Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [117,4,Mod(10,117)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(117, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("117.10");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 117 = 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 117.q (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.90322347067\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 70x^{8} + 1645x^{6} + 14700x^{4} + 44100x^{2} + 27648 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 82.3 | ||
Root | \(0.917374i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 117.82 |
Dual form | 117.4.q.e.10.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(92\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.794469 | + | 0.458687i | 0.280887 | + | 0.162170i | 0.633825 | − | 0.773476i | \(-0.281484\pi\) |
−0.352938 | + | 0.935647i | \(0.614817\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.57921 | − | 6.19938i | −0.447402 | − | 0.774922i | ||||
\(5\) | 15.4704i | 1.38372i | 0.722034 | + | 0.691858i | \(0.243208\pi\) | ||||
−0.722034 | + | 0.691858i | \(0.756792\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 17.8257 | − | 10.2917i | 0.962497 | − | 0.555698i | 0.0655563 | − | 0.997849i | \(-0.479118\pi\) |
0.896941 | + | 0.442151i | \(0.145784\pi\) | |||||||
\(8\) | − | 13.9059i | − | 0.614562i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −7.09608 | + | 12.2908i | −0.224398 | + | 0.388668i | ||||
\(11\) | 57.0209 | + | 32.9210i | 1.56295 | + | 0.902369i | 0.996957 | + | 0.0779583i | \(0.0248401\pi\) |
0.565992 | + | 0.824411i | \(0.308493\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 19.2429 | + | 42.7400i | 0.410540 | + | 0.911842i | ||||
\(14\) | 18.8826 | 0.360471 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −22.2552 | + | 38.5472i | −0.347738 | + | 0.602300i | ||||
\(17\) | −22.1478 | − | 38.3611i | −0.315979 | − | 0.547291i | 0.663666 | − | 0.748029i | \(-0.268999\pi\) |
−0.979645 | + | 0.200738i | \(0.935666\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 127.352 | − | 73.5266i | 1.53771 | − | 0.887798i | 0.538738 | − | 0.842473i | \(-0.318901\pi\) |
0.998972 | − | 0.0453247i | \(-0.0144322\pi\) | |||||||
\(20\) | 95.9069 | − | 55.3719i | 1.07227 | − | 0.619077i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 30.2009 | + | 52.3094i | 0.292675 | + | 0.506928i | ||||
\(23\) | −26.5793 | + | 46.0367i | −0.240964 | + | 0.417362i | −0.960989 | − | 0.276586i | \(-0.910797\pi\) |
0.720025 | + | 0.693948i | \(0.244130\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −114.334 | −0.914669 | ||||||||
\(26\) | −4.31639 | + | 42.7821i | −0.0325582 | + | 0.322702i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −127.604 | − | 73.6721i | −0.861245 | − | 0.497240i | ||||
\(29\) | −19.3128 | + | 33.4508i | −0.123666 | + | 0.214195i | −0.921211 | − | 0.389064i | \(-0.872798\pi\) |
0.797545 | + | 0.603260i | \(0.206132\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 88.3894i | 0.512104i | 0.966663 | + | 0.256052i | \(0.0824218\pi\) | ||||
−0.966663 | + | 0.256052i | \(0.917578\pi\) | |||||||
\(32\) | −131.705 | + | 76.0401i | −0.727576 | + | 0.420066i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 40.6357i | − | 0.204969i | ||||||
\(35\) | 159.216 | + | 275.771i | 0.768928 | + | 1.33182i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 68.3803 | + | 39.4794i | 0.303828 | + | 0.175415i | 0.644161 | − | 0.764890i | \(-0.277206\pi\) |
−0.340333 | + | 0.940305i | \(0.610540\pi\) | |||||||
\(38\) | 134.903 | 0.575898 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 215.131 | 0.850379 | ||||||||
\(41\) | −307.410 | − | 177.483i | −1.17096 | − | 0.676054i | −0.217053 | − | 0.976160i | \(-0.569645\pi\) |
−0.953906 | + | 0.300106i | \(0.902978\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −203.923 | − | 353.205i | −0.723208 | − | 1.25263i | −0.959707 | − | 0.281002i | \(-0.909333\pi\) |
0.236499 | − | 0.971632i | \(-0.424000\pi\) | |||||||
\(44\) | − | 471.325i | − | 1.61489i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −42.2329 | + | 24.3832i | −0.135367 | + | 0.0781544i | ||||
\(47\) | − | 67.9674i | − | 0.210938i | −0.994423 | − | 0.105469i | \(-0.966366\pi\) | ||
0.994423 | − | 0.105469i | \(-0.0336343\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 40.3369 | − | 69.8656i | 0.117600 | − | 0.203690i | ||||
\(50\) | −90.8345 | − | 52.4433i | −0.256919 | − | 0.148332i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 196.087 | − | 272.270i | 0.522931 | − | 0.726097i | ||||
\(53\) | −226.572 | −0.587209 | −0.293604 | − | 0.955927i | \(-0.594855\pi\) | ||||
−0.293604 | + | 0.955927i | \(0.594855\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −509.302 | + | 882.136i | −1.24862 | + | 2.16268i | ||||
\(56\) | −143.115 | − | 247.883i | −0.341511 | − | 0.591514i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −30.6869 | + | 17.7171i | −0.0694722 | + | 0.0401098i | ||||
\(59\) | 123.002 | − | 71.0154i | 0.271416 | − | 0.156702i | −0.358115 | − | 0.933677i | \(-0.616580\pi\) |
0.629531 | + | 0.776976i | \(0.283247\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −133.416 | − | 231.083i | −0.280035 | − | 0.485034i | 0.691358 | − | 0.722512i | \(-0.257013\pi\) |
−0.971393 | + | 0.237478i | \(0.923679\pi\) | |||||||
\(62\) | −40.5431 | + | 70.2227i | −0.0830480 | + | 0.143843i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 216.569 | 0.422987 | ||||||||
\(65\) | −661.206 | + | 297.696i | −1.26173 | + | 0.568071i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 356.098 | + | 205.593i | 0.649318 | + | 0.374884i | 0.788195 | − | 0.615426i | \(-0.211016\pi\) |
−0.138877 | + | 0.990310i | \(0.544349\pi\) | |||||||
\(68\) | −158.543 | + | 274.605i | −0.282739 | + | 0.489718i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 292.122i | 0.498789i | ||||||||
\(71\) | 79.2458 | − | 45.7526i | 0.132461 | − | 0.0764765i | −0.432305 | − | 0.901727i | \(-0.642300\pi\) |
0.564766 | + | 0.825251i | \(0.308966\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 63.1328i | − | 0.101221i | −0.998718 | − | 0.0506105i | \(-0.983883\pi\) | ||
0.998718 | − | 0.0506105i | \(-0.0161167\pi\) | |||||||
\(74\) | 36.2173 | + | 62.7303i | 0.0568943 | + | 0.0985439i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −911.638 | − | 526.335i | −1.37595 | − | 0.794404i | ||||
\(77\) | 1355.25 | 2.00578 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −287.115 | −0.408899 | −0.204449 | − | 0.978877i | \(-0.565540\pi\) | ||||
−0.204449 | + | 0.978877i | \(0.565540\pi\) | |||||||
\(80\) | −596.341 | − | 344.298i | −0.833412 | − | 0.481170i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −162.818 | − | 282.010i | −0.219272 | − | 0.379790i | ||||
\(83\) | 373.812i | 0.494352i | 0.968971 | + | 0.247176i | \(0.0795026\pi\) | ||||
−0.968971 | + | 0.247176i | \(0.920497\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 593.463 | − | 342.636i | 0.757295 | − | 0.437224i | ||||
\(86\) | − | 374.147i | − | 0.469132i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 457.798 | − | 792.929i | 0.554561 | − | 0.960528i | ||||
\(89\) | −103.406 | − | 59.7013i | −0.123157 | − | 0.0711047i | 0.437156 | − | 0.899386i | \(-0.355986\pi\) |
−0.560313 | + | 0.828281i | \(0.689319\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 782.885 | + | 563.829i | 0.901853 | + | 0.649509i | ||||
\(92\) | 380.532 | 0.431231 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 31.1758 | − | 53.9980i | 0.0342078 | − | 0.0592497i | ||||
\(95\) | 1137.49 | + | 1970.18i | 1.22846 | + | 2.12775i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 480.341 | − | 277.325i | 0.502796 | − | 0.290290i | −0.227071 | − | 0.973878i | \(-0.572915\pi\) |
0.729868 | + | 0.683589i | \(0.239582\pi\) | |||||||
\(98\) | 64.0928 | − | 37.0040i | 0.0660648 | − | 0.0381426i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 409.224 | + | 708.797i | 0.409224 | + | 0.708797i | ||||
\(101\) | 231.282 | − | 400.593i | 0.227856 | − | 0.394658i | −0.729317 | − | 0.684176i | \(-0.760162\pi\) |
0.957172 | + | 0.289518i | \(0.0934952\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1122.07 | −1.07341 | −0.536704 | − | 0.843771i | \(-0.680331\pi\) | ||||
−0.536704 | + | 0.843771i | \(0.680331\pi\) | |||||||
\(104\) | 594.340 | − | 267.591i | 0.560383 | − | 0.252302i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −180.005 | − | 103.926i | −0.164939 | − | 0.0952279i | ||||
\(107\) | 301.378 | − | 522.002i | 0.272293 | − | 0.471625i | −0.697156 | − | 0.716920i | \(-0.745551\pi\) |
