Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(2305,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.2305");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.q (of order \(3\), 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: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.309123.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2305.2 | ||
Root | \(0.500000 - 1.41036i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3024.2305 |
Dual form | 3024.2.q.h.2881.2 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.880438 | + | 1.52496i | 0.393744 | + | 0.681985i | 0.992940 | − | 0.118618i | \(-0.0378463\pi\) |
−0.599196 | + | 0.800602i | \(0.704513\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.710533 | + | 2.54856i | 0.268556 | + | 0.963264i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.06238 | + | 5.30420i | −0.923343 | + | 1.59928i | −0.129138 | + | 0.991627i | \(0.541221\pi\) |
−0.794205 | + | 0.607650i | \(0.792112\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.380438 | + | 0.658939i | −0.105515 | + | 0.182757i | −0.913948 | − | 0.405831i | \(-0.866982\pi\) |
0.808434 | + | 0.588587i | \(0.200316\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.42107 | + | 5.92546i | 0.829731 | + | 1.43714i | 0.898250 | + | 0.439486i | \(0.144839\pi\) |
−0.0685191 | + | 0.997650i | \(0.521827\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.971410 | + | 1.68253i | −0.222857 | + | 0.385999i | −0.955674 | − | 0.294426i | \(-0.904872\pi\) |
0.732818 | + | 0.680425i | \(0.238205\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.210533 | + | 0.364654i | 0.0438992 | + | 0.0760357i | 0.887140 | − | 0.461500i | \(-0.152689\pi\) |
−0.843241 | + | 0.537536i | \(0.819355\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.949657 | − | 1.64485i | 0.189931 | − | 0.328971i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.732287 | − | 1.26836i | −0.135982 | − | 0.235528i | 0.789990 | − | 0.613120i | \(-0.210086\pi\) |
−0.925972 | + | 0.377592i | \(0.876752\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.70370 | −1.38362 | −0.691812 | − | 0.722077i | \(-0.743187\pi\) | ||||
−0.691812 | + | 0.722077i | \(0.743187\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.26088 | + | 3.32738i | −0.551189 | + | 0.562431i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.44282 | − | 2.49904i | 0.237198 | − | 0.410839i | −0.722711 | − | 0.691150i | \(-0.757104\pi\) |
0.959909 | + | 0.280311i | \(0.0904376\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.47141 | − | 6.01266i | 0.542143 | − | 0.939020i | −0.456638 | − | 0.889653i | \(-0.650946\pi\) |
0.998781 | − | 0.0493667i | \(-0.0157203\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.33009 | − | 7.49994i | −0.660333 | − | 1.14373i | −0.980528 | − | 0.196379i | \(-0.937082\pi\) |
0.320195 | − | 0.947352i | \(-0.396252\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.66019 | 0.242164 | 0.121082 | − | 0.992643i | \(-0.461364\pi\) | ||||
0.121082 | + | 0.992643i | \(0.461364\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.99028 | + | 3.62167i | −0.855755 | + | 0.517381i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.112725 | + | 0.195246i | 0.0154840 | + | 0.0268190i | 0.873664 | − | 0.486531i | \(-0.161738\pi\) |
−0.858180 | + | 0.513350i | \(0.828404\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.7850 | −1.45424 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.98633 | 0.258598 | 0.129299 | − | 0.991606i | \(-0.458727\pi\) | ||||
0.129299 | + | 0.991606i | \(0.458727\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.3502 | −1.32521 | −0.662605 | − | 0.748969i | \(-0.730549\pi\) | ||||
−0.662605 | + | 0.748969i | \(0.730549\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.33981 | −0.166183 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.78495 | −0.828914 | −0.414457 | − | 0.910069i | \(-0.636028\pi\) | ||||
−0.414457 | + | 0.910069i | \(0.636028\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.7850 | 1.27994 | 0.639969 | − | 0.768401i | \(-0.278947\pi\) | ||||
0.639969 | + | 0.768401i | \(0.278947\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.153353 | + | 0.265616i | 0.0179487 | + | 0.0310880i | 0.874860 | − | 0.484375i | \(-0.160953\pi\) |
−0.856912 | + | 0.515463i | \(0.827620\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −15.6940 | − | 4.03584i | −1.78850 | − | 0.459927i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.4451 | 1.51270 | 0.756348 | − | 0.654169i | \(-0.226982\pi\) | ||||
0.756348 | + | 0.654169i | \(0.226982\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.56238 | − | 2.70612i | −0.171494 | − | 0.297036i | 0.767449 | − | 0.641110i | \(-0.221526\pi\) |
−0.938942 | + | 0.344075i | \(0.888193\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.02408 | + | 10.4340i | −0.653403 | + | 1.13173i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.30150 | + | 2.25427i | −0.137959 | + | 0.238952i | −0.926724 | − | 0.375743i | \(-0.877388\pi\) |
0.788765 | + | 0.614695i | \(0.210721\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.94966 | − | 0.501371i | −0.204380 | − | 0.0525580i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.42107 | −0.350994 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.81806 | − | 3.14897i | −0.184596 | − | 0.319729i | 0.758845 | − | 0.651272i | \(-0.225764\pi\) |
−0.943440 | + | 0.331543i | \(0.892431\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.00520 | + | 6.93721i | −0.398532 | + | 0.690278i | −0.993545 | − | 0.113438i | \(-0.963814\pi\) |
0.595013 | + | 0.803716i | \(0.297147\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.41423 | − | 5.91362i | −0.336414 | − | 0.582686i | 0.647341 | − | 0.762200i | \(-0.275881\pi\) |
