Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4014,2,Mod(4013,4014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4014, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4014.4013");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4014 = 2 \cdot 3^{2} \cdot 223 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4014.d (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: | \(32.0519513713\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4013.10 | ||
Character | \(\chi\) | \(=\) | 4014.4013 |
Dual form | 4014.2.d.a.4013.9 |
$q$-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 \(\left(\mathbb{Z}/4014\mathbb{Z}\right)^\times\).
\(n\) | \(893\) | \(2233\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 3.59603 | 1.60819 | 0.804096 | − | 0.594499i | \(-0.202650\pi\) | ||||
0.804096 | + | 0.594499i | \(0.202650\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.66381 | 1.76276 | 0.881378 | − | 0.472412i | \(-0.156617\pi\) | ||||
0.881378 | + | 0.472412i | \(0.156617\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.59603i | 1.13716i | ||||||||
\(11\) | −0.902432 | −0.272093 | −0.136047 | − | 0.990702i | \(-0.543440\pi\) | ||||
−0.136047 | + | 0.990702i | \(0.543440\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.90912i | 1.08419i | 0.840316 | + | 0.542097i | \(0.182369\pi\) | ||||
−0.840316 | + | 0.542097i | \(0.817631\pi\) | |||||||
\(14\) | 4.66381i | 1.24646i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 3.88874i | − | 0.943158i | −0.881824 | − | 0.471579i | \(-0.843684\pi\) | ||
0.881824 | − | 0.471579i | \(-0.156316\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00606 | 0.460222 | 0.230111 | − | 0.973164i | \(-0.426091\pi\) | ||||
0.230111 | + | 0.973164i | \(0.426091\pi\) | |||||||
\(20\) | −3.59603 | −0.804096 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 0.902432i | − | 0.192399i | ||||||
\(23\) | 9.11811 | 1.90126 | 0.950629 | − | 0.310331i | \(-0.100440\pi\) | ||||
0.950629 | + | 0.310331i | \(0.100440\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.93141 | 1.58628 | ||||||||
\(26\) | −3.90912 | −0.766641 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.66381 | −0.881378 | ||||||||
\(29\) | − | 5.06669i | − | 0.940861i | −0.882437 | − | 0.470431i | \(-0.844099\pi\) | ||
0.882437 | − | 0.470431i | \(-0.155901\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.64590 | −1.37324 | −0.686622 | − | 0.727014i | \(-0.740907\pi\) | ||||
−0.686622 | + | 0.727014i | \(0.740907\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.88874 | 0.666914 | ||||||||
\(35\) | 16.7712 | 2.83485 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.27714 | 0.374359 | 0.187180 | − | 0.982326i | \(-0.440065\pi\) | ||||
0.187180 | + | 0.982326i | \(0.440065\pi\) | |||||||
\(38\) | 2.00606i | 0.325426i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 3.59603i | − | 0.568582i | ||||||
\(41\) | 1.40849i | 0.219969i | 0.993933 | + | 0.109984i | \(0.0350801\pi\) | ||||
−0.993933 | + | 0.109984i | \(0.964920\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.26130 | −0.802341 | −0.401170 | − | 0.916003i | \(-0.631396\pi\) | ||||
−0.401170 | + | 0.916003i | \(0.631396\pi\) | |||||||
\(44\) | 0.902432 | 0.136047 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 9.11811i | 1.34439i | ||||||||
\(47\) | 5.68266i | 0.828901i | 0.910072 | + | 0.414451i | \(0.136026\pi\) | ||||
−0.910072 | + | 0.414451i | \(0.863974\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.7511 | 2.10731 | ||||||||
\(50\) | 7.93141i | 1.12167i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 3.90912i | − | 0.542097i | ||||||
\(53\) | 12.3390i | 1.69490i | 0.530878 | + | 0.847448i | \(0.321862\pi\) | ||||
−0.530878 | + | 0.847448i | \(0.678138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.24517 | −0.437579 | ||||||||
\(56\) | − | 4.66381i | − | 0.623228i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.06669 | 0.665289 | ||||||||
\(59\) | −1.09050 | −0.141972 | −0.0709858 | − | 0.997477i | \(-0.522614\pi\) | ||||
−0.0709858 | + | 0.997477i | \(0.522614\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.98011i | 0.253527i | 0.991933 | + | 0.126763i | \(0.0404589\pi\) | ||||
−0.991933 | + | 0.126763i | \(0.959541\pi\) | |||||||
\(62\) | − | 7.64590i | − | 0.971030i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 14.0573i | 1.74359i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 13.9899i | − | 1.70914i | −0.519340 | − | 0.854568i | \(-0.673822\pi\) | ||
0.519340 | − | 0.854568i | \(-0.326178\pi\) | |||||||
\(68\) | 3.88874i | 0.471579i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 16.7712i | 2.00454i | ||||||||
\(71\) | −6.23553 | −0.740021 | −0.370010 | − | 0.929028i | \(-0.620646\pi\) | ||||
−0.370010 | + | 0.929028i | \(0.620646\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.3293 | −1.79415 | −0.897077 | − | 0.441875i | \(-0.854313\pi\) | ||||
−0.897077 | + | 0.441875i | \(0.854313\pi\) | |||||||
\(74\) | 2.27714i | 0.264712i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.00606 | −0.230111 | ||||||||
\(77\) | −4.20877 | −0.479634 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 5.68601i | − | 0.639726i | −0.947464 | − | 0.319863i | \(-0.896363\pi\) | ||
0.947464 | − | 0.319863i | \(-0.103637\pi\) | |||||||
\(80\) | 3.59603 | 0.402048 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.40849 | −0.155541 | ||||||||
\(83\) | − | 2.04815i | − | 0.224813i | −0.993662 | − | 0.112407i | \(-0.964144\pi\) | ||
0.993662 | − | 0.112407i | \(-0.0358559\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 13.9840i | − | 1.51678i | ||||||
\(86\) | − | 5.26130i | − | 0.567341i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.902432i | 0.0961996i | ||||||||
\(89\) | − | 1.95797i | − | 0.207545i | −0.994601 | − | 0.103772i | \(-0.966909\pi\) | ||
0.994601 | − | 0.103772i | \(-0.0330914\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 18.2314i | 1.91117i | ||||||||
\(92\) | −9.11811 | −0.950629 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.68266 | −0.586122 | ||||||||
\(95\) | 7.21384 | 0.740125 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 10.0724i | − | 1.02270i | −0.859374 | − | 0.511348i | \(-0.829146\pi\) | ||
0.859374 | − | 0.511348i | \(-0.170854\pi\) | |||||||
\(98\) | 14.7511i | 1.49009i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.93141 | −0.793141 | ||||||||
\(101\) | − | 11.9250i | − | 1.18658i | −0.804988 | − | 0.593291i | \(-0.797828\pi\) | ||
0.804988 | − | 0.593291i | \(-0.202172\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.4768i | 1.52498i | 0.647003 | + | 0.762488i | \(0.276022\pi\) | ||||
−0.647003 | + | 0.762488i | \(0.723978\pi\) | |||||||
\(104\) | 3.90912 | 0.383320 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.3390 | −1.19847 | ||||||||
\(107\) | 18.9884 | 1.83568 | 0.917841 | − | 0.396948i | \(-0.129931\pi\) | ||||
