Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [165,4,Mod(34,165)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(165, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("165.34");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 165 = 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 165.c (of order \(2\), degree \(1\), 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: | \(9.73531515095\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 66x^{12} + 1705x^{10} + 22060x^{8} + 151880x^{6} + 537860x^{4} + 825344x^{2} + 262144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{4}\cdot 5 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 34.9 | ||
Root | \(2.41169i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 165.34 |
Dual form | 165.4.c.b.34.6 |
$q$-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 \(\left(\mathbb{Z}/165\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(56\) | \(67\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41169i | 0.499107i | 0.968361 | + | 0.249553i | \(0.0802838\pi\) | ||||
−0.968361 | + | 0.249553i | \(0.919716\pi\) | |||||||
\(3\) | − | 3.00000i | − | 0.577350i | ||||||
\(4\) | 6.00714 | 0.750892 | ||||||||
\(5\) | −11.1339 | − | 1.01772i | −0.995848 | − | 0.0910276i | ||||
\(6\) | 4.23506 | 0.288160 | ||||||||
\(7\) | 15.2844i | 0.825280i | 0.910894 | + | 0.412640i | \(0.135393\pi\) | ||||
−0.910894 | + | 0.412640i | \(0.864607\pi\) | |||||||
\(8\) | 19.7737i | 0.873882i | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 1.43670 | − | 15.7176i | 0.0454325 | − | 0.497035i | ||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | − | 18.0214i | − | 0.433528i | ||||||
\(13\) | 58.7385i | 1.25316i | 0.779355 | + | 0.626582i | \(0.215547\pi\) | ||||
−0.779355 | + | 0.626582i | \(0.784453\pi\) | |||||||
\(14\) | −21.5768 | −0.411903 | ||||||||
\(15\) | −3.05316 | + | 33.4018i | −0.0525548 | + | 0.574953i | ||||
\(16\) | 20.1428 | 0.314731 | ||||||||
\(17\) | 55.1122i | 0.786274i | 0.919480 | + | 0.393137i | \(0.128610\pi\) | ||||
−0.919480 | + | 0.393137i | \(0.871390\pi\) | |||||||
\(18\) | − | 12.7052i | − | 0.166369i | ||||||
\(19\) | 146.975 | 1.77465 | 0.887326 | − | 0.461142i | \(-0.152560\pi\) | ||||
0.887326 | + | 0.461142i | \(0.152560\pi\) | |||||||
\(20\) | −66.8830 | − | 6.11358i | −0.747775 | − | 0.0683519i | ||||
\(21\) | 45.8532 | 0.476475 | ||||||||
\(22\) | 15.5286i | 0.150486i | ||||||||
\(23\) | 4.30091i | 0.0389914i | 0.999810 | + | 0.0194957i | \(0.00620606\pi\) | ||||
−0.999810 | + | 0.0194957i | \(0.993794\pi\) | |||||||
\(24\) | 59.3211 | 0.504536 | ||||||||
\(25\) | 122.928 | + | 22.6624i | 0.983428 | + | 0.181299i | ||||
\(26\) | −82.9205 | −0.625463 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | 91.8155i | 0.619696i | ||||||||
\(29\) | −34.2412 | −0.219256 | −0.109628 | − | 0.993973i | \(-0.534966\pi\) | ||||
−0.109628 | + | 0.993973i | \(0.534966\pi\) | |||||||
\(30\) | −47.1529 | − | 4.31010i | −0.286963 | − | 0.0262305i | ||||
\(31\) | −255.359 | −1.47948 | −0.739740 | − | 0.672893i | \(-0.765051\pi\) | ||||
−0.739740 | + | 0.672893i | \(0.765051\pi\) | |||||||
\(32\) | 186.625i | 1.03097i | ||||||||
\(33\) | − | 33.0000i | − | 0.174078i | ||||||
\(34\) | −77.8012 | −0.392435 | ||||||||
\(35\) | 15.5552 | − | 170.175i | 0.0751232 | − | 0.821853i | ||||
\(36\) | −54.0642 | −0.250297 | ||||||||
\(37\) | 323.110i | 1.43565i | 0.696225 | + | 0.717824i | \(0.254862\pi\) | ||||
−0.696225 | + | 0.717824i | \(0.745138\pi\) | |||||||
\(38\) | 207.483i | 0.885742i | ||||||||
\(39\) | 176.216 | 0.723515 | ||||||||
\(40\) | 20.1241 | − | 220.159i | 0.0795474 | − | 0.870254i | ||||
\(41\) | −186.425 | −0.710116 | −0.355058 | − | 0.934844i | \(-0.615539\pi\) | ||||
−0.355058 | + | 0.934844i | \(0.615539\pi\) | |||||||
\(42\) | 64.7304i | 0.237812i | ||||||||
\(43\) | 119.302i | 0.423100i | 0.977367 | + | 0.211550i | \(0.0678512\pi\) | ||||
−0.977367 | + | 0.211550i | \(0.932149\pi\) | |||||||
\(44\) | 66.0785 | 0.226403 | ||||||||
\(45\) | 100.205 | + | 9.15947i | 0.331949 | + | 0.0303425i | ||||
\(46\) | −6.07154 | −0.0194609 | ||||||||
\(47\) | − | 484.663i | − | 1.50416i | −0.659074 | − | 0.752078i | \(-0.729052\pi\) | ||
0.659074 | − | 0.752078i | \(-0.270948\pi\) | |||||||
\(48\) | − | 60.4284i | − | 0.181710i | ||||||
\(49\) | 109.387 | 0.318913 | ||||||||
\(50\) | −31.9922 | + | 173.537i | −0.0904877 | + | 0.490836i | ||||
\(51\) | 165.337 | 0.453956 | ||||||||
\(52\) | 352.851i | 0.940992i | ||||||||
\(53\) | 44.8855i | 0.116330i | 0.998307 | + | 0.0581651i | \(0.0185250\pi\) | ||||
−0.998307 | + | 0.0581651i | \(0.981475\pi\) | |||||||
\(54\) | −38.1156 | −0.0960532 | ||||||||
\(55\) | −122.473 | − | 11.1949i | −0.300260 | − | 0.0274458i | ||||
\(56\) | −302.229 | −0.721197 | ||||||||
\(57\) | − | 440.925i | − | 1.02460i | ||||||
\(58\) | − | 48.3379i | − | 0.109432i | ||||||
\(59\) | −263.074 | −0.580498 | −0.290249 | − | 0.956951i | \(-0.593738\pi\) | ||||
−0.290249 | + | 0.956951i | \(0.593738\pi\) | |||||||
\(60\) | −18.3407 | + | 200.649i | −0.0394630 | + | 0.431728i | ||||
\(61\) | 27.5825 | 0.0578948 | 0.0289474 | − | 0.999581i | \(-0.490784\pi\) | ||||
0.0289474 | + | 0.999581i | \(0.490784\pi\) | |||||||
\(62\) | − | 360.487i | − | 0.738419i | ||||||
\(63\) | − | 137.560i | − | 0.275093i | ||||||
\(64\) | −102.314 | −0.199831 | ||||||||
\(65\) | 59.7793 | − | 653.990i | 0.114073 | − | 1.24796i | ||||
\(66\) | 46.5857 | 0.0868834 | ||||||||
\(67\) | − | 1053.61i | − | 1.92118i | −0.277969 | − | 0.960590i | \(-0.589661\pi\) | ||
0.277969 | − | 0.960590i | \(-0.410339\pi\) | |||||||
\(68\) | 331.066i | 0.590407i | ||||||||
\(69\) | 12.9027 | 0.0225117 | ||||||||
\(70\) | 240.234 | + | 21.9591i | 0.410193 | + | 0.0374945i | ||||
\(71\) | 81.3960 | 0.136055 | 0.0680276 | − | 0.997683i | \(-0.478329\pi\) | ||||
0.0680276 | + | 0.997683i | \(0.478329\pi\) | |||||||
\(72\) | − | 177.963i | − | 0.291294i | ||||||
\(73\) | − | 623.529i | − | 0.999707i | −0.866110 | − | 0.499853i | \(-0.833387\pi\) | ||
0.866110 | − | 0.499853i | \(-0.166613\pi\) | |||||||
\(74\) | −456.130 | −0.716542 | ||||||||
\(75\) | 67.9872 | − | 368.785i | 0.104673 | − | 0.567782i | ||||
\(76\) | 882.900 | 1.33257 | ||||||||
\(77\) | 168.128i | 0.248831i | ||||||||
\(78\) | 248.761i | 0.361111i | ||||||||
\(79\) | 896.394 | 1.27661 | 0.638305 | − | 0.769784i | \(-0.279636\pi\) | ||||
0.638305 | + | 0.769784i | \(0.279636\pi\) | |||||||
\(80\) | −224.269 | − | 20.4997i | −0.313425 | − | 0.0286492i | ||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | − | 263.174i | − | 0.354424i | ||||||
\(83\) | 575.180i | 0.760653i | 0.924852 | + | 0.380326i | \(0.124188\pi\) | ||||
−0.924852 | + | 0.380326i | \(0.875812\pi\) | |||||||
\(84\) | 275.446 | 0.357782 | ||||||||
\(85\) | 56.0887 | − | 613.615i | 0.0715727 | − | 0.783010i | ||||
\(86\) | −168.416 | −0.211172 | ||||||||
\(87\) | 102.724i | 0.126588i | ||||||||
\(88\) | 217.511i | 0.263485i | ||||||||
\(89\) | 1063.68 | 1.26685 | 0.633426 | − | 0.773803i | \(-0.281648\pi\) | ||||
0.633426 | + | 0.773803i | \(0.281648\pi\) | |||||||
\(90\) | −12.9303 | + | 141.459i | −0.0151442 | + | 0.165678i | ||||
\(91\) | −897.783 | −1.03421 | ||||||||
\(92\) | 25.8361i | 0.0292783i | ||||||||
\(93\) | 766.078i | 0.854178i | ||||||||
\(94\) | 684.192 | 0.750735 | ||||||||
\(95\) | −1636.41 | − | 149.579i | −1.76729 | − | 0.161542i | ||||
\(96\) | 559.875 | 0.595229 | ||||||||
\(97\) | − | 544.723i | − | 0.570188i | −0.958499 | − | 0.285094i | \(-0.907975\pi\) | ||
0.958499 | − | 0.285094i | \(-0.0920249\pi\) | |||||||
\(98\) | 154.421i | 0.159172i | ||||||||
\(99\) | −99.0000 | −0.100504 | ||||||||
\(100\) | 738.448 | + | 136.136i | 0.738448 | + | 0.136136i | ||||
\(101\) | −1124.51 | −1.10785 | −0.553925 | − | 0.832567i | \(-0.686871\pi\) | ||||
−0.553925 | + | 0.832567i | \(0.686871\pi\) | |||||||
\(102\) | 233.404i | 0.226572i | ||||||||
\(103\) | 1275.53i | 1.22021i | 0.792322 | + | 0.610103i | \(0.208872\pi\) | ||||
−0.792322 | + | 0.610103i | \(0.791128\pi\) | |||||||
\(104\) | −1161.48 | −1.09512 | ||||||||
\(105\) | −510.526 | − | 46.6657i | −0.474497 | − | 0.0433724i | ||||
\(106\) | −63.3644 | −0.0580612 | ||||||||
