | − | 0.299972i | \(-0.903023\pi\) |
0.299972 | + | 0.953948i | \(0.403023\pi\) | |||||||
\(384\) | 4427.79 | 0.588424 | ||||||||
\(385\) | 9579.07 | − | 1789.02i | 1.26804 | − | 0.236823i | ||||
\(386\) | −2073.64 | −0.273434 | ||||||||
\(387\) | −2984.17 | + | 2984.17i | −0.391974 | + | 0.391974i | ||||
\(388\) | 1420.10 | − | 1420.10i | 0.185810 | − | 0.185810i | ||||
\(389\) | 11003.6i | 1.43420i | 0.696969 | + | 0.717101i | \(0.254532\pi\) | ||||
−0.696969 | + | 0.717101i | \(0.745468\pi\) | |||||||
\(390\) | −322.984 | + | 124.019i | −0.0419357 | + | 0.0161024i | ||||
\(391\) | 3200.96i | 0.414014i | ||||||||
\(392\) | 5273.75 | − | 2364.19i | 0.679501 | − | 0.304616i | ||||
\(393\) | −4737.09 | − | 4737.09i | −0.608027 | − | 0.608027i | ||||
\(394\) | 1557.86i | 0.199198i | ||||||||
\(395\) | 12173.0 | + | 5418.33i | 1.55061 | + | 0.690192i | ||||
\(396\) | 2830.67 | 0.359208 | ||||||||
\(397\) | 10543.3 | + | 10543.3i | 1.33289 | + | 1.33289i | 0.902778 | + | 0.430107i | \(0.141524\pi\) |
0.430107 | + | 0.902778i | \(0.358476\pi\) | |||||||
\(398\) | 2559.50 | − | 2559.50i | 0.322352 | − | 0.322352i | ||||
\(399\) | 6704.85 | + | 1233.81i | 0.841259 | + | 0.154807i | ||||
\(400\) | 2855.23 | + | 3169.80i | 0.356904 | + | 0.396225i | ||||
\(401\) | −9885.66 | −1.23109 | −0.615544 | − | 0.788102i | \(-0.711064\pi\) | ||||
−0.615544 | + | 0.788102i | \(0.711064\pi\) | |||||||
\(402\) | −595.139 | − | 595.139i | −0.0738379 | − | 0.0738379i | ||||
\(403\) | 439.804 | + | 439.804i | 0.0543627 | + | 0.0543627i | ||||
\(404\) | 743.251 | 0.0915300 | ||||||||
\(405\) | −368.262 | + | 827.350i | −0.0451829 | + | 0.101510i | ||||
\(406\) | 429.990 | − | 2336.68i | 0.0525617 | − | 0.285634i | ||||
\(407\) | −10714.9 | + | 10714.9i | −1.30496 | + | 1.30496i | ||||
\(408\) | −2466.32 | − | 2466.32i | −0.299267 | − | 0.299267i | ||||
\(409\) | −1778.29 | −0.214989 | −0.107495 | − | 0.994206i | \(-0.534283\pi\) | ||||
−0.107495 | + | 0.994206i | \(0.534283\pi\) | |||||||
\(410\) | 3095.94 | − | 1188.77i | 0.372920 | − | 0.143193i | ||||
\(411\) | − | 940.736i | − | 0.112903i | ||||||
\(412\) | −2310.29 | − | 2310.29i | −0.276262 | − | 0.276262i | ||||
\(413\) | −1307.49 | − | 1897.21i | −0.155780 | − | 0.226042i | ||||
\(414\) | 479.118i | 0.0568777i | ||||||||
\(415\) | −191.643 | − | 499.101i | −0.0226684 | − | 0.0590359i | ||||
\(416\) | 1563.69i | 0.184294i | ||||||||
\(417\) | −3996.66 | + | 3996.66i | −0.469346 | + | 0.469346i | ||||
\(418\) | −4685.72 | + | 4685.72i | −0.548292 | + | 0.548292i | ||||
\(419\) | 12780.7 | 1.49016 | 0.745079 | − | 0.666976i | \(-0.232412\pi\) | ||||
0.745079 | + | 0.666976i | \(0.232412\pi\) | |||||||
\(420\) | 3424.58 | + | 2346.71i | 0.397862 | + | 0.272638i | ||||
\(421\) | 11972.9 | 1.38605 | 0.693023 | − | 0.720916i | \(-0.256279\pi\) | ||||
0.693023 | + | 0.720916i | \(0.256279\pi\) | |||||||
\(422\) | 804.751 | − | 804.751i | 0.0928310 | − | 0.0928310i | ||||
\(423\) | −2994.50 | + | 2994.50i | −0.344202 | + | 0.344202i | ||||
\(424\) | 9462.56i | 1.08383i | ||||||||
\(425\) | 449.702 | − | 8613.34i | 0.0513265 | − | 0.983078i | ||||
\(426\) | 505.844i | 0.0575311i | ||||||||
\(427\) | −5952.43 | + | 4102.20i | −0.674610 | + | 0.464917i | ||||
\(428\) | −9208.98 | − | 9208.98i | −1.04003 | − | 1.04003i | ||||
\(429\) | 1269.07i | 0.142823i | ||||||||
\(430\) | 2446.47 | − | 5496.33i | 0.274371 | − | 0.616410i | ||||
\(431\) | 1294.36 | 0.144657 | 0.0723287 | − | 0.997381i | \(-0.476957\pi\) | ||||
0.0723287 | + | 0.997381i | \(0.476957\pi\) | |||||||
\(432\) | 651.590 | + | 651.590i | 0.0725686 | + | 0.0725686i | ||||
\(433\) | 9248.52 | − | 9248.52i | 1.02646 | − | 1.02646i | 0.0268152 | − | 0.999640i | \(-0.491463\pi\) |
0.999640 | − | 0.0268152i | \(-0.00853657\pi\) | |||||||
\(434\) | −266.149 | + | 1446.32i | −0.0294367 | + | 0.159967i | ||||
\(435\) | 3500.44 | − | 1344.09i | 0.385823 | − | 0.148147i | ||||
\(436\) | 11439.0 | 1.25648 | ||||||||
\(437\) | 4024.99 | + | 4024.99i | 0.440598 | + | 0.440598i | ||||
\(438\) | 1239.62 | + | 1239.62i | 0.135232 | + | 0.135232i | ||||
\(439\) | −3709.27 | −0.403267 | −0.201633 | − | 0.979461i | \(-0.564625\pi\) | ||||
−0.201633 | + | 0.979461i | \(0.564625\pi\) | |||||||
\(440\) | −8276.52 | + | 3177.99i | −0.896744 | + | 0.344329i | ||||
\(441\) | 2884.78 | + | 1098.91i | 0.311498 | + | 0.118660i | ||||
\(442\) | 503.277 | − | 503.277i | 0.0541594 | − | 0.0541594i | ||||
\(443\) | 441.078 | + | 441.078i | 0.0473054 | + | 0.0473054i | 0.730364 | − | 0.683058i | \(-0.239351\pi\) |
−0.683058 | + | 0.730364i | \(0.739351\pi\) | |||||||
\(444\) | −6455.61 | −0.690022 | ||||||||
\(445\) | 5834.83 | − | 13108.7i | 0.621568 | − | 1.39643i | ||||
\(446\) | 4461.28i | 0.473650i | ||||||||
\(447\) | −4116.74 | − | 4116.74i | −0.435604 | − | 0.435604i | ||||
\(448\) | 1119.36 | − | 771.425i | 0.118047 | − | 0.0813535i | ||||
\(449\) | 7375.06i | 0.775168i | 0.921834 | + | 0.387584i | \(0.126690\pi\) | ||||
−0.921834 | + | 0.387584i | \(0.873310\pi\) | |||||||
\(450\) | 67.3111 | − | 1289.24i | 0.00705128 | − | 0.135056i | ||||
\(451\) | − | 12164.5i | − | 1.27008i | ||||||
\(452\) | 1523.22 | − | 1523.22i | 0.158510 | − | 0.158510i | ||||
\(453\) | 3138.52 | − | 3138.52i | 0.325520 | − | 0.325520i | ||||
\(454\) | 3972.43 | 0.410651 | ||||||||
\(455\) | −1052.10 | + | 1535.34i | −0.108402 | + | 0.158193i | ||||
\(456\) | −6202.46 | −0.636967 | ||||||||
\(457\) | 2880.31 | − | 2880.31i | 0.294826 | − | 0.294826i | −0.544157 | − | 0.838983i | \(-0.683151\pi\) |
0.838983 | + | 0.544157i | \(0.183151\pi\) | |||||||
\(458\) | −5188.87 | + | 5188.87i | −0.529388 | + | 0.529388i | ||||
\(459\) | − | 1863.02i | − | 0.189451i | ||||||
\(460\) | 1242.52 | + | 3235.92i | 0.125941 | + | 0.327990i | ||||