0.917841 | + | 0.396948i | \(0.129931\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.80760 | −0.460484 | −0.230242 | − | 0.973133i | \(-0.573952\pi\) | ||||
−0.230242 | + | 0.973133i | \(0.573952\pi\) | |||||||
\(110\) | − | 3.24517i | − | 0.309415i | ||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.66381 | 0.440689 | ||||||||
\(113\) | 18.1589 | 1.70825 | 0.854125 | − | 0.520068i | \(-0.174093\pi\) | ||||
0.854125 | + | 0.520068i | \(0.174093\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 32.7890 | 3.05759 | ||||||||
\(116\) | 5.06669i | 0.470431i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 1.09050i | − | 0.100389i | ||||||
\(119\) | − | 18.1364i | − | 1.66256i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.1856 | −0.925965 | ||||||||
\(122\) | −1.98011 | −0.179270 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.64590 | 0.686622 | ||||||||
\(125\) | 10.5414 | 0.942853 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.78190 | −0.335590 | −0.167795 | − | 0.985822i | \(-0.553665\pi\) | ||||
−0.167795 | + | 0.985822i | \(0.553665\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −14.0573 | −1.23291 | ||||||||
\(131\) | − | 9.66672i | − | 0.844585i | −0.906460 | − | 0.422293i | \(-0.861225\pi\) | ||
0.906460 | − | 0.422293i | \(-0.138775\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.35589 | 0.811258 | ||||||||
\(134\) | 13.9899 | 1.20854 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.88874 | −0.333457 | ||||||||
\(137\) | −0.470346 | −0.0401844 | −0.0200922 | − | 0.999798i | \(-0.506396\pi\) | ||||
−0.0200922 | + | 0.999798i | \(0.506396\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.4688 | −1.22722 | −0.613612 | − | 0.789607i | \(-0.710284\pi\) | ||||
−0.613612 | + | 0.789607i | \(0.710284\pi\) | |||||||
\(140\) | −16.7712 | −1.41742 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 6.23553i | − | 0.523274i | ||||||
\(143\) | − | 3.52771i | − | 0.295002i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 18.2200i | − | 1.51309i | ||||||
\(146\) | − | 15.3293i | − | 1.26866i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.27714 | −0.187180 | ||||||||
\(149\) | 0.978503 | 0.0801621 | 0.0400810 | − | 0.999196i | \(-0.487238\pi\) | ||||
0.0400810 | + | 0.999196i | \(0.487238\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 3.93932i | − | 0.320577i | −0.987070 | − | 0.160289i | \(-0.948757\pi\) | ||
0.987070 | − | 0.160289i | \(-0.0512425\pi\) | |||||||
\(152\) | − | 2.00606i | − | 0.162713i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 4.20877i | − | 0.339153i | ||||||
\(155\) | −27.4949 | −2.20844 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.1663i | 0.891167i | 0.895240 | + | 0.445583i | \(0.147004\pi\) | ||||
−0.895240 | + | 0.445583i | \(0.852996\pi\) | |||||||
\(158\) | 5.68601 | 0.452355 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.59603i | 0.284291i | ||||||||
\(161\) | 42.5251 | 3.35145 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.5956i | 1.22154i | 0.791807 | + | 0.610771i | \(0.209141\pi\) | ||||
−0.791807 | + | 0.610771i | \(0.790859\pi\) | |||||||
\(164\) | − | 1.40849i | − | 0.109984i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.04815 | 0.158967 | ||||||||
\(167\) | −7.90448 | −0.611667 | −0.305833 | − | 0.952085i | \(-0.598935\pi\) | ||||
−0.305833 | + | 0.952085i | \(0.598935\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.28120 | −0.175477 | ||||||||
\(170\) | 13.9840 | 1.07253 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.26130 | 0.401170 | ||||||||
\(173\) | −15.7797 | −1.19971 | −0.599856 | − | 0.800108i | \(-0.704775\pi\) | ||||
−0.599856 | + | 0.800108i | \(0.704775\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 36.9906 | 2.79623 | ||||||||
\(176\) | −0.902432 | −0.0680234 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.95797 | 0.146756 | ||||||||
\(179\) | 4.39415i | 0.328434i | 0.986424 | + | 0.164217i | \(0.0525098\pi\) | ||||
−0.986424 | + | 0.164217i | \(0.947490\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.91690 | −0.439800 | −0.219900 | − | 0.975522i | \(-0.570573\pi\) | ||||
−0.219900 | + | 0.975522i | \(0.570573\pi\) | |||||||
\(182\) | −18.2314 | −1.35140 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 9.11811i | − | 0.672196i | ||||||
\(185\) | 8.18865 | 0.602042 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.50932i | 0.256627i | ||||||||
\(188\) | − | 5.68266i | − | 0.414451i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.21384i | 0.523347i | ||||||||
\(191\) | 18.1304 | 1.31187 | 0.655936 | − | 0.754816i | \(-0.272274\pi\) | ||||
0.655936 | + | 0.754816i | \(0.272274\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 12.2241i | − | 0.879910i | −0.898020 | − | 0.439955i | \(-0.854994\pi\) | ||
0.898020 | − | 0.439955i | \(-0.145006\pi\) | |||||||
\(194\) | 10.0724 | 0.723155 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.7511 | −1.05365 | ||||||||
\(197\) | − | 2.60238i | − | 0.185412i | −0.995694 | − | 0.0927061i | \(-0.970448\pi\) | ||
0.995694 | − | 0.0927061i | \(-0.0295517\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.9269 | −1.05814 | −0.529071 | − | 0.848578i | \(-0.677459\pi\) | ||||
−0.529071 | + | 0.848578i | \(0.677459\pi\) | |||||||
\(200\) | − | 7.93141i | − | 0.560835i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 11.9250 | 0.839040 | ||||||||
\(203\) | − | 23.6301i | − | 1.65851i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.06496i | 0.353752i | ||||||||
\(206\) | −15.4768 | −1.07832 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.90912i | 0.271049i | ||||||||
\(209\) | −1.81033 | −0.125223 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.4855 | 1.13491 | 0.567455 | − | 0.823405i | \(-0.307928\pi\) | ||||
0.567455 | + | 0.823405i | \(0.307928\pi\) | |||||||
\(212\) | − | 12.3390i | − | 0.847448i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 18.9884i | 1.29802i | ||||||||
\(215\) | −18.9198 | −1.29032 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −35.6591 | −2.42069 | ||||||||
\(218\) | − | 4.80760i | − | 0.325612i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.24517 | 0.218789 | ||||||||
\(221\) | 15.2015 | 1.02257 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.326717 | + | 14.9296i | 0.0218786 | + | 0.999761i | ||||
\(224\) | 4.66381i | 0.311614i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 18.1589i | 1.20792i | ||||||||
\(227\) | 3.91525i | 0.259865i | 0.991523 | + | 0.129932i | \(0.0414760\pi\) | ||||
−0.991523 | + | 0.129932i | \(0.958524\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 5.35015i | − | 0.353548i | −0.984251 | − | 0.176774i | \(-0.943434\pi\) | ||
0.984251 | − | 0.176774i | \(-0.0565662\pi\) | |||||||
\(230\) | 32.7890i | 2.16204i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.06669 | −0.332645 | ||||||||
\(233\) | 15.0088 | 0.983258 | 0.491629 | − | 0.870805i | \(-0.336402\pi\) | ||||