0.969449 | + | 0.245295i | \(0.0788848\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1421.89i | 1.24947i | 0.780837 | + | 0.624735i | \(0.214793\pi\) | ||||
−0.780837 | + | 0.624735i | \(0.785207\pi\) | |||||||
\(110\) | −809.249 | + | 467.220i | −0.701444 | + | 0.404979i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 916.174i | 0.772949i | ||||||||
\(113\) | −198.359 | − | 343.569i | −0.165134 | − | 0.286020i | 0.771569 | − | 0.636145i | \(-0.219472\pi\) |
−0.936703 | + | 0.350126i | \(0.886139\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −712.207 | − | 411.193i | −0.577510 | − | 0.333426i | ||||
\(116\) | 276.499 | 0.221313 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 130.295 | 0.101650 | ||||||||
\(119\) | −789.600 | − | 455.876i | −0.608257 | − | 0.351177i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1502.09 | + | 2601.69i | 1.12854 | + | 1.95469i | ||||
\(122\) | − | 244.784i | − | 0.181653i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 547.960 | − | 316.365i | 0.396841 | − | 0.229116i | ||||
\(125\) | 165.013i | 0.118074i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 218.934 | − | 379.205i | 0.152970 | − | 0.264952i | −0.779348 | − | 0.626592i | \(-0.784449\pi\) |
0.932318 | + | 0.361639i | \(0.117783\pi\) | |||||||
\(128\) | 1225.70 | + | 707.659i | 0.846388 | + | 0.488662i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −661.857 | − | 66.7764i | −0.446528 | − | 0.0450514i | ||||
\(131\) | −1657.44 | −1.10543 | −0.552715 | − | 0.833370i | \(-0.686408\pi\) | ||||
−0.552715 | + | 0.833370i | \(0.686408\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1513.42 | − | 2621.33i | 0.986695 | − | 1.70901i | ||||
\(134\) | 188.606 | + | 326.675i | 0.121590 | + | 0.210600i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −533.448 | + | 307.986i | −0.336344 | + | 0.194188i | ||||
\(137\) | 1703.84 | − | 983.711i | 1.06254 | − | 0.613460i | 0.136410 | − | 0.990653i | \(-0.456444\pi\) |
0.926135 | + | 0.377192i | \(0.123110\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1412.57 | − | 2446.64i | −0.861960 | − | 1.49296i | −0.870035 | − | 0.492990i | \(-0.835904\pi\) |
0.00807518 | − | 0.999967i | \(-0.497430\pi\) | |||||||
\(140\) | 1139.74 | − | 1974.08i | 0.688039 | − | 1.19172i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 83.9445 | 0.0496089 | ||||||||
\(143\) | −309.797 | + | 3070.57i | −0.181165 | + | 1.79562i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −517.498 | − | 298.777i | −0.296385 | − | 0.171118i | ||||
\(146\) | 28.9582 | − | 50.1571i | 0.0164150 | − | 0.0284317i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 565.220i | − | 0.313924i | ||||||
\(149\) | −690.792 | + | 398.829i | −0.379811 | + | 0.219284i | −0.677736 | − | 0.735305i | \(-0.737039\pi\) |
0.297925 | + | 0.954589i | \(0.403706\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 161.987i | 0.0873003i | 0.999047 | + | 0.0436501i | \(0.0138987\pi\) | ||||
−0.999047 | + | 0.0436501i | \(0.986101\pi\) | |||||||
\(152\) | −1022.46 | − | 1770.95i | −0.545606 | − | 0.945018i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1076.70 | + | 621.635i | 0.563397 | + | 0.325278i | ||||
\(155\) | −1367.42 | −0.708606 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −342.000 | −0.173851 | −0.0869255 | − | 0.996215i | \(-0.527704\pi\) | ||||
−0.0869255 | + | 0.996215i | \(0.527704\pi\) | |||||||
\(158\) | −228.104 | − | 131.696i | −0.114854 | − | 0.0663112i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1176.37 | − | 2037.54i | −0.581252 | − | 1.00676i | ||||
\(161\) | 1094.18i | 0.535613i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 482.027 | − | 278.299i | 0.231628 | − | 0.133730i | −0.379695 | − | 0.925112i | \(-0.623971\pi\) |
0.611323 | + | 0.791381i | \(0.290638\pi\) | |||||||
\(164\) | 2541.00i | 1.20987i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −171.463 | + | 296.982i | −0.0801693 | + | 0.138857i | ||||
\(167\) | −2716.22 | − | 1568.21i | −1.25861 | − | 0.726658i | −0.285805 | − | 0.958288i | \(-0.592261\pi\) |
−0.972804 | + | 0.231630i | \(0.925594\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1456.42 | + | 1644.89i | −0.662913 | + | 0.748696i | ||||
\(170\) | 628.650 | 0.283619 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1459.77 | + | 2528.39i | −0.647129 | + | 1.12086i | ||||
\(173\) | −1662.10 | − | 2878.84i | −0.730444 | − | 1.26517i | −0.956693 | − | 0.291097i | \(-0.905980\pi\) |
0.226249 | − | 0.974070i | \(-0.427354\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2038.08 | + | 1176.68i | −0.880366 | + | 0.508280i | ||||
\(176\) | −2538.02 | + | 1465.33i | −1.08699 | + | 0.627576i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −54.7684 | − | 94.8616i | −0.0230622 | − | 0.0399448i | ||||
\(179\) | 1656.62 | − | 2869.36i | 0.691743 | − | 1.19813i | −0.279524 | − | 0.960139i | \(-0.590177\pi\) |
0.971266 | − | 0.237995i | \(-0.0764900\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −76.0118 | −0.0312150 | −0.0156075 | − | 0.999878i | \(-0.504968\pi\) | ||||
−0.0156075 | + | 0.999878i | \(0.504968\pi\) | |||||||
\(182\) | 363.357 | + | 807.044i | 0.147988 | + | 0.328693i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 640.184 | + | 369.610i | 0.256494 | + | 0.148087i | ||||
\(185\) | −610.762 | + | 1057.87i | −0.242725 | + | 0.420412i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 2916.51i | − | 1.14052i | ||||||
\(188\) | −421.356 | + | 243.270i | −0.163460 | + | 0.0943738i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2087.00i | 0.796879i | ||||||||
\(191\) | −2036.70 | − | 3527.66i | −0.771572 | − | 1.33640i | −0.936701 | − | 0.350130i | \(-0.886138\pi\) |
0.165129 | − | 0.986272i | \(-0.447196\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 751.347 | + | 433.791i | 0.280224 | + | 0.161787i | 0.633525 | − | 0.773723i | \(-0.281608\pi\) |
−0.353301 | + | 0.935510i | \(0.614941\pi\) | |||||||
\(194\) | 508.821 | 0.188305 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −577.497 | −0.210458 | ||||||||
\(197\) | −1634.79 | − | 943.846i | −0.591238 | − | 0.341352i | 0.174349 | − | 0.984684i | \(-0.444218\pi\) |
−0.765587 | + | 0.643332i | \(0.777551\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1393.11 | + | 2412.94i | 0.496256 | + | 0.859540i | 0.999991 | − | 0.00431832i | \(-0.00137457\pi\) |
−0.503735 | + | 0.863858i | \(0.668041\pi\) | |||||||
\(200\) | 1589.92i | 0.562120i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 367.493 | − | 212.172i | 0.128004 | − | 0.0739029i | ||||
\(203\) | 795.045i | 0.274883i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2745.74 | − | 4755.75i | 0.935466 | − | 1.62027i | ||||
\(206\) | −891.451 | − | 514.680i | −0.301507 | − | 0.174075i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2075.76 | − | 209.429i | −0.691963 | − | 0.0698139i | ||||
\(209\) | 9682.28 | 3.20448 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −354.395 | + | 613.830i | −0.115628 | + | 0.200274i | −0.918031 | − | 0.396509i | \(-0.870221\pi\) |
0.802403 | + | 0.596783i | \(0.203555\pi\) | |||||||
\(212\) | 810.950 | + | 1404.61i | 0.262718 | + | 0.455041i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 478.871 | − | 276.476i | 0.152967 | − | 0.0883156i | ||||
\(215\) | 5464.22 | − | 3154.77i | 1.73329 | − | 1.00071i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 909.675 | + | 1575.60i | 0.284575 | + | 0.492898i | ||||
\(218\) | −652.202 | + | 1129.65i | −0.202627 | + | 0.350960i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 7291.59 | 2.23454 | ||||||||
\(221\) | 1213.37 | − | 1684.78i | 0.369321 | − | 0.512808i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4673.62 | − | 2698.32i | −1.40345 | − | 0.810281i | −0.408703 | − | 0.912667i | \(-0.634019\pi\) |
−0.994745 | + | 0.102386i | \(0.967352\pi\) | |||||||
\(224\) | −1565.16 | + | 2710.94i | −0.466860 | + | 0.808625i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 363.940i | − | 0.107119i | ||||||
\(227\) | −2755.51 | + | 1590.90i | −0.805682 | + | 0.465160i | −0.845454 | − | 0.534048i | \(-0.820670\pi\) |
0.0397724 | + | 0.999209i | \(0.487337\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 2034.00i | − | 0.586945i | −0.955967 | − | 0.293473i | \(-0.905189\pi\) | ||
0.955967 | − | 0.293473i | \(-0.0948110\pi\) | |||||||
\(230\) | −377.218 | − | 653.360i | −0.108143 | − | 0.187310i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 465.165 | + | 268.563i | 0.131636 | + | 0.0760001i | ||||
\(233\) | −2794.22 | −0.785645 | −0.392823 | − | 0.919614i | \(-0.628501\pi\) | ||||
