Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [39,4,Mod(5,39)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(39, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("39.5");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 39 = 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 39.f (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: | \(2.30107449022\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 1316x^{16} + 520390x^{12} + 64668772x^{8} + 2536036097x^{4} + 8509693504 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 5.3 | ||
Root | \(-2.26335 + 2.26335i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 39.5 |
Dual form | 39.4.f.b.8.3 |
$q$-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 \(\left(\mathbb{Z}/39\mathbb{Z}\right)^\times\).
\(n\) | \(14\) | \(28\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.26335 | − | 2.26335i | −0.800217 | − | 0.800217i | 0.182912 | − | 0.983129i | \(-0.441448\pi\) |
−0.983129 | + | 0.182912i | \(0.941448\pi\) | |||||||
\(3\) | 2.15347 | − | 4.72891i | 0.414436 | − | 0.910079i | ||||
\(4\) | 2.24555i | 0.280694i | ||||||||
\(5\) | 0.350510 | + | 0.350510i | 0.0313506 | + | 0.0313506i | 0.722608 | − | 0.691258i | \(-0.242943\pi\) |
−0.691258 | + | 0.722608i | \(0.742943\pi\) | |||||||
\(6\) | −15.5773 | + | 5.82912i | −1.05990 | + | 0.396622i | ||||
\(7\) | −7.24142 | − | 7.24142i | −0.391000 | − | 0.391000i | 0.484044 | − | 0.875044i | \(-0.339167\pi\) |
−0.875044 | + | 0.484044i | \(0.839167\pi\) | |||||||
\(8\) | −13.0244 | + | 13.0244i | −0.575601 | + | 0.575601i | ||||
\(9\) | −17.7251 | − | 20.3671i | −0.656486 | − | 0.754338i | ||||
\(10\) | − | 1.58666i | − | 0.0501745i | ||||||
\(11\) | −0.0601824 | + | 0.0601824i | −0.00164961 | + | 0.00164961i | −0.707931 | − | 0.706281i | \(-0.750371\pi\) |
0.706281 | + | 0.707931i | \(0.250371\pi\) | |||||||
\(12\) | 10.6190 | + | 4.83573i | 0.255453 | + | 0.116330i | ||||
\(13\) | 38.0081 | − | 27.4297i | 0.810888 | − | 0.585202i | ||||
\(14\) | 32.7798i | 0.625769i | ||||||||
\(15\) | 2.41234 | − | 0.902716i | 0.0415243 | − | 0.0155387i | ||||
\(16\) | 76.9219 | 1.20190 | ||||||||
\(17\) | 58.1275 | 0.829293 | 0.414647 | − | 0.909982i | \(-0.363905\pi\) | ||||
0.414647 | + | 0.909982i | \(0.363905\pi\) | |||||||
\(18\) | −5.97982 | + | 86.2163i | −0.0783032 | + | 1.12897i | ||||
\(19\) | 20.4339 | − | 20.4339i | 0.246730 | − | 0.246730i | −0.572897 | − | 0.819627i | \(-0.694181\pi\) |
0.819627 | + | 0.572897i | \(0.194181\pi\) | |||||||
\(20\) | −0.787088 | + | 0.787088i | −0.00879991 | + | 0.00879991i | ||||
\(21\) | −49.8382 | + | 18.6498i | −0.517885 | + | 0.193796i | ||||
\(22\) | 0.272428 | 0.00264009 | ||||||||
\(23\) | 93.7819 | 0.850212 | 0.425106 | − | 0.905143i | \(-0.360237\pi\) | ||||
0.425106 | + | 0.905143i | \(0.360237\pi\) | |||||||
\(24\) | 33.5434 | + | 89.6386i | 0.285292 | + | 0.762392i | ||||
\(25\) | − | 124.754i | − | 0.998034i | ||||||
\(26\) | −148.109 | − | 23.9426i | −1.11717 | − | 0.180598i | ||||
\(27\) | −134.485 | + | 39.9604i | −0.958578 | + | 0.284829i | ||||
\(28\) | 16.2610 | − | 16.2610i | 0.109751 | − | 0.109751i | ||||
\(29\) | − | 189.233i | − | 1.21171i | −0.795574 | − | 0.605856i | \(-0.792831\pi\) | ||
0.795574 | − | 0.605856i | \(-0.207169\pi\) | |||||||
\(30\) | −7.50315 | − | 3.41682i | −0.0456627 | − | 0.0207941i | ||||
\(31\) | −173.538 | + | 173.538i | −1.00543 | + | 1.00543i | −0.00544479 | + | 0.999985i | \(0.501733\pi\) |
−0.999985 | + | 0.00544479i | \(0.998267\pi\) | |||||||
\(32\) | −69.9066 | − | 69.9066i | −0.386183 | − | 0.386183i | ||||
\(33\) | 0.154996 | + | 0.414198i | 0.000817616 | + | 0.00218493i | ||||
\(34\) | −131.563 | − | 131.563i | −0.663614 | − | 0.663614i | ||||
\(35\) | − | 5.07638i | − | 0.0245161i | ||||||
\(36\) | 45.7354 | − | 39.8026i | 0.211738 | − | 0.184271i | ||||
\(37\) | 247.149 | + | 247.149i | 1.09813 | + | 1.09813i | 0.994629 | + | 0.103506i | \(0.0330060\pi\) |
0.103506 | + | 0.994629i | \(0.466994\pi\) | |||||||
\(38\) | −92.4984 | −0.394874 | ||||||||
\(39\) | −47.8631 | − | 238.806i | −0.196519 | − | 0.980500i | ||||
\(40\) | −9.13034 | −0.0360908 | ||||||||
\(41\) | 132.516 | + | 132.516i | 0.504767 | + | 0.504767i | 0.912916 | − | 0.408148i | \(-0.133825\pi\) |
−0.408148 | + | 0.912916i | \(0.633825\pi\) | |||||||
\(42\) | 155.013 | + | 70.5903i | 0.569499 | + | 0.259341i | ||||
\(43\) | 277.604i | 0.984517i | 0.870449 | + | 0.492259i | \(0.163829\pi\) | ||||
−0.870449 | + | 0.492259i | \(0.836171\pi\) | |||||||
\(44\) | −0.135143 | − | 0.135143i | −0.000463034 | − | 0.000463034i | ||||
\(45\) | 0.926053 | − | 13.3517i | 0.00306773 | − | 0.0442302i | ||||
\(46\) | −212.262 | − | 212.262i | −0.680354 | − | 0.680354i | ||||
\(47\) | 219.429 | − | 219.429i | 0.681002 | − | 0.681002i | −0.279224 | − | 0.960226i | \(-0.590077\pi\) |
0.960226 | + | 0.279224i | \(0.0900773\pi\) | |||||||
\(48\) | 165.649 | − | 363.757i | 0.498112 | − | 1.09383i | ||||
\(49\) | − | 238.124i | − | 0.694238i | ||||||
\(50\) | −282.363 | + | 282.363i | −0.798644 | + | 0.798644i | ||||
\(51\) | 125.176 | − | 274.879i | 0.343689 | − | 0.754722i | ||||
\(52\) | 61.5947 | + | 85.3490i | 0.164262 | + | 0.227611i | ||||
\(53\) | 582.835i | 1.51054i | 0.655414 | + | 0.755270i | \(0.272494\pi\) | ||||
−0.655414 | + | 0.755270i | \(0.727506\pi\) | |||||||
\(54\) | 394.831 | + | 213.942i | 0.994995 | + | 0.539146i | ||||
\(55\) | −0.0421891 | −0.000103432 | ||||||||
\(56\) | 188.630 | 0.450120 | ||||||||
\(57\) | −52.6262 | − | 140.634i | −0.122290 | − | 0.326797i | ||||
\(58\) | −428.301 | + | 428.301i | −0.969633 | + | 0.969633i | ||||
\(59\) | −396.700 | + | 396.700i | −0.875356 | + | 0.875356i | −0.993050 | − | 0.117694i | \(-0.962450\pi\) |
0.117694 | + | 0.993050i | \(0.462450\pi\) | |||||||
\(60\) | 2.02709 | + | 5.41704i | 0.00436161 | + | 0.0116556i | ||||
\(61\) | −244.208 | −0.512585 | −0.256293 | − | 0.966599i | \(-0.582501\pi\) | ||||
−0.256293 | + | 0.966599i | \(0.582501\pi\) | |||||||
\(62\) | 785.556 | 1.60912 | ||||||||
\(63\) | −19.1319 | + | 275.842i | −0.0382603 | + | 0.551632i | ||||
\(64\) | − | 298.928i | − | 0.583844i | ||||||
\(65\) | 22.9366 | + | 3.70783i | 0.0437682 | + | 0.00707539i | ||||
\(66\) | 0.586667 | − | 1.28829i | 0.00109415 | − | 0.00240269i | ||||
\(67\) | −44.4298 | + | 44.4298i | −0.0810145 | + | 0.0810145i | −0.746453 | − | 0.665438i | \(-0.768245\pi\) |
0.665438 | + | 0.746453i | \(0.268245\pi\) | |||||||
\(68\) | 130.528i | 0.232777i | ||||||||
\(69\) | 201.957 | − | 443.486i | 0.352359 | − | 0.773760i | ||||
\(70\) | −11.4896 | + | 11.4896i | −0.0196182 | + | 0.0196182i | ||||
\(71\) | −454.877 | − | 454.877i | −0.760338 | − | 0.760338i | 0.216046 | − | 0.976383i | \(-0.430684\pi\) |
−0.976383 | + | 0.216046i | \(0.930684\pi\) | |||||||
\(72\) | 496.127 | + | 34.4106i | 0.812072 | + | 0.0563240i | ||||
\(73\) | 430.182 | + | 430.182i | 0.689712 | + | 0.689712i | 0.962168 | − | 0.272456i | \(-0.0878361\pi\) |
−0.272456 | + | 0.962168i | \(0.587836\pi\) | |||||||
\(74\) | − | 1118.77i | − | 1.75749i | ||||||
\(75\) | −589.951 | − | 268.655i | −0.908290 | − | 0.413621i | ||||
\(76\) | 45.8854 | + | 45.8854i | 0.0692555 | + | 0.0692555i | ||||
\(77\) | 0.871612 | 0.00128999 | ||||||||
\(78\) | −432.171 | + | 648.833i | −0.627355 | + | 0.941870i | ||||
\(79\) | 637.325 | 0.907653 | 0.453827 | − | 0.891090i | \(-0.350059\pi\) | ||||
0.453827 | + | 0.891090i | \(0.350059\pi\) | |||||||
\(80\) | 26.9619 | + | 26.9619i | 0.0376804 | + | 0.0376804i | ||||
\(81\) | −100.640 | + | 722.020i | −0.138053 | + | 0.990425i | ||||
\(82\) | − | 599.860i | − | 0.807846i | ||||||
\(83\) | −868.087 | − | 868.087i | −1.14801 | − | 1.14801i | −0.986943 | − | 0.161068i | \(-0.948506\pi\) |
−0.161068 | − | 0.986943i | \(-0.551494\pi\) | |||||||
\(84\) | −41.8790 | − | 111.914i | −0.0543974 | − | 0.145367i | ||||
\(85\) | 20.3743 | + | 20.3743i | 0.0259988 | + | 0.0259988i | ||||
\(86\) | 628.317 | − | 628.317i | 0.787827 | − | 0.787827i | ||||
\(87\) | −894.865 | − | 407.508i | −1.10275 | − | 0.502177i | ||||
\(88\) | − | 1.56768i | − | 0.00189903i | ||||||
\(89\) | −477.014 | + | 477.014i | −0.568128 | + | 0.568128i | −0.931604 | − | 0.363476i | \(-0.881590\pi\) |
0.363476 | + | 0.931604i | \(0.381590\pi\) | |||||||
\(90\) | −32.3157 | + | 28.1237i | −0.0378486 | + | 0.0329389i | ||||
\(91\) | −473.862 | − | 76.6025i | −0.545871 | − | 0.0882431i | ||||
\(92\) | 210.592i | 0.238649i | ||||||||
\(93\) | 446.936 | + | 1194.35i | 0.498334 | + | 1.33171i | ||||
\(94\) | −993.294 | −1.08990 | ||||||||
\(95\) | 14.3246 | 0.0154702 | ||||||||
\(96\) | −481.124 | + | 180.040i | −0.511505 | + | 0.191409i | ||||
\(97\) | 168.184 | − | 168.184i | 0.176046 | − | 0.176046i | −0.613584 | − | 0.789630i | \(-0.710273\pi\) |
0.789630 | + | 0.613584i | \(0.210273\pi\) | |||||||
\(98\) | −538.959 | + | 538.959i | −0.555541 | + | 0.555541i | ||||
\(99\) | 2.29248 | + | 0.159003i | 0.00232731 | + | 0.000161418i | ||||
\(100\) | 280.142 | 0.280142 | ||||||||
\(101\) | 1773.86 | 1.74758 | 0.873791 | − | 0.486301i | \(-0.161654\pi\) | ||||
0.873791 | + | 0.486301i | \(0.161654\pi\) | |||||||
\(102\) | −905.467 | + | 338.832i | −0.878967 | + | 0.328916i | ||||
\(103\) | 1309.11i | 1.25233i | 0.779689 | + | 0.626167i | \(0.215377\pi\) | ||||
−0.779689 | + | 0.626167i | \(0.784623\pi\) | |||||||
\(104\) | −137.777 | + | 852.285i | −0.129905 | + | 0.803590i | ||||
\(105\) | −24.0057 | − | 10.9318i | −0.0223116 | − | 0.0101604i | ||||
\(106\) | 1319.16 | − | 1319.16i | 1.20876 | − | 1.20876i | ||||
\(107\) | − | 373.388i | − | 0.337353i | −0.985671 | − | 0.168677i | \(-0.946051\pi\) | ||
0.985671 | − | 0.168677i | \(-0.0539494\pi\) | |||||||
\(108\) | −89.7330 | − | 301.992i | −0.0799497 | − | 0.269067i | ||||