\(461\) | 13598.8i | 1.37389i | 0.726711 | + | 0.686943i | \(0.241048\pi\) | ||||
−0.726711 | + | 0.686943i | \(0.758952\pi\) | |||||||
\(462\) | −2470.69 | + | 1702.71i | −0.248803 | + | 0.171466i | ||||
\(463\) | 3784.31 | + | 3784.31i | 0.379853 | + | 0.379853i | 0.871049 | − | 0.491196i | \(-0.163440\pi\) |
−0.491196 | + | 0.871049i | \(0.663440\pi\) | |||||||
\(464\) | − | 3815.37i | − | 0.381732i | ||||||
\(465\) | −2166.65 | + | 831.943i | −0.216077 | + | 0.0829687i | ||||
\(466\) | −1040.39 | −0.103424 | ||||||||
\(467\) | −2918.56 | − | 2918.56i | −0.289197 | − | 0.289197i | 0.547566 | − | 0.836763i | \(-0.315555\pi\) |
−0.836763 | + | 0.547566i | \(0.815555\pi\) | |||||||
\(468\) | −382.300 | + | 382.300i | −0.0377603 | + | 0.0377603i | ||||
\(469\) | −4453.03 | − | 819.436i | −0.438426 | − | 0.0806782i | ||||
\(470\) | 2454.94 | − | 5515.34i | 0.240932 | − | 0.541285i | ||||
\(471\) | −644.336 | −0.0630349 | ||||||||
\(472\) | 1482.28 | + | 1482.28i | 0.144550 | + | 0.144550i | ||||
\(473\) | −15604.4 | − | 15604.4i | −1.51690 | − | 1.51690i | ||||
\(474\) | −4102.86 | −0.397575 | ||||||||
\(475\) | −10265.2 | − | 11396.2i | −0.991580 | − | 1.10082i | ||||
\(476\) | −8399.39 | − | 1545.64i | −0.808793 | − | 0.148832i | ||||
\(477\) | −3573.93 | + | 3573.93i | −0.343058 | + | 0.343058i | ||||
\(478\) | 4628.55 | + | 4628.55i | 0.442897 | + | 0.442897i | ||||
\(479\) | −10671.2 | −1.01791 | −0.508957 | − | 0.860792i | \(-0.669969\pi\) | ||||
−0.508957 | + | 0.860792i | \(0.669969\pi\) | |||||||
\(480\) | −5330.65 | − | 2372.73i | −0.506895 | − | 0.225624i | ||||
\(481\) | − | 2894.24i | − | 0.274357i | ||||||
\(482\) | −3850.52 | − | 3850.52i | −0.363872 | − | 0.363872i | ||||
\(483\) | 1462.62 | + | 2122.30i | 0.137787 | + | 0.199934i | ||||
\(484\) | 5906.50i | 0.554705i | ||||||||
\(485\) | −3136.49 | + | 1204.34i | −0.293651 | + | 0.112755i | ||||
\(486\) | − | 278.855i | − | 0.0260270i | ||||||
\(487\) | −1867.09 | + | 1867.09i | −0.173728 | + | 0.173728i | −0.788615 | − | 0.614887i | \(-0.789202\pi\) |
0.614887 | + | 0.788615i | \(0.289202\pi\) | |||||||
\(488\) | 4650.63 | − | 4650.63i | 0.431402 | − | 0.431402i | ||||
\(489\) | 6697.03 | 0.619326 | ||||||||
\(490\) | −4400.68 | + | 11.6800i | −0.405719 | + | 0.00107683i | ||||
\(491\) | 15349.2 | 1.41079 | 0.705396 | − | 0.708813i | \(-0.250769\pi\) | ||||
0.705396 | + | 0.708813i | \(0.250769\pi\) | |||||||
\(492\) | 3664.50 | − | 3664.50i | 0.335790 | − | 0.335790i | ||||
\(493\) | −5454.41 | + | 5454.41i | −0.498285 | + | 0.498285i | ||||
\(494\) | − | 1265.67i | − | 0.115274i | ||||||
\(495\) | −4326.27 | − | 1925.67i | −0.392831 | − | 0.174853i | ||||
\(496\) | 2361.58i | 0.213786i | ||||||||
\(497\) | 1544.20 | + | 2240.69i | 0.139370 | + | 0.202231i | ||||
\(498\) | 116.406 | + | 116.406i | 0.0104745 | + | 0.0104745i | ||||
\(499\) | 7059.56i | 0.633325i | 0.948538 | + | 0.316663i | \(0.102562\pi\) | ||||
−0.948538 | + | 0.316663i | \(0.897438\pi\) | |||||||
\(500\) | −2888.83 | − | 8881.97i | −0.258385 | − | 0.794427i | ||||
\(501\) | −4223.83 | −0.376660 | ||||||||
\(502\) | −81.8053 | − | 81.8053i | −0.00727321 | − | 0.00727321i | ||||
\(503\) | 2440.13 | − | 2440.13i | 0.216302 | − | 0.216302i | −0.590636 | − | 0.806938i | \(-0.701123\pi\) |
0.806938 | + | 0.590636i | \(0.201123\pi\) | |||||||
\(504\) | −2762.16 | − | 508.287i | −0.244120 | − | 0.0449224i | ||||
\(505\) | −1135.95 | − | 505.625i | −0.100098 | − | 0.0445545i | ||||
\(506\) | −2505.34 | −0.220110 | ||||||||
\(507\) | 4489.14 | + | 4489.14i | 0.393235 | + | 0.393235i | ||||
\(508\) | −449.258 | − | 449.258i | −0.0392374 | − | 0.0392374i | ||||
\(509\) | −11565.4 | −1.00713 | −0.503564 | − | 0.863958i | \(-0.667978\pi\) | ||||
−0.503564 | + | 0.863958i | \(0.667978\pi\) | |||||||
\(510\) | 952.011 | + | 2479.34i | 0.0826583 | + | 0.215269i | ||||
\(511\) | 9275.27 | + | 1706.81i | 0.802963 | + | 0.147759i | ||||
\(512\) | −7451.28 | + | 7451.28i | −0.643170 | + | 0.643170i | ||||
\(513\) | −2342.62 | − | 2342.62i | −0.201616 | − | 0.201616i | ||||
\(514\) | 2522.96 | 0.216504 | ||||||||
\(515\) | 1959.29 | + | 5102.61i | 0.167644 | + | 0.436598i | ||||
\(516\) | − | 9401.49i | − | 0.802088i | ||||||
\(517\) | −15658.4 | − | 15658.4i | −1.33202 | − | 1.33202i | ||||
\(518\) | 5634.66 | − | 3883.21i | 0.477940 | − | 0.329379i | ||||
\(519\) | 4647.48i | 0.393067i | ||||||||
\(520\) | 688.589 | − | 1547.01i | 0.0580704 | − | 0.130463i | ||||
\(521\) | − | 6288.19i | − | 0.528773i | −0.964417 | − | 0.264387i | \(-0.914831\pi\) | ||
0.964417 | − | 0.264387i | \(-0.0851695\pi\) | |||||||
\(522\) | −816.414 | + | 816.414i | −0.0684549 | + | 0.0684549i | ||||
\(523\) | 3302.60 | − | 3302.60i | 0.276124 | − | 0.276124i | −0.555436 | − | 0.831559i | \(-0.687449\pi\) |
0.831559 | + | 0.555436i | \(0.187449\pi\) | |||||||
\(524\) | 14924.0 | 1.24419 | ||||||||
\(525\) | −3637.53 | − | 5916.31i | −0.302390 | − | 0.491827i | ||||
\(526\) | −6010.12 | −0.498201 | ||||||||
\(527\) | 3376.09 | − | 3376.09i | 0.279060 | − | 0.279060i | ||||
\(528\) | −3407.21 | + | 3407.21i | −0.280833 | + | 0.280833i | ||||
\(529\) | − | 10014.9i | − | 0.823123i | ||||||
\(530\) | 2929.96 | − | 6582.56i | 0.240131 | − | 0.539487i | ||||
\(531\) | 1119.69i | 0.0915075i | ||||||||
\(532\) | −12505.2 | + | 8618.13i | −1.01912 | + | 0.702337i | ||||
\(533\) | 1642.90 | + | 1642.90i | 0.133512 | + | 0.133512i | ||||
\(534\) | 4418.25i | 0.358045i | ||||||||
\(535\) | 7809.85 | + | 20339.4i | 0.631120 | + | 1.64364i | ||||
\(536\) | 4119.37 | 0.331958 | ||||||||
\(537\) | 1229.78 | + | 1229.78i | 0.0988245 | + | 0.0988245i | ||||
\(538\) | 592.767 | − | 592.767i | 0.0475018 | − | 0.0475018i | ||||
\(539\) | −5746.29 | + | 15084.7i | −0.459203 | + | 1.20546i | ||||