\(107\) | − | 946.142i | − | 0.854832i | −0.904055 | − | 0.427416i | \(-0.859424\pi\) | ||
0.904055 | − | 0.427416i | \(-0.140576\pi\) | |||||||
\(108\) | 162.193i | 0.144509i | ||||||||
\(109\) | −472.202 | −0.414943 | −0.207472 | − | 0.978241i | \(-0.566523\pi\) | ||||
−0.207472 | + | 0.978241i | \(0.566523\pi\) | |||||||
\(110\) | 15.8037 | − | 172.894i | 0.0136984 | − | 0.149862i | ||||
\(111\) | 969.330 | 0.828872 | ||||||||
\(112\) | 307.871i | 0.259742i | ||||||||
\(113\) | − | 185.707i | − | 0.154601i | −0.997008 | − | 0.0773004i | \(-0.975370\pi\) | ||
0.997008 | − | 0.0773004i | \(-0.0246300\pi\) | |||||||
\(114\) | 622.449 | 0.511383 | ||||||||
\(115\) | 4.37712 | − | 47.8860i | 0.00354929 | − | 0.0388295i | ||||
\(116\) | −205.692 | −0.164638 | ||||||||
\(117\) | − | 528.647i | − | 0.417722i | ||||||
\(118\) | − | 371.379i | − | 0.289731i | ||||||
\(119\) | −842.356 | −0.648896 | ||||||||
\(120\) | −660.477 | − | 60.3722i | −0.502442 | − | 0.0459267i | ||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 38.9379i | 0.0288957i | ||||||||
\(123\) | 559.276i | 0.409986i | ||||||||
\(124\) | −1533.98 | −1.11093 | ||||||||
\(125\) | −1345.61 | − | 377.428i | −0.962842 | − | 0.270066i | ||||
\(126\) | 194.191 | 0.137301 | ||||||||
\(127\) | − | 1866.06i | − | 1.30383i | −0.758294 | − | 0.651913i | \(-0.773967\pi\) | ||
0.758294 | − | 0.651913i | \(-0.226033\pi\) | |||||||
\(128\) | 1348.56i | 0.931230i | ||||||||
\(129\) | 357.905 | 0.244277 | ||||||||
\(130\) | 923.230 | + | 84.3897i | 0.622866 | + | 0.0569344i | ||||
\(131\) | 2163.02 | 1.44262 | 0.721311 | − | 0.692611i | \(-0.243540\pi\) | ||||
0.721311 | + | 0.692611i | \(0.243540\pi\) | |||||||
\(132\) | − | 198.236i | − | 0.130714i | ||||||
\(133\) | 2246.43i | 1.46459i | ||||||||
\(134\) | 1487.37 | 0.958874 | ||||||||
\(135\) | 27.4784 | − | 300.616i | 0.0175183 | − | 0.191651i | ||||
\(136\) | −1089.77 | −0.687111 | ||||||||
\(137\) | 2175.20i | 1.35650i | 0.734832 | + | 0.678249i | \(0.237261\pi\) | ||||
−0.734832 | + | 0.678249i | \(0.762739\pi\) | |||||||
\(138\) | 18.2146i | 0.0112357i | ||||||||
\(139\) | −1280.43 | −0.781331 | −0.390666 | − | 0.920533i | \(-0.627755\pi\) | ||||
−0.390666 | + | 0.920533i | \(0.627755\pi\) | |||||||
\(140\) | 93.4424 | − | 1022.27i | 0.0564094 | − | 0.617123i | ||||
\(141\) | −1453.99 | −0.868425 | ||||||||
\(142\) | 114.906i | 0.0679061i | ||||||||
\(143\) | 646.124i | 0.377843i | ||||||||
\(144\) | −181.285 | −0.104910 | ||||||||
\(145\) | 381.239 | + | 34.8480i | 0.218346 | + | 0.0199584i | ||||
\(146\) | 880.229 | 0.498961 | ||||||||
\(147\) | − | 328.162i | − | 0.184125i | ||||||
\(148\) | 1940.97i | 1.07802i | ||||||||
\(149\) | −440.136 | −0.241996 | −0.120998 | − | 0.992653i | \(-0.538609\pi\) | ||||
−0.120998 | + | 0.992653i | \(0.538609\pi\) | |||||||
\(150\) | 520.610 | + | 95.9767i | 0.283384 | + | 0.0522431i | ||||
\(151\) | 2100.57 | 1.13207 | 0.566034 | − | 0.824382i | \(-0.308477\pi\) | ||||
0.566034 | + | 0.824382i | \(0.308477\pi\) | |||||||
\(152\) | 2906.24i | 1.55084i | ||||||||
\(153\) | − | 496.010i | − | 0.262091i | ||||||
\(154\) | −237.345 | −0.124193 | ||||||||
\(155\) | 2843.15 | + | 259.884i | 1.47334 | + | 0.134673i | ||||
\(156\) | 1058.55 | 0.543282 | ||||||||
\(157\) | − | 688.807i | − | 0.350145i | −0.984556 | − | 0.175073i | \(-0.943984\pi\) | ||
0.984556 | − | 0.175073i | \(-0.0560160\pi\) | |||||||
\(158\) | 1265.43i | 0.637165i | ||||||||
\(159\) | 134.657 | 0.0671633 | ||||||||
\(160\) | 189.932 | − | 2077.87i | 0.0938464 | − | 1.02669i | ||||
\(161\) | −65.7368 | −0.0321788 | ||||||||
\(162\) | 114.347i | 0.0554563i | ||||||||
\(163\) | 1800.54i | 0.865207i | 0.901584 | + | 0.432604i | \(0.142405\pi\) | ||||
−0.901584 | + | 0.432604i | \(0.857595\pi\) | |||||||
\(164\) | −1119.88 | −0.533220 | ||||||||
\(165\) | −33.5847 | + | 367.419i | −0.0158459 | + | 0.173355i | ||||
\(166\) | −811.974 | −0.379647 | ||||||||
\(167\) | 3420.45i | 1.58493i | 0.609920 | + | 0.792463i | \(0.291201\pi\) | ||||
−0.609920 | + | 0.792463i | \(0.708799\pi\) | |||||||
\(168\) | 906.687i | 0.416384i | ||||||||
\(169\) | −1253.22 | −0.570421 | ||||||||
\(170\) | 866.232 | + | 79.1797i | 0.390806 | + | 0.0357224i | ||||
\(171\) | −1322.78 | −0.591551 | ||||||||
\(172\) | 716.661i | 0.317703i | ||||||||
\(173\) | − | 2326.51i | − | 1.02243i | −0.859452 | − | 0.511216i | \(-0.829195\pi\) | ||
0.859452 | − | 0.511216i | \(-0.170805\pi\) | |||||||
\(174\) | −145.014 | −0.0631808 | ||||||||
\(175\) | −346.381 | + | 1878.89i | −0.149623 | + | 0.811603i | ||||
\(176\) | 221.571 | 0.0948951 | ||||||||
\(177\) | 789.223i | 0.335151i | ||||||||
\(178\) | 1501.58i | 0.632295i | ||||||||
\(179\) | 4072.53 | 1.70053 | 0.850266 | − | 0.526353i | \(-0.176441\pi\) | ||||
0.850266 | + | 0.526353i | \(0.176441\pi\) | |||||||
\(180\) | 601.947 | + | 55.0222i | 0.249258 | + | 0.0227840i | ||||
\(181\) | 435.684 | 0.178918 | 0.0894590 | − | 0.995991i | \(-0.471486\pi\) | ||||
0.0894590 | + | 0.995991i | \(0.471486\pi\) | |||||||
\(182\) | − | 1267.39i | − | 0.516182i | ||||||
\(183\) | − | 82.7476i | − | 0.0334256i | ||||||
\(184\) | −85.0449 | −0.0340739 | ||||||||
\(185\) | 328.835 | − | 3597.48i | 0.130684 | − | 1.42969i | ||||
\(186\) | −1081.46 | −0.426326 | ||||||||
\(187\) | 606.234i | 0.237071i | ||||||||
\(188\) | − | 2911.44i | − | 1.12946i | ||||||
\(189\) | −412.679 | −0.158825 | ||||||||
\(190\) | 211.159 | − | 2310.10i | 0.0806269 | − | 0.882064i | ||||
\(191\) | 3120.75 | 1.18225 | 0.591125 | − | 0.806580i | \(-0.298684\pi\) | ||||
0.591125 | + | 0.806580i | \(0.298684\pi\) | |||||||
\(192\) | 306.941i | 0.115373i | ||||||||
\(193\) | − | 1100.45i | − | 0.410427i | −0.978717 | − | 0.205213i | \(-0.934211\pi\) | ||
0.978717 | − | 0.205213i | \(-0.0657888\pi\) | |||||||
\(194\) | 768.979 | 0.284585 | ||||||||
\(195\) | −1961.97 | − | 179.338i | −0.720511 | − | 0.0658598i | ||||
\(196\) | 657.105 | 0.239470 | ||||||||
\(197\) | − | 5347.12i | − | 1.93384i | −0.255082 | − | 0.966920i | \(-0.582102\pi\) | ||
0.255082 | − | 0.966920i | \(-0.417898\pi\) | |||||||
\(198\) | − | 139.757i | − | 0.0501621i | ||||||
\(199\) | −5103.80 | −1.81808 | −0.909042 | − | 0.416705i | \(-0.863185\pi\) | ||||
−0.909042 | + | 0.416705i | \(0.863185\pi\) | |||||||
\(200\) | −448.120 | + | 2430.75i | −0.158434 | + | 0.859400i | ||||
\(201\) | −3160.83 | −1.10919 | ||||||||
\(202\) | − | 1587.46i | − | 0.552935i | ||||||
\(203\) | − | 523.357i | − | 0.180948i | ||||||
\(204\) | 993.199 | 0.340872 | ||||||||
\(205\) | 2075.65 | + | 189.729i | 0.707168 | + | 0.0646401i | ||||
\(206\) | −1800.64 | −0.609013 | ||||||||
\(207\) | − | 38.7082i | − | 0.0129971i | ||||||
\(208\) | 1183.16i | 0.394410i | ||||||||
\(209\) | 1616.73 | 0.535078 | ||||||||
\(210\) | 65.8773 | − | 720.703i | 0.0216475 | − | 0.236825i | ||||
\(211\) | 1645.58 | 0.536902 | 0.268451 | − | 0.963293i | \(-0.413488\pi\) | ||||
0.268451 | + | 0.963293i | \(0.413488\pi\) | |||||||
\(212\) | 269.634i | 0.0873515i | ||||||||
\(213\) | − | 244.188i | − | 0.0785515i | ||||||
\(214\) | 1335.66 | 0.426653 | ||||||||
\(215\) | 121.415 | − | 1328.29i | 0.0385138 | − | 0.421344i | ||||
\(216\) | −533.890 | −0.168179 | ||||||||
\(217\) | − | 3903.01i | − | 1.22098i | ||||||
\(218\) | − | 666.602i | − | 0.207101i | ||||||
\(219\) | −1870.59 | −0.577181 | ||||||||
\(220\) | −735.713 | − | 67.2494i | −0.225463 | − | 0.0206089i | ||||
\(221\) | −3237.21 | −0.985331 | ||||||||
\(222\) | 1368.39i | 0.413696i | ||||||||
\(223\) | − | 2592.93i | − | 0.778635i | −0.921104 | − | 0.389318i | \(-0.872711\pi\) | ||
0.921104 | − | 0.389318i | \(-0.127289\pi\) | |||||||
\(224\) | −2852.45 | −0.850836 | ||||||||
\(225\) | −1106.36 | − | 203.962i | −0.327809 | − | 0.0604331i | ||||
\(226\) | 262.161 | 0.0771623 | ||||||||
\(227\) | − | 916.297i | − | 0.267915i | −0.990987 | − | 0.133958i | \(-0.957231\pi\) | ||
0.990987 | − | 0.133958i | \(-0.0427686\pi\) | |||||||
\(228\) | − | 2648.70i | − | 0.769361i | ||||||
\(229\) | −4300.85 | −1.24108 | −0.620542 | − | 0.784173i | \(-0.713087\pi\) | ||||
−0.620542 | + | 0.784173i | \(0.713087\pi\) | |||||||
\(230\) | 67.6000 | + | 6.17912i | 0.0193801 | + | 0.00177147i | ||||
\(231\) | 504.385 | 0.143663 | ||||||||