\(109\) | 1439.45 | − | 1439.45i | 1.26490 | − | 1.26490i | 0.316214 | − | 0.948688i | \(-0.397588\pi\) |
0.948688 | − | 0.316214i | \(-0.102412\pi\) | |||||||
\(110\) | 0.0954889 | + | 0.0954889i | 8.27682e−5 | + | 8.27682e-5i | ||||
\(111\) | 1700.97 | − | 636.515i | 1.45449 | − | 0.544282i | ||||
\(112\) | −557.023 | − | 557.023i | −0.469944 | − | 0.469944i | ||||
\(113\) | 1299.74i | 1.08203i | 0.841013 | + | 0.541014i | \(0.181960\pi\) | ||||
−0.841013 | + | 0.541014i | \(0.818040\pi\) | |||||||
\(114\) | −199.193 | + | 437.416i | −0.163650 | + | 0.359367i | ||||
\(115\) | 32.8715 | + | 32.8715i | 0.0266547 | + | 0.0266547i | ||||
\(116\) | 424.932 | 0.340120 | ||||||||
\(117\) | −1232.36 | − | 287.921i | −0.973776 | − | 0.227507i | ||||
\(118\) | 1795.75 | 1.40095 | ||||||||
\(119\) | −420.925 | − | 420.925i | −0.324253 | − | 0.324253i | ||||
\(120\) | −19.6619 | + | 43.1765i | −0.0149573 | + | 0.0328455i | ||||
\(121\) | 1330.99i | 0.999995i | ||||||||
\(122\) | 552.730 | + | 552.730i | 0.410179 | + | 0.410179i | ||||
\(123\) | 912.022 | − | 341.285i | 0.668572 | − | 0.250184i | ||||
\(124\) | −389.688 | − | 389.688i | −0.282218 | − | 0.282218i | ||||
\(125\) | 87.5414 | − | 87.5414i | 0.0626395 | − | 0.0626395i | ||||
\(126\) | 667.630 | − | 581.026i | 0.472042 | − | 0.410809i | ||||
\(127\) | − | 825.698i | − | 0.576920i | −0.957492 | − | 0.288460i | \(-0.906857\pi\) | ||
0.957492 | − | 0.288460i | \(-0.0931432\pi\) | |||||||
\(128\) | −1235.83 | + | 1235.83i | −0.853385 | + | 0.853385i | ||||
\(129\) | 1312.76 | + | 597.813i | 0.895988 | + | 0.408019i | ||||
\(130\) | −43.5215 | − | 60.3058i | −0.0293622 | − | 0.0406859i | ||||
\(131\) | 276.713i | 0.184554i | 0.995733 | + | 0.0922768i | \(0.0294144\pi\) | ||||
−0.995733 | + | 0.0922768i | \(0.970586\pi\) | |||||||
\(132\) | −0.930102 | + | 0.348051i | −0.000613296 | + | 0.000229500i | ||||
\(133\) | −295.941 | −0.192942 | ||||||||
\(134\) | 201.121 | 0.129658 | ||||||||
\(135\) | −61.1448 | − | 33.1318i | −0.0389815 | − | 0.0211224i | ||||
\(136\) | −757.074 | + | 757.074i | −0.477342 | + | 0.477342i | ||||
\(137\) | 144.788 | − | 144.788i | 0.0902925 | − | 0.0902925i | −0.660518 | − | 0.750810i | \(-0.729663\pi\) |
0.750810 | + | 0.660518i | \(0.229663\pi\) | |||||||
\(138\) | −1460.87 | + | 546.666i | −0.901139 | + | 0.337213i | ||||
\(139\) | −2444.55 | −1.49168 | −0.745841 | − | 0.666124i | \(-0.767952\pi\) | ||||
−0.745841 | + | 0.666124i | \(0.767952\pi\) | |||||||
\(140\) | 11.3993 | 0.00688152 | ||||||||
\(141\) | −565.126 | − | 1510.20i | −0.337534 | − | 0.901997i | ||||
\(142\) | 2059.10i | 1.21687i | ||||||||
\(143\) | −0.636633 | + | 3.93820i | −0.000372293 | + | 0.00230300i | ||||
\(144\) | −1363.45 | − | 1566.68i | −0.789033 | − | 0.906643i | ||||
\(145\) | 66.3280 | − | 66.3280i | 0.0379879 | − | 0.0379879i | ||||
\(146\) | − | 1947.31i | − | 1.10384i | ||||||
\(147\) | −1126.07 | − | 512.793i | −0.631812 | − | 0.287717i | ||||
\(148\) | −554.984 | + | 554.984i | −0.308239 | + | 0.308239i | ||||
\(149\) | −934.262 | − | 934.262i | −0.513676 | − | 0.513676i | 0.401975 | − | 0.915651i | \(-0.368324\pi\) |
−0.915651 | + | 0.401975i | \(0.868324\pi\) | |||||||
\(150\) | 727.208 | + | 1943.33i | 0.395842 | + | 1.05782i | ||||
\(151\) | −683.199 | − | 683.199i | −0.368198 | − | 0.368198i | 0.498621 | − | 0.866820i | \(-0.333840\pi\) |
−0.866820 | + | 0.498621i | \(0.833840\pi\) | |||||||
\(152\) | 532.278i | 0.284036i | ||||||||
\(153\) | −1030.32 | − | 1183.89i | −0.544419 | − | 0.625568i | ||||
\(154\) | −1.97277 | − | 1.97277i | −0.00103227 | − | 0.00103227i | ||||
\(155\) | −121.654 | −0.0630416 | ||||||||
\(156\) | 536.250 | − | 107.479i | 0.275220 | − | 0.0551615i | ||||
\(157\) | −116.097 | −0.0590160 | −0.0295080 | − | 0.999565i | \(-0.509394\pi\) | ||||
−0.0295080 | + | 0.999565i | \(0.509394\pi\) | |||||||
\(158\) | −1442.49 | − | 1442.49i | −0.726319 | − | 0.726319i | ||||
\(159\) | 2756.17 | + | 1255.12i | 1.37471 | + | 0.626022i | ||||
\(160\) | − | 49.0060i | − | 0.0242141i | ||||||
\(161\) | −679.114 | − | 679.114i | −0.332433 | − | 0.332433i | ||||
\(162\) | 1861.97 | − | 1406.40i | 0.903027 | − | 0.682083i | ||||
\(163\) | −267.153 | − | 267.153i | −0.128374 | − | 0.128374i | 0.640000 | − | 0.768375i | \(-0.278934\pi\) |
−0.768375 | + | 0.640000i | \(0.778934\pi\) | |||||||
\(164\) | −297.570 | + | 297.570i | −0.141685 | + | 0.141685i | ||||
\(165\) | −0.0908530 | + | 0.199508i | −4.28660e−5 | + | 9.41315e-5i | ||||
\(166\) | 3929.58i | 1.83732i | ||||||||
\(167\) | 2454.42 | − | 2454.42i | 1.13730 | − | 1.13730i | 0.148366 | − | 0.988932i | \(-0.452598\pi\) |
0.988932 | − | 0.148366i | \(-0.0474015\pi\) | |||||||
\(168\) | 406.209 | − | 892.012i | 0.186546 | − | 0.409644i | ||||
\(169\) | 692.226 | − | 2085.10i | 0.315078 | − | 0.949066i | ||||
\(170\) | − | 92.2284i | − | 0.0416094i | ||||||
\(171\) | −778.374 | − | 53.9868i | −0.348092 | − | 0.0241431i | ||||
\(172\) | −623.374 | −0.276348 | ||||||||
\(173\) | 702.152 | 0.308576 | 0.154288 | − | 0.988026i | \(-0.450692\pi\) | ||||
0.154288 | + | 0.988026i | \(0.450692\pi\) | |||||||
\(174\) | 1103.06 | + | 2947.73i | 0.480591 | + | 1.28429i | ||||
\(175\) | −903.398 | + | 903.398i | −0.390231 | + | 0.390231i | ||||
\(176\) | −4.62935 | + | 4.62935i | −0.00198267 | + | 0.00198267i | ||||
\(177\) | 1021.68 | + | 2730.24i | 0.433864 | + | 1.15942i | ||||
\(178\) | 2159.30 | 0.909251 | ||||||||
\(179\) | 343.109 | 0.143269 | 0.0716345 | − | 0.997431i | \(-0.477178\pi\) | ||||
0.0716345 | + | 0.997431i | \(0.477178\pi\) | |||||||
\(180\) | 29.9819 | + | 2.07950i | 0.0124151 | + | 0.000861093i | ||||
\(181\) | − | 2707.33i | − | 1.11179i | −0.831252 | − | 0.555895i | \(-0.812376\pi\) | ||
0.831252 | − | 0.555895i | \(-0.187624\pi\) | |||||||
\(182\) | 899.139 | + | 1245.90i | 0.366201 | + | 0.507428i | ||||
\(183\) | −525.896 | + | 1154.84i | −0.212434 | + | 0.466493i | ||||
\(184\) | −1221.45 | + | 1221.45i | −0.489383 | + | 0.489383i | ||||
\(185\) | 173.256i | 0.0688543i | ||||||||
\(186\) | 1691.67 | − | 3714.82i | 0.666879 | − | 1.46443i | ||||
\(187\) | −3.49825 | + | 3.49825i | −0.00136801 | + | 0.00136801i | ||||
\(188\) | 492.740 | + | 492.740i | 0.191153 | + | 0.191153i | ||||
\(189\) | 1263.23 | + | 684.491i | 0.486172 | + | 0.263436i | ||||
\(190\) | −32.4216 | − | 32.4216i | −0.0123795 | − | 0.0123795i | ||||
\(191\) | 3556.56i | 1.34735i | 0.739029 | + | 0.673674i | \(0.235285\pi\) | ||||
−0.739029 | + | 0.673674i | \(0.764715\pi\) | |||||||
\(192\) | −1413.60 | − | 643.733i | −0.531344 | − | 0.241966i | ||||
\(193\) | −59.4885 | − | 59.4885i | −0.0221869 | − | 0.0221869i | 0.695926 | − | 0.718113i | \(-0.254994\pi\) |
−0.718113 | + | 0.695926i | \(0.754994\pi\) | |||||||
\(194\) | −761.319 | −0.281750 | ||||||||
\(195\) | 66.9273 | − | 100.480i | 0.0245783 | − | 0.0369002i | ||||
\(196\) | 534.719 | 0.194868 | ||||||||
\(197\) | 229.292 | + | 229.292i | 0.0829258 | + | 0.0829258i | 0.747353 | − | 0.664427i | \(-0.231324\pi\) |
−0.664427 | + | 0.747353i | \(0.731324\pi\) | |||||||
\(198\) | −4.82882 | − | 5.54858i | −0.00173318 | − | 0.00199152i | ||||
\(199\) | 4289.02i | 1.52784i | 0.645310 | + | 0.763921i | \(0.276728\pi\) | ||||
−0.645310 | + | 0.763921i | \(0.723272\pi\) | |||||||
\(200\) | 1624.85 | + | 1624.85i | 0.574469 | + | 0.574469i | ||||
\(201\) | 114.426 | + | 305.783i | 0.0401542 | + | 0.107305i | ||||
\(202\) | −4014.88 | − | 4014.88i | −1.39844 | − | 1.39844i | ||||
\(203\) | −1370.31 | + | 1370.31i | −0.473779 | + | 0.473779i | ||||
\(204\) | 617.255 | + | 281.089i | 0.211846 | + | 0.0964713i | ||||
\(205\) | 92.8961i | 0.0316495i | ||||||||
\(206\) | 2962.98 | − | 2962.98i | 1.00214 | − | 1.00214i | ||||
\(207\) | −1662.30 | − | 1910.07i | −0.558152 | − | 0.641348i | ||||
\(208\) | 2923.65 | − | 2109.94i | 0.974610 | − | 0.703357i | ||||
\(209\) | 2.45953i | 0.000814014i | ||||||||
\(210\) | 29.5908 | + | 79.0761i | 0.00972363 | + | 0.0259846i | ||||
\(211\) | −927.050 | −0.302468 | −0.151234 | − | 0.988498i | \(-0.548325\pi\) | ||||
−0.151234 | + | 0.988498i | \(0.548325\pi\) | |||||||
\(212\) | −1308.79 | −0.423999 | ||||||||
\(213\) | −3130.64 | + | 1171.51i | −1.00708 | + | 0.376856i | ||||
\(214\) | −845.110 | + | 845.110i | −0.269956 | + | 0.269956i | ||||
\(215\) | −97.3031 | + | 97.3031i | −0.0308652 | + | 0.0308652i | ||||
\(216\) | 1231.12 | − | 2272.04i | 0.387811 | − | 0.715706i | ||||
\(217\) | 2513.32 | 0.786246 | ||||||||
\(218\) | −6515.97 | −2.02439 | ||||||||
\(219\) | 2960.67 | − | 1107.90i | 0.913533 | − | 0.341851i | ||||
\(220\) | − | 0.0947377i | − | 2.90328e-5i | ||||||
\(221\) | 2209.31 | − | 1594.42i | 0.672464 | − | 0.485304i | ||||
\(222\) | −5290.56 | − | 2409.24i | −1.59946 | − | 0.728367i | ||||
\(223\) | −287.402 | + | 287.402i | −0.0863043 | + | 0.0863043i | −0.748941 | − | 0.662637i | \(-0.769437\pi\) |
0.662637 | + | 0.748941i | \(0.269437\pi\) | |||||||
\(224\) | 1012.45i | 0.301995i | ||||||||
\(225\) | −2540.89 | + | 2211.28i | −0.752856 | + | 0.655195i | ||||
\(226\) | 2941.77 | − | 2941.77i | 0.865858 | − | 0.865858i | ||||
\(227\) | 3982.28 | + | 3982.28i | 1.16438 | + | 1.16438i | 0.983507 | + | 0.180869i | \(0.0578910\pi\) |
0.180869 | + | 0.983507i | \(0.442109\pi\) | |||||||
\(228\) | 315.801 | − | 118.175i | 0.0917298 | − | 0.0343260i | ||||
\(229\) | 1178.36 | + | 1178.36i | 0.340035 | + | 0.340035i | 0.856380 | − | 0.516346i | \(-0.172708\pi\) |
−0.516346 | + | 0.856380i | \(0.672708\pi\) | |||||||
\(230\) | − | 148.800i | − | 0.0426590i | ||||||
\(231\) | 1.87699 | − | 4.12177i | 0.000534619 | − | 0.00117399i | ||||
\(232\) | 2464.64 | + | 2464.64i | 0.697463 | + | 0.697463i | ||||
