Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,3,Mod(129,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("448.129");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.s (of order \(6\), degree \(2\), not 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: | \(12.2071158433\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 26 x^{14} - 16 x^{13} + 469 x^{12} + 144 x^{11} - 4526 x^{10} + 4440 x^{9} + 32608 x^{8} - 33728 x^{7} - 49760 x^{6} + 203528 x^{5} + 27401 x^{4} - 156928 x^{3} + \cdots + 208849 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{20}\cdot 7 \) |
Twist minimal: | no (minimal twist has level 224) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 129.5 | ||
Root | \(0.869658 + 0.314400i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 448.129 |
Dual form | 448.3.s.h.257.5 |
$q$-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 \(\left(\mathbb{Z}/448\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 0.729881 | + | 0.421397i | 0.243294 | + | 0.140466i | 0.616690 | − | 0.787206i | \(-0.288473\pi\) |
−0.373396 | + | 0.927672i | \(0.621807\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.21685 | − | 0.702550i | 0.243371 | − | 0.140510i | −0.373354 | − | 0.927689i | \(-0.621792\pi\) |
0.616725 | + | 0.787179i | \(0.288459\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.56553 | + | 6.82269i | 0.223647 | + | 0.974670i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.14485 | − | 7.17909i | −0.460539 | − | 0.797677i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 7.44562 | − | 12.8962i | 0.676874 | − | 1.17238i | −0.299043 | − | 0.954240i | \(-0.596667\pi\) |
0.975917 | − | 0.218141i | \(-0.0699994\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.67477i | − | 0.205752i | −0.994694 | − | 0.102876i | \(-0.967196\pi\) | ||
0.994694 | − | 0.102876i | \(-0.0328045\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.18421 | 0.0789474 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 11.7354 | + | 6.77544i | 0.690318 | + | 0.398555i | 0.803731 | − | 0.594993i | \(-0.202845\pi\) |
−0.113413 | + | 0.993548i | \(0.536178\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 25.2564 | − | 14.5818i | 1.32928 | − | 0.767462i | 0.344095 | − | 0.938935i | \(-0.388186\pi\) |
0.985189 | + | 0.171473i | \(0.0548526\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.73241 | + | 5.63947i | −0.0824958 | + | 0.268546i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 11.4367 | + | 19.8089i | 0.497247 | + | 0.861257i | 0.999995 | − | 0.00317621i | \(-0.00101102\pi\) |
−0.502748 | + | 0.864433i | \(0.667678\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −11.5128 | + | 19.9408i | −0.460514 | + | 0.797633i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 14.5717i | − | 0.539691i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.76543 | 0.129843 | 0.0649213 | − | 0.997890i | \(-0.479320\pi\) | ||||
0.0649213 | + | 0.997890i | \(0.479320\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 11.4937 | + | 6.63592i | 0.370766 | + | 0.214062i | 0.673793 | − | 0.738920i | \(-0.264664\pi\) |
−0.303027 | + | 0.952982i | \(0.597997\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 10.8688 | − | 6.27513i | 0.329359 | − | 0.190155i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.69830 | + | 7.20235i | 0.191380 | + | 0.205781i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.32272 | + | 2.29102i | 0.0357491 | + | 0.0619193i | 0.883346 | − | 0.468721i | \(-0.155285\pi\) |
−0.847597 | + | 0.530640i | \(0.821952\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.12714 | − | 1.95227i | 0.0289011 | − | 0.0500581i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 45.2712i | − | 1.10417i | −0.833786 | − | 0.552087i | \(-0.813832\pi\) | ||
0.833786 | − | 0.552087i | \(-0.186168\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 51.5858 | 1.19967 | 0.599834 | − | 0.800124i | \(-0.295233\pi\) | ||||
0.599834 | + | 0.800124i | \(0.295233\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −10.0873 | − | 5.82393i | −0.224163 | − | 0.129421i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 58.1281 | − | 33.5603i | 1.23677 | − | 0.714049i | 0.268336 | − | 0.963325i | \(-0.413526\pi\) |
0.968432 | + | 0.249276i | \(0.0801928\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −44.0982 | + | 21.3623i | −0.899964 | + | 0.435964i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.71030 | + | 9.89054i | 0.111967 | + | 0.193932i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 19.9616 | − | 34.5744i | 0.376633 | − | 0.652348i | −0.613937 | − | 0.789355i | \(-0.710415\pi\) |
0.990570 | + | 0.137007i | \(0.0437484\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 20.9237i | − | 0.380431i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 24.5789 | 0.431209 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.0804 | + | 6.39728i | 0.187804 | + | 0.108429i | 0.590954 | − | 0.806705i | \(-0.298751\pi\) |
−0.403150 | + | 0.915134i | \(0.632085\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −67.4084 | + | 38.9182i | −1.10506 | + | 0.638004i | −0.937544 | − | 0.347866i | \(-0.886906\pi\) |
−0.167511 | + | 0.985870i | \(0.553573\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 42.4918 | − | 39.5181i | 0.674473 | − | 0.627271i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.87916 | − | 3.25480i | −0.0289102 | − | 0.0500739i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −22.9199 | + | 39.6985i | −0.342089 | + | 0.592515i | −0.984820 | − | 0.173576i | \(-0.944468\pi\) |
0.642732 | + | 0.766091i | \(0.277801\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 19.2775i | 0.279385i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 40.6812 | 0.572975 | 0.286487 | − | 0.958084i | \(-0.407512\pi\) | ||||
0.286487 | + | 0.958084i | \(0.407512\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 55.6834 | + | 32.1488i | 0.762786 | + | 0.440395i | 0.830295 | − | 0.557324i | \(-0.188172\pi\) |
−0.0675092 | + | 0.997719i | \(0.521505\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −16.8060 | + | 9.70296i | −0.224080 | + | 0.129373i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 99.6431 | + | 30.6098i | 1.29407 | + | 0.397530i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −40.2603 | − | 69.7329i | −0.509624 | − | 0.882695i | −0.999938 | − | 0.0111488i | \(-0.996451\pi\) |
0.490314 | − | 0.871546i | \(-0.336882\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −31.1632 | + | 53.9762i | −0.384731 | + | 0.666373i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 121.864i | 1.46824i | 0.679021 | + | 0.734118i | \(0.262404\pi\) | ||||
−0.679021 | + | 0.734118i | \(0.737596\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 19.0403 | 0.224004 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.74832 | + | 1.58674i | 0.0315899 | + | 0.0182384i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −39.7614 | + | 22.9562i | −0.446757 | + | 0.257935i | −0.706460 | − | 0.707753i | \(-0.749709\pi\) |
0.259703 | + | 0.965689i | \(0.416375\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 18.2492 | − | 4.18744i | 0.200540 | − | 0.0460158i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.59271 | + | 9.68687i | 0.0601367 | + | 0.104160i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 20.4889 | − | 35.4878i | 0.215672 | − | 0.373555i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 134.268i | − | 1.38421i | −0.721798 | − | 0.692104i | \(-0.756684\pi\) | ||
0.721798 | − | 0.692104i | \(-0.243316\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −123.444 | −1.24691 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −170.810 | − | 98.6169i | −1.69118 | − | 0.976405i | −0.953565 | − | 0.301188i | \(-0.902617\pi\) |
−0.737619 | − | 0.675218i | \(-0.764050\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −121.371 | + | 70.0736i | −1.17836 | + | 0.680326i | −0.955635 | − | 0.294555i | \(-0.904829\pi\) |