\(232\) | − | 677.076i | − | 0.191604i | ||||||
\(233\) | 4196.20i | 1.17984i | 0.807463 | + | 0.589918i | \(0.200840\pi\) | ||||
−0.807463 | + | 0.589918i | \(0.799160\pi\) | |||||||
\(234\) | 746.284 | 0.208488 | ||||||||
\(235\) | −493.251 | + | 5396.20i | −0.136920 | + | 1.49791i | ||||
\(236\) | −1580.32 | −0.435891 | ||||||||
\(237\) | − | 2689.18i | − | 0.737051i | ||||||
\(238\) | − | 1189.14i | − | 0.323869i | ||||||
\(239\) | 3150.37 | 0.852639 | 0.426319 | − | 0.904573i | \(-0.359810\pi\) | ||||
0.426319 | + | 0.904573i | \(0.359810\pi\) | |||||||
\(240\) | −61.4992 | + | 672.806i | −0.0165406 | + | 0.180956i | ||||
\(241\) | 4864.06 | 1.30009 | 0.650044 | − | 0.759896i | \(-0.274750\pi\) | ||||
0.650044 | + | 0.759896i | \(0.274750\pi\) | |||||||
\(242\) | 170.814i | 0.0453734i | ||||||||
\(243\) | − | 243.000i | − | 0.0641500i | ||||||
\(244\) | 165.692 | 0.0434727 | ||||||||
\(245\) | −1217.91 | − | 111.326i | −0.317589 | − | 0.0290299i | ||||
\(246\) | −789.523 | −0.204627 | ||||||||
\(247\) | 8633.10i | 2.22393i | ||||||||
\(248\) | − | 5049.40i | − | 1.29289i | ||||||
\(249\) | 1725.54 | 0.439163 | ||||||||
\(250\) | 532.811 | − | 1899.58i | 0.134792 | − | 0.480561i | ||||
\(251\) | 5366.11 | 1.34942 | 0.674712 | − | 0.738081i | \(-0.264268\pi\) | ||||
0.674712 | + | 0.738081i | \(0.264268\pi\) | |||||||
\(252\) | − | 826.339i | − | 0.206565i | ||||||
\(253\) | 47.3100i | 0.0117563i | ||||||||
\(254\) | 2634.29 | 0.650749 | ||||||||
\(255\) | −1840.84 | − | 168.266i | −0.452071 | − | 0.0413225i | ||||
\(256\) | −2722.26 | −0.664615 | ||||||||
\(257\) | − | 406.491i | − | 0.0986624i | −0.998782 | − | 0.0493312i | \(-0.984291\pi\) | ||
0.998782 | − | 0.0493312i | \(-0.0157090\pi\) | |||||||
\(258\) | 505.249i | 0.121920i | ||||||||
\(259\) | −4938.54 | −1.18481 | ||||||||
\(260\) | 359.103 | − | 3928.61i | 0.0856562 | − | 0.937085i | ||||
\(261\) | 308.171 | 0.0730855 | ||||||||
\(262\) | 3053.50i | 0.720023i | ||||||||
\(263\) | 8009.69i | 1.87794i | 0.343996 | + | 0.938971i | \(0.388219\pi\) | ||||
−0.343996 | + | 0.938971i | \(0.611781\pi\) | |||||||
\(264\) | 652.532 | 0.152123 | ||||||||
\(265\) | 45.6809 | − | 499.752i | 0.0105893 | − | 0.115847i | ||||
\(266\) | −3171.25 | −0.730985 | ||||||||
\(267\) | − | 3191.04i | − | 0.731418i | ||||||
\(268\) | − | 6329.19i | − | 1.44260i | ||||||
\(269\) | 4762.72 | 1.07951 | 0.539755 | − | 0.841822i | \(-0.318517\pi\) | ||||
0.539755 | + | 0.841822i | \(0.318517\pi\) | |||||||
\(270\) | 424.376 | + | 38.7909i | 0.0956544 | + | 0.00874349i | ||||
\(271\) | −4454.85 | −0.998570 | −0.499285 | − | 0.866438i | \(-0.666404\pi\) | ||||
−0.499285 | + | 0.866438i | \(0.666404\pi\) | |||||||
\(272\) | 1110.11i | 0.247465i | ||||||||
\(273\) | 2693.35i | 0.597102i | ||||||||
\(274\) | −3070.71 | −0.677038 | ||||||||
\(275\) | 1352.21 | + | 249.287i | 0.296515 | + | 0.0546638i | ||||
\(276\) | 77.5084 | 0.0169038 | ||||||||
\(277\) | − | 2090.00i | − | 0.453343i | −0.973971 | − | 0.226671i | \(-0.927216\pi\) | ||
0.973971 | − | 0.226671i | \(-0.0727843\pi\) | |||||||
\(278\) | − | 1807.57i | − | 0.389968i | ||||||
\(279\) | 2298.23 | 0.493160 | ||||||||
\(280\) | 3365.00 | + | 307.584i | 0.718203 | + | 0.0656489i | ||||
\(281\) | 3261.96 | 0.692499 | 0.346250 | − | 0.938142i | \(-0.387455\pi\) | ||||
0.346250 | + | 0.938142i | \(0.387455\pi\) | |||||||
\(282\) | − | 2052.58i | − | 0.433437i | ||||||
\(283\) | − | 5421.25i | − | 1.13873i | −0.822086 | − | 0.569363i | \(-0.807190\pi\) | ||
0.822086 | − | 0.569363i | \(-0.192810\pi\) | |||||||
\(284\) | 488.957 | 0.102163 | ||||||||
\(285\) | −448.738 | + | 4909.23i | −0.0932665 | + | 1.02034i | ||||
\(286\) | −912.125 | −0.188584 | ||||||||
\(287\) | − | 2849.40i | − | 0.586044i | ||||||
\(288\) | − | 1679.62i | − | 0.343656i | ||||||
\(289\) | 1875.65 | 0.381772 | ||||||||
\(290\) | −49.1944 | + | 538.191i | −0.00996137 | + | 0.108978i | ||||
\(291\) | −1634.17 | −0.329198 | ||||||||
\(292\) | − | 3745.63i | − | 0.750672i | ||||||
\(293\) | − | 7383.35i | − | 1.47215i | −0.676900 | − | 0.736075i | \(-0.736677\pi\) | ||
0.676900 | − | 0.736075i | \(-0.263323\pi\) | |||||||
\(294\) | 463.262 | 0.0918979 | ||||||||
\(295\) | 2929.05 | + | 267.736i | 0.578088 | + | 0.0528413i | ||||
\(296\) | −6389.08 | −1.25459 | ||||||||
\(297\) | 297.000i | 0.0580259i | ||||||||
\(298\) | − | 621.335i | − | 0.120782i | ||||||
\(299\) | −252.629 | −0.0488626 | ||||||||
\(300\) | 408.409 | − | 2215.35i | 0.0785983 | − | 0.426343i | ||||
\(301\) | −1823.45 | −0.349176 | ||||||||
\(302\) | 2965.35i | 0.565023i | ||||||||
\(303\) | 3373.53i | 0.639617i | ||||||||
\(304\) | 2960.49 | 0.558539 | ||||||||
\(305\) | −307.102 | − | 28.0713i | −0.0576544 | − | 0.00527002i | ||||
\(306\) | 700.211 | 0.130812 | ||||||||
\(307\) | − | 397.190i | − | 0.0738399i | −0.999318 | − | 0.0369200i | \(-0.988245\pi\) | ||
0.999318 | − | 0.0369200i | \(-0.0117547\pi\) | |||||||
\(308\) | 1009.97i | 0.186845i | ||||||||
\(309\) | 3826.58 | 0.704486 | ||||||||
\(310\) | −366.875 | + | 4013.64i | −0.0672164 | + | 0.735353i | ||||
\(311\) | −163.865 | −0.0298775 | −0.0149388 | − | 0.999888i | \(-0.504755\pi\) | ||||
−0.0149388 | + | 0.999888i | \(0.504755\pi\) | |||||||
\(312\) | 3484.44i | 0.632267i | ||||||||
\(313\) | 2498.48i | 0.451189i | 0.974221 | + | 0.225595i | \(0.0724325\pi\) | ||||
−0.974221 | + | 0.225595i | \(0.927568\pi\) | |||||||
\(314\) | 972.381 | 0.174760 | ||||||||
\(315\) | −139.997 | + | 1531.58i | −0.0250411 | + | 0.273951i | ||||
\(316\) | 5384.76 | 0.958596 | ||||||||
\(317\) | − | 411.403i | − | 0.0728917i | −0.999336 | − | 0.0364459i | \(-0.988396\pi\) | ||
0.999336 | − | 0.0364459i | \(-0.0116036\pi\) | |||||||
\(318\) | 190.093i | 0.0335217i | ||||||||
\(319\) | −376.654 | −0.0661083 | ||||||||
\(320\) | 1139.15 | + | 104.127i | 0.199002 | + | 0.0181902i | ||||
\(321\) | −2838.43 | −0.493537 | ||||||||
\(322\) | − | 92.7998i | − | 0.0160607i | ||||||
\(323\) | 8100.12i | 1.39536i | ||||||||
\(324\) | 486.578 | 0.0834325 | ||||||||
\(325\) | −1331.16 | + | 7220.64i | −0.227198 | + | 1.23240i | ||||
\(326\) | −2541.79 | −0.431831 | ||||||||
\(327\) | 1416.61i | 0.239568i | ||||||||
\(328\) | − | 3686.32i | − | 0.620558i | ||||||
\(329\) | 7407.78 | 1.24135 | ||||||||
\(330\) | −518.681 | − | 47.4111i | −0.0865227 | − | 0.00790878i | ||||
\(331\) | −2282.08 | −0.378957 | −0.189478 | − | 0.981885i | \(-0.560680\pi\) | ||||
−0.189478 | + | 0.981885i | \(0.560680\pi\) | |||||||
\(332\) | 3455.18i | 0.571168i | ||||||||
\(333\) | − | 2907.99i | − | 0.478549i | ||||||
\(334\) | −4828.61 | −0.791047 | ||||||||
\(335\) | −1072.28 | + | 11730.8i | −0.174880 | + | 1.91320i | ||||
\(336\) | 923.612 | 0.149962 | ||||||||
\(337\) | − | 2451.29i | − | 0.396233i | −0.980179 | − | 0.198116i | \(-0.936518\pi\) | ||
0.980179 | − | 0.198116i | \(-0.0634824\pi\) | |||||||
\(338\) | − | 1769.15i | − | 0.284701i | ||||||
\(339\) | −557.122 | −0.0892588 | ||||||||
\(340\) | 336.933 | − | 3686.07i | 0.0537434 | − | 0.587956i | ||||
\(341\) | −2808.95 | −0.446080 | ||||||||
\(342\) | − | 1867.35i | − | 0.295247i | ||||||
\(343\) | 6914.47i | 1.08847i | ||||||||
\(344\) | −2359.03 | −0.369740 | ||||||||
\(345\) | −143.658 | − | 13.1313i | −0.0224182 | − | 0.00204918i | ||||
\(346\) | 3284.30 | 0.510303 | ||||||||
\(347\) | 3950.82i | 0.611214i | 0.952158 | + | 0.305607i | \(0.0988594\pi\) | ||||
−0.952158 | + | 0.305607i | \(0.901141\pi\) | |||||||
\(348\) | 617.075i | 0.0950538i | ||||||||
\(349\) | −8241.77 | −1.26410 | −0.632051 | − | 0.774926i | \(-0.717787\pi\) | ||||
−0.632051 | + | 0.774926i | \(0.717787\pi\) | |||||||
\(350\) | −2652.40 | − | 488.982i | −0.405077 | − | 0.0746777i | ||||
\(351\) | −1585.94 | −0.241172 | ||||||||
\(352\) | 2052.87i | 0.310848i | ||||||||
\(353\) | − | 4882.59i | − | 0.736187i | −0.929789 | − | 0.368094i | \(-0.880011\pi\) | ||
0.929789 | − | 0.368094i | \(-0.119989\pi\) | |||||||
\(354\) | −1114.14 | −0.167276 | ||||||||
\(355\) | −906.256 | − | 82.8382i | −0.135490 | − | 0.0123848i | ||||
\(356\) | 6389.67 | 0.951270 | ||||||||
\(357\) | 2527.07i | 0.374640i | ||||||||
\(358\) | 5749.14i | 0.848748i | ||||||||
