Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1020,3,Mod(749,1020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1020.749");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1020 = 2^{2} \cdot 3 \cdot 5 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1020.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(27.7929869648\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 749.10 | ||
Character | \(\chi\) | \(=\) | 1020.749 |
Dual form | 1020.3.c.a.749.9 |
$q$-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 \(\left(\mathbb{Z}/1020\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(341\) | \(511\) | \(817\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.75746 | + | 1.18170i | −0.919153 | + | 0.393901i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.98117 | − | 0.433573i | 0.996233 | − | 0.0867146i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 13.3287i | 1.90410i | 0.305950 | + | 0.952048i | \(0.401026\pi\) | ||||
−0.305950 | + | 0.952048i | \(0.598974\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.20715 | − | 6.51700i | 0.689684 | − | 0.724111i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 7.28217i | − | 0.662015i | −0.943628 | − | 0.331008i | \(-0.892611\pi\) | ||
0.943628 | − | 0.331008i | \(-0.107389\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 14.2252i | − | 1.09425i | −0.837052 | − | 0.547123i | \(-0.815723\pi\) | ||
0.837052 | − | 0.547123i | \(-0.184277\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −13.2230 | + | 7.08182i | −0.881534 | + | 0.472121i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.12311 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 30.5400 | 1.60737 | 0.803685 | − | 0.595055i | \(-0.202870\pi\) | ||||
0.803685 | + | 0.595055i | \(0.202870\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −15.7505 | − | 36.7532i | −0.750025 | − | 1.75015i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 29.9932 | 1.30405 | 0.652025 | − | 0.758197i | \(-0.273920\pi\) | ||||
0.652025 | + | 0.758197i | \(0.273920\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24.6240 | − | 4.31940i | 0.984961 | − | 0.172776i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −9.41481 | + | 25.3054i | −0.348697 | + | 0.937236i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 48.5070i | − | 1.67265i | −0.548231 | − | 0.836327i | \(-0.684699\pi\) | ||
0.548231 | − | 0.836327i | \(-0.315301\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −48.6377 | −1.56896 | −0.784479 | − | 0.620155i | \(-0.787070\pi\) | ||||
−0.784479 | + | 0.620155i | \(0.787070\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.60536 | + | 20.0803i | 0.260768 | + | 0.608493i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.77895 | + | 66.3923i | 0.165113 | + | 1.89692i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 13.4646i | 0.363908i | 0.983307 | + | 0.181954i | \(0.0582423\pi\) | ||||
−0.983307 | + | 0.181954i | \(0.941758\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 16.8100 | + | 39.2254i | 0.431025 | + | 1.00578i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 18.6706i | 0.455380i | 0.973734 | + | 0.227690i | \(0.0731173\pi\) | ||||
−0.973734 | + | 0.227690i | \(0.926883\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 70.3336i | − | 1.63567i | −0.575455 | − | 0.817833i | \(-0.695175\pi\) | ||
0.575455 | − | 0.817833i | \(-0.304825\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 28.0933 | − | 35.1535i | 0.624295 | − | 0.781189i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 39.8435 | 0.847733 | 0.423867 | − | 0.905725i | \(-0.360673\pi\) | ||||
0.423867 | + | 0.905725i | \(0.360673\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −128.653 | −2.62558 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11.3693 | + | 4.87229i | −0.222927 | + | 0.0955351i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 40.7085 | 0.768086 | 0.384043 | − | 0.923315i | \(-0.374531\pi\) | ||||
0.384043 | + | 0.923315i | \(0.374531\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.15735 | − | 36.2737i | −0.0574064 | − | 0.659521i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −84.2129 | + | 36.0893i | −1.47742 | + | 0.633145i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 9.13866i | − | 0.154892i | −0.996997 | − | 0.0774462i | \(-0.975323\pi\) | ||
0.996997 | − | 0.0774462i | \(-0.0246766\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 28.3187 | 0.464240 | 0.232120 | − | 0.972687i | \(-0.425434\pi\) | ||||
0.232120 | + | 0.972687i | \(0.425434\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 86.8629 | + | 82.7331i | 1.37878 | + | 1.31322i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.16767 | − | 70.8581i | −0.0948872 | − | 1.09012i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 46.3846i | 0.692308i | 0.938178 | + | 0.346154i | \(0.112513\pi\) | ||||
−0.938178 | + | 0.346154i | \(0.887487\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −82.7049 | + | 35.4430i | −1.19862 | + | 0.513667i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 95.5663i | 1.34600i | 0.739640 | + | 0.673002i | \(0.234996\pi\) | ||||
−0.739640 | + | 0.673002i | \(0.765004\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 73.9456i | 1.01295i | 0.862254 | + | 0.506477i | \(0.169052\pi\) | ||||
−0.862254 | + | 0.506477i | \(0.830948\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −62.7955 | + | 41.0089i | −0.837273 | + | 0.546785i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 97.0616 | 1.26054 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 46.8555 | 0.593108 | 0.296554 | − | 0.955016i | \(-0.404163\pi\) | ||||
0.296554 | + | 0.955016i | \(0.404163\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.94248 | − | 80.9040i | −0.0486725 | − | 0.998815i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 132.752 | 1.59943 | 0.799714 | − | 0.600382i | \(-0.204985\pi\) | ||||
0.799714 | + | 0.600382i | \(0.204985\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 20.5379 | − | 1.78767i | 0.241622 | − | 0.0210314i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 57.3208 | + | 133.756i | 0.658860 | + | 1.53742i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 18.7147i | − | 0.210277i | −0.994458 | − | 0.105139i | \(-0.966471\pi\) | ||
0.994458 | − | 0.105139i | \(-0.0335287\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 189.603 | 2.08355 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 134.116 | − | 57.4754i | 1.44211 | − | 0.618015i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 152.125 | − | 13.2413i | 1.60132 | − | 0.139383i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 43.0964i | 0.444293i | 0.975013 | + | 0.222146i | \(0.0713063\pi\) | ||||
−0.975013 | + | 0.222146i | \(0.928694\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −47.4578 | − | 45.2015i | −0.479372 | − | 0.456581i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 72.2619i | − | 0.715465i | −0.933824 | − | 0.357732i | \(-0.883550\pi\) | ||
0.933824 | − | 0.357732i | \(-0.116450\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 89.3407i | 0.867385i | 0.901061 | + | 0.433693i | \(0.142790\pi\) | ||||
−0.901061 | + | 0.433693i | \(0.857210\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −94.3912 | − | 176.245i | −0.898964 | − | 1.67852i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −93.5164 | −0.873985 | −0.436993 | − | 0.899465i | \(-0.643956\pi\) | ||||
