Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [100,4,Mod(7,100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(100, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("100.7");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 100 = 2^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 100.e (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: | \(5.90019100057\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.2342560000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 24x^{6} - 58x^{5} + 141x^{4} - 190x^{3} + 186x^{2} - 100x + 20 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.4 | ||
Root | \(0.500000 - 2.27635i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 100.43 |
Dual form | 100.4.e.d.7.4 |
$q$-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 \(\left(\mathbb{Z}/100\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(77\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.77635 | − | 0.540278i | 0.981587 | − | 0.191017i | ||||
\(3\) | 2.23607 | − | 2.23607i | 0.430331 | − | 0.430331i | −0.458410 | − | 0.888741i | \(-0.651581\pi\) |
0.888741 | + | 0.458410i | \(0.151581\pi\) | |||||||
\(4\) | 7.41620 | − | 3.00000i | 0.927025 | − | 0.375000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 5.00000 | − | 7.41620i | 0.340207 | − | 0.504608i | ||||
\(7\) | 11.1803 | + | 11.1803i | 0.603682 | + | 0.603682i | 0.941288 | − | 0.337606i | \(-0.109617\pi\) |
−0.337606 | + | 0.941288i | \(0.609617\pi\) | |||||||
\(8\) | 18.9691 | − | 12.3359i | 0.838324 | − | 0.545173i | ||||
\(9\) | 17.0000i | 0.629630i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 59.3296i | − | 1.62623i | −0.582102 | − | 0.813116i | \(-0.697770\pi\) | ||
0.582102 | − | 0.813116i | \(-0.302230\pi\) | |||||||
\(12\) | 9.87492 | − | 23.2913i | 0.237554 | − | 0.560302i | ||||
\(13\) | −26.5330 | − | 26.5330i | −0.566072 | − | 0.566072i | 0.364954 | − | 0.931026i | \(-0.381085\pi\) |
−0.931026 | + | 0.364954i | \(0.881085\pi\) | |||||||
\(14\) | 37.0810 | + | 25.0000i | 0.707879 | + | 0.477252i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 46.0000 | − | 44.4972i | 0.718750 | − | 0.695269i | ||||
\(17\) | −79.5990 | + | 79.5990i | −1.13562 | + | 1.13562i | −0.146397 | + | 0.989226i | \(0.546768\pi\) |
−0.989226 | + | 0.146397i | \(0.953232\pi\) | |||||||
\(18\) | 9.18473 | + | 47.1979i | 0.120270 | + | 0.618036i | ||||
\(19\) | 59.3296 | 0.716376 | 0.358188 | − | 0.933650i | \(-0.383395\pi\) | ||||
0.358188 | + | 0.933650i | \(0.383395\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 50.0000 | 0.519566 | ||||||||
\(22\) | −32.0545 | − | 164.719i | −0.310638 | − | 1.59629i | ||||
\(23\) | −105.095 | + | 105.095i | −0.952777 | + | 0.952777i | −0.998934 | − | 0.0461575i | \(-0.985302\pi\) |
0.0461575 | + | 0.998934i | \(0.485302\pi\) | |||||||
\(24\) | 14.8324 | − | 70.0000i | 0.126152 | − | 0.595362i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −88.0000 | − | 59.3296i | −0.663778 | − | 0.447519i | ||||
\(27\) | 98.3870 | + | 98.3870i | 0.701281 | + | 0.701281i | ||||
\(28\) | 116.457 | + | 49.3746i | 0.786008 | + | 0.333247i | ||||
\(29\) | − | 46.0000i | − | 0.294551i | −0.989095 | − | 0.147276i | \(-0.952950\pi\) | ||
0.989095 | − | 0.147276i | \(-0.0470504\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 118.659i | 0.687478i | 0.939065 | + | 0.343739i | \(0.111694\pi\) | ||||
−0.939065 | + | 0.343739i | \(0.888306\pi\) | |||||||
\(32\) | 103.671 | − | 148.392i | 0.572707 | − | 0.819760i | ||||
\(33\) | −132.665 | − | 132.665i | −0.699819 | − | 0.699819i | ||||
\(34\) | −177.989 | + | 264.000i | −0.897789 | + | 1.33164i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 51.0000 | + | 126.075i | 0.236111 | + | 0.583682i | ||||
\(37\) | −212.264 | + | 212.264i | −0.943135 | + | 0.943135i | −0.998468 | − | 0.0553332i | \(-0.982378\pi\) |
0.0553332 | + | 0.998468i | \(0.482378\pi\) | |||||||
\(38\) | 164.719 | − | 32.0545i | 0.703185 | − | 0.136840i | ||||
\(39\) | −118.659 | −0.487197 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −188.000 | −0.716114 | −0.358057 | − | 0.933700i | \(-0.616561\pi\) | ||||
−0.358057 | + | 0.933700i | \(0.616561\pi\) | |||||||
\(42\) | 138.817 | − | 27.0139i | 0.509999 | − | 0.0992462i | ||||
\(43\) | 122.984 | − | 122.984i | 0.436159 | − | 0.436159i | −0.454558 | − | 0.890717i | \(-0.650203\pi\) |
0.890717 | + | 0.454558i | \(0.150203\pi\) | |||||||
\(44\) | −177.989 | − | 440.000i | −0.609837 | − | 1.50756i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −235.000 | + | 348.561i | −0.753236 | + | 1.11723i | ||||
\(47\) | 194.538 | + | 194.538i | 0.603750 | + | 0.603750i | 0.941306 | − | 0.337555i | \(-0.109600\pi\) |
−0.337555 | + | 0.941306i | \(0.609600\pi\) | |||||||
\(48\) | 3.36038 | − | 202.358i | 0.0101048 | − | 0.608497i | ||||
\(49\) | − | 93.0000i | − | 0.271137i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 355.978i | 0.977389i | ||||||||
\(52\) | −276.373 | − | 117.175i | −0.737039 | − | 0.312486i | ||||
\(53\) | −26.5330 | − | 26.5330i | −0.0687658 | − | 0.0687658i | 0.671887 | − | 0.740653i | \(-0.265484\pi\) |
−0.740653 | + | 0.671887i | \(0.765484\pi\) | |||||||
\(54\) | 326.313 | + | 220.000i | 0.822325 | + | 0.554411i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 350.000 | + | 74.1620i | 0.835191 | + | 0.176970i | ||||
\(57\) | 132.665 | − | 132.665i | 0.308279 | − | 0.308279i | ||||
\(58\) | −24.8528 | − | 127.712i | −0.0562644 | − | 0.289128i | ||||
\(59\) | −415.307 | −0.916413 | −0.458207 | − | 0.888846i | \(-0.651508\pi\) | ||||
−0.458207 | + | 0.888846i | \(0.651508\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 72.0000 | 0.151125 | 0.0755627 | − | 0.997141i | \(-0.475925\pi\) | ||||
0.0755627 | + | 0.997141i | \(0.475925\pi\) | |||||||
\(62\) | 64.1090 | + | 329.439i | 0.131320 | + | 0.674819i | ||||
\(63\) | −190.066 | + | 190.066i | −0.380096 | + | 0.380096i | ||||
\(64\) | 207.654 | − | 468.000i | 0.405573 | − | 0.914062i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −440.000 | − | 296.648i | −0.820610 | − | 0.553255i | ||||
\(67\) | −597.030 | − | 597.030i | −1.08864 | − | 1.08864i | −0.995669 | − | 0.0929706i | \(-0.970364\pi\) |
−0.0929706 | − | 0.995669i | \(-0.529636\pi\) | |||||||
\(68\) | −351.525 | + | 829.119i | −0.626892 | + | 1.47861i | ||||
\(69\) | 470.000i | 0.820020i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 711.955i | − | 1.19005i | −0.803707 | − | 0.595025i | \(-0.797142\pi\) | ||
0.803707 | − | 0.595025i | \(-0.202858\pi\) | |||||||
\(72\) | 209.709 | + | 322.475i | 0.343257 | + | 0.527833i | ||||
\(73\) | 504.127 | + | 504.127i | 0.808268 | + | 0.808268i | 0.984372 | − | 0.176103i | \(-0.0563493\pi\) |
−0.176103 | + | 0.984372i | \(0.556349\pi\) | |||||||
\(74\) | −474.637 | + | 704.000i | −0.745613 | + | 1.10592i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 440.000 | − | 177.989i | 0.664098 | − | 0.268641i | ||||
\(77\) | 663.325 | − | 663.325i | 0.981726 | − | 0.981726i | ||||
\(78\) | −329.439 | + | 64.1090i | −0.478226 | + | 0.0930630i | ||||
\(79\) | 830.614 | 1.18293 | 0.591465 | − | 0.806331i | \(-0.298550\pi\) | ||||
0.591465 | + | 0.806331i | \(0.298550\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −19.0000 | −0.0260631 | ||||||||
\(82\) | −521.953 | + | 101.572i | −0.702928 | + | 0.136790i | ||||
\(83\) | 221.371 | − | 221.371i | 0.292754 | − | 0.292754i | −0.545413 | − | 0.838167i | \(-0.683627\pi\) |
0.838167 | + | 0.545413i | \(0.183627\pi\) | |||||||
\(84\) | 370.810 | − | 150.000i | 0.481651 | − | 0.194837i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 275.000 | − | 407.891i | 0.344814 | − | 0.511442i | ||||
\(87\) | −102.859 | − | 102.859i | −0.126755 | − | 0.126755i | ||||
\(88\) | −731.881 | − | 1125.43i | −0.886577 | − | 1.36331i | ||||
\(89\) | − | 726.000i | − | 0.864672i | −0.901712 | − | 0.432336i | \(-0.857689\pi\) | ||
0.901712 | − | 0.432336i | \(-0.142311\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 593.296i | − | 0.683454i | ||||||
\(92\) | −464.121 | + | 1094.69i | −0.525956 | + | 1.24054i | ||||
\(93\) | 265.330 | + | 265.330i | 0.295843 | + | 0.295843i | ||||
\(94\) | 645.209 | + | 435.000i | 0.707960 | + | 0.477307i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −100.000 | − | 563.631i | −0.106315 | − | 0.599222i | ||||
\(97\) | 451.061 | − | 451.061i | 0.472147 | − | 0.472147i | −0.430461 | − | 0.902609i | \(-0.641649\pi\) |
0.902609 | + | 0.430461i | \(0.141649\pi\) | |||||||
\(98\) | −50.2459 | − | 258.200i | −0.0517919 | − | 0.266144i | ||||
\(99\) | 1008.60 | 1.02392 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1382.00 | 1.36153 | 0.680763 | − | 0.732504i | \(-0.261648\pi\) | ||||
0.680763 | + | 0.732504i | \(0.261648\pi\) | |||||||
\(102\) | 192.327 | + | 988.317i | 0.186698 | + | 0.959392i | ||||
\(103\) | 1053.19 | − | 1053.19i | 1.00751 | − | 1.00751i | 0.00754007 | − | 0.999972i | \(-0.497600\pi\) |
0.999972 | − | 0.00754007i | \(-0.00240010\pi\) | |||||||
\(104\) | −830.614 | − | 176.000i | −0.783158 | − | 0.165944i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −88.0000 | − | 59.3296i | −0.0806351 | − | 0.0543641i | ||||