−0.983755 | + | 0.179514i | \(0.942548\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.77292 | − | 3.07078i | 0.171394 | − | 0.296863i | −0.767513 | − | 0.641033i | \(-0.778506\pi\) |
0.938908 | + | 0.344170i | \(0.111840\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.351848 | + | 0.609419i | 0.0337010 | + | 0.0583718i | 0.882384 | − | 0.470530i | \(-0.155937\pi\) |
−0.848683 | + | 0.528902i | \(0.822604\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.25116 | + | 7.36323i | −0.399916 | + | 0.692674i | −0.993715 | − | 0.111939i | \(-0.964294\pi\) |
0.593799 | + | 0.804613i | \(0.297627\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.370723 | + | 0.642111i | −0.0345701 | + | 0.0598772i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12.6706 | + | 12.9290i | −1.16151 | + | 1.18520i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13.2564 | − | 22.9607i | −1.20512 | − | 2.08734i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1488 | 1.08663 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.9532 | 1.68183 | 0.840913 | − | 0.541170i | \(-0.182018\pi\) | ||||
0.840913 | + | 0.541170i | \(0.182018\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.64652 | + | 6.31595i | 0.318598 | + | 0.551827i | 0.980196 | − | 0.198031i | \(-0.0634548\pi\) |
−0.661598 | + | 0.749859i | \(0.730121\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.97825 | − | 1.28020i | −0.431669 | − | 0.111007i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.09097 | + | 7.08577i | −0.349515 | + | 0.605378i | −0.986163 | − | 0.165776i | \(-0.946987\pi\) |
0.636648 | + | 0.771154i | \(0.280320\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.23229 | − | 10.7946i | 0.528616 | − | 0.915589i | −0.470828 | − | 0.882225i | \(-0.656045\pi\) |
0.999443 | − | 0.0333640i | \(-0.0106220\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.33009 | − | 4.03584i | −0.194852 | − | 0.337494i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.28947 | − | 2.23342i | 0.107084 | − | 0.185476i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.41423 | + | 7.64567i | 0.361628 | + | 0.626358i | 0.988229 | − | 0.152982i | \(-0.0488878\pi\) |
−0.626601 | + | 0.779340i | \(0.715554\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.49316 | + | 12.9785i | −0.609785 | + | 1.05618i | 0.381491 | + | 0.924373i | \(0.375411\pi\) |
−0.991276 | + | 0.131806i | \(0.957922\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.78263 | − | 11.7479i | −0.544794 | − | 0.943611i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.9806 | 1.51481 | 0.757407 | − | 0.652943i | \(-0.226466\pi\) | ||||
0.757407 | + | 0.652943i | \(0.226466\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.779752 | + | 0.795655i | −0.0614530 | + | 0.0627064i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.51887 | − | 13.0231i | 0.588924 | − | 1.02005i | −0.405450 | − | 0.914117i | \(-0.632885\pi\) |
0.994374 | − | 0.105929i | \(-0.0337815\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.572097 | − | 0.990901i | 0.0442702 | − | 0.0766782i | −0.843041 | − | 0.537849i | \(-0.819237\pi\) |
0.887311 | + | 0.461171i | \(0.152570\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.21053 | + | 10.7570i | 0.477733 | + | 0.827458i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.497677 | −0.0378377 | −0.0189188 | − | 0.999821i | \(-0.506022\pi\) | ||||
−0.0189188 | + | 0.999821i | \(0.506022\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.86677 | + | 1.25153i | 0.367893 | + | 0.0946068i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.41423 | + | 7.64567i | 0.329935 | + | 0.571464i | 0.982499 | − | 0.186270i | \(-0.0596398\pi\) |
−0.652564 | + | 0.757734i | \(0.726306\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.32941 | 0.0988140 | 0.0494070 | − | 0.998779i | \(-0.484267\pi\) | ||||
0.0494070 | + | 0.998779i | \(0.484267\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.08126 | 0.373581 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −41.9064 | −3.06450 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.1683 | −1.16989 | −0.584947 | − | 0.811071i | \(-0.698885\pi\) | ||||
−0.584947 | + | 0.811071i | \(0.698885\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.1683 | −1.01985 | −0.509927 | − | 0.860218i | \(-0.670328\pi\) | ||||
−0.509927 | + | 0.860218i | \(0.670328\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.8421 | −1.12871 | −0.564353 | − | 0.825534i | \(-0.690874\pi\) | ||||
−0.564353 | + | 0.825534i | \(0.690874\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.47141 | + | 7.74471i | 0.316970 | + | 0.549008i | 0.979854 | − | 0.199714i | \(-0.0640013\pi\) |
−0.662884 | + | 0.748722i | \(0.730668\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.71217 | − | 2.76748i | 0.190357 | − | 0.194239i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.2255 | 0.853862 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.94966 | − | 10.3051i | −0.411546 | − | 0.712819i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.3856 | + | 19.7205i | −0.783820 | + | 1.35762i | 0.145882 | + | 0.989302i | \(0.453398\pi\) |
−0.929702 | + | 0.368314i | \(0.879935\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.62476 | − | 13.2065i | 0.520005 | − | 0.900674i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.47373 | − | 19.6333i | −0.371581 | − | 1.33280i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.20602 | −0.350195 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.44282 | + | 11.1593i | 0.431443 | + | 0.747281i | 0.996998 | − | 0.0774293i | \(-0.0246712\pi\) |
−0.565555 | + | 0.824711i | \(0.691338\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.9984 | + | 19.0497i | −0.729987 | + | 1.26437i | 0.226901 | + | 0.973918i | \(0.427141\pi\) |
