Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3234,2,Mod(2155,3234)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3234, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("3234.2155");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3234.e (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: | \(25.8236200137\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2155.11 | ||
Character | \(\chi\) | \(=\) | 3234.2155 |
Dual form | 3234.2.e.c.2155.14 |
$q$-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 \(\left(\mathbb{Z}/3234\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(1079\) | \(2059\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 3.45711i | 1.54606i | 0.634366 | + | 0.773032i | \(0.281261\pi\) | ||||
−0.634366 | + | 0.773032i | \(0.718739\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 3.45711 | 1.09323 | ||||||||
\(11\) | 3.07598 | + | 1.24029i | 0.927444 | + | 0.373961i | ||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | −5.39143 | −1.49531 | −0.747656 | − | 0.664086i | \(-0.768821\pi\) | ||||
−0.747656 | + | 0.664086i | \(0.768821\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.45711 | 0.892621 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.0457263 | 0.0110903 | 0.00554513 | − | 0.999985i | \(-0.498235\pi\) | ||||
0.00554513 | + | 0.999985i | \(0.498235\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | −6.95062 | −1.59458 | −0.797291 | − | 0.603595i | \(-0.793734\pi\) | ||||
−0.797291 | + | 0.603595i | \(0.793734\pi\) | |||||||
\(20\) | − | 3.45711i | − | 0.773032i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.24029 | − | 3.07598i | 0.264431 | − | 0.655802i | ||||
\(23\) | 1.19252 | 0.248657 | 0.124329 | − | 0.992241i | \(-0.460322\pi\) | ||||
0.124329 | + | 0.992241i | \(0.460322\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −6.95158 | −1.39032 | ||||||||
\(26\) | 5.39143i | 1.05735i | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.78271i | 1.44521i | 0.691259 | + | 0.722607i | \(0.257056\pi\) | ||||
−0.691259 | + | 0.722607i | \(0.742944\pi\) | |||||||
\(30\) | − | 3.45711i | − | 0.631178i | ||||||
\(31\) | − | 6.61846i | − | 1.18871i | −0.804203 | − | 0.594355i | \(-0.797407\pi\) | ||
0.804203 | − | 0.594355i | \(-0.202593\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 1.24029 | − | 3.07598i | 0.215907 | − | 0.535460i | ||||
\(34\) | − | 0.0457263i | − | 0.00784200i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −1.51053 | −0.248330 | −0.124165 | − | 0.992262i | \(-0.539625\pi\) | ||||
−0.124165 | + | 0.992262i | \(0.539625\pi\) | |||||||
\(38\) | 6.95062i | 1.12754i | ||||||||
\(39\) | 5.39143i | 0.863319i | ||||||||
\(40\) | −3.45711 | −0.546617 | ||||||||
\(41\) | 4.87368 | 0.761140 | 0.380570 | − | 0.924752i | \(-0.375728\pi\) | ||||
0.380570 | + | 0.924752i | \(0.375728\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 3.27873i | − | 0.500001i | −0.968246 | − | 0.250001i | \(-0.919569\pi\) | ||
0.968246 | − | 0.250001i | \(-0.0804308\pi\) | |||||||
\(44\) | −3.07598 | − | 1.24029i | −0.463722 | − | 0.186981i | ||||
\(45\) | − | 3.45711i | − | 0.515355i | ||||||
\(46\) | − | 1.19252i | − | 0.175827i | ||||||
\(47\) | − | 12.1060i | − | 1.76584i | −0.469524 | − | 0.882920i | \(-0.655574\pi\) | ||
0.469524 | − | 0.882920i | \(-0.344426\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 6.95158i | 0.983102i | ||||||||
\(51\) | − | 0.0457263i | − | 0.00640297i | ||||||
\(52\) | 5.39143 | 0.747656 | ||||||||
\(53\) | −3.69054 | −0.506935 | −0.253467 | − | 0.967344i | \(-0.581571\pi\) | ||||
−0.253467 | + | 0.967344i | \(0.581571\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −4.28781 | + | 10.6340i | −0.578169 | + | 1.43389i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.95062i | 0.920632i | ||||||||
\(58\) | 7.78271 | 1.02192 | ||||||||
\(59\) | − | 14.8396i | − | 1.93195i | −0.258638 | − | 0.965974i | \(-0.583274\pi\) | ||
0.258638 | − | 0.965974i | \(-0.416726\pi\) | |||||||
\(60\) | −3.45711 | −0.446311 | ||||||||
\(61\) | −3.63129 | −0.464939 | −0.232469 | − | 0.972604i | \(-0.574681\pi\) | ||||
−0.232469 | + | 0.972604i | \(0.574681\pi\) | |||||||
\(62\) | −6.61846 | −0.840545 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 18.6387i | − | 2.31185i | ||||||
\(66\) | −3.07598 | − | 1.24029i | −0.378628 | − | 0.152669i | ||||
\(67\) | 6.66903 | 0.814751 | 0.407376 | − | 0.913261i | \(-0.366444\pi\) | ||||
0.407376 | + | 0.913261i | \(0.366444\pi\) | |||||||
\(68\) | −0.0457263 | −0.00554513 | ||||||||
\(69\) | − | 1.19252i | − | 0.143562i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.89741 | 0.818572 | 0.409286 | − | 0.912406i | \(-0.365778\pi\) | ||||
0.409286 | + | 0.912406i | \(0.365778\pi\) | |||||||
\(72\) | − | 1.00000i | − | 0.117851i | ||||||
\(73\) | −3.04272 | −0.356123 | −0.178062 | − | 0.984019i | \(-0.556983\pi\) | ||||
−0.178062 | + | 0.984019i | \(0.556983\pi\) | |||||||
\(74\) | 1.51053i | 0.175596i | ||||||||
\(75\) | 6.95158i | 0.802700i | ||||||||
\(76\) | 6.95062 | 0.797291 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 5.39143 | 0.610459 | ||||||||
\(79\) | − | 12.9709i | − | 1.45935i | −0.683796 | − | 0.729673i | \(-0.739672\pi\) | ||
0.683796 | − | 0.729673i | \(-0.260328\pi\) | |||||||
\(80\) | 3.45711i | 0.386516i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 4.87368i | − | 0.538207i | ||||||
\(83\) | −8.48330 | −0.931163 | −0.465582 | − | 0.885005i | \(-0.654155\pi\) | ||||
−0.465582 | + | 0.885005i | \(0.654155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.158081i | 0.0171463i | ||||||||
\(86\) | −3.27873 | −0.353554 | ||||||||
\(87\) | 7.78271 | 0.834395 | ||||||||
\(88\) | −1.24029 | + | 3.07598i | −0.132215 | + | 0.327901i | ||||
\(89\) | − | 4.20562i | − | 0.445795i | −0.974842 | − | 0.222897i | \(-0.928448\pi\) | ||
0.974842 | − | 0.222897i | \(-0.0715515\pi\) | |||||||
\(90\) | −3.45711 | −0.364411 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.19252 | −0.124329 | ||||||||
\(93\) | −6.61846 | −0.686302 | ||||||||
\(94\) | −12.1060 | −1.24864 | ||||||||
\(95\) | − | 24.0290i | − | 2.46533i | ||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 6.64551i | 0.674749i | 0.941370 | + | 0.337375i | \(0.109539\pi\) | ||||
−0.941370 | + | 0.337375i | \(0.890461\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.07598 | − | 1.24029i | −0.309148 | − | 0.124654i | ||||
\(100\) | 6.95158 | 0.695158 | ||||||||
\(101\) | −14.1963 | −1.41258 | −0.706290 | − | 0.707922i | \(-0.749633\pi\) | ||||
−0.706290 | + | 0.707922i | \(0.749633\pi\) | |||||||
\(102\) | −0.0457263 | −0.00452758 | ||||||||
\(103\) | 1.26090i | 0.124240i | 0.998069 | + | 0.0621200i | \(0.0197861\pi\) | ||||
−0.998069 | + | 0.0621200i | \(0.980214\pi\) | |||||||
\(104\) | − | 5.39143i | − | 0.528673i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.69054i | 0.358457i | ||||||||
\(107\) | 0.676179i | 0.0653687i | 0.999466 | + | 0.0326843i | \(0.0104056\pi\) | ||||
−0.999466 | + | 0.0326843i | \(0.989594\pi\) | |||||||
\(108\) | − | 1.00000i | − | 0.0962250i | ||||||
\(109\) | − | 19.6069i | − | 1.87800i | −0.343913 | − | 0.939002i | \(-0.611752\pi\) | ||
0.343913 | − | 0.939002i | \(-0.388248\pi\) | |||||||
\(110\) | 10.6340 | + | 4.28781i | 1.01391 | + | 0.408827i | ||||
\(111\) | 1.51053i | 0.143373i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.24860 | −0.211531 | −0.105765 | − | 0.994391i | \(-0.533729\pi\) | ||||