\(359\) | −232.369 | −0.0341615 | −0.0170808 | − | 0.999854i | \(-0.505437\pi\) | ||||
−0.0170808 | + | 0.999854i | \(0.505437\pi\) | |||||||
\(360\) | −181.117 | + | 1981.43i | −0.0265158 | + | 0.290085i | ||||
\(361\) | 14742.7 | 2.14939 | ||||||||
\(362\) | 615.050i | 0.0892992i | ||||||||
\(363\) | − | 363.000i | − | 0.0524864i | ||||||
\(364\) | −5393.11 | −0.776581 | ||||||||
\(365\) | −634.578 | + | 6942.33i | −0.0910009 | + | 0.995556i | ||||
\(366\) | 116.814 | 0.0166829 | ||||||||
\(367\) | 10953.0i | 1.55788i | 0.627099 | + | 0.778940i | \(0.284242\pi\) | ||||
−0.627099 | + | 0.778940i | \(0.715758\pi\) | |||||||
\(368\) | 86.6324i | 0.0122718i | ||||||||
\(369\) | 1677.83 | 0.236705 | ||||||||
\(370\) | 5078.52 | + | 464.213i | 0.713567 | + | 0.0652251i | ||||
\(371\) | −686.048 | −0.0960050 | ||||||||
\(372\) | 4601.93i | 0.641396i | ||||||||
\(373\) | − | 5165.78i | − | 0.717089i | −0.933513 | − | 0.358544i | \(-0.883273\pi\) | ||
0.933513 | − | 0.358544i | \(-0.116727\pi\) | |||||||
\(374\) | −855.813 | −0.118324 | ||||||||
\(375\) | −1132.28 | + | 4036.84i | −0.155922 | + | 0.555897i | ||||
\(376\) | 9583.58 | 1.31446 | ||||||||
\(377\) | − | 2011.28i | − | 0.274764i | ||||||
\(378\) | − | 582.573i | − | 0.0792707i | ||||||
\(379\) | −6076.10 | −0.823505 | −0.411752 | − | 0.911296i | \(-0.635083\pi\) | ||||
−0.411752 | + | 0.911296i | \(0.635083\pi\) | |||||||
\(380\) | −9830.14 | − | 898.544i | −1.32704 | − | 0.121301i | ||||
\(381\) | −5598.18 | −0.752764 | ||||||||
\(382\) | 4405.52i | 0.590069i | ||||||||
\(383\) | − | 4767.71i | − | 0.636080i | −0.948077 | − | 0.318040i | \(-0.896975\pi\) | ||
0.948077 | − | 0.318040i | \(-0.103025\pi\) | |||||||
\(384\) | 4045.69 | 0.537646 | ||||||||
\(385\) | 171.107 | − | 1871.93i | 0.0226505 | − | 0.247798i | ||||
\(386\) | 1553.50 | 0.204847 | ||||||||
\(387\) | − | 1073.71i | − | 0.141033i | ||||||
\(388\) | − | 3272.23i | − | 0.428150i | ||||||
\(389\) | 10533.7 | 1.37295 | 0.686476 | − | 0.727152i | \(-0.259157\pi\) | ||||
0.686476 | + | 0.727152i | \(0.259157\pi\) | |||||||
\(390\) | 253.169 | − | 2769.69i | 0.0328711 | − | 0.359612i | ||||
\(391\) | −237.032 | −0.0306579 | ||||||||
\(392\) | 2162.99i | 0.278693i | ||||||||
\(393\) | − | 6489.05i | − | 0.832898i | ||||||
\(394\) | 7548.46 | 0.965192 | ||||||||
\(395\) | −9980.38 | − | 912.277i | −1.27131 | − | 0.116207i | ||||
\(396\) | −594.707 | −0.0754675 | ||||||||
\(397\) | − | 3463.58i | − | 0.437865i | −0.975740 | − | 0.218932i | \(-0.929743\pi\) | ||
0.975740 | − | 0.218932i | \(-0.0702574\pi\) | |||||||
\(398\) | − | 7204.97i | − | 0.907418i | ||||||
\(399\) | 6739.28 | 0.845579 | ||||||||
\(400\) | 2476.13 | + | 456.485i | 0.309516 | + | 0.0570606i | ||||
\(401\) | −4337.43 | −0.540152 | −0.270076 | − | 0.962839i | \(-0.587049\pi\) | ||||
−0.270076 | + | 0.962839i | \(0.587049\pi\) | |||||||
\(402\) | − | 4462.11i | − | 0.553606i | ||||||
\(403\) | − | 14999.4i | − | 1.85403i | ||||||
\(404\) | −6755.08 | −0.831876 | ||||||||
\(405\) | −901.848 | − | 82.4353i | −0.110650 | − | 0.0101142i | ||||
\(406\) | 738.816 | 0.0903124 | ||||||||
\(407\) | 3554.21i | 0.432864i | ||||||||
\(408\) | 3269.32i | 0.396704i | ||||||||
\(409\) | −7287.09 | −0.880986 | −0.440493 | − | 0.897756i | \(-0.645196\pi\) | ||||
−0.440493 | + | 0.897756i | \(0.645196\pi\) | |||||||
\(410\) | −267.838 | + | 2930.16i | −0.0322623 | + | 0.352952i | ||||
\(411\) | 6525.61 | 0.783175 | ||||||||
\(412\) | 7662.26i | 0.916243i | ||||||||
\(413\) | − | 4020.93i | − | 0.479073i | ||||||
\(414\) | 54.6438 | 0.00648695 | ||||||||
\(415\) | 585.371 | − | 6404.01i | 0.0692404 | − | 0.757495i | ||||
\(416\) | −10962.1 | −1.29197 | ||||||||
\(417\) | 3841.30i | 0.451102i | ||||||||
\(418\) | 2282.31i | 0.267061i | ||||||||
\(419\) | −10603.5 | −1.23631 | −0.618156 | − | 0.786056i | \(-0.712120\pi\) | ||||
−0.618156 | + | 0.786056i | \(0.712120\pi\) | |||||||
\(420\) | −3066.80 | − | 280.327i | −0.356296 | − | 0.0325680i | ||||
\(421\) | 8344.14 | 0.965959 | 0.482979 | − | 0.875632i | \(-0.339555\pi\) | ||||
0.482979 | + | 0.875632i | \(0.339555\pi\) | |||||||
\(422\) | 2323.04i | 0.267971i | ||||||||
\(423\) | 4361.96i | 0.501385i | ||||||||
\(424\) | −887.553 | −0.101659 | ||||||||
\(425\) | −1248.97 | + | 6774.86i | −0.142551 | + | 0.773244i | ||||
\(426\) | 344.717 | 0.0392056 | ||||||||
\(427\) | 421.582i | 0.0477794i | ||||||||
\(428\) | − | 5683.61i | − | 0.641887i | ||||||
\(429\) | 1938.37 | 0.218148 | ||||||||
\(430\) | 1875.14 | + | 171.401i | 0.210296 | + | 0.0192225i | ||||
\(431\) | −1313.51 | −0.146797 | −0.0733987 | − | 0.997303i | \(-0.523385\pi\) | ||||
−0.0733987 | + | 0.997303i | \(0.523385\pi\) | |||||||
\(432\) | 543.856i | 0.0605701i | ||||||||
\(433\) | − | 11108.3i | − | 1.23287i | −0.787408 | − | 0.616433i | \(-0.788577\pi\) | ||
0.787408 | − | 0.616433i | \(-0.211423\pi\) | |||||||
\(434\) | 5509.83 | 0.609402 | ||||||||
\(435\) | 104.544 | − | 1143.72i | 0.0115230 | − | 0.126062i | ||||
\(436\) | −2836.59 | −0.311578 | ||||||||
\(437\) | 632.126i | 0.0691961i | ||||||||
\(438\) | − | 2640.69i | − | 0.288075i | ||||||
\(439\) | 5527.06 | 0.600894 | 0.300447 | − | 0.953799i | \(-0.402864\pi\) | ||||
0.300447 | + | 0.953799i | \(0.402864\pi\) | |||||||
\(440\) | 221.365 | − | 2421.75i | 0.0239844 | − | 0.262392i | ||||
\(441\) | −984.486 | −0.106304 | ||||||||
\(442\) | − | 4569.93i | − | 0.491786i | ||||||
\(443\) | 6792.28i | 0.728467i | 0.931308 | + | 0.364234i | \(0.118669\pi\) | ||||
−0.931308 | + | 0.364234i | \(0.881331\pi\) | |||||||
\(444\) | 5822.90 | 0.622393 | ||||||||
\(445\) | −11842.9 | − | 1082.53i | −1.26159 | − | 0.115318i | ||||
\(446\) | 3660.41 | 0.388622 | ||||||||
\(447\) | 1320.41i | 0.139716i | ||||||||
\(448\) | − | 1563.80i | − | 0.164917i | ||||||
\(449\) | −8575.87 | −0.901382 | −0.450691 | − | 0.892680i | \(-0.648822\pi\) | ||||
−0.450691 | + | 0.892680i | \(0.648822\pi\) | |||||||
\(450\) | 287.930 | − | 1561.83i | 0.0301626 | − | 0.163612i | ||||
\(451\) | −2050.68 | −0.214108 | ||||||||
\(452\) | − | 1115.57i | − | 0.116089i | ||||||
\(453\) | − | 6301.72i | − | 0.653599i | ||||||
\(454\) | 1293.52 | 0.133718 | ||||||||
\(455\) | 9995.85 | + | 913.691i | 1.02992 | + | 0.0941417i | ||||
\(456\) | 8718.73 | 0.895377 | ||||||||
\(457\) | − | 6527.74i | − | 0.668173i | −0.942542 | − | 0.334086i | \(-0.891572\pi\) | ||
0.942542 | − | 0.334086i | \(-0.108428\pi\) | |||||||
\(458\) | − | 6071.46i | − | 0.619434i | ||||||
\(459\) | −1488.03 | −0.151319 | ||||||||
\(460\) | 26.2939 | − | 287.658i | 0.00266513 | − | 0.0291568i | ||||
\(461\) | −3071.00 | −0.310262 | −0.155131 | − | 0.987894i | \(-0.549580\pi\) | ||||
−0.155131 | + | 0.987894i | \(0.549580\pi\) | |||||||
\(462\) | 712.034i | 0.0717031i | ||||||||
\(463\) | 18473.5i | 1.85429i | 0.374697 | + | 0.927147i | \(0.377747\pi\) | ||||
−0.374697 | + | 0.927147i | \(0.622253\pi\) | |||||||
\(464\) | −689.715 | −0.0690069 | ||||||||
\(465\) | 779.652 | − | 8529.45i | 0.0777537 | − | 0.850632i | ||||
\(466\) | −5923.72 | −0.588865 | ||||||||
\(467\) | − | 11967.1i | − | 1.18581i | −0.805273 | − | 0.592904i | \(-0.797981\pi\) | ||
0.805273 | − | 0.592904i | \(-0.202019\pi\) | |||||||
\(468\) | − | 3175.65i | − | 0.313664i | ||||||
\(469\) | 16103.8 | 1.58551 | ||||||||
\(470\) | −7617.74 | − | 696.316i | −0.747618 | − | 0.0683375i | ||||
\(471\) | −2066.42 | −0.202156 | ||||||||
\(472\) | − | 5201.96i | − | 0.507287i | ||||||
\(473\) | 1312.32i | 0.127570i | ||||||||
\(474\) | 3796.28 | 0.367867 | ||||||||
\(475\) | 18067.4 | + | 3330.81i | 1.74524 | + | 0.321743i | ||||
\(476\) | −5060.15 | −0.487251 | ||||||||
\(477\) | − | 403.970i | − | 0.0387768i | ||||||
\(478\) | 4447.34i | 0.425558i | ||||||||
\(479\) | 10463.1 | 0.998062 | 0.499031 | − | 0.866584i | \(-0.333689\pi\) | ||||
0.499031 | + | 0.866584i | \(0.333689\pi\) | |||||||
\(480\) | −6233.60 | − | 569.795i | −0.592758 | − | 0.0541823i | ||||
\(481\) | −18979.0 | −1.79910 | ||||||||
\(482\) | 6866.53i | 0.648883i | ||||||||
\(483\) | 197.210i | 0.0185784i | ||||||||
\(484\) | 726.864 | 0.0682629 | ||||||||
\(485\) | −554.375 | + | 6064.91i | −0.0519029 | + | 0.567821i | ||||
\(486\) | 343.040 | 0.0320177 | ||||||||