\(540\) | −723.168 | − | 1883.36i | −0.0576300 | − | 0.150087i | ||||
\(541\) | 11630.6 | 0.924289 | 0.462145 | − | 0.886805i | \(-0.347080\pi\) | ||||
0.462145 | + | 0.886805i | \(0.347080\pi\) | |||||||
\(542\) | −4600.77 | − | 4600.77i | −0.364613 | − | 0.364613i | ||||
\(543\) | 2519.57 | + | 2519.57i | 0.199125 | + | 0.199125i | ||||
\(544\) | 12003.5 | 0.946039 | ||||||||
\(545\) | −17482.8 | − | 7781.79i | −1.37409 | − | 0.611624i | ||||
\(546\) | 103.721 | − | 563.646i | 0.00812975 | − | 0.0441792i | ||||
\(547\) | 6512.62 | − | 6512.62i | 0.509066 | − | 0.509066i | −0.405173 | − | 0.914240i | \(-0.632789\pi\) |
0.914240 | + | 0.405173i | \(0.132789\pi\) | |||||||
\(548\) | 1481.87 | + | 1481.87i | 0.115515 | + | 0.115515i | ||||
\(549\) | 3513.00 | 0.273099 | ||||||||
\(550\) | 6741.52 | + | 351.974i | 0.522653 | + | 0.0272877i | ||||
\(551\) | 13717.1i | 1.06056i | ||||||||
\(552\) | −1658.15 | − | 1658.15i | −0.127854 | − | 0.127854i | ||||
\(553\) | −18174.1 | + | 12524.9i | −1.39754 | + | 0.963135i | ||||
\(554\) | − | 9705.25i | − | 0.744290i | ||||||
\(555\) | 9866.48 | + | 4391.67i | 0.754610 | + | 0.335885i | ||||
\(556\) | − | 12591.3i | − | 0.960413i | ||||||
\(557\) | −3672.75 | + | 3672.75i | −0.279389 | + | 0.279389i | −0.832865 | − | 0.553476i | \(-0.813301\pi\) |
0.553476 | + | 0.832865i | \(0.313301\pi\) | |||||||
\(558\) | 505.331 | − | 505.331i | 0.0383376 | − | 0.0383376i | ||||
\(559\) | 4214.96 | 0.318915 | ||||||||
\(560\) | −6946.76 | + | 1297.40i | −0.524204 | + | 0.0979020i | ||||
\(561\) | 9741.83 | 0.733156 | ||||||||
\(562\) | −3718.66 | + | 3718.66i | −0.279115 | + | 0.279115i | ||||
\(563\) | −3765.85 | + | 3765.85i | −0.281903 | + | 0.281903i | −0.833868 | − | 0.551964i | \(-0.813878\pi\) |
0.551964 | + | 0.833868i | \(0.313878\pi\) | |||||||
\(564\) | − | 9434.02i | − | 0.704333i | ||||||
\(565\) | −3364.26 | + | 1291.80i | −0.250505 | + | 0.0961883i | ||||
\(566\) | 2762.69i | 0.205167i | ||||||||
\(567\) | −851.268 | − | 1235.22i | −0.0630510 | − | 0.0914891i | ||||
\(568\) | −1750.65 | − | 1750.65i | −0.129323 | − | 0.129323i | ||||
\(569\) | 14873.6i | 1.09584i | 0.836529 | + | 0.547922i | \(0.184581\pi\) | ||||
−0.836529 | + | 0.547922i | \(0.815419\pi\) | |||||||
\(570\) | 4314.69 | + | 1920.52i | 0.317057 | + | 0.141126i | ||||
\(571\) | −13602.3 | −0.996916 | −0.498458 | − | 0.866914i | \(-0.666100\pi\) | ||||
−0.498458 | + | 0.866914i | \(0.666100\pi\) | |||||||
\(572\) | −1999.07 | − | 1999.07i | −0.146128 | − | 0.146128i | ||||
\(573\) | −2062.19 | + | 2062.19i | −0.150348 | + | 0.150348i | ||||
\(574\) | −994.207 | + | 5402.78i | −0.0722951 | + | 0.392870i | ||||
\(575\) | 302.343 | − | 5790.91i | 0.0219279 | − | 0.419996i | ||||
\(576\) | −660.624 | −0.0477882 | ||||||||
\(577\) | −4519.16 | − | 4519.16i | −0.326057 | − | 0.326057i | 0.525028 | − | 0.851085i | \(-0.324055\pi\) |
−0.851085 | + | 0.525028i | \(0.824055\pi\) | |||||||
\(578\) | 123.276 | + | 123.276i | 0.00887126 | + | 0.00887126i | ||||
\(579\) | 5421.04 | 0.389103 | ||||||||
\(580\) | −3396.74 | + | 7631.23i | −0.243176 | + | 0.546327i | ||||
\(581\) | 870.990 | + | 160.278i | 0.0621941 | + | 0.0114448i | ||||
\(582\) | 731.529 | − | 731.529i | 0.0521011 | − | 0.0521011i | ||||
\(583\) | −18688.3 | − | 18688.3i | −1.32760 | − | 1.32760i | ||||
\(584\) | −8580.29 | −0.607971 | ||||||||
\(585\) | 844.365 | − | 324.217i | 0.0596755 | − | 0.0229140i | ||||
\(586\) | − | 2545.23i | − | 0.179424i | ||||||
\(587\) | 17037.9 | + | 17037.9i | 1.19800 | + | 1.19800i | 0.974763 | + | 0.223241i | \(0.0716636\pi\) |
0.223241 | + | 0.974763i | \(0.428336\pi\) | |||||||
\(588\) | −6275.22 | + | 2813.15i | −0.440112 | + | 0.197300i | ||||
\(589\) | − | 8490.41i | − | 0.593958i | ||||||
\(590\) | −572.168 | − | 1490.11i | −0.0399251 | − | 0.103978i | ||||
\(591\) | − | 4072.66i | − | 0.283463i | ||||||
\(592\) | 7770.47 | − | 7770.47i | 0.539467 | − | 0.539467i | ||||
\(593\) | 5362.06 | − | 5362.06i | 0.371321 | − | 0.371321i | −0.496637 | − | 0.867958i | \(-0.665432\pi\) |
0.867958 | + | 0.496637i | \(0.165432\pi\) | |||||||
\(594\) | 1458.15 | 0.100722 | ||||||||
\(595\) | 11785.8 | + | 8076.29i | 0.812051 | + | 0.556463i | ||||
\(596\) | 12969.6 | 0.891368 | ||||||||
\(597\) | −6691.21 | + | 6691.21i | −0.458715 | + | 0.458715i | ||||
\(598\) | 338.362 | − | 338.362i | 0.0231382 | − | 0.0231382i | ||||
\(599\) | − | 5584.54i | − | 0.380932i | −0.981694 | − | 0.190466i | \(-0.939000\pi\) | ||
0.981694 | − | 0.190466i | \(-0.0609998\pi\) | |||||||
\(600\) | 4228.91 | + | 4694.81i | 0.287741 | + | 0.319442i | ||||
\(601\) | 19025.6i | 1.29130i | 0.763634 | + | 0.645649i | \(0.223413\pi\) | ||||
−0.763634 | + | 0.645649i | \(0.776587\pi\) | |||||||
\(602\) | 5655.22 | + | 8205.92i | 0.382873 | + | 0.555562i | ||||
\(603\) | 1555.85 | + | 1555.85i | 0.105073 | + | 0.105073i | ||||
\(604\) | 9887.76i | 0.666105i | ||||||||
\(605\) | 4018.12 | − | 9027.24i | 0.270016 | − | 0.606627i | ||||
\(606\) | 382.869 | 0.0256650 | ||||||||
\(607\) | −1636.42 | − | 1636.42i | −0.109424 | − | 0.109424i | 0.650275 | − | 0.759699i | \(-0.274654\pi\) |
−0.759699 | + | 0.650275i | \(0.774654\pi\) | |||||||
\(608\) | 15093.6 | − | 15093.6i | 1.00678 | − | 1.00678i | ||||
\(609\) | −1124.11 | + | 6108.68i | −0.0747965 | + | 0.406463i | ||||
\(610\) | −4675.18 | + | 1795.16i | −0.310316 | + | 0.119154i | ||||
\(611\) | 4229.54 | 0.280047 | ||||||||
\(612\) | 2934.67 | + | 2934.67i | 0.193835 | + | 0.193835i | ||||
\(613\) | −6492.66 | − | 6492.66i | −0.427791 | − | 0.427791i | 0.460084 | − | 0.887875i | \(-0.347819\pi\) |
−0.887875 | + | 0.460084i | \(0.847819\pi\) | |||||||
\(614\) | 10498.4 | 0.690031 | ||||||||
\(615\) | −8093.58 | + | 3107.75i | −0.530674 | + | 0.203767i | ||||