−0.956888 | + | 0.290457i | \(0.906193\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.89931 | + | 3.28971i | 0.125510 | + | 0.217390i | 0.921932 | − | 0.387351i | \(-0.126610\pi\) |
−0.796422 | + | 0.604741i | \(0.793277\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.33530 | − | 5.77690i | 0.218503 | − | 0.378458i | −0.735848 | − | 0.677147i | \(-0.763216\pi\) |
0.954350 | + | 0.298689i | \(0.0965495\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.46169 | + | 2.53173i | 0.0953505 | + | 0.165152i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.82038 | + | 13.5453i | −0.505858 | + | 0.876172i | 0.494119 | + | 0.869394i | \(0.335491\pi\) |
−0.999977 | + | 0.00677786i | \(0.997843\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.7060 | + | 18.5434i | −0.689635 | + | 1.19448i | 0.282320 | + | 0.959320i | \(0.408896\pi\) |
−0.971956 | + | 0.235163i | \(0.924437\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.7970 | − | 5.94631i | −0.689794 | − | 0.379896i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.739123 | − | 1.28020i | −0.0470293 | − | 0.0814571i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.6030 | −1.48981 | −0.744904 | − | 0.667171i | \(-0.767505\pi\) | ||||
−0.744904 | + | 0.667171i | \(0.767505\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.57893 | −0.162136 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.1300 | + | 17.5456i | 0.631890 | + | 1.09447i | 0.987165 | + | 0.159704i | \(0.0510538\pi\) |
−0.355275 | + | 0.934762i | \(0.615613\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.39411 | + | 1.90146i | 0.459448 | + | 0.118151i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.2443 | − | 19.4757i | 0.693355 | − | 1.20093i | −0.277377 | − | 0.960761i | \(-0.589465\pi\) |
0.970732 | − | 0.240165i | \(-0.0772014\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.198495 | + | 0.343803i | −0.0121935 | + | 0.0211197i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.6706 | + | 21.9461i | 0.772540 | + | 1.33808i | 0.936167 | + | 0.351556i | \(0.114347\pi\) |
−0.163627 | + | 0.986522i | \(0.552319\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.87880 | − | 11.9144i | 0.417858 | − | 0.723751i | −0.577866 | − | 0.816132i | \(-0.696114\pi\) |
0.995724 | + | 0.0923810i | \(0.0294478\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.81642 | + | 10.0743i | 0.350743 | + | 0.607505i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.64132 | − | 2.84284i | 0.0986171 | − | 0.170810i | −0.812495 | − | 0.582968i | \(-0.801891\pi\) |
0.911112 | + | 0.412158i | \(0.135225\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.634479 | − | 1.09895i | −0.0378498 | − | 0.0655578i | 0.846480 | − | 0.532421i | \(-0.178718\pi\) |
−0.884330 | + | 0.466863i | \(0.845384\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.19235 | 0.486984 | 0.243492 | − | 0.969903i | \(-0.421707\pi\) | ||||
0.243492 | + | 0.969903i | \(0.421707\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 17.7902 | + | 4.57489i | 1.05012 | + | 0.270047i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.9074 | + | 25.8204i | −0.876906 | + | 1.51884i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.72545 | + | 13.3809i | −0.451326 | + | 0.781719i | −0.998469 | − | 0.0553202i | \(-0.982382\pi\) |
0.547143 | + | 0.837039i | \(0.315715\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.74884 | + | 3.02908i | 0.101821 | + | 0.176360i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.320380 | −0.0185280 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.0374 | − | 16.3645i | 0.924378 | − | 0.943231i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.11273 | − | 15.7837i | −0.521793 | − | 0.903772i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.89931 | −0.279619 | −0.139809 | − | 0.990178i | \(-0.544649\pi\) | ||||
−0.139809 | + | 0.990178i | \(0.544649\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.69002 | −0.436061 | −0.218031 | − | 0.975942i | \(-0.569963\pi\) | ||||
−0.218031 | + | 0.975942i | \(0.569963\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.72313 | −0.0973969 | −0.0486985 | − | 0.998814i | \(-0.515507\pi\) | ||||
−0.0486985 | + | 0.998814i | \(0.515507\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −33.2028 | −1.86485 | −0.932426 | − | 0.361361i | \(-0.882312\pi\) | ||||
−0.932426 | + | 0.361361i | \(0.882312\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.97017 | 0.502233 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −13.2930 | −0.739644 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.722572 | + | 1.25153i | 0.0400811 | + | 0.0694224i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.17962 | + | 4.23109i | 0.0650346 | + | 0.233267i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.88891 | −0.158789 | −0.0793944 | − | 0.996843i | \(-0.525299\pi\) | ||||
−0.0793944 | + | 0.996843i | \(0.525299\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.97373 | − | 10.3468i | −0.326380 | − | 0.565307i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.36156 | + | 7.55445i | −0.237590 | + | 0.411517i | −0.960022 | − | 0.279924i | \(-0.909691\pi\) |
0.722433 | + | 0.691441i | \(0.243024\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 23.5917 | − | 40.8620i | 1.27756 | − | 2.21280i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.4863 | − | 12.6933i | −0.728193 | − | 0.685372i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.69467 | 0.520437 | 0.260219 | − | 0.965550i | \(-0.416205\pi\) | ||||
0.260219 | + | 0.965550i | \(0.416205\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.1992 | + | 24.5937i | 0.760065 | + | 1.31647i | 0.942817 | + | 0.333312i | \(0.108166\pi\) |
−0.182752 | + | 0.983159i | \(0.558500\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.19686 | + | 3.80507i | −0.116927 | + | 0.202524i | −0.918548 | − | 0.395308i | \(-0.870638\pi\) |