−0.392823 | + | 0.919614i | \(0.628501\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1051.48 | 0.291878 | ||||||||
\(236\) | −880.502 | − | 508.358i | −0.242864 | − | 0.140217i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −418.209 | − | 724.359i | −0.113901 | − | 0.197282i | ||||
\(239\) | 5493.81i | 1.48688i | 0.668800 | + | 0.743442i | \(0.266808\pi\) | ||||
−0.668800 | + | 0.743442i | \(0.733192\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3517.16 | + | 2030.63i | −0.940084 | + | 0.542758i | −0.889987 | − | 0.455986i | \(-0.849287\pi\) |
−0.0500976 | + | 0.998744i | \(0.515953\pi\) | |||||||
\(242\) | 2755.95i | 0.732062i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −955.046 | + | 1654.19i | −0.250576 | + | 0.434010i | ||||
\(245\) | 1080.85 | + | 624.028i | 0.281849 | + | 0.162725i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5593.15 | + | 4028.15i | 1.44082 | + | 1.03767i | ||||
\(248\) | 1229.14 | 0.314719 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −75.6894 | + | 131.098i | −0.0191481 | + | 0.0331654i | ||||
\(251\) | 1785.44 | + | 3092.47i | 0.448988 | + | 0.777670i | 0.998320 | − | 0.0579336i | \(-0.0184512\pi\) |
−0.549332 | + | 0.835604i | \(0.685118\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3031.15 | + | 1750.04i | −0.753228 | + | 0.434877i | ||||
\(254\) | 347.872 | − | 200.844i | 0.0859348 | − | 0.0496145i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −217.089 | − | 376.010i | −0.0530003 | − | 0.0917993i | ||||
\(257\) | 3759.13 | − | 6511.01i | 0.912405 | − | 1.58033i | 0.101749 | − | 0.994810i | \(-0.467556\pi\) |
0.810656 | − | 0.585522i | \(-0.199111\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1625.23 | 0.389912 | ||||||||
\(260\) | 4212.13 | + | 3033.55i | 1.00471 | + | 0.723587i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1316.79 | − | 760.246i | −0.310501 | − | 0.179268i | ||||
\(263\) | −2330.09 | + | 4035.84i | −0.546310 | + | 0.946237i | 0.452213 | + | 0.891910i | \(0.350635\pi\) |
−0.998523 | + | 0.0543273i | \(0.982699\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 3505.16i | − | 0.812530i | ||||||
\(266\) | 2404.73 | − | 1388.37i | 0.554300 | − | 0.320025i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 2943.45i | − | 0.670895i | ||||||
\(269\) | 2673.72 | + | 4631.02i | 0.606021 | + | 1.04966i | 0.991889 | + | 0.127105i | \(0.0405684\pi\) |
−0.385869 | + | 0.922554i | \(0.626098\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2574.76 | + | 1486.54i | 0.577143 | + | 0.333214i | 0.759997 | − | 0.649926i | \(-0.225200\pi\) |
−0.182854 | + | 0.983140i | \(0.558534\pi\) | |||||||
\(272\) | 1971.62 | 0.439511 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1804.86 | 0.397940 | ||||||||
\(275\) | −6519.40 | − | 3763.98i | −1.42958 | − | 0.825369i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −382.076 | − | 661.776i | −0.0828764 | − | 0.143546i | 0.821608 | − | 0.570053i | \(-0.193077\pi\) |
−0.904484 | + | 0.426507i | \(0.859744\pi\) | |||||||
\(278\) | − | 2591.70i | − | 0.559137i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3834.85 | − | 2214.05i | 0.818487 | − | 0.472554i | ||||
\(281\) | − | 7040.34i | − | 1.49463i | −0.664469 | − | 0.747316i | \(-0.731342\pi\) | ||
0.664469 | − | 0.747316i | \(-0.268658\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4517.58 | + | 7824.68i | −0.948913 | + | 1.64357i | −0.201194 | + | 0.979551i | \(0.564482\pi\) |
−0.747720 | + | 0.664015i | \(0.768851\pi\) | |||||||
\(284\) | −567.275 | − | 327.517i | −0.118527 | − | 0.0684314i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1654.55 | + | 2297.37i | −0.342083 | + | 0.474988i | ||||
\(287\) | −7306.39 | −1.50273 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1475.45 | − | 2555.55i | 0.300315 | − | 0.520161i | ||||
\(290\) | −274.091 | − | 474.739i | −0.0555005 | − | 0.0961297i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −391.384 | + | 225.966i | −0.0784384 | + | 0.0452865i | ||||
\(293\) | 1546.06 | − | 892.617i | 0.308265 | − | 0.177977i | −0.337885 | − | 0.941188i | \(-0.609711\pi\) |
0.646150 | + | 0.763211i | \(0.276378\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1098.64 | + | 1902.89i | 0.216831 | + | 0.375562i | ||||
\(296\) | 548.998 | − | 950.892i | 0.107804 | − | 0.186721i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −731.751 | −0.142246 | ||||||||
\(299\) | −2479.07 | − | 250.120i | −0.479494 | − | 0.0483773i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7270.13 | − | 4197.41i | −1.39217 | − | 0.803771i | ||||
\(302\) | −74.3015 | + | 128.694i | −0.0141575 | + | 0.0245215i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6545.40i | 1.23488i | ||||||||
\(305\) | 3574.94 | − | 2063.99i | 0.671150 | − | 0.387488i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 5323.13i | − | 0.989600i | −0.869007 | − | 0.494800i | \(-0.835241\pi\) | ||
0.869007 | − | 0.494800i | \(-0.164759\pi\) | |||||||
\(308\) | −4850.72 | − | 8401.70i | −0.897388 | − | 1.55432i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1086.37 | − | 627.218i | −0.199038 | − | 0.114915i | ||||
\(311\) | 6265.64 | 1.14242 | 0.571209 | − | 0.820805i | \(-0.306475\pi\) | ||||
0.571209 | + | 0.820805i | \(0.306475\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7193.77 | 1.29909 | 0.649547 | − | 0.760322i | \(-0.274959\pi\) | ||||
0.649547 | + | 0.760322i | \(0.274959\pi\) | |||||||
\(314\) | −271.709 | − | 156.871i | −0.0488325 | − | 0.0281935i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1027.65 | + | 1779.94i | 0.182942 | + | 0.316865i | ||||
\(317\) | 9576.87i | 1.69682i | 0.529343 | + | 0.848408i | \(0.322439\pi\) | ||||
−0.529343 | + | 0.848408i | \(0.677561\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2202.47 | + | 1271.60i | −0.386566 | + | 0.223184i | ||||
\(320\) | 3350.41i | 0.585293i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −501.887 | + | 869.294i | −0.0868604 | + | 0.150447i | ||||
\(323\) | −5641.13 | − | 3256.91i | −0.971767 | − | 0.561050i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2200.11 | − | 4886.62i | −0.375509 | − | 0.834034i | ||||
\(326\) | 510.608 | 0.0867483 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2468.07 | + | 4274.82i | −0.415477 | + | 0.719627i | ||||
\(329\) | −699.498 | − | 1211.57i | −0.117218 | − | 0.203027i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4999.68 | − | 2886.56i | 0.830233 | − | 0.479335i | −0.0236996 | − | 0.999719i | \(-0.507545\pi\) |
0.853932 | + | 0.520384i | \(0.174211\pi\) | |||||||
\(332\) | 2317.40 | − | 1337.95i | 0.383085 | − | 0.221174i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1438.64 | − | 2491.79i | −0.235685 | − | 0.408218i | ||||
\(335\) | −3180.61 | + | 5508.98i | −0.518733 | + | 0.898471i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1238.09 | −0.200127 | −0.100063 | − | 0.994981i | \(-0.531905\pi\) | ||||
−0.100063 | + | 0.994981i | \(0.531905\pi\) | |||||||
\(338\) | −1911.57 | + | 638.770i | −0.307620 | + | 0.102794i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4248.26 | − | 2452.73i | −0.677630 | − | 0.391230i | ||||
\(341\) | −2909.87 | + | 5040.04i | −0.462106 | + | 0.800392i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5399.55i | 0.849995i | ||||||||
\(344\) | −4911.65 | + | 2835.74i | −0.769820 | + | 0.444456i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 3049.53i | − | 0.473826i | ||||||
\(347\) | 2724.98 | + | 4719.81i | 0.421570 | + | 0.730181i | 0.996093 | − | 0.0883076i | \(-0.0281459\pi\) |
−0.574523 | + | 0.818488i | \(0.694813\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1189.95 | − | 687.016i | −0.182511 | − | 0.105373i | 0.405961 | − | 0.913890i | \(-0.366937\pi\) |
−0.588472 | + | 0.808518i | \(0.700270\pi\) | |||||||
\(350\) | −2158.92 | −0.329711 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −10013.3 | −1.51622 | ||||||||
\(353\) | −5170.55 | − | 2985.22i | −0.779606 | − | 0.450106i | 0.0566848 | − | 0.998392i | \(-0.481947\pi\) |
−0.836291 | + | 0.548287i | \(0.815280\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 707.811 | + | 1225.97i | 0.105822 | + | 0.183289i | ||||
\(356\) | 854.734i | 0.127249i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2632.27 | − | 1519.74i | 0.388603 | − | 0.224360i | ||||
\(359\) | − | 7813.71i | − | 1.14872i | −0.818602 | − | 0.574362i | \(-0.805250\pi\) | ||
0.818602 | − | 0.574362i | \(-0.194750\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7382.82 | − | 12787.4i | 1.07637 | − | 1.86433i | ||||
