Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,3,Mod(449,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(85.8312832735\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | 16.0.9671731157401600000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 7x^{12} + 753x^{8} + 112x^{4} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{28} \) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.12 | ||
Root | \(0.796626 + 0.359610i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.449 |
Dual form | 3150.3.c.f.449.13 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 2.64575i | − 0.377964i | ||||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 14.1001i | 1.28183i | 0.767611 | + | 0.640916i | \(0.221445\pi\) | ||||
−0.767611 | + | 0.640916i | \(0.778555\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.78360i | 0.137200i | 0.997644 | + | 0.0685998i | \(0.0218532\pi\) | ||||
−0.997644 | + | 0.0685998i | \(0.978147\pi\) | |||||||
\(14\) | − 3.74166i | − 0.267261i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | −32.2729 | −1.89841 | −0.949203 | − | 0.314665i | \(-0.898108\pi\) | ||||
−0.949203 | + | 0.314665i | \(0.898108\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −9.89548 | −0.520815 | −0.260407 | − | 0.965499i | \(-0.583857\pi\) | ||||
−0.260407 | + | 0.965499i | \(0.583857\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 19.9406i | 0.906392i | ||||||||
\(23\) | −9.58126 | −0.416577 | −0.208288 | − | 0.978067i | \(-0.566789\pi\) | ||||
−0.208288 | + | 0.978067i | \(0.566789\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.52238i | 0.0970148i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 5.29150i | − 0.188982i | ||||||||
\(29\) | − 40.5881i | − 1.39959i | −0.714343 | − | 0.699795i | \(-0.753274\pi\) | ||||
0.714343 | − | 0.699795i | \(-0.246726\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 48.5626 | 1.56653 | 0.783267 | − | 0.621685i | \(-0.213552\pi\) | ||||
0.783267 | + | 0.621685i | \(0.213552\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −45.6408 | −1.34238 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 62.8976i | − 1.69993i | −0.526835 | − | 0.849967i | \(-0.676622\pi\) | ||||
0.526835 | − | 0.849967i | \(-0.323378\pi\) | |||||||
\(38\) | −13.9943 | −0.368272 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 65.7349i | − 1.60329i | −0.597801 | − | 0.801645i | \(-0.703959\pi\) | ||||
0.597801 | − | 0.801645i | \(-0.296041\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 50.8420i | 1.18237i | 0.806535 | + | 0.591186i | \(0.201340\pi\) | ||||
−0.806535 | + | 0.591186i | \(0.798660\pi\) | |||||||
\(44\) | 28.2003i | 0.640916i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −13.5500 | −0.294564 | ||||||||
\(47\) | 65.3405 | 1.39022 | 0.695111 | − | 0.718902i | \(-0.255355\pi\) | ||||
0.695111 | + | 0.718902i | \(0.255355\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.56719i | 0.0685998i | ||||||||
\(53\) | −64.9575 | −1.22561 | −0.612807 | − | 0.790233i | \(-0.709960\pi\) | ||||
−0.612807 | + | 0.790233i | \(0.709960\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − 7.48331i | − 0.133631i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − 57.4003i | − 0.989660i | ||||||||
\(59\) | − 111.642i | − 1.89223i | −0.323824 | − | 0.946117i | \(-0.604968\pi\) | ||||
0.323824 | − | 0.946117i | \(-0.395032\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.69105 | 0.0441156 | 0.0220578 | − | 0.999757i | \(-0.492978\pi\) | ||||
0.0220578 | + | 0.999757i | \(0.492978\pi\) | |||||||
\(62\) | 68.6778 | 1.10771 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 72.1824i | − 1.07735i | −0.842514 | − | 0.538674i | \(-0.818925\pi\) | ||||
0.842514 | − | 0.538674i | \(-0.181075\pi\) | |||||||
\(68\) | −64.5458 | −0.949203 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 40.6525i | − 0.572570i | −0.958144 | − | 0.286285i | \(-0.907580\pi\) | ||||
0.958144 | − | 0.286285i | \(-0.0924205\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 63.6965i | − 0.872554i | −0.899812 | − | 0.436277i | \(-0.856297\pi\) | ||||
0.899812 | − | 0.436277i | \(-0.143703\pi\) | |||||||
\(74\) | − 88.9506i | − 1.20204i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −19.7910 | −0.260407 | ||||||||
\(77\) | 37.3055 | 0.484487 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 82.3035 | 1.04182 | 0.520908 | − | 0.853613i | \(-0.325593\pi\) | ||||
0.520908 | + | 0.853613i | \(0.325593\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 92.9631i | − 1.13370i | ||||||||
\(83\) | 99.9021 | 1.20364 | 0.601820 | − | 0.798632i | \(-0.294442\pi\) | ||||
0.601820 | + | 0.798632i | \(0.294442\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 71.9014i | 0.836063i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 39.8812i | 0.453196i | ||||||||
\(89\) | 88.5703i | 0.995172i | 0.867415 | + | 0.497586i | \(0.165780\pi\) | ||||
−0.867415 | + | 0.497586i | \(0.834220\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.71895 | 0.0518566 | ||||||||
\(92\) | −19.1625 | −0.208288 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 92.4054 | 0.983036 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 117.848i | − 1.21493i | −0.794348 | − | 0.607464i | \(-0.792187\pi\) | ||||
0.794348 | − | 0.607464i | \(-0.207813\pi\) | |||||||
\(98\) | −9.89949 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 36.0289i | 0.356722i | 0.983965 | + | 0.178361i | \(0.0570794\pi\) | ||||
−0.983965 | + | 0.178361i | \(0.942921\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 34.8611i | 0.338457i | 0.985577 | + | 0.169229i | \(0.0541276\pi\) | ||||
−0.985577 | + | 0.169229i | \(0.945872\pi\) | |||||||
\(104\) | 5.04477i | 0.0485074i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −91.8638 | −0.866639 | ||||||||
\(107\) | −81.8068 | −0.764550 | −0.382275 | − | 0.924049i | \(-0.624859\pi\) | ||||
−0.382275 | + | 0.924049i | \(0.624859\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −103.430 | −0.948903 | −0.474452 | − | 0.880282i | \(-0.657354\pi\) | ||||
−0.474452 | + | 0.880282i | \(0.657354\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 10.5830i | − 0.0944911i | ||||||||