\(107\) | −547.837 | − | 547.837i | −0.494966 | − | 0.494966i | 0.414901 | − | 0.909867i | \(-0.363816\pi\) |
−0.909867 | + | 0.414901i | \(0.863816\pi\) | |||||||
\(108\) | 1024.82 | + | 434.496i | 0.913085 | + | 0.387124i | ||||
\(109\) | 784.000i | 0.688932i | 0.938799 | + | 0.344466i | \(0.111940\pi\) | ||||
−0.938799 | + | 0.344466i | \(0.888060\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 949.273i | 0.811721i | ||||||||
\(112\) | 1011.79 | + | 16.8019i | 0.853617 | + | 0.0141753i | ||||
\(113\) | −159.198 | − | 159.198i | −0.132532 | − | 0.132532i | 0.637729 | − | 0.770261i | \(-0.279874\pi\) |
−0.770261 | + | 0.637729i | \(0.779874\pi\) | |||||||
\(114\) | 296.648 | − | 440.000i | 0.243716 | − | 0.361489i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −138.000 | − | 341.145i | −0.110457 | − | 0.273056i | ||||
\(117\) | 451.061 | − | 451.061i | 0.356415 | − | 0.356415i | ||||
\(118\) | −1153.04 | + | 224.381i | −0.899539 | + | 0.175051i | ||||
\(119\) | −1779.89 | −1.37111 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2189.00 | −1.64463 | ||||||||
\(122\) | 199.897 | − | 38.9000i | 0.148343 | − | 0.0288676i | ||||
\(123\) | −420.381 | + | 420.381i | −0.308166 | + | 0.308166i | ||||
\(124\) | 355.978 | + | 880.000i | 0.257804 | + | 0.637309i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −425.000 | + | 630.377i | −0.300492 | + | 0.445702i | ||||
\(127\) | 762.499 | + | 762.499i | 0.532763 | + | 0.532763i | 0.921394 | − | 0.388631i | \(-0.127052\pi\) |
−0.388631 | + | 0.921394i | \(0.627052\pi\) | |||||||
\(128\) | 323.668 | − | 1411.52i | 0.223504 | − | 0.974703i | ||||
\(129\) | − | 550.000i | − | 0.375386i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 177.989i | − | 0.118710i | −0.998237 | − | 0.0593548i | \(-0.981096\pi\) | ||
0.998237 | − | 0.0593548i | \(-0.0189043\pi\) | |||||||
\(132\) | −1381.86 | − | 585.875i | −0.911181 | − | 0.386317i | ||||
\(133\) | 663.325 | + | 663.325i | 0.432463 | + | 0.432463i | ||||
\(134\) | −1980.12 | − | 1335.00i | −1.27654 | − | 0.860645i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −528.000 | + | 2491.84i | −0.332909 | + | 1.57113i | ||||
\(137\) | −477.594 | + | 477.594i | −0.297837 | + | 0.297837i | −0.840166 | − | 0.542329i | \(-0.817542\pi\) |
0.542329 | + | 0.840166i | \(0.317542\pi\) | |||||||
\(138\) | 253.931 | + | 1304.88i | 0.156638 | + | 0.804920i | ||||
\(139\) | −771.285 | −0.470644 | −0.235322 | − | 0.971917i | \(-0.575614\pi\) | ||||
−0.235322 | + | 0.971917i | \(0.575614\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 870.000 | 0.519626 | ||||||||
\(142\) | −384.654 | − | 1976.63i | −0.227320 | − | 1.16814i | ||||
\(143\) | −1574.19 | + | 1574.19i | −0.920563 | + | 0.920563i | ||||
\(144\) | 756.452 | + | 782.000i | 0.437762 | + | 0.452546i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1672.00 | + | 1127.26i | 0.947779 | + | 0.638992i | ||||
\(147\) | −207.954 | − | 207.954i | −0.116679 | − | 0.116679i | ||||
\(148\) | −937.400 | + | 2210.98i | −0.520634 | + | 1.22798i | ||||
\(149\) | 104.000i | 0.0571813i | 0.999591 | + | 0.0285906i | \(0.00910193\pi\) | ||||
−0.999591 | + | 0.0285906i | \(0.990898\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1779.89i | 0.959240i | 0.877476 | + | 0.479620i | \(0.159225\pi\) | ||||
−0.877476 | + | 0.479620i | \(0.840775\pi\) | |||||||
\(152\) | 1125.43 | − | 731.881i | 0.600555 | − | 0.390549i | ||||
\(153\) | −1353.18 | − | 1353.18i | −0.715022 | − | 0.715022i | ||||
\(154\) | 1483.24 | − | 2200.00i | 0.776122 | − | 1.15118i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −880.000 | + | 355.978i | −0.451644 | + | 0.182699i | ||||
\(157\) | −2600.23 | + | 2600.23i | −1.32179 | + | 1.32179i | −0.409466 | + | 0.912325i | \(0.634285\pi\) |
−0.912325 | + | 0.409466i | \(0.865715\pi\) | |||||||
\(158\) | 2306.07 | − | 448.763i | 1.16115 | − | 0.225960i | ||||
\(159\) | −118.659 | −0.0591842 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2350.00 | −1.15035 | ||||||||
\(162\) | −52.7506 | + | 10.2653i | −0.0255832 | + | 0.00497850i | ||||
\(163\) | 15.6525 | − | 15.6525i | 0.00752145 | − | 0.00752145i | −0.703336 | − | 0.710858i | \(-0.748307\pi\) |
0.710858 | + | 0.703336i | \(0.248307\pi\) | |||||||
\(164\) | −1394.25 | + | 564.000i | −0.663855 | + | 0.268543i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 495.000 | − | 734.204i | 0.231442 | − | 0.343285i | ||||
\(167\) | 73.7902 | + | 73.7902i | 0.0341920 | + | 0.0341920i | 0.723996 | − | 0.689804i | \(-0.242303\pi\) |
−0.689804 | + | 0.723996i | \(0.742303\pi\) | |||||||
\(168\) | 948.455 | − | 616.793i | 0.435565 | − | 0.283253i | ||||
\(169\) | − | 789.000i | − | 0.359126i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1008.60i | 0.451051i | ||||||||
\(172\) | 543.121 | − | 1281.02i | 0.240771 | − | 0.567890i | ||||
\(173\) | −2281.84 | − | 2281.84i | −1.00280 | − | 1.00280i | −0.999996 | − | 0.00280694i | \(-0.999107\pi\) |
−0.00280694 | − | 0.999996i | \(-0.500893\pi\) | |||||||
\(174\) | −341.145 | − | 230.000i | −0.148633 | − | 0.100208i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2640.00 | − | 2729.16i | −1.13067 | − | 1.16885i | ||||
\(177\) | −928.655 | + | 928.655i | −0.394361 | + | 0.394361i | ||||
\(178\) | −392.242 | − | 2015.63i | −0.165167 | − | 0.848751i | ||||
\(179\) | −652.625 | −0.272511 | −0.136256 | − | 0.990674i | \(-0.543507\pi\) | ||||
−0.136256 | + | 0.990674i | \(0.543507\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4202.00 | 1.72559 | 0.862796 | − | 0.505552i | \(-0.168711\pi\) | ||||
0.862796 | + | 0.505552i | \(0.168711\pi\) | |||||||
\(182\) | −320.545 | − | 1647.19i | −0.130551 | − | 0.670869i | ||||
\(183\) | 160.997 | − | 160.997i | 0.0650341 | − | 0.0650341i | ||||
\(184\) | −697.123 | + | 3290.00i | −0.279307 | + | 1.31816i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 880.000 | + | 593.296i | 0.346907 | + | 0.233885i | ||||
\(187\) | 4722.58 | + | 4722.58i | 1.84679 | + | 1.84679i | ||||
\(188\) | 2026.35 | + | 859.118i | 0.786098 | + | 0.333285i | ||||
\(189\) | 2200.00i | 0.846701i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 3797.09i | − | 1.43847i | −0.694766 | − | 0.719236i | \(-0.744492\pi\) | ||
0.694766 | − | 0.719236i | \(-0.255508\pi\) | |||||||
\(192\) | −582.152 | − | 1510.81i | −0.218819 | − | 0.567881i | ||||
\(193\) | 1830.78 | + | 1830.78i | 0.682809 | + | 0.682809i | 0.960632 | − | 0.277823i | \(-0.0896129\pi\) |
−0.277823 | + | 0.960632i | \(0.589613\pi\) | |||||||
\(194\) | 1008.60 | − | 1496.00i | 0.373265 | − | 0.553642i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −279.000 | − | 689.706i | −0.101676 | − | 0.251351i | ||||
\(197\) | 185.731 | − | 185.731i | 0.0671715 | − | 0.0671715i | −0.672723 | − | 0.739894i | \(-0.734875\pi\) |
0.739894 | + | 0.672723i | \(0.234875\pi\) | |||||||
\(198\) | 2800.23 | − | 544.926i | 1.00507 | − | 0.195587i | ||||
\(199\) | 4746.37 | 1.69076 | 0.845379 | − | 0.534166i | \(-0.179374\pi\) | ||||
0.845379 | + | 0.534166i | \(0.179374\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2670.00 | −0.936952 | ||||||||
\(202\) | 3836.91 | − | 746.665i | 1.33646 | − | 0.260075i | ||||
\(203\) | 514.296 | − | 514.296i | 0.177815 | − | 0.177815i | ||||
\(204\) | 1067.93 | + | 2640.00i | 0.366521 | + | 0.906064i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2355.00 | − | 3493.03i | 0.796508 | − | 1.18141i | ||||
\(207\) | −1786.62 | − | 1786.62i | −0.599896 | − | 0.599896i | ||||
\(208\) | −2401.16 | − | 39.8740i | −0.800436 | − | 0.0132921i | ||||
\(209\) | − | 3520.00i | − | 1.16499i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 652.625i | − | 0.212932i | −0.994316 | − | 0.106466i | \(-0.966047\pi\) | ||
0.994316 | − | 0.106466i | \(-0.0339535\pi\) | |||||||
\(212\) | −276.373 | − | 117.175i | −0.0895348 | − | 0.0379604i | ||||
\(213\) | −1591.98 | − | 1591.98i | −0.512116 | − | 0.512116i | ||||
\(214\) | −1816.97 | − | 1225.00i | −0.580399 | − | 0.391305i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3080.00 | + | 652.625i | 0.970220 | + | 0.205581i | ||||
\(217\) | −1326.65 | + | 1326.65i | −0.415018 | + | 0.415018i | ||||
\(218\) | 423.578 | + | 2176.66i | 0.131598 | + | 0.676246i | ||||
\(219\) | 2254.52 | 0.695647 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4224.00 | 1.28569 | ||||||||
\(222\) | 512.872 | + | 2635.51i | 0.155053 | + | 0.796775i | ||||
\(223\) | −149.817 | + | 149.817i | −0.0449886 | + | 0.0449886i | −0.729243 | − | 0.684255i | \(-0.760128\pi\) |
0.684255 | + | 0.729243i | \(0.260128\pi\) | |||||||
\(224\) | 2818.16 | − | 500.000i | 0.840607 | − | 0.149141i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −528.000 | − | 355.978i | −0.155407 | − | 0.104776i | ||||
\(227\) | −1451.21 | − | 1451.21i | −0.424317 | − | 0.424317i | 0.462370 | − | 0.886687i | \(-0.346999\pi\) |
−0.886687 | + | 0.462370i | \(0.846999\pi\) | |||||||
\(228\) | 585.875 | − | 1381.86i | 0.170178 | − | 0.401387i | ||||
\(229\) | 3334.00i | 0.962083i | 0.876698 | + | 0.481041i | \(0.159741\pi\) | ||||
−0.876698 | + | 0.481041i | \(0.840259\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 2966.48i | − | 0.844935i | ||||||
\(232\) | −567.449 | − | 872.579i | −0.160581 | − | 0.246929i | ||||