−0.105765 | + | 0.994391i | \(0.533729\pi\) | |||||||
\(114\) | 6.95062 | 0.650985 | ||||||||
\(115\) | 4.12266i | 0.384440i | ||||||||
\(116\) | − | 7.78271i | − | 0.722607i | ||||||
\(117\) | 5.39143 | 0.498438 | ||||||||
\(118\) | −14.8396 | −1.36609 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.45711i | 0.315589i | ||||||||
\(121\) | 7.92336 | + | 7.63022i | 0.720306 | + | 0.693657i | ||||
\(122\) | 3.63129i | 0.328761i | ||||||||
\(123\) | − | 4.87368i | − | 0.439444i | ||||||
\(124\) | 6.61846i | 0.594355i | ||||||||
\(125\) | − | 6.74683i | − | 0.603455i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.24140i | − | 0.198892i | −0.995043 | − | 0.0994461i | \(-0.968293\pi\) | ||
0.995043 | − | 0.0994461i | \(-0.0317071\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −3.27873 | −0.288676 | ||||||||
\(130\) | −18.6387 | −1.63473 | ||||||||
\(131\) | −2.65048 | −0.231573 | −0.115787 | − | 0.993274i | \(-0.536939\pi\) | ||||
−0.115787 | + | 0.993274i | \(0.536939\pi\) | |||||||
\(132\) | −1.24029 | + | 3.07598i | −0.107953 | + | 0.267730i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 6.66903i | − | 0.576116i | ||||||
\(135\) | −3.45711 | −0.297540 | ||||||||
\(136\) | 0.0457263i | 0.00392100i | ||||||||
\(137\) | −14.9046 | −1.27339 | −0.636694 | − | 0.771117i | \(-0.719698\pi\) | ||||
−0.636694 | + | 0.771117i | \(0.719698\pi\) | |||||||
\(138\) | −1.19252 | −0.101514 | ||||||||
\(139\) | −17.4420 | −1.47941 | −0.739707 | − | 0.672929i | \(-0.765036\pi\) | ||||
−0.739707 | + | 0.672929i | \(0.765036\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.1060 | −1.01951 | ||||||||
\(142\) | − | 6.89741i | − | 0.578818i | ||||||
\(143\) | −16.5839 | − | 6.68693i | −1.38682 | − | 0.559189i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | −26.9057 | −2.23439 | ||||||||
\(146\) | 3.04272i | 0.251817i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.51053 | 0.124165 | ||||||||
\(149\) | 11.1458i | 0.913098i | 0.889698 | + | 0.456549i | \(0.150915\pi\) | ||||
−0.889698 | + | 0.456549i | \(0.849085\pi\) | |||||||
\(150\) | 6.95158 | 0.567594 | ||||||||
\(151\) | − | 13.7210i | − | 1.11660i | −0.829639 | − | 0.558300i | \(-0.811454\pi\) | ||
0.829639 | − | 0.558300i | \(-0.188546\pi\) | |||||||
\(152\) | − | 6.95062i | − | 0.563770i | ||||||
\(153\) | −0.0457263 | −0.00369676 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 22.8807 | 1.83782 | ||||||||
\(156\) | − | 5.39143i | − | 0.431660i | ||||||
\(157\) | 20.5517i | 1.64021i | 0.572215 | + | 0.820104i | \(0.306084\pi\) | ||||
−0.572215 | + | 0.820104i | \(0.693916\pi\) | |||||||
\(158\) | −12.9709 | −1.03191 | ||||||||
\(159\) | 3.69054i | 0.292679i | ||||||||
\(160\) | 3.45711 | 0.273308 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | −10.3412 | −0.809986 | −0.404993 | − | 0.914320i | \(-0.632726\pi\) | ||||
−0.404993 | + | 0.914320i | \(0.632726\pi\) | |||||||
\(164\) | −4.87368 | −0.380570 | ||||||||
\(165\) | 10.6340 | + | 4.28781i | 0.827856 | + | 0.333806i | ||||
\(166\) | 8.48330i | 0.658432i | ||||||||
\(167\) | 23.7721 | 1.83954 | 0.919769 | − | 0.392460i | \(-0.128376\pi\) | ||||
0.919769 | + | 0.392460i | \(0.128376\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.0675 | 1.23596 | ||||||||
\(170\) | 0.158081 | 0.0121242 | ||||||||
\(171\) | 6.95062 | 0.531527 | ||||||||
\(172\) | 3.27873i | 0.250001i | ||||||||
\(173\) | 13.5605 | 1.03099 | 0.515494 | − | 0.856893i | \(-0.327608\pi\) | ||||
0.515494 | + | 0.856893i | \(0.327608\pi\) | |||||||
\(174\) | − | 7.78271i | − | 0.590006i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.07598 | + | 1.24029i | 0.231861 | + | 0.0934903i | ||||
\(177\) | −14.8396 | −1.11541 | ||||||||
\(178\) | −4.20562 | −0.315225 | ||||||||
\(179\) | −16.1833 | −1.20960 | −0.604799 | − | 0.796378i | \(-0.706747\pi\) | ||||
−0.604799 | + | 0.796378i | \(0.706747\pi\) | |||||||
\(180\) | 3.45711i | 0.257677i | ||||||||
\(181\) | − | 15.6283i | − | 1.16164i | −0.814031 | − | 0.580821i | \(-0.802732\pi\) | ||
0.814031 | − | 0.580821i | \(-0.197268\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.63129i | 0.268433i | ||||||||
\(184\) | 1.19252i | 0.0879135i | ||||||||
\(185\) | − | 5.22206i | − | 0.383934i | ||||||
\(186\) | 6.61846i | 0.485289i | ||||||||
\(187\) | 0.140654 | + | 0.0567139i | 0.0102856 | + | 0.00414733i | ||||
\(188\) | 12.1060i | 0.882920i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −24.0290 | −1.74325 | ||||||||
\(191\) | −8.42409 | −0.609546 | −0.304773 | − | 0.952425i | \(-0.598581\pi\) | ||||
−0.304773 | + | 0.952425i | \(0.598581\pi\) | |||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | − | 9.14795i | − | 0.658484i | −0.944246 | − | 0.329242i | \(-0.893207\pi\) | ||
0.944246 | − | 0.329242i | \(-0.106793\pi\) | |||||||
\(194\) | 6.64551 | 0.477120 | ||||||||
\(195\) | −18.6387 | −1.33475 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.7101i | 0.976806i | 0.872618 | + | 0.488403i | \(0.162420\pi\) | ||||
−0.872618 | + | 0.488403i | \(0.837580\pi\) | |||||||
\(198\) | −1.24029 | + | 3.07598i | −0.0881435 | + | 0.218601i | ||||
\(199\) | 5.92036i | 0.419683i | 0.977735 | + | 0.209842i | \(0.0672948\pi\) | ||||
−0.977735 | + | 0.209842i | \(0.932705\pi\) | |||||||
\(200\) | − | 6.95158i | − | 0.491551i | ||||||
\(201\) | − | 6.66903i | − | 0.470397i | ||||||
\(202\) | 14.1963i | 0.998845i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.0457263i | 0.00320148i | ||||||||
\(205\) | 16.8488i | 1.17677i | ||||||||
\(206\) | 1.26090 | 0.0878509 | ||||||||
\(207\) | −1.19252 | −0.0828857 | ||||||||
\(208\) | −5.39143 | −0.373828 | ||||||||
\(209\) | −21.3800 | − | 8.62078i | −1.47889 | − | 0.596312i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.27732i | 0.432148i | 0.976377 | + | 0.216074i | \(0.0693253\pi\) | ||||
−0.976377 | + | 0.216074i | \(0.930675\pi\) | |||||||
\(212\) | 3.69054 | 0.253467 | ||||||||
\(213\) | − | 6.89741i | − | 0.472603i | ||||||
\(214\) | 0.676179 | 0.0462226 | ||||||||
\(215\) | 11.3349 | 0.773034 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −19.6069 | −1.32795 | ||||||||
\(219\) | 3.04272i | 0.205608i | ||||||||
\(220\) | 4.28781 | − | 10.6340i | 0.289084 | − | 0.716945i | ||||
\(221\) | −0.246530 | −0.0165834 | ||||||||
\(222\) | 1.51053 | 0.101380 | ||||||||
\(223\) | 23.9882i | 1.60637i | 0.595730 | + | 0.803185i | \(0.296863\pi\) | ||||
−0.595730 | + | 0.803185i | \(0.703137\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.95158 | 0.463439 | ||||||||
\(226\) | 2.24860i | 0.149575i | ||||||||
\(227\) | −27.9605 | −1.85581 | −0.927903 | − | 0.372823i | \(-0.878390\pi\) | ||||
−0.927903 | + | 0.372823i | \(0.878390\pi\) | |||||||
\(228\) | − | 6.95062i | − | 0.460316i | ||||||
\(229\) | − | 22.8477i | − | 1.50982i | −0.655830 | − | 0.754908i | \(-0.727681\pi\) | ||
0.655830 | − | 0.754908i | \(-0.272319\pi\) | |||||||
\(230\) | 4.12266 | 0.271840 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.78271 | −0.510960 | ||||||||
\(233\) | − | 5.11552i | − | 0.335129i | −0.985861 | − | 0.167564i | \(-0.946410\pi\) | ||
0.985861 | − | 0.167564i | \(-0.0535902\pi\) | |||||||
\(234\) | − | 5.39143i | − | 0.352449i | ||||||
\(235\) | 41.8517 | 2.73010 | ||||||||
\(236\) | 14.8396i | 0.965974i | ||||||||
\(237\) | −12.9709 | −0.842554 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 11.3940i | − | 0.737016i | −0.929625 | − | 0.368508i | \(-0.879869\pi\) | ||