\(616\) | 2657.86 | − | 14443.5i | 0.173845 | − | 0.944717i | ||||
\(617\) | 10437.9 | − | 10437.9i | 0.681060 | − | 0.681060i | −0.279179 | − | 0.960239i | \(-0.590062\pi\) |
0.960239 | + | 0.279179i | \(0.0900622\pi\) | |||||||
\(618\) | −1190.09 | − | 1190.09i | −0.0774636 | − | 0.0774636i | ||||
\(619\) | 11190.6 | 0.726636 | 0.363318 | − | 0.931665i | \(-0.381644\pi\) | ||||
0.363318 | + | 0.931665i | \(0.381644\pi\) | |||||||
\(620\) | 2102.46 | − | 4723.46i | 0.136189 | − | 0.305966i | ||||
\(621\) | − | 1252.54i | − | 0.0809383i | ||||||
\(622\) | 8465.38 | + | 8465.38i | 0.545708 | + | 0.545708i | ||||
\(623\) | 13487.7 | + | 19571.1i | 0.867373 | + | 1.25859i | ||||
\(624\) | − | 920.331i | − | 0.0590428i | ||||||
\(625\) | −1627.13 | + | 15540.0i | −0.104136 | + | 0.994563i | ||||
\(626\) | 8476.38i | 0.541189i | ||||||||
\(627\) | 12249.7 | − | 12249.7i | 0.780232 | − | 0.780232i | ||||
\(628\) | 1014.98 | − | 1014.98i | 0.0644935 | − | 0.0644935i | ||||
\(629\) | −22217.2 | −1.40836 | ||||||||
\(630\) | 1764.09 | + | 1208.85i | 0.111560 | + | 0.0764475i | ||||
\(631\) | −27632.2 | −1.74329 | −0.871647 | − | 0.490133i | \(-0.836948\pi\) | ||||
−0.871647 | + | 0.490133i | \(0.836948\pi\) | |||||||
\(632\) | 14199.4 | − | 14199.4i | 0.893704 | − | 0.893704i | ||||
\(633\) | −2103.83 | + | 2103.83i | −0.132101 | + | 0.132101i | ||||
\(634\) | − | 8638.74i | − | 0.541149i | ||||||
\(635\) | 381.002 | + | 992.251i | 0.0238104 | + | 0.0620099i | ||||
\(636\) | − | 11259.5i | − | 0.701994i | ||||||
\(637\) | −1261.21 | − | 2813.36i | −0.0784476 | − | 0.174991i | ||||
\(638\) | −4269.08 | − | 4269.08i | −0.264913 | − | 0.264913i | ||||
\(639\) | − | 1322.41i | − | 0.0818681i | ||||||
\(640\) | 15404.8 | − | 5915.09i | 0.951451 | − | 0.365335i | ||||
\(641\) | −2161.05 | −0.133161 | −0.0665806 | − | 0.997781i | \(-0.521209\pi\) | ||||
−0.0665806 | + | 0.997781i | \(0.521209\pi\) | |||||||
\(642\) | −4743.79 | − | 4743.79i | −0.291624 | − | 0.291624i | ||||
\(643\) | 10891.0 | − | 10891.0i | 0.667959 | − | 0.667959i | −0.289284 | − | 0.957243i | \(-0.593417\pi\) |
0.957243 | + | 0.289284i | \(0.0934173\pi\) | |||||||
\(644\) | −5647.07 | − | 1039.16i | −0.345537 | − | 0.0635849i | ||||
\(645\) | −6395.72 | + | 14368.8i | −0.390436 | + | 0.877166i | ||||
\(646\) | −9715.77 | −0.591737 | ||||||||
\(647\) | 9796.19 | + | 9796.19i | 0.595252 | + | 0.595252i | 0.939045 | − | 0.343794i | \(-0.111712\pi\) |
−0.343794 | + | 0.939045i | \(0.611712\pi\) | |||||||
\(648\) | 965.074 | + | 965.074i | 0.0585057 | + | 0.0585057i | ||||
\(649\) | −5854.94 | −0.354124 | ||||||||
\(650\) | −958.023 | + | 862.950i | −0.0578104 | + | 0.0520733i | ||||
\(651\) | 695.782 | − | 3781.06i | 0.0418892 | − | 0.227637i | ||||
\(652\) | −10549.4 | + | 10549.4i | −0.633657 | + | 0.633657i | ||||
\(653\) | 16668.7 | + | 16668.7i | 0.998925 | + | 0.998925i | 0.999999 | − | 0.00107454i | \(-0.000342037\pi\) |
−0.00107454 | + | 0.999999i | \(0.500342\pi\) | |||||||
\(654\) | 5892.52 | 0.352317 | ||||||||
\(655\) | −22809.2 | − | 10152.6i | −1.36065 | − | 0.605641i | ||||
\(656\) | 8821.75i | 0.525048i | ||||||||
\(657\) | −3240.70 | − | 3240.70i | −0.192438 | − | 0.192438i | ||||
\(658\) | 5674.79 | + | 8234.31i | 0.336210 | + | 0.487852i | ||||
\(659\) | − | 13534.7i | − | 0.800056i | −0.916503 | − | 0.400028i | \(-0.869000\pi\) | ||
0.916503 | − | 0.400028i | \(-0.131000\pi\) | |||||||
\(660\) | 9848.22 | − | 3781.49i | 0.580820 | − | 0.223022i | ||||
\(661\) | 4401.31i | 0.258988i | 0.991580 | + | 0.129494i | \(0.0413353\pi\) | ||||
−0.991580 | + | 0.129494i | \(0.958665\pi\) | |||||||
\(662\) | 6804.28 | − | 6804.28i | 0.399480 | − | 0.399480i | ||||
\(663\) | −1315.70 | + | 1315.70i | −0.0770701 | + | 0.0770701i | ||||
\(664\) | −805.728 | −0.0470908 | ||||||||
\(665\) | 24975.2 | − | 4664.45i | 1.45639 | − | 0.271999i | ||||
\(666\) | −3325.46 | −0.193482 | ||||||||
\(667\) | −3667.10 | + | 3667.10i | −0.212880 | + | 0.212880i | ||||
\(668\) | 6653.49 | − | 6653.49i | 0.385376 | − | 0.385376i | ||||
\(669\) | − | 11663.0i | − | 0.674015i | ||||||
\(670\) | −2865.61 | − | 1275.51i | −0.165236 | − | 0.0735482i | ||||
\(671\) | 18369.7i | 1.05686i | ||||||||
\(672\) | 7958.57 | − | 5484.76i | 0.456858 | − | 0.314850i | ||||
\(673\) | 13974.6 | + | 13974.6i | 0.800420 | + | 0.800420i | 0.983161 | − | 0.182741i | \(-0.0584971\pi\) |
−0.182741 | + | 0.983161i | \(0.558497\pi\) | |||||||
\(674\) | 963.851i | 0.0550833i | ||||||||
\(675\) | −175.969 | + | 3370.41i | −0.0100341 | + | 0.192188i | ||||
\(676\) | −14142.9 | −0.804668 | ||||||||
\(677\) | 9910.40 | + | 9910.40i | 0.562611 | + | 0.562611i | 0.930048 | − | 0.367437i | \(-0.119765\pi\) |
−0.367437 | + | 0.930048i | \(0.619765\pi\) | |||||||
\(678\) | 784.653 | − | 784.653i | 0.0444461 | − | 0.0444461i | ||||
\(679\) | 1007.23 | − | 5473.55i | 0.0569277 | − | 0.309360i | ||||
\(680\) | −11875.4 | − | 5285.86i | −0.669706 | − | 0.298093i | ||||
\(681\) | −10385.0 | −0.584366 | ||||||||
\(682\) | 2642.41 | + | 2642.41i | 0.148362 | + | 0.148362i | ||||
\(683\) | −11316.5 | − | 11316.5i | −0.633986 | − | 0.633986i | 0.315079 | − | 0.949065i | \(-0.397969\pi\) |
−0.949065 | + | 0.315079i | \(0.897969\pi\) | |||||||
\(684\) | 7380.31 | 0.412563 | ||||||||
\(685\) | −1256.73 | − | 3272.93i | −0.0700981 | − | 0.182558i | ||||
\(686\) | 3785.04 | − | 6230.10i | 0.210661 | − | 0.346744i | ||||
\(687\) | 13565.1 | − | 13565.1i | 0.753332 | − | 0.753332i | ||||
\(688\) | 11316.4 | + | 11316.4i | 0.627081 | + | 0.627081i | ||||
\(689\) | 5047.95 | 0.279117 | ||||||||
\(690\) | 640.054 | + | 1666.91i | 0.0353137 | + | 0.0919682i | ||||
\(691\) | 18547.8i | 1.02111i | 0.859844 | + | 0.510557i | \(0.170561\pi\) | ||||
