Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [29,3,Mod(12,29)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(29, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("29.12");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.c (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: | \(0.790192766645\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 18x^{6} + 91x^{4} + 126x^{2} + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 12.4 | ||
Root | \(-0.486981i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 29.12 |
Dual form | 29.3.c.a.17.4 |
$q$-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 \(\left(\mathbb{Z}/29\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.62492 | + | 2.62492i | 1.31246 | + | 1.31246i | 0.919599 | + | 0.392859i | \(0.128514\pi\) |
0.392859 | + | 0.919599i | \(0.371486\pi\) | |||||||
\(3\) | −3.11190 | − | 3.11190i | −1.03730 | − | 1.03730i | −0.999277 | − | 0.0380218i | \(-0.987894\pi\) |
−0.0380218 | − | 0.999277i | \(-0.512106\pi\) | |||||||
\(4\) | 9.78036i | 2.44509i | ||||||||
\(5\) | − | 4.53053i | − | 0.906106i | −0.891484 | − | 0.453053i | \(-0.850335\pi\) | ||
0.891484 | − | 0.453053i | \(-0.149665\pi\) | |||||||
\(6\) | − | 16.3369i | − | 2.72282i | ||||||
\(7\) | −0.745339 | −0.106477 | −0.0532385 | − | 0.998582i | \(-0.516954\pi\) | ||||
−0.0532385 | + | 0.998582i | \(0.516954\pi\) | |||||||
\(8\) | −15.1730 | + | 15.1730i | −1.89662 | + | 1.89662i | ||||
\(9\) | 10.3678i | 1.15198i | ||||||||
\(10\) | 11.8923 | − | 11.8923i | 1.18923 | − | 1.18923i | ||||
\(11\) | 0.0423096 | + | 0.0423096i | 0.00384632 | + | 0.00384632i | 0.709027 | − | 0.705181i | \(-0.249134\pi\) |
−0.705181 | + | 0.709027i | \(0.749134\pi\) | |||||||
\(12\) | 30.4355 | − | 30.4355i | 2.53629 | − | 2.53629i | ||||
\(13\) | 8.30191i | 0.638608i | 0.947652 | + | 0.319304i | \(0.103449\pi\) | ||||
−0.947652 | + | 0.319304i | \(0.896551\pi\) | |||||||
\(14\) | −1.95645 | − | 1.95645i | −0.139747 | − | 0.139747i | ||||
\(15\) | −14.0985 | + | 14.0985i | −0.939903 | + | 0.939903i | ||||
\(16\) | −40.5340 | −2.53338 | ||||||||
\(17\) | 15.2625 | + | 15.2625i | 0.897795 | + | 0.897795i | 0.995241 | − | 0.0974461i | \(-0.0310673\pi\) |
−0.0974461 | + | 0.995241i | \(0.531067\pi\) | |||||||
\(18\) | −27.2146 | + | 27.2146i | −1.51192 | + | 1.51192i | ||||
\(19\) | −25.1348 | − | 25.1348i | −1.32288 | − | 1.32288i | −0.911431 | − | 0.411453i | \(-0.865021\pi\) |
−0.411453 | − | 0.911431i | \(-0.634979\pi\) | |||||||
\(20\) | 44.3102 | 2.21551 | ||||||||
\(21\) | 2.31942 | + | 2.31942i | 0.110448 | + | 0.110448i | ||||
\(22\) | 0.222118i | 0.0100963i | ||||||||
\(23\) | 8.64367 | 0.375812 | 0.187906 | − | 0.982187i | \(-0.439830\pi\) | ||||
0.187906 | + | 0.982187i | \(0.439830\pi\) | |||||||
\(24\) | 94.4333 | 3.93472 | ||||||||
\(25\) | 4.47430 | 0.178972 | ||||||||
\(26\) | −21.7918 | + | 21.7918i | −0.838146 | + | 0.838146i | ||||
\(27\) | 4.25644 | − | 4.25644i | 0.157646 | − | 0.157646i | ||||
\(28\) | − | 7.28968i | − | 0.260346i | ||||||
\(29\) | 22.0908 | − | 18.7882i | 0.761752 | − | 0.647869i | ||||
\(30\) | −74.0149 | −2.46716 | ||||||||
\(31\) | −5.09325 | − | 5.09325i | −0.164298 | − | 0.164298i | 0.620169 | − | 0.784468i | \(-0.287064\pi\) |
−0.784468 | + | 0.620169i | \(0.787064\pi\) | |||||||
\(32\) | −45.7065 | − | 45.7065i | −1.42833 | − | 1.42833i | ||||
\(33\) | − | 0.263326i | − | 0.00797957i | ||||||
\(34\) | 80.1256i | 2.35664i | ||||||||
\(35\) | 3.37678i | 0.0964794i | ||||||||
\(36\) | −101.401 | −2.81669 | ||||||||
\(37\) | 10.0725 | − | 10.0725i | 0.272230 | − | 0.272230i | −0.557767 | − | 0.829997i | \(-0.688342\pi\) |
0.829997 | + | 0.557767i | \(0.188342\pi\) | |||||||
\(38\) | − | 131.953i | − | 3.47246i | ||||||
\(39\) | 25.8347 | − | 25.8347i | 0.662427 | − | 0.662427i | ||||
\(40\) | 68.7415 | + | 68.7415i | 1.71854 | + | 1.71854i | ||||
\(41\) | 2.50571 | − | 2.50571i | 0.0611149 | − | 0.0611149i | −0.675889 | − | 0.737004i | \(-0.736240\pi\) |
0.737004 | + | 0.675889i | \(0.236240\pi\) | |||||||
\(42\) | 12.1765i | 0.289918i | ||||||||
\(43\) | −11.2668 | − | 11.2668i | −0.262018 | − | 0.262018i | 0.563855 | − | 0.825874i | \(-0.309318\pi\) |
−0.825874 | + | 0.563855i | \(0.809318\pi\) | |||||||
\(44\) | −0.413803 | + | 0.413803i | −0.00940461 | + | 0.00940461i | ||||
\(45\) | 46.9716 | 1.04381 | ||||||||
\(46\) | 22.6889 | + | 22.6889i | 0.493237 | + | 0.493237i | ||||
\(47\) | −23.0132 | + | 23.0132i | −0.489643 | + | 0.489643i | −0.908194 | − | 0.418550i | \(-0.862538\pi\) |
0.418550 | + | 0.908194i | \(0.362538\pi\) | |||||||
\(48\) | 126.138 | + | 126.138i | 2.62787 | + | 2.62787i | ||||
\(49\) | −48.4445 | −0.988663 | ||||||||
\(50\) | 11.7447 | + | 11.7447i | 0.234893 | + | 0.234893i | ||||
\(51\) | − | 94.9907i | − | 1.86256i | ||||||
\(52\) | −81.1956 | −1.56145 | ||||||||
\(53\) | −42.8979 | −0.809394 | −0.404697 | − | 0.914451i | \(-0.632623\pi\) | ||||
−0.404697 | + | 0.914451i | \(0.632623\pi\) | |||||||
\(54\) | 22.3456 | 0.413807 | ||||||||
\(55\) | 0.191685 | − | 0.191685i | 0.00348518 | − | 0.00348518i | ||||
\(56\) | 11.3090 | − | 11.3090i | 0.201946 | − | 0.201946i | ||||
\(57\) | 156.434i | 2.74445i | ||||||||
\(58\) | 107.304 | + | 8.66900i | 1.85007 | + | 0.149466i | ||||
\(59\) | 106.413 | 1.80361 | 0.901806 | − | 0.432140i | \(-0.142241\pi\) | ||||
0.901806 | + | 0.432140i | \(0.142241\pi\) | |||||||
\(60\) | −137.889 | − | 137.889i | −2.29815 | − | 2.29815i | ||||
\(61\) | −42.3211 | − | 42.3211i | −0.693788 | − | 0.693788i | 0.269275 | − | 0.963063i | \(-0.413216\pi\) |
−0.963063 | + | 0.269275i | \(0.913216\pi\) | |||||||
\(62\) | − | 26.7387i | − | 0.431269i | ||||||
\(63\) | − | 7.72752i | − | 0.122659i | ||||||
\(64\) | − | 77.8154i | − | 1.21587i | ||||||
\(65\) | 37.6120 | 0.578647 | ||||||||
\(66\) | 0.691208 | − | 0.691208i | 0.0104729 | − | 0.0104729i | ||||
\(67\) | 75.7926i | 1.13123i | 0.824668 | + | 0.565616i | \(0.191362\pi\) | ||||
−0.824668 | + | 0.565616i | \(0.808638\pi\) | |||||||
\(68\) | −149.273 | + | 149.273i | −2.19519 | + | 2.19519i | ||||
\(69\) | −26.8982 | − | 26.8982i | −0.389829 | − | 0.389829i | ||||
\(70\) | −8.86376 | + | 8.86376i | −0.126625 | + | 0.126625i | ||||
\(71\) | 71.2051i | 1.00289i | 0.865190 | + | 0.501445i | \(0.167198\pi\) | ||||
−0.865190 | + | 0.501445i | \(0.832802\pi\) | |||||||
\(72\) | −157.310 | − | 157.310i | −2.18486 | − | 2.18486i | ||||
\(73\) | −73.7928 | + | 73.7928i | −1.01086 | + | 1.01086i | −0.0109201 | + | 0.999940i | \(0.503476\pi\) |
−0.999940 | + | 0.0109201i | \(0.996524\pi\) | |||||||
\(74\) | 52.8790 | 0.714581 | ||||||||
\(75\) | −13.9236 | − | 13.9236i | −0.185647 | − | 0.185647i | ||||
\(76\) | 245.827 | − | 245.827i | 3.23457 | − | 3.23457i | ||||
\(77\) | −0.0315350 | − | 0.0315350i | −0.000409545 | − | 0.000409545i | ||||
\(78\) | 135.628 | 1.73882 | ||||||||
\(79\) | −78.7399 | − | 78.7399i | −0.996707 | − | 0.996707i | 0.00328762 | − | 0.999995i | \(-0.498954\pi\) |
−0.999995 | + | 0.00328762i | \(0.998954\pi\) | |||||||
\(80\) | 183.641i | 2.29551i | ||||||||
\(81\) | 66.8190 | 0.824925 | ||||||||
\(82\) | 13.1546 | 0.160421 | ||||||||
\(83\) | 15.1749 | 0.182830 | 0.0914152 | − | 0.995813i | \(-0.470861\pi\) | ||||
0.0914152 | + | 0.995813i | \(0.470861\pi\) | |||||||
\(84\) | −22.6847 | + | 22.6847i | −0.270056 | + | 0.270056i | ||||
\(85\) | 69.1473 | − | 69.1473i | 0.813497 | − | 0.813497i | ||||
\(86\) | − | 59.1487i | − | 0.687775i | ||||||
\(87\) | −127.211 | − | 10.2773i | −1.46220 | − | 0.118130i | ||||
\(88\) | −1.28392 | −0.0145900 | ||||||||
\(89\) | −22.8417 | − | 22.8417i | −0.256648 | − | 0.256648i | 0.567041 | − | 0.823689i | \(-0.308088\pi\) |
−0.823689 | + | 0.567041i | \(0.808088\pi\) | |||||||
\(90\) | 123.296 | + | 123.296i | 1.36996 | + | 1.36996i | ||||
\(91\) | − | 6.18773i | − | 0.0679971i | ||||||
\(92\) | 84.5382i | 0.918893i | ||||||||
\(93\) | 31.6993i | 0.340853i | ||||||||
\(94\) | −120.816 | −1.28527 | ||||||||
\(95\) | −113.874 | + | 113.874i | −1.19867 | + | 1.19867i | ||||
\(96\) | 284.468i | 2.96321i | ||||||||
\(97\) | 42.8298 | − | 42.8298i | 0.441544 | − | 0.441544i | −0.450987 | − | 0.892531i | \(-0.648928\pi\) |
0.892531 | + | 0.450987i | \(0.148928\pi\) | |||||||
\(98\) | −127.163 | − | 127.163i | −1.29758 | − | 1.29758i | ||||
\(99\) | −0.438657 | + | 0.438657i | −0.00443088 | + | 0.00443088i | ||||
\(100\) | 43.7603i | 0.437603i | ||||||||
\(101\) | 36.4365 | + | 36.4365i | 0.360757 | + | 0.360757i | 0.864092 | − | 0.503334i | \(-0.167894\pi\) |
−0.503334 | + | 0.864092i | \(0.667894\pi\) | |||||||
\(102\) | 249.343 | − | 249.343i | 2.44453 | − | 2.44453i | ||||
\(103\) | 111.751 | 1.08496 | 0.542479 | − | 0.840070i | \(-0.317486\pi\) | ||||
0.542479 | + | 0.840070i | \(0.317486\pi\) | |||||||
\(104\) | −125.964 | − | 125.964i | −1.21120 | − | 1.21120i | ||||
\(105\) | 10.5082 | − | 10.5082i | 0.100078 | − | 0.100078i | ||||
\(106\) | −112.603 | − | 112.603i | −1.06230 | − | 1.06230i | ||||
\(107\) | 88.9678 | 0.831475 | 0.415737 | − | 0.909485i | \(-0.363524\pi\) | ||||
0.415737 | + | 0.909485i | \(0.363524\pi\) | |||||||