\(362\) | −60.3891 | − | 34.8656i | −0.00876790 | − | 0.00506215i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 693.279 | − | 6871.46i | 0.0998288 | − | 0.989457i | ||||
\(365\) | 976.690 | 0.140061 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −844.195 | + | 1462.19i | −0.120073 | + | 0.207972i | −0.919796 | − | 0.392397i | \(-0.871646\pi\) |
0.799724 | + | 0.600368i | \(0.204979\pi\) | |||||||
\(368\) | −1183.06 | − | 2049.12i | −0.167585 | − | 0.290265i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −970.463 | + | 560.297i | −0.136357 | + | 0.0787256i | ||||
\(371\) | −4038.80 | + | 2331.81i | −0.565187 | + | 0.326311i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −935.307 | − | 1620.00i | −0.129835 | − | 0.224880i | 0.793778 | − | 0.608208i | \(-0.208111\pi\) |
−0.923612 | + | 0.383328i | \(0.874778\pi\) | |||||||
\(374\) | 1337.77 | − | 2317.08i | 0.184958 | − | 0.320357i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −945.151 | −0.129634 | ||||||||
\(377\) | −1801.32 | − | 181.740i | −0.246082 | − | 0.0248278i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10103.9 | + | 5833.52i | 1.36941 | + | 0.790627i | 0.990852 | − | 0.134952i | \(-0.0430882\pi\) |
0.378554 | + | 0.925579i | \(0.376421\pi\) | |||||||
\(380\) | 8142.61 | − | 14103.4i | 1.09923 | − | 1.90392i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 3736.82i | − | 0.500504i | ||||||
\(383\) | −5782.11 | + | 3338.30i | −0.771415 | + | 0.445376i | −0.833379 | − | 0.552702i | \(-0.813597\pi\) |
0.0619643 | + | 0.998078i | \(0.480263\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 20966.3i | 2.77543i | ||||||||
\(386\) | 397.948 | + | 689.266i | 0.0524742 | + | 0.0908879i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3438.48 | − | 1985.21i | −0.449904 | − | 0.259752i | ||||
\(389\) | 14285.3 | 1.86194 | 0.930969 | − | 0.365099i | \(-0.118965\pi\) | ||||
0.930969 | + | 0.365099i | \(0.118965\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2354.69 | 0.304558 | ||||||||
\(392\) | −971.547 | − | 560.923i | −0.125180 | − | 0.0722726i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −865.860 | − | 1499.71i | −0.110714 | − | 0.191763i | ||||
\(395\) | − | 4441.79i | − | 0.565800i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3091.09 | − | 1784.64i | 0.390774 | − | 0.225614i | −0.291721 | − | 0.956503i | \(-0.594228\pi\) |
0.682496 | + | 0.730890i | \(0.260895\pi\) | |||||||
\(398\) | 2556.00i | 0.321912i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2544.52 | − | 4407.24i | 0.318065 | − | 0.550905i | ||||
\(401\) | 432.448 | + | 249.674i | 0.0538540 | + | 0.0310926i | 0.526685 | − | 0.850060i | \(-0.323435\pi\) |
−0.472831 | + | 0.881153i | \(0.656768\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3777.77 | + | 1700.87i | −0.466958 | + | 0.210239i | ||||
\(404\) | −3311.23 | −0.407772 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −364.677 | + | 631.639i | −0.0445778 | + | 0.0772111i | ||||
\(407\) | 2599.40 | + | 4502.30i | 0.316579 | + | 0.548331i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9056.46 | + | 5228.75i | −1.09490 | + | 0.632140i | −0.934876 | − | 0.354974i | \(-0.884490\pi\) |
−0.160022 | + | 0.987114i | \(0.551156\pi\) | |||||||
\(410\) | 4362.80 | − | 2518.87i | 0.525521 | − | 0.303410i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4016.13 | + | 6956.15i | 0.480245 | + | 0.831808i | ||||
\(413\) | 1461.73 | − | 2531.80i | 0.174158 | − | 0.301650i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5783.03 | −0.684043 | ||||||||
\(416\) | −5784.35 | − | 4165.86i | −0.681734 | − | 0.490981i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7692.27 | + | 4441.13i | 0.900099 | + | 0.519672i | ||||
\(419\) | −852.710 | + | 1476.94i | −0.0994215 | + | 0.172203i | −0.911445 | − | 0.411421i | \(-0.865033\pi\) |
0.812024 | + | 0.583624i | \(0.198366\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8765.57i | 1.01475i | 0.861727 | + | 0.507373i | \(0.169383\pi\) | ||||
−0.861727 | + | 0.507373i | \(0.830617\pi\) | |||||||
\(422\) | −563.111 | + | 325.112i | −0.0649569 | + | 0.0375029i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3150.70i | 0.360876i | ||||||||
\(425\) | 2532.24 | + | 4385.97i | 0.289016 | + | 0.500590i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4756.45 | − | 2746.14i | −0.539065 | − | 0.311229i | ||||
\(428\) | −4314.79 | −0.487297 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5788.21 | 0.649145 | ||||||||
\(431\) | 6997.81 | + | 4040.18i | 0.782071 | + | 0.451529i | 0.837164 | − | 0.546953i | \(-0.184212\pi\) |
−0.0550930 | + | 0.998481i | \(0.517546\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2062.24 | − | 3571.91i | −0.228880 | − | 0.396432i | 0.728596 | − | 0.684943i | \(-0.240173\pi\) |
−0.957476 | + | 0.288511i | \(0.906840\pi\) | |||||||
\(434\) | 1669.02i | 0.184598i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8814.83 | − | 5089.24i | 0.968242 | − | 0.559015i | ||||
\(437\) | 7817.14i | 0.855709i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3057.76 | + | 5296.19i | −0.332435 | + | 0.575794i | −0.982989 | − | 0.183666i | \(-0.941203\pi\) |
0.650554 | + | 0.759460i | \(0.274537\pi\) | |||||||
\(440\) | 12266.9 | + | 7082.32i | 1.32910 | + | 0.767355i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1736.77 | − | 781.948i | 0.186900 | − | 0.0841482i | ||||
\(443\) | 11058.8 | 1.18605 | 0.593025 | − | 0.805184i | \(-0.297933\pi\) | ||||
0.593025 | + | 0.805184i | \(0.297933\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 923.603 | − | 1599.73i | 0.0983887 | − | 0.170414i | ||||
\(446\) | −2475.37 | − | 4287.46i | −0.262807 | − | 0.455195i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3860.50 | − | 2228.86i | 0.407123 | − | 0.235053i | ||||
\(449\) | −209.588 | + | 121.006i | −0.0220291 | + | 0.0127185i | −0.510974 | − | 0.859596i | \(-0.670715\pi\) |
0.488945 | + | 0.872315i | \(0.337382\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11685.8 | − | 20240.5i | −1.22010 | − | 2.11327i | ||||
\(452\) | −1419.94 | + | 2459.41i | −0.147762 | + | 0.255931i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2918.89 | −0.301741 | ||||||||
\(455\) | −8722.67 | + | 12111.5i | −0.898736 | + | 1.24791i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9571.46 | + | 5526.08i | 0.979724 | + | 0.565644i | 0.902187 | − | 0.431346i | \(-0.141961\pi\) |
0.0775372 | + | 0.996989i | \(0.475294\pi\) | |||||||
\(458\) | 932.969 | − | 1615.95i | 0.0951851 | − | 0.164865i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5886.99i | 0.596700i | ||||||||
\(461\) | −237.086 | + | 136.882i | −0.0239527 | + | 0.0138291i | −0.511929 | − | 0.859028i | \(-0.671069\pi\) |
0.487976 | + | 0.872857i | \(0.337735\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 11579.2i | − | 1.16227i | −0.813808 | − | 0.581134i | \(-0.802609\pi\) | ||
0.813808 | − | 0.581134i | \(-0.197391\pi\) | |||||||
\(464\) | −859.623 | − | 1488.91i | −0.0860064 | − | 0.148968i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2219.92 | − | 1281.67i | −0.220678 | − | 0.127408i | ||||
\(467\) | 902.915 | 0.0894688 | 0.0447344 | − | 0.998999i | \(-0.485756\pi\) | ||||
0.0447344 | + | 0.998999i | \(0.485756\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8463.59 | 0.833289 | ||||||||
\(470\) | 835.372 | + | 482.302i | 0.0819847 | + | 0.0473339i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −987.535 | − | 1710.46i | −0.0963030 | − | 0.166802i | ||||
\(473\) | − | 26853.4i | − | 2.61040i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14560.6 | + | 8406.56i | −1.40650 | + | 0.812041i | ||||
\(476\) | 6526.71i | 0.628469i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2519.94 | + | 4364.67i | −0.241128 | + | 0.417647i | ||||
\(479\) | 10451.9 | + | 6034.38i | 0.996988 | + | 0.575611i | 0.907356 | − | 0.420364i | \(-0.138097\pi\) |
0.0896324 | + | 0.995975i | \(0.471431\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −371.514 | + | 3682.27i | −0.0352174 | + | 0.349059i | ||||
\(482\) | −3725.70 | −0.352077 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10752.6 | − | 18624.0i | 1.00982 | − | 1.74906i | ||||
\(485\) | 4290.33 | + | 7431.07i | 0.401678 | + | 0.695727i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9952.82 | − | 5746.26i | 0.926089 | − | 0.534678i | 0.0405163 | − | 0.999179i | \(-0.487100\pi\) |
0.885572 | + | 0.464501i | \(0.153766\pi\) | |||||||
\(488\) | −3213.42 | + | 1855.27i | −0.298084 | + | 0.172099i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 572.467 | + | 991.543i | 0.0527785 | + | 0.0914150i | ||||