−0.436993 | + | 0.899465i | \(0.643956\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 77.5459 | 0.711431 | 0.355715 | − | 0.934594i | \(-0.384237\pi\) | ||||
0.355715 | + | 0.934594i | \(0.384237\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −15.9112 | − | 37.1281i | −0.143344 | − | 0.334487i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.8816 | −0.140545 | −0.0702724 | − | 0.997528i | \(-0.522387\pi\) | ||||
−0.0702724 | + | 0.997528i | \(0.522387\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 149.401 | − | 13.0042i | 1.29914 | − | 0.113080i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −92.7056 | − | 88.2980i | −0.792356 | − | 0.754684i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 54.9555i | 0.461811i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 67.9701 | 0.561736 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −22.0631 | − | 51.4834i | −0.179375 | − | 0.418564i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 120.784 | − | 32.1920i | 0.966269 | − | 0.257536i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 92.8562i | − | 0.731151i | −0.930782 | − | 0.365575i | \(-0.880872\pi\) | ||
0.930782 | − | 0.365575i | \(-0.119128\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 83.1135 | + | 193.942i | 0.644291 | + | 1.50343i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 90.2128i | 0.688647i | 0.938851 | + | 0.344323i | \(0.111892\pi\) | ||||
−0.938851 | + | 0.344323i | \(0.888108\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 407.058i | 3.06059i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −35.9250 | + | 130.132i | −0.266111 | + | 0.963942i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 121.516 | 0.886977 | 0.443488 | − | 0.896280i | \(-0.353741\pi\) | ||||
0.443488 | + | 0.896280i | \(0.353741\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 31.9966 | 0.230192 | 0.115096 | − | 0.993354i | \(-0.463282\pi\) | ||||
0.115096 | + | 0.993354i | \(0.463282\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −109.867 | + | 47.0831i | −0.779196 | + | 0.333923i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −103.590 | −0.724408 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −21.0313 | − | 241.621i | −0.145044 | − | 1.66635i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 354.756 | − | 152.030i | 2.41331 | − | 1.03422i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 78.2024i | − | 0.524848i | −0.964953 | − | 0.262424i | \(-0.915478\pi\) | ||
0.964953 | − | 0.262424i | \(-0.0845220\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 149.668 | 0.991178 | 0.495589 | − | 0.868557i | \(-0.334952\pi\) | ||||
0.495589 | + | 0.868557i | \(0.334952\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 25.5928 | − | 26.8703i | 0.167273 | − | 0.175623i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −242.273 | + | 21.0880i | −1.56305 | + | 0.136052i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 201.290i | 1.28210i | 0.767498 | + | 0.641052i | \(0.221502\pi\) | ||||
−0.767498 | + | 0.641052i | \(0.778498\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −112.252 | + | 48.1054i | −0.705988 | + | 0.302550i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 399.769i | 2.48304i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 16.8171i | − | 0.103172i | −0.998669 | − | 0.0515861i | \(-0.983572\pi\) | ||
0.998669 | − | 0.0515861i | \(-0.0164277\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 51.5710 | + | 96.2921i | 0.312551 | + | 0.583588i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −170.328 | −1.01993 | −0.509963 | − | 0.860196i | \(-0.670341\pi\) | ||||
−0.509963 | + | 0.860196i | \(0.670341\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −33.3565 | −0.197375 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 189.567 | − | 199.029i | 1.10858 | − | 1.16391i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.8370 | −0.0857630 | −0.0428815 | − | 0.999080i | \(-0.513654\pi\) | ||||
−0.0428815 | + | 0.999080i | \(0.513654\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 57.5718 | + | 328.205i | 0.328982 | + | 1.87546i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.7992 | + | 25.1995i | 0.0610123 | + | 0.142370i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 155.033i | − | 0.866106i | −0.901368 | − | 0.433053i | \(-0.857436\pi\) | ||
0.901368 | − | 0.433053i | \(-0.142564\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −211.969 | −1.17110 | −0.585550 | − | 0.810636i | \(-0.699122\pi\) | ||||
−0.585550 | + | 0.810636i | \(0.699122\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −78.0876 | + | 33.4643i | −0.426708 | + | 0.182865i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.83789 | + | 67.0695i | 0.0315562 | + | 0.362538i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 30.0251i | − | 0.160562i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −337.287 | − | 125.487i | −1.78459 | − | 0.663952i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 298.521i | 1.56293i | 0.623946 | + | 0.781467i | \(0.285528\pi\) | ||||
−0.623946 | + | 0.781467i | \(0.714472\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 262.057i | 1.35781i | 0.734228 | + | 0.678903i | \(0.237544\pi\) | ||||
−0.734228 | + | 0.678903i | \(0.762456\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 100.740 | + | 188.100i | 0.516617 | + | 0.964615i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −271.215 | −1.37673 | −0.688364 | − | 0.725365i | \(-0.741671\pi\) | ||||
−0.688364 | + | 0.725365i | \(0.741671\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −175.753 | −0.883179 | −0.441590 | − | 0.897217i | \(-0.645585\pi\) | ||||
−0.441590 | + | 0.897217i | \(0.645585\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −54.8129 | − | 127.904i | −0.272701 | − | 0.636337i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 646.533 | 3.18489 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.09507 | + | 93.0013i | 0.0394881 | + | 0.453665i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 186.172 | − | 195.465i | 0.899382 | − | 0.944277i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 222.398i | − | 1.06410i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −198.030 | −0.938533 | −0.469267 | − | 0.883057i | \(-0.655482\pi\) | ||||
−0.469267 | + | 0.883057i | \(0.655482\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −112.931 | − | 263.520i | −0.530193 | − | 1.23718i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −30.4948 | − | 350.344i | −0.141836 | − | 1.62951i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 648.276i | − | 2.98745i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −87.3817 | − | 203.902i | −0.399003 | − | 0.931059i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 58.6520i | − | 0.265394i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 6.87693i | − | 0.0308382i | −0.999881 | − | 0.0154191i | \(-0.995092\pi\) | ||
0.999881 | − | 0.0154191i | \(-0.00490825\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 124.696 | − | 187.286i | 0.554203 | − | 0.832382i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −91.3375 | −0.402368 | −0.201184 | − | 0.979553i | \(-0.564479\pi\) | ||||
−0.201184 | + | 0.979553i | \(0.564479\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 155.566 | 0.679329 | 0.339664 | − | 0.940547i | \(-0.389687\pi\) | ||||
0.339664 | + | 0.940547i | \(0.389687\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −267.643 | + | 114.698i | −1.15863 | + | 0.496528i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −161.438 | −0.692866 | −0.346433 | − | 0.938075i | \(-0.612607\pi\) | ||||