\(108\) | 41.6295 | + | 41.6295i | 0.385459 | + | 0.385459i | ||||
\(109\) | 41.1196i | 0.377244i | 0.982050 | + | 0.188622i | \(0.0604020\pi\) | ||||
−0.982050 | + | 0.188622i | \(0.939598\pi\) | |||||||
\(110\) | 1.00631 | 0.00914829 | ||||||||
\(111\) | −62.6893 | −0.564768 | ||||||||
\(112\) | 30.2116 | 0.269746 | ||||||||
\(113\) | 104.104 | − | 104.104i | 0.921275 | − | 0.921275i | −0.0758450 | − | 0.997120i | \(-0.524165\pi\) |
0.997120 | + | 0.0758450i | \(0.0241654\pi\) | |||||||
\(114\) | −410.625 | + | 410.625i | −3.60198 | + | 3.60198i | ||||
\(115\) | − | 39.1604i | − | 0.340525i | ||||||
\(116\) | 183.755 | + | 216.056i | 1.58410 | + | 1.86255i | ||||
\(117\) | −86.0725 | −0.735662 | ||||||||
\(118\) | 279.326 | + | 279.326i | 2.36717 | + | 2.36717i | ||||
\(119\) | −11.3757 | − | 11.3757i | −0.0955945 | − | 0.0955945i | ||||
\(120\) | − | 427.833i | − | 3.56527i | ||||||
\(121\) | − | 120.996i | − | 0.999970i | ||||||
\(122\) | − | 222.179i | − | 1.82114i | ||||||
\(123\) | −15.5950 | −0.126789 | ||||||||
\(124\) | 49.8138 | − | 49.8138i | 0.401724 | − | 0.401724i | ||||
\(125\) | − | 133.534i | − | 1.06827i | ||||||
\(126\) | 20.2841 | − | 20.2841i | 0.160985 | − | 0.160985i | ||||
\(127\) | 8.26743 | + | 8.26743i | 0.0650978 | + | 0.0650978i | 0.738906 | − | 0.673808i | \(-0.235343\pi\) |
−0.673808 | + | 0.738906i | \(0.735343\pi\) | |||||||
\(128\) | 21.4328 | − | 21.4328i | 0.167443 | − | 0.167443i | ||||
\(129\) | 70.1221i | 0.543582i | ||||||||
\(130\) | 98.7284 | + | 98.7284i | 0.759449 | + | 0.759449i | ||||
\(131\) | −0.361622 | + | 0.361622i | −0.00276047 | + | 0.00276047i | −0.708486 | − | 0.705725i | \(-0.750621\pi\) |
0.705725 | + | 0.708486i | \(0.250621\pi\) | |||||||
\(132\) | 2.57542 | 0.0195108 | ||||||||
\(133\) | 18.7339 | + | 18.7339i | 0.140857 | + | 0.140857i | ||||
\(134\) | −198.949 | + | 198.949i | −1.48470 | + | 1.48470i | ||||
\(135\) | −19.2839 | − | 19.2839i | −0.142844 | − | 0.142844i | ||||
\(136\) | −463.155 | −3.40555 | ||||||||
\(137\) | −69.5740 | − | 69.5740i | −0.507840 | − | 0.507840i | 0.406023 | − | 0.913863i | \(-0.366915\pi\) |
−0.913863 | + | 0.406023i | \(0.866915\pi\) | |||||||
\(138\) | − | 141.211i | − | 1.02327i | ||||||
\(139\) | 111.380 | 0.801297 | 0.400649 | − | 0.916232i | \(-0.368785\pi\) | ||||
0.400649 | + | 0.916232i | \(0.368785\pi\) | |||||||
\(140\) | −33.0261 | −0.235901 | ||||||||
\(141\) | 143.230 | 1.01581 | ||||||||
\(142\) | −186.907 | + | 186.907i | −1.31625 | + | 1.31625i | ||||
\(143\) | −0.351250 | + | 0.351250i | −0.00245629 | + | 0.00245629i | ||||
\(144\) | − | 420.248i | − | 2.91839i | ||||||
\(145\) | −85.1205 | − | 100.083i | −0.587038 | − | 0.690228i | ||||
\(146\) | −387.400 | −2.65342 | ||||||||
\(147\) | 150.754 | + | 150.754i | 1.02554 | + | 1.02554i | ||||
\(148\) | 98.5129 | + | 98.5129i | 0.665628 | + | 0.665628i | ||||
\(149\) | 44.5177i | 0.298776i | 0.988779 | + | 0.149388i | \(0.0477304\pi\) | ||||
−0.988779 | + | 0.149388i | \(0.952270\pi\) | |||||||
\(150\) | − | 73.0963i | − | 0.487309i | ||||||
\(151\) | 70.6402i | 0.467816i | 0.972259 | + | 0.233908i | \(0.0751514\pi\) | ||||
−0.972259 | + | 0.233908i | \(0.924849\pi\) | |||||||
\(152\) | 762.738 | 5.01802 | ||||||||
\(153\) | −158.239 | + | 158.239i | −1.03424 | + | 1.03424i | ||||
\(154\) | − | 0.165553i | − | 0.00107502i | ||||||
\(155\) | −23.0751 | + | 23.0751i | −0.148872 | + | 0.148872i | ||||
\(156\) | 252.672 | + | 252.672i | 1.61969 | + | 1.61969i | ||||
\(157\) | −127.354 | + | 127.354i | −0.811173 | + | 0.811173i | −0.984810 | − | 0.173636i | \(-0.944448\pi\) |
0.173636 | + | 0.984810i | \(0.444448\pi\) | |||||||
\(158\) | − | 413.371i | − | 2.61627i | ||||||
\(159\) | 133.494 | + | 133.494i | 0.839583 | + | 0.839583i | ||||
\(160\) | −207.075 | + | 207.075i | −1.29422 | + | 1.29422i | ||||
\(161\) | −6.44246 | −0.0400153 | ||||||||
\(162\) | 175.394 | + | 175.394i | 1.08268 | + | 1.08268i | ||||
\(163\) | 83.4261 | − | 83.4261i | 0.511817 | − | 0.511817i | −0.403266 | − | 0.915083i | \(-0.632125\pi\) |
0.915083 | + | 0.403266i | \(0.132125\pi\) | |||||||
\(164\) | 24.5067 | + | 24.5067i | 0.149431 | + | 0.149431i | ||||
\(165\) | −1.19301 | −0.00723034 | ||||||||
\(166\) | 39.8329 | + | 39.8329i | 0.239957 | + | 0.239957i | ||||
\(167\) | 221.605i | 1.32697i | 0.748188 | + | 0.663487i | \(0.230924\pi\) | ||||
−0.748188 | + | 0.663487i | \(0.769076\pi\) | |||||||
\(168\) | −70.3848 | −0.418957 | ||||||||
\(169\) | 100.078 | 0.592180 | ||||||||
\(170\) | 363.011 | 2.13536 | ||||||||
\(171\) | 260.592 | − | 260.592i | 1.52393 | − | 1.52393i | ||||
\(172\) | 110.193 | − | 110.193i | 0.640658 | − | 0.640658i | ||||
\(173\) | 6.62034i | 0.0382679i | 0.999817 | + | 0.0191339i | \(0.00609089\pi\) | ||||
−0.999817 | + | 0.0191339i | \(0.993909\pi\) | |||||||
\(174\) | −306.942 | − | 360.896i | −1.76403 | − | 2.07411i | ||||
\(175\) | −3.33487 | −0.0190564 | ||||||||
\(176\) | −1.71498 | − | 1.71498i | −0.00974418 | − | 0.00974418i | ||||
\(177\) | −331.147 | − | 331.147i | −1.87089 | − | 1.87089i | ||||
\(178\) | − | 119.915i | − | 0.673679i | ||||||
\(179\) | − | 36.9603i | − | 0.206482i | −0.994656 | − | 0.103241i | \(-0.967079\pi\) | ||
0.994656 | − | 0.103241i | \(-0.0329213\pi\) | |||||||
\(180\) | 459.399i | 2.55222i | ||||||||
\(181\) | −192.039 | −1.06099 | −0.530494 | − | 0.847689i | \(-0.677994\pi\) | ||||
−0.530494 | + | 0.847689i | \(0.677994\pi\) | |||||||
\(182\) | 16.2423 | − | 16.2423i | 0.0892433 | − | 0.0892433i | ||||
\(183\) | 263.398i | 1.43933i | ||||||||
\(184\) | −131.150 | + | 131.150i | −0.712771 | + | 0.712771i | ||||
\(185\) | −45.6339 | − | 45.6339i | −0.246669 | − | 0.246669i | ||||
\(186\) | −83.2081 | + | 83.2081i | −0.447355 | + | 0.447355i | ||||
\(187\) | 1.29150i | 0.00690642i | ||||||||
\(188\) | −225.078 | − | 225.078i | −1.19722 | − | 1.19722i | ||||
\(189\) | −3.17249 | + | 3.17249i | −0.0167857 | + | 0.0167857i | ||||
\(190\) | −597.819 | −3.14642 | ||||||||
\(191\) | −215.351 | − | 215.351i | −1.12749 | − | 1.12749i | −0.990584 | − | 0.136906i | \(-0.956284\pi\) |
−0.136906 | − | 0.990584i | \(-0.543716\pi\) | |||||||
\(192\) | −242.153 | + | 242.153i | −1.26122 | + | 1.26122i | ||||
\(193\) | 130.679 | + | 130.679i | 0.677095 | + | 0.677095i | 0.959342 | − | 0.282247i | \(-0.0910797\pi\) |
−0.282247 | + | 0.959342i | \(0.591080\pi\) | |||||||
\(194\) | 224.849 | 1.15902 | ||||||||
\(195\) | −117.045 | − | 117.045i | −0.600229 | − | 0.600229i | ||||
\(196\) | − | 473.804i | − | 2.41737i | ||||||
\(197\) | −254.953 | −1.29418 | −0.647090 | − | 0.762414i | \(-0.724014\pi\) | ||||
−0.647090 | + | 0.762414i | \(0.724014\pi\) | |||||||
\(198\) | −2.30287 | −0.0116307 | ||||||||
\(199\) | 168.018 | 0.844311 | 0.422155 | − | 0.906524i | \(-0.361274\pi\) | ||||
0.422155 | + | 0.906524i | \(0.361274\pi\) | |||||||
\(200\) | −67.8884 | + | 67.8884i | −0.339442 | + | 0.339442i | ||||
\(201\) | 235.859 | − | 235.859i | 1.17343 | − | 1.17343i | ||||
\(202\) | 191.285i | 0.946957i | ||||||||
\(203\) | −16.4651 | + | 14.0036i | −0.0811090 | + | 0.0689832i | ||||
\(204\) | 929.043 | 4.55413 | ||||||||
\(205\) | −11.3522 | − | 11.3522i | −0.0553766 | − | 0.0553766i | ||||
\(206\) | 293.336 | + | 293.336i | 1.42396 | + | 1.42396i | ||||
\(207\) | 89.6158i | 0.432926i | ||||||||
\(208\) | − | 336.510i | − | 1.61783i | ||||||
\(209\) | − | 2.12688i | − | 0.0101765i | ||||||
\(210\) | 55.1662 | 0.262696 | ||||||||
\(211\) | −111.890 | + | 111.890i | −0.530285 | + | 0.530285i | −0.920657 | − | 0.390372i | \(-0.872346\pi\) |
0.390372 | + | 0.920657i | \(0.372346\pi\) | |||||||
\(212\) | − | 419.557i | − | 1.97904i | ||||||
\(213\) | 221.583 | − | 221.583i | 1.04030 | − | 1.04030i | ||||
\(214\) | 233.533 | + | 233.533i | 1.09128 | + | 1.09128i | ||||
\(215\) | −51.0445 | + | 51.0445i | −0.237416 | + | 0.237416i | ||||
\(216\) | 129.166i | 0.597989i | ||||||||
\(217\) | 3.79620 | + | 3.79620i | 0.0174940 | + | 0.0174940i | ||||
\(218\) | −107.935 | + | 107.935i | −0.495116 | + | 0.495116i | ||||
\(219\) | 459.271 | 2.09713 | ||||||||
\(220\) | 1.87475 | + | 1.87475i | 0.00852157 | + | 0.00852157i | ||||
\(221\) | −126.708 | + | 126.708i | −0.573339 | + | 0.573339i | ||||
\(222\) | −164.554 | − | 164.554i | −0.741234 | − | 0.741234i | ||||
\(223\) | −57.0256 | −0.255720 | −0.127860 | − | 0.991792i | \(-0.540811\pi\) | ||||
−0.127860 | + | 0.991792i | \(0.540811\pi\) | |||||||
\(224\) | 34.0668 | + | 34.0668i | 0.152084 | + | 0.152084i | ||||
\(225\) | 46.3886i | 0.206172i | ||||||||
\(226\) | 546.528 | 2.41827 | ||||||||
\(227\) | −173.750 | −0.765418 | −0.382709 | − | 0.923869i | \(-0.625009\pi\) | ||||
−0.382709 | + | 0.923869i | \(0.625009\pi\) | |||||||
\(228\) | −1529.98 | −6.71043 | ||||||||
\(229\) | −144.696 | + | 144.696i | −0.631859 | + | 0.631859i | −0.948534 | − | 0.316675i | \(-0.897433\pi\) |
0.316675 | + | 0.948534i | \(0.397433\pi\) | |||||||
\(230\) | 102.793 | − | 102.793i | 0.446925 | − | 0.446925i | ||||
\(231\) | 0.196267i | 0.000849641i | ||||||||
\(232\) | −50.1100 | + | 620.255i | −0.215991 | + | 2.67351i | ||||