0.801621 | + | 0.597832i | \(0.203971\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.49549 | + | 16.4467i | 0.503968 | + | 0.872898i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.0796 | − | 27.8507i | 0.848650 | − | 1.46990i | −0.0337633 | − | 0.999430i | \(-0.510749\pi\) |
0.882413 | − | 0.470475i | \(-0.155917\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.61273 | + | 13.1856i | 0.400670 | + | 0.693980i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.270036 | + | 0.467717i | −0.0141343 | + | 0.0244814i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.3015 | − | 29.9671i | 0.903131 | − | 1.56427i | 0.0797249 | − | 0.996817i | \(-0.474596\pi\) |
0.823406 | − | 0.567452i | \(-0.192071\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.417500 | + | 0.426015i | −0.0216755 | + | 0.0221176i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.48796 | − | 9.50543i | −0.284156 | − | 0.492172i | 0.688248 | − | 0.725475i | \(-0.258380\pi\) |
−0.972404 | + | 0.233303i | \(0.925047\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.11436 | 0.0573925 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −33.9877 | −1.74583 | −0.872916 | − | 0.487871i | \(-0.837774\pi\) | ||||
−0.872916 | + | 0.487871i | \(0.837774\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.5120 | + | 18.2074i | 0.537140 | + | 0.930354i | 0.999056 | + | 0.0434304i | \(0.0138287\pi\) |
−0.461916 | + | 0.886923i | \(0.652838\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.66307 | − | 27.4861i | −0.390546 | − | 1.40082i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.86909 | − | 11.8976i | 0.348277 | − | 0.603233i | −0.637667 | − | 0.770312i | \(-0.720100\pi\) |
0.985943 | + | 0.167080i | \(0.0534337\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.44050 | + | 2.49501i | −0.0728491 | + | 0.126178i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.8376 | + | 20.5034i | 0.595615 | + | 1.03164i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.57893 | + | 6.19889i | −0.179622 | + | 0.311114i | −0.941751 | − | 0.336311i | \(-0.890821\pi\) |
0.762129 | + | 0.647425i | \(0.224154\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.63968 | − | 8.03616i | −0.231695 | − | 0.401307i | 0.726612 | − | 0.687048i | \(-0.241094\pi\) |
−0.958307 | + | 0.285741i | \(0.907760\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.93078 | − | 5.07626i | 0.145993 | − | 0.252867i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.83693 | + | 15.3060i | 0.438030 | + | 0.758691i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.1683 | 0.750023 | 0.375011 | − | 0.927020i | \(-0.377639\pi\) | ||||
0.375011 | + | 0.927020i | \(0.377639\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.41135 | + | 5.06227i | 0.0694481 | + | 0.249098i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.75116 | − | 4.76515i | 0.135049 | − | 0.233912i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.16827 | + | 7.21966i | −0.203633 | + | 0.352703i | −0.949696 | − | 0.313172i | \(-0.898608\pi\) |
0.746063 | + | 0.665875i | \(0.231942\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.50232 | − | 6.06620i | −0.170693 | − | 0.295649i | 0.767969 | − | 0.640486i | \(-0.221267\pi\) |
−0.938662 | + | 0.344838i | \(0.887934\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.9954 | 0.630367 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.35417 | − | 26.3781i | −0.355893 | − | 1.27653i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.72545 | − | 2.98857i | −0.0831120 | − | 0.143954i | 0.821473 | − | 0.570247i | \(-0.193153\pi\) |
−0.904585 | + | 0.426293i | \(0.859819\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.2599 | 1.35809 | 0.679043 | − | 0.734099i | \(-0.262395\pi\) | ||||
0.679043 | + | 0.734099i | \(0.262395\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.818057 | −0.0391330 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.8960 | 1.37913 | 0.689566 | − | 0.724222i | \(-0.257801\pi\) | ||||
0.689566 | + | 0.724222i | \(0.257801\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.7609 | −0.653799 | −0.326899 | − | 0.945059i | \(-0.606004\pi\) | ||||
−0.326899 | + | 0.945059i | \(0.606004\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.58358 | −0.217283 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.2003 | 0.953309 | 0.476655 | − | 0.879091i | \(-0.341849\pi\) | ||||
0.476655 | + | 0.879091i | \(0.341849\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.2616 | + | 36.8261i | 1.00117 | + | 1.73407i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.951980 | − | 3.41458i | −0.0446295 | − | 0.160078i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.0298 | 0.936956 | 0.468478 | − | 0.883475i | \(-0.344803\pi\) | ||||
0.468478 | + | 0.883475i | \(0.344803\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.97661 | − | 10.3518i | −0.278359 | − | 0.482131i | 0.692618 | − | 0.721304i | \(-0.256457\pi\) |
−0.970977 | + | 0.239173i | \(0.923124\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.64527 | + | 11.5100i | −0.308832 | + | 0.534913i | −0.978107 | − | 0.208102i | \(-0.933271\pi\) |
0.669275 | + | 0.743015i | \(0.266605\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.61505 | + | 9.72555i | −0.259833 | + | 0.450045i | −0.966197 | − | 0.257804i | \(-0.917001\pi\) |
0.706364 | + | 0.707849i | \(0.250334\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.82094 | − | 17.2918i | −0.222610 | − | 0.798463i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 53.0416 | 2.43886 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.84501 | + | 3.19565i | 0.0846550 | + | 0.146627i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.3135 | − | 28.2559i | 0.745385 | − | 1.29104i | −0.204630 | − | 0.978839i | \(-0.565599\pi\) |