\(113\) | −187.400 | −1.65841 | −0.829204 | − | 0.558946i | \(-0.811206\pi\) | ||||
−0.829204 | + | 0.558946i | \(0.811206\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − 81.1763i | − 0.699795i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 157.885i | − 1.33801i | ||||||||
\(119\) | 85.3860i | 0.717530i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −77.8140 | −0.643091 | ||||||||
\(122\) | 3.80572 | 0.0311944 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 97.1251 | 0.783267 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 81.3040i | 0.640189i | 0.947386 | + | 0.320094i | \(0.103715\pi\) | ||||
−0.947386 | + | 0.320094i | \(0.896285\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.22925i | 0.0704523i | 0.999379 | + | 0.0352261i | \(0.0112152\pi\) | ||||
−0.999379 | + | 0.0352261i | \(0.988785\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 26.1810i | 0.196849i | ||||||||
\(134\) | − 102.081i | − 0.761801i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −91.2815 | −0.671188 | ||||||||
\(137\) | 27.8171 | 0.203044 | 0.101522 | − | 0.994833i | \(-0.467629\pi\) | ||||
0.101522 | + | 0.994833i | \(0.467629\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 101.074 | 0.727147 | 0.363574 | − | 0.931565i | \(-0.381556\pi\) | ||||
0.363574 | + | 0.931565i | \(0.381556\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − 57.4913i | − 0.404868i | ||||||||
\(143\) | −25.1489 | −0.175867 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − 90.0804i | − 0.616989i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − 125.795i | − 0.849967i | ||||||||
\(149\) | 119.738i | 0.803612i | 0.915725 | + | 0.401806i | \(0.131617\pi\) | ||||
−0.915725 | + | 0.401806i | \(0.868383\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 41.9026 | 0.277501 | 0.138750 | − | 0.990327i | \(-0.455691\pi\) | ||||
0.138750 | + | 0.990327i | \(0.455691\pi\) | |||||||
\(152\) | −27.9886 | −0.184136 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 52.7579 | 0.342584 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 130.984i | − 0.834295i | −0.908839 | − | 0.417148i | \(-0.863030\pi\) | ||||
0.908839 | − | 0.417148i | \(-0.136970\pi\) | |||||||
\(158\) | 116.395 | 0.736676 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 25.3496i | 0.157451i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 117.726i | 0.722246i | 0.932518 | + | 0.361123i | \(0.117607\pi\) | ||||
−0.932518 | + | 0.361123i | \(0.882393\pi\) | |||||||
\(164\) | − 131.470i | − 0.801645i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 141.283 | 0.851102 | ||||||||
\(167\) | −208.939 | −1.25113 | −0.625567 | − | 0.780170i | \(-0.715132\pi\) | ||||
−0.625567 | + | 0.780170i | \(0.715132\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 165.819 | 0.981176 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 101.684i | 0.591186i | ||||||||
\(173\) | 65.6170 | 0.379289 | 0.189644 | − | 0.981853i | \(-0.439266\pi\) | ||||
0.189644 | + | 0.981853i | \(0.439266\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 56.4006i | 0.320458i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 125.257i | 0.703693i | ||||||||
\(179\) | − 220.904i | − 1.23410i | −0.786924 | − | 0.617050i | \(-0.788328\pi\) | ||||
0.786924 | − | 0.617050i | \(-0.211672\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −84.5556 | −0.467158 | −0.233579 | − | 0.972338i | \(-0.575044\pi\) | ||||
−0.233579 | + | 0.972338i | \(0.575044\pi\) | |||||||
\(182\) | 6.67360 | 0.0366681 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −27.0999 | −0.147282 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 455.052i | − 2.43344i | ||||||||
\(188\) | 130.681 | 0.695111 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 308.870i | − 1.61712i | −0.588415 | − | 0.808559i | \(-0.700248\pi\) | ||||
0.588415 | − | 0.808559i | \(-0.299752\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 314.793i | − 1.63105i | −0.578720 | − | 0.815526i | \(-0.696448\pi\) | ||||
0.578720 | − | 0.815526i | \(-0.303552\pi\) | |||||||
\(194\) | − 166.662i | − 0.859083i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | −317.747 | −1.61293 | −0.806465 | − | 0.591282i | \(-0.798622\pi\) | ||||
−0.806465 | + | 0.591282i | \(0.798622\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −123.082 | −0.618502 | −0.309251 | − | 0.950980i | \(-0.600078\pi\) | ||||
−0.309251 | + | 0.950980i | \(0.600078\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 50.9526i | 0.252240i | ||||||||
\(203\) | −107.386 | −0.528996 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 49.3010i | 0.239325i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7.13438i | 0.0342999i | ||||||||
\(209\) | − 139.528i | − 0.667596i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −298.146 | −1.41302 | −0.706508 | − | 0.707705i | \(-0.749730\pi\) | ||||
−0.706508 | + | 0.707705i | \(0.749730\pi\) | |||||||
\(212\) | −129.915 | −0.612807 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −115.692 | −0.540618 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 128.484i | − 0.592094i | ||||||||
\(218\) | −146.273 | −0.670976 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 57.5618i | − 0.260460i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 83.8687i | 0.376093i | 0.982160 | + | 0.188046i | \(0.0602155\pi\) | ||||
−0.982160 | + | 0.188046i | \(0.939784\pi\) | |||||||
\(224\) | − 14.9666i | − 0.0668153i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −265.024 | −1.17267 | ||||||||
\(227\) | 94.6100 | 0.416784 | 0.208392 | − | 0.978045i | \(-0.433177\pi\) | ||||
0.208392 | + | 0.978045i | \(0.433177\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 318.779 | 1.39205 | 0.696025 | − | 0.718018i | \(-0.254950\pi\) | ||||
0.696025 | + | 0.718018i | \(0.254950\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 114.801i | − 0.494830i | ||||||||
\(233\) | 187.832 | 0.806147 | 0.403073 | − | 0.915168i | \(-0.367942\pi\) | ||||
0.403073 | + | 0.915168i | \(0.367942\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − 223.284i | − 0.946117i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 120.754i | 0.507370i | ||||||||