−0.346433 | + | 0.938075i | \(0.612607\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 198.467 | − | 17.2751i | 0.844540 | − | 0.0735109i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −129.202 | + | 55.3693i | −0.545157 | + | 0.233626i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 212.830i | − | 0.890501i | −0.895406 | − | 0.445250i | \(-0.853115\pi\) | ||
0.895406 | − | 0.445250i | \(-0.146885\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 445.835 | 1.84994 | 0.924969 | − | 0.380043i | \(-0.124091\pi\) | ||||
0.924969 | + | 0.380043i | \(0.124091\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 106.476 | + | 218.431i | 0.438172 | + | 0.898891i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −640.844 | + | 55.7806i | −2.61569 | + | 0.227676i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 434.438i | − | 1.75886i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −366.059 | + | 156.874i | −1.47012 | + | 0.630016i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 110.922i | − | 0.441922i | −0.975283 | − | 0.220961i | \(-0.929081\pi\) | ||
0.975283 | − | 0.220961i | \(-0.0709193\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 218.415i | − | 0.863301i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −54.5198 | + | 29.1991i | −0.213803 | + | 0.114506i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −56.1145 | −0.218344 | −0.109172 | − | 0.994023i | \(-0.534820\pi\) | ||||
−0.109172 | + | 0.994023i | \(0.534820\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −179.465 | −0.692916 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −316.120 | − | 301.090i | −1.21119 | − | 1.15360i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 171.027 | 0.650293 | 0.325146 | − | 0.945664i | \(-0.394586\pi\) | ||||
0.325146 | + | 0.945664i | \(0.394586\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 202.776 | − | 17.6501i | 0.765192 | − | 0.0666043i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 22.1152 | + | 51.6050i | 0.0828285 | + | 0.193277i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 200.140i | − | 0.744016i | −0.928230 | − | 0.372008i | \(-0.878669\pi\) | ||
0.928230 | − | 0.372008i | \(-0.121331\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.71558 | −0.0358508 | −0.0179254 | − | 0.999839i | \(-0.505706\pi\) | ||||
−0.0179254 | + | 0.999839i | \(0.505706\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −522.822 | + | 224.055i | −1.91510 | + | 0.820713i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −31.4546 | − | 179.316i | −0.114380 | − | 0.652059i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.2582i | 0.0550839i | 0.999621 | + | 0.0275420i | \(0.00876799\pi\) | ||||
−0.999621 | + | 0.0275420i | \(0.991232\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −301.902 | + | 316.972i | −1.08209 | + | 1.13610i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 140.166i | − | 0.498813i | −0.968399 | − | 0.249406i | \(-0.919764\pi\) | ||
0.968399 | − | 0.249406i | \(-0.0802355\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 36.7624i | − | 0.129903i | −0.997888 | − | 0.0649513i | \(-0.979311\pi\) | ||
0.997888 | − | 0.0649513i | \(-0.0206892\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −403.831 | + | 216.279i | −1.41695 | + | 0.758874i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −248.854 | −0.867088 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.0000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −50.9271 | − | 118.836i | −0.175007 | − | 0.408373i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −440.326 | −1.50282 | −0.751410 | − | 0.659836i | \(-0.770626\pi\) | ||||
−0.751410 | + | 0.659836i | \(0.770626\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.96228 | − | 45.5212i | −0.0134314 | − | 0.154309i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 184.278 | + | 68.5602i | 0.620464 | + | 0.230843i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 426.659i | − | 1.42695i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 937.454 | 3.11446 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 85.3922 | + | 199.259i | 0.281822 | + | 0.657621i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 141.060 | − | 12.2782i | 0.462492 | − | 0.0402564i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.3930i | 0.0599120i | 0.999551 | + | 0.0299560i | \(0.00953672\pi\) | ||||
−0.999551 | + | 0.0299560i | \(0.990463\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −105.574 | − | 246.353i | −0.341664 | − | 0.797260i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 121.314i | − | 0.390076i | −0.980796 | − | 0.195038i | \(-0.937517\pi\) | ||
0.980796 | − | 0.195038i | \(-0.0624830\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 241.333i | − | 0.771033i | −0.922701 | − | 0.385517i | \(-0.874023\pi\) | ||
0.922701 | − | 0.385517i | \(-0.125977\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 468.549 | + | 374.446i | 1.48746 | + | 1.18872i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 487.588 | 1.53813 | 0.769067 | − | 0.639169i | \(-0.220721\pi\) | ||||
0.769067 | + | 0.639169i | \(0.220721\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −353.236 | −1.10732 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 257.868 | − | 110.509i | 0.803326 | − | 0.344264i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 125.920 | 0.389845 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −61.4443 | − | 350.282i | −0.189059 | − | 1.07779i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −213.830 | + | 91.6363i | −0.653913 | + | 0.280233i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 531.060i | 1.61416i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −263.720 | −0.796736 | −0.398368 | − | 0.917226i | \(-0.630423\pi\) | ||||
−0.398368 | + | 0.917226i | \(0.630423\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 87.7488 | + | 83.5769i | 0.263510 | + | 0.250982i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 20.1111 | + | 231.050i | 0.0600332 | + | 0.689700i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 213.013i | − | 0.632087i | −0.948745 | − | 0.316044i | \(-0.897645\pi\) | ||
0.948745 | − | 0.316044i | \(-0.102355\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 43.7927 | − | 18.7673i | 0.129182 | − | 0.0553607i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 354.188i | 1.03867i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1061.67i | − | 3.09526i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −396.600 | + | 212.406i | −1.14956 | + | 0.615670i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −384.201 | −1.10721 | −0.553603 | − | 0.832781i | \(-0.686748\pi\) | ||||
−0.553603 | + | 0.832781i | \(0.686748\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 175.928 | 0.504090 | 0.252045 | − | 0.967715i | \(-0.418897\pi\) | ||||
0.252045 | + | 0.967715i | \(0.418897\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 359.974 | + | 133.928i | 1.02557 | + | 0.381560i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −504.077 | −1.42798 | −0.713990 | − | 0.700156i | \(-0.753114\pi\) | ||||
−0.713990 | + | 0.700156i | \(0.753114\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 41.4350 | + | 476.032i | 0.116718 | + | 1.34093i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −64.9411 | − | 151.537i | −0.181908 | − | 0.424475i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.62957i | 0.0268233i | 0.999910 | + | 0.0134117i | \(0.00426919\pi\) | ||||