\(233\) | −5811.46 | −1.63400 | −0.816999 | − | 0.576639i | \(-0.804364\pi\) | ||||
−0.816999 | + | 0.576639i | \(0.804364\pi\) | |||||||
\(234\) | 2137.60 | + | 3440.94i | 0.597177 | + | 0.961287i | ||||
\(235\) | 153.825 | 0.0426996 | ||||||||
\(236\) | −890.810 | − | 890.810i | −0.245707 | − | 0.245707i | ||||
\(237\) | 1372.46 | − | 3013.85i | 0.376164 | − | 0.826036i | ||||
\(238\) | 1905.41i | 0.518946i | ||||||||
\(239\) | −521.832 | − | 521.832i | −0.141232 | − | 0.141232i | 0.632956 | − | 0.774188i | \(-0.281841\pi\) |
−0.774188 | + | 0.632956i | \(0.781841\pi\) | |||||||
\(240\) | 185.562 | − | 69.4386i | 0.0499082 | − | 0.0186760i | ||||
\(241\) | −2758.93 | − | 2758.93i | −0.737421 | − | 0.737421i | 0.234657 | − | 0.972078i | \(-0.424603\pi\) |
−0.972078 | + | 0.234657i | \(0.924603\pi\) | |||||||
\(242\) | 3012.51 | − | 3012.51i | 0.800212 | − | 0.800212i | ||||
\(243\) | 3197.64 | + | 2030.77i | 0.844150 | + | 0.536106i | ||||
\(244\) | − | 548.382i | − | 0.143879i | ||||||
\(245\) | 83.4648 | − | 83.4648i | 0.0217648 | − | 0.0217648i | ||||
\(246\) | −2836.68 | − | 1291.78i | −0.735204 | − | 0.334801i | ||||
\(247\) | 216.158 | − | 1337.15i | 0.0556834 | − | 0.344457i | ||||
\(248\) | − | 4520.44i | − | 1.15745i | ||||||
\(249\) | −5974.50 | + | 2235.70i | −1.52056 | + | 0.569003i | ||||
\(250\) | −396.274 | −0.100250 | ||||||||
\(251\) | −2175.12 | −0.546981 | −0.273491 | − | 0.961875i | \(-0.588178\pi\) | ||||
−0.273491 | + | 0.961875i | \(0.588178\pi\) | |||||||
\(252\) | −619.416 | − | 42.9617i | −0.154840 | − | 0.0107394i | ||||
\(253\) | −5.64402 | + | 5.64402i | −0.00140252 | + | 0.00140252i | ||||
\(254\) | −1868.85 | + | 1868.85i | −0.461661 | + | 0.461661i | ||||
\(255\) | 140.223 | − | 52.4726i | 0.0344358 | − | 0.0128861i | ||||
\(256\) | 3202.83 | 0.781942 | ||||||||
\(257\) | 1163.64 | 0.282436 | 0.141218 | − | 0.989979i | \(-0.454898\pi\) | ||||
0.141218 | + | 0.989979i | \(0.454898\pi\) | |||||||
\(258\) | −1618.19 | − | 4324.31i | −0.390481 | − | 1.04349i | ||||
\(259\) | − | 3579.41i | − | 0.858741i | ||||||
\(260\) | −8.32612 | + | 51.5052i | −0.00198602 | + | 0.0122855i | ||||
\(261\) | −3854.13 | + | 3354.18i | −0.914041 | + | 0.795472i | ||||
\(262\) | 626.299 | − | 626.299i | 0.147683 | − | 0.147683i | ||||
\(263\) | 1652.99i | 0.387559i | 0.981045 | + | 0.193779i | \(0.0620746\pi\) | ||||
−0.981045 | + | 0.193779i | \(0.937925\pi\) | |||||||
\(264\) | −7.41339 | − | 3.37594i | −0.00172827 | − | 0.000787027i | ||||
\(265\) | −204.290 | + | 204.290i | −0.0473563 | + | 0.0473563i | ||||
\(266\) | 669.820 | + | 669.820i | 0.154396 | + | 0.154396i | ||||
\(267\) | 1228.52 | + | 3282.99i | 0.281588 | + | 0.752494i | ||||
\(268\) | −99.7694 | − | 99.7694i | −0.0227402 | − | 0.0227402i | ||||
\(269\) | − | 3584.47i | − | 0.812449i | −0.913773 | − | 0.406225i | \(-0.866845\pi\) | ||
0.913773 | − | 0.406225i | \(-0.133155\pi\) | |||||||
\(270\) | 63.4034 | + | 213.381i | 0.0142911 | + | 0.0480962i | ||||
\(271\) | −220.676 | − | 220.676i | −0.0494653 | − | 0.0494653i | 0.681941 | − | 0.731407i | \(-0.261136\pi\) |
−0.731407 | + | 0.681941i | \(0.761136\pi\) | |||||||
\(272\) | 4471.28 | 0.996732 | ||||||||
\(273\) | −1382.69 | + | 2075.89i | −0.306537 | + | 0.460214i | ||||
\(274\) | −655.413 | −0.144507 | ||||||||
\(275\) | 7.50801 | + | 7.50801i | 0.00164636 | + | 0.00164636i | ||||
\(276\) | 995.870 | + | 453.504i | 0.217190 | + | 0.0989048i | ||||
\(277\) | 550.383i | 0.119384i | 0.998217 | + | 0.0596919i | \(0.0190118\pi\) | ||||
−0.998217 | + | 0.0596919i | \(0.980988\pi\) | |||||||
\(278\) | 5532.88 | + | 5532.88i | 1.19367 | + | 1.19367i | ||||
\(279\) | 6610.45 | + | 458.490i | 1.41848 | + | 0.0983838i | ||||
\(280\) | 66.1166 | + | 66.1166i | 0.0141115 | + | 0.0141115i | ||||
\(281\) | −4713.18 | + | 4713.18i | −1.00059 | + | 1.00059i | −0.000586773 | 1.00000i | \(0.500187\pi\) | |
−1.00000 | 0.000586773i | \(0.999813\pi\) | ||||||||
\(282\) | −2139.03 | + | 4697.19i | −0.451693 | + | 0.991893i | ||||
\(283\) | − | 1465.49i | − | 0.307824i | −0.988085 | − | 0.153912i | \(-0.950813\pi\) | ||
0.988085 | − | 0.153912i | \(-0.0491872\pi\) | |||||||
\(284\) | 1021.45 | − | 1021.45i | 0.213422 | − | 0.213422i | ||||
\(285\) | 30.8476 | − | 67.7397i | 0.00641142 | − | 0.0140791i | ||||
\(286\) | 10.3545 | − | 7.47262i | 0.00214081 | − | 0.00154498i | ||||
\(287\) | − | 1919.20i | − | 0.394728i | ||||||
\(288\) | −184.695 | + | 2662.90i | −0.0377890 | + | 0.544837i | ||||
\(289\) | −1534.19 | −0.312272 | ||||||||
\(290\) | −300.248 | −0.0607971 | ||||||||
\(291\) | −433.147 | − | 1157.50i | −0.0872560 | − | 0.233176i | ||||
\(292\) | −965.994 | + | 965.994i | −0.193598 | + | 0.193598i | ||||
\(293\) | 4976.72 | − | 4976.72i | 0.992297 | − | 0.992297i | −0.00767353 | − | 0.999971i | \(-0.502443\pi\) |
0.999971 | + | 0.00767353i | \(0.00244258\pi\) | |||||||
\(294\) | 1388.05 | + | 3709.32i | 0.275350 | + | 0.735822i | ||||
\(295\) | −278.095 | −0.0548858 | ||||||||
\(296\) | −6437.91 | −1.26417 | ||||||||
\(297\) | 5.68871 | − | 10.4985i | 0.00111142 | − | 0.00205113i | ||||
\(298\) | 4229.13i | 0.822105i | ||||||||
\(299\) | 3564.47 | − | 2572.41i | 0.689427 | − | 0.497546i | ||||
\(300\) | 603.278 | − | 1324.76i | 0.116101 | − | 0.254951i | ||||
\(301\) | 2010.25 | − | 2010.25i | 0.384946 | − | 0.384946i | ||||
\(302\) | 3092.64i | 0.589277i | ||||||||
\(303\) | 3819.96 | − | 8388.43i | 0.724261 | − | 1.59044i | ||||
\(304\) | 1571.82 | − | 1571.82i | 0.296546 | − | 0.296546i | ||||
\(305\) | −85.5975 | − | 85.5975i | −0.0160698 | − | 0.0160698i | ||||
\(306\) | −347.592 | + | 5011.54i | −0.0649363 | + | 0.936243i | ||||
\(307\) | 1119.82 | + | 1119.82i | 0.208181 | + | 0.208181i | 0.803494 | − | 0.595313i | \(-0.202972\pi\) |
−0.595313 | + | 0.803494i | \(0.702972\pi\) | |||||||
\(308\) | 1.95725i | 0.000362093i | ||||||||
\(309\) | 6190.66 | + | 2819.13i | 1.13972 | + | 0.519013i | ||||
\(310\) | 275.345 | + | 275.345i | 0.0504470 | + | 0.0504470i | ||||
\(311\) | 1793.81 | 0.327067 | 0.163534 | − | 0.986538i | \(-0.447711\pi\) | ||||
0.163534 | + | 0.986538i | \(0.447711\pi\) | |||||||
\(312\) | 3733.68 | + | 2486.91i | 0.677493 | + | 0.451260i | ||||
\(313\) | 7542.23 | 1.36202 | 0.681010 | − | 0.732274i | \(-0.261541\pi\) | ||||
0.681010 | + | 0.732274i | \(0.261541\pi\) | |||||||
\(314\) | 262.768 | + | 262.768i | 0.0472256 | + | 0.0472256i | ||||
\(315\) | −103.391 | + | 89.9794i | −0.0184935 | + | 0.0160945i | ||||
\(316\) | 1431.14i | 0.254773i | ||||||||
\(317\) | −3785.41 | − | 3785.41i | −0.670693 | − | 0.670693i | 0.287183 | − | 0.957876i | \(-0.407281\pi\) |
−0.957876 | + | 0.287183i | \(0.907281\pi\) | |||||||
\(318\) | −3397.42 | − | 9078.98i | −0.599112 | − | 1.60102i | ||||
\(319\) | 11.3885 | + | 11.3885i | 0.00199885 | + | 0.00199885i | ||||
\(320\) | 104.777 | − | 104.777i | 0.0183038 | − | 0.0183038i | ||||
\(321\) | −1765.72 | − | 804.081i | −0.307018 | − | 0.139811i | ||||
\(322\) | 3074.15i | 0.532037i | ||||||||
\(323\) | 1187.77 | − | 1187.77i | 0.204611 | − | 0.204611i | ||||
\(324\) | −1621.33 | − | 225.993i | −0.278006 | − | 0.0387505i | ||||
\(325\) | −3421.97 | − | 4741.67i | −0.584051 | − | 0.809294i | ||||
\(326\) | 1209.32i | 0.205455i | ||||||||
\(327\) | −3707.21 | − | 9906.84i | −0.626939 | − | 1.67538i | ||||
\(328\) | −3451.86 | −0.581089 | ||||||||
\(329\) | −3177.96 | −0.532543 | ||||||||
\(330\) | 0.657191 | − | 0.245925i | 0.000109628 | − | 4.10235e-5i | ||||
\(331\) | −3829.32 | + | 3829.32i | −0.635886 | + | 0.635886i | −0.949538 | − | 0.313652i | \(-0.898447\pi\) |
0.313652 | + | 0.949538i | \(0.398447\pi\) | |||||||
\(332\) | 1949.33 | − | 1949.33i | 0.322240 | − | 0.322240i | ||||
\(333\) | 652.971 | − | 9414.45i | 0.107455 | − | 1.54927i | ||||
\(334\) | −11110.5 | −1.82017 | ||||||||
\(335\) | −31.1462 | −0.00507970 | ||||||||
\(336\) | −3833.65 | + | 1434.58i | −0.622448 | + | 0.232925i | ||||
\(337\) | 9715.03i | 1.57036i | 0.619268 | + | 0.785180i | \(0.287429\pi\) | ||||
−0.619268 | + | 0.785180i | \(0.712571\pi\) | |||||||
\(338\) | −6286.07 | + | 3152.56i | −1.01159 | + | 0.507328i | ||||
\(339\) | 6146.35 | + | 2798.95i | 0.984731 | + | 0.448432i | ||||
\(340\) | −45.7514 | + | 45.7514i | −0.00729771 | + | 0.00729771i | ||||
\(341\) | − | 20.8879i | − | 0.00331713i | ||||||
\(342\) | 1639.55 | + | 1883.93i | 0.259229 | + | 0.297869i | ||||
\(343\) | −4208.16 | + | 4208.16i | −0.662447 | + | 0.662447i | ||||
\(344\) | −3615.62 | − | 3615.62i | −0.566689 | − | 0.566689i | ||||
\(345\) | 226.234 | − | 84.6585i | 0.0353045 | − | 0.0132112i | ||||
\(346\) | −1589.22 | − | 1589.22i | −0.246928 | − | 0.246928i | ||||
\(347\) | 703.045i | 0.108765i | 0.998520 | + | 0.0543825i | \(0.0173190\pi\) | ||||
−0.998520 | + | 0.0543825i | \(0.982681\pi\) | |||||||
\(348\) | 915.079 | − | 2009.46i | 0.140958 | − | 0.309536i | ||||
\(349\) | −6231.70 | − | 6231.70i | −0.955802 | − | 0.955802i | 0.0432615 | − | 0.999064i | \(-0.486225\pi\) |
−0.999064 | + | 0.0432615i | \(0.986225\pi\) | |||||||
\(350\) | 4089.42 | 0.624539 | ||||||||
\(351\) | −4015.41 | + | 5207.69i | −0.610617 | + | 0.791926i | ||||
\(352\) | 8.41430 | 0.00127410 | ||||||||
\(353\) | 4606.02 | + | 4606.02i | 0.694486 | + | 0.694486i | 0.963216 | − | 0.268729i | \(-0.0866038\pi\) |
−0.268729 | + | 0.963216i | \(0.586604\pi\) | |||||||
\(354\) | 3867.09 | − | 8491.92i | 0.580603 | − | 1.27497i | ||||
\(355\) | − | 318.878i | − | 0.0476740i | ||||||
\(356\) | −1071.16 | − | 1071.16i | −0.159470 | − | 0.159470i | ||||
\(357\) | −2896.97 | + | 1084.07i | −0.429478 | + | 0.160714i | ||||
\(358\) | −776.577 | − | 776.577i | −0.114646 | − | 0.114646i | ||||
\(359\) | −8688.79 | + | 8688.79i | −1.27737 | + | 1.27737i | −0.335240 | + | 0.942133i | \(0.608818\pi\) |