\(233\) | 102.871 | 0.441507 | 0.220754 | − | 0.975330i | \(-0.429148\pi\) | ||||
0.220754 | + | 0.975330i | \(0.429148\pi\) | |||||||
\(234\) | −225.933 | − | 225.933i | −0.965525 | − | 0.965525i | ||||
\(235\) | 104.262 | + | 104.262i | 0.443669 | + | 0.443669i | ||||
\(236\) | 1040.76i | 4.41000i | ||||||||
\(237\) | 490.060i | 2.06777i | ||||||||
\(238\) | − | 59.7207i | − | 0.250927i | ||||||
\(239\) | −312.152 | −1.30607 | −0.653037 | − | 0.757326i | \(-0.726505\pi\) | ||||
−0.653037 | + | 0.757326i | \(0.726505\pi\) | |||||||
\(240\) | 571.470 | − | 571.470i | 2.38113 | − | 2.38113i | ||||
\(241\) | − | 313.004i | − | 1.29877i | −0.760460 | − | 0.649385i | \(-0.775026\pi\) | ||
0.760460 | − | 0.649385i | \(-0.224974\pi\) | |||||||
\(242\) | 317.605 | − | 317.605i | 1.31242 | − | 1.31242i | ||||
\(243\) | −246.242 | − | 246.242i | −1.01334 | − | 1.01334i | ||||
\(244\) | 413.916 | − | 413.916i | 1.69638 | − | 1.69638i | ||||
\(245\) | 219.479i | 0.895833i | ||||||||
\(246\) | −40.9356 | − | 40.9356i | −0.166405 | − | 0.166405i | ||||
\(247\) | 208.667 | − | 208.667i | 0.844805 | − | 0.844805i | ||||
\(248\) | 154.559 | 0.623223 | ||||||||
\(249\) | −47.2228 | − | 47.2228i | −0.189650 | − | 0.189650i | ||||
\(250\) | 350.516 | − | 350.516i | 1.40206 | − | 1.40206i | ||||
\(251\) | 7.83425 | + | 7.83425i | 0.0312121 | + | 0.0312121i | 0.722541 | − | 0.691328i | \(-0.242974\pi\) |
−0.691328 | + | 0.722541i | \(0.742974\pi\) | |||||||
\(252\) | 75.5779 | 0.299912 | ||||||||
\(253\) | 0.365710 | + | 0.365710i | 0.00144549 | + | 0.00144549i | ||||
\(254\) | 43.4026i | 0.170876i | ||||||||
\(255\) | −430.358 | −1.68768 | ||||||||
\(256\) | −198.743 | −0.776340 | ||||||||
\(257\) | 68.5603 | 0.266771 | 0.133386 | − | 0.991064i | \(-0.457415\pi\) | ||||
0.133386 | + | 0.991064i | \(0.457415\pi\) | |||||||
\(258\) | −184.065 | + | 184.065i | −0.713429 | + | 0.713429i | ||||
\(259\) | −7.50744 | + | 7.50744i | −0.0289863 | + | 0.0289863i | ||||
\(260\) | 367.859i | 1.41484i | ||||||||
\(261\) | 194.792 | + | 229.033i | 0.746331 | + | 0.877521i | ||||
\(262\) | −1.89845 | −0.00724600 | ||||||||
\(263\) | 153.717 | + | 153.717i | 0.584477 | + | 0.584477i | 0.936130 | − | 0.351653i | \(-0.114380\pi\) |
−0.351653 | + | 0.936130i | \(0.614380\pi\) | |||||||
\(264\) | 3.99543 | + | 3.99543i | 0.0151342 | + | 0.0151342i | ||||
\(265\) | 194.350i | 0.733397i | ||||||||
\(266\) | 98.3500i | 0.369737i | ||||||||
\(267\) | 142.162i | 0.532441i | ||||||||
\(268\) | −741.279 | −2.76597 | ||||||||
\(269\) | 272.419 | − | 272.419i | 1.01271 | − | 1.01271i | 0.0127932 | − | 0.999918i | \(-0.495928\pi\) |
0.999918 | − | 0.0127932i | \(-0.00407231\pi\) | |||||||
\(270\) | − | 101.237i | − | 0.374953i | ||||||
\(271\) | −304.778 | + | 304.778i | −1.12464 | + | 1.12464i | −0.133607 | + | 0.991034i | \(0.542656\pi\) |
−0.991034 | + | 0.133607i | \(0.957344\pi\) | |||||||
\(272\) | −618.651 | − | 618.651i | −2.27445 | − | 2.27445i | ||||
\(273\) | −19.2556 | + | 19.2556i | −0.0705333 | + | 0.0705333i | ||||
\(274\) | − | 365.252i | − | 1.33304i | ||||||
\(275\) | 0.189306 | + | 0.189306i | 0.000688384 | + | 0.000688384i | ||||
\(276\) | 263.074 | − | 263.074i | 0.953167 | − | 0.953167i | ||||
\(277\) | −26.7259 | −0.0964834 | −0.0482417 | − | 0.998836i | \(-0.515362\pi\) | ||||
−0.0482417 | + | 0.998836i | \(0.515362\pi\) | |||||||
\(278\) | 292.364 | + | 292.364i | 1.05167 | + | 1.05167i | ||||
\(279\) | 52.8058 | − | 52.8058i | 0.189268 | − | 0.189268i | ||||
\(280\) | −51.2357 | − | 51.2357i | −0.182985 | − | 0.182985i | ||||
\(281\) | 468.922 | 1.66876 | 0.834380 | − | 0.551189i | \(-0.185826\pi\) | ||||
0.834380 | + | 0.551189i | \(0.185826\pi\) | |||||||
\(282\) | 375.966 | + | 375.966i | 1.33321 | + | 1.33321i | ||||
\(283\) | − | 263.495i | − | 0.931079i | −0.885027 | − | 0.465540i | \(-0.845860\pi\) | ||
0.885027 | − | 0.465540i | \(-0.154140\pi\) | |||||||
\(284\) | −696.412 | −2.45215 | ||||||||
\(285\) | 708.728 | 2.48676 | ||||||||
\(286\) | −1.84400 | −0.00644756 | ||||||||
\(287\) | −1.86760 | + | 1.86760i | −0.00650733 | + | 0.00650733i | ||||
\(288\) | 473.876 | − | 473.876i | 1.64540 | − | 1.64540i | ||||
\(289\) | 176.888i | 0.612071i | ||||||||
\(290\) | 39.2752 | − | 486.144i | 0.135432 | − | 1.67636i | ||||
\(291\) | −266.564 | −0.916026 | ||||||||
\(292\) | −721.720 | − | 721.720i | −2.47164 | − | 2.47164i | ||||
\(293\) | −84.4413 | − | 84.4413i | −0.288196 | − | 0.288196i | 0.548171 | − | 0.836366i | \(-0.315324\pi\) |
−0.836366 | + | 0.548171i | \(0.815324\pi\) | |||||||
\(294\) | 791.434i | 2.69195i | ||||||||
\(295\) | − | 482.108i | − | 1.63426i | ||||||
\(296\) | 305.660i | 1.03263i | ||||||||
\(297\) | 0.360176 | 0.00121271 | ||||||||
\(298\) | −116.855 | + | 116.855i | −0.392131 | + | 0.392131i | ||||
\(299\) | 71.7589i | 0.239996i | ||||||||
\(300\) | 136.177 | − | 136.177i | 0.453925 | − | 0.453925i | ||||
\(301\) | 8.39757 | + | 8.39757i | 0.0278989 | + | 0.0278989i | ||||
\(302\) | −185.424 | + | 185.424i | −0.613988 | + | 0.613988i | ||||
\(303\) | − | 226.773i | − | 0.748426i | ||||||
\(304\) | 1018.81 | + | 1018.81i | 3.35136 | + | 3.35136i | ||||
\(305\) | −191.737 | + | 191.737i | −0.628646 | + | 0.628646i | ||||
\(306\) | −830.726 | −2.71479 | ||||||||
\(307\) | 193.086 | + | 193.086i | 0.628945 | + | 0.628945i | 0.947803 | − | 0.318858i | \(-0.103299\pi\) |
−0.318858 | + | 0.947803i | \(0.603299\pi\) | |||||||
\(308\) | 0.308423 | − | 0.308423i | 0.00100137 | − | 0.00100137i | ||||
\(309\) | −347.756 | − | 347.756i | −1.12542 | − | 1.12542i | ||||
\(310\) | −121.141 | −0.390776 | ||||||||
\(311\) | −138.374 | − | 138.374i | −0.444932 | − | 0.444932i | 0.448734 | − | 0.893666i | \(-0.351875\pi\) |
−0.893666 | + | 0.448734i | \(0.851875\pi\) | |||||||
\(312\) | 783.977i | 2.51275i | ||||||||
\(313\) | 316.089 | 1.00987 | 0.504934 | − | 0.863158i | \(-0.331517\pi\) | ||||
0.504934 | + | 0.863158i | \(0.331517\pi\) | |||||||
\(314\) | −668.588 | −2.12926 | ||||||||
\(315\) | −35.0098 | −0.111142 | ||||||||
\(316\) | 770.104 | − | 770.104i | 2.43704 | − | 2.43704i | ||||
\(317\) | 222.503 | − | 222.503i | 0.701902 | − | 0.701902i | −0.262916 | − | 0.964819i | \(-0.584684\pi\) |
0.964819 | + | 0.262916i | \(0.0846843\pi\) | |||||||
\(318\) | 700.820i | 2.20384i | ||||||||
\(319\) | 1.72957 | + | 0.139731i | 0.00542186 | + | 0.000438028i | ||||
\(320\) | −352.545 | −1.10170 | ||||||||
\(321\) | −276.859 | − | 276.859i | −0.862488 | − | 0.862488i | ||||
\(322\) | −16.9109 | − | 16.9109i | −0.0525184 | − | 0.0525184i | ||||
\(323\) | − | 767.240i | − | 2.37536i | ||||||
\(324\) | 653.514i | 2.01702i | ||||||||
\(325\) | 37.1452i | 0.114293i | ||||||||
\(326\) | 437.973 | 1.34348 | ||||||||
\(327\) | 127.960 | − | 127.960i | 0.391314 | − | 0.391314i | ||||
\(328\) | 76.0381i | 0.231823i | ||||||||
\(329\) | 17.1527 | − | 17.1527i | 0.0521358 | − | 0.0521358i | ||||
\(330\) | −3.13154 | − | 3.13154i | −0.00948951 | − | 0.00948951i | ||||
\(331\) | 240.645 | − | 240.645i | 0.727024 | − | 0.727024i | −0.243002 | − | 0.970026i | \(-0.578132\pi\) |
0.970026 | + | 0.243002i | \(0.0781322\pi\) | |||||||
\(332\) | 148.416i | 0.447037i | ||||||||
\(333\) | 104.430 | + | 104.430i | 0.313603 | + | 0.313603i | ||||
\(334\) | −581.693 | + | 581.693i | −1.74160 | + | 1.74160i | ||||
\(335\) | 343.381 | 1.02502 | ||||||||
\(336\) | −94.0153 | − | 94.0153i | −0.279807 | − | 0.279807i | ||||
\(337\) | −294.375 | + | 294.375i | −0.873517 | + | 0.873517i | −0.992854 | − | 0.119336i | \(-0.961923\pi\) |
0.119336 | + | 0.992854i | \(0.461923\pi\) | |||||||
\(338\) | 262.697 | + | 262.697i | 0.777211 | + | 0.777211i | ||||
\(339\) | −647.922 | −1.91127 | ||||||||
\(340\) | 676.285 | + | 676.285i | 1.98907 | + | 1.98907i | ||||
\(341\) | − | 0.430987i | − | 0.00126389i | ||||||
\(342\) | 1368.07 | 4.00019 | ||||||||
\(343\) | 72.6291 | 0.211747 | ||||||||
\(344\) | 341.901 | 0.993897 | ||||||||
\(345\) | −121.863 | + | 121.863i | −0.353226 | + | 0.353226i | ||||
\(346\) | −17.3778 | + | 17.3778i | −0.0502250 | + | 0.0502250i | ||||
\(347\) | − | 355.572i | − | 1.02470i | −0.858776 | − | 0.512351i | \(-0.828775\pi\) | ||
0.858776 | − | 0.512351i | \(-0.171225\pi\) | |||||||
\(348\) | 100.516 | − | 1244.17i | 0.288838 | − | 3.57521i | ||||
\(349\) | −239.336 | −0.685775 | −0.342888 | − | 0.939376i | \(-0.611405\pi\) | ||||
−0.342888 | + | 0.939376i | \(0.611405\pi\) | |||||||
\(350\) | −8.75375 | − | 8.75375i | −0.0250107 | − | 0.0250107i | ||||
\(351\) | 35.3366 | + | 35.3366i | 0.100674 | + | 0.100674i | ||||
\(352\) | − | 3.86764i | − | 0.0109876i | ||||||
\(353\) | − | 31.2450i | − | 0.0885128i | −0.999020 | − | 0.0442564i | \(-0.985908\pi\) | ||
0.999020 | − | 0.0442564i | \(-0.0140919\pi\) | |||||||
\(354\) | − | 1738.46i | − | 4.91092i | ||||||
\(355\) | 322.597 | 0.908724 | ||||||||
\(356\) | 223.400 | − | 223.400i | 0.627527 | − | 0.627527i | ||||
\(357\) | 70.8003i | 0.198320i | ||||||||
\(358\) | 97.0177 | − | 97.0177i | 0.270999 | − | 0.270999i | ||||
\(359\) | 259.580 | + | 259.580i | 0.723064 | + | 0.723064i | 0.969228 | − | 0.246164i | \(-0.0791702\pi\) |
−0.246164 | + | 0.969228i | \(0.579170\pi\) | |||||||