\(233\) | −1087.85 | − | 1087.85i | −0.305870 | − | 0.305870i | 0.537435 | − | 0.843305i | \(-0.319393\pi\) |
−0.843305 | + | 0.537435i | \(0.819393\pi\) | |||||||
\(234\) | 1008.60 | − | 1496.00i | 0.281771 | − | 0.417934i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3080.00 | + | 1245.92i | −0.849538 | + | 0.343655i | ||||
\(237\) | 1857.31 | − | 1857.31i | 0.509052 | − | 0.509052i | ||||
\(238\) | −4941.58 | + | 961.635i | −1.34586 | + | 0.261906i | ||||
\(239\) | −3441.12 | −0.931328 | −0.465664 | − | 0.884962i | \(-0.654184\pi\) | ||||
−0.465664 | + | 0.884962i | \(0.654184\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3028.00 | −0.809339 | −0.404669 | − | 0.914463i | \(-0.632613\pi\) | ||||
−0.404669 | + | 0.914463i | \(0.632613\pi\) | |||||||
\(242\) | −6077.42 | + | 1182.67i | −1.61435 | + | 0.314152i | ||||
\(243\) | −2698.93 | + | 2698.93i | −0.712497 | + | 0.712497i | ||||
\(244\) | 533.966 | − | 216.000i | 0.140097 | − | 0.0566721i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −940.000 | + | 1394.25i | −0.243627 | + | 0.361357i | ||||
\(247\) | −1574.19 | − | 1574.19i | −0.405520 | − | 0.405520i | ||||
\(248\) | 1463.76 | + | 2250.86i | 0.374794 | + | 0.576329i | ||||
\(249\) | − | 990.000i | − | 0.251963i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2076.54i | 0.522190i | 0.965313 | + | 0.261095i | \(0.0840836\pi\) | ||||
−0.965313 | + | 0.261095i | \(0.915916\pi\) | |||||||
\(252\) | −839.368 | + | 1979.76i | −0.209822 | + | 0.494894i | ||||
\(253\) | 6235.25 | + | 6235.25i | 1.54944 | + | 1.54944i | ||||
\(254\) | 2528.92 | + | 1705.00i | 0.624720 | + | 0.421186i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 136.000 | − | 4093.74i | 0.0332031 | − | 0.999449i | ||||
\(257\) | 2441.04 | − | 2441.04i | 0.592481 | − | 0.592481i | −0.345820 | − | 0.938301i | \(-0.612399\pi\) |
0.938301 | + | 0.345820i | \(0.112399\pi\) | |||||||
\(258\) | −297.153 | − | 1526.99i | −0.0717052 | − | 0.368474i | ||||
\(259\) | −4746.37 | −1.13871 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 782.000 | 0.185458 | ||||||||
\(262\) | −96.1635 | − | 494.158i | −0.0226756 | − | 0.116524i | ||||
\(263\) | 1402.01 | − | 1402.01i | 0.328715 | − | 0.328715i | −0.523383 | − | 0.852098i | \(-0.675330\pi\) |
0.852098 | + | 0.523383i | \(0.175330\pi\) | |||||||
\(264\) | −4153.07 | − | 880.000i | −0.968196 | − | 0.205152i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2200.00 | + | 1483.24i | 0.507108 | + | 0.341892i | ||||
\(267\) | −1623.39 | − | 1623.39i | −0.372096 | − | 0.372096i | ||||
\(268\) | −6218.78 | − | 2636.60i | −1.41744 | − | 0.600956i | ||||
\(269\) | 5544.00i | 1.25659i | 0.777974 | + | 0.628297i | \(0.216248\pi\) | ||||
−0.777974 | + | 0.628297i | \(0.783752\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4627.71i | 1.03732i | 0.854981 | + | 0.518659i | \(0.173569\pi\) | ||||
−0.854981 | + | 0.518659i | \(0.826431\pi\) | |||||||
\(272\) | −119.622 | + | 7203.49i | −0.0266660 | + | 1.60579i | ||||
\(273\) | −1326.65 | − | 1326.65i | −0.294112 | − | 0.294112i | ||||
\(274\) | −1067.93 | + | 1584.00i | −0.235460 | + | 0.349244i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1410.00 | + | 3485.61i | 0.307507 | + | 0.760178i | ||||
\(277\) | 1379.72 | − | 1379.72i | 0.299275 | − | 0.299275i | −0.541455 | − | 0.840730i | \(-0.682126\pi\) |
0.840730 | + | 0.541455i | \(0.182126\pi\) | |||||||
\(278\) | −2141.35 | + | 416.708i | −0.461978 | + | 0.0899011i | ||||
\(279\) | −2017.21 | −0.432857 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5308.00 | −1.12686 | −0.563432 | − | 0.826163i | \(-0.690519\pi\) | ||||
−0.563432 | + | 0.826163i | \(0.690519\pi\) | |||||||
\(282\) | 2415.42 | − | 470.042i | 0.510058 | − | 0.0992575i | ||||
\(283\) | 4894.75 | − | 4894.75i | 1.02814 | − | 1.02814i | 0.0285448 | − | 0.999593i | \(-0.490913\pi\) |
0.999593 | − | 0.0285448i | \(-0.00908732\pi\) | |||||||
\(284\) | −2135.87 | − | 5280.00i | −0.446269 | − | 1.10321i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3520.00 | + | 5221.00i | −0.727769 | + | 1.07946i | ||||
\(287\) | −2101.90 | − | 2101.90i | −0.432305 | − | 0.432305i | ||||
\(288\) | 2522.67 | + | 1762.41i | 0.516145 | + | 0.360593i | ||||
\(289\) | − | 7759.00i | − | 1.57928i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 2017.21i | − | 0.406360i | ||||||
\(292\) | 5251.09 | + | 2226.32i | 1.05239 | + | 0.446184i | ||||
\(293\) | 371.462 | + | 371.462i | 0.0740650 | + | 0.0740650i | 0.743169 | − | 0.669104i | \(-0.233322\pi\) |
−0.669104 | + | 0.743169i | \(0.733322\pi\) | |||||||
\(294\) | −689.706 | − | 465.000i | −0.136818 | − | 0.0922427i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1408.00 | + | 6644.91i | −0.276481 | + | 1.30482i | ||||
\(297\) | 5837.26 | − | 5837.26i | 1.14044 | − | 1.14044i | ||||
\(298\) | 56.1890 | + | 288.740i | 0.0109226 | + | 0.0561284i | ||||
\(299\) | 5576.98 | 1.07868 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2750.00 | 0.526603 | ||||||||
\(302\) | 961.635 | + | 4941.58i | 0.183231 | + | 0.941577i | ||||
\(303\) | 3090.25 | − | 3090.25i | 0.585908 | − | 0.585908i | ||||
\(304\) | 2729.16 | − | 2640.00i | 0.514895 | − | 0.498074i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −4488.00 | − | 3025.81i | −0.838438 | − | 0.565274i | ||||
\(307\) | 905.608 | + | 905.608i | 0.168357 | + | 0.168357i | 0.786257 | − | 0.617900i | \(-0.212016\pi\) |
−0.617900 | + | 0.786257i | \(0.712016\pi\) | |||||||
\(308\) | 2929.37 | − | 6909.32i | 0.541937 | − | 1.27823i | ||||
\(309\) | − | 4710.00i | − | 0.867128i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10323.3i | 1.88226i | 0.338043 | + | 0.941131i | \(0.390235\pi\) | ||||
−0.338043 | + | 0.941131i | \(0.609765\pi\) | |||||||
\(312\) | −2250.86 | + | 1463.76i | −0.408429 | + | 0.265606i | ||||
\(313\) | 4882.07 | + | 4882.07i | 0.881633 | + | 0.881633i | 0.993701 | − | 0.112068i | \(-0.0357474\pi\) |
−0.112068 | + | 0.993701i | \(0.535747\pi\) | |||||||
\(314\) | −5814.30 | + | 8624.00i | −1.04497 | + | 1.54994i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6160.00 | − | 2491.84i | 1.09660 | − | 0.443598i | ||||
\(317\) | 3104.36 | − | 3104.36i | 0.550026 | − | 0.550026i | −0.376422 | − | 0.926448i | \(-0.622846\pi\) |
0.926448 | + | 0.376422i | \(0.122846\pi\) | |||||||
\(318\) | −329.439 | + | 64.1090i | −0.0580944 | + | 0.0113052i | ||||
\(319\) | −2729.16 | −0.479008 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2450.00 | −0.425999 | ||||||||
\(322\) | −6524.41 | + | 1269.65i | −1.12917 | + | 0.219736i | ||||
\(323\) | −4722.58 | + | 4722.58i | −0.813533 | + | 0.813533i | ||||
\(324\) | −140.908 | + | 57.0000i | −0.0241611 | + | 0.00977366i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 35.0000 | − | 51.9134i | 0.00594623 | − | 0.00881968i | ||||
\(327\) | 1753.08 | + | 1753.08i | 0.296469 | + | 0.296469i | ||||
\(328\) | −3566.19 | + | 2319.14i | −0.600335 | + | 0.390406i | ||||
\(329\) | 4350.00i | 0.728946i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 3144.47i | − | 0.522162i | −0.965317 | − | 0.261081i | \(-0.915921\pi\) | ||
0.965317 | − | 0.261081i | \(-0.0840790\pi\) | |||||||
\(332\) | 977.617 | − | 2305.84i | 0.161608 | − | 0.381173i | ||||
\(333\) | −3608.49 | − | 3608.49i | −0.593826 | − | 0.593826i | ||||
\(334\) | 244.735 | + | 165.000i | 0.0400936 | + | 0.0270311i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2300.00 | − | 2224.86i | 0.373438 | − | 0.361238i | ||||
\(337\) | −4988.20 | + | 4988.20i | −0.806305 | + | 0.806305i | −0.984073 | − | 0.177768i | \(-0.943112\pi\) |
0.177768 | + | 0.984073i | \(0.443112\pi\) | |||||||
\(338\) | −426.280 | − | 2190.54i | −0.0685993 | − | 0.352513i | ||||
\(339\) | −711.955 | −0.114065 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7040.00 | 1.11800 | ||||||||
\(342\) | 544.926 | + | 2800.23i | 0.0861586 | + | 0.442746i | ||||
\(343\) | 4874.63 | − | 4874.63i | 0.767362 | − | 0.767362i | ||||
\(344\) | 815.782 | − | 3850.00i | 0.127860 | − | 0.603425i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7568.00 | − | 5102.34i | −1.17589 | − | 0.792785i | ||||
\(347\) | −3360.81 | − | 3360.81i | −0.519936 | − | 0.519936i | 0.397616 | − | 0.917552i | \(-0.369838\pi\) |
−0.917552 | + | 0.397616i | \(0.869838\pi\) | |||||||
\(348\) | −1071.40 | − | 454.246i | −0.165038 | − | 0.0699717i | ||||
\(349\) | 5774.00i | 0.885602i | 0.896620 | + | 0.442801i | \(0.146015\pi\) | ||||
−0.896620 | + | 0.442801i | \(0.853985\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 5221.00i | − | 0.793950i | ||||||
\(352\) | −8804.06 | − | 6150.76i | −1.33312 | − | 0.931354i | ||||
\(353\) | −424.528 | − | 424.528i | −0.0640095 | − | 0.0640095i | 0.674377 | − | 0.738387i | \(-0.264412\pi\) |
−0.738387 | + | 0.674377i | \(0.764412\pi\) | |||||||
\(354\) | −2076.54 | + | 3080.00i | −0.311770 | + | 0.462430i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2178.00 | − | 5384.16i | −0.324252 | − | 0.801573i | ||||
\(357\) | −3979.95 | + | 3979.95i | −0.590032 | + | 0.590032i | ||||
\(358\) | −1811.91 | + | 352.599i | −0.267493 | + | 0.0520544i | ||||
\(359\) | 7000.89 | 1.02923 | 0.514614 | − | 0.857422i | \(-0.327935\pi\) | ||||