−0.942133 | + | 0.335240i | \(0.891182\pi\) | |||||||
\(360\) | 161.836 | + | 185.959i | 0.0236931 | + | 0.0272247i | ||||
\(361\) | 6023.91i | 0.878249i | ||||||||
\(362\) | −6127.64 | + | 6127.64i | −0.889674 | + | 0.889674i | ||||
\(363\) | 6294.14 | + | 2866.26i | 0.910074 | + | 0.414434i | ||||
\(364\) | 172.015 | − | 1064.08i | 0.0247693 | − | 0.153222i | ||||
\(365\) | 301.566i | 0.0432457i | ||||||||
\(366\) | 3804.10 | − | 1423.52i | 0.543288 | − | 0.203302i | ||||
\(367\) | −3039.03 | −0.432251 | −0.216125 | − | 0.976366i | \(-0.569342\pi\) | ||||
−0.216125 | + | 0.976366i | \(0.569342\pi\) | |||||||
\(368\) | 7213.89 | 1.02187 | ||||||||
\(369\) | 350.108 | − | 5047.82i | 0.0493927 | − | 0.712138i | ||||
\(370\) | 392.140 | − | 392.140i | 0.0550984 | − | 0.0550984i | ||||
\(371\) | 4220.55 | − | 4220.55i | 0.590620 | − | 0.590620i | ||||
\(372\) | −2681.98 | + | 1003.62i | −0.373802 | + | 0.139879i | ||||
\(373\) | 4113.21 | 0.570975 | 0.285488 | − | 0.958382i | \(-0.407844\pi\) | ||||
0.285488 | + | 0.958382i | \(0.407844\pi\) | |||||||
\(374\) | 15.8356 | 0.00218941 | ||||||||
\(375\) | −225.457 | − | 602.493i | −0.0310468 | − | 0.0829670i | ||||
\(376\) | 5715.86i | 0.783970i | ||||||||
\(377\) | −5190.60 | − | 7192.38i | −0.709096 | − | 0.982563i | ||||
\(378\) | −1309.89 | − | 4408.38i | −0.178237 | − | 0.599849i | ||||
\(379\) | 3541.54 | − | 3541.54i | 0.479992 | − | 0.479992i | −0.425137 | − | 0.905129i | \(-0.639774\pi\) |
0.905129 | + | 0.425137i | \(0.139774\pi\) | |||||||
\(380\) | 32.1666i | 0.00434240i | ||||||||
\(381\) | −3904.65 | − | 1778.12i | −0.525042 | − | 0.239096i | ||||
\(382\) | 8049.75 | − | 8049.75i | 1.07817 | − | 1.07817i | ||||
\(383\) | −495.148 | − | 495.148i | −0.0660598 | − | 0.0660598i | 0.673305 | − | 0.739365i | \(-0.264874\pi\) |
−0.739365 | + | 0.673305i | \(0.764874\pi\) | |||||||
\(384\) | 3182.81 | + | 8505.47i | 0.422974 | + | 1.13032i | ||||
\(385\) | 0.305509 | + | 0.305509i | 4.04420e−5 | + | 4.04420e-5i | ||||
\(386\) | 269.287i | 0.0355087i | ||||||||
\(387\) | 5654.00 | − | 4920.57i | 0.742659 | − | 0.646322i | ||||
\(388\) | 377.665 | + | 377.665i | 0.0494151 | + | 0.0494151i | ||||
\(389\) | 7976.07 | 1.03960 | 0.519798 | − | 0.854289i | \(-0.326007\pi\) | ||||
0.519798 | + | 0.854289i | \(0.326007\pi\) | |||||||
\(390\) | −378.903 | + | 75.9423i | −0.0491961 | + | 0.00986023i | ||||
\(391\) | 5451.31 | 0.705076 | ||||||||
\(392\) | 3101.41 | + | 3101.41i | 0.399604 | + | 0.399604i | ||||
\(393\) | 1308.55 | + | 595.893i | 0.167958 | + | 0.0764856i | ||||
\(394\) | − | 1037.94i | − | 0.132717i | ||||||
\(395\) | 223.389 | + | 223.389i | 0.0284555 | + | 0.0284555i | ||||
\(396\) | −0.357049 | + | 5.14789i | −4.53090e−5 | + | 0.000653260i | ||||
\(397\) | 3273.29 | + | 3273.29i | 0.413807 | + | 0.413807i | 0.883063 | − | 0.469255i | \(-0.155478\pi\) |
−0.469255 | + | 0.883063i | \(0.655478\pi\) | |||||||
\(398\) | 9707.57 | − | 9707.57i | 1.22260 | − | 1.22260i | ||||
\(399\) | −637.301 | + | 1399.48i | −0.0799623 | + | 0.175593i | ||||
\(400\) | − | 9596.34i | − | 1.19954i | ||||||
\(401\) | −8314.24 | + | 8314.24i | −1.03539 | + | 1.03539i | −0.0360441 | + | 0.999350i | \(0.511476\pi\) |
−0.999350 | + | 0.0360441i | \(0.988524\pi\) | |||||||
\(402\) | 433.108 | − | 951.082i | 0.0537350 | − | 0.117999i | ||||
\(403\) | −1835.75 | + | 11355.9i | −0.226911 | + | 1.40367i | ||||
\(404\) | 3983.29i | 0.490535i | ||||||||
\(405\) | −288.351 | + | 217.800i | −0.0353784 | + | 0.0267224i | ||||
\(406\) | 6203.01 | 0.758252 | ||||||||
\(407\) | −29.7480 | −0.00362298 | ||||||||
\(408\) | 1949.79 | + | 5210.47i | 0.236591 | + | 0.632246i | ||||
\(409\) | 7048.05 | − | 7048.05i | 0.852087 | − | 0.852087i | −0.138303 | − | 0.990390i | \(-0.544165\pi\) |
0.990390 | + | 0.138303i | \(0.0441646\pi\) | |||||||
\(410\) | 210.257 | − | 210.257i | 0.0253265 | − | 0.0253265i | ||||
\(411\) | −372.892 | − | 996.486i | −0.0447528 | − | 0.119594i | ||||
\(412\) | −2939.67 | −0.351523 | ||||||||
\(413\) | 5745.35 | 0.684528 | ||||||||
\(414\) | −560.799 | + | 8085.53i | −0.0665743 | + | 0.959860i | ||||
\(415\) | − | 608.547i | − | 0.0719816i | ||||||
\(416\) | −4574.53 | − | 739.500i | −0.539146 | − | 0.0871562i | ||||
\(417\) | −5264.27 | + | 11560.0i | −0.618207 | + | 1.35755i | ||||
\(418\) | 5.56678 | − | 5.56678i | 0.000651388 | − | 0.000651388i | ||||
\(419\) | 7049.75i | 0.821963i | 0.911644 | + | 0.410982i | \(0.134814\pi\) | ||||
−0.911644 | + | 0.410982i | \(0.865186\pi\) | |||||||
\(420\) | 24.5480 | − | 53.9060i | 0.00285195 | − | 0.00626273i | ||||
\(421\) | −3428.49 | + | 3428.49i | −0.396899 | + | 0.396899i | −0.877138 | − | 0.480239i | \(-0.840550\pi\) |
0.480239 | + | 0.877138i | \(0.340550\pi\) | |||||||
\(422\) | 2098.24 | + | 2098.24i | 0.242040 | + | 0.242040i | ||||
\(423\) | −8358.56 | − | 579.736i | −0.960774 | − | 0.0666377i | ||||
\(424\) | −7591.06 | − | 7591.06i | −0.869468 | − | 0.869468i | ||||
\(425\) | − | 7251.65i | − | 0.827663i | ||||||
\(426\) | 9737.27 | + | 4434.21i | 1.10745 | + | 0.504314i | ||||
\(427\) | 1768.41 | + | 1768.41i | 0.200421 | + | 0.200421i | ||||
\(428\) | 838.462 | 0.0946930 | ||||||||
\(429\) | 17.2524 | + | 11.4914i | 0.00194162 | + | 0.00129326i | ||||
\(430\) | 440.463 | 0.0493977 | ||||||||
\(431\) | 5002.08 | + | 5002.08i | 0.559029 | + | 0.559029i | 0.929031 | − | 0.370002i | \(-0.120643\pi\) |
−0.370002 | + | 0.929031i | \(0.620643\pi\) | |||||||
\(432\) | −10344.8 | + | 3073.83i | −1.15212 | + | 0.342337i | ||||
\(433\) | 3256.29i | 0.361402i | 0.983538 | + | 0.180701i | \(0.0578367\pi\) | ||||
−0.983538 | + | 0.180701i | \(0.942163\pi\) | |||||||
\(434\) | −5688.54 | − | 5688.54i | −0.629167 | − | 0.629167i | ||||
\(435\) | −170.824 | − | 456.495i | −0.0188284 | − | 0.0503155i | ||||
\(436\) | 3232.36 | + | 3232.36i | 0.355050 | + | 0.355050i | ||||
\(437\) | 1916.33 | − | 1916.33i | 0.209773 | − | 0.209773i | ||||
\(438\) | −9208.63 | − | 4193.47i | −1.00458 | − | 0.457470i | ||||
\(439\) | − | 6361.30i | − | 0.691591i | −0.938310 | − | 0.345795i | \(-0.887609\pi\) | ||
0.938310 | − | 0.345795i | \(-0.112391\pi\) | |||||||
\(440\) | 0.549486 | − | 0.549486i | 5.95357e−5 | − | 5.95357e-5i | ||||
\(441\) | −4849.90 | + | 4220.77i | −0.523691 | + | 0.455758i | ||||
\(442\) | −8609.19 | − | 1391.73i | −0.926465 | − | 0.149768i | ||||
\(443\) | − | 11204.8i | − | 1.20171i | −0.799359 | − | 0.600854i | \(-0.794827\pi\) | ||
0.799359 | − | 0.600854i | \(-0.205173\pi\) | |||||||
\(444\) | 1429.33 | + | 3819.61i | 0.152777 | + | 0.408268i | ||||
\(445\) | −334.396 | −0.0356223 | ||||||||
\(446\) | 1300.99 | 0.138124 | ||||||||
\(447\) | −6429.95 | + | 2406.13i | −0.680372 | + | 0.254600i | ||||
\(448\) | −2164.66 | + | 2164.66i | −0.228283 | + | 0.228283i | ||||
\(449\) | −4510.62 | + | 4510.62i | −0.474096 | + | 0.474096i | −0.903237 | − | 0.429141i | \(-0.858816\pi\) |
0.429141 | + | 0.903237i | \(0.358816\pi\) | |||||||
\(450\) | 10755.9 | + | 746.008i | 1.12675 | + | 0.0781493i | ||||
\(451\) | −15.9502 | −0.00166534 | ||||||||
\(452\) | −2918.63 | −0.303719 | ||||||||
\(453\) | −4702.04 | + | 1759.54i | −0.487684 | + | 0.182495i | ||||
\(454\) | − | 18026.6i | − | 1.86351i | ||||||
\(455\) | −139.243 | − | 192.943i | −0.0143469 | − | 0.0198798i | ||||
\(456\) | 2517.09 | + | 1146.24i | 0.258495 | + | 0.117715i | ||||
\(457\) | 6380.62 | − | 6380.62i | 0.653113 | − | 0.653113i | −0.300628 | − | 0.953741i | \(-0.597196\pi\) |
0.953741 | + | 0.300628i | \(0.0971963\pi\) | |||||||
\(458\) | − | 5334.07i | − | 0.544203i | ||||||
\(459\) | −7817.27 | + | 2322.80i | −0.794943 | + | 0.236207i | ||||
\(460\) | −73.8146 | + | 73.8146i | −0.00748179 | + | 0.00748179i | ||||
\(461\) | −5380.50 | − | 5380.50i | −0.543590 | − | 0.543590i | 0.380990 | − | 0.924579i | \(-0.375583\pi\) |
−0.924579 | + | 0.380990i | \(0.875583\pi\) | |||||||
\(462\) | −13.5773 | + | 5.08073i | −0.00136726 | + | 0.000511639i | ||||
\(463\) | 5694.54 | + | 5694.54i | 0.571594 | + | 0.571594i | 0.932574 | − | 0.360980i | \(-0.117558\pi\) |
−0.360980 | + | 0.932574i | \(0.617558\pi\) | |||||||
\(464\) | − | 14556.2i | − | 1.45636i | ||||||
\(465\) | −261.978 | + | 575.288i | −0.0261267 | + | 0.0573728i | ||||
\(466\) | 13153.4 | + | 13153.4i | 1.30755 | + | 1.30755i | ||||
\(467\) | −13135.9 | −1.30162 | −0.650811 | − | 0.759240i | \(-0.725571\pi\) | ||||
−0.650811 | + | 0.759240i | \(0.725571\pi\) | |||||||
\(468\) | 646.541 | − | 2767.33i | 0.0638598 | − | 0.273333i | ||||
\(469\) | 643.470 | 0.0633533 | ||||||||
\(470\) | −348.159 | − | 348.159i | −0.0341689 | − | 0.0341689i | ||||
\(471\) | −250.011 | + | 549.010i | −0.0244583 | + | 0.0537092i | ||||
\(472\) | − | 10333.5i | − | 1.00771i | ||||||
\(473\) | −16.7069 | − | 16.7069i | −0.00162407 | − | 0.00162407i | ||||
\(474\) | −9927.77 | + | 3715.04i | −0.962021 | + | 0.359995i | ||||
\(475\) | −2549.22 | − | 2549.22i | −0.246245 | − | 0.246245i | ||||
\(476\) | 945.209 | − | 945.209i | 0.0910159 | − | 0.0910159i | ||||
\(477\) | 11870.7 | − | 10330.8i | 1.13946 | − | 0.991648i | ||||
\(478\) | 2362.18i | 0.226033i | ||||||||
\(479\) | 1999.71 | − | 1999.71i | 0.190749 | − | 0.190749i | −0.605270 | − | 0.796020i | \(-0.706935\pi\) |
0.796020 | + | 0.605270i | \(0.206935\pi\) | |||||||
\(480\) | −231.745 | − | 105.533i | −0.0220368 | − | 0.0100352i | ||||
\(481\) | 16172.8 | + | 2614.43i | 1.53309 | + | 0.247834i | ||||
\(482\) | 12488.9i | 1.18019i | ||||||||
\(483\) | −4673.92 | + | 1749.01i | −0.440312 | + | 0.164768i | ||||
\(484\) | −2988.81 | −0.280692 | ||||||||
\(485\) | 117.900 | 0.0110383 | ||||||||
\(486\) | −2641.04 | − | 11833.7i | −0.246502 | − | 1.10450i | ||||
\(487\) | −7192.22 | + | 7192.22i | −0.669220 | + | 0.669220i | −0.957536 | − | 0.288315i | \(-0.906905\pi\) |