\(360\) | −712.698 | + | 712.698i | −1.97972 | + | 1.97972i | ||||
\(361\) | 902.516i | 2.50004i | ||||||||
\(362\) | −504.086 | − | 504.086i | −1.39250 | − | 1.39250i | ||||
\(363\) | −376.528 | + | 376.528i | −1.03727 | + | 1.03727i | ||||
\(364\) | 60.5183 | 0.166259 | ||||||||
\(365\) | 334.321 | + | 334.321i | 0.915947 | + | 0.915947i | ||||
\(366\) | −691.397 | + | 691.397i | −1.88906 | + | 1.88906i | ||||
\(367\) | 130.207 | + | 130.207i | 0.354786 | + | 0.354786i | 0.861887 | − | 0.507100i | \(-0.169283\pi\) |
−0.507100 | + | 0.861887i | \(0.669283\pi\) | |||||||
\(368\) | −350.362 | −0.952072 | ||||||||
\(369\) | 25.9787 | + | 25.9787i | 0.0704030 | + | 0.0704030i | ||||
\(370\) | − | 239.570i | − | 0.647486i | ||||||
\(371\) | 31.9735 | 0.0861818 | ||||||||
\(372\) | −310.031 | −0.833417 | ||||||||
\(373\) | −638.263 | −1.71116 | −0.855581 | − | 0.517669i | \(-0.826800\pi\) | ||||
−0.855581 | + | 0.517669i | \(0.826800\pi\) | |||||||
\(374\) | −3.39008 | + | 3.39008i | −0.00906438 | + | 0.00906438i | ||||
\(375\) | −415.545 | + | 415.545i | −1.10812 | + | 1.10812i | ||||
\(376\) | − | 698.358i | − | 1.85733i | ||||||
\(377\) | 155.978 | + | 183.396i | 0.413735 | + | 0.486461i | ||||
\(378\) | −16.6550 | −0.0440609 | ||||||||
\(379\) | 91.7710 | + | 91.7710i | 0.242140 | + | 0.242140i | 0.817735 | − | 0.575595i | \(-0.195229\pi\) |
−0.575595 | + | 0.817735i | \(0.695229\pi\) | |||||||
\(380\) | −1113.73 | − | 1113.73i | −2.93086 | − | 2.93086i | ||||
\(381\) | − | 51.4547i | − | 0.135052i | ||||||
\(382\) | − | 1130.55i | − | 2.95957i | ||||||
\(383\) | 290.256i | 0.757848i | 0.925428 | + | 0.378924i | \(0.123706\pi\) | ||||
−0.925428 | + | 0.378924i | \(0.876294\pi\) | |||||||
\(384\) | −133.393 | −0.347378 | ||||||||
\(385\) | −0.142870 | + | 0.142870i | −0.000371091 | + | 0.000371091i | ||||
\(386\) | 686.044i | 1.77732i | ||||||||
\(387\) | 116.812 | − | 116.812i | 0.301839 | − | 0.301839i | ||||
\(388\) | 418.891 | + | 418.891i | 1.07962 | + | 1.07962i | ||||
\(389\) | 404.811 | − | 404.811i | 1.04065 | − | 1.04065i | 0.0415071 | − | 0.999138i | \(-0.486784\pi\) |
0.999138 | − | 0.0415071i | \(-0.0132159\pi\) | |||||||
\(390\) | − | 614.465i | − | 1.57555i | ||||||
\(391\) | 131.924 | + | 131.924i | 0.337402 | + | 0.337402i | ||||
\(392\) | 735.046 | − | 735.046i | 1.87512 | − | 1.87512i | ||||
\(393\) | 2.25066 | 0.00572686 | ||||||||
\(394\) | −669.231 | − | 669.231i | −1.69856 | − | 1.69856i | ||||
\(395\) | −356.733 | + | 356.733i | −0.903122 | + | 0.903122i | ||||
\(396\) | −4.29022 | − | 4.29022i | −0.0108339 | − | 0.0108339i | ||||
\(397\) | −485.501 | −1.22292 | −0.611462 | − | 0.791274i | \(-0.709418\pi\) | ||||
−0.611462 | + | 0.791274i | \(0.709418\pi\) | |||||||
\(398\) | 441.032 | + | 441.032i | 1.10812 | + | 1.10812i | ||||
\(399\) | − | 116.596i | − | 0.292221i | ||||||
\(400\) | −181.361 | −0.453403 | ||||||||
\(401\) | −144.170 | −0.359527 | −0.179763 | − | 0.983710i | \(-0.557533\pi\) | ||||
−0.179763 | + | 0.983710i | \(0.557533\pi\) | |||||||
\(402\) | 1238.22 | 3.08015 | ||||||||
\(403\) | 42.2837 | − | 42.2837i | 0.104922 | − | 0.104922i | ||||
\(404\) | −356.362 | + | 356.362i | −0.882084 | + | 0.882084i | ||||
\(405\) | − | 302.725i | − | 0.747470i | ||||||
\(406\) | −79.9778 | − | 6.46135i | −0.196990 | − | 0.0159146i | ||||
\(407\) | 0.852328 | 0.00209417 | ||||||||
\(408\) | 1441.29 | + | 1441.29i | 3.53257 | + | 3.53257i | ||||
\(409\) | 118.758 | + | 118.758i | 0.290361 | + | 0.290361i | 0.837223 | − | 0.546862i | \(-0.184178\pi\) |
−0.546862 | + | 0.837223i | \(0.684178\pi\) | |||||||
\(410\) | − | 59.5971i | − | 0.145359i | ||||||
\(411\) | 433.014i | 1.05356i | ||||||||
\(412\) | 1092.96i | 2.65282i | ||||||||
\(413\) | −79.3139 | −0.192043 | ||||||||
\(414\) | −235.234 | + | 235.234i | −0.568198 | + | 0.568198i | ||||
\(415\) | − | 68.7504i | − | 0.165664i | ||||||
\(416\) | 379.451 | − | 379.451i | 0.912142 | − | 0.912142i | ||||
\(417\) | −346.604 | − | 346.604i | −0.831185 | − | 0.831185i | ||||
\(418\) | 5.58289 | − | 5.58289i | 0.0133562 | − | 0.0133562i | ||||
\(419\) | − | 20.8124i | − | 0.0496715i | −0.999692 | − | 0.0248357i | \(-0.992094\pi\) | ||
0.999692 | − | 0.0248357i | \(-0.00790628\pi\) | |||||||
\(420\) | 102.774 | + | 102.774i | 0.244700 | + | 0.244700i | ||||
\(421\) | 199.204 | − | 199.204i | 0.473168 | − | 0.473168i | −0.429770 | − | 0.902938i | \(-0.641405\pi\) |
0.902938 | + | 0.429770i | \(0.141405\pi\) | |||||||
\(422\) | −587.404 | −1.39195 | ||||||||
\(423\) | −238.597 | − | 238.597i | −0.564058 | − | 0.564058i | ||||
\(424\) | 650.888 | − | 650.888i | 1.53511 | − | 1.53511i | ||||
\(425\) | 68.2891 | + | 68.2891i | 0.160680 | + | 0.160680i | ||||
\(426\) | 1163.27 | 2.73069 | ||||||||
\(427\) | 31.5436 | + | 31.5436i | 0.0738725 | + | 0.0738725i | ||||
\(428\) | 870.137i | 2.03303i | ||||||||
\(429\) | 2.18611 | 0.00509582 | ||||||||
\(430\) | −267.975 | −0.623197 | ||||||||
\(431\) | −193.044 | −0.447898 | −0.223949 | − | 0.974601i | \(-0.571895\pi\) | ||||
−0.223949 | + | 0.974601i | \(0.571895\pi\) | |||||||
\(432\) | −172.531 | + | 172.531i | −0.399376 | + | 0.399376i | ||||
\(433\) | 118.795 | − | 118.795i | 0.274353 | − | 0.274353i | −0.556497 | − | 0.830850i | \(-0.687855\pi\) |
0.830850 | + | 0.556497i | \(0.187855\pi\) | |||||||
\(434\) | 19.9294i | 0.0459203i | ||||||||
\(435\) | −46.5616 | + | 576.334i | −0.107038 | + | 1.32491i | ||||
\(436\) | −402.164 | −0.922395 | ||||||||
\(437\) | −217.257 | − | 217.257i | −0.497155 | − | 0.497155i | ||||
\(438\) | 1205.55 | + | 1205.55i | 2.75239 | + | 2.75239i | ||||
\(439\) | − | 660.370i | − | 1.50426i | −0.659015 | − | 0.752130i | \(-0.729027\pi\) | ||
0.659015 | − | 0.752130i | \(-0.270973\pi\) | |||||||
\(440\) | 5.81685i | 0.0132201i | ||||||||
\(441\) | − | 502.262i | − | 1.13892i | ||||||
\(442\) | −665.195 | −1.50497 | ||||||||
\(443\) | 222.343 | − | 222.343i | 0.501904 | − | 0.501904i | −0.410125 | − | 0.912029i | \(-0.634515\pi\) |
0.912029 | + | 0.410125i | \(0.134515\pi\) | |||||||
\(444\) | − | 613.124i | − | 1.38091i | ||||||
\(445\) | −103.485 | + | 103.485i | −0.232550 | + | 0.232550i | ||||
\(446\) | −149.687 | − | 149.687i | −0.335622 | − | 0.335622i | ||||
\(447\) | 138.534 | − | 138.534i | 0.309920 | − | 0.309920i | ||||
\(448\) | 57.9988i | 0.129462i | ||||||||
\(449\) | 289.500 | + | 289.500i | 0.644765 | + | 0.644765i | 0.951723 | − | 0.306958i | \(-0.0993111\pi\) |
−0.306958 | + | 0.951723i | \(0.599311\pi\) | |||||||
\(450\) | −121.766 | + | 121.766i | −0.270592 | + | 0.270592i | ||||
\(451\) | 0.212031 | 0.000470135 | ||||||||
\(452\) | 1018.17 | + | 1018.17i | 2.25260 | + | 2.25260i | ||||
\(453\) | 219.825 | − | 219.825i | 0.485265 | − | 0.485265i | ||||
\(454\) | −456.079 | − | 456.079i | −1.00458 | − | 1.00458i | ||||
\(455\) | −28.0337 | −0.0616125 | ||||||||
\(456\) | −2373.56 | − | 2373.56i | −5.20518 | − | 5.20518i | ||||
\(457\) | 263.854i | 0.577361i | 0.957426 | + | 0.288680i | \(0.0932165\pi\) | ||||
−0.957426 | + | 0.288680i | \(0.906784\pi\) | |||||||
\(458\) | −759.628 | −1.65858 | ||||||||
\(459\) | 129.928 | 0.283067 | ||||||||
\(460\) | 383.003 | 0.832614 | ||||||||
\(461\) | −489.859 | + | 489.859i | −1.06260 | + | 1.06260i | −0.0646957 | + | 0.997905i | \(0.520608\pi\) |
−0.997905 | + | 0.0646957i | \(0.979392\pi\) | |||||||
\(462\) | −0.515184 | + | 0.515184i | −0.00111512 | + | 0.00111512i | ||||
\(463\) | − | 606.327i | − | 1.30956i | −0.755819 | − | 0.654781i | \(-0.772761\pi\) | ||
0.755819 | − | 0.654781i | \(-0.227239\pi\) | |||||||
\(464\) | −895.428 | + | 761.561i | −1.92980 | + | 1.64130i | ||||
\(465\) | 143.615 | 0.308849 | ||||||||
\(466\) | 270.028 | + | 270.028i | 0.579459 | + | 0.579459i | ||||
\(467\) | 337.667 | + | 337.667i | 0.723056 | + | 0.723056i | 0.969227 | − | 0.246171i | \(-0.0791724\pi\) |
−0.246171 | + | 0.969227i | \(0.579172\pi\) | |||||||
\(468\) | − | 841.820i | − | 1.79876i | ||||||
\(469\) | − | 56.4912i | − | 0.120450i | ||||||
\(470\) | 547.359i | 1.16459i | ||||||||
\(471\) | 792.626 | 1.68286 | ||||||||
\(472\) | −1614.60 | + | 1614.60i | −3.42077 | + | 3.42077i | ||||
\(473\) | − | 0.953385i | − | 0.00201561i | ||||||
\(474\) | −1286.37 | + | 1286.37i | −2.71385 | + | 2.71385i | ||||
\(475\) | −112.461 | − | 112.461i | −0.236759 | − | 0.236759i | ||||
\(476\) | 111.259 | − | 111.259i | 0.233737 | − | 0.233737i | ||||
\(477\) | − | 444.757i | − | 0.932404i | ||||||
\(478\) | −819.372 | − | 819.372i | −1.71417 | − | 1.71417i | ||||
\(479\) | 431.509 | − | 431.509i | 0.900854 | − | 0.900854i | −0.0946564 | − | 0.995510i | \(-0.530175\pi\) |
0.995510 | + | 0.0946564i | \(0.0301753\pi\) | |||||||
\(480\) | 1288.79 | 2.68498 | ||||||||
\(481\) | 83.6211 | + | 83.6211i | 0.173848 | + | 0.173848i | ||||
\(482\) | 821.608 | − | 821.608i | 1.70458 | − | 1.70458i | ||||
\(483\) | 20.0483 | + | 20.0483i | 0.0415078 | + | 0.0415078i | ||||
\(484\) | 1183.39 | 2.44502 | ||||||||
\(485\) | −194.042 | − | 194.042i | −0.400086 | − | 0.400086i | ||||
\(486\) | − | 1292.73i | − | 2.65993i | ||||||