−0.222725 | + | 0.974881i | \(0.571495\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.85392 | + | 8.07950i | 0.0176564 | + | 0.0769477i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −53.0099 | − | 91.8159i | −0.495420 | − | 0.858093i | 0.504566 | − | 0.863373i | \(-0.331652\pi\) |
−0.999986 | + | 0.00528051i | \(0.998319\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 71.3762 | − | 123.627i | 0.654828 | − | 1.13419i | −0.327109 | − | 0.944986i | \(-0.606075\pi\) |
0.981937 | − | 0.189208i | \(-0.0605921\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.22956i | 0.0200861i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 108.519 | 0.960344 | 0.480172 | − | 0.877174i | \(-0.340574\pi\) | ||||
0.480172 | + | 0.877174i | \(0.340574\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 27.8335 | + | 16.0697i | 0.242030 | + | 0.139736i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −19.2024 | + | 11.0865i | −0.164123 | + | 0.0947567i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −27.8546 | + | 90.6742i | −0.234072 | + | 0.761968i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −50.3745 | − | 87.2512i | −0.416318 | − | 0.721084i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 19.0771 | − | 33.0426i | 0.155099 | − | 0.268639i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 67.4809i | 0.539847i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −139.789 | −1.10070 | −0.550351 | − | 0.834934i | \(-0.685506\pi\) | ||||
−0.550351 | + | 0.834934i | \(0.685506\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 37.6515 | + | 21.7381i | 0.291872 | + | 0.168512i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −82.2943 | + | 47.5126i | −0.628200 | + | 0.362692i | −0.780055 | − | 0.625711i | \(-0.784809\pi\) |
0.151854 | + | 0.988403i | \(0.451476\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 139.027 | + | 149.488i | 1.04531 | + | 1.12397i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −10.2373 | − | 17.7316i | −0.0758320 | − | 0.131345i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −76.7845 | + | 132.995i | −0.560471 | + | 0.970764i | 0.436984 | + | 0.899469i | \(0.356046\pi\) |
−0.997455 | + | 0.0712949i | \(0.977287\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 217.529i | − | 1.56496i | −0.622676 | − | 0.782480i | \(-0.713954\pi\) | ||
0.622676 | − | 0.782480i | \(-0.286046\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 56.5689 | 0.401198 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −34.4944 | − | 19.9153i | −0.241219 | − | 0.139268i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.58198 | − | 2.64541i | 0.0315998 | − | 0.0182442i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −41.1885 | − | 2.99096i | −0.280194 | − | 0.0203467i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 32.0451 | + | 55.5037i | 0.215068 | + | 0.372508i | 0.953294 | − | 0.302045i | \(-0.0976694\pi\) |
−0.738226 | + | 0.674554i | \(0.764336\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −136.023 | + | 235.598i | −0.900813 | + | 1.56025i | −0.0743729 | + | 0.997230i | \(0.523696\pi\) |
−0.826440 | + | 0.563024i | \(0.809638\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 112.333i | − | 0.734201i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 18.6483 | 0.120311 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −187.295 | − | 108.135i | −1.19296 | − | 0.688757i | −0.233984 | − | 0.972240i | \(-0.575176\pi\) |
−0.958977 | + | 0.283484i | \(0.908510\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 29.1391 | − | 16.8235i | 0.183265 | − | 0.105808i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −117.246 | + | 109.040i | −0.728233 | + | 0.677269i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 27.3465 | + | 47.3655i | 0.167770 | + | 0.290586i | 0.937635 | − | 0.347620i | \(-0.113010\pi\) |
−0.769866 | + | 0.638206i | \(0.779677\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.81718 | − | 15.2718i | 0.0534375 | − | 0.0925564i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 248.098i | 1.48562i | 0.669504 | + | 0.742809i | \(0.266507\pi\) | ||||
−0.669504 | + | 0.742809i | \(0.733493\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 161.846 | 0.957666 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −209.368 | − | 120.879i | −1.22437 | − | 0.706892i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −224.883 | + | 129.836i | −1.29990 | + | 0.750499i | −0.980387 | − | 0.197082i | \(-0.936853\pi\) |
−0.319515 | + | 0.947581i | \(0.603520\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −154.074 | − | 47.3306i | −0.880422 | − | 0.270461i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.39159 | + | 9.33851i | 0.0304610 | + | 0.0527600i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −69.0883 | + | 119.664i | −0.385968 | + | 0.668516i | −0.991903 | − | 0.126998i | \(-0.959466\pi\) |
0.605935 | + | 0.795514i | \(0.292799\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 114.497i | − | 0.632579i | −0.948663 | − | 0.316290i | \(-0.897563\pi\) | ||
0.948663 | − | 0.316290i | \(-0.102437\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −65.6001 | −0.358471 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.21911 | + | 1.85855i | 0.0174006 | + | 0.0100462i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 174.755 | − | 100.895i | 0.934517 | − | 0.539544i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 99.4180 | − | 22.8124i | 0.526021 | − | 0.120700i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 76.2145 | + | 132.007i | 0.399029 | + | 0.691138i | 0.993606 | − | 0.112900i | \(-0.0360141\pi\) |
−0.594578 | + | 0.804038i | \(0.702681\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −121.156 | + | 209.848i | −0.627749 | + | 1.08729i | 0.360253 | + | 0.932855i | \(0.382690\pi\) |
−0.988002 | + | 0.154439i | \(0.950643\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 3.16750i | − | 0.0162436i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 197.518 | 1.00263 | 0.501314 | − | 0.865265i | \(-0.332850\pi\) | ||||
0.501314 | + | 0.865265i | \(0.332850\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −142.172 | − | 82.0833i | −0.714435 | − | 0.412479i | 0.0982663 | − | 0.995160i | \(-0.468670\pi\) |
−0.812701 | + | 0.582681i | \(0.802004\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −33.4577 | + | 19.3168i | −0.166456 | + | 0.0961035i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.89490 | + | 25.6904i | 0.0290389 | + | 0.126554i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −31.8053 | − | 55.0883i | −0.155148 | − | 0.268724i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 94.8066 | − | 164.210i | 0.458003 | − | 0.793284i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 434.282i | − | 2.07790i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −53.1445 | −0.251870 | −0.125935 | − | 0.992039i | \(-0.540193\pi\) | ||||
−0.125935 | + | 0.992039i | \(0.540193\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 29.6925 | + | 17.1429i | 0.139401 | + | 0.0804833i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 62.7723 | − | 36.2416i | 0.291964 | − | 0.168565i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −27.2810 | + | 88.8070i | −0.125719 | + | 0.409249i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 27.0948 | + | 46.9296i | 0.123721 | + | 0.214291i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.1228 | − | 31.3896i | 0.0820035 | − | 0.142034i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 310.755i | − | 1.39352i | −0.717303 | − | 0.696761i | \(-0.754624\pi\) | ||
0.717303 | − | 0.696761i | \(-0.245376\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 190.876 | 0.848338 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 43.2131 | + | 24.9491i | 0.190366 | + | 0.109908i | 0.592154 | − | 0.805825i | \(-0.298278\pi\) |
−0.401788 | + | 0.915733i | \(0.631611\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −182.833 | + | 105.559i | −0.798398 | + | 0.460955i | −0.842911 | − | 0.538054i | \(-0.819160\pi\) |