0.288315 | + | 0.957536i | \(0.406905\pi\) | |||||||
\(488\) | 3180.66 | − | 3180.66i | 0.295044 | − | 0.295044i | ||||
\(489\) | −1838.65 | + | 688.034i | −0.170034 | + | 0.0636278i | ||||
\(490\) | −377.821 | −0.0348331 | ||||||||
\(491\) | 8860.19 | 0.814368 | 0.407184 | − | 0.913346i | \(-0.366511\pi\) | ||||
0.407184 | + | 0.913346i | \(0.366511\pi\) | |||||||
\(492\) | 766.373 | + | 2047.99i | 0.0702251 | + | 0.187664i | ||||
\(493\) | − | 10999.6i | − | 1.00487i | ||||||
\(494\) | −3515.69 | + | 2537.20i | −0.320199 | + | 0.231081i | ||||
\(495\) | 0.747807 | + | 0.859271i | 6.79018e−5 | + | 7.80229e-5i | ||||
\(496\) | −13348.9 | + | 13348.9i | −1.20843 | + | 1.20843i | ||||
\(497\) | 6587.91i | 0.594584i | ||||||||
\(498\) | 18582.6 | + | 8462.24i | 1.67210 | + | 0.761450i | ||||
\(499\) | −3607.76 | + | 3607.76i | −0.323659 | + | 0.323659i | −0.850169 | − | 0.526510i | \(-0.823500\pi\) |
0.526510 | + | 0.850169i | \(0.323500\pi\) | |||||||
\(500\) | 196.579 | + | 196.579i | 0.0175825 | + | 0.0175825i | ||||
\(501\) | −6321.21 | − | 16892.3i | −0.563694 | − | 1.50637i | ||||
\(502\) | 4923.07 | + | 4923.07i | 0.437704 | + | 0.437704i | ||||
\(503\) | − | 6518.68i | − | 0.577840i | −0.957353 | − | 0.288920i | \(-0.906704\pi\) | ||
0.957353 | − | 0.288920i | \(-0.0932962\pi\) | |||||||
\(504\) | −3343.48 | − | 3841.85i | −0.295497 | − | 0.339542i | ||||
\(505\) | 621.756 | + | 621.756i | 0.0547877 | + | 0.0547877i | ||||
\(506\) | 25.5489 | 0.00224463 | ||||||||
\(507\) | −8369.54 | − | 7763.67i | −0.733145 | − | 0.680072i | ||||
\(508\) | 1854.14 | 0.161938 | ||||||||
\(509\) | 8689.49 | + | 8689.49i | 0.756689 | + | 0.756689i | 0.975718 | − | 0.219029i | \(-0.0702890\pi\) |
−0.219029 | + | 0.975718i | \(0.570289\pi\) | |||||||
\(510\) | −436.140 | − | 198.611i | −0.0378678 | − | 0.0172444i | ||||
\(511\) | − | 6230.25i | − | 0.539354i | ||||||
\(512\) | 2637.52 | + | 2637.52i | 0.227662 | + | 0.227662i | ||||
\(513\) | −1931.51 | + | 3564.60i | −0.166234 | + | 0.306785i | ||||
\(514\) | −2633.74 | − | 2633.74i | −0.226010 | − | 0.226010i | ||||
\(515\) | −458.856 | + | 458.856i | −0.0392614 | + | 0.0392614i | ||||
\(516\) | −1342.42 | + | 2947.88i | −0.114528 | + | 0.251498i | ||||
\(517\) | 26.4116i | 0.00224677i | ||||||||
\(518\) | −8101.48 | + | 8101.48i | −0.687179 | + | 0.687179i | ||||
\(519\) | 1512.06 | − | 3320.41i | 0.127885 | − | 0.280828i | ||||
\(520\) | −347.027 | + | 250.442i | −0.0292656 | + | 0.0211204i | ||||
\(521\) | 21252.3i | 1.78710i | 0.448963 | + | 0.893550i | \(0.351793\pi\) | ||||
−0.448963 | + | 0.893550i | \(0.648207\pi\) | |||||||
\(522\) | 16315.0 | + | 1131.58i | 1.36798 | + | 0.0948810i | ||||
\(523\) | 3719.30 | 0.310963 | 0.155481 | − | 0.987839i | \(-0.450307\pi\) | ||||
0.155481 | + | 0.987839i | \(0.450307\pi\) | |||||||
\(524\) | −621.372 | −0.0518030 | ||||||||
\(525\) | 2326.64 | + | 6217.52i | 0.193415 | + | 0.516867i | ||||
\(526\) | 3741.31 | − | 3741.31i | 0.310131 | − | 0.310131i | ||||
\(527\) | −10087.3 | + | 10087.3i | −0.833796 | + | 0.833796i | ||||
\(528\) | 11.9226 | + | 31.8609i | 0.000982696 | + | 0.00262608i | ||||
\(529\) | −3371.95 | −0.277139 | ||||||||
\(530\) | 924.760 | 0.0757906 | ||||||||
\(531\) | 15111.2 | + | 1048.09i | 1.23497 | + | 0.0856557i | ||||
\(532\) | − | 664.550i | − | 0.0541577i | ||||||
\(533\) | 8671.52 | + | 1401.80i | 0.704700 | + | 0.113919i | ||||
\(534\) | 4650.00 | − | 10211.1i | 0.376826 | − | 0.827490i | ||||
\(535\) | 130.876 | − | 130.876i | 0.0105762 | − | 0.0105762i | ||||
\(536\) | − | 1157.34i | − | 0.0932640i | ||||||
\(537\) | 738.875 | − | 1622.53i | 0.0593758 | − | 0.130386i | ||||
\(538\) | −8112.92 | + | 8112.92i | −0.650136 | + | 0.650136i | ||||
\(539\) | 14.3309 | + | 14.3309i | 0.00114522 | + | 0.00114522i | ||||
\(540\) | 74.3990 | − | 137.304i | 0.00592893 | − | 0.0109419i | ||||
\(541\) | −935.454 | − | 935.454i | −0.0743407 | − | 0.0743407i | 0.668959 | − | 0.743299i | \(-0.266740\pi\) |
−0.743299 | + | 0.668959i | \(0.766740\pi\) | |||||||
\(542\) | 998.935i | 0.0791660i | ||||||||
\(543\) | −12802.7 | − | 5830.15i | −1.01182 | − | 0.460766i | ||||
\(544\) | −4063.50 | − | 4063.50i | −0.320259 | − | 0.320259i | ||||
\(545\) | 1009.08 | 0.0793108 | ||||||||
\(546\) | 7828.00 | − | 1568.94i | 0.613567 | − | 0.122975i | ||||
\(547\) | −24246.7 | −1.89528 | −0.947638 | − | 0.319348i | \(-0.896536\pi\) | ||||
−0.947638 | + | 0.319348i | \(0.896536\pi\) | |||||||
\(548\) | 325.129 | + | 325.129i | 0.0253445 | + | 0.0253445i | ||||
\(549\) | 4328.62 | + | 4973.83i | 0.336505 | + | 0.386663i | ||||
\(550\) | − | 33.9866i | − | 0.00263490i | ||||||
\(551\) | −3866.77 | − | 3866.77i | −0.298965 | − | 0.298965i | ||||
\(552\) | 3145.77 | + | 8406.48i | 0.242559 | + | 0.648195i | ||||
\(553\) | −4615.13 | − | 4615.13i | −0.354892 | − | 0.354892i | ||||
\(554\) | 1245.71 | − | 1245.71i | 0.0955330 | − | 0.0955330i | ||||
\(555\) | 819.312 | + | 373.102i | 0.0626628 | + | 0.0285357i | ||||
\(556\) | − | 5489.35i | − | 0.418706i | ||||||
\(557\) | 7890.32 | − | 7890.32i | 0.600222 | − | 0.600222i | −0.340150 | − | 0.940371i | \(-0.610478\pi\) |
0.940371 | + | 0.340150i | \(0.110478\pi\) | |||||||
\(558\) | −13924.1 | − | 15999.5i | −1.05637 | − | 1.21382i | ||||
\(559\) | 7614.59 | + | 10551.2i | 0.576141 | + | 0.798333i | ||||
\(560\) | − | 390.485i | − | 0.0294661i | ||||||
\(561\) | 9.00952 | + | 24.0763i | 0.000678043 | + | 0.00181195i | ||||
\(562\) | 21335.2 | 1.60137 | ||||||||
\(563\) | 9586.10 | 0.717595 | 0.358798 | − | 0.933415i | \(-0.383187\pi\) | ||||
0.358798 | + | 0.933415i | \(0.383187\pi\) | |||||||
\(564\) | 3391.22 | − | 1269.02i | 0.253185 | − | 0.0947435i | ||||
\(565\) | −455.572 | + | 455.572i | −0.0339222 | + | 0.0339222i | ||||
\(566\) | −3316.92 | + | 3316.92i | −0.246326 | + | 0.246326i | ||||
\(567\) | 5957.22 | − | 4499.67i | 0.441234 | − | 0.333277i | ||||
\(568\) | 11849.0 | 0.875302 | ||||||||
\(569\) | 12552.5 | 0.924831 | 0.462415 | − | 0.886663i | \(-0.346983\pi\) | ||||
0.462415 | + | 0.886663i | \(0.346983\pi\) | |||||||
\(570\) | −223.138 | + | 83.4998i | −0.0163969 | + | 0.00613583i | ||||
\(571\) | − | 276.603i | − | 0.0202723i | −0.999949 | − | 0.0101361i | \(-0.996774\pi\) | ||
0.999949 | − | 0.0101361i | \(-0.00322649\pi\) | |||||||
\(572\) | −8.84342 | − | 1.42959i | −0.000646437 | − | 0.000104500i | ||||
\(573\) | 16818.6 | + | 7658.94i | 1.22619 | + | 0.558389i | ||||
\(574\) | −4343.83 | + | 4343.83i | −0.315868 | + | 0.315868i | ||||
\(575\) | − | 11699.7i | − | 0.848541i | ||||||
\(576\) | −6088.31 | + | 5298.54i | −0.440416 | + | 0.383285i | ||||
\(577\) | −6032.82 | + | 6032.82i | −0.435268 | + | 0.435268i | −0.890416 | − | 0.455148i | \(-0.849586\pi\) |
0.455148 | + | 0.890416i | \(0.349586\pi\) | |||||||
\(578\) | 3472.43 | + | 3472.43i | 0.249886 | + | 0.249886i | ||||
\(579\) | −409.422 | + | 153.209i | −0.0293869 | + | 0.0109968i | ||||
\(580\) | 148.943 | + | 148.943i | 0.0106630 | + | 0.0106630i | ||||
\(581\) | 12572.4i | 0.897744i | ||||||||
\(582\) | −1639.48 | + | 3600.21i | −0.116767 | + | 0.256415i | ||||
\(583\) | −35.0764 | − | 35.0764i | −0.00249180 | − | 0.00249180i | ||||
\(584\) | −11205.7 | −0.793997 | ||||||||
\(585\) | −331.036 | − | 532.874i | −0.0233960 | − | 0.0376609i | ||||
\(586\) | −22528.2 | −1.58811 | ||||||||
\(587\) | −16607.1 | − | 16607.1i | −1.16772 | − | 1.16772i | −0.982743 | − | 0.184975i | \(-0.940780\pi\) |
−0.184975 | − | 0.982743i | \(-0.559220\pi\) | |||||||
\(588\) | 1151.50 | − | 2528.64i | 0.0807604 | − | 0.177345i | ||||
\(589\) | 7092.12i | 0.496139i | ||||||||
\(590\) | 629.428 | + | 629.428i | 0.0439206 | + | 0.0439206i | ||||
\(591\) | 1578.07 | − | 590.527i | 0.109836 | − | 0.0411016i | ||||
\(592\) | 19011.1 | + | 19011.1i | 1.31985 | + | 1.31985i | ||||
\(593\) | 7681.48 | − | 7681.48i | 0.531941 | − | 0.531941i | −0.389209 | − | 0.921149i | \(-0.627252\pi\) |
0.921149 | + | 0.389209i | \(0.127252\pi\) | |||||||
\(594\) | −36.6375 | + | 10.8863i | −0.00253073 | + | 0.000751973i | ||||
\(595\) | − | 295.077i | − | 0.0203311i | ||||||
\(596\) | 2097.93 | − | 2097.93i | 0.144186 | − | 0.144186i | ||||
\(597\) | 20282.4 | + | 9236.28i | 1.39046 | + | 0.633192i | ||||
\(598\) | −13889.9 | − | 2245.39i | −0.949835 | − | 0.153546i | ||||
\(599\) | − | 19722.5i | − | 1.34531i | −0.739956 | − | 0.672655i | \(-0.765154\pi\) | ||
0.739956 | − | 0.672655i | \(-0.234846\pi\) | |||||||
\(600\) | 11182.8 | − | 4184.68i | 0.760893 | − | 0.284732i | ||||
\(601\) | −6532.58 | −0.443377 | −0.221689 | − | 0.975118i | \(-0.571157\pi\) | ||||
−0.221689 | + | 0.975118i | \(0.571157\pi\) | |||||||
\(602\) | −9099.81 | −0.616080 | ||||||||
\(603\) | 1692.43 | + | 117.384i | 0.114297 | + | 0.00792746i | ||||
\(604\) | 1534.16 | − | 1534.16i | 0.103351 | − | 0.103351i | ||||
\(605\) | −466.526 | + | 466.526i | −0.0313504 | + | 0.0313504i | ||||
\(606\) | −27631.9 | + | 10340.1i | −1.85226 | + | 0.693129i | ||||
\(607\) | 2988.34 | 0.199824 | 0.0999120 | − | 0.994996i | \(-0.468144\pi\) | ||||
0.0999120 | + | 0.994996i | \(0.468144\pi\) | |||||||
\(608\) | −2856.93 | −0.190566 | ||||||||
\(609\) | 3529.16 | + | 9431.02i | 0.234825 | + | 0.627528i | ||||
\(610\) | 387.475i | 0.0257187i | ||||||||
\(611\) | 2321.21 | − | 14359.0i | 0.153693 | − | 0.950739i | ||||
\(612\) | 2658.48 | − | 2313.63i | 0.175593 | − | 0.152815i | ||||
\(613\) | −3030.04 | + | 3030.04i | −0.199645 | + | 0.199645i | −0.799848 | − | 0.600203i | \(-0.795086\pi\) |
0.600203 | + | 0.799848i | \(0.295086\pi\) | |||||||
\(614\) | − | 5069.10i | − | 0.333179i | ||||||
\(615\) | 439.297 | + | 200.049i | 0.0288035 | + | 0.0131167i | ||||
\(616\) | −11.3522 | + | 11.3522i | −0.000742521 | + | 0.000742521i | ||||