0.491629 | + | 0.870805i | \(0.336402\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 20.4350i | 1.33303i | ||||||||
\(236\) | 1.09050 | 0.0709858 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 18.1364 | 1.17561 | ||||||||
\(239\) | − | 22.7374i | − | 1.47076i | −0.677656 | − | 0.735379i | \(-0.737004\pi\) | ||
0.677656 | − | 0.735379i | \(-0.262996\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.5649 | −1.00263 | −0.501313 | − | 0.865266i | \(-0.667150\pi\) | ||||
−0.501313 | + | 0.865266i | \(0.667150\pi\) | |||||||
\(242\) | − | 10.1856i | − | 0.654756i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 1.98011i | − | 0.126763i | ||||||
\(245\) | 53.0455 | 3.38895 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.84192i | 0.498970i | ||||||||
\(248\) | 7.64590i | 0.485515i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 10.5414i | 0.666698i | ||||||||
\(251\) | − | 25.2944i | − | 1.59657i | −0.602280 | − | 0.798285i | \(-0.705741\pi\) | ||
0.602280 | − | 0.798285i | \(-0.294259\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.22847 | −0.517320 | ||||||||
\(254\) | − | 3.78190i | − | 0.237298i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 27.5846i | 1.72068i | 0.509720 | + | 0.860340i | \(0.329749\pi\) | ||||
−0.509720 | + | 0.860340i | \(0.670251\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.6201 | 0.659904 | ||||||||
\(260\) | − | 14.0573i | − | 0.871796i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9.66672 | 0.597212 | ||||||||
\(263\) | 7.69202 | 0.474310 | 0.237155 | − | 0.971472i | \(-0.423785\pi\) | ||||
0.237155 | + | 0.971472i | \(0.423785\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 44.3715i | 2.72572i | ||||||||
\(266\) | 9.35589i | 0.573646i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 13.9899i | 0.854568i | ||||||||
\(269\) | −31.7587 | −1.93636 | −0.968181 | − | 0.250251i | \(-0.919487\pi\) | ||||
−0.968181 | + | 0.250251i | \(0.919487\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 8.67132i | − | 0.526745i | −0.964694 | − | 0.263373i | \(-0.915165\pi\) | ||
0.964694 | − | 0.263373i | \(-0.0848348\pi\) | |||||||
\(272\) | − | 3.88874i | − | 0.235790i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 0.470346i | − | 0.0284147i | ||||||
\(275\) | −7.15756 | −0.431617 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.7339i | 1.72645i | 0.504815 | + | 0.863227i | \(0.331561\pi\) | ||||
−0.504815 | + | 0.863227i | \(0.668439\pi\) | |||||||
\(278\) | − | 14.4688i | − | 0.867779i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | − | 16.7712i | − | 1.00227i | ||||||
\(281\) | 23.8796i | 1.42454i | 0.701906 | + | 0.712270i | \(0.252333\pi\) | ||||
−0.701906 | + | 0.712270i | \(0.747667\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.3009 | −1.08787 | −0.543937 | − | 0.839126i | \(-0.683067\pi\) | ||||
−0.543937 | + | 0.839126i | \(0.683067\pi\) | |||||||
\(284\) | 6.23553 | 0.370010 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.52771 | 0.208598 | ||||||||
\(287\) | 6.56892i | 0.387751i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.87769 | 0.110452 | ||||||||
\(290\) | 18.2200 | 1.06991 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 15.3293 | 0.897077 | ||||||||
\(293\) | −18.0681 | −1.05555 | −0.527776 | − | 0.849384i | \(-0.676974\pi\) | ||||
−0.527776 | + | 0.849384i | \(0.676974\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.92148 | −0.228317 | ||||||||
\(296\) | − | 2.27714i | − | 0.132356i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.978503i | 0.0566832i | ||||||||
\(299\) | 35.6438i | 2.06133i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −24.5377 | −1.41433 | ||||||||
\(302\) | 3.93932 | 0.226682 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.00606 | 0.115055 | ||||||||
\(305\) | 7.12051i | 0.407719i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 4.70645i | − | 0.268611i | −0.990940 | − | 0.134306i | \(-0.957120\pi\) | ||
0.990940 | − | 0.134306i | \(-0.0428804\pi\) | |||||||
\(308\) | 4.20877 | 0.239817 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − | 27.4949i | − | 1.56160i | ||||||
\(311\) | 15.0235 | 0.851904 | 0.425952 | − | 0.904746i | \(-0.359939\pi\) | ||||
0.425952 | + | 0.904746i | \(0.359939\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 4.54957i | − | 0.257157i | −0.991699 | − | 0.128578i | \(-0.958959\pi\) | ||
0.991699 | − | 0.128578i | \(-0.0410414\pi\) | |||||||
\(314\) | −11.1663 | −0.630150 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.68601i | 0.319863i | ||||||||
\(317\) | 18.1436i | 1.01905i | 0.860457 | + | 0.509524i | \(0.170178\pi\) | ||||
−0.860457 | + | 0.509524i | \(0.829822\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.57235i | 0.256002i | ||||||||
\(320\) | −3.59603 | −0.201024 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 42.5251i | 2.36983i | ||||||||
\(323\) | − | 7.80105i | − | 0.434062i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 31.0048i | 1.71984i | ||||||||
\(326\) | −15.5956 | −0.863761 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.40849 | 0.0777707 | ||||||||
\(329\) | 26.5029i | 1.46115i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.3644i | 0.789537i | 0.918781 | + | 0.394769i | \(0.129175\pi\) | ||||
−0.918781 | + | 0.394769i | \(0.870825\pi\) | |||||||
\(332\) | 2.04815i | 0.112407i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 7.90448i | − | 0.432514i | ||||||
\(335\) | − | 50.3080i | − | 2.74862i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.9673i | 1.57795i | 0.614427 | + | 0.788974i | \(0.289387\pi\) | ||||
−0.614427 | + | 0.788974i | \(0.710613\pi\) | |||||||
\(338\) | − | 2.28120i | − | 0.124081i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 13.9840i | 0.758390i | ||||||||
\(341\) | 6.89991 | 0.373651 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 36.1499 | 1.95191 | ||||||||
\(344\) | 5.26130i | 0.283670i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 15.7797i | − | 0.848324i | ||||||
\(347\) | − | 11.7543i | − | 0.631003i | −0.948925 | − | 0.315501i | \(-0.897827\pi\) | ||
0.948925 | − | 0.315501i | \(-0.102173\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.58365 | −0.0847711 | −0.0423855 | − | 0.999101i | \(-0.513496\pi\) | ||||
−0.0423855 | + | 0.999101i | \(0.513496\pi\) | |||||||
\(350\) | 36.9906i | 1.97723i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 0.902432i | − | 0.0480998i | ||||||
\(353\) | 25.8563i | 1.37619i | 0.725619 | + | 0.688096i | \(0.241553\pi\) | ||||
−0.725619 | + | 0.688096i | \(0.758447\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −22.4231 | −1.19010 | ||||||||
\(356\) | 1.95797i | 0.103772i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.39415 | −0.232238 | ||||||||
\(359\) | 28.3204i | 1.49469i | 0.664434 | + | 0.747347i | \(0.268673\pi\) | ||||