\(491\) | −7852.08 | + | 13600.2i | −0.721710 | + | 1.25004i | 0.238605 | + | 0.971117i | \(0.423310\pi\) |
−0.960314 | + | 0.278921i | \(0.910023\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1710.95 | 0.156303 | ||||||||
\(494\) | 2595.92 | + | 5765.75i | 0.236429 | + | 0.525128i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3407.16 | − | 1967.13i | −0.308440 | − | 0.178078i | ||||
\(497\) | 941.741 | − | 1631.14i | 0.0849957 | − | 0.147217i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9019.80i | 0.809181i | 0.914498 | + | 0.404591i | \(0.132586\pi\) | ||||
−0.914498 | + | 0.404591i | \(0.867414\pi\) | |||||||
\(500\) | 1022.98 | − | 590.617i | 0.0914980 | − | 0.0528264i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3275.83i | 0.291250i | ||||||||
\(503\) | −3016.92 | − | 5225.46i | −0.267431 | − | 0.463204i | 0.700767 | − | 0.713391i | \(-0.252841\pi\) |
−0.968198 | + | 0.250186i | \(0.919508\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6197.33 | + | 3578.03i | 0.546094 | + | 0.315288i | ||||
\(506\) | −3210.87 | −0.282096 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3134.44 | −0.273757 | ||||||||
\(509\) | 19443.6 | + | 11225.8i | 1.69317 | + | 0.977551i | 0.951934 | + | 0.306304i | \(0.0990926\pi\) |
0.741234 | + | 0.671246i | \(0.234241\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −649.742 | − | 1125.39i | −0.0562483 | − | 0.0974249i | ||||
\(512\) | − | 11720.8i | − | 1.01170i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5973.03 | − | 3448.53i | 0.512566 | − | 0.295930i | ||||
\(515\) | − | 17358.9i | − | 1.48529i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2237.56 | − | 3875.56i | 0.190344 | − | 0.329685i | ||||
\(518\) | 1291.20 | + | 745.474i | 0.109521 | + | 0.0632321i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4139.74 | + | 9194.69i | 0.349115 | + | 0.775411i | ||||
\(521\) | −15674.7 | −1.31808 | −0.659040 | − | 0.752108i | \(-0.729037\pi\) | ||||
−0.659040 | + | 0.752108i | \(0.729037\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6755.39 | + | 11700.7i | −0.564804 | + | 0.978270i | 0.432264 | + | 0.901747i | \(0.357715\pi\) |
−0.997068 | + | 0.0765223i | \(0.975618\pi\) | |||||||
\(524\) | 5932.33 | + | 10275.1i | 0.494571 | + | 0.856622i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3702.37 | + | 2137.57i | −0.306903 | + | 0.177191i | ||||
\(527\) | 3390.72 | − | 1957.63i | 0.280270 | − | 0.161814i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4670.58 | + | 8089.68i | 0.383873 | + | 0.664887i | ||||
\(530\) | 1607.77 | − | 2784.74i | 0.131768 | − | 0.228229i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −21667.4 | −1.76580 | ||||||||
\(533\) | 1670.17 | − | 16554.0i | 0.135728 | − | 1.34528i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8075.59 | + | 4662.44i | 0.652595 | + | 0.376776i | ||||
\(536\) | 2858.97 | − | 4951.88i | 0.230389 | − | 0.399046i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4905.60i | 0.393114i | ||||||||
\(539\) | 4600.09 | − | 2655.86i | 0.367607 | − | 0.212238i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 12103.6i | − | 0.961875i | −0.876755 | − | 0.480937i | \(-0.840296\pi\) | ||
0.876755 | − | 0.480937i | \(-0.159704\pi\) | |||||||
\(542\) | 1363.71 | + | 2362.02i | 0.108075 | + | 0.187191i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5833.97 | + | 3368.25i | 0.459797 | + | 0.265464i | ||||
\(545\) | −21997.2 | −1.72891 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15228.6 | −1.19036 | −0.595181 | − | 0.803592i | \(-0.702920\pi\) | ||||
−0.595181 | + | 0.803592i | \(0.702920\pi\) | |||||||
\(548\) | −12196.8 | − | 7041.82i | −0.950768 | − | 0.548926i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3452.98 | − | 5980.73i | −0.267701 | − | 0.463671i | ||||
\(551\) | 5680.03i | 0.439160i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5118.03 | + | 2954.90i | −0.393564 | + | 0.227224i | ||||
\(554\) | − | 701.014i | − | 0.0537603i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10111.8 | + | 17514.1i | −0.771284 | + | 1.33590i | ||||
\(557\) | −20435.5 | − | 11798.5i | −1.55454 | − | 0.897516i | −0.997763 | − | 0.0668564i | \(-0.978703\pi\) |
−0.556781 | − | 0.830660i | \(-0.687964\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11171.9 | − | 15512.4i | 0.845298 | − | 1.17371i | ||||
\(560\) | −14173.6 | −1.06954 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3229.31 | − | 5593.33i | 0.242385 | − | 0.419823i | ||||
\(563\) | −3970.81 | − | 6877.64i | −0.297246 | − | 0.514846i | 0.678259 | − | 0.734823i | \(-0.262735\pi\) |
−0.975505 | + | 0.219978i | \(0.929402\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5315.15 | − | 3068.70i | 0.395770 | − | 0.228498i | ||||
\(566\) | −7178.16 | + | 4144.31i | −0.533075 | + | 0.307771i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −636.233 | − | 1101.99i | −0.0469995 | − | 0.0814056i | ||||
\(569\) | −1137.33 | + | 1969.91i | −0.0837948 | + | 0.145137i | −0.904877 | − | 0.425673i | \(-0.860037\pi\) |
0.821082 | + | 0.570810i | \(0.193371\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4499.84 | 0.329794 | 0.164897 | − | 0.986311i | \(-0.447271\pi\) | ||||
0.164897 | + | 0.986311i | \(0.447271\pi\) | |||||||
\(572\) | 20144.5 | − | 9069.67i | 1.47252 | − | 0.662975i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5804.70 | − | 3351.34i | −0.422097 | − | 0.243698i | ||||
\(575\) | 3038.91 | − | 5263.55i | 0.220402 | − | 0.381748i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 25253.3i | − | 1.82202i | −0.412381 | − | 0.911011i | \(-0.635303\pi\) | ||
0.412381 | − | 0.911011i | \(-0.364697\pi\) | |||||||
\(578\) | 2344.40 | − | 1353.54i | 0.168709 | − | 0.0974044i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4277.55i | 0.306234i | ||||||||
\(581\) | 3847.15 | + | 6663.47i | 0.274711 | + | 0.475813i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12919.3 | − | 7458.98i | −0.917777 | − | 0.529879i | ||||
\(584\) | −877.921 | −0.0622066 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1637.73 | 0.115450 | ||||||||
\(587\) | −9773.25 | − | 5642.59i | −0.687198 | − | 0.396754i | 0.115363 | − | 0.993323i | \(-0.463197\pi\) |
−0.802562 | + | 0.596569i | \(0.796530\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6498.97 | + | 11256.6i | 0.454644 | + | 0.787467i | ||||
\(590\) | 2015.72i | 0.140654i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3043.64 | + | 1757.24i | −0.211305 | + | 0.121997i | ||||
\(593\) | 12824.5i | 0.888090i | 0.896005 | + | 0.444045i | \(0.146457\pi\) | ||||
−0.896005 | + | 0.444045i | \(0.853543\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7052.59 | − | 12215.4i | 0.485929 | − | 0.841654i | ||||
\(596\) | 4944.99 | + | 2854.99i | 0.339857 | + | 0.196216i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1854.82 | − | 1335.83i | −0.126838 | − | 0.0913482i | ||||
\(599\) | 26180.3 | 1.78581 | 0.892905 | − | 0.450245i | \(-0.148664\pi\) | ||||
0.892905 | + | 0.450245i | \(0.148664\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8006.28 | + | 13867.3i | −0.543399 | + | 0.941195i | 0.455307 | + | 0.890335i | \(0.349530\pi\) |
−0.998706 | + | 0.0508602i | \(0.983804\pi\) | |||||||
\(602\) | −3850.60 | − | 6669.43i | −0.260695 | − | 0.451538i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1004.22 | − | 579.787i | 0.0676509 | − | 0.0390583i | ||||
\(605\) | −40249.2 | + | 23237.9i | −2.70473 | + | 1.56158i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4765.74 | + | 8254.50i | 0.318674 | + | 0.551960i | 0.980212 | − | 0.197952i | \(-0.0634290\pi\) |
−0.661537 | + | 0.749912i | \(0.730096\pi\) | |||||||
\(608\) | −11181.9 | + | 19367.7i | −0.745868 | + | 1.29188i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3786.91 | 0.251356 | ||||||||
\(611\) | 2904.93 | − | 1307.89i | 0.192342 | − | 0.0865984i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8822.27 | − | 5093.54i | −0.581286 | − | 0.335605i | 0.180359 | − | 0.983601i | \(-0.442274\pi\) |
−0.761644 | + | 0.647996i | \(0.775608\pi\) | |||||||
\(614\) | 2441.65 | − | 4229.06i | 0.160484 | − | 0.277966i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 18846.0i | − | 1.23267i | ||||||
\(617\) | −6939.13 | + | 4006.31i | −0.452770 | + | 0.261407i | −0.708999 | − | 0.705209i | \(-0.750853\pi\) |
0.256230 | + | 0.966616i | \(0.417520\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 1886.59i | − | 0.122501i | −0.998122 | − | 0.0612506i | \(-0.980491\pi\) | ||
0.998122 | − | 0.0612506i | \(-0.0195089\pi\) | |||||||