−0.999910 | + | 0.0134117i | \(0.995731\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 571.694 | 1.58364 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −187.425 | + | 80.3205i | −0.516321 | + | 0.221268i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 32.0608 | + | 368.335i | 0.0878378 | + | 1.00914i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 648.885i | 1.76808i | 0.467411 | + | 0.884040i | \(0.345187\pi\) | ||||
−0.467411 | + | 0.884040i | \(0.654813\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 121.676 | + | 115.891i | 0.329746 | + | 0.314068i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 542.591i | 1.46251i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 96.4552i | 0.258593i | 0.991606 | + | 0.129296i | \(0.0412719\pi\) | ||||
−0.991606 | + | 0.129296i | \(0.958728\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −295.014 | + | 231.498i | −0.786705 | + | 0.617329i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −690.021 | −1.83030 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.1078 | 0.0636091 | 0.0318045 | − | 0.999494i | \(-0.489875\pi\) | ||||
0.0318045 | + | 0.999494i | \(0.489875\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 109.728 | + | 256.047i | 0.288001 | + | 0.672039i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −535.837 | −1.39905 | −0.699526 | − | 0.714607i | \(-0.746606\pi\) | ||||
−0.699526 | + | 0.714607i | \(0.746606\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 483.480 | − | 42.0833i | 1.25579 | − | 0.109307i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −458.364 | − | 436.572i | −1.18440 | − | 1.12809i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 718.536i | 1.84714i | 0.383435 | + | 0.923568i | \(0.374741\pi\) | ||||
−0.383435 | + | 0.923568i | \(0.625259\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 123.665 | 0.316279 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −106.605 | − | 248.758i | −0.271259 | − | 0.632972i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 233.395 | − | 20.3153i | 0.590873 | − | 0.0514311i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 287.466i | 0.724096i | 0.932160 | + | 0.362048i | \(0.117922\pi\) | ||||
−0.932160 | + | 0.362048i | \(0.882078\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −481.022 | − | 1122.45i | −1.20557 | − | 2.81315i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 622.455i | − | 1.55226i | −0.630575 | − | 0.776128i | \(-0.717181\pi\) | ||
0.630575 | − | 0.776128i | \(-0.282819\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 691.881i | 1.71683i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −54.7159 | − | 401.287i | −0.135101 | − | 0.990832i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 98.0515 | 0.240913 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −352.901 | −0.862840 | −0.431420 | − | 0.902151i | \(-0.641987\pi\) | ||||
−0.431420 | + | 0.902151i | \(0.641987\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −335.075 | + | 143.596i | −0.815267 | + | 0.349381i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 121.806 | 0.294930 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 661.262 | − | 57.5579i | 1.59340 | − | 0.138694i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −88.2294 | + | 37.8105i | −0.211581 | + | 0.0906728i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 622.927i | 1.48670i | 0.668903 | + | 0.743350i | \(0.266764\pi\) | ||||
−0.668903 | + | 0.743350i | \(0.733236\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −242.097 | −0.575052 | −0.287526 | − | 0.957773i | \(-0.592833\pi\) | ||||
−0.287526 | + | 0.957773i | \(0.592833\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 247.314 | − | 259.660i | 0.584668 | − | 0.613853i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 101.527 | − | 17.8093i | 0.238888 | − | 0.0419043i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 377.450i | 0.883958i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 285.646 | − | 122.413i | 0.665841 | − | 0.285345i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 454.978i | 1.05563i | 0.849359 | + | 0.527816i | \(0.176989\pi\) | ||||
−0.849359 | + | 0.527816i | \(0.823011\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 382.897i | − | 0.884288i | −0.896944 | − | 0.442144i | \(-0.854218\pi\) | ||
0.896944 | − | 0.442144i | \(-0.145782\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 343.518 | + | 641.408i | 0.789695 | + | 1.47450i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 915.992 | 2.09609 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 126.812 | 0.288865 | 0.144433 | − | 0.989515i | \(-0.453864\pi\) | ||||
0.144433 | + | 0.989515i | \(0.453864\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −798.571 | + | 838.433i | −1.81082 | + | 1.90121i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 254.887 | 0.575365 | 0.287682 | − | 0.957726i | \(-0.407115\pi\) | ||||
0.287682 | + | 0.957726i | \(0.407115\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.11419 | − | 93.2210i | −0.0182341 | − | 0.209485i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 92.4120 | + | 215.640i | 0.206738 | + | 0.482416i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 863.869i | − | 1.92398i | −0.273076 | − | 0.961992i | \(-0.588041\pi\) | ||
0.273076 | − | 0.961992i | \(-0.411959\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 135.962 | 0.301469 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −412.703 | + | 176.863i | −0.911044 | + | 0.390426i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 944.444 | − | 82.2068i | 2.07570 | − | 0.180674i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 222.183i | 0.486178i | 0.970004 | + | 0.243089i | \(0.0781607\pi\) | ||||
−0.970004 | + | 0.243089i | \(0.921839\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −38.8183 | + | 104.337i | −0.0845714 | + | 0.227313i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 427.601i | − | 0.927551i | −0.885953 | − | 0.463775i | \(-0.846494\pi\) | ||
0.885953 | − | 0.463775i | \(-0.153506\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 437.238i | − | 0.944358i | −0.881503 | − | 0.472179i | \(-0.843468\pi\) | ||
0.881503 | − | 0.472179i | \(-0.156532\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 643.137 | − | 344.444i | 1.38309 | − | 0.740739i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 407.465 | 0.872516 | 0.436258 | − | 0.899822i | \(-0.356304\pi\) | ||||
0.436258 | + | 0.899822i | \(0.356304\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −618.245 | −1.31822 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −237.865 | − | 555.049i | −0.505022 | − | 1.17845i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −512.181 | −1.08284 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 752.019 | − | 131.915i | 1.58320 | − | 0.277715i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 252.684 | − | 265.297i | 0.529736 | − | 0.556179i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 510.262i | − | 1.06527i | −0.846347 | − | 0.532633i | \(-0.821203\pi\) | ||
0.846347 | − | 0.532633i | \(-0.178797\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 191.537 | 0.398206 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −472.408 | − | 1102.35i | −0.978071 | − | 2.28229i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 18.6854 | + | 214.670i | 0.0385267 | + | 0.442619i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 918.558i | 1.88616i | 0.332572 | + | 0.943078i | \(0.392084\pi\) | ||||