\(487\) | −317.203 | −0.651341 | −0.325670 | − | 0.945483i | \(-0.605590\pi\) | ||||
−0.325670 | + | 0.945483i | \(0.605590\pi\) | |||||||
\(488\) | 1284.27 | 2.63171 | ||||||||
\(489\) | −519.227 | −1.06181 | ||||||||
\(490\) | −576.114 | + | 576.114i | −1.17574 | + | 1.17574i | ||||
\(491\) | −440.067 | + | 440.067i | −0.896266 | + | 0.896266i | −0.995104 | − | 0.0988377i | \(-0.968488\pi\) |
0.0988377 | + | 0.995104i | \(0.468488\pi\) | |||||||
\(492\) | − | 152.525i | − | 0.310010i | ||||||
\(493\) | 623.916 | + | 50.4057i | 1.26555 | + | 0.102243i | ||||
\(494\) | 1095.47 | 2.21754 | ||||||||
\(495\) | 1.98735 | + | 1.98735i | 0.00401485 | + | 0.00401485i | ||||
\(496\) | 206.450 | + | 206.450i | 0.416230 | + | 0.416230i | ||||
\(497\) | − | 53.0720i | − | 0.106785i | ||||||
\(498\) | − | 247.912i | − | 0.497814i | ||||||
\(499\) | 847.151i | 1.69770i | 0.528635 | + | 0.848849i | \(0.322704\pi\) | ||||
−0.528635 | + | 0.848849i | \(0.677296\pi\) | |||||||
\(500\) | 1306.01 | 2.61203 | ||||||||
\(501\) | 689.610 | − | 689.610i | 1.37647 | − | 1.37647i | ||||
\(502\) | 41.1285i | 0.0819292i | ||||||||
\(503\) | −6.42815 | + | 6.42815i | −0.0127796 | + | 0.0127796i | −0.713468 | − | 0.700688i | \(-0.752876\pi\) |
0.700688 | + | 0.713468i | \(0.252876\pi\) | |||||||
\(504\) | 117.249 | + | 117.249i | 0.232638 | + | 0.232638i | ||||
\(505\) | 165.077 | − | 165.077i | 0.326884 | − | 0.326884i | ||||
\(506\) | 1.91991i | 0.00379430i | ||||||||
\(507\) | −311.433 | − | 311.433i | −0.614267 | − | 0.614267i | ||||
\(508\) | −80.8584 | + | 80.8584i | −0.159170 | + | 0.159170i | ||||
\(509\) | −476.056 | −0.935277 | −0.467638 | − | 0.883920i | \(-0.654895\pi\) | ||||
−0.467638 | + | 0.883920i | \(0.654895\pi\) | |||||||
\(510\) | −1129.65 | − | 1129.65i | −2.21501 | − | 2.21501i | ||||
\(511\) | 55.0007 | − | 55.0007i | 0.107633 | − | 0.107633i | ||||
\(512\) | −607.415 | − | 607.415i | −1.18636 | − | 1.18636i | ||||
\(513\) | −213.970 | −0.417095 | ||||||||
\(514\) | 179.965 | + | 179.965i | 0.350126 | + | 0.350126i | ||||
\(515\) | − | 506.289i | − | 0.983086i | ||||||
\(516\) | −685.819 | −1.32911 | ||||||||
\(517\) | −1.94736 | −0.00376665 | ||||||||
\(518\) | −39.4128 | −0.0760865 | ||||||||
\(519\) | 20.6018 | − | 20.6018i | 0.0396952 | − | 0.0396952i | ||||
\(520\) | −570.686 | + | 570.686i | −1.09747 | + | 1.09747i | ||||
\(521\) | 557.186i | 1.06946i | 0.845024 | + | 0.534728i | \(0.179586\pi\) | ||||
−0.845024 | + | 0.534728i | \(0.820414\pi\) | |||||||
\(522\) | −89.8785 | + | 1112.51i | −0.172181 | + | 2.13124i | ||||
\(523\) | 456.134 | 0.872149 | 0.436074 | − | 0.899911i | \(-0.356368\pi\) | ||||
0.436074 | + | 0.899911i | \(0.356368\pi\) | |||||||
\(524\) | −3.53679 | − | 3.53679i | −0.00674960 | − | 0.00674960i | ||||
\(525\) | 10.3778 | + | 10.3778i | 0.0197672 | + | 0.0197672i | ||||
\(526\) | 806.990i | 1.53420i | ||||||||
\(527\) | − | 155.472i | − | 0.295013i | ||||||
\(528\) | 10.6737i | 0.0202153i | ||||||||
\(529\) | −454.287 | −0.858766 | ||||||||
\(530\) | −510.153 | + | 510.153i | −0.962552 | + | 0.962552i | ||||
\(531\) | 1103.27i | 2.07772i | ||||||||
\(532\) | −183.225 | + | 183.225i | −0.344407 | + | 0.344407i | ||||
\(533\) | 20.8022 | + | 20.8022i | 0.0390285 | + | 0.0390285i | ||||
\(534\) | −373.163 | + | 373.163i | −0.698806 | + | 0.698806i | ||||
\(535\) | − | 403.071i | − | 0.753404i | ||||||
\(536\) | −1150.00 | − | 1150.00i | −2.14552 | − | 2.14552i | ||||
\(537\) | −115.017 | + | 115.017i | −0.214184 | + | 0.214184i | ||||
\(538\) | 1430.16 | 2.65828 | ||||||||
\(539\) | −2.04966 | − | 2.04966i | −0.00380272 | − | 0.00380272i | ||||
\(540\) | 188.604 | − | 188.604i | 0.349266 | − | 0.349266i | ||||
\(541\) | 537.048 | + | 537.048i | 0.992694 | + | 0.992694i | 0.999974 | − | 0.00727934i | \(-0.00231711\pi\) |
−0.00727934 | + | 0.999974i | \(0.502317\pi\) | |||||||
\(542\) | −1600.03 | −2.95209 | ||||||||
\(543\) | 597.605 | + | 597.605i | 1.10056 | + | 1.10056i | ||||
\(544\) | − | 1395.19i | − | 2.56469i | ||||||
\(545\) | 186.293 | 0.341823 | ||||||||
\(546\) | −101.089 | −0.185144 | ||||||||
\(547\) | 353.235 | 0.645768 | 0.322884 | − | 0.946439i | \(-0.395348\pi\) | ||||
0.322884 | + | 0.946439i | \(0.395348\pi\) | |||||||
\(548\) | 680.459 | − | 680.459i | 1.24171 | − | 1.24171i | ||||
\(549\) | 438.776 | − | 438.776i | 0.799229 | − | 0.799229i | ||||
\(550\) | 0.993823i | 0.00180695i | ||||||||
\(551\) | −1027.49 | − | 83.0098i | −1.86477 | − | 0.150653i | ||||
\(552\) | 816.250 | 1.47871 | ||||||||
\(553\) | 58.6879 | + | 58.6879i | 0.106126 | + | 0.106126i | ||||
\(554\) | −70.1532 | − | 70.1532i | −0.126630 | − | 0.126630i | ||||
\(555\) | 284.016i | 0.511740i | ||||||||
\(556\) | 1089.34i | 1.95924i | ||||||||
\(557\) | − | 916.424i | − | 1.64529i | −0.568558 | − | 0.822643i | \(-0.692499\pi\) | ||
0.568558 | − | 0.822643i | \(-0.307501\pi\) | |||||||
\(558\) | 277.221 | 0.496813 | ||||||||
\(559\) | 93.5358 | − | 93.5358i | 0.167327 | − | 0.167327i | ||||
\(560\) | − | 136.874i | − | 0.244419i | ||||||
\(561\) | 4.01902 | − | 4.01902i | 0.00716402 | − | 0.00716402i | ||||
\(562\) | 1230.88 | + | 1230.88i | 2.19018 | + | 2.19018i | ||||
\(563\) | −526.927 | + | 526.927i | −0.935928 | + | 0.935928i | −0.998067 | − | 0.0621396i | \(-0.980208\pi\) |
0.0621396 | + | 0.998067i | \(0.480208\pi\) | |||||||
\(564\) | 1400.84i | 2.48375i | ||||||||
\(565\) | −471.646 | − | 471.646i | −0.834772 | − | 0.834772i | ||||
\(566\) | 691.653 | − | 691.653i | 1.22200 | − | 1.22200i | ||||
\(567\) | −49.8028 | −0.0878356 | ||||||||
\(568\) | −1080.39 | − | 1080.39i | −1.90210 | − | 1.90210i | ||||
\(569\) | 394.074 | − | 394.074i | 0.692573 | − | 0.692573i | −0.270224 | − | 0.962797i | \(-0.587098\pi\) |
0.962797 | + | 0.270224i | \(0.0870979\pi\) | |||||||
\(570\) | 1860.35 | + | 1860.35i | 3.26377 | + | 3.26377i | ||||
\(571\) | −552.975 | −0.968432 | −0.484216 | − | 0.874949i | \(-0.660895\pi\) | ||||
−0.484216 | + | 0.874949i | \(0.660895\pi\) | |||||||
\(572\) | −3.43535 | − | 3.43535i | −0.00600586 | − | 0.00600586i | ||||
\(573\) | 1340.30i | 2.33909i | ||||||||
\(574\) | −9.80460 | −0.0170812 | ||||||||
\(575\) | 38.6744 | 0.0672598 | ||||||||
\(576\) | 806.774 | 1.40065 | ||||||||
\(577\) | 167.445 | − | 167.445i | 0.290200 | − | 0.290200i | −0.546959 | − | 0.837159i | \(-0.684215\pi\) |
0.837159 | + | 0.546959i | \(0.184215\pi\) | |||||||
\(578\) | −464.317 | + | 464.317i | −0.803317 | + | 0.803317i | ||||
\(579\) | − | 813.321i | − | 1.40470i | ||||||
\(580\) | 978.848 | − | 832.510i | 1.68767 | − | 1.43536i | ||||
\(581\) | −11.3105 | −0.0194672 | ||||||||
\(582\) | −699.707 | − | 699.707i | −1.20225 | − | 1.20225i | ||||
\(583\) | −1.81499 | − | 1.81499i | −0.00311319 | − | 0.00311319i | ||||
\(584\) | − | 2239.31i | − | 3.83444i | ||||||
\(585\) | 389.954i | 0.666588i | ||||||||
\(586\) | − | 443.303i | − | 0.756489i | ||||||
\(587\) | 38.0082 | 0.0647500 | 0.0323750 | − | 0.999476i | \(-0.489693\pi\) | ||||
0.0323750 | + | 0.999476i | \(0.489693\pi\) | |||||||
\(588\) | −1474.43 | + | 1474.43i | −2.50753 | + | 2.50753i | ||||
\(589\) | 256.036i | 0.434696i | ||||||||
\(590\) | 1265.49 | − | 1265.49i | 2.14490 | − | 2.14490i | ||||
\(591\) | 793.388 | + | 793.388i | 1.34245 | + | 1.34245i | ||||
\(592\) | −408.280 | + | 408.280i | −0.689661 | + | 0.689661i | ||||
\(593\) | − | 627.850i | − | 1.05877i | −0.848382 | − | 0.529385i | \(-0.822423\pi\) | ||
0.848382 | − | 0.529385i | \(-0.177577\pi\) | |||||||
\(594\) | 0.945432 | + | 0.945432i | 0.00159164 | + | 0.00159164i | ||||
\(595\) | −51.5381 | + | 51.5381i | −0.0866187 | + | 0.0866187i | ||||
\(596\) | −435.399 | −0.730535 | ||||||||
\(597\) | −522.854 | − | 522.854i | −0.875802 | − | 0.875802i | ||||
\(598\) | −188.361 | + | 188.361i | −0.314985 | + | 0.314985i | ||||
\(599\) | 674.702 | + | 674.702i | 1.12638 | + | 1.12638i | 0.990761 | + | 0.135619i | \(0.0433024\pi\) |
0.135619 | + | 0.990761i | \(0.456698\pi\) | |||||||
\(600\) | 422.523 | 0.704205 | ||||||||
\(601\) | −500.527 | − | 500.527i | −0.832823 | − | 0.832823i | 0.155079 | − | 0.987902i | \(-0.450437\pi\) |
−0.987902 | + | 0.155079i | \(0.950437\pi\) | |||||||
\(602\) | 44.0858i | 0.0732322i | ||||||||
\(603\) | −785.802 | −1.30315 | ||||||||
\(604\) | −690.886 | −1.14385 | ||||||||
\(605\) | −548.178 | −0.906079 | ||||||||
\(606\) | 595.260 | − | 595.260i | 0.982278 | − | 0.982278i | ||||
\(607\) | 780.373 | − | 780.373i | 1.28562 | − | 1.28562i | 0.348204 | − | 0.937419i | \(-0.386792\pi\) |
0.937419 | − | 0.348204i | \(-0.113208\pi\) | |||||||
\(608\) | 2297.65i | 3.77903i | ||||||||
\(609\) | 94.8155 | + | 7.66007i | 0.155690 | + | 0.0125781i | ||||
\(610\) | −1006.59 | −1.65014 | ||||||||
\(611\) | −191.054 | − | 191.054i | −0.312690 | − | 0.312690i | ||||
\(612\) | −1547.63 | − | 1547.63i | −2.52881 | − | 2.52881i | ||||
\(613\) | 830.453i | 1.35473i | 0.735645 | + | 0.677367i | \(0.236879\pi\) | ||||
−0.735645 | + | 0.677367i | \(0.763121\pi\) | |||||||
\(614\) | 1013.67i | 1.65093i | ||||||||
\(615\) | 70.6537i | 0.114884i | ||||||||
\(616\) | 0.956957 | 0.00155350 | ||||||||