0.950015 | − | 0.312205i | \(-0.101068\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.09781 | + | 1.90146i | 0.0500557 | + | 0.0866991i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.20137 | − | 5.54494i | 0.145367 | − | 0.251783i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.84897 | − | 3.20251i | −0.0837848 | − | 0.145120i | 0.821088 | − | 0.570802i | \(-0.193368\pi\) |
−0.904873 | + | 0.425682i | \(0.860034\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.7804 | + | 32.5287i | −0.847549 | + | 1.46800i | 0.0358393 | + | 0.999358i | \(0.488590\pi\) |
−0.883389 | + | 0.468641i | \(0.844744\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.01040 | − | 8.67827i | 0.225657 | − | 0.390850i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.66307 | + | 27.4861i | 0.343736 | + | 1.23292i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.8977 | − | 27.5356i | −0.711678 | − | 1.23266i | −0.964227 | − | 0.265078i | \(-0.914602\pi\) |
0.252549 | − | 0.967584i | \(-0.418731\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 30.8252 | 1.37443 | 0.687214 | − | 0.726455i | \(-0.258834\pi\) | ||||
0.687214 | + | 0.726455i | \(0.258834\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.1053 | −0.627679 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.00808 | + | 6.94220i | 0.177655 | + | 0.307708i | 0.941077 | − | 0.338193i | \(-0.109816\pi\) |
−0.763422 | + | 0.645900i | \(0.776482\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.567974 | + | 0.579559i | −0.0251257 | + | 0.0256382i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.01204 | − | 10.4132i | 0.264922 | − | 0.458858i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.08414 | + | 8.80598i | −0.223600 | + | 0.387287i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.8646 | − | 25.7462i | −0.651229 | − | 1.12796i | −0.982825 | − | 0.184540i | \(-0.940920\pi\) |
0.331596 | − | 0.943421i | \(-0.392413\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.4698 | + | 23.3303i | −0.588992 | + | 1.02016i | 0.405373 | + | 0.914152i | \(0.367142\pi\) |
−0.994365 | + | 0.106013i | \(0.966192\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −26.3549 | − | 45.6480i | −1.14804 | − | 1.98846i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.4114 | − | 19.7650i | 0.496146 | − | 0.859350i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.64132 | + | 4.57489i | 0.114408 | + | 0.198161i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.24377 | 0.269942 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.865521 | − | 42.8646i | −0.0372806 | − | 1.84631i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.15568 | − | 12.3940i | 0.307647 | − | 0.532859i | −0.670201 | − | 0.742180i | \(-0.733792\pi\) |
0.977847 | + | 0.209321i | \(0.0671252\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.619562 | + | 1.07311i | −0.0265391 | + | 0.0459671i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.02463 | − | 1.77471i | −0.0438101 | − | 0.0758813i | 0.843289 | − | 0.537461i | \(-0.180616\pi\) |
−0.887099 | + | 0.461579i | \(0.847283\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.84540 | 0.121218 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.55322 | + | 34.2657i | 0.406244 | + | 1.45713i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.84338 | − | 15.3172i | −0.374706 | − | 0.649010i | 0.615577 | − | 0.788077i | \(-0.288923\pi\) |
−0.990283 | + | 0.139067i | \(0.955590\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.58934 | 0.278699 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.937063 | 0.0394925 | 0.0197462 | − | 0.999805i | \(-0.493714\pi\) | ||||
0.0197462 | + | 0.999805i | \(0.493714\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.9715 | −0.629858 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23.5264 | −0.986278 | −0.493139 | − | 0.869951i | \(-0.664151\pi\) | ||||
−0.493139 | + | 0.869951i | \(0.664151\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.484004 | 0.0202549 | 0.0101275 | − | 0.999949i | \(-0.496776\pi\) | ||||
0.0101275 | + | 0.999949i | \(0.496776\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.799737 | 0.0333514 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.23065 | − | 3.86360i | −0.0928633 | − | 0.160844i | 0.815852 | − | 0.578261i | \(-0.196269\pi\) |
−0.908715 | + | 0.417417i | \(0.862935\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.78659 | − | 5.90461i | 0.240068 | − | 0.244965i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.38083 | −0.0571881 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.31518 | + | 14.4023i | 0.343204 | + | 0.594447i | 0.985026 | − | 0.172407i | \(-0.0551544\pi\) |
−0.641822 | + | 0.766854i | \(0.721821\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.48345 | − | 12.9617i | 0.308350 | − | 0.534078i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20.7632 | + | 35.9629i | −0.852642 | + | 1.47682i | 0.0261726 | + | 0.999657i | \(0.491668\pi\) |
−0.878815 | + | 0.477163i | \(0.841665\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −30.8720 | − | 7.93899i | −1.26563 | − | 0.325467i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.0766 | 0.616014 | 0.308007 | − | 0.951384i | \(-0.400338\pi\) | ||||
0.308007 | + | 0.951384i | \(0.400338\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.05555 | − | 13.9526i | −0.328593 | − | 0.569139i | 0.653640 | − | 0.756805i | \(-0.273241\pi\) |
−0.982233 | + | 0.187666i | \(0.939908\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 23.3428 | − | 40.4310i | 0.949021 | − | 1.64375i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.78659 | + | 16.9509i | 0.397225 | + | 0.688014i | 0.993382 | − | 0.114853i | \(-0.0366398\pi\) |