−0.664434 | + | 0.747347i | \(0.731327\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.9757 | −0.788196 | ||||||||
\(362\) | − | 5.91690i | − | 0.310986i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 18.2314i | − | 0.955585i | ||||||
\(365\) | −55.1244 | −2.88534 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.9073 | 0.621557 | 0.310778 | − | 0.950482i | \(-0.399410\pi\) | ||||
0.310778 | + | 0.950482i | \(0.399410\pi\) | |||||||
\(368\) | 9.11811 | 0.475314 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8.18865i | 0.425708i | ||||||||
\(371\) | 57.5469i | 2.98769i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.4501i | 0.955309i | 0.878548 | + | 0.477655i | \(0.158513\pi\) | ||||
−0.878548 | + | 0.477655i | \(0.841487\pi\) | |||||||
\(374\) | −3.50932 | −0.181463 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.68266 | 0.293061 | ||||||||
\(377\) | 19.8063 | 1.02008 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.95014 | −0.202905 | −0.101453 | − | 0.994840i | \(-0.532349\pi\) | ||||
−0.101453 | + | 0.994840i | \(0.532349\pi\) | |||||||
\(380\) | −7.21384 | −0.370062 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 18.1304i | 0.927634i | ||||||||
\(383\) | 2.90672 | 0.148526 | 0.0742632 | − | 0.997239i | \(-0.476340\pi\) | ||||
0.0742632 | + | 0.997239i | \(0.476340\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −15.1349 | −0.771344 | ||||||||
\(386\) | 12.2241 | 0.622191 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 10.0724i | 0.511348i | ||||||||
\(389\) | − | 13.6810i | − | 0.693655i | −0.937929 | − | 0.346827i | \(-0.887259\pi\) | ||
0.937929 | − | 0.346827i | \(-0.112741\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 35.4580i | − | 1.79319i | ||||||
\(392\) | − | 14.7511i | − | 0.745045i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.60238 | 0.131106 | ||||||||
\(395\) | − | 20.4471i | − | 1.02880i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 26.2699i | − | 1.31845i | −0.751946 | − | 0.659225i | \(-0.770885\pi\) | ||
0.751946 | − | 0.659225i | \(-0.229115\pi\) | |||||||
\(398\) | − | 14.9269i | − | 0.748219i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.93141 | 0.396570 | ||||||||
\(401\) | − | 1.64967i | − | 0.0823808i | −0.999151 | − | 0.0411904i | \(-0.986885\pi\) | ||
0.999151 | − | 0.0411904i | \(-0.0131150\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 29.8887i | − | 1.48886i | ||||||
\(404\) | 11.9250i | 0.593291i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 23.6301 | 1.17274 | ||||||||
\(407\) | −2.05496 | −0.101861 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 15.3942i | − | 0.761196i | −0.924741 | − | 0.380598i | \(-0.875718\pi\) | ||
0.924741 | − | 0.380598i | \(-0.124282\pi\) | |||||||
\(410\) | −5.06496 | −0.250141 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 15.4768i | − | 0.762488i | ||||||
\(413\) | −5.08591 | −0.250261 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 7.36519i | − | 0.361543i | ||||||
\(416\) | −3.90912 | −0.191660 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 1.81033i | − | 0.0885463i | ||||||
\(419\) | − | 24.8933i | − | 1.21612i | −0.793891 | − | 0.608060i | \(-0.791948\pi\) | ||
0.793891 | − | 0.608060i | \(-0.208052\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.89567i | 0.0923894i | 0.998932 | + | 0.0461947i | \(0.0147095\pi\) | ||||
−0.998932 | + | 0.0461947i | \(0.985291\pi\) | |||||||
\(422\) | 16.4855i | 0.802502i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 12.3390 | 0.599236 | ||||||||
\(425\) | − | 30.8432i | − | 1.49611i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.23484i | 0.446905i | ||||||||
\(428\) | −18.9884 | −0.917841 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 18.9198i | − | 0.912393i | ||||||
\(431\) | 20.7721 | 1.00056 | 0.500279 | − | 0.865865i | \(-0.333231\pi\) | ||||
0.500279 | + | 0.865865i | \(0.333231\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.5538 | 1.13192 | 0.565961 | − | 0.824432i | \(-0.308505\pi\) | ||||
0.565961 | + | 0.824432i | \(0.308505\pi\) | |||||||
\(434\) | − | 35.6591i | − | 1.71169i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.80760 | 0.230242 | ||||||||
\(437\) | 18.2915 | 0.875000 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 27.5002i | − | 1.31251i | −0.754538 | − | 0.656256i | \(-0.772139\pi\) | ||
0.754538 | − | 0.656256i | \(-0.227861\pi\) | |||||||
\(440\) | 3.24517i | 0.154707i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 15.2015i | 0.723064i | ||||||||
\(443\) | 24.3687i | 1.15779i | 0.815401 | + | 0.578896i | \(0.196516\pi\) | ||||
−0.815401 | + | 0.578896i | \(0.803484\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 7.04093i | − | 0.333772i | ||||||
\(446\) | −14.9296 | + | 0.326717i | −0.706938 | + | 0.0154705i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.66381 | −0.220344 | ||||||||
\(449\) | −22.6953 | −1.07106 | −0.535529 | − | 0.844517i | \(-0.679888\pi\) | ||||
−0.535529 | + | 0.844517i | \(0.679888\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 1.27106i | − | 0.0598521i | ||||||
\(452\) | −18.1589 | −0.854125 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.91525 | −0.183752 | ||||||||
\(455\) | 65.5606i | 3.07353i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.6720i | 0.966996i | 0.875345 | + | 0.483498i | \(0.160634\pi\) | ||||
−0.875345 | + | 0.483498i | \(0.839366\pi\) | |||||||
\(458\) | 5.35015 | 0.249996 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −32.7890 | −1.52879 | ||||||||
\(461\) | − | 25.4522i | − | 1.18543i | −0.805413 | − | 0.592714i | \(-0.798057\pi\) | ||
0.805413 | − | 0.592714i | \(-0.201943\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.3610 | 1.17863 | 0.589313 | − | 0.807905i | \(-0.299399\pi\) | ||||
0.589313 | + | 0.807905i | \(0.299399\pi\) | |||||||
\(464\) | − | 5.06669i | − | 0.235215i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 15.0088i | 0.695269i | ||||||||
\(467\) | 5.67695 | 0.262698 | 0.131349 | − | 0.991336i | \(-0.458069\pi\) | ||||
0.131349 | + | 0.991336i | \(0.458069\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 65.2462i | − | 3.01279i | ||||||
\(470\) | −20.4350 | −0.942596 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.09050i | 0.0501945i | ||||||||
\(473\) | 4.74797 | 0.218312 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.9109 | 0.730041 | ||||||||
\(476\) | 18.1364i | 0.831279i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 22.7374 | 1.03998 | ||||||||
\(479\) | 7.99218i | 0.365172i | 0.983190 | + | 0.182586i | \(0.0584468\pi\) | ||||
−0.983190 | + | 0.182586i | \(0.941553\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.90160i | 0.405878i | ||||||||
\(482\) | − | 15.5649i | − | 0.708964i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.1856 | 0.462983 | ||||||||
\(485\) | − | 36.2206i | − | 1.64469i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.2751 | 0.782810 | 0.391405 | − | 0.920219i | \(-0.371989\pi\) | ||||