0.0445127 | + | 0.999009i | \(0.485826\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 59.8287 | + | 64.3308i | 0.258999 | + | 0.278488i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −37.7274 | − | 65.3457i | −0.161920 | − | 0.280454i | 0.773637 | − | 0.633629i | \(-0.218435\pi\) |
−0.935557 | + | 0.353175i | \(0.885102\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 47.1556 | − | 81.6759i | 0.200662 | − | 0.347557i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 67.8623i | − | 0.286339i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 310.396 | 1.29873 | 0.649365 | − | 0.760477i | \(-0.275035\pi\) | ||||
0.649365 | + | 0.760477i | \(0.275035\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 93.7200 | + | 54.1093i | 0.388880 | + | 0.224520i | 0.681675 | − | 0.731656i | \(-0.261252\pi\) |
−0.292795 | + | 0.956175i | \(0.594585\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −159.066 | + | 91.8366i | −0.654591 | + | 0.377929i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −38.6530 | + | 56.9759i | −0.157767 | + | 0.232555i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −39.0030 | − | 67.5551i | −0.157907 | − | 0.273502i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −51.3530 | + | 88.9460i | −0.206237 | + | 0.357213i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 302.023i | 1.20328i | 0.798768 | + | 0.601639i | \(0.205485\pi\) | ||||
−0.798768 | + | 0.601639i | \(0.794515\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 340.613 | 1.34629 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 13.8972 | + | 8.02355i | 0.0544988 | + | 0.0314649i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −89.8068 | + | 51.8500i | −0.349443 | + | 0.201751i | −0.664440 | − | 0.747342i | \(-0.731330\pi\) |
0.314997 | + | 0.949093i | \(0.397996\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.5601 | + | 12.6112i | −0.0523557 | + | 0.0486917i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −15.6072 | − | 27.0324i | −0.0597975 | − | 0.103572i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 128.972 | − | 223.386i | 0.490387 | − | 0.849375i | −0.509552 | − | 0.860440i | \(-0.670189\pi\) |
0.999939 | + | 0.0110651i | \(0.00352220\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 56.0960i | − | 0.211683i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −38.6948 | −0.144924 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −140.523 | − | 81.1310i | −0.522390 | − | 0.301602i | 0.215522 | − | 0.976499i | \(-0.430855\pi\) |
−0.737912 | + | 0.674897i | \(0.764188\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 54.3429 | − | 31.3749i | 0.200527 | − | 0.115775i | −0.396374 | − | 0.918089i | \(-0.629732\pi\) |
0.596901 | + | 0.802315i | \(0.296398\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 15.0843 | + | 4.63381i | 0.0552538 | + | 0.0169737i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 171.441 | + | 296.944i | 0.623420 | + | 1.07980i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −128.576 | + | 222.701i | −0.464175 | + | 0.803974i | −0.999164 | − | 0.0408848i | \(-0.986982\pi\) |
0.534989 | + | 0.844859i | \(0.320316\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 110.019i | − | 0.394335i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 230.243 | 0.819369 | 0.409685 | − | 0.912227i | \(-0.365639\pi\) | ||||
0.409685 | + | 0.912227i | \(0.365639\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 354.637 | + | 204.750i | 1.25313 | + | 0.723497i | 0.971730 | − | 0.236093i | \(-0.0758671\pi\) |
0.281402 | + | 0.959590i | \(0.409200\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 29.9089 | − | 17.2679i | 0.104943 | − | 0.0605891i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 308.871 | − | 70.8733i | 1.07621 | − | 0.246945i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −52.6868 | − | 91.2562i | −0.182307 | − | 0.315765i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 56.5803 | − | 97.9999i | 0.194434 | − | 0.336769i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 438.106i | − | 1.49524i | −0.664126 | − | 0.747621i | \(-0.731196\pi\) | ||
0.664126 | − | 0.747621i | \(-0.268804\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.9776 | 0.0609412 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −187.919 | − | 108.495i | −0.632724 | − | 0.365303i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 52.9843 | − | 30.5905i | 0.177205 | − | 0.102309i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 80.7590 | + | 351.954i | 0.268302 | + | 1.16928i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −83.1138 | − | 143.957i | −0.274303 | − | 0.475107i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −54.6840 | + | 94.7155i | −0.179292 | + | 0.310543i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 136.514i | − | 0.444672i | −0.974970 | − | 0.222336i | \(-0.928632\pi\) | ||
0.974970 | − | 0.222336i | \(-0.0713682\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −118.115 | −0.382250 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 503.092 | + | 290.461i | 1.61766 | + | 0.933957i | 0.987523 | + | 0.157473i | \(0.0503348\pi\) |
0.630138 | + | 0.776484i | \(0.282999\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −162.118 | + | 93.5987i | −0.517948 | + | 0.299037i | −0.736095 | − | 0.676879i | \(-0.763332\pi\) |
0.218147 | + | 0.975916i | \(0.429999\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 23.9428 | − | 77.9403i | 0.0760090 | − | 0.247430i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 82.9440 | + | 143.663i | 0.261653 | + | 0.453196i | 0.966681 | − | 0.255983i | \(-0.0823991\pi\) |
−0.705028 | + | 0.709179i | \(0.749066\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 28.0360 | − | 48.5597i | 0.0878871 | − | 0.152225i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 89.3530i | − | 0.278358i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 395.192 | 1.22350 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 53.3372 | + | 30.7943i | 0.164115 | + | 0.0947516i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 104.192 | − | 60.1555i | 0.318631 | − | 0.183962i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 319.973 | + | 344.051i | 0.972562 | + | 1.04575i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −209.099 | − | 362.170i | −0.631719 | − | 1.09417i | −0.987200 | − | 0.159486i | \(-0.949016\pi\) |
0.355481 | − | 0.934683i | \(-0.384317\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.9649 | − | 18.9918i | 0.0329277 | − | 0.0570325i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 64.4096i | 0.192268i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 104.000 | 0.308607 | 0.154303 | − | 0.988024i | \(-0.450687\pi\) | ||||
0.154303 | + | 0.988024i | \(0.450687\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 79.2059 | + | 45.7295i | 0.233646 | + | 0.134895i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 171.156 | − | 98.8170i | 0.501924 | − | 0.289786i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −214.785 | − | 267.425i | −0.626196 | − | 0.779666i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 13.5434 | + | 23.4579i | 0.0392563 | + | 0.0679940i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 48.9796 | − | 84.8352i | 0.141152 | − | 0.244482i | −0.786779 | − | 0.617235i | \(-0.788253\pi\) |
0.927931 | + | 0.372753i | \(0.121586\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 248.606i | − | 0.712339i | −0.934421 | − | 0.356169i | \(-0.884083\pi\) | ||
0.934421 | − | 0.356169i | \(-0.115917\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −38.9759 | −0.111042 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −113.804 | − | 65.7047i | −0.322390 | − | 0.186132i | 0.330067 | − | 0.943957i | \(-0.392929\pi\) |
−0.652458 | + | 0.757825i | \(0.726262\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 49.5030 | − | 28.5806i | 0.139445 | − | 0.0805087i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −58.5404 | + | 54.4436i | −0.163979 | + | 0.152503i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 176.634 | + | 305.939i | 0.492016 | + | 0.852196i | 0.999958 | − | 0.00919491i | \(-0.00292687\pi\) |