\(487\) | − | 10438.9i | − | 0.971317i | −0.874149 | − | 0.485658i | \(-0.838580\pi\) | ||
0.874149 | − | 0.485658i | \(-0.161420\pi\) | |||||||
\(488\) | 545.409i | 0.0505932i | ||||||||
\(489\) | 5401.61 | 0.499528 | ||||||||
\(490\) | 157.157 | − | 1719.31i | 0.0144890 | − | 0.158511i | ||||
\(491\) | −1842.23 | −0.169325 | −0.0846625 | − | 0.996410i | \(-0.526981\pi\) | ||||
−0.0846625 | + | 0.996410i | \(0.526981\pi\) | |||||||
\(492\) | 3359.65i | 0.307855i | ||||||||
\(493\) | − | 1887.11i | − | 0.172396i | ||||||
\(494\) | −12187.2 | −1.10998 | ||||||||
\(495\) | 1102.26 | + | 100.754i | 0.100087 | + | 0.00914861i | ||||
\(496\) | −5143.65 | −0.465639 | ||||||||
\(497\) | 1244.09i | 0.112284i | ||||||||
\(498\) | 2435.92i | 0.219189i | ||||||||
\(499\) | −20277.4 | −1.81912 | −0.909561 | − | 0.415570i | \(-0.863582\pi\) | ||||
−0.909561 | + | 0.415570i | \(0.863582\pi\) | |||||||
\(500\) | −8083.28 | − | 2267.26i | −0.722991 | − | 0.202790i | ||||
\(501\) | 10261.4 | 0.915057 | ||||||||
\(502\) | 7575.27i | 0.673507i | ||||||||
\(503\) | − | 15694.8i | − | 1.39125i | −0.718406 | − | 0.695624i | \(-0.755128\pi\) | ||
0.718406 | − | 0.695624i | \(-0.244872\pi\) | |||||||
\(504\) | 2720.06 | 0.240399 | ||||||||
\(505\) | 12520.2 | + | 1144.43i | 1.10325 | + | 0.100845i | ||||
\(506\) | −66.7869 | −0.00586767 | ||||||||
\(507\) | 3759.65i | 0.329333i | ||||||||
\(508\) | − | 11209.7i | − | 0.979033i | ||||||
\(509\) | −13383.0 | −1.16541 | −0.582704 | − | 0.812684i | \(-0.698005\pi\) | ||||
−0.582704 | + | 0.812684i | \(0.698005\pi\) | |||||||
\(510\) | 237.539 | − | 2598.70i | 0.0206243 | − | 0.225632i | ||||
\(511\) | 9530.27 | 0.825038 | ||||||||
\(512\) | 6945.54i | 0.599516i | ||||||||
\(513\) | 3968.33i | 0.341532i | ||||||||
\(514\) | 573.839 | 0.0492431 | ||||||||
\(515\) | 1298.13 | − | 14201.6i | 0.111072 | − | 1.21514i | ||||
\(516\) | 2149.98 | 0.183426 | ||||||||
\(517\) | − | 5331.29i | − | 0.453520i | ||||||
\(518\) | − | 6971.68i | − | 0.591347i | ||||||
\(519\) | −6979.52 | −0.590302 | ||||||||
\(520\) | 12931.8 | + | 1182.06i | 1.09057 | + | 0.0996860i | ||||
\(521\) | −12346.1 | −1.03818 | −0.519089 | − | 0.854720i | \(-0.673729\pi\) | ||||
−0.519089 | + | 0.854720i | \(0.673729\pi\) | |||||||
\(522\) | 435.041i | 0.0364775i | ||||||||
\(523\) | − | 9814.80i | − | 0.820595i | −0.911952 | − | 0.410298i | \(-0.865425\pi\) | ||
0.911952 | − | 0.410298i | \(-0.134575\pi\) | |||||||
\(524\) | 12993.5 | 1.08325 | ||||||||
\(525\) | 5636.66 | + | 1039.14i | 0.468579 | + | 0.0863847i | ||||
\(526\) | −11307.2 | −0.937294 | ||||||||
\(527\) | − | 14073.4i | − | 1.16328i | ||||||
\(528\) | − | 664.713i | − | 0.0547877i | ||||||
\(529\) | 12148.5 | 0.998480 | ||||||||
\(530\) | 705.494 | + | 64.4871i | 0.0578202 | + | 0.00528517i | ||||
\(531\) | 2367.67 | 0.193499 | ||||||||
\(532\) | 13494.6i | 1.09975i | ||||||||
\(533\) | − | 10950.4i | − | 0.889892i | ||||||
\(534\) | 4504.75 | 0.365056 | ||||||||
\(535\) | −962.907 | + | 10534.3i | −0.0778133 | + | 0.851283i | ||||
\(536\) | 20833.8 | 1.67889 | ||||||||
\(537\) | − | 12217.6i | − | 0.981803i | ||||||
\(538\) | 6723.48i | 0.538791i | ||||||||
\(539\) | 1203.26 | 0.0961560 | ||||||||
\(540\) | 165.067 | − | 1805.84i | 0.0131543 | − | 0.143909i | ||||
\(541\) | 6943.74 | 0.551820 | 0.275910 | − | 0.961183i | \(-0.411021\pi\) | ||||
0.275910 | + | 0.961183i | \(0.411021\pi\) | |||||||
\(542\) | − | 6288.85i | − | 0.498393i | ||||||
\(543\) | − | 1307.05i | − | 0.103298i | ||||||
\(544\) | −10285.3 | −0.810623 | ||||||||
\(545\) | 5257.47 | + | 480.570i | 0.413220 | + | 0.0377713i | ||||
\(546\) | −3802.17 | −0.298018 | ||||||||
\(547\) | 5191.82i | 0.405825i | 0.979197 | + | 0.202913i | \(0.0650407\pi\) | ||||
−0.979197 | + | 0.202913i | \(0.934959\pi\) | |||||||
\(548\) | 13066.8i | 1.01858i | ||||||||
\(549\) | −248.243 | −0.0192983 | ||||||||
\(550\) | −351.915 | + | 1908.90i | −0.0272831 | + | 0.147993i | ||||
\(551\) | −5032.61 | −0.389104 | ||||||||
\(552\) | 255.135i | 0.0196726i | ||||||||
\(553\) | 13700.8i | 1.05356i | ||||||||
\(554\) | 2950.43 | 0.226266 | ||||||||
\(555\) | −10792.4 | − | 986.506i | −0.825430 | − | 0.0754502i | ||||
\(556\) | −7691.75 | −0.586696 | ||||||||
\(557\) | − | 2193.76i | − | 0.166881i | −0.996513 | − | 0.0834404i | \(-0.973409\pi\) | ||
0.996513 | − | 0.0834404i | \(-0.0265908\pi\) | |||||||
\(558\) | 3244.39i | 0.246140i | ||||||||
\(559\) | −7007.60 | −0.530214 | ||||||||
\(560\) | 313.326 | − | 3427.81i | 0.0236436 | − | 0.258663i | ||||
\(561\) | 1818.70 | 0.136873 | ||||||||
\(562\) | 4604.87i | 0.345631i | ||||||||
\(563\) | 15858.0i | 1.18709i | 0.804799 | + | 0.593547i | \(0.202273\pi\) | ||||
−0.804799 | + | 0.593547i | \(0.797727\pi\) | |||||||
\(564\) | −8734.31 | −0.652093 | ||||||||
\(565\) | −188.998 | + | 2067.65i | −0.0140729 | + | 0.153959i | ||||
\(566\) | 7653.11 | 0.568346 | ||||||||
\(567\) | 1238.04i | 0.0916977i | ||||||||
\(568\) | 1609.50i | 0.118896i | ||||||||
\(569\) | −1176.17 | −0.0866569 | −0.0433285 | − | 0.999061i | \(-0.513796\pi\) | ||||
−0.0433285 | + | 0.999061i | \(0.513796\pi\) | |||||||
\(570\) | −6930.30 | − | 633.478i | −0.509260 | − | 0.0465500i | ||||
\(571\) | 7715.30 | 0.565456 | 0.282728 | − | 0.959200i | \(-0.408761\pi\) | ||||
0.282728 | + | 0.959200i | \(0.408761\pi\) | |||||||
\(572\) | 3881.36i | 0.283720i | ||||||||
\(573\) | − | 9362.25i | − | 0.682572i | ||||||
\(574\) | 4022.46 | 0.292499 | ||||||||
\(575\) | −97.4689 | + | 528.704i | −0.00706911 | + | 0.0383452i | ||||
\(576\) | 920.823 | 0.0666105 | ||||||||
\(577\) | − | 22948.6i | − | 1.65574i | −0.560922 | − | 0.827869i | \(-0.689553\pi\) | ||
0.560922 | − | 0.827869i | \(-0.310447\pi\) | |||||||
\(578\) | 2647.83i | 0.190545i | ||||||||
\(579\) | −3301.36 | −0.236960 | ||||||||
\(580\) | 2290.16 | + | 209.337i | 0.163954 | + | 0.0149866i | ||||
\(581\) | −8791.27 | −0.627751 | ||||||||
\(582\) | − | 2306.94i | − | 0.164305i | ||||||
\(583\) | 493.741i | 0.0350749i | ||||||||
\(584\) | 12329.5 | 0.873626 | ||||||||
\(585\) | −538.014 | + | 5885.91i | −0.0380242 | + | 0.415987i | ||||
\(586\) | 10423.0 | 0.734761 | ||||||||
\(587\) | − | 23977.7i | − | 1.68597i | −0.537938 | − | 0.842985i | \(-0.680796\pi\) | ||
0.537938 | − | 0.842985i | \(-0.319204\pi\) | |||||||
\(588\) | − | 1971.31i | − | 0.138258i | ||||||
\(589\) | −37531.5 | −2.62556 | ||||||||
\(590\) | −377.960 | + | 4134.91i | −0.0263735 | + | 0.288528i | ||||
\(591\) | −16041.4 | −1.11650 | ||||||||
\(592\) | 6508.35i | 0.451844i | ||||||||
\(593\) | 23207.4i | 1.60711i | 0.595232 | + | 0.803554i | \(0.297060\pi\) | ||||
−0.595232 | + | 0.803554i | \(0.702940\pi\) | |||||||
\(594\) | −419.271 | −0.0289611 | ||||||||
\(595\) | 9378.73 | + | 857.282i | 0.646202 | + | 0.0590675i | ||||
\(596\) | −2643.96 | −0.181713 | ||||||||
\(597\) | 15311.4i | 1.04967i | ||||||||
\(598\) | − | 356.633i | − | 0.0243877i | ||||||
\(599\) | 1989.79 | 0.135727 | 0.0678636 | − | 0.997695i | \(-0.478382\pi\) | ||||
0.0678636 | + | 0.997695i | \(0.478382\pi\) | |||||||
\(600\) | 7292.25 | + | 1344.36i | 0.496175 | + | 0.0914721i | ||||
\(601\) | 17469.3 | 1.18567 | 0.592834 | − | 0.805325i | \(-0.298009\pi\) | ||||
0.592834 | + | 0.805325i | \(0.298009\pi\) | |||||||
\(602\) | − | 2574.14i | − | 0.174276i | ||||||
\(603\) | 9482.50i | 0.640393i | ||||||||
\(604\) | 12618.4 | 0.850060 | ||||||||
\(605\) | −1347.20 | − | 123.144i | −0.0905317 | − | 0.00827523i | ||||
\(606\) | −4762.37 | −0.319237 | ||||||||
\(607\) | 939.720i | 0.0628370i | 0.999506 | + | 0.0314185i | \(0.0100025\pi\) | ||||
−0.999506 | + | 0.0314185i | \(0.989998\pi\) | |||||||
\(608\) | 27429.2i | 1.82961i | ||||||||
\(609\) | −1570.07 | −0.104470 | ||||||||
\(610\) | 39.6279 | − | 433.532i | 0.00263030 | − | 0.0287757i | ||||
\(611\) | 28468.4 | 1.88495 | ||||||||
\(612\) | − | 2979.60i | − | 0.196802i | ||||||
\(613\) | 12099.9i | 0.797247i | 0.917115 | + | 0.398623i | \(0.130512\pi\) | ||||
−0.917115 | + | 0.398623i | \(0.869488\pi\) | |||||||
\(614\) | 560.709 | 0.0368540 | ||||||||
\(615\) | 569.186 | − | 6226.94i | 0.0373200 | − | 0.408283i | ||||
\(616\) | −3324.52 | −0.217449 | ||||||||
\(617\) | − | 5849.45i | − | 0.381670i | −0.981622 | − | 0.190835i | \(-0.938881\pi\) | ||