0.391405 | + | 0.920219i | \(0.371989\pi\) | |||||||
\(488\) | 1.98011 | 0.0896352 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 53.0455i | 2.39635i | ||||||||
\(491\) | 6.80166 | 0.306955 | 0.153477 | − | 0.988152i | \(-0.450953\pi\) | ||||
0.153477 | + | 0.988152i | \(0.450953\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.7031 | −0.887381 | ||||||||
\(494\) | −7.84192 | −0.352825 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.64590 | −0.343311 | ||||||||
\(497\) | −29.0813 | −1.30448 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −34.3509 | −1.53776 | −0.768879 | − | 0.639395i | \(-0.779185\pi\) | ||||
−0.768879 | + | 0.639395i | \(0.779185\pi\) | |||||||
\(500\) | −10.5414 | −0.471427 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 25.2944 | 1.12895 | ||||||||
\(503\) | 38.9506 | 1.73672 | 0.868360 | − | 0.495935i | \(-0.165174\pi\) | ||||
0.868360 | + | 0.495935i | \(0.165174\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 42.8826i | − | 1.90825i | ||||||
\(506\) | − | 8.22847i | − | 0.365800i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.78190 | 0.167795 | ||||||||
\(509\) | 7.69102i | 0.340898i | 0.985366 | + | 0.170449i | \(0.0545219\pi\) | ||||
−0.985366 | + | 0.170449i | \(0.945478\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −71.4928 | −3.16265 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −27.5846 | −1.21671 | ||||||||
\(515\) | 55.6550i | 2.45245i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 5.12821i | − | 0.225539i | ||||||
\(518\) | 10.6201i | 0.466622i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 14.0573 | 0.616453 | ||||||||
\(521\) | 6.39420 | 0.280135 | 0.140067 | − | 0.990142i | \(-0.455268\pi\) | ||||
0.140067 | + | 0.990142i | \(0.455268\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 4.03803i | − | 0.176571i | −0.996095 | − | 0.0882854i | \(-0.971861\pi\) | ||
0.996095 | − | 0.0882854i | \(-0.0281388\pi\) | |||||||
\(524\) | 9.66672i | 0.422293i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.69202i | 0.335388i | ||||||||
\(527\) | 29.7329i | 1.29519i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 60.1399 | 2.61478 | ||||||||
\(530\) | −44.3715 | −1.92737 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −9.35589 | −0.405629 | ||||||||
\(533\) | −5.50595 | −0.238489 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 68.2830 | 2.95213 | ||||||||
\(536\) | −13.9899 | −0.604271 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 31.7587i | − | 1.36921i | ||||||
\(539\) | −13.3119 | −0.573384 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.94748i | 0.341689i | 0.985298 | + | 0.170844i | \(0.0546495\pi\) | ||||
−0.985298 | + | 0.170844i | \(0.945350\pi\) | |||||||
\(542\) | 8.67132 | 0.372465 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.88874 | 0.166728 | ||||||||
\(545\) | −17.2883 | −0.740547 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.34285 | 0.313958 | 0.156979 | − | 0.987602i | \(-0.449825\pi\) | ||||
0.156979 | + | 0.987602i | \(0.449825\pi\) | |||||||
\(548\) | 0.470346 | 0.0200922 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | − | 7.15756i | − | 0.305199i | ||||||
\(551\) | − | 10.1641i | − | 0.433005i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 26.5185i | − | 1.12768i | ||||||
\(554\) | −28.7339 | −1.22079 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 14.4688 | 0.613612 | ||||||||
\(557\) | −23.3969 | −0.991360 | −0.495680 | − | 0.868505i | \(-0.665081\pi\) | ||||
−0.495680 | + | 0.868505i | \(0.665081\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 20.5670i | − | 0.869893i | ||||||
\(560\) | 16.7712 | 0.708712 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −23.8796 | −1.00730 | ||||||||
\(563\) | −9.73178 | −0.410146 | −0.205073 | − | 0.978747i | \(-0.565743\pi\) | ||||
−0.205073 | + | 0.978747i | \(0.565743\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 65.3001 | 2.74719 | ||||||||
\(566\) | − | 18.3009i | − | 0.769243i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.23553i | 0.261637i | ||||||||
\(569\) | 4.19768 | 0.175976 | 0.0879879 | − | 0.996122i | \(-0.471956\pi\) | ||||
0.0879879 | + | 0.996122i | \(0.471956\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 35.4089i | − | 1.48182i | −0.671606 | − | 0.740908i | \(-0.734395\pi\) | ||
0.671606 | − | 0.740908i | \(-0.265605\pi\) | |||||||
\(572\) | 3.52771i | 0.147501i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.56892 | −0.274182 | ||||||||
\(575\) | 72.3194 | 3.01593 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.2588 | −1.00991 | −0.504953 | − | 0.863147i | \(-0.668490\pi\) | ||||
−0.504953 | + | 0.863147i | \(0.668490\pi\) | |||||||
\(578\) | 1.87769i | 0.0781017i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 18.2200i | 0.756543i | ||||||||
\(581\) | − | 9.55217i | − | 0.396291i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 11.1351i | − | 0.461170i | ||||||
\(584\) | 15.3293i | 0.634329i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 18.0681i | − | 0.746388i | ||||||
\(587\) | 14.2496 | 0.588146 | 0.294073 | − | 0.955783i | \(-0.404989\pi\) | ||||
0.294073 | + | 0.955783i | \(0.404989\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.3381 | −0.631997 | ||||||||
\(590\) | − | 3.92148i | − | 0.161445i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.27714 | 0.0935898 | ||||||||
\(593\) | −18.9380 | −0.777690 | −0.388845 | − | 0.921303i | \(-0.627126\pi\) | ||||
−0.388845 | + | 0.921303i | \(0.627126\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 65.2188i | − | 2.67371i | ||||||
\(596\) | −0.978503 | −0.0400810 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −35.6438 | −1.45758 | ||||||||
\(599\) | − | 45.9774i | − | 1.87858i | −0.343118 | − | 0.939292i | \(-0.611483\pi\) | ||
0.343118 | − | 0.939292i | \(-0.388517\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 19.7024i | − | 0.803677i | −0.915711 | − | 0.401839i | \(-0.868371\pi\) | ||
0.915711 | − | 0.401839i | \(-0.131629\pi\) | |||||||
\(602\) | − | 24.5377i | − | 1.00008i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.93932i | 0.160289i | ||||||||
\(605\) | −36.6277 | −1.48913 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.8892i | 0.726099i | 0.931770 | + | 0.363049i | \(0.118264\pi\) | ||||
−0.931770 | + | 0.363049i | \(0.881736\pi\) | |||||||
\(608\) | 2.00606i | 0.0813565i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.12051 | −0.288301 | ||||||||
\(611\) | −22.2142 | −0.898690 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 1.04687i | − | 0.0422828i | −0.999776 | − | 0.0211414i | \(-0.993270\pi\) | ||
0.999776 | − | 0.0211414i | \(-0.00673001\pi\) | |||||||
\(614\) | 4.70645 | 0.189937 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.20877i | 0.169576i | ||||||||