−0.507942 | + | 0.861391i | \(0.669594\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 244.757 | − | 423.931i | 0.677996 | − | 1.17432i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 84.9107i | − | 0.233914i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 90.3446 | 0.247519 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 105.306 | + | 60.7983i | 0.286937 | + | 0.165663i | 0.636560 | − | 0.771228i | \(-0.280357\pi\) |
−0.349623 | + | 0.936891i | \(0.613690\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −325.006 | + | 187.642i | −0.880774 | + | 0.508515i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 267.141 | + | 82.0642i | 0.720057 | + | 0.221197i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −245.458 | − | 425.145i | −0.658063 | − | 1.13980i | −0.981116 | − | 0.193418i | \(-0.938043\pi\) |
0.323053 | − | 0.946381i | \(-0.395291\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −28.4363 | + | 49.2531i | −0.0758301 | + | 0.131342i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 10.0717i | − | 0.0267153i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 325.094 | 0.857768 | 0.428884 | − | 0.903360i | \(-0.358907\pi\) | ||||
0.428884 | + | 0.903360i | \(0.358907\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −102.029 | − | 58.9067i | −0.267794 | − | 0.154611i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −385.028 | + | 222.296i | −1.00529 | + | 0.580407i | −0.909810 | − | 0.415024i | \(-0.863773\pi\) |
−0.0954837 | + | 0.995431i | \(0.530440\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 142.756 | − | 32.7567i | 0.370794 | − | 0.0850822i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −213.815 | − | 370.339i | −0.552494 | − | 0.956948i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −209.219 | + | 362.379i | −0.537839 | + | 0.931565i | 0.461181 | + | 0.887306i | \(0.347426\pi\) |
−0.999020 | + | 0.0442585i | \(0.985907\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 309.954i | 0.792721i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −80.0867 | −0.203783 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −97.9817 | − | 56.5698i | −0.248055 | − | 0.143215i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −378.814 | + | 218.708i | −0.954192 | + | 0.550903i | −0.894381 | − | 0.447307i | \(-0.852383\pi\) |
−0.0598112 | + | 0.998210i | \(0.519050\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 38.4790 | + | 167.694i | 0.0964385 | + | 0.420286i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 45.2362 | + | 78.3513i | 0.112808 | + | 0.195390i | 0.916902 | − | 0.399113i | \(-0.130682\pi\) |
−0.804093 | + | 0.594503i | \(0.797349\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.7496 | − | 30.7432i | 0.0440436 | − | 0.0762858i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 87.5748i | 0.216234i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 39.3938 | 0.0967907 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −607.126 | − | 350.524i | −1.48442 | − | 0.857028i | −0.484573 | − | 0.874751i | \(-0.661025\pi\) |
−0.999843 | + | 0.0177233i | \(0.994358\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −112.087 | + | 64.7136i | −0.272718 | + | 0.157454i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −26.3000 | + | 85.6134i | −0.0636803 | + | 0.207296i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 85.6153 | + | 148.290i | 0.206302 | + | 0.357326i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 91.6663 | − | 158.771i | 0.219823 | − | 0.380745i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 374.252i | − | 0.893202i | −0.894733 | − | 0.446601i | \(-0.852634\pi\) | ||
0.894733 | − | 0.446601i | \(-0.147366\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 733.801 | 1.74299 | 0.871497 | − | 0.490400i | \(-0.163149\pi\) | ||||
0.871497 | + | 0.490400i | \(0.163149\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −481.865 | − | 278.205i | −1.13916 | − | 0.657694i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −270.216 | + | 156.009i | −0.635802 | + | 0.367081i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −371.057 | − | 398.979i | −0.868986 | − | 0.934376i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −16.7845 | − | 29.0717i | −0.0391248 | − | 0.0677662i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −416.503 | + | 721.405i | −0.966365 | + | 1.67379i | −0.260462 | + | 0.965484i | \(0.583875\pi\) |
−0.705903 | + | 0.708308i | \(0.749459\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 414.085i | 0.956316i | 0.878274 | + | 0.478158i | \(0.158695\pi\) | ||||
−0.878274 | + | 0.478158i | \(0.841305\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.45907 | 0.0102507 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 577.698 | + | 333.534i | 1.32196 | + | 0.763236i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 61.9802 | − | 35.7843i | 0.141185 | − | 0.0815132i | −0.427744 | − | 0.903900i | \(-0.640691\pi\) |
0.568929 | + | 0.822387i | \(0.307358\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 336.142 | + | 228.042i | 0.762227 | + | 0.517102i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 414.628 | + | 718.157i | 0.935956 | + | 1.62112i | 0.772921 | + | 0.634503i | \(0.218795\pi\) |
0.163035 | + | 0.986620i | \(0.447872\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −32.2558 | + | 55.8687i | −0.0724850 | + | 0.125548i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 54.0149i | 0.120839i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 247.153 | 0.550452 | 0.275226 | − | 0.961380i | \(-0.411247\pi\) | ||||
0.275226 | + | 0.961380i | \(0.411247\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −583.825 | − | 337.072i | −1.29451 | − | 0.747388i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −198.561 | + | 114.639i | −0.438325 | + | 0.253067i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 19.2646 | − | 17.9164i | 0.0423399 | − | 0.0393768i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 240.746 | + | 416.984i | 0.526796 | + | 0.912437i | 0.999512 | + | 0.0312226i | \(0.00994009\pi\) |
−0.472717 | + | 0.881214i | \(0.656727\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 98.7294 | − | 171.004i | 0.215097 | − | 0.372559i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 256.190i | − | 0.555727i | −0.960621 | − | 0.277863i | \(-0.910374\pi\) | ||
0.960621 | − | 0.277863i | \(-0.0896263\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −142.004 | −0.306705 | −0.153353 | − | 0.988172i | \(-0.549007\pi\) | ||||
−0.153353 | + | 0.988172i | \(0.549007\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13.6110 | + | 7.85832i | 0.0292710 | + | 0.0168996i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 375.153 | − | 216.594i | 0.803324 | − | 0.463800i | −0.0413078 | − | 0.999146i | \(-0.513152\pi\) |
0.844632 | + | 0.535347i | \(0.179819\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −306.732 | − | 94.2265i | −0.654014 | − | 0.200909i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −91.1354 | − | 157.851i | −0.193493 | − | 0.335140i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 384.088 | − | 665.260i | 0.812025 | − | 1.40647i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 671.511i | 1.41371i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −330.950 | −0.693816 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −227.894 | − | 131.575i | −0.475770 | − | 0.274686i | 0.242882 | − | 0.970056i | \(-0.421907\pi\) |
−0.718652 | + | 0.695370i | \(0.755241\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.12795 | − | 3.53797i | 0.0127400 | − | 0.00735545i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −131.525 | + | 30.1796i | −0.272308 | + | 0.0624836i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −94.3302 | − | 163.385i | −0.194495 | − | 0.336876i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 338.504 | − | 586.307i | 0.695081 | − | 1.20392i | −0.275072 | − | 0.961424i | \(-0.588702\pi\) |