0.981622 | − | 0.190835i | \(-0.0611195\pi\) | |||||||
\(618\) | 5401.93i | 0.351614i | ||||||||
\(619\) | −7870.96 | −0.511083 | −0.255542 | − | 0.966798i | \(-0.582254\pi\) | ||||
−0.255542 | + | 0.966798i | \(0.582254\pi\) | |||||||
\(620\) | 17079.2 | + | 1561.16i | 1.10632 | + | 0.101125i | ||||
\(621\) | −116.125 | −0.00750389 | ||||||||
\(622\) | − | 231.326i | − | 0.0149121i | ||||||
\(623\) | 16257.7i | 1.04551i | ||||||||
\(624\) | 3549.48 | 0.227713 | ||||||||
\(625\) | 14597.8 | + | 5571.71i | 0.934261 | + | 0.356590i | ||||
\(626\) | −3527.07 | −0.225192 | ||||||||
\(627\) | − | 4850.18i | − | 0.308927i | ||||||
\(628\) | − | 4137.76i | − | 0.262921i | ||||||
\(629\) | −17807.3 | −1.12881 | ||||||||
\(630\) | −2162.11 | − | 197.632i | −0.136731 | − | 0.0124982i | ||||
\(631\) | −7754.68 | −0.489238 | −0.244619 | − | 0.969619i | \(-0.578663\pi\) | ||||
−0.244619 | + | 0.969619i | \(0.578663\pi\) | |||||||
\(632\) | 17725.0i | 1.11561i | ||||||||
\(633\) | − | 4936.73i | − | 0.309980i | ||||||
\(634\) | 580.772 | 0.0363808 | ||||||||
\(635\) | −1899.12 | + | 20776.6i | −0.118684 | + | 1.29841i | ||||
\(636\) | 808.901 | 0.0504324 | ||||||||
\(637\) | 6425.25i | 0.399651i | ||||||||
\(638\) | − | 531.717i | − | 0.0329951i | ||||||
\(639\) | −732.564 | −0.0453517 | ||||||||
\(640\) | 1372.46 | − | 15014.8i | 0.0847676 | − | 0.927364i | ||||
\(641\) | −6179.14 | −0.380751 | −0.190376 | − | 0.981711i | \(-0.560971\pi\) | ||||
−0.190376 | + | 0.981711i | \(0.560971\pi\) | |||||||
\(642\) | − | 4006.97i | − | 0.246328i | ||||||
\(643\) | − | 5816.66i | − | 0.356745i | −0.983963 | − | 0.178372i | \(-0.942917\pi\) | ||
0.983963 | − | 0.178372i | \(-0.0570832\pi\) | |||||||
\(644\) | −394.890 | −0.0241628 | ||||||||
\(645\) | −3984.88 | − | 364.246i | −0.243263 | − | 0.0222359i | ||||
\(646\) | −11434.8 | −0.696436 | ||||||||
\(647\) | 451.104i | 0.0274107i | 0.999906 | + | 0.0137053i | \(0.00436268\pi\) | ||||
−0.999906 | + | 0.0137053i | \(0.995637\pi\) | |||||||
\(648\) | 1601.67i | 0.0970981i | ||||||||
\(649\) | −2893.82 | −0.175027 | ||||||||
\(650\) | −10193.3 | − | 1879.18i | −0.615098 | − | 0.113396i | ||||
\(651\) | −11709.0 | −0.704936 | ||||||||
\(652\) | 10816.1i | 0.649678i | ||||||||
\(653\) | − | 17071.3i | − | 1.02305i | −0.859269 | − | 0.511525i | \(-0.829081\pi\) | ||
0.859269 | − | 0.511525i | \(-0.170919\pi\) | |||||||
\(654\) | −1999.81 | −0.119570 | ||||||||
\(655\) | −24082.8 | − | 2201.34i | −1.43663 | − | 0.131318i | ||||
\(656\) | −3755.13 | −0.223496 | ||||||||
\(657\) | 5611.76i | 0.333236i | ||||||||
\(658\) | 10457.5i | 0.619566i | ||||||||
\(659\) | 24970.1 | 1.47602 | 0.738011 | − | 0.674789i | \(-0.235765\pi\) | ||||
0.738011 | + | 0.674789i | \(0.235765\pi\) | |||||||
\(660\) | −201.748 | + | 2207.14i | −0.0118985 | + | 0.130171i | ||||
\(661\) | −13170.6 | −0.775006 | −0.387503 | − | 0.921869i | \(-0.626662\pi\) | ||||
−0.387503 | + | 0.921869i | \(0.626662\pi\) | |||||||
\(662\) | − | 3221.59i | − | 0.189140i | ||||||
\(663\) | 9711.63i | 0.568881i | ||||||||
\(664\) | −11373.4 | −0.664721 | ||||||||
\(665\) | 2286.23 | − | 25011.5i | 0.133318 | − | 1.45850i | ||||
\(666\) | 4105.17 | 0.238847 | ||||||||
\(667\) | − | 147.268i | − | 0.00854911i | ||||||
\(668\) | 20547.1i | 1.19011i | ||||||||
\(669\) | −7778.80 | −0.449545 | ||||||||
\(670\) | −16560.3 | − | 1513.72i | −0.954893 | − | 0.0872840i | ||||
\(671\) | 303.408 | 0.0174559 | ||||||||
\(672\) | 8557.35i | 0.491231i | ||||||||
\(673\) | − | 15152.7i | − | 0.867893i | −0.900939 | − | 0.433947i | \(-0.857121\pi\) | ||
0.900939 | − | 0.433947i | \(-0.142879\pi\) | |||||||
\(674\) | 3460.46 | 0.197763 | ||||||||
\(675\) | −611.885 | + | 3319.07i | −0.0348911 | + | 0.189261i | ||||
\(676\) | −7528.24 | −0.428325 | ||||||||
\(677\) | 13795.6i | 0.783173i | 0.920141 | + | 0.391587i | \(0.128074\pi\) | ||||
−0.920141 | + | 0.391587i | \(0.871926\pi\) | |||||||
\(678\) | − | 786.483i | − | 0.0445497i | ||||||
\(679\) | 8325.77 | 0.470565 | ||||||||
\(680\) | 12133.4 | + | 1109.08i | 0.684259 | + | 0.0625461i | ||||
\(681\) | −2748.89 | −0.154681 | ||||||||
\(682\) | − | 3965.36i | − | 0.222642i | ||||||
\(683\) | 12455.4i | 0.697791i | 0.937162 | + | 0.348896i | \(0.113443\pi\) | ||||
−0.937162 | + | 0.348896i | \(0.886557\pi\) | |||||||
\(684\) | −7946.10 | −0.444191 | ||||||||
\(685\) | 2213.75 | − | 24218.6i | 0.123479 | − | 1.35087i | ||||
\(686\) | −9761.07 | −0.543264 | ||||||||
\(687\) | 12902.6i | 0.716540i | ||||||||
\(688\) | 2403.07i | 0.133163i | ||||||||
\(689\) | −2636.51 | −0.145781 | ||||||||
\(690\) | 18.5374 | − | 202.800i | 0.00102276 | − | 0.0111891i | ||||
\(691\) | 17389.1 | 0.957327 | 0.478664 | − | 0.877998i | \(-0.341121\pi\) | ||||
0.478664 | + | 0.877998i | \(0.341121\pi\) | |||||||
\(692\) | − | 13975.6i | − | 0.767737i | ||||||
\(693\) | − | 1513.15i | − | 0.0829437i | ||||||
\(694\) | −5577.33 | −0.305061 | ||||||||
\(695\) | 14256.3 | + | 1303.12i | 0.778087 | + | 0.0711227i | ||||
\(696\) | −2031.23 | −0.110623 | ||||||||
\(697\) | − | 10274.3i | − | 0.558346i | ||||||
\(698\) | − | 11634.8i | − | 0.630922i | ||||||
\(699\) | 12588.6 | 0.681179 | ||||||||
\(700\) | −2080.76 | + | 11286.7i | −0.112350 | + | 0.609427i | ||||
\(701\) | 30534.7 | 1.64519 | 0.822596 | − | 0.568626i | \(-0.192525\pi\) | ||||
0.822596 | + | 0.568626i | \(0.192525\pi\) | |||||||
\(702\) | − | 2238.85i | − | 0.120370i | ||||||
\(703\) | 47489.1i | 2.54778i | ||||||||
\(704\) | −1125.45 | −0.0602514 | ||||||||
\(705\) | 16188.6 | + | 1479.75i | 0.864819 | + | 0.0790506i | ||||
\(706\) | 6892.69 | 0.367436 | ||||||||
\(707\) | − | 17187.4i | − | 0.914286i | ||||||
\(708\) | 4740.97i | 0.251662i | ||||||||
\(709\) | 17762.5 | 0.940880 | 0.470440 | − | 0.882432i | \(-0.344095\pi\) | ||||
0.470440 | + | 0.882432i | \(0.344095\pi\) | |||||||
\(710\) | 116.942 | − | 1279.35i | 0.00618133 | − | 0.0676242i | ||||
\(711\) | −8067.54 | −0.425537 | ||||||||
\(712\) | 21032.9i | 1.10708i | ||||||||
\(713\) | − | 1098.28i | − | 0.0576869i | ||||||
\(714\) | −3567.43 | −0.186986 | ||||||||
\(715\) | 657.573 | − | 7193.89i | 0.0343942 | − | 0.376275i | ||||
\(716\) | 24464.3 | 1.27692 | ||||||||
\(717\) | − | 9451.12i | − | 0.492271i | ||||||
\(718\) | − | 328.033i | − | 0.0170502i | ||||||
\(719\) | 30661.9 | 1.59040 | 0.795200 | − | 0.606347i | \(-0.207366\pi\) | ||||
0.795200 | + | 0.606347i | \(0.207366\pi\) | |||||||
\(720\) | 2018.42 | + | 184.498i | 0.104475 | + | 0.00954975i | ||||
\(721\) | −19495.6 | −1.00701 | ||||||||
\(722\) | 20812.1i | 1.07278i | ||||||||
\(723\) | − | 14592.2i | − | 0.750607i | ||||||
\(724\) | 2617.21 | 0.134348 | ||||||||
\(725\) | −4209.22 | − | 775.989i | −0.215623 | − | 0.0397510i | ||||
\(726\) | 512.443 | 0.0261963 | ||||||||
\(727\) | − | 9028.13i | − | 0.460570i | −0.973123 | − | 0.230285i | \(-0.926034\pi\) | ||
0.973123 | − | 0.230285i | \(-0.0739659\pi\) | |||||||
\(728\) | − | 17752.5i | − | 0.903779i | ||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | −9800.40 | − | 895.826i | −0.496889 | − | 0.0454192i | ||||
\(731\) | −6574.97 | −0.332673 | ||||||||
\(732\) | − | 497.076i | − | 0.0250990i | ||||||
\(733\) | − | 5574.59i | − | 0.280904i | −0.990088 | − | 0.140452i | \(-0.955145\pi\) | ||
0.990088 | − | 0.140452i | \(-0.0448555\pi\) | |||||||
\(734\) | −15462.2 | −0.777548 | ||||||||
\(735\) | −333.977 | + | 3653.73i | −0.0167604 | + | 0.183360i | ||||
\(736\) | −802.657 | −0.0401988 | ||||||||
\(737\) | − | 11589.7i | − | 0.579258i | ||||||
\(738\) | 2368.57i | 0.118141i | ||||||||
\(739\) | 17032.3 | 0.847826 | 0.423913 | − | 0.905703i | \(-0.360656\pi\) | ||||
0.423913 | + | 0.905703i | \(0.360656\pi\) | |||||||
\(740\) | 1975.36 | − | 21610.6i | 0.0981292 | − | 1.07354i | ||||
\(741\) | 25899.3 | 1.28399 | ||||||||
\(742\) | − | 968.486i | − | 0.0479168i | ||||||
\(743\) | 20888.9i | 1.03141i | 0.856765 | + | 0.515707i | \(0.172471\pi\) | ||||
−0.856765 | + | 0.515707i | \(0.827529\pi\) | |||||||
\(744\) | −15148.2 | −0.746451 | ||||||||
\(745\) | 4900.44 | + | 447.935i | 0.240991 | + | 0.0220283i | ||||
\(746\) | 7292.47 | 0.357904 | ||||||||
\(747\) | − | 5176.62i | − | 0.253551i | ||||||