\(617\) | −11141.2 | − | 11141.2i | −0.726948 | − | 0.726948i | 0.243062 | − | 0.970011i | \(-0.421848\pi\) |
−0.970011 | + | 0.243062i | \(0.921848\pi\) | |||||||
\(618\) | −7630.97 | − | 20392.4i | −0.496703 | − | 1.32735i | ||||
\(619\) | −11973.1 | − | 11973.1i | −0.777444 | − | 0.777444i | 0.201951 | − | 0.979396i | \(-0.435272\pi\) |
−0.979396 | + | 0.201951i | \(0.935272\pi\) | |||||||
\(620\) | − | 273.179i | − | 0.0176954i | ||||||
\(621\) | −12612.2 | + | 3747.56i | −0.814995 | + | 0.242165i | ||||
\(622\) | −4060.04 | − | 4060.04i | −0.261725 | − | 0.261725i | ||||
\(623\) | 6908.51 | 0.444276 | ||||||||
\(624\) | −3681.72 | − | 18369.4i | −0.236197 | − | 1.17847i | ||||
\(625\) | −15532.9 | −0.994107 | ||||||||
\(626\) | −17070.7 | − | 17070.7i | −1.08991 | − | 1.08991i | ||||
\(627\) | 11.6309 | + | 5.29652i | 0.000740817 | + | 0.000337357i | ||||
\(628\) | − | 260.701i | − | 0.0165654i | ||||||
\(629\) | 14366.1 | + | 14366.1i | 0.910676 | + | 0.910676i | ||||
\(630\) | 437.666 | + | 30.3558i | 0.0276779 | + | 0.00191969i | ||||
\(631\) | 10462.6 | + | 10462.6i | 0.660079 | + | 0.660079i | 0.955398 | − | 0.295320i | \(-0.0954262\pi\) |
−0.295320 | + | 0.955398i | \(0.595426\pi\) | |||||||
\(632\) | −8300.75 | + | 8300.75i | −0.522446 | + | 0.522446i | ||||
\(633\) | −1996.38 | + | 4383.93i | −0.125354 | + | 0.275270i | ||||
\(634\) | 17135.4i | 1.07340i | ||||||||
\(635\) | 289.415 | − | 289.415i | 0.0180868 | − | 0.0180868i | ||||
\(636\) | −2818.43 | + | 6189.12i | −0.175720 | + | 0.385872i | ||||
\(637\) | −6531.66 | − | 9050.62i | −0.406270 | − | 0.562949i | ||||
\(638\) | − | 51.5524i | − | 0.00319903i | ||||||
\(639\) | −1201.79 | + | 17327.3i | −0.0744009 | + | 1.07270i | ||||
\(640\) | −866.344 | −0.0535082 | ||||||||
\(641\) | −11375.1 | −0.700922 | −0.350461 | − | 0.936577i | \(-0.613975\pi\) | ||||
−0.350461 | + | 0.936577i | \(0.613975\pi\) | |||||||
\(642\) | 2176.53 | + | 5816.37i | 0.133802 | + | 0.357560i | ||||
\(643\) | 20708.6 | − | 20708.6i | 1.27009 | − | 1.27009i | 0.324054 | − | 0.946039i | \(-0.394954\pi\) |
0.946039 | − | 0.324054i | \(-0.105046\pi\) | |||||||
\(644\) | 1524.98 | − | 1524.98i | 0.0933118 | − | 0.0933118i | ||||
\(645\) | 250.598 | + | 669.677i | 0.0152981 | + | 0.0408814i | ||||
\(646\) | −5376.70 | −0.327467 | ||||||||
\(647\) | −4586.05 | −0.278665 | −0.139333 | − | 0.990246i | \(-0.544496\pi\) | ||||
−0.139333 | + | 0.990246i | \(0.544496\pi\) | |||||||
\(648\) | −8093.07 | − | 10714.6i | −0.490626 | − | 0.649553i | ||||
\(649\) | − | 47.7488i | − | 0.00288799i | ||||||
\(650\) | −2986.95 | + | 18477.2i | −0.180243 | + | 1.11498i | ||||
\(651\) | 5412.36 | − | 11885.3i | 0.325848 | − | 0.715545i | ||||
\(652\) | 599.905 | − | 599.905i | 0.0360339 | − | 0.0360339i | ||||
\(653\) | − | 21589.3i | − | 1.29380i | −0.762573 | − | 0.646902i | \(-0.776064\pi\) | ||
0.762573 | − | 0.646902i | \(-0.223936\pi\) | |||||||
\(654\) | −14032.0 | + | 30813.4i | −0.838980 | + | 1.84236i | ||||
\(655\) | −96.9906 | + | 96.9906i | −0.00578586 | + | 0.00578586i | ||||
\(656\) | 10193.4 | + | 10193.4i | 0.606682 | + | 0.606682i | ||||
\(657\) | 1136.55 | − | 16386.6i | 0.0674900 | − | 0.973062i | ||||
\(658\) | 7192.85 | + | 7192.85i | 0.426150 | + | 0.426150i | ||||
\(659\) | 32017.7i | 1.89261i | 0.323271 | + | 0.946306i | \(0.395218\pi\) | ||||
−0.323271 | + | 0.946306i | \(0.604782\pi\) | |||||||
\(660\) | −0.448006 | − | 0.204015i | −2.64221e−5 | − | 1.20322e-5i | ||||
\(661\) | −5903.99 | − | 5903.99i | −0.347411 | − | 0.347411i | 0.511733 | − | 0.859144i | \(-0.329004\pi\) |
−0.859144 | + | 0.511733i | \(0.829004\pi\) | |||||||
\(662\) | 17334.2 | 1.01769 | ||||||||
\(663\) | −2782.16 | − | 13881.2i | −0.162972 | − | 0.813122i | ||||
\(664\) | 22612.6 | 1.32159 | ||||||||
\(665\) | −103.730 | − | 103.730i | −0.00604886 | − | 0.00604886i | ||||
\(666\) | −22786.1 | + | 19830.3i | −1.32574 | + | 1.15377i | ||||
\(667\) | − | 17746.6i | − | 1.03021i | ||||||
\(668\) | 5511.53 | + | 5511.53i | 0.319233 | + | 0.319233i | ||||
\(669\) | 740.185 | + | 1978.01i | 0.0427761 | + | 0.114311i | ||||
\(670\) | 70.4949 | + | 70.4949i | 0.00406486 | + | 0.00406486i | ||||
\(671\) | 14.6971 | − | 14.6971i | 0.000845564 | − | 0.000845564i | ||||
\(672\) | 4787.76 | + | 2180.27i | 0.274839 | + | 0.125158i | ||||
\(673\) | − | 4597.39i | − | 0.263323i | −0.991295 | − | 0.131662i | \(-0.957969\pi\) | ||
0.991295 | − | 0.131662i | \(-0.0420312\pi\) | |||||||
\(674\) | 21988.5 | − | 21988.5i | 1.25663 | − | 1.25663i | ||||
\(675\) | 4985.23 | + | 16777.6i | 0.284269 | + | 0.956694i | ||||
\(676\) | 4682.19 | + | 1554.43i | 0.266397 | + | 0.0884403i | ||||
\(677\) | − | 4282.28i | − | 0.243104i | −0.992585 | − | 0.121552i | \(-0.961213\pi\) | ||
0.992585 | − | 0.121552i | \(-0.0387871\pi\) | |||||||
\(678\) | −7576.34 | − | 20246.4i | −0.429156 | − | 1.14684i | ||||
\(679\) | −2435.78 | −0.137668 | ||||||||
\(680\) | −530.724 | −0.0299299 | ||||||||
\(681\) | 27407.6 | − | 10256.1i | 1.54223 | − | 0.577115i | ||||
\(682\) | −47.2766 | + | 47.2766i | −0.00265442 | + | 0.00265442i | ||||
\(683\) | −20404.1 | + | 20404.1i | −1.14310 | + | 1.14310i | −0.155224 | + | 0.987879i | \(0.549610\pi\) |
−0.987879 | + | 0.155224i | \(0.950390\pi\) | |||||||
\(684\) | 121.230 | − | 1747.88i | 0.00677682 | − | 0.0977073i | ||||
\(685\) | 101.499 | 0.00566144 | ||||||||
\(686\) | 19049.1 | 1.06020 | ||||||||
\(687\) | 8109.89 | − | 3034.78i | 0.450381 | − | 0.168536i | ||||
\(688\) | 21353.8i | 1.18330i | ||||||||
\(689\) | 15987.0 | + | 22152.4i | 0.883970 | + | 1.22488i | ||||
\(690\) | −703.660 | − | 320.436i | −0.0388230 | − | 0.0176794i | ||||
\(691\) | 10715.7 | − | 10715.7i | 0.589936 | − | 0.589936i | −0.347678 | − | 0.937614i | \(-0.613030\pi\) |
0.937614 | + | 0.347678i | \(0.113030\pi\) | |||||||
\(692\) | 1576.72i | 0.0866153i | ||||||||
\(693\) | −15.4494 | − | 17.7522i | −0.000846861 | − | 0.000973090i | ||||
\(694\) | 1591.24 | − | 1591.24i | 0.0870356 | − | 0.0870356i | ||||
\(695\) | −856.839 | − | 856.839i | −0.0467651 | − | 0.0467651i | ||||
\(696\) | 16962.6 | − | 6347.52i | 0.923800 | − | 0.345692i | ||||
\(697\) | 7702.80 | + | 7702.80i | 0.418600 | + | 0.418600i | ||||
\(698\) | 28209.1i | 1.52970i | ||||||||
\(699\) | −12514.8 | + | 27481.9i | −0.677187 | + | 1.48707i | ||||
\(700\) | −2028.62 | − | 2028.62i | −0.109535 | − | 0.109535i | ||||
\(701\) | −22279.2 | −1.20039 | −0.600195 | − | 0.799854i | \(-0.704910\pi\) | ||||
−0.600195 | + | 0.799854i | \(0.704910\pi\) | |||||||
\(702\) | 20875.1 | − | 2698.56i | 1.12234 | − | 0.145086i | ||||
\(703\) | 10100.4 | 0.541885 | ||||||||
\(704\) | 17.9902 | + | 17.9902i | 0.000963113 | + | 0.000963113i | ||||
\(705\) | 331.257 | − | 727.422i | 0.0176962 | − | 0.0388600i | ||||
\(706\) | − | 20850.1i | − | 1.11148i | ||||||
\(707\) | −12845.3 | − | 12845.3i | −0.683304 | − | 0.683304i | ||||
\(708\) | −6130.89 | + | 2294.22i | −0.325442 | + | 0.121783i | ||||
\(709\) | 10387.2 | + | 10387.2i | 0.550213 | + | 0.550213i | 0.926502 | − | 0.376289i | \(-0.122800\pi\) |
−0.376289 | + | 0.926502i | \(0.622800\pi\) | |||||||
\(710\) | −721.734 | + | 721.734i | −0.0381496 | + | 0.0381496i | ||||
\(711\) | −11296.7 | − | 12980.5i | −0.595862 | − | 0.684678i | ||||
\(712\) | − | 12425.6i | − | 0.654030i | ||||||
\(713\) | −16274.7 | + | 16274.7i | −0.854829 | + | 0.854829i | ||||
\(714\) | 9010.49 | + | 4103.24i | 0.472282 | + | 0.215070i | ||||
\(715\) | −1.60353 | + | 1.15723i | −8.38720e−5 | + | 6.05287e-5i | ||||
\(716\) | 770.468i | 0.0402147i | ||||||||
\(717\) | −3591.44 | + | 1343.94i | −0.187064 | + | 0.0700007i | ||||
\(718\) | 39331.6 | 2.04435 | ||||||||
\(719\) | 29006.9 | 1.50455 | 0.752276 | − | 0.658848i | \(-0.228956\pi\) | ||||
0.752276 | + | 0.658848i | \(0.228956\pi\) | |||||||
\(720\) | 71.2338 | − | 1027.04i | 0.00368712 | − | 0.0531604i | ||||
\(721\) | 9479.81 | − | 9479.81i | 0.489663 | − | 0.489663i | ||||
\(722\) | 13634.2 | − | 13634.2i | 0.702790 | − | 0.702790i | ||||
\(723\) | −18988.0 | + | 7105.46i | −0.976725 | + | 0.365498i | ||||
\(724\) | 6079.44 | 0.312073 | ||||||||
\(725\) | −23607.6 | −1.20933 | ||||||||
\(726\) | −7758.52 | − | 20733.2i | −0.396619 | − | 1.05989i | ||||
\(727\) | 1301.34i | 0.0663881i | 0.999449 | + | 0.0331941i | \(0.0105679\pi\) | ||||
−0.999449 | + | 0.0331941i | \(0.989432\pi\) | |||||||
\(728\) | 7169.45 | − | 5174.05i | 0.364996 | − | 0.263411i | ||||
\(729\) | 16489.3 | − | 10748.1i | 0.837745 | − | 0.546062i | ||||
\(730\) | 682.551 | − | 682.551i | 0.0346059 | − | 0.0346059i | ||||
\(731\) | 16136.4i | 0.816454i | ||||||||
\(732\) | −2593.25 | − | 1180.93i | −0.130942 | − | 0.0596288i | ||||
\(733\) | 7575.76 | − | 7575.76i | 0.381742 | − | 0.381742i | −0.489987 | − | 0.871730i | \(-0.662999\pi\) |
0.871730 | + | 0.489987i | \(0.162999\pi\) | |||||||
\(734\) | 6878.40 | + | 6878.40i | 0.345894 | + | 0.345894i | ||||
\(735\) | −214.958 | − | 574.436i | −0.0107876 | − | 0.0288278i | ||||
\(736\) | −6555.98 | − | 6555.98i | −0.328338 | − | 0.328338i | ||||
\(737\) | − | 5.34779i | − | 0.000267284i | ||||||
\(738\) | −12217.4 | + | 10632.6i | −0.609390 | + | 0.530340i | ||||
\(739\) | −26362.3 | − | 26362.3i | −1.31225 | − | 1.31225i | −0.919752 | − | 0.392500i | \(-0.871610\pi\) |
−0.392500 | − | 0.919752i | \(-0.628390\pi\) | |||||||
\(740\) | −389.055 | −0.0193270 | ||||||||
\(741\) | −5857.77 | − | 3901.71i | −0.290405 | − | 0.193431i | ||||
\(742\) | −19105.2 | −0.945249 | ||||||||
\(743\) | −14985.2 | − | 14985.2i | −0.739913 | − | 0.739913i | 0.232648 | − | 0.972561i | \(-0.425261\pi\) |
−0.972561 | + | 0.232648i | \(0.925261\pi\) | |||||||
\(744\) | −21376.7 | − | 9734.64i | −1.05337 | − | 0.479690i | ||||