−0.859844 | + | 0.510557i | \(0.829439\pi\) | |||||||
\(692\) | −7320.84 | − | 7320.84i | −0.402163 | − | 0.402163i | ||||
\(693\) | 6459.04 | − | 4451.34i | 0.354053 | − | 0.244000i | ||||
\(694\) | 1974.38i | 0.107992i | ||||||||
\(695\) | −8565.70 | + | 19244.0i | −0.467504 | + | 1.05031i | ||||
\(696\) | − | 5650.96i | − | 0.307758i | ||||||
\(697\) | 12611.5 | − | 12611.5i | 0.685358 | − | 0.685358i | ||||
\(698\) | −2775.85 | + | 2775.85i | −0.150526 | + | 0.150526i | ||||
\(699\) | 2719.86 | 0.147174 | ||||||||
\(700\) | 15049.5 | + | 3589.59i | 0.812595 | + | 0.193820i | ||||
\(701\) | −9679.24 | −0.521512 | −0.260756 | − | 0.965405i | \(-0.583972\pi\) | ||||
−0.260756 | + | 0.965405i | \(0.583972\pi\) | |||||||
\(702\) | −196.933 | + | 196.933i | −0.0105880 | + | 0.0105880i | ||||
\(703\) | −27936.6 | + | 27936.6i | −1.49879 | + | 1.49879i | ||||
\(704\) | − | 3454.45i | − | 0.184935i | ||||||
\(705\) | −6417.85 | + | 14418.6i | −0.342851 | + | 0.770261i | ||||
\(706\) | − | 110.123i | − | 0.00587045i | ||||||
\(707\) | 1695.96 | − | 1168.79i | 0.0902165 | − | 0.0621739i | ||||
\(708\) | −1763.77 | − | 1763.77i | −0.0936250 | − | 0.0936250i | ||||
\(709\) | 15134.7i | 0.801686i | 0.916147 | + | 0.400843i | \(0.131283\pi\) | ||||
−0.916147 | + | 0.400843i | \(0.868717\pi\) | |||||||
\(710\) | 675.758 | + | 1759.89i | 0.0357194 | + | 0.0930247i | ||||
\(711\) | 10726.0 | 0.565759 | ||||||||
\(712\) | −15290.9 | − | 15290.9i | −0.804845 | − | 0.804845i | ||||
\(713\) | 2269.81 | − | 2269.81i | 0.119222 | − | 0.119222i | ||||
\(714\) | −4326.75 | − | 796.199i | −0.226785 | − | 0.0417325i | ||||
\(715\) | 1695.35 | + | 4415.24i | 0.0886749 | + | 0.230938i | ||||
\(716\) | −3874.36 | −0.202223 | ||||||||
\(717\) | −12100.2 | − | 12100.2i | −0.630253 | − | 0.630253i | ||||
\(718\) | 5562.42 | + | 5562.42i | 0.289119 | + | 0.289119i | ||||
\(719\) | −16820.2 | −0.872445 | −0.436222 | − | 0.899839i | \(-0.643684\pi\) | ||||
−0.436222 | + | 0.899839i | \(0.643684\pi\) | |||||||
\(720\) | 3137.42 | + | 1396.50i | 0.162395 | + | 0.0722839i | ||||
\(721\) | −8904.66 | − | 1638.62i | −0.459954 | − | 0.0846397i | ||||
\(722\) | −6651.25 | + | 6651.25i | −0.342844 | + | 0.342844i | ||||
\(723\) | 10066.3 | + | 10066.3i | 0.517798 | + | 0.517798i | ||||
\(724\) | −7937.78 | −0.407466 | ||||||||
\(725\) | 10382.9 | − | 9352.48i | 0.531875 | − | 0.479093i | ||||
\(726\) | 3042.59i | 0.155539i | ||||||||
\(727\) | 6865.13 | + | 6865.13i | 0.350225 | + | 0.350225i | 0.860193 | − | 0.509968i | \(-0.170343\pi\) |
−0.509968 | + | 0.860193i | \(0.670343\pi\) | |||||||
\(728\) | 1591.73 | + | 2309.65i | 0.0810349 | + | 0.117584i | ||||
\(729\) | 729.000i | 0.0370370i | ||||||||
\(730\) | 5968.81 | + | 2656.78i | 0.302624 | + | 0.134701i | ||||
\(731\) | − | 32355.5i | − | 1.63709i | ||||||
\(732\) | −5533.78 | + | 5533.78i | −0.279418 | + | 0.279418i | ||||
\(733\) | 5472.36 | − | 5472.36i | 0.275752 | − | 0.275752i | −0.555659 | − | 0.831411i | \(-0.687534\pi\) |
0.831411 | + | 0.555659i | \(0.187534\pi\) | |||||||
\(734\) | −9480.81 | −0.476762 | ||||||||
\(735\) | 11504.5 | − | 30.5346i | 0.577348 | − | 0.00153236i | ||||
\(736\) | 8070.16 | 0.404171 | ||||||||
\(737\) | −8135.64 | + | 8135.64i | −0.406621 | + | 0.406621i | ||||
\(738\) | 1887.68 | − | 1887.68i | 0.0941552 | − | 0.0941552i | ||||
\(739\) | − | 13345.3i | − | 0.664295i | −0.943227 | − | 0.332147i | \(-0.892227\pi\) | ||
0.943227 | − | 0.332147i | \(-0.107773\pi\) | |||||||
\(740\) | −22459.8 | + | 8624.07i | −1.11573 | + | 0.428415i | ||||
\(741\) | 3308.80i | 0.164038i | ||||||||
\(742\) | 6772.85 | + | 9827.64i | 0.335093 | + | 0.486232i | ||||
\(743\) | 1331.63 | + | 1331.63i | 0.0657505 | + | 0.0657505i | 0.739217 | − | 0.673467i | \(-0.235196\pi\) |
−0.673467 | + | 0.739217i | \(0.735196\pi\) | |||||||
\(744\) | 3497.75i | 0.172357i | ||||||||
\(745\) | −19822.2 | − | 8823.05i | −0.974802 | − | 0.433895i | ||||
\(746\) | 8655.10 | 0.424780 | ||||||||
\(747\) | −304.316 | − | 304.316i | −0.0149054 | − | 0.0149054i | ||||
\(748\) | −15345.6 | + | 15345.6i | −0.750121 | + | 0.750121i | ||||
\(749\) | −35494.6 | − | 6531.64i | −1.73157 | − | 0.318639i | ||||
\(750\) | −1488.11 | − | 4575.34i | −0.0724510 | − | 0.222757i | ||||
\(751\) | −10872.5 | −0.528287 | −0.264144 | − | 0.964483i | \(-0.585089\pi\) | ||||
−0.264144 | + | 0.964483i | \(0.585089\pi\) | |||||||
\(752\) | 11355.5 | + | 11355.5i | 0.550655 | + | 0.550655i | ||||
\(753\) | 213.861 | + | 213.861i | 0.0103499 | + | 0.0103499i | ||||
\(754\) | 1153.13 | 0.0556959 | ||||||||
\(755\) | 6726.52 | − | 15112.0i | 0.324243 | − | 0.728454i | ||||
\(756\) | 3286.69 | + | 604.810i | 0.158116 | + | 0.0290962i | ||||
\(757\) | −6114.57 | + | 6114.57i | −0.293577 | + | 0.293577i | −0.838492 | − | 0.544915i | \(-0.816562\pi\) |
0.544915 | + | 0.838492i | \(0.316562\pi\) | |||||||
\(758\) | 7253.94 | + | 7253.94i | 0.347592 | + | 0.347592i | ||||
\(759\) | 6549.61 | 0.313222 | ||||||||
\(760\) | −21579.1 | + | 8285.88i | −1.02994 | + | 0.395474i | ||||
\(761\) | − | 12938.4i | − | 0.616318i | −0.951335 | − | 0.308159i | \(-0.900287\pi\) | ||
0.951335 | − | 0.308159i | \(-0.0997129\pi\) | |||||||
\(762\) | −231.425 | − | 231.425i | −0.0110021 | − | 0.0110021i | ||||
\(763\) | 26101.5 | − | 17988.2i | 1.23845 | − | 0.853497i | ||||
\(764\) | − | 6496.84i | − | 0.307653i | ||||||
\(765\) | −2488.81 | − | 6481.65i | −0.117625 | − | 0.306333i | ||||
\(766\) | − | 7955.13i | − | 0.375236i | ||||||
\(767\) | 790.748 | − | 790.748i | 0.0372259 | − | 0.0372259i | ||||
\(768\) | −2347.21 | + | 2347.21i | −0.110283 | + | 0.110283i | ||||
\(769\) | 30980.7 | 1.45278 | 0.726392 | − | 0.687281i | \(-0.241196\pi\) | ||||
0.726392 | + | 0.687281i | \(0.241196\pi\) | |||||||