−0.332572 | + | 0.943078i | \(0.607916\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.8728 | + | 46.3724i | 0.0406396 | + | 0.0948310i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 293.290i | − | 0.597332i | −0.954358 | − | 0.298666i | \(-0.903458\pi\) | ||
0.954358 | − | 0.298666i | \(-0.0965417\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 199.999i | − | 0.405678i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −255.994 | − | 204.580i | −0.517159 | − | 0.413293i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1273.77 | −2.56292 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 47.2362 | 0.0946618 | 0.0473309 | − | 0.998879i | \(-0.484928\pi\) | ||||
0.0473309 | + | 0.998879i | \(0.484928\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 469.671 | − | 201.277i | 0.937468 | − | 0.401750i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −45.4136 | −0.0902855 | −0.0451428 | − | 0.998981i | \(-0.514374\pi\) | ||||
−0.0451428 | + | 0.998981i | \(0.514374\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −31.3308 | − | 359.949i | −0.0620412 | − | 0.712770i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 91.9790 | − | 39.4174i | 0.181418 | − | 0.0777464i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 864.768i | − | 1.69896i | −0.527625 | − | 0.849478i | \(-0.676917\pi\) | ||
0.527625 | − | 0.849478i | \(-0.323083\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −985.596 | −1.92876 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −287.529 | + | 772.827i | −0.560485 | + | 1.50648i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 38.7357 | + | 445.021i | 0.0752150 | + | 0.864118i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 290.147i | − | 0.561212i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 40.9124 | − | 17.5329i | 0.0788293 | − | 0.0337821i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 474.781i | − | 0.911287i | −0.890162 | − | 0.455644i | \(-0.849409\pi\) | ||
0.890162 | − | 0.455644i | \(-0.150591\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 956.640i | 1.82914i | 0.404427 | + | 0.914570i | \(0.367471\pi\) | ||||
−0.404427 | + | 0.914570i | \(0.632529\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −546.593 | − | 836.980i | −1.04113 | − | 1.59425i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −200.538 | −0.380528 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 370.589 | 0.700547 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −59.5566 | − | 56.7250i | −0.112159 | − | 0.106827i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 265.593 | 0.498298 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −465.821 | + | 40.5462i | −0.870693 | + | 0.0757873i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 183.203 | + | 427.497i | 0.341160 | + | 0.796084i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 936.875i | 1.73817i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 220.979 | 0.408464 | 0.204232 | − | 0.978923i | \(-0.434530\pi\) | ||||
0.204232 | + | 0.978923i | \(0.434530\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 584.496 | − | 250.485i | 1.07642 | − | 0.461298i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 386.269 | − | 33.6218i | 0.708751 | − | 0.0616914i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 314.582i | − | 0.575104i | −0.957765 | − | 0.287552i | \(-0.907159\pi\) | ||
0.957765 | − | 0.287552i | \(-0.0928413\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 175.778 | − | 184.553i | 0.320179 | − | 0.336161i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 1481.40i | − | 2.68857i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 624.521i | 1.12933i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −95.3540 | − | 178.043i | −0.171809 | − | 0.320797i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1096.11 | −1.96788 | −0.983940 | − | 0.178497i | \(-0.942877\pi\) | ||||
−0.983940 | + | 0.178497i | \(0.942877\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1000.51 | −1.78982 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 35.4808 | + | 82.7931i | 0.0632456 | + | 0.147581i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 386.925 | 0.687257 | 0.343628 | − | 0.939106i | \(-0.388344\pi\) | ||||
0.343628 | + | 0.939106i | \(0.388344\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −79.1086 | + | 6.88581i | −0.140015 | + | 0.0121873i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1078.34 | − | 52.5479i | 1.90184 | − | 0.0926771i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 113.274i | − | 0.199076i | −0.995034 | − | 0.0995381i | \(-0.968263\pi\) | ||
0.995034 | − | 0.0995381i | \(-0.0317365\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 434.868 | 0.761589 | 0.380795 | − | 0.924660i | \(-0.375650\pi\) | ||||
0.380795 | + | 0.924660i | \(0.375650\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −352.763 | − | 823.158i | −0.615642 | − | 1.43658i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 738.552 | − | 129.552i | 1.28444 | − | 0.225309i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 283.194i | 0.490805i | 0.969421 | + | 0.245402i | \(0.0789200\pi\) | ||||
−0.969421 | + | 0.245402i | \(0.921080\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −309.673 | − | 722.610i | −0.534842 | − | 1.24803i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1769.41i | 3.04546i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 296.446i | − | 0.508484i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −500.066 | − | 399.633i | −0.854813 | − | 0.683133i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 80.5141 | 0.137162 | 0.0685810 | − | 0.997646i | \(-0.478153\pi\) | ||||
0.0685810 | + | 0.997646i | \(0.478153\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1485.40 | −2.52190 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 747.865 | − | 320.496i | 1.26542 | − | 0.542295i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 583.731 | 0.984370 | 0.492185 | − | 0.870491i | \(-0.336198\pi\) | ||||
0.492185 | + | 0.870491i | \(0.336198\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 23.8272 | + | 273.742i | 0.0400458 | + | 0.460071i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 484.631 | − | 207.688i | 0.811777 | − | 0.347885i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1080.54i | 1.80391i | 0.431834 | + | 0.901953i | \(0.357867\pi\) | ||||
−0.431834 | + | 0.901953i | \(0.642133\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 689.594 | 1.14741 | 0.573706 | − | 0.819062i | \(-0.305505\pi\) | ||||
0.573706 | + | 0.819062i | \(0.305505\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 302.289 | + | 287.917i | 0.501308 | + | 0.477474i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 338.570 | − | 29.4700i | 0.559620 | − | 0.0487107i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 466.053i | 0.767798i | 0.923375 | + | 0.383899i | \(0.125419\pi\) | ||||
−0.923375 | + | 0.383899i | \(0.874581\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1782.79 | + | 764.010i | −2.92740 | + | 1.25453i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 566.781i | − | 0.927629i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 754.913i | − | 1.23151i | −0.787939 | − | 0.615753i | \(-0.788852\pi\) | ||
0.787939 | − | 0.615753i | \(-0.211148\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −132.222 | − | 246.881i | −0.214995 | − | 0.401433i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 685.857 | 1.11160 | 0.555800 | − | 0.831316i | \(-0.312412\pi\) | ||||