\(745\) | − | 654.937i | − | 0.0322081i | ||||||
\(746\) | −9309.65 | − | 9309.65i | −0.456904 | − | 0.456904i | ||||
\(747\) | −2293.50 | + | 33067.4i | −0.112336 | + | 1.61964i | ||||
\(748\) | −7.85550 | − | 7.85550i | −0.000383991 | − | 0.000383991i | ||||
\(749\) | −2703.86 | + | 2703.86i | −0.131905 | + | 0.131905i | ||||
\(750\) | −853.366 | + | 1873.95i | −0.0415474 | + | 0.0912357i | ||||
\(751\) | 349.933i | 0.0170030i | 0.999964 | + | 0.00850149i | \(0.00270614\pi\) | ||||
−0.999964 | + | 0.00850149i | \(0.997294\pi\) | |||||||
\(752\) | 16878.9 | − | 16878.9i | 0.818499 | − | 0.818499i | ||||
\(753\) | −4684.06 | + | 10285.9i | −0.226689 | + | 0.497796i | ||||
\(754\) | −4530.74 | + | 28027.1i | −0.218833 | + | 1.35369i | ||||
\(755\) | − | 478.936i | − | 0.0230865i | ||||||
\(756\) | −1537.06 | + | 2836.65i | −0.0739448 | + | 0.136465i | ||||
\(757\) | −24519.0 | −1.17722 | −0.588612 | − | 0.808416i | \(-0.700325\pi\) | ||||
−0.588612 | + | 0.808416i | \(0.700325\pi\) | |||||||
\(758\) | −16031.5 | −0.768195 | ||||||||
\(759\) | 14.5358 | + | 38.8443i | 0.000695147 | + | 0.00185765i | ||||
\(760\) | −186.569 | + | 186.569i | −0.00890468 | + | 0.00890468i | ||||
\(761\) | 20497.4 | − | 20497.4i | 0.976387 | − | 0.976387i | −0.0233407 | − | 0.999728i | \(-0.507430\pi\) |
0.999728 | + | 0.0233407i | \(0.00743024\pi\) | |||||||
\(762\) | 4813.09 | + | 12862.1i | 0.228819 | + | 0.611476i | ||||
\(763\) | −20847.3 | −0.989153 | ||||||||
\(764\) | −7986.42 | −0.378192 | ||||||||
\(765\) | 53.8292 | − | 776.102i | 0.00254405 | − | 0.0366798i | ||||
\(766\) | 2241.39i | 0.105724i | ||||||||
\(767\) | −4196.45 | + | 25959.2i | −0.197556 | + | 1.22208i | ||||
\(768\) | 6897.21 | − | 15145.9i | 0.324065 | − | 0.711629i | ||||
\(769\) | −16748.3 | + | 16748.3i | −0.785381 | + | 0.785381i | −0.980733 | − | 0.195352i | \(-0.937415\pi\) |
0.195352 | + | 0.980733i | \(0.437415\pi\) | |||||||
\(770\) | − | 1.38295i | − | 6.47247e-5i | ||||||
\(771\) | 2505.87 | − | 5502.76i | 0.117052 | − | 0.257039i | ||||
\(772\) | 133.584 | − | 133.584i | 0.00622772 | − | 0.00622772i | ||||
\(773\) | −3346.88 | − | 3346.88i | −0.155730 | − | 0.155730i | 0.624942 | − | 0.780671i | \(-0.285123\pi\) |
−0.780671 | + | 0.624942i | \(0.785123\pi\) | |||||||
\(774\) | −23934.0 | − | 1660.02i | −1.11149 | − | 0.0770908i | ||||
\(775\) | 21649.6 | + | 21649.6i | 1.00345 | + | 1.00345i | ||||
\(776\) | 4380.97i | 0.202665i | ||||||||
\(777\) | −16926.7 | − | 7708.16i | −0.781521 | − | 0.355893i | ||||
\(778\) | −18052.7 | − | 18052.7i | −0.831902 | − | 0.831902i | ||||
\(779\) | 5415.63 | 0.249082 | ||||||||
\(780\) | 225.633 | + | 150.289i | 0.0103577 | + | 0.00689897i | ||||
\(781\) | 54.7512 | 0.00250852 | ||||||||
\(782\) | −12338.2 | − | 12338.2i | −0.564213 | − | 0.564213i | ||||
\(783\) | 7561.82 | + | 25449.0i | 0.345131 | + | 1.16152i | ||||
\(784\) | − | 18316.9i | − | 0.834409i | ||||||
\(785\) | −40.6930 | − | 40.6930i | −0.00185019 | − | 0.00185019i | ||||
\(786\) | −1612.99 | − | 4310.43i | −0.0731979 | − | 0.195608i | ||||
\(787\) | 24752.5 | + | 24752.5i | 1.12113 | + | 1.12113i | 0.991572 | + | 0.129559i | \(0.0413561\pi\) |
0.129559 | + | 0.991572i | \(0.458644\pi\) | |||||||
\(788\) | −514.887 | + | 514.887i | −0.0232768 | + | 0.0232768i | ||||
\(789\) | 7816.85 | + | 3559.68i | 0.352709 | + | 0.160618i | ||||
\(790\) | − | 1011.22i | − | 0.0455411i | ||||||
\(791\) | 9411.96 | − | 9411.96i | 0.423073 | − | 0.423073i | ||||
\(792\) | −31.9291 | + | 27.7872i | −0.00143251 | + | 0.00124669i | ||||
\(793\) | −9281.89 | + | 6698.56i | −0.415649 | + | 0.299966i | ||||
\(794\) | − | 14817.2i | − | 0.662271i | ||||||
\(795\) | 526.135 | + | 1406.00i | 0.0234718 | + | 0.0627241i | ||||
\(796\) | −9631.20 | −0.428855 | ||||||||
\(797\) | −15529.1 | −0.690176 | −0.345088 | − | 0.938570i | \(-0.612151\pi\) | ||||
−0.345088 | + | 0.938570i | \(0.612151\pi\) | |||||||
\(798\) | 4609.95 | − | 1725.08i | 0.204499 | − | 0.0765251i | ||||
\(799\) | 12754.9 | − | 12754.9i | 0.564750 | − | 0.564750i | ||||
\(800\) | −8721.15 | + | 8721.15i | −0.385424 | + | 0.385424i | ||||
\(801\) | 18170.5 | + | 1260.28i | 0.801529 | + | 0.0555927i | ||||
\(802\) | 37636.1 | 1.65708 | ||||||||
\(803\) | −51.7787 | −0.00227551 | ||||||||
\(804\) | −686.651 | + | 256.950i | −0.0301198 | + | 0.0112710i | ||||
\(805\) | − | 476.073i | − | 0.0208439i | ||||||
\(806\) | 29857.5 | − | 21547.5i | 1.30482 | − | 0.941662i | ||||
\(807\) | −16950.6 | − | 7719.05i | −0.739393 | − | 0.336708i | ||||
\(808\) | −23103.4 | + | 23103.4i | −1.00591 | + | 1.00591i | ||||
\(809\) | − | 37192.7i | − | 1.61635i | −0.588943 | − | 0.808175i | \(-0.700456\pi\) | ||
0.588943 | − | 0.808175i | \(-0.299544\pi\) | |||||||
\(810\) | 1145.60 | + | 159.682i | 0.0496941 | + | 0.00692672i | ||||
\(811\) | 12080.9 | − | 12080.9i | 0.523080 | − | 0.523080i | −0.395420 | − | 0.918500i | \(-0.629401\pi\) |
0.918500 | + | 0.395420i | \(0.129401\pi\) | |||||||
\(812\) | −3077.11 | − | 3077.11i | −0.132987 | − | 0.132987i | ||||
\(813\) | −1518.77 | + | 568.336i | −0.0655175 | + | 0.0245171i | ||||
\(814\) | 67.3303 | + | 67.3303i | 0.00289917 | + | 0.00289917i | ||||
\(815\) | − | 187.279i | − | 0.00804922i | ||||||
\(816\) | 9628.77 | − | 21144.3i | 0.413081 | − | 0.907104i | ||||
\(817\) | 5672.54 | + | 5672.54i | 0.242910 | + | 0.242910i | ||||
\(818\) | −31904.5 | −1.36371 | ||||||||
\(819\) | 6839.08 | + | 11009.0i | 0.291791 | + | 0.469701i | ||||
\(820\) | −208.603 | −0.00888381 | ||||||||
\(821\) | 4210.80 | + | 4210.80i | 0.178999 | + | 0.178999i | 0.790919 | − | 0.611921i | \(-0.209603\pi\) |
−0.611921 | + | 0.790919i | \(0.709603\pi\) | |||||||
\(822\) | −1411.41 | + | 3099.39i | −0.0598889 | + | 0.131513i | ||||
\(823\) | 30867.3i | 1.30737i | 0.756766 | + | 0.653686i | \(0.226778\pi\) | ||||
−0.756766 | + | 0.653686i | \(0.773222\pi\) | |||||||
\(824\) | −17050.3 | − | 17050.3i | −0.720845 | − | 0.720845i | ||||
\(825\) | 51.6730 | − | 19.3364i | 0.00218063 | − | 0.000816009i | ||||
\(826\) | −13003.8 | − | 13003.8i | −0.547771 | − | 0.547771i | ||||
\(827\) | 15143.3 | − | 15143.3i | 0.636739 | − | 0.636739i | −0.313010 | − | 0.949750i | \(-0.601337\pi\) |
0.949750 | + | 0.313010i | \(0.101337\pi\) | |||||||
\(828\) | 4289.16 | − | 3732.77i | 0.180022 | − | 0.156670i | ||||
\(829\) | 23785.9i | 0.996525i | 0.867026 | + | 0.498263i | \(0.166028\pi\) | ||||
−0.867026 | + | 0.498263i | \(0.833972\pi\) | |||||||
\(830\) | −1377.36 | + | 1377.36i | −0.0576009 | + | 0.0576009i | ||||
\(831\) | 2602.71 | + | 1185.24i | 0.108649 | + | 0.0494770i | ||||
\(832\) | −8199.50 | − | 11361.7i | −0.341667 | − | 0.473432i | ||||
\(833\) | − | 13841.5i | − | 0.575727i | ||||||
\(834\) | 38079.4 | − | 14249.6i | 1.58103 | − | 0.591634i | ||||
\(835\) | 1720.60 | 0.0713100 | ||||||||
\(836\) | −5.52299 | −0.000228489 | ||||||||
\(837\) | 16403.6 | − | 30272.9i | 0.677408 | − | 1.25016i | ||||
\(838\) | 15956.1 | − | 15956.1i | 0.657749 | − | 0.657749i | ||||
\(839\) | −5042.71 | + | 5042.71i | −0.207501 | + | 0.207501i | −0.803205 | − | 0.595703i | \(-0.796873\pi\) |
0.595703 | + | 0.803205i | \(0.296873\pi\) | |||||||
\(840\) | 455.039 | − | 170.279i | 0.0186909 | − | 0.00699427i | ||||
\(841\) | −11420.1 | −0.468248 | ||||||||
\(842\) | 15519.8 | 0.635210 | ||||||||
\(843\) | 12138.5 | + | 32437.9i | 0.495933 | + | 1.32529i | ||||
\(844\) | − | 2081.74i | − | 0.0849008i | ||||||
\(845\) | 973.480 | − | 488.216i | 0.0396316 | − | 0.0198759i | ||||
\(846\) | 17606.2 | + | 20230.5i | 0.715503 | + | 0.822152i | ||||
\(847\) | 9638.27 | − | 9638.27i | 0.390998 | − | 0.390998i | ||||
\(848\) | 44832.8i | 1.81552i | ||||||||
\(849\) | −6930.16 | − | 3155.89i | −0.280144 | − | 0.127573i | ||||
\(850\) | −16413.1 | + | 16413.1i | −0.662310 | + | 0.662310i | ||||
\(851\) | 23178.1 | + | 23178.1i | 0.933648 | + | 0.933648i | ||||
\(852\) | −2630.67 | − | 7030.00i | −0.105781 | − | 0.282680i | ||||
\(853\) | −6010.39 | − | 6010.39i | −0.241257 | − | 0.241257i | 0.576113 | − | 0.817370i | \(-0.304569\pi\) |
−0.817370 | + | 0.576113i | \(0.804569\pi\) | |||||||
\(854\) | − | 8005.10i | − | 0.320760i | ||||||
\(855\) | −253.905 | − | 291.751i | −0.0101560 | − | 0.0116698i | ||||
\(856\) | 4863.15 | + | 4863.15i | 0.194181 | + | 0.194181i | ||||
\(857\) | 3348.20 | 0.133457 | 0.0667284 | − | 0.997771i | \(-0.478744\pi\) | ||||
0.0667284 | + | 0.997771i | \(0.478744\pi\) | |||||||
\(858\) | −13.0393 | − | 65.0574i | −0.000518826 | − | 0.00258861i | ||||
\(859\) | −19432.4 | −0.771858 | −0.385929 | − | 0.922529i | \(-0.626119\pi\) | ||||
−0.385929 | + | 0.922529i | \(0.626119\pi\) | |||||||
\(860\) | −218.499 | − | 218.499i | −0.00866366 | − | 0.00866366i | ||||
\(861\) | −9075.72 | − | 4132.95i | −0.359233 | − | 0.163589i | ||||
\(862\) | − | 22642.9i | − | 0.894689i | ||||||
\(863\) | 32959.0 | + | 32959.0i | 1.30004 | + | 1.30004i | 0.928359 | + | 0.371685i | \(0.121220\pi\) |
0.371685 | + | 0.928359i | \(0.378780\pi\) | |||||||
\(864\) | 12194.9 | + | 6607.89i | 0.480183 | + | 0.260191i | ||||
\(865\) | 246.111 | + | 246.111i | 0.00967403 | + | 0.00967403i | ||||
\(866\) | 7370.13 | − | 7370.13i | 0.289200 | − | 0.289200i | ||||
\(867\) | −3303.85 | + | 7255.06i | −0.129417 | + | 0.284192i | ||||
\(868\) | 5643.78i | 0.220694i | ||||||||
\(869\) | −38.3557 | + | 38.3557i | −0.00149727 | + | 0.00149727i | ||||
\(870\) | −646.575 | + | 1419.84i | −0.0251965 | + | 0.0553301i | ||||
\(871\) | −469.996 | + | 2907.39i | −0.0182838 | + | 0.113103i | ||||
\(872\) | 37495.8i | 1.45616i | ||||||||
\(873\) | −6406.50 | − | 444.344i | −0.248370 | − | 0.0172266i | ||||
\(874\) | −8674.68 | −0.335727 | ||||||||
\(875\) | −1267.85 | −0.0489841 | ||||||||