\(620\) | 4894.29 | + | 8477.16i | 0.317031 | + | 0.549114i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4977.86 | + | 2873.97i | 0.320891 | + | 0.185266i | ||||
\(623\) | −2457.70 | −0.158051 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16844.5 | −1.07805 | ||||||||
\(626\) | 5715.23 | + | 3299.69i | 0.364899 | + | 0.210674i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1224.09 | + | 2120.19i | 0.0777812 | + | 0.134721i | ||||
\(629\) | − | 3497.53i | − | 0.221710i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12952.3 | + | 7478.04i | −0.817154 | + | 0.471784i | −0.849434 | − | 0.527695i | \(-0.823057\pi\) |
0.0322798 | + | 0.999479i | \(0.489723\pi\) | |||||||
\(632\) | 3992.61i | 0.251293i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4392.79 | + | 7608.53i | −0.275173 | + | 0.476614i | ||||
\(635\) | 5866.45 | + | 3387.00i | 0.366619 | + | 0.211667i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3762.26 | + | 379.583i | 0.234013 | + | 0.0236101i | ||||
\(638\) | −2333.06 | −0.144775 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −10947.8 | + | 18962.1i | −0.676170 | + | 1.17116i | ||||
\(641\) | −11845.9 | − | 20517.6i | −0.729927 | − | 1.26427i | −0.956913 | − | 0.290373i | \(-0.906221\pi\) |
0.226986 | − | 0.973898i | \(-0.427113\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11822.4 | − | 6825.65i | 0.725083 | − | 0.418627i | −0.0915374 | − | 0.995802i | \(-0.529178\pi\) |
0.816621 | + | 0.577175i | \(0.195845\pi\) | |||||||
\(644\) | 6783.25 | − | 3916.31i | 0.415058 | − | 0.239634i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2987.80 | − | 5175.02i | −0.181971 | − | 0.315184i | ||||
\(647\) | 9066.14 | − | 15703.0i | 0.550892 | − | 0.954172i | −0.447319 | − | 0.894375i | \(-0.647621\pi\) |
0.998211 | − | 0.0597977i | \(-0.0190456\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9351.59 | 0.565612 | ||||||||
\(650\) | 493.509 | − | 4891.43i | 0.0297800 | − | 0.295166i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3450.56 | − | 1992.18i | −0.207261 | − | 0.119662i | ||||
\(653\) | 3181.74 | − | 5510.93i | 0.190675 | − | 0.330259i | −0.754799 | − | 0.655956i | \(-0.772266\pi\) |
0.945474 | + | 0.325697i | \(0.105599\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 25641.3i | − | 1.52960i | ||||||
\(656\) | 13682.9 | − | 7899.85i | 0.814374 | − | 0.470179i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 1283.40i | − | 0.0760369i | ||||||
\(659\) | −525.717 | − | 910.568i | −0.0310759 | − | 0.0538250i | 0.850069 | − | 0.526671i | \(-0.176560\pi\) |
−0.881145 | + | 0.472846i | \(0.843227\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7031.91 | + | 4059.87i | 0.413781 | + | 0.238897i | 0.692413 | − | 0.721501i | \(-0.256548\pi\) |
−0.278632 | + | 0.960398i | \(0.589881\pi\) | |||||||
\(662\) | 5296.12 | 0.310936 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5198.21 | 0.303810 | ||||||||
\(665\) | 40553.0 | + | 23413.3i | 2.36478 | + | 1.36530i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1026.64 | − | 1778.20i | −0.0595979 | − | 0.103227i | ||||
\(668\) | 22451.9i | 1.30043i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5053.80 | + | 2917.81i | −0.291411 | + | 0.168246i | ||||
\(671\) | − | 17568.7i | − | 1.01078i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −95.1322 | + | 164.774i | −0.00544885 | + | 0.00943769i | −0.868737 | − | 0.495274i | \(-0.835068\pi\) |
0.863288 | + | 0.504711i | \(0.168401\pi\) | |||||||
\(674\) | −983.620 | − | 567.893i | −0.0562131 | − | 0.0324547i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 15410.1 | + | 3141.51i | 0.876770 | + | 0.178738i | ||||
\(677\) | −4861.93 | −0.276010 | −0.138005 | − | 0.990431i | \(-0.544069\pi\) | ||||
−0.138005 | + | 0.990431i | \(0.544069\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5708.27 | − | 9887.02i | 0.322627 | − | 0.558806i | ||||
\(680\) | −4764.67 | − | 8252.66i | −0.268701 | − | 0.465404i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4623.60 | + | 2669.44i | −0.259600 | + | 0.149880i | ||||
\(683\) | −12591.7 | + | 7269.80i | −0.705426 | + | 0.407278i | −0.809365 | − | 0.587306i | \(-0.800189\pi\) |
0.103939 | + | 0.994584i | \(0.466855\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15218.4 | + | 26359.1i | 0.848855 | + | 1.47026i | ||||
\(686\) | −2476.70 | + | 4289.77i | −0.137844 | + | 0.238753i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 18153.4 | 1.00595 | ||||||||
\(689\) | −4359.91 | − | 9683.70i | −0.241073 | − | 0.535442i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19144.8 | + | 11053.2i | 1.05398 | + | 0.608517i | 0.923762 | − | 0.382968i | \(-0.125098\pi\) |
0.130221 | + | 0.991485i | \(0.458431\pi\) | |||||||
\(692\) | −11898.0 | + | 20607.9i | −0.653604 | + | 1.13208i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4999.66i | 0.273465i | ||||||||
\(695\) | 37850.5 | − | 21853.0i | 2.06583 | − | 1.19271i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15723.4i | 0.854474i | ||||||||
\(698\) | −630.251 | − | 1091.63i | −0.0341767 | − | 0.0591958i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 14589.4 | + | 8423.20i | 0.787754 | + | 0.454810i | ||||
\(701\) | 229.971 | 0.0123907 | 0.00619535 | − | 0.999981i | \(-0.498028\pi\) | ||||
0.00619535 | + | 0.999981i | \(0.498028\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11611.1 | 0.622934 | ||||||||
\(704\) | 12349.0 | + | 7129.68i | 0.661107 | + | 0.381690i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2738.56 | − | 4743.33i | −0.145988 | − | 0.252858i | ||||
\(707\) | − | 9521.12i | − | 0.506476i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4158.85 | − | 2401.11i | 0.220294 | − | 0.127187i | −0.385792 | − | 0.922586i | \(-0.626072\pi\) |
0.606087 | + | 0.795399i | \(0.292738\pi\) | |||||||
\(710\) | 1298.66i | 0.0686446i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −830.202 | + | 1437.95i | −0.0436982 | + | 0.0756876i | ||||
\(713\) | −4069.16 | − | 2349.33i | −0.213732 | − | 0.123398i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −47503.0 | − | 4792.69i | −2.48463 | − | 0.250681i | ||||
\(716\) | −23717.6 | −1.23795 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3584.05 | − | 6207.75i | 0.186289 | − | 0.322662i | ||||
\(719\) | 5508.46 | + | 9540.94i | 0.285718 | + | 0.494878i | 0.972783 | − | 0.231718i | \(-0.0744347\pi\) |
−0.687065 | + | 0.726596i | \(0.741101\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20001.7 | + | 11548.0i | −1.03315 | + | 0.596491i | ||||
\(722\) | 11730.8 | − | 6772.81i | 0.604677 | − | 0.349110i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 272.063 | + | 471.226i | 0.0139656 | + | 0.0241892i | ||||
\(725\) | 2208.11 | − | 3824.55i | 0.113113 | − | 0.195918i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13498.2 | 0.688612 | 0.344306 | − | 0.938857i | \(-0.388114\pi\) | ||||
0.344306 | + | 0.938857i | \(0.388114\pi\) | |||||||
\(728\) | 7840.57 | − | 10886.7i | 0.399163 | − | 0.554244i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 775.950 | + | 447.995i | 0.0393414 | + | 0.0227138i | ||||
\(731\) | −9032.89 | + | 15645.4i | −0.457037 | + | 0.791610i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 17014.7i | − | 0.857368i | −0.903455 | − | 0.428684i | \(-0.858977\pi\) | ||
0.903455 | − | 0.428684i | \(-0.141023\pi\) | |||||||
\(734\) | −1341.37 | + | 774.442i | −0.0674537 | + | 0.0389444i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 8084.38i | − | 0.404883i | ||||||
\(737\) | 13536.7 | + | 23446.2i | 0.676567 | + | 1.17185i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11598.3 | + | 6696.31i | 0.577337 | + | 0.333326i | 0.760074 | − | 0.649836i | \(-0.225162\pi\) |
−0.182737 | + | 0.983162i | \(0.558496\pi\) | |||||||
\(740\) | 8744.19 | 0.434382 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4278.27 | −0.211672 | ||||||||
\(743\) | 10216.1 | + | 5898.26i | 0.504431 | + | 0.291233i | 0.730541 | − | 0.682868i | \(-0.239268\pi\) |
−0.226111 | + | 0.974102i | \(0.572601\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6170.05 | − | 10686.8i | −0.303427 | − | 0.525551i | ||||
\(746\) | − | 1716.05i | − | 0.0842214i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −18080.6 | + | 10438.8i | −0.883812 | + | 0.510269i | ||||
\(749\) | − | 12406.7i | − | 0.605250i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6225.26 | + | 10782.5i | −0.302480 | + | 0.523911i | −0.976697 | − | 0.214622i | \(-0.931148\pi\) |
0.674217 | + | 0.738534i | \(0.264481\pi\) | |||||||