0.929625 | − | 0.368508i | \(-0.120131\pi\) | |||||||
\(240\) | 3.45711 | 0.223155 | ||||||||
\(241\) | 20.6584 | 1.33072 | 0.665361 | − | 0.746521i | \(-0.268277\pi\) | ||||
0.665361 | + | 0.746521i | \(0.268277\pi\) | |||||||
\(242\) | 7.63022 | − | 7.92336i | 0.490489 | − | 0.509333i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 3.63129 | 0.232469 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.87368 | −0.310734 | ||||||||
\(247\) | 37.4738 | 2.38440 | ||||||||
\(248\) | 6.61846 | 0.420273 | ||||||||
\(249\) | 8.48330i | 0.537607i | ||||||||
\(250\) | −6.74683 | −0.426707 | ||||||||
\(251\) | 15.9325i | 1.00565i | 0.864389 | + | 0.502824i | \(0.167706\pi\) | ||||
−0.864389 | + | 0.502824i | \(0.832294\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.66816 | + | 1.47907i | 0.230616 | + | 0.0929881i | ||||
\(254\) | −2.24140 | −0.140638 | ||||||||
\(255\) | 0.158081 | 0.00989941 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 2.50401i | − | 0.156196i | −0.996946 | − | 0.0780979i | \(-0.975115\pi\) | ||
0.996946 | − | 0.0780979i | \(-0.0248847\pi\) | |||||||
\(258\) | 3.27873i | 0.204125i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 18.6387i | 1.15593i | ||||||||
\(261\) | − | 7.78271i | − | 0.481738i | ||||||
\(262\) | 2.65048i | 0.163747i | ||||||||
\(263\) | − | 21.6317i | − | 1.33387i | −0.745117 | − | 0.666934i | \(-0.767606\pi\) | ||
0.745117 | − | 0.666934i | \(-0.232394\pi\) | |||||||
\(264\) | 3.07598 | + | 1.24029i | 0.189314 | + | 0.0763345i | ||||
\(265\) | − | 12.7586i | − | 0.783754i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.20562 | −0.257380 | ||||||||
\(268\) | −6.66903 | −0.407376 | ||||||||
\(269\) | 6.05738i | 0.369325i | 0.982802 | + | 0.184663i | \(0.0591192\pi\) | ||||
−0.982802 | + | 0.184663i | \(0.940881\pi\) | |||||||
\(270\) | 3.45711i | 0.210393i | ||||||||
\(271\) | 17.7596 | 1.07882 | 0.539409 | − | 0.842044i | \(-0.318648\pi\) | ||||
0.539409 | + | 0.842044i | \(0.318648\pi\) | |||||||
\(272\) | 0.0457263 | 0.00277257 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.9046i | 0.900421i | ||||||||
\(275\) | −21.3830 | − | 8.62198i | −1.28944 | − | 0.519925i | ||||
\(276\) | 1.19252i | 0.0717811i | ||||||||
\(277\) | 28.8259i | 1.73198i | 0.500059 | + | 0.865992i | \(0.333312\pi\) | ||||
−0.500059 | + | 0.865992i | \(0.666688\pi\) | |||||||
\(278\) | 17.4420i | 1.04610i | ||||||||
\(279\) | 6.61846i | 0.396237i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 21.1314i | − | 1.26060i | −0.776354 | − | 0.630298i | \(-0.782933\pi\) | ||
0.776354 | − | 0.630298i | \(-0.217067\pi\) | |||||||
\(282\) | 12.1060i | 0.720901i | ||||||||
\(283\) | −3.10856 | −0.184785 | −0.0923924 | − | 0.995723i | \(-0.529451\pi\) | ||||
−0.0923924 | + | 0.995723i | \(0.529451\pi\) | |||||||
\(284\) | −6.89741 | −0.409286 | ||||||||
\(285\) | −24.0290 | −1.42336 | ||||||||
\(286\) | −6.68693 | + | 16.5839i | −0.395407 | + | 0.980629i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | −16.9979 | −0.999877 | ||||||||
\(290\) | 26.9057i | 1.57996i | ||||||||
\(291\) | 6.64551 | 0.389567 | ||||||||
\(292\) | 3.04272 | 0.178062 | ||||||||
\(293\) | −24.9692 | −1.45872 | −0.729358 | − | 0.684132i | \(-0.760181\pi\) | ||||
−0.729358 | + | 0.684132i | \(0.760181\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 51.3020 | 2.98692 | ||||||||
\(296\) | − | 1.51053i | − | 0.0877978i | ||||||
\(297\) | −1.24029 | + | 3.07598i | −0.0719689 | + | 0.178487i | ||||
\(298\) | 11.1458 | 0.645658 | ||||||||
\(299\) | −6.42937 | −0.371820 | ||||||||
\(300\) | − | 6.95158i | − | 0.401350i | ||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −13.7210 | −0.789556 | ||||||||
\(303\) | 14.1963i | 0.815554i | ||||||||
\(304\) | −6.95062 | −0.398646 | ||||||||
\(305\) | − | 12.5538i | − | 0.718826i | ||||||
\(306\) | 0.0457263i | 0.00261400i | ||||||||
\(307\) | 13.6795 | 0.780732 | 0.390366 | − | 0.920660i | \(-0.372348\pi\) | ||||
0.390366 | + | 0.920660i | \(0.372348\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.26090 | 0.0717300 | ||||||||
\(310\) | − | 22.8807i | − | 1.29954i | ||||||
\(311\) | 10.5374i | 0.597521i | 0.954328 | + | 0.298760i | \(0.0965731\pi\) | ||||
−0.954328 | + | 0.298760i | \(0.903427\pi\) | |||||||
\(312\) | −5.39143 | −0.305229 | ||||||||
\(313\) | 9.21844i | 0.521057i | 0.965466 | + | 0.260528i | \(0.0838968\pi\) | ||||
−0.965466 | + | 0.260528i | \(0.916103\pi\) | |||||||
\(314\) | 20.5517 | 1.15980 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.9709i | 0.729673i | ||||||||
\(317\) | 9.13510 | 0.513078 | 0.256539 | − | 0.966534i | \(-0.417418\pi\) | ||||
0.256539 | + | 0.966534i | \(0.417418\pi\) | |||||||
\(318\) | 3.69054 | 0.206955 | ||||||||
\(319\) | −9.65282 | + | 23.9395i | −0.540454 | + | 1.34036i | ||||
\(320\) | − | 3.45711i | − | 0.193258i | ||||||
\(321\) | 0.676179 | 0.0377406 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.317827 | −0.0176843 | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 37.4790 | 2.07896 | ||||||||
\(326\) | 10.3412i | 0.572746i | ||||||||
\(327\) | −19.6069 | −1.08427 | ||||||||
\(328\) | 4.87368i | 0.269104i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 4.28781 | − | 10.6340i | 0.236036 | − | 0.585383i | ||||
\(331\) | −9.48566 | −0.521379 | −0.260690 | − | 0.965423i | \(-0.583950\pi\) | ||||
−0.260690 | + | 0.965423i | \(0.583950\pi\) | |||||||
\(332\) | 8.48330 | 0.465582 | ||||||||
\(333\) | 1.51053 | 0.0827765 | ||||||||
\(334\) | − | 23.7721i | − | 1.30075i | ||||||
\(335\) | 23.0555i | 1.25966i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.0197i | 1.14501i | 0.819900 | + | 0.572507i | \(0.194029\pi\) | ||||
−0.819900 | + | 0.572507i | \(0.805971\pi\) | |||||||
\(338\) | − | 16.0675i | − | 0.873956i | ||||||
\(339\) | 2.24860i | 0.122127i | ||||||||
\(340\) | − | 0.158081i | − | 0.00857314i | ||||||
\(341\) | 8.20881 | − | 20.3583i | 0.444532 | − | 1.10246i | ||||
\(342\) | − | 6.95062i | − | 0.375847i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3.27873 | 0.176777 | ||||||||
\(345\) | 4.12266 | 0.221957 | ||||||||
\(346\) | − | 13.5605i | − | 0.729019i | ||||||
\(347\) | − | 1.87391i | − | 0.100597i | −0.998734 | − | 0.0502984i | \(-0.983983\pi\) | ||
0.998734 | − | 0.0502984i | \(-0.0160172\pi\) | |||||||
\(348\) | −7.78271 | −0.417197 | ||||||||
\(349\) | −32.8189 | −1.75675 | −0.878377 | − | 0.477969i | \(-0.841373\pi\) | ||||
−0.878377 | + | 0.477969i | \(0.841373\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 5.39143i | − | 0.287773i | ||||||
\(352\) | 1.24029 | − | 3.07598i | 0.0661077 | − | 0.163951i | ||||
\(353\) | 19.8071i | 1.05422i | 0.849796 | + | 0.527112i | \(0.176725\pi\) | ||||
−0.849796 | + | 0.527112i | \(0.823275\pi\) | |||||||
\(354\) | 14.8396i | 0.788715i | ||||||||
\(355\) | 23.8451i | 1.26557i | ||||||||
\(356\) | 4.20562i | 0.222897i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 16.1833i | 0.855316i | ||||||||
\(359\) | 27.4211i | 1.44723i | 0.690203 | + | 0.723616i | \(0.257521\pi\) | ||||
−0.690203 | + | 0.723616i | \(0.742479\pi\) | |||||||
\(360\) | 3.45711 | 0.182206 | ||||||||
\(361\) | 29.3112 | 1.54269 | ||||||||
\(362\) | −15.6283 | −0.821405 | ||||||||
\(363\) | 7.63022 | − | 7.92336i | 0.400483 | − | 0.415869i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 10.5190i | − | 0.550590i | ||||||