0.970153 | − | 0.242492i | \(-0.0779649\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 46.0950i | 0.0942637i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −807.748 | −1.64511 | −0.822554 | − | 0.568686i | \(-0.807452\pi\) | ||||
−0.822554 | + | 0.568686i | \(0.807452\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 44.1889 | + | 25.5125i | 0.0896326 | + | 0.0517494i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −150.213 | + | 86.7255i | −0.303461 | + | 0.175203i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 63.6876 | + | 277.555i | 0.128144 | + | 0.558461i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −78.2519 | − | 135.536i | −0.156817 | − | 0.271616i | 0.776902 | − | 0.629622i | \(-0.216790\pi\) |
−0.933719 | + | 0.358006i | \(0.883457\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −104.548 | + | 181.082i | −0.208678 | + | 0.361441i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 499.753i | − | 0.993545i | −0.867881 | − | 0.496773i | \(-0.834518\pi\) | ||
0.867881 | − | 0.496773i | \(-0.165482\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −277.133 | −0.548779 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 118.128 | + | 68.2013i | 0.232994 | + | 0.134519i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 462.478 | − | 267.012i | 0.908602 | − | 0.524582i | 0.0286209 | − | 0.999590i | \(-0.490888\pi\) |
0.879981 | + | 0.475009i | \(0.157555\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −132.167 | + | 430.240i | −0.258645 | + | 0.841958i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −212.481 | − | 368.027i | −0.414193 | − | 0.717403i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −98.4604 | + | 170.538i | −0.191185 | + | 0.331143i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 999.509i | − | 1.93329i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −218.851 | −0.421677 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −623.856 | − | 360.184i | −1.19742 | − | 0.691331i | −0.237442 | − | 0.971402i | \(-0.576309\pi\) |
−0.959979 | + | 0.280070i | \(0.909642\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −523.499 | + | 302.243i | −1.00095 | + | 0.577902i | −0.908531 | − | 0.417818i | \(-0.862795\pi\) |
−0.0924242 | + | 0.995720i | \(0.529462\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −92.5107 | − | 99.4721i | −0.176211 | − | 0.189471i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 89.9225 | + | 155.750i | 0.170631 | + | 0.295542i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.90487 | − | 5.03138i | 0.00549125 | − | 0.00951112i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 106.063i | − | 0.199742i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −121.090 | −0.227186 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −129.011 | − | 74.4843i | −0.241141 | − | 0.139223i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −100.853 | + | 58.2272i | −0.187807 | + | 0.108431i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −52.8470 | + | 727.754i | −0.0980463 | + | 1.35019i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 177.344 | + | 307.168i | 0.327807 | + | 0.567779i | 0.982077 | − | 0.188483i | \(-0.0603570\pi\) |
−0.654269 | + | 0.756262i | \(0.727024\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 48.2487 | − | 83.5692i | 0.0888557 | − | 0.153903i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 200.581i | − | 0.368039i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −867.407 | −1.58575 | −0.792877 | − | 0.609382i | \(-0.791417\pi\) | ||||
−0.792877 | + | 0.609382i | \(0.791417\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 558.795 | + | 322.620i | 1.01784 | + | 0.587651i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 95.1012 | − | 54.9067i | 0.172597 | − | 0.0996492i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 412.737 | − | 383.853i | 0.746360 | − | 0.694128i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.56638 | + | 2.71304i | 0.00282230 | + | 0.00488837i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −67.3674 | + | 116.684i | −0.120947 | + | 0.209486i | −0.920141 | − | 0.391586i | \(-0.871926\pi\) |
0.799194 | + | 0.601073i | \(0.205260\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 137.980i | − | 0.246834i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 170.067 | 0.303150 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 413.611 | + | 238.798i | 0.734655 | + | 0.424153i | 0.820123 | − | 0.572188i | \(-0.193905\pi\) |
−0.0854680 | + | 0.996341i | \(0.527239\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 132.051 | − | 76.2399i | 0.233719 | − | 0.134938i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −417.050 | − | 128.115i | −0.735538 | − | 0.225953i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 166.341 | + | 288.110i | 0.292338 | + | 0.506345i | 0.974362 | − | 0.224985i | \(-0.0722333\pi\) |
−0.682024 | + | 0.731330i | \(0.738900\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −525.564 | + | 910.304i | −0.920427 | + | 1.59423i | −0.121672 | + | 0.992570i | \(0.538826\pi\) |
−0.798755 | + | 0.601657i | \(0.794508\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 128.466i | 0.224199i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −526.675 | −0.915956 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 350.366 | + | 202.284i | 0.607221 | + | 0.350579i | 0.771877 | − | 0.635772i | \(-0.219318\pi\) |
−0.164656 | + | 0.986351i | \(0.552651\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −176.858 | + | 102.109i | −0.305455 | + | 0.176355i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −831.438 | + | 190.781i | −1.43105 | + | 0.328367i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −297.252 | − | 514.856i | −0.509867 | − | 0.883115i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −15.5777 | + | 26.9813i | −0.0266285 | + | 0.0461220i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 64.6639i | − | 0.110160i | −0.998482 | − | 0.0550800i | \(-0.982459\pi\) | ||
0.998482 | − | 0.0550800i | \(-0.0175414\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 387.054 | 0.657137 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 144.165 | + | 83.2335i | 0.243933 | + | 0.140835i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 36.0843 | − | 20.8333i | 0.0608504 | − | 0.0351320i | −0.469266 | − | 0.883057i | \(-0.655482\pi\) |
0.530117 | + | 0.847925i | \(0.322148\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 29.8082 | + | 129.906i | 0.0500979 | + | 0.218330i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −69.1794 | − | 119.822i | −0.115878 | − | 0.200707i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 60.0025 | − | 103.927i | 0.100171 | − | 0.173502i | −0.811584 | − | 0.584236i | \(-0.801394\pi\) |
0.911755 | + | 0.410734i | \(0.134728\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1120.08i | 1.86369i | 0.362858 | + | 0.931844i | \(0.381801\pi\) | ||||
−0.362858 | + | 0.931844i | \(0.618199\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 379.999 | 0.630180 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −122.597 | − | 70.7812i | −0.202639 | − | 0.116994i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 383.831 | − | 221.605i | 0.632342 | − | 0.365083i | −0.149317 | − | 0.988789i | \(-0.547707\pi\) |
0.781658 | + | 0.623707i | \(0.214374\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.52328 | + | 21.2350i | −0.0107115 | + | 0.0348687i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −89.7662 | − | 155.480i | −0.146917 | − | 0.254467i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −568.642 | + | 984.916i | −0.927637 | + | 1.60672i | −0.140374 | + | 0.990099i | \(0.544830\pi\) |
−0.787264 | + | 0.616617i | \(0.788503\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 53.6106i | − | 0.0871717i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −357.454 | −0.579343 | −0.289671 | − | 0.957126i | \(-0.593546\pi\) | ||||
−0.289671 | + | 0.957126i | \(0.593546\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −686.616 | − | 396.418i | −1.10923 | − | 0.640416i | −0.170603 | − | 0.985340i | \(-0.554572\pi\) |