−0.596157 | + | 0.802868i | \(0.703306\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.631600 | + | 1.09396i | −0.0255518 | + | 0.0442570i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.77579 | − | 4.80782i | −0.112113 | − | 0.194186i | 0.804509 | − | 0.593941i | \(-0.202429\pi\) |
−0.916622 | + | 0.399755i | \(0.869095\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.634479 | + | 1.09895i | −0.0255431 | + | 0.0442420i | −0.878514 | − | 0.477716i | \(-0.841465\pi\) |
0.852971 | + | 0.521958i | \(0.174798\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.25116 | − | 3.89913i | 0.0904818 | − | 0.156719i | −0.817232 | − | 0.576309i | \(-0.804493\pi\) |
0.907714 | + | 0.419589i | \(0.137826\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.66991 | − | 1.71522i | −0.267224 | − | 0.0687190i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.94802 | + | 10.3023i | 0.237921 | + | 0.412091i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 19.7439 | 0.787242 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.69905 | 0.0676381 | 0.0338191 | − | 0.999428i | \(-0.489233\pi\) | ||||
0.0338191 | + | 0.999428i | \(0.489233\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16.6871 | + | 28.9030i | 0.662209 | + | 1.14698i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.107523 | − | 5.32505i | −0.00426023 | − | 0.210986i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.474289 | + | 0.821492i | −0.0187333 | + | 0.0324470i | −0.875240 | − | 0.483689i | \(-0.839297\pi\) |
0.856507 | + | 0.516136i | \(0.172630\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.84897 | − | 17.0589i | 0.388405 | − | 0.672738i | −0.603830 | − | 0.797113i | \(-0.706359\pi\) |
0.992235 | + | 0.124375i | \(0.0396927\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.7271 | + | 20.3119i | 0.461039 | + | 0.798543i | 0.999013 | − | 0.0444181i | \(-0.0141434\pi\) |
−0.537974 | + | 0.842962i | \(0.680810\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.08289 | + | 10.5359i | −0.238774 | + | 0.413569i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.3954 | + | 19.7373i | 0.445935 | + | 0.772382i | 0.998117 | − | 0.0613420i | \(-0.0195380\pi\) |
−0.552182 | + | 0.833724i | \(0.686205\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.42107 | + | 11.1216i | −0.250892 | + | 0.434557i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.2398 | − | 22.9320i | −0.515750 | − | 0.893305i | −0.999833 | − | 0.0182828i | \(-0.994180\pi\) |
0.484083 | − | 0.875022i | \(-0.339153\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.7382 | −1.03999 | −0.519997 | − | 0.854168i | \(-0.674067\pi\) | ||||
−0.519997 | + | 0.854168i | \(0.674067\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.43078 | − | 8.71878i | −0.0942617 | − | 0.338100i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.308342 | − | 0.534063i | 0.0119390 | − | 0.0206790i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 31.6963 | − | 54.8996i | 1.22362 | − | 2.11938i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.3856 | − | 17.9885i | −0.400337 | − | 0.693404i | 0.593429 | − | 0.804886i | \(-0.297774\pi\) |
−0.993766 | + | 0.111482i | \(0.964440\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.6979 | 0.795486 | 0.397743 | − | 0.917497i | \(-0.369793\pi\) | ||||
0.397743 | + | 0.917497i | \(0.369793\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.73353 | − | 6.87087i | 0.258409 | − | 0.263680i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.2918 | + | 24.7541i | 0.546860 | + | 0.947190i | 0.998487 | + | 0.0549828i | \(0.0175104\pi\) |
−0.451627 | + | 0.892207i | \(0.649156\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.4074 | −0.550478 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.171540 | −0.00653515 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.69794 | 0.254802 | 0.127401 | − | 0.991851i | \(-0.459337\pi\) | ||||
0.127401 | + | 0.991851i | \(0.459337\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21.9486 | 0.832557 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 47.5037 | 1.79933 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.1442 | 0.949683 | 0.474842 | − | 0.880071i | \(-0.342505\pi\) | ||||
0.474842 | + | 0.880071i | \(0.342505\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.80314 | + | 4.85518i | 0.105722 | + | 0.183117i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −20.5257 | − | 5.27836i | −0.771949 | − | 0.198513i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.86621 | 0.332977 | 0.166489 | − | 0.986043i | \(-0.446757\pi\) | ||||
0.166489 | + | 0.986043i | \(0.446757\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.62188 | − | 2.80919i | −0.0607401 | − | 0.105205i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.10301 | − | 7.10662i | 0.153444 | − | 0.265773i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.8015 | − | 20.4408i | 0.440122 | − | 0.762313i | −0.557576 | − | 0.830126i | \(-0.688269\pi\) |
0.997698 | + | 0.0678123i | \(0.0216019\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.6453 | − | 12.9032i | 0.470935 | − | 0.480540i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.78168 | −0.103309 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.25692 | − | 5.64115i | −0.120792 | − | 0.209219i | 0.799288 | − | 0.600948i | \(-0.205210\pi\) |
−0.920080 | + | 0.391730i | \(0.871877\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 29.6271 | − | 51.3156i | 1.09580 | − | 1.89798i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.5991 | + | 20.0901i | 0.428421 | + | 0.742047i | 0.996733 | − | 0.0807664i | \(-0.0257368\pi\) |
−0.568312 | + | 0.822813i | \(0.692403\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 20.7781 | − | 35.9888i | 0.765372 | − | 1.32566i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.57838 | + | 13.1261i | 0.278775 | + | 0.482853i | 0.971081 | − | 0.238752i | \(-0.0767383\pi\) |