\(617\) | − | 2.67707i | − | 0.107775i | −0.998547 | − | 0.0538873i | \(-0.982839\pi\) | ||
0.998547 | − | 0.0538873i | \(-0.0171612\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.8865i | 1.28163i | 0.767696 | + | 0.640814i | \(0.221403\pi\) | ||||
−0.767696 | + | 0.640814i | \(0.778597\pi\) | |||||||
\(620\) | 27.4949 | 1.10422 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15.0235i | 0.602387i | ||||||||
\(623\) | − | 9.13162i | − | 0.365851i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.74981 | −0.0699925 | ||||||||
\(626\) | 4.54957 | 0.181837 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 11.1663i | − | 0.445583i | ||||||
\(629\) | − | 8.85520i | − | 0.353080i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 46.9308i | 1.86828i | 0.356901 | + | 0.934142i | \(0.383833\pi\) | ||||
−0.356901 | + | 0.934142i | \(0.616167\pi\) | |||||||
\(632\) | −5.68601 | −0.226177 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −18.1436 | −0.720576 | ||||||||
\(635\) | −13.5998 | −0.539693 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 57.6640i | 2.28473i | ||||||||
\(638\) | −4.57235 | −0.181021 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 3.59603i | − | 0.142145i | ||||||
\(641\) | −10.6710 | −0.421480 | −0.210740 | − | 0.977542i | \(-0.567587\pi\) | ||||
−0.210740 | + | 0.977542i | \(0.567587\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.07541 | −0.0818463 | −0.0409231 | − | 0.999162i | \(-0.513030\pi\) | ||||
−0.0409231 | + | 0.999162i | \(0.513030\pi\) | |||||||
\(644\) | −42.5251 | −1.67573 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.80105 | 0.306928 | ||||||||
\(647\) | − | 25.0950i | − | 0.986587i | −0.869863 | − | 0.493294i | \(-0.835793\pi\) | ||
0.869863 | − | 0.493294i | \(-0.164207\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.984106 | 0.0386295 | ||||||||
\(650\) | −31.0048 | −1.21611 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 15.5956i | − | 0.610771i | ||||||
\(653\) | −13.3767 | −0.523470 | −0.261735 | − | 0.965140i | \(-0.584295\pi\) | ||||
−0.261735 | + | 0.965140i | \(0.584295\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 34.7618i | − | 1.35826i | ||||||
\(656\) | 1.40849i | 0.0549922i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −26.5029 | −1.03319 | ||||||||
\(659\) | − | 44.7250i | − | 1.74224i | −0.491072 | − | 0.871119i | \(-0.663395\pi\) | ||
0.491072 | − | 0.871119i | \(-0.336605\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 32.3751i | − | 1.25924i | −0.776901 | − | 0.629622i | \(-0.783210\pi\) | ||
0.776901 | − | 0.629622i | \(-0.216790\pi\) | |||||||
\(662\) | −14.3644 | −0.558287 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.04815 | −0.0794835 | ||||||||
\(665\) | 33.6440 | 1.30466 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 46.1987i | − | 1.78882i | ||||||
\(668\) | 7.90448 | 0.305833 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 50.3080 | 1.94357 | ||||||||
\(671\) | − | 1.78691i | − | 0.0689829i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −44.4949 | −1.71515 | −0.857575 | − | 0.514358i | \(-0.828030\pi\) | ||||
−0.857575 | + | 0.514358i | \(0.828030\pi\) | |||||||
\(674\) | −28.9673 | −1.11578 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.28120 | 0.0877384 | ||||||||
\(677\) | − | 5.75638i | − | 0.221236i | −0.993863 | − | 0.110618i | \(-0.964717\pi\) | ||
0.993863 | − | 0.110618i | \(-0.0352830\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 46.9757i | − | 1.80276i | ||||||
\(680\) | −13.9840 | −0.536263 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.89991i | 0.264211i | ||||||||
\(683\) | 36.0279i | 1.37857i | 0.724490 | + | 0.689285i | \(0.242075\pi\) | ||||
−0.724490 | + | 0.689285i | \(0.757925\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.69138 | −0.0646242 | ||||||||
\(686\) | 36.1499i | 1.38021i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.26130 | −0.200585 | ||||||||
\(689\) | −48.2347 | −1.83760 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.5987i | 1.20207i | 0.799222 | + | 0.601036i | \(0.205245\pi\) | ||||
−0.799222 | + | 0.601036i | \(0.794755\pi\) | |||||||
\(692\) | 15.7797 | 0.599856 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11.7543 | 0.446186 | ||||||||
\(695\) | −52.0301 | −1.97361 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.47725 | 0.207465 | ||||||||
\(698\) | − | 1.58365i | − | 0.0599422i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −36.9906 | −1.39811 | ||||||||
\(701\) | − | 24.6638i | − | 0.931538i | −0.884906 | − | 0.465769i | \(-0.845778\pi\) | ||
0.884906 | − | 0.465769i | \(-0.154222\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.56808 | 0.172288 | ||||||||
\(704\) | 0.902432 | 0.0340117 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −25.8563 | −0.973115 | ||||||||
\(707\) | − | 55.6160i | − | 2.09165i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 14.3003i | − | 0.537060i | −0.963271 | − | 0.268530i | \(-0.913462\pi\) | ||
0.963271 | − | 0.268530i | \(-0.0865378\pi\) | |||||||
\(710\) | − | 22.4231i | − | 0.841525i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.95797 | −0.0733782 | ||||||||
\(713\) | −69.7162 | −2.61089 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 12.6857i | − | 0.474420i | ||||||
\(716\) | − | 4.39415i | − | 0.164217i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −28.3204 | −1.05691 | ||||||||
\(719\) | − | 3.36040i | − | 0.125322i | −0.998035 | − | 0.0626609i | \(-0.980041\pi\) | ||
0.998035 | − | 0.0626609i | \(-0.0199586\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 72.1809i | 2.68816i | ||||||||
\(722\) | − | 14.9757i | − | 0.557339i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.91690 | 0.219900 | ||||||||
\(725\) | − | 40.1860i | − | 1.49247i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.6392 | 0.580025 | 0.290013 | − | 0.957023i | \(-0.406340\pi\) | ||||
0.290013 | + | 0.957023i | \(0.406340\pi\) | |||||||
\(728\) | 18.2314 | 0.675700 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | − | 55.1244i | − | 2.04025i | ||||||
\(731\) | 20.4598i | 0.756734i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.7550 | −0.508051 | −0.254025 | − | 0.967198i | \(-0.581755\pi\) | ||||
−0.254025 | + | 0.967198i | \(0.581755\pi\) | |||||||
\(734\) | 11.9073i | 0.439507i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.11811i | 0.336098i | ||||||||
\(737\) | 12.6249i | 0.465045i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 22.3492i | − | 0.822127i | −0.911607 | − | 0.411064i | \(-0.865157\pi\) | ||
0.911607 | − | 0.411064i | \(-0.134843\pi\) | |||||||
\(740\) | −8.18865 | −0.301021 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −57.5469 | −2.11261 | ||||||||
\(743\) | − | 43.1880i | − | 1.58441i | −0.610252 | − | 0.792207i | \(-0.708932\pi\) | ||
0.610252 | − | 0.792207i | \(-0.291068\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.51872 | 0.128916 | ||||||||