\(770\) | −6321.18 | + | 9224.54i | −0.295843 | + | 0.431727i | ||||
\(771\) | −6595.67 | −0.308090 | ||||||||
\(772\) | −8539.38 | + | 8539.38i | −0.398107 | + | 0.398107i | ||||
\(773\) | −2711.05 | + | 2711.05i | −0.126144 | + | 0.126144i | −0.767360 | − | 0.641216i | \(-0.778430\pi\) |
0.641216 | + | 0.767360i | \(0.278430\pi\) | |||||||
\(774\) | − | 4842.96i | − | 0.224905i | ||||||
\(775\) | −6426.62 | + | 5788.85i | −0.297872 | + | 0.268312i | ||||
\(776\) | 5063.42i | 0.234235i | ||||||||
\(777\) | −14730.5 | + | 10151.7i | −0.680120 | + | 0.468714i | ||||
\(778\) | −8928.78 | − | 8928.78i | −0.411456 | − | 0.411456i | ||||
\(779\) | − | 31716.2i | − | 1.45873i | ||||||
\(780\) | −819.351 | + | 1840.78i | −0.0376122 | + | 0.0845007i | ||||
\(781\) | 6914.97 | 0.316821 | ||||||||
\(782\) | −2597.39 | − | 2597.39i | −0.118776 | − | 0.118776i | ||||
\(783\) | 2134.32 | − | 2134.32i | 0.0974129 | − | 0.0974129i | ||||
\(784\) | 4167.22 | − | 10939.5i | 0.189833 | − | 0.498335i | ||||
\(785\) | −2241.72 | + | 860.770i | −0.101924 | + | 0.0391365i | ||||
\(786\) | 7687.74 | 0.348871 | ||||||||
\(787\) | −17187.2 | − | 17187.2i | −0.778473 | − | 0.778473i | 0.201098 | − | 0.979571i | \(-0.435549\pi\) |
−0.979571 | + | 0.201098i | \(0.935549\pi\) | |||||||
\(788\) | 6415.37 | + | 6415.37i | 0.290023 | + | 0.290023i | ||||
\(789\) | 15712.0 | 0.708951 | ||||||||
\(790\) | −14274.3 | + | 5481.02i | −0.642859 | + | 0.246843i | ||||
\(791\) | 1080.38 | − | 5871.04i | 0.0485635 | − | 0.263907i | ||||
\(792\) | −5046.44 | + | 5046.44i | −0.226411 | + | 0.226411i | ||||
\(793\) | −2480.95 | − | 2480.95i | −0.111099 | − | 0.111099i | ||||
\(794\) | −17110.6 | −0.764777 | ||||||||
\(795\) | −7659.69 | + | 17208.5i | −0.341712 | + | 0.767702i | ||||
\(796\) | − | 21080.3i | − | 0.938660i | ||||||
\(797\) | −9725.84 | − | 9725.84i | −0.432254 | − | 0.432254i | 0.457140 | − | 0.889395i | \(-0.348874\pi\) |
−0.889395 | + | 0.457140i | \(0.848874\pi\) | |||||||
\(798\) | −6441.76 | + | 4439.43i | −0.285759 | + | 0.196935i | ||||
\(799\) | − | 32467.5i | − | 1.43757i | ||||||
\(800\) | −21715.7 | − | 1133.77i | −0.959707 | − | 0.0501062i | ||||
\(801\) | − | 11550.5i | − | 0.509507i | ||||||
\(802\) | 8021.64 | − | 8021.64i | 0.353184 | − | 0.353184i | ||||
\(803\) | 16945.8 | − | 16945.8i | 0.744714 | − | 0.744714i | ||||
\(804\) | −4901.63 | −0.215009 | ||||||||
\(805\) | 7923.80 | + | 5429.84i | 0.346928 | + | 0.237735i | ||||
\(806\) | −713.750 | −0.0311920 | ||||||||
\(807\) | −1549.65 | + | 1549.65i | −0.0675962 | + | 0.0675962i | ||||
\(808\) | −1325.05 | + | 1325.05i | −0.0576919 | + | 0.0576919i | ||||
\(809\) | 13840.9i | 0.601507i | 0.953702 | + | 0.300754i | \(0.0972382\pi\) | ||||
−0.953702 | + | 0.300754i | \(0.902762\pi\) | |||||||
\(810\) | −372.523 | − | 970.169i | −0.0161594 | − | 0.0420843i | ||||
\(811\) | 6459.17i | 0.279670i | 0.990175 | + | 0.139835i | \(0.0446571\pi\) | ||||
−0.990175 | + | 0.139835i | \(0.955343\pi\) | |||||||
\(812\) | −7851.84 | − | 11393.3i | −0.339342 | − | 0.492396i | ||||
\(813\) | 12027.6 | + | 12027.6i | 0.518853 | + | 0.518853i | ||||
\(814\) | − | 17389.0i | − | 0.748754i | ||||||
\(815\) | 23299.8 | − | 8946.58i | 1.00142 | − | 0.384521i | ||||
\(816\) | −7064.79 | −0.303085 | ||||||||
\(817\) | −40684.9 | − | 40684.9i | −1.74221 | − | 1.74221i | ||||
\(818\) | 1442.98 | − | 1442.98i | 0.0616779 | − | 0.0616779i | ||||
\(819\) | −271.153 | + | 1473.52i | −0.0115688 | + | 0.0628680i | ||||
\(820\) | 7853.82 | − | 17644.7i | 0.334472 | − | 0.751437i | ||||
\(821\) | −29095.0 | −1.23681 | −0.618407 | − | 0.785858i | \(-0.712222\pi\) | ||||
−0.618407 | + | 0.785858i | \(0.712222\pi\) | |||||||
\(822\) | 763.352 | + | 763.352i | 0.0323905 | + | 0.0323905i | ||||
\(823\) | 28670.5 | + | 28670.5i | 1.21433 | + | 1.21433i | 0.969589 | + | 0.244737i | \(0.0787018\pi\) |
0.244737 | + | 0.969589i | \(0.421298\pi\) | |||||||
\(824\) | 8237.45 | 0.348259 | ||||||||
\(825\) | −17624.1 | − | 920.153i | −0.743748 | − | 0.0388310i | ||||
\(826\) | 2600.42 | + | 478.524i | 0.109540 | + | 0.0201573i | ||||
\(827\) | 26904.3 | − | 26904.3i | 1.13126 | − | 1.13126i | 0.141293 | − | 0.989968i | \(-0.454874\pi\) |
0.989968 | − | 0.141293i | \(-0.0451260\pi\) | |||||||
\(828\) | 1973.03 | + | 1973.03i | 0.0828112 | + | 0.0828112i | ||||
\(829\) | −5672.16 | −0.237638 | −0.118819 | − | 0.992916i | \(-0.537911\pi\) | ||||
−0.118819 | + | 0.992916i | \(0.537911\pi\) | |||||||
\(830\) | 560.498 | + | 249.484i | 0.0234400 | + | 0.0104334i | ||||
\(831\) | 25372.1i | 1.05914i | ||||||||
\(832\) | 466.546 | + | 466.546i | 0.0194406 | + | 0.0194406i | ||||
\(833\) | −21596.4 | + | 9681.54i | −0.898284 | + | 0.402695i | ||||
\(834\) | − | 6486.11i | − | 0.269299i | ||||||
\(835\) | −14695.2 | + | 5642.62i | −0.609039 | + | 0.233857i | ||||
\(836\) | 38592.1i | 1.59657i | ||||||||
\(837\) | −1321.07 | + | 1321.07i | −0.0545553 | + | 0.0545553i | ||||
\(838\) | −10370.8 | + | 10370.8i | −0.427508 | + | 0.427508i | ||||
\(839\) | −17815.9 | −0.733102 | −0.366551 | − | 0.930398i | \(-0.619461\pi\) | ||||
−0.366551 | + | 0.930398i | \(0.619461\pi\) | |||||||
\(840\) | −10288.9 | + | 1921.59i | −0.422620 | + | 0.0789298i | ||||
\(841\) | 11891.6 | 0.487579 | ||||||||
\(842\) | −9715.34 | + | 9715.34i | −0.397640 | + | 0.397640i | ||||
\(843\) | 9721.56 | − | 9721.56i | 0.397187 | − | 0.397187i | ||||
\(844\) | − | 6628.02i | − | 0.270315i | ||||||
\(845\) | 21615.3 | + | 9621.20i | 0.879988 | + | 0.391692i | ||||
\(846\) | − | 4859.72i | − | 0.197495i | ||||||
\(847\) | 9288.21 | + | 13477.5i | 0.376796 | + | 0.546744i | ||||
\(848\) | 13552.8 | + | 13552.8i | 0.548826 | + | 0.548826i | ||||
\(849\) | − | 7222.40i | − | 0.291958i | ||||||