−0.938631 | + | 0.344923i | \(0.887905\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 288.649 | − | 166.651i | 0.464813 | − | 0.268360i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −218.871 | − | 235.341i | −0.351318 | − | 0.377754i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −240.412 | − | 416.407i | −0.384660 | − | 0.666250i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 183.005 | − | 316.974i | 0.291874 | − | 0.505541i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 35.8480i | 0.0569920i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 587.326 | 0.930786 | 0.465393 | − | 0.885104i | \(-0.345913\pi\) | ||||
0.465393 | + | 0.885104i | \(0.345913\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −38.7892 | − | 22.3950i | −0.0612783 | − | 0.0353791i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −170.103 | + | 98.2088i | −0.267878 | + | 0.154660i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 57.1392 | + | 117.953i | 0.0897004 | + | 0.185169i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −168.617 | − | 292.054i | −0.263877 | − | 0.457048i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −229.349 | + | 397.244i | −0.357798 | + | 0.619725i | −0.987593 | − | 0.157037i | \(-0.949806\pi\) |
0.629794 | + | 0.776762i | \(0.283139\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 242.009i | − | 0.376374i | −0.982133 | − | 0.188187i | \(-0.939739\pi\) | ||
0.982133 | − | 0.188187i | \(-0.0602611\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 61.0884 | 0.0947107 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 68.6970 | + | 39.6622i | 0.106178 | + | 0.0613017i | 0.552148 | − | 0.833746i | \(-0.313808\pi\) |
−0.445971 | + | 0.895048i | \(0.647141\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 165.001 | − | 95.2634i | 0.254239 | − | 0.146785i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −57.3349 | + | 53.3224i | −0.0880721 | + | 0.0819085i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −56.1079 | − | 97.1817i | −0.0859232 | − | 0.148823i | 0.819861 | − | 0.572563i | \(-0.194051\pi\) |
−0.905784 | + | 0.423739i | \(0.860717\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −66.7600 | + | 115.632i | −0.101924 | + | 0.176537i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 533.008i | − | 0.811275i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 811.930 | 1.23206 | 0.616032 | − | 0.787721i | \(-0.288739\pi\) | ||||
0.616032 | + | 0.787721i | \(0.288739\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 317.842 | + | 183.506i | 0.480850 | + | 0.277619i | 0.720771 | − | 0.693174i | \(-0.243788\pi\) |
−0.239921 | + | 0.970792i | \(0.577121\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 26.4549 | − | 15.2738i | 0.0399019 | − | 0.0230374i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 274.198 | + | 84.2321i | 0.412328 | + | 0.126665i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 43.0640 | + | 74.5891i | 0.0645638 | + | 0.111828i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 130.952 | − | 226.815i | 0.195742 | − | 0.339035i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1159.08i | 1.72739i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −504.526 | −0.749668 | −0.374834 | − | 0.927092i | \(-0.622300\pi\) | ||||
−0.374834 | + | 0.927092i | \(0.622300\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 290.571 | + | 167.761i | 0.430476 | + | 0.248535i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 519.740 | − | 300.072i | 0.767710 | − | 0.443238i | −0.0643468 | − | 0.997928i | \(-0.520496\pi\) |
0.832057 | + | 0.554690i | \(0.187163\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 916.071 | − | 210.201i | 1.34915 | − | 0.309574i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21.0270 | + | 36.4198i | 0.0308766 | + | 0.0534798i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −105.717 | + | 183.107i | −0.154783 | + | 0.268093i | −0.932980 | − | 0.359928i | \(-0.882801\pi\) |
0.778197 | + | 0.628020i | \(0.216135\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 215.780i | 0.315007i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −177.929 | −0.258994 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −92.4787 | − | 53.3926i | −0.134222 | − | 0.0774929i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.6678 | + | 9.62318i | −0.0241213 | + | 0.0139265i | −0.512012 | − | 0.858978i | \(-0.671100\pi\) |
0.487891 | + | 0.872905i | \(0.337766\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −193.255 | − | 842.219i | −0.278867 | − | 1.21532i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −152.825 | − | 264.701i | −0.219893 | − | 0.380865i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 306.732 | − | 531.275i | 0.440075 | − | 0.762232i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 63.5928i | − | 0.0909768i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1073.36 | −1.53119 | −0.765595 | − | 0.643323i | \(-0.777555\pi\) | ||||
−0.765595 | + | 0.643323i | \(0.777555\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 66.8142 | + | 38.5752i | 0.0950415 | + | 0.0548722i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 68.8360 | − | 39.7425i | 0.0976397 | − | 0.0563723i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 405.425 | − | 1319.77i | 0.573445 | − | 1.86672i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −128.799 | − | 223.086i | −0.181663 | − | 0.314649i | 0.760784 | − | 0.649005i | \(-0.224815\pi\) |
−0.942447 | + | 0.334356i | \(0.891481\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −333.746 | + | 578.065i | −0.469403 | + | 0.813030i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 303.571i | 0.425766i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −55.9661 | −0.0782743 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 226.553 | + | 130.800i | 0.315973 | + | 0.182427i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −278.533 | + | 160.811i | −0.387389 | + | 0.223659i | −0.681028 | − | 0.732257i | \(-0.738467\pi\) |
0.293639 | + | 0.955916i | \(0.405134\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −668.101 | − | 718.375i | −0.926630 | − | 0.996359i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 45.6030 | + | 78.9867i | 0.0630747 | + | 0.109249i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −43.3509 | + | 75.0859i | −0.0597943 | + | 0.103567i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 19.9115i | − | 0.0273886i | −0.999906 | − | 0.0136943i | \(-0.995641\pi\) | ||
0.999906 | − | 0.0136943i | \(-0.00435917\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 406.138 | 0.557117 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 605.380 | + | 349.516i | 0.828153 | + | 0.478134i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −514.080 | + | 296.804i | −0.701337 | + | 0.404917i | −0.807845 | − | 0.589395i | \(-0.799366\pi\) |
0.106508 | + | 0.994312i | \(0.466033\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −52.2216 | + | 25.2974i | −0.0710498 | + | 0.0344182i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 341.306 | + | 591.160i | 0.463102 | + | 0.802116i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 505.499 | − | 875.550i | 0.684031 | − | 1.18478i | −0.289709 | − | 0.957115i | \(-0.593559\pi\) |
0.973740 | − | 0.227662i | \(-0.0731080\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 65.7430i | − | 0.0887219i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 581.910 | 0.783189 | 0.391595 | − | 0.920138i | \(-0.371924\pi\) | ||||
0.391595 | + | 0.920138i | \(0.371924\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 77.9883 | + | 45.0266i | 0.104682 | + | 0.0604383i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 874.870 | − | 505.106i | 1.17118 | − | 0.676180i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 543.443 | − | 505.411i | 0.725558 | − | 0.674781i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 605.277 | + | 1048.37i | 0.805962 | + | 1.39597i | 0.915640 | + | 0.402000i | \(0.131685\pi\) |