\(746\) | −18.4501 | −0.675506 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 3.50932i | − | 0.128314i | ||||||
\(749\) | 88.5586 | 3.23586 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.0187 | −0.985925 | −0.492962 | − | 0.870051i | \(-0.664086\pi\) | ||||
−0.492962 | + | 0.870051i | \(0.664086\pi\) | |||||||
\(752\) | 5.68266i | 0.207225i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 19.8063i | 0.721303i | ||||||||
\(755\) | − | 14.1659i | − | 0.515550i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.1030i | 1.16680i | 0.812184 | + | 0.583402i | \(0.198279\pi\) | ||||
−0.812184 | + | 0.583402i | \(0.801721\pi\) | |||||||
\(758\) | − | 3.95014i | − | 0.143476i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | − | 7.21384i | − | 0.261674i | ||||||
\(761\) | 22.6216 | 0.820031 | 0.410016 | − | 0.912078i | \(-0.365523\pi\) | ||||
0.410016 | + | 0.912078i | \(0.365523\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22.4217 | −0.811721 | ||||||||
\(764\) | −18.1304 | −0.655936 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.90672i | 0.105024i | ||||||||
\(767\) | − | 4.26291i | − | 0.153925i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −38.3830 | −1.38413 | −0.692063 | − | 0.721837i | \(-0.743298\pi\) | ||||
−0.692063 | + | 0.721837i | \(0.743298\pi\) | |||||||
\(770\) | − | 15.1349i | − | 0.545423i | ||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 12.2241i | 0.439955i | ||||||||
\(773\) | −41.3477 | −1.48717 | −0.743586 | − | 0.668640i | \(-0.766877\pi\) | ||||
−0.743586 | + | 0.668640i | \(0.766877\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −60.6428 | −2.17835 | ||||||||
\(776\) | −10.0724 | −0.361577 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13.6810 | 0.490488 | ||||||||
\(779\) | 2.82551i | 0.101234i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.62714 | 0.201355 | ||||||||
\(782\) | 35.4580 | 1.26797 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 14.7511 | 0.526827 | ||||||||
\(785\) | 40.1543i | 1.43317i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.4917i | 1.08691i | 0.839437 | + | 0.543456i | \(0.182885\pi\) | ||||
−0.839437 | + | 0.543456i | \(0.817115\pi\) | |||||||
\(788\) | 2.60238i | 0.0927061i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 20.4471 | 0.727473 | ||||||||
\(791\) | 84.6899 | 3.01123 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.74047 | −0.274872 | ||||||||
\(794\) | 26.2699 | 0.932284 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 14.9269 | 0.529071 | ||||||||
\(797\) | − | 1.28996i | − | 0.0456928i | −0.999739 | − | 0.0228464i | \(-0.992727\pi\) | ||
0.999739 | − | 0.0228464i | \(-0.00727286\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.0984 | 0.781785 | ||||||||
\(800\) | 7.93141i | 0.280418i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.64967 | 0.0582520 | ||||||||
\(803\) | 13.8336 | 0.488177 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 152.922 | 5.38978 | ||||||||
\(806\) | 29.8887 | 1.05279 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −11.9250 | −0.419520 | ||||||||
\(809\) | 41.9767 | 1.47582 | 0.737911 | − | 0.674898i | \(-0.235813\pi\) | ||||
0.737911 | + | 0.674898i | \(0.235813\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.73208i | 0.0959365i | 0.998849 | + | 0.0479682i | \(0.0152746\pi\) | ||||
−0.998849 | + | 0.0479682i | \(0.984725\pi\) | |||||||
\(812\) | 23.6301i | 0.829254i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 2.05496i | − | 0.0720264i | ||||||
\(815\) | 56.0822i | 1.96448i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.5545 | −0.369255 | ||||||||
\(818\) | 15.3942 | 0.538247 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 5.06496i | − | 0.176876i | ||||||
\(821\) | 52.4879i | 1.83184i | 0.401359 | + | 0.915921i | \(0.368538\pi\) | ||||
−0.401359 | + | 0.915921i | \(0.631462\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 48.4730i | − | 1.68966i | −0.535032 | − | 0.844832i | \(-0.679701\pi\) | ||
0.535032 | − | 0.844832i | \(-0.320299\pi\) | |||||||
\(824\) | 15.4768 | 0.539160 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | − | 5.08591i | − | 0.176961i | ||||||
\(827\) | 19.6698 | 0.683987 | 0.341994 | − | 0.939702i | \(-0.388898\pi\) | ||||
0.341994 | + | 0.939702i | \(0.388898\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 0.791876i | − | 0.0275030i | −0.999905 | − | 0.0137515i | \(-0.995623\pi\) | ||
0.999905 | − | 0.0137515i | \(-0.00437737\pi\) | |||||||
\(830\) | 7.36519 | 0.255649 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 3.90912i | − | 0.135524i | ||||||
\(833\) | − | 57.3634i | − | 1.98752i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −28.4247 | −0.983678 | ||||||||
\(836\) | 1.81033 | 0.0626117 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 24.8933 | 0.859926 | ||||||||
\(839\) | −21.2090 | −0.732215 | −0.366108 | − | 0.930573i | \(-0.619310\pi\) | ||||
−0.366108 | + | 0.930573i | \(0.619310\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.32862 | 0.114780 | ||||||||
\(842\) | −1.89567 | −0.0653292 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −16.4855 | −0.567455 | ||||||||
\(845\) | −8.20325 | −0.282200 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −47.5038 | −1.63225 | ||||||||
\(848\) | 12.3390i | 0.423724i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 30.8432 | 1.05791 | ||||||||
\(851\) | 20.7632 | 0.711753 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 12.6616i | − | 0.433525i | −0.976224 | − | 0.216762i | \(-0.930450\pi\) | ||
0.976224 | − | 0.216762i | \(-0.0695497\pi\) | |||||||
\(854\) | −9.23484 | −0.316010 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 18.9884i | − | 0.649012i | ||||||
\(857\) | 27.3655i | 0.934786i | 0.884050 | + | 0.467393i | \(0.154807\pi\) | ||||
−0.884050 | + | 0.467393i | \(0.845193\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.0721i | 0.991927i | 0.868343 | + | 0.495963i | \(0.165185\pi\) | ||||
−0.868343 | + | 0.495963i | \(0.834815\pi\) | |||||||
\(860\) | 18.9198 | 0.645159 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 20.7721i | 0.707501i | ||||||||
\(863\) | 26.9203 | 0.916379 | 0.458190 | − | 0.888854i | \(-0.348498\pi\) | ||||
0.458190 | + | 0.888854i | \(0.348498\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −56.7444 | −1.92937 | ||||||||
\(866\) | 23.5538i | 0.800389i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 35.6591 | 1.21035 | ||||||||
\(869\) | 5.13124i | 0.174065i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 54.6881 | 1.85303 | ||||||||
\(872\) | 4.80760i | 0.162806i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 18.2915i | 0.618718i | ||||||||
\(875\) | 49.1632 | 1.66202 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 51.7787i | 1.74844i | 0.485529 | + | 0.874220i | \(0.338627\pi\) | ||||
−0.485529 | + | 0.874220i | \(0.661373\pi\) | |||||||