0.514614 | + | 0.857422i | \(0.327935\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3339.00 | −0.486806 | ||||||||
\(362\) | 11666.2 | − | 2270.25i | 1.69382 | − | 0.329618i | ||||
\(363\) | −4894.75 | + | 4894.75i | −0.707735 | + | 0.707735i | ||||
\(364\) | −1779.89 | − | 4400.00i | −0.256295 | − | 0.633579i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 360.000 | − | 533.966i | 0.0514139 | − | 0.0762592i | ||||
\(367\) | −1603.26 | − | 1603.26i | −0.228037 | − | 0.228037i | 0.583835 | − | 0.811872i | \(-0.301551\pi\) |
−0.811872 | + | 0.583835i | \(0.801551\pi\) | |||||||
\(368\) | −157.938 | + | 9510.82i | −0.0223725 | + | 1.34724i | ||||
\(369\) | − | 3196.00i | − | 0.450886i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 593.296i | − | 0.0830253i | ||||||
\(372\) | 2763.73 | + | 1171.75i | 0.385195 | + | 0.163313i | ||||
\(373\) | −1220.52 | − | 1220.52i | −0.169426 | − | 0.169426i | 0.617301 | − | 0.786727i | \(-0.288226\pi\) |
−0.786727 | + | 0.617301i | \(0.788226\pi\) | |||||||
\(374\) | 15663.0 | + | 10560.0i | 2.16555 | + | 1.46001i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6090.00 | + | 1290.42i | 0.835287 | + | 0.176990i | ||||
\(377\) | −1220.52 | + | 1220.52i | −0.166737 | + | 0.166737i | ||||
\(378\) | 1188.61 | + | 6107.96i | 0.161734 | + | 0.831110i | ||||
\(379\) | −1839.22 | −0.249272 | −0.124636 | − | 0.992203i | \(-0.539776\pi\) | ||||
−0.124636 | + | 0.992203i | \(0.539776\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3410.00 | 0.458529 | ||||||||
\(382\) | −2051.49 | − | 10542.0i | −0.274773 | − | 1.41198i | ||||
\(383\) | −8789.98 | + | 8789.98i | −1.17271 | + | 1.17271i | −0.191146 | + | 0.981562i | \(0.561221\pi\) |
−0.981562 | + | 0.191146i | \(0.938779\pi\) | |||||||
\(384\) | −2432.51 | − | 3880.00i | −0.323265 | − | 0.515626i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6072.00 | + | 4093.74i | 0.800665 | + | 0.539808i | ||||
\(387\) | 2090.72 | + | 2090.72i | 0.274619 | + | 0.274619i | ||||
\(388\) | 1991.97 | − | 4698.34i | 0.260637 | − | 0.614748i | ||||
\(389\) | − | 3096.00i | − | 0.403531i | −0.979434 | − | 0.201765i | \(-0.935332\pi\) | ||
0.979434 | − | 0.201765i | \(-0.0646678\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 16730.9i | − | 2.16399i | ||||||
\(392\) | −1147.23 | − | 1764.13i | −0.147817 | − | 0.227301i | ||||
\(393\) | −397.995 | − | 397.995i | −0.0510845 | − | 0.0510845i | ||||
\(394\) | 415.307 | − | 616.000i | 0.0531037 | − | 0.0787656i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 7480.00 | − | 3025.81i | 0.949202 | − | 0.383971i | ||||
\(397\) | −2998.23 | + | 2998.23i | −0.379035 | + | 0.379035i | −0.870754 | − | 0.491719i | \(-0.836369\pi\) |
0.491719 | + | 0.870754i | \(0.336369\pi\) | |||||||
\(398\) | 13177.6 | − | 2564.36i | 1.65963 | − | 0.322964i | ||||
\(399\) | 2966.48 | 0.372205 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1778.00 | −0.221419 | −0.110710 | − | 0.993853i | \(-0.535312\pi\) | ||||
−0.110710 | + | 0.993853i | \(0.535312\pi\) | |||||||
\(402\) | −7412.84 | + | 1442.54i | −0.919699 | + | 0.178974i | ||||
\(403\) | 3148.38 | − | 3148.38i | 0.389162 | − | 0.389162i | ||||
\(404\) | 10249.2 | − | 4146.00i | 1.26217 | − | 0.510572i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1150.00 | − | 1705.73i | 0.140575 | − | 0.208507i | ||||
\(407\) | 12593.5 | + | 12593.5i | 1.53376 | + | 1.53376i | ||||
\(408\) | 4391.29 | + | 6752.57i | 0.532846 | + | 0.819368i | ||||
\(409\) | 5804.00i | 0.701685i | 0.936434 | + | 0.350843i | \(0.114105\pi\) | ||||
−0.936434 | + | 0.350843i | \(0.885895\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2135.87i | 0.256337i | ||||||||
\(412\) | 4651.09 | − | 10970.2i | 0.556171 | − | 1.31181i | ||||
\(413\) | −4643.27 | − | 4643.27i | −0.553222 | − | 0.553222i | ||||
\(414\) | −5925.54 | − | 3995.00i | −0.703441 | − | 0.474260i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −6688.00 | + | 1186.59i | −0.788236 | + | 0.139850i | ||||
\(417\) | −1724.64 | + | 1724.64i | −0.202533 | + | 0.202533i | ||||
\(418\) | −1901.78 | − | 9772.74i | −0.222534 | − | 1.14354i | ||||
\(419\) | 4805.70 | 0.560319 | 0.280159 | − | 0.959953i | \(-0.409613\pi\) | ||||
0.280159 | + | 0.959953i | \(0.409613\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1672.00 | 0.193559 | 0.0967794 | − | 0.995306i | \(-0.469146\pi\) | ||||
0.0967794 | + | 0.995306i | \(0.469146\pi\) | |||||||
\(422\) | −352.599 | − | 1811.91i | −0.0406736 | − | 0.209011i | ||||
\(423\) | −3307.14 | + | 3307.14i | −0.380139 | + | 0.380139i | ||||
\(424\) | −830.614 | − | 176.000i | −0.0951372 | − | 0.0201588i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5280.00 | − | 3559.78i | −0.600509 | − | 0.404863i | ||||
\(427\) | 804.984 | + | 804.984i | 0.0912317 | + | 0.0912317i | ||||
\(428\) | −5706.38 | − | 2419.36i | −0.644458 | − | 0.273234i | ||||
\(429\) | 7040.00i | 0.792295i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 118.659i | 0.0132613i | 0.999978 | + | 0.00663064i | \(0.00211061\pi\) | ||||
−0.999978 | + | 0.00663064i | \(0.997889\pi\) | |||||||
\(432\) | 8903.75 | + | 147.857i | 0.991624 | + | 0.0164671i | ||||
\(433\) | −6394.45 | − | 6394.45i | −0.709695 | − | 0.709695i | 0.256776 | − | 0.966471i | \(-0.417340\pi\) |
−0.966471 | + | 0.256776i | \(0.917340\pi\) | |||||||
\(434\) | −2966.48 | + | 4400.00i | −0.328100 | + | 0.486652i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2352.00 | + | 5814.30i | 0.258349 | + | 0.638657i | ||||
\(437\) | −6235.25 | + | 6235.25i | −0.682546 | + | 0.682546i | ||||
\(438\) | 6259.34 | − | 1218.07i | 0.682838 | − | 0.132881i | ||||
\(439\) | −10560.7 | −1.14814 | −0.574070 | − | 0.818806i | \(-0.694636\pi\) | ||||
−0.574070 | + | 0.818806i | \(0.694636\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1581.00 | 0.170716 | ||||||||
\(442\) | 11727.3 | − | 2282.14i | 1.26201 | − | 0.245589i | ||||
\(443\) | 12153.0 | − | 12153.0i | 1.30340 | − | 1.30340i | 0.377321 | − | 0.926082i | \(-0.376845\pi\) |
0.926082 | − | 0.377321i | \(-0.123155\pi\) | |||||||
\(444\) | 2847.82 | + | 7040.00i | 0.304395 | + | 0.752486i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −335.000 | + | 496.885i | −0.0355666 | + | 0.0527538i | ||||
\(447\) | 232.551 | + | 232.551i | 0.0246069 | + | 0.0246069i | ||||
\(448\) | 7554.04 | − | 2910.76i | 0.796640 | − | 0.306966i | ||||
\(449\) | − | 2476.00i | − | 0.260244i | −0.991498 | − | 0.130122i | \(-0.958463\pi\) | ||
0.991498 | − | 0.130122i | \(-0.0415369\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11154.0i | 1.16457i | ||||||||
\(452\) | −1658.24 | − | 703.050i | −0.172560 | − | 0.0731608i | ||||
\(453\) | 3979.95 | + | 3979.95i | 0.412791 | + | 0.412791i | ||||
\(454\) | −4813.11 | − | 3245.00i | −0.497556 | − | 0.335452i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 880.000 | − | 4153.07i | 0.0903723 | − | 0.426503i | ||||
\(457\) | −8702.82 | + | 8702.82i | −0.890812 | + | 0.890812i | −0.994599 | − | 0.103788i | \(-0.966904\pi\) |
0.103788 | + | 0.994599i | \(0.466904\pi\) | |||||||
\(458\) | 1801.29 | + | 9256.34i | 0.183774 | + | 0.944367i | ||||
\(459\) | −15663.0 | −1.59278 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13918.0 | −1.40613 | −0.703065 | − | 0.711126i | \(-0.748186\pi\) | ||||
−0.703065 | + | 0.711126i | \(0.748186\pi\) | |||||||
\(462\) | −1602.72 | − | 8235.97i | −0.161397 | − | 0.829377i | ||||
\(463\) | −3204.29 | + | 3204.29i | −0.321632 | + | 0.321632i | −0.849393 | − | 0.527761i | \(-0.823032\pi\) |
0.527761 | + | 0.849393i | \(0.323032\pi\) | |||||||
\(464\) | −2046.87 | − | 2116.00i | −0.204792 | − | 0.211709i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3608.00 | − | 2432.51i | −0.358664 | − | 0.241811i | ||||
\(467\) | 1415.43 | + | 1415.43i | 0.140253 | + | 0.140253i | 0.773748 | − | 0.633494i | \(-0.218380\pi\) |
−0.633494 | + | 0.773748i | \(0.718380\pi\) | |||||||
\(468\) | 1991.97 | − | 4698.34i | 0.196750 | − | 0.464062i | ||||
\(469\) | − | 13350.0i | − | 1.31438i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11628.6i | 1.13762i | ||||||||
\(472\) | −7878.00 | + | 5123.17i | −0.768251 | + | 0.499604i | ||||
\(473\) | −7296.57 | − | 7296.57i | −0.709296 | − | 0.709296i | ||||
\(474\) | 4153.07 | − | 6160.00i | 0.402441 | − | 0.596916i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −13200.0 | + | 5339.66i | −1.27105 | + | 0.514166i | ||||
\(477\) | 451.061 | − | 451.061i | 0.0432970 | − | 0.0432970i | ||||
\(478\) | −9553.73 | + | 1859.16i | −0.914179 | + | 0.177900i | ||||
\(479\) | 14476.4 | 1.38089 | 0.690443 | − | 0.723387i | \(-0.257416\pi\) | ||||
0.690443 | + | 0.723387i | \(0.257416\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11264.0 | 1.06776 | ||||||||
\(482\) | −8406.78 | + | 1635.96i | −0.794436 | + | 0.154598i | ||||
\(483\) | −5254.76 | + | 5254.76i | −0.495031 | + | 0.495031i | ||||
\(484\) | −16234.1 | + | 6567.00i | −1.52461 | + | 0.616736i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −6035.00 | + | 8951.35i | −0.563278 | + | 0.835476i | ||||
\(487\) | −494.171 | − | 494.171i | −0.0459816 | − | 0.0459816i | 0.683742 | − | 0.729724i | \(-0.260351\pi\) |
−0.729724 | + | 0.683742i | \(0.760351\pi\) | |||||||