\(239\) | 361.090i | 1.51084i | 0.655243 | + | 0.755418i | \(0.272566\pi\) | ||||
−0.655243 | + | 0.755418i | \(0.727434\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.5899 | −0.0605391 | −0.0302695 | − | 0.999542i | \(-0.509637\pi\) | ||||
−0.0302695 | + | 0.999542i | \(0.509637\pi\) | |||||||
\(242\) | −110.046 | −0.454734 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.38210 | 0.0220578 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 17.6495i | − 0.0714556i | ||||||||
\(248\) | 137.356 | 0.553854 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 359.495i | − 1.43225i | −0.697971 | − | 0.716126i | \(-0.745914\pi\) | ||||
0.697971 | − | 0.716126i | \(-0.254086\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 135.097i | − 0.533981i | ||||||||
\(254\) | 114.981i | 0.452682i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 196.720 | 0.765447 | 0.382724 | − | 0.923863i | \(-0.374986\pi\) | ||||
0.382724 | + | 0.923863i | \(0.374986\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −166.411 | −0.642515 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 13.0521i | 0.0498173i | ||||||||
\(263\) | −396.028 | −1.50581 | −0.752905 | − | 0.658129i | \(-0.771348\pi\) | ||||
−0.752905 | + | 0.658129i | \(0.771348\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 37.0255i | 0.139194i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − 144.365i | − 0.538674i | ||||||||
\(269\) | − 203.497i | − 0.756494i | −0.925705 | − | 0.378247i | \(-0.876527\pi\) | ||||
0.925705 | − | 0.378247i | \(-0.123473\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −173.701 | −0.640964 | −0.320482 | − | 0.947255i | \(-0.603845\pi\) | ||||
−0.320482 | + | 0.947255i | \(0.603845\pi\) | |||||||
\(272\) | −129.092 | −0.474601 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 39.3393 | 0.143574 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 130.018i | 0.469380i | 0.972070 | + | 0.234690i | \(0.0754075\pi\) | ||||
−0.972070 | + | 0.234690i | \(0.924593\pi\) | |||||||
\(278\) | 142.940 | 0.514171 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 476.464i | 1.69560i | 0.530314 | + | 0.847801i | \(0.322074\pi\) | ||||
−0.530314 | + | 0.847801i | \(0.677926\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 56.5824i | − 0.199938i | −0.994991 | − | 0.0999690i | \(-0.968126\pi\) | ||||
0.994991 | − | 0.0999690i | \(-0.0318744\pi\) | |||||||
\(284\) | − 81.3050i | − 0.286285i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −35.5660 | −0.124357 | ||||||||
\(287\) | −173.918 | −0.605986 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 752.540 | 2.60394 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 127.393i | − 0.436277i | ||||||||
\(293\) | 124.651 | 0.425431 | 0.212715 | − | 0.977114i | \(-0.431769\pi\) | ||||
0.212715 | + | 0.977114i | \(0.431769\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − 177.901i | − 0.601018i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 169.335i | 0.568239i | ||||||||
\(299\) | − 17.0891i | − 0.0571542i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 134.515 | 0.446895 | ||||||||
\(302\) | 59.2592 | 0.196223 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −39.5819 | −0.130204 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 27.2322i | − 0.0887042i | −0.999016 | − | 0.0443521i | \(-0.985878\pi\) | ||||
0.999016 | − | 0.0443521i | \(-0.0141223\pi\) | |||||||
\(308\) | 74.6109 | 0.242243 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 63.9207i | 0.205533i | 0.994706 | + | 0.102766i | \(0.0327694\pi\) | ||||
−0.994706 | + | 0.102766i | \(0.967231\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 277.105i | 0.885320i | 0.896689 | + | 0.442660i | \(0.145965\pi\) | ||||
−0.896689 | + | 0.442660i | \(0.854035\pi\) | |||||||
\(314\) | − 185.240i | − 0.589936i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 164.607 | 0.520908 | ||||||||
\(317\) | −407.861 | −1.28663 | −0.643313 | − | 0.765603i | \(-0.722441\pi\) | ||||
−0.643313 | + | 0.765603i | \(0.722441\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 572.299 | 1.79404 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 35.8498i | 0.111335i | ||||||||
\(323\) | 319.356 | 0.988717 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 166.490i | 0.510705i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 185.926i | − 0.566848i | ||||||||
\(329\) | − 172.875i | − 0.525455i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 350.438 | 1.05872 | 0.529362 | − | 0.848396i | \(-0.322431\pi\) | ||||
0.529362 | + | 0.848396i | \(0.322431\pi\) | |||||||
\(332\) | 199.804 | 0.601820 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −295.485 | −0.884686 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 506.953i | − 1.50431i | −0.658985 | − | 0.752156i | \(-0.729014\pi\) | ||||
0.658985 | − | 0.752156i | \(-0.270986\pi\) | |||||||
\(338\) | 234.503 | 0.693796 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 684.739i | 2.00803i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5203i | 0.0539949i | ||||||||
\(344\) | 143.803i | 0.418032i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 92.7964 | 0.268198 | ||||||||
\(347\) | −143.703 | −0.414131 | −0.207065 | − | 0.978327i | \(-0.566391\pi\) | ||||
−0.207065 | + | 0.978327i | \(0.566391\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 168.383 | 0.482473 | 0.241237 | − | 0.970466i | \(-0.422447\pi\) | ||||
0.241237 | + | 0.970466i | \(0.422447\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 79.7625i | 0.226598i | ||||||||
\(353\) | −531.562 | −1.50584 | −0.752921 | − | 0.658111i | \(-0.771356\pi\) | ||||
−0.752921 | + | 0.658111i | \(0.771356\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 177.141i | 0.497586i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 312.405i | − 0.872640i | ||||||||
\(359\) | 63.2884i | 0.176291i | 0.996108 | + | 0.0881454i | \(0.0280940\pi\) | ||||
−0.996108 | + | 0.0881454i | \(0.971906\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −263.080 | −0.728752 | ||||||||
\(362\) | −119.580 | −0.330331 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.43790 | 0.0259283 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 252.555i | − 0.688160i | −0.938940 | − | 0.344080i | \(-0.888191\pi\) | ||||