\(878\) | 27.5002 | 0.928086 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.24517 | −0.109395 | ||||||||
\(881\) | 4.09113i | 0.137834i | 0.997622 | + | 0.0689168i | \(0.0219543\pi\) | ||||
−0.997622 | + | 0.0689168i | \(0.978046\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.63618i | 0.122367i | 0.998127 | + | 0.0611837i | \(0.0194875\pi\) | ||||
−0.998127 | + | 0.0611837i | \(0.980512\pi\) | |||||||
\(884\) | −15.2015 | −0.511283 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −24.3687 | −0.818683 | ||||||||
\(887\) | 7.58846i | 0.254796i | 0.991852 | + | 0.127398i | \(0.0406625\pi\) | ||||
−0.991852 | + | 0.127398i | \(0.959338\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.6381 | −0.591563 | ||||||||
\(890\) | 7.04093 | 0.236012 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.326717 | − | 14.9296i | −0.0109393 | − | 0.499880i | ||||
\(893\) | 11.3998i | 0.381478i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.8015i | 0.528186i | ||||||||
\(896\) | − | 4.66381i | − | 0.155807i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 22.6953i | − | 0.757352i | ||||||
\(899\) | 38.7394i | 1.29203i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 47.9833 | 1.59856 | ||||||||
\(902\) | 1.27106 | 0.0423218 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 18.1589i | − | 0.603958i | ||||||
\(905\) | −21.2773 | −0.707283 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.2633 | −1.07129 | −0.535643 | − | 0.844444i | \(-0.679931\pi\) | ||||
−0.535643 | + | 0.844444i | \(0.679931\pi\) | |||||||
\(908\) | − | 3.91525i | − | 0.129932i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −65.5606 | −2.17331 | ||||||||
\(911\) | − | 18.1569i | − | 0.601564i | −0.953693 | − | 0.300782i | \(-0.902752\pi\) | ||
0.953693 | − | 0.300782i | \(-0.0972477\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.84831i | 0.0611702i | ||||||||
\(914\) | −20.6720 | −0.683769 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.35015i | 0.176774i | ||||||||
\(917\) | − | 45.0838i | − | 1.48880i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 49.5535i | − | 1.63462i | −0.576200 | − | 0.817309i | \(-0.695465\pi\) | ||
0.576200 | − | 0.817309i | \(-0.304535\pi\) | |||||||
\(920\) | − | 32.7890i | − | 1.08102i | ||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 25.4522 | 0.838224 | ||||||||
\(923\) | − | 24.3754i | − | 0.802326i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.0609 | 0.593839 | ||||||||
\(926\) | 25.3610i | 0.833414i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.06669 | 0.166322 | ||||||||
\(929\) | − | 24.2071i | − | 0.794208i | −0.917774 | − | 0.397104i | \(-0.870015\pi\) | ||
0.917774 | − | 0.397104i | \(-0.129985\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 29.5917 | 0.969828 | ||||||||
\(932\) | −15.0088 | −0.491629 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5.67695i | 0.185756i | ||||||||
\(935\) | 12.6196i | 0.412706i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 22.3246i | − | 0.729314i | −0.931142 | − | 0.364657i | \(-0.881186\pi\) | ||
0.931142 | − | 0.364657i | \(-0.118814\pi\) | |||||||
\(938\) | 65.2462 | 2.13036 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | − | 20.4350i | − | 0.666516i | ||||||
\(941\) | 17.3826i | 0.566657i | 0.959023 | + | 0.283328i | \(0.0914386\pi\) | ||||
−0.959023 | + | 0.283328i | \(0.908561\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.8427i | 0.418217i | ||||||||
\(944\) | −1.09050 | −0.0354929 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.74797i | 0.154370i | ||||||||
\(947\) | − | 13.8285i | − | 0.449365i | −0.974432 | − | 0.224682i | \(-0.927866\pi\) | ||
0.974432 | − | 0.224682i | \(-0.0721344\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 59.9238i | − | 1.94521i | ||||||
\(950\) | 15.9109i | 0.516217i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −18.1364 | −0.587803 | ||||||||
\(953\) | −23.3803 | −0.757363 | −0.378682 | − | 0.925527i | \(-0.623622\pi\) | ||||
−0.378682 | + | 0.925527i | \(0.623622\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 65.1975 | 2.10974 | ||||||||
\(956\) | 22.7374i | 0.735379i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7.99218 | −0.258216 | ||||||||
\(959\) | −2.19361 | −0.0708353 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.4598 | 0.885800 | ||||||||
\(962\) | −8.90160 | −0.286999 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 15.5649 | 0.501313 | ||||||||
\(965\) | − | 43.9582i | − | 1.41506i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 31.7180i | − | 1.01998i | −0.860179 | − | 0.509992i | \(-0.829649\pi\) | ||
0.860179 | − | 0.509992i | \(-0.170351\pi\) | |||||||
\(968\) | 10.1856i | 0.327378i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 36.2206 | 1.16297 | ||||||||
\(971\) | −43.6042 | −1.39933 | −0.699663 | − | 0.714473i | \(-0.746667\pi\) | ||||
−0.699663 | + | 0.714473i | \(0.746667\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −67.4796 | −2.16330 | ||||||||
\(974\) | 17.2751i | 0.553530i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.98011i | 0.0633816i | ||||||||
\(977\) | −35.3637 | −1.13139 | −0.565693 | − | 0.824616i | \(-0.691391\pi\) | ||||
−0.565693 | + | 0.824616i | \(0.691391\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.76694i | 0.0564716i | ||||||||
\(980\) | −53.0455 | −1.69448 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.80166i | 0.217050i | ||||||||
\(983\) | 42.9170 | 1.36884 | 0.684420 | − | 0.729088i | \(-0.260056\pi\) | ||||
0.684420 | + | 0.729088i | \(0.260056\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 9.35825i | − | 0.298178i | ||||||
\(986\) | − | 19.7031i | − | 0.627473i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 7.84192i | − | 0.249485i | ||||||
\(989\) | −47.9731 | −1.52546 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 31.2085i | − | 0.991371i | −0.868502 | − | 0.495685i | \(-0.834917\pi\) | ||
0.868502 | − | 0.495685i | \(-0.165083\pi\) | |||||||
\(992\) | − | 7.64590i | − | 0.242758i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 29.0813i | − | 0.922404i | ||||||
\(995\) | −53.6776 | −1.70170 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.6931 | −0.560347 | −0.280174 | − | 0.959949i | \(-0.590392\pi\) | ||||
−0.280174 | + | 0.959949i | \(0.590392\pi\) | |||||||
\(998\) | − | 34.3509i | − | 1.08736i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4014.2.d.a.4013.10 | yes | 72 | |
3.2 | odd | 2 | inner | 4014.2.d.a.4013.37 | yes | 72 | |
223.222 | odd | 2 | inner | 4014.2.d.a.4013.38 | yes | 72 | |
669.668 | even | 2 | inner | 4014.2.d.a.4013.9 | ✓ | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4014.2.d.a.4013.9 | ✓ | 72 | 669.668 | even | 2 | inner | |
4014.2.d.a.4013.10 | yes | 72 | 1.1 | even | 1 | trivial | |
4014.2.d.a.4013.37 | yes | 72 | 3.2 | odd | 2 | inner | |
4014.2.d.a.4013.38 | yes | 72 | 223.222 | odd | 2 | inner |