\(488\) | 1365.78 | − | 888.181i | 0.126692 | − | 0.0823895i | ||||
\(489\) | − | 70.0000i | − | 0.00647343i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1245.92i | 0.114517i | 0.998359 | + | 0.0572583i | \(0.0182359\pi\) | ||||
−0.998359 | + | 0.0572583i | \(0.981764\pi\) | |||||||
\(492\) | −1856.48 | + | 4378.77i | −0.170115 | + | 0.401240i | ||||
\(493\) | 3661.55 | + | 3661.55i | 0.334499 | + | 0.334499i | ||||
\(494\) | −5221.00 | − | 3520.00i | −0.475514 | − | 0.320592i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5280.00 | + | 5458.32i | 0.477982 | + | 0.494125i | ||||
\(497\) | 7959.90 | − | 7959.90i | 0.718411 | − | 0.718411i | ||||
\(498\) | −534.876 | − | 2748.58i | −0.0481292 | − | 0.247323i | ||||
\(499\) | 11569.3 | 1.03790 | 0.518950 | − | 0.854805i | \(-0.326323\pi\) | ||||
0.518950 | + | 0.854805i | \(0.326323\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 330.000 | 0.0294278 | ||||||||
\(502\) | 1121.91 | + | 5765.18i | 0.0997474 | + | 0.512575i | ||||
\(503\) | −6549.44 | + | 6549.44i | −0.580567 | + | 0.580567i | −0.935059 | − | 0.354492i | \(-0.884654\pi\) |
0.354492 | + | 0.935059i | \(0.384654\pi\) | |||||||
\(504\) | −1260.75 | + | 5950.00i | −0.111425 | + | 0.525861i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 20680.0 | + | 13942.5i | 1.81687 | + | 1.22494i | ||||
\(507\) | −1764.26 | − | 1764.26i | −0.154543 | − | 0.154543i | ||||
\(508\) | 7942.34 | + | 3367.35i | 0.693670 | + | 0.294098i | ||||
\(509\) | 1554.00i | 0.135324i | 0.997708 | + | 0.0676619i | \(0.0215539\pi\) | ||||
−0.997708 | + | 0.0676619i | \(0.978446\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11272.6i | 0.975874i | ||||||||
\(512\) | −1834.18 | − | 11439.1i | −0.158320 | − | 0.987388i | ||||
\(513\) | 5837.26 | + | 5837.26i | 0.502381 | + | 0.502381i | ||||
\(514\) | 5458.32 | − | 8096.00i | 0.468397 | − | 0.694746i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1650.00 | − | 4078.91i | −0.140770 | − | 0.347992i | ||||
\(517\) | 11541.9 | − | 11541.9i | 0.981838 | − | 0.981838i | ||||
\(518\) | −13177.6 | + | 2564.36i | −1.11774 | + | 0.217513i | ||||
\(519\) | −10204.7 | −0.863075 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5638.00 | −0.474098 | −0.237049 | − | 0.971498i | \(-0.576180\pi\) | ||||
−0.237049 | + | 0.971498i | \(0.576180\pi\) | |||||||
\(522\) | 2171.10 | − | 422.498i | 0.182043 | − | 0.0354257i | ||||
\(523\) | −2475.33 | + | 2475.33i | −0.206957 | + | 0.206957i | −0.802973 | − | 0.596016i | \(-0.796750\pi\) |
0.596016 | + | 0.802973i | \(0.296750\pi\) | |||||||
\(524\) | −533.966 | − | 1320.00i | −0.0445161 | − | 0.110047i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3135.00 | − | 4649.96i | 0.259872 | − | 0.385452i | ||||
\(527\) | −9445.15 | − | 9445.15i | −0.780716 | − | 0.780716i | ||||
\(528\) | −12005.8 | − | 199.370i | −0.989556 | − | 0.0164327i | ||||
\(529\) | − | 9923.00i | − | 0.815567i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 7060.22i | − | 0.577001i | ||||||
\(532\) | 6909.32 | + | 2929.37i | 0.563077 | + | 0.238730i | ||||
\(533\) | 4988.20 | + | 4988.20i | 0.405372 | + | 0.405372i | ||||
\(534\) | −5384.16 | − | 3630.00i | −0.436321 | − | 0.294168i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −18690.0 | − | 3960.25i | −1.50613 | − | 0.319136i | ||||
\(537\) | −1459.31 | + | 1459.31i | −0.117270 | + | 0.117270i | ||||
\(538\) | 2995.30 | + | 15392.1i | 0.240031 | + | 1.23346i | ||||
\(539\) | −5517.65 | −0.440932 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16078.0 | −1.27772 | −0.638861 | − | 0.769322i | \(-0.720594\pi\) | ||||
−0.638861 | + | 0.769322i | \(0.720594\pi\) | |||||||
\(542\) | 2500.25 | + | 12848.1i | 0.198146 | + | 1.01822i | ||||
\(543\) | 9395.96 | − | 9395.96i | 0.742577 | − | 0.742577i | ||||
\(544\) | 3559.78 | + | 20064.0i | 0.280559 | + | 1.58132i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4400.00 | − | 2966.48i | −0.344877 | − | 0.232516i | ||||
\(547\) | −7944.75 | − | 7944.75i | −0.621011 | − | 0.621011i | 0.324779 | − | 0.945790i | \(-0.394710\pi\) |
−0.945790 | + | 0.324779i | \(0.894710\pi\) | |||||||
\(548\) | −2109.15 | + | 4974.71i | −0.164413 | + | 0.387791i | ||||
\(549\) | 1224.00i | 0.0951531i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 2729.16i | − | 0.211009i | ||||||
\(552\) | 5797.85 | + | 8915.48i | 0.447052 | + | 0.687442i | ||||
\(553\) | 9286.55 | + | 9286.55i | 0.714113 | + | 0.714113i | ||||
\(554\) | 3085.14 | − | 4576.00i | 0.236597 | − | 0.350931i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5720.00 | + | 2313.85i | −0.436299 | + | 0.176491i | ||||
\(557\) | −1273.58 | + | 1273.58i | −0.0968824 | + | 0.0968824i | −0.753887 | − | 0.657004i | \(-0.771823\pi\) |
0.657004 | + | 0.753887i | \(0.271823\pi\) | |||||||
\(558\) | −5600.46 | + | 1089.85i | −0.424886 | + | 0.0826831i | ||||
\(559\) | −6526.25 | −0.493795 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21120.0 | 1.58946 | ||||||||
\(562\) | −14736.8 | + | 2867.80i | −1.10611 | + | 0.215250i | ||||
\(563\) | 8803.40 | − | 8803.40i | 0.659004 | − | 0.659004i | −0.296141 | − | 0.955144i | \(-0.595700\pi\) |
0.955144 | + | 0.296141i | \(0.0956997\pi\) | |||||||
\(564\) | 6452.09 | − | 2610.00i | 0.481706 | − | 0.194860i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 10945.0 | − | 16234.1i | 0.812814 | − | 1.20560i | ||||
\(567\) | −212.426 | − | 212.426i | −0.0157338 | − | 0.0157338i | ||||
\(568\) | −8782.57 | − | 13505.1i | −0.648783 | − | 0.997647i | ||||
\(569\) | 24564.0i | 1.80980i | 0.425624 | + | 0.904900i | \(0.360055\pi\) | ||||
−0.425624 | + | 0.904900i | \(0.639945\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 17027.6i | − | 1.24796i | −0.781442 | − | 0.623978i | \(-0.785516\pi\) | ||
0.781442 | − | 0.623978i | \(-0.214484\pi\) | |||||||
\(572\) | −6951.94 | + | 16397.1i | −0.508174 | + | 1.19860i | ||||
\(573\) | −8490.56 | − | 8490.56i | −0.619020 | − | 0.619020i | ||||
\(574\) | −6971.23 | − | 4700.00i | −0.506922 | − | 0.341767i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 7956.00 | + | 3530.11i | 0.575521 | + | 0.255361i | ||||
\(577\) | 13850.2 | − | 13850.2i | 0.999294 | − | 0.999294i | −0.000706135 | − | 1.00000i | \(-0.500225\pi\) |
1.00000 | 0.000706135i | \(0.000224770\pi\) | ||||||||
\(578\) | −4192.02 | − | 21541.7i | −0.301670 | − | 1.55020i | ||||
\(579\) | 8187.48 | 0.587669 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4950.00 | 0.353461 | ||||||||
\(582\) | −1089.85 | − | 5600.46i | −0.0776217 | − | 0.398877i | ||||
\(583\) | −1574.19 | + | 1574.19i | −0.111829 | + | 0.111829i | ||||
\(584\) | 15781.7 | + | 3344.00i | 1.11824 | + | 0.236945i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1232.00 | + | 830.614i | 0.0868489 | + | 0.0585535i | ||||
\(587\) | −2774.96 | − | 2774.96i | −0.195119 | − | 0.195119i | 0.602785 | − | 0.797904i | \(-0.294058\pi\) |
−0.797904 | + | 0.602785i | \(0.794058\pi\) | |||||||
\(588\) | −2166.09 | − | 918.368i | −0.151919 | − | 0.0644096i | ||||
\(589\) | 7040.00i | 0.492493i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 830.614i | − | 0.0578120i | ||||||
\(592\) | −318.992 | + | 19209.3i | −0.0221461 | + | 1.33361i | ||||
\(593\) | 13638.0 | + | 13638.0i | 0.944425 | + | 0.944425i | 0.998535 | − | 0.0541101i | \(-0.0172322\pi\) |
−0.0541101 | + | 0.998535i | \(0.517232\pi\) | |||||||
\(594\) | 13052.5 | − | 19360.0i | 0.901601 | − | 1.33729i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 312.000 | + | 771.285i | 0.0214430 | + | 0.0530085i | ||||
\(597\) | 10613.2 | − | 10613.2i | 0.727587 | − | 0.727587i | ||||
\(598\) | 15483.6 | − | 3013.12i | 1.05882 | − | 0.206046i | ||||
\(599\) | −3559.78 | −0.242819 | −0.121409 | − | 0.992603i | \(-0.538741\pi\) | ||||
−0.121409 | + | 0.992603i | \(0.538741\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2572.00 | 0.174566 | 0.0872829 | − | 0.996184i | \(-0.472182\pi\) | ||||
0.0872829 | + | 0.996184i | \(0.472182\pi\) | |||||||
\(602\) | 7634.95 | − | 1485.77i | 0.516906 | − | 0.100590i | ||||
\(603\) | 10149.5 | − | 10149.5i | 0.685440 | − | 0.685440i | ||||
\(604\) | 5339.66 | + | 13200.0i | 0.359715 | + | 0.889239i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 6910.00 | − | 10249.2i | 0.463201 | − | 0.687038i | ||||
\(607\) | 10945.6 | + | 10945.6i | 0.731905 | + | 0.731905i | 0.970997 | − | 0.239092i | \(-0.0768498\pi\) |
−0.239092 | + | 0.970997i | \(0.576850\pi\) | |||||||
\(608\) | 6150.76 | − | 8804.06i | 0.410274 | − | 0.587256i | ||||
\(609\) | − | 2300.00i | − | 0.153039i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 10323.3i | − | 0.683532i | ||||||
\(612\) | −14095.0 | − | 5975.92i | −0.930976 | − | 0.394710i | ||||
\(613\) | −10109.1 | − | 10109.1i | −0.666071 | − | 0.666071i | 0.290733 | − | 0.956804i | \(-0.406101\pi\) |
−0.956804 | + | 0.290733i | \(0.906101\pi\) | |||||||
\(614\) | 3003.56 | + | 2025.00i | 0.197417 | + | 0.133098i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4400.00 | − | 20765.4i | 0.287794 | − | 1.35821i | ||||
\(617\) | 4961.67 | − | 4961.67i | 0.323743 | − | 0.323743i | −0.526458 | − | 0.850201i | \(-0.676480\pi\) |
0.850201 | + | 0.526458i | \(0.176480\pi\) | |||||||