\(366\) | 3.63129 | 0.189811 | ||||||||
\(367\) | 17.2117i | 0.898444i | 0.893420 | + | 0.449222i | \(0.148299\pi\) | ||||
−0.893420 | + | 0.449222i | \(0.851701\pi\) | |||||||
\(368\) | 1.19252 | 0.0621643 | ||||||||
\(369\) | −4.87368 | −0.253713 | ||||||||
\(370\) | −5.22206 | −0.271482 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 6.61846 | 0.343151 | ||||||||
\(373\) | − | 23.5811i | − | 1.22099i | −0.792022 | − | 0.610493i | \(-0.790971\pi\) | ||
0.792022 | − | 0.610493i | \(-0.209029\pi\) | |||||||
\(374\) | 0.0567139 | − | 0.140654i | 0.00293261 | − | 0.00727302i | ||||
\(375\) | −6.74683 | −0.348405 | ||||||||
\(376\) | 12.1060 | 0.624319 | ||||||||
\(377\) | − | 41.9599i | − | 2.16105i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.82325 | 0.350487 | 0.175243 | − | 0.984525i | \(-0.443929\pi\) | ||||
0.175243 | + | 0.984525i | \(0.443929\pi\) | |||||||
\(380\) | 24.0290i | 1.23266i | ||||||||
\(381\) | −2.24140 | −0.114830 | ||||||||
\(382\) | 8.42409i | 0.431014i | ||||||||
\(383\) | 10.0655i | 0.514321i | 0.966369 | + | 0.257160i | \(0.0827869\pi\) | ||||
−0.966369 | + | 0.257160i | \(0.917213\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.14795 | −0.465618 | ||||||||
\(387\) | 3.27873i | 0.166667i | ||||||||
\(388\) | − | 6.64551i | − | 0.337375i | ||||||
\(389\) | 11.3167 | 0.573778 | 0.286889 | − | 0.957964i | \(-0.407379\pi\) | ||||
0.286889 | + | 0.957964i | \(0.407379\pi\) | |||||||
\(390\) | 18.6387i | 0.943809i | ||||||||
\(391\) | 0.0545295 | 0.00275767 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.65048i | 0.133699i | ||||||||
\(394\) | 13.7101 | 0.690706 | ||||||||
\(395\) | 44.8419 | 2.25624 | ||||||||
\(396\) | 3.07598 | + | 1.24029i | 0.154574 | + | 0.0623269i | ||||
\(397\) | − | 26.8201i | − | 1.34606i | −0.739614 | − | 0.673031i | \(-0.764992\pi\) | ||
0.739614 | − | 0.673031i | \(-0.235008\pi\) | |||||||
\(398\) | 5.92036 | 0.296761 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.95158 | −0.347579 | ||||||||
\(401\) | −14.0066 | −0.699457 | −0.349728 | − | 0.936851i | \(-0.613726\pi\) | ||||
−0.349728 | + | 0.936851i | \(0.613726\pi\) | |||||||
\(402\) | −6.66903 | −0.332621 | ||||||||
\(403\) | 35.6829i | 1.77749i | ||||||||
\(404\) | 14.1963 | 0.706290 | ||||||||
\(405\) | 3.45711i | 0.171785i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.64637 | − | 1.87349i | −0.230312 | − | 0.0928657i | ||||
\(408\) | 0.0457263 | 0.00226379 | ||||||||
\(409\) | −6.38532 | −0.315734 | −0.157867 | − | 0.987460i | \(-0.550462\pi\) | ||||
−0.157867 | + | 0.987460i | \(0.550462\pi\) | |||||||
\(410\) | 16.8488 | 0.832104 | ||||||||
\(411\) | 14.9046i | 0.735190i | ||||||||
\(412\) | − | 1.26090i | − | 0.0621200i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.19252i | 0.0586090i | ||||||||
\(415\) | − | 29.3277i | − | 1.43964i | ||||||
\(416\) | 5.39143i | 0.264336i | ||||||||
\(417\) | 17.4420i | 0.854140i | ||||||||
\(418\) | −8.62078 | + | 21.3800i | −0.421656 | + | 1.04573i | ||||
\(419\) | − | 18.9490i | − | 0.925718i | −0.886432 | − | 0.462859i | \(-0.846824\pi\) | ||
0.886432 | − | 0.462859i | \(-0.153176\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.8148 | −1.06319 | −0.531595 | − | 0.846999i | \(-0.678407\pi\) | ||||
−0.531595 | + | 0.846999i | \(0.678407\pi\) | |||||||
\(422\) | 6.27732 | 0.305575 | ||||||||
\(423\) | 12.1060i | 0.588613i | ||||||||
\(424\) | − | 3.69054i | − | 0.179229i | ||||||
\(425\) | −0.317871 | −0.0154190 | ||||||||
\(426\) | −6.89741 | −0.334181 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 0.676179i | − | 0.0326843i | ||||||
\(429\) | −6.68693 | + | 16.5839i | −0.322848 | + | 0.800680i | ||||
\(430\) | − | 11.3349i | − | 0.546618i | ||||||
\(431\) | − | 6.96363i | − | 0.335426i | −0.985836 | − | 0.167713i | \(-0.946362\pi\) | ||
0.985836 | − | 0.167713i | \(-0.0536383\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | − | 4.32631i | − | 0.207909i | −0.994582 | − | 0.103955i | \(-0.966850\pi\) | ||
0.994582 | − | 0.103955i | \(-0.0331496\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 26.9057i | 1.29003i | ||||||||
\(436\) | 19.6069i | 0.939002i | ||||||||
\(437\) | −8.28874 | −0.396504 | ||||||||
\(438\) | 3.04272 | 0.145387 | ||||||||
\(439\) | −1.95568 | −0.0933395 | −0.0466698 | − | 0.998910i | \(-0.514861\pi\) | ||||
−0.0466698 | + | 0.998910i | \(0.514861\pi\) | |||||||
\(440\) | −10.6340 | − | 4.28781i | −0.506956 | − | 0.204413i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.246530i | 0.0117262i | ||||||||
\(443\) | −13.8098 | −0.656122 | −0.328061 | − | 0.944656i | \(-0.606395\pi\) | ||||
−0.328061 | + | 0.944656i | \(0.606395\pi\) | |||||||
\(444\) | − | 1.51053i | − | 0.0716866i | ||||||
\(445\) | 14.5393 | 0.689228 | ||||||||
\(446\) | 23.9882 | 1.13588 | ||||||||
\(447\) | 11.1458 | 0.527178 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −34.4653 | −1.62652 | −0.813259 | − | 0.581901i | \(-0.802309\pi\) | ||||
−0.813259 | + | 0.581901i | \(0.802309\pi\) | |||||||
\(450\) | − | 6.95158i | − | 0.327701i | ||||||
\(451\) | 14.9913 | + | 6.04477i | 0.705915 | + | 0.284637i | ||||
\(452\) | 2.24860 | 0.105765 | ||||||||
\(453\) | −13.7210 | −0.644670 | ||||||||
\(454\) | 27.9605i | 1.31225i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.95062 | −0.325493 | ||||||||
\(457\) | 24.0756i | 1.12621i | 0.826386 | + | 0.563104i | \(0.190393\pi\) | ||||
−0.826386 | + | 0.563104i | \(0.809607\pi\) | |||||||
\(458\) | −22.8477 | −1.06760 | ||||||||
\(459\) | 0.0457263i | 0.00213432i | ||||||||
\(460\) | − | 4.12266i | − | 0.192220i | ||||||
\(461\) | 6.27016 | 0.292030 | 0.146015 | − | 0.989282i | \(-0.453355\pi\) | ||||
0.146015 | + | 0.989282i | \(0.453355\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.766178 | −0.0356073 | −0.0178036 | − | 0.999842i | \(-0.505667\pi\) | ||||
−0.0178036 | + | 0.999842i | \(0.505667\pi\) | |||||||
\(464\) | 7.78271i | 0.361303i | ||||||||
\(465\) | − | 22.8807i | − | 1.06107i | ||||||
\(466\) | −5.11552 | −0.236972 | ||||||||
\(467\) | − | 27.5152i | − | 1.27325i | −0.771172 | − | 0.636626i | \(-0.780329\pi\) | ||
0.771172 | − | 0.636626i | \(-0.219671\pi\) | |||||||
\(468\) | −5.39143 | −0.249219 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 41.8517i | − | 1.93047i | ||||||
\(471\) | 20.5517 | 0.946974 | ||||||||
\(472\) | 14.8396 | 0.683047 | ||||||||
\(473\) | 4.06657 | − | 10.0853i | 0.186981 | − | 0.463723i | ||||
\(474\) | 12.9709i | 0.595775i | ||||||||
\(475\) | 48.3178 | 2.21697 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.69054 | 0.168978 | ||||||||
\(478\) | −11.3940 | −0.521149 | ||||||||
\(479\) | −14.3917 | −0.657575 | −0.328788 | − | 0.944404i | \(-0.606640\pi\) | ||||
−0.328788 | + | 0.944404i | \(0.606640\pi\) | |||||||
\(480\) | − | 3.45711i | − | 0.157795i | ||||||
\(481\) | 8.14391 | 0.371330 | ||||||||
\(482\) | − | 20.6584i | − | 0.940963i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.92336 | − | 7.63022i | −0.360153 | − | 0.346828i | ||||
\(485\) | −22.9742 | −1.04321 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −15.4033 | −0.697988 | −0.348994 | − | 0.937125i | \(-0.613477\pi\) | ||||
−0.348994 | + | 0.937125i | \(0.613477\pi\) | |||||||
\(488\) | − | 3.63129i | − | 0.164381i | ||||||
\(489\) | 10.3412i | 0.467646i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 5.09884i | − | 0.230107i | −0.993359 | − | 0.115054i | \(-0.963296\pi\) | ||