−0.109678 | + | 0.993967i | \(0.534982\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −127.272 | + | 220.441i | −0.169019 | + | 0.292750i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 382.251i | 0.506293i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 245.833 | 0.324746 | 0.162373 | − | 0.986729i | \(-0.448085\pi\) | ||||
0.162373 | + | 0.986729i | \(0.448085\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 248.607 | + | 143.533i | 0.327545 | + | 0.189108i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 59.4109 | − | 34.3009i | 0.0780694 | − | 0.0450734i | −0.460457 | − | 0.887682i | \(-0.652314\pi\) |
0.538527 | + | 0.842609i | \(0.318981\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 955.212 | + | 293.436i | 1.25192 | + | 0.384582i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −78.9194 | − | 136.692i | −0.103163 | − | 0.178683i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17.1113 | − | 29.6376i | 0.0223094 | − | 0.0386409i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 540.953i | 0.703450i | 0.936103 | + | 0.351725i | \(0.114405\pi\) | ||||
−0.936103 | + | 0.351725i | \(0.885595\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −87.3977 | −0.113356 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 223.462 | + | 129.016i | 0.289085 | + | 0.166903i | 0.637529 | − | 0.770426i | \(-0.279957\pi\) |
−0.348444 | + | 0.937329i | \(0.613290\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −264.651 | + | 152.797i | −0.341486 | + | 0.197157i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −15.2116 | + | 3.49044i | −0.0195773 | + | 0.00449220i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −660.134 | − | 1143.39i | −0.847412 | − | 1.46776i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 302.897 | − | 524.633i | 0.387832 | − | 0.671745i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 54.8686i | − | 0.0700749i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −303.880 | −0.387109 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −156.307 | − | 90.2438i | −0.198611 | − | 0.114668i | 0.397396 | − | 0.917647i | \(-0.369914\pi\) |
−0.596007 | + | 0.802979i | \(0.703247\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 188.268 | − | 108.697i | 0.238616 | − | 0.137765i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 169.889 | + | 740.391i | 0.214778 | + | 0.936018i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 104.097 | + | 180.302i | 0.131270 | + | 0.227367i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 23.6387 | − | 40.9434i | 0.0297342 | − | 0.0515011i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1387.83i | 1.74132i | 0.491886 | + | 0.870660i | \(0.336308\pi\) | ||||
−0.491886 | + | 0.870660i | \(0.663692\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 909.543 | 1.13835 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 329.610 | + | 190.300i | 0.411498 | + | 0.237578i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 829.194 | − | 478.736i | 1.03262 | − | 0.596184i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −66.0643 | + | 215.057i | −0.0820674 | + | 0.267151i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −68.3767 | − | 118.432i | −0.0847295 | − | 0.146756i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 354.447 | − | 613.920i | 0.438130 | − | 0.758863i | −0.559415 | − | 0.828887i | \(-0.688974\pi\) |
0.997545 | + | 0.0700243i | \(0.0223077\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 281.652i | − | 0.347289i | −0.984808 | − | 0.173645i | \(-0.944446\pi\) | ||
0.984808 | − | 0.173645i | \(-0.0555544\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 52.8852 | 0.0650495 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 66.5533 | + | 38.4246i | 0.0816605 | + | 0.0471467i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1302.87 | − | 752.212i | 1.59470 | − | 0.920700i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −105.702 | − | 113.656i | −0.129062 | − | 0.138774i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 610.722 | + | 1057.80i | 0.743876 | + | 1.28843i | 0.950718 | + | 0.310057i | \(0.100348\pi\) |
−0.206842 | + | 0.978374i | \(0.566319\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.7002 | − | 72.2268i | 0.0506685 | − | 0.0877604i | −0.839579 | − | 0.543238i | \(-0.817198\pi\) |
0.890247 | + | 0.455478i | \(0.150531\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 288.978i | 0.350277i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 804.602 | 0.972916 | 0.486458 | − | 0.873704i | \(-0.338289\pi\) | ||||
0.486458 | + | 0.873704i | \(0.338289\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −891.302 | − | 514.593i | −1.07515 | − | 0.620740i | −0.145568 | − | 0.989348i | \(-0.546501\pi\) |
−0.929585 | + | 0.368608i | \(0.879834\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −187.691 | + | 108.363i | −0.225862 | + | 0.130401i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −662.249 | − | 48.0902i | −0.795017 | − | 0.0577314i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 174.301 | + | 301.899i | 0.208744 | + | 0.361555i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 96.6963 | − | 167.483i | 0.115527 | − | 0.200099i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 864.563i | − | 1.03047i | −0.857049 | − | 0.515234i | \(-0.827705\pi\) | ||
0.857049 | − | 0.515234i | \(-0.172295\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −826.822 | −0.983141 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 168.050 | + | 97.0237i | 0.199348 | + | 0.115093i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 196.942 | − | 113.705i | 0.233068 | − | 0.134562i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 516.425 | − | 480.284i | 0.609711 | − | 0.567041i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 172.562 | + | 298.886i | 0.203253 | + | 0.352044i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −30.2550 | + | 52.4032i | −0.0355523 | + | 0.0615784i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 285.568i | 0.334781i | 0.985891 | + | 0.167391i | \(0.0535341\pi\) | ||||
−0.985891 | + | 0.167391i | \(0.946466\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −339.693 | −0.397302 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −565.510 | − | 326.497i | −0.659872 | − | 0.380977i | 0.132356 | − | 0.991202i | \(-0.457746\pi\) |
−0.792228 | + | 0.610225i | \(0.791079\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −75.6507 | + | 43.6770i | −0.0880683 | + | 0.0508463i | −0.543387 | − | 0.839482i | \(-0.682859\pi\) |
0.455319 | + | 0.890328i | \(0.349525\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 255.305 | + | 78.4283i | 0.296522 | + | 0.0910898i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −213.639 | − | 370.034i | −0.247554 | − | 0.428776i | 0.715293 | − | 0.698825i | \(-0.246293\pi\) |
−0.962847 | + | 0.270049i | \(0.912960\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −182.433 | + | 315.983i | −0.210905 | + | 0.365299i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 88.8083i | − | 0.102432i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1199.05 | −1.37981 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 106.184 | + | 61.3056i | 0.121911 | + | 0.0703853i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −963.923 | + | 556.521i | −1.10415 | + | 0.637482i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −460.401 | + | 105.643i | −0.526173 | + | 0.120735i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −290.651 | − | 503.422i | −0.331415 | − | 0.574028i | 0.651374 | − | 0.758756i | \(-0.274193\pi\) |
−0.982790 | + | 0.184729i | \(0.940859\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 184.617 | − | 319.765i | 0.210030 | − | 0.363783i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 617.976i | − | 0.701448i | −0.936479 | − | 0.350724i | \(-0.885936\pi\) | ||
0.936479 | − | 0.350724i | \(-0.114064\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −150.782 | −0.170761 | −0.0853807 | − | 0.996348i | \(-0.527211\pi\) | ||||