\(617\) | 69.2239 | − | 69.2239i | 0.112194 | − | 0.112194i | −0.648781 | − | 0.760975i | \(-0.724721\pi\) |
0.760975 | + | 0.648781i | \(0.224721\pi\) | |||||||
\(618\) | − | 1825.66i | − | 2.95414i | ||||||
\(619\) | −331.072 | + | 331.072i | −0.534849 | + | 0.534849i | −0.922012 | − | 0.387162i | \(-0.873455\pi\) |
0.387162 | + | 0.922012i | \(0.373455\pi\) | |||||||
\(620\) | −225.683 | − | 225.683i | −0.364005 | − | 0.364005i | ||||
\(621\) | 36.7912 | − | 36.7912i | 0.0592452 | − | 0.0592452i | ||||
\(622\) | − | 726.439i | − | 1.16791i | ||||||
\(623\) | 17.0248 | + | 17.0248i | 0.0273271 | + | 0.0273271i | ||||
\(624\) | −1047.18 | + | 1047.18i | −1.67818 | + | 1.67818i | ||||
\(625\) | −493.123 | −0.788997 | ||||||||
\(626\) | 829.706 | + | 829.706i | 1.32541 | + | 1.32541i | ||||
\(627\) | −6.61864 | + | 6.61864i | −0.0105561 | + | 0.0105561i | ||||
\(628\) | −1245.57 | − | 1245.57i | −1.98339 | − | 1.98339i | ||||
\(629\) | 307.464 | 0.488814 | ||||||||
\(630\) | −91.8977 | − | 91.8977i | −0.145869 | − | 0.145869i | ||||
\(631\) | 681.376i | 1.07984i | 0.841718 | + | 0.539918i | \(0.181545\pi\) | ||||
−0.841718 | + | 0.539918i | \(0.818455\pi\) | |||||||
\(632\) | 2389.43 | 3.78075 | ||||||||
\(633\) | 696.381 | 1.10013 | ||||||||
\(634\) | 1168.10 | 1.84243 | ||||||||
\(635\) | 37.4558 | − | 37.4558i | 0.0589855 | − | 0.0589855i | ||||
\(636\) | −1305.62 | + | 1305.62i | −2.05286 | + | 2.05286i | ||||
\(637\) | − | 402.181i | − | 0.631368i | ||||||
\(638\) | 4.17320 | + | 4.90676i | 0.00654107 | + | 0.00769085i | ||||
\(639\) | −738.240 | −1.15531 | ||||||||
\(640\) | −97.1018 | − | 97.1018i | −0.151722 | − | 0.151722i | ||||
\(641\) | −517.626 | − | 517.626i | −0.807529 | − | 0.807529i | 0.176730 | − | 0.984259i | \(-0.443448\pi\) |
−0.984259 | + | 0.176730i | \(0.943448\pi\) | |||||||
\(642\) | − | 1453.46i | − | 2.26396i | ||||||
\(643\) | − | 867.657i | − | 1.34939i | −0.738097 | − | 0.674694i | \(-0.764275\pi\) | ||
0.738097 | − | 0.674694i | \(-0.235725\pi\) | |||||||
\(644\) | − | 63.0096i | − | 0.0978410i | ||||||
\(645\) | 317.690 | 0.492543 | ||||||||
\(646\) | 2013.94 | − | 2013.94i | 3.11756 | − | 3.11756i | ||||
\(647\) | 357.347i | 0.552314i | 0.961113 | + | 0.276157i | \(0.0890609\pi\) | ||||
−0.961113 | + | 0.276157i | \(0.910939\pi\) | |||||||
\(648\) | −1013.84 | + | 1013.84i | −1.56457 | + | 1.56457i | ||||
\(649\) | 4.50229 | + | 4.50229i | 0.00693728 | + | 0.00693728i | ||||
\(650\) | −97.5031 | + | 97.5031i | −0.150005 | + | 0.150005i | ||||
\(651\) | − | 23.6268i | − | 0.0362930i | ||||||
\(652\) | 815.937 | + | 815.937i | 1.25144 | + | 1.25144i | ||||
\(653\) | −700.906 | + | 700.906i | −1.07336 | + | 1.07336i | −0.0762758 | + | 0.997087i | \(0.524303\pi\) |
−0.997087 | + | 0.0762758i | \(0.975697\pi\) | |||||||
\(654\) | 671.767 | 1.02717 | ||||||||
\(655\) | 1.63834 | + | 1.63834i | 0.00250128 | + | 0.00250128i | ||||
\(656\) | −101.566 | + | 101.566i | −0.154827 | + | 0.154827i | ||||
\(657\) | −765.069 | − | 765.069i | −1.16449 | − | 1.16449i | ||||
\(658\) | 90.0486 | 0.136852 | ||||||||
\(659\) | 760.878 | + | 760.878i | 1.15459 | + | 1.15459i | 0.985621 | + | 0.168974i | \(0.0540453\pi\) |
0.168974 | + | 0.985621i | \(0.445955\pi\) | |||||||
\(660\) | − | 11.6680i | − | 0.0176788i | ||||||
\(661\) | −204.176 | −0.308889 | −0.154444 | − | 0.988001i | \(-0.549359\pi\) | ||||
−0.154444 | + | 0.988001i | \(0.549359\pi\) | |||||||
\(662\) | 1263.34 | 1.90838 | ||||||||
\(663\) | 788.604 | 1.18945 | ||||||||
\(664\) | −230.248 | + | 230.248i | −0.346760 | + | 0.346760i | ||||
\(665\) | 84.8747 | − | 84.8747i | 0.127631 | − | 0.127631i | ||||
\(666\) | 548.239i | 0.823182i | ||||||||
\(667\) | 190.945 | − | 162.399i | 0.286275 | − | 0.243477i | ||||
\(668\) | −2167.37 | −3.24457 | ||||||||
\(669\) | 177.458 | + | 177.458i | 0.265258 | + | 0.265258i | ||||
\(670\) | 901.345 | + | 901.345i | 1.34529 | + | 1.34529i | ||||
\(671\) | − | 3.58117i | − | 0.00533707i | ||||||
\(672\) | − | 212.025i | − | 0.315513i | ||||||
\(673\) | − | 255.714i | − | 0.379962i | −0.981788 | − | 0.189981i | \(-0.939157\pi\) | ||
0.981788 | − | 0.189981i | \(-0.0608426\pi\) | |||||||
\(674\) | −1545.42 | −2.29291 | ||||||||
\(675\) | 19.0446 | − | 19.0446i | 0.0282142 | − | 0.0282142i | ||||
\(676\) | 978.802i | 1.44793i | ||||||||
\(677\) | −778.876 | + | 778.876i | −1.15048 | + | 1.15048i | −0.164026 | + | 0.986456i | \(0.552448\pi\) |
−0.986456 | + | 0.164026i | \(0.947552\pi\) | |||||||
\(678\) | −1700.74 | − | 1700.74i | −2.50847 | − | 2.50847i | ||||
\(679\) | −31.9227 | + | 31.9227i | −0.0470143 | + | 0.0470143i | ||||
\(680\) | 2098.34i | 3.08579i | ||||||||
\(681\) | 540.692 | + | 540.692i | 0.793967 | + | 0.793967i | ||||
\(682\) | 1.13130 | − | 1.13130i | 0.00165880 | − | 0.00165880i | ||||
\(683\) | −712.500 | −1.04319 | −0.521596 | − | 0.853193i | \(-0.674663\pi\) | ||||
−0.521596 | + | 0.853193i | \(0.674663\pi\) | |||||||
\(684\) | 2548.69 | + | 2548.69i | 3.72615 | + | 3.72615i | ||||
\(685\) | −315.207 | + | 315.207i | −0.460156 | + | 0.460156i | ||||
\(686\) | 190.645 | + | 190.645i | 0.277909 | + | 0.277909i | ||||
\(687\) | 900.556 | 1.31085 | ||||||||
\(688\) | 456.688 | + | 456.688i | 0.663790 | + | 0.663790i | ||||
\(689\) | − | 356.134i | − | 0.516886i | ||||||
\(690\) | −639.760 | −0.927189 | ||||||||
\(691\) | 85.2702 | 0.123401 | 0.0617006 | − | 0.998095i | \(-0.480348\pi\) | ||||
0.0617006 | + | 0.998095i | \(0.480348\pi\) | |||||||
\(692\) | −64.7493 | −0.0935684 | ||||||||
\(693\) | 0.326948 | − | 0.326948i | 0.000471787 | − | 0.000471787i | ||||
\(694\) | 933.346 | − | 933.346i | 1.34488 | − | 1.34488i | ||||
\(695\) | − | 504.612i | − | 0.726060i | ||||||
\(696\) | 2086.11 | − | 1774.23i | 2.99728 | − | 2.54919i | ||||
\(697\) | 76.4869 | 0.109737 | ||||||||
\(698\) | −628.235 | − | 628.235i | −0.900051 | − | 0.900051i | ||||
\(699\) | −320.124 | − | 320.124i | −0.457975 | − | 0.457975i | ||||
\(700\) | − | 32.6162i | − | 0.0465946i | ||||||
\(701\) | − | 389.567i | − | 0.555731i | −0.960620 | − | 0.277865i | \(-0.910373\pi\) | ||
0.960620 | − | 0.277865i | \(-0.0896269\pi\) | |||||||
\(702\) | 185.511i | 0.264261i | ||||||||
\(703\) | −506.342 | −0.720258 | ||||||||
\(704\) | 3.29233 | − | 3.29233i | 0.00467661 | − | 0.00467661i | ||||
\(705\) | − | 648.906i | − | 0.920434i | ||||||
\(706\) | 82.0155 | − | 82.0155i | 0.116169 | − | 0.116169i | ||||
\(707\) | −27.1575 | − | 27.1575i | −0.0384123 | − | 0.0384123i | ||||
\(708\) | 3238.73 | − | 3238.73i | 4.57448 | − | 4.57448i | ||||
\(709\) | − | 616.933i | − | 0.870145i | −0.900396 | − | 0.435072i | \(-0.856723\pi\) | ||
0.900396 | − | 0.435072i | \(-0.143277\pi\) | |||||||
\(710\) | 846.790 | + | 846.790i | 1.19266 | + | 1.19266i | ||||
\(711\) | 816.359 | − | 816.359i | 1.14818 | − | 1.14818i | ||||
\(712\) | 693.151 | 0.973527 | ||||||||
\(713\) | −44.0244 | − | 44.0244i | −0.0617452 | − | 0.0617452i | ||||
\(714\) | −185.845 | + | 185.845i | −0.260287 | + | 0.260287i | ||||
\(715\) | 1.59135 | + | 1.59135i | 0.00222566 | + | 0.00222566i | ||||
\(716\) | 361.485 | 0.504868 | ||||||||
\(717\) | 971.384 | + | 971.384i | 1.35479 | + | 1.35479i | ||||
\(718\) | 1362.75i | 1.89798i | ||||||||
\(719\) | 273.210 | 0.379986 | 0.189993 | − | 0.981785i | \(-0.439153\pi\) | ||||
0.189993 | + | 0.981785i | \(0.439153\pi\) | |||||||
\(720\) | −1903.95 | −2.64437 | ||||||||
\(721\) | −83.2920 | −0.115523 | ||||||||
\(722\) | −2369.03 | + | 2369.03i | −3.28120 | + | 3.28120i | ||||
\(723\) | −974.035 | + | 974.035i | −1.34721 | + | 1.34721i | ||||
\(724\) | − | 1878.21i | − | 2.59421i | ||||||
\(725\) | 98.8409 | − | 84.0641i | 0.136332 | − | 0.115950i | ||||
\(726\) | −1976.71 | −2.72274 | ||||||||
\(727\) | 136.415 | + | 136.415i | 0.187641 | + | 0.187641i | 0.794676 | − | 0.607034i | \(-0.207641\pi\) |
−0.607034 | + | 0.794676i | \(0.707641\pi\) | |||||||
\(728\) | 93.8862 | + | 93.8862i | 0.128965 | + | 0.128965i | ||||
\(729\) | 931.186i | 1.27735i | ||||||||
\(730\) | 1755.13i | 2.40428i | ||||||||
\(731\) | − | 343.919i | − | 0.470477i | ||||||
\(732\) | −2576.12 | −3.51930 | ||||||||
\(733\) | −580.859 | + | 580.859i | −0.792441 | + | 0.792441i | −0.981890 | − | 0.189449i | \(-0.939330\pi\) |
0.189449 | + | 0.981890i | \(0.439330\pi\) | |||||||
\(734\) | 683.563i | 0.931284i | ||||||||
\(735\) | 682.996 | − | 682.996i | 0.929247 | − | 0.929247i | ||||
\(736\) | −395.072 | − | 395.072i | −0.536782 | − | 0.536782i | ||||
\(737\) | −3.20675 | + | 3.20675i | −0.00435109 | + | 0.00435109i | ||||
\(738\) | 136.384i | 0.184802i | ||||||||
\(739\) | −688.432 | − | 688.432i | −0.931572 | − | 0.931572i | 0.0662318 | − | 0.997804i | \(-0.478902\pi\) |
−0.997804 | + | 0.0662318i | \(0.978902\pi\) | |||||||
\(740\) | 446.316 | − | 446.316i | 0.603129 | − | 0.603129i | ||||
\(741\) | −1298.70 | −1.75263 | ||||||||
\(742\) | 83.9276 | + | 83.9276i | 0.113110 | + | 0.113110i | ||||
\(743\) | 108.284 | − | 108.284i | 0.145739 | − | 0.145739i | −0.630472 | − | 0.776212i | \(-0.717139\pi\) |
0.776212 | + | 0.630472i | \(0.217139\pi\) | |||||||
\(744\) | −480.973 | − | 480.973i | −0.646469 | − | 0.646469i | ||||