0.555800 | + | 0.831316i | \(0.312412\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −633.092 | −1.02277 | −0.511383 | − | 0.859353i | \(-0.670867\pi\) | ||||
−0.511383 | + | 0.859353i | \(0.670867\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −282.380 | + | 758.988i | −0.454718 | + | 1.22220i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 249.442 | 0.400388 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 587.686 | − | 212.722i | 0.940297 | − | 0.340355i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 262.808 | + | 613.252i | 0.419152 | + | 0.978074i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 55.5160i | 0.0882608i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 374.848 | 0.594054 | 0.297027 | − | 0.954869i | \(-0.404005\pi\) | ||||
0.297027 | + | 0.954869i | \(0.404005\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 546.061 | − | 234.013i | 0.862655 | − | 0.369689i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −40.2599 | − | 462.532i | −0.0634015 | − | 0.728397i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1830.12i | 2.87303i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 622.805 | + | 593.195i | 0.974656 | + | 0.928317i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 36.2900i | 0.0566147i | 0.999599 | + | 0.0283073i | \(0.00901171\pi\) | ||||
−0.999599 | + | 0.0283073i | \(0.990988\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 421.273i | − | 0.655168i | −0.944822 | − | 0.327584i | \(-0.893766\pi\) | ||
0.944822 | − | 0.327584i | \(-0.106234\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 498.090 | + | 930.022i | 0.772233 | + | 1.44189i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −999.955 | −1.54553 | −0.772763 | − | 0.634695i | \(-0.781126\pi\) | ||||
−0.772763 | + | 0.634695i | \(0.781126\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −66.5492 | −0.102541 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 766.070 | + | 1787.59i | 1.17676 | + | 2.74592i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 783.570 | 1.19995 | 0.599977 | − | 0.800017i | \(-0.295176\pi\) | ||||
0.599977 | + | 0.800017i | \(0.295176\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 39.1138 | + | 449.365i | 0.0597158 | + | 0.686053i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 481.903 | + | 458.992i | 0.733490 | + | 0.698617i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 123.974i | − | 0.188124i | −0.995566 | − | 0.0940620i | \(-0.970015\pi\) | ||
0.995566 | − | 0.0940620i | \(-0.0299852\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 117.706 | 0.178072 | 0.0890360 | − | 0.996028i | \(-0.471621\pi\) | ||||
0.0890360 | + | 0.996028i | \(0.471621\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 69.3093 | + | 161.731i | 0.104539 | + | 0.243937i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 176.489 | + | 2027.62i | 0.265398 | + | 3.04906i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1454.88i | − | 2.18122i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.12649 | + | 18.9628i | 0.0121472 | + | 0.0283451i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 206.221i | − | 0.307334i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 539.523i | − | 0.801669i | −0.916150 | − | 0.400835i | \(-0.868720\pi\) | ||
0.916150 | − | 0.400835i | \(-0.131280\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −122.527 | + | 663.786i | −0.181521 | + | 0.983387i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 645.528 | 0.953512 | 0.476756 | − | 0.879036i | \(-0.341812\pi\) | ||||
0.476756 | + | 0.879036i | \(0.341812\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −574.417 | −0.845975 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 251.859 | − | 107.934i | 0.369837 | − | 0.158493i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −796.825 | −1.16665 | −0.583327 | − | 0.812237i | \(-0.698249\pi\) | ||||
−0.583327 | + | 0.812237i | \(0.698249\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 605.290 | − | 52.6860i | 0.883636 | − | 0.0769139i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −428.968 | + | 183.833i | −0.624407 | + | 0.267588i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 579.087i | − | 0.840475i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1302.35 | −1.88474 | −0.942369 | − | 0.334575i | \(-0.891407\pi\) | ||||
−0.942369 | + | 0.334575i | \(0.891407\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 602.476 | − | 632.550i | 0.869374 | − | 0.912770i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 159.381 | − | 13.8729i | 0.229325 | − | 0.0199610i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 76.9808i | 0.110446i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 445.158 | − | 190.772i | 0.636850 | − | 0.272921i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 260.882i | 0.372157i | 0.982535 | + | 0.186078i | \(0.0595778\pi\) | ||||
−0.982535 | + | 0.186078i | \(0.940422\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 411.210i | 0.584936i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −526.850 | + | 282.164i | −0.747305 | + | 0.400233i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 963.155 | 1.36231 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 440.863 | 0.621809 | 0.310905 | − | 0.950441i | \(-0.399368\pi\) | ||||
0.310905 | + | 0.950441i | \(0.399368\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 290.839 | − | 305.357i | 0.409057 | − | 0.429476i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1458.80 | −2.04600 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −516.000 | + | 44.9140i | −0.721679 | + | 0.0628167i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 251.502 | + | 586.869i | 0.350769 | + | 0.818506i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1359.12i | − | 1.89029i | −0.326648 | − | 0.945146i | \(-0.605919\pi\) | ||
0.326648 | − | 0.945146i | \(-0.394081\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1190.79 | −1.65158 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1229.37 | + | 526.845i | −1.70038 | + | 0.728692i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −209.521 | − | 1194.44i | −0.288994 | − | 1.64750i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 67.9032i | − | 0.0934019i | −0.998909 | − | 0.0467009i | \(-0.985129\pi\) | ||
0.998909 | − | 0.0467009i | \(-0.0148708\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −551.723 | − | 476.490i | −0.756821 | − | 0.653622i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 289.993i | − | 0.396707i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 728.945i | − | 0.994468i | −0.867617 | − | 0.497234i | \(-0.834349\pi\) | ||
0.867617 | − | 0.497234i | \(-0.165651\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1701.18 | − | 911.100i | 2.31454 | − | 1.23959i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 337.781 | 0.458318 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1008.11 | 1.36416 | 0.682080 | − | 0.731278i | \(-0.261076\pi\) | ||||
0.682080 | + | 0.731278i | \(0.261076\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 513.377 | + | 1197.95i | 0.692817 | + | 1.61666i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 696.093 | 0.936869 | 0.468434 | − | 0.883498i | \(-0.344818\pi\) | ||||