\(618\) | −2544.71 | − | 13076.6i | −0.165636 | − | 0.851161i | ||||
\(619\) | 19638.1 | 1.27516 | 0.637578 | − | 0.770386i | \(-0.279936\pi\) | ||||
0.637578 | + | 0.770386i | \(0.279936\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −20680.0 | −1.33633 | ||||||||
\(622\) | 5577.48 | + | 28661.2i | 0.359544 | + | 1.84760i | ||||
\(623\) | 8116.93 | − | 8116.93i | 0.521987 | − | 0.521987i | ||||
\(624\) | −5458.32 | + | 5280.00i | −0.350173 | + | 0.338733i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 16192.0 | + | 10916.6i | 1.03381 | + | 0.696992i | ||||
\(627\) | −7870.96 | − | 7870.96i | −0.501333 | − | 0.501333i | ||||
\(628\) | −11483.1 | + | 27084.6i | −0.729662 | + | 1.72101i | ||||
\(629\) | − | 33792.0i | − | 2.14209i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 16493.6i | − | 1.04057i | −0.853992 | − | 0.520286i | \(-0.825825\pi\) | ||
0.853992 | − | 0.520286i | \(-0.174175\pi\) | |||||||
\(632\) | 15756.0 | − | 10246.3i | 0.991678 | − | 0.644901i | ||||
\(633\) | −1459.31 | − | 1459.31i | −0.0916312 | − | 0.0916312i | ||||
\(634\) | 6941.56 | − | 10296.0i | 0.434834 | − | 0.644963i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −880.000 | + | 355.978i | −0.0548652 | + | 0.0221941i | ||||
\(637\) | −2467.57 | + | 2467.57i | −0.153483 | + | 0.153483i | ||||
\(638\) | −7577.10 | + | 1474.51i | −0.470188 | + | 0.0914989i | ||||
\(639\) | 12103.2 | 0.749290 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27492.0 | 1.69402 | 0.847011 | − | 0.531575i | \(-0.178399\pi\) | ||||
0.847011 | + | 0.531575i | \(0.178399\pi\) | |||||||
\(642\) | −6802.05 | + | 1323.68i | −0.418155 | + | 0.0813732i | ||||
\(643\) | −10095.8 | + | 10095.8i | −0.619193 | + | 0.619193i | −0.945325 | − | 0.326131i | \(-0.894255\pi\) |
0.326131 | + | 0.945325i | \(0.394255\pi\) | |||||||
\(644\) | −17428.1 | + | 7050.00i | −1.06640 | + | 0.431380i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10560.0 | + | 15663.0i | −0.643154 | + | 0.953952i | ||||
\(647\) | −14429.3 | − | 14429.3i | −0.876779 | − | 0.876779i | 0.116421 | − | 0.993200i | \(-0.462858\pi\) |
−0.993200 | + | 0.116421i | \(0.962858\pi\) | |||||||
\(648\) | −360.413 | + | 234.381i | −0.0218493 | + | 0.0142089i | ||||
\(649\) | 24640.0i | 1.49030i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5932.96i | 0.357190i | ||||||||
\(652\) | 69.1244 | − | 163.039i | 0.00415203 | − | 0.00979312i | ||||
\(653\) | 21730.5 | + | 21730.5i | 1.30227 | + | 1.30227i | 0.926859 | + | 0.375409i | \(0.122498\pi\) |
0.375409 | + | 0.926859i | \(0.377502\pi\) | |||||||
\(654\) | 5814.30 | + | 3920.00i | 0.347641 | + | 0.234379i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −8648.00 | + | 8365.47i | −0.514707 | + | 0.497891i | ||||
\(657\) | −8570.16 | + | 8570.16i | −0.508910 | + | 0.508910i | ||||
\(658\) | 2350.21 | + | 12077.1i | 0.139241 | + | 0.715524i | ||||
\(659\) | −19400.8 | −1.14681 | −0.573404 | − | 0.819273i | \(-0.694378\pi\) | ||||
−0.573404 | + | 0.819273i | \(0.694378\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6048.00 | −0.355885 | −0.177942 | − | 0.984041i | \(-0.556944\pi\) | ||||
−0.177942 | + | 0.984041i | \(0.556944\pi\) | |||||||
\(662\) | −1698.89 | − | 8730.13i | −0.0997419 | − | 0.512547i | ||||
\(663\) | 9445.15 | − | 9445.15i | 0.553272 | − | 0.553272i | ||||
\(664\) | 1468.41 | − | 6930.00i | 0.0858212 | − | 0.405024i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −11968.0 | − | 8068.82i | −0.696322 | − | 0.469460i | ||||
\(667\) | 4834.38 | + | 4834.38i | 0.280642 | + | 0.280642i | ||||
\(668\) | 768.614 | + | 325.872i | 0.0445188 | + | 0.0188748i | ||||
\(669\) | 670.000i | 0.0387200i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 4271.73i | − | 0.245765i | ||||||
\(672\) | 5183.55 | − | 7419.62i | 0.297559 | − | 0.425920i | ||||
\(673\) | −17538.3 | − | 17538.3i | −1.00454 | − | 1.00454i | −0.999990 | − | 0.00454561i | \(-0.998553\pi\) |
−0.00454561 | − | 0.999990i | \(-0.501447\pi\) | |||||||
\(674\) | −11154.0 | + | 16544.0i | −0.637440 | + | 0.945476i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2367.00 | − | 5851.38i | −0.134672 | − | 0.332919i | ||||
\(677\) | −6712.85 | + | 6712.85i | −0.381087 | + | 0.381087i | −0.871494 | − | 0.490407i | \(-0.836848\pi\) |
0.490407 | + | 0.871494i | \(0.336848\pi\) | |||||||
\(678\) | −1976.63 | + | 384.654i | −0.111965 | + | 0.0217884i | ||||
\(679\) | 10086.0 | 0.570053 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6490.00 | −0.365194 | ||||||||
\(682\) | 19545.5 | − | 3803.56i | 1.09741 | − | 0.213557i | ||||
\(683\) | −22720.7 | + | 22720.7i | −1.27289 | + | 1.27289i | −0.328323 | + | 0.944565i | \(0.606483\pi\) |
−0.944565 | + | 0.328323i | \(0.893517\pi\) | |||||||
\(684\) | 3025.81 | + | 7480.00i | 0.169144 | + | 0.418136i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 10900.0 | − | 16167.3i | 0.606653 | − | 0.899812i | ||||
\(687\) | 7455.05 | + | 7455.05i | 0.414014 | + | 0.414014i | ||||
\(688\) | 184.821 | − | 11129.7i | 0.0102416 | − | 0.616737i | ||||
\(689\) | 1408.00i | 0.0778527i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33877.2i | 1.86505i | 0.361106 | + | 0.932525i | \(0.382399\pi\) | ||||
−0.361106 | + | 0.932525i | \(0.617601\pi\) | |||||||
\(692\) | −23768.1 | − | 10077.0i | −1.30567 | − | 0.553572i | ||||
\(693\) | 11276.5 | + | 11276.5i | 0.618124 | + | 0.618124i | ||||
\(694\) | −11146.5 | − | 7515.00i | −0.609679 | − | 0.411045i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3220.00 | − | 682.290i | −0.175365 | − | 0.0371583i | ||||
\(697\) | 14964.6 | − | 14964.6i | 0.813235 | − | 0.813235i | ||||
\(698\) | 3119.57 | + | 16030.6i | 0.169165 | + | 0.869295i | ||||
\(699\) | −4865.03 | −0.263251 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14928.0 | −0.804312 | −0.402156 | − | 0.915571i | \(-0.631739\pi\) | ||||
−0.402156 | + | 0.915571i | \(0.631739\pi\) | |||||||
\(702\) | −2820.80 | − | 14495.3i | −0.151658 | − | 0.779331i | ||||
\(703\) | −12593.5 | + | 12593.5i | −0.675639 | + | 0.675639i | ||||
\(704\) | −27766.2 | − | 12320.0i | −1.48648 | − | 0.659556i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1408.00 | − | 949.273i | −0.0750578 | − | 0.0506039i | ||||
\(707\) | 15451.2 | + | 15451.2i | 0.821928 | + | 0.821928i | ||||
\(708\) | −4101.12 | + | 9673.05i | −0.217697 | + | 0.513468i | ||||
\(709\) | − | 20966.0i | − | 1.11057i | −0.831660 | − | 0.555285i | \(-0.812609\pi\) | ||
0.831660 | − | 0.555285i | \(-0.187391\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14120.4i | 0.744807i | ||||||||
\(712\) | −8955.83 | − | 13771.6i | −0.471396 | − | 0.724875i | ||||
\(713\) | −12470.5 | − | 12470.5i | −0.655013 | − | 0.655013i | ||||
\(714\) | −8899.44 | + | 13200.0i | −0.466461 | + | 0.691873i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4840.00 | + | 1957.88i | −0.252625 | + | 0.102192i | ||||
\(717\) | −7694.57 | + | 7694.57i | −0.400780 | + | 0.400780i | ||||
\(718\) | 19436.9 | − | 3782.43i | 1.01028 | − | 0.196600i | ||||
\(719\) | −13883.1 | −0.720102 | −0.360051 | − | 0.932933i | \(-0.617241\pi\) | ||||
−0.360051 | + | 0.932933i | \(0.617241\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23550.0 | 1.21643 | ||||||||
\(722\) | −9270.22 | + | 1803.99i | −0.477842 | + | 0.0929883i | ||||
\(723\) | −6770.81 | + | 6770.81i | −0.348284 | + | 0.348284i | ||||
\(724\) | 31162.9 | − | 12606.0i | 1.59967 | − | 0.647097i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −10945.0 | + | 16234.1i | −0.559514 | + | 0.829893i | ||||
\(727\) | −11222.8 | − | 11222.8i | −0.572533 | − | 0.572533i | 0.360302 | − | 0.932836i | \(-0.382673\pi\) |
−0.932836 | + | 0.360302i | \(0.882673\pi\) | |||||||
\(728\) | −7318.81 | − | 11254.3i | −0.372600 | − | 0.572956i | ||||
\(729\) | 11557.0i | 0.587156i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19578.8i | 0.990625i | ||||||||
\(732\) | 710.994 | − | 1676.98i | 0.0359004 | − | 0.0846760i | ||||
\(733\) | −18732.3 | − | 18732.3i | −0.943920 | − | 0.943920i | 0.0545892 | − | 0.998509i | \(-0.482615\pi\) |
−0.998509 | + | 0.0545892i | \(0.982615\pi\) | |||||||
\(734\) | −5317.41 | − | 3585.00i | −0.267397 | − | 0.180279i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4700.00 | + | 26490.7i | 0.235386 | + | 1.32671i | ||||
\(737\) | −35421.6 | + | 35421.6i | −1.77038 | + | 1.77038i | ||||
\(738\) | −1726.73 | − | 8873.20i | −0.0861271 | − | 0.442584i | ||||
\(739\) | −16790.3 | −0.835778 | −0.417889 | − | 0.908498i | \(-0.637230\pi\) | ||||
−0.417889 | + | 0.908498i | \(0.637230\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7040.00 | −0.349016 | ||||||||
\(742\) | −320.545 | − | 1647.19i | −0.0158593 | − | 0.0814965i | ||||
\(743\) | 18078.6 | − | 18078.6i | 0.892651 | − | 0.892651i | −0.102121 | − | 0.994772i | \(-0.532563\pi\) |
0.994772 | + | 0.102121i | \(0.0325628\pi\) | |||||||
\(744\) | 8306.14 | + | 1760.00i | 0.409298 | + | 0.0867268i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −4048.00 | − | 2729.16i | −0.198670 | − | 0.133943i | ||||
\(747\) | 3763.30 | + | 3763.30i | 0.184327 | + | 0.184327i | ||||
\(748\) | 49191.3 | + | 20855.8i | 2.40456 | + | 1.01947i | ||||