\(850\) | 6624.32 | + | 7354.13i | 0.267308 | + | 0.296758i | ||||
\(851\) | −14937.0 | −0.601686 | ||||||||
\(852\) | 2083.10 | + | 2083.10i | 0.0837625 | + | 0.0837625i | ||||
\(853\) | 14900.6 | − | 14900.6i | 0.598110 | − | 0.598110i | −0.341699 | − | 0.939809i | \(-0.611002\pi\) |
0.939809 | + | 0.341699i | \(0.111002\pi\) | |||||||
\(854\) | 1501.35 | − | 8158.75i | 0.0601584 | − | 0.326917i | ||||
\(855\) | −11279.7 | − | 5020.73i | −0.451180 | − | 0.200825i | ||||
\(856\) | 32835.1 | 1.31107 | ||||||||
\(857\) | 15227.9 | + | 15227.9i | 0.606973 | + | 0.606973i | 0.942154 | − | 0.335181i | \(-0.108797\pi\) |
−0.335181 | + | 0.942154i | \(0.608797\pi\) | |||||||
\(858\) | −1029.77 | − | 1029.77i | −0.0409743 | − | 0.0409743i | ||||
\(859\) | 28883.5 | 1.14726 | 0.573628 | − | 0.819116i | \(-0.305536\pi\) | ||||
0.573628 | + | 0.819116i | \(0.305536\pi\) | |||||||
\(860\) | −12559.5 | − | 32708.9i | −0.497993 | − | 1.29693i | ||||
\(861\) | 2599.12 | − | 14124.3i | 0.102878 | − | 0.559064i | ||||
\(862\) | −1050.30 | + | 1050.30i | −0.0415005 | + | 0.0415005i | ||||
\(863\) | 23740.1 | + | 23740.1i | 0.936410 | + | 0.936410i | 0.998096 | − | 0.0616857i | \(-0.0196476\pi\) |
−0.0616857 | + | 0.998096i | \(0.519648\pi\) | |||||||
\(864\) | −4696.98 | −0.184947 | ||||||||
\(865\) | 6208.58 | + | 16169.1i | 0.244044 | + | 0.635569i | ||||
\(866\) | 15009.3i | 0.588955i | ||||||||
\(867\) | −322.275 | − | 322.275i | −0.0126240 | − | 0.0126240i | ||||
\(868\) | 4860.01 | + | 7052.04i | 0.190046 | + | 0.275763i | ||||
\(869\) | 56086.7i | 2.18943i | ||||||||
\(870\) | −1749.75 | + | 3931.05i | −0.0681863 | + | 0.153190i | ||||
\(871\) | − | 2197.54i | − | 0.0854889i | ||||||
\(872\) | −20393.1 | + | 20393.1i | −0.791969 | + | 0.791969i | ||||
\(873\) | −1912.41 | + | 1912.41i | −0.0741411 | + | 0.0741411i | ||||
\(874\) | −6532.09 | −0.252805 | ||||||||
\(875\) | −20559.0 | − | 15724.1i | −0.794310 | − | 0.607512i | ||||
\(876\) | 10209.7 | 0.393782 | ||||||||
\(877\) | 26994.5 | − | 26994.5i | 1.03939 | − | 1.03939i | 0.0401931 | − | 0.999192i | \(-0.487203\pi\) |
0.999192 | − | 0.0401931i | \(-0.0127973\pi\) | |||||||
\(878\) | 3009.86 | − | 3009.86i | 0.115692 | − | 0.115692i | ||||
\(879\) | 6653.91i | 0.255325i | ||||||||
\(880\) | −7302.38 | + | 16405.8i | −0.279731 | + | 0.628452i | ||||
\(881\) | 14885.5i | 0.569244i | 0.958640 | + | 0.284622i | \(0.0918681\pi\) | ||||
−0.958640 | + | 0.284622i | \(0.908132\pi\) | |||||||
\(882\) | −3232.54 | + | 1449.13i | −0.123407 | + | 0.0553227i | ||||
\(883\) | −1000.38 | − | 1000.38i | −0.0381264 | − | 0.0381264i | 0.687787 | − | 0.725913i | \(-0.258582\pi\) |
−0.725913 | + | 0.687787i | \(0.758582\pi\) | |||||||
\(884\) | − | 4145.05i | − | 0.157707i | ||||||
\(885\) | 1495.80 | + | 3895.54i | 0.0568143 | + | 0.147963i | ||||
\(886\) | −715.819 | −0.0271427 | ||||||||
\(887\) | 32848.8 | + | 32848.8i | 1.24347 | + | 1.24347i | 0.958553 | + | 0.284915i | \(0.0919655\pi\) |
0.284915 | + | 0.958553i | \(0.408034\pi\) | |||||||
\(888\) | 11508.9 | − | 11508.9i | 0.434925 | − | 0.434925i | ||||
\(889\) | −1731.60 | − | 318.645i | −0.0653272 | − | 0.0120214i | ||||
\(890\) | 5902.34 | + | 15371.6i | 0.222300 | + | 0.578941i | ||||
\(891\) | −3811.99 | −0.143329 | ||||||||
\(892\) | 18371.8 | + | 18371.8i | 0.689612 | + | 0.689612i | ||||
\(893\) | −40825.7 | − | 40825.7i | −1.52988 | − | 1.52988i | ||||
\(894\) | 6680.98 | 0.249939 | ||||||||
\(895\) | 5921.40 | + | 2635.68i | 0.221151 | + | 0.0984368i | ||||
\(896\) | −4946.99 | + | 26883.2i | −0.184450 | + | 1.00235i | ||||
\(897\) | −884.568 | + | 884.568i | −0.0329263 | + | 0.0329263i | ||||
\(898\) | −5984.43 | − | 5984.43i | −0.222386 | − | 0.222386i | ||||
\(899\) | 7735.48 | 0.286977 | ||||||||
\(900\) | −5031.97 | − | 5586.35i | −0.186369 | − | 0.206902i | ||||
\(901\) | − | 38749.9i | − | 1.43279i | ||||||
\(902\) | 9870.82 | + | 9870.82i | 0.364371 | + | 0.364371i | ||||
\(903\) | −14784.2 | − | 21452.4i | −0.544837 | − | 0.790577i | ||||
\(904\) | 5431.13i | 0.199819i | ||||||||
\(905\) | 12131.8 | + | 5399.98i | 0.445606 | + | 0.198344i | ||||
\(906\) | 5093.45i | 0.186775i | ||||||||
\(907\) | −3132.55 | + | 3132.55i | −0.114680 | + | 0.114680i | −0.762118 | − | 0.647438i | \(-0.775840\pi\) |
0.647438 | + | 0.762118i | \(0.275840\pi\) | |||||||
\(908\) | 16358.7 | − | 16358.7i | 0.597888 | − | 0.597888i | ||||
\(909\) | −1000.92 | −0.0365219 | ||||||||
\(910\) | −392.119 | − | 2099.55i | −0.0142842 | − | 0.0764829i | ||||
\(911\) | −18810.6 | −0.684108 | −0.342054 | − | 0.939680i | \(-0.611123\pi\) | ||||
−0.342054 | + | 0.939680i | \(0.611123\pi\) | |||||||
\(912\) | −8883.50 | + | 8883.50i | −0.322546 | + | 0.322546i | ||||
\(913\) | 1591.29 | − | 1591.29i | 0.0576824 | − | 0.0576824i | ||||
\(914\) | 4674.41i | 0.169164i | ||||||||
\(915\) | 12222.1 | − | 4693.02i | 0.441586 | − | 0.169559i | ||||
\(916\) | 42736.1i | 1.54153i | ||||||||
\(917\) | 34053.7 | − | 23468.6i | 1.22634 | − | 0.845148i | ||||
\(918\) | 1511.73 | + | 1511.73i | 0.0543513 | + | 0.0543513i | ||||
\(919\) | 30657.2i | 1.10042i | 0.835025 | + | 0.550212i | \(0.185453\pi\) | ||||
−0.835025 | + | 0.550212i | \(0.814547\pi\) | |||||||
\(920\) | −7984.04 | − | 3553.78i | −0.286115 | − | 0.127353i | ||||
\(921\) | −27445.4 | −0.981931 | ||||||||
\(922\) | −11034.7 | − | 11034.7i | −0.394151 | − | 0.394151i | ||||
\(923\) | −933.911 | + | 933.911i | −0.0333045 | + | 0.0333045i | ||||
\(924\) | −3162.59 | + | 17186.3i | −0.112599 | + | 0.611892i | ||||
\(925\) | 40193.5 | + | 2098.50i | 1.42871 | + | 0.0745927i | ||||
\(926\) | −6141.50 | −0.217951 | ||||||||
\(927\) | 3111.21 | + | 3111.21i | 0.110233 | + | 0.110233i | ||||
\(928\) | 13751.5 | + | 13751.5i | 0.486439 | + | 0.486439i | ||||