\(745\) | 201.689 | 0.270723 | ||||||||
\(746\) | −1675.39 | − | 1675.39i | −2.24583 | − | 2.24583i | ||||
\(747\) | 157.330i | 0.210616i | ||||||||
\(748\) | −12.6313 | −0.0168868 | ||||||||
\(749\) | −66.3112 | −0.0885329 | ||||||||
\(750\) | −2181.54 | −2.90872 | ||||||||
\(751\) | 474.687 | − | 474.687i | 0.632074 | − | 0.632074i | −0.316514 | − | 0.948588i | \(-0.602512\pi\) |
0.948588 | + | 0.316514i | \(0.102512\pi\) | |||||||
\(752\) | 932.819 | − | 932.819i | 1.24045 | − | 1.24045i | ||||
\(753\) | − | 48.7587i | − | 0.0647526i | ||||||
\(754\) | −71.9693 | + | 890.827i | −0.0954500 | + | 1.18147i | ||||
\(755\) | 320.037 | 0.423891 | ||||||||
\(756\) | −31.0281 | − | 31.0281i | −0.0410425 | − | 0.0410425i | ||||
\(757\) | 144.571 | + | 144.571i | 0.190979 | + | 0.190979i | 0.796119 | − | 0.605140i | \(-0.206883\pi\) |
−0.605140 | + | 0.796119i | \(0.706883\pi\) | |||||||
\(758\) | 481.782i | 0.635597i | ||||||||
\(759\) | − | 2.27610i | − | 0.00299882i | ||||||
\(760\) | − | 3455.61i | − | 4.54685i | ||||||
\(761\) | 279.009 | 0.366635 | 0.183318 | − | 0.983054i | \(-0.441316\pi\) | ||||
0.183318 | + | 0.983054i | \(0.441316\pi\) | |||||||
\(762\) | 135.064 | − | 135.064i | 0.177250 | − | 0.177250i | ||||
\(763\) | − | 30.6480i | − | 0.0401678i | ||||||
\(764\) | 2106.21 | − | 2106.21i | 2.75681 | − | 2.75681i | ||||
\(765\) | 716.905 | + | 716.905i | 0.937130 | + | 0.937130i | ||||
\(766\) | −761.897 | + | 761.897i | −0.994644 | + | 0.994644i | ||||
\(767\) | 883.432i | 1.15180i | ||||||||
\(768\) | 618.468 | + | 618.468i | 0.805297 | + | 0.805297i | ||||
\(769\) | 270.425 | − | 270.425i | 0.351658 | − | 0.351658i | −0.509068 | − | 0.860726i | \(-0.670010\pi\) |
0.860726 | + | 0.509068i | \(0.170010\pi\) | |||||||
\(770\) | −0.750044 | −0.000974083 | ||||||||
\(771\) | −213.352 | − | 213.352i | −0.276722 | − | 0.276722i | ||||
\(772\) | −1278.09 | + | 1278.09i | −1.65556 | + | 1.65556i | ||||
\(773\) | 933.705 | + | 933.705i | 1.20790 | + | 1.20790i | 0.971707 | + | 0.236191i | \(0.0758991\pi\) |
0.236191 | + | 0.971707i | \(0.424101\pi\) | |||||||
\(774\) | 613.242 | 0.792302 | ||||||||
\(775\) | −22.7887 | − | 22.7887i | −0.0294048 | − | 0.0294048i | ||||
\(776\) | 1299.71i | 1.67488i | ||||||||
\(777\) | 46.7248 | 0.0601348 | ||||||||
\(778\) | 2125.19 | 2.73161 | ||||||||
\(779\) | −125.961 | −0.161696 | ||||||||
\(780\) | 1144.74 | − | 1144.74i | 1.46762 | − | 1.46762i | ||||
\(781\) | −3.01266 | + | 3.01266i | −0.00385744 | + | 0.00385744i | ||||
\(782\) | 692.579i | 0.885651i | ||||||||
\(783\) | 14.0573 | − | 173.999i | 0.0179531 | − | 0.222221i | ||||
\(784\) | 1963.65 | 2.50465 | ||||||||
\(785\) | 576.982 | + | 576.982i | 0.735009 | + | 0.735009i | ||||
\(786\) | 5.90779 | + | 5.90779i | 0.00751627 | + | 0.00751627i | ||||
\(787\) | 377.592i | 0.479786i | 0.970799 | + | 0.239893i | \(0.0771124\pi\) | ||||
−0.970799 | + | 0.239893i | \(0.922888\pi\) | |||||||
\(788\) | − | 2493.54i | − | 3.16438i | ||||||
\(789\) | − | 956.705i | − | 1.21255i | ||||||
\(790\) | −1872.79 | −2.37062 | ||||||||
\(791\) | −77.5928 | + | 77.5928i | −0.0980945 | + | 0.0980945i | ||||
\(792\) | − | 13.3114i | − | 0.0168074i | ||||||
\(793\) | 351.346 | − | 351.346i | 0.443059 | − | 0.443059i | ||||
\(794\) | −1274.40 | − | 1274.40i | −1.60504 | − | 1.60504i | ||||
\(795\) | 604.797 | − | 604.797i | 0.760751 | − | 0.760751i | ||||
\(796\) | 1643.27i | 2.06442i | ||||||||
\(797\) | 350.486 | + | 350.486i | 0.439756 | + | 0.439756i | 0.891930 | − | 0.452174i | \(-0.149351\pi\) |
−0.452174 | + | 0.891930i | \(0.649351\pi\) | |||||||
\(798\) | 306.055 | − | 306.055i | 0.383528 | − | 0.383528i | ||||
\(799\) | −702.480 | −0.879199 | ||||||||
\(800\) | −204.505 | − | 204.505i | −0.255631 | − | 0.255631i | ||||
\(801\) | 236.818 | − | 236.818i | 0.295653 | − | 0.295653i | ||||
\(802\) | −378.434 | − | 378.434i | −0.471863 | − | 0.471863i | ||||
\(803\) | −6.24428 | −0.00777619 | ||||||||
\(804\) | 2306.78 | + | 2306.78i | 2.86913 | + | 2.86913i | ||||
\(805\) | 29.1878i | 0.0362581i | ||||||||
\(806\) | 221.982 | 0.275412 | ||||||||
\(807\) | −1695.48 | −2.10097 | ||||||||
\(808\) | −1105.70 | −1.36844 | ||||||||
\(809\) | −303.271 | + | 303.271i | −0.374872 | + | 0.374872i | −0.869248 | − | 0.494376i | \(-0.835397\pi\) |
0.494376 | + | 0.869248i | \(0.335397\pi\) | |||||||
\(810\) | 794.628 | − | 794.628i | 0.981023 | − | 0.981023i | ||||
\(811\) | 1521.59i | 1.87619i | 0.346380 | + | 0.938094i | \(0.387411\pi\) | ||||
−0.346380 | + | 0.938094i | \(0.612589\pi\) | |||||||
\(812\) | −136.960 | − | 161.035i | −0.168670 | − | 0.198319i | ||||
\(813\) | 1896.87 | 2.33318 | ||||||||
\(814\) | 2.23729 | + | 2.23729i | 0.00274851 | + | 0.00274851i | ||||
\(815\) | −377.964 | − | 377.964i | −0.463760 | − | 0.463760i | ||||
\(816\) | 3850.35i | 4.71857i | ||||||||
\(817\) | 566.376i | 0.693239i | ||||||||
\(818\) | 623.458i | 0.762174i | ||||||||
\(819\) | 64.1532 | 0.0783311 | ||||||||
\(820\) | 111.029 | − | 111.029i | 0.135401 | − | 0.135401i | ||||
\(821\) | − | 307.159i | − | 0.374128i | −0.982348 | − | 0.187064i | \(-0.940103\pi\) | ||
0.982348 | − | 0.187064i | \(-0.0598972\pi\) | |||||||
\(822\) | −1136.63 | + | 1136.63i | −1.38276 | + | 1.38276i | ||||
\(823\) | −861.491 | − | 861.491i | −1.04677 | − | 1.04677i | −0.998851 | − | 0.0479183i | \(-0.984741\pi\) |
−0.0479183 | − | 0.998851i | \(-0.515259\pi\) | |||||||
\(824\) | −1695.59 | + | 1695.59i | −2.05775 | + | 2.05775i | ||||
\(825\) | − | 1.17820i | − | 0.00142812i | ||||||
\(826\) | −208.192 | − | 208.192i | −0.252049 | − | 0.252049i | ||||
\(827\) | 18.3000 | − | 18.3000i | 0.0221282 | − | 0.0221282i | −0.695956 | − | 0.718084i | \(-0.745019\pi\) |
0.718084 | + | 0.695956i | \(0.245019\pi\) | |||||||
\(828\) | −876.474 | −1.05854 | ||||||||
\(829\) | −211.234 | − | 211.234i | −0.254806 | − | 0.254806i | 0.568132 | − | 0.822938i | \(-0.307666\pi\) |
−0.822938 | + | 0.568132i | \(0.807666\pi\) | |||||||
\(830\) | 180.464 | − | 180.464i | 0.217426 | − | 0.217426i | ||||
\(831\) | 83.1683 | + | 83.1683i | 0.100082 | + | 0.100082i | ||||
\(832\) | 646.016 | 0.776462 | ||||||||
\(833\) | −739.384 | − | 739.384i | −0.887616 | − | 0.887616i | ||||
\(834\) | − | 1819.61i | − | 2.18179i | ||||||
\(835\) | 1003.99 | 1.20238 | ||||||||
\(836\) | 20.8017 | 0.0248824 | ||||||||
\(837\) | −43.3582 | −0.0518020 | ||||||||
\(838\) | 54.6307 | − | 54.6307i | 0.0651917 | − | 0.0651917i | ||||
\(839\) | 479.471 | − | 479.471i | 0.571479 | − | 0.571479i | −0.361063 | − | 0.932542i | \(-0.617586\pi\) |
0.932542 | + | 0.361063i | \(0.117586\pi\) | |||||||
\(840\) | 318.881i | 0.379620i | ||||||||
\(841\) | 135.006 | − | 830.093i | 0.160531 | − | 0.987031i | ||||
\(842\) | 1045.79 | 1.24203 | ||||||||
\(843\) | −1459.24 | − | 1459.24i | −1.73100 | − | 1.73100i | ||||
\(844\) | −1094.33 | − | 1094.33i | −1.29659 | − | 1.29659i | ||||
\(845\) | − | 453.408i | − | 0.536577i | ||||||
\(846\) | − | 1252.59i | − | 1.48060i | ||||||
\(847\) | 90.1833i | 0.106474i | ||||||||
\(848\) | 1738.82 | 2.05050 | ||||||||
\(849\) | −819.970 | + | 819.970i | −0.965807 | + | 0.965807i | ||||
\(850\) | 358.506i | 0.421772i | ||||||||
\(851\) | 87.0635 | − | 87.0635i | 0.102307 | − | 0.102307i | ||||
\(852\) | 2167.16 | + | 2167.16i | 2.54362 | + | 2.54362i | ||||
\(853\) | −74.8941 | + | 74.8941i | −0.0878008 | + | 0.0878008i | −0.749643 | − | 0.661842i | \(-0.769775\pi\) |
0.661842 | + | 0.749643i | \(0.269775\pi\) | |||||||
\(854\) | 165.598i | 0.193909i | ||||||||
\(855\) | −1180.62 | − | 1180.62i | −1.38084 | − | 1.38084i | ||||
\(856\) | −1349.90 | + | 1349.90i | −1.57699 | + | 1.57699i | ||||
\(857\) | 1145.50 | 1.33664 | 0.668321 | − | 0.743873i | \(-0.267013\pi\) | ||||
0.668321 | + | 0.743873i | \(0.267013\pi\) | |||||||
\(858\) | 5.73835 | + | 5.73835i | 0.00668805 | + | 0.00668805i | ||||
\(859\) | −307.151 | + | 307.151i | −0.357568 | + | 0.357568i | −0.862916 | − | 0.505348i | \(-0.831364\pi\) |
0.505348 | + | 0.862916i | \(0.331364\pi\) | |||||||
\(860\) | −499.233 | − | 499.233i | −0.580504 | − | 0.580504i | ||||
\(861\) | 11.6236 | 0.0135001 | ||||||||
\(862\) | −506.724 | − | 506.724i | −0.587847 | − | 0.587847i | ||||
\(863\) | − | 181.269i | − | 0.210046i | −0.994470 | − | 0.105023i | \(-0.966508\pi\) | ||
0.994470 | − | 0.105023i | \(-0.0334916\pi\) | |||||||
\(864\) | −389.094 | −0.450340 | ||||||||
\(865\) | 29.9937 | 0.0346747 | ||||||||
\(866\) | 623.653 | 0.720153 | ||||||||
\(867\) | 550.459 | − | 550.459i | 0.634900 | − | 0.634900i | ||||
\(868\) | −37.1282 | + | 37.1282i | −0.0427744 | + | 0.0427744i | ||||
\(869\) | − | 6.66290i | − | 0.00766732i | ||||||
\(870\) | −1635.05 | + | 1390.61i | −1.87937 | + | 1.59840i | ||||
\(871\) | −629.223 | −0.722415 | ||||||||
\(872\) | −623.905 | − | 623.905i | −0.715488 | − | 0.715488i | ||||
\(873\) | 444.050 | + | 444.050i | 0.508649 | + | 0.508649i | ||||
\(874\) | − | 1140.56i | − | 1.30499i | ||||||
\(875\) | 99.5282i | 0.113747i | ||||||||
\(876\) | 4491.84i | 5.12767i | ||||||||
\(877\) | 1730.81 | 1.97355 | 0.986777 | − | 0.162083i | \(-0.0518211\pi\) | ||||