\(752\) | 2619.95 | + | 1512.63i | 0.127048 | + | 0.0733510i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1347.73 | − | 970.630i | −0.0650949 | − | 0.0468810i | ||||
\(755\) | −2506.01 | −0.120799 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3514.92 | − | 6088.02i | 0.168761 | − | 0.292302i | −0.769224 | − | 0.638980i | \(-0.779357\pi\) |
0.937984 | + | 0.346677i | \(0.112690\pi\) | |||||||
\(758\) | 5351.51 | + | 9269.10i | 0.256432 | + | 0.444154i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 27397.3 | − | 15817.8i | 1.30764 | − | 0.754964i | ||||
\(761\) | 15363.8 | − | 8870.29i | 0.731849 | − | 0.422533i | −0.0872491 | − | 0.996187i | \(-0.527808\pi\) |
0.819098 | + | 0.573653i | \(0.194474\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14633.6 | + | 25346.2i | 0.694328 | + | 1.20261i | ||||
\(764\) | −14579.5 | + | 25252.5i | −0.690405 | + | 1.19582i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6124.94 | −0.288907 | ||||||||
\(767\) | 5402.12 | + | 3890.58i | 0.254314 | + | 0.183156i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27692.4 | − | 15988.2i | −1.29859 | − | 0.749741i | −0.318429 | − | 0.947947i | \(-0.603155\pi\) |
−0.980160 | + | 0.198206i | \(0.936489\pi\) | |||||||
\(770\) | −9616.95 | + | 16657.0i | −0.450092 | + | 0.779582i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 6210.51i | − | 0.289535i | ||||||
\(773\) | 1849.06 | − | 1067.56i | 0.0860364 | − | 0.0496732i | −0.456365 | − | 0.889793i | \(-0.650849\pi\) |
0.542401 | + | 0.840120i | \(0.317515\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 10105.9i | − | 0.468405i | ||||||
\(776\) | −3856.47 | − | 6679.59i | −0.178401 | − | 0.308999i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11349.2 | + | 6552.48i | 0.522994 | + | 0.301951i | ||||
\(779\) | −52198.9 | −2.40080 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6024.89 | 0.276040 | ||||||||
\(782\) | 1870.73 | + | 1080.07i | 0.0855464 | + | 0.0493902i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1795.41 | + | 3109.75i | 0.0817882 | + | 0.141661i | ||||
\(785\) | − | 5290.89i | − | 0.240560i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10136.3 | − | 5852.18i | 0.459109 | − | 0.265067i | −0.252560 | − | 0.967581i | \(-0.581273\pi\) |
0.711670 | + | 0.702514i | \(0.247939\pi\) | |||||||
\(788\) | 13512.9i | 0.610885i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2037.39 | − | 3528.87i | 0.0917559 | − | 0.158926i | ||||
\(791\) | −7071.79 | − | 4082.90i | −0.317881 | − | 0.183529i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7309.17 | − | 10148.9i | 0.327309 | − | 0.454474i | ||||
\(794\) | 3274.37 | 0.146351 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9972.46 | − | 17272.8i | 0.444051 | − | 0.769119i | ||||
\(797\) | 74.8667 | + | 129.673i | 0.00332737 | + | 0.00576317i | 0.867684 | − | 0.497116i | \(-0.165608\pi\) |
−0.864357 | + | 0.502879i | \(0.832274\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2607.31 | + | 1505.33i | −0.115444 | + | 0.0666518i | ||||
\(800\) | 15058.4 | − | 8693.94i | 0.665491 | − | 0.384222i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 229.045 | + | 396.717i | 0.0100846 | + | 0.0174670i | ||||
\(803\) | 2078.40 | − | 3599.89i | 0.0913387 | − | 0.158203i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −16927.4 | −0.741135 | ||||||||
\(806\) | −3781.49 | − | 381.524i | −0.165257 | − | 0.0166732i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5570.62 | − | 3216.20i | −0.242542 | − | 0.140031i | ||||
\(809\) | 11760.4 | − | 20369.6i | 0.511093 | − | 0.885239i | −0.488825 | − | 0.872382i | \(-0.662574\pi\) |
0.999917 | − | 0.0128565i | \(-0.00409245\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29604.8i | 1.28183i | 0.767612 | + | 0.640915i | \(0.221445\pi\) | ||||
−0.767612 | + | 0.640915i | \(0.778555\pi\) | |||||||
\(812\) | 4928.79 | − | 2845.64i | 0.213013 | − | 0.122983i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4769.25i | 0.205359i | ||||||||
\(815\) | 4305.39 | + | 7457.16i | 0.185045 | + | 0.320507i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −51939.9 | − | 29987.5i | −2.22417 | − | 1.28413i | ||||
\(818\) | −9593.44 | −0.410057 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −39310.3 | −1.67412 | ||||||||
\(821\) | 37269.2 | + | 21517.4i | 1.58429 | + | 0.914691i | 0.994223 | + | 0.107338i | \(0.0342326\pi\) |
0.590068 | + | 0.807353i | \(0.299101\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2792.47 | + | 4836.71i | 0.118274 | + | 0.204857i | 0.919084 | − | 0.394062i | \(-0.128931\pi\) |
−0.800810 | + | 0.598919i | \(0.795597\pi\) | |||||||
\(824\) | 15603.5i | 0.659675i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2322.60 | − | 1340.96i | 0.0978374 | − | 0.0564865i | ||||
\(827\) | − | 4788.13i | − | 0.201330i | −0.994920 | − | 0.100665i | \(-0.967903\pi\) | ||
0.994920 | − | 0.100665i | \(-0.0320970\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16196.1 | + | 28052.5i | −0.678546 | + | 1.17528i | 0.296873 | + | 0.954917i | \(0.404056\pi\) |
−0.975419 | + | 0.220359i | \(0.929277\pi\) | |||||||
\(830\) | −4594.44 | − | 2652.60i | −0.192139 | − | 0.110931i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4167.42 | + | 9256.17i | 0.173653 | + | 0.385697i | ||||
\(833\) | −3573.50 | −0.148637 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 24260.9 | − | 42021.1i | 1.00549 | − | 1.74156i | ||||
\(836\) | −34654.9 | − | 60024.1i | −1.43369 | − | 2.48323i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1354.90 | + | 782.254i | −0.0558525 | + | 0.0322464i | ||||
\(839\) | 11777.0 | − | 6799.43i | 0.484607 | − | 0.279788i | −0.237727 | − | 0.971332i | \(-0.576402\pi\) |
0.722335 | + | 0.691544i | \(0.243069\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11448.5 | + | 19829.4i | 0.469414 | + | 0.813048i | ||||
\(842\) | −4020.65 | + | 6963.97i | −0.164562 | + | 0.285029i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5073.82 | 0.206929 | ||||||||
\(845\) | −25447.1 | − | 22531.4i | −1.03598 | − | 0.917284i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 53551.4 | + | 30917.9i | 2.17243 | + | 1.25425i | ||||
\(848\) | 5042.41 | − | 8733.72i | 0.204195 | − | 0.353676i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4646.02i | 0.187479i | ||||||||
\(851\) | −3635.00 | + | 2098.67i | −0.146423 | + | 0.0845375i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 41037.0i | − | 1.64722i | −0.567155 | − | 0.823611i | \(-0.691956\pi\) | ||
0.567155 | − | 0.823611i | \(-0.308044\pi\) | |||||||
\(854\) | −2519.24 | − | 4363.44i | −0.100944 | − | 0.174841i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7258.93 | − | 4190.95i | −0.289843 | − | 0.167341i | ||||
\(857\) | −39959.3 | −1.59275 | −0.796374 | − | 0.604804i | \(-0.793251\pi\) | ||||
−0.796374 | + | 0.604804i | \(0.793251\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32570.5 | −1.29371 | −0.646853 | − | 0.762615i | \(-0.723915\pi\) | ||||
−0.646853 | + | 0.762615i | \(0.723915\pi\) | |||||||
\(860\) | −39115.2 | − | 22583.2i | −1.55095 | − | 0.895442i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3706.36 | + | 6419.60i | 0.146449 | + | 0.253657i | ||||
\(863\) | 16951.8i | 0.668652i | 0.942457 | + | 0.334326i | \(0.108509\pi\) | ||||
−0.942457 | + | 0.334326i | \(0.891491\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 44536.8 | − | 25713.3i | 1.75063 | − | 1.01073i | ||||
\(866\) | − | 3783.69i | − | 0.148470i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6511.84 | − | 11278.8i | 0.254639 | − | 0.441047i | ||||
\(869\) | −16371.6 | − | 9452.13i | −0.639088 | − | 0.368978i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1934.70 | + | 19175.9i | −0.0752639 | + | 0.745981i | ||||
\(872\) | 19772.7 | 0.767876 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3585.62 | + | 6210.48i | −0.138771 | + | 0.240358i | ||||
\(875\) | 1698.26 | + | 2941.47i | 0.0656134 | + | 0.113646i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −39784.5 | + | 22969.6i | −1.53184 | + | 0.884411i | −0.532568 | + | 0.846388i | \(0.678773\pi\) |
−0.999277 | + | 0.0380232i | \(0.987894\pi\) | |||||||
\(878\) | −4858.59 | + | 2805.11i | −0.186753 | + | 0.107822i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −22669.2 | − | 39264.3i | −0.868386 | − | 1.50409i | ||||
\(881\) | −18980.3 | + | 32874.8i | −0.725836 | + | 1.25718i | 0.232793 | + | 0.972526i | \(0.425213\pi\) |
−0.958629 | + | 0.284658i | \(0.908120\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −43172.9 | −1.64539 | −0.822697 | − | 0.568480i | \(-0.807532\pi\) | ||||