−0.692305 | + | 0.721605i | \(0.743405\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.21737 | + | 9.03675i | −0.191407 | + | 0.331526i | −0.945717 | − | 0.324992i | \(-0.894638\pi\) |
0.754310 | + | 0.656518i | \(0.227972\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.77292 | + | 13.4631i | −0.284778 | + | 0.493249i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.08577 | + | 2.33648i | 0.331987 | + | 0.0853733i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.1059 | + | 34.8244i | 0.733674 | + | 1.27076i | 0.955303 | + | 0.295630i | \(0.0955295\pi\) |
−0.221628 | + | 0.975131i | \(0.571137\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −26.3891 | −0.960397 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.5206 | −0.782181 | −0.391091 | − | 0.920352i | \(-0.627902\pi\) | ||||
−0.391091 | + | 0.920352i | \(0.627902\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.8313 | − | 20.4925i | −0.428886 | − | 0.742852i | 0.567889 | − | 0.823105i | \(-0.307760\pi\) |
−0.996774 | + | 0.0802535i | \(0.974427\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.30314 | + | 1.32972i | −0.0471768 | + | 0.0481390i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.755675 | + | 1.30887i | −0.0272858 | + | 0.0472605i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.62764 | + | 9.74736i | −0.202938 | + | 0.351499i | −0.949474 | − | 0.313846i | \(-0.898382\pi\) |
0.746536 | + | 0.665345i | \(0.231716\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.138992 | − | 0.240741i | −0.00499919 | − | 0.00865886i | 0.863515 | − | 0.504323i | \(-0.168258\pi\) |
−0.868514 | + | 0.495664i | \(0.834925\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.31587 | + | 12.6715i | −0.262794 | + | 0.455172i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.74433 | + | 11.6815i | 0.241641 | + | 0.418534i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −33.0276 | + | 57.2056i | −1.18182 | + | 2.04698i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.7112 | + | 28.9447i | 0.596449 | + | 1.03308i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.3880 | 1.04757 | 0.523784 | − | 0.851851i | \(-0.324520\pi\) | ||||
0.523784 | + | 0.851851i | \(0.324520\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21.7862 | − | 5.60251i | −0.774628 | − | 0.199202i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.93762 | − | 6.82015i | 0.139829 | − | 0.242191i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.433105 | + | 0.750160i | −0.0153414 | + | 0.0265720i | −0.873594 | − | 0.486655i | \(-0.838217\pi\) |
0.858253 | + | 0.513227i | \(0.171550\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.67962 | + | 9.83739i | 0.200931 | + | 0.348022i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.87851 | −0.0662910 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.89987 | − | 0.488568i | −0.0669616 | − | 0.0172197i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.66703 | − | 16.7438i | −0.339875 | − | 0.588680i | 0.644534 | − | 0.764575i | \(-0.277051\pi\) |
−0.984409 | + | 0.175895i | \(0.943718\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 47.0391 | 1.65177 | 0.825884 | − | 0.563841i | \(-0.190677\pi\) | ||||
0.825884 | + | 0.563841i | \(0.190677\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 26.4796 | 0.927541 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.8252 | 0.588639 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.41066 | −0.0492325 | −0.0246162 | − | 0.999697i | \(-0.507836\pi\) | ||||
−0.0246162 | + | 0.999697i | \(0.507836\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 35.0391 | 1.22139 | 0.610694 | − | 0.791867i | \(-0.290891\pi\) | ||||
0.610694 | + | 0.791867i | \(0.290891\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.5997 | −0.646776 | −0.323388 | − | 0.946266i | \(-0.604822\pi\) | ||||
−0.323388 | + | 0.946266i | \(0.604822\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.0848 | + | 33.0559i | 0.662843 | + | 1.14808i | 0.979865 | + | 0.199660i | \(0.0639838\pi\) |
−0.317022 | + | 0.948418i | \(0.602683\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −41.9532 | − | 23.1052i | −1.45359 | − | 0.800549i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.01478 | 0.0697245 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17.3691 | + | 30.0841i | 0.599648 | + | 1.03862i | 0.992873 | + | 0.119178i | \(0.0380259\pi\) |
−0.393225 | + | 0.919442i | \(0.628641\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.4275 | − | 23.2571i | 0.463018 | − | 0.801970i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.9360 | + | 18.9417i | −0.376209 | + | 0.651614i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 49.0976 | − | 50.0989i | 1.68701 | − | 1.72142i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.21505 | 0.0416513 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.1586 | − | 36.6477i | −0.724455 | − | 1.25479i | −0.959198 | − | 0.282736i | \(-0.908758\pi\) |
0.234743 | − | 0.972058i | \(-0.424575\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.46169 | − | 12.9240i | 0.254887 | − | 0.441477i | −0.709978 | − | 0.704224i | \(-0.751295\pi\) |
0.964865 | + | 0.262747i | \(0.0846285\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.70658 | + | 16.8123i | 0.331184 | + | 0.573628i | 0.982744 | − | 0.184969i | \(-0.0592186\pi\) |
−0.651560 | + | 0.758597i | \(0.725885\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.542263 | + | 0.939227i | −0.0184588 | + | 0.0319717i | −0.875107 | − | 0.483929i | \(-0.839209\pi\) |