0.938940 | − | 0.344080i | \(-0.111809\pi\) | |||||||
\(368\) | −38.3251 | −0.104144 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 171.861i | 0.463238i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 223.925i | − 0.600336i | −0.953886 | − | 0.300168i | \(-0.902957\pi\) | ||||
0.953886 | − | 0.300168i | \(-0.0970427\pi\) | |||||||
\(374\) | − 643.541i | − 1.72070i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 184.811 | 0.491518 | ||||||||
\(377\) | 72.3928 | 0.192023 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 503.313 | 1.32800 | 0.664001 | − | 0.747732i | \(-0.268857\pi\) | ||||
0.664001 | + | 0.747732i | \(0.268857\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 436.808i | − 1.14348i | ||||||||
\(383\) | −446.558 | −1.16595 | −0.582974 | − | 0.812491i | \(-0.698111\pi\) | ||||
−0.582974 | + | 0.812491i | \(0.698111\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − 445.185i | − 1.15333i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 235.696i | − 0.607464i | ||||||||
\(389\) | − 18.4450i | − 0.0474165i | −0.999719 | − | 0.0237083i | \(-0.992453\pi\) | ||||
0.999719 | − | 0.0237083i | \(-0.00754728\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 309.215 | 0.790831 | ||||||||
\(392\) | −19.7990 | −0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −449.362 | −1.14051 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 209.590i | 0.527934i | 0.964532 | + | 0.263967i | \(0.0850310\pi\) | ||||
−0.964532 | + | 0.263967i | \(0.914969\pi\) | |||||||
\(398\) | −174.064 | −0.437347 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 277.998i | 0.693261i | 0.938002 | + | 0.346631i | \(0.112674\pi\) | ||||
−0.938002 | + | 0.346631i | \(0.887326\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 86.6160i | 0.214928i | ||||||||
\(404\) | 72.0578i | 0.178361i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −151.867 | −0.374056 | ||||||||
\(407\) | 886.865 | 2.17903 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 506.079 | 1.23736 | 0.618678 | − | 0.785644i | \(-0.287668\pi\) | ||||
0.618678 | + | 0.785644i | \(0.287668\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 69.7221i | 0.169229i | ||||||||
\(413\) | −295.377 | −0.715198 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 10.0895i | 0.0242537i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 197.322i | − 0.472062i | ||||||||
\(419\) | 95.9760i | 0.229060i | 0.993420 | + | 0.114530i | \(0.0365362\pi\) | ||||
−0.993420 | + | 0.114530i | \(0.963464\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −236.741 | −0.562330 | −0.281165 | − | 0.959659i | \(-0.590721\pi\) | ||||
−0.281165 | + | 0.959659i | \(0.590721\pi\) | |||||||
\(422\) | −421.642 | −0.999153 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −183.728 | −0.433320 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 7.11985i | − 0.0166741i | ||||||||
\(428\) | −163.614 | −0.382275 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 494.406i | 1.14711i | 0.819166 | + | 0.573557i | \(0.194437\pi\) | ||||
−0.819166 | + | 0.573557i | \(0.805563\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 426.179i | − 0.984247i | −0.870526 | − | 0.492123i | \(-0.836221\pi\) | ||||
0.870526 | − | 0.492123i | \(-0.163779\pi\) | |||||||
\(434\) | − 181.705i | − 0.418674i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −206.861 | −0.474452 | ||||||||
\(437\) | 94.8112 | 0.216959 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −374.522 | −0.853125 | −0.426562 | − | 0.904458i | \(-0.640276\pi\) | ||||
−0.426562 | + | 0.904458i | \(0.640276\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 81.4046i | − 0.184173i | ||||||||
\(443\) | 38.1307 | 0.0860739 | 0.0430370 | − | 0.999073i | \(-0.486297\pi\) | ||||
0.0430370 | + | 0.999073i | \(0.486297\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 118.608i | 0.265938i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 21.1660i | − 0.0472456i | ||||||||
\(449\) | − 1.52774i | − 0.00340253i | −0.999999 | − | 0.00170126i | \(-0.999458\pi\) | ||||
0.999999 | − | 0.00170126i | \(-0.000541529\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 926.871 | 2.05515 | ||||||||
\(452\) | −374.800 | −0.829204 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 133.799 | 0.294711 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 141.016i | 0.308569i | 0.988026 | + | 0.154284i | \(0.0493072\pi\) | ||||
−0.988026 | + | 0.154284i | \(0.950693\pi\) | |||||||
\(458\) | 450.822 | 0.984327 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 10.4463i | − 0.0226601i | −0.999936 | − | 0.0113301i | \(-0.996393\pi\) | ||||
0.999936 | − | 0.0113301i | \(-0.00360655\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 159.805i | 0.345152i | 0.984996 | + | 0.172576i | \(0.0552091\pi\) | ||||
−0.984996 | + | 0.172576i | \(0.944791\pi\) | |||||||
\(464\) | − 162.353i | − 0.349898i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 265.635 | 0.570032 | ||||||||
\(467\) | 58.0764 | 0.124361 | 0.0621803 | − | 0.998065i | \(-0.480195\pi\) | ||||
0.0621803 | + | 0.998065i | \(0.480195\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −190.977 | −0.407200 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 315.771i | − 0.669006i | ||||||||
\(473\) | −716.879 | −1.51560 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 170.772i | 0.358765i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 510.658i | 1.06832i | ||||||||
\(479\) | 134.072i | 0.279899i | 0.990159 | + | 0.139950i | \(0.0446940\pi\) | ||||
−0.990159 | + | 0.139950i | \(0.955306\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 112.184 | 0.233230 | ||||||||
\(482\) | −20.6333 | −0.0428076 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −155.628 | −0.321546 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 277.859i | − 0.570552i | −0.958445 | − | 0.285276i | \(-0.907915\pi\) | ||||
0.958445 | − | 0.285276i | \(-0.0920853\pi\) | |||||||
\(488\) | 7.61144 | 0.0155972 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 514.975i | − 1.04883i | −0.851463 | − | 0.524414i | \(-0.824284\pi\) | ||||