\(749\) | − | 12250.0i | − | 0.597604i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1186.59i | − | 0.0576556i | −0.999584 | − | 0.0288278i | \(-0.990823\pi\) | ||
0.999584 | − | 0.0288278i | \(-0.00917744\pi\) | |||||||
\(752\) | 17605.1 | + | 292.353i | 0.853714 | + | 0.0141769i | ||||
\(753\) | 4643.27 | + | 4643.27i | 0.224715 | + | 0.224715i | ||||
\(754\) | −2729.16 | + | 4048.00i | −0.131817 | + | 0.195517i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 6600.00 | + | 16315.6i | 0.317513 | + | 0.784913i | ||||
\(757\) | −14805.4 | + | 14805.4i | −0.710848 | + | 0.710848i | −0.966713 | − | 0.255865i | \(-0.917640\pi\) |
0.255865 | + | 0.966713i | \(0.417640\pi\) | |||||||
\(758\) | −5106.30 | + | 993.689i | −0.244682 | + | 0.0476153i | ||||
\(759\) | 27884.9 | 1.33354 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −678.000 | −0.0322963 | −0.0161481 | − | 0.999870i | \(-0.505140\pi\) | ||||
−0.0161481 | + | 0.999870i | \(0.505140\pi\) | |||||||
\(762\) | 9467.34 | − | 1842.35i | 0.450086 | − | 0.0875870i | ||||
\(763\) | −8765.39 | + | 8765.39i | −0.415896 | + | 0.415896i | ||||
\(764\) | −11391.3 | − | 28160.0i | −0.539427 | − | 1.33350i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −19655.0 | + | 29153.1i | −0.927107 | + | 1.37512i | ||||
\(767\) | 11019.3 | + | 11019.3i | 0.518755 | + | 0.518755i | ||||
\(768\) | −8849.78 | − | 9457.99i | −0.415806 | − | 0.444383i | ||||
\(769\) | − | 10546.0i | − | 0.494536i | −0.968947 | − | 0.247268i | \(-0.920467\pi\) | ||
0.968947 | − | 0.247268i | \(-0.0795329\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 10916.6i | − | 0.509927i | ||||||
\(772\) | 19069.7 | + | 8085.07i | 0.889035 | + | 0.376928i | ||||
\(773\) | −19395.6 | − | 19395.6i | −0.902474 | − | 0.902474i | 0.0931761 | − | 0.995650i | \(-0.470298\pi\) |
−0.995650 | + | 0.0931761i | \(0.970298\pi\) | |||||||
\(774\) | 6934.15 | + | 4675.00i | 0.322019 | + | 0.217105i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2992.00 | − | 14120.4i | 0.138410 | − | 0.653214i | ||||
\(777\) | −10613.2 | + | 10613.2i | −0.490021 | + | 0.490021i | ||||
\(778\) | −1672.70 | − | 8595.57i | −0.0770813 | − | 0.396100i | ||||
\(779\) | −11154.0 | −0.513007 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −42240.0 | −1.93530 | ||||||||
\(782\) | −9039.37 | − | 46450.9i | −0.413359 | − | 2.12414i | ||||
\(783\) | 4525.80 | − | 4525.80i | 0.206563 | − | 0.206563i | ||||
\(784\) | −4138.24 | − | 4278.00i | −0.188513 | − | 0.194880i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1320.00 | − | 889.944i | −0.0599018 | − | 0.0403858i | ||||
\(787\) | 15068.9 | + | 15068.9i | 0.682525 | + | 0.682525i | 0.960568 | − | 0.278044i | \(-0.0896860\pi\) |
−0.278044 | + | 0.960568i | \(0.589686\pi\) | |||||||
\(788\) | 820.225 | − | 1934.61i | 0.0370803 | − | 0.0874590i | ||||
\(789\) | − | 6270.00i | − | 0.282912i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 3559.78i | − | 0.160014i | ||||||
\(792\) | 19132.3 | − | 12442.0i | 0.858379 | − | 0.558215i | ||||
\(793\) | −1910.38 | − | 1910.38i | −0.0855478 | − | 0.0855478i | ||||
\(794\) | −6704.24 | + | 9944.00i | −0.299653 | + | 0.444458i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 35200.0 | − | 14239.1i | 1.56738 | − | 0.634035i | ||||
\(797\) | 17432.2 | − | 17432.2i | 0.774755 | − | 0.774755i | −0.204179 | − | 0.978934i | \(-0.565452\pi\) |
0.978934 | + | 0.204179i | \(0.0654524\pi\) | |||||||
\(798\) | 8235.97 | − | 1602.72i | 0.365351 | − | 0.0710975i | ||||
\(799\) | −30970.0 | −1.37127 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12342.0 | 0.544423 | ||||||||
\(802\) | −4936.34 | + | 960.615i | −0.217342 | + | 0.0422949i | ||||
\(803\) | 29909.6 | − | 29909.6i | 1.31443 | − | 1.31443i | ||||
\(804\) | −19801.2 | + | 8010.00i | −0.868577 | + | 0.351357i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7040.00 | − | 10442.0i | 0.307659 | − | 0.456333i | ||||
\(807\) | 12396.8 | + | 12396.8i | 0.540752 | + | 0.540752i | ||||
\(808\) | 26215.3 | − | 17048.1i | 1.14140 | − | 0.742267i | ||||
\(809\) | 34854.0i | 1.51471i | 0.653003 | + | 0.757356i | \(0.273509\pi\) | ||||
−0.653003 | + | 0.757356i | \(0.726491\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 10738.7i | − | 0.464963i | −0.972601 | − | 0.232482i | \(-0.925315\pi\) | ||
0.972601 | − | 0.232482i | \(-0.0746846\pi\) | |||||||
\(812\) | 2271.23 | − | 5357.01i | 0.0981584 | − | 0.231520i | ||||
\(813\) | 10347.9 | + | 10347.9i | 0.446391 | + | 0.446391i | ||||
\(814\) | 41768.0 | + | 28160.0i | 1.79849 | + | 1.21254i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 15840.0 | + | 16375.0i | 0.679548 | + | 0.702498i | ||||
\(817\) | 7296.57 | − | 7296.57i | 0.312454 | − | 0.312454i | ||||
\(818\) | 3135.78 | + | 16113.9i | 0.134034 | + | 0.688765i | ||||
\(819\) | 10086.0 | 0.430323 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9392.00 | 0.399249 | 0.199624 | − | 0.979873i | \(-0.436028\pi\) | ||||
0.199624 | + | 0.979873i | \(0.436028\pi\) | |||||||
\(822\) | 1153.96 | + | 5929.90i | 0.0489648 | + | 0.251617i | ||||
\(823\) | −31499.5 | + | 31499.5i | −1.33415 | + | 1.33415i | −0.432526 | + | 0.901622i | \(0.642377\pi\) |
−0.901622 | + | 0.432526i | \(0.857623\pi\) | |||||||
\(824\) | 6986.06 | − | 32970.0i | 0.295353 | − | 1.39389i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −15400.0 | − | 10382.7i | −0.648710 | − | 0.437360i | ||||
\(827\) | 22631.2 | + | 22631.2i | 0.951591 | + | 0.951591i | 0.998881 | − | 0.0472905i | \(-0.0150587\pi\) |
−0.0472905 | + | 0.998881i | \(0.515059\pi\) | |||||||
\(828\) | −18609.8 | − | 7890.06i | −0.781080 | − | 0.331158i | ||||
\(829\) | 43384.0i | 1.81760i | 0.417234 | + | 0.908799i | \(0.362999\pi\) | ||||
−0.417234 | + | 0.908799i | \(0.637001\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 6170.28i | − | 0.257575i | ||||||
\(832\) | −17927.1 | + | 6907.77i | −0.747008 | + | 0.287841i | ||||
\(833\) | 7402.71 | + | 7402.71i | 0.307909 | + | 0.307909i | ||||
\(834\) | −3856.42 | + | 5720.00i | −0.160116 | + | 0.237491i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −10560.0 | − | 26105.0i | −0.436872 | − | 1.07998i | ||||
\(837\) | −11674.5 | + | 11674.5i | −0.482115 | + | 0.482115i | ||||
\(838\) | 13342.3 | − | 2596.41i | 0.550002 | − | 0.107031i | ||||
\(839\) | −11747.3 | −0.483385 | −0.241693 | − | 0.970353i | \(-0.577703\pi\) | ||||
−0.241693 | + | 0.970353i | \(0.577703\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22273.0 | 0.913240 | ||||||||
\(842\) | 4642.05 | − | 903.345i | 0.189995 | − | 0.0369731i | ||||
\(843\) | −11869.0 | + | 11869.0i | −0.484925 | + | 0.484925i | ||||
\(844\) | −1957.88 | − | 4840.00i | −0.0798494 | − | 0.197393i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7395.00 | + | 10968.6i | −0.300526 | + | 0.445753i | ||||
\(847\) | −24473.8 | − | 24473.8i | −0.992832 | − | 0.992832i | ||||
\(848\) | −2401.16 | − | 39.8740i | −0.0972361 | − | 0.00161472i | ||||
\(849\) | − | 21890.0i | − | 0.884880i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 44615.9i | − | 1.79719i | ||||||
\(852\) | −16582.4 | − | 7030.50i | −0.666787 | − | 0.282701i | ||||
\(853\) | −17273.0 | − | 17273.0i | −0.693336 | − | 0.693336i | 0.269628 | − | 0.962964i | \(-0.413099\pi\) |
−0.962964 | + | 0.269628i | \(0.913099\pi\) | |||||||
\(854\) | 2669.83 | + | 1800.00i | 0.106979 | + | 0.0721250i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −17150.0 | − | 3633.94i | −0.684784 | − | 0.145100i | ||||
\(857\) | −7376.17 | + | 7376.17i | −0.294009 | + | 0.294009i | −0.838662 | − | 0.544653i | \(-0.816661\pi\) |
0.544653 | + | 0.838662i | \(0.316661\pi\) | |||||||
\(858\) | 3803.56 | + | 19545.5i | 0.151342 | + | 0.777706i | ||||
\(859\) | 43488.6 | 1.72737 | 0.863685 | − | 0.504031i | \(-0.168150\pi\) | ||||
0.863685 | + | 0.504031i | \(0.168150\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9400.00 | −0.372069 | ||||||||
\(862\) | 64.1090 | + | 329.439i | 0.00253313 | + | 0.0130171i | ||||
\(863\) | −8816.82 | + | 8816.82i | −0.347773 | + | 0.347773i | −0.859279 | − | 0.511507i | \(-0.829088\pi\) |
0.511507 | + | 0.859279i | \(0.329088\pi\) | |||||||
\(864\) | 24799.8 | − | 4400.00i | 0.976511 | − | 0.173254i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −21208.0 | − | 14298.4i | −0.832191 | − | 0.561063i | ||||
\(867\) | −17349.7 | − | 17349.7i | −0.679614 | − | 0.679614i | ||||
\(868\) | −5858.75 | + | 13818.6i | −0.229100 | + | 0.540363i | ||||
\(869\) | − | 49280.0i | − | 1.92372i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31682.0i | 1.23250i | ||||||||
\(872\) | 9671.31 | + | 14871.8i | 0.375587 | + | 0.577548i | ||||
\(873\) | 7668.04 | + | 7668.04i | 0.297278 | + | 0.297278i | ||||
\(874\) | −13942.5 | + | 20680.0i | −0.539600 | + | 0.800356i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 16720.0 | − | 6763.57i | 0.644882 | − | 0.260868i | ||||
\(877\) | 6420.99 | − | 6420.99i | 0.247231 | − | 0.247231i | −0.572602 | − | 0.819833i | \(-0.694066\pi\) |
0.819833 | + | 0.572602i | \(0.194066\pi\) | |||||||
\(878\) | −29320.1 | + | 5705.70i | −1.12700 | + | 0.219314i | ||||
\(879\) | 1661.23 | 0.0637450 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22372.0 | 0.855541 | 0.427771 | − | 0.903887i | \(-0.359299\pi\) | ||||