\(748\) | 3641.73i | 0.178015i | ||||||||
\(749\) | 14461.2 | 0.705475 | ||||||||
\(750\) | −5698.75 | − | 1598.43i | −0.277452 | − | 0.0778220i | ||||
\(751\) | −15666.1 | −0.761205 | −0.380602 | − | 0.924739i | \(-0.624283\pi\) | ||||
−0.380602 | + | 0.924739i | \(0.624283\pi\) | |||||||
\(752\) | − | 9762.47i | − | 0.473405i | ||||||
\(753\) | − | 16098.3i | − | 0.779091i | ||||||
\(754\) | 2839.30 | 0.137137 | ||||||||
\(755\) | −23387.6 | − | 2137.79i | −1.12737 | − | 0.103049i | ||||
\(756\) | −2479.02 | −0.119261 | ||||||||
\(757\) | − | 22613.4i | − | 1.08573i | −0.839820 | − | 0.542865i | \(-0.817340\pi\) | ||
0.839820 | − | 0.542865i | \(-0.182660\pi\) | |||||||
\(758\) | − | 8577.56i | − | 0.411017i | ||||||
\(759\) | 141.930 | 0.00678752 | ||||||||
\(760\) | 2957.74 | − | 32357.9i | 0.141169 | − | 1.54440i | ||||
\(761\) | −11761.9 | −0.560272 | −0.280136 | − | 0.959960i | \(-0.590380\pi\) | ||||
−0.280136 | + | 0.959960i | \(0.590380\pi\) | |||||||
\(762\) | − | 7902.87i | − | 0.375710i | ||||||
\(763\) | − | 7217.33i | − | 0.342444i | ||||||
\(764\) | 18746.8 | 0.887742 | ||||||||
\(765\) | −504.798 | + | 5522.53i | −0.0238576 | + | 0.261003i | ||||
\(766\) | 6730.52 | 0.317472 | ||||||||
\(767\) | − | 15452.6i | − | 0.727459i | ||||||
\(768\) | 8166.78i | 0.383715i | ||||||||
\(769\) | −644.074 | −0.0302027 | −0.0151014 | − | 0.999886i | \(-0.504807\pi\) | ||||
−0.0151014 | + | 0.999886i | \(0.504807\pi\) | |||||||
\(770\) | 2642.58 | + | 241.550i | 0.123678 | + | 0.0113050i | ||||
\(771\) | −1219.47 | −0.0569628 | ||||||||
\(772\) | − | 6610.58i | − | 0.308186i | ||||||
\(773\) | 40800.8i | 1.89845i | 0.314598 | + | 0.949225i | \(0.398130\pi\) | ||||
−0.314598 | + | 0.949225i | \(0.601870\pi\) | |||||||
\(774\) | 1515.75 | 0.0703908 | ||||||||
\(775\) | −31390.9 | − | 5787.06i | −1.45496 | − | 0.268229i | ||||
\(776\) | 10771.2 | 0.498278 | ||||||||
\(777\) | 14815.6i | 0.684051i | ||||||||
\(778\) | 14870.3i | 0.685250i | ||||||||
\(779\) | −27399.9 | −1.26021 | ||||||||
\(780\) | −11785.8 | − | 1077.31i | −0.541026 | − | 0.0494536i | ||||
\(781\) | 895.356 | 0.0410222 | ||||||||
\(782\) | − | 334.616i | − | 0.0153016i | ||||||
\(783\) | − | 924.513i | − | 0.0421959i | ||||||
\(784\) | 2203.37 | 0.100372 | ||||||||
\(785\) | −701.012 | + | 7669.13i | −0.0318729 | + | 0.348692i | ||||
\(786\) | 9160.51 | 0.415705 | ||||||||
\(787\) | 20784.5i | 0.941407i | 0.882292 | + | 0.470703i | \(0.156000\pi\) | ||||
−0.882292 | + | 0.470703i | \(0.844000\pi\) | |||||||
\(788\) | − | 32120.9i | − | 1.45210i | ||||||
\(789\) | 24029.1 | 1.08423 | ||||||||
\(790\) | 1287.85 | − | 14089.2i | 0.0579996 | − | 0.634520i | ||||
\(791\) | 2838.43 | 0.127589 | ||||||||
\(792\) | − | 1957.60i | − | 0.0878285i | ||||||
\(793\) | 1620.16i | 0.0725517i | ||||||||
\(794\) | 4889.50 | 0.218541 | ||||||||
\(795\) | −1499.26 | − | 137.043i | −0.0668845 | − | 0.00611371i | ||||
\(796\) | −30659.2 | −1.36518 | ||||||||
\(797\) | − | 36547.2i | − | 1.62430i | −0.583446 | − | 0.812152i | \(-0.698296\pi\) | ||
0.583446 | − | 0.812152i | \(-0.301704\pi\) | |||||||
\(798\) | 9513.75i | 0.422034i | ||||||||
\(799\) | 26710.8 | 1.18268 | ||||||||
\(800\) | −4229.37 | + | 22941.5i | −0.186914 | + | 1.01388i | ||||
\(801\) | −9573.12 | −0.422284 | ||||||||
\(802\) | − | 6123.10i | − | 0.269594i | ||||||
\(803\) | − | 6858.82i | − | 0.301423i | ||||||
\(804\) | −18987.6 | −0.832885 | ||||||||
\(805\) | 731.908 | + | 66.9016i | 0.0320452 | + | 0.00292916i | ||||
\(806\) | 21174.5 | 0.925360 | ||||||||
\(807\) | − | 14288.2i | − | 0.623256i | ||||||
\(808\) | − | 22235.7i | − | 0.968130i | ||||||
\(809\) | −6326.13 | −0.274926 | −0.137463 | − | 0.990507i | \(-0.543895\pi\) | ||||
−0.137463 | + | 0.990507i | \(0.543895\pi\) | |||||||
\(810\) | 116.373 | − | 1273.13i | 0.00504805 | − | 0.0552261i | ||||
\(811\) | 24501.7 | 1.06088 | 0.530438 | − | 0.847724i | \(-0.322028\pi\) | ||||
0.530438 | + | 0.847724i | \(0.322028\pi\) | |||||||
\(812\) | − | 3143.87i | − | 0.135872i | ||||||
\(813\) | 13364.5i | 0.576525i | ||||||||
\(814\) | −5017.44 | −0.216045 | ||||||||
\(815\) | 1832.44 | − | 20047.0i | 0.0787577 | − | 0.861615i | ||||
\(816\) | 3330.34 | 0.142874 | ||||||||
\(817\) | 17534.4i | 0.750856i | ||||||||
\(818\) | − | 10287.1i | − | 0.439706i | ||||||
\(819\) | 8080.05 | 0.344737 | ||||||||
\(820\) | 12468.7 | + | 1139.73i | 0.531007 | + | 0.0485378i | ||||
\(821\) | −38165.9 | −1.62241 | −0.811204 | − | 0.584763i | \(-0.801188\pi\) | ||||
−0.811204 | + | 0.584763i | \(0.801188\pi\) | |||||||
\(822\) | 9212.13i | 0.390888i | ||||||||
\(823\) | − | 20194.9i | − | 0.855344i | −0.903934 | − | 0.427672i | \(-0.859334\pi\) | ||
0.903934 | − | 0.427672i | \(-0.140666\pi\) | |||||||
\(824\) | −25221.9 | −1.06632 | ||||||||
\(825\) | 747.860 | − | 4056.64i | 0.0315602 | − | 0.171193i | ||||
\(826\) | 5676.30 | 0.239109 | ||||||||
\(827\) | 12875.4i | 0.541380i | 0.962667 | + | 0.270690i | \(0.0872518\pi\) | ||||
−0.962667 | + | 0.270690i | \(0.912748\pi\) | |||||||
\(828\) | − | 232.525i | − | 0.00975944i | ||||||
\(829\) | −35670.2 | −1.49442 | −0.747212 | − | 0.664586i | \(-0.768608\pi\) | ||||
−0.747212 | + | 0.664586i | \(0.768608\pi\) | |||||||
\(830\) | 9040.46 | + | 826.362i | 0.378071 | + | 0.0345583i | ||||
\(831\) | −6270.00 | −0.261737 | ||||||||
\(832\) | − | 6009.75i | − | 0.250422i | ||||||
\(833\) | 6028.57i | 0.250753i | ||||||||
\(834\) | −5422.72 | −0.225148 | ||||||||
\(835\) | 3481.06 | − | 38083.1i | 0.144272 | − | 1.57835i | ||||
\(836\) | 9711.90 | 0.401786 | ||||||||
\(837\) | − | 6894.70i | − | 0.284726i | ||||||
\(838\) | − | 14968.8i | − | 0.617051i | ||||||
\(839\) | −9.05023 | −0.000372406 | −0.000186203 | − | 1.00000i | \(-0.500059\pi\) | ||||
−0.000186203 | 1.00000i | \(0.500059\pi\) | ||||||||
\(840\) | 922.753 | − | 10095.0i | 0.0379024 | − | 0.414655i | ||||
\(841\) | −23216.5 | −0.951927 | ||||||||
\(842\) | 11779.3i | 0.482117i | ||||||||
\(843\) | − | 9785.89i | − | 0.399815i | ||||||
\(844\) | 9885.22 | 0.403155 | ||||||||
\(845\) | 13953.2 | + | 1275.42i | 0.568053 | + | 0.0519241i | ||||
\(846\) | −6157.73 | −0.250245 | ||||||||
\(847\) | 1849.41i | 0.0750254i | ||||||||
\(848\) | 904.121i | 0.0366128i | ||||||||
\(849\) | −16263.7 | −0.657444 | ||||||||
\(850\) | −9563.98 | − | 1763.16i | −0.385932 | − | 0.0711482i | ||||
\(851\) | −1389.67 | −0.0559779 | ||||||||
\(852\) | − | 1466.87i | − | 0.0589837i | ||||||
\(853\) | 42635.9i | 1.71140i | 0.517472 | + | 0.855700i | \(0.326873\pi\) | ||||
−0.517472 | + | 0.855700i | \(0.673127\pi\) | |||||||
\(854\) | −595.143 | −0.0238470 | ||||||||
\(855\) | 14727.7 | + | 1346.21i | 0.589095 | + | 0.0538474i | ||||
\(856\) | 18708.7 | 0.747023 | ||||||||
\(857\) | 28082.3i | 1.11934i | 0.828716 | + | 0.559669i | \(0.189072\pi\) | ||||
−0.828716 | + | 0.559669i | \(0.810928\pi\) | |||||||
\(858\) | 2736.38i | 0.108879i | ||||||||
\(859\) | −20954.6 | −0.832320 | −0.416160 | − | 0.909291i | \(-0.636624\pi\) | ||||
−0.416160 | + | 0.909291i | \(0.636624\pi\) | |||||||
\(860\) | 729.359 | − | 7979.25i | 0.0289197 | − | 0.316384i | ||||
\(861\) | −8548.20 | −0.338353 | ||||||||
\(862\) | − | 1854.27i | − | 0.0732676i | ||||||
\(863\) | 36811.3i | 1.45199i | 0.687698 | + | 0.725997i | \(0.258621\pi\) | ||||
−0.687698 | + | 0.725997i | \(0.741379\pi\) | |||||||
\(864\) | −5038.87 | −0.198410 | ||||||||
\(865\) | −2367.73 | + | 25903.1i | −0.0930696 | + | 1.01819i | ||||
\(866\) | 15681.4 | 0.615332 | ||||||||
\(867\) | − | 5626.94i | − | 0.220416i | ||||||
\(868\) | − | 23445.9i | − | 0.916828i | ||||||
\(869\) | 9860.33 | 0.384912 | ||||||||
\(870\) | 1614.57 | + | 147.583i | 0.0629185 | + | 0.00575120i | ||||
\(871\) | 61887.6 | 2.40755 | ||||||||
\(872\) | − | 9337.19i | − | 0.362611i | ||||||
\(873\) | 4902.51i | 0.190063i | ||||||||
\(874\) | −892.365 | −0.0345363 | ||||||||
\(875\) | 5768.76 | − | 20566.9i | 0.222880 | − | 0.794614i | ||||
\(876\) | −11236.9 | −0.433401 | ||||||||
\(877\) | 253.241i | 0.00975069i | 0.999988 | + | 0.00487534i | \(0.00155188\pi\) | ||||
−0.999988 | + | 0.00487534i | \(0.998448\pi\) | |||||||
\(878\) | 7802.48i | 0.299910i | ||||||||
\(879\) | −22150.1 | −0.849947 | ||||||||