0.851463 | − | 0.524414i | \(-0.175716\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1309.90i | 2.65699i | ||||||||
\(494\) | − 24.9602i | − 0.0505267i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 194.250 | 0.391634 | ||||||||
\(497\) | −107.556 | −0.216411 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 144.052 | 0.288682 | 0.144341 | − | 0.989528i | \(-0.453894\pi\) | ||||
0.144341 | + | 0.989528i | \(0.453894\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 508.403i | − 1.01275i | ||||||||
\(503\) | −596.609 | −1.18610 | −0.593051 | − | 0.805165i | \(-0.702077\pi\) | ||||
−0.593051 | + | 0.805165i | \(0.702077\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − 191.056i | − 0.377582i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 162.608i | 0.320094i | ||||||||
\(509\) | − 7.91201i | − 0.0155442i | −0.999970 | − | 0.00777211i | \(-0.997526\pi\) | ||||
0.999970 | − | 0.00777211i | \(-0.00247397\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −168.525 | −0.329794 | ||||||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 278.204 | 0.541253 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 921.310i | 1.78203i | ||||||||
\(518\) | −235.341 | −0.454327 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 746.931i | 1.43365i | 0.697253 | + | 0.716825i | \(0.254405\pi\) | ||||
−0.697253 | + | 0.716825i | \(0.745595\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 138.896i | − 0.265576i | −0.991144 | − | 0.132788i | \(-0.957607\pi\) | ||||
0.991144 | − | 0.132788i | \(-0.0423929\pi\) | |||||||
\(524\) | 18.4585i | 0.0352261i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −560.068 | −1.06477 | ||||||||
\(527\) | −1567.25 | −2.97392 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −437.199 | −0.826464 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 52.3619i | 0.0984247i | ||||||||
\(533\) | 117.244 | 0.219971 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − 204.163i | − 0.380900i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 287.788i | − 0.534922i | ||||||||
\(539\) | − 98.7010i | − 0.183119i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −684.033 | −1.26439 | −0.632193 | − | 0.774811i | \(-0.717845\pi\) | ||||
−0.632193 | + | 0.774811i | \(0.717845\pi\) | |||||||
\(542\) | −245.651 | −0.453230 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −182.563 | −0.335594 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 485.135i | − 0.886901i | −0.896299 | − | 0.443451i | \(-0.853754\pi\) | ||||
0.896299 | − | 0.443451i | \(-0.146246\pi\) | |||||||
\(548\) | 55.6341 | 0.101522 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 401.639i | 0.728927i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 217.755i | − 0.393770i | ||||||||
\(554\) | 183.874i | 0.331902i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 202.147 | 0.363574 | ||||||||
\(557\) | 227.641 | 0.408692 | 0.204346 | − | 0.978899i | \(-0.434493\pi\) | ||||
0.204346 | + | 0.978899i | \(0.434493\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −90.6815 | −0.162221 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 673.822i | 1.19897i | ||||||||
\(563\) | 69.7030 | 0.123806 | 0.0619032 | − | 0.998082i | \(-0.480283\pi\) | ||||
0.0619032 | + | 0.998082i | \(0.480283\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − 80.0197i | − 0.141378i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − 114.983i | − 0.202434i | ||||||||
\(569\) | − 573.975i | − 1.00874i | −0.863487 | − | 0.504372i | \(-0.831724\pi\) | ||||
0.863487 | − | 0.504372i | \(-0.168276\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 289.675 | 0.507312 | 0.253656 | − | 0.967294i | \(-0.418367\pi\) | ||||
0.253656 | + | 0.967294i | \(0.418367\pi\) | |||||||
\(572\) | −50.2979 | −0.0879334 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −245.957 | −0.428497 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 122.652i | − 0.212569i | −0.994336 | − | 0.106285i | \(-0.966105\pi\) | ||||
0.994336 | − | 0.106285i | \(-0.0338955\pi\) | |||||||
\(578\) | 1064.25 | 1.84127 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 264.316i | − 0.454933i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 915.910i | − 1.57103i | ||||||||
\(584\) | − 180.161i | − 0.308494i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 176.283 | 0.300825 | ||||||||
\(587\) | −156.694 | −0.266940 | −0.133470 | − | 0.991053i | \(-0.542612\pi\) | ||||
−0.133470 | + | 0.991053i | \(0.542612\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −480.550 | −0.815874 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − 251.590i | − 0.424984i | ||||||||
\(593\) | 78.4823 | 0.132348 | 0.0661739 | − | 0.997808i | \(-0.478921\pi\) | ||||
0.0661739 | + | 0.997808i | \(0.478921\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 239.476i | 0.401806i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 24.1676i | − 0.0404141i | ||||||||
\(599\) | 104.010i | 0.173639i | 0.996224 | + | 0.0868195i | \(0.0276703\pi\) | ||||
−0.996224 | + | 0.0868195i | \(0.972330\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 773.253 | 1.28661 | 0.643305 | − | 0.765610i | \(-0.277563\pi\) | ||||
0.643305 | + | 0.765610i | \(0.277563\pi\) | |||||||
\(602\) | 190.233 | 0.316002 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 83.8052 | 0.138750 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 349.051i | − 0.575044i | −0.957774 | − | 0.287522i | \(-0.907169\pi\) | ||||
0.957774 | − | 0.287522i | \(-0.0928314\pi\) | |||||||
\(608\) | −55.9773 | −0.0920679 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 116.541i | 0.190738i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 323.779i | − 0.528188i | −0.964497 | − | 0.264094i | \(-0.914927\pi\) | ||||
0.964497 | − | 0.264094i | \(-0.0850729\pi\) | |||||||
\(614\) | − 38.5121i | − 0.0627233i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 105.516 | 0.171292 | ||||||||
\(617\) | −1040.96 | −1.68713 | −0.843567 | − | 0.537023i | \(-0.819549\pi\) | ||||
−0.843567 | + | 0.537023i | \(0.819549\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 783.600 | 1.26591 | 0.632957 | − | 0.774187i | \(-0.281841\pi\) | ||||