0.468434 | + | 0.883498i | \(0.344818\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −33.9065 | − | 389.539i | −0.0455120 | − | 0.522871i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 824.015 | − | 865.147i | 1.10310 | − | 1.15816i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 1246.45i | − | 1.66415i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 783.678 | 1.04351 | 0.521756 | − | 0.853095i | \(-0.325277\pi\) | ||||
0.521756 | + | 0.853095i | \(0.325277\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 131.077 | + | 305.864i | 0.174073 | + | 0.406193i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 745.520 | − | 64.8919i | 0.987444 | − | 0.0859496i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 511.207i | 0.675307i | 0.941270 | + | 0.337654i | \(0.109633\pi\) | ||||
−0.941270 | + | 0.337654i | \(0.890367\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 258.102 | + | 602.271i | 0.340055 | + | 0.793505i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 371.165i | 0.487734i | 0.969809 | + | 0.243867i | \(0.0784160\pi\) | ||||
−0.969809 | + | 0.243867i | \(0.921584\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1033.58i | 1.35463i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 115.832 | − | 144.942i | 0.151414 | − | 0.189466i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −129.999 | −0.169491 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −61.6158 | −0.0801245 | −0.0400623 | − | 0.999197i | \(-0.512756\pi\) | ||||
−0.0400623 | + | 0.999197i | \(0.512756\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 154.733 | − | 66.3107i | 0.200692 | − | 0.0860061i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −87.8197 | −0.113609 | −0.0568045 | − | 0.998385i | \(-0.518091\pi\) | ||||
−0.0568045 | + | 0.998385i | \(0.518091\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1197.66 | + | 210.086i | −1.54536 | + | 0.271078i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 494.868 | − | 212.075i | 0.636896 | − | 0.272940i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 570.201i | 0.731965i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 695.930 | 0.891075 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1227.49 | + | 456.684i | 1.56767 | + | 0.583249i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 87.2740 | + | 1002.66i | 0.111177 | + | 1.27727i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1333.59i | − | 1.69453i | −0.531171 | − | 0.847264i | \(-0.678248\pi\) | ||
0.531171 | − | 0.847264i | \(-0.321752\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −471.600 | + | 202.103i | −0.597719 | + | 0.256151i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 211.680i | − | 0.267610i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 402.839i | − | 0.507994i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −538.289 | + | 288.291i | −0.677093 | + | 0.362630i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 309.090 | 0.387817 | 0.193908 | − | 0.981020i | \(-0.437884\pi\) | ||||
0.193908 | + | 0.981020i | \(0.437884\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 164.279 | 0.205605 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −121.964 | − | 116.165i | −0.152264 | − | 0.145025i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 538.484 | 0.670590 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 173.329 | + | 1991.31i | 0.215315 | + | 2.47368i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 236.506 | + | 551.879i | 0.293069 | + | 0.683864i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1189.17i | − | 1.46992i | −0.678110 | − | 0.734960i | \(-0.737201\pi\) | ||
0.678110 | − | 0.734960i | \(-0.262799\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 960.641 | 1.18451 | 0.592257 | − | 0.805749i | \(-0.298237\pi\) | ||||
0.592257 | + | 0.805749i | \(0.298237\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 26.7903 | − | 11.4809i | 0.0329524 | − | 0.0141217i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.29143 | − | 83.7686i | −0.00894654 | − | 0.102784i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 2147.99i | − | 2.62912i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1176.90 | − | 1235.64i | 1.43699 | − | 1.50872i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1071.24i | 1.30480i | 0.757877 | + | 0.652398i | \(0.226237\pi\) | ||||
−0.757877 | + | 0.652398i | \(0.773763\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 915.823i | − | 1.11279i | −0.830919 | − | 0.556393i | \(-0.812185\pi\) | ||
0.830919 | − | 0.556393i | \(-0.187815\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 298.633 | + | 457.287i | 0.361980 | + | 0.554287i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −505.257 | −0.610952 | −0.305476 | − | 0.952200i | \(-0.598816\pi\) | ||||
−0.305476 | + | 0.952200i | \(0.598816\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −386.448 | −0.466161 | −0.233081 | − | 0.972457i | \(-0.574881\pi\) | ||||
−0.233081 | + | 0.972457i | \(0.574881\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.0307 | − | 42.0740i | −0.0216976 | − | 0.0506305i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −530.451 | −0.636796 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −848.430 | + | 73.8495i | −1.01608 | + | 0.0884425i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 457.915 | − | 1230.79i | 0.547091 | − | 1.47048i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 610.689i | 0.727877i | 0.931423 | + | 0.363939i | \(0.118568\pi\) | ||||
−0.931423 | + | 0.363939i | \(0.881432\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1511.92 | −1.79777 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 165.635 | + | 386.503i | 0.196483 | + | 0.458485i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −166.154 | + | 14.4625i | −0.196632 | + | 0.0171153i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 905.950i | 1.06960i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 43.4423 | + | 101.371i | 0.0511688 | + | 0.119400i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 403.846i | 0.474555i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1500.11i | 1.75863i | 0.476243 | + | 0.879314i | \(0.341998\pi\) | ||||
−0.476243 | + | 0.879314i | \(0.658002\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 857.970 | − | 1073.59i | 1.00347 | − | 1.25566i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 127.645 | 0.148944 | 0.0744721 | − | 0.997223i | \(-0.476273\pi\) | ||||
0.0744721 | + | 0.997223i | \(0.476273\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 46.8391 | 0.0545274 | 0.0272637 | − | 0.999628i | \(-0.491321\pi\) | ||||
0.0272637 | + | 0.999628i | \(0.491321\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 686.205 | − | 294.072i | 0.796986 | − | 0.341547i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −554.819 | −0.642895 | −0.321448 | − | 0.946927i | \(-0.604169\pi\) | ||||
−0.321448 | + | 0.946927i | \(0.604169\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −73.9056 | + | 6.43292i | −0.0854400 | + | 0.00743691i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −46.8768 | + | 20.0890i | −0.0540678 | + | 0.0231707i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 341.210i | − | 0.392646i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 659.831 | 0.757556 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 280.859 | + | 267.506i | 0.321717 | + | 0.306421i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 429.076 | + | 1609.88i | 0.490372 | + | 1.83987i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 775.419i | − | 0.884172i | −0.896973 | − | 0.442086i | \(-0.854239\pi\) | ||