0.993359 | − | 0.115054i | \(-0.0367040\pi\) | |||||||
\(492\) | 4.87368i | 0.219722i | ||||||||
\(493\) | 0.355875i | 0.0160278i | ||||||||
\(494\) | − | 37.4738i | − | 1.68602i | ||||||
\(495\) | 4.28781 | − | 10.6340i | 0.192723 | − | 0.477963i | ||||
\(496\) | − | 6.61846i | − | 0.297178i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 8.48330 | 0.380146 | ||||||||
\(499\) | −23.7056 | −1.06121 | −0.530605 | − | 0.847619i | \(-0.678035\pi\) | ||||
−0.530605 | + | 0.847619i | \(0.678035\pi\) | |||||||
\(500\) | 6.74683i | 0.301728i | ||||||||
\(501\) | − | 23.7721i | − | 1.06206i | ||||||
\(502\) | 15.9325 | 0.711101 | ||||||||
\(503\) | 38.3613 | 1.71045 | 0.855223 | − | 0.518260i | \(-0.173420\pi\) | ||||
0.855223 | + | 0.518260i | \(0.173420\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 49.0780i | − | 2.18394i | ||||||
\(506\) | 1.47907 | − | 3.66816i | 0.0657525 | − | 0.163070i | ||||
\(507\) | − | 16.0675i | − | 0.713582i | ||||||
\(508\) | 2.24140i | 0.0994461i | ||||||||
\(509\) | 30.6547i | 1.35874i | 0.733794 | + | 0.679372i | \(0.237748\pi\) | ||||
−0.733794 | + | 0.679372i | \(0.762252\pi\) | |||||||
\(510\) | − | 0.158081i | − | 0.00699994i | ||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | − | 6.95062i | − | 0.306877i | ||||||
\(514\) | −2.50401 | −0.110447 | ||||||||
\(515\) | −4.35906 | −0.192083 | ||||||||
\(516\) | 3.27873 | 0.144338 | ||||||||
\(517\) | 15.0149 | − | 37.2378i | 0.660356 | − | 1.63772i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 13.5605i | − | 0.595242i | ||||||
\(520\) | 18.6387 | 0.817363 | ||||||||
\(521\) | − | 41.7976i | − | 1.83119i | −0.402106 | − | 0.915593i | \(-0.631722\pi\) | ||
0.402106 | − | 0.915593i | \(-0.368278\pi\) | |||||||
\(522\) | −7.78271 | −0.340640 | ||||||||
\(523\) | 13.0947 | 0.572591 | 0.286296 | − | 0.958141i | \(-0.407576\pi\) | ||||
0.286296 | + | 0.958141i | \(0.407576\pi\) | |||||||
\(524\) | 2.65048 | 0.115787 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −21.6317 | −0.943187 | ||||||||
\(527\) | − | 0.302638i | − | 0.0131831i | ||||||
\(528\) | 1.24029 | − | 3.07598i | 0.0539767 | − | 0.133865i | ||||
\(529\) | −21.5779 | −0.938170 | ||||||||
\(530\) | −12.7586 | −0.554198 | ||||||||
\(531\) | 14.8396i | 0.643983i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −26.2761 | −1.13814 | ||||||||
\(534\) | 4.20562i | 0.181995i | ||||||||
\(535\) | −2.33762 | −0.101064 | ||||||||
\(536\) | 6.66903i | 0.288058i | ||||||||
\(537\) | 16.1833i | 0.698362i | ||||||||
\(538\) | 6.05738 | 0.261152 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.45711 | 0.148770 | ||||||||
\(541\) | − | 9.85167i | − | 0.423556i | −0.977318 | − | 0.211778i | \(-0.932075\pi\) | ||
0.977318 | − | 0.211778i | \(-0.0679254\pi\) | |||||||
\(542\) | − | 17.7596i | − | 0.762840i | ||||||
\(543\) | −15.6283 | −0.670675 | ||||||||
\(544\) | − | 0.0457263i | − | 0.00196050i | ||||||
\(545\) | 67.7832 | 2.90352 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 7.17541i | − | 0.306798i | −0.988164 | − | 0.153399i | \(-0.950978\pi\) | ||
0.988164 | − | 0.153399i | \(-0.0490220\pi\) | |||||||
\(548\) | 14.9046 | 0.636694 | ||||||||
\(549\) | 3.63129 | 0.154980 | ||||||||
\(550\) | −8.62198 | + | 21.3830i | −0.367642 | + | 0.911773i | ||||
\(551\) | − | 54.0947i | − | 2.30451i | ||||||
\(552\) | 1.19252 | 0.0507569 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 28.8259 | 1.22470 | ||||||||
\(555\) | −5.22206 | −0.221664 | ||||||||
\(556\) | 17.4420 | 0.739707 | ||||||||
\(557\) | − | 38.2620i | − | 1.62121i | −0.585590 | − | 0.810607i | \(-0.699137\pi\) | ||
0.585590 | − | 0.810607i | \(-0.300863\pi\) | |||||||
\(558\) | 6.61846 | 0.280182 | ||||||||
\(559\) | 17.6770i | 0.747658i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.0567139 | − | 0.140654i | 0.00239446 | − | 0.00593840i | ||||
\(562\) | −21.1314 | −0.891375 | ||||||||
\(563\) | −39.6058 | −1.66918 | −0.834592 | − | 0.550868i | \(-0.814297\pi\) | ||||
−0.834592 | + | 0.550868i | \(0.814297\pi\) | |||||||
\(564\) | 12.1060 | 0.509754 | ||||||||
\(565\) | − | 7.77366i | − | 0.327040i | ||||||
\(566\) | 3.10856i | 0.130663i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.89741i | 0.289409i | ||||||||
\(569\) | − | 9.08146i | − | 0.380715i | −0.981715 | − | 0.190357i | \(-0.939035\pi\) | ||
0.981715 | − | 0.190357i | \(-0.0609646\pi\) | |||||||
\(570\) | 24.0290i | 1.00647i | ||||||||
\(571\) | 18.5109i | 0.774659i | 0.921941 | + | 0.387329i | \(0.126602\pi\) | ||||
−0.921941 | + | 0.387329i | \(0.873398\pi\) | |||||||
\(572\) | 16.5839 | + | 6.68693i | 0.693410 | + | 0.279595i | ||||
\(573\) | 8.42409i | 0.351921i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.28988 | −0.345712 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | − | 35.6857i | − | 1.48562i | −0.669505 | − | 0.742808i | \(-0.733494\pi\) | ||
0.669505 | − | 0.742808i | \(-0.266506\pi\) | |||||||
\(578\) | 16.9979i | 0.707020i | ||||||||
\(579\) | −9.14795 | −0.380176 | ||||||||
\(580\) | 26.9057 | 1.11720 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | − | 6.64551i | − | 0.275465i | ||||||
\(583\) | −11.3520 | − | 4.57734i | −0.470154 | − | 0.189574i | ||||
\(584\) | − | 3.04272i | − | 0.125909i | ||||||
\(585\) | 18.6387i | 0.770617i | ||||||||
\(586\) | 24.9692i | 1.03147i | ||||||||
\(587\) | 11.3534i | 0.468606i | 0.972164 | + | 0.234303i | \(0.0752808\pi\) | ||||
−0.972164 | + | 0.234303i | \(0.924719\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 46.0024i | 1.89550i | ||||||||
\(590\) | − | 51.3020i | − | 2.11207i | ||||||
\(591\) | 13.7101 | 0.563959 | ||||||||
\(592\) | −1.51053 | −0.0620824 | ||||||||
\(593\) | 18.1657 | 0.745974 | 0.372987 | − | 0.927837i | \(-0.378334\pi\) | ||||
0.372987 | + | 0.927837i | \(0.378334\pi\) | |||||||
\(594\) | 3.07598 | + | 1.24029i | 0.126209 | + | 0.0508897i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 11.1458i | − | 0.456549i | ||||||
\(597\) | 5.92036 | 0.242304 | ||||||||
\(598\) | 6.42937i | 0.262916i | ||||||||
\(599\) | 34.4805 | 1.40884 | 0.704419 | − | 0.709785i | \(-0.251208\pi\) | ||||
0.704419 | + | 0.709785i | \(0.251208\pi\) | |||||||
\(600\) | −6.95158 | −0.283797 | ||||||||
\(601\) | −19.6808 | −0.802797 | −0.401398 | − | 0.915904i | \(-0.631476\pi\) | ||||
−0.401398 | + | 0.915904i | \(0.631476\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.66903 | −0.271584 | ||||||||
\(604\) | 13.7210i | 0.558300i | ||||||||
\(605\) | −26.3785 | + | 27.3919i | −1.07244 | + | 1.11364i | ||||
\(606\) | 14.1963 | 0.576684 | ||||||||
\(607\) | −16.2385 | −0.659102 | −0.329551 | − | 0.944138i | \(-0.606897\pi\) | ||||
−0.329551 | + | 0.944138i | \(0.606897\pi\) | |||||||
\(608\) | 6.95062i | 0.281885i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.5538 | −0.508287 | ||||||||
\(611\) | 65.2685i | 2.64048i | ||||||||
\(612\) | 0.0457263 | 0.00184838 | ||||||||
\(613\) | 15.9340i | 0.643567i | 0.946813 | + | 0.321783i | \(0.104282\pi\) | ||||
−0.946813 | + | 0.321783i | \(0.895718\pi\) | |||||||
\(614\) | − | 13.6795i | − | 0.552061i | ||||||
\(615\) | 16.8488 | 0.679410 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.30634 | 0.334401 | 0.167200 | − | 0.985923i | \(-0.446527\pi\) | ||||
0.167200 | + | 0.985923i | \(0.446527\pi\) | |||||||
\(618\) | − | 1.26090i | − | 0.0507207i | ||||||