0.632957 | + | 0.774187i | \(0.281841\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 90.3976i | 0.145334i | ||||||||
\(623\) | 234.335 | 0.376140 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 391.886i | 0.626016i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 261.969i | − 0.417148i | ||||||||
\(629\) | 2029.89i | 3.22717i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 967.921 | 1.53395 | 0.766974 | − | 0.641678i | \(-0.221762\pi\) | ||||
0.766974 | + | 0.641678i | \(0.221762\pi\) | |||||||
\(632\) | 232.790 | 0.368338 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −576.802 | −0.909783 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 12.4852i | − 0.0195999i | ||||||||
\(638\) | 809.352 | 1.26858 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 38.9129i | − 0.0607066i | −0.999539 | − | 0.0303533i | \(-0.990337\pi\) | ||||
0.999539 | − | 0.0303533i | \(-0.00966324\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1123.77i | 1.74771i | 0.486191 | + | 0.873853i | \(0.338386\pi\) | ||||
−0.486191 | + | 0.873853i | \(0.661614\pi\) | |||||||
\(644\) | 50.6993i | 0.0787256i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 451.637 | 0.699129 | ||||||||
\(647\) | −635.461 | −0.982165 | −0.491083 | − | 0.871113i | \(-0.663399\pi\) | ||||
−0.491083 | + | 0.871113i | \(0.663399\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1574.17 | 2.42553 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 235.452i | 0.361123i | ||||||||
\(653\) | 361.063 | 0.552929 | 0.276465 | − | 0.961024i | \(-0.410837\pi\) | ||||
0.276465 | + | 0.961024i | \(0.410837\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − 262.939i | − 0.400822i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − 244.482i | − 0.371553i | ||||||||
\(659\) | 1284.71i | 1.94949i | 0.223327 | + | 0.974744i | \(0.428308\pi\) | ||||
−0.223327 | + | 0.974744i | \(0.571692\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 605.603 | 0.916192 | 0.458096 | − | 0.888903i | \(-0.348532\pi\) | ||||
0.458096 | + | 0.888903i | \(0.348532\pi\) | |||||||
\(662\) | 495.594 | 0.748632 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 282.566 | 0.425551 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 388.886i | 0.583037i | ||||||||
\(668\) | −417.879 | −0.625567 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 37.9442i | 0.0565487i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 863.984i | − 1.28378i | −0.766797 | − | 0.641890i | \(-0.778151\pi\) | ||||
0.766797 | − | 0.641890i | \(-0.221849\pi\) | |||||||
\(674\) | − 716.940i | − 1.06371i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 331.638 | 0.490588 | ||||||||
\(677\) | 1009.59 | 1.49127 | 0.745635 | − | 0.666354i | \(-0.232146\pi\) | ||||
0.745635 | + | 0.666354i | \(0.232146\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −311.796 | −0.459199 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 968.367i | 1.41989i | ||||||||
\(683\) | −786.887 | −1.15210 | −0.576052 | − | 0.817413i | \(-0.695407\pi\) | ||||
−0.576052 | + | 0.817413i | \(0.695407\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 26.1916i | 0.0381802i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 203.368i | 0.295593i | ||||||||
\(689\) | − 115.858i | − 0.168154i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1285.82 | −1.86081 | −0.930405 | − | 0.366534i | \(-0.880544\pi\) | ||||
−0.930405 | + | 0.366534i | \(0.880544\pi\) | |||||||
\(692\) | 131.234 | 0.189644 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −203.227 | −0.292835 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2121.45i | 3.04369i | ||||||||
\(698\) | 238.130 | 0.341160 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 717.153i | 1.02304i | 0.859271 | + | 0.511521i | \(0.170918\pi\) | ||||
−0.859271 | + | 0.511521i | \(0.829082\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 622.402i | 0.885351i | ||||||||
\(704\) | 112.801i | 0.160229i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −751.742 | −1.06479 | ||||||||
\(707\) | 95.3235 | 0.134828 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −197.923 | −0.279158 | −0.139579 | − | 0.990211i | \(-0.544575\pi\) | ||||
−0.139579 | + | 0.990211i | \(0.544575\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 250.515i | 0.351847i | ||||||||
\(713\) | −465.291 | −0.652582 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − 441.808i | − 0.617050i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 89.5033i | 0.124656i | ||||||||
\(719\) | − 168.511i | − 0.234369i | −0.993110 | − | 0.117185i | \(-0.962613\pi\) | ||||
0.993110 | − | 0.117185i | \(-0.0373869\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 92.2337 | 0.127925 | ||||||||
\(722\) | −372.051 | −0.515306 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −169.111 | −0.233579 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 906.873i | − 1.24742i | −0.781657 | − | 0.623709i | \(-0.785625\pi\) | ||||
0.781657 | − | 0.623709i | \(-0.214375\pi\) | |||||||
\(728\) | 13.3472 | 0.0183341 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 1640.82i | − 2.24462i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 22.6632i | − 0.0309184i | −0.999880 | − | 0.0154592i | \(-0.995079\pi\) | ||||
0.999880 | − | 0.0154592i | \(-0.00492101\pi\) | |||||||
\(734\) | − 357.166i | − 0.486602i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −54.1998 | −0.0736410 | ||||||||
\(737\) | 1017.78 | 1.38098 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −614.258 | −0.831202 | −0.415601 | − | 0.909547i | \(-0.636429\pi\) | ||||
−0.415601 | + | 0.909547i | \(0.636429\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 243.049i | 0.327559i | ||||||||
\(743\) | −33.0291 | −0.0444537 | −0.0222268 | − | 0.999753i | \(-0.507076\pi\) | ||||
−0.0222268 | + | 0.999753i | \(0.507076\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − 316.678i | − 0.424501i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 910.105i | − 1.21672i | ||||||||
\(749\) | 216.441i | 0.288973i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −905.403 | −1.20560 | −0.602798 | − | 0.797894i | \(-0.705948\pi\) | ||||
−0.602798 | + | 0.797894i | \(0.705948\pi\) | |||||||