0.986777 | + | 0.162083i | \(0.0518211\pi\) | |||||||
\(878\) | 1733.41 | − | 1733.41i | 1.97428 | − | 1.97428i | ||||
\(879\) | 525.545i | 0.597890i | ||||||||
\(880\) | −7.76975 | + | 7.76975i | −0.00882926 | + | 0.00882926i | ||||
\(881\) | 433.391 | + | 433.391i | 0.491931 | + | 0.491931i | 0.908914 | − | 0.416983i | \(-0.136913\pi\) |
−0.416983 | + | 0.908914i | \(0.636913\pi\) | |||||||
\(882\) | 1318.40 | − | 1318.40i | 1.49478 | − | 1.49478i | ||||
\(883\) | − | 589.072i | − | 0.667126i | −0.942728 | − | 0.333563i | \(-0.891749\pi\) | ||
0.942728 | − | 0.333563i | \(-0.108251\pi\) | |||||||
\(884\) | −1239.25 | − | 1239.25i | −1.40187 | − | 1.40187i | ||||
\(885\) | −1500.27 | + | 1500.27i | −1.69522 | + | 1.69522i | ||||
\(886\) | 1167.26 | 1.31745 | ||||||||
\(887\) | 136.134 | + | 136.134i | 0.153477 | + | 0.153477i | 0.779669 | − | 0.626192i | \(-0.215387\pi\) |
−0.626192 | + | 0.779669i | \(0.715387\pi\) | |||||||
\(888\) | 951.182 | − | 951.182i | 1.07115 | − | 1.07115i | ||||
\(889\) | −6.16203 | − | 6.16203i | −0.00693142 | − | 0.00693142i | ||||
\(890\) | −543.278 | −0.610425 | ||||||||
\(891\) | 2.82708 | + | 2.82708i | 0.00317293 | + | 0.00317293i | ||||
\(892\) | − | 557.731i | − | 0.625259i | ||||||
\(893\) | 1156.87 | 1.29548 | ||||||||
\(894\) | 727.282 | 0.813514 | ||||||||
\(895\) | −167.450 | −0.187095 | ||||||||
\(896\) | −15.9747 | + | 15.9747i | −0.0178289 | + | 0.0178289i | ||||
\(897\) | 223.306 | − | 223.306i | 0.248948 | − | 0.248948i | ||||
\(898\) | 1519.82i | 1.69245i | ||||||||
\(899\) | −208.207 | − | 16.8209i | −0.231599 | − | 0.0187107i | ||||
\(900\) | −453.698 | −0.504108 | ||||||||
\(901\) | −654.729 | − | 654.729i | −0.726670 | − | 0.726670i | ||||
\(902\) | 0.556563 | + | 0.556563i | 0.000617033 | + | 0.000617033i | ||||
\(903\) | − | 52.2647i | − | 0.0578790i | ||||||
\(904\) | 3159.13i | 3.49461i | ||||||||
\(905\) | 870.038i | 0.961368i | ||||||||
\(906\) | 1154.04 | 1.27378 | ||||||||
\(907\) | −490.744 | + | 490.744i | −0.541063 | + | 0.541063i | −0.923840 | − | 0.382778i | \(-0.874967\pi\) |
0.382778 | + | 0.923840i | \(0.374967\pi\) | |||||||
\(908\) | − | 1699.34i | − | 1.87152i | ||||||
\(909\) | −377.766 | + | 377.766i | −0.415584 | + | 0.415584i | ||||
\(910\) | −73.5861 | − | 73.5861i | −0.0808639 | − | 0.0808639i | ||||
\(911\) | 686.245 | − | 686.245i | 0.753287 | − | 0.753287i | −0.221804 | − | 0.975091i | \(-0.571195\pi\) |
0.975091 | + | 0.221804i | \(0.0711945\pi\) | |||||||
\(912\) | − | 6340.89i | − | 6.95273i | ||||||
\(913\) | 0.642044 | + | 0.642044i | 0.000703225 | + | 0.000703225i | ||||
\(914\) | −692.594 | + | 692.594i | −0.757762 | + | 0.757762i | ||||
\(915\) | 1193.33 | 1.30419 | ||||||||
\(916\) | −1415.18 | − | 1415.18i | −1.54495 | − | 1.54495i | ||||
\(917\) | 0.269531 | − | 0.269531i | 0.000293927 | − | 0.000293927i | ||||
\(918\) | 341.050 | + | 341.050i | 0.371514 | + | 0.371514i | ||||
\(919\) | 94.8391 | 0.103198 | 0.0515991 | − | 0.998668i | \(-0.483568\pi\) | ||||
0.0515991 | + | 0.998668i | \(0.483568\pi\) | |||||||
\(920\) | 594.179 | + | 594.179i | 0.645846 | + | 0.645846i | ||||
\(921\) | − | 1201.73i | − | 1.30481i | ||||||
\(922\) | −2571.68 | −2.78924 | ||||||||
\(923\) | −591.138 | −0.640453 | ||||||||
\(924\) | −1.91956 | −0.00207745 | ||||||||
\(925\) | 45.0675 | − | 45.0675i | 0.0487216 | − | 0.0487216i | ||||
\(926\) | 1591.56 | − | 1591.56i | 1.71874 | − | 1.71874i | ||||
\(927\) | 1158.61i | 1.24985i | ||||||||
\(928\) | −1868.44 | − | 150.950i | −2.01340 | − | 0.162661i | ||||
\(929\) | −382.605 | −0.411846 | −0.205923 | − | 0.978568i | \(-0.566020\pi\) | ||||
−0.205923 | + | 0.978568i | \(0.566020\pi\) | |||||||
\(930\) | 376.977 | + | 376.977i | 0.405351 | + | 0.405351i | ||||
\(931\) | 1217.64 | + | 1217.64i | 1.30789 | + | 1.30789i | ||||
\(932\) | 1006.12i | 1.07952i | ||||||||
\(933\) | 861.210i | 0.923054i | ||||||||
\(934\) | 1772.70i | 1.89796i | ||||||||
\(935\) | 5.85118 | 0.00625795 | ||||||||
\(936\) | 1305.97 | − | 1305.97i | 1.39527 | − | 1.39527i | ||||
\(937\) | − | 1462.55i | − | 1.56089i | −0.625227 | − | 0.780443i | \(-0.714994\pi\) | ||
0.625227 | − | 0.780443i | \(-0.285006\pi\) | |||||||
\(938\) | 148.285 | − | 148.285i | 0.158086 | − | 0.158086i | ||||
\(939\) | −983.635 | − | 983.635i | −1.04753 | − | 1.04753i | ||||
\(940\) | −1019.72 | + | 1019.72i | −1.08481 | + | 1.08481i | ||||
\(941\) | 828.617i | 0.880571i | 0.897858 | + | 0.440285i | \(0.145123\pi\) | ||||
−0.897858 | + | 0.440285i | \(0.854877\pi\) | |||||||
\(942\) | 2080.58 | + | 2080.58i | 2.20868 | + | 2.20868i | ||||
\(943\) | 21.6585 | − | 21.6585i | 0.0229677 | − | 0.0229677i | ||||
\(944\) | −4313.35 | −4.56923 | ||||||||
\(945\) | 14.3731 | + | 14.3731i | 0.0152096 | + | 0.0152096i | ||||
\(946\) | 2.50256 | − | 2.50256i | 0.00264541 | − | 0.00264541i | ||||
\(947\) | −612.076 | − | 612.076i | −0.646331 | − | 0.646331i | 0.305773 | − | 0.952104i | \(-0.401085\pi\) |
−0.952104 | + | 0.305773i | \(0.901085\pi\) | |||||||
\(948\) | −4792.97 | −5.05587 | ||||||||
\(949\) | −612.621 | − | 612.621i | −0.645544 | − | 0.645544i | ||||
\(950\) | − | 590.399i | − | 0.621473i | ||||||
\(951\) | −1384.81 | −1.45617 | ||||||||
\(952\) | 345.207 | 0.362613 | ||||||||
\(953\) | 884.227 | 0.927835 | 0.463917 | − | 0.885878i | \(-0.346443\pi\) | ||||
0.463917 | + | 0.885878i | \(0.346443\pi\) | |||||||
\(954\) | 1167.45 | − | 1167.45i | 1.22374 | − | 1.22374i | ||||
\(955\) | −975.652 | + | 975.652i | −1.02163 | + | 1.02163i | ||||
\(956\) | − | 3052.96i | − | 3.19347i | ||||||
\(957\) | −4.94742 | − | 5.81708i | −0.00516972 | − | 0.00607845i | ||||
\(958\) | 2265.35 | 2.36466 | ||||||||
\(959\) | 51.8562 | + | 51.8562i | 0.0540732 | + | 0.0540732i | ||||
\(960\) | 1097.08 | + | 1097.08i | 1.14279 | + | 1.14279i | ||||
\(961\) | − | 909.118i | − | 0.946012i | ||||||
\(962\) | 438.997i | 0.456338i | ||||||||
\(963\) | 922.400i | 0.957840i | ||||||||
\(964\) | 3061.29 | 3.17561 | ||||||||
\(965\) | 592.047 | − | 592.047i | 0.613520 | − | 0.613520i | ||||
\(966\) | 105.250i | 0.108954i | ||||||||
\(967\) | −1022.14 | + | 1022.14i | −1.05702 | + | 1.05702i | −0.0587468 | + | 0.998273i | \(0.518710\pi\) |
−0.998273 | + | 0.0587468i | \(0.981290\pi\) | |||||||
\(968\) | 1835.87 | + | 1835.87i | 1.89656 | + | 1.89656i | ||||
\(969\) | −2387.57 | + | 2387.57i | −2.46395 | + | 2.46395i | ||||
\(970\) | − | 1018.69i | − | 1.05019i | ||||||
\(971\) | 118.570 | + | 118.570i | 0.122111 | + | 0.122111i | 0.765522 | − | 0.643410i | \(-0.222481\pi\) |
−0.643410 | + | 0.765522i | \(0.722481\pi\) | |||||||
\(972\) | 2408.33 | − | 2408.33i | 2.47771 | − | 2.47771i | ||||
\(973\) | −83.0161 | −0.0853197 | ||||||||
\(974\) | −832.631 | − | 832.631i | −0.854857 | − | 0.854857i | ||||
\(975\) | 115.592 | − | 115.592i | 0.118556 | − | 0.118556i | ||||
\(976\) | 1715.44 | + | 1715.44i | 1.75763 | + | 1.75763i | ||||
\(977\) | 722.204 | 0.739205 | 0.369603 | − | 0.929190i | \(-0.379494\pi\) | ||||
0.369603 | + | 0.929190i | \(0.379494\pi\) | |||||||
\(978\) | −1362.93 | − | 1362.93i | −1.39359 | − | 1.39359i | ||||
\(979\) | − | 1.93284i | − | 0.00197430i | ||||||
\(980\) | −2146.58 | −2.19039 | ||||||||
\(981\) | −426.319 | −0.434576 | ||||||||
\(982\) | −2310.27 | −2.35262 | ||||||||
\(983\) | −295.211 | + | 295.211i | −0.300317 | + | 0.300317i | −0.841138 | − | 0.540821i | \(-0.818114\pi\) |
0.540821 | + | 0.841138i | \(0.318114\pi\) | |||||||
\(984\) | 236.623 | − | 236.623i | 0.240470 | − | 0.240470i | ||||
\(985\) | 1155.07i | 1.17266i | ||||||||
\(986\) | 1505.42 | + | 1770.04i | 1.52679 | + | 1.79517i | ||||
\(987\) | −106.755 | −0.108161 | ||||||||
\(988\) | 2040.84 | + | 2040.84i | 2.06562 | + | 2.06562i | ||||
\(989\) | −97.3863 | − | 97.3863i | −0.0984694 | − | 0.0984694i | ||||
\(990\) | 10.4332i | 0.0105386i | ||||||||
\(991\) | − | 1627.14i | − | 1.64191i | −0.570991 | − | 0.820956i | \(-0.693441\pi\) | ||
0.570991 | − | 0.820956i | \(-0.306559\pi\) | |||||||
\(992\) | 465.589i | 0.469344i | ||||||||
\(993\) | −1497.72 | −1.50828 | ||||||||
\(994\) | 139.309 | − | 139.309i | 0.140150 | − | 0.140150i | ||||
\(995\) | − | 761.210i | − | 0.765035i | ||||||
\(996\) | 461.856 | − | 461.856i | 0.463710 | − | 0.463710i | ||||
\(997\) | 472.423 | + | 472.423i | 0.473845 | + | 0.473845i | 0.903156 | − | 0.429312i | \(-0.141244\pi\) |
−0.429312 | + | 0.903156i | \(0.641244\pi\) | |||||||
\(998\) | −2223.70 | + | 2223.70i | −2.22816 | + | 2.22816i | ||||
\(999\) | − | 85.7462i | − | 0.0858320i |
(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 | 29.3.c.a.12.4 | ✓ | 8 | |
3.2 | odd | 2 | 261.3.f.a.244.1 | 8 | |||
4.3 | odd | 2 | 464.3.l.c.273.4 | 8 | |||
29.17 | odd | 4 | inner | 29.3.c.a.17.4 | yes | 8 | |
87.17 | even | 4 | 261.3.f.a.46.1 | 8 | |||
116.75 | even | 4 | 464.3.l.c.17.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.3.c.a.12.4 | ✓ | 8 | 1.1 | even | 1 | trivial | |
29.3.c.a.17.4 | yes | 8 | 29.17 | odd | 4 | inner | |
261.3.f.a.46.1 | 8 | 87.17 | even | 4 | |||
261.3.f.a.244.1 | 8 | 3.2 | odd | 2 | |||
464.3.l.c.17.4 | 8 | 116.75 | even | 4 | |||
464.3.l.c.273.4 | 8 | 4.3 | odd | 2 |