0.427771 | + | 0.903887i | \(0.359299\pi\) | |||||||
\(882\) | 4389.40 | − | 854.180i | 0.167572 | − | 0.0326097i | ||||
\(883\) | 16477.6 | − | 16477.6i | 0.627990 | − | 0.627990i | −0.319572 | − | 0.947562i | \(-0.603539\pi\) |
0.947562 | + | 0.319572i | \(0.103539\pi\) | |||||||
\(884\) | 31326.0 | − | 12672.0i | 1.19186 | − | 0.482133i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 27175.0 | − | 40307.0i | 1.03043 | − | 1.52838i | ||||
\(887\) | −16750.4 | − | 16750.4i | −0.634073 | − | 0.634073i | 0.315014 | − | 0.949087i | \(-0.397991\pi\) |
−0.949087 | + | 0.315014i | \(0.897991\pi\) | |||||||
\(888\) | 11710.1 | + | 18006.9i | 0.442528 | + | 0.680485i | ||||
\(889\) | 17050.0i | 0.643238i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1127.26i | 0.0423846i | ||||||||
\(892\) | −661.620 | + | 1560.52i | −0.0248348 | + | 0.0585763i | ||||
\(893\) | 11541.9 | + | 11541.9i | 0.432512 | + | 0.432512i | ||||
\(894\) | 771.285 | + | 520.000i | 0.0288542 | + | 0.0194535i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 19400.0 | − | 12162.6i | 0.723335 | − | 0.453485i | ||||
\(897\) | 12470.5 | − | 12470.5i | 0.464190 | − | 0.464190i | ||||
\(898\) | −1337.73 | − | 6874.23i | −0.0497111 | − | 0.255452i | ||||
\(899\) | 5458.32 | 0.202497 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4224.00 | 0.156184 | ||||||||
\(902\) | 6026.25 | + | 30967.3i | 0.222452 | + | 1.14312i | ||||
\(903\) | 6149.19 | − | 6149.19i | 0.226614 | − | 0.226614i | ||||
\(904\) | −4983.69 | − | 1056.00i | −0.183357 | − | 0.0388518i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 13200.0 | + | 8899.44i | 0.484040 | + | 0.326340i | ||||
\(907\) | −22886.2 | − | 22886.2i | −0.837842 | − | 0.837842i | 0.150733 | − | 0.988575i | \(-0.451837\pi\) |
−0.988575 | + | 0.150733i | \(0.951837\pi\) | |||||||
\(908\) | −15116.1 | − | 6408.82i | −0.552472 | − | 0.234234i | ||||
\(909\) | 23494.0i | 0.857257i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 24087.8i | − | 0.876032i | −0.898967 | − | 0.438016i | \(-0.855681\pi\) | ||
0.898967 | − | 0.438016i | \(-0.144319\pi\) | |||||||
\(912\) | 199.370 | − | 12005.8i | 0.00723882 | − | 0.435912i | ||||
\(913\) | −13133.8 | − | 13133.8i | −0.476086 | − | 0.476086i | ||||
\(914\) | −19460.1 | + | 28864.0i | −0.704248 | + | 1.04457i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10002.0 | + | 24725.6i | 0.360781 | + | 0.891874i | ||||
\(917\) | 1989.97 | − | 1989.97i | 0.0716628 | − | 0.0716628i | ||||
\(918\) | −43485.9 | + | 8462.39i | −1.56345 | + | 0.304249i | ||||
\(919\) | 34173.8 | 1.22665 | 0.613325 | − | 0.789831i | \(-0.289832\pi\) | ||||
0.613325 | + | 0.789831i | \(0.289832\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4050.00 | 0.144899 | ||||||||
\(922\) | −38641.2 | + | 7519.59i | −1.38024 | + | 0.268595i | ||||
\(923\) | −18890.3 | + | 18890.3i | −0.673653 | + | 0.673653i | ||||
\(924\) | −8899.44 | − | 22000.0i | −0.316851 | − | 0.783276i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −7165.00 | + | 10627.4i | −0.254273 | + | 0.377147i | ||||
\(927\) | 17904.2 | + | 17904.2i | 0.634359 | + | 0.634359i | ||||
\(928\) | −6826.05 | − | 4768.87i | −0.241461 | − | 0.168692i | ||||
\(929\) | − | 13996.0i | − | 0.494288i | −0.968979 | − | 0.247144i | \(-0.920508\pi\) | ||
0.968979 | − | 0.247144i | \(-0.0794921\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 5517.65i | − | 0.194236i | ||||||
\(932\) | −11331.3 | − | 4804.17i | −0.398250 | − | 0.168848i | ||||
\(933\) | 23083.7 | + | 23083.7i | 0.809996 | + | 0.809996i | ||||
\(934\) | 4694.45 | + | 3165.00i | 0.164462 | + | 0.110880i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2992.00 | − | 14120.4i | 0.104484 | − | 0.493099i | ||||
\(937\) | 21677.5 | − | 21677.5i | 0.755786 | − | 0.755786i | −0.219766 | − | 0.975553i | \(-0.570529\pi\) |
0.975553 | + | 0.219766i | \(0.0705295\pi\) | |||||||
\(938\) | −7212.72 | − | 37064.2i | −0.251070 | − | 1.29018i | ||||
\(939\) | 21833.3 | 0.758789 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18078.0 | −0.626276 | −0.313138 | − | 0.949708i | \(-0.601380\pi\) | ||||
−0.313138 | + | 0.949708i | \(0.601380\pi\) | |||||||
\(942\) | 6282.68 | + | 32285.0i | 0.217304 | + | 1.11667i | ||||
\(943\) | 19757.9 | − | 19757.9i | 0.682297 | − | 0.682297i | ||||
\(944\) | −19104.1 | + | 18480.0i | −0.658672 | + | 0.637153i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −24200.0 | − | 16315.6i | −0.831723 | − | 0.560747i | ||||
\(947\) | 7864.25 | + | 7864.25i | 0.269856 | + | 0.269856i | 0.829042 | − | 0.559186i | \(-0.188886\pi\) |
−0.559186 | + | 0.829042i | \(0.688886\pi\) | |||||||
\(948\) | 8202.25 | − | 19346.1i | 0.281009 | − | 0.662798i | ||||
\(949\) | − | 26752.0i | − | 0.915076i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 13883.1i | − | 0.473387i | ||||||
\(952\) | −33762.9 | + | 21956.4i | −1.14943 | + | 0.747492i | ||||
\(953\) | 31680.4 | + | 31680.4i | 1.07684 | + | 1.07684i | 0.996791 | + | 0.0800494i | \(0.0255078\pi\) |
0.0800494 | + | 0.996791i | \(0.474492\pi\) | |||||||
\(954\) | 1008.60 | − | 1496.00i | 0.0342293 | − | 0.0507702i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −25520.0 | + | 10323.3i | −0.863364 | + | 0.349248i | ||||
\(957\) | −6102.59 | + | 6102.59i | −0.206132 | + | 0.206132i | ||||
\(958\) | 40191.6 | − | 7821.30i | 1.35546 | − | 0.263773i | ||||
\(959\) | −10679.3 | −0.359597 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15711.0 | 0.527374 | ||||||||
\(962\) | 31272.8 | − | 6085.70i | 1.04810 | − | 0.203961i | ||||
\(963\) | 9313.22 | − | 9313.22i | 0.311645 | − | 0.311645i | ||||
\(964\) | −22456.2 | + | 9084.00i | −0.750277 | + | 0.303502i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −11750.0 | + | 17428.1i | −0.391356 | + | 0.580475i | ||||
\(967\) | −27228.6 | − | 27228.6i | −0.905494 | − | 0.905494i | 0.0904105 | − | 0.995905i | \(-0.471182\pi\) |
−0.995905 | + | 0.0904105i | \(0.971182\pi\) | |||||||
\(968\) | −41523.4 | + | 27003.2i | −1.37873 | + | 0.896606i | ||||
\(969\) | 21120.0i | 0.700178i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17976.9i | 0.594135i | 0.954856 | + | 0.297067i | \(0.0960086\pi\) | ||||
−0.954856 | + | 0.297067i | \(0.903991\pi\) | |||||||
\(972\) | −11919.0 | + | 28112.6i | −0.393316 | + | 0.927688i | ||||
\(973\) | −8623.22 | − | 8623.22i | −0.284119 | − | 0.284119i | ||||
\(974\) | −1638.98 | − | 1105.00i | −0.0539182 | − | 0.0363516i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3312.00 | − | 3203.80i | 0.108621 | − | 0.105073i | ||||
\(977\) | 36270.6 | − | 36270.6i | 1.18772 | − | 1.18772i | 0.210020 | − | 0.977697i | \(-0.432647\pi\) |
0.977697 | − | 0.210020i | \(-0.0673529\pi\) | |||||||
\(978\) | −37.8195 | − | 194.344i | −0.00123654 | − | 0.00635424i | ||||
\(979\) | −43073.3 | −1.40616 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13328.0 | −0.433772 | ||||||||
\(982\) | 673.144 | + | 3459.11i | 0.0218746 | + | 0.112408i | ||||
\(983\) | 3709.64 | − | 3709.64i | 0.120365 | − | 0.120365i | −0.644358 | − | 0.764724i | \(-0.722875\pi\) |
0.764724 | + | 0.644358i | \(0.222875\pi\) | |||||||
\(984\) | −2788.49 | + | 13160.0i | −0.0903393 | + | 0.426347i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 12144.0 | + | 8187.48i | 0.392235 | + | 0.264445i | ||||
\(987\) | 9726.90 | + | 9726.90i | 0.313688 | + | 0.313688i | ||||
\(988\) | −16397.1 | − | 6951.94i | −0.527997 | − | 0.223857i | ||||
\(989\) | 25850.0i | 0.831125i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30614.1i | 0.981320i | 0.871351 | + | 0.490660i | \(0.163244\pi\) | ||||
−0.871351 | + | 0.490660i | \(0.836756\pi\) | |||||||
\(992\) | 17608.1 | + | 12301.5i | 0.563567 | + | 0.393724i | ||||
\(993\) | −7031.24 | − | 7031.24i | −0.224703 | − | 0.224703i | ||||
\(994\) | 17798.9 | − | 26400.0i | 0.567954 | − | 0.842412i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2970.00 | − | 7342.04i | −0.0944860 | − | 0.233576i | ||||
\(997\) | 34148.0 | − | 34148.0i | 1.08473 | − | 1.08473i | 0.0886702 | − | 0.996061i | \(-0.471738\pi\) |
0.996061 | − | 0.0886702i | \(-0.0282617\pi\) | |||||||
\(998\) | 32120.3 | − | 6250.63i | 1.01879 | − | 0.198257i | ||||
\(999\) | −41768.0 | −1.32280 |
(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 | 100.4.e.d.43.4 | yes | 8 | |
4.3 | odd | 2 | inner | 100.4.e.d.43.3 | yes | 8 | |
5.2 | odd | 4 | inner | 100.4.e.d.7.3 | yes | 8 | |
5.3 | odd | 4 | inner | 100.4.e.d.7.2 | yes | 8 | |
5.4 | even | 2 | inner | 100.4.e.d.43.1 | yes | 8 | |
20.3 | even | 4 | inner | 100.4.e.d.7.1 | ✓ | 8 | |
20.7 | even | 4 | inner | 100.4.e.d.7.4 | yes | 8 | |
20.19 | odd | 2 | inner | 100.4.e.d.43.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
100.4.e.d.7.1 | ✓ | 8 | 20.3 | even | 4 | inner | |
100.4.e.d.7.2 | yes | 8 | 5.3 | odd | 4 | inner | |
100.4.e.d.7.3 | yes | 8 | 5.2 | odd | 4 | inner | |
100.4.e.d.7.4 | yes | 8 | 20.7 | even | 4 | inner | |
100.4.e.d.43.1 | yes | 8 | 5.4 | even | 2 | inner | |
100.4.e.d.43.2 | yes | 8 | 20.19 | odd | 2 | inner | |
100.4.e.d.43.3 | yes | 8 | 4.3 | odd | 2 | inner | |
100.4.e.d.43.4 | yes | 8 | 1.1 | even | 1 | trivial |