\(619\) | 13.0920i | 0.526212i | 0.964767 | + | 0.263106i | \(0.0847468\pi\) | ||||
−0.964767 | + | 0.263106i | \(0.915253\pi\) | |||||||
\(620\) | −22.8807 | −0.918912 | ||||||||
\(621\) | 1.19252i | 0.0478541i | ||||||||
\(622\) | 10.5374 | 0.422511 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 5.39143i | 0.215830i | ||||||||
\(625\) | −11.4334 | −0.457336 | ||||||||
\(626\) | 9.21844 | 0.368443 | ||||||||
\(627\) | −8.62078 | + | 21.3800i | −0.344281 | + | 0.853835i | ||||
\(628\) | − | 20.5517i | − | 0.820104i | ||||||
\(629\) | −0.0690710 | −0.00275404 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.60081 | 0.183155 | 0.0915776 | − | 0.995798i | \(-0.470809\pi\) | ||||
0.0915776 | + | 0.995798i | \(0.470809\pi\) | |||||||
\(632\) | 12.9709 | 0.515957 | ||||||||
\(633\) | 6.27732 | 0.249501 | ||||||||
\(634\) | − | 9.13510i | − | 0.362801i | ||||||
\(635\) | 7.74876 | 0.307500 | ||||||||
\(636\) | − | 3.69054i | − | 0.146339i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 23.9395 | + | 9.65282i | 0.947774 | + | 0.382159i | ||||
\(639\) | −6.89741 | −0.272857 | ||||||||
\(640\) | −3.45711 | −0.136654 | ||||||||
\(641\) | −20.5868 | −0.813131 | −0.406565 | − | 0.913622i | \(-0.633274\pi\) | ||||
−0.406565 | + | 0.913622i | \(0.633274\pi\) | |||||||
\(642\) | − | 0.676179i | − | 0.0266866i | ||||||
\(643\) | 3.20879i | 0.126542i | 0.997996 | + | 0.0632712i | \(0.0201533\pi\) | ||||
−0.997996 | + | 0.0632712i | \(0.979847\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 11.3349i | − | 0.446312i | ||||||
\(646\) | 0.317827i | 0.0125047i | ||||||||
\(647\) | 3.22975i | 0.126974i | 0.997983 | + | 0.0634872i | \(0.0202222\pi\) | ||||
−0.997983 | + | 0.0634872i | \(0.979778\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | 18.4054 | − | 45.6463i | 0.722474 | − | 1.79177i | ||||
\(650\) | − | 37.4790i | − | 1.47005i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.3412 | 0.404993 | ||||||||
\(653\) | 38.6968 | 1.51432 | 0.757162 | − | 0.653227i | \(-0.226585\pi\) | ||||
0.757162 | + | 0.653227i | \(0.226585\pi\) | |||||||
\(654\) | 19.6069i | 0.766692i | ||||||||
\(655\) | − | 9.16298i | − | 0.358027i | ||||||
\(656\) | 4.87368 | 0.190285 | ||||||||
\(657\) | 3.04272 | 0.118708 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.9199i | 0.620150i | 0.950712 | + | 0.310075i | \(0.100354\pi\) | ||||
−0.950712 | + | 0.310075i | \(0.899646\pi\) | |||||||
\(660\) | −10.6340 | − | 4.28781i | −0.413928 | − | 0.166903i | ||||
\(661\) | 13.1465i | 0.511338i | 0.966764 | + | 0.255669i | \(0.0822958\pi\) | ||||
−0.966764 | + | 0.255669i | \(0.917704\pi\) | |||||||
\(662\) | 9.48566i | 0.368671i | ||||||||
\(663\) | 0.246530i | 0.00957444i | ||||||||
\(664\) | − | 8.48330i | − | 0.329216i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | − | 1.51053i | − | 0.0585319i | ||||||
\(667\) | 9.28102i | 0.359363i | ||||||||
\(668\) | −23.7721 | −0.919769 | ||||||||
\(669\) | 23.9882 | 0.927438 | ||||||||
\(670\) | 23.0555 | 0.890713 | ||||||||
\(671\) | −11.1698 | − | 4.50385i | −0.431205 | − | 0.173869i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 3.87040i | − | 0.149193i | −0.997214 | − | 0.0745965i | \(-0.976233\pi\) | ||
0.997214 | − | 0.0745965i | \(-0.0237669\pi\) | |||||||
\(674\) | 21.0197 | 0.809647 | ||||||||
\(675\) | − | 6.95158i | − | 0.267567i | ||||||
\(676\) | −16.0675 | −0.617980 | ||||||||
\(677\) | 39.9138 | 1.53401 | 0.767006 | − | 0.641640i | \(-0.221746\pi\) | ||||
0.767006 | + | 0.641640i | \(0.221746\pi\) | |||||||
\(678\) | 2.24860 | 0.0863571 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.158081 | −0.00606212 | ||||||||
\(681\) | 27.9605i | 1.07145i | ||||||||
\(682\) | −20.3583 | − | 8.20881i | −0.779559 | − | 0.314331i | ||||
\(683\) | −30.6358 | −1.17225 | −0.586124 | − | 0.810222i | \(-0.699347\pi\) | ||||
−0.586124 | + | 0.810222i | \(0.699347\pi\) | |||||||
\(684\) | −6.95062 | −0.265764 | ||||||||
\(685\) | − | 51.5268i | − | 1.96874i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −22.8477 | −0.871693 | ||||||||
\(688\) | − | 3.27873i | − | 0.125000i | ||||||
\(689\) | 19.8973 | 0.758026 | ||||||||
\(690\) | − | 4.12266i | − | 0.156947i | ||||||
\(691\) | 14.2288i | 0.541290i | 0.962679 | + | 0.270645i | \(0.0872369\pi\) | ||||
−0.962679 | + | 0.270645i | \(0.912763\pi\) | |||||||
\(692\) | −13.5605 | −0.515494 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.87391 | −0.0711326 | ||||||||
\(695\) | − | 60.2989i | − | 2.28727i | ||||||
\(696\) | 7.78271i | 0.295003i | ||||||||
\(697\) | 0.222855 | 0.00844125 | ||||||||
\(698\) | 32.8189i | 1.24221i | ||||||||
\(699\) | −5.11552 | −0.193487 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 44.8935i | − | 1.69560i | −0.530312 | − | 0.847802i | \(-0.677925\pi\) | ||
0.530312 | − | 0.847802i | \(-0.322075\pi\) | |||||||
\(702\) | −5.39143 | −0.203486 | ||||||||
\(703\) | 10.4991 | 0.395982 | ||||||||
\(704\) | −3.07598 | − | 1.24029i | −0.115931 | − | 0.0467452i | ||||
\(705\) | − | 41.8517i | − | 1.57623i | ||||||
\(706\) | 19.8071 | 0.745449 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 14.8396 | 0.557706 | ||||||||
\(709\) | 19.5243 | 0.733252 | 0.366626 | − | 0.930368i | \(-0.380513\pi\) | ||||
0.366626 | + | 0.930368i | \(0.380513\pi\) | |||||||
\(710\) | 23.8451 | 0.894890 | ||||||||
\(711\) | 12.9709i | 0.486449i | ||||||||
\(712\) | 4.20562 | 0.157612 | ||||||||
\(713\) | − | 7.89263i | − | 0.295581i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 23.1174 | − | 57.3325i | 0.864543 | − | 2.14411i | ||||
\(716\) | 16.1833 | 0.604799 | ||||||||
\(717\) | −11.3940 | −0.425516 | ||||||||
\(718\) | 27.4211 | 1.02335 | ||||||||
\(719\) | − | 34.6102i | − | 1.29074i | −0.763870 | − | 0.645371i | \(-0.776703\pi\) | ||
0.763870 | − | 0.645371i | \(-0.223297\pi\) | |||||||
\(720\) | − | 3.45711i | − | 0.128839i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 29.3112i | − | 1.09085i | ||||||
\(723\) | − | 20.6584i | − | 0.768293i | ||||||
\(724\) | 15.6283i | 0.580821i | ||||||||
\(725\) | − | 54.1022i | − | 2.00930i | ||||||
\(726\) | −7.92336 | − | 7.63022i | −0.294064 | − | 0.283184i | ||||
\(727\) | 17.5486i | 0.650840i | 0.945570 | + | 0.325420i | \(0.105506\pi\) | ||||
−0.945570 | + | 0.325420i | \(0.894494\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −10.5190 | −0.389326 | ||||||||
\(731\) | − | 0.149924i | − | 0.00554515i | ||||||
\(732\) | − | 3.63129i | − | 0.134216i | ||||||
\(733\) | −39.1221 | −1.44501 | −0.722504 | − | 0.691367i | \(-0.757009\pi\) | ||||
−0.722504 | + | 0.691367i | \(0.757009\pi\) | |||||||
\(734\) | 17.2117 | 0.635296 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 1.19252i | − | 0.0439568i | ||||||
\(737\) | 20.5138 | + | 8.27153i | 0.755637 | + | 0.304686i | ||||
\(738\) | 4.87368i | 0.179402i | ||||||||
\(739\) | − | 33.6557i | − | 1.23804i | −0.785374 | − | 0.619022i | \(-0.787529\pi\) | ||
0.785374 | − | 0.619022i | \(-0.212471\pi\) | |||||||
\(740\) | 5.22206i | 0.191967i | ||||||||
\(741\) | − | 37.4738i | − | 1.37663i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 32.1198i | − | 1.17836i | −0.808001 | − | 0.589181i | \(-0.799450\pi\) | ||
0.808001 | − | 0.589181i | \(-0.200550\pi\) | |||||||
\(744\) | − | 6.61846i | − | 0.242644i | ||||||
\(745\) | −38.5322 | −1.41171 | ||||||||
\(746\) | −23.5811 | −0.863367 | ||||||||
\(747\) | 8.48330 | 0.310388 | ||||||||