\(880\) | −2466.95 | − | 225.497i | −0.0945011 | − | 0.00863807i | ||||
\(881\) | −13595.0 | −0.519896 | −0.259948 | − | 0.965623i | \(-0.583705\pi\) | ||||
−0.259948 | + | 0.965623i | \(0.583705\pi\) | |||||||
\(882\) | − | 1389.79i | − | 0.0530573i | ||||||
\(883\) | 41418.2i | 1.57852i | 0.614059 | + | 0.789260i | \(0.289536\pi\) | ||||
−0.614059 | + | 0.789260i | \(0.710464\pi\) | |||||||
\(884\) | −19446.4 | −0.739878 | ||||||||
\(885\) | 803.208 | − | 8787.15i | 0.0305080 | − | 0.333759i | ||||
\(886\) | −9588.58 | −0.363583 | ||||||||
\(887\) | 19752.3i | 0.747708i | 0.927488 | + | 0.373854i | \(0.121964\pi\) | ||||
−0.927488 | + | 0.373854i | \(0.878036\pi\) | |||||||
\(888\) | 19167.2i | 0.724336i | ||||||||
\(889\) | 28521.6 | 1.07602 | ||||||||
\(890\) | 1528.19 | − | 16718.5i | 0.0575563 | − | 0.629670i | ||||
\(891\) | 891.000 | 0.0335013 | ||||||||
\(892\) | − | 15576.1i | − | 0.584671i | ||||||
\(893\) | − | 71233.4i | − | 2.66935i | ||||||
\(894\) | −1864.00 | −0.0697333 | ||||||||
\(895\) | −45343.3 | − | 4144.69i | −1.69347 | − | 0.154795i | ||||
\(896\) | −20612.0 | −0.768525 | ||||||||
\(897\) | 757.887i | 0.0282108i | ||||||||
\(898\) | − | 12106.5i | − | 0.449886i | ||||||
\(899\) | 8743.81 | 0.324385 | ||||||||
\(900\) | −6646.04 | − | 1225.23i | −0.246149 | − | 0.0453788i | ||||
\(901\) | −2473.74 | −0.0914675 | ||||||||
\(902\) | − | 2894.92i | − | 0.106863i | ||||||
\(903\) | 5470.35i | 0.201597i | ||||||||
\(904\) | 3672.12 | 0.135103 | ||||||||
\(905\) | −4850.87 | − | 443.404i | −0.178175 | − | 0.0162865i | ||||
\(906\) | 8896.06 | 0.326216 | ||||||||
\(907\) | − | 43641.5i | − | 1.59767i | −0.601547 | − | 0.798837i | \(-0.705449\pi\) | ||
0.601547 | − | 0.798837i | \(-0.294551\pi\) | |||||||
\(908\) | − | 5504.32i | − | 0.201175i | ||||||
\(909\) | 10120.6 | 0.369283 | ||||||||
\(910\) | −1289.85 | + | 14111.0i | −0.0469868 | + | 0.514039i | ||||
\(911\) | −4915.73 | −0.178777 | −0.0893883 | − | 0.995997i | \(-0.528491\pi\) | ||||
−0.0893883 | + | 0.995997i | \(0.528491\pi\) | |||||||
\(912\) | − | 8881.48i | − | 0.322473i | ||||||
\(913\) | 6326.98i | 0.229345i | ||||||||
\(914\) | 9215.13 | 0.333490 | ||||||||
\(915\) | −84.2138 | + | 921.305i | −0.00304265 | + | 0.0332868i | ||||
\(916\) | −25835.8 | −0.931921 | ||||||||
\(917\) | 33060.4i | 1.19057i | ||||||||
\(918\) | − | 2100.63i | − | 0.0755242i | ||||||
\(919\) | 10069.5 | 0.361439 | 0.180720 | − | 0.983535i | \(-0.442157\pi\) | ||||
0.180720 | + | 0.983535i | \(0.442157\pi\) | |||||||
\(920\) | 946.883 | + | 86.5518i | 0.0339324 | + | 0.00310166i | ||||
\(921\) | −1191.57 | −0.0426315 | ||||||||
\(922\) | − | 4335.30i | − | 0.154854i | ||||||
\(923\) | 4781.08i | 0.170500i | ||||||||
\(924\) | 3029.91 | 0.107875 | ||||||||
\(925\) | −7322.45 | + | 39719.4i | −0.260282 | + | 1.41186i | ||||
\(926\) | −26078.9 | −0.925491 | ||||||||
\(927\) | − | 11479.7i | − | 0.406735i | ||||||
\(928\) | − | 6390.27i | − | 0.226046i | ||||||
\(929\) | −10460.2 | −0.369416 | −0.184708 | − | 0.982793i | \(-0.559134\pi\) | ||||
−0.184708 | + | 0.982793i | \(0.559134\pi\) | |||||||
\(930\) | 12040.9 | + | 1100.62i | 0.424556 | + | 0.0388074i | ||||
\(931\) | 16077.2 | 0.565961 | ||||||||
\(932\) | 25207.1i | 0.885930i | ||||||||
\(933\) | 491.594i | 0.0172498i | ||||||||
\(934\) | 16893.8 | 0.591845 | ||||||||
\(935\) | 616.976 | − | 6749.76i | 0.0215800 | − | 0.236086i | ||||
\(936\) | 10453.3 | 0.365040 | ||||||||
\(937\) | 16835.9i | 0.586984i | 0.955961 | + | 0.293492i | \(0.0948174\pi\) | ||||
−0.955961 | + | 0.293492i | \(0.905183\pi\) | |||||||
\(938\) | 22733.5i | 0.791339i | ||||||||
\(939\) | 7495.43 | 0.260494 | ||||||||
\(940\) | −2963.02 | + | 32415.7i | −0.102812 | + | 1.12477i | ||||
\(941\) | −19862.2 | −0.688088 | −0.344044 | − | 0.938954i | \(-0.611797\pi\) | ||||
−0.344044 | + | 0.938954i | \(0.611797\pi\) | |||||||
\(942\) | − | 2917.14i | − | 0.100898i | ||||||
\(943\) | − | 801.798i | − | 0.0276884i | ||||||
\(944\) | −5299.06 | −0.182701 | ||||||||
\(945\) | 4594.73 | + | 419.991i | 0.158166 | + | 0.0144575i | ||||
\(946\) | −1852.58 | −0.0636708 | ||||||||
\(947\) | 43730.5i | 1.50058i | 0.661107 | + | 0.750291i | \(0.270087\pi\) | ||||
−0.661107 | + | 0.750291i | \(0.729913\pi\) | |||||||
\(948\) | − | 16154.3i | − | 0.553446i | ||||||
\(949\) | 36625.2 | 1.25280 | ||||||||
\(950\) | −4702.06 | + | 25505.6i | −0.160584 | + | 0.871063i | ||||
\(951\) | −1234.21 | −0.0420841 | ||||||||
\(952\) | − | 16656.5i | − | 0.567059i | ||||||
\(953\) | − | 9765.34i | − | 0.331931i | −0.986132 | − | 0.165966i | \(-0.946926\pi\) | ||
0.986132 | − | 0.165966i | \(-0.0530741\pi\) | |||||||
\(954\) | 570.279 | 0.0193537 | ||||||||
\(955\) | −34746.2 | − | 3176.05i | −1.17734 | − | 0.107617i | ||||
\(956\) | 18924.7 | 0.640240 | ||||||||
\(957\) | 1129.96i | 0.0381677i | ||||||||
\(958\) | 14770.6i | 0.498140i | ||||||||
\(959\) | −33246.7 | −1.11949 | ||||||||
\(960\) | 312.380 | − | 3417.46i | 0.0105021 | − | 0.114894i | ||||
\(961\) | 35417.3 | 1.18886 | ||||||||
\(962\) | − | 26792.4i | − | 0.897945i | ||||||
\(963\) | 8515.28i | 0.284944i | ||||||||
\(964\) | 29219.1 | 0.976227 | ||||||||
\(965\) | −1119.95 | + | 12252.4i | −0.0373602 | + | 0.408723i | ||||
\(966\) | −278.399 | −0.00927262 | ||||||||
\(967\) | 20857.3i | 0.693614i | 0.937936 | + | 0.346807i | \(0.112734\pi\) | ||||
−0.937936 | + | 0.346807i | \(0.887266\pi\) | |||||||
\(968\) | 2392.62i | 0.0794439i | ||||||||
\(969\) | 24300.4 | 0.805614 | ||||||||
\(970\) | −8561.76 | − | 782.605i | −0.283404 | − | 0.0259051i | ||||
\(971\) | 11205.1 | 0.370328 | 0.185164 | − | 0.982708i | \(-0.440718\pi\) | ||||
0.185164 | + | 0.982708i | \(0.440718\pi\) | |||||||
\(972\) | − | 1459.73i | − | 0.0481698i | ||||||
\(973\) | − | 19570.7i | − | 0.644817i | ||||||
\(974\) | 14736.5 | 0.484791 | ||||||||
\(975\) | 21661.9 | + | 3993.47i | 0.711525 | + | 0.131173i | ||||
\(976\) | 555.590 | 0.0182213 | ||||||||
\(977\) | − | 37128.3i | − | 1.21580i | −0.794013 | − | 0.607901i | \(-0.792012\pi\) | ||
0.794013 | − | 0.607901i | \(-0.207988\pi\) | |||||||
\(978\) | 7625.38i | 0.249318i | ||||||||
\(979\) | 11700.5 | 0.381970 | ||||||||
\(980\) | −7316.15 | − | 668.748i | −0.238475 | − | 0.0217983i | ||||
\(981\) | 4249.82 | 0.138314 | ||||||||
\(982\) | − | 2600.65i | − | 0.0845112i | ||||||
\(983\) | − | 30593.0i | − | 0.992640i | −0.868140 | − | 0.496320i | \(-0.834684\pi\) | ||
0.868140 | − | 0.496320i | \(-0.165316\pi\) | |||||||
\(984\) | −11059.0 | −0.358279 | ||||||||
\(985\) | −5441.86 | + | 59534.4i | −0.176033 | + | 1.92581i | ||||
\(986\) | 2664.01 | 0.0860439 | ||||||||
\(987\) | − | 22223.3i | − | 0.716693i | ||||||
\(988\) | 51860.2i | 1.66993i | ||||||||
\(989\) | −513.105 | −0.0164973 | ||||||||
\(990\) | −142.233 | + | 1556.04i | −0.00456614 | + | 0.0499539i | ||||
\(991\) | −14998.6 | −0.480773 | −0.240387 | − | 0.970677i | \(-0.577274\pi\) | ||||
−0.240387 | + | 0.970677i | \(0.577274\pi\) | |||||||
\(992\) | − | 47656.4i | − | 1.52529i | ||||||
\(993\) | 6846.25i | 0.218791i | ||||||||
\(994\) | −1756.26 | −0.0560415 | ||||||||
\(995\) | 56825.3 | + | 5194.23i | 1.81054 | + | 0.165496i | ||||
\(996\) | 10365.6 | 0.329764 | ||||||||
\(997\) | 30874.3i | 0.980741i | 0.871514 | + | 0.490370i | \(0.163139\pi\) | ||||
−0.871514 | + | 0.490370i | \(0.836861\pi\) | |||||||
\(998\) | − | 28625.4i | − | 0.907937i | ||||||
\(999\) | −8723.97 | −0.276291 |
(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 | 165.4.c.b.34.9 | yes | 14 | |
3.2 | odd | 2 | 495.4.c.d.199.6 | 14 | |||
5.2 | odd | 4 | 825.4.a.bd.1.3 | 7 | |||
5.3 | odd | 4 | 825.4.a.ba.1.5 | 7 | |||
5.4 | even | 2 | inner | 165.4.c.b.34.6 | ✓ | 14 | |
15.2 | even | 4 | 2475.4.a.bo.1.5 | 7 | |||
15.8 | even | 4 | 2475.4.a.bs.1.3 | 7 | |||
15.14 | odd | 2 | 495.4.c.d.199.9 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.4.c.b.34.6 | ✓ | 14 | 5.4 | even | 2 | inner | |
165.4.c.b.34.9 | yes | 14 | 1.1 | even | 1 | trivial | |
495.4.c.d.199.6 | 14 | 3.2 | odd | 2 | |||
495.4.c.d.199.9 | 14 | 15.14 | odd | 2 | |||
825.4.a.ba.1.5 | 7 | 5.3 | odd | 4 | |||
825.4.a.bd.1.3 | 7 | 5.2 | odd | 4 | |||
2475.4.a.bo.1.5 | 7 | 15.2 | even | 4 | |||
2475.4.a.bs.1.3 | 7 | 15.8 | even | 4 |