\(752\) | 261.362 | 0.347556 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 102.379 | 0.135781 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 64.4031i | − 0.0850768i | −0.999095 | − | 0.0425384i | \(-0.986456\pi\) | ||||
0.999095 | − | 0.0425384i | \(-0.0135445\pi\) | |||||||
\(758\) | 711.791 | 0.939039 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 508.718i | − 0.668486i | −0.942487 | − | 0.334243i | \(-0.891519\pi\) | ||||
0.942487 | − | 0.334243i | \(-0.108481\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 273.651i | 0.358652i | ||||||||
\(764\) | − 617.739i | − 0.808559i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −631.528 | −0.824449 | ||||||||
\(767\) | 199.124 | 0.259614 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 934.507 | 1.21522 | 0.607612 | − | 0.794234i | \(-0.292128\pi\) | ||||
0.607612 | + | 0.794234i | \(0.292128\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 629.586i | − 0.815526i | ||||||||
\(773\) | 1013.90 | 1.31164 | 0.655821 | − | 0.754917i | \(-0.272323\pi\) | ||||
0.655821 | + | 0.754917i | \(0.272323\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − 333.324i | − 0.429542i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 26.0852i | − 0.0335285i | ||||||||
\(779\) | 650.478i | 0.835017i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 573.206 | 0.733939 | ||||||||
\(782\) | 437.296 | 0.559202 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −28.0000 | −0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 374.605i | − 0.475991i | −0.971266 | − | 0.237996i | \(-0.923510\pi\) | ||||
0.971266 | − | 0.237996i | \(-0.0764904\pi\) | |||||||
\(788\) | −635.494 | −0.806465 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 495.814i | 0.626819i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.79975i | 0.00605264i | ||||||||
\(794\) | 296.405i | 0.373306i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −246.164 | −0.309251 | ||||||||
\(797\) | 734.515 | 0.921600 | 0.460800 | − | 0.887504i | \(-0.347563\pi\) | ||||
0.460800 | + | 0.887504i | \(0.347563\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2108.73 | −2.63921 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 393.148i | 0.490210i | ||||||||
\(803\) | 898.129 | 1.11847 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 122.493i | 0.151977i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 101.905i | 0.126120i | ||||||||
\(809\) | 212.258i | 0.262371i | 0.991358 | + | 0.131186i | \(0.0418784\pi\) | ||||
−0.991358 | + | 0.131186i | \(0.958122\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1343.78 | −1.65694 | −0.828470 | − | 0.560034i | \(-0.810788\pi\) | ||||
−0.828470 | + | 0.560034i | \(0.810788\pi\) | |||||||
\(812\) | −214.772 | −0.264498 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1254.22 | 1.54081 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 503.106i | − 0.615797i | ||||||||
\(818\) | 715.703 | 0.874943 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 126.090i | 0.153582i | 0.997047 | + | 0.0767908i | \(0.0244674\pi\) | ||||
−0.997047 | + | 0.0767908i | \(0.975533\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 74.0891i | − 0.0900232i | −0.998986 | − | 0.0450116i | \(-0.985668\pi\) | ||||
0.998986 | − | 0.0450116i | \(-0.0143325\pi\) | |||||||
\(824\) | 98.6020i | 0.119663i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −417.726 | −0.505721 | ||||||||
\(827\) | 626.689 | 0.757786 | 0.378893 | − | 0.925441i | \(-0.376305\pi\) | ||||
0.378893 | + | 0.925441i | \(0.376305\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −605.458 | −0.730348 | −0.365174 | − | 0.930939i | \(-0.618990\pi\) | ||||
−0.365174 | + | 0.930939i | \(0.618990\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 14.2688i | 0.0171500i | ||||||||
\(833\) | 225.910 | 0.271201 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − 279.055i | − 0.333798i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 135.731i | 0.161970i | ||||||||
\(839\) | 1303.81i | 1.55400i | 0.629499 | + | 0.777001i | \(0.283260\pi\) | ||||
−0.629499 | + | 0.777001i | \(0.716740\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −806.397 | −0.958855 | ||||||||
\(842\) | −334.802 | −0.397627 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −596.293 | −0.706508 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 205.877i | 0.243066i | ||||||||
\(848\) | −259.830 | −0.306403 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 602.638i | 0.708153i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 34.1253i | − 0.0400062i | −0.999800 | − | 0.0200031i | \(-0.993632\pi\) | ||||
0.999800 | − | 0.0200031i | \(-0.00636761\pi\) | |||||||
\(854\) | − 10.0690i | − 0.0117904i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −231.385 | −0.270309 | ||||||||
\(857\) | −1513.23 | −1.76573 | −0.882866 | − | 0.469626i | \(-0.844389\pi\) | ||||
−0.882866 | + | 0.469626i | \(0.844389\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1089.68 | 1.26855 | 0.634273 | − | 0.773109i | \(-0.281299\pi\) | ||||
0.634273 | + | 0.773109i | \(0.281299\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 699.196i | 0.811132i | ||||||||
\(863\) | 643.590 | 0.745759 | 0.372880 | − | 0.927880i | \(-0.378370\pi\) | ||||
0.372880 | + | 0.927880i | \(0.378370\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − 602.708i | − 0.695967i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − 256.969i | − 0.296047i | ||||||||
\(869\) | 1160.49i | 1.33543i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 128.744 | 0.147812 | ||||||||
\(872\) | −292.545 | −0.335488 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 134.083 | 0.153413 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 766.776i | 0.874317i | 0.899385 | + | 0.437158i | \(0.144015\pi\) | ||||
−0.899385 | + | 0.437158i | \(0.855985\pi\) | |||||||
\(878\) | −529.654 | −0.603250 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 157.211i | − 0.178446i | −0.996012 | − | 0.0892229i | \(-0.971562\pi\) | ||||
0.996012 | − | 0.0892229i | \(-0.0284384\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 14.1471i | − 0.0160216i | −0.999968 | − | 0.00801079i | \(-0.997450\pi\) | ||||