−0.0853807 | + | 0.996348i | \(0.527211\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.1215 | + | 7.57573i | 0.0148266 | + | 0.00856015i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1158.00 | − | 668.569i | 1.30552 | − | 0.753742i | 0.324174 | − | 0.945997i | \(-0.394914\pi\) |
0.981345 | + | 0.192256i | \(0.0615804\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −218.844 | − | 953.737i | −0.246169 | − | 1.07282i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 464.058 | + | 803.773i | 0.520829 | + | 0.902102i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 978.738 | − | 1695.22i | 1.09601 | − | 1.89835i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 194.152i | 0.216930i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 51.5630 | 0.0574839 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 43.2789 | + | 24.9871i | 0.0481412 | + | 0.0277943i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 468.514 | − | 270.497i | 0.519993 | − | 0.300218i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −89.3678 | + | 290.916i | −0.0989677 | + | 0.322166i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −80.4398 | − | 139.326i | −0.0888838 | − | 0.153951i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 322.677 | − | 558.894i | 0.355763 | − | 0.616200i | −0.631485 | − | 0.775388i | \(-0.717554\pi\) |
0.987248 | + | 0.159188i | \(0.0508876\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1635.01i | 1.79869i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −865.195 | −0.949720 | −0.474860 | − | 0.880061i | \(-0.657501\pi\) | ||||
−0.474860 | + | 0.880061i | \(0.657501\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1571.58 | + | 907.350i | 1.72133 | + | 0.993812i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −79.8257 | + | 46.0874i | −0.0872412 | + | 0.0503687i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −452.998 | − | 487.086i | −0.494000 | − | 0.531173i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31.6093 | + | 54.7489i | 0.0343953 | + | 0.0595745i | 0.882711 | − | 0.469917i | \(-0.155716\pi\) |
−0.848315 | + | 0.529491i | \(0.822383\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 57.5268 | − | 99.6393i | 0.0624612 | − | 0.108186i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 108.813i | − | 0.117891i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −60.9130 | −0.0658519 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1006.13 | + | 580.889i | 1.08536 | + | 0.626633i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1109.30 | − | 640.454i | 1.19408 | − | 0.689402i | 0.234850 | − | 0.972032i | \(-0.424540\pi\) |
0.959229 | + | 0.282630i | \(0.0912069\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −802.262 | + | 1182.56i | −0.861721 | + | 1.27021i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 244.799 | + | 424.004i | 0.262378 | + | 0.454452i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 141.767 | − | 245.548i | 0.151623 | − | 0.262618i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1176.84i | 1.25597i | 0.778227 | + | 0.627983i | \(0.216119\pi\) | ||||
−0.778227 | + | 0.627983i | \(0.783881\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −157.769 | −0.168018 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1184.64 | − | 683.950i | −1.25891 | − | 0.726833i | −0.286048 | − | 0.958215i | \(-0.592342\pi\) |
−0.972863 | + | 0.231382i | \(0.925675\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 896.772 | − | 517.752i | 0.950978 | − | 0.549047i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 104.950 | − | 97.6054i | 0.111058 | − | 0.103286i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 87.6049 | + | 151.736i | 0.0925078 | + | 0.160228i | 0.908566 | − | 0.417742i | \(-0.137178\pi\) |
−0.816058 | + | 0.577970i | \(0.803845\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 85.9908 | − | 148.940i | 0.0906120 | − | 0.156945i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 139.809i | 0.147013i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 89.5669 | 0.0939842 | 0.0469921 | − | 0.998895i | \(-0.485036\pi\) | ||||
0.0469921 | + | 0.998895i | \(0.485036\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 185.484 | + | 107.089i | 0.194224 | + | 0.112135i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 40.9259 | − | 23.6286i | 0.0427648 | − | 0.0246903i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1027.59 | − | 315.670i | −1.07152 | − | 0.329166i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −392.429 | − | 679.707i | −0.408355 | − | 0.707292i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −439.436 | + | 761.126i | −0.456320 | + | 0.790370i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 340.472i | 0.352820i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −640.201 | −0.662049 | −0.331024 | − | 0.943622i | \(-0.607394\pi\) | ||||
−0.331024 | + | 0.943622i | \(0.607394\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 288.443 | + | 166.533i | 0.297671 | + | 0.171860i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −990.220 | + | 571.704i | −1.01979 | + | 0.588779i | −0.914044 | − | 0.405614i | \(-0.867058\pi\) |
−0.105750 | + | 0.994393i | \(0.533724\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1484.14 | − | 340.549i | 1.52532 | − | 0.349999i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 25.9532 | + | 44.9523i | 0.0266187 | + | 0.0461049i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −801.534 | + | 1388.30i | −0.820403 | + | 1.42098i | 0.0849795 | + | 0.996383i | \(0.472918\pi\) |
−0.905382 | + | 0.424597i | \(0.860416\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 683.694i | 0.698359i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1183.37 | −1.20629 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −850.237 | − | 490.885i | −0.864941 | − | 0.499374i | 0.000722851 | − | 1.00000i | \(-0.499770\pi\) |
−0.865664 | + | 0.500626i | \(0.833103\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 240.350 | − | 138.766i | 0.244010 | − | 0.140879i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 88.5602 | + | 385.952i | 0.0897267 | + | 0.391035i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 589.970 | + | 1021.86i | 0.596531 | + | 1.03322i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 413.854 | − | 716.817i | 0.417613 | − | 0.723327i | −0.578086 | − | 0.815976i | \(-0.696200\pi\) |
0.995699 | + | 0.0926491i | \(0.0295335\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 352.455i | − | 0.354939i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −230.671 | −0.231830 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 156.575 | + | 90.3985i | 0.157046 | + | 0.0906705i | 0.576463 | − | 0.817123i | \(-0.304432\pi\) |
−0.419418 | + | 0.907793i | \(0.637766\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 33.3839 | − | 19.2742i | 0.0334173 | − | 0.0192935i |
(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 | 448.3.s.h.129.5 | 16 | ||
4.3 | odd | 2 | inner | 448.3.s.h.129.4 | 16 | ||
7.5 | odd | 6 | inner | 448.3.s.h.257.5 | 16 | ||
8.3 | odd | 2 | 224.3.s.b.129.5 | yes | 16 | ||
8.5 | even | 2 | 224.3.s.b.129.4 | yes | 16 | ||
28.19 | even | 6 | inner | 448.3.s.h.257.4 | 16 | ||
56.3 | even | 6 | 1568.3.c.g.97.10 | 16 | |||
56.5 | odd | 6 | 224.3.s.b.33.4 | ✓ | 16 | ||
56.11 | odd | 6 | 1568.3.c.g.97.7 | 16 | |||
56.19 | even | 6 | 224.3.s.b.33.5 | yes | 16 | ||
56.45 | odd | 6 | 1568.3.c.g.97.8 | 16 | |||
56.53 | even | 6 | 1568.3.c.g.97.9 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.s.b.33.4 | ✓ | 16 | 56.5 | odd | 6 | ||
224.3.s.b.33.5 | yes | 16 | 56.19 | even | 6 | ||
224.3.s.b.129.4 | yes | 16 | 8.5 | even | 2 | ||
224.3.s.b.129.5 | yes | 16 | 8.3 | odd | 2 | ||
448.3.s.h.129.4 | 16 | 4.3 | odd | 2 | inner | ||
448.3.s.h.129.5 | 16 | 1.1 | even | 1 | trivial | ||
448.3.s.h.257.4 | 16 | 28.19 | even | 6 | inner | ||
448.3.s.h.257.5 | 16 | 7.5 | odd | 6 | inner | ||
1568.3.c.g.97.7 | 16 | 56.11 | odd | 6 | |||
1568.3.c.g.97.8 | 16 | 56.45 | odd | 6 | |||
1568.3.c.g.97.9 | 16 | 56.53 | even | 6 | |||
1568.3.c.g.97.10 | 16 | 56.3 | even | 6 |