\(876\) | 2487.85 | + | 6648.34i | 0.0959553 | + | 0.256423i | ||||
\(877\) | −28070.1 | + | 28070.1i | −1.08080 | + | 1.08080i | −0.0843650 | + | 0.996435i | \(0.526886\pi\) |
−0.996435 | + | 0.0843650i | \(0.973114\pi\) | |||||||
\(878\) | −14397.9 | + | 14397.9i | −0.553423 | + | 0.553423i | ||||
\(879\) | −12817.2 | − | 34251.7i | −0.491825 | − | 1.31431i | ||||
\(880\) | −3.24526 | −0.000124316 | ||||||||
\(881\) | −16588.0 | −0.634353 | −0.317176 | − | 0.948367i | \(-0.602735\pi\) | ||||
−0.317176 | + | 0.948367i | \(0.602735\pi\) | |||||||
\(882\) | 20530.1 | + | 1423.94i | 0.783771 | + | 0.0543611i | ||||
\(883\) | − | 45423.1i | − | 1.73115i | −0.500776 | − | 0.865577i | \(-0.666952\pi\) | ||
0.500776 | − | 0.865577i | \(-0.333048\pi\) | |||||||
\(884\) | 3580.34 | + | 4961.12i | 0.136222 | + | 0.188756i | ||||
\(885\) | −598.870 | + | 1315.09i | −0.0227467 | + | 0.0499504i | ||||
\(886\) | −25360.5 | + | 25360.5i | −0.961627 | + | 0.961627i | ||||
\(887\) | 21141.8i | 0.800308i | 0.916448 | + | 0.400154i | \(0.131043\pi\) | ||||
−0.916448 | + | 0.400154i | \(0.868957\pi\) | |||||||
\(888\) | −13863.8 | + | 30444.3i | −0.523919 | + | 1.15050i | ||||
\(889\) | −5979.22 | + | 5979.22i | −0.225575 | + | 0.225575i | ||||
\(890\) | 756.858 | + | 756.858i | 0.0285055 | + | 0.0285055i | ||||
\(891\) | −37.3961 | − | 49.5097i | −0.00140608 | − | 0.00186154i | ||||
\(892\) | −645.376 | − | 645.376i | −0.0242251 | − | 0.0242251i | ||||
\(893\) | − | 8967.61i | − | 0.336047i | ||||||
\(894\) | 19999.2 | + | 9107.32i | 0.748180 | + | 0.340710i | ||||
\(895\) | 120.263 | + | 120.263i | 0.00449157 | + | 0.00449157i | ||||
\(896\) | 17898.4 | 0.667347 | ||||||||
\(897\) | −4488.69 | − | 22395.7i | −0.167083 | − | 0.833633i | ||||
\(898\) | 20418.3 | 0.758759 | ||||||||
\(899\) | 32839.1 | + | 32839.1i | 1.21829 | + | 1.21829i | ||||
\(900\) | −4965.55 | − | 5705.69i | −0.183909 | − | 0.211322i | ||||
\(901\) | 33878.8i | 1.25268i | ||||||||
\(902\) | 36.1010 | + | 36.1010i | 0.00133263 | + | 0.00133263i | ||||
\(903\) | −5177.26 | − | 13835.3i | −0.190796 | − | 0.509866i | ||||
\(904\) | −16928.3 | − | 16928.3i | −0.622817 | − | 0.622817i | ||||
\(905\) | 948.946 | − | 948.946i | 0.0348553 | − | 0.0348553i | ||||
\(906\) | 14624.8 | + | 6659.92i | 0.536288 | + | 0.244218i | ||||
\(907\) | − | 31242.6i | − | 1.14376i | −0.820336 | − | 0.571881i | \(-0.806214\pi\) | ||
0.820336 | − | 0.571881i | \(-0.193786\pi\) | |||||||
\(908\) | −8942.41 | + | 8942.41i | −0.326833 | + | 0.326833i | ||||
\(909\) | −31441.9 | − | 36128.5i | −1.14726 | − | 1.31827i | ||||
\(910\) | −121.542 | + | 751.856i | −0.00442756 | + | 0.0273888i | ||||
\(911\) | − | 28667.7i | − | 1.04260i | −0.853375 | − | 0.521298i | \(-0.825448\pi\) | ||
0.853375 | − | 0.521298i | \(-0.174552\pi\) | |||||||
\(912\) | −4048.11 | − | 10817.8i | −0.146981 | − | 0.392779i | ||||
\(913\) | 104.487 | 0.00378754 | ||||||||
\(914\) | −28883.2 | −1.04526 | ||||||||
\(915\) | −589.115 | + | 220.451i | −0.0212847 | + | 0.00796490i | ||||
\(916\) | −2646.06 | + | 2646.06i | −0.0954456 | + | 0.0954456i | ||||
\(917\) | 2003.79 | − | 2003.79i | 0.0721604 | − | 0.0721604i | ||||
\(918\) | 22950.6 | + | 12435.9i | 0.825143 | + | 0.447110i | ||||
\(919\) | 16605.4 | 0.596040 | 0.298020 | − | 0.954560i | \(-0.403674\pi\) | ||||
0.298020 | + | 0.954560i | \(0.403674\pi\) | |||||||
\(920\) | −856.261 | −0.0306849 | ||||||||
\(921\) | 7707.02 | − | 2884.02i | 0.275738 | − | 0.103183i | ||||
\(922\) | 24355.9i | 0.869979i | ||||||||
\(923\) | −29766.1 | − | 4811.87i | −1.06150 | − | 0.171598i | ||||
\(924\) | 9.25564 | + | 4.21488i | 0.000329533 | + | 0.000150064i | ||||
\(925\) | 30832.8 | − | 30832.8i | 1.09598 | − | 1.09598i | ||||
\(926\) | − | 25777.5i | − | 0.914798i | ||||||
\(927\) | 26662.8 | − | 23204.1i | 0.944684 | − | 0.822140i | ||||
\(928\) | −13228.6 | + | 13228.6i | −0.467943 | + | 0.467943i | ||||
\(929\) | −18663.1 | − | 18663.1i | −0.659112 | − | 0.659112i | 0.296058 | − | 0.955170i | \(-0.404328\pi\) |
−0.955170 | + | 0.296058i | \(0.904328\pi\) | |||||||
\(930\) | 1895.03 | − | 709.134i | 0.0668177 | − | 0.0250037i | ||||
\(931\) | −4865.80 | − | 4865.80i | −0.171289 | − | 0.171289i | ||||
\(932\) | − | 13049.9i | − | 0.458653i | ||||||
\(933\) | 3862.93 | − | 8482.78i | 0.135548 | − | 0.297657i | ||||
\(934\) | 29731.2 | + | 29731.2i | 1.04158 | + | 1.04158i | ||||
\(935\) | −2.45235 | −8.57757e−5 | ||||||||
\(936\) | 19800.7 | − | 12300.7i | 0.691460 | − | 0.429553i | ||||
\(937\) | −24863.9 | −0.866881 | −0.433440 | − | 0.901182i | \(-0.642701\pi\) | ||||
−0.433440 | + | 0.901182i | \(0.642701\pi\) | |||||||
\(938\) | −1456.40 | − | 1456.40i | −0.0506963 | − | 0.0506963i | ||||
\(939\) | 16242.0 | − | 35666.5i | 0.564470 | − | 1.23954i | ||||
\(940\) | 345.421i | 0.0119855i | ||||||||
\(941\) | 10173.1 | + | 10173.1i | 0.352426 | + | 0.352426i | 0.861011 | − | 0.508586i | \(-0.169831\pi\) |
−0.508586 | + | 0.861011i | \(0.669831\pi\) | |||||||
\(942\) | 1808.47 | − | 676.741i | 0.0625510 | − | 0.0234070i | ||||
\(943\) | 12427.6 | + | 12427.6i | 0.429159 | + | 0.429159i | ||||
\(944\) | −30515.0 | + | 30515.0i | −1.05209 | + | 1.05209i | ||||
\(945\) | 202.854 | + | 682.696i | 0.00698290 | + | 0.0235006i | ||||
\(946\) | 75.6272i | 0.00259921i | ||||||||
\(947\) | −6473.47 | + | 6473.47i | −0.222132 | + | 0.222132i | −0.809396 | − | 0.587263i | \(-0.800205\pi\) |
0.587263 | + | 0.809396i | \(0.300205\pi\) | |||||||
\(948\) | 6767.75 | + | 3081.93i | 0.231863 | + | 0.105587i | ||||
\(949\) | 28150.1 | + | 4550.63i | 0.962899 | + | 0.155658i | ||||
\(950\) | 11539.6i | 0.394098i | ||||||||
\(951\) | −26052.6 | + | 9749.07i | −0.888343 | + | 0.332424i | ||||
\(952\) | 10964.6 | 0.373281 | ||||||||
\(953\) | 28943.0 | 0.983793 | 0.491897 | − | 0.870654i | \(-0.336304\pi\) | ||||
0.491897 | + | 0.870654i | \(0.336304\pi\) | |||||||
\(954\) | −50249.9 | − | 3485.25i | −1.70535 | − | 0.118280i | ||||
\(955\) | −1246.61 | + | 1246.61i | −0.0422401 | + | 0.0422401i | ||||
\(956\) | 1171.80 | − | 1171.80i | 0.0396430 | − | 0.0396430i | ||||
\(957\) | 78.3799 | − | 29.3303i | 0.00264751 | − | 0.000990715i | ||||
\(958\) | −9052.09 | −0.305282 | ||||||||
\(959\) | −2096.94 | −0.0706087 | ||||||||
\(960\) | −269.847 | − | 721.117i | −0.00907217 | − | 0.0242437i | ||||
\(961\) | − | 30439.8i | − | 1.02178i | ||||||
\(962\) | −30687.5 | − | 42522.3i | −1.02849 | − | 1.42513i | ||||
\(963\) | −7604.85 | + | 6618.35i | −0.254479 | + | 0.221468i | ||||
\(964\) | 6195.32 | − | 6195.32i | 0.206990 | − | 0.206990i | ||||
\(965\) | − | 41.7026i | − | 0.00139114i | ||||||
\(966\) | 14537.4 | + | 6620.10i | 0.484195 | + | 0.220495i | ||||
\(967\) | −6194.98 | + | 6194.98i | −0.206016 | + | 0.206016i | −0.802572 | − | 0.596556i | \(-0.796535\pi\) |
0.596556 | + | 0.802572i | \(0.296535\pi\) | |||||||
\(968\) | −17335.3 | − | 17335.3i | −0.575598 | − | 0.575598i | ||||
\(969\) | −3059.03 | − | 8174.70i | −0.101414 | − | 0.271011i | ||||
\(970\) | −266.850 | − | 266.850i | −0.00883303 | − | 0.00883303i | ||||
\(971\) | − | 47616.7i | − | 1.57373i | −0.617124 | − | 0.786866i | \(-0.711702\pi\) | ||
0.617124 | − | 0.786866i | \(-0.288298\pi\) | |||||||
\(972\) | −4560.19 | + | 7180.45i | −0.150482 | + | 0.236948i | ||||
\(973\) | 17702.0 | + | 17702.0i | 0.583248 | + | 0.583248i | ||||
\(974\) | 32557.1 | 1.07104 | ||||||||
\(975\) | −29792.0 | + | 5971.12i | −0.978573 | + | 0.196132i | ||||
\(976\) | −18785.0 | −0.616078 | ||||||||
\(977\) | 1901.80 | + | 1901.80i | 0.0622764 | + | 0.0622764i | 0.737559 | − | 0.675283i | \(-0.235978\pi\) |
−0.675283 | + | 0.737559i | \(0.735978\pi\) | |||||||
\(978\) | 5718.77 | + | 2604.24i | 0.186980 | + | 0.0851477i | ||||
\(979\) | − | 57.4157i | − | 0.00187438i | ||||||
\(980\) | 187.424 | + | 187.424i | 0.00610923 | + | 0.00610923i | ||||
\(981\) | −54831.9 | − | 3803.05i | −1.78455 | − | 0.123774i | ||||
\(982\) | −20053.7 | − | 20053.7i | −0.651671 | − | 0.651671i | ||||
\(983\) | 9735.99 | − | 9735.99i | 0.315900 | − | 0.315900i | −0.531290 | − | 0.847190i | \(-0.678293\pi\) |
0.847190 | + | 0.531290i | \(0.178293\pi\) | |||||||
\(984\) | −7433.49 | + | 16323.5i | −0.240824 | + | 0.528837i | ||||
\(985\) | 160.738i | 0.00519954i | ||||||||
\(986\) | −24896.1 | + | 24896.1i | −0.804110 | + | 0.804110i | ||||
\(987\) | −6843.65 | + | 15028.3i | −0.220705 | + | 0.484656i | ||||
\(988\) | 3002.64 | + | 485.393i | 0.0966868 | + | 0.0156300i | ||||
\(989\) | 26034.3i | 0.837049i | ||||||||
\(990\) | 0.252283 | − | 3.63739i | 8.09908e−6 | − | 0.000116771i | ||||
\(991\) | 62313.0 | 1.99741 | 0.998707 | − | 0.0508357i | \(-0.0161885\pi\) | ||||
0.998707 | + | 0.0508357i | \(0.0161885\pi\) | |||||||
\(992\) | 24262.9 | 0.776561 | ||||||||
\(993\) | 9862.16 | + | 26354.8i | 0.315172 | + | 0.842240i | ||||
\(994\) | 14910.8 | − | 14910.8i | 0.475796 | − | 0.475796i | ||||
\(995\) | −1503.34 | + | 1503.34i | −0.0478987 | + | 0.0478987i | ||||
\(996\) | −5020.38 | − | 13416.0i | −0.159716 | − | 0.426811i | ||||
\(997\) | −40277.8 | −1.27945 | −0.639725 | − | 0.768604i | \(-0.720952\pi\) | ||||
−0.639725 | + | 0.768604i | \(0.720952\pi\) | |||||||
\(998\) | 16331.3 | 0.517994 | ||||||||
\(999\) | −43113.9 | − | 23361.6i | −1.36543 | − | 0.739868i |
(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 | 39.4.f.b.5.3 | ✓ | 20 | |
3.2 | odd | 2 | inner | 39.4.f.b.5.8 | yes | 20 | |
13.8 | odd | 4 | inner | 39.4.f.b.8.8 | yes | 20 | |
39.8 | even | 4 | inner | 39.4.f.b.8.3 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.f.b.5.3 | ✓ | 20 | 1.1 | even | 1 | trivial | |
39.4.f.b.5.8 | yes | 20 | 3.2 | odd | 2 | inner | |
39.4.f.b.8.3 | yes | 20 | 39.8 | even | 4 | inner | |
39.4.f.b.8.8 | yes | 20 | 13.8 | odd | 4 | inner |