\(748\) | −0.140654 | − | 0.0567139i | −0.00514280 | − | 0.00207367i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 6.74683i | 0.246360i | ||||||||
\(751\) | 51.6804 | 1.88584 | 0.942922 | − | 0.333014i | \(-0.108065\pi\) | ||||
0.942922 | + | 0.333014i | \(0.108065\pi\) | |||||||
\(752\) | − | 12.1060i | − | 0.441460i | ||||||
\(753\) | 15.9325 | 0.580611 | ||||||||
\(754\) | −41.9599 | −1.52809 | ||||||||
\(755\) | 47.4350 | 1.72634 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 43.1042 | 1.56665 | 0.783324 | − | 0.621614i | \(-0.213523\pi\) | ||||
0.783324 | + | 0.621614i | \(0.213523\pi\) | |||||||
\(758\) | − | 6.82325i | − | 0.247831i | ||||||
\(759\) | 1.47907 | − | 3.66816i | 0.0536867 | − | 0.133146i | ||||
\(760\) | 24.0290 | 0.871625 | ||||||||
\(761\) | 6.05142 | 0.219364 | 0.109682 | − | 0.993967i | \(-0.465017\pi\) | ||||
0.109682 | + | 0.993967i | \(0.465017\pi\) | |||||||
\(762\) | 2.24140i | 0.0811974i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 8.42409 | 0.304773 | ||||||||
\(765\) | − | 0.158081i | − | 0.00571543i | ||||||
\(766\) | 10.0655 | 0.363680 | ||||||||
\(767\) | 80.0065i | 2.88887i | ||||||||
\(768\) | − | 1.00000i | − | 0.0360844i | ||||||
\(769\) | 44.3139 | 1.59800 | 0.799000 | − | 0.601331i | \(-0.205363\pi\) | ||||
0.799000 | + | 0.601331i | \(0.205363\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.50401 | −0.0901797 | ||||||||
\(772\) | 9.14795i | 0.329242i | ||||||||
\(773\) | 0.830514i | 0.0298715i | 0.999888 | + | 0.0149358i | \(0.00475437\pi\) | ||||
−0.999888 | + | 0.0149358i | \(0.995246\pi\) | |||||||
\(774\) | 3.27873 | 0.117851 | ||||||||
\(775\) | 46.0088i | 1.65268i | ||||||||
\(776\) | −6.64551 | −0.238560 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 11.3167i | − | 0.405722i | ||||||
\(779\) | −33.8751 | −1.21370 | ||||||||
\(780\) | 18.6387 | 0.667374 | ||||||||
\(781\) | 21.2163 | + | 8.55479i | 0.759180 | + | 0.306114i | ||||
\(782\) | − | 0.0545295i | − | 0.00194997i | ||||||
\(783\) | −7.78271 | −0.278132 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −71.0496 | −2.53587 | ||||||||
\(786\) | 2.65048 | 0.0945394 | ||||||||
\(787\) | 41.5963 | 1.48275 | 0.741374 | − | 0.671092i | \(-0.234174\pi\) | ||||
0.741374 | + | 0.671092i | \(0.234174\pi\) | |||||||
\(788\) | − | 13.7101i | − | 0.488403i | ||||||
\(789\) | −21.6317 | −0.770109 | ||||||||
\(790\) | − | 44.8419i | − | 1.59540i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.24029 | − | 3.07598i | 0.0440718 | − | 0.109300i | ||||
\(793\) | 19.5778 | 0.695229 | ||||||||
\(794\) | −26.8201 | −0.951810 | ||||||||
\(795\) | −12.7586 | −0.452501 | ||||||||
\(796\) | − | 5.92036i | − | 0.209842i | ||||||
\(797\) | 13.1136i | 0.464507i | 0.972655 | + | 0.232254i | \(0.0746099\pi\) | ||||
−0.972655 | + | 0.232254i | \(0.925390\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 0.553563i | − | 0.0195836i | ||||||
\(800\) | 6.95158i | 0.245776i | ||||||||
\(801\) | 4.20562i | 0.148598i | ||||||||
\(802\) | 14.0066i | 0.494591i | ||||||||
\(803\) | −9.35936 | − | 3.77385i | −0.330285 | − | 0.133176i | ||||
\(804\) | 6.66903i | 0.235198i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 35.6829 | 1.25688 | ||||||||
\(807\) | 6.05738 | 0.213230 | ||||||||
\(808\) | − | 14.1963i | − | 0.499423i | ||||||
\(809\) | 11.7322i | 0.412481i | 0.978501 | + | 0.206240i | \(0.0661229\pi\) | ||||
−0.978501 | + | 0.206240i | \(0.933877\pi\) | |||||||
\(810\) | 3.45711 | 0.121470 | ||||||||
\(811\) | −45.2773 | −1.58990 | −0.794950 | − | 0.606675i | \(-0.792503\pi\) | ||||
−0.794950 | + | 0.606675i | \(0.792503\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 17.7596i | − | 0.622856i | ||||||
\(814\) | −1.87349 | + | 4.64637i | −0.0656660 | + | 0.162855i | ||||
\(815\) | − | 35.7506i | − | 1.25229i | ||||||
\(816\) | − | 0.0457263i | − | 0.00160074i | ||||||
\(817\) | 22.7892i | 0.797293i | ||||||||
\(818\) | 6.38532i | 0.223258i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 16.8488i | − | 0.588386i | ||||||
\(821\) | − | 4.57149i | − | 0.159546i | −0.996813 | − | 0.0797730i | \(-0.974580\pi\) | ||
0.996813 | − | 0.0797730i | \(-0.0254195\pi\) | |||||||
\(822\) | 14.9046 | 0.519858 | ||||||||
\(823\) | 3.85368 | 0.134331 | 0.0671655 | − | 0.997742i | \(-0.478604\pi\) | ||||
0.0671655 | + | 0.997742i | \(0.478604\pi\) | |||||||
\(824\) | −1.26090 | −0.0439255 | ||||||||
\(825\) | −8.62198 | + | 21.3830i | −0.300179 | + | 0.744459i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.321085i | 0.0111652i | 0.999984 | + | 0.00558261i | \(0.00177701\pi\) | ||||
−0.999984 | + | 0.00558261i | \(0.998223\pi\) | |||||||
\(828\) | 1.19252 | 0.0414428 | ||||||||
\(829\) | − | 9.89076i | − | 0.343520i | −0.985139 | − | 0.171760i | \(-0.945055\pi\) | ||
0.985139 | − | 0.171760i | \(-0.0549454\pi\) | |||||||
\(830\) | −29.3277 | −1.01798 | ||||||||
\(831\) | 28.8259 | 0.999961 | ||||||||
\(832\) | 5.39143 | 0.186914 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 17.4420 | 0.603968 | ||||||||
\(835\) | 82.1826i | 2.84404i | ||||||||
\(836\) | 21.3800 | + | 8.62078i | 0.739443 | + | 0.298156i | ||||
\(837\) | 6.61846 | 0.228767 | ||||||||
\(838\) | −18.9490 | −0.654581 | ||||||||
\(839\) | 19.1031i | 0.659512i | 0.944066 | + | 0.329756i | \(0.106967\pi\) | ||||
−0.944066 | + | 0.329756i | \(0.893033\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −31.5706 | −1.08864 | ||||||||
\(842\) | 21.8148i | 0.751789i | ||||||||
\(843\) | −21.1314 | −0.727805 | ||||||||
\(844\) | − | 6.27732i | − | 0.216074i | ||||||
\(845\) | 55.5470i | 1.91087i | ||||||||
\(846\) | 12.1060 | 0.416212 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.69054 | −0.126734 | ||||||||
\(849\) | 3.10856i | 0.106686i | ||||||||
\(850\) | 0.317871i | 0.0109029i | ||||||||
\(851\) | −1.80133 | −0.0617489 | ||||||||
\(852\) | 6.89741i | 0.236301i | ||||||||
\(853\) | −6.65956 | −0.228019 | −0.114009 | − | 0.993480i | \(-0.536369\pi\) | ||||
−0.114009 | + | 0.993480i | \(0.536369\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 24.0290i | 0.821776i | ||||||||
\(856\) | −0.676179 | −0.0231113 | ||||||||
\(857\) | −18.2342 | −0.622867 | −0.311434 | − | 0.950268i | \(-0.600809\pi\) | ||||
−0.311434 | + | 0.950268i | \(0.600809\pi\) | |||||||
\(858\) | 16.5839 | + | 6.68693i | 0.566167 | + | 0.228288i | ||||
\(859\) | 47.3128i | 1.61429i | 0.590352 | + | 0.807146i | \(0.298989\pi\) | ||||
−0.590352 | + | 0.807146i | \(0.701011\pi\) | |||||||
\(860\) | −11.3349 | −0.386517 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.96363 | −0.237182 | ||||||||
\(863\) | 47.4281 | 1.61447 | 0.807236 | − | 0.590228i | \(-0.200962\pi\) | ||||
0.807236 | + | 0.590228i | \(0.200962\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 46.8802i | 1.59398i | ||||||||
\(866\) | −4.32631 | −0.147014 | ||||||||
\(867\) | 16.9979i | 0.577279i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16.0877 | − | 39.8984i | 0.545739 | − | 1.35346i | ||||
\(870\) | 26.9057 | 0.912188 | ||||||||
\(871\) | −35.9556 | −1.21831 | ||||||||
\(872\) | 19.6069 | 0.663974 | ||||||||
\(873\) | − | 6.64551i | − | 0.224916i | ||||||
\(874\) | 8.28874i | 0.280371i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 3.04272i | − | 0.102804i | ||||||
\(877\) | 16.9463i | 0.572236i | 0.958194 | + | 0.286118i | \(0.0923649\pi\) | ||||
−0.958194 | + | 0.286118i | \(0.907635\pi\) | |||||||