0.856648 | + | 0.515901i | \(0.172543\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.438174 | − | 0.758939i | −0.0148984 | − | 0.0258047i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −41.1742 | + | 71.3157i | −1.39674 | + | 2.41922i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.58126 | − | 4.47087i | 0.0874625 | − | 0.151490i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.63216 | + | 30.9620i | 0.291820 | + | 1.04671i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.2850 | + | 24.7423i | 0.482369 | + | 0.835487i | 0.999795 | − | 0.0202407i | \(-0.00644326\pi\) |
−0.517427 | + | 0.855728i | \(0.673110\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −45.9967 | −1.54967 | −0.774835 | − | 0.632164i | \(-0.782167\pi\) | ||||
−0.774835 | + | 0.632164i | \(0.782167\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32.9384 | −1.10847 | −0.554233 | − | 0.832361i | \(-0.686988\pi\) | ||||
−0.554233 | + | 0.832361i | \(0.686988\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.1699 | + | 24.5430i | 0.475779 | + | 0.824073i | 0.999615 | − | 0.0277459i | \(-0.00883293\pi\) |
−0.523836 | + | 0.851819i | \(0.675500\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.4669 | + | 48.3034i | 0.451665 | + | 1.62004i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.61273 | + | 2.79332i | −0.0539678 | + | 0.0934750i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.77292 | + | 13.4631i | −0.259820 | + | 0.450021i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.64132 | + | 9.77104i | 0.188148 | + | 0.325883i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.771280 | + | 1.33590i | −0.0256951 | + | 0.0445052i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.17046 | + | 2.02730i | 0.0389074 | + | 0.0673896i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.97373 | − | 6.88271i | 0.131946 | − | 0.228537i | −0.792481 | − | 0.609897i | \(-0.791211\pi\) |
0.924427 | + | 0.381360i | \(0.124544\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.00808 | − | 6.94220i | −0.132794 | − | 0.230005i | 0.791959 | − | 0.610575i | \(-0.209061\pi\) |
−0.924752 | + | 0.380569i | \(0.875728\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.1384 | 0.633390 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.5056 | + | 13.7811i | −0.445994 | + | 0.455090i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.0224 | − | 20.8235i | 0.396584 | − | 0.686903i | −0.596718 | − | 0.802451i | \(-0.703529\pi\) |
0.993302 | + | 0.115548i | \(0.0368623\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.10301 | + | 7.10662i | −0.135052 | + | 0.233917i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.74037 | − | 4.74646i | −0.0901027 | − | 0.156062i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27.8662 | −0.914261 | −0.457130 | − | 0.889400i | \(-0.651123\pi\) | ||||
−0.457130 | + | 0.889400i | \(0.651123\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.274550 | − | 13.5970i | −0.00899801 | − | 0.445623i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −36.8960 | − | 63.9058i | −1.20663 | − | 2.08994i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 53.2211 | 1.73866 | 0.869328 | − | 0.494235i | \(-0.164552\pi\) | ||||
0.869328 | + | 0.494235i | \(0.164552\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.0482 | 0.979542 | 0.489771 | − | 0.871851i | \(-0.337080\pi\) | ||||
0.489771 | + | 0.871851i | \(0.337080\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.92339 | 0.0951987 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −39.6889 | −1.28972 | −0.644858 | − | 0.764302i | \(-0.723084\pi\) | ||||
−0.644858 | + | 0.764302i | \(0.723084\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.233366 | −0.00757538 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −23.0643 | −0.747126 | −0.373563 | − | 0.927605i | \(-0.621864\pi\) | ||||
−0.373563 | + | 0.927605i | \(0.621864\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.2352 | − | 24.6560i | −0.460639 | − | 0.797850i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20.9653 | − | 5.39140i | −0.677004 | − | 0.174097i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.3469 | 0.914418 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.4743 | − | 21.6061i | −0.401562 | − | 0.695525i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.2902 | + | 26.4833i | −0.491698 | + | 0.851646i | −0.999954 | − | 0.00955967i | \(-0.996957\pi\) |
0.508256 | + | 0.861206i | \(0.330290\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.1030 | − | 22.6951i | 0.420496 | − | 0.728320i | −0.575492 | − | 0.817807i | \(-0.695190\pi\) |
0.995988 | + | 0.0894874i | \(0.0285229\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 31.9390 | + | 8.21339i | 1.02392 | + | 0.263309i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.0539 | −0.673574 | −0.336787 | − | 0.941581i | \(-0.609340\pi\) | ||||
−0.336787 | + | 0.941581i | \(0.609340\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.97141 | − | 13.8069i | −0.254767 | − | 0.441270i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.76483 | − | 16.9132i | 0.311450 | − | 0.539447i | −0.667227 | − | 0.744855i | \(-0.732519\pi\) |
0.978676 | + | 0.205408i | \(0.0658521\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.9480 | − | 24.1587i | −0.444421 | − | 0.769760i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.82326 | − | 3.15798i | 0.0579762 | − | 0.100418i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.49837 | + | 12.9875i | 0.238193 | + | 0.412563i | 0.960196 | − | 0.279327i | \(-0.0901114\pi\) |
−0.722003 | + | 0.691890i | \(0.756778\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.87360 | + | 13.6375i | −0.249610 | + | 0.432337i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.2821 | − | 50.7180i | 0.927373 | − | 1.60626i | 0.139672 | − | 0.990198i | \(-0.455395\pi\) |
0.787700 | − | 0.616059i | \(-0.211272\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))