\(929\) | −1690.64 | −0.0597072 | −0.0298536 | − | 0.999554i | \(-0.509504\pi\) | ||||
−0.0298536 | + | 0.999554i | \(0.509504\pi\) | |||||||
\(930\) | 1083.03 | − | 2433.18i | 0.0381872 | − | 0.0857926i | ||||
\(931\) | −14982.1 | + | 39329.9i | −0.527410 | + | 1.38452i | ||||
\(932\) | −4284.40 | + | 4284.40i | −0.150580 | + | 0.150580i | ||||
\(933\) | −22130.7 | − | 22130.7i | −0.776556 | − | 0.776556i | ||||
\(934\) | 4736.49 | 0.165934 | ||||||||
\(935\) | 33893.0 | − | 13014.1i | 1.18547 | − | 0.455195i | ||||
\(936\) | − | 1363.11i | − | 0.0476011i | ||||||
\(937\) | 9415.33 | + | 9415.33i | 0.328266 | + | 0.328266i | 0.851927 | − | 0.523661i | \(-0.175434\pi\) |
−0.523661 | + | 0.851927i | \(0.675434\pi\) | |||||||
\(938\) | 4278.30 | − | 2948.45i | 0.148925 | − | 0.102634i | ||||
\(939\) | − | 22159.5i | − | 0.770124i | ||||||
\(940\) | −12602.9 | − | 32822.1i | −0.437300 | − | 1.13887i | ||||
\(941\) | − | 40817.7i | − | 1.41405i | −0.707190 | − | 0.707024i | \(-0.750037\pi\) | ||
0.707190 | − | 0.707024i | \(-0.249963\pi\) | |||||||
\(942\) | 522.841 | − | 522.841i | 0.0180840 | − | 0.0180840i | ||||
\(943\) | 8478.95 | − | 8478.95i | 0.292802 | − | 0.292802i | ||||
\(944\) | 4246.01 | 0.146394 | ||||||||
\(945\) | −4611.79 | − | 3160.26i | −0.158753 | − | 0.108787i | ||||
\(946\) | 25324.1 | 0.870358 | ||||||||
\(947\) | 36885.1 | − | 36885.1i | 1.26569 | − | 1.26569i | 0.317394 | − | 0.948294i | \(-0.397192\pi\) |
0.948294 | − | 0.317394i | \(-0.102808\pi\) | |||||||
\(948\) | −16895.8 | + | 16895.8i | −0.578851 | + | 0.578851i | ||||
\(949\) | 4577.29i | 0.156570i | ||||||||
\(950\) | 17576.9 | + | 917.691i | 0.600286 | + | 0.0313409i | ||||
\(951\) | 22583.9i | 0.770067i | ||||||||
\(952\) | 17729.7 | − | 12218.7i | 0.603597 | − | 0.415977i | ||||
\(953\) | −19383.6 | − | 19383.6i | −0.658864 | − | 0.658864i | 0.296247 | − | 0.955111i | \(-0.404265\pi\) |
−0.955111 | + | 0.296247i | \(0.904265\pi\) | |||||||
\(954\) | − | 5800.06i | − | 0.196839i | ||||||
\(955\) | −4419.72 | + | 9929.48i | −0.149758 | + | 0.336451i | ||||
\(956\) | 38121.2 | 1.28967 | ||||||||
\(957\) | 11160.5 | + | 11160.5i | 0.376977 | + | 0.376977i | ||||
\(958\) | 8659.07 | − | 8659.07i | 0.292027 | − | 0.292027i | ||||
\(959\) | 5711.66 | + | 1051.05i | 0.192324 | + | 0.0353911i | ||||
\(960\) | −2298.39 | + | 882.529i | −0.0772710 | + | 0.0296703i | ||||
\(961\) | 25003.0 | 0.839281 | ||||||||
\(962\) | 2348.50 | + | 2348.50i | 0.0787098 | + | 0.0787098i | ||||
\(963\) | 12401.5 | + | 12401.5i | 0.414988 | + | 0.414988i | ||||
\(964\) | −31713.3 | −1.05956 | ||||||||
\(965\) | 18860.4 | − | 7241.98i | 0.629160 | − | 0.241583i | ||||
\(966\) | −2908.95 | − | 535.299i | −0.0968882 | − | 0.0178292i | ||||
\(967\) | 10511.9 | − | 10511.9i | 0.349578 | − | 0.349578i | −0.510375 | − | 0.859952i | \(-0.670493\pi\) |
0.859952 | + | 0.510375i | \(0.170493\pi\) | |||||||
\(968\) | −10530.0 | − | 10530.0i | −0.349634 | − | 0.349634i | ||||
\(969\) | 25399.6 | 0.842055 | ||||||||
\(970\) | 1567.82 | − | 3522.33i | 0.0518967 | − | 0.116593i | ||||
\(971\) | − | 11937.1i | − | 0.394520i | −0.980351 | − | 0.197260i | \(-0.936796\pi\) | ||
0.980351 | − | 0.197260i | \(-0.0632042\pi\) | |||||||
\(972\) | −1148.34 | − | 1148.34i | −0.0378941 | − | 0.0378941i | ||||
\(973\) | −19800.3 | − | 28730.9i | −0.652383 | − | 0.946630i | ||||
\(974\) | − | 3030.06i | − | 0.0996811i | ||||||
\(975\) | 2504.52 | − | 2255.98i | 0.0822655 | − | 0.0741016i | ||||
\(976\) | − | 13321.8i | − | 0.436905i | ||||||
\(977\) | −35517.3 | + | 35517.3i | −1.16305 | + | 1.16305i | −0.179244 | + | 0.983805i | \(0.557365\pi\) |
−0.983805 | + | 0.179244i | \(0.942635\pi\) | |||||||
\(978\) | −5434.25 | + | 5434.25i | −0.177677 | + | 0.177677i | ||||
\(979\) | 60398.1 | 1.97174 | ||||||||
\(980\) | −18074.2 | + | 18170.4i | −0.589140 | + | 0.592276i | ||||
\(981\) | −15404.6 | −0.501356 | ||||||||
\(982\) | −12455.0 | + | 12455.0i | −0.404739 | + | 0.404739i | ||||
\(983\) | −32641.2 | + | 32641.2i | −1.05910 | + | 1.05910i | −0.0609579 | + | 0.998140i | \(0.519416\pi\) |
−0.998140 | + | 0.0609579i | \(0.980584\pi\) | |||||||
\(984\) | 13066.0i | 0.423300i | ||||||||
\(985\) | −5440.68 | − | 14169.3i | −0.175994 | − | 0.458346i | ||||
\(986\) | − | 8851.88i | − | 0.285904i | ||||||
\(987\) | −14835.4 | − | 21526.6i | −0.478435 | − | 0.694225i | ||||
\(988\) | −5212.12 | − | 5212.12i | −0.167834 | − | 0.167834i | ||||
\(989\) | − | 21753.2i | − | 0.699406i | ||||||
\(990\) | 5073.08 | − | 1947.95i | 0.162862 | − | 0.0625352i | ||||
\(991\) | 2297.54 | 0.0736465 | 0.0368232 | − | 0.999322i | \(-0.488276\pi\) | ||||
0.0368232 | + | 0.999322i | \(0.488276\pi\) | |||||||
\(992\) | −8511.70 | − | 8511.70i | −0.272426 | − | 0.272426i | ||||
\(993\) | −17788.2 | + | 17788.2i | −0.568470 | + | 0.568470i | ||||
\(994\) | −3071.22 | − | 565.160i | −0.0980013 | − | 0.0180340i | ||||
\(995\) | −14340.7 | + | 32218.3i | −0.456915 | + | 1.02652i | ||||
\(996\) | 958.735 | 0.0305007 | ||||||||
\(997\) | 4284.98 | + | 4284.98i | 0.136115 | + | 0.136115i | 0.771882 | − | 0.635766i | \(-0.219316\pi\) |
−0.635766 | + | 0.771882i | \(0.719316\pi\) | |||||||
\(998\) | −5728.42 | − | 5728.42i | −0.181693 | − | 0.181693i | ||||
\(999\) | 8693.62 | 0.275329 |
(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 | 105.4.m.a.13.12 | yes | 48 | |
5.2 | odd | 4 | inner | 105.4.m.a.97.11 | yes | 48 | |
7.6 | odd | 2 | inner | 105.4.m.a.13.11 | ✓ | 48 | |
35.27 | even | 4 | inner | 105.4.m.a.97.12 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.m.a.13.11 | ✓ | 48 | 7.6 | odd | 2 | inner | |
105.4.m.a.13.12 | yes | 48 | 1.1 | even | 1 | trivial | |
105.4.m.a.97.11 | yes | 48 | 5.2 | odd | 4 | inner | |
105.4.m.a.97.12 | yes | 48 | 35.27 | even | 4 | inner |