\(878\) | 1.95568i | 0.0660010i | ||||||||
\(879\) | 24.9692i | 0.842190i | ||||||||
\(880\) | −4.28781 | + | 10.6340i | −0.144542 | + | 0.358472i | ||||
\(881\) | 34.5802i | 1.16504i | 0.812817 | + | 0.582518i | \(0.197933\pi\) | ||||
−0.812817 | + | 0.582518i | \(0.802067\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.6051 | −0.525154 | −0.262577 | − | 0.964911i | \(-0.584572\pi\) | ||||
−0.262577 | + | 0.964911i | \(0.584572\pi\) | |||||||
\(884\) | 0.246530 | 0.00829171 | ||||||||
\(885\) | − | 51.3020i | − | 1.72450i | ||||||
\(886\) | 13.8098i | 0.463949i | ||||||||
\(887\) | 1.12794 | 0.0378727 | 0.0189363 | − | 0.999821i | \(-0.493972\pi\) | ||||
0.0189363 | + | 0.999821i | \(0.493972\pi\) | |||||||
\(888\) | −1.51053 | −0.0506901 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 14.5393i | − | 0.487358i | ||||||
\(891\) | 3.07598 | + | 1.24029i | 0.103049 | + | 0.0415513i | ||||
\(892\) | − | 23.9882i | − | 0.803185i | ||||||
\(893\) | 84.1441i | 2.81578i | ||||||||
\(894\) | − | 11.1458i | − | 0.372771i | ||||||
\(895\) | − | 55.9475i | − | 1.87012i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.42937i | 0.214670i | ||||||||
\(898\) | 34.4653i | 1.15012i | ||||||||
\(899\) | 51.5096 | 1.71794 | ||||||||
\(900\) | −6.95158 | −0.231719 | ||||||||
\(901\) | −0.168755 | −0.00562204 | ||||||||
\(902\) | 6.04477 | − | 14.9913i | 0.201269 | − | 0.499157i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 2.24860i | − | 0.0747875i | ||||||
\(905\) | 54.0287 | 1.79597 | ||||||||
\(906\) | 13.7210i | 0.455850i | ||||||||
\(907\) | −43.2193 | −1.43507 | −0.717537 | − | 0.696521i | \(-0.754730\pi\) | ||||
−0.717537 | + | 0.696521i | \(0.754730\pi\) | |||||||
\(908\) | 27.9605 | 0.927903 | ||||||||
\(909\) | 14.1963 | 0.470860 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.2783 | 0.439928 | 0.219964 | − | 0.975508i | \(-0.429406\pi\) | ||||
0.219964 | + | 0.975508i | \(0.429406\pi\) | |||||||
\(912\) | 6.95062i | 0.230158i | ||||||||
\(913\) | −26.0945 | − | 10.5217i | −0.863602 | − | 0.348219i | ||||
\(914\) | 24.0756 | 0.796349 | ||||||||
\(915\) | −12.5538 | −0.415014 | ||||||||
\(916\) | 22.8477i | 0.754908i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.0457263 | 0.00150919 | ||||||||
\(919\) | 15.5661i | 0.513478i | 0.966481 | + | 0.256739i | \(0.0826481\pi\) | ||||
−0.966481 | + | 0.256739i | \(0.917352\pi\) | |||||||
\(920\) | −4.12266 | −0.135920 | ||||||||
\(921\) | − | 13.6795i | − | 0.450756i | ||||||
\(922\) | − | 6.27016i | − | 0.206497i | ||||||
\(923\) | −37.1869 | −1.22402 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.5006 | 0.345257 | ||||||||
\(926\) | 0.766178i | 0.0251782i | ||||||||
\(927\) | − | 1.26090i | − | 0.0414133i | ||||||
\(928\) | 7.78271 | 0.255480 | ||||||||
\(929\) | − | 21.8356i | − | 0.716403i | −0.933644 | − | 0.358201i | \(-0.883390\pi\) | ||
0.933644 | − | 0.358201i | \(-0.116610\pi\) | |||||||
\(930\) | −22.8807 | −0.750288 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 5.11552i | 0.167564i | ||||||||
\(933\) | 10.5374 | 0.344979 | ||||||||
\(934\) | −27.5152 | −0.900326 | ||||||||
\(935\) | −0.196066 | + | 0.486254i | −0.00641205 | + | 0.0159022i | ||||
\(936\) | 5.39143i | 0.176224i | ||||||||
\(937\) | −40.9973 | −1.33932 | −0.669661 | − | 0.742667i | \(-0.733561\pi\) | ||||
−0.669661 | + | 0.742667i | \(0.733561\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.21844 | 0.300832 | ||||||||
\(940\) | −41.8517 | −1.36505 | ||||||||
\(941\) | 30.0564 | 0.979811 | 0.489905 | − | 0.871776i | \(-0.337031\pi\) | ||||
0.489905 | + | 0.871776i | \(0.337031\pi\) | |||||||
\(942\) | − | 20.5517i | − | 0.669612i | ||||||
\(943\) | 5.81194 | 0.189263 | ||||||||
\(944\) | − | 14.8396i | − | 0.482987i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.0853 | − | 4.06657i | −0.327902 | − | 0.132216i | ||||
\(947\) | −49.6856 | −1.61457 | −0.807283 | − | 0.590165i | \(-0.799063\pi\) | ||||
−0.807283 | + | 0.590165i | \(0.799063\pi\) | |||||||
\(948\) | 12.9709 | 0.421277 | ||||||||
\(949\) | 16.4046 | 0.532516 | ||||||||
\(950\) | − | 48.3178i | − | 1.56764i | ||||||
\(951\) | − | 9.13510i | − | 0.296226i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 55.8496i | 1.80915i | 0.426319 | + | 0.904573i | \(0.359810\pi\) | ||||
−0.426319 | + | 0.904573i | \(0.640190\pi\) | |||||||
\(954\) | − | 3.69054i | − | 0.119486i | ||||||
\(955\) | − | 29.1230i | − | 0.942397i | ||||||
\(956\) | 11.3940i | 0.368508i | ||||||||
\(957\) | 23.9395 | + | 9.65282i | 0.773854 | + | 0.312031i | ||||
\(958\) | 14.3917i | 0.464976i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3.45711 | −0.111578 | ||||||||
\(961\) | −12.8040 | −0.413032 | ||||||||
\(962\) | − | 8.14391i | − | 0.262570i | ||||||
\(963\) | − | 0.676179i | − | 0.0217896i | ||||||
\(964\) | −20.6584 | −0.665361 | ||||||||
\(965\) | 31.6254 | 1.01806 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 38.2830i | 1.23110i | 0.788098 | + | 0.615549i | \(0.211066\pi\) | ||||
−0.788098 | + | 0.615549i | \(0.788934\pi\) | |||||||
\(968\) | −7.63022 | + | 7.92336i | −0.245245 | + | 0.254667i | ||||
\(969\) | 0.317827i | 0.0102101i | ||||||||
\(970\) | 22.9742i | 0.737658i | ||||||||
\(971\) | − | 16.1758i | − | 0.519107i | −0.965729 | − | 0.259554i | \(-0.916425\pi\) | ||
0.965729 | − | 0.259554i | \(-0.0835754\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 15.4033i | 0.493552i | ||||||||
\(975\) | − | 37.4790i | − | 1.20029i | ||||||
\(976\) | −3.63129 | −0.116235 | ||||||||
\(977\) | 29.2417 | 0.935525 | 0.467763 | − | 0.883854i | \(-0.345060\pi\) | ||||
0.467763 | + | 0.883854i | \(0.345060\pi\) | |||||||
\(978\) | 10.3412 | 0.330675 | ||||||||
\(979\) | 5.21619 | − | 12.9364i | 0.166710 | − | 0.413450i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 19.6069i | 0.626001i | ||||||||
\(982\) | −5.09884 | −0.162710 | ||||||||
\(983\) | 23.6960i | 0.755784i | 0.925850 | + | 0.377892i | \(0.123351\pi\) | ||||
−0.925850 | + | 0.377892i | \(0.876649\pi\) | |||||||
\(984\) | 4.87368 | 0.155367 | ||||||||
\(985\) | −47.3974 | −1.51021 | ||||||||
\(986\) | 0.355875 | 0.0113334 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −37.4738 | −1.19220 | ||||||||
\(989\) | − | 3.90994i | − | 0.124329i | ||||||
\(990\) | −10.6340 | − | 4.28781i | −0.337971 | − | 0.136276i | ||||
\(991\) | −56.4659 | −1.79370 | −0.896849 | − | 0.442337i | \(-0.854150\pi\) | ||||
−0.896849 | + | 0.442337i | \(0.854150\pi\) | |||||||
\(992\) | −6.61846 | −0.210136 | ||||||||
\(993\) | 9.48566i | 0.301018i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −20.4673 | −0.648858 | ||||||||
\(996\) | − | 8.48330i | − | 0.268804i | ||||||
\(997\) | 9.69675 | 0.307099 | 0.153550 | − | 0.988141i | \(-0.450930\pi\) | ||||
0.153550 | + | 0.988141i | \(0.450930\pi\) | |||||||
\(998\) | 23.7056i | 0.750388i | ||||||||
\(999\) | − | 1.51053i | − | 0.0477911i |
(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 | 3234.2.e.c.2155.11 | ✓ | 24 | |
7.6 | odd | 2 | 3234.2.e.d.2155.2 | yes | 24 | ||
11.10 | odd | 2 | 3234.2.e.d.2155.23 | yes | 24 | ||
77.76 | even | 2 | inner | 3234.2.e.c.2155.14 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3234.2.e.c.2155.11 | ✓ | 24 | 1.1 | even | 1 | trivial | |
3234.2.e.c.2155.14 | yes | 24 | 77.76 | even | 2 | inner | |
3234.2.e.d.2155.2 | yes | 24 | 7.6 | odd | 2 | ||
3234.2.e.d.2155.23 | yes | 24 | 11.10 | odd | 2 |