0.999968 | − | 0.00801079i | \(-0.00254994\pi\) | |||||||
\(884\) | − 115.124i | − 0.130230i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 53.9250 | 0.0608635 | ||||||||
\(887\) | 1741.26 | 1.96309 | 0.981547 | − | 0.191220i | \(-0.0612444\pi\) | ||||
0.981547 | + | 0.191220i | \(0.0612444\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 215.110 | 0.241969 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 167.737i | 0.188046i | ||||||||
\(893\) | −646.575 | −0.724048 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − 29.9333i | − 0.0334077i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − 2.16054i | − 0.00240595i | ||||||||
\(899\) | − 1971.06i | − 2.19251i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2096.37 | 2.32671 | ||||||||
\(902\) | 1310.79 | 1.45321 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −530.047 | −0.586336 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1290.67i | 1.42301i | 0.702681 | + | 0.711505i | \(0.251986\pi\) | ||||
−0.702681 | + | 0.711505i | \(0.748014\pi\) | |||||||
\(908\) | 189.220 | 0.208392 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 906.341i | − 0.994886i | −0.867497 | − | 0.497443i | \(-0.834272\pi\) | ||||
0.867497 | − | 0.497443i | \(-0.165728\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1408.63i | 1.54286i | ||||||||
\(914\) | 199.427i | 0.218191i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 637.559 | 0.696025 | ||||||||
\(917\) | 24.4183 | 0.0266285 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1738.74 | −1.89199 | −0.945994 | − | 0.324185i | \(-0.894910\pi\) | ||||
−0.945994 | + | 0.324185i | \(0.894910\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 14.7733i | − 0.0160231i | ||||||||
\(923\) | 72.5076 | 0.0785564 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 225.999i | 0.244059i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − 229.601i | − 0.247415i | ||||||||
\(929\) | 529.634i | 0.570112i | 0.958511 | + | 0.285056i | \(0.0920122\pi\) | ||||
−0.958511 | + | 0.285056i | \(0.907988\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 69.2683 | 0.0744021 | ||||||||
\(932\) | 375.664 | 0.403073 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 82.1324 | 0.0879362 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1354.47i | 1.44553i | 0.691091 | + | 0.722767i | \(0.257130\pi\) | ||||
−0.691091 | + | 0.722767i | \(0.742870\pi\) | |||||||
\(938\) | −270.082 | −0.287934 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 1406.13i | − 1.49429i | −0.664662 | − | 0.747144i | \(-0.731425\pi\) | ||||
0.664662 | − | 0.747144i | \(-0.268575\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 629.823i | 0.667893i | ||||||||
\(944\) | − 446.567i | − 0.473059i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1013.82 | −1.07169 | ||||||||
\(947\) | 1168.66 | 1.23406 | 0.617032 | − | 0.786938i | \(-0.288335\pi\) | ||||
0.617032 | + | 0.786938i | \(0.288335\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 113.609 | 0.119714 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 241.508i | 0.253685i | ||||||||
\(953\) | 65.5411 | 0.0687735 | 0.0343867 | − | 0.999409i | \(-0.489052\pi\) | ||||
0.0343867 | + | 0.999409i | \(0.489052\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 722.179i | 0.755418i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 189.606i | 0.197918i | ||||||||
\(959\) | − 73.5971i | − 0.0767435i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1397.32 | 1.45403 | ||||||||
\(962\) | 158.652 | 0.164919 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −29.1798 | −0.0302695 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1095.49i | 1.13287i | 0.824106 | + | 0.566436i | \(0.191678\pi\) | ||||
−0.824106 | + | 0.566436i | \(0.808322\pi\) | |||||||
\(968\) | −220.091 | −0.227367 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 143.575i | − 0.147863i | −0.997263 | − | 0.0739313i | \(-0.976445\pi\) | ||||
0.997263 | − | 0.0739313i | \(-0.0235546\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 267.415i | − 0.274836i | ||||||||
\(974\) | − 392.952i | − 0.403441i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.7642 | 0.0110289 | ||||||||
\(977\) | −1259.60 | −1.28925 | −0.644627 | − | 0.764498i | \(-0.722987\pi\) | ||||
−0.644627 | + | 0.764498i | \(0.722987\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1248.85 | −1.27564 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − 728.285i | − 0.741634i | ||||||||
\(983\) | 275.176 | 0.279935 | 0.139968 | − | 0.990156i | \(-0.455300\pi\) | ||||
0.139968 | + | 0.990156i | \(0.455300\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1852.47i | 1.87878i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − 35.2991i | − 0.0357278i | ||||||||
\(989\) | − 487.131i | − 0.492549i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1111.90 | −1.12200 | −0.560998 | − | 0.827817i | \(-0.689583\pi\) | ||||
−0.560998 | + | 0.827817i | \(0.689583\pi\) | |||||||
\(992\) | 274.711 | 0.276927 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −152.108 | −0.153026 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1008.42i | 1.01145i | 0.862693 | + | 0.505727i | \(0.168776\pi\) | ||||
−0.862693 | + | 0.505727i | \(0.831224\pi\) | |||||||
\(998\) | 203.720 | 0.204129 | ||||||||
\(999\) | 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 | 3150.3.c.f.449.12 | 16 | ||
3.2 | odd | 2 | inner | 3150.3.c.f.449.1 | 16 | ||
5.2 | odd | 4 | 630.3.e.b.71.6 | yes | 8 | ||
5.3 | odd | 4 | 3150.3.e.f.701.2 | 8 | |||
5.4 | even | 2 | inner | 3150.3.c.f.449.8 | 16 | ||
15.2 | even | 4 | 630.3.e.b.71.4 | ✓ | 8 | ||
15.8 | even | 4 | 3150.3.e.f.701.5 | 8 | |||
15.14 | odd | 2 | inner | 3150.3.c.f.449.13 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.3.e.b.71.4 | ✓ | 8 | 15.2 | even | 4 | ||
630.3.e.b.71.6 | yes | 8 | 5.2 | odd | 4 | ||
3150.3.c.f.449.1 | 16 | 3.2 | odd | 2 | inner | ||
3150.3.c.f.449.8 | 16 | 5.4 | even | 2 | inner | ||
3150.3.c.f.449.12 | 16 | 1.1 | even | 1 | trivial | ||
3150.3.c.f.449.13 | 16 | 15.14 | odd | 2 | inner | ||
3150.3.e.f.701.2 | 8 | 5.3 | odd | 4 | |||
3150.3.e.f.701.5 | 8 | 15.8 | even | 4 |