0.896973 | − | 0.442086i | \(-0.145761\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1214.18 | − | 520.335i | 1.38132 | − | 0.591962i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 826.534i | − | 0.938177i | −0.883151 | − | 0.469089i | \(-0.844582\pi\) | ||
0.883151 | − | 0.469089i | \(-0.155418\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1422.79i | 1.61131i | 0.592383 | + | 0.805657i | \(0.298187\pi\) | ||||
−0.592383 | + | 0.805657i | \(0.701813\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 64.7183 | + | 120.840i | 0.0731280 | + | 0.136543i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 503.369 | 0.567496 | 0.283748 | − | 0.958899i | \(-0.408422\pi\) | ||||
0.283748 | + | 0.958899i | \(0.408422\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1237.65 | 1.39218 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −589.156 | + | 28.7098i | −0.661230 | + | 0.0322220i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1216.82 | 1.36262 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −67.2182 | − | 772.245i | −0.0751041 | − | 0.862844i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 504.184 | + | 1176.49i | 0.562078 | + | 1.31159i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2359.27i | 2.62432i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 167.846 | 0.186288 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2584.99 | + | 1107.79i | −2.86267 | + | 1.22679i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1055.85 | + | 91.9041i | −1.16669 | + | 0.101552i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1552.85i | − | 1.71208i | −0.516911 | − | 0.856039i | \(-0.672918\pi\) | ||
0.516911 | − | 0.856039i | \(-0.327082\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −470.931 | − | 448.541i | −0.518076 | − | 0.493444i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1017.10i | − | 1.11646i | −0.829686 | − | 0.558230i | \(-0.811481\pi\) | ||
0.829686 | − | 0.558230i | \(-0.188519\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 966.725i | − | 1.05884i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −374.458 | + | 200.548i | −0.409244 | + | 0.219178i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1202.42 | −1.31125 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1102.70 | −1.19989 | −0.599946 | − | 0.800040i | \(-0.704811\pi\) | ||||
−0.599946 | + | 0.800040i | \(0.704811\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21.7351 | − | 50.7179i | −0.0235994 | − | 0.0550683i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1359.45 | 1.47286 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 58.1590 | + | 331.553i | 0.0628746 | + | 0.358436i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 582.233 | + | 554.552i | 0.628083 | + | 0.598222i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 560.608i | 0.603454i | 0.953394 | + | 0.301727i | \(0.0975631\pi\) | ||||
−0.953394 | + | 0.301727i | \(0.902437\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3929.08 | −4.22028 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 143.357 | + | 334.517i | 0.153651 | + | 0.358539i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −13.0181 | − | 149.560i | −0.0139231 | − | 0.159957i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 673.304i | − | 0.718574i | −0.933227 | − | 0.359287i | \(-0.883020\pi\) | ||
0.933227 | − | 0.359287i | \(-0.116980\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 285.184 | + | 665.467i | 0.303711 | + | 0.708697i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 438.910i | − | 0.466429i | −0.972425 | − | 0.233214i | \(-0.925076\pi\) | ||
0.972425 | − | 0.233214i | \(-0.0749244\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 559.990i | 0.593839i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1734.49 | − | 478.833i | −1.83544 | − | 0.506701i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1842.75 | −1.94588 | −0.972939 | − | 0.231063i | \(-0.925780\pi\) | ||||
−0.972939 | + | 0.231063i | \(0.925780\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1051.89 | 1.10842 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1344.50 | + | 576.185i | −1.41378 | + | 0.605872i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 198.284 | 0.208063 | 0.104031 | − | 0.994574i | \(-0.466826\pi\) | ||||
0.104031 | + | 0.994574i | \(0.466826\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 129.430 | + | 1486.98i | 0.135529 | + | 1.55705i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 974.033 | − | 417.420i | 1.01780 | − | 0.436175i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1619.64i | 1.68889i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1404.63 | 1.46163 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −580.471 | + | 609.446i | −0.602773 | + | 0.632862i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 113.621 | + | 1305.35i | 0.117742 | + | 1.35269i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 889.888i | − | 0.920256i | −0.887853 | − | 0.460128i | \(-0.847803\pi\) | ||
0.887853 | − | 0.460128i | \(-0.152197\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −347.219 | + | 148.800i | −0.358327 | + | 0.153560i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 553.795i | − | 0.570335i | −0.958478 | − | 0.285167i | \(-0.907951\pi\) | ||
0.958478 | − | 0.285167i | \(-0.0920492\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 426.473i | 0.438307i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 583.359 | + | 893.279i | 0.598317 | + | 0.916183i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1047.10 | −1.07175 | −0.535877 | − | 0.844296i | \(-0.680019\pi\) | ||||
−0.535877 | + | 0.844296i | \(0.680019\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −136.283 | −0.139207 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 481.340 | − | 505.367i | 0.490662 | − | 0.515155i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 257.621 | 0.262076 | 0.131038 | − | 0.991377i | \(-0.458169\pi\) | ||||
0.131038 | + | 0.991377i | \(0.458169\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1350.97 | + | 117.592i | −1.37154 | + | 0.119382i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −627.556 | − | 1464.38i | −0.635821 | − | 1.48366i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 2109.53i | − | 2.13299i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1574.78 | −1.58909 | −0.794543 | − | 0.607208i | \(-0.792289\pi\) | ||||
−0.794543 | + | 0.607208i | \(0.792289\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 727.196 | − | 311.638i | 0.732322 | − | 0.313835i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −875.453 | + | 76.2016i | −0.879853 | + | 0.0765846i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1435.38i | 1.43970i | 0.694129 | + | 0.719850i | \(0.255790\pi\) | ||||
−0.694129 | + | 0.719850i | \(0.744210\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −340.727 | − | 126.767i | −0.341068 | − | 0.126894i |
(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 | 1020.3.c.a.749.10 | yes | 64 | |
3.2 | odd | 2 | inner | 1020.3.c.a.749.56 | yes | 64 | |
5.4 | even | 2 | inner | 1020.3.c.a.749.55 | yes | 64 | |
15.14 | odd | 2 | inner | 1020.3.c.a.749.9 | ✓ | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1020.3.c.a.749.9 | ✓ | 64 | 15.14 | odd | 2 | inner | |
1020.3.c.a.749.10 | yes | 64 | 1.1 | even | 1 | trivial | |
1020.3.c.a.749.55 | yes | 64 | 5.4 | even | 2 | inner | |
1020.3.c.a.749.56 | yes | 64 | 3.2 | odd | 2 | inner |