−0.822697 | + | 0.568480i | \(0.807532\pi\) | |||||||
\(884\) | −14787.5 | − | 1491.95i | −0.562621 | − | 0.0567642i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8785.89 | + | 5072.54i | 0.333146 | + | 0.192342i | ||||
\(887\) | 14353.1 | − | 24860.4i | 0.543327 | − | 0.941071i | −0.455383 | − | 0.890296i | \(-0.650498\pi\) |
0.998710 | − | 0.0507749i | \(-0.0161691\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 9012.78i | − | 0.340021i | ||||||
\(890\) | 1467.55 | − | 847.289i | 0.0552723 | − | 0.0319115i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 38631.4i | 1.45008i | ||||||||
\(893\) | −4997.41 | − | 8655.78i | −0.187270 | − | 0.324361i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 44390.1 | + | 25628.7i | 1.65788 | + | 0.957175i | ||||
\(896\) | 29131.9 | 1.08619 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −222.015 | −0.00825027 | ||||||||
\(899\) | −2956.70 | − | 1707.05i | −0.109690 | − | 0.0633296i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5018.08 | + | 8691.57i | 0.185545 | + | 0.321374i | ||||
\(902\) | − | 21440.6i | − | 0.791456i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4777.65 | + | 2758.38i | −0.175777 | + | 0.101485i | ||||
\(905\) | − | 1175.93i | − | 0.0431927i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11178.0 | + | 19360.9i | −0.409218 | + | 0.708786i | −0.994802 | − | 0.101826i | \(-0.967532\pi\) |
0.585585 | + | 0.810611i | \(0.300865\pi\) | |||||||
\(908\) | 19725.1 | + | 11388.3i | 0.720926 | + | 0.416227i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −12485.3 | + | 5621.28i | −0.454817 | + | 0.204773i | ||||
\(911\) | −6953.80 | −0.252897 | −0.126449 | − | 0.991973i | \(-0.540358\pi\) | ||||
−0.126449 | + | 0.991973i | \(0.540358\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12306.3 | + | 21315.1i | −0.446088 | + | 0.772647i | ||||
\(914\) | 5069.48 | + | 8780.60i | 0.183461 | + | 0.317764i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −12609.5 | + | 7280.12i | −0.454837 | + | 0.262600i | ||||
\(917\) | −29545.0 | + | 17057.8i | −1.06397 | + | 0.614285i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20312.6 | − | 35182.4i | −0.729108 | − | 1.26285i | −0.957261 | − | 0.289227i | \(-0.906602\pi\) |
0.228153 | − | 0.973625i | \(-0.426731\pi\) | |||||||
\(920\) | −5718.02 | + | 9903.91i | −0.204911 | + | 0.354915i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −251.143 | −0.00897068 | ||||||||
\(923\) | 3480.39 | + | 2506.56i | 0.124115 | + | 0.0893871i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7818.17 | − | 4513.82i | −0.277902 | − | 0.160447i | ||||
\(926\) | 5311.22 | − | 9199.30i | 0.188485 | − | 0.326466i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 5874.20i | − | 0.207791i | ||||||
\(929\) | −37077.8 | + | 21406.9i | −1.30946 | + | 0.756014i | −0.982005 | − | 0.188854i | \(-0.939523\pi\) |
−0.327450 | + | 0.944869i | \(0.606189\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 11863.3i | − | 0.417621i | ||||||
\(932\) | 10001.1 | + | 17322.4i | 0.351499 | + | 0.608814i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 717.338 | + | 414.155i | 0.0251306 | + | 0.0145092i | ||||
\(935\) | 45119.7 | 1.57815 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43484.1 | 1.51608 | 0.758038 | − | 0.652210i | \(-0.226158\pi\) | ||||
0.758038 | + | 0.652210i | \(0.226158\pi\) | |||||||
\(938\) | 6724.06 | + | 3882.14i | 0.234060 | + | 0.135135i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3763.49 | − | 6518.55i | −0.130587 | − | 0.226183i | ||||
\(941\) | 7108.58i | 0.246263i | 0.992390 | + | 0.123131i | \(0.0392936\pi\) | ||||
−0.992390 | + | 0.123131i | \(0.960706\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16341.5 | − | 9434.75i | 0.564318 | − | 0.325809i | ||||
\(944\) | 6321.85i | 0.217965i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12317.3 | − | 21334.2i | 0.423330 | − | 0.733229i | ||||
\(947\) | −1679.22 | − | 969.496i | −0.0576211 | − | 0.0332676i | 0.470913 | − | 0.882180i | \(-0.343925\pi\) |
−0.528534 | + | 0.848912i | \(0.677258\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2698.30 | − | 1214.86i | 0.0922976 | − | 0.0415553i | ||||
\(950\) | −15423.9 | −0.526756 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −6339.39 | + | 10980.1i | −0.215820 | + | 0.373811i | ||||
\(953\) | 23903.3 | + | 41401.8i | 0.812492 | + | 1.40728i | 0.911115 | + | 0.412153i | \(0.135223\pi\) |
−0.0986228 | + | 0.995125i | \(0.531444\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 54574.4 | − | 31508.5i | 1.84920 | − | 1.06764i | ||||
\(956\) | 34058.2 | − | 19663.5i | 1.15222 | − | 0.665234i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 5535.78 | + | 9588.26i | 0.186694 | + | 0.323364i | ||||
\(959\) | 20248.1 | − | 35070.7i | 0.681797 | − | 1.18091i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21978.3 | 0.737750 | ||||||||
\(962\) | −1984.17 | + | 2755.04i | −0.0664991 | + | 0.0923349i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 25177.3 | + | 14536.1i | 0.841190 | + | 0.485662i | ||||
\(965\) | −6710.92 | + | 11623.7i | −0.223867 | + | 0.387750i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 2832.71i | − | 0.0942025i | −0.998890 | − | 0.0471013i | \(-0.985002\pi\) | ||
0.998890 | − | 0.0471013i | \(-0.0149983\pi\) | |||||||
\(968\) | 36178.9 | − | 20887.9i | 1.20128 | − | 0.693557i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 7871.68i | 0.260561i | ||||||||
\(971\) | −20638.1 | − | 35746.3i | −0.682090 | − | 1.18142i | −0.974342 | − | 0.225074i | \(-0.927738\pi\) |
0.292251 | − | 0.956342i | \(-0.405596\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −50360.0 | − | 29075.3i | −1.65927 | − | 0.957978i | ||||
\(974\) | 10542.9 | 0.346835 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11876.8 | 0.389515 | ||||||||
\(977\) | 3705.63 | + | 2139.45i | 0.121344 | + | 0.0700583i | 0.559444 | − | 0.828868i | \(-0.311015\pi\) |
−0.438099 | + | 0.898927i | \(0.644348\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3930.85 | − | 6808.43i | −0.128325 | − | 0.222266i | ||||
\(980\) | − | 8934.12i | − | 0.291214i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −12476.5 | + | 7203.29i | −0.405438 | + | 0.234080i | ||||
\(983\) | 22652.9i | 0.735011i | 0.930021 | + | 0.367505i | \(0.119788\pi\) | ||||
−0.930021 | + | 0.367505i | \(0.880212\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14601.7 | − | 25290.9i | 0.472333 | − | 0.818105i | ||||
\(986\) | 1359.30 | + | 784.790i | 0.0439034 | + | 0.0253477i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4952.98 | − | 49091.7i | 0.159489 | − | 1.58078i | ||||
\(989\) | 21680.5 | 0.697068 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11030.1 | + | 19104.7i | −0.353565 | + | 0.612393i | −0.986871 | − | 0.161508i | \(-0.948364\pi\) |
0.633306 | + | 0.773901i | \(0.281697\pi\) | |||||||
\(992\) | −6721.15 | − | 11641.4i | −0.215118 | − | 0.372594i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1496.37 | − | 863.929i | 0.0477484 | − | 0.0275676i | ||||
\(995\) | −37329.1 | + | 21552.0i | −1.18936 | + | 0.686677i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17817.8 | − | 30861.3i | −0.565992 | − | 0.980327i | −0.996957 | − | 0.0779583i | \(-0.975160\pi\) |
0.430964 | − | 0.902369i | \(-0.358173\pi\) | |||||||
\(998\) | −4137.26 | + | 7165.95i | −0.131225 | + | 0.227289i | ||||
\(999\) | 0 | 0 |
(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 | 117.4.q.e.82.3 | 10 | ||
3.2 | odd | 2 | 39.4.j.c.4.3 | ✓ | 10 | ||
12.11 | even | 2 | 624.4.bv.h.433.2 | 10 | |||
13.6 | odd | 12 | 1521.4.a.bk.1.5 | 10 | |||
13.7 | odd | 12 | 1521.4.a.bk.1.6 | 10 | |||
13.10 | even | 6 | inner | 117.4.q.e.10.3 | 10 | ||
39.17 | odd | 6 | 507.4.b.i.337.5 | 10 | |||
39.20 | even | 12 | 507.4.a.r.1.5 | 10 | |||
39.23 | odd | 6 | 39.4.j.c.10.3 | yes | 10 | ||
39.32 | even | 12 | 507.4.a.r.1.6 | 10 | |||
39.35 | odd | 6 | 507.4.b.i.337.6 | 10 | |||
156.23 | even | 6 | 624.4.bv.h.49.4 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.j.c.4.3 | ✓ | 10 | 3.2 | odd | 2 | ||
39.4.j.c.10.3 | yes | 10 | 39.23 | odd | 6 | ||
117.4.q.e.10.3 | 10 | 13.10 | even | 6 | inner | ||
117.4.q.e.82.3 | 10 | 1.1 | even | 1 | trivial | ||
507.4.a.r.1.5 | 10 | 39.20 | even | 12 | |||
507.4.a.r.1.6 | 10 | 39.32 | even | 12 | |||
507.4.b.i.337.5 | 10 | 39.17 | odd | 6 | |||
507.4.b.i.337.6 | 10 | 39.35 | odd | 6 | |||
624.4.bv.h.49.4 | 10 | 156.23 | even | 6 | |||
624.4.bv.h.433.2 | 10 | 12.11 | even | 2 | |||
1521.4.a.bk.1.5 | 10 | 13.6 | odd | 12 | |||
1521.4.a.bk.1.6 | 10 | 13.7 | odd | 12 |